tanh 3x faster, and <1.5 ULP vs 2.0 ULP for master #38382
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stevengj
approved these changes
Nov 11, 2020
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(It looks like we already have test coverage for this.) |
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Good to also have @simonbyrne take a quick look if possible. |
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One specific question about this. At this point, I'm pretty sure we aren't using |
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If not related to this PR, then make it a separate PR so that this one can go through. |
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The speedup comes from using
expinstead ofexpm1for mostx. For smallx(less thanlog(2)/2or.5depending on the datatype), just use a minimax polynomial. This solution is faster, more accurate, and simpler. I believe accuracy is strictly below 1.5 ULP for all inputs, but I wouldn't be shocked if a 1.6 ULP slipped in somewhere. Either way, current behavior has over 2 ulps for0.233002233002233and 1.95 for0.46070245f0, so this is a major accuracy improvement in addition to the speed improvement.