| commit | 1e135c54c52a71ae9267011f13fded21cc05fcc3 | [log] [tgz] |
|---|---|---|
| author | David Majnemer <majnemer@google.com> | Mon Feb 22 11:16:22 2021 -0800 |
| committer | TensorFlower Gardener <gardener@tensorflow.org> | Mon Feb 22 11:29:40 2021 -0800 |
| tree | 97f4574c01c9007cb241eeb9313a6cbcb08e4d7e | |
| parent | 4856f23a49dfe44fb697d5affcf10fb2a2585523 [diff] |
[XLA:CPU] More accurate expm1 when x is small, take two
We approximate it with:
expm1(x) = tanh(x/2)*(exp(x)+1)
Additional care is taken to handle the case when x/2 underflows but x does not
by simply approximating the result with x itself.
Yet further care must be taken to handle the case when exp(x) would not be all that close to 1, in which case we simply use:
expm1(x) = exp(x)-1
The pseudo-code for this is roughly:
if x/2 == 0:
return x
exp_x = exp(x)
if |x| > .5:
return exp_x - 1
return tanh(x/2)*(exp_x+1)
The actual code sequence emitted preserves vectorization in the case where different lanes observe inputs where the magnitudes are entirely different.
This suffices to get us within a relative error of 4.76e-7 or about eight ULPs when
compared against libm.
PiperOrigin-RevId: 358861023
Change-Id: I4a51ec8e2a16a95b6cbaa2af3305ce3a16201c54
Documentation |
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