[PATCH] D42879: InstCombine: 1./x >= 0. -> x >= 0.

[Matthias Braun via Phabricator via llvm-commits]

MatzeB created this revision.
MatzeB added reviewers: majnemer, spatel, arsenm, craig.topper, nlopes.
Herald added subscribers: wdng, mcrosier.

This adds the following two rules when the "no infs" fast-math
flag is set:

  fcmp ninf pred (fdiv ninf 1., x), 0   ->   fcmp pred x, 0
  fcmp ninf pred (fdiv ninf -1., x), 0  ->   fcmp swap(pred) x, 0

To justify the first rule:

- All of the following cases show that with or without fdiv the sign is the same and 0 does not occur.
- fdiv 1., small number  <-> + large number or +inf on overflow
- fidv 1., -small number <-> - large number or -inf on overflow
- fdiv 1., big number    <-> + small normal or denormal number (Example: 1./FLT_MAX = 1./0x0x1.fffffep+127 = 0x1p-128)
- fdiv 1., big number    <-> - small normal or denormal number

NaN is preserved:

- fdiv 1., nan  <-> nan
- fdiv 1., -nan <-> -nan

The following cases do not work correctly:

- fdiv 1., 0  <-> inf
- fdiv 1., -0 <-> -inf
- fdiv 1., inf  </-> 0
- fdiv 1., -inf </-> -0

However having a "no inf" fast-math flag on the fcmp and the fdiv allows
us to ignore these cases.

The 2nd rule can be shown to be a variant of the first:

  fcmp pred (fdiv -1., x), 0  -> fcmp pred fneg (fdiv 1., x), 0
       -> fcmp swap(pred) (fdiv 1., x), 0 -> fcmp swap(pred) x, 0

Question to reviewers: Is it correct to assume that with `fcmp ninf (fdiv 1.0, x)` the input to fcmp cannot be +/- infinity and hence x cannot be +/- 0?


Repository:
  rL LLVM

https://reviews.llvm.org/D42879

Files:
  lib/Transforms/InstCombine/InstCombineCompares.cpp
  test/Transforms/InstCombine/fcmp_reciproc.ll

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