[PATCH] D122757: [InstCombine] Fold (ctpop(X) == N) || (X != 0) into X != 0 where N > 0

[Hirochika Matsumoto via Phabricator via llvm-commits]

hkmatsumoto added a comment.

Proof (This is first time writing proof in English, so sorry for any inconveniences)
Suppose X: i32

1. For 0 < N < 32
  - ctpop(X) == N --> X > 0.
  - Hence (ctpop(X) == N) || (X != 0) --> X > 0 || X != 0.
  - Intuitively X > 0 || X != 0 --> X != 0.
2. For 32 < N
  - ctpop(X) == N is always false, because of the semantics of ctpop().
  - Hence (ctpop(X) == N) || (X != 0) --> false || X != 0 --> X != 0.


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  https://reviews.llvm.org/D122757/new/

https://reviews.llvm.org/D122757