[llvm] [InstCombinePHI] Enhance PHI CSE to remove redundant phis (PR #163453)

[Yingwei Zheng via llvm-commits]

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@@ -4866,6 +4866,89 @@ static Value *simplifySelectWithFCmp(Value *Cond, Value *T, Value *F,
   return nullptr;
 }
 
+// Look for the following pattern and simplify %1 to %identicalPhi.
+// Here %phi, %1 and %phi.next perform the same functionality as
+// %identicalPhi and hence the select instruction %1 can be folded
+// into %identicalPhi.
+//
+// BB1:
+//   %identicalPhi = phi [ X, %BB0 ], [ %identicalPhi.next, %BB1 ]
+//   %phi = phi [ X, %BB0 ], [ %phi.next, %BB1 ]
+//   ...
+//   %identicalPhi.next = select %cmp, %val, %identicalPhi
+//                      (or select %cmp, %identicalPhi, %val)
+//   %1 = select %cmp2, %identicalPhi, %phi
+//   %phi.next = select %cmp, %val, %1
+//             (or select %cmp, %1, %val)
+//
+// Prove that %phi and %identicalPhi are the same by induction:
+//
+// Base case: Both %phi and %identicalPhi are equal on entry to the loop.
+// Inductive case:
+// Suppose %phi and %identicalPhi are equal at iteration i.
+// We look at their values at iteration i+1 which are %phi.next and
+// %identicalPhi.next. They would have become different only when %cmp is
+// false and the corresponding values %1 and %identicalPhi differ
+// (similar reason for the other "or" case in the bracket).
+//
+// The only condition when %1 and %identicalPh could differ is when %cmp2
+// is false and %1 is %phi, which contradicts our inductive hypothesis
+// that %phi and %identicalPhi are equal. Thus %phi and %identicalPhi are
+// always equal at iteration i+1.
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dtcxzyw wrote:

Use `///` for header comments.

https://github.com/llvm/llvm-project/pull/163453