InstCombine: Simplify (A ^ B) or/and (A ^ B ^ C)
While we can already transform A | (A ^ B) into A | B, things get bad
once we have (A ^ B) | (A ^ B ^ Cst) because reassociation will morph
this into (A ^ B) | ((A ^ Cst) ^ B). Our existing patterns fail once
this happens.
To fix this, we add a new pattern which looks through the tree of xor
binary operators to see that, in fact, there exists a redundant xor
operation.
What follows bellow is a correctness proof of the transform using CVC3.
$ cat t.cvc
A, B, C : BITVECTOR(64);
QUERY BVXOR(A, B) | BVXOR(BVXOR(B, C), A) = BVXOR(A, B) | C;
QUERY BVXOR(BVXOR(A, C), B) | BVXOR(A, B) = BVXOR(A, B) | C;
QUERY BVXOR(A, B) & BVXOR(BVXOR(B, C), A) = BVXOR(A, B) & ~C;
QUERY BVXOR(BVXOR(A, C), B) & BVXOR(A, B) = BVXOR(A, B) & ~C;
$ cvc3 < t.cvc
Valid.
Valid.
Valid.
Valid.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@214342
91177308-0d34-0410-b5e6-
96231b3b80d8