[SCEV] Recognize binary xor as bit-wise add

https://alive2.llvm.org/ce/z/ULuZxB

We could transparently handle wider bitwidths,
by effectively casting iN to <N x i1> and performing the `add`
bit/element -wise, the expression will be rather large,
so let's not do that for now.

llvm/lib/Analysis/ScalarEvolution.cpp

@@ -5067,6 +5067,9 @@ static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
       // Instcombine turns add of signmask into xor as a strength reduction step.
       if (RHSC->getValue().isSignMask())
         return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
+    // Binary `xor` is a bit-wise `add`.
+    if (V->getType()->isIntegerTy(1))
+      return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
     return BinaryOp(Op);
 
   case Instruction::LShr:

llvm/test/Analysis/ScalarEvolution/logical-operations.ll

@@ -86,7 +86,7 @@ define i1 @binary_xor.i1(i1 %x, i1 %y) {
 ; CHECK-LABEL: 'binary_xor.i1'
 ; CHECK-NEXT:  Classifying expressions for: @binary_xor.i1
 ; CHECK-NEXT:    %r = xor i1 %x, %y
-; CHECK-NEXT:    --> %r U: full-set S: full-set
+; CHECK-NEXT:    --> (%x + %y) U: full-set S: full-set
 ; CHECK-NEXT:  Determining loop execution counts for: @binary_xor.i1
 ;
   %r = xor i1 %x, %y
@@ -108,11 +108,11 @@ define i1 @binary_xor.4ops.i1(i1 %x, i1 %y, i1 %z, i1 %a) {
 ; CHECK-LABEL: 'binary_xor.4ops.i1'
 ; CHECK-NEXT:  Classifying expressions for: @binary_xor.4ops.i1
 ; CHECK-NEXT:    %t0 = xor i1 %x, %y
-; CHECK-NEXT:    --> %t0 U: full-set S: full-set
+; CHECK-NEXT:    --> (%x + %y) U: full-set S: full-set
 ; CHECK-NEXT:    %t1 = xor i1 %z, %a
-; CHECK-NEXT:    --> %t1 U: full-set S: full-set
+; CHECK-NEXT:    --> (%z + %a) U: full-set S: full-set
 ; CHECK-NEXT:    %r = xor i1 %t0, %t1
-; CHECK-NEXT:    --> %r U: full-set S: full-set
+; CHECK-NEXT:    --> (%x + %y + %z + %a) U: full-set S: full-set
 ; CHECK-NEXT:  Determining loop execution counts for: @binary_xor.4ops.i1
 ;
   %t0 = xor i1 %x, %y