diff --git a/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp b/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
@@ -1165,15 +1165,32 @@
 ///
 /// We can't replace %sel with %add unless we strip away the flags.
 /// TODO: Wrapping flags could be preserved in some cases with better analysis.
-static Value *foldSelectValueEquivalence(SelectInst &Sel, ICmpInst &Cmp,
-                                         const SimplifyQuery &Q) {
+static Instruction *foldSelectValueEquivalence(SelectInst &Sel, ICmpInst &Cmp,
+                                               const SimplifyQuery &Q,
+                                               InstCombiner &IC) {
   if (!Cmp.isEquality())
     return nullptr;
 
   // Canonicalize the pattern to ICMP_EQ by swapping the select operands.
   Value *TrueVal = Sel.getTrueValue(), *FalseVal = Sel.getFalseValue();
-  if (Cmp.getPredicate() == ICmpInst::ICMP_NE)
+  bool Swapped = false;
+  if (Cmp.getPredicate() == ICmpInst::ICMP_NE) {
     std::swap(TrueVal, FalseVal);
+    Swapped = true;
+  }
+
+  // In X == Y ? f(X) : Z, try to evaluate f(X) and replace the operand.
+  // Take care to avoid replacing X == Y ? X : Z with X == Y ? Y : Z, as that
+  // would lead to an infinite replacement cycle.
+  Value *CmpLHS = Cmp.getOperand(0), *CmpRHS = Cmp.getOperand(1);
+  if (TrueVal != CmpLHS)
+    if (Value *V = SimplifyWithOpReplaced(TrueVal, CmpLHS, CmpRHS, Q,
+                                          /* AllowRefinement */ true))
+      return IC.replaceOperand(Sel, Swapped ? 2 : 1, V);
+  if (TrueVal != CmpRHS)
+    if (Value *V = SimplifyWithOpReplaced(TrueVal, CmpRHS, CmpLHS, Q,
+                                          /* AllowRefinement */ true))
+      return IC.replaceOperand(Sel, Swapped ? 2 : 1, V);
 
   auto *FalseInst = dyn_cast<Instruction>(FalseVal);
   if (!FalseInst)
@@ -1198,12 +1215,11 @@
   // We have an 'EQ' comparison, so the select's false value will propagate.
   // Example:
   // (X == 42) ? 43 : (X + 1) --> (X == 42) ? (X + 1) : (X + 1) --> X + 1
-  Value *CmpLHS = Cmp.getOperand(0), *CmpRHS = Cmp.getOperand(1);
   if (SimplifyWithOpReplaced(FalseVal, CmpLHS, CmpRHS, Q,
                              /* AllowRefinement */ false) == TrueVal ||
       SimplifyWithOpReplaced(FalseVal, CmpRHS, CmpLHS, Q,
                              /* AllowRefinement */ false) == TrueVal) {
-    return FalseVal;
+    return IC.replaceInstUsesWith(Sel, FalseVal);
   }
 
   // Restore poison-generating flags if the transform did not apply.
@@ -1439,8 +1455,8 @@
 /// Visit a SelectInst that has an ICmpInst as its first operand.
 Instruction *InstCombinerImpl::foldSelectInstWithICmp(SelectInst &SI,
                                                       ICmpInst *ICI) {
-  if (Value *V = foldSelectValueEquivalence(SI, *ICI, SQ))
-    return replaceInstUsesWith(SI, V);
+  if (Instruction *NewSel = foldSelectValueEquivalence(SI, *ICI, SQ, *this))
+    return NewSel;
 
   if (Instruction *NewSel = canonicalizeMinMaxWithConstant(SI, *ICI, *this))
     return NewSel;
diff --git a/llvm/test/Transforms/InstCombine/rem.ll b/llvm/test/Transforms/InstCombine/rem.ll
--- a/llvm/test/Transforms/InstCombine/rem.ll
+++ b/llvm/test/Transforms/InstCombine/rem.ll
@@ -50,8 +50,7 @@
 define i5 @biggest_divisor(i5 %x) {
 ; CHECK-LABEL: @biggest_divisor(
 ; CHECK-NEXT:    [[DOTNOT:%.*]] = icmp eq i5 [[X:%.*]], -1
-; CHECK-NEXT:    [[TMP1:%.*]] = zext i1 [[DOTNOT]] to i5
-; CHECK-NEXT:    [[REM:%.*]] = add i5 [[TMP1]], [[X]]
+; CHECK-NEXT:    [[REM:%.*]] = select i1 [[DOTNOT]], i5 0, i5 [[X]]
 ; CHECK-NEXT:    ret i5 [[REM]]
 ;
   %rem = urem i5 %x, -1
diff --git a/llvm/test/Transforms/InstCombine/select-binop-cmp.ll b/llvm/test/Transforms/InstCombine/select-binop-cmp.ll
--- a/llvm/test/Transforms/InstCombine/select-binop-cmp.ll
+++ b/llvm/test/Transforms/InstCombine/select-binop-cmp.ll
@@ -564,12 +564,10 @@
   ret <2 x i8>  %C
 }
 
-; TODO: support for undefs, check for an identity constant does not handle them yet
-define <2 x i8> @select_xor_icmp_vec_bad_2(<2 x i8> %x, <2 x i8> %y, <2 x i8> %z) {
-; CHECK-LABEL: @select_xor_icmp_vec_bad_2(
+define <2 x i8> @select_xor_icmp_vec_undef(<2 x i8> %x, <2 x i8> %y, <2 x i8> %z) {
+; CHECK-LABEL: @select_xor_icmp_vec_undef(
 ; CHECK-NEXT:    [[A:%.*]] = icmp eq <2 x i8> [[X:%.*]], <i8 0, i8 undef>
-; CHECK-NEXT:    [[B:%.*]] = xor <2 x i8> [[X]], [[Z:%.*]]
-; CHECK-NEXT:    [[C:%.*]] = select <2 x i1> [[A]], <2 x i8> [[B]], <2 x i8> [[Y:%.*]]
+; CHECK-NEXT:    [[C:%.*]] = select <2 x i1> [[A]], <2 x i8> [[Z:%.*]], <2 x i8> [[Y:%.*]]
 ; CHECK-NEXT:    ret <2 x i8> [[C]]
 ;
   %A = icmp eq <2 x i8>  %x, <i8 0, i8 undef>
@@ -604,11 +602,10 @@
   ret i32 %C
 }
 
-define i32 @select_and_icmp_bad(i32 %x, i32 %y, i32 %z) {
-; CHECK-LABEL: @select_and_icmp_bad(
+define i32 @select_and_icmp_zero(i32 %x, i32 %y, i32 %z) {
+; CHECK-LABEL: @select_and_icmp_zero(
 ; CHECK-NEXT:    [[A:%.*]] = icmp eq i32 [[X:%.*]], 0
-; CHECK-NEXT:    [[B:%.*]] = and i32 [[X]], [[Z:%.*]]
-; CHECK-NEXT:    [[C:%.*]] = select i1 [[A]], i32 [[B]], i32 [[Y:%.*]]
+; CHECK-NEXT:    [[C:%.*]] = select i1 [[A]], i32 0, i32 [[Y:%.*]]
 ; CHECK-NEXT:    ret i32 [[C]]
 ;
   %A = icmp eq i32 %x, 0
diff --git a/llvm/test/Transforms/InstCombine/select.ll b/llvm/test/Transforms/InstCombine/select.ll
--- a/llvm/test/Transforms/InstCombine/select.ll
+++ b/llvm/test/Transforms/InstCombine/select.ll
@@ -2606,8 +2606,7 @@
 define i8 @select_replacement_add_eq(i8 %x, i8 %y) {
 ; CHECK-LABEL: @select_replacement_add_eq(
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X:%.*]], 1
-; CHECK-NEXT:    [[ADD:%.*]] = add i8 [[X]], 1
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[ADD]], i8 [[Y:%.*]]
+; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 2, i8 [[Y:%.*]]
 ; CHECK-NEXT:    ret i8 [[SEL]]
 ;
   %cmp = icmp eq i8 %x, 1
@@ -2620,8 +2619,7 @@
 ; CHECK-LABEL: @select_replacement_add_ne(
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp ne i8 [[X:%.*]], 1
 ; CHECK-NEXT:    call void @use(i1 [[CMP]])
-; CHECK-NEXT:    [[ADD:%.*]] = add i8 [[X]], 1
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[Y:%.*]], i8 [[ADD]]
+; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[Y:%.*]], i8 2
 ; CHECK-NEXT:    ret i8 [[SEL]]
 ;
   %cmp = icmp ne i8 %x, 1
@@ -2634,8 +2632,7 @@
 define i8 @select_replacement_add_nuw(i8 %x, i8 %y) {
 ; CHECK-LABEL: @select_replacement_add_nuw(
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X:%.*]], 1
-; CHECK-NEXT:    [[ADD:%.*]] = add nuw i8 [[X]], 1
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[ADD]], i8 [[Y:%.*]]
+; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 2, i8 [[Y:%.*]]
 ; CHECK-NEXT:    ret i8 [[SEL]]
 ;
   %cmp = icmp eq i8 %x, 1
@@ -2647,8 +2644,7 @@
 define i8 @select_replacement_sub(i8 %x, i8 %y, i8 %z) {
 ; CHECK-LABEL: @select_replacement_sub(
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[X:%.*]], [[Y:%.*]]
-; CHECK-NEXT:    [[SUB:%.*]] = sub i8 [[X]], [[Y]]
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[SUB]], i8 [[Z:%.*]]
+; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 0, i8 [[Z:%.*]]
 ; CHECK-NEXT:    ret i8 [[SEL]]
 ;
   %cmp = icmp eq i8 %x, %y
@@ -2661,8 +2657,7 @@
 ; CHECK-LABEL: @select_replacement_shift(
 ; CHECK-NEXT:    [[SHR:%.*]] = lshr exact i8 [[X:%.*]], 1
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp eq i8 [[SHR]], [[Y:%.*]]
-; CHECK-NEXT:    [[SHL:%.*]] = shl i8 [[Y]], 1
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[SHL]], i8 [[Z:%.*]]
+; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 [[X]], i8 [[Z:%.*]]
 ; CHECK-NEXT:    ret i8 [[SEL]]
 ;
   %shr = lshr exact i8 %x, 1