Index: lib/Transforms/InstCombine/InstCombineCompares.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -2824,6 +2824,31 @@
   if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_SLT && match(D, m_One()))
     return new ICmpInst(CmpInst::ICMP_SLE, Op0, C);
 
+  // TODO: The subtraction-related identities shown below also hold, but
+  // canonicalization from (X -nuw 1) to (X + -1) means that the combinations
+  // wouldn't happen even if they were implemented.
+  //
+  // icmp ult (X - 1), Y -> icmp ule X, Y
+  // icmp uge (X - 1), Y -> icmp ugt X, Y
+  // icmp ugt X, (Y - 1) -> icmp uge X, Y
+  // icmp ule X, (Y - 1) -> icmp ult X, Y
+
+  // icmp ule (X + 1), Y -> icmp ult X, Y
+  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_ULE && match(B, m_One()))
+    return new ICmpInst(CmpInst::ICMP_ULT, A, Op1);
+
+  // icmp ugt (X + 1), Y -> icmp uge X, Y
+  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_UGT && match(B, m_One()))
+    return new ICmpInst(CmpInst::ICMP_UGE, A, Op1);
+
+  // icmp uge X, (Y + 1) -> icmp ugt X, Y
+  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_UGE && match(D, m_One()))
+    return new ICmpInst(CmpInst::ICMP_UGT, Op0, C);
+
+  // icmp ult X, (Y + 1) -> icmp ule X, Y
+  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_ULT && match(D, m_One()))
+    return new ICmpInst(CmpInst::ICMP_ULE, Op0, C);
+
   // if C1 has greater magnitude than C2:
   //  icmp (X + C1), (Y + C2) -> icmp (X + C3), Y
   //  s.t. C3 = C1 - C2
Index: test/Transforms/InstCombine/icmp.ll
===================================================================
--- test/Transforms/InstCombine/icmp.ll
+++ test/Transforms/InstCombine/icmp.ll
@@ -2761,3 +2761,47 @@
   %b = icmp eq i64 %o, 0
   ret i1 %b
 }
+
+define i1 @icmp_add1_ugt(i32 %x, i32 %y) {
+; CHECK-LABEL: @icmp_add1_ugt(
+; CHECK-NEXT:    [[CMP:%.*]] = icmp uge i32 %x, %y
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %add = add nuw i32 %x, 1
+  %cmp = icmp ugt i32 %add, %y
+  ret i1 %cmp
+}
+
+define i1 @icmp_add1_ule(i32 %x, i32 %y) {
+; CHECK-LABEL: @icmp_add1_ule(
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i32 %x, %y
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %add = add nuw i32 %x, 1
+  %cmp = icmp ule i32 %add, %y
+  ret i1 %cmp
+}
+
+define i1 @cmp_uge_rhs_inc(float %x, i32 %i) {
+; CHECK-LABEL: @cmp_uge_rhs_inc(
+; CHECK-NEXT:    [[CONV:%.*]] = fptosi float %x to i32
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ugt i32 [[CONV]], %i
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %conv = fptosi float %x to i32
+  %inc = add nuw i32 %i, 1
+  %cmp = icmp uge i32 %conv, %inc
+  ret i1 %cmp
+}
+
+define i1 @cmp_ult_rhs_inc(float %x, i32 %i) {
+; CHECK-LABEL: @cmp_ult_rhs_inc(
+; CHECK-NEXT:    [[CONV:%.*]] = fptosi float %x to i32
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i32 [[CONV]], %i
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %conv = fptosi float %x to i32
+  %inc = add nuw i32 %i, 1
+  %cmp = icmp ult i32 %conv, %inc
+  ret i1 %cmp
+}