Index: lib/Transforms/InstCombine/InstCombineCompares.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -3030,6 +3030,48 @@
   return nullptr;
 }
 
+/// Fold icmp Pred smin(X, Y), X.
+Instruction *InstCombiner::foldICmpWithSMin(ICmpInst &Cmp) {
+  ICmpInst::Predicate Pred = Cmp.getPredicate();
+  Value *Op0 = Cmp.getOperand(0);
+  Value *X = Cmp.getOperand(1);
+
+  // Canonicalize minimum operand to LHS of the icmp.
+  if (match(X, m_SMin(m_Specific(Op0), m_Value())) ||
+      match(X, m_SMin(m_Value(), m_Specific(Op0)))) {
+    std::swap(Op0, X);
+    Pred = Cmp.getSwappedPredicate();
+  }
+
+  Value *Y;
+  if (!match(Op0, m_SMin(m_Specific(X), m_Value(Y))) &&
+      !match(Op0, m_SMin(m_Value(Y), m_Specific(X))))
+    return nullptr;
+
+  // TODO: The cases where we fold to a constant should be handled by
+  // InstSimplify, so we could assert on those?
+  switch (Pred) {
+  case CmpInst::ICMP_EQ:
+  case CmpInst::ICMP_SGE:
+    // smin(X, Y) == X --> X <= Y
+    // smin(X, Y) >= X --> X <= Y
+    return new ICmpInst(ICmpInst::ICMP_SLE, X, Y);
+  case CmpInst::ICMP_NE:
+  case CmpInst::ICMP_SLT:
+    // smin(X, Y) != X --> X > Y
+    // smin(X, Y) <  X --> X > Y
+    return new ICmpInst(ICmpInst::ICMP_SGT, X, Y);
+  case CmpInst::ICMP_SLE:
+    // smin(X, Y) <= X --> true
+    return replaceInstUsesWith(Cmp, ConstantInt::getTrue(Cmp.getType()));
+  case CmpInst::ICMP_SGT:
+    // smin(X, Y) > X --> false
+    return replaceInstUsesWith(Cmp, ConstantInt::getFalse(Cmp.getType()));
+  default:
+    return nullptr;
+  }
+}
+
 Instruction *InstCombiner::foldICmpEquality(ICmpInst &I) {
   if (!I.isEquality())
     return nullptr;
@@ -4277,6 +4319,9 @@
   if (Instruction *Res = foldICmpBinOp(I))
     return Res;
 
+  if (Instruction *Res = foldICmpWithSMin(I))
+    return Res;
+
   {
     Value *A, *B;
     // Transform (A & ~B) == 0 --> (A & B) != 0
Index: lib/Transforms/InstCombine/InstCombineInternal.h
===================================================================
--- lib/Transforms/InstCombine/InstCombineInternal.h
+++ lib/Transforms/InstCombine/InstCombineInternal.h
@@ -571,6 +571,7 @@
   Instruction *foldICmpInstWithConstant(ICmpInst &Cmp);
   Instruction *foldICmpInstWithConstantNotInt(ICmpInst &Cmp);
   Instruction *foldICmpBinOp(ICmpInst &Cmp);
+  Instruction *foldICmpWithSMin(ICmpInst &Cmp);
   Instruction *foldICmpEquality(ICmpInst &Cmp);
 
   Instruction *foldICmpTruncConstant(ICmpInst &Cmp, Instruction *Trunc,
Index: test/Transforms/InstCombine/smin-icmp.ll
===================================================================
--- test/Transforms/InstCombine/smin-icmp.ll
+++ test/Transforms/InstCombine/smin-icmp.ll
@@ -11,9 +11,7 @@
 
 define i1 @eq_smin1(i32 %x, i32 %y) {
 ; CHECK-LABEL: @eq_smin1(
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 %x, %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %x, i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i32 [[SEL]], %x
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 %x, %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %cmp1 = icmp slt i32 %x, %y
@@ -26,9 +24,7 @@
 
 define i1 @eq_smin2(i32 %x, i32 %y) {
 ; CHECK-LABEL: @eq_smin2(
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 %y, %x
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %y, i32 %x
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i32 [[SEL]], %x
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 %x, %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %cmp1 = icmp slt i32 %y, %x
@@ -42,9 +38,7 @@
 define i1 @eq_smin3(i32 %a, i32 %y) {
 ; CHECK-LABEL: @eq_smin3(
 ; CHECK-NEXT:    [[X:%.*]] = add i32 %a, 3
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[X]], %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 [[X]], i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i32 [[X]], [[SEL]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 [[X]], %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %x = add i32 %a, 3 ; thwart complexity-based canonicalization
@@ -59,9 +53,7 @@
 define i1 @eq_smin4(i32 %a, i32 %y) {
 ; CHECK-LABEL: @eq_smin4(
 ; CHECK-NEXT:    [[X:%.*]] = add i32 %a, 3
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp sgt i32 [[X]], %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %y, i32 [[X]]
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i32 [[X]], [[SEL]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 [[X]], %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %x = add i32 %a, 3 ; thwart complexity-based canonicalization
@@ -75,9 +67,7 @@
 
 define i1 @sge_smin1(i32 %x, i32 %y) {
 ; CHECK-LABEL: @sge_smin1(
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 %x, %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %x, i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp sge i32 [[SEL]], %x
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 %x, %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %cmp1 = icmp slt i32 %x, %y
@@ -90,9 +80,7 @@
 
 define i1 @sge_smin2(i32 %x, i32 %y) {
 ; CHECK-LABEL: @sge_smin2(
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 %y, %x
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %y, i32 %x
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp sge i32 [[SEL]], %x
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 %x, %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %cmp1 = icmp slt i32 %y, %x
@@ -106,9 +94,7 @@
 define i1 @sge_smin3(i32 %a, i32 %y) {
 ; CHECK-LABEL: @sge_smin3(
 ; CHECK-NEXT:    [[X:%.*]] = add i32 %a, 3
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[X]], %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 [[X]], i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 [[X]], [[SEL]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 [[X]], %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %x = add i32 %a, 3 ; thwart complexity-based canonicalization
@@ -123,9 +109,7 @@
 define i1 @sge_smin4(i32 %a, i32 %y) {
 ; CHECK-LABEL: @sge_smin4(
 ; CHECK-NEXT:    [[X:%.*]] = add i32 %a, 3
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp sgt i32 [[X]], %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %y, i32 [[X]]
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 [[X]], [[SEL]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sle i32 [[X]], %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %x = add i32 %a, 3 ; thwart complexity-based canonicalization
@@ -139,9 +123,7 @@
 
 define i1 @ne_smin1(i32 %x, i32 %y) {
 ; CHECK-LABEL: @ne_smin1(
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 %x, %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %x, i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp ne i32 [[SEL]], %x
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sgt i32 %x, %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %cmp1 = icmp slt i32 %x, %y
@@ -168,9 +150,7 @@
 define i1 @ne_smin3(i32 %a, i32 %y) {
 ; CHECK-LABEL: @ne_smin3(
 ; CHECK-NEXT:    [[X:%.*]] = add i32 %a, 3
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[X]], %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 [[X]], i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp ne i32 [[X]], [[SEL]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[X]], %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %x = add i32 %a, 3 ; thwart complexity-based canonicalization
@@ -199,9 +179,7 @@
 
 define i1 @slt_smin1(i32 %x, i32 %y) {
 ; CHECK-LABEL: @slt_smin1(
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 %x, %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 %x, i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp slt i32 [[SEL]], %x
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sgt i32 %x, %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %cmp1 = icmp slt i32 %x, %y
@@ -228,9 +206,7 @@
 define i1 @slt_smin3(i32 %a, i32 %y) {
 ; CHECK-LABEL: @slt_smin3(
 ; CHECK-NEXT:    [[X:%.*]] = add i32 %a, 3
-; CHECK-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[X]], %y
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP1]], i32 [[X]], i32 %y
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[X]], [[SEL]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[X]], %y
 ; CHECK-NEXT:    ret i1 [[CMP2]]
 ;
   %x = add i32 %a, 3 ; thwart complexity-based canonicalization