Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -4250,6 +4250,24 @@
     std::swap(LHS, RHS);
   // fall through
   case ICmpInst::ICMP_SGT:
+    // a+1 >s b ? a+x : b+x  ->  smax(a, b)+x
+    // a+1 >s b ? b+x : a+x  ->  smin(a, b)+x
+    if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
+      const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
+      const SCEV *LSMinusOne = getMinusSCEV(LS, getOne(I->getType()));
+      const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
+      const SCEV *LA = getSCEV(TrueVal);
+      const SCEV *RA = getSCEV(FalseVal);
+      const SCEV *LDiff = getMinusSCEV(LA, LSMinusOne);
+      const SCEV *RDiff = getMinusSCEV(RA, RS);
+      if (LDiff == RDiff)
+        return getAddExpr(getSMaxExpr(LSMinusOne, RS), RDiff);
+      LDiff = getMinusSCEV(LA, RS);
+      RDiff = getMinusSCEV(RA, LSMinusOne);
+      if (LDiff == RDiff)
+        return getAddExpr(getSMinExpr(LSMinusOne, RS), LDiff);
+    }
+  // fall through
   case ICmpInst::ICMP_SGE:
     // a >s b ? a+x : b+x  ->  smax(a, b)+x
     // a >s b ? b+x : a+x  ->  smin(a, b)+x
@@ -4273,6 +4291,24 @@
     std::swap(LHS, RHS);
   // fall through
   case ICmpInst::ICMP_UGT:
+    // a+1 >u b ? a+x : b+x  ->  umax(a, b)+x
+    // a+1 >u b ? b+x : a+x  ->  umin(a, b)+x
+    if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
+      const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
+      const SCEV *LSMinusOne = getMinusSCEV(LS, getOne(I->getType()));
+      const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
+      const SCEV *LA = getSCEV(TrueVal);
+      const SCEV *RA = getSCEV(FalseVal);
+      const SCEV *LDiff = getMinusSCEV(LA, LSMinusOne);
+      const SCEV *RDiff = getMinusSCEV(RA, RS);
+      if (LDiff == RDiff)
+        return getAddExpr(getUMaxExpr(LSMinusOne, RS), RDiff);
+      LDiff = getMinusSCEV(LA, RS);
+      RDiff = getMinusSCEV(RA, LSMinusOne);
+      if (LDiff == RDiff)
+        return getAddExpr(getUMinExpr(LSMinusOne, RS), LDiff);
+    }
+  // fall through
   case ICmpInst::ICMP_UGE:
     // a >u b ? a+x : b+x  ->  umax(a, b)+x
     // a >u b ? b+x : a+x  ->  umin(a, b)+x
Index: test/Analysis/ScalarEvolution/min-max-patterns.ll
===================================================================
--- /dev/null
+++ test/Analysis/ScalarEvolution/min-max-patterns.ll
@@ -0,0 +1,56 @@
+; RUN: opt -analyze -scalar-evolution < %s | FileCheck %s
+;
+; This file contains test cases that verify that some simple uses of ICMP and
+; SELECT are recognized as SMAX/UMAX or SMIN/UMIN.
+
+; Try to match the following pattern in function f0:
+; a+1 >s b ? a+x : b+x  ->  smax(a, b)+x
+define void @f0(i64 %x, i64 %y) {
+; CHECK-LABEL: Classifying expressions for: @f0
+entry:
+  %z = add i64 %x, 1
+  %cond = icmp sgt i64 %z, %y
+  %max = select i1 %cond, i64 %x, i64 %y
+; CHECK: %max = select i1 %cond, i64 %x, i64 %y
+; CHECK-NEXT: -->  (%x smax %y)
+  ret void
+}
+
+; Try to match the following pattern in function f1:
+; a+1 >s b ? b+x : a+x  ->  smin(a, b)+x
+define void @f1(i64 %x, i64 %y) {
+; CHECK-LABEL: Classifying expressions for: @f1
+entry:
+  %z = add i64 %x, 1
+  %cond = icmp sgt i64 %z, %y
+  %min = select i1 %cond, i64 %y, i64 %x
+; CHECK: %min = select i1 %cond, i64 %y, i64 %x
+; CHECK-NEXT: -->  (-1 + (-1 * ((-1 + (-1 * %x)) smax (-1 + (-1 * %y)))))
+  ret void
+}
+
+; Try to match the following pattern in function f2:
+; a+1 >u b ? a+x : b+x  ->  umax(a, b)+x
+define void @f2(i64 %x, i64 %y) {
+; CHECK-LABEL: Classifying expressions for: @f2
+entry:
+  %z = add i64 %x, 1
+  %cond = icmp ugt i64 %z, %y
+  %max = select i1 %cond, i64 %x, i64 %y
+; CHECK: %max = select i1 %cond, i64 %x, i64 %y
+; CHECK-NEXT: -->  (%x umax %y)
+  ret void
+}
+
+; Try to match the following pattern in function f3:
+; a+1 >u b ? b+x : a+x  ->  umin(a, b)+x
+define void @f3(i64 %x, i64 %y) {
+; CHECK-LABEL: Classifying expressions for: @f3
+entry:
+  %z = add i64 %x, 1
+  %cond = icmp ugt i64 %z, %y
+  %min = select i1 %cond, i64 %y, i64 %x
+; CHECK: %min = select i1 %cond, i64 %y, i64 %x
+; CHECK-NEXT: -->  (-1 + (-1 * ((-1 + (-1 * %x)) umax (-1 + (-1 * %y)))))
+  ret void
+}