diff --git a/include/llvm/Analysis/ScalarEvolution.h b/include/llvm/Analysis/ScalarEvolution.h
index d9104067711..4706c09e791 100644
--- a/include/llvm/Analysis/ScalarEvolution.h
+++ b/include/llvm/Analysis/ScalarEvolution.h
@@ -539,7 +539,8 @@ namespace llvm {
 
     /// getMinusSCEV - Return LHS-RHS.
     ///
-    const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS);
+    const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
+                             bool HasNUW = false, bool HasNSW = false);
 
     /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
     /// of the input value to the specified type.  If the type must be
diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
index b675e286bad..d3d65847cbc 100644
--- a/lib/Analysis/ScalarEvolution.cpp
+++ b/lib/Analysis/ScalarEvolution.cpp
@@ -2448,22 +2448,21 @@ const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
 
 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
 ///
-const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
-                                          const SCEV *RHS) {
+const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
+                                          bool HasNUW, bool HasNSW) {
   // Fast path: X - X --> 0.
   if (LHS == RHS)
     return getConstant(LHS->getType(), 0);
 
   // X - Y --> X + -Y
-  return getAddExpr(LHS, getNegativeSCEV(RHS));
+  return getAddExpr(LHS, getNegativeSCEV(RHS), HasNUW, HasNSW);
 }
 
 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
 /// input value to the specified type.  If the type must be extended, it is zero
 /// extended.
 const SCEV *
-ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
-                                         const Type *Ty) {
+ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) {
   const Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
@@ -3942,6 +3941,105 @@ ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
   return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
 }
 
+static const SCEVAddRecExpr *
+isSimpleUnwrappingAddRec(const SCEV *S, const Loop *L) {
+  const SCEVAddRecExpr *SA = dyn_cast<SCEVAddRecExpr>(S);
+  
+  // The SCEV must be an addrec of this loop.
+  if (!SA || SA->getLoop() != L || !SA->isAffine())
+    return 0;
+  
+  // The SCEV must be known to not wrap in some way to be interesting.
+  if (!SA->hasNoUnsignedWrap() && !SA->hasNoSignedWrap())
+    return 0;
+
+  // The stride must be a constant so that we know if it is striding up or down.
+  if (!isa<SCEVConstant>(SA->getOperand(1)))
+    return 0;
+  return SA;
+}
+
+/// getMinusSCEVForExitTest - When considering an exit test for a loop with a
+/// "x != y" exit test, we turn this into a computation that evaluates x-y != 0,
+/// and this function returns the expression to use for x-y.  We know and take
+/// advantage of the fact that this subtraction is only being used in a
+/// comparison by zero context.
+///
+static const SCEV *getMinusSCEVForExitTest(const SCEV *LHS, const SCEV *RHS,
+                                           const Loop *L, ScalarEvolution &SE) {
+  // If either LHS or RHS is an AddRec SCEV (of this loop) that is known to not
+  // wrap (either NSW or NUW), then we know that the value will either become
+  // the other one (and thus the loop terminates), that the loop will terminate
+  // through some other exit condition first, or that the loop has undefined
+  // behavior.  This information is useful when the addrec has a stride that is
+  // != 1 or -1, because it means we can't "miss" the exit value.
+  //
+  // In any of these three cases, it is safe to turn the exit condition into a
+  // "counting down" AddRec (to zero) by subtracting the two inputs as normal,
+  // but since we know that the "end cannot be missed" we can force the
+  // resulting AddRec to be a NUW addrec.  Since it is counting down, this means
+  // that the AddRec *cannot* pass zero.
+
+  // See if LHS and RHS are addrec's we can handle.
+  const SCEVAddRecExpr *LHSA = isSimpleUnwrappingAddRec(LHS, L);
+  const SCEVAddRecExpr *RHSA = isSimpleUnwrappingAddRec(RHS, L);
+  
+  // If neither addrec is interesting, just return a minus.
+  if (RHSA == 0 && LHSA == 0)
+    return SE.getMinusSCEV(LHS, RHS);
+  
+  // If only one of LHS and RHS are an AddRec of this loop, make sure it is LHS.
+  if (RHSA && LHSA == 0) {
+    // Safe because a-b === b-a for comparisons against zero.
+    std::swap(LHS, RHS);
+    std::swap(LHSA, RHSA);
+  }
+  
+  // Handle the case when only one is advancing in a non-overflowing way.
+  if (RHSA == 0) {
+    // If RHS is loop varying, then we can't predict when LHS will cross it.
+    if (!SE.isLoopInvariant(RHS, L))
+      return SE.getMinusSCEV(LHS, RHS);
+    
+    // If LHS has a positive stride, then we compute RHS-LHS, because the loop
+    // is counting up until it crosses RHS (which must be larger than LHS).  If
+    // it is negative, we compute LHS-RHS because we're counting down to RHS.
+    const ConstantInt *Stride =
+      cast<SCEVConstant>(LHSA->getOperand(1))->getValue();
+    if (Stride->getValue().isNegative())
+      std::swap(LHS, RHS);
+
+    return SE.getMinusSCEV(RHS, LHS, true /*HasNUW*/);
+  }
+  
+  // If both LHS and RHS are interesting, we have something like:
+  //  a+i*4 != b+i*8.
+  const ConstantInt *LHSStride =
+    cast<SCEVConstant>(LHSA->getOperand(1))->getValue();
+  const ConstantInt *RHSStride =
+    cast<SCEVConstant>(RHSA->getOperand(1))->getValue();
+  
+  // If the strides are equal, then this is just a (complex) loop invariant
+  // comparison of a/b.
+  if (LHSStride == RHSStride)
+    return SE.getMinusSCEV(LHSA->getStart(), RHSA->getStart());
+  
+  // If the signs of the strides differ, then the negative stride is counting
+  // down to the positive stride.
+  if (LHSStride->getValue().isNegative() != RHSStride->getValue().isNegative()){
+    if (RHSStride->getValue().isNegative())
+      std::swap(LHS, RHS);
+  } else {
+    // If LHS's stride is smaller than RHS's stride, then "b" must be less than
+    // "a" and "b" is RHS is counting up (catching up) to LHS.  This is true
+    // whether the strides are positive or negative.
+    if (RHSStride->getValue().slt(LHSStride->getValue()))
+      std::swap(LHS, RHS);
+  }
+    
+  return SE.getMinusSCEV(LHS, RHS, true /*HasNUW*/);
+}
+
 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
 /// backedge of the specified loop will execute if its exit condition
 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
@@ -4001,7 +4099,8 @@ ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
   switch (Cond) {
   case ICmpInst::ICMP_NE: {                     // while (X != Y)
     // Convert to: while (X-Y != 0)
-    BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
+    BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEVForExitTest(LHS, RHS, L,
+                                                                 *this), L);
     if (BTI.hasAnyInfo()) return BTI;
     break;
   }