diff --git a/include/llvm/Analysis/ScalarEvolution.h b/include/llvm/Analysis/ScalarEvolution.h
index e3be8ee..548f8f6 100644
--- a/include/llvm/Analysis/ScalarEvolution.h
+++ b/include/llvm/Analysis/ScalarEvolution.h
@@ -253,7 +253,8 @@
     /// CouldNotCompute if an intermediate computation overflows.
     const SCEV *getBECount(const SCEV *Start,
                            const SCEV *End,
-                           const SCEV *Step);
+                           const SCEV *Step,
+                           bool NoWrap);
 
     /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
     /// loop, lazily computing new values if the loop hasn't been analyzed
diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
index 6466386..fa45235 100644
--- a/lib/Analysis/ScalarEvolution.cpp
+++ b/lib/Analysis/ScalarEvolution.cpp
@@ -2972,8 +2972,20 @@
       const SCEV *LHS = getSCEV(U->getOperand(0));
       const APInt &CIVal = CI->getValue();
       if (GetMinTrailingZeros(LHS) >=
-          (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
-        return getAddExpr(LHS, getSCEV(U->getOperand(1)));
+          (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
+        // Build a plain add SCEV.
+        const SCEV *S = getAddExpr(LHS, getSCEV(CI));
+        // If the LHS of the add was an addrec and it has no-wrap flags,
+        // transfer the no-wrap flags, since an or won't introduce a wrap.
+        if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
+          const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
+          if (OldAR->hasNoUnsignedWrap())
+            const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
+          if (OldAR->hasNoSignedWrap())
+            const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
+        }
+        return S;
+      }
     }
     break;
   case Instruction::Xor:
@@ -4795,7 +4807,8 @@
 /// CouldNotCompute if an intermediate computation overflows.
 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
                                         const SCEV *End,
-                                        const SCEV *Step) {
+                                        const SCEV *Step,
+                                        bool NoWrap) {
   const Type *Ty = Start->getType();
   const SCEV *NegOne = getIntegerSCEV(-1, Ty);
   const SCEV *Diff = getMinusSCEV(End, Start);
@@ -4805,15 +4818,17 @@
   // the division will effectively round up.
   const SCEV *Add = getAddExpr(Diff, RoundUp);
 
-  // Check Add for unsigned overflow.
-  // TODO: More sophisticated things could be done here.
-  const Type *WideTy = IntegerType::get(getContext(),
-                                        getTypeSizeInBits(Ty) + 1);
-  const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
-  const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
-  const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
-  if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
-    return getCouldNotCompute();
+  if (!NoWrap) {
+    // Check Add for unsigned overflow.
+    // TODO: More sophisticated things could be done here.
+    const Type *WideTy = IntegerType::get(getContext(),
+                                          getTypeSizeInBits(Ty) + 1);
+    const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
+    const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
+    const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
+    if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
+      return getCouldNotCompute();
+  }
 
   return getUDivExpr(Add, Step);
 }
@@ -4831,6 +4846,10 @@
   if (!AddRec || AddRec->getLoop() != L)
     return getCouldNotCompute();
 
+  // Check to see if we have a flag which makes analysis easy.
+  bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
+                           AddRec->hasNoUnsignedWrap();
+
   if (AddRec->isAffine()) {
     // FORNOW: We only support unit strides.
     unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
@@ -4843,7 +4862,10 @@
     if (CStep->isOne()) {
       // With unit stride, the iteration never steps past the limit value.
     } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
-      if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
+      if (NoWrap) {
+        // We know the iteration won't step past the maximum value for its type.
+        ;
+      } else if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
         // Test whether a positive iteration iteration can step past the limit
         // value and past the maximum value for its type in a single step.
         if (isSigned) {
@@ -4896,11 +4918,11 @@
 
     // Finally, we subtract these two values and divide, rounding up, to get
     // the number of times the backedge is executed.
-    const SCEV *BECount = getBECount(Start, End, Step);
+    const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
 
     // The maximum backedge count is similar, except using the minimum start
     // value and the maximum end value.
-    const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step);
+    const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
 
     return BackedgeTakenInfo(BECount, MaxBECount);
   }
diff --git a/test/Analysis/ScalarEvolution/nsw-offset.ll b/test/Analysis/ScalarEvolution/nsw-offset.ll
new file mode 100644
index 0000000..1e165bf6
--- /dev/null
+++ b/test/Analysis/ScalarEvolution/nsw-offset.ll
@@ -0,0 +1,76 @@
+; RUN: opt < %s -S -analyze -scalar-evolution -disable-output | FileCheck %s
+
+; ScalarEvolution should be able to fold away the sign-extensions
+; on this loop with a primary induction variable incremented with
+; a nsw add of 2.
+
+target datalayout = "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128"
+
+define void @foo(i32 %n, double* nocapture %d, double* nocapture %q) nounwind {
+entry:
+  %0 = icmp sgt i32 %n, 0                         ; <i1> [#uses=1]
+  br i1 %0, label %bb.nph, label %return
+
+bb.nph:                                           ; preds = %entry
+  br label %bb
+
+bb:                                               ; preds = %bb.nph, %bb1
+  %i.01 = phi i32 [ %16, %bb1 ], [ 0, %bb.nph ]   ; <i32> [#uses=5]
+
+; CHECK: %1 = sext i32 %i.01 to i64
+; CHECK: -->  {0,+,2}<bb>
+  %1 = sext i32 %i.01 to i64                      ; <i64> [#uses=1]
+
+; CHECK: %2 = getelementptr inbounds double* %d, i64 %1
+; CHECK: -->  {%d,+,16}<bb>
+  %2 = getelementptr inbounds double* %d, i64 %1  ; <double*> [#uses=1]
+
+  %3 = load double* %2, align 8                   ; <double> [#uses=1]
+  %4 = sext i32 %i.01 to i64                      ; <i64> [#uses=1]
+  %5 = getelementptr inbounds double* %q, i64 %4  ; <double*> [#uses=1]
+  %6 = load double* %5, align 8                   ; <double> [#uses=1]
+  %7 = or i32 %i.01, 1                            ; <i32> [#uses=1]
+
+; CHECK: %8 = sext i32 %7 to i64
+; CHECK: -->  {1,+,2}<bb>
+  %8 = sext i32 %7 to i64                         ; <i64> [#uses=1]
+
+; CHECK: %9 = getelementptr inbounds double* %q, i64 %8
+; CHECK: {(8 + %q),+,16}<bb>
+  %9 = getelementptr inbounds double* %q, i64 %8  ; <double*> [#uses=1]
+
+; Artificially repeat the above three instructions, this time using
+; add nsw instead of or.
+  %t7 = add nsw i32 %i.01, 1                            ; <i32> [#uses=1]
+
+; CHECK: %t8 = sext i32 %t7 to i64
+; CHECK: -->  {1,+,2}<bb>
+  %t8 = sext i32 %t7 to i64                         ; <i64> [#uses=1]
+
+; CHECK: %t9 = getelementptr inbounds double* %q, i64 %t8
+; CHECK: {(8 + %q),+,16}<bb>
+  %t9 = getelementptr inbounds double* %q, i64 %t8  ; <double*> [#uses=1]
+
+  %10 = load double* %9, align 8                  ; <double> [#uses=1]
+  %11 = fadd double %6, %10                       ; <double> [#uses=1]
+  %12 = fadd double %11, 3.200000e+00             ; <double> [#uses=1]
+  %13 = fmul double %3, %12                       ; <double> [#uses=1]
+  %14 = sext i32 %i.01 to i64                     ; <i64> [#uses=1]
+  %15 = getelementptr inbounds double* %d, i64 %14 ; <double*> [#uses=1]
+  store double %13, double* %15, align 8
+  %16 = add nsw i32 %i.01, 2                      ; <i32> [#uses=2]
+  br label %bb1
+
+bb1:                                              ; preds = %bb
+  %17 = icmp slt i32 %16, %n                      ; <i1> [#uses=1]
+  br i1 %17, label %bb, label %bb1.return_crit_edge
+
+bb1.return_crit_edge:                             ; preds = %bb1
+  br label %return
+
+return:                                           ; preds = %bb1.return_crit_edge, %entry
+  ret void
+}
+
+; CHECK: Loop bb: backedge-taken count is ((-1 + %n) /u 2)
+; CHECK: Loop bb: max backedge-taken count is 1073741823