Index: llvm/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- llvm/lib/Analysis/ScalarEvolution.cpp
+++ llvm/lib/Analysis/ScalarEvolution.cpp
@@ -5654,11 +5654,17 @@
   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
     // If there's no unsigned wrap, the value will never be less than its
     // initial value.
-    if (AddRec->hasNoUnsignedWrap())
-      if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
-        if (!C->getValue()->isZero())
-          ConservativeResult = ConservativeResult.intersectWith(
-              ConstantRange(C->getAPInt(), APInt(BitWidth, 0)), RangeType);
+    if (AddRec->hasNoUnsignedWrap()) {
+      APInt MinValue = APInt(BitWidth, 0);
+      const SCEV *Start = AddRec->getStart();
+      if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
+        MinValue = getUnsignedRangeMin(AddRec->getStart());
+      else if (isKnownNonNegative(Start) || isKnownNonPositive(Start))
+        MinValue = getSignedRangeMin(Start);
+      if (!MinValue.isNullValue())
+        ConservativeResult = ConservativeResult.intersectWith(
+            ConstantRange(MinValue, APInt(BitWidth, 0)), RangeType);
+    }
 
     // If there's no signed wrap, and all the operands have the same sign or
     // zero, the value won't ever change sign.
Index: llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll
===================================================================
--- llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll
+++ llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll
@@ -20,7 +20,7 @@
 }
 
 ; CHECK-LABEL: @test-addrec-nuw
-; CHECK: -->  {(1 + (10 smax %offset))<nuw>,+,1}<nuw><%loop> U: full-set S: full-set 
+; CHECK: -->  {(1 + (10 smax %offset))<nuw>,+,1}<nuw><%loop> U: [11,0) S: full-set
 define void @test-addrec-nuw(float* %input, i32 %offset, i32 %numIterations) {
 entry:
   %cmp = icmp sgt i32 %offset, 10