diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -5672,11 +5672,12 @@
   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 UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
+      if (!UnsignedMinValue.isNullValue())
+        ConservativeResult = ConservativeResult.intersectWith(
+            ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
+    }
 
     // If there's no signed wrap, and all the operands except initial value have
     // the same sign or zero, the value won't ever be:
diff --git a/llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll b/llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll
--- a/llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll
+++ b/llvm/test/Analysis/ScalarEvolution/range_nw_flag.ll
@@ -2,7 +2,7 @@
 
 ; copied from flags-from-poison.ll
 ; CHECK-LABEL: @test-add-nuw
-; CHECK: -->  {(1 + %offset)<nuw>,+,1}<nuw><%loop> U: full-set S: full-set
+; CHECK: -->  {(1 + %offset)<nuw>,+,1}<nuw><%loop> U: [1,0) S: [1,0)
 define void @test-add-nuw(float* %input, i32 %offset, i32 %numIterations) {
 entry:
   br label %loop
@@ -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: [11,0)
 define void @test-addrec-nuw(float* %input, i32 %offset, i32 %numIterations) {
 entry:
   %cmp = icmp sgt i32 %offset, 10