Index: include/llvm/Analysis/ScalarEvolution.h
===================================================================
--- include/llvm/Analysis/ScalarEvolution.h
+++ include/llvm/Analysis/ScalarEvolution.h
@@ -1838,7 +1838,7 @@
   /// assert these preconditions so please be careful.
   const SCEV *computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride,
                                      const SCEV *End, unsigned BitWidth,
-                                     bool IsSigned);
+                                     bool IsSigned, const Loop *L);
 
   /// Verify if an linear IV with positive stride can overflow when in a
   /// less-than comparison, knowing the invariant term of the comparison,
Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -10465,8 +10465,8 @@
                                                     const SCEV *Stride,
                                                     const SCEV *End,
                                                     unsigned BitWidth,
-                                                    bool IsSigned) {
-
+                                                    bool IsSigned,
+                                                    const Loop *L) {
   assert(!isKnownNonPositive(Stride) &&
          "Stride is expected strictly positive!");
   // Calculate the maximum backedge count based on the range of values
@@ -10475,6 +10475,34 @@
   APInt MinStart =
       IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
 
+  // For this loop:
+  // entry:
+  //   %x = load i32, i32* @global, align 4
+  //   %0 = icmp ult i32 %x, 17
+  //   br i1 %0, label %loop, label %exit
+  //
+  // loop:
+  //   %iv = phi i32 [ %x, %entry ], [ %iv.next, %loop ]
+  //   %iv.next = add nuw i32 %iv, 8
+  //   %1 = icmp ult i32 %iv.next, 17
+  //   br i1 %1, label %loop, label %exit
+  //
+  // exit:
+  //   ret void
+  //
+  // Start is (%x + 8), Stride is 8, End is 17. Given that loop entry is guarded
+  // by ult %x, 17, we know %x is in [0, 17) if loop is entered, and min start
+  // shall be 8.
+  auto *S = getMinusSCEV(Start, Stride);
+  if (!IsSigned && isa<SCEVConstant>(Stride) && isLoopInvariant(End, L) &&
+      // Prove that (Start - Stride) is in [0, End)
+      isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, S, End) &&
+      // Prove that (Start - Stride) doesn't overflow.
+      isKnownNonNegative(Stride) && isKnownNonNegative(End))
+    // Compute MinStart as getUnsignedRangeMin(Start-Stride) + Stride.
+    MinStart = getUnsignedRangeMin(S) +
+               dyn_cast<SCEVConstant>(Stride)->getAPInt();
+
   APInt StrideForMaxBECount =
       IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
 
@@ -10598,7 +10626,7 @@
   // checked above).
   if (!isLoopInvariant(RHS, L)) {
     const SCEV *MaxBECount = computeMaxBECountForLT(
-        Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
+        Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned, L);
     return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
                      false /*MaxOrZero*/, Predicates);
   }
@@ -10635,7 +10663,7 @@
     MaxOrZero = true;
   } else {
     MaxBECount = computeMaxBECountForLT(
-        Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
+        Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned, L);
   }
 
   if (isa<SCEVCouldNotCompute>(MaxBECount) &&
Index: test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll
===================================================================
--- test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll
+++ test/Analysis/ScalarEvolution/2008-11-18-Stride2.ll
@@ -1,7 +1,7 @@
 ; RUN: opt < %s -analyze -scalar-evolution 2>&1 | FileCheck %s
 
 ; CHECK: Loop %bb: backedge-taken count is ((999 + (-1 * %x)) /u 3)
-; CHECK: Loop %bb: max backedge-taken count is 334
+; CHECK: Loop %bb: max backedge-taken count is 333
 
 
 ; This is a tricky testcase for unsigned wrap detection which ScalarEvolution