Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -7206,17 +7206,27 @@
   // 1*N = -Start; -1*N = Start (mod 2^BW), so:
   //   N = Distance (as unsigned)
   if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
-    ConstantRange CR = getUnsignedRange(Start);
-    const SCEV *MaxBECount;
-    if (!CountDown && CR.getUnsignedMin().isMinValue())
-      // When counting up, the worst starting value is 1, not 0.
-      MaxBECount = CR.getUnsignedMax().isMinValue()
-        ? getConstant(APInt::getMinValue(CR.getBitWidth()))
-        : getConstant(APInt::getMaxValue(CR.getBitWidth()));
-    else
-      MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
-                                         : -CR.getUnsignedMin());
-    return ExitLimit(Distance, MaxBECount, false, Predicates);
+    APInt MaxBECount = getUnsignedRange(Distance).getUnsignedMax();
+
+    // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
+    // we end up with a loop whose backedge-taken count is n - 1.  Detect this
+    // case, and see if we can improve the bound.
+    //
+    // Explicitly handling this here is necessary because getUnsignedRange
+    // isn't context-sensitive; it doesn't know that we only care about the
+    // range inside the loop.
+    const SCEV *Zero = getZero(Distance->getType());
+    const SCEVConstant *One = cast<SCEVConstant>(getOne(Distance->getType()));
+    const SCEV *DistancePlusOne = getAddExpr(Distance, getOne(Distance->getType()));
+    if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
+      // If Distance + 1 doesn't overflow, we can compute the maximum distance
+      // as "unsigned_max(Distance + 1) - 1".
+      ConstantRange CR = getUnsignedRange(DistancePlusOne);
+      APInt NewMaxBECount = CR.getUnsignedMax() - One->getAPInt();
+      if (NewMaxBECount.ult(MaxBECount))
+        MaxBECount = NewMaxBECount;
+    }
+    return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
   }
 
   // As a special case, handle the instance where Step is a positive power of
Index: test/Analysis/ScalarEvolution/max-trip-count.ll
===================================================================
--- test/Analysis/ScalarEvolution/max-trip-count.ll
+++ test/Analysis/ScalarEvolution/max-trip-count.ll
@@ -207,3 +207,84 @@
 bar.exit:                                         ; preds = %for.cond.i, %for.body.i
   ret i32 0
 }
+
+; CHECK-LABEL: @ne_max_trip_count_1
+; CHECK: Loop %for.body: max backedge-taken count is 7
+define i32 @ne_max_trip_count_1(i32 %n) {
+entry:
+  %masked = and i32 %n, 7
+  br label %for.body
+
+for.body:
+  %i = phi i32 [ 0, %entry ], [ %add, %for.body ]
+  %add = add nsw i32 %i, 1
+  %cmp = icmp ne i32 %i, %masked
+  br i1 %cmp, label %for.body, label %bar.exit
+
+bar.exit:
+  ret i32 0
+}
+
+; CHECK-LABEL: @ne_max_trip_count_2
+; CHECK: Loop %for.body: max backedge-taken count is -1
+define i32 @ne_max_trip_count_2(i32 %n) {
+entry:
+  %masked = and i32 %n, 7
+  br label %for.body
+
+for.body:
+  %i = phi i32 [ 0, %entry ], [ %add, %for.body ]
+  %add = add nsw i32 %i, 1
+  %cmp = icmp ne i32 %add, %masked
+  br i1 %cmp, label %for.body, label %bar.exit
+
+bar.exit:
+  ret i32 0
+}
+
+; CHECK-LABEL: @ne_max_trip_count_3
+; CHECK: Loop %for.body: max backedge-taken count is 6
+define i32 @ne_max_trip_count_3(i32 %n) {
+entry:
+  %masked = and i32 %n, 7
+  %guard = icmp eq i32 %masked, 0
+  br i1 %guard, label %exit, label %for.preheader
+
+for.preheader:
+  br label %for.body
+
+for.body:
+  %i = phi i32 [ 0, %for.preheader ], [ %add, %for.body ]
+  %add = add nsw i32 %i, 1
+  %cmp = icmp ne i32 %add, %masked
+  br i1 %cmp, label %for.body, label %loop.exit
+
+loop.exit:
+  br label %exit
+
+exit:
+  ret i32 0
+}
+
+; CHECK-LABEL: @ne_max_trip_count_4
+; CHECK: Loop %for.body: max backedge-taken count is -2
+define i32 @ne_max_trip_count_4(i32 %n) {
+entry:
+  %guard = icmp eq i32 %n, 0
+  br i1 %guard, label %exit, label %for.preheader
+
+for.preheader:
+  br label %for.body
+
+for.body:
+  %i = phi i32 [ 0, %for.preheader ], [ %add, %for.body ]
+  %add = add nsw i32 %i, 1
+  %cmp = icmp ne i32 %add, %n
+  br i1 %cmp, label %for.body, label %loop.exit
+
+loop.exit:
+  br label %exit
+
+exit:
+  ret i32 0
+}