Index: llvm/trunk/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- llvm/trunk/lib/Analysis/ScalarEvolution.cpp
+++ llvm/trunk/lib/Analysis/ScalarEvolution.cpp
@@ -8655,43 +8655,68 @@
                                       : ICmpInst::ICMP_ULT;
   const SCEV *Start = IV->getStart();
   const SCEV *End = RHS;
-  if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
+  // If the backedge is taken at least once, then it will be taken
+  // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
+  // is the LHS value of the less-than comparison the first time it is evaluated
+  // and End is the RHS.
+  const SCEV *BECountIfBackedgeTaken =
+    computeBECount(getMinusSCEV(End, Start), Stride, false);
+  // If the loop entry is guarded by the result of the backedge test of the
+  // first loop iteration, then we know the backedge will be taken at least
+  // once and so the backedge taken count is as above. If not then we use the
+  // expression (max(End,Start)-Start)/Stride to describe the backedge count,
+  // as if the backedge is taken at least once max(End,Start) is End and so the
+  // result is as above, and if not max(End,Start) is Start so we get a backedge
+  // count of zero.
+  const SCEV *BECount;
+  if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
+    BECount = BECountIfBackedgeTaken;
+  else {
     End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
+    BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
+  }
 
-  const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
-
-  APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
-                            : getUnsignedRange(Start).getUnsignedMin();
-
-  unsigned BitWidth = getTypeSizeInBits(LHS->getType());
-
-  APInt StrideForMaxBECount;
-
-  if (PositiveStride)
-    StrideForMaxBECount = IsSigned ? getSignedRange(Stride).getSignedMin()
-                                   : getUnsignedRange(Stride).getUnsignedMin();
-  else
-    // Using a stride of 1 is safe when computing max backedge taken count for
-    // a loop with unknown stride.
-    StrideForMaxBECount = APInt(BitWidth, 1, IsSigned);
+  const SCEV *MaxBECount;
+  if (isa<SCEVConstant>(BECount))
+    MaxBECount = BECount;
+  else if (isa<SCEVConstant>(BECountIfBackedgeTaken))
+    // If we know exactly how many times the backedge will be taken if it's
+    // taken at least once, then the backedge count will either be that or
+    // zero.
+    MaxBECount = BECountIfBackedgeTaken;
+  else {
+    // Calculate the maximum backedge count based on the range of values
+    // permitted by Start, End, and Stride.
+    APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
+                              : getUnsignedRange(Start).getUnsignedMin();
+
+    unsigned BitWidth = getTypeSizeInBits(LHS->getType());
+
+    APInt StrideForMaxBECount;
+
+    if (PositiveStride)
+      StrideForMaxBECount =
+        IsSigned ? getSignedRange(Stride).getSignedMin()
+                 : getUnsignedRange(Stride).getUnsignedMin();
+    else
+      // Using a stride of 1 is safe when computing max backedge taken count for
+      // a loop with unknown stride.
+      StrideForMaxBECount = APInt(BitWidth, 1, IsSigned);
 
-  APInt Limit =
+    APInt Limit =
       IsSigned ? APInt::getSignedMaxValue(BitWidth) - (StrideForMaxBECount - 1)
                : APInt::getMaxValue(BitWidth) - (StrideForMaxBECount - 1);
 
-  // Although End can be a MAX expression we estimate MaxEnd considering only
-  // the case End = RHS. This is safe because in the other case (End - Start)
-  // is zero, leading to a zero maximum backedge taken count.
-  APInt MaxEnd =
-    IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
-             : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
+    // Although End can be a MAX expression we estimate MaxEnd considering only
+    // the case End = RHS. This is safe because in the other case (End - Start)
+    // is zero, leading to a zero maximum backedge taken count.
+    APInt MaxEnd =
+      IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
+               : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
 
-  const SCEV *MaxBECount;
-  if (isa<SCEVConstant>(BECount))
-    MaxBECount = BECount;
-  else
     MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
                                 getConstant(StrideForMaxBECount), false);
+  }
 
   if (isa<SCEVCouldNotCompute>(MaxBECount))
     MaxBECount = BECount;
Index: llvm/trunk/test/Analysis/ScalarEvolution/trip-count13.ll
===================================================================
--- llvm/trunk/test/Analysis/ScalarEvolution/trip-count13.ll
+++ llvm/trunk/test/Analysis/ScalarEvolution/trip-count13.ll
@@ -14,7 +14,7 @@
 
 ; CHECK-LABEL: Determining loop execution counts for: @u_0
 ; CHECK-NEXT: Loop %loop: backedge-taken count is (-100 + (-1 * %rhs) + ((100 + %rhs) umax %rhs))
-; CHECK-NEXT: Loop %loop: max backedge-taken count is -1
+; CHECK-NEXT: Loop %loop: max backedge-taken count is -100
 
 leave:
   ret void
@@ -34,7 +34,7 @@
 
 ; CHECK-LABEL: Determining loop execution counts for: @u_1
 ; CHECK-NEXT: Loop %loop: backedge-taken count is ((-1 * %start) + ((-100 + %start) umax %start))
-; CHECK-NEXT: Loop %loop: max backedge-taken count is -1
+; CHECK-NEXT: Loop %loop: max backedge-taken count is -100
 
 leave:
   ret void
@@ -54,7 +54,7 @@
 
 ; CHECK-LABEL: Determining loop execution counts for: @s_0
 ; CHECK-NEXT: Loop %loop: backedge-taken count is (-100 + (-1 * %rhs) + ((100 + %rhs) smax %rhs))
-; CHECK-NEXT: Loop %loop: max backedge-taken count is -1
+; CHECK-NEXT: Loop %loop: max backedge-taken count is -100
 
 leave:
   ret void
@@ -74,7 +74,7 @@
 
 ; CHECK-LABEL: Determining loop execution counts for: @s_1
 ; CHECK-NEXT: Loop %loop: backedge-taken count is ((-1 * %start) + ((-100 + %start) smax %start))
-; CHECK-NEXT: Loop %loop: max backedge-taken count is -1
+; CHECK-NEXT: Loop %loop: max backedge-taken count is -100
 
 leave:
   ret void
Index: llvm/trunk/test/Analysis/ScalarEvolution/trip-count14.ll
===================================================================
--- llvm/trunk/test/Analysis/ScalarEvolution/trip-count14.ll
+++ llvm/trunk/test/Analysis/ScalarEvolution/trip-count14.ll
@@ -0,0 +1,177 @@
+; RUN: opt -S -analyze -scalar-evolution < %s | FileCheck %s
+
+define void @s32_max1(i32 %n, i32* %p) {
+entry:
+  %add = add i32 %n, 1
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %do.body ]
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp = icmp slt i32 %i.0, %add
+  br i1 %cmp, label %do.body, label %do.end ; taken either 0 or 1 times
+
+; CHECK-LABEL: Determining loop execution counts for: @s32_max1
+; CHECK-NEXT: Loop %do.body: backedge-taken count is ((-1 * %n) + ((1 + %n) smax %n))
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is 1
+
+do.end:
+  ret void
+}
+
+define void @s32_max2(i32 %n, i32* %p) {
+entry:
+  %add = add i32 %n, 2
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %do.body ]
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp = icmp slt i32 %i.0, %add
+  br i1 %cmp, label %do.body, label %do.end ; taken either 0 or 2 times
+
+; CHECK-LABEL: Determining loop execution counts for: @s32_max2
+; CHECK-NEXT: Loop %do.body: backedge-taken count is ((-1 * %n) + ((2 + %n) smax %n))
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is 2
+
+do.end:
+  ret void
+}
+
+define void @s32_maxx(i32 %n, i32 %x, i32* %p) {
+entry:
+  %add = add i32 %x, %n
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %do.body ]
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp = icmp slt i32 %i.0, %add
+  br i1 %cmp, label %do.body, label %do.end ; taken either 0 or x times
+
+; CHECK-LABEL: Determining loop execution counts for: @s32_maxx
+; CHECK-NEXT: Loop %do.body: backedge-taken count is ((-1 * %n) + ((%n + %x) smax %n))
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is -1
+
+do.end:
+  ret void
+}
+
+define void @s32_max2_unpredictable_exit(i32 %n, i32 %x, i32* %p) {
+entry:
+  %add = add i32 %n, 2
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %if.end ]
+  %cmp = icmp eq i32 %i.0, %x
+  br i1 %cmp, label %do.end, label %if.end ; unpredictable
+
+if.end:
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp1 = icmp slt i32 %i.0, %add
+  br i1 %cmp1, label %do.body, label %do.end ; taken either 0 or 2 times
+
+; CHECK-LABEL: Determining loop execution counts for: @s32_max2_unpredictable_exit
+; CHECK-NEXT: Loop %do.body: <multiple exits> Unpredictable backedge-taken count.
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is 2
+
+do.end:
+  ret void
+}
+
+define void @u32_max1(i32 %n, i32* %p) {
+entry:
+  %add = add i32 %n, 1
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %do.body ]
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp = icmp ult i32 %i.0, %add
+  br i1 %cmp, label %do.body, label %do.end ; taken either 0 or 1 times
+
+; CHECK-LABEL: Determining loop execution counts for: @u32_max1
+; CHECK-NEXT: Loop %do.body: backedge-taken count is ((-1 * %n) + ((1 + %n) umax %n))
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is 1
+
+do.end:
+  ret void
+}
+
+define void @u32_max2(i32 %n, i32* %p) {
+entry:
+  %add = add i32 %n, 2
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %do.body ]
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp = icmp ult i32 %i.0, %add
+  br i1 %cmp, label %do.body, label %do.end ; taken either 0 or 2 times
+
+; CHECK-LABEL: Determining loop execution counts for: @u32_max2
+; CHECK-NEXT: Loop %do.body: backedge-taken count is ((-1 * %n) + ((2 + %n) umax %n))
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is 2
+
+do.end:
+  ret void
+}
+
+define void @u32_maxx(i32 %n, i32 %x, i32* %p) {
+entry:
+  %add = add i32 %x, %n
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %do.body ]
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp = icmp ult i32 %i.0, %add
+  br i1 %cmp, label %do.body, label %do.end ; taken either 0 or x times
+
+; CHECK-LABEL: Determining loop execution counts for: @u32_maxx
+; CHECK-NEXT: Loop %do.body: backedge-taken count is ((-1 * %n) + ((%n + %x) umax %n))
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is -1
+
+do.end:
+  ret void
+}
+
+define void @u32_max2_unpredictable_exit(i32 %n, i32 %x, i32* %p) {
+entry:
+  %add = add i32 %n, 2
+  br label %do.body
+
+do.body:
+  %i.0 = phi i32 [ %n, %entry ], [ %inc, %if.end ]
+  %cmp = icmp eq i32 %i.0, %x
+  br i1 %cmp, label %do.end, label %if.end ; unpredictable
+
+if.end:
+  %arrayidx = getelementptr i32, i32* %p, i32 %i.0
+  store i32 %i.0, i32* %arrayidx, align 4
+  %inc = add i32 %i.0, 1
+  %cmp1 = icmp ult i32 %i.0, %add
+  br i1 %cmp1, label %do.body, label %do.end ; taken either 0 or 2 times
+
+; CHECK-LABEL: Determining loop execution counts for: @u32_max2_unpredictable_exit
+; CHECK-NEXT: Loop %do.body: <multiple exits> Unpredictable backedge-taken count.
+; CHECK-NEXT: Loop %do.body: max backedge-taken count is 2
+
+do.end:
+  ret void
+}