Index: include/llvm/Analysis/BlockFrequencyInfoImpl.h
===================================================================
--- include/llvm/Analysis/BlockFrequencyInfoImpl.h
+++ include/llvm/Analysis/BlockFrequencyInfoImpl.h
@@ -718,9 +718,6 @@
 ///
 /// It has some known flaws.
 ///
-///   - Loop scale is limited to 4096 per loop (2^12) to avoid exhausting
-///     BlockFrequency's 64-bit integer precision.
-///
 ///   - The model of irreducible control flow is a rough approximation.
 ///
 ///     Modelling irreducible control flow exactly involves setting up and
Index: lib/Analysis/BlockFrequencyInfoImpl.cpp
===================================================================
--- lib/Analysis/BlockFrequencyInfoImpl.cpp
+++ lib/Analysis/BlockFrequencyInfoImpl.cpp
@@ -331,32 +331,35 @@
   return true;
 }
 
-/// \brief Get the maximum allowed loop scale.
-///
-/// Gives the maximum number of estimated iterations allowed for a loop.  Very
-/// large numbers cause problems downstream (even within 64-bits).
-static Scaled64 getMaxLoopScale() { return Scaled64(1, 12); }
-
 /// \brief Compute the loop scale for a loop.
 void BlockFrequencyInfoImplBase::computeLoopScale(LoopData &Loop) {
   // Compute loop scale.
   DEBUG(dbgs() << "compute-loop-scale: " << getLoopName(Loop) << "\n");
 
+  // Infinite loops need special handling. If we give the back edge an infinite
+  // mass, they may saturate all the other scales in the function down to 1,
+  // making all the other region temperatures look exactly the same. Choose an
+  // arbitrary scale to avoid these issues.
+  //
+  // TODO: An alternate way would be to select a symbolic scale which is later
+  // replaced to be the maximum of all computed scales plus 1. This would
+  // appropriately describe the loop as having a large scale, without skewing
+  // the final frequency computation.
+  const Scaled64 InifiniteLoopScale(1, 12);
+
   // LoopScale == 1 / ExitMass
   // ExitMass == HeadMass - BackedgeMass
   BlockMass ExitMass = BlockMass::getFull() - Loop.BackedgeMass;
 
-  // Block scale stores the inverse of the scale.
-  Loop.Scale = ExitMass.toScaled().inverse();
+  // Block scale stores the inverse of the scale. If this is an
+  // infinite loop, its exit mass will be zero. In this case, use an
+  // arbitrary scale for the loop scale.
+  Loop.Scale =
+      ExitMass.isEmpty() ? InifiniteLoopScale : ExitMass.toScaled().inverse();
 
   DEBUG(dbgs() << " - exit-mass = " << ExitMass << " (" << BlockMass::getFull()
                << " - " << Loop.BackedgeMass << ")\n"
                << " - scale = " << Loop.Scale << "\n");
-
-  if (Loop.Scale > getMaxLoopScale()) {
-    Loop.Scale = getMaxLoopScale();
-    DEBUG(dbgs() << " - reduced-to-max-scale: " << getMaxLoopScale() << "\n");
-  }
 }
 
 /// \brief Package up a loop.
@@ -427,12 +430,19 @@
   // differentiated.  However, the register allocator currently deals poorly
   // with large numbers.  Instead, push Min up a little from 1 to give some
   // room to differentiate small, unequal numbers.
-  //
-  // TODO: fix issues downstream so that ScalingFactor can be
-  // Scaled64(1,64)/Max.
+  const unsigned MaxBits = 32;
+  const unsigned SpreadBits = (Max / Min).lg();
   Scaled64 ScalingFactor = Min.inverse();
-  if ((Max / Min).lg() < 60)
+  if (SpreadBits <= MaxBits - 3) {
+    // If the values are small enough, make the scaling factor at least 8 to
+    // allow distinguishing small values.
     ScalingFactor <<= 3;
+  } else if (SpreadBits > MaxBits) {
+    // If the values need more than MaxBits to be represented, saturate small
+    // frequency values down to 1 by using a scaling factor that benefits large
+    // frequency values.
+    ScalingFactor = Scaled64(1, MaxBits) / Max;
+  }
 
   // Translate the floats to integers.
   DEBUG(dbgs() << "float-to-int: min = " << Min << ", max = " << Max
Index: test/Analysis/BlockFrequencyInfo/bad_input.ll
===================================================================
--- test/Analysis/BlockFrequencyInfo/bad_input.ll
+++ test/Analysis/BlockFrequencyInfo/bad_input.ll
@@ -32,7 +32,8 @@
 entry:
   br i1 %x, label %for.body, label %for.end, !prof !1
 
-; Check that the loop scale maxes out at 4096, giving 2048 here.
+; Check that the infinite loop is arbitrarily scaled to max out a 4096,
+; giving 2048 here.
 ; CHECK-NEXT: for.body: float = 2048.0,
 for.body:
   %i = phi i32 [ 0, %entry ], [ %inc, %for.body ]
Index: test/Analysis/BlockFrequencyInfo/loops_with_profile_info.ll
===================================================================
--- /dev/null
+++ test/Analysis/BlockFrequencyInfo/loops_with_profile_info.ll
@@ -0,0 +1,204 @@
+; RUN: opt < %s -analyze -block-freq | FileCheck %s
+
+; This code contains three loops. One is triple-nested, the
+; second is double nested and the third is a single loop. At
+; runtime, all three loops execute 1,000,000 times each. We use to
+; give different frequencies to each of the loops because loop
+; scales were limited to no more than 4,096.
+;
+; This was penalizing the hotness of the second and third loops
+; because BFI was reducing the loop scale for for.cond16 and
+; for.cond26 to a max of 4,096.
+;
+; Without this restriction, all loops are now correctly given the same
+; frequency values.
+;
+; Original C code:
+;
+;
+; int g;
+; __attribute__((noinline)) void bar() {
+;  g++;
+; }
+;
+; extern int printf(const char*, ...);
+;
+; int main()
+; {
+;   int i, j, k;
+;
+;   g = 0;
+;   for (i = 0; i < 100; i++)
+;     for (j = 0; j < 100; j++)
+;        for (k = 0; k < 100; k++)
+;            bar();
+;
+;   printf ("g = %d\n", g);
+;   g = 0;
+;
+;   for (i = 0; i < 100; i++)
+;     for (j = 0; j < 10000; j++)
+;         bar();
+;
+;   printf ("g = %d\n", g);
+;   g = 0;
+;
+;
+;   for (i = 0; i < 1000000; i++)
+;     bar();
+;
+;   printf ("g = %d\n", g);
+;   g = 0;
+; }
+
+@g = common global i32 0, align 4
+@.str = private unnamed_addr constant [8 x i8] c"g = %d\0A\00", align 1
+
+declare void @bar()
+declare i32 @printf(i8*, ...)
+
+; CHECK: Printing analysis {{.*}} for function 'main':
+; CHECK-NEXT: block-frequency-info: main
+define i32 @main() {
+entry:
+  %retval = alloca i32, align 4
+  %i = alloca i32, align 4
+  %j = alloca i32, align 4
+  %k = alloca i32, align 4
+  store i32 0, i32* %retval
+  store i32 0, i32* @g, align 4
+  store i32 0, i32* %i, align 4
+  br label %for.cond
+
+for.cond:                                         ; preds = %for.inc10, %entry
+  %0 = load i32, i32* %i, align 4
+  %cmp = icmp slt i32 %0, 100
+  br i1 %cmp, label %for.body, label %for.end12, !prof !1
+
+for.body:                                         ; preds = %for.cond
+  store i32 0, i32* %j, align 4
+  br label %for.cond1
+
+for.cond1:                                        ; preds = %for.inc7, %for.body
+  %1 = load i32, i32* %j, align 4
+  %cmp2 = icmp slt i32 %1, 100
+  br i1 %cmp2, label %for.body3, label %for.end9, !prof !2
+
+for.body3:                                        ; preds = %for.cond1
+  store i32 0, i32* %k, align 4
+  br label %for.cond4
+
+for.cond4:                                        ; preds = %for.inc, %for.body3
+  %2 = load i32, i32* %k, align 4
+  %cmp5 = icmp slt i32 %2, 100
+  br i1 %cmp5, label %for.body6, label %for.end, !prof !3
+
+; CHECK: - for.body6: float = 500000.5, int = 4000003
+for.body6:                                        ; preds = %for.cond4
+  call void @bar()
+  br label %for.inc
+
+for.inc:                                          ; preds = %for.body6
+  %3 = load i32, i32* %k, align 4
+  %inc = add nsw i32 %3, 1
+  store i32 %inc, i32* %k, align 4
+  br label %for.cond4
+
+for.end:                                          ; preds = %for.cond4
+  br label %for.inc7
+
+for.inc7:                                         ; preds = %for.end
+  %4 = load i32, i32* %j, align 4
+  %inc8 = add nsw i32 %4, 1
+  store i32 %inc8, i32* %j, align 4
+  br label %for.cond1
+
+for.end9:                                         ; preds = %for.cond1
+  br label %for.inc10
+
+for.inc10:                                        ; preds = %for.end9
+  %5 = load i32, i32* %i, align 4
+  %inc11 = add nsw i32 %5, 1
+  store i32 %inc11, i32* %i, align 4
+  br label %for.cond
+
+for.end12:                                        ; preds = %for.cond
+  %6 = load i32, i32* @g, align 4
+  %call = call i32 (i8*, ...)* @printf(i8* getelementptr inbounds ([8 x i8], [8 x i8]* @.str, i32 0, i32 0), i32 %6)
+  store i32 0, i32* @g, align 4
+  store i32 0, i32* %i, align 4
+  br label %for.cond13
+
+for.cond13:                                       ; preds = %for.inc22, %for.end12
+  %7 = load i32, i32* %i, align 4
+  %cmp14 = icmp slt i32 %7, 100
+  br i1 %cmp14, label %for.body15, label %for.end24, !prof !1
+
+for.body15:                                       ; preds = %for.cond13
+  store i32 0, i32* %j, align 4
+  br label %for.cond16
+
+for.cond16:                                       ; preds = %for.inc19, %for.body15
+  %8 = load i32, i32* %j, align 4
+  %cmp17 = icmp slt i32 %8, 10000
+  br i1 %cmp17, label %for.body18, label %for.end21, !prof !4
+
+; CHECK: - for.body18: float = 500000.5, int = 4000003
+for.body18:                                       ; preds = %for.cond16
+  call void @bar()
+  br label %for.inc19
+
+for.inc19:                                        ; preds = %for.body18
+  %9 = load i32, i32* %j, align 4
+  %inc20 = add nsw i32 %9, 1
+  store i32 %inc20, i32* %j, align 4
+  br label %for.cond16
+
+for.end21:                                        ; preds = %for.cond16
+  br label %for.inc22
+
+for.inc22:                                        ; preds = %for.end21
+  %10 = load i32, i32* %i, align 4
+  %inc23 = add nsw i32 %10, 1
+  store i32 %inc23, i32* %i, align 4
+  br label %for.cond13
+
+for.end24:                                        ; preds = %for.cond13
+  %11 = load i32, i32* @g, align 4
+  %call25 = call i32 (i8*, ...)* @printf(i8* getelementptr inbounds ([8 x i8], [8 x i8]* @.str, i32 0, i32 0), i32 %11)
+  store i32 0, i32* @g, align 4
+  store i32 0, i32* %i, align 4
+  br label %for.cond26
+
+for.cond26:                                       ; preds = %for.inc29, %for.end24
+  %12 = load i32, i32* %i, align 4
+  %cmp27 = icmp slt i32 %12, 1000000
+  br i1 %cmp27, label %for.body28, label %for.end31, !prof !5
+
+; CHECK: - for.body28: float = 500000.5, int = 4000003
+for.body28:                                       ; preds = %for.cond26
+  call void @bar()
+  br label %for.inc29
+
+for.inc29:                                        ; preds = %for.body28
+  %13 = load i32, i32* %i, align 4
+  %inc30 = add nsw i32 %13, 1
+  store i32 %inc30, i32* %i, align 4
+  br label %for.cond26
+
+for.end31:                                        ; preds = %for.cond26
+  %14 = load i32, i32* @g, align 4
+  %call32 = call i32 (i8*, ...)* @printf(i8* getelementptr inbounds ([8 x i8], [8 x i8]* @.str, i32 0, i32 0), i32 %14)
+  store i32 0, i32* @g, align 4
+  %15 = load i32, i32* %retval
+  ret i32 %15
+}
+
+!llvm.ident = !{!0}
+
+!0 = !{!"clang version 3.7.0 (trunk 232635) (llvm/trunk 232636)"}
+!1 = !{!"branch_weights", i32 101, i32 2}
+!2 = !{!"branch_weights", i32 10001, i32 101}
+!3 = !{!"branch_weights", i32 1000001, i32 10001}
+!4 = !{!"branch_weights", i32 1000001, i32 101}
+!5 = !{!"branch_weights", i32 1000001, i32 2}