Index: llvm/trunk/include/llvm/Analysis/ScalarEvolution.h
===================================================================
--- llvm/trunk/include/llvm/Analysis/ScalarEvolution.h
+++ llvm/trunk/include/llvm/Analysis/ScalarEvolution.h
@@ -253,6 +253,10 @@
     /// conditions dominating the backedge of a loop.
     bool WalkingBEDominatingConds;
 
+    /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
+    /// predicate by splitting it into a set of independent predicates.
+    bool ProvingSplitPredicate;
+
     /// Information about the number of loop iterations for which a loop exit's
     /// branch condition evaluates to the not-taken path.  This is a temporary
     /// pair of exact and max expressions that are eventually summarized in
@@ -559,6 +563,11 @@
     bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
                                     const SCEV *LHS, const SCEV *RHS);
 
+    /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
+    /// prove them individually.
+    bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
+                                      const SCEV *RHS);
+
     /// Drop memoized information computed for S.
     void forgetMemoizedResults(const SCEV *S);
 
Index: llvm/trunk/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- llvm/trunk/lib/Analysis/ScalarEvolution.cpp
+++ llvm/trunk/lib/Analysis/ScalarEvolution.cpp
@@ -6764,6 +6764,9 @@
   if (LeftGuarded && RightGuarded)
     return true;
 
+  if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
+    return true;
+
   // Otherwise see what can be done with known constant ranges.
   return isKnownPredicateWithRanges(Pred, LHS, RHS);
 }
@@ -6969,6 +6972,31 @@
   return false;
 }
 
+bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
+                                                   const SCEV *LHS,
+                                                   const SCEV *RHS) {
+  if (ProvingSplitPredicate)
+    return false;
+
+  // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
+  // the stack can result in exponential time complexity.
+  SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
+
+  // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
+  //
+  // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
+  // isKnownPredicate.  isKnownPredicate is more powerful, but also more
+  // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
+  // interesting cases seen in practice.  We can consider "upgrading" L >= 0 to
+  // use isKnownPredicate later if needed.
+  if (Pred == ICmpInst::ICMP_ULT && isKnownNonNegative(RHS) &&
+      isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
+      isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS))
+    return true;
+
+  return false;
+}
+
 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
 /// protected by a conditional between LHS and RHS.  This is used to
 /// to eliminate casts.
@@ -8529,14 +8557,15 @@
                                  LoopInfo &LI)
     : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
       CouldNotCompute(new SCEVCouldNotCompute()),
-      WalkingBEDominatingConds(false), ValuesAtScopes(64), LoopDispositions(64),
-      BlockDispositions(64), FirstUnknown(nullptr) {}
+      WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
+      ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
+      FirstUnknown(nullptr) {}
 
 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
     : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
       CouldNotCompute(std::move(Arg.CouldNotCompute)),
       ValueExprMap(std::move(Arg.ValueExprMap)),
-      WalkingBEDominatingConds(false),
+      WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
       BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
       ConstantEvolutionLoopExitValue(
           std::move(Arg.ConstantEvolutionLoopExitValue)),
@@ -8573,6 +8602,7 @@
 
   assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
   assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
+  assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
 }
 
 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
Index: llvm/trunk/test/Transforms/IndVarSimplify/eliminate-comparison.ll
===================================================================
--- llvm/trunk/test/Transforms/IndVarSimplify/eliminate-comparison.ll
+++ llvm/trunk/test/Transforms/IndVarSimplify/eliminate-comparison.ll
@@ -394,4 +394,87 @@
   ret i1 true
 }
 
+define void @func_19(i32* %length.ptr) {
+; CHECK-LABEL: @func_19(
+ entry:
+  %length = load i32, i32* %length.ptr, !range !0
+  %length.is.nonzero = icmp ne i32 %length, 0
+  br i1 %length.is.nonzero, label %loop, label %leave
+
+ loop:
+; CHECK: loop:
+  %iv = phi i32 [ 0, %entry ], [ %iv.inc, %be ]
+  %iv.inc = add i32 %iv, 1
+  %range.check = icmp ult i32 %iv, %length
+  br i1 %range.check, label %be, label %leave
+; CHECK:   br i1 true, label %be, label %leave.loopexit
+; CHECK: be:
+
+ be:
+  call void @side_effect()
+  %be.cond = icmp slt i32 %iv.inc, %length
+  br i1 %be.cond, label %loop, label %leave
+
+ leave:
+  ret void
+}
+
+define void @func_20(i32* %length.ptr) {
+; Like @func_19, but %length is no longer provably positive, so
+; %range.check cannot be proved to be always true.
+
+; CHECK-LABEL: @func_20(
+ entry:
+  %length = load i32, i32* %length.ptr
+  %length.is.nonzero = icmp ne i32 %length, 0
+  br i1 %length.is.nonzero, label %loop, label %leave
+
+ loop:
+; CHECK: loop:
+  %iv = phi i32 [ 0, %entry ], [ %iv.inc, %be ]
+  %iv.inc = add i32 %iv, 1
+  %range.check = icmp ult i32 %iv, %length
+  br i1 %range.check, label %be, label %leave
+; CHECK:   br i1 %range.check, label %be, label %leave.loopexit
+; CHECK: be:
+
+ be:
+  call void @side_effect()
+  %be.cond = icmp slt i32 %iv.inc, %length
+  br i1 %be.cond, label %loop, label %leave
+
+ leave:
+  ret void
+}
+
+define void @func_21(i32* %length.ptr, i32 %init) {
+; Like @func_19, but it is no longer possible to prove %iv's start
+; value is positive without doing some control flow analysis.
+
+; CHECK-LABEL: @func_21(
+ entry:
+  %length = load i32, i32* %length.ptr, !range !0
+  %length.is.nonzero = icmp ne i32 %length, 0
+  %init.is.positive = icmp sgt i32 %init, 0
+  %entry.cond = and i1 %length.is.nonzero, %init.is.positive
+  br i1 %length.is.nonzero, label %loop, label %leave
+
+ loop:
+; CHECK: loop:
+  %iv = phi i32 [ 0, %entry ], [ %iv.inc, %be ]
+  %iv.inc = add i32 %iv, 1
+  %range.check = icmp ult i32 %iv, %length
+  br i1 %range.check, label %be, label %leave
+; CHECK:   br i1 true, label %be, label %leave.loopexit
+; CHECK: be:
+
+ be:
+  call void @side_effect()
+  %be.cond = icmp slt i32 %iv.inc, %length
+  br i1 %be.cond, label %loop, label %leave
+
+ leave:
+  ret void
+}
+
 !0 = !{i32 0, i32 2147483647}