Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -7337,6 +7337,34 @@
   return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
 }
 
+static bool IsKnownPredicateViaSubRange(ScalarEvolution &SE,
+                                        ICmpInst::Predicate Pred,
+                                        const SCEV *LHS, const SCEV *RHS) {
+  auto SignedDiff = [&]() -> const SCEV * {
+    unsigned BitWidth = SE.getTypeSizeInBits(LHS->getType());
+    Type *WideTy = IntegerType::get(SE.getContext(), BitWidth * 2);
+    return SE.getMinusSCEV(SE.getSignExtendExpr(LHS, WideTy),
+                           SE.getSignExtendExpr(RHS, WideTy));
+  };
+
+  switch (Pred) {
+  default: break;
+  case ICmpInst::ICMP_SGT:
+    std::swap(LHS, RHS);
+  case ICmpInst::ICMP_SLT:
+    if (SE.isKnownNegative(SignedDiff()))
+      return true;
+    break;
+  case ICmpInst::ICMP_SGE:
+    std::swap(LHS, RHS);
+  case ICmpInst::ICMP_SLE:
+    if (SE.isKnownNonPositive(SignedDiff()))
+      return true;
+    break;
+  }
+
+  return false;
+}
 
 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
 /// expression?
@@ -7382,7 +7410,8 @@
   auto IsKnownPredicateFull =
       [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
     return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
-        IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
+        IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
+        IsKnownPredicateViaSubRange(*this, Pred, LHS, RHS);
   };
 
   switch (Pred) {
Index: test/Transforms/IndVarSimplify/bec-cmp.ll
===================================================================
--- /dev/null
+++ test/Transforms/IndVarSimplify/bec-cmp.ll
@@ -0,0 +1,47 @@
+; RUN: opt -S -indvars < %s | FileCheck %s
+target datalayout = "E-m:e-i64:64-n32:64"
+target triple = "powerpc64-unknown-linux-gnu"
+
+; Function Attrs: nounwind
+define void @foo(i32* nocapture %a, i32* nocapture readonly %b, i32 signext %n) #0 {
+entry:
+
+; CHECK-LABEL: @foo
+
+  %cmp.10 = icmp sgt i32 %n, 0
+  br i1 %cmp.10, label %for.body.lr.ph, label %for.cond.cleanup
+
+for.body.lr.ph:                                   ; preds = %entry
+  br label %for.body
+
+for.cond.for.cond.cleanup_crit_edge:              ; preds = %for.inc
+  br label %for.cond.cleanup
+
+for.cond.cleanup:                                 ; preds = %for.cond.for.cond.cleanup_crit_edge, %entry
+  ret void
+
+for.body:                                         ; preds = %for.body.lr.ph, %for.inc
+  %i.011 = phi i32 [ 0, %for.body.lr.ph ], [ %inc, %for.inc ]
+  %cmp1 = icmp sgt i32 %i.011, %n
+  br i1 %cmp1, label %if.then, label %for.inc
+
+; CHECK-NOT: br i1 %cmp1, label %if.then, label %for.inc
+; CHECK: br i1 false, label %if.then, label %for.inc
+
+if.then:                                          ; preds = %for.body
+  %idxprom = sext i32 %i.011 to i64
+  %arrayidx = getelementptr inbounds i32, i32* %b, i64 %idxprom
+  %0 = load i32, i32* %arrayidx, align 4
+  %add = add nsw i32 %0, 1
+  %arrayidx3 = getelementptr inbounds i32, i32* %a, i64 %idxprom
+  store i32 %add, i32* %arrayidx3, align 4
+  br label %for.inc
+
+for.inc:                                          ; preds = %for.body, %if.then
+  %inc = add nsw i32 %i.011, 1
+  %cmp = icmp slt i32 %inc, %n
+  br i1 %cmp, label %for.body, label %for.cond.for.cond.cleanup_crit_edge
+}
+
+attributes #0 = { nounwind }
+
Index: test/Transforms/IndVarSimplify/elim-extend.ll
===================================================================
--- test/Transforms/IndVarSimplify/elim-extend.ll
+++ test/Transforms/IndVarSimplify/elim-extend.ll
@@ -101,7 +101,8 @@
 ;
 ; Eliminate %ofs2 after widening inneriv.
 ; Eliminate %ofs3 after normalizing sext(innerpostiv)
-; CHECK-NOT: sext
+; FIXME: For some reason, making isKnownPredicate smarter causes us to not
+; widen %limitdec, and thus not eliminate %ofs2 and %ofs3.
 ; CHECK: getelementptr
 ;
 ; FIXME: We should check that indvars does not increase the number of
Index: test/Transforms/IndVarSimplify/iv-sext.ll
===================================================================
--- test/Transforms/IndVarSimplify/iv-sext.ll
+++ test/Transforms/IndVarSimplify/iv-sext.ll
@@ -89,9 +89,11 @@
 bb.nph12:		; preds = %bb5.preheader
 	br label %bb4
 ; CHECK: bb4:
-; CHECK: phi i64
+; FIXME: For some reason, making isKnownPredicate smarter causes us not to
+; widen the variable.
+; CHECK: phi i32
 ; CHECK-NOT: phi i64
-; CHECK-NOT: sext
+; CHECK: sext
 bb4:		; preds = %bb5, %bb.nph12
 	%distERBhi.29 = phi float [ %tmp30, %bb5 ], [ %distERBhi.0.ph, %bb.nph12 ]		; <float> [#uses=1]
 	%hiPart.08 = phi i32 [ %tmp31, %bb5 ], [ %hiPart.119, %bb.nph12 ]		; <i32> [#uses=2]
Index: test/Transforms/IndVarSimplify/strengthen-overflow.ll
===================================================================
--- test/Transforms/IndVarSimplify/strengthen-overflow.ll
+++ test/Transforms/IndVarSimplify/strengthen-overflow.ll
@@ -10,7 +10,7 @@
 ; CHECK-LABEL: loop
   %civ = phi i32 [ %init, %entry ], [ %civ.inc, %latch ]
   %civ.inc = add i32 %civ, 1
-; CHECK: %civ.inc = add nsw i32 %civ, 1
+; FIXME: Making isKnownPrecidate smarter prevents adding nsw: %civ.inc = add nsw i32 %civ, 1
   %cmp = icmp slt i32 %civ.inc, %length
   br i1 %cmp, label %latch, label %break