Index: llvm/trunk/include/llvm/Analysis/ScalarEvolution.h
===================================================================
--- llvm/trunk/include/llvm/Analysis/ScalarEvolution.h
+++ llvm/trunk/include/llvm/Analysis/ScalarEvolution.h
@@ -1761,10 +1761,18 @@
   const SCEV *getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
                                  SCEV::NoWrapFlags Flags);
 
+  /// Find all of the loops transitively used in \p S, and update \c LoopUsers
+  /// accordingly.
+  void addToLoopUseLists(const SCEV *S);
+
   FoldingSet<SCEV> UniqueSCEVs;
   FoldingSet<SCEVPredicate> UniquePreds;
   BumpPtrAllocator SCEVAllocator;
 
+  /// This maps loops to a list of SCEV expressions that (transitively) use said
+  /// loop.
+  DenseMap<const Loop *, SmallVector<const SCEV *, 4>> LoopUsers;
+
   /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
   /// they can be rewritten into under certain predicates.
   DenseMap<std::pair<const SCEVUnknown *, const Loop *>,
Index: llvm/trunk/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- llvm/trunk/lib/Analysis/ScalarEvolution.cpp
+++ llvm/trunk/lib/Analysis/ScalarEvolution.cpp
@@ -1290,6 +1290,7 @@
   SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
                                                  Op, Ty);
   UniqueSCEVs.InsertNode(S, IP);
+  addToLoopUseLists(S);
   return S;
 }
 
@@ -1580,6 +1581,7 @@
     SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
                                                      Op, Ty);
     UniqueSCEVs.InsertNode(S, IP);
+    addToLoopUseLists(S);
     return S;
   }
 
@@ -1766,6 +1768,7 @@
   SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
                                                    Op, Ty);
   UniqueSCEVs.InsertNode(S, IP);
+  addToLoopUseLists(S);
   return S;
 }
 
@@ -1803,6 +1806,7 @@
     SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
                                                      Op, Ty);
     UniqueSCEVs.InsertNode(S, IP);
+    addToLoopUseLists(S);
     return S;
   }
 
@@ -2014,6 +2018,7 @@
   SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
                                                    Op, Ty);
   UniqueSCEVs.InsertNode(S, IP);
+  addToLoopUseLists(S);
   return S;
 }
 
@@ -2662,6 +2667,7 @@
     S = new (SCEVAllocator)
         SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
     UniqueSCEVs.InsertNode(S, IP);
+    addToLoopUseLists(S);
   }
   S->setNoWrapFlags(Flags);
   return S;
@@ -2683,6 +2689,7 @@
     S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
                                         O, Ops.size());
     UniqueSCEVs.InsertNode(S, IP);
+    addToLoopUseLists(S);
   }
   S->setNoWrapFlags(Flags);
   return S;
@@ -3135,6 +3142,7 @@
   SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
                                              LHS, RHS);
   UniqueSCEVs.InsertNode(S, IP);
+  addToLoopUseLists(S);
   return S;
 }
 
@@ -3315,6 +3323,7 @@
     S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
                                            O, Operands.size(), L);
     UniqueSCEVs.InsertNode(S, IP);
+    addToLoopUseLists(S);
   }
   S->setNoWrapFlags(Flags);
   return S;
@@ -3470,6 +3479,7 @@
   SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
                                              O, Ops.size());
   UniqueSCEVs.InsertNode(S, IP);
+  addToLoopUseLists(S);
   return S;
 }
 
@@ -3571,6 +3581,7 @@
   SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
                                              O, Ops.size());
   UniqueSCEVs.InsertNode(S, IP);
+  addToLoopUseLists(S);
   return S;
 }
 
@@ -6392,6 +6403,13 @@
         ++I;
     }
 
+    auto LoopUsersItr = LoopUsers.find(CurrL);
+    if (LoopUsersItr != LoopUsers.end()) {
+      for (auto *S : LoopUsersItr->second)
+        forgetMemoizedResults(S);
+      LoopUsers.erase(LoopUsersItr);
+    }
+
     // Drop information about expressions based on loop-header PHIs.
     PushLoopPHIs(CurrL, Worklist);
 
@@ -10574,6 +10592,7 @@
       UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
       UniquePreds(std::move(Arg.UniquePreds)),
       SCEVAllocator(std::move(Arg.SCEVAllocator)),
+      LoopUsers(std::move(Arg.LoopUsers)),
       PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
       FirstUnknown(Arg.FirstUnknown) {
   Arg.FirstUnknown = nullptr;
@@ -11016,6 +11035,25 @@
         ExitLimits.erase(I);
 }
 
+void ScalarEvolution::addToLoopUseLists(const SCEV *S) {
+  struct FindUsedLoops {
+    SmallPtrSet<const Loop *, 8> LoopsUsed;
+    bool follow(const SCEV *S) {
+      if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
+        LoopsUsed.insert(AR->getLoop());
+      return true;
+    }
+
+    bool isDone() const { return false; }
+  };
+
+  FindUsedLoops F;
+  SCEVTraversal<FindUsedLoops>(F).visitAll(S);
+
+  for (auto *L : F.LoopsUsed)
+    LoopUsers[L].push_back(S);
+}
+
 void ScalarEvolution::verify() const {
   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
   ScalarEvolution SE2(F, TLI, AC, DT, LI);
Index: llvm/trunk/unittests/Analysis/ScalarEvolutionTest.cpp
===================================================================
--- llvm/trunk/unittests/Analysis/ScalarEvolutionTest.cpp
+++ llvm/trunk/unittests/Analysis/ScalarEvolutionTest.cpp
@@ -856,6 +856,17 @@
   EXPECT_TRUE(isa<SCEVConstant>(EC));
   EXPECT_EQ(cast<SCEVConstant>(EC)->getAPInt().getLimitedValue(), 999u);
 
+  // The add recurrence {5,+,1} does not correspond to any PHI in the IR, and
+  // that is relevant to this test.
+  auto *Five = SE.getConstant(APInt(/*numBits=*/64, 5));
+  auto *AR =
+      SE.getAddRecExpr(Five, SE.getOne(T_int64), Loop, SCEV::FlagAnyWrap);
+  const SCEV *ARAtLoopExit = SE.getSCEVAtScope(AR, nullptr);
+  EXPECT_FALSE(isa<SCEVCouldNotCompute>(ARAtLoopExit));
+  EXPECT_TRUE(isa<SCEVConstant>(ARAtLoopExit));
+  EXPECT_EQ(cast<SCEVConstant>(ARAtLoopExit)->getAPInt().getLimitedValue(),
+            1004u);
+
   SE.forgetLoop(Loop);
   Br->eraseFromParent();
   Cond->eraseFromParent();
@@ -868,6 +879,11 @@
   EXPECT_FALSE(isa<SCEVCouldNotCompute>(NewEC));
   EXPECT_TRUE(isa<SCEVConstant>(NewEC));
   EXPECT_EQ(cast<SCEVConstant>(NewEC)->getAPInt().getLimitedValue(), 1999u);
+  const SCEV *NewARAtLoopExit = SE.getSCEVAtScope(AR, nullptr);
+  EXPECT_FALSE(isa<SCEVCouldNotCompute>(NewARAtLoopExit));
+  EXPECT_TRUE(isa<SCEVConstant>(NewARAtLoopExit));
+  EXPECT_EQ(cast<SCEVConstant>(NewARAtLoopExit)->getAPInt().getLimitedValue(),
+            2004u);
 }
 
 // Make sure that SCEV invalidates exit limits after invalidating the values it