[LCG] Construct an actual call graph with call-edge SCCs nested inside

reference-edge SCCs.

This essentially builds a more normal call graph as a subgraph of the
"reference graph" that was the old model. This allows both to exist and
the different use cases to use the aspect which addresses their needs.
Specifically, the pass manager and other *ordering* constrained logic
can use the reference graph to achieve conservative order of visit,
while analyses reasoning about attributes and other properties derived
from reachability can reason about the direct call graph.

Note that this isn't necessarily complete: it doesn't model edges to
declarations or indirect calls. Those can be found by scanning the
instructions of the function if desirable, and in fact every user
currently does this in order to handle things like calls to instrinsics.
If useful, we could consider caching this information in the call graph
to save the instruction scans, but currently that doesn't seem to be
important.

An important realization for why the representation chosen here works is
that the call graph is a formal subset of the reference graph and thus
both can live within the same data structure. All SCCs of the call graph
are necessarily contained within an SCC of the reference graph, etc.

The design is to build 'RefSCC's to model SCCs of the reference graph,
and then within them more literal SCCs for the call graph.

The formation of actual call edge SCCs is not done lazily, unlike
reference edge 'RefSCC's. Instead, once a reference SCC is formed, it
directly builds the call SCCs within it and stores them in a post-order
sequence. This is used to provide a consistent platform for mutation and
update of the graph. The post-order also allows for very efficient
updates in common cases by bounding the number of nodes (and thus edges)
considered.

There is considerable common code that I'm still looking for the best
way to factor out between the various DFS implementations here. So far,
my attempts have made the code harder to read and understand despite
reducing the duplication, which seems a poor tradeoff. I've not given up
on figuring out the right way to do this, but I wanted to wait until
I at least had the system working and tested to continue attempting to
factor it differently.

This also requires introducing several new algorithms in order to handle
all of the incremental update scenarios for the more complex structure
involving two edge colorings. I've tried to comment the algorithms
sufficiently to make it clear how this is expected to work, but they may
still need more extensive documentation.

I know that there are some changes which are not strictly necessarily
coupled here. The process of developing this started out with a very
focused set of changes for the new structure of the graph and
algorithms, but subsequent changes to bring the APIs and code into
consistent and understandable patterns also ended up touching on other
aspects. There was no good way to separate these out without causing
*massive* merge conflicts. Ultimately, to a large degree this is
a rewrite of most of the core algorithms in the LCG class and so I don't
think it really matters much.

Many thanks to the careful review by Sanjoy Das!

Differential Revision: http://reviews.llvm.org/D16802

llvm-svn: 261040

1 files changed, 1181 insertions, 388 deletions

diff --git a/llvm/lib/Analysis/LazyCallGraph.cpp b/llvm/lib/Analysis/LazyCallGraph.cpp
index 11e1166001a..5de90782a31 100644
--- a/llvm/lib/Analysis/LazyCallGraph.cpp
+++ b/llvm/lib/Analysis/LazyCallGraph.cpp
@@ -21,7 +21,7 @@ using namespace llvm;
 #define DEBUG_TYPE "lcg"
 
 static void addEdge(SmallVectorImpl<LazyCallGraph::Edge> &Edges,
-                    DenseMap<Function *, size_t> &EdgeIndexMap, Function &F,
+                    DenseMap<Function *, int> &EdgeIndexMap, Function &F,
                     LazyCallGraph::Edge::Kind EK) {
   // Note that we consider *any* function with a definition to be a viable
   // edge. Even if the function's definition is subject to replacement by
@@ -34,17 +34,16 @@ static void addEdge(SmallVectorImpl<LazyCallGraph::Edge> &Edges,
   // strong definition's address would be an effective way to determine the
   // safety of optimizing a direct call edge.
   if (!F.isDeclaration() &&
-      EdgeIndexMap.insert(std::make_pair(&F, Edges.size())).second) {
+      EdgeIndexMap.insert({&F, Edges.size()}).second) {
     DEBUG(dbgs() << "    Added callable function: " << F.getName() << "\n");
     Edges.emplace_back(LazyCallGraph::Edge(F, EK));
   }
 }
 
-static void findReferences(
-                      SmallVectorImpl<Constant *> &Worklist,
-                      SmallPtrSetImpl<Constant *> &Visited,
-                      SmallVectorImpl<LazyCallGraph::Edge> &Edges,
-                      DenseMap<Function *, size_t> &EdgeIndexMap) {
+static void findReferences(SmallVectorImpl<Constant *> &Worklist,
+                           SmallPtrSetImpl<Constant *> &Visited,
+                           SmallVectorImpl<LazyCallGraph::Edge> &Edges,
+                           DenseMap<Function *, int> &EdgeIndexMap) {
   while (!Worklist.empty()) {
     Constant *C = Worklist.pop_back_val();
 
@@ -94,23 +93,27 @@ LazyCallGraph::Node::Node(LazyCallGraph &G, Function &F)
   findReferences(Worklist, Visited, Edges, EdgeIndexMap);
 }
 
-void LazyCallGraph::Node::insertEdgeInternal(Function &Child, Edge::Kind EK) {
-  if (Node *N = G->lookup(Child))
+void LazyCallGraph::Node::insertEdgeInternal(Function &Target, Edge::Kind EK) {
+  if (Node *N = G->lookup(Target))
     return insertEdgeInternal(*N, EK);
 
-  EdgeIndexMap.insert(std::make_pair(&Child, Edges.size()));
-  Edges.emplace_back(Child, EK);
+  EdgeIndexMap.insert({&Target, Edges.size()});
+  Edges.emplace_back(Target, EK);
 }
 
-void LazyCallGraph::Node::insertEdgeInternal(Node &ChildN, Edge::Kind EK) {
-  EdgeIndexMap.insert(std::make_pair(&ChildN.getFunction(), Edges.size()));
-  Edges.emplace_back(ChildN, EK);
+void LazyCallGraph::Node::insertEdgeInternal(Node &TargetN, Edge::Kind EK) {
+  EdgeIndexMap.insert({&TargetN.getFunction(), Edges.size()});
+  Edges.emplace_back(TargetN, EK);
 }
 
-void LazyCallGraph::Node::removeEdgeInternal(Function &Child) {
-  auto IndexMapI = EdgeIndexMap.find(&Child);
+void LazyCallGraph::Node::setEdgeKind(Function &TargetF, Edge::Kind EK) {
+  Edges[EdgeIndexMap.find(&TargetF)->second].setKind(EK);
+}
+
+void LazyCallGraph::Node::removeEdgeInternal(Function &Target) {
+  auto IndexMapI = EdgeIndexMap.find(&Target);
   assert(IndexMapI != EdgeIndexMap.end() &&
-         "Child not in the edge set for this caller?");
+         "Target not in the edge set for this caller?");
 
   Edges[IndexMapI->second] = Edge();
   EdgeIndexMap.erase(IndexMapI);
@@ -121,7 +124,7 @@ LazyCallGraph::LazyCallGraph(Module &M) : NextDFSNumber(0) {
                << "\n");
   for (Function &F : M)
     if (!F.isDeclaration() && !F.hasLocalLinkage())
-      if (EntryIndexMap.insert(std::make_pair(&F, EntryEdges.size())).second) {
+      if (EntryIndexMap.insert({&F, EntryEdges.size()}).second) {
         DEBUG(dbgs() << "  Adding '" << F.getName()
                      << "' to entry set of the graph.\n");
         EntryEdges.emplace_back(F, Edge::Ref);
@@ -140,16 +143,16 @@ LazyCallGraph::LazyCallGraph(Module &M) : NextDFSNumber(0) {
   findReferences(Worklist, Visited, EntryEdges, EntryIndexMap);
 
   for (const Edge &E : EntryEdges)
-    SCCEntryNodes.push_back(&E.getFunction());
+    RefSCCEntryNodes.push_back(&E.getFunction());
 }
 
 LazyCallGraph::LazyCallGraph(LazyCallGraph &&G)
     : BPA(std::move(G.BPA)), NodeMap(std::move(G.NodeMap)),
       EntryEdges(std::move(G.EntryEdges)),
       EntryIndexMap(std::move(G.EntryIndexMap)), SCCBPA(std::move(G.SCCBPA)),
-      SCCMap(std::move(G.SCCMap)), LeafSCCs(std::move(G.LeafSCCs)),
+      SCCMap(std::move(G.SCCMap)), LeafRefSCCs(std::move(G.LeafRefSCCs)),
       DFSStack(std::move(G.DFSStack)),
-      SCCEntryNodes(std::move(G.SCCEntryNodes)),
+      RefSCCEntryNodes(std::move(G.RefSCCEntryNodes)),
       NextDFSNumber(G.NextDFSNumber) {
   updateGraphPtrs();
 }
@@ -161,405 +164,1068 @@ LazyCallGraph &LazyCallGraph::operator=(LazyCallGraph &&G) {
   EntryIndexMap = std::move(G.EntryIndexMap);
   SCCBPA = std::move(G.SCCBPA);
   SCCMap = std::move(G.SCCMap);
-  LeafSCCs = std::move(G.LeafSCCs);
+  LeafRefSCCs = std::move(G.LeafRefSCCs);
   DFSStack = std::move(G.DFSStack);
-  SCCEntryNodes = std::move(G.SCCEntryNodes);
+  RefSCCEntryNodes = std::move(G.RefSCCEntryNodes);
   NextDFSNumber = G.NextDFSNumber;
   updateGraphPtrs();
   return *this;
 }
 
-void LazyCallGraph::SCC::insert(Node &N) {
-  N.DFSNumber = N.LowLink = -1;
-  Nodes.push_back(&N);
-  G->SCCMap[&N] = this;
+#ifndef NDEBUG
+void LazyCallGraph::SCC::verify() {
+  assert(OuterRefSCC && "Can't have a null RefSCC!");
+  assert(!Nodes.empty() && "Can't have an empty SCC!");
+
+  for (Node *N : Nodes) {
+    assert(N && "Can't have a null node!");
+    assert(OuterRefSCC->G->lookupSCC(*N) == this &&
+           "Node does not map to this SCC!");
+    assert(N->DFSNumber == -1 &&
+           "Must set DFS numbers to -1 when adding a node to an SCC!");
+    assert(N->LowLink == -1 &&
+           "Must set low link to -1 when adding a node to an SCC!");
+    for (Edge &E : *N)
+      assert(E.getNode() && "Can't have an edge to a raw function!");
+  }
 }
+#endif
 
-bool LazyCallGraph::SCC::isDescendantOf(const SCC &C) const {
+LazyCallGraph::RefSCC::RefSCC(LazyCallGraph &G) : G(&G) {}
+
+#ifndef NDEBUG
+void LazyCallGraph::RefSCC::verify() {
+  assert(G && "Can't have a null graph!");
+  assert(!SCCs.empty() && "Can't have an empty SCC!");
+
+  // Verify basic properties of the SCCs.
+  for (SCC *C : SCCs) {
+    assert(C && "Can't have a null SCC!");
+    C->verify();
+    assert(&C->getOuterRefSCC() == this &&
+           "SCC doesn't think it is inside this RefSCC!");
+  }
+
+  // Check that our indices map correctly.
+  for (auto &SCCIndexPair : SCCIndices) {
+    SCC *C = SCCIndexPair.first;
+    int i = SCCIndexPair.second;
+    assert(C && "Can't have a null SCC in the indices!");
+    assert(SCCs[i] == C && "Index doesn't point to SCC!");
+  }
+
+  // Check that the SCCs are in fact in post-order.
+  for (int i = 0, Size = SCCs.size(); i < Size; ++i) {
+    SCC &SourceSCC = *SCCs[i];
+    for (Node &N : SourceSCC)
+      for (Edge &E : N) {
+        if (!E.isCall())
+          continue;
+        SCC &TargetSCC = *G->lookupSCC(*E.getNode());
+        if (&TargetSCC.getOuterRefSCC() == this) {
+          assert(SCCIndices.find(&TargetSCC)->second <= i &&
+                 "Edge between SCCs violates post-order relationship.");
+          continue;
+        }
+        assert(TargetSCC.getOuterRefSCC().Parents.count(this) &&
+               "Edge to a RefSCC missing us in its parent set.");
+      }
+  }
+}
+#endif
+
+bool LazyCallGraph::RefSCC::isDescendantOf(const RefSCC &C) const {
   // Walk up the parents of this SCC and verify that we eventually find C.
-  SmallVector<const SCC *, 4> AncestorWorklist;
+  SmallVector<const RefSCC *, 4> AncestorWorklist;
   AncestorWorklist.push_back(this);
   do {
-    const SCC *AncestorC = AncestorWorklist.pop_back_val();
+    const RefSCC *AncestorC = AncestorWorklist.pop_back_val();
     if (AncestorC->isChildOf(C))
       return true;
-    for (const SCC *ParentC : AncestorC->ParentSCCs)
+    for (const RefSCC *ParentC : AncestorC->Parents)
       AncestorWorklist.push_back(ParentC);
   } while (!AncestorWorklist.empty());
 
   return false;
 }
 
-void LazyCallGraph::SCC::insertIntraSCCEdge(Node &ParentN, Node &ChildN,
-                                            Edge::Kind EK) {
-  // First insert it into the caller.
-  ParentN.insertEdgeInternal(ChildN, EK);
+SmallVector<LazyCallGraph::SCC *, 1>
+LazyCallGraph::RefSCC::switchInternalEdgeToCall(Node &SourceN, Node &TargetN) {
+  assert(!SourceN[TargetN].isCall() && "Must start with a ref edge!");
+
+  SmallVector<SCC *, 1> DeletedSCCs;
+
+  SCC &SourceSCC = *G->lookupSCC(SourceN);
+  SCC &TargetSCC = *G->lookupSCC(TargetN);
+
+  // If the two nodes are already part of the same SCC, we're also done as
+  // we've just added more connectivity.
+  if (&SourceSCC == &TargetSCC) {
+    SourceN.setEdgeKind(TargetN.getFunction(), Edge::Call);
+#ifndef NDEBUG
+    // Check that the RefSCC is still valid.
+    verify();
+#endif
+    return DeletedSCCs;
+  }
 
-  assert(G->SCCMap.lookup(&ParentN) == this && "Parent must be in this SCC.");
-  assert(G->SCCMap.lookup(&ChildN) == this && "Child must be in this SCC.");
+  // At this point we leverage the postorder list of SCCs to detect when the
+  // insertion of an edge changes the SCC structure in any way.
+  //
+  // First and foremost, we can eliminate the need for any changes when the
+  // edge is toward the beginning of the postorder sequence because all edges
+  // flow in that direction already. Thus adding a new one cannot form a cycle.
+  int SourceIdx = SCCIndices[&SourceSCC];
+  int TargetIdx = SCCIndices[&TargetSCC];
+  if (TargetIdx < SourceIdx) {
+    SourceN.setEdgeKind(TargetN.getFunction(), Edge::Call);
+#ifndef NDEBUG
+    // Check that the RefSCC is still valid.
+    verify();
+#endif
+    return DeletedSCCs;
+  }
 
-  // Nothing changes about this SCC or any other.
+  // When we do have an edge from an earlier SCC to a later SCC in the
+  // postorder sequence, all of the SCCs which may be impacted are in the
+  // closed range of those two within the postorder sequence. The algorithm to
+  // restore the state is as follows:
+  //
+  // 1) Starting from the source SCC, construct a set of SCCs which reach the
+  //    source SCC consisting of just the source SCC. Then scan toward the
+  //    target SCC in postorder and for each SCC, if it has an edge to an SCC
+  //    in the set, add it to the set. Otherwise, the source SCC is not
+  //    a successor, move it in the postorder sequence to immediately before
+  //    the source SCC, shifting the source SCC and all SCCs in the set one
+  //    position toward the target SCC. Stop scanning after processing the
+  //    target SCC.
+  // 2) If the source SCC is now past the target SCC in the postorder sequence,
+  //    and thus the new edge will flow toward the start, we are done.
+  // 3) Otherwise, starting from the target SCC, walk all edges which reach an
+  //    SCC between the source and the target, and add them to the set of
+  //    connected SCCs, then recurse through them. Once a complete set of the
+  //    SCCs the target connects to is known, hoist the remaining SCCs between
+  //    the source and the target to be above the target. Note that there is no
+  //    need to process the source SCC, it is already known to connect.
+  // 4) At this point, all of the SCCs in the closed range between the source
+  //    SCC and the target SCC in the postorder sequence are connected,
+  //    including the target SCC and the source SCC. Inserting the edge from
+  //    the source SCC to the target SCC will form a cycle out of precisely
+  //    these SCCs. Thus we can merge all of the SCCs in this closed range into
+  //    a single SCC.
+  //
+  // This process has various important properties:
+  // - Only mutates the SCCs when adding the edge actually changes the SCC
+  //   structure.
+  // - Never mutates SCCs which are unaffected by the change.
+  // - Updates the postorder sequence to correctly satisfy the postorder
+  //   constraint after the edge is inserted.
+  // - Only reorders SCCs in the closed postorder sequence from the source to
+  //   the target, so easy to bound how much has changed even in the ordering.
+  // - Big-O is the number of edges in the closed postorder range of SCCs from
+  //   source to target.
+
+  assert(SourceIdx < TargetIdx && "Cannot have equal indices here!");
+  SmallPtrSet<SCC *, 4> ConnectedSet;
+
+  // Compute the SCCs which (transitively) reach the source.
+  ConnectedSet.insert(&SourceSCC);
+  auto IsConnected = [&](SCC &C) {
+    for (Node &N : C)
+      for (Edge &E : N.calls()) {
+        assert(E.getNode() && "Must have formed a node within an SCC!");
+        if (ConnectedSet.count(G->lookupSCC(*E.getNode())))
+          return true;
+      }
+
+    return false;
+  };
+
+  for (SCC *C :
+       make_range(SCCs.begin() + SourceIdx + 1, SCCs.begin() + TargetIdx + 1))
+    if (IsConnected(*C))
+      ConnectedSet.insert(C);
+
+  // Partition the SCCs in this part of the port-order sequence so only SCCs
+  // connecting to the source remain between it and the target. This is
+  // a benign partition as it preserves postorder.
+  auto SourceI = std::stable_partition(
+      SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx + 1,
+      [&ConnectedSet](SCC *C) { return !ConnectedSet.count(C); });
+  for (int i = SourceIdx, e = TargetIdx + 1; i < e; ++i)
+    SCCIndices.find(SCCs[i])->second = i;
+
+  // If the target doesn't connect to the source, then we've corrected the
+  // post-order and there are no cycles formed.
+  if (!ConnectedSet.count(&TargetSCC)) {
+    assert(SourceI > (SCCs.begin() + SourceIdx) &&
+           "Must have moved the source to fix the post-order.");
+    assert(*std::prev(SourceI) == &TargetSCC &&
+           "Last SCC to move should have bene the target.");
+    SourceN.setEdgeKind(TargetN.getFunction(), Edge::Call);
+#ifndef NDEBUG
+    verify();
+#endif
+    return DeletedSCCs;
+  }
+
+  assert(SCCs[TargetIdx] == &TargetSCC &&
+         "Should not have moved target if connected!");
+  SourceIdx = SourceI - SCCs.begin();
+
+#ifndef NDEBUG
+  // Check that the RefSCC is still valid.
+  verify();
+#endif
+
+  // See whether there are any remaining intervening SCCs between the source
+  // and target. If so we need to make sure they all are reachable form the
+  // target.
+  if (SourceIdx + 1 < TargetIdx) {
+    // Use a normal worklist to find which SCCs the target connects to. We still
+    // bound the search based on the range in the postorder list we care about,
+    // but because this is forward connectivity we just "recurse" through the
+    // edges.
+    ConnectedSet.clear();
+    ConnectedSet.insert(&TargetSCC);
+    SmallVector<SCC *, 4> Worklist;
+    Worklist.push_back(&TargetSCC);
+    do {
+      SCC &C = *Worklist.pop_back_val();
+      for (Node &N : C)
+        for (Edge &E : N) {
+          assert(E.getNode() && "Must have formed a node within an SCC!");
+          if (!E.isCall())
+            continue;
+          SCC &EdgeC = *G->lookupSCC(*E.getNode());
+          if (&EdgeC.getOuterRefSCC() != this)
+            // Not in this RefSCC...
+            continue;
+          if (SCCIndices.find(&EdgeC)->second <= SourceIdx)
+            // Not in the postorder sequence between source and target.
+            continue;
+
+          if (ConnectedSet.insert(&EdgeC).second)
+            Worklist.push_back(&EdgeC);
+        }
+    } while (!Worklist.empty());
+
+    // Partition SCCs so that only SCCs reached from the target remain between
+    // the source and the target. This preserves postorder.
+    auto TargetI = std::stable_partition(
+        SCCs.begin() + SourceIdx + 1, SCCs.begin() + TargetIdx + 1,
+        [&ConnectedSet](SCC *C) { return ConnectedSet.count(C); });
+    for (int i = SourceIdx + 1, e = TargetIdx + 1; i < e; ++i)
+      SCCIndices.find(SCCs[i])->second = i;
+    TargetIdx = std::prev(TargetI) - SCCs.begin();
+    assert(SCCs[TargetIdx] == &TargetSCC &&
+           "Should always end with the target!");
+
+#ifndef NDEBUG
+    // Check that the RefSCC is still valid.
+    verify();
+#endif
+  }
+
+  // At this point, we know that connecting source to target forms a cycle
+  // because target connects back to source, and we know that all of the SCCs
+  // between the source and target in the postorder sequence participate in that
+  // cycle. This means that we need to merge all of these SCCs into a single
+  // result SCC.
+  //
+  // NB: We merge into the target because all of these functions were already
+  // reachable from the target, meaning any SCC-wide properties deduced about it
+  // other than the set of functions within it will not have changed.
+  auto MergeRange =
+      make_range(SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx);
+  for (SCC *C : MergeRange) {
+    assert(C != &TargetSCC &&
+           "We merge *into* the target and shouldn't process it here!");
+    SCCIndices.erase(C);
+    TargetSCC.Nodes.append(C->Nodes.begin(), C->Nodes.end());
+    for (Node *N : C->Nodes)
+      G->SCCMap[N] = &TargetSCC;
+    C->clear();
+    DeletedSCCs.push_back(C);
+  }
+
+  // Erase the merged SCCs from the list and update the indices of the
+  // remaining SCCs.
+  int IndexOffset = MergeRange.end() - MergeRange.begin();
+  auto EraseEnd = SCCs.erase(MergeRange.begin(), MergeRange.end());
+  for (SCC *C : make_range(EraseEnd, SCCs.end()))
+    SCCIndices[C] -= IndexOffset;
+
+  // Now that the SCC structure is finalized, flip the kind to call.
+  SourceN.setEdgeKind(TargetN.getFunction(), Edge::Call);
+
+#ifndef NDEBUG
+  // And we're done! Verify in debug builds that the RefSCC is coherent.
+  verify();
+#endif
+  return DeletedSCCs;
 }
 
-void LazyCallGraph::SCC::insertOutgoingEdge(Node &ParentN, Node &ChildN,
-                                            Edge::Kind EK) {
+void LazyCallGraph::RefSCC::switchInternalEdgeToRef(Node &SourceN,
+                                                    Node &TargetN) {
+  assert(SourceN[TargetN].isCall() && "Must start with a call edge!");
+
+  SCC &SourceSCC = *G->lookupSCC(SourceN);
+  SCC &TargetSCC = *G->lookupSCC(TargetN);
+
+  assert(&SourceSCC.getOuterRefSCC() == this &&
+         "Source must be in this RefSCC.");
+  assert(&TargetSCC.getOuterRefSCC() == this &&
+         "Target must be in this RefSCC.");
+
+  // Set the edge kind.
+  SourceN.setEdgeKind(TargetN.getFunction(), Edge::Ref);
+
+  // If this call edge is just connecting two separate SCCs within this RefSCC,
+  // there is nothing to do.
+  if (&SourceSCC != &TargetSCC) {
+#ifndef NDEBUG
+    // Check that the RefSCC is still valid.
+    verify();
+#endif
+    return;
+  }
+
+  // Otherwise we are removing a call edge from a single SCC. This may break
+  // the cycle. In order to compute the new set of SCCs, we need to do a small
+  // DFS over the nodes within the SCC to form any sub-cycles that remain as
+  // distinct SCCs and compute a postorder over the resulting SCCs.
+  //
+  // However, we specially handle the target node. The target node is known to
+  // reach all other nodes in the original SCC by definition. This means that
+  // we want the old SCC to be replaced with an SCC contaning that node as it
+  // will be the root of whatever SCC DAG results from the DFS. Assumptions
+  // about an SCC such as the set of functions called will continue to hold,
+  // etc.
+
+  SCC &OldSCC = TargetSCC;
+  SmallVector<std::pair<Node *, call_edge_iterator>, 16> DFSStack;
+  SmallVector<Node *, 16> PendingSCCStack;
+  SmallVector<SCC *, 4> NewSCCs;
+
+  // Prepare the nodes for a fresh DFS.
+  SmallVector<Node *, 16> Worklist;
+  Worklist.swap(OldSCC.Nodes);
+  for (Node *N : Worklist) {
+    N->DFSNumber = N->LowLink = 0;
+    G->SCCMap.erase(N);
+  }
+
+  // Force the target node to be in the old SCC. This also enables us to take
+  // a very significant short-cut in the standard Tarjan walk to re-form SCCs
+  // below: whenever we build an edge that reaches the target node, we know
+  // that the target node eventually connects back to all other nodes in our
+  // walk. As a consequence, we can detect and handle participants in that
+  // cycle without walking all the edges that form this connection, and instead
+  // by relying on the fundamental guarantee coming into this operation (all
+  // nodes are reachable from the target due to previously forming an SCC).
+  TargetN.DFSNumber = TargetN.LowLink = -1;
+  OldSCC.Nodes.push_back(&TargetN);
+  G->SCCMap[&TargetN] = &OldSCC;
+
+  // Scan down the stack and DFS across the call edges.
+  for (Node *RootN : Worklist) {
+    assert(DFSStack.empty() &&
+           "Cannot begin a new root with a non-empty DFS stack!");
+    assert(PendingSCCStack.empty() &&
+           "Cannot begin a new root with pending nodes for an SCC!");
+
+    // Skip any nodes we've already reached in the DFS.
+    if (RootN->DFSNumber != 0) {
+      assert(RootN->DFSNumber == -1 &&
+             "Shouldn't have any mid-DFS root nodes!");
+      continue;
+    }
+
+    RootN->DFSNumber = RootN->LowLink = 1;
+    int NextDFSNumber = 2;
+
+    DFSStack.push_back({RootN, RootN->call_begin()});
+    do {
+      Node *N;
+      call_edge_iterator I;
+      std::tie(N, I) = DFSStack.pop_back_val();
+      auto E = N->call_end();
+      while (I != E) {
+        Node &ChildN = *I->getNode();
+        if (ChildN.DFSNumber == 0) {
+          // We haven't yet visited this child, so descend, pushing the current
+          // node onto the stack.
+          DFSStack.push_back({N, I});
+
+          assert(!G->SCCMap.count(&ChildN) &&
+                 "Found a node with 0 DFS number but already in an SCC!");
+          ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
+          N = &ChildN;
+          I = N->call_begin();
+          E = N->call_end();
+          continue;
+        }
+
+        // Check for the child already being part of some component.
+        if (ChildN.DFSNumber == -1) {
+          if (G->lookupSCC(ChildN) == &OldSCC) {
+            // If the child is part of the old SCC, we know that it can reach
+            // every other node, so we have formed a cycle. Pull the entire DFS
+            // and pending stacks into it. See the comment above about setting
+            // up the old SCC for why we do this.
+            int OldSize = OldSCC.size();
+            OldSCC.Nodes.push_back(N);
+            OldSCC.Nodes.append(PendingSCCStack.begin(), PendingSCCStack.end());
+            PendingSCCStack.clear();
+            while (!DFSStack.empty())
+              OldSCC.Nodes.push_back(DFSStack.pop_back_val().first);
+            for (Node &N : make_range(OldSCC.begin() + OldSize, OldSCC.end())) {
+              N.DFSNumber = N.LowLink = -1;
+              G->SCCMap[&N] = &OldSCC;
+            }
+            N = nullptr;
+            break;
+          }
+
+          // If the child has already been added to some child component, it
+          // couldn't impact the low-link of this parent because it isn't
+          // connected, and thus its low-link isn't relevant so skip it.
+          ++I;
+          continue;
+        }
+
+        // Track the lowest linked child as the lowest link for this node.
+        assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
+        if (ChildN.LowLink < N->LowLink)
+          N->LowLink = ChildN.LowLink;
+
+        // Move to the next edge.
+        ++I;
+      }
+      if (!N)
+        // Cleared the DFS early, start another round.
+        break;
+
+      // We've finished processing N and its descendents, put it on our pending
+      // SCC stack to eventually get merged into an SCC of nodes.
+      PendingSCCStack.push_back(N);
+
+      // If this node is linked to some lower entry, continue walking up the
+      // stack.
+      if (N->LowLink != N->DFSNumber)
+        continue;
+
+      // Otherwise, we've completed an SCC. Append it to our post order list of
+      // SCCs.
+      int RootDFSNumber = N->DFSNumber;
+      // Find the range of the node stack by walking down until we pass the
+      // root DFS number.
+      auto SCCNodes = make_range(
+          PendingSCCStack.rbegin(),
+          std::find_if(PendingSCCStack.rbegin(), PendingSCCStack.rend(),
+                       [RootDFSNumber](Node *N) {
+                         return N->DFSNumber < RootDFSNumber;
+                       }));
+
+      // Form a new SCC out of these nodes and then clear them off our pending
+      // stack.
+      NewSCCs.push_back(G->createSCC(*this, SCCNodes));
+      for (Node &N : *NewSCCs.back()) {
+        N.DFSNumber = N.LowLink = -1;
+        G->SCCMap[&N] = NewSCCs.back();
+      }
+      PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
+    } while (!DFSStack.empty());
+  }
+
+  // Insert the remaining SCCs before the old one. The old SCC can reach all
+  // other SCCs we form because it contains the target node of the removed edge
+  // of the old SCC. This means that we will have edges into all of the new
+  // SCCs, which means the old one must come last for postorder.
+  int OldIdx = SCCIndices[&OldSCC];
+  SCCs.insert(SCCs.begin() + OldIdx, NewSCCs.begin(), NewSCCs.end());
+
+  // Update the mapping from SCC* to index to use the new SCC*s, and remove the
+  // old SCC from the mapping.
+  for (int Idx = OldIdx, Size = SCCs.size(); Idx < Size; ++Idx)
+    SCCIndices[SCCs[Idx]] = Idx;
+
+#ifndef NDEBUG
+  // We're done. Check the validity on our way out.
+  verify();
+#endif
+}
+
+void LazyCallGraph::RefSCC::switchOutgoingEdgeToCall(Node &SourceN,
+                                                     Node &TargetN) {
+  assert(!SourceN[TargetN].isCall() && "Must start with a ref edge!");
+
+  assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
+  assert(G->lookupRefSCC(TargetN) != this &&
+         "Target must not be in this RefSCC.");
+  assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
+         "Target must be a descendant of the Source.");
+
+  // Edges between RefSCCs are the same regardless of call or ref, so we can
+  // just flip the edge here.
+  SourceN.setEdgeKind(TargetN.getFunction(), Edge::Call);
+
+#ifndef NDEBUG
+  // Check that the RefSCC is still valid.
+  verify();
+#endif
+}
+
+void LazyCallGraph::RefSCC::switchOutgoingEdgeToRef(Node &SourceN,
+                                                    Node &TargetN) {
+  assert(SourceN[TargetN].isCall() && "Must start with a call edge!");
+
+  assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
+  assert(G->lookupRefSCC(TargetN) != this &&
+         "Target must not be in this RefSCC.");
+  assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
+         "Target must be a descendant of the Source.");
+
+  // Edges between RefSCCs are the same regardless of call or ref, so we can
+  // just flip the edge here.
+  SourceN.setEdgeKind(TargetN.getFunction(), Edge::Ref);
+
+#ifndef NDEBUG
+  // Check that the RefSCC is still valid.
+  verify();
+#endif
+}
+
+void LazyCallGraph::RefSCC::insertInternalRefEdge(Node &SourceN,
+                                                  Node &TargetN) {
+  assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
+  assert(G->lookupRefSCC(TargetN) == this && "Target must be in this RefSCC.");
+
+  SourceN.insertEdgeInternal(TargetN, Edge::Ref);
+
+#ifndef NDEBUG
+  // Check that the RefSCC is still valid.
+  verify();
+#endif
+}
+
+void LazyCallGraph::RefSCC::insertOutgoingEdge(Node &SourceN, Node &TargetN,
+                                               Edge::Kind EK) {
   // First insert it into the caller.
-  ParentN.insertEdgeInternal(ChildN, EK);
+  SourceN.insertEdgeInternal(TargetN, EK);
 
-  assert(G->SCCMap.lookup(&ParentN) == this && "Parent must be in this SCC.");
+  assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
 
-  SCC &ChildC = *G->SCCMap.lookup(&ChildN);
-  assert(&ChildC != this && "Child must not be in this SCC.");
-  assert(ChildC.isDescendantOf(*this) &&
-         "Child must be a descendant of the Parent.");
+  RefSCC &TargetC = *G->lookupRefSCC(TargetN);
+  assert(&TargetC != this && "Target must not be in this RefSCC.");
+  assert(TargetC.isDescendantOf(*this) &&
+         "Target must be a descendant of the Source.");
 
   // The only change required is to add this SCC to the parent set of the
   // callee.
-  ChildC.ParentSCCs.insert(this);
+  TargetC.Parents.insert(this);
+
+#ifndef NDEBUG
+  // Check that the RefSCC is still valid.
+  verify();
+#endif
 }
 
-SmallVector<LazyCallGraph::SCC *, 1>
-LazyCallGraph::SCC::insertIncomingEdge(Node &ParentN, Node &ChildN,
-                                       Edge::Kind EK) {
-  // First insert it into the caller.
-  ParentN.insertEdgeInternal(ChildN, EK);
+SmallVector<LazyCallGraph::RefSCC *, 1>
+LazyCallGraph::RefSCC::insertIncomingRefEdge(Node &SourceN, Node &TargetN) {
+  assert(G->lookupRefSCC(TargetN) == this && "Target must be in this SCC.");
 
-  assert(G->SCCMap.lookup(&ChildN) == this && "Child must be in this SCC.");
+  // We store the RefSCCs found to be connected in postorder so that we can use
+  // that when merging. We also return this to the caller to allow them to
+  // invalidate information pertaining to these RefSCCs.
+  SmallVector<RefSCC *, 1> Connected;
 
-  SCC &ParentC = *G->SCCMap.lookup(&ParentN);
-  assert(&ParentC != this && "Parent must not be in this SCC.");
-  assert(ParentC.isDescendantOf(*this) &&
-         "Parent must be a descendant of the Child.");
+  RefSCC &SourceC = *G->lookupRefSCC(SourceN);
+  assert(&SourceC != this && "Source must not be in this SCC.");
+  assert(SourceC.isDescendantOf(*this) &&
+         "Source must be a descendant of the Target.");
 
   // The algorithm we use for merging SCCs based on the cycle introduced here
-  // is to walk the SCC inverted DAG formed by the parent SCC sets. The inverse
-  // graph has the same cycle properties as the actual DAG of the SCCs, and
-  // when forming SCCs lazily by a DFS, the bottom of the graph won't exist in
-  // many cases which should prune the search space.
+  // is to walk the RefSCC inverted DAG formed by the parent sets. The inverse
+  // graph has the same cycle properties as the actual DAG of the RefSCCs, and
+  // when forming RefSCCs lazily by a DFS, the bottom of the graph won't exist
+  // in many cases which should prune the search space.
   //
-  // FIXME: We can get this pruning behavior even after the incremental SCC
+  // FIXME: We can get this pruning behavior even after the incremental RefSCC
   // formation by leaving behind (conservative) DFS numberings in the nodes,
   // and pruning the search with them. These would need to be cleverly updated
   // during the removal of intra-SCC edges, but could be preserved
   // conservatively.
+  //
+  // FIXME: This operation currently creates ordering stability problems
+  // because we don't use stably ordered containers for the parent SCCs.
 
-  // The set of SCCs that are connected to the caller, and thus will
+  // The set of RefSCCs that are connected to the parent, and thus will
   // participate in the merged connected component.
-  SmallPtrSet<SCC *, 8> ConnectedSCCs;
-  ConnectedSCCs.insert(this);
-  ConnectedSCCs.insert(&ParentC);
+  SmallPtrSet<RefSCC *, 8> ConnectedSet;
+  ConnectedSet.insert(this);
 
   // We build up a DFS stack of the parents chains.
-  SmallVector<std::pair<SCC *, SCC::parent_iterator>, 8> DFSSCCs;
-  SmallPtrSet<SCC *, 8> VisitedSCCs;
+  SmallVector<std::pair<RefSCC *, parent_iterator>, 8> DFSStack;
+  SmallPtrSet<RefSCC *, 8> Visited;
   int ConnectedDepth = -1;
-  SCC *C = this;
-  parent_iterator I = parent_begin(), E = parent_end();
-  for (;;) {
+  DFSStack.push_back({&SourceC, SourceC.parent_begin()});
+  do {
+    auto DFSPair = DFSStack.pop_back_val();
+    RefSCC *C = DFSPair.first;
+    parent_iterator I = DFSPair.second;
+    auto E = C->parent_end();
+
     while (I != E) {
-      SCC &ParentSCC = *I++;
+      RefSCC &Parent = *I++;
 
       // If we have already processed this parent SCC, skip it, and remember
       // whether it was connected so we don't have to check the rest of the
       // stack. This also handles when we reach a child of the 'this' SCC (the
       // callee) which terminates the search.
-      if (ConnectedSCCs.count(&ParentSCC)) {
-        ConnectedDepth = std::max<int>(ConnectedDepth, DFSSCCs.size());
+      if (ConnectedSet.count(&Parent)) {
+        assert(ConnectedDepth < (int)DFSStack.size() &&
+               "Cannot have a connected depth greater than the DFS depth!");
+        ConnectedDepth = DFSStack.size();
         continue;
       }
-      if (VisitedSCCs.count(&ParentSCC))
+      if (Visited.count(&Parent))
         continue;
 
       // We fully explore the depth-first space, adding nodes to the connected
       // set only as we pop them off, so "recurse" by rotating to the parent.
-      DFSSCCs.push_back(std::make_pair(C, I));
-      C = &ParentSCC;
-      I = ParentSCC.parent_begin();
-      E = ParentSCC.parent_end();
+      DFSStack.push_back({C, I});
+      C = &Parent;
+      I = C->parent_begin();
+      E = C->parent_end();
     }
 
     // If we've found a connection anywhere below this point on the stack (and
     // thus up the parent graph from the caller), the current node needs to be
     // added to the connected set now that we've processed all of its parents.
-    if ((int)DFSSCCs.size() == ConnectedDepth) {
+    if ((int)DFSStack.size() == ConnectedDepth) {
       --ConnectedDepth; // We're finished with this connection.
-      ConnectedSCCs.insert(C);
+      bool Inserted = ConnectedSet.insert(C).second;
+      (void)Inserted;
+      assert(Inserted && "Cannot insert a refSCC multiple times!");
+      Connected.push_back(C);
     } else {
       // Otherwise remember that its parents don't ever connect.
-      assert(ConnectedDepth < (int)DFSSCCs.size() &&
+      assert(ConnectedDepth < (int)DFSStack.size() &&
              "Cannot have a connected depth greater than the DFS depth!");
-      VisitedSCCs.insert(C);
+      Visited.insert(C);
     }
-
-    if (DFSSCCs.empty())
-      break; // We've walked all the parents of the caller transitively.
-
-    // Pop off the prior node and position to unwind the depth first recursion.
-    std::tie(C, I) = DFSSCCs.pop_back_val();
-    E = C->parent_end();
-  }
+  } while (!DFSStack.empty());
 
   // Now that we have identified all of the SCCs which need to be merged into
   // a connected set with the inserted edge, merge all of them into this SCC.
-  // FIXME: This operation currently creates ordering stability problems
-  // because we don't use stably ordered containers for the parent SCCs or the
-  // connected SCCs.
-  unsigned NewNodeBeginIdx = Nodes.size();
-  for (SCC *C : ConnectedSCCs) {
-    if (C == this)
-      continue;
-    for (SCC *ParentC : C->ParentSCCs)
-      if (!ConnectedSCCs.count(ParentC))
-        ParentSCCs.insert(ParentC);
-    C->ParentSCCs.clear();
-
-    for (Node *N : *C) {
-      for (Edge &E : *N) {
-        assert(E.getNode() && "Cannot have a null node within a visited SCC!");
-        SCC &ChildC = *G->SCCMap.lookup(E.getNode());
-        if (&ChildC != C)
-          ChildC.ParentSCCs.erase(C);
+  // We walk the newly connected RefSCCs in the reverse postorder of the parent
+  // DAG walk above and merge in each of their SCC postorder lists. This
+  // ensures a merged postorder SCC list.
+  SmallVector<SCC *, 16> MergedSCCs;
+  int SCCIndex = 0;
+  for (RefSCC *C : reverse(Connected)) {
+    assert(C != this &&
+           "This RefSCC should terminate the DFS without being reached.");
+
+    // Merge the parents which aren't part of the merge into the our parents.
+    for (RefSCC *ParentC : C->Parents)
+      if (!ConnectedSet.count(ParentC))
+        Parents.insert(ParentC);
+    C->Parents.clear();
+
+    // Walk the inner SCCs to update their up-pointer and walk all the edges to
+    // update any parent sets.
+    // FIXME: We should try to find a way to avoid this (rather expensive) edge
+    // walk by updating the parent sets in some other manner.
+    for (SCC &InnerC : *C) {
+      InnerC.OuterRefSCC = this;
+      SCCIndices[&InnerC] = SCCIndex++;
+      for (Node &N : InnerC) {
+        G->SCCMap[&N] = &InnerC;
+        for (Edge &E : N) {
+          assert(E.getNode() &&
+                 "Cannot have a null node within a visited SCC!");
+          RefSCC &ChildRC = *G->lookupRefSCC(*E.getNode());
+          if (ConnectedSet.count(&ChildRC))
+            continue;
+          ChildRC.Parents.erase(C);
+          ChildRC.Parents.insert(this);
+        }
       }
-      G->SCCMap[N] = this;
-      Nodes.push_back(N);
     }
-    C->Nodes.clear();
+
+    // Now merge in the SCCs. We can actually move here so try to reuse storage
+    // the first time through.
+    if (MergedSCCs.empty())
+      MergedSCCs = std::move(C->SCCs);
+    else
+      MergedSCCs.append(C->SCCs.begin(), C->SCCs.end());
+    C->SCCs.clear();
   }
-  for (auto I = Nodes.begin() + NewNodeBeginIdx, E = Nodes.end(); I != E; ++I)
-    for (Edge &E : **I) {
-      assert(E.getNode() && "Cannot have a null node within a visited SCC!");
-      SCC &ChildC = *G->SCCMap.lookup(E.getNode());
-      if (&ChildC != this)
-        ChildC.ParentSCCs.insert(this);
-    }
+
+  // Finally append our original SCCs to the merged list and move it into
+  // place.
+  for (SCC &InnerC : *this)
+    SCCIndices[&InnerC] = SCCIndex++;
+  MergedSCCs.append(SCCs.begin(), SCCs.end());
+  SCCs = std::move(MergedSCCs);
+
+  // At this point we have a merged RefSCC with a post-order SCCs list, just
+  // connect the nodes to form the new edge.
+  SourceN.insertEdgeInternal(TargetN, Edge::Ref);
+
+#ifndef NDEBUG
+  // Check that the RefSCC is still valid.
+  verify();
+#endif
 
   // We return the list of SCCs which were merged so that callers can
   // invalidate any data they have associated with those SCCs. Note that these
   // SCCs are no longer in an interesting state (they are totally empty) but
   // the pointers will remain stable for the life of the graph itself.
-  return SmallVector<SCC *, 1>(ConnectedSCCs.begin(), ConnectedSCCs.end());
+  return Connected;
 }
 
-void LazyCallGraph::SCC::removeInterSCCEdge(Node &ParentN, Node &ChildN) {
+void LazyCallGraph::RefSCC::removeOutgoingEdge(Node &SourceN, Node &TargetN) {
+  assert(G->lookupRefSCC(SourceN) == this &&
+         "The source must be a member of this RefSCC.");
+
+  RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
+  assert(&TargetRC != this && "The target must not be a member of this RefSCC");
+
+  assert(std::find(G->LeafRefSCCs.begin(), G->LeafRefSCCs.end(), this) ==
+             G->LeafRefSCCs.end() &&
+         "Cannot have a leaf RefSCC source.");
+
   // First remove it from the node.
-  ParentN.removeEdgeInternal(ChildN.getFunction());
-
-  assert(G->SCCMap.lookup(&ParentN) == this &&
-         "The caller must be a member of this SCC.");
-
-  SCC &ChildC = *G->SCCMap.lookup(&ChildN);
-  assert(&ChildC != this &&
-         "This API only supports the rmoval of inter-SCC edges.");
-
-  assert(std::find(G->LeafSCCs.begin(), G->LeafSCCs.end(), this) ==
-             G->LeafSCCs.end() &&
-         "Cannot have a leaf SCC caller with a different SCC callee.");
-
-  bool HasOtherEdgeToChildC = false;
-  bool HasOtherChildC = false;
-  for (Node *N : *this) {
-    for (Edge &E : *N) {
-      assert(E.getNode() && "Cannot have a missing node in a visited SCC!");
-      SCC &OtherChildC = *G->SCCMap.lookup(E.getNode());
-      if (&OtherChildC == &ChildC) {
-        HasOtherEdgeToChildC = true;
-        break;
+  SourceN.removeEdgeInternal(TargetN.getFunction());
+
+  bool HasOtherEdgeToChildRC = false;
+  bool HasOtherChildRC = false;
+  for (SCC *InnerC : SCCs) {
+    for (Node &N : *InnerC) {
+      for (Edge &E : N) {
+        assert(E.getNode() && "Cannot have a missing node in a visited SCC!");
+        RefSCC &OtherChildRC = *G->lookupRefSCC(*E.getNode());
+        if (&OtherChildRC == &TargetRC) {
+          HasOtherEdgeToChildRC = true;
+          break;
+        }
+        if (&OtherChildRC != this)
+          HasOtherChildRC = true;
       }
-      if (&OtherChildC != this)
-        HasOtherChildC = true;
+      if (HasOtherEdgeToChildRC)
+        break;
     }
-    if (HasOtherEdgeToChildC)
+    if (HasOtherEdgeToChildRC)
       break;
   }
   // Because the SCCs form a DAG, deleting such an edge cannot change the set
   // of SCCs in the graph. However, it may cut an edge of the SCC DAG, making
-  // the parent SCC no longer connected to the child SCC. If so, we need to
-  // update the child SCC's map of its parents.
-  if (!HasOtherEdgeToChildC) {
-    bool Removed = ChildC.ParentSCCs.erase(this);
+  // the source SCC no longer connected to the target SCC. If so, we need to
+  // update the target SCC's map of its parents.
+  if (!HasOtherEdgeToChildRC) {
+    bool Removed = TargetRC.Parents.erase(this);
     (void)Removed;
     assert(Removed &&
-           "Did not find the parent SCC in the child SCC's parent list!");
+           "Did not find the source SCC in the target SCC's parent list!");
 
     // It may orphan an SCC if it is the last edge reaching it, but that does
     // not violate any invariants of the graph.
-    if (ChildC.ParentSCCs.empty())
-      DEBUG(dbgs() << "LCG: Update removing " << ParentN.getFunction().getName()
-                   << " -> " << ChildN.getFunction().getName()
+    if (TargetRC.Parents.empty())
+      DEBUG(dbgs() << "LCG: Update removing " << SourceN.getFunction().getName()
+                   << " -> " << TargetN.getFunction().getName()
                    << " edge orphaned the callee's SCC!\n");
-  }
 
-  // It may make the Parent SCC a leaf SCC.
-  if (!HasOtherChildC)
-    G->LeafSCCs.push_back(this);
+    // It may make the Source SCC a leaf SCC.
+    if (!HasOtherChildRC)
+      G->LeafRefSCCs.push_back(this);
+  }
 }
 
-void LazyCallGraph::SCC::internalDFS(
-    SmallVectorImpl<std::pair<Node *, Node::edge_iterator>> &DFSStack,
-    SmallVectorImpl<Node *> &PendingSCCStack, Node *N,
-    SmallVectorImpl<SCC *> &ResultSCCs) {
-  auto I = N->begin();
-  N->LowLink = N->DFSNumber = 1;
-  int NextDFSNumber = 2;
-  for (;;) {
-    assert(N->DFSNumber != 0 && "We should always assign a DFS number "
-                                "before processing a node.");
+SmallVector<LazyCallGraph::RefSCC *, 1>
+LazyCallGraph::RefSCC::removeInternalRefEdge(Node &SourceN, Node &TargetN) {
+  assert(!SourceN[TargetN].isCall() &&
+         "Cannot remove a call edge, it must first be made a ref edge");
 
-    // We simulate recursion by popping out of the nested loop and continuing.
-    auto E = N->end();
-    while (I != E) {
-      Node &ChildN = I->getNode(*G);
-      if (SCC *ChildSCC = G->SCCMap.lookup(&ChildN)) {
-        // Check if we have reached a node in the new (known connected) set of
-        // this SCC. If so, the entire stack is necessarily in that set and we
-        // can re-start.
-        if (ChildSCC == this) {
-          insert(*N);
-          while (!PendingSCCStack.empty())
-            insert(*PendingSCCStack.pop_back_val());
-          while (!DFSStack.empty())
-            insert(*DFSStack.pop_back_val().first);
-          return;
-        }
+  // First remove the actual edge.
+  SourceN.removeEdgeInternal(TargetN.getFunction());
 
-        // If this child isn't currently in this SCC, no need to process it.
-        // However, we do need to remove this SCC from its SCC's parent set.
-        ChildSCC->ParentSCCs.erase(this);
-        ++I;
-        continue;
-      }
+  // We return a list of the resulting *new* RefSCCs in post-order.
+  SmallVector<RefSCC *, 1> Result;
 
-      if (ChildN.DFSNumber == 0) {
-        // Mark that we should start at this child when next this node is the
-        // top of the stack. We don't start at the next child to ensure this
-        // child's lowlink is reflected.
-        DFSStack.push_back(std::make_pair(N, I));
+  // Direct recursion doesn't impact the SCC graph at all.
+  if (&SourceN == &TargetN)
+    return Result;
+
+  // We build somewhat synthetic new RefSCCs by providing a postorder mapping
+  // for each inner SCC. We also store these associated with *nodes* rather
+  // than SCCs because this saves a round-trip through the node->SCC map and in
+  // the common case, SCCs are small. We will verify that we always give the
+  // same number to every node in the SCC such that these are equivalent.
+  const int RootPostOrderNumber = 0;
+  int PostOrderNumber = RootPostOrderNumber + 1;
+  SmallDenseMap<Node *, int> PostOrderMapping;
+
+  // Every node in the target SCC can already reach every node in this RefSCC
+  // (by definition). It is the only node we know will stay inside this RefSCC.
+  // Everything which transitively reaches Target will also remain in the
+  // RefSCC. We handle this by pre-marking that the nodes in the target SCC map
+  // back to the root post order number.
+  //
+  // This also enables us to take a very significant short-cut in the standard
+  // Tarjan walk to re-form RefSCCs below: whenever we build an edge that
+  // references the target node, we know that the target node eventually
+  // references all other nodes in our walk. As a consequence, we can detect
+  // and handle participants in that cycle without walking all the edges that
+  // form the connections, and instead by relying on the fundamental guarantee
+  // coming into this operation.
+  SCC &TargetC = *G->lookupSCC(TargetN);
+  for (Node &N : TargetC)
+    PostOrderMapping[&N] = RootPostOrderNumber;
+
+  // Reset all the other nodes to prepare for a DFS over them, and add them to
+  // our worklist.
+  SmallVector<Node *, 8> Worklist;
+  for (SCC *C : SCCs) {
+    if (C == &TargetC)
+      continue;
 
-        // Continue, resetting to the child node.
-        ChildN.LowLink = ChildN.DFSNumber = NextDFSNumber++;
-        N = &ChildN;
-        I = ChildN.begin();
-        E = ChildN.end();
-        continue;
-      }
+    for (Node &N : *C)
+      N.DFSNumber = N.LowLink = 0;
 
-      // Track the lowest link of the children, if any are still in the stack.
-      // Any child not on the stack will have a LowLink of -1.
-      assert(ChildN.LowLink != 0 &&
-             "Low-link must not be zero with a non-zero DFS number.");
-      if (ChildN.LowLink >= 0 && ChildN.LowLink < N->LowLink)
-        N->LowLink = ChildN.LowLink;
-      ++I;
-    }
+    Worklist.append(C->Nodes.begin(), C->Nodes.end());
+  }
 
-    if (N->LowLink == N->DFSNumber) {
-      ResultSCCs.push_back(G->formSCC(N, PendingSCCStack));
-      if (DFSStack.empty())
-        return;
-    } else {
-      // At this point we know that N cannot ever be an SCC root. Its low-link
-      // is not its dfs-number, and we've processed all of its children. It is
-      // just sitting here waiting until some node further down the stack gets
-      // low-link == dfs-number and pops it off as well. Move it to the pending
-      // stack which is pulled into the next SCC to be formed.
-      PendingSCCStack.push_back(N);
+  auto MarkNodeForSCCNumber = [&PostOrderMapping](Node &N, int Number) {
+    N.DFSNumber = N.LowLink = -1;
+    PostOrderMapping[&N] = Number;
+  };
 
-      assert(!DFSStack.empty() && "We shouldn't have an empty stack!");
+  SmallVector<std::pair<Node *, edge_iterator>, 4> DFSStack;
+  SmallVector<Node *, 4> PendingRefSCCStack;
+  do {
+    assert(DFSStack.empty() &&
+           "Cannot begin a new root with a non-empty DFS stack!");
+    assert(PendingRefSCCStack.empty() &&
+           "Cannot begin a new root with pending nodes for an SCC!");
+
+    Node *RootN = Worklist.pop_back_val();
+    // Skip any nodes we've already reached in the DFS.
+    if (RootN->DFSNumber != 0) {
+      assert(RootN->DFSNumber == -1 &&
+             "Shouldn't have any mid-DFS root nodes!");
+      continue;
     }
 
-    N = DFSStack.back().first;
-    I = DFSStack.back().second;
-    DFSStack.pop_back();
-  }
-}
+    RootN->DFSNumber = RootN->LowLink = 1;
+    int NextDFSNumber = 2;
 
-SmallVector<LazyCallGraph::SCC *, 1>
-LazyCallGraph::SCC::removeIntraSCCEdge(Node &ParentN, Node &ChildN) {
-  // First remove it from the node.
-  ParentN.removeEdgeInternal(ChildN.getFunction());
+    DFSStack.push_back({RootN, RootN->begin()});
+    do {
+      Node *N;
+      edge_iterator I;
+      std::tie(N, I) = DFSStack.pop_back_val();
+      auto E = N->end();
+
+      assert(N->DFSNumber != 0 && "We should always assign a DFS number "
+                                  "before processing a node.");
+
+      while (I != E) {
+        Node &ChildN = I->getNode(*G);
+        if (ChildN.DFSNumber == 0) {
+          // Mark that we should start at this child when next this node is the
+          // top of the stack. We don't start at the next child to ensure this
+          // child's lowlink is reflected.
+          DFSStack.push_back({N, I});
+
+          // Continue, resetting to the child node.
+          ChildN.LowLink = ChildN.DFSNumber = NextDFSNumber++;
+          N = &ChildN;
+          I = ChildN.begin();
+          E = ChildN.end();
+          continue;
+        }
+        if (ChildN.DFSNumber == -1) {
+          // Check if this edge's target node connects to the deleted edge's
+          // target node. If so, we know that every node connected will end up
+          // in this RefSCC, so collapse the entire current stack into the root
+          // slot in our SCC numbering. See above for the motivation of
+          // optimizing the target connected nodes in this way.
+          auto PostOrderI = PostOrderMapping.find(&ChildN);
+          if (PostOrderI != PostOrderMapping.end() &&
+              PostOrderI->second == RootPostOrderNumber) {
+            MarkNodeForSCCNumber(*N, RootPostOrderNumber);
+            while (!PendingRefSCCStack.empty())
+              MarkNodeForSCCNumber(*PendingRefSCCStack.pop_back_val(),
+                                   RootPostOrderNumber);
+            while (!DFSStack.empty())
+              MarkNodeForSCCNumber(*DFSStack.pop_back_val().first,
+                                   RootPostOrderNumber);
+            // Ensure we break all the way out of the enclosing loop.
+            N = nullptr;
+            break;
+          }
 
-  // We return a list of the resulting *new* SCCs in postorder.
-  SmallVector<SCC *, 1> ResultSCCs;
+          // If this child isn't currently in this RefSCC, no need to process
+          // it.
+          // However, we do need to remove this RefSCC from its RefSCC's parent
+          // set.
+          RefSCC &ChildRC = *G->lookupRefSCC(ChildN);
+          ChildRC.Parents.erase(this);
+          ++I;
+          continue;
+        }
 
-  // Direct recursion doesn't impact the SCC graph at all.
-  if (&ParentN == &ChildN)
-    return ResultSCCs;
+        // Track the lowest link of the children, if any are still in the stack.
+        // Any child not on the stack will have a LowLink of -1.
+        assert(ChildN.LowLink != 0 &&
+               "Low-link must not be zero with a non-zero DFS number.");
+        if (ChildN.LowLink >= 0 && ChildN.LowLink < N->LowLink)
+          N->LowLink = ChildN.LowLink;
+        ++I;
+      }
+      if (!N)
+        // We short-circuited this node.
+        break;
 
-  // The worklist is every node in the original SCC.
-  SmallVector<Node *, 1> Worklist;
-  Worklist.swap(Nodes);
-  for (Node *N : Worklist) {
-    // The nodes formerly in this SCC are no longer in any SCC.
-    N->DFSNumber = 0;
-    N->LowLink = 0;
-    G->SCCMap.erase(N);
-  }
-  assert(Worklist.size() > 1 && "We have to have at least two nodes to have an "
-                                "edge between them that is within the SCC.");
-
-  // The child can already reach every node in this SCC (by definition). It is
-  // the only node we know will stay inside this SCC. Everything which
-  // transitively reaches Child will also remain in the SCC. To model this we
-  // incrementally add any chain of nodes which reaches something in the new
-  // node set to the new node set. This short circuits one side of the Tarjan's
-  // walk.
-  insert(ChildN);
-
-  // We're going to do a full mini-Tarjan's walk using a local stack here.
-  SmallVector<std::pair<Node *, Node::edge_iterator>, 4> DFSStack;
-  SmallVector<Node *, 4> PendingSCCStack;
-  do {
-    Node *N = Worklist.pop_back_val();
-    if (N->DFSNumber == 0)
-      internalDFS(DFSStack, PendingSCCStack, N, ResultSCCs);
+      // We've finished processing N and its descendents, put it on our pending
+      // stack to eventually get merged into a RefSCC.
+      PendingRefSCCStack.push_back(N);
+
+      // If this node is linked to some lower entry, continue walking up the
+      // stack.
+      if (N->LowLink != N->DFSNumber) {
+        assert(!DFSStack.empty() &&
+               "We never found a viable root for a RefSCC to pop off!");
+        continue;
+      }
+
+      // Otherwise, form a new RefSCC from the top of the pending node stack.
+      int RootDFSNumber = N->DFSNumber;
+      // Find the range of the node stack by walking down until we pass the
+      // root DFS number.
+      auto RefSCCNodes = make_range(
+          PendingRefSCCStack.rbegin(),
+          std::find_if(PendingRefSCCStack.rbegin(), PendingRefSCCStack.rend(),
+                       [RootDFSNumber](Node *N) {
+                         return N->DFSNumber < RootDFSNumber;
+                       }));
+
+      // Mark the postorder number for these nodes and clear them off the
+      // stack. We'll use the postorder number to pull them into RefSCCs at the
+      // end. FIXME: Fuse with the loop above.
+      int RefSCCNumber = PostOrderNumber++;
+      for (Node *N : RefSCCNodes)
+        MarkNodeForSCCNumber(*N, RefSCCNumber);
+
+      PendingRefSCCStack.erase(RefSCCNodes.end().base(),
+                               PendingRefSCCStack.end());
+    } while (!DFSStack.empty());
 
     assert(DFSStack.empty() && "Didn't flush the entire DFS stack!");
-    assert(PendingSCCStack.empty() && "Didn't flush all pending SCC nodes!");
+    assert(PendingRefSCCStack.empty() && "Didn't flush all pending nodes!");
   } while (!Worklist.empty());
 
-  // Now we need to reconnect the current SCC to the graph.
-  bool IsLeafSCC = true;
-  for (Node *N : Nodes) {
-    for (Edge &E : *N) {
-      assert(E.getNode() && "Cannot have a missing node in a visited SCC!");
-      SCC &ChildSCC = *G->SCCMap.lookup(E.getNode());
-      if (&ChildSCC == this)
-        continue;
-      ChildSCC.ParentSCCs.insert(this);
-      IsLeafSCC = false;
-    }
+  // We now have a post-order numbering for RefSCCs and a mapping from each
+  // node in this RefSCC to its final RefSCC. We create each new RefSCC node
+  // (re-using this RefSCC node for the root) and build a radix-sort style map
+  // from postorder number to the RefSCC. We then append SCCs to each of these
+  // RefSCCs in the order they occured in the original SCCs container.
+  for (int i = 1; i < PostOrderNumber; ++i)
+    Result.push_back(G->createRefSCC(*G));
+
+  for (SCC *C : SCCs) {
+    auto PostOrderI = PostOrderMapping.find(&*C->begin());
+    assert(PostOrderI != PostOrderMapping.end() &&
+           "Cannot have missing mappings for nodes!");
+    int SCCNumber = PostOrderI->second;
+#ifndef NDEBUG
+    for (Node &N : *C)
+      assert(PostOrderMapping.find(&N)->second == SCCNumber &&
+             "Cannot have different numbers for nodes in the same SCC!");
+#endif
+    if (SCCNumber == 0)
+      // The root node is handled separately by removing the SCCs.
+      continue;
+
+    RefSCC &RC = *Result[SCCNumber - 1];
+    int SCCIndex = RC.SCCs.size();
+    RC.SCCs.push_back(C);
+    SCCIndices[C] = SCCIndex;
+    C->OuterRefSCC = &RC;
   }
+
+  // FIXME: We re-walk the edges in each RefSCC to establish whether it is
+  // a leaf and connect it to the rest of the graph's parents lists. This is
+  // really wasteful. We should instead do this during the DFS to avoid yet
+  // another edge walk.
+  for (RefSCC *RC : Result)
+    G->connectRefSCC(*RC);
+
+  // Now erase all but the root's SCCs.
+  SCCs.erase(std::remove_if(SCCs.begin(), SCCs.end(),
+                            [&](SCC *C) {
+                              return PostOrderMapping.lookup(&*C->begin()) !=
+                                     RootPostOrderNumber;
+                            }),
+             SCCs.end());
+
+#ifndef NDEBUG
+  // Now we need to reconnect the current (root) SCC to the graph. We do this
+  // manually because we can special case our leaf handling and detect errors.
+  bool IsLeaf = true;
+#endif
+  for (SCC *C : SCCs)
+    for (Node &N : *C) {
+      for (Edge &E : N) {
+        assert(E.getNode() && "Cannot have a missing node in a visited SCC!");
+        RefSCC &ChildRC = *G->lookupRefSCC(*E.getNode());
+        if (&ChildRC == this)
+          continue;
+        ChildRC.Parents.insert(this);
+#ifndef NDEBUG
+        IsLeaf = false;
+#endif
+      }
+    }
 #ifndef NDEBUG
-  if (!ResultSCCs.empty())
-    assert(!IsLeafSCC && "This SCC cannot be a leaf as we have split out new "
-                         "SCCs by removing this edge.");
-  if (!std::any_of(G->LeafSCCs.begin(), G->LeafSCCs.end(),
-                   [&](SCC *C) { return C == this; }))
-    assert(!IsLeafSCC && "This SCC cannot be a leaf as it already had child "
-                         "SCCs before we removed this edge.");
+  if (!Result.empty())
+    assert(!IsLeaf && "This SCC cannot be a leaf as we have split out new "
+                      "SCCs by removing this edge.");
+  if (!std::any_of(G->LeafRefSCCs.begin(), G->LeafRefSCCs.end(),
+                   [&](RefSCC *C) { return C == this; }))
+    assert(!IsLeaf && "This SCC cannot be a leaf as it already had child "
+                      "SCCs before we removed this edge.");
 #endif
   // If this SCC stopped being a leaf through this edge removal, remove it from
-  // the leaf SCC list.
-  if (!IsLeafSCC && !ResultSCCs.empty())
-    G->LeafSCCs.erase(std::remove(G->LeafSCCs.begin(), G->LeafSCCs.end(), this),
-                      G->LeafSCCs.end());
+  // the leaf SCC list. Note that this DTRT in the case where this was never
+  // a leaf.
+  // FIXME: As LeafRefSCCs could be very large, we might want to not walk the
+  // entire list if this RefSCC wasn't a leaf before the edge removal.
+  if (!Result.empty())
+    G->LeafRefSCCs.erase(
+        std::remove(G->LeafRefSCCs.begin(), G->LeafRefSCCs.end(), this),
+        G->LeafRefSCCs.end());
 
   // Return the new list of SCCs.
-  return ResultSCCs;
+  return Result;
 }
 
-void LazyCallGraph::insertEdge(Node &ParentN, Function &Child, Edge::Kind EK) {
+void LazyCallGraph::insertEdge(Node &SourceN, Function &Target, Edge::Kind EK) {
   assert(SCCMap.empty() && DFSStack.empty() &&
          "This method cannot be called after SCCs have been formed!");
 
-  return ParentN.insertEdgeInternal(Child, EK);
+  return SourceN.insertEdgeInternal(Target, EK);
 }
 
-void LazyCallGraph::removeEdge(Node &ParentN, Function &Child) {
+void LazyCallGraph::removeEdge(Node &SourceN, Function &Target) {
   assert(SCCMap.empty() && DFSStack.empty() &&
          "This method cannot be called after SCCs have been formed!");
 
-  return ParentN.removeEdgeInternal(Child);
+  return SourceN.removeEdgeInternal(Target);
 }
 
 LazyCallGraph::Node &LazyCallGraph::insertInto(Function &F, Node *&MappedN) {
@@ -578,125 +1244,258 @@ void LazyCallGraph::updateGraphPtrs() {
       Node *N = Worklist.pop_back_val();
       N->G = this;
       for (Edge &E : N->Edges)
-        if (Node *ChildN = E.getNode())
-          Worklist.push_back(ChildN);
+        if (Node *TargetN = E.getNode())
+          Worklist.push_back(TargetN);
     }
   }
 
   // Process all SCCs updating the graph pointers.
   {
-    SmallVector<SCC *, 16> Worklist(LeafSCCs.begin(), LeafSCCs.end());
+    SmallVector<RefSCC *, 16> Worklist(LeafRefSCCs.begin(), LeafRefSCCs.end());
 
     while (!Worklist.empty()) {
-      SCC *C = Worklist.pop_back_val();
-      C->G = this;
-      Worklist.insert(Worklist.end(), C->ParentSCCs.begin(),
-                      C->ParentSCCs.end());
+      RefSCC &C = *Worklist.pop_back_val();
+      C.G = this;
+      for (RefSCC &ParentC : C.parents())
+        Worklist.push_back(&ParentC);
     }
   }
 }
 
-LazyCallGraph::SCC *LazyCallGraph::formSCC(Node *RootN,
-                                           SmallVectorImpl<Node *> &NodeStack) {
-  // The tail of the stack is the new SCC. Allocate the SCC and pop the stack
-  // into it.
-  SCC *NewSCC = new (SCCBPA.Allocate()) SCC(*this);
+/// Build the internal SCCs for a RefSCC from a sequence of nodes.
+///
+/// Appends the SCCs to the provided vector and updates the map with their
+/// indices. Both the vector and map must be empty when passed into this
+/// routine.
+void LazyCallGraph::buildSCCs(RefSCC &RC, node_stack_range Nodes) {
+  assert(RC.SCCs.empty() && "Already built SCCs!");
+  assert(RC.SCCIndices.empty() && "Already mapped SCC indices!");
 
-  while (!NodeStack.empty() && NodeStack.back()->DFSNumber > RootN->DFSNumber) {
-    assert(NodeStack.back()->LowLink >= RootN->LowLink &&
+  for (Node *N : Nodes) {
+    assert(N->LowLink >= (*Nodes.begin())->LowLink &&
            "We cannot have a low link in an SCC lower than its root on the "
            "stack!");
-    NewSCC->insert(*NodeStack.pop_back_val());
+
+    // This node will go into the next RefSCC, clear out its DFS and low link
+    // as we scan.
+    N->DFSNumber = N->LowLink = 0;
   }
-  NewSCC->insert(*RootN);
-
-  // A final pass over all edges in the SCC (this remains linear as we only
-  // do this once when we build the SCC) to connect it to the parent sets of
-  // its children.
-  bool IsLeafSCC = true;
-  for (Node *SCCN : NewSCC->Nodes)
-    for (Edge &E : *SCCN) {
-      assert(E.getNode() && "Cannot have a missing node in a visited SCC!");
-      SCC &ChildSCC = *SCCMap.lookup(E.getNode());
-      if (&ChildSCC == NewSCC)
-        continue;
-      ChildSCC.ParentSCCs.insert(NewSCC);
-      IsLeafSCC = false;
+
+  // Each RefSCC contains a DAG of the call SCCs. To build these, we do
+  // a direct walk of the call edges using Tarjan's algorithm. We reuse the
+  // internal storage as we won't need it for the outer graph's DFS any longer.
+
+  SmallVector<std::pair<Node *, call_edge_iterator>, 16> DFSStack;
+  SmallVector<Node *, 16> PendingSCCStack;
+
+  // Scan down the stack and DFS across the call edges.
+  for (Node *RootN : Nodes) {
+    assert(DFSStack.empty() &&
+           "Cannot begin a new root with a non-empty DFS stack!");
+    assert(PendingSCCStack.empty() &&
+           "Cannot begin a new root with pending nodes for an SCC!");
+
+    // Skip any nodes we've already reached in the DFS.
+    if (RootN->DFSNumber != 0) {
+      assert(RootN->DFSNumber == -1 &&
+             "Shouldn't have any mid-DFS root nodes!");
+      continue;
     }
 
-  // For the SCCs where we fine no child SCCs, add them to the leaf list.
-  if (IsLeafSCC)
-    LeafSCCs.push_back(NewSCC);
+    RootN->DFSNumber = RootN->LowLink = 1;
+    int NextDFSNumber = 2;
+
+    DFSStack.push_back({RootN, RootN->call_begin()});
+    do {
+      Node *N;
+      call_edge_iterator I;
+      std::tie(N, I) = DFSStack.pop_back_val();
+      auto E = N->call_end();
+      while (I != E) {
+        Node &ChildN = *I->getNode();
+        if (ChildN.DFSNumber == 0) {
+          // We haven't yet visited this child, so descend, pushing the current
+          // node onto the stack.
+          DFSStack.push_back({N, I});
+
+          assert(!lookupSCC(ChildN) &&
+                 "Found a node with 0 DFS number but already in an SCC!");
+          ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
+          N = &ChildN;
+          I = N->call_begin();
+          E = N->call_end();
+          continue;
+        }
+
+        // If the child has already been added to some child component, it
+        // couldn't impact the low-link of this parent because it isn't
+        // connected, and thus its low-link isn't relevant so skip it.
+        if (ChildN.DFSNumber == -1) {
+          ++I;
+          continue;
+        }
+
+        // Track the lowest linked child as the lowest link for this node.
+        assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
+        if (ChildN.LowLink < N->LowLink)
+          N->LowLink = ChildN.LowLink;
+
+        // Move to the next edge.
+        ++I;
+      }
+
+      // We've finished processing N and its descendents, put it on our pending
+      // SCC stack to eventually get merged into an SCC of nodes.
+      PendingSCCStack.push_back(N);
+
+      // If this node is linked to some lower entry, continue walking up the
+      // stack.
+      if (N->LowLink != N->DFSNumber)
+        continue;
+
+      // Otherwise, we've completed an SCC. Append it to our post order list of
+      // SCCs.
+      int RootDFSNumber = N->DFSNumber;
+      // Find the range of the node stack by walking down until we pass the
+      // root DFS number.
+      auto SCCNodes = make_range(
+          PendingSCCStack.rbegin(),
+          std::find_if(PendingSCCStack.rbegin(), PendingSCCStack.rend(),
+                       [RootDFSNumber](Node *N) {
+                         return N->DFSNumber < RootDFSNumber;
+                       }));
+      // Form a new SCC out of these nodes and then clear them off our pending
+      // stack.
+      RC.SCCs.push_back(createSCC(RC, SCCNodes));
+      for (Node &N : *RC.SCCs.back()) {
+        N.DFSNumber = N.LowLink = -1;
+        SCCMap[&N] = RC.SCCs.back();
+      }
+      PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
+    } while (!DFSStack.empty());
+  }
 
-  return NewSCC;
+  // Wire up the SCC indices.
+  for (int i = 0, Size = RC.SCCs.size(); i < Size; ++i)
+    RC.SCCIndices[RC.SCCs[i]] = i;
 }
 
-LazyCallGraph::SCC *LazyCallGraph::getNextSCCInPostOrder() {
-  Node *N;
-  Node::edge_iterator I;
-  if (!DFSStack.empty()) {
-    N = DFSStack.back().first;
-    I = DFSStack.back().second;
-    DFSStack.pop_back();
-  } else {
-    // If we've handled all candidate entry nodes to the SCC forest, we're done.
+// FIXME: We should move callers of this to embed the parent linking and leaf
+// tracking into their DFS in order to remove a full walk of all edges.
+void LazyCallGraph::connectRefSCC(RefSCC &RC) {
+  // Walk all edges in the RefSCC (this remains linear as we only do this once
+  // when we build the RefSCC) to connect it to the parent sets of its
+  // children.
+  bool IsLeaf = true;
+  for (SCC &C : RC)
+    for (Node &N : C)
+      for (Edge &E : N) {
+        assert(E.getNode() &&
+               "Cannot have a missing node in a visited part of the graph!");
+        RefSCC &ChildRC = *lookupRefSCC(*E.getNode());
+        if (&ChildRC == &RC)
+          continue;
+        ChildRC.Parents.insert(&RC);
+        IsLeaf = false;
+      }
+
+  // For the SCCs where we fine no child SCCs, add them to the leaf list.
+  if (IsLeaf)
+    LeafRefSCCs.push_back(&RC);
+}
+
+LazyCallGraph::RefSCC *LazyCallGraph::getNextRefSCCInPostOrder() {
+  if (DFSStack.empty()) {
+    Node *N;
     do {
-      if (SCCEntryNodes.empty())
+      // If we've handled all candidate entry nodes to the SCC forest, we're
+      // done.
+      if (RefSCCEntryNodes.empty())
         return nullptr;
 
-      N = &get(*SCCEntryNodes.pop_back_val());
+      N = &get(*RefSCCEntryNodes.pop_back_val());
     } while (N->DFSNumber != 0);
-    I = N->begin();
+
+    // Found a new root, begin the DFS here.
     N->LowLink = N->DFSNumber = 1;
     NextDFSNumber = 2;
+    DFSStack.push_back({N, N->begin()});
   }
 
   for (;;) {
-    assert(N->DFSNumber != 0 && "We should always assign a DFS number "
-                                "before placing a node onto the stack.");
+    Node *N;
+    edge_iterator I;
+    std::tie(N, I) = DFSStack.pop_back_val();
+
+    assert(N->DFSNumber > 0 && "We should always assign a DFS number "
+                               "before placing a node onto the stack.");
 
     auto E = N->end();
     while (I != E) {
       Node &ChildN = I->getNode(*this);
       if (ChildN.DFSNumber == 0) {
-        // Mark that we should start at this child when next this node is the
-        // top of the stack. We don't start at the next child to ensure this
-        // child's lowlink is reflected.
-        DFSStack.push_back(std::make_pair(N, N->begin()));
+        // We haven't yet visited this child, so descend, pushing the current
+        // node onto the stack.
+        DFSStack.push_back({N, N->begin()});
 
-        // Recurse onto this node via a tail call.
         assert(!SCCMap.count(&ChildN) &&
                "Found a node with 0 DFS number but already in an SCC!");
         ChildN.LowLink = ChildN.DFSNumber = NextDFSNumber++;
         N = &ChildN;
-        I = ChildN.begin();
-        E = ChildN.end();
+        I = N->begin();
+        E = N->end();
+        continue;
+      }
+
+      // If the child has already been added to some child component, it
+      // couldn't impact the low-link of this parent because it isn't
+      // connected, and thus its low-link isn't relevant so skip it.
+      if (ChildN.DFSNumber == -1) {
+        ++I;
         continue;
       }
 
-      // Track the lowest link of the children, if any are still in the stack.
-      assert(ChildN.LowLink != 0 &&
-             "Low-link must not be zero with a non-zero DFS number.");
-      if (ChildN.LowLink >= 0 && ChildN.LowLink < N->LowLink)
+      // Track the lowest linked child as the lowest link for this node.
+      assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
+      if (ChildN.LowLink < N->LowLink)
         N->LowLink = ChildN.LowLink;
+
+      // Move to the next edge.
       ++I;
     }
 
-    if (N->LowLink == N->DFSNumber)
-      // Form the new SCC out of the top of the DFS stack.
-      return formSCC(N, PendingSCCStack);
-
-    // At this point we know that N cannot ever be an SCC root. Its low-link
-    // is not its dfs-number, and we've processed all of its children. It is
-    // just sitting here waiting until some node further down the stack gets
-    // low-link == dfs-number and pops it off as well. Move it to the pending
-    // stack which is pulled into the next SCC to be formed.
-    PendingSCCStack.push_back(N);
-
-    assert(!DFSStack.empty() && "We never found a viable root!");
-    N = DFSStack.back().first;
-    I = DFSStack.back().second;
-    DFSStack.pop_back();
+    // We've finished processing N and its descendents, put it on our pending
+    // SCC stack to eventually get merged into an SCC of nodes.
+    PendingRefSCCStack.push_back(N);
+
+    // If this node is linked to some lower entry, continue walking up the
+    // stack.
+    if (N->LowLink != N->DFSNumber) {
+      assert(!DFSStack.empty() &&
+             "We never found a viable root for an SCC to pop off!");
+      continue;
+    }
+
+    // Otherwise, form a new RefSCC from the top of the pending node stack.
+    int RootDFSNumber = N->DFSNumber;
+    // Find the range of the node stack by walking down until we pass the
+    // root DFS number.
+    auto RefSCCNodes = node_stack_range(
+        PendingRefSCCStack.rbegin(),
+        std::find_if(
+            PendingRefSCCStack.rbegin(), PendingRefSCCStack.rend(),
+            [RootDFSNumber](Node *N) { return N->DFSNumber < RootDFSNumber; }));
+    // Form a new RefSCC out of these nodes and then clear them off our pending
+    // stack.
+    RefSCC *NewRC = createRefSCC(*this);
+    buildSCCs(*NewRC, RefSCCNodes);
+    connectRefSCC(*NewRC);
+    PendingRefSCCStack.erase(RefSCCNodes.end().base(),
+                             PendingRefSCCStack.end());
+
+    // We return the new node here. This essentially suspends the DFS walk
+    // until another RefSCC is requested.
+    return NewRC;
   }
 }
 
@@ -704,17 +1503,7 @@ char LazyCallGraphAnalysis::PassID;
 
 LazyCallGraphPrinterPass::LazyCallGraphPrinterPass(raw_ostream &OS) : OS(OS) {}
 
-static void printNodes(raw_ostream &OS, LazyCallGraph::Node &N,
-                       SmallPtrSetImpl<LazyCallGraph::Node *> &Printed) {
-  LazyCallGraph &G = N.getGraph();
-
-  // Recurse depth first through the nodes.
-  for (LazyCallGraph::Edge &E : N) {
-    LazyCallGraph::Node &ChildN = E.getNode(G);
-    if (Printed.insert(&ChildN).second)
-      printNodes(OS, ChildN, Printed);
-  }
-
+static void printNode(raw_ostream &OS, LazyCallGraph::Node &N) {
   OS << "  Edges in function: " << N.getFunction().getName() << "\n";
   for (const LazyCallGraph::Edge &E : N)
     OS << "    " << (E.isCall() ? "call" : "ref ") << " -> "
@@ -723,12 +1512,20 @@ static void printNodes(raw_ostream &OS, LazyCallGraph::Node &N,
   OS << "\n";
 }
 
-static void printSCC(raw_ostream &OS, LazyCallGraph::SCC &SCC) {
-  ptrdiff_t SCCSize = std::distance(SCC.begin(), SCC.end());
-  OS << "  SCC with " << SCCSize << " functions:\n";
+static void printSCC(raw_ostream &OS, LazyCallGraph::SCC &C) {
+  ptrdiff_t Size = std::distance(C.begin(), C.end());
+  OS << "    SCC with " << Size << " functions:\n";
+
+  for (LazyCallGraph::Node &N : C)
+    OS << "      " << N.getFunction().getName() << "\n";
+}
+
+static void printRefSCC(raw_ostream &OS, LazyCallGraph::RefSCC &C) {
+  ptrdiff_t Size = std::distance(C.begin(), C.end());
+  OS << "  RefSCC with " << Size << " call SCCs:\n";
 
-  for (LazyCallGraph::Node *N : SCC)
-    OS << "    " << N->getFunction().getName() << "\n";
+  for (LazyCallGraph::SCC &InnerC : C)
+    printSCC(OS, InnerC);
 
   OS << "\n";
 }
@@ -740,15 +1537,11 @@ PreservedAnalyses LazyCallGraphPrinterPass::run(Module &M,
   OS << "Printing the call graph for module: " << M.getModuleIdentifier()
      << "\n\n";
 
-  SmallPtrSet<LazyCallGraph::Node *, 16> Printed;
-  for (LazyCallGraph::Edge &E : G) {
-    LazyCallGraph::Node &N = E.getNode(G);
-    if (Printed.insert(&N).second)
-      printNodes(OS, N, Printed);
-  }
+  for (Function &F : M)
+    printNode(OS, G.get(F));
 
-  for (LazyCallGraph::SCC &SCC : G.postorder_sccs())
-    printSCC(OS, SCC);
+  for (LazyCallGraph::RefSCC &C : G.postorder_ref_sccs())
+    printRefSCC(OS, C);
 
   return PreservedAnalyses::all();
 }