text: //===- LazyCallGraph.cpp - Analysis of a Module's call graph --------------===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  
  #include "llvm/Analysis/LazyCallGraph.h"
  #include "llvm/ADT/STLExtras.h"
  #include "llvm/ADT/ScopeExit.h"
  #include "llvm/ADT/Sequence.h"
  #include "llvm/IR/CallSite.h"
  #include "llvm/IR/InstVisitor.h"
  #include "llvm/IR/Instructions.h"
  #include "llvm/IR/PassManager.h"
  #include "llvm/Support/Debug.h"
  #include "llvm/Support/GraphWriter.h"
  #include <utility>
  
  using namespace llvm;
  
  #define DEBUG_TYPE "lcg"
  
  void LazyCallGraph::EdgeSequence::insertEdgeInternal(Node &TargetN,
                                                       Edge::Kind EK) {
    EdgeIndexMap.insert({&TargetN, Edges.size()});
    Edges.emplace_back(TargetN, EK);
  }
  
  void LazyCallGraph::EdgeSequence::setEdgeKind(Node &TargetN, Edge::Kind EK) {
    Edges[EdgeIndexMap.find(&TargetN)->second].setKind(EK);
  }
  
  bool LazyCallGraph::EdgeSequence::removeEdgeInternal(Node &TargetN) {
    auto IndexMapI = EdgeIndexMap.find(&TargetN);
    if (IndexMapI == EdgeIndexMap.end())
      return false;
  
    Edges[IndexMapI->second] = Edge();
    EdgeIndexMap.erase(IndexMapI);
    return true;
  }
  
  static void addEdge(SmallVectorImpl<LazyCallGraph::Edge> &Edges,
                      DenseMap<LazyCallGraph::Node *, int> &EdgeIndexMap,
                      LazyCallGraph::Node &N, LazyCallGraph::Edge::Kind EK) {
    if (!EdgeIndexMap.insert({&N, Edges.size()}).second)
      return;
  
    DEBUG(dbgs() << "    Added callable function: " << N.getName() << "\n");
    Edges.emplace_back(LazyCallGraph::Edge(N, EK));
  }
  
  LazyCallGraph::EdgeSequence &LazyCallGraph::Node::populateSlow() {
    assert(!Edges && "Must not have already populated the edges for this node!");
  
    DEBUG(dbgs() << "  Adding functions called by '" << getName()
                 << "' to the graph.\n");
  
    Edges = EdgeSequence();
  
    SmallVector<Constant *, 16> Worklist;
    SmallPtrSet<Function *, 4> Callees;
    SmallPtrSet<Constant *, 16> Visited;
  
    // Find all the potential call graph edges in this function. We track both
    // actual call edges and indirect references to functions. The direct calls
    // are trivially added, but to accumulate the latter we walk the instructions
    // and add every operand which is a constant to the worklist to process
    // afterward.
    //
    // 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
    // some other module (say, a weak definition) there may still be
    // optimizations which essentially speculate based on the definition and
    // a way to check that the specific definition is in fact the one being
    // used. For example, this could be done by moving the weak definition to
    // a strong (internal) definition and making the weak definition be an
    // alias. Then a test of the address of the weak function against the new
    // strong definition's address would be an effective way to determine the
    // safety of optimizing a direct call edge.
    for (BasicBlock &BB : *F)
      for (Instruction &I : BB) {
        if (auto CS = CallSite(&I))
          if (Function *Callee = CS.getCalledFunction())
            if (!Callee->isDeclaration())
              if (Callees.insert(Callee).second) {
                Visited.insert(Callee);
                addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(*Callee),
                        LazyCallGraph::Edge::Call);
              }
  
        for (Value *Op : I.operand_values())
          if (Constant *C = dyn_cast<Constant>(Op))
            if (Visited.insert(C).second)
              Worklist.push_back(C);
      }
  
    // We've collected all the constant (and thus potentially function or
    // function containing) operands to all of the instructions in the function.
    // Process them (recursively) collecting every function found.
    visitReferences(Worklist, Visited, [&](Function &F) {
      addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(F),
              LazyCallGraph::Edge::Ref);
    });
  
    // Add implicit reference edges to any defined libcall functions (if we
    // haven't found an explicit edge).
    for (auto *F : G->LibFunctions)
      if (!Visited.count(F))
        addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(*F),
                LazyCallGraph::Edge::Ref);
  
    return *Edges;
  }
  
  void LazyCallGraph::Node::replaceFunction(Function &NewF) {
    assert(F != &NewF && "Must not replace a function with itself!");
    F = &NewF;
  }
  
  #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
  LLVM_DUMP_METHOD void LazyCallGraph::Node::dump() const {
    dbgs() << *this << '\n';
  }
  #endif
  
  static bool isKnownLibFunction(Function &F, TargetLibraryInfo &TLI) {
    LibFunc LF;
  
    // Either this is a normal library function or a "vectorizable" function.
    return TLI.getLibFunc(F, LF) || TLI.isFunctionVectorizable(F.getName());
  }
  
  LazyCallGraph::LazyCallGraph(Module &M, TargetLibraryInfo &TLI) {
    DEBUG(dbgs() << "Building CG for module: " << M.getModuleIdentifier()
                 << "\n");
    for (Function &F : M) {
      if (F.isDeclaration())
        continue;
      // If this function is a known lib function to LLVM then we want to
      // synthesize reference edges to it to model the fact that LLVM can turn
      // arbitrary code into a library function call.
      if (isKnownLibFunction(F, TLI))
        LibFunctions.insert(&F);
  
      if (F.hasLocalLinkage())
        continue;
  
      // External linkage defined functions have edges to them from other
      // modules.
      DEBUG(dbgs() << "  Adding '" << F.getName()
                   << "' to entry set of the graph.\n");
      addEdge(EntryEdges.Edges, EntryEdges.EdgeIndexMap, get(F), Edge::Ref);
    }
  
    // Now add entry nodes for functions reachable via initializers to globals.
    SmallVector<Constant *, 16> Worklist;
    SmallPtrSet<Constant *, 16> Visited;
    for (GlobalVariable &GV : M.globals())
      if (GV.hasInitializer())
        if (Visited.insert(GV.getInitializer()).second)
          Worklist.push_back(GV.getInitializer());
  
    DEBUG(dbgs() << "  Adding functions referenced by global initializers to the "
                    "entry set.\n");
    visitReferences(Worklist, Visited, [&](Function &F) {
      addEdge(EntryEdges.Edges, EntryEdges.EdgeIndexMap, get(F),
              LazyCallGraph::Edge::Ref);
    });
  }
  
  LazyCallGraph::LazyCallGraph(LazyCallGraph &&G)
      : BPA(std::move(G.BPA)), NodeMap(std::move(G.NodeMap)),
        EntryEdges(std::move(G.EntryEdges)), SCCBPA(std::move(G.SCCBPA)),
        SCCMap(std::move(G.SCCMap)), LeafRefSCCs(std::move(G.LeafRefSCCs)),
        LibFunctions(std::move(G.LibFunctions)) {
    updateGraphPtrs();
  }
  
  LazyCallGraph &LazyCallGraph::operator=(LazyCallGraph &&G) {
    BPA = std::move(G.BPA);
    NodeMap = std::move(G.NodeMap);
    EntryEdges = std::move(G.EntryEdges);
    SCCBPA = std::move(G.SCCBPA);
    SCCMap = std::move(G.SCCMap);
    LeafRefSCCs = std::move(G.LeafRefSCCs);
    LibFunctions = std::move(G.LibFunctions);
    updateGraphPtrs();
    return *this;
  }
  
  #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
  LLVM_DUMP_METHOD void LazyCallGraph::SCC::dump() const {
    dbgs() << *this << '\n';
  }
  #endif
  
  #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 unpopulated node!");
    }
  }
  #endif
  
  bool LazyCallGraph::SCC::isParentOf(const SCC &C) const {
    if (this == &C)
      return false;
  
    for (Node &N : *this)
      for (Edge &E : N->calls())
        if (OuterRefSCC->G->lookupSCC(E.getNode()) == &C)
          return true;
  
    // No edges found.
    return false;
  }
  
  bool LazyCallGraph::SCC::isAncestorOf(const SCC &TargetC) const {
    if (this == &TargetC)
      return false;
  
    LazyCallGraph &G = *OuterRefSCC->G;
  
    // Start with this SCC.
    SmallPtrSet<const SCC *, 16> Visited = {this};
    SmallVector<const SCC *, 16> Worklist = {this};
  
    // Walk down the graph until we run out of edges or find a path to TargetC.
    do {
      const SCC &C = *Worklist.pop_back_val();
      for (Node &N : C)
        for (Edge &E : N->calls()) {
          SCC *CalleeC = G.lookupSCC(E.getNode());
          if (!CalleeC)
            continue;
  
          // If the callee's SCC is the TargetC, we're done.
          if (CalleeC == &TargetC)
            return true;
  
          // If this is the first time we've reached this SCC, put it on the
          // worklist to recurse through.
          if (Visited.insert(CalleeC).second)
            Worklist.push_back(CalleeC);
        }
    } while (!Worklist.empty());
  
    // No paths found.
    return false;
  }
  
  LazyCallGraph::RefSCC::RefSCC(LazyCallGraph &G) : G(&G) {}
  
  #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
  LLVM_DUMP_METHOD void LazyCallGraph::RefSCC::dump() const {
    dbgs() << *this << '\n';
  }
  #endif
  
  #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.
    SmallPtrSet<SCC *, 4> SCCSet;
    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!");
      bool Inserted = SCCSet.insert(C).second;
      assert(Inserted && "Found a duplicate SCC!");
      auto IndexIt = SCCIndices.find(C);
      assert(IndexIt != SCCIndices.end() &&
             "Found an SCC that doesn't have an index!");
    }
  
    // 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(SCCSet.count(C) && "Found an index for an SCC not in the RefSCC!");
      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.");
        }
    }
  
    // Check that our parents are actually parents.
    for (RefSCC *ParentRC : Parents) {
      assert(ParentRC != this && "Cannot be our own parent!");
      auto HasConnectingEdge = [&] {
        for (SCC &C : *ParentRC)
          for (Node &N : C)
            for (Edge &E : *N)
              if (G->lookupRefSCC(E.getNode()) == this)
                return true;
        return false;
      };
      assert(HasConnectingEdge() && "No edge connects the parent to us!");
    }
  }
  #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 RefSCC *, 4> AncestorWorklist;
    AncestorWorklist.push_back(this);
    do {
      const RefSCC *AncestorC = AncestorWorklist.pop_back_val();
      if (AncestorC->isChildOf(C))
        return true;
      for (const RefSCC *ParentC : AncestorC->Parents)
        AncestorWorklist.push_back(ParentC);
    } while (!AncestorWorklist.empty());
  
    return false;
  }
  
  /// Generic helper that updates a postorder sequence of SCCs for a potentially
  /// cycle-introducing edge insertion.
  ///
  /// A postorder sequence of SCCs of a directed graph has one fundamental
  /// property: all deges in the DAG of SCCs point "up" the sequence. That is,
  /// all edges in the SCC DAG point to prior SCCs in the sequence.
  ///
  /// This routine both updates a postorder sequence and uses that sequence to
  /// compute the set of SCCs connected into a cycle. It should only be called to
  /// insert a "downward" edge which will require changing the sequence to
  /// restore it to a postorder.
  ///
  /// When inserting an edge from an earlier SCC to a later SCC in some postorder
  /// sequence, all of the SCCs which may be impacted are in the closed range of
  /// those two within the postorder sequence. The algorithm used here 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.
  ///
  /// This helper routine, in addition to updating the postorder sequence itself
  /// will also update a map from SCCs to indices within that sequecne.
  ///
  /// The sequence and the map must operate on pointers to the SCC type.
  ///
  /// Two callbacks must be provided. The first computes the subset of SCCs in
  /// the postorder closed range from the source to the target which connect to
  /// the source SCC via some (transitive) set of edges. The second computes the
  /// subset of the same range which the target SCC connects to via some
  /// (transitive) set of edges. Both callbacks should populate the set argument
  /// provided.
  template <typename SCCT, typename PostorderSequenceT, typename SCCIndexMapT,
            typename ComputeSourceConnectedSetCallableT,
            typename ComputeTargetConnectedSetCallableT>
  static iterator_range<typename PostorderSequenceT::iterator>
  updatePostorderSequenceForEdgeInsertion(
      SCCT &SourceSCC, SCCT &TargetSCC, PostorderSequenceT &SCCs,
      SCCIndexMapT &SCCIndices,
      ComputeSourceConnectedSetCallableT ComputeSourceConnectedSet,
      ComputeTargetConnectedSetCallableT ComputeTargetConnectedSet) {
    int SourceIdx = SCCIndices[&SourceSCC];
    int TargetIdx = SCCIndices[&TargetSCC];
    assert(SourceIdx < TargetIdx && "Cannot have equal indices here!");
  
    SmallPtrSet<SCCT *, 4> ConnectedSet;
  
    // Compute the SCCs which (transitively) reach the source.
    ComputeSourceConnectedSet(ConnectedSet);
  
    // 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](SCCT *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.");
  
      // Return an empty range at the target SCC indicating there is nothing to
      // merge.
      return make_range(std::prev(SourceI), std::prev(SourceI));
    }
  
    assert(SCCs[TargetIdx] == &TargetSCC &&
           "Should not have moved target if connected!");
    SourceIdx = SourceI - SCCs.begin();
    assert(SCCs[SourceIdx] == &SourceSCC &&
           "Bad updated index computation for the source SCC!");
  
  
    // 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) {
      ConnectedSet.clear();
      ComputeTargetConnectedSet(ConnectedSet);
  
      // 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](SCCT *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!");
    }
  
    // 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.
    return make_range(SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx);
  }
  
  bool
  LazyCallGraph::RefSCC::switchInternalEdgeToCall(
      Node &SourceN, Node &TargetN,
      function_ref<void(ArrayRef<SCC *> MergeSCCs)> MergeCB) {
    assert(!(*SourceN)[TargetN].isCall() && "Must start with a ref edge!");
    SmallVector<SCC *, 1> DeletedSCCs;
  
  #ifndef NDEBUG
    // In a debug build, verify the RefSCC is valid to start with and when this
    // routine finishes.
    verify();
    auto VerifyOnExit = make_scope_exit([&]() { verify(); });
  #endif
  
    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, Edge::Call);
      return false; // No new cycle.
    }
  
    // 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, Edge::Call);
      return false; // No new cycle.
    }
  
    // Compute the SCCs which (transitively) reach the source.
    auto ComputeSourceConnectedSet = [&](SmallPtrSetImpl<SCC *> &ConnectedSet) {
  #ifndef NDEBUG
      // Check that the RefSCC is still valid before computing this as the
      // results will be nonsensical of we've broken its invariants.
      verify();
  #endif
      ConnectedSet.insert(&SourceSCC);
      auto IsConnected = [&](SCC &C) {
        for (Node &N : C)
          for (Edge &E : N->calls())
            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);
    };
  
    // 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.
    auto ComputeTargetConnectedSet = [&](SmallPtrSetImpl<SCC *> &ConnectedSet) {
  #ifndef NDEBUG
      // Check that the RefSCC is still valid before computing this as the
      // results will be nonsensical of we've broken its invariants.
      verify();
  #endif
      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) {
            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());
    };
  
    // Use a generic helper to update the postorder sequence of SCCs and return
    // a range of any SCCs connected into a cycle by inserting this edge. This
    // routine will also take care of updating the indices into the postorder
    // sequence.
    auto MergeRange = updatePostorderSequenceForEdgeInsertion(
        SourceSCC, TargetSCC, SCCs, SCCIndices, ComputeSourceConnectedSet,
        ComputeTargetConnectedSet);
  
    // Run the user's callback on the merged SCCs before we actually merge them.
    if (MergeCB)
      MergeCB(makeArrayRef(MergeRange.begin(), MergeRange.end()));
  
    // If the merge range is empty, then adding the edge didn't actually form any
    // new cycles. We're done.
    if (MergeRange.begin() == MergeRange.end()) {
      // Now that the SCC structure is finalized, flip the kind to call.
      SourceN->setEdgeKind(TargetN, Edge::Call);
      return false; // No new cycle.
    }
  
  #ifndef NDEBUG
    // Before merging, check that the RefSCC remains valid after all the
    // postorder updates.
    verify();
  #endif
  
    // Otherwise we need to merge all of the SCCs in the cycle 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.
    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, Edge::Call);
  
    // And we're done, but we did form a new cycle.
    return true;
  }
  
  void LazyCallGraph::RefSCC::switchTrivialInternalEdgeToRef(Node &SourceN,
                                                             Node &TargetN) {
    assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
  
  #ifndef NDEBUG
    // In a debug build, verify the RefSCC is valid to start with and when this
    // routine finishes.
    verify();
    auto VerifyOnExit = make_scope_exit([&]() { verify(); });
  #endif
  
    assert(G->lookupRefSCC(SourceN) == this &&
           "Source must be in this RefSCC.");
    assert(G->lookupRefSCC(TargetN) == this &&
           "Target must be in this RefSCC.");
    assert(G->lookupSCC(SourceN) != G->lookupSCC(TargetN) &&
           "Source and Target must be in separate SCCs for this to be trivial!");
  
    // Set the edge kind.
    SourceN->setEdgeKind(TargetN, Edge::Ref);
  }
  
  iterator_range<LazyCallGraph::RefSCC::iterator>
  LazyCallGraph::RefSCC::switchInternalEdgeToRef(Node &SourceN, Node &TargetN) {
    assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
  
  #ifndef NDEBUG
    // In a debug build, verify the RefSCC is valid to start with and when this
    // routine finishes.
    verify();
    auto VerifyOnExit = make_scope_exit([&]() { verify(); });
  #endif
  
    assert(G->lookupRefSCC(SourceN) == this &&
           "Source must be in this RefSCC.");
    assert(G->lookupRefSCC(TargetN) == this &&
           "Target must be in this RefSCC.");
  
    SCC &TargetSCC = *G->lookupSCC(TargetN);
    assert(G->lookupSCC(SourceN) == &TargetSCC && "Source and Target must be in "
                                                  "the same SCC to require the "
                                                  "full CG update.");
  
    // Set the edge kind.
    SourceN->setEdgeKind(TargetN, Edge::Ref);
  
    // 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 *, EdgeSequence::call_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;
        EdgeSequence::call_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(),
            find_if(reverse(PendingSCCStack), [RootDFSNumber](const 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;
  
    return make_range(SCCs.begin() + OldIdx,
                      SCCs.begin() + OldIdx + NewSCCs.size());
  }
  
  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.");
  #ifdef EXPENSIVE_CHECKS
    assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
           "Target must be a descendant of the Source.");
  #endif
  
    // Edges between RefSCCs are the same regardless of call or ref, so we can
    // just flip the edge here.
    SourceN->setEdgeKind(TargetN, 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.");
  #ifdef EXPENSIVE_CHECKS
    assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
           "Target must be a descendant of the Source.");
  #endif
  
    // Edges between RefSCCs are the same regardless of call or ref, so we can
    // just flip the edge here.
    SourceN->setEdgeKind(TargetN, 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.
    SourceN->insertEdgeInternal(TargetN, EK);
  
    assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
  
    RefSCC &TargetC = *G->lookupRefSCC(TargetN);
    assert(&TargetC != this && "Target must not be in this RefSCC.");
  #ifdef EXPENSIVE_CHECKS
    assert(TargetC.isDescendantOf(*this) &&
           "Target must be a descendant of the Source.");
  #endif
  
    // The only change required is to add this SCC to the parent set of the
    // callee.
    TargetC.Parents.insert(this);
  
  #ifndef NDEBUG
    // Check that the RefSCC is still valid.
    verify();
  #endif
  }
  
  SmallVector<LazyCallGraph::RefSCC *, 1>
  LazyCallGraph::RefSCC::insertIncomingRefEdge(Node &SourceN, Node &TargetN) {
    assert(G->lookupRefSCC(TargetN) == this && "Target must be in this RefSCC.");
    RefSCC &SourceC = *G->lookupRefSCC(SourceN);
    assert(&SourceC != this && "Source must not be in this RefSCC.");
  #ifdef EXPENSIVE_CHECKS
    assert(SourceC.isDescendantOf(*this) &&
           "Source must be a descendant of the Target.");
  #endif
  
    SmallVector<RefSCC *, 1> DeletedRefSCCs;
  
  #ifndef NDEBUG
    // In a debug build, verify the RefSCC is valid to start with and when this
    // routine finishes.
    verify();
    auto VerifyOnExit = make_scope_exit([&]() { verify(); });
  #endif
  
    int SourceIdx = G->RefSCCIndices[&SourceC];
    int TargetIdx = G->RefSCCIndices[this];
    assert(SourceIdx < TargetIdx &&
           "Postorder list doesn't see edge as incoming!");
  
    // Compute the RefSCCs which (transitively) reach the source. We do this by
    // working backwards from the source using the parent set in each RefSCC,
    // skipping any RefSCCs that don't fall in the postorder range. This has the
    // advantage of walking the sparser parent edge (in high fan-out graphs) but
    // more importantly this removes examining all forward edges in all RefSCCs
    // within the postorder range which aren't in fact connected. Only connected
    // RefSCCs (and their edges) are visited here.
    auto ComputeSourceConnectedSet = [&](SmallPtrSetImpl<RefSCC *> &Set) {
      Set.insert(&SourceC);
      SmallVector<RefSCC *, 4> Worklist;
      Worklist.push_back(&SourceC);
      do {
        RefSCC &RC = *Worklist.pop_back_val();
        for (RefSCC &ParentRC : RC.parents()) {
          // Skip any RefSCCs outside the range of source to target in the
          // postorder sequence.
          int ParentIdx = G->getRefSCCIndex(ParentRC);
          assert(ParentIdx > SourceIdx && "Parent cannot precede source in postorder!");
          if (ParentIdx > TargetIdx)
            continue;
          if (Set.insert(&ParentRC).second)
            // First edge connecting to this parent, add it to our worklist.
            Worklist.push_back(&ParentRC);
        }
      } while (!Worklist.empty());
    };
  
    // 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.
    auto ComputeTargetConnectedSet = [&](SmallPtrSetImpl<RefSCC *> &Set) {
      Set.insert(this);
      SmallVector<RefSCC *, 4> Worklist;
      Worklist.push_back(this);
      do {
        RefSCC &RC = *Worklist.pop_back_val();
        for (SCC &C : RC)
          for (Node &N : C)
            for (Edge &E : *N) {
              RefSCC &EdgeRC = *G->lookupRefSCC(E.getNode());
              if (G->getRefSCCIndex(EdgeRC) <= SourceIdx)
                // Not in the postorder sequence between source and target.
                continue;
  
              if (Set.insert(&EdgeRC).second)
                Worklist.push_back(&EdgeRC);
            }
      } while (!Worklist.empty());
    };
  
    // Use a generic helper to update the postorder sequence of RefSCCs and return
    // a range of any RefSCCs connected into a cycle by inserting this edge. This
    // routine will also take care of updating the indices into the postorder
    // sequence.
    iterator_range<SmallVectorImpl<RefSCC *>::iterator> MergeRange =
        updatePostorderSequenceForEdgeInsertion(
            SourceC, *this, G->PostOrderRefSCCs, G->RefSCCIndices,
            ComputeSourceConnectedSet, ComputeTargetConnectedSet);
  
    // Build a set so we can do fast tests for whether a RefSCC will end up as
    // part of the merged RefSCC.
    SmallPtrSet<RefSCC *, 16> MergeSet(MergeRange.begin(), MergeRange.end());
  
    // This RefSCC will always be part of that set, so just insert it here.
    MergeSet.insert(this);
  
    // 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.
    SmallVector<SCC *, 16> MergedSCCs;
    int SCCIndex = 0;
    for (RefSCC *RC : MergeRange) {
      assert(RC != this && "We're merging into the target RefSCC, so it "
                           "shouldn't be in the range.");
  
      // Merge the parents which aren't part of the merge into the our parents.
      for (RefSCC *ParentRC : RC->Parents)
        if (!MergeSet.count(ParentRC))
          Parents.insert(ParentRC);
      RC->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 : *RC) {
        InnerC.OuterRefSCC = this;
        SCCIndices[&InnerC] = SCCIndex++;
        for (Node &N : InnerC) {
          G->SCCMap[&N] = &InnerC;
          for (Edge &E : *N) {
            RefSCC &ChildRC = *G->lookupRefSCC(E.getNode());
            if (MergeSet.count(&ChildRC))
              continue;
            ChildRC.Parents.erase(RC);
            ChildRC.Parents.insert(this);
          }
        }
      }
  
      // 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(RC->SCCs);
      else
        MergedSCCs.append(RC->SCCs.begin(), RC->SCCs.end());
      RC->SCCs.clear();
      DeletedRefSCCs.push_back(RC);
    }
  
    // 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);
  
    // Remove the merged away RefSCCs from the post order sequence.
    for (RefSCC *RC : MergeRange)
      G->RefSCCIndices.erase(RC);
    int IndexOffset = MergeRange.end() - MergeRange.begin();
    auto EraseEnd =
        G->PostOrderRefSCCs.erase(MergeRange.begin(), MergeRange.end());
    for (RefSCC *RC : make_range(EraseEnd, G->PostOrderRefSCCs.end()))
      G->RefSCCIndices[RC] -= IndexOffset;
  
    // 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);
  
    // 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 DeletedRefSCCs;
  }
  
  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(!is_contained(G->LeafRefSCCs, this) &&
           "Cannot have a leaf RefSCC source.");
  
  #ifndef NDEBUG
    // In a debug build, verify the RefSCC is valid to start with and when this
    // routine finishes.
    verify();
    auto VerifyOnExit = make_scope_exit([&]() { verify(); });
  #endif
  
    // First remove it from the node.
    bool Removed = SourceN->removeEdgeInternal(TargetN);
    (void)Removed;
    assert(Removed && "Target not in the edge set for this caller?");
  
    bool HasOtherEdgeToChildRC = false;
    bool HasOtherChildRC = false;
    for (SCC *InnerC : SCCs) {
      for (Node &N : *InnerC) {
        for (Edge &E : *N) {
          RefSCC &OtherChildRC = *G->lookupRefSCC(E.getNode());
          if (&OtherChildRC == &TargetRC) {
            HasOtherEdgeToChildRC = true;
            break;
          }
          if (&OtherChildRC != this)
            HasOtherChildRC = true;
        }
        if (HasOtherEdgeToChildRC)
          break;
      }
      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 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 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 (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 Source SCC a leaf SCC.
      if (!HasOtherChildRC)
        G->LeafRefSCCs.push_back(this);
    }
  }
  
  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");
  
  #ifndef NDEBUG
    // In a debug build, verify the RefSCC is valid to start with and when this
    // routine finishes.
    verify();
    auto VerifyOnExit = make_scope_exit([&]() { verify(); });
  #endif
  
    // First remove the actual edge.
    bool Removed = SourceN->removeEdgeInternal(TargetN);
    (void)Removed;
    assert(Removed && "Target not in the edge set for this caller?");
  
    // We return a list of the resulting *new* RefSCCs in post-order.
    SmallVector<RefSCC *, 1> Result;
  
    // Direct recursion doesn't impact the SCC graph at all.
    if (&SourceN == &TargetN)
      return Result;
  
    // If this ref edge is within an SCC then there are sufficient other edges to
    // form a cycle without this edge so removing it is a no-op.
    SCC &SourceC = *G->lookupSCC(SourceN);
    SCC &TargetC = *G->lookupSCC(TargetN);
    if (&SourceC == &TargetC)
      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.
    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;
  
      for (Node &N : *C)
        N.DFSNumber = N.LowLink = 0;
  
      Worklist.append(C->Nodes.begin(), C->Nodes.end());
    }
  
    auto MarkNodeForSCCNumber = [&PostOrderMapping](Node &N, int Number) {
      N.DFSNumber = N.LowLink = -1;
      PostOrderMapping[&N] = Number;
    };
  
    SmallVector<std::pair<Node *, EdgeSequence::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;
      }
  
      RootN->DFSNumber = RootN->LowLink = 1;
      int NextDFSNumber = 2;
  
      DFSStack.push_back({RootN, (*RootN)->begin()});
      do {
        Node *N;
        EdgeSequence::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();
          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;
            }
  
            // 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;
          }
  
          // 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;
  
        // 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(),
            find_if(reverse(PendingRefSCCStack), [RootDFSNumber](const 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(PendingRefSCCStack.empty() && "Didn't flush all pending nodes!");
    } while (!Worklist.empty());
  
    // 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));
  
    // Insert the resulting postorder sequence into the global graph postorder
    // sequence before the current RefSCC in that sequence. The idea being that
    // this RefSCC is the target of the reference edge removed, and thus has
    // a direct or indirect edge to every other RefSCC formed and so must be at
    // the end of any postorder traversal.
    //
    // FIXME: It'd be nice to change the APIs so that we returned an iterator
    // range over the global postorder sequence and generally use that sequence
    // rather than building a separate result vector here.
    if (!Result.empty()) {
      int Idx = G->getRefSCCIndex(*this);
      G->PostOrderRefSCCs.insert(G->PostOrderRefSCCs.begin() + Idx,
                                 Result.begin(), Result.end());
      for (int i : seq<int>(Idx, G->PostOrderRefSCCs.size()))
        G->RefSCCIndices[G->PostOrderRefSCCs[i]] = i;
      assert(G->PostOrderRefSCCs[G->getRefSCCIndex(*this)] == this &&
             "Failed to update this RefSCC's index after insertion!");
    }
  
    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);
      RC.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(remove_if(SCCs,
                         [&](SCC *C) {
                           return PostOrderMapping.lookup(&*C->begin()) !=
                                  RootPostOrderNumber;
                         }),
               SCCs.end());
    SCCIndices.clear();
    for (int i = 0, Size = SCCs.size(); i < Size; ++i)
      SCCIndices[SCCs[i]] = i;
  
  #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) {
          RefSCC &ChildRC = *G->lookupRefSCC(E.getNode());
          if (&ChildRC == this)
            continue;
          ChildRC.Parents.insert(this);
  #ifndef NDEBUG
          IsLeaf = false;
  #endif
        }
      }
  #ifndef NDEBUG
    if (!Result.empty())
      assert(!IsLeaf && "This SCC cannot be a leaf as we have split out new "
                        "SCCs by removing this edge.");
    if (none_of(G->LeafRefSCCs, [&](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
    // And connect both this RefSCC and all the new ones to the correct parents.
    // The easiest way to do this is just to re-analyze the old parent set.
    SmallVector<RefSCC *, 4> OldParents(Parents.begin(), Parents.end());
    Parents.clear();
    for (RefSCC *ParentRC : OldParents)
      for (SCC &ParentC : *ParentRC)
        for (Node &ParentN : ParentC)
          for (Edge &E : *ParentN) {
            RefSCC &RC = *G->lookupRefSCC(E.getNode());
            if (&RC != ParentRC)
              RC.Parents.insert(ParentRC);
          }
  
    // If this SCC stopped being a leaf through this edge removal, remove it from
    // 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());
  
  #ifndef NDEBUG
    // Verify all of the new RefSCCs.
    for (RefSCC *RC : Result)
      RC->verify();
  #endif
  
    // Return the new list of SCCs.
    return Result;
  }
  
  void LazyCallGraph::RefSCC::handleTrivialEdgeInsertion(Node &SourceN,
                                                         Node &TargetN) {
    // The only trivial case that requires any graph updates is when we add new
    // ref edge and may connect different RefSCCs along that path. This is only
    // because of the parents set. Every other part of the graph remains constant
    // after this edge insertion.
    assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
    RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
    if (&TargetRC == this) {
  
      return;
    }
  
  #ifdef EXPENSIVE_CHECKS
    assert(TargetRC.isDescendantOf(*this) &&
           "Target must be a descendant of the Source.");
  #endif
    // The only change required is to add this RefSCC to the parent set of the
    // target. This is a set and so idempotent if the edge already existed.
    TargetRC.Parents.insert(this);
  }
  
  void LazyCallGraph::RefSCC::insertTrivialCallEdge(Node &SourceN,
                                                    Node &TargetN) {
  #ifndef NDEBUG
    // Check that the RefSCC is still valid when we finish.
    auto ExitVerifier = make_scope_exit([this] { verify(); });
  
  #ifdef EXPENSIVE_CHECKS
    // Check that we aren't breaking some invariants of the SCC graph. Note that
    // this is quadratic in the number of edges in the call graph!
    SCC &SourceC = *G->lookupSCC(SourceN);
    SCC &TargetC = *G->lookupSCC(TargetN);
    if (&SourceC != &TargetC)
      assert(SourceC.isAncestorOf(TargetC) &&
             "Call edge is not trivial in the SCC graph!");
  #endif // EXPENSIVE_CHECKS
  #endif // NDEBUG
  
    // First insert it into the source or find the existing edge.
    auto InsertResult =
        SourceN->EdgeIndexMap.insert({&TargetN, SourceN->Edges.size()});
    if (!InsertResult.second) {
      // Already an edge, just update it.
      Edge &E = SourceN->Edges[InsertResult.first->second];
      if (E.isCall())
        return; // Nothing to do!
      E.setKind(Edge::Call);
    } else {
      // Create the new edge.
      SourceN->Edges.emplace_back(TargetN, Edge::Call);
    }
  
    // Now that we have the edge, handle the graph fallout.
    handleTrivialEdgeInsertion(SourceN, TargetN);
  }
  
  void LazyCallGraph::RefSCC::insertTrivialRefEdge(Node &SourceN, Node &TargetN) {
  #ifndef NDEBUG
    // Check that the RefSCC is still valid when we finish.
    auto ExitVerifier = make_scope_exit([this] { verify(); });
  
  #ifdef EXPENSIVE_CHECKS
    // Check that we aren't breaking some invariants of the RefSCC graph.
    RefSCC &SourceRC = *G->lookupRefSCC(SourceN);
    RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
    if (&SourceRC != &TargetRC)
      assert(SourceRC.isAncestorOf(TargetRC) &&
             "Ref edge is not trivial in the RefSCC graph!");
  #endif // EXPENSIVE_CHECKS
  #endif // NDEBUG
  
    // First insert it into the source or find the existing edge.
    auto InsertResult =
        SourceN->EdgeIndexMap.insert({&TargetN, SourceN->Edges.size()});
    if (!InsertResult.second)
      // Already an edge, we're done.
      return;
  
    // Create the new edge.
    SourceN->Edges.emplace_back(TargetN, Edge::Ref);
  
    // Now that we have the edge, handle the graph fallout.
    handleTrivialEdgeInsertion(SourceN, TargetN);
  }
  
  void LazyCallGraph::RefSCC::replaceNodeFunction(Node &N, Function &NewF) {
    Function &OldF = N.getFunction();
  
  #ifndef NDEBUG
    // Check that the RefSCC is still valid when we finish.
    auto ExitVerifier = make_scope_exit([this] { verify(); });
  
    assert(G->lookupRefSCC(N) == this &&
           "Cannot replace the function of a node outside this RefSCC.");
  
    assert(G->NodeMap.find(&NewF) == G->NodeMap.end() &&
           "Must not have already walked the new function!'");
  
    // It is important that this replacement not introduce graph changes so we
    // insist that the caller has already removed every use of the original
    // function and that all uses of the new function correspond to existing
    // edges in the graph. The common and expected way to use this is when
    // replacing the function itself in the IR without changing the call graph
    // shape and just updating the analysis based on that.
    assert(&OldF != &NewF && "Cannot replace a function with itself!");
    assert(OldF.use_empty() &&
           "Must have moved all uses from the old function to the new!");
  #endif
  
    N.replaceFunction(NewF);
  
    // Update various call graph maps.
    G->NodeMap.erase(&OldF);
    G->NodeMap[&NewF] = &N;
  }
  
  void LazyCallGraph::insertEdge(Node &SourceN, Node &TargetN, Edge::Kind EK) {
    assert(SCCMap.empty() &&
           "This method cannot be called after SCCs have been formed!");
  
    return SourceN->insertEdgeInternal(TargetN, EK);
  }
  
  void LazyCallGraph::removeEdge(Node &SourceN, Node &TargetN) {
    assert(SCCMap.empty() &&
           "This method cannot be called after SCCs have been formed!");
  
    bool Removed = SourceN->removeEdgeInternal(TargetN);
    (void)Removed;
    assert(Removed && "Target not in the edge set for this caller?");
  }
  
  void LazyCallGraph::removeDeadFunction(Function &F) {
    // FIXME: This is unnecessarily restrictive. We should be able to remove
    // functions which recursively call themselves.
    assert(F.use_empty() &&
           "This routine should only be called on trivially dead functions!");
  
    // We shouldn't remove library functions as they are never really dead while
    // the call graph is in use -- every function definition refers to them.
    assert(!isLibFunction(F) &&
           "Must not remove lib functions from the call graph!");
  
    auto NI = NodeMap.find(&F);
    if (NI == NodeMap.end())
      // Not in the graph at all!
      return;
  
    Node &N = *NI->second;
    NodeMap.erase(NI);
  
    // Remove this from the entry edges if present.
    EntryEdges.removeEdgeInternal(N);
  
    if (SCCMap.empty()) {
      // No SCCs have been formed, so removing this is fine and there is nothing
      // else necessary at this point but clearing out the node.
      N.clear();
      return;
    }
  
    // Cannot remove a function which has yet to be visited in the DFS walk, so
    // if we have a node at all then we must have an SCC and RefSCC.
    auto CI = SCCMap.find(&N);
    assert(CI != SCCMap.end() &&
           "Tried to remove a node without an SCC after DFS walk started!");
    SCC &C = *CI->second;
    SCCMap.erase(CI);
    RefSCC &RC = C.getOuterRefSCC();
  
    // This node must be the only member of its SCC as it has no callers, and
    // that SCC must be the only member of a RefSCC as it has no references.
    // Validate these properties first.
    assert(C.size() == 1 && "Dead functions must be in a singular SCC");
    assert(RC.size() == 1 && "Dead functions must be in a singular RefSCC");
  
    // Clean up any remaining reference edges. Note that we walk an unordered set
    // here but are just removing and so the order doesn't matter.
    for (RefSCC &ParentRC : RC.parents())
      for (SCC &ParentC : ParentRC)
        for (Node &ParentN : ParentC)
          if (ParentN)
            ParentN->removeEdgeInternal(N);
  
    // Now remove this RefSCC from any parents sets and the leaf list.
    for (Edge &E : *N)
      if (RefSCC *TargetRC = lookupRefSCC(E.getNode()))
        TargetRC->Parents.erase(&RC);
    // FIXME: This is a linear operation which could become hot and benefit from
    // an index map.
    auto LRI = find(LeafRefSCCs, &RC);
    if (LRI != LeafRefSCCs.end())
      LeafRefSCCs.erase(LRI);
  
    auto RCIndexI = RefSCCIndices.find(&RC);
    int RCIndex = RCIndexI->second;
    PostOrderRefSCCs.erase(PostOrderRefSCCs.begin() + RCIndex);
    RefSCCIndices.erase(RCIndexI);
    for (int i = RCIndex, Size = PostOrderRefSCCs.size(); i < Size; ++i)
      RefSCCIndices[PostOrderRefSCCs[i]] = i;
  
    // Finally clear out all the data structures from the node down through the
    // components.
    N.clear();
    C.clear();
    RC.clear();
  
    // Nothing to delete as all the objects are allocated in stable bump pointer
    // allocators.
  }
  
  LazyCallGraph::Node &LazyCallGraph::insertInto(Function &F, Node *&MappedN) {
    return *new (MappedN = BPA.Allocate()) Node(*this, F);
  }
  
  void LazyCallGraph::updateGraphPtrs() {
    // Process all nodes updating the graph pointers.
    {
      SmallVector<Node *, 16> Worklist;
      for (Edge &E : EntryEdges)
        Worklist.push_back(&E.getNode());
  
      while (!Worklist.empty()) {
        Node &N = *Worklist.pop_back_val();
        N.G = this;
        if (N)
          for (Edge &E : *N)
            Worklist.push_back(&E.getNode());
      }
    }
  
    // Process all SCCs updating the graph pointers.
    {
      SmallVector<RefSCC *, 16> Worklist(LeafRefSCCs.begin(), LeafRefSCCs.end());
  
      while (!Worklist.empty()) {
        RefSCC &C = *Worklist.pop_back_val();
        C.G = this;
        for (RefSCC &ParentC : C.parents())
          Worklist.push_back(&ParentC);
      }
    }
  }
  
  template <typename RootsT, typename GetBeginT, typename GetEndT,
            typename GetNodeT, typename FormSCCCallbackT>
  void LazyCallGraph::buildGenericSCCs(RootsT &&Roots, GetBeginT &&GetBegin,
                                       GetEndT &&GetEnd, GetNodeT &&GetNode,
                                       FormSCCCallbackT &&FormSCC) {
    typedef decltype(GetBegin(std::declval<Node &>())) EdgeItT;
  
    SmallVector<std::pair<Node *, EdgeItT>, 16> DFSStack;
    SmallVector<Node *, 16> PendingSCCStack;
  
    // Scan down the stack and DFS across the call edges.
    for (Node *RootN : Roots) {
      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, GetBegin(*RootN)});
      do {
        Node *N;
        EdgeItT I;
        std::tie(N, I) = DFSStack.pop_back_val();
        auto E = GetEnd(*N);
        while (I != E) {
          Node &ChildN = GetNode(I);
          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});
  
            ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
            N = &ChildN;
            I = GetBegin(*N);
            E = GetEnd(*N);
            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(),
            find_if(reverse(PendingSCCStack), [RootDFSNumber](const Node *N) {
              return N->DFSNumber < RootDFSNumber;
            }));
        // Form a new SCC out of these nodes and then clear them off our pending
        // stack.
        FormSCC(SCCNodes);
        PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
      } while (!DFSStack.empty());
    }
  }
  
  /// 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!");
  
    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!");
  
      // This node will go into the next RefSCC, clear out its DFS and low link
      // as we scan.
      N->DFSNumber = N->LowLink = 0;
    }
  
    // 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.
    buildGenericSCCs(
        Nodes, [](Node &N) { return N->call_begin(); },
        [](Node &N) { return N->call_end(); },
        [](EdgeSequence::call_iterator I) -> Node & { return I->getNode(); },
        [this, &RC](node_stack_range Nodes) {
          RC.SCCs.push_back(createSCC(RC, Nodes));
          for (Node &N : *RC.SCCs.back()) {
            N.DFSNumber = N.LowLink = -1;
            SCCMap[&N] = RC.SCCs.back();
          }
        });
  
    // Wire up the SCC indices.
    for (int i = 0, Size = RC.SCCs.size(); i < Size; ++i)
      RC.SCCIndices[RC.SCCs[i]] = i;
  }
  
  void LazyCallGraph::buildRefSCCs() {
    if (EntryEdges.empty() || !PostOrderRefSCCs.empty())
      // RefSCCs are either non-existent or already built!
      return;
  
    assert(RefSCCIndices.empty() && "Already mapped RefSCC indices!");
  
    SmallVector<Node *, 16> Roots;
    for (Edge &E : *this)
      Roots.push_back(&E.getNode());
  
    // The roots will be popped of a stack, so use reverse to get a less
    // surprising order. This doesn't change any of the semantics anywhere.
    std::reverse(Roots.begin(), Roots.end());
  
    buildGenericSCCs(
        Roots,
        [](Node &N) {
          // We need to populate each node as we begin to walk its edges.
          N.populate();
          return N->begin();
        },
        [](Node &N) { return N->end(); },
        [](EdgeSequence::iterator I) -> Node & { return I->getNode(); },
        [this](node_stack_range Nodes) {
          RefSCC *NewRC = createRefSCC(*this);
          buildSCCs(*NewRC, Nodes);
          connectRefSCC(*NewRC);
  
          // Push the new node into the postorder list and remember its position
          // in the index map.
          bool Inserted =
              RefSCCIndices.insert({NewRC, PostOrderRefSCCs.size()}).second;
          (void)Inserted;
          assert(Inserted && "Cannot already have this RefSCC in the index map!");
          PostOrderRefSCCs.push_back(NewRC);
  #ifndef NDEBUG
          NewRC->verify();
  #endif
        });
  }
  
  // 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) {
          RefSCC &ChildRC = *lookupRefSCC(E.getNode());
          if (&ChildRC == &RC)
            continue;
          ChildRC.Parents.insert(&RC);
          IsLeaf = false;
        }
  
    // For the SCCs where we find no child SCCs, add them to the leaf list.
    if (IsLeaf)
      LeafRefSCCs.push_back(&RC);
  }
  
  AnalysisKey LazyCallGraphAnalysis::Key;
  
  LazyCallGraphPrinterPass::LazyCallGraphPrinterPass(raw_ostream &OS) : OS(OS) {}
  
  static void printNode(raw_ostream &OS, LazyCallGraph::Node &N) {
    OS << "  Edges in function: " << N.getFunction().getName() << "\n";
    for (LazyCallGraph::Edge &E : N.populate())
      OS << "    " << (E.isCall() ? "call" : "ref ") << " -> "
         << E.getFunction().getName() << "\n";
  
    OS << "\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::SCC &InnerC : C)
      printSCC(OS, InnerC);
  
    OS << "\n";
  }
  
  PreservedAnalyses LazyCallGraphPrinterPass::run(Module &M,
                                                  ModuleAnalysisManager &AM) {
    LazyCallGraph &G = AM.getResult<LazyCallGraphAnalysis>(M);
  
    OS << "Printing the call graph for module: " << M.getModuleIdentifier()
       << "\n\n";
  
    for (Function &F : M)
      printNode(OS, G.get(F));
  
    G.buildRefSCCs();
    for (LazyCallGraph::RefSCC &C : G.postorder_ref_sccs())
      printRefSCC(OS, C);
  
    return PreservedAnalyses::all();
  }
  
  LazyCallGraphDOTPrinterPass::LazyCallGraphDOTPrinterPass(raw_ostream &OS)
      : OS(OS) {}
  
  static void printNodeDOT(raw_ostream &OS, LazyCallGraph::Node &N) {
    std::string Name = "\"" + DOT::EscapeString(N.getFunction().getName()) + "\"";
  
    for (LazyCallGraph::Edge &E : N.populate()) {
      OS << "  " << Name << " -> \""
         << DOT::EscapeString(E.getFunction().getName()) << "\"";
      if (!E.isCall()) // It is a ref edge.
        OS << " [style=dashed,label=\"ref\"]";
      OS << ";\n";
    }
  
    OS << "\n";
  }
  
  PreservedAnalyses LazyCallGraphDOTPrinterPass::run(Module &M,
                                                     ModuleAnalysisManager &AM) {
    LazyCallGraph &G = AM.getResult<LazyCallGraphAnalysis>(M);
  
    OS << "digraph \"" << DOT::EscapeString(M.getModuleIdentifier()) << "\" {\n";
  
    for (Function &F : M)
      printNodeDOT(OS, G.get(F));
  
    OS << "}\n";
  
    return PreservedAnalyses::all();
  }
  