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

[chandlerc]

Summary

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 yet complete: it doesn't model edges to
declarations or indirect calls yet. Those are planned for subsequent
patches to complete the set of information needed for traditional call
graph based analyses.

An important realization 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 call graph SCCs is not done lazily, unlike reference
SCCs. Instead, once a reference SCC is formed, it directly builds the
call SCCs within it and stores them in post-order. 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 have worked through the core algorithms on a whiteboard and I think
their underpinnings are largely correct. However, I still have a lot of
testing to do here. Several of the previous tests have not yet been
updated (and are commented out currently) and new tests have not been
written covering all of the intricasies of the new algorithms. I'm
planning to continue working on the testing, but based on discussions
with Sanjoy, it seemed worthwhile to start the review early. This seems
especially worthwhile considering the very sizable amount of code change
due to introducing both new structures and new algorithms.

I also 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.

Anyways, looking forward to comments. I'll also update this as I make
more progress carefully testing the rest of the mutation logic.

[sanjoy]

Okay, this is a lot of code to review at once. :)

I'm okay with the general structure (SCC's nested in RefSCCs). I've only skimmed through the code so far, and have added some minor comments inline based on that.

lib/Analysis/LazyCallGraph.cpp

354

Here and below in the later std::stable_partition, do you need to update SCCIndices?

410

Should this be return ConnectedSet.count(C);? Since I understand you want { nodes reachable from Target } Target { nodes not reachable from Target } ?

426

any SCC-wide properties except norecurse?

471

Minor: assert message is wrong.

737

This may be naive of me, but why can't this do exactly what switchInternalEdgeToCall does when it discovers that it needs to merge a set of SCC's into a new SCC (perhaps even share code with some suitable abstraction)? If it is expensive to keep a postorder of RefSCCs due to lazy generation (since you'll have to prepend onto a vector), can we apply essentially the same algorithm to the reverse postorder (that is always up to date) of RefSCCs?

[sanjoy]

include/llvm/Analysis/LazyCallGraph.h

481–515

Nit: "existing"

495

Nit: "existing"

507

Nit: "existing"

775

Why not map these to unsigned? Is making the integer type signed a semantic change?

lib/Analysis/LazyCallGraph.cpp

351

Should this be !ConnectedSet.count(&TargetSCC)?

[chandlerc]

Fleshed out unit tests, numerous bug fixes and missing APIs in order to write
unit tests effectively, and addressed Sanjoy's feedback.

[chandlerc]

Thanks so much for the review Sanjoy.

Now with much better testing (still checking on the last bit of coverage) and many, many bugs fixed. I've also replied inline to some of your questions and fixed all the issues you pointed out (that I could).

include/llvm/Analysis/LazyCallGraph.h

775

Because I don't want 2^32 modular arithmetic behavior.

I use signed integers unless I *need* an unsigned integer. It makes me much more comfortable writing relational comparisons, etc.

lib/Analysis/LazyCallGraph.cpp

351

Yep.

New unit tests catch this as well.

354

Yep. Unit tests also catch this now.

I've also been able to merge some of the calls to this to simplify things.

410

Yep. Again, unit tests now catch this and fixed.

426

readnone? most of them are...

737

So, I've not thought of a good way to retain the postorder of RefSCCs and use them here. It's made tricky because one of the goals of RefSCCS is for updates to one RefSCC to not impact other ones (for parallelism etc) and mutating a postorder list would likely do just that.

But it is a delightful optimization so I'm going to keep thinking about this. Maybe something will present itself once we have the users in hand and know what their usage looks like?

[sanjoy]

First round of comments and questions (I'll do a second pass soon):

(PS: I haven't reviewed the tests yet)

include/llvm/Analysis/LazyCallGraph.h

452

I don't see where slice, Begin and End above are used.

458

Why can't Parents be a container of const RefSCC *?

526–527

Minor: Might want to change this to "existing path from \p SourceN to \p TargetN" since the edge being inserted is not necessarily a call edge.

526–527

Minor: "does not change the set of SCCs and RefSCCs" may be clearer (esp. since you use that language elsewhere).

541

s/SCC/RefSCC

565

Was this FIXME for the postorder optimization we do in this change, or something else? If the former, then perhaps this FIXME should be removed now?

lib/Analysis/LazyCallGraph.cpp

224

I'd remove the &TargetSCC == &SourceSCC clause, and instead just have this assert be <= i.

302

Nit: sequence

336

Minor: I'd use llvm::any_of for the inner loop over the outgoing edges.

360

Nit: "the correct post-order"

373

This special case here makes me slightly uncomfortable. Unless you think it is important for performance (or other reasons I don't see yet), perhaps we can get rid of the // Force the target node to be in the old SCC. bit above (so that the ChildN.DFSNumber == -1 case is never "spuriously" taken), and instead down below add SCCNodes to OldSCC if it contains TargetN?

406

Minor: I'd use SCCIndices.find(&EdgeC)->second here, just so that we crash if &EdgeC didn't end up in SCCIndices due to a bug earlier.

464

Nit: indentation

741

Nit: spelling

850

Given that you've used this pattern a lot, perhaps the interface should be Node &getNode() (which asserts that node exists) and perhaps an Node *getNodePtr() or bool hasNode() interface for clients that want to handle edges that don't yet have a node?

1028

Why not have this DFS be over SCC s as nodes? That way we won't waste cycles DFS'ing inside an SCC; and it fits in better with the "SCC 's nested within RefSCC" design.

1051

Might be useful to explicitly document (on the field) that DFSNumber for RefSCC (and SCC?) instances is -1 for all nodes unless we're mid-DFS. Perhaps we can even stick this invariant in verify()?

1060

As I said earlier, unless there are cases where this really matters, I'd rather not have this special case here; but instead have a check on RefSCCNodes to see if it should be put in a new SCC or into TargetC.

1074

Nit: "RefSCC"

1196

Can there be cases where Result is empty, IsLeaf is false, and this was a leaf RefSCC before removeInternalRefEdge was called? If not, we can get rid of IsLeaf and update G->LeafRefSCCs only if Result is non-empty.

1204–1211

[Edit: also see above]

Doesn't !Result.empty() imply !IsLeaf (from the assert above)?

I think you need if (!WasLeafBeforeEdgeRemoval && !Result.empty()), but I think just checking for !IsLeaf will Do The Right Thing, since std::remove doesn't break if this isn't present in G->LeafRefSCCs.

[sanjoy]

include/llvm/Analysis/LazyCallGraph.h

707

Why can't this (i.e. ContainingSCC) live as a field in Node?

[chandlerc]

Update based on code review comments.

[chandlerc]

Updated resolving most of the code review comments. Some questions and responses below:

include/llvm/Analysis/LazyCallGraph.h

452

I'm expecting clients to want to do:

for (auto &C : make_range(RC.begin(), RC.find(SomeOldC)))
  ...

And thought it would be good to directly support this rather than forcing the use of make_range by providing:

for (auto &C : RC.slice(RC.Begin, SomeOldC))
  ...

It happened to end up cleaner to write the tests using direct iterators instead. I can add a unit test specifically for this API or I can wait to add the API until I have the first user?

458

I guess it can, but there are some places where we walk the parents container and we are really planning to mutate stuff... I was mostly trying to reduce the number of const_casts I have to write. I don't feel very strongly about any of this.

565

In this case, the postorder optimization doesn't apply.

This comment is about the fact that the DFS over the inverse DAG formed with the 'parents' sets is potentially quite far reaching. We could do some things to try to prune this space in common cases. That's all.

707

I was originally trying to avoid digging into the Node object. Essentially, to allow the DFS to just find the SCC from the address of the node.

But I'm not sure any more that this is the right tradeoff.

Either way, moving completely away from the map seems like it could be usefully separated into a follow-up change.

lib/Analysis/LazyCallGraph.cpp

336

For all_of, I tend to agree. But I'm not sure that this:

return std::any_of(C.begin(), C.end(), [&](Node &N) {
  return std::any_of(N.call_begin(), N.call_end(), [&](Edge &E) {
    assert(E.getNode() && "Must have formed a node within an SCC!");
    return ConnectedSet.count(G->lookupSCC(*E.getNode()));
  });
});

Is more readable than:

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;

360

I think this should be "corrected the post-order" (which I've made it) but check me.

373

Well, this clearly doesn't change the big-O, but I think it pretty dramatically shifts the average case. Whenever we hit this, we skip visiting all other edges on the "pop" half of the DFS which should be a really significant savings.

Is there anything that would make you more comfortable with it? We do this optimization in two places so I'd like to get it right.

406

Yea, much better.

850

I think you're totally right. Should that go here or in a follow-up patch?

1028

I thought a lot about this, but I don't think it helps much. Let me see if I can explain why.

Ultimately, the DFS is actually over *edges*, and the edges are fundamentally attached to nodes. We could use the SCC as the "node" in the DFS, but we'd have to include both an edge_iterator and a node_iterator to mark the position in the DFS stack, and we'd still visit exactly the same number of edges.

So while it makes the code a bit awkward, I don't think we really lose anything by directly DFS-ing the nodes, and we get a significantly simpler edge iterator model.

1060

See above.

1196

No, there can't (as you indicate below).

1204–1211

Yea, the IsLeaf is essentially just a debug check. I've made it now in fact just a debug check and left a FIXME about the cost of relying on std::remove rather than knowing if this RefSCC was already a leaf RefSCC.

[sanjoy]

include/llvm/Analysis/LazyCallGraph.h

452

I'd say lets wait till we have a user?

458

If having the parents be a container of const RefSCC * increases the number of const_casts then what you have here is fine.

565

Ah, I misread it as inserting an incoming call edge.

707

Either way, moving completely away from the map seems like it could be usefully separated into a follow-up change.

SGTM. Might save a few hashtable lookups.

lib/Analysis/LazyCallGraph.cpp

336

As discussed on IRC, the for loop is fine.

360

SGTM

733

Is there anything that would make you more comfortable with it? We do this optimization in two places so I'd like to get it right.

Might be helpful to explicitly document that this is a performance optimization then -- I couldn't easily tell if there's something fundamentally different going on here.

850

SGTM

1028

we'd still visit exactly the same number of edges.

Wouldn't you be able to skip pushing intra-SCC edges, if you're considering an SCC as a node?

we get a significantly simpler edge iterator model.

This I agree with: for the code to be readable, we'll need to add an outgoing_edges iterator to SCC, that skips intra-SCC edges.

[chandlerc]

More updates to address review comments.

include/llvm/Analysis/LazyCallGraph.h

452

Fine fine. ;] And I was so happy to have figured out a nice pattern here. Will try to remember it.

lib/Analysis/LazyCallGraph.cpp

733

I've tried to expand the comments about this in both algorithms, and reference those comments from the place where we do the short-circuit. Let me know if this is helping.

1028

I'm really not sure this is the right tradeoff... The iterator itself has to carry 2x the state in order to remember where we "paused" in our walk. But we do get to only have 1 frame in the DFS stack for each SCC.

My expectation is that SCCs with >1 node are *quite* rare in practice, and RefSCCs with >1 SCC are somewhat rare (probably under 50%, maybe under 20% in most code). Given that, I suspect that the state would almost always be a bunch of zeros and we wouldn't save a lot of depth on the stack.

But I think this is still something to potentially revisit as we go along. But I'd like to keep the algorithm as-is for now. It's a complex change and there is already too much of that here.

I'd be interested in re-visiting this and trying to see if there is a way to get the best of both worlds -- simple DFS stack and walk over edges, but handle SCCs at once so that we actually skip redundant work in the face of large SCCs.

[chandlerc]

Ping. I think this patch is getting close?

[sanjoy]

Some more mostly minor comments:

include/llvm/Analysis/LazyCallGraph.h

52

Looks like this header is unused.

485

Minor: I'd be specific about "remain valid till ... (destruction of the parent LCG?)"

497

SourceN ant? This first sentence sounds malformed.

lib/Analysis/LazyCallGraph.cpp

105

Here and elsewhere: why not {&TargetN.getFunction(), Edges.size()} instead of an explicit std::make_pair?

110

Why not (*this)[&TargetF].setKind(EK)?

733

The doc updates lgtm

788

I think this can just be ConnectedDepth = DFSStack.size() (with an assert(ConnectedDepth < (int)DFSStack.size())).

1028

SGTM

[chandlerc]

Update to address comments from Sanjoy.

[chandlerc]

Comments addressed.

include/llvm/Analysis/LazyCallGraph.h

52

std::pair comes from here.

497

Cleaned it up, sorry about that.

lib/Analysis/LazyCallGraph.cpp

105

When I first wrote the code, not all of our compilers supported {} syntax, and this make_pair didn't end up getting completely rewritten. I can update more of them though.

110

The public interface doesn't expose a mutable edge.

[sanjoy]

Looks great!

include/llvm/Analysis/CGSCCPassManager.h

PreservedAnalyses run(Module &M, ModuleAnalysisManager *AM) {
     // Setup the CGSCC analysis manager from its proxy.
     CGSCCAnalysisManager &CGAM =
         AM->getResult<CGSCCAnalysisManagerModuleProxy>(M).getManager();
 
     // Get the call graph for this module.
     LazyCallGraph &CG = AM->getResult<LazyCallGraphAnalysis>(M);
 
     PreservedAnalyses PA = PreservedAnalyses::all();
-    for (LazyCallGraph::SCC &C : CG.postorder_sccs()) {
+    for (LazyCallGraph::RefSCC &OuterC : CG.postorder_ref_sccs())
+      for (LazyCallGraph::SCC &C : OuterC) {
         PreservedAnalyses PassPA = Pass.run(C, &CGAM);
 
         // We know that the CGSCC pass couldn't have invalidated any other
         // SCC's analyses (that's the contract of a CGSCC pass), so
         // directly handle the CGSCC analysis manager's invalidation here. We
         // also update the preserved set of analyses to reflect that invalidated
         // analyses are now safe to preserve.
         // FIXME: This isn't quite correct. We need to handle the case where the
         // pass updated the CG, particularly some child of the current SCC, and
         // invalidate its analyses.
         PassPA = CGAM.invalidate(C, std::move(PassPA));
 
         // Then intersect the preserved set so that invalidation of module
         // analyses will eventually occur when the module pass completes.
         PA.intersect(std::move(PassPA));
       }
 
     // By definition we preserve the proxy. This precludes *any* invalidation
     // of CGSCC analyses by the proxy, but that's OK because we've taken
     // care to invalidate analyses in the CGSCC analysis manager
     // incrementally above.
     PA.preserve<CGSCCAnalysisManagerModuleProxy>();
     return PA;
   }
public:
   /// \brief Runs the function pass across every function in the module.
   PreservedAnalyses run(LazyCallGraph::SCC &C, CGSCCAnalysisManager *AM) {
     FunctionAnalysisManager *FAM = nullptr;
     if (AM)
       // Setup the function analysis manager from its proxy.
       FAM = &AM->getResult<FunctionAnalysisManagerCGSCCProxy>(C).getManager();
 
     PreservedAnalyses PA = PreservedAnalyses::all();
-    for (LazyCallGraph::Node *N : C) {
-      PreservedAnalyses PassPA = Pass.run(N->getFunction(), FAM);
+    for (LazyCallGraph::Node &N : C) {
+      PreservedAnalyses PassPA = Pass.run(N.getFunction(), FAM);
 
       // We know that the function pass couldn't have invalidated any other
       // function's analyses (that's the contract of a function pass), so
       // directly handle the function analysis manager's invalidation here.
       // Also, update the preserved analyses to reflect that once invalidated
       // these can again be preserved.
       if (FAM)
-        PassPA = FAM->invalidate(N->getFunction(), std::move(PassPA));
+        PassPA = FAM->invalidate(N.getFunction(), std::move(PassPA));
 
       // Then intersect the preserved set so that invalidation of module
       // analyses will eventually occur when the module pass completes.
       PA.intersect(std::move(PassPA));
     }
 
     // By definition we preserve the proxy. This precludes *any* invalidation
     // of function analyses by the proxy, but that's OK because we've taken

include/llvm/Analysis/LazyCallGraph.h

 #include "llvm/ADT/iterator.h"
 #include "llvm/ADT/iterator_range.h"
 #include "llvm/IR/BasicBlock.h"
 #include "llvm/IR/Function.h"
 #include "llvm/IR/Module.h"
 #include "llvm/IR/PassManager.h"
 #include "llvm/Support/Allocator.h"
 #include <iterator>
+#include <utility>
 
 namespace llvm {
 class PreservedAnalyses;
 class raw_ostream;
 
 /// A lazily constructed view of the call graph of a module.
 ///
 /// With the edges of this graph, the motivating constraint that we are

 ///
 /// FIXME: This class is named LazyCallGraph in a lame attempt to distinguish
 /// it from the existing CallGraph. At some point, it is expected that this
 /// will be the only call graph and it will be renamed accordingly.
 class LazyCallGraph {
 public:
   class Node;
   class SCC;
+  class RefSCC;
   class edge_iterator;
+  class call_edge_iterator;
 
   /// A class used to represent edges in the call graph.
   ///
   /// The lazy call graph models both *call* edges and *reference* edges. Call
   /// edges are much what you would expect, and exist when there is a 'call' or
   /// 'invoke' instruction of some function. Reference edges are also tracked
   /// along side these, and exist whenever any instruction (transitively
   /// through its operands) references a function. All call edges are
public:
     ///
     /// This requires that the edge is not null. If we have not yet built
     /// a graph node for the function this edge points to, this will first ask
     /// the graph to build that node, inserting it into all the relevant
     /// structures.
     Node &getNode(LazyCallGraph &G);
 
   private:
+    friend class LazyCallGraph::Node;
+
     PointerIntPair<PointerUnion<Function *, Node *>, 1, Kind> Value;
+
+    void setKind(Kind K) { Value.setInt(K); }
   };
 
   typedef SmallVector<Edge, 4> EdgeVectorT;
   typedef SmallVectorImpl<Edge> EdgeVectorImplT;
 
   /// A node in the call graph.
   ///
   /// This represents a single node. It's primary roles are to cache the list of
   /// callees, de-duplicate and provide fast testing of whether a function is
   /// a callee, and facilitate iteration of child nodes in the graph.
   class Node {
     friend class LazyCallGraph;
     friend class LazyCallGraph::SCC;
 
     LazyCallGraph *G;
     Function &F;
 
     // We provide for the DFS numbering and Tarjan walk lowlink numbers to be
-    // stored directly within the node.
+    // stored directly within the node. These are both '-1' when nodes are part
+    // of an SCC (or RefSCC), or '0' when not yet reached in a DFS walk.
     int DFSNumber;
     int LowLink;
 
     mutable EdgeVectorT Edges;
-    DenseMap<Function *, size_t> EdgeIndexMap;
+    DenseMap<Function *, int> EdgeIndexMap;
 
     /// Basic constructor implements the scanning of F into Edges and
     /// EdgeIndexMap.
     Node(LazyCallGraph &G, Function &F);
 
     /// Internal helper to insert an edge to a function.
     void insertEdgeInternal(Function &ChildF, Edge::Kind EK);
 
     /// Internal helper to insert an edge to a node.
     void insertEdgeInternal(Node &ChildN, Edge::Kind EK);
 
+    /// Internal helper to change an edge kind.
+    void setEdgeKind(Function &ChildF, Edge::Kind EK);
+
     /// Internal helper to remove the edge to the given function.
     void removeEdgeInternal(Function &ChildF);
 
   public:
-    typedef LazyCallGraph::edge_iterator edge_iterator;
-
     LazyCallGraph &getGraph() const { return *G; }
 
     Function &getFunction() const { return F; }
 
     edge_iterator begin() const {
       return edge_iterator(Edges.begin(), Edges.end());
     }
     edge_iterator end() const { return edge_iterator(Edges.end(), Edges.end()); }
 
+    const Edge &operator[](int i) const { return Edges[i]; }
+    const Edge &operator[](Function &F) const {
+      assert(EdgeIndexMap.find(&F) != EdgeIndexMap.end() && "No such edge!");
+      return Edges[EdgeIndexMap.find(&F)->second];
+    }
+    const Edge &operator[](Node &N) const { return (*this)[N.getFunction()]; }
+
+    call_edge_iterator call_begin() const {
+      return call_edge_iterator(Edges.begin(), Edges.end());
+    }
+    call_edge_iterator call_end() const {
+      return call_edge_iterator(Edges.end(), Edges.end());
+    }
+
+    iterator_range<call_edge_iterator> calls() const {
+      return make_range(call_begin(), call_end());
+    }
+
     /// Equality is defined as address equality.
     bool operator==(const Node &N) const { return this == &N; }
     bool operator!=(const Node &N) const { return !operator==(N); }
   };
 
   /// A lazy iterator used for both the entry nodes and child nodes.
   ///
   /// When this iterator is dereferenced, if not yet available, a function will
call_edge_iterator &operator++() {
       ++I;
       advanceToNextEdge();
       return *this;
     }
   };
 
   /// An SCC of the call graph.
   ///
-  /// This represents a Strongly Connected Component of the call graph as
+  /// This represents a Strongly Connected Component of the direct call graph
+  /// -- ignoring indirect calls and function references. It stores this as
   /// a collection of call graph nodes. While the order of nodes in the SCC is
   /// stable, it is not any particular order.
+  ///
+  /// The SCCs are nested within a \c RefSCC, see below for details about that
+  /// outer structure. SCCs do not support mutation of the call graph, that
+  /// must be done through the containing \c RefSCC in order to fully reason
+  /// about the ordering and connections of the graph.
   class SCC {
     friend class LazyCallGraph;
     friend class LazyCallGraph::Node;
 
-    LazyCallGraph *G;
-    SmallPtrSet<SCC *, 1> ParentSCCs;
+    RefSCC *OuterRefSCC;
     SmallVector<Node *, 1> Nodes;
 
-    SCC(LazyCallGraph &G) : G(&G) {}
+    template <typename NodeRangeT>
+    SCC(RefSCC &OuterRefSCC, NodeRangeT &&Nodes)
+        : OuterRefSCC(&OuterRefSCC), Nodes(std::forward<NodeRangeT>(Nodes)) {}
+
+    void clear() {
+      OuterRefSCC = nullptr;
+      Nodes.clear();
+    }
+
+#ifndef NDEBUG
+    /// Verify invariants about the SCC.
+    ///
+    /// This will attempt to validate all of the basic invariants within an
+    /// SCC, but not that it is a strongly connected componet per-se. Primarily
+    /// useful while building and updating the graph to check that basic
+    /// properties are in place rather than having inexplicable crashes later.
+    void verify();
+#endif
 
-    void insert(Node &N);
+  public:
+    typedef pointee_iterator<SmallVectorImpl<Node *>::const_iterator> iterator;
 
-    void
-    internalDFS(SmallVectorImpl<std::pair<Node *, Node::edge_iterator>> &DFSStack,
-                SmallVectorImpl<Node *> &PendingSCCStack, Node *N,
-                SmallVectorImpl<SCC *> &ResultSCCs);
+    iterator begin() const { return Nodes.begin(); }
+    iterator end() const { return Nodes.end(); }
+
+    int size() const { return Nodes.size(); }
+
+    RefSCC &getOuterRefSCC() const { return *OuterRefSCC; }
+
+    /// Short name useful for debugging or logging.
+    ///
+    /// We use the name of the first function in the SCC to name the SCC for
+    /// the purposes of debugging and logging.
+    StringRef getName() const { return begin()->getFunction().getName(); }
+  };
+
+  /// A RefSCC of the call graph.
+  ///
+  /// This models a Strongly Connected Component of function reference edges in
+  /// the call graph. As opposed to actual SCCs, these can be used to scope
+  /// subgraphs of the module which are independent from other subgraphs of the
+  /// module because they do not reference it in any way. This is also the unit
+  /// where we do mutation of the graph in order to restrict mutations to those
+  /// which don't violate this independence.
+  ///
+  /// A RefSCC contains a DAG of actual SCCs. All the nodes within the RefSCC
+  /// are necessarily within some actual SCC that nests within it. Since
+  /// a direct call *is* a reference, there will always be at least one RefSCC
+  /// around any SCC.
+  class RefSCC {
+    friend class LazyCallGraph;
+    friend class LazyCallGraph::Node;
+
+    LazyCallGraph *G;
+    SmallPtrSet<RefSCC *, 1> Parents;
+
+    /// A postorder list of the inner SCCs.
+    SmallVector<SCC *, 4> SCCs;
+
+    /// A map from SCC to index in the postorder list.
+    SmallDenseMap<SCC *, int, 4> SCCIndices;
+
+    /// Fast-path constructor. RefSCCs should instead be constructed by calling
+    /// formRefSCCFast on the graph itself.
+    RefSCC(LazyCallGraph &G);
+
+#ifndef NDEBUG
+    /// Verify invariants about the RefSCC and all its SCCs.
+    ///
+    /// This will attempt to validate all of the invariants *within* the
+    /// RefSCC, but not that it is a strongly connected component of the larger
+    /// graph. This makes it useful even when partially through an update.
+    ///
+    /// Invariants checked:
+    /// - SCCs and their indices match.
+    /// - The SCCs list is in fact in post-order.
+    void verify();
+#endif
 
   public:
-    typedef SmallVectorImpl<Node *>::const_iterator iterator;
-    typedef pointee_iterator<SmallPtrSet<SCC *, 1>::const_iterator>
+    typedef pointee_iterator<SmallVectorImpl<SCC *>::const_iterator> iterator;
+    typedef iterator_range<iterator> range;
+    typedef pointee_iterator<SmallPtrSetImpl<RefSCC *>::const_iterator>
         parent_iterator;
 
-    iterator begin() const { return Nodes.begin(); }
-    iterator end() const { return Nodes.end(); }
+    iterator begin() const { return SCCs.begin(); }
+    iterator end() const { return SCCs.end(); }
 
-    parent_iterator parent_begin() const { return ParentSCCs.begin(); }
-    parent_iterator parent_end() const { return ParentSCCs.end(); }
+    ssize_t size() const { return SCCs.size(); }
+
+    SCC &operator[](int Idx) { return *SCCs[Idx]; }
+
+    iterator find(SCC &C) const {
+      return SCCs.begin() + SCCIndices.find(&C)->second;
+    }
+
+    parent_iterator parent_begin() const { return Parents.begin(); }
+    parent_iterator parent_end() const { return Parents.end(); }
 
     iterator_range<parent_iterator> parents() const {
       return make_range(parent_begin(), parent_end());
     }
 
     /// Test if this SCC is a parent of \a C.
-    bool isParentOf(const SCC &C) const { return C.isChildOf(*this); }
+    bool isParentOf(const RefSCC &C) const { return C.isChildOf(*this); }
 
-    /// Test if this SCC is an ancestor of \a C.
-    bool isAncestorOf(const SCC &C) const { return C.isDescendantOf(*this); }
+    /// Test if this RefSCC is an ancestor of \a C.
+    bool isAncestorOf(const RefSCC &C) const { return C.isDescendantOf(*this); }
 
-    /// Test if this SCC is a child of \a C.
-    bool isChildOf(const SCC &C) const {
-      return ParentSCCs.count(const_cast<SCC *>(&C));
+    /// Test if this RefSCC is a child of \a C.
+    bool isChildOf(const RefSCC &C) const {
+      return Parents.count(const_cast<RefSCC *>(&C));
     }
 
-    /// Test if this SCC is a descendant of \a C.
-    bool isDescendantOf(const SCC &C) const;
+    /// Test if this RefSCC is a descendant of \a C.
+    bool isDescendantOf(const RefSCC &C) const;
 
     /// Short name useful for debugging or logging.
     ///
     /// We use the name of the first function in the SCC to name the SCC for
     /// the purposes of debugging and logging.
-    StringRef getName() const { return (*begin())->getFunction().getName(); }
+    StringRef getName() const {
+      return begin()->begin()->getFunction().getName();
+    }
 
     ///@{
     /// \name Mutation API
     ///
     /// These methods provide the core API for updating the call graph in the
     /// presence of a (potentially still in-flight) DFS-found SCCs.
     ///
     /// Note that these methods sometimes have complex runtimes, so be careful
     /// how you call them.
 
-    /// Insert an edge from one node in this SCC to another in this SCC.
+    /// Make an existing internal ref edge into a call edge.
     ///
-    /// By the definition of an SCC, this does not change the nature or make-up
-    /// of any SCCs.
-    void insertIntraSCCEdge(Node &ParentN, Node &ChildN, Edge::Kind EK);
-
-    /// Insert an edge whose tail is in this SCC and head is in some child SCC.
-    ///
-    /// There must be an existing path from the caller to the callee. This
-    /// operation is inexpensive and does not change the set of SCCs in the
-    /// graph.
-    void insertOutgoingEdge(Node &ParentN, Node &ChildN, Edge::Kind EK);
-
-    /// Insert an edge whose tail is in a descendant SCC and head is in this
-    /// SCC.
-    ///
-    /// There must be an existing path from the callee to the caller in this
-    /// case. NB! This is has the potential to be a very expensive function. It
-    /// inherently forms a cycle in the prior SCC DAG and we have to merge SCCs
-    /// to resolve that cycle. But finding all of the SCCs which participate in
-    /// the cycle can in the worst case require traversing every SCC in the
-    /// graph. Every attempt is made to avoid that, but passes must still
-    /// exercise caution calling this routine repeatedly.
+    /// This may form a larger cycle and thus collapse SCCs into TargetN's SCC.
+    /// If that happens, the deleted SCC pointers are returned. These SCCs are
+    /// not in a valid state any longer but the pointers will remain valid
+    /// until destruction of the parent graph instance for the purpose of
+    /// clearing cached information.
+    ///
+    /// After this operation, both SourceN's SCC and TargetN's SCC may move
+    /// position within this RefSCC's postorder list. Any SCCs merged are
+    /// merged into the TargetN's SCC in order to preserve reachability analyses
+    /// which took place on that SCC.
+    SmallVector<SCC *, 1> switchInternalEdgeToCall(Node &SourceN,
+                                                   Node &TargetN);
+
+    /// Make an existing internal call edge into a ref edge.
+    ///
+    /// If SourceN and TargetN are part of a single SCC, it may be split up due
+    /// to breaking a cycle in the call edges that formed it. If that happens,
+    /// then this routine will insert new SCCs into the postorder list *before*
+    /// the SCC of TargetN (previously the SCC of both). This preserves
+    /// postorder as the TargetN can reach all of the other nodes by definition
+    /// of previously being in a single SCC formed by the cycle from SourceN to
+    /// TargetN. The newly added nodes are added *immediately* and contiguously
+    /// prior to the TargetN SCC and so they may be iterated starting from
+    /// there.
+    void switchInternalEdgeToRef(Node &SourceN, Node &TargetN);
+
+    /// Make an existing outgoing ref edge into a call edge.
+    ///
+    /// Note that this is trivial as there are no cyclic impacts and there
+    /// remains a reference edge.
+    void switchOutgoingEdgeToCall(Node &SourceN, Node &TargetN);
+
+    /// Make an existing outgoing call edge into a ref edge.
+    ///
+    /// This is trivial as there are no cyclic impacts and there remains
+    /// a reference edge.
+    void switchOutgoingEdgeToRef(Node &SourceN, Node &TargetN);
+
+    /// Insert a ref edge from one node in this RefSCC to another in this
+    /// RefSCC.
+    ///
+    /// This is always a trivial operation as it doesn't change any part of the
+    /// graph structure besides connecting the two nodes.
+    ///
+    /// Note that we don't support directly inserting internal *call* edges
+    /// because that could change the graph structure and requires returning
+    /// information about what became invalid. As a consequence, the pattern
+    /// should be to first insert the necessary ref edge, and then to switch it
+    /// to a call edge if needed and handle any invalidation that results. See
+    /// the \c switchInternalEdgeToCall routine for details.
+    void insertInternalRefEdge(Node &SourceN, Node &TargetN);
+
+    /// Insert an edge whose parent is in this RefSCC and child is in some
+    /// child RefSCC.
+    ///
+    /// There must be an existing path from the \p SourceN to the \p TargetN.
+    /// This operation is inexpensive and does not change the set of SCCs and
+    /// RefSCCs in the graph.
+    void insertOutgoingEdge(Node &SourceN, Node &TargetN, Edge::Kind EK);
+
+    /// Insert an edge whose source is in a descendant RefSCC and target is in
+    /// this RefSCC.
+    ///
+    /// There must be an existing path from the target to the source in this
+    /// case.
+    ///
+    /// NB! This is has the potential to be a very expensive function. It
+    /// inherently forms a cycle in the prior RefSCC DAG and we have to merge
+    /// RefSCCs to resolve that cycle. But finding all of the RefSCCs which
+    /// participate in the cycle can in the worst case require traversing every
+    /// RefSCC in the graph. Every attempt is made to avoid that, but passes
+    /// must still exercise caution calling this routine repeatedly.
+    ///
+    /// Also note that this can only insert ref edges. In order to insert
+    /// a call edge, first insert a ref edge and then switch it to a call edge.
+    /// These are intentionally kept as separate interfaces because each step
+    /// of the operation invalidates a different set of data structures.
+    ///
+    /// This returns all the RefSCCs which were merged into the this RefSCC
+    /// (the target's). This allows callers to invalidate any cached
+    /// information.
     ///
     /// FIXME: We could possibly optimize this quite a bit for cases where the
     /// caller and callee are very nearby in the graph. See comments in the
     /// implementation for details, but that use case might impact users.
-    SmallVector<SCC *, 1> insertIncomingEdge(Node &ParentN, Node &ChildN,
-                                             Edge::Kind EK);
+    SmallVector<RefSCC *, 1> insertIncomingRefEdge(Node &SourceN,
+                                                   Node &TargetN);
 
-    /// Remove an edge whose source is in this SCC and target is *not*.
+    /// Remove an edge whose source is in this RefSCC and target is *not*.
     ///
-    /// This removes an inter-SCC edge. All inter-SCC edges originating from
-    /// this SCC have been fully explored by any in-flight DFS SCC formation,
-    /// so this is always safe to call once you have the source SCC.
-    ///
-    /// This operation does not change the set of SCCs or the members of the
-    /// SCCs and so is very inexpensive. It may change the connectivity graph
-    /// of the SCCs though, so be careful calling this while iterating over
-    /// them.
-    void removeInterSCCEdge(Node &ParentN, Node &ChildN);
-
-    /// Remove an edge which is entirely within this SCC.
-    ///
-    /// Both the \a ParentN and the \a ChildN must be within this SCC. Removing
-    /// such an edge make break cycles that form this SCC and thus this
-    /// operation may change the SCC graph significantly. In particular, this
-    /// operation will re-form new SCCs based on the remaining connectivity of
-    /// the graph. The following invariants are guaranteed to hold after
-    /// calling this method:
-    ///
-    /// 1) This SCC is still an SCC in the graph.
-    /// 2) This SCC will be the parent of any new SCCs. Thus, this SCC is
-    ///    preserved as the root of any new SCC directed graph formed.
-    /// 3) No SCC other than this SCC has its member set changed (this is
+    /// This removes an inter-RefSCC edge. All inter-RefSCC edges originating
+    /// from this SCC have been fully explored by any in-flight DFS graph
+    /// formation, so this is always safe to call once you have the source
+    /// RefSCC.
+    ///
+    /// This operation does not change the cyclic structure of the graph and so
+    /// is very inexpensive. It may change the connectivity graph of the SCCs
+    /// though, so be careful calling this while iterating over them.
+    void removeOutgoingEdge(Node &SourceN, Node &TargetN);
+
+    /// Remove a ref edge which is entirely within this RefSCC.
+    ///
+    /// Both the \a SourceN and the \a TargetN must be within this RefSCC.
+    /// Removing such an edge may break cycles that form this RefSCC and thus
+    /// this operation may change the RefSCC graph significantly. In
+    /// particular, this operation will re-form new RefSCCs based on the
+    /// remaining connectivity of the graph. The following invariants are
+    /// guaranteed to hold after calling this method:
+    ///
+    /// 1) This RefSCC is still a RefSCC in the graph.
+    /// 2) This RefSCC will be the parent of any new RefSCCs. Thus, this RefSCC
+    ///    is preserved as the root of any new RefSCC DAG formed.
+    /// 3) No RefSCC other than this RefSCC has its member set changed (this is
     ///    inherent in the definition of removing such an edge).
-    /// 4) All of the parent links of the SCC graph will be updated to reflect
-    ///    the new SCC structure.
-    /// 5) All SCCs formed out of this SCC, excluding this SCC, will be
-    ///    returned in a vector.
-    /// 6) The order of the SCCs in the vector will be a valid postorder
-    ///    traversal of the new SCCs.
+    /// 4) All of the parent links of the RefSCC graph will be updated to
+    ///    reflect the new RefSCC structure.
+    /// 5) All RefSCCs formed out of this RefSCC, excluding this RefSCC, will
+    ///    be returned in post-order.
+    /// 6) The order of the RefSCCs in the vector will be a valid postorder
+    ///    traversal of the new RefSCCs.
     ///
     /// These invariants are very important to ensure that we can build
-    /// optimization pipeliens on top of the CGSCC pass manager which
-    /// intelligently update the SCC graph without invalidating other parts of
-    /// the SCC graph.
+    /// optimization pipelines on top of the CGSCC pass manager which
+    /// intelligently update the RefSCC graph without invalidating other parts
+    /// of the RefSCC graph.
+    ///
+    /// Note that we provide no routine to remove a *call* edge. Instead, you
+    /// must first switch it to a ref edge using \c switchInternalEdgeToRef.
+    /// This split API is intentional as each of these two steps can invalidate
+    /// a different aspect of the graph structure and needs to have the
+    /// invalidation handled independently.
     ///
     /// The runtime complexity of this method is, in the worst case, O(V+E)
-    /// where V is the number of nodes in this SCC and E is the number of edges
-    /// leaving the nodes in this SCC. Note that E includes both edges within
-    /// this SCC and edges from this SCC to child SCCs. Some effort has been
-    /// made to minimize the overhead of common cases such as self-edges and
-    /// edge removals which result in a spanning tree with no more cycles.
-    SmallVector<SCC *, 1> removeIntraSCCEdge(Node &ParentN, Node &ChildN);
+    /// where V is the number of nodes in this RefSCC and E is the number of
+    /// edges leaving the nodes in this RefSCC. Note that E includes both edges
+    /// within this RefSCC and edges from this RefSCC to child RefSCCs. Some
+    /// effort has been made to minimize the overhead of common cases such as
+    /// self-edges and edge removals which result in a spanning tree with no
+    /// more cycles. There are also detailed comments within the implementation
+    /// on techniques which could substantially improve this routine's
+    /// efficiency.
+    SmallVector<RefSCC *, 1> removeInternalRefEdge(Node &SourceN,
+                                                   Node &TargetN);
 
     ///@}
   };
 
   /// A post-order depth-first SCC iterator over the call graph.
   ///
   /// This iterator triggers the Tarjan DFS-based formation of the SCC DAG for
   /// the call graph, walking it lazily in depth-first post-order. That is, it
   /// always visits SCCs for a callee prior to visiting the SCC for a caller
   /// (when they are in different SCCs).
-  class postorder_scc_iterator
-      : public iterator_facade_base<postorder_scc_iterator,
-                                    std::forward_iterator_tag, SCC> {
+  class postorder_ref_scc_iterator
+      : public iterator_facade_base<postorder_ref_scc_iterator,
+                                    std::forward_iterator_tag, RefSCC> {
     friend class LazyCallGraph;
     friend class LazyCallGraph::Node;
 
     /// Nonce type to select the constructor for the end iterator.
     struct IsAtEndT {};
 
     LazyCallGraph *G;
-    SCC *C;
+    RefSCC *C;
 
     // Build the begin iterator for a node.
-    postorder_scc_iterator(LazyCallGraph &G) : G(&G) {
-      C = G.getNextSCCInPostOrder();
+    postorder_ref_scc_iterator(LazyCallGraph &G) : G(&G) {
+      C = G.getNextRefSCCInPostOrder();
     }
 
     // Build the end iterator for a node. This is selected purely by overload.
-    postorder_scc_iterator(LazyCallGraph &G, IsAtEndT /*Nonce*/)
+    postorder_ref_scc_iterator(LazyCallGraph &G, IsAtEndT /*Nonce*/)
         : G(&G), C(nullptr) {}
 
   public:
-    bool operator==(const postorder_scc_iterator &Arg) const {
+    bool operator==(const postorder_ref_scc_iterator &Arg) const {
       return G == Arg.G && C == Arg.C;
     }
 
     reference operator*() const { return *C; }
 
     using iterator_facade_base::operator++;
-    postorder_scc_iterator &operator++() {
-      C = G->getNextSCCInPostOrder();
+    postorder_ref_scc_iterator &operator++() {
+      C = G->getNextRefSCCInPostOrder();
       return *this;
     }
   };
 
   /// Construct a graph for the given module.
   ///
   /// This sets up the graph and computes all of the entry points of the graph.
   /// No function definitions are scanned until their nodes in the graph are
   /// requested during traversal.
   LazyCallGraph(Module &M);
 
   LazyCallGraph(LazyCallGraph &&G);
   LazyCallGraph &operator=(LazyCallGraph &&RHS);
 
   edge_iterator begin() {
     return edge_iterator(EntryEdges.begin(), EntryEdges.end());
   }
   edge_iterator end() {
     return edge_iterator(EntryEdges.end(), EntryEdges.end());
   }
 
-  postorder_scc_iterator postorder_scc_begin() {
-    return postorder_scc_iterator(*this);
+  postorder_ref_scc_iterator postorder_ref_scc_begin() {
+    return postorder_ref_scc_iterator(*this);
   }
-  postorder_scc_iterator postorder_scc_end() {
-    return postorder_scc_iterator(*this, postorder_scc_iterator::IsAtEndT());
+  postorder_ref_scc_iterator postorder_ref_scc_end() {
+    return postorder_ref_scc_iterator(*this,
+                                      postorder_ref_scc_iterator::IsAtEndT());
   }
 
-  iterator_range<postorder_scc_iterator> postorder_sccs() {
-    return make_range(postorder_scc_begin(), postorder_scc_end());
+  iterator_range<postorder_ref_scc_iterator> postorder_ref_sccs() {
+    return make_range(postorder_ref_scc_begin(), postorder_ref_scc_end());
   }
 
   /// Lookup a function in the graph which has already been scanned and added.
   Node *lookup(const Function &F) const { return NodeMap.lookup(&F); }
 
   /// Lookup a function's SCC in the graph.
   ///
   /// \returns null if the function hasn't been assigned an SCC via the SCC
   /// iterator walk.
   SCC *lookupSCC(Node &N) const { return SCCMap.lookup(&N); }
 
+  /// Lookup a function's RefSCC in the graph.
+  ///
+  /// \returns null if the function hasn't been assigned a RefSCC via the
+  /// RefSCC iterator walk.
+  RefSCC *lookupRefSCC(Node &N) const {
+    if (SCC *C = lookupSCC(N))
+      return &C->getOuterRefSCC();
+
+    return nullptr;
+  }
+
   /// Get a graph node for a given function, scanning it to populate the graph
   /// data as necessary.
   Node &get(Function &F) {
     Node *&N = NodeMap[&F];
     if (N)
       return *N;
 
     return insertInto(F, N);
#endif
   /// Update the call graph after deleting an edge.
   void removeEdge(Function &Caller, Function &Callee) {
     return removeEdge(get(Caller), Callee);
   }
 
   ///@}
 
 private:
+  typedef SmallVectorImpl<Node *>::reverse_iterator node_stack_iterator;
+  typedef iterator_range<node_stack_iterator> node_stack_range;
+
   /// Allocator that holds all the call graph nodes.
   SpecificBumpPtrAllocator<Node> BPA;
 
   /// Maps function->node for fast lookup.
   DenseMap<const Function *, Node *> NodeMap;
 
   /// The entry nodes to the graph.
   ///
   /// These nodes are reachable through "external" means. Put another way, they
   /// escape at the module scope.
   EdgeVectorT EntryEdges;
 
   /// Map of the entry nodes in the graph to their indices in \c EntryEdges.
-  DenseMap<Function *, size_t> EntryIndexMap;
+  DenseMap<Function *, int> EntryIndexMap;
 
   /// Allocator that holds all the call graph SCCs.
   SpecificBumpPtrAllocator<SCC> SCCBPA;
 
   /// Maps Function -> SCC for fast lookup.
   DenseMap<Node *, SCC *> SCCMap;
 
-  /// The leaf SCCs of the graph.
+  /// Allocator that holds all the call graph RefSCCs.
+  SpecificBumpPtrAllocator<RefSCC> RefSCCBPA;
+
+  /// The leaf RefSCCs of the graph.
   ///
-  /// These are all of the SCCs which have no children.
-  SmallVector<SCC *, 4> LeafSCCs;
+  /// These are all of the RefSCCs which have no children.
+  SmallVector<RefSCC *, 4> LeafRefSCCs;
 
   /// Stack of nodes in the DFS walk.
   SmallVector<std::pair<Node *, edge_iterator>, 4> DFSStack;
 
-  /// Set of entry nodes not-yet-processed into SCCs.
-  SmallVector<Function *, 4> SCCEntryNodes;
+  /// Set of entry nodes not-yet-processed into RefSCCs.
+  SmallVector<Function *, 4> RefSCCEntryNodes;
 
   /// Stack of nodes the DFS has walked but not yet put into a SCC.
-  SmallVector<Node *, 4> PendingSCCStack;
+  SmallVector<Node *, 4> PendingRefSCCStack;
 
   /// Counter for the next DFS number to assign.
   int NextDFSNumber;
 
   /// Helper to insert a new function, with an already looked-up entry in
   /// the NodeMap.
   Node &insertInto(Function &F, Node *&MappedN);
 
   /// Helper to update pointers back to the graph object during moves.
   void updateGraphPtrs();
 
-  /// Helper to form a new SCC out of the top of a DFSStack-like
-  /// structure.
-  SCC *formSCC(Node *RootN, SmallVectorImpl<Node *> &NodeStack);
+  /// Allocates an SCC and constructs it using the graph allocator.
+  ///
+  /// The arguments are forwarded to the constructor.
+  template <typename... Ts> SCC *createSCC(Ts &&... Args) {
+    return new (SCCBPA.Allocate()) SCC(std::forward<Ts>(Args)...);
+  }
+
+  /// Allocates a RefSCC and constructs it using the graph allocator.
+  ///
+  /// The arguments are forwarded to the constructor.
+  template <typename... Ts> RefSCC *createRefSCC(Ts &&... Args) {
+    return new (RefSCCBPA.Allocate()) RefSCC(std::forward<Ts>(Args)...);
+  }
+
+  /// Build the SCCs for a RefSCC out of a list of nodes.
+  void buildSCCs(RefSCC &RC, node_stack_range Nodes);
+
+  /// Connect a RefSCC into the larger graph.
+  ///
+  /// This walks the edges to connect the RefSCC to its children's parent set,
+  /// and updates the root leaf list.
+  void connectRefSCC(RefSCC &RC);
 
-  /// Retrieve the next node in the post-order SCC walk of the call graph.
-  SCC *getNextSCCInPostOrder();
+  /// Retrieve the next node in the post-order RefSCC walk of the call graph.
+  RefSCC *getNextRefSCCInPostOrder();
 };
 
 inline LazyCallGraph::Edge::Edge() : Value() {}
 inline LazyCallGraph::Edge::Edge(Function &F, Kind K) : Value(&F, K) {}
 inline LazyCallGraph::Edge::Edge(Node &N, Kind K) : Value(&N, K) {}
 
 inline LazyCallGraph::Edge::operator bool() const {
   return !Value.getPointer().isNull();

lib/Analysis/LazyCallGraph.cpp

 #include "llvm/Support/Debug.h"
 #include "llvm/Support/raw_ostream.h"
 
 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
   // 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.
   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,
+static void findReferences(SmallVectorImpl<Constant *> &Worklist,
                            SmallPtrSetImpl<Constant *> &Visited,
                            SmallVectorImpl<LazyCallGraph::Edge> &Edges,
-                      DenseMap<Function *, size_t> &EdgeIndexMap) {
+                           DenseMap<Function *, int> &EdgeIndexMap) {
   while (!Worklist.empty()) {
     Constant *C = Worklist.pop_back_val();
 
     if (Function *F = dyn_cast<Function>(C)) {
       addEdge(Edges, EdgeIndexMap, *F, LazyCallGraph::Edge::Ref);
       continue;
     }
 
for (BasicBlock &BB : F)
     }
 
   // 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.
   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);
 }
 
 LazyCallGraph::LazyCallGraph(Module &M) : NextDFSNumber(0) {
   DEBUG(dbgs() << "Building CG for module: " << M.getModuleIdentifier()
                << "\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);
       }
 
   // 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");
   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();
 }
 
 LazyCallGraph &LazyCallGraph::operator=(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);
+  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
+
+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::SCC::isDescendantOf(const SCC &C) const {
+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;
 
-  assert(G->SCCMap.lookup(&ParentN) == this && "Parent must be in this SCC.");
-  assert(G->SCCMap.lookup(&ChildN) == this && "Child must be in this SCC.");
+  SCC &SourceSCC = *G->lookupSCC(SourceN);
+  SCC &TargetSCC = *G->lookupSCC(TargetN);
 
-  // Nothing changes about this SCC or any other.
+  // 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;
   }
 
-void LazyCallGraph::SCC::insertOutgoingEdge(Node &ParentN, Node &ChildN,
-                                            Edge::Kind EK) {
-  // First insert it into the caller.
-  ParentN.insertEdgeInternal(ChildN, EK);
+  // 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;
+  }
 
-  assert(G->SCCMap.lookup(&ParentN) == this && "Parent must be in this SCC.");
+  // 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;
+      }
 
-  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.");
+    return false;
+  };
 
-  // The only change required is to add this SCC to the parent set of the
-  // callee.
-  ChildC.ParentSCCs.insert(this);
+  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;
   }
 
-SmallVector<LazyCallGraph::SCC *, 1>
-LazyCallGraph::SCC::insertIncomingEdge(Node &ParentN, Node &ChildN,
+  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::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->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
+
+  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.");
 
-  assert(G->SCCMap.lookup(&ChildN) == this && "Child must be in this SCC.");
+  // The only change required is to add this SCC to the parent set of the
+  // callee.
+  TargetC.Parents.insert(this);
 
-  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.");
+#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 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;
+
+  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);
-    }
-
-    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();
+      Visited.insert(C);
     }
+  } 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);
-      }
-      G->SCCMap[N] = this;
-      Nodes.push_back(N);
-    }
-    C->Nodes.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);
+  // 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);
         }
+      }
+    }
+
+    // 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();
+  }
+
+  // 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) {
-  // First remove it from the node.
-  ParentN.removeEdgeInternal(ChildN.getFunction());
+void LazyCallGraph::RefSCC::removeOutgoingEdge(Node &SourceN, Node &TargetN) {
+  assert(G->lookupRefSCC(SourceN) == this &&
+         "The source must be a member of this RefSCC.");
 
-  assert(G->SCCMap.lookup(&ParentN) == this &&
-         "The caller must be a member of this SCC.");
+  RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
+  assert(&TargetRC != this && "The target must not be a member of this RefSCC");
 
-  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(std::find(G->LeafRefSCCs.begin(), G->LeafRefSCCs.end(), this) ==
+             G->LeafRefSCCs.end() &&
+         "Cannot have a leaf RefSCC source.");
+
+  // First remove it from the node.
+  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!");
-      SCC &OtherChildC = *G->SCCMap.lookup(E.getNode());
-      if (&OtherChildC == &ChildC) {
-        HasOtherEdgeToChildC = true;
+        RefSCC &OtherChildRC = *G->lookupRefSCC(*E.getNode());
+        if (&OtherChildRC == &TargetRC) {
+          HasOtherEdgeToChildRC = true;
           break;
         }
-      if (&OtherChildC != this)
-        HasOtherChildC = true;
+        if (&OtherChildRC != this)
+          HasOtherChildRC = 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 Source SCC a leaf SCC.
+    if (!HasOtherChildRC)
+      G->LeafRefSCCs.push_back(this);
+  }
 
-  // It may make the Parent SCC a leaf SCC.
-  if (!HasOtherChildC)
-    G->LeafSCCs.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");
+
+  // First remove the actual edge.
+  SourceN.removeEdgeInternal(TargetN.getFunction());
+
+  // 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;
+
+  // 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;
+
+    for (Node &N : *C)
+      N.DFSNumber = N.LowLink = 0;
+
+    Worklist.append(C->Nodes.begin(), C->Nodes.end());
   }
 
-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;
+  auto MarkNodeForSCCNumber = [&PostOrderMapping](Node &N, int Number) {
+    N.DFSNumber = N.LowLink = -1;
+    PostOrderMapping[&N] = Number;
+  };
+
+  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;
+    }
+
+    RootN->DFSNumber = RootN->LowLink = 1;
     int NextDFSNumber = 2;
-  for (;;) {
+
+    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.");
 
-    // 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;
-        }
-
-        // 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;
-      }
-
         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));
+          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;
 
-    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);
-
-      assert(!DFSStack.empty() && "We shouldn't have an empty stack!");
-    }
-
-    N = DFSStack.back().first;
-    I = DFSStack.back().second;
-    DFSStack.pop_back();
-  }
-}
-
-SmallVector<LazyCallGraph::SCC *, 1>
-LazyCallGraph::SCC::removeIntraSCCEdge(Node &ParentN, Node &ChildN) {
-  // First remove it from the node.
-  ParentN.removeEdgeInternal(ChildN.getFunction());
-
-  // We return a list of the resulting *new* SCCs in postorder.
-  SmallVector<SCC *, 1> ResultSCCs;
-
-  // Direct recursion doesn't impact the SCC graph at all.
-  if (&ParentN == &ChildN)
-    return ResultSCCs;
-
-  // 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);
+      // 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;
       }
-  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);
+      // 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) {
+  // 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!");
-      SCC &ChildSCC = *G->SCCMap.lookup(E.getNode());
-      if (&ChildSCC == this)
+        RefSCC &ChildRC = *G->lookupRefSCC(*E.getNode());
+        if (&ChildRC == this)
           continue;
-      ChildSCC.ParentSCCs.insert(this);
-      IsLeafSCC = false;
+        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 "
+  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 "
 #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) {
   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)
       if (Node *EntryN = E.getNode())
         Worklist.push_back(EntryN);
 
     while (!Worklist.empty()) {
       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;
+  }
+
+  // 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;
     }
-  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)
+    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;
-      ChildSCC.ParentSCCs.insert(NewSCC);
-      IsLeafSCC = false;
         }
 
-  // For the SCCs where we fine no child SCCs, add them to the leaf list.
-  if (IsLeafSCC)
-    LeafSCCs.push_back(NewSCC);
+        // 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;
 
-  return NewSCC;
+      // 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());
+  }
+
+  // Wire up the SCC indices.
+  for (int i = 0, Size = RC.SCCs.size(); i < Size; ++i)
+    RC.SCCIndices[RC.SCCs[i]] = i;
+}
+
+// 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;
       }
 
-LazyCallGraph::SCC *LazyCallGraph::getNextSCCInPostOrder() {
+  // 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;
-  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.
     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 "
 
     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;
       }
 
-      // 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)
+      // 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;
     }
 
-    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);
+    // 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;
+    }
 
-    assert(!DFSStack.empty() && "We never found a viable root!");
-    N = DFSStack.back().first;
-    I = DFSStack.back().second;
-    DFSStack.pop_back();
+    // 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;
   }
 }
 
 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 ") << " -> "
        << E.getFunction().getName() << "\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 : SCC)
-    OS << "    " << N->getFunction().getName() << "\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";
 
-  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();
 }

test/Analysis/LazyCallGraph/basic.ll

; CHECK-NOT: ->
 
   load i8*, i8** bitcast (void ()** @g to i8**)
   load i8*, i8** bitcast (void ()** getelementptr ([4 x void ()*], [4 x void ()*]* @g1, i32 0, i32 2) to i8**)
   load i8*, i8** bitcast (void ()** getelementptr ({i8, void ()*, i8}, {i8, void ()*, i8}* @g2, i32 0, i32 1) to i8**)
   load i8*, i8** bitcast (void ()** @h to i8**)
   ret void
 }
 
+@test3_ptr = external global void ()*
+
+define void @test3_aa1() {
+; CHECK-LABEL: Edges in function: test3_aa1
+; CHECK-NEXT: call -> test3_aa2
+; CHECK-NEXT: ref -> test3_ab1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_aa2()
+  store void ()* @test3_ab1, void ()** @test3_ptr
+  ret void
+}
+
+define void @test3_aa2() {
+; CHECK-LABEL: Edges in function: test3_aa2
+; CHECK-NEXT: call -> test3_aa1
+; CHECK-NEXT: call -> test3_ab2
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_aa1()
+  call void @test3_ab2()
+  ret void
+}
+
+define void @test3_ab1() {
+; CHECK-LABEL: Edges in function: test3_ab1
+; CHECK-NEXT: call -> test3_ab2
+; CHECK-NEXT: call -> test3_ac1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ab2()
+  call void @test3_ac1()
+  ret void
+}
+
+define void @test3_ab2() {
+; CHECK-LABEL: Edges in function: test3_ab2
+; CHECK-NEXT: call -> test3_ab1
+; CHECK-NEXT: call -> test3_ba1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ab1()
+  call void @test3_ba1()
+  ret void
+}
+
+define void @test3_ac1() {
+; CHECK-LABEL: Edges in function: test3_ac1
+; CHECK-NEXT: call -> test3_ac2
+; CHECK-NEXT: ref -> test3_aa2
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ac2()
+  store void ()* @test3_aa2, void ()** @test3_ptr
+  ret void
+}
+
+define void @test3_ac2() {
+; CHECK-LABEL: Edges in function: test3_ac2
+; CHECK-NEXT: call -> test3_ac1
+; CHECK-NEXT: ref -> test3_ba1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ac1()
+  store void ()* @test3_ba1, void ()** @test3_ptr
+  ret void
+}
+
+define void @test3_ba1() {
+; CHECK-LABEL: Edges in function: test3_ba1
+; CHECK-NEXT: call -> test3_bb1
+; CHECK-NEXT: ref -> test3_ca1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_bb1()
+  store void ()* @test3_ca1, void ()** @test3_ptr
+  ret void
+}
+
+define void @test3_bb1() {
+; CHECK-LABEL: Edges in function: test3_bb1
+; CHECK-NEXT: call -> test3_ca2
+; CHECK-NEXT: ref -> test3_ba1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ca2()
+  store void ()* @test3_ba1, void ()** @test3_ptr
+  ret void
+}
+
+define void @test3_ca1() {
+; CHECK-LABEL: Edges in function: test3_ca1
+; CHECK-NEXT: call -> test3_ca2
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ca2()
+  ret void
+}
+
+define void @test3_ca2() {
+; CHECK-LABEL: Edges in function: test3_ca2
+; CHECK-NEXT: call -> test3_ca3
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ca3()
+  ret void
+}
+
+define void @test3_ca3() {
+; CHECK-LABEL: Edges in function: test3_ca3
+; CHECK-NEXT: call -> test3_ca1
+; CHECK-NOT: ->
+
+entry:
+  call void @test3_ca1()
+  ret void
+}
+
 ; Verify the SCCs formed.
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f7
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 3 functions:
+; CHECK-NEXT:      test3_ca3
+; CHECK-NEXT:      test3_ca1
+; CHECK-NEXT:      test3_ca2
+;
+; CHECK-LABEL: RefSCC with 2 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      test3_bb1
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      test3_ba1
+;
+; CHECK-LABEL: RefSCC with 3 call SCCs:
+; CHECK-NEXT:    SCC with 2 functions:
+; CHECK-NEXT:      test3_ac2
+; CHECK-NEXT:      test3_ac1
+; CHECK-NEXT:    SCC with 2 functions:
+; CHECK-NEXT:      test3_ab2
+; CHECK-NEXT:      test3_ab1
+; CHECK-NEXT:    SCC with 2 functions:
+; CHECK-NEXT:      test3_aa2
+; CHECK-NEXT:      test3_aa1
+;
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f7
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f6
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f6
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f5
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f5
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f4
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f4
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f3
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f3
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f2
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f2
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f1
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f1
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    test2
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      test2
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f10
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f10
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f12
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f12
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f11
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f11
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f9
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f9
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f8
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f8
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    test1
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      test1
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    f
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      f
 ;
-; CHECK-LABEL: SCC with 1 functions:
-; CHECK-NEXT:    test0
+; CHECK-LABEL: RefSCC with 1 call SCCs:
+; CHECK-NEXT:    SCC with 1 functions:
+; CHECK-NEXT:      test0

unittests/Analysis/LazyCallGraphTest.cpp

TEST(LazyCallGraphTest, BasicGraphFormation) {
 
   EXPECT_EQ(D1.end(), std::next(D1.begin()));
   EXPECT_EQ("d2", D1.begin()->getFunction().getName());
   EXPECT_EQ(D2.end(), std::next(D2.begin()));
   EXPECT_EQ("d3", D2.begin()->getFunction().getName());
   EXPECT_EQ(D3.end(), std::next(D3.begin()));
   EXPECT_EQ("d1", D3.begin()->getFunction().getName());
 
-  // Now lets look at the SCCs.
-  auto SCCI = CG.postorder_scc_begin();
+  // Now lets look at the RefSCCs and SCCs.
+  auto J = CG.postorder_ref_scc_begin();
 
-  LazyCallGraph::SCC &D = *SCCI++;
-  for (LazyCallGraph::Node *N : D)
-    Nodes.push_back(N->getFunction().getName());
+  LazyCallGraph::RefSCC &D = *J++;
+  ASSERT_EQ(1, D.size());
+  for (LazyCallGraph::Node &N : *D.begin())
+    Nodes.push_back(N.getFunction().getName());
   std::sort(Nodes.begin(), Nodes.end());
   EXPECT_EQ(3u, Nodes.size());
   EXPECT_EQ("d1", Nodes[0]);
   EXPECT_EQ("d2", Nodes[1]);
   EXPECT_EQ("d3", Nodes[2]);
   Nodes.clear();
   EXPECT_FALSE(D.isParentOf(D));
   EXPECT_FALSE(D.isChildOf(D));
   EXPECT_FALSE(D.isAncestorOf(D));
   EXPECT_FALSE(D.isDescendantOf(D));
 
-  LazyCallGraph::SCC &C = *SCCI++;
-  for (LazyCallGraph::Node *N : C)
-    Nodes.push_back(N->getFunction().getName());
+  LazyCallGraph::RefSCC &C = *J++;
+  ASSERT_EQ(1, C.size());
+  for (LazyCallGraph::Node &N : *C.begin())
+    Nodes.push_back(N.getFunction().getName());
   std::sort(Nodes.begin(), Nodes.end());
   EXPECT_EQ(3u, Nodes.size());
   EXPECT_EQ("c1", Nodes[0]);
   EXPECT_EQ("c2", Nodes[1]);
   EXPECT_EQ("c3", Nodes[2]);
   Nodes.clear();
   EXPECT_TRUE(C.isParentOf(D));
   EXPECT_FALSE(C.isChildOf(D));
   EXPECT_TRUE(C.isAncestorOf(D));
   EXPECT_FALSE(C.isDescendantOf(D));
 
-  LazyCallGraph::SCC &B = *SCCI++;
-  for (LazyCallGraph::Node *N : B)
-    Nodes.push_back(N->getFunction().getName());
+  LazyCallGraph::RefSCC &B = *J++;
+  ASSERT_EQ(1, B.size());
+  for (LazyCallGraph::Node &N : *B.begin())
+    Nodes.push_back(N.getFunction().getName());
   std::sort(Nodes.begin(), Nodes.end());
   EXPECT_EQ(3u, Nodes.size());
   EXPECT_EQ("b1", Nodes[0]);
   EXPECT_EQ("b2", Nodes[1]);
   EXPECT_EQ("b3", Nodes[2]);
   Nodes.clear();
   EXPECT_TRUE(B.isParentOf(D));
   EXPECT_FALSE(B.isChildOf(D));
   EXPECT_TRUE(B.isAncestorOf(D));
   EXPECT_FALSE(B.isDescendantOf(D));
   EXPECT_FALSE(B.isAncestorOf(C));
   EXPECT_FALSE(C.isAncestorOf(B));
 
-  LazyCallGraph::SCC &A = *SCCI++;
-  for (LazyCallGraph::Node *N : A)
-    Nodes.push_back(N->getFunction().getName());
+  LazyCallGraph::RefSCC &A = *J++;
+  ASSERT_EQ(1, A.size());
+  for (LazyCallGraph::Node &N : *A.begin())
+    Nodes.push_back(N.getFunction().getName());
   std::sort(Nodes.begin(), Nodes.end());
   EXPECT_EQ(3u, Nodes.size());
   EXPECT_EQ("a1", Nodes[0]);
   EXPECT_EQ("a2", Nodes[1]);
   EXPECT_EQ("a3", Nodes[2]);
   Nodes.clear();
   EXPECT_TRUE(A.isParentOf(B));
   EXPECT_TRUE(A.isParentOf(C));
   EXPECT_FALSE(A.isParentOf(D));
   EXPECT_TRUE(A.isAncestorOf(B));
   EXPECT_TRUE(A.isAncestorOf(C));
   EXPECT_TRUE(A.isAncestorOf(D));
 
-  EXPECT_EQ(CG.postorder_scc_end(), SCCI);
+  EXPECT_EQ(CG.postorder_ref_scc_end(), J);
 }
 
 static Function &lookupFunction(Module &M, StringRef Name) {
   for (Function &F : M)
     if (F.getName() == Name)
       return F;
   report_fatal_error("Couldn't find function!");
 }
TEST(LazyCallGraphTest, BasicGraphMutation) {
 
   CG.removeEdge(C, C.getFunction());
   EXPECT_EQ(0, std::distance(C.begin(), C.end()));
 
   CG.removeEdge(B, C.getFunction());
   EXPECT_EQ(0, std::distance(B.begin(), B.end()));
 }
 
+TEST(LazyCallGraphTest, InnerSCCFormation) {
+  std::unique_ptr<Module> M = parseAssembly(DiamondOfTriangles);
+  LazyCallGraph CG(*M);
+
+  // Now mutate the graph to connect every node into a single RefSCC to ensure
+  // that our inner SCC formation handles the rest.
+  CG.insertEdge(lookupFunction(*M, "d1"), lookupFunction(*M, "a1"),
+                LazyCallGraph::Edge::Ref);
+
+  // Build vectors and sort them for the rest of the assertions to make them
+  // independent of order.
+  std::vector<std::string> Nodes;
+
+  // We should build a single RefSCC for the entire graph.
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
+
+  // Now walk the four SCCs which should be in post-order.
+  auto J = RC.begin();
+  LazyCallGraph::SCC &D = *J++;
+  for (LazyCallGraph::Node &N : D)
+    Nodes.push_back(N.getFunction().getName());
+  std::sort(Nodes.begin(), Nodes.end());
+  EXPECT_EQ(3u, Nodes.size());
+  EXPECT_EQ("d1", Nodes[0]);
+  EXPECT_EQ("d2", Nodes[1]);
+  EXPECT_EQ("d3", Nodes[2]);
+  Nodes.clear();
+
+  LazyCallGraph::SCC &B = *J++;
+  for (LazyCallGraph::Node &N : B)
+    Nodes.push_back(N.getFunction().getName());
+  std::sort(Nodes.begin(), Nodes.end());
+  EXPECT_EQ(3u, Nodes.size());
+  EXPECT_EQ("b1", Nodes[0]);
+  EXPECT_EQ("b2", Nodes[1]);
+  EXPECT_EQ("b3", Nodes[2]);
+  Nodes.clear();
+
+  LazyCallGraph::SCC &C = *J++;
+  for (LazyCallGraph::Node &N : C)
+    Nodes.push_back(N.getFunction().getName());
+  std::sort(Nodes.begin(), Nodes.end());
+  EXPECT_EQ(3u, Nodes.size());
+  EXPECT_EQ("c1", Nodes[0]);
+  EXPECT_EQ("c2", Nodes[1]);
+  EXPECT_EQ("c3", Nodes[2]);
+  Nodes.clear();
+
+  LazyCallGraph::SCC &A = *J++;
+  for (LazyCallGraph::Node &N : A)
+    Nodes.push_back(N.getFunction().getName());
+  std::sort(Nodes.begin(), Nodes.end());
+  EXPECT_EQ(3u, Nodes.size());
+  EXPECT_EQ("a1", Nodes[0]);
+  EXPECT_EQ("a2", Nodes[1]);
+  EXPECT_EQ("a3", Nodes[2]);
+  Nodes.clear();
+
+  EXPECT_EQ(RC.end(), J);
+}
+
 TEST(LazyCallGraphTest, MultiArmSCC) {
   // Two interlocking cycles. The really useful thing about this SCC is that it
   // will require Tarjan's DFS to backtrack and finish processing all of the
-  // children of each node in the SCC.
+  // children of each node in the SCC. Since this involves call edges, both
+  // Tarjan implementations will have to successfully navigate the structure.
   std::unique_ptr<Module> M = parseAssembly(
-      "define void @a() {\n"
+      "define void @f1() {\n"
       "entry:\n"
-      "  call void @b()\n"
-      "  call void @d()\n"
+      "  call void @f2()\n"
+      "  call void @f4()\n"
       "  ret void\n"
       "}\n"
-      "define void @b() {\n"
+      "define void @f2() {\n"
       "entry:\n"
-      "  call void @c()\n"
+      "  call void @f3()\n"
       "  ret void\n"
       "}\n"
-      "define void @c() {\n"
+      "define void @f3() {\n"
       "entry:\n"
-      "  call void @a()\n"
+      "  call void @f1()\n"
       "  ret void\n"
       "}\n"
-      "define void @d() {\n"
+      "define void @f4() {\n"
       "entry:\n"
-      "  call void @e()\n"
+      "  call void @f5()\n"
       "  ret void\n"
       "}\n"
-      "define void @e() {\n"
+      "define void @f5() {\n"
       "entry:\n"
-      "  call void @a()\n"
+      "  call void @f1()\n"
       "  ret void\n"
       "}\n");
   LazyCallGraph CG(*M);
 
   // Force the graph to be fully expanded.
-  auto SCCI = CG.postorder_scc_begin();
-  LazyCallGraph::SCC &SCC = *SCCI++;
-  EXPECT_EQ(CG.postorder_scc_end(), SCCI);
-
-  LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
-  LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
-  LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
-  LazyCallGraph::Node &D = *CG.lookup(lookupFunction(*M, "d"));
-  LazyCallGraph::Node &E = *CG.lookup(lookupFunction(*M, "e"));
-  EXPECT_EQ(&SCC, CG.lookupSCC(A));
-  EXPECT_EQ(&SCC, CG.lookupSCC(B));
-  EXPECT_EQ(&SCC, CG.lookupSCC(C));
-  EXPECT_EQ(&SCC, CG.lookupSCC(D));
-  EXPECT_EQ(&SCC, CG.lookupSCC(E));
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
+
+  LazyCallGraph::Node &N1 = *CG.lookup(lookupFunction(*M, "f1"));
+  LazyCallGraph::Node &N2 = *CG.lookup(lookupFunction(*M, "f2"));
+  LazyCallGraph::Node &N3 = *CG.lookup(lookupFunction(*M, "f3"));
+  LazyCallGraph::Node &N4 = *CG.lookup(lookupFunction(*M, "f4"));
+  LazyCallGraph::Node &N5 = *CG.lookup(lookupFunction(*M, "f4"));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(N1));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(N2));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(N3));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(N4));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(N5));
+
+  ASSERT_EQ(1, RC.size());
+
+  LazyCallGraph::SCC &C = *RC.begin();
+  EXPECT_EQ(&C, CG.lookupSCC(N1));
+  EXPECT_EQ(&C, CG.lookupSCC(N2));
+  EXPECT_EQ(&C, CG.lookupSCC(N3));
+  EXPECT_EQ(&C, CG.lookupSCC(N4));
+  EXPECT_EQ(&C, CG.lookupSCC(N5));
 }
 
-TEST(LazyCallGraphTest, OutgoingSCCEdgeInsertion) {
+TEST(LazyCallGraphTest, OutgoingEdgeMutation) {
   std::unique_ptr<Module> M = parseAssembly(
       "define void @a() {\n"
       "entry:\n"
       "  call void @b()\n"
       "  call void @c()\n"
       "  ret void\n"
       "}\n"
       "define void @b() {\n"
       "entry:\n"
       "  call void @d()\n"
       "  ret void\n"
       "}\n"
       "define void @c() {\n"
       "entry:\n"
       "  call void @d()\n"
       "  ret void\n"
       "}\n"
       "define void @d() {\n"
       "entry:\n"
       "  ret void\n"
       "}\n");
   LazyCallGraph CG(*M);
 
   // Force the graph to be fully expanded.
-  for (LazyCallGraph::SCC &C : CG.postorder_sccs())
-    (void)C;
+  for (LazyCallGraph::RefSCC &RC : CG.postorder_ref_sccs())
+    (void)RC;
 
   LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
   LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
   LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
   LazyCallGraph::Node &D = *CG.lookup(lookupFunction(*M, "d"));
   LazyCallGraph::SCC &AC = *CG.lookupSCC(A);
   LazyCallGraph::SCC &BC = *CG.lookupSCC(B);
   LazyCallGraph::SCC &CC = *CG.lookupSCC(C);
   LazyCallGraph::SCC &DC = *CG.lookupSCC(D);
-  EXPECT_TRUE(AC.isAncestorOf(BC));
-  EXPECT_TRUE(AC.isAncestorOf(CC));
-  EXPECT_TRUE(AC.isAncestorOf(DC));
-  EXPECT_TRUE(DC.isDescendantOf(AC));
-  EXPECT_TRUE(DC.isDescendantOf(BC));
-  EXPECT_TRUE(DC.isDescendantOf(CC));
+  LazyCallGraph::RefSCC &ARC = *CG.lookupRefSCC(A);
+  LazyCallGraph::RefSCC &BRC = *CG.lookupRefSCC(B);
+  LazyCallGraph::RefSCC &CRC = *CG.lookupRefSCC(C);
+  LazyCallGraph::RefSCC &DRC = *CG.lookupRefSCC(D);
+  EXPECT_TRUE(ARC.isParentOf(BRC));
+  EXPECT_TRUE(ARC.isParentOf(CRC));
+  EXPECT_FALSE(ARC.isParentOf(DRC));
+  EXPECT_TRUE(ARC.isAncestorOf(DRC));
+  EXPECT_FALSE(DRC.isChildOf(ARC));
+  EXPECT_TRUE(DRC.isDescendantOf(ARC));
+  EXPECT_TRUE(DRC.isChildOf(BRC));
+  EXPECT_TRUE(DRC.isChildOf(CRC));
 
   EXPECT_EQ(2, std::distance(A.begin(), A.end()));
-  AC.insertOutgoingEdge(A, D, LazyCallGraph::Edge::Call);
+  ARC.insertOutgoingEdge(A, D, LazyCallGraph::Edge::Call);
   EXPECT_EQ(3, std::distance(A.begin(), A.end()));
-  EXPECT_TRUE(AC.isParentOf(DC));
+  const LazyCallGraph::Edge &NewE = A[D];
+  EXPECT_TRUE(NewE);
+  EXPECT_TRUE(NewE.isCall());
+  EXPECT_EQ(&D, NewE.getNode());
+
+  // Only the parent and child tests sholud have changed. The rest of the graph
+  // remains the same.
+  EXPECT_TRUE(ARC.isParentOf(DRC));
+  EXPECT_TRUE(ARC.isAncestorOf(DRC));
+  EXPECT_TRUE(DRC.isChildOf(ARC));
+  EXPECT_TRUE(DRC.isDescendantOf(ARC));
+  EXPECT_EQ(&AC, CG.lookupSCC(A));
+  EXPECT_EQ(&BC, CG.lookupSCC(B));
+  EXPECT_EQ(&CC, CG.lookupSCC(C));
+  EXPECT_EQ(&DC, CG.lookupSCC(D));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C));
+  EXPECT_EQ(&DRC, CG.lookupRefSCC(D));
+
+  ARC.switchOutgoingEdgeToRef(A, D);
+  EXPECT_FALSE(NewE.isCall());
+
+  // Verify the graph remains the same.
+  EXPECT_TRUE(ARC.isParentOf(DRC));
+  EXPECT_TRUE(ARC.isAncestorOf(DRC));
+  EXPECT_TRUE(DRC.isChildOf(ARC));
+  EXPECT_TRUE(DRC.isDescendantOf(ARC));
+  EXPECT_EQ(&AC, CG.lookupSCC(A));
+  EXPECT_EQ(&BC, CG.lookupSCC(B));
+  EXPECT_EQ(&CC, CG.lookupSCC(C));
+  EXPECT_EQ(&DC, CG.lookupSCC(D));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C));
+  EXPECT_EQ(&DRC, CG.lookupRefSCC(D));
+
+  ARC.switchOutgoingEdgeToCall(A, D);
+  EXPECT_TRUE(NewE.isCall());
+
+  // Verify the graph remains the same.
+  EXPECT_TRUE(ARC.isParentOf(DRC));
+  EXPECT_TRUE(ARC.isAncestorOf(DRC));
+  EXPECT_TRUE(DRC.isChildOf(ARC));
+  EXPECT_TRUE(DRC.isDescendantOf(ARC));
+  EXPECT_EQ(&AC, CG.lookupSCC(A));
+  EXPECT_EQ(&BC, CG.lookupSCC(B));
+  EXPECT_EQ(&CC, CG.lookupSCC(C));
+  EXPECT_EQ(&DC, CG.lookupSCC(D));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C));
+  EXPECT_EQ(&DRC, CG.lookupRefSCC(D));
+
+  ARC.removeOutgoingEdge(A, D);
+  EXPECT_EQ(2, std::distance(A.begin(), A.end()));
+
+  // Now the parent and child tests fail again but the rest remains the same.
+  EXPECT_FALSE(ARC.isParentOf(DRC));
+  EXPECT_TRUE(ARC.isAncestorOf(DRC));
+  EXPECT_FALSE(DRC.isChildOf(ARC));
+  EXPECT_TRUE(DRC.isDescendantOf(ARC));
   EXPECT_EQ(&AC, CG.lookupSCC(A));
   EXPECT_EQ(&BC, CG.lookupSCC(B));
   EXPECT_EQ(&CC, CG.lookupSCC(C));
   EXPECT_EQ(&DC, CG.lookupSCC(D));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C));
+  EXPECT_EQ(&DRC, CG.lookupRefSCC(D));
 }
 
-TEST(LazyCallGraphTest, IncomingSCCEdgeInsertion) {
+TEST(LazyCallGraphTest, IncomingEdgeInsertion) {
   // We want to ensure we can add edges even across complex diamond graphs, so
   // we use the diamond of triangles graph defined above. The ascii diagram is
   // repeated here for easy reference.
   //
   //         d1       |
   //        /  \      |
   //       d3--d2     |
   //      /     \     |
   //     b1     c1    |
   //   /  \    /  \   |
   //  b3--b2  c3--c2  |
   //       \  /       |
   //        a1        |
   //       /  \       |
   //      a3--a2      |
   //
   std::unique_ptr<Module> M = parseAssembly(DiamondOfTriangles);
   LazyCallGraph CG(*M);
 
   // Force the graph to be fully expanded.
-  for (LazyCallGraph::SCC &C : CG.postorder_sccs())
-    (void)C;
+  for (LazyCallGraph::RefSCC &RC : CG.postorder_ref_sccs())
+    (void)RC;
 
   LazyCallGraph::Node &A1 = *CG.lookup(lookupFunction(*M, "a1"));
   LazyCallGraph::Node &A2 = *CG.lookup(lookupFunction(*M, "a2"));
   LazyCallGraph::Node &A3 = *CG.lookup(lookupFunction(*M, "a3"));
   LazyCallGraph::Node &B1 = *CG.lookup(lookupFunction(*M, "b1"));
   LazyCallGraph::Node &B2 = *CG.lookup(lookupFunction(*M, "b2"));
   LazyCallGraph::Node &B3 = *CG.lookup(lookupFunction(*M, "b3"));
   LazyCallGraph::Node &C1 = *CG.lookup(lookupFunction(*M, "c1"));
   LazyCallGraph::Node &C2 = *CG.lookup(lookupFunction(*M, "c2"));
   LazyCallGraph::Node &C3 = *CG.lookup(lookupFunction(*M, "c3"));
   LazyCallGraph::Node &D1 = *CG.lookup(lookupFunction(*M, "d1"));
   LazyCallGraph::Node &D2 = *CG.lookup(lookupFunction(*M, "d2"));
   LazyCallGraph::Node &D3 = *CG.lookup(lookupFunction(*M, "d3"));
-  LazyCallGraph::SCC &AC = *CG.lookupSCC(A1);
-  LazyCallGraph::SCC &BC = *CG.lookupSCC(B1);
-  LazyCallGraph::SCC &CC = *CG.lookupSCC(C1);
-  LazyCallGraph::SCC &DC = *CG.lookupSCC(D1);
-  ASSERT_EQ(&AC, CG.lookupSCC(A2));
-  ASSERT_EQ(&AC, CG.lookupSCC(A3));
-  ASSERT_EQ(&BC, CG.lookupSCC(B2));
-  ASSERT_EQ(&BC, CG.lookupSCC(B3));
-  ASSERT_EQ(&CC, CG.lookupSCC(C2));
-  ASSERT_EQ(&CC, CG.lookupSCC(C3));
-  ASSERT_EQ(&DC, CG.lookupSCC(D2));
-  ASSERT_EQ(&DC, CG.lookupSCC(D3));
+  LazyCallGraph::RefSCC &ARC = *CG.lookupRefSCC(A1);
+  LazyCallGraph::RefSCC &BRC = *CG.lookupRefSCC(B1);
+  LazyCallGraph::RefSCC &CRC = *CG.lookupRefSCC(C1);
+  LazyCallGraph::RefSCC &DRC = *CG.lookupRefSCC(D1);
+  ASSERT_EQ(&ARC, CG.lookupRefSCC(A2));
+  ASSERT_EQ(&ARC, CG.lookupRefSCC(A3));
+  ASSERT_EQ(&BRC, CG.lookupRefSCC(B2));
+  ASSERT_EQ(&BRC, CG.lookupRefSCC(B3));
+  ASSERT_EQ(&CRC, CG.lookupRefSCC(C2));
+  ASSERT_EQ(&CRC, CG.lookupRefSCC(C3));
+  ASSERT_EQ(&DRC, CG.lookupRefSCC(D2));
+  ASSERT_EQ(&DRC, CG.lookupRefSCC(D3));
   ASSERT_EQ(1, std::distance(D2.begin(), D2.end()));
 
   // Add an edge to make the graph:
   //
   //         d1         |
   //        /  \        |
   //       d3--d2---.   |
   //      /     \    |  |
   //     b1     c1   |  |
   //   /  \    /  \ /   |
   //  b3--b2  c3--c2    |
   //       \  /         |
   //        a1          |
   //       /  \         |
   //      a3--a2        |
-  CC.insertIncomingEdge(D2, C2, LazyCallGraph::Edge::Call);
+  auto MergedRCs = CRC.insertIncomingRefEdge(D2, C2);
   // Make sure we connected the nodes.
-  EXPECT_EQ(2, std::distance(D2.begin(), D2.end()));
+  for (LazyCallGraph::Edge E : D2) {
+    if (E.getNode() == &D3)
+      continue;
+    EXPECT_EQ(&C2, E.getNode());
+  }
+  // And marked the D ref-SCC as no longer valid.
+  EXPECT_EQ(1u, MergedRCs.size());
+  EXPECT_EQ(&DRC, MergedRCs[0]);
 
   // Make sure we have the correct nodes in the SCC sets.
-  EXPECT_EQ(&AC, CG.lookupSCC(A1));
-  EXPECT_EQ(&AC, CG.lookupSCC(A2));
-  EXPECT_EQ(&AC, CG.lookupSCC(A3));
-  EXPECT_EQ(&BC, CG.lookupSCC(B1));
-  EXPECT_EQ(&BC, CG.lookupSCC(B2));
-  EXPECT_EQ(&BC, CG.lookupSCC(B3));
-  EXPECT_EQ(&CC, CG.lookupSCC(C1));
-  EXPECT_EQ(&CC, CG.lookupSCC(C2));
-  EXPECT_EQ(&CC, CG.lookupSCC(C3));
-  EXPECT_EQ(&CC, CG.lookupSCC(D1));
-  EXPECT_EQ(&CC, CG.lookupSCC(D2));
-  EXPECT_EQ(&CC, CG.lookupSCC(D3));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A1));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A2));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(A3));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B1));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B2));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(B3));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C1));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C2));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C3));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(D1));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(D2));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(D3));
 
   // And that ancestry tests have been updated.
-  EXPECT_TRUE(AC.isParentOf(BC));
-  EXPECT_TRUE(AC.isParentOf(CC));
-  EXPECT_FALSE(AC.isAncestorOf(DC));
-  EXPECT_FALSE(BC.isAncestorOf(DC));
-  EXPECT_FALSE(CC.isAncestorOf(DC));
+  EXPECT_TRUE(ARC.isParentOf(CRC));
+  EXPECT_TRUE(BRC.isParentOf(CRC));
 }
 
-TEST(LazyCallGraphTest, IncomingSCCEdgeInsertionMidTraversal) {
+TEST(LazyCallGraphTest, IncomingEdgeInsertionMidTraversal) {
   // This is the same fundamental test as the previous, but we perform it
-  // having only partially walked the SCCs of the graph.
+  // having only partially walked the RefSCCs of the graph.
   std::unique_ptr<Module> M = parseAssembly(DiamondOfTriangles);
   LazyCallGraph CG(*M);
 
-  // Walk the SCCs until we find the one containing 'c1'.
-  auto SCCI = CG.postorder_scc_begin(), SCCE = CG.postorder_scc_end();
-  ASSERT_NE(SCCI, SCCE);
-  LazyCallGraph::SCC &DC = *SCCI;
-  ASSERT_NE(&DC, nullptr);
-  ++SCCI;
-  ASSERT_NE(SCCI, SCCE);
-  LazyCallGraph::SCC &CC = *SCCI;
-  ASSERT_NE(&CC, nullptr);
+  // Walk the RefSCCs until we find the one containing 'c1'.
+  auto I = CG.postorder_ref_scc_begin(), E = CG.postorder_ref_scc_end();
+  ASSERT_NE(I, E);
+  LazyCallGraph::RefSCC &DRC = *I;
+  ASSERT_NE(&DRC, nullptr);
+  ++I;
+  ASSERT_NE(I, E);
+  LazyCallGraph::RefSCC &CRC = *I;
+  ASSERT_NE(&CRC, nullptr);
 
   ASSERT_EQ(nullptr, CG.lookup(lookupFunction(*M, "a1")));
   ASSERT_EQ(nullptr, CG.lookup(lookupFunction(*M, "a2")));
   ASSERT_EQ(nullptr, CG.lookup(lookupFunction(*M, "a3")));
   ASSERT_EQ(nullptr, CG.lookup(lookupFunction(*M, "b1")));
   ASSERT_EQ(nullptr, CG.lookup(lookupFunction(*M, "b2")));
   ASSERT_EQ(nullptr, CG.lookup(lookupFunction(*M, "b3")));
   LazyCallGraph::Node &C1 = *CG.lookup(lookupFunction(*M, "c1"));
   LazyCallGraph::Node &C2 = *CG.lookup(lookupFunction(*M, "c2"));
   LazyCallGraph::Node &C3 = *CG.lookup(lookupFunction(*M, "c3"));
   LazyCallGraph::Node &D1 = *CG.lookup(lookupFunction(*M, "d1"));
   LazyCallGraph::Node &D2 = *CG.lookup(lookupFunction(*M, "d2"));
   LazyCallGraph::Node &D3 = *CG.lookup(lookupFunction(*M, "d3"));
-  ASSERT_EQ(&CC, CG.lookupSCC(C1));
-  ASSERT_EQ(&CC, CG.lookupSCC(C2));
-  ASSERT_EQ(&CC, CG.lookupSCC(C3));
-  ASSERT_EQ(&DC, CG.lookupSCC(D1));
-  ASSERT_EQ(&DC, CG.lookupSCC(D2));
-  ASSERT_EQ(&DC, CG.lookupSCC(D3));
+  ASSERT_EQ(&CRC, CG.lookupRefSCC(C1));
+  ASSERT_EQ(&CRC, CG.lookupRefSCC(C2));
+  ASSERT_EQ(&CRC, CG.lookupRefSCC(C3));
+  ASSERT_EQ(&DRC, CG.lookupRefSCC(D1));
+  ASSERT_EQ(&DRC, CG.lookupRefSCC(D2));
+  ASSERT_EQ(&DRC, CG.lookupRefSCC(D3));
   ASSERT_EQ(1, std::distance(D2.begin(), D2.end()));
 
-  CC.insertIncomingEdge(D2, C2, LazyCallGraph::Edge::Call);
-  EXPECT_EQ(2, std::distance(D2.begin(), D2.end()));
-
-  // Make sure we have the correct nodes in the SCC sets.
-  EXPECT_EQ(&CC, CG.lookupSCC(C1));
-  EXPECT_EQ(&CC, CG.lookupSCC(C2));
-  EXPECT_EQ(&CC, CG.lookupSCC(C3));
-  EXPECT_EQ(&CC, CG.lookupSCC(D1));
-  EXPECT_EQ(&CC, CG.lookupSCC(D2));
-  EXPECT_EQ(&CC, CG.lookupSCC(D3));
-
-  // Check that we can form the last two SCCs now in a coherent way.
-  ++SCCI;
-  EXPECT_NE(SCCI, SCCE);
-  LazyCallGraph::SCC &BC = *SCCI;
-  EXPECT_NE(&BC, nullptr);
-  EXPECT_EQ(&BC, CG.lookupSCC(*CG.lookup(lookupFunction(*M, "b1"))));
-  EXPECT_EQ(&BC, CG.lookupSCC(*CG.lookup(lookupFunction(*M, "b2"))));
-  EXPECT_EQ(&BC, CG.lookupSCC(*CG.lookup(lookupFunction(*M, "b3"))));
-  ++SCCI;
-  EXPECT_NE(SCCI, SCCE);
-  LazyCallGraph::SCC &AC = *SCCI;
-  EXPECT_NE(&AC, nullptr);
-  EXPECT_EQ(&AC, CG.lookupSCC(*CG.lookup(lookupFunction(*M, "a1"))));
-  EXPECT_EQ(&AC, CG.lookupSCC(*CG.lookup(lookupFunction(*M, "a2"))));
-  EXPECT_EQ(&AC, CG.lookupSCC(*CG.lookup(lookupFunction(*M, "a3"))));
-  ++SCCI;
-  EXPECT_EQ(SCCI, SCCE);
+  auto MergedRCs = CRC.insertIncomingRefEdge(D2, C2);
+  // Make sure we connected the nodes.
+  for (LazyCallGraph::Edge E : D2) {
+    if (E.getNode() == &D3)
+      continue;
+    EXPECT_EQ(&C2, E.getNode());
+  }
+  // And marked the D ref-SCC as no longer valid.
+  EXPECT_EQ(1u, MergedRCs.size());
+  EXPECT_EQ(&DRC, MergedRCs[0]);
+
+  // Make sure we have the correct nodes in the RefSCCs.
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C1));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C2));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(C3));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(D1));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(D2));
+  EXPECT_EQ(&CRC, CG.lookupRefSCC(D3));
+
+  // Check that we can form the last two RefSCCs now in a coherent way.
+  ++I;
+  EXPECT_NE(I, E);
+  LazyCallGraph::RefSCC &BRC = *I;
+  EXPECT_NE(&BRC, nullptr);
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(*CG.lookup(lookupFunction(*M, "b1"))));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(*CG.lookup(lookupFunction(*M, "b2"))));
+  EXPECT_EQ(&BRC, CG.lookupRefSCC(*CG.lookup(lookupFunction(*M, "b3"))));
+  EXPECT_TRUE(BRC.isParentOf(CRC));
+  ++I;
+  EXPECT_NE(I, E);
+  LazyCallGraph::RefSCC &ARC = *I;
+  EXPECT_NE(&ARC, nullptr);
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(*CG.lookup(lookupFunction(*M, "a1"))));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(*CG.lookup(lookupFunction(*M, "a2"))));
+  EXPECT_EQ(&ARC, CG.lookupRefSCC(*CG.lookup(lookupFunction(*M, "a3"))));
+  EXPECT_TRUE(ARC.isParentOf(CRC));
+  ++I;
+  EXPECT_EQ(E, I);
 }
 
-TEST(LazyCallGraphTest, InterSCCEdgeRemoval) {
+TEST(LazyCallGraphTest, InternalEdgeMutation) {
   std::unique_ptr<Module> M = parseAssembly(
       "define void @a() {\n"
       "entry:\n"
       "  call void @b()\n"
       "  ret void\n"
       "}\n"
       "define void @b() {\n"
       "entry:\n"
+      "  call void @c()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @c() {\n"
+      "entry:\n"
+      "  call void @a()\n"
       "  ret void\n"
       "}\n");
   LazyCallGraph CG(*M);
 
   // Force the graph to be fully expanded.
-  for (LazyCallGraph::SCC &C : CG.postorder_sccs())
-    (void)C;
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
 
   LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
   LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
+  LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(C));
+  EXPECT_EQ(1, RC.size());
+  EXPECT_EQ(&*RC.begin(), CG.lookupSCC(A));
+  EXPECT_EQ(&*RC.begin(), CG.lookupSCC(B));
+  EXPECT_EQ(&*RC.begin(), CG.lookupSCC(C));
+
+  // Insert an edge from 'a' to 'c'. Nothing changes about the graph.
+  RC.insertInternalRefEdge(A, C);
+  EXPECT_EQ(2, std::distance(A.begin(), A.end()));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(C));
+  EXPECT_EQ(1, RC.size());
+  EXPECT_EQ(&*RC.begin(), CG.lookupSCC(A));
+  EXPECT_EQ(&*RC.begin(), CG.lookupSCC(B));
+  EXPECT_EQ(&*RC.begin(), CG.lookupSCC(C));
+
+  // Switch the call edge from 'b' to 'c' to a ref edge. This will break the
+  // call cycle and cause us to form more SCCs. The RefSCC will remain the same
+  // though.
+  RC.switchInternalEdgeToRef(B, C);
+  EXPECT_EQ(&RC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(C));
+  auto J = RC.begin();
+  // The SCCs must be in *post-order* which means successors before
+  // predecessors. At this point we have call edges from C to A and from A to
+  // B. The only valid postorder is B, A, C.
+  EXPECT_EQ(&*J++, CG.lookupSCC(B));
+  EXPECT_EQ(&*J++, CG.lookupSCC(A));
+  EXPECT_EQ(&*J++, CG.lookupSCC(C));
+  EXPECT_EQ(RC.end(), J);
+
+  // Test turning the ref edge from A to C into a call edge. This will form an
+  // SCC out of A and C. Since we previously had a call edge from C to A, the
+  // C SCC should be preserved and have A merged into it while the A SCC should
+  // be invalidated.
   LazyCallGraph::SCC &AC = *CG.lookupSCC(A);
-  LazyCallGraph::SCC &BC = *CG.lookupSCC(B);
+  LazyCallGraph::SCC &CC = *CG.lookupSCC(C);
+  auto InvalidatedSCCs = RC.switchInternalEdgeToCall(A, C);
+  ASSERT_EQ(1u, InvalidatedSCCs.size());
+  EXPECT_EQ(&AC, InvalidatedSCCs[0]);
+  EXPECT_EQ(2, CC.size());
+  EXPECT_EQ(&CC, CG.lookupSCC(A));
+  EXPECT_EQ(&CC, CG.lookupSCC(C));
+  J = RC.begin();
+  EXPECT_EQ(&*J++, CG.lookupSCC(B));
+  EXPECT_EQ(&*J++, CG.lookupSCC(C));
+  EXPECT_EQ(RC.end(), J);
+}
+
+TEST(LazyCallGraphTest, InternalEdgeRemoval) {
+  // A nice fully connected (including self-edges) RefSCC.
+  std::unique_ptr<Module> M = parseAssembly(
+      "define void @a(i8** %ptr) {\n"
+      "entry:\n"
+      "  store i8* bitcast (void(i8**)* @a to i8*), i8** %ptr\n"
+      "  store i8* bitcast (void(i8**)* @b to i8*), i8** %ptr\n"
+      "  store i8* bitcast (void(i8**)* @c to i8*), i8** %ptr\n"
+      "  ret void\n"
+      "}\n"
+      "define void @b(i8** %ptr) {\n"
+      "entry:\n"
+      "  store i8* bitcast (void(i8**)* @a to i8*), i8** %ptr\n"
+      "  store i8* bitcast (void(i8**)* @b to i8*), i8** %ptr\n"
+      "  store i8* bitcast (void(i8**)* @c to i8*), i8** %ptr\n"
+      "  ret void\n"
+      "}\n"
+      "define void @c(i8** %ptr) {\n"
+      "entry:\n"
+      "  store i8* bitcast (void(i8**)* @a to i8*), i8** %ptr\n"
+      "  store i8* bitcast (void(i8**)* @b to i8*), i8** %ptr\n"
+      "  store i8* bitcast (void(i8**)* @c to i8*), i8** %ptr\n"
+      "  ret void\n"
+      "}\n");
+  LazyCallGraph CG(*M);
 
-  EXPECT_EQ("b", A.begin()->getFunction().getName());
-  EXPECT_EQ(B.end(), B.begin());
-  EXPECT_EQ(&AC, &*BC.parent_begin());
+  // Force the graph to be fully expanded.
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
 
-  AC.removeInterSCCEdge(A, B);
+  LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
+  LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
+  LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(C));
 
-  EXPECT_EQ(A.end(), A.begin());
-  EXPECT_EQ(B.end(), B.begin());
-  EXPECT_EQ(BC.parent_end(), BC.parent_begin());
+  // Remove the edge from b -> a, which should leave the 3 functions still in
+  // a single connected component because of a -> b -> c -> a.
+  SmallVector<LazyCallGraph::RefSCC *, 1> NewRCs =
+      RC.removeInternalRefEdge(B, A);
+  EXPECT_EQ(0u, NewRCs.size());
+  EXPECT_EQ(&RC, CG.lookupRefSCC(A));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(B));
+  EXPECT_EQ(&RC, CG.lookupRefSCC(C));
+
+  // Remove the edge from c -> a, which should leave 'a' in the original RefSCC
+  // and form a new RefSCC for 'b' and 'c'.
+  NewRCs = RC.removeInternalRefEdge(C, A);
+  EXPECT_EQ(1u, NewRCs.size());
+  EXPECT_EQ(&RC, CG.lookupRefSCC(A));
+  EXPECT_EQ(1, std::distance(RC.begin(), RC.end()));
+  LazyCallGraph::RefSCC *RC2 = CG.lookupRefSCC(B);
+  EXPECT_EQ(RC2, CG.lookupRefSCC(C));
+  EXPECT_EQ(RC2, NewRCs[0]);
 }
 
-TEST(LazyCallGraphTest, IntraSCCEdgeInsertion) {
-  std::unique_ptr<Module> M1 = parseAssembly(
+TEST(LazyCallGraphTest, InternalCallEdgeToRef) {
+  // A nice fully connected (including self-edges) SCC (and RefSCC)
+  std::unique_ptr<Module> M = parseAssembly(
       "define void @a() {\n"
       "entry:\n"
+      "  call void @a()\n"
       "  call void @b()\n"
+      "  call void @c()\n"
       "  ret void\n"
       "}\n"
       "define void @b() {\n"
       "entry:\n"
+      "  call void @a()\n"
+      "  call void @b()\n"
       "  call void @c()\n"
       "  ret void\n"
       "}\n"
       "define void @c() {\n"
       "entry:\n"
       "  call void @a()\n"
+      "  call void @b()\n"
+      "  call void @c()\n"
       "  ret void\n"
       "}\n");
-  LazyCallGraph CG1(*M1);
+  LazyCallGraph CG(*M);
 
   // Force the graph to be fully expanded.
-  auto SCCI = CG1.postorder_scc_begin();
-  LazyCallGraph::SCC &SCC = *SCCI++;
-  EXPECT_EQ(CG1.postorder_scc_end(), SCCI);
-
-  LazyCallGraph::Node &A = *CG1.lookup(lookupFunction(*M1, "a"));
-  LazyCallGraph::Node &B = *CG1.lookup(lookupFunction(*M1, "b"));
-  LazyCallGraph::Node &C = *CG1.lookup(lookupFunction(*M1, "c"));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(A));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(B));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(C));
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
 
-  // Insert an edge from 'a' to 'c'. Nothing changes about the SCCs.
-  SCC.insertIntraSCCEdge(A, C, LazyCallGraph::Edge::Call);
-  EXPECT_EQ(2, std::distance(A.begin(), A.end()));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(A));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(B));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(C));
+  EXPECT_EQ(1, RC.size());
+  LazyCallGraph::SCC &CallC = *RC.begin();
 
-  // Insert a self edge from 'a' back to 'a'.
-  SCC.insertIntraSCCEdge(A, A, LazyCallGraph::Edge::Call);
-  EXPECT_EQ(3, std::distance(A.begin(), A.end()));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(A));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(B));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(C));
+  LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
+  LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
+  LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
+  EXPECT_EQ(&CallC, CG.lookupSCC(A));
+  EXPECT_EQ(&CallC, CG.lookupSCC(B));
+  EXPECT_EQ(&CallC, CG.lookupSCC(C));
+
+  // Remove the call edge from b -> a to a ref edge, which should leave the
+  // 3 functions still in a single connected component because of a -> b ->
+  // c -> a.
+  RC.switchInternalEdgeToRef(B, A);
+  EXPECT_EQ(1, RC.size());
+  EXPECT_EQ(&CallC, CG.lookupSCC(A));
+  EXPECT_EQ(&CallC, CG.lookupSCC(B));
+  EXPECT_EQ(&CallC, CG.lookupSCC(C));
+
+  // Remove the edge from c -> a, which should leave 'a' in the original SCC
+  // and form a new SCC for 'b' and 'c'.
+  RC.switchInternalEdgeToRef(C, A);
+  EXPECT_EQ(2, RC.size());
+  EXPECT_EQ(&CallC, CG.lookupSCC(A));
+  LazyCallGraph::SCC &BCallC = *CG.lookupSCC(B);
+  EXPECT_NE(&BCallC, &CallC);
+  EXPECT_EQ(&BCallC, CG.lookupSCC(C));
+  auto J = RC.find(CallC);
+  EXPECT_EQ(&CallC, &*J);
+  --J;
+  EXPECT_EQ(&BCallC, &*J);
+  EXPECT_EQ(RC.begin(), J);
+
+  // Remove the edge from c -> b, which should leave 'b' in the original SCC
+  // and form a new SCC for 'c'. It shouldn't change 'a's SCC.
+  RC.switchInternalEdgeToRef(C, B);
+  EXPECT_EQ(3, RC.size());
+  EXPECT_EQ(&CallC, CG.lookupSCC(A));
+  EXPECT_EQ(&BCallC, CG.lookupSCC(B));
+  LazyCallGraph::SCC &CCallC = *CG.lookupSCC(C);
+  EXPECT_NE(&CCallC, &CallC);
+  EXPECT_NE(&CCallC, &BCallC);
+  J = RC.find(CallC);
+  EXPECT_EQ(&CallC, &*J);
+  --J;
+  EXPECT_EQ(&BCallC, &*J);
+  --J;
+  EXPECT_EQ(&CCallC, &*J);
+  EXPECT_EQ(RC.begin(), J);
 }
 
-TEST(LazyCallGraphTest, IntraSCCEdgeRemoval) {
-  // A nice fully connected (including self-edges) SCC.
-  std::unique_ptr<Module> M1 = parseAssembly(
+TEST(LazyCallGraphTest, InternalRefEdgeToCall) {
+  // Basic tests for making a ref edge a call. This hits the basics of the
+  // process only.
+  std::unique_ptr<Module> M = parseAssembly(
       "define void @a() {\n"
       "entry:\n"
-      "  call void @a()\n"
       "  call void @b()\n"
       "  call void @c()\n"
+      "  store void()* @d, void()** undef\n"
       "  ret void\n"
       "}\n"
       "define void @b() {\n"
       "entry:\n"
-      "  call void @a()\n"
-      "  call void @b()\n"
-      "  call void @c()\n"
+      "  store void()* @c, void()** undef\n"
+      "  call void @d()\n"
       "  ret void\n"
       "}\n"
       "define void @c() {\n"
       "entry:\n"
-      "  call void @a()\n"
+      "  store void()* @b, void()** undef\n"
+      "  call void @d()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @d() {\n"
+      "entry:\n"
+      "  store void()* @a, void()** undef\n"
+      "  ret void\n"
+      "}\n");
+  LazyCallGraph CG(*M);
+
+  // Force the graph to be fully expanded.
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
+
+  LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
+  LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
+  LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
+  LazyCallGraph::Node &D = *CG.lookup(lookupFunction(*M, "d"));
+  LazyCallGraph::SCC &AC = *CG.lookupSCC(A);
+  LazyCallGraph::SCC &BC = *CG.lookupSCC(B);
+  LazyCallGraph::SCC &CC = *CG.lookupSCC(C);
+  LazyCallGraph::SCC &DC = *CG.lookupSCC(D);
+
+  // Check the initial post-order. Note that B and C could be flipped here (and
+  // in our mutation) without changing the nature of this test.
+  ASSERT_EQ(4, RC.size());
+  EXPECT_EQ(&DC, &RC[0]);
+  EXPECT_EQ(&BC, &RC[1]);
+  EXPECT_EQ(&CC, &RC[2]);
+  EXPECT_EQ(&AC, &RC[3]);
+
+  // Switch the ref edge from A -> D to a call edge. This should have no
+  // effect as it is already in postorder and no new cycles are formed.
+  auto MergedCs = RC.switchInternalEdgeToCall(A, D);
+  EXPECT_EQ(0u, MergedCs.size());
+  ASSERT_EQ(4, RC.size());
+  EXPECT_EQ(&DC, &RC[0]);
+  EXPECT_EQ(&BC, &RC[1]);
+  EXPECT_EQ(&CC, &RC[2]);
+  EXPECT_EQ(&AC, &RC[3]);
+
+  // Switch B -> C to a call edge. This doesn't form any new cycles but does
+  // require reordering the SCCs.
+  MergedCs = RC.switchInternalEdgeToCall(B, C);
+  EXPECT_EQ(0u, MergedCs.size());
+  ASSERT_EQ(4, RC.size());
+  EXPECT_EQ(&DC, &RC[0]);
+  EXPECT_EQ(&CC, &RC[1]);
+  EXPECT_EQ(&BC, &RC[2]);
+  EXPECT_EQ(&AC, &RC[3]);
+
+  // Switch C -> B to a call edge. This forms a cycle and forces merging SCCs.
+  MergedCs = RC.switchInternalEdgeToCall(C, B);
+  ASSERT_EQ(1u, MergedCs.size());
+  EXPECT_EQ(&CC, MergedCs[0]);
+  ASSERT_EQ(3, RC.size());
+  EXPECT_EQ(&DC, &RC[0]);
+  EXPECT_EQ(&BC, &RC[1]);
+  EXPECT_EQ(&AC, &RC[2]);
+  EXPECT_EQ(2, BC.size());
+  EXPECT_EQ(&BC, CG.lookupSCC(B));
+  EXPECT_EQ(&BC, CG.lookupSCC(C));
+}
+
+TEST(LazyCallGraphTest, InternalRefEdgeToCallNoCycleInterleaved) {
+  // Test for having a post-order prior to changing a ref edge to a call edge
+  // with SCCs connecting to the source and connecting to the target, but not
+  // connecting to both, interleaved between the source and target. This
+  // ensures we correctly partition the range rather than simply moving one or
+  // the other.
+  std::unique_ptr<Module> M = parseAssembly(
+      "define void @a() {\n"
+      "entry:\n"
+      "  call void @b1()\n"
+      "  call void @c1()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @b1() {\n"
+      "entry:\n"
+      "  call void @c1()\n"
+      "  call void @b2()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @c1() {\n"
+      "entry:\n"
+      "  call void @b2()\n"
+      "  call void @c2()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @b2() {\n"
+      "entry:\n"
+      "  call void @c2()\n"
+      "  call void @b3()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @c2() {\n"
+      "entry:\n"
+      "  call void @b3()\n"
+      "  call void @c3()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @b3() {\n"
+      "entry:\n"
+      "  call void @c3()\n"
+      "  call void @d()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @c3() {\n"
+      "entry:\n"
+      "  store void()* @b1, void()** undef\n"
+      "  call void @d()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @d() {\n"
+      "entry:\n"
+      "  store void()* @a, void()** undef\n"
+      "  ret void\n"
+      "}\n");
+  LazyCallGraph CG(*M);
+
+  // Force the graph to be fully expanded.
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
+
+  LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
+  LazyCallGraph::Node &B1 = *CG.lookup(lookupFunction(*M, "b1"));
+  LazyCallGraph::Node &B2 = *CG.lookup(lookupFunction(*M, "b2"));
+  LazyCallGraph::Node &B3 = *CG.lookup(lookupFunction(*M, "b3"));
+  LazyCallGraph::Node &C1 = *CG.lookup(lookupFunction(*M, "c1"));
+  LazyCallGraph::Node &C2 = *CG.lookup(lookupFunction(*M, "c2"));
+  LazyCallGraph::Node &C3 = *CG.lookup(lookupFunction(*M, "c3"));
+  LazyCallGraph::Node &D = *CG.lookup(lookupFunction(*M, "d"));
+  LazyCallGraph::SCC &AC = *CG.lookupSCC(A);
+  LazyCallGraph::SCC &B1C = *CG.lookupSCC(B1);
+  LazyCallGraph::SCC &B2C = *CG.lookupSCC(B2);
+  LazyCallGraph::SCC &B3C = *CG.lookupSCC(B3);
+  LazyCallGraph::SCC &C1C = *CG.lookupSCC(C1);
+  LazyCallGraph::SCC &C2C = *CG.lookupSCC(C2);
+  LazyCallGraph::SCC &C3C = *CG.lookupSCC(C3);
+  LazyCallGraph::SCC &DC = *CG.lookupSCC(D);
+
+  // Several call edges are initially present to force a particual post-order.
+  // Remove them now, leaving an interleaved post-order pattern.
+  RC.switchInternalEdgeToRef(B3, C3);
+  RC.switchInternalEdgeToRef(C2, B3);
+  RC.switchInternalEdgeToRef(B2, C2);
+  RC.switchInternalEdgeToRef(C1, B2);
+  RC.switchInternalEdgeToRef(B1, C1);
+
+  // Check the initial post-order. We ensure this order with the extra edges
+  // that are nuked above.
+  ASSERT_EQ(8, RC.size());
+  EXPECT_EQ(&DC, &RC[0]);
+  EXPECT_EQ(&C3C, &RC[1]);
+  EXPECT_EQ(&B3C, &RC[2]);
+  EXPECT_EQ(&C2C, &RC[3]);
+  EXPECT_EQ(&B2C, &RC[4]);
+  EXPECT_EQ(&C1C, &RC[5]);
+  EXPECT_EQ(&B1C, &RC[6]);
+  EXPECT_EQ(&AC, &RC[7]);
+
+  // Switch C3 -> B1 to a call edge. This doesn't form any new cycles but does
+  // require reordering the SCCs in the face of tricky internal node
+  // structures.
+  auto MergedCs = RC.switchInternalEdgeToCall(C3, B1);
+  EXPECT_EQ(0u, MergedCs.size());
+  ASSERT_EQ(8, RC.size());
+  EXPECT_EQ(&DC, &RC[0]);
+  EXPECT_EQ(&B3C, &RC[1]);
+  EXPECT_EQ(&B2C, &RC[2]);
+  EXPECT_EQ(&B1C, &RC[3]);
+  EXPECT_EQ(&C3C, &RC[4]);
+  EXPECT_EQ(&C2C, &RC[5]);
+  EXPECT_EQ(&C1C, &RC[6]);
+  EXPECT_EQ(&AC, &RC[7]);
+}
+
+TEST(LazyCallGraphTest, InternalRefEdgeToCallBothPartitionAndMerge) {
+  // Test for having a postorder where between the source and target are all
+  // three kinds of other SCCs:
+  // 1) One connected to the target only that have to be shifted below the
+  //    source.
+  // 2) One connected to the source only that have to be shifted below the
+  //    target.
+  // 3) One connected to both source and target that has to remain and get
+  //    merged away.
+  //
+  // To achieve this we construct a heavily connected graph to force
+  // a particular post-order. Then we remove the forcing edges and connect
+  // a cycle.
+  //
+  // Diagram for the graph we want on the left and the graph we use to force
+  // the ordering on the right. Edges ponit down or right.
+  //
+  //   A    |    A    |
+  //  / \   |   / \   |
+  // B   E  |  B   \  |
+  // |\  |  |  |\  |  |
+  // | D |  |  C-D-E  |
+  // |  \|  |  |  \|  |
+  // C   F  |  \   F  |
+  //  \ /   |   \ /   |
+  //   G    |    G    |
+  //
+  // And we form a cycle by connecting F to B.
+  std::unique_ptr<Module> M = parseAssembly(
+      "define void @a() {\n"
+      "entry:\n"
       "  call void @b()\n"
+      "  call void @e()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @b() {\n"
+      "entry:\n"
       "  call void @c()\n"
+      "  call void @d()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @c() {\n"
+      "entry:\n"
+      "  call void @d()\n"
+      "  call void @g()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @d() {\n"
+      "entry:\n"
+      "  call void @e()\n"
+      "  call void @f()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @e() {\n"
+      "entry:\n"
+      "  call void @f()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @f() {\n"
+      "entry:\n"
+      "  store void()* @b, void()** undef\n"
+      "  call void @g()\n"
+      "  ret void\n"
+      "}\n"
+      "define void @g() {\n"
+      "entry:\n"
+      "  store void()* @a, void()** undef\n"
       "  ret void\n"
       "}\n");
-  LazyCallGraph CG1(*M1);
+  LazyCallGraph CG(*M);
 
   // Force the graph to be fully expanded.
-  auto SCCI = CG1.postorder_scc_begin();
-  LazyCallGraph::SCC &SCC = *SCCI++;
-  EXPECT_EQ(CG1.postorder_scc_end(), SCCI);
-
-  LazyCallGraph::Node &A = *CG1.lookup(lookupFunction(*M1, "a"));
-  LazyCallGraph::Node &B = *CG1.lookup(lookupFunction(*M1, "b"));
-  LazyCallGraph::Node &C = *CG1.lookup(lookupFunction(*M1, "c"));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(A));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(B));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(C));
-
-  // Remove the edge from b -> a, which should leave the 3 functions still in
-  // a single connected component because of a -> b -> c -> a.
-  SmallVector<LazyCallGraph::SCC *, 1> NewSCCs = SCC.removeIntraSCCEdge(B, A);
-  EXPECT_EQ(0u, NewSCCs.size());
-  EXPECT_EQ(&SCC, CG1.lookupSCC(A));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(B));
-  EXPECT_EQ(&SCC, CG1.lookupSCC(C));
+  auto I = CG.postorder_ref_scc_begin();
+  LazyCallGraph::RefSCC &RC = *I++;
+  EXPECT_EQ(CG.postorder_ref_scc_end(), I);
 
-  // Remove the edge from c -> a, which should leave 'a' in the original SCC
-  // and form a new SCC for 'b' and 'c'.
-  NewSCCs = SCC.removeIntraSCCEdge(C, A);
-  EXPECT_EQ(1u, NewSCCs.size());
-  EXPECT_EQ(&SCC, CG1.lookupSCC(A));
-  EXPECT_EQ(1, std::distance(SCC.begin(), SCC.end()));
-  LazyCallGraph::SCC *SCC2 = CG1.lookupSCC(B);
-  EXPECT_EQ(SCC2, CG1.lookupSCC(C));
-  EXPECT_EQ(SCC2, NewSCCs[0]);
+  LazyCallGraph::Node &A = *CG.lookup(lookupFunction(*M, "a"));
+  LazyCallGraph::Node &B = *CG.lookup(lookupFunction(*M, "b"));
+  LazyCallGraph::Node &C = *CG.lookup(lookupFunction(*M, "c"));
+  LazyCallGraph::Node &D = *CG.lookup(lookupFunction(*M, "d"));
+  LazyCallGraph::Node &E = *CG.lookup(lookupFunction(*M, "e"));
+  LazyCallGraph::Node &F = *CG.lookup(lookupFunction(*M, "f"));
+  LazyCallGraph::Node &G = *CG.lookup(lookupFunction(*M, "g"));
+  LazyCallGraph::SCC &AC = *CG.lookupSCC(A);
+  LazyCallGraph::SCC &BC = *CG.lookupSCC(B);
+  LazyCallGraph::SCC &CC = *CG.lookupSCC(C);
+  LazyCallGraph::SCC &DC = *CG.lookupSCC(D);
+  LazyCallGraph::SCC &EC = *CG.lookupSCC(E);
+  LazyCallGraph::SCC &FC = *CG.lookupSCC(F);
+  LazyCallGraph::SCC &GC = *CG.lookupSCC(G);
+
+  // Remove the extra edges that were used to force a particular post-order.
+  RC.switchInternalEdgeToRef(C, D);
+  RC.switchInternalEdgeToRef(D, E);
+
+  // Check the initial post-order. We ensure this order with the extra edges
+  // that are nuked above.
+  ASSERT_EQ(7, RC.size());
+  EXPECT_EQ(&GC, &RC[0]);
+  EXPECT_EQ(&FC, &RC[1]);
+  EXPECT_EQ(&EC, &RC[2]);
+  EXPECT_EQ(&DC, &RC[3]);
+  EXPECT_EQ(&CC, &RC[4]);
+  EXPECT_EQ(&BC, &RC[5]);
+  EXPECT_EQ(&AC, &RC[6]);
+
+  // Switch F -> B to a call edge. This merges B, D, and F into a single SCC,
+  // and has to place the C and E SCCs on either side of it:
+  //   A          A    |
+  //  / \        / \   |
+  // B   E      |   E  |
+  // |\  |       \ /   |
+  // | D |  ->    B    |
+  // |  \|       / \   |
+  // C   F      C   |  |
+  //  \ /        \ /   |
+  //   G          G    |
+  auto MergedCs = RC.switchInternalEdgeToCall(F, B);
+  ASSERT_EQ(2u, MergedCs.size());
+  EXPECT_EQ(&FC, MergedCs[0]);
+  EXPECT_EQ(&DC, MergedCs[1]);
+  EXPECT_EQ(3, BC.size());
+
+  // And make sure the postorder was updated.
+  ASSERT_EQ(5, RC.size());
+  EXPECT_EQ(&GC, &RC[0]);
+  EXPECT_EQ(&CC, &RC[1]);
+  EXPECT_EQ(&BC, &RC[2]);
+  EXPECT_EQ(&EC, &RC[3]);
+  EXPECT_EQ(&AC, &RC[4]);
 }
 
 }