llvm-mirror/include/llvm/Analysis/LazyCallGraph.h

//===- LazyCallGraph.h - Analysis of a Module's call graph ------*- C++ -*-===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
/// \file
///
/// Implements a lazy call graph analysis and related passes for the new pass
/// manager.
///
/// NB: This is *not* a traditional call graph! It is a graph which models both
/// the current calls and potential calls. As a consequence there are many
/// edges in this call graph that do not correspond to a 'call' or 'invoke'
/// instruction.
///
/// The primary use cases of this graph analysis is to facilitate iterating
/// across the functions of a module in ways that ensure all callees are
/// visited prior to a caller (given any SCC constraints), or vice versa. As
/// such is it particularly well suited to organizing CGSCC optimizations such
/// as inlining, outlining, argument promotion, etc. That is its primary use
/// case and motivates the design. It may not be appropriate for other
/// purposes. The use graph of functions or some other conservative analysis of
/// call instructions may be interesting for optimizations and subsequent
/// analyses which don't work in the context of an overly specified
/// potential-call-edge graph.
///
/// To understand the specific rules and nature of this call graph analysis,
/// see the documentation of the \c LazyCallGraph below.
///
//===----------------------------------------------------------------------===//

#ifndef LLVM_ANALYSIS_LAZYCALLGRAPH_H
#define LLVM_ANALYSIS_LAZYCALLGRAPH_H

#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/PointerUnion.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallVector.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 "llvm/Support/raw_ostream.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
/// attempting to maintain is that function-local optimization, CGSCC-local
/// optimizations, and optimizations transforming a pair of functions connected
/// by an edge in the graph, do not invalidate a bottom-up traversal of the SCC
/// DAG. That is, no optimizations will delete, remove, or add an edge such
/// that functions already visited in a bottom-up order of the SCC DAG are no
/// longer valid to have visited, or such that functions not yet visited in
/// a bottom-up order of the SCC DAG are not required to have already been
/// visited.
///
/// Within this constraint, the desire is to minimize the merge points of the
/// SCC DAG. The greater the fanout of the SCC DAG and the fewer merge points
/// in the SCC DAG, the more independence there is in optimizing within it.
/// There is a strong desire to enable parallelization of optimizations over
/// the call graph, and both limited fanout and merge points will (artificially
/// in some cases) limit the scaling of such an effort.
///
/// To this end, graph represents both direct and any potential resolution to
/// an indirect call edge. Another way to think about it is that it represents
/// both the direct call edges and any direct call edges that might be formed
/// through static optimizations. Specifically, it considers taking the address
/// of a function to be an edge in the call graph because this might be
/// forwarded to become a direct call by some subsequent function-local
/// optimization. The result is that the graph closely follows the use-def
/// edges for functions. Walking "up" the graph can be done by looking at all
/// of the uses of a function.
///
/// The roots of the call graph are the external functions and functions
/// escaped into global variables. Those functions can be called from outside
/// of the module or via unknowable means in the IR -- we may not be able to
/// form even a potential call edge from a function body which may dynamically
/// load the function and call it.
///
/// This analysis still requires updates to remain valid after optimizations
/// which could potentially change the set of potential callees. The
/// constraints it operates under only make the traversal order remain valid.
///
/// The entire analysis must be re-computed if full interprocedural
/// optimizations run at any point. For example, globalopt completely
/// invalidates the information in this analysis.
///
/// 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
  /// inherently reference edges, and so the reference graph forms a superset
  /// of the formal call graph.
  ///
  /// Furthermore, edges also may point to raw \c Function objects when those
  /// functions have not been scanned and incorporated into the graph (yet).
  /// This is one of the primary ways in which the graph can be lazy. When
  /// functions are scanned and fully incorporated into the graph, all of the
  /// edges referencing them are updated to point to the graph \c Node objects
  /// instead of to the raw \c Function objects. This class even provides
  /// methods to trigger this scan on-demand by attempting to get the target
  /// node of the graph and providing a reference back to the graph in order to
  /// lazily build it if necessary.
  ///
  /// All of these forms of edges are fundamentally represented as outgoing
  /// edges. The edges are stored in the source node and point at the target
  /// node. This allows the edge structure itself to be a very compact data
  /// structure: essentially a tagged pointer.
  class Edge {
  public:
    /// The kind of edge in the graph.
    enum Kind : bool { Ref = false, Call = true };

    Edge();
    explicit Edge(Function &F, Kind K);
    explicit Edge(Node &N, Kind K);

    /// Test whether the edge is null.
    ///
    /// This happens when an edge has been deleted. We leave the edge objects
    /// around but clear them.
    operator bool() const;

    /// Returnss the \c Kind of the edge.
    Kind getKind() const;

    /// Test whether the edge represents a direct call to a function.
    ///
    /// This requires that the edge is not null.
    bool isCall() const;

    /// Get the function referenced by this edge.
    ///
    /// This requires that the edge is not null, but will succeed whether we
    /// have built a graph node for the function yet or not.
    Function &getFunction() const;

    /// Get the call graph node referenced by this edge if one exists.
    ///
    /// This requires that the edge is not null. If we have built a graph node
    /// for the function this edge points to, this will return that node,
    /// otherwise it will return null.
    Node *getNode() const;

    /// Get the call graph node for this edge, building it if necessary.
    ///
    /// 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;
    friend class LazyCallGraph::RefSCC;

    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;
    friend class LazyCallGraph::RefSCC;

    LazyCallGraph *G;
    Function &F;

    // We provide for the DFS numbering and Tarjan walk lowlink numbers to be
    // 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 *, 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);

    void clear() {
      Edges.clear();
      EdgeIndexMap.clear();
    }

    /// Print the name of this node's function.
    friend raw_ostream &operator<<(raw_ostream &OS, const Node &N) {
      return OS << N.F.getName();
    }

    /// Dump the name of this node's function to stderr.
    void dump() const;

  public:
    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()]; }

    const Edge *lookup(Function &F) const {
      auto EI = EdgeIndexMap.find(&F);
      return EI != EdgeIndexMap.end() ? &Edges[EI->second] : nullptr;
    }

    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
  /// be scanned for "calls" or uses of functions and its child information
  /// will be constructed. All of these results are accumulated and cached in
  /// the graph.
  class edge_iterator
      : public iterator_adaptor_base<edge_iterator, EdgeVectorImplT::iterator,
                                     std::forward_iterator_tag> {
    friend class LazyCallGraph;
    friend class LazyCallGraph::Node;

    EdgeVectorImplT::iterator E;

    // Build the iterator for a specific position in the edge list.
    edge_iterator(EdgeVectorImplT::iterator BaseI,
                  EdgeVectorImplT::iterator E)
        : iterator_adaptor_base(BaseI), E(E) {
      while (I != E && !*I)
        ++I;
    }

  public:
    edge_iterator() {}

    using iterator_adaptor_base::operator++;
    edge_iterator &operator++() {
      do {
        ++I;
      } while (I != E && !*I);
      return *this;
    }
  };

  /// A lazy iterator over specifically call edges.
  ///
  /// This has the same iteration properties as the \c edge_iterator, but
  /// restricts itself to edges which represent actual calls.
  class call_edge_iterator
      : public iterator_adaptor_base<call_edge_iterator,
                                     EdgeVectorImplT::iterator,
                                     std::forward_iterator_tag> {
    friend class LazyCallGraph;
    friend class LazyCallGraph::Node;

    EdgeVectorImplT::iterator E;

    /// Advance the iterator to the next valid, call edge.
    void advanceToNextEdge() {
      while (I != E && (!*I || !I->isCall()))
        ++I;
    }

    // Build the iterator for a specific position in the edge list.
    call_edge_iterator(EdgeVectorImplT::iterator BaseI,
                       EdgeVectorImplT::iterator E)
        : iterator_adaptor_base(BaseI), E(E) {
      advanceToNextEdge();
    }

  public:
    call_edge_iterator() {}

    using iterator_adaptor_base::operator++;
    call_edge_iterator &operator++() {
      ++I;
      advanceToNextEdge();
      return *this;
    }
  };

  /// An SCC of the call graph.
  ///
  /// 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;

    RefSCC *OuterRefSCC;
    SmallVector<Node *, 1> Nodes;

    template <typename NodeRangeT>
    SCC(RefSCC &OuterRefSCC, NodeRangeT &&Nodes)
        : OuterRefSCC(&OuterRefSCC), Nodes(std::forward<NodeRangeT>(Nodes)) {}

    void clear() {
      OuterRefSCC = nullptr;
      Nodes.clear();
    }

    /// Print a short descrtiption useful for debugging or logging.
    ///
    /// We print the function names in the SCC wrapped in '()'s and skipping
    /// the middle functions if there are a large number.
    //
    // Note: this is defined inline to dodge issues with GCC's interpretation
    // of enclosing namespaces for friend function declarations.
    friend raw_ostream &operator<<(raw_ostream &OS, const SCC &C) {
      OS << '(';
      int i = 0;
      for (LazyCallGraph::Node &N : C) {
        if (i > 0)
          OS << ", ";
        // Elide the inner elements if there are too many.
        if (i > 8) {
          OS << "..., " << *C.Nodes.back();
          break;
        }
        OS << N;
        ++i;
      }
      OS << ')';
      return OS;
    }

    /// Dump a short description of this SCC to stderr.
    void dump() const;

#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

  public:
    typedef pointee_iterator<SmallVectorImpl<Node *>::const_iterator> iterator;

    iterator begin() const { return Nodes.begin(); }
    iterator end() const { return Nodes.end(); }

    int size() const { return Nodes.size(); }

    RefSCC &getOuterRefSCC() const { return *OuterRefSCC; }

    /// Provide a short name by printing this SCC to a std::string.
    ///
    /// This copes with the fact that we don't have a name per-se for an SCC
    /// while still making the use of this in debugging and logging useful.
    std::string getName() const {
      std::string Name;
      raw_string_ostream OS(Name);
      OS << *this;
      OS.flush();
      return Name;
    }
  };

  /// 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);

    void clear() {
      Parents.clear();
      SCCs.clear();
      SCCIndices.clear();
    }

    /// Print a short description useful for debugging or logging.
    ///
    /// We print the SCCs wrapped in '[]'s and skipping the middle SCCs if
    /// there are a large number.
    //
    // Note: this is defined inline to dodge issues with GCC's interpretation
    // of enclosing namespaces for friend function declarations.
    friend raw_ostream &operator<<(raw_ostream &OS, const RefSCC &RC) {
      OS << '[';
      int i = 0;
      for (LazyCallGraph::SCC &C : RC) {
        if (i > 0)
          OS << ", ";
        // Elide the inner elements if there are too many.
        if (i > 4) {
          OS << "..., " << *RC.SCCs.back();
          break;
        }
        OS << C;
        ++i;
      }
      OS << ']';
      return OS;
    }

    /// Dump a short description of this RefSCC to stderr.
    void dump() const;

#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

    /// Handle any necessary parent set updates after inserting a trivial ref
    /// or call edge.
    void handleTrivialEdgeInsertion(Node &SourceN, Node &TargetN);

  public:
    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 SCCs.begin(); }
    iterator end() const { return SCCs.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 RefSCC &C) const { return C.isChildOf(*this); }

    /// Test if this RefSCC is an ancestor of \a C.
    bool isAncestorOf(const RefSCC &C) const { return C.isDescendantOf(*this); }

    /// 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 RefSCC is a descendant of \a C.
    bool isDescendantOf(const RefSCC &C) const;

    /// Provide a short name by printing this SCC to a std::string.
    ///
    /// This copes with the fact that we don't have a name per-se for an SCC
    /// while still making the use of this in debugging and logging useful.
    std::string getName() const {
      std::string Name;
      raw_string_ostream OS(Name);
      OS << *this;
      OS.flush();
      return Name;
    }

    ///@{
    /// \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.

    /// Make an existing internal ref edge into a call edge.
    ///
    /// 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 SCCs are added *immediately* and contiguously
    /// prior to the TargetN SCC and return the range covering the new SCCs in
    /// the RefSCC's postorder sequence. You can directly iterate the returned
    /// range to observe all of the new SCCs in postorder.
    iterator_range<iterator> 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<RefSCC *, 1> insertIncomingRefEdge(Node &SourceN,
                                                   Node &TargetN);

    /// Remove an edge whose source is in this RefSCC and target is *not*.
    ///
    /// 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 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 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 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 convenience wrapper around the above to handle trivial cases of
    /// inserting a new call edge.
    ///
    /// This is trivial whenever the target is in the same SCC as the source or
    /// the edge is an outgoing edge to some descendant SCC. In these cases
    /// there is no change to the cyclic structure of SCCs or RefSCCs.
    ///
    /// To further make calling this convenient, it also handles inserting
    /// already existing edges.
    void insertTrivialCallEdge(Node &SourceN, Node &TargetN);

    /// A convenience wrapper around the above to handle trivial cases of
    /// inserting a new ref edge.
    ///
    /// This is trivial whenever the target is in the same RefSCC as the source
    /// or the edge is an outgoing edge to some descendant RefSCC. In these
    /// cases there is no change to the cyclic structure of the RefSCCs.
    ///
    /// To further make calling this convenient, it also handles inserting
    /// already existing edges.
    void insertTrivialRefEdge(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_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;
    RefSCC *RC;

    /// Build the begin iterator for a node.
    postorder_ref_scc_iterator(LazyCallGraph &G) : G(&G), RC(getRC(G, 0)) {}

    /// Build the end iterator for a node. This is selected purely by overload.
    postorder_ref_scc_iterator(LazyCallGraph &G, IsAtEndT /*Nonce*/)
        : G(&G), RC(nullptr) {}

    /// Get the post-order RefSCC at the given index of the postorder walk,
    /// populating it if necessary.
    static RefSCC *getRC(LazyCallGraph &G, int Index) {
      if (Index == (int)G.PostOrderRefSCCs.size())
        if (!G.buildNextRefSCCInPostOrder())
          // We're at the end.
          return nullptr;

      assert(Index < (int)G.PostOrderRefSCCs.size() &&
             "Built the next post-order RefSCC without growing list!");
      return G.PostOrderRefSCCs[Index];
    }

  public:
    bool operator==(const postorder_ref_scc_iterator &Arg) const {
      return G == Arg.G && RC == Arg.RC;
    }

    reference operator*() const { return *RC; }

    using iterator_facade_base::operator++;
    postorder_ref_scc_iterator &operator++() {
      assert(RC && "Cannot increment the end iterator!");
      RC = getRC(*G, G->RefSCCIndices.find(RC)->second + 1);
      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_ref_scc_iterator postorder_ref_scc_begin() {
    return postorder_ref_scc_iterator(*this);
  }
  postorder_ref_scc_iterator postorder_ref_scc_end() {
    return postorder_ref_scc_iterator(*this,
                                      postorder_ref_scc_iterator::IsAtEndT());
  }

  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);
  }

  ///@{
  /// \name Pre-SCC Mutation API
  ///
  /// These methods are only valid to call prior to forming any SCCs for this
  /// call graph. They can be used to update the core node-graph during
  /// a node-based inorder traversal that precedes any SCC-based traversal.
  ///
  /// Once you begin manipulating a call graph's SCCs, most mutation of the
  /// graph must be performed via a RefSCC method. There are some exceptions
  /// below.

  /// Update the call graph after inserting a new edge.
  void insertEdge(Node &Caller, Function &Callee, Edge::Kind EK);

  /// Update the call graph after inserting a new edge.
  void insertEdge(Function &Caller, Function &Callee, Edge::Kind EK) {
    return insertEdge(get(Caller), Callee, EK);
  }

  /// Update the call graph after deleting an edge.
  void removeEdge(Node &Caller, Function &Callee);

  /// Update the call graph after deleting an edge.
  void removeEdge(Function &Caller, Function &Callee) {
    return removeEdge(get(Caller), Callee);
  }

  ///@}

  ///@{
  /// \name General Mutation API
  ///
  /// There are a very limited set of mutations allowed on the graph as a whole
  /// once SCCs have started to be formed. These routines have strict contracts
  /// but may be called at any point.

  /// Remove a dead function from the call graph (typically to delete it).
  ///
  /// Note that the function must have an empty use list, and the call graph
  /// must be up-to-date prior to calling this. That means it is by itself in
  /// a maximal SCC which is by itself in a maximal RefSCC, etc. No structural
  /// changes result from calling this routine other than potentially removing
  /// entry points into the call graph.
  ///
  /// If SCC formation has begun, this function must not be part of the current
  /// DFS in order to call this safely. Typically, the function will have been
  /// fully visited by the DFS prior to calling this routine.
  void removeDeadFunction(Function &F);

  ///@}

  ///@{
  /// \name Static helpers for code doing updates to the call graph.
  ///
  /// These helpers are used to implement parts of the call graph but are also
  /// useful to code doing updates or otherwise wanting to walk the IR in the
  /// same patterns as when we build the call graph.

  template <typename CallbackT>
  static void visitReferences(SmallVectorImpl<Constant *> &Worklist,
                              SmallPtrSetImpl<Constant *> &Visited,
                              CallbackT Callback) {
    while (!Worklist.empty()) {
      Constant *C = Worklist.pop_back_val();

      if (Function *F = dyn_cast<Function>(C)) {
        Callback(*F);
        continue;
      }

      for (Value *Op : C->operand_values())
        if (Visited.insert(cast<Constant>(Op)).second)
          Worklist.push_back(cast<Constant>(Op));
    }

    ///@}
  }

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 *, int> EntryIndexMap;

  /// Allocator that holds all the call graph SCCs.
  SpecificBumpPtrAllocator<SCC> SCCBPA;

  /// Maps Function -> SCC for fast lookup.
  DenseMap<Node *, SCC *> SCCMap;

  /// Allocator that holds all the call graph RefSCCs.
  SpecificBumpPtrAllocator<RefSCC> RefSCCBPA;

  /// The post-order sequence of RefSCCs.
  ///
  /// This list is lazily formed the first time we walk the graph.
  SmallVector<RefSCC *, 16> PostOrderRefSCCs;

  /// A map from RefSCC to the index for it in the postorder sequence of
  /// RefSCCs.
  DenseMap<RefSCC *, int> RefSCCIndices;

  /// The leaf RefSCCs of the graph.
  ///
  /// 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 RefSCCs.
  SmallVector<Function *, 4> RefSCCEntryNodes;

  /// Stack of nodes the DFS has walked but not yet put into a SCC.
  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();

  /// 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);

  /// Get the index of a RefSCC within the postorder traversal.
  ///
  /// Requires that this RefSCC is a valid one in the (perhaps partial)
  /// postorder traversed part of the graph.
  int getRefSCCIndex(RefSCC &RC) {
    auto IndexIt = RefSCCIndices.find(&RC);
    assert(IndexIt != RefSCCIndices.end() && "RefSCC doesn't have an index!");
    assert(PostOrderRefSCCs[IndexIt->second] == &RC &&
           "Index does not point back at RC!");
    return IndexIt->second;
  }

  /// Builds the next node in the post-order RefSCC walk of the call graph and
  /// appends it to the \c PostOrderRefSCCs vector.
  ///
  /// Returns true if a new RefSCC was successfully constructed, and false if
  /// there are no more RefSCCs to build in the graph.
  bool buildNextRefSCCInPostOrder();
};

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();
}

inline LazyCallGraph::Edge::Kind LazyCallGraph::Edge::getKind() const {
  assert(*this && "Queried a null edge!");
  return Value.getInt();
}

inline bool LazyCallGraph::Edge::isCall() const {
  assert(*this && "Queried a null edge!");
  return getKind() == Call;
}

inline Function &LazyCallGraph::Edge::getFunction() const {
  assert(*this && "Queried a null edge!");
  auto P = Value.getPointer();
  if (auto *F = P.dyn_cast<Function *>())
    return *F;

  return P.get<Node *>()->getFunction();
}

inline LazyCallGraph::Node *LazyCallGraph::Edge::getNode() const {
  assert(*this && "Queried a null edge!");
  auto P = Value.getPointer();
  if (auto *N = P.dyn_cast<Node *>())
    return N;

  return nullptr;
}

inline LazyCallGraph::Node &LazyCallGraph::Edge::getNode(LazyCallGraph &G) {
  assert(*this && "Queried a null edge!");
  auto P = Value.getPointer();
  if (auto *N = P.dyn_cast<Node *>())
    return *N;

  Node &N = G.get(*P.get<Function *>());
  Value.setPointer(&N);
  return N;
}

// Provide GraphTraits specializations for call graphs.
template <> struct GraphTraits<LazyCallGraph::Node *> {
  typedef LazyCallGraph::Node *NodeRef;
  typedef LazyCallGraph::edge_iterator ChildIteratorType;

  static NodeRef getEntryNode(NodeRef N) { return N; }
  static ChildIteratorType child_begin(NodeRef N) { return N->begin(); }
  static ChildIteratorType child_end(NodeRef N) { return N->end(); }
};
template <> struct GraphTraits<LazyCallGraph *> {
  typedef LazyCallGraph::Node *NodeRef;
  typedef LazyCallGraph::edge_iterator ChildIteratorType;

  static NodeRef getEntryNode(NodeRef N) { return N; }
  static ChildIteratorType child_begin(NodeRef N) { return N->begin(); }
  static ChildIteratorType child_end(NodeRef N) { return N->end(); }
};

/// An analysis pass which computes the call graph for a module.
class LazyCallGraphAnalysis : public AnalysisInfoMixin<LazyCallGraphAnalysis> {
  friend AnalysisInfoMixin<LazyCallGraphAnalysis>;
  static char PassID;

public:
  /// Inform generic clients of the result type.
  typedef LazyCallGraph Result;

  /// Compute the \c LazyCallGraph for the module \c M.
  ///
  /// This just builds the set of entry points to the call graph. The rest is
  /// built lazily as it is walked.
  LazyCallGraph run(Module &M, ModuleAnalysisManager &) {
    return LazyCallGraph(M);
  }
};

/// A pass which prints the call graph to a \c raw_ostream.
///
/// This is primarily useful for testing the analysis.
class LazyCallGraphPrinterPass
    : public PassInfoMixin<LazyCallGraphPrinterPass> {
  raw_ostream &OS;

public:
  explicit LazyCallGraphPrinterPass(raw_ostream &OS);

  PreservedAnalyses run(Module &M, ModuleAnalysisManager &AM);
};

/// A pass which prints the call graph as a DOT file to a \c raw_ostream.
///
/// This is primarily useful for visualization purposes.
class LazyCallGraphDOTPrinterPass
    : public PassInfoMixin<LazyCallGraphDOTPrinterPass> {
  raw_ostream &OS;

public:
  explicit LazyCallGraphDOTPrinterPass(raw_ostream &OS);

  PreservedAnalyses run(Module &M, ModuleAnalysisManager &AM);
};
}

#endif