text: //===- 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/ArrayRef.h"
  #include "llvm/ADT/DenseMap.h"
  #include "llvm/ADT/Optional.h"
  #include "llvm/ADT/PointerIntPair.h"
  #include "llvm/ADT/SetVector.h"
  #include "llvm/ADT/SmallPtrSet.h"
  #include "llvm/ADT/SmallVector.h"
  #include "llvm/ADT/StringRef.h"
  #include "llvm/ADT/iterator.h"
  #include "llvm/ADT/iterator_range.h"
  #include "llvm/Analysis/TargetLibraryInfo.h"
  #include "llvm/IR/Constant.h"
  #include "llvm/IR/Constants.h"
  #include "llvm/IR/Function.h"
  #include "llvm/IR/PassManager.h"
  #include "llvm/Support/Allocator.h"
  #include "llvm/Support/Casting.h"
  #include "llvm/Support/raw_ostream.h"
  #include <cassert>
  #include <iterator>
  #include <string>
  #include <utility>
  
  namespace llvm {
  
  class Module;
  class Value;
  
  /// 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 EdgeSequence;
    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.
    ///
    /// 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(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.
      explicit 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 call graph node referenced by this edge.
      ///
      /// This requires that the edge is not null.
      Node &getNode() const;
  
      /// Get the function referenced by this edge.
      ///
      /// This requires that the edge is not null.
      Function &getFunction() const;
  
    private:
      friend class LazyCallGraph::EdgeSequence;
      friend class LazyCallGraph::RefSCC;
  
      PointerIntPair<Node *, 1, Kind> Value;
  
      void setKind(Kind K) { Value.setInt(K); }
    };
  
    /// The edge sequence object.
    ///
    /// This typically exists entirely within the node but is exposed as
    /// a separate type because a node doesn't initially have edges. An explicit
    /// population step is required to produce this sequence at first and it is
    /// then cached in the node. It is also used to represent edges entering the
    /// graph from outside the module to model the graph's roots.
    ///
    /// The sequence itself both iterable and indexable. The indexes remain
    /// stable even as the sequence mutates (including removal).
    class EdgeSequence {
      friend class LazyCallGraph;
      friend class LazyCallGraph::Node;
      friend class LazyCallGraph::RefSCC;
  
      using VectorT = SmallVector<Edge, 4>;
      using VectorImplT = SmallVectorImpl<Edge>;
  
    public:
      /// An iterator used for the edges to both entry nodes and child nodes.
      class iterator
          : public iterator_adaptor_base<iterator, VectorImplT::iterator,
                                         std::forward_iterator_tag> {
        friend class LazyCallGraph;
        friend class LazyCallGraph::Node;
  
        VectorImplT::iterator E;
  
        // Build the iterator for a specific position in the edge list.
        iterator(VectorImplT::iterator BaseI, VectorImplT::iterator E)
            : iterator_adaptor_base(BaseI), E(E) {
          while (I != E && !*I)
            ++I;
        }
  
      public:
        iterator() = default;
  
        using iterator_adaptor_base::operator++;
        iterator &operator++() {
          do {
            ++I;
          } while (I != E && !*I);
          return *this;
        }
      };
  
      /// An iterator over specifically call edges.
      ///
      /// This has the same iteration properties as the \c iterator, but
      /// restricts itself to edges which represent actual calls.
      class call_iterator
          : public iterator_adaptor_base<call_iterator, VectorImplT::iterator,
                                         std::forward_iterator_tag> {
        friend class LazyCallGraph;
        friend class LazyCallGraph::Node;
  
        VectorImplT::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_iterator(VectorImplT::iterator BaseI, VectorImplT::iterator E)
            : iterator_adaptor_base(BaseI), E(E) {
          advanceToNextEdge();
        }
  
      public:
        call_iterator() = default;
  
        using iterator_adaptor_base::operator++;
        call_iterator &operator++() {
          ++I;
          advanceToNextEdge();
          return *this;
        }
      };
  
      iterator begin() { return iterator(Edges.begin(), Edges.end()); }
      iterator end() { return iterator(Edges.end(), Edges.end()); }
  
      Edge &operator[](int i) { return Edges[i]; }
      Edge &operator[](Node &N) {
        assert(EdgeIndexMap.find(&N) != EdgeIndexMap.end() && "No such edge!");
        auto &E = Edges[EdgeIndexMap.find(&N)->second];
        assert(E && "Dead or null edge!");
        return E;
      }
  
      Edge *lookup(Node &N) {
        auto EI = EdgeIndexMap.find(&N);
        if (EI == EdgeIndexMap.end())
          return nullptr;
        auto &E = Edges[EI->second];
        return E ? &E : nullptr;
      }
  
      call_iterator call_begin() {
        return call_iterator(Edges.begin(), Edges.end());
      }
      call_iterator call_end() { return call_iterator(Edges.end(), Edges.end()); }
  
      iterator_range<call_iterator> calls() {
        return make_range(call_begin(), call_end());
      }
  
      bool empty() {
        for (auto &E : Edges)
          if (E)
            return false;
  
        return true;
      }
  
    private:
      VectorT Edges;
      DenseMap<Node *, int> EdgeIndexMap;
  
      EdgeSequence() = default;
  
      /// 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(Node &ChildN, Edge::Kind EK);
  
      /// Internal helper to remove the edge to the given function.
      bool removeEdgeInternal(Node &ChildN);
  
      /// Internal helper to replace an edge key with a new one.
      ///
      /// This should be used when the function for a particular node in the
      /// graph gets replaced and we are updating all of the edges to that node
      /// to use the new function as the key.
      void replaceEdgeKey(Function &OldTarget, Function &NewTarget);
    };
  
    /// 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.
    ///
    /// The node works much like an optional in order to lazily populate the
    /// edges of each node. Until populated, there are no edges. Once populated,
    /// you can access the edges by dereferencing the node or using the `->`
    /// operator as if the node was an `Optional<EdgeSequence>`.
    class Node {
      friend class LazyCallGraph;
      friend class LazyCallGraph::RefSCC;
  
    public:
      LazyCallGraph &getGraph() const { return *G; }
  
      Function &getFunction() const { return *F; }
  
      StringRef getName() const { return F->getName(); }
  
      /// Equality is defined as address equality.
      bool operator==(const Node &N) const { return this == &N; }
      bool operator!=(const Node &N) const { return !operator==(N); }
  
      /// Tests whether the node has been populated with edges.
      bool isPopulated() const { return Edges.hasValue(); }
  
      /// Tests whether this is actually a dead node and no longer valid.
      ///
      /// Users rarely interact with nodes in this state and other methods are
      /// invalid. This is used to model a node in an edge list where the
      /// function has been completely removed.
      bool isDead() const {
        assert(!G == !F &&
               "Both graph and function pointers should be null or non-null.");
        return !G;
      }
  
      // We allow accessing the edges by dereferencing or using the arrow
      // operator, essentially wrapping the internal optional.
      EdgeSequence &operator*() const {
        // Rip const off because the node itself isn't changing here.
        return const_cast<EdgeSequence &>(*Edges);
      }
      EdgeSequence *operator->() const { return &**this; }
  
      /// Populate the edges of this node if necessary.
      ///
      /// The first time this is called it will populate the edges for this node
      /// in the graph. It does this by scanning the underlying function, so once
      /// this is done, any changes to that function must be explicitly reflected
      /// in updates to the graph.
      ///
      /// \returns the populated \c EdgeSequence to simplify walking it.
      ///
      /// This will not update or re-scan anything if called repeatedly. Instead,
      /// the edge sequence is cached and returned immediately on subsequent
      /// calls.
      EdgeSequence &populate() {
        if (Edges)
          return *Edges;
  
        return populateSlow();
      }
  
    private:
      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 = 0;
      int LowLink = 0;
  
      Optional<EdgeSequence> Edges;
  
      /// Basic constructor implements the scanning of F into Edges and
      /// EdgeIndexMap.
      Node(LazyCallGraph &G, Function &F) : G(&G), F(&F) {}
  
      /// Implementation of the scan when populating.
      EdgeSequence &populateSlow();
  
      /// Internal helper to directly replace the function with a new one.
      ///
      /// This is used to facilitate tranfsormations which need to replace the
      /// formal Function object but directly move the body and users from one to
      /// the other.
      void replaceFunction(Function &NewF);
  
      void clear() { Edges.reset(); }
  
      /// 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;
    };
  
    /// 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:
      using iterator = pointee_iterator<SmallVectorImpl<Node *>::const_iterator>;
  
      iterator begin() const { return Nodes.begin(); }
      iterator end() const { return Nodes.end(); }
  
      int size() const { return Nodes.size(); }
  
      RefSCC &getOuterRefSCC() const { return *OuterRefSCC; }
  
      /// Test if this SCC is a parent of \a C.
      ///
      /// Note that this is linear in the number of edges departing the current
      /// SCC.
      bool isParentOf(const SCC &C) const;
  
      /// Test if this SCC is an ancestor of \a C.
      ///
      /// Note that in the worst case this is linear in the number of edges
      /// departing the current SCC and every SCC in the entire graph reachable
      /// from this SCC. Thus this very well may walk every edge in the entire
      /// call graph! Do not call this in a tight loop!
      bool isAncestorOf(const SCC &C) const;
  
      /// Test if this SCC is a child of \a C.
      ///
      /// See the comments for \c isParentOf for detailed notes about the
      /// complexity of this routine.
      bool isChildOf(const SCC &C) const { return C.isParentOf(*this); }
  
      /// Test if this SCC is a descendant of \a C.
      ///
      /// See the comments for \c isParentOf for detailed notes about the
      /// complexity of this routine.
      bool isDescendantOf(const SCC &C) const { return C.isAncestorOf(*this); }
  
      /// 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;
  
      /// 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() {
        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:
      using iterator = pointee_iterator<SmallVectorImpl<SCC *>::const_iterator>;
      using range = iterator_range<iterator>;
      using parent_iterator =
          pointee_iterator<SmallPtrSetImpl<RefSCC *>::const_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;
      }
  
      /// Test if this RefSCC is a parent of \a RC.
      ///
      /// CAUTION: This method walks every edge in the \c RefSCC, it can be very
      /// expensive.
      bool isParentOf(const RefSCC &RC) const;
  
      /// Test if this RefSCC is an ancestor of \a RC.
      ///
      /// CAUTION: This method walks the directed graph of edges as far as
      /// necessary to find a possible path to the argument. In the worst case
      /// this may walk the entire graph and can be extremely expensive.
      bool isAncestorOf(const RefSCC &RC) const;
  
      /// Test if this RefSCC is a child of \a RC.
      ///
      /// CAUTION: This method walks every edge in the argument \c RefSCC, it can
      /// be very expensive.
      bool isChildOf(const RefSCC &RC) const { return RC.isParentOf(*this); }
  
      /// Test if this RefSCC is a descendant of \a RC.
      ///
      /// CAUTION: This method walks the directed graph of edges as far as
      /// necessary to find a possible path from the argument. In the worst case
      /// this may walk the entire graph and can be extremely expensive.
      bool isDescendantOf(const RefSCC &RC) const {
        return RC.isAncestorOf(*this);
      }
  
      /// Provide a short name by printing this RefSCC to a std::string.
      ///
      /// This copes with the fact that we don't have a name per-se for an RefSCC
      /// 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 (potentially still in-flight) DFS-found RefSCCs and 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 optional callback \p MergedCB will be invoked (if
      /// provided) on the SCCs being merged away prior to actually performing
      /// the merge. Note that this will never include the target SCC as that
      /// will be the SCC functions are merged into to resolve the cycle. Once
      /// this function returns, these merged SCCs are not in a valid state but
      /// the pointers will remain valid until destruction of the parent graph
      /// instance for the purpose of clearing cached information. This function
      /// also returns 'true' if a cycle was formed and some SCCs merged away as
      /// a convenience.
      ///
      /// 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.
      bool switchInternalEdgeToCall(
          Node &SourceN, Node &TargetN,
          function_ref<void(ArrayRef<SCC *> MergedSCCs)> MergeCB = {});
  
      /// Make an existing internal call edge between separate SCCs into a ref
      /// edge.
      ///
      /// If SourceN and TargetN in separate SCCs within this RefSCC, changing
      /// the call edge between them to a ref edge is a trivial operation that
      /// does not require any structural changes to the call graph.
      void switchTrivialInternalEdgeToRef(Node &SourceN, Node &TargetN);
  
      /// Make an existing internal call edge within a single SCC into a ref
      /// edge.
      ///
      /// Since SourceN and TargetN are part of a single SCC, this SCC 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.
      ///
      /// Note that if SourceN and TargetN are in separate SCCs, the simpler
      /// routine `switchTrivialInternalEdgeToRef` should be used instead.
      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 list of ref edges which are entirely within this RefSCC.
      ///
      /// Both the \a SourceN and all of the \a TargetNs must be within this
      /// RefSCC. Removing these edges 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) If a ref-cycle remains after removal, it leaves this RefSCC intact
      ///    and in the graph. No new RefSCCs are built.
      /// 2) Otherwise, this RefSCC will be dead after this call and no longer in
      ///    the graph or the postorder traversal of the call graph. Any iterator
      ///    pointing at this RefSCC will become invalid.
      /// 3) All newly formed RefSCCs will be returned and the order of the
      ///    RefSCCs returned will be a valid postorder traversal of the new
      ///    RefSCCs.
      /// 4) No RefSCC other than this RefSCC has its member set changed (this is
      ///    inherent in the definition of removing such an edge).
      ///
      /// 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.
      SmallVector<RefSCC *, 1> removeInternalRefEdge(Node &SourceN,
                                                     ArrayRef<Node *> TargetNs);
  
      /// 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);
  
      /// Directly replace a node's function with a new function.
      ///
      /// This should be used when moving the body and users of a function to
      /// a new formal function object but not otherwise changing the call graph
      /// structure in any way.
      ///
      /// It requires that the old function in the provided node have zero uses
      /// and the new function must have calls and references to it establishing
      /// an equivalent graph.
      void replaceNodeFunction(Node &N, Function &NewF);
  
      ///@}
    };
  
    /// A post-order depth-first RefSCC iterator over the call graph.
    ///
    /// This iterator walks the cached post-order sequence of RefSCCs. However,
    /// it trades stability for flexibility. It is restricted to a forward
    /// iterator but will survive mutations which insert new RefSCCs and continue
    /// to point to the same RefSCC even if it moves in the post-order sequence.
    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 = nullptr;
  
      /// 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) {}
  
      /// 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())
          // We're at the end.
          return nullptr;
  
        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, TargetLibraryInfo &TLI);
  
    LazyCallGraph(LazyCallGraph &&G);
    LazyCallGraph &operator=(LazyCallGraph &&RHS);
  
    EdgeSequence::iterator begin() { return EntryEdges.begin(); }
    EdgeSequence::iterator end() { return EntryEdges.end(); }
  
    void buildRefSCCs();
  
    postorder_ref_scc_iterator postorder_ref_scc_begin() {
      if (!EntryEdges.empty())
        assert(!PostOrderRefSCCs.empty() &&
               "Must form RefSCCs before iterating them!");
      return postorder_ref_scc_iterator(*this);
    }
    postorder_ref_scc_iterator postorder_ref_scc_end() {
      if (!EntryEdges.empty())
        assert(!PostOrderRefSCCs.empty() &&
               "Must form RefSCCs before iterating them!");
      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 RefSCC
    /// 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);
    }
  
    /// Get the sequence of known and defined library functions.
    ///
    /// These functions, because they are known to LLVM, can have calls
    /// introduced out of thin air from arbitrary IR.
    ArrayRef<Function *> getLibFunctions() const {
      return LibFunctions.getArrayRef();
    }
  
    /// Test whether a function is a known and defined library function tracked by
    /// the call graph.
    ///
    /// Because these functions are known to LLVM they are specially modeled in
    /// the call graph and even when all IR-level references have been removed
    /// remain active and reachable.
    bool isLibFunction(Function &F) const { return LibFunctions.count(&F); }
  
    ///@{
    /// \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 &SourceN, Node &TargetN, Edge::Kind EK);
  
    /// Update the call graph after inserting a new edge.
    void insertEdge(Function &Source, Function &Target, Edge::Kind EK) {
      return insertEdge(get(Source), get(Target), EK);
    }
  
    /// Update the call graph after deleting an edge.
    void removeEdge(Node &SourceN, Node &TargetN);
  
    /// Update the call graph after deleting an edge.
    void removeEdge(Function &Source, Function &Target) {
      return removeEdge(get(Source), get(Target));
    }
  
    ///@}
  
    ///@{
    /// \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.
  
    /// Recursively visits the defined functions whose address is reachable from
    /// every constant in the \p Worklist.
    ///
    /// Doesn't recurse through any constants already in the \p Visited set, and
    /// updates that set with every constant visited.
    ///
    /// For each defined function, calls \p Callback with that function.
    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)) {
          if (!F->isDeclaration())
            Callback(*F);
          continue;
        }
  
        if (BlockAddress *BA = dyn_cast<BlockAddress>(C)) {
          // The blockaddress constant expression is a weird special case, we
          // can't generically walk its operands the way we do for all other
          // constants.
          if (Visited.insert(BA->getFunction()).second)
            Worklist.push_back(BA->getFunction());
          continue;
        }
  
        for (Value *Op : C->operand_values())
          if (Visited.insert(cast<Constant>(Op)).second)
            Worklist.push_back(cast<Constant>(Op));
      }
    }
  
    ///@}
  
  private:
    using node_stack_iterator = SmallVectorImpl<Node *>::reverse_iterator;
    using node_stack_range = iterator_range<node_stack_iterator>;
  
    /// Allocator that holds all the call graph nodes.
    SpecificBumpPtrAllocator<Node> BPA;
  
    /// Maps function->node for fast lookup.
    DenseMap<const Function *, Node *> NodeMap;
  
    /// The entry edges into the graph.
    ///
    /// These edges are from "external" sources. Put another way, they
    /// escape at the module scope.
    EdgeSequence EntryEdges;
  
    /// 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;
  
    /// Defined functions that are also known library functions which the
    /// optimizer can reason about and therefore might introduce calls to out of
    /// thin air.
    SmallSetVector<Function *, 4> LibFunctions;
  
    /// 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)...);
    }
  
    /// Common logic for building SCCs from a sequence of roots.
    ///
    /// This is a very generic implementation of the depth-first walk and SCC
    /// formation algorithm. It uses a generic sequence of roots and generic
    /// callbacks for each step. This is designed to be used to implement both
    /// the RefSCC formation and SCC formation with shared logic.
    ///
    /// Currently this is a relatively naive implementation of Tarjan's DFS
    /// algorithm to form the SCCs.
    ///
    /// FIXME: We should consider newer variants such as Nuutila.
    template <typename RootsT, typename GetBeginT, typename GetEndT,
              typename GetNodeT, typename FormSCCCallbackT>
    static void buildGenericSCCs(RootsT &&Roots, GetBeginT &&GetBegin,
                                 GetEndT &&GetEnd, GetNodeT &&GetNode,
                                 FormSCCCallbackT &&FormSCC);
  
    /// Build the SCCs for a RefSCC out of a list of nodes.
    void buildSCCs(RefSCC &RC, node_stack_range Nodes);
  
    /// 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;
    }
  };
  
  inline LazyCallGraph::Edge::Edge() : Value() {}
  inline LazyCallGraph::Edge::Edge(Node &N, Kind K) : Value(&N, K) {}
  
  inline LazyCallGraph::Edge::operator bool() const {
    return Value.getPointer() && !Value.getPointer()->isDead();
  }
  
  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 LazyCallGraph::Node &LazyCallGraph::Edge::getNode() const {
    assert(*this && "Queried a null edge!");
    return *Value.getPointer();
  }
  
  inline Function &LazyCallGraph::Edge::getFunction() const {
    assert(*this && "Queried a null edge!");
    return getNode().getFunction();
  }
  
  // Provide GraphTraits specializations for call graphs.
  template <> struct GraphTraits<LazyCallGraph::Node *> {
    using NodeRef = LazyCallGraph::Node *;
    using ChildIteratorType = LazyCallGraph::EdgeSequence::iterator;
  
    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 *> {
    using NodeRef = LazyCallGraph::Node *;
    using ChildIteratorType = LazyCallGraph::EdgeSequence::iterator;
  
    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 AnalysisKey Key;
  
  public:
    /// Inform generic clients of the result type.
    using Result = LazyCallGraph;
  
    /// 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 &AM) {
      return LazyCallGraph(M, AM.getResult<TargetLibraryAnalysis>(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);
  };
  
  } // end namespace llvm
  
  #endif // LLVM_ANALYSIS_LAZYCALLGRAPH_H
  