llvm-mirror/lib/Analysis/CFLAliasAnalysis.cpp

//===- CFLAliasAnalysis.cpp - CFL-Based Alias Analysis Implementation ------==//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file implements a CFL-based context-insensitive alias analysis
// algorithm. It does not depend on types. The algorithm is a mixture of the one
// described in "Demand-driven alias analysis for C" by Xin Zheng and Radu
// Rugina, and "Fast algorithms for Dyck-CFL-reachability with applications to
// Alias Analysis" by Zhang Q, Lyu M R, Yuan H, and Su Z. -- to summarize the
// papers, we build a graph of the uses of a variable, where each node is a
// memory location, and each edge is an action that happened on that memory
// location.  The "actions" can be one of Dereference, Reference, or Assign.
//
// Two variables are considered as aliasing iff you can reach one value's node
// from the other value's node and the language formed by concatenating all of
// the edge labels (actions) conforms to a context-free grammar.
//
// Because this algorithm requires a graph search on each query, we execute the
// algorithm outlined in "Fast algorithms..." (mentioned above)
// in order to transform the graph into sets of variables that may alias in
// ~nlogn time (n = number of variables), which makes queries take constant
// time.
//===----------------------------------------------------------------------===//

// N.B. AliasAnalysis as a whole is phrased as a FunctionPass at the moment, and
// CFLAA is interprocedural. This is *technically* A Bad Thing, because
// FunctionPasses are only allowed to inspect the Function that they're being
// run on. Realistically, this likely isn't a problem until we allow
// FunctionPasses to run concurrently.

#include "llvm/Analysis/CFLAliasAnalysis.h"
#include "StratifiedSets.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/None.h"
#include "llvm/ADT/Optional.h"
#include "llvm/Analysis/MemoryBuiltins.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/InstVisitor.h"
#include "llvm/IR/Instructions.h"
#include "llvm/Pass.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
#include <cassert>
#include <memory>
#include <tuple>

using namespace llvm;

#define DEBUG_TYPE "cfl-aa"

CFLAAResult::CFLAAResult(const TargetLibraryInfo &TLI)
    : AAResultBase(), TLI(TLI) {}
CFLAAResult::CFLAAResult(CFLAAResult &&Arg)
    : AAResultBase(std::move(Arg)), TLI(Arg.TLI) {}
CFLAAResult::~CFLAAResult() {}

/// Information we have about a function and would like to keep around.
struct CFLAAResult::FunctionInfo {
  StratifiedSets<Value *> Sets;
  // Lots of functions have < 4 returns. Adjust as necessary.
  SmallVector<Value *, 4> ReturnedValues;

  FunctionInfo(StratifiedSets<Value *> &&S, SmallVector<Value *, 4> &&RV)
      : Sets(std::move(S)), ReturnedValues(std::move(RV)) {}
};

/// Try to go from a Value* to a Function*. Never returns nullptr.
static Optional<Function *> parentFunctionOfValue(Value *);

/// Returns possible functions called by the Inst* into the given
/// SmallVectorImpl. Returns true if targets found, false otherwise. This is
/// templated so we can use it with CallInsts and InvokeInsts.
template <typename Inst>
static bool getPossibleTargets(Inst *, SmallVectorImpl<Function *> &);

/// Some instructions need to have their users tracked. Instructions like
/// `add` require you to get the users of the Instruction* itself, other
/// instructions like `store` require you to get the users of the first
/// operand. This function gets the "proper" value to track for each
/// type of instruction we support.
static Optional<Value *> getTargetValue(Instruction *);

/// Determines whether or not we an instruction is useless to us (e.g.
/// FenceInst)
static bool hasUsefulEdges(Instruction *);

const StratifiedIndex StratifiedLink::SetSentinel =
    std::numeric_limits<StratifiedIndex>::max();

namespace {
/// StratifiedInfo Attribute things.
typedef unsigned StratifiedAttr;
LLVM_CONSTEXPR unsigned MaxStratifiedAttrIndex = NumStratifiedAttrs;
LLVM_CONSTEXPR unsigned AttrEscapedIndex = 0;
LLVM_CONSTEXPR unsigned AttrUnknownIndex = 1;
LLVM_CONSTEXPR unsigned AttrGlobalIndex = 2;
LLVM_CONSTEXPR unsigned AttrFirstArgIndex = 3;
LLVM_CONSTEXPR unsigned AttrLastArgIndex = MaxStratifiedAttrIndex;
LLVM_CONSTEXPR unsigned AttrMaxNumArgs = AttrLastArgIndex - AttrFirstArgIndex;

LLVM_CONSTEXPR StratifiedAttr AttrNone = 0;
LLVM_CONSTEXPR StratifiedAttr AttrEscaped = 1 << AttrEscapedIndex;
LLVM_CONSTEXPR StratifiedAttr AttrUnknown = 1 << AttrUnknownIndex;
LLVM_CONSTEXPR StratifiedAttr AttrGlobal = 1 << AttrGlobalIndex;

/// StratifiedSets call for knowledge of "direction", so this is how we
/// represent that locally.
enum class Level { Same, Above, Below };

/// Edges can be one of four "weights" -- each weight must have an inverse
/// weight (Assign has Assign; Reference has Dereference).
enum class EdgeType {
  /// The weight assigned when assigning from or to a value. For example, in:
  /// %b = getelementptr %a, 0
  /// ...The relationships are %b assign %a, and %a assign %b. This used to be
  /// two edges, but having a distinction bought us nothing.
  Assign,

  /// The edge used when we have an edge going from some handle to a Value.
  /// Examples of this include:
  /// %b = load %a              (%b Dereference %a)
  /// %b = extractelement %a, 0 (%a Dereference %b)
  Dereference,

  /// The edge used when our edge goes from a value to a handle that may have
  /// contained it at some point. Examples:
  /// %b = load %a              (%a Reference %b)
  /// %b = extractelement %a, 0 (%b Reference %a)
  Reference
};

// \brief Encodes the notion of a "use"
struct Edge {
  /// Which value the edge is coming from
  Value *From;

  /// Which value the edge is pointing to
  Value *To;

  /// Edge weight
  EdgeType Weight;

  /// Whether we aliased any external values along the way that may be
  /// invisible to the analysis (i.e. landingpad for exceptions, calls for
  /// interprocedural analysis, etc.)
  StratifiedAttrs AdditionalAttrs;

  Edge(Value *From, Value *To, EdgeType W, StratifiedAttrs A)
      : From(From), To(To), Weight(W), AdditionalAttrs(A) {}
};

/// Gets the edges our graph should have, based on an Instruction*
class GetEdgesVisitor : public InstVisitor<GetEdgesVisitor, void> {
  CFLAAResult &AA;
  SmallVectorImpl<Edge> &Output;
  const TargetLibraryInfo &TLI;

public:
  GetEdgesVisitor(CFLAAResult &AA, SmallVectorImpl<Edge> &Output,
                  const TargetLibraryInfo &TLI)
      : AA(AA), Output(Output), TLI(TLI) {}

  void visitInstruction(Instruction &) {
    llvm_unreachable("Unsupported instruction encountered");
  }

  void visitPtrToIntInst(PtrToIntInst &Inst) {
    auto *Ptr = Inst.getOperand(0);
    Output.push_back(Edge(Ptr, &Inst, EdgeType::Assign, AttrEscaped));
  }

  void visitIntToPtrInst(IntToPtrInst &Inst) {
    auto *Ptr = &Inst;
    Output.push_back(Edge(Ptr, Ptr, EdgeType::Assign, AttrUnknown));
  }

  void visitCastInst(CastInst &Inst) {
    Output.push_back(
        Edge(&Inst, Inst.getOperand(0), EdgeType::Assign, AttrNone));
  }

  void visitBinaryOperator(BinaryOperator &Inst) {
    auto *Op1 = Inst.getOperand(0);
    auto *Op2 = Inst.getOperand(1);
    Output.push_back(Edge(&Inst, Op1, EdgeType::Assign, AttrNone));
    Output.push_back(Edge(&Inst, Op2, EdgeType::Assign, AttrNone));
  }

  void visitAtomicCmpXchgInst(AtomicCmpXchgInst &Inst) {
    auto *Ptr = Inst.getPointerOperand();
    auto *Val = Inst.getNewValOperand();
    Output.push_back(Edge(Ptr, Val, EdgeType::Dereference, AttrNone));
  }

  void visitAtomicRMWInst(AtomicRMWInst &Inst) {
    auto *Ptr = Inst.getPointerOperand();
    auto *Val = Inst.getValOperand();
    Output.push_back(Edge(Ptr, Val, EdgeType::Dereference, AttrNone));
  }

  void visitPHINode(PHINode &Inst) {
    for (Value *Val : Inst.incoming_values())
      Output.push_back(Edge(&Inst, Val, EdgeType::Assign, AttrNone));
  }

  void visitGetElementPtrInst(GetElementPtrInst &Inst) {
    auto *Op = Inst.getPointerOperand();
    Output.push_back(Edge(&Inst, Op, EdgeType::Assign, AttrNone));
  }

  void visitSelectInst(SelectInst &Inst) {
    // Condition is not processed here (The actual statement producing
    // the condition result is processed elsewhere). For select, the
    // condition is evaluated, but not loaded, stored, or assigned
    // simply as a result of being the condition of a select.

    auto *TrueVal = Inst.getTrueValue();
    Output.push_back(Edge(&Inst, TrueVal, EdgeType::Assign, AttrNone));
    auto *FalseVal = Inst.getFalseValue();
    Output.push_back(Edge(&Inst, FalseVal, EdgeType::Assign, AttrNone));
  }

  void visitAllocaInst(AllocaInst &) {}

  void visitLoadInst(LoadInst &Inst) {
    auto *Ptr = Inst.getPointerOperand();
    auto *Val = &Inst;
    Output.push_back(Edge(Val, Ptr, EdgeType::Reference, AttrNone));
  }

  void visitStoreInst(StoreInst &Inst) {
    auto *Ptr = Inst.getPointerOperand();
    auto *Val = Inst.getValueOperand();
    Output.push_back(Edge(Ptr, Val, EdgeType::Dereference, AttrNone));
  }

  void visitVAArgInst(VAArgInst &Inst) {
    // We can't fully model va_arg here. For *Ptr = Inst.getOperand(0), it does
    // two things:
    //  1. Loads a value from *((T*)*Ptr).
    //  2. Increments (stores to) *Ptr by some target-specific amount.
    // For now, we'll handle this like a landingpad instruction (by placing the
    // result in its own group, and having that group alias externals).
    auto *Val = &Inst;
    Output.push_back(Edge(Val, Val, EdgeType::Assign, AttrUnknown));
  }

  static bool isFunctionExternal(Function *Fn) {
    return Fn->isDeclaration() || !Fn->hasLocalLinkage();
  }

  /// Gets whether the sets at Index1 above, below, or equal to the sets at
  /// Index2. Returns None if they are not in the same set chain.
  static Optional<Level> getIndexRelation(const StratifiedSets<Value *> &Sets,
                                          StratifiedIndex Index1,
                                          StratifiedIndex Index2) {
    if (Index1 == Index2)
      return Level::Same;

    const auto *Current = &Sets.getLink(Index1);
    while (Current->hasBelow()) {
      if (Current->Below == Index2)
        return Level::Below;
      Current = &Sets.getLink(Current->Below);
    }

    Current = &Sets.getLink(Index1);
    while (Current->hasAbove()) {
      if (Current->Above == Index2)
        return Level::Above;
      Current = &Sets.getLink(Current->Above);
    }

    return None;
  }

  bool
  tryInterproceduralAnalysis(const SmallVectorImpl<Function *> &Fns,
                             Value *FuncValue,
                             const iterator_range<User::op_iterator> &Args) {
    const unsigned ExpectedMaxArgs = 8;
    const unsigned MaxSupportedArgs = 50;
    assert(Fns.size() > 0);

    // This algorithm is n^2, so an arbitrary upper-bound of 50 args was
    // selected, so it doesn't take too long in insane cases.
    if (std::distance(Args.begin(), Args.end()) > (int)MaxSupportedArgs)
      return false;

    // Exit early if we'll fail anyway
    for (auto *Fn : Fns) {
      if (isFunctionExternal(Fn) || Fn->isVarArg())
        return false;
      auto &MaybeInfo = AA.ensureCached(Fn);
      if (!MaybeInfo.hasValue())
        return false;
    }

    SmallVector<Value *, ExpectedMaxArgs> Arguments(Args.begin(), Args.end());
    SmallVector<StratifiedInfo, ExpectedMaxArgs> Parameters;
    for (auto *Fn : Fns) {
      auto &Info = *AA.ensureCached(Fn);
      auto &Sets = Info.Sets;
      auto &RetVals = Info.ReturnedValues;

      Parameters.clear();
      for (auto &Param : Fn->args()) {
        auto MaybeInfo = Sets.find(&Param);
        // Did a new parameter somehow get added to the function/slip by?
        if (!MaybeInfo.hasValue())
          return false;
        Parameters.push_back(*MaybeInfo);
      }

      // Adding an edge from argument -> return value for each parameter that
      // may alias the return value
      for (unsigned I = 0, E = Parameters.size(); I != E; ++I) {
        auto &ParamInfo = Parameters[I];
        auto &ArgVal = Arguments[I];
        bool AddEdge = false;
        StratifiedAttrs Externals;
        for (unsigned X = 0, XE = RetVals.size(); X != XE; ++X) {
          auto MaybeInfo = Sets.find(RetVals[X]);
          if (!MaybeInfo.hasValue())
            return false;

          auto &RetInfo = *MaybeInfo;
          auto RetAttrs = Sets.getLink(RetInfo.Index).Attrs;
          auto ParamAttrs = Sets.getLink(ParamInfo.Index).Attrs;
          auto MaybeRelation =
              getIndexRelation(Sets, ParamInfo.Index, RetInfo.Index);
          if (MaybeRelation.hasValue()) {
            AddEdge = true;
            Externals |= RetAttrs | ParamAttrs;
          }
        }
        if (AddEdge)
          Output.push_back(
              Edge(FuncValue, ArgVal, EdgeType::Assign, Externals));
      }

      if (Parameters.size() != Arguments.size())
        return false;

      /// Adding edges between arguments for arguments that may end up aliasing
      /// each other. This is necessary for functions such as
      /// void foo(int** a, int** b) { *a = *b; }
      /// (Technically, the proper sets for this would be those below
      /// Arguments[I] and Arguments[X], but our algorithm will produce
      /// extremely similar, and equally correct, results either way)
      for (unsigned I = 0, E = Arguments.size(); I != E; ++I) {
        auto &MainVal = Arguments[I];
        auto &MainInfo = Parameters[I];
        auto &MainAttrs = Sets.getLink(MainInfo.Index).Attrs;
        for (unsigned X = I + 1; X != E; ++X) {
          auto &SubInfo = Parameters[X];
          auto &SubVal = Arguments[X];
          auto &SubAttrs = Sets.getLink(SubInfo.Index).Attrs;
          auto MaybeRelation =
              getIndexRelation(Sets, MainInfo.Index, SubInfo.Index);

          if (!MaybeRelation.hasValue())
            continue;

          auto NewAttrs = SubAttrs | MainAttrs;
          Output.push_back(Edge(MainVal, SubVal, EdgeType::Assign, NewAttrs));
        }
      }
    }
    return true;
  }

  template <typename InstT> void visitCallLikeInst(InstT &Inst) {
    // Check if Inst is a call to a library function that allocates/deallocates
    // on the heap. Those kinds of functions do not introduce any aliases.
    // TODO: address other common library functions such as realloc(), strdup(),
    // etc.
    if (isMallocLikeFn(&Inst, &TLI) || isCallocLikeFn(&Inst, &TLI)) {
      Output.push_back(Edge(&Inst, &Inst, EdgeType::Assign, AttrNone));
      return;
    } else if (isFreeCall(&Inst, &TLI)) {
      assert(Inst.getNumArgOperands() == 1);
      auto argVal = Inst.arg_begin()->get();
      Output.push_back(Edge(argVal, argVal, EdgeType::Assign, AttrNone));
      return;
    }

    // TODO: Add support for noalias args/all the other fun function attributes
    // that we can tack on.
    SmallVector<Function *, 4> Targets;
    if (getPossibleTargets(&Inst, Targets)) {
      if (tryInterproceduralAnalysis(Targets, &Inst, Inst.arg_operands()))
        return;
      // Cleanup from interprocedural analysis
      Output.clear();
    }

    // Because the function is opaque, we need to note that anything
    // could have happened to the arguments, and that the result could alias
    // just about anything, too.
    // The goal of the loop is in part to unify many Values into one set, so we
    // don't care if the function is void there.
    for (Value *V : Inst.arg_operands())
      Output.push_back(Edge(&Inst, V, EdgeType::Assign, AttrUnknown));
    if (Inst.getNumArgOperands() == 0 &&
        Inst.getType() != Type::getVoidTy(Inst.getContext()))
      Output.push_back(Edge(&Inst, &Inst, EdgeType::Assign, AttrUnknown));
  }

  void visitCallInst(CallInst &Inst) { visitCallLikeInst(Inst); }

  void visitInvokeInst(InvokeInst &Inst) { visitCallLikeInst(Inst); }

  /// Because vectors/aggregates are immutable and unaddressable, there's
  /// nothing we can do to coax a value out of them, other than calling
  /// Extract{Element,Value}. We can effectively treat them as pointers to
  /// arbitrary memory locations we can store in and load from.
  void visitExtractElementInst(ExtractElementInst &Inst) {
    auto *Ptr = Inst.getVectorOperand();
    auto *Val = &Inst;
    Output.push_back(Edge(Val, Ptr, EdgeType::Reference, AttrNone));
  }

  void visitInsertElementInst(InsertElementInst &Inst) {
    auto *Vec = Inst.getOperand(0);
    auto *Val = Inst.getOperand(1);
    Output.push_back(Edge(&Inst, Vec, EdgeType::Assign, AttrNone));
    Output.push_back(Edge(&Inst, Val, EdgeType::Dereference, AttrNone));
  }

  void visitLandingPadInst(LandingPadInst &Inst) {
    // Exceptions come from "nowhere", from our analysis' perspective.
    // So we place the instruction its own group, noting that said group may
    // alias externals
    Output.push_back(Edge(&Inst, &Inst, EdgeType::Assign, AttrUnknown));
  }

  void visitInsertValueInst(InsertValueInst &Inst) {
    auto *Agg = Inst.getOperand(0);
    auto *Val = Inst.getOperand(1);
    Output.push_back(Edge(&Inst, Agg, EdgeType::Assign, AttrNone));
    Output.push_back(Edge(&Inst, Val, EdgeType::Dereference, AttrNone));
  }

  void visitExtractValueInst(ExtractValueInst &Inst) {
    auto *Ptr = Inst.getAggregateOperand();
    Output.push_back(Edge(&Inst, Ptr, EdgeType::Reference, AttrNone));
  }

  void visitShuffleVectorInst(ShuffleVectorInst &Inst) {
    auto *From1 = Inst.getOperand(0);
    auto *From2 = Inst.getOperand(1);
    Output.push_back(Edge(&Inst, From1, EdgeType::Assign, AttrNone));
    Output.push_back(Edge(&Inst, From2, EdgeType::Assign, AttrNone));
  }

  void visitConstantExpr(ConstantExpr *CE) {
    switch (CE->getOpcode()) {
    default:
      llvm_unreachable("Unknown instruction type encountered!");
// Build the switch statement using the Instruction.def file.
#define HANDLE_INST(NUM, OPCODE, CLASS)                                        \
  case Instruction::OPCODE:                                                    \
    visit##OPCODE(*(CLASS *)CE);                                               \
    break;
#include "llvm/IR/Instruction.def"
    }
  }
};

/// For a given instruction, we need to know which Value* to get the
/// users of in order to build our graph. In some cases (i.e. add),
/// we simply need the Instruction*. In other cases (i.e. store),
/// finding the users of the Instruction* is useless; we need to find
/// the users of the first operand. This handles determining which
/// value to follow for us.
///
/// Note: we *need* to keep this in sync with GetEdgesVisitor. Add
/// something to GetEdgesVisitor, add it here -- remove something from
/// GetEdgesVisitor, remove it here.
class GetTargetValueVisitor
    : public InstVisitor<GetTargetValueVisitor, Value *> {
public:
  Value *visitInstruction(Instruction &Inst) { return &Inst; }

  Value *visitStoreInst(StoreInst &Inst) { return Inst.getPointerOperand(); }

  Value *visitAtomicCmpXchgInst(AtomicCmpXchgInst &Inst) {
    return Inst.getPointerOperand();
  }

  Value *visitAtomicRMWInst(AtomicRMWInst &Inst) {
    return Inst.getPointerOperand();
  }

  Value *visitInsertElementInst(InsertElementInst &Inst) {
    return Inst.getOperand(0);
  }

  Value *visitInsertValueInst(InsertValueInst &Inst) {
    return Inst.getAggregateOperand();
  }
};

/// Set building requires a weighted bidirectional graph.
template <typename EdgeTypeT> class WeightedBidirectionalGraph {
public:
  typedef std::size_t Node;

private:
  const static Node StartNode = Node(0);

  struct Edge {
    EdgeTypeT Weight;
    Node Other;

    Edge(const EdgeTypeT &W, const Node &N) : Weight(W), Other(N) {}

    bool operator==(const Edge &E) const {
      return Weight == E.Weight && Other == E.Other;
    }

    bool operator!=(const Edge &E) const { return !operator==(E); }
  };

  struct NodeImpl {
    std::vector<Edge> Edges;
  };

  std::vector<NodeImpl> NodeImpls;

  bool inbounds(Node NodeIndex) const { return NodeIndex < NodeImpls.size(); }

  const NodeImpl &getNode(Node N) const { return NodeImpls[N]; }
  NodeImpl &getNode(Node N) { return NodeImpls[N]; }

public:
  /// \brief Iterator for edges. Because this graph is bidirected, we don't
  /// allow modification of the edges using this iterator. Additionally, the
  /// iterator becomes invalid if you add edges to or from the node you're
  /// getting the edges of.
  struct EdgeIterator : public std::iterator<std::forward_iterator_tag,
                                             std::tuple<EdgeTypeT, Node *>> {
    EdgeIterator(const typename std::vector<Edge>::const_iterator &Iter)
        : Current(Iter) {}

    EdgeIterator(NodeImpl &Impl) : Current(Impl.begin()) {}

    EdgeIterator &operator++() {
      ++Current;
      return *this;
    }

    EdgeIterator operator++(int) {
      EdgeIterator Copy(Current);
      operator++();
      return Copy;
    }

    std::tuple<EdgeTypeT, Node> &operator*() {
      Store = std::make_tuple(Current->Weight, Current->Other);
      return Store;
    }

    bool operator==(const EdgeIterator &Other) const {
      return Current == Other.Current;
    }

    bool operator!=(const EdgeIterator &Other) const {
      return !operator==(Other);
    }

  private:
    typename std::vector<Edge>::const_iterator Current;
    std::tuple<EdgeTypeT, Node> Store;
  };

  /// Wrapper for EdgeIterator with begin()/end() calls.
  struct EdgeIterable {
    EdgeIterable(const std::vector<Edge> &Edges)
        : BeginIter(Edges.begin()), EndIter(Edges.end()) {}

    EdgeIterator begin() { return EdgeIterator(BeginIter); }

    EdgeIterator end() { return EdgeIterator(EndIter); }

  private:
    typename std::vector<Edge>::const_iterator BeginIter;
    typename std::vector<Edge>::const_iterator EndIter;
  };

  // ----- Actual graph-related things ----- //

  WeightedBidirectionalGraph() {}

  WeightedBidirectionalGraph(WeightedBidirectionalGraph<EdgeTypeT> &&Other)
      : NodeImpls(std::move(Other.NodeImpls)) {}

  WeightedBidirectionalGraph<EdgeTypeT> &
  operator=(WeightedBidirectionalGraph<EdgeTypeT> &&Other) {
    NodeImpls = std::move(Other.NodeImpls);
    return *this;
  }

  Node addNode() {
    auto Index = NodeImpls.size();
    auto NewNode = Node(Index);
    NodeImpls.push_back(NodeImpl());
    return NewNode;
  }

  void addEdge(Node From, Node To, const EdgeTypeT &Weight,
               const EdgeTypeT &ReverseWeight) {
    assert(inbounds(From));
    assert(inbounds(To));
    auto &FromNode = getNode(From);
    auto &ToNode = getNode(To);
    FromNode.Edges.push_back(Edge(Weight, To));
    ToNode.Edges.push_back(Edge(ReverseWeight, From));
  }

  iterator_range<EdgeIterator> edgesFor(const Node &N) const {
    const auto &Node = getNode(N);
    return make_range(EdgeIterator(Node.Edges.begin()),
                      EdgeIterator(Node.Edges.end()));
  }

  bool empty() const { return NodeImpls.empty(); }
  std::size_t size() const { return NodeImpls.size(); }

  /// Gets an arbitrary node in the graph as a starting point for traversal.
  Node getEntryNode() {
    assert(inbounds(StartNode));
    return StartNode;
  }
};

typedef WeightedBidirectionalGraph<std::pair<EdgeType, StratifiedAttrs>> GraphT;
typedef DenseMap<Value *, GraphT::Node> NodeMapT;
}

//===----------------------------------------------------------------------===//
// Function declarations that require types defined in the namespace above
//===----------------------------------------------------------------------===//

/// Given a StratifiedAttrs, returns true if it marks the corresponding values
/// as globals or arguments
static bool isGlobalOrArgAttr(StratifiedAttrs Attr);

/// Given a StratifiedAttrs, returns true if the corresponding values come from
/// an unknown source (such as opaque memory or an integer cast)
static bool isUnknownAttr(StratifiedAttrs Attr);

/// Given an argument number, returns the appropriate StratifiedAttr to set.
static StratifiedAttr argNumberToAttr(unsigned ArgNum);

/// Given a Value, potentially return which StratifiedAttr it maps to.
static Optional<StratifiedAttr> valueToAttr(Value *Val);

/// Gets the inverse of a given EdgeType.
static EdgeType flipWeight(EdgeType Initial);

/// Gets edges of the given Instruction*, writing them to the SmallVector*.
static void argsToEdges(CFLAAResult &, Instruction *, SmallVectorImpl<Edge> &,
                        const TargetLibraryInfo &);

/// Gets edges of the given ConstantExpr*, writing them to the SmallVector*.
static void argsToEdges(CFLAAResult &, ConstantExpr *, SmallVectorImpl<Edge> &,
                        const TargetLibraryInfo &);

/// Gets the "Level" that one should travel in StratifiedSets
/// given an EdgeType.
static Level directionOfEdgeType(EdgeType);

/// Builds the graph needed for constructing the StratifiedSets for the
/// given function
static void buildGraphFrom(CFLAAResult &, Function *,
                           SmallVectorImpl<Value *> &, NodeMapT &, GraphT &,
                           const TargetLibraryInfo &);

/// Gets the edges of a ConstantExpr as if it was an Instruction. This function
/// also acts on any nested ConstantExprs, adding the edges of those to the
/// given SmallVector as well.
static void constexprToEdges(CFLAAResult &, ConstantExpr &,
                             SmallVectorImpl<Edge> &,
                             const TargetLibraryInfo &);

/// Given an Instruction, this will add it to the graph, along with any
/// Instructions that are potentially only available from said Instruction
/// For example, given the following line:
///   %0 = load i16* getelementptr ([1 x i16]* @a, 0, 0), align 2
/// addInstructionToGraph would add both the `load` and `getelementptr`
/// instructions to the graph appropriately.
static void addInstructionToGraph(CFLAAResult &, Instruction &,
                                  SmallVectorImpl<Value *> &, NodeMapT &,
                                  GraphT &, const TargetLibraryInfo &);

/// Determines whether it would be pointless to add the given Value to our sets.
static bool canSkipAddingToSets(Value *Val);

static Optional<Function *> parentFunctionOfValue(Value *Val) {
  if (auto *Inst = dyn_cast<Instruction>(Val)) {
    auto *Bb = Inst->getParent();
    return Bb->getParent();
  }

  if (auto *Arg = dyn_cast<Argument>(Val))
    return Arg->getParent();
  return None;
}

template <typename Inst>
static bool getPossibleTargets(Inst *Call,
                               SmallVectorImpl<Function *> &Output) {
  if (auto *Fn = Call->getCalledFunction()) {
    Output.push_back(Fn);
    return true;
  }

  // TODO: If the call is indirect, we might be able to enumerate all potential
  // targets of the call and return them, rather than just failing.
  return false;
}

static Optional<Value *> getTargetValue(Instruction *Inst) {
  GetTargetValueVisitor V;
  return V.visit(Inst);
}

static bool hasUsefulEdges(Instruction *Inst) {
  bool IsNonInvokeTerminator =
      isa<TerminatorInst>(Inst) && !isa<InvokeInst>(Inst);
  return !isa<CmpInst>(Inst) && !isa<FenceInst>(Inst) && !IsNonInvokeTerminator;
}

static bool hasUsefulEdges(ConstantExpr *CE) {
  // ConstantExpr doesn't have terminators, invokes, or fences, so only needs
  // to check for compares.
  return CE->getOpcode() != Instruction::ICmp &&
         CE->getOpcode() != Instruction::FCmp;
}

static bool isGlobalOrArgAttr(StratifiedAttrs Attr) {
  return Attr.reset(AttrEscapedIndex).reset(AttrUnknownIndex).any();
}

static bool isUnknownAttr(StratifiedAttrs Attr) {
  return Attr.test(AttrUnknownIndex);
}

static Optional<StratifiedAttr> valueToAttr(Value *Val) {
  if (isa<GlobalValue>(Val))
    return AttrGlobal;

  if (auto *Arg = dyn_cast<Argument>(Val))
    // Only pointer arguments should have the argument attribute,
    // because things can't escape through scalars without us seeing a
    // cast, and thus, interaction with them doesn't matter.
    if (!Arg->hasNoAliasAttr() && Arg->getType()->isPointerTy())
      return argNumberToAttr(Arg->getArgNo());
  return None;
}

static StratifiedAttr argNumberToAttr(unsigned ArgNum) {
  if (ArgNum >= AttrMaxNumArgs)
    return AttrUnknown;
  return 1 << (ArgNum + AttrFirstArgIndex);
}

static EdgeType flipWeight(EdgeType Initial) {
  switch (Initial) {
  case EdgeType::Assign:
    return EdgeType::Assign;
  case EdgeType::Dereference:
    return EdgeType::Reference;
  case EdgeType::Reference:
    return EdgeType::Dereference;
  }
  llvm_unreachable("Incomplete coverage of EdgeType enum");
}

static void argsToEdges(CFLAAResult &Analysis, Instruction *Inst,
                        SmallVectorImpl<Edge> &Output,
                        const TargetLibraryInfo &TLI) {
  assert(hasUsefulEdges(Inst) &&
         "Expected instructions to have 'useful' edges");
  GetEdgesVisitor v(Analysis, Output, TLI);
  v.visit(Inst);
}

static void argsToEdges(CFLAAResult &Analysis, ConstantExpr *CE,
                        SmallVectorImpl<Edge> &Output,
                        const TargetLibraryInfo &TLI) {
  assert(hasUsefulEdges(CE) && "Expected constant expr to have 'useful' edges");
  GetEdgesVisitor v(Analysis, Output, TLI);
  v.visitConstantExpr(CE);
}

static Level directionOfEdgeType(EdgeType Weight) {
  switch (Weight) {
  case EdgeType::Reference:
    return Level::Above;
  case EdgeType::Dereference:
    return Level::Below;
  case EdgeType::Assign:
    return Level::Same;
  }
  llvm_unreachable("Incomplete switch coverage");
}

static void constexprToEdges(CFLAAResult &Analysis,
                             ConstantExpr &CExprToCollapse,
                             SmallVectorImpl<Edge> &Results,
                             const TargetLibraryInfo &TLI) {
  SmallVector<ConstantExpr *, 4> Worklist;
  Worklist.push_back(&CExprToCollapse);

  SmallVector<Edge, 8> ConstexprEdges;
  SmallPtrSet<ConstantExpr *, 4> Visited;
  while (!Worklist.empty()) {
    auto *CExpr = Worklist.pop_back_val();

    if (!hasUsefulEdges(CExpr))
      continue;

    ConstexprEdges.clear();
    argsToEdges(Analysis, CExpr, ConstexprEdges, TLI);
    for (auto &Edge : ConstexprEdges) {
      if (auto *Nested = dyn_cast<ConstantExpr>(Edge.From))
        if (Visited.insert(Nested).second)
          Worklist.push_back(Nested);

      if (auto *Nested = dyn_cast<ConstantExpr>(Edge.To))
        if (Visited.insert(Nested).second)
          Worklist.push_back(Nested);
    }

    Results.append(ConstexprEdges.begin(), ConstexprEdges.end());
  }
}

static void addInstructionToGraph(CFLAAResult &Analysis, Instruction &Inst,
                                  SmallVectorImpl<Value *> &ReturnedValues,
                                  NodeMapT &Map, GraphT &Graph,
                                  const TargetLibraryInfo &TLI) {
  const auto findOrInsertNode = [&Map, &Graph](Value *Val) {
    auto Pair = Map.insert(std::make_pair(Val, GraphT::Node()));
    auto &Iter = Pair.first;
    if (Pair.second) {
      auto NewNode = Graph.addNode();
      Iter->second = NewNode;
    }
    return Iter->second;
  };

  // We don't want the edges of most "return" instructions, but we *do* want
  // to know what can be returned.
  if (isa<ReturnInst>(&Inst))
    ReturnedValues.push_back(&Inst);

  if (!hasUsefulEdges(&Inst))
    return;

  SmallVector<Edge, 8> Edges;
  argsToEdges(Analysis, &Inst, Edges, TLI);

  // In the case of an unused alloca (or similar), edges may be empty. Note
  // that it exists so we can potentially answer NoAlias.
  if (Edges.empty()) {
    auto MaybeVal = getTargetValue(&Inst);
    assert(MaybeVal.hasValue());
    auto *Target = *MaybeVal;
    findOrInsertNode(Target);
    return;
  }

  auto addEdgeToGraph = [&](const Edge &E) {
    auto To = findOrInsertNode(E.To);
    auto From = findOrInsertNode(E.From);
    auto FlippedWeight = flipWeight(E.Weight);
    auto Attrs = E.AdditionalAttrs;
    Graph.addEdge(From, To, std::make_pair(E.Weight, Attrs),
                  std::make_pair(FlippedWeight, Attrs));
  };

  SmallVector<ConstantExpr *, 4> ConstantExprs;
  for (const Edge &E : Edges) {
    addEdgeToGraph(E);
    if (auto *Constexpr = dyn_cast<ConstantExpr>(E.To))
      ConstantExprs.push_back(Constexpr);
    if (auto *Constexpr = dyn_cast<ConstantExpr>(E.From))
      ConstantExprs.push_back(Constexpr);
  }

  for (ConstantExpr *CE : ConstantExprs) {
    Edges.clear();
    constexprToEdges(Analysis, *CE, Edges, TLI);
    std::for_each(Edges.begin(), Edges.end(), addEdgeToGraph);
  }
}

static void buildGraphFrom(CFLAAResult &Analysis, Function *Fn,
                           SmallVectorImpl<Value *> &ReturnedValues,
                           NodeMapT &Map, GraphT &Graph,
                           const TargetLibraryInfo &TLI) {
  // (N.B. We may remove graph construction entirely, because it doesn't really
  // buy us much.)
  for (auto &Bb : Fn->getBasicBlockList())
    for (auto &Inst : Bb.getInstList())
      addInstructionToGraph(Analysis, Inst, ReturnedValues, Map, Graph, TLI);
}

static bool canSkipAddingToSets(Value *Val) {
  // Constants can share instances, which may falsely unify multiple
  // sets, e.g. in
  // store i32* null, i32** %ptr1
  // store i32* null, i32** %ptr2
  // clearly ptr1 and ptr2 should not be unified into the same set, so
  // we should filter out the (potentially shared) instance to
  // i32* null.
  if (isa<Constant>(Val)) {
    // TODO: Because all of these things are constant, we can determine whether
    // the data is *actually* mutable at graph building time. This will probably
    // come for free/cheap with offset awareness.
    bool CanStoreMutableData = isa<GlobalValue>(Val) ||
                               isa<ConstantExpr>(Val) ||
                               isa<ConstantAggregate>(Val);
    return !CanStoreMutableData;
  }

  return false;
}

// Builds the graph + StratifiedSets for a function.
CFLAAResult::FunctionInfo CFLAAResult::buildSetsFrom(Function *Fn) {
  NodeMapT Map;
  GraphT Graph;
  SmallVector<Value *, 4> ReturnedValues;

  buildGraphFrom(*this, Fn, ReturnedValues, Map, Graph, TLI);

  DenseMap<GraphT::Node, Value *> NodeValueMap;
  NodeValueMap.reserve(Map.size());
  for (const auto &Pair : Map)
    NodeValueMap.insert(std::make_pair(Pair.second, Pair.first));

  const auto findValueOrDie = [&NodeValueMap](GraphT::Node Node) {
    auto ValIter = NodeValueMap.find(Node);
    assert(ValIter != NodeValueMap.end());
    return ValIter->second;
  };

  StratifiedSetsBuilder<Value *> Builder;

  SmallVector<GraphT::Node, 16> Worklist;
  SmallPtrSet<Value *, 16> Globals;
  for (auto &Pair : Map) {
    Worklist.clear();

    auto *Value = Pair.first;
    Builder.add(Value);
    auto InitialNode = Pair.second;
    Worklist.push_back(InitialNode);
    while (!Worklist.empty()) {
      auto Node = Worklist.pop_back_val();
      auto *CurValue = findValueOrDie(Node);
      if (canSkipAddingToSets(CurValue))
        continue;

      if (isa<GlobalValue>(CurValue))
        Globals.insert(CurValue);

      for (const auto &EdgeTuple : Graph.edgesFor(Node)) {
        auto Weight = std::get<0>(EdgeTuple);
        auto Label = Weight.first;
        auto &OtherNode = std::get<1>(EdgeTuple);
        auto *OtherValue = findValueOrDie(OtherNode);

        if (canSkipAddingToSets(OtherValue))
          continue;
        if (isa<GlobalValue>(OtherValue))
          Globals.insert(OtherValue);

        bool Added;
        switch (directionOfEdgeType(Label)) {
        case Level::Above:
          Added = Builder.addAbove(CurValue, OtherValue);
          break;
        case Level::Below:
          Added = Builder.addBelow(CurValue, OtherValue);
          break;
        case Level::Same:
          Added = Builder.addWith(CurValue, OtherValue);
          break;
        }

        auto Aliasing = Weight.second;
        Builder.noteAttributes(CurValue, Aliasing);
        Builder.noteAttributes(OtherValue, Aliasing);

        if (Added)
          Worklist.push_back(OtherNode);
      }
    }
  }

  // Special handling for globals and arguments
  auto ProcessGlobalOrArgValue = [&Builder](Value &Val) {
    Builder.add(&Val);
    auto Attr = valueToAttr(&Val);
    if (Attr.hasValue()) {
      Builder.noteAttributes(&Val, *Attr);
      // TODO: do we need to filter out non-pointer values here?
      Builder.addAttributesBelow(&Val, AttrUnknown);
    }
  };

  for (auto &Arg : Fn->args())
    ProcessGlobalOrArgValue(Arg);
  for (auto *Global : Globals)
    ProcessGlobalOrArgValue(*Global);

  return FunctionInfo(Builder.build(), std::move(ReturnedValues));
}

void CFLAAResult::scan(Function *Fn) {
  auto InsertPair = Cache.insert(std::make_pair(Fn, Optional<FunctionInfo>()));
  (void)InsertPair;
  assert(InsertPair.second &&
         "Trying to scan a function that has already been cached");

  // Note that we can't do Cache[Fn] = buildSetsFrom(Fn) here: the function call
  // may get evaluated after operator[], potentially triggering a DenseMap
  // resize and invalidating the reference returned by operator[]
  auto FunInfo = buildSetsFrom(Fn);
  Cache[Fn] = std::move(FunInfo);

  Handles.push_front(FunctionHandle(Fn, this));
}

void CFLAAResult::evict(Function *Fn) { Cache.erase(Fn); }

/// Ensures that the given function is available in the cache, and returns the
/// entry.
const Optional<CFLAAResult::FunctionInfo> &
CFLAAResult::ensureCached(Function *Fn) {
  auto Iter = Cache.find(Fn);
  if (Iter == Cache.end()) {
    scan(Fn);
    Iter = Cache.find(Fn);
    assert(Iter != Cache.end());
    assert(Iter->second.hasValue());
  }
  return Iter->second;
}

AliasResult CFLAAResult::query(const MemoryLocation &LocA,
                               const MemoryLocation &LocB) {
  auto *ValA = const_cast<Value *>(LocA.Ptr);
  auto *ValB = const_cast<Value *>(LocB.Ptr);

  Function *Fn = nullptr;
  auto MaybeFnA = parentFunctionOfValue(ValA);
  auto MaybeFnB = parentFunctionOfValue(ValB);
  if (!MaybeFnA.hasValue() && !MaybeFnB.hasValue()) {
    // The only times this is known to happen are when globals + InlineAsm are
    // involved
    DEBUG(dbgs() << "CFLAA: could not extract parent function information.\n");
    return MayAlias;
  }

  if (MaybeFnA.hasValue()) {
    Fn = *MaybeFnA;
    assert((!MaybeFnB.hasValue() || *MaybeFnB == *MaybeFnA) &&
           "Interprocedural queries not supported");
  } else {
    Fn = *MaybeFnB;
  }

  assert(Fn != nullptr);
  auto &MaybeInfo = ensureCached(Fn);
  assert(MaybeInfo.hasValue());

  auto &Sets = MaybeInfo->Sets;
  auto MaybeA = Sets.find(ValA);
  if (!MaybeA.hasValue())
    return MayAlias;

  auto MaybeB = Sets.find(ValB);
  if (!MaybeB.hasValue())
    return MayAlias;

  auto SetA = *MaybeA;
  auto SetB = *MaybeB;
  auto AttrsA = Sets.getLink(SetA.Index).Attrs;
  auto AttrsB = Sets.getLink(SetB.Index).Attrs;

  // If both values are local (meaning the corresponding set has attribute
  // AttrNone or AttrEscaped), then we know that CFLAA fully models them: they
  // may-alias each other if and only if they are in the same set
  // If at least one value is non-local (meaning it either is global/argument or
  // it comes from unknown sources like integer cast), the situation becomes a
  // bit more interesting. We follow three general rules described below:
  // - Non-local values may alias each other
  // - AttrNone values do not alias any non-local values
  // - AttrEscaped do not alias globals/arguments, but they may alias
  // AttrUnknown values
  if (SetA.Index == SetB.Index)
    return MayAlias;
  if (AttrsA.none() || AttrsB.none())
    return NoAlias;
  if (isUnknownAttr(AttrsA) || isUnknownAttr(AttrsB))
    return MayAlias;
  if (isGlobalOrArgAttr(AttrsA) && isGlobalOrArgAttr(AttrsB))
    return MayAlias;
  return NoAlias;
}

char CFLAA::PassID;

CFLAAResult CFLAA::run(Function &F, AnalysisManager<Function> &AM) {
  return CFLAAResult(AM.getResult<TargetLibraryAnalysis>(F));
}

char CFLAAWrapperPass::ID = 0;
INITIALIZE_PASS(CFLAAWrapperPass, "cfl-aa", "CFL-Based Alias Analysis", false,
                true)

ImmutablePass *llvm::createCFLAAWrapperPass() { return new CFLAAWrapperPass(); }

CFLAAWrapperPass::CFLAAWrapperPass() : ImmutablePass(ID) {
  initializeCFLAAWrapperPassPass(*PassRegistry::getPassRegistry());
}

void CFLAAWrapperPass::initializePass() {
  auto &TLIWP = getAnalysis<TargetLibraryInfoWrapperPass>();
  Result.reset(new CFLAAResult(TLIWP.getTLI()));
}

void CFLAAWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
  AU.setPreservesAll();
  AU.addRequired<TargetLibraryInfoWrapperPass>();
}