DataFlowFramework.h

Go to the documentation of this file.

//===- DataFlowFramework.h - A generic framework for data-flow analysis ---===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file defines a generic framework for writing data-flow analysis in MLIR.
// The framework consists of a solver, which runs the fixed-point iteration and
// manages analysis dependencies, and a data-flow analysis class used to
// implement specific analyses.
//
//===----------------------------------------------------------------------===//
 
#ifndef MLIR_ANALYSIS_DATAFLOWFRAMEWORK_H
#define MLIR_ANALYSIS_DATAFLOWFRAMEWORK_H
 
#include "mlir/IR/Operation.h"
#include "mlir/Support/StorageUniquer.h"
#include "llvm/ADT/Hashing.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/TypeName.h"
#include <queue>
#include <tuple>
 
namespace mlir {
 
//===----------------------------------------------------------------------===//
// ChangeResult
//===----------------------------------------------------------------------===//
 
/// A result type used to indicate if a change happened. Boolean operations on
/// ChangeResult behave as though `Change` is truth.
enum class [[nodiscard]] ChangeResult {
  NoChange,
  Change,
};
inline ChangeResult operator|(ChangeResult lhs, ChangeResult rhs) {
  return lhs == ChangeResult::Change ? lhs : rhs;
}
inline ChangeResult &operator|=(ChangeResult &lhs, ChangeResult rhs) {
  lhs = lhs | rhs;
  return lhs;
}
inline ChangeResult operator&(ChangeResult lhs, ChangeResult rhs) {
  return lhs == ChangeResult::NoChange ? lhs : rhs;
}
 
/// Forward declare the analysis state class.
class AnalysisState;
 
/// Program point represents a specific location in the execution of a program.
/// A sequence of program points can be combined into a control flow graph.
struct ProgramPoint : public StorageUniquer::BaseStorage {
  /// Creates a new program point at the given location.
  ProgramPoint(Block *parentBlock, Block::iterator pp)
      : block(parentBlock), point(pp) {}
 
  /// Creates a new program point at the given operation.
  ProgramPoint(Operation *op) : op(op) {}
 
  /// The concrete key type used by the storage uniquer. This class is uniqued
  /// by its contents.
  using KeyTy = std::tuple<Block *, Block::iterator, Operation *>;
 
  /// Create a empty program point.
  ProgramPoint() {}
 
  /// Create a new program point from the given program point.
  ProgramPoint(const ProgramPoint &point) {
    this->block = point.getBlock();
    this->point = point.getPoint();
    this->op = point.getOperation();
  }
 
  static ProgramPoint *construct(StorageUniquer::StorageAllocator &alloc,
                                 KeyTy &&key) {
    if (std::get<0>(key)) {
      return new (alloc.allocate<ProgramPoint>())
          ProgramPoint(std::get<0>(key), std::get<1>(key));
    }
    return new (alloc.allocate<ProgramPoint>()) ProgramPoint(std::get<2>(key));
  }
 
  /// Returns true if this program point is set.
  bool isNull() const { return block == nullptr && op == nullptr; }
 
  /// Two program points are equal if their block and iterator are equal.
  bool operator==(const KeyTy &key) const {
    return block == std::get<0>(key) && point == std::get<1>(key) &&
           op == std::get<2>(key);
  }
 
  bool operator==(const ProgramPoint &pp) const {
    return block == pp.block && point == pp.point && op == pp.op;
  }
 
  /// Get the block contains this program point.
  Block *getBlock() const { return block; }
 
  /// Get the the iterator this program point refers to.
  Block::iterator getPoint() const { return point; }
 
  /// Get the the iterator this program point refers to.
  Operation *getOperation() const { return op; }
 
  /// Get the next operation of this program point.
  Operation *getNextOp() const {
    assert(!isBlockEnd());
    // If the current program point has no parent block, both the next op and
    // the previous op point to the op corresponding to the current program
    // point.
    if (block == nullptr) {
      return op;
    }
    return &*point;
  }
 
  /// Get the previous operation of this program point.
  Operation *getPrevOp() const {
    assert(!isBlockStart());
    // If the current program point has no parent block, both the next op and
    // the previous op point to the op corresponding to the current program
    // point.
    if (block == nullptr) {
      return op;
    }
    return &*(--Block::iterator(point));
  }
 
  bool isBlockStart() const { return block && block->begin() == point; }
 
  bool isBlockEnd() const { return block && block->end() == point; }
 
  /// Print the program point.
  void print(raw_ostream &os) const;
 
private:
  Block *block = nullptr;
  Block::iterator point;
 
  /// For operations without a parent block, we record the operation itself as
  /// its program point.
  Operation *op = nullptr;
};
 
inline raw_ostream &operator<<(raw_ostream &os, ProgramPoint point) {
  point.print(os);
  return os;
}
 
//===----------------------------------------------------------------------===//
// GenericLatticeAnchor
//===----------------------------------------------------------------------===//
 
/// Abstract class for generic lattice anchor. In classical data-flow analysis,
/// lattice anchor represent positions in a program to which lattice elements
/// are attached. In sparse data-flow analysis, these can be SSA values, and in
/// dense data-flow analysis, these are the program points before and after
/// every operation.
///
/// Lattice anchor are implemented using MLIR's storage uniquer framework and
/// type ID system to provide RTTI.
class GenericLatticeAnchor : public StorageUniquer::BaseStorage {
public:
  virtual ~GenericLatticeAnchor();
 
  /// Get the abstract lattice anchor's type identifier.
  TypeID getTypeID() const { return typeID; }
 
  /// Get a derived source location for the lattice anchor.
  virtual Location getLoc() const = 0;
 
  /// Print the lattice anchor.
  virtual void print(raw_ostream &os) const = 0;
 
protected:
  /// Create an abstract lattice anchor with type identifier.
  explicit GenericLatticeAnchor(TypeID typeID) : typeID(typeID) {}
 
private:
  /// The type identifier of the lattice anchor.
  TypeID typeID;
};
 
//===----------------------------------------------------------------------===//
// GenericLatticeAnchorBase
//===----------------------------------------------------------------------===//
 
/// Base class for generic lattice anchor based on a concrete lattice anchor
/// type and a content key. This class defines the common methods required for
/// operability with the storage uniquer framework.
///
/// The provided key type uniquely identifies the concrete lattice anchor
/// instance and are the data members of the class.
template <typename ConcreteT, typename Value>
class GenericLatticeAnchorBase : public GenericLatticeAnchor {
public:
  /// The concrete key type used by the storage uniquer. This class is uniqued
  /// by its contents.
  using KeyTy = Value;
  /// Alias for the base class.
  using Base = GenericLatticeAnchorBase<ConcreteT, Value>;
 
  /// Construct an instance of the lattice anchor using the provided value and
  /// the type ID of the concrete type.
  template <typename ValueT>
  explicit GenericLatticeAnchorBase(ValueT &&value)
      : GenericLatticeAnchor(TypeID::get<ConcreteT>()),
        value(std::forward<ValueT>(value)) {}
 
  /// Get a uniqued instance of this lattice anchor class with the given
  /// arguments.
  template <typename... Args>
  static ConcreteT *get(StorageUniquer &uniquer, Args &&...args) {
    return uniquer.get<ConcreteT>(/*initFn=*/{}, std::forward<Args>(args)...);
  }
 
  /// Allocate space for a lattice anchor and construct it in-place.
  template <typename ValueT>
  static ConcreteT *construct(StorageUniquer::StorageAllocator &alloc,
                              ValueT &&value) {
    return new (alloc.allocate<ConcreteT>())
        ConcreteT(std::forward<ValueT>(value));
  }
 
  /// Two lattice anchors are equal if their values are equal.
  bool operator==(const Value &value) const { return this->value == value; }
 
  /// Provide LLVM-style RTTI using type IDs.
  static bool classof(const GenericLatticeAnchor *point) {
    return point->getTypeID() == TypeID::get<ConcreteT>();
  }
 
  /// Get the contents of the lattice anchor.
  const Value &getValue() const { return value; }
 
private:
  /// The lattice anchor value.
  Value value;
};
 
//===----------------------------------------------------------------------===//
// LatticeAnchor
//===----------------------------------------------------------------------===//
 
/// Fundamental IR components are supported as first-class lattice anchor.
struct LatticeAnchor
    : public PointerUnion<GenericLatticeAnchor *, ProgramPoint *, Value> {
  using ParentTy = PointerUnion<GenericLatticeAnchor *, ProgramPoint *, Value>;
  /// Inherit constructors.
  using ParentTy::PointerUnion;
  /// Allow implicit conversion from the parent type.
  LatticeAnchor(ParentTy point = nullptr) : ParentTy(point) {}
 
  /// Print the lattice anchor.
  void print(raw_ostream &os) const;
 
  /// Get the source location of the lattice anchor.
  Location getLoc() const;
};
 
/// Forward declaration of the data-flow analysis class.
class DataFlowAnalysis;
 
//===----------------------------------------------------------------------===//
// DataFlowConfig
//===----------------------------------------------------------------------===//
 
/// Configuration class for data flow solver and child analyses. Follows the
/// fluent API pattern.
class DataFlowConfig {
public:
  DataFlowConfig() = default;
 
  /// Set whether the solver should operate interpocedurally, i.e. enter the
  /// callee body when available. Interprocedural analyses may be more precise,
  /// but also more expensive as more states need to be computed and the
  /// fixpoint convergence takes longer.
  DataFlowConfig &setInterprocedural(bool enable) {
    interprocedural = enable;
    return *this;
  }
 
  /// Return `true` if the solver operates interprocedurally, `false` otherwise.
  bool isInterprocedural() const { return interprocedural; }
 
private:
  bool interprocedural = true;
};
 
//===----------------------------------------------------------------------===//
// DataFlowSolver
//===----------------------------------------------------------------------===//
 
/// The general data-flow analysis solver. This class is responsible for
/// orchestrating child data-flow analyses, running the fixed-point iteration
/// algorithm, managing analysis state and lattice anchor memory, and tracking
/// dependencies between analyses, lattice anchor, and analysis states.
///
/// Steps to run a data-flow analysis:
///
/// 1. Load and initialize children analyses. Children analyses are instantiated
///    in the solver and initialized, building their dependency relations.
/// 2. Configure and run the analysis. The solver invokes the children analyses
///    according to their dependency relations until a fixed point is reached.
/// 3. Query analysis state results from the solver.
///
/// TODO: Optimize the internal implementation of the solver.
class DataFlowSolver {
public:
  explicit DataFlowSolver(const DataFlowConfig &config = DataFlowConfig())
      : config(config) {
    uniquer.registerParametricStorageType<ProgramPoint>();
  }
 
  /// Load an analysis into the solver. Return the analysis instance.
  template <typename AnalysisT, typename... Args>
  AnalysisT *load(Args &&...args);
 
  /// Initialize the children analyses starting from the provided top-level
  /// operation and run the analysis until fixpoint.
  LogicalResult initializeAndRun(Operation *top);
 
  /// Lookup an analysis state for the given lattice anchor. Returns null if one
  /// does not exist.
  template <typename StateT, typename AnchorT>
  const StateT *lookupState(AnchorT anchor) const {
    auto it =
        analysisStates.find({LatticeAnchor(anchor), TypeID::get<StateT>()});
    if (it == analysisStates.end())
      return nullptr;
    return static_cast<const StateT *>(it->second.get());
  }
 
  /// Erase any analysis state associated with the given lattice anchor.
  template <typename AnchorT>
  void eraseState(AnchorT anchor) {
    LatticeAnchor la(anchor);
 
    for (auto it = analysisStates.begin(); it != analysisStates.end(); ++it) {
      if (it->first.first == la)
        analysisStates.erase(it);
    }
  }
 
  /// Get a uniqued lattice anchor instance. If one is not present, it is
  /// created with the provided arguments.
  template <typename AnchorT, typename... Args>
  AnchorT *getLatticeAnchor(Args &&...args) {
    return AnchorT::get(uniquer, std::forward<Args>(args)...);
  }
 
  /// Get a uniqued program point instance.
  ProgramPoint *getProgramPointBefore(Operation *op) {
    if (op->getBlock())
      return uniquer.get<ProgramPoint>(/*initFn*/ {}, op->getBlock(),
                                       Block::iterator(op), nullptr);
    else
      return uniquer.get<ProgramPoint>(/*initFn*/ {}, nullptr,
                                       Block::iterator(), op);
  }
 
  ProgramPoint *getProgramPointBefore(Block *block) {
    return uniquer.get<ProgramPoint>(/*initFn*/ {}, block, block->begin(),
                                     nullptr);
  }
 
  ProgramPoint *getProgramPointAfter(Operation *op) {
    if (op->getBlock())
      return uniquer.get<ProgramPoint>(/*initFn*/ {}, op->getBlock(),
                                       ++Block::iterator(op), nullptr);
    else
      return uniquer.get<ProgramPoint>(/*initFn*/ {}, nullptr,
                                       Block::iterator(), op);
  }
 
  ProgramPoint *getProgramPointAfter(Block *block) {
    return uniquer.get<ProgramPoint>(/*initFn*/ {}, block, block->end(),
                                     nullptr);
  }
 
  /// A work item on the solver queue is a program point, child analysis pair.
  /// Each item is processed by invoking the child analysis at the program
  /// point.
  using WorkItem = std::pair<ProgramPoint *, DataFlowAnalysis *>;
  /// Push a work item onto the worklist.
  void enqueue(WorkItem item) { worklist.push(std::move(item)); }
 
  /// Get the state associated with the given lattice anchor. If it does not
  /// exist, create an uninitialized state.
  template <typename StateT, typename AnchorT>
  StateT *getOrCreateState(AnchorT anchor);
 
  /// Propagate an update to an analysis state if it changed by pushing
  /// dependent work items to the back of the queue.
  void propagateIfChanged(AnalysisState *state, ChangeResult changed);
 
  /// Get the configuration of the solver.
  const DataFlowConfig &getConfig() const { return config; }
 
private:
  /// Configuration of the dataflow solver.
  DataFlowConfig config;
 
  /// The solver's work queue. Work items can be inserted to the front of the
  /// queue to be processed greedily, speeding up computations that otherwise
  /// quickly degenerate to quadratic due to propagation of state updates.
  std::queue<WorkItem> worklist;
 
  /// Type-erased instances of the children analyses.
  SmallVector<std::unique_ptr<DataFlowAnalysis>> childAnalyses;
 
  /// The storage uniquer instance that owns the memory of the allocated lattice
  /// anchors
  StorageUniquer uniquer;
 
  /// A type-erased map of lattice anchors to associated analysis states for
  /// first-class lattice anchors.
  DenseMap<std::pair<LatticeAnchor, TypeID>, std::unique_ptr<AnalysisState>>
      analysisStates;
 
  /// Allow the base child analysis class to access the internals of the solver.
  friend class DataFlowAnalysis;
};
 
//===----------------------------------------------------------------------===//
// AnalysisState
//===----------------------------------------------------------------------===//
 
/// Base class for generic analysis states. Analysis states contain data-flow
/// information that are attached to lattice anchors and which evolve as the
/// analysis iterates.
///
/// This class places no restrictions on the semantics of analysis states beyond
/// these requirements.
///
/// 1. Querying the state of a lattice anchor prior to visiting that anchor
///    results in uninitialized state. Analyses must be aware of unintialized
///    states.
/// 2. Analysis states can reach fixpoints, where subsequent updates will never
///    trigger a change in the state.
/// 3. Analysis states that are uninitialized can be forcefully initialized to a
///    default value.
class AnalysisState {
public:
  virtual ~AnalysisState();
 
  /// Create the analysis state on the given lattice anchor.
  AnalysisState(LatticeAnchor anchor) : anchor(anchor) {}
 
  /// Returns the lattice anchor this state is located at.
  LatticeAnchor getAnchor() const { return anchor; }
 
  /// Print the contents of the analysis state.
  virtual void print(raw_ostream &os) const = 0;
  LLVM_DUMP_METHOD void dump() const;
 
  /// Add a dependency to this analysis state on a lattice anchor and an
  /// analysis. If this state is updated, the analysis will be invoked on the
  /// given lattice anchor again (in onUpdate()).
  void addDependency(ProgramPoint *point, DataFlowAnalysis *analysis);
 
protected:
  /// This function is called by the solver when the analysis state is updated
  /// to enqueue more work items. For example, if a state tracks dependents
  /// through the IR (e.g. use-def chains), this function can be implemented to
  /// push those dependents on the worklist.
  virtual void onUpdate(DataFlowSolver *solver) const {
    for (const DataFlowSolver::WorkItem &item : dependents)
      solver->enqueue(item);
  }
 
  /// The lattice anchor to which the state belongs.
  LatticeAnchor anchor;
 
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
  /// When compiling with debugging, keep a name for the analysis state.
  StringRef debugName;
#endif // LLVM_ENABLE_ABI_BREAKING_CHECKS
 
private:
  /// The dependency relations originating from this analysis state. An entry
  /// `state -> (analysis, anchor)` is created when `analysis` queries `state`
  /// when updating `anchor`.
  ///
  /// When this state is updated, all dependent child analysis invocations are
  /// pushed to the back of the queue. Use a `SetVector` to keep the analysis
  /// deterministic.
  ///
  /// Store the dependents on the analysis state for efficiency.
  SetVector<DataFlowSolver::WorkItem> dependents;
 
  /// Allow the framework to access the dependents.
  friend class DataFlowSolver;
};
 
//===----------------------------------------------------------------------===//
// DataFlowAnalysis
//===----------------------------------------------------------------------===//
 
/// Base class for all data-flow analyses. A child analysis is expected to build
/// an initial dependency graph (and optionally provide an initial state) when
/// initialized and define transfer functions when visiting program points.
///
/// In classical data-flow analysis, the dependency graph is fixed and analyses
/// define explicit transfer functions between input states and output states.
/// In this framework, however, the dependency graph can change during the
/// analysis, and transfer functions are opaque such that the solver doesn't
/// know what states calling `visit` on an analysis will be updated. This allows
/// multiple analyses to plug in and provide values for the same state.
///
/// Generally, when an analysis queries an uninitialized state, it is expected
/// to "bail out", i.e., not provide any updates. When the value is initialized,
/// the solver will re-invoke the analysis. If the solver exhausts its worklist,
/// however, and there are still uninitialized states, the solver "nudges" the
/// analyses by default-initializing those states.
class DataFlowAnalysis {
public:
  virtual ~DataFlowAnalysis();
 
  /// Create an analysis with a reference to the parent solver.
  explicit DataFlowAnalysis(DataFlowSolver &solver);
 
  /// Initialize the analysis from the provided top-level operation by building
  /// an initial dependency graph between all lattice anchors of interest. This
  /// can be implemented by calling `visit` on all program points of interest
  /// below the top-level operation.
  ///
  /// An analysis can optionally provide initial values to certain analysis
  /// states to influence the evolution of the analysis.
  virtual LogicalResult initialize(Operation *top) = 0;
 
  /// Visit the given program point. This function is invoked by the solver on
  /// this analysis with a given program point when a dependent analysis state
  /// is updated. The function is similar to a transfer function; it queries
  /// certain analysis states and sets other states.
  ///
  /// The function is expected to create dependencies on queried states and
  /// propagate updates on changed states. A dependency can be created by
  /// calling `addDependency` between the input state and a program point,
  /// indicating that, if the state is updated, the solver should invoke `solve`
  /// on the program point. The dependent point does not have to be the same as
  /// the provided point. An update to a state is propagated by calling
  /// `propagateIfChange` on the state. If the state has changed, then all its
  /// dependents are placed on the worklist.
  ///
  /// The dependency graph does not need to be static. Each invocation of
  /// `visit` can add new dependencies, but these dependencies will not be
  /// dynamically added to the worklist because the solver doesn't know what
  /// will provide a value for then.
  virtual LogicalResult visit(ProgramPoint *point) = 0;
 
protected:
  /// Create a dependency between the given analysis state and lattice anchor
  /// on this analysis.
  void addDependency(AnalysisState *state, ProgramPoint *point);
 
  /// Propagate an update to a state if it changed.
  void propagateIfChanged(AnalysisState *state, ChangeResult changed);
 
  /// Register a custom lattice anchor class.
  template <typename AnchorT>
  void registerAnchorKind() {
    solver.uniquer.registerParametricStorageType<AnchorT>();
  }
 
  /// Get or create a custom lattice anchor.
  template <typename AnchorT, typename... Args>
  AnchorT *getLatticeAnchor(Args &&...args) {
    return solver.getLatticeAnchor<AnchorT>(std::forward<Args>(args)...);
  }
 
  /// Get the analysis state associated with the lattice anchor. The returned
  /// state is expected to be "write-only", and any updates need to be
  /// propagated by `propagateIfChanged`.
  template <typename StateT, typename AnchorT>
  StateT *getOrCreate(AnchorT anchor) {
    return solver.getOrCreateState<StateT>(anchor);
  }
 
  /// Get a read-only analysis state for the given point and create a dependency
  /// on `dependent`. If the return state is updated elsewhere, this analysis is
  /// re-invoked on the dependent.
  template <typename StateT, typename AnchorT>
  const StateT *getOrCreateFor(ProgramPoint *dependent, AnchorT anchor) {
    StateT *state = getOrCreate<StateT>(anchor);
    addDependency(state, dependent);
    return state;
  }
 
  /// Get a uniqued program point instance.
  ProgramPoint *getProgramPointBefore(Operation *op) {
    return solver.getProgramPointBefore(op);
  }
 
  ProgramPoint *getProgramPointBefore(Block *block) {
    return solver.getProgramPointBefore(block);
  }
 
  ProgramPoint *getProgramPointAfter(Operation *op) {
    return solver.getProgramPointAfter(op);
  }
 
  ProgramPoint *getProgramPointAfter(Block *block) {
    return solver.getProgramPointAfter(block);
  }
 
  /// Return the configuration of the solver used for this analysis.
  const DataFlowConfig &getSolverConfig() const { return solver.getConfig(); }
 
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
  /// When compiling with debugging, keep a name for the analyis.
  StringRef debugName;
#endif // LLVM_ENABLE_ABI_BREAKING_CHECKS
 
private:
  /// The parent data-flow solver.
  DataFlowSolver &solver;
 
  /// Allow the data-flow solver to access the internals of this class.
  friend class DataFlowSolver;
};
 
template <typename AnalysisT, typename... Args>
AnalysisT *DataFlowSolver::load(Args &&...args) {
  childAnalyses.emplace_back(new AnalysisT(*this, std::forward<Args>(args)...));
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
  childAnalyses.back().get()->debugName = llvm::getTypeName<AnalysisT>();
#endif // LLVM_ENABLE_ABI_BREAKING_CHECKS
  return static_cast<AnalysisT *>(childAnalyses.back().get());
}
 
template <typename StateT, typename AnchorT>
StateT *DataFlowSolver::getOrCreateState(AnchorT anchor) {
  std::unique_ptr<AnalysisState> &state =
      analysisStates[{LatticeAnchor(anchor), TypeID::get<StateT>()}];
  if (!state) {
    state = std::unique_ptr<StateT>(new StateT(anchor));
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
    state->debugName = llvm::getTypeName<StateT>();
#endif // LLVM_ENABLE_ABI_BREAKING_CHECKS
  }
  return static_cast<StateT *>(state.get());
}
 
inline raw_ostream &operator<<(raw_ostream &os, const AnalysisState &state) {
  state.print(os);
  return os;
}
 
inline raw_ostream &operator<<(raw_ostream &os, LatticeAnchor anchor) {
  anchor.print(os);
  return os;
}
 
} // end namespace mlir
 
namespace llvm {
/// Allow hashing of lattice anchors and program points.
template <>
struct DenseMapInfo<mlir::ProgramPoint> {
  static mlir::ProgramPoint getEmptyKey() {
    void *pointer = llvm::DenseMapInfo<void *>::getEmptyKey();
    return mlir::ProgramPoint(
        (mlir::Block *)pointer,
        mlir::Block::iterator((mlir::Operation *)pointer));
  }
  static mlir::ProgramPoint getTombstoneKey() {
    void *pointer = llvm::DenseMapInfo<void *>::getTombstoneKey();
    return mlir::ProgramPoint(
        (mlir::Block *)pointer,
        mlir::Block::iterator((mlir::Operation *)pointer));
  }
  static unsigned getHashValue(mlir::ProgramPoint pp) {
    return hash_combine(pp.getBlock(), pp.getPoint().getNodePtr());
  }
  static bool isEqual(mlir::ProgramPoint lhs, mlir::ProgramPoint rhs) {
    return lhs == rhs;
  }
};
 
template <>
struct DenseMapInfo<mlir::LatticeAnchor>
    : public DenseMapInfo<mlir::LatticeAnchor::ParentTy> {};
 
// Allow llvm::cast style functions.
template <typename To>
struct CastInfo<To, mlir::LatticeAnchor>
    : public CastInfo<To, mlir::LatticeAnchor::PointerUnion> {};
 
template <typename To>
struct CastInfo<To, const mlir::LatticeAnchor>
    : public CastInfo<To, const mlir::LatticeAnchor::PointerUnion> {};
 
} // end namespace llvm
 
#endif // MLIR_ANALYSIS_DATAFLOWFRAMEWORK_H