DependenceAnalysis.h

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//===-- llvm/Analysis/DependenceAnalysis.h -------------------- -*- C++ -*-===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// DependenceAnalysis is an LLVM pass that analyses dependences between memory
// accesses. Currently, it is an implementation of the approach described in
//
//            Practical Dependence Testing
//            Goff, Kennedy, Tseng
//            PLDI 1991
//
// There's a single entry point that analyzes the dependence between a pair
// of memory references in a function, returning either NULL, for no dependence,
// or a more-or-less detailed description of the dependence between them.
//
// This pass exists to support the DependenceGraph pass. There are two separate
// passes because there's a useful separation of concerns. A dependence exists
// if two conditions are met:
//
//    1) Two instructions reference the same memory location, and
//    2) There is a flow of control leading from one instruction to the other.
//
// DependenceAnalysis attacks the first condition; DependenceGraph will attack
// the second (it's not yet ready).
//
// Please note that this is work in progress and the interface is subject to
// change.
//
// Plausible changes:
//    Return a set of more precise dependences instead of just one dependence
//    summarizing all.
//
//===----------------------------------------------------------------------===//
 
#ifndef LLVM_ANALYSIS_DEPENDENCEANALYSIS_H
#define LLVM_ANALYSIS_DEPENDENCEANALYSIS_H
 
#include "llvm/ADT/SmallBitVector.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/PassManager.h"
#include "llvm/Pass.h"
#include "llvm/Support/Compiler.h"
 
namespace llvm {
class AAResults;
struct AnalysisOptions;
template <typename T> class ArrayRef;
class Loop;
class LoopInfo;
class SCEVConstant;
class raw_ostream;
 
/// Dependence - This class represents a dependence between two memory
/// memory references in a function. It contains minimal information and
/// is used in the very common situation where the compiler is unable to
/// determine anything beyond the existence of a dependence; that is, it
/// represents a confused dependence (see also FullDependence). In most
/// cases (for output, flow, and anti dependences), the dependence implies
/// an ordering, where the source must precede the destination; in contrast,
/// input dependences are unordered.
///
/// When a dependence graph is built, each Dependence will be a member of
/// the set of predecessor edges for its destination instruction and a set
/// if successor edges for its source instruction. These sets are represented
/// as singly-linked lists, with the "next" fields stored in the dependence
/// itelf.
class LLVM_ABI Dependence {
protected:
  Dependence(Dependence &&) = default;
  Dependence &operator=(Dependence &&) = default;
 
public:
  Dependence(Instruction *Source, Instruction *Destination,
             const SCEVUnionPredicate &A)
      : Src(Source), Dst(Destination), Assumptions(A) {}
  virtual ~Dependence() = default;
 
  /// Dependence::DVEntry - Each level in the distance/direction vector
  /// has a direction (or perhaps a union of several directions), and
  /// perhaps a distance.
  /// The dependency information could be across a single loop level or across
  /// two separate levels that have the same trip count and nesting depth,
  /// which helps to provide information for loop fusion candidation.
  /// For example, loops b and c have the same iteration count and depth:
  ///    for (a = ...) {
  ///      for (b = 0; b < 10; b++) {
  ///      }
  ///      for (c = 0; c < 10; c++) {
  ///      }
  ///    }
  struct DVEntry {
    enum : unsigned char {
      NONE = 0,
      LT = 1,
      EQ = 2,
      LE = 3,
      GT = 4,
      NE = 5,
      GE = 6,
      ALL = 7
    };
    unsigned char Direction : 3; // Init to ALL, then refine.
    bool Scalar : 1;             // Init to true.
    const SCEV *Distance = nullptr; // NULL implies no distance available.
    DVEntry() : Direction(ALL), Scalar(true) {}
  };
 
  /// getSrc - Returns the source instruction for this dependence.
  Instruction *getSrc() const { return Src; }
 
  /// getDst - Returns the destination instruction for this dependence.
  Instruction *getDst() const { return Dst; }
 
  /// isInput - Returns true if this is an input dependence.
  bool isInput() const;
 
  /// isOutput - Returns true if this is an output dependence.
  bool isOutput() const;
 
  /// isFlow - Returns true if this is a flow (aka true) dependence.
  bool isFlow() const;
 
  /// isAnti - Returns true if this is an anti dependence.
  bool isAnti() const;
 
  /// isOrdered - Returns true if dependence is Output, Flow, or Anti
  bool isOrdered() const { return isOutput() || isFlow() || isAnti(); }
 
  /// isUnordered - Returns true if dependence is Input
  bool isUnordered() const { return isInput(); }
 
  /// isLoopIndependent - Returns true if this is a loop-independent
  /// dependence.
  virtual bool isLoopIndependent() const { return true; }
 
  /// isConfused - Returns true if this dependence is confused
  /// (the compiler understands nothing and makes worst-case assumptions).
  virtual bool isConfused() const { return true; }
 
  /// getLevels - Returns the number of common loops surrounding the
  /// source and destination of the dependence.
  virtual unsigned getLevels() const { return 0; }
 
  /// getSameSDLevels - Returns the number of separate SameSD loops surrounding
  /// the source and destination of the dependence.
  virtual unsigned getSameSDLevels() const { return 0; }
 
  /// getDirection - Returns the direction associated with a particular
  /// common or SameSD level.
  virtual unsigned getDirection(unsigned Level, bool SameSD = false) const {
    return DVEntry::ALL;
  }
 
  /// getDistance - Returns the distance (or NULL) associated with a
  /// particular common or SameSD level.
  virtual const SCEV *getDistance(unsigned Level, bool SameSD = false) const {
    return nullptr;
  }
 
  /// Check if the direction vector is negative. A negative direction
  /// vector means Src and Dst are reversed in the actual program.
  virtual bool isDirectionNegative() const { return false; }
 
  /// Negate the dependence by swapping the source and destination, and
  /// reversing the direction and distance information.
  virtual void negate(ScalarEvolution &SE) {}
 
  /// If the direction vector is negative, normalize the direction
  /// vector to make it non-negative. Normalization is done by reversing
  /// Src and Dst, plus reversing the dependence directions and distances
  /// in the vector.
  virtual bool normalize(ScalarEvolution *SE) { return false; }
 
  /// inSameSDLoops - Returns true if this level is an SameSD level, i.e.,
  /// performed across two separate loop nests that have the Same Iteration and
  /// Depth.
  virtual bool inSameSDLoops(unsigned Level) const { return false; }
 
  /// isScalar - Returns true if a particular regular or SameSD level is
  /// scalar; that is, if no subscript in the source or destination mention
  /// the induction variable associated with the loop at this level.
  virtual bool isScalar(unsigned Level, bool SameSD = false) const;
 
  /// getNextPredecessor - Returns the value of the NextPredecessor field.
  const Dependence *getNextPredecessor() const { return NextPredecessor; }
 
  /// getNextSuccessor - Returns the value of the NextSuccessor field.
  const Dependence *getNextSuccessor() const { return NextSuccessor; }
 
  /// setNextPredecessor - Sets the value of the NextPredecessor
  /// field.
  void setNextPredecessor(const Dependence *pred) { NextPredecessor = pred; }
 
  /// setNextSuccessor - Sets the value of the NextSuccessor field.
  void setNextSuccessor(const Dependence *succ) { NextSuccessor = succ; }
 
  /// getRuntimeAssumptions - Returns the runtime assumptions under which this
  /// Dependence relation is valid.
  SCEVUnionPredicate getRuntimeAssumptions() const { return Assumptions; }
 
  /// dump - For debugging purposes, dumps a dependence to OS.
  void dump(raw_ostream &OS) const;
 
  /// dumpImp - For debugging purposes. Dumps a dependence to OS with or
  /// without considering the SameSD levels.
  void dumpImp(raw_ostream &OS, bool IsSameSD = false) const;
 
protected:
  Instruction *Src, *Dst;
 
private:
  SCEVUnionPredicate Assumptions;
  const Dependence *NextPredecessor = nullptr, *NextSuccessor = nullptr;
  friend class DependenceInfo;
};
 
/// FullDependence - This class represents a dependence between two memory
/// references in a function. It contains detailed information about the
/// dependence (direction vectors, etc.) and is used when the compiler is
/// able to accurately analyze the interaction of the references; that is,
/// it is not a confused dependence (see Dependence). In most cases
/// (for output, flow, and anti dependences), the dependence implies an
/// ordering, where the source must precede the destination; in contrast,
/// input dependences are unordered.
class LLVM_ABI FullDependence final : public Dependence {
public:
  FullDependence(Instruction *Source, Instruction *Destination,
                 const SCEVUnionPredicate &Assumes,
                 bool PossiblyLoopIndependent, unsigned Levels);
 
  /// isLoopIndependent - Returns true if this is a loop-independent
  /// dependence.
  bool isLoopIndependent() const override { return LoopIndependent; }
 
  /// isConfused - Returns true if this dependence is confused
  /// (the compiler understands nothing and makes worst-case
  /// assumptions).
  bool isConfused() const override { return false; }
 
  /// getLevels - Returns the number of common loops surrounding the
  /// source and destination of the dependence.
  unsigned getLevels() const override { return Levels; }
 
  /// getSameSDLevels - Returns the number of separate SameSD loops surrounding
  /// the source and destination of the dependence.
  unsigned getSameSDLevels() const override { return SameSDLevels; }
 
  /// getDVEntry - Returns the DV entry associated with a regular or a
  /// SameSD level.
  DVEntry getDVEntry(unsigned Level, bool IsSameSD) const {
    if (!IsSameSD) {
      assert(0 < Level && Level <= Levels && "Level out of range");
      return DV[Level - 1];
    } else {
      assert(Levels < Level &&
             Level <= static_cast<unsigned>(Levels) + SameSDLevels &&
             "isSameSD level out of range");
      return DVSameSD[Level - Levels - 1];
    }
  }
 
  /// getDirection - Returns the direction associated with a particular
  /// common or SameSD level.
  unsigned getDirection(unsigned Level, bool SameSD = false) const override;
 
  /// getDistance - Returns the distance (or NULL) associated with a
  /// particular common or SameSD level.
  const SCEV *getDistance(unsigned Level, bool SameSD = false) const override;
 
  /// Check if the direction vector is negative. A negative direction
  /// vector means Src and Dst are reversed in the actual program.
  bool isDirectionNegative() const override;
 
  void negate(ScalarEvolution &SE) override;
 
  /// If the direction vector is negative, normalize the direction
  /// vector to make it non-negative. Normalization is done by reversing
  /// Src and Dst, plus reversing the dependence directions and distances
  /// in the vector.
  bool normalize(ScalarEvolution *SE) override;
 
  /// inSameSDLoops - Returns true if this level is an SameSD level, i.e.,
  /// performed across two separate loop nests that have the Same Iteration and
  /// Depth.
  bool inSameSDLoops(unsigned Level) const override;
 
  /// isScalar - Returns true if a particular regular or SameSD level is
  /// scalar; that is, if no subscript in the source or destination mention
  /// the induction variable associated with the loop at this level.
  bool isScalar(unsigned Level, bool SameSD = false) const override;
 
private:
  unsigned short Levels;
  unsigned short SameSDLevels;
  bool LoopIndependent;
  std::unique_ptr<DVEntry[]> DV;
  std::unique_ptr<DVEntry[]> DVSameSD; // DV entries on SameSD levels
  friend class DependenceInfo;
};
 
/// DependenceInfo - This class is the main dependence-analysis driver.
class DependenceInfo {
public:
  LLVM_ABI DependenceInfo(Function *F, AAResults *AA, ScalarEvolution *SE,
                          LoopInfo *LI);
 
  /// Handle transitive invalidation when the cached analysis results go away.
  LLVM_ABI bool invalidate(Function &F, const PreservedAnalyses &PA,
                           FunctionAnalysisManager::Invalidator &Inv);
 
  /// depends - Tests for a dependence between the Src and Dst instructions.
  /// Returns NULL if no dependence; otherwise, returns a Dependence (or a
  /// FullDependence) with as much information as can be gleaned. By default,
  /// the dependence test collects a set of runtime assumptions that cannot be
  /// solved at compilation time. By default UnderRuntimeAssumptions is false
  /// for a safe approximation of the dependence relation that does not
  /// require runtime checks.
  LLVM_ABI std::unique_ptr<Dependence>
  depends(Instruction *Src, Instruction *Dst,
          bool UnderRuntimeAssumptions = false);
 
  Function *getFunction() const { return F; }
 
private:
  const AnalysisOptions &Opts;
  AAResults *AA;
  ScalarEvolution *SE;
  LoopInfo *LI;
  Function *F;
 
  /// Subscript - This private struct represents a pair of subscripts from
  /// a pair of potentially multi-dimensional array references. We use a
  /// vector of them to guide subscript partitioning.
  struct Subscript {
    const SCEV *Src;
    const SCEV *Dst;
    enum ClassificationKind { ZIV, SIV, RDIV, MIV, NonLinear } Classification;
    SmallBitVector Loops;
  };
 
  struct CoefficientInfo {
    const SCEV *SrcCoeff;
    const SCEV *DstCoeff;
    const SCEV *MaxIterIndex;
  };
 
  struct BoundInfo {
    const SCEV *Upper[8];
    const SCEV *Lower[8];
    unsigned char Direction;
    unsigned char DirSet;
  };
 
  /// Returns true if two loops have the Same iteration Space and Depth. To be
  /// more specific, two loops have SameSD if they are in the same nesting
  /// depth and have the same backedge count. SameSD stands for Same iteration
  /// Space and Depth.
  bool haveSameSD(const Loop *SrcLoop, const Loop *DstLoop) const;
 
  /// establishNestingLevels - Examines the loop nesting of the Src and Dst
  /// instructions and establishes their shared loops. Sets the variables
  /// CommonLevels, SrcLevels, and MaxLevels.
  /// The source and destination instructions needn't be contained in the same
  /// loop. The routine establishNestingLevels finds the level of most deeply
  /// nested loop that contains them both, CommonLevels. An instruction that's
  /// not contained in a loop is at level = 0. MaxLevels is equal to the level
  /// of the source plus the level of the destination, minus CommonLevels.
  /// This lets us allocate vectors MaxLevels in length, with room for every
  /// distinct loop referenced in both the source and destination subscripts.
  /// The variable SrcLevels is the nesting depth of the source instruction.
  /// It's used to help calculate distinct loops referenced by the destination.
  /// Here's the map from loops to levels:
  ///            0 - unused
  ///            1 - outermost common loop
  ///          ... - other common loops
  /// CommonLevels - innermost common loop
  ///          ... - loops containing Src but not Dst
  ///    SrcLevels - innermost loop containing Src but not Dst
  ///          ... - loops containing Dst but not Src
  ///    MaxLevels - innermost loop containing Dst but not Src
  /// Consider the follow code fragment:
  ///    for (a = ...) {
  ///      for (b = ...) {
  ///        for (c = ...) {
  ///          for (d = ...) {
  ///            A[] = ...;
  ///          }
  ///        }
  ///        for (e = ...) {
  ///          for (f = ...) {
  ///            for (g = ...) {
  ///              ... = A[];
  ///            }
  ///          }
  ///        }
  ///      }
  ///    }
  /// If we're looking at the possibility of a dependence between the store
  /// to A (the Src) and the load from A (the Dst), we'll note that they
  /// have 2 loops in common, so CommonLevels will equal 2 and the direction
  /// vector for Result will have 2 entries. SrcLevels = 4 and MaxLevels = 7.
  /// A map from loop names to level indices would look like
  ///     a - 1
  ///     b - 2 = CommonLevels
  ///     c - 3
  ///     d - 4 = SrcLevels
  ///     e - 5
  ///     f - 6
  ///     g - 7 = MaxLevels
  /// SameSDLevels counts the number of levels after common levels that are
  /// not common but have the same iteration space and depth. Internally this
  /// is checked using haveSameSD. Assume that in this code fragment, levels c
  /// and e have the same iteration space and depth, but levels d and f does
  /// not. Then SameSDLevels is set to 1. In that case the level numbers for the
  /// previous code look like
  ///     a   - 1
  ///     b   - 2
  ///     c,e - 3 = CommonLevels
  ///     d   - 4 = SrcLevels
  ///     f   - 5
  ///     g   - 6 = MaxLevels
  void establishNestingLevels(const Instruction *Src, const Instruction *Dst);
 
  unsigned CommonLevels, SrcLevels, MaxLevels, SameSDLevels;
 
  /// mapSrcLoop - Given one of the loops containing the source, return
  /// its level index in our numbering scheme.
  unsigned mapSrcLoop(const Loop *SrcLoop) const;
 
  /// mapDstLoop - Given one of the loops containing the destination,
  /// return its level index in our numbering scheme.
  unsigned mapDstLoop(const Loop *DstLoop) const;
 
  /// isLoopInvariant - Returns true if Expression is loop invariant
  /// in LoopNest.
  bool isLoopInvariant(const SCEV *Expression, const Loop *LoopNest) const;
 
  /// collectCommonLoops - Finds the set of loops from the LoopNest that
  /// have a level <= CommonLevels and are referred to by the SCEV Expression.
  void collectCommonLoops(const SCEV *Expression, const Loop *LoopNest,
                          SmallBitVector &Loops) const;
 
  /// checkSrcSubscript - Examines the SCEV Src, returning true iff it's
  /// linear. Collect the set of loops mentioned by Src.
  bool checkSrcSubscript(const SCEV *Src, const Loop *LoopNest,
                         SmallBitVector &Loops);
 
  /// checkDstSubscript - Examines the SCEV Dst, returning true iff it's
  /// linear. Collect the set of loops mentioned by Dst.
  bool checkDstSubscript(const SCEV *Dst, const Loop *LoopNest,
                         SmallBitVector &Loops);
 
  /// collectUpperBound - All subscripts are the same type (on my machine,
  /// an i64). The loop bound may be a smaller type. collectUpperBound
  /// find the bound, if available, and zero extends it to the Type T.
  /// (I zero extend since the bound should always be >= 0.)
  /// If no upper bound is available, return NULL.
  const SCEV *collectUpperBound(const Loop *l, Type *T) const;
 
  /// collectNonNegativeConstantUpperBound - Calls collectUpperBound(), then
  /// attempts to cast it to APInt. If the cast fails, or the value is negative,
  /// returns std::nullopt.
  std::optional<APInt> collectNonNegativeConstantUpperBound(const Loop *L,
                                                            Type *T) const;
 
  /// classifyPair - Examines the subscript pair (the Src and Dst SCEVs)
  /// and classifies it as either ZIV, SIV, RDIV, MIV, or Nonlinear.
  /// Collects the associated loops in a set.
  Subscript::ClassificationKind
  classifyPair(const SCEV *Src, const Loop *SrcLoopNest, const SCEV *Dst,
               const Loop *DstLoopNest, SmallBitVector &Loops);
 
  /// testZIV - Tests the ZIV subscript pair (Src and Dst) for dependence.
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// If the dependence isn't proven to exist,
  bool testZIV(const SCEV *Src, const SCEV *Dst, FullDependence &Result) const;
 
  /// testSIV - Tests the SIV subscript pair (Src and Dst) for dependence.
  /// Things of the form [c1 + a1*i] and [c2 + a2*j], where
  /// i and j are induction variables, c1 and c2 are loop invariant,
  /// and a1 and a2 are constant.
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// Sets appropriate direction vector entry and, when possible,
  /// the distance vector entry.
  /// If the dependence isn't proven to exist,
  bool testSIV(const SCEV *Src, const SCEV *Dst, unsigned &Level,
               FullDependence &Result, bool UnderRuntimeAssumptions);
 
  /// testRDIV - Tests the RDIV subscript pair (Src and Dst) for dependence.
  /// Things of the form [c1 + a1*i] and [c2 + a2*j]
  /// where i and j are induction variables, c1 and c2 are loop invariant,
  /// and a1 and a2 are constant.
  /// With minor algebra, this test can also be used for things like
  /// [c1 + a1*i + a2*j][c2].
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  bool testRDIV(const SCEV *Src, const SCEV *Dst, FullDependence &Result) const;
 
  /// testMIV - Tests the MIV subscript pair (Src and Dst) for dependence.
  /// Returns true if dependence disproved.
  /// Can sometimes refine direction vectors.
  bool testMIV(const SCEV *Src, const SCEV *Dst, const SmallBitVector &Loops,
               FullDependence &Result) const;
 
  /// strongSIVtest - Tests the strong SIV subscript pair (\p Src and \p Dst)
  /// for dependence.
  /// Things of the form [c1 + a*i] and [c2 + a*i],
  /// where i is an induction variable, c1 and c2 are loop invariant,
  /// and a is a constant
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// Sets appropriate direction and distance.
  bool strongSIVtest(const SCEVAddRecExpr *Src, const SCEVAddRecExpr *Dst,
                     unsigned Level, FullDependence &Result,
                     bool UnderRuntimeAssumptions);
 
  /// weakCrossingSIVtest - Tests the weak-crossing SIV subscript pair
  /// (Src and Dst) for dependence.
  /// Things of the form [c1 + a*i] and [c2 - a*i],
  /// where i is an induction variable, c1 and c2 are loop invariant,
  /// and a is a constant.
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// Sets appropriate direction entry.
  bool weakCrossingSIVtest(const SCEVAddRecExpr *Src, const SCEVAddRecExpr *Dst,
                           unsigned Level, FullDependence &Result) const;
 
  /// ExactSIVtest - Tests the SIV subscript pair
  /// (Src and Dst) for dependence.
  /// Things of the form [c1 + a1*i] and [c2 + a2*i],
  /// where i is an induction variable, c1 and c2 are loop invariant,
  /// and a1 and a2 are constant.
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// Sets appropriate direction entry.
  bool exactSIVtest(const SCEVAddRecExpr *Src, const SCEVAddRecExpr *Dst,
                    unsigned Level, FullDependence &Result) const;
 
  /// weakZeroSIVtestImpl - Core implementation for weakZeroSrcSIVtest and
  /// weakZeroDstSIVtest.
  bool weakZeroSIVtestImpl(const SCEVAddRecExpr *AR, const SCEV *Const,
                           unsigned Level, FullDependence &Result) const;
 
  /// weakZeroSrcSIVtest - Tests the weak-zero SIV subscript pair
  /// (Src and Dst) for dependence.
  /// Things of the form [c1] and [c2 + a*i],
  /// where i is an induction variable, c1 and c2 are loop invariant,
  /// and a is a constant. See also weakZeroDstSIVtest.
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// Sets appropriate direction entry.
  bool weakZeroSrcSIVtest(const SCEV *SrcConst, const SCEVAddRecExpr *Dst,
                          unsigned Level, FullDependence &Result) const;
 
  /// weakZeroDstSIVtest - Tests the weak-zero SIV subscript pair
  /// (Src and Dst) for dependence.
  /// Things of the form [c1 + a*i] and [c2],
  /// where i is an induction variable, c1 and c2 are loop invariant,
  /// and a is a constant. See also weakZeroSrcSIVtest.
  /// Returns true if any possible dependence is disproved.
  /// If there might be a dependence, returns false.
  /// Sets appropriate direction entry.
  bool weakZeroDstSIVtest(const SCEVAddRecExpr *Src, const SCEV *DstConst,
                          unsigned Level, FullDependence &Result) const;
 
  /// exactRDIVtest - Tests the RDIV subscript pair for dependence.
  /// Things of the form [c1 + a*i] and [c2 + b*j],
  /// where i and j are induction variable, c1 and c2 are loop invariant,
  /// and a and b are constants.
  /// Returns true if any possible dependence is disproved.
  /// Works in some cases that symbolicRDIVtest doesn't,
  /// and vice versa.
  bool exactRDIVtest(const SCEVAddRecExpr *Src, const SCEVAddRecExpr *Dst,
                     FullDependence &Result) const;
 
  /// exactTestImpl - Core implementation shared by the Exact SIV test and the
  /// Exact RDIV test. Returns true if any possible dependence is disproved. If
  /// \p Level is provided, this function will also attempt to explore
  /// directions and refine \p Result for the given level.
  bool exactTestImpl(const SCEVAddRecExpr *Src, const SCEVAddRecExpr *Dst,
                     FullDependence &Result,
                     std::optional<unsigned> Level) const;
 
  /// gcdMIVtest - Tests an MIV subscript pair for dependence.
  /// Returns true if any possible dependence is disproved.
  /// Can sometimes disprove the equal direction for 1 or more loops.
  //  Can handle some symbolics that even the SIV tests don't get,
  /// so we use it as a backup for everything.
  bool gcdMIVtest(const SCEV *Src, const SCEV *Dst,
                  FullDependence &Result) const;
 
  /// banerjeeMIVtest - Tests an MIV subscript pair for dependence.
  /// Returns true if any possible dependence is disproved.
  /// Computes directions.
  bool banerjeeMIVtest(const SCEV *Src, const SCEV *Dst,
                       const SmallBitVector &Loops,
                       FullDependence &Result) const;
 
  /// collectCoeffInfo - Walks through the subscript, collecting each
  /// coefficient and the associated maximum iteration index in the
  /// widened analysis type. Returns the widened constant term.
  const SCEV *collectCoeffInfo(const SCEV *Subscript, bool SrcFlag,
                               Type *WideType,
                               MutableArrayRef<CoefficientInfo> CI) const;
 
  /// Given \p Expr of the form
  ///
  ///   c_0*X_0*i_0 + c_1*X_1*i_1 + ...c_n*X_n*i_n + C
  ///
  /// compute
  ///
  ///   RunningGCD = gcd(RunningGCD, c_0, c_1, ..., c_n)
  ///
  /// where c_0, c_1, ..., and c_n are the constant values. The result is stored
  /// in \p RunningGCD. Also, the initial value of \p RunningGCD affects the
  /// result. If we find a term like (c_k * X_k * i_k), where i_k is the
  /// induction variable of \p CurLoop, c_k is stored in \p CurLoopCoeff and not
  /// included in the GCD computation. Returns nullptr if we fail to find a
  /// constant coefficient for some loop, e.g., when a term like (X+Y)*i is
  /// present. Otherwise returns the remaining constant term C.
  const SCEV *accumulateCoefficientsGCD(const SCEV *Expr, const Loop *CurLoop,
                                        const SCEV *&CurLoopCoeff,
                                        APInt &RunningGCD) const;
 
  /// getLowerBound - Looks through all the bounds info and
  /// computes the lower bound given the current direction settings
  /// at each level.
  const SCEV *getLowerBound(ArrayRef<BoundInfo> Bound) const;
 
  /// getUpperBound - Looks through all the bounds info and
  /// computes the upper bound given the current direction settings
  /// at each level.
  const SCEV *getUpperBound(ArrayRef<BoundInfo> Bound) const;
 
  /// exploreDirections - Hierarchically expands the direction vector
  /// search space, combining the directions of discovered dependences
  /// in the DirSet field of Bound. Returns the number of distinct
  /// dependences discovered. If the dependence is disproved,
  /// it will return 0.
  unsigned exploreDirections(unsigned Level, MutableArrayRef<BoundInfo> Bound,
                             const SmallBitVector &Loops, const SCEV *Delta,
                             const FullDependence &Result) const;
 
  /// testBounds - Returns true when the current bounds may be feasible
  /// or their feasibility is unknown.
  bool testBounds(unsigned char DirKind, unsigned Level,
                  MutableArrayRef<BoundInfo> Bound, const SCEV *Delta) const;
 
  /// findBoundsALL - Computes the upper and lower bounds for level K
  /// using the * direction. Records them in Bound.
  void findBoundsALL(ArrayRef<CoefficientInfo> CI,
                     MutableArrayRef<BoundInfo> Bound, unsigned K) const;
 
  /// findBoundsLT - Computes the upper and lower bounds for level K
  /// using the < direction. Records them in Bound.
  void findBoundsLT(ArrayRef<CoefficientInfo> CI,
                    MutableArrayRef<BoundInfo> Bound, unsigned K) const;
 
  /// findBoundsGT - Computes the upper and lower bounds for level K
  /// using the > direction. Records them in Bound.
  void findBoundsGT(ArrayRef<CoefficientInfo> CI,
                    MutableArrayRef<BoundInfo> Bound, unsigned K) const;
 
  /// findBoundsEQ - Computes the upper and lower bounds for level K
  /// using the = direction. Records them in Bound.
  void findBoundsEQ(ArrayRef<CoefficientInfo> CI,
                    MutableArrayRef<BoundInfo> Bound, unsigned K) const;
 
  /// Given a linear access function, tries to recover subscripts
  /// for each dimension of the array element access.
  bool tryDelinearize(Instruction *Src, Instruction *Dst,
                      SmallVectorImpl<Subscript> &Pair);
 
  /// Tries to delinearize \p Src and \p Dst access functions for a fixed size
  /// multi-dimensional array. Calls delinearizeFixedSizeArray() to delinearize
  /// \p Src and \p Dst separately,
  bool tryDelinearizeFixedSize(Instruction *Src, Instruction *Dst,
                               const SCEV *SrcAccessFn, const SCEV *DstAccessFn,
                               SmallVectorImpl<const SCEV *> &SrcSubscripts,
                               SmallVectorImpl<const SCEV *> &DstSubscripts);
 
  /// Tries to delinearize access function for a multi-dimensional array with
  /// symbolic runtime sizes.
  /// Returns true upon success and false otherwise.
  bool
  tryDelinearizeParametricSize(Instruction *Src, Instruction *Dst,
                               const SCEV *SrcAccessFn, const SCEV *DstAccessFn,
                               SmallVectorImpl<const SCEV *> &SrcSubscripts,
                               SmallVectorImpl<const SCEV *> &DstSubscripts);
 
  /// checkSubscript - Helper function for checkSrcSubscript and
  /// checkDstSubscript to avoid duplicate code
  bool checkSubscript(const SCEV *Expr, const Loop *LoopNest,
                      SmallBitVector &Loops, bool IsSrc);
}; // class DependenceInfo
 
/// AnalysisPass to compute dependence information in a function
class DependenceAnalysis : public AnalysisInfoMixin<DependenceAnalysis> {
public:
  typedef DependenceInfo Result;
  LLVM_ABI Result run(Function &F, FunctionAnalysisManager &FAM);
 
private:
  LLVM_ABI static AnalysisKey Key;
  friend struct AnalysisInfoMixin<DependenceAnalysis>;
}; // class DependenceAnalysis
 
/// Printer pass to dump DA results.
struct DependenceAnalysisPrinterPass
    : public RequiredPassInfoMixin<DependenceAnalysisPrinterPass> {
  DependenceAnalysisPrinterPass(raw_ostream &OS, bool NormalizeResults = false)
      : OS(OS), NormalizeResults(NormalizeResults) {}
 
  LLVM_ABI PreservedAnalyses run(Function &F, FunctionAnalysisManager &FAM);
 
private:
  raw_ostream &OS;
  bool NormalizeResults;
}; // class DependenceAnalysisPrinterPass
 
/// Legacy pass manager pass to access dependence information
class LLVM_ABI DependenceAnalysisWrapperPass : public FunctionPass {
public:
  static char ID; // Class identification, replacement for typeinfo
  DependenceAnalysisWrapperPass();
 
  bool runOnFunction(Function &F) override;
  void releaseMemory() override;
  void getAnalysisUsage(AnalysisUsage &) const override;
  void print(raw_ostream &, const Module * = nullptr) const override;
  DependenceInfo &getDI() const;
 
private:
  std::unique_ptr<DependenceInfo> info;
}; // class DependenceAnalysisWrapperPass
 
/// createDependenceAnalysisPass - This creates an instance of the
/// DependenceAnalysis wrapper pass.
LLVM_ABI FunctionPass *createDependenceAnalysisWrapperPass();
 
} // namespace llvm
 
#endif