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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/IR/Instructions.h"

#include "llvm/IR/PassManager.h"

#include "llvm/Pass.h"

namespace llvm {

  class AAResults;

  template <typename T> class ArrayRef;

  class Loop;

  class LoopInfo;

  class ScalarEvolution;

  class SCEV;

  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 Dependence {

  protected:

    Dependence(Dependence &&) = default;

    Dependence &operator=(Dependence &&) = default;

  public:

    Dependence(Instruction *Source, Instruction *Destination)

        : Src(Source), Dst(Destination) {}

    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.

    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.

      bool PeelFirst : 1; // Peeling the first iteration will break dependence.

      bool PeelLast  : 1; // Peeling the last iteration will break the dependence.

      bool Splitable : 1; // Splitting the loop will break dependence.

      const SCEV *Distance = nullptr; // NULL implies no distance available.

      DVEntry()

          : Direction(ALL), Scalar(true), PeelFirst(false), PeelLast(false),

            Splitable(false) {}

    };

    /// 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; }

    /// isConsistent - Returns true if this dependence is consistent

    /// (occurs every time the source and destination are executed).

    virtual bool isConsistent() const { return false; }

    /// getLevels - Returns the number of common loops surrounding the

    /// source and destination of the dependence.

    virtual unsigned getLevels() const { return 0; }

    /// getDirection - Returns the direction associated with a particular

    /// level.

    virtual unsigned getDirection(unsigned Level) const { return DVEntry::ALL; }

    /// getDistance - Returns the distance (or NULL) associated with a

    /// particular level.

    virtual const SCEV *getDistance(unsigned Level) 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; }

    /// 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; }

    /// isPeelFirst - Returns true if peeling the first iteration from

    /// this loop will break this dependence.

    virtual bool isPeelFirst(unsigned Level) const { return false; }

    /// isPeelLast - Returns true if peeling the last iteration from

    /// this loop will break this dependence.

    virtual bool isPeelLast(unsigned Level) const { return false; }

    /// isSplitable - Returns true if splitting this loop will break

    /// the dependence.

    virtual bool isSplitable(unsigned Level) const { return false; }

    /// isScalar - Returns true if a particular 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) 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; }

    /// dump - For debugging purposes, dumps a dependence to OS.

    ///

    void dump(raw_ostream &OS) const;

  protected:

    Instruction *Src, *Dst;

  private:

    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 FullDependence final : public Dependence {

  public:

    FullDependence(Instruction *Src, Instruction *Dst, bool LoopIndependent,

                   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; }

    /// isConsistent - Returns true if this dependence is consistent

    /// (occurs every time the source and destination are executed).

    bool isConsistent() const override { return Consistent; }

    /// getLevels - Returns the number of common loops surrounding the

    /// source and destination of the dependence.

    unsigned getLevels() const override { return Levels; }

    /// getDirection - Returns the direction associated with a particular

    /// level.

    unsigned getDirection(unsigned Level) const override;

    /// getDistance - Returns the distance (or NULL) associated with a

    /// particular level.

    const SCEV *getDistance(unsigned Level) 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;

    /// 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;

    /// isPeelFirst - Returns true if peeling the first iteration from

    /// this loop will break this dependence.

    bool isPeelFirst(unsigned Level) const override;

    /// isPeelLast - Returns true if peeling the last iteration from

    /// this loop will break this dependence.

    bool isPeelLast(unsigned Level) const override;

    /// isSplitable - Returns true if splitting the loop will break

    /// the dependence.

    bool isSplitable(unsigned Level) const override;

    /// isScalar - Returns true if a particular 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) const override;

  private:

    unsigned short Levels;

    bool LoopIndependent;

    bool Consistent; // Init to true, then refine.

    std::unique_ptr<DVEntry[]> DV;

    friend class DependenceInfo;

  };

  /// DependenceInfo - This class is the main dependence-analysis driver.

  ///

  class DependenceInfo {

  public:

    DependenceInfo(Function *F, AAResults *AA, ScalarEvolution *SE,

                   LoopInfo *LI)

        : AA(AA), SE(SE), LI(LI), F(F) {}

    /// Handle transitive invalidation when the cached analysis results go away.

    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.

    /// The flag PossiblyLoopIndependent should be set by the caller

    /// if it appears that control flow can reach from Src to Dst

    /// without traversing a loop back edge.

    std::unique_ptr<Dependence> depends(Instruction *Src,

                                        Instruction *Dst,

                                        bool PossiblyLoopIndependent);

    /// getSplitIteration - Give a dependence that's splittable at some

    /// particular level, return the iteration that should be used to split

    /// the loop.

    ///

    /// Generally, the dependence analyzer will be used to build

    /// a dependence graph for a function (basically a map from instructions

    /// to dependences). Looking for cycles in the graph shows us loops

    /// that cannot be trivially vectorized/parallelized.

    ///

    /// We can try to improve the situation by examining all the dependences

    /// that make up the cycle, looking for ones we can break.

    /// Sometimes, peeling the first or last iteration of a loop will break

    /// dependences, and there are flags for those possibilities.

    /// Sometimes, splitting a loop at some other iteration will do the trick,

    /// and we've got a flag for that case. Rather than waste the space to

    /// record the exact iteration (since we rarely know), we provide

    /// a method that calculates the iteration. It's a drag that it must work

    /// from scratch, but wonderful in that it's possible.

    ///

    /// Here's an example:

    ///

    ///    for (i = 0; i < 10; i++)

    ///        A[i] = ...

    ///        ... = A[11 - i]

    ///

    /// There's a loop-carried flow dependence from the store to the load,

    /// found by the weak-crossing SIV test. The dependence will have a flag,

    /// indicating that the dependence can be broken by splitting the loop.

    /// Calling getSplitIteration will return 5.

    /// Splitting the loop breaks the dependence, like so:

    ///

    ///    for (i = 0; i <= 5; i++)

    ///        A[i] = ...

    ///        ... = A[11 - i]

    ///    for (i = 6; i < 10; i++)

    ///        A[i] = ...

    ///        ... = A[11 - i]

    ///

    /// breaks the dependence and allows us to vectorize/parallelize

    /// both loops.

    const SCEV *getSplitIteration(const Dependence &Dep, unsigned Level);

    Function *getFunction() const { return F; }

  private:

    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;

      SmallBitVector GroupLoops;

      SmallBitVector Group;

    };

    struct CoefficientInfo {

      const SCEV *Coeff;

      const SCEV *PosPart;

      const SCEV *NegPart;

      const SCEV *Iterations;

    };

    struct BoundInfo {

      const SCEV *Iterations;

      const SCEV *Upper[8];

      const SCEV *Lower[8];

      unsigned char Direction;

      unsigned char DirSet;

    };

    /// Constraint - This private class represents a constraint, as defined

    /// in the paper

    ///

    ///           Practical Dependence Testing

    ///           Goff, Kennedy, Tseng

    ///           PLDI 1991

    ///

    /// There are 5 kinds of constraint, in a hierarchy.

    ///   1) Any - indicates no constraint, any dependence is possible.

    ///   2) Line - A line ax + by = c, where a, b, and c are parameters,

    ///             representing the dependence equation.

    ///   3) Distance - The value d of the dependence distance;

    ///   4) Point - A point <x, y> representing the dependence from

    ///              iteration x to iteration y.

    ///   5) Empty - No dependence is possible.

    class Constraint {

    private:

      enum ConstraintKind { Empty, Point, Distance, Line, Any } Kind;

      ScalarEvolution *SE;

      const SCEV *A;

      const SCEV *B;

      const SCEV *C;

      const Loop *AssociatedLoop;

    public:

      /// isEmpty - Return true if the constraint is of kind Empty.

      bool isEmpty() const { return Kind == Empty; }

      /// isPoint - Return true if the constraint is of kind Point.

      bool isPoint() const { return Kind == Point; }

      /// isDistance - Return true if the constraint is of kind Distance.

      bool isDistance() const { return Kind == Distance; }

      /// isLine - Return true if the constraint is of kind Line.

      /// Since Distance's can also be represented as Lines, we also return

      /// true if the constraint is of kind Distance.

      bool isLine() const { return Kind == Line || Kind == Distance; }

      /// isAny - Return true if the constraint is of kind Any;

      bool isAny() const { return Kind == Any; }

      /// getX - If constraint is a point <X, Y>, returns X.

      /// Otherwise assert.

      const SCEV *getX() const;

      /// getY - If constraint is a point <X, Y>, returns Y.

      /// Otherwise assert.

      const SCEV *getY() const;

      /// getA - If constraint is a line AX + BY = C, returns A.

      /// Otherwise assert.

      const SCEV *getA() const;

      /// getB - If constraint is a line AX + BY = C, returns B.

      /// Otherwise assert.

      const SCEV *getB() const;

      /// getC - If constraint is a line AX + BY = C, returns C.

      /// Otherwise assert.

      const SCEV *getC() const;

      /// getD - If constraint is a distance, returns D.

      /// Otherwise assert.

      const SCEV *getD() const;

      /// getAssociatedLoop - Returns the loop associated with this constraint.

      const Loop *getAssociatedLoop() const;

      /// setPoint - Change a constraint to Point.

      void setPoint(const SCEV *X, const SCEV *Y, const Loop *CurrentLoop);

      /// setLine - Change a constraint to Line.

      void setLine(const SCEV *A, const SCEV *B,

                   const SCEV *C, const Loop *CurrentLoop);

      /// setDistance - Change a constraint to Distance.

      void setDistance(const SCEV *D, const Loop *CurrentLoop);

      /// setEmpty - Change a constraint to Empty.

      void setEmpty();

      /// setAny - Change a constraint to Any.

      void setAny(ScalarEvolution *SE);

      /// dump - For debugging purposes. Dumps the constraint

      /// out to OS.

      void dump(raw_ostream &OS) 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

    void establishNestingLevels(const Instruction *Src,

                                const Instruction *Dst);

    unsigned CommonLevels, SrcLevels, MaxLevels;

    /// 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;

    /// Makes sure all subscript pairs share the same integer type by

    /// sign-extending as necessary.

    /// Sign-extending a subscript is safe because getelementptr assumes the

    /// array subscripts are signed.

    void unifySubscriptType(ArrayRef<Subscript *> Pairs);

    /// removeMatchingExtensions - Examines a subscript pair.

    /// If the source and destination are identically sign (or zero)

    /// extended, it strips off the extension in an effort to

    /// simplify the actual analysis.

    void removeMatchingExtensions(Subscript *Pair);

    /// 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);

    /// isKnownPredicate - Compare X and Y using the predicate Pred.

    /// Basically a wrapper for SCEV::isKnownPredicate,

    /// but tries harder, especially in the presence of sign and zero

    /// extensions and symbolics.

    bool isKnownPredicate(ICmpInst::Predicate Pred,

                          const SCEV *X,

                          const SCEV *Y) const;

    /// isKnownLessThan - Compare to see if S is less than Size

    /// Another wrapper for isKnownNegative(S - max(Size, 1)) with some extra

    /// checking if S is an AddRec and we can prove lessthan using the loop

    /// bounds.

    bool isKnownLessThan(const SCEV *S, const SCEV *Size) const;

    /// isKnownNonNegative - Compare to see if S is known not to be negative

    /// Uses the fact that S comes from Ptr, which may be an inbound GEP,

    /// Proving there is no wrapping going on.

    bool isKnownNonNegative(const SCEV *S, const Value *Ptr) const;

    /// 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;

    /// collectConstantUpperBound - Calls collectUpperBound(), then

    /// attempts to cast it to SCEVConstant. If the cast fails,

    /// returns NULL.

    const SCEVConstant *collectConstantUpperBound(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,

    /// marks the Result as inconsistent.

    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,

    /// marks the Result as inconsistent.

    bool testSIV(const SCEV *Src,

                 const SCEV *Dst,

                 unsigned &Level,

                 FullDependence &Result,

                 Constraint &NewConstraint,

                 const SCEV *&SplitIter) const;

    /// 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.

    /// Marks the Result as inconsistent.

    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 (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 and distance.

    bool strongSIVtest(const SCEV *Coeff,

                       const SCEV *SrcConst,

                       const SCEV *DstConst,

                       const Loop *CurrentLoop,

                       unsigned Level,

                       FullDependence &Result,

                       Constraint &NewConstraint) const;

    /// 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.

    /// Set consistent to false.

    /// Marks the dependence as splitable.

    bool weakCrossingSIVtest(const SCEV *SrcCoeff,

                             const SCEV *SrcConst,

                             const SCEV *DstConst,

                             const Loop *CurrentLoop,

                             unsigned Level,

                             FullDependence &Result,

                             Constraint &NewConstraint,

                             const SCEV *&SplitIter) 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.

    /// Set consistent to false.

    bool exactSIVtest(const SCEV *SrcCoeff,

                      const SCEV *DstCoeff,

                      const SCEV *SrcConst,

                      const SCEV *DstConst,

                      const Loop *CurrentLoop,

                      unsigned Level,

                      FullDependence &Result,

                      Constraint &NewConstraint) 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.

    /// Set consistent to false.

    /// If loop peeling will break the dependence, mark appropriately.

    bool weakZeroSrcSIVtest(const SCEV *DstCoeff,

                            const SCEV *SrcConst,

                            const SCEV *DstConst,

                            const Loop *CurrentLoop,

                            unsigned Level,

                            FullDependence &Result,

                            Constraint &NewConstraint) 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.

    /// Set consistent to false.

    /// If loop peeling will break the dependence, mark appropriately.

    bool weakZeroDstSIVtest(const SCEV *SrcCoeff,

                            const SCEV *SrcConst,

                            const SCEV *DstConst,

                            const Loop *CurrentLoop,

                            unsigned Level,

                            FullDependence &Result,

                            Constraint &NewConstraint) 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.

    /// Marks the result as inconsistent.

    /// Works in some cases that symbolicRDIVtest doesn't,

    /// and vice versa.

    bool exactRDIVtest(const SCEV *SrcCoeff,

                       const SCEV *DstCoeff,

                       const SCEV *SrcConst,

                       const SCEV *DstConst,

                       const Loop *SrcLoop,

                       const Loop *DstLoop,

                       FullDependence &Result) const;

    /// symbolicRDIVtest - 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.

    /// Marks the result as inconsistent.

    /// Works in some cases that exactRDIVtest doesn't,

    /// and vice versa. Can also be used as a backup for

    /// ordinary SIV tests.

    bool symbolicRDIVtest(const SCEV *SrcCoeff,

                          const SCEV *DstCoeff,

                          const SCEV *SrcConst,

                          const SCEV *DstConst,

                          const Loop *SrcLoop,

                          const Loop *DstLoop) const;

    /// gcdMIVtest - Tests an MIV subscript pair for dependence.

    /// Returns true if any possible dependence is disproved.

    /// Marks the result as inconsistent.

    /// 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.

    /// Marks the result as inconsistent.

    /// Computes directions.

    bool banerjeeMIVtest(const SCEV *Src,

                         const SCEV *Dst,

                         const SmallBitVector &Loops,

                         FullDependence &Result) const;

    /// collectCoefficientInfo - Walks through the subscript,

    /// collecting each coefficient, the associated loop bounds,

    /// and recording its positive and negative parts for later use.

    CoefficientInfo *collectCoeffInfo(const SCEV *Subscript,

                                      bool SrcFlag,

                                      const SCEV *&Constant) const;

    /// getPositivePart - X^+ = max(X, 0).

    ///

    const SCEV *getPositivePart(const SCEV *X) const;

    /// getNegativePart - X^- = min(X, 0).

    ///

    const SCEV *getNegativePart(const SCEV *X) const;

    /// getLowerBound - Looks through all the bounds info and

    /// computes the lower bound given the current direction settings

    /// at each level.

    const SCEV *getLowerBound(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(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,

                               CoefficientInfo *A,

                               CoefficientInfo *B,

                               BoundInfo *Bound,

                               const SmallBitVector &Loops,

                               unsigned &DepthExpanded,

                               const SCEV *Delta) const;

    /// testBounds - Returns true iff the current bounds are plausible.

    bool testBounds(unsigned char DirKind,

                    unsigned Level,

                    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(CoefficientInfo *A,

                       CoefficientInfo *B,

                       BoundInfo *Bound,

                       unsigned K) const;

    /// findBoundsLT - Computes the upper and lower bounds for level K

    /// using the < direction. Records them in Bound.

    void findBoundsLT(CoefficientInfo *A,

                      CoefficientInfo *B,

                      BoundInfo *Bound,

                      unsigned K) const;

    /// findBoundsGT - Computes the upper and lower bounds for level K

    /// using the > direction. Records them in Bound.

    void findBoundsGT(CoefficientInfo *A,

                      CoefficientInfo *B,

                      BoundInfo *Bound,

                      unsigned K) const;

    /// findBoundsEQ - Computes the upper and lower bounds for level K

    /// using the = direction. Records them in Bound.

    void findBoundsEQ(CoefficientInfo *A,

                      CoefficientInfo *B,

                      BoundInfo *Bound,

                      unsigned K) const;

    /// intersectConstraints - Updates X with the intersection

    /// of the Constraints X and Y. Returns true if X has changed.

    bool intersectConstraints(Constraint *X,

                              const Constraint *Y);

    /// propagate - Review the constraints, looking for opportunities

    /// to simplify a subscript pair (Src and Dst).

    /// Return true if some simplification occurs.

    /// If the simplification isn't exact (that is, if it is conservative

    /// in terms of dependence), set consistent to false.

    bool propagate(const SCEV *&Src,

                   const SCEV *&Dst,