ScalarEvolutionExpressions.h

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//===- llvm/Analysis/ScalarEvolutionExpressions.h - SCEV Exprs --*- 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
//
//===----------------------------------------------------------------------===//
//
// This file defines the classes used to represent and build scalar expressions.
//
//===----------------------------------------------------------------------===//
 
#ifndef LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H
#define LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H
 
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/FoldingSet.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/iterator_range.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/ErrorHandling.h"
#include <cassert>
#include <cstddef>
 
namespace llvm {
 
class APInt;
class Constant;
class ConstantRange;
class Loop;
class Type;
 
  enum SCEVTypes : unsigned short {
    // These should be ordered in terms of increasing complexity to make the
    // folders simpler.
    scConstant, scTruncate, scZeroExtend, scSignExtend, scAddExpr, scMulExpr,
    scUDivExpr, scAddRecExpr, scUMaxExpr, scSMaxExpr, scUMinExpr, scSMinExpr,
    scPtrToInt, scUnknown, scCouldNotCompute
  };
 
  /// This class represents a constant integer value.
  class SCEVConstant : public SCEV {
    friend class ScalarEvolution;
 
    ConstantInt *V;
 
    SCEVConstant(const FoldingSetNodeIDRef ID, ConstantInt *v) :
      SCEV(ID, scConstant, 1), V(v) {}
 
  public:
    ConstantInt *getValue() const { return V; }
    const APInt &getAPInt() const { return getValue()->getValue(); }
 
    Type *getType() const { return V->getType(); }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scConstant;
    }
  };
 
  inline unsigned short computeExpressionSize(ArrayRef<const SCEV *> Args) {
    APInt Size(16, 1);
    for (auto *Arg : Args)
      Size = Size.uadd_sat(APInt(16, Arg->getExpressionSize()));
    return (unsigned short)Size.getZExtValue();
  }
 
  /// This is the base class for unary cast operator classes.
  class SCEVCastExpr : public SCEV {
  protected:
    std::array<const SCEV *, 1> Operands;
    Type *Ty;
 
    SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy, const SCEV *op,
                 Type *ty);
 
  public:
    const SCEV *getOperand() const { return Operands[0]; }
    const SCEV *getOperand(unsigned i) const {
      assert(i == 0 && "Operand index out of range!");
      return Operands[0];
    }
    using op_iterator = std::array<const SCEV *, 1>::const_iterator;
    using op_range = iterator_range<op_iterator>;
 
    op_range operands() const {
      return make_range(Operands.begin(), Operands.end());
    }
    size_t getNumOperands() const { return 1; }
    Type *getType() const { return Ty; }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scPtrToInt || S->getSCEVType() == scTruncate ||
             S->getSCEVType() == scZeroExtend ||
             S->getSCEVType() == scSignExtend;
    }
  };
 
  /// This class represents a cast from a pointer to a pointer-sized integer
  /// value.
  class SCEVPtrToIntExpr : public SCEVCastExpr {
    friend class ScalarEvolution;
 
    SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op, Type *ITy);
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scPtrToInt;
    }
  };
 
  /// This is the base class for unary integral cast operator classes.
  class SCEVIntegralCastExpr : public SCEVCastExpr {
  protected:
    SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy,
                         const SCEV *op, Type *ty);
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scTruncate ||
             S->getSCEVType() == scZeroExtend ||
             S->getSCEVType() == scSignExtend;
    }
  };
 
  /// This class represents a truncation of an integer value to a
  /// smaller integer value.
  class SCEVTruncateExpr : public SCEVIntegralCastExpr {
    friend class ScalarEvolution;
 
    SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
                     const SCEV *op, Type *ty);
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scTruncate;
    }
  };
 
  /// This class represents a zero extension of a small integer value
  /// to a larger integer value.
  class SCEVZeroExtendExpr : public SCEVIntegralCastExpr {
    friend class ScalarEvolution;
 
    SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
                       const SCEV *op, Type *ty);
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scZeroExtend;
    }
  };
 
  /// This class represents a sign extension of a small integer value
  /// to a larger integer value.
  class SCEVSignExtendExpr : public SCEVIntegralCastExpr {
    friend class ScalarEvolution;
 
    SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
                       const SCEV *op, Type *ty);
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scSignExtend;
    }
  };
 
  /// This node is a base class providing common functionality for
  /// n'ary operators.
  class SCEVNAryExpr : public SCEV {
  protected:
    // Since SCEVs are immutable, ScalarEvolution allocates operand
    // arrays with its SCEVAllocator, so this class just needs a simple
    // pointer rather than a more elaborate vector-like data structure.
    // This also avoids the need for a non-trivial destructor.
    const SCEV *const *Operands;
    size_t NumOperands;
 
    SCEVNAryExpr(const FoldingSetNodeIDRef ID, enum SCEVTypes T,
                 const SCEV *const *O, size_t N)
        : SCEV(ID, T, computeExpressionSize(makeArrayRef(O, N))), Operands(O),
          NumOperands(N) {}
 
  public:
    size_t getNumOperands() const { return NumOperands; }
 
    const SCEV *getOperand(unsigned i) const {
      assert(i < NumOperands && "Operand index out of range!");
      return Operands[i];
    }
 
    using op_iterator = const SCEV *const *;
    using op_range = iterator_range<op_iterator>;
 
    op_iterator op_begin() const { return Operands; }
    op_iterator op_end() const { return Operands + NumOperands; }
    op_range operands() const {
      return make_range(op_begin(), op_end());
    }
 
    NoWrapFlags getNoWrapFlags(NoWrapFlags Mask = NoWrapMask) const {
      return (NoWrapFlags)(SubclassData & Mask);
    }
 
    bool hasNoUnsignedWrap() const {
      return getNoWrapFlags(FlagNUW) != FlagAnyWrap;
    }
 
    bool hasNoSignedWrap() const {
      return getNoWrapFlags(FlagNSW) != FlagAnyWrap;
    }
 
    bool hasNoSelfWrap() const {
      return getNoWrapFlags(FlagNW) != FlagAnyWrap;
    }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddExpr || S->getSCEVType() == scMulExpr ||
             S->getSCEVType() == scSMaxExpr || S->getSCEVType() == scUMaxExpr ||
             S->getSCEVType() == scSMinExpr || S->getSCEVType() == scUMinExpr ||
             S->getSCEVType() == scAddRecExpr;
    }
  };
 
  /// This node is the base class for n'ary commutative operators.
  class SCEVCommutativeExpr : public SCEVNAryExpr {
  protected:
    SCEVCommutativeExpr(const FoldingSetNodeIDRef ID,
                        enum SCEVTypes T, const SCEV *const *O, size_t N)
      : SCEVNAryExpr(ID, T, O, N) {}
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddExpr || S->getSCEVType() == scMulExpr ||
             S->getSCEVType() == scSMaxExpr || S->getSCEVType() == scUMaxExpr ||
             S->getSCEVType() == scSMinExpr || S->getSCEVType() == scUMinExpr;
    }
 
    /// Set flags for a non-recurrence without clearing previously set flags.
    void setNoWrapFlags(NoWrapFlags Flags) {
      SubclassData |= Flags;
    }
  };
 
  /// This node represents an addition of some number of SCEVs.
  class SCEVAddExpr : public SCEVCommutativeExpr {
    friend class ScalarEvolution;
 
    Type *Ty;
 
    SCEVAddExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
        : SCEVCommutativeExpr(ID, scAddExpr, O, N) {
      auto *FirstPointerTypedOp = find_if(operands(), [](const SCEV *Op) {
        return Op->getType()->isPointerTy();
      });
      if (FirstPointerTypedOp != operands().end())
        Ty = (*FirstPointerTypedOp)->getType();
      else
        Ty = getOperand(0)->getType();
    }
 
  public:
    Type *getType() const { return Ty; }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddExpr;
    }
  };
 
  /// This node represents multiplication of some number of SCEVs.
  class SCEVMulExpr : public SCEVCommutativeExpr {
    friend class ScalarEvolution;
 
    SCEVMulExpr(const FoldingSetNodeIDRef ID,
                const SCEV *const *O, size_t N)
      : SCEVCommutativeExpr(ID, scMulExpr, O, N) {}
 
  public:
    Type *getType() const { return getOperand(0)->getType(); }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scMulExpr;
    }
  };
 
  /// This class represents a binary unsigned division operation.
  class SCEVUDivExpr : public SCEV {
    friend class ScalarEvolution;
 
    std::array<const SCEV *, 2> Operands;
 
    SCEVUDivExpr(const FoldingSetNodeIDRef ID, const SCEV *lhs, const SCEV *rhs)
        : SCEV(ID, scUDivExpr, computeExpressionSize({lhs, rhs})) {
        Operands[0] = lhs;
        Operands[1] = rhs;
      }
 
  public:
    const SCEV *getLHS() const { return Operands[0]; }
    const SCEV *getRHS() const { return Operands[1]; }
    size_t getNumOperands() const { return 2; }
    const SCEV *getOperand(unsigned i) const {
      assert((i == 0 || i == 1) && "Operand index out of range!");
      return i == 0 ? getLHS() : getRHS();
    }
 
    using op_iterator = std::array<const SCEV *, 2>::const_iterator;
    using op_range = iterator_range<op_iterator>;
    op_range operands() const {
      return make_range(Operands.begin(), Operands.end());
    }
 
    Type *getType() const {
      // In most cases the types of LHS and RHS will be the same, but in some
      // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
      // depend on the type for correctness, but handling types carefully can
      // avoid extra casts in the SCEVExpander. The LHS is more likely to be
      // a pointer type than the RHS, so use the RHS' type here.
      return getRHS()->getType();
    }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scUDivExpr;
    }
  };
 
  /// This node represents a polynomial recurrence on the trip count
  /// of the specified loop.  This is the primary focus of the
  /// ScalarEvolution framework; all the other SCEV subclasses are
  /// mostly just supporting infrastructure to allow SCEVAddRecExpr
  /// expressions to be created and analyzed.
  ///
  /// All operands of an AddRec are required to be loop invariant.
  ///
  class SCEVAddRecExpr : public SCEVNAryExpr {
    friend class ScalarEvolution;
 
    const Loop *L;
 
    SCEVAddRecExpr(const FoldingSetNodeIDRef ID,
                   const SCEV *const *O, size_t N, const Loop *l)
      : SCEVNAryExpr(ID, scAddRecExpr, O, N), L(l) {}
 
  public:
    Type *getType() const { return getStart()->getType(); }
    const SCEV *getStart() const { return Operands[0]; }
    const Loop *getLoop() const { return L; }
 
    /// Constructs and returns the recurrence indicating how much this
    /// expression steps by.  If this is a polynomial of degree N, it
    /// returns a chrec of degree N-1.  We cannot determine whether
    /// the step recurrence has self-wraparound.
    const SCEV *getStepRecurrence(ScalarEvolution &SE) const {
      if (isAffine()) return getOperand(1);
      return SE.getAddRecExpr(SmallVector<const SCEV *, 3>(op_begin()+1,
                                                           op_end()),
                              getLoop(), FlagAnyWrap);
    }
 
    /// Return true if this represents an expression A + B*x where A
    /// and B are loop invariant values.
    bool isAffine() const {
      // We know that the start value is invariant.  This expression is thus
      // affine iff the step is also invariant.
      return getNumOperands() == 2;
    }
 
    /// Return true if this represents an expression A + B*x + C*x^2
    /// where A, B and C are loop invariant values.  This corresponds
    /// to an addrec of the form {L,+,M,+,N}
    bool isQuadratic() const {
      return getNumOperands() == 3;
    }
 
    /// Set flags for a recurrence without clearing any previously set flags.
    /// For AddRec, either NUW or NSW implies NW. Keep track of this fact here
    /// to make it easier to propagate flags.
    void setNoWrapFlags(NoWrapFlags Flags) {
      if (Flags & (FlagNUW | FlagNSW))
        Flags = ScalarEvolution::setFlags(Flags, FlagNW);
      SubclassData |= Flags;
    }
 
    /// Return the value of this chain of recurrences at the specified
    /// iteration number.
    const SCEV *evaluateAtIteration(const SCEV *It, ScalarEvolution &SE) const;
 
    /// Return the value of this chain of recurrences at the specified iteration
    /// number. Takes an explicit list of operands to represent an AddRec.
    static const SCEV *evaluateAtIteration(ArrayRef<const SCEV *> Operands,
                                           const SCEV *It, ScalarEvolution &SE);
 
    /// Return the number of iterations of this loop that produce
    /// values in the specified constant range.  Another way of
    /// looking at this is that it returns the first iteration number
    /// where the value is not in the condition, thus computing the
    /// exit count.  If the iteration count can't be computed, an
    /// instance of SCEVCouldNotCompute is returned.
    const SCEV *getNumIterationsInRange(const ConstantRange &Range,
                                        ScalarEvolution &SE) const;
 
    /// Return an expression representing the value of this expression
    /// one iteration of the loop ahead.
    const SCEVAddRecExpr *getPostIncExpr(ScalarEvolution &SE) const;
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddRecExpr;
    }
  };
 
  /// This node is the base class min/max selections.
  class SCEVMinMaxExpr : public SCEVCommutativeExpr {
    friend class ScalarEvolution;
 
    static bool isMinMaxType(enum SCEVTypes T) {
      return T == scSMaxExpr || T == scUMaxExpr || T == scSMinExpr ||
             T == scUMinExpr;
    }
 
  protected:
    /// Note: Constructing subclasses via this constructor is allowed
    SCEVMinMaxExpr(const FoldingSetNodeIDRef ID, enum SCEVTypes T,
                   const SCEV *const *O, size_t N)
        : SCEVCommutativeExpr(ID, T, O, N) {
      assert(isMinMaxType(T));
      // Min and max never overflow
      setNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW));
    }
 
  public:
    Type *getType() const { return getOperand(0)->getType(); }
 
    static bool classof(const SCEV *S) {
      return isMinMaxType(S->getSCEVType());
    }
 
    static enum SCEVTypes negate(enum SCEVTypes T) {
      switch (T) {
      case scSMaxExpr:
        return scSMinExpr;
      case scSMinExpr:
        return scSMaxExpr;
      case scUMaxExpr:
        return scUMinExpr;
      case scUMinExpr:
        return scUMaxExpr;
      default:
        llvm_unreachable("Not a min or max SCEV type!");
      }
    }
  };
 
  /// This class represents a signed maximum selection.
  class SCEVSMaxExpr : public SCEVMinMaxExpr {
    friend class ScalarEvolution;
 
    SCEVSMaxExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
        : SCEVMinMaxExpr(ID, scSMaxExpr, O, N) {}
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scSMaxExpr;
    }
  };
 
  /// This class represents an unsigned maximum selection.
  class SCEVUMaxExpr : public SCEVMinMaxExpr {
    friend class ScalarEvolution;
 
    SCEVUMaxExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
        : SCEVMinMaxExpr(ID, scUMaxExpr, O, N) {}
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scUMaxExpr;
    }
  };
 
  /// This class represents a signed minimum selection.
  class SCEVSMinExpr : public SCEVMinMaxExpr {
    friend class ScalarEvolution;
 
    SCEVSMinExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
        : SCEVMinMaxExpr(ID, scSMinExpr, O, N) {}
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scSMinExpr;
    }
  };
 
  /// This class represents an unsigned minimum selection.
  class SCEVUMinExpr : public SCEVMinMaxExpr {
    friend class ScalarEvolution;
 
    SCEVUMinExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
        : SCEVMinMaxExpr(ID, scUMinExpr, O, N) {}
 
  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scUMinExpr;
    }
  };
 
  /// This means that we are dealing with an entirely unknown SCEV
  /// value, and only represent it as its LLVM Value.  This is the
  /// "bottom" value for the analysis.
  class SCEVUnknown final : public SCEV, private CallbackVH {
    friend class ScalarEvolution;
 
    /// The parent ScalarEvolution value. This is used to update the
    /// parent's maps when the value associated with a SCEVUnknown is
    /// deleted or RAUW'd.
    ScalarEvolution *SE;
 
    /// The next pointer in the linked list of all SCEVUnknown
    /// instances owned by a ScalarEvolution.
    SCEVUnknown *Next;
 
    SCEVUnknown(const FoldingSetNodeIDRef ID, Value *V,
                ScalarEvolution *se, SCEVUnknown *next) :
      SCEV(ID, scUnknown, 1), CallbackVH(V), SE(se), Next(next) {}
 
    // Implement CallbackVH.
    void deleted() override;
    void allUsesReplacedWith(Value *New) override;
 
  public:
    Value *getValue() const { return getValPtr(); }
 
    /// @{
    /// Test whether this is a special constant representing a type
    /// size, alignment, or field offset in a target-independent
    /// manner, and hasn't happened to have been folded with other
    /// operations into something unrecognizable. This is mainly only
    /// useful for pretty-printing and other situations where it isn't
    /// absolutely required for these to succeed.
    bool isSizeOf(Type *&AllocTy) const;
    bool isAlignOf(Type *&AllocTy) const;
    bool isOffsetOf(Type *&STy, Constant *&FieldNo) const;
    /// @}
 
    Type *getType() const { return getValPtr()->getType(); }
 
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static bool classof(const SCEV *S) {
      return S->getSCEVType() == scUnknown;
    }
  };
 
  /// This class defines a simple visitor class that may be used for
  /// various SCEV analysis purposes.
  template<typename SC, typename RetVal=void>
  struct SCEVVisitor {
    RetVal visit(const SCEV *S) {
      switch (S->getSCEVType()) {
      case scConstant:
        return ((SC*)this)->visitConstant((const SCEVConstant*)S);
      case scPtrToInt:
        return ((SC *)this)->visitPtrToIntExpr((const SCEVPtrToIntExpr *)S);
      case scTruncate:
        return ((SC*)this)->visitTruncateExpr((const SCEVTruncateExpr*)S);
      case scZeroExtend:
        return ((SC*)this)->visitZeroExtendExpr((const SCEVZeroExtendExpr*)S);
      case scSignExtend:
        return ((SC*)this)->visitSignExtendExpr((const SCEVSignExtendExpr*)S);
      case scAddExpr:
        return ((SC*)this)->visitAddExpr((const SCEVAddExpr*)S);
      case scMulExpr:
        return ((SC*)this)->visitMulExpr((const SCEVMulExpr*)S);
      case scUDivExpr:
        return ((SC*)this)->visitUDivExpr((const SCEVUDivExpr*)S);
      case scAddRecExpr:
        return ((SC*)this)->visitAddRecExpr((const SCEVAddRecExpr*)S);
      case scSMaxExpr:
        return ((SC*)this)->visitSMaxExpr((const SCEVSMaxExpr*)S);
      case scUMaxExpr:
        return ((SC*)this)->visitUMaxExpr((const SCEVUMaxExpr*)S);
      case scSMinExpr:
        return ((SC *)this)->visitSMinExpr((const SCEVSMinExpr *)S);
      case scUMinExpr:
        return ((SC *)this)->visitUMinExpr((const SCEVUMinExpr *)S);
      case scUnknown:
        return ((SC*)this)->visitUnknown((const SCEVUnknown*)S);
      case scCouldNotCompute:
        return ((SC*)this)->visitCouldNotCompute((const SCEVCouldNotCompute*)S);
      }
      llvm_unreachable("Unknown SCEV kind!");
    }
 
    RetVal visitCouldNotCompute(const SCEVCouldNotCompute *S) {
      llvm_unreachable("Invalid use of SCEVCouldNotCompute!");
    }
  };
 
  /// Visit all nodes in the expression tree using worklist traversal.
  ///
  /// Visitor implements:
  ///   // return true to follow this node.
  ///   bool follow(const SCEV *S);
  ///   // return true to terminate the search.
  ///   bool isDone();
  template<typename SV>
  class SCEVTraversal {
    SV &Visitor;
    SmallVector<const SCEV *, 8> Worklist;
    SmallPtrSet<const SCEV *, 8> Visited;
 
    void push(const SCEV *S) {
      if (Visited.insert(S).second && Visitor.follow(S))
        Worklist.push_back(S);
    }
 
  public:
    SCEVTraversal(SV& V): Visitor(V) {}
 
    void visitAll(const SCEV *Root) {
      push(Root);
      while (!Worklist.empty() && !Visitor.isDone()) {
        const SCEV *S = Worklist.pop_back_val();
 
        switch (S->getSCEVType()) {
        case scConstant:
        case scUnknown:
          continue;
        case scPtrToInt:
        case scTruncate:
        case scZeroExtend:
        case scSignExtend:
          push(cast<SCEVCastExpr>(S)->getOperand());
          continue;
        case scAddExpr:
        case scMulExpr:
        case scSMaxExpr:
        case scUMaxExpr:
        case scSMinExpr:
        case scUMinExpr:
        case scAddRecExpr:
          for (const auto *Op : cast<SCEVNAryExpr>(S)->operands())
            push(Op);
          continue;
        case scUDivExpr: {
          const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
          push(UDiv->getLHS());
          push(UDiv->getRHS());
          continue;
        }
        case scCouldNotCompute:
          llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
        }
        llvm_unreachable("Unknown SCEV kind!");
      }
    }
  };
 
  /// Use SCEVTraversal to visit all nodes in the given expression tree.
  template<typename SV>
  void visitAll(const SCEV *Root, SV& Visitor) {
    SCEVTraversal<SV> T(Visitor);
    T.visitAll(Root);
  }
 
  /// Return true if any node in \p Root satisfies the predicate \p Pred.
  template <typename PredTy>
  bool SCEVExprContains(const SCEV *Root, PredTy Pred) {
    struct FindClosure {
      bool Found = false;
      PredTy Pred;
 
      FindClosure(PredTy Pred) : Pred(Pred) {}
 
      bool follow(const SCEV *S) {
        if (!Pred(S))
          return true;
 
        Found = true;
        return false;
      }
 
      bool isDone() const { return Found; }
    };
 
    FindClosure FC(Pred);
    visitAll(Root, FC);
    return FC.Found;
  }
 
  /// This visitor recursively visits a SCEV expression and re-writes it.
  /// The result from each visit is cached, so it will return the same
  /// SCEV for the same input.
  template<typename SC>
  class SCEVRewriteVisitor : public SCEVVisitor<SC, const SCEV *> {
  protected:
    ScalarEvolution &SE;
    // Memoize the result of each visit so that we only compute once for
    // the same input SCEV. This is to avoid redundant computations when
    // a SCEV is referenced by multiple SCEVs. Without memoization, this
    // visit algorithm would have exponential time complexity in the worst
    // case, causing the compiler to hang on certain tests.
    DenseMap<const SCEV *, const SCEV *> RewriteResults;
 
  public:
    SCEVRewriteVisitor(ScalarEvolution &SE) : SE(SE) {}
 
    const SCEV *visit(const SCEV *S) {
      auto It = RewriteResults.find(S);
      if (It != RewriteResults.end())
        return It->second;
      auto* Visited = SCEVVisitor<SC, const SCEV *>::visit(S);
      auto Result = RewriteResults.try_emplace(S, Visited);
      assert(Result.second && "Should insert a new entry");
      return Result.first->second;
    }
 
    const SCEV *visitConstant(const SCEVConstant *Constant) {
      return Constant;
    }
 
    const SCEV *visitPtrToIntExpr(const SCEVPtrToIntExpr *Expr) {
      const SCEV *Operand = ((SC *)this)->visit(Expr->getOperand());
      return Operand == Expr->getOperand()
                 ? Expr
                 : SE.getPtrToIntExpr(Operand, Expr->getType());
    }
 
    const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
      const SCEV *Operand = ((SC*)this)->visit(Expr->getOperand());
      return Operand == Expr->getOperand()
                 ? Expr
                 : SE.getTruncateExpr(Operand, Expr->getType());
    }
 
    const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
      const SCEV *Operand = ((SC*)this)->visit(Expr->getOperand());
      return Operand == Expr->getOperand()
                 ? Expr
                 : SE.getZeroExtendExpr(Operand, Expr->getType());
    }
 
    const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
      const SCEV *Operand = ((SC*)this)->visit(Expr->getOperand());
      return Operand == Expr->getOperand()
                 ? Expr
                 : SE.getSignExtendExpr(Operand, Expr->getType());
    }
 
    const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC*)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr : SE.getAddExpr(Operands);
    }
 
    const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC*)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr : SE.getMulExpr(Operands);
    }
 
    const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
      auto *LHS = ((SC *)this)->visit(Expr->getLHS());
      auto *RHS = ((SC *)this)->visit(Expr->getRHS());
      bool Changed = LHS != Expr->getLHS() || RHS != Expr->getRHS();
      return !Changed ? Expr : SE.getUDivExpr(LHS, RHS);
    }
 
    const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC*)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr
                      : SE.getAddRecExpr(Operands, Expr->getLoop(),
                                         Expr->getNoWrapFlags());
    }
 
    const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC *)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr : SE.getSMaxExpr(Operands);
    }
 
    const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC*)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr : SE.getUMaxExpr(Operands);
    }
 
    const SCEV *visitSMinExpr(const SCEVSMinExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC *)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr : SE.getSMinExpr(Operands);
    }
 
    const SCEV *visitUMinExpr(const SCEVUMinExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      bool Changed = false;
      for (auto *Op : Expr->operands()) {
        Operands.push_back(((SC *)this)->visit(Op));
        Changed |= Op != Operands.back();
      }
      return !Changed ? Expr : SE.getUMinExpr(Operands);
    }
 
    const SCEV *visitUnknown(const SCEVUnknown *Expr) {
      return Expr;
    }
 
    const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
      return Expr;
    }
  };
 
  using ValueToValueMap = DenseMap<const Value *, Value *>;
  using ValueToSCEVMapTy = DenseMap<const Value *, const SCEV *>;
 
  /// The SCEVParameterRewriter takes a scalar evolution expression and updates
  /// the SCEVUnknown components following the Map (Value -> SCEV).
  class SCEVParameterRewriter : public SCEVRewriteVisitor<SCEVParameterRewriter> {
  public:
    static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
                               ValueToSCEVMapTy &Map) {
      SCEVParameterRewriter Rewriter(SE, Map);
      return Rewriter.visit(Scev);
    }
 
    SCEVParameterRewriter(ScalarEvolution &SE, ValueToSCEVMapTy &M)
        : SCEVRewriteVisitor(SE), Map(M) {}
 
    const SCEV *visitUnknown(const SCEVUnknown *Expr) {
      auto I = Map.find(Expr->getValue());
      if (I == Map.end())
        return Expr;
      return I->second;
    }
 
  private:
    ValueToSCEVMapTy &Map;
  };
 
  using LoopToScevMapT = DenseMap<const Loop *, const SCEV *>;
 
  /// The SCEVLoopAddRecRewriter takes a scalar evolution expression and applies
  /// the Map (Loop -> SCEV) to all AddRecExprs.
  class SCEVLoopAddRecRewriter
      : public SCEVRewriteVisitor<SCEVLoopAddRecRewriter> {
  public:
    SCEVLoopAddRecRewriter(ScalarEvolution &SE, LoopToScevMapT &M)
        : SCEVRewriteVisitor(SE), Map(M) {}
 
    static const SCEV *rewrite(const SCEV *Scev, LoopToScevMapT &Map,
                               ScalarEvolution &SE) {
      SCEVLoopAddRecRewriter Rewriter(SE, Map);
      return Rewriter.visit(Scev);
    }
 
    const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (const SCEV *Op : Expr->operands())
        Operands.push_back(visit(Op));
 
      const Loop *L = Expr->getLoop();
      if (0 == Map.count(L))
        return SE.getAddRecExpr(Operands, L, Expr->getNoWrapFlags());
 
      return SCEVAddRecExpr::evaluateAtIteration(Operands, Map[L], SE);
    }
 
  private:
    LoopToScevMapT &Map;
  };
 
} // end namespace llvm
 
#endif // LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H