ScalarEvolutionExpressions.h

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//===- llvm/Analysis/ScalarEvolutionExpressions.h - SCEV Exprs --*- C++ -*-===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// 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/iterator_range.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Support/ErrorHandling.h"

namespace llvm {
  class ConstantInt;
  class ConstantRange;
  class DominatorTree;

  enum SCEVTypes {
    // These should be ordered in terms of increasing complexity to make the
    // folders simpler.
    scConstant, scTruncate, scZeroExtend, scSignExtend, scAddExpr, scMulExpr,
    scUDivExpr, scAddRecExpr, scUMaxExpr, scSMaxExpr,
    scUnknown, scCouldNotCompute
  };

  //===--------------------------------------------------------------------===//
  /// SCEVConstant - 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), V(v) {}
  public:
    ConstantInt *getValue() const { return V; }

    Type *getType() const { return V->getType(); }

    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scConstant;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVCastExpr - This is the base class for unary cast operator classes.
  ///
  class SCEVCastExpr : public SCEV {
  protected:
    const SCEV *Op;
    Type *Ty;

    SCEVCastExpr(const FoldingSetNodeIDRef ID,
                 unsigned SCEVTy, const SCEV *op, Type *ty);

  public:
    const SCEV *getOperand() const { return Op; }
    Type *getType() const { return Ty; }

    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scTruncate ||
             S->getSCEVType() == scZeroExtend ||
             S->getSCEVType() == scSignExtend;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVTruncateExpr - This class represents a truncation of an integer value
  /// to a smaller integer value.
  ///
  class SCEVTruncateExpr : public SCEVCastExpr {
    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 inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scTruncate;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVZeroExtendExpr - This class represents a zero extension of a small
  /// integer value to a larger integer value.
  ///
  class SCEVZeroExtendExpr : public SCEVCastExpr {
    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 inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scZeroExtend;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVSignExtendExpr - This class represents a sign extension of a small
  /// integer value to a larger integer value.
  ///
  class SCEVSignExtendExpr : public SCEVCastExpr {
    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 inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scSignExtend;
    }
  };


  //===--------------------------------------------------------------------===//
  /// SCEVNAryExpr - 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), 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];
    }

    typedef const SCEV *const *op_iterator;
    typedef iterator_range<op_iterator> op_range;
    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());
    }

    Type *getType() const { return getOperand(0)->getType(); }

    NoWrapFlags getNoWrapFlags(NoWrapFlags Mask = NoWrapMask) const {
      return (NoWrapFlags)(SubclassData & Mask);
    }

    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddExpr ||
             S->getSCEVType() == scMulExpr ||
             S->getSCEVType() == scSMaxExpr ||
             S->getSCEVType() == scUMaxExpr ||
             S->getSCEVType() == scAddRecExpr;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVCommutativeExpr - 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 inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddExpr ||
             S->getSCEVType() == scMulExpr ||
             S->getSCEVType() == scSMaxExpr ||
             S->getSCEVType() == scUMaxExpr;
    }

    /// Set flags for a non-recurrence without clearing previously set flags.
    void setNoWrapFlags(NoWrapFlags Flags) {
      SubclassData |= Flags;
    }
  };


  //===--------------------------------------------------------------------===//
  /// SCEVAddExpr - This node represents an addition of some number of SCEVs.
  ///
  class SCEVAddExpr : public SCEVCommutativeExpr {
    friend class ScalarEvolution;

    SCEVAddExpr(const FoldingSetNodeIDRef ID,
                const SCEV *const *O, size_t N)
      : SCEVCommutativeExpr(ID, scAddExpr, O, N) {
    }

  public:
    Type *getType() const {
      // Use the type of the last operand, which is likely to be a pointer
      // type, if there is one. This doesn't usually matter, but it can help
      // reduce casts when the expressions are expanded.
      return getOperand(getNumOperands() - 1)->getType();
    }

    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddExpr;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVMulExpr - 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:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scMulExpr;
    }
  };


  //===--------------------------------------------------------------------===//
  /// SCEVUDivExpr - This class represents a binary unsigned division operation.
  ///
  class SCEVUDivExpr : public SCEV {
    friend class ScalarEvolution;

    const SCEV *LHS;
    const SCEV *RHS;
    SCEVUDivExpr(const FoldingSetNodeIDRef ID, const SCEV *lhs, const SCEV *rhs)
      : SCEV(ID, scUDivExpr), LHS(lhs), RHS(rhs) {}

  public:
    const SCEV *getLHS() const { return LHS; }
    const SCEV *getRHS() const { return RHS; }

    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 inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scUDivExpr;
    }
  };


  //===--------------------------------------------------------------------===//
  /// SCEVAddRecExpr - 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:
    const SCEV *getStart() const { return Operands[0]; }
    const Loop *getLoop() const { return L; }

    /// getStepRecurrence - This method 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);
    }

    /// isAffine - 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;
    }

    /// isQuadratic - 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;
    }

    /// evaluateAtIteration - Return the value of this chain of recurrences at
    /// the specified iteration number.
    const SCEV *evaluateAtIteration(const SCEV *It, ScalarEvolution &SE) const;

    /// getNumIterationsInRange - 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(ConstantRange Range,
                                       ScalarEvolution &SE) const;

    /// getPostIncExpr - Return an expression representing the value of
    /// this expression one iteration of the loop ahead.
    const SCEVAddRecExpr *getPostIncExpr(ScalarEvolution &SE) const {
      return cast<SCEVAddRecExpr>(SE.getAddExpr(this, getStepRecurrence(SE)));
    }

    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scAddRecExpr;
    }

    /// Collect parametric terms occurring in step expressions.
    void collectParametricTerms(ScalarEvolution &SE,
                                SmallVectorImpl<const SCEV *> &Terms) const;

    /// Return in Subscripts the access functions for each dimension in Sizes.
    void computeAccessFunctions(ScalarEvolution &SE,
                                SmallVectorImpl<const SCEV *> &Subscripts,
                                SmallVectorImpl<const SCEV *> &Sizes) const;

    /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
    /// subscripts and sizes of an array access.
    ///
    /// The delinearization is a 3 step process: the first two steps compute the
    /// sizes of each subscript and the third step computes the access functions
    /// for the delinearized array:
    ///
    /// 1. Find the terms in the step functions
    /// 2. Compute the array size
    /// 3. Compute the access function: divide the SCEV by the array size
    ///    starting with the innermost dimensions found in step 2. The Quotient
    ///    is the SCEV to be divided in the next step of the recursion. The
    ///    Remainder is the subscript of the innermost dimension. Loop over all
    ///    array dimensions computed in step 2.
    ///
    /// To compute a uniform array size for several memory accesses to the same
    /// object, one can collect in step 1 all the step terms for all the memory
    /// accesses, and compute in step 2 a unique array shape. This guarantees
    /// that the array shape will be the same across all memory accesses.
    ///
    /// FIXME: We could derive the result of steps 1 and 2 from a description of
    /// the array shape given in metadata.
    ///
    /// Example:
    ///
    /// A[][n][m]
    ///
    /// for i
    ///   for j
    ///     for k
    ///       A[j+k][2i][5i] =
    ///
    /// The initial SCEV:
    ///
    /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
    ///
    /// 1. Find the different terms in the step functions:
    /// -> [2*m, 5, n*m, n*m]
    ///
    /// 2. Compute the array size: sort and unique them
    /// -> [n*m, 2*m, 5]
    /// find the GCD of all the terms = 1
    /// divide by the GCD and erase constant terms
    /// -> [n*m, 2*m]
    /// GCD = m
    /// divide by GCD -> [n, 2]
    /// remove constant terms
    /// -> [n]
    /// size of the array is A[unknown][n][m]
    ///
    /// 3. Compute the access function
    /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
    /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
    /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
    /// The remainder is the subscript of the innermost array dimension: [5i].
    ///
    /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
    /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
    /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
    /// The Remainder is the subscript of the next array dimension: [2i].
    ///
    /// The subscript of the outermost dimension is the Quotient: [j+k].
    ///
    /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
    void delinearize(ScalarEvolution &SE,
                     SmallVectorImpl<const SCEV *> &Subscripts,
                     SmallVectorImpl<const SCEV *> &Sizes,
                     const SCEV *ElementSize) const;
  };

  //===--------------------------------------------------------------------===//
  /// SCEVSMaxExpr - This class represents a signed maximum selection.
  ///
  class SCEVSMaxExpr : public SCEVCommutativeExpr {
    friend class ScalarEvolution;

    SCEVSMaxExpr(const FoldingSetNodeIDRef ID,
                 const SCEV *const *O, size_t N)
      : SCEVCommutativeExpr(ID, scSMaxExpr, O, N) {
      // Max never overflows.
      setNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW));
    }

  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scSMaxExpr;
    }
  };


  //===--------------------------------------------------------------------===//
  /// SCEVUMaxExpr - This class represents an unsigned maximum selection.
  ///
  class SCEVUMaxExpr : public SCEVCommutativeExpr {
    friend class ScalarEvolution;

    SCEVUMaxExpr(const FoldingSetNodeIDRef ID,
                 const SCEV *const *O, size_t N)
      : SCEVCommutativeExpr(ID, scUMaxExpr, O, N) {
      // Max never overflows.
      setNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW));
    }

  public:
    /// Methods for support type inquiry through isa, cast, and dyn_cast:
    static inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scUMaxExpr;
    }
  };

  //===--------------------------------------------------------------------===//
  /// SCEVUnknown - 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 : public SCEV, private CallbackVH {
    friend class ScalarEvolution;

    // Implement CallbackVH.
    void deleted() override;
    void allUsesReplacedWith(Value *New) override;

    /// SE - 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;

    /// Next - 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), CallbackVH(V), SE(se), Next(next) {}

  public:
    Value *getValue() const { return getValPtr(); }

    /// isSizeOf, isAlignOf, isOffsetOf - 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 inline bool classof(const SCEV *S) {
      return S->getSCEVType() == scUnknown;
    }
  };

  /// SCEVVisitor - 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 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 scUnknown:
        return ((SC*)this)->visitUnknown((const SCEVUnknown*)S);
      case scCouldNotCompute:
        return ((SC*)this)->visitCouldNotCompute((const SCEVCouldNotCompute*)S);
      default:
        llvm_unreachable("Unknown SCEV type!");
      }
    }

    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) && 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:
          break;
        case scTruncate:
        case scZeroExtend:
        case scSignExtend:
          push(cast<SCEVCastExpr>(S)->getOperand());
          break;
        case scAddExpr:
        case scMulExpr:
        case scSMaxExpr:
        case scUMaxExpr:
        case scAddRecExpr: {
          const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
          for (SCEVNAryExpr::op_iterator I = NAry->op_begin(),
                 E = NAry->op_end(); I != E; ++I) {
            push(*I);
          }
          break;
        }
        case scUDivExpr: {
          const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
          push(UDiv->getLHS());
          push(UDiv->getRHS());
          break;
        }
        case scCouldNotCompute:
          llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
        default:
          llvm_unreachable("Unknown SCEV kind!");
        }
      }
    }
  };

  /// Use SCEVTraversal to visit all nodes in the givien expression tree.
  template<typename SV>
  void visitAll(const SCEV *Root, SV& Visitor) {
    SCEVTraversal<SV> T(Visitor);
    T.visitAll(Root);
  }

  typedef DenseMap<const Value*, Value*> ValueToValueMap;

  /// The SCEVParameterRewriter takes a scalar evolution expression and updates
  /// the SCEVUnknown components following the Map (Value -> Value).
  struct SCEVParameterRewriter
    : public SCEVVisitor<SCEVParameterRewriter, const SCEV*> {
  public:
    static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
                               ValueToValueMap &Map,
                               bool InterpretConsts = false) {
      SCEVParameterRewriter Rewriter(SE, Map, InterpretConsts);
      return Rewriter.visit(Scev);
    }

    SCEVParameterRewriter(ScalarEvolution &S, ValueToValueMap &M, bool C)
      : SE(S), Map(M), InterpretConsts(C) {}

    const SCEV *visitConstant(const SCEVConstant *Constant) {
      return Constant;
    }

    const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
      const SCEV *Operand = visit(Expr->getOperand());
      return SE.getTruncateExpr(Operand, Expr->getType());
    }

    const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
      const SCEV *Operand = visit(Expr->getOperand());
      return SE.getZeroExtendExpr(Operand, Expr->getType());
    }

    const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
      const SCEV *Operand = visit(Expr->getOperand());
      return SE.getSignExtendExpr(Operand, Expr->getType());
    }

    const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getAddExpr(Operands);
    }

    const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getMulExpr(Operands);
    }

    const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
      return SE.getUDivExpr(visit(Expr->getLHS()), visit(Expr->getRHS()));
    }

    const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getAddRecExpr(Operands, Expr->getLoop(),
                              Expr->getNoWrapFlags());
    }

    const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getSMaxExpr(Operands);
    }

    const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getUMaxExpr(Operands);
    }

    const SCEV *visitUnknown(const SCEVUnknown *Expr) {
      Value *V = Expr->getValue();
      if (Map.count(V)) {
        Value *NV = Map[V];
        if (InterpretConsts && isa<ConstantInt>(NV))
          return SE.getConstant(cast<ConstantInt>(NV));
        return SE.getUnknown(NV);
      }
      return Expr;
    }

    const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
      return Expr;
    }

  private:
    ScalarEvolution &SE;
    ValueToValueMap &Map;
    bool InterpretConsts;
  };

  typedef DenseMap<const Loop*, const SCEV*> LoopToScevMapT;

  /// The SCEVApplyRewriter takes a scalar evolution expression and applies
  /// the Map (Loop -> SCEV) to all AddRecExprs.
  struct SCEVApplyRewriter
    : public SCEVVisitor<SCEVApplyRewriter, const SCEV*> {
  public:
    static const SCEV *rewrite(const SCEV *Scev, LoopToScevMapT &Map,
                               ScalarEvolution &SE) {
      SCEVApplyRewriter Rewriter(SE, Map);
      return Rewriter.visit(Scev);
    }

    SCEVApplyRewriter(ScalarEvolution &S, LoopToScevMapT &M)
      : SE(S), Map(M) {}

    const SCEV *visitConstant(const SCEVConstant *Constant) {
      return Constant;
    }

    const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
      const SCEV *Operand = visit(Expr->getOperand());
      return SE.getTruncateExpr(Operand, Expr->getType());
    }

    const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
      const SCEV *Operand = visit(Expr->getOperand());
      return SE.getZeroExtendExpr(Operand, Expr->getType());
    }

    const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
      const SCEV *Operand = visit(Expr->getOperand());
      return SE.getSignExtendExpr(Operand, Expr->getType());
    }

    const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getAddExpr(Operands);
    }

    const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getMulExpr(Operands);
    }

    const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
      return SE.getUDivExpr(visit(Expr->getLHS()), visit(Expr->getRHS()));
    }

    const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));

      const Loop *L = Expr->getLoop();
      const SCEV *Res = SE.getAddRecExpr(Operands, L, Expr->getNoWrapFlags());

      if (0 == Map.count(L))
        return Res;

      const SCEVAddRecExpr *Rec = (const SCEVAddRecExpr *) Res;
      return Rec->evaluateAtIteration(Map[L], SE);
    }

    const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getSMaxExpr(Operands);
    }

    const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
      SmallVector<const SCEV *, 2> Operands;
      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
        Operands.push_back(visit(Expr->getOperand(i)));
      return SE.getUMaxExpr(Operands);
    }

    const SCEV *visitUnknown(const SCEVUnknown *Expr) {
      return Expr;
    }

    const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
      return Expr;
    }

  private:
    ScalarEvolution &SE;
    LoopToScevMapT &Map;
  };

/// Applies the Map (Loop -> SCEV) to the given Scev.
static inline const SCEV *apply(const SCEV *Scev, LoopToScevMapT &Map,
                                ScalarEvolution &SE) {
  return SCEVApplyRewriter::rewrite(Scev, Map, SE);
}

}

#endif