include/llvm/Analysis/ScalarEvolutionExpressions.h - llvm - Git at Google

 //===- 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_SCALAREVOLUTION_EXPRESSIONS_H
 #define LLVM_ANALYSIS_SCALAREVOLUTION_EXPRESSIONS_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 SCEVConstant *S) { return true; }
     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 SCEVCastExpr *S) { return true; }
     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 SCEVTruncateExpr *S) { return true; }
     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 SCEVZeroExtendExpr *S) { return true; }
     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 SCEVSignExtendExpr *S) { return true; }
     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;
     op_iterator op_begin() const { return Operands; }
     op_iterator op_end() const { return Operands + NumOperands; }

     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 SCEVNAryExpr *S) { return true; }
     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 SCEVCommutativeExpr *S) { return true; }
     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 SCEVAddExpr *S) { return true; }
     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 SCEVMulExpr *S) { return true; }
     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 SCEVUDivExpr *S) { return true; }
     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 is an affine AddRec (i.e., it represents
     /// an expressions 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 is an quadratic AddRec (i.e., it
     /// represents an expressions 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 SCEVAddRecExpr *S) { return true; }
     static inline bool classof(const SCEV *S) {
       return S->getSCEVType() == scAddRecExpr;
     }
   };


   //===--------------------------------------------------------------------===//
   /// 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 SCEVSMaxExpr *S) { return true; }
     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 SCEVUMaxExpr *S) { return true; }
     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.
     virtual void deleted();
     virtual void allUsesReplacedWith(Value *New);

     /// 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 SCEVUnknown *S) { return true; }
     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!");
       return RetVal();
     }
   };
 }

 #endif
	//===- 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_SCALAREVOLUTION_EXPRESSIONS_H
	#define LLVM_ANALYSIS_SCALAREVOLUTION_EXPRESSIONS_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 SCEVConstant *S) { return true; }
	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 SCEVCastExpr *S) { return true; }
	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 SCEVTruncateExpr *S) { return true; }
	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 SCEVZeroExtendExpr *S) { return true; }
	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 SCEVSignExtendExpr *S) { return true; }
	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;
	op_iterator op_begin() const { return Operands; }
	op_iterator op_end() const { return Operands + NumOperands; }

	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 SCEVNAryExpr *S) { return true; }
	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 SCEVCommutativeExpr *S) { return true; }
	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 SCEVAddExpr *S) { return true; }
	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 SCEVMulExpr *S) { return true; }
	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 SCEVUDivExpr *S) { return true; }
	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 is an affine AddRec (i.e., it represents
	/// an expressions 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 is an quadratic AddRec (i.e., it
	/// represents an expressions A+Bx+Cx^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 SCEVAddRecExpr *S) { return true; }
	static inline bool classof(const SCEV *S) {
	return S->getSCEVType() == scAddRecExpr;
	}
	};


	//===--------------------------------------------------------------------===//
	/// 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 SCEVSMaxExpr *S) { return true; }
	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 SCEVUMaxExpr *S) { return true; }
	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.
	virtual void deleted();
	virtual void allUsesReplacedWith(Value *New);

	/// 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 SCEVUnknown *S) { return true; }
	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!");
	return RetVal();
	}
	};
	}

	#endif