include/llvm/Analysis/IVDescriptors.h - llvm-project/llvm - Git at Google

 //===- llvm/Analysis/IVDescriptors.h - IndVar Descriptors -------*- 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 "describes" induction and recurrence variables.
 //
 //===----------------------------------------------------------------------===//

 #ifndef LLVM_ANALYSIS_IVDESCRIPTORS_H
 #define LLVM_ANALYSIS_IVDESCRIPTORS_H

 #include "llvm/ADT/DenseMap.h"
 #include "llvm/ADT/SmallPtrSet.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/StringRef.h"
 #include "llvm/IR/InstrTypes.h"
 #include "llvm/IR/Instruction.h"
 #include "llvm/IR/Operator.h"
 #include "llvm/IR/ValueHandle.h"
 #include "llvm/Support/Casting.h"

 namespace llvm {

 class DemandedBits;
 class AssumptionCache;
 class Loop;
 class PredicatedScalarEvolution;
 class ScalarEvolution;
 class SCEV;
 class DominatorTree;

 /// These are the kinds of recurrences that we support.
 enum class RecurKind {
   None,   ///< Not a recurrence.
   Add,    ///< Sum of integers.
   Mul,    ///< Product of integers.
   Or,     ///< Bitwise or logical OR of integers.
   And,    ///< Bitwise or logical AND of integers.
   Xor,    ///< Bitwise or logical XOR of integers.
   SMin,   ///< Signed integer min implemented in terms of select(cmp()).
   SMax,   ///< Signed integer max implemented in terms of select(cmp()).
   UMin,   ///< Unisgned integer min implemented in terms of select(cmp()).
   UMax,   ///< Unsigned integer max implemented in terms of select(cmp()).
   FAdd,   ///< Sum of floats.
   FMul,   ///< Product of floats.
   FMin,   ///< FP min implemented in terms of select(cmp()).
   FMax    ///< FP max implemented in terms of select(cmp()).
 };

 /// The RecurrenceDescriptor is used to identify recurrences variables in a
 /// loop. Reduction is a special case of recurrence that has uses of the
 /// recurrence variable outside the loop. The method isReductionPHI identifies
 /// reductions that are basic recurrences.
 ///
 /// Basic recurrences are defined as the summation, product, OR, AND, XOR, min,
 /// or max of a set of terms. For example: for(i=0; i<n; i++) { total +=
 /// array[i]; } is a summation of array elements. Basic recurrences are a
 /// special case of chains of recurrences (CR). See ScalarEvolution for CR
 /// references.

 /// This struct holds information about recurrence variables.
 class RecurrenceDescriptor {
 public:
   RecurrenceDescriptor() = default;

   RecurrenceDescriptor(Value *Start, Instruction *Exit, RecurKind K,
                        FastMathFlags FMF, Instruction *ExactFP, Type *RT,
                        bool Signed, bool Ordered,
                        SmallPtrSetImpl<Instruction *> &CI)
       : StartValue(Start), LoopExitInstr(Exit), Kind(K), FMF(FMF),
         ExactFPMathInst(ExactFP), RecurrenceType(RT), IsSigned(Signed),
         IsOrdered(Ordered) {
     CastInsts.insert(CI.begin(), CI.end());
   }

   /// This POD struct holds information about a potential recurrence operation.
   class InstDesc {
   public:
     InstDesc(bool IsRecur, Instruction *I, Instruction *ExactFP = nullptr)
         : IsRecurrence(IsRecur), PatternLastInst(I),
           RecKind(RecurKind::None), ExactFPMathInst(ExactFP) {}

     InstDesc(Instruction *I, RecurKind K, Instruction *ExactFP = nullptr)
         : IsRecurrence(true), PatternLastInst(I), RecKind(K),
           ExactFPMathInst(ExactFP) {}

     bool isRecurrence() const { return IsRecurrence; }

     bool needsExactFPMath() const { return ExactFPMathInst != nullptr; }

     Instruction *getExactFPMathInst() const { return ExactFPMathInst; }

     RecurKind getRecKind() const { return RecKind; }

     Instruction *getPatternInst() const { return PatternLastInst; }

   private:
     // Is this instruction a recurrence candidate.
     bool IsRecurrence;
     // The last instruction in a min/max pattern (select of the select(icmp())
     // pattern), or the current recurrence instruction otherwise.
     Instruction *PatternLastInst;
     // If this is a min/max pattern.
     RecurKind RecKind;
     // Recurrence does not allow floating-point reassociation.
     Instruction *ExactFPMathInst;
   };

   /// Returns a struct describing if the instruction 'I' can be a recurrence
   /// variable of type 'Kind'. If the recurrence is a min/max pattern of
   /// select(icmp()) this function advances the instruction pointer 'I' from the
   /// compare instruction to the select instruction and stores this pointer in
   /// 'PatternLastInst' member of the returned struct.
   static InstDesc isRecurrenceInstr(Instruction *I, RecurKind Kind,
                                     InstDesc &Prev, FastMathFlags FMF);

   /// Returns true if instruction I has multiple uses in Insts
   static bool hasMultipleUsesOf(Instruction *I,
                                 SmallPtrSetImpl<Instruction *> &Insts,
                                 unsigned MaxNumUses);

   /// Returns true if all uses of the instruction I is within the Set.
   static bool areAllUsesIn(Instruction *I, SmallPtrSetImpl<Instruction *> &Set);

   /// Returns a struct describing if the instruction is a
   /// Select(ICmp(X, Y), X, Y) instruction pattern corresponding to a min(X, Y)
   /// or max(X, Y). \p Prev specifies the description of an already processed
   /// select instruction, so its corresponding cmp can be matched to it.
   static InstDesc isMinMaxSelectCmpPattern(Instruction *I,
                                            const InstDesc &Prev);

   /// Returns a struct describing if the instruction is a
   /// Select(FCmp(X, Y), (Z = X op PHINode), PHINode) instruction pattern.
   static InstDesc isConditionalRdxPattern(RecurKind Kind, Instruction *I);

   /// Returns identity corresponding to the RecurrenceKind.
   static Constant *getRecurrenceIdentity(RecurKind K, Type *Tp,
                                          FastMathFlags FMF);

   /// Returns the opcode corresponding to the RecurrenceKind.
   static unsigned getOpcode(RecurKind Kind);

   /// Returns true if Phi is a reduction of type Kind and adds it to the
   /// RecurrenceDescriptor. If either \p DB is non-null or \p AC and \p DT are
   /// non-null, the minimal bit width needed to compute the reduction will be
   /// computed.
   static bool AddReductionVar(PHINode *Phi, RecurKind Kind, Loop *TheLoop,
                               FastMathFlags FMF,
                               RecurrenceDescriptor &RedDes,
                               DemandedBits *DB = nullptr,
                               AssumptionCache *AC = nullptr,
                               DominatorTree *DT = nullptr);

   /// Returns true if Phi is a reduction in TheLoop. The RecurrenceDescriptor
   /// is returned in RedDes. If either \p DB is non-null or \p AC and \p DT are
   /// non-null, the minimal bit width needed to compute the reduction will be
   /// computed.
   static bool isReductionPHI(PHINode *Phi, Loop *TheLoop,
                              RecurrenceDescriptor &RedDes,
                              DemandedBits *DB = nullptr,
                              AssumptionCache *AC = nullptr,
                              DominatorTree *DT = nullptr);

   /// Returns true if Phi is a first-order recurrence. A first-order recurrence
   /// is a non-reduction recurrence relation in which the value of the
   /// recurrence in the current loop iteration equals a value defined in the
   /// previous iteration. \p SinkAfter includes pairs of instructions where the
   /// first will be rescheduled to appear after the second if/when the loop is
   /// vectorized. It may be augmented with additional pairs if needed in order
   /// to handle Phi as a first-order recurrence.
   static bool
   isFirstOrderRecurrence(PHINode *Phi, Loop *TheLoop,
                          DenseMap<Instruction *, Instruction *> &SinkAfter,
                          DominatorTree *DT);

   RecurKind getRecurrenceKind() const { return Kind; }

   unsigned getOpcode() const { return getOpcode(getRecurrenceKind()); }

   FastMathFlags getFastMathFlags() const { return FMF; }

   TrackingVH<Value> getRecurrenceStartValue() const { return StartValue; }

   Instruction *getLoopExitInstr() const { return LoopExitInstr; }

   /// Returns true if the recurrence has floating-point math that requires
   /// precise (ordered) operations.
   bool hasExactFPMath() const { return ExactFPMathInst != nullptr; }

   /// Returns 1st non-reassociative FP instruction in the PHI node's use-chain.
   Instruction *getExactFPMathInst() const { return ExactFPMathInst; }

   /// Returns true if the recurrence kind is an integer kind.
   static bool isIntegerRecurrenceKind(RecurKind Kind);

   /// Returns true if the recurrence kind is a floating point kind.
   static bool isFloatingPointRecurrenceKind(RecurKind Kind);

   /// Returns true if the recurrence kind is an arithmetic kind.
   static bool isArithmeticRecurrenceKind(RecurKind Kind);

   /// Returns true if the recurrence kind is an integer min/max kind.
   static bool isIntMinMaxRecurrenceKind(RecurKind Kind) {
     return Kind == RecurKind::UMin || Kind == RecurKind::UMax ||
            Kind == RecurKind::SMin || Kind == RecurKind::SMax;
   }

   /// Returns true if the recurrence kind is a floating-point min/max kind.
   static bool isFPMinMaxRecurrenceKind(RecurKind Kind) {
     return Kind == RecurKind::FMin || Kind == RecurKind::FMax;
   }

   /// Returns true if the recurrence kind is any min/max kind.
   static bool isMinMaxRecurrenceKind(RecurKind Kind) {
     return isIntMinMaxRecurrenceKind(Kind) || isFPMinMaxRecurrenceKind(Kind);
   }

   /// Returns the type of the recurrence. This type can be narrower than the
   /// actual type of the Phi if the recurrence has been type-promoted.
   Type *getRecurrenceType() const { return RecurrenceType; }

   /// Returns a reference to the instructions used for type-promoting the
   /// recurrence.
   const SmallPtrSet<Instruction *, 8> &getCastInsts() const { return CastInsts; }

   /// Returns true if all source operands of the recurrence are SExtInsts.
   bool isSigned() const { return IsSigned; }

   /// Expose an ordered FP reduction to the instance users.
   bool isOrdered() const { return IsOrdered; }

   /// Attempts to find a chain of operations from Phi to LoopExitInst that can
   /// be treated as a set of reductions instructions for in-loop reductions.
   SmallVector<Instruction *, 4> getReductionOpChain(PHINode *Phi,
                                                     Loop *L) const;

 private:
   // The starting value of the recurrence.
   // It does not have to be zero!
   TrackingVH<Value> StartValue;
   // The instruction who's value is used outside the loop.
   Instruction *LoopExitInstr = nullptr;
   // The kind of the recurrence.
   RecurKind Kind = RecurKind::None;
   // The fast-math flags on the recurrent instructions.  We propagate these
   // fast-math flags into the vectorized FP instructions we generate.
   FastMathFlags FMF;
   // First instance of non-reassociative floating-point in the PHI's use-chain.
   Instruction *ExactFPMathInst = nullptr;
   // The type of the recurrence.
   Type *RecurrenceType = nullptr;
   // True if all source operands of the recurrence are SExtInsts.
   bool IsSigned = false;
   // True if this recurrence can be treated as an in-order reduction.
   // Currently only a non-reassociative FAdd can be considered in-order,
   // if it is also the only FAdd in the PHI's use chain.
   bool IsOrdered = false;
   // Instructions used for type-promoting the recurrence.
   SmallPtrSet<Instruction *, 8> CastInsts;
 };

 /// A struct for saving information about induction variables.
 class InductionDescriptor {
 public:
   /// This enum represents the kinds of inductions that we support.
   enum InductionKind {
     IK_NoInduction,  ///< Not an induction variable.
     IK_IntInduction, ///< Integer induction variable. Step = C.
     IK_PtrInduction, ///< Pointer induction var. Step = C / sizeof(elem).
     IK_FpInduction   ///< Floating point induction variable.
   };

 public:
   /// Default constructor - creates an invalid induction.
   InductionDescriptor() = default;

   Value *getStartValue() const { return StartValue; }
   InductionKind getKind() const { return IK; }
   const SCEV *getStep() const { return Step; }
   BinaryOperator *getInductionBinOp() const { return InductionBinOp; }
   ConstantInt *getConstIntStepValue() const;

   /// Returns true if \p Phi is an induction in the loop \p L. If \p Phi is an
   /// induction, the induction descriptor \p D will contain the data describing
   /// this induction. If by some other means the caller has a better SCEV
   /// expression for \p Phi than the one returned by the ScalarEvolution
   /// analysis, it can be passed through \p Expr. If the def-use chain
   /// associated with the phi includes casts (that we know we can ignore
   /// under proper runtime checks), they are passed through \p CastsToIgnore.
   static bool
   isInductionPHI(PHINode *Phi, const Loop *L, ScalarEvolution *SE,
                  InductionDescriptor &D, const SCEV *Expr = nullptr,
                  SmallVectorImpl<Instruction *> *CastsToIgnore = nullptr);

   /// Returns true if \p Phi is a floating point induction in the loop \p L.
   /// If \p Phi is an induction, the induction descriptor \p D will contain
   /// the data describing this induction.
   static bool isFPInductionPHI(PHINode *Phi, const Loop *L, ScalarEvolution *SE,
                                InductionDescriptor &D);

   /// Returns true if \p Phi is a loop \p L induction, in the context associated
   /// with the run-time predicate of PSE. If \p Assume is true, this can add
   /// further SCEV predicates to \p PSE in order to prove that \p Phi is an
   /// induction.
   /// If \p Phi is an induction, \p D will contain the data describing this
   /// induction.
   static bool isInductionPHI(PHINode *Phi, const Loop *L,
                              PredicatedScalarEvolution &PSE,
                              InductionDescriptor &D, bool Assume = false);

   /// Returns floating-point induction operator that does not allow
   /// reassociation (transforming the induction requires an override of normal
   /// floating-point rules).
   Instruction *getExactFPMathInst() {
     if (IK == IK_FpInduction && InductionBinOp &&
         !InductionBinOp->hasAllowReassoc())
       return InductionBinOp;
     return nullptr;
   }

   /// Returns binary opcode of the induction operator.
   Instruction::BinaryOps getInductionOpcode() const {
     return InductionBinOp ? InductionBinOp->getOpcode()
                           : Instruction::BinaryOpsEnd;
   }

   /// Returns a reference to the type cast instructions in the induction
   /// update chain, that are redundant when guarded with a runtime
   /// SCEV overflow check.
   const SmallVectorImpl<Instruction *> &getCastInsts() const {
     return RedundantCasts;
   }

 private:
   /// Private constructor - used by \c isInductionPHI.
   InductionDescriptor(Value *Start, InductionKind K, const SCEV *Step,
                       BinaryOperator *InductionBinOp = nullptr,
                       SmallVectorImpl<Instruction *> *Casts = nullptr);

   /// Start value.
   TrackingVH<Value> StartValue;
   /// Induction kind.
   InductionKind IK = IK_NoInduction;
   /// Step value.
   const SCEV *Step = nullptr;
   // Instruction that advances induction variable.
   BinaryOperator *InductionBinOp = nullptr;
   // Instructions used for type-casts of the induction variable,
   // that are redundant when guarded with a runtime SCEV overflow check.
   SmallVector<Instruction *, 2> RedundantCasts;
 };

 } // end namespace llvm

 #endif // LLVM_ANALYSIS_IVDESCRIPTORS_H
	//===- llvm/Analysis/IVDescriptors.h - IndVar Descriptors -------- 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 "describes" induction and recurrence variables.
	//
	//===----------------------------------------------------------------------===//

	#ifndef LLVM_ANALYSIS_IVDESCRIPTORS_H
	#define LLVM_ANALYSIS_IVDESCRIPTORS_H

	#include "llvm/ADT/DenseMap.h"
	#include "llvm/ADT/SmallPtrSet.h"
	#include "llvm/ADT/SmallVector.h"
	#include "llvm/ADT/StringRef.h"
	#include "llvm/IR/InstrTypes.h"
	#include "llvm/IR/Instruction.h"
	#include "llvm/IR/Operator.h"
	#include "llvm/IR/ValueHandle.h"
	#include "llvm/Support/Casting.h"

	namespace llvm {

	class DemandedBits;
	class AssumptionCache;
	class Loop;
	class PredicatedScalarEvolution;
	class ScalarEvolution;
	class SCEV;
	class DominatorTree;

	/// These are the kinds of recurrences that we support.
	enum class RecurKind {
	None, ///< Not a recurrence.
	Add, ///< Sum of integers.
	Mul, ///< Product of integers.
	Or, ///< Bitwise or logical OR of integers.
	And, ///< Bitwise or logical AND of integers.
	Xor, ///< Bitwise or logical XOR of integers.
	SMin, ///< Signed integer min implemented in terms of select(cmp()).
	SMax, ///< Signed integer max implemented in terms of select(cmp()).
	UMin, ///< Unisgned integer min implemented in terms of select(cmp()).
	UMax, ///< Unsigned integer max implemented in terms of select(cmp()).
	FAdd, ///< Sum of floats.
	FMul, ///< Product of floats.
	FMin, ///< FP min implemented in terms of select(cmp()).
	FMax ///< FP max implemented in terms of select(cmp()).
	};

	/// The RecurrenceDescriptor is used to identify recurrences variables in a
	/// loop. Reduction is a special case of recurrence that has uses of the
	/// recurrence variable outside the loop. The method isReductionPHI identifies
	/// reductions that are basic recurrences.
	///
	/// Basic recurrences are defined as the summation, product, OR, AND, XOR, min,
	/// or max of a set of terms. For example: for(i=0; i<n; i++) { total +=
	/// array[i]; } is a summation of array elements. Basic recurrences are a
	/// special case of chains of recurrences (CR). See ScalarEvolution for CR
	/// references.

	/// This struct holds information about recurrence variables.
	class RecurrenceDescriptor {
	public:
	RecurrenceDescriptor() = default;

	RecurrenceDescriptor(Value Start, Instruction Exit, RecurKind K,
	FastMathFlags FMF, Instruction ExactFP, Type RT,
	bool Signed, bool Ordered,
	SmallPtrSetImpl<Instruction *> &CI)
	: StartValue(Start), LoopExitInstr(Exit), Kind(K), FMF(FMF),
	ExactFPMathInst(ExactFP), RecurrenceType(RT), IsSigned(Signed),
	IsOrdered(Ordered) {
	CastInsts.insert(CI.begin(), CI.end());
	}

	/// This POD struct holds information about a potential recurrence operation.
	class InstDesc {
	public:
	InstDesc(bool IsRecur, Instruction I, Instruction ExactFP = nullptr)
	: IsRecurrence(IsRecur), PatternLastInst(I),
	RecKind(RecurKind::None), ExactFPMathInst(ExactFP) {}

	InstDesc(Instruction I, RecurKind K, Instruction ExactFP = nullptr)
	: IsRecurrence(true), PatternLastInst(I), RecKind(K),
	ExactFPMathInst(ExactFP) {}

	bool isRecurrence() const { return IsRecurrence; }

	bool needsExactFPMath() const { return ExactFPMathInst != nullptr; }

	Instruction *getExactFPMathInst() const { return ExactFPMathInst; }

	RecurKind getRecKind() const { return RecKind; }

	Instruction *getPatternInst() const { return PatternLastInst; }

	private:
	// Is this instruction a recurrence candidate.
	bool IsRecurrence;
	// The last instruction in a min/max pattern (select of the select(icmp())
	// pattern), or the current recurrence instruction otherwise.
	Instruction *PatternLastInst;
	// If this is a min/max pattern.
	RecurKind RecKind;
	// Recurrence does not allow floating-point reassociation.
	Instruction *ExactFPMathInst;
	};

	/// Returns a struct describing if the instruction 'I' can be a recurrence
	/// variable of type 'Kind'. If the recurrence is a min/max pattern of
	/// select(icmp()) this function advances the instruction pointer 'I' from the
	/// compare instruction to the select instruction and stores this pointer in
	/// 'PatternLastInst' member of the returned struct.
	static InstDesc isRecurrenceInstr(Instruction *I, RecurKind Kind,
	InstDesc &Prev, FastMathFlags FMF);

	/// Returns true if instruction I has multiple uses in Insts
	static bool hasMultipleUsesOf(Instruction *I,
	SmallPtrSetImpl<Instruction *> &Insts,
	unsigned MaxNumUses);

	/// Returns true if all uses of the instruction I is within the Set.
	static bool areAllUsesIn(Instruction I, SmallPtrSetImpl<Instruction > &Set);

	/// Returns a struct describing if the instruction is a
	/// Select(ICmp(X, Y), X, Y) instruction pattern corresponding to a min(X, Y)
	/// or max(X, Y). \p Prev specifies the description of an already processed
	/// select instruction, so its corresponding cmp can be matched to it.
	static InstDesc isMinMaxSelectCmpPattern(Instruction *I,
	const InstDesc &Prev);

	/// Returns a struct describing if the instruction is a
	/// Select(FCmp(X, Y), (Z = X op PHINode), PHINode) instruction pattern.
	static InstDesc isConditionalRdxPattern(RecurKind Kind, Instruction *I);

	/// Returns identity corresponding to the RecurrenceKind.
	static Constant getRecurrenceIdentity(RecurKind K, Type Tp,
	FastMathFlags FMF);

	/// Returns the opcode corresponding to the RecurrenceKind.
	static unsigned getOpcode(RecurKind Kind);

	/// Returns true if Phi is a reduction of type Kind and adds it to the
	/// RecurrenceDescriptor. If either \p DB is non-null or \p AC and \p DT are
	/// non-null, the minimal bit width needed to compute the reduction will be
	/// computed.
	static bool AddReductionVar(PHINode Phi, RecurKind Kind, Loop TheLoop,
	FastMathFlags FMF,
	RecurrenceDescriptor &RedDes,
	DemandedBits *DB = nullptr,
	AssumptionCache *AC = nullptr,
	DominatorTree *DT = nullptr);

	/// Returns true if Phi is a reduction in TheLoop. The RecurrenceDescriptor
	/// is returned in RedDes. If either \p DB is non-null or \p AC and \p DT are
	/// non-null, the minimal bit width needed to compute the reduction will be
	/// computed.
	static bool isReductionPHI(PHINode Phi, Loop TheLoop,
	RecurrenceDescriptor &RedDes,
	DemandedBits *DB = nullptr,
	AssumptionCache *AC = nullptr,
	DominatorTree *DT = nullptr);

	/// Returns true if Phi is a first-order recurrence. A first-order recurrence
	/// is a non-reduction recurrence relation in which the value of the
	/// recurrence in the current loop iteration equals a value defined in the
	/// previous iteration. \p SinkAfter includes pairs of instructions where the
	/// first will be rescheduled to appear after the second if/when the loop is
	/// vectorized. It may be augmented with additional pairs if needed in order
	/// to handle Phi as a first-order recurrence.
	static bool
	isFirstOrderRecurrence(PHINode Phi, Loop TheLoop,
	DenseMap<Instruction , Instruction > &SinkAfter,
	DominatorTree *DT);

	RecurKind getRecurrenceKind() const { return Kind; }

	unsigned getOpcode() const { return getOpcode(getRecurrenceKind()); }

	FastMathFlags getFastMathFlags() const { return FMF; }

	TrackingVH<Value> getRecurrenceStartValue() const { return StartValue; }

	Instruction *getLoopExitInstr() const { return LoopExitInstr; }

	/// Returns true if the recurrence has floating-point math that requires
	/// precise (ordered) operations.
	bool hasExactFPMath() const { return ExactFPMathInst != nullptr; }

	/// Returns 1st non-reassociative FP instruction in the PHI node's use-chain.
	Instruction *getExactFPMathInst() const { return ExactFPMathInst; }

	/// Returns true if the recurrence kind is an integer kind.
	static bool isIntegerRecurrenceKind(RecurKind Kind);

	/// Returns true if the recurrence kind is a floating point kind.
	static bool isFloatingPointRecurrenceKind(RecurKind Kind);

	/// Returns true if the recurrence kind is an arithmetic kind.
	static bool isArithmeticRecurrenceKind(RecurKind Kind);

	/// Returns true if the recurrence kind is an integer min/max kind.
	static bool isIntMinMaxRecurrenceKind(RecurKind Kind) {
	return Kind == RecurKind::UMin \|\| Kind == RecurKind::UMax \|\|
	Kind == RecurKind::SMin \|\| Kind == RecurKind::SMax;
	}

	/// Returns true if the recurrence kind is a floating-point min/max kind.
	static bool isFPMinMaxRecurrenceKind(RecurKind Kind) {
	return Kind == RecurKind::FMin \|\| Kind == RecurKind::FMax;
	}

	/// Returns true if the recurrence kind is any min/max kind.
	static bool isMinMaxRecurrenceKind(RecurKind Kind) {
	return isIntMinMaxRecurrenceKind(Kind) \|\| isFPMinMaxRecurrenceKind(Kind);
	}

	/// Returns the type of the recurrence. This type can be narrower than the
	/// actual type of the Phi if the recurrence has been type-promoted.
	Type *getRecurrenceType() const { return RecurrenceType; }

	/// Returns a reference to the instructions used for type-promoting the
	/// recurrence.
	const SmallPtrSet<Instruction *, 8> &getCastInsts() const { return CastInsts; }

	/// Returns true if all source operands of the recurrence are SExtInsts.
	bool isSigned() const { return IsSigned; }

	/// Expose an ordered FP reduction to the instance users.
	bool isOrdered() const { return IsOrdered; }

	/// Attempts to find a chain of operations from Phi to LoopExitInst that can
	/// be treated as a set of reductions instructions for in-loop reductions.
	SmallVector<Instruction , 4> getReductionOpChain(PHINode Phi,
	Loop *L) const;

	private:
	// The starting value of the recurrence.
	// It does not have to be zero!
	TrackingVH<Value> StartValue;
	// The instruction who's value is used outside the loop.
	Instruction *LoopExitInstr = nullptr;
	// The kind of the recurrence.
	RecurKind Kind = RecurKind::None;
	// The fast-math flags on the recurrent instructions. We propagate these
	// fast-math flags into the vectorized FP instructions we generate.
	FastMathFlags FMF;
	// First instance of non-reassociative floating-point in the PHI's use-chain.
	Instruction *ExactFPMathInst = nullptr;
	// The type of the recurrence.
	Type *RecurrenceType = nullptr;
	// True if all source operands of the recurrence are SExtInsts.
	bool IsSigned = false;
	// True if this recurrence can be treated as an in-order reduction.
	// Currently only a non-reassociative FAdd can be considered in-order,
	// if it is also the only FAdd in the PHI's use chain.
	bool IsOrdered = false;
	// Instructions used for type-promoting the recurrence.
	SmallPtrSet<Instruction *, 8> CastInsts;
	};

	/// A struct for saving information about induction variables.
	class InductionDescriptor {
	public:
	/// This enum represents the kinds of inductions that we support.
	enum InductionKind {
	IK_NoInduction, ///< Not an induction variable.
	IK_IntInduction, ///< Integer induction variable. Step = C.
	IK_PtrInduction, ///< Pointer induction var. Step = C / sizeof(elem).
	IK_FpInduction ///< Floating point induction variable.
	};

	public:
	/// Default constructor - creates an invalid induction.
	InductionDescriptor() = default;

	Value *getStartValue() const { return StartValue; }
	InductionKind getKind() const { return IK; }
	const SCEV *getStep() const { return Step; }
	BinaryOperator *getInductionBinOp() const { return InductionBinOp; }
	ConstantInt *getConstIntStepValue() const;

	/// Returns true if \p Phi is an induction in the loop \p L. If \p Phi is an
	/// induction, the induction descriptor \p D will contain the data describing
	/// this induction. If by some other means the caller has a better SCEV
	/// expression for \p Phi than the one returned by the ScalarEvolution
	/// analysis, it can be passed through \p Expr. If the def-use chain
	/// associated with the phi includes casts (that we know we can ignore
	/// under proper runtime checks), they are passed through \p CastsToIgnore.
	static bool
	isInductionPHI(PHINode Phi, const Loop L, ScalarEvolution *SE,
	InductionDescriptor &D, const SCEV *Expr = nullptr,
	SmallVectorImpl<Instruction > CastsToIgnore = nullptr);

	/// Returns true if \p Phi is a floating point induction in the loop \p L.
	/// If \p Phi is an induction, the induction descriptor \p D will contain
	/// the data describing this induction.
	static bool isFPInductionPHI(PHINode Phi, const Loop L, ScalarEvolution *SE,
	InductionDescriptor &D);

	/// Returns true if \p Phi is a loop \p L induction, in the context associated
	/// with the run-time predicate of PSE. If \p Assume is true, this can add
	/// further SCEV predicates to \p PSE in order to prove that \p Phi is an
	/// induction.
	/// If \p Phi is an induction, \p D will contain the data describing this
	/// induction.
	static bool isInductionPHI(PHINode Phi, const Loop L,
	PredicatedScalarEvolution &PSE,
	InductionDescriptor &D, bool Assume = false);

	/// Returns floating-point induction operator that does not allow
	/// reassociation (transforming the induction requires an override of normal
	/// floating-point rules).
	Instruction *getExactFPMathInst() {
	if (IK == IK_FpInduction && InductionBinOp &&
	!InductionBinOp->hasAllowReassoc())
	return InductionBinOp;
	return nullptr;
	}

	/// Returns binary opcode of the induction operator.
	Instruction::BinaryOps getInductionOpcode() const {
	return InductionBinOp ? InductionBinOp->getOpcode()
	: Instruction::BinaryOpsEnd;
	}

	/// Returns a reference to the type cast instructions in the induction
	/// update chain, that are redundant when guarded with a runtime
	/// SCEV overflow check.
	const SmallVectorImpl<Instruction *> &getCastInsts() const {
	return RedundantCasts;
	}

	private:
	/// Private constructor - used by \c isInductionPHI.
	InductionDescriptor(Value Start, InductionKind K, const SCEV Step,
	BinaryOperator *InductionBinOp = nullptr,
	SmallVectorImpl<Instruction > Casts = nullptr);

	/// Start value.
	TrackingVH<Value> StartValue;
	/// Induction kind.
	InductionKind IK = IK_NoInduction;
	/// Step value.
	const SCEV *Step = nullptr;
	// Instruction that advances induction variable.
	BinaryOperator *InductionBinOp = nullptr;
	// Instructions used for type-casts of the induction variable,
	// that are redundant when guarded with a runtime SCEV overflow check.
	SmallVector<Instruction *, 2> RedundantCasts;
	};

	} // end namespace llvm

	#endif // LLVM_ANALYSIS_IVDESCRIPTORS_H