include/llvm/Analysis/ValueTracking.h - platform/external/llvm - Git at Google

 //===- llvm/Analysis/ValueTracking.h - Walk computations --------*- C++ -*-===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // This file contains routines that help analyze properties that chains of
 // computations have.
 //
 //===----------------------------------------------------------------------===//

 #ifndef LLVM_ANALYSIS_VALUETRACKING_H
 #define LLVM_ANALYSIS_VALUETRACKING_H

 #include "llvm/ADT/ArrayRef.h"
 #include "llvm/IR/ConstantRange.h"
 #include "llvm/IR/Instruction.h"
 #include "llvm/Support/DataTypes.h"

 namespace llvm {
   class APInt;
   class AddOperator;
   class AssumptionCache;
   class DataLayout;
   class DominatorTree;
   class Instruction;
   class Loop;
   class LoopInfo;
   class MDNode;
   class StringRef;
   class TargetLibraryInfo;
   class Value;

   /// Determine which bits of V are known to be either zero or one and return
   /// them in the KnownZero/KnownOne bit sets.
   ///
   /// This function is defined on values with integer type, values with pointer
   /// type, and vectors of integers.  In the case
   /// where V is a vector, the known zero and known one values are the
   /// same width as the vector element, and the bit is set only if it is true
   /// for all of the elements in the vector.
   void computeKnownBits(Value *V, APInt &KnownZero, APInt &KnownOne,
                         const DataLayout &DL, unsigned Depth = 0,
                         AssumptionCache *AC = nullptr,
                         const Instruction *CxtI = nullptr,
                         const DominatorTree *DT = nullptr);
   /// Compute known bits from the range metadata.
   /// \p KnownZero the set of bits that are known to be zero
   /// \p KnownOne the set of bits that are known to be one
   void computeKnownBitsFromRangeMetadata(const MDNode &Ranges,
                                          APInt &KnownZero, APInt &KnownOne);
   /// Return true if LHS and RHS have no common bits set.
   bool haveNoCommonBitsSet(Value *LHS, Value *RHS, const DataLayout &DL,
                            AssumptionCache *AC = nullptr,
                            const Instruction *CxtI = nullptr,
                            const DominatorTree *DT = nullptr);

   /// ComputeSignBit - Determine whether the sign bit is known to be zero or
   /// one.  Convenience wrapper around computeKnownBits.
   void ComputeSignBit(Value *V, bool &KnownZero, bool &KnownOne,
                       const DataLayout &DL, unsigned Depth = 0,
                       AssumptionCache *AC = nullptr,
                       const Instruction *CxtI = nullptr,
                       const DominatorTree *DT = nullptr);

   /// isKnownToBeAPowerOfTwo - Return true if the given value is known to have
   /// exactly one bit set when defined. For vectors return true if every
   /// element is known to be a power of two when defined.  Supports values with
   /// integer or pointer type and vectors of integers.  If 'OrZero' is set then
   /// return true if the given value is either a power of two or zero.
   bool isKnownToBeAPowerOfTwo(Value *V, const DataLayout &DL,
                               bool OrZero = false, unsigned Depth = 0,
                               AssumptionCache *AC = nullptr,
                               const Instruction *CxtI = nullptr,
                               const DominatorTree *DT = nullptr);

   /// isKnownNonZero - Return true if the given value is known to be non-zero
   /// when defined.  For vectors return true if every element is known to be
   /// non-zero when defined.  Supports values with integer or pointer type and
   /// vectors of integers.
   bool isKnownNonZero(Value *V, const DataLayout &DL, unsigned Depth = 0,
                       AssumptionCache *AC = nullptr,
                       const Instruction *CxtI = nullptr,
                       const DominatorTree *DT = nullptr);

   /// Returns true if the give value is known to be non-negative.
   bool isKnownNonNegative(Value *V, const DataLayout &DL, unsigned Depth = 0,
                           AssumptionCache *AC = nullptr,
                           const Instruction *CxtI = nullptr,
                           const DominatorTree *DT = nullptr);

   /// isKnownNonEqual - Return true if the given values are known to be
   /// non-equal when defined. Supports scalar integer types only.
   bool isKnownNonEqual(Value *V1, Value *V2, const DataLayout &DL,
                       AssumptionCache *AC = nullptr,
                       const Instruction *CxtI = nullptr,
                       const DominatorTree *DT = nullptr);

   /// MaskedValueIsZero - Return true if 'V & Mask' is known to be zero.  We use
   /// this predicate to simplify operations downstream.  Mask is known to be
   /// zero for bits that V cannot have.
   ///
   /// This function is defined on values with integer type, values with pointer
   /// type, and vectors of integers.  In the case
   /// where V is a vector, the mask, known zero, and known one values are the
   /// same width as the vector element, and the bit is set only if it is true
   /// for all of the elements in the vector.
   bool MaskedValueIsZero(Value *V, const APInt &Mask, const DataLayout &DL,
                          unsigned Depth = 0, AssumptionCache *AC = nullptr,
                          const Instruction *CxtI = nullptr,
                          const DominatorTree *DT = nullptr);

   /// ComputeNumSignBits - Return the number of times the sign bit of the
   /// register is replicated into the other bits.  We know that at least 1 bit
   /// is always equal to the sign bit (itself), but other cases can give us
   /// information.  For example, immediately after an "ashr X, 2", we know that
   /// the top 3 bits are all equal to each other, so we return 3.
   ///
   /// 'Op' must have a scalar integer type.
   ///
   unsigned ComputeNumSignBits(Value *Op, const DataLayout &DL,
                               unsigned Depth = 0, AssumptionCache *AC = nullptr,
                               const Instruction *CxtI = nullptr,
                               const DominatorTree *DT = nullptr);

   /// ComputeMultiple - This function computes the integer multiple of Base that
   /// equals V.  If successful, it returns true and returns the multiple in
   /// Multiple.  If unsuccessful, it returns false.  Also, if V can be
   /// simplified to an integer, then the simplified V is returned in Val.  Look
   /// through sext only if LookThroughSExt=true.
   bool ComputeMultiple(Value *V, unsigned Base, Value *&Multiple,
                        bool LookThroughSExt = false,
                        unsigned Depth = 0);

   /// CannotBeNegativeZero - Return true if we can prove that the specified FP
   /// value is never equal to -0.0.
   ///
   bool CannotBeNegativeZero(const Value *V, unsigned Depth = 0);

   /// CannotBeOrderedLessThanZero - Return true if we can prove that the
   /// specified FP value is either a NaN or never less than 0.0.
   ///
   bool CannotBeOrderedLessThanZero(const Value *V, unsigned Depth = 0);

   /// isBytewiseValue - If the specified value can be set by repeating the same
   /// byte in memory, return the i8 value that it is represented with.  This is
   /// true for all i8 values obviously, but is also true for i32 0, i32 -1,
   /// i16 0xF0F0, double 0.0 etc.  If the value can't be handled with a repeated
   /// byte store (e.g. i16 0x1234), return null.
   Value *isBytewiseValue(Value *V);

   /// FindInsertedValue - Given an aggregrate and an sequence of indices, see if
   /// the scalar value indexed is already around as a register, for example if
   /// it were inserted directly into the aggregrate.
   ///
   /// If InsertBefore is not null, this function will duplicate (modified)
   /// insertvalues when a part of a nested struct is extracted.
   Value *FindInsertedValue(Value *V,
                            ArrayRef<unsigned> idx_range,
                            Instruction *InsertBefore = nullptr);

   /// GetPointerBaseWithConstantOffset - Analyze the specified pointer to see if
   /// it can be expressed as a base pointer plus a constant offset.  Return the
   /// base and offset to the caller.
   Value *GetPointerBaseWithConstantOffset(Value *Ptr, int64_t &Offset,
                                           const DataLayout &DL);
   static inline const Value *
   GetPointerBaseWithConstantOffset(const Value *Ptr, int64_t &Offset,
                                    const DataLayout &DL) {
     return GetPointerBaseWithConstantOffset(const_cast<Value *>(Ptr), Offset,
                                             DL);
   }

   /// getConstantStringInfo - This function computes the length of a
   /// null-terminated C string pointed to by V.  If successful, it returns true
   /// and returns the string in Str.  If unsuccessful, it returns false.  This
   /// does not include the trailing nul character by default.  If TrimAtNul is
   /// set to false, then this returns any trailing nul characters as well as any
   /// other characters that come after it.
   bool getConstantStringInfo(const Value *V, StringRef &Str,
                              uint64_t Offset = 0, bool TrimAtNul = true);

   /// GetStringLength - If we can compute the length of the string pointed to by
   /// the specified pointer, return 'len+1'.  If we can't, return 0.
   uint64_t GetStringLength(Value *V);

   /// GetUnderlyingObject - This method strips off any GEP address adjustments
   /// and pointer casts from the specified value, returning the original object
   /// being addressed.  Note that the returned value has pointer type if the
   /// specified value does.  If the MaxLookup value is non-zero, it limits the
   /// number of instructions to be stripped off.
   Value *GetUnderlyingObject(Value *V, const DataLayout &DL,
                              unsigned MaxLookup = 6);
   static inline const Value *GetUnderlyingObject(const Value *V,
                                                  const DataLayout &DL,
                                                  unsigned MaxLookup = 6) {
     return GetUnderlyingObject(const_cast<Value *>(V), DL, MaxLookup);
   }

   /// \brief This method is similar to GetUnderlyingObject except that it can
   /// look through phi and select instructions and return multiple objects.
   ///
   /// If LoopInfo is passed, loop phis are further analyzed.  If a pointer
   /// accesses different objects in each iteration, we don't look through the
   /// phi node. E.g. consider this loop nest:
   ///
   ///   int **A;
   ///   for (i)
   ///     for (j) {
   ///        A[i][j] = A[i-1][j] * B[j]
   ///     }
   ///
   /// This is transformed by Load-PRE to stash away A[i] for the next iteration
   /// of the outer loop:
   ///
   ///   Curr = A[0];          // Prev_0
   ///   for (i: 1..N) {
   ///     Prev = Curr;        // Prev = PHI (Prev_0, Curr)
   ///     Curr = A[i];
   ///     for (j: 0..N) {
   ///        Curr[j] = Prev[j] * B[j]
   ///     }
   ///   }
   ///
   /// Since A[i] and A[i-1] are independent pointers, getUnderlyingObjects
   /// should not assume that Curr and Prev share the same underlying object thus
   /// it shouldn't look through the phi above.
   void GetUnderlyingObjects(Value *V, SmallVectorImpl<Value *> &Objects,
                             const DataLayout &DL, LoopInfo *LI = nullptr,
                             unsigned MaxLookup = 6);

   /// onlyUsedByLifetimeMarkers - Return true if the only users of this pointer
   /// are lifetime markers.
   bool onlyUsedByLifetimeMarkers(const Value *V);

   /// isDereferenceablePointer - Return true if this is always a dereferenceable
   /// pointer. If the context instruction is specified perform context-sensitive
   /// analysis and return true if the pointer is dereferenceable at the
   /// specified instruction.
   bool isDereferenceablePointer(const Value *V, const DataLayout &DL,
                                 const Instruction *CtxI = nullptr,
                                 const DominatorTree *DT = nullptr,
                                 const TargetLibraryInfo *TLI = nullptr);

   /// Returns true if V is always a dereferenceable pointer with alignment
   /// greater or equal than requested. If the context instruction is specified
   /// performs context-sensitive analysis and returns true if the pointer is
   /// dereferenceable at the specified instruction.
   bool isDereferenceableAndAlignedPointer(const Value *V, unsigned Align,
                                           const DataLayout &DL,
                                           const Instruction *CtxI = nullptr,
                                           const DominatorTree *DT = nullptr,
                                           const TargetLibraryInfo *TLI = nullptr);

   /// isSafeToSpeculativelyExecute - Return true if the instruction does not
   /// have any effects besides calculating the result and does not have
   /// undefined behavior.
   ///
   /// This method never returns true for an instruction that returns true for
   /// mayHaveSideEffects; however, this method also does some other checks in
   /// addition. It checks for undefined behavior, like dividing by zero or
   /// loading from an invalid pointer (but not for undefined results, like a
   /// shift with a shift amount larger than the width of the result). It checks
   /// for malloc and alloca because speculatively executing them might cause a
   /// memory leak. It also returns false for instructions related to control
   /// flow, specifically terminators and PHI nodes.
   ///
   /// If the CtxI is specified this method performs context-sensitive analysis
   /// and returns true if it is safe to execute the instruction immediately
   /// before the CtxI.
   ///
   /// If the CtxI is NOT specified this method only looks at the instruction
   /// itself and its operands, so if this method returns true, it is safe to
   /// move the instruction as long as the correct dominance relationships for
   /// the operands and users hold.
   ///
   /// This method can return true for instructions that read memory;
   /// for such instructions, moving them may change the resulting value.
   bool isSafeToSpeculativelyExecute(const Value *V,
                                     const Instruction *CtxI = nullptr,
                                     const DominatorTree *DT = nullptr,
                                     const TargetLibraryInfo *TLI = nullptr);

   /// Returns true if the result or effects of the given instructions \p I
   /// depend on or influence global memory.
   /// Memory dependence arises for example if the instruction reads from
   /// memory or may produce effects or undefined behaviour. Memory dependent
   /// instructions generally cannot be reorderd with respect to other memory
   /// dependent instructions or moved into non-dominated basic blocks.
   /// Instructions which just compute a value based on the values of their
   /// operands are not memory dependent.
   bool mayBeMemoryDependent(const Instruction &I);

   /// isKnownNonNull - Return true if this pointer couldn't possibly be null by
   /// its definition.  This returns true for allocas, non-extern-weak globals
   /// and byval arguments.
   bool isKnownNonNull(const Value *V, const TargetLibraryInfo *TLI = nullptr);

   /// isKnownNonNullAt - Return true if this pointer couldn't possibly be null.
   /// If the context instruction is specified perform context-sensitive analysis
   /// and return true if the pointer couldn't possibly be null at the specified
   /// instruction.
   bool isKnownNonNullAt(const Value *V,
                         const Instruction *CtxI = nullptr,
                         const DominatorTree *DT  = nullptr,
                         const TargetLibraryInfo *TLI = nullptr);

   /// Return true if it is valid to use the assumptions provided by an
   /// assume intrinsic, I, at the point in the control-flow identified by the
   /// context instruction, CxtI.
   bool isValidAssumeForContext(const Instruction *I, const Instruction *CxtI,
                                const DominatorTree *DT = nullptr);

   enum class OverflowResult { AlwaysOverflows, MayOverflow, NeverOverflows };
   OverflowResult computeOverflowForUnsignedMul(Value *LHS, Value *RHS,
                                                const DataLayout &DL,
                                                AssumptionCache *AC,
                                                const Instruction *CxtI,
                                                const DominatorTree *DT);
   OverflowResult computeOverflowForUnsignedAdd(Value *LHS, Value *RHS,
                                                const DataLayout &DL,
                                                AssumptionCache *AC,
                                                const Instruction *CxtI,
                                                const DominatorTree *DT);
   OverflowResult computeOverflowForSignedAdd(Value *LHS, Value *RHS,
                                              const DataLayout &DL,
                                              AssumptionCache *AC = nullptr,
                                              const Instruction *CxtI = nullptr,
                                              const DominatorTree *DT = nullptr);
   /// This version also leverages the sign bit of Add if known.
   OverflowResult computeOverflowForSignedAdd(AddOperator *Add,
                                              const DataLayout &DL,
                                              AssumptionCache *AC = nullptr,
                                              const Instruction *CxtI = nullptr,
                                              const DominatorTree *DT = nullptr);

   /// Return true if this function can prove that the instruction I will
   /// always transfer execution to one of its successors (including the next
   /// instruction that follows within a basic block). E.g. this is not
   /// guaranteed for function calls that could loop infinitely.
   ///
   /// In other words, this function returns false for instructions that may
   /// transfer execution or fail to transfer execution in a way that is not
   /// captured in the CFG nor in the sequence of instructions within a basic
   /// block.
   ///
   /// Undefined behavior is assumed not to happen, so e.g. division is
   /// guaranteed to transfer execution to the following instruction even
   /// though division by zero might cause undefined behavior.
   bool isGuaranteedToTransferExecutionToSuccessor(const Instruction *I);

   /// Return true if this function can prove that the instruction I
   /// is executed for every iteration of the loop L.
   ///
   /// Note that this currently only considers the loop header.
   bool isGuaranteedToExecuteForEveryIteration(const Instruction *I,
                                               const Loop *L);

   /// Return true if this function can prove that I is guaranteed to yield
   /// full-poison (all bits poison) if at least one of its operands are
   /// full-poison (all bits poison).
   ///
   /// The exact rules for how poison propagates through instructions have
   /// not been settled as of 2015-07-10, so this function is conservative
   /// and only considers poison to be propagated in uncontroversial
   /// cases. There is no attempt to track values that may be only partially
   /// poison.
   bool propagatesFullPoison(const Instruction *I);

   /// Return either nullptr or an operand of I such that I will trigger
   /// undefined behavior if I is executed and that operand has a full-poison
   /// value (all bits poison).
   const Value *getGuaranteedNonFullPoisonOp(const Instruction *I);

   /// Return true if this function can prove that if PoisonI is executed
   /// and yields a full-poison value (all bits poison), then that will
   /// trigger undefined behavior.
   ///
   /// Note that this currently only considers the basic block that is
   /// the parent of I.
   bool isKnownNotFullPoison(const Instruction *PoisonI);

   /// \brief Specific patterns of select instructions we can match.
   enum SelectPatternFlavor {
     SPF_UNKNOWN = 0,
     SPF_SMIN,                   /// Signed minimum
     SPF_UMIN,                   /// Unsigned minimum
     SPF_SMAX,                   /// Signed maximum
     SPF_UMAX,                   /// Unsigned maximum
     SPF_FMINNUM,                /// Floating point minnum
     SPF_FMAXNUM,                /// Floating point maxnum
     SPF_ABS,                    /// Absolute value
     SPF_NABS                    /// Negated absolute value
   };
   /// \brief Behavior when a floating point min/max is given one NaN and one
   /// non-NaN as input.
   enum SelectPatternNaNBehavior {
     SPNB_NA = 0,                /// NaN behavior not applicable.
     SPNB_RETURNS_NAN,           /// Given one NaN input, returns the NaN.
     SPNB_RETURNS_OTHER,         /// Given one NaN input, returns the non-NaN.
     SPNB_RETURNS_ANY            /// Given one NaN input, can return either (or
                                 /// it has been determined that no operands can
                                 /// be NaN).
   };
   struct SelectPatternResult {
     SelectPatternFlavor Flavor;
     SelectPatternNaNBehavior NaNBehavior; /// Only applicable if Flavor is
                                           /// SPF_FMINNUM or SPF_FMAXNUM.
     bool Ordered;               /// When implementing this min/max pattern as
                                 /// fcmp; select, does the fcmp have to be
                                 /// ordered?

     /// \brief Return true if \p SPF is a min or a max pattern.
     static bool isMinOrMax(SelectPatternFlavor SPF) {
       return !(SPF == SPF_UNKNOWN || SPF == SPF_ABS || SPF == SPF_NABS);
     }
   };
   /// Pattern match integer [SU]MIN, [SU]MAX and ABS idioms, returning the kind
   /// and providing the out parameter results if we successfully match.
   ///
   /// If CastOp is not nullptr, also match MIN/MAX idioms where the type does
   /// not match that of the original select. If this is the case, the cast
   /// operation (one of Trunc,SExt,Zext) that must be done to transform the
   /// type of LHS and RHS into the type of V is returned in CastOp.
   ///
   /// For example:
   ///   %1 = icmp slt i32 %a, i32 4
   ///   %2 = sext i32 %a to i64
   ///   %3 = select i1 %1, i64 %2, i64 4
   ///
   /// -> LHS = %a, RHS = i32 4, *CastOp = Instruction::SExt
   ///
   SelectPatternResult matchSelectPattern(Value *V, Value *&LHS, Value *&RHS,
                                          Instruction::CastOps *CastOp = nullptr);

   /// Parse out a conservative ConstantRange from !range metadata.
   ///
   /// E.g. if RangeMD is !{i32 0, i32 10, i32 15, i32 20} then return [0, 20).
   ConstantRange getConstantRangeFromMetadata(MDNode &RangeMD);

   /// Return true if RHS is known to be implied by LHS.  A & B must be i1
   /// (boolean) values or a vector of such values. Note that the truth table for
   /// implication is the same as <=u on i1 values (but not <=s!).  The truth
   /// table for both is:
   ///    | T | F (B)
   ///  T | T | F
   ///  F | T | T
   /// (A)
   bool isImpliedCondition(Value *LHS, Value *RHS, const DataLayout &DL,
                           unsigned Depth = 0, AssumptionCache *AC = nullptr,
                           const Instruction *CxtI = nullptr,
                           const DominatorTree *DT = nullptr);
 } // end namespace llvm

 #endif
	//===- llvm/Analysis/ValueTracking.h - Walk computations --------- C++ --===//
	//
	// The LLVM Compiler Infrastructure
	//
	// This file is distributed under the University of Illinois Open Source
	// License. See LICENSE.TXT for details.
	//
	//===----------------------------------------------------------------------===//
	//
	// This file contains routines that help analyze properties that chains of
	// computations have.
	//
	//===----------------------------------------------------------------------===//

	#ifndef LLVM_ANALYSIS_VALUETRACKING_H
	#define LLVM_ANALYSIS_VALUETRACKING_H

	#include "llvm/ADT/ArrayRef.h"
	#include "llvm/IR/ConstantRange.h"
	#include "llvm/IR/Instruction.h"
	#include "llvm/Support/DataTypes.h"

	namespace llvm {
	class APInt;
	class AddOperator;
	class AssumptionCache;
	class DataLayout;
	class DominatorTree;
	class Instruction;
	class Loop;
	class LoopInfo;
	class MDNode;
	class StringRef;
	class TargetLibraryInfo;
	class Value;

	/// Determine which bits of V are known to be either zero or one and return
	/// them in the KnownZero/KnownOne bit sets.
	///
	/// This function is defined on values with integer type, values with pointer
	/// type, and vectors of integers. In the case
	/// where V is a vector, the known zero and known one values are the
	/// same width as the vector element, and the bit is set only if it is true
	/// for all of the elements in the vector.
	void computeKnownBits(Value *V, APInt &KnownZero, APInt &KnownOne,
	const DataLayout &DL, unsigned Depth = 0,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);
	/// Compute known bits from the range metadata.
	/// \p KnownZero the set of bits that are known to be zero
	/// \p KnownOne the set of bits that are known to be one
	void computeKnownBitsFromRangeMetadata(const MDNode &Ranges,
	APInt &KnownZero, APInt &KnownOne);
	/// Return true if LHS and RHS have no common bits set.
	bool haveNoCommonBitsSet(Value LHS, Value RHS, const DataLayout &DL,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// ComputeSignBit - Determine whether the sign bit is known to be zero or
	/// one. Convenience wrapper around computeKnownBits.
	void ComputeSignBit(Value *V, bool &KnownZero, bool &KnownOne,
	const DataLayout &DL, unsigned Depth = 0,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// isKnownToBeAPowerOfTwo - Return true if the given value is known to have
	/// exactly one bit set when defined. For vectors return true if every
	/// element is known to be a power of two when defined. Supports values with
	/// integer or pointer type and vectors of integers. If 'OrZero' is set then
	/// return true if the given value is either a power of two or zero.
	bool isKnownToBeAPowerOfTwo(Value *V, const DataLayout &DL,
	bool OrZero = false, unsigned Depth = 0,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// isKnownNonZero - Return true if the given value is known to be non-zero
	/// when defined. For vectors return true if every element is known to be
	/// non-zero when defined. Supports values with integer or pointer type and
	/// vectors of integers.
	bool isKnownNonZero(Value *V, const DataLayout &DL, unsigned Depth = 0,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// Returns true if the give value is known to be non-negative.
	bool isKnownNonNegative(Value *V, const DataLayout &DL, unsigned Depth = 0,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// isKnownNonEqual - Return true if the given values are known to be
	/// non-equal when defined. Supports scalar integer types only.
	bool isKnownNonEqual(Value V1, Value V2, const DataLayout &DL,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// MaskedValueIsZero - Return true if 'V & Mask' is known to be zero. We use
	/// this predicate to simplify operations downstream. Mask is known to be
	/// zero for bits that V cannot have.
	///
	/// This function is defined on values with integer type, values with pointer
	/// type, and vectors of integers. In the case
	/// where V is a vector, the mask, known zero, and known one values are the
	/// same width as the vector element, and the bit is set only if it is true
	/// for all of the elements in the vector.
	bool MaskedValueIsZero(Value *V, const APInt &Mask, const DataLayout &DL,
	unsigned Depth = 0, AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// ComputeNumSignBits - Return the number of times the sign bit of the
	/// register is replicated into the other bits. We know that at least 1 bit
	/// is always equal to the sign bit (itself), but other cases can give us
	/// information. For example, immediately after an "ashr X, 2", we know that
	/// the top 3 bits are all equal to each other, so we return 3.
	///
	/// 'Op' must have a scalar integer type.
	///
	unsigned ComputeNumSignBits(Value *Op, const DataLayout &DL,
	unsigned Depth = 0, AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// ComputeMultiple - This function computes the integer multiple of Base that
	/// equals V. If successful, it returns true and returns the multiple in
	/// Multiple. If unsuccessful, it returns false. Also, if V can be
	/// simplified to an integer, then the simplified V is returned in Val. Look
	/// through sext only if LookThroughSExt=true.
	bool ComputeMultiple(Value V, unsigned Base, Value &Multiple,
	bool LookThroughSExt = false,
	unsigned Depth = 0);

	/// CannotBeNegativeZero - Return true if we can prove that the specified FP
	/// value is never equal to -0.0.
	///
	bool CannotBeNegativeZero(const Value *V, unsigned Depth = 0);

	/// CannotBeOrderedLessThanZero - Return true if we can prove that the
	/// specified FP value is either a NaN or never less than 0.0.
	///
	bool CannotBeOrderedLessThanZero(const Value *V, unsigned Depth = 0);

	/// isBytewiseValue - If the specified value can be set by repeating the same
	/// byte in memory, return the i8 value that it is represented with. This is
	/// true for all i8 values obviously, but is also true for i32 0, i32 -1,
	/// i16 0xF0F0, double 0.0 etc. If the value can't be handled with a repeated
	/// byte store (e.g. i16 0x1234), return null.
	Value isBytewiseValue(Value V);

	/// FindInsertedValue - Given an aggregrate and an sequence of indices, see if
	/// the scalar value indexed is already around as a register, for example if
	/// it were inserted directly into the aggregrate.
	///
	/// If InsertBefore is not null, this function will duplicate (modified)
	/// insertvalues when a part of a nested struct is extracted.
	Value FindInsertedValue(Value V,
	ArrayRef<unsigned> idx_range,
	Instruction *InsertBefore = nullptr);

	/// GetPointerBaseWithConstantOffset - Analyze the specified pointer to see if
	/// it can be expressed as a base pointer plus a constant offset. Return the
	/// base and offset to the caller.
	Value GetPointerBaseWithConstantOffset(Value Ptr, int64_t &Offset,
	const DataLayout &DL);
	static inline const Value *
	GetPointerBaseWithConstantOffset(const Value *Ptr, int64_t &Offset,
	const DataLayout &DL) {
	return GetPointerBaseWithConstantOffset(const_cast<Value *>(Ptr), Offset,
	DL);
	}

	/// getConstantStringInfo - This function computes the length of a
	/// null-terminated C string pointed to by V. If successful, it returns true
	/// and returns the string in Str. If unsuccessful, it returns false. This
	/// does not include the trailing nul character by default. If TrimAtNul is
	/// set to false, then this returns any trailing nul characters as well as any
	/// other characters that come after it.
	bool getConstantStringInfo(const Value *V, StringRef &Str,
	uint64_t Offset = 0, bool TrimAtNul = true);

	/// GetStringLength - If we can compute the length of the string pointed to by
	/// the specified pointer, return 'len+1'. If we can't, return 0.
	uint64_t GetStringLength(Value *V);

	/// GetUnderlyingObject - This method strips off any GEP address adjustments
	/// and pointer casts from the specified value, returning the original object
	/// being addressed. Note that the returned value has pointer type if the
	/// specified value does. If the MaxLookup value is non-zero, it limits the
	/// number of instructions to be stripped off.
	Value GetUnderlyingObject(Value V, const DataLayout &DL,
	unsigned MaxLookup = 6);
	static inline const Value GetUnderlyingObject(const Value V,
	const DataLayout &DL,
	unsigned MaxLookup = 6) {
	return GetUnderlyingObject(const_cast<Value *>(V), DL, MaxLookup);
	}

	/// \brief This method is similar to GetUnderlyingObject except that it can
	/// look through phi and select instructions and return multiple objects.
	///
	/// If LoopInfo is passed, loop phis are further analyzed. If a pointer
	/// accesses different objects in each iteration, we don't look through the
	/// phi node. E.g. consider this loop nest:
	///
	/// int **A;
	/// for (i)
	/// for (j) {
	/// A[i][j] = A[i-1][j] * B[j]
	/// }
	///
	/// This is transformed by Load-PRE to stash away A[i] for the next iteration
	/// of the outer loop:
	///
	/// Curr = A[0]; // Prev_0
	/// for (i: 1..N) {
	/// Prev = Curr; // Prev = PHI (Prev_0, Curr)
	/// Curr = A[i];
	/// for (j: 0..N) {
	/// Curr[j] = Prev[j] * B[j]
	/// }
	/// }
	///
	/// Since A[i] and A[i-1] are independent pointers, getUnderlyingObjects
	/// should not assume that Curr and Prev share the same underlying object thus
	/// it shouldn't look through the phi above.
	void GetUnderlyingObjects(Value V, SmallVectorImpl<Value > &Objects,
	const DataLayout &DL, LoopInfo *LI = nullptr,
	unsigned MaxLookup = 6);

	/// onlyUsedByLifetimeMarkers - Return true if the only users of this pointer
	/// are lifetime markers.
	bool onlyUsedByLifetimeMarkers(const Value *V);

	/// isDereferenceablePointer - Return true if this is always a dereferenceable
	/// pointer. If the context instruction is specified perform context-sensitive
	/// analysis and return true if the pointer is dereferenceable at the
	/// specified instruction.
	bool isDereferenceablePointer(const Value *V, const DataLayout &DL,
	const Instruction *CtxI = nullptr,
	const DominatorTree *DT = nullptr,
	const TargetLibraryInfo *TLI = nullptr);

	/// Returns true if V is always a dereferenceable pointer with alignment
	/// greater or equal than requested. If the context instruction is specified
	/// performs context-sensitive analysis and returns true if the pointer is
	/// dereferenceable at the specified instruction.
	bool isDereferenceableAndAlignedPointer(const Value *V, unsigned Align,
	const DataLayout &DL,
	const Instruction *CtxI = nullptr,
	const DominatorTree *DT = nullptr,
	const TargetLibraryInfo *TLI = nullptr);

	/// isSafeToSpeculativelyExecute - Return true if the instruction does not
	/// have any effects besides calculating the result and does not have
	/// undefined behavior.
	///
	/// This method never returns true for an instruction that returns true for
	/// mayHaveSideEffects; however, this method also does some other checks in
	/// addition. It checks for undefined behavior, like dividing by zero or
	/// loading from an invalid pointer (but not for undefined results, like a
	/// shift with a shift amount larger than the width of the result). It checks
	/// for malloc and alloca because speculatively executing them might cause a
	/// memory leak. It also returns false for instructions related to control
	/// flow, specifically terminators and PHI nodes.
	///
	/// If the CtxI is specified this method performs context-sensitive analysis
	/// and returns true if it is safe to execute the instruction immediately
	/// before the CtxI.
	///
	/// If the CtxI is NOT specified this method only looks at the instruction
	/// itself and its operands, so if this method returns true, it is safe to
	/// move the instruction as long as the correct dominance relationships for
	/// the operands and users hold.
	///
	/// This method can return true for instructions that read memory;
	/// for such instructions, moving them may change the resulting value.
	bool isSafeToSpeculativelyExecute(const Value *V,
	const Instruction *CtxI = nullptr,
	const DominatorTree *DT = nullptr,
	const TargetLibraryInfo *TLI = nullptr);

	/// Returns true if the result or effects of the given instructions \p I
	/// depend on or influence global memory.
	/// Memory dependence arises for example if the instruction reads from
	/// memory or may produce effects or undefined behaviour. Memory dependent
	/// instructions generally cannot be reorderd with respect to other memory
	/// dependent instructions or moved into non-dominated basic blocks.
	/// Instructions which just compute a value based on the values of their
	/// operands are not memory dependent.
	bool mayBeMemoryDependent(const Instruction &I);

	/// isKnownNonNull - Return true if this pointer couldn't possibly be null by
	/// its definition. This returns true for allocas, non-extern-weak globals
	/// and byval arguments.
	bool isKnownNonNull(const Value V, const TargetLibraryInfo TLI = nullptr);

	/// isKnownNonNullAt - Return true if this pointer couldn't possibly be null.
	/// If the context instruction is specified perform context-sensitive analysis
	/// and return true if the pointer couldn't possibly be null at the specified
	/// instruction.
	bool isKnownNonNullAt(const Value *V,
	const Instruction *CtxI = nullptr,
	const DominatorTree *DT = nullptr,
	const TargetLibraryInfo *TLI = nullptr);

	/// Return true if it is valid to use the assumptions provided by an
	/// assume intrinsic, I, at the point in the control-flow identified by the
	/// context instruction, CxtI.
	bool isValidAssumeForContext(const Instruction I, const Instruction CxtI,
	const DominatorTree *DT = nullptr);

	enum class OverflowResult { AlwaysOverflows, MayOverflow, NeverOverflows };
	OverflowResult computeOverflowForUnsignedMul(Value LHS, Value RHS,
	const DataLayout &DL,
	AssumptionCache *AC,
	const Instruction *CxtI,
	const DominatorTree *DT);
	OverflowResult computeOverflowForUnsignedAdd(Value LHS, Value RHS,
	const DataLayout &DL,
	AssumptionCache *AC,
	const Instruction *CxtI,
	const DominatorTree *DT);
	OverflowResult computeOverflowForSignedAdd(Value LHS, Value RHS,
	const DataLayout &DL,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);
	/// This version also leverages the sign bit of Add if known.
	OverflowResult computeOverflowForSignedAdd(AddOperator *Add,
	const DataLayout &DL,
	AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);

	/// Return true if this function can prove that the instruction I will
	/// always transfer execution to one of its successors (including the next
	/// instruction that follows within a basic block). E.g. this is not
	/// guaranteed for function calls that could loop infinitely.
	///
	/// In other words, this function returns false for instructions that may
	/// transfer execution or fail to transfer execution in a way that is not
	/// captured in the CFG nor in the sequence of instructions within a basic
	/// block.
	///
	/// Undefined behavior is assumed not to happen, so e.g. division is
	/// guaranteed to transfer execution to the following instruction even
	/// though division by zero might cause undefined behavior.
	bool isGuaranteedToTransferExecutionToSuccessor(const Instruction *I);

	/// Return true if this function can prove that the instruction I
	/// is executed for every iteration of the loop L.
	///
	/// Note that this currently only considers the loop header.
	bool isGuaranteedToExecuteForEveryIteration(const Instruction *I,
	const Loop *L);

	/// Return true if this function can prove that I is guaranteed to yield
	/// full-poison (all bits poison) if at least one of its operands are
	/// full-poison (all bits poison).
	///
	/// The exact rules for how poison propagates through instructions have
	/// not been settled as of 2015-07-10, so this function is conservative
	/// and only considers poison to be propagated in uncontroversial
	/// cases. There is no attempt to track values that may be only partially
	/// poison.
	bool propagatesFullPoison(const Instruction *I);

	/// Return either nullptr or an operand of I such that I will trigger
	/// undefined behavior if I is executed and that operand has a full-poison
	/// value (all bits poison).
	const Value getGuaranteedNonFullPoisonOp(const Instruction I);

	/// Return true if this function can prove that if PoisonI is executed
	/// and yields a full-poison value (all bits poison), then that will
	/// trigger undefined behavior.
	///
	/// Note that this currently only considers the basic block that is
	/// the parent of I.
	bool isKnownNotFullPoison(const Instruction *PoisonI);

	/// \brief Specific patterns of select instructions we can match.
	enum SelectPatternFlavor {
	SPF_UNKNOWN = 0,
	SPF_SMIN, /// Signed minimum
	SPF_UMIN, /// Unsigned minimum
	SPF_SMAX, /// Signed maximum
	SPF_UMAX, /// Unsigned maximum
	SPF_FMINNUM, /// Floating point minnum
	SPF_FMAXNUM, /// Floating point maxnum
	SPF_ABS, /// Absolute value
	SPF_NABS /// Negated absolute value
	};
	/// \brief Behavior when a floating point min/max is given one NaN and one
	/// non-NaN as input.
	enum SelectPatternNaNBehavior {
	SPNB_NA = 0, /// NaN behavior not applicable.
	SPNB_RETURNS_NAN, /// Given one NaN input, returns the NaN.
	SPNB_RETURNS_OTHER, /// Given one NaN input, returns the non-NaN.
	SPNB_RETURNS_ANY /// Given one NaN input, can return either (or
	/// it has been determined that no operands can
	/// be NaN).
	};
	struct SelectPatternResult {
	SelectPatternFlavor Flavor;
	SelectPatternNaNBehavior NaNBehavior; /// Only applicable if Flavor is
	/// SPF_FMINNUM or SPF_FMAXNUM.
	bool Ordered; /// When implementing this min/max pattern as
	/// fcmp; select, does the fcmp have to be
	/// ordered?

	/// \brief Return true if \p SPF is a min or a max pattern.
	static bool isMinOrMax(SelectPatternFlavor SPF) {
	return !(SPF == SPF_UNKNOWN \|\| SPF == SPF_ABS \|\| SPF == SPF_NABS);
	}
	};
	/// Pattern match integer [SU]MIN, [SU]MAX and ABS idioms, returning the kind
	/// and providing the out parameter results if we successfully match.
	///
	/// If CastOp is not nullptr, also match MIN/MAX idioms where the type does
	/// not match that of the original select. If this is the case, the cast
	/// operation (one of Trunc,SExt,Zext) that must be done to transform the
	/// type of LHS and RHS into the type of V is returned in CastOp.
	///
	/// For example:
	/// %1 = icmp slt i32 %a, i32 4
	/// %2 = sext i32 %a to i64
	/// %3 = select i1 %1, i64 %2, i64 4
	///
	/// -> LHS = %a, RHS = i32 4, *CastOp = Instruction::SExt
	///
	SelectPatternResult matchSelectPattern(Value V, Value &LHS, Value *&RHS,
	Instruction::CastOps *CastOp = nullptr);

	/// Parse out a conservative ConstantRange from !range metadata.
	///
	/// E.g. if RangeMD is !{i32 0, i32 10, i32 15, i32 20} then return [0, 20).
	ConstantRange getConstantRangeFromMetadata(MDNode &RangeMD);

	/// Return true if RHS is known to be implied by LHS. A & B must be i1
	/// (boolean) values or a vector of such values. Note that the truth table for
	/// implication is the same as <=u on i1 values (but not <=s!). The truth
	/// table for both is:
	/// \| T \| F (B)
	/// T \| T \| F
	/// F \| T \| T
	/// (A)
	bool isImpliedCondition(Value LHS, Value RHS, const DataLayout &DL,
	unsigned Depth = 0, AssumptionCache *AC = nullptr,
	const Instruction *CxtI = nullptr,
	const DominatorTree *DT = nullptr);
	} // end namespace llvm

	#endif