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 //===- llvm/Analysis/ValueTracking.h - Walk computations --------*- 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 contains routines that help analyze properties that chains of
 // computations have.
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef LLVM_ANALYSIS_VALUETRACKING_H
 #define LLVM_ANALYSIS_VALUETRACKING_H
 
 #include "llvm/Analysis/SimplifyQuery.h"
 #include "llvm/Analysis/WithCache.h"
 #include "llvm/IR/Constants.h"
 #include "llvm/IR/DataLayout.h"
 #include "llvm/IR/FMF.h"
 #include "llvm/IR/Instructions.h"
 #include "llvm/IR/InstrTypes.h"
 #include "llvm/IR/Intrinsics.h"
 #include <cassert>
 #include <cstdint>
 
 namespace llvm {
 
 class Operator;
 class AddOperator;
 class AssumptionCache;
 class DominatorTree;
 class GEPOperator;
 class WithOverflowInst;
 struct KnownBits;
 class Loop;
 class LoopInfo;
 class MDNode;
 class StringRef;
 class TargetLibraryInfo;
 template <typename T> class ArrayRef;
 
 constexpr unsigned MaxAnalysisRecursionDepth = 6;
 
 /// 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(const Value *V, KnownBits &Known, const DataLayout &DL,
                       unsigned Depth = 0, AssumptionCache *AC = nullptr,
                       const Instruction *CxtI = nullptr,
                       const DominatorTree *DT = nullptr,
                       bool UseInstrInfo = true);
 
 /// Returns the known bits rather than passing by reference.
 KnownBits computeKnownBits(const Value *V, const DataLayout &DL,
                            unsigned Depth = 0, AssumptionCache *AC = nullptr,
                            const Instruction *CxtI = nullptr,
                            const DominatorTree *DT = nullptr,
                            bool UseInstrInfo = true);
 
 /// Returns the known bits rather than passing by reference.
 KnownBits computeKnownBits(const Value *V, const APInt &DemandedElts,
                            const DataLayout &DL, unsigned Depth = 0,
                            AssumptionCache *AC = nullptr,
                            const Instruction *CxtI = nullptr,
                            const DominatorTree *DT = nullptr,
                            bool UseInstrInfo = true);
 
 KnownBits computeKnownBits(const Value *V, const APInt &DemandedElts,
                            unsigned Depth, const SimplifyQuery &Q);
 
 KnownBits computeKnownBits(const Value *V, unsigned Depth,
                            const SimplifyQuery &Q);
 
 void computeKnownBits(const Value *V, KnownBits &Known, unsigned Depth,
                       const SimplifyQuery &Q);
 
 /// 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, KnownBits &Known);
 
 /// Merge bits known from context-dependent facts into Known.
 void computeKnownBitsFromContext(const Value *V, KnownBits &Known,
                                  unsigned Depth, const SimplifyQuery &Q);
 
 /// Using KnownBits LHS/RHS produce the known bits for logic op (and/xor/or).
 KnownBits analyzeKnownBitsFromAndXorOr(const Operator *I,
                                        const KnownBits &KnownLHS,
                                        const KnownBits &KnownRHS,
                                        unsigned Depth, const SimplifyQuery &SQ);
 
 /// Adjust \p Known for the given select \p Arm to include information from the
 /// select \p Cond.
 void adjustKnownBitsForSelectArm(KnownBits &Known, Value *Cond, Value *Arm,
                                  bool Invert, unsigned Depth,
                                  const SimplifyQuery &Q);
 
 /// Return true if LHS and RHS have no common bits set.
 bool haveNoCommonBitsSet(const WithCache<const Value *> &LHSCache,
                          const WithCache<const Value *> &RHSCache,
                          const SimplifyQuery &SQ);
 
 /// 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(const Value *V, const DataLayout &DL,
                             bool OrZero = false, unsigned Depth = 0,
                             AssumptionCache *AC = nullptr,
                             const Instruction *CxtI = nullptr,
                             const DominatorTree *DT = nullptr,
                             bool UseInstrInfo = true);
 
 bool isKnownToBeAPowerOfTwo(const Value *V, bool OrZero, unsigned Depth,
                             const SimplifyQuery &Q);
 
 bool isOnlyUsedInZeroComparison(const Instruction *CxtI);
 
 bool isOnlyUsedInZeroEqualityComparison(const Instruction *CxtI);
 
 /// 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. For pointers, if the context instruction and dominator tree are
 /// specified, perform context-sensitive analysis and return true if the
 /// pointer couldn't possibly be null at the specified instruction.
 /// Supports values with integer or pointer type and vectors of integers.
 bool isKnownNonZero(const Value *V, const SimplifyQuery &Q, unsigned Depth = 0);
 
 /// Return true if the two given values are negation.
 /// Currently can recoginze Value pair:
 /// 1: <X, Y> if X = sub (0, Y) or Y = sub (0, X)
 /// 2: <X, Y> if X = sub (A, B) and Y = sub (B, A)
 bool isKnownNegation(const Value *X, const Value *Y, bool NeedNSW = false,
                      bool AllowPoison = true);
 
 /// Return true iff:
 /// 1. X is poison implies Y is poison.
 /// 2. X is true implies Y is false.
 /// 3. X is false implies Y is true.
 /// Otherwise, return false.
 bool isKnownInversion(const Value *X, const Value *Y);
 
 /// Returns true if the give value is known to be non-negative.
 bool isKnownNonNegative(const Value *V, const SimplifyQuery &SQ,
                         unsigned Depth = 0);
 
 /// Returns true if the given value is known be positive (i.e. non-negative
 /// and non-zero).
 bool isKnownPositive(const Value *V, const SimplifyQuery &SQ,
                      unsigned Depth = 0);
 
 /// Returns true if the given value is known be negative (i.e. non-positive
 /// and non-zero).
 bool isKnownNegative(const Value *V, const SimplifyQuery &SQ,
                      unsigned Depth = 0);
 
 /// Return true if the given values are known to be non-equal when defined.
 /// Supports scalar integer types only.
 bool isKnownNonEqual(const Value *V1, const Value *V2, const DataLayout &DL,
                      AssumptionCache *AC = nullptr,
                      const Instruction *CxtI = nullptr,
                      const DominatorTree *DT = nullptr,
                      bool UseInstrInfo = true);
 
 /// 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(const Value *V, const APInt &Mask,
                        const SimplifyQuery &SQ, unsigned Depth = 0);
 
 /// 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. For vectors, return the number of
 /// sign bits for the vector element with the mininum number of known sign
 /// bits.
 unsigned ComputeNumSignBits(const Value *Op, const DataLayout &DL,
                             unsigned Depth = 0, AssumptionCache *AC = nullptr,
                             const Instruction *CxtI = nullptr,
                             const DominatorTree *DT = nullptr,
                             bool UseInstrInfo = true);
 
 /// Get the upper bound on bit size for this Value \p Op as a signed integer.
 /// i.e.  x == sext(trunc(x to MaxSignificantBits) to bitwidth(x)).
 /// Similar to the APInt::getSignificantBits function.
 unsigned ComputeMaxSignificantBits(const Value *Op, const DataLayout &DL,
                                    unsigned Depth = 0,
                                    AssumptionCache *AC = nullptr,
                                    const Instruction *CxtI = nullptr,
                                    const DominatorTree *DT = nullptr);
 
 /// Map a call instruction to an intrinsic ID.  Libcalls which have equivalent
 /// intrinsics are treated as-if they were intrinsics.
 Intrinsic::ID getIntrinsicForCallSite(const CallBase &CB,
                                       const TargetLibraryInfo *TLI);
 
 /// Given an exploded icmp instruction, return true if the comparison only
 /// checks the sign bit. If it only checks the sign bit, set TrueIfSigned if
 /// the result of the comparison is true when the input value is signed.
 bool isSignBitCheck(ICmpInst::Predicate Pred, const APInt &RHS,
                     bool &TrueIfSigned);
 
 /// Returns a pair of values, which if passed to llvm.is.fpclass, returns the
 /// same result as an fcmp with the given operands.
 ///
 /// If \p LookThroughSrc is true, consider the input value when computing the
 /// mask.
 ///
 /// If \p LookThroughSrc is false, ignore the source value (i.e. the first pair
 /// element will always be LHS.
 std::pair<Value *, FPClassTest> fcmpToClassTest(CmpInst::Predicate Pred,
                                                 const Function &F, Value *LHS,
                                                 Value *RHS,
                                                 bool LookThroughSrc = true);
 std::pair<Value *, FPClassTest> fcmpToClassTest(CmpInst::Predicate Pred,
                                                 const Function &F, Value *LHS,
                                                 const APFloat *ConstRHS,
                                                 bool LookThroughSrc = true);
 
 /// Compute the possible floating-point classes that \p LHS could be based on
 /// fcmp \Pred \p LHS, \p RHS.
 ///
 /// \returns { TestedValue, ClassesIfTrue, ClassesIfFalse }
 ///
 /// If the compare returns an exact class test, ClassesIfTrue == ~ClassesIfFalse
 ///
 /// This is a less exact version of fcmpToClassTest (e.g. fcmpToClassTest will
 /// only succeed for a test of x > 0 implies positive, but not x > 1).
 ///
 /// If \p LookThroughSrc is true, consider the input value when computing the
 /// mask. This may look through sign bit operations.
 ///
 /// If \p LookThroughSrc is false, ignore the source value (i.e. the first pair
 /// element will always be LHS.
 ///
 std::tuple<Value *, FPClassTest, FPClassTest>
 fcmpImpliesClass(CmpInst::Predicate Pred, const Function &F, Value *LHS,
                  Value *RHS, bool LookThroughSrc = true);
 std::tuple<Value *, FPClassTest, FPClassTest>
 fcmpImpliesClass(CmpInst::Predicate Pred, const Function &F, Value *LHS,
                  FPClassTest RHS, bool LookThroughSrc = true);
 std::tuple<Value *, FPClassTest, FPClassTest>
 fcmpImpliesClass(CmpInst::Predicate Pred, const Function &F, Value *LHS,
                  const APFloat &RHS, bool LookThroughSrc = true);
 
 struct KnownFPClass {
   /// Floating-point classes the value could be one of.
   FPClassTest KnownFPClasses = fcAllFlags;
 
   /// std::nullopt if the sign bit is unknown, true if the sign bit is
   /// definitely set or false if the sign bit is definitely unset.
   std::optional<bool> SignBit;
 
   bool operator==(KnownFPClass Other) const {
     return KnownFPClasses == Other.KnownFPClasses && SignBit == Other.SignBit;
   }
 
   /// Return true if it's known this can never be one of the mask entries.
   bool isKnownNever(FPClassTest Mask) const {
     return (KnownFPClasses & Mask) == fcNone;
   }
 
   bool isKnownAlways(FPClassTest Mask) const { return isKnownNever(~Mask); }
 
   bool isUnknown() const {
     return KnownFPClasses == fcAllFlags && !SignBit;
   }
 
   /// Return true if it's known this can never be a nan.
   bool isKnownNeverNaN() const {
     return isKnownNever(fcNan);
   }
 
   /// Return true if it's known this must always be a nan.
   bool isKnownAlwaysNaN() const { return isKnownAlways(fcNan); }
 
   /// Return true if it's known this can never be an infinity.
   bool isKnownNeverInfinity() const {
     return isKnownNever(fcInf);
   }
 
   /// Return true if it's known this can never be +infinity.
   bool isKnownNeverPosInfinity() const {
     return isKnownNever(fcPosInf);
   }
 
   /// Return true if it's known this can never be -infinity.
   bool isKnownNeverNegInfinity() const {
     return isKnownNever(fcNegInf);
   }
 
   /// Return true if it's known this can never be a subnormal
   bool isKnownNeverSubnormal() const {
     return isKnownNever(fcSubnormal);
   }
 
   /// Return true if it's known this can never be a positive subnormal
   bool isKnownNeverPosSubnormal() const {
     return isKnownNever(fcPosSubnormal);
   }
 
   /// Return true if it's known this can never be a negative subnormal
   bool isKnownNeverNegSubnormal() const {
     return isKnownNever(fcNegSubnormal);
   }
 
   /// Return true if it's known this can never be a zero. This means a literal
   /// [+-]0, and does not include denormal inputs implicitly treated as [+-]0.
   bool isKnownNeverZero() const {
     return isKnownNever(fcZero);
   }
 
   /// Return true if it's known this can never be a literal positive zero.
   bool isKnownNeverPosZero() const {
     return isKnownNever(fcPosZero);
   }
 
   /// Return true if it's known this can never be a negative zero. This means a
   /// literal -0 and does not include denormal inputs implicitly treated as -0.
   bool isKnownNeverNegZero() const {
     return isKnownNever(fcNegZero);
   }
 
   /// Return true if it's know this can never be interpreted as a zero. This
   /// extends isKnownNeverZero to cover the case where the assumed
   /// floating-point mode for the function interprets denormals as zero.
   bool isKnownNeverLogicalZero(const Function &F, Type *Ty) const;
 
   /// Return true if it's know this can never be interpreted as a negative zero.
   bool isKnownNeverLogicalNegZero(const Function &F, Type *Ty) const;
 
   /// Return true if it's know this can never be interpreted as a positive zero.
   bool isKnownNeverLogicalPosZero(const Function &F, Type *Ty) const;
 
   static constexpr FPClassTest OrderedLessThanZeroMask =
       fcNegSubnormal | fcNegNormal | fcNegInf;
   static constexpr FPClassTest OrderedGreaterThanZeroMask =
       fcPosSubnormal | fcPosNormal | fcPosInf;
 
   /// Return true if we can prove that the analyzed floating-point value is
   /// either NaN or never less than -0.0.
   ///
   ///      NaN --> true
   ///       +0 --> true
   ///       -0 --> true
   ///   x > +0 --> true
   ///   x < -0 --> false
   bool cannotBeOrderedLessThanZero() const {
     return isKnownNever(OrderedLessThanZeroMask);
   }
 
   /// Return true if we can prove that the analyzed floating-point value is
   /// either NaN or never greater than -0.0.
   ///      NaN --> true
   ///       +0 --> true
   ///       -0 --> true
   ///   x > +0 --> false
   ///   x < -0 --> true
   bool cannotBeOrderedGreaterThanZero() const {
     return isKnownNever(OrderedGreaterThanZeroMask);
   }
 
   KnownFPClass &operator|=(const KnownFPClass &RHS) {
     KnownFPClasses = KnownFPClasses | RHS.KnownFPClasses;
 
     if (SignBit != RHS.SignBit)
       SignBit = std::nullopt;
     return *this;
   }
 
   void knownNot(FPClassTest RuleOut) {
     KnownFPClasses = KnownFPClasses & ~RuleOut;
     if (isKnownNever(fcNan) && !SignBit) {
       if (isKnownNever(fcNegative))
         SignBit = false;
       else if (isKnownNever(fcPositive))
         SignBit = true;
     }
   }
 
   void fneg() {
     KnownFPClasses = llvm::fneg(KnownFPClasses);
     if (SignBit)
       SignBit = !*SignBit;
   }
 
   void fabs() {
     if (KnownFPClasses & fcNegZero)
       KnownFPClasses |= fcPosZero;
 
     if (KnownFPClasses & fcNegInf)
       KnownFPClasses |= fcPosInf;
 
     if (KnownFPClasses & fcNegSubnormal)
       KnownFPClasses |= fcPosSubnormal;
 
     if (KnownFPClasses & fcNegNormal)
       KnownFPClasses |= fcPosNormal;
 
     signBitMustBeZero();
   }
 
   /// Return true if the sign bit must be 0, ignoring the sign of nans.
   bool signBitIsZeroOrNaN() const {
     return isKnownNever(fcNegative);
   }
 
   /// Assume the sign bit is zero.
   void signBitMustBeZero() {
     KnownFPClasses &= (fcPositive | fcNan);
     SignBit = false;
   }
 
   /// Assume the sign bit is one.
   void signBitMustBeOne() {
     KnownFPClasses &= (fcNegative | fcNan);
     SignBit = true;
   }
 
   void copysign(const KnownFPClass &Sign) {
     // Don't know anything about the sign of the source. Expand the possible set
     // to its opposite sign pair.
     if (KnownFPClasses & fcZero)
       KnownFPClasses |= fcZero;
     if (KnownFPClasses & fcSubnormal)
       KnownFPClasses |= fcSubnormal;
     if (KnownFPClasses & fcNormal)
       KnownFPClasses |= fcNormal;
     if (KnownFPClasses & fcInf)
       KnownFPClasses |= fcInf;
 
     // Sign bit is exactly preserved even for nans.
     SignBit = Sign.SignBit;
 
     // Clear sign bits based on the input sign mask.
     if (Sign.isKnownNever(fcPositive | fcNan) || (SignBit && *SignBit))
       KnownFPClasses &= (fcNegative | fcNan);
     if (Sign.isKnownNever(fcNegative | fcNan) || (SignBit && !*SignBit))
       KnownFPClasses &= (fcPositive | fcNan);
   }
 
   // Propagate knowledge that a non-NaN source implies the result can also not
   // be a NaN. For unconstrained operations, signaling nans are not guaranteed
   // to be quieted but cannot be introduced.
   void propagateNaN(const KnownFPClass &Src, bool PreserveSign = false) {
     if (Src.isKnownNever(fcNan)) {
       knownNot(fcNan);
       if (PreserveSign)
         SignBit = Src.SignBit;
     } else if (Src.isKnownNever(fcSNan))
       knownNot(fcSNan);
   }
 
   /// Propagate knowledge from a source value that could be a denormal or
   /// zero. We have to be conservative since output flushing is not guaranteed,
   /// so known-never-zero may not hold.
   ///
   /// This assumes a copy-like operation and will replace any currently known
   /// information.
   void propagateDenormal(const KnownFPClass &Src, const Function &F, Type *Ty);
 
   /// Report known classes if \p Src is evaluated through a potentially
   /// canonicalizing operation. We can assume signaling nans will not be
   /// introduced, but cannot assume a denormal will be flushed under FTZ/DAZ.
   ///
   /// This assumes a copy-like operation and will replace any currently known
   /// information.
   void propagateCanonicalizingSrc(const KnownFPClass &Src, const Function &F,
                                   Type *Ty);
 
   void resetAll() { *this = KnownFPClass(); }
 };
 
 inline KnownFPClass operator|(KnownFPClass LHS, const KnownFPClass &RHS) {
   LHS |= RHS;
   return LHS;
 }
 
 inline KnownFPClass operator|(const KnownFPClass &LHS, KnownFPClass &&RHS) {
   RHS |= LHS;
   return std::move(RHS);
 }
 
 /// Determine which floating-point classes are valid for \p V, and return them
 /// in KnownFPClass bit sets.
 ///
 /// This function is defined on values with floating-point type, values vectors
 /// of floating-point type, and arrays of floating-point type.
 
 /// \p InterestedClasses is a compile time optimization hint for which floating
 /// point classes should be queried. Queries not specified in \p
 /// InterestedClasses should be reliable if they are determined during the
 /// query.
 KnownFPClass computeKnownFPClass(const Value *V, const APInt &DemandedElts,
                                  FPClassTest InterestedClasses, unsigned Depth,
                                  const SimplifyQuery &SQ);
 
 KnownFPClass computeKnownFPClass(const Value *V, FPClassTest InterestedClasses,
                                  unsigned Depth, const SimplifyQuery &SQ);
 
 inline KnownFPClass computeKnownFPClass(
     const Value *V, const DataLayout &DL,
     FPClassTest InterestedClasses = fcAllFlags, unsigned Depth = 0,
     const TargetLibraryInfo *TLI = nullptr, AssumptionCache *AC = nullptr,
     const Instruction *CxtI = nullptr, const DominatorTree *DT = nullptr,
     bool UseInstrInfo = true) {
   return computeKnownFPClass(
       V, InterestedClasses, Depth,
       SimplifyQuery(DL, TLI, DT, AC, CxtI, UseInstrInfo));
 }
 
 /// Wrapper to account for known fast math flags at the use instruction.
 inline KnownFPClass
 computeKnownFPClass(const Value *V, const APInt &DemandedElts,
                     FastMathFlags FMF, FPClassTest InterestedClasses,
                     unsigned Depth, const SimplifyQuery &SQ) {
   if (FMF.noNaNs())
     InterestedClasses &= ~fcNan;
   if (FMF.noInfs())
     InterestedClasses &= ~fcInf;
 
   KnownFPClass Result =
       computeKnownFPClass(V, DemandedElts, InterestedClasses, Depth, SQ);
 
   if (FMF.noNaNs())
     Result.KnownFPClasses &= ~fcNan;
   if (FMF.noInfs())
     Result.KnownFPClasses &= ~fcInf;
   return Result;
 }
 
 inline KnownFPClass computeKnownFPClass(const Value *V, FastMathFlags FMF,
                                         FPClassTest InterestedClasses,
                                         unsigned Depth,
                                         const SimplifyQuery &SQ) {
   auto *FVTy = dyn_cast<FixedVectorType>(V->getType());
   APInt DemandedElts =
       FVTy ? APInt::getAllOnes(FVTy->getNumElements()) : APInt(1, 1);
   return computeKnownFPClass(V, DemandedElts, FMF, InterestedClasses, Depth,
                              SQ);
 }
 
 /// Return true if we can prove that the specified FP value is never equal to
 /// -0.0. Users should use caution when considering PreserveSign
 /// denormal-fp-math.
 inline bool cannotBeNegativeZero(const Value *V, unsigned Depth,
                                  const SimplifyQuery &SQ) {
   KnownFPClass Known = computeKnownFPClass(V, fcNegZero, Depth, SQ);
   return Known.isKnownNeverNegZero();
 }
 
 /// Return true if we can prove that the specified FP value is either NaN or
 /// never less than -0.0.
 ///
 ///      NaN --> true
 ///       +0 --> true
 ///       -0 --> true
 ///   x > +0 --> true
 ///   x < -0 --> false
 inline bool cannotBeOrderedLessThanZero(const Value *V, unsigned Depth,
                                         const SimplifyQuery &SQ) {
   KnownFPClass Known =
       computeKnownFPClass(V, KnownFPClass::OrderedLessThanZeroMask, Depth, SQ);
   return Known.cannotBeOrderedLessThanZero();
 }
 
 /// Return true if the floating-point scalar value is not an infinity or if
 /// the floating-point vector value has no infinities. Return false if a value
 /// could ever be infinity.
 inline bool isKnownNeverInfinity(const Value *V, unsigned Depth,
                                  const SimplifyQuery &SQ) {
   KnownFPClass Known = computeKnownFPClass(V, fcInf, Depth, SQ);
   return Known.isKnownNeverInfinity();
 }
 
 /// Return true if the floating-point value can never contain a NaN or infinity.
 inline bool isKnownNeverInfOrNaN(const Value *V, unsigned Depth,
                                  const SimplifyQuery &SQ) {
   KnownFPClass Known = computeKnownFPClass(V, fcInf | fcNan, Depth, SQ);
   return Known.isKnownNeverNaN() && Known.isKnownNeverInfinity();
 }
 
 /// Return true if the floating-point scalar value is not a NaN or if the
 /// floating-point vector value has no NaN elements. Return false if a value
 /// could ever be NaN.
 inline bool isKnownNeverNaN(const Value *V, unsigned Depth,
                             const SimplifyQuery &SQ) {
   KnownFPClass Known = computeKnownFPClass(V, fcNan, Depth, SQ);
   return Known.isKnownNeverNaN();
 }
 
 /// Return false if we can prove that the specified FP value's sign bit is 0.
 /// Return true if we can prove that the specified FP value's sign bit is 1.
 /// Otherwise return std::nullopt.
 inline std::optional<bool> computeKnownFPSignBit(const Value *V, unsigned Depth,
                                                  const SimplifyQuery &SQ) {
   KnownFPClass Known = computeKnownFPClass(V, fcAllFlags, Depth, SQ);
   return Known.SignBit;
 }
 
 /// 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. If the value is entirely undef and padding,
 /// return undef.
 Value *isBytewiseValue(Value *V, const DataLayout &DL);
 
 /// Given an aggregate 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 aggregate.
 ///
 /// If InsertBefore is not empty, this function will duplicate (modified)
 /// insertvalues when a part of a nested struct is extracted.
 Value *FindInsertedValue(
     Value *V, ArrayRef<unsigned> idx_range,
     std::optional<BasicBlock::iterator> InsertBefore = std::nullopt);
 
 /// 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.
 ///
 /// This is a wrapper around Value::stripAndAccumulateConstantOffsets that
 /// creates and later unpacks the required APInt.
 inline Value *GetPointerBaseWithConstantOffset(Value *Ptr, int64_t &Offset,
                                                const DataLayout &DL,
                                                bool AllowNonInbounds = true) {
   APInt OffsetAPInt(DL.getIndexTypeSizeInBits(Ptr->getType()), 0);
   Value *Base =
       Ptr->stripAndAccumulateConstantOffsets(DL, OffsetAPInt, AllowNonInbounds);
 
   Offset = OffsetAPInt.getSExtValue();
   return Base;
 }
 inline const Value *
 GetPointerBaseWithConstantOffset(const Value *Ptr, int64_t &Offset,
                                  const DataLayout &DL,
                                  bool AllowNonInbounds = true) {
   return GetPointerBaseWithConstantOffset(const_cast<Value *>(Ptr), Offset, DL,
                                           AllowNonInbounds);
 }
 
 /// Returns true if the GEP is based on a pointer to a string (array of
 // \p CharSize integers) and is indexing into this string.
 bool isGEPBasedOnPointerToString(const GEPOperator *GEP, unsigned CharSize = 8);
 
 /// Represents offset+length into a ConstantDataArray.
 struct ConstantDataArraySlice {
   /// ConstantDataArray pointer. nullptr indicates a zeroinitializer (a valid
   /// initializer, it just doesn't fit the ConstantDataArray interface).
   const ConstantDataArray *Array;
 
   /// Slice starts at this Offset.
   uint64_t Offset;
 
   /// Length of the slice.
   uint64_t Length;
 
   /// Moves the Offset and adjusts Length accordingly.
   void move(uint64_t Delta) {
     assert(Delta < Length);
     Offset += Delta;
     Length -= Delta;
   }
 
   /// Convenience accessor for elements in the slice.
   uint64_t operator[](unsigned I) const {
     return Array == nullptr ? 0 : Array->getElementAsInteger(I + Offset);
   }
 };
 
 /// Returns true if the value \p V is a pointer into a ConstantDataArray.
 /// If successful \p Slice will point to a ConstantDataArray info object
 /// with an appropriate offset.
 bool getConstantDataArrayInfo(const Value *V, ConstantDataArraySlice &Slice,
                               unsigned ElementSize, uint64_t Offset = 0);
 
 /// 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 null
 /// character by default. If TrimAtNul is set to false, then this returns any
 /// trailing null characters as well as any other characters that come after
 /// it.
 bool getConstantStringInfo(const Value *V, StringRef &Str,
                            bool TrimAtNul = true);
 
 /// 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(const Value *V, unsigned CharSize = 8);
 
 /// This function returns call pointer argument that is considered the same by
 /// aliasing rules. You CAN'T use it to replace one value with another. If
 /// \p MustPreserveNullness is true, the call must preserve the nullness of
 /// the pointer.
 const Value *getArgumentAliasingToReturnedPointer(const CallBase *Call,
                                                   bool MustPreserveNullness);
 inline Value *getArgumentAliasingToReturnedPointer(CallBase *Call,
                                                    bool MustPreserveNullness) {
   return const_cast<Value *>(getArgumentAliasingToReturnedPointer(
       const_cast<const CallBase *>(Call), MustPreserveNullness));
 }
 
 /// {launder,strip}.invariant.group returns pointer that aliases its argument,
 /// and it only captures pointer by returning it.
 /// These intrinsics are not marked as nocapture, because returning is
 /// considered as capture. The arguments are not marked as returned neither,
 /// because it would make it useless. If \p MustPreserveNullness is true,
 /// the intrinsic must preserve the nullness of the pointer.
 bool isIntrinsicReturningPointerAliasingArgumentWithoutCapturing(
     const CallBase *Call, bool MustPreserveNullness);
 
 /// This method strips off any GEP address adjustments, pointer casts
 /// or `llvm.threadlocal.address` from the specified value \p V, returning the
 /// original object being addressed. Note that the returned value has pointer
 /// type if the specified value does. If the \p MaxLookup value is non-zero, it
 /// limits the number of instructions to be stripped off.
 const Value *getUnderlyingObject(const Value *V, unsigned MaxLookup = 6);
 inline Value *getUnderlyingObject(Value *V, unsigned MaxLookup = 6) {
   // Force const to avoid infinite recursion.
   const Value *VConst = V;
   return const_cast<Value *>(getUnderlyingObject(VConst, MaxLookup));
 }
 
 /// Like getUnderlyingObject(), but will try harder to find a single underlying
 /// object. In particular, this function also looks through selects and phis.
 const Value *getUnderlyingObjectAggressive(const Value *V);
 
 /// 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(const Value *V,
                           SmallVectorImpl<const Value *> &Objects,
                           const LoopInfo *LI = nullptr, unsigned MaxLookup = 6);
 
 /// This is a wrapper around getUnderlyingObjects and adds support for basic
 /// ptrtoint+arithmetic+inttoptr sequences.
 bool getUnderlyingObjectsForCodeGen(const Value *V,
                                     SmallVectorImpl<Value *> &Objects);
 
 /// Returns unique alloca where the value comes from, or nullptr.
 /// If OffsetZero is true check that V points to the begining of the alloca.
 AllocaInst *findAllocaForValue(Value *V, bool OffsetZero = false);
 inline const AllocaInst *findAllocaForValue(const Value *V,
                                             bool OffsetZero = false) {
   return findAllocaForValue(const_cast<Value *>(V), OffsetZero);
 }
 
 /// Return true if the only users of this pointer are lifetime markers.
 bool onlyUsedByLifetimeMarkers(const Value *V);
 
 /// Return true if the only users of this pointer are lifetime markers or
 /// droppable instructions.
 bool onlyUsedByLifetimeMarkersOrDroppableInsts(const Value *V);
 
 /// Return true if the instruction doesn't potentially cross vector lanes. This
 /// condition is weaker than checking that the instruction is lanewise: lanewise
 /// means that the same operation is splatted across all lanes, but we also
 /// include the case where there is a different operation on each lane, as long
 /// as the operation only uses data from that lane. An example of an operation
 /// that is not lanewise, but doesn't cross vector lanes is insertelement.
 bool isNotCrossLaneOperation(const Instruction *I);
 
 /// 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 instruction has (transitive) operands that don't
 /// dominate CtxI, the analysis is performed under the assumption that these
 /// operands will also be speculated to a point before CxtI.
 ///
 /// 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 Instruction *I,
                                   const Instruction *CtxI = nullptr,
                                   AssumptionCache *AC = nullptr,
                                   const DominatorTree *DT = nullptr,
                                   const TargetLibraryInfo *TLI = nullptr,
                                   bool UseVariableInfo = true);
 
 inline bool isSafeToSpeculativelyExecute(const Instruction *I,
                                          BasicBlock::iterator CtxI,
                                          AssumptionCache *AC = nullptr,
                                          const DominatorTree *DT = nullptr,
                                          const TargetLibraryInfo *TLI = nullptr,
                                          bool UseVariableInfo = true) {
   // Take an iterator, and unwrap it into an Instruction *.
   return isSafeToSpeculativelyExecute(I, &*CtxI, AC, DT, TLI, UseVariableInfo);
 }
 
 /// Don't use information from its non-constant operands. This helper is used
 /// when its operands are going to be replaced.
 inline bool
 isSafeToSpeculativelyExecuteWithVariableReplaced(const Instruction *I) {
   return isSafeToSpeculativelyExecute(I, nullptr, nullptr, nullptr, nullptr,
                                       /*UseVariableInfo=*/false);
 }
 
 /// This returns the same result as isSafeToSpeculativelyExecute if Opcode is
 /// the actual opcode of Inst. If the provided and actual opcode differ, the
 /// function (virtually) overrides the opcode of Inst with the provided
 /// Opcode. There are come constraints in this case:
 /// * If Opcode has a fixed number of operands (eg, as binary operators do),
 ///   then Inst has to have at least as many leading operands. The function
 ///   will ignore all trailing operands beyond that number.
 /// * If Opcode allows for an arbitrary number of operands (eg, as CallInsts
 ///   do), then all operands are considered.
 /// * The virtual instruction has to satisfy all typing rules of the provided
 ///   Opcode.
 /// * This function is pessimistic in the following sense: If one actually
 ///   materialized the virtual instruction, then isSafeToSpeculativelyExecute
 ///   may say that the materialized instruction is speculatable whereas this
 ///   function may have said that the instruction wouldn't be speculatable.
 ///   This behavior is a shortcoming in the current implementation and not
 ///   intentional.
 bool isSafeToSpeculativelyExecuteWithOpcode(
     unsigned Opcode, const Instruction *Inst, const Instruction *CtxI = nullptr,
     AssumptionCache *AC = nullptr, const DominatorTree *DT = nullptr,
     const TargetLibraryInfo *TLI = nullptr, bool UseVariableInfo = true);
 
 /// Returns true if the result or effects of the given instructions \p I
 /// depend values not reachable through the def use graph.
 /// * 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.
 /// * Control dependence arises for example if the instruction may fault
 ///   if lifted above a throwing call or infinite loop.
 bool mayHaveNonDefUseDependency(const Instruction &I);
 
 /// Return true if it is an intrinsic that cannot be speculated but also
 /// cannot trap.
 bool isAssumeLikeIntrinsic(const Instruction *I);
 
 /// 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. By default, ephemeral values of the assumption
 /// are treated as an invalid context, to prevent the assumption from being used
 /// to optimize away its argument. If the caller can ensure that this won't
 /// happen, it can call with AllowEphemerals set to true to get more valid
 /// assumptions.
 bool isValidAssumeForContext(const Instruction *I, const Instruction *CxtI,
                              const DominatorTree *DT = nullptr,
                              bool AllowEphemerals = false);
 
 enum class OverflowResult {
   /// Always overflows in the direction of signed/unsigned min value.
   AlwaysOverflowsLow,
   /// Always overflows in the direction of signed/unsigned max value.
   AlwaysOverflowsHigh,
   /// May or may not overflow.
   MayOverflow,
   /// Never overflows.
   NeverOverflows,
 };
 
 OverflowResult computeOverflowForUnsignedMul(const Value *LHS, const Value *RHS,
                                              const SimplifyQuery &SQ,
                                              bool IsNSW = false);
 OverflowResult computeOverflowForSignedMul(const Value *LHS, const Value *RHS,
                                            const SimplifyQuery &SQ);
 OverflowResult
 computeOverflowForUnsignedAdd(const WithCache<const Value *> &LHS,
                               const WithCache<const Value *> &RHS,
                               const SimplifyQuery &SQ);
 OverflowResult computeOverflowForSignedAdd(const WithCache<const Value *> &LHS,
                                            const WithCache<const Value *> &RHS,
                                            const SimplifyQuery &SQ);
 /// This version also leverages the sign bit of Add if known.
 OverflowResult computeOverflowForSignedAdd(const AddOperator *Add,
                                            const SimplifyQuery &SQ);
 OverflowResult computeOverflowForUnsignedSub(const Value *LHS, const Value *RHS,
                                              const SimplifyQuery &SQ);
 OverflowResult computeOverflowForSignedSub(const Value *LHS, const Value *RHS,
                                            const SimplifyQuery &SQ);
 
 /// Returns true if the arithmetic part of the \p WO 's result is
 /// used only along the paths control dependent on the computation
 /// not overflowing, \p WO being an <op>.with.overflow intrinsic.
 bool isOverflowIntrinsicNoWrap(const WithOverflowInst *WO,
                                const DominatorTree &DT);
 
 /// Determine the possible constant range of vscale with the given bit width,
 /// based on the vscale_range function attribute.
 ConstantRange getVScaleRange(const Function *F, unsigned BitWidth);
 
 /// Determine the possible constant range of an integer or vector of integer
 /// value. This is intended as a cheap, non-recursive check.
 ConstantRange computeConstantRange(const Value *V, bool ForSigned,
                                    bool UseInstrInfo = true,
                                    AssumptionCache *AC = nullptr,
                                    const Instruction *CtxI = nullptr,
                                    const DominatorTree *DT = nullptr,
                                    unsigned Depth = 0);
 
 /// Combine constant ranges from computeConstantRange() and computeKnownBits().
 ConstantRange
 computeConstantRangeIncludingKnownBits(const WithCache<const Value *> &V,
                                        bool ForSigned, const SimplifyQuery &SQ);
 
 /// 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);
 
 /// Returns true if this block does not contain a potential implicit exit.
 /// This is equivelent to saying that all instructions within the basic block
 /// are guaranteed to transfer execution to their successor within the basic
 /// block. This has the same assumptions w.r.t. undefined behavior as the
 /// instruction variant of this function.
 bool isGuaranteedToTransferExecutionToSuccessor(const BasicBlock *BB);
 
 /// Return true if every instruction in the range (Begin, End) is
 /// guaranteed to transfer execution to its static successor. \p ScanLimit
 /// bounds the search to avoid scanning huge blocks.
 bool isGuaranteedToTransferExecutionToSuccessor(
     BasicBlock::const_iterator Begin, BasicBlock::const_iterator End,
     unsigned ScanLimit = 32);
 
 /// Same as previous, but with range expressed via iterator_range.
 bool isGuaranteedToTransferExecutionToSuccessor(
     iterator_range<BasicBlock::const_iterator> Range, unsigned ScanLimit = 32);
 
 /// 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 \p PoisonOp's user yields poison or raises UB if its
 /// operand \p PoisonOp is poison.
 ///
 /// If \p PoisonOp is a vector or an aggregate and the operation's result is a
 /// single value, any poison element in /p PoisonOp should make the result
 /// poison or raise UB.
 ///
 /// To filter out operands that raise UB on poison, you can use
 /// getGuaranteedNonPoisonOp.
 bool propagatesPoison(const Use &PoisonOp);
 
 /// Insert operands of I into Ops such that I will trigger undefined behavior
 /// if I is executed and that operand has a poison value.
 void getGuaranteedNonPoisonOps(const Instruction *I,
                                SmallVectorImpl<const Value *> &Ops);
 
 /// Insert operands of I into Ops such that I will trigger undefined behavior
 /// if I is executed and that operand is not a well-defined value
 /// (i.e. has undef bits or poison).
 void getGuaranteedWellDefinedOps(const Instruction *I,
                                  SmallVectorImpl<const Value *> &Ops);
 
 /// Return true if the given instruction must trigger undefined behavior
 /// when I is executed with any operands which appear in KnownPoison holding
 /// a poison value at the point of execution.
 bool mustTriggerUB(const Instruction *I,
                    const SmallPtrSetImpl<const Value *> &KnownPoison);
 
 /// Return true if this function can prove that if Inst is executed
 /// and yields a poison value or undef bits, then that will trigger
 /// undefined behavior.
 ///
 /// Note that this currently only considers the basic block that is
 /// the parent of Inst.
 bool programUndefinedIfUndefOrPoison(const Instruction *Inst);
 bool programUndefinedIfPoison(const Instruction *Inst);
 
 /// canCreateUndefOrPoison returns true if Op can create undef or poison from
 /// non-undef & non-poison operands.
 /// For vectors, canCreateUndefOrPoison returns true if there is potential
 /// poison or undef in any element of the result when vectors without
 /// undef/poison poison are given as operands.
 /// For example, given `Op = shl <2 x i32> %x, <0, 32>`, this function returns
 /// true. If Op raises immediate UB but never creates poison or undef
 /// (e.g. sdiv I, 0), canCreatePoison returns false.
 ///
 /// \p ConsiderFlagsAndMetadata controls whether poison producing flags and
 /// metadata on the instruction are considered.  This can be used to see if the
 /// instruction could still introduce undef or poison even without poison
 /// generating flags and metadata which might be on the instruction.
 /// (i.e. could the result of Op->dropPoisonGeneratingFlags() still create
 /// poison or undef)
 ///
 /// canCreatePoison returns true if Op can create poison from non-poison
 /// operands.
 bool canCreateUndefOrPoison(const Operator *Op,
                             bool ConsiderFlagsAndMetadata = true);
 bool canCreatePoison(const Operator *Op, bool ConsiderFlagsAndMetadata = true);
 
 /// Return true if V is poison given that ValAssumedPoison is already poison.
 /// For example, if ValAssumedPoison is `icmp X, 10` and V is `icmp X, 5`,
 /// impliesPoison returns true.
 bool impliesPoison(const Value *ValAssumedPoison, const Value *V);
 
 /// Return true if this function can prove that V does not have undef bits
 /// and is never poison. If V is an aggregate value or vector, check whether
 /// all elements (except padding) are not undef or poison.
 /// Note that this is different from canCreateUndefOrPoison because the
 /// function assumes Op's operands are not poison/undef.
 ///
 /// If CtxI and DT are specified this method performs flow-sensitive analysis
 /// and returns true if it is guaranteed to be never undef or poison
 /// immediately before the CtxI.
 bool isGuaranteedNotToBeUndefOrPoison(const Value *V,
                                       AssumptionCache *AC = nullptr,
                                       const Instruction *CtxI = nullptr,
                                       const DominatorTree *DT = nullptr,
                                       unsigned Depth = 0);
 
 /// Returns true if V cannot be poison, but may be undef.
 bool isGuaranteedNotToBePoison(const Value *V, AssumptionCache *AC = nullptr,
                                const Instruction *CtxI = nullptr,
                                const DominatorTree *DT = nullptr,
                                unsigned Depth = 0);
 
 inline bool isGuaranteedNotToBePoison(const Value *V, AssumptionCache *AC,
                                       BasicBlock::iterator CtxI,
                                       const DominatorTree *DT = nullptr,
                                       unsigned Depth = 0) {
   // Takes an iterator as a position, passes down to Instruction *
   // implementation.
   return isGuaranteedNotToBePoison(V, AC, &*CtxI, DT, Depth);
 }
 
 /// Returns true if V cannot be undef, but may be poison.
 bool isGuaranteedNotToBeUndef(const Value *V, AssumptionCache *AC = nullptr,
                               const Instruction *CtxI = nullptr,
                               const DominatorTree *DT = nullptr,
                               unsigned Depth = 0);
 
 /// Return true if undefined behavior would provable be executed on the path to
 /// OnPathTo if Root produced a posion result.  Note that this doesn't say
 /// anything about whether OnPathTo is actually executed or whether Root is
 /// actually poison.  This can be used to assess whether a new use of Root can
 /// be added at a location which is control equivalent with OnPathTo (such as
 /// immediately before it) without introducing UB which didn't previously
 /// exist.  Note that a false result conveys no information.
 bool mustExecuteUBIfPoisonOnPathTo(Instruction *Root,
                                    Instruction *OnPathTo,
                                    DominatorTree *DT);
 
 /// Convert an integer comparison with a constant RHS into an equivalent
 /// form with the strictness flipped predicate. Return the new predicate and
 /// corresponding constant RHS if possible. Otherwise return std::nullopt.
 /// E.g., (icmp sgt X, 0) -> (icmp sle X, 1).
 std::optional<std::pair<CmpPredicate, Constant *>>
 getFlippedStrictnessPredicateAndConstant(CmpPredicate Pred, Constant *C);
 
 /// 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
 };
 
 /// 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?
 
   /// 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.
 ///
 /// For ABS/NABS, LHS will be set to the input to the abs idiom. RHS will be
 /// the negation instruction from the idiom.
 ///
 /// 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,
                                        unsigned Depth = 0);
 
 inline SelectPatternResult matchSelectPattern(const Value *V, const Value *&LHS,
                                               const Value *&RHS) {
   Value *L = const_cast<Value *>(LHS);
   Value *R = const_cast<Value *>(RHS);
   auto Result = matchSelectPattern(const_cast<Value *>(V), L, R);
   LHS = L;
   RHS = R;
   return Result;
 }
 
 /// Determine the pattern that a select with the given compare as its
 /// predicate and given values as its true/false operands would match.
 SelectPatternResult matchDecomposedSelectPattern(
     CmpInst *CmpI, Value *TrueVal, Value *FalseVal, Value *&LHS, Value *&RHS,
     Instruction::CastOps *CastOp = nullptr, unsigned Depth = 0);
 
 /// Determine the pattern for predicate `X Pred Y ? X : Y`.
 SelectPatternResult
 getSelectPattern(CmpInst::Predicate Pred,
                  SelectPatternNaNBehavior NaNBehavior = SPNB_NA,
                  bool Ordered = false);
 
 /// Return the canonical comparison predicate for the specified
 /// minimum/maximum flavor.
 CmpInst::Predicate getMinMaxPred(SelectPatternFlavor SPF, bool Ordered = false);
 
 /// Convert given `SPF` to equivalent min/max intrinsic.
 /// Caller must ensure `SPF` is an integer min or max pattern.
 Intrinsic::ID getMinMaxIntrinsic(SelectPatternFlavor SPF);
 
 /// Return the inverse minimum/maximum flavor of the specified flavor.
 /// For example, signed minimum is the inverse of signed maximum.
 SelectPatternFlavor getInverseMinMaxFlavor(SelectPatternFlavor SPF);
 
 Intrinsic::ID getInverseMinMaxIntrinsic(Intrinsic::ID MinMaxID);
 
 /// Return the minimum or maximum constant value for the specified integer
 /// min/max flavor and type.
 APInt getMinMaxLimit(SelectPatternFlavor SPF, unsigned BitWidth);
 
 /// Check if the values in \p VL are select instructions that can be converted
 /// to a min or max (vector) intrinsic. Returns the intrinsic ID, if such a
 /// conversion is possible, together with a bool indicating whether all select
 /// conditions are only used by the selects. Otherwise return
 /// Intrinsic::not_intrinsic.
 std::pair<Intrinsic::ID, bool>
 canConvertToMinOrMaxIntrinsic(ArrayRef<Value *> VL);
 
 /// Attempt to match a simple first order recurrence cycle of the form:
 ///   %iv = phi Ty [%Start, %Entry], [%Inc, %backedge]
 ///   %inc = binop %iv, %step
 /// OR
 ///   %iv = phi Ty [%Start, %Entry], [%Inc, %backedge]
 ///   %inc = binop %step, %iv
 ///
 /// A first order recurrence is a formula with the form: X_n = f(X_(n-1))
 ///
 /// A couple of notes on subtleties in that definition:
 /// * The Step does not have to be loop invariant.  In math terms, it can
 ///   be a free variable.  We allow recurrences with both constant and
 ///   variable coefficients. Callers may wish to filter cases where Step
 ///   does not dominate P.
 /// * For non-commutative operators, we will match both forms.  This
 ///   results in some odd recurrence structures.  Callers may wish to filter
 ///   out recurrences where the phi is not the LHS of the returned operator.
 /// * Because of the structure matched, the caller can assume as a post
 ///   condition of the match the presence of a Loop with P's parent as it's
 ///   header *except* in unreachable code.  (Dominance decays in unreachable
 ///   code.)
 ///
 /// NOTE: This is intentional simple.  If you want the ability to analyze
 /// non-trivial loop conditons, see ScalarEvolution instead.
 bool matchSimpleRecurrence(const PHINode *P, BinaryOperator *&BO, Value *&Start,
                            Value *&Step);
 
 /// Analogous to the above, but starting from the binary operator
 bool matchSimpleRecurrence(const BinaryOperator *I, PHINode *&P, Value *&Start,
                            Value *&Step);
 
 /// Return true if RHS is known to be implied true by LHS.  Return false if
 /// RHS is known to be implied false by LHS.  Otherwise, return std::nullopt if
 /// no implication can be made. 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)
 std::optional<bool> isImpliedCondition(const Value *LHS, const Value *RHS,
                                        const DataLayout &DL,
                                        bool LHSIsTrue = true,
                                        unsigned Depth = 0);
 std::optional<bool> isImpliedCondition(const Value *LHS, CmpPredicate RHSPred,
                                        const Value *RHSOp0, const Value *RHSOp1,
                                        const DataLayout &DL,
                                        bool LHSIsTrue = true,
                                        unsigned Depth = 0);
 
 /// Return the boolean condition value in the context of the given instruction
 /// if it is known based on dominating conditions.
 std::optional<bool> isImpliedByDomCondition(const Value *Cond,
                                             const Instruction *ContextI,
                                             const DataLayout &DL);
 std::optional<bool> isImpliedByDomCondition(CmpPredicate Pred, const Value *LHS,
                                             const Value *RHS,
                                             const Instruction *ContextI,
                                             const DataLayout &DL);
 
 /// Call \p InsertAffected on all Values whose known bits / value may be
 /// affected by the condition \p Cond. Used by AssumptionCache and
 /// DomConditionCache.
 void findValuesAffectedByCondition(Value *Cond, bool IsAssume,
                                    function_ref<void(Value *)> InsertAffected);
 
 } // end namespace llvm
 
 #endif // LLVM_ANALYSIS_VALUETRACKING_H

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