ValueTracking.cpp

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//===- ValueTracking.cpp - Walk computations to compute properties --------===//
//
// 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.
//
//===----------------------------------------------------------------------===//
 
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/ADT/APFloat.h"
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/None.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/StringRef.h"
#include "llvm/ADT/iterator_range.h"
#include "llvm/Analysis/AliasAnalysis.h"
#include "llvm/Analysis/AssumeBundleQueries.h"
#include "llvm/Analysis/AssumptionCache.h"
#include "llvm/Analysis/EHPersonalities.h"
#include "llvm/Analysis/GuardUtils.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/Loads.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/OptimizationRemarkEmitter.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/IR/Argument.h"
#include "llvm/IR/Attributes.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/Constant.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/DiagnosticInfo.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/GetElementPtrTypeIterator.h"
#include "llvm/IR/GlobalAlias.h"
#include "llvm/IR/GlobalValue.h"
#include "llvm/IR/GlobalVariable.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Intrinsics.h"
#include "llvm/IR/IntrinsicsAArch64.h"
#include "llvm/IR/IntrinsicsRISCV.h"
#include "llvm/IR/IntrinsicsX86.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/User.h"
#include "llvm/IR/Value.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/KnownBits.h"
#include "llvm/Support/MathExtras.h"
#include <algorithm>
#include <array>
#include <cassert>
#include <cstdint>
#include <iterator>
#include <utility>
 
using namespace llvm;
using namespace llvm::PatternMatch;
 
// Controls the number of uses of the value searched for possible
// dominating comparisons.
static cl::opt<unsigned> DomConditionsMaxUses("dom-conditions-max-uses",
                                              cl::Hidden, cl::init(20));
 
// According to the LangRef, branching on a poison condition is absolutely
// immediate full UB.  However, historically we haven't implemented that
// consistently as we have an important transformation (non-trivial unswitch)
// which introduces instances of branch on poison/undef to otherwise well
// defined programs.  This flag exists to let us test optimization benefit
// of exploiting the specified behavior (in combination with enabling the
// unswitch fix.)
static cl::opt<bool> BranchOnPoisonAsUB("branch-on-poison-as-ub",
                                        cl::Hidden, cl::init(false));
 
 
/// Returns the bitwidth of the given scalar or pointer type. For vector types,
/// returns the element type's bitwidth.
static unsigned getBitWidth(Type *Ty, const DataLayout &DL) {
  if (unsigned BitWidth = Ty->getScalarSizeInBits())
    return BitWidth;
 
  return DL.getPointerTypeSizeInBits(Ty);
}
 
namespace {
 
// Simplifying using an assume can only be done in a particular control-flow
// context (the context instruction provides that context). If an assume and
// the context instruction are not in the same block then the DT helps in
// figuring out if we can use it.
struct Query {
  const DataLayout &DL;
  AssumptionCache *AC;
  const Instruction *CxtI;
  const DominatorTree *DT;
 
  // Unlike the other analyses, this may be a nullptr because not all clients
  // provide it currently.
  OptimizationRemarkEmitter *ORE;
 
  /// If true, it is safe to use metadata during simplification.
  InstrInfoQuery IIQ;
 
  Query(const DataLayout &DL, AssumptionCache *AC, const Instruction *CxtI,
        const DominatorTree *DT, bool UseInstrInfo,
        OptimizationRemarkEmitter *ORE = nullptr)
      : DL(DL), AC(AC), CxtI(CxtI), DT(DT), ORE(ORE), IIQ(UseInstrInfo) {}
};
 
} // end anonymous namespace
 
// Given the provided Value and, potentially, a context instruction, return
// the preferred context instruction (if any).
static const Instruction *safeCxtI(const Value *V, const Instruction *CxtI) {
  // If we've been provided with a context instruction, then use that (provided
  // it has been inserted).
  if (CxtI && CxtI->getParent())
    return CxtI;
 
  // If the value is really an already-inserted instruction, then use that.
  CxtI = dyn_cast<Instruction>(V);
  if (CxtI && CxtI->getParent())
    return CxtI;
 
  return nullptr;
}
 
static const Instruction *safeCxtI(const Value *V1, const Value *V2, const Instruction *CxtI) {
  // If we've been provided with a context instruction, then use that (provided
  // it has been inserted).
  if (CxtI && CxtI->getParent())
    return CxtI;
 
  // If the value is really an already-inserted instruction, then use that.
  CxtI = dyn_cast<Instruction>(V1);
  if (CxtI && CxtI->getParent())
    return CxtI;
 
  CxtI = dyn_cast<Instruction>(V2);
  if (CxtI && CxtI->getParent())
    return CxtI;
 
  return nullptr;
}
 
static bool getShuffleDemandedElts(const ShuffleVectorInst *Shuf,
                                   const APInt &DemandedElts,
                                   APInt &DemandedLHS, APInt &DemandedRHS) {
  // The length of scalable vectors is unknown at compile time, thus we
  // cannot check their values
  if (isa<ScalableVectorType>(Shuf->getType()))
    return false;
 
  int NumElts =
      cast<FixedVectorType>(Shuf->getOperand(0)->getType())->getNumElements();
  int NumMaskElts = cast<FixedVectorType>(Shuf->getType())->getNumElements();
  DemandedLHS = DemandedRHS = APInt::getZero(NumElts);
  if (DemandedElts.isZero())
    return true;
  // Simple case of a shuffle with zeroinitializer.
  if (all_of(Shuf->getShuffleMask(), [](int Elt) { return Elt == 0; })) {
    DemandedLHS.setBit(0);
    return true;
  }
  for (int i = 0; i != NumMaskElts; ++i) {
    if (!DemandedElts[i])
      continue;
    int M = Shuf->getMaskValue(i);
    assert(M < (NumElts * 2) && "Invalid shuffle mask constant");
 
    // For undef elements, we don't know anything about the common state of
    // the shuffle result.
    if (M == -1)
      return false;
    if (M < NumElts)
      DemandedLHS.setBit(M % NumElts);
    else
      DemandedRHS.setBit(M % NumElts);
  }
 
  return true;
}
 
static void computeKnownBits(const Value *V, const APInt &DemandedElts,
                             KnownBits &Known, unsigned Depth, const Query &Q);
 
static void computeKnownBits(const Value *V, KnownBits &Known, unsigned Depth,
                             const Query &Q) {
  // FIXME: We currently have no way to represent the DemandedElts of a scalable
  // vector
  if (isa<ScalableVectorType>(V->getType())) {
    Known.resetAll();
    return;
  }
 
  auto *FVTy = dyn_cast<FixedVectorType>(V->getType());
  APInt DemandedElts =
      FVTy ? APInt::getAllOnes(FVTy->getNumElements()) : APInt(1, 1);
  computeKnownBits(V, DemandedElts, Known, Depth, Q);
}
 
void llvm::computeKnownBits(const Value *V, KnownBits &Known,
                            const DataLayout &DL, unsigned Depth,
                            AssumptionCache *AC, const Instruction *CxtI,
                            const DominatorTree *DT,
                            OptimizationRemarkEmitter *ORE, bool UseInstrInfo) {
  ::computeKnownBits(V, Known, Depth,
                     Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo, ORE));
}
 
void llvm::computeKnownBits(const Value *V, const APInt &DemandedElts,
                            KnownBits &Known, const DataLayout &DL,
                            unsigned Depth, AssumptionCache *AC,
                            const Instruction *CxtI, const DominatorTree *DT,
                            OptimizationRemarkEmitter *ORE, bool UseInstrInfo) {
  ::computeKnownBits(V, DemandedElts, Known, Depth,
                     Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo, ORE));
}
 
static KnownBits computeKnownBits(const Value *V, const APInt &DemandedElts,
                                  unsigned Depth, const Query &Q);
 
static KnownBits computeKnownBits(const Value *V, unsigned Depth,
                                  const Query &Q);
 
KnownBits llvm::computeKnownBits(const Value *V, const DataLayout &DL,
                                 unsigned Depth, AssumptionCache *AC,
                                 const Instruction *CxtI,
                                 const DominatorTree *DT,
                                 OptimizationRemarkEmitter *ORE,
                                 bool UseInstrInfo) {
  return ::computeKnownBits(
      V, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo, ORE));
}
 
KnownBits llvm::computeKnownBits(const Value *V, const APInt &DemandedElts,
                                 const DataLayout &DL, unsigned Depth,
                                 AssumptionCache *AC, const Instruction *CxtI,
                                 const DominatorTree *DT,
                                 OptimizationRemarkEmitter *ORE,
                                 bool UseInstrInfo) {
  return ::computeKnownBits(
      V, DemandedElts, Depth,
      Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo, ORE));
}
 
bool llvm::haveNoCommonBitsSet(const Value *LHS, const Value *RHS,
                               const DataLayout &DL, AssumptionCache *AC,
                               const Instruction *CxtI, const DominatorTree *DT,
                               bool UseInstrInfo) {
  assert(LHS->getType() == RHS->getType() &&
         "LHS and RHS should have the same type");
  assert(LHS->getType()->isIntOrIntVectorTy() &&
         "LHS and RHS should be integers");
  // Look for an inverted mask: (X & ~M) op (Y & M).
  Value *M;
  if (match(LHS, m_c_And(m_Not(m_Value(M)), m_Value())) &&
      match(RHS, m_c_And(m_Specific(M), m_Value())))
    return true;
  if (match(RHS, m_c_And(m_Not(m_Value(M)), m_Value())) &&
      match(LHS, m_c_And(m_Specific(M), m_Value())))
    return true;
  IntegerType *IT = cast<IntegerType>(LHS->getType()->getScalarType());
  KnownBits LHSKnown(IT->getBitWidth());
  KnownBits RHSKnown(IT->getBitWidth());
  computeKnownBits(LHS, LHSKnown, DL, 0, AC, CxtI, DT, nullptr, UseInstrInfo);
  computeKnownBits(RHS, RHSKnown, DL, 0, AC, CxtI, DT, nullptr, UseInstrInfo);
  return KnownBits::haveNoCommonBitsSet(LHSKnown, RHSKnown);
}
 
bool llvm::isOnlyUsedInZeroEqualityComparison(const Instruction *I) {
  return !I->user_empty() && all_of(I->users(), [](const User *U) {
    ICmpInst::Predicate P;
    return match(U, m_ICmp(P, m_Value(), m_Zero())) && ICmpInst::isEquality(P);
  });
}
 
static bool isKnownToBeAPowerOfTwo(const Value *V, bool OrZero, unsigned Depth,
                                   const Query &Q);
 
bool llvm::isKnownToBeAPowerOfTwo(const Value *V, const DataLayout &DL,
                                  bool OrZero, unsigned Depth,
                                  AssumptionCache *AC, const Instruction *CxtI,
                                  const DominatorTree *DT, bool UseInstrInfo) {
  return ::isKnownToBeAPowerOfTwo(
      V, OrZero, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
}
 
static bool isKnownNonZero(const Value *V, const APInt &DemandedElts,
                           unsigned Depth, const Query &Q);
 
static bool isKnownNonZero(const Value *V, unsigned Depth, const Query &Q);
 
bool llvm::isKnownNonZero(const Value *V, const DataLayout &DL, unsigned Depth,
                          AssumptionCache *AC, const Instruction *CxtI,
                          const DominatorTree *DT, bool UseInstrInfo) {
  return ::isKnownNonZero(V, Depth,
                          Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
}
 
bool llvm::isKnownNonNegative(const Value *V, const DataLayout &DL,
                              unsigned Depth, AssumptionCache *AC,
                              const Instruction *CxtI, const DominatorTree *DT,
                              bool UseInstrInfo) {
  KnownBits Known =
      computeKnownBits(V, DL, Depth, AC, CxtI, DT, nullptr, UseInstrInfo);
  return Known.isNonNegative();
}
 
bool llvm::isKnownPositive(const Value *V, const DataLayout &DL, unsigned Depth,
                           AssumptionCache *AC, const Instruction *CxtI,
                           const DominatorTree *DT, bool UseInstrInfo) {
  if (auto *CI = dyn_cast<ConstantInt>(V))
    return CI->getValue().isStrictlyPositive();
 
  // TODO: We'd doing two recursive queries here.  We should factor this such
  // that only a single query is needed.
  return isKnownNonNegative(V, DL, Depth, AC, CxtI, DT, UseInstrInfo) &&
         isKnownNonZero(V, DL, Depth, AC, CxtI, DT, UseInstrInfo);
}
 
bool llvm::isKnownNegative(const Value *V, const DataLayout &DL, unsigned Depth,
                           AssumptionCache *AC, const Instruction *CxtI,
                           const DominatorTree *DT, bool UseInstrInfo) {
  KnownBits Known =
      computeKnownBits(V, DL, Depth, AC, CxtI, DT, nullptr, UseInstrInfo);
  return Known.isNegative();
}
 
static bool isKnownNonEqual(const Value *V1, const Value *V2, unsigned Depth,
                            const Query &Q);
 
bool llvm::isKnownNonEqual(const Value *V1, const Value *V2,
                           const DataLayout &DL, AssumptionCache *AC,
                           const Instruction *CxtI, const DominatorTree *DT,
                           bool UseInstrInfo) {
  return ::isKnownNonEqual(V1, V2, 0,
                           Query(DL, AC, safeCxtI(V2, V1, CxtI), DT,
                                 UseInstrInfo, /*ORE=*/nullptr));
}
 
static bool MaskedValueIsZero(const Value *V, const APInt &Mask, unsigned Depth,
                              const Query &Q);
 
bool llvm::MaskedValueIsZero(const Value *V, const APInt &Mask,
                             const DataLayout &DL, unsigned Depth,
                             AssumptionCache *AC, const Instruction *CxtI,
                             const DominatorTree *DT, bool UseInstrInfo) {
  return ::MaskedValueIsZero(
      V, Mask, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
}
 
static unsigned ComputeNumSignBits(const Value *V, const APInt &DemandedElts,
                                   unsigned Depth, const Query &Q);
 
static unsigned ComputeNumSignBits(const Value *V, unsigned Depth,
                                   const Query &Q) {
  // FIXME: We currently have no way to represent the DemandedElts of a scalable
  // vector
  if (isa<ScalableVectorType>(V->getType()))
    return 1;
 
  auto *FVTy = dyn_cast<FixedVectorType>(V->getType());
  APInt DemandedElts =
      FVTy ? APInt::getAllOnes(FVTy->getNumElements()) : APInt(1, 1);
  return ComputeNumSignBits(V, DemandedElts, Depth, Q);
}
 
unsigned llvm::ComputeNumSignBits(const Value *V, const DataLayout &DL,
                                  unsigned Depth, AssumptionCache *AC,
                                  const Instruction *CxtI,
                                  const DominatorTree *DT, bool UseInstrInfo) {
  return ::ComputeNumSignBits(
      V, Depth, Query(DL, AC, safeCxtI(V, CxtI), DT, UseInstrInfo));
}
 
unsigned llvm::ComputeMaxSignificantBits(const Value *V, const DataLayout &DL,
                                         unsigned Depth, AssumptionCache *AC,
                                         const Instruction *CxtI,
                                         const DominatorTree *DT) {
  unsigned SignBits = ComputeNumSignBits(V, DL, Depth, AC, CxtI, DT);
  return V->getType()->getScalarSizeInBits() - SignBits + 1;
}
 
static void computeKnownBitsAddSub(bool Add, const Value *Op0, const Value *Op1,
                                   bool NSW, const APInt &DemandedElts,
                                   KnownBits &KnownOut, KnownBits &Known2,
                                   unsigned Depth, const Query &Q) {
  computeKnownBits(Op1, DemandedElts, KnownOut, Depth + 1, Q);
 
  // If one operand is unknown and we have no nowrap information,
  // the result will be unknown independently of the second operand.
  if (KnownOut.isUnknown() && !NSW)
    return;
 
  computeKnownBits(Op0, DemandedElts, Known2, Depth + 1, Q);
  KnownOut = KnownBits::computeForAddSub(Add, NSW, Known2, KnownOut);
}
 
static void computeKnownBitsMul(const Value *Op0, const Value *Op1, bool NSW,
                                const APInt &DemandedElts, KnownBits &Known,
                                KnownBits &Known2, unsigned Depth,
                                const Query &Q) {
  computeKnownBits(Op1, DemandedElts, Known, Depth + 1, Q);
  computeKnownBits(Op0, DemandedElts, Known2, Depth + 1, Q);
 
  bool isKnownNegative = false;
  bool isKnownNonNegative = false;
  // If the multiplication is known not to overflow, compute the sign bit.
  if (NSW) {
    if (Op0 == Op1) {
      // The product of a number with itself is non-negative.
      isKnownNonNegative = true;
    } else {
      bool isKnownNonNegativeOp1 = Known.isNonNegative();
      bool isKnownNonNegativeOp0 = Known2.isNonNegative();
      bool isKnownNegativeOp1 = Known.isNegative();
      bool isKnownNegativeOp0 = Known2.isNegative();
      // The product of two numbers with the same sign is non-negative.
      isKnownNonNegative = (isKnownNegativeOp1 && isKnownNegativeOp0) ||
                           (isKnownNonNegativeOp1 && isKnownNonNegativeOp0);
      // The product of a negative number and a non-negative number is either
      // negative or zero.
      if (!isKnownNonNegative)
        isKnownNegative =
            (isKnownNegativeOp1 && isKnownNonNegativeOp0 &&
             Known2.isNonZero()) ||
            (isKnownNegativeOp0 && isKnownNonNegativeOp1 && Known.isNonZero());
    }
  }
 
  Known = KnownBits::mul(Known, Known2);
 
  // Only make use of no-wrap flags if we failed to compute the sign bit
  // directly.  This matters if the multiplication always overflows, in
  // which case we prefer to follow the result of the direct computation,
  // though as the program is invoking undefined behaviour we can choose
  // whatever we like here.
  if (isKnownNonNegative && !Known.isNegative())
    Known.makeNonNegative();
  else if (isKnownNegative && !Known.isNonNegative())
    Known.makeNegative();
}
 
void llvm::computeKnownBitsFromRangeMetadata(const MDNode &Ranges,
                                             KnownBits &Known) {
  unsigned BitWidth = Known.getBitWidth();
  unsigned NumRanges = Ranges.getNumOperands() / 2;
  assert(NumRanges >= 1);
 
  Known.Zero.setAllBits();
  Known.One.setAllBits();
 
  for (unsigned i = 0; i < NumRanges; ++i) {
    ConstantInt *Lower =
        mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 0));
    ConstantInt *Upper =
        mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 1));
    ConstantRange Range(Lower->getValue(), Upper->getValue());
 
    // The first CommonPrefixBits of all values in Range are equal.
    unsigned CommonPrefixBits =
        (Range.getUnsignedMax() ^ Range.getUnsignedMin()).countLeadingZeros();
    APInt Mask = APInt::getHighBitsSet(BitWidth, CommonPrefixBits);
    APInt UnsignedMax = Range.getUnsignedMax().zextOrTrunc(BitWidth);
    Known.One &= UnsignedMax & Mask;
    Known.Zero &= ~UnsignedMax & Mask;
  }
}
 
static bool isEphemeralValueOf(const Instruction *I, const Value *E) {
  SmallVector<const Value *, 16> WorkSet(1, I);
  SmallPtrSet<const Value *, 32> Visited;
  SmallPtrSet<const Value *, 16> EphValues;
 
  // The instruction defining an assumption's condition itself is always
  // considered ephemeral to that assumption (even if it has other
  // non-ephemeral users). See r246696's test case for an example.
  if (is_contained(I->operands(), E))
    return true;
 
  while (!WorkSet.empty()) {
    const Value *V = WorkSet.pop_back_val();
    if (!Visited.insert(V).second)
      continue;
 
    // If all uses of this value are ephemeral, then so is this value.
    if (llvm::all_of(V->users(), [&](const User *U) {
                                   return EphValues.count(U);
                                 })) {
      if (V == E)
        return true;
 
      if (V == I || (isa<Instruction>(V) &&
                     !cast<Instruction>(V)->mayHaveSideEffects() &&
                     !cast<Instruction>(V)->isTerminator())) {
       EphValues.insert(V);
       if (const User *U = dyn_cast<User>(V))
         append_range(WorkSet, U->operands());
      }
    }
  }
 
  return false;
}
 
// Is this an intrinsic that cannot be speculated but also cannot trap?
bool llvm::isAssumeLikeIntrinsic(const Instruction *I) {
  if (const IntrinsicInst *CI = dyn_cast<IntrinsicInst>(I))
    return CI->isAssumeLikeIntrinsic();
 
  return false;
}
 
bool llvm::isValidAssumeForContext(const Instruction *Inv,
                                   const Instruction *CxtI,
                                   const DominatorTree *DT) {
  // There are two restrictions on the use of an assume:
  //  1. The assume must dominate the context (or the control flow must
  //     reach the assume whenever it reaches the context).
  //  2. The context must not be in the assume's set of ephemeral values
  //     (otherwise we will use the assume to prove that the condition
  //     feeding the assume is trivially true, thus causing the removal of
  //     the assume).
 
  if (Inv->getParent() == CxtI->getParent()) {
    // If Inv and CtxI are in the same block, check if the assume (Inv) is first
    // in the BB.
    if (Inv->comesBefore(CxtI))
      return true;
 
    // Don't let an assume affect itself - this would cause the problems
    // `isEphemeralValueOf` is trying to prevent, and it would also make
    // the loop below go out of bounds.
    if (Inv == CxtI)
      return false;
 
    // The context comes first, but they're both in the same block.
    // Make sure there is nothing in between that might interrupt
    // the control flow, not even CxtI itself.
    // We limit the scan distance between the assume and its context instruction
    // to avoid a compile-time explosion. This limit is chosen arbitrarily, so
    // it can be adjusted if needed (could be turned into a cl::opt).
    auto Range = make_range(CxtI->getIterator(), Inv->getIterator());
    if (!isGuaranteedToTransferExecutionToSuccessor(Range, 15))
      return false;
 
    return !isEphemeralValueOf(Inv, CxtI);
  }
 
  // Inv and CxtI are in different blocks.
  if (DT) {
    if (DT->dominates(Inv, CxtI))
      return true;
  } else if (Inv->getParent() == CxtI->getParent()->getSinglePredecessor()) {
    // We don't have a DT, but this trivially dominates.
    return true;
  }
 
  return false;
}
 
static bool cmpExcludesZero(CmpInst::Predicate Pred, const Value *RHS) {
  // v u> y implies v != 0.
  if (Pred == ICmpInst::ICMP_UGT)
    return true;
 
  // Special-case v != 0 to also handle v != null.
  if (Pred == ICmpInst::ICMP_NE)
    return match(RHS, m_Zero());
 
  // All other predicates - rely on generic ConstantRange handling.
  const APInt *C;
  if (!match(RHS, m_APInt(C)))
    return false;
 
  ConstantRange TrueValues = ConstantRange::makeExactICmpRegion(Pred, *C);
  return !TrueValues.contains(APInt::getZero(C->getBitWidth()));
}
 
static bool isKnownNonZeroFromAssume(const Value *V, const Query &Q) {
  // Use of assumptions is context-sensitive. If we don't have a context, we
  // cannot use them!
  if (!Q.AC || !Q.CxtI)
    return false;
 
  if (Q.CxtI && V->getType()->isPointerTy()) {
    SmallVector<Attribute::AttrKind, 2> AttrKinds{Attribute::NonNull};
    if (!NullPointerIsDefined(Q.CxtI->getFunction(),
                              V->getType()->getPointerAddressSpace()))
      AttrKinds.push_back(Attribute::Dereferenceable);
 
    if (getKnowledgeValidInContext(V, AttrKinds, Q.CxtI, Q.DT, Q.AC))
      return true;
  }
 
  for (auto &AssumeVH : Q.AC->assumptionsFor(V)) {
    if (!AssumeVH)
      continue;
    CallInst *I = cast<CallInst>(AssumeVH);
    assert(I->getFunction() == Q.CxtI->getFunction() &&
           "Got assumption for the wrong function!");
 
    // Warning: This loop can end up being somewhat performance sensitive.
    // We're running this loop for once for each value queried resulting in a
    // runtime of ~O(#assumes * #values).
 
    assert(I->getCalledFunction()->getIntrinsicID() == Intrinsic::assume &&
           "must be an assume intrinsic");
 
    Value *RHS;
    CmpInst::Predicate Pred;
    auto m_V = m_CombineOr(m_Specific(V), m_PtrToInt(m_Specific(V)));
    if (!match(I->getArgOperand(0), m_c_ICmp(Pred, m_V, m_Value(RHS))))
      return false;
 
    if (cmpExcludesZero(Pred, RHS) && isValidAssumeForContext(I, Q.CxtI, Q.DT))
      return true;
  }
 
  return false;
}
 
static void computeKnownBitsFromAssume(const Value *V, KnownBits &Known,
                                       unsigned Depth, const Query &Q) {
  // Use of assumptions is context-sensitive. If we don't have a context, we
  // cannot use them!
  if (!Q.AC || !Q.CxtI)
    return;
 
  unsigned BitWidth = Known.getBitWidth();
 
  // Refine Known set if the pointer alignment is set by assume bundles.
  if (V->getType()->isPointerTy()) {
    if (RetainedKnowledge RK = getKnowledgeValidInContext(
            V, {Attribute::Alignment}, Q.CxtI, Q.DT, Q.AC)) {
      Known.Zero.setLowBits(Log2_64(RK.ArgValue));
    }
  }
 
  // Note that the patterns below need to be kept in sync with the code
  // in AssumptionCache::updateAffectedValues.
 
  for (auto &AssumeVH : Q.AC->assumptionsFor(V)) {
    if (!AssumeVH)
      continue;
    CallInst *I = cast<CallInst>(AssumeVH);
    assert(I->getParent()->getParent() == Q.CxtI->getParent()->getParent() &&
           "Got assumption for the wrong function!");
 
    // Warning: This loop can end up being somewhat performance sensitive.
    // We're running this loop for once for each value queried resulting in a
    // runtime of ~O(#assumes * #values).
 
    assert(I->getCalledFunction()->getIntrinsicID() == Intrinsic::assume &&
           "must be an assume intrinsic");
 
    Value *Arg = I->getArgOperand(0);
 
    if (Arg == V && isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
      assert(BitWidth == 1 && "assume operand is not i1?");
      Known.setAllOnes();
      return;
    }
    if (match(Arg, m_Not(m_Specific(V))) &&
        isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
      assert(BitWidth == 1 && "assume operand is not i1?");
      Known.setAllZero();
      return;
    }
 
    // The remaining tests are all recursive, so bail out if we hit the limit.
    if (Depth == MaxAnalysisRecursionDepth)
      continue;
 
    ICmpInst *Cmp = dyn_cast<ICmpInst>(Arg);
    if (!Cmp)
      continue;
 
    // We are attempting to compute known bits for the operands of an assume.
    // Do not try to use other assumptions for those recursive calls because
    // that can lead to mutual recursion and a compile-time explosion.
    // An example of the mutual recursion: computeKnownBits can call
    // isKnownNonZero which calls computeKnownBitsFromAssume (this function)
    // and so on.
    Query QueryNoAC = Q;
    QueryNoAC.AC = nullptr;
 
    // Note that ptrtoint may change the bitwidth.
    Value *A, *B;
    auto m_V = m_CombineOr(m_Specific(V), m_PtrToInt(m_Specific(V)));
 
    CmpInst::Predicate Pred;
    uint64_t C;
    switch (Cmp->getPredicate()) {
    default:
      break;
    case ICmpInst::ICMP_EQ:
      // assume(v = a)
      if (match(Cmp, m_c_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        Known.Zero |= RHSKnown.Zero;
        Known.One  |= RHSKnown.One;
      // assume(v & b = a)
      } else if (match(Cmp,
                       m_c_ICmp(Pred, m_c_And(m_V, m_Value(B)), m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        KnownBits MaskKnown =
            computeKnownBits(B, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in the mask that are known to be one, we can propagate
        // known bits from the RHS to V.
        Known.Zero |= RHSKnown.Zero & MaskKnown.One;
        Known.One  |= RHSKnown.One  & MaskKnown.One;
      // assume(~(v & b) = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_c_And(m_V, m_Value(B))),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        KnownBits MaskKnown =
            computeKnownBits(B, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in the mask that are known to be one, we can propagate
        // inverted known bits from the RHS to V.
        Known.Zero |= RHSKnown.One  & MaskKnown.One;
        Known.One  |= RHSKnown.Zero & MaskKnown.One;
      // assume(v | b = a)
      } else if (match(Cmp,
                       m_c_ICmp(Pred, m_c_Or(m_V, m_Value(B)), m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        KnownBits BKnown =
            computeKnownBits(B, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in B that are known to be zero, we can propagate known
        // bits from the RHS to V.
        Known.Zero |= RHSKnown.Zero & BKnown.Zero;
        Known.One  |= RHSKnown.One  & BKnown.Zero;
      // assume(~(v | b) = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_c_Or(m_V, m_Value(B))),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        KnownBits BKnown =
            computeKnownBits(B, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in B that are known to be zero, we can propagate
        // inverted known bits from the RHS to V.
        Known.Zero |= RHSKnown.One  & BKnown.Zero;
        Known.One  |= RHSKnown.Zero & BKnown.Zero;
      // assume(v ^ b = a)
      } else if (match(Cmp,
                       m_c_ICmp(Pred, m_c_Xor(m_V, m_Value(B)), m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        KnownBits BKnown =
            computeKnownBits(B, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in B that are known to be zero, we can propagate known
        // bits from the RHS to V. For those bits in B that are known to be one,
        // we can propagate inverted known bits from the RHS to V.
        Known.Zero |= RHSKnown.Zero & BKnown.Zero;
        Known.One  |= RHSKnown.One  & BKnown.Zero;
        Known.Zero |= RHSKnown.One  & BKnown.One;
        Known.One  |= RHSKnown.Zero & BKnown.One;
      // assume(~(v ^ b) = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_c_Xor(m_V, m_Value(B))),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        KnownBits BKnown =
            computeKnownBits(B, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in B that are known to be zero, we can propagate
        // inverted known bits from the RHS to V. For those bits in B that are
        // known to be one, we can propagate known bits from the RHS to V.
        Known.Zero |= RHSKnown.One  & BKnown.Zero;
        Known.One  |= RHSKnown.Zero & BKnown.Zero;
        Known.Zero |= RHSKnown.Zero & BKnown.One;
        Known.One  |= RHSKnown.One  & BKnown.One;
      // assume(v << c = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Shl(m_V, m_ConstantInt(C)),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // For those bits in RHS that are known, we can propagate them to known
        // bits in V shifted to the right by C.
        RHSKnown.Zero.lshrInPlace(C);
        Known.Zero |= RHSKnown.Zero;
        RHSKnown.One.lshrInPlace(C);
        Known.One  |= RHSKnown.One;
      // assume(~(v << c) = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_Shl(m_V, m_ConstantInt(C))),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        // For those bits in RHS that are known, we can propagate them inverted
        // to known bits in V shifted to the right by C.
        RHSKnown.One.lshrInPlace(C);
        Known.Zero |= RHSKnown.One;
        RHSKnown.Zero.lshrInPlace(C);
        Known.One  |= RHSKnown.Zero;
      // assume(v >> c = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Shr(m_V, m_ConstantInt(C)),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        // For those bits in RHS that are known, we can propagate them to known
        // bits in V shifted to the right by C.
        Known.Zero |= RHSKnown.Zero << C;
        Known.One  |= RHSKnown.One  << C;
      // assume(~(v >> c) = a)
      } else if (match(Cmp, m_c_ICmp(Pred, m_Not(m_Shr(m_V, m_ConstantInt(C))),
                                     m_Value(A))) &&
                 isValidAssumeForContext(I, Q.CxtI, Q.DT) && C < BitWidth) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
        // For those bits in RHS that are known, we can propagate them inverted
        // to known bits in V shifted to the right by C.
        Known.Zero |= RHSKnown.One  << C;
        Known.One  |= RHSKnown.Zero << C;
      }
      break;
    case ICmpInst::ICMP_SGE:
      // assume(v >=_s c) where c is non-negative
      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth + 1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        if (RHSKnown.isNonNegative()) {
          // We know that the sign bit is zero.
          Known.makeNonNegative();
        }
      }
      break;
    case ICmpInst::ICMP_SGT:
      // assume(v >_s c) where c is at least -1.
      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth + 1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        if (RHSKnown.isAllOnes() || RHSKnown.isNonNegative()) {
          // We know that the sign bit is zero.
          Known.makeNonNegative();
        }
      }
      break;
    case ICmpInst::ICMP_SLE:
      // assume(v <=_s c) where c is negative
      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth + 1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        if (RHSKnown.isNegative()) {
          // We know that the sign bit is one.
          Known.makeNegative();
        }
      }
      break;
    case ICmpInst::ICMP_SLT:
      // assume(v <_s c) where c is non-positive
      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        if (RHSKnown.isZero() || RHSKnown.isNegative()) {
          // We know that the sign bit is one.
          Known.makeNegative();
        }
      }
      break;
    case ICmpInst::ICMP_ULE:
      // assume(v <=_u c)
      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // Whatever high bits in c are zero are known to be zero.
        Known.Zero.setHighBits(RHSKnown.countMinLeadingZeros());
      }
      break;
    case ICmpInst::ICMP_ULT:
      // assume(v <_u c)
      if (match(Cmp, m_ICmp(Pred, m_V, m_Value(A))) &&
          isValidAssumeForContext(I, Q.CxtI, Q.DT)) {
        KnownBits RHSKnown =
            computeKnownBits(A, Depth+1, QueryNoAC).anyextOrTrunc(BitWidth);
 
        // If the RHS is known zero, then this assumption must be wrong (nothing
        // is unsigned less than zero). Signal a conflict and get out of here.
        if (RHSKnown.isZero()) {
          Known.Zero.setAllBits();
          Known.One.setAllBits();
          break;
        }
 
        // Whatever high bits in c are zero are known to be zero (if c is a power
        // of 2, then one more).
        if (isKnownToBeAPowerOfTwo(A, false, Depth + 1, QueryNoAC))
          Known.Zero.setHighBits(RHSKnown.countMinLeadingZeros() + 1);
        else
          Known.Zero.setHighBits(RHSKnown.countMinLeadingZeros());
      }
      break;
    }
  }
 
  // If assumptions conflict with each other or previous known bits, then we
  // have a logical fallacy. It's possible that the assumption is not reachable,
  // so this isn't a real bug. On the other hand, the program may have undefined
  // behavior, or we might have a bug in the compiler. We can't assert/crash, so
  // clear out the known bits, try to warn the user, and hope for the best.
  if (Known.Zero.intersects(Known.One)) {
    Known.resetAll();
 
    if (Q.ORE)
      Q.ORE->emit([&]() {
        auto *CxtI = const_cast<Instruction *>(Q.CxtI);
        return OptimizationRemarkAnalysis("value-tracking", "BadAssumption",
                                          CxtI)
               << "Detected conflicting code assumptions. Program may "
                  "have undefined behavior, or compiler may have "
                  "internal error.";
      });
  }
}
 
/// Compute known bits from a shift operator, including those with a
/// non-constant shift amount. Known is the output of this function. Known2 is a
/// pre-allocated temporary with the same bit width as Known and on return
/// contains the known bit of the shift value source. KF is an
/// operator-specific function that, given the known-bits and a shift amount,
/// compute the implied known-bits of the shift operator's result respectively
/// for that shift amount. The results from calling KF are conservatively
/// combined for all permitted shift amounts.
static void computeKnownBitsFromShiftOperator(
    const Operator *I, const APInt &DemandedElts, KnownBits &Known,
    KnownBits &Known2, unsigned Depth, const Query &Q,
    function_ref<KnownBits(const KnownBits &, const KnownBits &)> KF) {
  unsigned BitWidth = Known.getBitWidth();
  computeKnownBits(I->getOperand(0), DemandedElts, Known2, Depth + 1, Q);
  computeKnownBits(I->getOperand(1), DemandedElts, Known, Depth + 1, Q);
 
  // Note: We cannot use Known.Zero.getLimitedValue() here, because if
  // BitWidth > 64 and any upper bits are known, we'll end up returning the
  // limit value (which implies all bits are known).
  uint64_t ShiftAmtKZ = Known.Zero.zextOrTrunc(64).getZExtValue();
  uint64_t ShiftAmtKO = Known.One.zextOrTrunc(64).getZExtValue();
  bool ShiftAmtIsConstant = Known.isConstant();
  bool MaxShiftAmtIsOutOfRange = Known.getMaxValue().uge(BitWidth);
 
  if (ShiftAmtIsConstant) {
    Known = KF(Known2, Known);
 
    // If the known bits conflict, this must be an overflowing left shift, so
    // the shift result is poison. We can return anything we want. Choose 0 for
    // the best folding opportunity.
    if (Known.hasConflict())
      Known.setAllZero();
 
    return;
  }
 
  // If the shift amount could be greater than or equal to the bit-width of the
  // LHS, the value could be poison, but bail out because the check below is
  // expensive.
  // TODO: Should we just carry on?
  if (MaxShiftAmtIsOutOfRange) {
    Known.resetAll();
    return;
  }
 
  // It would be more-clearly correct to use the two temporaries for this
  // calculation. Reusing the APInts here to prevent unnecessary allocations.
  Known.resetAll();
 
  // If we know the shifter operand is nonzero, we can sometimes infer more
  // known bits. However this is expensive to compute, so be lazy about it and
  // only compute it when absolutely necessary.
  Optional<bool> ShifterOperandIsNonZero;
 
  // Early exit if we can't constrain any well-defined shift amount.
  if (!(ShiftAmtKZ & (PowerOf2Ceil(BitWidth) - 1)) &&
      !(ShiftAmtKO & (PowerOf2Ceil(BitWidth) - 1))) {
    ShifterOperandIsNonZero =
        isKnownNonZero(I->getOperand(1), DemandedElts, Depth + 1, Q);
    if (!*ShifterOperandIsNonZero)
      return;
  }
 
  Known.Zero.setAllBits();
  Known.One.setAllBits();
  for (unsigned ShiftAmt = 0; ShiftAmt < BitWidth; ++ShiftAmt) {
    // Combine the shifted known input bits only for those shift amounts
    // compatible with its known constraints.
    if ((ShiftAmt & ~ShiftAmtKZ) != ShiftAmt)
      continue;
    if ((ShiftAmt | ShiftAmtKO) != ShiftAmt)
      continue;
    // If we know the shifter is nonzero, we may be able to infer more known
    // bits. This check is sunk down as far as possible to avoid the expensive
    // call to isKnownNonZero if the cheaper checks above fail.
    if (ShiftAmt == 0) {
      if (!ShifterOperandIsNonZero.hasValue())
        ShifterOperandIsNonZero =
            isKnownNonZero(I->getOperand(1), DemandedElts, Depth + 1, Q);
      if (*ShifterOperandIsNonZero)
        continue;
    }
 
    Known = KnownBits::commonBits(
        Known, KF(Known2, KnownBits::makeConstant(APInt(32, ShiftAmt))));
  }
 
  // If the known bits conflict, the result is poison. Return a 0 and hope the
  // caller can further optimize that.
  if (Known.hasConflict())
    Known.setAllZero();
}
 
static void computeKnownBitsFromOperator(const Operator *I,
                                         const APInt &DemandedElts,
                                         KnownBits &Known, unsigned Depth,
                                         const Query &Q) {
  unsigned BitWidth = Known.getBitWidth();
 
  KnownBits Known2(BitWidth);
  switch (I->getOpcode()) {
  default: break;
  case Instruction::Load:
    if (MDNode *MD =
            Q.IIQ.getMetadata(cast<LoadInst>(I), LLVMContext::MD_range))
      computeKnownBitsFromRangeMetadata(*MD, Known);
    break;
  case Instruction::And: {
    // If either the LHS or the RHS are Zero, the result is zero.
    computeKnownBits(I->getOperand(1), DemandedElts, Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(0), DemandedElts, Known2, Depth + 1, Q);
 
    Known &= Known2;
 
    // and(x, add (x, -1)) is a common idiom that always clears the low bit;
    // here we handle the more general case of adding any odd number by
    // matching the form add(x, add(x, y)) where y is odd.
    // TODO: This could be generalized to clearing any bit set in y where the
    // following bit is known to be unset in y.
    Value *X = nullptr, *Y = nullptr;
    if (!Known.Zero[0] && !Known.One[0] &&
        match(I, m_c_BinOp(m_Value(X), m_Add(m_Deferred(X), m_Value(Y))))) {
      Known2.resetAll();
      computeKnownBits(Y, DemandedElts, Known2, Depth + 1, Q);
      if (Known2.countMinTrailingOnes() > 0)
        Known.Zero.setBit(0);
    }
    break;
  }
  case Instruction::Or:
    computeKnownBits(I->getOperand(1), DemandedElts, Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(0), DemandedElts, Known2, Depth + 1, Q);
 
    Known |= Known2;
    break;
  case Instruction::Xor:
    computeKnownBits(I->getOperand(1), DemandedElts, Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(0), DemandedElts, Known2, Depth + 1, Q);
 
    Known ^= Known2;
    break;
  case Instruction::Mul: {
    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
    computeKnownBitsMul(I->getOperand(0), I->getOperand(1), NSW, DemandedElts,
                        Known, Known2, Depth, Q);
    break;
  }
  case Instruction::UDiv: {
    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
    Known = KnownBits::udiv(Known, Known2);
    break;
  }
  case Instruction::Select: {
    const Value *LHS = nullptr, *RHS = nullptr;
    SelectPatternFlavor SPF = matchSelectPattern(I, LHS, RHS).Flavor;
    if (SelectPatternResult::isMinOrMax(SPF)) {
      computeKnownBits(RHS, Known, Depth + 1, Q);
      computeKnownBits(LHS, Known2, Depth + 1, Q);
      switch (SPF) {
      default:
        llvm_unreachable("Unhandled select pattern flavor!");
      case SPF_SMAX:
        Known = KnownBits::smax(Known, Known2);
        break;
      case SPF_SMIN:
        Known = KnownBits::smin(Known, Known2);
        break;
      case SPF_UMAX:
        Known = KnownBits::umax(Known, Known2);
        break;
      case SPF_UMIN:
        Known = KnownBits::umin(Known, Known2);
        break;
      }
      break;
    }
 
    computeKnownBits(I->getOperand(2), Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
 
    // Only known if known in both the LHS and RHS.
    Known = KnownBits::commonBits(Known, Known2);
 
    if (SPF == SPF_ABS) {
      // RHS from matchSelectPattern returns the negation part of abs pattern.
      // If the negate has an NSW flag we can assume the sign bit of the result
      // will be 0 because that makes abs(INT_MIN) undefined.
      if (match(RHS, m_Neg(m_Specific(LHS))) &&
          Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(RHS)))
        Known.Zero.setSignBit();
    }
 
    break;
  }
  case Instruction::FPTrunc:
  case Instruction::FPExt:
  case Instruction::FPToUI:
  case Instruction::FPToSI:
  case Instruction::SIToFP:
  case Instruction::UIToFP:
    break; // Can't work with floating point.
  case Instruction::PtrToInt:
  case Instruction::IntToPtr:
    // Fall through and handle them the same as zext/trunc.
    LLVM_FALLTHROUGH;
  case Instruction::ZExt:
  case Instruction::Trunc: {
    Type *SrcTy = I->getOperand(0)->getType();
 
    unsigned SrcBitWidth;
    // Note that we handle pointer operands here because of inttoptr/ptrtoint
    // which fall through here.
    Type *ScalarTy = SrcTy->getScalarType();
    SrcBitWidth = ScalarTy->isPointerTy() ?
      Q.DL.getPointerTypeSizeInBits(ScalarTy) :
      Q.DL.getTypeSizeInBits(ScalarTy);
 
    assert(SrcBitWidth && "SrcBitWidth can't be zero");
    Known = Known.anyextOrTrunc(SrcBitWidth);
    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    Known = Known.zextOrTrunc(BitWidth);
    break;
  }
  case Instruction::BitCast: {
    Type *SrcTy = I->getOperand(0)->getType();
    if (SrcTy->isIntOrPtrTy() &&
        // TODO: For now, not handling conversions like:
        // (bitcast i64 %x to <2 x i32>)
        !I->getType()->isVectorTy()) {
      computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
      break;
    }
 
    // Handle cast from vector integer type to scalar or vector integer.
    auto *SrcVecTy = dyn_cast<FixedVectorType>(SrcTy);
    if (!SrcVecTy || !SrcVecTy->getElementType()->isIntegerTy() ||
        !I->getType()->isIntOrIntVectorTy())
      break;
 
    // Look through a cast from narrow vector elements to wider type.
    // Examples: v4i32 -> v2i64, v3i8 -> v24
    unsigned SubBitWidth = SrcVecTy->getScalarSizeInBits();
    if (BitWidth % SubBitWidth == 0) {
      // Known bits are automatically intersected across demanded elements of a
      // vector. So for example, if a bit is computed as known zero, it must be
      // zero across all demanded elements of the vector.
      //
      // For this bitcast, each demanded element of the output is sub-divided
      // across a set of smaller vector elements in the source vector. To get
      // the known bits for an entire element of the output, compute the known
      // bits for each sub-element sequentially. This is done by shifting the
      // one-set-bit demanded elements parameter across the sub-elements for
      // consecutive calls to computeKnownBits. We are using the demanded
      // elements parameter as a mask operator.
      //
      // The known bits of each sub-element are then inserted into place
      // (dependent on endian) to form the full result of known bits.
      unsigned NumElts = DemandedElts.getBitWidth();
      unsigned SubScale = BitWidth / SubBitWidth;
      APInt SubDemandedElts = APInt::getZero(NumElts * SubScale);
      for (unsigned i = 0; i != NumElts; ++i) {
        if (DemandedElts[i])
          SubDemandedElts.setBit(i * SubScale);
      }
 
      KnownBits KnownSrc(SubBitWidth);
      for (unsigned i = 0; i != SubScale; ++i) {
        computeKnownBits(I->getOperand(0), SubDemandedElts.shl(i), KnownSrc,
                         Depth + 1, Q);
        unsigned ShiftElt = Q.DL.isLittleEndian() ? i : SubScale - 1 - i;
        Known.insertBits(KnownSrc, ShiftElt * SubBitWidth);
      }
    }
    break;
  }
  case Instruction::SExt: {
    // Compute the bits in the result that are not present in the input.
    unsigned SrcBitWidth = I->getOperand(0)->getType()->getScalarSizeInBits();
 
    Known = Known.trunc(SrcBitWidth);
    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    // If the sign bit of the input is known set or clear, then we know the
    // top bits of the result.
    Known = Known.sext(BitWidth);
    break;
  }
  case Instruction::Shl: {
    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
    auto KF = [NSW](const KnownBits &KnownVal, const KnownBits &KnownAmt) {
      KnownBits Result = KnownBits::shl(KnownVal, KnownAmt);
      // If this shift has "nsw" keyword, then the result is either a poison
      // value or has the same sign bit as the first operand.
      if (NSW) {
        if (KnownVal.Zero.isSignBitSet())
          Result.Zero.setSignBit();
        if (KnownVal.One.isSignBitSet())
          Result.One.setSignBit();
      }
      return Result;
    };
    computeKnownBitsFromShiftOperator(I, DemandedElts, Known, Known2, Depth, Q,
                                      KF);
    // Trailing zeros of a right-shifted constant never decrease.
    const APInt *C;
    if (match(I->getOperand(0), m_APInt(C)))
      Known.Zero.setLowBits(C->countTrailingZeros());
    break;
  }
  case Instruction::LShr: {
    auto KF = [](const KnownBits &KnownVal, const KnownBits &KnownAmt) {
      return KnownBits::lshr(KnownVal, KnownAmt);
    };
    computeKnownBitsFromShiftOperator(I, DemandedElts, Known, Known2, Depth, Q,
                                      KF);
    // Leading zeros of a left-shifted constant never decrease.
    const APInt *C;
    if (match(I->getOperand(0), m_APInt(C)))
      Known.Zero.setHighBits(C->countLeadingZeros());
    break;
  }
  case Instruction::AShr: {
    auto KF = [](const KnownBits &KnownVal, const KnownBits &KnownAmt) {
      return KnownBits::ashr(KnownVal, KnownAmt);
    };
    computeKnownBitsFromShiftOperator(I, DemandedElts, Known, Known2, Depth, Q,
                                      KF);
    break;
  }
  case Instruction::Sub: {
    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
    computeKnownBitsAddSub(false, I->getOperand(0), I->getOperand(1), NSW,
                           DemandedElts, Known, Known2, Depth, Q);
    break;
  }
  case Instruction::Add: {
    bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
    computeKnownBitsAddSub(true, I->getOperand(0), I->getOperand(1), NSW,
                           DemandedElts, Known, Known2, Depth, Q);
    break;
  }
  case Instruction::SRem:
    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
    Known = KnownBits::srem(Known, Known2);
    break;
 
  case Instruction::URem:
    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
    Known = KnownBits::urem(Known, Known2);
    break;
  case Instruction::Alloca:
    Known.Zero.setLowBits(Log2(cast<AllocaInst>(I)->getAlign()));
    break;
  case Instruction::GetElementPtr: {
    // Analyze all of the subscripts of this getelementptr instruction
    // to determine if we can prove known low zero bits.
    computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    // Accumulate the constant indices in a separate variable
    // to minimize the number of calls to computeForAddSub.
    APInt AccConstIndices(BitWidth, 0, /*IsSigned*/ true);
 
    gep_type_iterator GTI = gep_type_begin(I);
    for (unsigned i = 1, e = I->getNumOperands(); i != e; ++i, ++GTI) {
      // TrailZ can only become smaller, short-circuit if we hit zero.
      if (Known.isUnknown())
        break;
 
      Value *Index = I->getOperand(i);
 
      // Handle case when index is zero.
      Constant *CIndex = dyn_cast<Constant>(Index);
      if (CIndex && CIndex->isZeroValue())
        continue;
 
      if (StructType *STy = GTI.getStructTypeOrNull()) {
        // Handle struct member offset arithmetic.
 
        assert(CIndex &&
               "Access to structure field must be known at compile time");
 
        if (CIndex->getType()->isVectorTy())
          Index = CIndex->getSplatValue();
 
        unsigned Idx = cast<ConstantInt>(Index)->getZExtValue();
        const StructLayout *SL = Q.DL.getStructLayout(STy);
        uint64_t Offset = SL->getElementOffset(Idx);
        AccConstIndices += Offset;
        continue;
      }
 
      // Handle array index arithmetic.
      Type *IndexedTy = GTI.getIndexedType();
      if (!IndexedTy->isSized()) {
        Known.resetAll();
        break;
      }
 
      unsigned IndexBitWidth = Index->getType()->getScalarSizeInBits();
      KnownBits IndexBits(IndexBitWidth);
      computeKnownBits(Index, IndexBits, Depth + 1, Q);
      TypeSize IndexTypeSize = Q.DL.getTypeAllocSize(IndexedTy);
      uint64_t TypeSizeInBytes = IndexTypeSize.getKnownMinSize();
      KnownBits ScalingFactor(IndexBitWidth);
      // Multiply by current sizeof type.
      // &A[i] == A + i * sizeof(*A[i]).
      if (IndexTypeSize.isScalable()) {
        // For scalable types the only thing we know about sizeof is
        // that this is a multiple of the minimum size.
        ScalingFactor.Zero.setLowBits(countTrailingZeros(TypeSizeInBytes));
      } else if (IndexBits.isConstant()) {
        APInt IndexConst = IndexBits.getConstant();
        APInt ScalingFactor(IndexBitWidth, TypeSizeInBytes);
        IndexConst *= ScalingFactor;
        AccConstIndices += IndexConst.sextOrTrunc(BitWidth);
        continue;
      } else {
        ScalingFactor =
            KnownBits::makeConstant(APInt(IndexBitWidth, TypeSizeInBytes));
      }
      IndexBits = KnownBits::mul(IndexBits, ScalingFactor);
 
      // If the offsets have a different width from the pointer, according
      // to the language reference we need to sign-extend or truncate them
      // to the width of the pointer.
      IndexBits = IndexBits.sextOrTrunc(BitWidth);
 
      // Note that inbounds does *not* guarantee nsw for the addition, as only
      // the offset is signed, while the base address is unsigned.
      Known = KnownBits::computeForAddSub(
          /*Add=*/true, /*NSW=*/false, Known, IndexBits);
    }
    if (!Known.isUnknown() && !AccConstIndices.isZero()) {
      KnownBits Index = KnownBits::makeConstant(AccConstIndices);
      Known = KnownBits::computeForAddSub(
          /*Add=*/true, /*NSW=*/false, Known, Index);
    }
    break;
  }
  case Instruction::PHI: {
    const PHINode *P = cast<PHINode>(I);
    BinaryOperator *BO = nullptr;
    Value *R = nullptr, *L = nullptr;
    if (matchSimpleRecurrence(P, BO, R, L)) {
      // Handle the case of a simple two-predecessor recurrence PHI.
      // There's a lot more that could theoretically be done here, but
      // this is sufficient to catch some interesting cases.
      unsigned Opcode = BO->getOpcode();
 
      // If this is a shift recurrence, we know the bits being shifted in.
      // We can combine that with information about the start value of the
      // recurrence to conclude facts about the result.
      if ((Opcode == Instruction::LShr || Opcode == Instruction::AShr ||
           Opcode == Instruction::Shl) &&
          BO->getOperand(0) == I) {
 
        // We have matched a recurrence of the form:
        // %iv = [R, %entry], [%iv.next, %backedge]
        // %iv.next = shift_op %iv, L
 
        // Recurse with the phi context to avoid concern about whether facts
        // inferred hold at original context instruction.  TODO: It may be
        // correct to use the original context.  IF warranted, explore and
        // add sufficient tests to cover.
        Query RecQ = Q;
        RecQ.CxtI = P;
        computeKnownBits(R, DemandedElts, Known2, Depth + 1, RecQ);
        switch (Opcode) {
        case Instruction::Shl:
          // A shl recurrence will only increase the tailing zeros
          Known.Zero.setLowBits(Known2.countMinTrailingZeros());
          break;
        case Instruction::LShr:
          // A lshr recurrence will preserve the leading zeros of the
          // start value
          Known.Zero.setHighBits(Known2.countMinLeadingZeros());
          break;
        case Instruction::AShr:
          // An ashr recurrence will extend the initial sign bit
          Known.Zero.setHighBits(Known2.countMinLeadingZeros());
          Known.One.setHighBits(Known2.countMinLeadingOnes());
          break;
        };
      }
 
      // Check for operations that have the property that if
      // both their operands have low zero bits, the result
      // will have low zero bits.
      if (Opcode == Instruction::Add ||
          Opcode == Instruction::Sub ||
          Opcode == Instruction::And ||
          Opcode == Instruction::Or ||
          Opcode == Instruction::Mul) {
        // Change the context instruction to the "edge" that flows into the
        // phi. This is important because that is where the value is actually
        // "evaluated" even though it is used later somewhere else. (see also
        // D69571).
        Query RecQ = Q;
 
        unsigned OpNum = P->getOperand(0) == R ? 0 : 1;
        Instruction *RInst = P->getIncomingBlock(OpNum)->getTerminator();
        Instruction *LInst = P->getIncomingBlock(1-OpNum)->getTerminator();
 
        // Ok, we have a PHI of the form L op= R. Check for low
        // zero bits.
        RecQ.CxtI = RInst;
        computeKnownBits(R, Known2, Depth + 1, RecQ);
 
        // We need to take the minimum number of known bits
        KnownBits Known3(BitWidth);
        RecQ.CxtI = LInst;
        computeKnownBits(L, Known3, Depth + 1, RecQ);
 
        Known.Zero.setLowBits(std::min(Known2.countMinTrailingZeros(),
                                       Known3.countMinTrailingZeros()));
 
        auto *OverflowOp = dyn_cast<OverflowingBinaryOperator>(BO);
        if (OverflowOp && Q.IIQ.hasNoSignedWrap(OverflowOp)) {
          // If initial value of recurrence is nonnegative, and we are adding
          // a nonnegative number with nsw, the result can only be nonnegative
          // or poison value regardless of the number of times we execute the
          // add in phi recurrence. If initial value is negative and we are
          // adding a negative number with nsw, the result can only be
          // negative or poison value. Similar arguments apply to sub and mul.
          //
          // (add non-negative, non-negative) --> non-negative
          // (add negative, negative) --> negative
          if (Opcode == Instruction::Add) {
            if (Known2.isNonNegative() && Known3.isNonNegative())
              Known.makeNonNegative();
            else if (Known2.isNegative() && Known3.isNegative())
              Known.makeNegative();
          }
 
          // (sub nsw non-negative, negative) --> non-negative
          // (sub nsw negative, non-negative) --> negative
          else if (Opcode == Instruction::Sub && BO->getOperand(0) == I) {
            if (Known2.isNonNegative() && Known3.isNegative())
              Known.makeNonNegative();
            else if (Known2.isNegative() && Known3.isNonNegative())
              Known.makeNegative();
          }
 
          // (mul nsw non-negative, non-negative) --> non-negative
          else if (Opcode == Instruction::Mul && Known2.isNonNegative() &&
                   Known3.isNonNegative())
            Known.makeNonNegative();
        }
 
        break;
      }
    }
 
    // Unreachable blocks may have zero-operand PHI nodes.
    if (P->getNumIncomingValues() == 0)
      break;
 
    // Otherwise take the unions of the known bit sets of the operands,
    // taking conservative care to avoid excessive recursion.
    if (Depth < MaxAnalysisRecursionDepth - 1 && !Known.Zero && !Known.One) {
      // Skip if every incoming value references to ourself.
      if (isa_and_nonnull<UndefValue>(P->hasConstantValue()))
        break;
 
      Known.Zero.setAllBits();
      Known.One.setAllBits();
      for (unsigned u = 0, e = P->getNumIncomingValues(); u < e; ++u) {
        Value *IncValue = P->getIncomingValue(u);
        // Skip direct self references.
        if (IncValue == P) continue;
 
        // Change the context instruction to the "edge" that flows into the
        // phi. This is important because that is where the value is actually
        // "evaluated" even though it is used later somewhere else. (see also
        // D69571).
        Query RecQ = Q;
        RecQ.CxtI = P->getIncomingBlock(u)->getTerminator();
 
        Known2 = KnownBits(BitWidth);
        // Recurse, but cap the recursion to one level, because we don't
        // want to waste time spinning around in loops.
        computeKnownBits(IncValue, Known2, MaxAnalysisRecursionDepth - 1, RecQ);
        Known = KnownBits::commonBits(Known, Known2);
        // If all bits have been ruled out, there's no need to check
        // more operands.
        if (Known.isUnknown())
          break;
      }
    }
    break;
  }
  case Instruction::Call:
  case Instruction::Invoke:
    // If range metadata is attached to this call, set known bits from that,
    // and then intersect with known bits based on other properties of the
    // function.
    if (MDNode *MD =
            Q.IIQ.getMetadata(cast<Instruction>(I), LLVMContext::MD_range))
      computeKnownBitsFromRangeMetadata(*MD, Known);
    if (const Value *RV = cast<CallBase>(I)->getReturnedArgOperand()) {
      computeKnownBits(RV, Known2, Depth + 1, Q);
      Known.Zero |= Known2.Zero;
      Known.One |= Known2.One;
    }
    if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(I)) {
      switch (II->getIntrinsicID()) {
      default: break;
      case Intrinsic::abs: {
        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
        bool IntMinIsPoison = match(II->getArgOperand(1), m_One());
        Known = Known2.abs(IntMinIsPoison);
        break;
      }
      case Intrinsic::bitreverse:
        computeKnownBits(I->getOperand(0), DemandedElts, Known2, Depth + 1, Q);
        Known.Zero |= Known2.Zero.reverseBits();
        Known.One |= Known2.One.reverseBits();
        break;
      case Intrinsic::bswap:
        computeKnownBits(I->getOperand(0), DemandedElts, Known2, Depth + 1, Q);
        Known.Zero |= Known2.Zero.byteSwap();
        Known.One |= Known2.One.byteSwap();
        break;
      case Intrinsic::ctlz: {
        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
        // If we have a known 1, its position is our upper bound.
        unsigned PossibleLZ = Known2.countMaxLeadingZeros();
        // If this call is undefined for 0, the result will be less than 2^n.
        if (II->getArgOperand(1) == ConstantInt::getTrue(II->getContext()))
          PossibleLZ = std::min(PossibleLZ, BitWidth - 1);
        unsigned LowBits = Log2_32(PossibleLZ)+1;
        Known.Zero.setBitsFrom(LowBits);
        break;
      }
      case Intrinsic::cttz: {
        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
        // If we have a known 1, its position is our upper bound.
        unsigned PossibleTZ = Known2.countMaxTrailingZeros();
        // If this call is undefined for 0, the result will be less than 2^n.
        if (II->getArgOperand(1) == ConstantInt::getTrue(II->getContext()))
          PossibleTZ = std::min(PossibleTZ, BitWidth - 1);
        unsigned LowBits = Log2_32(PossibleTZ)+1;
        Known.Zero.setBitsFrom(LowBits);
        break;
      }
      case Intrinsic::ctpop: {
        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
        // We can bound the space the count needs.  Also, bits known to be zero
        // can't contribute to the population.
        unsigned BitsPossiblySet = Known2.countMaxPopulation();
        unsigned LowBits = Log2_32(BitsPossiblySet)+1;
        Known.Zero.setBitsFrom(LowBits);
        // TODO: we could bound KnownOne using the lower bound on the number
        // of bits which might be set provided by popcnt KnownOne2.
        break;
      }
      case Intrinsic::fshr:
      case Intrinsic::fshl: {
        const APInt *SA;
        if (!match(I->getOperand(2), m_APInt(SA)))
          break;
 
        // Normalize to funnel shift left.
        uint64_t ShiftAmt = SA->urem(BitWidth);
        if (II->getIntrinsicID() == Intrinsic::fshr)
          ShiftAmt = BitWidth - ShiftAmt;
 
        KnownBits Known3(BitWidth);
        computeKnownBits(I->getOperand(0), Known2, Depth + 1, Q);
        computeKnownBits(I->getOperand(1), Known3, Depth + 1, Q);
 
        Known.Zero =
            Known2.Zero.shl(ShiftAmt) | Known3.Zero.lshr(BitWidth - ShiftAmt);
        Known.One =
            Known2.One.shl(ShiftAmt) | Known3.One.lshr(BitWidth - ShiftAmt);
        break;
      }
      case Intrinsic::uadd_sat:
      case Intrinsic::usub_sat: {
        bool IsAdd = II->getIntrinsicID() == Intrinsic::uadd_sat;
        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
        computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
 
        // Add: Leading ones of either operand are preserved.
        // Sub: Leading zeros of LHS and leading ones of RHS are preserved
        // as leading zeros in the result.
        unsigned LeadingKnown;
        if (IsAdd)
          LeadingKnown = std::max(Known.countMinLeadingOnes(),
                                  Known2.countMinLeadingOnes());
        else
          LeadingKnown = std::max(Known.countMinLeadingZeros(),
                                  Known2.countMinLeadingOnes());
 
        Known = KnownBits::computeForAddSub(
            IsAdd, /* NSW */ false, Known, Known2);
 
        // We select between the operation result and all-ones/zero
        // respectively, so we can preserve known ones/zeros.
        if (IsAdd) {
          Known.One.setHighBits(LeadingKnown);
          Known.Zero.clearAllBits();
        } else {
          Known.Zero.setHighBits(LeadingKnown);
          Known.One.clearAllBits();
        }
        break;
      }
      case Intrinsic::umin:
        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
        computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
        Known = KnownBits::umin(Known, Known2);
        break;
      case Intrinsic::umax:
        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
        computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
        Known = KnownBits::umax(Known, Known2);
        break;
      case Intrinsic::smin:
        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
        computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
        Known = KnownBits::smin(Known, Known2);
        break;
      case Intrinsic::smax:
        computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
        computeKnownBits(I->getOperand(1), Known2, Depth + 1, Q);
        Known = KnownBits::smax(Known, Known2);
        break;
      case Intrinsic::x86_sse42_crc32_64_64:
        Known.Zero.setBitsFrom(32);
        break;
      case Intrinsic::riscv_vsetvli:
      case Intrinsic::riscv_vsetvlimax:
        // Assume that VL output is positive and would fit in an int32_t.
        // TODO: VLEN might be capped at 16 bits in a future V spec update.
        if (BitWidth >= 32)
          Known.Zero.setBitsFrom(31);
        break;
      case Intrinsic::vscale: {
        if (!II->getParent() || !II->getFunction() ||
            !II->getFunction()->hasFnAttribute(Attribute::VScaleRange))
          break;
 
        auto Attr = II->getFunction()->getFnAttribute(Attribute::VScaleRange);
        Optional<unsigned> VScaleMax = Attr.getVScaleRangeMax();
 
        if (!VScaleMax)
          break;
 
        unsigned VScaleMin = Attr.getVScaleRangeMin();
 
        // If vscale min = max then we know the exact value at compile time
        // and hence we know the exact bits.
        if (VScaleMin == VScaleMax) {
          Known.One = VScaleMin;
          Known.Zero = VScaleMin;
          Known.Zero.flipAllBits();
          break;
        }
 
        unsigned FirstZeroHighBit =
            32 - countLeadingZeros(VScaleMax.getValue());
        if (FirstZeroHighBit < BitWidth)
          Known.Zero.setBitsFrom(FirstZeroHighBit);
 
        break;
      }
      }
    }
    break;
  case Instruction::ShuffleVector: {
    auto *Shuf = dyn_cast<ShuffleVectorInst>(I);
    // FIXME: Do we need to handle ConstantExpr involving shufflevectors?
    if (!Shuf) {
      Known.resetAll();
      return;
    }
    // For undef elements, we don't know anything about the common state of
    // the shuffle result.
    APInt DemandedLHS, DemandedRHS;
    if (!getShuffleDemandedElts(Shuf, DemandedElts, DemandedLHS, DemandedRHS)) {
      Known.resetAll();
      return;
    }
    Known.One.setAllBits();
    Known.Zero.setAllBits();
    if (!!DemandedLHS) {
      const Value *LHS = Shuf->getOperand(0);
      computeKnownBits(LHS, DemandedLHS, Known, Depth + 1, Q);
      // If we don't know any bits, early out.
      if (Known.isUnknown())
        break;
    }
    if (!!DemandedRHS) {
      const Value *RHS = Shuf->getOperand(1);
      computeKnownBits(RHS, DemandedRHS, Known2, Depth + 1, Q);
      Known = KnownBits::commonBits(Known, Known2);
    }
    break;
  }
  case Instruction::InsertElement: {
    const Value *Vec = I->getOperand(0);
    const Value *Elt = I->getOperand(1);
    auto *CIdx = dyn_cast<ConstantInt>(I->getOperand(2));
    // Early out if the index is non-constant or out-of-range.
    unsigned NumElts = DemandedElts.getBitWidth();
    if (!CIdx || CIdx->getValue().uge(NumElts)) {
      Known.resetAll();
      return;
    }
    Known.One.setAllBits();
    Known.Zero.setAllBits();
    unsigned EltIdx = CIdx->getZExtValue();
    // Do we demand the inserted element?
    if (DemandedElts[EltIdx]) {
      computeKnownBits(Elt, Known, Depth + 1, Q);
      // If we don't know any bits, early out.
      if (Known.isUnknown())
        break;
    }
    // We don't need the base vector element that has been inserted.
    APInt DemandedVecElts = DemandedElts;
    DemandedVecElts.clearBit(EltIdx);
    if (!!DemandedVecElts) {
      computeKnownBits(Vec, DemandedVecElts, Known2, Depth + 1, Q);
      Known = KnownBits::commonBits(Known, Known2);
    }
    break;
  }
  case Instruction::ExtractElement: {
    // Look through extract element. If the index is non-constant or
    // out-of-range demand all elements, otherwise just the extracted element.
    const Value *Vec = I->getOperand(0);
    const Value *Idx = I->getOperand(1);
    auto *CIdx = dyn_cast<ConstantInt>(Idx);
    if (isa<ScalableVectorType>(Vec->getType())) {
      // FIXME: there's probably *something* we can do with scalable vectors
      Known.resetAll();
      break;
    }
    unsigned NumElts = cast<FixedVectorType>(Vec->getType())->getNumElements();
    APInt DemandedVecElts = APInt::getAllOnes(NumElts);
    if (CIdx && CIdx->getValue().ult(NumElts))
      DemandedVecElts = APInt::getOneBitSet(NumElts, CIdx->getZExtValue());
    computeKnownBits(Vec, DemandedVecElts, Known, Depth + 1, Q);
    break;
  }
  case Instruction::ExtractValue:
    if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(I->getOperand(0))) {
      const ExtractValueInst *EVI = cast<ExtractValueInst>(I);
      if (EVI->getNumIndices() != 1) break;
      if (EVI->getIndices()[0] == 0) {
        switch (II->getIntrinsicID()) {
        default: break;
        case Intrinsic::uadd_with_overflow:
        case Intrinsic::sadd_with_overflow:
          computeKnownBitsAddSub(true, II->getArgOperand(0),
                                 II->getArgOperand(1), false, DemandedElts,
                                 Known, Known2, Depth, Q);
          break;
        case Intrinsic::usub_with_overflow:
        case Intrinsic::ssub_with_overflow:
          computeKnownBitsAddSub(false, II->getArgOperand(0),
                                 II->getArgOperand(1), false, DemandedElts,
                                 Known, Known2, Depth, Q);
          break;
        case Intrinsic::umul_with_overflow:
        case Intrinsic::smul_with_overflow:
          computeKnownBitsMul(II->getArgOperand(0), II->getArgOperand(1), false,
                              DemandedElts, Known, Known2, Depth, Q);
          break;
        }
      }
    }
    break;
  case Instruction::Freeze:
    if (isGuaranteedNotToBePoison(I->getOperand(0), Q.AC, Q.CxtI, Q.DT,
                                  Depth + 1))
      computeKnownBits(I->getOperand(0), Known, Depth + 1, Q);
    break;
  }
}
 
/// Determine which bits of V are known to be either zero or one and return
/// them.
KnownBits computeKnownBits(const Value *V, const APInt &DemandedElts,
                           unsigned Depth, const Query &Q) {
  KnownBits Known(getBitWidth(V->getType(), Q.DL));
  computeKnownBits(V, DemandedElts, Known, Depth, Q);
  return Known;
}
 
/// Determine which bits of V are known to be either zero or one and return
/// them.
KnownBits computeKnownBits(const Value *V, unsigned Depth, const Query &Q) {
  KnownBits Known(getBitWidth(V->getType(), Q.DL));
  computeKnownBits(V, Known, Depth, Q);
  return Known;
}
 
/// Determine which bits of V are known to be either zero or one and return
/// them in the Known bit set.
///
/// NOTE: we cannot consider 'undef' to be "IsZero" here.  The problem is that
/// we cannot optimize based on the assumption that it is zero without changing
/// it to be an explicit zero.  If we don't change it to zero, other code could
/// optimized based on the contradictory assumption that it is non-zero.
/// Because instcombine aggressively folds operations with undef args anyway,
/// this won't lose us code quality.
///
/// 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, 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 demanded elements in the vector specified by DemandedElts.
void computeKnownBits(const Value *V, const APInt &DemandedElts,
                      KnownBits &Known, unsigned Depth, const Query &Q) {
  if (!DemandedElts || isa<ScalableVectorType>(V->getType())) {
    // No demanded elts or V is a scalable vector, better to assume we don't
    // know anything.
    Known.resetAll();
    return;
  }
 
  assert(V && "No Value?");
  assert(Depth <= MaxAnalysisRecursionDepth && "Limit Search Depth");
 
#ifndef NDEBUG
  Type *Ty = V->getType();
  unsigned BitWidth = Known.getBitWidth();
 
  assert((Ty->isIntOrIntVectorTy(BitWidth) || Ty->isPtrOrPtrVectorTy()) &&
         "Not integer or pointer type!");
 
  if (auto *FVTy = dyn_cast<FixedVectorType>(Ty)) {
    assert(
        FVTy->getNumElements() == DemandedElts.getBitWidth() &&
        "DemandedElt width should equal the fixed vector number of elements");
  } else {
    assert(DemandedElts == APInt(1, 1) &&
           "DemandedElt width should be 1 for scalars");
  }
 
  Type *ScalarTy = Ty->getScalarType();
  if (ScalarTy->isPointerTy()) {
    assert(BitWidth == Q.DL.getPointerTypeSizeInBits(ScalarTy) &&
           "V and Known should have same BitWidth");
  } else {
    assert(BitWidth == Q.DL.getTypeSizeInBits(ScalarTy) &&
           "V and Known should have same BitWidth");
  }
#endif
 
  const APInt *C;
  if (match(V, m_APInt(C))) {
    // We know all of the bits for a scalar constant or a splat vector constant!
    Known = KnownBits::makeConstant(*C);
    return;
  }
  // Null and aggregate-zero are all-zeros.
  if (isa<ConstantPointerNull>(V) || isa<ConstantAggregateZero>(V)) {
    Known.setAllZero();
    return;
  }
  // Handle a constant vector by taking the intersection of the known bits of
  // each element.
  if (const ConstantDataVector *CDV = dyn_cast<ConstantDataVector>(V)) {
    // We know that CDV must be a vector of integers. Take the intersection of
    // each element.
    Known.Zero.setAllBits(); Known.One.setAllBits();
    for (unsigned i = 0, e = CDV->getNumElements(); i != e; ++i) {
      if (!DemandedElts[i])
        continue;
      APInt Elt = CDV->getElementAsAPInt(i);
      Known.Zero &= ~Elt;
      Known.One &= Elt;
    }
    return;
  }
 
  if (const auto *CV = dyn_cast<ConstantVector>(V)) {
    // We know that CV must be a vector of integers. Take the intersection of
    // each element.
    Known.Zero.setAllBits(); Known.One.setAllBits();
    for (unsigned i = 0, e = CV->getNumOperands(); i != e; ++i) {
      if (!DemandedElts[i])
        continue;
      Constant *Element = CV->getAggregateElement(i);
      auto *ElementCI = dyn_cast_or_null<ConstantInt>(Element);
      if (!ElementCI) {
        Known.resetAll();
        return;
      }
      const APInt &Elt = ElementCI->getValue();
      Known.Zero &= ~Elt;
      Known.One &= Elt;
    }
    return;
  }
 
  // Start out not knowing anything.
  Known.resetAll();
 
  // We can't imply anything about undefs.
  if (isa<UndefValue>(V))
    return;
 
  // There's no point in looking through other users of ConstantData for
  // assumptions.  Confirm that we've handled them all.
  assert(!isa<ConstantData>(V) && "Unhandled constant data!");
 
  // All recursive calls that increase depth must come after this.
  if (Depth == MaxAnalysisRecursionDepth)
    return;
 
  // A weak GlobalAlias is totally unknown. A non-weak GlobalAlias has
  // the bits of its aliasee.
  if (const GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
    if (!GA->isInterposable())
      computeKnownBits(GA->getAliasee(), Known, Depth + 1, Q);
    return;
  }
 
  if (const Operator *I = dyn_cast<Operator>(V))
    computeKnownBitsFromOperator(I, DemandedElts, Known, Depth, Q);
 
  // Aligned pointers have trailing zeros - refine Known.Zero set
  if (isa<PointerType>(V->getType())) {
    Align Alignment = V->getPointerAlignment(Q.DL);
    Known.Zero.setLowBits(Log2(Alignment));
  }
 
  // computeKnownBitsFromAssume strictly refines Known.
  // Therefore, we run them after computeKnownBitsFromOperator.
 
  // Check whether a nearby assume intrinsic can determine some known bits.
  computeKnownBitsFromAssume(V, Known, Depth, Q);
 
  assert((Known.Zero & Known.One) == 0 && "Bits known to be one AND zero?");
}
 
/// 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
/// types and vectors of integers.
bool isKnownToBeAPowerOfTwo(const Value *V, bool OrZero, unsigned Depth,
                            const Query &Q) {
  assert(Depth <= MaxAnalysisRecursionDepth && "Limit Search Depth");
 
  // Attempt to match against constants.
  if (OrZero && match(V, m_Power2OrZero()))
      return true;
  if (match(V, m_Power2()))
      return true;
 
  // 1 << X is clearly a power of two if the one is not shifted off the end.  If
  // it is shifted off the end then the result is undefined.
  if (match(V, m_Shl(m_One(), m_Value())))
    return true;
 
  // (signmask) >>l X is clearly a power of two if the one is not shifted off
  // the bottom.  If it is shifted off the bottom then the result is undefined.
  if (match(V, m_LShr(m_SignMask(), m_Value())))
    return true;
 
  // The remaining tests are all recursive, so bail out if we hit the limit.
  if (Depth++ == MaxAnalysisRecursionDepth)
    return false;
 
  Value *X = nullptr, *Y = nullptr;
  // A shift left or a logical shift right of a power of two is a power of two
  // or zero.
  if (OrZero && (match(V, m_Shl(m_Value(X), m_Value())) ||
                 match(V, m_LShr(m_Value(X), m_Value()))))
    return isKnownToBeAPowerOfTwo(X, /*OrZero*/ true, Depth, Q);
 
  if (const ZExtInst *ZI = dyn_cast<ZExtInst>(V))
    return isKnownToBeAPowerOfTwo(ZI->getOperand(0), OrZero, Depth, Q);
 
  if (const SelectInst *SI = dyn_cast<SelectInst>(V))
    return isKnownToBeAPowerOfTwo(SI->getTrueValue(), OrZero, Depth, Q) &&
           isKnownToBeAPowerOfTwo(SI->getFalseValue(), OrZero, Depth, Q);
 
  // Peek through min/max.
  if (match(V, m_MaxOrMin(m_Value(X), m_Value(Y)))) {
    return isKnownToBeAPowerOfTwo(X, OrZero, Depth, Q) &&
           isKnownToBeAPowerOfTwo(Y, OrZero, Depth, Q);
  }
 
  if (OrZero && match(V, m_And(m_Value(X), m_Value(Y)))) {
    // A power of two and'd with anything is a power of two or zero.
    if (isKnownToBeAPowerOfTwo(X, /*OrZero*/ true, Depth, Q) ||
        isKnownToBeAPowerOfTwo(Y, /*OrZero*/ true, Depth, Q))
      return true;
    // X & (-X) is always a power of two or zero.
    if (match(X, m_Neg(m_Specific(Y))) || match(Y, m_Neg(m_Specific(X))))
      return true;
    return false;
  }
 
  // Adding a power-of-two or zero to the same power-of-two or zero yields
  // either the original power-of-two, a larger power-of-two or zero.
  if (match(V, m_Add(m_Value(X), m_Value(Y)))) {
    const OverflowingBinaryOperator *VOBO = cast<OverflowingBinaryOperator>(V);
    if (OrZero || Q.IIQ.hasNoUnsignedWrap(VOBO) ||
        Q.IIQ.hasNoSignedWrap(VOBO)) {
      if (match(X, m_And(m_Specific(Y), m_Value())) ||
          match(X, m_And(m_Value(), m_Specific(Y))))
        if (isKnownToBeAPowerOfTwo(Y, OrZero, Depth, Q))
          return true;
      if (match(Y, m_And(m_Specific(X), m_Value())) ||
          match(Y, m_And(m_Value(), m_Specific(X))))
        if (isKnownToBeAPowerOfTwo(X, OrZero, Depth, Q))
          return true;
 
      unsigned BitWidth = V->getType()->getScalarSizeInBits();
      KnownBits LHSBits(BitWidth);
      computeKnownBits(X, LHSBits, Depth, Q);
 
      KnownBits RHSBits(BitWidth);
      computeKnownBits(Y, RHSBits, Depth, Q);
      // If i8 V is a power of two or zero:
      //  ZeroBits: 1 1 1 0 1 1 1 1
      // ~ZeroBits: 0 0 0 1 0 0 0 0
      if ((~(LHSBits.Zero & RHSBits.Zero)).isPowerOf2())
        // If OrZero isn't set, we cannot give back a zero result.
        // Make sure either the LHS or RHS has a bit set.
        if (OrZero || RHSBits.One.getBoolValue() || LHSBits.One.getBoolValue())
          return true;
    }
  }
 
  // An exact divide or right shift can only shift off zero bits, so the result
  // is a power of two only if the first operand is a power of two and not
  // copying a sign bit (sdiv int_min, 2).
  if (match(V, m_Exact(m_LShr(m_Value(), m_Value()))) ||
      match(V, m_Exact(m_UDiv(m_Value(), m_Value())))) {
    return isKnownToBeAPowerOfTwo(cast<Operator>(V)->getOperand(0), OrZero,
                                  Depth, Q);
  }
 
  return false;
}
 
/// Test whether a GEP's result is known to be non-null.
///
/// Uses properties inherent in a GEP to try to determine whether it is known
/// to be non-null.
///
/// Currently this routine does not support vector GEPs.
static bool isGEPKnownNonNull(const GEPOperator *GEP, unsigned Depth,
                              const Query &Q) {
  const Function *F = nullptr;
  if (const Instruction *I = dyn_cast<Instruction>(GEP))
    F = I->getFunction();
 
  if (!GEP->isInBounds() ||
      NullPointerIsDefined(F, GEP->getPointerAddressSpace()))
    return false;
 
  // FIXME: Support vector-GEPs.
  assert(GEP->getType()->isPointerTy() && "We only support plain pointer GEP");
 
  // If the base pointer is non-null, we cannot walk to a null address with an
  // inbounds GEP in address space zero.
  if (isKnownNonZero(GEP->getPointerOperand(), Depth, Q))
    return true;
 
  // Walk the GEP operands and see if any operand introduces a non-zero offset.
  // If so, then the GEP cannot produce a null pointer, as doing so would
  // inherently violate the inbounds contract within address space zero.
  for (gep_type_iterator GTI = gep_type_begin(GEP), GTE = gep_type_end(GEP);
       GTI != GTE; ++GTI) {
    // Struct types are easy -- they must always be indexed by a constant.
    if (StructType *STy = GTI.getStructTypeOrNull()) {
      ConstantInt *OpC = cast<ConstantInt>(GTI.getOperand());
      unsigned ElementIdx = OpC->getZExtValue();
      const StructLayout *SL = Q.DL.getStructLayout(STy);
      uint64_t ElementOffset = SL->getElementOffset(ElementIdx);
      if (ElementOffset > 0)
        return true;
      continue;
    }
 
    // If we have a zero-sized type, the index doesn't matter. Keep looping.
    if (Q.DL.getTypeAllocSize(GTI.getIndexedType()).getKnownMinSize() == 0)
      continue;
 
    // Fast path the constant operand case both for efficiency and so we don't
    // increment Depth when just zipping down an all-constant GEP.
    if (ConstantInt *OpC = dyn_cast<ConstantInt>(GTI.getOperand())) {
      if (!OpC->isZero())
        return true;
      continue;
    }
 
    // We post-increment Depth here because while isKnownNonZero increments it
    // as well, when we pop back up that increment won't persist. We don't want
    // to recurse 10k times just because we have 10k GEP operands. We don't
    // bail completely out because we want to handle constant GEPs regardless
    // of depth.
    if (Depth++ >= MaxAnalysisRecursionDepth)
      continue;
 
    if (isKnownNonZero(GTI.getOperand(), Depth, Q))
      return true;
  }
 
  return false;
}
 
static bool isKnownNonNullFromDominatingCondition(const Value *V,
                                                  const Instruction *CtxI,
                                                  const DominatorTree *DT) {
  if (isa<Constant>(V))
    return false;
 
  if (!CtxI || !DT)
    return false;
 
  unsigned NumUsesExplored = 0;
  for (auto *U : V->users()) {
    // Avoid massive lists
    if (NumUsesExplored >= DomConditionsMaxUses)
      break;
    NumUsesExplored++;
 
    // If the value is used as an argument to a call or invoke, then argument
    // attributes may provide an answer about null-ness.
    if (const auto *CB = dyn_cast<CallBase>(U))
      if (auto *CalledFunc = CB->getCalledFunction())
        for (const Argument &Arg : CalledFunc->args())
          if (CB->getArgOperand(Arg.getArgNo()) == V &&
              Arg.hasNonNullAttr(/* AllowUndefOrPoison */ false) &&
              DT->dominates(CB, CtxI))
            return true;
 
    // If the value is used as a load/store, then the pointer must be non null.
    if (V == getLoadStorePointerOperand(U)) {
      const Instruction *I = cast<Instruction>(U);
      if (!NullPointerIsDefined(I->getFunction(),
                                V->getType()->getPointerAddressSpace()) &&
          DT->dominates(I, CtxI))
        return true;
    }
 
    // Consider only compare instructions uniquely controlling a branch
    Value *RHS;
    CmpInst::Predicate Pred;
    if (!match(U, m_c_ICmp(Pred, m_Specific(V), m_Value(RHS))))
      continue;
 
    bool NonNullIfTrue;
    if (cmpExcludesZero(Pred, RHS))
      NonNullIfTrue = true;
    else if (cmpExcludesZero(CmpInst::getInversePredicate(Pred), RHS))
      NonNullIfTrue = false;
    else
      continue;
 
    SmallVector<const User *, 4> WorkList;
    SmallPtrSet<const User *, 4> Visited;
    for (auto *CmpU : U->users()) {
      assert(WorkList.empty() && "Should be!");
      if (Visited.insert(CmpU).second)
        WorkList.push_back(CmpU);
 
      while (!WorkList.empty()) {
        auto *Curr = WorkList.pop_back_val();
 
        // If a user is an AND, add all its users to the work list. We only
        // propagate "pred != null" condition through AND because it is only
        // correct to assume that all conditions of AND are met in true branch.
        // TODO: Support similar logic of OR and EQ predicate?
        if (NonNullIfTrue)
          if (match(Curr, m_LogicalAnd(m_Value(), m_Value()))) {
            for (auto *CurrU : Curr->users())
              if (Visited.insert(CurrU).second)
                WorkList.push_back(CurrU);
            continue;
          }
 
        if (const BranchInst *BI = dyn_cast<BranchInst>(Curr)) {
          assert(BI->isConditional() && "uses a comparison!");
 
          BasicBlock *NonNullSuccessor =
              BI->getSuccessor(NonNullIfTrue ? 0 : 1);
          BasicBlockEdge Edge(BI->getParent(), NonNullSuccessor);
          if (Edge.isSingleEdge() && DT->dominates(Edge, CtxI->getParent()))
            return true;
        } else if (NonNullIfTrue && isGuard(Curr) &&
                   DT->dominates(cast<Instruction>(Curr), CtxI)) {
          return true;
        }
      }
    }
  }
 
  return false;
}
 
/// Does the 'Range' metadata (which must be a valid MD_range operand list)
/// ensure that the value it's attached to is never Value?  'RangeType' is
/// is the type of the value described by the range.
static bool rangeMetadataExcludesValue(const MDNode* Ranges, const APInt& Value) {
  const unsigned NumRanges = Ranges->getNumOperands() / 2;
  assert(NumRanges >= 1);
  for (unsigned i = 0; i < NumRanges; ++i) {
    ConstantInt *Lower =
        mdconst::extract<ConstantInt>(Ranges->getOperand(2 * i + 0));
    ConstantInt *Upper =
        mdconst::extract<ConstantInt>(Ranges->getOperand(2 * i + 1));
    ConstantRange Range(Lower->getValue(), Upper->getValue());
    if (Range.contains(Value))
      return false;
  }
  return true;
}
 
/// Try to detect a recurrence that monotonically increases/decreases from a
/// non-zero starting value. These are common as induction variables.
static bool isNonZeroRecurrence(const PHINode *PN) {
  BinaryOperator *BO = nullptr;
  Value *Start = nullptr, *Step = nullptr;
  const APInt *StartC, *StepC;
  if (!matchSimpleRecurrence(PN, BO, Start, Step) ||
      !match(Start, m_APInt(StartC)) || StartC->isZero())
    return false;
 
  switch (BO->getOpcode()) {
  case Instruction::Add:
    // Starting from non-zero and stepping away from zero can never wrap back
    // to zero.
    return BO->hasNoUnsignedWrap() ||
           (BO->hasNoSignedWrap() && match(Step, m_APInt(StepC)) &&
            StartC->isNegative() == StepC->isNegative());
  case Instruction::Mul:
    return (BO->hasNoUnsignedWrap() || BO->hasNoSignedWrap()) &&
           match(Step, m_APInt(StepC)) && !StepC->isZero();
  case Instruction::Shl:
    return BO->hasNoUnsignedWrap() || BO->hasNoSignedWrap();
  case Instruction::AShr:
  case Instruction::LShr:
    return BO->isExact();
  default:
    return false;
  }
}
 
/// Return true if the given value is known to be non-zero when defined. For
/// vectors, return true if every demanded 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 APInt &DemandedElts, unsigned Depth,
                    const Query &Q) {
  // FIXME: We currently have no way to represent the DemandedElts of a scalable
  // vector
  if (isa<ScalableVectorType>(V->getType()))
    return false;
 
  if (auto *C = dyn_cast<Constant>(V)) {
    if (C->isNullValue())
      return false;
    if (isa<ConstantInt>(C))
      // Must be non-zero due to null test above.
      return true;
 
    if (auto *CE = dyn_cast<ConstantExpr>(C)) {
      // See the comment for IntToPtr/PtrToInt instructions below.
      if (CE->getOpcode() == Instruction::IntToPtr ||
          CE->getOpcode() == Instruction::PtrToInt)
        if (Q.DL.getTypeSizeInBits(CE->getOperand(0)->getType())
                .getFixedSize() <=
            Q.DL.getTypeSizeInBits(CE->getType()).getFixedSize())
          return isKnownNonZero(CE->getOperand(0), Depth, Q);
    }
 
    // For constant vectors, check that all elements are undefined or known
    // non-zero to determine that the whole vector is known non-zero.
    if (auto *VecTy = dyn_cast<FixedVectorType>(C->getType())) {
      for (unsigned i = 0, e = VecTy->getNumElements(); i != e; ++i) {
        if (!DemandedElts[i])
          continue;
        Constant *Elt = C->getAggregateElement(i);
        if (!Elt || Elt->isNullValue())
          return false;
        if (!isa<UndefValue>(Elt) && !isa<ConstantInt>(Elt))
          return false;
      }
      return true;
    }
 
    // A global variable in address space 0 is non null unless extern weak
    // or an absolute symbol reference. Other address spaces may have null as a
    // valid address for a global, so we can't assume anything.
    if (const GlobalValue *GV = dyn_cast<GlobalValue>(V)) {
      if (!GV->isAbsoluteSymbolRef() && !GV->hasExternalWeakLinkage() &&
          GV->getType()->getAddressSpace() == 0)
        return true;
    } else
      return false;
  }
 
  if (auto *I = dyn_cast<Instruction>(V)) {
    if (MDNode *Ranges = Q.IIQ.getMetadata(I, LLVMContext::MD_range)) {
      // If the possible ranges don't contain zero, then the value is
      // definitely non-zero.
      if (auto *Ty = dyn_cast<IntegerType>(V->getType())) {
        const APInt ZeroValue(Ty->getBitWidth(), 0);
        if (rangeMetadataExcludesValue(Ranges, ZeroValue))
          return true;
      }
    }
  }
 
  if (isKnownNonZeroFromAssume(V, Q))
    return true;
 
  // Some of the tests below are recursive, so bail out if we hit the limit.
  if (Depth++ >= MaxAnalysisRecursionDepth)
    return false;
 
  // Check for pointer simplifications.
 
  if (PointerType *PtrTy = dyn_cast<PointerType>(V->getType())) {
    // Alloca never returns null, malloc might.
    if (isa<AllocaInst>(V) && Q.DL.getAllocaAddrSpace() == 0)
      return true;
 
    // A byval, inalloca may not be null in a non-default addres space. A
    // nonnull argument is assumed never 0.
    if (const Argument *A = dyn_cast<Argument>(V)) {
      if (((A->hasPassPointeeByValueCopyAttr() &&
            !NullPointerIsDefined(A->getParent(), PtrTy->getAddressSpace())) ||
           A->hasNonNullAttr()))
        return true;
    }
 
    // A Load tagged with nonnull metadata is never null.
    if (const LoadInst *LI = dyn_cast<LoadInst>(V))
      if (Q.IIQ.getMetadata(LI, LLVMContext::MD_nonnull))
        return true;
 
    if (const auto *Call = dyn_cast<CallBase>(V)) {
      if (Call->isReturnNonNull())
        return true;
      if (const auto *RP = getArgumentAliasingToReturnedPointer(Call, true))
        return isKnownNonZero(RP, Depth, Q);
    }
  }
 
  if (isKnownNonNullFromDominatingCondition(V, Q.CxtI, Q.DT))
    return true;
 
  // Check for recursive pointer simplifications.
  if (V->getType()->isPointerTy()) {
    // Look through bitcast operations, GEPs, and int2ptr instructions as they
    // do not alter the value, or at least not the nullness property of the
    // value, e.g., int2ptr is allowed to zero/sign extend the value.
    //
    // Note that we have to take special care to avoid looking through
    // truncating casts, e.g., int2ptr/ptr2int with appropriate sizes, as well
    // as casts that can alter the value, e.g., AddrSpaceCasts.
    if (const GEPOperator *GEP = dyn_cast<GEPOperator>(V))
      return isGEPKnownNonNull(GEP, Depth, Q);
 
    if (auto *BCO = dyn_cast<BitCastOperator>(V))
      return isKnownNonZero(BCO->getOperand(0), Depth, Q);
 
    if (auto *I2P = dyn_cast<IntToPtrInst>(V))
      if (Q.DL.getTypeSizeInBits(I2P->getSrcTy()).getFixedSize() <=
          Q.DL.getTypeSizeInBits(I2P->getDestTy()).getFixedSize())
        return isKnownNonZero(I2P->getOperand(0), Depth, Q);
  }
 
  // Similar to int2ptr above, we can look through ptr2int here if the cast
  // is a no-op or an extend and not a truncate.
  if (auto *P2I = dyn_cast<PtrToIntInst>(V))
    if (Q.DL.getTypeSizeInBits(P2I->getSrcTy()).getFixedSize() <=
        Q.DL.getTypeSizeInBits(P2I->getDestTy()).getFixedSize())
      return isKnownNonZero(P2I->getOperand(0), Depth, Q);
 
  unsigned BitWidth = getBitWidth(V->getType()->getScalarType(), Q.DL);
 
  // X | Y != 0 if X != 0 or Y != 0.
  Value *X = nullptr, *Y = nullptr;
  if (match(V, m_Or(m_Value(X), m_Value(Y))))
    return isKnownNonZero(X, DemandedElts, Depth, Q) ||
           isKnownNonZero(Y, DemandedElts, Depth, Q);
 
  // ext X != 0 if X != 0.
  if (isa<SExtInst>(V) || isa<ZExtInst>(V))
    return isKnownNonZero(cast<Instruction>(V)->getOperand(0), Depth, Q);
 
  // shl X, Y != 0 if X is odd.  Note that the value of the shift is undefined
  // if the lowest bit is shifted off the end.
  if (match(V, m_Shl(m_Value(X), m_Value(Y)))) {
    // shl nuw can't remove any non-zero bits.
    const OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
    if (Q.IIQ.hasNoUnsignedWrap(BO))
      return isKnownNonZero(X, Depth, Q);
 
    KnownBits Known(BitWidth);
    computeKnownBits(X, DemandedElts, Known, Depth, Q);
    if (Known.One[0])
      return true;
  }
  // shr X, Y != 0 if X is negative.  Note that the value of the shift is not
  // defined if the sign bit is shifted off the end.
  else if (match(V, m_Shr(m_Value(X), m_Value(Y)))) {
    // shr exact can only shift out zero bits.
    const PossiblyExactOperator *BO = cast<PossiblyExactOperator>(V);
    if (BO->isExact())
      return isKnownNonZero(X, Depth, Q);
 
    KnownBits Known = computeKnownBits(X, DemandedElts, Depth, Q);
    if (Known.isNegative())
      return true;
 
    // If the shifter operand is a constant, and all of the bits shifted
    // out are known to be zero, and X is known non-zero then at least one
    // non-zero bit must remain.
    if (ConstantInt *Shift = dyn_cast<ConstantInt>(Y)) {
      auto ShiftVal = Shift->getLimitedValue(BitWidth - 1);
      // Is there a known one in the portion not shifted out?
      if (Known.countMaxLeadingZeros() < BitWidth - ShiftVal)
        return true;
      // Are all the bits to be shifted out known zero?
      if (Known.countMinTrailingZeros() >= ShiftVal)
        return isKnownNonZero(X, DemandedElts, Depth, Q);
    }
  }
  // div exact can only produce a zero if the dividend is zero.
  else if (match(V, m_Exact(m_IDiv(m_Value(X), m_Value())))) {
    return isKnownNonZero(X, DemandedElts, Depth, Q);
  }
  // X + Y.
  else if (match(V, m_Add(m_Value(X), m_Value(Y)))) {
    KnownBits XKnown = computeKnownBits(X, DemandedElts, Depth, Q);
    KnownBits YKnown = computeKnownBits(Y, DemandedElts, Depth, Q);
 
    // If X and Y are both non-negative (as signed values) then their sum is not
    // zero unless both X and Y are zero.
    if (XKnown.isNonNegative() && YKnown.isNonNegative())
      if (isKnownNonZero(X, DemandedElts, Depth, Q) ||
          isKnownNonZero(Y, DemandedElts, Depth, Q))
        return true;
 
    // If X and Y are both negative (as signed values) then their sum is not
    // zero unless both X and Y equal INT_MIN.
    if (XKnown.isNegative() && YKnown.isNegative()) {
      APInt Mask = APInt::getSignedMaxValue(BitWidth);
      // The sign bit of X is set.  If some other bit is set then X is not equal
      // to INT_MIN.
      if (XKnown.One.intersects(Mask))
        return true;
      // The sign bit of Y is set.  If some other bit is set then Y is not equal
      // to INT_MIN.
      if (YKnown.One.intersects(Mask))
        return true;
    }
 
    // The sum of a non-negative number and a power of two is not zero.
    if (XKnown.isNonNegative() &&
        isKnownToBeAPowerOfTwo(Y, /*OrZero*/ false, Depth, Q))
      return true;
    if (YKnown.isNonNegative() &&
        isKnownToBeAPowerOfTwo(X, /*OrZero*/ false, Depth, Q))
      return true;
  }
  // X * Y.
  else if (match(V, m_Mul(m_Value(X), m_Value(Y)))) {
    const OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
    // If X and Y are non-zero then so is X * Y as long as the multiplication
    // does not overflow.
    if ((Q.IIQ.hasNoSignedWrap(BO) || Q.IIQ.hasNoUnsignedWrap(BO)) &&
        isKnownNonZero(X, DemandedElts, Depth, Q) &&
        isKnownNonZero(Y, DemandedElts, Depth, Q))
      return true;
  }
  // (C ? X : Y) != 0 if X != 0 and Y != 0.
  else if (const SelectInst *SI = dyn_cast<SelectInst>(V)) {
    if (isKnownNonZero(SI->getTrueValue(), DemandedElts, Depth, Q) &&
        isKnownNonZero(SI->getFalseValue(), DemandedElts, Depth, Q))
      return true;
  }
  // PHI
  else if (const PHINode *PN = dyn_cast<PHINode>(V)) {
    if (Q.IIQ.UseInstrInfo && isNonZeroRecurrence(PN))
      return true;
 
    // Check if all incoming values are non-zero using recursion.
    Query RecQ = Q;
    unsigned NewDepth = std::max(Depth, MaxAnalysisRecursionDepth - 1);
    return llvm::all_of(PN->operands(), [&](const Use &U) {
      if (U.get() == PN)
        return true;
      RecQ.CxtI = PN->getIncomingBlock(U)->getTerminator();
      return isKnownNonZero(U.get(), DemandedElts, NewDepth, RecQ);
    });
  }
  // ExtractElement
  else if (const auto *EEI = dyn_cast<ExtractElementInst>(V)) {
    const Value *Vec = EEI->getVectorOperand();
    const Value *Idx = EEI->getIndexOperand();
    auto *CIdx = dyn_cast<ConstantInt>(Idx);
    if (auto *VecTy = dyn_cast<FixedVectorType>(Vec->getType())) {
      unsigned NumElts = VecTy->getNumElements();
      APInt DemandedVecElts = APInt::getAllOnes(NumElts);
      if (CIdx && CIdx->getValue().ult(NumElts))
        DemandedVecElts = APInt::getOneBitSet(NumElts, CIdx->getZExtValue());
      return isKnownNonZero(Vec, DemandedVecElts, Depth, Q);
    }
  }
  // Freeze
  else if (const FreezeInst *FI = dyn_cast<FreezeInst>(V)) {
    auto *Op = FI->getOperand(0);
    if (isKnownNonZero(Op, Depth, Q) &&
        isGuaranteedNotToBePoison(Op, Q.AC, Q.CxtI, Q.DT, Depth))
      return true;
  }
 
  KnownBits Known(BitWidth);
  computeKnownBits(V, DemandedElts, Known, Depth, Q);
  return Known.One != 0;
}
 
bool isKnownNonZero(const Value* V, unsigned Depth, const Query& Q) {
  // FIXME: We currently have no way to represent the DemandedElts of a scalable
  // vector
  if (isa<ScalableVectorType>(V->getType()))
    return false;
 
  auto *FVTy = dyn_cast<FixedVectorType>(V->getType());
  APInt DemandedElts =
      FVTy ? APInt::getAllOnes(FVTy->getNumElements()) : APInt(1, 1);
  return isKnownNonZero(V, DemandedElts, Depth, Q);
}
 
/// If the pair of operators are the same invertible function, return the
/// the operands of the function corresponding to each input. Otherwise,
/// return None.  An invertible function is one that is 1-to-1 and maps
/// every input value to exactly one output value.  This is equivalent to
/// saying that Op1 and Op2 are equal exactly when the specified pair of
/// operands are equal, (except that Op1 and Op2 may be poison more often.)
static Optional<std::pair<Value*, Value*>>
getInvertibleOperands(const Operator *Op1,
                      const Operator *Op2) {
  if (Op1->getOpcode() != Op2->getOpcode())
    return None;
 
  auto getOperands = [&](unsigned OpNum) -> auto {
    return std::make_pair(Op1->getOperand(OpNum), Op2->getOperand(OpNum));
  };
 
  switch (Op1->getOpcode()) {
  default:
    break;
  case Instruction::Add:
  case Instruction::Sub:
    if (Op1->getOperand(0) == Op2->getOperand(0))
      return getOperands(1);
    if (Op1->getOperand(1) == Op2->getOperand(1))
      return getOperands(0);
    break;
  case Instruction::Mul: {
    // invertible if A * B == (A * B) mod 2^N where A, and B are integers
    // and N is the bitwdith.  The nsw case is non-obvious, but proven by
    // alive2: https://alive2.llvm.org/ce/z/Z6D5qK
    auto *OBO1 = cast<OverflowingBinaryOperator>(Op1);
    auto *OBO2 = cast<OverflowingBinaryOperator>(Op2);
    if ((!OBO1->hasNoUnsignedWrap() || !OBO2->hasNoUnsignedWrap()) &&
        (!OBO1->hasNoSignedWrap() || !OBO2->hasNoSignedWrap()))
      break;
 
    // Assume operand order has been canonicalized
    if (Op1->getOperand(1) == Op2->getOperand(1) &&
        isa<ConstantInt>(Op1->getOperand(1)) &&
        !cast<ConstantInt>(Op1->getOperand(1))->isZero())
      return getOperands(0);
    break;
  }
  case Instruction::Shl: {
    // Same as multiplies, with the difference that we don't need to check
    // for a non-zero multiply. Shifts always multiply by non-zero.
    auto *OBO1 = cast<OverflowingBinaryOperator>(Op1);
    auto *OBO2 = cast<OverflowingBinaryOperator>(Op2);
    if ((!OBO1->hasNoUnsignedWrap() || !OBO2->hasNoUnsignedWrap()) &&
        (!OBO1->hasNoSignedWrap() || !OBO2->hasNoSignedWrap()))
      break;
 
    if (Op1->getOperand(1) == Op2->getOperand(1))
      return getOperands(0);
    break;
  }
  case Instruction::AShr:
  case Instruction::LShr: {
    auto *PEO1 = cast<PossiblyExactOperator>(Op1);
    auto *PEO2 = cast<PossiblyExactOperator>(Op2);
    if (!PEO1->isExact() || !PEO2->isExact())
      break;
 
    if (Op1->getOperand(1) == Op2->getOperand(1))
      return getOperands(0);
    break;
  }
  case Instruction::SExt:
  case Instruction::ZExt:
    if (Op1->getOperand(0)->getType() == Op2->getOperand(0)->getType())
      return getOperands(0);
    break;
  case Instruction::PHI: {
    const PHINode *PN1 = cast<PHINode>(Op1);
    const PHINode *PN2 = cast<PHINode>(Op2);
 
    // If PN1 and PN2 are both recurrences, can we prove the entire recurrences
    // are a single invertible function of the start values? Note that repeated
    // application of an invertible function is also invertible
    BinaryOperator *BO1 = nullptr;
    Value *Start1 = nullptr, *Step1 = nullptr;
    BinaryOperator *BO2 = nullptr;
    Value *Start2 = nullptr, *Step2 = nullptr;
    if (PN1->getParent() != PN2->getParent() ||
        !matchSimpleRecurrence(PN1, BO1, Start1, Step1) ||
        !matchSimpleRecurrence(PN2, BO2, Start2, Step2))
      break;
 
    auto Values = getInvertibleOperands(cast<Operator>(BO1),
                                        cast<Operator>(BO2));
    if (!Values)
       break;
 
    // We have to be careful of mutually defined recurrences here.  Ex:
    // * X_i = X_(i-1) OP Y_(i-1), and Y_i = X_(i-1) OP V
    // * X_i = Y_i = X_(i-1) OP Y_(i-1)
    // The invertibility of these is complicated, and not worth reasoning
    // about (yet?).
    if (Values->first != PN1 || Values->second != PN2)
      break;
 
    return std::make_pair(Start1, Start2);
  }
  }
  return None;
}
 
/// Return true if V2 == V1 + X, where X is known non-zero.
static bool isAddOfNonZero(const Value *V1, const Value *V2, unsigned Depth,
                           const Query &Q) {
  const BinaryOperator *BO = dyn_cast<BinaryOperator>(V1);
  if (!BO || BO->getOpcode() != Instruction::Add)
    return false;
  Value *Op = nullptr;
  if (V2 == BO->getOperand(0))
    Op = BO->getOperand(1);
  else if (V2 == BO->getOperand(1))
    Op = BO->getOperand(0);
  else
    return false;
  return isKnownNonZero(Op, Depth + 1, Q);
}
 
/// Return true if V2 == V1 * C, where V1 is known non-zero, C is not 0/1 and
/// the multiplication is nuw or nsw.
static bool isNonEqualMul(const Value *V1, const Value *V2, unsigned Depth,
                          const Query &Q) {
  if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(V2)) {
    const APInt *C;
    return match(OBO, m_Mul(m_Specific(V1), m_APInt(C))) &&
           (OBO->hasNoUnsignedWrap() || OBO->hasNoSignedWrap()) &&
           !C->isZero() && !C->isOne() && isKnownNonZero(V1, Depth + 1, Q);
  }
  return false;
}
 
/// Return true if V2 == V1 << C, where V1 is known non-zero, C is not 0 and
/// the shift is nuw or nsw.
static bool isNonEqualShl(const Value *V1, const Value *V2, unsigned Depth,
                          const Query &Q) {
  if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(V2)) {
    const APInt *C;
    return match(OBO, m_Shl(m_Specific(V1), m_APInt(C))) &&
           (OBO->hasNoUnsignedWrap() || OBO->hasNoSignedWrap()) &&
           !C->isZero() && isKnownNonZero(V1, Depth + 1, Q);
  }
  return false;
}
 
static bool isNonEqualPHIs(const PHINode *PN1, const PHINode *PN2,
                           unsigned Depth, const Query &Q) {
  // Check two PHIs are in same block.
  if (PN1->getParent() != PN2->getParent())
    return false;
 
  SmallPtrSet<const BasicBlock *, 8> VisitedBBs;
  bool UsedFullRecursion = false;
  for (const BasicBlock *IncomBB : PN1->blocks()) {
    if (!VisitedBBs.insert(IncomBB).second)
      continue; // Don't reprocess blocks that we have dealt with already.
    const Value *IV1 = PN1->getIncomingValueForBlock(IncomBB);
    const Value *IV2 = PN2->getIncomingValueForBlock(IncomBB);
    const APInt *C1, *C2;
    if (match(IV1, m_APInt(C1)) && match(IV2, m_APInt(C2)) && *C1 != *C2)
      continue;
 
    // Only one pair of phi operands is allowed for full recursion.
    if (UsedFullRecursion)
      return false;
 
    Query RecQ = Q;
    RecQ.CxtI = IncomBB->getTerminator();
    if (!isKnownNonEqual(IV1, IV2, Depth + 1, RecQ))
      return false;
    UsedFullRecursion = true;
  }
  return true;
}
 
/// Return true if it is known that V1 != V2.
static bool isKnownNonEqual(const Value *V1, const Value *V2, unsigned Depth,
                            const Query &Q) {
  if (V1 == V2)
    return false;
  if (V1->getType() != V2->getType())
    // We can't look through casts yet.
    return false;
 
  if (Depth >= MaxAnalysisRecursionDepth)
    return false;
 
  // See if we can recurse through (exactly one of) our operands.  This
  // requires our operation be 1-to-1 and map every input value to exactly
  // one output value.  Such an operation is invertible.
  auto *O1 = dyn_cast<Operator>(V1);
  auto *O2 = dyn_cast<Operator>(V2);
  if (O1 && O2 && O1->getOpcode() == O2->getOpcode()) {
    if (auto Values = getInvertibleOperands(O1, O2))
      return isKnownNonEqual(Values->first, Values->second, Depth + 1, Q);
 
    if (const PHINode *PN1 = dyn_cast<PHINode>(V1)) {
      const PHINode *PN2 = cast<PHINode>(V2);
      // FIXME: This is missing a generalization to handle the case where one is
      // a PHI and another one isn't.
      if (isNonEqualPHIs(PN1, PN2, Depth, Q))
        return true;
    };
  }
 
  if (isAddOfNonZero(V1, V2, Depth, Q) || isAddOfNonZero(V2, V1, Depth, Q))
    return true;
 
  if (isNonEqualMul(V1, V2, Depth, Q) || isNonEqualMul(V2, V1, Depth, Q))
    return true;
 
  if (isNonEqualShl(V1, V2, Depth, Q) || isNonEqualShl(V2, V1, Depth, Q))
    return true;
 
  if (V1->getType()->isIntOrIntVectorTy()) {
    // Are any known bits in V1 contradictory to known bits in V2? If V1
    // has a known zero where V2 has a known one, they must not be equal.
    KnownBits Known1 = computeKnownBits(V1, Depth, Q);
    KnownBits Known2 = computeKnownBits(V2, Depth, Q);
 
    if (Known1.Zero.intersects(Known2.One) ||
        Known2.Zero.intersects(Known1.One))
      return true;
  }
  return false;
}
 
/// 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, unsigned Depth,
                       const Query &Q) {
  KnownBits Known(Mask.getBitWidth());
  computeKnownBits(V, Known, Depth, Q);
  return Mask.isSubsetOf(Known.Zero);
}
 
// Match a signed min+max clamp pattern like smax(smin(In, CHigh), CLow).
// Returns the input and lower/upper bounds.
static bool isSignedMinMaxClamp(const Value *Select, const Value *&In,
                                const APInt *&CLow, const APInt *&CHigh) {
  assert(isa<Operator>(Select) &&
         cast<Operator>(Select)->getOpcode() == Instruction::Select &&
         "Input should be a Select!");
 
  const Value *LHS = nullptr, *RHS = nullptr;
  SelectPatternFlavor SPF = matchSelectPattern(Select, LHS, RHS).Flavor;
  if (SPF != SPF_SMAX && SPF != SPF_SMIN)
    return false;
 
  if (!match(RHS, m_APInt(CLow)))
    return false;
 
  const Value *LHS2 = nullptr, *RHS2 = nullptr;
  SelectPatternFlavor SPF2 = matchSelectPattern(LHS, LHS2, RHS2).Flavor;
  if (getInverseMinMaxFlavor(SPF) != SPF2)
    return false;
 
  if (!match(RHS2, m_APInt(CHigh)))
    return false;
 
  if (SPF == SPF_SMIN)
    std::swap(CLow, CHigh);
 
  In = LHS2;
  return CLow->sle(*CHigh);
}
 
/// For vector constants, loop over the elements and find the constant with the
/// minimum number of sign bits. Return 0 if the value is not a vector constant
/// or if any element was not analyzed; otherwise, return the count for the
/// element with the minimum number of sign bits.
static unsigned computeNumSignBitsVectorConstant(const Value *V,
                                                 const APInt &DemandedElts,
                                                 unsigned TyBits) {
  const auto *CV = dyn_cast<Constant>(V);
  if (!CV || !isa<FixedVectorType>(CV->getType()))
    return 0;
 
  unsigned MinSignBits = TyBits;
  unsigned NumElts = cast<FixedVectorType>(CV->getType())->getNumElements();
  for (unsigned i = 0; i != NumElts; ++i) {
    if (!DemandedElts[i])
      continue;
    // If we find a non-ConstantInt, bail out.
    auto *Elt = dyn_cast_or_null<ConstantInt>(CV->getAggregateElement(i));
    if (!Elt)
      return 0;
 
    MinSignBits = std::min(MinSignBits, Elt->getValue().getNumSignBits());
  }
 
  return MinSignBits;
}
 
static unsigned ComputeNumSignBitsImpl(const Value *V,
                                       const APInt &DemandedElts,
                                       unsigned Depth, const Query &Q);
 
static unsigned ComputeNumSignBits(const Value *V, const APInt &DemandedElts,
                                   unsigned Depth, const Query &Q) {
  unsigned Result = ComputeNumSignBitsImpl(V, DemandedElts, Depth, Q);
  assert(Result > 0 && "At least one sign bit needs to be present!");
  return Result;
}
 
/// 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 minimum number of known sign bits of the demanded
/// elements in the vector specified by DemandedElts.
static unsigned ComputeNumSignBitsImpl(const Value *V,
                                       const APInt &DemandedElts,
                                       unsigned Depth, const Query &Q) {
  Type *Ty = V->getType();
 
  // FIXME: We currently have no way to represent the DemandedElts of a scalable
  // vector
  if (isa<ScalableVectorType>(Ty))
    return 1;
 
#ifndef NDEBUG
  assert(Depth <= MaxAnalysisRecursionDepth && "Limit Search Depth");
 
  if (auto *FVTy = dyn_cast<FixedVectorType>(Ty)) {
    assert(
        FVTy->getNumElements() == DemandedElts.getBitWidth() &&
        "DemandedElt width should equal the fixed vector number of elements");
  } else {
    assert(DemandedElts == APInt(1, 1) &&
           "DemandedElt width should be 1 for scalars");
  }
#endif
 
  // We return the minimum number of sign bits that are guaranteed to be present
  // in V, so for undef we have to conservatively return 1.  We don't have the
  // same behavior for poison though -- that's a FIXME today.
 
  Type *ScalarTy = Ty->getScalarType();
  unsigned TyBits = ScalarTy->isPointerTy() ?
    Q.DL.getPointerTypeSizeInBits(ScalarTy) :
    Q.DL.getTypeSizeInBits(ScalarTy);
 
  unsigned Tmp, Tmp2;
  unsigned FirstAnswer = 1;
 
  // Note that ConstantInt is handled by the general computeKnownBits case
  // below.
 
  if (Depth == MaxAnalysisRecursionDepth)
    return 1;
 
  if (auto *U = dyn_cast<Operator>(V)) {
    switch (Operator::getOpcode(V)) {
    default: break;
    case Instruction::SExt:
      Tmp = TyBits - U->getOperand(0)->getType()->getScalarSizeInBits();
      return ComputeNumSignBits(U->getOperand(0), Depth + 1, Q) + Tmp;
 
    case Instruction::SDiv: {
      const APInt *Denominator;
      // sdiv X, C -> adds log(C) sign bits.
      if (match(U->getOperand(1), m_APInt(Denominator))) {
 
        // Ignore non-positive denominator.
        if (!Denominator->isStrictlyPositive())
          break;
 
        // Calculate the incoming numerator bits.
        unsigned NumBits = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
 
        // Add floor(log(C)) bits to the numerator bits.
        return std::min(TyBits, NumBits + Denominator->logBase2());
      }
      break;
    }
 
    case Instruction::SRem: {
      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
 
      const APInt *Denominator;
      // srem X, C -> we know that the result is within [-C+1,C) when C is a
      // positive constant.  This let us put a lower bound on the number of sign
      // bits.
      if (match(U->getOperand(1), m_APInt(Denominator))) {
 
        // Ignore non-positive denominator.
        if (Denominator->isStrictlyPositive()) {
          // Calculate the leading sign bit constraints by examining the
          // denominator.  Given that the denominator is positive, there are two
          // cases:
          //
          //  1. The numerator is positive. The result range is [0,C) and
          //     [0,C) u< (1 << ceilLogBase2(C)).
          //
          //  2. The numerator is negative. Then the result range is (-C,0] and
          //     integers in (-C,0] are either 0 or >u (-1 << ceilLogBase2(C)).
          //
          // Thus a lower bound on the number of sign bits is `TyBits -
          // ceilLogBase2(C)`.
 
          unsigned ResBits = TyBits - Denominator->ceilLogBase2();
          Tmp = std::max(Tmp, ResBits);
        }
      }
      return Tmp;
    }
 
    case Instruction::AShr: {
      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
      // ashr X, C   -> adds C sign bits.  Vectors too.
      const APInt *ShAmt;
      if (match(U->getOperand(1), m_APInt(ShAmt))) {
        if (ShAmt->uge(TyBits))
          break; // Bad shift.
        unsigned ShAmtLimited = ShAmt->getZExtValue();
        Tmp += ShAmtLimited;
        if (Tmp > TyBits) Tmp = TyBits;
      }
      return Tmp;
    }
    case Instruction::Shl: {
      const APInt *ShAmt;
      if (match(U->getOperand(1), m_APInt(ShAmt))) {
        // shl destroys sign bits.
        Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
        if (ShAmt->uge(TyBits) ||   // Bad shift.
            ShAmt->uge(Tmp)) break; // Shifted all sign bits out.
        Tmp2 = ShAmt->getZExtValue();
        return Tmp - Tmp2;
      }
      break;
    }
    case Instruction::And:
    case Instruction::Or:
    case Instruction::Xor: // NOT is handled here.
      // Logical binary ops preserve the number of sign bits at the worst.
      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
      if (Tmp != 1) {
        Tmp2 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
        FirstAnswer = std::min(Tmp, Tmp2);
        // We computed what we know about the sign bits as our first
        // answer. Now proceed to the generic code that uses
        // computeKnownBits, and pick whichever answer is better.
      }
      break;
 
    case Instruction::Select: {
      // If we have a clamp pattern, we know that the number of sign bits will
      // be the minimum of the clamp min/max range.
      const Value *X;
      const APInt *CLow, *CHigh;
      if (isSignedMinMaxClamp(U, X, CLow, CHigh))
        return std::min(CLow->getNumSignBits(), CHigh->getNumSignBits());
 
      Tmp = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
      if (Tmp == 1) break;
      Tmp2 = ComputeNumSignBits(U->getOperand(2), Depth + 1, Q);
      return std::min(Tmp, Tmp2);
    }
 
    case Instruction::Add:
      // Add can have at most one carry bit.  Thus we know that the output
      // is, at worst, one more bit than the inputs.
      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
      if (Tmp == 1) break;
 
      // Special case decrementing a value (ADD X, -1):
      if (const auto *CRHS = dyn_cast<Constant>(U->getOperand(1)))
        if (CRHS->isAllOnesValue()) {
          KnownBits Known(TyBits);
          computeKnownBits(U->getOperand(0), Known, Depth + 1, Q);
 
          // If the input is known to be 0 or 1, the output is 0/-1, which is
          // all sign bits set.
          if ((Known.Zero | 1).isAllOnes())
            return TyBits;
 
          // If we are subtracting one from a positive number, there is no carry
          // out of the result.
          if (Known.isNonNegative())
            return Tmp;
        }
 
      Tmp2 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
      if (Tmp2 == 1) break;
      return std::min(Tmp, Tmp2) - 1;
 
    case Instruction::Sub:
      Tmp2 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
      if (Tmp2 == 1) break;
 
      // Handle NEG.
      if (const auto *CLHS = dyn_cast<Constant>(U->getOperand(0)))
        if (CLHS->isNullValue()) {
          KnownBits Known(TyBits);
          computeKnownBits(U->getOperand(1), Known, Depth + 1, Q);
          // If the input is known to be 0 or 1, the output is 0/-1, which is
          // all sign bits set.
          if ((Known.Zero | 1).isAllOnes())
            return TyBits;
 
          // If the input is known to be positive (the sign bit is known clear),
          // the output of the NEG has the same number of sign bits as the
          // input.
          if (Known.isNonNegative())
            return Tmp2;
 
          // Otherwise, we treat this like a SUB.
        }
 
      // Sub can have at most one carry bit.  Thus we know that the output
      // is, at worst, one more bit than the inputs.
      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
      if (Tmp == 1) break;
      return std::min(Tmp, Tmp2) - 1;
 
    case Instruction::Mul: {
      // The output of the Mul can be at most twice the valid bits in the
      // inputs.
      unsigned SignBitsOp0 = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
      if (SignBitsOp0 == 1) break;
      unsigned SignBitsOp1 = ComputeNumSignBits(U->getOperand(1), Depth + 1, Q);
      if (SignBitsOp1 == 1) break;
      unsigned OutValidBits =
          (TyBits - SignBitsOp0 + 1) + (TyBits - SignBitsOp1 + 1);
      return OutValidBits > TyBits ? 1 : TyBits - OutValidBits + 1;
    }
 
    case Instruction::PHI: {
      const PHINode *PN = cast<PHINode>(U);
      unsigned NumIncomingValues = PN->getNumIncomingValues();
      // Don't analyze large in-degree PHIs.
      if (NumIncomingValues > 4) break;
      // Unreachable blocks may have zero-operand PHI nodes.
      if (NumIncomingValues == 0) break;
 
      // Take the minimum of all incoming values.  This can't infinitely loop
      // because of our depth threshold.
      Query RecQ = Q;
      Tmp = TyBits;
      for (unsigned i = 0, e = NumIncomingValues; i != e; ++i) {
        if (Tmp == 1) return Tmp;
        RecQ.CxtI = PN->getIncomingBlock(i)->getTerminator();
        Tmp = std::min(
            Tmp, ComputeNumSignBits(PN->getIncomingValue(i), Depth + 1, RecQ));
      }
      return Tmp;
    }
 
    case Instruction::Trunc:
      // FIXME: it's tricky to do anything useful for this, but it is an
      // important case for targets like X86.
      break;
 
    case Instruction::ExtractElement:
      // Look through extract element. At the moment we keep this simple and
      // skip tracking the specific element. But at least we might find
      // information valid for all elements of the vector (for example if vector
      // is sign extended, shifted, etc).
      return ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
 
    case Instruction::ShuffleVector: {
      // Collect the minimum number of sign bits that are shared by every vector
      // element referenced by the shuffle.
      auto *Shuf = dyn_cast<ShuffleVectorInst>(U);
      if (!Shuf) {
        // FIXME: Add support for shufflevector constant expressions.
        return 1;
      }
      APInt DemandedLHS, DemandedRHS;
      // For undef elements, we don't know anything about the common state of
      // the shuffle result.
      if (!getShuffleDemandedElts(Shuf, DemandedElts, DemandedLHS, DemandedRHS))
        return 1;
      Tmp = std::numeric_limits<unsigned>::max();
      if (!!DemandedLHS) {
        const Value *LHS = Shuf->getOperand(0);
        Tmp = ComputeNumSignBits(LHS, DemandedLHS, Depth + 1, Q);
      }
      // If we don't know anything, early out and try computeKnownBits
      // fall-back.
      if (Tmp == 1)
        break;
      if (!!DemandedRHS) {
        const Value *RHS = Shuf->getOperand(1);
        Tmp2 = ComputeNumSignBits(RHS, DemandedRHS, Depth + 1, Q);
        Tmp = std::min(Tmp, Tmp2);
      }
      // If we don't know anything, early out and try computeKnownBits
      // fall-back.
      if (Tmp == 1)
        break;
      assert(Tmp <= TyBits && "Failed to determine minimum sign bits");
      return Tmp;
    }
    case Instruction::Call: {
      if (const auto *II = dyn_cast<IntrinsicInst>(U)) {
        switch (II->getIntrinsicID()) {
        default: break;
        case Intrinsic::abs:
          Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
          if (Tmp == 1) break;
 
          // Absolute value reduces number of sign bits by at most 1.
          return Tmp - 1;
        }
      }
    }
    }
  }
 
  // Finally, if we can prove that the top bits of the result are 0's or 1's,
  // use this information.
 
  // If we can examine all elements of a vector constant successfully, we're
  // done (we can't do any better than that). If not, keep trying.
  if (unsigned VecSignBits =
          computeNumSignBitsVectorConstant(V, DemandedElts, TyBits))
    return VecSignBits;
 
  KnownBits Known(TyBits);
  computeKnownBits(V, DemandedElts, Known, Depth, Q);
 
  // If we know that the sign bit is either zero or one, determine the number of
  // identical bits in the top of the input value.
  return std::max(FirstAnswer, Known.countMinSignBits());
}
 
Intrinsic::ID llvm::getIntrinsicForCallSite(const CallBase &CB,
                                            const TargetLibraryInfo *TLI) {
  const Function *F = CB.getCalledFunction();
  if (!F)
    return Intrinsic::not_intrinsic;
 
  if (F->isIntrinsic())
    return F->getIntrinsicID();
 
  // We are going to infer semantics of a library function based on mapping it
  // to an LLVM intrinsic. Check that the library function is available from
  // this callbase and in this environment.
  LibFunc Func;
  if (F->hasLocalLinkage() || !TLI || !TLI->getLibFunc(CB, Func) ||
      !CB.onlyReadsMemory())
    return Intrinsic::not_intrinsic;
 
  switch (Func) {
  default:
    break;
  case LibFunc_sin:
  case LibFunc_sinf:
  case LibFunc_sinl:
    return Intrinsic::sin;
  case LibFunc_cos:
  case LibFunc_cosf:
  case LibFunc_cosl:
    return Intrinsic::cos;
  case LibFunc_exp:
  case LibFunc_expf:
  case LibFunc_expl:
    return Intrinsic::exp;
  case LibFunc_exp2:
  case LibFunc_exp2f:
  case LibFunc_exp2l:
    return Intrinsic::exp2;
  case LibFunc_log:
  case LibFunc_logf:
  case LibFunc_logl:
    return Intrinsic::log;
  case LibFunc_log10:
  case LibFunc_log10f:
  case LibFunc_log10l:
    return Intrinsic::log10;
  case LibFunc_log2:
  case LibFunc_log2f:
  case LibFunc_log2l:
    return Intrinsic::log2;
  case LibFunc_fabs:
  case LibFunc_fabsf:
  case LibFunc_fabsl:
    return Intrinsic::fabs;
  case LibFunc_fmin:
  case LibFunc_fminf:
  case LibFunc_fminl:
    return Intrinsic::minnum;
  case LibFunc_fmax:
  case LibFunc_fmaxf:
  case LibFunc_fmaxl:
    return Intrinsic::maxnum;
  case LibFunc_copysign:
  case LibFunc_copysignf:
  case LibFunc_copysignl:
    return Intrinsic::copysign;
  case LibFunc_floor:
  case LibFunc_floorf:
  case LibFunc_floorl:
    return Intrinsic::floor;
  case LibFunc_ceil:
  case LibFunc_ceilf:
  case LibFunc_ceill:
    return Intrinsic::ceil;
  case LibFunc_trunc:
  case LibFunc_truncf:
  case LibFunc_truncl:
    return Intrinsic::trunc;
  case LibFunc_rint:
  case LibFunc_rintf:
  case LibFunc_rintl:
    return Intrinsic::rint;
  case LibFunc_nearbyint:
  case LibFunc_nearbyintf:
  case LibFunc_nearbyintl:
    return Intrinsic::nearbyint;
  case LibFunc_round:
  case LibFunc_roundf:
  case LibFunc_roundl:
    return Intrinsic::round;
  case LibFunc_roundeven:
  case LibFunc_roundevenf:
  case LibFunc_roundevenl:
    return Intrinsic::roundeven;
  case LibFunc_pow:
  case LibFunc_powf:
  case LibFunc_powl:
    return Intrinsic::pow;
  case LibFunc_sqrt:
  case LibFunc_sqrtf:
  case LibFunc_sqrtl:
    return Intrinsic::sqrt;
  }
 
  return Intrinsic::not_intrinsic;
}
 
/// Return true if we can prove that the specified FP value is never equal to
/// -0.0.
/// NOTE: Do not check 'nsz' here because that fast-math-flag does not guarantee
///       that a value is not -0.0. It only guarantees that -0.0 may be treated
///       the same as +0.0 in floating-point ops.
///
/// NOTE: this function will need to be revisited when we support non-default
/// rounding modes!
bool llvm::CannotBeNegativeZero(const Value *V, const TargetLibraryInfo *TLI,
                                unsigned Depth) {
  if (auto *CFP = dyn_cast<ConstantFP>(V))
    return !CFP->getValueAPF().isNegZero();
 
  if (Depth == MaxAnalysisRecursionDepth)
    return false;
 
  auto *Op = dyn_cast<Operator>(V);
  if (!Op)
    return false;
 
  // (fadd x, 0.0) is guaranteed to return +0.0, not -0.0.
  if (match(Op, m_FAdd(m_Value(), m_PosZeroFP())))
    return true;
 
  // sitofp and uitofp turn into +0.0 for zero.
  if (isa<SIToFPInst>(Op) || isa<UIToFPInst>(Op))
    return true;
 
  if (auto *Call = dyn_cast<CallInst>(Op)) {
    Intrinsic::ID IID = getIntrinsicForCallSite(*Call, TLI);
    switch (IID) {
    default:
      break;
    // sqrt(-0.0) = -0.0, no other negative results are possible.
    case Intrinsic::sqrt:
    case Intrinsic::canonicalize:
      return CannotBeNegativeZero(Call->getArgOperand(0), TLI, Depth + 1);
    // fabs(x) != -0.0
    case Intrinsic::fabs:
      return true;
    }
  }
 
  return false;
}
 
/// If \p SignBitOnly is true, test for a known 0 sign bit rather than a
/// standard ordered compare. e.g. make -0.0 olt 0.0 be true because of the sign
/// bit despite comparing equal.
static bool cannotBeOrderedLessThanZeroImpl(const Value *V,
                                            const TargetLibraryInfo *TLI,
                                            bool SignBitOnly,
                                            unsigned Depth) {
  // TODO: This function does not do the right thing when SignBitOnly is true
  // and we're lowering to a hypothetical IEEE 754-compliant-but-evil platform
  // which flips the sign bits of NaNs.  See
  // https://llvm.org/bugs/show_bug.cgi?id=31702.
 
  if (const ConstantFP *CFP = dyn_cast<ConstantFP>(V)) {
    return !CFP->getValueAPF().isNegative() ||
           (!SignBitOnly && CFP->getValueAPF().isZero());
  }
 
  // Handle vector of constants.
  if (auto *CV = dyn_cast<Constant>(V)) {
    if (auto *CVFVTy = dyn_cast<FixedVectorType>(CV->getType())) {
      unsigned NumElts = CVFVTy->getNumElements();
      for (unsigned i = 0; i != NumElts; ++i) {
        auto *CFP = dyn_cast_or_null<ConstantFP>(CV->getAggregateElement(i));
        if (!CFP)
          return false;
        if (CFP->getValueAPF().isNegative() &&
            (SignBitOnly || !CFP->getValueAPF().isZero()))
          return false;
      }
 
      // All non-negative ConstantFPs.
      return true;
    }
  }
 
  if (Depth == MaxAnalysisRecursionDepth)
    return false;
 
  const Operator *I = dyn_cast<Operator>(V);
  if (!I)
    return false;
 
  switch (I->getOpcode()) {
  default:
    break;
  // Unsigned integers are always nonnegative.
  case Instruction::UIToFP:
    return true;
  case Instruction::FMul:
  case Instruction::FDiv:
    // X * X is always non-negative or a NaN.
    // X / X is always exactly 1.0 or a NaN.
    if (I->getOperand(0) == I->getOperand(1) &&
        (!SignBitOnly || cast<FPMathOperator>(I)->hasNoNaNs()))
      return true;
 
    LLVM_FALLTHROUGH;
  case Instruction::FAdd:
  case Instruction::FRem:
    return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                           Depth + 1) &&
           cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
                                           Depth + 1);
  case Instruction::Select:
    return cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
                                           Depth + 1) &&
           cannotBeOrderedLessThanZeroImpl(I->getOperand(2), TLI, SignBitOnly,
                                           Depth + 1);
  case Instruction::FPExt:
  case Instruction::FPTrunc:
    // Widening/narrowing never change sign.
    return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                           Depth + 1);
  case Instruction::ExtractElement:
    // Look through extract element. At the moment we keep this simple and skip
    // tracking the specific element. But at least we might find information
    // valid for all elements of the vector.
    return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                           Depth + 1);
  case Instruction::Call:
    const auto *CI = cast<CallInst>(I);
    Intrinsic::ID IID = getIntrinsicForCallSite(*CI, TLI);
    switch (IID) {
    default:
      break;
    case Intrinsic::maxnum: {
      Value *V0 = I->getOperand(0), *V1 = I->getOperand(1);
      auto isPositiveNum = [&](Value *V) {
        if (SignBitOnly) {
          // With SignBitOnly, this is tricky because the result of
          // maxnum(+0.0, -0.0) is unspecified. Just check if the operand is
          // a constant strictly greater than 0.0.
          const APFloat *C;
          return match(V, m_APFloat(C)) &&
                 *C > APFloat::getZero(C->getSemantics());
        }
 
        // -0.0 compares equal to 0.0, so if this operand is at least -0.0,
        // maxnum can't be ordered-less-than-zero.
        return isKnownNeverNaN(V, TLI) &&
               cannotBeOrderedLessThanZeroImpl(V, TLI, false, Depth + 1);
      };
 
      // TODO: This could be improved. We could also check that neither operand
      //       has its sign bit set (and at least 1 is not-NAN?).
      return isPositiveNum(V0) || isPositiveNum(V1);
    }
 
    case Intrinsic::maximum:
      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                             Depth + 1) ||
             cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
                                             Depth + 1);
    case Intrinsic::minnum:
    case Intrinsic::minimum:
      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                             Depth + 1) &&
             cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
                                             Depth + 1);
    case Intrinsic::exp:
    case Intrinsic::exp2:
    case Intrinsic::fabs:
      return true;
 
    case Intrinsic::sqrt:
      // sqrt(x) is always >= -0 or NaN.  Moreover, sqrt(x) == -0 iff x == -0.
      if (!SignBitOnly)
        return true;
      return CI->hasNoNaNs() && (CI->hasNoSignedZeros() ||
                                 CannotBeNegativeZero(CI->getOperand(0), TLI));
 
    case Intrinsic::powi:
      if (ConstantInt *Exponent = dyn_cast<ConstantInt>(I->getOperand(1))) {
        // powi(x,n) is non-negative if n is even.
        if (Exponent->getBitWidth() <= 64 && Exponent->getSExtValue() % 2u == 0)
          return true;
      }
      // TODO: This is not correct.  Given that exp is an integer, here are the
      // ways that pow can return a negative value:
      //
      //   pow(x, exp)    --> negative if exp is odd and x is negative.
      //   pow(-0, exp)   --> -inf if exp is negative odd.
      //   pow(-0, exp)   --> -0 if exp is positive odd.
      //   pow(-inf, exp) --> -0 if exp is negative odd.
      //   pow(-inf, exp) --> -inf if exp is positive odd.
      //
      // Therefore, if !SignBitOnly, we can return true if x >= +0 or x is NaN,
      // but we must return false if x == -0.  Unfortunately we do not currently
      // have a way of expressing this constraint.  See details in
      // https://llvm.org/bugs/show_bug.cgi?id=31702.
      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                             Depth + 1);
 
    case Intrinsic::fma:
    case Intrinsic::fmuladd:
      // x*x+y is non-negative if y is non-negative.
      return I->getOperand(0) == I->getOperand(1) &&
             (!SignBitOnly || cast<FPMathOperator>(I)->hasNoNaNs()) &&
             cannotBeOrderedLessThanZeroImpl(I->getOperand(2), TLI, SignBitOnly,
                                             Depth + 1);
    }
    break;
  }
  return false;
}
 
bool llvm::CannotBeOrderedLessThanZero(const Value *V,
                                       const TargetLibraryInfo *TLI) {
  return cannotBeOrderedLessThanZeroImpl(V, TLI, false, 0);
}
 
bool llvm::SignBitMustBeZero(const Value *V, const TargetLibraryInfo *TLI) {
  return cannotBeOrderedLessThanZeroImpl(V, TLI, true, 0);
}
 
bool llvm::isKnownNeverInfinity(const Value *V, const TargetLibraryInfo *TLI,
                                unsigned Depth) {
  assert(V->getType()->isFPOrFPVectorTy() && "Querying for Inf on non-FP type");
 
  // If we're told that infinities won't happen, assume they won't.
  if (auto *FPMathOp = dyn_cast<FPMathOperator>(V))
    if (FPMathOp->hasNoInfs())
      return true;
 
  // Handle scalar constants.
  if (auto *CFP = dyn_cast<ConstantFP>(V))
    return !CFP->isInfinity();
 
  if (Depth == MaxAnalysisRecursionDepth)
    return false;
 
  if (auto *Inst = dyn_cast<Instruction>(V)) {
    switch (Inst->getOpcode()) {
    case Instruction::Select: {
      return isKnownNeverInfinity(Inst->getOperand(1), TLI, Depth + 1) &&
             isKnownNeverInfinity(Inst->getOperand(2), TLI, Depth + 1);
    }
    case Instruction::SIToFP:
    case Instruction::UIToFP: {
      // Get width of largest magnitude integer (remove a bit if signed).
      // This still works for a signed minimum value because the largest FP
      // value is scaled by some fraction close to 2.0 (1.0 + 0.xxxx).
      int IntSize = Inst->getOperand(0)->getType()->getScalarSizeInBits();
      if (Inst->getOpcode() == Instruction::SIToFP)
        --IntSize;
 
      // If the exponent of the largest finite FP value can hold the largest
      // integer, the result of the cast must be finite.
      Type *FPTy = Inst->getType()->getScalarType();
      return ilogb(APFloat::getLargest(FPTy->getFltSemantics())) >= IntSize;
    }
    default:
      break;
    }
  }
 
  // try to handle fixed width vector constants
  auto *VFVTy = dyn_cast<FixedVectorType>(V->getType());
  if (VFVTy && isa<Constant>(V)) {
    // For vectors, verify that each element is not infinity.
    unsigned NumElts = VFVTy->getNumElements();
    for (unsigned i = 0; i != NumElts; ++i) {
      Constant *Elt = cast<Constant>(V)->getAggregateElement(i);
      if (!Elt)
        return false;
      if (isa<UndefValue>(Elt))
        continue;
      auto *CElt = dyn_cast<ConstantFP>(Elt);
      if (!CElt || CElt->isInfinity())
        return false;
    }
    // All elements were confirmed non-infinity or undefined.
    return true;
  }
 
  // was not able to prove that V never contains infinity
  return false;
}
 
bool llvm::isKnownNeverNaN(const Value *V, const TargetLibraryInfo *TLI,
                           unsigned Depth) {
  assert(V->getType()->isFPOrFPVectorTy() && "Querying for NaN on non-FP type");
 
  // If we're told that NaNs won't happen, assume they won't.
  if (auto *FPMathOp = dyn_cast<FPMathOperator>(V))
    if (FPMathOp->hasNoNaNs())
      return true;
 
  // Handle scalar constants.
  if (auto *CFP = dyn_cast<ConstantFP>(V))
    return !CFP->isNaN();
 
  if (Depth == MaxAnalysisRecursionDepth)
    return false;
 
  if (auto *Inst = dyn_cast<Instruction>(V)) {
    switch (Inst->getOpcode()) {
    case Instruction::FAdd:
    case Instruction::FSub:
      // Adding positive and negative infinity produces NaN.
      return isKnownNeverNaN(Inst->getOperand(0), TLI, Depth + 1) &&
             isKnownNeverNaN(Inst->getOperand(1), TLI, Depth + 1) &&
             (isKnownNeverInfinity(Inst->getOperand(0), TLI, Depth + 1) ||
              isKnownNeverInfinity(Inst->getOperand(1), TLI, Depth + 1));
 
    case Instruction::FMul:
      // Zero multiplied with infinity produces NaN.
      // FIXME: If neither side can be zero fmul never produces NaN.
      return isKnownNeverNaN(Inst->getOperand(0), TLI, Depth + 1) &&
             isKnownNeverInfinity(Inst->getOperand(0), TLI, Depth + 1) &&
             isKnownNeverNaN(Inst->getOperand(1), TLI, Depth + 1) &&
             isKnownNeverInfinity(Inst->getOperand(1), TLI, Depth + 1);
 
    case Instruction::FDiv:
    case Instruction::FRem:
      // FIXME: Only 0/0, Inf/Inf, Inf REM x and x REM 0 produce NaN.
      return false;
 
    case Instruction::Select: {
      return isKnownNeverNaN(Inst->getOperand(1), TLI, Depth + 1) &&
             isKnownNeverNaN(Inst->getOperand(2), TLI, Depth + 1);
    }
    case Instruction::SIToFP:
    case Instruction::UIToFP:
      return true;
    case Instruction::FPTrunc:
    case Instruction::FPExt:
      return isKnownNeverNaN(Inst->getOperand(0), TLI, Depth + 1);
    default:
      break;
    }
  }
 
  if (const auto *II = dyn_cast<IntrinsicInst>(V)) {
    switch (II->getIntrinsicID()) {
    case Intrinsic::canonicalize:
    case Intrinsic::fabs:
    case Intrinsic::copysign:
    case Intrinsic::exp:
    case Intrinsic::exp2:
    case Intrinsic::floor:
    case Intrinsic::ceil:
    case Intrinsic::trunc:
    case Intrinsic::rint:
    case Intrinsic::nearbyint:
    case Intrinsic::round:
    case Intrinsic::roundeven:
      return isKnownNeverNaN(II->getArgOperand(0), TLI, Depth + 1);
    case Intrinsic::sqrt:
      return isKnownNeverNaN(II->getArgOperand(0), TLI, Depth + 1) &&
             CannotBeOrderedLessThanZero(II->getArgOperand(0), TLI);
    case Intrinsic::minnum:
    case Intrinsic::maxnum:
      // If either operand is not NaN, the result is not NaN.
      return isKnownNeverNaN(II->getArgOperand(0), TLI, Depth + 1) ||
             isKnownNeverNaN(II->getArgOperand(1), TLI, Depth + 1);
    default:
      return false;
    }
  }
 
  // Try to handle fixed width vector constants
  auto *VFVTy = dyn_cast<FixedVectorType>(V->getType());
  if (VFVTy && isa<Constant>(V)) {
    // For vectors, verify that each element is not NaN.
    unsigned NumElts = VFVTy->getNumElements();
    for (unsigned i = 0; i != NumElts; ++i) {
      Constant *Elt = cast<Constant>(V)->getAggregateElement(i);
      if (!Elt)
        return false;
      if (isa<UndefValue>(Elt))
        continue;
      auto *CElt = dyn_cast<ConstantFP>(Elt);
      if (!CElt || CElt->isNaN())
        return false;
    }
    // All elements were confirmed not-NaN or undefined.
    return true;
  }
 
  // Was not able to prove that V never contains NaN
  return false;
}
 
Value *llvm::isBytewiseValue(Value *V, const DataLayout &DL) {
 
  // All byte-wide stores are splatable, even of arbitrary variables.
  if (V->getType()->isIntegerTy(8))
    return V;
 
  LLVMContext &Ctx = V->getContext();
 
  // Undef don't care.
  auto *UndefInt8 = UndefValue::get(Type::getInt8Ty(Ctx));
  if (isa<UndefValue>(V))
    return UndefInt8;
 
  // Return Undef for zero-sized type.
  if (!DL.getTypeStoreSize(V->getType()).isNonZero())
    return UndefInt8;
 
  Constant *C = dyn_cast<Constant>(V);
  if (!C) {
    // Conceptually, we could handle things like:
    //   %a = zext i8 %X to i16
    //   %b = shl i16 %a, 8
    //   %c = or i16 %a, %b
    // but until there is an example that actually needs this, it doesn't seem
    // worth worrying about.
    return nullptr;
  }
 
  // Handle 'null' ConstantArrayZero etc.
  if (C->isNullValue())
    return Constant::getNullValue(Type::getInt8Ty(Ctx));
 
  // Constant floating-point values can be handled as integer values if the
  // corresponding integer value is "byteable".  An important case is 0.0.
  if (ConstantFP *CFP = dyn_cast<ConstantFP>(C)) {
    Type *Ty = nullptr;
    if (CFP->getType()->isHalfTy())
      Ty = Type::getInt16Ty(Ctx);
    else if (CFP->getType()->isFloatTy())
      Ty = Type::getInt32Ty(Ctx);
    else if (CFP->getType()->isDoubleTy())
      Ty = Type::getInt64Ty(Ctx);
    // Don't handle long double formats, which have strange constraints.
    return Ty ? isBytewiseValue(ConstantExpr::getBitCast(CFP, Ty), DL)
              : nullptr;
  }
 
  // We can handle constant integers that are multiple of 8 bits.
  if (ConstantInt *CI = dyn_cast<ConstantInt>(C)) {
    if (CI->getBitWidth() % 8 == 0) {
      assert(CI->getBitWidth() > 8 && "8 bits should be handled above!");
      if (!CI->getValue().isSplat(8))
        return nullptr;
      return ConstantInt::get(Ctx, CI->getValue().trunc(8));
    }
  }
 
  if (auto *CE = dyn_cast<ConstantExpr>(C)) {
    if (CE->getOpcode() == Instruction::IntToPtr) {
      if (auto *PtrTy = dyn_cast<PointerType>(CE->getType())) {
        unsigned BitWidth = DL.getPointerSizeInBits(PtrTy->getAddressSpace());
        return isBytewiseValue(
            ConstantExpr::getIntegerCast(CE->getOperand(0),
                                         Type::getIntNTy(Ctx, BitWidth), false),
            DL);
      }
    }
  }
 
  auto Merge = [&](Value *LHS, Value *RHS) -> Value * {
    if (LHS == RHS)
      return LHS;
    if (!LHS || !RHS)
      return nullptr;
    if (LHS == UndefInt8)
      return RHS;
    if (RHS == UndefInt8)
      return LHS;
    return nullptr;
  };
 
  if (ConstantDataSequential *CA = dyn_cast<ConstantDataSequential>(C)) {
    Value *Val = UndefInt8;
    for (unsigned I = 0, E = CA->getNumElements(); I != E; ++I)
      if (!(Val = Merge(Val, isBytewiseValue(CA->getElementAsConstant(I), DL))))
        return nullptr;
    return Val;
  }
 
  if (isa<ConstantAggregate>(C)) {
    Value *Val = UndefInt8;
    for (unsigned I = 0, E = C->getNumOperands(); I != E; ++I)
      if (!(Val = Merge(Val, isBytewiseValue(C->getOperand(I), DL))))
        return nullptr;
    return Val;
  }
 
  // Don't try to handle the handful of other constants.
  return nullptr;
}
 
// This is the recursive version of BuildSubAggregate. It takes a few different
// arguments. Idxs is the index within the nested struct From that we are
// looking at now (which is of type IndexedType). IdxSkip is the number of
// indices from Idxs that should be left out when inserting into the resulting
// struct. To is the result struct built so far, new insertvalue instructions
// build on that.
static Value *BuildSubAggregate(Value *From, Value* To, Type *IndexedType,
                                SmallVectorImpl<unsigned> &Idxs,
                                unsigned IdxSkip,
                                Instruction *InsertBefore) {
  StructType *STy = dyn_cast<StructType>(IndexedType);
  if (STy) {
    // Save the original To argument so we can modify it
    Value *OrigTo = To;
    // General case, the type indexed by Idxs is a struct
    for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i) {
      // Process each struct element recursively
      Idxs.push_back(i);
      Value *PrevTo = To;
      To = BuildSubAggregate(From, To, STy->getElementType(i), Idxs, IdxSkip,
                             InsertBefore);
      Idxs.pop_back();
      if (!To) {
        // Couldn't find any inserted value for this index? Cleanup
        while (PrevTo != OrigTo) {
          InsertValueInst* Del = cast<InsertValueInst>(PrevTo);
          PrevTo = Del->getAggregateOperand();
          Del->eraseFromParent();
        }
        // Stop processing elements
        break;
      }
    }
    // If we successfully found a value for each of our subaggregates
    if (To)
      return To;
  }
  // Base case, the type indexed by SourceIdxs is not a struct, or not all of
  // the struct's elements had a value that was inserted directly. In the latter
  // case, perhaps we can't determine each of the subelements individually, but
  // we might be able to find the complete struct somewhere.
 
  // Find the value that is at that particular spot
  Value *V = FindInsertedValue(From, Idxs);
 
  if (!V)
    return nullptr;
 
  // Insert the value in the new (sub) aggregate
  return InsertValueInst::Create(To, V, makeArrayRef(Idxs).slice(IdxSkip),
                                 "tmp", InsertBefore);
}
 
// This helper takes a nested struct and extracts a part of it (which is again a
// struct) into a new value. For example, given the struct:
// { a, { b, { c, d }, e } }
// and the indices "1, 1" this returns
// { c, d }.
//
// It does this by inserting an insertvalue for each element in the resulting
// struct, as opposed to just inserting a single struct. This will only work if
// each of the elements of the substruct are known (ie, inserted into From by an
// insertvalue instruction somewhere).
//
// All inserted insertvalue instructions are inserted before InsertBefore
static Value *BuildSubAggregate(Value *From, ArrayRef<unsigned> idx_range,
                                Instruction *InsertBefore) {
  assert(InsertBefore && "Must have someplace to insert!");
  Type *IndexedType = ExtractValueInst::getIndexedType(From->getType(),
                                                             idx_range);
  Value *To = UndefValue::get(IndexedType);
  SmallVector<unsigned, 10> Idxs(idx_range.begin(), idx_range.end());
  unsigned IdxSkip = Idxs.size();
 
  return BuildSubAggregate(From, To, IndexedType, Idxs, IdxSkip, InsertBefore);
}
 
/// Given an aggregate and a sequence of indices, see if the scalar value
/// indexed is already around as a register, for example if it was inserted
/// directly into the aggregate.
///
/// If InsertBefore is not null, this function will duplicate (modified)
/// insertvalues when a part of a nested struct is extracted.
Value *llvm::FindInsertedValue(Value *V, ArrayRef<unsigned> idx_range,
                               Instruction *InsertBefore) {
  // Nothing to index? Just return V then (this is useful at the end of our
  // recursion).
  if (idx_range.empty())
    return V;
  // We have indices, so V should have an indexable type.
  assert((V->getType()->isStructTy() || V->getType()->isArrayTy()) &&
         "Not looking at a struct or array?");
  assert(ExtractValueInst::getIndexedType(V->getType(), idx_range) &&
         "Invalid indices for type?");
 
  if (Constant *C = dyn_cast<Constant>(V)) {
    C = C->getAggregateElement(idx_range[0]);
    if (!C) return nullptr;
    return FindInsertedValue(C, idx_range.slice(1), InsertBefore);
  }
 
  if (InsertValueInst *I = dyn_cast<InsertValueInst>(V)) {
    // Loop the indices for the insertvalue instruction in parallel with the
    // requested indices
    const unsigned *req_idx = idx_range.begin();
    for (const unsigned *i = I->idx_begin(), *e = I->idx_end();
         i != e; ++i, ++req_idx) {
      if (req_idx == idx_range.end()) {
        // We can't handle this without inserting insertvalues
        if (!InsertBefore)
          return nullptr;
 
        // The requested index identifies a part of a nested aggregate. Handle
        // this specially. For example,
        // %A = insertvalue { i32, {i32, i32 } } undef, i32 10, 1, 0
        // %B = insertvalue { i32, {i32, i32 } } %A, i32 11, 1, 1
        // %C = extractvalue {i32, { i32, i32 } } %B, 1
        // This can be changed into
        // %A = insertvalue {i32, i32 } undef, i32 10, 0
        // %C = insertvalue {i32, i32 } %A, i32 11, 1
        // which allows the unused 0,0 element from the nested struct to be
        // removed.
        return BuildSubAggregate(V, makeArrayRef(idx_range.begin(), req_idx),
                                 InsertBefore);
      }
 
      // This insert value inserts something else than what we are looking for.
      // See if the (aggregate) value inserted into has the value we are
      // looking for, then.
      if (*req_idx != *i)
        return FindInsertedValue(I->getAggregateOperand(), idx_range,
                                 InsertBefore);
    }
    // If we end up here, the indices of the insertvalue match with those
    // requested (though possibly only partially). Now we recursively look at
    // the inserted value, passing any remaining indices.
    return FindInsertedValue(I->getInsertedValueOperand(),
                             makeArrayRef(req_idx, idx_range.end()),
                             InsertBefore);
  }
 
  if (ExtractValueInst *I = dyn_cast<ExtractValueInst>(V)) {
    // If we're extracting a value from an aggregate that was extracted from
    // something else, we can extract from that something else directly instead.
    // However, we will need to chain I's indices with the requested indices.
 
    // Calculate the number of indices required
    unsigned size = I->getNumIndices() + idx_range.size();
    // Allocate some space to put the new indices in
    SmallVector<unsigned, 5> Idxs;
    Idxs.reserve(size);
    // Add indices from the extract value instruction
    Idxs.append(I->idx_begin(), I->idx_end());
 
    // Add requested indices
    Idxs.append(idx_range.begin(), idx_range.end());
 
    assert(Idxs.size() == size
           && "Number of indices added not correct?");
 
    return FindInsertedValue(I->getAggregateOperand(), Idxs, InsertBefore);
  }
  // Otherwise, we don't know (such as, extracting from a function return value
  // or load instruction)
  return nullptr;
}
 
bool llvm::isGEPBasedOnPointerToString(const GEPOperator *GEP,
                                       unsigned CharSize) {
  // Make sure the GEP has exactly three arguments.
  if (GEP->getNumOperands() != 3)
    return false;
 
  // Make sure the index-ee is a pointer to array of \p CharSize integers.
  // CharSize.
  ArrayType *AT = dyn_cast<ArrayType>(GEP->getSourceElementType());
  if (!AT || !AT->getElementType()->isIntegerTy(CharSize))
    return false;
 
  // Check to make sure that the first operand of the GEP is an integer and
  // has value 0 so that we are sure we're indexing into the initializer.
  const ConstantInt *FirstIdx = dyn_cast<ConstantInt>(GEP->getOperand(1));
  if (!FirstIdx || !FirstIdx->isZero())
    return false;
 
  return true;
}
 
bool llvm::getConstantDataArrayInfo(const Value *V,
                                    ConstantDataArraySlice &Slice,
                                    unsigned ElementSize, uint64_t Offset) {
  assert(V);
 
  // Look through bitcast instructions and geps.
  V = V->stripPointerCasts();
 
  // If the value is a GEP instruction or constant expression, treat it as an
  // offset.
  if (const GEPOperator *GEP = dyn_cast<GEPOperator>(V)) {
    // The GEP operator should be based on a pointer to string constant, and is
    // indexing into the string constant.
    if (!isGEPBasedOnPointerToString(GEP, ElementSize))
      return false;
 
    // If the second index isn't a ConstantInt, then this is a variable index
    // into the array.  If this occurs, we can't say anything meaningful about
    // the string.
    uint64_t StartIdx = 0;
    if (const ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(2)))
      StartIdx = CI->getZExtValue();
    else
      return false;
    return getConstantDataArrayInfo(GEP->getOperand(0), Slice, ElementSize,
                                    StartIdx + Offset);
  }
 
  // The GEP instruction, constant or instruction, must reference a global
  // variable that is a constant and is initialized. The referenced constant
  // initializer is the array that we'll use for optimization.
  const GlobalVariable *GV = dyn_cast<GlobalVariable>(V);
  if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer())
    return false;
 
  const ConstantDataArray *Array;
  ArrayType *ArrayTy;
  if (GV->getInitializer()->isNullValue()) {
    Type *GVTy = GV->getValueType();
    if ( (ArrayTy = dyn_cast<ArrayType>(GVTy)) ) {
      // A zeroinitializer for the array; there is no ConstantDataArray.
      Array = nullptr;
    } else {
      const DataLayout &DL = GV->getParent()->getDataLayout();
      uint64_t SizeInBytes = DL.getTypeStoreSize(GVTy).getFixedSize();
      uint64_t Length = SizeInBytes / (ElementSize / 8);
      if (Length <= Offset)
        return false;
 
      Slice.Array = nullptr;
      Slice.Offset = 0;
      Slice.Length = Length - Offset;
      return true;
    }
  } else {
    // This must be a ConstantDataArray.
    Array = dyn_cast<ConstantDataArray>(GV->getInitializer());
    if (!Array)
      return false;
    ArrayTy = Array->getType();
  }
  if (!ArrayTy->getElementType()->isIntegerTy(ElementSize))
    return false;
 
  uint64_t NumElts = ArrayTy->getArrayNumElements();
  if (Offset > NumElts)
    return false;
 
  Slice.Array = Array;
  Slice.Offset = Offset;
  Slice.Length = NumElts - Offset;
  return true;
}
 
/// 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.
bool llvm::getConstantStringInfo(const Value *V, StringRef &Str,
                                 uint64_t Offset, bool TrimAtNul) {
  ConstantDataArraySlice Slice;
  if (!getConstantDataArrayInfo(V, Slice, 8, Offset))
    return false;
 
  if (Slice.Array == nullptr) {
    if (TrimAtNul) {
      Str = StringRef();
      return true;
    }
    if (Slice.Length == 1) {
      Str = StringRef("", 1);
      return true;
    }
    // We cannot instantiate a StringRef as we do not have an appropriate string
    // of 0s at hand.
    return false;
  }
 
  // Start out with the entire array in the StringRef.
  Str = Slice.Array->getAsString();
  // Skip over 'offset' bytes.
  Str = Str.substr(Slice.Offset);
 
  if (TrimAtNul) {
    // Trim off the \0 and anything after it.  If the array is not nul
    // terminated, we just return the whole end of string.  The client may know
    // some other way that the string is length-bound.
    Str = Str.substr(0, Str.find('\0'));
  }
  return true;
}
 
// These next two are very similar to the above, but also look through PHI
// nodes.
// TODO: See if we can integrate these two together.
 
/// If we can compute the length of the string pointed to by
/// the specified pointer, return 'len+1'.  If we can't, return 0.
static uint64_t GetStringLengthH(const Value *V,
                                 SmallPtrSetImpl<const PHINode*> &PHIs,
                                 unsigned CharSize) {
  // Look through noop bitcast instructions.
  V = V->stripPointerCasts();
 
  // If this is a PHI node, there are two cases: either we have already seen it
  // or we haven't.
  if (const PHINode *PN = dyn_cast<PHINode>(V)) {
    if (!PHIs.insert(PN).second)
      return ~0ULL;  // already in the set.
 
    // If it was new, see if all the input strings are the same length.
    uint64_t LenSoFar = ~0ULL;
    for (Value *IncValue : PN->incoming_values()) {
      uint64_t Len = GetStringLengthH(IncValue, PHIs, CharSize);
      if (Len == 0) return 0; // Unknown length -> unknown.
 
      if (Len == ~0ULL) continue;
 
      if (Len != LenSoFar && LenSoFar != ~0ULL)
        return 0;    // Disagree -> unknown.
      LenSoFar = Len;
    }
 
    // Success, all agree.
    return LenSoFar;
  }
 
  // strlen(select(c,x,y)) -> strlen(x) ^ strlen(y)
  if (const SelectInst *SI = dyn_cast<SelectInst>(V)) {
    uint64_t Len1 = GetStringLengthH(SI->getTrueValue(), PHIs, CharSize);
    if (Len1 == 0) return 0;
    uint64_t Len2 = GetStringLengthH(SI->getFalseValue(), PHIs, CharSize);
    if (Len2 == 0) return 0;
    if (Len1 == ~0ULL) return Len2;
    if (Len2 == ~0ULL) return Len1;
    if (Len1 != Len2) return 0;
    return Len1;
  }
 
  // Otherwise, see if we can read the string.
  ConstantDataArraySlice Slice;
  if (!getConstantDataArrayInfo(V, Slice, CharSize))
    return 0;
 
  if (Slice.Array == nullptr)
    return 1;
 
  // Search for nul characters
  unsigned NullIndex = 0;
  for (unsigned E = Slice.Length; NullIndex < E; ++NullIndex) {
    if (Slice.Array->getElementAsInteger(Slice.Offset + NullIndex) == 0)
      break;
  }
 
  return NullIndex + 1;
}
 
/// 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 llvm::GetStringLength(const Value *V, unsigned CharSize) {
  if (!V->getType()->isPointerTy())
    return 0;
 
  SmallPtrSet<const PHINode*, 32> PHIs;
  uint64_t Len = GetStringLengthH(V, PHIs, CharSize);
  // If Len is ~0ULL, we had an infinite phi cycle: this is dead code, so return
  // an empty string as a length.
  return Len == ~0ULL ? 1 : Len;
}
 
const Value *
llvm::getArgumentAliasingToReturnedPointer(const CallBase *Call,
                                           bool MustPreserveNullness) {
  assert(Call &&
         "getArgumentAliasingToReturnedPointer only works on nonnull calls");
  if (const Value *RV = Call->getReturnedArgOperand())
    return RV;
  // This can be used only as a aliasing property.
  if (isIntrinsicReturningPointerAliasingArgumentWithoutCapturing(
          Call, MustPreserveNullness))
    return Call->getArgOperand(0);
  return nullptr;
}
 
bool llvm::isIntrinsicReturningPointerAliasingArgumentWithoutCapturing(
    const CallBase *Call, bool MustPreserveNullness) {
  switch (Call->getIntrinsicID()) {
  case Intrinsic::launder_invariant_group:
  case Intrinsic::strip_invariant_group:
  case Intrinsic::aarch64_irg:
  case Intrinsic::aarch64_tagp:
    return true;
  case Intrinsic::ptrmask:
    return !MustPreserveNullness;
  default:
    return false;
  }
}
 
/// \p PN defines a loop-variant pointer to an object.  Check if the
/// previous iteration of the loop was referring to the same object as \p PN.
static bool isSameUnderlyingObjectInLoop(const PHINode *PN,
                                         const LoopInfo *LI) {
  // Find the loop-defined value.
  Loop *L = LI->getLoopFor(PN->getParent());
  if (PN->getNumIncomingValues() != 2)
    return true;
 
  // Find the value from previous iteration.
  auto *PrevValue = dyn_cast<Instruction>(PN->getIncomingValue(0));
  if (!PrevValue || LI->getLoopFor(PrevValue->getParent()) != L)
    PrevValue = dyn_cast<Instruction>(PN->getIncomingValue(1));
  if (!PrevValue || LI->getLoopFor(PrevValue->getParent()) != L)
    return true;
 
  // If a new pointer is loaded in the loop, the pointer references a different
  // object in every iteration.  E.g.:
  //    for (i)
  //       int *p = a[i];
  //       ...
  if (auto *Load = dyn_cast<LoadInst>(PrevValue))
    if (!L->isLoopInvariant(Load->getPointerOperand()))
      return false;
  return true;
}
 
const Value *llvm::getUnderlyingObject(const Value *V, unsigned MaxLookup) {
  if (!V->getType()->isPointerTy())
    return V;
  for (unsigned Count = 0; MaxLookup == 0 || Count < MaxLookup; ++Count) {
    if (auto *GEP = dyn_cast<GEPOperator>(V)) {
      V = GEP->getPointerOperand();
    } else if (Operator::getOpcode(V) == Instruction::BitCast ||
               Operator::getOpcode(V) == Instruction::AddrSpaceCast) {
      V = cast<Operator>(V)->getOperand(0);
      if (!V->getType()->isPointerTy())
        return V;
    } else if (auto *GA = dyn_cast<GlobalAlias>(V)) {
      if (GA->isInterposable())
        return V;
      V = GA->getAliasee();
    } else {
      if (auto *PHI = dyn_cast<PHINode>(V)) {
        // Look through single-arg phi nodes created by LCSSA.
        if (PHI->getNumIncomingValues() == 1) {
          V = PHI->getIncomingValue(0);
          continue;
        }
      } else if (auto *Call = dyn_cast<CallBase>(V)) {
        // CaptureTracking can know about special capturing properties of some
        // intrinsics like launder.invariant.group, that can't be expressed with
        // the attributes, but have properties like returning aliasing pointer.
        // Because some analysis may assume that nocaptured pointer is not
        // returned from some special intrinsic (because function would have to
        // be marked with returns attribute), it is crucial to use this function
        // because it should be in sync with CaptureTracking. Not using it may
        // cause weird miscompilations where 2 aliasing pointers are assumed to
        // noalias.
        if (auto *RP = getArgumentAliasingToReturnedPointer(Call, false)) {
          V = RP;
          continue;
        }
      }
 
      return V;
    }
    assert(V->getType()->isPointerTy() && "Unexpected operand type!");
  }
  return V;
}
 
void llvm::getUnderlyingObjects(const Value *V,
                                SmallVectorImpl<const Value *> &Objects,
                                LoopInfo *LI, unsigned MaxLookup) {
  SmallPtrSet<const Value *, 4> Visited;
  SmallVector<const Value *, 4> Worklist;
  Worklist.push_back(V);
  do {
    const Value *P = Worklist.pop_back_val();
    P = getUnderlyingObject(P, MaxLookup);
 
    if (!Visited.insert(P).second)
      continue;
 
    if (auto *SI = dyn_cast<SelectInst>(P)) {
      Worklist.push_back(SI->getTrueValue());
      Worklist.push_back(SI->getFalseValue());
      continue;
    }
 
    if (auto *PN = dyn_cast<PHINode>(P)) {
      // If this PHI changes the underlying object in every iteration of the
      // loop, don't look through it.  Consider:
      //   int **A;
      //   for (i) {
      //     Prev = Curr;     // Prev = PHI (Prev_0, Curr)
      //     Curr = A[i];
      //     *Prev, *Curr;
      //
      // Prev is tracking Curr one iteration behind so they refer to different
      // underlying objects.
      if (!LI || !LI->isLoopHeader(PN->getParent()) ||
          isSameUnderlyingObjectInLoop(PN, LI))
        append_range(Worklist, PN->incoming_values());
      continue;
    }
 
    Objects.push_back(P);
  } while (!Worklist.empty());
}
 
/// This is the function that does the work of looking through basic
/// ptrtoint+arithmetic+inttoptr sequences.
static const Value *getUnderlyingObjectFromInt(const Value *V) {
  do {
    if (const Operator *U = dyn_cast<Operator>(V)) {
      // If we find a ptrtoint, we can transfer control back to the
      // regular getUnderlyingObjectFromInt.
      if (U->getOpcode() == Instruction::PtrToInt)
        return U->getOperand(0);
      // If we find an add of a constant, a multiplied value, or a phi, it's
      // likely that the other operand will lead us to the base
      // object. We don't have to worry about the case where the
      // object address is somehow being computed by the multiply,
      // because our callers only care when the result is an
      // identifiable object.
      if (U->getOpcode() != Instruction::Add ||
          (!isa<ConstantInt>(U->getOperand(1)) &&
           Operator::getOpcode(U->getOperand(1)) != Instruction::Mul &&
           !isa<PHINode>(U->getOperand(1))))
        return V;
      V = U->getOperand(0);
    } else {
      return V;
    }
    assert(V->getType()->isIntegerTy() && "Unexpected operand type!");
  } while (true);
}
 
/// This is a wrapper around getUnderlyingObjects and adds support for basic
/// ptrtoint+arithmetic+inttoptr sequences.
/// It returns false if unidentified object is found in getUnderlyingObjects.
bool llvm::getUnderlyingObjectsForCodeGen(const Value *V,
                                          SmallVectorImpl<Value *> &Objects) {
  SmallPtrSet<const Value *, 16> Visited;
  SmallVector<const Value *, 4> Working(1, V);
  do {
    V = Working.pop_back_val();
 
    SmallVector<const Value *, 4> Objs;
    getUnderlyingObjects(V, Objs);
 
    for (const Value *V : Objs) {
      if (!Visited.insert(V).second)
        continue;
      if (Operator::getOpcode(V) == Instruction::IntToPtr) {
        const Value *O =
          getUnderlyingObjectFromInt(cast<User>(V)->getOperand(0));
        if (O->getType()->isPointerTy()) {
          Working.push_back(O);
          continue;
        }
      }
      // If getUnderlyingObjects fails to find an identifiable object,
      // getUnderlyingObjectsForCodeGen also fails for safety.
      if (!isIdentifiedObject(V)) {
        Objects.clear();
        return false;
      }
      Objects.push_back(const_cast<Value *>(V));
    }
  } while (!Working.empty());
  return true;
}
 
AllocaInst *llvm::findAllocaForValue(Value *V, bool OffsetZero) {
  AllocaInst *Result = nullptr;
  SmallPtrSet<Value *, 4> Visited;
  SmallVector<Value *, 4> Worklist;
 
  auto AddWork = [&](Value *V) {
    if (Visited.insert(V).second)
      Worklist.push_back(V);
  };
 
  AddWork(V);
  do {
    V = Worklist.pop_back_val();
    assert(Visited.count(V));
 
    if (AllocaInst *AI = dyn_cast<AllocaInst>(V)) {
      if (Result && Result != AI)
        return nullptr;
      Result = AI;
    } else if (CastInst *CI = dyn_cast<CastInst>(V)) {
      AddWork(CI->getOperand(0));
    } else if (PHINode *PN = dyn_cast<PHINode>(V)) {
      for (Value *IncValue : PN->incoming_values())
        AddWork(IncValue);
    } else if (auto *SI = dyn_cast<SelectInst>(V)) {
      AddWork(SI->getTrueValue());
      AddWork(SI->getFalseValue());
    } else if (GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(V)) {
      if (OffsetZero && !GEP->hasAllZeroIndices())
        return nullptr;
      AddWork(GEP->getPointerOperand());
    } else if (CallBase *CB = dyn_cast<CallBase>(V)) {
      Value *Returned = CB->getReturnedArgOperand();
      if (Returned)
        AddWork(Returned);
      else
        return nullptr;
    } else {
      return nullptr;
    }
  } while (!Worklist.empty());
 
  return Result;
}
 
static bool onlyUsedByLifetimeMarkersOrDroppableInstsHelper(
    const Value *V, bool AllowLifetime, bool AllowDroppable) {
  for (const User *U : V->users()) {
    const IntrinsicInst *II = dyn_cast<IntrinsicInst>(U);
    if (!II)
      return false;
 
    if (AllowLifetime && II->isLifetimeStartOrEnd())
      continue;
 
    if (AllowDroppable && II->isDroppable())
      continue;
 
    return false;
  }
  return true;
}
 
bool llvm::onlyUsedByLifetimeMarkers(const Value *V) {
  return onlyUsedByLifetimeMarkersOrDroppableInstsHelper(
      V, /* AllowLifetime */ true, /* AllowDroppable */ false);
}
bool llvm::onlyUsedByLifetimeMarkersOrDroppableInsts(const Value *V) {
  return onlyUsedByLifetimeMarkersOrDroppableInstsHelper(
      V, /* AllowLifetime */ true, /* AllowDroppable */ true);
}
 
bool llvm::mustSuppressSpeculation(const LoadInst &LI) {
  if (!LI.isUnordered())
    return true;
  const Function &F = *LI.getFunction();
  // Speculative load may create a race that did not exist in the source.
  return F.hasFnAttribute(Attribute::SanitizeThread) ||
    // Speculative load may load data from dirty regions.
    F.hasFnAttribute(Attribute::SanitizeAddress) ||
    F.hasFnAttribute(Attribute::SanitizeHWAddress);
}
 
 
bool llvm::isSafeToSpeculativelyExecute(const Value *V,
                                        const Instruction *CtxI,
                                        const DominatorTree *DT,
                                        const TargetLibraryInfo *TLI) {
  const Operator *Inst = dyn_cast<Operator>(V);
  if (!Inst)
    return false;
 
  for (unsigned i = 0, e = Inst->getNumOperands(); i != e; ++i)
    if (Constant *C = dyn_cast<Constant>(Inst->getOperand(i)))
      if (C->canTrap())
        return false;
 
  switch (Inst->getOpcode()) {
  default:
    return true;
  case Instruction::UDiv:
  case Instruction::URem: {
    // x / y is undefined if y == 0.
    const APInt *V;
    if (match(Inst->getOperand(1), m_APInt(V)))
      return *V != 0;
    return false;
  }
  case Instruction::SDiv:
  case Instruction::SRem: {
    // x / y is undefined if y == 0 or x == INT_MIN and y == -1
    const APInt *Numerator, *Denominator;
    if (!match(Inst->getOperand(1), m_APInt(Denominator)))
      return false;
    // We cannot hoist this division if the denominator is 0.
    if (*Denominator == 0)
      return false;
    // It's safe to hoist if the denominator is not 0 or -1.
    if (!Denominator->isAllOnes())
      return true;
    // At this point we know that the denominator is -1.  It is safe to hoist as
    // long we know that the numerator is not INT_MIN.
    if (match(Inst->getOperand(0), m_APInt(Numerator)))
      return !Numerator->isMinSignedValue();
    // The numerator *might* be MinSignedValue.
    return false;
  }
  case Instruction::Load: {
    const LoadInst *LI = cast<LoadInst>(Inst);
    if (mustSuppressSpeculation(*LI))
      return false;
    const DataLayout &DL = LI->getModule()->getDataLayout();
    return isDereferenceableAndAlignedPointer(
        LI->getPointerOperand(), LI->getType(), MaybeAlign(LI->getAlign()), DL,
        CtxI, DT, TLI);
  }
  case Instruction::Call: {
    auto *CI = cast<const CallInst>(Inst);
    const Function *Callee = CI->getCalledFunction();
 
    // The called function could have undefined behavior or side-effects, even
    // if marked readnone nounwind.
    return Callee && Callee->isSpeculatable();
  }
  case Instruction::VAArg:
  case Instruction::Alloca:
  case Instruction::Invoke:
  case Instruction::CallBr:
  case Instruction::PHI:
  case Instruction::Store:
  case Instruction::Ret:
  case Instruction::Br:
  case Instruction::IndirectBr:
  case Instruction::Switch:
  case Instruction::Unreachable:
  case Instruction::Fence:
  case Instruction::AtomicRMW:
  case Instruction::AtomicCmpXchg:
  case Instruction::LandingPad:
  case Instruction::Resume:
  case Instruction::CatchSwitch:
  case Instruction::CatchPad:
  case Instruction::CatchRet:
  case Instruction::CleanupPad:
  case Instruction::CleanupRet:
    return false; // Misc instructions which have effects
  }
}
 
bool llvm::mayBeMemoryDependent(const Instruction &I) {
  return I.mayReadOrWriteMemory() || !isSafeToSpeculativelyExecute(&I);
}
 
/// Convert ConstantRange OverflowResult into ValueTracking OverflowResult.
static OverflowResult mapOverflowResult(ConstantRange::OverflowResult OR) {
  switch (OR) {
    case ConstantRange::OverflowResult::MayOverflow:
      return OverflowResult::MayOverflow;
    case ConstantRange::OverflowResult::AlwaysOverflowsLow:
      return OverflowResult::AlwaysOverflowsLow;
    case ConstantRange::OverflowResult::AlwaysOverflowsHigh:
      return OverflowResult::AlwaysOverflowsHigh;
    case ConstantRange::OverflowResult::NeverOverflows:
      return OverflowResult::NeverOverflows;
  }
  llvm_unreachable("Unknown OverflowResult");
}
 
/// Combine constant ranges from computeConstantRange() and computeKnownBits().
static ConstantRange computeConstantRangeIncludingKnownBits(
    const Value *V, bool ForSigned, const DataLayout &DL, unsigned Depth,
    AssumptionCache *AC, const Instruction *CxtI, const DominatorTree *DT,
    OptimizationRemarkEmitter *ORE = nullptr, bool UseInstrInfo = true) {
  KnownBits Known = computeKnownBits(
      V, DL, Depth, AC, CxtI, DT, ORE, UseInstrInfo);
  ConstantRange CR1 = ConstantRange::fromKnownBits(Known, ForSigned);
  ConstantRange CR2 = computeConstantRange(V, UseInstrInfo);
  ConstantRange::PreferredRangeType RangeType =
      ForSigned ? ConstantRange::Signed : ConstantRange::Unsigned;
  return CR1.intersectWith(CR2, RangeType);
}
 
OverflowResult llvm::computeOverflowForUnsignedMul(
    const Value *LHS, const Value *RHS, const DataLayout &DL,
    AssumptionCache *AC, const Instruction *CxtI, const DominatorTree *DT,
    bool UseInstrInfo) {
  KnownBits LHSKnown = computeKnownBits(LHS, DL, /*Depth=*/0, AC, CxtI, DT,
                                        nullptr, UseInstrInfo);
  KnownBits RHSKnown = computeKnownBits(RHS, DL, /*Depth=*/0, AC, CxtI, DT,
                                        nullptr, UseInstrInfo);
  ConstantRange LHSRange = ConstantRange::fromKnownBits(LHSKnown, false);
  ConstantRange RHSRange = ConstantRange::fromKnownBits(RHSKnown, false);
  return mapOverflowResult(LHSRange.unsignedMulMayOverflow(RHSRange));
}
 
OverflowResult
llvm::computeOverflowForSignedMul(const Value *LHS, const Value *RHS,
                                  const DataLayout &DL, AssumptionCache *AC,
                                  const Instruction *CxtI,
                                  const DominatorTree *DT, bool UseInstrInfo) {
  // Multiplying n * m significant bits yields a result of n + m significant
  // bits. If the total number of significant bits does not exceed the
  // result bit width (minus 1), there is no overflow.
  // This means if we have enough leading sign bits in the operands
  // we can guarantee that the result does not overflow.
  // Ref: "Hacker's Delight" by Henry Warren
  unsigned BitWidth = LHS->getType()->getScalarSizeInBits();
 
  // Note that underestimating the number of sign bits gives a more
  // conservative answer.
  unsigned SignBits = ComputeNumSignBits(LHS, DL, 0, AC, CxtI, DT) +
                      ComputeNumSignBits(RHS, DL, 0, AC, CxtI, DT);
 
  // First handle the easy case: if we have enough sign bits there's
  // definitely no overflow.
  if (SignBits > BitWidth + 1)
    return OverflowResult::NeverOverflows;
 
  // There are two ambiguous cases where there can be no overflow:
  //   SignBits == BitWidth + 1    and
  //   SignBits == BitWidth
  // The second case is difficult to check, therefore we only handle the
  // first case.
  if (SignBits == BitWidth + 1) {
    // It overflows only when both arguments are negative and the true
    // product is exactly the minimum negative number.
    // E.g. mul i16 with 17 sign bits: 0xff00 * 0xff80 = 0x8000
    // For simplicity we just check if at least one side is not negative.
    KnownBits LHSKnown = computeKnownBits(LHS, DL, /*Depth=*/0, AC, CxtI, DT,
                                          nullptr, UseInstrInfo);
    KnownBits RHSKnown = computeKnownBits(RHS, DL, /*Depth=*/0, AC, CxtI, DT,
                                          nullptr, UseInstrInfo);
    if (LHSKnown.isNonNegative() || RHSKnown.isNonNegative())
      return OverflowResult::NeverOverflows;
  }
  return OverflowResult::MayOverflow;
}
 
OverflowResult llvm::computeOverflowForUnsignedAdd(
    const Value *LHS, const Value *RHS, const DataLayout &DL,
    AssumptionCache *AC, const Instruction *CxtI, const DominatorTree *DT,
    bool UseInstrInfo) {
  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
      LHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT,
      nullptr, UseInstrInfo);
  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
      RHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT,
      nullptr, UseInstrInfo);
  return mapOverflowResult(LHSRange.unsignedAddMayOverflow(RHSRange));
}
 
static OverflowResult computeOverflowForSignedAdd(const Value *LHS,
                                                  const Value *RHS,
                                                  const AddOperator *Add,
                                                  const DataLayout &DL,
                                                  AssumptionCache *AC,
                                                  const Instruction *CxtI,
                                                  const DominatorTree *DT) {
  if (Add && Add->hasNoSignedWrap()) {
    return OverflowResult::NeverOverflows;
  }
 
  // If LHS and RHS each have at least two sign bits, the addition will look
  // like
  //
  // XX..... +
  // YY.....
  //
  // If the carry into the most significant position is 0, X and Y can't both
  // be 1 and therefore the carry out of the addition is also 0.
  //
  // If the carry into the most significant position is 1, X and Y can't both
  // be 0 and therefore the carry out of the addition is also 1.
  //
  // Since the carry into the most significant position is always equal to
  // the carry out of the addition, there is no signed overflow.
  if (ComputeNumSignBits(LHS, DL, 0, AC, CxtI, DT) > 1 &&
      ComputeNumSignBits(RHS, DL, 0, AC, CxtI, DT) > 1)
    return OverflowResult::NeverOverflows;
 
  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
      LHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
      RHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
  OverflowResult OR =
      mapOverflowResult(LHSRange.signedAddMayOverflow(RHSRange));
  if (OR != OverflowResult::MayOverflow)
    return OR;
 
  // The remaining code needs Add to be available. Early returns if not so.
  if (!Add)
    return OverflowResult::MayOverflow;
 
  // If the sign of Add is the same as at least one of the operands, this add
  // CANNOT overflow. If this can be determined from the known bits of the
  // operands the above signedAddMayOverflow() check will have already done so.
  // The only other way to improve on the known bits is from an assumption, so
  // call computeKnownBitsFromAssume() directly.
  bool LHSOrRHSKnownNonNegative =
      (LHSRange.isAllNonNegative() || RHSRange.isAllNonNegative());
  bool LHSOrRHSKnownNegative =
      (LHSRange.isAllNegative() || RHSRange.isAllNegative());
  if (LHSOrRHSKnownNonNegative || LHSOrRHSKnownNegative) {
    KnownBits AddKnown(LHSRange.getBitWidth());
    computeKnownBitsFromAssume(
        Add, AddKnown, /*Depth=*/0, Query(DL, AC, CxtI, DT, true));
    if ((AddKnown.isNonNegative() && LHSOrRHSKnownNonNegative) ||
        (AddKnown.isNegative() && LHSOrRHSKnownNegative))
      return OverflowResult::NeverOverflows;
  }
 
  return OverflowResult::MayOverflow;
}
 
OverflowResult llvm::computeOverflowForUnsignedSub(const Value *LHS,
                                                   const Value *RHS,
                                                   const DataLayout &DL,
                                                   AssumptionCache *AC,
                                                   const Instruction *CxtI,
                                                   const DominatorTree *DT) {
  // Checking for conditions implied by dominating conditions may be expensive.
  // Limit it to usub_with_overflow calls for now.
  if (match(CxtI,
            m_Intrinsic<Intrinsic::usub_with_overflow>(m_Value(), m_Value())))
    if (auto C =
            isImpliedByDomCondition(CmpInst::ICMP_UGE, LHS, RHS, CxtI, DL)) {
      if (*C)
        return OverflowResult::NeverOverflows;
      return OverflowResult::AlwaysOverflowsLow;
    }
  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
      LHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT);
  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
      RHS, /*ForSigned=*/false, DL, /*Depth=*/0, AC, CxtI, DT);
  return mapOverflowResult(LHSRange.unsignedSubMayOverflow(RHSRange));
}
 
OverflowResult llvm::computeOverflowForSignedSub(const Value *LHS,
                                                 const Value *RHS,
                                                 const DataLayout &DL,
                                                 AssumptionCache *AC,
                                                 const Instruction *CxtI,
                                                 const DominatorTree *DT) {
  // If LHS and RHS each have at least two sign bits, the subtraction
  // cannot overflow.
  if (ComputeNumSignBits(LHS, DL, 0, AC, CxtI, DT) > 1 &&
      ComputeNumSignBits(RHS, DL, 0, AC, CxtI, DT) > 1)
    return OverflowResult::NeverOverflows;
 
  ConstantRange LHSRange = computeConstantRangeIncludingKnownBits(
      LHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
  ConstantRange RHSRange = computeConstantRangeIncludingKnownBits(
      RHS, /*ForSigned=*/true, DL, /*Depth=*/0, AC, CxtI, DT);
  return mapOverflowResult(LHSRange.signedSubMayOverflow(RHSRange));
}
 
bool llvm::isOverflowIntrinsicNoWrap(const WithOverflowInst *WO,
                                     const DominatorTree &DT) {
  SmallVector<const BranchInst *, 2> GuardingBranches;
  SmallVector<const ExtractValueInst *, 2> Results;
 
  for (const User *U : WO->users()) {
    if (const auto *EVI = dyn_cast<ExtractValueInst>(U)) {
      assert(EVI->getNumIndices() == 1 && "Obvious from CI's type");
 
      if (EVI->getIndices()[0] == 0)
        Results.push_back(EVI);
      else {
        assert(EVI->getIndices()[0] == 1 && "Obvious from CI's type");
 
        for (const auto *U : EVI->users())
          if (const auto *B = dyn_cast<BranchInst>(U)) {
            assert(B->isConditional() && "How else is it using an i1?");
            GuardingBranches.push_back(B);
          }
      }
    } else {
      // We are using the aggregate directly in a way we don't want to analyze
      // here (storing it to a global, say).
      return false;
    }
  }
 
  auto AllUsesGuardedByBranch = [&](const BranchInst *BI) {
    BasicBlockEdge NoWrapEdge(BI->getParent(), BI->getSuccessor(1));
    if (!NoWrapEdge.isSingleEdge())
      return false;
 
    // Check if all users of the add are provably no-wrap.
    for (const auto *Result : Results) {
      // If the extractvalue itself is not executed on overflow, the we don't
      // need to check each use separately, since domination is transitive.
      if (DT.dominates(NoWrapEdge, Result->getParent()))
        continue;
 
      for (auto &RU : Result->uses())
        if (!DT.dominates(NoWrapEdge, RU))
          return false;
    }
 
    return true;
  };
 
  return llvm::any_of(GuardingBranches, AllUsesGuardedByBranch);
}
 
static bool canCreateUndefOrPoison(const Operator *Op, bool PoisonOnly,
                                   bool ConsiderFlags) {
 
  if (ConsiderFlags && Op->hasPoisonGeneratingFlags())
    return true;
 
  unsigned Opcode = Op->getOpcode();
 
  // Check whether opcode is a poison/undef-generating operation
  switch (Opcode) {
  case Instruction::Shl:
  case Instruction::AShr:
  case Instruction::LShr: {
    // Shifts return poison if shiftwidth is larger than the bitwidth.
    if (auto *C = dyn_cast<Constant>(Op->getOperand(1))) {
      SmallVector<Constant *, 4> ShiftAmounts;
      if (auto *FVTy = dyn_cast<FixedVectorType>(C->getType())) {
        unsigned NumElts = FVTy->getNumElements();
        for (unsigned i = 0; i < NumElts; ++i)
          ShiftAmounts.push_back(C->getAggregateElement(i));
      } else if (isa<ScalableVectorType>(C->getType()))
        return true; // Can't tell, just return true to be safe
      else
        ShiftAmounts.push_back(C);
 
      bool Safe = llvm::all_of(ShiftAmounts, [](Constant *C) {
        auto *CI = dyn_cast_or_null<ConstantInt>(C);
        return CI && CI->getValue().ult(C->getType()->getIntegerBitWidth());
      });
      return !Safe;
    }
    return true;
  }
  case Instruction::FPToSI:
  case Instruction::FPToUI:
    // fptosi/ui yields poison if the resulting value does not fit in the
    // destination type.
    return true;