InstructionSimplify.cpp

Go to the documentation of this file.

//===- InstructionSimplify.cpp - Fold instruction operands ----------------===//
//
// 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 implements routines for folding instructions into simpler forms
// that do not require creating new instructions.  This does constant folding
// ("add i32 1, 1" -> "2") but can also handle non-constant operands, either
// returning a constant ("and i32 %x, 0" -> "0") or an already existing value
// ("and i32 %x, %x" -> "%x").  All operands are assumed to have already been
// simplified: This is usually true and assuming it simplifies the logic (if
// they have not been simplified then results are correct but maybe suboptimal).
//
//===----------------------------------------------------------------------===//
 
#include "llvm/Analysis/InstructionSimplify.h"
 
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Analysis/AliasAnalysis.h"
#include "llvm/Analysis/AssumptionCache.h"
#include "llvm/Analysis/CaptureTracking.h"
#include "llvm/Analysis/CmpInstAnalysis.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/InstSimplifyFolder.h"
#include "llvm/Analysis/LoopAnalysisManager.h"
#include "llvm/Analysis/MemoryBuiltins.h"
#include "llvm/Analysis/OverflowInstAnalysis.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/Analysis/VectorUtils.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Support/KnownBits.h"
#include <algorithm>
#include <optional>
using namespace llvm;
using namespace llvm::PatternMatch;
 
#define DEBUG_TYPE "instsimplify"
 
enum { RecursionLimit = 3 };
 
STATISTIC(NumExpand, "Number of expansions");
STATISTIC(NumReassoc, "Number of reassociations");
 
static Value *simplifyAndInst(Value *, Value *, const SimplifyQuery &,
                              unsigned);
static Value *simplifyUnOp(unsigned, Value *, const SimplifyQuery &, unsigned);
static Value *simplifyFPUnOp(unsigned, Value *, const FastMathFlags &,
                             const SimplifyQuery &, unsigned);
static Value *simplifyBinOp(unsigned, Value *, Value *, const SimplifyQuery &,
                            unsigned);
static Value *simplifyBinOp(unsigned, Value *, Value *, const FastMathFlags &,
                            const SimplifyQuery &, unsigned);
static Value *simplifyCmpInst(unsigned, Value *, Value *, const SimplifyQuery &,
                              unsigned);
static Value *simplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q, unsigned MaxRecurse);
static Value *simplifyOrInst(Value *, Value *, const SimplifyQuery &, unsigned);
static Value *simplifyXorInst(Value *, Value *, const SimplifyQuery &,
                              unsigned);
static Value *simplifyCastInst(unsigned, Value *, Type *, const SimplifyQuery &,
                               unsigned);
static Value *simplifyGEPInst(Type *, Value *, ArrayRef<Value *>, bool,
                              const SimplifyQuery &, unsigned);
static Value *simplifySelectInst(Value *, Value *, Value *,
                                 const SimplifyQuery &, unsigned);
 
static Value *foldSelectWithBinaryOp(Value *Cond, Value *TrueVal,
                                     Value *FalseVal) {
  BinaryOperator::BinaryOps BinOpCode;
  if (auto *BO = dyn_cast<BinaryOperator>(Cond))
    BinOpCode = BO->getOpcode();
  else
    return nullptr;
 
  CmpInst::Predicate ExpectedPred, Pred1, Pred2;
  if (BinOpCode == BinaryOperator::Or) {
    ExpectedPred = ICmpInst::ICMP_NE;
  } else if (BinOpCode == BinaryOperator::And) {
    ExpectedPred = ICmpInst::ICMP_EQ;
  } else
    return nullptr;
 
  // %A = icmp eq %TV, %FV
  // %B = icmp eq %X, %Y (and one of these is a select operand)
  // %C = and %A, %B
  // %D = select %C, %TV, %FV
  // -->
  // %FV
 
  // %A = icmp ne %TV, %FV
  // %B = icmp ne %X, %Y (and one of these is a select operand)
  // %C = or %A, %B
  // %D = select %C, %TV, %FV
  // -->
  // %TV
  Value *X, *Y;
  if (!match(Cond, m_c_BinOp(m_c_ICmp(Pred1, m_Specific(TrueVal),
                                      m_Specific(FalseVal)),
                             m_ICmp(Pred2, m_Value(X), m_Value(Y)))) ||
      Pred1 != Pred2 || Pred1 != ExpectedPred)
    return nullptr;
 
  if (X == TrueVal || X == FalseVal || Y == TrueVal || Y == FalseVal)
    return BinOpCode == BinaryOperator::Or ? TrueVal : FalseVal;
 
  return nullptr;
}
 
/// For a boolean type or a vector of boolean type, return false or a vector
/// with every element false.
static Constant *getFalse(Type *Ty) { return ConstantInt::getFalse(Ty); }
 
/// For a boolean type or a vector of boolean type, return true or a vector
/// with every element true.
static Constant *getTrue(Type *Ty) { return ConstantInt::getTrue(Ty); }
 
/// isSameCompare - Is V equivalent to the comparison "LHS Pred RHS"?
static bool isSameCompare(Value *V, CmpInst::Predicate Pred, Value *LHS,
                          Value *RHS) {
  CmpInst *Cmp = dyn_cast<CmpInst>(V);
  if (!Cmp)
    return false;
  CmpInst::Predicate CPred = Cmp->getPredicate();
  Value *CLHS = Cmp->getOperand(0), *CRHS = Cmp->getOperand(1);
  if (CPred == Pred && CLHS == LHS && CRHS == RHS)
    return true;
  return CPred == CmpInst::getSwappedPredicate(Pred) && CLHS == RHS &&
         CRHS == LHS;
}
 
/// Simplify comparison with true or false branch of select:
///  %sel = select i1 %cond, i32 %tv, i32 %fv
///  %cmp = icmp sle i32 %sel, %rhs
/// Compose new comparison by substituting %sel with either %tv or %fv
/// and see if it simplifies.
static Value *simplifyCmpSelCase(CmpInst::Predicate Pred, Value *LHS,
                                 Value *RHS, Value *Cond,
                                 const SimplifyQuery &Q, unsigned MaxRecurse,
                                 Constant *TrueOrFalse) {
  Value *SimplifiedCmp = simplifyCmpInst(Pred, LHS, RHS, Q, MaxRecurse);
  if (SimplifiedCmp == Cond) {
    // %cmp simplified to the select condition (%cond).
    return TrueOrFalse;
  } else if (!SimplifiedCmp && isSameCompare(Cond, Pred, LHS, RHS)) {
    // It didn't simplify. However, if composed comparison is equivalent
    // to the select condition (%cond) then we can replace it.
    return TrueOrFalse;
  }
  return SimplifiedCmp;
}
 
/// Simplify comparison with true branch of select
static Value *simplifyCmpSelTrueCase(CmpInst::Predicate Pred, Value *LHS,
                                     Value *RHS, Value *Cond,
                                     const SimplifyQuery &Q,
                                     unsigned MaxRecurse) {
  return simplifyCmpSelCase(Pred, LHS, RHS, Cond, Q, MaxRecurse,
                            getTrue(Cond->getType()));
}
 
/// Simplify comparison with false branch of select
static Value *simplifyCmpSelFalseCase(CmpInst::Predicate Pred, Value *LHS,
                                      Value *RHS, Value *Cond,
                                      const SimplifyQuery &Q,
                                      unsigned MaxRecurse) {
  return simplifyCmpSelCase(Pred, LHS, RHS, Cond, Q, MaxRecurse,
                            getFalse(Cond->getType()));
}
 
/// We know comparison with both branches of select can be simplified, but they
/// are not equal. This routine handles some logical simplifications.
static Value *handleOtherCmpSelSimplifications(Value *TCmp, Value *FCmp,
                                               Value *Cond,
                                               const SimplifyQuery &Q,
                                               unsigned MaxRecurse) {
  // If the false value simplified to false, then the result of the compare
  // is equal to "Cond && TCmp".  This also catches the case when the false
  // value simplified to false and the true value to true, returning "Cond".
  // Folding select to and/or isn't poison-safe in general; impliesPoison
  // checks whether folding it does not convert a well-defined value into
  // poison.
  if (match(FCmp, m_Zero()) && impliesPoison(TCmp, Cond))
    if (Value *V = simplifyAndInst(Cond, TCmp, Q, MaxRecurse))
      return V;
  // If the true value simplified to true, then the result of the compare
  // is equal to "Cond || FCmp".
  if (match(TCmp, m_One()) && impliesPoison(FCmp, Cond))
    if (Value *V = simplifyOrInst(Cond, FCmp, Q, MaxRecurse))
      return V;
  // Finally, if the false value simplified to true and the true value to
  // false, then the result of the compare is equal to "!Cond".
  if (match(FCmp, m_One()) && match(TCmp, m_Zero()))
    if (Value *V = simplifyXorInst(
            Cond, Constant::getAllOnesValue(Cond->getType()), Q, MaxRecurse))
      return V;
  return nullptr;
}
 
/// Does the given value dominate the specified phi node?
static bool valueDominatesPHI(Value *V, PHINode *P, const DominatorTree *DT) {
  Instruction *I = dyn_cast<Instruction>(V);
  if (!I)
    // Arguments and constants dominate all instructions.
    return true;
 
  // If we are processing instructions (and/or basic blocks) that have not been
  // fully added to a function, the parent nodes may still be null. Simply
  // return the conservative answer in these cases.
  if (!I->getParent() || !P->getParent() || !I->getFunction())
    return false;
 
  // If we have a DominatorTree then do a precise test.
  if (DT)
    return DT->dominates(I, P);
 
  // Otherwise, if the instruction is in the entry block and is not an invoke,
  // then it obviously dominates all phi nodes.
  if (I->getParent()->isEntryBlock() && !isa<InvokeInst>(I) &&
      !isa<CallBrInst>(I))
    return true;
 
  return false;
}
 
/// Try to simplify a binary operator of form "V op OtherOp" where V is
/// "(B0 opex B1)" by distributing 'op' across 'opex' as
/// "(B0 op OtherOp) opex (B1 op OtherOp)".
static Value *expandBinOp(Instruction::BinaryOps Opcode, Value *V,
                          Value *OtherOp, Instruction::BinaryOps OpcodeToExpand,
                          const SimplifyQuery &Q, unsigned MaxRecurse) {
  auto *B = dyn_cast<BinaryOperator>(V);
  if (!B || B->getOpcode() != OpcodeToExpand)
    return nullptr;
  Value *B0 = B->getOperand(0), *B1 = B->getOperand(1);
  Value *L =
      simplifyBinOp(Opcode, B0, OtherOp, Q.getWithoutUndef(), MaxRecurse);
  if (!L)
    return nullptr;
  Value *R =
      simplifyBinOp(Opcode, B1, OtherOp, Q.getWithoutUndef(), MaxRecurse);
  if (!R)
    return nullptr;
 
  // Does the expanded pair of binops simplify to the existing binop?
  if ((L == B0 && R == B1) ||
      (Instruction::isCommutative(OpcodeToExpand) && L == B1 && R == B0)) {
    ++NumExpand;
    return B;
  }
 
  // Otherwise, return "L op' R" if it simplifies.
  Value *S = simplifyBinOp(OpcodeToExpand, L, R, Q, MaxRecurse);
  if (!S)
    return nullptr;
 
  ++NumExpand;
  return S;
}
 
/// Try to simplify binops of form "A op (B op' C)" or the commuted variant by
/// distributing op over op'.
static Value *expandCommutativeBinOp(Instruction::BinaryOps Opcode, Value *L,
                                     Value *R,
                                     Instruction::BinaryOps OpcodeToExpand,
                                     const SimplifyQuery &Q,
                                     unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;
 
  if (Value *V = expandBinOp(Opcode, L, R, OpcodeToExpand, Q, MaxRecurse))
    return V;
  if (Value *V = expandBinOp(Opcode, R, L, OpcodeToExpand, Q, MaxRecurse))
    return V;
  return nullptr;
}
 
/// Generic simplifications for associative binary operations.
/// Returns the simpler value, or null if none was found.
static Value *simplifyAssociativeBinOp(Instruction::BinaryOps Opcode,
                                       Value *LHS, Value *RHS,
                                       const SimplifyQuery &Q,
                                       unsigned MaxRecurse) {
  assert(Instruction::isAssociative(Opcode) && "Not an associative operation!");
 
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;
 
  BinaryOperator *Op0 = dyn_cast<BinaryOperator>(LHS);
  BinaryOperator *Op1 = dyn_cast<BinaryOperator>(RHS);
 
  // Transform: "(A op B) op C" ==> "A op (B op C)" if it simplifies completely.
  if (Op0 && Op0->getOpcode() == Opcode) {
    Value *A = Op0->getOperand(0);
    Value *B = Op0->getOperand(1);
    Value *C = RHS;
 
    // Does "B op C" simplify?
    if (Value *V = simplifyBinOp(Opcode, B, C, Q, MaxRecurse)) {
      // It does!  Return "A op V" if it simplifies or is already available.
      // If V equals B then "A op V" is just the LHS.
      if (V == B)
        return LHS;
      // Otherwise return "A op V" if it simplifies.
      if (Value *W = simplifyBinOp(Opcode, A, V, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }
 
  // Transform: "A op (B op C)" ==> "(A op B) op C" if it simplifies completely.
  if (Op1 && Op1->getOpcode() == Opcode) {
    Value *A = LHS;
    Value *B = Op1->getOperand(0);
    Value *C = Op1->getOperand(1);
 
    // Does "A op B" simplify?
    if (Value *V = simplifyBinOp(Opcode, A, B, Q, MaxRecurse)) {
      // It does!  Return "V op C" if it simplifies or is already available.
      // If V equals B then "V op C" is just the RHS.
      if (V == B)
        return RHS;
      // Otherwise return "V op C" if it simplifies.
      if (Value *W = simplifyBinOp(Opcode, V, C, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }
 
  // The remaining transforms require commutativity as well as associativity.
  if (!Instruction::isCommutative(Opcode))
    return nullptr;
 
  // Transform: "(A op B) op C" ==> "(C op A) op B" if it simplifies completely.
  if (Op0 && Op0->getOpcode() == Opcode) {
    Value *A = Op0->getOperand(0);
    Value *B = Op0->getOperand(1);
    Value *C = RHS;
 
    // Does "C op A" simplify?
    if (Value *V = simplifyBinOp(Opcode, C, A, Q, MaxRecurse)) {
      // It does!  Return "V op B" if it simplifies or is already available.
      // If V equals A then "V op B" is just the LHS.
      if (V == A)
        return LHS;
      // Otherwise return "V op B" if it simplifies.
      if (Value *W = simplifyBinOp(Opcode, V, B, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }
 
  // Transform: "A op (B op C)" ==> "B op (C op A)" if it simplifies completely.
  if (Op1 && Op1->getOpcode() == Opcode) {
    Value *A = LHS;
    Value *B = Op1->getOperand(0);
    Value *C = Op1->getOperand(1);
 
    // Does "C op A" simplify?
    if (Value *V = simplifyBinOp(Opcode, C, A, Q, MaxRecurse)) {
      // It does!  Return "B op V" if it simplifies or is already available.
      // If V equals C then "B op V" is just the RHS.
      if (V == C)
        return RHS;
      // Otherwise return "B op V" if it simplifies.
      if (Value *W = simplifyBinOp(Opcode, B, V, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }
 
  return nullptr;
}
 
/// In the case of a binary operation with a select instruction as an operand,
/// try to simplify the binop by seeing whether evaluating it on both branches
/// of the select results in the same value. Returns the common value if so,
/// otherwise returns null.
static Value *threadBinOpOverSelect(Instruction::BinaryOps Opcode, Value *LHS,
                                    Value *RHS, const SimplifyQuery &Q,
                                    unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;
 
  SelectInst *SI;
  if (isa<SelectInst>(LHS)) {
    SI = cast<SelectInst>(LHS);
  } else {
    assert(isa<SelectInst>(RHS) && "No select instruction operand!");
    SI = cast<SelectInst>(RHS);
  }
 
  // Evaluate the BinOp on the true and false branches of the select.
  Value *TV;
  Value *FV;
  if (SI == LHS) {
    TV = simplifyBinOp(Opcode, SI->getTrueValue(), RHS, Q, MaxRecurse);
    FV = simplifyBinOp(Opcode, SI->getFalseValue(), RHS, Q, MaxRecurse);
  } else {
    TV = simplifyBinOp(Opcode, LHS, SI->getTrueValue(), Q, MaxRecurse);
    FV = simplifyBinOp(Opcode, LHS, SI->getFalseValue(), Q, MaxRecurse);
  }
 
  // If they simplified to the same value, then return the common value.
  // If they both failed to simplify then return null.
  if (TV == FV)
    return TV;
 
  // If one branch simplified to undef, return the other one.
  if (TV && Q.isUndefValue(TV))
    return FV;
  if (FV && Q.isUndefValue(FV))
    return TV;
 
  // If applying the operation did not change the true and false select values,
  // then the result of the binop is the select itself.
  if (TV == SI->getTrueValue() && FV == SI->getFalseValue())
    return SI;
 
  // If one branch simplified and the other did not, and the simplified
  // value is equal to the unsimplified one, return the simplified value.
  // For example, select (cond, X, X & Z) & Z -> X & Z.
  if ((FV && !TV) || (TV && !FV)) {
    // Check that the simplified value has the form "X op Y" where "op" is the
    // same as the original operation.
    Instruction *Simplified = dyn_cast<Instruction>(FV ? FV : TV);
    if (Simplified && Simplified->getOpcode() == unsigned(Opcode)) {
      // The value that didn't simplify is "UnsimplifiedLHS op UnsimplifiedRHS".
      // We already know that "op" is the same as for the simplified value.  See
      // if the operands match too.  If so, return the simplified value.
      Value *UnsimplifiedBranch = FV ? SI->getTrueValue() : SI->getFalseValue();
      Value *UnsimplifiedLHS = SI == LHS ? UnsimplifiedBranch : LHS;
      Value *UnsimplifiedRHS = SI == LHS ? RHS : UnsimplifiedBranch;
      if (Simplified->getOperand(0) == UnsimplifiedLHS &&
          Simplified->getOperand(1) == UnsimplifiedRHS)
        return Simplified;
      if (Simplified->isCommutative() &&
          Simplified->getOperand(1) == UnsimplifiedLHS &&
          Simplified->getOperand(0) == UnsimplifiedRHS)
        return Simplified;
    }
  }
 
  return nullptr;
}
 
/// In the case of a comparison with a select instruction, try to simplify the
/// comparison by seeing whether both branches of the select result in the same
/// value. Returns the common value if so, otherwise returns null.
/// For example, if we have:
///  %tmp = select i1 %cmp, i32 1, i32 2
///  %cmp1 = icmp sle i32 %tmp, 3
/// We can simplify %cmp1 to true, because both branches of select are
/// less than 3. We compose new comparison by substituting %tmp with both
/// branches of select and see if it can be simplified.
static Value *threadCmpOverSelect(CmpInst::Predicate Pred, Value *LHS,
                                  Value *RHS, const SimplifyQuery &Q,
                                  unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;
 
  // Make sure the select is on the LHS.
  if (!isa<SelectInst>(LHS)) {
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }
  assert(isa<SelectInst>(LHS) && "Not comparing with a select instruction!");
  SelectInst *SI = cast<SelectInst>(LHS);
  Value *Cond = SI->getCondition();
  Value *TV = SI->getTrueValue();
  Value *FV = SI->getFalseValue();
 
  // Now that we have "cmp select(Cond, TV, FV), RHS", analyse it.
  // Does "cmp TV, RHS" simplify?
  Value *TCmp = simplifyCmpSelTrueCase(Pred, TV, RHS, Cond, Q, MaxRecurse);
  if (!TCmp)
    return nullptr;
 
  // Does "cmp FV, RHS" simplify?
  Value *FCmp = simplifyCmpSelFalseCase(Pred, FV, RHS, Cond, Q, MaxRecurse);
  if (!FCmp)
    return nullptr;
 
  // If both sides simplified to the same value, then use it as the result of
  // the original comparison.
  if (TCmp == FCmp)
    return TCmp;
 
  // The remaining cases only make sense if the select condition has the same
  // type as the result of the comparison, so bail out if this is not so.
  if (Cond->getType()->isVectorTy() == RHS->getType()->isVectorTy())
    return handleOtherCmpSelSimplifications(TCmp, FCmp, Cond, Q, MaxRecurse);
 
  return nullptr;
}
 
/// In the case of a binary operation with an operand that is a PHI instruction,
/// try to simplify the binop by seeing whether evaluating it on the incoming
/// phi values yields the same result for every value. If so returns the common
/// value, otherwise returns null.
static Value *threadBinOpOverPHI(Instruction::BinaryOps Opcode, Value *LHS,
                                 Value *RHS, const SimplifyQuery &Q,
                                 unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;
 
  PHINode *PI;
  if (isa<PHINode>(LHS)) {
    PI = cast<PHINode>(LHS);
    // Bail out if RHS and the phi may be mutually interdependent due to a loop.
    if (!valueDominatesPHI(RHS, PI, Q.DT))
      return nullptr;
  } else {
    assert(isa<PHINode>(RHS) && "No PHI instruction operand!");
    PI = cast<PHINode>(RHS);
    // Bail out if LHS and the phi may be mutually interdependent due to a loop.
    if (!valueDominatesPHI(LHS, PI, Q.DT))
      return nullptr;
  }
 
  // Evaluate the BinOp on the incoming phi values.
  Value *CommonValue = nullptr;
  for (Use &Incoming : PI->incoming_values()) {
    // If the incoming value is the phi node itself, it can safely be skipped.
    if (Incoming == PI)
      continue;
    Instruction *InTI = PI->getIncomingBlock(Incoming)->getTerminator();
    Value *V = PI == LHS
                   ? simplifyBinOp(Opcode, Incoming, RHS,
                                   Q.getWithInstruction(InTI), MaxRecurse)
                   : simplifyBinOp(Opcode, LHS, Incoming,
                                   Q.getWithInstruction(InTI), MaxRecurse);
    // If the operation failed to simplify, or simplified to a different value
    // to previously, then give up.
    if (!V || (CommonValue && V != CommonValue))
      return nullptr;
    CommonValue = V;
  }
 
  return CommonValue;
}
 
/// In the case of a comparison with a PHI instruction, try to simplify the
/// comparison by seeing whether comparing with all of the incoming phi values
/// yields the same result every time. If so returns the common result,
/// otherwise returns null.
static Value *threadCmpOverPHI(CmpInst::Predicate Pred, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;
 
  // Make sure the phi is on the LHS.
  if (!isa<PHINode>(LHS)) {
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }
  assert(isa<PHINode>(LHS) && "Not comparing with a phi instruction!");
  PHINode *PI = cast<PHINode>(LHS);
 
  // Bail out if RHS and the phi may be mutually interdependent due to a loop.
  if (!valueDominatesPHI(RHS, PI, Q.DT))
    return nullptr;
 
  // Evaluate the BinOp on the incoming phi values.
  Value *CommonValue = nullptr;
  for (unsigned u = 0, e = PI->getNumIncomingValues(); u < e; ++u) {
    Value *Incoming = PI->getIncomingValue(u);
    Instruction *InTI = PI->getIncomingBlock(u)->getTerminator();
    // If the incoming value is the phi node itself, it can safely be skipped.
    if (Incoming == PI)
      continue;
    // Change the context instruction to the "edge" that flows into the phi.
    // This is important because that is where incoming is actually "evaluated"
    // even though it is used later somewhere else.
    Value *V = simplifyCmpInst(Pred, Incoming, RHS, Q.getWithInstruction(InTI),
                               MaxRecurse);
    // If the operation failed to simplify, or simplified to a different value
    // to previously, then give up.
    if (!V || (CommonValue && V != CommonValue))
      return nullptr;
    CommonValue = V;
  }
 
  return CommonValue;
}
 
static Constant *foldOrCommuteConstant(Instruction::BinaryOps Opcode,
                                       Value *&Op0, Value *&Op1,
                                       const SimplifyQuery &Q) {
  if (auto *CLHS = dyn_cast<Constant>(Op0)) {
    if (auto *CRHS = dyn_cast<Constant>(Op1)) {
      switch (Opcode) {
      default:
        break;
      case Instruction::FAdd:
      case Instruction::FSub:
      case Instruction::FMul:
      case Instruction::FDiv:
      case Instruction::FRem:
        if (Q.CxtI != nullptr)
          return ConstantFoldFPInstOperands(Opcode, CLHS, CRHS, Q.DL, Q.CxtI);
      }
      return ConstantFoldBinaryOpOperands(Opcode, CLHS, CRHS, Q.DL);
    }
 
    // Canonicalize the constant to the RHS if this is a commutative operation.
    if (Instruction::isCommutative(Opcode))
      std::swap(Op0, Op1);
  }
  return nullptr;
}
 
/// Given operands for an Add, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyAddInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Add, Op0, Op1, Q))
    return C;
 
  // X + poison -> poison
  if (isa<PoisonValue>(Op1))
    return Op1;
 
  // X + undef -> undef
  if (Q.isUndefValue(Op1))
    return Op1;
 
  // X + 0 -> X
  if (match(Op1, m_Zero()))
    return Op0;
 
  // If two operands are negative, return 0.
  if (isKnownNegation(Op0, Op1))
    return Constant::getNullValue(Op0->getType());
 
  // X + (Y - X) -> Y
  // (Y - X) + X -> Y
  // Eg: X + -X -> 0
  Value *Y = nullptr;
  if (match(Op1, m_Sub(m_Value(Y), m_Specific(Op0))) ||
      match(Op0, m_Sub(m_Value(Y), m_Specific(Op1))))
    return Y;
 
  // X + ~X -> -1   since   ~X = -X-1
  Type *Ty = Op0->getType();
  if (match(Op0, m_Not(m_Specific(Op1))) || match(Op1, m_Not(m_Specific(Op0))))
    return Constant::getAllOnesValue(Ty);
 
  // add nsw/nuw (xor Y, signmask), signmask --> Y
  // The no-wrapping add guarantees that the top bit will be set by the add.
  // Therefore, the xor must be clearing the already set sign bit of Y.
  if ((IsNSW || IsNUW) && match(Op1, m_SignMask()) &&
      match(Op0, m_Xor(m_Value(Y), m_SignMask())))
    return Y;
 
  // add nuw %x, -1  ->  -1, because %x can only be 0.
  if (IsNUW && match(Op1, m_AllOnes()))
    return Op1; // Which is -1.
 
  /// i1 add -> xor.
  if (MaxRecurse && Op0->getType()->isIntOrIntVectorTy(1))
    if (Value *V = simplifyXorInst(Op0, Op1, Q, MaxRecurse - 1))
      return V;
 
  // Try some generic simplifications for associative operations.
  if (Value *V =
          simplifyAssociativeBinOp(Instruction::Add, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // Threading Add over selects and phi nodes is pointless, so don't bother.
  // Threading over the select in "A + select(cond, B, C)" means evaluating
  // "A+B" and "A+C" and seeing if they are equal; but they are equal if and
  // only if B and C are equal.  If B and C are equal then (since we assume
  // that operands have already been simplified) "select(cond, B, C)" should
  // have been simplified to the common value of B and C already.  Analysing
  // "A+B" and "A+C" thus gains nothing, but costs compile time.  Similarly
  // for threading over phi nodes.
 
  return nullptr;
}
 
Value *llvm::simplifyAddInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                             const SimplifyQuery &Query) {
  return ::simplifyAddInst(Op0, Op1, IsNSW, IsNUW, Query, RecursionLimit);
}
 
/// Compute the base pointer and cumulative constant offsets for V.
///
/// This strips all constant offsets off of V, leaving it the base pointer, and
/// accumulates the total constant offset applied in the returned constant.
/// It returns zero if there are no constant offsets applied.
///
/// This is very similar to stripAndAccumulateConstantOffsets(), except it
/// normalizes the offset bitwidth to the stripped pointer type, not the
/// original pointer type.
static APInt stripAndComputeConstantOffsets(const DataLayout &DL, Value *&V,
                                            bool AllowNonInbounds = false) {
  assert(V->getType()->isPtrOrPtrVectorTy());
 
  APInt Offset = APInt::getZero(DL.getIndexTypeSizeInBits(V->getType()));
  V = V->stripAndAccumulateConstantOffsets(DL, Offset, AllowNonInbounds);
  // As that strip may trace through `addrspacecast`, need to sext or trunc
  // the offset calculated.
  return Offset.sextOrTrunc(DL.getIndexTypeSizeInBits(V->getType()));
}
 
/// Compute the constant difference between two pointer values.
/// If the difference is not a constant, returns zero.
static Constant *computePointerDifference(const DataLayout &DL, Value *LHS,
                                          Value *RHS) {
  APInt LHSOffset = stripAndComputeConstantOffsets(DL, LHS);
  APInt RHSOffset = stripAndComputeConstantOffsets(DL, RHS);
 
  // If LHS and RHS are not related via constant offsets to the same base
  // value, there is nothing we can do here.
  if (LHS != RHS)
    return nullptr;
 
  // Otherwise, the difference of LHS - RHS can be computed as:
  //    LHS - RHS
  //  = (LHSOffset + Base) - (RHSOffset + Base)
  //  = LHSOffset - RHSOffset
  Constant *Res = ConstantInt::get(LHS->getContext(), LHSOffset - RHSOffset);
  if (auto *VecTy = dyn_cast<VectorType>(LHS->getType()))
    Res = ConstantVector::getSplat(VecTy->getElementCount(), Res);
  return Res;
}
 
/// Test if there is a dominating equivalence condition for the
/// two operands. If there is, try to reduce the binary operation
/// between the two operands.
/// Example: Op0 - Op1 --> 0 when Op0 == Op1
static Value *simplifyByDomEq(unsigned Opcode, Value *Op0, Value *Op1,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  // Recursive run it can not get any benefit
  if (MaxRecurse != RecursionLimit)
    return nullptr;
 
  std::optional<bool> Imp =
      isImpliedByDomCondition(CmpInst::ICMP_EQ, Op0, Op1, Q.CxtI, Q.DL);
  if (Imp && *Imp) {
    Type *Ty = Op0->getType();
    switch (Opcode) {
    case Instruction::Sub:
    case Instruction::Xor:
    case Instruction::URem:
    case Instruction::SRem:
      return Constant::getNullValue(Ty);
 
    case Instruction::SDiv:
    case Instruction::UDiv:
      return ConstantInt::get(Ty, 1);
 
    case Instruction::And:
    case Instruction::Or:
      // Could be either one - choose Op1 since that's more likely a constant.
      return Op1;
    default:
      break;
    }
  }
  return nullptr;
}
 
/// Given operands for a Sub, see if we can fold the result.
/// If not, this returns null.
static Value *simplifySubInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Sub, Op0, Op1, Q))
    return C;
 
  // X - poison -> poison
  // poison - X -> poison
  if (isa<PoisonValue>(Op0) || isa<PoisonValue>(Op1))
    return PoisonValue::get(Op0->getType());
 
  // X - undef -> undef
  // undef - X -> undef
  if (Q.isUndefValue(Op0) || Q.isUndefValue(Op1))
    return UndefValue::get(Op0->getType());
 
  // X - 0 -> X
  if (match(Op1, m_Zero()))
    return Op0;
 
  // X - X -> 0
  if (Op0 == Op1)
    return Constant::getNullValue(Op0->getType());
 
  // Is this a negation?
  if (match(Op0, m_Zero())) {
    // 0 - X -> 0 if the sub is NUW.
    if (IsNUW)
      return Constant::getNullValue(Op0->getType());
 
    KnownBits Known = computeKnownBits(Op1, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (Known.Zero.isMaxSignedValue()) {
      // Op1 is either 0 or the minimum signed value. If the sub is NSW, then
      // Op1 must be 0 because negating the minimum signed value is undefined.
      if (IsNSW)
        return Constant::getNullValue(Op0->getType());
 
      // 0 - X -> X if X is 0 or the minimum signed value.
      return Op1;
    }
  }
 
  // (X + Y) - Z -> X + (Y - Z) or Y + (X - Z) if everything simplifies.
  // For example, (X + Y) - Y -> X; (Y + X) - Y -> X
  Value *X = nullptr, *Y = nullptr, *Z = Op1;
  if (MaxRecurse && match(Op0, m_Add(m_Value(X), m_Value(Y)))) { // (X + Y) - Z
    // See if "V === Y - Z" simplifies.
    if (Value *V = simplifyBinOp(Instruction::Sub, Y, Z, Q, MaxRecurse - 1))
      // It does!  Now see if "X + V" simplifies.
      if (Value *W = simplifyBinOp(Instruction::Add, X, V, Q, MaxRecurse - 1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
    // See if "V === X - Z" simplifies.
    if (Value *V = simplifyBinOp(Instruction::Sub, X, Z, Q, MaxRecurse - 1))
      // It does!  Now see if "Y + V" simplifies.
      if (Value *W = simplifyBinOp(Instruction::Add, Y, V, Q, MaxRecurse - 1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
  }
 
  // X - (Y + Z) -> (X - Y) - Z or (X - Z) - Y if everything simplifies.
  // For example, X - (X + 1) -> -1
  X = Op0;
  if (MaxRecurse && match(Op1, m_Add(m_Value(Y), m_Value(Z)))) { // X - (Y + Z)
    // See if "V === X - Y" simplifies.
    if (Value *V = simplifyBinOp(Instruction::Sub, X, Y, Q, MaxRecurse - 1))
      // It does!  Now see if "V - Z" simplifies.
      if (Value *W = simplifyBinOp(Instruction::Sub, V, Z, Q, MaxRecurse - 1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
    // See if "V === X - Z" simplifies.
    if (Value *V = simplifyBinOp(Instruction::Sub, X, Z, Q, MaxRecurse - 1))
      // It does!  Now see if "V - Y" simplifies.
      if (Value *W = simplifyBinOp(Instruction::Sub, V, Y, Q, MaxRecurse - 1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
  }
 
  // Z - (X - Y) -> (Z - X) + Y if everything simplifies.
  // For example, X - (X - Y) -> Y.
  Z = Op0;
  if (MaxRecurse && match(Op1, m_Sub(m_Value(X), m_Value(Y)))) // Z - (X - Y)
    // See if "V === Z - X" simplifies.
    if (Value *V = simplifyBinOp(Instruction::Sub, Z, X, Q, MaxRecurse - 1))
      // It does!  Now see if "V + Y" simplifies.
      if (Value *W = simplifyBinOp(Instruction::Add, V, Y, Q, MaxRecurse - 1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
 
  // trunc(X) - trunc(Y) -> trunc(X - Y) if everything simplifies.
  if (MaxRecurse && match(Op0, m_Trunc(m_Value(X))) &&
      match(Op1, m_Trunc(m_Value(Y))))
    if (X->getType() == Y->getType())
      // See if "V === X - Y" simplifies.
      if (Value *V = simplifyBinOp(Instruction::Sub, X, Y, Q, MaxRecurse - 1))
        // It does!  Now see if "trunc V" simplifies.
        if (Value *W = simplifyCastInst(Instruction::Trunc, V, Op0->getType(),
                                        Q, MaxRecurse - 1))
          // It does, return the simplified "trunc V".
          return W;
 
  // Variations on GEP(base, I, ...) - GEP(base, i, ...) -> GEP(null, I-i, ...).
  if (match(Op0, m_PtrToInt(m_Value(X))) && match(Op1, m_PtrToInt(m_Value(Y))))
    if (Constant *Result = computePointerDifference(Q.DL, X, Y))
      return ConstantExpr::getIntegerCast(Result, Op0->getType(), true);
 
  // i1 sub -> xor.
  if (MaxRecurse && Op0->getType()->isIntOrIntVectorTy(1))
    if (Value *V = simplifyXorInst(Op0, Op1, Q, MaxRecurse - 1))
      return V;
 
  // Threading Sub over selects and phi nodes is pointless, so don't bother.
  // Threading over the select in "A - select(cond, B, C)" means evaluating
  // "A-B" and "A-C" and seeing if they are equal; but they are equal if and
  // only if B and C are equal.  If B and C are equal then (since we assume
  // that operands have already been simplified) "select(cond, B, C)" should
  // have been simplified to the common value of B and C already.  Analysing
  // "A-B" and "A-C" thus gains nothing, but costs compile time.  Similarly
  // for threading over phi nodes.
 
  if (Value *V = simplifyByDomEq(Instruction::Sub, Op0, Op1, Q, MaxRecurse))
    return V;
 
  return nullptr;
}
 
Value *llvm::simplifySubInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                             const SimplifyQuery &Q) {
  return ::simplifySubInst(Op0, Op1, IsNSW, IsNUW, Q, RecursionLimit);
}
 
/// Given operands for a Mul, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyMulInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Mul, Op0, Op1, Q))
    return C;
 
  // X * poison -> poison
  if (isa<PoisonValue>(Op1))
    return Op1;
 
  // X * undef -> 0
  // X * 0 -> 0
  if (Q.isUndefValue(Op1) || match(Op1, m_Zero()))
    return Constant::getNullValue(Op0->getType());
 
  // X * 1 -> X
  if (match(Op1, m_One()))
    return Op0;
 
  // (X / Y) * Y -> X if the division is exact.
  Value *X = nullptr;
  if (Q.IIQ.UseInstrInfo &&
      (match(Op0,
             m_Exact(m_IDiv(m_Value(X), m_Specific(Op1)))) ||     // (X / Y) * Y
       match(Op1, m_Exact(m_IDiv(m_Value(X), m_Specific(Op0)))))) // Y * (X / Y)
    return X;
 
   if (Op0->getType()->isIntOrIntVectorTy(1)) {
    // mul i1 nsw is a special-case because -1 * -1 is poison (+1 is not
    // representable). All other cases reduce to 0, so just return 0.
    if (IsNSW)
      return ConstantInt::getNullValue(Op0->getType());
 
    // Treat "mul i1" as "and i1".
    if (MaxRecurse)
      if (Value *V = simplifyAndInst(Op0, Op1, Q, MaxRecurse - 1))
        return V;
  }
 
  // Try some generic simplifications for associative operations.
  if (Value *V =
          simplifyAssociativeBinOp(Instruction::Mul, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // Mul distributes over Add. Try some generic simplifications based on this.
  if (Value *V = expandCommutativeBinOp(Instruction::Mul, Op0, Op1,
                                        Instruction::Add, Q, MaxRecurse))
    return V;
 
  // If the operation is with the result of a select instruction, check whether
  // operating on either branch of the select always yields the same value.
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
    if (Value *V =
            threadBinOpOverSelect(Instruction::Mul, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V =
            threadBinOpOverPHI(Instruction::Mul, Op0, Op1, Q, MaxRecurse))
      return V;
 
  return nullptr;
}
 
Value *llvm::simplifyMulInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                             const SimplifyQuery &Q) {
  return ::simplifyMulInst(Op0, Op1, IsNSW, IsNUW, Q, RecursionLimit);
}
 
/// Check for common or similar folds of integer division or integer remainder.
/// This applies to all 4 opcodes (sdiv/udiv/srem/urem).
static Value *simplifyDivRem(Instruction::BinaryOps Opcode, Value *Op0,
                             Value *Op1, const SimplifyQuery &Q,
                             unsigned MaxRecurse) {
  bool IsDiv = (Opcode == Instruction::SDiv || Opcode == Instruction::UDiv);
  bool IsSigned = (Opcode == Instruction::SDiv || Opcode == Instruction::SRem);
 
  Type *Ty = Op0->getType();
 
  // X / undef -> poison
  // X % undef -> poison
  if (Q.isUndefValue(Op1) || isa<PoisonValue>(Op1))
    return PoisonValue::get(Ty);
 
  // X / 0 -> poison
  // X % 0 -> poison
  // We don't need to preserve faults!
  if (match(Op1, m_Zero()))
    return PoisonValue::get(Ty);
 
  // If any element of a constant divisor fixed width vector is zero or undef
  // the behavior is undefined and we can fold the whole op to poison.
  auto *Op1C = dyn_cast<Constant>(Op1);
  auto *VTy = dyn_cast<FixedVectorType>(Ty);
  if (Op1C && VTy) {
    unsigned NumElts = VTy->getNumElements();
    for (unsigned i = 0; i != NumElts; ++i) {
      Constant *Elt = Op1C->getAggregateElement(i);
      if (Elt && (Elt->isNullValue() || Q.isUndefValue(Elt)))
        return PoisonValue::get(Ty);
    }
  }
 
  // poison / X -> poison
  // poison % X -> poison
  if (isa<PoisonValue>(Op0))
    return Op0;
 
  // undef / X -> 0
  // undef % X -> 0
  if (Q.isUndefValue(Op0))
    return Constant::getNullValue(Ty);
 
  // 0 / X -> 0
  // 0 % X -> 0
  if (match(Op0, m_Zero()))
    return Constant::getNullValue(Op0->getType());
 
  // X / X -> 1
  // X % X -> 0
  if (Op0 == Op1)
    return IsDiv ? ConstantInt::get(Ty, 1) : Constant::getNullValue(Ty);
 
  // X / 1 -> X
  // X % 1 -> 0
  // If this is a boolean op (single-bit element type), we can't have
  // division-by-zero or remainder-by-zero, so assume the divisor is 1.
  // Similarly, if we're zero-extending a boolean divisor, then assume it's a 1.
  Value *X;
  if (match(Op1, m_One()) || Ty->isIntOrIntVectorTy(1) ||
      (match(Op1, m_ZExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1)))
    return IsDiv ? Op0 : Constant::getNullValue(Ty);
 
  // If X * Y does not overflow, then:
  //   X * Y / Y -> X
  //   X * Y % Y -> 0
  if (match(Op0, m_c_Mul(m_Value(X), m_Specific(Op1)))) {
    auto *Mul = cast<OverflowingBinaryOperator>(Op0);
    // The multiplication can't overflow if it is defined not to, or if
    // X == A / Y for some A.
    if ((IsSigned && Q.IIQ.hasNoSignedWrap(Mul)) ||
        (!IsSigned && Q.IIQ.hasNoUnsignedWrap(Mul)) ||
        (IsSigned && match(X, m_SDiv(m_Value(), m_Specific(Op1)))) ||
        (!IsSigned && match(X, m_UDiv(m_Value(), m_Specific(Op1))))) {
      return IsDiv ? X : Constant::getNullValue(Op0->getType());
    }
  }
 
  if (Value *V = simplifyByDomEq(Opcode, Op0, Op1, Q, MaxRecurse))
    return V;
 
  return nullptr;
}
 
/// Given a predicate and two operands, return true if the comparison is true.
/// This is a helper for div/rem simplification where we return some other value
/// when we can prove a relationship between the operands.
static bool isICmpTrue(ICmpInst::Predicate Pred, Value *LHS, Value *RHS,
                       const SimplifyQuery &Q, unsigned MaxRecurse) {
  Value *V = simplifyICmpInst(Pred, LHS, RHS, Q, MaxRecurse);
  Constant *C = dyn_cast_or_null<Constant>(V);
  return (C && C->isAllOnesValue());
}
 
/// Return true if we can simplify X / Y to 0. Remainder can adapt that answer
/// to simplify X % Y to X.
static bool isDivZero(Value *X, Value *Y, const SimplifyQuery &Q,
                      unsigned MaxRecurse, bool IsSigned) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return false;
 
  if (IsSigned) {
    // |X| / |Y| --> 0
    //
    // We require that 1 operand is a simple constant. That could be extended to
    // 2 variables if we computed the sign bit for each.
    //
    // Make sure that a constant is not the minimum signed value because taking
    // the abs() of that is undefined.
    Type *Ty = X->getType();
    const APInt *C;
    if (match(X, m_APInt(C)) && !C->isMinSignedValue()) {
      // Is the variable divisor magnitude always greater than the constant
      // dividend magnitude?
      // |Y| > |C| --> Y < -abs(C) or Y > abs(C)
      Constant *PosDividendC = ConstantInt::get(Ty, C->abs());
      Constant *NegDividendC = ConstantInt::get(Ty, -C->abs());
      if (isICmpTrue(CmpInst::ICMP_SLT, Y, NegDividendC, Q, MaxRecurse) ||
          isICmpTrue(CmpInst::ICMP_SGT, Y, PosDividendC, Q, MaxRecurse))
        return true;
    }
    if (match(Y, m_APInt(C))) {
      // Special-case: we can't take the abs() of a minimum signed value. If
      // that's the divisor, then all we have to do is prove that the dividend
      // is also not the minimum signed value.
      if (C->isMinSignedValue())
        return isICmpTrue(CmpInst::ICMP_NE, X, Y, Q, MaxRecurse);
 
      // Is the variable dividend magnitude always less than the constant
      // divisor magnitude?
      // |X| < |C| --> X > -abs(C) and X < abs(C)
      Constant *PosDivisorC = ConstantInt::get(Ty, C->abs());
      Constant *NegDivisorC = ConstantInt::get(Ty, -C->abs());
      if (isICmpTrue(CmpInst::ICMP_SGT, X, NegDivisorC, Q, MaxRecurse) &&
          isICmpTrue(CmpInst::ICMP_SLT, X, PosDivisorC, Q, MaxRecurse))
        return true;
    }
    return false;
  }
 
  // IsSigned == false.
 
  // Is the unsigned dividend known to be less than a constant divisor?
  // TODO: Convert this (and above) to range analysis
  //      ("computeConstantRangeIncludingKnownBits")?
  const APInt *C;
  if (match(Y, m_APInt(C)) &&
      computeKnownBits(X, Q.DL, 0, Q.AC, Q.CxtI, Q.DT).getMaxValue().ult(*C))
    return true;
 
  // Try again for any divisor:
  // Is the dividend unsigned less than the divisor?
  return isICmpTrue(ICmpInst::ICMP_ULT, X, Y, Q, MaxRecurse);
}
 
/// These are simplifications common to SDiv and UDiv.
static Value *simplifyDiv(Instruction::BinaryOps Opcode, Value *Op0, Value *Op1,
                          bool IsExact, const SimplifyQuery &Q,
                          unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
    return C;
 
  if (Value *V = simplifyDivRem(Opcode, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // If this is an exact divide by a constant, then the dividend (Op0) must have
  // at least as many trailing zeros as the divisor to divide evenly. If it has
  // less trailing zeros, then the result must be poison.
  const APInt *DivC;
  if (IsExact && match(Op1, m_APInt(DivC)) && DivC->countr_zero()) {
    KnownBits KnownOp0 = computeKnownBits(Op0, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (KnownOp0.countMaxTrailingZeros() < DivC->countr_zero())
      return PoisonValue::get(Op0->getType());
  }
 
  bool IsSigned = Opcode == Instruction::SDiv;
 
  // (X rem Y) / Y -> 0
  if ((IsSigned && match(Op0, m_SRem(m_Value(), m_Specific(Op1)))) ||
      (!IsSigned && match(Op0, m_URem(m_Value(), m_Specific(Op1)))))
    return Constant::getNullValue(Op0->getType());
 
  // (X /u C1) /u C2 -> 0 if C1 * C2 overflow
  ConstantInt *C1, *C2;
  if (!IsSigned && match(Op0, m_UDiv(m_Value(), m_ConstantInt(C1))) &&
      match(Op1, m_ConstantInt(C2))) {
    bool Overflow;
    (void)C1->getValue().umul_ov(C2->getValue(), Overflow);
    if (Overflow)
      return Constant::getNullValue(Op0->getType());
  }
 
  // If the operation is with the result of a select instruction, check whether
  // operating on either branch of the select always yields the same value.
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
    if (Value *V = threadBinOpOverSelect(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V = threadBinOpOverPHI(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;
 
  if (isDivZero(Op0, Op1, Q, MaxRecurse, IsSigned))
    return Constant::getNullValue(Op0->getType());
 
  return nullptr;
}
 
/// These are simplifications common to SRem and URem.
static Value *simplifyRem(Instruction::BinaryOps Opcode, Value *Op0, Value *Op1,
                          const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
    return C;
 
  if (Value *V = simplifyDivRem(Opcode, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // (X % Y) % Y -> X % Y
  if ((Opcode == Instruction::SRem &&
       match(Op0, m_SRem(m_Value(), m_Specific(Op1)))) ||
      (Opcode == Instruction::URem &&
       match(Op0, m_URem(m_Value(), m_Specific(Op1)))))
    return Op0;
 
  // (X << Y) % X -> 0
  if (Q.IIQ.UseInstrInfo &&
      ((Opcode == Instruction::SRem &&
        match(Op0, m_NSWShl(m_Specific(Op1), m_Value()))) ||
       (Opcode == Instruction::URem &&
        match(Op0, m_NUWShl(m_Specific(Op1), m_Value())))))
    return Constant::getNullValue(Op0->getType());
 
  // If the operation is with the result of a select instruction, check whether
  // operating on either branch of the select always yields the same value.
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
    if (Value *V = threadBinOpOverSelect(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V = threadBinOpOverPHI(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // If X / Y == 0, then X % Y == X.
  if (isDivZero(Op0, Op1, Q, MaxRecurse, Opcode == Instruction::SRem))
    return Op0;
 
  return nullptr;
}
 
/// Given operands for an SDiv, see if we can fold the result.
/// If not, this returns null.
static Value *simplifySDivInst(Value *Op0, Value *Op1, bool IsExact,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  // If two operands are negated and no signed overflow, return -1.
  if (isKnownNegation(Op0, Op1, /*NeedNSW=*/true))
    return Constant::getAllOnesValue(Op0->getType());
 
  return simplifyDiv(Instruction::SDiv, Op0, Op1, IsExact, Q, MaxRecurse);
}
 
Value *llvm::simplifySDivInst(Value *Op0, Value *Op1, bool IsExact,
                              const SimplifyQuery &Q) {
  return ::simplifySDivInst(Op0, Op1, IsExact, Q, RecursionLimit);
}
 
/// Given operands for a UDiv, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyUDivInst(Value *Op0, Value *Op1, bool IsExact,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  return simplifyDiv(Instruction::UDiv, Op0, Op1, IsExact, Q, MaxRecurse);
}
 
Value *llvm::simplifyUDivInst(Value *Op0, Value *Op1, bool IsExact,
                              const SimplifyQuery &Q) {
  return ::simplifyUDivInst(Op0, Op1, IsExact, Q, RecursionLimit);
}
 
/// Given operands for an SRem, see if we can fold the result.
/// If not, this returns null.
static Value *simplifySRemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  // If the divisor is 0, the result is undefined, so assume the divisor is -1.
  // srem Op0, (sext i1 X) --> srem Op0, -1 --> 0
  Value *X;
  if (match(Op1, m_SExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1))
    return ConstantInt::getNullValue(Op0->getType());
 
  // If the two operands are negated, return 0.
  if (isKnownNegation(Op0, Op1))
    return ConstantInt::getNullValue(Op0->getType());
 
  return simplifyRem(Instruction::SRem, Op0, Op1, Q, MaxRecurse);
}
 
Value *llvm::simplifySRemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::simplifySRemInst(Op0, Op1, Q, RecursionLimit);
}
 
/// Given operands for a URem, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyURemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  return simplifyRem(Instruction::URem, Op0, Op1, Q, MaxRecurse);
}
 
Value *llvm::simplifyURemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::simplifyURemInst(Op0, Op1, Q, RecursionLimit);
}
 
/// Returns true if a shift by \c Amount always yields poison.
static bool isPoisonShift(Value *Amount, const SimplifyQuery &Q) {
  Constant *C = dyn_cast<Constant>(Amount);
  if (!C)
    return false;
 
  // X shift by undef -> poison because it may shift by the bitwidth.
  if (Q.isUndefValue(C))
    return true;
 
  // Shifting by the bitwidth or more is poison. This covers scalars and
  // fixed/scalable vectors with splat constants.
  const APInt *AmountC;
  if (match(C, m_APInt(AmountC)) && AmountC->uge(AmountC->getBitWidth()))
    return true;
 
  // Try harder for fixed-length vectors:
  // If all lanes of a vector shift are poison, the whole shift is poison.
  if (isa<ConstantVector>(C) || isa<ConstantDataVector>(C)) {
    for (unsigned I = 0,
                  E = cast<FixedVectorType>(C->getType())->getNumElements();
         I != E; ++I)
      if (!isPoisonShift(C->getAggregateElement(I), Q))
        return false;
    return true;
  }
 
  return false;
}
 
/// Given operands for an Shl, LShr or AShr, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyShift(Instruction::BinaryOps Opcode, Value *Op0,
                            Value *Op1, bool IsNSW, const SimplifyQuery &Q,
                            unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
    return C;
 
  // poison shift by X -> poison
  if (isa<PoisonValue>(Op0))
    return Op0;
 
  // 0 shift by X -> 0
  if (match(Op0, m_Zero()))
    return Constant::getNullValue(Op0->getType());
 
  // X shift by 0 -> X
  // Shift-by-sign-extended bool must be shift-by-0 because shift-by-all-ones
  // would be poison.
  Value *X;
  if (match(Op1, m_Zero()) ||
      (match(Op1, m_SExt(m_Value(X))) && X->getType()->isIntOrIntVectorTy(1)))
    return Op0;
 
  // Fold undefined shifts.
  if (isPoisonShift(Op1, Q))
    return PoisonValue::get(Op0->getType());
 
  // If the operation is with the result of a select instruction, check whether
  // operating on either branch of the select always yields the same value.
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
    if (Value *V = threadBinOpOverSelect(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V = threadBinOpOverPHI(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // If any bits in the shift amount make that value greater than or equal to
  // the number of bits in the type, the shift is undefined.
  KnownBits KnownAmt = computeKnownBits(Op1, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
  if (KnownAmt.getMinValue().uge(KnownAmt.getBitWidth()))
    return PoisonValue::get(Op0->getType());
 
  // If all valid bits in the shift amount are known zero, the first operand is
  // unchanged.
  unsigned NumValidShiftBits = Log2_32_Ceil(KnownAmt.getBitWidth());
  if (KnownAmt.countMinTrailingZeros() >= NumValidShiftBits)
    return Op0;
 
  // Check for nsw shl leading to a poison value.
  if (IsNSW) {
    assert(Opcode == Instruction::Shl && "Expected shl for nsw instruction");
    KnownBits KnownVal = computeKnownBits(Op0, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    KnownBits KnownShl = KnownBits::shl(KnownVal, KnownAmt);
 
    if (KnownVal.Zero.isSignBitSet())
      KnownShl.Zero.setSignBit();
    if (KnownVal.One.isSignBitSet())
      KnownShl.One.setSignBit();
 
    if (KnownShl.hasConflict())
      return PoisonValue::get(Op0->getType());
  }
 
  return nullptr;
}
 
/// Given operands for an LShr or AShr, see if we can fold the result.  If not,
/// this returns null.
static Value *simplifyRightShift(Instruction::BinaryOps Opcode, Value *Op0,
                                 Value *Op1, bool IsExact,
                                 const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V =
          simplifyShift(Opcode, Op0, Op1, /*IsNSW*/ false, Q, MaxRecurse))
    return V;
 
  // X >> X -> 0
  if (Op0 == Op1)
    return Constant::getNullValue(Op0->getType());
 
  // undef >> X -> 0
  // undef >> X -> undef (if it's exact)
  if (Q.isUndefValue(Op0))
    return IsExact ? Op0 : Constant::getNullValue(Op0->getType());
 
  // The low bit cannot be shifted out of an exact shift if it is set.
  // TODO: Generalize by counting trailing zeros (see fold for exact division).
  if (IsExact) {
    KnownBits Op0Known =
        computeKnownBits(Op0, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT);
    if (Op0Known.One[0])
      return Op0;
  }
 
  return nullptr;
}
 
/// Given operands for an Shl, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyShlInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V =
          simplifyShift(Instruction::Shl, Op0, Op1, IsNSW, Q, MaxRecurse))
    return V;
 
  Type *Ty = Op0->getType();
  // undef << X -> 0
  // undef << X -> undef if (if it's NSW/NUW)
  if (Q.isUndefValue(Op0))
    return IsNSW || IsNUW ? Op0 : Constant::getNullValue(Ty);
 
  // (X >> A) << A -> X
  Value *X;
  if (Q.IIQ.UseInstrInfo &&
      match(Op0, m_Exact(m_Shr(m_Value(X), m_Specific(Op1)))))
    return X;
 
  // shl nuw i8 C, %x  ->  C  iff C has sign bit set.
  if (IsNUW && match(Op0, m_Negative()))
    return Op0;
  // NOTE: could use computeKnownBits() / LazyValueInfo,
  // but the cost-benefit analysis suggests it isn't worth it.
 
  // "nuw" guarantees that only zeros are shifted out, and "nsw" guarantees
  // that the sign-bit does not change, so the only input that does not
  // produce poison is 0, and "0 << (bitwidth-1) --> 0".
  if (IsNSW && IsNUW &&
      match(Op1, m_SpecificInt(Ty->getScalarSizeInBits() - 1)))
    return Constant::getNullValue(Ty);
 
  return nullptr;
}
 
Value *llvm::simplifyShlInst(Value *Op0, Value *Op1, bool IsNSW, bool IsNUW,
                             const SimplifyQuery &Q) {
  return ::simplifyShlInst(Op0, Op1, IsNSW, IsNUW, Q, RecursionLimit);
}
 
/// Given operands for an LShr, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyLShrInst(Value *Op0, Value *Op1, bool IsExact,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V = simplifyRightShift(Instruction::LShr, Op0, Op1, IsExact, Q,
                                    MaxRecurse))
    return V;
 
  // (X << A) >> A -> X
  Value *X;
  if (match(Op0, m_NUWShl(m_Value(X), m_Specific(Op1))))
    return X;
 
  // ((X << A) | Y) >> A -> X  if effective width of Y is not larger than A.
  // We can return X as we do in the above case since OR alters no bits in X.
  // SimplifyDemandedBits in InstCombine can do more general optimization for
  // bit manipulation. This pattern aims to provide opportunities for other
  // optimizers by supporting a simple but common case in InstSimplify.
  Value *Y;
  const APInt *ShRAmt, *ShLAmt;
  if (match(Op1, m_APInt(ShRAmt)) &&
      match(Op0, m_c_Or(m_NUWShl(m_Value(X), m_APInt(ShLAmt)), m_Value(Y))) &&
      *ShRAmt == *ShLAmt) {
    const KnownBits YKnown = computeKnownBits(Y, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    const unsigned EffWidthY = YKnown.countMaxActiveBits();
    if (ShRAmt->uge(EffWidthY))
      return X;
  }
 
  return nullptr;
}
 
Value *llvm::simplifyLShrInst(Value *Op0, Value *Op1, bool IsExact,
                              const SimplifyQuery &Q) {
  return ::simplifyLShrInst(Op0, Op1, IsExact, Q, RecursionLimit);
}
 
/// Given operands for an AShr, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyAShrInst(Value *Op0, Value *Op1, bool IsExact,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V = simplifyRightShift(Instruction::AShr, Op0, Op1, IsExact, Q,
                                    MaxRecurse))
    return V;
 
  // -1 >>a X --> -1
  // (-1 << X) a>> X --> -1
  // Do not return Op0 because it may contain undef elements if it's a vector.
  if (match(Op0, m_AllOnes()) ||
      match(Op0, m_Shl(m_AllOnes(), m_Specific(Op1))))
    return Constant::getAllOnesValue(Op0->getType());
 
  // (X << A) >> A -> X
  Value *X;
  if (Q.IIQ.UseInstrInfo && match(Op0, m_NSWShl(m_Value(X), m_Specific(Op1))))
    return X;
 
  // Arithmetic shifting an all-sign-bit value is a no-op.
  unsigned NumSignBits = ComputeNumSignBits(Op0, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
  if (NumSignBits == Op0->getType()->getScalarSizeInBits())
    return Op0;
 
  return nullptr;
}
 
Value *llvm::simplifyAShrInst(Value *Op0, Value *Op1, bool IsExact,
                              const SimplifyQuery &Q) {
  return ::simplifyAShrInst(Op0, Op1, IsExact, Q, RecursionLimit);
}
 
/// Commuted variants are assumed to be handled by calling this function again
/// with the parameters swapped.
static Value *simplifyUnsignedRangeCheck(ICmpInst *ZeroICmp,
                                         ICmpInst *UnsignedICmp, bool IsAnd,
                                         const SimplifyQuery &Q) {
  Value *X, *Y;
 
  ICmpInst::Predicate EqPred;
  if (!match(ZeroICmp, m_ICmp(EqPred, m_Value(Y), m_Zero())) ||
      !ICmpInst::isEquality(EqPred))
    return nullptr;
 
  ICmpInst::Predicate UnsignedPred;
 
  Value *A, *B;
  // Y = (A - B);
  if (match(Y, m_Sub(m_Value(A), m_Value(B)))) {
    if (match(UnsignedICmp,
              m_c_ICmp(UnsignedPred, m_Specific(A), m_Specific(B))) &&
        ICmpInst::isUnsigned(UnsignedPred)) {
      // A >=/<= B || (A - B) != 0  <-->  true
      if ((UnsignedPred == ICmpInst::ICMP_UGE ||
           UnsignedPred == ICmpInst::ICMP_ULE) &&
          EqPred == ICmpInst::ICMP_NE && !IsAnd)
        return ConstantInt::getTrue(UnsignedICmp->getType());
      // A </> B && (A - B) == 0  <-->  false
      if ((UnsignedPred == ICmpInst::ICMP_ULT ||
           UnsignedPred == ICmpInst::ICMP_UGT) &&
          EqPred == ICmpInst::ICMP_EQ && IsAnd)
        return ConstantInt::getFalse(UnsignedICmp->getType());
 
      // A </> B && (A - B) != 0  <-->  A </> B
      // A </> B || (A - B) != 0  <-->  (A - B) != 0
      if (EqPred == ICmpInst::ICMP_NE && (UnsignedPred == ICmpInst::ICMP_ULT ||
                                          UnsignedPred == ICmpInst::ICMP_UGT))
        return IsAnd ? UnsignedICmp : ZeroICmp;
 
      // A <=/>= B && (A - B) == 0  <-->  (A - B) == 0
      // A <=/>= B || (A - B) == 0  <-->  A <=/>= B
      if (EqPred == ICmpInst::ICMP_EQ && (UnsignedPred == ICmpInst::ICMP_ULE ||
                                          UnsignedPred == ICmpInst::ICMP_UGE))
        return IsAnd ? ZeroICmp : UnsignedICmp;
    }
 
    // Given  Y = (A - B)
    //   Y >= A && Y != 0  --> Y >= A  iff B != 0
    //   Y <  A || Y == 0  --> Y <  A  iff B != 0
    if (match(UnsignedICmp,
              m_c_ICmp(UnsignedPred, m_Specific(Y), m_Specific(A)))) {
      if (UnsignedPred == ICmpInst::ICMP_UGE && IsAnd &&
          EqPred == ICmpInst::ICMP_NE &&
          isKnownNonZero(B, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT))
        return UnsignedICmp;
      if (UnsignedPred == ICmpInst::ICMP_ULT && !IsAnd &&
          EqPred == ICmpInst::ICMP_EQ &&
          isKnownNonZero(B, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT))
        return UnsignedICmp;
    }
  }
 
  if (match(UnsignedICmp, m_ICmp(UnsignedPred, m_Value(X), m_Specific(Y))) &&
      ICmpInst::isUnsigned(UnsignedPred))
    ;
  else if (match(UnsignedICmp,
                 m_ICmp(UnsignedPred, m_Specific(Y), m_Value(X))) &&
           ICmpInst::isUnsigned(UnsignedPred))
    UnsignedPred = ICmpInst::getSwappedPredicate(UnsignedPred);
  else
    return nullptr;
 
  // X > Y && Y == 0  -->  Y == 0  iff X != 0
  // X > Y || Y == 0  -->  X > Y   iff X != 0
  if (UnsignedPred == ICmpInst::ICMP_UGT && EqPred == ICmpInst::ICMP_EQ &&
      isKnownNonZero(X, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT))
    return IsAnd ? ZeroICmp : UnsignedICmp;
 
  // X <= Y && Y != 0  -->  X <= Y  iff X != 0
  // X <= Y || Y != 0  -->  Y != 0  iff X != 0
  if (UnsignedPred == ICmpInst::ICMP_ULE && EqPred == ICmpInst::ICMP_NE &&
      isKnownNonZero(X, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT))
    return IsAnd ? UnsignedICmp : ZeroICmp;
 
  // The transforms below here are expected to be handled more generally with
  // simplifyAndOrOfICmpsWithLimitConst() or in InstCombine's
  // foldAndOrOfICmpsWithConstEq(). If we are looking to trim optimizer overlap,
  // these are candidates for removal.
 
  // X < Y && Y != 0  -->  X < Y
  // X < Y || Y != 0  -->  Y != 0
  if (UnsignedPred == ICmpInst::ICMP_ULT && EqPred == ICmpInst::ICMP_NE)
    return IsAnd ? UnsignedICmp : ZeroICmp;
 
  // X >= Y && Y == 0  -->  Y == 0
  // X >= Y || Y == 0  -->  X >= Y
  if (UnsignedPred == ICmpInst::ICMP_UGE && EqPred == ICmpInst::ICMP_EQ)
    return IsAnd ? ZeroICmp : UnsignedICmp;
 
  // X < Y && Y == 0  -->  false
  if (UnsignedPred == ICmpInst::ICMP_ULT && EqPred == ICmpInst::ICMP_EQ &&
      IsAnd)
    return getFalse(UnsignedICmp->getType());
 
  // X >= Y || Y != 0  -->  true
  if (UnsignedPred == ICmpInst::ICMP_UGE && EqPred == ICmpInst::ICMP_NE &&
      !IsAnd)
    return getTrue(UnsignedICmp->getType());
 
  return nullptr;
}
 
/// Test if a pair of compares with a shared operand and 2 constants has an
/// empty set intersection, full set union, or if one compare is a superset of
/// the other.
static Value *simplifyAndOrOfICmpsWithConstants(ICmpInst *Cmp0, ICmpInst *Cmp1,
                                                bool IsAnd) {
  // Look for this pattern: {and/or} (icmp X, C0), (icmp X, C1)).
  if (Cmp0->getOperand(0) != Cmp1->getOperand(0))
    return nullptr;
 
  const APInt *C0, *C1;
  if (!match(Cmp0->getOperand(1), m_APInt(C0)) ||
      !match(Cmp1->getOperand(1), m_APInt(C1)))
    return nullptr;
 
  auto Range0 = ConstantRange::makeExactICmpRegion(Cmp0->getPredicate(), *C0);
  auto Range1 = ConstantRange::makeExactICmpRegion(Cmp1->getPredicate(), *C1);
 
  // For and-of-compares, check if the intersection is empty:
  // (icmp X, C0) && (icmp X, C1) --> empty set --> false
  if (IsAnd && Range0.intersectWith(Range1).isEmptySet())
    return getFalse(Cmp0->getType());
 
  // For or-of-compares, check if the union is full:
  // (icmp X, C0) || (icmp X, C1) --> full set --> true
  if (!IsAnd && Range0.unionWith(Range1).isFullSet())
    return getTrue(Cmp0->getType());
 
  // Is one range a superset of the other?
  // If this is and-of-compares, take the smaller set:
  // (icmp sgt X, 4) && (icmp sgt X, 42) --> icmp sgt X, 42
  // If this is or-of-compares, take the larger set:
  // (icmp sgt X, 4) || (icmp sgt X, 42) --> icmp sgt X, 4
  if (Range0.contains(Range1))
    return IsAnd ? Cmp1 : Cmp0;
  if (Range1.contains(Range0))
    return IsAnd ? Cmp0 : Cmp1;
 
  return nullptr;
}
 
static Value *simplifyAndOrOfICmpsWithZero(ICmpInst *Cmp0, ICmpInst *Cmp1,
                                           bool IsAnd) {
  ICmpInst::Predicate P0 = Cmp0->getPredicate(), P1 = Cmp1->getPredicate();
  if (!match(Cmp0->getOperand(1), m_Zero()) ||
      !match(Cmp1->getOperand(1), m_Zero()) || P0 != P1)
    return nullptr;
 
  if ((IsAnd && P0 != ICmpInst::ICMP_NE) || (!IsAnd && P1 != ICmpInst::ICMP_EQ))
    return nullptr;
 
  // We have either "(X == 0 || Y == 0)" or "(X != 0 && Y != 0)".
  Value *X = Cmp0->getOperand(0);
  Value *Y = Cmp1->getOperand(0);
 
  // If one of the compares is a masked version of a (not) null check, then
  // that compare implies the other, so we eliminate the other. Optionally, look
  // through a pointer-to-int cast to match a null check of a pointer type.
 
  // (X == 0) || (([ptrtoint] X & ?) == 0) --> ([ptrtoint] X & ?) == 0
  // (X == 0) || ((? & [ptrtoint] X) == 0) --> (? & [ptrtoint] X) == 0
  // (X != 0) && (([ptrtoint] X & ?) != 0) --> ([ptrtoint] X & ?) != 0
  // (X != 0) && ((? & [ptrtoint] X) != 0) --> (? & [ptrtoint] X) != 0
  if (match(Y, m_c_And(m_Specific(X), m_Value())) ||
      match(Y, m_c_And(m_PtrToInt(m_Specific(X)), m_Value())))
    return Cmp1;
 
  // (([ptrtoint] Y & ?) == 0) || (Y == 0) --> ([ptrtoint] Y & ?) == 0
  // ((? & [ptrtoint] Y) == 0) || (Y == 0) --> (? & [ptrtoint] Y) == 0
  // (([ptrtoint] Y & ?) != 0) && (Y != 0) --> ([ptrtoint] Y & ?) != 0
  // ((? & [ptrtoint] Y) != 0) && (Y != 0) --> (? & [ptrtoint] Y) != 0
  if (match(X, m_c_And(m_Specific(Y), m_Value())) ||
      match(X, m_c_And(m_PtrToInt(m_Specific(Y)), m_Value())))
    return Cmp0;
 
  return nullptr;
}
 
static Value *simplifyAndOfICmpsWithAdd(ICmpInst *Op0, ICmpInst *Op1,
                                        const InstrInfoQuery &IIQ) {
  // (icmp (add V, C0), C1) & (icmp V, C0)
  ICmpInst::Predicate Pred0, Pred1;
  const APInt *C0, *C1;
  Value *V;
  if (!match(Op0, m_ICmp(Pred0, m_Add(m_Value(V), m_APInt(C0)), m_APInt(C1))))
    return nullptr;
 
  if (!match(Op1, m_ICmp(Pred1, m_Specific(V), m_Value())))
    return nullptr;
 
  auto *AddInst = cast<OverflowingBinaryOperator>(Op0->getOperand(0));
  if (AddInst->getOperand(1) != Op1->getOperand(1))
    return nullptr;
 
  Type *ITy = Op0->getType();
  bool IsNSW = IIQ.hasNoSignedWrap(AddInst);
  bool IsNUW = IIQ.hasNoUnsignedWrap(AddInst);
 
  const APInt Delta = *C1 - *C0;
  if (C0->isStrictlyPositive()) {
    if (Delta == 2) {
      if (Pred0 == ICmpInst::ICMP_ULT && Pred1 == ICmpInst::ICMP_SGT)
        return getFalse(ITy);
      if (Pred0 == ICmpInst::ICMP_SLT && Pred1 == ICmpInst::ICMP_SGT && IsNSW)
        return getFalse(ITy);
    }
    if (Delta == 1) {
      if (Pred0 == ICmpInst::ICMP_ULE && Pred1 == ICmpInst::ICMP_SGT)
        return getFalse(ITy);
      if (Pred0 == ICmpInst::ICMP_SLE && Pred1 == ICmpInst::ICMP_SGT && IsNSW)
        return getFalse(ITy);
    }
  }
  if (C0->getBoolValue() && IsNUW) {
    if (Delta == 2)
      if (Pred0 == ICmpInst::ICMP_ULT && Pred1 == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
    if (Delta == 1)
      if (Pred0 == ICmpInst::ICMP_ULE && Pred1 == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
  }
 
  return nullptr;
}
 
/// Try to eliminate compares with signed or unsigned min/max constants.
static Value *simplifyAndOrOfICmpsWithLimitConst(ICmpInst *Cmp0, ICmpInst *Cmp1,
                                                 bool IsAnd) {
  // Canonicalize an equality compare as Cmp0.
  if (Cmp1->isEquality())
    std::swap(Cmp0, Cmp1);
  if (!Cmp0->isEquality())
    return nullptr;
 
  // The non-equality compare must include a common operand (X). Canonicalize
  // the common operand as operand 0 (the predicate is swapped if the common
  // operand was operand 1).
  ICmpInst::Predicate Pred0 = Cmp0->getPredicate();
  Value *X = Cmp0->getOperand(0);
  ICmpInst::Predicate Pred1;
  bool HasNotOp = match(Cmp1, m_c_ICmp(Pred1, m_Not(m_Specific(X)), m_Value()));
  if (!HasNotOp && !match(Cmp1, m_c_ICmp(Pred1, m_Specific(X), m_Value())))
    return nullptr;
  if (ICmpInst::isEquality(Pred1))
    return nullptr;
 
  // The equality compare must be against a constant. Flip bits if we matched
  // a bitwise not. Convert a null pointer constant to an integer zero value.
  APInt MinMaxC;
  const APInt *C;
  if (match(Cmp0->getOperand(1), m_APInt(C)))
    MinMaxC = HasNotOp ? ~*C : *C;
  else if (isa<ConstantPointerNull>(Cmp0->getOperand(1)))
    MinMaxC = APInt::getZero(8);
  else
    return nullptr;
 
  // DeMorganize if this is 'or': P0 || P1 --> !P0 && !P1.
  if (!IsAnd) {
    Pred0 = ICmpInst::getInversePredicate(Pred0);
    Pred1 = ICmpInst::getInversePredicate(Pred1);
  }
 
  // Normalize to unsigned compare and unsigned min/max value.
  // Example for 8-bit: -128 + 128 -> 0; 127 + 128 -> 255
  if (ICmpInst::isSigned(Pred1)) {
    Pred1 = ICmpInst::getUnsignedPredicate(Pred1);
    MinMaxC += APInt::getSignedMinValue(MinMaxC.getBitWidth());
  }
 
  // (X != MAX) && (X < Y) --> X < Y
  // (X == MAX) || (X >= Y) --> X >= Y
  if (MinMaxC.isMaxValue())
    if (Pred0 == ICmpInst::ICMP_NE && Pred1 == ICmpInst::ICMP_ULT)
      return Cmp1;
 
  // (X != MIN) && (X > Y) -->  X > Y
  // (X == MIN) || (X <= Y) --> X <= Y
  if (MinMaxC.isMinValue())
    if (Pred0 == ICmpInst::ICMP_NE && Pred1 == ICmpInst::ICMP_UGT)
      return Cmp1;
 
  return nullptr;
}
 
/// Try to simplify and/or of icmp with ctpop intrinsic.
static Value *simplifyAndOrOfICmpsWithCtpop(ICmpInst *Cmp0, ICmpInst *Cmp1,
                                            bool IsAnd) {
  ICmpInst::Predicate Pred0, Pred1;
  Value *X;
  const APInt *C;
  if (!match(Cmp0, m_ICmp(Pred0, m_Intrinsic<Intrinsic::ctpop>(m_Value(X)),
                          m_APInt(C))) ||
      !match(Cmp1, m_ICmp(Pred1, m_Specific(X), m_ZeroInt())) || C->isZero())
    return nullptr;
 
  // (ctpop(X) == C) || (X != 0) --> X != 0 where C > 0
  if (!IsAnd && Pred0 == ICmpInst::ICMP_EQ && Pred1 == ICmpInst::ICMP_NE)
    return Cmp1;
  // (ctpop(X) != C) && (X == 0) --> X == 0 where C > 0
  if (IsAnd && Pred0 == ICmpInst::ICMP_NE && Pred1 == ICmpInst::ICMP_EQ)
    return Cmp1;
 
  return nullptr;
}
 
static Value *simplifyAndOfICmps(ICmpInst *Op0, ICmpInst *Op1,
                                 const SimplifyQuery &Q) {
  if (Value *X = simplifyUnsignedRangeCheck(Op0, Op1, /*IsAnd=*/true, Q))
    return X;
  if (Value *X = simplifyUnsignedRangeCheck(Op1, Op0, /*IsAnd=*/true, Q))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithConstants(Op0, Op1, true))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithLimitConst(Op0, Op1, true))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithZero(Op0, Op1, true))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithCtpop(Op0, Op1, true))
    return X;
  if (Value *X = simplifyAndOrOfICmpsWithCtpop(Op1, Op0, true))
    return X;
 
  if (Value *X = simplifyAndOfICmpsWithAdd(Op0, Op1, Q.IIQ))
    return X;
  if (Value *X = simplifyAndOfICmpsWithAdd(Op1, Op0, Q.IIQ))
    return X;
 
  return nullptr;
}
 
static Value *simplifyOrOfICmpsWithAdd(ICmpInst *Op0, ICmpInst *Op1,
                                       const InstrInfoQuery &IIQ) {
  // (icmp (add V, C0), C1) | (icmp V, C0)
  ICmpInst::Predicate Pred0, Pred1;
  const APInt *C0, *C1;
  Value *V;
  if (!match(Op0, m_ICmp(Pred0, m_Add(m_Value(V), m_APInt(C0)), m_APInt(C1))))
    return nullptr;
 
  if (!match(Op1, m_ICmp(Pred1, m_Specific(V), m_Value())))
    return nullptr;
 
  auto *AddInst = cast<BinaryOperator>(Op0->getOperand(0));
  if (AddInst->getOperand(1) != Op1->getOperand(1))
    return nullptr;
 
  Type *ITy = Op0->getType();
  bool IsNSW = IIQ.hasNoSignedWrap(AddInst);
  bool IsNUW = IIQ.hasNoUnsignedWrap(AddInst);
 
  const APInt Delta = *C1 - *C0;
  if (C0->isStrictlyPositive()) {
    if (Delta == 2) {
      if (Pred0 == ICmpInst::ICMP_UGE && Pred1 == ICmpInst::ICMP_SLE)
        return getTrue(ITy);
      if (Pred0 == ICmpInst::ICMP_SGE && Pred1 == ICmpInst::ICMP_SLE && IsNSW)
        return getTrue(ITy);
    }
    if (Delta == 1) {
      if (Pred0 == ICmpInst::ICMP_UGT && Pred1 == ICmpInst::ICMP_SLE)
        return getTrue(ITy);
      if (Pred0 == ICmpInst::ICMP_SGT && Pred1 == ICmpInst::ICMP_SLE && IsNSW)
        return getTrue(ITy);
    }
  }
  if (C0->getBoolValue() && IsNUW) {
    if (Delta == 2)
      if (Pred0 == ICmpInst::ICMP_UGE && Pred1 == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
    if (Delta == 1)
      if (Pred0 == ICmpInst::ICMP_UGT && Pred1 == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
  }
 
  return nullptr;
}
 
static Value *simplifyOrOfICmps(ICmpInst *Op0, ICmpInst *Op1,
                                const SimplifyQuery &Q) {
  if (Value *X = simplifyUnsignedRangeCheck(Op0, Op1, /*IsAnd=*/false, Q))
    return X;
  if (Value *X = simplifyUnsignedRangeCheck(Op1, Op0, /*IsAnd=*/false, Q))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithConstants(Op0, Op1, false))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithLimitConst(Op0, Op1, false))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithZero(Op0, Op1, false))
    return X;
 
  if (Value *X = simplifyAndOrOfICmpsWithCtpop(Op0, Op1, false))
    return X;
  if (Value *X = simplifyAndOrOfICmpsWithCtpop(Op1, Op0, false))
    return X;
 
  if (Value *X = simplifyOrOfICmpsWithAdd(Op0, Op1, Q.IIQ))
    return X;
  if (Value *X = simplifyOrOfICmpsWithAdd(Op1, Op0, Q.IIQ))
    return X;
 
  return nullptr;
}
 
static Value *simplifyAndOrOfFCmps(const TargetLibraryInfo *TLI, FCmpInst *LHS,
                                   FCmpInst *RHS, bool IsAnd) {
  Value *LHS0 = LHS->getOperand(0), *LHS1 = LHS->getOperand(1);
  Value *RHS0 = RHS->getOperand(0), *RHS1 = RHS->getOperand(1);
  if (LHS0->getType() != RHS0->getType())
    return nullptr;
 
  FCmpInst::Predicate PredL = LHS->getPredicate(), PredR = RHS->getPredicate();
  if ((PredL == FCmpInst::FCMP_ORD && PredR == FCmpInst::FCMP_ORD && IsAnd) ||
      (PredL == FCmpInst::FCMP_UNO && PredR == FCmpInst::FCMP_UNO && !IsAnd)) {
    // (fcmp ord NNAN, X) & (fcmp ord X, Y) --> fcmp ord X, Y
    // (fcmp ord NNAN, X) & (fcmp ord Y, X) --> fcmp ord Y, X
    // (fcmp ord X, NNAN) & (fcmp ord X, Y) --> fcmp ord X, Y
    // (fcmp ord X, NNAN) & (fcmp ord Y, X) --> fcmp ord Y, X
    // (fcmp uno NNAN, X) | (fcmp uno X, Y) --> fcmp uno X, Y
    // (fcmp uno NNAN, X) | (fcmp uno Y, X) --> fcmp uno Y, X
    // (fcmp uno X, NNAN) | (fcmp uno X, Y) --> fcmp uno X, Y
    // (fcmp uno X, NNAN) | (fcmp uno Y, X) --> fcmp uno Y, X
    if ((isKnownNeverNaN(LHS0, TLI) && (LHS1 == RHS0 || LHS1 == RHS1)) ||
        (isKnownNeverNaN(LHS1, TLI) && (LHS0 == RHS0 || LHS0 == RHS1)))
      return RHS;
 
    // (fcmp ord X, Y) & (fcmp ord NNAN, X) --> fcmp ord X, Y
    // (fcmp ord Y, X) & (fcmp ord NNAN, X) --> fcmp ord Y, X
    // (fcmp ord X, Y) & (fcmp ord X, NNAN) --> fcmp ord X, Y
    // (fcmp ord Y, X) & (fcmp ord X, NNAN) --> fcmp ord Y, X
    // (fcmp uno X, Y) | (fcmp uno NNAN, X) --> fcmp uno X, Y
    // (fcmp uno Y, X) | (fcmp uno NNAN, X) --> fcmp uno Y, X
    // (fcmp uno X, Y) | (fcmp uno X, NNAN) --> fcmp uno X, Y
    // (fcmp uno Y, X) | (fcmp uno X, NNAN) --> fcmp uno Y, X
    if ((isKnownNeverNaN(RHS0, TLI) && (RHS1 == LHS0 || RHS1 == LHS1)) ||
        (isKnownNeverNaN(RHS1, TLI) && (RHS0 == LHS0 || RHS0 == LHS1)))
      return LHS;
  }
 
  return nullptr;
}
 
static Value *simplifyAndOrOfCmps(const SimplifyQuery &Q, Value *Op0,
                                  Value *Op1, bool IsAnd) {
  // Look through casts of the 'and' operands to find compares.
  auto *Cast0 = dyn_cast<CastInst>(Op0);
  auto *Cast1 = dyn_cast<CastInst>(Op1);
  if (Cast0 && Cast1 && Cast0->getOpcode() == Cast1->getOpcode() &&
      Cast0->getSrcTy() == Cast1->getSrcTy()) {
    Op0 = Cast0->getOperand(0);
    Op1 = Cast1->getOperand(0);
  }
 
  Value *V = nullptr;
  auto *ICmp0 = dyn_cast<ICmpInst>(Op0);
  auto *ICmp1 = dyn_cast<ICmpInst>(Op1);
  if (ICmp0 && ICmp1)
    V = IsAnd ? simplifyAndOfICmps(ICmp0, ICmp1, Q)
              : simplifyOrOfICmps(ICmp0, ICmp1, Q);
 
  auto *FCmp0 = dyn_cast<FCmpInst>(Op0);
  auto *FCmp1 = dyn_cast<FCmpInst>(Op1);
  if (FCmp0 && FCmp1)
    V = simplifyAndOrOfFCmps(Q.TLI, FCmp0, FCmp1, IsAnd);
 
  if (!V)
    return nullptr;
  if (!Cast0)
    return V;
 
  // If we looked through casts, we can only handle a constant simplification
  // because we are not allowed to create a cast instruction here.
  if (auto *C = dyn_cast<Constant>(V))
    return ConstantExpr::getCast(Cast0->getOpcode(), C, Cast0->getType());
 
  return nullptr;
}
 
/// Given a bitwise logic op, check if the operands are add/sub with a common
/// source value and inverted constant (identity: C - X -> ~(X + ~C)).
static Value *simplifyLogicOfAddSub(Value *Op0, Value *Op1,
                                    Instruction::BinaryOps Opcode) {
  assert(Op0->getType() == Op1->getType() && "Mismatched binop types");
  assert(BinaryOperator::isBitwiseLogicOp(Opcode) && "Expected logic op");
  Value *X;
  Constant *C1, *C2;
  if ((match(Op0, m_Add(m_Value(X), m_Constant(C1))) &&
       match(Op1, m_Sub(m_Constant(C2), m_Specific(X)))) ||
      (match(Op1, m_Add(m_Value(X), m_Constant(C1))) &&
       match(Op0, m_Sub(m_Constant(C2), m_Specific(X))))) {
    if (ConstantExpr::getNot(C1) == C2) {
      // (X + C) & (~C - X) --> (X + C) & ~(X + C) --> 0
      // (X + C) | (~C - X) --> (X + C) | ~(X + C) --> -1
      // (X + C) ^ (~C - X) --> (X + C) ^ ~(X + C) --> -1
      Type *Ty = Op0->getType();
      return Opcode == Instruction::And ? ConstantInt::getNullValue(Ty)
                                        : ConstantInt::getAllOnesValue(Ty);
    }
  }
  return nullptr;
}
 
/// Given operands for an And, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyAndInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                              unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::And, Op0, Op1, Q))
    return C;
 
  // X & poison -> poison
  if (isa<PoisonValue>(Op1))
    return Op1;
 
  // X & undef -> 0
  if (Q.isUndefValue(Op1))
    return Constant::getNullValue(Op0->getType());
 
  // X & X = X
  if (Op0 == Op1)
    return Op0;
 
  // X & 0 = 0
  if (match(Op1, m_Zero()))
    return Constant::getNullValue(Op0->getType());
 
  // X & -1 = X
  if (match(Op1, m_AllOnes()))
    return Op0;
 
  // A & ~A  =  ~A & A  =  0
  if (match(Op0, m_Not(m_Specific(Op1))) || match(Op1, m_Not(m_Specific(Op0))))
    return Constant::getNullValue(Op0->getType());
 
  // (A | ?) & A = A
  if (match(Op0, m_c_Or(m_Specific(Op1), m_Value())))
    return Op1;
 
  // A & (A | ?) = A
  if (match(Op1, m_c_Or(m_Specific(Op0), m_Value())))
    return Op0;
 
  // (X | Y) & (X | ~Y) --> X (commuted 8 ways)
  Value *X, *Y;
  if (match(Op0, m_c_Or(m_Value(X), m_Not(m_Value(Y)))) &&
      match(Op1, m_c_Or(m_Deferred(X), m_Deferred(Y))))
    return X;
  if (match(Op1, m_c_Or(m_Value(X), m_Not(m_Value(Y)))) &&
      match(Op0, m_c_Or(m_Deferred(X), m_Deferred(Y))))
    return X;
 
  if (Value *V = simplifyLogicOfAddSub(Op0, Op1, Instruction::And))
    return V;
 
  // A mask that only clears known zeros of a shifted value is a no-op.
  const APInt *Mask;
  const APInt *ShAmt;
  if (match(Op1, m_APInt(Mask))) {
    // If all bits in the inverted and shifted mask are clear:
    // and (shl X, ShAmt), Mask --> shl X, ShAmt
    if (match(Op0, m_Shl(m_Value(X), m_APInt(ShAmt))) &&
        (~(*Mask)).lshr(*ShAmt).isZero())
      return Op0;
 
    // If all bits in the inverted and shifted mask are clear:
    // and (lshr X, ShAmt), Mask --> lshr X, ShAmt
    if (match(Op0, m_LShr(m_Value(X), m_APInt(ShAmt))) &&
        (~(*Mask)).shl(*ShAmt).isZero())
      return Op0;
  }
 
  // If we have a multiplication overflow check that is being 'and'ed with a
  // check that one of the multipliers is not zero, we can omit the 'and', and
  // only keep the overflow check.
  if (isCheckForZeroAndMulWithOverflow(Op0, Op1, true))
    return Op1;
  if (isCheckForZeroAndMulWithOverflow(Op1, Op0, true))
    return Op0;
 
  // A & (-A) = A if A is a power of two or zero.
  if (match(Op0, m_Neg(m_Specific(Op1))) ||
      match(Op1, m_Neg(m_Specific(Op0)))) {
    if (isKnownToBeAPowerOfTwo(Op0, Q.DL, /*OrZero*/ true, 0, Q.AC, Q.CxtI,
                               Q.DT))
      return Op0;
    if (isKnownToBeAPowerOfTwo(Op1, Q.DL, /*OrZero*/ true, 0, Q.AC, Q.CxtI,
                               Q.DT))
      return Op1;
  }
 
  // This is a similar pattern used for checking if a value is a power-of-2:
  // (A - 1) & A --> 0 (if A is a power-of-2 or 0)
  // A & (A - 1) --> 0 (if A is a power-of-2 or 0)
  if (match(Op0, m_Add(m_Specific(Op1), m_AllOnes())) &&
      isKnownToBeAPowerOfTwo(Op1, Q.DL, /*OrZero*/ true, 0, Q.AC, Q.CxtI, Q.DT))
    return Constant::getNullValue(Op1->getType());
  if (match(Op1, m_Add(m_Specific(Op0), m_AllOnes())) &&
      isKnownToBeAPowerOfTwo(Op0, Q.DL, /*OrZero*/ true, 0, Q.AC, Q.CxtI, Q.DT))
    return Constant::getNullValue(Op0->getType());
 
  if (Value *V = simplifyAndOrOfCmps(Q, Op0, Op1, true))
    return V;
 
  // Try some generic simplifications for associative operations.
  if (Value *V =
          simplifyAssociativeBinOp(Instruction::And, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // And distributes over Or.  Try some generic simplifications based on this.
  if (Value *V = expandCommutativeBinOp(Instruction::And, Op0, Op1,
                                        Instruction::Or, Q, MaxRecurse))
    return V;
 
  // And distributes over Xor.  Try some generic simplifications based on this.
  if (Value *V = expandCommutativeBinOp(Instruction::And, Op0, Op1,
                                        Instruction::Xor, Q, MaxRecurse))
    return V;
 
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1)) {
    if (Op0->getType()->isIntOrIntVectorTy(1)) {
      // A & (A && B) -> A && B
      if (match(Op1, m_Select(m_Specific(Op0), m_Value(), m_Zero())))
        return Op1;
      else if (match(Op0, m_Select(m_Specific(Op1), m_Value(), m_Zero())))
        return Op0;
    }
    // If the operation is with the result of a select instruction, check
    // whether operating on either branch of the select always yields the same
    // value.
    if (Value *V =
            threadBinOpOverSelect(Instruction::And, Op0, Op1, Q, MaxRecurse))
      return V;
  }
 
  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V =
            threadBinOpOverPHI(Instruction::And, Op0, Op1, Q, MaxRecurse))
      return V;
 
  // Assuming the effective width of Y is not larger than A, i.e. all bits
  // from X and Y are disjoint in (X << A) | Y,
  // if the mask of this AND op covers all bits of X or Y, while it covers
  // no bits from the other, we can bypass this AND op. E.g.,
  // ((X << A) | Y) & Mask -> Y,
  //     if Mask = ((1 << effective_width_of(Y)) - 1)
  // ((X << A) | Y) & Mask -> X << A,
  //     if Mask = ((1 << effective_width_of(X)) - 1) << A
  // SimplifyDemandedBits in InstCombine can optimize the general case.
  // This pattern aims to help other passes for a common case.
  Value *XShifted;
  if (match(Op1, m_APInt(Mask)) &&
      match(Op0, m_c_Or(m_CombineAnd(m_NUWShl(m_Value(X), m_APInt(ShAmt)),
                                     m_Value(XShifted)),
                        m_Value(Y)))) {
    const unsigned Width = Op0->getType()->getScalarSizeInBits();
    const unsigned ShftCnt = ShAmt->getLimitedValue(Width);
    const KnownBits YKnown = computeKnownBits(Y, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    const unsigned EffWidthY = YKnown.countMaxActiveBits();
    if (EffWidthY <= ShftCnt) {
      const KnownBits XKnown = computeKnownBits(X, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
      const unsigned EffWidthX = XKnown.countMaxActiveBits();
      const APInt EffBitsY = APInt::getLowBitsSet(Width, EffWidthY);
      const APInt EffBitsX = APInt::getLowBitsSet(Width, EffWidthX) << ShftCnt;
      // If the mask is extracting all bits from X or Y as is, we can skip
      // this AND op.
      if (EffBitsY.isSubsetOf(*Mask) && !EffBitsX.intersects(*Mask))
        return Y;
      if (EffBitsX.isSubsetOf(*Mask) && !EffBitsY.intersects(*Mask))
        return XShifted;
    }
  }
 
  // ((X | Y) ^ X ) & ((X | Y) ^ Y) --> 0
  // ((X | Y) ^ Y ) & ((X | Y) ^ X) --> 0
  BinaryOperator *Or;
  if (match(Op0, m_c_Xor(m_Value(X),
                         m_CombineAnd(m_BinOp(Or),
                                      m_c_Or(m_Deferred(X), m_Value(Y))))) &&
      match(Op1, m_c_Xor(m_Specific(Or), m_Specific(Y))))
    return Constant::getNullValue(Op0->getType());
 
  if (Op0->getType()->isIntOrIntVectorTy(1)) {
    if (std::optional<bool> Implied = isImpliedCondition(Op0, Op1, Q.DL)) {
      // If Op0 is true implies Op1 is true, then Op0 is a subset of Op1.
      if (*Implied == true)
        return Op0;
      // If Op0 is true implies Op1 is false, then they are not true together.
      if (*Implied == false)
        return ConstantInt::getFalse(Op0->getType());
    }
    if (std::optional<bool> Implied = isImpliedCondition(Op1, Op0, Q.DL)) {
      // If Op1 is true implies Op0 is true, then Op1 is a subset of Op0.
      if (*Implied)
        return Op1;
      // If Op1 is true implies Op0 is false, then they are not true together.
      if (!*Implied)
        return ConstantInt::getFalse(Op1->getType());
    }
  }
 
  if (Value *V = simplifyByDomEq(Instruction::And, Op0, Op1, Q, MaxRecurse))
    return V;
 
  return nullptr;
}
 
Value *llvm::simplifyAndInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::simplifyAndInst(Op0, Op1, Q, RecursionLimit);
}
 
// TODO: Many of these folds could use LogicalAnd/LogicalOr.
static Value *simplifyOrLogic(Value *X, Value *Y) {
  assert(X->getType() == Y->getType() && "Expected same type for 'or' ops");
  Type *Ty = X->getType();
 
  // X | ~X --> -1
  if (match(Y, m_Not(m_Specific(X))))
    return ConstantInt::getAllOnesValue(Ty);
 
  // X | ~(X & ?) = -1
  if (match(Y, m_Not(m_c_And(m_Specific(X), m_Value()))))
    return ConstantInt::getAllOnesValue(Ty);
 
  // X | (X & ?) --> X
  if (match(Y, m_c_And(m_Specific(X), m_Value())))
    return X;
 
  Value *A, *B;
 
  // (A ^ B) | (A | B) --> A | B
  // (A ^ B) | (B | A) --> B | A
  if (match(X, m_Xor(m_Value(A), m_Value(B))) &&
      match(Y, m_c_Or(m_Specific(A), m_Specific(B))))
    return Y;
 
  // ~(A ^ B) | (A | B) --> -1
  // ~(A ^ B) | (B | A) --> -1
  if (match(X, m_Not(m_Xor(m_Value(A), m_Value(B)))) &&
      match(Y, m_c_Or(m_Specific(A), m_Specific(B))))
    return ConstantInt::getAllOnesValue(Ty);
 
  // (A & ~B) | (A ^ B) --> A ^ B
  // (~B & A) | (A ^ B) --> A ^ B
  // (A & ~B) | (B ^ A) --> B ^ A
  // (~B & A) | (B ^ A) --> B ^ A
  if (match(X, m_c_And(m_Value(A), m_Not(m_Value(B)))) &&
      match(Y, m_c_Xor(m_Specific(A), m_Specific(B))))
    return Y;
 
  // (~A ^ B) | (A & B) --> ~A ^ B
  // (B ^ ~A) | (A & B) --> B ^ ~A
  // (~A ^ B) | (B & A) --> ~A ^ B
  // (B ^ ~A) | (B & A) --> B ^ ~A
  if (match(X, m_c_Xor(m_NotForbidUndef(m_Value(A)), m_Value(B))) &&
      match(Y, m_c_And(m_Specific(A), m_Specific(B))))
    return X;
 
  // (~A | B) | (A ^ B) --> -1
  // (~A | B) | (B ^ A) --> -1
  // (B | ~A) | (A ^ B) --> -1
  // (B | ~A) | (B ^ A) --> -1
  if (match(X, m_c_Or(m_Not(m_Value(A)), m_Value(B))) &&
      match(Y, m_c_Xor(m_Specific(A), m_Specific(B))))
    return ConstantInt::getAllOnesValue(Ty);
 
  // (~A & B) | ~(A | B) --> ~A
  // (~A & B) | ~(B | A) --> ~A
  // (B & ~A) | ~(A | B) --> ~A
  // (B & ~A) | ~(B | A) --> ~A
  Value *NotA;
  if (match(X,
            m_c_And(m_CombineAnd(m_Value(NotA), m_NotForbidUndef(m_Value(A))),
                    m_Value(B))) &&
      match(Y, m_Not(m_c_Or(m_Specific(A), m_Specific(B)))))
    return NotA;
  // The same is true of Logical And
  // TODO: This could share the logic of the version above if there was a
  // version of LogicalAnd that allowed more than just i1 types.
  if (match(X, m_c_LogicalAnd(
                   m_CombineAnd(m_Value(NotA), m_NotForbidUndef(m_Value(A))),
                   m_Value(B))) &&
      match(Y, m_Not(m_c_LogicalOr(m_Specific(A), m_Specific(B)))))
    return NotA;
 
  // ~(A ^ B) | (A & B) --> ~(A ^ B)
  // ~(A ^ B) | (B & A) --> ~(A ^ B)
  Value *NotAB;
  if (match(X, m_CombineAnd(m_NotForbidUndef(m_Xor(m_Value(A), m_Value(B))),
                            m_Value(NotAB))) &&
      match(Y, m_c_And(m_Specific(A), m_Specific(B))))
    return NotAB;
 
  // ~(A & B) | (A ^ B) --> ~(A & B)
  // ~(A & B) | (B ^ A) --> ~(A & B)
  if (match(X, m_CombineAnd(m_NotForbidUndef(m_And(m_Value(A), m_Value(B))),
                            m_Value(NotAB))) &&
      match(Y, m_c_Xor(m_Specific(A), m_Specific(B))))
    return NotAB;
 
  return nullptr;
}
 
/// Given operands for an Or, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyOrInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                             unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Or, Op0, Op1, Q))
    return C;
 
  // X | poison -> poison
  if (isa<PoisonValue>(Op1))
    return Op1;
 
  // X | undef -> -1
  // X | -1 = -1
  // Do not return Op1 because it may contain undef elements if it's a vector.
  if (Q.isUndefValue(Op1) || match(Op1, m_AllOnes()))
    return Constant::getAllOnesValue(Op0->getType());
 
  // X | X = X
  // X | 0 = X
  if (Op0 == Op1 || match(Op1, m_Zero()))
    return Op0;
 
  if (Value *R = simplifyOrLogic(Op0, Op1))
    return R;
  if (Value *R = simplifyOrLogic(Op1, Op0))
    return R;
 
  if (Value *V = simplifyLogicOfAddSub(Op0, Op1, Instruction::Or))
    return V;
 
  // Rotated -1 is still -1:
  // (-1 << X) | (-1 >> (C - X)) --> -1
  // (-1 >> X) | (-1 << (C - X)) --> -1
  // ...with C <= bitwidth (and commuted variants).
  Value *X, *Y;
  if ((match(Op0, m_Shl(m_AllOnes(), m_Value(X))) &&
       match(Op1, m_LShr(m_AllOnes(), m_Value(Y)))) ||
      (match(Op1, m_Shl(m_AllOnes(), m_Value(X))) &&
       match(Op0, m_LShr(m_AllOnes(), m_Value(Y))))) {
    const APInt *C;
    if ((match(X, m_Sub(m_APInt(C), m_Specific(Y))) ||
         match(Y, m_Sub(m_APInt(C), m_Specific(X)))) &&
        C->ule(X->getType()->getScalarSizeInBits())) {
      return ConstantInt::getAllOnesValue(X->getType());
    }
  }
 
  // A funnel shift (rotate) can be decomposed into simpler shifts. See if we
  // are mixing in another shift that is redundant with the funnel shift.
 
  // (fshl X, ?, Y) | (shl X, Y) --> fshl X, ?, Y
  // (shl X, Y) | (fshl X, ?, Y) --> fshl X, ?, Y
  if (match(Op0,
            m_Intrinsic<Intrinsic::fshl>(m_Value(X), m_Value(), m_Value(Y))) &&
      match(Op1, m_Shl(m_Specific(X), m_Specific(Y))))
    return Op0;
  if (match(Op1,
            m_Intrinsic<Intrinsic::fshl>(m_Value(X), m_Value(), m_Value(Y))) &&
      match(Op0, m_Shl(m_Specific(X), m_Specific(Y))))
    return Op1;
 
  // (fshr ?, X, Y) | (lshr X, Y) --> fshr ?, X, Y
  // (lshr X, Y) | (fshr ?, X, Y) --> fshr ?, X, Y
  if (match(Op0,
            m_Intrinsic<Intrinsic::fshr>(m_Value(), m_Value(X), m_Value(Y))) &&
      match(Op1, m_LShr(m_Specific(X), m_Specific(Y))))
    return Op0;
  if (match(Op1,
            m_Intrinsic<Intrinsic::fshr>(m_Value(), m_Value(X), m_Value(Y))) &&
      match(Op0, m_LShr(m_Specific(X), m_Specific(Y))))
    return Op1;
 
  if (Value *V = simplifyAndOrOfCmps(Q, Op0, Op1, false))
    return V;
 
  // If we have a multiplication overflow check that is being 'and'ed with a
  // check that one of the multipliers is not zero, we can omit the 'and', and
  // only keep the overflow check.
  if (isCheckForZeroAndMulWithOverflow(Op0, Op1, false))
    return Op1;
  if (isCheckForZeroAndMulWithOverflow(Op1, Op0, false))
    return Op0;
 
  // Try some generic simplifications for associative operations.
  if (Value *V =
          simplifyAssociativeBinOp(Instruction::Or, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // Or distributes over And.  Try some generic simplifications based on this.
  if (Value *V = expandCommutativeBinOp(Instruction::Or, Op0, Op1,
                                        Instruction::And, Q, MaxRecurse))
    return V;
 
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1)) {
    if (Op0->getType()->isIntOrIntVectorTy(1)) {
      // A | (A || B) -> A || B
      if (match(Op1, m_Select(m_Specific(Op0), m_One(), m_Value())))
        return Op1;
      else if (match(Op0, m_Select(m_Specific(Op1), m_One(), m_Value())))
        return Op0;
    }
    // If the operation is with the result of a select instruction, check
    // whether operating on either branch of the select always yields the same
    // value.
    if (Value *V =
            threadBinOpOverSelect(Instruction::Or, Op0, Op1, Q, MaxRecurse))
      return V;
  }
 
  // (A & C1)|(B & C2)
  Value *A, *B;
  const APInt *C1, *C2;
  if (match(Op0, m_And(m_Value(A), m_APInt(C1))) &&
      match(Op1, m_And(m_Value(B), m_APInt(C2)))) {
    if (*C1 == ~*C2) {
      // (A & C1)|(B & C2)
      // If we have: ((V + N) & C1) | (V & C2)
      // .. and C2 = ~C1 and C2 is 0+1+ and (N & C2) == 0
      // replace with V+N.
      Value *N;
      if (C2->isMask() && // C2 == 0+1+
          match(A, m_c_Add(m_Specific(B), m_Value(N)))) {
        // Add commutes, try both ways.
        if (MaskedValueIsZero(N, *C2, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
          return A;
      }
      // Or commutes, try both ways.
      if (C1->isMask() && match(B, m_c_Add(m_Specific(A), m_Value(N)))) {
        // Add commutes, try both ways.
        if (MaskedValueIsZero(N, *C1, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
          return B;
      }
    }
  }
 
  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V = threadBinOpOverPHI(Instruction::Or, Op0, Op1, Q, MaxRecurse))
      return V;
 
  if (Op0->getType()->isIntOrIntVectorTy(1)) {
    if (std::optional<bool> Implied =
            isImpliedCondition(Op0, Op1, Q.DL, false)) {
      // If Op0 is false implies Op1 is false, then Op1 is a subset of Op0.
      if (*Implied == false)
        return Op0;
      // If Op0 is false implies Op1 is true, then at least one is always true.
      if (*Implied == true)
        return ConstantInt::getTrue(Op0->getType());
    }
    if (std::optional<bool> Implied =
            isImpliedCondition(Op1, Op0, Q.DL, false)) {
      // If Op1 is false implies Op0 is false, then Op0 is a subset of Op1.
      if (*Implied == false)
        return Op1;
      // If Op1 is false implies Op0 is true, then at least one is always true.
      if (*Implied == true)
        return ConstantInt::getTrue(Op1->getType());
    }
  }
 
  if (Value *V = simplifyByDomEq(Instruction::Or, Op0, Op1, Q, MaxRecurse))
    return V;
 
  return nullptr;
}
 
Value *llvm::simplifyOrInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::simplifyOrInst(Op0, Op1, Q, RecursionLimit);
}
 
/// Given operands for a Xor, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyXorInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                              unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Xor, Op0, Op1, Q))
    return C;
 
  // X ^ poison -> poison
  if (isa<PoisonValue>(Op1))
    return Op1;
 
  // A ^ undef -> undef
  if (Q.isUndefValue(Op1))
    return Op1;
 
  // A ^ 0 = A
  if (match(Op1, m_Zero()))
    return Op0;
 
  // A ^ A = 0
  if (Op0 == Op1)
    return Constant::getNullValue(Op0->getType());
 
  // A ^ ~A  =  ~A ^ A  =  -1
  if (match(Op0, m_Not(m_Specific(Op1))) || match(Op1, m_Not(m_Specific(Op0))))
    return Constant::getAllOnesValue(Op0->getType());
 
  auto foldAndOrNot = [](Value *X, Value *Y) -> Value * {
    Value *A, *B;
    // (~A & B) ^ (A | B) --> A -- There are 8 commuted variants.
    if (match(X, m_c_And(m_Not(m_Value(A)), m_Value(B))) &&
        match(Y, m_c_Or(m_Specific(A), m_Specific(B))))
      return A;
 
    // (~A | B) ^ (A & B) --> ~A -- There are 8 commuted variants.
    // The 'not' op must contain a complete -1 operand (no undef elements for
    // vector) for the transform to be safe.
    Value *NotA;
    if (match(X,
              m_c_Or(m_CombineAnd(m_NotForbidUndef(m_Value(A)), m_Value(NotA)),
                     m_Value(B))) &&
        match(Y, m_c_And(m_Specific(A), m_Specific(B))))
      return NotA;
 
    return nullptr;
  };
  if (Value *R = foldAndOrNot(Op0, Op1))
    return R;
  if (Value *R = foldAndOrNot(Op1, Op0))
    return R;
 
  if (Value *V = simplifyLogicOfAddSub(Op0, Op1, Instruction::Xor))
    return V;
 
  // Try some generic simplifications for associative operations.
  if (Value *V =
          simplifyAssociativeBinOp(Instruction::Xor, Op0, Op1, Q, MaxRecurse))
    return V;
 
  // Threading Xor over selects and phi nodes is pointless, so don't bother.
  // Threading over the select in "A ^ select(cond, B, C)" means evaluating
  // "A^B" and "A^C" and seeing if they are equal; but they are equal if and
  // only if B and C are equal.  If B and C are equal then (since we assume
  // that operands have already been simplified) "select(cond, B, C)" should
  // have been simplified to the common value of B and C already.  Analysing
  // "A^B" and "A^C" thus gains nothing, but costs compile time.  Similarly
  // for threading over phi nodes.
 
  if (Value *V = simplifyByDomEq(Instruction::Xor, Op0, Op1, Q, MaxRecurse))
    return V;
 
  return nullptr;
}
 
Value *llvm::simplifyXorInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::simplifyXorInst(Op0, Op1, Q, RecursionLimit);
}
 
static Type *getCompareTy(Value *Op) {
  return CmpInst::makeCmpResultType(Op->getType());
}
 
/// Rummage around inside V looking for something equivalent to the comparison
/// "LHS Pred RHS". Return such a value if found, otherwise return null.
/// Helper function for analyzing max/min idioms.
static Value *extractEquivalentCondition(Value *V, CmpInst::Predicate Pred,
                                         Value *LHS, Value *RHS) {
  SelectInst *SI = dyn_cast<SelectInst>(V);
  if (!SI)
    return nullptr;
  CmpInst *Cmp = dyn_cast<CmpInst>(SI->getCondition());
  if (!Cmp)
    return nullptr;
  Value *CmpLHS = Cmp->getOperand(0), *CmpRHS = Cmp->getOperand(1);
  if (Pred == Cmp->getPredicate() && LHS == CmpLHS && RHS == CmpRHS)
    return Cmp;
  if (Pred == CmpInst::getSwappedPredicate(Cmp->getPredicate()) &&
      LHS == CmpRHS && RHS == CmpLHS)
    return Cmp;
  return nullptr;
}
 
/// Return true if the underlying object (storage) must be disjoint from
/// storage returned by any noalias return call.
static bool isAllocDisjoint(const Value *V) {
  // For allocas, we consider only static ones (dynamic
  // allocas might be transformed into calls to malloc not simultaneously
  // live with the compared-to allocation). For globals, we exclude symbols
  // that might be resolve lazily to symbols in another dynamically-loaded
  // library (and, thus, could be malloc'ed by the implementation).
  if (const AllocaInst *AI = dyn_cast<AllocaInst>(V))
    return AI->getParent() && AI->getFunction() && AI->isStaticAlloca();
  if (const GlobalValue *GV = dyn_cast<GlobalValue>(V))
    return (GV->hasLocalLinkage() || GV->hasHiddenVisibility() ||
            GV->hasProtectedVisibility() || GV->hasGlobalUnnamedAddr()) &&
           !GV->isThreadLocal();
  if (const Argument *A = dyn_cast<Argument>(V))
    return A->hasByValAttr();
  return false;
}
 
/// Return true if V1 and V2 are each the base of some distict storage region
/// [V, object_size(V)] which do not overlap.  Note that zero sized regions
/// *are* possible, and that zero sized regions do not overlap with any other.
static bool haveNonOverlappingStorage(const Value *V1, const Value *V2) {
  // Global variables always exist, so they always exist during the lifetime
  // of each other and all allocas.  Global variables themselves usually have
  // non-overlapping storage, but since their addresses are constants, the
  // case involving two globals does not reach here and is instead handled in
  // constant folding.
  //
  // Two different allocas usually have different addresses...
  //
  // However, if there's an @llvm.stackrestore dynamically in between two
  // allocas, they may have the same address. It's tempting to reduce the
  // scope of the problem by only looking at *static* allocas here. That would
  // cover the majority of allocas while significantly reducing the likelihood
  // of having an @llvm.stackrestore pop up in the middle. However, it's not
  // actually impossible for an @llvm.stackrestore to pop up in the middle of
  // an entry block. Also, if we have a block that's not attached to a
  // function, we can't tell if it's "static" under the current definition.
  // Theoretically, this problem could be fixed by creating a new kind of
  // instruction kind specifically for static allocas. Such a new instruction
  // could be required to be at the top of the entry block, thus preventing it
  // from being subject to a @llvm.stackrestore. Instcombine could even
  // convert regular allocas into these special allocas. It'd be nifty.
  // However, until then, this problem remains open.
  //
  // So, we'll assume that two non-empty allocas have different addresses
  // for now.
  auto isByValArg = [](const Value *V) {
    const Argument *A = dyn_cast<Argument>(V);
    return A && A->hasByValAttr();
  };
 
  // Byval args are backed by store which does not overlap with each other,
  // allocas, or globals.
  if (isByValArg(V1))
    return isa<AllocaInst>(V2) || isa<GlobalVariable>(V2) || isByValArg(V2);
  if (isByValArg(V2))
    return isa<AllocaInst>(V1) || isa<GlobalVariable>(V1) || isByValArg(V1);
 
  return isa<AllocaInst>(V1) &&
         (isa<AllocaInst>(V2) || isa<GlobalVariable>(V2));
}
 
// A significant optimization not implemented here is assuming that alloca
// addresses are not equal to incoming argument values. They don't *alias*,
// as we say, but that doesn't mean they aren't equal, so we take a
// conservative approach.
//
// This is inspired in part by C++11 5.10p1:
//   "Two pointers of the same type compare equal if and only if they are both
//    null, both point to the same function, or both represent the same
//    address."
//
// This is pretty permissive.
//
// It's also partly due to C11 6.5.9p6:
//   "Two pointers compare equal if and only if both are null pointers, both are
//    pointers to the same object (including a pointer to an object and a
//    subobject at its beginning) or function, both are pointers to one past the
//    last element of the same array object, or one is a pointer to one past the
//    end of one array object and the other is a pointer to the start of a
//    different array object that happens to immediately follow the first array
//    object in the address space.)
//
// C11's version is more restrictive, however there's no reason why an argument
// couldn't be a one-past-the-end value for a stack object in the caller and be
// equal to the beginning of a stack object in the callee.
//
// If the C and C++ standards are ever made sufficiently restrictive in this
// area, it may be possible to update LLVM's semantics accordingly and reinstate
// this optimization.
static Constant *computePointerICmp(CmpInst::Predicate Pred, Value *LHS,
                                    Value *RHS, const SimplifyQuery &Q) {
  const DataLayout &DL = Q.DL;
  const TargetLibraryInfo *TLI = Q.TLI;
  const DominatorTree *DT = Q.DT;
  const Instruction *CxtI = Q.CxtI;
  const InstrInfoQuery &IIQ = Q.IIQ;
 
  // First, skip past any trivial no-ops.
  LHS = LHS->stripPointerCasts();
  RHS = RHS->stripPointerCasts();
 
  // A non-null pointer is not equal to a null pointer.
  if (isa<ConstantPointerNull>(RHS) && ICmpInst::isEquality(Pred) &&
      llvm::isKnownNonZero(LHS, DL, 0, nullptr, nullptr, nullptr,
                           IIQ.UseInstrInfo))
    return ConstantInt::get(getCompareTy(LHS), !CmpInst::isTrueWhenEqual(Pred));
 
  // We can only fold certain predicates on pointer comparisons.
  switch (Pred) {
  default:
    return nullptr;
 
    // Equality comparisons are easy to fold.
  case CmpInst::ICMP_EQ:
  case CmpInst::ICMP_NE:
    break;
 
    // We can only handle unsigned relational comparisons because 'inbounds' on
    // a GEP only protects against unsigned wrapping.
  case CmpInst::ICMP_UGT:
  case CmpInst::ICMP_UGE:
  case CmpInst::ICMP_ULT:
  case CmpInst::ICMP_ULE:
    // However, we have to switch them to their signed variants to handle
    // negative indices from the base pointer.
    Pred = ICmpInst::getSignedPredicate(Pred);
    break;
  }
 
  // Strip off any constant offsets so that we can reason about them.
  // It's tempting to use getUnderlyingObject or even just stripInBoundsOffsets
  // here and compare base addresses like AliasAnalysis does, however there are
  // numerous hazards. AliasAnalysis and its utilities rely on special rules
  // governing loads and stores which don't apply to icmps. Also, AliasAnalysis
  // doesn't need to guarantee pointer inequality when it says NoAlias.
 
  // Even if an non-inbounds GEP occurs along the path we can still optimize
  // equality comparisons concerning the result.
  bool AllowNonInbounds = ICmpInst::isEquality(Pred);
  APInt LHSOffset = stripAndComputeConstantOffsets(DL, LHS, AllowNonInbounds);
  APInt RHSOffset = stripAndComputeConstantOffsets(DL, RHS, AllowNonInbounds);
 
  // If LHS and RHS are related via constant offsets to the same base
  // value, we can replace it with an icmp which just compares the offsets.
  if (LHS == RHS)
    return ConstantInt::get(getCompareTy(LHS),
                            ICmpInst::compare(LHSOffset, RHSOffset, Pred));
 
  // Various optimizations for (in)equality comparisons.
  if (Pred == CmpInst::ICMP_EQ || Pred == CmpInst::ICMP_NE) {
    // Different non-empty allocations that exist at the same time have
    // different addresses (if the program can tell). If the offsets are
    // within the bounds of their allocations (and not one-past-the-end!
    // so we can't use inbounds!), and their allocations aren't the same,
    // the pointers are not equal.
    if (haveNonOverlappingStorage(LHS, RHS)) {
      uint64_t LHSSize, RHSSize;
      ObjectSizeOpts Opts;
      Opts.EvalMode = ObjectSizeOpts::Mode::Min;
      auto *F = [](Value *V) -> Function * {
        if (auto *I = dyn_cast<Instruction>(V))
          return I->getFunction();
        if (auto *A = dyn_cast<Argument>(V))
          return A->getParent();
        return nullptr;
      }(LHS);
      Opts.NullIsUnknownSize = F ? NullPointerIsDefined(F) : true;
      if (getObjectSize(LHS, LHSSize, DL, TLI, Opts) &&
          getObjectSize(RHS, RHSSize, DL, TLI, Opts) &&
          !LHSOffset.isNegative() && !RHSOffset.isNegative() &&
          LHSOffset.ult(LHSSize) && RHSOffset.ult(RHSSize)) {
        return ConstantInt::get(getCompareTy(LHS),
                                !CmpInst::isTrueWhenEqual(Pred));
      }
    }
 
    // If one side of the equality comparison must come from a noalias call
    // (meaning a system memory allocation function), and the other side must
    // come from a pointer that cannot overlap with dynamically-allocated
    // memory within the lifetime of the current function (allocas, byval
    // arguments, globals), then determine the comparison result here.
    SmallVector<const Value *, 8> LHSUObjs, RHSUObjs;
    getUnderlyingObjects(LHS, LHSUObjs);
    getUnderlyingObjects(RHS, RHSUObjs);
 
    // Is the set of underlying objects all noalias calls?
    auto IsNAC = [](ArrayRef<const Value *> Objects) {
      return all_of(Objects, isNoAliasCall);
    };
 
    // Is the set of underlying objects all things which must be disjoint from
    // noalias calls.  We assume that indexing from such disjoint storage
    // into the heap is undefined, and thus offsets can be safely ignored.
    auto IsAllocDisjoint = [](ArrayRef<const Value *> Objects) {
      return all_of(Objects, ::isAllocDisjoint);
    };
 
    if ((IsNAC(LHSUObjs) && IsAllocDisjoint(RHSUObjs)) ||
        (IsNAC(RHSUObjs) && IsAllocDisjoint(LHSUObjs)))
      return ConstantInt::get(getCompareTy(LHS),
                              !CmpInst::isTrueWhenEqual(Pred));
 
    // Fold comparisons for non-escaping pointer even if the allocation call
    // cannot be elided. We cannot fold malloc comparison to null. Also, the
    // dynamic allocation call could be either of the operands.  Note that
    // the other operand can not be based on the alloc - if it were, then
    // the cmp itself would be a capture.
    Value *MI = nullptr;
    if (isAllocLikeFn(LHS, TLI) &&
        llvm::isKnownNonZero(RHS, DL, 0, nullptr, CxtI, DT))
      MI = LHS;
    else if (isAllocLikeFn(RHS, TLI) &&
             llvm::isKnownNonZero(LHS, DL, 0, nullptr, CxtI, DT))
      MI = RHS;
    if (MI) {
      // FIXME: This is incorrect, see PR54002. While we can assume that the
      // allocation is at an address that makes the comparison false, this
      // requires that *all* comparisons to that address be false, which
      // InstSimplify cannot guarantee.
      struct CustomCaptureTracker : public CaptureTracker {
        bool Captured = false;
        void tooManyUses() override { Captured = true; }
        bool captured(const Use *U) override {
          if (auto *ICmp = dyn_cast<ICmpInst>(U->getUser())) {
            // Comparison against value stored in global variable. Given the
            // pointer does not escape, its value cannot be guessed and stored
            // separately in a global variable.
            unsigned OtherIdx = 1 - U->getOperandNo();
            auto *LI = dyn_cast<LoadInst>(ICmp->getOperand(OtherIdx));
            if (LI && isa<GlobalVariable>(LI->getPointerOperand()))
              return false;
          }
 
          Captured = true;
          return true;
        }
      };
      CustomCaptureTracker Tracker;
      PointerMayBeCaptured(MI, &Tracker);
      if (!Tracker.Captured)
        return ConstantInt::get(getCompareTy(LHS),
                                CmpInst::isFalseWhenEqual(Pred));
    }
  }
 
  // Otherwise, fail.
  return nullptr;
}
 
/// Fold an icmp when its operands have i1 scalar type.
static Value *simplifyICmpOfBools(CmpInst::Predicate Pred, Value *LHS,
                                  Value *RHS, const SimplifyQuery &Q) {
  Type *ITy = getCompareTy(LHS); // The return type.
  Type *OpTy = LHS->getType();   // The operand type.
  if (!OpTy->isIntOrIntVectorTy(1))
    return nullptr;
 
  // A boolean compared to true/false can be reduced in 14 out of the 20
  // (10 predicates * 2 constants) possible combinations. The other
  // 6 cases require a 'not' of the LHS.
 
  auto ExtractNotLHS = [](Value *V) -> Value * {
    Value *X;
    if (match(V, m_Not(m_Value(X))))
      return X;
    return nullptr;
  };
 
  if (match(RHS, m_Zero())) {
    switch (Pred) {
    case CmpInst::ICMP_NE:  // X !=  0 -> X
    case CmpInst::ICMP_UGT: // X >u  0 -> X
    case CmpInst::ICMP_SLT: // X <s  0 -> X
      return LHS;
 
    case CmpInst::ICMP_EQ:  // not(X) ==  0 -> X != 0 -> X
    case CmpInst::ICMP_ULE: // not(X) <=u 0 -> X >u 0 -> X
    case CmpInst::ICMP_SGE: // not(X) >=s 0 -> X <s 0 -> X
      if (Value *X = ExtractNotLHS(LHS))
        return X;
      break;
 
    case CmpInst::ICMP_ULT: // X <u  0 -> false
    case CmpInst::ICMP_SGT: // X >s  0 -> false
      return getFalse(ITy);
 
    case CmpInst::ICMP_UGE: // X >=u 0 -> true
    case CmpInst::ICMP_SLE: // X <=s 0 -> true
      return getTrue(ITy);
 
    default:
      break;
    }
  } else if (match(RHS, m_One())) {
    switch (Pred) {
    case CmpInst::ICMP_EQ:  // X ==   1 -> X
    case CmpInst::ICMP_UGE: // X >=u  1 -> X
    case CmpInst::ICMP_SLE: // X <=s -1 -> X
      return LHS;
 
    case CmpInst::ICMP_NE:  // not(X) !=  1 -> X ==   1 -> X
    case CmpInst::ICMP_ULT: // not(X) <=u 1 -> X >=u  1 -> X
    case CmpInst::ICMP_SGT: // not(X) >s  1 -> X <=s -1 -> X
      if (Value *X = ExtractNotLHS(LHS))
        return X;
      break;
 
    case CmpInst::ICMP_UGT: // X >u   1 -> false
    case CmpInst::ICMP_SLT: // X <s  -1 -> false
      return getFalse(ITy);
 
    case CmpInst::ICMP_ULE: // X <=u  1 -> true
    case CmpInst::ICMP_SGE: // X >=s -1 -> true
      return getTrue(ITy);
 
    default:
      break;
    }
  }
 
  switch (Pred) {
  default:
    break;
  case ICmpInst::ICMP_UGE:
    if (isImpliedCondition(RHS, LHS, Q.DL).value_or(false))
      return getTrue(ITy);
    break;
  case ICmpInst::ICMP_SGE:
    /// For signed comparison, the values for an i1 are 0 and -1
    /// respectively. This maps into a truth table of:
    /// LHS | RHS | LHS >=s RHS   | LHS implies RHS
    ///  0  |  0  |  1 (0 >= 0)   |  1
    ///  0  |  1  |  1 (0 >= -1)  |  1
    ///  1  |  0  |  0 (-1 >= 0)  |  0
    ///  1  |  1  |  1 (-1 >= -1) |  1
    if (isImpliedCondition(LHS, RHS, Q.DL).value_or(false))
      return getTrue(ITy);
    break;
  case ICmpInst::ICMP_ULE:
    if (isImpliedCondition(LHS, RHS, Q.DL).value_or(false))
      return getTrue(ITy);
    break;
  case ICmpInst::ICMP_SLE:
    /// SLE follows the same logic as SGE with the LHS and RHS swapped.
    if (isImpliedCondition(RHS, LHS, Q.DL).value_or(false))
      return getTrue(ITy);
    break;
  }
 
  return nullptr;
}
 
/// Try hard to fold icmp with zero RHS because this is a common case.
static Value *simplifyICmpWithZero(CmpInst::Predicate Pred, Value *LHS,
                                   Value *RHS, const SimplifyQuery &Q) {
  if (!match(RHS, m_Zero()))
    return nullptr;
 
  Type *ITy = getCompareTy(LHS); // The return type.
  switch (Pred) {
  default:
    llvm_unreachable("Unknown ICmp predicate!");
  case ICmpInst::ICMP_ULT:
    return getFalse(ITy);
  case ICmpInst::ICMP_UGE:
    return getTrue(ITy);
  case ICmpInst::ICMP_EQ:
  case ICmpInst::ICMP_ULE:
    if (isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT, Q.IIQ.UseInstrInfo))
      return getFalse(ITy);
    break;
  case ICmpInst::ICMP_NE:
  case ICmpInst::ICMP_UGT:
    if (isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT, Q.IIQ.UseInstrInfo))
      return getTrue(ITy);
    break;
  case ICmpInst::ICMP_SLT: {
    KnownBits LHSKnown = computeKnownBits(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (LHSKnown.isNegative())
      return getTrue(ITy);
    if (LHSKnown.isNonNegative())
      return getFalse(ITy);
    break;
  }
  case ICmpInst::ICMP_SLE: {
    KnownBits LHSKnown = computeKnownBits(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (LHSKnown.isNegative())
      return getTrue(ITy);
    if (LHSKnown.isNonNegative() &&
        isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
      return getFalse(ITy);
    break;
  }
  case ICmpInst::ICMP_SGE: {
    KnownBits LHSKnown = computeKnownBits(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (LHSKnown.isNegative())
      return getFalse(ITy);
    if (LHSKnown.isNonNegative())
      return getTrue(ITy);
    break;
  }
  case ICmpInst::ICMP_SGT: {
    KnownBits LHSKnown = computeKnownBits(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (LHSKnown.isNegative())
      return getFalse(ITy);
    if (LHSKnown.isNonNegative() &&
        isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
      return getTrue(ITy);
    break;
  }
  }
 
  return nullptr;
}
 
static Value *simplifyICmpWithConstant(CmpInst::Predicate Pred, Value *LHS,
                                       Value *RHS, const InstrInfoQuery &IIQ) {
  Type *ITy = getCompareTy(RHS); // The return type.
 
  Value *X;
  // Sign-bit checks can be optimized to true/false after unsigned
  // floating-point casts:
  // icmp slt (bitcast (uitofp X)),  0 --> false
  // icmp sgt (bitcast (uitofp X)), -1 --> true
  if (match(LHS, m_BitCast(m_UIToFP(m_Value(X))))) {
    if (Pred == ICmpInst::ICMP_SLT && match(RHS, m_Zero()))
      return ConstantInt::getFalse(ITy);
    if (Pred == ICmpInst::ICMP_SGT && match(RHS, m_AllOnes()))
      return ConstantInt::getTrue(ITy);
  }
 
  const APInt *C;
  if (!match(RHS, m_APIntAllowUndef(C)))
    return nullptr;
 
  // Rule out tautological comparisons (eg., ult 0 or uge 0).
  ConstantRange RHS_CR = ConstantRange::makeExactICmpRegion(Pred, *C);
  if (RHS_CR.isEmptySet())
    return ConstantInt::getFalse(ITy);
  if (RHS_CR.isFullSet())
    return ConstantInt::getTrue(ITy);
 
  ConstantRange LHS_CR =
      computeConstantRange(LHS, CmpInst::isSigned(Pred), IIQ.UseInstrInfo);
  if (!LHS_CR.isFullSet()) {
    if (RHS_CR.contains(LHS_CR))
      return ConstantInt::getTrue(ITy);
    if (RHS_CR.inverse().contains(LHS_CR))
      return ConstantInt::getFalse(ITy);
  }
 
  // (mul nuw/nsw X, MulC) != C --> true  (if C is not a multiple of MulC)
  // (mul nuw/nsw X, MulC) == C --> false (if C is not a multiple of MulC)
  const APInt *MulC;
  if (ICmpInst::isEquality(Pred) &&
      ((match(LHS, m_NUWMul(m_Value(), m_APIntAllowUndef(MulC))) &&
        *MulC != 0 && C->urem(*MulC) != 0) ||
       (match(LHS, m_NSWMul(m_Value(), m_APIntAllowUndef(MulC))) &&
        *MulC != 0 && C->srem(*MulC) != 0)))
    return ConstantInt::get(ITy, Pred == ICmpInst::ICMP_NE);
 
  return nullptr;
}
 
static Value *simplifyICmpWithBinOpOnLHS(CmpInst::Predicate Pred,
                                         BinaryOperator *LBO, Value *RHS,
                                         const SimplifyQuery &Q,
                                         unsigned MaxRecurse) {
  Type *ITy = getCompareTy(RHS); // The return type.
 
  Value *Y = nullptr;
  // icmp pred (or X, Y), X
  if (match(LBO, m_c_Or(m_Value(Y), m_Specific(RHS)))) {
    if (Pred == ICmpInst::ICMP_ULT)
      return getFalse(ITy);
    if (Pred == ICmpInst::ICMP_UGE)
      return getTrue(ITy);
 
    if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SGE) {
      KnownBits RHSKnown = computeKnownBits(RHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
      KnownBits YKnown = computeKnownBits(Y, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
      if (RHSKnown.isNonNegative() && YKnown.isNegative())
        return Pred == ICmpInst::ICMP_SLT ? getTrue(ITy) : getFalse(ITy);
      if (RHSKnown.isNegative() || YKnown.isNonNegative())
        return Pred == ICmpInst::ICMP_SLT ? getFalse(ITy) : getTrue(ITy);
    }
  }
 
  // icmp pred (and X, Y), X
  if (match(LBO, m_c_And(m_Value(), m_Specific(RHS)))) {
    if (Pred == ICmpInst::ICMP_UGT)
      return getFalse(ITy);
    if (Pred == ICmpInst::ICMP_ULE)
      return getTrue(ITy);
  }
 
  // icmp pred (urem X, Y), Y
  if (match(LBO, m_URem(m_Value(), m_Specific(RHS)))) {
    switch (Pred) {
    default:
      break;
    case ICmpInst::ICMP_SGT:
    case ICmpInst::ICMP_SGE: {
      KnownBits Known = computeKnownBits(RHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
      if (!Known.isNonNegative())
        break;
      [[fallthrough]];
    }
    case ICmpInst::ICMP_EQ:
    case ICmpInst::ICMP_UGT:
    case ICmpInst::ICMP_UGE:
      return getFalse(ITy);
    case ICmpInst::ICMP_SLT:
    case ICmpInst::ICMP_SLE: {
      KnownBits Known = computeKnownBits(RHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
      if (!Known.isNonNegative())
        break;
      [[fallthrough]];
    }
    case ICmpInst::ICMP_NE:
    case ICmpInst::ICMP_ULT:
    case ICmpInst::ICMP_ULE:
      return getTrue(ITy);
    }
  }
 
  // icmp pred (urem X, Y), X
  if (match(LBO, m_URem(m_Specific(RHS), m_Value()))) {
    if (Pred == ICmpInst::ICMP_ULE)
      return getTrue(ITy);
    if (Pred == ICmpInst::ICMP_UGT)
      return getFalse(ITy);
  }
 
  // x >>u y <=u x --> true.
  // x >>u y >u  x --> false.
  // x udiv y <=u x --> true.
  // x udiv y >u  x --> false.
  if (match(LBO, m_LShr(m_Specific(RHS), m_Value())) ||
      match(LBO, m_UDiv(m_Specific(RHS), m_Value()))) {
    // icmp pred (X op Y), X
    if (Pred == ICmpInst::ICMP_UGT)
      return getFalse(ITy);
    if (Pred == ICmpInst::ICMP_ULE)
      return getTrue(ITy);
  }
 
  // If x is nonzero:
  // x >>u C <u  x --> true  for C != 0.
  // x >>u C !=  x --> true  for C != 0.
  // x >>u C >=u x --> false for C != 0.
  // x >>u C ==  x --> false for C != 0.
  // x udiv C <u  x --> true  for C != 1.
  // x udiv C !=  x --> true  for C != 1.
  // x udiv C >=u x --> false for C != 1.
  // x udiv C ==  x --> false for C != 1.
  // TODO: allow non-constant shift amount/divisor
  const APInt *C;
  if ((match(LBO, m_LShr(m_Specific(RHS), m_APInt(C))) && *C != 0) ||
      (match(LBO, m_UDiv(m_Specific(RHS), m_APInt(C))) && *C != 1)) {
    if (isKnownNonZero(RHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT)) {
      switch (Pred) {
      default:
        break;
      case ICmpInst::ICMP_EQ:
      case ICmpInst::ICMP_UGE:
        return getFalse(ITy);
      case ICmpInst::ICMP_NE:
      case ICmpInst::ICMP_ULT:
        return getTrue(ITy);
      case ICmpInst::ICMP_UGT:
      case ICmpInst::ICMP_ULE:
        // UGT/ULE are handled by the more general case just above
        llvm_unreachable("Unexpected UGT/ULE, should have been handled");
      }
    }
  }
 
  // (x*C1)/C2 <= x for C1 <= C2.
  // This holds even if the multiplication overflows: Assume that x != 0 and
  // arithmetic is modulo M. For overflow to occur we must have C1 >= M/x and
  // thus C2 >= M/x. It follows that (x*C1)/C2 <= (M-1)/C2 <= ((M-1)*x)/M < x.
  //
  // Additionally, either the multiplication and division might be represented
  // as shifts:
  // (x*C1)>>C2 <= x for C1 < 2**C2.
  // (x<<C1)/C2 <= x for 2**C1 < C2.
  const APInt *C1, *C2;
  if ((match(LBO, m_UDiv(m_Mul(m_Specific(RHS), m_APInt(C1)), m_APInt(C2))) &&
       C1->ule(*C2)) ||
      (match(LBO, m_LShr(m_Mul(m_Specific(RHS), m_APInt(C1)), m_APInt(C2))) &&
       C1->ule(APInt(C2->getBitWidth(), 1) << *C2)) ||
      (match(LBO, m_UDiv(m_Shl(m_Specific(RHS), m_APInt(C1)), m_APInt(C2))) &&
       (APInt(C1->getBitWidth(), 1) << *C1).ule(*C2))) {
    if (Pred == ICmpInst::ICMP_UGT)
      return getFalse(ITy);
    if (Pred == ICmpInst::ICMP_ULE)
      return getTrue(ITy);
  }
 
  // (sub C, X) == X, C is odd  --> false
  // (sub C, X) != X, C is odd  --> true
  if (match(LBO, m_Sub(m_APIntAllowUndef(C), m_Specific(RHS))) &&
      (*C & 1) == 1 && ICmpInst::isEquality(Pred))
    return (Pred == ICmpInst::ICMP_EQ) ? getFalse(ITy) : getTrue(ITy);
 
  return nullptr;
}
 
// If only one of the icmp's operands has NSW flags, try to prove that:
//
//   icmp slt (x + C1), (x +nsw C2)
//
// is equivalent to:
//
//   icmp slt C1, C2
//
// which is true if x + C2 has the NSW flags set and:
// *) C1 < C2 && C1 >= 0, or
// *) C2 < C1 && C1 <= 0.
//
static bool trySimplifyICmpWithAdds(CmpInst::Predicate Pred, Value *LHS,
                                    Value *RHS) {
  // TODO: only support icmp slt for now.
  if (Pred != CmpInst::ICMP_SLT)
    return false;
 
  // Canonicalize nsw add as RHS.
  if (!match(RHS, m_NSWAdd(m_Value(), m_Value())))
    std::swap(LHS, RHS);
  if (!match(RHS, m_NSWAdd(m_Value(), m_Value())))
    return false;
 
  Value *X;
  const APInt *C1, *C2;
  if (!match(LHS, m_c_Add(m_Value(X), m_APInt(C1))) ||
      !match(RHS, m_c_Add(m_Specific(X), m_APInt(C2))))
    return false;
 
  return (C1->slt(*C2) && C1->isNonNegative()) ||
         (C2->slt(*C1) && C1->isNonPositive());
}
 
/// TODO: A large part of this logic is duplicated in InstCombine's
/// foldICmpBinOp(). We should be able to share that and avoid the code
/// duplication.
static Value *simplifyICmpWithBinOp(CmpInst::Predicate Pred, Value *LHS,
                                    Value *RHS, const SimplifyQuery &Q,
                                    unsigned MaxRecurse) {
  BinaryOperator *LBO = dyn_cast<BinaryOperator>(LHS);
  BinaryOperator *RBO = dyn_cast<BinaryOperator>(RHS);
  if (MaxRecurse && (LBO || RBO)) {
    // Analyze the case when either LHS or RHS is an add instruction.
    Value *A = nullptr, *B = nullptr, *C = nullptr, *D = nullptr;
    // LHS = A + B (or A and B are null); RHS = C + D (or C and D are null).
    bool NoLHSWrapProblem = false, NoRHSWrapProblem = false;
    if (LBO && LBO->getOpcode() == Instruction::Add) {
      A = LBO->getOperand(0);
      B = LBO->getOperand(1);
      NoLHSWrapProblem =
          ICmpInst::isEquality(Pred) ||
          (CmpInst::isUnsigned(Pred) &&
           Q.IIQ.hasNoUnsignedWrap(cast<OverflowingBinaryOperator>(LBO))) ||
          (CmpInst::isSigned(Pred) &&
           Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(LBO)));
    }
    if (RBO && RBO->getOpcode() == Instruction::Add) {
      C = RBO->getOperand(0);
      D = RBO->getOperand(1);
      NoRHSWrapProblem =
          ICmpInst::isEquality(Pred) ||
          (CmpInst::isUnsigned(Pred) &&
           Q.IIQ.hasNoUnsignedWrap(cast<OverflowingBinaryOperator>(RBO))) ||
          (CmpInst::isSigned(Pred) &&
           Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(RBO)));
    }
 
    // icmp (X+Y), X -> icmp Y, 0 for equalities or if there is no overflow.
    if ((A == RHS || B == RHS) && NoLHSWrapProblem)
      if (Value *V = simplifyICmpInst(Pred, A == RHS ? B : A,
                                      Constant::getNullValue(RHS->getType()), Q,
                                      MaxRecurse - 1))
        return V;
 
    // icmp X, (X+Y) -> icmp 0, Y for equalities or if there is no overflow.
    if ((C == LHS || D == LHS) && NoRHSWrapProblem)
      if (Value *V =
              simplifyICmpInst(Pred, Constant::getNullValue(LHS->getType()),
                               C == LHS ? D : C, Q, MaxRecurse - 1))
        return V;
 
    // icmp (X+Y), (X+Z) -> icmp Y,Z for equalities or if there is no overflow.
    bool CanSimplify = (NoLHSWrapProblem && NoRHSWrapProblem) ||
                       trySimplifyICmpWithAdds(Pred, LHS, RHS);
    if (A && C && (A == C || A == D || B == C || B == D) && CanSimplify) {
      // Determine Y and Z in the form icmp (X+Y), (X+Z).
      Value *Y, *Z;
      if (A == C) {
        // C + B == C + D  ->  B == D
        Y = B;
        Z = D;
      } else if (A == D) {
        // D + B == C + D  ->  B == C
        Y = B;
        Z = C;
      } else if (B == C) {
        // A + C == C + D  ->  A == D
        Y = A;
        Z = D;
      } else {
        assert(B == D);
        // A + D == C + D  ->  A == C
        Y = A;
        Z = C;
      }
      if (Value *V = simplifyICmpInst(Pred, Y, Z, Q, MaxRecurse - 1))
        return V;
    }
  }
 
  if (LBO)
    if (Value *V = simplifyICmpWithBinOpOnLHS(Pred, LBO, RHS, Q, MaxRecurse))
      return V;
 
  if (RBO)
    if (Value *V = simplifyICmpWithBinOpOnLHS(
            ICmpInst::getSwappedPredicate(Pred), RBO, LHS, Q, MaxRecurse))
      return V;
 
  // 0 - (zext X) pred C
  if (!CmpInst::isUnsigned(Pred) && match(LHS, m_Neg(m_ZExt(m_Value())))) {
    const APInt *C;
    if (match(RHS, m_APInt(C))) {
      if (C->isStrictlyPositive()) {
        if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_NE)
          return ConstantInt::getTrue(getCompareTy(RHS));
        if (Pred == ICmpInst::ICMP_SGE || Pred == ICmpInst::ICMP_EQ)
          return ConstantInt::getFalse(getCompareTy(RHS));
      }
      if (C->isNonNegative()) {
        if (Pred == ICmpInst::ICMP_SLE)
          return ConstantInt::getTrue(getCompareTy(RHS));
        if (Pred == ICmpInst::ICMP_SGT)
          return ConstantInt::getFalse(getCompareTy(RHS));
      }
    }
  }
 
  //   If C2 is a power-of-2 and C is not:
  //   (C2 << X) == C --> false
  //   (C2 << X) != C --> true
  const APInt *C;
  if (match(LHS, m_Shl(m_Power2(), m_Value())) &&
      match(RHS, m_APIntAllowUndef(C)) && !C->isPowerOf2()) {
    // C2 << X can equal zero in some circumstances.
    // This simplification might be unsafe if C is zero.
    //
    // We know it is safe if:
    // - The shift is nsw. We can't shift out the one bit.
    // - The shift is nuw. We can't shift out the one bit.
    // - C2 is one.
    // - C isn't zero.
    if (Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(LBO)) ||
        Q.IIQ.hasNoUnsignedWrap(cast<OverflowingBinaryOperator>(LBO)) ||
        match(LHS, m_Shl(m_One(), m_Value())) || !C->isZero()) {
      if (Pred == ICmpInst::ICMP_EQ)
        return ConstantInt::getFalse(getCompareTy(RHS));
      if (Pred == ICmpInst::ICMP_NE)
        return ConstantInt::getTrue(getCompareTy(RHS));
    }
  }
 
  // TODO: This is overly constrained. LHS can be any power-of-2.
  // (1 << X)  >u 0x8000 --> false
  // (1 << X) <=u 0x8000 --> true
  if (match(LHS, m_Shl(m_One(), m_Value())) && match(RHS, m_SignMask())) {
    if (Pred == ICmpInst::ICMP_UGT)
      return ConstantInt::getFalse(getCompareTy(RHS));
    if (Pred == ICmpInst::ICMP_ULE)
      return ConstantInt::getTrue(getCompareTy(RHS));
  }
 
  if (!MaxRecurse || !LBO || !RBO || LBO->getOpcode() != RBO->getOpcode())
    return nullptr;
 
  if (LBO->getOperand(0) == RBO->getOperand(0)) {
    switch (LBO->getOpcode()) {
    default:
      break;
    case Instruction::Shl:
      bool NUW = Q.IIQ.hasNoUnsignedWrap(LBO) && Q.IIQ.hasNoUnsignedWrap(RBO);
      bool NSW = Q.IIQ.hasNoSignedWrap(LBO) && Q.IIQ.hasNoSignedWrap(RBO);
      if (!NUW || (ICmpInst::isSigned(Pred) && !NSW) ||
          !isKnownNonZero(LBO->getOperand(0), Q.DL))
        break;
      if (Value *V = simplifyICmpInst(Pred, LBO->getOperand(1),
                                      RBO->getOperand(1), Q, MaxRecurse - 1))
        return V;
    }
  }
 
  if (LBO->getOperand(1) == RBO->getOperand(1)) {
    switch (LBO->getOpcode()) {
    default:
      break;
    case Instruction::UDiv:
    case Instruction::LShr:
      if (ICmpInst::isSigned(Pred) || !Q.IIQ.isExact(LBO) ||
          !Q.IIQ.isExact(RBO))
        break;
      if (Value *V = simplifyICmpInst(Pred, LBO->getOperand(0),
                                      RBO->getOperand(0), Q, MaxRecurse - 1))
        return V;
      break;
    case Instruction::SDiv:
      if (!ICmpInst::isEquality(Pred) || !Q.IIQ.isExact(LBO) ||
          !Q.IIQ.isExact(RBO))
        break;
      if (Value *V = simplifyICmpInst(Pred, LBO->getOperand(0),
                                      RBO->getOperand(0), Q, MaxRecurse - 1))
        return V;
      break;
    case Instruction::AShr:
      if (!Q.IIQ.isExact(LBO) || !Q.IIQ.isExact(RBO))
        break;
      if (Value *V = simplifyICmpInst(Pred, LBO->getOperand(0),
                                      RBO->getOperand(0), Q, MaxRecurse - 1))
        return V;
      break;
    case Instruction::Shl: {
      bool NUW = Q.IIQ.hasNoUnsignedWrap(LBO) && Q.IIQ.hasNoUnsignedWrap(RBO);
      bool NSW = Q.IIQ.hasNoSignedWrap(LBO) && Q.IIQ.hasNoSignedWrap(RBO);
      if (!NUW && !NSW)
        break;
      if (!NSW && ICmpInst::isSigned(Pred))
        break;
      if (Value *V = simplifyICmpInst(Pred, LBO->getOperand(0),
                                      RBO->getOperand(0), Q, MaxRecurse - 1))
        return V;
      break;
    }
    }
  }
  return nullptr;
}
 
/// simplify integer comparisons where at least one operand of the compare
/// matches an integer min/max idiom.
static Value *simplifyICmpWithMinMax(CmpInst::Predicate Pred, Value *LHS,
                                     Value *RHS, const SimplifyQuery &Q,
                                     unsigned MaxRecurse) {
  Type *ITy = getCompareTy(LHS); // The return type.
  Value *A, *B;
  CmpInst::Predicate P = CmpInst::BAD_ICMP_PREDICATE;
  CmpInst::Predicate EqP; // Chosen so that "A == max/min(A,B)" iff "A EqP B".
 
  // Signed variants on "max(a,b)>=a -> true".
  if (match(LHS, m_SMax(m_Value(A), m_Value(B))) && (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // smax(A, B) pred A.
    EqP = CmpInst::ICMP_SGE; // "A == smax(A, B)" iff "A sge B".
    // We analyze this as smax(A, B) pred A.
    P = Pred;
  } else if (match(RHS, m_SMax(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred smax(A, B).
    EqP = CmpInst::ICMP_SGE; // "A == smax(A, B)" iff "A sge B".
    // We analyze this as smax(A, B) swapped-pred A.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(LHS, m_SMin(m_Value(A), m_Value(B))) &&
             (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // smin(A, B) pred A.
    EqP = CmpInst::ICMP_SLE; // "A == smin(A, B)" iff "A sle B".
    // We analyze this as smax(-A, -B) swapped-pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(RHS, m_SMin(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred smin(A, B).
    EqP = CmpInst::ICMP_SLE; // "A == smin(A, B)" iff "A sle B".
    // We analyze this as smax(-A, -B) pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = Pred;
  }
  if (P != CmpInst::BAD_ICMP_PREDICATE) {
    // Cases correspond to "max(A, B) p A".
    switch (P) {
    default:
      break;
    case CmpInst::ICMP_EQ:
    case CmpInst::ICMP_SLE:
      // Equivalent to "A EqP B".  This may be the same as the condition tested
      // in the max/min; if so, we can just return that.
      if (Value *V = extractEquivalentCondition(LHS, EqP, A, B))
        return V;
      if (Value *V = extractEquivalentCondition(RHS, EqP, A, B))
        return V;
      // Otherwise, see if "A EqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = simplifyICmpInst(EqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    case CmpInst::ICMP_NE:
    case CmpInst::ICMP_SGT: {
      CmpInst::Predicate InvEqP = CmpInst::getInversePredicate(EqP);
      // Equivalent to "A InvEqP B".  This may be the same as the condition
      // tested in the max/min; if so, we can just return that.
      if (Value *V = extractEquivalentCondition(LHS, InvEqP, A, B))
        return V;
      if (Value *V = extractEquivalentCondition(RHS, InvEqP, A, B))
        return V;
      // Otherwise, see if "A InvEqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = simplifyICmpInst(InvEqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    }
    case CmpInst::ICMP_SGE:
      // Always true.
      return getTrue(ITy);
    case CmpInst::ICMP_SLT:
      // Always false.
      return getFalse(ITy);
    }
  }
 
  // Unsigned variants on "max(a,b)>=a -> true".
  P = CmpInst::BAD_ICMP_PREDICATE;
  if (match(LHS, m_UMax(m_Value(A), m_Value(B))) && (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // umax(A, B) pred A.
    EqP = CmpInst::ICMP_UGE; // "A == umax(A, B)" iff "A uge B".
    // We analyze this as umax(A, B) pred A.
    P = Pred;
  } else if (match(RHS, m_UMax(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred umax(A, B).
    EqP = CmpInst::ICMP_UGE; // "A == umax(A, B)" iff "A uge B".
    // We analyze this as umax(A, B) swapped-pred A.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(LHS, m_UMin(m_Value(A), m_Value(B))) &&
             (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // umin(A, B) pred A.
    EqP = CmpInst::ICMP_ULE; // "A == umin(A, B)" iff "A ule B".
    // We analyze this as umax(-A, -B) swapped-pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(RHS, m_UMin(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred umin(A, B).
    EqP = CmpInst::ICMP_ULE; // "A == umin(A, B)" iff "A ule B".
    // We analyze this as umax(-A, -B) pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = Pred;
  }
  if (P != CmpInst::BAD_ICMP_PREDICATE) {
    // Cases correspond to "max(A, B) p A".
    switch (P) {
    default:
      break;
    case CmpInst::ICMP_EQ:
    case CmpInst::ICMP_ULE:
      // Equivalent to "A EqP B".  This may be the same as the condition tested
      // in the max/min; if so, we can just return that.
      if (Value *V = extractEquivalentCondition(LHS, EqP, A, B))
        return V;
      if (Value *V = extractEquivalentCondition(RHS, EqP, A, B))
        return V;
      // Otherwise, see if "A EqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = simplifyICmpInst(EqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    case CmpInst::ICMP_NE:
    case CmpInst::ICMP_UGT: {
      CmpInst::Predicate InvEqP = CmpInst::getInversePredicate(EqP);
      // Equivalent to "A InvEqP B".  This may be the same as the condition
      // tested in the max/min; if so, we can just return that.
      if (Value *V = extractEquivalentCondition(LHS, InvEqP, A, B))
        return V;
      if (Value *V = extractEquivalentCondition(RHS, InvEqP, A, B))
        return V;
      // Otherwise, see if "A InvEqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = simplifyICmpInst(InvEqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    }
    case CmpInst::ICMP_UGE:
      return getTrue(ITy);
    case CmpInst::ICMP_ULT:
      return getFalse(ITy);
    }
  }
 
  // Comparing 1 each of min/max with a common operand?
  // Canonicalize min operand to RHS.
  if (match(LHS, m_UMin(m_Value(), m_Value())) ||
      match(LHS, m_SMin(m_Value(), m_Value()))) {
    std::swap(LHS, RHS);
    Pred = ICmpInst::getSwappedPredicate(Pred);
  }
 
  Value *C, *D;
  if (match(LHS, m_SMax(m_Value(A), m_Value(B))) &&
      match(RHS, m_SMin(m_Value(C), m_Value(D))) &&
      (A == C || A == D || B == C || B == D)) {
    // smax(A, B) >=s smin(A, D) --> true
    if (Pred == CmpInst::ICMP_SGE)
      return getTrue(ITy);
    // smax(A, B) <s smin(A, D) --> false
    if (Pred == CmpInst::ICMP_SLT)
      return getFalse(ITy);
  } else if (match(LHS, m_UMax(m_Value(A), m_Value(B))) &&
             match(RHS, m_UMin(m_Value(C), m_Value(D))) &&
             (A == C || A == D || B == C || B == D)) {
    // umax(A, B) >=u umin(A, D) --> true
    if (Pred == CmpInst::ICMP_UGE)
      return getTrue(ITy);
    // umax(A, B) <u umin(A, D) --> false
    if (Pred == CmpInst::ICMP_ULT)
      return getFalse(ITy);
  }
 
  return nullptr;
}
 
static Value *simplifyICmpWithDominatingAssume(CmpInst::Predicate Predicate,
                                               Value *LHS, Value *RHS,
                                               const SimplifyQuery &Q) {
  // Gracefully handle instructions that have not been inserted yet.
  if (!Q.AC || !Q.CxtI || !Q.CxtI->getParent())
    return nullptr;
 
  for (Value *AssumeBaseOp : {LHS, RHS}) {
    for (auto &AssumeVH : Q.AC->assumptionsFor(AssumeBaseOp)) {
      if (!AssumeVH)
        continue;
 
      CallInst *Assume = cast<CallInst>(AssumeVH);
      if (std::optional<bool> Imp = isImpliedCondition(
              Assume->getArgOperand(0), Predicate, LHS, RHS, Q.DL))
        if (isValidAssumeForContext(Assume, Q.CxtI, Q.DT))
          return ConstantInt::get(getCompareTy(LHS), *Imp);
    }
  }
 
  return nullptr;
}
 
/// Given operands for an ICmpInst, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  CmpInst::Predicate Pred = (CmpInst::Predicate)Predicate;
  assert(CmpInst::isIntPredicate(Pred) && "Not an integer compare!");
 
  if (Constant *CLHS = dyn_cast<Constant>(LHS)) {
    if (Constant *CRHS = dyn_cast<Constant>(RHS))
      return ConstantFoldCompareInstOperands(Pred, CLHS, CRHS, Q.DL, Q.TLI);
 
    // If we have a constant, make sure it is on the RHS.
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }
  assert(!isa<UndefValue>(LHS) && "Unexpected icmp undef,%X");
 
  Type *ITy = getCompareTy(LHS); // The return type.
 
  // icmp poison, X -> poison
  if (isa<PoisonValue>(RHS))
    return PoisonValue::get(ITy);
 
  // For EQ and NE, we can always pick a value for the undef to make the
  // predicate pass or fail, so we can return undef.
  // Matches behavior in llvm::ConstantFoldCompareInstruction.
  if (Q.isUndefValue(RHS) && ICmpInst::isEquality(Pred))
    return UndefValue::get(ITy);
 
  // icmp X, X -> true/false
  // icmp X, undef -> true/false because undef could be X.
  if (LHS == RHS || Q.isUndefValue(RHS))
    return ConstantInt::get(ITy, CmpInst::isTrueWhenEqual(Pred));
 
  if (Value *V = simplifyICmpOfBools(Pred, LHS, RHS, Q))
    return V;
 
  // TODO: Sink/common this with other potentially expensive calls that use
  //       ValueTracking? See comment below for isKnownNonEqual().
  if (Value *V = simplifyICmpWithZero(Pred, LHS, RHS, Q))
    return V;
 
  if (Value *V = simplifyICmpWithConstant(Pred, LHS, RHS, Q.IIQ))
    return V;
 
  // If both operands have range metadata, use the metadata
  // to simplify the comparison.
  if (isa<Instruction>(RHS) && isa<Instruction>(LHS)) {
    auto RHS_Instr = cast<Instruction>(RHS);
    auto LHS_Instr = cast<Instruction>(LHS);
 
    if (Q.IIQ.getMetadata(RHS_Instr, LLVMContext::MD_range) &&
        Q.IIQ.getMetadata(LHS_Instr, LLVMContext::MD_range)) {
      auto RHS_CR = getConstantRangeFromMetadata(
          *RHS_Instr->getMetadata(LLVMContext::MD_range));
      auto LHS_CR = getConstantRangeFromMetadata(
          *LHS_Instr->getMetadata(LLVMContext::MD_range));
 
      if (LHS_CR.icmp(Pred, RHS_CR))
        return ConstantInt::getTrue(RHS->getContext());
 
      if (LHS_CR.icmp(CmpInst::getInversePredicate(Pred), RHS_CR))
        return ConstantInt::getFalse(RHS->getContext());
    }
  }
 
  // Compare of cast, for example (zext X) != 0 -> X != 0
  if (isa<CastInst>(LHS) && (isa<Constant>(RHS) || isa<CastInst>(RHS))) {
    Instruction *LI = cast<CastInst>(LHS);
    Value *SrcOp = LI->getOperand(0);
    Type *SrcTy = SrcOp->getType();
    Type *DstTy = LI->getType();
 
    // Turn icmp (ptrtoint x), (ptrtoint/constant) into a compare of the input
    // if the integer type is the same size as the pointer type.
    if (MaxRecurse && isa<PtrToIntInst>(LI) &&
        Q.DL.getTypeSizeInBits(SrcTy) == DstTy->getPrimitiveSizeInBits()) {
      if (Constant *RHSC = dyn_cast<Constant>(RHS)) {
        // Transfer the cast to the constant.
        if (Value *V = simplifyICmpInst(Pred, SrcOp,
                                        ConstantExpr::getIntToPtr(RHSC, SrcTy),
                                        Q, MaxRecurse - 1))
          return V;
      } else if (PtrToIntInst *RI = dyn_cast<PtrToIntInst>(RHS)) {
        if (RI->getOperand(0)->getType() == SrcTy)
          // Compare without the cast.
          if (Value *V = simplifyICmpInst(Pred, SrcOp, RI->getOperand(0), Q,
                                          MaxRecurse - 1))
            return V;
      }
    }
 
    if (isa<ZExtInst>(LHS)) {
      // Turn icmp (zext X), (zext Y) into a compare of X and Y if they have the
      // same type.
      if (ZExtInst *RI = dyn_cast<ZExtInst>(RHS)) {
        if (MaxRecurse && SrcTy == RI->getOperand(0)->getType())
          // Compare X and Y.  Note that signed predicates become unsigned.
          if (Value *V =
                  simplifyICmpInst(ICmpInst::getUnsignedPredicate(Pred), SrcOp,
                                   RI->getOperand(0), Q, MaxRecurse - 1))
            return V;
      }
      // Fold (zext X) ule (sext X), (zext X) sge (sext X) to true.
      else if (SExtInst *RI = dyn_cast<SExtInst>(RHS)) {
        if (SrcOp == RI->getOperand(0)) {
          if (Pred == ICmpInst::ICMP_ULE || Pred == ICmpInst::ICMP_SGE)
            return ConstantInt::getTrue(ITy);
          if (Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_SLT)
            return ConstantInt::getFalse(ITy);
        }
      }
      // Turn icmp (zext X), Cst into a compare of X and Cst if Cst is extended
      // too.  If not, then try to deduce the result of the comparison.
      else if (ConstantInt *CI = dyn_cast<ConstantInt>(RHS)) {
        // Compute the constant that would happen if we truncated to SrcTy then
        // reextended to DstTy.
        Constant *Trunc = ConstantExpr::getTrunc(CI, SrcTy);
        Constant *RExt = ConstantExpr::getCast(CastInst::ZExt, Trunc, DstTy);
 
        // If the re-extended constant didn't change then this is effectively
        // also a case of comparing two zero-extended values.
        if (RExt == CI && MaxRecurse)
          if (Value *V = simplifyICmpInst(ICmpInst::getUnsignedPredicate(Pred),
                                          SrcOp, Trunc, Q, MaxRecurse - 1))
            return V;
 
        // Otherwise the upper bits of LHS are zero while RHS has a non-zero bit
        // there.  Use this to work out the result of the comparison.
        if (RExt != CI) {
          switch (Pred) {
          default:
            llvm_unreachable("Unknown ICmp predicate!");
          // LHS <u RHS.
          case ICmpInst::ICMP_EQ:
          case ICmpInst::ICMP_UGT:
          case ICmpInst::ICMP_UGE:
            return ConstantInt::getFalse(CI->getContext());
 
          case ICmpInst::ICMP_NE:
          case ICmpInst::ICMP_ULT:
          case ICmpInst::ICMP_ULE:
            return ConstantInt::getTrue(CI->getContext());
 
          // LHS is non-negative.  If RHS is negative then LHS >s LHS.  If RHS
          // is non-negative then LHS <s RHS.
          case ICmpInst::ICMP_SGT:
          case ICmpInst::ICMP_SGE:
            return CI->getValue().isNegative()
                       ? ConstantInt::getTrue(CI->getContext())
                       : ConstantInt::getFalse(CI->getContext());
 
          case ICmpInst::ICMP_SLT:
          case ICmpInst::ICMP_SLE:
            return CI->getValue().isNegative()
                       ? ConstantInt::getFalse(CI->getContext())
                       : ConstantInt::getTrue(CI->getContext());
          }
        }
      }
    }
 
    if (isa<SExtInst>(LHS)) {
      // Turn icmp (sext X), (sext Y) into a compare of X and Y if they have the
      // same type.
      if (SExtInst *RI = dyn_cast<SExtInst>(RHS)) {
        if (MaxRecurse && SrcTy == RI->getOperand(0)->getType())
          // Compare X and Y.  Note that the predicate does not change.
          if (Value *V = simplifyICmpInst(Pred, SrcOp, RI->getOperand(0), Q,
                                          MaxRecurse - 1))
            return V;
      }
      // Fold (sext X) uge (zext X), (sext X) sle (zext X) to true.
      else if (ZExtInst *RI = dyn_cast<ZExtInst>(RHS)) {
        if (SrcOp == RI->getOperand(0)) {
          if (Pred == ICmpInst::ICMP_UGE || Pred == ICmpInst::ICMP_SLE)
            return ConstantInt::getTrue(ITy);
          if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_SGT)
            return ConstantInt::getFalse(ITy);
        }
      }
      // Turn icmp (sext X), Cst into a compare of X and Cst if Cst is extended
      // too.  If not, then try to deduce the result of the comparison.
      else if (ConstantInt *CI = dyn_cast<ConstantInt>(RHS)) {
        // Compute the constant that would happen if we truncated to SrcTy then
        // reextended to DstTy.
        Constant *Trunc = ConstantExpr::getTrunc(CI, SrcTy);
        Constant *RExt = ConstantExpr::getCast(CastInst::SExt, Trunc, DstTy);
 
        // If the re-extended constant didn't change then this is effectively
        // also a case of comparing two sign-extended values.
        if (RExt == CI && MaxRecurse)
          if (Value *V =
                  simplifyICmpInst(Pred, SrcOp, Trunc, Q, MaxRecurse - 1))
            return V;
 
        // Otherwise the upper bits of LHS are all equal, while RHS has varying
        // bits there.  Use this to work out the result of the comparison.
        if (RExt != CI) {
          switch (Pred) {
          default:
            llvm_unreachable("Unknown ICmp predicate!");
          case ICmpInst::ICMP_EQ:
            return ConstantInt::getFalse(CI->getContext());
          case ICmpInst::ICMP_NE:
            return ConstantInt::getTrue(CI->getContext());
 
          // If RHS is non-negative then LHS <s RHS.  If RHS is negative then
          // LHS >s RHS.
          case ICmpInst::ICMP_SGT:
          case ICmpInst::ICMP_SGE:
            return CI->getValue().isNegative()
                       ? ConstantInt::getTrue(CI->getContext())
                       : ConstantInt::getFalse(CI->getContext());
          case ICmpInst::ICMP_SLT:
          case ICmpInst::ICMP_SLE:
            return CI->getValue().isNegative()
                       ? ConstantInt::getFalse(CI->getContext())
                       : ConstantInt::getTrue(CI->getContext());
 
          // If LHS is non-negative then LHS <u RHS.  If LHS is negative then
          // LHS >u RHS.
          case ICmpInst::ICMP_UGT:
          case ICmpInst::ICMP_UGE:
            // Comparison is true iff the LHS <s 0.
            if (MaxRecurse)
              if (Value *V = simplifyICmpInst(ICmpInst::ICMP_SLT, SrcOp,
                                              Constant::getNullValue(SrcTy), Q,
                                              MaxRecurse - 1))
                return V;
            break;
          case ICmpInst::ICMP_ULT:
          case ICmpInst::ICMP_ULE:
            // Comparison is true iff the LHS >=s 0.
            if (MaxRecurse)
              if (Value *V = simplifyICmpInst(ICmpInst::ICMP_SGE, SrcOp,
                                              Constant::getNullValue(SrcTy), Q,
                                              MaxRecurse - 1))
                return V;
            break;
          }
        }
      }
    }
  }
 
  // icmp eq|ne X, Y -> false|true if X != Y
  // This is potentially expensive, and we have already computedKnownBits for
  // compares with 0 above here, so only try this for a non-zero compare.
  if (ICmpInst::isEquality(Pred) && !match(RHS, m_Zero()) &&
      isKnownNonEqual(LHS, RHS, Q.DL, Q.AC, Q.CxtI, Q.DT, Q.IIQ.UseInstrInfo)) {
    return Pred == ICmpInst::ICMP_NE ? getTrue(ITy) : getFalse(ITy);
  }
 
  if (Value *V = simplifyICmpWithBinOp(Pred, LHS, RHS, Q, MaxRecurse))
    return V;
 
  if (Value *V = simplifyICmpWithMinMax(Pred, LHS, RHS, Q, MaxRecurse))
    return V;
 
  if (Value *V = simplifyICmpWithDominatingAssume(Pred, LHS, RHS, Q))
    return V;
 
  if (std::optional<bool> Res =
          isImpliedByDomCondition(Pred, LHS, RHS, Q.CxtI, Q.DL))
    return ConstantInt::getBool(ITy, *Res);
 
  // Simplify comparisons of related pointers using a powerful, recursive
  // GEP-walk when we have target data available..
  if (LHS->getType()->isPointerTy())
    if (auto *C = computePointerICmp(Pred, LHS, RHS, Q))
      return C;
  if (auto *CLHS = dyn_cast<PtrToIntOperator>(LHS))
    if (auto *CRHS = dyn_cast<PtrToIntOperator>(RHS))
      if (Q.DL.getTypeSizeInBits(CLHS->getPointerOperandType()) ==
              Q.DL.getTypeSizeInBits(CLHS->getType()) &&
          Q.DL.getTypeSizeInBits(CRHS->getPointerOperandType()) ==
              Q.DL.getTypeSizeInBits(CRHS->getType()))
        if (auto *C = computePointerICmp(Pred, CLHS->getPointerOperand(),
                                         CRHS->getPointerOperand(), Q))
          return C;
 
  // If the comparison is with the result of a select instruction, check whether
  // comparing with either branch of the select always yields the same value.
  if (isa<SelectInst>(LHS) || isa<SelectInst>(RHS))
    if (Value *V = threadCmpOverSelect(Pred, LHS, RHS, Q, MaxRecurse))
      return V;
 
  // If the comparison is with the result of a phi instruction, check whether
  // doing the compare with each incoming phi value yields a common result.
  if (isa<PHINode>(LHS) || isa<PHINode>(RHS))
    if (Value *V = threadCmpOverPHI(Pred, LHS, RHS, Q, MaxRecurse))
      return V;
 
  return nullptr;
}
 
Value *llvm::simplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                              const SimplifyQuery &Q) {
  return ::simplifyICmpInst(Predicate, LHS, RHS, Q, RecursionLimit);
}
 
/// Given operands for an FCmpInst, see if we can fold the result.
/// If not, this returns null.
static Value *simplifyFCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               FastMathFlags FMF, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  CmpInst::Predicate Pred = (CmpInst::Predicate)Predicate;
  assert(CmpInst::isFPPredicate(Pred) && "Not an FP compare!");
 
  if (Constant *CLHS = dyn_cast<Constant>(LHS)) {
    if (Constant *CRHS = dyn_cast<Constant>(RHS))
      return ConstantFoldCompareInstOperands(Pred, CLHS, CRHS, Q.DL, Q.TLI,
                                             Q.CxtI);
 
    // If we have a constant, make sure it is on the RHS.
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }
 
  // Fold trivial predicates.
  Type *RetTy = getCompareTy(LHS);
  if (Pred == FCmpInst::FCMP_FALSE)
    return getFalse(RetTy);
  if (Pred == FCmpInst::FCMP_TRUE)
    return getTrue(RetTy);
 
  // Fold (un)ordered comparison if we can determine there are no NaNs.
  if (Pred == FCmpInst::FCMP_UNO || Pred == FCmpInst::FCMP_ORD)
    if (FMF.noNaNs() ||
        (isKnownNeverNaN(LHS, Q.TLI) && isKnownNeverNaN(RHS, Q.TLI)))
      return ConstantInt::get(RetTy, Pred == FCmpInst::FCMP_ORD);
 
  // NaN is unordered; NaN is not ordered.
  assert((FCmpInst::isOrdered(Pred) || FCmpInst::isUnordered(Pred)) &&
         "Comparison must be either ordered or unordered");
  if (match(RHS, m_NaN()))
    return ConstantInt::get(RetTy, CmpInst::isUnordered(Pred));
 
  // fcmp pred x, poison and  fcmp pred poison, x
  // fold to poison
  if (isa<PoisonValue>(LHS) || isa<PoisonValue>(RHS))
    return PoisonValue::get(RetTy);
 
  // fcmp pred x, undef  and  fcmp pred undef, x
  // fold to true if unordered, false if ordered
  if (Q.isUndefValue(LHS) || Q.isUndefValue(RHS)) {
    // Choosing NaN for the undef will always make unordered comparison succeed
    // and ordered comparison fail.
    return ConstantInt::get(RetTy, CmpInst::isUnordered(Pred));
  }
 
  // fcmp x,x -> true/false.  Not all compares are foldable.
  if (LHS == RHS) {
    if (CmpInst::isTrueWhenEqual(Pred))
      return getTrue(RetTy);
    if (CmpInst::isFalseWhenEqual(Pred))
      return getFalse(RetTy);
  }
 
  // Handle fcmp with constant RHS.
  // TODO: Use match with a specific FP value, so these work with vectors with
  // undef lanes.
  const APFloat *C;
  if (match(RHS, m_APFloat(C))) {
    // Check whether the constant is an infinity.
    if (C->isInfinity()) {
      if (C->isNegative()) {
        switch (Pred) {
        case FCmpInst::FCMP_OLT:
          // No value is ordered and less than negative infinity.
          return getFalse(RetTy);
        case FCmpInst::FCMP_UGE:
          // All values are unordered with or at least negative infinity.
          return getTrue(RetTy);
        default:
          break;
        }
      } else {
        switch (Pred) {
        case FCmpInst::FCMP_OGT:
          // No value is ordered and greater than infinity.
          return getFalse(RetTy);
        case FCmpInst::FCMP_ULE:
          // All values are unordered with and at most infinity.
          return getTrue(RetTy);
        default:
          break;
        }
      }
 
      // LHS == Inf
      if (Pred == FCmpInst::FCMP_OEQ && isKnownNeverInfinity(LHS, Q.TLI))
        return getFalse(RetTy);
      // LHS != Inf
      if (Pred == FCmpInst::FCMP_UNE && isKnownNeverInfinity(LHS, Q.TLI))
        return getTrue(RetTy);
      // LHS == Inf || LHS == NaN
      if (Pred == FCmpInst::FCMP_UEQ && isKnownNeverInfinity(LHS, Q.TLI) &&
          isKnownNeverNaN(LHS, Q.TLI))
        return getFalse(RetTy);
      // LHS != Inf && LHS != NaN
      if (Pred == FCmpInst::FCMP_ONE && isKnownNeverInfinity(LHS, Q.TLI) &&
          isKnownNeverNaN(LHS, Q.TLI))
        return getTrue(RetTy);
    }
    if (C->isNegative() && !C->isNegZero()) {
      assert(!C->isNaN() && "Unexpected NaN constant!");
      // TODO: We can catch more cases by using a range check rather than
      //       relying on CannotBeOrderedLessThanZero.
      switch (Pred) {
      case FCmpInst::FCMP_UGE:
      case FCmpInst::FCMP_UGT:
      case FCmpInst::FCMP_UNE:
        // (X >= 0) implies (X > C) when (C < 0)
        if (CannotBeOrderedLessThanZero(LHS, Q.TLI))
          return getTrue(RetTy);
        break;
      case FCmpInst::FCMP_OEQ:
      case FCmpInst::FCMP_OLE:
      case FCmpInst::FCMP_OLT:
        // (X >= 0) implies !(X < C) when (C < 0)
        if (CannotBeOrderedLessThanZero(LHS, Q.TLI))
          return getFalse(RetTy);
        break;
      default:
        break;
      }
    }
 
    // Check comparison of [minnum/maxnum with constant] with other constant.
    const APFloat *C2;
    if ((match(LHS, m_Intrinsic<Intrinsic::minnum>(m_Value(), m_APFloat(C2))) &&
         *C2 < *C) ||
        (match(LHS, m_Intrinsic<Intrinsic::maxnum>(m_Value(), m_APFloat(C2))) &&
         *C2 > *C)) {
      bool IsMaxNum =
          cast<IntrinsicInst>(LHS)->getIntrinsicID() == Intrinsic::maxnum;
      // The ordered relationship and minnum/maxnum guarantee that we do not
      // have NaN constants, so ordered/unordered preds are handled the same.
      switch (Pred) {
      case FCmpInst::FCMP_OEQ:
      case FCmpInst::FCMP_UEQ:
        // minnum(X, LesserC)  == C --> false
        // maxnum(X, GreaterC) == C --> false
        return getFalse(RetTy);
      case FCmpInst::FCMP_ONE:
      case FCmpInst::FCMP_UNE:
        // minnum(X, LesserC)  != C --> true
        // maxnum(X, GreaterC) != C --> true
        return getTrue(RetTy);
      case FCmpInst::FCMP_OGE:
      case FCmpInst::FCMP_UGE:
      case FCmpInst::FCMP_OGT:
      case FCmpInst::FCMP_UGT:
        // minnum(X, LesserC)  >= C --> false
        // minnum(X, LesserC)  >  C --> false
        // maxnum(X, GreaterC) >= C --> true
        // maxnum(X, GreaterC) >  C --> true
        return ConstantInt::get(RetTy, IsMaxNum);
      case FCmpInst::FCMP_OLE:
      case FCmpInst::FCMP_ULE:
      case FCmpInst::FCMP_OLT:
      case FCmpInst::FCMP_ULT:
        // minnum(X, LesserC)  <= C --> true
        // minnum(X, LesserC)  <  C --> true
        // maxnum(X, GreaterC) <= C --> false
        // maxnum(X, GreaterC) <  C --> false
        return ConstantInt::get(RetTy, !IsMaxNum);
      default:
        // TRUE/FALSE/ORD/UNO should be handled before this.
        llvm_unreachable("Unexpected fcmp predicate");
      }
    }
  }
 
  if (match(RHS, m_AnyZeroFP())) {
    switch (Pred) {
    case FCmpInst::FCMP_OGE:
    case FCmpInst::FCMP_ULT:
      // Positive or zero X >= 0.0 --> true
      // Positive or zero X <  0.0 --> false
      if ((FMF.noNaNs() || isKnownNeverNaN(LHS, Q.TLI)) &&
          CannotBeOrderedLessThanZero(LHS, Q.TLI))
        return Pred == FCmpInst::FCMP_OGE ? getTrue(RetTy) : getFalse(RetTy);
      break;
    case FCmpInst::FCMP_UGE:
    case FCmpInst::FCMP_OLT:
      // Positive or zero or nan X >= 0.0 --> true
      // Positive or zero or nan X <  0.0 --> false