text: //===- 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/SetVector.h"
  #include "llvm/ADT/SmallPtrSet.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/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/GetElementPtrTypeIterator.h"
  #include "llvm/IR/GlobalAlias.h"
  #include "llvm/IR/InstrTypes.h"
  #include "llvm/IR/Instructions.h"
  #include "llvm/IR/Operator.h"
  #include "llvm/IR/PatternMatch.h"
  #include "llvm/IR/ValueHandle.h"
  #include "llvm/Support/KnownBits.h"
  #include <algorithm>
  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 *, ArrayRef<Value *>, 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".
    if (match(FCmp, m_Zero()))
      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()))
      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 (Value *Incoming : PI->incoming_values()) {
      // If the incoming value is the phi node itself, it can safely be skipped.
      if (Incoming == PI) continue;
      Value *V = PI == LHS ?
        SimplifyBinOp(Opcode, Incoming, RHS, Q, MaxRecurse) :
        SimplifyBinOp(Opcode, LHS, Incoming, Q, 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))
        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 + 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 0 if V is not a pointer, and returns the constant '0' if there are
  /// no constant offsets applied.
  ///
  /// This is very similar to GetPointerBaseWithConstantOffset except it doesn't
  /// follow non-inbounds geps. This allows it to remain usable for icmp ult/etc.
  /// folding.
  static Constant *stripAndComputeConstantOffsets(const DataLayout &DL, Value *&V,
                                                  bool AllowNonInbounds = false) {
    assert(V->getType()->isPtrOrPtrVectorTy());
  
    Type *IntIdxTy = DL.getIndexType(V->getType())->getScalarType();
    APInt Offset = APInt::getNullValue(IntIdxTy->getIntegerBitWidth());
  
    V = V->stripAndAccumulateConstantOffsets(DL, Offset, AllowNonInbounds);
    // As that strip may trace through `addrspacecast`, need to sext or trunc
    // the offset calculated.
    IntIdxTy = DL.getIndexType(V->getType())->getScalarType();
    Offset = Offset.sextOrTrunc(IntIdxTy->getIntegerBitWidth());
  
    Constant *OffsetIntPtr = ConstantInt::get(IntIdxTy, Offset);
    if (VectorType *VecTy = dyn_cast<VectorType>(V->getType()))
      return ConstantVector::getSplat(VecTy->getElementCount(), OffsetIntPtr);
    return OffsetIntPtr;
  }
  
  /// 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) {
    Constant *LHSOffset = stripAndComputeConstantOffsets(DL, LHS);
    Constant *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
    return ConstantExpr::getSub(LHSOffset, RHSOffset);
  }
  
  /// 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.
  
    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, 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;
  
    // i1 mul -> and.
    if (MaxRecurse && Op0->getType()->isIntOrIntVectorTy(1))
      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, const SimplifyQuery &Q) {
    return ::SimplifyMulInst(Op0, Op1, 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) {
    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))
      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());
      }
    }
  
    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 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,
                            const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
      return C;
  
    if (Value *V = simplifyDivRem(Opcode, Op0, Op1, Q))
      return V;
  
    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))
      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, 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, Q, MaxRecurse);
  }
  
  Value *llvm::SimplifySDivInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
    return ::SimplifySDivInst(Op0, Op1, 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, const SimplifyQuery &Q,
                                 unsigned MaxRecurse) {
    return simplifyDiv(Instruction::UDiv, Op0, Op1, Q, MaxRecurse);
  }
  
  Value *llvm::SimplifyUDivInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
    return ::SimplifyUDivInst(Op0, Op1, 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 undefined.
    if (ConstantInt *CI = dyn_cast<ConstantInt>(C))
      if (CI->getValue().uge(CI->getType()->getScalarSizeInBits()))
        return true;
  
    // If all lanes of a vector shift are undefined the whole shift is.
    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 Shl, 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.
    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;
  
    // undef << X -> 0
    // undef << X -> undef if (if it's NSW/NUW)
    if (Q.isUndefValue(Op0))
      return isNSW || isNUW ? Op0 : Constant::getNullValue(Op0->getType());
  
    // (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.
  
    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 Width = Op0->getType()->getScalarSizeInBits();
      const unsigned EffWidthY = Width - YKnown.countMinLeadingZeros();
      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;
  
    // all ones >>a X -> -1
    // Do not return Op0 because it may contain undef elements if it's a vector.
    if (match(Op0, m_AllOnes()))
      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;
  }
  
  /// Commuted variants are assumed to be handled by calling this function again
  /// with the parameters swapped.
  static Value *simplifyAndOfICmpsWithSameOperands(ICmpInst *Op0, ICmpInst *Op1) {
    ICmpInst::Predicate Pred0, Pred1;
    Value *A ,*B;
    if (!match(Op0, m_ICmp(Pred0, m_Value(A), m_Value(B))) ||
        !match(Op1, m_ICmp(Pred1, m_Specific(A), m_Specific(B))))
      return nullptr;
  
    // We have (icmp Pred0, A, B) & (icmp Pred1, A, B).
    // If Op1 is always implied true by Op0, then Op0 is a subset of Op1, and we
    // can eliminate Op1 from this 'and'.
    if (ICmpInst::isImpliedTrueByMatchingCmp(Pred0, Pred1))
      return Op0;
  
    // Check for any combination of predicates that are guaranteed to be disjoint.
    if ((Pred0 == ICmpInst::getInversePredicate(Pred1)) ||
        (Pred0 == ICmpInst::ICMP_EQ && ICmpInst::isFalseWhenEqual(Pred1)) ||
        (Pred0 == ICmpInst::ICMP_SLT && Pred1 == ICmpInst::ICMP_SGT) ||
        (Pred0 == ICmpInst::ICMP_ULT && Pred1 == ICmpInst::ICMP_UGT))
      return getFalse(Op0->getType());
  
    return nullptr;
  }
  
  /// Commuted variants are assumed to be handled by calling this function again
  /// with the parameters swapped.
  static Value *simplifyOrOfICmpsWithSameOperands(ICmpInst *Op0, ICmpInst *Op1) {
    ICmpInst::Predicate Pred0, Pred1;
    Value *A ,*B;
    if (!match(Op0, m_ICmp(Pred0, m_Value(A), m_Value(B))) ||
        !match(Op1, m_ICmp(Pred1, m_Specific(A), m_Specific(B))))
      return nullptr;
  
    // We have (icmp Pred0, A, B) | (icmp Pred1, A, B).
    // If Op1 is always implied true by Op0, then Op0 is a subset of Op1, and we
    // can eliminate Op0 from this 'or'.
    if (ICmpInst::isImpliedTrueByMatchingCmp(Pred0, Pred1))
      return Op1;
  
    // Check for any combination of predicates that cover the entire range of
    // possibilities.
    if ((Pred0 == ICmpInst::getInversePredicate(Pred1)) ||
        (Pred0 == ICmpInst::ICMP_NE && ICmpInst::isTrueWhenEqual(Pred1)) ||
        (Pred0 == ICmpInst::ICMP_SLE && Pred1 == ICmpInst::ICMP_SGE) ||
        (Pred0 == ICmpInst::ICMP_ULE && Pred1 == ICmpInst::ICMP_UGE))
      return getTrue(Op0->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::getNullValue(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;
  }
  
  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 = simplifyAndOfICmpsWithSameOperands(Op0, Op1))
      return X;
    if (Value *X = simplifyAndOfICmpsWithSameOperands(Op1, Op0))
      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 = 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 = simplifyOrOfICmpsWithSameOperands(Op0, Op1))
      return X;
    if (Value *X = simplifyOrOfICmpsWithSameOperands(Op1, Op0))
      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 = 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;
  
    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.
    Value *X;
    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).isNullValue())
        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).isNullValue())
        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 *Y, *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 = Width - YKnown.countMinLeadingZeros();
      if (EffWidthY <= ShftCnt) {
        const KnownBits XKnown = computeKnownBits(X, Q.DL, 0, Q.AC, Q.CxtI,
                                                  Q.DT);
        const unsigned EffWidthX = Width - XKnown.countMinLeadingZeros();
        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;
      }
    }
  
    return nullptr;
  }
  
  Value *llvm::SimplifyAndInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
    return ::SimplifyAndInst(Op0, Op1, Q, RecursionLimit);
  }
  
  /// 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;
  
    // 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());
  
    // (A & ?) | A = A
    if (match(Op0, m_c_And(m_Specific(Op1), m_Value())))
      return Op1;
  
    // A | (A & ?) = A
    if (match(Op1, m_c_And(m_Specific(Op0), m_Value())))
      return Op0;
  
    // ~(A & ?) | A = -1
    if (match(Op0, m_Not(m_c_And(m_Specific(Op1), m_Value()))))
      return Constant::getAllOnesValue(Op1->getType());
  
    // A | ~(A & ?) = -1
    if (match(Op1, m_Not(m_c_And(m_Specific(Op0), m_Value()))))
      return Constant::getAllOnesValue(Op0->getType());
  
    if (Value *V = simplifyLogicOfAddSub(Op0, Op1, Instruction::Or))
      return V;
  
    Value *A, *B, *NotA;
    // (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(Op1, m_Xor(m_Value(A), m_Value(B))) &&
        (match(Op0, m_c_And(m_Specific(A), m_Not(m_Specific(B)))) ||
         match(Op0, m_c_And(m_Not(m_Specific(A)), m_Specific(B)))))
      return Op1;
  
    // Commute the 'or' operands.
    // (A ^ B) | (A & ~B) -> (A ^ B)
    // (A ^ B) | (~B & A) -> (A ^ B)
    // (B ^ A) | (A & ~B) -> (B ^ A)
    // (B ^ A) | (~B & A) -> (B ^ A)
    if (match(Op0, m_Xor(m_Value(A), m_Value(B))) &&
        (match(Op1, m_c_And(m_Specific(A), m_Not(m_Specific(B)))) ||
         match(Op1, m_c_And(m_Not(m_Specific(A)), m_Specific(B)))))
      return Op0;
  
    // (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(Op0, m_And(m_Value(A), m_Value(B))) &&
        (match(Op1, m_c_Xor(m_Specific(A), m_Not(m_Specific(B)))) ||
         match(Op1, m_c_Xor(m_Not(m_Specific(A)), m_Specific(B)))))
      return Op1;
  
    // Commute the 'or' operands.
    // (~A ^ B) | (A & B) -> (~A ^ B)
    // (~A ^ B) | (B & A) -> (~A ^ B)
    // (B ^ ~A) | (A & B) -> (B ^ ~A)
    // (B ^ ~A) | (B & A) -> (B ^ ~A)
    if (match(Op1, m_And(m_Value(A), m_Value(B))) &&
        (match(Op0, m_c_Xor(m_Specific(A), m_Not(m_Specific(B)))) ||
         match(Op0, m_c_Xor(m_Not(m_Specific(A)), m_Specific(B)))))
      return Op0;
  
    // (~A & B) | ~(A | B) --> ~A
    // (~A & B) | ~(B | A) --> ~A
    // (B & ~A) | ~(A | B) --> ~A
    // (B & ~A) | ~(B | A) --> ~A
    if (match(Op0, m_c_And(m_CombineAnd(m_Value(NotA), m_Not(m_Value(A))),
                           m_Value(B))) &&
        match(Op1, m_Not(m_c_Or(m_Specific(A), m_Specific(B)))))
      return NotA;
  
    // Commute the 'or' operands.
    // ~(A | B) | (~A & B) --> ~A
    // ~(B | A) | (~A & B) --> ~A
    // ~(A | B) | (B & ~A) --> ~A
    // ~(B | A) | (B & ~A) --> ~A
    if (match(Op1, m_c_And(m_CombineAnd(m_Value(NotA), m_Not(m_Value(A))),
                           m_Value(B))) &&
        match(Op0, m_Not(m_c_Or(m_Specific(A), m_Specific(B)))))
      return NotA;
  
    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)
    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;
  
    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;
  
    // 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());
  
    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.
  
    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;
  }
  
  // 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 comaprisons 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.
    Constant *LHSOffset = stripAndComputeConstantOffsets(DL, LHS);
    Constant *RHSOffset = stripAndComputeConstantOffsets(DL, RHS);
  
    // 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 ConstantExpr::getICmp(Pred, LHSOffset, RHSOffset);
  
    // 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). Global variables always
      // exist, so they always exist during the lifetime of each other and all
      // allocas. 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.
      //
      // With all that, 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.
      //
      // Note that it's not necessary to check for LHS being a global variable
      // address, due to canonicalization and constant folding.
      if (isa<AllocaInst>(LHS) &&
          (isa<AllocaInst>(RHS) || isa<GlobalVariable>(RHS))) {
        ConstantInt *LHSOffsetCI = dyn_cast<ConstantInt>(LHSOffset);
        ConstantInt *RHSOffsetCI = dyn_cast<ConstantInt>(RHSOffset);
        uint64_t LHSSize, RHSSize;
        ObjectSizeOpts Opts;
        Opts.NullIsUnknownSize =
            NullPointerIsDefined(cast<AllocaInst>(LHS)->getFunction());
        if (LHSOffsetCI && RHSOffsetCI &&
            getObjectSize(LHS, LHSSize, DL, TLI, Opts) &&
            getObjectSize(RHS, RHSSize, DL, TLI, Opts)) {
          const APInt &LHSOffsetValue = LHSOffsetCI->getValue();
          const APInt &RHSOffsetValue = RHSOffsetCI->getValue();
          if (!LHSOffsetValue.isNegative() &&
              !RHSOffsetValue.isNegative() &&
              LHSOffsetValue.ult(LHSSize) &&
              RHSOffsetValue.ult(RHSSize)) {
            return ConstantInt::get(GetCompareTy(LHS),
                                    !CmpInst::isTrueWhenEqual(Pred));
          }
        }
  
        // Repeat the above check but this time without depending on DataLayout
        // or being able to compute a precise size.
        if (!cast<PointerType>(LHS->getType())->isEmptyTy() &&
            !cast<PointerType>(RHS->getType())->isEmptyTy() &&
            LHSOffset->isNullValue() &&
            RHSOffset->isNullValue())
          return ConstantInt::get(GetCompareTy(LHS),
                                  !CmpInst::isTrueWhenEqual(Pred));
      }
  
      // Even if an non-inbounds GEP occurs along the path we can still optimize
      // equality comparisons concerning the result. We avoid walking the whole
      // chain again by starting where the last calls to
      // stripAndComputeConstantOffsets left off and accumulate the offsets.
      Constant *LHSNoBound = stripAndComputeConstantOffsets(DL, LHS, true);
      Constant *RHSNoBound = stripAndComputeConstantOffsets(DL, RHS, true);
      if (LHS == RHS)
        return ConstantExpr::getICmp(Pred,
                                     ConstantExpr::getAdd(LHSOffset, LHSNoBound),
                                     ConstantExpr::getAdd(RHSOffset, RHSNoBound));
  
      // 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. 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).
      auto IsAllocDisjoint = [](ArrayRef<const Value *> Objects) {
        return all_of(Objects, [](const Value *V) {
          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;
        });
      };
  
      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.
      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;
      // FIXME: We should also fold the compare when the pointer escapes, but the
      // compare dominates the pointer escape
      if (MI && !PointerMayBeCaptured(MI, true, true))
        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 simplified in 14 out of the 20
    // (10 predicates * 2 constants) possible combinations. Cases not handled here
    // require a 'not' of the LHS, so those must be transformed in InstCombine.
    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_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_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).getValueOr(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).getValueOr(false))
        return getTrue(ITy);
      break;
    case ICmpInst::ICMP_ULE:
      if (isImpliedCondition(LHS, RHS, Q.DL).getValueOr(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, 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;
        LLVM_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;
        LLVM_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 >> y <=u x
    // x udiv y <=u x.
    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);
    }
  
    // (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);
    }
  
    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->isNullValue()) {
        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() &&
        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 (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;
  
    // 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 (GetElementPtrInst *GLHS = dyn_cast<GetElementPtrInst>(LHS)) {
      if (GEPOperator *GRHS = dyn_cast<GEPOperator>(RHS)) {
        if (GLHS->getPointerOperand() == GRHS->getPointerOperand() &&
            GLHS->hasAllConstantIndices() && GRHS->hasAllConstantIndices() &&
            (ICmpInst::isEquality(Pred) ||
             (GLHS->isInBounds() && GRHS->isInBounds() &&
              Pred == ICmpInst::getSignedPredicate(Pred)))) {
          // The bases are equal and the indices are constant.  Build a constant
          // expression GEP with the same indices and a null base pointer to see
          // what constant folding can make out of it.
          Constant *Null = Constant::getNullValue(GLHS->getPointerOperandType());
          SmallVector<Value *, 4> IndicesLHS(GLHS->indices());
          Constant *NewLHS = ConstantExpr::getGetElementPtr(
              GLHS->getSourceElementType(), Null, IndicesLHS);
  
          SmallVector<Value *, 4> IndicesRHS(GRHS->idx_begin(), GRHS->idx_end());
          Constant *NewRHS = ConstantExpr::getGetElementPtr(
              GLHS->getSourceElementType(), Null, IndicesRHS);
          Constant *NewICmp = ConstantExpr::getICmp(Pred, NewLHS, NewRHS);
          return ConstantFoldConstant(NewICmp, Q.DL);
        }
      }
    }
  
    // 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);
  
      // 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
        if (CannotBeOrderedLessThanZero(LHS, Q.TLI))
          return Pred == FCmpInst::FCMP_UGE ? getTrue(RetTy) : getFalse(RetTy);
        break;
      default:
        break;
      }
    }
  
    // 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::SimplifyFCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                                FastMathFlags FMF, const SimplifyQuery &Q) {
    return ::SimplifyFCmpInst(Predicate, LHS, RHS, FMF, Q, RecursionLimit);
  }
  
  static Value *simplifyWithOpReplaced(Value *V, Value *Op, Value *RepOp,
                                       const SimplifyQuery &Q,
                                       bool AllowRefinement,
                                       unsigned MaxRecurse) {
    assert(!Op->getType()->isVectorTy() && "This is not safe for vectors");
  
    // Trivial replacement.
    if (V == Op)
      return RepOp;
  
    // We cannot replace a constant, and shouldn't even try.
    if (isa<Constant>(Op))
      return nullptr;
  
    auto *I = dyn_cast<Instruction>(V);
    if (!I || !is_contained(I->operands(), Op))
      return nullptr;
  
    // Replace Op with RepOp in instruction operands.
    SmallVector<Value *, 8> NewOps(I->getNumOperands());
    transform(I->operands(), NewOps.begin(),
              [&](Value *V) { return V == Op ? RepOp : V; });
  
    if (!AllowRefinement) {
      // General InstSimplify functions may refine the result, e.g. by returning
      // a constant for a potentially poison value. To avoid this, implement only
      // a few non-refining but profitable transforms here.
  
      if (auto *BO = dyn_cast<BinaryOperator>(I)) {
        unsigned Opcode = BO->getOpcode();
        // id op x -> x, x op id -> x
        if (NewOps[0] == ConstantExpr::getBinOpIdentity(Opcode, I->getType()))
          return NewOps[1];
        if (NewOps[1] == ConstantExpr::getBinOpIdentity(Opcode, I->getType(),
                                                        /* RHS */ true))
          return NewOps[0];
  
        // x & x -> x, x | x -> x
        if ((Opcode == Instruction::And || Opcode == Instruction::Or) &&
            NewOps[0] == NewOps[1])
          return NewOps[0];
      }
  
      if (auto *GEP = dyn_cast<GetElementPtrInst>(I)) {
        // getelementptr x, 0 -> x
        if (NewOps.size() == 2 && match(NewOps[1], m_Zero()) &&
            !GEP->isInBounds())
          return NewOps[0];
      }
    } else if (MaxRecurse) {
      // The simplification queries below may return the original value. Consider:
      //   %div = udiv i32 %arg, %arg2
      //   %mul = mul nsw i32 %div, %arg2
      //   %cmp = icmp eq i32 %mul, %arg
      //   %sel = select i1 %cmp, i32 %div, i32 undef
      // Replacing %arg by %mul, %div becomes "udiv i32 %mul, %arg2", which
      // simplifies back to %arg. This can only happen because %mul does not
      // dominate %div. To ensure a consistent return value contract, we make sure
      // that this case returns nullptr as well.
      auto PreventSelfSimplify = [V](Value *Simplified) {
        return Simplified != V ? Simplified : nullptr;
      };
  
      if (auto *B = dyn_cast<BinaryOperator>(I))
        return PreventSelfSimplify(SimplifyBinOp(B->getOpcode(), NewOps[0],
                                                 NewOps[1], Q, MaxRecurse - 1));
  
      if (CmpInst *C = dyn_cast<CmpInst>(I))
        return PreventSelfSimplify(SimplifyCmpInst(C->getPredicate(), NewOps[0],
                                                   NewOps[1], Q, MaxRecurse - 1));
  
      if (auto *GEP = dyn_cast<GetElementPtrInst>(I))
        return PreventSelfSimplify(SimplifyGEPInst(GEP->getSourceElementType(),
                                                   NewOps, Q, MaxRecurse - 1));
  
      if (isa<SelectInst>(I))
        return PreventSelfSimplify(
            SimplifySelectInst(NewOps[0], NewOps[1], NewOps[2], Q,
                               MaxRecurse - 1));
      // TODO: We could hand off more cases to instsimplify here.
    }
  
    // If all operands are constant after substituting Op for RepOp then we can
    // constant fold the instruction.
    SmallVector<Constant *, 8> ConstOps;
    for (Value *NewOp : NewOps) {
      if (Constant *ConstOp = dyn_cast<Constant>(NewOp))
        ConstOps.push_back(ConstOp);
      else
        return nullptr;
    }
  
    // Consider:
    //   %cmp = icmp eq i32 %x, 2147483647
    //   %add = add nsw i32 %x, 1
    //   %sel = select i1 %cmp, i32 -2147483648, i32 %add
    //
    // We can't replace %sel with %add unless we strip away the flags (which
    // will be done in InstCombine).
    // TODO: This may be unsound, because it only catches some forms of
    // refinement.
    if (!AllowRefinement && canCreatePoison(cast<Operator>(I)))
      return nullptr;
  
    if (CmpInst *C = dyn_cast<CmpInst>(I))
      return ConstantFoldCompareInstOperands(C->getPredicate(), ConstOps[0],
                                             ConstOps[1], Q.DL, Q.TLI);
  
    if (LoadInst *LI = dyn_cast<LoadInst>(I))
      if (!LI->isVolatile())
        return ConstantFoldLoadFromConstPtr(ConstOps[0], LI->getType(), Q.DL);
  
    return ConstantFoldInstOperands(I, ConstOps, Q.DL, Q.TLI);
  }
  
  Value *llvm::simplifyWithOpReplaced(Value *V, Value *Op, Value *RepOp,
                                      const SimplifyQuery &Q,
                                      bool AllowRefinement) {
    return ::simplifyWithOpReplaced(V, Op, RepOp, Q, AllowRefinement,
                                    RecursionLimit);
  }
  
  /// Try to simplify a select instruction when its condition operand is an
  /// integer comparison where one operand of the compare is a constant.
  static Value *simplifySelectBitTest(Value *TrueVal, Value *FalseVal, Value *X,
                                      const APInt *Y, bool TrueWhenUnset) {
    const APInt *C;
  
    // (X & Y) == 0 ? X & ~Y : X  --> X
    // (X & Y) != 0 ? X & ~Y : X  --> X & ~Y
    if (FalseVal == X && match(TrueVal, m_And(m_Specific(X), m_APInt(C))) &&
        *Y == ~*C)
      return TrueWhenUnset ? FalseVal : TrueVal;
  
    // (X & Y) == 0 ? X : X & ~Y  --> X & ~Y
    // (X & Y) != 0 ? X : X & ~Y  --> X
    if (TrueVal == X && match(FalseVal, m_And(m_Specific(X), m_APInt(C))) &&
        *Y == ~*C)
      return TrueWhenUnset ? FalseVal : TrueVal;
  
    if (Y->isPowerOf2()) {
      // (X & Y) == 0 ? X | Y : X  --> X | Y
      // (X & Y) != 0 ? X | Y : X  --> X
      if (FalseVal == X && match(TrueVal, m_Or(m_Specific(X), m_APInt(C))) &&
          *Y == *C)
        return TrueWhenUnset ? TrueVal : FalseVal;
  
      // (X & Y) == 0 ? X : X | Y  --> X
      // (X & Y) != 0 ? X : X | Y  --> X | Y
      if (TrueVal == X && match(FalseVal, m_Or(m_Specific(X), m_APInt(C))) &&
          *Y == *C)
        return TrueWhenUnset ? TrueVal : FalseVal;
    }
  
    return nullptr;
  }
  
  /// An alternative way to test if a bit is set or not uses sgt/slt instead of
  /// eq/ne.
  static Value *simplifySelectWithFakeICmpEq(Value *CmpLHS, Value *CmpRHS,
                                             ICmpInst::Predicate Pred,
                                             Value *TrueVal, Value *FalseVal) {
    Value *X;
    APInt Mask;
    if (!decomposeBitTestICmp(CmpLHS, CmpRHS, Pred, X, Mask))
      return nullptr;
  
    return simplifySelectBitTest(TrueVal, FalseVal, X, &Mask,
                                 Pred == ICmpInst::ICMP_EQ);
  }
  
  /// Try to simplify a select instruction when its condition operand is an
  /// integer comparison.
  static Value *simplifySelectWithICmpCond(Value *CondVal, Value *TrueVal,
                                           Value *FalseVal, const SimplifyQuery &Q,
                                           unsigned MaxRecurse) {
    ICmpInst::Predicate Pred;
    Value *CmpLHS, *CmpRHS;
    if (!match(CondVal, m_ICmp(Pred, m_Value(CmpLHS), m_Value(CmpRHS))))
      return nullptr;
  
    // Canonicalize ne to eq predicate.
    if (Pred == ICmpInst::ICMP_NE) {
      Pred = ICmpInst::ICMP_EQ;
      std::swap(TrueVal, FalseVal);
    }
  
    if (Pred == ICmpInst::ICMP_EQ && match(CmpRHS, m_Zero())) {
      Value *X;
      const APInt *Y;
      if (match(CmpLHS, m_And(m_Value(X), m_APInt(Y))))
        if (Value *V = simplifySelectBitTest(TrueVal, FalseVal, X, Y,
                                             /*TrueWhenUnset=*/true))
          return V;
  
      // Test for a bogus zero-shift-guard-op around funnel-shift or rotate.
      Value *ShAmt;
      auto isFsh = m_CombineOr(m_FShl(m_Value(X), m_Value(), m_Value(ShAmt)),
                               m_FShr(m_Value(), m_Value(X), m_Value(ShAmt)));
      // (ShAmt == 0) ? fshl(X, *, ShAmt) : X --> X
      // (ShAmt == 0) ? fshr(*, X, ShAmt) : X --> X
      if (match(TrueVal, isFsh) && FalseVal == X && CmpLHS == ShAmt)
        return X;
  
      // Test for a zero-shift-guard-op around rotates. These are used to
      // avoid UB from oversized shifts in raw IR rotate patterns, but the
      // intrinsics do not have that problem.
      // We do not allow this transform for the general funnel shift case because
      // that would not preserve the poison safety of the original code.
      auto isRotate =
          m_CombineOr(m_FShl(m_Value(X), m_Deferred(X), m_Value(ShAmt)),
                      m_FShr(m_Value(X), m_Deferred(X), m_Value(ShAmt)));
      // (ShAmt == 0) ? X : fshl(X, X, ShAmt) --> fshl(X, X, ShAmt)
      // (ShAmt == 0) ? X : fshr(X, X, ShAmt) --> fshr(X, X, ShAmt)
      if (match(FalseVal, isRotate) && TrueVal == X && CmpLHS == ShAmt &&
          Pred == ICmpInst::ICMP_EQ)
        return FalseVal;
  
      // X == 0 ? abs(X) : -abs(X) --> -abs(X)
      // X == 0 ? -abs(X) : abs(X) --> abs(X)
      if (match(TrueVal, m_Intrinsic<Intrinsic::abs>(m_Specific(CmpLHS))) &&
          match(FalseVal, m_Neg(m_Intrinsic<Intrinsic::abs>(m_Specific(CmpLHS)))))
        return FalseVal;
      if (match(TrueVal,
                m_Neg(m_Intrinsic<Intrinsic::abs>(m_Specific(CmpLHS)))) &&
          match(FalseVal, m_Intrinsic<Intrinsic::abs>(m_Specific(CmpLHS))))
        return FalseVal;
    }
  
    // Check for other compares that behave like bit test.
    if (Value *V = simplifySelectWithFakeICmpEq(CmpLHS, CmpRHS, Pred,
                                                TrueVal, FalseVal))
      return V;
  
    // If we have a scalar equality comparison, then we know the value in one of
    // the arms of the select. See if substituting this value into the arm and
    // simplifying the result yields the same value as the other arm.
    // Note that the equivalence/replacement opportunity does not hold for vectors
    // because each element of a vector select is chosen independently.
    if (Pred == ICmpInst::ICMP_EQ && !CondVal->getType()->isVectorTy()) {
      if (simplifyWithOpReplaced(FalseVal, CmpLHS, CmpRHS, Q,
                                 /* AllowRefinement */ false, MaxRecurse) ==
              TrueVal ||
          simplifyWithOpReplaced(FalseVal, CmpRHS, CmpLHS, Q,
                                 /* AllowRefinement */ false, MaxRecurse) ==
              TrueVal)
        return FalseVal;
      if (simplifyWithOpReplaced(TrueVal, CmpLHS, CmpRHS, Q,
                                 /* AllowRefinement */ true, MaxRecurse) ==
              FalseVal ||
          simplifyWithOpReplaced(TrueVal, CmpRHS, CmpLHS, Q,
                                 /* AllowRefinement */ true, MaxRecurse) ==
              FalseVal)
        return FalseVal;
    }
  
    return nullptr;
  }
  
  /// Try to simplify a select instruction when its condition operand is a
  /// floating-point comparison.
  static Value *simplifySelectWithFCmp(Value *Cond, Value *T, Value *F,
                                       const SimplifyQuery &Q) {
    FCmpInst::Predicate Pred;
    if (!match(Cond, m_FCmp(Pred, m_Specific(T), m_Specific(F))) &&
        !match(Cond, m_FCmp(Pred, m_Specific(F), m_Specific(T))))
      return nullptr;
  
    // This transform is safe if we do not have (do not care about) -0.0 or if
    // at least one operand is known to not be -0.0. Otherwise, the select can
    // change the sign of a zero operand.
    bool HasNoSignedZeros = Q.CxtI && isa<FPMathOperator>(Q.CxtI) &&
                            Q.CxtI->hasNoSignedZeros();
    const APFloat *C;
    if (HasNoSignedZeros || (match(T, m_APFloat(C)) && C->isNonZero()) ||
                            (match(F, m_APFloat(C)) && C->isNonZero())) {
      // (T == F) ? T : F --> F
      // (F == T) ? T : F --> F
      if (Pred == FCmpInst::FCMP_OEQ)
        return F;
  
      // (T != F) ? T : F --> T
      // (F != T) ? T : F --> T
      if (Pred == FCmpInst::FCMP_UNE)
        return T;
    }
  
    return nullptr;
  }
  
  /// Given operands for a SelectInst, see if we can fold the result.
  /// If not, this returns null.
  static Value *SimplifySelectInst(Value *Cond, Value *TrueVal, Value *FalseVal,
                                   const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (auto *CondC = dyn_cast<Constant>(Cond)) {
      if (auto *TrueC = dyn_cast<Constant>(TrueVal))
        if (auto *FalseC = dyn_cast<Constant>(FalseVal))
          return ConstantFoldSelectInstruction(CondC, TrueC, FalseC);
  
      // select poison, X, Y -> poison
      if (isa<PoisonValue>(CondC))
        return PoisonValue::get(TrueVal->getType());
  
      // select undef, X, Y -> X or Y
      if (Q.isUndefValue(CondC))
        return isa<Constant>(FalseVal) ? FalseVal : TrueVal;
  
      // select true,  X, Y --> X
      // select false, X, Y --> Y
      // For vectors, allow undef/poison elements in the condition to match the
      // defined elements, so we can eliminate the select.
      if (match(CondC, m_One()))
        return TrueVal;
      if (match(CondC, m_Zero()))
        return FalseVal;
    }
  
    // select i1 Cond, i1 true, i1 false --> i1 Cond
    assert(Cond->getType()->isIntOrIntVectorTy(1) &&
           "Select must have bool or bool vector condition");
    assert(TrueVal->getType() == FalseVal->getType() &&
           "Select must have same types for true/false ops");
    if (Cond->getType() == TrueVal->getType() &&
        match(TrueVal, m_One()) && match(FalseVal, m_ZeroInt()))
      return Cond;
  
    // select ?, X, X -> X
    if (TrueVal == FalseVal)
      return TrueVal;
  
    // If the true or false value is poison, we can fold to the other value.
    // If the true or false value is undef, we can fold to the other value as
    // long as the other value isn't poison.
    // select ?, poison, X -> X
    // select ?, undef,  X -> X
    if (isa<PoisonValue>(TrueVal) ||
        (Q.isUndefValue(TrueVal) &&
         isGuaranteedNotToBePoison(FalseVal, Q.AC, Q.CxtI, Q.DT)))
      return FalseVal;
    // select ?, X, poison -> X
    // select ?, X, undef  -> X
    if (isa<PoisonValue>(FalseVal) ||
        (Q.isUndefValue(FalseVal) &&
         isGuaranteedNotToBePoison(TrueVal, Q.AC, Q.CxtI, Q.DT)))
      return TrueVal;
  
    // Deal with partial undef vector constants: select ?, VecC, VecC' --> VecC''
    Constant *TrueC, *FalseC;
    if (isa<FixedVectorType>(TrueVal->getType()) &&
        match(TrueVal, m_Constant(TrueC)) &&
        match(FalseVal, m_Constant(FalseC))) {
      unsigned NumElts =
          cast<FixedVectorType>(TrueC->getType())->getNumElements();
      SmallVector<Constant *, 16> NewC;
      for (unsigned i = 0; i != NumElts; ++i) {
        // Bail out on incomplete vector constants.
        Constant *TEltC = TrueC->getAggregateElement(i);
        Constant *FEltC = FalseC->getAggregateElement(i);
        if (!TEltC || !FEltC)
          break;
  
        // If the elements match (undef or not), that value is the result. If only
        // one element is undef, choose the defined element as the safe result.
        if (TEltC == FEltC)
          NewC.push_back(TEltC);
        else if (isa<PoisonValue>(TEltC) ||
                 (Q.isUndefValue(TEltC) && isGuaranteedNotToBePoison(FEltC)))
          NewC.push_back(FEltC);
        else if (isa<PoisonValue>(FEltC) ||
                 (Q.isUndefValue(FEltC) && isGuaranteedNotToBePoison(TEltC)))
          NewC.push_back(TEltC);
        else
          break;
      }
      if (NewC.size() == NumElts)
        return ConstantVector::get(NewC);
    }
  
    if (Value *V =
            simplifySelectWithICmpCond(Cond, TrueVal, FalseVal, Q, MaxRecurse))
      return V;
  
    if (Value *V = simplifySelectWithFCmp(Cond, TrueVal, FalseVal, Q))
      return V;
  
    if (Value *V = foldSelectWithBinaryOp(Cond, TrueVal, FalseVal))
      return V;
  
    Optional<bool> Imp = isImpliedByDomCondition(Cond, Q.CxtI, Q.DL);
    if (Imp)
      return *Imp ? TrueVal : FalseVal;
  
    return nullptr;
  }
  
  Value *llvm::SimplifySelectInst(Value *Cond, Value *TrueVal, Value *FalseVal,
                                  const SimplifyQuery &Q) {
    return ::SimplifySelectInst(Cond, TrueVal, FalseVal, Q, RecursionLimit);
  }
  
  /// Given operands for an GetElementPtrInst, see if we can fold the result.
  /// If not, this returns null.
  static Value *SimplifyGEPInst(Type *SrcTy, ArrayRef<Value *> Ops,
                                const SimplifyQuery &Q, unsigned) {
    // The type of the GEP pointer operand.
    unsigned AS =
        cast<PointerType>(Ops[0]->getType()->getScalarType())->getAddressSpace();
  
    // getelementptr P -> P.
    if (Ops.size() == 1)
      return Ops[0];
  
    // Compute the (pointer) type returned by the GEP instruction.
    Type *LastType = GetElementPtrInst::getIndexedType(SrcTy, Ops.slice(1));
    Type *GEPTy = PointerType::get(LastType, AS);
    for (Value *Op : Ops) {
      // If one of the operands is a vector, the result type is a vector of
      // pointers. All vector operands must have the same number of elements.
      if (VectorType *VT = dyn_cast<VectorType>(Op->getType())) {
        GEPTy = VectorType::get(GEPTy, VT->getElementCount());
        break;
      }
    }
  
    // getelementptr poison, idx -> poison
    // getelementptr baseptr, poison -> poison
    if (any_of(Ops, [](const auto *V) { return isa<PoisonValue>(V); }))
      return PoisonValue::get(GEPTy);
  
    if (Q.isUndefValue(Ops[0]))
      return UndefValue::get(GEPTy);
  
    bool IsScalableVec =
        isa<ScalableVectorType>(SrcTy) || any_of(Ops, [](const Value *V) {
          return isa<ScalableVectorType>(V->getType());
        });
  
    if (Ops.size() == 2) {
      // getelementptr P, 0 -> P.
      if (match(Ops[1], m_Zero()) && Ops[0]->getType() == GEPTy)
        return Ops[0];
  
      Type *Ty = SrcTy;
      if (!IsScalableVec && Ty->isSized()) {
        Value *P;
        uint64_t C;
        uint64_t TyAllocSize = Q.DL.getTypeAllocSize(Ty);
        // getelementptr P, N -> P if P points to a type of zero size.
        if (TyAllocSize == 0 && Ops[0]->getType() == GEPTy)
          return Ops[0];
  
        // The following transforms are only safe if the ptrtoint cast
        // doesn't truncate the pointers.
        if (Ops[1]->getType()->getScalarSizeInBits() ==
            Q.DL.getPointerSizeInBits(AS)) {
          auto CanSimplify = [GEPTy, &P, V = Ops[0]]() -> bool {
            return P->getType() == GEPTy &&
                   getUnderlyingObject(P) == getUnderlyingObject(V);
          };
          // getelementptr V, (sub P, V) -> P if P points to a type of size 1.
          if (TyAllocSize == 1 &&
              match(Ops[1], m_Sub(m_PtrToInt(m_Value(P)),
                                  m_PtrToInt(m_Specific(Ops[0])))) &&
              CanSimplify())
            return P;
  
          // getelementptr V, (ashr (sub P, V), C) -> P if P points to a type of
          // size 1 << C.
          if (match(Ops[1], m_AShr(m_Sub(m_PtrToInt(m_Value(P)),
                                         m_PtrToInt(m_Specific(Ops[0]))),
                                   m_ConstantInt(C))) &&
              TyAllocSize == 1ULL << C && CanSimplify())
            return P;
  
          // getelementptr V, (sdiv (sub P, V), C) -> P if P points to a type of
          // size C.
          if (match(Ops[1], m_SDiv(m_Sub(m_PtrToInt(m_Value(P)),
                                         m_PtrToInt(m_Specific(Ops[0]))),
                                   m_SpecificInt(TyAllocSize))) &&
              CanSimplify())
            return P;
        }
      }
    }
  
    if (!IsScalableVec && Q.DL.getTypeAllocSize(LastType) == 1 &&
        all_of(Ops.slice(1).drop_back(1),
               [](Value *Idx) { return match(Idx, m_Zero()); })) {
      unsigned IdxWidth =
          Q.DL.getIndexSizeInBits(Ops[0]->getType()->getPointerAddressSpace());
      if (Q.DL.getTypeSizeInBits(Ops.back()->getType()) == IdxWidth) {
        APInt BasePtrOffset(IdxWidth, 0);
        Value *StrippedBasePtr =
            Ops[0]->stripAndAccumulateInBoundsConstantOffsets(Q.DL,
                                                              BasePtrOffset);
  
        // Avoid creating inttoptr of zero here: While LLVMs treatment of
        // inttoptr is generally conservative, this particular case is folded to
        // a null pointer, which will have incorrect provenance.
  
        // gep (gep V, C), (sub 0, V) -> C
        if (match(Ops.back(),
                  m_Sub(m_Zero(), m_PtrToInt(m_Specific(StrippedBasePtr)))) &&
            !BasePtrOffset.isNullValue()) {
          auto *CI = ConstantInt::get(GEPTy->getContext(), BasePtrOffset);
          return ConstantExpr::getIntToPtr(CI, GEPTy);
        }
        // gep (gep V, C), (xor V, -1) -> C-1
        if (match(Ops.back(),
                  m_Xor(m_PtrToInt(m_Specific(StrippedBasePtr)), m_AllOnes())) &&
            !BasePtrOffset.isOneValue()) {
          auto *CI = ConstantInt::get(GEPTy->getContext(), BasePtrOffset - 1);
          return ConstantExpr::getIntToPtr(CI, GEPTy);
        }
      }
    }
  
    // Check to see if this is constant foldable.
    if (!all_of(Ops, [](Value *V) { return isa<Constant>(V); }))
      return nullptr;
  
    auto *CE = ConstantExpr::getGetElementPtr(SrcTy, cast<Constant>(Ops[0]),
                                              Ops.slice(1));
    return ConstantFoldConstant(CE, Q.DL);
  }
  
  Value *llvm::SimplifyGEPInst(Type *SrcTy, ArrayRef<Value *> Ops,
                               const SimplifyQuery &Q) {
    return ::SimplifyGEPInst(SrcTy, Ops, Q, RecursionLimit);
  }
  
  /// Given operands for an InsertValueInst, see if we can fold the result.
  /// If not, this returns null.
  static Value *SimplifyInsertValueInst(Value *Agg, Value *Val,
                                        ArrayRef<unsigned> Idxs, const SimplifyQuery &Q,
                                        unsigned) {
    if (Constant *CAgg = dyn_cast<Constant>(Agg))
      if (Constant *CVal = dyn_cast<Constant>(Val))
        return ConstantFoldInsertValueInstruction(CAgg, CVal, Idxs);
  
    // insertvalue x, undef, n -> x
    if (Q.isUndefValue(Val))
      return Agg;
  
    // insertvalue x, (extractvalue y, n), n
    if (ExtractValueInst *EV = dyn_cast<ExtractValueInst>(Val))
      if (EV->getAggregateOperand()->getType() == Agg->getType() &&
          EV->getIndices() == Idxs) {
        // insertvalue undef, (extractvalue y, n), n -> y
        if (Q.isUndefValue(Agg))
          return EV->getAggregateOperand();
  
        // insertvalue y, (extractvalue y, n), n -> y
        if (Agg == EV->getAggregateOperand())
          return Agg;
      }
  
    return nullptr;
  }
  
  Value *llvm::SimplifyInsertValueInst(Value *Agg, Value *Val,
                                       ArrayRef<unsigned> Idxs,
                                       const SimplifyQuery &Q) {
    return ::SimplifyInsertValueInst(Agg, Val, Idxs, Q, RecursionLimit);
  }
  
  Value *llvm::SimplifyInsertElementInst(Value *Vec, Value *Val, Value *Idx,
                                         const SimplifyQuery &Q) {
    // Try to constant fold.
    auto *VecC = dyn_cast<Constant>(Vec);
    auto *ValC = dyn_cast<Constant>(Val);
    auto *IdxC = dyn_cast<Constant>(Idx);
    if (VecC && ValC && IdxC)
      return ConstantExpr::getInsertElement(VecC, ValC, IdxC);
  
    // For fixed-length vector, fold into poison if index is out of bounds.
    if (auto *CI = dyn_cast<ConstantInt>(Idx)) {
      if (isa<FixedVectorType>(Vec->getType()) &&
          CI->uge(cast<FixedVectorType>(Vec->getType())->getNumElements()))
        return PoisonValue::get(Vec->getType());
    }
  
    // If index is undef, it might be out of bounds (see above case)
    if (Q.isUndefValue(Idx))
      return PoisonValue::get(Vec->getType());
  
    // If the scalar is poison, or it is undef and there is no risk of
    // propagating poison from the vector value, simplify to the vector value.
    if (isa<PoisonValue>(Val) ||
        (Q.isUndefValue(Val) && isGuaranteedNotToBePoison(Vec)))
      return Vec;
  
    // If we are extracting a value from a vector, then inserting it into the same
    // place, that's the input vector:
    // insertelt Vec, (extractelt Vec, Idx), Idx --> Vec
    if (match(Val, m_ExtractElt(m_Specific(Vec), m_Specific(Idx))))
      return Vec;
  
    return nullptr;
  }
  
  /// Given operands for an ExtractValueInst, see if we can fold the result.
  /// If not, this returns null.
  static Value *SimplifyExtractValueInst(Value *Agg, ArrayRef<unsigned> Idxs,
                                         const SimplifyQuery &, unsigned) {
    if (auto *CAgg = dyn_cast<Constant>(Agg))
      return ConstantFoldExtractValueInstruction(CAgg, Idxs);
  
    // extractvalue x, (insertvalue y, elt, n), n -> elt
    unsigned NumIdxs = Idxs.size();
    for (auto *IVI = dyn_cast<InsertValueInst>(Agg); IVI != nullptr;
         IVI = dyn_cast<InsertValueInst>(IVI->getAggregateOperand())) {
      ArrayRef<unsigned> InsertValueIdxs = IVI->getIndices();
      unsigned NumInsertValueIdxs = InsertValueIdxs.size();
      unsigned NumCommonIdxs = std::min(NumInsertValueIdxs, NumIdxs);
      if (InsertValueIdxs.slice(0, NumCommonIdxs) ==
          Idxs.slice(0, NumCommonIdxs)) {
        if (NumIdxs == NumInsertValueIdxs)
          return IVI->getInsertedValueOperand();
        break;
      }
    }
  
    return nullptr;
  }
  
  Value *llvm::SimplifyExtractValueInst(Value *Agg, ArrayRef<unsigned> Idxs,
                                        const SimplifyQuery &Q) {
    return ::SimplifyExtractValueInst(Agg, Idxs, Q, RecursionLimit);
  }
  
  /// Given operands for an ExtractElementInst, see if we can fold the result.
  /// If not, this returns null.
  static Value *SimplifyExtractElementInst(Value *Vec, Value *Idx,
                                           const SimplifyQuery &Q, unsigned) {
    auto *VecVTy = cast<VectorType>(Vec->getType());
    if (auto *CVec = dyn_cast<Constant>(Vec)) {
      if (auto *CIdx = dyn_cast<Constant>(Idx))
        return ConstantExpr::getExtractElement(CVec, CIdx);
  
      // The index is not relevant if our vector is a splat.
      if (auto *Splat = CVec->getSplatValue())
        return Splat;
  
      if (Q.isUndefValue(Vec))
        return UndefValue::get(VecVTy->getElementType());
    }
  
    // An undef extract index can be arbitrarily chosen to be an out-of-range
    // index value, which would result in the instruction being poison.
    if (Q.isUndefValue(Idx))
      return PoisonValue::get(VecVTy->getElementType());
  
    // If extracting a specified index from the vector, see if we can recursively
    // find a previously computed scalar that was inserted into the vector.
    if (auto *IdxC = dyn_cast<ConstantInt>(Idx)) {
      // For fixed-length vector, fold into undef if index is out of bounds.
      unsigned MinNumElts = VecVTy->getElementCount().getKnownMinValue();
      if (isa<FixedVectorType>(VecVTy) && IdxC->getValue().uge(MinNumElts))
        return PoisonValue::get(VecVTy->getElementType());
      // Handle case where an element is extracted from a splat.
      if (IdxC->getValue().ult(MinNumElts))
        if (auto *Splat = getSplatValue(Vec))
          return Splat;
      if (Value *Elt = findScalarElement(Vec, IdxC->getZExtValue()))
        return Elt;
    }
    return nullptr;
  }
  
  Value *llvm::SimplifyExtractElementInst(Value *Vec, Value *Idx,
                                          const SimplifyQuery &Q) {
    return ::SimplifyExtractElementInst(Vec, Idx, Q, RecursionLimit);
  }
  
  /// See if we can fold the given phi. If not, returns null.
  static Value *SimplifyPHINode(PHINode *PN, const SimplifyQuery &Q) {
    // WARNING: no matter how worthwhile it may seem, we can not perform PHI CSE
    //          here, because the PHI we may succeed simplifying to was not
    //          def-reachable from the original PHI!
  
    // If all of the PHI's incoming values are the same then replace the PHI node
    // with the common value.
    Value *CommonValue = nullptr;
    bool HasUndefInput = false;
    for (Value *Incoming : PN->incoming_values()) {
      // If the incoming value is the phi node itself, it can safely be skipped.
      if (Incoming == PN) continue;
      if (Q.isUndefValue(Incoming)) {
        // Remember that we saw an undef value, but otherwise ignore them.
        HasUndefInput = true;
        continue;
      }
      if (CommonValue && Incoming != CommonValue)
        return nullptr;  // Not the same, bail out.
      CommonValue = Incoming;
    }
  
    // If CommonValue is null then all of the incoming values were either undef or
    // equal to the phi node itself.
    if (!CommonValue)
      return UndefValue::get(PN->getType());
  
    // If we have a PHI node like phi(X, undef, X), where X is defined by some
    // instruction, we cannot return X as the result of the PHI node unless it
    // dominates the PHI block.
    if (HasUndefInput)
      return valueDominatesPHI(CommonValue, PN, Q.DT) ? CommonValue : nullptr;
  
    return CommonValue;
  }
  
  static Value *SimplifyCastInst(unsigned CastOpc, Value *Op,
                                 Type *Ty, const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (auto *C = dyn_cast<Constant>(Op))
      return ConstantFoldCastOperand(CastOpc, C, Ty, Q.DL);
  
    if (auto *CI = dyn_cast<CastInst>(Op)) {
      auto *Src = CI->getOperand(0);
      Type *SrcTy = Src->getType();
      Type *MidTy = CI->getType();
      Type *DstTy = Ty;
      if (Src->getType() == Ty) {
        auto FirstOp = static_cast<Instruction::CastOps>(CI->getOpcode());
        auto SecondOp = static_cast<Instruction::CastOps>(CastOpc);
        Type *SrcIntPtrTy =
            SrcTy->isPtrOrPtrVectorTy() ? Q.DL.getIntPtrType(SrcTy) : nullptr;
        Type *MidIntPtrTy =
            MidTy->isPtrOrPtrVectorTy() ? Q.DL.getIntPtrType(MidTy) : nullptr;
        Type *DstIntPtrTy =
            DstTy->isPtrOrPtrVectorTy() ? Q.DL.getIntPtrType(DstTy) : nullptr;
        if (CastInst::isEliminableCastPair(FirstOp, SecondOp, SrcTy, MidTy, DstTy,
                                           SrcIntPtrTy, MidIntPtrTy,
                                           DstIntPtrTy) == Instruction::BitCast)
          return Src;
      }
    }
  
    // bitcast x -> x
    if (CastOpc == Instruction::BitCast)
      if (Op->getType() == Ty)
        return Op;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyCastInst(unsigned CastOpc, Value *Op, Type *Ty,
                                const SimplifyQuery &Q) {
    return ::SimplifyCastInst(CastOpc, Op, Ty, Q, RecursionLimit);
  }
  
  /// For the given destination element of a shuffle, peek through shuffles to
  /// match a root vector source operand that contains that element in the same
  /// vector lane (ie, the same mask index), so we can eliminate the shuffle(s).
  static Value *foldIdentityShuffles(int DestElt, Value *Op0, Value *Op1,
                                     int MaskVal, Value *RootVec,
                                     unsigned MaxRecurse) {
    if (!MaxRecurse--)
      return nullptr;
  
    // Bail out if any mask value is undefined. That kind of shuffle may be
    // simplified further based on demanded bits or other folds.
    if (MaskVal == -1)
      return nullptr;
  
    // The mask value chooses which source operand we need to look at next.
    int InVecNumElts = cast<FixedVectorType>(Op0->getType())->getNumElements();
    int RootElt = MaskVal;
    Value *SourceOp = Op0;
    if (MaskVal >= InVecNumElts) {
      RootElt = MaskVal - InVecNumElts;
      SourceOp = Op1;
    }
  
    // If the source operand is a shuffle itself, look through it to find the
    // matching root vector.
    if (auto *SourceShuf = dyn_cast<ShuffleVectorInst>(SourceOp)) {
      return foldIdentityShuffles(
          DestElt, SourceShuf->getOperand(0), SourceShuf->getOperand(1),
          SourceShuf->getMaskValue(RootElt), RootVec, MaxRecurse);
    }
  
    // TODO: Look through bitcasts? What if the bitcast changes the vector element
    // size?
  
    // The source operand is not a shuffle. Initialize the root vector value for
    // this shuffle if that has not been done yet.
    if (!RootVec)
      RootVec = SourceOp;
  
    // Give up as soon as a source operand does not match the existing root value.
    if (RootVec != SourceOp)
      return nullptr;
  
    // The element must be coming from the same lane in the source vector
    // (although it may have crossed lanes in intermediate shuffles).
    if (RootElt != DestElt)
      return nullptr;
  
    return RootVec;
  }
  
  static Value *SimplifyShuffleVectorInst(Value *Op0, Value *Op1,
                                          ArrayRef<int> Mask, Type *RetTy,
                                          const SimplifyQuery &Q,
                                          unsigned MaxRecurse) {
    if (all_of(Mask, [](int Elem) { return Elem == UndefMaskElem; }))
      return UndefValue::get(RetTy);
  
    auto *InVecTy = cast<VectorType>(Op0->getType());
    unsigned MaskNumElts = Mask.size();
    ElementCount InVecEltCount = InVecTy->getElementCount();
  
    bool Scalable = InVecEltCount.isScalable();
  
    SmallVector<int, 32> Indices;
    Indices.assign(Mask.begin(), Mask.end());
  
    // Canonicalization: If mask does not select elements from an input vector,
    // replace that input vector with poison.
    if (!Scalable) {
      bool MaskSelects0 = false, MaskSelects1 = false;
      unsigned InVecNumElts = InVecEltCount.getKnownMinValue();
      for (unsigned i = 0; i != MaskNumElts; ++i) {
        if (Indices[i] == -1)
          continue;
        if ((unsigned)Indices[i] < InVecNumElts)
          MaskSelects0 = true;
        else
          MaskSelects1 = true;
      }
      if (!MaskSelects0)
        Op0 = PoisonValue::get(InVecTy);
      if (!MaskSelects1)
        Op1 = PoisonValue::get(InVecTy);
    }
  
    auto *Op0Const = dyn_cast<Constant>(Op0);
    auto *Op1Const = dyn_cast<Constant>(Op1);
  
    // If all operands are constant, constant fold the shuffle. This
    // transformation depends on the value of the mask which is not known at
    // compile time for scalable vectors
    if (Op0Const && Op1Const)
      return ConstantExpr::getShuffleVector(Op0Const, Op1Const, Mask);
  
    // Canonicalization: if only one input vector is constant, it shall be the
    // second one. This transformation depends on the value of the mask which
    // is not known at compile time for scalable vectors
    if (!Scalable && Op0Const && !Op1Const) {
      std::swap(Op0, Op1);
      ShuffleVectorInst::commuteShuffleMask(Indices,
                                            InVecEltCount.getKnownMinValue());
    }
  
    // A splat of an inserted scalar constant becomes a vector constant:
    // shuf (inselt ?, C, IndexC), undef, <IndexC, IndexC...> --> <C, C...>
    // NOTE: We may have commuted above, so analyze the updated Indices, not the
    //       original mask constant.
    // NOTE: This transformation depends on the value of the mask which is not
    // known at compile time for scalable vectors
    Constant *C;
    ConstantInt *IndexC;
    if (!Scalable && match(Op0, m_InsertElt(m_Value(), m_Constant(C),
                                            m_ConstantInt(IndexC)))) {
      // Match a splat shuffle mask of the insert index allowing undef elements.
      int InsertIndex = IndexC->getZExtValue();
      if (all_of(Indices, [InsertIndex](int MaskElt) {
            return MaskElt == InsertIndex || MaskElt == -1;
          })) {
        assert(isa<UndefValue>(Op1) && "Expected undef operand 1 for splat");
  
        // Shuffle mask undefs become undefined constant result elements.
        SmallVector<Constant *, 16> VecC(MaskNumElts, C);
        for (unsigned i = 0; i != MaskNumElts; ++i)
          if (Indices[i] == -1)
            VecC[i] = UndefValue::get(C->getType());
        return ConstantVector::get(VecC);
      }
    }
  
    // A shuffle of a splat is always the splat itself. Legal if the shuffle's
    // value type is same as the input vectors' type.
    if (auto *OpShuf = dyn_cast<ShuffleVectorInst>(Op0))
      if (Q.isUndefValue(Op1) && RetTy == InVecTy &&
          is_splat(OpShuf->getShuffleMask()))
        return Op0;
  
    // All remaining transformation depend on the value of the mask, which is
    // not known at compile time for scalable vectors.
    if (Scalable)
      return nullptr;
  
    // Don't fold a shuffle with undef mask elements. This may get folded in a
    // better way using demanded bits or other analysis.
    // TODO: Should we allow this?
    if (is_contained(Indices, -1))
      return nullptr;
  
    // Check if every element of this shuffle can be mapped back to the
    // corresponding element of a single root vector. If so, we don't need this
    // shuffle. This handles simple identity shuffles as well as chains of
    // shuffles that may widen/narrow and/or move elements across lanes and back.
    Value *RootVec = nullptr;
    for (unsigned i = 0; i != MaskNumElts; ++i) {
      // Note that recursion is limited for each vector element, so if any element
      // exceeds the limit, this will fail to simplify.
      RootVec =
          foldIdentityShuffles(i, Op0, Op1, Indices[i], RootVec, MaxRecurse);
  
      // We can't replace a widening/narrowing shuffle with one of its operands.
      if (!RootVec || RootVec->getType() != RetTy)
        return nullptr;
    }
    return RootVec;
  }
  
  /// Given operands for a ShuffleVectorInst, fold the result or return null.
  Value *llvm::SimplifyShuffleVectorInst(Value *Op0, Value *Op1,
                                         ArrayRef<int> Mask, Type *RetTy,
                                         const SimplifyQuery &Q) {
    return ::SimplifyShuffleVectorInst(Op0, Op1, Mask, RetTy, Q, RecursionLimit);
  }
  
  static Constant *foldConstant(Instruction::UnaryOps Opcode,
                                Value *&Op, const SimplifyQuery &Q) {
    if (auto *C = dyn_cast<Constant>(Op))
      return ConstantFoldUnaryOpOperand(Opcode, C, Q.DL);
    return nullptr;
  }
  
  /// Given the operand for an FNeg, see if we can fold the result.  If not, this
  /// returns null.
  static Value *simplifyFNegInst(Value *Op, FastMathFlags FMF,
                                 const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (Constant *C = foldConstant(Instruction::FNeg, Op, Q))
      return C;
  
    Value *X;
    // fneg (fneg X) ==> X
    if (match(Op, m_FNeg(m_Value(X))))
      return X;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyFNegInst(Value *Op, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    return ::simplifyFNegInst(Op, FMF, Q, RecursionLimit);
  }
  
  static Constant *propagateNaN(Constant *In) {
    // If the input is a vector with undef elements, just return a default NaN.
    if (!In->isNaN())
      return ConstantFP::getNaN(In->getType());
  
    // Propagate the existing NaN constant when possible.
    // TODO: Should we quiet a signaling NaN?
    return In;
  }
  
  /// Perform folds that are common to any floating-point operation. This implies
  /// transforms based on poison/undef/NaN because the operation itself makes no
  /// difference to the result.
  static Constant *simplifyFPOp(ArrayRef<Value *> Ops, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    for (Value *V : Ops) {
      // Poison is independent of anything else. It always propagates from an
      // operand to a math result.
      if (match(V, m_Poison()))
        return PoisonValue::get(V->getType());
  
      bool IsNan = match(V, m_NaN());
      bool IsInf = match(V, m_Inf());
      bool IsUndef = Q.isUndefValue(V);
  
      // If this operation has 'nnan' or 'ninf' and at least 1 disallowed operand
      // (an undef operand can be chosen to be Nan/Inf), then the result of
      // this operation is poison.
      if (FMF.noNaNs() && (IsNan || IsUndef))
        return PoisonValue::get(V->getType());
      if (FMF.noInfs() && (IsInf || IsUndef))
        return PoisonValue::get(V->getType());
  
      if (IsUndef || IsNan)
        return propagateNaN(cast<Constant>(V));
    }
    return nullptr;
  }
  
  /// Given operands for an FAdd, see if we can fold the result.  If not, this
  /// returns null.
  static Value *SimplifyFAddInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (Constant *C = foldOrCommuteConstant(Instruction::FAdd, Op0, Op1, Q))
      return C;
  
    if (Constant *C = simplifyFPOp({Op0, Op1}, FMF, Q))
      return C;
  
    // fadd X, -0 ==> X
    if (match(Op1, m_NegZeroFP()))
      return Op0;
  
    // fadd X, 0 ==> X, when we know X is not -0
    if (match(Op1, m_PosZeroFP()) &&
        (FMF.noSignedZeros() || CannotBeNegativeZero(Op0, Q.TLI)))
      return Op0;
  
    // With nnan: -X + X --> 0.0 (and commuted variant)
    // We don't have to explicitly exclude infinities (ninf): INF + -INF == NaN.
    // Negative zeros are allowed because we always end up with positive zero:
    // X = -0.0: (-0.0 - (-0.0)) + (-0.0) == ( 0.0) + (-0.0) == 0.0
    // X = -0.0: ( 0.0 - (-0.0)) + (-0.0) == ( 0.0) + (-0.0) == 0.0
    // X =  0.0: (-0.0 - ( 0.0)) + ( 0.0) == (-0.0) + ( 0.0) == 0.0
    // X =  0.0: ( 0.0 - ( 0.0)) + ( 0.0) == ( 0.0) + ( 0.0) == 0.0
    if (FMF.noNaNs()) {
      if (match(Op0, m_FSub(m_AnyZeroFP(), m_Specific(Op1))) ||
          match(Op1, m_FSub(m_AnyZeroFP(), m_Specific(Op0))))
        return ConstantFP::getNullValue(Op0->getType());
  
      if (match(Op0, m_FNeg(m_Specific(Op1))) ||
          match(Op1, m_FNeg(m_Specific(Op0))))
        return ConstantFP::getNullValue(Op0->getType());
    }
  
    // (X - Y) + Y --> X
    // Y + (X - Y) --> X
    Value *X;
    if (FMF.noSignedZeros() && FMF.allowReassoc() &&
        (match(Op0, m_FSub(m_Value(X), m_Specific(Op1))) ||
         match(Op1, m_FSub(m_Value(X), m_Specific(Op0)))))
      return X;
  
    return nullptr;
  }
  
  /// Given operands for an FSub, see if we can fold the result.  If not, this
  /// returns null.
  static Value *SimplifyFSubInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (Constant *C = foldOrCommuteConstant(Instruction::FSub, Op0, Op1, Q))
      return C;
  
    if (Constant *C = simplifyFPOp({Op0, Op1}, FMF, Q))
      return C;
  
    // fsub X, +0 ==> X
    if (match(Op1, m_PosZeroFP()))
      return Op0;
  
    // fsub X, -0 ==> X, when we know X is not -0
    if (match(Op1, m_NegZeroFP()) &&
        (FMF.noSignedZeros() || CannotBeNegativeZero(Op0, Q.TLI)))
      return Op0;
  
    // fsub -0.0, (fsub -0.0, X) ==> X
    // fsub -0.0, (fneg X) ==> X
    Value *X;
    if (match(Op0, m_NegZeroFP()) &&
        match(Op1, m_FNeg(m_Value(X))))
      return X;
  
    // fsub 0.0, (fsub 0.0, X) ==> X if signed zeros are ignored.
    // fsub 0.0, (fneg X) ==> X if signed zeros are ignored.
    if (FMF.noSignedZeros() && match(Op0, m_AnyZeroFP()) &&
        (match(Op1, m_FSub(m_AnyZeroFP(), m_Value(X))) ||
         match(Op1, m_FNeg(m_Value(X)))))
      return X;
  
    // fsub nnan x, x ==> 0.0
    if (FMF.noNaNs() && Op0 == Op1)
      return Constant::getNullValue(Op0->getType());
  
    // Y - (Y - X) --> X
    // (X + Y) - Y --> X
    if (FMF.noSignedZeros() && FMF.allowReassoc() &&
        (match(Op1, m_FSub(m_Specific(Op0), m_Value(X))) ||
         match(Op0, m_c_FAdd(m_Specific(Op1), m_Value(X)))))
      return X;
  
    return nullptr;
  }
  
  static Value *SimplifyFMAFMul(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (Constant *C = simplifyFPOp({Op0, Op1}, FMF, Q))
      return C;
  
    // fmul X, 1.0 ==> X
    if (match(Op1, m_FPOne()))
      return Op0;
  
    // fmul 1.0, X ==> X
    if (match(Op0, m_FPOne()))
      return Op1;
  
    // fmul nnan nsz X, 0 ==> 0
    if (FMF.noNaNs() && FMF.noSignedZeros() && match(Op1, m_AnyZeroFP()))
      return ConstantFP::getNullValue(Op0->getType());
  
    // fmul nnan nsz 0, X ==> 0
    if (FMF.noNaNs() && FMF.noSignedZeros() && match(Op0, m_AnyZeroFP()))
      return ConstantFP::getNullValue(Op1->getType());
  
    // sqrt(X) * sqrt(X) --> X, if we can:
    // 1. Remove the intermediate rounding (reassociate).
    // 2. Ignore non-zero negative numbers because sqrt would produce NAN.
    // 3. Ignore -0.0 because sqrt(-0.0) == -0.0, but -0.0 * -0.0 == 0.0.
    Value *X;
    if (Op0 == Op1 && match(Op0, m_Intrinsic<Intrinsic::sqrt>(m_Value(X))) &&
        FMF.allowReassoc() && FMF.noNaNs() && FMF.noSignedZeros())
      return X;
  
    return nullptr;
  }
  
  /// Given the operands for an FMul, see if we can fold the result
  static Value *SimplifyFMulInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (Constant *C = foldOrCommuteConstant(Instruction::FMul, Op0, Op1, Q))
      return C;
  
    // Now apply simplifications that do not require rounding.
    return SimplifyFMAFMul(Op0, Op1, FMF, Q, MaxRecurse);
  }
  
  Value *llvm::SimplifyFAddInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    return ::SimplifyFAddInst(Op0, Op1, FMF, Q, RecursionLimit);
  }
  
  
  Value *llvm::SimplifyFSubInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    return ::SimplifyFSubInst(Op0, Op1, FMF, Q, RecursionLimit);
  }
  
  Value *llvm::SimplifyFMulInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    return ::SimplifyFMulInst(Op0, Op1, FMF, Q, RecursionLimit);
  }
  
  Value *llvm::SimplifyFMAFMul(Value *Op0, Value *Op1, FastMathFlags FMF,
                               const SimplifyQuery &Q) {
    return ::SimplifyFMAFMul(Op0, Op1, FMF, Q, RecursionLimit);
  }
  
  static Value *SimplifyFDivInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const SimplifyQuery &Q, unsigned) {
    if (Constant *C = foldOrCommuteConstant(Instruction::FDiv, Op0, Op1, Q))
      return C;
  
    if (Constant *C = simplifyFPOp({Op0, Op1}, FMF, Q))
      return C;
  
    // X / 1.0 -> X
    if (match(Op1, m_FPOne()))
      return Op0;
  
    // 0 / X -> 0
    // Requires that NaNs are off (X could be zero) and signed zeroes are
    // ignored (X could be positive or negative, so the output sign is unknown).
    if (FMF.noNaNs() && FMF.noSignedZeros() && match(Op0, m_AnyZeroFP()))
      return ConstantFP::getNullValue(Op0->getType());
  
    if (FMF.noNaNs()) {
      // X / X -> 1.0 is legal when NaNs are ignored.
      // We can ignore infinities because INF/INF is NaN.
      if (Op0 == Op1)
        return ConstantFP::get(Op0->getType(), 1.0);
  
      // (X * Y) / Y --> X if we can reassociate to the above form.
      Value *X;
      if (FMF.allowReassoc() && match(Op0, m_c_FMul(m_Value(X), m_Specific(Op1))))
        return X;
  
      // -X /  X -> -1.0 and
      //  X / -X -> -1.0 are legal when NaNs are ignored.
      // We can ignore signed zeros because +-0.0/+-0.0 is NaN and ignored.
      if (match(Op0, m_FNegNSZ(m_Specific(Op1))) ||
          match(Op1, m_FNegNSZ(m_Specific(Op0))))
        return ConstantFP::get(Op0->getType(), -1.0);
    }
  
    return nullptr;
  }
  
  Value *llvm::SimplifyFDivInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    return ::SimplifyFDivInst(Op0, Op1, FMF, Q, RecursionLimit);
  }
  
  static Value *SimplifyFRemInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const SimplifyQuery &Q, unsigned) {
    if (Constant *C = foldOrCommuteConstant(Instruction::FRem, Op0, Op1, Q))
      return C;
  
    if (Constant *C = simplifyFPOp({Op0, Op1}, FMF, Q))
      return C;
  
    // Unlike fdiv, the result of frem always matches the sign of the dividend.
    // The constant match may include undef elements in a vector, so return a full
    // zero constant as the result.
    if (FMF.noNaNs()) {
      // +0 % X -> 0
      if (match(Op0, m_PosZeroFP()))
        return ConstantFP::getNullValue(Op0->getType());
      // -0 % X -> -0
      if (match(Op0, m_NegZeroFP()))
        return ConstantFP::getNegativeZero(Op0->getType());
    }
  
    return nullptr;
  }
  
  Value *llvm::SimplifyFRemInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const SimplifyQuery &Q) {
    return ::SimplifyFRemInst(Op0, Op1, FMF, Q, RecursionLimit);
  }
  
  //=== Helper functions for higher up the class hierarchy.
  
  /// Given the operand for a UnaryOperator, see if we can fold the result.
  /// If not, this returns null.
  static Value *simplifyUnOp(unsigned Opcode, Value *Op, const SimplifyQuery &Q,
                             unsigned MaxRecurse) {
    switch (Opcode) {
    case Instruction::FNeg:
      return simplifyFNegInst(Op, FastMathFlags(), Q, MaxRecurse);
    default:
      llvm_unreachable("Unexpected opcode");
    }
  }
  
  /// Given the operand for a UnaryOperator, see if we can fold the result.
  /// If not, this returns null.
  /// Try to use FastMathFlags when folding the result.
  static Value *simplifyFPUnOp(unsigned Opcode, Value *Op,
                               const FastMathFlags &FMF,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
    switch (Opcode) {
    case Instruction::FNeg:
      return simplifyFNegInst(Op, FMF, Q, MaxRecurse);
    default:
      return simplifyUnOp(Opcode, Op, Q, MaxRecurse);
    }
  }
  
  Value *llvm::SimplifyUnOp(unsigned Opcode, Value *Op, const SimplifyQuery &Q) {
    return ::simplifyUnOp(Opcode, Op, Q, RecursionLimit);
  }
  
  Value *llvm::SimplifyUnOp(unsigned Opcode, Value *Op, FastMathFlags FMF,
                            const SimplifyQuery &Q) {
    return ::simplifyFPUnOp(Opcode, Op, FMF, Q, RecursionLimit);
  }
  
  /// Given operands for a BinaryOperator, see if we can fold the result.
  /// If not, this returns null.
  static Value *SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
    switch (Opcode) {
    case Instruction::Add:
      return SimplifyAddInst(LHS, RHS, false, false, Q, MaxRecurse);
    case Instruction::Sub:
      return SimplifySubInst(LHS, RHS, false, false, Q, MaxRecurse);
    case Instruction::Mul:
      return SimplifyMulInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::SDiv:
      return SimplifySDivInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::UDiv:
      return SimplifyUDivInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::SRem:
      return SimplifySRemInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::URem:
      return SimplifyURemInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::Shl:
      return SimplifyShlInst(LHS, RHS, false, false, Q, MaxRecurse);
    case Instruction::LShr:
      return SimplifyLShrInst(LHS, RHS, false, Q, MaxRecurse);
    case Instruction::AShr:
      return SimplifyAShrInst(LHS, RHS, false, Q, MaxRecurse);
    case Instruction::And:
      return SimplifyAndInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::Or:
      return SimplifyOrInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::Xor:
      return SimplifyXorInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::FAdd:
      return SimplifyFAddInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::FSub:
      return SimplifyFSubInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::FMul:
      return SimplifyFMulInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::FDiv:
      return SimplifyFDivInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::FRem:
      return SimplifyFRemInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    default:
      llvm_unreachable("Unexpected opcode");
    }
  }
  
  /// Given operands for a BinaryOperator, see if we can fold the result.
  /// If not, this returns null.
  /// Try to use FastMathFlags when folding the result.
  static Value *SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                              const FastMathFlags &FMF, const SimplifyQuery &Q,
                              unsigned MaxRecurse) {
    switch (Opcode) {
    case Instruction::FAdd:
      return SimplifyFAddInst(LHS, RHS, FMF, Q, MaxRecurse);
    case Instruction::FSub:
      return SimplifyFSubInst(LHS, RHS, FMF, Q, MaxRecurse);
    case Instruction::FMul:
      return SimplifyFMulInst(LHS, RHS, FMF, Q, MaxRecurse);
    case Instruction::FDiv:
      return SimplifyFDivInst(LHS, RHS, FMF, Q, MaxRecurse);
    default:
      return SimplifyBinOp(Opcode, LHS, RHS, Q, MaxRecurse);
    }
  }
  
  Value *llvm::SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                             const SimplifyQuery &Q) {
    return ::SimplifyBinOp(Opcode, LHS, RHS, Q, RecursionLimit);
  }
  
  Value *llvm::SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                             FastMathFlags FMF, const SimplifyQuery &Q) {
    return ::SimplifyBinOp(Opcode, LHS, RHS, FMF, Q, RecursionLimit);
  }
  
  /// Given operands for a CmpInst, see if we can fold the result.
  static Value *SimplifyCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                                const SimplifyQuery &Q, unsigned MaxRecurse) {
    if (CmpInst::isIntPredicate((CmpInst::Predicate)Predicate))
      return SimplifyICmpInst(Predicate, LHS, RHS, Q, MaxRecurse);
    return SimplifyFCmpInst(Predicate, LHS, RHS, FastMathFlags(), Q, MaxRecurse);
  }
  
  Value *llvm::SimplifyCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q) {
    return ::SimplifyCmpInst(Predicate, LHS, RHS, Q, RecursionLimit);
  }
  
  static bool IsIdempotent(Intrinsic::ID ID) {
    switch (ID) {
    default: return false;
  
    // Unary idempotent: f(f(x)) = f(x)
    case Intrinsic::fabs:
    case Intrinsic::floor:
    case Intrinsic::ceil:
    case Intrinsic::trunc:
    case Intrinsic::rint:
    case Intrinsic::nearbyint:
    case Intrinsic::round:
    case Intrinsic::roundeven:
    case Intrinsic::canonicalize:
      return true;
    }
  }
  
  static Value *SimplifyRelativeLoad(Constant *Ptr, Constant *Offset,
                                     const DataLayout &DL) {
    GlobalValue *PtrSym;
    APInt PtrOffset;
    if (!IsConstantOffsetFromGlobal(Ptr, PtrSym, PtrOffset, DL))
      return nullptr;
  
    Type *Int8PtrTy = Type::getInt8PtrTy(Ptr->getContext());
    Type *Int32Ty = Type::getInt32Ty(Ptr->getContext());
    Type *Int32PtrTy = Int32Ty->getPointerTo();
    Type *Int64Ty = Type::getInt64Ty(Ptr->getContext());
  
    auto *OffsetConstInt = dyn_cast<ConstantInt>(Offset);
    if (!OffsetConstInt || OffsetConstInt->getType()->getBitWidth() > 64)
      return nullptr;
  
    uint64_t OffsetInt = OffsetConstInt->getSExtValue();
    if (OffsetInt % 4 != 0)
      return nullptr;
  
    Constant *C = ConstantExpr::getGetElementPtr(
        Int32Ty, ConstantExpr::getBitCast(Ptr, Int32PtrTy),
        ConstantInt::get(Int64Ty, OffsetInt / 4));
    Constant *Loaded = ConstantFoldLoadFromConstPtr(C, Int32Ty, DL);
    if (!Loaded)
      return nullptr;
  
    auto *LoadedCE = dyn_cast<ConstantExpr>(Loaded);
    if (!LoadedCE)
      return nullptr;
  
    if (LoadedCE->getOpcode() == Instruction::Trunc) {
      LoadedCE = dyn_cast<ConstantExpr>(LoadedCE->getOperand(0));
      if (!LoadedCE)
        return nullptr;
    }
  
    if (LoadedCE->getOpcode() != Instruction::Sub)
      return nullptr;
  
    auto *LoadedLHS = dyn_cast<ConstantExpr>(LoadedCE->getOperand(0));
    if (!LoadedLHS || LoadedLHS->getOpcode() != Instruction::PtrToInt)
      return nullptr;
    auto *LoadedLHSPtr = LoadedLHS->getOperand(0);
  
    Constant *LoadedRHS = LoadedCE->getOperand(1);
    GlobalValue *LoadedRHSSym;
    APInt LoadedRHSOffset;
    if (!IsConstantOffsetFromGlobal(LoadedRHS, LoadedRHSSym, LoadedRHSOffset,
                                    DL) ||
        PtrSym != LoadedRHSSym || PtrOffset != LoadedRHSOffset)
      return nullptr;
  
    return ConstantExpr::getBitCast(LoadedLHSPtr, Int8PtrTy);
  }
  
  static Value *simplifyUnaryIntrinsic(Function *F, Value *Op0,
                                       const SimplifyQuery &Q) {
    // Idempotent functions return the same result when called repeatedly.
    Intrinsic::ID IID = F->getIntrinsicID();
    if (IsIdempotent(IID))
      if (auto *II = dyn_cast<IntrinsicInst>(Op0))
        if (II->getIntrinsicID() == IID)
          return II;
  
    Value *X;
    switch (IID) {
    case Intrinsic::fabs:
      if (SignBitMustBeZero(Op0, Q.TLI)) return Op0;
      break;
    case Intrinsic::bswap:
      // bswap(bswap(x)) -> x
      if (match(Op0, m_BSwap(m_Value(X)))) return X;
      break;
    case Intrinsic::bitreverse:
      // bitreverse(bitreverse(x)) -> x
      if (match(Op0, m_BitReverse(m_Value(X)))) return X;
      break;
    case Intrinsic::ctpop: {
      // If everything but the lowest bit is zero, that bit is the pop-count. Ex:
      // ctpop(and X, 1) --> and X, 1
      unsigned BitWidth = Op0->getType()->getScalarSizeInBits();
      if (MaskedValueIsZero(Op0, APInt::getHighBitsSet(BitWidth, BitWidth - 1),
                            Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
        return Op0;
      break;
    }
    case Intrinsic::exp:
      // exp(log(x)) -> x
      if (Q.CxtI->hasAllowReassoc() &&
          match(Op0, m_Intrinsic<Intrinsic::log>(m_Value(X)))) return X;
      break;
    case Intrinsic::exp2:
      // exp2(log2(x)) -> x
      if (Q.CxtI->hasAllowReassoc() &&
          match(Op0, m_Intrinsic<Intrinsic::log2>(m_Value(X)))) return X;
      break;
    case Intrinsic::log:
      // log(exp(x)) -> x
      if (Q.CxtI->hasAllowReassoc() &&
          match(Op0, m_Intrinsic<Intrinsic::exp>(m_Value(X)))) return X;
      break;
    case Intrinsic::log2:
      // log2(exp2(x)) -> x
      if (Q.CxtI->hasAllowReassoc() &&
          (match(Op0, m_Intrinsic<Intrinsic::exp2>(m_Value(X))) ||
           match(Op0, m_Intrinsic<Intrinsic::pow>(m_SpecificFP(2.0),
                                                  m_Value(X))))) return X;
      break;
    case Intrinsic::log10:
      // log10(pow(10.0, x)) -> x
      if (Q.CxtI->hasAllowReassoc() &&
          match(Op0, m_Intrinsic<Intrinsic::pow>(m_SpecificFP(10.0),
                                                 m_Value(X)))) return X;
      break;
    case Intrinsic::floor:
    case Intrinsic::trunc:
    case Intrinsic::ceil:
    case Intrinsic::round:
    case Intrinsic::roundeven:
    case Intrinsic::nearbyint:
    case Intrinsic::rint: {
      // floor (sitofp x) -> sitofp x
      // floor (uitofp x) -> uitofp x
      //
      // Converting from int always results in a finite integral number or
      // infinity. For either of those inputs, these rounding functions always
      // return the same value, so the rounding can be eliminated.
      if (match(Op0, m_SIToFP(m_Value())) || match(Op0, m_UIToFP(m_Value())))
        return Op0;
      break;
    }
    case Intrinsic::experimental_vector_reverse:
      // experimental.vector.reverse(experimental.vector.reverse(x)) -> x
      if (match(Op0,
                m_Intrinsic<Intrinsic::experimental_vector_reverse>(m_Value(X))))
        return X;
      break;
    default:
      break;
    }
  
    return nullptr;
  }
  
  static APInt getMaxMinLimit(Intrinsic::ID IID, unsigned BitWidth) {
    switch (IID) {
    case Intrinsic::smax: return APInt::getSignedMaxValue(BitWidth);
    case Intrinsic::smin: return APInt::getSignedMinValue(BitWidth);
    case Intrinsic::umax: return APInt::getMaxValue(BitWidth);
    case Intrinsic::umin: return APInt::getMinValue(BitWidth);
    default: llvm_unreachable("Unexpected intrinsic");
    }
  }
  
  static ICmpInst::Predicate getMaxMinPredicate(Intrinsic::ID IID) {
    switch (IID) {
    case Intrinsic::smax: return ICmpInst::ICMP_SGE;
    case Intrinsic::smin: return ICmpInst::ICMP_SLE;
    case Intrinsic::umax: return ICmpInst::ICMP_UGE;
    case Intrinsic::umin: return ICmpInst::ICMP_ULE;
    default: llvm_unreachable("Unexpected intrinsic");
    }
  }
  
  /// Given a min/max intrinsic, see if it can be removed based on having an
  /// operand that is another min/max intrinsic with shared operand(s). The caller
  /// is expected to swap the operand arguments to handle commutation.
  static Value *foldMinMaxSharedOp(Intrinsic::ID IID, Value *Op0, Value *Op1) {
    Value *X, *Y;
    if (!match(Op0, m_MaxOrMin(m_Value(X), m_Value(Y))))
      return nullptr;
  
    auto *MM0 = dyn_cast<IntrinsicInst>(Op0);
    if (!MM0)
      return nullptr;
    Intrinsic::ID IID0 = MM0->getIntrinsicID();
  
    if (Op1 == X || Op1 == Y ||
        match(Op1, m_c_MaxOrMin(m_Specific(X), m_Specific(Y)))) {
      // max (max X, Y), X --> max X, Y
      if (IID0 == IID)
        return MM0;
      // max (min X, Y), X --> X
      if (IID0 == getInverseMinMaxIntrinsic(IID))
        return Op1;
    }
    return nullptr;
  }
  
  static Value *simplifyBinaryIntrinsic(Function *F, Value *Op0, Value *Op1,
                                        const SimplifyQuery &Q) {
    Intrinsic::ID IID = F->getIntrinsicID();
    Type *ReturnType = F->getReturnType();
    unsigned BitWidth = ReturnType->getScalarSizeInBits();
    switch (IID) {
    case Intrinsic::abs:
      // abs(abs(x)) -> abs(x). We don't need to worry about the nsw arg here.
      // It is always ok to pick the earlier abs. We'll just lose nsw if its only
      // on the outer abs.
      if (match(Op0, m_Intrinsic<Intrinsic::abs>(m_Value(), m_Value())))
        return Op0;
      break;
  
    case Intrinsic::cttz: {
      Value *X;
      if (match(Op0, m_Shl(m_One(), m_Value(X))))
        return X;
      break;
    }
    case Intrinsic::ctlz: {
      Value *X;
      if (match(Op0, m_LShr(m_Negative(), m_Value(X))))
        return X;
      if (match(Op0, m_AShr(m_Negative(), m_Value())))
        return Constant::getNullValue(ReturnType);
      break;
    }
    case Intrinsic::smax:
    case Intrinsic::smin:
    case Intrinsic::umax:
    case Intrinsic::umin: {
      // If the arguments are the same, this is a no-op.
      if (Op0 == Op1)
        return Op0;
  
      // Canonicalize constant operand as Op1.
      if (isa<Constant>(Op0))
        std::swap(Op0, Op1);
  
      // Assume undef is the limit value.
      if (Q.isUndefValue(Op1))
        return ConstantInt::get(ReturnType, getMaxMinLimit(IID, BitWidth));
  
      const APInt *C;
      if (match(Op1, m_APIntAllowUndef(C))) {
        // Clamp to limit value. For example:
        // umax(i8 %x, i8 255) --> 255
        if (*C == getMaxMinLimit(IID, BitWidth))
          return ConstantInt::get(ReturnType, *C);
  
        // If the constant op is the opposite of the limit value, the other must
        // be larger/smaller or equal. For example:
        // umin(i8 %x, i8 255) --> %x
        if (*C == getMaxMinLimit(getInverseMinMaxIntrinsic(IID), BitWidth))
          return Op0;
  
        // Remove nested call if constant operands allow it. Example:
        // max (max X, 7), 5 -> max X, 7
        auto *MinMax0 = dyn_cast<IntrinsicInst>(Op0);
        if (MinMax0 && MinMax0->getIntrinsicID() == IID) {
          // TODO: loosen undef/splat restrictions for vector constants.
          Value *M00 = MinMax0->getOperand(0), *M01 = MinMax0->getOperand(1);
          const APInt *InnerC;
          if ((match(M00, m_APInt(InnerC)) || match(M01, m_APInt(InnerC))) &&
              ((IID == Intrinsic::smax && InnerC->sge(*C)) ||
               (IID == Intrinsic::smin && InnerC->sle(*C)) ||
               (IID == Intrinsic::umax && InnerC->uge(*C)) ||
               (IID == Intrinsic::umin && InnerC->ule(*C))))
            return Op0;
        }
      }
  
      if (Value *V = foldMinMaxSharedOp(IID, Op0, Op1))
        return V;
      if (Value *V = foldMinMaxSharedOp(IID, Op1, Op0))
        return V;
  
      ICmpInst::Predicate Pred = getMaxMinPredicate(IID);
      if (isICmpTrue(Pred, Op0, Op1, Q.getWithoutUndef(), RecursionLimit))
        return Op0;
      if (isICmpTrue(Pred, Op1, Op0, Q.getWithoutUndef(), RecursionLimit))
        return Op1;
  
      if (Optional<bool> Imp =
              isImpliedByDomCondition(Pred, Op0, Op1, Q.CxtI, Q.DL))
        return *Imp ? Op0 : Op1;
      if (Optional<bool> Imp =
              isImpliedByDomCondition(Pred, Op1, Op0, Q.CxtI, Q.DL))
        return *Imp ? Op1 : Op0;
  
      break;
    }
    case Intrinsic::usub_with_overflow:
    case Intrinsic::ssub_with_overflow:
      // X - X -> { 0, false }
      // X - undef -> { 0, false }
      // undef - X -> { 0, false }
      if (Op0 == Op1 || Q.isUndefValue(Op0) || Q.isUndefValue(Op1))
        return Constant::getNullValue(ReturnType);
      break;
    case Intrinsic::uadd_with_overflow:
    case Intrinsic::sadd_with_overflow:
      // X + undef -> { -1, false }
      // undef + x -> { -1, false }
      if (Q.isUndefValue(Op0) || Q.isUndefValue(Op1)) {
        return ConstantStruct::get(
            cast<StructType>(ReturnType),
            {Constant::getAllOnesValue(ReturnType->getStructElementType(0)),
             Constant::getNullValue(ReturnType->getStructElementType(1))});
      }
      break;
    case Intrinsic::umul_with_overflow:
    case Intrinsic::smul_with_overflow:
      // 0 * X -> { 0, false }
      // X * 0 -> { 0, false }
      if (match(Op0, m_Zero()) || match(Op1, m_Zero()))
        return Constant::getNullValue(ReturnType);
      // undef * X -> { 0, false }
      // X * undef -> { 0, false }
      if (Q.isUndefValue(Op0) || Q.isUndefValue(Op1))
        return Constant::getNullValue(ReturnType);
      break;
    case Intrinsic::uadd_sat:
      // sat(MAX + X) -> MAX
      // sat(X + MAX) -> MAX
      if (match(Op0, m_AllOnes()) || match(Op1, m_AllOnes()))
        return Constant::getAllOnesValue(ReturnType);
      LLVM_FALLTHROUGH;
    case Intrinsic::sadd_sat:
      // sat(X + undef) -> -1
      // sat(undef + X) -> -1
      // For unsigned: Assume undef is MAX, thus we saturate to MAX (-1).
      // For signed: Assume undef is ~X, in which case X + ~X = -1.
      if (Q.isUndefValue(Op0) || Q.isUndefValue(Op1))
        return Constant::getAllOnesValue(ReturnType);
  
      // X + 0 -> X
      if (match(Op1, m_Zero()))
        return Op0;
      // 0 + X -> X
      if (match(Op0, m_Zero()))
        return Op1;
      break;
    case Intrinsic::usub_sat:
      // sat(0 - X) -> 0, sat(X - MAX) -> 0
      if (match(Op0, m_Zero()) || match(Op1, m_AllOnes()))
        return Constant::getNullValue(ReturnType);
      LLVM_FALLTHROUGH;
    case Intrinsic::ssub_sat:
      // X - X -> 0, X - undef -> 0, undef - X -> 0
      if (Op0 == Op1 || Q.isUndefValue(Op0) || Q.isUndefValue(Op1))
        return Constant::getNullValue(ReturnType);
      // X - 0 -> X
      if (match(Op1, m_Zero()))
        return Op0;
      break;
    case Intrinsic::load_relative:
      if (auto *C0 = dyn_cast<Constant>(Op0))
        if (auto *C1 = dyn_cast<Constant>(Op1))
          return SimplifyRelativeLoad(C0, C1, Q.DL);
      break;
    case Intrinsic::powi:
      if (auto *Power = dyn_cast<ConstantInt>(Op1)) {
        // powi(x, 0) -> 1.0
        if (Power->isZero())
          return ConstantFP::get(Op0->getType(), 1.0);
        // powi(x, 1) -> x
        if (Power->isOne())
          return Op0;
      }
      break;
    case Intrinsic::copysign:
      // copysign X, X --> X
      if (Op0 == Op1)
        return Op0;
      // copysign -X, X --> X
      // copysign X, -X --> -X
      if (match(Op0, m_FNeg(m_Specific(Op1))) ||
          match(Op1, m_FNeg(m_Specific(Op0))))
        return Op1;
      break;
    case Intrinsic::maxnum:
    case Intrinsic::minnum:
    case Intrinsic::maximum:
    case Intrinsic::minimum: {
      // If the arguments are the same, this is a no-op.
      if (Op0 == Op1) return Op0;
  
      // Canonicalize constant operand as Op1.
      if (isa<Constant>(Op0))
        std::swap(Op0, Op1);
  
      // If an argument is undef, return the other argument.
      if (Q.isUndefValue(Op1))
        return Op0;
  
      bool PropagateNaN = IID == Intrinsic::minimum || IID == Intrinsic::maximum;
      bool IsMin = IID == Intrinsic::minimum || IID == Intrinsic::minnum;
  
      // minnum(X, nan) -> X
      // maxnum(X, nan) -> X
      // minimum(X, nan) -> nan
      // maximum(X, nan) -> nan
      if (match(Op1, m_NaN()))
        return PropagateNaN ? propagateNaN(cast<Constant>(Op1)) : Op0;
  
      // In the following folds, inf can be replaced with the largest finite
      // float, if the ninf flag is set.
      const APFloat *C;
      if (match(Op1, m_APFloat(C)) &&
          (C->isInfinity() || (Q.CxtI->hasNoInfs() && C->isLargest()))) {
        // minnum(X, -inf) -> -inf
        // maxnum(X, +inf) -> +inf
        // minimum(X, -inf) -> -inf if nnan
        // maximum(X, +inf) -> +inf if nnan
        if (C->isNegative() == IsMin && (!PropagateNaN || Q.CxtI->hasNoNaNs()))
          return ConstantFP::get(ReturnType, *C);
  
        // minnum(X, +inf) -> X if nnan
        // maxnum(X, -inf) -> X if nnan
        // minimum(X, +inf) -> X
        // maximum(X, -inf) -> X
        if (C->isNegative() != IsMin && (PropagateNaN || Q.CxtI->hasNoNaNs()))
          return Op0;
      }
  
      // Min/max of the same operation with common operand:
      // m(m(X, Y)), X --> m(X, Y) (4 commuted variants)
      if (auto *M0 = dyn_cast<IntrinsicInst>(Op0))
        if (M0->getIntrinsicID() == IID &&
            (M0->getOperand(0) == Op1 || M0->getOperand(1) == Op1))
          return Op0;
      if (auto *M1 = dyn_cast<IntrinsicInst>(Op1))
        if (M1->getIntrinsicID() == IID &&
            (M1->getOperand(0) == Op0 || M1->getOperand(1) == Op0))
          return Op1;
  
      break;
    }
    case Intrinsic::experimental_vector_extract: {
      Type *ReturnType = F->getReturnType();
  
      // (extract_vector (insert_vector _, X, 0), 0) -> X
      unsigned IdxN = cast<ConstantInt>(Op1)->getZExtValue();
      Value *X = nullptr;
      if (match(Op0, m_Intrinsic<Intrinsic::experimental_vector_insert>(
                         m_Value(), m_Value(X), m_Zero())) &&
          IdxN == 0 && X->getType() == ReturnType)
        return X;
  
      break;
    }
    default:
      break;
    }
  
    return nullptr;
  }
  
  static Value *simplifyIntrinsic(CallBase *Call, const SimplifyQuery &Q) {
  
    // Intrinsics with no operands have some kind of side effect. Don't simplify.
    unsigned NumOperands = Call->getNumArgOperands();
    if (!NumOperands)
      return nullptr;
  
    Function *F = cast<Function>(Call->getCalledFunction());
    Intrinsic::ID IID = F->getIntrinsicID();
    if (NumOperands == 1)
      return simplifyUnaryIntrinsic(F, Call->getArgOperand(0), Q);
  
    if (NumOperands == 2)
      return simplifyBinaryIntrinsic(F, Call->getArgOperand(0),
                                     Call->getArgOperand(1), Q);
  
    // Handle intrinsics with 3 or more arguments.
    switch (IID) {
    case Intrinsic::masked_load:
    case Intrinsic::masked_gather: {
      Value *MaskArg = Call->getArgOperand(2);
      Value *PassthruArg = Call->getArgOperand(3);
      // If the mask is all zeros or undef, the "passthru" argument is the result.
      if (maskIsAllZeroOrUndef(MaskArg))
        return PassthruArg;
      return nullptr;
    }
    case Intrinsic::fshl:
    case Intrinsic::fshr: {
      Value *Op0 = Call->getArgOperand(0), *Op1 = Call->getArgOperand(1),
            *ShAmtArg = Call->getArgOperand(2);
  
      // If both operands are undef, the result is undef.
      if (Q.isUndefValue(Op0) && Q.isUndefValue(Op1))
        return UndefValue::get(F->getReturnType());
  
      // If shift amount is undef, assume it is zero.
      if (Q.isUndefValue(ShAmtArg))
        return Call->getArgOperand(IID == Intrinsic::fshl ? 0 : 1);
  
      const APInt *ShAmtC;
      if (match(ShAmtArg, m_APInt(ShAmtC))) {
        // If there's effectively no shift, return the 1st arg or 2nd arg.
        APInt BitWidth = APInt(ShAmtC->getBitWidth(), ShAmtC->getBitWidth());
        if (ShAmtC->urem(BitWidth).isNullValue())
          return Call->getArgOperand(IID == Intrinsic::fshl ? 0 : 1);
      }
      return nullptr;
    }
    case Intrinsic::fma:
    case Intrinsic::fmuladd: {
      Value *Op0 = Call->getArgOperand(0);
      Value *Op1 = Call->getArgOperand(1);
      Value *Op2 = Call->getArgOperand(2);
      if (Value *V = simplifyFPOp({ Op0, Op1, Op2 }, {}, Q))
        return V;
      return nullptr;
    }
    case Intrinsic::smul_fix:
    case Intrinsic::smul_fix_sat: {
      Value *Op0 = Call->getArgOperand(0);
      Value *Op1 = Call->getArgOperand(1);
      Value *Op2 = Call->getArgOperand(2);
      Type *ReturnType = F->getReturnType();
  
      // Canonicalize constant operand as Op1 (ConstantFolding handles the case
      // when both Op0 and Op1 are constant so we do not care about that special
      // case here).
      if (isa<Constant>(Op0))
        std::swap(Op0, Op1);
  
      // X * 0 -> 0
      if (match(Op1, m_Zero()))
        return Constant::getNullValue(ReturnType);
  
      // X * undef -> 0
      if (Q.isUndefValue(Op1))
        return Constant::getNullValue(ReturnType);
  
      // X * (1 << Scale) -> X
      APInt ScaledOne =
          APInt::getOneBitSet(ReturnType->getScalarSizeInBits(),
                              cast<ConstantInt>(Op2)->getZExtValue());
      if (ScaledOne.isNonNegative() && match(Op1, m_SpecificInt(ScaledOne)))
        return Op0;
  
      return nullptr;
    }
    case Intrinsic::experimental_vector_insert: {
      Value *Vec = Call->getArgOperand(0);
      Value *SubVec = Call->getArgOperand(1);
      Value *Idx = Call->getArgOperand(2);
      Type *ReturnType = F->getReturnType();
  
      // (insert_vector Y, (extract_vector X, 0), 0) -> X
      // where: Y is X, or Y is undef
      unsigned IdxN = cast<ConstantInt>(Idx)->getZExtValue();
      Value *X = nullptr;
      if (match(SubVec, m_Intrinsic<Intrinsic::experimental_vector_extract>(
                            m_Value(X), m_Zero())) &&
          (Q.isUndefValue(Vec) || Vec == X) && IdxN == 0 &&
          X->getType() == ReturnType)
        return X;
  
      return nullptr;
    }
    default:
      return nullptr;
    }
  }
  
  static Value *tryConstantFoldCall(CallBase *Call, const SimplifyQuery &Q) {
    auto *F = dyn_cast<Function>(Call->getCalledOperand());
    if (!F || !canConstantFoldCallTo(Call, F))
      return nullptr;
  
    SmallVector<Constant *, 4> ConstantArgs;
    unsigned NumArgs = Call->getNumArgOperands();
    ConstantArgs.reserve(NumArgs);
    for (auto &Arg : Call->args()) {
      Constant *C = dyn_cast<Constant>(&Arg);
      if (!C) {
        if (isa<MetadataAsValue>(Arg.get()))
          continue;
        return nullptr;
      }
      ConstantArgs.push_back(C);
    }
  
    return ConstantFoldCall(Call, F, ConstantArgs, Q.TLI);
  }
  
  Value *llvm::SimplifyCall(CallBase *Call, const SimplifyQuery &Q) {
    // musttail calls can only be simplified if they are also DCEd.
    // As we can't guarantee this here, don't simplify them.
    if (Call->isMustTailCall())
      return nullptr;
  
    // call undef -> poison
    // call null -> poison
    Value *Callee = Call->getCalledOperand();
    if (isa<UndefValue>(Callee) || isa<ConstantPointerNull>(Callee))
      return PoisonValue::get(Call->getType());
  
    if (Value *V = tryConstantFoldCall(Call, Q))
      return V;
  
    auto *F = dyn_cast<Function>(Callee);
    if (F && F->isIntrinsic())
      if (Value *Ret = simplifyIntrinsic(Call, Q))
        return Ret;
  
    return nullptr;
  }
  
  /// Given operands for a Freeze, see if we can fold the result.
  static Value *SimplifyFreezeInst(Value *Op0, const SimplifyQuery &Q) {
    // Use a utility function defined in ValueTracking.
    if (llvm::isGuaranteedNotToBeUndefOrPoison(Op0, Q.AC, Q.CxtI, Q.DT))
      return Op0;
    // We have room for improvement.
    return nullptr;
  }
  
  Value *llvm::SimplifyFreezeInst(Value *Op0, const SimplifyQuery &Q) {
    return ::SimplifyFreezeInst(Op0, Q);
  }
  
  static Constant *ConstructLoadOperandConstant(Value *Op) {
    SmallVector<Value *, 4> Worklist;
    // Invalid IR in unreachable code may contain self-referential values. Don't infinitely loop.
    SmallPtrSet<Value *, 4> Visited;
    Worklist.push_back(Op);
    while (true) {
      Value *CurOp = Worklist.back();
      if (!Visited.insert(CurOp).second)
        return nullptr;
      if (isa<Constant>(CurOp))
        break;
      if (auto *BC = dyn_cast<BitCastOperator>(CurOp)) {
        Worklist.push_back(BC->getOperand(0));
      } else if (auto *GEP = dyn_cast<GEPOperator>(CurOp)) {
        for (unsigned I = 1; I != GEP->getNumOperands(); ++I) {
          if (!isa<Constant>(GEP->getOperand(I)))
            return nullptr;
        }
        Worklist.push_back(GEP->getOperand(0));
      } else if (auto *II = dyn_cast<IntrinsicInst>(CurOp)) {
        if (II->isLaunderOrStripInvariantGroup())
          Worklist.push_back(II->getOperand(0));
        else
          return nullptr;
      } else {
        return nullptr;
      }
    }
  
    Constant *NewOp = cast<Constant>(Worklist.pop_back_val());
    while (!Worklist.empty()) {
      Value *CurOp = Worklist.pop_back_val();
      if (isa<BitCastOperator>(CurOp)) {
        NewOp = ConstantExpr::getBitCast(NewOp, CurOp->getType());
      } else if (auto *GEP = dyn_cast<GEPOperator>(CurOp)) {
        SmallVector<Constant *> Idxs;
        Idxs.reserve(GEP->getNumOperands() - 1);
        for (unsigned I = 1, E = GEP->getNumOperands(); I != E; ++I) {
          Idxs.push_back(cast<Constant>(GEP->getOperand(I)));
        }
        NewOp = ConstantExpr::getGetElementPtr(GEP->getSourceElementType(), NewOp,
                                               Idxs, GEP->isInBounds(),
                                               GEP->getInRangeIndex());
      } else {
        assert(isa<IntrinsicInst>(CurOp) &&
               cast<IntrinsicInst>(CurOp)->isLaunderOrStripInvariantGroup() &&
               "expected invariant group intrinsic");
        NewOp = ConstantExpr::getBitCast(NewOp, CurOp->getType());
      }
    }
    return NewOp;
  }
  
  static Value *SimplifyLoadInst(LoadInst *LI, const SimplifyQuery &Q) {
    if (LI->isVolatile())
      return nullptr;
  
    if (auto *C = ConstantFoldInstruction(LI, Q.DL))
      return C;
  
    // The following only catches more cases than ConstantFoldInstruction() if the
    // load operand wasn't a constant. Specifically, invariant.group intrinsics.
    if (isa<Constant>(LI->getPointerOperand()))
      return nullptr;
  
    if (auto *C = dyn_cast_or_null<Constant>(
            ConstructLoadOperandConstant(LI->getPointerOperand())))
      return ConstantFoldLoadFromConstPtr(C, LI->getType(), Q.DL);
  
    return nullptr;
  }
  
  /// See if we can compute a simplified version of this instruction.
  /// If not, this returns null.
  
  Value *llvm::SimplifyInstruction(Instruction *I, const SimplifyQuery &SQ,
                                   OptimizationRemarkEmitter *ORE) {
    const SimplifyQuery Q = SQ.CxtI ? SQ : SQ.getWithInstruction(I);
    Value *Result;
  
    switch (I->getOpcode()) {
    default:
      Result = ConstantFoldInstruction(I, Q.DL, Q.TLI);
      break;
    case Instruction::FNeg:
      Result = SimplifyFNegInst(I->getOperand(0), I->getFastMathFlags(), Q);
      break;
    case Instruction::FAdd:
      Result = SimplifyFAddInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), Q);
      break;
    case Instruction::Add:
      Result =
          SimplifyAddInst(I->getOperand(0), I->getOperand(1),
                          Q.IIQ.hasNoSignedWrap(cast<BinaryOperator>(I)),
                          Q.IIQ.hasNoUnsignedWrap(cast<BinaryOperator>(I)), Q);
      break;
    case Instruction::FSub:
      Result = SimplifyFSubInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), Q);
      break;
    case Instruction::Sub:
      Result =
          SimplifySubInst(I->getOperand(0), I->getOperand(1),
                          Q.IIQ.hasNoSignedWrap(cast<BinaryOperator>(I)),
                          Q.IIQ.hasNoUnsignedWrap(cast<BinaryOperator>(I)), Q);
      break;
    case Instruction::FMul:
      Result = SimplifyFMulInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), Q);
      break;
    case Instruction::Mul:
      Result = SimplifyMulInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::SDiv:
      Result = SimplifySDivInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::UDiv:
      Result = SimplifyUDivInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::FDiv:
      Result = SimplifyFDivInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), Q);
      break;
    case Instruction::SRem:
      Result = SimplifySRemInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::URem:
      Result = SimplifyURemInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::FRem:
      Result = SimplifyFRemInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), Q);
      break;
    case Instruction::Shl:
      Result =
          SimplifyShlInst(I->getOperand(0), I->getOperand(1),
                          Q.IIQ.hasNoSignedWrap(cast<BinaryOperator>(I)),
                          Q.IIQ.hasNoUnsignedWrap(cast<BinaryOperator>(I)), Q);
      break;
    case Instruction::LShr:
      Result = SimplifyLShrInst(I->getOperand(0), I->getOperand(1),
                                Q.IIQ.isExact(cast<BinaryOperator>(I)), Q);
      break;
    case Instruction::AShr:
      Result = SimplifyAShrInst(I->getOperand(0), I->getOperand(1),
                                Q.IIQ.isExact(cast<BinaryOperator>(I)), Q);
      break;
    case Instruction::And:
      Result = SimplifyAndInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::Or:
      Result = SimplifyOrInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::Xor:
      Result = SimplifyXorInst(I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::ICmp:
      Result = SimplifyICmpInst(cast<ICmpInst>(I)->getPredicate(),
                                I->getOperand(0), I->getOperand(1), Q);
      break;
    case Instruction::FCmp:
      Result =
          SimplifyFCmpInst(cast<FCmpInst>(I)->getPredicate(), I->getOperand(0),
                           I->getOperand(1), I->getFastMathFlags(), Q);
      break;
    case Instruction::Select:
      Result = SimplifySelectInst(I->getOperand(0), I->getOperand(1),
                                  I->getOperand(2), Q);
      break;
    case Instruction::GetElementPtr: {
      SmallVector<Value *, 8> Ops(I->operands());
      Result = SimplifyGEPInst(cast<GetElementPtrInst>(I)->getSourceElementType(),
                               Ops, Q);
      break;
    }
    case Instruction::InsertValue: {
      InsertValueInst *IV = cast<InsertValueInst>(I);
      Result = SimplifyInsertValueInst(IV->getAggregateOperand(),
                                       IV->getInsertedValueOperand(),
                                       IV->getIndices(), Q);
      break;
    }
    case Instruction::InsertElement: {
      auto *IE = cast<InsertElementInst>(I);
      Result = SimplifyInsertElementInst(IE->getOperand(0), IE->getOperand(1),
                                         IE->getOperand(2), Q);
      break;
    }
    case Instruction::ExtractValue: {
      auto *EVI = cast<ExtractValueInst>(I);
      Result = SimplifyExtractValueInst(EVI->getAggregateOperand(),
                                        EVI->getIndices(), Q);
      break;
    }
    case Instruction::ExtractElement: {
      auto *EEI = cast<ExtractElementInst>(I);
      Result = SimplifyExtractElementInst(EEI->getVectorOperand(),
                                          EEI->getIndexOperand(), Q);
      break;
    }
    case Instruction::ShuffleVector: {
      auto *SVI = cast<ShuffleVectorInst>(I);
      Result =
          SimplifyShuffleVectorInst(SVI->getOperand(0), SVI->getOperand(1),
                                    SVI->getShuffleMask(), SVI->getType(), Q);
      break;
    }
    case Instruction::PHI:
      Result = SimplifyPHINode(cast<PHINode>(I), Q);
      break;
    case Instruction::Call: {
      Result = SimplifyCall(cast<CallInst>(I), Q);
      break;
    }
    case Instruction::Freeze:
      Result = SimplifyFreezeInst(I->getOperand(0), Q);
      break;
  #define HANDLE_CAST_INST(num, opc, clas) case Instruction::opc:
  #include "llvm/IR/Instruction.def"
  #undef HANDLE_CAST_INST
      Result =
          SimplifyCastInst(I->getOpcode(), I->getOperand(0), I->getType(), Q);
      break;
    case Instruction::Alloca:
      // No simplifications for Alloca and it can't be constant folded.
      Result = nullptr;
      break;
    case Instruction::Load:
      Result = SimplifyLoadInst(cast<LoadInst>(I), Q);
      break;
    }
  
    /// If called on unreachable code, the above logic may report that the
    /// instruction simplified to itself.  Make life easier for users by
    /// detecting that case here, returning a safe value instead.
    return Result == I ? UndefValue::get(I->getType()) : Result;
  }
  
  /// Implementation of recursive simplification through an instruction's
  /// uses.
  ///
  /// This is the common implementation of the recursive simplification routines.
  /// If we have a pre-simplified value in 'SimpleV', that is forcibly used to
  /// replace the instruction 'I'. Otherwise, we simply add 'I' to the list of
  /// instructions to process and attempt to simplify it using
  /// InstructionSimplify. Recursively visited users which could not be
  /// simplified themselves are to the optional UnsimplifiedUsers set for
  /// further processing by the caller.
  ///
  /// This routine returns 'true' only when *it* simplifies something. The passed
  /// in simplified value does not count toward this.
  static bool replaceAndRecursivelySimplifyImpl(
      Instruction *I, Value *SimpleV, const TargetLibraryInfo *TLI,
      const DominatorTree *DT, AssumptionCache *AC,
      SmallSetVector<Instruction *, 8> *UnsimplifiedUsers = nullptr) {
    bool Simplified = false;
    SmallSetVector<Instruction *, 8> Worklist;
    const DataLayout &DL = I->getModule()->getDataLayout();
  
    // If we have an explicit value to collapse to, do that round of the
    // simplification loop by hand initially.
    if (SimpleV) {
      for (User *U : I->users())
        if (U != I)
          Worklist.insert(cast<Instruction>(U));
  
      // Replace the instruction with its simplified value.
      I->replaceAllUsesWith(SimpleV);
  
      // Gracefully handle edge cases where the instruction is not wired into any
      // parent block.
      if (I->getParent() && !I->isEHPad() && !I->isTerminator() &&
          !I->mayHaveSideEffects())
        I->eraseFromParent();
    } else {
      Worklist.insert(I);
    }
  
    // Note that we must test the size on each iteration, the worklist can grow.
    for (unsigned Idx = 0; Idx != Worklist.size(); ++Idx) {
      I = Worklist[Idx];
  
      // See if this instruction simplifies.
      SimpleV = SimplifyInstruction(I, {DL, TLI, DT, AC});
      if (!SimpleV) {
        if (UnsimplifiedUsers)
          UnsimplifiedUsers->insert(I);
        continue;
      }
  
      Simplified = true;
  
      // Stash away all the uses of the old instruction so we can check them for
      // recursive simplifications after a RAUW. This is cheaper than checking all
      // uses of To on the recursive step in most cases.
      for (User *U : I->users())
        Worklist.insert(cast<Instruction>(U));
  
      // Replace the instruction with its simplified value.
      I->replaceAllUsesWith(SimpleV);
  
      // Gracefully handle edge cases where the instruction is not wired into any
      // parent block.
      if (I->getParent() && !I->isEHPad() && !I->isTerminator() &&
          !I->mayHaveSideEffects())
        I->eraseFromParent();
    }
    return Simplified;
  }
  
  bool llvm::replaceAndRecursivelySimplify(
      Instruction *I, Value *SimpleV, const TargetLibraryInfo *TLI,
      const DominatorTree *DT, AssumptionCache *AC,
      SmallSetVector<Instruction *, 8> *UnsimplifiedUsers) {
    assert(I != SimpleV && "replaceAndRecursivelySimplify(X,X) is not valid!");
    assert(SimpleV && "Must provide a simplified value.");
    return replaceAndRecursivelySimplifyImpl(I, SimpleV, TLI, DT, AC,
                                             UnsimplifiedUsers);
  }
  
  namespace llvm {
  const SimplifyQuery getBestSimplifyQuery(Pass &P, Function &F) {
    auto *DTWP = P.getAnalysisIfAvailable<DominatorTreeWrapperPass>();
    auto *DT = DTWP ? &DTWP->getDomTree() : nullptr;
    auto *TLIWP = P.getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
    auto *TLI = TLIWP ? &TLIWP->getTLI(F) : nullptr;
    auto *ACWP = P.getAnalysisIfAvailable<AssumptionCacheTracker>();
    auto *AC = ACWP ? &ACWP->getAssumptionCache(F) : nullptr;
    return {F.getParent()->getDataLayout(), TLI, DT, AC};
  }
  
  const SimplifyQuery getBestSimplifyQuery(LoopStandardAnalysisResults &AR,
                                           const DataLayout &DL) {
    return {DL, &AR.TLI, &AR.DT, &AR.AC};
  }
  
  template <class T, class... TArgs>
  const SimplifyQuery getBestSimplifyQuery(AnalysisManager<T, TArgs...> &AM,
                                           Function &F) {
    auto *DT = AM.template getCachedResult<DominatorTreeAnalysis>(F);
    auto *TLI = AM.template getCachedResult<TargetLibraryAnalysis>(F);
    auto *AC = AM.template getCachedResult<AssumptionAnalysis>(F);
    return {F.getParent()->getDataLayout(), TLI, DT, AC};
  }
  template const SimplifyQuery getBestSimplifyQuery(AnalysisManager<Function> &,
                                                    Function &);
  }
  