text: //===- InstructionSimplify.cpp - Fold instruction operands ----------------===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // 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/Statistic.h"
  #include "llvm/Analysis/AliasAnalysis.h"
  #include "llvm/Analysis/ConstantFolding.h"
  #include "llvm/Analysis/MemoryBuiltins.h"
  #include "llvm/Analysis/ValueTracking.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/Operator.h"
  #include "llvm/IR/PatternMatch.h"
  #include "llvm/IR/ValueHandle.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");
  
  namespace {
  struct Query {
    const DataLayout &DL;
    const TargetLibraryInfo *TLI;
    const DominatorTree *DT;
    AssumptionCache *AC;
    const Instruction *CxtI;
  
    Query(const DataLayout &DL, const TargetLibraryInfo *tli,
          const DominatorTree *dt, AssumptionCache *ac = nullptr,
          const Instruction *cxti = nullptr)
        : DL(DL), TLI(tli), DT(dt), AC(ac), CxtI(cxti) {}
  };
  } // end anonymous namespace
  
  static Value *SimplifyAndInst(Value *, Value *, const Query &, unsigned);
  static Value *SimplifyBinOp(unsigned, Value *, Value *, const Query &,
                              unsigned);
  static Value *SimplifyFPBinOp(unsigned, Value *, Value *, const FastMathFlags &,
                                const Query &, unsigned);
  static Value *SimplifyCmpInst(unsigned, Value *, Value *, const Query &,
                                unsigned);
  static Value *SimplifyOrInst(Value *, Value *, const Query &, unsigned);
  static Value *SimplifyXorInst(Value *, Value *, const Query &, unsigned);
  static Value *SimplifyTruncInst(Value *, Type *, const Query &, unsigned);
  
  /// getFalse - For a boolean type, or a vector of boolean type, return false, or
  /// a vector with every element false, as appropriate for the type.
  static Constant *getFalse(Type *Ty) {
    assert(Ty->getScalarType()->isIntegerTy(1) &&
           "Expected i1 type or a vector of i1!");
    return Constant::getNullValue(Ty);
  }
  
  /// getTrue - For a boolean type, or a vector of boolean type, return true, or
  /// a vector with every element true, as appropriate for the type.
  static Constant *getTrue(Type *Ty) {
    assert(Ty->getScalarType()->isIntegerTy(1) &&
           "Expected i1 type or a vector of i1!");
    return Constant::getAllOnesValue(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;
  }
  
  /// ValueDominatesPHI - 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->getParent()->getParent())
      return false;
  
    // If we have a DominatorTree then do a precise test.
    if (DT) {
      if (!DT->isReachableFromEntry(P->getParent()))
        return true;
      if (!DT->isReachableFromEntry(I->getParent()))
        return false;
      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() == &I->getParent()->getParent()->getEntryBlock() &&
        !isa<InvokeInst>(I))
      return true;
  
    return false;
  }
  
  /// ExpandBinOp - Simplify "A op (B op' C)" by distributing op over op', turning
  /// it into "(A op B) op' (A op C)".  Here "op" is given by Opcode and "op'" is
  /// given by OpcodeToExpand, while "A" corresponds to LHS and "B op' C" to RHS.
  /// Also performs the transform "(A op' B) op C" -> "(A op C) op' (B op C)".
  /// Returns the simplified value, or null if no simplification was performed.
  static Value *ExpandBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                            unsigned OpcToExpand, const Query &Q,
                            unsigned MaxRecurse) {
    Instruction::BinaryOps OpcodeToExpand = (Instruction::BinaryOps)OpcToExpand;
    // Recursion is always used, so bail out at once if we already hit the limit.
    if (!MaxRecurse--)
      return nullptr;
  
    // Check whether the expression has the form "(A op' B) op C".
    if (BinaryOperator *Op0 = dyn_cast<BinaryOperator>(LHS))
      if (Op0->getOpcode() == OpcodeToExpand) {
        // It does!  Try turning it into "(A op C) op' (B op C)".
        Value *A = Op0->getOperand(0), *B = Op0->getOperand(1), *C = RHS;
        // Do "A op C" and "B op C" both simplify?
        if (Value *L = SimplifyBinOp(Opcode, A, C, Q, MaxRecurse))
          if (Value *R = SimplifyBinOp(Opcode, B, C, Q, MaxRecurse)) {
            // They do! Return "L op' R" if it simplifies or is already available.
            // If "L op' R" equals "A op' B" then "L op' R" is just the LHS.
            if ((L == A && R == B) || (Instruction::isCommutative(OpcodeToExpand)
                                       && L == B && R == A)) {
              ++NumExpand;
              return LHS;
            }
            // Otherwise return "L op' R" if it simplifies.
            if (Value *V = SimplifyBinOp(OpcodeToExpand, L, R, Q, MaxRecurse)) {
              ++NumExpand;
              return V;
            }
          }
      }
  
    // Check whether the expression has the form "A op (B op' C)".
    if (BinaryOperator *Op1 = dyn_cast<BinaryOperator>(RHS))
      if (Op1->getOpcode() == OpcodeToExpand) {
        // It does!  Try turning it into "(A op B) op' (A op C)".
        Value *A = LHS, *B = Op1->getOperand(0), *C = Op1->getOperand(1);
        // Do "A op B" and "A op C" both simplify?
        if (Value *L = SimplifyBinOp(Opcode, A, B, Q, MaxRecurse))
          if (Value *R = SimplifyBinOp(Opcode, A, C, Q, MaxRecurse)) {
            // They do! Return "L op' R" if it simplifies or is already available.
            // If "L op' R" equals "B op' C" then "L op' R" is just the RHS.
            if ((L == B && R == C) || (Instruction::isCommutative(OpcodeToExpand)
                                       && L == C && R == B)) {
              ++NumExpand;
              return RHS;
            }
            // Otherwise return "L op' R" if it simplifies.
            if (Value *V = SimplifyBinOp(OpcodeToExpand, L, R, Q, MaxRecurse)) {
              ++NumExpand;
              return V;
            }
          }
      }
  
    return nullptr;
  }
  
  /// SimplifyAssociativeBinOp - Generic simplifications for associative binary
  /// operations.  Returns the simpler value, or null if none was found.
  static Value *SimplifyAssociativeBinOp(unsigned Opc, Value *LHS, Value *RHS,
                                         const Query &Q, unsigned MaxRecurse) {
    Instruction::BinaryOps Opcode = (Instruction::BinaryOps)Opc;
    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;
  }
  
  /// ThreadBinOpOverSelect - 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(unsigned Opcode, Value *LHS, Value *RHS,
                                      const Query &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 && isa<UndefValue>(TV))
      return FV;
    if (FV && isa<UndefValue>(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() == 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;
  }
  
  /// ThreadCmpOverSelect - 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.
  static Value *ThreadCmpOverSelect(CmpInst::Predicate Pred, Value *LHS,
                                    Value *RHS, const Query &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 = SimplifyCmpInst(Pred, TV, RHS, Q, MaxRecurse);
    if (TCmp == Cond) {
      // It not only simplified, it simplified to the select condition.  Replace
      // it with 'true'.
      TCmp = getTrue(Cond->getType());
    } else if (!TCmp) {
      // It didn't simplify.  However if "cmp TV, RHS" is equal to the select
      // condition then we can replace it with 'true'.  Otherwise give up.
      if (!isSameCompare(Cond, Pred, TV, RHS))
        return nullptr;
      TCmp = getTrue(Cond->getType());
    }
  
    // Does "cmp FV, RHS" simplify?
    Value *FCmp = SimplifyCmpInst(Pred, FV, RHS, Q, MaxRecurse);
    if (FCmp == Cond) {
      // It not only simplified, it simplified to the select condition.  Replace
      // it with 'false'.
      FCmp = getFalse(Cond->getType());
    } else if (!FCmp) {
      // It didn't simplify.  However if "cmp FV, RHS" is equal to the select
      // condition then we can replace it with 'false'.  Otherwise give up.
      if (!isSameCompare(Cond, Pred, FV, RHS))
        return nullptr;
      FCmp = getFalse(Cond->getType());
    }
  
    // 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 nullptr;
    // 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;
  }
  
  /// ThreadBinOpOverPHI - 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(unsigned Opcode, Value *LHS, Value *RHS,
                                   const Query &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 (unsigned i = 0, e = PI->getNumIncomingValues(); i != e; ++i) {
      Value *Incoming = PI->getIncomingValue(i);
      // 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;
  }
  
  /// ThreadCmpOverPHI - In the case of a comparison with a PHI instruction, try
  /// 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 Query &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 i = 0, e = PI->getNumIncomingValues(); i != e; ++i) {
      Value *Incoming = PI->getIncomingValue(i);
      // If the incoming value is the phi node itself, it can safely be skipped.
      if (Incoming == PI) continue;
      Value *V = SimplifyCmpInst(Pred, Incoming, RHS, 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;
  }
  
  /// SimplifyAddInst - 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 Query &Q, unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::Add, CLHS->getType(), Ops,
                                        Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
    }
  
    // X + undef -> undef
    if (match(Op1, m_Undef()))
      return Op1;
  
    // X + 0 -> X
    if (match(Op1, m_Zero()))
      return Op0;
  
    // 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
    if (match(Op0, m_Not(m_Specific(Op1))) ||
        match(Op1, m_Not(m_Specific(Op0))))
      return Constant::getAllOnesValue(Op0->getType());
  
    /// i1 add -> xor.
    if (MaxRecurse && Op0->getType()->isIntegerTy(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 DataLayout &DL, const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyAddInst(Op0, Op1, isNSW, isNUW, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  /// \brief 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()->getScalarType()->isPointerTy());
  
    Type *IntPtrTy = DL.getIntPtrType(V->getType())->getScalarType();
    APInt Offset = APInt::getNullValue(IntPtrTy->getIntegerBitWidth());
  
    // Even though we don't look through PHI nodes, we could be called on an
    // instruction in an unreachable block, which may be on a cycle.
    SmallPtrSet<Value *, 4> Visited;
    Visited.insert(V);
    do {
      if (GEPOperator *GEP = dyn_cast<GEPOperator>(V)) {
        if ((!AllowNonInbounds && !GEP->isInBounds()) ||
            !GEP->accumulateConstantOffset(DL, Offset))
          break;
        V = GEP->getPointerOperand();
      } else if (Operator::getOpcode(V) == Instruction::BitCast) {
        V = cast<Operator>(V)->getOperand(0);
      } else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
        if (GA->mayBeOverridden())
          break;
        V = GA->getAliasee();
      } else {
        break;
      }
      assert(V->getType()->getScalarType()->isPointerTy() &&
             "Unexpected operand type!");
    } while (Visited.insert(V).second);
  
    Constant *OffsetIntPtr = ConstantInt::get(IntPtrTy, Offset);
    if (V->getType()->isVectorTy())
      return ConstantVector::getSplat(V->getType()->getVectorNumElements(),
                                      OffsetIntPtr);
    return OffsetIntPtr;
  }
  
  /// \brief 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);
  }
  
  /// SimplifySubInst - 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 Query &Q, unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0))
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::Sub, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
    // X - undef -> undef
    // undef - X -> undef
    if (match(Op0, m_Undef()) || match(Op1, m_Undef()))
      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());
  
    // 0 - X -> 0 if the sub is NUW.
    if (isNUW && match(Op0, m_Zero()))
      return Op0;
  
    // (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 = SimplifyTruncInst(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()->isIntegerTy(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 DataLayout &DL, const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifySubInst(Op0, Op1, isNSW, isNUW, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  /// 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 Query &Q, unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::FAdd, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
    }
  
    // fadd X, -0 ==> X
    if (match(Op1, m_NegZero()))
      return Op0;
  
    // fadd X, 0 ==> X, when we know X is not -0
    if (match(Op1, m_Zero()) &&
        (FMF.noSignedZeros() || CannotBeNegativeZero(Op0)))
      return Op0;
  
    // fadd [nnan ninf] X, (fsub [nnan ninf] 0, X) ==> 0
    //   where nnan and ninf have to occur at least once somewhere in this
    //   expression
    Value *SubOp = nullptr;
    if (match(Op1, m_FSub(m_AnyZero(), m_Specific(Op0))))
      SubOp = Op1;
    else if (match(Op0, m_FSub(m_AnyZero(), m_Specific(Op1))))
      SubOp = Op0;
    if (SubOp) {
      Instruction *FSub = cast<Instruction>(SubOp);
      if ((FMF.noNaNs() || FSub->hasNoNaNs()) &&
          (FMF.noInfs() || FSub->hasNoInfs()))
        return Constant::getNullValue(Op0->getType());
    }
  
    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 Query &Q, unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::FSub, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
    }
  
    // fsub X, 0 ==> X
    if (match(Op1, m_Zero()))
      return Op0;
  
    // fsub X, -0 ==> X, when we know X is not -0
    if (match(Op1, m_NegZero()) &&
        (FMF.noSignedZeros() || CannotBeNegativeZero(Op0)))
      return Op0;
  
    // fsub 0, (fsub -0.0, X) ==> X
    Value *X;
    if (match(Op0, m_AnyZero())) {
      if (match(Op1, m_FSub(m_NegZero(), m_Value(X))))
        return X;
      if (FMF.noSignedZeros() && match(Op1, m_FSub(m_AnyZero(), m_Value(X))))
        return X;
    }
  
    // fsub nnan ninf x, x ==> 0.0
    if (FMF.noNaNs() && FMF.noInfs() && Op0 == Op1)
      return Constant::getNullValue(Op0->getType());
  
    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 Query &Q,
                                 unsigned MaxRecurse) {
   if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::FMul, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
   }
  
   // fmul X, 1.0 ==> X
   if (match(Op1, m_FPOne()))
     return Op0;
  
   // fmul nnan nsz X, 0 ==> 0
   if (FMF.noNaNs() && FMF.noSignedZeros() && match(Op1, m_AnyZero()))
     return Op1;
  
   return nullptr;
  }
  
  /// SimplifyMulInst - 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 Query &Q,
                                unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::Mul, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
    }
  
    // X * undef -> 0
    if (match(Op1, m_Undef()))
      return Constant::getNullValue(Op0->getType());
  
    // X * 0 -> 0
    if (match(Op1, m_Zero()))
      return Op1;
  
    // X * 1 -> X
    if (match(Op1, m_One()))
      return Op0;
  
    // (X / Y) * Y -> X if the division is exact.
    Value *X = nullptr;
    if (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()->isIntegerTy(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 = ExpandBinOp(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::SimplifyFAddInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyFAddInst(Op0, Op1, FMF, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  Value *llvm::SimplifyFSubInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyFSubInst(Op0, Op1, FMF, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  Value *llvm::SimplifyFMulInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyFMulInst(Op0, Op1, FMF, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  Value *llvm::SimplifyMulInst(Value *Op0, Value *Op1, const DataLayout &DL,
                               const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyMulInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  /// SimplifyDiv - Given operands for an SDiv or UDiv, see if we can
  /// fold the result.  If not, this returns null.
  static Value *SimplifyDiv(Instruction::BinaryOps Opcode, Value *Op0, Value *Op1,
                            const Query &Q, unsigned MaxRecurse) {
    if (Constant *C0 = dyn_cast<Constant>(Op0)) {
      if (Constant *C1 = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { C0, C1 };
        return ConstantFoldInstOperands(Opcode, C0->getType(), Ops, Q.DL, Q.TLI);
      }
    }
  
    bool isSigned = Opcode == Instruction::SDiv;
  
    // X / undef -> undef
    if (match(Op1, m_Undef()))
      return Op1;
  
    // X / 0 -> undef, we don't need to preserve faults!
    if (match(Op1, m_Zero()))
      return UndefValue::get(Op1->getType());
  
    // undef / X -> 0
    if (match(Op0, m_Undef()))
      return Constant::getNullValue(Op0->getType());
  
    // 0 / X -> 0, we don't need to preserve faults!
    if (match(Op0, m_Zero()))
      return Op0;
  
    // X / 1 -> X
    if (match(Op1, m_One()))
      return Op0;
  
    if (Op0->getType()->isIntegerTy(1))
      // It can't be division by zero, hence it must be division by one.
      return Op0;
  
    // X / X -> 1
    if (Op0 == Op1)
      return ConstantInt::get(Op0->getType(), 1);
  
    // (X * Y) / Y -> X if the multiplication does not overflow.
    Value *X = nullptr, *Y = nullptr;
    if (match(Op0, m_Mul(m_Value(X), m_Value(Y))) && (X == Op1 || Y == Op1)) {
      if (Y != Op1) std::swap(X, Y); // Ensure expression is (X * Y) / Y, Y = Op1
      OverflowingBinaryOperator *Mul = cast<OverflowingBinaryOperator>(Op0);
      // If the Mul knows it does not overflow, then we are good to go.
      if ((isSigned && Mul->hasNoSignedWrap()) ||
          (!isSigned && Mul->hasNoUnsignedWrap()))
        return X;
      // If X has the form X = A / Y then X * Y cannot overflow.
      if (BinaryOperator *Div = dyn_cast<BinaryOperator>(X))
        if (Div->getOpcode() == Opcode && Div->getOperand(1) == Y)
          return X;
    }
  
    // (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(X), m_ConstantInt(C1))) &&
        match(Op1, m_ConstantInt(C2))) {
      bool Overflow;
      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;
  
    return nullptr;
  }
  
  /// SimplifySDivInst - 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 Query &Q,
                                 unsigned MaxRecurse) {
    if (Value *V = SimplifyDiv(Instruction::SDiv, Op0, Op1, Q, MaxRecurse))
      return V;
  
    return nullptr;
  }
  
  Value *llvm::SimplifySDivInst(Value *Op0, Value *Op1, const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifySDivInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// SimplifyUDivInst - 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 Query &Q,
                                 unsigned MaxRecurse) {
    if (Value *V = SimplifyDiv(Instruction::UDiv, Op0, Op1, Q, MaxRecurse))
      return V;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyUDivInst(Value *Op0, Value *Op1, const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyUDivInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  static Value *SimplifyFDivInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const Query &Q, unsigned) {
    // undef / X -> undef    (the undef could be a snan).
    if (match(Op0, m_Undef()))
      return Op0;
  
    // X / undef -> undef
    if (match(Op1, m_Undef()))
      return Op1;
  
    // 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_AnyZero()))
      return Op0;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyFDivInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyFDivInst(Op0, Op1, FMF, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// SimplifyRem - Given operands for an SRem or URem, see if we can
  /// fold the result.  If not, this returns null.
  static Value *SimplifyRem(Instruction::BinaryOps Opcode, Value *Op0, Value *Op1,
                            const Query &Q, unsigned MaxRecurse) {
    if (Constant *C0 = dyn_cast<Constant>(Op0)) {
      if (Constant *C1 = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { C0, C1 };
        return ConstantFoldInstOperands(Opcode, C0->getType(), Ops, Q.DL, Q.TLI);
      }
    }
  
    // X % undef -> undef
    if (match(Op1, m_Undef()))
      return Op1;
  
    // undef % X -> 0
    if (match(Op0, m_Undef()))
      return Constant::getNullValue(Op0->getType());
  
    // 0 % X -> 0, we don't need to preserve faults!
    if (match(Op0, m_Zero()))
      return Op0;
  
    // X % 0 -> undef, we don't need to preserve faults!
    if (match(Op1, m_Zero()))
      return UndefValue::get(Op0->getType());
  
    // X % 1 -> 0
    if (match(Op1, m_One()))
      return Constant::getNullValue(Op0->getType());
  
    if (Op0->getType()->isIntegerTy(1))
      // It can't be remainder by zero, hence it must be remainder by one.
      return Constant::getNullValue(Op0->getType());
  
    // X % X -> 0
    if (Op0 == Op1)
      return Constant::getNullValue(Op0->getType());
  
    // (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;
  
    // 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;
  
    return nullptr;
  }
  
  /// SimplifySRemInst - 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 Query &Q,
                                 unsigned MaxRecurse) {
    if (Value *V = SimplifyRem(Instruction::SRem, Op0, Op1, Q, MaxRecurse))
      return V;
  
    return nullptr;
  }
  
  Value *llvm::SimplifySRemInst(Value *Op0, Value *Op1, const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifySRemInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// SimplifyURemInst - 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 Query &Q,
                                 unsigned MaxRecurse) {
    if (Value *V = SimplifyRem(Instruction::URem, Op0, Op1, Q, MaxRecurse))
      return V;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyURemInst(Value *Op0, Value *Op1, const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyURemInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  static Value *SimplifyFRemInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                 const Query &, unsigned) {
    // undef % X -> undef    (the undef could be a snan).
    if (match(Op0, m_Undef()))
      return Op0;
  
    // X % undef -> undef
    if (match(Op1, m_Undef()))
      return Op1;
  
    // 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_AnyZero()))
      return Op0;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyFRemInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyFRemInst(Op0, Op1, FMF, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// isUndefShift - Returns true if a shift by \c Amount always yields undef.
  static bool isUndefShift(Value *Amount) {
    Constant *C = dyn_cast<Constant>(Amount);
    if (!C)
      return false;
  
    // X shift by undef -> undef because it may shift by the bitwidth.
    if (isa<UndefValue>(C))
      return true;
  
    // Shifting by the bitwidth or more is undefined.
    if (ConstantInt *CI = dyn_cast<ConstantInt>(C))
      if (CI->getValue().getLimitedValue() >=
          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 = C->getType()->getVectorNumElements(); I != E; ++I)
        if (!isUndefShift(C->getAggregateElement(I)))
          return false;
      return true;
    }
  
    return false;
  }
  
  /// SimplifyShift - Given operands for an Shl, LShr or AShr, see if we can
  /// fold the result.  If not, this returns null.
  static Value *SimplifyShift(unsigned Opcode, Value *Op0, Value *Op1,
                              const Query &Q, unsigned MaxRecurse) {
    if (Constant *C0 = dyn_cast<Constant>(Op0)) {
      if (Constant *C1 = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { C0, C1 };
        return ConstantFoldInstOperands(Opcode, C0->getType(), Ops, Q.DL, Q.TLI);
      }
    }
  
    // 0 shift by X -> 0
    if (match(Op0, m_Zero()))
      return Op0;
  
    // X shift by 0 -> X
    if (match(Op1, m_Zero()))
      return Op0;
  
    // Fold undefined shifts.
    if (isUndefShift(Op1))
      return UndefValue::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;
  
    return nullptr;
  }
  
  /// \brief Given operands for an Shl, LShr or AShr, see if we can
  /// fold the result.  If not, this returns null.
  static Value *SimplifyRightShift(unsigned Opcode, Value *Op0, Value *Op1,
                                   bool isExact, const Query &Q,
                                   unsigned MaxRecurse) {
    if (Value *V = SimplifyShift(Opcode, Op0, Op1, 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 (match(Op0, m_Undef()))
      return isExact ? Op0 : Constant::getNullValue(Op0->getType());
  
    // The low bit cannot be shifted out of an exact shift if it is set.
    if (isExact) {
      unsigned BitWidth = Op0->getType()->getScalarSizeInBits();
      APInt Op0KnownZero(BitWidth, 0);
      APInt Op0KnownOne(BitWidth, 0);
      computeKnownBits(Op0, Op0KnownZero, Op0KnownOne, Q.DL, /*Depth=*/0, Q.AC,
                       Q.CxtI, Q.DT);
      if (Op0KnownOne[0])
        return Op0;
    }
  
    return nullptr;
  }
  
  /// SimplifyShlInst - 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 Query &Q, unsigned MaxRecurse) {
    if (Value *V = SimplifyShift(Instruction::Shl, Op0, Op1, Q, MaxRecurse))
      return V;
  
    // undef << X -> 0
    // undef << X -> undef if (if it's NSW/NUW)
    if (match(Op0, m_Undef()))
      return isNSW || isNUW ? Op0 : Constant::getNullValue(Op0->getType());
  
    // (X >> A) << A -> X
    Value *X;
    if (match(Op0, m_Exact(m_Shr(m_Value(X), m_Specific(Op1)))))
      return X;
    return nullptr;
  }
  
  Value *llvm::SimplifyShlInst(Value *Op0, Value *Op1, bool isNSW, bool isNUW,
                               const DataLayout &DL, const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyShlInst(Op0, Op1, isNSW, isNUW, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  /// SimplifyLShrInst - 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 Query &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;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyLShrInst(Value *Op0, Value *Op1, bool isExact,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyLShrInst(Op0, Op1, isExact, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// SimplifyAShrInst - 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 Query &Q, unsigned MaxRecurse) {
    if (Value *V = SimplifyRightShift(Instruction::AShr, Op0, Op1, isExact, Q,
                                      MaxRecurse))
      return V;
  
    // all ones >>a X -> all ones
    if (match(Op0, m_AllOnes()))
      return Op0;
  
    // (X << A) >> A -> X
    Value *X;
    if (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 DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyAShrInst(Op0, Op1, isExact, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  static Value *simplifyUnsignedRangeCheck(ICmpInst *ZeroICmp,
                                           ICmpInst *UnsignedICmp, bool IsAnd) {
    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;
    if (match(UnsignedICmp, m_ICmp(UnsignedPred, m_Value(X), m_Specific(Y))) &&
        ICmpInst::isUnsigned(UnsignedPred))
      ;
    else if (match(UnsignedICmp,
                   m_ICmp(UnsignedPred, m_Value(Y), m_Specific(X))) &&
             ICmpInst::isUnsigned(UnsignedPred))
      UnsignedPred = ICmpInst::getSwappedPredicate(UnsignedPred);
    else
      return nullptr;
  
    // 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  -->  true
    // X >= Y || Y == 0  -->  X >= Y
    if (UnsignedPred == ICmpInst::ICMP_UGE && !IsAnd) {
      if (EqPred == ICmpInst::ICMP_NE)
        return getTrue(UnsignedICmp->getType());
      return UnsignedICmp;
    }
  
    // X < Y && Y == 0  -->  false
    if (UnsignedPred == ICmpInst::ICMP_ULT && EqPred == ICmpInst::ICMP_EQ &&
        IsAnd)
      return getFalse(UnsignedICmp->getType());
  
    return nullptr;
  }
  
  // Simplify (and (icmp ...) (icmp ...)) to true when we can tell that the range
  // of possible values cannot be satisfied.
  static Value *SimplifyAndOfICmps(ICmpInst *Op0, ICmpInst *Op1) {
    ICmpInst::Predicate Pred0, Pred1;
    ConstantInt *CI1, *CI2;
    Value *V;
  
    if (Value *X = simplifyUnsignedRangeCheck(Op0, Op1, /*IsAnd=*/true))
      return X;
  
    if (!match(Op0, m_ICmp(Pred0, m_Add(m_Value(V), m_ConstantInt(CI1)),
                           m_ConstantInt(CI2))))
     return nullptr;
  
    if (!match(Op1, m_ICmp(Pred1, m_Specific(V), m_Specific(CI1))))
      return nullptr;
  
    Type *ITy = Op0->getType();
  
    auto *AddInst = cast<BinaryOperator>(Op0->getOperand(0));
    bool isNSW = AddInst->hasNoSignedWrap();
    bool isNUW = AddInst->hasNoUnsignedWrap();
  
    const APInt &CI1V = CI1->getValue();
    const APInt &CI2V = CI2->getValue();
    const APInt Delta = CI2V - CI1V;
    if (CI1V.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 (CI1V.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;
  }
  
  /// SimplifyAndInst - 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 Query &Q,
                                unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::And, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
    }
  
    // X & undef -> 0
    if (match(Op1, m_Undef()))
      return Constant::getNullValue(Op0->getType());
  
    // X & X = X
    if (Op0 == Op1)
      return Op0;
  
    // X & 0 = 0
    if (match(Op1, m_Zero()))
      return Op1;
  
    // 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
    Value *A = nullptr, *B = nullptr;
    if (match(Op0, m_Or(m_Value(A), m_Value(B))) &&
        (A == Op1 || B == Op1))
      return Op1;
  
    // A & (A | ?) = A
    if (match(Op1, m_Or(m_Value(A), m_Value(B))) &&
        (A == Op0 || B == Op0))
      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;
    }
  
    if (auto *ICILHS = dyn_cast<ICmpInst>(Op0)) {
      if (auto *ICIRHS = dyn_cast<ICmpInst>(Op1)) {
        if (Value *V = SimplifyAndOfICmps(ICILHS, ICIRHS))
          return V;
        if (Value *V = SimplifyAndOfICmps(ICIRHS, ICILHS))
          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 = ExpandBinOp(Instruction::And, Op0, Op1, Instruction::Or,
                               Q, MaxRecurse))
      return V;
  
    // And distributes over Xor.  Try some generic simplifications based on this.
    if (Value *V = ExpandBinOp(Instruction::And, Op0, Op1, Instruction::Xor,
                               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::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;
  
    return nullptr;
  }
  
  Value *llvm::SimplifyAndInst(Value *Op0, Value *Op1, const DataLayout &DL,
                               const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyAndInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  // Simplify (or (icmp ...) (icmp ...)) to true when we can tell that the union
  // contains all possible values.
  static Value *SimplifyOrOfICmps(ICmpInst *Op0, ICmpInst *Op1) {
    ICmpInst::Predicate Pred0, Pred1;
    ConstantInt *CI1, *CI2;
    Value *V;
  
    if (Value *X = simplifyUnsignedRangeCheck(Op0, Op1, /*IsAnd=*/false))
      return X;
  
    if (!match(Op0, m_ICmp(Pred0, m_Add(m_Value(V), m_ConstantInt(CI1)),
                           m_ConstantInt(CI2))))
     return nullptr;
  
    if (!match(Op1, m_ICmp(Pred1, m_Specific(V), m_Specific(CI1))))
      return nullptr;
  
    Type *ITy = Op0->getType();
  
    auto *AddInst = cast<BinaryOperator>(Op0->getOperand(0));
    bool isNSW = AddInst->hasNoSignedWrap();
    bool isNUW = AddInst->hasNoUnsignedWrap();
  
    const APInt &CI1V = CI1->getValue();
    const APInt &CI2V = CI2->getValue();
    const APInt Delta = CI2V - CI1V;
    if (CI1V.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 (CI1V.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;
  }
  
  /// SimplifyOrInst - 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 Query &Q,
                               unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::Or, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
    }
  
    // X | undef -> -1
    if (match(Op1, m_Undef()))
      return Constant::getAllOnesValue(Op0->getType());
  
    // X | X = X
    if (Op0 == Op1)
      return Op0;
  
    // X | 0 = X
    if (match(Op1, m_Zero()))
      return Op0;
  
    // X | -1 = -1
    if (match(Op1, m_AllOnes()))
      return Op1;
  
    // 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
    Value *A = nullptr, *B = nullptr;
    if (match(Op0, m_And(m_Value(A), m_Value(B))) &&
        (A == Op1 || B == Op1))
      return Op1;
  
    // A | (A & ?) = A
    if (match(Op1, m_And(m_Value(A), m_Value(B))) &&
        (A == Op0 || B == Op0))
      return Op0;
  
    // ~(A & ?) | A = -1
    if (match(Op0, m_Not(m_And(m_Value(A), m_Value(B)))) &&
        (A == Op1 || B == Op1))
      return Constant::getAllOnesValue(Op1->getType());
  
    // A | ~(A & ?) = -1
    if (match(Op1, m_Not(m_And(m_Value(A), m_Value(B)))) &&
        (A == Op0 || B == Op0))
      return Constant::getAllOnesValue(Op0->getType());
  
    if (auto *ICILHS = dyn_cast<ICmpInst>(Op0)) {
      if (auto *ICIRHS = dyn_cast<ICmpInst>(Op1)) {
        if (Value *V = SimplifyOrOfICmps(ICILHS, ICIRHS))
          return V;
        if (Value *V = SimplifyOrOfICmps(ICIRHS, ICILHS))
          return V;
      }
    }
  
    // 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 = ExpandBinOp(Instruction::Or, Op0, Op1, Instruction::And, 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::Or, Op0, Op1, Q,
                                           MaxRecurse))
        return V;
  
    // (A & C)|(B & D)
    Value *C = nullptr, *D = nullptr;
    if (match(Op0, m_And(m_Value(A), m_Value(C))) &&
        match(Op1, m_And(m_Value(B), m_Value(D)))) {
      ConstantInt *C1 = dyn_cast<ConstantInt>(C);
      ConstantInt *C2 = dyn_cast<ConstantInt>(D);
      if (C1 && C2 && (C1->getValue() == ~C2->getValue())) {
        // (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 *V1, *V2;
        if ((C2->getValue() & (C2->getValue() + 1)) == 0 && // C2 == 0+1+
            match(A, m_Add(m_Value(V1), m_Value(V2)))) {
          // Add commutes, try both ways.
          if (V1 == B &&
              MaskedValueIsZero(V2, C2->getValue(), Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
            return A;
          if (V2 == B &&
              MaskedValueIsZero(V1, C2->getValue(), Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
            return A;
        }
        // Or commutes, try both ways.
        if ((C1->getValue() & (C1->getValue() + 1)) == 0 &&
            match(B, m_Add(m_Value(V1), m_Value(V2)))) {
          // Add commutes, try both ways.
          if (V1 == A &&
              MaskedValueIsZero(V2, C1->getValue(), Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
            return B;
          if (V2 == A &&
              MaskedValueIsZero(V1, C1->getValue(), 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 DataLayout &DL,
                              const TargetLibraryInfo *TLI,
                              const DominatorTree *DT, AssumptionCache *AC,
                              const Instruction *CxtI) {
    return ::SimplifyOrInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                            RecursionLimit);
  }
  
  /// SimplifyXorInst - 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 Query &Q,
                                unsigned MaxRecurse) {
    if (Constant *CLHS = dyn_cast<Constant>(Op0)) {
      if (Constant *CRHS = dyn_cast<Constant>(Op1)) {
        Constant *Ops[] = { CLHS, CRHS };
        return ConstantFoldInstOperands(Instruction::Xor, CLHS->getType(),
                                        Ops, Q.DL, Q.TLI);
      }
  
      // Canonicalize the constant to the RHS.
      std::swap(Op0, Op1);
    }
  
    // A ^ undef -> undef
    if (match(Op1, m_Undef()))
      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());
  
    // 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 DataLayout &DL,
                               const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyXorInst(Op0, Op1, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  static Type *GetCompareTy(Value *Op) {
    return CmpInst::makeCmpResultType(Op->getType());
  }
  
  /// ExtractEquivalentCondition - 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(const DataLayout &DL,
                                      const TargetLibraryInfo *TLI,
                                      CmpInst::Predicate Pred, Value *LHS,
                                      Value *RHS) {
    // 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 (llvm::isKnownNonNull(LHS, TLI) && isa<ConstantPointerNull>(RHS) &&
        (Pred == CmpInst::ICMP_EQ || Pred == CmpInst::ICMP_NE))
      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;
        if (LHSOffsetCI && RHSOffsetCI &&
            getObjectSize(LHS, LHSSize, DL, TLI) &&
            getObjectSize(RHS, RHSSize, DL, TLI)) {
          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<Value *, 8> LHSUObjs, RHSUObjs;
      GetUnderlyingObjects(LHS, LHSUObjs, DL);
      GetUnderlyingObjects(RHS, RHSUObjs, DL);
  
      // Is the set of underlying objects all noalias calls?
      auto IsNAC = [](SmallVectorImpl<Value *> &Objects) {
        return std::all_of(Objects.begin(), Objects.end(),
                           [](Value *V){ return isNoAliasCall(V); });
      };
  
      // 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 = [](SmallVectorImpl<Value *> &Objects) {
        return std::all_of(Objects.begin(), Objects.end(),
                           [](Value *V){
                             if (const AllocaInst *AI = dyn_cast<AllocaInst>(V))
                               return AI->getParent() && AI->getParent()->getParent() &&
                                      AI->isStaticAlloca();
                             if (const GlobalValue *GV = dyn_cast<GlobalValue>(V))
                               return (GV->hasLocalLinkage() ||
                                       GV->hasHiddenVisibility() ||
                                       GV->hasProtectedVisibility() ||
                                       GV->hasUnnamedAddr()) &&
                                      !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));
    }
  
    // Otherwise, fail.
    return nullptr;
  }
  
  /// SimplifyICmpInst - 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 Query &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);
    }
  
    Type *ITy = GetCompareTy(LHS); // The return type.
    Type *OpTy = LHS->getType();   // The operand type.
  
    // icmp X, X -> true/false
    // X icmp undef -> true/false.  For example, icmp ugt %X, undef -> false
    // because X could be 0.
    if (LHS == RHS || isa<UndefValue>(RHS))
      return ConstantInt::get(ITy, CmpInst::isTrueWhenEqual(Pred));
  
    // Special case logic when the operands have i1 type.
    if (OpTy->getScalarType()->isIntegerTy(1)) {
      switch (Pred) {
      default: break;
      case ICmpInst::ICMP_EQ:
        // X == 1 -> X
        if (match(RHS, m_One()))
          return LHS;
        break;
      case ICmpInst::ICMP_NE:
        // X != 0 -> X
        if (match(RHS, m_Zero()))
          return LHS;
        break;
      case ICmpInst::ICMP_UGT:
        // X >u 0 -> X
        if (match(RHS, m_Zero()))
          return LHS;
        break;
      case ICmpInst::ICMP_UGE:
        // X >=u 1 -> X
        if (match(RHS, m_One()))
          return LHS;
        break;
      case ICmpInst::ICMP_SLT:
        // X <s 0 -> X
        if (match(RHS, m_Zero()))
          return LHS;
        break;
      case ICmpInst::ICMP_SLE:
        // X <=s -1 -> X
        if (match(RHS, m_One()))
          return LHS;
        break;
      }
    }
  
    // If we are comparing with zero then try hard since this is a common case.
    if (match(RHS, m_Zero())) {
      bool LHSKnownNonNegative, LHSKnownNegative;
      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))
          return getFalse(ITy);
        break;
      case ICmpInst::ICMP_NE:
      case ICmpInst::ICMP_UGT:
        if (isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
          return getTrue(ITy);
        break;
      case ICmpInst::ICMP_SLT:
        ComputeSignBit(LHS, LHSKnownNonNegative, LHSKnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (LHSKnownNegative)
          return getTrue(ITy);
        if (LHSKnownNonNegative)
          return getFalse(ITy);
        break;
      case ICmpInst::ICMP_SLE:
        ComputeSignBit(LHS, LHSKnownNonNegative, LHSKnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (LHSKnownNegative)
          return getTrue(ITy);
        if (LHSKnownNonNegative &&
            isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
          return getFalse(ITy);
        break;
      case ICmpInst::ICMP_SGE:
        ComputeSignBit(LHS, LHSKnownNonNegative, LHSKnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (LHSKnownNegative)
          return getFalse(ITy);
        if (LHSKnownNonNegative)
          return getTrue(ITy);
        break;
      case ICmpInst::ICMP_SGT:
        ComputeSignBit(LHS, LHSKnownNonNegative, LHSKnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (LHSKnownNegative)
          return getFalse(ITy);
        if (LHSKnownNonNegative &&
            isKnownNonZero(LHS, Q.DL, 0, Q.AC, Q.CxtI, Q.DT))
          return getTrue(ITy);
        break;
      }
    }
  
    // See if we are doing a comparison with a constant integer.
    if (ConstantInt *CI = dyn_cast<ConstantInt>(RHS)) {
      // Rule out tautological comparisons (eg., ult 0 or uge 0).
      ConstantRange RHS_CR = ICmpInst::makeConstantRange(Pred, CI->getValue());
      if (RHS_CR.isEmptySet())
        return ConstantInt::getFalse(CI->getContext());
      if (RHS_CR.isFullSet())
        return ConstantInt::getTrue(CI->getContext());
  
      // Many binary operators with constant RHS have easy to compute constant
      // range.  Use them to check whether the comparison is a tautology.
      unsigned Width = CI->getBitWidth();
      APInt Lower = APInt(Width, 0);
      APInt Upper = APInt(Width, 0);
      ConstantInt *CI2;
      if (match(LHS, m_URem(m_Value(), m_ConstantInt(CI2)))) {
        // 'urem x, CI2' produces [0, CI2).
        Upper = CI2->getValue();
      } else if (match(LHS, m_SRem(m_Value(), m_ConstantInt(CI2)))) {
        // 'srem x, CI2' produces (-|CI2|, |CI2|).
        Upper = CI2->getValue().abs();
        Lower = (-Upper) + 1;
      } else if (match(LHS, m_UDiv(m_ConstantInt(CI2), m_Value()))) {
        // 'udiv CI2, x' produces [0, CI2].
        Upper = CI2->getValue() + 1;
      } else if (match(LHS, m_UDiv(m_Value(), m_ConstantInt(CI2)))) {
        // 'udiv x, CI2' produces [0, UINT_MAX / CI2].
        APInt NegOne = APInt::getAllOnesValue(Width);
        if (!CI2->isZero())
          Upper = NegOne.udiv(CI2->getValue()) + 1;
      } else if (match(LHS, m_SDiv(m_ConstantInt(CI2), m_Value()))) {
        if (CI2->isMinSignedValue()) {
          // 'sdiv INT_MIN, x' produces [INT_MIN, INT_MIN / -2].
          Lower = CI2->getValue();
          Upper = Lower.lshr(1) + 1;
        } else {
          // 'sdiv CI2, x' produces [-|CI2|, |CI2|].
          Upper = CI2->getValue().abs() + 1;
          Lower = (-Upper) + 1;
        }
      } else if (match(LHS, m_SDiv(m_Value(), m_ConstantInt(CI2)))) {
        APInt IntMin = APInt::getSignedMinValue(Width);
        APInt IntMax = APInt::getSignedMaxValue(Width);
        APInt Val = CI2->getValue();
        if (Val.isAllOnesValue()) {
          // 'sdiv x, -1' produces [INT_MIN + 1, INT_MAX]
          //    where CI2 != -1 and CI2 != 0 and CI2 != 1
          Lower = IntMin + 1;
          Upper = IntMax + 1;
        } else if (Val.countLeadingZeros() < Width - 1) {
          // 'sdiv x, CI2' produces [INT_MIN / CI2, INT_MAX / CI2]
          //    where CI2 != -1 and CI2 != 0 and CI2 != 1
          Lower = IntMin.sdiv(Val);
          Upper = IntMax.sdiv(Val);
          if (Lower.sgt(Upper))
            std::swap(Lower, Upper);
          Upper = Upper + 1;
          assert(Upper != Lower && "Upper part of range has wrapped!");
        }
      } else if (match(LHS, m_NUWShl(m_ConstantInt(CI2), m_Value()))) {
        // 'shl nuw CI2, x' produces [CI2, CI2 << CLZ(CI2)]
        Lower = CI2->getValue();
        Upper = Lower.shl(Lower.countLeadingZeros()) + 1;
      } else if (match(LHS, m_NSWShl(m_ConstantInt(CI2), m_Value()))) {
        if (CI2->isNegative()) {
          // 'shl nsw CI2, x' produces [CI2 << CLO(CI2)-1, CI2]
          unsigned ShiftAmount = CI2->getValue().countLeadingOnes() - 1;
          Lower = CI2->getValue().shl(ShiftAmount);
          Upper = CI2->getValue() + 1;
        } else {
          // 'shl nsw CI2, x' produces [CI2, CI2 << CLZ(CI2)-1]
          unsigned ShiftAmount = CI2->getValue().countLeadingZeros() - 1;
          Lower = CI2->getValue();
          Upper = CI2->getValue().shl(ShiftAmount) + 1;
        }
      } else if (match(LHS, m_LShr(m_Value(), m_ConstantInt(CI2)))) {
        // 'lshr x, CI2' produces [0, UINT_MAX >> CI2].
        APInt NegOne = APInt::getAllOnesValue(Width);
        if (CI2->getValue().ult(Width))
          Upper = NegOne.lshr(CI2->getValue()) + 1;
      } else if (match(LHS, m_LShr(m_ConstantInt(CI2), m_Value()))) {
        // 'lshr CI2, x' produces [CI2 >> (Width-1), CI2].
        unsigned ShiftAmount = Width - 1;
        if (!CI2->isZero() && cast<BinaryOperator>(LHS)->isExact())
          ShiftAmount = CI2->getValue().countTrailingZeros();
        Lower = CI2->getValue().lshr(ShiftAmount);
        Upper = CI2->getValue() + 1;
      } else if (match(LHS, m_AShr(m_Value(), m_ConstantInt(CI2)))) {
        // 'ashr x, CI2' produces [INT_MIN >> CI2, INT_MAX >> CI2].
        APInt IntMin = APInt::getSignedMinValue(Width);
        APInt IntMax = APInt::getSignedMaxValue(Width);
        if (CI2->getValue().ult(Width)) {
          Lower = IntMin.ashr(CI2->getValue());
          Upper = IntMax.ashr(CI2->getValue()) + 1;
        }
      } else if (match(LHS, m_AShr(m_ConstantInt(CI2), m_Value()))) {
        unsigned ShiftAmount = Width - 1;
        if (!CI2->isZero() && cast<BinaryOperator>(LHS)->isExact())
          ShiftAmount = CI2->getValue().countTrailingZeros();
        if (CI2->isNegative()) {
          // 'ashr CI2, x' produces [CI2, CI2 >> (Width-1)]
          Lower = CI2->getValue();
          Upper = CI2->getValue().ashr(ShiftAmount) + 1;
        } else {
          // 'ashr CI2, x' produces [CI2 >> (Width-1), CI2]
          Lower = CI2->getValue().ashr(ShiftAmount);
          Upper = CI2->getValue() + 1;
        }
      } else if (match(LHS, m_Or(m_Value(), m_ConstantInt(CI2)))) {
        // 'or x, CI2' produces [CI2, UINT_MAX].
        Lower = CI2->getValue();
      } else if (match(LHS, m_And(m_Value(), m_ConstantInt(CI2)))) {
        // 'and x, CI2' produces [0, CI2].
        Upper = CI2->getValue() + 1;
      }
      if (Lower != Upper) {
        ConstantRange LHS_CR = ConstantRange(Lower, Upper);
        if (RHS_CR.contains(LHS_CR))
          return ConstantInt::getTrue(RHS->getContext());
        if (RHS_CR.inverse().contains(LHS_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;
        }
        // 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;
        }
        // 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;
            }
          }
        }
      }
    }
  
    // Special logic for binary operators.
    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) && LBO->hasNoUnsignedWrap()) ||
          (CmpInst::isSigned(Pred) && LBO->hasNoSignedWrap());
      }
      if (RBO && RBO->getOpcode() == Instruction::Add) {
        C = RBO->getOperand(0); D = RBO->getOperand(1);
        NoRHSWrapProblem = ICmpInst::isEquality(Pred) ||
          (CmpInst::isUnsigned(Pred) && RBO->hasNoUnsignedWrap()) ||
          (CmpInst::isSigned(Pred) && RBO->hasNoSignedWrap());
      }
  
      // 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.
      if (A && C && (A == C || A == D || B == C || B == D) &&
          NoLHSWrapProblem && NoRHSWrapProblem) {
        // 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;
      }
    }
  
    // icmp pred (or X, Y), X
    if (LBO && match(LBO, m_CombineOr(m_Or(m_Value(), m_Specific(RHS)),
                                      m_Or(m_Specific(RHS), m_Value())))) {
      if (Pred == ICmpInst::ICMP_ULT)
        return getFalse(ITy);
      if (Pred == ICmpInst::ICMP_UGE)
        return getTrue(ITy);
    }
    // icmp pred X, (or X, Y)
    if (RBO && match(RBO, m_CombineOr(m_Or(m_Value(), m_Specific(LHS)),
                                      m_Or(m_Specific(LHS), m_Value())))) {
      if (Pred == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
      if (Pred == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
    }
  
    // icmp pred (and X, Y), X
    if (LBO && match(LBO, m_CombineOr(m_And(m_Value(), m_Specific(RHS)),
                                      m_And(m_Specific(RHS), m_Value())))) {
      if (Pred == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
      if (Pred == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
    }
    // icmp pred X, (and X, Y)
    if (RBO && match(RBO, m_CombineOr(m_And(m_Value(), m_Specific(LHS)),
                                      m_And(m_Specific(LHS), m_Value())))) {
      if (Pred == ICmpInst::ICMP_UGE)
        return getTrue(ITy);
      if (Pred == ICmpInst::ICMP_ULT)
        return getFalse(ITy);
    }
  
    // 0 - (zext X) pred C
    if (!CmpInst::isUnsigned(Pred) && match(LHS, m_Neg(m_ZExt(m_Value())))) {
      if (ConstantInt *RHSC = dyn_cast<ConstantInt>(RHS)) {
        if (RHSC->getValue().isStrictlyPositive()) {
          if (Pred == ICmpInst::ICMP_SLT)
            return ConstantInt::getTrue(RHSC->getContext());
          if (Pred == ICmpInst::ICMP_SGE)
            return ConstantInt::getFalse(RHSC->getContext());
          if (Pred == ICmpInst::ICMP_EQ)
            return ConstantInt::getFalse(RHSC->getContext());
          if (Pred == ICmpInst::ICMP_NE)
            return ConstantInt::getTrue(RHSC->getContext());
        }
        if (RHSC->getValue().isNonNegative()) {
          if (Pred == ICmpInst::ICMP_SLE)
            return ConstantInt::getTrue(RHSC->getContext());
          if (Pred == ICmpInst::ICMP_SGT)
            return ConstantInt::getFalse(RHSC->getContext());
        }
      }
    }
  
    // icmp pred (urem X, Y), Y
    if (LBO && match(LBO, m_URem(m_Value(), m_Specific(RHS)))) {
      bool KnownNonNegative, KnownNegative;
      switch (Pred) {
      default:
        break;
      case ICmpInst::ICMP_SGT:
      case ICmpInst::ICMP_SGE:
        ComputeSignBit(RHS, KnownNonNegative, KnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (!KnownNonNegative)
          break;
        // fall-through
      case ICmpInst::ICMP_EQ:
      case ICmpInst::ICMP_UGT:
      case ICmpInst::ICMP_UGE:
        return getFalse(ITy);
      case ICmpInst::ICMP_SLT:
      case ICmpInst::ICMP_SLE:
        ComputeSignBit(RHS, KnownNonNegative, KnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (!KnownNonNegative)
          break;
        // fall-through
      case ICmpInst::ICMP_NE:
      case ICmpInst::ICMP_ULT:
      case ICmpInst::ICMP_ULE:
        return getTrue(ITy);
      }
    }
  
    // icmp pred X, (urem Y, X)
    if (RBO && match(RBO, m_URem(m_Value(), m_Specific(LHS)))) {
      bool KnownNonNegative, KnownNegative;
      switch (Pred) {
      default:
        break;
      case ICmpInst::ICMP_SGT:
      case ICmpInst::ICMP_SGE:
        ComputeSignBit(LHS, KnownNonNegative, KnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (!KnownNonNegative)
          break;
        // fall-through
      case ICmpInst::ICMP_NE:
      case ICmpInst::ICMP_UGT:
      case ICmpInst::ICMP_UGE:
        return getTrue(ITy);
      case ICmpInst::ICMP_SLT:
      case ICmpInst::ICMP_SLE:
        ComputeSignBit(LHS, KnownNonNegative, KnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (!KnownNonNegative)
          break;
        // fall-through
      case ICmpInst::ICMP_EQ:
      case ICmpInst::ICMP_ULT:
      case ICmpInst::ICMP_ULE:
        return getFalse(ITy);
      }
    }
  
    // x udiv y <=u x.
    if (LBO && match(LBO, m_UDiv(m_Specific(RHS), m_Value()))) {
      // icmp pred (X /u Y), X
      if (Pred == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
      if (Pred == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
    }
  
    // handle:
    //   CI2 << X == CI
    //   CI2 << X != CI
    //
    //   where CI2 is a power of 2 and CI isn't
    if (auto *CI = dyn_cast<ConstantInt>(RHS)) {
      const APInt *CI2Val, *CIVal = &CI->getValue();
      if (LBO && match(LBO, m_Shl(m_APInt(CI2Val), m_Value())) &&
          CI2Val->isPowerOf2()) {
        if (!CIVal->isPowerOf2()) {
          // CI2 << X can equal zero in some circumstances,
          // this simplification is unsafe if CI 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.
          // - CI2 is one
          // - CI isn't zero
          if (LBO->hasNoSignedWrap() || LBO->hasNoUnsignedWrap() ||
              *CI2Val == 1 || !CI->isZero()) {
            if (Pred == ICmpInst::ICMP_EQ)
              return ConstantInt::getFalse(RHS->getContext());
            if (Pred == ICmpInst::ICMP_NE)
              return ConstantInt::getTrue(RHS->getContext());
          }
        }
        if (CIVal->isSignBit() && *CI2Val == 1) {
          if (Pred == ICmpInst::ICMP_UGT)
            return ConstantInt::getFalse(RHS->getContext());
          if (Pred == ICmpInst::ICMP_ULE)
            return ConstantInt::getTrue(RHS->getContext());
        }
      }
    }
  
    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))
          break;
        // fall-through
      case Instruction::SDiv:
      case Instruction::AShr:
        if (!LBO->isExact() || !RBO->isExact())
          break;
        if (Value *V = SimplifyICmpInst(Pred, LBO->getOperand(0),
                                        RBO->getOperand(0), Q, MaxRecurse-1))
          return V;
        break;
      case Instruction::Shl: {
        bool NUW = LBO->hasNoUnsignedWrap() && RBO->hasNoUnsignedWrap();
        bool NSW = LBO->hasNoSignedWrap() && RBO->hasNoSignedWrap();
        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;
      }
      }
    }
  
    // Simplify comparisons involving max/min.
    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:
        // Always true.
        return getTrue(ITy);
      case CmpInst::ICMP_ULT:
        // Always false.
        return getFalse(ITy);
      }
    }
  
    // Variants on "max(x,y) >= min(x,z)".
    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)) {
      // max(x, ?) pred min(x, ?).
      if (Pred == CmpInst::ICMP_SGE)
        // Always true.
        return getTrue(ITy);
      if (Pred == CmpInst::ICMP_SLT)
        // Always false.
        return getFalse(ITy);
    } else if (match(LHS, m_SMin(m_Value(A), m_Value(B))) &&
               match(RHS, m_SMax(m_Value(C), m_Value(D))) &&
               (A == C || A == D || B == C || B == D)) {
      // min(x, ?) pred max(x, ?).
      if (Pred == CmpInst::ICMP_SLE)
        // Always true.
        return getTrue(ITy);
      if (Pred == CmpInst::ICMP_SGT)
        // Always false.
        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)) {
      // max(x, ?) pred min(x, ?).
      if (Pred == CmpInst::ICMP_UGE)
        // Always true.
        return getTrue(ITy);
      if (Pred == CmpInst::ICMP_ULT)
        // Always false.
        return getFalse(ITy);
    } else if (match(LHS, m_UMin(m_Value(A), m_Value(B))) &&
               match(RHS, m_UMax(m_Value(C), m_Value(D))) &&
               (A == C || A == D || B == C || B == D)) {
      // min(x, ?) pred max(x, ?).
      if (Pred == CmpInst::ICMP_ULE)
        // Always true.
        return getTrue(ITy);
      if (Pred == CmpInst::ICMP_UGT)
        // Always false.
        return getFalse(ITy);
    }
  
    // Simplify comparisons of related pointers using a powerful, recursive
    // GEP-walk when we have target data available..
    if (LHS->getType()->isPointerTy())
      if (Constant *C = computePointerICmp(Q.DL, Q.TLI, Pred, LHS, RHS))
        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->idx_begin(), GLHS->idx_end());
          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);
          return ConstantExpr::getICmp(Pred, NewLHS, NewRHS);
        }
      }
    }
  
    // If a bit is known to be zero for A and known to be one for B,
    // then A and B cannot be equal.
    if (ICmpInst::isEquality(Pred)) {
      if (ConstantInt *CI = dyn_cast<ConstantInt>(RHS)) {
        uint32_t BitWidth = CI->getBitWidth();
        APInt LHSKnownZero(BitWidth, 0);
        APInt LHSKnownOne(BitWidth, 0);
        computeKnownBits(LHS, LHSKnownZero, LHSKnownOne, Q.DL, /*Depth=*/0, Q.AC,
                         Q.CxtI, Q.DT);
        const APInt &RHSVal = CI->getValue();
        if (((LHSKnownZero & RHSVal) != 0) || ((LHSKnownOne & ~RHSVal) != 0))
          return Pred == ICmpInst::ICMP_EQ
                     ? ConstantInt::getFalse(CI->getContext())
                     : ConstantInt::getTrue(CI->getContext());
      }
    }
  
    // 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 DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                Instruction *CxtI) {
    return ::SimplifyICmpInst(Predicate, LHS, RHS, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// SimplifyFCmpInst - 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,
                                 const Query &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.
    if (Pred == FCmpInst::FCMP_FALSE)
      return ConstantInt::get(GetCompareTy(LHS), 0);
    if (Pred == FCmpInst::FCMP_TRUE)
      return ConstantInt::get(GetCompareTy(LHS), 1);
  
    // fcmp pred x, undef  and  fcmp pred undef, x
    // fold to true if unordered, false if ordered
    if (isa<UndefValue>(LHS) || isa<UndefValue>(RHS)) {
      // Choosing NaN for the undef will always make unordered comparison succeed
      // and ordered comparison fail.
      return ConstantInt::get(GetCompareTy(LHS), CmpInst::isUnordered(Pred));
    }
  
    // fcmp x,x -> true/false.  Not all compares are foldable.
    if (LHS == RHS) {
      if (CmpInst::isTrueWhenEqual(Pred))
        return ConstantInt::get(GetCompareTy(LHS), 1);
      if (CmpInst::isFalseWhenEqual(Pred))
        return ConstantInt::get(GetCompareTy(LHS), 0);
    }
  
    // Handle fcmp with constant RHS
    if (ConstantFP *CFP = dyn_cast<ConstantFP>(RHS)) {
      // If the constant is a nan, see if we can fold the comparison based on it.
      if (CFP->getValueAPF().isNaN()) {
        if (FCmpInst::isOrdered(Pred)) // True "if ordered and foo"
          return ConstantInt::getFalse(CFP->getContext());
        assert(FCmpInst::isUnordered(Pred) &&
               "Comparison must be either ordered or unordered!");
        // True if unordered.
        return ConstantInt::getTrue(CFP->getContext());
      }
      // Check whether the constant is an infinity.
      if (CFP->getValueAPF().isInfinity()) {
        if (CFP->getValueAPF().isNegative()) {
          switch (Pred) {
          case FCmpInst::FCMP_OLT:
            // No value is ordered and less than negative infinity.
            return ConstantInt::getFalse(CFP->getContext());
          case FCmpInst::FCMP_UGE:
            // All values are unordered with or at least negative infinity.
            return ConstantInt::getTrue(CFP->getContext());
          default:
            break;
          }
        } else {
          switch (Pred) {
          case FCmpInst::FCMP_OGT:
            // No value is ordered and greater than infinity.
            return ConstantInt::getFalse(CFP->getContext());
          case FCmpInst::FCMP_ULE:
            // All values are unordered with and at most infinity.
            return ConstantInt::getTrue(CFP->getContext());
          default:
            break;
          }
        }
      }
      if (CFP->getValueAPF().isZero()) {
        switch (Pred) {
        case FCmpInst::FCMP_UGE:
          if (CannotBeOrderedLessThanZero(LHS))
            return ConstantInt::getTrue(CFP->getContext());
          break;
        case FCmpInst::FCMP_OLT:
          // X < 0
          if (CannotBeOrderedLessThanZero(LHS))
            return ConstantInt::getFalse(CFP->getContext());
          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,
                                const DataLayout &DL,
                                const TargetLibraryInfo *TLI,
                                const DominatorTree *DT, AssumptionCache *AC,
                                const Instruction *CxtI) {
    return ::SimplifyFCmpInst(Predicate, LHS, RHS, Query(DL, TLI, DT, AC, CxtI),
                              RecursionLimit);
  }
  
  /// SimplifySelectInst - Given operands for a SelectInst, see if we can fold
  /// the result.  If not, this returns null.
  static Value *SimplifySelectInst(Value *CondVal, Value *TrueVal,
                                   Value *FalseVal, const Query &Q,
                                   unsigned MaxRecurse) {
    // select true, X, Y  -> X
    // select false, X, Y -> Y
    if (Constant *CB = dyn_cast<Constant>(CondVal)) {
      if (CB->isAllOnesValue())
        return TrueVal;
      if (CB->isNullValue())
        return FalseVal;
    }
  
    // select C, X, X -> X
    if (TrueVal == FalseVal)
      return TrueVal;
  
    if (isa<UndefValue>(CondVal)) {  // select undef, X, Y -> X or Y
      if (isa<Constant>(TrueVal))
        return TrueVal;
      return FalseVal;
    }
    if (isa<UndefValue>(TrueVal))   // select C, undef, X -> X
      return FalseVal;
    if (isa<UndefValue>(FalseVal))   // select C, X, undef -> X
      return TrueVal;
  
    const auto *ICI = dyn_cast<ICmpInst>(CondVal);
    unsigned BitWidth = TrueVal->getType()->getScalarSizeInBits();
    if (ICI && BitWidth) {
      ICmpInst::Predicate Pred = ICI->getPredicate();
      APInt MinSignedValue = APInt::getSignBit(BitWidth);
      Value *X;
      const APInt *Y;
      bool TrueWhenUnset;
      bool IsBitTest = false;
      if (ICmpInst::isEquality(Pred) &&
          match(ICI->getOperand(0), m_And(m_Value(X), m_APInt(Y))) &&
          match(ICI->getOperand(1), m_Zero())) {
        IsBitTest = true;
        TrueWhenUnset = Pred == ICmpInst::ICMP_EQ;
      } else if (Pred == ICmpInst::ICMP_SLT &&
                 match(ICI->getOperand(1), m_Zero())) {
        X = ICI->getOperand(0);
        Y = &MinSignedValue;
        IsBitTest = true;
        TrueWhenUnset = false;
      } else if (Pred == ICmpInst::ICMP_SGT &&
                 match(ICI->getOperand(1), m_AllOnes())) {
        X = ICI->getOperand(0);
        Y = &MinSignedValue;
        IsBitTest = true;
        TrueWhenUnset = true;
      }
      if (IsBitTest) {
        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;
  }
  
  Value *llvm::SimplifySelectInst(Value *Cond, Value *TrueVal, Value *FalseVal,
                                  const DataLayout &DL,
                                  const TargetLibraryInfo *TLI,
                                  const DominatorTree *DT, AssumptionCache *AC,
                                  const Instruction *CxtI) {
    return ::SimplifySelectInst(Cond, TrueVal, FalseVal,
                                Query(DL, TLI, DT, AC, CxtI), RecursionLimit);
  }
  
  /// SimplifyGEPInst - 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 Query &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);
    if (VectorType *VT = dyn_cast<VectorType>(Ops[0]->getType()))
      GEPTy = VectorType::get(GEPTy, VT->getNumElements());
  
    if (isa<UndefValue>(Ops[0]))
      return UndefValue::get(GEPTy);
  
    if (Ops.size() == 2) {
      // getelementptr P, 0 -> P.
      if (match(Ops[1], m_Zero()))
        return Ops[0];
  
      Type *Ty = SrcTy;
      if (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)
          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 PtrToIntOrZero = [GEPTy](Value *P) -> Value * {
            if (match(P, m_Zero()))
              return Constant::getNullValue(GEPTy);
            Value *Temp;
            if (match(P, m_PtrToInt(m_Value(Temp))))
              if (Temp->getType() == GEPTy)
                return Temp;
            return nullptr;
          };
  
          // getelementptr V, (sub P, V) -> P if P points to a type of size 1.
          if (TyAllocSize == 1 &&
              match(Ops[1], m_Sub(m_Value(P), m_PtrToInt(m_Specific(Ops[0])))))
            if (Value *R = PtrToIntOrZero(P))
              return R;
  
          // getelementptr V, (ashr (sub P, V), C) -> Q
          // if P points to a type of size 1 << C.
          if (match(Ops[1],
                    m_AShr(m_Sub(m_Value(P), m_PtrToInt(m_Specific(Ops[0]))),
                           m_ConstantInt(C))) &&
              TyAllocSize == 1ULL << C)
            if (Value *R = PtrToIntOrZero(P))
              return R;
  
          // getelementptr V, (sdiv (sub P, V), C) -> Q
          // if P points to a type of size C.
          if (match(Ops[1],
                    m_SDiv(m_Sub(m_Value(P), m_PtrToInt(m_Specific(Ops[0]))),
                           m_SpecificInt(TyAllocSize))))
            if (Value *R = PtrToIntOrZero(P))
              return R;
        }
      }
    }
  
    // Check to see if this is constant foldable.
    for (unsigned i = 0, e = Ops.size(); i != e; ++i)
      if (!isa<Constant>(Ops[i]))
        return nullptr;
  
    return ConstantExpr::getGetElementPtr(SrcTy, cast<Constant>(Ops[0]),
                                          Ops.slice(1));
  }
  
  Value *llvm::SimplifyGEPInst(ArrayRef<Value *> Ops, const DataLayout &DL,
                               const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyGEPInst(
        cast<PointerType>(Ops[0]->getType()->getScalarType())->getElementType(),
        Ops, Query(DL, TLI, DT, AC, CxtI), RecursionLimit);
  }
  
  /// SimplifyInsertValueInst - 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 Query &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 (match(Val, m_Undef()))
      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 (match(Agg, m_Undef()))
          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 DataLayout &DL,
      const TargetLibraryInfo *TLI, const DominatorTree *DT, AssumptionCache *AC,
      const Instruction *CxtI) {
    return ::SimplifyInsertValueInst(Agg, Val, Idxs, Query(DL, TLI, DT, AC, CxtI),
                                     RecursionLimit);
  }
  
  /// SimplifyPHINode - See if we can fold the given phi.  If not, returns null.
  static Value *SimplifyPHINode(PHINode *PN, const Query &Q) {
    // 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 (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
      Value *Incoming = PN->getIncomingValue(i);
      // If the incoming value is the phi node itself, it can safely be skipped.
      if (Incoming == PN) continue;
      if (isa<UndefValue>(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 *SimplifyTruncInst(Value *Op, Type *Ty, const Query &Q, unsigned) {
    if (Constant *C = dyn_cast<Constant>(Op))
      return ConstantFoldInstOperands(Instruction::Trunc, Ty, C, Q.DL, Q.TLI);
  
    return nullptr;
  }
  
  Value *llvm::SimplifyTruncInst(Value *Op, Type *Ty, const DataLayout &DL,
                                 const TargetLibraryInfo *TLI,
                                 const DominatorTree *DT, AssumptionCache *AC,
                                 const Instruction *CxtI) {
    return ::SimplifyTruncInst(Op, Ty, Query(DL, TLI, DT, AC, CxtI),
                               RecursionLimit);
  }
  
  //=== Helper functions for higher up the class hierarchy.
  
  /// SimplifyBinOp - 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 Query &Q, unsigned MaxRecurse) {
    switch (Opcode) {
    case Instruction::Add:
      return SimplifyAddInst(LHS, RHS, /*isNSW*/false, /*isNUW*/false,
                             Q, MaxRecurse);
    case Instruction::FAdd:
      return SimplifyFAddInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
  
    case Instruction::Sub:
      return SimplifySubInst(LHS, RHS, /*isNSW*/false, /*isNUW*/false,
                             Q, MaxRecurse);
    case Instruction::FSub:
      return SimplifyFSubInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
  
    case Instruction::Mul:  return SimplifyMulInst (LHS, RHS, Q, MaxRecurse);
    case Instruction::FMul:
      return SimplifyFMulInst (LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::SDiv: return SimplifySDivInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::UDiv: return SimplifyUDivInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::FDiv:
        return SimplifyFDivInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::SRem: return SimplifySRemInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::URem: return SimplifyURemInst(LHS, RHS, Q, MaxRecurse);
    case Instruction::FRem:
        return SimplifyFRemInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
    case Instruction::Shl:
      return SimplifyShlInst(LHS, RHS, /*isNSW*/false, /*isNUW*/false,
                             Q, MaxRecurse);
    case Instruction::LShr:
      return SimplifyLShrInst(LHS, RHS, /*isExact*/false, Q, MaxRecurse);
    case Instruction::AShr:
      return SimplifyAShrInst(LHS, RHS, /*isExact*/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);
    default:
      if (Constant *CLHS = dyn_cast<Constant>(LHS))
        if (Constant *CRHS = dyn_cast<Constant>(RHS)) {
          Constant *COps[] = {CLHS, CRHS};
          return ConstantFoldInstOperands(Opcode, LHS->getType(), COps, Q.DL,
                                          Q.TLI);
        }
  
      // If the operation is associative, try some generic simplifications.
      if (Instruction::isAssociative(Opcode))
        if (Value *V = SimplifyAssociativeBinOp(Opcode, LHS, RHS, 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>(LHS) || isa<SelectInst>(RHS))
        if (Value *V = ThreadBinOpOverSelect(Opcode, LHS, RHS, 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>(LHS) || isa<PHINode>(RHS))
        if (Value *V = ThreadBinOpOverPHI(Opcode, LHS, RHS, Q, MaxRecurse))
          return V;
  
      return nullptr;
    }
  }
  
  /// SimplifyFPBinOp - Given operands for a BinaryOperator, see if we can
  /// fold the result.  If not, this returns null.
  /// In contrast to SimplifyBinOp, try to use FastMathFlag when folding the
  /// result. In case we don't need FastMathFlags, simply fall to SimplifyBinOp.
  static Value *SimplifyFPBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                                const FastMathFlags &FMF, const Query &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);
    default:
      return SimplifyBinOp(Opcode, LHS, RHS, Q, MaxRecurse);
    }
  }
  
  Value *llvm::SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                             const DataLayout &DL, const TargetLibraryInfo *TLI,
                             const DominatorTree *DT, AssumptionCache *AC,
                             const Instruction *CxtI) {
    return ::SimplifyBinOp(Opcode, LHS, RHS, Query(DL, TLI, DT, AC, CxtI),
                           RecursionLimit);
  }
  
  Value *llvm::SimplifyFPBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                               const FastMathFlags &FMF, const DataLayout &DL,
                               const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyFPBinOp(Opcode, LHS, RHS, FMF, Query(DL, TLI, DT, AC, CxtI),
                             RecursionLimit);
  }
  
  /// SimplifyCmpInst - Given operands for a CmpInst, see if we can
  /// fold the result.
  static Value *SimplifyCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                                const Query &Q, unsigned MaxRecurse) {
    if (CmpInst::isIntPredicate((CmpInst::Predicate)Predicate))
      return SimplifyICmpInst(Predicate, LHS, RHS, Q, MaxRecurse);
    return SimplifyFCmpInst(Predicate, LHS, RHS, Q, MaxRecurse);
  }
  
  Value *llvm::SimplifyCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               const DataLayout &DL, const TargetLibraryInfo *TLI,
                               const DominatorTree *DT, AssumptionCache *AC,
                               const Instruction *CxtI) {
    return ::SimplifyCmpInst(Predicate, LHS, RHS, Query(DL, TLI, DT, AC, CxtI),
                             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:
      return true;
    }
  }
  
  template <typename IterTy>
  static Value *SimplifyIntrinsic(Intrinsic::ID IID, IterTy ArgBegin, IterTy ArgEnd,
                                  const Query &Q, unsigned MaxRecurse) {
    // Perform idempotent optimizations
    if (!IsIdempotent(IID))
      return nullptr;
  
    // Unary Ops
    if (std::distance(ArgBegin, ArgEnd) == 1)
      if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(*ArgBegin))
        if (II->getIntrinsicID() == IID)
          return II;
  
    return nullptr;
  }
  
  template <typename IterTy>
  static Value *SimplifyCall(Value *V, IterTy ArgBegin, IterTy ArgEnd,
                             const Query &Q, unsigned MaxRecurse) {
    Type *Ty = V->getType();
    if (PointerType *PTy = dyn_cast<PointerType>(Ty))
      Ty = PTy->getElementType();
    FunctionType *FTy = cast<FunctionType>(Ty);
  
    // call undef -> undef
    if (isa<UndefValue>(V))
      return UndefValue::get(FTy->getReturnType());
  
    Function *F = dyn_cast<Function>(V);
    if (!F)
      return nullptr;
  
    if (unsigned IID = F->getIntrinsicID())
      if (Value *Ret =
          SimplifyIntrinsic((Intrinsic::ID) IID, ArgBegin, ArgEnd, Q, MaxRecurse))
        return Ret;
  
    if (!canConstantFoldCallTo(F))
      return nullptr;
  
    SmallVector<Constant *, 4> ConstantArgs;
    ConstantArgs.reserve(ArgEnd - ArgBegin);
    for (IterTy I = ArgBegin, E = ArgEnd; I != E; ++I) {
      Constant *C = dyn_cast<Constant>(*I);
      if (!C)
        return nullptr;
      ConstantArgs.push_back(C);
    }
  
    return ConstantFoldCall(F, ConstantArgs, Q.TLI);
  }
  
  Value *llvm::SimplifyCall(Value *V, User::op_iterator ArgBegin,
                            User::op_iterator ArgEnd, const DataLayout &DL,
                            const TargetLibraryInfo *TLI, const DominatorTree *DT,
                            AssumptionCache *AC, const Instruction *CxtI) {
    return ::SimplifyCall(V, ArgBegin, ArgEnd, Query(DL, TLI, DT, AC, CxtI),
                          RecursionLimit);
  }
  
  Value *llvm::SimplifyCall(Value *V, ArrayRef<Value *> Args,
                            const DataLayout &DL, const TargetLibraryInfo *TLI,
                            const DominatorTree *DT, AssumptionCache *AC,
                            const Instruction *CxtI) {
    return ::SimplifyCall(V, Args.begin(), Args.end(),
                          Query(DL, TLI, DT, AC, CxtI), RecursionLimit);
  }
  
  /// SimplifyInstruction - See if we can compute a simplified version of this
  /// instruction.  If not, this returns null.
  Value *llvm::SimplifyInstruction(Instruction *I, const DataLayout &DL,
                                   const TargetLibraryInfo *TLI,
                                   const DominatorTree *DT, AssumptionCache *AC) {
    Value *Result;
  
    switch (I->getOpcode()) {
    default:
      Result = ConstantFoldInstruction(I, DL, TLI);
      break;
    case Instruction::FAdd:
      Result = SimplifyFAddInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), DL, TLI, DT, AC, I);
      break;
    case Instruction::Add:
      Result = SimplifyAddInst(I->getOperand(0), I->getOperand(1),
                               cast<BinaryOperator>(I)->hasNoSignedWrap(),
                               cast<BinaryOperator>(I)->hasNoUnsignedWrap(), DL,
                               TLI, DT, AC, I);
      break;
    case Instruction::FSub:
      Result = SimplifyFSubInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), DL, TLI, DT, AC, I);
      break;
    case Instruction::Sub:
      Result = SimplifySubInst(I->getOperand(0), I->getOperand(1),
                               cast<BinaryOperator>(I)->hasNoSignedWrap(),
                               cast<BinaryOperator>(I)->hasNoUnsignedWrap(), DL,
                               TLI, DT, AC, I);
      break;
    case Instruction::FMul:
      Result = SimplifyFMulInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), DL, TLI, DT, AC, I);
      break;
    case Instruction::Mul:
      Result =
          SimplifyMulInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT, AC, I);
      break;
    case Instruction::SDiv:
      Result = SimplifySDivInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT,
                                AC, I);
      break;
    case Instruction::UDiv:
      Result = SimplifyUDivInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT,
                                AC, I);
      break;
    case Instruction::FDiv:
      Result = SimplifyFDivInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), DL, TLI, DT, AC, I);
      break;
    case Instruction::SRem:
      Result = SimplifySRemInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT,
                                AC, I);
      break;
    case Instruction::URem:
      Result = SimplifyURemInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT,
                                AC, I);
      break;
    case Instruction::FRem:
      Result = SimplifyFRemInst(I->getOperand(0), I->getOperand(1),
                                I->getFastMathFlags(), DL, TLI, DT, AC, I);
      break;
    case Instruction::Shl:
      Result = SimplifyShlInst(I->getOperand(0), I->getOperand(1),
                               cast<BinaryOperator>(I)->hasNoSignedWrap(),
                               cast<BinaryOperator>(I)->hasNoUnsignedWrap(), DL,
                               TLI, DT, AC, I);
      break;
    case Instruction::LShr:
      Result = SimplifyLShrInst(I->getOperand(0), I->getOperand(1),
                                cast<BinaryOperator>(I)->isExact(), DL, TLI, DT,
                                AC, I);
      break;
    case Instruction::AShr:
      Result = SimplifyAShrInst(I->getOperand(0), I->getOperand(1),
                                cast<BinaryOperator>(I)->isExact(), DL, TLI, DT,
                                AC, I);
      break;
    case Instruction::And:
      Result =
          SimplifyAndInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT, AC, I);
      break;
    case Instruction::Or:
      Result =
          SimplifyOrInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT, AC, I);
      break;
    case Instruction::Xor:
      Result =
          SimplifyXorInst(I->getOperand(0), I->getOperand(1), DL, TLI, DT, AC, I);
      break;
    case Instruction::ICmp:
      Result =
          SimplifyICmpInst(cast<ICmpInst>(I)->getPredicate(), I->getOperand(0),
                           I->getOperand(1), DL, TLI, DT, AC, I);
      break;
    case Instruction::FCmp:
      Result =
          SimplifyFCmpInst(cast<FCmpInst>(I)->getPredicate(), I->getOperand(0),
                           I->getOperand(1), DL, TLI, DT, AC, I);
      break;
    case Instruction::Select:
      Result = SimplifySelectInst(I->getOperand(0), I->getOperand(1),
                                  I->getOperand(2), DL, TLI, DT, AC, I);
      break;
    case Instruction::GetElementPtr: {
      SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end());
      Result = SimplifyGEPInst(Ops, DL, TLI, DT, AC, I);
      break;
    }
    case Instruction::InsertValue: {
      InsertValueInst *IV = cast<InsertValueInst>(I);
      Result = SimplifyInsertValueInst(IV->getAggregateOperand(),
                                       IV->getInsertedValueOperand(),
                                       IV->getIndices(), DL, TLI, DT, AC, I);
      break;
    }
    case Instruction::PHI:
      Result = SimplifyPHINode(cast<PHINode>(I), Query(DL, TLI, DT, AC, I));
      break;
    case Instruction::Call: {
      CallSite CS(cast<CallInst>(I));
      Result = SimplifyCall(CS.getCalledValue(), CS.arg_begin(), CS.arg_end(), DL,
                            TLI, DT, AC, I);
      break;
    }
    case Instruction::Trunc:
      Result =
          SimplifyTruncInst(I->getOperand(0), I->getType(), DL, TLI, DT, AC, I);
      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;
  }
  
  /// \brief Implementation of recursive simplification through an instructions
  /// 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.
  ///
  /// 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) {
    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->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)
        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->eraseFromParent();
    }
    return Simplified;
  }
  
  bool llvm::recursivelySimplifyInstruction(Instruction *I,
                                            const TargetLibraryInfo *TLI,
                                            const DominatorTree *DT,
                                            AssumptionCache *AC) {
    return replaceAndRecursivelySimplifyImpl(I, nullptr, TLI, DT, AC);
  }
  
  bool llvm::replaceAndRecursivelySimplify(Instruction *I, Value *SimpleV,
                                           const TargetLibraryInfo *TLI,
                                           const DominatorTree *DT,
                                           AssumptionCache *AC) {
    assert(I != SimpleV && "replaceAndRecursivelySimplify(X,X) is not valid!");
    assert(SimpleV && "Must provide a simplified value.");
    return replaceAndRecursivelySimplifyImpl(I, SimpleV, TLI, DT, AC);
  }
  