llvm/lib/Analysis/InstructionSimplify.cpp

//===- 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/AssumptionCache.h"
#include "llvm/Analysis/CaptureTracking.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/LoopAnalysisManager.h"
#include "llvm/Analysis/MemoryBuiltins.h"
#include "llvm/Analysis/OptimizationDiagnosticInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/Analysis/VectorUtils.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/GetElementPtrTypeIterator.h"
#include "llvm/IR/GlobalAlias.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/Support/KnownBits.h"
#include <algorithm>
using namespace llvm;
using namespace llvm::PatternMatch;

#define DEBUG_TYPE "instsimplify"

enum { RecursionLimit = 3 };

STATISTIC(NumExpand,  "Number of expansions");
STATISTIC(NumReassoc, "Number of reassociations");

static Value *SimplifyAndInst(Value *, Value *, const SimplifyQuery &, unsigned);
static Value *SimplifyBinOp(unsigned, Value *, Value *, const SimplifyQuery &,
                            unsigned);
static Value *SimplifyFPBinOp(unsigned, Value *, Value *, const FastMathFlags &,
                              const SimplifyQuery &, unsigned);
static Value *SimplifyCmpInst(unsigned, Value *, Value *, const SimplifyQuery &,
                              unsigned);
static Value *SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q, unsigned MaxRecurse);
static Value *SimplifyOrInst(Value *, Value *, const SimplifyQuery &, unsigned);
static Value *SimplifyXorInst(Value *, Value *, const SimplifyQuery &, unsigned);
static Value *SimplifyCastInst(unsigned, Value *, Type *,
                               const SimplifyQuery &, unsigned);

/// For a boolean type or a vector of boolean type, return false or a vector
/// with every element false.
static Constant *getFalse(Type *Ty) {
  return ConstantInt::getFalse(Ty);
}

/// For a boolean type or a vector of boolean type, return true or a vector
/// with every element true.
static Constant *getTrue(Type *Ty) {
  return ConstantInt::getTrue(Ty);
}

/// isSameCompare - Is V equivalent to the comparison "LHS Pred RHS"?
static bool isSameCompare(Value *V, CmpInst::Predicate Pred, Value *LHS,
                          Value *RHS) {
  CmpInst *Cmp = dyn_cast<CmpInst>(V);
  if (!Cmp)
    return false;
  CmpInst::Predicate CPred = Cmp->getPredicate();
  Value *CLHS = Cmp->getOperand(0), *CRHS = Cmp->getOperand(1);
  if (CPred == Pred && CLHS == LHS && CRHS == RHS)
    return true;
  return CPred == CmpInst::getSwappedPredicate(Pred) && CLHS == RHS &&
    CRHS == LHS;
}

/// 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;
}

/// 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(Instruction::BinaryOps Opcode, Value *LHS, Value *RHS,
                          Instruction::BinaryOps OpcodeToExpand, const SimplifyQuery &Q,
                          unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;

  // 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;
}

/// Generic simplifications for associative binary operations.
/// Returns the simpler value, or null if none was found.
static Value *SimplifyAssociativeBinOp(Instruction::BinaryOps Opcode,
                                       Value *LHS, Value *RHS, const SimplifyQuery &Q,
                                       unsigned MaxRecurse) {
  assert(Instruction::isAssociative(Opcode) && "Not an associative operation!");

  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;

  BinaryOperator *Op0 = dyn_cast<BinaryOperator>(LHS);
  BinaryOperator *Op1 = dyn_cast<BinaryOperator>(RHS);

  // Transform: "(A op B) op C" ==> "A op (B op C)" if it simplifies completely.
  if (Op0 && Op0->getOpcode() == Opcode) {
    Value *A = Op0->getOperand(0);
    Value *B = Op0->getOperand(1);
    Value *C = RHS;

    // Does "B op C" simplify?
    if (Value *V = SimplifyBinOp(Opcode, B, C, Q, MaxRecurse)) {
      // It does!  Return "A op V" if it simplifies or is already available.
      // If V equals B then "A op V" is just the LHS.
      if (V == B) return LHS;
      // Otherwise return "A op V" if it simplifies.
      if (Value *W = SimplifyBinOp(Opcode, A, V, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }

  // Transform: "A op (B op C)" ==> "(A op B) op C" if it simplifies completely.
  if (Op1 && Op1->getOpcode() == Opcode) {
    Value *A = LHS;
    Value *B = Op1->getOperand(0);
    Value *C = Op1->getOperand(1);

    // Does "A op B" simplify?
    if (Value *V = SimplifyBinOp(Opcode, A, B, Q, MaxRecurse)) {
      // It does!  Return "V op C" if it simplifies or is already available.
      // If V equals B then "V op C" is just the RHS.
      if (V == B) return RHS;
      // Otherwise return "V op C" if it simplifies.
      if (Value *W = SimplifyBinOp(Opcode, V, C, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }

  // The remaining transforms require commutativity as well as associativity.
  if (!Instruction::isCommutative(Opcode))
    return nullptr;

  // Transform: "(A op B) op C" ==> "(C op A) op B" if it simplifies completely.
  if (Op0 && Op0->getOpcode() == Opcode) {
    Value *A = Op0->getOperand(0);
    Value *B = Op0->getOperand(1);
    Value *C = RHS;

    // Does "C op A" simplify?
    if (Value *V = SimplifyBinOp(Opcode, C, A, Q, MaxRecurse)) {
      // It does!  Return "V op B" if it simplifies or is already available.
      // If V equals A then "V op B" is just the LHS.
      if (V == A) return LHS;
      // Otherwise return "V op B" if it simplifies.
      if (Value *W = SimplifyBinOp(Opcode, V, B, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }

  // Transform: "A op (B op C)" ==> "B op (C op A)" if it simplifies completely.
  if (Op1 && Op1->getOpcode() == Opcode) {
    Value *A = LHS;
    Value *B = Op1->getOperand(0);
    Value *C = Op1->getOperand(1);

    // Does "C op A" simplify?
    if (Value *V = SimplifyBinOp(Opcode, C, A, Q, MaxRecurse)) {
      // It does!  Return "B op V" if it simplifies or is already available.
      // If V equals C then "B op V" is just the RHS.
      if (V == C) return RHS;
      // Otherwise return "B op V" if it simplifies.
      if (Value *W = SimplifyBinOp(Opcode, B, V, Q, MaxRecurse)) {
        ++NumReassoc;
        return W;
      }
    }
  }

  return nullptr;
}

/// In the case of a binary operation with a select instruction as an operand,
/// try to simplify the binop by seeing whether evaluating it on both branches
/// of the select results in the same value. Returns the common value if so,
/// otherwise returns null.
static Value *ThreadBinOpOverSelect(Instruction::BinaryOps Opcode, Value *LHS,
                                    Value *RHS, const SimplifyQuery &Q,
                                    unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;

  SelectInst *SI;
  if (isa<SelectInst>(LHS)) {
    SI = cast<SelectInst>(LHS);
  } else {
    assert(isa<SelectInst>(RHS) && "No select instruction operand!");
    SI = cast<SelectInst>(RHS);
  }

  // Evaluate the BinOp on the true and false branches of the select.
  Value *TV;
  Value *FV;
  if (SI == LHS) {
    TV = SimplifyBinOp(Opcode, SI->getTrueValue(), RHS, Q, MaxRecurse);
    FV = SimplifyBinOp(Opcode, SI->getFalseValue(), RHS, Q, MaxRecurse);
  } else {
    TV = SimplifyBinOp(Opcode, LHS, SI->getTrueValue(), Q, MaxRecurse);
    FV = SimplifyBinOp(Opcode, LHS, SI->getFalseValue(), Q, MaxRecurse);
  }

  // If they simplified to the same value, then return the common value.
  // If they both failed to simplify then return null.
  if (TV == FV)
    return TV;

  // If one branch simplified to undef, return the other one.
  if (TV && 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;
}

/// 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 SimplifyQuery &Q,
                                  unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;

  // Make sure the select is on the LHS.
  if (!isa<SelectInst>(LHS)) {
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }
  assert(isa<SelectInst>(LHS) && "Not comparing with a select instruction!");
  SelectInst *SI = cast<SelectInst>(LHS);
  Value *Cond = SI->getCondition();
  Value *TV = SI->getTrueValue();
  Value *FV = SI->getFalseValue();

  // Now that we have "cmp select(Cond, TV, FV), RHS", analyse it.
  // Does "cmp TV, RHS" simplify?
  Value *TCmp = 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;
}

/// In the case of a binary operation with an operand that is a PHI instruction,
/// try to simplify the binop by seeing whether evaluating it on the incoming
/// phi values yields the same result for every value. If so returns the common
/// value, otherwise returns null.
static Value *ThreadBinOpOverPHI(Instruction::BinaryOps Opcode, Value *LHS,
                                 Value *RHS, const SimplifyQuery &Q,
                                 unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;

  PHINode *PI;
  if (isa<PHINode>(LHS)) {
    PI = cast<PHINode>(LHS);
    // Bail out if RHS and the phi may be mutually interdependent due to a loop.
    if (!ValueDominatesPHI(RHS, PI, Q.DT))
      return nullptr;
  } else {
    assert(isa<PHINode>(RHS) && "No PHI instruction operand!");
    PI = cast<PHINode>(RHS);
    // Bail out if LHS and the phi may be mutually interdependent due to a loop.
    if (!ValueDominatesPHI(LHS, PI, Q.DT))
      return nullptr;
  }

  // Evaluate the BinOp on the incoming phi values.
  Value *CommonValue = nullptr;
  for (Value *Incoming : PI->incoming_values()) {
    // If the incoming value is the phi node itself, it can safely be skipped.
    if (Incoming == PI) continue;
    Value *V = PI == LHS ?
      SimplifyBinOp(Opcode, Incoming, RHS, Q, MaxRecurse) :
      SimplifyBinOp(Opcode, LHS, Incoming, Q, MaxRecurse);
    // If the operation failed to simplify, or simplified to a different value
    // to previously, then give up.
    if (!V || (CommonValue && V != CommonValue))
      return nullptr;
    CommonValue = V;
  }

  return CommonValue;
}

/// In the case of a comparison with a PHI instruction, try to simplify the
/// comparison by seeing whether comparing with all of the incoming phi values
/// yields the same result every time. If so returns the common result,
/// otherwise returns null.
static Value *ThreadCmpOverPHI(CmpInst::Predicate Pred, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  // Recursion is always used, so bail out at once if we already hit the limit.
  if (!MaxRecurse--)
    return nullptr;

  // Make sure the phi is on the LHS.
  if (!isa<PHINode>(LHS)) {
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }
  assert(isa<PHINode>(LHS) && "Not comparing with a phi instruction!");
  PHINode *PI = cast<PHINode>(LHS);

  // Bail out if RHS and the phi may be mutually interdependent due to a loop.
  if (!ValueDominatesPHI(RHS, PI, Q.DT))
    return nullptr;

  // Evaluate the BinOp on the incoming phi values.
  Value *CommonValue = nullptr;
  for (Value *Incoming : PI->incoming_values()) {
    // If the incoming value is the phi node itself, it can safely be skipped.
    if (Incoming == PI) continue;
    Value *V = 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;
}

static Constant *foldOrCommuteConstant(Instruction::BinaryOps Opcode,
                                       Value *&Op0, Value *&Op1,
                                       const SimplifyQuery &Q) {
  if (auto *CLHS = dyn_cast<Constant>(Op0)) {
    if (auto *CRHS = dyn_cast<Constant>(Op1))
      return ConstantFoldBinaryOpOperands(Opcode, CLHS, CRHS, Q.DL);

    // Canonicalize the constant to the RHS if this is a commutative operation.
    if (Instruction::isCommutative(Opcode))
      std::swap(Op0, Op1);
  }
  return nullptr;
}

/// Given operands for an Add, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyAddInst(Value *Op0, Value *Op1, bool isNSW, bool isNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Add, Op0, Op1, Q))
    return C;

  // X + undef -> undef
  if (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
  Type *Ty = Op0->getType();
  if (match(Op0, m_Not(m_Specific(Op1))) ||
      match(Op1, m_Not(m_Specific(Op0))))
    return Constant::getAllOnesValue(Ty);

  // add nsw/nuw (xor Y, signmask), signmask --> Y
  // The no-wrapping add guarantees that the top bit will be set by the add.
  // Therefore, the xor must be clearing the already set sign bit of Y.
  if ((isNSW || isNUW) && match(Op1, m_SignMask()) &&
      match(Op0, m_Xor(m_Value(Y), m_SignMask())))
    return Y;

  /// i1 add -> xor.
  if (MaxRecurse && Op0->getType()->getScalarType()->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 SimplifyQuery &Query) {
  return ::SimplifyAddInst(Op0, Op1, isNSW, isNUW, Query, 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->isInterposable())
        break;
      V = GA->getAliasee();
    } else {
      if (auto CS = CallSite(V))
        if (Value *RV = CS.getReturnedArgOperand()) {
          V = RV;
          continue;
        }
      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);
}

/// Given operands for a Sub, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifySubInst(Value *Op0, Value *Op1, bool isNSW, bool isNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Sub, Op0, Op1, Q))
    return C;

  // X - 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());

  // Is this a negation?
  if (match(Op0, m_Zero())) {
    // 0 - X -> 0 if the sub is NUW.
    if (isNUW)
      return Op0;

    unsigned BitWidth = Op1->getType()->getScalarSizeInBits();
    KnownBits Known(BitWidth);
    computeKnownBits(Op1, Known, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
    if (Known.Zero.isMaxSignedValue()) {
      // Op1 is either 0 or the minimum signed value. If the sub is NSW, then
      // Op1 must be 0 because negating the minimum signed value is undefined.
      if (isNSW)
        return Op0;

      // 0 - X -> X if X is 0 or the minimum signed value.
      return Op1;
    }
  }

  // (X + Y) - Z -> X + (Y - Z) or Y + (X - Z) if everything simplifies.
  // For example, (X + Y) - Y -> X; (Y + X) - Y -> X
  Value *X = nullptr, *Y = nullptr, *Z = Op1;
  if (MaxRecurse && match(Op0, m_Add(m_Value(X), m_Value(Y)))) { // (X + Y) - Z
    // See if "V === Y - Z" simplifies.
    if (Value *V = SimplifyBinOp(Instruction::Sub, Y, Z, Q, MaxRecurse-1))
      // It does!  Now see if "X + V" simplifies.
      if (Value *W = SimplifyBinOp(Instruction::Add, X, V, Q, MaxRecurse-1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
    // See if "V === X - Z" simplifies.
    if (Value *V = SimplifyBinOp(Instruction::Sub, X, Z, Q, MaxRecurse-1))
      // It does!  Now see if "Y + V" simplifies.
      if (Value *W = SimplifyBinOp(Instruction::Add, Y, V, Q, MaxRecurse-1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
  }

  // X - (Y + Z) -> (X - Y) - Z or (X - Z) - Y if everything simplifies.
  // For example, X - (X + 1) -> -1
  X = Op0;
  if (MaxRecurse && match(Op1, m_Add(m_Value(Y), m_Value(Z)))) { // X - (Y + Z)
    // See if "V === X - Y" simplifies.
    if (Value *V = SimplifyBinOp(Instruction::Sub, X, Y, Q, MaxRecurse-1))
      // It does!  Now see if "V - Z" simplifies.
      if (Value *W = SimplifyBinOp(Instruction::Sub, V, Z, Q, MaxRecurse-1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
    // See if "V === X - Z" simplifies.
    if (Value *V = SimplifyBinOp(Instruction::Sub, X, Z, Q, MaxRecurse-1))
      // It does!  Now see if "V - Y" simplifies.
      if (Value *W = SimplifyBinOp(Instruction::Sub, V, Y, Q, MaxRecurse-1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }
  }

  // Z - (X - Y) -> (Z - X) + Y if everything simplifies.
  // For example, X - (X - Y) -> Y.
  Z = Op0;
  if (MaxRecurse && match(Op1, m_Sub(m_Value(X), m_Value(Y)))) // Z - (X - Y)
    // See if "V === Z - X" simplifies.
    if (Value *V = SimplifyBinOp(Instruction::Sub, Z, X, Q, MaxRecurse-1))
      // It does!  Now see if "V + Y" simplifies.
      if (Value *W = SimplifyBinOp(Instruction::Add, V, Y, Q, MaxRecurse-1)) {
        // It does, we successfully reassociated!
        ++NumReassoc;
        return W;
      }

  // trunc(X) - trunc(Y) -> trunc(X - Y) if everything simplifies.
  if (MaxRecurse && match(Op0, m_Trunc(m_Value(X))) &&
      match(Op1, m_Trunc(m_Value(Y))))
    if (X->getType() == Y->getType())
      // See if "V === X - Y" simplifies.
      if (Value *V = SimplifyBinOp(Instruction::Sub, X, Y, Q, MaxRecurse-1))
        // It does!  Now see if "trunc V" simplifies.
        if (Value *W = SimplifyCastInst(Instruction::Trunc, V, Op0->getType(),
                                        Q, MaxRecurse - 1))
          // It does, return the simplified "trunc V".
          return W;

  // Variations on GEP(base, I, ...) - GEP(base, i, ...) -> GEP(null, I-i, ...).
  if (match(Op0, m_PtrToInt(m_Value(X))) &&
      match(Op1, m_PtrToInt(m_Value(Y))))
    if (Constant *Result = computePointerDifference(Q.DL, X, Y))
      return ConstantExpr::getIntegerCast(Result, Op0->getType(), true);

  // i1 sub -> xor.
  if (MaxRecurse && Op0->getType()->getScalarType()->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 SimplifyQuery &Q) {
  return ::SimplifySubInst(Op0, Op1, isNSW, isNUW, Q, 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 SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::FAdd, Op0, Op1, Q))
    return C;

  // 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, Q.TLI)))
    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 SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::FSub, Op0, Op1, Q))
    return C;

  // 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, Q.TLI)))
    return Op0;

  // fsub -0.0, (fsub -0.0, X) ==> X
  Value *X;
  if (match(Op0, m_NegZero()) && match(Op1, m_FSub(m_NegZero(), m_Value(X))))
    return X;

  // fsub 0.0, (fsub 0.0, X) ==> X if signed zeros are ignored.
  if (FMF.noSignedZeros() && match(Op0, m_AnyZero()) &&
      match(Op1, m_FSub(m_AnyZero(), m_Value(X))))
    return X;

  // fsub nnan x, x ==> 0.0
  if (FMF.noNaNs() && 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 SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::FMul, Op0, Op1, Q))
    return C;

  // 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;
}

/// Given operands for a Mul, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyMulInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                              unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Mul, Op0, Op1, Q))
    return C;

  // X * 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()->getScalarType()->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 SimplifyQuery &Q) {
  return ::SimplifyFAddInst(Op0, Op1, FMF, Q, RecursionLimit);
}


Value *llvm::SimplifyFSubInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                              const SimplifyQuery &Q) {
  return ::SimplifyFSubInst(Op0, Op1, FMF, Q, RecursionLimit);
}

Value *llvm::SimplifyFMulInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                              const SimplifyQuery &Q) {
  return ::SimplifyFMulInst(Op0, Op1, FMF, Q, RecursionLimit);
}

Value *llvm::SimplifyMulInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::SimplifyMulInst(Op0, Op1, Q, RecursionLimit);
}

/// Check for common or similar folds of integer division or integer remainder.
static Value *simplifyDivRem(Value *Op0, Value *Op1, bool IsDiv) {
  Type *Ty = Op0->getType();

  // X / undef -> undef
  // X % undef -> undef
  if (match(Op1, m_Undef()))
    return Op1;

  // X / 0 -> undef
  // X % 0 -> undef
  // We don't need to preserve faults!
  if (match(Op1, m_Zero()))
    return UndefValue::get(Ty);

  // If any element of a constant divisor vector is zero, the whole op is undef.
  auto *Op1C = dyn_cast<Constant>(Op1);
  if (Op1C && Ty->isVectorTy()) {
    unsigned NumElts = Ty->getVectorNumElements();
    for (unsigned i = 0; i != NumElts; ++i) {
      Constant *Elt = Op1C->getAggregateElement(i);
      if (Elt && Elt->isNullValue())
        return UndefValue::get(Ty);
    }
  }

  // undef / X -> 0
  // undef % X -> 0
  if (match(Op0, m_Undef()))
    return Constant::getNullValue(Ty);

  // 0 / X -> 0
  // 0 % X -> 0
  if (match(Op0, m_Zero()))
    return Op0;

  // X / X -> 1
  // X % X -> 0
  if (Op0 == Op1)
    return IsDiv ? ConstantInt::get(Ty, 1) : Constant::getNullValue(Ty);

  // X / 1 -> X
  // X % 1 -> 0
  // If this is a boolean op (single-bit element type), we can't have
  // division-by-zero or remainder-by-zero, so assume the divisor is 1.
  if (match(Op1, m_One()) || Ty->getScalarType()->isIntegerTy(1))
    return IsDiv ? Op0 : Constant::getNullValue(Ty);

  return nullptr;
}

/// 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 SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
    return C;

  if (Value *V = simplifyDivRem(Op0, Op1, true))
    return V;

  bool isSigned = Opcode == Instruction::SDiv;

  // (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;
    (void)C1->getValue().umul_ov(C2->getValue(), Overflow);
    if (Overflow)
      return Constant::getNullValue(Op0->getType());
  }

  // If the operation is with the result of a select instruction, check whether
  // operating on either branch of the select always yields the same value.
  if (isa<SelectInst>(Op0) || isa<SelectInst>(Op1))
    if (Value *V = ThreadBinOpOverSelect(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;

  // If the operation is with the result of a phi instruction, check whether
  // operating on all incoming values of the phi always yields the same value.
  if (isa<PHINode>(Op0) || isa<PHINode>(Op1))
    if (Value *V = ThreadBinOpOverPHI(Opcode, Op0, Op1, Q, MaxRecurse))
      return V;

  return nullptr;
}

/// Given operands for an SDiv, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifySDivInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  if (Value *V = SimplifyDiv(Instruction::SDiv, Op0, Op1, Q, MaxRecurse))
    return V;

  return nullptr;
}

Value *llvm::SimplifySDivInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::SimplifySDivInst(Op0, Op1, Q, RecursionLimit);
}

/// Given operands for a UDiv, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyUDivInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  if (Value *V = SimplifyDiv(Instruction::UDiv, Op0, Op1, Q, MaxRecurse))
    return V;

  // udiv %V, C -> 0 if %V < C
  if (MaxRecurse) {
    if (Constant *C = dyn_cast_or_null<Constant>(SimplifyICmpInst(
            ICmpInst::ICMP_ULT, Op0, Op1, Q, MaxRecurse - 1))) {
      if (C->isAllOnesValue()) {
        return Constant::getNullValue(Op0->getType());
      }
    }
  }

  return nullptr;
}

Value *llvm::SimplifyUDivInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::SimplifyUDivInst(Op0, Op1, Q, RecursionLimit);
}

static Value *SimplifyFDivInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                               const SimplifyQuery &Q, unsigned) {
  if (Constant *C = foldOrCommuteConstant(Instruction::FDiv, Op0, Op1, Q))
    return C;

  // 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;

  // X / 1.0 -> X
  if (match(Op1, m_FPOne()))
    return Op0;

  // 0 / X -> 0
  // Requires that NaNs are off (X could be zero) and signed zeroes are
  // ignored (X could be positive or negative, so the output sign is unknown).
  if (FMF.noNaNs() && FMF.noSignedZeros() && match(Op0, m_AnyZero()))
    return Op0;

  if (FMF.noNaNs()) {
    // X / X -> 1.0 is legal when NaNs are ignored.
    if (Op0 == Op1)
      return ConstantFP::get(Op0->getType(), 1.0);

    // -X /  X -> -1.0 and
    //  X / -X -> -1.0 are legal when NaNs are ignored.
    // We can ignore signed zeros because +-0.0/+-0.0 is NaN and ignored.
    if ((BinaryOperator::isFNeg(Op0, /*IgnoreZeroSign=*/true) &&
         BinaryOperator::getFNegArgument(Op0) == Op1) ||
        (BinaryOperator::isFNeg(Op1, /*IgnoreZeroSign=*/true) &&
         BinaryOperator::getFNegArgument(Op1) == Op0))
      return ConstantFP::get(Op0->getType(), -1.0);
  }

  return nullptr;
}

Value *llvm::SimplifyFDivInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                              const SimplifyQuery &Q) {
  return ::SimplifyFDivInst(Op0, Op1, FMF, Q, RecursionLimit);
}

/// 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 SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
    return C;

  if (Value *V = simplifyDivRem(Op0, Op1, false))
    return V;

  // (X % Y) % Y -> X % Y
  if ((Opcode == Instruction::SRem &&
       match(Op0, m_SRem(m_Value(), m_Specific(Op1)))) ||
      (Opcode == Instruction::URem &&
       match(Op0, m_URem(m_Value(), m_Specific(Op1)))))
    return Op0;

  // 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;
}

/// Given operands for an SRem, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifySRemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  if (Value *V = SimplifyRem(Instruction::SRem, Op0, Op1, Q, MaxRecurse))
    return V;

  return nullptr;
}

Value *llvm::SimplifySRemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::SimplifySRemInst(Op0, Op1, Q, RecursionLimit);
}

/// Given operands for a URem, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyURemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  if (Value *V = SimplifyRem(Instruction::URem, Op0, Op1, Q, MaxRecurse))
    return V;

  // urem %V, C -> %V if %V < C
  if (MaxRecurse) {
    if (Constant *C = dyn_cast_or_null<Constant>(SimplifyICmpInst(
            ICmpInst::ICMP_ULT, Op0, Op1, Q, MaxRecurse - 1))) {
      if (C->isAllOnesValue()) {
        return Op0;
      }
    }
  }

  return nullptr;
}

Value *llvm::SimplifyURemInst(Value *Op0, Value *Op1, const SimplifyQuery &Q) {
  return ::SimplifyURemInst(Op0, Op1, Q, RecursionLimit);
}

static Value *SimplifyFRemInst(Value *Op0, Value *Op1, FastMathFlags FMF,
                               const SimplifyQuery &Q, unsigned) {
  if (Constant *C = foldOrCommuteConstant(Instruction::FRem, Op0, Op1, Q))
    return C;

  // 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 SimplifyQuery &Q) {
  return ::SimplifyFRemInst(Op0, Op1, FMF, Q, RecursionLimit);
}

/// 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;
}

/// Given operands for an Shl, LShr or AShr, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyShift(Instruction::BinaryOps Opcode, Value *Op0,
                            Value *Op1, const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Opcode, Op0, Op1, Q))
    return C;

  // 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;

  // If any bits in the shift amount make that value greater than or equal to
  // the number of bits in the type, the shift is undefined.
  unsigned BitWidth = Op1->getType()->getScalarSizeInBits();
  KnownBits Known(BitWidth);
  computeKnownBits(Op1, Known, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
  if (Known.One.getLimitedValue() >= BitWidth)
    return UndefValue::get(Op0->getType());

  // If all valid bits in the shift amount are known zero, the first operand is
  // unchanged.
  unsigned NumValidShiftBits = Log2_32_Ceil(BitWidth);
  if (Known.Zero.countTrailingOnes() >= NumValidShiftBits)
    return Op0;

  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(Instruction::BinaryOps Opcode, Value *Op0,
                                 Value *Op1, bool isExact, const SimplifyQuery &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();
    KnownBits Op0Known(BitWidth);
    computeKnownBits(Op0, Op0Known, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT);
    if (Op0Known.One[0])
      return Op0;
  }

  return nullptr;
}

/// Given operands for an Shl, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyShlInst(Value *Op0, Value *Op1, bool isNSW, bool isNUW,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V = SimplifyShift(Instruction::Shl, Op0, Op1, 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 SimplifyQuery &Q) {
  return ::SimplifyShlInst(Op0, Op1, isNSW, isNUW, Q, RecursionLimit);
}

/// Given operands for an LShr, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyLShrInst(Value *Op0, Value *Op1, bool isExact,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V = SimplifyRightShift(Instruction::LShr, Op0, Op1, isExact, Q,
                                    MaxRecurse))
      return V;

  // (X << A) >> A -> X
  Value *X;
  if (match(Op0, m_NUWShl(m_Value(X), m_Specific(Op1))))
    return X;

  return nullptr;
}

Value *llvm::SimplifyLShrInst(Value *Op0, Value *Op1, bool isExact,
                              const SimplifyQuery &Q) {
  return ::SimplifyLShrInst(Op0, Op1, isExact, Q, RecursionLimit);
}

/// Given operands for an AShr, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyAShrInst(Value *Op0, Value *Op1, bool isExact,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (Value *V = SimplifyRightShift(Instruction::AShr, Op0, Op1, isExact, Q,
                                    MaxRecurse))
    return V;

  // all ones >>a X -> 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 SimplifyQuery &Q) {
  return ::SimplifyAShrInst(Op0, Op1, isExact, Q, 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;
}

/// Commuted variants are assumed to be handled by calling this function again
/// with the parameters swapped.
static Value *simplifyAndOfICmpsWithSameOperands(ICmpInst *Op0, ICmpInst *Op1) {
  ICmpInst::Predicate Pred0, Pred1;
  Value *A ,*B;
  if (!match(Op0, m_ICmp(Pred0, m_Value(A), m_Value(B))) ||
      !match(Op1, m_ICmp(Pred1, m_Specific(A), m_Specific(B))))
    return nullptr;

  // We have (icmp Pred0, A, B) & (icmp Pred1, A, B).
  // If Op1 is always implied true by Op0, then Op0 is a subset of Op1, and we
  // can eliminate Op1 from this 'and'.
  if (ICmpInst::isImpliedTrueByMatchingCmp(Pred0, Pred1))
    return Op0;

  // Check for any combination of predicates that are guaranteed to be disjoint.
  if ((Pred0 == ICmpInst::getInversePredicate(Pred1)) ||
      (Pred0 == ICmpInst::ICMP_EQ && ICmpInst::isFalseWhenEqual(Pred1)) ||
      (Pred0 == ICmpInst::ICMP_SLT && Pred1 == ICmpInst::ICMP_SGT) ||
      (Pred0 == ICmpInst::ICMP_ULT && Pred1 == ICmpInst::ICMP_UGT))
    return getFalse(Op0->getType());

  return nullptr;
}

/// Commuted variants are assumed to be handled by calling this function again
/// with the parameters swapped.
static Value *SimplifyAndOfICmps(ICmpInst *Op0, ICmpInst *Op1) {
  if (Value *X = simplifyUnsignedRangeCheck(Op0, Op1, /*IsAnd=*/true))
    return X;

  if (Value *X = simplifyAndOfICmpsWithSameOperands(Op0, Op1))
    return X;

  // FIXME: This should be shared with or-of-icmps.
  // Look for this pattern: (icmp V, C0) & (icmp V, C1)).
  Type *ITy = Op0->getType();
  ICmpInst::Predicate Pred0, Pred1;
  const APInt *C0, *C1;
  Value *V;
  if (match(Op0, m_ICmp(Pred0, m_Value(V), m_APInt(C0))) &&
      match(Op1, m_ICmp(Pred1, m_Specific(V), m_APInt(C1)))) {
    // Make a constant range that's the intersection of the two icmp ranges.
    // If the intersection is empty, we know that the result is false.
    auto Range0 = ConstantRange::makeExactICmpRegion(Pred0, *C0);
    auto Range1 = ConstantRange::makeExactICmpRegion(Pred1, *C1);
    if (Range0.intersectWith(Range1).isEmptySet())
      return getFalse(ITy);

    // If a range is a superset of the other, the smaller set is all we need.
    if (Range0.contains(Range1))
      return Op1;
    if (Range1.contains(Range0))
      return Op0;
  }

  // (icmp (add V, C0), C1) & (icmp V, C0)
  if (!match(Op0, m_ICmp(Pred0, m_Add(m_Value(V), m_APInt(C0)), m_APInt(C1))))
    return nullptr;

  if (!match(Op1, m_ICmp(Pred1, m_Specific(V), m_Value())))
    return nullptr;

  auto *AddInst = cast<BinaryOperator>(Op0->getOperand(0));
  if (AddInst->getOperand(1) != Op1->getOperand(1))
    return nullptr;

  bool isNSW = AddInst->hasNoSignedWrap();
  bool isNUW = AddInst->hasNoUnsignedWrap();

  const APInt Delta = *C1 - *C0;
  if (C0->isStrictlyPositive()) {
    if (Delta == 2) {
      if (Pred0 == ICmpInst::ICMP_ULT && Pred1 == ICmpInst::ICMP_SGT)
        return getFalse(ITy);
      if (Pred0 == ICmpInst::ICMP_SLT && Pred1 == ICmpInst::ICMP_SGT && isNSW)
        return getFalse(ITy);
    }
    if (Delta == 1) {
      if (Pred0 == ICmpInst::ICMP_ULE && Pred1 == ICmpInst::ICMP_SGT)
        return getFalse(ITy);
      if (Pred0 == ICmpInst::ICMP_SLE && Pred1 == ICmpInst::ICMP_SGT && isNSW)
        return getFalse(ITy);
    }
  }
  if (C0->getBoolValue() && isNUW) {
    if (Delta == 2)
      if (Pred0 == ICmpInst::ICMP_ULT && Pred1 == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
    if (Delta == 1)
      if (Pred0 == ICmpInst::ICMP_ULE && Pred1 == ICmpInst::ICMP_UGT)
        return getFalse(ITy);
  }

  return nullptr;
}

/// Given operands for an And, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyAndInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                              unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::And, Op0, Op1, Q))
    return C;

  // X & 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;
    }
  }

  // The compares may be hidden behind casts. Look through those and try the
  // same folds as above.
  auto *Cast0 = dyn_cast<CastInst>(Op0);
  auto *Cast1 = dyn_cast<CastInst>(Op1);
  if (Cast0 && Cast1 && Cast0->getOpcode() == Cast1->getOpcode() &&
      Cast0->getSrcTy() == Cast1->getSrcTy()) {
    auto *Cmp0 = dyn_cast<ICmpInst>(Cast0->getOperand(0));
    auto *Cmp1 = dyn_cast<ICmpInst>(Cast1->getOperand(0));
    if (Cmp0 && Cmp1) {
      Instruction::CastOps CastOpc = Cast0->getOpcode();
      Type *ResultType = Cast0->getType();
      if (auto *V = dyn_cast_or_null<Constant>(SimplifyAndOfICmps(Cmp0, Cmp1)))
        return ConstantExpr::getCast(CastOpc, V, ResultType);
      if (auto *V = dyn_cast_or_null<Constant>(SimplifyAndOfICmps(Cmp1, Cmp0)))
        return ConstantExpr::getCast(CastOpc, V, ResultType);
    }
  }

  // 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 SimplifyQuery &Q) {
  return ::SimplifyAndInst(Op0, Op1, Q, RecursionLimit);
}

/// Commuted variants are assumed to be handled by calling this function again
/// with the parameters swapped.
static Value *simplifyOrOfICmpsWithSameOperands(ICmpInst *Op0, ICmpInst *Op1) {
  ICmpInst::Predicate Pred0, Pred1;
  Value *A ,*B;
  if (!match(Op0, m_ICmp(Pred0, m_Value(A), m_Value(B))) ||
      !match(Op1, m_ICmp(Pred1, m_Specific(A), m_Specific(B))))
    return nullptr;

  // We have (icmp Pred0, A, B) | (icmp Pred1, A, B).
  // If Op1 is always implied true by Op0, then Op0 is a subset of Op1, and we
  // can eliminate Op0 from this 'or'.
  if (ICmpInst::isImpliedTrueByMatchingCmp(Pred0, Pred1))
    return Op1;

  // Check for any combination of predicates that cover the entire range of
  // possibilities.
  if ((Pred0 == ICmpInst::getInversePredicate(Pred1)) ||
      (Pred0 == ICmpInst::ICMP_NE && ICmpInst::isTrueWhenEqual(Pred1)) ||
      (Pred0 == ICmpInst::ICMP_SLE && Pred1 == ICmpInst::ICMP_SGE) ||
      (Pred0 == ICmpInst::ICMP_ULE && Pred1 == ICmpInst::ICMP_UGE))
    return getTrue(Op0->getType());

  return nullptr;
}

/// Commuted variants are assumed to be handled by calling this function again
/// with the parameters swapped.
static Value *SimplifyOrOfICmps(ICmpInst *Op0, ICmpInst *Op1) {
  if (Value *X = simplifyUnsignedRangeCheck(Op0, Op1, /*IsAnd=*/false))
    return X;

  if (Value *X = simplifyOrOfICmpsWithSameOperands(Op0, Op1))
    return X;

  // (icmp (add V, C0), C1) | (icmp V, C0)
  ICmpInst::Predicate Pred0, Pred1;
  const APInt *C0, *C1;
  Value *V;
  if (!match(Op0, m_ICmp(Pred0, m_Add(m_Value(V), m_APInt(C0)), m_APInt(C1))))
    return nullptr;

  if (!match(Op1, m_ICmp(Pred1, m_Specific(V), m_Value())))
    return nullptr;

  auto *AddInst = cast<BinaryOperator>(Op0->getOperand(0));
  if (AddInst->getOperand(1) != Op1->getOperand(1))
    return nullptr;

  Type *ITy = Op0->getType();
  bool isNSW = AddInst->hasNoSignedWrap();
  bool isNUW = AddInst->hasNoUnsignedWrap();

  const APInt Delta = *C1 - *C0;
  if (C0->isStrictlyPositive()) {
    if (Delta == 2) {
      if (Pred0 == ICmpInst::ICMP_UGE && Pred1 == ICmpInst::ICMP_SLE)
        return getTrue(ITy);
      if (Pred0 == ICmpInst::ICMP_SGE && Pred1 == ICmpInst::ICMP_SLE && isNSW)
        return getTrue(ITy);
    }
    if (Delta == 1) {
      if (Pred0 == ICmpInst::ICMP_UGT && Pred1 == ICmpInst::ICMP_SLE)
        return getTrue(ITy);
      if (Pred0 == ICmpInst::ICMP_SGT && Pred1 == ICmpInst::ICMP_SLE && isNSW)
        return getTrue(ITy);
    }
  }
  if (C0->getBoolValue() && isNUW) {
    if (Delta == 2)
      if (Pred0 == ICmpInst::ICMP_UGE && Pred1 == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
    if (Delta == 1)
      if (Pred0 == ICmpInst::ICMP_UGT && Pred1 == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
  }

  return nullptr;
}

/// Given operands for an Or, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyOrInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                             unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Or, Op0, Op1, Q))
    return C;

  // X | 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());

  // (A & ~B) | (A ^ B) -> (A ^ B)
  // (~B & A) | (A ^ B) -> (A ^ B)
  // (A & ~B) | (B ^ A) -> (B ^ A)
  // (~B & A) | (B ^ A) -> (B ^ A)
  if (match(Op1, m_Xor(m_Value(A), m_Value(B))) &&
      (match(Op0, m_c_And(m_Specific(A), m_Not(m_Specific(B)))) ||
       match(Op0, m_c_And(m_Not(m_Specific(A)), m_Specific(B)))))
    return Op1;

  // Commute the 'or' operands.
  // (A ^ B) | (A & ~B) -> (A ^ B)
  // (A ^ B) | (~B & A) -> (A ^ B)
  // (B ^ A) | (A & ~B) -> (B ^ A)
  // (B ^ A) | (~B & A) -> (B ^ A)
  if (match(Op0, m_Xor(m_Value(A), m_Value(B))) &&
      (match(Op1, m_c_And(m_Specific(A), m_Not(m_Specific(B)))) ||
       match(Op1, m_c_And(m_Not(m_Specific(A)), m_Specific(B)))))
    return Op0;

  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 SimplifyQuery &Q) {
  return ::SimplifyOrInst(Op0, Op1, Q, RecursionLimit);
}

/// Given operands for a Xor, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyXorInst(Value *Op0, Value *Op1, const SimplifyQuery &Q,
                              unsigned MaxRecurse) {
  if (Constant *C = foldOrCommuteConstant(Instruction::Xor, Op0, Op1, Q))
    return C;

  // A ^ undef -> undef
  if (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 SimplifyQuery &Q) {
  return ::SimplifyXorInst(Op0, Op1, Q, RecursionLimit);
}


static Type *GetCompareTy(Value *Op) {
  return CmpInst::makeCmpResultType(Op->getType());
}

/// Rummage around inside V looking for something equivalent to the comparison
/// "LHS Pred RHS". Return such a value if found, otherwise return null.
/// Helper function for analyzing max/min idioms.
static Value *ExtractEquivalentCondition(Value *V, CmpInst::Predicate Pred,
                                         Value *LHS, Value *RHS) {
  SelectInst *SI = dyn_cast<SelectInst>(V);
  if (!SI)
    return nullptr;
  CmpInst *Cmp = dyn_cast<CmpInst>(SI->getCondition());
  if (!Cmp)
    return nullptr;
  Value *CmpLHS = Cmp->getOperand(0), *CmpRHS = Cmp->getOperand(1);
  if (Pred == Cmp->getPredicate() && LHS == CmpLHS && RHS == CmpRHS)
    return Cmp;
  if (Pred == CmpInst::getSwappedPredicate(Cmp->getPredicate()) &&
      LHS == CmpRHS && RHS == CmpLHS)
    return Cmp;
  return nullptr;
}

// A significant optimization not implemented here is assuming that alloca
// addresses are not equal to incoming argument values. They don't *alias*,
// as we say, but that doesn't mean they aren't equal, so we take a
// conservative approach.
//
// This is inspired in part by C++11 5.10p1:
//   "Two pointers of the same type compare equal if and only if they are both
//    null, both point to the same function, or both represent the same
//    address."
//
// This is pretty permissive.
//
// It's also partly due to C11 6.5.9p6:
//   "Two pointers compare equal if and only if both are null pointers, both are
//    pointers to the same object (including a pointer to an object and a
//    subobject at its beginning) or function, both are pointers to one past the
//    last element of the same array object, or one is a pointer to one past the
//    end of one array object and the other is a pointer to the start of a
//    different array object that happens to immediately follow the first array
//    object in the address space.)
//
// C11's version is more restrictive, however there's no reason why an argument
// couldn't be a one-past-the-end value for a stack object in the caller and be
// equal to the beginning of a stack object in the callee.
//
// If the C and C++ standards are ever made sufficiently restrictive in this
// area, it may be possible to update LLVM's semantics accordingly and reinstate
// this optimization.
static Constant *
computePointerICmp(const DataLayout &DL, const TargetLibraryInfo *TLI,
                   const DominatorTree *DT, CmpInst::Predicate Pred,
                   const Instruction *CxtI, 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) && 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 = [](ArrayRef<Value *> Objects) {
      return all_of(Objects, isNoAliasCall);
    };

    // Is the set of underlying objects all things which must be disjoint from
    // noalias calls. For allocas, we consider only static ones (dynamic
    // allocas might be transformed into calls to malloc not simultaneously
    // live with the compared-to allocation). For globals, we exclude symbols
    // that might be resolve lazily to symbols in another dynamically-loaded
    // library (and, thus, could be malloc'ed by the implementation).
    auto IsAllocDisjoint = [](ArrayRef<Value *> Objects) {
      return all_of(Objects, [](Value *V) {
        if (const AllocaInst *AI = dyn_cast<AllocaInst>(V))
          return AI->getParent() && AI->getFunction() && AI->isStaticAlloca();
        if (const GlobalValue *GV = dyn_cast<GlobalValue>(V))
          return (GV->hasLocalLinkage() || GV->hasHiddenVisibility() ||
                  GV->hasProtectedVisibility() || GV->hasGlobalUnnamedAddr()) &&
                 !GV->isThreadLocal();
        if (const Argument *A = dyn_cast<Argument>(V))
          return A->hasByValAttr();
        return false;
      });
    };

    if ((IsNAC(LHSUObjs) && IsAllocDisjoint(RHSUObjs)) ||
        (IsNAC(RHSUObjs) && IsAllocDisjoint(LHSUObjs)))
        return ConstantInt::get(GetCompareTy(LHS),
                                !CmpInst::isTrueWhenEqual(Pred));

    // Fold comparisons for non-escaping pointer even if the allocation call
    // cannot be elided. We cannot fold malloc comparison to null. Also, the
    // dynamic allocation call could be either of the operands.
    Value *MI = nullptr;
    if (isAllocLikeFn(LHS, TLI) && llvm::isKnownNonNullAt(RHS, CxtI, DT))
      MI = LHS;
    else if (isAllocLikeFn(RHS, TLI) && llvm::isKnownNonNullAt(LHS, CxtI, DT))
      MI = RHS;
    // FIXME: We should also fold the compare when the pointer escapes, but the
    // compare dominates the pointer escape
    if (MI && !PointerMayBeCaptured(MI, true, true))
      return ConstantInt::get(GetCompareTy(LHS),
                              CmpInst::isFalseWhenEqual(Pred));
  }

  // Otherwise, fail.
  return nullptr;
}

/// Fold an icmp when its operands have i1 scalar type.
static Value *simplifyICmpOfBools(CmpInst::Predicate Pred, Value *LHS,
                                  Value *RHS, const SimplifyQuery &Q) {
  Type *ITy = GetCompareTy(LHS); // The return type.
  Type *OpTy = LHS->getType();   // The operand type.
  if (!OpTy->getScalarType()->isIntegerTy(1))
    return nullptr;

  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;
    if (isImpliedCondition(RHS, LHS, Q.DL).getValueOr(false))
      return getTrue(ITy);
    break;
  case ICmpInst::ICMP_SGE:
    /// For signed comparison, the values for an i1 are 0 and -1
    /// respectively. This maps into a truth table of:
    /// LHS | RHS | LHS >=s RHS   | LHS implies RHS
    ///  0  |  0  |  1 (0 >= 0)   |  1
    ///  0  |  1  |  1 (0 >= -1)  |  1
    ///  1  |  0  |  0 (-1 >= 0)  |  0
    ///  1  |  1  |  1 (-1 >= -1) |  1
    if (isImpliedCondition(LHS, RHS, Q.DL).getValueOr(false))
      return getTrue(ITy);
    break;
  case ICmpInst::ICMP_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;
  case ICmpInst::ICMP_ULE:
    if (isImpliedCondition(LHS, RHS, Q.DL).getValueOr(false))
      return getTrue(ITy);
    break;
  }

  return nullptr;
}

/// Try hard to fold icmp with zero RHS because this is a common case.
static Value *simplifyICmpWithZero(CmpInst::Predicate Pred, Value *LHS,
                                   Value *RHS, const SimplifyQuery &Q) {
  if (!match(RHS, m_Zero()))
    return nullptr;

  Type *ITy = GetCompareTy(LHS); // The return type.
  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;
  }

  return nullptr;
}

/// Many binary operators with a constant operand have an easy-to-compute
/// range of outputs. This can be used to fold a comparison to always true or
/// always false.
static void setLimitsForBinOp(BinaryOperator &BO, APInt &Lower, APInt &Upper) {
  unsigned Width = Lower.getBitWidth();
  const APInt *C;
  switch (BO.getOpcode()) {
  case Instruction::Add:
    if (match(BO.getOperand(1), m_APInt(C)) && *C != 0) {
      // FIXME: If we have both nuw and nsw, we should reduce the range further.
      if (BO.hasNoUnsignedWrap()) {
        // 'add nuw x, C' produces [C, UINT_MAX].
        Lower = *C;
      } else if (BO.hasNoSignedWrap()) {
        if (C->isNegative()) {
          // 'add nsw x, -C' produces [SINT_MIN, SINT_MAX - C].
          Lower = APInt::getSignedMinValue(Width);
          Upper = APInt::getSignedMaxValue(Width) + *C + 1;
        } else {
          // 'add nsw x, +C' produces [SINT_MIN + C, SINT_MAX].
          Lower = APInt::getSignedMinValue(Width) + *C;
          Upper = APInt::getSignedMaxValue(Width) + 1;
        }
      }
    }
    break;

  case Instruction::And:
    if (match(BO.getOperand(1), m_APInt(C)))
      // 'and x, C' produces [0, C].
      Upper = *C + 1;
    break;

  case Instruction::Or:
    if (match(BO.getOperand(1), m_APInt(C)))
      // 'or x, C' produces [C, UINT_MAX].
      Lower = *C;
    break;

  case Instruction::AShr:
    if (match(BO.getOperand(1), m_APInt(C)) && C->ult(Width)) {
      // 'ashr x, C' produces [INT_MIN >> C, INT_MAX >> C].
      Lower = APInt::getSignedMinValue(Width).ashr(*C);
      Upper = APInt::getSignedMaxValue(Width).ashr(*C) + 1;
    } else if (match(BO.getOperand(0), m_APInt(C))) {
      unsigned ShiftAmount = Width - 1;
      if (*C != 0 && BO.isExact())
        ShiftAmount = C->countTrailingZeros();
      if (C->isNegative()) {
        // 'ashr C, x' produces [C, C >> (Width-1)]
        Lower = *C;
        Upper = C->ashr(ShiftAmount) + 1;
      } else {
        // 'ashr C, x' produces [C >> (Width-1), C]
        Lower = C->ashr(ShiftAmount);
        Upper = *C + 1;
      }
    }
    break;

  case Instruction::LShr:
    if (match(BO.getOperand(1), m_APInt(C)) && C->ult(Width)) {
      // 'lshr x, C' produces [0, UINT_MAX >> C].
      Upper = APInt::getAllOnesValue(Width).lshr(*C) + 1;
    } else if (match(BO.getOperand(0), m_APInt(C))) {
      // 'lshr C, x' produces [C >> (Width-1), C].
      unsigned ShiftAmount = Width - 1;
      if (*C != 0 && BO.isExact())
        ShiftAmount = C->countTrailingZeros();
      Lower = C->lshr(ShiftAmount);
      Upper = *C + 1;
    }
    break;

  case Instruction::Shl:
    if (match(BO.getOperand(0), m_APInt(C))) {
      if (BO.hasNoUnsignedWrap()) {
        // 'shl nuw C, x' produces [C, C << CLZ(C)]
        Lower = *C;
        Upper = Lower.shl(Lower.countLeadingZeros()) + 1;
      } else if (BO.hasNoSignedWrap()) { // TODO: What if both nuw+nsw?
        if (C->isNegative()) {
          // 'shl nsw C, x' produces [C << CLO(C)-1, C]
          unsigned ShiftAmount = C->countLeadingOnes() - 1;
          Lower = C->shl(ShiftAmount);
          Upper = *C + 1;
        } else {
          // 'shl nsw C, x' produces [C, C << CLZ(C)-1]
          unsigned ShiftAmount = C->countLeadingZeros() - 1;
          Lower = *C;
          Upper = C->shl(ShiftAmount) + 1;
        }
      }
    }
    break;

  case Instruction::SDiv:
    if (match(BO.getOperand(1), m_APInt(C))) {
      APInt IntMin = APInt::getSignedMinValue(Width);
      APInt IntMax = APInt::getSignedMaxValue(Width);
      if (C->isAllOnesValue()) {
        // 'sdiv x, -1' produces [INT_MIN + 1, INT_MAX]
        //    where C != -1 and C != 0 and C != 1
        Lower = IntMin + 1;
        Upper = IntMax + 1;
      } else if (C->countLeadingZeros() < Width - 1) {
        // 'sdiv x, C' produces [INT_MIN / C, INT_MAX / C]
        //    where C != -1 and C != 0 and C != 1
        Lower = IntMin.sdiv(*C);
        Upper = IntMax.sdiv(*C);
        if (Lower.sgt(Upper))
          std::swap(Lower, Upper);
        Upper = Upper + 1;
        assert(Upper != Lower && "Upper part of range has wrapped!");
      }
    } else if (match(BO.getOperand(0), m_APInt(C))) {
      if (C->isMinSignedValue()) {
        // 'sdiv INT_MIN, x' produces [INT_MIN, INT_MIN / -2].
        Lower = *C;
        Upper = Lower.lshr(1) + 1;
      } else {
        // 'sdiv C, x' produces [-|C|, |C|].
        Upper = C->abs() + 1;
        Lower = (-Upper) + 1;
      }
    }
    break;

  case Instruction::UDiv:
    if (match(BO.getOperand(1), m_APInt(C)) && *C != 0) {
      // 'udiv x, C' produces [0, UINT_MAX / C].
      Upper = APInt::getMaxValue(Width).udiv(*C) + 1;
    } else if (match(BO.getOperand(0), m_APInt(C))) {
      // 'udiv C, x' produces [0, C].
      Upper = *C + 1;
    }
    break;

  case Instruction::SRem:
    if (match(BO.getOperand(1), m_APInt(C))) {
      // 'srem x, C' produces (-|C|, |C|).
      Upper = C->abs();
      Lower = (-Upper) + 1;
    }
    break;

  case Instruction::URem:
    if (match(BO.getOperand(1), m_APInt(C)))
      // 'urem x, C' produces [0, C).
      Upper = *C;
    break;

  default:
    break;
  }
}

static Value *simplifyICmpWithConstant(CmpInst::Predicate Pred, Value *LHS,
                                       Value *RHS) {
  const APInt *C;
  if (!match(RHS, m_APInt(C)))
    return nullptr;

  // Rule out tautological comparisons (eg., ult 0 or uge 0).
  ConstantRange RHS_CR = ConstantRange::makeExactICmpRegion(Pred, *C);
  if (RHS_CR.isEmptySet())
    return ConstantInt::getFalse(GetCompareTy(RHS));
  if (RHS_CR.isFullSet())
    return ConstantInt::getTrue(GetCompareTy(RHS));

  // Find the range of possible values for binary operators.
  unsigned Width = C->getBitWidth();
  APInt Lower = APInt(Width, 0);
  APInt Upper = APInt(Width, 0);
  if (auto *BO = dyn_cast<BinaryOperator>(LHS))
    setLimitsForBinOp(*BO, Lower, Upper);

  ConstantRange LHS_CR =
      Lower != Upper ? ConstantRange(Lower, Upper) : ConstantRange(Width, true);

  if (auto *I = dyn_cast<Instruction>(LHS))
    if (auto *Ranges = I->getMetadata(LLVMContext::MD_range))
      LHS_CR = LHS_CR.intersectWith(getConstantRangeFromMetadata(*Ranges));

  if (!LHS_CR.isFullSet()) {
    if (RHS_CR.contains(LHS_CR))
      return ConstantInt::getTrue(GetCompareTy(RHS));
    if (RHS_CR.inverse().contains(LHS_CR))
      return ConstantInt::getFalse(GetCompareTy(RHS));
  }

  return nullptr;
}

static Value *simplifyICmpWithBinOp(CmpInst::Predicate Pred, Value *LHS,
                                    Value *RHS, const SimplifyQuery &Q,
                                    unsigned MaxRecurse) {
  Type *ITy = GetCompareTy(LHS); // The return type.

  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;
    }
  }

  {
    Value *Y = nullptr;
    // icmp pred (or X, Y), X
    if (LBO && match(LBO, m_c_Or(m_Value(Y), m_Specific(RHS)))) {
      if (Pred == ICmpInst::ICMP_ULT)
        return getFalse(ITy);
      if (Pred == ICmpInst::ICMP_UGE)
        return getTrue(ITy);

      if (Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SGE) {
        bool RHSKnownNonNegative, RHSKnownNegative;
        bool YKnownNonNegative, YKnownNegative;
        ComputeSignBit(RHS, RHSKnownNonNegative, RHSKnownNegative, Q.DL, 0,
                       Q.AC, Q.CxtI, Q.DT);
        ComputeSignBit(Y, YKnownNonNegative, YKnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (RHSKnownNonNegative && YKnownNegative)
          return Pred == ICmpInst::ICMP_SLT ? getTrue(ITy) : getFalse(ITy);
        if (RHSKnownNegative || YKnownNonNegative)
          return Pred == ICmpInst::ICMP_SLT ? getFalse(ITy) : getTrue(ITy);
      }
    }
    // icmp pred X, (or X, Y)
    if (RBO && match(RBO, m_c_Or(m_Value(Y), m_Specific(LHS)))) {
      if (Pred == ICmpInst::ICMP_ULE)
        return getTrue(ITy);
      if (Pred == ICmpInst::ICMP_UGT)
        return getFalse(ITy);

      if (Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SLE) {
        bool LHSKnownNonNegative, LHSKnownNegative;
        bool YKnownNonNegative, YKnownNegative;
        ComputeSignBit(LHS, LHSKnownNonNegative, LHSKnownNegative, Q.DL, 0,
                       Q.AC, Q.CxtI, Q.DT);
        ComputeSignBit(Y, YKnownNonNegative, YKnownNegative, Q.DL, 0, Q.AC,
                       Q.CxtI, Q.DT);
        if (LHSKnownNonNegative && YKnownNegative)
          return Pred == ICmpInst::ICMP_SGT ? getTrue(ITy) : getFalse(ITy);
        if (LHSKnownNegative || YKnownNonNegative)
          return Pred == ICmpInst::ICMP_SGT ? getFalse(ITy) : getTrue(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;
      LLVM_FALLTHROUGH;
    case ICmpInst::ICMP_EQ:
    case ICmpInst::ICMP_UGT:
    case ICmpInst::ICMP_UGE:
      return getFalse(ITy);
    case ICmpInst::ICMP_SLT:
    case ICmpInst::ICMP_SLE:
      ComputeSignBit(RHS, KnownNonNegative, KnownNegative, Q.DL, 0, Q.AC,
                     Q.CxtI, Q.DT);
      if (!KnownNonNegative)
        break;
      LLVM_FALLTHROUGH;
    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;
      LLVM_FALLTHROUGH;
    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;
      LLVM_FALLTHROUGH;
    case ICmpInst::ICMP_EQ:
    case ICmpInst::ICMP_ULT:
    case ICmpInst::ICMP_ULE:
      return getFalse(ITy);
    }
  }

  // x >> y <=u x
  // x udiv y <=u x.
  if (LBO && (match(LBO, m_LShr(m_Specific(RHS), m_Value())) ||
              match(LBO, m_UDiv(m_Specific(RHS), m_Value())))) {
    // icmp pred (X op Y), X
    if (Pred == ICmpInst::ICMP_UGT)
      return getFalse(ITy);
    if (Pred == ICmpInst::ICMP_ULE)
      return getTrue(ITy);
  }

  // x >=u x >> y
  // x >=u x udiv y.
  if (RBO && (match(RBO, m_LShr(m_Specific(LHS), m_Value())) ||
              match(RBO, m_UDiv(m_Specific(LHS), m_Value())))) {
    // icmp pred X, (X op Y)
    if (Pred == ICmpInst::ICMP_ULT)
      return getFalse(ITy);
    if (Pred == ICmpInst::ICMP_UGE)
      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->isSignMask() && *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;
      LLVM_FALLTHROUGH;
    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;
    }
    }
  }
  return nullptr;
}

/// Simplify integer comparisons where at least one operand of the compare
/// matches an integer min/max idiom.
static Value *simplifyICmpWithMinMax(CmpInst::Predicate Pred, Value *LHS,
                                     Value *RHS, const SimplifyQuery &Q,
                                     unsigned MaxRecurse) {
  Type *ITy = GetCompareTy(LHS); // The return type.
  Value *A, *B;
  CmpInst::Predicate P = CmpInst::BAD_ICMP_PREDICATE;
  CmpInst::Predicate EqP; // Chosen so that "A == max/min(A,B)" iff "A EqP B".

  // Signed variants on "max(a,b)>=a -> true".
  if (match(LHS, m_SMax(m_Value(A), m_Value(B))) && (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // smax(A, B) pred A.
    EqP = CmpInst::ICMP_SGE; // "A == smax(A, B)" iff "A sge B".
    // We analyze this as smax(A, B) pred A.
    P = Pred;
  } else if (match(RHS, m_SMax(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred smax(A, B).
    EqP = CmpInst::ICMP_SGE; // "A == smax(A, B)" iff "A sge B".
    // We analyze this as smax(A, B) swapped-pred A.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(LHS, m_SMin(m_Value(A), m_Value(B))) &&
             (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // smin(A, B) pred A.
    EqP = CmpInst::ICMP_SLE; // "A == smin(A, B)" iff "A sle B".
    // We analyze this as smax(-A, -B) swapped-pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(RHS, m_SMin(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred smin(A, B).
    EqP = CmpInst::ICMP_SLE; // "A == smin(A, B)" iff "A sle B".
    // We analyze this as smax(-A, -B) pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = Pred;
  }
  if (P != CmpInst::BAD_ICMP_PREDICATE) {
    // Cases correspond to "max(A, B) p A".
    switch (P) {
    default:
      break;
    case CmpInst::ICMP_EQ:
    case CmpInst::ICMP_SLE:
      // Equivalent to "A EqP B".  This may be the same as the condition tested
      // in the max/min; if so, we can just return that.
      if (Value *V = ExtractEquivalentCondition(LHS, EqP, A, B))
        return V;
      if (Value *V = ExtractEquivalentCondition(RHS, EqP, A, B))
        return V;
      // Otherwise, see if "A EqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = SimplifyICmpInst(EqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    case CmpInst::ICMP_NE:
    case CmpInst::ICMP_SGT: {
      CmpInst::Predicate InvEqP = CmpInst::getInversePredicate(EqP);
      // Equivalent to "A InvEqP B".  This may be the same as the condition
      // tested in the max/min; if so, we can just return that.
      if (Value *V = ExtractEquivalentCondition(LHS, InvEqP, A, B))
        return V;
      if (Value *V = ExtractEquivalentCondition(RHS, InvEqP, A, B))
        return V;
      // Otherwise, see if "A InvEqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = SimplifyICmpInst(InvEqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    }
    case CmpInst::ICMP_SGE:
      // Always true.
      return getTrue(ITy);
    case CmpInst::ICMP_SLT:
      // Always false.
      return getFalse(ITy);
    }
  }

  // Unsigned variants on "max(a,b)>=a -> true".
  P = CmpInst::BAD_ICMP_PREDICATE;
  if (match(LHS, m_UMax(m_Value(A), m_Value(B))) && (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // umax(A, B) pred A.
    EqP = CmpInst::ICMP_UGE; // "A == umax(A, B)" iff "A uge B".
    // We analyze this as umax(A, B) pred A.
    P = Pred;
  } else if (match(RHS, m_UMax(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred umax(A, B).
    EqP = CmpInst::ICMP_UGE; // "A == umax(A, B)" iff "A uge B".
    // We analyze this as umax(A, B) swapped-pred A.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(LHS, m_UMin(m_Value(A), m_Value(B))) &&
             (A == RHS || B == RHS)) {
    if (A != RHS)
      std::swap(A, B);       // umin(A, B) pred A.
    EqP = CmpInst::ICMP_ULE; // "A == umin(A, B)" iff "A ule B".
    // We analyze this as umax(-A, -B) swapped-pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = CmpInst::getSwappedPredicate(Pred);
  } else if (match(RHS, m_UMin(m_Value(A), m_Value(B))) &&
             (A == LHS || B == LHS)) {
    if (A != LHS)
      std::swap(A, B);       // A pred umin(A, B).
    EqP = CmpInst::ICMP_ULE; // "A == umin(A, B)" iff "A ule B".
    // We analyze this as umax(-A, -B) pred -A.
    // Note that we do not need to actually form -A or -B thanks to EqP.
    P = Pred;
  }
  if (P != CmpInst::BAD_ICMP_PREDICATE) {
    // Cases correspond to "max(A, B) p A".
    switch (P) {
    default:
      break;
    case CmpInst::ICMP_EQ:
    case CmpInst::ICMP_ULE:
      // Equivalent to "A EqP B".  This may be the same as the condition tested
      // in the max/min; if so, we can just return that.
      if (Value *V = ExtractEquivalentCondition(LHS, EqP, A, B))
        return V;
      if (Value *V = ExtractEquivalentCondition(RHS, EqP, A, B))
        return V;
      // Otherwise, see if "A EqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = SimplifyICmpInst(EqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    case CmpInst::ICMP_NE:
    case CmpInst::ICMP_UGT: {
      CmpInst::Predicate InvEqP = CmpInst::getInversePredicate(EqP);
      // Equivalent to "A InvEqP B".  This may be the same as the condition
      // tested in the max/min; if so, we can just return that.
      if (Value *V = ExtractEquivalentCondition(LHS, InvEqP, A, B))
        return V;
      if (Value *V = ExtractEquivalentCondition(RHS, InvEqP, A, B))
        return V;
      // Otherwise, see if "A InvEqP B" simplifies.
      if (MaxRecurse)
        if (Value *V = SimplifyICmpInst(InvEqP, A, B, Q, MaxRecurse - 1))
          return V;
      break;
    }
    case CmpInst::ICMP_UGE:
      // 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);
  }

  return nullptr;
}

/// Given operands for an ICmpInst, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               const SimplifyQuery &Q, unsigned MaxRecurse) {
  CmpInst::Predicate Pred = (CmpInst::Predicate)Predicate;
  assert(CmpInst::isIntPredicate(Pred) && "Not an integer compare!");

  if (Constant *CLHS = dyn_cast<Constant>(LHS)) {
    if (Constant *CRHS = dyn_cast<Constant>(RHS))
      return ConstantFoldCompareInstOperands(Pred, CLHS, CRHS, Q.DL, Q.TLI);

    // If we have a constant, make sure it is on the RHS.
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }

  Type *ITy = GetCompareTy(LHS); // The return 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));

  if (Value *V = simplifyICmpOfBools(Pred, LHS, RHS, Q))
    return V;

  if (Value *V = simplifyICmpWithZero(Pred, LHS, RHS, Q))
    return V;

  if (Value *V = simplifyICmpWithConstant(Pred, LHS, RHS))
    return V;

  // If both operands have range metadata, use the metadata
  // to simplify the comparison.
  if (isa<Instruction>(RHS) && isa<Instruction>(LHS)) {
    auto RHS_Instr = cast<Instruction>(RHS);
    auto LHS_Instr = cast<Instruction>(LHS);

    if (RHS_Instr->getMetadata(LLVMContext::MD_range) &&
        LHS_Instr->getMetadata(LLVMContext::MD_range)) {
      auto RHS_CR = getConstantRangeFromMetadata(
          *RHS_Instr->getMetadata(LLVMContext::MD_range));
      auto LHS_CR = getConstantRangeFromMetadata(
          *LHS_Instr->getMetadata(LLVMContext::MD_range));

      auto Satisfied_CR = ConstantRange::makeSatisfyingICmpRegion(Pred, RHS_CR);
      if (Satisfied_CR.contains(LHS_CR))
        return ConstantInt::getTrue(RHS->getContext());

      auto InversedSatisfied_CR = ConstantRange::makeSatisfyingICmpRegion(
                CmpInst::getInversePredicate(Pred), RHS_CR);
      if (InversedSatisfied_CR.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;
          }
        }
      }
    }
  }

  // icmp eq|ne X, Y -> false|true if X != Y
  if ((Pred == ICmpInst::ICMP_EQ || Pred == ICmpInst::ICMP_NE) &&
      isKnownNonEqual(LHS, RHS, Q.DL, Q.AC, Q.CxtI, Q.DT)) {
    LLVMContext &Ctx = LHS->getType()->getContext();
    return Pred == ICmpInst::ICMP_NE ?
      ConstantInt::getTrue(Ctx) : ConstantInt::getFalse(Ctx);
  }

  if (Value *V = simplifyICmpWithBinOp(Pred, LHS, RHS, Q, MaxRecurse))
    return V;

  if (Value *V = simplifyICmpWithMinMax(Pred, LHS, RHS, Q, MaxRecurse))
    return V;

  // Simplify comparisons of related pointers using a powerful, recursive
  // GEP-walk when we have target data available..
  if (LHS->getType()->isPointerTy())
    if (auto *C = computePointerICmp(Q.DL, Q.TLI, Q.DT, Pred, Q.CxtI, LHS, RHS))
      return C;
  if (auto *CLHS = dyn_cast<PtrToIntOperator>(LHS))
    if (auto *CRHS = dyn_cast<PtrToIntOperator>(RHS))
      if (Q.DL.getTypeSizeInBits(CLHS->getPointerOperandType()) ==
              Q.DL.getTypeSizeInBits(CLHS->getType()) &&
          Q.DL.getTypeSizeInBits(CRHS->getPointerOperandType()) ==
              Q.DL.getTypeSizeInBits(CRHS->getType()))
        if (auto *C = computePointerICmp(Q.DL, Q.TLI, Q.DT, Pred, Q.CxtI,
                                         CLHS->getPointerOperand(),
                                         CRHS->getPointerOperand()))
          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)) {
    const APInt *RHSVal;
    if (match(RHS, m_APInt(RHSVal))) {
      unsigned BitWidth = RHSVal->getBitWidth();
      KnownBits LHSKnown(BitWidth);
      computeKnownBits(LHS, LHSKnown, Q.DL, /*Depth=*/0, Q.AC, Q.CxtI, Q.DT);
      if (LHSKnown.Zero.intersects(*RHSVal) ||
          !LHSKnown.One.isSubsetOf(*RHSVal))
        return Pred == ICmpInst::ICMP_EQ ? ConstantInt::getFalse(ITy)
                                         : ConstantInt::getTrue(ITy);
    }
  }

  // If the comparison is with the result of a select instruction, check whether
  // comparing with either branch of the select always yields the same value.
  if (isa<SelectInst>(LHS) || isa<SelectInst>(RHS))
    if (Value *V = ThreadCmpOverSelect(Pred, LHS, RHS, Q, MaxRecurse))
      return V;

  // If the comparison is with the result of a phi instruction, check whether
  // doing the compare with each incoming phi value yields a common result.
  if (isa<PHINode>(LHS) || isa<PHINode>(RHS))
    if (Value *V = ThreadCmpOverPHI(Pred, LHS, RHS, Q, MaxRecurse))
      return V;

  return nullptr;
}

Value *llvm::SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                              const SimplifyQuery &Q) {
  return ::SimplifyICmpInst(Predicate, LHS, RHS, Q, RecursionLimit);
}

/// Given operands for an FCmpInst, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyFCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                               FastMathFlags FMF, const SimplifyQuery &Q,
                               unsigned MaxRecurse) {
  CmpInst::Predicate Pred = (CmpInst::Predicate)Predicate;
  assert(CmpInst::isFPPredicate(Pred) && "Not an FP compare!");

  if (Constant *CLHS = dyn_cast<Constant>(LHS)) {
    if (Constant *CRHS = dyn_cast<Constant>(RHS))
      return ConstantFoldCompareInstOperands(Pred, CLHS, CRHS, Q.DL, Q.TLI);

    // If we have a constant, make sure it is on the RHS.
    std::swap(LHS, RHS);
    Pred = CmpInst::getSwappedPredicate(Pred);
  }

  // Fold trivial predicates.
  Type *RetTy = GetCompareTy(LHS);
  if (Pred == FCmpInst::FCMP_FALSE)
    return getFalse(RetTy);
  if (Pred == FCmpInst::FCMP_TRUE)
    return getTrue(RetTy);

  // UNO/ORD predicates can be trivially folded if NaNs are ignored.
  if (FMF.noNaNs()) {
    if (Pred == FCmpInst::FCMP_UNO)
      return getFalse(RetTy);
    if (Pred == FCmpInst::FCMP_ORD)
      return getTrue(RetTy);
  }

  // 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(RetTy, CmpInst::isUnordered(Pred));
  }

  // fcmp x,x -> true/false.  Not all compares are foldable.
  if (LHS == RHS) {
    if (CmpInst::isTrueWhenEqual(Pred))
      return getTrue(RetTy);
    if (CmpInst::isFalseWhenEqual(Pred))
      return getFalse(RetTy);
  }

  // Handle fcmp with constant RHS
  const ConstantFP *CFP = nullptr;
  if (const auto *RHSC = dyn_cast<Constant>(RHS)) {
    if (RHS->getType()->isVectorTy())
      CFP = dyn_cast_or_null<ConstantFP>(RHSC->getSplatValue());
    else
      CFP = dyn_cast<ConstantFP>(RHSC);
  }
  if (CFP) {
    // 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 getFalse(RetTy);
      assert(FCmpInst::isUnordered(Pred) &&
             "Comparison must be either ordered or unordered!");
      // True if unordered.
      return getTrue(RetTy);
    }
    // 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 getFalse(RetTy);
        case FCmpInst::FCMP_UGE:
          // All values are unordered with or at least negative infinity.
          return getTrue(RetTy);
        default:
          break;
        }
      } else {
        switch (Pred) {
        case FCmpInst::FCMP_OGT:
          // No value is ordered and greater than infinity.
          return getFalse(RetTy);
        case FCmpInst::FCMP_ULE:
          // All values are unordered with and at most infinity.
          return getTrue(RetTy);
        default:
          break;
        }
      }
    }
    if (CFP->getValueAPF().isZero()) {
      switch (Pred) {
      case FCmpInst::FCMP_UGE:
        if (CannotBeOrderedLessThanZero(LHS, Q.TLI))
          return getTrue(RetTy);
        break;
      case FCmpInst::FCMP_OLT:
        // X < 0
        if (CannotBeOrderedLessThanZero(LHS, Q.TLI))
          return getFalse(RetTy);
        break;
      default:
        break;
      }
    }
  }

  // If the comparison is with the result of a select instruction, check whether
  // comparing with either branch of the select always yields the same value.
  if (isa<SelectInst>(LHS) || isa<SelectInst>(RHS))
    if (Value *V = ThreadCmpOverSelect(Pred, LHS, RHS, Q, MaxRecurse))
      return V;

  // If the comparison is with the result of a phi instruction, check whether
  // doing the compare with each incoming phi value yields a common result.
  if (isa<PHINode>(LHS) || isa<PHINode>(RHS))
    if (Value *V = ThreadCmpOverPHI(Pred, LHS, RHS, Q, MaxRecurse))
      return V;

  return nullptr;
}

Value *llvm::SimplifyFCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                              FastMathFlags FMF, const SimplifyQuery &Q) {
  return ::SimplifyFCmpInst(Predicate, LHS, RHS, FMF, Q, RecursionLimit);
}

/// See if V simplifies when its operand Op is replaced with RepOp.
static const Value *SimplifyWithOpReplaced(Value *V, Value *Op, Value *RepOp,
                                           const SimplifyQuery &Q,
                                           unsigned MaxRecurse) {
  // Trivial replacement.
  if (V == Op)
    return RepOp;

  auto *I = dyn_cast<Instruction>(V);
  if (!I)
    return nullptr;

  // If this is a binary operator, try to simplify it with the replaced op.
  if (auto *B = dyn_cast<BinaryOperator>(I)) {
    // Consider:
    //   %cmp = icmp eq i32 %x, 2147483647
    //   %add = add nsw i32 %x, 1
    //   %sel = select i1 %cmp, i32 -2147483648, i32 %add
    //
    // We can't replace %sel with %add unless we strip away the flags.
    if (isa<OverflowingBinaryOperator>(B))
      if (B->hasNoSignedWrap() || B->hasNoUnsignedWrap())
        return nullptr;
    if (isa<PossiblyExactOperator>(B))
      if (B->isExact())
        return nullptr;

    if (MaxRecurse) {
      if (B->getOperand(0) == Op)
        return SimplifyBinOp(B->getOpcode(), RepOp, B->getOperand(1), Q,
                             MaxRecurse - 1);
      if (B->getOperand(1) == Op)
        return SimplifyBinOp(B->getOpcode(), B->getOperand(0), RepOp, Q,
                             MaxRecurse - 1);
    }
  }

  // Same for CmpInsts.
  if (CmpInst *C = dyn_cast<CmpInst>(I)) {
    if (MaxRecurse) {
      if (C->getOperand(0) == Op)
        return SimplifyCmpInst(C->getPredicate(), RepOp, C->getOperand(1), Q,
                               MaxRecurse - 1);
      if (C->getOperand(1) == Op)
        return SimplifyCmpInst(C->getPredicate(), C->getOperand(0), RepOp, Q,
                               MaxRecurse - 1);
    }
  }

  // TODO: We could hand off more cases to instsimplify here.

  // If all operands are constant after substituting Op for RepOp then we can
  // constant fold the instruction.
  if (Constant *CRepOp = dyn_cast<Constant>(RepOp)) {
    // Build a list of all constant operands.
    SmallVector<Constant *, 8> ConstOps;
    for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
      if (I->getOperand(i) == Op)
        ConstOps.push_back(CRepOp);
      else if (Constant *COp = dyn_cast<Constant>(I->getOperand(i)))
        ConstOps.push_back(COp);
      else
        break;
    }

    // All operands were constants, fold it.
    if (ConstOps.size() == I->getNumOperands()) {
      if (CmpInst *C = dyn_cast<CmpInst>(I))
        return ConstantFoldCompareInstOperands(C->getPredicate(), ConstOps[0],
                                               ConstOps[1], Q.DL, Q.TLI);

      if (LoadInst *LI = dyn_cast<LoadInst>(I))
        if (!LI->isVolatile())
          return ConstantFoldLoadFromConstPtr(ConstOps[0], LI->getType(), Q.DL);

      return ConstantFoldInstOperands(I, ConstOps, Q.DL, Q.TLI);
    }
  }

  return nullptr;
}

/// Try to simplify a select instruction when its condition operand is an
/// integer comparison where one operand of the compare is a constant.
static Value *simplifySelectBitTest(Value *TrueVal, Value *FalseVal, Value *X,
                                    const APInt *Y, bool TrueWhenUnset) {
  const APInt *C;

  // (X & Y) == 0 ? X & ~Y : X  --> X
  // (X & Y) != 0 ? X & ~Y : X  --> X & ~Y
  if (FalseVal == X && match(TrueVal, m_And(m_Specific(X), m_APInt(C))) &&
      *Y == ~*C)
    return TrueWhenUnset ? FalseVal : TrueVal;

  // (X & Y) == 0 ? X : X & ~Y  --> X & ~Y
  // (X & Y) != 0 ? X : X & ~Y  --> X
  if (TrueVal == X && match(FalseVal, m_And(m_Specific(X), m_APInt(C))) &&
      *Y == ~*C)
    return TrueWhenUnset ? FalseVal : TrueVal;

  if (Y->isPowerOf2()) {
    // (X & Y) == 0 ? X | Y : X  --> X | Y
    // (X & Y) != 0 ? X | Y : X  --> X
    if (FalseVal == X && match(TrueVal, m_Or(m_Specific(X), m_APInt(C))) &&
        *Y == *C)
      return TrueWhenUnset ? TrueVal : FalseVal;

    // (X & Y) == 0 ? X : X | Y  --> X
    // (X & Y) != 0 ? X : X | Y  --> X | Y
    if (TrueVal == X && match(FalseVal, m_Or(m_Specific(X), m_APInt(C))) &&
        *Y == *C)
      return TrueWhenUnset ? TrueVal : FalseVal;
  }

  return nullptr;
}

/// An alternative way to test if a bit is set or not uses sgt/slt instead of
/// eq/ne.
static Value *simplifySelectWithFakeICmpEq(Value *CmpLHS, Value *TrueVal,
                                           Value *FalseVal,
                                           bool TrueWhenUnset) {
  unsigned BitWidth = TrueVal->getType()->getScalarSizeInBits();
  if (!BitWidth)
    return nullptr;

  APInt MinSignedValue;
  Value *X;
  if (match(CmpLHS, m_Trunc(m_Value(X))) && (X == TrueVal || X == FalseVal)) {
    // icmp slt (trunc X), 0  <--> icmp ne (and X, C), 0
    // icmp sgt (trunc X), -1 <--> icmp eq (and X, C), 0
    unsigned DestSize = CmpLHS->getType()->getScalarSizeInBits();
    MinSignedValue = APInt::getSignedMinValue(DestSize).zext(BitWidth);
  } else {
    // icmp slt X, 0  <--> icmp ne (and X, C), 0
    // icmp sgt X, -1 <--> icmp eq (and X, C), 0
    X = CmpLHS;
    MinSignedValue = APInt::getSignedMinValue(BitWidth);
  }

  if (Value *V = simplifySelectBitTest(TrueVal, FalseVal, X, &MinSignedValue,
                                       TrueWhenUnset))
    return V;

  return nullptr;
}

/// Try to simplify a select instruction when its condition operand is an
/// integer comparison.
static Value *simplifySelectWithICmpCond(Value *CondVal, Value *TrueVal,
                                         Value *FalseVal, const SimplifyQuery &Q,
                                         unsigned MaxRecurse) {
  ICmpInst::Predicate Pred;
  Value *CmpLHS, *CmpRHS;
  if (!match(CondVal, m_ICmp(Pred, m_Value(CmpLHS), m_Value(CmpRHS))))
    return nullptr;

  // FIXME: This code is nearly duplicated in InstCombine. Using/refactoring
  // decomposeBitTestICmp() might help.
  if (ICmpInst::isEquality(Pred) && match(CmpRHS, m_Zero())) {
    Value *X;
    const APInt *Y;
    if (match(CmpLHS, m_And(m_Value(X), m_APInt(Y))))
      if (Value *V = simplifySelectBitTest(TrueVal, FalseVal, X, Y,
                                           Pred == ICmpInst::ICMP_EQ))
        return V;
  } else if (Pred == ICmpInst::ICMP_SLT && match(CmpRHS, m_Zero())) {
    // Comparing signed-less-than 0 checks if the sign bit is set.
    if (Value *V = simplifySelectWithFakeICmpEq(CmpLHS, TrueVal, FalseVal,
                                                false))
      return V;
  } else if (Pred == ICmpInst::ICMP_SGT && match(CmpRHS, m_AllOnes())) {
    // Comparing signed-greater-than -1 checks if the sign bit is not set.
    if (Value *V = simplifySelectWithFakeICmpEq(CmpLHS, TrueVal, FalseVal,
                                                true))
      return V;
  }

  if (CondVal->hasOneUse()) {
    const APInt *C;
    if (match(CmpRHS, m_APInt(C))) {
      // X < MIN ? T : F  -->  F
      if (Pred == ICmpInst::ICMP_SLT && C->isMinSignedValue())
        return FalseVal;
      // X < MIN ? T : F  -->  F
      if (Pred == ICmpInst::ICMP_ULT && C->isMinValue())
        return FalseVal;
      // X > MAX ? T : F  -->  F
      if (Pred == ICmpInst::ICMP_SGT && C->isMaxSignedValue())
        return FalseVal;
      // X > MAX ? T : F  -->  F
      if (Pred == ICmpInst::ICMP_UGT && C->isMaxValue())
        return FalseVal;
    }
  }

  // If we have an equality comparison, then we know the value in one of the
  // arms of the select. See if substituting this value into the arm and
  // simplifying the result yields the same value as the other arm.
  if (Pred == ICmpInst::ICMP_EQ) {
    if (SimplifyWithOpReplaced(FalseVal, CmpLHS, CmpRHS, Q, MaxRecurse) ==
            TrueVal ||
        SimplifyWithOpReplaced(FalseVal, CmpRHS, CmpLHS, Q, MaxRecurse) ==
            TrueVal)
      return FalseVal;
    if (SimplifyWithOpReplaced(TrueVal, CmpLHS, CmpRHS, Q, MaxRecurse) ==
            FalseVal ||
        SimplifyWithOpReplaced(TrueVal, CmpRHS, CmpLHS, Q, MaxRecurse) ==
            FalseVal)
      return FalseVal;
  } else if (Pred == ICmpInst::ICMP_NE) {
    if (SimplifyWithOpReplaced(TrueVal, CmpLHS, CmpRHS, Q, MaxRecurse) ==
            FalseVal ||
        SimplifyWithOpReplaced(TrueVal, CmpRHS, CmpLHS, Q, MaxRecurse) ==
            FalseVal)
      return TrueVal;
    if (SimplifyWithOpReplaced(FalseVal, CmpLHS, CmpRHS, Q, MaxRecurse) ==
            TrueVal ||
        SimplifyWithOpReplaced(FalseVal, CmpRHS, CmpLHS, Q, MaxRecurse) ==
            TrueVal)
      return TrueVal;
  }

  return nullptr;
}

/// 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 SimplifyQuery &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>(FalseVal))
      return FalseVal;
    return TrueVal;
  }
  if (isa<UndefValue>(TrueVal))   // select C, undef, X -> X
    return FalseVal;
  if (isa<UndefValue>(FalseVal))   // select C, X, undef -> X
    return TrueVal;

  if (Value *V =
          simplifySelectWithICmpCond(CondVal, TrueVal, FalseVal, Q, MaxRecurse))
    return V;

  return nullptr;
}

Value *llvm::SimplifySelectInst(Value *Cond, Value *TrueVal, Value *FalseVal,
                                const SimplifyQuery &Q) {
  return ::SimplifySelectInst(Cond, TrueVal, FalseVal, Q, RecursionLimit);
}

/// Given operands for an GetElementPtrInst, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyGEPInst(Type *SrcTy, ArrayRef<Value *> Ops,
                              const SimplifyQuery &Q, unsigned) {
  // The type of the GEP pointer operand.
  unsigned AS =
      cast<PointerType>(Ops[0]->getType()->getScalarType())->getAddressSpace();

  // getelementptr P -> P.
  if (Ops.size() == 1)
    return Ops[0];

  // Compute the (pointer) type returned by the GEP instruction.
  Type *LastType = GetElementPtrInst::getIndexedType(SrcTy, Ops.slice(1));
  Type *GEPTy = PointerType::get(LastType, AS);
  if (VectorType *VT = dyn_cast<VectorType>(Ops[0]->getType()))
    GEPTy = VectorType::get(GEPTy, VT->getNumElements());
  else if (VectorType *VT = dyn_cast<VectorType>(Ops[1]->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;
      }
    }
  }

  if (Q.DL.getTypeAllocSize(LastType) == 1 &&
      all_of(Ops.slice(1).drop_back(1),
             [](Value *Idx) { return match(Idx, m_Zero()); })) {
    unsigned PtrWidth =
        Q.DL.getPointerSizeInBits(Ops[0]->getType()->getPointerAddressSpace());
    if (Q.DL.getTypeSizeInBits(Ops.back()->getType()) == PtrWidth) {
      APInt BasePtrOffset(PtrWidth, 0);
      Value *StrippedBasePtr =
          Ops[0]->stripAndAccumulateInBoundsConstantOffsets(Q.DL,
                                                            BasePtrOffset);

      // gep (gep V, C), (sub 0, V) -> C
      if (match(Ops.back(),
                m_Sub(m_Zero(), m_PtrToInt(m_Specific(StrippedBasePtr))))) {
        auto *CI = ConstantInt::get(GEPTy->getContext(), BasePtrOffset);
        return ConstantExpr::getIntToPtr(CI, GEPTy);
      }
      // gep (gep V, C), (xor V, -1) -> C-1
      if (match(Ops.back(),
                m_Xor(m_PtrToInt(m_Specific(StrippedBasePtr)), m_AllOnes()))) {
        auto *CI = ConstantInt::get(GEPTy->getContext(), BasePtrOffset - 1);
        return ConstantExpr::getIntToPtr(CI, GEPTy);
      }
    }
  }

  // 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(Type *SrcTy, ArrayRef<Value *> Ops,
                             const SimplifyQuery &Q) {
  return ::SimplifyGEPInst(SrcTy, Ops, Q, RecursionLimit);
}

/// Given operands for an InsertValueInst, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyInsertValueInst(Value *Agg, Value *Val,
                                      ArrayRef<unsigned> Idxs, const SimplifyQuery &Q,
                                      unsigned) {
  if (Constant *CAgg = dyn_cast<Constant>(Agg))
    if (Constant *CVal = dyn_cast<Constant>(Val))
      return ConstantFoldInsertValueInstruction(CAgg, CVal, Idxs);

  // insertvalue x, undef, n -> x
  if (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 SimplifyQuery &Q) {
  return ::SimplifyInsertValueInst(Agg, Val, Idxs, Q, RecursionLimit);
}

/// Given operands for an ExtractValueInst, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyExtractValueInst(Value *Agg, ArrayRef<unsigned> Idxs,
                                       const SimplifyQuery &, unsigned) {
  if (auto *CAgg = dyn_cast<Constant>(Agg))
    return ConstantFoldExtractValueInstruction(CAgg, Idxs);

  // extractvalue x, (insertvalue y, elt, n), n -> elt
  unsigned NumIdxs = Idxs.size();
  for (auto *IVI = dyn_cast<InsertValueInst>(Agg); IVI != nullptr;
       IVI = dyn_cast<InsertValueInst>(IVI->getAggregateOperand())) {
    ArrayRef<unsigned> InsertValueIdxs = IVI->getIndices();
    unsigned NumInsertValueIdxs = InsertValueIdxs.size();
    unsigned NumCommonIdxs = std::min(NumInsertValueIdxs, NumIdxs);
    if (InsertValueIdxs.slice(0, NumCommonIdxs) ==
        Idxs.slice(0, NumCommonIdxs)) {
      if (NumIdxs == NumInsertValueIdxs)
        return IVI->getInsertedValueOperand();
      break;
    }
  }

  return nullptr;
}

Value *llvm::SimplifyExtractValueInst(Value *Agg, ArrayRef<unsigned> Idxs,
                                      const SimplifyQuery &Q) {
  return ::SimplifyExtractValueInst(Agg, Idxs, Q, RecursionLimit);
}

/// Given operands for an ExtractElementInst, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyExtractElementInst(Value *Vec, Value *Idx, const SimplifyQuery &,
                                         unsigned) {
  if (auto *CVec = dyn_cast<Constant>(Vec)) {
    if (auto *CIdx = dyn_cast<Constant>(Idx))
      return ConstantFoldExtractElementInstruction(CVec, CIdx);

    // The index is not relevant if our vector is a splat.
    if (auto *Splat = CVec->getSplatValue())
      return Splat;

    if (isa<UndefValue>(Vec))
      return UndefValue::get(Vec->getType()->getVectorElementType());
  }

  // If extracting a specified index from the vector, see if we can recursively
  // find a previously computed scalar that was inserted into the vector.
  if (auto *IdxC = dyn_cast<ConstantInt>(Idx))
    if (Value *Elt = findScalarElement(Vec, IdxC->getZExtValue()))
      return Elt;

  return nullptr;
}

Value *llvm::SimplifyExtractElementInst(Value *Vec, Value *Idx,
                                        const SimplifyQuery &Q) {
  return ::SimplifyExtractElementInst(Vec, Idx, Q, RecursionLimit);
}

/// See if we can fold the given phi. If not, returns null.
static Value *SimplifyPHINode(PHINode *PN, const SimplifyQuery &Q) {
  // If all of the PHI's incoming values are the same then replace the PHI node
  // with the common value.
  Value *CommonValue = nullptr;
  bool HasUndefInput = false;
  for (Value *Incoming : PN->incoming_values()) {
    // If the incoming value is the phi node itself, it can safely be skipped.
    if (Incoming == PN) continue;
    if (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 *SimplifyCastInst(unsigned CastOpc, Value *Op,
                               Type *Ty, const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (auto *C = dyn_cast<Constant>(Op))
    return ConstantFoldCastOperand(CastOpc, C, Ty, Q.DL);

  if (auto *CI = dyn_cast<CastInst>(Op)) {
    auto *Src = CI->getOperand(0);
    Type *SrcTy = Src->getType();
    Type *MidTy = CI->getType();
    Type *DstTy = Ty;
    if (Src->getType() == Ty) {
      auto FirstOp = static_cast<Instruction::CastOps>(CI->getOpcode());
      auto SecondOp = static_cast<Instruction::CastOps>(CastOpc);
      Type *SrcIntPtrTy =
          SrcTy->isPtrOrPtrVectorTy() ? Q.DL.getIntPtrType(SrcTy) : nullptr;
      Type *MidIntPtrTy =
          MidTy->isPtrOrPtrVectorTy() ? Q.DL.getIntPtrType(MidTy) : nullptr;
      Type *DstIntPtrTy =
          DstTy->isPtrOrPtrVectorTy() ? Q.DL.getIntPtrType(DstTy) : nullptr;
      if (CastInst::isEliminableCastPair(FirstOp, SecondOp, SrcTy, MidTy, DstTy,
                                         SrcIntPtrTy, MidIntPtrTy,
                                         DstIntPtrTy) == Instruction::BitCast)
        return Src;
    }
  }

  // bitcast x -> x
  if (CastOpc == Instruction::BitCast)
    if (Op->getType() == Ty)
      return Op;

  return nullptr;
}

Value *llvm::SimplifyCastInst(unsigned CastOpc, Value *Op, Type *Ty,
                              const SimplifyQuery &Q) {
  return ::SimplifyCastInst(CastOpc, Op, Ty, Q, RecursionLimit);
}

/// For the given destination element of a shuffle, peek through shuffles to
/// match a root vector source operand that contains that element in the same
/// vector lane (ie, the same mask index), so we can eliminate the shuffle(s).
static Value *foldIdentityShuffles(int DestElt, Value *Op0, Value *Op1,
                                   Constant *Mask, Value *RootVec, int RootElt,
                                   unsigned MaxRecurse) {
  if (!MaxRecurse--)
    return nullptr;

  // Bail out if any mask value is undefined. That kind of shuffle may be
  // simplified further based on demanded bits or other folds.
  int MaskVal = ShuffleVectorInst::getMaskValue(Mask, RootElt);
  if (MaskVal == -1)
    return nullptr;

  // The mask value chooses which source operand we need to look at next.
  Value *SourceOp;
  int InVecNumElts = Op0->getType()->getVectorNumElements();
  if (MaskVal < InVecNumElts) {
    RootElt = MaskVal;
    SourceOp = Op0;
  } else {
    RootElt = MaskVal - InVecNumElts;
    SourceOp = Op1;
  }

  // If the source operand is a shuffle itself, look through it to find the
  // matching root vector.
  if (auto *SourceShuf = dyn_cast<ShuffleVectorInst>(SourceOp)) {
    return foldIdentityShuffles(
        DestElt, SourceShuf->getOperand(0), SourceShuf->getOperand(1),
        SourceShuf->getMask(), RootVec, RootElt, MaxRecurse);
  }

  // TODO: Look through bitcasts? What if the bitcast changes the vector element
  // size?

  // The source operand is not a shuffle. Initialize the root vector value for
  // this shuffle if that has not been done yet.
  if (!RootVec)
    RootVec = SourceOp;

  // Give up as soon as a source operand does not match the existing root value.
  if (RootVec != SourceOp)
    return nullptr;

  // The element must be coming from the same lane in the source vector
  // (although it may have crossed lanes in intermediate shuffles).
  if (RootElt != DestElt)
    return nullptr;

  return RootVec;
}

static Value *SimplifyShuffleVectorInst(Value *Op0, Value *Op1, Constant *Mask,
                                        Type *RetTy, const SimplifyQuery &Q,
                                        unsigned MaxRecurse) {
  if (isa<UndefValue>(Mask))
    return UndefValue::get(RetTy);

  Type *InVecTy = Op0->getType();
  unsigned MaskNumElts = Mask->getType()->getVectorNumElements();
  unsigned InVecNumElts = InVecTy->getVectorNumElements();

  auto *Op0Const = dyn_cast<Constant>(Op0);
  auto *Op1Const = dyn_cast<Constant>(Op1);

  // If all operands are constant, constant fold the shuffle.
  if (Op0Const && Op1Const)
    return ConstantFoldShuffleVectorInstruction(Op0Const, Op1Const, Mask);

  // If only one of the operands is constant, constant fold the shuffle if the
  // mask does not select elements from the variable operand.
  bool MaskSelects0 = false, MaskSelects1 = false;
  for (unsigned i = 0; i != MaskNumElts; ++i) {
    int Idx = ShuffleVectorInst::getMaskValue(Mask, i);
    if (Idx == -1)
      continue;
    if ((unsigned)Idx < InVecNumElts)
      MaskSelects0 = true;
    else
      MaskSelects1 = true;
  }
  if (!MaskSelects0 && Op1Const)
    return ConstantFoldShuffleVectorInstruction(UndefValue::get(InVecTy),
                                                Op1Const, Mask);
  if (!MaskSelects1 && Op0Const)
    return ConstantFoldShuffleVectorInstruction(Op0Const,
                                                UndefValue::get(InVecTy), Mask);

  // A shuffle of a splat is always the splat itself. Legal if the shuffle's
  // value type is same as the input vectors' type.
  if (auto *OpShuf = dyn_cast<ShuffleVectorInst>(Op0))
    if (!MaskSelects1 && RetTy == InVecTy &&
        OpShuf->getMask()->getSplatValue())
      return Op0;
  if (auto *OpShuf = dyn_cast<ShuffleVectorInst>(Op1))
    if (!MaskSelects0 && RetTy == InVecTy &&
        OpShuf->getMask()->getSplatValue())
      return Op1;

  // Don't fold a shuffle with undef mask elements. This may get folded in a
  // better way using demanded bits or other analysis.
  // TODO: Should we allow this?
  for (unsigned i = 0; i != MaskNumElts; ++i)
    if (ShuffleVectorInst::getMaskValue(Mask, i) == -1)
      return nullptr;

  // Check if every element of this shuffle can be mapped back to the
  // corresponding element of a single root vector. If so, we don't need this
  // shuffle. This handles simple identity shuffles as well as chains of
  // shuffles that may widen/narrow and/or move elements across lanes and back.
  Value *RootVec = nullptr;
  for (unsigned i = 0; i != MaskNumElts; ++i) {
    // Note that recursion is limited for each vector element, so if any element
    // exceeds the limit, this will fail to simplify.
    RootVec = foldIdentityShuffles(i, Op0, Op1, Mask, RootVec, i, MaxRecurse);

    // We can't replace a widening/narrowing shuffle with one of its operands.
    if (!RootVec || RootVec->getType() != RetTy)
      return nullptr;
  }
  return RootVec;
}

/// Given operands for a ShuffleVectorInst, fold the result or return null.
Value *llvm::SimplifyShuffleVectorInst(Value *Op0, Value *Op1, Constant *Mask,
                                       Type *RetTy, const SimplifyQuery &Q) {
  return ::SimplifyShuffleVectorInst(Op0, Op1, Mask, RetTy, Q, RecursionLimit);
}

//=== Helper functions for higher up the class hierarchy.

/// Given operands for a BinaryOperator, see if we can fold the result.
/// If not, this returns null.
static Value *SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                            const SimplifyQuery &Q, unsigned MaxRecurse) {
  switch (Opcode) {
  case Instruction::Add:
    return SimplifyAddInst(LHS, RHS, false, false, Q, MaxRecurse);
  case Instruction::FAdd:
    return SimplifyFAddInst(LHS, RHS, FastMathFlags(), Q, MaxRecurse);
  case Instruction::Sub:
    return SimplifySubInst(LHS, RHS, false, 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, false, false, Q, MaxRecurse);
  case Instruction::LShr:
    return SimplifyLShrInst(LHS, RHS, false, Q, MaxRecurse);
  case Instruction::AShr:
    return SimplifyAShrInst(LHS, RHS, false, Q, MaxRecurse);
  case Instruction::And:
    return SimplifyAndInst(LHS, RHS, Q, MaxRecurse);
  case Instruction::Or:
    return SimplifyOrInst(LHS, RHS, Q, MaxRecurse);
  case Instruction::Xor:
    return SimplifyXorInst(LHS, RHS, Q, MaxRecurse);
  default:
    llvm_unreachable("Unexpected opcode");
  }
}

/// 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 SimplifyQuery &Q,
                              unsigned MaxRecurse) {
  switch (Opcode) {
  case Instruction::FAdd:
    return SimplifyFAddInst(LHS, RHS, FMF, Q, MaxRecurse);
  case Instruction::FSub:
    return SimplifyFSubInst(LHS, RHS, FMF, Q, MaxRecurse);
  case Instruction::FMul:
    return SimplifyFMulInst(LHS, RHS, FMF, Q, MaxRecurse);
  case Instruction::FDiv:
    return SimplifyFDivInst(LHS, RHS, FMF, Q, MaxRecurse);
  default:
    return SimplifyBinOp(Opcode, LHS, RHS, Q, MaxRecurse);
  }
}

Value *llvm::SimplifyBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                           const SimplifyQuery &Q) {
  return ::SimplifyBinOp(Opcode, LHS, RHS, Q, RecursionLimit);
}

Value *llvm::SimplifyFPBinOp(unsigned Opcode, Value *LHS, Value *RHS,
                             FastMathFlags FMF, const SimplifyQuery &Q) {
  return ::SimplifyFPBinOp(Opcode, LHS, RHS, FMF, Q, RecursionLimit);
}

/// Given operands for a CmpInst, see if we can fold the result.
static Value *SimplifyCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                              const SimplifyQuery &Q, unsigned MaxRecurse) {
  if (CmpInst::isIntPredicate((CmpInst::Predicate)Predicate))
    return SimplifyICmpInst(Predicate, LHS, RHS, Q, MaxRecurse);
  return SimplifyFCmpInst(Predicate, LHS, RHS, FastMathFlags(), Q, MaxRecurse);
}

Value *llvm::SimplifyCmpInst(unsigned Predicate, Value *LHS, Value *RHS,
                             const SimplifyQuery &Q) {
  return ::SimplifyCmpInst(Predicate, LHS, RHS, Q, RecursionLimit);
}

static bool IsIdempotent(Intrinsic::ID ID) {
  switch (ID) {
  default: return false;

  // Unary idempotent: f(f(x)) = f(x)
  case Intrinsic::fabs:
  case Intrinsic::floor:
  case Intrinsic::ceil:
  case Intrinsic::trunc:
  case Intrinsic::rint:
  case Intrinsic::nearbyint:
  case Intrinsic::round:
    return true;
  }
}

static Value *SimplifyRelativeLoad(Constant *Ptr, Constant *Offset,
                                   const DataLayout &DL) {
  GlobalValue *PtrSym;
  APInt PtrOffset;
  if (!IsConstantOffsetFromGlobal(Ptr, PtrSym, PtrOffset, DL))
    return nullptr;

  Type *Int8PtrTy = Type::getInt8PtrTy(Ptr->getContext());
  Type *Int32Ty = Type::getInt32Ty(Ptr->getContext());
  Type *Int32PtrTy = Int32Ty->getPointerTo();
  Type *Int64Ty = Type::getInt64Ty(Ptr->getContext());

  auto *OffsetConstInt = dyn_cast<ConstantInt>(Offset);
  if (!OffsetConstInt || OffsetConstInt->getType()->getBitWidth() > 64)
    return nullptr;

  uint64_t OffsetInt = OffsetConstInt->getSExtValue();
  if (OffsetInt % 4 != 0)
    return nullptr;

  Constant *C = ConstantExpr::getGetElementPtr(
      Int32Ty, ConstantExpr::getBitCast(Ptr, Int32PtrTy),
      ConstantInt::get(Int64Ty, OffsetInt / 4));
  Constant *Loaded = ConstantFoldLoadFromConstPtr(C, Int32Ty, DL);
  if (!Loaded)
    return nullptr;

  auto *LoadedCE = dyn_cast<ConstantExpr>(Loaded);
  if (!LoadedCE)
    return nullptr;

  if (LoadedCE->getOpcode() == Instruction::Trunc) {
    LoadedCE = dyn_cast<ConstantExpr>(LoadedCE->getOperand(0));
    if (!LoadedCE)
      return nullptr;
  }

  if (LoadedCE->getOpcode() != Instruction::Sub)
    return nullptr;

  auto *LoadedLHS = dyn_cast<ConstantExpr>(LoadedCE->getOperand(0));
  if (!LoadedLHS || LoadedLHS->getOpcode() != Instruction::PtrToInt)
    return nullptr;
  auto *LoadedLHSPtr = LoadedLHS->getOperand(0);

  Constant *LoadedRHS = LoadedCE->getOperand(1);
  GlobalValue *LoadedRHSSym;
  APInt LoadedRHSOffset;
  if (!IsConstantOffsetFromGlobal(LoadedRHS, LoadedRHSSym, LoadedRHSOffset,
                                  DL) ||
      PtrSym != LoadedRHSSym || PtrOffset != LoadedRHSOffset)
    return nullptr;

  return ConstantExpr::getBitCast(LoadedLHSPtr, Int8PtrTy);
}

static bool maskIsAllZeroOrUndef(Value *Mask) {
  auto *ConstMask = dyn_cast<Constant>(Mask);
  if (!ConstMask)
    return false;
  if (ConstMask->isNullValue() || isa<UndefValue>(ConstMask))
    return true;
  for (unsigned I = 0, E = ConstMask->getType()->getVectorNumElements(); I != E;
       ++I) {
    if (auto *MaskElt = ConstMask->getAggregateElement(I))
      if (MaskElt->isNullValue() || isa<UndefValue>(MaskElt))
        continue;
    return false;
  }
  return true;
}

template <typename IterTy>
static Value *SimplifyIntrinsic(Function *F, IterTy ArgBegin, IterTy ArgEnd,
                                const SimplifyQuery &Q, unsigned MaxRecurse) {
  Intrinsic::ID IID = F->getIntrinsicID();
  unsigned NumOperands = std::distance(ArgBegin, ArgEnd);

  // Unary Ops
  if (NumOperands == 1) {
    // Perform idempotent optimizations
    if (IsIdempotent(IID)) {
      if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(*ArgBegin)) {
        if (II->getIntrinsicID() == IID)
          return II;
      }
    }

    switch (IID) {
    case Intrinsic::fabs: {
      if (SignBitMustBeZero(*ArgBegin, Q.TLI))
        return *ArgBegin;
      return nullptr;
    }
    default:
      return nullptr;
    }
  }

  // Binary Ops
  if (NumOperands == 2) {
    Value *LHS = *ArgBegin;
    Value *RHS = *(ArgBegin + 1);
    Type *ReturnType = F->getReturnType();

    switch (IID) {
    case Intrinsic::usub_with_overflow:
    case Intrinsic::ssub_with_overflow: {
      // X - X -> { 0, false }
      if (LHS == RHS)
        return Constant::getNullValue(ReturnType);

      // X - undef -> undef
      // undef - X -> undef
      if (isa<UndefValue>(LHS) || isa<UndefValue>(RHS))
        return UndefValue::get(ReturnType);

      return nullptr;
    }
    case Intrinsic::uadd_with_overflow:
    case Intrinsic::sadd_with_overflow: {
      // X + undef -> undef
      if (isa<UndefValue>(RHS))
        return UndefValue::get(ReturnType);

      return nullptr;
    }
    case Intrinsic::umul_with_overflow:
    case Intrinsic::smul_with_overflow: {
      // X * 0 -> { 0, false }
      if (match(RHS, m_Zero()))
        return Constant::getNullValue(ReturnType);

      // X * undef -> { 0, false }
      if (match(RHS, m_Undef()))
        return Constant::getNullValue(ReturnType);

      return nullptr;
    }
    case Intrinsic::load_relative: {
      Constant *C0 = dyn_cast<Constant>(LHS);
      Constant *C1 = dyn_cast<Constant>(RHS);
      if (C0 && C1)
        return SimplifyRelativeLoad(C0, C1, Q.DL);
      return nullptr;
    }
    default:
      return nullptr;
    }
  }

  // Simplify calls to llvm.masked.load.*
  switch (IID) {
  case Intrinsic::masked_load: {
    Value *MaskArg = ArgBegin[2];
    Value *PassthruArg = ArgBegin[3];
    // If the mask is all zeros or undef, the "passthru" argument is the result.
    if (maskIsAllZeroOrUndef(MaskArg))
      return PassthruArg;
    return nullptr;
  }
  default:
    return nullptr;
  }
}

template <typename IterTy>
static Value *SimplifyCall(Value *V, IterTy ArgBegin, IterTy ArgEnd,
                           const SimplifyQuery &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
  // call null -> undef
  if (isa<UndefValue>(V) || isa<ConstantPointerNull>(V))
    return UndefValue::get(FTy->getReturnType());

  Function *F = dyn_cast<Function>(V);
  if (!F)
    return nullptr;

  if (F->isIntrinsic())
    if (Value *Ret = SimplifyIntrinsic(F, 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 SimplifyQuery &Q) {
  return ::SimplifyCall(V, ArgBegin, ArgEnd, Q, RecursionLimit);
}

Value *llvm::SimplifyCall(Value *V, ArrayRef<Value *> Args,
                          const SimplifyQuery &Q) {
  return ::SimplifyCall(V, Args.begin(), Args.end(), Q, RecursionLimit);
}

/// See if we can compute a simplified version of this instruction.
/// If not, this returns null.

Value *llvm::SimplifyInstruction(Instruction *I, const SimplifyQuery &SQ,
                                 OptimizationRemarkEmitter *ORE) {
  const SimplifyQuery Q = SQ.CxtI ? SQ : SQ.getWithInstruction(I);
  Value *Result;

  switch (I->getOpcode()) {
  default:
    Result = ConstantFoldInstruction(I, Q.DL, Q.TLI);
    break;
  case Instruction::FAdd:
    Result = SimplifyFAddInst(I->getOperand(0), I->getOperand(1),
                              I->getFastMathFlags(), Q);
    break;
  case Instruction::Add:
    Result = SimplifyAddInst(I->getOperand(0), I->getOperand(1),
                             cast<BinaryOperator>(I)->hasNoSignedWrap(),
                             cast<BinaryOperator>(I)->hasNoUnsignedWrap(), Q);
    break;
  case Instruction::FSub:
    Result = SimplifyFSubInst(I->getOperand(0), I->getOperand(1),
                              I->getFastMathFlags(), Q);
    break;
  case Instruction::Sub:
    Result = SimplifySubInst(I->getOperand(0), I->getOperand(1),
                             cast<BinaryOperator>(I)->hasNoSignedWrap(),
                             cast<BinaryOperator>(I)->hasNoUnsignedWrap(), Q);
    break;
  case Instruction::FMul:
    Result = SimplifyFMulInst(I->getOperand(0), I->getOperand(1),
                              I->getFastMathFlags(), Q);
    break;
  case Instruction::Mul:
    Result = SimplifyMulInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::SDiv:
    Result = SimplifySDivInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::UDiv:
    Result = SimplifyUDivInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::FDiv:
    Result = SimplifyFDivInst(I->getOperand(0), I->getOperand(1),
                              I->getFastMathFlags(), Q);
    break;
  case Instruction::SRem:
    Result = SimplifySRemInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::URem:
    Result = SimplifyURemInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::FRem:
    Result = SimplifyFRemInst(I->getOperand(0), I->getOperand(1),
                              I->getFastMathFlags(), Q);
    break;
  case Instruction::Shl:
    Result = SimplifyShlInst(I->getOperand(0), I->getOperand(1),
                             cast<BinaryOperator>(I)->hasNoSignedWrap(),
                             cast<BinaryOperator>(I)->hasNoUnsignedWrap(), Q);
    break;
  case Instruction::LShr:
    Result = SimplifyLShrInst(I->getOperand(0), I->getOperand(1),
                              cast<BinaryOperator>(I)->isExact(), Q);
    break;
  case Instruction::AShr:
    Result = SimplifyAShrInst(I->getOperand(0), I->getOperand(1),
                              cast<BinaryOperator>(I)->isExact(), Q);
    break;
  case Instruction::And:
    Result = SimplifyAndInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::Or:
    Result = SimplifyOrInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::Xor:
    Result = SimplifyXorInst(I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::ICmp:
    Result = SimplifyICmpInst(cast<ICmpInst>(I)->getPredicate(),
                              I->getOperand(0), I->getOperand(1), Q);
    break;
  case Instruction::FCmp:
    Result =
        SimplifyFCmpInst(cast<FCmpInst>(I)->getPredicate(), I->getOperand(0),
                         I->getOperand(1), I->getFastMathFlags(), Q);
    break;
  case Instruction::Select:
    Result = SimplifySelectInst(I->getOperand(0), I->getOperand(1),
                                I->getOperand(2), Q);
    break;
  case Instruction::GetElementPtr: {
    SmallVector<Value *, 8> Ops(I->op_begin(), I->op_end());
    Result = SimplifyGEPInst(cast<GetElementPtrInst>(I)->getSourceElementType(),
                             Ops, Q);
    break;
  }
  case Instruction::InsertValue: {
    InsertValueInst *IV = cast<InsertValueInst>(I);
    Result = SimplifyInsertValueInst(IV->getAggregateOperand(),
                                     IV->getInsertedValueOperand(),
                                     IV->getIndices(), Q);
    break;
  }
  case Instruction::ExtractValue: {
    auto *EVI = cast<ExtractValueInst>(I);
    Result = SimplifyExtractValueInst(EVI->getAggregateOperand(),
                                      EVI->getIndices(), Q);
    break;
  }
  case Instruction::ExtractElement: {
    auto *EEI = cast<ExtractElementInst>(I);
    Result = SimplifyExtractElementInst(EEI->getVectorOperand(),
                                        EEI->getIndexOperand(), Q);
    break;
  }
  case Instruction::ShuffleVector: {
    auto *SVI = cast<ShuffleVectorInst>(I);
    Result = SimplifyShuffleVectorInst(SVI->getOperand(0), SVI->getOperand(1),
                                       SVI->getMask(), SVI->getType(), Q);
    break;
  }
  case Instruction::PHI:
    Result = SimplifyPHINode(cast<PHINode>(I), Q);
    break;
  case Instruction::Call: {
    CallSite CS(cast<CallInst>(I));
    Result = SimplifyCall(CS.getCalledValue(), CS.arg_begin(), CS.arg_end(), Q);
    break;
  }
#define HANDLE_CAST_INST(num, opc, clas) case Instruction::opc:
#include "llvm/IR/Instruction.def"
#undef HANDLE_CAST_INST
    Result =
        SimplifyCastInst(I->getOpcode(), I->getOperand(0), I->getType(), Q);
    break;
  case Instruction::Alloca:
    // No simplifications for Alloca and it can't be constant folded.
    Result = nullptr;
    break;
  }

  // In general, it is possible for computeKnownBits to determine all bits in a
  // value even when the operands are not all constants.
  if (!Result && I->getType()->isIntOrIntVectorTy()) {
    unsigned BitWidth = I->getType()->getScalarSizeInBits();
    KnownBits Known(BitWidth);
    computeKnownBits(I, Known, Q.DL, /*Depth*/ 0, Q.AC, I, Q.DT, ORE);
    if ((Known.Zero | Known.One).isAllOnesValue())
      Result = ConstantInt::get(I->getType(), Known.One);
  }

  /// 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 instruction's
/// uses.
///
/// This is the common implementation of the recursive simplification routines.
/// If we have a pre-simplified value in 'SimpleV', that is forcibly used to
/// replace the instruction 'I'. Otherwise, we simply add 'I' to the list of
/// instructions to process and attempt to simplify it using
/// InstructionSimplify.
///
/// 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->isEHPad() && !isa<TerminatorInst>(I) &&
        !I->mayHaveSideEffects())
      I->eraseFromParent();
  } else {
    Worklist.insert(I);
  }

  // Note that we must test the size on each iteration, the worklist can grow.
  for (unsigned Idx = 0; Idx != Worklist.size(); ++Idx) {
    I = Worklist[Idx];

    // See if this instruction simplifies.
    SimpleV = SimplifyInstruction(I, {DL, TLI, DT, AC});
    if (!SimpleV)
      continue;

    Simplified = true;

    // Stash away all the uses of the old instruction so we can check them for
    // recursive simplifications after a RAUW. This is cheaper than checking all
    // uses of To on the recursive step in most cases.
    for (User *U : I->users())
      Worklist.insert(cast<Instruction>(U));

    // Replace the instruction with its simplified value.
    I->replaceAllUsesWith(SimpleV);

    // Gracefully handle edge cases where the instruction is not wired into any
    // parent block.
    if (I->getParent() && !I->isEHPad() && !isa<TerminatorInst>(I) &&
        !I->mayHaveSideEffects())
      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);
}

namespace llvm {
const SimplifyQuery getBestSimplifyQuery(Pass &P, Function &F) {
  auto *DTWP = P.getAnalysisIfAvailable<DominatorTreeWrapperPass>();
  auto *DT = DTWP ? &DTWP->getDomTree() : nullptr;
  auto *TLIWP = P.getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
  auto *TLI = TLIWP ? &TLIWP->getTLI() : nullptr;
  auto *ACWP = P.getAnalysisIfAvailable<AssumptionCacheTracker>();
  auto *AC = ACWP ? &ACWP->getAssumptionCache(F) : nullptr;
  return {F.getParent()->getDataLayout(), TLI, DT, AC};
}

const SimplifyQuery getBestSimplifyQuery(LoopStandardAnalysisResults &AR,
                                         const DataLayout &DL) {
  return {DL, &AR.TLI, &AR.DT, &AR.AC};
}

template <class T, class... TArgs>
const SimplifyQuery getBestSimplifyQuery(AnalysisManager<T, TArgs...> &AM,
                                         Function &F) {
  auto *DT = AM.template getCachedResult<DominatorTreeAnalysis>(F);
  auto *TLI = AM.template getCachedResult<TargetLibraryAnalysis>(F);
  auto *AC = AM.template getCachedResult<AssumptionAnalysis>(F);
  return {F.getParent()->getDataLayout(), TLI, DT, AC};
}
template const SimplifyQuery getBestSimplifyQuery(AnalysisManager<Function> &,
                                                  Function &);
}