HexagonLoopIdiomRecognition.cpp

//===--- HexagonLoopIdiomRecognition.cpp ----------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#define DEBUG_TYPE "hexagon-lir"

#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/Analysis/AliasAnalysis.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"

#include <algorithm>
#include <array>

using namespace llvm;

static cl::opt<bool> DisableMemcpyIdiom("disable-memcpy-idiom",
  cl::Hidden, cl::init(false),
  cl::desc("Disable generation of memcpy in loop idiom recognition"));

static cl::opt<bool> DisableMemmoveIdiom("disable-memmove-idiom",
  cl::Hidden, cl::init(false),
  cl::desc("Disable generation of memmove in loop idiom recognition"));

static cl::opt<unsigned> RuntimeMemSizeThreshold("runtime-mem-idiom-threshold",
  cl::Hidden, cl::init(0), cl::desc("Threshold (in bytes) for the runtime "
  "check guarding the memmove."));

static cl::opt<unsigned> CompileTimeMemSizeThreshold(
  "compile-time-mem-idiom-threshold", cl::Hidden, cl::init(64),
  cl::desc("Threshold (in bytes) to perform the transformation, if the "
    "runtime loop count (mem transfer size) is known at compile-time."));

static cl::opt<bool> OnlyNonNestedMemmove("only-nonnested-memmove-idiom",
  cl::Hidden, cl::init(true),
  cl::desc("Only enable generating memmove in non-nested loops"));

cl::opt<bool> HexagonVolatileMemcpy("disable-hexagon-volatile-memcpy",
  cl::Hidden, cl::init(false),
  cl::desc("Enable Hexagon-specific memcpy for volatile destination."));

static const char *HexagonVolatileMemcpyName
  = "hexagon_memcpy_forward_vp4cp4n2";


namespace llvm {
  void initializeHexagonLoopIdiomRecognizePass(PassRegistry&);
  Pass *createHexagonLoopIdiomPass();
}

namespace {
  class HexagonLoopIdiomRecognize : public LoopPass {
  public:
    static char ID;
    explicit HexagonLoopIdiomRecognize() : LoopPass(ID) {
      initializeHexagonLoopIdiomRecognizePass(*PassRegistry::getPassRegistry());
    }
    StringRef getPassName() const override {
      return "Recognize Hexagon-specific loop idioms";
    }

   void getAnalysisUsage(AnalysisUsage &AU) const override {
      AU.addRequired<LoopInfoWrapperPass>();
      AU.addRequiredID(LoopSimplifyID);
      AU.addRequiredID(LCSSAID);
      AU.addRequired<AAResultsWrapperPass>();
      AU.addPreserved<AAResultsWrapperPass>();
      AU.addRequired<ScalarEvolutionWrapperPass>();
      AU.addRequired<DominatorTreeWrapperPass>();
      AU.addRequired<TargetLibraryInfoWrapperPass>();
      AU.addPreserved<TargetLibraryInfoWrapperPass>();
    }

    bool runOnLoop(Loop *L, LPPassManager &LPM) override;

  private:
    unsigned getStoreSizeInBytes(StoreInst *SI);
    int getSCEVStride(const SCEVAddRecExpr *StoreEv);
    bool isLegalStore(Loop *CurLoop, StoreInst *SI);
    void collectStores(Loop *CurLoop, BasicBlock *BB,
        SmallVectorImpl<StoreInst*> &Stores);
    bool processCopyingStore(Loop *CurLoop, StoreInst *SI, const SCEV *BECount);
    bool coverLoop(Loop *L, SmallVectorImpl<Instruction*> &Insts) const;
    bool runOnLoopBlock(Loop *CurLoop, BasicBlock *BB, const SCEV *BECount,
        SmallVectorImpl<BasicBlock*> &ExitBlocks);
    bool runOnCountableLoop(Loop *L);

    AliasAnalysis *AA;
    const DataLayout *DL;
    DominatorTree *DT;
    LoopInfo *LF;
    const TargetLibraryInfo *TLI;
    ScalarEvolution *SE;
    bool HasMemcpy, HasMemmove;
  };
}

char HexagonLoopIdiomRecognize::ID = 0;

INITIALIZE_PASS_BEGIN(HexagonLoopIdiomRecognize, "hexagon-loop-idiom",
    "Recognize Hexagon-specific loop idioms", false, false)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(LoopSimplify)
INITIALIZE_PASS_DEPENDENCY(LCSSAWrapperPass)
INITIALIZE_PASS_DEPENDENCY(ScalarEvolutionWrapperPass)
INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(AAResultsWrapperPass)
INITIALIZE_PASS_END(HexagonLoopIdiomRecognize, "hexagon-loop-idiom",
    "Recognize Hexagon-specific loop idioms", false, false)


namespace {
  struct Simplifier {
    typedef std::function<Value* (Instruction*, LLVMContext&)> Rule;

    void addRule(const Rule &R) { Rules.push_back(R); }

  private:
    struct WorkListType {
      WorkListType() = default;

      void push_back(Value* V) {
        // Do not push back duplicates.
        if (!S.count(V)) { Q.push_back(V); S.insert(V); }
      }
      Value *pop_front_val() {
        Value *V = Q.front(); Q.pop_front(); S.erase(V);
        return V;
      }
      bool empty() const { return Q.empty(); }

    private:
      std::deque<Value*> Q;
      std::set<Value*> S;
    };

    typedef std::set<Value*> ValueSetType;
    std::vector<Rule> Rules;

  public:
    struct Context {
      typedef DenseMap<Value*,Value*> ValueMapType;

      Value *Root;
      ValueSetType Used;    // The set of all cloned values used by Root.
      ValueSetType Clones;  // The set of all cloned values.
      LLVMContext &Ctx;

      Context(Instruction *Exp)
        : Ctx(Exp->getParent()->getParent()->getContext()) {
        initialize(Exp);
      }
      ~Context() { cleanup(); }
      void print(raw_ostream &OS, const Value *V) const;

      Value *materialize(BasicBlock *B, BasicBlock::iterator At);

    private:
      void initialize(Instruction *Exp);
      void cleanup();

      template <typename FuncT> void traverse(Value *V, FuncT F);
      void record(Value *V);
      void use(Value *V);
      void unuse(Value *V);

      bool equal(const Instruction *I, const Instruction *J) const;
      Value *find(Value *Tree, Value *Sub) const;
      Value *subst(Value *Tree, Value *OldV, Value *NewV);
      void replace(Value *OldV, Value *NewV);
      void link(Instruction *I, BasicBlock *B, BasicBlock::iterator At);

      friend struct Simplifier;
    };

    Value *simplify(Context &C);
  };

  struct PE {
    PE(const Simplifier::Context &c, Value *v = nullptr) : C(c), V(v) {}
    const Simplifier::Context &C;
    const Value *V;
  };

  raw_ostream &operator<< (raw_ostream &OS, const PE &P) LLVM_ATTRIBUTE_USED;
  raw_ostream &operator<< (raw_ostream &OS, const PE &P) {
    P.C.print(OS, P.V ? P.V : P.C.Root);
    return OS;
  }
}


template <typename FuncT>
void Simplifier::Context::traverse(Value *V, FuncT F) {
  WorkListType Q;
  Q.push_back(V);

  while (!Q.empty()) {
    Instruction *U = dyn_cast<Instruction>(Q.pop_front_val());
    if (!U || U->getParent())
      continue;
    if (!F(U))
      continue;
    for (Value *Op : U->operands())
      Q.push_back(Op);
  }
}


void Simplifier::Context::print(raw_ostream &OS, const Value *V) const {
  const auto *U = dyn_cast<const Instruction>(V);
  if (!U) {
    OS << V << '(' << *V << ')';
    return;
  }

  if (U->getParent()) {
    OS << U << '(';
    U->printAsOperand(OS, true);
    OS << ')';
    return;
  }

  unsigned N = U->getNumOperands();
  if (N != 0)
    OS << U << '(';
  OS << U->getOpcodeName();
  for (const Value *Op : U->operands()) {
    OS << ' ';
    print(OS, Op);
  }
  if (N != 0)
    OS << ')';
}


void Simplifier::Context::initialize(Instruction *Exp) {
  // Perform a deep clone of the expression, set Root to the root
  // of the clone, and build a map from the cloned values to the
  // original ones.
  ValueMapType M;
  BasicBlock *Block = Exp->getParent();
  WorkListType Q;
  Q.push_back(Exp);

  while (!Q.empty()) {
    Value *V = Q.pop_front_val();
    if (M.find(V) != M.end())
      continue;
    if (Instruction *U = dyn_cast<Instruction>(V)) {
      if (isa<PHINode>(U) || U->getParent() != Block)
        continue;
      for (Value *Op : U->operands())
        Q.push_back(Op);
      M.insert({U, U->clone()});
    }
  }

  for (std::pair<Value*,Value*> P : M) {
    Instruction *U = cast<Instruction>(P.second);
    for (unsigned i = 0, n = U->getNumOperands(); i != n; ++i) {
      auto F = M.find(U->getOperand(i));
      if (F != M.end())
        U->setOperand(i, F->second);
    }
  }

  auto R = M.find(Exp);
  assert(R != M.end());
  Root = R->second;

  record(Root);
  use(Root);
}


void Simplifier::Context::record(Value *V) {
  auto Record = [this](Instruction *U) -> bool {
    Clones.insert(U);
    return true;
  };
  traverse(V, Record);
}


void Simplifier::Context::use(Value *V) {
  auto Use = [this](Instruction *U) -> bool {
    Used.insert(U);
    return true;
  };
  traverse(V, Use);
}


void Simplifier::Context::unuse(Value *V) {
  if (!isa<Instruction>(V) || cast<Instruction>(V)->getParent() != nullptr)
    return;

  auto Unuse = [this](Instruction *U) -> bool {
    if (!U->use_empty())
      return false;
    Used.erase(U);
    return true;
  };
  traverse(V, Unuse);
}


Value *Simplifier::Context::subst(Value *Tree, Value *OldV, Value *NewV) {
  if (Tree == OldV)
    return NewV;
  if (OldV == NewV)
    return Tree;

  WorkListType Q;
  Q.push_back(Tree);
  while (!Q.empty()) {
    Instruction *U = dyn_cast<Instruction>(Q.pop_front_val());
    // If U is not an instruction, or it's not a clone, skip it.
    if (!U || U->getParent())
      continue;
    for (unsigned i = 0, n = U->getNumOperands(); i != n; ++i) {
      Value *Op = U->getOperand(i);
      if (Op == OldV) {
        U->setOperand(i, NewV);
        unuse(OldV);
      } else {
        Q.push_back(Op);
      }
    }
  }
  return Tree;
}


void Simplifier::Context::replace(Value *OldV, Value *NewV) {
  if (Root == OldV) {
    Root = NewV;
    use(Root);
    return;
  }

  // NewV may be a complex tree that has just been created by one of the
  // transformation rules. We need to make sure that it is commoned with
  // the existing Root to the maximum extent possible.
  // Identify all subtrees of NewV (including NewV itself) that have
  // equivalent counterparts in Root, and replace those subtrees with
  // these counterparts.
  WorkListType Q;
  Q.push_back(NewV);
  while (!Q.empty()) {
    Value *V = Q.pop_front_val();
    Instruction *U = dyn_cast<Instruction>(V);
    if (!U || U->getParent())
      continue;
    if (Value *DupV = find(Root, V)) {
      if (DupV != V)
        NewV = subst(NewV, V, DupV);
    } else {
      for (Value *Op : U->operands())
        Q.push_back(Op);
    }
  }

  // Now, simply replace OldV with NewV in Root.
  Root = subst(Root, OldV, NewV);
  use(Root);
}


void Simplifier::Context::cleanup() {
  for (Value *V : Clones) {
    Instruction *U = cast<Instruction>(V);
    if (!U->getParent())
      U->dropAllReferences();
  }

  for (Value *V : Clones) {
    Instruction *U = cast<Instruction>(V);
    if (!U->getParent())
      delete U;
  }
}


bool Simplifier::Context::equal(const Instruction *I,
                                const Instruction *J) const {
  if (I == J)
    return true;
  if (!I->isSameOperationAs(J))
    return false;
  if (isa<PHINode>(I))
    return I->isIdenticalTo(J);

  for (unsigned i = 0, n = I->getNumOperands(); i != n; ++i) {
    Value *OpI = I->getOperand(i), *OpJ = J->getOperand(i);
    if (OpI == OpJ)
      continue;
    auto *InI = dyn_cast<const Instruction>(OpI);
    auto *InJ = dyn_cast<const Instruction>(OpJ);
    if (InI && InJ) {
      if (!equal(InI, InJ))
        return false;
    } else if (InI != InJ || !InI)
      return false;
  }
  return true;
}


Value *Simplifier::Context::find(Value *Tree, Value *Sub) const {
  Instruction *SubI = dyn_cast<Instruction>(Sub);
  WorkListType Q;
  Q.push_back(Tree);

  while (!Q.empty()) {
    Value *V = Q.pop_front_val();
    if (V == Sub)
      return V;
    Instruction *U = dyn_cast<Instruction>(V);
    if (!U || U->getParent())
      continue;
    if (SubI && equal(SubI, U))
      return U;
    assert(!isa<PHINode>(U));
    for (Value *Op : U->operands())
      Q.push_back(Op);
  }
  return nullptr;
}


void Simplifier::Context::link(Instruction *I, BasicBlock *B,
      BasicBlock::iterator At) {
  if (I->getParent())
    return;

  for (Value *Op : I->operands()) {
    if (Instruction *OpI = dyn_cast<Instruction>(Op))
      link(OpI, B, At);
  }

  B->getInstList().insert(At, I);
}


Value *Simplifier::Context::materialize(BasicBlock *B,
      BasicBlock::iterator At) {
  if (Instruction *RootI = dyn_cast<Instruction>(Root))
    link(RootI, B, At);
  return Root;
}


Value *Simplifier::simplify(Context &C) {
  WorkListType Q;
  Q.push_back(C.Root);
  unsigned Count = 0;
  const unsigned Limit = 100000;

  while (!Q.empty()) {
    if (Count++ >= Limit)
      break;
    Instruction *U = dyn_cast<Instruction>(Q.pop_front_val());
    if (!U || U->getParent() || !C.Used.count(U))
      continue;
    bool Changed = false;
    for (Rule &R : Rules) {
      Value *W = R(U, C.Ctx);
      if (!W)
        continue;
      Changed = true;
      C.record(W);
      C.replace(U, W);
      Q.push_back(C.Root);
      break;
    }
    if (!Changed) {
      for (Value *Op : U->operands())
        Q.push_back(Op);
    }
  }
  assert(Count < Limit && "Infinite loop in HLIR/simplify?");
  return C.Root;
}


//===----------------------------------------------------------------------===//
//
//          Implementation of PolynomialMultiplyRecognize
//
//===----------------------------------------------------------------------===//

namespace {
  class PolynomialMultiplyRecognize {
  public:
    explicit PolynomialMultiplyRecognize(Loop *loop, const DataLayout &dl,
        const DominatorTree &dt, const TargetLibraryInfo &tli,
        ScalarEvolution &se)
      : CurLoop(loop), DL(dl), DT(dt), TLI(tli), SE(se) {}

    bool recognize();
  private:
    typedef SetVector<Value*> ValueSeq;

    IntegerType *getPmpyType() const {
      LLVMContext &Ctx = CurLoop->getHeader()->getParent()->getContext();
      return IntegerType::get(Ctx, 32);
    }
    bool isPromotableTo(Value *V, IntegerType *Ty);
    void promoteTo(Instruction *In, IntegerType *DestTy, BasicBlock *LoopB);
    bool promoteTypes(BasicBlock *LoopB, BasicBlock *ExitB);

    Value *getCountIV(BasicBlock *BB);
    bool findCycle(Value *Out, Value *In, ValueSeq &Cycle);
    void classifyCycle(Instruction *DivI, ValueSeq &Cycle, ValueSeq &Early,
          ValueSeq &Late);
    bool classifyInst(Instruction *UseI, ValueSeq &Early, ValueSeq &Late);
    bool commutesWithShift(Instruction *I);
    bool highBitsAreZero(Value *V, unsigned IterCount);
    bool keepsHighBitsZero(Value *V, unsigned IterCount);
    bool isOperandShifted(Instruction *I, Value *Op);
    bool convertShiftsToLeft(BasicBlock *LoopB, BasicBlock *ExitB,
          unsigned IterCount);
    void cleanupLoopBody(BasicBlock *LoopB);

    struct ParsedValues {
      ParsedValues() : M(nullptr), P(nullptr), Q(nullptr), R(nullptr),
          X(nullptr), Res(nullptr), IterCount(0), Left(false), Inv(false) {}
      Value *M, *P, *Q, *R, *X;
      Instruction *Res;
      unsigned IterCount;
      bool Left, Inv;
    };

    bool matchLeftShift(SelectInst *SelI, Value *CIV, ParsedValues &PV);
    bool matchRightShift(SelectInst *SelI, ParsedValues &PV);
    bool scanSelect(SelectInst *SI, BasicBlock *LoopB, BasicBlock *PrehB,
          Value *CIV, ParsedValues &PV, bool PreScan);
    unsigned getInverseMxN(unsigned QP);
    Value *generate(BasicBlock::iterator At, ParsedValues &PV);

    void setupSimplifier();

    Simplifier Simp;
    Loop *CurLoop;
    const DataLayout &DL;
    const DominatorTree &DT;
    const TargetLibraryInfo &TLI;
    ScalarEvolution &SE;
  };
}


Value *PolynomialMultiplyRecognize::getCountIV(BasicBlock *BB) {
  pred_iterator PI = pred_begin(BB), PE = pred_end(BB);
  if (std::distance(PI, PE) != 2)
    return nullptr;
  BasicBlock *PB = (*PI == BB) ? *std::next(PI) : *PI;

  for (auto I = BB->begin(), E = BB->end(); I != E && isa<PHINode>(I); ++I) {
    auto *PN = cast<PHINode>(I);
    Value *InitV = PN->getIncomingValueForBlock(PB);
    if (!isa<ConstantInt>(InitV) || !cast<ConstantInt>(InitV)->isZero())
      continue;
    Value *IterV = PN->getIncomingValueForBlock(BB);
    if (!isa<BinaryOperator>(IterV))
      continue;
    auto *BO = dyn_cast<BinaryOperator>(IterV);
    if (BO->getOpcode() != Instruction::Add)
      continue;
    Value *IncV = nullptr;
    if (BO->getOperand(0) == PN)
      IncV = BO->getOperand(1);
    else if (BO->getOperand(1) == PN)
      IncV = BO->getOperand(0);
    if (IncV == nullptr)
      continue;

    if (auto *T = dyn_cast<ConstantInt>(IncV))
      if (T->getZExtValue() == 1)
        return PN;
  }
  return nullptr;
}


static void replaceAllUsesOfWithIn(Value *I, Value *J, BasicBlock *BB) {
  for (auto UI = I->user_begin(), UE = I->user_end(); UI != UE;) {
    Use &TheUse = UI.getUse();
    ++UI;
    if (auto *II = dyn_cast<Instruction>(TheUse.getUser()))
      if (BB == II->getParent())
        II->replaceUsesOfWith(I, J);
  }
}


bool PolynomialMultiplyRecognize::matchLeftShift(SelectInst *SelI,
      Value *CIV, ParsedValues &PV) {
  // Match the following:
  //   select (X & (1 << i)) != 0 ? R ^ (Q << i) : R
  //   select (X & (1 << i)) == 0 ? R : R ^ (Q << i)
  // The condition may also check for equality with the masked value, i.e
  //   select (X & (1 << i)) == (1 << i) ? R ^ (Q << i) : R
  //   select (X & (1 << i)) != (1 << i) ? R : R ^ (Q << i);

  Value *CondV = SelI->getCondition();
  Value *TrueV = SelI->getTrueValue();
  Value *FalseV = SelI->getFalseValue();

  using namespace PatternMatch;

  CmpInst::Predicate P;
  Value *A = nullptr, *B = nullptr, *C = nullptr;

  if (!match(CondV, m_ICmp(P, m_And(m_Value(A), m_Value(B)), m_Value(C))) &&
      !match(CondV, m_ICmp(P, m_Value(C), m_And(m_Value(A), m_Value(B)))))
    return false;
  if (P != CmpInst::ICMP_EQ && P != CmpInst::ICMP_NE)
    return false;
  // Matched: select (A & B) == C ? ... : ...
  //          select (A & B) != C ? ... : ...

  Value *X = nullptr, *Sh1 = nullptr;
  // Check (A & B) for (X & (1 << i)):
  if (match(A, m_Shl(m_One(), m_Specific(CIV)))) {
    Sh1 = A;
    X = B;
  } else if (match(B, m_Shl(m_One(), m_Specific(CIV)))) {
    Sh1 = B;
    X = A;
  } else {
    // TODO: Could also check for an induction variable containing single
    // bit shifted left by 1 in each iteration.
    return false;
  }

  bool TrueIfZero;

  // Check C against the possible values for comparison: 0 and (1 << i):
  if (match(C, m_Zero()))
    TrueIfZero = (P == CmpInst::ICMP_EQ);
  else if (C == Sh1)
    TrueIfZero = (P == CmpInst::ICMP_NE);
  else
    return false;

  // So far, matched:
  //   select (X & (1 << i)) ? ... : ...
  // including variations of the check against zero/non-zero value.

  Value *ShouldSameV = nullptr, *ShouldXoredV = nullptr;
  if (TrueIfZero) {
    ShouldSameV = TrueV;
    ShouldXoredV = FalseV;
  } else {
    ShouldSameV = FalseV;
    ShouldXoredV = TrueV;
  }

  Value *Q = nullptr, *R = nullptr, *Y = nullptr, *Z = nullptr;
  Value *T = nullptr;
  if (match(ShouldXoredV, m_Xor(m_Value(Y), m_Value(Z)))) {
    // Matched: select +++ ? ... : Y ^ Z
    //          select +++ ? Y ^ Z : ...
    // where +++ denotes previously checked matches.
    if (ShouldSameV == Y)
      T = Z;
    else if (ShouldSameV == Z)
      T = Y;
    else
      return false;
    R = ShouldSameV;
    // Matched: select +++ ? R : R ^ T
    //          select +++ ? R ^ T : R
    // depending on TrueIfZero.

  } else if (match(ShouldSameV, m_Zero())) {
    // Matched: select +++ ? 0 : ...
    //          select +++ ? ... : 0
    if (!SelI->hasOneUse())
      return false;
    T = ShouldXoredV;
    // Matched: select +++ ? 0 : T
    //          select +++ ? T : 0

    Value *U = *SelI->user_begin();
    if (!match(U, m_Xor(m_Specific(SelI), m_Value(R))) &&
        !match(U, m_Xor(m_Value(R), m_Specific(SelI))))
      return false;
    // Matched: xor (select +++ ? 0 : T), R
    //          xor (select +++ ? T : 0), R
  } else
    return false;

  // The xor input value T is isolated into its own match so that it could
  // be checked against an induction variable containing a shifted bit
  // (todo).
  // For now, check against (Q << i).
  if (!match(T, m_Shl(m_Value(Q), m_Specific(CIV))) &&
      !match(T, m_Shl(m_ZExt(m_Value(Q)), m_ZExt(m_Specific(CIV)))))
    return false;
  // Matched: select +++ ? R : R ^ (Q << i)
  //          select +++ ? R ^ (Q << i) : R

  PV.X = X;
  PV.Q = Q;
  PV.R = R;
  PV.Left = true;
  return true;
}


bool PolynomialMultiplyRecognize::matchRightShift(SelectInst *SelI,
      ParsedValues &PV) {
  // Match the following:
  //   select (X & 1) != 0 ? (R >> 1) ^ Q : (R >> 1)
  //   select (X & 1) == 0 ? (R >> 1) : (R >> 1) ^ Q
  // The condition may also check for equality with the masked value, i.e
  //   select (X & 1) == 1 ? (R >> 1) ^ Q : (R >> 1)
  //   select (X & 1) != 1 ? (R >> 1) : (R >> 1) ^ Q

  Value *CondV = SelI->getCondition();
  Value *TrueV = SelI->getTrueValue();
  Value *FalseV = SelI->getFalseValue();

  using namespace PatternMatch;

  Value *C = nullptr;
  CmpInst::Predicate P;
  bool TrueIfZero;

  if (match(CondV, m_ICmp(P, m_Value(C), m_Zero())) ||
      match(CondV, m_ICmp(P, m_Zero(), m_Value(C)))) {
    if (P != CmpInst::ICMP_EQ && P != CmpInst::ICMP_NE)
      return false;
    // Matched: select C == 0 ? ... : ...
    //          select C != 0 ? ... : ...
    TrueIfZero = (P == CmpInst::ICMP_EQ);
  } else if (match(CondV, m_ICmp(P, m_Value(C), m_One())) ||
             match(CondV, m_ICmp(P, m_One(), m_Value(C)))) {
    if (P != CmpInst::ICMP_EQ && P != CmpInst::ICMP_NE)
      return false;
    // Matched: select C == 1 ? ... : ...
    //          select C != 1 ? ... : ...
    TrueIfZero = (P == CmpInst::ICMP_NE);
  } else
    return false;

  Value *X = nullptr;
  if (!match(C, m_And(m_Value(X), m_One())) &&
      !match(C, m_And(m_One(), m_Value(X))))
    return false;
  // Matched: select (X & 1) == +++ ? ... : ...
  //          select (X & 1) != +++ ? ... : ...

  Value *R = nullptr, *Q = nullptr;
  if (TrueIfZero) {
    // The select's condition is true if the tested bit is 0.
    // TrueV must be the shift, FalseV must be the xor.
    if (!match(TrueV, m_LShr(m_Value(R), m_One())))
      return false;
    // Matched: select +++ ? (R >> 1) : ...
    if (!match(FalseV, m_Xor(m_Specific(TrueV), m_Value(Q))) &&
        !match(FalseV, m_Xor(m_Value(Q), m_Specific(TrueV))))
      return false;
    // Matched: select +++ ? (R >> 1) : (R >> 1) ^ Q
    // with commuting ^.
  } else {
    // The select's condition is true if the tested bit is 1.
    // TrueV must be the xor, FalseV must be the shift.
    if (!match(FalseV, m_LShr(m_Value(R), m_One())))
      return false;
    // Matched: select +++ ? ... : (R >> 1)
    if (!match(TrueV, m_Xor(m_Specific(FalseV), m_Value(Q))) &&
        !match(TrueV, m_Xor(m_Value(Q), m_Specific(FalseV))))
      return false;
    // Matched: select +++ ? (R >> 1) ^ Q : (R >> 1)
    // with commuting ^.
  }

  PV.X = X;
  PV.Q = Q;
  PV.R = R;
  PV.Left = false;
  return true;
}


bool PolynomialMultiplyRecognize::scanSelect(SelectInst *SelI,
      BasicBlock *LoopB, BasicBlock *PrehB, Value *CIV, ParsedValues &PV,
      bool PreScan) {
  using namespace PatternMatch;
  // The basic pattern for R = P.Q is:
  // for i = 0..31
  //   R = phi (0, R')
  //   if (P & (1 << i))        ; test-bit(P, i)
  //     R' = R ^ (Q << i)
  //
  // Similarly, the basic pattern for R = (P/Q).Q - P
  // for i = 0..31
  //   R = phi(P, R')
  //   if (R & (1 << i))
  //     R' = R ^ (Q << i)

  // There exist idioms, where instead of Q being shifted left, P is shifted
  // right. This produces a result that is shifted right by 32 bits (the
  // non-shifted result is 64-bit).
  //
  // For R = P.Q, this would be:
  // for i = 0..31
  //   R = phi (0, R')
  //   if ((P >> i) & 1)
  //     R' = (R >> 1) ^ Q      ; R is cycled through the loop, so it must
  //   else                     ; be shifted by 1, not i.
  //     R' = R >> 1
  //
  // And for the inverse:
  // for i = 0..31
  //   R = phi (P, R')
  //   if (R & 1)
  //     R' = (R >> 1) ^ Q
  //   else
  //     R' = R >> 1

  // The left-shifting idioms share the same pattern:
  //   select (X & (1 << i)) ? R ^ (Q << i) : R
  // Similarly for right-shifting idioms:
  //   select (X & 1) ? (R >> 1) ^ Q

  if (matchLeftShift(SelI, CIV, PV)) {
    // If this is a pre-scan, getting this far is sufficient.
    if (PreScan)
      return true;

    // Need to make sure that the SelI goes back into R.
    auto *RPhi = dyn_cast<PHINode>(PV.R);
    if (!RPhi)
      return false;
    if (SelI != RPhi->getIncomingValueForBlock(LoopB))
      return false;
    PV.Res = SelI;

    // If X is loop invariant, it must be the input polynomial, and the
    // idiom is the basic polynomial multiply.
    if (CurLoop->isLoopInvariant(PV.X)) {
      PV.P = PV.X;
      PV.Inv = false;
    } else {
      // X is not loop invariant. If X == R, this is the inverse pmpy.
      // Otherwise, check for an xor with an invariant value. If the
      // variable argument to the xor is R, then this is still a valid
      // inverse pmpy.
      PV.Inv = true;
      if (PV.X != PV.R) {
        Value *Var = nullptr, *Inv = nullptr, *X1 = nullptr, *X2 = nullptr;
        if (!match(PV.X, m_Xor(m_Value(X1), m_Value(X2))))
          return false;
        auto *I1 = dyn_cast<Instruction>(X1);
        auto *I2 = dyn_cast<Instruction>(X2);
        if (!I1 || I1->getParent() != LoopB) {
          Var = X2;
          Inv = X1;
        } else if (!I2 || I2->getParent() != LoopB) {
          Var = X1;
          Inv = X2;
        } else
          return false;
        if (Var != PV.R)
          return false;
        PV.M = Inv;
      }
      // The input polynomial P still needs to be determined. It will be
      // the entry value of R.
      Value *EntryP = RPhi->getIncomingValueForBlock(PrehB);
      PV.P = EntryP;
    }

    return true;
  }

  if (matchRightShift(SelI, PV)) {
    // If this is an inverse pattern, the Q polynomial must be known at
    // compile time.
    if (PV.Inv && !isa<ConstantInt>(PV.Q))
      return false;
    if (PreScan)
      return true;
    // There is no exact matching of right-shift pmpy.
    return false;
  }

  return false;
}


bool PolynomialMultiplyRecognize::isPromotableTo(Value *Val,
      IntegerType *DestTy) {
  IntegerType *T = dyn_cast<IntegerType>(Val->getType());
  if (!T || T->getBitWidth() > DestTy->getBitWidth())
    return false;
  if (T->getBitWidth() == DestTy->getBitWidth())
    return true;
  // Non-instructions are promotable. The reason why an instruction may not
  // be promotable is that it may produce a different result if its operands
  // and the result are promoted, for example, it may produce more non-zero
  // bits. While it would still be possible to represent the proper result
  // in a wider type, it may require adding additional instructions (which
  // we don't want to do).
  Instruction *In = dyn_cast<Instruction>(Val);
  if (!In)
    return true;
  // The bitwidth of the source type is smaller than the destination.
  // Check if the individual operation can be promoted.
  switch (In->getOpcode()) {
    case Instruction::PHI:
    case Instruction::ZExt:
    case Instruction::And:
    case Instruction::Or:
    case Instruction::Xor:
    case Instruction::LShr: // Shift right is ok.
    case Instruction::Select:
      return true;
    case Instruction::ICmp:
      if (CmpInst *CI = cast<CmpInst>(In))
        return CI->isEquality() || CI->isUnsigned();
      llvm_unreachable("Cast failed unexpectedly");
    case Instruction::Add:
      return In->hasNoSignedWrap() && In->hasNoUnsignedWrap();
  }
  return false;
}


void PolynomialMultiplyRecognize::promoteTo(Instruction *In,
      IntegerType *DestTy, BasicBlock *LoopB) {
  // Leave boolean values alone.
  if (!In->getType()->isIntegerTy(1))
    In->mutateType(DestTy);
  unsigned DestBW = DestTy->getBitWidth();

  // Handle PHIs.
  if (PHINode *P = dyn_cast<PHINode>(In)) {
    unsigned N = P->getNumIncomingValues();
    for (unsigned i = 0; i != N; ++i) {
      BasicBlock *InB = P->getIncomingBlock(i);
      if (InB == LoopB)
        continue;
      Value *InV = P->getIncomingValue(i);
      IntegerType *Ty = cast<IntegerType>(InV->getType());
      // Do not promote values in PHI nodes of type i1.
      if (Ty != P->getType()) {
        // If the value type does not match the PHI type, the PHI type
        // must have been promoted.
        assert(Ty->getBitWidth() < DestBW);
        InV = IRBuilder<>(InB->getTerminator()).CreateZExt(InV, DestTy);
        P->setIncomingValue(i, InV);
      }
    }
  } else if (ZExtInst *Z = dyn_cast<ZExtInst>(In)) {
    Value *Op = Z->getOperand(0);
    if (Op->getType() == Z->getType())
      Z->replaceAllUsesWith(Op);
    Z->eraseFromParent();
    return;
  }

  // Promote immediates.
  for (unsigned i = 0, n = In->getNumOperands(); i != n; ++i) {
    if (ConstantInt *CI = dyn_cast<ConstantInt>(In->getOperand(i)))
      if (CI->getType()->getBitWidth() < DestBW)
        In->setOperand(i, ConstantInt::get(DestTy, CI->getZExtValue()));
  }
}


bool PolynomialMultiplyRecognize::promoteTypes(BasicBlock *LoopB,
      BasicBlock *ExitB) {
  assert(LoopB);
  // Skip loops where the exit block has more than one predecessor. The values
  // coming from the loop block will be promoted to another type, and so the
  // values coming into the exit block from other predecessors would also have
  // to be promoted.
  if (!ExitB || (ExitB->getSinglePredecessor() != LoopB))
    return false;
  IntegerType *DestTy = getPmpyType();
  // Check if the exit values have types that are no wider than the type
  // that we want to promote to.
  unsigned DestBW = DestTy->getBitWidth();
  for (Instruction &In : *ExitB) {
    PHINode *P = dyn_cast<PHINode>(&In);
    if (!P)
      break;
    if (P->getNumIncomingValues() != 1)
      return false;
    assert(P->getIncomingBlock(0) == LoopB);
    IntegerType *T = dyn_cast<IntegerType>(P->getType());
    if (!T || T->getBitWidth() > DestBW)
      return false;
  }

  // Check all instructions in the loop.
  for (Instruction &In : *LoopB)
    if (!In.isTerminator() && !isPromotableTo(&In, DestTy))
      return false;

  // Perform the promotion.
  std::vector<Instruction*> LoopIns;
  std::transform(LoopB->begin(), LoopB->end(), std::back_inserter(LoopIns),
                 [](Instruction &In) { return &In; });
  for (Instruction *In : LoopIns)
    promoteTo(In, DestTy, LoopB);

  // Fix up the PHI nodes in the exit block.
  Instruction *EndI = ExitB->getFirstNonPHI();
  BasicBlock::iterator End = EndI ? EndI->getIterator() : ExitB->end();
  for (auto I = ExitB->begin(); I != End; ++I) {
    PHINode *P = dyn_cast<PHINode>(I);
    if (!P)
      break;
    Type *Ty0 = P->getIncomingValue(0)->getType();
    Type *PTy = P->getType();
    if (PTy != Ty0) {
      assert(Ty0 == DestTy);
      // In order to create the trunc, P must have the promoted type.
      P->mutateType(Ty0);
      Value *T = IRBuilder<>(ExitB, End).CreateTrunc(P, PTy);
      // In order for the RAUW to work, the types of P and T must match.
      P->mutateType(PTy);
      P->replaceAllUsesWith(T);
      // Final update of the P's type.
      P->mutateType(Ty0);
      cast<Instruction>(T)->setOperand(0, P);
    }
  }

  return true;
}


bool PolynomialMultiplyRecognize::findCycle(Value *Out, Value *In,
      ValueSeq &Cycle) {
  // Out = ..., In, ...
  if (Out == In)
    return true;

  auto *BB = cast<Instruction>(Out)->getParent();
  bool HadPhi = false;

  for (auto U : Out->users()) {
    auto *I = dyn_cast<Instruction>(&*U);
    if (I == nullptr || I->getParent() != BB)
      continue;
    // Make sure that there are no multi-iteration cycles, e.g.
    //   p1 = phi(p2)
    //   p2 = phi(p1)
    // The cycle p1->p2->p1 would span two loop iterations.
    // Check that there is only one phi in the cycle.
    bool IsPhi = isa<PHINode>(I);
    if (IsPhi && HadPhi)
      return false;
    HadPhi |= IsPhi;
    if (Cycle.count(I))
      return false;
    Cycle.insert(I);
    if (findCycle(I, In, Cycle))
      break;
    Cycle.remove(I);
  }
  return !Cycle.empty();
}


void PolynomialMultiplyRecognize::classifyCycle(Instruction *DivI,
      ValueSeq &Cycle, ValueSeq &Early, ValueSeq &Late) {
  // All the values in the cycle that are between the phi node and the
  // divider instruction will be classified as "early", all other values
  // will be "late".

  bool IsE = true;
  unsigned I, N = Cycle.size();
  for (I = 0; I < N; ++I) {
    Value *V = Cycle[I];
    if (DivI == V)
      IsE = false;
    else if (!isa<PHINode>(V))
      continue;
    // Stop if found either.
    break;
  }
  // "I" is the index of either DivI or the phi node, whichever was first.
  // "E" is "false" or "true" respectively.
  ValueSeq &First = !IsE ? Early : Late;
  for (unsigned J = 0; J < I; ++J)
    First.insert(Cycle[J]);

  ValueSeq &Second = IsE ? Early : Late;
  Second.insert(Cycle[I]);
  for (++I; I < N; ++I) {
    Value *V = Cycle[I];
    if (DivI == V || isa<PHINode>(V))
      break;
    Second.insert(V);
  }

  for (; I < N; ++I)
    First.insert(Cycle[I]);
}


bool PolynomialMultiplyRecognize::classifyInst(Instruction *UseI,
      ValueSeq &Early, ValueSeq &Late) {
  // Select is an exception, since the condition value does not have to be
  // classified in the same way as the true/false values. The true/false
  // values do have to be both early or both late.
  if (UseI->getOpcode() == Instruction::Select) {
    Value *TV = UseI->getOperand(1), *FV = UseI->getOperand(2);
    if (Early.count(TV) || Early.count(FV)) {
      if (Late.count(TV) || Late.count(FV))
        return false;
      Early.insert(UseI);
    } else if (Late.count(TV) || Late.count(FV)) {
      if (Early.count(TV) || Early.count(FV))
        return false;
      Late.insert(UseI);
    }
    return true;
  }

  // Not sure what would be the example of this, but the code below relies
  // on having at least one operand.
  if (UseI->getNumOperands() == 0)
    return true;

  bool AE = true, AL = true;
  for (auto &I : UseI->operands()) {
    if (Early.count(&*I))
      AL = false;
    else if (Late.count(&*I))
      AE = false;
  }
  // If the operands appear "all early" and "all late" at the same time,
  // then it means that none of them are actually classified as either.
  // This is harmless.
  if (AE && AL)
    return true;
  // Conversely, if they are neither "all early" nor "all late", then
  // we have a mixture of early and late operands that is not a known
  // exception.
  if (!AE && !AL)
    return false;

  // Check that we have covered the two special cases.
  assert(AE != AL);

  if (AE)
    Early.insert(UseI);
  else
    Late.insert(UseI);
  return true;
}


bool PolynomialMultiplyRecognize::commutesWithShift(Instruction *I) {
  switch (I->getOpcode()) {
    case Instruction::And:
    case Instruction::Or:
    case Instruction::Xor:
    case Instruction::LShr:
    case Instruction::Shl:
    case Instruction::Select:
    case Instruction::ICmp:
    case Instruction::PHI:
      break;
    default:
      return false;
  }
  return true;
}


bool PolynomialMultiplyRecognize::highBitsAreZero(Value *V,
      unsigned IterCount) {
  auto *T = dyn_cast<IntegerType>(V->getType());
  if (!T)
    return false;

  unsigned BW = T->getBitWidth();
  APInt K0(BW, 0), K1(BW, 0);
  computeKnownBits(V, K0, K1, DL);
  return K0.countLeadingOnes() >= IterCount;
}


bool PolynomialMultiplyRecognize::keepsHighBitsZero(Value *V,
      unsigned IterCount) {
  // Assume that all inputs to the value have the high bits zero.
  // Check if the value itself preserves the zeros in the high bits.
  if (auto *C = dyn_cast<ConstantInt>(V))
    return C->getValue().countLeadingZeros() >= IterCount;

  if (auto *I = dyn_cast<Instruction>(V)) {
    switch (I->getOpcode()) {
      case Instruction::And:
      case Instruction::Or:
      case Instruction::Xor:
      case Instruction::LShr:
      case Instruction::Select:
      case Instruction::ICmp:
      case Instruction::PHI:
      case Instruction::ZExt:
        return true;
    }
  }

  return false;
}


bool PolynomialMultiplyRecognize::isOperandShifted(Instruction *I, Value *Op) {
  unsigned Opc = I->getOpcode();
  if (Opc == Instruction::Shl || Opc == Instruction::LShr)
    return Op != I->getOperand(1);
  return true;
}


bool PolynomialMultiplyRecognize::convertShiftsToLeft(BasicBlock *LoopB,
      BasicBlock *ExitB, unsigned IterCount) {
  Value *CIV = getCountIV(LoopB);
  if (CIV == nullptr)
    return false;
  auto *CIVTy = dyn_cast<IntegerType>(CIV->getType());
  if (CIVTy == nullptr)
    return false;

  ValueSeq RShifts;
  ValueSeq Early, Late, Cycled;

  // Find all value cycles that contain logical right shifts by 1.
  for (Instruction &I : *LoopB) {
    using namespace PatternMatch;
    Value *V = nullptr;
    if (!match(&I, m_LShr(m_Value(V), m_One())))
      continue;
    ValueSeq C;
    if (!findCycle(&I, V, C))
      continue;

    // Found a cycle.
    C.insert(&I);
    classifyCycle(&I, C, Early, Late);
    Cycled.insert(C.begin(), C.end());
    RShifts.insert(&I);
  }

  // Find the set of all values affected by the shift cycles, i.e. all
  // cycled values, and (recursively) all their users.
  ValueSeq Users(Cycled.begin(), Cycled.end());
  for (unsigned i = 0; i < Users.size(); ++i) {
    Value *V = Users[i];
    if (!isa<IntegerType>(V->getType()))
      return false;
    auto *R = cast<Instruction>(V);
    // If the instruction does not commute with shifts, the loop cannot
    // be unshifted.
    if (!commutesWithShift(R))
      return false;
    for (auto I = R->user_begin(), E = R->user_end(); I != E; ++I) {
      auto *T = cast<Instruction>(*I);
      // Skip users from outside of the loop. They will be handled later.
      // Also, skip the right-shifts and phi nodes, since they mix early
      // and late values.
      if (T->getParent() != LoopB || RShifts.count(T) || isa<PHINode>(T))
        continue;

      Users.insert(T);
      if (!classifyInst(T, Early, Late))
        return false;
    }
  }

  if (Users.size() == 0)
    return false;

  // Verify that high bits remain zero.
  ValueSeq Internal(Users.begin(), Users.end());
  ValueSeq Inputs;
  for (unsigned i = 0; i < Internal.size(); ++i) {
    auto *R = dyn_cast<Instruction>(Internal[i]);
    if (!R)
      continue;
    for (Value *Op : R->operands()) {
      auto *T = dyn_cast<Instruction>(Op);
      if (T && T->getParent() != LoopB)
        Inputs.insert(Op);
      else
        Internal.insert(Op);
    }
  }
  for (Value *V : Inputs)
    if (!highBitsAreZero(V, IterCount))
      return false;
  for (Value *V : Internal)
    if (!keepsHighBitsZero(V, IterCount))
      return false;

  // Finally, the work can be done. Unshift each user.
  IRBuilder<> IRB(LoopB);
  std::map<Value*,Value*> ShiftMap;
  typedef std::map<std::pair<Value*,Type*>,Value*> CastMapType;
  CastMapType CastMap;

  auto upcast = [] (CastMapType &CM, IRBuilder<> &IRB, Value *V,
        IntegerType *Ty) -> Value* {
    auto H = CM.find(std::make_pair(V, Ty));
    if (H != CM.end())
      return H->second;
    Value *CV = IRB.CreateIntCast(V, Ty, false);
    CM.insert(std::make_pair(std::make_pair(V, Ty), CV));
    return CV;
  };

  for (auto I = LoopB->begin(), E = LoopB->end(); I != E; ++I) {
    if (isa<PHINode>(I) || !Users.count(&*I))
      continue;
    using namespace PatternMatch;
    // Match lshr x, 1.
    Value *V = nullptr;
    if (match(&*I, m_LShr(m_Value(V), m_One()))) {
      replaceAllUsesOfWithIn(&*I, V, LoopB);
      continue;
    }
    // For each non-cycled operand, replace it with the corresponding
    // value shifted left.
    for (auto &J : I->operands()) {
      Value *Op = J.get();
      if (!isOperandShifted(&*I, Op))
        continue;
      if (Users.count(Op))
        continue;
      // Skip shifting zeros.
      if (isa<ConstantInt>(Op) && cast<ConstantInt>(Op)->isZero())
        continue;
      // Check if we have already generated a shift for this value.
      auto F = ShiftMap.find(Op);
      Value *W = (F != ShiftMap.end()) ? F->second : nullptr;
      if (W == nullptr) {
        IRB.SetInsertPoint(&*I);
        // First, the shift amount will be CIV or CIV+1, depending on
        // whether the value is early or late. Instead of creating CIV+1,
        // do a single shift of the value.
        Value *ShAmt = CIV, *ShVal = Op;
        auto *VTy = cast<IntegerType>(ShVal->getType());
        auto *ATy = cast<IntegerType>(ShAmt->getType());
        if (Late.count(&*I))
          ShVal = IRB.CreateShl(Op, ConstantInt::get(VTy, 1));
        // Second, the types of the shifted value and the shift amount
        // must match.
        if (VTy != ATy) {
          if (VTy->getBitWidth() < ATy->getBitWidth())
            ShVal = upcast(CastMap, IRB, ShVal, ATy);
          else
            ShAmt = upcast(CastMap, IRB, ShAmt, VTy);
        }
        // Ready to generate the shift and memoize it.
        W = IRB.CreateShl(ShVal, ShAmt);
        ShiftMap.insert(std::make_pair(Op, W));
      }
      I->replaceUsesOfWith(Op, W);
    }
  }

  // Update the users outside of the loop to account for having left
  // shifts. They would normally be shifted right in the loop, so shift
  // them right after the loop exit.
  // Take advantage of the loop-closed SSA form, which has all the post-
  // loop values in phi nodes.
  IRB.SetInsertPoint(ExitB, ExitB->getFirstInsertionPt());
  for (auto P = ExitB->begin(), Q = ExitB->end(); P != Q; ++P) {
    if (!isa<PHINode>(P))
      break;
    auto *PN = cast<PHINode>(P);
    Value *U = PN->getIncomingValueForBlock(LoopB);
    if (!Users.count(U))
      continue;
    Value *S = IRB.CreateLShr(PN, ConstantInt::get(PN->getType(), IterCount));
    PN->replaceAllUsesWith(S);
    // The above RAUW will create
    //   S = lshr S, IterCount
    // so we need to fix it back into
    //   S = lshr PN, IterCount
    cast<User>(S)->replaceUsesOfWith(S, PN);
  }

  return true;
}


void PolynomialMultiplyRecognize::cleanupLoopBody(BasicBlock *LoopB) {
  for (auto &I : *LoopB)
    if (Value *SV = SimplifyInstruction(&I, DL, &TLI, &DT))
      I.replaceAllUsesWith(SV);

  for (auto I = LoopB->begin(), N = I; I != LoopB->end(); I = N) {
    N = std::next(I);
    RecursivelyDeleteTriviallyDeadInstructions(&*I, &TLI);
  }
}


unsigned PolynomialMultiplyRecognize::getInverseMxN(unsigned QP) {
  // Arrays of coefficients of Q and the inverse, C.
  // Q[i] = coefficient at x^i.
  std::array<char,32> Q, C;

  for (unsigned i = 0; i < 32; ++i) {
    Q[i] = QP & 1;
    QP >>= 1;
  }
  assert(Q[0] == 1);

  // Find C, such that
  // (Q[n]*x^n + ... + Q[1]*x + Q[0]) * (C[n]*x^n + ... + C[1]*x + C[0]) = 1
  //
  // For it to have a solution, Q[0] must be 1. Since this is Z2[x], the
  // operations * and + are & and ^ respectively.
  //
  // Find C[i] recursively, by comparing i-th coefficient in the product
  // with 0 (or 1 for i=0).
  //
  // C[0] = 1, since C[0] = Q[0], and Q[0] = 1.
  C[0] = 1;
  for (unsigned i = 1; i < 32; ++i) {
    // Solve for C[i] in:
    //   C[0]Q[i] ^ C[1]Q[i-1] ^ ... ^ C[i-1]Q[1] ^ C[i]Q[0] = 0
    // This is equivalent to
    //   C[0]Q[i] ^ C[1]Q[i-1] ^ ... ^ C[i-1]Q[1] ^ C[i] = 0
    // which is
    //   C[0]Q[i] ^ C[1]Q[i-1] ^ ... ^ C[i-1]Q[1] = C[i]
    unsigned T = 0;
    for (unsigned j = 0; j < i; ++j)
      T = T ^ (C[j] & Q[i-j]);
    C[i] = T;
  }

  unsigned QV = 0;
  for (unsigned i = 0; i < 32; ++i)
    if (C[i])
      QV |= (1 << i);

  return QV;
}


Value *PolynomialMultiplyRecognize::generate(BasicBlock::iterator At,
      ParsedValues &PV) {
  IRBuilder<> B(&*At);
  Module *M = At->getParent()->getParent()->getParent();
  Value *PMF = Intrinsic::getDeclaration(M, Intrinsic::hexagon_M4_pmpyw);

  Value *P = PV.P, *Q = PV.Q, *P0 = P;
  unsigned IC = PV.IterCount;

  if (PV.M != nullptr)
    P0 = P = B.CreateXor(P, PV.M);

  // Create a bit mask to clear the high bits beyond IterCount.
  auto *BMI = ConstantInt::get(P->getType(), APInt::getLowBitsSet(32, IC));

  if (PV.IterCount != 32)
    P = B.CreateAnd(P, BMI);

  if (PV.Inv) {
    auto *QI = dyn_cast<ConstantInt>(PV.Q);
    assert(QI && QI->getBitWidth() <= 32);

    // Again, clearing bits beyond IterCount.
    unsigned M = (1 << PV.IterCount) - 1;
    unsigned Tmp = (QI->getZExtValue() | 1) & M;
    unsigned QV = getInverseMxN(Tmp) & M;
    auto *QVI = ConstantInt::get(QI->getType(), QV);
    P = B.CreateCall(PMF, {P, QVI});
    P = B.CreateTrunc(P, QI->getType());
    if (IC != 32)
      P = B.CreateAnd(P, BMI);
  }

  Value *R = B.CreateCall(PMF, {P, Q});

  if (PV.M != nullptr)
    R = B.CreateXor(R, B.CreateIntCast(P0, R->getType(), false));

  return R;
}


void PolynomialMultiplyRecognize::setupSimplifier() {
  Simp.addRule(
    // Sink zext past bitwise operations.
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      if (I->getOpcode() != Instruction::ZExt)
        return nullptr;
      Instruction *T = dyn_cast<Instruction>(I->getOperand(0));
      if (!T)
        return nullptr;
      switch (T->getOpcode()) {
        case Instruction::And:
        case Instruction::Or:
        case Instruction::Xor:
          break;
        default:
          return nullptr;
      }
      IRBuilder<> B(Ctx);
      return B.CreateBinOp(cast<BinaryOperator>(T)->getOpcode(),
                           B.CreateZExt(T->getOperand(0), I->getType()),
                           B.CreateZExt(T->getOperand(1), I->getType()));
    });
  Simp.addRule(
    // (xor (and x a) (and y a)) -> (and (xor x y) a)
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      if (I->getOpcode() != Instruction::Xor)
        return nullptr;
      Instruction *And0 = dyn_cast<Instruction>(I->getOperand(0));
      Instruction *And1 = dyn_cast<Instruction>(I->getOperand(1));
      if (!And0 || !And1)
        return nullptr;
      if (And0->getOpcode() != Instruction::And ||
          And1->getOpcode() != Instruction::And)
        return nullptr;
      if (And0->getOperand(1) != And1->getOperand(1))
        return nullptr;
      IRBuilder<> B(Ctx);
      return B.CreateAnd(B.CreateXor(And0->getOperand(0), And1->getOperand(0)),
                         And0->getOperand(1));
    });
  Simp.addRule(
    // (Op (select c x y) z) -> (select c (Op x z) (Op y z))
    // (Op x (select c y z)) -> (select c (Op x y) (Op x z))
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      BinaryOperator *BO = dyn_cast<BinaryOperator>(I);
      if (!BO)
        return nullptr;
      Instruction::BinaryOps Op = BO->getOpcode();
      if (SelectInst *Sel = dyn_cast<SelectInst>(BO->getOperand(0))) {
        IRBuilder<> B(Ctx);
        Value *X = Sel->getTrueValue(), *Y = Sel->getFalseValue();
        Value *Z = BO->getOperand(1);
        return B.CreateSelect(Sel->getCondition(),
                              B.CreateBinOp(Op, X, Z),
                              B.CreateBinOp(Op, Y, Z));
      }
      if (SelectInst *Sel = dyn_cast<SelectInst>(BO->getOperand(1))) {
        IRBuilder<> B(Ctx);
        Value *X = BO->getOperand(0);
        Value *Y = Sel->getTrueValue(), *Z = Sel->getFalseValue();
        return B.CreateSelect(Sel->getCondition(),
                              B.CreateBinOp(Op, X, Y),
                              B.CreateBinOp(Op, X, Z));
      }
      return nullptr;
    });
  Simp.addRule(
    // (select c (select c x y) z) -> (select c x z)
    // (select c x (select c y z)) -> (select c x z)
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      SelectInst *Sel = dyn_cast<SelectInst>(I);
      if (!Sel)
        return nullptr;
      IRBuilder<> B(Ctx);
      Value *C = Sel->getCondition();
      if (SelectInst *Sel0 = dyn_cast<SelectInst>(Sel->getTrueValue())) {
        if (Sel0->getCondition() == C)
          return B.CreateSelect(C, Sel0->getTrueValue(), Sel->getFalseValue());
      }
      if (SelectInst *Sel1 = dyn_cast<SelectInst>(Sel->getFalseValue())) {
        if (Sel1->getCondition() == C)
          return B.CreateSelect(C, Sel->getTrueValue(), Sel1->getFalseValue());
      }
      return nullptr;
    });
  Simp.addRule(
    // (or (lshr x 1) 0x800.0) -> (xor (lshr x 1) 0x800.0)
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      if (I->getOpcode() != Instruction::Or)
        return nullptr;
      Instruction *LShr = dyn_cast<Instruction>(I->getOperand(0));
      if (!LShr || LShr->getOpcode() != Instruction::LShr)
        return nullptr;
      ConstantInt *One = dyn_cast<ConstantInt>(LShr->getOperand(1));
      if (!One || One->getZExtValue() != 1)
        return nullptr;
      ConstantInt *Msb = dyn_cast<ConstantInt>(I->getOperand(1));
      if (!Msb || Msb->getZExtValue() != Msb->getType()->getSignBit())
        return nullptr;
      return IRBuilder<>(Ctx).CreateXor(LShr, Msb);
    });
  Simp.addRule(
    // (lshr (BitOp x y) c) -> (BitOp (lshr x c) (lshr y c))
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      if (I->getOpcode() != Instruction::LShr)
        return nullptr;
      BinaryOperator *BitOp = dyn_cast<BinaryOperator>(I->getOperand(0));
      if (!BitOp)
        return nullptr;
      switch (BitOp->getOpcode()) {
        case Instruction::And:
        case Instruction::Or:
        case Instruction::Xor:
          break;
        default:
          return nullptr;
      }
      IRBuilder<> B(Ctx);
      Value *S = I->getOperand(1);
      return B.CreateBinOp(BitOp->getOpcode(),
                B.CreateLShr(BitOp->getOperand(0), S),
                B.CreateLShr(BitOp->getOperand(1), S));
    });
  Simp.addRule(
    // (BitOp1 (BitOp2 x a) b) -> (BitOp2 x (BitOp1 a b))
    [](Instruction *I, LLVMContext &Ctx) -> Value* {
      auto IsBitOp = [](unsigned Op) -> bool {
        switch (Op) {
          case Instruction::And:
          case Instruction::Or:
          case Instruction::Xor:
            return true;
        }
        return false;
      };
      BinaryOperator *BitOp1 = dyn_cast<BinaryOperator>(I);
      if (!BitOp1 || !IsBitOp(BitOp1->getOpcode()))
        return nullptr;
      BinaryOperator *BitOp2 = dyn_cast<BinaryOperator>(BitOp1->getOperand(0));
      if (!BitOp2 || !IsBitOp(BitOp2->getOpcode()))
        return nullptr;
      ConstantInt *CA = dyn_cast<ConstantInt>(BitOp2->getOperand(1));
      ConstantInt *CB = dyn_cast<ConstantInt>(BitOp1->getOperand(1));
      if (!CA || !CB)
        return nullptr;
      IRBuilder<> B(Ctx);
      Value *X = BitOp2->getOperand(0);
      return B.CreateBinOp(BitOp2->getOpcode(), X,
                B.CreateBinOp(BitOp1->getOpcode(), CA, CB));
    });
}


bool PolynomialMultiplyRecognize::recognize() {
  DEBUG(dbgs() << "Starting PolynomialMultiplyRecognize on loop\n"
               << *CurLoop << '\n');
  // Restrictions:
  // - The loop must consist of a single block.
  // - The iteration count must be known at compile-time.
  // - The loop must have an induction variable starting from 0, and
  //   incremented in each iteration of the loop.
  BasicBlock *LoopB = CurLoop->getHeader();
  DEBUG(dbgs() << "Loop header:\n" << *LoopB);

  if (LoopB != CurLoop->getLoopLatch())
    return false;
  BasicBlock *ExitB = CurLoop->getExitBlock();
  if (ExitB == nullptr)
    return false;
  BasicBlock *EntryB = CurLoop->getLoopPreheader();
  if (EntryB == nullptr)
    return false;

  unsigned IterCount = 0;
  const SCEV *CT = SE.getBackedgeTakenCount(CurLoop);
  if (isa<SCEVCouldNotCompute>(CT))
    return false;
  if (auto *CV = dyn_cast<SCEVConstant>(CT))
    IterCount = CV->getValue()->getZExtValue() + 1;

  Value *CIV = getCountIV(LoopB);
  ParsedValues PV;
  PV.IterCount = IterCount;
  DEBUG(dbgs() << "Loop IV: " << *CIV << "\nIterCount: " << IterCount << '\n');

  setupSimplifier();

  // Perform a preliminary scan of select instructions to see if any of them
  // looks like a generator of the polynomial multiply steps. Assume that a
  // loop can only contain a single transformable operation, so stop the
  // traversal after the first reasonable candidate was found.
  // XXX: Currently this approach can modify the loop before being 100% sure
  // that the transformation can be carried out.
  bool FoundPreScan = false;
  for (Instruction &In : *LoopB) {
    SelectInst *SI = dyn_cast<SelectInst>(&In);
    if (!SI)
      continue;

    Simplifier::Context C(SI);
    Value *T = Simp.simplify(C);
    SelectInst *SelI = (T && isa<SelectInst>(T)) ? cast<SelectInst>(T) : SI;
    DEBUG(dbgs() << "scanSelect(pre-scan): " << PE(C, SelI) << '\n');
    if (scanSelect(SelI, LoopB, EntryB, CIV, PV, true)) {
      FoundPreScan = true;
      if (SelI != SI) {
        Value *NewSel = C.materialize(LoopB, SI->getIterator());
        SI->replaceAllUsesWith(NewSel);
        RecursivelyDeleteTriviallyDeadInstructions(SI, &TLI);
      }
      break;
    }
  }

  if (!FoundPreScan) {
    DEBUG(dbgs() << "Have not found candidates for pmpy\n");
    return false;
  }

  if (!PV.Left) {
    // The right shift version actually only returns the higher bits of
    // the result (each iteration discards the LSB). If we want to convert it
    // to a left-shifting loop, the working data type must be at least as
    // wide as the target's pmpy instruction.
    if (!promoteTypes(LoopB, ExitB))
      return false;
    convertShiftsToLeft(LoopB, ExitB, IterCount);
    cleanupLoopBody(LoopB);
  }

  // Scan the loop again, find the generating select instruction.
  bool FoundScan = false;
  for (Instruction &In : *LoopB) {
    SelectInst *SelI = dyn_cast<SelectInst>(&In);
    if (!SelI)
      continue;
    DEBUG(dbgs() << "scanSelect: " << *SelI << '\n');
    FoundScan = scanSelect(SelI, LoopB, EntryB, CIV, PV, false);
    if (FoundScan)
      break;
  }
  assert(FoundScan);

  DEBUG({
    StringRef PP = (PV.M ? "(P+M)" : "P");
    if (!PV.Inv)
      dbgs() << "Found pmpy idiom: R = " << PP << ".Q\n";
    else
      dbgs() << "Found inverse pmpy idiom: R = (" << PP << "/Q).Q) + "
             << PP << "\n";
    dbgs() << "  Res:" << *PV.Res << "\n  P:" << *PV.P << "\n";
    if (PV.M)
      dbgs() << "  M:" << *PV.M << "\n";
    dbgs() << "  Q:" << *PV.Q << "\n";
    dbgs() << "  Iteration count:" << PV.IterCount << "\n";
  });

  BasicBlock::iterator At(EntryB->getTerminator());
  Value *PM = generate(At, PV);
  if (PM == nullptr)
    return false;

  if (PM->getType() != PV.Res->getType())
    PM = IRBuilder<>(&*At).CreateIntCast(PM, PV.Res->getType(), false);

  PV.Res->replaceAllUsesWith(PM);
  PV.Res->eraseFromParent();
  return true;
}


unsigned HexagonLoopIdiomRecognize::getStoreSizeInBytes(StoreInst *SI) {
  uint64_t SizeInBits = DL->getTypeSizeInBits(SI->getValueOperand()->getType());
  assert(((SizeInBits & 7) || (SizeInBits >> 32) == 0) &&
         "Don't overflow unsigned.");
  return (unsigned)SizeInBits >> 3;
}


int HexagonLoopIdiomRecognize::getSCEVStride(const SCEVAddRecExpr *S) {
  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getOperand(1)))
    return SC->getAPInt().getSExtValue();
  return 0;
}


bool HexagonLoopIdiomRecognize::isLegalStore(Loop *CurLoop, StoreInst *SI) {
  // Allow volatile stores if HexagonVolatileMemcpy is enabled.
  if (!(SI->isVolatile() && HexagonVolatileMemcpy) && !SI->isSimple())
    return false;

  Value *StoredVal = SI->getValueOperand();
  Value *StorePtr = SI->getPointerOperand();

  // Reject stores that are so large that they overflow an unsigned.
  uint64_t SizeInBits = DL->getTypeSizeInBits(StoredVal->getType());
  if ((SizeInBits & 7) || (SizeInBits >> 32) != 0)
    return false;

  // See if the pointer expression is an AddRec like {base,+,1} on the current
  // loop, which indicates a strided store.  If we have something else, it's a
  // random store we can't handle.
  auto *StoreEv = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(StorePtr));
  if (!StoreEv || StoreEv->getLoop() != CurLoop || !StoreEv->isAffine())
    return false;

  // Check to see if the stride matches the size of the store.  If so, then we
  // know that every byte is touched in the loop.
  int Stride = getSCEVStride(StoreEv);
  if (Stride == 0)
    return false;
  unsigned StoreSize = getStoreSizeInBytes(SI);
  if (StoreSize != unsigned(std::abs(Stride)))
    return false;

  // The store must be feeding a non-volatile load.
  LoadInst *LI = dyn_cast<LoadInst>(SI->getValueOperand());
  if (!LI || !LI->isSimple())
    return false;

  // See if the pointer expression is an AddRec like {base,+,1} on the current
  // loop, which indicates a strided load.  If we have something else, it's a
  // random load we can't handle.
  Value *LoadPtr = LI->getPointerOperand();
  auto *LoadEv = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(LoadPtr));
  if (!LoadEv || LoadEv->getLoop() != CurLoop || !LoadEv->isAffine())
    return false;

  // The store and load must share the same stride.
  if (StoreEv->getOperand(1) != LoadEv->getOperand(1))
    return false;

  // Success.  This store can be converted into a memcpy.
  return true;
}


/// mayLoopAccessLocation - Return true if the specified loop might access the
/// specified pointer location, which is a loop-strided access.  The 'Access'
/// argument specifies what the verboten forms of access are (read or write).
static bool
mayLoopAccessLocation(Value *Ptr, ModRefInfo Access, Loop *L,
                      const SCEV *BECount, unsigned StoreSize,
                      AliasAnalysis &AA,
                      SmallPtrSetImpl<Instruction *> &Ignored) {
  // Get the location that may be stored across the loop.  Since the access
  // is strided positively through memory, we say that the modified location
  // starts at the pointer and has infinite size.
  uint64_t AccessSize = MemoryLocation::UnknownSize;

  // If the loop iterates a fixed number of times, we can refine the access
  // size to be exactly the size of the memset, which is (BECount+1)*StoreSize
  if (const SCEVConstant *BECst = dyn_cast<SCEVConstant>(BECount))
    AccessSize = (BECst->getValue()->getZExtValue() + 1) * StoreSize;

  // TODO: For this to be really effective, we have to dive into the pointer
  // operand in the store.  Store to &A[i] of 100 will always return may alias
  // with store of &A[100], we need to StoreLoc to be "A" with size of 100,
  // which will then no-alias a store to &A[100].
  MemoryLocation StoreLoc(Ptr, AccessSize);

  for (auto *B : L->blocks())
    for (auto &I : *B)
      if (Ignored.count(&I) == 0 && (AA.getModRefInfo(&I, StoreLoc) & Access))
        return true;

  return false;
}


void HexagonLoopIdiomRecognize::collectStores(Loop *CurLoop, BasicBlock *BB,
      SmallVectorImpl<StoreInst*> &Stores) {
  Stores.clear();
  for (Instruction &I : *BB)
    if (StoreInst *SI = dyn_cast<StoreInst>(&I))
      if (isLegalStore(CurLoop, SI))
        Stores.push_back(SI);
}


bool HexagonLoopIdiomRecognize::processCopyingStore(Loop *CurLoop,
      StoreInst *SI, const SCEV *BECount) {
  assert((SI->isSimple() || (SI->isVolatile() && HexagonVolatileMemcpy)) &&
         "Expected only non-volatile stores, or Hexagon-specific memcpy"
         "to volatile destination.");

  Value *StorePtr = SI->getPointerOperand();
  auto *StoreEv = cast<SCEVAddRecExpr>(SE->getSCEV(StorePtr));
  unsigned Stride = getSCEVStride(StoreEv);
  unsigned StoreSize = getStoreSizeInBytes(SI);
  if (Stride != StoreSize)
    return false;

  // See if the pointer expression is an AddRec like {base,+,1} on the current
  // loop, which indicates a strided load.  If we have something else, it's a
  // random load we can't handle.
  LoadInst *LI = dyn_cast<LoadInst>(SI->getValueOperand());
  auto *LoadEv = cast<SCEVAddRecExpr>(SE->getSCEV(LI->getPointerOperand()));

  // The trip count of the loop and the base pointer of the addrec SCEV is
  // guaranteed to be loop invariant, which means that it should dominate the
  // header.  This allows us to insert code for it in the preheader.
  BasicBlock *Preheader = CurLoop->getLoopPreheader();
  Instruction *ExpPt = Preheader->getTerminator();
  IRBuilder<> Builder(ExpPt);
  SCEVExpander Expander(*SE, *DL, "hexagon-loop-idiom");

  Type *IntPtrTy = Builder.getIntPtrTy(*DL, SI->getPointerAddressSpace());

  // Okay, we have a strided store "p[i]" of a loaded value.  We can turn
  // this into a memcpy/memmove in the loop preheader now if we want.  However,
  // this would be unsafe to do if there is anything else in the loop that may
  // read or write the memory region we're storing to.  For memcpy, this
  // includes the load that feeds the stores.  Check for an alias by generating
  // the base address and checking everything.
  Value *StoreBasePtr = Expander.expandCodeFor(StoreEv->getStart(),
      Builder.getInt8PtrTy(SI->getPointerAddressSpace()), ExpPt);
  Value *LoadBasePtr = nullptr;

  bool Overlap = false;
  bool DestVolatile = SI->isVolatile();
  Type *BECountTy = BECount->getType();

  if (DestVolatile) {
    // The trip count must fit in i32, since it is the type of the "num_words"
    // argument to hexagon_memcpy_forward_vp4cp4n2.
    if (StoreSize != 4 || DL->getTypeSizeInBits(BECountTy) > 32) {
CleanupAndExit:
      // If we generated new code for the base pointer, clean up.
      Expander.clear();
      if (StoreBasePtr && (LoadBasePtr != StoreBasePtr)) {
        RecursivelyDeleteTriviallyDeadInstructions(StoreBasePtr, TLI);
        StoreBasePtr = nullptr;
      }
      if (LoadBasePtr) {
        RecursivelyDeleteTriviallyDeadInstructions(LoadBasePtr, TLI);
        LoadBasePtr = nullptr;
      }
      return false;
    }
  }

  SmallPtrSet<Instruction*, 2> Ignore1;
  Ignore1.insert(SI);
  if (mayLoopAccessLocation(StoreBasePtr, MRI_ModRef, CurLoop, BECount,
                            StoreSize, *AA, Ignore1)) {
    // Check if the load is the offending instruction.
    Ignore1.insert(LI);
    if (mayLoopAccessLocation(StoreBasePtr, MRI_ModRef, CurLoop, BECount,
                              StoreSize, *AA, Ignore1)) {
      // Still bad. Nothing we can do.
      goto CleanupAndExit;
    }
    // It worked with the load ignored.
    Overlap = true;
  }

  if (!Overlap) {
    if (DisableMemcpyIdiom || !HasMemcpy)
      goto CleanupAndExit;
  } else {
    // Don't generate memmove if this function will be inlined. This is
    // because the caller will undergo this transformation after inlining.
    Function *Func = CurLoop->getHeader()->getParent();
    if (Func->hasFnAttribute(Attribute::AlwaysInline))
      goto CleanupAndExit;

    // In case of a memmove, the call to memmove will be executed instead
    // of the loop, so we need to make sure that there is nothing else in
    // the loop than the load, store and instructions that these two depend
    // on.
    SmallVector<Instruction*,2> Insts;
    Insts.push_back(SI);
    Insts.push_back(LI);
    if (!coverLoop(CurLoop, Insts))
      goto CleanupAndExit;

    if (DisableMemmoveIdiom || !HasMemmove)
      goto CleanupAndExit;
    bool IsNested = CurLoop->getParentLoop() != 0;
    if (IsNested && OnlyNonNestedMemmove)
      goto CleanupAndExit;
  }

  // For a memcpy, we have to make sure that the input array is not being
  // mutated by the loop.
  LoadBasePtr = Expander.expandCodeFor(LoadEv->getStart(),
      Builder.getInt8PtrTy(LI->getPointerAddressSpace()), ExpPt);

  SmallPtrSet<Instruction*, 2> Ignore2;
  Ignore2.insert(SI);
  if (mayLoopAccessLocation(LoadBasePtr, MRI_Mod, CurLoop, BECount, StoreSize,
                            *AA, Ignore2))
    goto CleanupAndExit;

  // Check the stride.
  bool StridePos = getSCEVStride(LoadEv) >= 0;

  // Currently, the volatile memcpy only emulates traversing memory forward.
  if (!StridePos && DestVolatile)
    goto CleanupAndExit;

  bool RuntimeCheck = (Overlap || DestVolatile);

  BasicBlock *ExitB;
  if (RuntimeCheck) {
    // The runtime check needs a single exit block.
    SmallVector<BasicBlock*, 8> ExitBlocks;
    CurLoop->getUniqueExitBlocks(ExitBlocks);
    if (ExitBlocks.size() != 1)
      goto CleanupAndExit;
    ExitB = ExitBlocks[0];
  }

  // The # stored bytes is (BECount+1)*Size.  Expand the trip count out to
  // pointer size if it isn't already.
  LLVMContext &Ctx = SI->getContext();
  BECount = SE->getTruncateOrZeroExtend(BECount, IntPtrTy);
  unsigned Alignment = std::min(SI->getAlignment(), LI->getAlignment());
  DebugLoc DLoc = SI->getDebugLoc();

  const SCEV *NumBytesS =
      SE->getAddExpr(BECount, SE->getOne(IntPtrTy), SCEV::FlagNUW);
  if (StoreSize != 1)
    NumBytesS = SE->getMulExpr(NumBytesS, SE->getConstant(IntPtrTy, StoreSize),
                               SCEV::FlagNUW);
  Value *NumBytes = Expander.expandCodeFor(NumBytesS, IntPtrTy, ExpPt);
  if (Instruction *In = dyn_cast<Instruction>(NumBytes))
    if (Value *Simp = SimplifyInstruction(In, *DL, TLI, DT))
      NumBytes = Simp;

  CallInst *NewCall;

  if (RuntimeCheck) {
    unsigned Threshold = RuntimeMemSizeThreshold;
    if (ConstantInt *CI = dyn_cast<ConstantInt>(NumBytes)) {
      uint64_t C = CI->getZExtValue();
      if (Threshold != 0 && C < Threshold)
        goto CleanupAndExit;
      if (C < CompileTimeMemSizeThreshold)
        goto CleanupAndExit;
    }

    BasicBlock *Header = CurLoop->getHeader();
    Function *Func = Header->getParent();
    Loop *ParentL = LF->getLoopFor(Preheader);
    StringRef HeaderName = Header->getName();

    // Create a new (empty) preheader, and update the PHI nodes in the
    // header to use the new preheader.
    BasicBlock *NewPreheader = BasicBlock::Create(Ctx, HeaderName+".rtli.ph",
                                                  Func, Header);
    if (ParentL)
      ParentL->addBasicBlockToLoop(NewPreheader, *LF);
    IRBuilder<>(NewPreheader).CreateBr(Header);
    for (auto &In : *Header) {
      PHINode *PN = dyn_cast<PHINode>(&In);
      if (!PN)
        break;
      int bx = PN->getBasicBlockIndex(Preheader);
      if (bx >= 0)
        PN->setIncomingBlock(bx, NewPreheader);
    }
    DT->addNewBlock(NewPreheader, Preheader);
    DT->changeImmediateDominator(Header, NewPreheader);

    // Check for safe conditions to execute memmove.
    // If stride is positive, copying things from higher to lower addresses
    // is equivalent to memmove.  For negative stride, it's the other way
    // around.  Copying forward in memory with positive stride may not be
    // same as memmove since we may be copying values that we just stored
    // in some previous iteration.
    Value *LA = Builder.CreatePtrToInt(LoadBasePtr, IntPtrTy);
    Value *SA = Builder.CreatePtrToInt(StoreBasePtr, IntPtrTy);
    Value *LowA = StridePos ? SA : LA;
    Value *HighA = StridePos ? LA : SA;
    Value *CmpA = Builder.CreateICmpULT(LowA, HighA);
    Value *Cond = CmpA;

    // Check for distance between pointers.
    Value *Dist = Builder.CreateSub(HighA, LowA);
    Value *CmpD = Builder.CreateICmpSLT(NumBytes, Dist);
    Value *CmpEither = Builder.CreateOr(Cond, CmpD);
    Cond = CmpEither;

    if (Threshold != 0) {
      Type *Ty = NumBytes->getType();
      Value *Thr = ConstantInt::get(Ty, Threshold);
      Value *CmpB = Builder.CreateICmpULT(Thr, NumBytes);
      Value *CmpBoth = Builder.CreateAnd(Cond, CmpB);
      Cond = CmpBoth;
    }
    BasicBlock *MemmoveB = BasicBlock::Create(Ctx, Header->getName()+".rtli",
                                              Func, NewPreheader);
    if (ParentL)
      ParentL->addBasicBlockToLoop(MemmoveB, *LF);
    Instruction *OldT = Preheader->getTerminator();
    Builder.CreateCondBr(Cond, MemmoveB, NewPreheader);
    OldT->eraseFromParent();
    Preheader->setName(Preheader->getName()+".old");
    DT->addNewBlock(MemmoveB, Preheader);
    // Find the new immediate dominator of the exit block.
    BasicBlock *ExitD = Preheader;
    for (auto PI = pred_begin(ExitB), PE = pred_end(ExitB); PI != PE; ++PI) {
      BasicBlock *PB = *PI;
      ExitD = DT->findNearestCommonDominator(ExitD, PB);
      if (!ExitD)
        break;
    }
    // If the prior immediate dominator of ExitB was dominated by the
    // old preheader, then the old preheader becomes the new immediate
    // dominator.  Otherwise don't change anything (because the newly
    // added blocks are dominated by the old preheader).
    if (ExitD && DT->dominates(Preheader, ExitD)) {
      DomTreeNode *BN = DT->getNode(ExitB);
      DomTreeNode *DN = DT->getNode(ExitD);
      BN->setIDom(DN);
    }

    // Add a call to memmove to the conditional block.
    IRBuilder<> CondBuilder(MemmoveB);
    CondBuilder.CreateBr(ExitB);
    CondBuilder.SetInsertPoint(MemmoveB->getTerminator());

    if (DestVolatile) {
      Type *Int32Ty = Type::getInt32Ty(Ctx);
      Type *Int32PtrTy = Type::getInt32PtrTy(Ctx);
      Type *VoidTy = Type::getVoidTy(Ctx);
      Module *M = Func->getParent();
      Constant *CF = M->getOrInsertFunction(HexagonVolatileMemcpyName, VoidTy,
                                            Int32PtrTy, Int32PtrTy, Int32Ty);
      Function *Fn = cast<Function>(CF);
      Fn->setLinkage(Function::ExternalLinkage);

      const SCEV *OneS = SE->getConstant(Int32Ty, 1);
      const SCEV *BECount32 = SE->getTruncateOrZeroExtend(BECount, Int32Ty);
      const SCEV *NumWordsS = SE->getAddExpr(BECount32, OneS, SCEV::FlagNUW);
      Value *NumWords = Expander.expandCodeFor(NumWordsS, Int32Ty,
                                               MemmoveB->getTerminator());
      if (Instruction *In = dyn_cast<Instruction>(NumWords))
        if (Value *Simp = SimplifyInstruction(In, *DL, TLI, DT))
          NumWords = Simp;

      Value *Op0 = (StoreBasePtr->getType() == Int32PtrTy)
                      ? StoreBasePtr
                      : CondBuilder.CreateBitCast(StoreBasePtr, Int32PtrTy);
      Value *Op1 = (LoadBasePtr->getType() == Int32PtrTy)
                      ? LoadBasePtr
                      : CondBuilder.CreateBitCast(LoadBasePtr, Int32PtrTy);
      NewCall = CondBuilder.CreateCall(Fn, {Op0, Op1, NumWords});
    } else {
      NewCall = CondBuilder.CreateMemMove(StoreBasePtr, LoadBasePtr,
                                          NumBytes, Alignment);
    }
  } else {
    NewCall = Builder.CreateMemCpy(StoreBasePtr, LoadBasePtr,
                                   NumBytes, Alignment);
    // Okay, the memcpy has been formed.  Zap the original store and
    // anything that feeds into it.
    RecursivelyDeleteTriviallyDeadInstructions(SI, TLI);
  }

  NewCall->setDebugLoc(DLoc);

  DEBUG(dbgs() << "  Formed " << (Overlap ? "memmove: " : "memcpy: ")
               << *NewCall << "\n"
               << "    from load ptr=" << *LoadEv << " at: " << *LI << "\n"
               << "    from store ptr=" << *StoreEv << " at: " << *SI << "\n");

  return true;
}


// \brief Check if the instructions in Insts, together with their dependencies
// cover the loop in the sense that the loop could be safely eliminated once
// the instructions in Insts are removed.
bool HexagonLoopIdiomRecognize::coverLoop(Loop *L,
      SmallVectorImpl<Instruction*> &Insts) const {
  SmallSet<BasicBlock*,8> LoopBlocks;
  for (auto *B : L->blocks())
    LoopBlocks.insert(B);

  SetVector<Instruction*> Worklist(Insts.begin(), Insts.end());

  // Collect all instructions from the loop that the instructions in Insts
  // depend on (plus their dependencies, etc.).  These instructions will
  // constitute the expression trees that feed those in Insts, but the trees
  // will be limited only to instructions contained in the loop.
  for (unsigned i = 0; i < Worklist.size(); ++i) {
    Instruction *In = Worklist[i];
    for (auto I = In->op_begin(), E = In->op_end(); I != E; ++I) {
      Instruction *OpI = dyn_cast<Instruction>(I);
      if (!OpI)
        continue;
      BasicBlock *PB = OpI->getParent();
      if (!LoopBlocks.count(PB))
        continue;
      Worklist.insert(OpI);
    }
  }

  // Scan all instructions in the loop, if any of them have a user outside
  // of the loop, or outside of the expressions collected above, then either
  // the loop has a side-effect visible outside of it, or there are
  // instructions in it that are not involved in the original set Insts.
  for (auto *B : L->blocks()) {
    for (auto &In : *B) {
      if (isa<BranchInst>(In) || isa<DbgInfoIntrinsic>(In))
        continue;
      if (!Worklist.count(&In) && In.mayHaveSideEffects())
        return false;
      for (const auto &K : In.users()) {
        Instruction *UseI = dyn_cast<Instruction>(K);
        if (!UseI)
          continue;
        BasicBlock *UseB = UseI->getParent();
        if (LF->getLoopFor(UseB) != L)
          return false;
      }
    }
  }

  return true;
}

/// runOnLoopBlock - Process the specified block, which lives in a counted loop
/// with the specified backedge count.  This block is known to be in the current
/// loop and not in any subloops.
bool HexagonLoopIdiomRecognize::runOnLoopBlock(Loop *CurLoop, BasicBlock *BB,
      const SCEV *BECount, SmallVectorImpl<BasicBlock*> &ExitBlocks) {
  // We can only promote stores in this block if they are unconditionally
  // executed in the loop.  For a block to be unconditionally executed, it has
  // to dominate all the exit blocks of the loop.  Verify this now.
  auto DominatedByBB = [this,BB] (BasicBlock *EB) -> bool {
    return DT->dominates(BB, EB);
  };
  if (!std::all_of(ExitBlocks.begin(), ExitBlocks.end(), DominatedByBB))
    return false;

  bool MadeChange = false;
  // Look for store instructions, which may be optimized to memset/memcpy.
  SmallVector<StoreInst*,8> Stores;
  collectStores(CurLoop, BB, Stores);

  // Optimize the store into a memcpy, if it feeds an similarly strided load.
  for (auto &SI : Stores)
    MadeChange |= processCopyingStore(CurLoop, SI, BECount);

  return MadeChange;
}


bool HexagonLoopIdiomRecognize::runOnCountableLoop(Loop *L) {
  PolynomialMultiplyRecognize PMR(L, *DL, *DT, *TLI, *SE);
  if (PMR.recognize())
    return true;

  if (!HasMemcpy && !HasMemmove)
    return false;

  const SCEV *BECount = SE->getBackedgeTakenCount(L);
  assert(!isa<SCEVCouldNotCompute>(BECount) &&
         "runOnCountableLoop() called on a loop without a predictable"
         "backedge-taken count");

  SmallVector<BasicBlock *, 8> ExitBlocks;
  L->getUniqueExitBlocks(ExitBlocks);

  bool Changed = false;

  // Scan all the blocks in the loop that are not in subloops.
  for (auto *BB : L->getBlocks()) {
    // Ignore blocks in subloops.
    if (LF->getLoopFor(BB) != L)
      continue;
    Changed |= runOnLoopBlock(L, BB, BECount, ExitBlocks);
  }

  return Changed;
}


bool HexagonLoopIdiomRecognize::runOnLoop(Loop *L, LPPassManager &LPM) {
  const Module &M = *L->getHeader()->getParent()->getParent();
  if (Triple(M.getTargetTriple()).getArch() != Triple::hexagon)
    return false;

  if (skipLoop(L))
    return false;

  // If the loop could not be converted to canonical form, it must have an
  // indirectbr in it, just give up.
  if (!L->getLoopPreheader())
    return false;

  // Disable loop idiom recognition if the function's name is a common idiom.
  StringRef Name = L->getHeader()->getParent()->getName();
  if (Name == "memset" || Name == "memcpy" || Name == "memmove")
    return false;

  AA = &getAnalysis<AAResultsWrapperPass>().getAAResults();
  DL = &L->getHeader()->getModule()->getDataLayout();
  DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
  LF = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
  TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
  SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();

  HasMemcpy = TLI->has(LibFunc_memcpy);
  HasMemmove = TLI->has(LibFunc_memmove);

  if (SE->hasLoopInvariantBackedgeTakenCount(L))
    return runOnCountableLoop(L);
  return false;
}


Pass *llvm::createHexagonLoopIdiomPass() {
  return new HexagonLoopIdiomRecognize();
}