LoopStrengthReduce.cpp

//===- LoopStrengthReduce.cpp - Strength Reduce IVs in Loops --------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This transformation analyzes and transforms the induction variables (and
// computations derived from them) into forms suitable for efficient execution
// on the target.
//
// This pass performs a strength reduction on array references inside loops that
// have as one or more of their components the loop induction variable, it
// rewrites expressions to take advantage of scaled-index addressing modes
// available on the target, and it performs a variety of other optimizations
// related to loop induction variables.
//
// Terminology note: this code has a lot of handling for "post-increment" or
// "post-inc" users. This is not talking about post-increment addressing modes;
// it is instead talking about code like this:
//
//   %i = phi [ 0, %entry ], [ %i.next, %latch ]
//   ...
//   %i.next = add %i, 1
//   %c = icmp eq %i.next, %n
//
// The SCEV for %i is {0,+,1}<%L>. The SCEV for %i.next is {1,+,1}<%L>, however
// it's useful to think about these as the same register, with some uses using
// the value of the register before the add and some using // it after. In this
// example, the icmp is a post-increment user, since it uses %i.next, which is
// the value of the induction variable after the increment. The other common
// case of post-increment users is users outside the loop.
//
// TODO: More sophistication in the way Formulae are generated and filtered.
//
// TODO: Handle multiple loops at a time.
//
// TODO: Should TargetLowering::AddrMode::BaseGV be changed to a ConstantExpr
//       instead of a GlobalValue?
//
// TODO: When truncation is free, truncate ICmp users' operands to make it a
//       smaller encoding (on x86 at least).
//
// TODO: When a negated register is used by an add (such as in a list of
//       multiple base registers, or as the increment expression in an addrec),
//       we may not actually need both reg and (-1 * reg) in registers; the
//       negation can be implemented by using a sub instead of an add. The
//       lack of support for taking this into consideration when making
//       register pressure decisions is partly worked around by the "Special"
//       use kind.
//
//===----------------------------------------------------------------------===//

#define DEBUG_TYPE "loop-reduce"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Constants.h"
#include "llvm/Instructions.h"
#include "llvm/IntrinsicInst.h"
#include "llvm/DerivedTypes.h"
#include "llvm/Analysis/IVUsers.h"
#include "llvm/Analysis/Dominators.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Assembly/Writer.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/ADT/SmallBitVector.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/DenseSet.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ValueHandle.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Target/TargetLowering.h"
#include <algorithm>
using namespace llvm;

namespace {

/// RegSortData - This class holds data which is used to order reuse candidates.
class RegSortData {
public:
  /// UsedByIndices - This represents the set of LSRUse indices which reference
  /// a particular register.
  SmallBitVector UsedByIndices;

  RegSortData() {}

  void print(raw_ostream &OS) const;
  void dump() const;
};

}

void RegSortData::print(raw_ostream &OS) const {
  OS << "[NumUses=" << UsedByIndices.count() << ']';
}

void RegSortData::dump() const {
  print(errs()); errs() << '\n';
}

namespace {

/// RegUseTracker - Map register candidates to information about how they are
/// used.
class RegUseTracker {
  typedef DenseMap<const SCEV *, RegSortData> RegUsesTy;

  RegUsesTy RegUsesMap;
  SmallVector<const SCEV *, 16> RegSequence;

public:
  void CountRegister(const SCEV *Reg, size_t LUIdx);
  void DropRegister(const SCEV *Reg, size_t LUIdx);
  void SwapAndDropUse(size_t LUIdx, size_t LastLUIdx);

  bool isRegUsedByUsesOtherThan(const SCEV *Reg, size_t LUIdx) const;

  const SmallBitVector &getUsedByIndices(const SCEV *Reg) const;

  void clear();

  typedef SmallVectorImpl<const SCEV *>::iterator iterator;
  typedef SmallVectorImpl<const SCEV *>::const_iterator const_iterator;
  iterator begin() { return RegSequence.begin(); }
  iterator end()   { return RegSequence.end(); }
  const_iterator begin() const { return RegSequence.begin(); }
  const_iterator end() const   { return RegSequence.end(); }
};

}

void
RegUseTracker::CountRegister(const SCEV *Reg, size_t LUIdx) {
  std::pair<RegUsesTy::iterator, bool> Pair =
    RegUsesMap.insert(std::make_pair(Reg, RegSortData()));
  RegSortData &RSD = Pair.first->second;
  if (Pair.second)
    RegSequence.push_back(Reg);
  RSD.UsedByIndices.resize(std::max(RSD.UsedByIndices.size(), LUIdx + 1));
  RSD.UsedByIndices.set(LUIdx);
}

void
RegUseTracker::DropRegister(const SCEV *Reg, size_t LUIdx) {
  RegUsesTy::iterator It = RegUsesMap.find(Reg);
  assert(It != RegUsesMap.end());
  RegSortData &RSD = It->second;
  assert(RSD.UsedByIndices.size() > LUIdx);
  RSD.UsedByIndices.reset(LUIdx);
}

void
RegUseTracker::SwapAndDropUse(size_t LUIdx, size_t LastLUIdx) {
  assert(LUIdx <= LastLUIdx);

  // Update RegUses. The data structure is not optimized for this purpose;
  // we must iterate through it and update each of the bit vectors.
  for (RegUsesTy::iterator I = RegUsesMap.begin(), E = RegUsesMap.end();
       I != E; ++I) {
    SmallBitVector &UsedByIndices = I->second.UsedByIndices;
    if (LUIdx < UsedByIndices.size())
      UsedByIndices[LUIdx] =
        LastLUIdx < UsedByIndices.size() ? UsedByIndices[LastLUIdx] : 0;
    UsedByIndices.resize(std::min(UsedByIndices.size(), LastLUIdx));
  }
}

bool
RegUseTracker::isRegUsedByUsesOtherThan(const SCEV *Reg, size_t LUIdx) const {
  RegUsesTy::const_iterator I = RegUsesMap.find(Reg);
  if (I == RegUsesMap.end())
    return false;
  const SmallBitVector &UsedByIndices = I->second.UsedByIndices;
  int i = UsedByIndices.find_first();
  if (i == -1) return false;
  if ((size_t)i != LUIdx) return true;
  return UsedByIndices.find_next(i) != -1;
}

const SmallBitVector &RegUseTracker::getUsedByIndices(const SCEV *Reg) const {
  RegUsesTy::const_iterator I = RegUsesMap.find(Reg);
  assert(I != RegUsesMap.end() && "Unknown register!");
  return I->second.UsedByIndices;
}

void RegUseTracker::clear() {
  RegUsesMap.clear();
  RegSequence.clear();
}

namespace {

/// Formula - This class holds information that describes a formula for
/// computing satisfying a use. It may include broken-out immediates and scaled
/// registers.
struct Formula {
  /// AM - This is used to represent complex addressing, as well as other kinds
  /// of interesting uses.
  TargetLowering::AddrMode AM;

  /// BaseRegs - The list of "base" registers for this use. When this is
  /// non-empty, AM.HasBaseReg should be set to true.
  SmallVector<const SCEV *, 2> BaseRegs;

  /// ScaledReg - The 'scaled' register for this use. This should be non-null
  /// when AM.Scale is not zero.
  const SCEV *ScaledReg;

  Formula() : ScaledReg(0) {}

  void InitialMatch(const SCEV *S, Loop *L, ScalarEvolution &SE);

  unsigned getNumRegs() const;
  const Type *getType() const;

  void DeleteBaseReg(const SCEV *&S);

  bool referencesReg(const SCEV *S) const;
  bool hasRegsUsedByUsesOtherThan(size_t LUIdx,
                                  const RegUseTracker &RegUses) const;

  void print(raw_ostream &OS) const;
  void dump() const;
};

}

/// DoInitialMatch - Recursion helper for InitialMatch.
static void DoInitialMatch(const SCEV *S, Loop *L,
                           SmallVectorImpl<const SCEV *> &Good,
                           SmallVectorImpl<const SCEV *> &Bad,
                           ScalarEvolution &SE) {
  // Collect expressions which properly dominate the loop header.
  if (SE.properlyDominates(S, L->getHeader())) {
    Good.push_back(S);
    return;
  }

  // Look at add operands.
  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
    for (SCEVAddExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
         I != E; ++I)
      DoInitialMatch(*I, L, Good, Bad, SE);
    return;
  }

  // Look at addrec operands.
  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
    if (!AR->getStart()->isZero()) {
      DoInitialMatch(AR->getStart(), L, Good, Bad, SE);
      DoInitialMatch(SE.getAddRecExpr(SE.getConstant(AR->getType(), 0),
                                      AR->getStepRecurrence(SE),
                                      AR->getLoop()),
                     L, Good, Bad, SE);
      return;
    }

  // Handle a multiplication by -1 (negation) if it didn't fold.
  if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S))
    if (Mul->getOperand(0)->isAllOnesValue()) {
      SmallVector<const SCEV *, 4> Ops(Mul->op_begin()+1, Mul->op_end());
      const SCEV *NewMul = SE.getMulExpr(Ops);

      SmallVector<const SCEV *, 4> MyGood;
      SmallVector<const SCEV *, 4> MyBad;
      DoInitialMatch(NewMul, L, MyGood, MyBad, SE);
      const SCEV *NegOne = SE.getSCEV(ConstantInt::getAllOnesValue(
        SE.getEffectiveSCEVType(NewMul->getType())));
      for (SmallVectorImpl<const SCEV *>::const_iterator I = MyGood.begin(),
           E = MyGood.end(); I != E; ++I)
        Good.push_back(SE.getMulExpr(NegOne, *I));
      for (SmallVectorImpl<const SCEV *>::const_iterator I = MyBad.begin(),
           E = MyBad.end(); I != E; ++I)
        Bad.push_back(SE.getMulExpr(NegOne, *I));
      return;
    }

  // Ok, we can't do anything interesting. Just stuff the whole thing into a
  // register and hope for the best.
  Bad.push_back(S);
}

/// InitialMatch - Incorporate loop-variant parts of S into this Formula,
/// attempting to keep all loop-invariant and loop-computable values in a
/// single base register.
void Formula::InitialMatch(const SCEV *S, Loop *L, ScalarEvolution &SE) {
  SmallVector<const SCEV *, 4> Good;
  SmallVector<const SCEV *, 4> Bad;
  DoInitialMatch(S, L, Good, Bad, SE);
  if (!Good.empty()) {
    const SCEV *Sum = SE.getAddExpr(Good);
    if (!Sum->isZero())
      BaseRegs.push_back(Sum);
    AM.HasBaseReg = true;
  }
  if (!Bad.empty()) {
    const SCEV *Sum = SE.getAddExpr(Bad);
    if (!Sum->isZero())
      BaseRegs.push_back(Sum);
    AM.HasBaseReg = true;
  }
}

/// getNumRegs - Return the total number of register operands used by this
/// formula. This does not include register uses implied by non-constant
/// addrec strides.
unsigned Formula::getNumRegs() const {
  return !!ScaledReg + BaseRegs.size();
}

/// getType - Return the type of this formula, if it has one, or null
/// otherwise. This type is meaningless except for the bit size.
const Type *Formula::getType() const {
  return !BaseRegs.empty() ? BaseRegs.front()->getType() :
         ScaledReg ? ScaledReg->getType() :
         AM.BaseGV ? AM.BaseGV->getType() :
         0;
}

/// DeleteBaseReg - Delete the given base reg from the BaseRegs list.
void Formula::DeleteBaseReg(const SCEV *&S) {
  if (&S != &BaseRegs.back())
    std::swap(S, BaseRegs.back());
  BaseRegs.pop_back();
}

/// referencesReg - Test if this formula references the given register.
bool Formula::referencesReg(const SCEV *S) const {
  return S == ScaledReg ||
         std::find(BaseRegs.begin(), BaseRegs.end(), S) != BaseRegs.end();
}

/// hasRegsUsedByUsesOtherThan - Test whether this formula uses registers
/// which are used by uses other than the use with the given index.
bool Formula::hasRegsUsedByUsesOtherThan(size_t LUIdx,
                                         const RegUseTracker &RegUses) const {
  if (ScaledReg)
    if (RegUses.isRegUsedByUsesOtherThan(ScaledReg, LUIdx))
      return true;
  for (SmallVectorImpl<const SCEV *>::const_iterator I = BaseRegs.begin(),
       E = BaseRegs.end(); I != E; ++I)
    if (RegUses.isRegUsedByUsesOtherThan(*I, LUIdx))
      return true;
  return false;
}

void Formula::print(raw_ostream &OS) const {
  bool First = true;
  if (AM.BaseGV) {
    if (!First) OS << " + "; else First = false;
    WriteAsOperand(OS, AM.BaseGV, /*PrintType=*/false);
  }
  if (AM.BaseOffs != 0) {
    if (!First) OS << " + "; else First = false;
    OS << AM.BaseOffs;
  }
  for (SmallVectorImpl<const SCEV *>::const_iterator I = BaseRegs.begin(),
       E = BaseRegs.end(); I != E; ++I) {
    if (!First) OS << " + "; else First = false;
    OS << "reg(" << **I << ')';
  }
  if (AM.HasBaseReg && BaseRegs.empty()) {
    if (!First) OS << " + "; else First = false;
    OS << "**error: HasBaseReg**";
  } else if (!AM.HasBaseReg && !BaseRegs.empty()) {
    if (!First) OS << " + "; else First = false;
    OS << "**error: !HasBaseReg**";
  }
  if (AM.Scale != 0) {
    if (!First) OS << " + "; else First = false;
    OS << AM.Scale << "*reg(";
    if (ScaledReg)
      OS << *ScaledReg;
    else
      OS << "<unknown>";
    OS << ')';
  }
}

void Formula::dump() const {
  print(errs()); errs() << '\n';
}

/// isAddRecSExtable - Return true if the given addrec can be sign-extended
/// without changing its value.
static bool isAddRecSExtable(const SCEVAddRecExpr *AR, ScalarEvolution &SE) {
  const Type *WideTy =
    IntegerType::get(SE.getContext(), SE.getTypeSizeInBits(AR->getType()) + 1);
  return isa<SCEVAddRecExpr>(SE.getSignExtendExpr(AR, WideTy));
}

/// isAddSExtable - Return true if the given add can be sign-extended
/// without changing its value.
static bool isAddSExtable(const SCEVAddExpr *A, ScalarEvolution &SE) {
  const Type *WideTy =
    IntegerType::get(SE.getContext(), SE.getTypeSizeInBits(A->getType()) + 1);
  return isa<SCEVAddExpr>(SE.getSignExtendExpr(A, WideTy));
}

/// isMulSExtable - Return true if the given mul can be sign-extended
/// without changing its value.
static bool isMulSExtable(const SCEVMulExpr *M, ScalarEvolution &SE) {
  const Type *WideTy =
    IntegerType::get(SE.getContext(),
                     SE.getTypeSizeInBits(M->getType()) * M->getNumOperands());
  return isa<SCEVMulExpr>(SE.getSignExtendExpr(M, WideTy));
}

/// getExactSDiv - Return an expression for LHS /s RHS, if it can be determined
/// and if the remainder is known to be zero,  or null otherwise. If
/// IgnoreSignificantBits is true, expressions like (X * Y) /s Y are simplified
/// to Y, ignoring that the multiplication may overflow, which is useful when
/// the result will be used in a context where the most significant bits are
/// ignored.
static const SCEV *getExactSDiv(const SCEV *LHS, const SCEV *RHS,
                                ScalarEvolution &SE,
                                bool IgnoreSignificantBits = false) {
  // Handle the trivial case, which works for any SCEV type.
  if (LHS == RHS)
    return SE.getConstant(LHS->getType(), 1);

  // Handle a few RHS special cases.
  const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS);
  if (RC) {
    const APInt &RA = RC->getValue()->getValue();
    // Handle x /s -1 as x * -1, to give ScalarEvolution a chance to do
    // some folding.
    if (RA.isAllOnesValue())
      return SE.getMulExpr(LHS, RC);
    // Handle x /s 1 as x.
    if (RA == 1)
      return LHS;
  }

  // Check for a division of a constant by a constant.
  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(LHS)) {
    if (!RC)
      return 0;
    const APInt &LA = C->getValue()->getValue();
    const APInt &RA = RC->getValue()->getValue();
    if (LA.srem(RA) != 0)
      return 0;
    return SE.getConstant(LA.sdiv(RA));
  }

  // Distribute the sdiv over addrec operands, if the addrec doesn't overflow.
  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) {
    if (IgnoreSignificantBits || isAddRecSExtable(AR, SE)) {
      const SCEV *Step = getExactSDiv(AR->getStepRecurrence(SE), RHS, SE,
                                      IgnoreSignificantBits);
      if (!Step) return 0;
      const SCEV *Start = getExactSDiv(AR->getStart(), RHS, SE,
                                       IgnoreSignificantBits);
      if (!Start) return 0;
      return SE.getAddRecExpr(Start, Step, AR->getLoop());
    }
    return 0;
  }

  // Distribute the sdiv over add operands, if the add doesn't overflow.
  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(LHS)) {
    if (IgnoreSignificantBits || isAddSExtable(Add, SE)) {
      SmallVector<const SCEV *, 8> Ops;
      for (SCEVAddExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
           I != E; ++I) {
        const SCEV *Op = getExactSDiv(*I, RHS, SE,
                                      IgnoreSignificantBits);
        if (!Op) return 0;
        Ops.push_back(Op);
      }
      return SE.getAddExpr(Ops);
    }
    return 0;
  }

  // Check for a multiply operand that we can pull RHS out of.
  if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS)) {
    if (IgnoreSignificantBits || isMulSExtable(Mul, SE)) {
      SmallVector<const SCEV *, 4> Ops;
      bool Found = false;
      for (SCEVMulExpr::op_iterator I = Mul->op_begin(), E = Mul->op_end();
           I != E; ++I) {
        const SCEV *S = *I;
        if (!Found)
          if (const SCEV *Q = getExactSDiv(S, RHS, SE,
                                           IgnoreSignificantBits)) {
            S = Q;
            Found = true;
          }
        Ops.push_back(S);
      }
      return Found ? SE.getMulExpr(Ops) : 0;
    }
    return 0;
  }

  // Otherwise we don't know.
  return 0;
}

/// ExtractImmediate - If S involves the addition of a constant integer value,
/// return that integer value, and mutate S to point to a new SCEV with that
/// value excluded.
static int64_t ExtractImmediate(const SCEV *&S, ScalarEvolution &SE) {
  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
    if (C->getValue()->getValue().getMinSignedBits() <= 64) {
      S = SE.getConstant(C->getType(), 0);
      return C->getValue()->getSExtValue();
    }
  } else if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
    SmallVector<const SCEV *, 8> NewOps(Add->op_begin(), Add->op_end());
    int64_t Result = ExtractImmediate(NewOps.front(), SE);
    if (Result != 0)
      S = SE.getAddExpr(NewOps);
    return Result;
  } else if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
    SmallVector<const SCEV *, 8> NewOps(AR->op_begin(), AR->op_end());
    int64_t Result = ExtractImmediate(NewOps.front(), SE);
    if (Result != 0)
      S = SE.getAddRecExpr(NewOps, AR->getLoop());
    return Result;
  }
  return 0;
}

/// ExtractSymbol - If S involves the addition of a GlobalValue address,
/// return that symbol, and mutate S to point to a new SCEV with that
/// value excluded.
static GlobalValue *ExtractSymbol(const SCEV *&S, ScalarEvolution &SE) {
  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
    if (GlobalValue *GV = dyn_cast<GlobalValue>(U->getValue())) {
      S = SE.getConstant(GV->getType(), 0);
      return GV;
    }
  } else if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
    SmallVector<const SCEV *, 8> NewOps(Add->op_begin(), Add->op_end());
    GlobalValue *Result = ExtractSymbol(NewOps.back(), SE);
    if (Result)
      S = SE.getAddExpr(NewOps);
    return Result;
  } else if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
    SmallVector<const SCEV *, 8> NewOps(AR->op_begin(), AR->op_end());
    GlobalValue *Result = ExtractSymbol(NewOps.front(), SE);
    if (Result)
      S = SE.getAddRecExpr(NewOps, AR->getLoop());
    return Result;
  }
  return 0;
}

/// isAddressUse - Returns true if the specified instruction is using the
/// specified value as an address.
static bool isAddressUse(Instruction *Inst, Value *OperandVal) {
  bool isAddress = isa<LoadInst>(Inst);
  if (StoreInst *SI = dyn_cast<StoreInst>(Inst)) {
    if (SI->getOperand(1) == OperandVal)
      isAddress = true;
  } else if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(Inst)) {
    // Addressing modes can also be folded into prefetches and a variety
    // of intrinsics.
    switch (II->getIntrinsicID()) {
      default: break;
      case Intrinsic::prefetch:
      case Intrinsic::x86_sse2_loadu_dq:
      case Intrinsic::x86_sse2_loadu_pd:
      case Intrinsic::x86_sse_loadu_ps:
      case Intrinsic::x86_sse_storeu_ps:
      case Intrinsic::x86_sse2_storeu_pd:
      case Intrinsic::x86_sse2_storeu_dq:
      case Intrinsic::x86_sse2_storel_dq:
        if (II->getArgOperand(0) == OperandVal)
          isAddress = true;
        break;
    }
  }
  return isAddress;
}

/// getAccessType - Return the type of the memory being accessed.
static const Type *getAccessType(const Instruction *Inst) {
  const Type *AccessTy = Inst->getType();
  if (const StoreInst *SI = dyn_cast<StoreInst>(Inst))
    AccessTy = SI->getOperand(0)->getType();
  else if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(Inst)) {
    // Addressing modes can also be folded into prefetches and a variety
    // of intrinsics.
    switch (II->getIntrinsicID()) {
    default: break;
    case Intrinsic::x86_sse_storeu_ps:
    case Intrinsic::x86_sse2_storeu_pd:
    case Intrinsic::x86_sse2_storeu_dq:
    case Intrinsic::x86_sse2_storel_dq:
      AccessTy = II->getArgOperand(0)->getType();
      break;
    }
  }

  // All pointers have the same requirements, so canonicalize them to an
  // arbitrary pointer type to minimize variation.
  if (const PointerType *PTy = dyn_cast<PointerType>(AccessTy))
    AccessTy = PointerType::get(IntegerType::get(PTy->getContext(), 1),
                                PTy->getAddressSpace());

  return AccessTy;
}

/// DeleteTriviallyDeadInstructions - If any of the instructions is the
/// specified set are trivially dead, delete them and see if this makes any of
/// their operands subsequently dead.
static bool
DeleteTriviallyDeadInstructions(SmallVectorImpl<WeakVH> &DeadInsts) {
  bool Changed = false;

  while (!DeadInsts.empty()) {
    Instruction *I = dyn_cast_or_null<Instruction>(&*DeadInsts.pop_back_val());

    if (I == 0 || !isInstructionTriviallyDead(I))
      continue;

    for (User::op_iterator OI = I->op_begin(), E = I->op_end(); OI != E; ++OI)
      if (Instruction *U = dyn_cast<Instruction>(*OI)) {
        *OI = 0;
        if (U->use_empty())
          DeadInsts.push_back(U);
      }

    I->eraseFromParent();
    Changed = true;
  }

  return Changed;
}

namespace {

/// Cost - This class is used to measure and compare candidate formulae.
class Cost {
  /// TODO: Some of these could be merged. Also, a lexical ordering
  /// isn't always optimal.
  unsigned NumRegs;
  unsigned AddRecCost;
  unsigned NumIVMuls;
  unsigned NumBaseAdds;
  unsigned ImmCost;
  unsigned SetupCost;

public:
  Cost()
    : NumRegs(0), AddRecCost(0), NumIVMuls(0), NumBaseAdds(0), ImmCost(0),
      SetupCost(0) {}

  bool operator<(const Cost &Other) const;

  void Loose();

  void RateFormula(const Formula &F,
                   SmallPtrSet<const SCEV *, 16> &Regs,
                   const DenseSet<const SCEV *> &VisitedRegs,
                   const Loop *L,
                   const SmallVectorImpl<int64_t> &Offsets,
                   ScalarEvolution &SE, DominatorTree &DT);

  void print(raw_ostream &OS) const;
  void dump() const;

private:
  void RateRegister(const SCEV *Reg,
                    SmallPtrSet<const SCEV *, 16> &Regs,
                    const Loop *L,
                    ScalarEvolution &SE, DominatorTree &DT);
  void RatePrimaryRegister(const SCEV *Reg,
                           SmallPtrSet<const SCEV *, 16> &Regs,
                           const Loop *L,
                           ScalarEvolution &SE, DominatorTree &DT);
};

}

/// RateRegister - Tally up interesting quantities from the given register.
void Cost::RateRegister(const SCEV *Reg,
                        SmallPtrSet<const SCEV *, 16> &Regs,
                        const Loop *L,
                        ScalarEvolution &SE, DominatorTree &DT) {
  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Reg)) {
    if (AR->getLoop() == L)
      AddRecCost += 1; /// TODO: This should be a function of the stride.

    // If this is an addrec for a loop that's already been visited by LSR,
    // don't second-guess its addrec phi nodes. LSR isn't currently smart
    // enough to reason about more than one loop at a time. Consider these
    // registers free and leave them alone.
    else if (L->contains(AR->getLoop()) ||
             (!AR->getLoop()->contains(L) &&
              DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))) {
      for (BasicBlock::iterator I = AR->getLoop()->getHeader()->begin();
           PHINode *PN = dyn_cast<PHINode>(I); ++I)
        if (SE.isSCEVable(PN->getType()) &&
            (SE.getEffectiveSCEVType(PN->getType()) ==
             SE.getEffectiveSCEVType(AR->getType())) &&
            SE.getSCEV(PN) == AR)
          return;

      // If this isn't one of the addrecs that the loop already has, it
      // would require a costly new phi and add. TODO: This isn't
      // precisely modeled right now.
      ++NumBaseAdds;
      if (!Regs.count(AR->getStart()))
        RateRegister(AR->getStart(), Regs, L, SE, DT);
    }

    // Add the step value register, if it needs one.
    // TODO: The non-affine case isn't precisely modeled here.
    if (!AR->isAffine() || !isa<SCEVConstant>(AR->getOperand(1)))
      if (!Regs.count(AR->getStart()))
        RateRegister(AR->getOperand(1), Regs, L, SE, DT);
  }
  ++NumRegs;

  // Rough heuristic; favor registers which don't require extra setup
  // instructions in the preheader.
  if (!isa<SCEVUnknown>(Reg) &&
      !isa<SCEVConstant>(Reg) &&
      !(isa<SCEVAddRecExpr>(Reg) &&
        (isa<SCEVUnknown>(cast<SCEVAddRecExpr>(Reg)->getStart()) ||
         isa<SCEVConstant>(cast<SCEVAddRecExpr>(Reg)->getStart()))))
    ++SetupCost;

    NumIVMuls += isa<SCEVMulExpr>(Reg) &&
                 SE.hasComputableLoopEvolution(Reg, L);
}

/// RatePrimaryRegister - Record this register in the set. If we haven't seen it
/// before, rate it.
void Cost::RatePrimaryRegister(const SCEV *Reg,
                               SmallPtrSet<const SCEV *, 16> &Regs,
                               const Loop *L,
                               ScalarEvolution &SE, DominatorTree &DT) {
  if (Regs.insert(Reg))
    RateRegister(Reg, Regs, L, SE, DT);
}

void Cost::RateFormula(const Formula &F,
                       SmallPtrSet<const SCEV *, 16> &Regs,
                       const DenseSet<const SCEV *> &VisitedRegs,
                       const Loop *L,
                       const SmallVectorImpl<int64_t> &Offsets,
                       ScalarEvolution &SE, DominatorTree &DT) {
  // Tally up the registers.
  if (const SCEV *ScaledReg = F.ScaledReg) {
    if (VisitedRegs.count(ScaledReg)) {
      Loose();
      return;
    }
    RatePrimaryRegister(ScaledReg, Regs, L, SE, DT);
  }
  for (SmallVectorImpl<const SCEV *>::const_iterator I = F.BaseRegs.begin(),
       E = F.BaseRegs.end(); I != E; ++I) {
    const SCEV *BaseReg = *I;
    if (VisitedRegs.count(BaseReg)) {
      Loose();
      return;
    }
    RatePrimaryRegister(BaseReg, Regs, L, SE, DT);
  }

  if (F.BaseRegs.size() > 1)
    NumBaseAdds += F.BaseRegs.size() - 1;

  // Tally up the non-zero immediates.
  for (SmallVectorImpl<int64_t>::const_iterator I = Offsets.begin(),
       E = Offsets.end(); I != E; ++I) {
    int64_t Offset = (uint64_t)*I + F.AM.BaseOffs;
    if (F.AM.BaseGV)
      ImmCost += 64; // Handle symbolic values conservatively.
                     // TODO: This should probably be the pointer size.
    else if (Offset != 0)
      ImmCost += APInt(64, Offset, true).getMinSignedBits();
  }
}

/// Loose - Set this cost to a loosing value.
void Cost::Loose() {
  NumRegs = ~0u;
  AddRecCost = ~0u;
  NumIVMuls = ~0u;
  NumBaseAdds = ~0u;
  ImmCost = ~0u;
  SetupCost = ~0u;
}

/// operator< - Choose the lower cost.
bool Cost::operator<(const Cost &Other) const {
  if (NumRegs != Other.NumRegs)
    return NumRegs < Other.NumRegs;
  if (AddRecCost != Other.AddRecCost)
    return AddRecCost < Other.AddRecCost;
  if (NumIVMuls != Other.NumIVMuls)
    return NumIVMuls < Other.NumIVMuls;
  if (NumBaseAdds != Other.NumBaseAdds)
    return NumBaseAdds < Other.NumBaseAdds;
  if (ImmCost != Other.ImmCost)
    return ImmCost < Other.ImmCost;
  if (SetupCost != Other.SetupCost)
    return SetupCost < Other.SetupCost;
  return false;
}

void Cost::print(raw_ostream &OS) const {
  OS << NumRegs << " reg" << (NumRegs == 1 ? "" : "s");
  if (AddRecCost != 0)
    OS << ", with addrec cost " << AddRecCost;
  if (NumIVMuls != 0)
    OS << ", plus " << NumIVMuls << " IV mul" << (NumIVMuls == 1 ? "" : "s");
  if (NumBaseAdds != 0)
    OS << ", plus " << NumBaseAdds << " base add"
       << (NumBaseAdds == 1 ? "" : "s");
  if (ImmCost != 0)
    OS << ", plus " << ImmCost << " imm cost";
  if (SetupCost != 0)
    OS << ", plus " << SetupCost << " setup cost";
}

void Cost::dump() const {
  print(errs()); errs() << '\n';
}

namespace {

/// LSRFixup - An operand value in an instruction which is to be replaced
/// with some equivalent, possibly strength-reduced, replacement.
struct LSRFixup {
  /// UserInst - The instruction which will be updated.
  Instruction *UserInst;

  /// OperandValToReplace - The operand of the instruction which will
  /// be replaced. The operand may be used more than once; every instance
  /// will be replaced.
  Value *OperandValToReplace;

  /// PostIncLoops - If this user is to use the post-incremented value of an
  /// induction variable, this variable is non-null and holds the loop
  /// associated with the induction variable.
  PostIncLoopSet PostIncLoops;

  /// LUIdx - The index of the LSRUse describing the expression which
  /// this fixup needs, minus an offset (below).
  size_t LUIdx;

  /// Offset - A constant offset to be added to the LSRUse expression.
  /// This allows multiple fixups to share the same LSRUse with different
  /// offsets, for example in an unrolled loop.
  int64_t Offset;

  bool isUseFullyOutsideLoop(const Loop *L) const;

  LSRFixup();

  void print(raw_ostream &OS) const;
  void dump() const;
};

}

LSRFixup::LSRFixup()
  : UserInst(0), OperandValToReplace(0), LUIdx(~size_t(0)), Offset(0) {}

/// isUseFullyOutsideLoop - Test whether this fixup always uses its
/// value outside of the given loop.
bool LSRFixup::isUseFullyOutsideLoop(const Loop *L) const {
  // PHI nodes use their value in their incoming blocks.
  if (const PHINode *PN = dyn_cast<PHINode>(UserInst)) {
    for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
      if (PN->getIncomingValue(i) == OperandValToReplace &&
          L->contains(PN->getIncomingBlock(i)))
        return false;
    return true;
  }

  return !L->contains(UserInst);
}

void LSRFixup::print(raw_ostream &OS) const {
  OS << "UserInst=";
  // Store is common and interesting enough to be worth special-casing.
  if (StoreInst *Store = dyn_cast<StoreInst>(UserInst)) {
    OS << "store ";
    WriteAsOperand(OS, Store->getOperand(0), /*PrintType=*/false);
  } else if (UserInst->getType()->isVoidTy())
    OS << UserInst->getOpcodeName();
  else
    WriteAsOperand(OS, UserInst, /*PrintType=*/false);

  OS << ", OperandValToReplace=";
  WriteAsOperand(OS, OperandValToReplace, /*PrintType=*/false);

  for (PostIncLoopSet::const_iterator I = PostIncLoops.begin(),
       E = PostIncLoops.end(); I != E; ++I) {
    OS << ", PostIncLoop=";
    WriteAsOperand(OS, (*I)->getHeader(), /*PrintType=*/false);
  }

  if (LUIdx != ~size_t(0))
    OS << ", LUIdx=" << LUIdx;

  if (Offset != 0)
    OS << ", Offset=" << Offset;
}

void LSRFixup::dump() const {
  print(errs()); errs() << '\n';
}

namespace {

/// UniquifierDenseMapInfo - A DenseMapInfo implementation for holding
/// DenseMaps and DenseSets of sorted SmallVectors of const SCEV*.
struct UniquifierDenseMapInfo {
  static SmallVector<const SCEV *, 2> getEmptyKey() {
    SmallVector<const SCEV *, 2> V;
    V.push_back(reinterpret_cast<const SCEV *>(-1));
    return V;
  }

  static SmallVector<const SCEV *, 2> getTombstoneKey() {
    SmallVector<const SCEV *, 2> V;
    V.push_back(reinterpret_cast<const SCEV *>(-2));
    return V;
  }

  static unsigned getHashValue(const SmallVector<const SCEV *, 2> &V) {
    unsigned Result = 0;
    for (SmallVectorImpl<const SCEV *>::const_iterator I = V.begin(),
         E = V.end(); I != E; ++I)
      Result ^= DenseMapInfo<const SCEV *>::getHashValue(*I);
    return Result;
  }

  static bool isEqual(const SmallVector<const SCEV *, 2> &LHS,
                      const SmallVector<const SCEV *, 2> &RHS) {
    return LHS == RHS;
  }
};

/// LSRUse - This class holds the state that LSR keeps for each use in
/// IVUsers, as well as uses invented by LSR itself. It includes information
/// about what kinds of things can be folded into the user, information about
/// the user itself, and information about how the use may be satisfied.
/// TODO: Represent multiple users of the same expression in common?
class LSRUse {
  DenseSet<SmallVector<const SCEV *, 2>, UniquifierDenseMapInfo> Uniquifier;

public:
  /// KindType - An enum for a kind of use, indicating what types of
  /// scaled and immediate operands it might support.
  enum KindType {
    Basic,   ///< A normal use, with no folding.
    Special, ///< A special case of basic, allowing -1 scales.
    Address, ///< An address use; folding according to TargetLowering
    ICmpZero ///< An equality icmp with both operands folded into one.
    // TODO: Add a generic icmp too?
  };

  KindType Kind;
  const Type *AccessTy;

  SmallVector<int64_t, 8> Offsets;
  int64_t MinOffset;
  int64_t MaxOffset;

  /// AllFixupsOutsideLoop - This records whether all of the fixups using this
  /// LSRUse are outside of the loop, in which case some special-case heuristics
  /// may be used.
  bool AllFixupsOutsideLoop;

  /// WidestFixupType - This records the widest use type for any fixup using
  /// this LSRUse. FindUseWithSimilarFormula can't consider uses with different
  /// max fixup widths to be equivalent, because the narrower one may be relying
  /// on the implicit truncation to truncate away bogus bits.
  const Type *WidestFixupType;

  /// Formulae - A list of ways to build a value that can satisfy this user.
  /// After the list is populated, one of these is selected heuristically and
  /// used to formulate a replacement for OperandValToReplace in UserInst.
  SmallVector<Formula, 12> Formulae;

  /// Regs - The set of register candidates used by all formulae in this LSRUse.
  SmallPtrSet<const SCEV *, 4> Regs;

  LSRUse(KindType K, const Type *T) : Kind(K), AccessTy(T),
                                      MinOffset(INT64_MAX),
                                      MaxOffset(INT64_MIN),
                                      AllFixupsOutsideLoop(true),
                                      WidestFixupType(0) {}

  bool HasFormulaWithSameRegs(const Formula &F) const;
  bool InsertFormula(const Formula &F);
  void DeleteFormula(Formula &F);