LoopStrengthReduce.cpp

        SME->getNumOperands() == 2 && SME->isLoopInvariant(L)) {

      SCEVHandle SubImm = SE->getIntegerSCEV(0, Val->getType());
      SCEVHandle NewOp = SME->getOperand(1);
      MoveImmediateValues(TLI, User, NewOp, SubImm, isAddress, L, SE);
      
      // If we extracted something out of the subexpressions, see if we can 
      // simplify this!
      if (NewOp != SME->getOperand(1)) {
        // Scale SubImm up by "8".  If the result is a target constant, we are
        // good.
        SubImm = SE->getMulExpr(SubImm, SME->getOperand(0));
        if (fitsInAddressMode(SubImm, UseTy, TLI, false)) {
          // Accumulate the immediate.
          Imm = SE->getAddExpr(Imm, SubImm);
          
          // Update what is left of 'Val'.
          Val = SE->getMulExpr(SME->getOperand(0), NewOp);
          return;
        }
      }
    }
  }

  // Loop-variant expressions must stay in the immediate field of the
  // expression.
  if ((isAddress && fitsInAddressMode(Val, UseTy, TLI, false)) ||
      !Val->isLoopInvariant(L)) {
    Imm = SE->getAddExpr(Imm, Val);
    Val = SE->getIntegerSCEV(0, Val->getType());
    return;
  }

  // Otherwise, no immediates to move.
}


/// SeparateSubExprs - Decompose Expr into all of the subexpressions that are
/// added together.  This is used to reassociate common addition subexprs
/// together for maximal sharing when rewriting bases.
static void SeparateSubExprs(std::vector<SCEVHandle> &SubExprs,
                             SCEVHandle Expr,
                             ScalarEvolution *SE) {
  if (SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(Expr)) {
    for (unsigned j = 0, e = AE->getNumOperands(); j != e; ++j)
      SeparateSubExprs(SubExprs, AE->getOperand(j), SE);
  } else if (SCEVAddRecExpr *SARE = dyn_cast<SCEVAddRecExpr>(Expr)) {
    SCEVHandle Zero = SE->getIntegerSCEV(0, Expr->getType());
    if (SARE->getOperand(0) == Zero) {
      SubExprs.push_back(Expr);
    } else {
      // Compute the addrec with zero as its base.
      std::vector<SCEVHandle> Ops(SARE->op_begin(), SARE->op_end());
      Ops[0] = Zero;   // Start with zero base.
      SubExprs.push_back(SE->getAddRecExpr(Ops, SARE->getLoop()));
      

      SeparateSubExprs(SubExprs, SARE->getOperand(0), SE);
    }
  } else if (!Expr->isZero()) {
    // Do not add zero.
    SubExprs.push_back(Expr);
  }
}

// This is logically local to the following function, but C++ says we have 
// to make it file scope.
struct SubExprUseData { unsigned Count; bool notAllUsesAreFree; };

/// RemoveCommonExpressionsFromUseBases - Look through all of the Bases of all
/// the Uses, removing any common subexpressions, except that if all such
/// subexpressions can be folded into an addressing mode for all uses inside
/// the loop (this case is referred to as "free" in comments herein) we do
/// not remove anything.  This looks for things like (a+b+c) and
/// (a+c+d) and computes the common (a+c) subexpression.  The common expression
/// is *removed* from the Bases and returned.
static SCEVHandle 
RemoveCommonExpressionsFromUseBases(std::vector<BasedUser> &Uses,
                                    ScalarEvolution *SE, Loop *L,
                                    const TargetLowering *TLI) {
  unsigned NumUses = Uses.size();

  // Only one use?  This is a very common case, so we handle it specially and
  // cheaply.
  SCEVHandle Zero = SE->getIntegerSCEV(0, Uses[0].Base->getType());
  SCEVHandle Result = Zero;
  SCEVHandle FreeResult = Zero;
  if (NumUses == 1) {
    // If the use is inside the loop, use its base, regardless of what it is:
    // it is clearly shared across all the IV's.  If the use is outside the loop
    // (which means after it) we don't want to factor anything *into* the loop,
    // so just use 0 as the base.
    if (L->contains(Uses[0].Inst->getParent()))
      std::swap(Result, Uses[0].Base);
    return Result;
  }

  // To find common subexpressions, count how many of Uses use each expression.
  // If any subexpressions are used Uses.size() times, they are common.
  // Also track whether all uses of each expression can be moved into an
  // an addressing mode "for free"; such expressions are left within the loop.
  // struct SubExprUseData { unsigned Count; bool notAllUsesAreFree; };
  std::map<SCEVHandle, SubExprUseData> SubExpressionUseData;
  
  // UniqueSubExprs - Keep track of all of the subexpressions we see in the
  // order we see them.
  std::vector<SCEVHandle> UniqueSubExprs;

  std::vector<SCEVHandle> SubExprs;
  unsigned NumUsesInsideLoop = 0;
  for (unsigned i = 0; i != NumUses; ++i) {
    // If the user is outside the loop, just ignore it for base computation.
    // Since the user is outside the loop, it must be *after* the loop (if it
    // were before, it could not be based on the loop IV).  We don't want users
    // after the loop to affect base computation of values *inside* the loop,
    // because we can always add their offsets to the result IV after the loop
    // is done, ensuring we get good code inside the loop.
    if (!L->contains(Uses[i].Inst->getParent()))
      continue;
    NumUsesInsideLoop++;
    
    // If the base is zero (which is common), return zero now, there are no
    // CSEs we can find.
    if (Uses[i].Base == Zero) return Zero;

    // If this use is as an address we may be able to put CSEs in the addressing
    // mode rather than hoisting them.
    bool isAddrUse = isAddressUse(Uses[i].Inst, Uses[i].OperandValToReplace);
    // We may need the UseTy below, but only when isAddrUse, so compute it
    // only in that case.
    const Type *UseTy = 0;
    if (isAddrUse) {
      UseTy  = Uses[i].Inst->getType();
      if (StoreInst *SI = dyn_cast<StoreInst>(Uses[i].Inst))
        UseTy = SI->getOperand(0)->getType();
    }

    // Split the expression into subexprs.
    SeparateSubExprs(SubExprs, Uses[i].Base, SE);
    // Add one to SubExpressionUseData.Count for each subexpr present, and
    // if the subexpr is not a valid immediate within an addressing mode use,
    // set SubExpressionUseData.notAllUsesAreFree.  We definitely want to
    // hoist these out of the loop (if they are common to all uses).
    for (unsigned j = 0, e = SubExprs.size(); j != e; ++j) {
      if (++SubExpressionUseData[SubExprs[j]].Count == 1)
        UniqueSubExprs.push_back(SubExprs[j]);
      if (!isAddrUse || !fitsInAddressMode(SubExprs[j], UseTy, TLI, false))
        SubExpressionUseData[SubExprs[j]].notAllUsesAreFree = true;
    }
    SubExprs.clear();
  }

  // Now that we know how many times each is used, build Result.  Iterate over
  // UniqueSubexprs so that we have a stable ordering.
  for (unsigned i = 0, e = UniqueSubExprs.size(); i != e; ++i) {
    std::map<SCEVHandle, SubExprUseData>::iterator I = 
       SubExpressionUseData.find(UniqueSubExprs[i]);
    assert(I != SubExpressionUseData.end() && "Entry not found?");
    if (I->second.Count == NumUsesInsideLoop) { // Found CSE! 
      if (I->second.notAllUsesAreFree)
        Result = SE->getAddExpr(Result, I->first);
      else 
        FreeResult = SE->getAddExpr(FreeResult, I->first);
    } else
      // Remove non-cse's from SubExpressionUseData.
      SubExpressionUseData.erase(I);
  }

  if (FreeResult != Zero) {
    // We have some subexpressions that can be subsumed into addressing
    // modes in every use inside the loop.  However, it's possible that
    // there are so many of them that the combined FreeResult cannot
    // be subsumed, or that the target cannot handle both a FreeResult
    // and a Result in the same instruction (for example because it would
    // require too many registers).  Check this.
    for (unsigned i=0; i<NumUses; ++i) {
      if (!L->contains(Uses[i].Inst->getParent()))
        continue;
      // We know this is an addressing mode use; if there are any uses that
      // are not, FreeResult would be Zero.
      const Type *UseTy = Uses[i].Inst->getType();
      if (StoreInst *SI = dyn_cast<StoreInst>(Uses[i].Inst))
        UseTy = SI->getOperand(0)->getType();
      if (!fitsInAddressMode(FreeResult, UseTy, TLI, Result!=Zero)) {
        // FIXME:  could split up FreeResult into pieces here, some hoisted
        // and some not.  There is no obvious advantage to this.
        Result = SE->getAddExpr(Result, FreeResult);
        FreeResult = Zero;
        break;
      }
    }
  }

  // If we found no CSE's, return now.
  if (Result == Zero) return Result;
  
  // If we still have a FreeResult, remove its subexpressions from
  // SubExpressionUseData.  This means they will remain in the use Bases.
  if (FreeResult != Zero) {
    SeparateSubExprs(SubExprs, FreeResult, SE);
    for (unsigned j = 0, e = SubExprs.size(); j != e; ++j) {
      std::map<SCEVHandle, SubExprUseData>::iterator I = 
         SubExpressionUseData.find(SubExprs[j]);
      SubExpressionUseData.erase(I);
    }
    SubExprs.clear();
  }

  // Otherwise, remove all of the CSE's we found from each of the base values.
  for (unsigned i = 0; i != NumUses; ++i) {
    // Uses outside the loop don't necessarily include the common base, but
    // the final IV value coming into those uses does.  Instead of trying to
    // remove the pieces of the common base, which might not be there,
    // subtract off the base to compensate for this.
    if (!L->contains(Uses[i].Inst->getParent())) {
      Uses[i].Base = SE->getMinusSCEV(Uses[i].Base, Result);
      continue;
    }

    // Split the expression into subexprs.
    SeparateSubExprs(SubExprs, Uses[i].Base, SE);

    // Remove any common subexpressions.
    for (unsigned j = 0, e = SubExprs.size(); j != e; ++j)
      if (SubExpressionUseData.count(SubExprs[j])) {
        SubExprs.erase(SubExprs.begin()+j);
        --j; --e;
      }
    
    // Finally, add the non-shared expressions together.
    if (SubExprs.empty())
      Uses[i].Base = Zero;
    else
      Uses[i].Base = SE->getAddExpr(SubExprs);
    SubExprs.clear();
  }
 
  return Result;
}

/// ValidStride - Check whether the given Scale is valid for all loads and 
/// stores in UsersToProcess.
///
bool LoopStrengthReduce::ValidStride(bool HasBaseReg,
                               int64_t Scale, 
                               const std::vector<BasedUser>& UsersToProcess) {
  if (!TLI)
    return true;

  for (unsigned i=0, e = UsersToProcess.size(); i!=e; ++i) {
    // If this is a load or other access, pass the type of the access in.
    const Type *AccessTy = Type::VoidTy;
    if (StoreInst *SI = dyn_cast<StoreInst>(UsersToProcess[i].Inst))
      AccessTy = SI->getOperand(0)->getType();
    else if (LoadInst *LI = dyn_cast<LoadInst>(UsersToProcess[i].Inst))
      AccessTy = LI->getType();
    else if (isa<PHINode>(UsersToProcess[i].Inst))
      continue;
    
    TargetLowering::AddrMode AM;
    if (SCEVConstant *SC = dyn_cast<SCEVConstant>(UsersToProcess[i].Imm))
      AM.BaseOffs = SC->getValue()->getSExtValue();
    AM.HasBaseReg = HasBaseReg || !UsersToProcess[i].Base->isZero();
    AM.Scale = Scale;

    // If load[imm+r*scale] is illegal, bail out.
    if (!TLI->isLegalAddressingMode(AM, AccessTy))
      return false;
  }
  return true;
}

/// RequiresTypeConversion - Returns true if converting Ty1 to Ty2 is not
/// a nop.
bool LoopStrengthReduce::RequiresTypeConversion(const Type *Ty1,
                                                const Type *Ty2) {
  if (Ty1 == Ty2)
    return false;
  if (Ty1->canLosslesslyBitCastTo(Ty2))
    return false;
  if (TLI && TLI->isTruncateFree(Ty1, Ty2))
    return false;
  if (isa<PointerType>(Ty2) && Ty1->canLosslesslyBitCastTo(UIntPtrTy))
    return false;
  if (isa<PointerType>(Ty1) && Ty2->canLosslesslyBitCastTo(UIntPtrTy))
    return false;
  return true;
}

/// CheckForIVReuse - Returns the multiple if the stride is the multiple
/// of a previous stride and it is a legal value for the target addressing
/// mode scale component and optional base reg. This allows the users of
/// this stride to be rewritten as prev iv * factor. It returns 0 if no
/// reuse is possible.  Factors can be negative on same targets, e.g. ARM.
///
/// If all uses are outside the loop, we don't require that all multiplies
/// be folded into the addressing mode, nor even that the factor be constant; 
/// a multiply (executed once) outside the loop is better than another IV 
/// within.  Well, usually.
SCEVHandle LoopStrengthReduce::CheckForIVReuse(bool HasBaseReg,
                                bool AllUsesAreAddresses,
                                bool AllUsesAreOutsideLoop,
                                const SCEVHandle &Stride, 
                                IVExpr &IV, const Type *Ty,
                                const std::vector<BasedUser>& UsersToProcess) {
  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Stride)) {
    int64_t SInt = SC->getValue()->getSExtValue();
    for (unsigned NewStride = 0, e = StrideOrder.size(); NewStride != e;
         ++NewStride) {
      std::map<SCEVHandle, IVsOfOneStride>::iterator SI = 
                IVsByStride.find(StrideOrder[NewStride]);
      if (SI == IVsByStride.end() || !isa<SCEVConstant>(SI->first))
        continue;
      int64_t SSInt = cast<SCEVConstant>(SI->first)->getValue()->getSExtValue();
      if (SI->first != Stride &&
          (unsigned(abs(SInt)) < SSInt || (SInt % SSInt) != 0))
        continue;
      int64_t Scale = SInt / SSInt;
      // Check that this stride is valid for all the types used for loads and
      // stores; if it can be used for some and not others, we might as well use
      // the original stride everywhere, since we have to create the IV for it
      // anyway. If the scale is 1, then we don't need to worry about folding
      // multiplications.
      if (Scale == 1 ||
          (AllUsesAreAddresses &&
           ValidStride(HasBaseReg, Scale, UsersToProcess)))
        for (std::vector<IVExpr>::iterator II = SI->second.IVs.begin(),
               IE = SI->second.IVs.end(); II != IE; ++II)
          // FIXME: Only handle base == 0 for now.
          // Only reuse previous IV if it would not require a type conversion.
          if (II->Base->isZero() &&
              !RequiresTypeConversion(II->Base->getType(), Ty)) {
            IV = *II;
            return SE->getIntegerSCEV(Scale, Stride->getType());
          }
    }
  } else if (AllUsesAreOutsideLoop) {
    // Accept nonconstant strides here; it is really really right to substitute
    // an existing IV if we can.
    for (unsigned NewStride = 0, e = StrideOrder.size(); NewStride != e;
         ++NewStride) {
      std::map<SCEVHandle, IVsOfOneStride>::iterator SI = 
                IVsByStride.find(StrideOrder[NewStride]);
      if (SI == IVsByStride.end() || !isa<SCEVConstant>(SI->first))
        continue;
      int64_t SSInt = cast<SCEVConstant>(SI->first)->getValue()->getSExtValue();
      if (SI->first != Stride && SSInt != 1)
        continue;
      for (std::vector<IVExpr>::iterator II = SI->second.IVs.begin(),
             IE = SI->second.IVs.end(); II != IE; ++II)
        // Accept nonzero base here.
        // Only reuse previous IV if it would not require a type conversion.
        if (!RequiresTypeConversion(II->Base->getType(), Ty)) {
          IV = *II;
          return Stride;
        }
    }
    // Special case, old IV is -1*x and this one is x.  Can treat this one as
    // -1*old.
    for (unsigned NewStride = 0, e = StrideOrder.size(); NewStride != e;
         ++NewStride) {
      std::map<SCEVHandle, IVsOfOneStride>::iterator SI = 
                IVsByStride.find(StrideOrder[NewStride]);
      if (SI == IVsByStride.end()) 
        continue;
      if (SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(SI->first))
        if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ME->getOperand(0)))
          if (Stride == ME->getOperand(1) &&
              SC->getValue()->getSExtValue() == -1LL)
            for (std::vector<IVExpr>::iterator II = SI->second.IVs.begin(),
                   IE = SI->second.IVs.end(); II != IE; ++II)
              // Accept nonzero base here.
              // Only reuse previous IV if it would not require type conversion.
              if (!RequiresTypeConversion(II->Base->getType(), Ty)) {
                IV = *II;
                return SE->getIntegerSCEV(-1LL, Stride->getType());
              }
    }
  }
  return SE->getIntegerSCEV(0, Stride->getType());
}

/// PartitionByIsUseOfPostIncrementedValue - Simple boolean predicate that
/// returns true if Val's isUseOfPostIncrementedValue is true.
static bool PartitionByIsUseOfPostIncrementedValue(const BasedUser &Val) {
  return Val.isUseOfPostIncrementedValue;
}

/// isNonConstantNegative - Return true if the specified scev is negated, but
/// not a constant.
static bool isNonConstantNegative(const SCEVHandle &Expr) {
  SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Expr);
  if (!Mul) return false;
  
  // If there is a constant factor, it will be first.
  SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
  if (!SC) return false;
  
  // Return true if the value is negative, this matches things like (-42 * V).
  return SC->getValue()->getValue().isNegative();
}

// CollectIVUsers - Transform our list of users and offsets to a bit more
// complex table. In this new vector, each 'BasedUser' contains 'Base', the base
// of the strided accesses, as well as the old information from Uses. We
// progressively move information from the Base field to the Imm field, until
// we eventually have the full access expression to rewrite the use.
SCEVHandle LoopStrengthReduce::CollectIVUsers(const SCEVHandle &Stride,
                                              IVUsersOfOneStride &Uses,
                                              Loop *L,
                                              bool &AllUsesAreAddresses,
                                              bool &AllUsesAreOutsideLoop,
                                       std::vector<BasedUser> &UsersToProcess) {
  UsersToProcess.reserve(Uses.Users.size());
  for (unsigned i = 0, e = Uses.Users.size(); i != e; ++i) {
    UsersToProcess.push_back(BasedUser(Uses.Users[i], SE));
    
    // Move any loop variant operands from the offset field to the immediate
    // field of the use, so that we don't try to use something before it is
    // computed.
    MoveLoopVariantsToImmediateField(UsersToProcess.back().Base,
                                    UsersToProcess.back().Imm, L, SE);
    assert(UsersToProcess.back().Base->isLoopInvariant(L) &&
           "Base value is not loop invariant!");
  }

  // We now have a whole bunch of uses of like-strided induction variables, but
  // they might all have different bases.  We want to emit one PHI node for this
  // stride which we fold as many common expressions (between the IVs) into as
  // possible.  Start by identifying the common expressions in the base values 
  // for the strides (e.g. if we have "A+C+B" and "A+B+D" as our bases, find
  // "A+B"), emit it to the preheader, then remove the expression from the
  // UsersToProcess base values.
  SCEVHandle CommonExprs =
    RemoveCommonExpressionsFromUseBases(UsersToProcess, SE, L, TLI);

  // Next, figure out what we can represent in the immediate fields of
  // instructions.  If we can represent anything there, move it to the imm
  // fields of the BasedUsers.  We do this so that it increases the commonality
  // of the remaining uses.
  unsigned NumPHI = 0;
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ++i) {
    // If the user is not in the current loop, this means it is using the exit
    // value of the IV.  Do not put anything in the base, make sure it's all in
    // the immediate field to allow as much factoring as possible.
    if (!L->contains(UsersToProcess[i].Inst->getParent())) {
      UsersToProcess[i].Imm = SE->getAddExpr(UsersToProcess[i].Imm,
                                             UsersToProcess[i].Base);
      UsersToProcess[i].Base = 
        SE->getIntegerSCEV(0, UsersToProcess[i].Base->getType());
    } else {

      // Addressing modes can be folded into loads and stores.  Be careful that
      // the store is through the expression, not of the expression though.
      bool isPHI = false;
      bool isAddress = isAddressUse(UsersToProcess[i].Inst,
                                    UsersToProcess[i].OperandValToReplace);
      if (isa<PHINode>(UsersToProcess[i].Inst)) {
        isPHI = true;
        ++NumPHI;
      }

      // Not all uses are outside the loop.
      AllUsesAreOutsideLoop = false; 
     
      // If this use isn't an address, then not all uses are addresses.
      if (!isAddress && !isPHI)
        AllUsesAreAddresses = false;
      
      MoveImmediateValues(TLI, UsersToProcess[i].Inst, UsersToProcess[i].Base,
                          UsersToProcess[i].Imm, isAddress, L, SE);
    }
  }

  // If one of the use if a PHI node and all other uses are addresses, still
  // allow iv reuse. Essentially we are trading one constant multiplication
  // for one fewer iv.
  if (NumPHI > 1)
    AllUsesAreAddresses = false;

  return CommonExprs;
}

/// ShouldUseFullStrengthReductionMode - Test whether full strength-reduction
/// is valid and profitable for the given set of users of a stride. In
/// full strength-reduction mode, all addresses at the current stride are
/// strength-reduced all the way down to pointer arithmetic.
///
bool LoopStrengthReduce::ShouldUseFullStrengthReductionMode(
                                   const std::vector<BasedUser> &UsersToProcess,
                                   const Loop *L,
                                   bool AllUsesAreAddresses,
                                   SCEVHandle Stride) {
  if (!EnableFullLSRMode)
    return false;

  // The heuristics below aim to avoid increasing register pressure, but
  // fully strength-reducing all the addresses increases the number of
  // add instructions, so don't do this when optimizing for size.
  // TODO: If the loop is large, the savings due to simpler addresses
  // may oughtweight the costs of the extra increment instructions.
  if (L->getHeader()->getParent()->hasFnAttr(Attribute::OptimizeForSize))
    return false;

  // TODO: For now, don't do full strength reduction if there could
  // potentially be greater-stride multiples of the current stride
  // which could reuse the current stride IV.
  if (StrideOrder.back() != Stride)
    return false;

  // Iterate through the uses to find conditions that automatically rule out
  // full-lsr mode.
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ) {
    SCEV *Base = UsersToProcess[i].Base;
    SCEV *Imm = UsersToProcess[i].Imm;
    // If any users have a loop-variant component, they can't be fully
    // strength-reduced.
    if (Imm && !Imm->isLoopInvariant(L))
      return false;
    // If there are to users with the same base and the difference between
    // the two Imm values can't be folded into the address, full
    // strength reduction would increase register pressure.
    do {
      SCEV *CurImm = UsersToProcess[i].Imm;
      if (CurImm || Imm && CurImm != Imm) {
        if (!CurImm) CurImm = SE->getIntegerSCEV(0, Stride->getType());
        if (!Imm)       Imm = SE->getIntegerSCEV(0, Stride->getType());
        const Instruction *Inst = UsersToProcess[i].Inst;
        const Type *UseTy = Inst->getType();
        if (const StoreInst *SI = dyn_cast<StoreInst>(Inst))
          UseTy = SI->getOperand(0)->getType();
        SCEVHandle Diff = SE->getMinusSCEV(UsersToProcess[i].Imm, Imm);
        if (!Diff->isZero() &&
            (!AllUsesAreAddresses ||
             !fitsInAddressMode(Diff, UseTy, TLI, /*HasBaseReg=*/true)))
          return false;
      }
    } while (++i != e && Base == UsersToProcess[i].Base);
  }

  // If there's exactly one user in this stride, fully strength-reducing it
  // won't increase register pressure. If it's starting from a non-zero base,
  // it'll be simpler this way.
  if (UsersToProcess.size() == 1 && !UsersToProcess[0].Base->isZero())
    return true;

  // Otherwise, if there are any users in this stride that don't require
  // a register for their base, full strength-reduction will increase
  // register pressure.
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ++i)
    if (UsersToProcess[i].Base->isZero())
      return false;

  // Otherwise, go for it.
  return true;
}

/// InsertAffinePhi Create and insert a PHI node for an induction variable
/// with the specified start and step values in the specified loop.
///
/// If NegateStride is true, the stride should be negated by using a
/// subtract instead of an add.
///
/// Return the created phi node, and return the step instruction by
/// reference in IncV.
///
static PHINode *InsertAffinePhi(SCEVHandle Start, SCEVHandle Step,
                                const Loop *L,
                                SCEVExpander &Rewriter,
                                Value *&IncV) {
  assert(Start->isLoopInvariant(L) && "New PHI start is not loop invariant!");
  assert(Step->isLoopInvariant(L) && "New PHI stride is not loop invariant!");

  BasicBlock *Header = L->getHeader();
  BasicBlock *Preheader = L->getLoopPreheader();

  PHINode *PN = PHINode::Create(Start->getType(), "lsr.iv", Header->begin());
  PN->addIncoming(Rewriter.expandCodeFor(Start, Preheader->getTerminator()),
                  Preheader);

  pred_iterator HPI = pred_begin(Header);
  assert(HPI != pred_end(Header) && "Loop with zero preds???");
  if (!L->contains(*HPI)) ++HPI;
  assert(HPI != pred_end(Header) && L->contains(*HPI) &&
         "No backedge in loop?");

  // If the stride is negative, insert a sub instead of an add for the
  // increment.
  bool isNegative = isNonConstantNegative(Step);
  SCEVHandle IncAmount = Step;
  if (isNegative)
    IncAmount = Rewriter.SE.getNegativeSCEV(Step);

  // Insert an add instruction right before the terminator corresponding
  // to the back-edge.
  Value *StepV = Rewriter.expandCodeFor(IncAmount, Preheader->getTerminator());
  if (isNegative) {
    IncV = BinaryOperator::CreateSub(PN, StepV, "lsr.iv.next",
                                     (*HPI)->getTerminator());
  } else {
    IncV = BinaryOperator::CreateAdd(PN, StepV, "lsr.iv.next",
                                     (*HPI)->getTerminator());
  }
  if (!isa<ConstantInt>(StepV)) ++NumVariable;

  pred_iterator PI = pred_begin(Header);
  if (*PI == L->getLoopPreheader())
    ++PI;
  PN->addIncoming(IncV, *PI);

  ++NumInserted;
  return PN;
}

static void SortUsersToProcess(std::vector<BasedUser> &UsersToProcess) {
  // We want to emit code for users inside the loop first.  To do this, we
  // rearrange BasedUser so that the entries at the end have
  // isUseOfPostIncrementedValue = false, because we pop off the end of the
  // vector (so we handle them first).
  std::partition(UsersToProcess.begin(), UsersToProcess.end(),
                 PartitionByIsUseOfPostIncrementedValue);

  // Sort this by base, so that things with the same base are handled
  // together.  By partitioning first and stable-sorting later, we are
  // guaranteed that within each base we will pop off users from within the
  // loop before users outside of the loop with a particular base.
  //
  // We would like to use stable_sort here, but we can't.  The problem is that
  // SCEVHandle's don't have a deterministic ordering w.r.t to each other, so
  // we don't have anything to do a '<' comparison on.  Because we think the
  // number of uses is small, do a horrible bubble sort which just relies on
  // ==.
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ++i) {
    // Get a base value.
    SCEVHandle Base = UsersToProcess[i].Base;

    // Compact everything with this base to be consecutive with this one.
    for (unsigned j = i+1; j != e; ++j) {
      if (UsersToProcess[j].Base == Base) {
        std::swap(UsersToProcess[i+1], UsersToProcess[j]);
        ++i;
      }
    }
  }
}

/// PrepareToStrengthReduceFully - Prepare to fully strength-reduce UsersToProcess,
/// meaning lowering addresses all the way down to direct pointer arithmetic.
///
void
LoopStrengthReduce::PrepareToStrengthReduceFully(
                                        std::vector<BasedUser> &UsersToProcess,
                                        SCEVHandle Stride,
                                        SCEVHandle CommonExprs,
                                        const Loop *L,
                                        SCEVExpander &PreheaderRewriter) {
  DOUT << "  Fully reducing all users\n";

  // Rewrite the UsersToProcess records, creating a separate PHI for each
  // unique Base value.
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ) {
    // TODO: The uses are grouped by base, but not sorted. We arbitrarily
    // pick the first Imm value here to start with, and adjust it for the
    // other uses.
    SCEVHandle Imm = UsersToProcess[i].Imm;
    SCEVHandle Base = UsersToProcess[i].Base;
    SCEVHandle Start = SE->getAddExpr(CommonExprs, Base, Imm);
    Value *IncV;
    PHINode *Phi = InsertAffinePhi(Start, Stride, L,
                                   PreheaderRewriter,
                                   IncV);
    // Loop over all the users with the same base.
    do {
      UsersToProcess[i].Base = SE->getIntegerSCEV(0, Stride->getType());
      UsersToProcess[i].Imm = SE->getMinusSCEV(UsersToProcess[i].Imm, Imm);
      UsersToProcess[i].Phi = Phi;
      UsersToProcess[i].IncV = IncV;
      assert(UsersToProcess[i].Imm->isLoopInvariant(L) &&
             "ShouldUseFullStrengthReductionMode should reject this!");
    } while (++i != e && Base == UsersToProcess[i].Base);
  }
}

/// PrepareToStrengthReduceWithNewPhi - Insert a new induction variable for the
/// given users to share.
///
void
LoopStrengthReduce::PrepareToStrengthReduceWithNewPhi(
                                         std::vector<BasedUser> &UsersToProcess,
                                         SCEVHandle Stride,
                                         SCEVHandle CommonExprs,
                                         Value *CommonBaseV,
                                         const Loop *L,
                                         SCEVExpander &PreheaderRewriter) {
  DOUT << "  Inserting new PHI:\n";

  Value *IncV;
  PHINode *Phi = InsertAffinePhi(SE->getUnknown(CommonBaseV),
                                 Stride, L,
                                 PreheaderRewriter,
                                 IncV);

  // Remember this in case a later stride is multiple of this.
  IVsByStride[Stride].addIV(Stride, CommonExprs, Phi, IncV);

  // All the users will share this new IV.
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ++i) {
    UsersToProcess[i].Phi = Phi;
    UsersToProcess[i].IncV = IncV;
  }

  DOUT << "    IV=";
  DEBUG(WriteAsOperand(*DOUT, Phi, /*PrintType=*/false));
  DOUT << ", INC=";
  DEBUG(WriteAsOperand(*DOUT, IncV, /*PrintType=*/false));
  DOUT << "\n";
}

/// PrepareToStrengthReduceWithNewPhi - Prepare for the given users to reuse
/// an induction variable with a stride that is a factor of the current
/// induction variable.
///
void
LoopStrengthReduce::PrepareToStrengthReduceFromSmallerStride(
                                         std::vector<BasedUser> &UsersToProcess,
                                         Value *CommonBaseV,
                                         const IVExpr &ReuseIV,
                                         Instruction *PreInsertPt) {
  DOUT << "  Rewriting in terms of existing IV of STRIDE " << *ReuseIV.Stride
       << " and BASE " << *ReuseIV.Base << "\n";

  // All the users will share the reused IV.
  for (unsigned i = 0, e = UsersToProcess.size(); i != e; ++i) {
    UsersToProcess[i].Phi = ReuseIV.PHI;
    UsersToProcess[i].IncV = ReuseIV.IncV;
  }

  Constant *C = dyn_cast<Constant>(CommonBaseV);
  if (C &&
      (!C->isNullValue() &&
       !fitsInAddressMode(SE->getUnknown(CommonBaseV), CommonBaseV->getType(),
                         TLI, false)))
    // We want the common base emitted into the preheader! This is just
    // using cast as a copy so BitCast (no-op cast) is appropriate
    CommonBaseV = new BitCastInst(CommonBaseV, CommonBaseV->getType(),
                                  "commonbase", PreInsertPt);
}

/// StrengthReduceStridedIVUsers - Strength reduce all of the users of a single
/// stride of IV.  All of the users may have different starting values, and this
/// may not be the only stride (we know it is if isOnlyStride is true).
void LoopStrengthReduce::StrengthReduceStridedIVUsers(const SCEVHandle &Stride,
                                                      IVUsersOfOneStride &Uses,
                                                      Loop *L,
                                                      bool isOnlyStride) {
  // If all the users are moved to another stride, then there is nothing to do.
  if (Uses.Users.empty())
    return;

  // Keep track if every use in UsersToProcess is an address. If they all are,
  // we may be able to rewrite the entire collection of them in terms of a
  // smaller-stride IV.
  bool AllUsesAreAddresses = true;

  // Keep track if every use of a single stride is outside the loop.  If so,
  // we want to be more aggressive about reusing a smaller-stride IV; a
  // multiply outside the loop is better than another IV inside.  Well, usually.
  bool AllUsesAreOutsideLoop = true;

  // Transform our list of users and offsets to a bit more complex table.  In
  // this new vector, each 'BasedUser' contains 'Base' the base of the
  // strided accessas well as the old information from Uses.  We progressively
  // move information from the Base field to the Imm field, until we eventually
  // have the full access expression to rewrite the use.
  std::vector<BasedUser> UsersToProcess;
  SCEVHandle CommonExprs = CollectIVUsers(Stride, Uses, L, AllUsesAreAddresses,
                                          AllUsesAreOutsideLoop,
                                          UsersToProcess);

  // Sort the UsersToProcess array so that users with common bases are
  // next to each other.
  SortUsersToProcess(UsersToProcess);

  // If we managed to find some expressions in common, we'll need to carry
  // their value in a register and add it in for each use. This will take up
  // a register operand, which potentially restricts what stride values are
  // valid.
  bool HaveCommonExprs = !CommonExprs->isZero();

  const Type *ReplacedTy = CommonExprs->getType();

  // Now that we know what we need to do, insert the PHI node itself.
  //
  DOUT << "LSR: Examining IVs of TYPE " << *ReplacedTy << " of STRIDE "
       << *Stride << ":\n"
       << "  Common base: " << *CommonExprs << "\n";

  SCEVExpander Rewriter(*SE, *LI);
  SCEVExpander PreheaderRewriter(*SE, *LI);

  BasicBlock  *Preheader = L->getLoopPreheader();
  Instruction *PreInsertPt = Preheader->getTerminator();
  BasicBlock *LatchBlock = L->getLoopLatch();

  Value *CommonBaseV = ConstantInt::get(ReplacedTy, 0);

  SCEVHandle RewriteFactor = SE->getIntegerSCEV(0, ReplacedTy);
  IVExpr   ReuseIV(SE->getIntegerSCEV(0, Type::Int32Ty),
                   SE->getIntegerSCEV(0, Type::Int32Ty),
                   0, 0);

  /// Choose a strength-reduction strategy and prepare for it by creating
  /// the necessary PHIs and adjusting the bookkeeping.
  if (ShouldUseFullStrengthReductionMode(UsersToProcess, L,
                                         AllUsesAreAddresses, Stride)) {
    PrepareToStrengthReduceFully(UsersToProcess, Stride, CommonExprs, L,
                                 PreheaderRewriter);
  } else {
    // Emit the initial base value into the loop preheader.
    CommonBaseV = PreheaderRewriter.expandCodeFor(CommonExprs, PreInsertPt);

    // If all uses are addresses, check if it is possible to reuse an IV with a
    // stride that is a factor of this stride. And that the multiple is a number
    // that can be encoded in the scale field of the target addressing mode. And
    // that we will have a valid instruction after this substition, including the
    // immediate field, if any.
    RewriteFactor = CheckForIVReuse(HaveCommonExprs, AllUsesAreAddresses,
                                    AllUsesAreOutsideLoop,
                                    Stride, ReuseIV, CommonExprs->getType(),
                                    UsersToProcess);
    if (isa<SCEVConstant>(RewriteFactor) &&
        cast<SCEVConstant>(RewriteFactor)->isZero())
      PrepareToStrengthReduceWithNewPhi(UsersToProcess, Stride, CommonExprs,
                                        CommonBaseV, L, PreheaderRewriter);
    else
      PrepareToStrengthReduceFromSmallerStride(UsersToProcess, CommonBaseV,
                                               ReuseIV, PreInsertPt);
  }

  // Process all the users now, replacing their strided uses with
  // strength-reduced forms.  This outer loop handles all bases, the inner
  // loop handles all users of a particular base.
  while (!UsersToProcess.empty()) {
    SCEVHandle Base = UsersToProcess.back().Base;
    Instruction *Inst = UsersToProcess.back().Inst;

    // Emit the code for Base into the preheader.
    Value *BaseV = PreheaderRewriter.expandCodeFor(Base, PreInsertPt);

    DOUT << "  Examining uses with BASE ";
    DEBUG(WriteAsOperand(*DOUT, BaseV, /*PrintType=*/false));
    DOUT << ":\n";

    // If BaseV is a constant other than 0, make sure that it gets inserted into
    // the preheader, instead of being forward substituted into the uses.  We do
    // this by forcing a BitCast (noop cast) to be inserted into the preheader 
    // in this case.
    if (Constant *C = dyn_cast<Constant>(BaseV)) {
      if (!C->isNullValue() && !fitsInAddressMode(Base, ReplacedTy, 
                                                 TLI, false)) {
        // We want this constant emitted into the preheader! This is just
        // using cast as a copy so BitCast (no-op cast) is appropriate
        BaseV = new BitCastInst(BaseV, BaseV->getType(), "preheaderinsert",
                                PreInsertPt);       
      }
    }

    // Emit the code to add the immediate offset to the Phi value, just before
    // the instructions that we identified as using this stride and base.
    do {
      // FIXME: Use emitted users to emit other users.
      BasedUser &User = UsersToProcess.back();

      DOUT << "    Examining use ";
      DEBUG(WriteAsOperand(*DOUT, UsersToProcess.back().OperandValToReplace,
                           /*PrintType=*/false));
      DOUT << " in Inst: " << *Inst;

      // If this instruction wants to use the post-incremented value, move it
      // after the post-inc and use its value instead of the PHI.
      Value *RewriteOp = User.Phi;
      if (User.isUseOfPostIncrementedValue) {
        RewriteOp = User.IncV;

        // If this user is in the loop, make sure it is the last thing in the
        // loop to ensure it is dominated by the increment.
        if (L->contains(User.Inst->getParent()))
          User.Inst->moveBefore(LatchBlock->getTerminator());
      }
      if (RewriteOp->getType() != ReplacedTy) {
        Instruction::CastOps opcode = Instruction::Trunc;
        if (ReplacedTy->getPrimitiveSizeInBits() ==
            RewriteOp->getType()->getPrimitiveSizeInBits())
          opcode = Instruction::BitCast;
        RewriteOp = SCEVExpander::InsertCastOfTo(opcode, RewriteOp, ReplacedTy);
      }

      SCEVHandle RewriteExpr = SE->getUnknown(RewriteOp);

      // If we had to insert new instructions for RewriteOp, we have to
      // consider that they may not have been able to end up immediately
      // next to RewriteOp, because non-PHI instructions may never precede
      // PHI instructions in a block. In this case, remember where the last
      // instruction was inserted so that if we're replacing a different
      // PHI node, we can use the later point to expand the final
      // RewriteExpr.
      Instruction *NewBasePt = dyn_cast<Instruction>(RewriteOp);
      if (RewriteOp == User.Phi) NewBasePt = 0;

      // Clear the SCEVExpander's expression map so that we are guaranteed
      // to have the code emitted where we expect it.
      Rewriter.clear();

      // If we are reusing the iv, then it must be multiplied by a constant
      // factor to take advantage of the addressing mode scale component.
      if (!isa<SCEVConstant>(RewriteFactor) ||
          !cast<SCEVConstant>(RewriteFactor)->isZero()) {
        // If we're reusing an IV with a nonzero base (currently this happens
        // only when all reuses are outside the loop) subtract that base here.
        // The base has been used to initialize the PHI node but we don't want
        // it here.
        if (!ReuseIV.Base->isZero()) {
          SCEVHandle typedBase = ReuseIV.Base;
          if (RewriteExpr->getType()->getPrimitiveSizeInBits() !=
              ReuseIV.Base->getType()->getPrimitiveSizeInBits()) {
            // It's possible the original IV is a larger type than the new IV,
            // in which case we have to truncate the Base.  We checked in
            // RequiresTypeConversion that this is valid.
            assert (RewriteExpr->getType()->getPrimitiveSizeInBits() <
                    ReuseIV.Base->getType()->getPrimitiveSizeInBits() &&
                    "Unexpected lengthening conversion!");
            typedBase = SE->getTruncateExpr(ReuseIV.Base, 
                                            RewriteExpr->getType());
          }
          RewriteExpr = SE->getMinusSCEV(RewriteExpr, typedBase);
        }

        // Multiply old variable, with base removed, by new scale factor.
        RewriteExpr = SE->getMulExpr(RewriteFactor,
                                     RewriteExpr);

        // The common base is emitted in the loop preheader. But since we
        // are reusing an IV, it has not been used to initialize the PHI node.
        // Add it to the expression used to rewrite the uses.
        // When this use is outside the loop, we earlier subtracted the
        // common base, and are adding it back here.  Use the same expression
        // as before, rather than CommonBaseV, so DAGCombiner will zap it.
        if (!isa<ConstantInt>(CommonBaseV) ||
            !cast<ConstantInt>(CommonBaseV)->isZero()) {
          if (L->contains(User.Inst->getParent()))
            RewriteExpr = SE->getAddExpr(RewriteExpr,
                                       SE->getUnknown(CommonBaseV));
          else
            RewriteExpr = SE->getAddExpr(RewriteExpr, CommonExprs);
        }
      }

      // Now that we know what we need to do, insert code before User for the
      // immediate and any loop-variant expressions.
      if (!isa<ConstantInt>(BaseV) || !cast<ConstantInt>(BaseV)->isZero())
        // Add BaseV to the PHI value if needed.
        RewriteExpr = SE->getAddExpr(RewriteExpr, SE->getUnknown(BaseV));

      User.RewriteInstructionToUseNewBase(RewriteExpr, NewBasePt,
                                          Rewriter, L, this,
                                          DeadInsts);

      // Mark old value we replaced as possibly dead, so that it is eliminated
      // if we just replaced the last use of that value.
      DeadInsts.push_back(cast<Instruction>(User.OperandValToReplace));

      UsersToProcess.pop_back();
      ++NumReduced;

      // If there are any more users to process with the same base, process them
      // now.  We sorted by base above, so we just have to check the last elt.
    } while (!UsersToProcess.empty() && UsersToProcess.back().Base == Base);
    // TODO: Next, find out which base index is the most common, pull it out.
  }

  // IMPORTANT TODO: Figure out how to partition the IV's with this stride, but
  // different starting values, into different PHIs.
}

/// FindIVUserForCond - If Cond has an operand that is an expression of an IV,
/// set the IV user and stride information and return true, otherwise return
/// false.
bool LoopStrengthReduce::FindIVUserForCond(ICmpInst *Cond, IVStrideUse *&CondUse,
                                       const SCEVHandle *&CondStride) {
  for (unsigned Stride = 0, e = StrideOrder.size(); Stride != e && !CondUse;
       ++Stride) {
    std::map<SCEVHandle, IVUsersOfOneStride>::iterator SI = 
    IVUsesByStride.find(StrideOrder[Stride]);
    assert(SI != IVUsesByStride.end() && "Stride doesn't exist!");
    
    for (std::vector<IVStrideUse>::iterator UI = SI->second.Users.begin(),
         E = SI->second.Users.end(); UI != E; ++UI)
      if (UI->User == Cond) {
        // NOTE: we could handle setcc instructions with multiple uses here, but
        // InstCombine does it as well for simple uses, it's not clear that it