lib/Transforms/Scalar/LoopStrengthReduce.cpp

//===- LoopStrengthReduce.cpp - Strength Reduce GEPs in Loops -------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This pass performs a strength reduction on array references inside loops that
// have as one or more of their components the loop induction variable.  This is
// accomplished by creating a new Value to hold the initial value of the array
// access for the first iteration, and then creating a new GEP instruction in
// the loop to increment the value by the appropriate amount.
//
//===----------------------------------------------------------------------===//

#define DEBUG_TYPE "loop-reduce"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Constants.h"
#include "llvm/Instructions.h"
#include "llvm/IntrinsicInst.h"
#include "llvm/Type.h"
#include "llvm/DerivedTypes.h"
#include "llvm/Analysis/Dominators.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/GetElementPtrTypeIterator.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Target/TargetData.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Target/TargetLowering.h"
#include <algorithm>
#include <set>
using namespace llvm;

STATISTIC(NumReduced ,    "Number of GEPs strength reduced");
STATISTIC(NumInserted,    "Number of PHIs inserted");
STATISTIC(NumVariable,    "Number of PHIs with variable strides");
STATISTIC(NumEliminated,  "Number of strides eliminated");
STATISTIC(NumShadow,      "Number of Shadow IVs optimized");

namespace {

  struct BasedUser;

  /// IVStrideUse - Keep track of one use of a strided induction variable, where
  /// the stride is stored externally.  The Offset member keeps track of the 
  /// offset from the IV, User is the actual user of the operand, and
  /// 'OperandValToReplace' is the operand of the User that is the use.
  struct VISIBILITY_HIDDEN IVStrideUse {
    SCEVHandle Offset;
    Instruction *User;
    Value *OperandValToReplace;

    // isUseOfPostIncrementedValue - True if this should use the
    // post-incremented version of this IV, not the preincremented version.
    // This can only be set in special cases, such as the terminating setcc
    // instruction for a loop or uses dominated by the loop.
    bool isUseOfPostIncrementedValue;
    
    IVStrideUse(const SCEVHandle &Offs, Instruction *U, Value *O)
      : Offset(Offs), User(U), OperandValToReplace(O),
        isUseOfPostIncrementedValue(false) {}
  };
  
  /// IVUsersOfOneStride - This structure keeps track of all instructions that
  /// have an operand that is based on the trip count multiplied by some stride.
  /// The stride for all of these users is common and kept external to this
  /// structure.
  struct VISIBILITY_HIDDEN IVUsersOfOneStride {
    /// Users - Keep track of all of the users of this stride as well as the
    /// initial value and the operand that uses the IV.
    std::vector<IVStrideUse> Users;
    
    void addUser(const SCEVHandle &Offset,Instruction *User, Value *Operand) {
      Users.push_back(IVStrideUse(Offset, User, Operand));
    }
  };

  /// IVInfo - This structure keeps track of one IV expression inserted during
  /// StrengthReduceStridedIVUsers. It contains the stride, the common base, as
  /// well as the PHI node and increment value created for rewrite.
  struct VISIBILITY_HIDDEN IVExpr {
    SCEVHandle  Stride;
    SCEVHandle  Base;
    PHINode    *PHI;
    Value      *IncV;

    IVExpr(const SCEVHandle &stride, const SCEVHandle &base, PHINode *phi,
           Value *incv)
      : Stride(stride), Base(base), PHI(phi), IncV(incv) {}
  };

  /// IVsOfOneStride - This structure keeps track of all IV expression inserted
  /// during StrengthReduceStridedIVUsers for a particular stride of the IV.
  struct VISIBILITY_HIDDEN IVsOfOneStride {
    std::vector<IVExpr> IVs;

    void addIV(const SCEVHandle &Stride, const SCEVHandle &Base, PHINode *PHI,
               Value *IncV) {
      IVs.push_back(IVExpr(Stride, Base, PHI, IncV));
    }
  };

  class VISIBILITY_HIDDEN LoopStrengthReduce : public LoopPass {
    LoopInfo *LI;
    DominatorTree *DT;
    ScalarEvolution *SE;
    const TargetData *TD;
    const Type *UIntPtrTy;
    bool Changed;

    /// IVUsesByStride - Keep track of all uses of induction variables that we
    /// are interested in.  The key of the map is the stride of the access.
    std::map<SCEVHandle, IVUsersOfOneStride> IVUsesByStride;

    /// IVsByStride - Keep track of all IVs that have been inserted for a
    /// particular stride.
    std::map<SCEVHandle, IVsOfOneStride> IVsByStride;

    /// StrideOrder - An ordering of the keys in IVUsesByStride that is stable:
    /// We use this to iterate over the IVUsesByStride collection without being
    /// dependent on random ordering of pointers in the process.
    SmallVector<SCEVHandle, 16> StrideOrder;

    /// CastedValues - As we need to cast values to uintptr_t, this keeps track
    /// of the casted version of each value.  This is accessed by
    /// getCastedVersionOf.
    DenseMap<Value*, Value*> CastedPointers;

    /// DeadInsts - Keep track of instructions we may have made dead, so that
    /// we can remove them after we are done working.
    SetVector<Instruction*> DeadInsts;

    /// TLI - Keep a pointer of a TargetLowering to consult for determining
    /// transformation profitability.
    const TargetLowering *TLI;

  public:
    static char ID; // Pass ID, replacement for typeid
    explicit LoopStrengthReduce(const TargetLowering *tli = NULL) : 
      LoopPass(&ID), TLI(tli) {
    }

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

    virtual void getAnalysisUsage(AnalysisUsage &AU) const {
      // We split critical edges, so we change the CFG.  However, we do update
      // many analyses if they are around.
      AU.addPreservedID(LoopSimplifyID);
      AU.addPreserved<LoopInfo>();
      AU.addPreserved<DominanceFrontier>();
      AU.addPreserved<DominatorTree>();

      AU.addRequiredID(LoopSimplifyID);
      AU.addRequired<LoopInfo>();
      AU.addRequired<DominatorTree>();
      AU.addRequired<TargetData>();
      AU.addRequired<ScalarEvolution>();
      AU.addPreserved<ScalarEvolution>();
    }
    
    /// getCastedVersionOf - Return the specified value casted to uintptr_t.
    ///
    Value *getCastedVersionOf(Instruction::CastOps opcode, Value *V);
private:
    bool AddUsersIfInteresting(Instruction *I, Loop *L,
                               SmallPtrSet<Instruction*,16> &Processed);
    SCEVHandle GetExpressionSCEV(Instruction *E);
    ICmpInst *ChangeCompareStride(Loop *L, ICmpInst *Cond,
                                  IVStrideUse* &CondUse,
                                  const SCEVHandle* &CondStride);
    void OptimizeIndvars(Loop *L);

    /// OptimizeShadowIV - If IV is used in a int-to-float cast
    /// inside the loop then try to eliminate the cast opeation.
    void OptimizeShadowIV(Loop *L);

    /// OptimizeSMax - Rewrite the loop's terminating condition
    /// if it uses an smax computation.
    ICmpInst *OptimizeSMax(Loop *L, ICmpInst *Cond,
                           IVStrideUse* &CondUse);

    bool FindIVUserForCond(ICmpInst *Cond, IVStrideUse *&CondUse,
                           const SCEVHandle *&CondStride);
    bool RequiresTypeConversion(const Type *Ty, const Type *NewTy);
    unsigned CheckForIVReuse(bool, bool, const SCEVHandle&,
                             IVExpr&, const Type*,
                             const std::vector<BasedUser>& UsersToProcess);
    bool ValidStride(bool, int64_t,
                     const std::vector<BasedUser>& UsersToProcess);
    SCEVHandle CollectIVUsers(const SCEVHandle &Stride,
                              IVUsersOfOneStride &Uses,
                              Loop *L,
                              bool &AllUsesAreAddresses,
                              std::vector<BasedUser> &UsersToProcess);
    void StrengthReduceStridedIVUsers(const SCEVHandle &Stride,
                                      IVUsersOfOneStride &Uses,
                                      Loop *L, bool isOnlyStride);
    void DeleteTriviallyDeadInstructions(SetVector<Instruction*> &Insts);
  };
}

char LoopStrengthReduce::ID = 0;
static RegisterPass<LoopStrengthReduce>
X("loop-reduce", "Loop Strength Reduction");

LoopPass *llvm::createLoopStrengthReducePass(const TargetLowering *TLI) {
  return new LoopStrengthReduce(TLI);
}

/// getCastedVersionOf - Return the specified value casted to uintptr_t. This
/// assumes that the Value* V is of integer or pointer type only.
///
Value *LoopStrengthReduce::getCastedVersionOf(Instruction::CastOps opcode, 
                                              Value *V) {
  if (V->getType() == UIntPtrTy) return V;
  if (Constant *CB = dyn_cast<Constant>(V))
    return ConstantExpr::getCast(opcode, CB, UIntPtrTy);

  Value *&New = CastedPointers[V];
  if (New) return New;
  
  New = SCEVExpander::InsertCastOfTo(opcode, V, UIntPtrTy);
  DeadInsts.insert(cast<Instruction>(New));
  return New;
}


/// 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.
void LoopStrengthReduce::
DeleteTriviallyDeadInstructions(SetVector<Instruction*> &Insts) {
  while (!Insts.empty()) {
    Instruction *I = Insts.back();
    Insts.pop_back();

    if (PHINode *PN = dyn_cast<PHINode>(I)) {
      // If all incoming values to the Phi are the same, we can replace the Phi
      // with that value.
      if (Value *PNV = PN->hasConstantValue()) {
        if (Instruction *U = dyn_cast<Instruction>(PNV))
          Insts.insert(U);
        SE->deleteValueFromRecords(PN);
        PN->replaceAllUsesWith(PNV);
        PN->eraseFromParent();
        Changed = true;
        continue;
      }
    }

    if (isInstructionTriviallyDead(I)) {
      for (User::op_iterator i = I->op_begin(), e = I->op_end(); i != e; ++i)
        if (Instruction *U = dyn_cast<Instruction>(*i))
          Insts.insert(U);
      SE->deleteValueFromRecords(I);
      I->eraseFromParent();
      Changed = true;
    }
  }
}


/// GetExpressionSCEV - Compute and return the SCEV for the specified
/// instruction.
SCEVHandle LoopStrengthReduce::GetExpressionSCEV(Instruction *Exp) {
  // Pointer to pointer bitcast instructions return the same value as their
  // operand.
  if (BitCastInst *BCI = dyn_cast<BitCastInst>(Exp)) {
    if (SE->hasSCEV(BCI) || !isa<Instruction>(BCI->getOperand(0)))
      return SE->getSCEV(BCI);
    SCEVHandle R = GetExpressionSCEV(cast<Instruction>(BCI->getOperand(0)));
    SE->setSCEV(BCI, R);
    return R;
  }

  // Scalar Evolutions doesn't know how to compute SCEV's for GEP instructions.
  // If this is a GEP that SE doesn't know about, compute it now and insert it.
  // If this is not a GEP, or if we have already done this computation, just let
  // SE figure it out.
  GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(Exp);
  if (!GEP || SE->hasSCEV(GEP))
    return SE->getSCEV(Exp);
    
  // Analyze all of the subscripts of this getelementptr instruction, looking
  // for uses that are determined by the trip count of the loop.  First, skip
  // all operands the are not dependent on the IV.

  // Build up the base expression.  Insert an LLVM cast of the pointer to
  // uintptr_t first.
  SCEVHandle GEPVal = SE->getUnknown(
      getCastedVersionOf(Instruction::PtrToInt, GEP->getOperand(0)));

  gep_type_iterator GTI = gep_type_begin(GEP);
  
  for (User::op_iterator i = GEP->op_begin() + 1, e = GEP->op_end();
       i != e; ++i, ++GTI) {
    // If this is a use of a recurrence that we can analyze, and it comes before
    // Op does in the GEP operand list, we will handle this when we process this
    // operand.
    if (const StructType *STy = dyn_cast<StructType>(*GTI)) {
      const StructLayout *SL = TD->getStructLayout(STy);
      unsigned Idx = cast<ConstantInt>(*i)->getZExtValue();
      uint64_t Offset = SL->getElementOffset(Idx);
      GEPVal = SE->getAddExpr(GEPVal,
                             SE->getIntegerSCEV(Offset, UIntPtrTy));
    } else {
      unsigned GEPOpiBits = 
        (*i)->getType()->getPrimitiveSizeInBits();
      unsigned IntPtrBits = UIntPtrTy->getPrimitiveSizeInBits();
      Instruction::CastOps opcode = (GEPOpiBits < IntPtrBits ? 
          Instruction::SExt : (GEPOpiBits > IntPtrBits ? Instruction::Trunc :
            Instruction::BitCast));
      Value *OpVal = getCastedVersionOf(opcode, *i);
      SCEVHandle Idx = SE->getSCEV(OpVal);

      uint64_t TypeSize = TD->getABITypeSize(GTI.getIndexedType());
      if (TypeSize != 1)
        Idx = SE->getMulExpr(Idx,
                            SE->getConstant(ConstantInt::get(UIntPtrTy,
                                                             TypeSize)));
      GEPVal = SE->getAddExpr(GEPVal, Idx);
    }
  }

  SE->setSCEV(GEP, GEPVal);
  return GEPVal;
}

/// getSCEVStartAndStride - Compute the start and stride of this expression,
/// returning false if the expression is not a start/stride pair, or true if it
/// is.  The stride must be a loop invariant expression, but the start may be
/// a mix of loop invariant and loop variant expressions.
static bool getSCEVStartAndStride(const SCEVHandle &SH, Loop *L,
                                  SCEVHandle &Start, SCEVHandle &Stride,
                                  ScalarEvolution *SE) {
  SCEVHandle TheAddRec = Start;   // Initialize to zero.

  // If the outer level is an AddExpr, the operands are all start values except
  // for a nested AddRecExpr.
  if (SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(SH)) {
    for (unsigned i = 0, e = AE->getNumOperands(); i != e; ++i)
      if (SCEVAddRecExpr *AddRec =
             dyn_cast<SCEVAddRecExpr>(AE->getOperand(i))) {
        if (AddRec->getLoop() == L)
          TheAddRec = SE->getAddExpr(AddRec, TheAddRec);
        else
          return false;  // Nested IV of some sort?
      } else {
        Start = SE->getAddExpr(Start, AE->getOperand(i));
      }
        
  } else if (isa<SCEVAddRecExpr>(SH)) {
    TheAddRec = SH;
  } else {
    return false;  // not analyzable.
  }
  
  SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(TheAddRec);
  if (!AddRec || AddRec->getLoop() != L) return false;
  
  // FIXME: Generalize to non-affine IV's.
  if (!AddRec->isAffine()) return false;

  Start = SE->getAddExpr(Start, AddRec->getOperand(0));
  
  if (!isa<SCEVConstant>(AddRec->getOperand(1)))
    DOUT << "[" << L->getHeader()->getName()
         << "] Variable stride: " << *AddRec << "\n";

  Stride = AddRec->getOperand(1);
  return true;
}

/// IVUseShouldUsePostIncValue - We have discovered a "User" of an IV expression
/// and now we need to decide whether the user should use the preinc or post-inc
/// value.  If this user should use the post-inc version of the IV, return true.
///
/// Choosing wrong here can break dominance properties (if we choose to use the
/// post-inc value when we cannot) or it can end up adding extra live-ranges to
/// the loop, resulting in reg-reg copies (if we use the pre-inc value when we
/// should use the post-inc value).
static bool IVUseShouldUsePostIncValue(Instruction *User, Instruction *IV,
                                       Loop *L, DominatorTree *DT, Pass *P,
                                       SetVector<Instruction*> &DeadInsts){
  // If the user is in the loop, use the preinc value.
  if (L->contains(User->getParent())) return false;
  
  BasicBlock *LatchBlock = L->getLoopLatch();
  
  // Ok, the user is outside of the loop.  If it is dominated by the latch
  // block, use the post-inc value.
  if (DT->dominates(LatchBlock, User->getParent()))
    return true;

  // There is one case we have to be careful of: PHI nodes.  These little guys
  // can live in blocks that do not dominate the latch block, but (since their
  // uses occur in the predecessor block, not the block the PHI lives in) should
  // still use the post-inc value.  Check for this case now.
  PHINode *PN = dyn_cast<PHINode>(User);
  if (!PN) return false;  // not a phi, not dominated by latch block.
  
  // Look at all of the uses of IV by the PHI node.  If any use corresponds to
  // a block that is not dominated by the latch block, give up and use the
  // preincremented value.
  unsigned NumUses = 0;
  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
    if (PN->getIncomingValue(i) == IV) {
      ++NumUses;
      if (!DT->dominates(LatchBlock, PN->getIncomingBlock(i)))
        return false;
    }

  // Okay, all uses of IV by PN are in predecessor blocks that really are
  // dominated by the latch block.  Split the critical edges and use the
  // post-incremented value.
  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
    if (PN->getIncomingValue(i) == IV) {
      SplitCriticalEdge(PN->getIncomingBlock(i), PN->getParent(), P, false);
      // Splitting the critical edge can reduce the number of entries in this
      // PHI.
      e = PN->getNumIncomingValues();
      if (--NumUses == 0) break;
    }

  // PHI node might have become a constant value after SplitCriticalEdge.
  DeadInsts.insert(User);
  
  return true;
}

  

/// AddUsersIfInteresting - Inspect the specified instruction.  If it is a
/// reducible SCEV, recursively add its users to the IVUsesByStride set and
/// return true.  Otherwise, return false.
bool LoopStrengthReduce::AddUsersIfInteresting(Instruction *I, Loop *L,
                                      SmallPtrSet<Instruction*,16> &Processed) {
  if (!I->getType()->isInteger() && !isa<PointerType>(I->getType()))
    return false;   // Void and FP expressions cannot be reduced.
  if (!Processed.insert(I))
    return true;    // Instruction already handled.
  
  // Get the symbolic expression for this instruction.
  SCEVHandle ISE = GetExpressionSCEV(I);
  if (isa<SCEVCouldNotCompute>(ISE)) return false;
  
  // Get the start and stride for this expression.
  SCEVHandle Start = SE->getIntegerSCEV(0, ISE->getType());
  SCEVHandle Stride = Start;
  if (!getSCEVStartAndStride(ISE, L, Start, Stride, SE))
    return false;  // Non-reducible symbolic expression, bail out.

  std::vector<Instruction *> IUsers;
  // Collect all I uses now because IVUseShouldUsePostIncValue may 
  // invalidate use_iterator.
  for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); UI != E; ++UI)
    IUsers.push_back(cast<Instruction>(*UI));

  for (unsigned iused_index = 0, iused_size = IUsers.size(); 
       iused_index != iused_size; ++iused_index) {

    Instruction *User = IUsers[iused_index];

    // Do not infinitely recurse on PHI nodes.
    if (isa<PHINode>(User) && Processed.count(User))
      continue;

    // If this is an instruction defined in a nested loop, or outside this loop,
    // don't recurse into it.
    bool AddUserToIVUsers = false;
    if (LI->getLoopFor(User->getParent()) != L) {
      DOUT << "FOUND USER in other loop: " << *User
           << "   OF SCEV: " << *ISE << "\n";
      AddUserToIVUsers = true;
    } else if (!AddUsersIfInteresting(User, L, Processed)) {
      DOUT << "FOUND USER: " << *User
           << "   OF SCEV: " << *ISE << "\n";
      AddUserToIVUsers = true;
    }

    if (AddUserToIVUsers) {
      IVUsersOfOneStride &StrideUses = IVUsesByStride[Stride];
      if (StrideUses.Users.empty())     // First occurance of this stride?
        StrideOrder.push_back(Stride);
      
      // Okay, we found a user that we cannot reduce.  Analyze the instruction
      // and decide what to do with it.  If we are a use inside of the loop, use
      // the value before incrementation, otherwise use it after incrementation.
      if (IVUseShouldUsePostIncValue(User, I, L, DT, this, DeadInsts)) {
        // The value used will be incremented by the stride more than we are
        // expecting, so subtract this off.
        SCEVHandle NewStart = SE->getMinusSCEV(Start, Stride);
        StrideUses.addUser(NewStart, User, I);
        StrideUses.Users.back().isUseOfPostIncrementedValue = true;
        DOUT << "   USING POSTINC SCEV, START=" << *NewStart<< "\n";
      } else {        
        StrideUses.addUser(Start, User, I);
      }
    }
  }
  return true;
}

namespace {
  /// BasedUser - For a particular base value, keep information about how we've
  /// partitioned the expression so far.
  struct BasedUser {
    /// SE - The current ScalarEvolution object.
    ScalarEvolution *SE;

    /// Base - The Base value for the PHI node that needs to be inserted for
    /// this use.  As the use is processed, information gets moved from this
    /// field to the Imm field (below).  BasedUser values are sorted by this
    /// field.
    SCEVHandle Base;
    
    /// Inst - The instruction using the induction variable.
    Instruction *Inst;

    /// OperandValToReplace - The operand value of Inst to replace with the
    /// EmittedBase.
    Value *OperandValToReplace;

    /// Imm - The immediate value that should be added to the base immediately
    /// before Inst, because it will be folded into the imm field of the
    /// instruction.
    SCEVHandle Imm;

    /// EmittedBase - The actual value* to use for the base value of this
    /// operation.  This is null if we should just use zero so far.
    Value *EmittedBase;

    // isUseOfPostIncrementedValue - True if this should use the
    // post-incremented version of this IV, not the preincremented version.
    // This can only be set in special cases, such as the terminating setcc
    // instruction for a loop and uses outside the loop that are dominated by
    // the loop.
    bool isUseOfPostIncrementedValue;
    
    BasedUser(IVStrideUse &IVSU, ScalarEvolution *se)
      : SE(se), Base(IVSU.Offset), Inst(IVSU.User), 
        OperandValToReplace(IVSU.OperandValToReplace), 
        Imm(SE->getIntegerSCEV(0, Base->getType())), EmittedBase(0),
        isUseOfPostIncrementedValue(IVSU.isUseOfPostIncrementedValue) {}

    // Once we rewrite the code to insert the new IVs we want, update the
    // operands of Inst to use the new expression 'NewBase', with 'Imm' added
    // to it.
    void RewriteInstructionToUseNewBase(const SCEVHandle &NewBase,
                                        Instruction *InsertPt,
                                       SCEVExpander &Rewriter, Loop *L, Pass *P,
                                       SetVector<Instruction*> &DeadInsts);
    
    Value *InsertCodeForBaseAtPosition(const SCEVHandle &NewBase, 
                                       SCEVExpander &Rewriter,
                                       Instruction *IP, Loop *L);
    void dump() const;
  };
}

void BasedUser::dump() const {
  cerr << " Base=" << *Base;
  cerr << " Imm=" << *Imm;
  if (EmittedBase)
    cerr << "  EB=" << *EmittedBase;

  cerr << "   Inst: " << *Inst;
}

Value *BasedUser::InsertCodeForBaseAtPosition(const SCEVHandle &NewBase, 
                                              SCEVExpander &Rewriter,
                                              Instruction *IP, Loop *L) {
  // Figure out where we *really* want to insert this code.  In particular, if
  // the user is inside of a loop that is nested inside of L, we really don't
  // want to insert this expression before the user, we'd rather pull it out as
  // many loops as possible.
  LoopInfo &LI = Rewriter.getLoopInfo();
  Instruction *BaseInsertPt = IP;
  
  // Figure out the most-nested loop that IP is in.
  Loop *InsertLoop = LI.getLoopFor(IP->getParent());
  
  // If InsertLoop is not L, and InsertLoop is nested inside of L, figure out
  // the preheader of the outer-most loop where NewBase is not loop invariant.
  while (InsertLoop && NewBase->isLoopInvariant(InsertLoop)) {
    BaseInsertPt = InsertLoop->getLoopPreheader()->getTerminator();
    InsertLoop = InsertLoop->getParentLoop();
  }
  
  // If there is no immediate value, skip the next part.
  if (Imm->isZero())
    return Rewriter.expandCodeFor(NewBase, BaseInsertPt);

  Value *Base = Rewriter.expandCodeFor(NewBase, BaseInsertPt);

  // If we are inserting the base and imm values in the same block, make sure to
  // adjust the IP position if insertion reused a result.
  if (IP == BaseInsertPt)
    IP = Rewriter.getInsertionPoint();
  
  // Always emit the immediate (if non-zero) into the same block as the user.
  SCEVHandle NewValSCEV = SE->getAddExpr(SE->getUnknown(Base), Imm);
  return Rewriter.expandCodeFor(NewValSCEV, IP);
  
}


// Once we rewrite the code to insert the new IVs we want, update the
// operands of Inst to use the new expression 'NewBase', with 'Imm' added
// to it. NewBasePt is the last instruction which contributes to the
// value of NewBase in the case that it's a diffferent instruction from
// the PHI that NewBase is computed from, or null otherwise.
//
void BasedUser::RewriteInstructionToUseNewBase(const SCEVHandle &NewBase,
                                               Instruction *NewBasePt,
                                      SCEVExpander &Rewriter, Loop *L, Pass *P,
                                      SetVector<Instruction*> &DeadInsts) {
  if (!isa<PHINode>(Inst)) {
    // By default, insert code at the user instruction.
    BasicBlock::iterator InsertPt = Inst;
    
    // However, if the Operand is itself an instruction, the (potentially
    // complex) inserted code may be shared by many users.  Because of this, we
    // want to emit code for the computation of the operand right before its old
    // computation.  This is usually safe, because we obviously used to use the
    // computation when it was computed in its current block.  However, in some
    // cases (e.g. use of a post-incremented induction variable) the NewBase
    // value will be pinned to live somewhere after the original computation.
    // In this case, we have to back off.
    if (!isUseOfPostIncrementedValue) {
      if (NewBasePt && isa<PHINode>(OperandValToReplace)) {
        InsertPt = NewBasePt;
        ++InsertPt;
      } else if (Instruction *OpInst
                 = dyn_cast<Instruction>(OperandValToReplace)) {
        InsertPt = OpInst;
        while (isa<PHINode>(InsertPt)) ++InsertPt;
      }
    }
    Value *NewVal = InsertCodeForBaseAtPosition(NewBase, Rewriter, InsertPt, L);
    // Adjust the type back to match the Inst. Note that we can't use InsertPt
    // here because the SCEVExpander may have inserted the instructions after
    // that point, in its efforts to avoid inserting redundant expressions.
    if (isa<PointerType>(OperandValToReplace->getType())) {
      NewVal = SCEVExpander::InsertCastOfTo(Instruction::IntToPtr,
                                            NewVal,
                                            OperandValToReplace->getType());
    }
    // Replace the use of the operand Value with the new Phi we just created.
    Inst->replaceUsesOfWith(OperandValToReplace, NewVal);
    DOUT << "    CHANGED: IMM =" << *Imm;
    DOUT << "  \tNEWBASE =" << *NewBase;
    DOUT << "  \tInst = " << *Inst;
    return;
  }
  
  // PHI nodes are more complex.  We have to insert one copy of the NewBase+Imm
  // expression into each operand block that uses it.  Note that PHI nodes can
  // have multiple entries for the same predecessor.  We use a map to make sure
  // that a PHI node only has a single Value* for each predecessor (which also
  // prevents us from inserting duplicate code in some blocks).
  DenseMap<BasicBlock*, Value*> InsertedCode;
  PHINode *PN = cast<PHINode>(Inst);
  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
    if (PN->getIncomingValue(i) == OperandValToReplace) {
      // If this is a critical edge, split the edge so that we do not insert the
      // code on all predecessor/successor paths.  We do this unless this is the
      // canonical backedge for this loop, as this can make some inserted code
      // be in an illegal position.
      BasicBlock *PHIPred = PN->getIncomingBlock(i);
      if (e != 1 && PHIPred->getTerminator()->getNumSuccessors() > 1 &&
          (PN->getParent() != L->getHeader() || !L->contains(PHIPred))) {
        
        // First step, split the critical edge.
        SplitCriticalEdge(PHIPred, PN->getParent(), P, false);
            
        // Next step: move the basic block.  In particular, if the PHI node
        // is outside of the loop, and PredTI is in the loop, we want to
        // move the block to be immediately before the PHI block, not
        // immediately after PredTI.
        if (L->contains(PHIPred) && !L->contains(PN->getParent())) {
          BasicBlock *NewBB = PN->getIncomingBlock(i);
          NewBB->moveBefore(PN->getParent());
        }
        
        // Splitting the edge can reduce the number of PHI entries we have.
        e = PN->getNumIncomingValues();
      }

      Value *&Code = InsertedCode[PN->getIncomingBlock(i)];
      if (!Code) {
        // Insert the code into the end of the predecessor block.
        Instruction *InsertPt = PN->getIncomingBlock(i)->getTerminator();
        Code = InsertCodeForBaseAtPosition(NewBase, Rewriter, InsertPt, L);

        // Adjust the type back to match the PHI. Note that we can't use
        // InsertPt here because the SCEVExpander may have inserted its
        // instructions after that point, in its efforts to avoid inserting
        // redundant expressions.
        if (isa<PointerType>(PN->getType())) {
          Code = SCEVExpander::InsertCastOfTo(Instruction::IntToPtr,
                                              Code,
                                              PN->getType());
        }
      }
      
      // Replace the use of the operand Value with the new Phi we just created.
      PN->setIncomingValue(i, Code);
      Rewriter.clear();
    }
  }

  // PHI node might have become a constant value after SplitCriticalEdge.
  DeadInsts.insert(Inst);

  DOUT << "    CHANGED: IMM =" << *Imm << "  Inst = " << *Inst;
}


/// isTargetConstant - Return true if the following can be referenced by the
/// immediate field of a target instruction.
static bool isTargetConstant(const SCEVHandle &V, const Type *UseTy,
                             const TargetLowering *TLI) {
  if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
    int64_t VC = SC->getValue()->getSExtValue();
    if (TLI) {
      TargetLowering::AddrMode AM;
      AM.BaseOffs = VC;
      return TLI->isLegalAddressingMode(AM, UseTy);
    } else {
      // Defaults to PPC. PPC allows a sign-extended 16-bit immediate field.
      return (VC > -(1 << 16) && VC < (1 << 16)-1);
    }
  }

  if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V))
    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(SU->getValue()))
      if (TLI && CE->getOpcode() == Instruction::PtrToInt) {
        Constant *Op0 = CE->getOperand(0);
        if (GlobalValue *GV = dyn_cast<GlobalValue>(Op0)) {
          TargetLowering::AddrMode AM;
          AM.BaseGV = GV;
          return TLI->isLegalAddressingMode(AM, UseTy);
        }
      }
  return false;
}

/// MoveLoopVariantsToImediateField - Move any subexpressions from Val that are
/// loop varying to the Imm operand.
static void MoveLoopVariantsToImediateField(SCEVHandle &Val, SCEVHandle &Imm,
                                            Loop *L, ScalarEvolution *SE) {
  if (Val->isLoopInvariant(L)) return;  // Nothing to do.
  
  if (SCEVAddExpr *SAE = dyn_cast<SCEVAddExpr>(Val)) {
    std::vector<SCEVHandle> NewOps;
    NewOps.reserve(SAE->getNumOperands());
    
    for (unsigned i = 0; i != SAE->getNumOperands(); ++i)
      if (!SAE->getOperand(i)->isLoopInvariant(L)) {
        // If this is a loop-variant expression, it must stay in the immediate
        // field of the expression.
        Imm = SE->getAddExpr(Imm, SAE->getOperand(i));
      } else {
        NewOps.push_back(SAE->getOperand(i));
      }

    if (NewOps.empty())
      Val = SE->getIntegerSCEV(0, Val->getType());
    else
      Val = SE->getAddExpr(NewOps);
  } else if (SCEVAddRecExpr *SARE = dyn_cast<SCEVAddRecExpr>(Val)) {
    // Try to pull immediates out of the start value of nested addrec's.
    SCEVHandle Start = SARE->getStart();
    MoveLoopVariantsToImediateField(Start, Imm, L, SE);
    
    std::vector<SCEVHandle> Ops(SARE->op_begin(), SARE->op_end());
    Ops[0] = Start;
    Val = SE->getAddRecExpr(Ops, SARE->getLoop());
  } else {
    // Otherwise, all of Val is variant, move the whole thing over.
    Imm = SE->getAddExpr(Imm, Val);
    Val = SE->getIntegerSCEV(0, Val->getType());
  }
}


/// MoveImmediateValues - Look at Val, and pull out any additions of constants
/// that can fit into the immediate field of instructions in the target.
/// Accumulate these immediate values into the Imm value.
static void MoveImmediateValues(const TargetLowering *TLI,
                                Instruction *User,
                                SCEVHandle &Val, SCEVHandle &Imm,
                                bool isAddress, Loop *L,
                                ScalarEvolution *SE) {
  const Type *UseTy = User->getType();
  if (StoreInst *SI = dyn_cast<StoreInst>(User))
    UseTy = SI->getOperand(0)->getType();

  if (SCEVAddExpr *SAE = dyn_cast<SCEVAddExpr>(Val)) {
    std::vector<SCEVHandle> NewOps;
    NewOps.reserve(SAE->getNumOperands());
    
    for (unsigned i = 0; i != SAE->getNumOperands(); ++i) {
      SCEVHandle NewOp = SAE->getOperand(i);
      MoveImmediateValues(TLI, User, NewOp, Imm, isAddress, L, SE);
      
      if (!NewOp->isLoopInvariant(L)) {
        // If this is a loop-variant expression, it must stay in the immediate
        // field of the expression.
        Imm = SE->getAddExpr(Imm, NewOp);
      } else {
        NewOps.push_back(NewOp);
      }
    }

    if (NewOps.empty())
      Val = SE->getIntegerSCEV(0, Val->getType());
    else
      Val = SE->getAddExpr(NewOps);
    return;
  } else if (SCEVAddRecExpr *SARE = dyn_cast<SCEVAddRecExpr>(Val)) {
    // Try to pull immediates out of the start value of nested addrec's.
    SCEVHandle Start = SARE->getStart();
    MoveImmediateValues(TLI, User, Start, Imm, isAddress, L, SE);
    
    if (Start != SARE->getStart()) {
      std::vector<SCEVHandle> Ops(SARE->op_begin(), SARE->op_end());
      Ops[0] = Start;
      Val = SE->getAddRecExpr(Ops, SARE->getLoop());
    }
    return;
  } else if (SCEVMulExpr *SME = dyn_cast<SCEVMulExpr>(Val)) {
    // Transform "8 * (4 + v)" -> "32 + 8*V" if "32" fits in the immed field.
    if (isAddress && isTargetConstant(SME->getOperand(0), UseTy, TLI) &&
        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 (isTargetConstant(SubImm, UseTy, TLI)) {
          // 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 && isTargetConstant(Val, UseTy, TLI)) ||
      !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);
  }
}


/// RemoveCommonExpressionsFromUseBases - Look through all of the uses in Bases,
/// removing any common subexpressions from it.  Anything truly common is
/// removed, accumulated, and returned.  This looks for things like (a+b+c) and
/// (a+c+d) -> (a+c).  The common expression is *removed* from the Bases.
static SCEVHandle 
RemoveCommonExpressionsFromUseBases(std::vector<BasedUser> &Uses,
                                    ScalarEvolution *SE) {
  unsigned NumUses = Uses.size();

  // Only one use?  Use its base, regardless of what it is!
  SCEVHandle Zero = SE->getIntegerSCEV(0, Uses[0].Base->getType());
  SCEVHandle Result = Zero;
  if (NumUses == 1) {
    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.
  std::map<SCEVHandle, unsigned> SubExpressionUseCounts;
  
  // UniqueSubExprs - Keep track of all of the subexpressions we see in the
  // order we see them.
  std::vector<SCEVHandle> UniqueSubExprs;

  std::vector<SCEVHandle> SubExprs;
  for (unsigned i = 0; i != NumUses; ++i) {
    // 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;

    // Split the expression into subexprs.
    SeparateSubExprs(SubExprs, Uses[i].Base, SE);
    // Add one to SubExpressionUseCounts for each subexpr present.
    for (unsigned j = 0, e = SubExprs.size(); j != e; ++j)
      if (++SubExpressionUseCounts[SubExprs[j]] == 1)
        UniqueSubExprs.push_back(SubExprs[j]);
    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, unsigned>::iterator I = 
       SubExpressionUseCounts.find(UniqueSubExprs[i]);
    assert(I != SubExpressionUseCounts.end() && "Entry not found?");
    if (I->second == NumUses) {  // Found CSE!
      Result = SE->getAddExpr(Result, I->first);
    } else {
      // Remove non-cse's from SubExpressionUseCounts.
      SubExpressionUseCounts.erase(I);
    }
  }
  
  // If we found no CSE's, return now.
  if (Result == Zero) return Result;
  
  // Otherwise, remove all of the CSE's we found from each of the base values.
  for (unsigned i = 0; i != NumUses; ++i) {
    // 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 (SubExpressionUseCounts.count(SubExprs[j])) {
        SubExprs.erase(SubExprs.begin()+j);
        --j; --e;
      }
    
    // Finally, 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 Ty to NewTy is not
/// a nop.
bool LoopStrengthReduce::RequiresTypeConversion(const Type *Ty1,
                                                const Type *Ty2) {
  if (Ty1 == Ty2)
    return false;
  if (TLI && TLI->isTruncateFree(Ty1, Ty2))
    return false;
  return (!Ty1->canLosslesslyBitCastTo(Ty2) &&
          !(isa<PointerType>(Ty2) &&
            Ty1->canLosslesslyBitCastTo(UIntPtrTy)) &&
          !(isa<PointerType>(Ty1) &&
            Ty2->canLosslesslyBitCastTo(UIntPtrTy)));
}

/// 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.
unsigned LoopStrengthReduce::CheckForIVReuse(bool HasBaseReg,
                                bool AllUsesAreAddresses,
                                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()) 
        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 Scale;
          }
    }
  }
  return 0;
}

/// 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();
}

/// isAddress - 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->getOperand(1) == OperandVal)
          isAddress = true;
        break;
    }
  }
  return isAddress;
}

// 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,
                                       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 invariant 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.
    MoveLoopVariantsToImediateField(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);

  // 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;
      }

      // 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;
}

/// 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;

  // 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,
                                          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();
  
  // 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.
  PHINode *NewPHI = NULL;
  Value   *IncV   = NULL;
  IVExpr   ReuseIV(SE->getIntegerSCEV(0, Type::Int32Ty),
                   SE->getIntegerSCEV(0, Type::Int32Ty),
                   0, 0);
  unsigned RewriteFactor = 0;
  RewriteFactor = CheckForIVReuse(HaveCommonExprs, AllUsesAreAddresses,
                                  Stride, ReuseIV, CommonExprs->getType(),
                                  UsersToProcess);
  if (RewriteFactor != 0) {
    DOUT << "BASED ON IV of STRIDE " << *ReuseIV.Stride
         << " and BASE " << *ReuseIV.Base << " :\n";
    NewPHI = ReuseIV.PHI;
    IncV   = ReuseIV.IncV;
  }

  const Type *ReplacedTy = CommonExprs->getType();
  
  // Now that we know what we need to do, insert the PHI node itself.
  //
  DOUT << "INSERTING IV of TYPE " << *ReplacedTy << " of STRIDE "
       << *Stride << " and BASE " << *CommonExprs << ": ";

  SCEVExpander Rewriter(*SE, *LI);
  SCEVExpander PreheaderRewriter(*SE, *LI);
  
  BasicBlock  *Preheader = L->getLoopPreheader();
  Instruction *PreInsertPt = Preheader->getTerminator();
  Instruction *PhiInsertBefore = L->getHeader()->begin();
  
  BasicBlock *LatchBlock = L->getLoopLatch();


  // Emit the initial base value into the loop preheader.
  Value *CommonBaseV
    = PreheaderRewriter.expandCodeFor(CommonExprs, PreInsertPt);

  if (RewriteFactor == 0) {
    // Create a new Phi for this base, and stick it in the loop header.
    NewPHI = PHINode::Create(ReplacedTy, "iv.", PhiInsertBefore);
    ++NumInserted;
  
    // Add common base to the new Phi node.
    NewPHI->addIncoming(CommonBaseV, Preheader);

    // If the stride is negative, insert a sub instead of an add for the
    // increment.
    bool isNegative = isNonConstantNegative(Stride);
    SCEVHandle IncAmount = Stride;
    if (isNegative)
      IncAmount = SE->getNegativeSCEV(Stride);
    
    // Insert the stride into the preheader.
    Value *StrideV = PreheaderRewriter.expandCodeFor(IncAmount, PreInsertPt);
    if (!isa<ConstantInt>(StrideV)) ++NumVariable;

    // Emit the increment of the base value before the terminator of the loop
    // latch block, and add it to the Phi node.
    SCEVHandle IncExp = SE->getUnknown(StrideV);
    if (isNegative)
      IncExp = SE->getNegativeSCEV(IncExp);
    IncExp = SE->getAddExpr(SE->getUnknown(NewPHI), IncExp);
  
    IncV = Rewriter.expandCodeFor(IncExp, LatchBlock->getTerminator());
    IncV->setName(NewPHI->getName()+".inc");
    NewPHI->addIncoming(IncV, LatchBlock);

    // Remember this in case a later stride is multiple of this.
    IVsByStride[Stride].addIV(Stride, CommonExprs, NewPHI, IncV);
    
    DOUT << " IV=%" << NewPHI->getNameStr() << " INC=%" << IncV->getNameStr();
  } else {
    Constant *C = dyn_cast<Constant>(CommonBaseV);
    if (!C ||
        (!C->isNullValue() &&
         !isTargetConstant(SE->getUnknown(CommonBaseV), ReplacedTy, TLI)))
      // 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);
  }
  DOUT << "\n";

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

  // Process all the users now.  This outer loop handles all bases, the inner
  // loop handles all users of a particular base.
  while (!UsersToProcess.empty()) {
    SCEVHandle Base = UsersToProcess.back().Base;

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

    DOUT << "  INSERTING code for BASE = " << *Base << ":";
    if (BaseV->hasName())
      DOUT << " Result value name = %" << BaseV->getNameStr();
    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() && !isTargetConstant(Base, ReplacedTy, TLI)) {
        // 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();

      // 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 = NewPHI;
      if (User.isUseOfPostIncrementedValue) {
        RewriteOp = 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 instrutions 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 == NewPHI) 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 take advantage of addressing mode scale component.
      if (RewriteFactor != 0) {
        RewriteExpr = SE->getMulExpr(SE->getIntegerSCEV(RewriteFactor,
                                                        RewriteExpr->getType()),
                                     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.
        if (!isa<ConstantInt>(CommonBaseV) ||
            !cast<ConstantInt>(CommonBaseV)->isZero())
          RewriteExpr = SE->getAddExpr(RewriteExpr,
                                      SE->getUnknown(CommonBaseV));
      }

      // 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 elminated
      // if we just replaced the last use of that value.
      DeadInsts.insert(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
        // occurs enough in real life to handle.
        CondUse = &*UI;
        CondStride = &SI->first;
        return true;
      }
  }
  return false;
}    

namespace {
  // Constant strides come first which in turns are sorted by their absolute
  // values. If absolute values are the same, then positive strides comes first.
  // e.g.
  // 4, -1, X, 1, 2 ==> 1, -1, 2, 4, X
  struct StrideCompare {
    bool operator()(const SCEVHandle &LHS, const SCEVHandle &RHS) {
      SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS);
      SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS);
      if (LHSC && RHSC) {
        int64_t  LV = LHSC->getValue()->getSExtValue();
        int64_t  RV = RHSC->getValue()->getSExtValue();
        uint64_t ALV = (LV < 0) ? -LV : LV;
        uint64_t ARV = (RV < 0) ? -RV : RV;
        if (ALV == ARV)
          return LV > RV;
        else
          return ALV < ARV;
      }
      return (LHSC && !RHSC);
    }
  };
}

/// ChangeCompareStride - If a loop termination compare instruction is the
/// only use of its stride, and the compaison is against a constant value,
/// try eliminate the stride by moving the compare instruction to another
/// stride and change its constant operand accordingly. e.g.
///
/// loop:
/// ...
/// v1 = v1 + 3
/// v2 = v2 + 1
/// if (v2 < 10) goto loop
/// =>
/// loop:
/// ...
/// v1 = v1 + 3
/// if (v1 < 30) goto loop
ICmpInst *LoopStrengthReduce::ChangeCompareStride(Loop *L, ICmpInst *Cond,
                                                IVStrideUse* &CondUse,
                                                const SCEVHandle* &CondStride) {
  if (StrideOrder.size() < 2 ||
      IVUsesByStride[*CondStride].Users.size() != 1)
    return Cond;
  const SCEVConstant *SC = dyn_cast<SCEVConstant>(*CondStride);
  if (!SC) return Cond;
  ConstantInt *C = dyn_cast<ConstantInt>(Cond->getOperand(1));
  if (!C) return Cond;

  ICmpInst::Predicate Predicate = Cond->getPredicate();
  int64_t CmpSSInt = SC->getValue()->getSExtValue();
  int64_t CmpVal = C->getValue().getSExtValue();
  unsigned BitWidth = C->getValue().getBitWidth();
  uint64_t SignBit = 1ULL << (BitWidth-1);
  const Type *CmpTy = C->getType();
  const Type *NewCmpTy = NULL;
  unsigned TyBits = CmpTy->getPrimitiveSizeInBits();
  unsigned NewTyBits = 0;
  int64_t NewCmpVal = CmpVal;
  SCEVHandle *NewStride = NULL;
  Value *NewIncV = NULL;
  int64_t Scale = 1;

  // Check stride constant and the comparision constant signs to detect
  // overflow.
  if ((CmpVal & SignBit) != (CmpSSInt & SignBit))
    return Cond;

  // Look for a suitable stride / iv as replacement.
  std::stable_sort(StrideOrder.begin(), StrideOrder.end(), StrideCompare());
  for (unsigned i = 0, e = StrideOrder.size(); i != e; ++i) {
    std::map<SCEVHandle, IVUsersOfOneStride>::iterator SI = 
      IVUsesByStride.find(StrideOrder[i]);
    if (!isa<SCEVConstant>(SI->first))
      continue;
    int64_t SSInt = cast<SCEVConstant>(SI->first)->getValue()->getSExtValue();
    if (abs(SSInt) <= abs(CmpSSInt) || (SSInt % CmpSSInt) != 0)
      continue;

    Scale = SSInt / CmpSSInt;
    NewCmpVal = CmpVal * Scale;
    APInt Mul = APInt(BitWidth, NewCmpVal);
    // Check for overflow.
    if (Mul.getSExtValue() != NewCmpVal) {
      NewCmpVal = CmpVal;
      continue;
    }

    // Watch out for overflow.
    if (ICmpInst::isSignedPredicate(Predicate) &&
        (CmpVal & SignBit) != (NewCmpVal & SignBit))
      NewCmpVal = CmpVal;

    if (NewCmpVal != CmpVal) {
      // Pick the best iv to use trying to avoid a cast.
      NewIncV = NULL;
      for (std::vector<IVStrideUse>::iterator UI = SI->second.Users.begin(),
             E = SI->second.Users.end(); UI != E; ++UI) {
        NewIncV = UI->OperandValToReplace;
        if (NewIncV->getType() == CmpTy)
          break;
      }
      if (!NewIncV) {
        NewCmpVal = CmpVal;
        continue;
      }

      NewCmpTy = NewIncV->getType();
      NewTyBits = isa<PointerType>(NewCmpTy)
        ? UIntPtrTy->getPrimitiveSizeInBits()
        : NewCmpTy->getPrimitiveSizeInBits();
      if (RequiresTypeConversion(NewCmpTy, CmpTy)) {
        // Check if it is possible to rewrite it using
        // an iv / stride of a smaller integer type.
        bool TruncOk = false;
        if (NewCmpTy->isInteger()) {
          unsigned Bits = NewTyBits;
          if (ICmpInst::isSignedPredicate(Predicate))
            --Bits;
          uint64_t Mask = (1ULL << Bits) - 1;
          if (((uint64_t)NewCmpVal & Mask) == (uint64_t)NewCmpVal)
            TruncOk = true;
        }
        if (!TruncOk) {
          NewCmpVal = CmpVal;
          continue;
        }
      }

      // Don't rewrite if use offset is non-constant and the new type is
      // of a different type.
      // FIXME: too conservative?
      if (NewTyBits != TyBits && !isa<SCEVConstant>(CondUse->Offset)) {
        NewCmpVal = CmpVal;
        continue;
      }

      bool AllUsesAreAddresses = true;
      std::vector<BasedUser> UsersToProcess;
      SCEVHandle CommonExprs = CollectIVUsers(SI->first, SI->second, L,
                                              AllUsesAreAddresses,
                                              UsersToProcess);
      // Avoid rewriting the compare instruction with an iv of new stride
      // if it's likely the new stride uses will be rewritten using the
      if (AllUsesAreAddresses &&
          ValidStride(!CommonExprs->isZero(), Scale, UsersToProcess)) {
        NewCmpVal = CmpVal;
        continue;
      }

      // If scale is negative, use swapped predicate unless it's testing
      // for equality.
      if (Scale < 0 && !Cond->isEquality())
        Predicate = ICmpInst::getSwappedPredicate(Predicate);

      NewStride = &StrideOrder[i];
      break;
    }
  }

  // Forgo this transformation if it the increment happens to be
  // unfortunately positioned after the condition, and the condition
  // has multiple uses which prevent it from being moved immediately
  // before the branch. See
  // test/Transforms/LoopStrengthReduce/change-compare-stride-trickiness-*.ll
  // for an example of this situation.
  if (!Cond->hasOneUse()) {
    for (BasicBlock::iterator I = Cond, E = Cond->getParent()->end();
         I != E; ++I)
      if (I == NewIncV)
        return Cond;
  }

  if (NewCmpVal != CmpVal) {
    // Create a new compare instruction using new stride / iv.
    ICmpInst *OldCond = Cond;
    Value *RHS;
    if (!isa<PointerType>(NewCmpTy))
      RHS = ConstantInt::get(NewCmpTy, NewCmpVal);
    else {
      RHS = ConstantInt::get(UIntPtrTy, NewCmpVal);
      RHS = SCEVExpander::InsertCastOfTo(Instruction::IntToPtr, RHS, NewCmpTy);
    }
    // Insert new compare instruction.
    Cond = new ICmpInst(Predicate, NewIncV, RHS,
                        L->getHeader()->getName() + ".termcond",
                        OldCond);

    // Remove the old compare instruction. The old indvar is probably dead too.
    DeadInsts.insert(cast<Instruction>(CondUse->OperandValToReplace));
    SE->deleteValueFromRecords(OldCond);
    OldCond->replaceAllUsesWith(Cond);
    OldCond->eraseFromParent();

    IVUsesByStride[*CondStride].Users.pop_back();
    SCEVHandle NewOffset = TyBits == NewTyBits
      ? SE->getMulExpr(CondUse->Offset,
                       SE->getConstant(ConstantInt::get(CmpTy, Scale)))
      : SE->getConstant(ConstantInt::get(NewCmpTy,
        cast<SCEVConstant>(CondUse->Offset)->getValue()->getSExtValue()*Scale));
    IVUsesByStride[*NewStride].addUser(NewOffset, Cond, NewIncV);
    CondUse = &IVUsesByStride[*NewStride].Users.back();
    CondStride = NewStride;
    ++NumEliminated;
  }

  return Cond;
}

/// OptimizeSMax - Rewrite the loop's terminating condition if it uses
/// an smax computation.
///
/// This is a narrow solution to a specific, but acute, problem. For loops
/// like this:
///
///   i = 0;
///   do {
///     p[i] = 0.0;
///   } while (++i < n);
///
/// where the comparison is signed, the trip count isn't just 'n', because
/// 'n' could be negative. And unfortunately this can come up even for loops
/// where the user didn't use a C do-while loop. For example, seemingly
/// well-behaved top-test loops will commonly be lowered like this:
//
///   if (n > 0) {
///     i = 0;
///     do {
///       p[i] = 0.0;
///     } while (++i < n);
///   }
///
/// and then it's possible for subsequent optimization to obscure the if
/// test in such a way that indvars can't find it.
///
/// When indvars can't find the if test in loops like this, it creates a
/// signed-max expression, which allows it to give the loop a canonical
/// induction variable:
///
///   i = 0;
///   smax = n < 1 ? 1 : n;
///   do {
///     p[i] = 0.0;
///   } while (++i != smax);
///
/// Canonical induction variables are necessary because the loop passes
/// are designed around them. The most obvious example of this is the
/// LoopInfo analysis, which doesn't remember trip count values. It
/// expects to be able to rediscover the trip count each time it is
/// needed, and it does this using a simple analyis that only succeeds if
/// the loop has a canonical induction variable.
///
/// However, when it comes time to generate code, the maximum operation
/// can be quite costly, especially if it's inside of an outer loop.
///
/// This function solves this problem by detecting this type of loop and
/// rewriting their conditions from ICMP_NE back to ICMP_SLT, and deleting
/// the instructions for the maximum computation.
///
ICmpInst *LoopStrengthReduce::OptimizeSMax(Loop *L, ICmpInst *Cond,
                                           IVStrideUse* &CondUse) {
  // Check that the loop matches the pattern we're looking for.
  if (Cond->getPredicate() != CmpInst::ICMP_EQ &&
      Cond->getPredicate() != CmpInst::ICMP_NE)
    return Cond;

  SelectInst *Sel = dyn_cast<SelectInst>(Cond->getOperand(1));
  if (!Sel || !Sel->hasOneUse()) return Cond;

  SCEVHandle IterationCount = SE->getIterationCount(L);
  if (isa<SCEVCouldNotCompute>(IterationCount))
    return Cond;
  SCEVHandle One = SE->getIntegerSCEV(1, IterationCount->getType());

  // Adjust for an annoying getIterationCount quirk.
  IterationCount = SE->getAddExpr(IterationCount, One);

  // Check for a max calculation that matches the pattern.
  SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(IterationCount);
  if (!SMax || SMax != SE->getSCEV(Sel)) return Cond;

  SCEVHandle SMaxLHS = SMax->getOperand(0);
  SCEVHandle SMaxRHS = SMax->getOperand(1);
  if (!SMaxLHS || SMaxLHS != One) return Cond;

  // Check the relevant induction variable for conformance to
  // the pattern.
  SCEVHandle IV = SE->getSCEV(Cond->getOperand(0));
  SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(IV);
  if (!AR || !AR->isAffine() ||
      AR->getStart() != One ||
      AR->getStepRecurrence(*SE) != One)
    return Cond;

  // Check the right operand of the select, and remember it, as it will
  // be used in the new comparison instruction.
  Value *NewRHS = 0;
  if (SE->getSCEV(Sel->getOperand(1)) == SMaxRHS)
    NewRHS = Sel->getOperand(1);
  else if (SE->getSCEV(Sel->getOperand(2)) == SMaxRHS)
    NewRHS = Sel->getOperand(2);
  if (!NewRHS) return Cond;

  // Ok, everything looks ok to change the condition into an SLT or SGE and
  // delete the max calculation.
  ICmpInst *NewCond =
    new ICmpInst(Cond->getPredicate() == CmpInst::ICMP_NE ?
                   CmpInst::ICMP_SLT :
                   CmpInst::ICMP_SGE,
                 Cond->getOperand(0), NewRHS, "scmp", Cond);

  // Delete the max calculation instructions.
  Cond->replaceAllUsesWith(NewCond);
  Cond->eraseFromParent();
  SE->deleteValueFromRecords(Cond);
  Instruction *Cmp = cast<Instruction>(Sel->getOperand(0));
  Sel->eraseFromParent();
  SE->deleteValueFromRecords(Sel);
  if (Cmp->use_empty()) {
    Cmp->eraseFromParent();
    SE->deleteValueFromRecords(Cmp);
  }
  CondUse->User = NewCond;
  return NewCond;
}

/// OptimizeShadowIV - If IV is used in a int-to-float cast
/// inside the loop then try to eliminate the cast opeation.
void LoopStrengthReduce::OptimizeShadowIV(Loop *L) {

  SCEVHandle IterationCount = SE->getIterationCount(L);
  if (isa<SCEVCouldNotCompute>(IterationCount))
    return;

  for (unsigned Stride = 0, e = StrideOrder.size(); Stride != e;
       ++Stride) {
    std::map<SCEVHandle, IVUsersOfOneStride>::iterator SI = 
      IVUsesByStride.find(StrideOrder[Stride]);
    assert(SI != IVUsesByStride.end() && "Stride doesn't exist!");
    if (!isa<SCEVConstant>(SI->first))
      continue;

    for (std::vector<IVStrideUse>::iterator UI = SI->second.Users.begin(),
           E = SI->second.Users.end(); UI != E; /* empty */) {
      std::vector<IVStrideUse>::iterator CandidateUI = UI;
      ++UI;
      Instruction *ShadowUse = CandidateUI->User;
      const Type *DestTy = NULL;

      /* If shadow use is a int->float cast then insert a second IV
         to eliminate this cast.

           for (unsigned i = 0; i < n; ++i) 
             foo((double)i);

         is transformed into

           double d = 0.0;
           for (unsigned i = 0; i < n; ++i, ++d) 
             foo(d);
      */
      if (UIToFPInst *UCast = dyn_cast<UIToFPInst>(CandidateUI->User))
        DestTy = UCast->getDestTy();
      else if (SIToFPInst *SCast = dyn_cast<SIToFPInst>(CandidateUI->User))
        DestTy = SCast->getDestTy();
      if (!DestTy) continue;

      if (TLI) {
        /* If target does not support DestTy natively then do not apply
           this transformation. */
        MVT DVT = TLI->getValueType(DestTy);
        if (!TLI->isTypeLegal(DVT)) continue;
      }

      PHINode *PH = dyn_cast<PHINode>(ShadowUse->getOperand(0));
      if (!PH) continue;
      if (PH->getNumIncomingValues() != 2) continue;

      const Type *SrcTy = PH->getType();
      int Mantissa = DestTy->getFPMantissaWidth();
      if (Mantissa == -1) continue; 
      if ((int)TD->getTypeSizeInBits(SrcTy) > Mantissa)
        continue;

      unsigned Entry, Latch;
      if (PH->getIncomingBlock(0) == L->getLoopPreheader()) {
        Entry = 0;
        Latch = 1;
      } else {
        Entry = 1;
        Latch = 0;
      }
        
      ConstantInt *Init = dyn_cast<ConstantInt>(PH->getIncomingValue(Entry));
      if (!Init) continue;
      ConstantFP *NewInit = ConstantFP::get(DestTy, Init->getZExtValue());

      BinaryOperator *Incr = 
        dyn_cast<BinaryOperator>(PH->getIncomingValue(Latch));
      if (!Incr) continue;
      if (Incr->getOpcode() != Instruction::Add
          && Incr->getOpcode() != Instruction::Sub)
        continue;

      /* Initialize new IV, double d = 0.0 in above example. */
      ConstantInt *C = NULL;
      if (Incr->getOperand(0) == PH)
        C = dyn_cast<ConstantInt>(Incr->getOperand(1));
      else if (Incr->getOperand(1) == PH)
        C = dyn_cast<ConstantInt>(Incr->getOperand(0));
      else
        continue;

      if (!C) continue;

      /* Add new PHINode. */
      PHINode *NewPH = PHINode::Create(DestTy, "IV.S.", PH);

      /* create new increment. '++d' in above example. */
      ConstantFP *CFP = ConstantFP::get(DestTy, C->getZExtValue());
      BinaryOperator *NewIncr = 
        BinaryOperator::Create(Incr->getOpcode(),
                               NewPH, CFP, "IV.S.next.", Incr);

      NewPH->addIncoming(NewInit, PH->getIncomingBlock(Entry));
      NewPH->addIncoming(NewIncr, PH->getIncomingBlock(Latch));

      /* Remove cast operation */
      SE->deleteValueFromRecords(ShadowUse);
      ShadowUse->replaceAllUsesWith(NewPH);
      ShadowUse->eraseFromParent();
      SI->second.Users.erase(CandidateUI);
      NumShadow++;
      break;
    }
  }
}

// OptimizeIndvars - Now that IVUsesByStride is set up with all of the indvar
// uses in the loop, look to see if we can eliminate some, in favor of using
// common indvars for the different uses.
void LoopStrengthReduce::OptimizeIndvars(Loop *L) {
  // TODO: implement optzns here.

  OptimizeShadowIV(L);

  // Finally, get the terminating condition for the loop if possible.  If we
  // can, we want to change it to use a post-incremented version of its
  // induction variable, to allow coalescing the live ranges for the IV into
  // one register value.
  PHINode *SomePHI = cast<PHINode>(L->getHeader()->begin());
  BasicBlock  *Preheader = L->getLoopPreheader();
  BasicBlock *LatchBlock =
   SomePHI->getIncomingBlock(SomePHI->getIncomingBlock(0) == Preheader);
  BranchInst *TermBr = dyn_cast<BranchInst>(LatchBlock->getTerminator());
  if (!TermBr || TermBr->isUnconditional() || 
      !isa<ICmpInst>(TermBr->getCondition()))
    return;
  ICmpInst *Cond = cast<ICmpInst>(TermBr->getCondition());

  // Search IVUsesByStride to find Cond's IVUse if there is one.
  IVStrideUse *CondUse = 0;
  const SCEVHandle *CondStride = 0;

  if (!FindIVUserForCond(Cond, CondUse, CondStride))
    return; // setcc doesn't use the IV.

  // If the trip count is computed in terms of an smax (due to ScalarEvolution
  // being unable to find a sufficient guard, for example), change the loop
  // comparison to use SLT instead of NE.
  Cond = OptimizeSMax(L, Cond, CondUse);

  // If possible, change stride and operands of the compare instruction to
  // eliminate one stride.
  Cond = ChangeCompareStride(L, Cond, CondUse, CondStride);

  // It's possible for the setcc instruction to be anywhere in the loop, and
  // possible for it to have multiple users.  If it is not immediately before
  // the latch block branch, move it.
  if (&*++BasicBlock::iterator(Cond) != (Instruction*)TermBr) {
    if (Cond->hasOneUse()) {   // Condition has a single use, just move it.
      Cond->moveBefore(TermBr);
    } else {
      // Otherwise, clone the terminating condition and insert into the loopend.
      Cond = cast<ICmpInst>(Cond->clone());
      Cond->setName(L->getHeader()->getName() + ".termcond");
      LatchBlock->getInstList().insert(TermBr, Cond);
      
      // Clone the IVUse, as the old use still exists!
      IVUsesByStride[*CondStride].addUser(CondUse->Offset, Cond,
                                         CondUse->OperandValToReplace);
      CondUse = &IVUsesByStride[*CondStride].Users.back();
    }
  }

  // If we get to here, we know that we can transform the setcc instruction to
  // use the post-incremented version of the IV, allowing us to coalesce the
  // live ranges for the IV correctly.
  CondUse->Offset = SE->getMinusSCEV(CondUse->Offset, *CondStride);
  CondUse->isUseOfPostIncrementedValue = true;
  Changed = true;
}

bool LoopStrengthReduce::runOnLoop(Loop *L, LPPassManager &LPM) {

  LI = &getAnalysis<LoopInfo>();
  DT = &getAnalysis<DominatorTree>();
  SE = &getAnalysis<ScalarEvolution>();
  TD = &getAnalysis<TargetData>();
  UIntPtrTy = TD->getIntPtrType();
  Changed = false;

  // Find all uses of induction variables in this loop, and catagorize
  // them by stride.  Start by finding all of the PHI nodes in the header for
  // this loop.  If they are induction variables, inspect their uses.
  SmallPtrSet<Instruction*,16> Processed;   // Don't reprocess instructions.
  for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I)
    AddUsersIfInteresting(I, L, Processed);

  if (!IVUsesByStride.empty()) {
    // Optimize induction variables.  Some indvar uses can be transformed to use
    // strides that will be needed for other purposes.  A common example of this
    // is the exit test for the loop, which can often be rewritten to use the
    // computation of some other indvar to decide when to terminate the loop.
    OptimizeIndvars(L);

    // FIXME: We can widen subreg IV's here for RISC targets.  e.g. instead of
    // doing computation in byte values, promote to 32-bit values if safe.

    // FIXME: Attempt to reuse values across multiple IV's.  In particular, we
    // could have something like "for(i) { foo(i*8); bar(i*16) }", which should
    // be codegened as "for (j = 0;; j+=8) { foo(j); bar(j+j); }" on X86/PPC.
    // Need to be careful that IV's are all the same type.  Only works for
    // intptr_t indvars.

    // If we only have one stride, we can more aggressively eliminate some
    // things.
    bool HasOneStride = IVUsesByStride.size() == 1;

#ifndef NDEBUG
    DOUT << "\nLSR on ";
    DEBUG(L->dump());
#endif

    // IVsByStride keeps IVs for one particular loop.
    assert(IVsByStride.empty() && "Stale entries in IVsByStride?");

    // Sort the StrideOrder so we process larger strides first.
    std::stable_sort(StrideOrder.begin(), StrideOrder.end(), StrideCompare());

    // Note: this processes each stride/type pair individually.  All users
    // passed into StrengthReduceStridedIVUsers have the same type AND stride.
    // Also, note that we iterate over IVUsesByStride indirectly by using
    // StrideOrder. This extra layer of indirection makes the ordering of
    // strides deterministic - not dependent on map order.
    for (unsigned Stride = 0, e = StrideOrder.size(); Stride != e; ++Stride) {
      std::map<SCEVHandle, IVUsersOfOneStride>::iterator SI = 
        IVUsesByStride.find(StrideOrder[Stride]);
      assert(SI != IVUsesByStride.end() && "Stride doesn't exist!");
      StrengthReduceStridedIVUsers(SI->first, SI->second, L, HasOneStride);
    }
  }

  // We're done analyzing this loop; release all the state we built up for it.
  CastedPointers.clear();
  IVUsesByStride.clear();
  IVsByStride.clear();
  StrideOrder.clear();

  // Clean up after ourselves
  if (!DeadInsts.empty()) {
    DeleteTriviallyDeadInstructions(DeadInsts);

    BasicBlock::iterator I = L->getHeader()->begin();
    while (PHINode *PN = dyn_cast<PHINode>(I++)) {
      // At this point, we know that we have killed one or more IV users.
      // It is worth checking to see if the cann indvar is also
      // dead, so that we can remove it as well.
      //
      // We can remove a PHI if it is on a cycle in the def-use graph
      // where each node in the cycle has degree one, i.e. only one use,
      // and is an instruction with no side effects.
      //
      // FIXME: this needs to eliminate an induction variable even if it's being
      // compared against some value to decide loop termination.
      if (PN->hasOneUse()) {
        SmallPtrSet<PHINode *, 2> PHIs;
        for (Instruction *J = dyn_cast<Instruction>(*PN->use_begin());
             J && J->hasOneUse() && !J->mayWriteToMemory();
             J = dyn_cast<Instruction>(*J->use_begin())) {
          // If we find the original PHI, we've discovered a cycle.
          if (J == PN) {
            // Break the cycle and mark the PHI for deletion.
            SE->deleteValueFromRecords(PN);
            PN->replaceAllUsesWith(UndefValue::get(PN->getType()));
            DeadInsts.insert(PN);
            Changed = true;
            break;
          }
          // If we find a PHI more than once, we're on a cycle that
          // won't prove fruitful.
          if (isa<PHINode>(J) && !PHIs.insert(cast<PHINode>(J)))
            break;
        }
      }
    }
    DeleteTriviallyDeadInstructions(DeadInsts);
  }
  return Changed;
}