LoopStrengthReduce.cpp

//===- LoopStrengthReduce.cpp - Strength Reduce IVs in Loops --------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This pass performs a strength reduction on array references inside loops that
// have as one or more of their components the loop induction variable.
//
//===----------------------------------------------------------------------===//

#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/Transforms/Utils/AddrModeMatcher.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Target/TargetLowering.h"
#include <algorithm>
using namespace llvm;

STATISTIC(NumReduced ,    "Number of IV uses 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");
STATISTIC(NumImmSunk,     "Number of common expr immediates sunk into uses");

static cl::opt<bool> EnableFullLSRMode("enable-full-lsr",
                                       cl::init(false),
                                       cl::Hidden);

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;

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

  /// 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) {
      IVs.push_back(IVExpr(Stride, Base, PHI));
    }
  };

  class VISIBILITY_HIDDEN LoopStrengthReduce : public LoopPass {
    LoopInfo *LI;
    DominatorTree *DT;
    ScalarEvolution *SE;
    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;

    /// DeadInsts - Keep track of instructions we may have made dead, so that
    /// we can remove them after we are done working.
    SmallVector<Instruction*, 16> 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<ScalarEvolution>();
      AU.addPreserved<ScalarEvolution>();
    }

  private:
    bool AddUsersIfInteresting(Instruction *I, Loop *L,
                               SmallPtrSet<Instruction*,16> &Processed);
    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);
    SCEVHandle CheckForIVReuse(bool, 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,
                              bool &AllUsesAreOutsideLoop,
                              std::vector<BasedUser> &UsersToProcess);
    bool ShouldUseFullStrengthReductionMode(
                                const std::vector<BasedUser> &UsersToProcess,
                                const Loop *L,
                                bool AllUsesAreAddresses,
                                SCEVHandle Stride);
    void PrepareToStrengthReduceFully(
                             std::vector<BasedUser> &UsersToProcess,
                             SCEVHandle Stride,
                             SCEVHandle CommonExprs,
                             const Loop *L,
                             SCEVExpander &PreheaderRewriter);
    void PrepareToStrengthReduceFromSmallerStride(
                                         std::vector<BasedUser> &UsersToProcess,
                                         Value *CommonBaseV,
                                         const IVExpr &ReuseIV,
                                         Instruction *PreInsertPt);
    void PrepareToStrengthReduceWithNewPhi(
                                  std::vector<BasedUser> &UsersToProcess,
                                  SCEVHandle Stride,
                                  SCEVHandle CommonExprs,
                                  Value *CommonBaseV,
                                  const Loop *L,
                                  SCEVExpander &PreheaderRewriter);
    void StrengthReduceStridedIVUsers(const SCEVHandle &Stride,
                                      IVUsersOfOneStride &Uses,
                                      Loop *L);
    void DeleteTriviallyDeadInstructions();
  };
}

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

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

/// 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() {
  if (DeadInsts.empty()) return;
  
  // Sort the deadinsts list so that we can trivially eliminate duplicates as we
  // go.  The code below never adds a non-dead instruction to the worklist, but
  // callers may not be so careful.
  array_pod_sort(DeadInsts.begin(), DeadInsts.end());

  // Drop duplicate instructions and those with uses.
  for (unsigned i = 0, e = DeadInsts.size()-1; i < e; ++i) {
    Instruction *I = DeadInsts[i];
    if (!I->use_empty()) DeadInsts[i] = 0;
    while (i != e && DeadInsts[i+1] == I)
      DeadInsts[++i] = 0;
  }
  
  while (!DeadInsts.empty()) {
    Instruction *I = DeadInsts.back();
    DeadInsts.pop_back();
    
    if (I == 0 || !isInstructionTriviallyDead(I))
      continue;

    SE->deleteValueFromRecords(I);

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

/// containsAddRecFromDifferentLoop - Determine whether expression S involves a 
/// subexpression that is an AddRec from a loop other than L.  An outer loop 
/// of L is OK, but not an inner loop nor a disjoint loop.
static bool containsAddRecFromDifferentLoop(SCEVHandle S, Loop *L) {
  // This is very common, put it first.
  if (isa<SCEVConstant>(S))
    return false;
  if (const SCEVCommutativeExpr *AE = dyn_cast<SCEVCommutativeExpr>(S)) {
    for (unsigned int i=0; i< AE->getNumOperands(); i++)
      if (containsAddRecFromDifferentLoop(AE->getOperand(i), L))
        return true;
    return false;
  }
  if (const SCEVAddRecExpr *AE = dyn_cast<SCEVAddRecExpr>(S)) {
    if (const Loop *newLoop = AE->getLoop()) {
      if (newLoop == L)
        return false;
      // if newLoop is an outer loop of L, this is OK.
      if (!LoopInfoBase<BasicBlock>::isNotAlreadyContainedIn(L, newLoop))
        return false;
    }
    return true;
  }
  if (const SCEVUDivExpr *DE = dyn_cast<SCEVUDivExpr>(S))
    return containsAddRecFromDifferentLoop(DE->getLHS(), L) ||
           containsAddRecFromDifferentLoop(DE->getRHS(), L);
#if 0
  // SCEVSDivExpr has been backed out temporarily, but will be back; we'll 
  // need this when it is.
  if (const SCEVSDivExpr *DE = dyn_cast<SCEVSDivExpr>(S))
    return containsAddRecFromDifferentLoop(DE->getLHS(), L) ||
           containsAddRecFromDifferentLoop(DE->getRHS(), L);
#endif
  if (const SCEVCastExpr *CE = dyn_cast<SCEVCastExpr>(S))
    return containsAddRecFromDifferentLoop(CE->getOperand(), L);
  return false;
}

/// 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.  The start cannot,
/// however, contain an AddRec from a different loop, unless that loop is an
/// outer loop of the current loop.
static bool getSCEVStartAndStride(const SCEVHandle &SH, Loop *L,
                                  SCEVHandle &Start, SCEVHandle &Stride,
                                  ScalarEvolution *SE, DominatorTree *DT) {
  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 (const 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.
  }
  
  const 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;

  // If Start contains an SCEVAddRecExpr from a different loop, other than an
  // outer loop of the current loop, reject it.  SCEV has no concept of 
  // operating on more than one loop at a time so don't confuse it with such
  // expressions.
  if (containsAddRecFromDifferentLoop(AddRec->getOperand(0), L))
    return false;

  Start = SE->getAddExpr(Start, AddRec->getOperand(0));
  
  if (!isa<SCEVConstant>(AddRec->getOperand(1))) {
    // If stride is an instruction, make sure it dominates the loop preheader.
    // Otherwise we could end up with a use before def situation.
    BasicBlock *Preheader = L->getLoopPreheader();
    if (!AddRec->getOperand(1)->dominates(Preheader, DT))
      return false;

    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,
                                      SmallVectorImpl<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.  Use the post-incremented value.
  return true;
}

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

/// getAccessType - Return the type of the memory being accessed.
static const Type *getAccessType(const Instruction *Inst) {
  const Type *UseTy = Inst->getType();
  if (const StoreInst *SI = dyn_cast<StoreInst>(Inst))
    UseTy = SI->getOperand(0)->getType();
  else if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(Inst)) {
    // Addressing modes can also be folded into prefetches and a variety
    // of intrinsics.
    switch (II->getIntrinsicID()) {
    default: break;
    case Intrinsic::x86_sse_storeu_ps:
    case Intrinsic::x86_sse2_storeu_pd:
    case Intrinsic::x86_sse2_storeu_dq:
    case Intrinsic::x86_sse2_storel_dq:
      UseTy = II->getOperand(1)->getType();
      break;
    }
  }
  return UseTy;
}

/// 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 (!SE->isSCEVable(I->getType()))
    return false;   // Void and FP expressions cannot be reduced.

  // LSR is not APInt clean, do not touch integers bigger than 64-bits.
  if (SE->getTypeSizeInBits(I->getType()) > 64)
    return false;
  
  if (!Processed.insert(I))
    return true;    // Instruction already handled.
  
  // Get the symbolic expression for this instruction.
  SCEVHandle ISE = SE->getSCEV(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, DT))
    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;

    // Descend recursively, but not into PHI nodes outside the current loop.
    // It's important to see the entire expression outside the loop to get
    // choices that depend on addressing mode use right, although we won't
    // consider references ouside the loop in all cases.
    // If User is already in Processed, we don't want to recurse into it again,
    // but do want to record a second reference in the same instruction.
    bool AddUserToIVUsers = false;
    if (LI->getLoopFor(User->getParent()) != L) {
      if (isa<PHINode>(User) || Processed.count(User) ||
          !AddUsersIfInteresting(User, L, Processed)) {
        DOUT << "FOUND USER in other loop: " << *User
             << "   OF SCEV: " << *ISE << "\n";
        AddUserToIVUsers = true;
      }
    } else if (Processed.count(User) || 
               !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 occurrence 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.  This is also sometimes used for loop-variant values that
    /// must be added inside the loop.
    SCEVHandle Imm;

    /// Phi - The induction variable that performs the striding that
    /// should be used for this user.
    PHINode *Phi;

    // 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())), 
        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,
                                      SmallVectorImpl<Instruction*> &DeadInsts);
    
    Value *InsertCodeForBaseAtPosition(const SCEVHandle &NewBase, 
                                       const Type *Ty,
                                       SCEVExpander &Rewriter,
                                       Instruction *IP, Loop *L);
    void dump() const;
  };
}

void BasedUser::dump() const {
  cerr << " Base=" << *Base;
  cerr << " Imm=" << *Imm;
  cerr << "   Inst: " << *Inst;
}

Value *BasedUser::InsertCodeForBaseAtPosition(const SCEVHandle &NewBase, 
                                              const Type *Ty,
                                              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.
  if (L->contains(IP->getParent()))
    while (InsertLoop && NewBase->isLoopInvariant(InsertLoop)) {
      BaseInsertPt = InsertLoop->getLoopPreheader()->getTerminator();
      InsertLoop = InsertLoop->getParentLoop();
    }
  
  Value *Base = Rewriter.expandCodeFor(NewBase, Ty, BaseInsertPt);

  // If there is no immediate value, skip the next part.
  if (Imm->isZero())
    return Base;

  // 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, Ty, 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,
                                      SmallVectorImpl<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 this is a use outside the loop (which means after, since it is based
    // on a loop indvar) we use the post-incremented value, so that we don't
    // artificially make the preinc value live out the bottom of the loop. 
    if (!isUseOfPostIncrementedValue && L->contains(Inst->getParent())) {
      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,
                                                OperandValToReplace->getType(),
                                                Rewriter, InsertPt, L);
    // Replace the use of the operand Value with the new Phi we just created.
    Inst->replaceUsesOfWith(OperandValToReplace, NewVal);

    DOUT << "      Replacing with ";
    DEBUG(WriteAsOperand(*DOUT, NewVal, /*PrintType=*/false));
    DOUT << ", which has value " << *NewBase << " plus IMM " << *Imm << "\n";
    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 the original expression is outside the loop, put the replacement
      // code in the same place as the original expression,
      // which need not be an immediate predecessor of this PHI.  This way we 
      // need only one copy of it even if it is referenced multiple times in
      // the PHI.  We don't do this when the original expression is inside the
      // loop because multiple copies sometimes do useful sinking of code in
      // that case(?).
      Instruction *OldLoc = dyn_cast<Instruction>(OperandValToReplace);
      if (L->contains(OldLoc->getParent())) {
        // 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 = (L->contains(OldLoc->getParent())) ?
                                PN->getIncomingBlock(i)->getTerminator() :
                                OldLoc->getParent()->getTerminator();
        Code = InsertCodeForBaseAtPosition(NewBase, PN->getType(),
                                           Rewriter, InsertPt, L);

        DOUT << "      Changing PHI use to ";
        DEBUG(WriteAsOperand(*DOUT, Code, /*PrintType=*/false));
        DOUT << ", which has value " << *NewBase << " plus IMM " << *Imm << "\n";
      }

      // 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.push_back(Inst);
}


/// fitsInAddressMode - Return true if V can be subsumed within an addressing
/// mode, and does not need to be put in a register first.
static bool fitsInAddressMode(const SCEVHandle &V, const Type *UseTy,
                             const TargetLowering *TLI, bool HasBaseReg) {
  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
    int64_t VC = SC->getValue()->getSExtValue();
    if (TLI) {
      TargetLowering::AddrMode AM;
      AM.BaseOffs = VC;
      AM.HasBaseReg = HasBaseReg;
      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 (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V))
    if (GlobalValue *GV = dyn_cast<GlobalValue>(SU->getValue())) {
      if (TLI) {
        TargetLowering::AddrMode AM;
        AM.BaseGV = GV;
        AM.HasBaseReg = HasBaseReg;
        return TLI->isLegalAddressingMode(AM, UseTy);
      } else {
        // Default: assume global addresses are not legal.
      }
    }

  return false;
}

/// MoveLoopVariantsToImmediateField - Move any subexpressions from Val that are
/// loop varying to the Imm operand.
static void MoveLoopVariantsToImmediateField(SCEVHandle &Val, SCEVHandle &Imm,
                                            Loop *L, ScalarEvolution *SE) {
  if (Val->isLoopInvariant(L)) return;  // Nothing to do.
  
  if (const 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 (const SCEVAddRecExpr *SARE = dyn_cast<SCEVAddRecExpr>(Val)) {
    // Try to pull immediates out of the start value of nested addrec's.
    SCEVHandle Start = SARE->getStart();
    MoveLoopVariantsToImmediateField(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,
                                const Type *UseTy,
                                SCEVHandle &Val, SCEVHandle &Imm,
                                bool isAddress, Loop *L,
                                ScalarEvolution *SE) {
  if (const 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, UseTy, 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 (const 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, UseTy, 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 (const SCEVMulExpr *SME = dyn_cast<SCEVMulExpr>(Val)) {
    // Transform "8 * (4 + v)" -> "32 + 8*V" if "32" fits in the immed field.
    if (isAddress && fitsInAddressMode(SME->getOperand(0), UseTy, TLI, false) &&
        SME->getNumOperands() == 2 && SME->isLoopInvariant(L)) {

      SCEVHandle SubImm = SE->getIntegerSCEV(0, Val->getType());
      SCEVHandle NewOp = SME->getOperand(1);
      MoveImmediateValues(TLI, UseTy, 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.
}

static void MoveImmediateValues(const TargetLowering *TLI,
                                Instruction *User,
                                SCEVHandle &Val, SCEVHandle &Imm,
                                bool isAddress, Loop *L,
                                ScalarEvolution *SE) {
  const Type *UseTy = getAccessType(User);
  MoveImmediateValues(TLI, UseTy, Val, Imm, isAddress, L, SE);
}

/// 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 (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(Expr)) {
    for (unsigned j = 0, e = AE->getNumOperands(); j != e; ++j)
      SeparateSubExprs(SubExprs, AE->getOperand(j), SE);
  } else if (const 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