lib/Transforms/Scalar/IndVarSimplify.cpp

//===- IndVarSimplify.cpp - Induction Variable Elimination ----------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This transformation analyzes and transforms the induction variables (and
// computations derived from them) into simpler forms suitable for subsequent
// analysis and transformation.
//
// This transformation makes the following changes to each loop with an
// identifiable induction variable:
//   1. All loops are transformed to have a SINGLE canonical induction variable
//      which starts at zero and steps by one.
//   2. The canonical induction variable is guaranteed to be the first PHI node
//      in the loop header block.
//   3. Any pointer arithmetic recurrences are raised to use array subscripts.
//
// If the trip count of a loop is computable, this pass also makes the following
// changes:
//   1. The exit condition for the loop is canonicalized to compare the
//      induction value against the exit value.  This turns loops like:
//        'for (i = 7; i*i < 1000; ++i)' into 'for (i = 0; i != 25; ++i)'
//   2. Any use outside of the loop of an expression derived from the indvar
//      is changed to compute the derived value outside of the loop, eliminating
//      the dependence on the exit value of the induction variable.  If the only
//      purpose of the loop is to compute the exit value of some derived
//      expression, this transformation will make the loop dead.
//
// This transformation should be followed by strength reduction after all of the
// desired loop transformations have been performed.  Additionally, on targets
// where it is profitable, the loop could be transformed to count down to zero
// (the "do loop" optimization).
//
//===----------------------------------------------------------------------===//

#define DEBUG_TYPE "indvars"
#include "llvm/Transforms/Scalar.h"
#include "llvm/BasicBlock.h"
#include "llvm/Constants.h"
#include "llvm/Instructions.h"
#include "llvm/Type.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/GetElementPtrTypeIterator.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/Statistic.h"
using namespace llvm;

STATISTIC(NumRemoved , "Number of aux indvars removed");
STATISTIC(NumPointer , "Number of pointer indvars promoted");
STATISTIC(NumInserted, "Number of canonical indvars added");
STATISTIC(NumReplaced, "Number of exit values replaced");
STATISTIC(NumLFTR    , "Number of loop exit tests replaced");

namespace {
  class VISIBILITY_HIDDEN IndVarSimplify : public LoopPass {
    LoopInfo        *LI;
    ScalarEvolution *SE;
    bool Changed;
  public:

   static char ID; // Pass identification, replacement for typeid
   IndVarSimplify() : LoopPass(&ID) {}

   bool runOnLoop(Loop *L, LPPassManager &LPM);
   bool doInitialization(Loop *L, LPPassManager &LPM);
   virtual void getAnalysisUsage(AnalysisUsage &AU) const {
     AU.addRequired<ScalarEvolution>();
     AU.addRequiredID(LCSSAID);
     AU.addRequiredID(LoopSimplifyID);
     AU.addRequired<LoopInfo>();
     AU.addPreservedID(LoopSimplifyID);
     AU.addPreservedID(LCSSAID);
     AU.setPreservesCFG();
   }

  private:

    void EliminatePointerRecurrence(PHINode *PN, BasicBlock *Preheader,
                                    SmallPtrSet<Instruction*, 16> &DeadInsts);
    void LinearFunctionTestReplace(Loop *L, SCEVHandle IterationCount, Value *IndVar,
                                   BasicBlock *ExitingBlock,
                                   BranchInst *BI,
                                   SCEVExpander &Rewriter);
    void RewriteLoopExitValues(Loop *L, SCEV *IterationCount);

    void DeleteTriviallyDeadInstructions(SmallPtrSet<Instruction*, 16> &Insts);

    void HandleFloatingPointIV(Loop *L, PHINode *PH, 
                               SmallPtrSet<Instruction*, 16> &DeadInsts);
  };
}

char IndVarSimplify::ID = 0;
static RegisterPass<IndVarSimplify>
X("indvars", "Canonicalize Induction Variables");

Pass *llvm::createIndVarSimplifyPass() {
  return new IndVarSimplify();
}

/// 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 IndVarSimplify::
DeleteTriviallyDeadInstructions(SmallPtrSet<Instruction*, 16> &Insts) {
  while (!Insts.empty()) {
    Instruction *I = *Insts.begin();
    Insts.erase(I);
    if (isInstructionTriviallyDead(I)) {
      for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i)
        if (Instruction *U = dyn_cast<Instruction>(I->getOperand(i)))
          Insts.insert(U);
      SE->deleteValueFromRecords(I);
      DOUT << "INDVARS: Deleting: " << *I;
      I->eraseFromParent();
      Changed = true;
    }
  }
}


/// EliminatePointerRecurrence - Check to see if this is a trivial GEP pointer
/// recurrence.  If so, change it into an integer recurrence, permitting
/// analysis by the SCEV routines.
void IndVarSimplify::EliminatePointerRecurrence(PHINode *PN,
                                                BasicBlock *Preheader,
                                     SmallPtrSet<Instruction*, 16> &DeadInsts) {
  assert(PN->getNumIncomingValues() == 2 && "Noncanonicalized loop!");
  unsigned PreheaderIdx = PN->getBasicBlockIndex(Preheader);
  unsigned BackedgeIdx = PreheaderIdx^1;
  if (GetElementPtrInst *GEPI =
          dyn_cast<GetElementPtrInst>(PN->getIncomingValue(BackedgeIdx)))
    if (GEPI->getOperand(0) == PN) {
      assert(GEPI->getNumOperands() == 2 && "GEP types must match!");
      DOUT << "INDVARS: Eliminating pointer recurrence: " << *GEPI;
      
      // Okay, we found a pointer recurrence.  Transform this pointer
      // recurrence into an integer recurrence.  Compute the value that gets
      // added to the pointer at every iteration.
      Value *AddedVal = GEPI->getOperand(1);

      // Insert a new integer PHI node into the top of the block.
      PHINode *NewPhi = PHINode::Create(AddedVal->getType(),
                                        PN->getName()+".rec", PN);
      NewPhi->addIncoming(Constant::getNullValue(NewPhi->getType()), Preheader);

      // Create the new add instruction.
      Value *NewAdd = BinaryOperator::CreateAdd(NewPhi, AddedVal,
                                                GEPI->getName()+".rec", GEPI);
      NewPhi->addIncoming(NewAdd, PN->getIncomingBlock(BackedgeIdx));

      // Update the existing GEP to use the recurrence.
      GEPI->setOperand(0, PN->getIncomingValue(PreheaderIdx));

      // Update the GEP to use the new recurrence we just inserted.
      GEPI->setOperand(1, NewAdd);

      // If the incoming value is a constant expr GEP, try peeling out the array
      // 0 index if possible to make things simpler.
      if (ConstantExpr *CE = dyn_cast<ConstantExpr>(GEPI->getOperand(0)))
        if (CE->getOpcode() == Instruction::GetElementPtr) {
          unsigned NumOps = CE->getNumOperands();
          assert(NumOps > 1 && "CE folding didn't work!");
          if (CE->getOperand(NumOps-1)->isNullValue()) {
            // Check to make sure the last index really is an array index.
            gep_type_iterator GTI = gep_type_begin(CE);
            for (unsigned i = 1, e = CE->getNumOperands()-1;
                 i != e; ++i, ++GTI)
              /*empty*/;
            if (isa<SequentialType>(*GTI)) {
              // Pull the last index out of the constant expr GEP.
              SmallVector<Value*, 8> CEIdxs(CE->op_begin()+1, CE->op_end()-1);
              Constant *NCE = ConstantExpr::getGetElementPtr(CE->getOperand(0),
                                                             &CEIdxs[0],
                                                             CEIdxs.size());
              Value *Idx[2];
              Idx[0] = Constant::getNullValue(Type::Int32Ty);
              Idx[1] = NewAdd;
              GetElementPtrInst *NGEPI = GetElementPtrInst::Create(
                  NCE, Idx, Idx + 2, 
                  GEPI->getName(), GEPI);
              SE->deleteValueFromRecords(GEPI);
              GEPI->replaceAllUsesWith(NGEPI);
              GEPI->eraseFromParent();
              GEPI = NGEPI;
            }
          }
        }


      // Finally, if there are any other users of the PHI node, we must
      // insert a new GEP instruction that uses the pre-incremented version
      // of the induction amount.
      if (!PN->use_empty()) {
        BasicBlock::iterator InsertPos = PN; ++InsertPos;
        while (isa<PHINode>(InsertPos)) ++InsertPos;
        Value *PreInc =
          GetElementPtrInst::Create(PN->getIncomingValue(PreheaderIdx),
                                    NewPhi, "", InsertPos);
        PreInc->takeName(PN);
        PN->replaceAllUsesWith(PreInc);
      }

      // Delete the old PHI for sure, and the GEP if its otherwise unused.
      DeadInsts.insert(PN);

      ++NumPointer;
      Changed = true;
    }
}

/// LinearFunctionTestReplace - This method rewrites the exit condition of the
/// loop to be a canonical != comparison against the incremented loop induction
/// variable.  This pass is able to rewrite the exit tests of any loop where the
/// SCEV analysis can determine a loop-invariant trip count of the loop, which
/// is actually a much broader range than just linear tests.
void IndVarSimplify::LinearFunctionTestReplace(Loop *L,
                                   SCEVHandle IterationCount,
                                   Value *IndVar,
                                   BasicBlock *ExitingBlock,
                                   BranchInst *BI,
                                   SCEVExpander &Rewriter) {
  // If the exiting block is not the same as the backedge block, we must compare
  // against the preincremented value, otherwise we prefer to compare against
  // the post-incremented value.
  Value *CmpIndVar;
  if (ExitingBlock == L->getLoopLatch()) {
    // What ScalarEvolution calls the "iteration count" is actually the
    // number of times the branch is taken. Add one to get the number
    // of times the branch is executed. If this addition may overflow,
    // we have to be more pessimistic and cast the induction variable
    // before doing the add.
    SCEVHandle Zero = SE->getIntegerSCEV(0, IterationCount->getType());
    SCEVHandle N =
      SE->getAddExpr(IterationCount,
                     SE->getIntegerSCEV(1, IterationCount->getType()));
    if ((isa<SCEVConstant>(N) && !N->isZero()) ||
        SE->isLoopGuardedByCond(L, ICmpInst::ICMP_NE, N, Zero)) {
      // No overflow. Cast the sum.
      IterationCount = SE->getTruncateOrZeroExtend(N, IndVar->getType());
    } else {
      // Potential overflow. Cast before doing the add.
      IterationCount = SE->getTruncateOrZeroExtend(IterationCount,
                                                   IndVar->getType());
      IterationCount =
        SE->getAddExpr(IterationCount,
                       SE->getIntegerSCEV(1, IndVar->getType()));
    }

    // The IterationCount expression contains the number of times that the
    // backedge actually branches to the loop header.  This is one less than the
    // number of times the loop executes, so add one to it.
    CmpIndVar = L->getCanonicalInductionVariableIncrement();
  } else {
    // We have to use the preincremented value...
    IterationCount = SE->getTruncateOrZeroExtend(IterationCount,
                                                 IndVar->getType());
    CmpIndVar = IndVar;
  }

  // Expand the code for the iteration count into the preheader of the loop.
  BasicBlock *Preheader = L->getLoopPreheader();
  Value *ExitCnt = Rewriter.expandCodeFor(IterationCount,
                                          Preheader->getTerminator());

  // Insert a new icmp_ne or icmp_eq instruction before the branch.
  ICmpInst::Predicate Opcode;
  if (L->contains(BI->getSuccessor(0)))
    Opcode = ICmpInst::ICMP_NE;
  else
    Opcode = ICmpInst::ICMP_EQ;

  DOUT << "INDVARS: Rewriting loop exit condition to:\n"
       << "      LHS:" << *CmpIndVar // includes a newline
       << "       op:\t"
       << (Opcode == ICmpInst::ICMP_NE ? "!=" : "=") << "\n"
       << "      RHS:\t" << *IterationCount << "\n";

  Value *Cond = new ICmpInst(Opcode, CmpIndVar, ExitCnt, "exitcond", BI);
  BI->setCondition(Cond);
  ++NumLFTR;
  Changed = true;
}

/// RewriteLoopExitValues - Check to see if this loop has a computable
/// loop-invariant execution count.  If so, this means that we can compute the
/// final value of any expressions that are recurrent in the loop, and
/// substitute the exit values from the loop into any instructions outside of
/// the loop that use the final values of the current expressions.
void IndVarSimplify::RewriteLoopExitValues(Loop *L, SCEV *IterationCount) {
  BasicBlock *Preheader = L->getLoopPreheader();

  // Scan all of the instructions in the loop, looking at those that have
  // extra-loop users and which are recurrences.
  SCEVExpander Rewriter(*SE, *LI);

  // We insert the code into the preheader of the loop if the loop contains
  // multiple exit blocks, or in the exit block if there is exactly one.
  BasicBlock *BlockToInsertInto;
  SmallVector<BasicBlock*, 8> ExitBlocks;
  L->getUniqueExitBlocks(ExitBlocks);
  if (ExitBlocks.size() == 1)
    BlockToInsertInto = ExitBlocks[0];
  else
    BlockToInsertInto = Preheader;
  BasicBlock::iterator InsertPt = BlockToInsertInto->getFirstNonPHI();

  bool HasConstantItCount = isa<SCEVConstant>(IterationCount);

  SmallPtrSet<Instruction*, 16> InstructionsToDelete;
  std::map<Instruction*, Value*> ExitValues;

  // Find all values that are computed inside the loop, but used outside of it.
  // Because of LCSSA, these values will only occur in LCSSA PHI Nodes.  Scan
  // the exit blocks of the loop to find them.
  for (unsigned i = 0, e = ExitBlocks.size(); i != e; ++i) {
    BasicBlock *ExitBB = ExitBlocks[i];
    
    // If there are no PHI nodes in this exit block, then no values defined
    // inside the loop are used on this path, skip it.
    PHINode *PN = dyn_cast<PHINode>(ExitBB->begin());
    if (!PN) continue;
    
    unsigned NumPreds = PN->getNumIncomingValues();
    
    // Iterate over all of the PHI nodes.
    BasicBlock::iterator BBI = ExitBB->begin();
    while ((PN = dyn_cast<PHINode>(BBI++))) {
      
      // Iterate over all of the values in all the PHI nodes.
      for (unsigned i = 0; i != NumPreds; ++i) {
        // If the value being merged in is not integer or is not defined
        // in the loop, skip it.
        Value *InVal = PN->getIncomingValue(i);
        if (!isa<Instruction>(InVal) ||
            // SCEV only supports integer expressions for now.
            !isa<IntegerType>(InVal->getType()))
          continue;

        // If this pred is for a subloop, not L itself, skip it.
        if (LI->getLoopFor(PN->getIncomingBlock(i)) != L) 
          continue; // The Block is in a subloop, skip it.

        // Check that InVal is defined in the loop.
        Instruction *Inst = cast<Instruction>(InVal);
        if (!L->contains(Inst->getParent()))
          continue;
        
        // We require that this value either have a computable evolution or that
        // the loop have a constant iteration count.  In the case where the loop
        // has a constant iteration count, we can sometimes force evaluation of
        // the exit value through brute force.
        SCEVHandle SH = SE->getSCEV(Inst);
        if (!SH->hasComputableLoopEvolution(L) && !HasConstantItCount)
          continue;          // Cannot get exit evolution for the loop value.
        
        // Okay, this instruction has a user outside of the current loop
        // and varies predictably *inside* the loop.  Evaluate the value it
        // contains when the loop exits, if possible.
        SCEVHandle ExitValue = SE->getSCEVAtScope(Inst, L->getParentLoop());
        if (isa<SCEVCouldNotCompute>(ExitValue) ||
            !ExitValue->isLoopInvariant(L))
          continue;

        Changed = true;
        ++NumReplaced;
        
        // See if we already computed the exit value for the instruction, if so,
        // just reuse it.
        Value *&ExitVal = ExitValues[Inst];
        if (!ExitVal)
          ExitVal = Rewriter.expandCodeFor(ExitValue, InsertPt);
        
        DOUT << "INDVARS: RLEV: AfterLoopVal = " << *ExitVal
             << "  LoopVal = " << *Inst << "\n";

        PN->setIncomingValue(i, ExitVal);
        
        // If this instruction is dead now, schedule it to be removed.
        if (Inst->use_empty())
          InstructionsToDelete.insert(Inst);
        
        // See if this is a single-entry LCSSA PHI node.  If so, we can (and
        // have to) remove
        // the PHI entirely.  This is safe, because the NewVal won't be variant
        // in the loop, so we don't need an LCSSA phi node anymore.
        if (NumPreds == 1) {
          SE->deleteValueFromRecords(PN);
          PN->replaceAllUsesWith(ExitVal);
          PN->eraseFromParent();
          break;
        }
      }
    }
  }
  
  DeleteTriviallyDeadInstructions(InstructionsToDelete);
}

bool IndVarSimplify::doInitialization(Loop *L, LPPassManager &LPM) {

  Changed = false;
  // First step.  Check to see if there are any trivial GEP pointer recurrences.
  // If there are, change them into integer recurrences, permitting analysis by
  // the SCEV routines.
  //
  BasicBlock *Header    = L->getHeader();
  BasicBlock *Preheader = L->getLoopPreheader();
  SE = &LPM.getAnalysis<ScalarEvolution>();

  SmallPtrSet<Instruction*, 16> DeadInsts;
  for (BasicBlock::iterator I = Header->begin(); isa<PHINode>(I); ++I) {
    PHINode *PN = cast<PHINode>(I);
    if (isa<PointerType>(PN->getType()))
      EliminatePointerRecurrence(PN, Preheader, DeadInsts);
    else
      HandleFloatingPointIV(L, PN, DeadInsts);
  }

  if (!DeadInsts.empty())
    DeleteTriviallyDeadInstructions(DeadInsts);

  return Changed;
}

/// getEffectiveIndvarType - Determine the widest type that the
/// induction-variable PHINode Phi is cast to.
///
static const Type *getEffectiveIndvarType(const PHINode *Phi) {
  const Type *Ty = Phi->getType();

  for (Value::use_const_iterator UI = Phi->use_begin(), UE = Phi->use_end();
       UI != UE; ++UI) {
    const Type *CandidateType = NULL;
    if (const ZExtInst *ZI = dyn_cast<ZExtInst>(UI))
      CandidateType = ZI->getDestTy();
    else if (const SExtInst *SI = dyn_cast<SExtInst>(UI))
      CandidateType = SI->getDestTy();
    if (CandidateType &&
        CandidateType->getPrimitiveSizeInBits() >
          Ty->getPrimitiveSizeInBits())
      Ty = CandidateType;
  }

  return Ty;
}

/// isOrigIVAlwaysNonNegative - Analyze the original induction variable
/// in the loop to determine whether it would ever have a negative
/// value.
///
/// TODO: This duplicates a fair amount of ScalarEvolution logic.
/// Perhaps this can be merged with ScalarEvolution::getIterationCount.
///
static bool isOrigIVAlwaysNonNegative(const Loop *L,
                                      const Instruction *OrigCond) {
  // Verify that the loop is sane and find the exit condition.
  const ICmpInst *Cmp = dyn_cast<ICmpInst>(OrigCond);
  if (!Cmp) return false;

  // For now, analyze only SLT loops for signed overflow.
  if (Cmp->getPredicate() != ICmpInst::ICMP_SLT) return false;

  // Get the increment instruction. Look past SExtInsts if we will
  // be able to prove that the original induction variable doesn't
  // undergo signed overflow.
  const Value *OrigIncrVal = Cmp->getOperand(0);
  const Value *IncrVal = OrigIncrVal;
  if (SExtInst *SI = dyn_cast<SExtInst>(Cmp->getOperand(0))) {
    if (!isa<ConstantInt>(Cmp->getOperand(1)) ||
        !cast<ConstantInt>(Cmp->getOperand(1))->getValue()
          .isSignedIntN(IncrVal->getType()->getPrimitiveSizeInBits()))
      return false;
    IncrVal = SI->getOperand(0);
  }

  // For now, only analyze induction variables that have simple increments.
  const BinaryOperator *IncrOp = dyn_cast<BinaryOperator>(IncrVal);
  if (!IncrOp ||
      IncrOp->getOpcode() != Instruction::Add ||
      !isa<ConstantInt>(IncrOp->getOperand(1)) ||
      !cast<ConstantInt>(IncrOp->getOperand(1))->equalsInt(1))
    return false;

  // Make sure the PHI looks like a normal IV.
  const PHINode *PN = dyn_cast<PHINode>(IncrOp->getOperand(0));
  if (!PN || PN->getNumIncomingValues() != 2)
    return false;
  unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
  unsigned BackEdge = !IncomingEdge;
  if (!L->contains(PN->getIncomingBlock(BackEdge)) ||
      PN->getIncomingValue(BackEdge) != IncrOp)
    return false;

  // For now, only analyze loops with a constant start value, so that
  // we can easily determine if the start value is non-negative and
  // not a maximum value which would wrap on the first iteration.
  const Value *InitialVal = PN->getIncomingValue(IncomingEdge);
  if (!isa<ConstantInt>(InitialVal) ||
      cast<ConstantInt>(InitialVal)->getValue().isNegative() ||
      cast<ConstantInt>(InitialVal)->getValue().isMaxSignedValue())
    return false;

  // The original induction variable will start at some non-negative
  // non-max value, it counts up by one, and the loop iterates only
  // while it remans less than (signed) some value in the same type.
  // As such, it will always be non-negative.
  return true;
}

bool IndVarSimplify::runOnLoop(Loop *L, LPPassManager &LPM) {
  LI = &getAnalysis<LoopInfo>();
  SE = &getAnalysis<ScalarEvolution>();

  Changed = false;
  BasicBlock *Header       = L->getHeader();
  BasicBlock *ExitingBlock = L->getExitingBlock();
  SmallPtrSet<Instruction*, 16> DeadInsts;

  // Verify the input to the pass in already in LCSSA form.
  assert(L->isLCSSAForm());

  // Check to see if this loop has a computable loop-invariant execution count.
  // If so, this means that we can compute the final value of any expressions
  // that are recurrent in the loop, and substitute the exit values from the
  // loop into any instructions outside of the loop that use the final values of
  // the current expressions.
  //
  SCEVHandle IterationCount = SE->getIterationCount(L);
  if (!isa<SCEVCouldNotCompute>(IterationCount))
    RewriteLoopExitValues(L, IterationCount);

  // Next, analyze all of the induction variables in the loop, canonicalizing
  // auxillary induction variables.
  std::vector<std::pair<PHINode*, SCEVHandle> > IndVars;

  for (BasicBlock::iterator I = Header->begin(); isa<PHINode>(I); ++I) {
    PHINode *PN = cast<PHINode>(I);
    if (PN->getType()->isInteger()) { // FIXME: when we have fast-math, enable!
      SCEVHandle SCEV = SE->getSCEV(PN);
      if (SCEV->hasComputableLoopEvolution(L))
        // FIXME: It is an extremely bad idea to indvar substitute anything more
        // complex than affine induction variables.  Doing so will put expensive
        // polynomial evaluations inside of the loop, and the str reduction pass
        // currently can only reduce affine polynomials.  For now just disable
        // indvar subst on anything more complex than an affine addrec.
        if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SCEV))
          if (AR->isAffine())
            IndVars.push_back(std::make_pair(PN, SCEV));
    }
  }

  // Compute the type of the largest recurrence expression, and collect
  // the set of the types of the other recurrence expressions.
  const Type *LargestType = 0;
  SmallSetVector<const Type *, 4> SizesToInsert;
  if (!isa<SCEVCouldNotCompute>(IterationCount)) {
    LargestType = IterationCount->getType();
    SizesToInsert.insert(IterationCount->getType());
  }
  for (unsigned i = 0, e = IndVars.size(); i != e; ++i) {
    const PHINode *PN = IndVars[i].first;
    SizesToInsert.insert(PN->getType());
    const Type *EffTy = getEffectiveIndvarType(PN);
    SizesToInsert.insert(EffTy);
    if (!LargestType ||
        EffTy->getPrimitiveSizeInBits() >
          LargestType->getPrimitiveSizeInBits())
      LargestType = EffTy;
  }

  // Create a rewriter object which we'll use to transform the code with.
  SCEVExpander Rewriter(*SE, *LI);

  // Now that we know the largest of of the induction variables in this loop,
  // insert a canonical induction variable of the largest size.
  Value *IndVar = 0;
  if (!SizesToInsert.empty()) {
    IndVar = Rewriter.getOrInsertCanonicalInductionVariable(L,LargestType);
    ++NumInserted;
    Changed = true;
    DOUT << "INDVARS: New CanIV: " << *IndVar;
  }

  // If we have a trip count expression, rewrite the loop's exit condition
  // using it.  We can currently only handle loops with a single exit.
  bool OrigIVAlwaysNonNegative = false;
  if (!isa<SCEVCouldNotCompute>(IterationCount) && ExitingBlock)
    // Can't rewrite non-branch yet.
    if (BranchInst *BI = dyn_cast<BranchInst>(ExitingBlock->getTerminator())) {
      if (Instruction *OrigCond = dyn_cast<Instruction>(BI->getCondition())) {
        // Determine if the OrigIV will ever have a non-zero sign bit.
        OrigIVAlwaysNonNegative = isOrigIVAlwaysNonNegative(L, OrigCond);

        // We'll be replacing the original condition, so it'll be dead.
        DeadInsts.insert(OrigCond);
      }

      LinearFunctionTestReplace(L, IterationCount, IndVar,
                                ExitingBlock, BI, Rewriter);
    }

  // Now that we have a canonical induction variable, we can rewrite any
  // recurrences in terms of the induction variable.  Start with the auxillary
  // induction variables, and recursively rewrite any of their uses.
  BasicBlock::iterator InsertPt = Header->getFirstNonPHI();

  // If there were induction variables of other sizes, cast the primary
  // induction variable to the right size for them, avoiding the need for the
  // code evaluation methods to insert induction variables of different sizes.
  for (unsigned i = 0, e = SizesToInsert.size(); i != e; ++i) {
    const Type *Ty = SizesToInsert[i];
    if (Ty != LargestType) {
      Instruction *New = new TruncInst(IndVar, Ty, "indvar", InsertPt);
      Rewriter.addInsertedValue(New, SE->getSCEV(New));
      DOUT << "INDVARS: Made trunc IV for type " << *Ty << ": "
           << *New << "\n";
    }
  }

  // Rewrite all induction variables in terms of the canonical induction
  // variable.
  while (!IndVars.empty()) {
    PHINode *PN = IndVars.back().first;
    Value *NewVal = Rewriter.expandCodeFor(IndVars.back().second, InsertPt);
    DOUT << "INDVARS: Rewrote IV '" << *IndVars.back().second << "' " << *PN
         << "   into = " << *NewVal << "\n";
    NewVal->takeName(PN);

    /// If the new canonical induction variable is wider than the original,
    /// and the original has uses that are casts to wider types, see if the
    /// truncate and extend can be omitted.
    if (isa<TruncInst>(NewVal))
      for (Value::use_iterator UI = PN->use_begin(), UE = PN->use_end();
           UI != UE; ++UI)
        if (isa<ZExtInst>(UI) ||
            (isa<SExtInst>(UI) && OrigIVAlwaysNonNegative)) {
          Value *TruncIndVar = IndVar;
          if (TruncIndVar->getType() != UI->getType())
            TruncIndVar = new TruncInst(IndVar, UI->getType(), "truncindvar",
                                        InsertPt);
          UI->replaceAllUsesWith(TruncIndVar);
          if (Instruction *DeadUse = dyn_cast<Instruction>(*UI))
            DeadInsts.insert(DeadUse);
        }

    // Replace the old PHI Node with the inserted computation.
    PN->replaceAllUsesWith(NewVal);
    DeadInsts.insert(PN);
    IndVars.pop_back();
    ++NumRemoved;
    Changed = true;
  }

#if 0
  // Now replace all derived expressions in the loop body with simpler
  // expressions.
  for (LoopInfo::block_iterator I = L->block_begin(), E = L->block_end();
       I != E; ++I) {
    BasicBlock *BB = *I;
    if (LI->getLoopFor(BB) == L) {  // Not in a subloop...
      for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I)
        if (I->getType()->isInteger() &&      // Is an integer instruction
            !I->use_empty() &&
            !Rewriter.isInsertedInstruction(I)) {
          SCEVHandle SH = SE->getSCEV(I);
          Value *V = Rewriter.expandCodeFor(SH, I, I->getType());
          if (V != I) {
            if (isa<Instruction>(V))
              V->takeName(I);
            I->replaceAllUsesWith(V);
            DeadInsts.insert(I);
            ++NumRemoved;
            Changed = true;
          }
        }
    }
  }
#endif

  DeleteTriviallyDeadInstructions(DeadInsts);
  assert(L->isLCSSAForm());
  return Changed;
}

/// Return true if it is OK to use SIToFPInst for an inducation variable
/// with given inital and exit values.
static bool useSIToFPInst(ConstantFP &InitV, ConstantFP &ExitV,
                          uint64_t intIV, uint64_t intEV) {

  if (InitV.getValueAPF().isNegative() || ExitV.getValueAPF().isNegative()) 
    return true;

  // If the iteration range can be handled by SIToFPInst then use it.
  APInt Max = APInt::getSignedMaxValue(32);
  if (Max.getZExtValue() > static_cast<uint64_t>(abs(intEV - intIV)))
    return true;
  
  return false;
}

/// convertToInt - Convert APF to an integer, if possible.
static bool convertToInt(const APFloat &APF, uint64_t *intVal) {

  bool isExact = false;
  if (&APF.getSemantics() == &APFloat::PPCDoubleDouble)
    return false;
  if (APF.convertToInteger(intVal, 32, APF.isNegative(), 
                           APFloat::rmTowardZero, &isExact)
      != APFloat::opOK)
    return false;
  if (!isExact) 
    return false;
  return true;

}

/// HandleFloatingPointIV - If the loop has floating induction variable
/// then insert corresponding integer induction variable if possible.
/// For example,
/// for(double i = 0; i < 10000; ++i)
///   bar(i)
/// is converted into
/// for(int i = 0; i < 10000; ++i)
///   bar((double)i);
///
void IndVarSimplify::HandleFloatingPointIV(Loop *L, PHINode *PH, 
                                   SmallPtrSet<Instruction*, 16> &DeadInsts) {

  unsigned IncomingEdge = L->contains(PH->getIncomingBlock(0));
  unsigned BackEdge     = IncomingEdge^1;
  
  // Check incoming value.
  ConstantFP *InitValue = dyn_cast<ConstantFP>(PH->getIncomingValue(IncomingEdge));
  if (!InitValue) return;
  uint64_t newInitValue = Type::Int32Ty->getPrimitiveSizeInBits();
  if (!convertToInt(InitValue->getValueAPF(), &newInitValue))
    return;

  // Check IV increment. Reject this PH if increement operation is not
  // an add or increment value can not be represented by an integer.
  BinaryOperator *Incr = 
    dyn_cast<BinaryOperator>(PH->getIncomingValue(BackEdge));
  if (!Incr) return;
  if (Incr->getOpcode() != Instruction::Add) return;
  ConstantFP *IncrValue = NULL;
  unsigned IncrVIndex = 1;
  if (Incr->getOperand(1) == PH)
    IncrVIndex = 0;
  IncrValue = dyn_cast<ConstantFP>(Incr->getOperand(IncrVIndex));
  if (!IncrValue) return;
  uint64_t newIncrValue = Type::Int32Ty->getPrimitiveSizeInBits();
  if (!convertToInt(IncrValue->getValueAPF(), &newIncrValue))
    return;
  
  // Check Incr uses. One user is PH and the other users is exit condition used
  // by the conditional terminator.
  Value::use_iterator IncrUse = Incr->use_begin();
  Instruction *U1 = cast<Instruction>(IncrUse++);
  if (IncrUse == Incr->use_end()) return;
  Instruction *U2 = cast<Instruction>(IncrUse++);
  if (IncrUse != Incr->use_end()) return;
  
  // Find exit condition.
  FCmpInst *EC = dyn_cast<FCmpInst>(U1);
  if (!EC)
    EC = dyn_cast<FCmpInst>(U2);
  if (!EC) return;

  if (BranchInst *BI = dyn_cast<BranchInst>(EC->getParent()->getTerminator())) {
    if (!BI->isConditional()) return;
    if (BI->getCondition() != EC) return;
  }

  // Find exit value. If exit value can not be represented as an interger then
  // do not handle this floating point PH.
  ConstantFP *EV = NULL;
  unsigned EVIndex = 1;
  if (EC->getOperand(1) == Incr)
    EVIndex = 0;
  EV = dyn_cast<ConstantFP>(EC->getOperand(EVIndex));
  if (!EV) return;
  uint64_t intEV = Type::Int32Ty->getPrimitiveSizeInBits();
  if (!convertToInt(EV->getValueAPF(), &intEV))
    return;
  
  // Find new predicate for integer comparison.
  CmpInst::Predicate NewPred = CmpInst::BAD_ICMP_PREDICATE;
  switch (EC->getPredicate()) {
  case CmpInst::FCMP_OEQ:
  case CmpInst::FCMP_UEQ:
    NewPred = CmpInst::ICMP_EQ;
    break;
  case CmpInst::FCMP_OGT:
  case CmpInst::FCMP_UGT:
    NewPred = CmpInst::ICMP_UGT;
    break;
  case CmpInst::FCMP_OGE:
  case CmpInst::FCMP_UGE:
    NewPred = CmpInst::ICMP_UGE;
    break;
  case CmpInst::FCMP_OLT:
  case CmpInst::FCMP_ULT:
    NewPred = CmpInst::ICMP_ULT;
    break;
  case CmpInst::FCMP_OLE:
  case CmpInst::FCMP_ULE:
    NewPred = CmpInst::ICMP_ULE;
    break;
  default:
    break;
  }
  if (NewPred == CmpInst::BAD_ICMP_PREDICATE) return;
  
  // Insert new integer induction variable.
  PHINode *NewPHI = PHINode::Create(Type::Int32Ty,
                                    PH->getName()+".int", PH);
  NewPHI->addIncoming(ConstantInt::get(Type::Int32Ty, newInitValue),
                      PH->getIncomingBlock(IncomingEdge));

  Value *NewAdd = BinaryOperator::CreateAdd(NewPHI, 
                                            ConstantInt::get(Type::Int32Ty, 
                                                             newIncrValue),
                                            Incr->getName()+".int", Incr);
  NewPHI->addIncoming(NewAdd, PH->getIncomingBlock(BackEdge));

  ConstantInt *NewEV = ConstantInt::get(Type::Int32Ty, intEV);
  Value *LHS = (EVIndex == 1 ? NewPHI->getIncomingValue(BackEdge) : NewEV);
  Value *RHS = (EVIndex == 1 ? NewEV : NewPHI->getIncomingValue(BackEdge));
  ICmpInst *NewEC = new ICmpInst(NewPred, LHS, RHS, EC->getNameStart(), 
                                 EC->getParent()->getTerminator());
  
  // Delete old, floating point, exit comparision instruction.
  EC->replaceAllUsesWith(NewEC);
  DeadInsts.insert(EC);
  
  // Delete old, floating point, increment instruction.
  Incr->replaceAllUsesWith(UndefValue::get(Incr->getType()));
  DeadInsts.insert(Incr);
  
  // Replace floating induction variable. Give SIToFPInst preference over
  // UIToFPInst because it is faster on platforms that are widely used.
  if (useSIToFPInst(*InitValue, *EV, newInitValue, intEV)) {
    SIToFPInst *Conv = new SIToFPInst(NewPHI, PH->getType(), "indvar.conv", 
                                      PH->getParent()->getFirstNonPHI());
    PH->replaceAllUsesWith(Conv);
  } else {
    UIToFPInst *Conv = new UIToFPInst(NewPHI, PH->getType(), "indvar.conv", 
                                      PH->getParent()->getFirstNonPHI());
    PH->replaceAllUsesWith(Conv);
  }
  DeadInsts.insert(PH);
}