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. The canonical induction variable is guaranteed to be in a wide enough
//      type so that IV expressions need not be (directly) zero-extended or
//      sign-extended.
//   4. 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.
//
//===----------------------------------------------------------------------===//

#define DEBUG_TYPE "indvars"
#include "llvm/Transforms/Scalar.h"
#include "llvm/BasicBlock.h"
#include "llvm/Constants.h"
#include "llvm/Instructions.h"
#include "llvm/IntrinsicInst.h"
#include "llvm/LLVMContext.h"
#include "llvm/Type.h"
#include "llvm/Analysis/Dominators.h"
#include "llvm/Analysis/IVUsers.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Target/TargetData.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/STLExtras.h"
using namespace llvm;

STATISTIC(NumRemoved     , "Number of aux indvars removed");
STATISTIC(NumWidened     , "Number of indvars widened");
STATISTIC(NumInserted    , "Number of canonical indvars added");
STATISTIC(NumReplaced    , "Number of exit values replaced");
STATISTIC(NumLFTR        , "Number of loop exit tests replaced");
STATISTIC(NumElimIdentity, "Number of IV identities eliminated");
STATISTIC(NumElimOperand,  "Number of IV operands folded into a use");
STATISTIC(NumElimExt     , "Number of IV sign/zero extends eliminated");
STATISTIC(NumElimRem     , "Number of IV remainder operations eliminated");
STATISTIC(NumElimCmp     , "Number of IV comparisons eliminated");
STATISTIC(NumElimIV      , "Number of congruent IVs eliminated");

static cl::opt<bool> DisableIVRewrite(
  "disable-iv-rewrite", cl::Hidden,
  cl::desc("Disable canonical induction variable rewriting"));

// Temporary flag for use with -disable-iv-rewrite to force a canonical IV for
// LFTR purposes.
static cl::opt<bool> ForceLFTR(
  "force-lftr", cl::Hidden,
  cl::desc("Enable forced linear function test replacement"));

namespace {
  class IndVarSimplify : public LoopPass {
    IVUsers         *IU;
    LoopInfo        *LI;
    ScalarEvolution *SE;
    DominatorTree   *DT;
    TargetData      *TD;

    SmallVector<WeakVH, 16> DeadInsts;
    bool Changed;
  public:

    static char ID; // Pass identification, replacement for typeid
    IndVarSimplify() : LoopPass(ID), IU(0), LI(0), SE(0), DT(0), TD(0),
                       Changed(false) {
      initializeIndVarSimplifyPass(*PassRegistry::getPassRegistry());
    }

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

    virtual void getAnalysisUsage(AnalysisUsage &AU) const {
      AU.addRequired<DominatorTree>();
      AU.addRequired<LoopInfo>();
      AU.addRequired<ScalarEvolution>();
      AU.addRequiredID(LoopSimplifyID);
      AU.addRequiredID(LCSSAID);
      if (!DisableIVRewrite)
        AU.addRequired<IVUsers>();
      AU.addPreserved<ScalarEvolution>();
      AU.addPreservedID(LoopSimplifyID);
      AU.addPreservedID(LCSSAID);
      if (!DisableIVRewrite)
        AU.addPreserved<IVUsers>();
      AU.setPreservesCFG();
    }

  private:
    virtual void releaseMemory() {
      DeadInsts.clear();
    }

    bool isValidRewrite(Value *FromVal, Value *ToVal);

    void HandleFloatingPointIV(Loop *L, PHINode *PH);
    void RewriteNonIntegerIVs(Loop *L);

    void RewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter);

    void SimplifyIVUsers(SCEVExpander &Rewriter);
    void SimplifyIVUsersNoRewrite(Loop *L, SCEVExpander &Rewriter);

    bool EliminateIVUser(Instruction *UseInst, Instruction *IVOperand);
    void EliminateIVComparison(ICmpInst *ICmp, Value *IVOperand);
    void EliminateIVRemainder(BinaryOperator *Rem,
                              Value *IVOperand,
                              bool IsSigned);

    bool FoldIVUser(Instruction *UseInst, Instruction *IVOperand);

    void SimplifyCongruentIVs(Loop *L);

    void RewriteIVExpressions(Loop *L, SCEVExpander &Rewriter);

    Value *LinearFunctionTestReplace(Loop *L, const SCEV *BackedgeTakenCount,
                                     PHINode *IndVar, SCEVExpander &Rewriter);

    void SinkUnusedInvariants(Loop *L);
  };
}

char IndVarSimplify::ID = 0;
INITIALIZE_PASS_BEGIN(IndVarSimplify, "indvars",
                "Induction Variable Simplification", false, false)
INITIALIZE_PASS_DEPENDENCY(DominatorTree)
INITIALIZE_PASS_DEPENDENCY(LoopInfo)
INITIALIZE_PASS_DEPENDENCY(ScalarEvolution)
INITIALIZE_PASS_DEPENDENCY(LoopSimplify)
INITIALIZE_PASS_DEPENDENCY(LCSSA)
INITIALIZE_PASS_DEPENDENCY(IVUsers)
INITIALIZE_PASS_END(IndVarSimplify, "indvars",
                "Induction Variable Simplification", false, false)

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

/// isValidRewrite - Return true if the SCEV expansion generated by the
/// rewriter can replace the original value. SCEV guarantees that it
/// produces the same value, but the way it is produced may be illegal IR.
/// Ideally, this function will only be called for verification.
bool IndVarSimplify::isValidRewrite(Value *FromVal, Value *ToVal) {
  // If an SCEV expression subsumed multiple pointers, its expansion could
  // reassociate the GEP changing the base pointer. This is illegal because the
  // final address produced by a GEP chain must be inbounds relative to its
  // underlying object. Otherwise basic alias analysis, among other things,
  // could fail in a dangerous way. Ultimately, SCEV will be improved to avoid
  // producing an expression involving multiple pointers. Until then, we must
  // bail out here.
  //
  // Retrieve the pointer operand of the GEP. Don't use GetUnderlyingObject
  // because it understands lcssa phis while SCEV does not.
  Value *FromPtr = FromVal;
  Value *ToPtr = ToVal;
  if (GEPOperator *GEP = dyn_cast<GEPOperator>(FromVal)) {
    FromPtr = GEP->getPointerOperand();
  }
  if (GEPOperator *GEP = dyn_cast<GEPOperator>(ToVal)) {
    ToPtr = GEP->getPointerOperand();
  }
  if (FromPtr != FromVal || ToPtr != ToVal) {
    // Quickly check the common case
    if (FromPtr == ToPtr)
      return true;

    // SCEV may have rewritten an expression that produces the GEP's pointer
    // operand. That's ok as long as the pointer operand has the same base
    // pointer. Unlike GetUnderlyingObject(), getPointerBase() will find the
    // base of a recurrence. This handles the case in which SCEV expansion
    // converts a pointer type recurrence into a nonrecurrent pointer base
    // indexed by an integer recurrence.
    const SCEV *FromBase = SE->getPointerBase(SE->getSCEV(FromPtr));
    const SCEV *ToBase = SE->getPointerBase(SE->getSCEV(ToPtr));
    if (FromBase == ToBase)
      return true;

    DEBUG(dbgs() << "INDVARS: GEP rewrite bail out "
          << *FromBase << " != " << *ToBase << "\n");

    return false;
  }
  return true;
}

/// Determine the insertion point for this user. By default, insert immediately
/// before the user. SCEVExpander or LICM will hoist loop invariants out of the
/// loop. For PHI nodes, there may be multiple uses, so compute the nearest
/// common dominator for the incoming blocks.
static Instruction *getInsertPointForUses(Instruction *User, Value *Def,
                                          DominatorTree *DT) {
  PHINode *PHI = dyn_cast<PHINode>(User);
  if (!PHI)
    return User;

  Instruction *InsertPt = 0;
  for (unsigned i = 0, e = PHI->getNumIncomingValues(); i != e; ++i) {
    if (PHI->getIncomingValue(i) != Def)
      continue;

    BasicBlock *InsertBB = PHI->getIncomingBlock(i);
    if (!InsertPt) {
      InsertPt = InsertBB->getTerminator();
      continue;
    }
    InsertBB = DT->findNearestCommonDominator(InsertPt->getParent(), InsertBB);
    InsertPt = InsertBB->getTerminator();
  }
  assert(InsertPt && "Missing phi operand");
  assert((!isa<Instruction>(Def) ||
          DT->dominates(cast<Instruction>(Def), InsertPt)) &&
         "def does not dominate all uses");
  return InsertPt;
}

//===----------------------------------------------------------------------===//
// RewriteNonIntegerIVs and helpers. Prefer integer IVs.
//===----------------------------------------------------------------------===//

/// ConvertToSInt - Convert APF to an integer, if possible.
static bool ConvertToSInt(const APFloat &APF, int64_t &IntVal) {
  bool isExact = false;
  if (&APF.getSemantics() == &APFloat::PPCDoubleDouble)
    return false;
  // See if we can convert this to an int64_t
  uint64_t UIntVal;
  if (APF.convertToInteger(&UIntVal, 64, true, APFloat::rmTowardZero,
                           &isExact) != APFloat::opOK || !isExact)
    return false;
  IntVal = UIntVal;
  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 *PN) {
  unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
  unsigned BackEdge     = IncomingEdge^1;

  // Check incoming value.
  ConstantFP *InitValueVal =
    dyn_cast<ConstantFP>(PN->getIncomingValue(IncomingEdge));

  int64_t InitValue;
  if (!InitValueVal || !ConvertToSInt(InitValueVal->getValueAPF(), InitValue))
    return;

  // Check IV increment. Reject this PN if increment operation is not
  // an add or increment value can not be represented by an integer.
  BinaryOperator *Incr =
    dyn_cast<BinaryOperator>(PN->getIncomingValue(BackEdge));
  if (Incr == 0 || Incr->getOpcode() != Instruction::FAdd) return;

  // If this is not an add of the PHI with a constantfp, or if the constant fp
  // is not an integer, bail out.
  ConstantFP *IncValueVal = dyn_cast<ConstantFP>(Incr->getOperand(1));
  int64_t IncValue;
  if (IncValueVal == 0 || Incr->getOperand(0) != PN ||
      !ConvertToSInt(IncValueVal->getValueAPF(), IncValue))
    return;

  // Check Incr uses. One user is PN and the other user is an 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, which is an fcmp.  If it doesn't exist, or if it isn't
  // only used by a branch, we can't transform it.
  FCmpInst *Compare = dyn_cast<FCmpInst>(U1);
  if (!Compare)
    Compare = dyn_cast<FCmpInst>(U2);
  if (Compare == 0 || !Compare->hasOneUse() ||
      !isa<BranchInst>(Compare->use_back()))
    return;

  BranchInst *TheBr = cast<BranchInst>(Compare->use_back());

  // We need to verify that the branch actually controls the iteration count
  // of the loop.  If not, the new IV can overflow and no one will notice.
  // The branch block must be in the loop and one of the successors must be out
  // of the loop.
  assert(TheBr->isConditional() && "Can't use fcmp if not conditional");
  if (!L->contains(TheBr->getParent()) ||
      (L->contains(TheBr->getSuccessor(0)) &&
       L->contains(TheBr->getSuccessor(1))))
    return;


  // If it isn't a comparison with an integer-as-fp (the exit value), we can't
  // transform it.
  ConstantFP *ExitValueVal = dyn_cast<ConstantFP>(Compare->getOperand(1));
  int64_t ExitValue;
  if (ExitValueVal == 0 ||
      !ConvertToSInt(ExitValueVal->getValueAPF(), ExitValue))
    return;

  // Find new predicate for integer comparison.
  CmpInst::Predicate NewPred = CmpInst::BAD_ICMP_PREDICATE;
  switch (Compare->getPredicate()) {
  default: return;  // Unknown comparison.
  case CmpInst::FCMP_OEQ:
  case CmpInst::FCMP_UEQ: NewPred = CmpInst::ICMP_EQ; break;
  case CmpInst::FCMP_ONE:
  case CmpInst::FCMP_UNE: NewPred = CmpInst::ICMP_NE; break;
  case CmpInst::FCMP_OGT:
  case CmpInst::FCMP_UGT: NewPred = CmpInst::ICMP_SGT; break;
  case CmpInst::FCMP_OGE:
  case CmpInst::FCMP_UGE: NewPred = CmpInst::ICMP_SGE; break;
  case CmpInst::FCMP_OLT:
  case CmpInst::FCMP_ULT: NewPred = CmpInst::ICMP_SLT; break;
  case CmpInst::FCMP_OLE:
  case CmpInst::FCMP_ULE: NewPred = CmpInst::ICMP_SLE; break;
  }

  // We convert the floating point induction variable to a signed i32 value if
  // we can.  This is only safe if the comparison will not overflow in a way
  // that won't be trapped by the integer equivalent operations.  Check for this
  // now.
  // TODO: We could use i64 if it is native and the range requires it.

  // The start/stride/exit values must all fit in signed i32.
  if (!isInt<32>(InitValue) || !isInt<32>(IncValue) || !isInt<32>(ExitValue))
    return;

  // If not actually striding (add x, 0.0), avoid touching the code.
  if (IncValue == 0)
    return;

  // Positive and negative strides have different safety conditions.
  if (IncValue > 0) {
    // If we have a positive stride, we require the init to be less than the
    // exit value and an equality or less than comparison.
    if (InitValue >= ExitValue ||
        NewPred == CmpInst::ICMP_SGT || NewPred == CmpInst::ICMP_SGE)
      return;

    uint32_t Range = uint32_t(ExitValue-InitValue);
    if (NewPred == CmpInst::ICMP_SLE) {
      // Normalize SLE -> SLT, check for infinite loop.
      if (++Range == 0) return;  // Range overflows.
    }

    unsigned Leftover = Range % uint32_t(IncValue);

    // If this is an equality comparison, we require that the strided value
    // exactly land on the exit value, otherwise the IV condition will wrap
    // around and do things the fp IV wouldn't.
    if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
        Leftover != 0)
      return;

    // If the stride would wrap around the i32 before exiting, we can't
    // transform the IV.
    if (Leftover != 0 && int32_t(ExitValue+IncValue) < ExitValue)
      return;

  } else {
    // If we have a negative stride, we require the init to be greater than the
    // exit value and an equality or greater than comparison.
    if (InitValue >= ExitValue ||
        NewPred == CmpInst::ICMP_SLT || NewPred == CmpInst::ICMP_SLE)
      return;

    uint32_t Range = uint32_t(InitValue-ExitValue);
    if (NewPred == CmpInst::ICMP_SGE) {
      // Normalize SGE -> SGT, check for infinite loop.
      if (++Range == 0) return;  // Range overflows.
    }

    unsigned Leftover = Range % uint32_t(-IncValue);

    // If this is an equality comparison, we require that the strided value
    // exactly land on the exit value, otherwise the IV condition will wrap
    // around and do things the fp IV wouldn't.
    if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
        Leftover != 0)
      return;

    // If the stride would wrap around the i32 before exiting, we can't
    // transform the IV.
    if (Leftover != 0 && int32_t(ExitValue+IncValue) > ExitValue)
      return;
  }

  IntegerType *Int32Ty = Type::getInt32Ty(PN->getContext());

  // Insert new integer induction variable.
  PHINode *NewPHI = PHINode::Create(Int32Ty, 2, PN->getName()+".int", PN);
  NewPHI->addIncoming(ConstantInt::get(Int32Ty, InitValue),
                      PN->getIncomingBlock(IncomingEdge));

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

  ICmpInst *NewCompare = new ICmpInst(TheBr, NewPred, NewAdd,
                                      ConstantInt::get(Int32Ty, ExitValue),
                                      Compare->getName());

  // In the following deletions, PN may become dead and may be deleted.
  // Use a WeakVH to observe whether this happens.
  WeakVH WeakPH = PN;

  // Delete the old floating point exit comparison.  The branch starts using the
  // new comparison.
  NewCompare->takeName(Compare);
  Compare->replaceAllUsesWith(NewCompare);
  RecursivelyDeleteTriviallyDeadInstructions(Compare);

  // Delete the old floating point increment.
  Incr->replaceAllUsesWith(UndefValue::get(Incr->getType()));
  RecursivelyDeleteTriviallyDeadInstructions(Incr);

  // If the FP induction variable still has uses, this is because something else
  // in the loop uses its value.  In order to canonicalize the induction
  // variable, we chose to eliminate the IV and rewrite it in terms of an
  // int->fp cast.
  //
  // We give preference to sitofp over uitofp because it is faster on most
  // platforms.
  if (WeakPH) {
    Value *Conv = new SIToFPInst(NewPHI, PN->getType(), "indvar.conv",
                                 PN->getParent()->getFirstNonPHI());
    PN->replaceAllUsesWith(Conv);
    RecursivelyDeleteTriviallyDeadInstructions(PN);
  }

  // Add a new IVUsers entry for the newly-created integer PHI.
  if (IU)
    IU->AddUsersIfInteresting(NewPHI);
}

void IndVarSimplify::RewriteNonIntegerIVs(Loop *L) {
  // First step.  Check to see if there are any floating-point recurrences.
  // If there are, change them into integer recurrences, permitting analysis by
  // the SCEV routines.
  //
  BasicBlock *Header = L->getHeader();

  SmallVector<WeakVH, 8> PHIs;
  for (BasicBlock::iterator I = Header->begin();
       PHINode *PN = dyn_cast<PHINode>(I); ++I)
    PHIs.push_back(PN);

  for (unsigned i = 0, e = PHIs.size(); i != e; ++i)
    if (PHINode *PN = dyn_cast_or_null<PHINode>(&*PHIs[i]))
      HandleFloatingPointIV(L, PN);

  // If the loop previously had floating-point IV, ScalarEvolution
  // may not have been able to compute a trip count. Now that we've done some
  // re-writing, the trip count may be computable.
  if (Changed)
    SE->forgetLoop(L);
}

//===----------------------------------------------------------------------===//
// RewriteLoopExitValues - Optimize IV users outside the loop.
// As a side effect, reduces the amount of IV processing within the loop.
//===----------------------------------------------------------------------===//

/// 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.
///
/// This is mostly redundant with the regular IndVarSimplify activities that
/// happen later, except that it's more powerful in some cases, because it's
/// able to brute-force evaluate arbitrary instructions as long as they have
/// constant operands at the beginning of the loop.
void IndVarSimplify::RewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter) {
  // Verify the input to the pass in already in LCSSA form.
  assert(L->isLCSSAForm(*DT));

  SmallVector<BasicBlock*, 8> ExitBlocks;
  L->getUniqueExitBlocks(ExitBlocks);

  // 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++))) {
      if (PN->use_empty())
        continue; // dead use, don't replace it

      // SCEV only supports integer expressions for now.
      if (!PN->getType()->isIntegerTy() && !PN->getType()->isPointerTy())
        continue;

      // It's necessary to tell ScalarEvolution about this explicitly so that
      // it can walk the def-use list and forget all SCEVs, as it may not be
      // watching the PHI itself. Once the new exit value is in place, there
      // may not be a def-use connection between the loop and every instruction
      // which got a SCEVAddRecExpr for that loop.
      SE->forgetValue(PN);

      // 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))
          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))
          continue;

        // 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.
        const SCEV *ExitValue = SE->getSCEVAtScope(Inst, L->getParentLoop());
        if (!SE->isLoopInvariant(ExitValue, L))
          continue;

        Value *ExitVal = Rewriter.expandCodeFor(ExitValue, PN->getType(), Inst);

        DEBUG(dbgs() << "INDVARS: RLEV: AfterLoopVal = " << *ExitVal << '\n'
                     << "  LoopVal = " << *Inst << "\n");

        if (!isValidRewrite(Inst, ExitVal)) {
          DeadInsts.push_back(ExitVal);
          continue;
        }
        Changed = true;
        ++NumReplaced;

        PN->setIncomingValue(i, ExitVal);

        // If this instruction is dead now, delete it.
        RecursivelyDeleteTriviallyDeadInstructions(Inst);

        if (NumPreds == 1) {
          // Completely replace a single-pred PHI. This is safe, because the
          // NewVal won't be variant in the loop, so we don't need an LCSSA phi
          // node anymore.
          PN->replaceAllUsesWith(ExitVal);
          RecursivelyDeleteTriviallyDeadInstructions(PN);
        }
      }
      if (NumPreds != 1) {
        // Clone the PHI and delete the original one. This lets IVUsers and
        // any other maps purge the original user from their records.
        PHINode *NewPN = cast<PHINode>(PN->clone());
        NewPN->takeName(PN);
        NewPN->insertBefore(PN);
        PN->replaceAllUsesWith(NewPN);
        PN->eraseFromParent();
      }
    }
  }

  // The insertion point instruction may have been deleted; clear it out
  // so that the rewriter doesn't trip over it later.
  Rewriter.clearInsertPoint();
}

//===----------------------------------------------------------------------===//
//  Rewrite IV users based on a canonical IV.
//  To be replaced by -disable-iv-rewrite.
//===----------------------------------------------------------------------===//

/// SimplifyIVUsers - Iteratively perform simplification on IVUsers within this
/// loop. IVUsers is treated as a worklist. Each successive simplification may
/// push more users which may themselves be candidates for simplification.
///
/// This is the old approach to IV simplification to be replaced by
/// SimplifyIVUsersNoRewrite.
///
void IndVarSimplify::SimplifyIVUsers(SCEVExpander &Rewriter) {
  // Each round of simplification involves a round of eliminating operations
  // followed by a round of widening IVs. A single IVUsers worklist is used
  // across all rounds. The inner loop advances the user. If widening exposes
  // more uses, then another pass through the outer loop is triggered.
  for (IVUsers::iterator I = IU->begin(); I != IU->end(); ++I) {
    Instruction *UseInst = I->getUser();
    Value *IVOperand = I->getOperandValToReplace();

    if (ICmpInst *ICmp = dyn_cast<ICmpInst>(UseInst)) {
      EliminateIVComparison(ICmp, IVOperand);
      continue;
    }
    if (BinaryOperator *Rem = dyn_cast<BinaryOperator>(UseInst)) {
      bool IsSigned = Rem->getOpcode() == Instruction::SRem;
      if (IsSigned || Rem->getOpcode() == Instruction::URem) {
        EliminateIVRemainder(Rem, IVOperand, IsSigned);
        continue;
      }
    }
  }
}

// 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, unless
// it can be expanded to a trivial value.
static bool isSafe(const SCEV *S, const Loop *L, ScalarEvolution *SE) {
  // Loop-invariant values are safe.
  if (SE->isLoopInvariant(S, L)) return true;

  // Affine addrecs are safe. Non-affine are not, because LSR doesn't know how
  // to transform them into efficient code.
  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
    return AR->isAffine();

  // An add is safe it all its operands are safe.
  if (const SCEVCommutativeExpr *Commutative = dyn_cast<SCEVCommutativeExpr>(S)) {
    for (SCEVCommutativeExpr::op_iterator I = Commutative->op_begin(),
         E = Commutative->op_end(); I != E; ++I)
      if (!isSafe(*I, L, SE)) return false;
    return true;
  }

  // A cast is safe if its operand is.
  if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(S))
    return isSafe(C->getOperand(), L, SE);

  // A udiv is safe if its operands are.
  if (const SCEVUDivExpr *UD = dyn_cast<SCEVUDivExpr>(S))
    return isSafe(UD->getLHS(), L, SE) &&
           isSafe(UD->getRHS(), L, SE);

  // SCEVUnknown is always safe.
  if (isa<SCEVUnknown>(S))
    return true;

  // Nothing else is safe.
  return false;
}

void IndVarSimplify::RewriteIVExpressions(Loop *L, SCEVExpander &Rewriter) {
  // Rewrite all induction variable expressions in terms of the canonical
  // induction variable.
  //
  // If there were induction variables of other sizes or offsets, manually
  // add the offsets to the primary induction variable and cast, avoiding
  // the need for the code evaluation methods to insert induction variables
  // of different sizes.
  for (IVUsers::iterator UI = IU->begin(), E = IU->end(); UI != E; ++UI) {
    Value *Op = UI->getOperandValToReplace();
    Type *UseTy = Op->getType();
    Instruction *User = UI->getUser();

    // Compute the final addrec to expand into code.
    const SCEV *AR = IU->getReplacementExpr(*UI);

    // Evaluate the expression out of the loop, if possible.
    if (!L->contains(UI->getUser())) {
      const SCEV *ExitVal = SE->getSCEVAtScope(AR, L->getParentLoop());
      if (SE->isLoopInvariant(ExitVal, L))
        AR = ExitVal;
    }

    // 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, unless
    // it can be expanded to a trivial value.
    if (!isSafe(AR, L, SE))
      continue;

    // Determine the insertion point for this user. By default, insert
    // immediately before the user. The SCEVExpander class will automatically
    // hoist loop invariants out of the loop. For PHI nodes, there may be
    // multiple uses, so compute the nearest common dominator for the
    // incoming blocks.
    Instruction *InsertPt = getInsertPointForUses(User, Op, DT);

    // Now expand it into actual Instructions and patch it into place.
    Value *NewVal = Rewriter.expandCodeFor(AR, UseTy, InsertPt);

    DEBUG(dbgs() << "INDVARS: Rewrote IV '" << *AR << "' " << *Op << '\n'
                 << "   into = " << *NewVal << "\n");

    if (!isValidRewrite(Op, NewVal)) {
      DeadInsts.push_back(NewVal);
      continue;
    }
    // Inform ScalarEvolution that this value is changing. The change doesn't
    // affect its value, but it does potentially affect which use lists the
    // value will be on after the replacement, which affects ScalarEvolution's
    // ability to walk use lists and drop dangling pointers when a value is
    // deleted.
    SE->forgetValue(User);

    // Patch the new value into place.
    if (Op->hasName())
      NewVal->takeName(Op);
    if (Instruction *NewValI = dyn_cast<Instruction>(NewVal))
      NewValI->setDebugLoc(User->getDebugLoc());
    User->replaceUsesOfWith(Op, NewVal);
    UI->setOperandValToReplace(NewVal);

    ++NumRemoved;
    Changed = true;

    // The old value may be dead now.
    DeadInsts.push_back(Op);
  }
}

//===----------------------------------------------------------------------===//
//  IV Widening - Extend the width of an IV to cover its widest uses.
//===----------------------------------------------------------------------===//

namespace {
  // Collect information about induction variables that are used by sign/zero
  // extend operations. This information is recorded by CollectExtend and
  // provides the input to WidenIV.
  struct WideIVInfo {
    Type *WidestNativeType; // Widest integer type created [sz]ext
    bool IsSigned;                // Was an sext user seen before a zext?

    WideIVInfo() : WidestNativeType(0), IsSigned(false) {}
  };
}

/// CollectExtend - Update information about the induction variable that is
/// extended by this sign or zero extend operation. This is used to determine
/// the final width of the IV before actually widening it.
static void CollectExtend(CastInst *Cast, bool IsSigned, WideIVInfo &WI,
                          ScalarEvolution *SE, const TargetData *TD) {
  Type *Ty = Cast->getType();
  uint64_t Width = SE->getTypeSizeInBits(Ty);
  if (TD && !TD->isLegalInteger(Width))
    return;

  if (!WI.WidestNativeType) {
    WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
    WI.IsSigned = IsSigned;
    return;
  }

  // We extend the IV to satisfy the sign of its first user, arbitrarily.
  if (WI.IsSigned != IsSigned)
    return;

  if (Width > SE->getTypeSizeInBits(WI.WidestNativeType))
    WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
}

namespace {

/// NarrowIVDefUse - Record a link in the Narrow IV def-use chain along with the
/// WideIV that computes the same value as the Narrow IV def.  This avoids
/// caching Use* pointers.
struct NarrowIVDefUse {
  Instruction *NarrowDef;
  Instruction *NarrowUse;
  Instruction *WideDef;

  NarrowIVDefUse(): NarrowDef(0), NarrowUse(0), WideDef(0) {}

  NarrowIVDefUse(Instruction *ND, Instruction *NU, Instruction *WD):
    NarrowDef(ND), NarrowUse(NU), WideDef(WD) {}
};

/// WidenIV - The goal of this transform is to remove sign and zero extends
/// without creating any new induction variables. To do this, it creates a new
/// phi of the wider type and redirects all users, either removing extends or
/// inserting truncs whenever we stop propagating the type.
///
class WidenIV {
  // Parameters
  PHINode *OrigPhi;
  Type *WideType;
  bool IsSigned;

  // Context
  LoopInfo        *LI;
  Loop            *L;
  ScalarEvolution *SE;
  DominatorTree   *DT;

  // Result
  PHINode *WidePhi;
  Instruction *WideInc;
  const SCEV *WideIncExpr;
  SmallVectorImpl<WeakVH> &DeadInsts;

  SmallPtrSet<Instruction*,16> Widened;
  SmallVector<NarrowIVDefUse, 8> NarrowIVUsers;

public:
  WidenIV(PHINode *PN, const WideIVInfo &WI, LoopInfo *LInfo,
          ScalarEvolution *SEv, DominatorTree *DTree,
          SmallVectorImpl<WeakVH> &DI) :
    OrigPhi(PN),
    WideType(WI.WidestNativeType),
    IsSigned(WI.IsSigned),
    LI(LInfo),
    L(LI->getLoopFor(OrigPhi->getParent())),
    SE(SEv),
    DT(DTree),
    WidePhi(0),
    WideInc(0),
    WideIncExpr(0),
    DeadInsts(DI) {
    assert(L->getHeader() == OrigPhi->getParent() && "Phi must be an IV");
  }

  PHINode *CreateWideIV(SCEVExpander &Rewriter);

protected:
  Instruction *CloneIVUser(NarrowIVDefUse DU);

  const SCEVAddRecExpr *GetWideRecurrence(Instruction *NarrowUse);

  Instruction *WidenIVUse(NarrowIVDefUse DU);

  void pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef);
};
} // anonymous namespace

static Value *getExtend( Value *NarrowOper, Type *WideType,
                               bool IsSigned, IRBuilder<> &Builder) {
  return IsSigned ? Builder.CreateSExt(NarrowOper, WideType) :
                    Builder.CreateZExt(NarrowOper, WideType);
}

/// CloneIVUser - Instantiate a wide operation to replace a narrow
/// operation. This only needs to handle operations that can evaluation to
/// SCEVAddRec. It can safely return 0 for any operation we decide not to clone.
Instruction *WidenIV::CloneIVUser(NarrowIVDefUse DU) {
  unsigned Opcode = DU.NarrowUse->getOpcode();
  switch (Opcode) {
  default:
    return 0;
  case Instruction::Add:
  case Instruction::Mul:
  case Instruction::UDiv:
  case Instruction::Sub:
  case Instruction::And:
  case Instruction::Or:
  case Instruction::Xor:
  case Instruction::Shl:
  case Instruction::LShr:
  case Instruction::AShr:
    DEBUG(dbgs() << "Cloning IVUser: " << *DU.NarrowUse << "\n");

    IRBuilder<> Builder(DU.NarrowUse);

    // Replace NarrowDef operands with WideDef. Otherwise, we don't know
    // anything about the narrow operand yet so must insert a [sz]ext. It is
    // probably loop invariant and will be folded or hoisted. If it actually
    // comes from a widened IV, it should be removed during a future call to
    // WidenIVUse.
    Value *LHS = (DU.NarrowUse->getOperand(0) == DU.NarrowDef) ? DU.WideDef :
      getExtend(DU.NarrowUse->getOperand(0), WideType, IsSigned, Builder);
    Value *RHS = (DU.NarrowUse->getOperand(1) == DU.NarrowDef) ? DU.WideDef :
      getExtend(DU.NarrowUse->getOperand(1), WideType, IsSigned, Builder);

    BinaryOperator *NarrowBO = cast<BinaryOperator>(DU.NarrowUse);
    BinaryOperator *WideBO = BinaryOperator::Create(NarrowBO->getOpcode(),
                                                    LHS, RHS,
                                                    NarrowBO->getName());
    Builder.Insert(WideBO);
    if (const OverflowingBinaryOperator *OBO =
        dyn_cast<OverflowingBinaryOperator>(NarrowBO)) {
      if (OBO->hasNoUnsignedWrap()) WideBO->setHasNoUnsignedWrap();
      if (OBO->hasNoSignedWrap()) WideBO->setHasNoSignedWrap();
    }
    return WideBO;
  }
  llvm_unreachable(0);
}

/// HoistStep - Attempt to hoist an IV increment above a potential use.
///
/// To successfully hoist, two criteria must be met:
/// - IncV operands dominate InsertPos and
/// - InsertPos dominates IncV
///
/// Meeting the second condition means that we don't need to check all of IncV's
/// existing uses (it's moving up in the domtree).
///
/// This does not yet recursively hoist the operands, although that would
/// not be difficult.
static bool HoistStep(Instruction *IncV, Instruction *InsertPos,
                      const DominatorTree *DT)
{
  if (DT->dominates(IncV, InsertPos))
    return true;

  if (!DT->dominates(InsertPos->getParent(), IncV->getParent()))
    return false;

  if (IncV->mayHaveSideEffects())
    return false;

  // Attempt to hoist IncV
  for (User::op_iterator OI = IncV->op_begin(), OE = IncV->op_end();
       OI != OE; ++OI) {
    Instruction *OInst = dyn_cast<Instruction>(OI);
    if (OInst && !DT->dominates(OInst, InsertPos))
      return false;
  }
  IncV->moveBefore(InsertPos);
  return true;
}

// GetWideRecurrence - Is this instruction potentially interesting from IVUsers'
// perspective after widening it's type? In other words, can the extend be
// safely hoisted out of the loop with SCEV reducing the value to a recurrence
// on the same loop. If so, return the sign or zero extended
// recurrence. Otherwise return NULL.
const SCEVAddRecExpr *WidenIV::GetWideRecurrence(Instruction *NarrowUse) {
  if (!SE->isSCEVable(NarrowUse->getType()))
    return 0;

  const SCEV *NarrowExpr = SE->getSCEV(NarrowUse);
  if (SE->getTypeSizeInBits(NarrowExpr->getType())
      >= SE->getTypeSizeInBits(WideType)) {
    // NarrowUse implicitly widens its operand. e.g. a gep with a narrow
    // index. So don't follow this use.
    return 0;
  }

  const SCEV *WideExpr = IsSigned ?
    SE->getSignExtendExpr(NarrowExpr, WideType) :
    SE->getZeroExtendExpr(NarrowExpr, WideType);
  const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(WideExpr);
  if (!AddRec || AddRec->getLoop() != L)
    return 0;

  return AddRec;
}

/// WidenIVUse - Determine whether an individual user of the narrow IV can be
/// widened. If so, return the wide clone of the user.
Instruction *WidenIV::WidenIVUse(NarrowIVDefUse DU) {

  // Stop traversing the def-use chain at inner-loop phis or post-loop phis.
  if (isa<PHINode>(DU.NarrowUse) &&