llvm-mirror/lib/Analysis/LoopInfo.cpp

//===- LoopInfo.cpp - Natural Loop Calculator -----------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file defines the LoopInfo class that is used to identify natural loops
// and determine the loop depth of various nodes of the CFG.  Note that the
// loops identified may actually be several natural loops that share the same
// header node... not just a single natural loop.
//
//===----------------------------------------------------------------------===//

#include "llvm/Analysis/LoopInfo.h"
#include "llvm/ADT/DepthFirstIterator.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/Analysis/LoopInfoImpl.h"
#include "llvm/Analysis/LoopIterator.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/CFG.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/PassManager.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
using namespace llvm;

// Explicitly instantiate methods in LoopInfoImpl.h for IR-level Loops.
template class llvm::LoopBase<BasicBlock, Loop>;
template class llvm::LoopInfoBase<BasicBlock, Loop>;

// Always verify loopinfo if expensive checking is enabled.
#ifdef EXPENSIVE_CHECKS
static bool VerifyLoopInfo = true;
#else
static bool VerifyLoopInfo = false;
#endif
static cl::opt<bool,true>
VerifyLoopInfoX("verify-loop-info", cl::location(VerifyLoopInfo),
                cl::desc("Verify loop info (time consuming)"));

//===----------------------------------------------------------------------===//
// Loop implementation
//

bool Loop::isLoopInvariant(const Value *V) const {
  if (const Instruction *I = dyn_cast<Instruction>(V))
    return !contains(I);
  return true;  // All non-instructions are loop invariant
}

bool Loop::hasLoopInvariantOperands(const Instruction *I) const {
  return all_of(I->operands(), [this](Value *V) { return isLoopInvariant(V); });
}

bool Loop::makeLoopInvariant(Value *V, bool &Changed,
                             Instruction *InsertPt) const {
  if (Instruction *I = dyn_cast<Instruction>(V))
    return makeLoopInvariant(I, Changed, InsertPt);
  return true;  // All non-instructions are loop-invariant.
}

bool Loop::makeLoopInvariant(Instruction *I, bool &Changed,
                             Instruction *InsertPt) const {
  // Test if the value is already loop-invariant.
  if (isLoopInvariant(I))
    return true;
  if (!isSafeToSpeculativelyExecute(I))
    return false;
  if (I->mayReadFromMemory())
    return false;
  // EH block instructions are immobile.
  if (I->isEHPad())
    return false;
  // Determine the insertion point, unless one was given.
  if (!InsertPt) {
    BasicBlock *Preheader = getLoopPreheader();
    // Without a preheader, hoisting is not feasible.
    if (!Preheader)
      return false;
    InsertPt = Preheader->getTerminator();
  }
  // Don't hoist instructions with loop-variant operands.
  for (Value *Operand : I->operands())
    if (!makeLoopInvariant(Operand, Changed, InsertPt))
      return false;

  // Hoist.
  I->moveBefore(InsertPt);

  // There is possibility of hoisting this instruction above some arbitrary
  // condition. Any metadata defined on it can be control dependent on this
  // condition. Conservatively strip it here so that we don't give any wrong
  // information to the optimizer.
  I->dropUnknownNonDebugMetadata();

  Changed = true;
  return true;
}

PHINode *Loop::getCanonicalInductionVariable() const {
  BasicBlock *H = getHeader();

  BasicBlock *Incoming = nullptr, *Backedge = nullptr;
  pred_iterator PI = pred_begin(H);
  assert(PI != pred_end(H) &&
         "Loop must have at least one backedge!");
  Backedge = *PI++;
  if (PI == pred_end(H)) return nullptr;  // dead loop
  Incoming = *PI++;
  if (PI != pred_end(H)) return nullptr;  // multiple backedges?

  if (contains(Incoming)) {
    if (contains(Backedge))
      return nullptr;
    std::swap(Incoming, Backedge);
  } else if (!contains(Backedge))
    return nullptr;

  // Loop over all of the PHI nodes, looking for a canonical indvar.
  for (BasicBlock::iterator I = H->begin(); isa<PHINode>(I); ++I) {
    PHINode *PN = cast<PHINode>(I);
    if (ConstantInt *CI =
        dyn_cast<ConstantInt>(PN->getIncomingValueForBlock(Incoming)))
      if (CI->isNullValue())
        if (Instruction *Inc =
            dyn_cast<Instruction>(PN->getIncomingValueForBlock(Backedge)))
          if (Inc->getOpcode() == Instruction::Add &&
                Inc->getOperand(0) == PN)
            if (ConstantInt *CI = dyn_cast<ConstantInt>(Inc->getOperand(1)))
              if (CI->equalsInt(1))
                return PN;
  }
  return nullptr;
}

bool Loop::isLCSSAForm(DominatorTree &DT) const {
  for (BasicBlock *BB : this->blocks()) {
    for (Instruction &I : *BB) {
      // Tokens can't be used in PHI nodes and live-out tokens prevent loop
      // optimizations, so for the purposes of considered LCSSA form, we
      // can ignore them.
      if (I.getType()->isTokenTy())
        continue;

      for (Use &U : I.uses()) {
        Instruction *UI = cast<Instruction>(U.getUser());
        BasicBlock *UserBB = UI->getParent();
        if (PHINode *P = dyn_cast<PHINode>(UI))
          UserBB = P->getIncomingBlock(U);

        // Check the current block, as a fast-path, before checking whether
        // the use is anywhere in the loop.  Most values are used in the same
        // block they are defined in.  Also, blocks not reachable from the
        // entry are special; uses in them don't need to go through PHIs.
        if (UserBB != BB &&
            !contains(UserBB) &&
            DT.isReachableFromEntry(UserBB))
          return false;
      }
    }
  }

  return true;
}

bool Loop::isRecursivelyLCSSAForm(DominatorTree &DT) const {
  if (!isLCSSAForm(DT))
    return false;

  return std::all_of(begin(), end(), [&](const Loop *L) {
    return L->isRecursivelyLCSSAForm(DT);
  });
}

bool Loop::isLoopSimplifyForm() const {
  // Normal-form loops have a preheader, a single backedge, and all of their
  // exits have all their predecessors inside the loop.
  return getLoopPreheader() && getLoopLatch() && hasDedicatedExits();
}

// Routines that reform the loop CFG and split edges often fail on indirectbr.
bool Loop::isSafeToClone() const {
  // Return false if any loop blocks contain indirectbrs, or there are any calls
  // to noduplicate functions.
  for (BasicBlock *BB : this->blocks()) {
    if (isa<IndirectBrInst>(BB->getTerminator()))
      return false;

    for (Instruction &I : *BB)
      if (auto CS = CallSite(&I))
        if (CS.cannotDuplicate())
          return false;
  }
  return true;
}

MDNode *Loop::getLoopID() const {
  MDNode *LoopID = nullptr;
  if (isLoopSimplifyForm()) {
    LoopID = getLoopLatch()->getTerminator()->getMetadata(LLVMContext::MD_loop);
  } else {
    // Go through each predecessor of the loop header and check the
    // terminator for the metadata.
    BasicBlock *H = getHeader();
    for (BasicBlock *BB : this->blocks()) {
      TerminatorInst *TI = BB->getTerminator();
      MDNode *MD = nullptr;

      // Check if this terminator branches to the loop header.
      for (BasicBlock *Successor : TI->successors()) {
        if (Successor == H) {
          MD = TI->getMetadata(LLVMContext::MD_loop);
          break;
        }
      }
      if (!MD)
        return nullptr;

      if (!LoopID)
        LoopID = MD;
      else if (MD != LoopID)
        return nullptr;
    }
  }
  if (!LoopID || LoopID->getNumOperands() == 0 ||
      LoopID->getOperand(0) != LoopID)
    return nullptr;
  return LoopID;
}

void Loop::setLoopID(MDNode *LoopID) const {
  assert(LoopID && "Loop ID should not be null");
  assert(LoopID->getNumOperands() > 0 && "Loop ID needs at least one operand");
  assert(LoopID->getOperand(0) == LoopID && "Loop ID should refer to itself");

  if (isLoopSimplifyForm()) {
    getLoopLatch()->getTerminator()->setMetadata(LLVMContext::MD_loop, LoopID);
    return;
  }

  BasicBlock *H = getHeader();
  for (BasicBlock *BB : this->blocks()) {
    TerminatorInst *TI = BB->getTerminator();
    for (BasicBlock *Successor : TI->successors()) {
      if (Successor == H)
        TI->setMetadata(LLVMContext::MD_loop, LoopID);
    }
  }
}

bool Loop::isAnnotatedParallel() const {
  MDNode *DesiredLoopIdMetadata = getLoopID();

  if (!DesiredLoopIdMetadata)
      return false;

  // The loop branch contains the parallel loop metadata. In order to ensure
  // that any parallel-loop-unaware optimization pass hasn't added loop-carried
  // dependencies (thus converted the loop back to a sequential loop), check
  // that all the memory instructions in the loop contain parallelism metadata
  // that point to the same unique "loop id metadata" the loop branch does.
  for (BasicBlock *BB : this->blocks()) {
    for (Instruction &I : *BB) {
      if (!I.mayReadOrWriteMemory())
        continue;

      // The memory instruction can refer to the loop identifier metadata
      // directly or indirectly through another list metadata (in case of
      // nested parallel loops). The loop identifier metadata refers to
      // itself so we can check both cases with the same routine.
      MDNode *LoopIdMD =
          I.getMetadata(LLVMContext::MD_mem_parallel_loop_access);

      if (!LoopIdMD)
        return false;

      bool LoopIdMDFound = false;
      for (const MDOperand &MDOp : LoopIdMD->operands()) {
        if (MDOp == DesiredLoopIdMetadata) {
          LoopIdMDFound = true;
          break;
        }
      }

      if (!LoopIdMDFound)
        return false;
    }
  }
  return true;
}

bool Loop::hasDedicatedExits() const {
  // Each predecessor of each exit block of a normal loop is contained
  // within the loop.
  SmallVector<BasicBlock *, 4> ExitBlocks;
  getExitBlocks(ExitBlocks);
  for (BasicBlock *BB : ExitBlocks)
    for (BasicBlock *Predecessor : predecessors(BB))
      if (!contains(Predecessor))
        return false;
  // All the requirements are met.
  return true;
}

void
Loop::getUniqueExitBlocks(SmallVectorImpl<BasicBlock *> &ExitBlocks) const {
  assert(hasDedicatedExits() &&
         "getUniqueExitBlocks assumes the loop has canonical form exits!");

  SmallVector<BasicBlock *, 32> SwitchExitBlocks;
  for (BasicBlock *BB : this->blocks()) {
    SwitchExitBlocks.clear();
    for (BasicBlock *Successor : successors(BB)) {
      // If block is inside the loop then it is not an exit block.
      if (contains(Successor))
        continue;

      pred_iterator PI = pred_begin(Successor);
      BasicBlock *FirstPred = *PI;

      // If current basic block is this exit block's first predecessor
      // then only insert exit block in to the output ExitBlocks vector.
      // This ensures that same exit block is not inserted twice into
      // ExitBlocks vector.
      if (BB != FirstPred)
        continue;

      // If a terminator has more then two successors, for example SwitchInst,
      // then it is possible that there are multiple edges from current block
      // to one exit block.
      if (std::distance(succ_begin(BB), succ_end(BB)) <= 2) {
        ExitBlocks.push_back(Successor);
        continue;
      }

      // In case of multiple edges from current block to exit block, collect
      // only one edge in ExitBlocks. Use switchExitBlocks to keep track of
      // duplicate edges.
      if (std::find(SwitchExitBlocks.begin(), SwitchExitBlocks.end(), Successor)
          == SwitchExitBlocks.end()) {
        SwitchExitBlocks.push_back(Successor);
        ExitBlocks.push_back(Successor);
      }
    }
  }
}

BasicBlock *Loop::getUniqueExitBlock() const {
  SmallVector<BasicBlock *, 8> UniqueExitBlocks;
  getUniqueExitBlocks(UniqueExitBlocks);
  if (UniqueExitBlocks.size() == 1)
    return UniqueExitBlocks[0];
  return nullptr;
}

#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void Loop::dump() const {
  print(dbgs());
}
#endif

//===----------------------------------------------------------------------===//
// UnloopUpdater implementation
//

namespace {
/// Find the new parent loop for all blocks within the "unloop" whose last
/// backedges has just been removed.
class UnloopUpdater {
  Loop *Unloop;
  LoopInfo *LI;

  LoopBlocksDFS DFS;

  // Map unloop's immediate subloops to their nearest reachable parents. Nested
  // loops within these subloops will not change parents. However, an immediate
  // subloop's new parent will be the nearest loop reachable from either its own
  // exits *or* any of its nested loop's exits.
  DenseMap<Loop*, Loop*> SubloopParents;

  // Flag the presence of an irreducible backedge whose destination is a block
  // directly contained by the original unloop.
  bool FoundIB;

public:
  UnloopUpdater(Loop *UL, LoopInfo *LInfo) :
    Unloop(UL), LI(LInfo), DFS(UL), FoundIB(false) {}

  void updateBlockParents();

  void removeBlocksFromAncestors();

  void updateSubloopParents();

protected:
  Loop *getNearestLoop(BasicBlock *BB, Loop *BBLoop);
};
} // end anonymous namespace

/// Update the parent loop for all blocks that are directly contained within the
/// original "unloop".
void UnloopUpdater::updateBlockParents() {
  if (Unloop->getNumBlocks()) {
    // Perform a post order CFG traversal of all blocks within this loop,
    // propagating the nearest loop from sucessors to predecessors.
    LoopBlocksTraversal Traversal(DFS, LI);
    for (LoopBlocksTraversal::POTIterator POI = Traversal.begin(),
           POE = Traversal.end(); POI != POE; ++POI) {

      Loop *L = LI->getLoopFor(*POI);
      Loop *NL = getNearestLoop(*POI, L);

      if (NL != L) {
        // For reducible loops, NL is now an ancestor of Unloop.
        assert((NL != Unloop && (!NL || NL->contains(Unloop))) &&
               "uninitialized successor");
        LI->changeLoopFor(*POI, NL);
      }
      else {
        // Or the current block is part of a subloop, in which case its parent
        // is unchanged.
        assert((FoundIB || Unloop->contains(L)) && "uninitialized successor");
      }
    }
  }
  // Each irreducible loop within the unloop induces a round of iteration using
  // the DFS result cached by Traversal.
  bool Changed = FoundIB;
  for (unsigned NIters = 0; Changed; ++NIters) {
    assert(NIters < Unloop->getNumBlocks() && "runaway iterative algorithm");

    // Iterate over the postorder list of blocks, propagating the nearest loop
    // from successors to predecessors as before.
    Changed = false;
    for (LoopBlocksDFS::POIterator POI = DFS.beginPostorder(),
           POE = DFS.endPostorder(); POI != POE; ++POI) {

      Loop *L = LI->getLoopFor(*POI);
      Loop *NL = getNearestLoop(*POI, L);
      if (NL != L) {
        assert(NL != Unloop && (!NL || NL->contains(Unloop)) &&
               "uninitialized successor");
        LI->changeLoopFor(*POI, NL);
        Changed = true;
      }
    }
  }
}

/// Remove unloop's blocks from all ancestors below their new parents.
void UnloopUpdater::removeBlocksFromAncestors() {
  // Remove all unloop's blocks (including those in nested subloops) from
  // ancestors below the new parent loop.
  for (Loop::block_iterator BI = Unloop->block_begin(),
         BE = Unloop->block_end(); BI != BE; ++BI) {
    Loop *OuterParent = LI->getLoopFor(*BI);
    if (Unloop->contains(OuterParent)) {
      while (OuterParent->getParentLoop() != Unloop)
        OuterParent = OuterParent->getParentLoop();
      OuterParent = SubloopParents[OuterParent];
    }
    // Remove blocks from former Ancestors except Unloop itself which will be
    // deleted.
    for (Loop *OldParent = Unloop->getParentLoop(); OldParent != OuterParent;
         OldParent = OldParent->getParentLoop()) {
      assert(OldParent && "new loop is not an ancestor of the original");
      OldParent->removeBlockFromLoop(*BI);
    }
  }
}

/// Update the parent loop for all subloops directly nested within unloop.
void UnloopUpdater::updateSubloopParents() {
  while (!Unloop->empty()) {
    Loop *Subloop = *std::prev(Unloop->end());
    Unloop->removeChildLoop(std::prev(Unloop->end()));

    assert(SubloopParents.count(Subloop) && "DFS failed to visit subloop");
    if (Loop *Parent = SubloopParents[Subloop])
      Parent->addChildLoop(Subloop);
    else
      LI->addTopLevelLoop(Subloop);
  }
}

/// Return the nearest parent loop among this block's successors. If a successor
/// is a subloop header, consider its parent to be the nearest parent of the
/// subloop's exits.
///
/// For subloop blocks, simply update SubloopParents and return NULL.
Loop *UnloopUpdater::getNearestLoop(BasicBlock *BB, Loop *BBLoop) {

  // Initially for blocks directly contained by Unloop, NearLoop == Unloop and
  // is considered uninitialized.
  Loop *NearLoop = BBLoop;

  Loop *Subloop = nullptr;
  if (NearLoop != Unloop && Unloop->contains(NearLoop)) {
    Subloop = NearLoop;
    // Find the subloop ancestor that is directly contained within Unloop.
    while (Subloop->getParentLoop() != Unloop) {
      Subloop = Subloop->getParentLoop();
      assert(Subloop && "subloop is not an ancestor of the original loop");
    }
    // Get the current nearest parent of the Subloop exits, initially Unloop.
    NearLoop =
      SubloopParents.insert(std::make_pair(Subloop, Unloop)).first->second;
  }

  succ_iterator I = succ_begin(BB), E = succ_end(BB);
  if (I == E) {
    assert(!Subloop && "subloop blocks must have a successor");
    NearLoop = nullptr; // unloop blocks may now exit the function.
  }
  for (; I != E; ++I) {
    if (*I == BB)
      continue; // self loops are uninteresting

    Loop *L = LI->getLoopFor(*I);
    if (L == Unloop) {
      // This successor has not been processed. This path must lead to an
      // irreducible backedge.
      assert((FoundIB || !DFS.hasPostorder(*I)) && "should have seen IB");
      FoundIB = true;
    }
    if (L != Unloop && Unloop->contains(L)) {
      // Successor is in a subloop.
      if (Subloop)
        continue; // Branching within subloops. Ignore it.

      // BB branches from the original into a subloop header.
      assert(L->getParentLoop() == Unloop && "cannot skip into nested loops");

      // Get the current nearest parent of the Subloop's exits.
      L = SubloopParents[L];
      // L could be Unloop if the only exit was an irreducible backedge.
    }
    if (L == Unloop) {
      continue;
    }
    // Handle critical edges from Unloop into a sibling loop.
    if (L && !L->contains(Unloop)) {
      L = L->getParentLoop();
    }
    // Remember the nearest parent loop among successors or subloop exits.
    if (NearLoop == Unloop || !NearLoop || NearLoop->contains(L))
      NearLoop = L;
  }
  if (Subloop) {
    SubloopParents[Subloop] = NearLoop;
    return BBLoop;
  }
  return NearLoop;
}

LoopInfo::LoopInfo(const DominatorTreeBase<BasicBlock> &DomTree) {
  analyze(DomTree);
}

void LoopInfo::markAsRemoved(Loop *Unloop) {
  assert(!Unloop->isInvalid() && "Loop has already been removed");
  Unloop->invalidate();
  RemovedLoops.push_back(Unloop);

  // First handle the special case of no parent loop to simplify the algorithm.
  if (!Unloop->getParentLoop()) {
    // Since BBLoop had no parent, Unloop blocks are no longer in a loop.
    for (Loop::block_iterator I = Unloop->block_begin(),
                              E = Unloop->block_end();
         I != E; ++I) {

      // Don't reparent blocks in subloops.
      if (getLoopFor(*I) != Unloop)
        continue;

      // Blocks no longer have a parent but are still referenced by Unloop until
      // the Unloop object is deleted.
      changeLoopFor(*I, nullptr);
    }

    // Remove the loop from the top-level LoopInfo object.
    for (iterator I = begin();; ++I) {
      assert(I != end() && "Couldn't find loop");
      if (*I == Unloop) {
        removeLoop(I);
        break;
      }
    }

    // Move all of the subloops to the top-level.
    while (!Unloop->empty())
      addTopLevelLoop(Unloop->removeChildLoop(std::prev(Unloop->end())));

    return;
  }

  // Update the parent loop for all blocks within the loop. Blocks within
  // subloops will not change parents.
  UnloopUpdater Updater(Unloop, this);
  Updater.updateBlockParents();

  // Remove blocks from former ancestor loops.
  Updater.removeBlocksFromAncestors();

  // Add direct subloops as children in their new parent loop.
  Updater.updateSubloopParents();

  // Remove unloop from its parent loop.
  Loop *ParentLoop = Unloop->getParentLoop();
  for (Loop::iterator I = ParentLoop->begin();; ++I) {
    assert(I != ParentLoop->end() && "Couldn't find loop");
    if (*I == Unloop) {
      ParentLoop->removeChildLoop(I);
      break;
    }
  }
}

char LoopAnalysis::PassID;

LoopInfo LoopAnalysis::run(Function &F, AnalysisManager<Function> &AM) {
  // FIXME: Currently we create a LoopInfo from scratch for every function.
  // This may prove to be too wasteful due to deallocating and re-allocating
  // memory each time for the underlying map and vector datastructures. At some
  // point it may prove worthwhile to use a freelist and recycle LoopInfo
  // objects. I don't want to add that kind of complexity until the scope of
  // the problem is better understood.
  LoopInfo LI;
  LI.analyze(AM.getResult<DominatorTreeAnalysis>(F));
  return LI;
}

PreservedAnalyses LoopPrinterPass::run(Function &F,
                                       AnalysisManager<Function> &AM) {
  AM.getResult<LoopAnalysis>(F).print(OS);
  return PreservedAnalyses::all();
}

PrintLoopPass::PrintLoopPass() : OS(dbgs()) {}
PrintLoopPass::PrintLoopPass(raw_ostream &OS, const std::string &Banner)
    : OS(OS), Banner(Banner) {}

PreservedAnalyses PrintLoopPass::run(Loop &L) {
  OS << Banner;
  for (auto *Block : L.blocks())
    if (Block)
      Block->print(OS);
    else
      OS << "Printing <null> block";
  return PreservedAnalyses::all();
}

//===----------------------------------------------------------------------===//
// LoopInfo implementation
//

char LoopInfoWrapperPass::ID = 0;
INITIALIZE_PASS_BEGIN(LoopInfoWrapperPass, "loops", "Natural Loop Information",
                      true, true)
INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
INITIALIZE_PASS_END(LoopInfoWrapperPass, "loops", "Natural Loop Information",
                    true, true)

bool LoopInfoWrapperPass::runOnFunction(Function &) {
  releaseMemory();
  LI.analyze(getAnalysis<DominatorTreeWrapperPass>().getDomTree());
  return false;
}

void LoopInfoWrapperPass::verifyAnalysis() const {
  // LoopInfoWrapperPass is a FunctionPass, but verifying every loop in the
  // function each time verifyAnalysis is called is very expensive. The
  // -verify-loop-info option can enable this. In order to perform some
  // checking by default, LoopPass has been taught to call verifyLoop manually
  // during loop pass sequences.
  if (VerifyLoopInfo)
    LI.verify();
}

void LoopInfoWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
  AU.setPreservesAll();
  AU.addRequired<DominatorTreeWrapperPass>();
}

void LoopInfoWrapperPass::print(raw_ostream &OS, const Module *) const {
  LI.print(OS);
}

//===----------------------------------------------------------------------===//
// LoopBlocksDFS implementation
//

/// Traverse the loop blocks and store the DFS result.
/// Useful for clients that just want the final DFS result and don't need to
/// visit blocks during the initial traversal.
void LoopBlocksDFS::perform(LoopInfo *LI) {
  LoopBlocksTraversal Traversal(*this, LI);
  for (LoopBlocksTraversal::POTIterator POI = Traversal.begin(),
         POE = Traversal.end(); POI != POE; ++POI) ;
}