LiveVariables.cpp revision a93d0f280693b8418bc88cf7a8c93325f7fcf4c6 
1//=- LiveVariables.cpp - Live Variable Analysis for Source CFGs ----------*-==//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9//
10// This file implements Live Variables analysis for source-level CFGs.
11//
12//===----------------------------------------------------------------------===//
13
14#include "clang/Analysis/Analyses/LiveVariables.h"
15#include "clang/Analysis/Analyses/PostOrderCFGView.h"
16#include "clang/Analysis/CFG.h"
17#include "clang/Analysis/AnalysisContext.h"
18#include "clang/AST/Stmt.h"
19#include "clang/AST/StmtVisitor.h"
20#include "llvm/ADT/DenseMap.h"
21#include "llvm/ADT/PostOrderIterator.h"
22#include "llvm/Support/raw_ostream.h"
23#include <algorithm>
24#include <vector>
25
26using namespace clang;
27
28namespace {
29
30class DataflowWorklist {
31  SmallVector<const CFGBlock *, 20> worklist;
32  llvm::BitVector enqueuedBlocks;
33  PostOrderCFGView *POV;
34public:
35  DataflowWorklist(const CFG &cfg, AnalysisDeclContext &Ctx)
36    : enqueuedBlocks(cfg.getNumBlockIDs()),
37      POV(Ctx.getAnalysis<PostOrderCFGView>()) {}
38
39  void enqueueBlock(const CFGBlock *block);
40  void enqueueSuccessors(const CFGBlock *block);
41  void enqueuePredecessors(const CFGBlock *block);
42
43  const CFGBlock *dequeue();
44
45  void sortWorklist();
46};
47
48}
49
50void DataflowWorklist::enqueueBlock(const clang::CFGBlock *block) {
51  if (block && !enqueuedBlocks[block->getBlockID()]) {
52    enqueuedBlocks[block->getBlockID()] = true;
53    worklist.push_back(block);
54  }
55}
56
57void DataflowWorklist::enqueueSuccessors(const clang::CFGBlock *block) {
58  const unsigned OldWorklistSize = worklist.size();
59  for (CFGBlock::const_succ_iterator I = block->succ_begin(),
60       E = block->succ_end(); I != E; ++I) {
61    enqueueBlock(*I);
62  }
63
64  if (OldWorklistSize == 0 || OldWorklistSize == worklist.size())
65    return;
66
67  sortWorklist();
68}
69
70void DataflowWorklist::enqueuePredecessors(const clang::CFGBlock *block) {
71  const unsigned OldWorklistSize = worklist.size();
72  for (CFGBlock::const_pred_iterator I = block->pred_begin(),
73       E = block->pred_end(); I != E; ++I) {
74    enqueueBlock(*I);
75  }
76
77  if (OldWorklistSize == 0 || OldWorklistSize == worklist.size())
78    return;
79
80  sortWorklist();
81}
82
83void DataflowWorklist::sortWorklist() {
84  std::sort(worklist.begin(), worklist.end(), POV->getComparator());
85}
86
87const CFGBlock *DataflowWorklist::dequeue() {
88  if (worklist.empty())
89    return 0;
90  const CFGBlock *b = worklist.back();
91  worklist.pop_back();
92  enqueuedBlocks[b->getBlockID()] = false;
93  return b;
94}
95
96namespace {
97class LiveVariablesImpl {
98public:
99  AnalysisDeclContext &analysisContext;
100  std::vector<LiveVariables::LivenessValues> cfgBlockValues;
101  llvm::ImmutableSet<const Stmt *>::Factory SSetFact;
102  llvm::ImmutableSet<const VarDecl *>::Factory DSetFact;
103  llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues> blocksEndToLiveness;
104  llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues> blocksBeginToLiveness;
105  llvm::DenseMap<const Stmt *, LiveVariables::LivenessValues> stmtsToLiveness;
106  llvm::DenseMap<const DeclRefExpr *, unsigned> inAssignment;
107  const bool killAtAssign;
108
109  LiveVariables::LivenessValues
110  merge(LiveVariables::LivenessValues valsA,
111        LiveVariables::LivenessValues valsB);
112
113  LiveVariables::LivenessValues runOnBlock(const CFGBlock *block,
114                                           LiveVariables::LivenessValues val,
115                                           LiveVariables::Observer *obs = 0);
116
117  void dumpBlockLiveness(const SourceManager& M);
118
119  LiveVariablesImpl(AnalysisDeclContext &ac, bool KillAtAssign)
120    : analysisContext(ac),
121      SSetFact(false), // Do not canonicalize ImmutableSets by default.
122      DSetFact(false), // This is a *major* performance win.
123      killAtAssign(KillAtAssign) {}
124};
125}
126
127static LiveVariablesImpl &getImpl(void *x) {
128  return *((LiveVariablesImpl *) x);
129}
130
131//===----------------------------------------------------------------------===//
132// Operations and queries on LivenessValues.
133//===----------------------------------------------------------------------===//
134
135bool LiveVariables::LivenessValues::isLive(const Stmt *S) const {
136  return liveStmts.contains(S);
137}
138
139bool LiveVariables::LivenessValues::isLive(const VarDecl *D) const {
140  return liveDecls.contains(D);
141}
142
143namespace {
144  template <typename SET>
145  SET mergeSets(SET A, SET B) {
146    if (A.isEmpty())
147      return B;
148
149    for (typename SET::iterator it = B.begin(), ei = B.end(); it != ei; ++it) {
150      A = A.add(*it);
151    }
152    return A;
153  }
154}
155
156void LiveVariables::Observer::anchor() { }
157
158LiveVariables::LivenessValues
159LiveVariablesImpl::merge(LiveVariables::LivenessValues valsA,
160                         LiveVariables::LivenessValues valsB) {
161
162  llvm::ImmutableSetRef<const Stmt *>
163    SSetRefA(valsA.liveStmts.getRootWithoutRetain(), SSetFact.getTreeFactory()),
164    SSetRefB(valsB.liveStmts.getRootWithoutRetain(), SSetFact.getTreeFactory());
165
166
167  llvm::ImmutableSetRef<const VarDecl *>
168    DSetRefA(valsA.liveDecls.getRootWithoutRetain(), DSetFact.getTreeFactory()),
169    DSetRefB(valsB.liveDecls.getRootWithoutRetain(), DSetFact.getTreeFactory());
170
171
172  SSetRefA = mergeSets(SSetRefA, SSetRefB);
173  DSetRefA = mergeSets(DSetRefA, DSetRefB);
174
175  // asImmutableSet() canonicalizes the tree, allowing us to do an easy
176  // comparison afterwards.
177  return LiveVariables::LivenessValues(SSetRefA.asImmutableSet(),
178                                       DSetRefA.asImmutableSet());
179}
180
181bool LiveVariables::LivenessValues::equals(const LivenessValues &V) const {
182  return liveStmts == V.liveStmts && liveDecls == V.liveDecls;
183}
184
185//===----------------------------------------------------------------------===//
186// Query methods.
187//===----------------------------------------------------------------------===//
188
189static bool isAlwaysAlive(const VarDecl *D) {
190  return D->hasGlobalStorage();
191}
192
193bool LiveVariables::isLive(const CFGBlock *B, const VarDecl *D) {
194  return isAlwaysAlive(D) || getImpl(impl).blocksEndToLiveness[B].isLive(D);
195}
196
197bool LiveVariables::isLive(const Stmt *S, const VarDecl *D) {
198  return isAlwaysAlive(D) || getImpl(impl).stmtsToLiveness[S].isLive(D);
199}
200
201bool LiveVariables::isLive(const Stmt *Loc, const Stmt *S) {
202  return getImpl(impl).stmtsToLiveness[Loc].isLive(S);
203}
204
205//===----------------------------------------------------------------------===//
206// Dataflow computation.
207//===----------------------------------------------------------------------===//
208
209namespace {
210class TransferFunctions : public StmtVisitor<TransferFunctions> {
211  LiveVariablesImpl &LV;
212  LiveVariables::LivenessValues &val;
213  LiveVariables::Observer *observer;
214  const CFGBlock *currentBlock;
215public:
216  TransferFunctions(LiveVariablesImpl &im,
217                    LiveVariables::LivenessValues &Val,
218                    LiveVariables::Observer *Observer,
219                    const CFGBlock *CurrentBlock)
220  : LV(im), val(Val), observer(Observer), currentBlock(CurrentBlock) {}
221
222  void VisitBinaryOperator(BinaryOperator *BO);
223  void VisitBlockExpr(BlockExpr *BE);
224  void VisitDeclRefExpr(DeclRefExpr *DR);
225  void VisitDeclStmt(DeclStmt *DS);
226  void VisitObjCForCollectionStmt(ObjCForCollectionStmt *OS);
227  void VisitUnaryExprOrTypeTraitExpr(UnaryExprOrTypeTraitExpr *UE);
228  void VisitUnaryOperator(UnaryOperator *UO);
229  void Visit(Stmt *S);
230};
231}
232
233static const VariableArrayType *FindVA(QualType Ty) {
234  const Type *ty = Ty.getTypePtr();
235  while (const ArrayType *VT = dyn_cast<ArrayType>(ty)) {
236    if (const VariableArrayType *VAT = dyn_cast<VariableArrayType>(VT))
237      if (VAT->getSizeExpr())
238        return VAT;
239
240    ty = VT->getElementType().getTypePtr();
241  }
242
243  return 0;
244}
245
246static const Stmt *LookThroughStmt(const Stmt *S) {
247  while (S) {
248    if (const Expr *Ex = dyn_cast<Expr>(S))
249      S = Ex->IgnoreParens();
250    if (const ExprWithCleanups *EWC = dyn_cast<ExprWithCleanups>(S)) {
251      S = EWC->getSubExpr();
252      continue;
253    }
254    if (const OpaqueValueExpr *OVE = dyn_cast<OpaqueValueExpr>(S)) {
255      S = OVE->getSourceExpr();
256      continue;
257    }
258    break;
259  }
260  return S;
261}
262
263static void AddLiveStmt(llvm::ImmutableSet<const Stmt *> &Set,
264                        llvm::ImmutableSet<const Stmt *>::Factory &F,
265                        const Stmt *S) {
266  Set = F.add(Set, LookThroughStmt(S));
267}
268
269void TransferFunctions::Visit(Stmt *S) {
270  if (observer)
271    observer->observeStmt(S, currentBlock, val);
272
273  StmtVisitor<TransferFunctions>::Visit(S);
274
275  if (isa<Expr>(S)) {
276    val.liveStmts = LV.SSetFact.remove(val.liveStmts, S);
277  }
278
279  // Mark all children expressions live.
280
281  switch (S->getStmtClass()) {
282    default:
283      break;
284    case Stmt::StmtExprClass: {
285      // For statement expressions, look through the compound statement.
286      S = cast<StmtExpr>(S)->getSubStmt();
287      break;
288    }
289    case Stmt::CXXMemberCallExprClass: {
290      // Include the implicit "this" pointer as being live.
291      CXXMemberCallExpr *CE = cast<CXXMemberCallExpr>(S);
292      if (Expr *ImplicitObj = CE->getImplicitObjectArgument()) {
293        AddLiveStmt(val.liveStmts, LV.SSetFact, ImplicitObj);
294      }
295      break;
296    }
297    case Stmt::ObjCMessageExprClass: {
298      // In calls to super, include the implicit "self" pointer as being live.
299      ObjCMessageExpr *CE = cast<ObjCMessageExpr>(S);
300      if (CE->getReceiverKind() == ObjCMessageExpr::SuperInstance)
301        val.liveDecls = LV.DSetFact.add(val.liveDecls,
302                                        LV.analysisContext.getSelfDecl());
303      break;
304    }
305    case Stmt::DeclStmtClass: {
306      const DeclStmt *DS = cast<DeclStmt>(S);
307      if (const VarDecl *VD = dyn_cast<VarDecl>(DS->getSingleDecl())) {
308        for (const VariableArrayType* VA = FindVA(VD->getType());
309             VA != 0; VA = FindVA(VA->getElementType())) {
310          AddLiveStmt(val.liveStmts, LV.SSetFact, VA->getSizeExpr());
311        }
312      }
313      break;
314    }
315    case Stmt::PseudoObjectExprClass: {
316      // A pseudo-object operation only directly consumes its result
317      // expression.
318      Expr *child = cast<PseudoObjectExpr>(S)->getResultExpr();
319      if (!child) return;
320      if (OpaqueValueExpr *OV = dyn_cast<OpaqueValueExpr>(child))
321        child = OV->getSourceExpr();
322      child = child->IgnoreParens();
323      val.liveStmts = LV.SSetFact.add(val.liveStmts, child);
324      return;
325    }
326
327    // FIXME: These cases eventually shouldn't be needed.
328    case Stmt::ExprWithCleanupsClass: {
329      S = cast<ExprWithCleanups>(S)->getSubExpr();
330      break;
331    }
332    case Stmt::CXXBindTemporaryExprClass: {
333      S = cast<CXXBindTemporaryExpr>(S)->getSubExpr();
334      break;
335    }
336    case Stmt::UnaryExprOrTypeTraitExprClass: {
337      // No need to unconditionally visit subexpressions.
338      return;
339    }
340  }
341
342  for (Stmt::child_iterator it = S->child_begin(), ei = S->child_end();
343       it != ei; ++it) {
344    if (Stmt *child = *it)
345      AddLiveStmt(val.liveStmts, LV.SSetFact, child);
346  }
347}
348
349void TransferFunctions::VisitBinaryOperator(BinaryOperator *B) {
350  if (B->isAssignmentOp()) {
351    if (!LV.killAtAssign)
352      return;
353
354    // Assigning to a variable?
355    Expr *LHS = B->getLHS()->IgnoreParens();
356
357    if (DeclRefExpr *DR = dyn_cast<DeclRefExpr>(LHS))
358      if (const VarDecl *VD = dyn_cast<VarDecl>(DR->getDecl())) {
359        // Assignments to references don't kill the ref's address
360        if (VD->getType()->isReferenceType())
361          return;
362
363        if (!isAlwaysAlive(VD)) {
364          // The variable is now dead.
365          val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
366        }
367
368        if (observer)
369          observer->observerKill(DR);
370      }
371  }
372}
373
374void TransferFunctions::VisitBlockExpr(BlockExpr *BE) {
375  AnalysisDeclContext::referenced_decls_iterator I, E;
376  llvm::tie(I, E) =
377    LV.analysisContext.getReferencedBlockVars(BE->getBlockDecl());
378  for ( ; I != E ; ++I) {
379    const VarDecl *VD = *I;
380    if (isAlwaysAlive(VD))
381      continue;
382    val.liveDecls = LV.DSetFact.add(val.liveDecls, VD);
383  }
384}
385
386void TransferFunctions::VisitDeclRefExpr(DeclRefExpr *DR) {
387  if (const VarDecl *D = dyn_cast<VarDecl>(DR->getDecl()))
388    if (!isAlwaysAlive(D) && LV.inAssignment.find(DR) == LV.inAssignment.end())
389      val.liveDecls = LV.DSetFact.add(val.liveDecls, D);
390}
391
392void TransferFunctions::VisitDeclStmt(DeclStmt *DS) {
393  for (DeclStmt::decl_iterator DI=DS->decl_begin(), DE = DS->decl_end();
394       DI != DE; ++DI)
395    if (VarDecl *VD = dyn_cast<VarDecl>(*DI)) {
396      if (!isAlwaysAlive(VD))
397        val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
398    }
399}
400
401void TransferFunctions::VisitObjCForCollectionStmt(ObjCForCollectionStmt *OS) {
402  // Kill the iteration variable.
403  DeclRefExpr *DR = 0;
404  const VarDecl *VD = 0;
405
406  Stmt *element = OS->getElement();
407  if (DeclStmt *DS = dyn_cast<DeclStmt>(element)) {
408    VD = cast<VarDecl>(DS->getSingleDecl());
409  }
410  else if ((DR = dyn_cast<DeclRefExpr>(cast<Expr>(element)->IgnoreParens()))) {
411    VD = cast<VarDecl>(DR->getDecl());
412  }
413
414  if (VD) {
415    val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
416    if (observer && DR)
417      observer->observerKill(DR);
418  }
419}
420
421void TransferFunctions::
422VisitUnaryExprOrTypeTraitExpr(UnaryExprOrTypeTraitExpr *UE)
423{
424  // While sizeof(var) doesn't technically extend the liveness of 'var', it
425  // does extent the liveness of metadata if 'var' is a VariableArrayType.
426  // We handle that special case here.
427  if (UE->getKind() != UETT_SizeOf || UE->isArgumentType())
428    return;
429
430  const Expr *subEx = UE->getArgumentExpr();
431  if (subEx->getType()->isVariableArrayType()) {
432    assert(subEx->isLValue());
433    val.liveStmts = LV.SSetFact.add(val.liveStmts, subEx->IgnoreParens());
434  }
435}
436
437void TransferFunctions::VisitUnaryOperator(UnaryOperator *UO) {
438  // Treat ++/-- as a kill.
439  // Note we don't actually have to do anything if we don't have an observer,
440  // since a ++/-- acts as both a kill and a "use".
441  if (!observer)
442    return;
443
444  switch (UO->getOpcode()) {
445  default:
446    return;
447  case UO_PostInc:
448  case UO_PostDec:
449  case UO_PreInc:
450  case UO_PreDec:
451    break;
452  }
453
454  if (DeclRefExpr *DR = dyn_cast<DeclRefExpr>(UO->getSubExpr()->IgnoreParens()))
455    if (isa<VarDecl>(DR->getDecl())) {
456      // Treat ++/-- as a kill.
457      observer->observerKill(DR);
458    }
459}
460
461LiveVariables::LivenessValues
462LiveVariablesImpl::runOnBlock(const CFGBlock *block,
463                              LiveVariables::LivenessValues val,
464                              LiveVariables::Observer *obs) {
465
466  TransferFunctions TF(*this, val, obs, block);
467
468  // Visit the terminator (if any).
469  if (const Stmt *term = block->getTerminator())
470    TF.Visit(const_cast<Stmt*>(term));
471
472  // Apply the transfer function for all Stmts in the block.
473  for (CFGBlock::const_reverse_iterator it = block->rbegin(),
474       ei = block->rend(); it != ei; ++it) {
475    const CFGElement &elem = *it;
476
477    if (const CFGAutomaticObjDtor *Dtor = dyn_cast<CFGAutomaticObjDtor>(&elem)){
478      val.liveDecls = DSetFact.add(val.liveDecls, Dtor->getVarDecl());
479      continue;
480    }
481
482    if (!isa<CFGStmt>(elem))
483      continue;
484
485    const Stmt *S = cast<CFGStmt>(elem).getStmt();
486    TF.Visit(const_cast<Stmt*>(S));
487    stmtsToLiveness[S] = val;
488  }
489  return val;
490}
491
492void LiveVariables::runOnAllBlocks(LiveVariables::Observer &obs) {
493  const CFG *cfg = getImpl(impl).analysisContext.getCFG();
494  for (CFG::const_iterator it = cfg->begin(), ei = cfg->end(); it != ei; ++it)
495    getImpl(impl).runOnBlock(*it, getImpl(impl).blocksEndToLiveness[*it], &obs);
496}
497
498LiveVariables::LiveVariables(void *im) : impl(im) {}
499
500LiveVariables::~LiveVariables() {
501  delete (LiveVariablesImpl*) impl;
502}
503
504LiveVariables *
505LiveVariables::computeLiveness(AnalysisDeclContext &AC,
506                                 bool killAtAssign) {
507
508  // No CFG?  Bail out.
509  CFG *cfg = AC.getCFG();
510  if (!cfg)
511    return 0;
512
513  // The analysis currently has scalability issues for very large CFGs.
514  // Bail out if it looks too large.
515  if (cfg->getNumBlockIDs() > 300000)
516    return 0;
517
518  LiveVariablesImpl *LV = new LiveVariablesImpl(AC, killAtAssign);
519
520  // Construct the dataflow worklist.  Enqueue the exit block as the
521  // start of the analysis.
522  DataflowWorklist worklist(*cfg, AC);
523  llvm::BitVector everAnalyzedBlock(cfg->getNumBlockIDs());
524
525  // FIXME: we should enqueue using post order.
526  for (CFG::const_iterator it = cfg->begin(), ei = cfg->end(); it != ei; ++it) {
527    const CFGBlock *block = *it;
528    worklist.enqueueBlock(block);
529
530    // FIXME: Scan for DeclRefExprs using in the LHS of an assignment.
531    // We need to do this because we lack context in the reverse analysis
532    // to determine if a DeclRefExpr appears in such a context, and thus
533    // doesn't constitute a "use".
534    if (killAtAssign)
535      for (CFGBlock::const_iterator bi = block->begin(), be = block->end();
536           bi != be; ++bi) {
537        if (const CFGStmt *cs = bi->getAs<CFGStmt>()) {
538          if (const BinaryOperator *BO = dyn_cast<BinaryOperator>(cs->getStmt())) {
539            if (BO->getOpcode() == BO_Assign) {
540              if (const DeclRefExpr *DR =
541                    dyn_cast<DeclRefExpr>(BO->getLHS()->IgnoreParens())) {
542                LV->inAssignment[DR] = 1;
543              }
544            }
545          }
546        }
547      }
548  }
549
550  worklist.sortWorklist();
551
552  while (const CFGBlock *block = worklist.dequeue()) {
553    // Determine if the block's end value has changed.  If not, we
554    // have nothing left to do for this block.
555    LivenessValues &prevVal = LV->blocksEndToLiveness[block];
556
557    // Merge the values of all successor blocks.
558    LivenessValues val;
559    for (CFGBlock::const_succ_iterator it = block->succ_begin(),
560                                       ei = block->succ_end(); it != ei; ++it) {
561      if (const CFGBlock *succ = *it) {
562        val = LV->merge(val, LV->blocksBeginToLiveness[succ]);
563      }
564    }
565
566    if (!everAnalyzedBlock[block->getBlockID()])
567      everAnalyzedBlock[block->getBlockID()] = true;
568    else if (prevVal.equals(val))
569      continue;
570
571    prevVal = val;
572
573    // Update the dataflow value for the start of this block.
574    LV->blocksBeginToLiveness[block] = LV->runOnBlock(block, val);
575
576    // Enqueue the value to the predecessors.
577    worklist.enqueuePredecessors(block);
578  }
579
580  return new LiveVariables(LV);
581}
582
583static bool compare_entries(const CFGBlock *A, const CFGBlock *B) {
584  return A->getBlockID() < B->getBlockID();
585}
586
587static bool compare_vd_entries(const Decl *A, const Decl *B) {
588  SourceLocation ALoc = A->getLocStart();
589  SourceLocation BLoc = B->getLocStart();
590  return ALoc.getRawEncoding() < BLoc.getRawEncoding();
591}
592
593void LiveVariables::dumpBlockLiveness(const SourceManager &M) {
594  getImpl(impl).dumpBlockLiveness(M);
595}
596
597void LiveVariablesImpl::dumpBlockLiveness(const SourceManager &M) {
598  std::vector<const CFGBlock *> vec;
599  for (llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues>::iterator
600       it = blocksEndToLiveness.begin(), ei = blocksEndToLiveness.end();
601       it != ei; ++it) {
602    vec.push_back(it->first);
603  }
604  std::sort(vec.begin(), vec.end(), compare_entries);
605
606  std::vector<const VarDecl*> declVec;
607
608  for (std::vector<const CFGBlock *>::iterator
609        it = vec.begin(), ei = vec.end(); it != ei; ++it) {
610    llvm::errs() << "\n[ B" << (*it)->getBlockID()
611                 << " (live variables at block exit) ]\n";
612
613    LiveVariables::LivenessValues vals = blocksEndToLiveness[*it];
614    declVec.clear();
615
616    for (llvm::ImmutableSet<const VarDecl *>::iterator si =
617          vals.liveDecls.begin(),
618          se = vals.liveDecls.end(); si != se; ++si) {
619      declVec.push_back(*si);
620    }
621
622    std::sort(declVec.begin(), declVec.end(), compare_vd_entries);
623
624    for (std::vector<const VarDecl*>::iterator di = declVec.begin(),
625         de = declVec.end(); di != de; ++di) {
626      llvm::errs() << " " << (*di)->getDeclName().getAsString()
627                   << " <";
628      (*di)->getLocation().dump(M);
629      llvm::errs() << ">\n";
630    }
631  }
632  llvm::errs() << "\n";
633}
634
635const void *LiveVariables::getTag() { static int x; return &x; }
636const void *RelaxedLiveVariables::getTag() { static int x; return &x; }
637