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