clang/lib/Analysis/LiveVariables.cpp - toolchain/llvm-project - Gitiles

 //=- LiveVariables.cpp - Live Variable Analysis for Source CFGs ----------*-==//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // This file implements Live Variables analysis for source-level CFGs.
 //
 //===----------------------------------------------------------------------===//

 #include "clang/Analysis/Analyses/LiveVariables.h"
 #include "clang/AST/Stmt.h"
 #include "clang/AST/StmtVisitor.h"
 #include "clang/Analysis/Analyses/PostOrderCFGView.h"
 #include "clang/Analysis/AnalysisContext.h"
 #include "clang/Analysis/CFG.h"
 #include "llvm/ADT/DenseMap.h"
 #include "llvm/ADT/PostOrderIterator.h"
 #include "llvm/Support/raw_ostream.h"
 #include <algorithm>
 #include <vector>

 using namespace clang;

 namespace {

 class DataflowWorklist {
   SmallVector<const CFGBlock *, 20> worklist;
   llvm::BitVector enqueuedBlocks;
   PostOrderCFGView *POV;
 public:
   DataflowWorklist(const CFG &cfg, AnalysisDeclContext &Ctx)
     : enqueuedBlocks(cfg.getNumBlockIDs()),
       POV(Ctx.getAnalysis<PostOrderCFGView>()) {}

   void enqueueBlock(const CFGBlock *block);
   void enqueuePredecessors(const CFGBlock *block);

   const CFGBlock *dequeue();

   void sortWorklist();
 };

 }

 void DataflowWorklist::enqueueBlock(const clang::CFGBlock *block) {
   if (block && !enqueuedBlocks[block->getBlockID()]) {
     enqueuedBlocks[block->getBlockID()] = true;
     worklist.push_back(block);
   }
 }

 void DataflowWorklist::enqueuePredecessors(const clang::CFGBlock *block) {
   const unsigned OldWorklistSize = worklist.size();
   for (CFGBlock::const_pred_iterator I = block->pred_begin(),
        E = block->pred_end(); I != E; ++I) {
     enqueueBlock(*I);
   }

   if (OldWorklistSize == 0 || OldWorklistSize == worklist.size())
     return;

   sortWorklist();
 }

 void DataflowWorklist::sortWorklist() {
   std::sort(worklist.begin(), worklist.end(), POV->getComparator());
 }

 const CFGBlock *DataflowWorklist::dequeue() {
   if (worklist.empty())
     return nullptr;
   const CFGBlock *b = worklist.pop_back_val();
   enqueuedBlocks[b->getBlockID()] = false;
   return b;
 }

 namespace {
 class LiveVariablesImpl {
 public:
   AnalysisDeclContext &analysisContext;
   llvm::ImmutableSet<const Stmt *>::Factory SSetFact;
   llvm::ImmutableSet<const VarDecl *>::Factory DSetFact;
   llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues> blocksEndToLiveness;
   llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues> blocksBeginToLiveness;
   llvm::DenseMap<const Stmt *, LiveVariables::LivenessValues> stmtsToLiveness;
   llvm::DenseMap<const DeclRefExpr *, unsigned> inAssignment;
   const bool killAtAssign;

   LiveVariables::LivenessValues
   merge(LiveVariables::LivenessValues valsA,
         LiveVariables::LivenessValues valsB);

   LiveVariables::LivenessValues
   runOnBlock(const CFGBlock *block, LiveVariables::LivenessValues val,
              LiveVariables::Observer *obs = nullptr);

   void dumpBlockLiveness(const SourceManager& M);

   LiveVariablesImpl(AnalysisDeclContext &ac, bool KillAtAssign)
     : analysisContext(ac),
       SSetFact(false), // Do not canonicalize ImmutableSets by default.
       DSetFact(false), // This is a *major* performance win.
       killAtAssign(KillAtAssign) {}
 };
 }

 static LiveVariablesImpl &getImpl(void *x) {
   return *((LiveVariablesImpl *) x);
 }

 //===----------------------------------------------------------------------===//
 // Operations and queries on LivenessValues.
 //===----------------------------------------------------------------------===//

 bool LiveVariables::LivenessValues::isLive(const Stmt *S) const {
   return liveStmts.contains(S);
 }

 bool LiveVariables::LivenessValues::isLive(const VarDecl *D) const {
   return liveDecls.contains(D);
 }

 namespace {
   template <typename SET>
   SET mergeSets(SET A, SET B) {
     if (A.isEmpty())
       return B;

     for (typename SET::iterator it = B.begin(), ei = B.end(); it != ei; ++it) {
       A = A.add(*it);
     }
     return A;
   }
 }

 void LiveVariables::Observer::anchor() { }

 LiveVariables::LivenessValues
 LiveVariablesImpl::merge(LiveVariables::LivenessValues valsA,
                          LiveVariables::LivenessValues valsB) {

   llvm::ImmutableSetRef<const Stmt *>
     SSetRefA(valsA.liveStmts.getRootWithoutRetain(), SSetFact.getTreeFactory()),
     SSetRefB(valsB.liveStmts.getRootWithoutRetain(), SSetFact.getTreeFactory());


   llvm::ImmutableSetRef<const VarDecl *>
     DSetRefA(valsA.liveDecls.getRootWithoutRetain(), DSetFact.getTreeFactory()),
     DSetRefB(valsB.liveDecls.getRootWithoutRetain(), DSetFact.getTreeFactory());


   SSetRefA = mergeSets(SSetRefA, SSetRefB);
   DSetRefA = mergeSets(DSetRefA, DSetRefB);

   // asImmutableSet() canonicalizes the tree, allowing us to do an easy
   // comparison afterwards.
   return LiveVariables::LivenessValues(SSetRefA.asImmutableSet(),
                                        DSetRefA.asImmutableSet());
 }

 bool LiveVariables::LivenessValues::equals(const LivenessValues &V) const {
   return liveStmts == V.liveStmts && liveDecls == V.liveDecls;
 }

 //===----------------------------------------------------------------------===//
 // Query methods.
 //===----------------------------------------------------------------------===//

 static bool isAlwaysAlive(const VarDecl *D) {
   return D->hasGlobalStorage();
 }

 bool LiveVariables::isLive(const CFGBlock *B, const VarDecl *D) {
   return isAlwaysAlive(D) || getImpl(impl).blocksEndToLiveness[B].isLive(D);
 }

 bool LiveVariables::isLive(const Stmt *S, const VarDecl *D) {
   return isAlwaysAlive(D) || getImpl(impl).stmtsToLiveness[S].isLive(D);
 }

 bool LiveVariables::isLive(const Stmt *Loc, const Stmt *S) {
   return getImpl(impl).stmtsToLiveness[Loc].isLive(S);
 }

 //===----------------------------------------------------------------------===//
 // Dataflow computation.
 //===----------------------------------------------------------------------===//

 namespace {
 class TransferFunctions : public StmtVisitor<TransferFunctions> {
   LiveVariablesImpl &LV;
   LiveVariables::LivenessValues &val;
   LiveVariables::Observer *observer;
   const CFGBlock *currentBlock;
 public:
   TransferFunctions(LiveVariablesImpl &im,
                     LiveVariables::LivenessValues &Val,
                     LiveVariables::Observer *Observer,
                     const CFGBlock *CurrentBlock)
   : LV(im), val(Val), observer(Observer), currentBlock(CurrentBlock) {}

   void VisitBinaryOperator(BinaryOperator *BO);
   void VisitBlockExpr(BlockExpr *BE);
   void VisitDeclRefExpr(DeclRefExpr *DR);
   void VisitDeclStmt(DeclStmt *DS);
   void VisitObjCForCollectionStmt(ObjCForCollectionStmt *OS);
   void VisitUnaryExprOrTypeTraitExpr(UnaryExprOrTypeTraitExpr *UE);
   void VisitUnaryOperator(UnaryOperator *UO);
   void Visit(Stmt *S);
 };
 }

 static const VariableArrayType *FindVA(QualType Ty) {
   const Type *ty = Ty.getTypePtr();
   while (const ArrayType *VT = dyn_cast<ArrayType>(ty)) {
     if (const VariableArrayType *VAT = dyn_cast<VariableArrayType>(VT))
       if (VAT->getSizeExpr())
         return VAT;

     ty = VT->getElementType().getTypePtr();
   }

   return nullptr;
 }

 static const Stmt *LookThroughStmt(const Stmt *S) {
   while (S) {
     if (const Expr *Ex = dyn_cast<Expr>(S))
       S = Ex->IgnoreParens();
     if (const ExprWithCleanups *EWC = dyn_cast<ExprWithCleanups>(S)) {
       S = EWC->getSubExpr();
       continue;
     }
     if (const OpaqueValueExpr *OVE = dyn_cast<OpaqueValueExpr>(S)) {
       S = OVE->getSourceExpr();
       continue;
     }
     break;
   }
   return S;
 }

 static void AddLiveStmt(llvm::ImmutableSet<const Stmt *> &Set,
                         llvm::ImmutableSet<const Stmt *>::Factory &F,
                         const Stmt *S) {
   Set = F.add(Set, LookThroughStmt(S));
 }

 void TransferFunctions::Visit(Stmt *S) {
   if (observer)
     observer->observeStmt(S, currentBlock, val);

   StmtVisitor<TransferFunctions>::Visit(S);

   if (isa<Expr>(S)) {
     val.liveStmts = LV.SSetFact.remove(val.liveStmts, S);
   }

   // Mark all children expressions live.

   switch (S->getStmtClass()) {
     default:
       break;
     case Stmt::StmtExprClass: {
       // For statement expressions, look through the compound statement.
       S = cast<StmtExpr>(S)->getSubStmt();
       break;
     }
     case Stmt::CXXMemberCallExprClass: {
       // Include the implicit "this" pointer as being live.
       CXXMemberCallExpr *CE = cast<CXXMemberCallExpr>(S);
       if (Expr *ImplicitObj = CE->getImplicitObjectArgument()) {
         AddLiveStmt(val.liveStmts, LV.SSetFact, ImplicitObj);
       }
       break;
     }
     case Stmt::ObjCMessageExprClass: {
       // In calls to super, include the implicit "self" pointer as being live.
       ObjCMessageExpr *CE = cast<ObjCMessageExpr>(S);
       if (CE->getReceiverKind() == ObjCMessageExpr::SuperInstance)
         val.liveDecls = LV.DSetFact.add(val.liveDecls,
                                         LV.analysisContext.getSelfDecl());
       break;
     }
     case Stmt::DeclStmtClass: {
       const DeclStmt *DS = cast<DeclStmt>(S);
       if (const VarDecl *VD = dyn_cast<VarDecl>(DS->getSingleDecl())) {
         for (const VariableArrayType* VA = FindVA(VD->getType());
              VA != nullptr; VA = FindVA(VA->getElementType())) {
           AddLiveStmt(val.liveStmts, LV.SSetFact, VA->getSizeExpr());
         }
       }
       break;
     }
     case Stmt::PseudoObjectExprClass: {
       // A pseudo-object operation only directly consumes its result
       // expression.
       Expr *child = cast<PseudoObjectExpr>(S)->getResultExpr();
       if (!child) return;
       if (OpaqueValueExpr *OV = dyn_cast<OpaqueValueExpr>(child))
         child = OV->getSourceExpr();
       child = child->IgnoreParens();
       val.liveStmts = LV.SSetFact.add(val.liveStmts, child);
       return;
     }

     // FIXME: These cases eventually shouldn't be needed.
     case Stmt::ExprWithCleanupsClass: {
       S = cast<ExprWithCleanups>(S)->getSubExpr();
       break;
     }
     case Stmt::CXXBindTemporaryExprClass: {
       S = cast<CXXBindTemporaryExpr>(S)->getSubExpr();
       break;
     }
     case Stmt::UnaryExprOrTypeTraitExprClass: {
       // No need to unconditionally visit subexpressions.
       return;
     }
   }

   for (Stmt *Child : S->children()) {
     if (Child)
       AddLiveStmt(val.liveStmts, LV.SSetFact, Child);
   }
 }

 void TransferFunctions::VisitBinaryOperator(BinaryOperator *B) {
   if (B->isAssignmentOp()) {
     if (!LV.killAtAssign)
       return;

     // Assigning to a variable?
     Expr *LHS = B->getLHS()->IgnoreParens();

     if (DeclRefExpr *DR = dyn_cast<DeclRefExpr>(LHS))
       if (const VarDecl *VD = dyn_cast<VarDecl>(DR->getDecl())) {
         // Assignments to references don't kill the ref's address
         if (VD->getType()->isReferenceType())
           return;

         if (!isAlwaysAlive(VD)) {
           // The variable is now dead.
           val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
         }

         if (observer)
           observer->observerKill(DR);
       }
   }
 }

 void TransferFunctions::VisitBlockExpr(BlockExpr *BE) {
   for (const VarDecl *VD :
        LV.analysisContext.getReferencedBlockVars(BE->getBlockDecl())) {
     if (isAlwaysAlive(VD))
       continue;
     val.liveDecls = LV.DSetFact.add(val.liveDecls, VD);
   }
 }

 void TransferFunctions::VisitDeclRefExpr(DeclRefExpr *DR) {
   if (const VarDecl *D = dyn_cast<VarDecl>(DR->getDecl()))
     if (!isAlwaysAlive(D) && LV.inAssignment.find(DR) == LV.inAssignment.end())
       val.liveDecls = LV.DSetFact.add(val.liveDecls, D);
 }

 void TransferFunctions::VisitDeclStmt(DeclStmt *DS) {
   for (const auto *DI : DS->decls())
     if (const auto *VD = dyn_cast<VarDecl>(DI)) {
       if (!isAlwaysAlive(VD))
         val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
     }
 }

 void TransferFunctions::VisitObjCForCollectionStmt(ObjCForCollectionStmt *OS) {
   // Kill the iteration variable.
   DeclRefExpr *DR = nullptr;
   const VarDecl *VD = nullptr;

   Stmt *element = OS->getElement();
   if (DeclStmt *DS = dyn_cast<DeclStmt>(element)) {
     VD = cast<VarDecl>(DS->getSingleDecl());
   }
   else if ((DR = dyn_cast<DeclRefExpr>(cast<Expr>(element)->IgnoreParens()))) {
     VD = cast<VarDecl>(DR->getDecl());
   }

   if (VD) {
     val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
     if (observer && DR)
       observer->observerKill(DR);
   }
 }

 void TransferFunctions::
 VisitUnaryExprOrTypeTraitExpr(UnaryExprOrTypeTraitExpr *UE)
 {
   // While sizeof(var) doesn't technically extend the liveness of 'var', it
   // does extent the liveness of metadata if 'var' is a VariableArrayType.
   // We handle that special case here.
   if (UE->getKind() != UETT_SizeOf || UE->isArgumentType())
     return;

   const Expr *subEx = UE->getArgumentExpr();
   if (subEx->getType()->isVariableArrayType()) {
     assert(subEx->isLValue());
     val.liveStmts = LV.SSetFact.add(val.liveStmts, subEx->IgnoreParens());
   }
 }

 void TransferFunctions::VisitUnaryOperator(UnaryOperator *UO) {
   // Treat ++/-- as a kill.
   // Note we don't actually have to do anything if we don't have an observer,
   // since a ++/-- acts as both a kill and a "use".
   if (!observer)
     return;

   switch (UO->getOpcode()) {
   default:
     return;
   case UO_PostInc:
   case UO_PostDec:
   case UO_PreInc:
   case UO_PreDec:
     break;
   }

   if (DeclRefExpr *DR = dyn_cast<DeclRefExpr>(UO->getSubExpr()->IgnoreParens()))
     if (isa<VarDecl>(DR->getDecl())) {
       // Treat ++/-- as a kill.
       observer->observerKill(DR);
     }
 }

 LiveVariables::LivenessValues
 LiveVariablesImpl::runOnBlock(const CFGBlock *block,
                               LiveVariables::LivenessValues val,
                               LiveVariables::Observer *obs) {

   TransferFunctions TF(*this, val, obs, block);

   // Visit the terminator (if any).
   if (const Stmt *term = block->getTerminator())
     TF.Visit(const_cast<Stmt*>(term));

   // Apply the transfer function for all Stmts in the block.
   for (CFGBlock::const_reverse_iterator it = block->rbegin(),
        ei = block->rend(); it != ei; ++it) {
     const CFGElement &elem = *it;

     if (Optional<CFGAutomaticObjDtor> Dtor =
             elem.getAs<CFGAutomaticObjDtor>()) {
       val.liveDecls = DSetFact.add(val.liveDecls, Dtor->getVarDecl());
       continue;
     }

     if (!elem.getAs<CFGStmt>())
       continue;

     const Stmt *S = elem.castAs<CFGStmt>().getStmt();
     TF.Visit(const_cast<Stmt*>(S));
     stmtsToLiveness[S] = val;
   }
   return val;
 }

 void LiveVariables::runOnAllBlocks(LiveVariables::Observer &obs) {
   const CFG *cfg = getImpl(impl).analysisContext.getCFG();
   for (CFG::const_iterator it = cfg->begin(), ei = cfg->end(); it != ei; ++it)
     getImpl(impl).runOnBlock(*it, getImpl(impl).blocksEndToLiveness[*it], &obs);
 }

 LiveVariables::LiveVariables(void *im) : impl(im) {}

 LiveVariables::~LiveVariables() {
   delete (LiveVariablesImpl*) impl;
 }

 LiveVariables *
 LiveVariables::computeLiveness(AnalysisDeclContext &AC,
                                  bool killAtAssign) {

   // No CFG?  Bail out.
   CFG *cfg = AC.getCFG();
   if (!cfg)
     return nullptr;

   // The analysis currently has scalability issues for very large CFGs.
   // Bail out if it looks too large.
   if (cfg->getNumBlockIDs() > 300000)
     return nullptr;

   LiveVariablesImpl *LV = new LiveVariablesImpl(AC, killAtAssign);

   // Construct the dataflow worklist.  Enqueue the exit block as the
   // start of the analysis.
   DataflowWorklist worklist(*cfg, AC);
   llvm::BitVector everAnalyzedBlock(cfg->getNumBlockIDs());

   // FIXME: we should enqueue using post order.
   for (CFG::const_iterator it = cfg->begin(), ei = cfg->end(); it != ei; ++it) {
     const CFGBlock *block = *it;
     worklist.enqueueBlock(block);

     // FIXME: Scan for DeclRefExprs using in the LHS of an assignment.
     // We need to do this because we lack context in the reverse analysis
     // to determine if a DeclRefExpr appears in such a context, and thus
     // doesn't constitute a "use".
     if (killAtAssign)
       for (CFGBlock::const_iterator bi = block->begin(), be = block->end();
            bi != be; ++bi) {
         if (Optional<CFGStmt> cs = bi->getAs<CFGStmt>()) {
           if (const BinaryOperator *BO =
                   dyn_cast<BinaryOperator>(cs->getStmt())) {
             if (BO->getOpcode() == BO_Assign) {
               if (const DeclRefExpr *DR =
                     dyn_cast<DeclRefExpr>(BO->getLHS()->IgnoreParens())) {
                 LV->inAssignment[DR] = 1;
               }
             }
           }
         }
       }
   }

   worklist.sortWorklist();

   while (const CFGBlock *block = worklist.dequeue()) {
     // Determine if the block's end value has changed.  If not, we
     // have nothing left to do for this block.
     LivenessValues &prevVal = LV->blocksEndToLiveness[block];

     // Merge the values of all successor blocks.
     LivenessValues val;
     for (CFGBlock::const_succ_iterator it = block->succ_begin(),
                                        ei = block->succ_end(); it != ei; ++it) {
       if (const CFGBlock *succ = *it) {
         val = LV->merge(val, LV->blocksBeginToLiveness[succ]);
       }
     }

     if (!everAnalyzedBlock[block->getBlockID()])
       everAnalyzedBlock[block->getBlockID()] = true;
     else if (prevVal.equals(val))
       continue;

     prevVal = val;

     // Update the dataflow value for the start of this block.
     LV->blocksBeginToLiveness[block] = LV->runOnBlock(block, val);

     // Enqueue the value to the predecessors.
     worklist.enqueuePredecessors(block);
   }

   return new LiveVariables(LV);
 }

 void LiveVariables::dumpBlockLiveness(const SourceManager &M) {
   getImpl(impl).dumpBlockLiveness(M);
 }

 void LiveVariablesImpl::dumpBlockLiveness(const SourceManager &M) {
   std::vector<const CFGBlock *> vec;
   for (llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues>::iterator
        it = blocksEndToLiveness.begin(), ei = blocksEndToLiveness.end();
        it != ei; ++it) {
     vec.push_back(it->first);
   }
   std::sort(vec.begin(), vec.end(), [](const CFGBlock *A, const CFGBlock *B) {
     return A->getBlockID() < B->getBlockID();
   });

   std::vector<const VarDecl*> declVec;

   for (std::vector<const CFGBlock *>::iterator
         it = vec.begin(), ei = vec.end(); it != ei; ++it) {
     llvm::errs() << "\n[ B" << (*it)->getBlockID()
                  << " (live variables at block exit) ]\n";

     LiveVariables::LivenessValues vals = blocksEndToLiveness[*it];
     declVec.clear();

     for (llvm::ImmutableSet<const VarDecl *>::iterator si =
           vals.liveDecls.begin(),
           se = vals.liveDecls.end(); si != se; ++si) {
       declVec.push_back(*si);
     }

     std::sort(declVec.begin(), declVec.end(), [](const Decl *A, const Decl *B) {
       return A->getLocStart() < B->getLocStart();
     });

     for (std::vector<const VarDecl*>::iterator di = declVec.begin(),
          de = declVec.end(); di != de; ++di) {
       llvm::errs() << " " << (*di)->getDeclName().getAsString()
                    << " <";
       (*di)->getLocation().dump(M);
       llvm::errs() << ">\n";
     }
   }
   llvm::errs() << "\n";
 }

 const void *LiveVariables::getTag() { static int x; return &x; }
 const void *RelaxedLiveVariables::getTag() { static int x; return &x; }
	//=- LiveVariables.cpp - Live Variable Analysis for Source CFGs ----------*-==//
	//
	// The LLVM Compiler Infrastructure
	//
	// This file is distributed under the University of Illinois Open Source
	// License. See LICENSE.TXT for details.
	//
	//===----------------------------------------------------------------------===//
	//
	// This file implements Live Variables analysis for source-level CFGs.
	//
	//===----------------------------------------------------------------------===//

	#include "clang/Analysis/Analyses/LiveVariables.h"
	#include "clang/AST/Stmt.h"
	#include "clang/AST/StmtVisitor.h"
	#include "clang/Analysis/Analyses/PostOrderCFGView.h"
	#include "clang/Analysis/AnalysisContext.h"
	#include "clang/Analysis/CFG.h"
	#include "llvm/ADT/DenseMap.h"
	#include "llvm/ADT/PostOrderIterator.h"
	#include "llvm/Support/raw_ostream.h"
	#include <algorithm>
	#include <vector>

	using namespace clang;

	namespace {

	class DataflowWorklist {
	SmallVector<const CFGBlock *, 20> worklist;
	llvm::BitVector enqueuedBlocks;
	PostOrderCFGView *POV;
	public:
	DataflowWorklist(const CFG &cfg, AnalysisDeclContext &Ctx)
	: enqueuedBlocks(cfg.getNumBlockIDs()),
	POV(Ctx.getAnalysis<PostOrderCFGView>()) {}

	void enqueueBlock(const CFGBlock *block);
	void enqueuePredecessors(const CFGBlock *block);

	const CFGBlock *dequeue();

	void sortWorklist();
	};

	}

	void DataflowWorklist::enqueueBlock(const clang::CFGBlock *block) {
	if (block && !enqueuedBlocks[block->getBlockID()]) {
	enqueuedBlocks[block->getBlockID()] = true;
	worklist.push_back(block);
	}
	}

	void DataflowWorklist::enqueuePredecessors(const clang::CFGBlock *block) {
	const unsigned OldWorklistSize = worklist.size();
	for (CFGBlock::const_pred_iterator I = block->pred_begin(),
	E = block->pred_end(); I != E; ++I) {
	enqueueBlock(*I);
	}

	if (OldWorklistSize == 0 \|\| OldWorklistSize == worklist.size())
	return;

	sortWorklist();
	}

	void DataflowWorklist::sortWorklist() {
	std::sort(worklist.begin(), worklist.end(), POV->getComparator());
	}

	const CFGBlock *DataflowWorklist::dequeue() {
	if (worklist.empty())
	return nullptr;
	const CFGBlock *b = worklist.pop_back_val();
	enqueuedBlocks[b->getBlockID()] = false;
	return b;
	}

	namespace {
	class LiveVariablesImpl {
	public:
	AnalysisDeclContext &analysisContext;
	llvm::ImmutableSet<const Stmt *>::Factory SSetFact;
	llvm::ImmutableSet<const VarDecl *>::Factory DSetFact;
	llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues> blocksEndToLiveness;
	llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues> blocksBeginToLiveness;
	llvm::DenseMap<const Stmt *, LiveVariables::LivenessValues> stmtsToLiveness;
	llvm::DenseMap<const DeclRefExpr *, unsigned> inAssignment;
	const bool killAtAssign;

	LiveVariables::LivenessValues
	merge(LiveVariables::LivenessValues valsA,
	LiveVariables::LivenessValues valsB);

	LiveVariables::LivenessValues
	runOnBlock(const CFGBlock *block, LiveVariables::LivenessValues val,
	LiveVariables::Observer *obs = nullptr);

	void dumpBlockLiveness(const SourceManager& M);

	LiveVariablesImpl(AnalysisDeclContext &ac, bool KillAtAssign)
	: analysisContext(ac),
	SSetFact(false), // Do not canonicalize ImmutableSets by default.
	DSetFact(false), // This is a major performance win.
	killAtAssign(KillAtAssign) {}
	};
	}

	static LiveVariablesImpl &getImpl(void *x) {
	return ((LiveVariablesImpl ) x);
	}

	//===----------------------------------------------------------------------===//
	// Operations and queries on LivenessValues.
	//===----------------------------------------------------------------------===//

	bool LiveVariables::LivenessValues::isLive(const Stmt *S) const {
	return liveStmts.contains(S);
	}

	bool LiveVariables::LivenessValues::isLive(const VarDecl *D) const {
	return liveDecls.contains(D);
	}

	namespace {
	template <typename SET>
	SET mergeSets(SET A, SET B) {
	if (A.isEmpty())
	return B;

	for (typename SET::iterator it = B.begin(), ei = B.end(); it != ei; ++it) {
	A = A.add(*it);
	}
	return A;
	}
	}

	void LiveVariables::Observer::anchor() { }

	LiveVariables::LivenessValues
	LiveVariablesImpl::merge(LiveVariables::LivenessValues valsA,
	LiveVariables::LivenessValues valsB) {

	llvm::ImmutableSetRef<const Stmt *>
	SSetRefA(valsA.liveStmts.getRootWithoutRetain(), SSetFact.getTreeFactory()),
	SSetRefB(valsB.liveStmts.getRootWithoutRetain(), SSetFact.getTreeFactory());


	llvm::ImmutableSetRef<const VarDecl *>
	DSetRefA(valsA.liveDecls.getRootWithoutRetain(), DSetFact.getTreeFactory()),
	DSetRefB(valsB.liveDecls.getRootWithoutRetain(), DSetFact.getTreeFactory());


	SSetRefA = mergeSets(SSetRefA, SSetRefB);
	DSetRefA = mergeSets(DSetRefA, DSetRefB);

	// asImmutableSet() canonicalizes the tree, allowing us to do an easy
	// comparison afterwards.
	return LiveVariables::LivenessValues(SSetRefA.asImmutableSet(),
	DSetRefA.asImmutableSet());
	}

	bool LiveVariables::LivenessValues::equals(const LivenessValues &V) const {
	return liveStmts == V.liveStmts && liveDecls == V.liveDecls;
	}

	//===----------------------------------------------------------------------===//
	// Query methods.
	//===----------------------------------------------------------------------===//

	static bool isAlwaysAlive(const VarDecl *D) {
	return D->hasGlobalStorage();
	}

	bool LiveVariables::isLive(const CFGBlock B, const VarDecl D) {
	return isAlwaysAlive(D) \|\| getImpl(impl).blocksEndToLiveness[B].isLive(D);
	}

	bool LiveVariables::isLive(const Stmt S, const VarDecl D) {
	return isAlwaysAlive(D) \|\| getImpl(impl).stmtsToLiveness[S].isLive(D);
	}

	bool LiveVariables::isLive(const Stmt Loc, const Stmt S) {
	return getImpl(impl).stmtsToLiveness[Loc].isLive(S);
	}

	//===----------------------------------------------------------------------===//
	// Dataflow computation.
	//===----------------------------------------------------------------------===//

	namespace {
	class TransferFunctions : public StmtVisitor<TransferFunctions> {
	LiveVariablesImpl &LV;
	LiveVariables::LivenessValues &val;
	LiveVariables::Observer *observer;
	const CFGBlock *currentBlock;
	public:
	TransferFunctions(LiveVariablesImpl &im,
	LiveVariables::LivenessValues &Val,
	LiveVariables::Observer *Observer,
	const CFGBlock *CurrentBlock)
	: LV(im), val(Val), observer(Observer), currentBlock(CurrentBlock) {}

	void VisitBinaryOperator(BinaryOperator *BO);
	void VisitBlockExpr(BlockExpr *BE);
	void VisitDeclRefExpr(DeclRefExpr *DR);
	void VisitDeclStmt(DeclStmt *DS);
	void VisitObjCForCollectionStmt(ObjCForCollectionStmt *OS);
	void VisitUnaryExprOrTypeTraitExpr(UnaryExprOrTypeTraitExpr *UE);
	void VisitUnaryOperator(UnaryOperator *UO);
	void Visit(Stmt *S);
	};
	}

	static const VariableArrayType *FindVA(QualType Ty) {
	const Type *ty = Ty.getTypePtr();
	while (const ArrayType *VT = dyn_cast<ArrayType>(ty)) {
	if (const VariableArrayType *VAT = dyn_cast<VariableArrayType>(VT))
	if (VAT->getSizeExpr())
	return VAT;

	ty = VT->getElementType().getTypePtr();
	}

	return nullptr;
	}

	static const Stmt LookThroughStmt(const Stmt S) {
	while (S) {
	if (const Expr *Ex = dyn_cast<Expr>(S))
	S = Ex->IgnoreParens();
	if (const ExprWithCleanups *EWC = dyn_cast<ExprWithCleanups>(S)) {
	S = EWC->getSubExpr();
	continue;
	}
	if (const OpaqueValueExpr *OVE = dyn_cast<OpaqueValueExpr>(S)) {
	S = OVE->getSourceExpr();
	continue;
	}
	break;
	}
	return S;
	}

	static void AddLiveStmt(llvm::ImmutableSet<const Stmt *> &Set,
	llvm::ImmutableSet<const Stmt *>::Factory &F,
	const Stmt *S) {
	Set = F.add(Set, LookThroughStmt(S));
	}

	void TransferFunctions::Visit(Stmt *S) {
	if (observer)
	observer->observeStmt(S, currentBlock, val);

	StmtVisitor<TransferFunctions>::Visit(S);

	if (isa<Expr>(S)) {
	val.liveStmts = LV.SSetFact.remove(val.liveStmts, S);
	}

	// Mark all children expressions live.

	switch (S->getStmtClass()) {
	default:
	break;
	case Stmt::StmtExprClass: {
	// For statement expressions, look through the compound statement.
	S = cast<StmtExpr>(S)->getSubStmt();
	break;
	}
	case Stmt::CXXMemberCallExprClass: {
	// Include the implicit "this" pointer as being live.
	CXXMemberCallExpr *CE = cast<CXXMemberCallExpr>(S);
	if (Expr *ImplicitObj = CE->getImplicitObjectArgument()) {
	AddLiveStmt(val.liveStmts, LV.SSetFact, ImplicitObj);
	}
	break;
	}
	case Stmt::ObjCMessageExprClass: {
	// In calls to super, include the implicit "self" pointer as being live.
	ObjCMessageExpr *CE = cast<ObjCMessageExpr>(S);
	if (CE->getReceiverKind() == ObjCMessageExpr::SuperInstance)
	val.liveDecls = LV.DSetFact.add(val.liveDecls,
	LV.analysisContext.getSelfDecl());
	break;
	}
	case Stmt::DeclStmtClass: {
	const DeclStmt *DS = cast<DeclStmt>(S);
	if (const VarDecl *VD = dyn_cast<VarDecl>(DS->getSingleDecl())) {
	for (const VariableArrayType* VA = FindVA(VD->getType());
	VA != nullptr; VA = FindVA(VA->getElementType())) {
	AddLiveStmt(val.liveStmts, LV.SSetFact, VA->getSizeExpr());
	}
	}
	break;
	}
	case Stmt::PseudoObjectExprClass: {
	// A pseudo-object operation only directly consumes its result
	// expression.
	Expr *child = cast<PseudoObjectExpr>(S)->getResultExpr();
	if (!child) return;
	if (OpaqueValueExpr *OV = dyn_cast<OpaqueValueExpr>(child))
	child = OV->getSourceExpr();
	child = child->IgnoreParens();
	val.liveStmts = LV.SSetFact.add(val.liveStmts, child);
	return;
	}

	// FIXME: These cases eventually shouldn't be needed.
	case Stmt::ExprWithCleanupsClass: {
	S = cast<ExprWithCleanups>(S)->getSubExpr();
	break;
	}
	case Stmt::CXXBindTemporaryExprClass: {
	S = cast<CXXBindTemporaryExpr>(S)->getSubExpr();
	break;
	}
	case Stmt::UnaryExprOrTypeTraitExprClass: {
	// No need to unconditionally visit subexpressions.
	return;
	}
	}

	for (Stmt *Child : S->children()) {
	if (Child)
	AddLiveStmt(val.liveStmts, LV.SSetFact, Child);
	}
	}

	void TransferFunctions::VisitBinaryOperator(BinaryOperator *B) {
	if (B->isAssignmentOp()) {
	if (!LV.killAtAssign)
	return;

	// Assigning to a variable?
	Expr *LHS = B->getLHS()->IgnoreParens();

	if (DeclRefExpr *DR = dyn_cast<DeclRefExpr>(LHS))
	if (const VarDecl *VD = dyn_cast<VarDecl>(DR->getDecl())) {
	// Assignments to references don't kill the ref's address
	if (VD->getType()->isReferenceType())
	return;

	if (!isAlwaysAlive(VD)) {
	// The variable is now dead.
	val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
	}

	if (observer)
	observer->observerKill(DR);
	}
	}
	}

	void TransferFunctions::VisitBlockExpr(BlockExpr *BE) {
	for (const VarDecl *VD :
	LV.analysisContext.getReferencedBlockVars(BE->getBlockDecl())) {
	if (isAlwaysAlive(VD))
	continue;
	val.liveDecls = LV.DSetFact.add(val.liveDecls, VD);
	}
	}

	void TransferFunctions::VisitDeclRefExpr(DeclRefExpr *DR) {
	if (const VarDecl *D = dyn_cast<VarDecl>(DR->getDecl()))
	if (!isAlwaysAlive(D) && LV.inAssignment.find(DR) == LV.inAssignment.end())
	val.liveDecls = LV.DSetFact.add(val.liveDecls, D);
	}

	void TransferFunctions::VisitDeclStmt(DeclStmt *DS) {
	for (const auto *DI : DS->decls())
	if (const auto *VD = dyn_cast<VarDecl>(DI)) {
	if (!isAlwaysAlive(VD))
	val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
	}
	}

	void TransferFunctions::VisitObjCForCollectionStmt(ObjCForCollectionStmt *OS) {
	// Kill the iteration variable.
	DeclRefExpr *DR = nullptr;
	const VarDecl *VD = nullptr;

	Stmt *element = OS->getElement();
	if (DeclStmt *DS = dyn_cast<DeclStmt>(element)) {
	VD = cast<VarDecl>(DS->getSingleDecl());
	}
	else if ((DR = dyn_cast<DeclRefExpr>(cast<Expr>(element)->IgnoreParens()))) {
	VD = cast<VarDecl>(DR->getDecl());
	}

	if (VD) {
	val.liveDecls = LV.DSetFact.remove(val.liveDecls, VD);
	if (observer && DR)
	observer->observerKill(DR);
	}
	}

	void TransferFunctions::
	VisitUnaryExprOrTypeTraitExpr(UnaryExprOrTypeTraitExpr *UE)
	{
	// While sizeof(var) doesn't technically extend the liveness of 'var', it
	// does extent the liveness of metadata if 'var' is a VariableArrayType.
	// We handle that special case here.
	if (UE->getKind() != UETT_SizeOf \|\| UE->isArgumentType())
	return;

	const Expr *subEx = UE->getArgumentExpr();
	if (subEx->getType()->isVariableArrayType()) {
	assert(subEx->isLValue());
	val.liveStmts = LV.SSetFact.add(val.liveStmts, subEx->IgnoreParens());
	}
	}

	void TransferFunctions::VisitUnaryOperator(UnaryOperator *UO) {
	// Treat ++/-- as a kill.
	// Note we don't actually have to do anything if we don't have an observer,
	// since a ++/-- acts as both a kill and a "use".
	if (!observer)
	return;

	switch (UO->getOpcode()) {
	default:
	return;
	case UO_PostInc:
	case UO_PostDec:
	case UO_PreInc:
	case UO_PreDec:
	break;
	}

	if (DeclRefExpr *DR = dyn_cast<DeclRefExpr>(UO->getSubExpr()->IgnoreParens()))
	if (isa<VarDecl>(DR->getDecl())) {
	// Treat ++/-- as a kill.
	observer->observerKill(DR);
	}
	}

	LiveVariables::LivenessValues
	LiveVariablesImpl::runOnBlock(const CFGBlock *block,
	LiveVariables::LivenessValues val,
	LiveVariables::Observer *obs) {

	TransferFunctions TF(*this, val, obs, block);

	// Visit the terminator (if any).
	if (const Stmt *term = block->getTerminator())
	TF.Visit(const_cast<Stmt*>(term));

	// Apply the transfer function for all Stmts in the block.
	for (CFGBlock::const_reverse_iterator it = block->rbegin(),
	ei = block->rend(); it != ei; ++it) {
	const CFGElement &elem = *it;

	if (Optional<CFGAutomaticObjDtor> Dtor =
	elem.getAs<CFGAutomaticObjDtor>()) {
	val.liveDecls = DSetFact.add(val.liveDecls, Dtor->getVarDecl());
	continue;
	}

	if (!elem.getAs<CFGStmt>())
	continue;

	const Stmt *S = elem.castAs<CFGStmt>().getStmt();
	TF.Visit(const_cast<Stmt*>(S));
	stmtsToLiveness[S] = val;
	}
	return val;
	}

	void LiveVariables::runOnAllBlocks(LiveVariables::Observer &obs) {
	const CFG *cfg = getImpl(impl).analysisContext.getCFG();
	for (CFG::const_iterator it = cfg->begin(), ei = cfg->end(); it != ei; ++it)
	getImpl(impl).runOnBlock(it, getImpl(impl).blocksEndToLiveness[it], &obs);
	}

	LiveVariables::LiveVariables(void *im) : impl(im) {}

	LiveVariables::~LiveVariables() {
	delete (LiveVariablesImpl*) impl;
	}

	LiveVariables *
	LiveVariables::computeLiveness(AnalysisDeclContext &AC,
	bool killAtAssign) {

	// No CFG? Bail out.
	CFG *cfg = AC.getCFG();
	if (!cfg)
	return nullptr;

	// The analysis currently has scalability issues for very large CFGs.
	// Bail out if it looks too large.
	if (cfg->getNumBlockIDs() > 300000)
	return nullptr;

	LiveVariablesImpl *LV = new LiveVariablesImpl(AC, killAtAssign);

	// Construct the dataflow worklist. Enqueue the exit block as the
	// start of the analysis.
	DataflowWorklist worklist(*cfg, AC);
	llvm::BitVector everAnalyzedBlock(cfg->getNumBlockIDs());

	// FIXME: we should enqueue using post order.
	for (CFG::const_iterator it = cfg->begin(), ei = cfg->end(); it != ei; ++it) {
	const CFGBlock block = it;
	worklist.enqueueBlock(block);

	// FIXME: Scan for DeclRefExprs using in the LHS of an assignment.
	// We need to do this because we lack context in the reverse analysis
	// to determine if a DeclRefExpr appears in such a context, and thus
	// doesn't constitute a "use".
	if (killAtAssign)
	for (CFGBlock::const_iterator bi = block->begin(), be = block->end();
	bi != be; ++bi) {
	if (Optional<CFGStmt> cs = bi->getAs<CFGStmt>()) {
	if (const BinaryOperator *BO =
	dyn_cast<BinaryOperator>(cs->getStmt())) {
	if (BO->getOpcode() == BO_Assign) {
	if (const DeclRefExpr *DR =
	dyn_cast<DeclRefExpr>(BO->getLHS()->IgnoreParens())) {
	LV->inAssignment[DR] = 1;
	}
	}
	}
	}
	}
	}

	worklist.sortWorklist();

	while (const CFGBlock *block = worklist.dequeue()) {
	// Determine if the block's end value has changed. If not, we
	// have nothing left to do for this block.
	LivenessValues &prevVal = LV->blocksEndToLiveness[block];

	// Merge the values of all successor blocks.
	LivenessValues val;
	for (CFGBlock::const_succ_iterator it = block->succ_begin(),
	ei = block->succ_end(); it != ei; ++it) {
	if (const CFGBlock succ = it) {
	val = LV->merge(val, LV->blocksBeginToLiveness[succ]);
	}
	}

	if (!everAnalyzedBlock[block->getBlockID()])
	everAnalyzedBlock[block->getBlockID()] = true;
	else if (prevVal.equals(val))
	continue;

	prevVal = val;

	// Update the dataflow value for the start of this block.
	LV->blocksBeginToLiveness[block] = LV->runOnBlock(block, val);

	// Enqueue the value to the predecessors.
	worklist.enqueuePredecessors(block);
	}

	return new LiveVariables(LV);
	}

	void LiveVariables::dumpBlockLiveness(const SourceManager &M) {
	getImpl(impl).dumpBlockLiveness(M);
	}

	void LiveVariablesImpl::dumpBlockLiveness(const SourceManager &M) {
	std::vector<const CFGBlock *> vec;
	for (llvm::DenseMap<const CFGBlock *, LiveVariables::LivenessValues>::iterator
	it = blocksEndToLiveness.begin(), ei = blocksEndToLiveness.end();
	it != ei; ++it) {
	vec.push_back(it->first);
	}
	std::sort(vec.begin(), vec.end(), [](const CFGBlock A, const CFGBlock B) {
	return A->getBlockID() < B->getBlockID();
	});

	std::vector<const VarDecl*> declVec;

	for (std::vector<const CFGBlock *>::iterator
	it = vec.begin(), ei = vec.end(); it != ei; ++it) {
	llvm::errs() << "\n[ B" << (*it)->getBlockID()
	<< " (live variables at block exit) ]\n";

	LiveVariables::LivenessValues vals = blocksEndToLiveness[*it];
	declVec.clear();

	for (llvm::ImmutableSet<const VarDecl *>::iterator si =
	vals.liveDecls.begin(),
	se = vals.liveDecls.end(); si != se; ++si) {
	declVec.push_back(*si);
	}

	std::sort(declVec.begin(), declVec.end(), [](const Decl A, const Decl B) {
	return A->getLocStart() < B->getLocStart();
	});

	for (std::vector<const VarDecl*>::iterator di = declVec.begin(),
	de = declVec.end(); di != de; ++di) {
	llvm::errs() << " " << (*di)->getDeclName().getAsString()
	<< " <";
	(*di)->getLocation().dump(M);
	llvm::errs() << ">\n";
	}
	}
	llvm::errs() << "\n";
	}

	const void *LiveVariables::getTag() { static int x; return &x; }
	const void *RelaxedLiveVariables::getTag() { static int x; return &x; }