IdempotentOperationChecker.cpp

//==- IdempotentOperationChecker.cpp - Idempotent Operations ----*- C++ -*-==//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file defines a set of path-sensitive checks for idempotent and/or
// tautological operations. Each potential operation is checked along all paths
// to see if every path results in a pointless operation.
//                 +-------------------------------------------+
//                 |Table of idempotent/tautological operations|
//                 +-------------------------------------------+
//+--------------------------------------------------------------------------+
//|Operator | x op x | x op 1 | 1 op x | x op 0 | 0 op x | x op ~0 | ~0 op x |
//+--------------------------------------------------------------------------+
//  +, +=   |        |        |        |   x    |   x    |         |
//  -, -=   |        |        |        |   x    |   -x   |         |
//  *, *=   |        |   x    |   x    |   0    |   0    |         |
//  /, /=   |   1    |   x    |        |  N/A   |   0    |         |
//  &, &=   |   x    |        |        |   0    |   0    |   x     |    x
//  |, |=   |   x    |        |        |   x    |   x    |   ~0    |    ~0
//  ^, ^=   |   0    |        |        |   x    |   x    |         |
//  <<, <<= |        |        |        |   x    |   0    |         |
//  >>, >>= |        |        |        |   x    |   0    |         |
//  ||      |   1    |   1    |   1    |   x    |   x    |   1     |    1
//  &&      |   1    |   x    |   x    |   0    |   0    |   x     |    x
//  =       |   x    |        |        |        |        |         |
//  ==      |   1    |        |        |        |        |         |
//  >=      |   1    |        |        |        |        |         |
//  <=      |   1    |        |        |        |        |         |
//  >       |   0    |        |        |        |        |         |
//  <       |   0    |        |        |        |        |         |
//  !=      |   0    |        |        |        |        |         |
//===----------------------------------------------------------------------===//
//
// Things TODO:
// - Improved error messages
// - Handle mixed assumptions (which assumptions can belong together?)
// - Finer grained false positive control (levels)
// - Handling ~0 values

#include "GRExprEngineExperimentalChecks.h"
#include "clang/Analysis/CFGStmtMap.h"
#include "clang/Analysis/Analyses/PseudoConstantAnalysis.h"
#include "clang/Checker/BugReporter/BugReporter.h"
#include "clang/Checker/BugReporter/BugType.h"
#include "clang/Checker/PathSensitive/CheckerHelpers.h"
#include "clang/Checker/PathSensitive/CheckerVisitor.h"
#include "clang/Checker/PathSensitive/GRCoreEngine.h"
#include "clang/Checker/PathSensitive/SVals.h"
#include "clang/AST/Stmt.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/Support/ErrorHandling.h"
#include <deque>

using namespace clang;

namespace {
class IdempotentOperationChecker
  : public CheckerVisitor<IdempotentOperationChecker> {
public:
  static void *getTag();
  void PreVisitBinaryOperator(CheckerContext &C, const BinaryOperator *B);
  void PostVisitBinaryOperator(CheckerContext &C, const BinaryOperator *B);
  void VisitEndAnalysis(ExplodedGraph &G, BugReporter &B, GRExprEngine &Eng);

private:
  // Our assumption about a particular operation.
  enum Assumption { Possible = 0, Impossible, Equal, LHSis1, RHSis1, LHSis0,
      RHSis0 };

  void UpdateAssumption(Assumption &A, const Assumption &New);

  // False positive reduction methods
  static bool isSelfAssign(const Expr *LHS, const Expr *RHS);
  static bool isUnused(const Expr *E, AnalysisContext *AC);
  static bool isTruncationExtensionAssignment(const Expr *LHS,
                                              const Expr *RHS);
  bool PathWasCompletelyAnalyzed(const CFG *C,
                                 const CFGBlock *CB,
                                 const GRCoreEngine &CE);
  static bool CanVary(const Expr *Ex,
                      AnalysisContext *AC);
  static bool isConstantOrPseudoConstant(const DeclRefExpr *DR,
                                         AnalysisContext *AC);
  static bool containsNonLocalVarDecl(const Stmt *S);
  const ExplodedNodeSet getLastRelevantNodes(const CFGBlock *Begin,
                                             const ExplodedNode *N);

  // Hash table and related data structures
  struct BinaryOperatorData {
    BinaryOperatorData() : assumption(Possible), analysisContext(0) {}

    Assumption assumption;
    AnalysisContext *analysisContext;
    ExplodedNodeSet explodedNodes; // Set of ExplodedNodes that refer to a
                                   // BinaryOperator
  };
  typedef llvm::DenseMap<const BinaryOperator *, BinaryOperatorData>
      AssumptionMap;
  AssumptionMap hash;

  // A class that performs reachability queries for CFGBlocks. Several internal
  // checks in this checker require reachability information. The requests all
  // tend to have a common destination, so we lazily do a predecessor search
  // from the destination node and cache the results to prevent work
  // duplication.
  class CFGReachabilityAnalysis {
    typedef llvm::SmallSet<unsigned, 32> ReachableSet;
    typedef llvm::DenseMap<unsigned, ReachableSet> ReachableMap;
    ReachableSet analyzed;
    ReachableMap reachable;
  public:
    inline bool isReachable(const CFGBlock *Src, const CFGBlock *Dst);
  private:
    void MapReachability(const CFGBlock *Dst);
  };
  CFGReachabilityAnalysis CRA;
};
}

void *IdempotentOperationChecker::getTag() {
  static int x = 0;
  return &x;
}

void clang::RegisterIdempotentOperationChecker(GRExprEngine &Eng) {
  Eng.registerCheck(new IdempotentOperationChecker());
}

void IdempotentOperationChecker::PreVisitBinaryOperator(
                                                      CheckerContext &C,
                                                      const BinaryOperator *B) {
  // Find or create an entry in the hash for this BinaryOperator instance.
  // If we haven't done a lookup before, it will get default initialized to
  // 'Possible'. At this stage we do not store the ExplodedNode, as it has not
  // been created yet.
  BinaryOperatorData &Data = hash[B];
  Assumption &A = Data.assumption;
  AnalysisContext *AC = C.getCurrentAnalysisContext();
  Data.analysisContext = AC;

  // If we already have visited this node on a path that does not contain an
  // idempotent operation, return immediately.
  if (A == Impossible)
    return;

  // Retrieve both sides of the operator and determine if they can vary (which
  // may mean this is a false positive.
  const Expr *LHS = B->getLHS();
  const Expr *RHS = B->getRHS();

  // At this stage we can calculate whether each side contains a false positive
  // that applies to all operators. We only need to calculate this the first
  // time.
  bool LHSContainsFalsePositive = false, RHSContainsFalsePositive = false;
  if (A == Possible) {
    // An expression contains a false positive if it can't vary, or if it
    // contains a known false positive VarDecl.
    LHSContainsFalsePositive = !CanVary(LHS, AC)
        || containsNonLocalVarDecl(LHS);
    RHSContainsFalsePositive = !CanVary(RHS, AC)
        || containsNonLocalVarDecl(RHS);
  }

  const GRState *state = C.getState();

  SVal LHSVal = state->getSVal(LHS);
  SVal RHSVal = state->getSVal(RHS);

  // If either value is unknown, we can't be 100% sure of all paths.
  if (LHSVal.isUnknownOrUndef() || RHSVal.isUnknownOrUndef()) {
    A = Impossible;
    return;
  }
  BinaryOperator::Opcode Op = B->getOpcode();

  // Dereference the LHS SVal if this is an assign operation
  switch (Op) {
  default:
    break;

  // Fall through intentional
  case BO_AddAssign:
  case BO_SubAssign:
  case BO_MulAssign:
  case BO_DivAssign:
  case BO_AndAssign:
  case BO_OrAssign:
  case BO_XorAssign:
  case BO_ShlAssign:
  case BO_ShrAssign:
  case BO_Assign:
  // Assign statements have one extra level of indirection
    if (!isa<Loc>(LHSVal)) {
      A = Impossible;
      return;
    }
    LHSVal = state->getSVal(cast<Loc>(LHSVal), LHS->getType());
  }


  // We now check for various cases which result in an idempotent operation.

  // x op x
  switch (Op) {
  default:
    break; // We don't care about any other operators.

  // Fall through intentional
  case BO_Assign:
    // x Assign x can be used to silence unused variable warnings intentionally.
    // If this is a self assignment and the variable is referenced elsewhere,
    // and the assignment is not a truncation or extension, then it is a false
    // positive.
    if (isSelfAssign(LHS, RHS)) {
      if (!isUnused(LHS, AC) && !isTruncationExtensionAssignment(LHS, RHS)) {
        UpdateAssumption(A, Equal);
        return;
      }
      else {
        A = Impossible;
        return;
      }
    }

  case BO_SubAssign:
  case BO_DivAssign:
  case BO_AndAssign:
  case BO_OrAssign:
  case BO_XorAssign:
  case BO_Sub:
  case BO_Div:
  case BO_And:
  case BO_Or:
  case BO_Xor:
  case BO_LOr:
  case BO_LAnd:
  case BO_EQ:
  case BO_NE:
    if (LHSVal != RHSVal || LHSContainsFalsePositive
        || RHSContainsFalsePositive)
      break;
    UpdateAssumption(A, Equal);
    return;
  }

  // x op 1
  switch (Op) {
   default:
     break; // We don't care about any other operators.

   // Fall through intentional
   case BO_MulAssign:
   case BO_DivAssign:
   case BO_Mul:
   case BO_Div:
   case BO_LOr:
   case BO_LAnd:
     if (!RHSVal.isConstant(1) || RHSContainsFalsePositive)
       break;
     UpdateAssumption(A, RHSis1);
     return;
  }

  // 1 op x
  switch (Op) {
  default:
    break; // We don't care about any other operators.

  // Fall through intentional
  case BO_MulAssign:
  case BO_Mul:
  case BO_LOr:
  case BO_LAnd:
    if (!LHSVal.isConstant(1) || LHSContainsFalsePositive)
      break;
    UpdateAssumption(A, LHSis1);
    return;
  }

  // x op 0
  switch (Op) {
  default:
    break; // We don't care about any other operators.

  // Fall through intentional
  case BO_AddAssign:
  case BO_SubAssign:
  case BO_MulAssign:
  case BO_AndAssign:
  case BO_OrAssign:
  case BO_XorAssign:
  case BO_Add:
  case BO_Sub:
  case BO_Mul:
  case BO_And:
  case BO_Or:
  case BO_Xor:
  case BO_Shl:
  case BO_Shr:
  case BO_LOr:
  case BO_LAnd:
    if (!RHSVal.isConstant(0) || RHSContainsFalsePositive)
      break;
    UpdateAssumption(A, RHSis0);
    return;
  }

  // 0 op x
  switch (Op) {
  default:
    break; // We don't care about any other operators.

  // Fall through intentional
  //case BO_AddAssign: // Common false positive
  case BO_SubAssign: // Check only if unsigned
  case BO_MulAssign:
  case BO_DivAssign:
  case BO_AndAssign:
  //case BO_OrAssign: // Common false positive
  //case BO_XorAssign: // Common false positive
  case BO_ShlAssign:
  case BO_ShrAssign:
  case BO_Add:
  case BO_Sub:
  case BO_Mul:
  case BO_Div:
  case BO_And:
  case BO_Or:
  case BO_Xor:
  case BO_Shl:
  case BO_Shr:
  case BO_LOr:
  case BO_LAnd:
    if (!LHSVal.isConstant(0) || LHSContainsFalsePositive)
      break;
    UpdateAssumption(A, LHSis0);
    return;
  }

  // If we get to this point, there has been a valid use of this operation.
  A = Impossible;
}

// At the post visit stage, the predecessor ExplodedNode will be the
// BinaryOperator that was just created. We use this hook to collect the
// ExplodedNode.
void IdempotentOperationChecker::PostVisitBinaryOperator(
                                                      CheckerContext &C,
                                                      const BinaryOperator *B) {
  // Add the ExplodedNode we just visited
  BinaryOperatorData &Data = hash[B];
  assert(isa<BinaryOperator>(cast<StmtPoint>(C.getPredecessor()
                                             ->getLocation()).getStmt()));
  Data.explodedNodes.Add(C.getPredecessor());
}

void IdempotentOperationChecker::VisitEndAnalysis(ExplodedGraph &G,
                                                  BugReporter &BR,
                                                  GRExprEngine &Eng) {
  BugType *BT = new BugType("Idempotent operation", "Dead code");
  // Iterate over the hash to see if we have any paths with definite
  // idempotent operations.
  for (AssumptionMap::const_iterator i = hash.begin(); i != hash.end(); ++i) {
    // Unpack the hash contents
    const BinaryOperatorData &Data = i->second;
    const Assumption &A = Data.assumption;
    AnalysisContext *AC = Data.analysisContext;
    const ExplodedNodeSet &ES = Data.explodedNodes;

    const BinaryOperator *B = i->first;

    if (A == Impossible)
      continue;

    // If the analyzer did not finish, check to see if we can still emit this
    // warning
    if (Eng.hasWorkRemaining()) {
      const CFGStmtMap *CBM = CFGStmtMap::Build(AC->getCFG(),
                                                &AC->getParentMap());

      // If we can trace back
      if (!PathWasCompletelyAnalyzed(AC->getCFG(),
                                     CBM->getBlock(B),
                                     Eng.getCoreEngine()))
        continue;

      delete CBM;
    }

    // Select the error message and SourceRanges to report.
    llvm::SmallString<128> buf;
    llvm::raw_svector_ostream os(buf);
    bool LHSRelevant = false, RHSRelevant = false;
    switch (A) {
    case Equal:
      LHSRelevant = true;
      RHSRelevant = true;
      if (B->getOpcode() == BO_Assign)
        os << "Assigned value is always the same as the existing value";
      else
        os << "Both operands to '" << B->getOpcodeStr()
           << "' always have the same value";
      break;
    case LHSis1:
      LHSRelevant = true;
      os << "The left operand to '" << B->getOpcodeStr() << "' is always 1";
      break;
    case RHSis1:
      RHSRelevant = true;
      os << "The right operand to '" << B->getOpcodeStr() << "' is always 1";
      break;
    case LHSis0:
      LHSRelevant = true;
      os << "The left operand to '" << B->getOpcodeStr() << "' is always 0";
      break;
    case RHSis0:
      RHSRelevant = true;
      os << "The right operand to '" << B->getOpcodeStr() << "' is always 0";
      break;
    case Possible:
      llvm_unreachable("Operation was never marked with an assumption");
    case Impossible:
      llvm_unreachable(0);
    }

    // Add a report for each ExplodedNode
    for (ExplodedNodeSet::iterator I = ES.begin(), E = ES.end(); I != E; ++I) {
      EnhancedBugReport *report = new EnhancedBugReport(*BT, os.str(), *I);

      // Add source ranges and visitor hooks
      if (LHSRelevant) {
        const Expr *LHS = i->first->getLHS();
        report->addRange(LHS->getSourceRange());
        report->addVisitorCreator(bugreporter::registerVarDeclsLastStore, LHS);
      }
      if (RHSRelevant) {
        const Expr *RHS = i->first->getRHS();
        report->addRange(i->first->getRHS()->getSourceRange());
        report->addVisitorCreator(bugreporter::registerVarDeclsLastStore, RHS);
      }

      BR.EmitReport(report);
    }
  }
}

// Updates the current assumption given the new assumption
inline void IdempotentOperationChecker::UpdateAssumption(Assumption &A,
                                                        const Assumption &New) {
// If the assumption is the same, there is nothing to do
  if (A == New)
    return;

  switch (A) {
  // If we don't currently have an assumption, set it
  case Possible:
    A = New;
    return;

  // If we have determined that a valid state happened, ignore the new
  // assumption.
  case Impossible:
    return;

  // Any other case means that we had a different assumption last time. We don't
  // currently support mixing assumptions for diagnostic reasons, so we set
  // our assumption to be impossible.
  default:
    A = Impossible;
    return;
  }
}

// Check for a statement where a variable is self assigned to possibly avoid an
// unused variable warning.
bool IdempotentOperationChecker::isSelfAssign(const Expr *LHS, const Expr *RHS) {
  LHS = LHS->IgnoreParenCasts();
  RHS = RHS->IgnoreParenCasts();

  const DeclRefExpr *LHS_DR = dyn_cast<DeclRefExpr>(LHS);
  if (!LHS_DR)
    return false;

  const VarDecl *VD = dyn_cast<VarDecl>(LHS_DR->getDecl());
  if (!VD)
    return false;

  const DeclRefExpr *RHS_DR = dyn_cast<DeclRefExpr>(RHS);
  if (!RHS_DR)
    return false;

  if (VD != RHS_DR->getDecl())
    return false;

  return true;
}

// Returns true if the Expr points to a VarDecl that is not read anywhere
// outside of self-assignments.
bool IdempotentOperationChecker::isUnused(const Expr *E,
                                          AnalysisContext *AC) {
  if (!E)
    return false;

  const DeclRefExpr *DR = dyn_cast<DeclRefExpr>(E->IgnoreParenCasts());
  if (!DR)
    return false;

  const VarDecl *VD = dyn_cast<VarDecl>(DR->getDecl());
  if (!VD)
    return false;

  if (AC->getPseudoConstantAnalysis()->wasReferenced(VD))
    return false;

  return true;
}

// Check for self casts truncating/extending a variable
bool IdempotentOperationChecker::isTruncationExtensionAssignment(
                                                              const Expr *LHS,
                                                              const Expr *RHS) {

  const DeclRefExpr *LHS_DR = dyn_cast<DeclRefExpr>(LHS->IgnoreParenCasts());
  if (!LHS_DR)
    return false;

  const VarDecl *VD = dyn_cast<VarDecl>(LHS_DR->getDecl());
  if (!VD)
    return false;

  const DeclRefExpr *RHS_DR = dyn_cast<DeclRefExpr>(RHS->IgnoreParenCasts());
  if (!RHS_DR)
    return false;

  if (VD != RHS_DR->getDecl())
     return false;

  return dyn_cast<DeclRefExpr>(RHS->IgnoreParens()) == NULL;
}

// Returns false if a path to this block was not completely analyzed, or true
// otherwise.
bool IdempotentOperationChecker::PathWasCompletelyAnalyzed(
                                                       const CFG *C,
                                                       const CFGBlock *CB,
                                                       const GRCoreEngine &CE) {
  // Test for reachability from any aborted blocks to this block
  typedef GRCoreEngine::BlocksAborted::const_iterator AbortedIterator;
  for (AbortedIterator I = CE.blocks_aborted_begin(),
      E = CE.blocks_aborted_end(); I != E; ++I) {
    const BlockEdge &BE =  I->first;

    // The destination block on the BlockEdge is the first block that was not
    // analyzed. If we can reach this block from the aborted block, then this
    // block was not completely analyzed.
    if (CRA.isReachable(BE.getDst(), CB))
      return false;
  }

  // Verify that this block is reachable from the entry block
  if (!CRA.isReachable(&C->getEntry(), CB))
    return false;

  // If we get to this point, there is no connection to the entry block or an
  // aborted block. This path is unreachable and we can report the error.
  return true;
}

// Recursive function that determines whether an expression contains any element
// that varies. This could be due to a compile-time constant like sizeof. An
// expression may also involve a variable that behaves like a constant. The
// function returns true if the expression varies, and false otherwise.
bool IdempotentOperationChecker::CanVary(const Expr *Ex,
                                         AnalysisContext *AC) {
  // Parentheses and casts are irrelevant here
  Ex = Ex->IgnoreParenCasts();

  if (Ex->getLocStart().isMacroID())
    return false;

  switch (Ex->getStmtClass()) {
  // Trivially true cases
  case Stmt::ArraySubscriptExprClass:
  case Stmt::MemberExprClass:
  case Stmt::StmtExprClass:
  case Stmt::CallExprClass:
  case Stmt::VAArgExprClass:
  case Stmt::ShuffleVectorExprClass:
    return true;
  default:
    return true;

  // Trivially false cases
  case Stmt::IntegerLiteralClass:
  case Stmt::CharacterLiteralClass:
  case Stmt::FloatingLiteralClass:
  case Stmt::PredefinedExprClass:
  case Stmt::ImaginaryLiteralClass:
  case Stmt::StringLiteralClass:
  case Stmt::OffsetOfExprClass:
  case Stmt::CompoundLiteralExprClass:
  case Stmt::AddrLabelExprClass:
  case Stmt::TypesCompatibleExprClass:
  case Stmt::GNUNullExprClass:
  case Stmt::InitListExprClass:
  case Stmt::DesignatedInitExprClass:
  case Stmt::BlockExprClass:
  case Stmt::BlockDeclRefExprClass:
    return false;

  // Cases requiring custom logic
  case Stmt::SizeOfAlignOfExprClass: {
    const SizeOfAlignOfExpr *SE = cast<const SizeOfAlignOfExpr>(Ex);
    if (!SE->isSizeOf())
      return false;
    return SE->getTypeOfArgument()->isVariableArrayType();
  }
  case Stmt::DeclRefExprClass:
    // Check for constants/pseudoconstants
    return !isConstantOrPseudoConstant(cast<DeclRefExpr>(Ex), AC);

  // The next cases require recursion for subexpressions
  case Stmt::BinaryOperatorClass: {
    const BinaryOperator *B = cast<const BinaryOperator>(Ex);

    // Exclude cases involving pointer arithmetic.  These are usually
    // false positives.
    if (B->getOpcode() == BO_Sub || B->getOpcode() == BO_Add)
      if (B->getLHS()->getType()->getAs<PointerType>())
        return false;

    return CanVary(B->getRHS(), AC)
        || CanVary(B->getLHS(), AC);
   }
  case Stmt::UnaryOperatorClass: {
    const UnaryOperator *U = cast<const UnaryOperator>(Ex);
    // Handle trivial case first
    switch (U->getOpcode()) {
    case UO_Extension:
      return false;
    default:
      return CanVary(U->getSubExpr(), AC);
    }
  }
  case Stmt::ChooseExprClass:
    return CanVary(cast<const ChooseExpr>(Ex)->getChosenSubExpr(
        AC->getASTContext()), AC);
  case Stmt::ConditionalOperatorClass:
    return CanVary(cast<const ConditionalOperator>(Ex)->getCond(), AC);
  }
}

// Returns true if a DeclRefExpr is or behaves like a constant.
bool IdempotentOperationChecker::isConstantOrPseudoConstant(
                                                          const DeclRefExpr *DR,
                                                          AnalysisContext *AC) {
  // Check if the type of the Decl is const-qualified
  if (DR->getType().isConstQualified())
    return true;

  // Check for an enum
  if (isa<EnumConstantDecl>(DR->getDecl()))
    return true;

  const VarDecl *VD = dyn_cast<VarDecl>(DR->getDecl());
  if (!VD)
    return true;

  // Check if the Decl behaves like a constant. This check also takes care of
  // static variables, which can only change between function calls if they are
  // modified in the AST.
  PseudoConstantAnalysis *PCA = AC->getPseudoConstantAnalysis();
  if (PCA->isPseudoConstant(VD))
    return true;

  return false;
}

// Recursively find any substatements containing VarDecl's with storage other
// than local
bool IdempotentOperationChecker::containsNonLocalVarDecl(const Stmt *S) {
  const DeclRefExpr *DR = dyn_cast<DeclRefExpr>(S);

  if (DR)
    if (const VarDecl *VD = dyn_cast<VarDecl>(DR->getDecl()))
      if (!VD->hasLocalStorage())
        return true;

  for (Stmt::const_child_iterator I = S->child_begin(); I != S->child_end();
      ++I)
    if (const Stmt *child = *I)
      if (containsNonLocalVarDecl(child))
        return true;

  return false;
}

// Returns the successor nodes of N whose CFGBlocks cannot reach N's CFGBlock.
// This effectively gives us a set of points in the ExplodedGraph where
// subsequent execution could not affect the idempotent operation on this path.
// This is useful for displaying paths after the point of the error, providing
// an example of how this idempotent operation cannot change.
const ExplodedNodeSet IdempotentOperationChecker::getLastRelevantNodes(
    const CFGBlock *Begin, const ExplodedNode *N) {
  std::deque<const ExplodedNode *> WorkList;
  llvm::SmallPtrSet<const ExplodedNode *, 32> Visited;
  ExplodedNodeSet Result;

  WorkList.push_back(N);

  while (!WorkList.empty()) {
    const ExplodedNode *Head = WorkList.front();
    WorkList.pop_front();
    Visited.insert(Head);

    const ProgramPoint &PP = Head->getLocation();
    if (const BlockEntrance *BE = dyn_cast<BlockEntrance>(&PP)) {
      // Get the CFGBlock and test the reachability
      const CFGBlock *CB = BE->getBlock();

      // If we cannot reach the beginning CFGBlock from this block, then we are
      // finished
      if (!CRA.isReachable(CB, Begin)) {
        Result.Add(const_cast<ExplodedNode *>(Head));
        continue;
      }
    }

    // Add unvisited children to the worklist
    for (ExplodedNode::const_succ_iterator I = Head->succ_begin(),
        E = Head->succ_end(); I != E; ++I)
      if (!Visited.count(*I))
        WorkList.push_back(*I);
  }

  // Return the ExplodedNodes that were found
  return Result;
}

bool IdempotentOperationChecker::CFGReachabilityAnalysis::isReachable(
                                                          const CFGBlock *Src,
                                                          const CFGBlock *Dst) {
  const unsigned DstBlockID = Dst->getBlockID();

  // If we haven't analyzed the destination node, run the analysis now
  if (!analyzed.count(DstBlockID)) {
    MapReachability(Dst);
    analyzed.insert(DstBlockID);
  }

  // Return the cached result
  return reachable[DstBlockID].count(Src->getBlockID());
}

// Maps reachability to a common node by walking the predecessors of the
// destination node.
void IdempotentOperationChecker::CFGReachabilityAnalysis::MapReachability(
                                                          const CFGBlock *Dst) {
  std::deque<const CFGBlock *> WorkList;
  // Maintain a visited list to ensure we don't get stuck on cycles
  llvm::SmallSet<unsigned, 32> Visited;
  ReachableSet &DstReachability = reachable[Dst->getBlockID()];

  // Start searching from the destination node, since we commonly will perform
  // multiple queries relating to a destination node.
  WorkList.push_back(Dst);

  bool firstRun = true;
  while (!WorkList.empty()) {
    const CFGBlock *Head = WorkList.front();
    WorkList.pop_front();
    Visited.insert(Head->getBlockID());

    // Update reachability information for this node -> Dst
    if (!firstRun)
      // Don't insert Dst -> Dst unless it was a predecessor of itself
      DstReachability.insert(Head->getBlockID());
    else
      firstRun = false;

    // Add the predecessors to the worklist unless we have already visited them
    for (CFGBlock::const_pred_iterator I = Head->pred_begin();
        I != Head->pred_end(); ++I)
      if (!Visited.count((*I)->getBlockID()))
        WorkList.push_back(*I);
  }
}