StackAddrEscapeChecker.cpp revision 9ef6537a894c33003359b1f9b9676e9178e028b7
11622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//=== StackAddrLeakChecker.cpp ------------------------------------*- C++ -*--//
21622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//
31622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//                     The LLVM Compiler Infrastructure
41622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//
51622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu// This file is distributed under the University of Illinois Open Source
61622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu// License. See LICENSE.TXT for details.
71622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//
81622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//===----------------------------------------------------------------------===//
91622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//
101622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu// This file defines stack address leak checker, which checks if an invalid
111622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu// stack address is stored into a global or heap location. See CERT DCL30-C.
121622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//
131622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu//===----------------------------------------------------------------------===//
141622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu
15d2592a34a059e7cbb2b11dc53649ac4912422909Argyrios Kyrtzidis#include "ExprEngineInternalChecks.h"
1698cabbad47a4d9db6b7e95c950d3302c110d1b02Argyrios Kyrtzidis#include "clang/GR/BugReporter/BugType.h"
1798cabbad47a4d9db6b7e95c950d3302c110d1b02Argyrios Kyrtzidis#include "clang/GR/PathSensitive/CheckerVisitor.h"
1898cabbad47a4d9db6b7e95c950d3302c110d1b02Argyrios Kyrtzidis#include "clang/GR/PathSensitive/GRState.h"
199b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu#include "clang/Basic/SourceManager.h"
209b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu#include "llvm/ADT/SmallString.h"
211622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xuusing namespace clang;
229ef6537a894c33003359b1f9b9676e9178e028b7Ted Kremenekusing namespace ento;
231622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu
241622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xunamespace {
259b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xuclass StackAddrLeakChecker : public CheckerVisitor<StackAddrLeakChecker> {
261622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu  BuiltinBug *BT_stackleak;
279b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  BuiltinBug *BT_returnstack;
281622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu
291622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xupublic:
309b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  StackAddrLeakChecker() : BT_stackleak(0), BT_returnstack(0) {}
311622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu  static void *getTag() {
321622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu    static int x;
331622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu    return &x;
341622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu  }
359b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  void PreVisitReturnStmt(CheckerContext &C, const ReturnStmt *RS);
36d2592a34a059e7cbb2b11dc53649ac4912422909Argyrios Kyrtzidis  void evalEndPath(EndPathNodeBuilder &B, void *tag, ExprEngine &Eng);
379b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xuprivate:
389b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  void EmitStackError(CheckerContext &C, const MemRegion *R, const Expr *RetE);
39a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  SourceRange GenName(llvm::raw_ostream &os, const MemRegion *R,
40a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                      SourceManager &SM);
411622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu};
421622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu}
431622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu
449ef6537a894c33003359b1f9b9676e9178e028b7Ted Kremenekvoid ento::RegisterStackAddrLeakChecker(ExprEngine &Eng) {
451622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu  Eng.registerCheck(new StackAddrLeakChecker());
461622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu}
479b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
48a8166156a6414ddd6a68514dc4f48e95d2259977Ted KremenekSourceRange StackAddrLeakChecker::GenName(llvm::raw_ostream &os,
49a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                                          const MemRegion *R,
50a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                                          SourceManager &SM) {
51a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    // Get the base region, stripping away fields and elements.
529b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  R = R->getBaseRegion();
53a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  SourceRange range;
54a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  os << "Address of ";
55a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
569b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  // Check if the region is a compound literal.
579b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  if (const CompoundLiteralRegion* CR = dyn_cast<CompoundLiteralRegion>(R)) {
589b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    const CompoundLiteralExpr* CL = CR->getLiteralExpr();
59a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    os << "stack memory associated with a compound literal "
60a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek          "declared on line "
61a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek        << SM.getInstantiationLineNumber(CL->getLocStart())
62a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek        << " returned to caller";
639b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    range = CL->getSourceRange();
649b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  }
659b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  else if (const AllocaRegion* AR = dyn_cast<AllocaRegion>(R)) {
669b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    const Expr* ARE = AR->getExpr();
679b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    SourceLocation L = ARE->getLocStart();
689b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    range = ARE->getSourceRange();
69a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    os << "stack memory allocated by call to alloca() on line "
70a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek       << SM.getInstantiationLineNumber(L);
719b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  }
729b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  else if (const BlockDataRegion *BR = dyn_cast<BlockDataRegion>(R)) {
739b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    const BlockDecl *BD = BR->getCodeRegion()->getDecl();
749b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    SourceLocation L = BD->getLocStart();
759b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    range = BD->getSourceRange();
76a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    os << "stack-allocated block declared on line "
77a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek       << SM.getInstantiationLineNumber(L);
789b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  }
799b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  else if (const VarRegion *VR = dyn_cast<VarRegion>(R)) {
80a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    os << "stack memory associated with local variable '"
81a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek       << VR->getString() << '\'';
829b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    range = VR->getDecl()->getSourceRange();
839b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  }
849b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  else {
859b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    assert(false && "Invalid region in ReturnStackAddressChecker.");
86a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  }
87a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
88a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  return range;
89a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek}
90a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
91a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenekvoid StackAddrLeakChecker::EmitStackError(CheckerContext &C, const MemRegion *R,
92a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                                          const Expr *RetE) {
93d048c6ef5b6cfaa0cecb8cc1d4bdace32ed21d07Ted Kremenek  ExplodedNode *N = C.generateSink();
94a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
95a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  if (!N)
969b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    return;
979b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
98a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  if (!BT_returnstack)
99a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek   BT_returnstack=new BuiltinBug("Return of address to stack-allocated memory");
100a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
101a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  // Generate a report for this bug.
102a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  llvm::SmallString<512> buf;
103a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  llvm::raw_svector_ostream os(buf);
104a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  SourceRange range = GenName(os, R, C.getSourceManager());
105a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  os << " returned to caller";
1069b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  RangedBugReport *report = new RangedBugReport(*BT_returnstack, os.str(), N);
1079b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  report->addRange(RetE->getSourceRange());
1089b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  if (range.isValid())
1099b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    report->addRange(range);
1109b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
1119b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  C.EmitReport(report);
112a7e6845660f91ec611427e1db842780e1ec12bdbEli Friedman}
1139b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
1149b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xuvoid StackAddrLeakChecker::PreVisitReturnStmt(CheckerContext &C,
1159b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu                                              const ReturnStmt *RS) {
1169b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
1179b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  const Expr *RetE = RS->getRetValue();
1189b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  if (!RetE)
1199b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    return;
1209b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
1219b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  SVal V = C.getState()->getSVal(RetE);
1229b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  const MemRegion *R = V.getAsRegion();
1239b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
1249b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  if (!R || !R->hasStackStorage())
1259b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    return;
1269b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu
1279b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  if (R->hasStackStorage()) {
1289b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    EmitStackError(C, R, RetE);
1299b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu    return;
1309b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu  }
1319b1468311d625ac8920adda5440ce8ffb1a5a5d2Zhongxing Xu}
1321622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu
133d2592a34a059e7cbb2b11dc53649ac4912422909Argyrios Kyrtzidisvoid StackAddrLeakChecker::evalEndPath(EndPathNodeBuilder &B, void *tag,
134d2592a34a059e7cbb2b11dc53649ac4912422909Argyrios Kyrtzidis                                       ExprEngine &Eng) {
1351622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu  SaveAndRestore<bool> OldHasGen(B.HasGeneratedNode);
1361622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu  const GRState *state = B.getState();
137551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
138551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  // Iterate over all bindings to global variables and see if it contains
139551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  // a memory region in the stack space.
140551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  class CallBack : public StoreManager::BindingsHandler {
141551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  private:
142551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek    const StackFrameContext *CurSFC;
143551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  public:
144a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    llvm::SmallVector<std::pair<const MemRegion*, const MemRegion*>, 10> V;
145551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
146551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek    CallBack(const LocationContext *LCtx)
147a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek      : CurSFC(LCtx->getCurrentStackFrame()) {}
148551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
149551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek    bool HandleBinding(StoreManager &SMgr, Store store,
150551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek                       const MemRegion *region, SVal val) {
151551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
152551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek      if (!isa<GlobalsSpaceRegion>(region->getMemorySpace()))
153551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek        return true;
154551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
155551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek      const MemRegion *vR = val.getAsRegion();
156551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek      if (!vR)
157551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek        return true;
158551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
159551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek      if (const StackSpaceRegion *SSR =
160551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek          dyn_cast<StackSpaceRegion>(vR->getMemorySpace())) {
161551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek        // If the global variable holds a location in the current stack frame,
162551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek        // record the binding to emit a warning.
163a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek        if (SSR->getStackFrame() == CurSFC)
164a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek          V.push_back(std::make_pair(region, vR));
1651622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu      }
166551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
167551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek      return true;
1681622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu    }
169551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  };
170551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
171551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  CallBack cb(B.getPredecessor()->getLocationContext());
172551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  state->getStateManager().getStoreManager().iterBindings(state->getStore(),cb);
173a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
174a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  if (cb.V.empty())
175551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek    return;
176551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
177551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  // Generate an error node.
178551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  ExplodedNode *N = B.generateNode(state, tag, B.getPredecessor());
179551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  if (!N)
180551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek    return;
181a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
182551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek  if (!BT_stackleak)
183a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    BT_stackleak =
184a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek      new BuiltinBug("Stack address stored into global variable",
185a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                     "Stack address was saved into a global variable. "
186a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                     "This is dangerous because the address will become "
187a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                     "invalid after returning from the function");
188551bd1f9191af0eecdc29764e34e01803c73ae31Ted Kremenek
189a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  for (unsigned i = 0, e = cb.V.size(); i != e; ++i) {
190a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    // Generate a report for this bug.
191a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    llvm::SmallString<512> buf;
192a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    llvm::raw_svector_ostream os(buf);
193a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    SourceRange range = GenName(os, cb.V[i].second,
194a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek                                Eng.getContext().getSourceManager());
195a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    os << " is still referred to by the global variable '";
196a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    const VarRegion *VR = cast<VarRegion>(cb.V[i].first->getBaseRegion());
197a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    os << VR->getDecl()->getNameAsString()
198a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek       << "' upon returning to the caller.  This will be a dangling reference";
199a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    RangedBugReport *report = new RangedBugReport(*BT_stackleak, os.str(), N);
200a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    if (range.isValid())
201a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek      report->addRange(range);
202a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek
203a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek    Eng.getBugReporter().EmitReport(report);
204a8166156a6414ddd6a68514dc4f48e95d2259977Ted Kremenek  }
2051622a547971cee50e386b4cdfe62ed1fcee1036dZhongxing Xu}
206