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Zhongxing Xud19e21b2008-08-29 15:09:12 +00001//== BasicConstraintManager.cpp - Manage basic constraints.------*- C++ -*--==//
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 defines BasicConstraintManager, a class that tracks simple
11// equality and inequality constraints on symbolic values of GRState.
12//
13//===----------------------------------------------------------------------===//
14
Zhongxing Xu30ad1672008-08-27 14:03:33 +000015#include "clang/Analysis/PathSensitive/ConstraintManager.h"
16#include "clang/Analysis/PathSensitive/GRState.h"
Zhongxing Xu39cfed32008-08-29 14:52:36 +000017#include "clang/Analysis/PathSensitive/GRStateTrait.h"
Zhongxing Xu30ad1672008-08-27 14:03:33 +000018#include "llvm/Support/Compiler.h"
Zhongxing Xu39cfed32008-08-29 14:52:36 +000019#include "llvm/Support/raw_ostream.h"
Zhongxing Xu30ad1672008-08-27 14:03:33 +000020
21using namespace clang;
22
23namespace {
24
Zhongxing Xu39cfed32008-08-29 14:52:36 +000025typedef llvm::ImmutableMap<SymbolID,GRState::IntSetTy> ConstNotEqTy;
26typedef llvm::ImmutableMap<SymbolID,const llvm::APSInt*> ConstEqTy;
27
Zhongxing Xu30ad1672008-08-27 14:03:33 +000028// BasicConstraintManager only tracks equality and inequality constraints of
29// constants and integer variables.
30class VISIBILITY_HIDDEN BasicConstraintManager : public ConstraintManager {
Zhongxing Xu30ad1672008-08-27 14:03:33 +000031 GRStateManager& StateMgr;
32
33public:
34 BasicConstraintManager(GRStateManager& statemgr) : StateMgr(statemgr) {}
35
Zhongxing Xu1c96b242008-10-17 05:57:07 +000036 virtual const GRState* Assume(const GRState* St, SVal Cond,
Zhongxing Xu30ad1672008-08-27 14:03:33 +000037 bool Assumption, bool& isFeasible);
38
Zhongxing Xu1c96b242008-10-17 05:57:07 +000039 const GRState* Assume(const GRState* St, Loc Cond, bool Assumption,
Zhongxing Xu30ad1672008-08-27 14:03:33 +000040 bool& isFeasible);
41
Zhongxing Xu1c96b242008-10-17 05:57:07 +000042 const GRState* AssumeAux(const GRState* St, Loc Cond,bool Assumption,
Zhongxing Xu30ad1672008-08-27 14:03:33 +000043 bool& isFeasible);
44
Zhongxing Xu1c96b242008-10-17 05:57:07 +000045 const GRState* Assume(const GRState* St, NonLoc Cond, bool Assumption,
Zhongxing Xu30ad1672008-08-27 14:03:33 +000046 bool& isFeasible);
47
Zhongxing Xu1c96b242008-10-17 05:57:07 +000048 const GRState* AssumeAux(const GRState* St, NonLoc Cond, bool Assumption,
Zhongxing Xu30ad1672008-08-27 14:03:33 +000049 bool& isFeasible);
50
51 const GRState* AssumeSymInt(const GRState* St, bool Assumption,
52 const SymIntConstraint& C, bool& isFeasible);
53
54 const GRState* AssumeSymNE(const GRState* St, SymbolID sym,
55 const llvm::APSInt& V, bool& isFeasible);
56
57 const GRState* AssumeSymEQ(const GRState* St, SymbolID sym,
58 const llvm::APSInt& V, bool& isFeasible);
59
60 const GRState* AssumeSymLT(const GRState* St, SymbolID sym,
61 const llvm::APSInt& V, bool& isFeasible);
62
63 const GRState* AssumeSymGT(const GRState* St, SymbolID sym,
64 const llvm::APSInt& V, bool& isFeasible);
65
66 const GRState* AssumeSymGE(const GRState* St, SymbolID sym,
67 const llvm::APSInt& V, bool& isFeasible);
68
69 const GRState* AssumeSymLE(const GRState* St, SymbolID sym,
70 const llvm::APSInt& V, bool& isFeasible);
Zhongxing Xu39cfed32008-08-29 14:52:36 +000071
72 const GRState* AddEQ(const GRState* St, SymbolID sym, const llvm::APSInt& V);
73
74 const GRState* AddNE(const GRState* St, SymbolID sym, const llvm::APSInt& V);
75
76 const llvm::APSInt* getSymVal(const GRState* St, SymbolID sym);
77 bool isNotEqual(const GRState* St, SymbolID sym, const llvm::APSInt& V) const;
78 bool isEqual(const GRState* St, SymbolID sym, const llvm::APSInt& V) const;
79
80 const GRState* RemoveDeadBindings(const GRState* St,
81 StoreManager::LiveSymbolsTy& LSymbols,
82 StoreManager::DeadSymbolsTy& DSymbols);
83
84 void print(const GRState* St, std::ostream& Out,
85 const char* nl, const char *sep);
86};
Zhongxing Xu30ad1672008-08-27 14:03:33 +000087
88} // end anonymous namespace
89
90ConstraintManager* clang::CreateBasicConstraintManager(GRStateManager& StateMgr)
91{
92 return new BasicConstraintManager(StateMgr);
93}
94
Zhongxing Xu1c96b242008-10-17 05:57:07 +000095const GRState* BasicConstraintManager::Assume(const GRState* St, SVal Cond,
Zhongxing Xu30ad1672008-08-27 14:03:33 +000096 bool Assumption, bool& isFeasible) {
97 if (Cond.isUnknown()) {
98 isFeasible = true;
99 return St;
100 }
101
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000102 if (isa<NonLoc>(Cond))
103 return Assume(St, cast<NonLoc>(Cond), Assumption, isFeasible);
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000104 else
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000105 return Assume(St, cast<Loc>(Cond), Assumption, isFeasible);
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000106}
107
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000108const GRState* BasicConstraintManager::Assume(const GRState* St, Loc Cond,
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000109 bool Assumption, bool& isFeasible) {
110 St = AssumeAux(St, Cond, Assumption, isFeasible);
111 // TF->EvalAssume(*this, St, Cond, Assumption, isFeasible)
112 return St;
113}
114
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000115const GRState* BasicConstraintManager::AssumeAux(const GRState* St, Loc Cond,
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000116 bool Assumption, bool& isFeasible) {
117 BasicValueFactory& BasicVals = StateMgr.getBasicVals();
118
119 switch (Cond.getSubKind()) {
120 default:
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000121 assert (false && "'Assume' not implemented for this Loc.");
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000122 return St;
123
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000124 case loc::SymbolValKind:
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000125 if (Assumption)
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000126 return AssumeSymNE(St, cast<loc::SymbolVal>(Cond).getSymbol(),
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000127 BasicVals.getZeroWithPtrWidth(), isFeasible);
128 else
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000129 return AssumeSymEQ(St, cast<loc::SymbolVal>(Cond).getSymbol(),
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000130 BasicVals.getZeroWithPtrWidth(), isFeasible);
131
Ted Kremenekc5234712008-10-17 21:22:20 +0000132 case loc::MemRegionKind: {
133 // FIXME: Should this go into the storemanager?
134
135 const MemRegion* R = cast<loc::MemRegionVal>(Cond).getRegion();
136
137 while (R) {
138 if (const SubRegion* SubR = dyn_cast<SubRegion>(R)) {
139 R = SubR->getSuperRegion();
140 continue;
141 }
142 else if (const SymbolicRegion* SymR = dyn_cast<SymbolicRegion>(R))
143 return AssumeAux(St, loc::SymbolVal(SymR->getSymbol()), Assumption,
144 isFeasible);
145
146 break;
147 }
148
149 // FALL-THROUGH.
150 }
151
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000152 case loc::FuncValKind:
153 case loc::GotoLabelKind:
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000154 isFeasible = Assumption;
155 return St;
156
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000157 case loc::ConcreteIntKind: {
158 bool b = cast<loc::ConcreteInt>(Cond).getValue() != 0;
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000159 isFeasible = b ? Assumption : !Assumption;
160 return St;
161 }
162 } // end switch
163}
164
165const GRState*
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000166BasicConstraintManager::Assume(const GRState* St, NonLoc Cond, bool Assumption,
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000167 bool& isFeasible) {
168 St = AssumeAux(St, Cond, Assumption, isFeasible);
169 // TF->EvalAssume() does nothing now.
170 return St;
171}
172
173const GRState*
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000174BasicConstraintManager::AssumeAux(const GRState* St,NonLoc Cond,
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000175 bool Assumption, bool& isFeasible) {
176 BasicValueFactory& BasicVals = StateMgr.getBasicVals();
177 SymbolManager& SymMgr = StateMgr.getSymbolManager();
178
179 switch (Cond.getSubKind()) {
180 default:
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000181 assert(false && "'Assume' not implemented for this NonLoc");
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000182
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000183 case nonloc::SymbolValKind: {
184 nonloc::SymbolVal& SV = cast<nonloc::SymbolVal>(Cond);
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000185 SymbolID sym = SV.getSymbol();
186
187 if (Assumption)
188 return AssumeSymNE(St, sym, BasicVals.getValue(0, SymMgr.getType(sym)),
189 isFeasible);
190 else
191 return AssumeSymEQ(St, sym, BasicVals.getValue(0, SymMgr.getType(sym)),
192 isFeasible);
193 }
194
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000195 case nonloc::SymIntConstraintValKind:
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000196 return
197 AssumeSymInt(St, Assumption,
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000198 cast<nonloc::SymIntConstraintVal>(Cond).getConstraint(),
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000199 isFeasible);
200
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000201 case nonloc::ConcreteIntKind: {
202 bool b = cast<nonloc::ConcreteInt>(Cond).getValue() != 0;
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000203 isFeasible = b ? Assumption : !Assumption;
204 return St;
205 }
206
Zhongxing Xu1c96b242008-10-17 05:57:07 +0000207 case nonloc::LocAsIntegerKind:
208 return AssumeAux(St, cast<nonloc::LocAsInteger>(Cond).getLoc(),
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000209 Assumption, isFeasible);
210 } // end switch
211}
212
213const GRState*
214BasicConstraintManager::AssumeSymInt(const GRState* St, bool Assumption,
215 const SymIntConstraint& C, bool& isFeasible) {
216
217 switch (C.getOpcode()) {
218 default:
219 // No logic yet for other operators.
220 isFeasible = true;
221 return St;
222
223 case BinaryOperator::EQ:
224 if (Assumption)
225 return AssumeSymEQ(St, C.getSymbol(), C.getInt(), isFeasible);
226 else
227 return AssumeSymNE(St, C.getSymbol(), C.getInt(), isFeasible);
228
229 case BinaryOperator::NE:
230 if (Assumption)
231 return AssumeSymNE(St, C.getSymbol(), C.getInt(), isFeasible);
232 else
233 return AssumeSymEQ(St, C.getSymbol(), C.getInt(), isFeasible);
234
Zhongxing Xu94b83122008-09-19 06:07:59 +0000235 case BinaryOperator::GT:
236 if (Assumption)
237 return AssumeSymGT(St, C.getSymbol(), C.getInt(), isFeasible);
238 else
239 return AssumeSymLE(St, C.getSymbol(), C.getInt(), isFeasible);
240
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000241 case BinaryOperator::GE:
242 if (Assumption)
243 return AssumeSymGE(St, C.getSymbol(), C.getInt(), isFeasible);
244 else
245 return AssumeSymLT(St, C.getSymbol(), C.getInt(), isFeasible);
246
Ted Kremenek8c3e7fb2008-09-16 23:24:45 +0000247 case BinaryOperator::LT:
248 if (Assumption)
249 return AssumeSymLT(St, C.getSymbol(), C.getInt(), isFeasible);
250 else
251 return AssumeSymGE(St, C.getSymbol(), C.getInt(), isFeasible);
252
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000253 case BinaryOperator::LE:
254 if (Assumption)
255 return AssumeSymLE(St, C.getSymbol(), C.getInt(), isFeasible);
256 else
257 return AssumeSymGT(St, C.getSymbol(), C.getInt(), isFeasible);
258 } // end switch
259}
260
261const GRState*
262BasicConstraintManager::AssumeSymNE(const GRState* St, SymbolID sym,
263 const llvm::APSInt& V, bool& isFeasible) {
264 // First, determine if sym == X, where X != V.
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000265 if (const llvm::APSInt* X = getSymVal(St, sym)) {
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000266 isFeasible = (*X != V);
267 return St;
268 }
269
270 // Second, determine if sym != V.
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000271 if (isNotEqual(St, sym, V)) {
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000272 isFeasible = true;
273 return St;
274 }
275
276 // If we reach here, sym is not a constant and we don't know if it is != V.
277 // Make that assumption.
278 isFeasible = true;
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000279 return AddNE(St, sym, V);
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000280}
281
282const GRState*
283BasicConstraintManager::AssumeSymEQ(const GRState* St, SymbolID sym,
284 const llvm::APSInt& V, bool& isFeasible) {
285 // First, determine if sym == X, where X != V.
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000286 if (const llvm::APSInt* X = getSymVal(St, sym)) {
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000287 isFeasible = *X == V;
288 return St;
289 }
290
291 // Second, determine if sym != V.
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000292 if (isNotEqual(St, sym, V)) {
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000293 isFeasible = false;
294 return St;
295 }
296
297 // If we reach here, sym is not a constant and we don't know if it is == V.
298 // Make that assumption.
299
300 isFeasible = true;
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000301 return AddEQ(St, sym, V);
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000302}
303
304// These logic will be handled in another ConstraintManager.
305const GRState*
306BasicConstraintManager::AssumeSymLT(const GRState* St, SymbolID sym,
307 const llvm::APSInt& V, bool& isFeasible) {
308
309 // FIXME: For now have assuming x < y be the same as assuming sym != V;
310 return AssumeSymNE(St, sym, V, isFeasible);
311}
312
313const GRState*
314BasicConstraintManager::AssumeSymGT(const GRState* St, SymbolID sym,
315 const llvm::APSInt& V, bool& isFeasible) {
316
317 // FIXME: For now have assuming x > y be the same as assuming sym != V;
318 return AssumeSymNE(St, sym, V, isFeasible);
319}
320
321const GRState*
322BasicConstraintManager::AssumeSymGE(const GRState* St, SymbolID sym,
323 const llvm::APSInt& V, bool& isFeasible) {
324
Ted Kremenek8c3e7fb2008-09-16 23:24:45 +0000325 // Reject a path if the value of sym is a constant X and !(X >= V).
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000326 if (const llvm::APSInt* X = getSymVal(St, sym)) {
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000327 isFeasible = *X >= V;
328 return St;
329 }
330
Ted Kremenek0a41e5a2008-09-19 18:00:36 +0000331 isFeasible = !isNotEqual(St, sym, V) ||
332 (V != llvm::APSInt::getMaxValue(V.getBitWidth(), V.isSigned()));
333
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000334 return St;
335}
336
337const GRState*
338BasicConstraintManager::AssumeSymLE(const GRState* St, SymbolID sym,
339 const llvm::APSInt& V, bool& isFeasible) {
340
341 // FIXME: Primitive logic for now. Only reject a path if the value of
342 // sym is a constant X and !(X <= V).
343
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000344 if (const llvm::APSInt* X = getSymVal(St, sym)) {
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000345 isFeasible = *X <= V;
346 return St;
347 }
Ted Kremenek0a41e5a2008-09-19 18:00:36 +0000348
349 isFeasible = !isNotEqual(St, sym, V) ||
350 (V != llvm::APSInt::getMinValue(V.getBitWidth(), V.isSigned()));
351
Zhongxing Xu30ad1672008-08-27 14:03:33 +0000352 return St;
353}
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000354
355static int ConstEqTyIndex = 0;
356static int ConstNotEqTyIndex = 0;
357
358namespace clang {
359 template<>
360 struct GRStateTrait<ConstNotEqTy> : public GRStatePartialTrait<ConstNotEqTy> {
361 static inline void* GDMIndex() { return &ConstNotEqTyIndex; }
362 };
363
364 template<>
365 struct GRStateTrait<ConstEqTy> : public GRStatePartialTrait<ConstEqTy> {
366 static inline void* GDMIndex() { return &ConstEqTyIndex; }
367 };
368}
369
370const GRState* BasicConstraintManager::AddEQ(const GRState* St, SymbolID sym,
371 const llvm::APSInt& V) {
372 // Create a new state with the old binding replaced.
373 GRStateRef state(St, StateMgr);
374 return state.set<ConstEqTy>(sym, &V);
375}
376
377const GRState* BasicConstraintManager::AddNE(const GRState* St, SymbolID sym,
378 const llvm::APSInt& V) {
379 GRState::IntSetTy::Factory ISetFactory(StateMgr.getAllocator());
380 GRStateRef state(St, StateMgr);
381
382 // First, retrieve the NE-set associated with the given symbol.
383 ConstNotEqTy::data_type* T = state.get<ConstNotEqTy>(sym);
384 GRState::IntSetTy S = T ? *T : ISetFactory.GetEmptySet();
385
386
387 // Now add V to the NE set.
388 S = ISetFactory.Add(S, &V);
389
390 // Create a new state with the old binding replaced.
391 return state.set<ConstNotEqTy>(sym, S);
392}
393
394const llvm::APSInt* BasicConstraintManager::getSymVal(const GRState* St,
395 SymbolID sym) {
396 const ConstEqTy::data_type* T = St->get<ConstEqTy>(sym);
397 return T ? *T : NULL;
398}
399
400bool BasicConstraintManager::isNotEqual(const GRState* St, SymbolID sym,
401 const llvm::APSInt& V) const {
402
403 // Retrieve the NE-set associated with the given symbol.
404 const ConstNotEqTy::data_type* T = St->get<ConstNotEqTy>(sym);
405
406 // See if V is present in the NE-set.
407 return T ? T->contains(&V) : false;
408}
409
410bool BasicConstraintManager::isEqual(const GRState* St, SymbolID sym,
411 const llvm::APSInt& V) const {
412 // Retrieve the EQ-set associated with the given symbol.
413 const ConstEqTy::data_type* T = St->get<ConstEqTy>(sym);
414 // See if V is present in the EQ-set.
415 return T ? **T == V : false;
416}
417
418const GRState* BasicConstraintManager::RemoveDeadBindings(const GRState* St,
419 StoreManager::LiveSymbolsTy& LSymbols,
420 StoreManager::DeadSymbolsTy& DSymbols) {
421 GRStateRef state(St, StateMgr);
422 ConstEqTy CE = state.get<ConstEqTy>();
423 ConstEqTy::Factory& CEFactory = state.get_context<ConstEqTy>();
424
425 for (ConstEqTy::iterator I = CE.begin(), E = CE.end(); I!=E; ++I) {
426 SymbolID sym = I.getKey();
427 if (!LSymbols.count(sym)) {
428 DSymbols.insert(sym);
429 CE = CEFactory.Remove(CE, sym);
430 }
431 }
432 state = state.set<ConstEqTy>(CE);
433
434 ConstNotEqTy CNE = state.get<ConstNotEqTy>();
435 ConstNotEqTy::Factory& CNEFactory = state.get_context<ConstNotEqTy>();
436
437 for (ConstNotEqTy::iterator I = CNE.begin(), E = CNE.end(); I != E; ++I) {
438 SymbolID sym = I.getKey();
439 if (!LSymbols.count(sym)) {
440 DSymbols.insert(sym);
441 CNE = CNEFactory.Remove(CNE, sym);
442 }
443 }
444
445 return state.set<ConstNotEqTy>(CNE);
446}
447
448void BasicConstraintManager::print(const GRState* St, std::ostream& Out,
449 const char* nl, const char *sep) {
450 // Print equality constraints.
451
452 ConstEqTy CE = St->get<ConstEqTy>();
453
454 if (!CE.isEmpty()) {
455 Out << nl << sep << "'==' constraints:";
456
457 for (ConstEqTy::iterator I = CE.begin(), E = CE.end(); I!=E; ++I) {
458 Out << nl << " $" << I.getKey();
459 llvm::raw_os_ostream OS(Out);
460 OS << " : " << *I.getData();
461 }
462 }
463
464 // Print != constraints.
465
466 ConstNotEqTy CNE = St->get<ConstNotEqTy>();
467
468 if (!CNE.isEmpty()) {
469 Out << nl << sep << "'!=' constraints:";
470
471 for (ConstNotEqTy::iterator I = CNE.begin(), EI = CNE.end(); I!=EI; ++I) {
472 Out << nl << " $" << I.getKey() << " : ";
473 bool isFirst = true;
474
475 GRState::IntSetTy::iterator J = I.getData().begin(),
476 EJ = I.getData().end();
477
478 for ( ; J != EJ; ++J) {
479 if (isFirst) isFirst = false;
480 else Out << ", ";
481
Zhongxing Xu7d94e262008-11-10 05:00:06 +0000482 Out << (*J)->getSExtValue(); // Hack: should print to raw_ostream.
Zhongxing Xu39cfed32008-08-29 14:52:36 +0000483 }
484 }
485 }
Daniel Dunbar0e194dd2008-08-30 02:06:22 +0000486}