1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
|
//===-- CachingSolver.cpp - Caching expression solver ---------------------===//
//
// The KLEE Symbolic Virtual Machine
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#include "klee/Solver/Solver.h"
#include "klee/Expr/Constraints.h"
#include "klee/Expr/Expr.h"
#include "klee/Solver/IncompleteSolver.h"
#include "klee/Solver/SolverImpl.h"
#include "klee/Solver/SolverStats.h"
#include <unordered_map>
using namespace klee;
class CachingSolver : public SolverImpl {
private:
ref<Expr> canonicalizeQuery(ref<Expr> originalQuery,
bool &negationUsed);
void cacheInsert(const Query& query,
IncompleteSolver::PartialValidity result);
bool cacheLookup(const Query& query,
IncompleteSolver::PartialValidity &result);
struct CacheEntry {
CacheEntry(const ConstraintSet &c, ref<Expr> q)
: constraints(c), query(q) {}
CacheEntry(const CacheEntry &ce)
: constraints(ce.constraints), query(ce.query) {}
ConstraintSet constraints;
ref<Expr> query;
bool operator==(const CacheEntry &b) const {
return constraints==b.constraints && *query.get()==*b.query.get();
}
};
struct CacheEntryHash {
unsigned operator()(const CacheEntry &ce) const {
unsigned result = ce.query->hash();
for (auto const &constraint : ce.constraints) {
result ^= constraint->hash();
}
return result;
}
};
typedef std::unordered_map<CacheEntry, IncompleteSolver::PartialValidity,
CacheEntryHash>
cache_map;
Solver *solver;
cache_map cache;
public:
CachingSolver(Solver *s) : solver(s) {}
~CachingSolver() { cache.clear(); delete solver; }
bool computeValidity(const Query&, Solver::Validity &result);
bool computeTruth(const Query&, bool &isValid);
bool computeValue(const Query& query, ref<Expr> &result) {
++stats::queryCacheMisses;
return solver->impl->computeValue(query, result);
}
bool computeInitialValues(const Query& query,
const std::vector<const Array*> &objects,
std::vector< std::vector<unsigned char> > &values,
bool &hasSolution) {
++stats::queryCacheMisses;
return solver->impl->computeInitialValues(query, objects, values,
hasSolution);
}
SolverRunStatus getOperationStatusCode();
char *getConstraintLog(const Query&);
void setCoreSolverTimeout(time::Span timeout);
};
/** @returns the canonical version of the given query. The reference
negationUsed is set to true if the original query was negated in
the canonicalization process. */
ref<Expr> CachingSolver::canonicalizeQuery(ref<Expr> originalQuery,
bool &negationUsed) {
ref<Expr> negatedQuery = Expr::createIsZero(originalQuery);
// select the "smaller" query to the be canonical representation
if (originalQuery.compare(negatedQuery) < 0) {
negationUsed = false;
return originalQuery;
} else {
negationUsed = true;
return negatedQuery;
}
}
/** @returns true on a cache hit, false of a cache miss. Reference
value result only valid on a cache hit. */
bool CachingSolver::cacheLookup(const Query& query,
IncompleteSolver::PartialValidity &result) {
bool negationUsed;
ref<Expr> canonicalQuery = canonicalizeQuery(query.expr, negationUsed);
CacheEntry ce(query.constraints, canonicalQuery);
cache_map::iterator it = cache.find(ce);
if (it != cache.end()) {
result = (negationUsed ?
IncompleteSolver::negatePartialValidity(it->second) :
it->second);
return true;
}
return false;
}
/// Inserts the given query, result pair into the cache.
void CachingSolver::cacheInsert(const Query& query,
IncompleteSolver::PartialValidity result) {
bool negationUsed;
ref<Expr> canonicalQuery = canonicalizeQuery(query.expr, negationUsed);
CacheEntry ce(query.constraints, canonicalQuery);
IncompleteSolver::PartialValidity cachedResult =
(negationUsed ? IncompleteSolver::negatePartialValidity(result) : result);
cache.insert(std::make_pair(ce, cachedResult));
}
bool CachingSolver::computeValidity(const Query& query,
Solver::Validity &result) {
IncompleteSolver::PartialValidity cachedResult;
bool tmp, cacheHit = cacheLookup(query, cachedResult);
if (cacheHit) {
switch(cachedResult) {
case IncompleteSolver::MustBeTrue:
result = Solver::True;
++stats::queryCacheHits;
return true;
case IncompleteSolver::MustBeFalse:
result = Solver::False;
++stats::queryCacheHits;
return true;
case IncompleteSolver::TrueOrFalse:
result = Solver::Unknown;
++stats::queryCacheHits;
return true;
case IncompleteSolver::MayBeTrue: {
++stats::queryCacheMisses;
if (!solver->impl->computeTruth(query, tmp))
return false;
if (tmp) {
cacheInsert(query, IncompleteSolver::MustBeTrue);
result = Solver::True;
return true;
} else {
cacheInsert(query, IncompleteSolver::TrueOrFalse);
result = Solver::Unknown;
return true;
}
}
case IncompleteSolver::MayBeFalse: {
++stats::queryCacheMisses;
if (!solver->impl->computeTruth(query.negateExpr(), tmp))
return false;
if (tmp) {
cacheInsert(query, IncompleteSolver::MustBeFalse);
result = Solver::False;
return true;
} else {
cacheInsert(query, IncompleteSolver::TrueOrFalse);
result = Solver::Unknown;
return true;
}
}
default: assert(0 && "unreachable");
}
}
++stats::queryCacheMisses;
if (!solver->impl->computeValidity(query, result))
return false;
switch (result) {
case Solver::True:
cachedResult = IncompleteSolver::MustBeTrue; break;
case Solver::False:
cachedResult = IncompleteSolver::MustBeFalse; break;
default:
cachedResult = IncompleteSolver::TrueOrFalse; break;
}
cacheInsert(query, cachedResult);
return true;
}
bool CachingSolver::computeTruth(const Query& query,
bool &isValid) {
IncompleteSolver::PartialValidity cachedResult;
bool cacheHit = cacheLookup(query, cachedResult);
// a cached result of MayBeTrue forces us to check whether
// a False assignment exists.
if (cacheHit && cachedResult != IncompleteSolver::MayBeTrue) {
++stats::queryCacheHits;
isValid = (cachedResult == IncompleteSolver::MustBeTrue);
return true;
}
++stats::queryCacheMisses;
// cache miss: query solver
if (!solver->impl->computeTruth(query, isValid))
return false;
if (isValid) {
cachedResult = IncompleteSolver::MustBeTrue;
} else if (cacheHit) {
// We know a true assignment exists, and query isn't valid, so
// must be TrueOrFalse.
assert(cachedResult == IncompleteSolver::MayBeTrue);
cachedResult = IncompleteSolver::TrueOrFalse;
} else {
cachedResult = IncompleteSolver::MayBeFalse;
}
cacheInsert(query, cachedResult);
return true;
}
SolverImpl::SolverRunStatus CachingSolver::getOperationStatusCode() {
return solver->impl->getOperationStatusCode();
}
char *CachingSolver::getConstraintLog(const Query& query) {
return solver->impl->getConstraintLog(query);
}
void CachingSolver::setCoreSolverTimeout(time::Span timeout) {
solver->impl->setCoreSolverTimeout(timeout);
}
///
Solver *klee::createCachingSolver(Solver *_solver) {
return new Solver(new CachingSolver(_solver));
}
|