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
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
|
/**CFile****************************************************************
FileName [abcReach.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [Network and node package.]
Synopsis [Performs reachability analysis.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - June 20, 2005.]
Revision [$Id: abcReach.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
***********************************************************************/
#include "abc.h"
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
/**Function*************************************************************
Synopsis [Computes the initial state and sets up the variable map.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
DdNode * Abc_NtkInitStateVarMap( DdManager * dd, Abc_Ntk_t * pNtk, int fVerbose )
{
DdNode ** pbVarsX, ** pbVarsY;
DdNode * bTemp, * bProd, * bVar;
Abc_Obj_t * pLatch;
int i;
// set the variable mapping for Cudd_bddVarMap()
pbVarsX = ALLOC( DdNode *, dd->size );
pbVarsY = ALLOC( DdNode *, dd->size );
bProd = b1; Cudd_Ref( bProd );
Abc_NtkForEachLatch( pNtk, pLatch, i )
{
pbVarsX[i] = dd->vars[ Abc_NtkPiNum(pNtk) + i ];
pbVarsY[i] = dd->vars[ Abc_NtkCiNum(pNtk) + i ];
// get the initial value of the latch
bVar = Cudd_NotCond( pbVarsX[i], !Abc_LatchIsInit1(pLatch) );
bProd = Cudd_bddAnd( dd, bTemp = bProd, bVar ); Cudd_Ref( bProd );
Cudd_RecursiveDeref( dd, bTemp );
}
Cudd_SetVarMap( dd, pbVarsX, pbVarsY, Abc_NtkLatchNum(pNtk) );
FREE( pbVarsX );
FREE( pbVarsY );
Cudd_Deref( bProd );
return bProd;
}
/**Function*************************************************************
Synopsis []
Description []
SideEffects []
SeeAlso []
***********************************************************************/
DdNode ** Abc_NtkCreatePartitions( DdManager * dd, Abc_Ntk_t * pNtk, int fReorder, int fVerbose )
{
DdNode ** pbParts;
DdNode * bVar;
Abc_Obj_t * pNode;
int i;
// extand the BDD manager to represent NS variables
assert( dd->size == Abc_NtkCiNum(pNtk) );
Cudd_bddIthVar( dd, Abc_NtkCiNum(pNtk) + Abc_NtkLatchNum(pNtk) - 1 );
// enable reordering
if ( fReorder )
Cudd_AutodynEnable( dd, CUDD_REORDER_SYMM_SIFT );
else
Cudd_AutodynDisable( dd );
// compute the transition relation
pbParts = ALLOC( DdNode *, Abc_NtkLatchNum(pNtk) );
Abc_NtkForEachLatch( pNtk, pNode, i )
{
bVar = Cudd_bddIthVar( dd, Abc_NtkCiNum(pNtk) + i );
pbParts[i] = Cudd_bddXnor( dd, bVar, Abc_ObjGlobalBdd(Abc_ObjFanin0(pNode)) ); Cudd_Ref( pbParts[i] );
}
// free the global BDDs
Abc_NtkFreeGlobalBdds( pNtk, 0 );
// reorder and disable reordering
if ( fReorder )
{
if ( fVerbose )
fprintf( stdout, "BDD nodes in the partitions before reordering %d.\n", Cudd_SharingSize(pbParts,Abc_NtkLatchNum(pNtk)) );
Cudd_ReduceHeap( dd, CUDD_REORDER_SYMM_SIFT, 100 );
Cudd_AutodynDisable( dd );
if ( fVerbose )
fprintf( stdout, "BDD nodes in the partitions after reordering %d.\n", Cudd_SharingSize(pbParts,Abc_NtkLatchNum(pNtk)) );
}
return pbParts;
}
/**Function*************************************************************
Synopsis [Computes the set of unreachable states.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
DdNode * Abc_NtkComputeReachable( DdManager * dd, Abc_Ntk_t * pNtk, DdNode ** pbParts, DdNode * bInitial, DdNode * bOutput, int nBddMax, int nIterMax, int fPartition, int fReorder, int fVerbose )
{
int fInternalReorder = 0;
Extra_ImageTree_t * pTree;
Extra_ImageTree2_t * pTree2;
DdNode * bReached, * bCubeCs;
DdNode * bCurrent, * bNext, * bTemp;
DdNode ** pbVarsY;
Abc_Obj_t * pLatch;
int i, nIters, nBddSize;
int nThreshold = 10000;
// collect the NS variables
// set the variable mapping for Cudd_bddVarMap()
pbVarsY = ALLOC( DdNode *, dd->size );
Abc_NtkForEachLatch( pNtk, pLatch, i )
pbVarsY[i] = dd->vars[ Abc_NtkCiNum(pNtk) + i ];
// start the image computation
bCubeCs = Extra_bddComputeRangeCube( dd, Abc_NtkPiNum(pNtk), Abc_NtkCiNum(pNtk) ); Cudd_Ref( bCubeCs );
if ( fPartition )
pTree = Extra_bddImageStart( dd, bCubeCs, Abc_NtkLatchNum(pNtk), pbParts, Abc_NtkLatchNum(pNtk), pbVarsY, fVerbose );
else
pTree2 = Extra_bddImageStart2( dd, bCubeCs, Abc_NtkLatchNum(pNtk), pbParts, Abc_NtkLatchNum(pNtk), pbVarsY, fVerbose );
free( pbVarsY );
Cudd_RecursiveDeref( dd, bCubeCs );
// perform reachability analisys
bCurrent = bInitial; Cudd_Ref( bCurrent );
bReached = bInitial; Cudd_Ref( bReached );
for ( nIters = 1; nIters <= nIterMax; nIters++ )
{
// compute the next states
if ( fPartition )
bNext = Extra_bddImageCompute( pTree, bCurrent );
else
bNext = Extra_bddImageCompute2( pTree2, bCurrent );
Cudd_Ref( bNext );
Cudd_RecursiveDeref( dd, bCurrent );
// remap these states into the current state vars
bNext = Cudd_bddVarMap( dd, bTemp = bNext ); Cudd_Ref( bNext );
Cudd_RecursiveDeref( dd, bTemp );
// check if there are any new states
if ( Cudd_bddLeq( dd, bNext, bReached ) )
break;
// check the BDD size
nBddSize = Cudd_DagSize(bNext);
if ( nBddSize > nBddMax )
break;
// check the result
if ( !Cudd_bddLeq( dd, bNext, Cudd_Not(bOutput) ) )
{
printf( "The miter is proved REACHABLE in %d iterations. ", nIters );
Cudd_RecursiveDeref( dd, bReached );
bReached = NULL;
break;
}
// get the new states
bCurrent = Cudd_bddAnd( dd, bNext, Cudd_Not(bReached) ); Cudd_Ref( bCurrent );
// minimize the new states with the reached states
// bCurrent = Cudd_bddConstrain( dd, bTemp = bCurrent, Cudd_Not(bReached) ); Cudd_Ref( bCurrent );
// Cudd_RecursiveDeref( dd, bTemp );
// add to the reached states
bReached = Cudd_bddOr( dd, bTemp = bReached, bNext ); Cudd_Ref( bReached );
Cudd_RecursiveDeref( dd, bTemp );
Cudd_RecursiveDeref( dd, bNext );
if ( fVerbose )
fprintf( stdout, "Iteration = %3d. BDD = %5d. ", nIters, nBddSize );
if ( fInternalReorder && fReorder && nBddSize > nThreshold )
{
if ( fVerbose )
fprintf( stdout, "Reordering... Before = %5d. ", Cudd_DagSize(bReached) );
Cudd_ReduceHeap( dd, CUDD_REORDER_SYMM_SIFT, 100 );
Cudd_AutodynDisable( dd );
if ( fVerbose )
fprintf( stdout, "After = %5d.\r", Cudd_DagSize(bReached) );
nThreshold *= 2;
}
if ( fVerbose )
fprintf( stdout, "\r" );
}
Cudd_RecursiveDeref( dd, bNext );
// undo the image tree
if ( fPartition )
Extra_bddImageTreeDelete( pTree );
else
Extra_bddImageTreeDelete2( pTree2 );
if ( bReached == NULL )
return NULL;
// report the stats
if ( fVerbose )
{
double nMints = Cudd_CountMinterm(dd, bReached, Abc_NtkLatchNum(pNtk) );
if ( nIters > nIterMax || Cudd_DagSize(bReached) > nBddMax )
fprintf( stdout, "Reachability analysis is stopped after %d iterations.\n", nIters );
else
fprintf( stdout, "Reachability analysis completed in %d iterations.\n", nIters );
fprintf( stdout, "Reachable states = %.0f. (Ratio = %.4f %%)\n", nMints, 100.0*nMints/pow(2.0, Abc_NtkLatchNum(pNtk)) );
fflush( stdout );
}
//PRB( dd, bReached );
Cudd_Deref( bReached );
if ( nIters > nIterMax || Cudd_DagSize(bReached) > nBddMax )
printf( "Verified ONLY FOR STATES REACHED in %d iterations. \n", nIters );
printf( "The miter is proved unreachable in %d iteration. ", nIters );
return bReached;
}
/**Function*************************************************************
Synopsis [Performs reachability to see if any .]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Abc_NtkVerifyUsingBdds( Abc_Ntk_t * pNtk, int nBddMax, int nIterMax, int fPartition, int fReorder, int fVerbose )
{
DdManager * dd;
DdNode ** pbParts;
DdNode * bOutput, * bReached, * bInitial;
int i, clk = clock();
assert( Abc_NtkIsStrash(pNtk) );
assert( Abc_NtkPoNum(pNtk) == 1 );
assert( Abc_ObjFanoutNum(Abc_NtkPo(pNtk,0)) == 0 ); // PO should go first
// compute the global BDDs of the latches
dd = Abc_NtkBuildGlobalBdds( pNtk, nBddMax, 1, fReorder, fVerbose );
if ( dd == NULL )
{
printf( "The number of intermediate BDD nodes exceeded the limit (%d).\n", nBddMax );
return;
}
if ( fVerbose )
printf( "Shared BDD size is %6d nodes.\n", Cudd_ReadKeys(dd) - Cudd_ReadDead(dd) );
// save the output BDD
bOutput = Abc_ObjGlobalBdd(Abc_NtkPo(pNtk,0)); Cudd_Ref( bOutput );
// create partitions
pbParts = Abc_NtkCreatePartitions( dd, pNtk, fReorder, fVerbose );
// create the initial state and the variable map
bInitial = Abc_NtkInitStateVarMap( dd, pNtk, fVerbose ); Cudd_Ref( bInitial );
// check the result
if ( !Cudd_bddLeq( dd, bInitial, Cudd_Not(bOutput) ) )
printf( "The miter is proved REACHABLE in the initial state. " );
else
{
// compute the reachable states
bReached = Abc_NtkComputeReachable( dd, pNtk, pbParts, bInitial, bOutput, nBddMax, nIterMax, fPartition, fReorder, fVerbose );
if ( bReached != NULL )
{
Cudd_Ref( bReached );
Cudd_RecursiveDeref( dd, bReached );
}
}
// cleanup
Cudd_RecursiveDeref( dd, bOutput );
Cudd_RecursiveDeref( dd, bInitial );
for ( i = 0; i < Abc_NtkLatchNum(pNtk); i++ )
Cudd_RecursiveDeref( dd, pbParts[i] );
free( pbParts );
Extra_StopManager( dd );
// report the runtime
PRT( "Time", clock() - clk );
fflush( stdout );
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
|
