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
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
|
/**CFile****************************************************************
FileName [abcQuant.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [Network and node package.]
Synopsis [AIG-based variable quantification.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - June 20, 2005.]
Revision [$Id: abcQuant.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
***********************************************************************/
#include "abc.h"
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
/**Function*************************************************************
Synopsis [Performs fast synthesis.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Abc_NtkSynthesize( Abc_Ntk_t ** ppNtk, int fMoreEffort )
{
Abc_Ntk_t * pNtk, * pNtkTemp;
pNtk = *ppNtk;
Abc_NtkRewrite( pNtk, 0, 0, 0, 0, 0 );
Abc_NtkRefactor( pNtk, 10, 16, 0, 0, 0, 0 );
pNtk = Abc_NtkBalance( pNtkTemp = pNtk, 0, 0, 0 );
Abc_NtkDelete( pNtkTemp );
if ( fMoreEffort )
{
Abc_NtkRewrite( pNtk, 0, 0, 0, 0, 0 );
Abc_NtkRefactor( pNtk, 10, 16, 0, 0, 0, 0 );
pNtk = Abc_NtkBalance( pNtkTemp = pNtk, 0, 0, 0 );
Abc_NtkDelete( pNtkTemp );
}
*ppNtk = pNtk;
}
/**Function*************************************************************
Synopsis [Existentially quantifies one variable.]
Description []
SideEffects [This procedure creates dangling nodes in the AIG.]
SeeAlso []
***********************************************************************/
int Abc_NtkQuantify( Abc_Ntk_t * pNtk, int fUniv, int iVar, int fVerbose )
{
Vec_Ptr_t * vNodes;
Abc_Obj_t * pObj, * pNext, * pFanin;
int i;
assert( Abc_NtkIsStrash(pNtk) );
assert( iVar < Abc_NtkCiNum(pNtk) );
// collect the internal nodes
pObj = Abc_NtkCi( pNtk, iVar );
vNodes = Abc_NtkDfsReverseNodes( pNtk, &pObj, 1 );
// assign the cofactors of the CI node to be constants
pObj->pCopy = Abc_ObjNot( Abc_AigConst1(pNtk) );
pObj->pData = Abc_AigConst1(pNtk);
// quantify the nodes
Vec_PtrForEachEntry( vNodes, pObj, i )
{
for ( pNext = pObj? pObj->pCopy : pObj; pObj; pObj = pNext, pNext = pObj? pObj->pCopy : pObj )
{
pFanin = Abc_ObjFanin0(pObj);
if ( !Abc_NodeIsTravIdCurrent(pFanin) )
pFanin->pCopy = pFanin->pData = pFanin;
pFanin = Abc_ObjFanin1(pObj);
if ( !Abc_NodeIsTravIdCurrent(pFanin) )
pFanin->pCopy = pFanin->pData = pFanin;
pObj->pCopy = Abc_AigAnd( pNtk->pManFunc, Abc_ObjChild0Copy(pObj), Abc_ObjChild1Copy(pObj) );
pObj->pData = Abc_AigAnd( pNtk->pManFunc, Abc_ObjChild0Data(pObj), Abc_ObjChild1Data(pObj) );
}
}
Vec_PtrFree( vNodes );
// update the affected COs
Abc_NtkForEachCo( pNtk, pObj, i )
{
if ( !Abc_NodeIsTravIdCurrent(pObj) )
continue;
pFanin = Abc_ObjFanin0(pObj);
// get the result of quantification
if ( fUniv )
pNext = Abc_AigAnd( pNtk->pManFunc, Abc_ObjChild0Copy(pObj), Abc_ObjChild0Data(pObj) );
else
pNext = Abc_AigOr( pNtk->pManFunc, Abc_ObjChild0Copy(pObj), Abc_ObjChild0Data(pObj) );
pNext = Abc_ObjNotCond( pNext, Abc_ObjFaninC0(pObj) );
if ( Abc_ObjRegular(pNext) == pFanin )
continue;
// update the fanins of the CO
Abc_ObjPatchFanin( pObj, pFanin, pNext );
// if ( Abc_ObjFanoutNum(pFanin) == 0 )
// Abc_AigDeleteNode( pNtk->pManFunc, pFanin );
}
// make sure the node has no fanouts
// pObj = Abc_NtkCi( pNtk, iVar );
// assert( Abc_ObjFanoutNum(pObj) == 0 );
return 1;
}
/**Function*************************************************************
Synopsis [Constructs the transition relation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Abc_Ntk_t * Abc_NtkTransRel( Abc_Ntk_t * pNtk, int fInputs, int fVerbose )
{
char Buffer[1000];
Vec_Ptr_t * vPairs;
Abc_Ntk_t * pNtkNew;
Abc_Obj_t * pObj, * pMiter;
int i, nLatches;
int fSynthesis = 1;
assert( Abc_NtkIsStrash(pNtk) );
assert( Abc_NtkLatchNum(pNtk) );
nLatches = Abc_NtkLatchNum(pNtk);
// start the network
pNtkNew = Abc_NtkAlloc( ABC_NTK_STRASH, ABC_FUNC_AIG, 1 );
// duplicate the name and the spec
sprintf( Buffer, "%s_TR", pNtk->pName );
pNtkNew->pName = Extra_UtilStrsav(pNtk->pName);
// pNtkNew->pSpec = Extra_UtilStrsav(pNtk->pSpec);
Abc_NtkCleanCopy( pNtk );
// create current state variables
Abc_NtkForEachLatchOutput( pNtk, pObj, i )
{
pObj->pCopy = Abc_NtkCreatePi(pNtkNew);
Abc_ObjAssignName( pObj->pCopy, Abc_ObjName(pObj), NULL );
}
// create next state variables
Abc_NtkForEachLatchInput( pNtk, pObj, i )
Abc_ObjAssignName( Abc_NtkCreatePi(pNtkNew), Abc_ObjName(pObj), NULL );
// create PI variables
Abc_NtkForEachPi( pNtk, pObj, i )
Abc_NtkDupObj( pNtkNew, pObj, 1 );
// create the PO
Abc_NtkCreatePo( pNtkNew );
// restrash the nodes (assuming a topological order of the old network)
Abc_AigConst1(pNtk)->pCopy = Abc_AigConst1(pNtkNew);
Abc_NtkForEachNode( pNtk, pObj, i )
pObj->pCopy = Abc_AigAnd( pNtkNew->pManFunc, Abc_ObjChild0Copy(pObj), Abc_ObjChild1Copy(pObj) );
// create the function of the primary output
assert( Abc_NtkBoxNum(pNtk) == Abc_NtkLatchNum(pNtk) );
vPairs = Vec_PtrAlloc( 2*nLatches );
Abc_NtkForEachLatchInput( pNtk, pObj, i )
{
Vec_PtrPush( vPairs, Abc_ObjChild0Copy(pObj) );
Vec_PtrPush( vPairs, Abc_NtkPi(pNtkNew, i+nLatches) );
}
pMiter = Abc_AigMiter( pNtkNew->pManFunc, vPairs );
Vec_PtrFree( vPairs );
// add the primary output
Abc_ObjAddFanin( Abc_NtkPo(pNtkNew,0), Abc_ObjNot(pMiter) );
Abc_ObjAssignName( Abc_NtkPo(pNtkNew,0), "rel", NULL );
// quantify inputs
if ( fInputs )
{
assert( Abc_NtkPiNum(pNtkNew) == Abc_NtkPiNum(pNtk) + 2*nLatches );
for ( i = Abc_NtkPiNum(pNtkNew) - 1; i >= 2*nLatches; i-- )
// for ( i = 2*nLatches; i < Abc_NtkPiNum(pNtkNew); i++ )
{
Abc_NtkQuantify( pNtkNew, 0, i, fVerbose );
// if ( fSynthesis && (i % 3 == 2) )
if ( fSynthesis )
{
Abc_NtkCleanData( pNtkNew );
Abc_AigCleanup( pNtkNew->pManFunc );
Abc_NtkSynthesize( &pNtkNew, 1 );
}
// printf( "Var = %3d. Nodes = %6d. ", Abc_NtkPiNum(pNtkNew) - 1 - i, Abc_NtkNodeNum(pNtkNew) );
// printf( "Var = %3d. Nodes = %6d. ", i - 2*nLatches, Abc_NtkNodeNum(pNtkNew) );
}
// printf( "\n" );
Abc_NtkCleanData( pNtkNew );
Abc_AigCleanup( pNtkNew->pManFunc );
for ( i = Abc_NtkPiNum(pNtkNew) - 1; i >= 2*nLatches; i-- )
{
pObj = Abc_NtkPi( pNtkNew, i );
assert( Abc_ObjFanoutNum(pObj) == 0 );
Abc_NtkDeleteObj( pObj );
}
}
// check consistency of the network
if ( !Abc_NtkCheck( pNtkNew ) )
{
printf( "Abc_NtkTransRel: The network check has failed.\n" );
Abc_NtkDelete( pNtkNew );
return NULL;
}
return pNtkNew;
}
/**Function*************************************************************
Synopsis [Performs one image computation.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Abc_Ntk_t * Abc_NtkInitialState( Abc_Ntk_t * pNtk )
{
Abc_Ntk_t * pNtkNew;
Abc_Obj_t * pMiter;
int i, nVars = Abc_NtkPiNum(pNtk)/2;
assert( Abc_NtkIsStrash(pNtk) );
// start the new network
pNtkNew = Abc_NtkStartFrom( pNtk, ABC_NTK_STRASH, ABC_FUNC_AIG );
// compute the all-zero state in terms of the CS variables
pMiter = Abc_AigConst1(pNtkNew);
for ( i = 0; i < nVars; i++ )
pMiter = Abc_AigAnd( pNtkNew->pManFunc, pMiter, Abc_ObjNot( Abc_NtkPi(pNtkNew, i) ) );
// add the PO
Abc_ObjAddFanin( Abc_NtkPo(pNtkNew,0), pMiter );
return pNtkNew;
}
/**Function*************************************************************
Synopsis [Swaps current state and next state variables.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Abc_Ntk_t * Abc_NtkSwapVariables( Abc_Ntk_t * pNtk )
{
Abc_Ntk_t * pNtkNew;
Abc_Obj_t * pMiter, * pObj, * pObj0, * pObj1;
int i, nVars = Abc_NtkPiNum(pNtk)/2;
assert( Abc_NtkIsStrash(pNtk) );
// start the new network
pNtkNew = Abc_NtkStartFrom( pNtk, ABC_NTK_STRASH, ABC_FUNC_AIG );
// update the PIs
for ( i = 0; i < nVars; i++ )
{
pObj0 = Abc_NtkPi( pNtk, i );
pObj1 = Abc_NtkPi( pNtk, i+nVars );
pMiter = pObj0->pCopy;
pObj0->pCopy = pObj1->pCopy;
pObj1->pCopy = pMiter;
}
// restrash
Abc_NtkForEachNode( pNtk, pObj, i )
pObj->pCopy = Abc_AigAnd( pNtkNew->pManFunc, Abc_ObjChild0Copy(pObj), Abc_ObjChild1Copy(pObj) );
// add the PO
pMiter = Abc_ObjChild0Copy( Abc_NtkPo(pNtk,0) );
Abc_ObjAddFanin( Abc_NtkPo(pNtkNew,0), pMiter );
return pNtkNew;
}
/**Function*************************************************************
Synopsis [Performs reachability analisys.]
Description [Assumes that the input is the transition relation.]
SideEffects []
SeeAlso []
***********************************************************************/
Abc_Ntk_t * Abc_NtkReachability( Abc_Ntk_t * pNtkRel, int nIters, int fVerbose )
{
Abc_Obj_t * pObj;
Abc_Ntk_t * pNtkFront, * pNtkReached, * pNtkNext, * pNtkTemp;
int clk, i, v, nVars, nNodesOld, nNodesNew, nNodesPrev;
int fFixedPoint = 0;
int fSynthesis = 1;
int fMoreEffort = 1;
assert( Abc_NtkIsStrash(pNtkRel) );
assert( Abc_NtkLatchNum(pNtkRel) == 0 );
assert( Abc_NtkPiNum(pNtkRel) % 2 == 0 );
// compute the network composed of the initial states
pNtkFront = Abc_NtkInitialState( pNtkRel );
pNtkReached = Abc_NtkDup( pNtkFront );
//Abc_NtkShow( pNtkReached, 0, 0, 0 );
// if ( fVerbose )
// printf( "Transition relation = %6d.\n", Abc_NtkNodeNum(pNtkRel) );
// perform iterations of reachability analysis
nNodesPrev = Abc_NtkNodeNum(pNtkFront);
nVars = Abc_NtkPiNum(pNtkRel)/2;
for ( i = 0; i < nIters; i++ )
{
clk = clock();
// get the set of next states
pNtkNext = Abc_NtkMiterAnd( pNtkRel, pNtkFront, 0, 0 );
Abc_NtkDelete( pNtkFront );
// quantify the current state variables
for ( v = 0; v < nVars; v++ )
{
Abc_NtkQuantify( pNtkNext, 0, v, fVerbose );
if ( fSynthesis && (v % 3 == 2) )
{
Abc_NtkCleanData( pNtkNext );
Abc_AigCleanup( pNtkNext->pManFunc );
Abc_NtkSynthesize( &pNtkNext, fMoreEffort );
}
}
Abc_NtkCleanData( pNtkNext );
Abc_AigCleanup( pNtkNext->pManFunc );
if ( fSynthesis )
Abc_NtkSynthesize( &pNtkNext, 1 );
// map the next states into the current states
pNtkNext = Abc_NtkSwapVariables( pNtkTemp = pNtkNext );
Abc_NtkDelete( pNtkTemp );
// check the termination condition
if ( Abc_ObjFanin0(Abc_NtkPo(pNtkNext,0)) == Abc_AigConst1(pNtkNext) )
{
fFixedPoint = 1;
printf( "Fixed point is reached!\n" );
Abc_NtkDelete( pNtkNext );
break;
}
// compute new front
pNtkFront = Abc_NtkMiterAnd( pNtkNext, pNtkReached, 0, 1 );
Abc_NtkDelete( pNtkNext );
// add the reached states
pNtkReached = Abc_NtkMiterAnd( pNtkTemp = pNtkReached, pNtkFront, 1, 0 );
Abc_NtkDelete( pNtkTemp );
// compress the size of Front
nNodesOld = Abc_NtkNodeNum(pNtkFront);
if ( fSynthesis )
{
Abc_NtkSynthesize( &pNtkFront, fMoreEffort );
Abc_NtkSynthesize( &pNtkReached, fMoreEffort );
}
nNodesNew = Abc_NtkNodeNum(pNtkFront);
// print statistics
if ( fVerbose )
{
printf( "I = %3d : Reach = %6d Fr = %6d FrM = %6d %7.2f %% ",
i + 1, Abc_NtkNodeNum(pNtkReached), nNodesOld, nNodesNew, 100.0*(nNodesNew-nNodesPrev)/nNodesPrev );
PRT( "T", clock() - clk );
}
nNodesPrev = Abc_NtkNodeNum(pNtkFront);
}
if ( !fFixedPoint )
fprintf( stdout, "Reachability analysis stopped after %d iterations.\n", nIters );
// complement the output to represent the set of unreachable states
Abc_ObjXorFaninC( Abc_NtkPo(pNtkReached,0), 0 );
// remove next state variables
for ( i = 2*nVars - 1; i >= nVars; i-- )
{
pObj = Abc_NtkPi( pNtkReached, i );
assert( Abc_ObjFanoutNum(pObj) == 0 );
Abc_NtkDeleteObj( pObj );
}
// check consistency of the network
if ( !Abc_NtkCheck( pNtkReached ) )
{
printf( "Abc_NtkReachability: The network check has failed.\n" );
Abc_NtkDelete( pNtkReached );
return NULL;
}
return pNtkReached;
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
|
