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
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
|
/**CFile****************************************************************
FileName [kitSop.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [Computation kit.]
Synopsis [Procedures involving SOPs.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - Dec 6, 2006.]
Revision [$Id: kitSop.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
***********************************************************************/
#include "kit.h"
ABC_NAMESPACE_IMPL_START
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
/**Function*************************************************************
Synopsis [Creates SOP from the cube array.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopCreate( Kit_Sop_t * cResult, Vec_Int_t * vInput, int nVars, Vec_Int_t * vMemory )
{
unsigned uCube;
int i;
// start the cover
cResult->nCubes = 0;
cResult->pCubes = Vec_IntFetch( vMemory, Vec_IntSize(vInput) );
// add the cubes
Vec_IntForEachEntry( vInput, uCube, i )
Kit_SopPushCube( cResult, uCube );
}
/**Function*************************************************************
Synopsis [Creates SOP from the cube array.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopCreateInverse( Kit_Sop_t * cResult, Vec_Int_t * vInput, int nLits, Vec_Int_t * vMemory )
{
unsigned uCube, uMask = 0;
int i, nCubes = Vec_IntSize(vInput);
// start the cover
cResult->nCubes = 0;
cResult->pCubes = Vec_IntFetch( vMemory, nCubes );
// add the cubes
// Vec_IntForEachEntry( vInput, uCube, i )
for ( i = 0; i < nCubes; i++ )
{
uCube = Vec_IntEntry( vInput, i );
uMask = ((uCube | (uCube >> 1)) & 0x55555555);
uMask |= (uMask << 1);
Kit_SopPushCube( cResult, uCube ^ uMask );
}
}
/**Function*************************************************************
Synopsis [Duplicates SOP.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopDup( Kit_Sop_t * cResult, Kit_Sop_t * cSop, Vec_Int_t * vMemory )
{
unsigned uCube;
int i;
// start the cover
cResult->nCubes = 0;
cResult->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) );
// add the cubes
Kit_SopForEachCube( cSop, uCube, i )
Kit_SopPushCube( cResult, uCube );
}
/**Function*************************************************************
Synopsis [Derives the quotient of division by literal.]
Description [Reduces the cover to be equal to the result of
division of the given cover by the literal.]
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopDivideByLiteralQuo( Kit_Sop_t * cSop, int iLit )
{
unsigned uCube;
int i, k = 0;
Kit_SopForEachCube( cSop, uCube, i )
{
if ( Kit_CubeHasLit(uCube, iLit) )
Kit_SopWriteCube( cSop, Kit_CubeRemLit(uCube, iLit), k++ );
}
Kit_SopShrink( cSop, k );
}
/**Function*************************************************************
Synopsis [Divides cover by one cube.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopDivideByCube( Kit_Sop_t * cSop, Kit_Sop_t * cDiv, Kit_Sop_t * vQuo, Kit_Sop_t * vRem, Vec_Int_t * vMemory )
{
unsigned uCube, uDiv;
int i;
// get the only cube
assert( Kit_SopCubeNum(cDiv) == 1 );
uDiv = Kit_SopCube(cDiv, 0);
// allocate covers
vQuo->nCubes = 0;
vQuo->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) );
vRem->nCubes = 0;
vRem->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) );
// sort the cubes
Kit_SopForEachCube( cSop, uCube, i )
{
if ( Kit_CubeContains( uCube, uDiv ) )
Kit_SopPushCube( vQuo, Kit_CubeSharp(uCube, uDiv) );
else
Kit_SopPushCube( vRem, uCube );
}
}
/**Function*************************************************************
Synopsis [Divides cover by one cube.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopDivideInternal( Kit_Sop_t * cSop, Kit_Sop_t * cDiv, Kit_Sop_t * vQuo, Kit_Sop_t * vRem, Vec_Int_t * vMemory )
{
unsigned uCube, uDiv;
unsigned uCube2 = 0; // Suppress "might be used uninitialized"
unsigned uDiv2, uQuo;
int i, i2, k, k2, nCubesRem;
assert( Kit_SopCubeNum(cSop) >= Kit_SopCubeNum(cDiv) );
// consider special case
if ( Kit_SopCubeNum(cDiv) == 1 )
{
Kit_SopDivideByCube( cSop, cDiv, vQuo, vRem, vMemory );
return;
}
// allocate quotient
vQuo->nCubes = 0;
vQuo->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) / Kit_SopCubeNum(cDiv) );
// for each cube of the cover
// it either belongs to the quotient or to the remainder
Kit_SopForEachCube( cSop, uCube, i )
{
// skip taken cubes
if ( Kit_CubeIsMarked(uCube) )
continue;
// find a matching cube in the divisor
uDiv = ~0;
Kit_SopForEachCube( cDiv, uDiv, k )
if ( Kit_CubeContains( uCube, uDiv ) )
break;
// the cube is not found
if ( k == Kit_SopCubeNum(cDiv) )
continue;
// the quotient cube exists
uQuo = Kit_CubeSharp( uCube, uDiv );
// find corresponding cubes for other cubes of the divisor
uDiv2 = ~0;
Kit_SopForEachCube( cDiv, uDiv2, k2 )
{
if ( k2 == k )
continue;
// find a matching cube
Kit_SopForEachCube( cSop, uCube2, i2 )
{
// skip taken cubes
if ( Kit_CubeIsMarked(uCube2) )
continue;
// check if the cube can be used
if ( Kit_CubeContains( uCube2, uDiv2 ) && uQuo == Kit_CubeSharp( uCube2, uDiv2 ) )
break;
}
// the case when the cube is not found
if ( i2 == Kit_SopCubeNum(cSop) )
break;
}
// we did not find some cubes - continue looking at other cubes
if ( k2 != Kit_SopCubeNum(cDiv) )
continue;
// we found all cubes - add the quotient cube
Kit_SopPushCube( vQuo, uQuo );
// mark the first cube
Kit_SopWriteCube( cSop, Kit_CubeMark(uCube), i );
// mark other cubes that have this quotient
Kit_SopForEachCube( cDiv, uDiv2, k2 )
{
if ( k2 == k )
continue;
// find a matching cube
Kit_SopForEachCube( cSop, uCube2, i2 )
{
// skip taken cubes
if ( Kit_CubeIsMarked(uCube2) )
continue;
// check if the cube can be used
if ( Kit_CubeContains( uCube2, uDiv2 ) && uQuo == Kit_CubeSharp( uCube2, uDiv2 ) )
break;
}
assert( i2 < Kit_SopCubeNum(cSop) );
// the cube is found, mark it
// (later we will add all unmarked cubes to the remainder)
Kit_SopWriteCube( cSop, Kit_CubeMark(uCube2), i2 );
}
}
// determine the number of cubes in the remainder
nCubesRem = Kit_SopCubeNum(cSop) - Kit_SopCubeNum(vQuo) * Kit_SopCubeNum(cDiv);
// allocate remainder
vRem->nCubes = 0;
vRem->pCubes = Vec_IntFetch( vMemory, nCubesRem );
// finally add the remaining unmarked cubes to the remainder
// and clean the marked cubes in the cover
Kit_SopForEachCube( cSop, uCube, i )
{
if ( !Kit_CubeIsMarked(uCube) )
{
Kit_SopPushCube( vRem, uCube );
continue;
}
Kit_SopWriteCube( cSop, Kit_CubeUnmark(uCube), i );
}
assert( nCubesRem == Kit_SopCubeNum(vRem) );
}
/**Function*************************************************************
Synopsis [Returns the common cube.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
static inline unsigned Kit_SopCommonCube( Kit_Sop_t * cSop )
{
unsigned uMask, uCube;
int i;
uMask = ~(unsigned)0;
Kit_SopForEachCube( cSop, uCube, i )
uMask &= uCube;
return uMask;
}
/**Function*************************************************************
Synopsis [Makes the cover cube-ABC_FREE.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopMakeCubeFree( Kit_Sop_t * cSop )
{
unsigned uMask, uCube;
int i;
uMask = Kit_SopCommonCube( cSop );
if ( uMask == 0 )
return;
// remove the common cube
Kit_SopForEachCube( cSop, uCube, i )
Kit_SopWriteCube( cSop, Kit_CubeSharp(uCube, uMask), i );
}
/**Function*************************************************************
Synopsis [Checks if the cover is cube-ABC_FREE.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Kit_SopIsCubeFree( Kit_Sop_t * cSop )
{
return Kit_SopCommonCube( cSop ) == 0;
}
/**Function*************************************************************
Synopsis [Creates SOP composes of the common cube of the given SOP.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopCommonCubeCover( Kit_Sop_t * cResult, Kit_Sop_t * cSop, Vec_Int_t * vMemory )
{
assert( Kit_SopCubeNum(cSop) > 0 );
cResult->nCubes = 0;
cResult->pCubes = Vec_IntFetch( vMemory, 1 );
Kit_SopPushCube( cResult, Kit_SopCommonCube(cSop) );
}
/**Function*************************************************************
Synopsis [Find any literal that occurs more than once.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Kit_SopAnyLiteral( Kit_Sop_t * cSop, int nLits )
{
unsigned uCube;
int i, k, nLitsCur;
// go through each literal
for ( i = 0; i < nLits; i++ )
{
// go through all the cubes
nLitsCur = 0;
Kit_SopForEachCube( cSop, uCube, k )
if ( Kit_CubeHasLit(uCube, i) )
nLitsCur++;
if ( nLitsCur > 1 )
return i;
}
return -1;
}
/**Function*************************************************************
Synopsis [Find the least often occurring literal.]
Description [Find the least often occurring literal among those
that occur more than once.]
SideEffects []
SeeAlso []
***********************************************************************/
int Kit_SopWorstLiteral( Kit_Sop_t * cSop, int nLits )
{
unsigned uCube;
int i, k, iMin, nLitsMin, nLitsCur;
int fUseFirst = 1;
// go through each literal
iMin = -1;
nLitsMin = 1000000;
for ( i = 0; i < nLits; i++ )
{
// go through all the cubes
nLitsCur = 0;
Kit_SopForEachCube( cSop, uCube, k )
if ( Kit_CubeHasLit(uCube, i) )
nLitsCur++;
// skip the literal that does not occur or occurs once
if ( nLitsCur < 2 )
continue;
// check if this is the best literal
if ( fUseFirst )
{
if ( nLitsMin > nLitsCur )
{
nLitsMin = nLitsCur;
iMin = i;
}
}
else
{
if ( nLitsMin >= nLitsCur )
{
nLitsMin = nLitsCur;
iMin = i;
}
}
}
if ( nLitsMin < 1000000 )
return iMin;
return -1;
}
/**Function*************************************************************
Synopsis [Find the least often occurring literal.]
Description [Find the least often occurring literal among those
that occur more than once.]
SideEffects []
SeeAlso []
***********************************************************************/
int Kit_SopBestLiteral( Kit_Sop_t * cSop, int nLits, unsigned uMask )
{
unsigned uCube;
int i, k, iMax, nLitsMax, nLitsCur;
int fUseFirst = 1;
// go through each literal
iMax = -1;
nLitsMax = -1;
for ( i = 0; i < nLits; i++ )
{
if ( !Kit_CubeHasLit(uMask, i) )
continue;
// go through all the cubes
nLitsCur = 0;
Kit_SopForEachCube( cSop, uCube, k )
if ( Kit_CubeHasLit(uCube, i) )
nLitsCur++;
// skip the literal that does not occur or occurs once
if ( nLitsCur < 2 )
continue;
// check if this is the best literal
if ( fUseFirst )
{
if ( nLitsMax < nLitsCur )
{
nLitsMax = nLitsCur;
iMax = i;
}
}
else
{
if ( nLitsMax <= nLitsCur )
{
nLitsMax = nLitsCur;
iMax = i;
}
}
}
if ( nLitsMax >= 0 )
return iMax;
return -1;
}
/**Function*************************************************************
Synopsis [Computes a level-zero kernel.]
Description [Modifies the cover to contain one level-zero kernel.]
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopDivisorZeroKernel_rec( Kit_Sop_t * cSop, int nLits )
{
int iLit;
// find any literal that occurs at least two times
iLit = Kit_SopWorstLiteral( cSop, nLits );
if ( iLit == -1 )
return;
// derive the cube-free quotient
Kit_SopDivideByLiteralQuo( cSop, iLit ); // the same cover
Kit_SopMakeCubeFree( cSop ); // the same cover
// call recursively
Kit_SopDivisorZeroKernel_rec( cSop, nLits ); // the same cover
}
/**Function*************************************************************
Synopsis [Computes the quick divisor of the cover.]
Description [Returns 0, if there is no divisor other than trivial.]
SideEffects []
SeeAlso []
***********************************************************************/
int Kit_SopDivisor( Kit_Sop_t * cResult, Kit_Sop_t * cSop, int nLits, Vec_Int_t * vMemory )
{
if ( Kit_SopCubeNum(cSop) <= 1 )
return 0;
if ( Kit_SopAnyLiteral( cSop, nLits ) == -1 )
return 0;
// duplicate the cover
Kit_SopDup( cResult, cSop, vMemory );
// perform the kerneling
Kit_SopDivisorZeroKernel_rec( cResult, nLits );
assert( Kit_SopCubeNum(cResult) > 0 );
return 1;
}
/**Function*************************************************************
Synopsis [Create the one-literal cover with the best literal from cSop.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Kit_SopBestLiteralCover( Kit_Sop_t * cResult, Kit_Sop_t * cSop, unsigned uCube, int nLits, Vec_Int_t * vMemory )
{
int iLitBest;
// get the best literal
iLitBest = Kit_SopBestLiteral( cSop, nLits, uCube );
// start the cover
cResult->nCubes = 0;
cResult->pCubes = Vec_IntFetch( vMemory, 1 );
// set the cube
Kit_SopPushCube( cResult, Kit_CubeSetLit(0, iLitBest) );
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
ABC_NAMESPACE_IMPL_END
|
