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
|
/**CFile****************************************************************
FileName [ifDec.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [FPGA mapping based on priority cuts.]
Synopsis [Performs additional check.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - November 21, 2006.]
Revision [$Id: ifDec.c,v 1.00 2006/11/21 00:00:00 alanmi Exp $]
***********************************************************************/
#include "if.h"
ABC_NAMESPACE_IMPL_START
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
// the bit count for the first 256 integer numbers
static int BitCount8[256] = {
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8
};
// variable swapping code
static word PMasks[5][3] = {
{ 0x9999999999999999, 0x2222222222222222, 0x4444444444444444 },
{ 0xC3C3C3C3C3C3C3C3, 0x0C0C0C0C0C0C0C0C, 0x3030303030303030 },
{ 0xF00FF00FF00FF00F, 0x00F000F000F000F0, 0x0F000F000F000F00 },
{ 0xFF0000FFFF0000FF, 0x0000FF000000FF00, 0x00FF000000FF0000 },
{ 0xFFFF00000000FFFF, 0x00000000FFFF0000, 0x0000FFFF00000000 }
};
// elementary truth tables
static word Truth6[6] = {
0xAAAAAAAAAAAAAAAA,
0xCCCCCCCCCCCCCCCC,
0xF0F0F0F0F0F0F0F0,
0xFF00FF00FF00FF00,
0xFFFF0000FFFF0000,
0xFFFFFFFF00000000
};
static word Truth7[7][2] = {
0xAAAAAAAAAAAAAAAA,0xAAAAAAAAAAAAAAAA,
0xCCCCCCCCCCCCCCCC,0xCCCCCCCCCCCCCCCC,
0xF0F0F0F0F0F0F0F0,0xF0F0F0F0F0F0F0F0,
0xFF00FF00FF00FF00,0xFF00FF00FF00FF00,
0xFFFF0000FFFF0000,0xFFFF0000FFFF0000,
0xFFFFFFFF00000000,0xFFFFFFFF00000000,
0x0000000000000000,0xFFFFFFFFFFFFFFFF
};
extern void Kit_DsdPrintFromTruth( unsigned * pTruth, int nVars );
extern void Extra_PrintBinary( FILE * pFile, unsigned Sign[], int nBits );
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
static void If_DecPrintConfig( word z )
{
unsigned S[1];
S[0] = (z & 0xffff) | ((z & 0xffff) << 16);
Extra_PrintBinary( stdout, S, 16 );
printf( " " );
Kit_DsdPrintFromTruth( S, 4 );
printf( " " );
printf( " %d", (z >> 16) & 7 );
printf( " %d", (z >> 20) & 7 );
printf( " %d", (z >> 24) & 7 );
printf( " %d", (z >> 28) & 7 );
printf( " " );
S[0] = ((z >> 32) & 0xffff) | (((z >> 32) & 0xffff) << 16);
Extra_PrintBinary( stdout, S, 16 );
printf( " " );
Kit_DsdPrintFromTruth( S, 4 );
printf( " " );
printf( " %d", (z >> 48) & 7 );
printf( " %d", (z >> 52) & 7 );
printf( " %d", (z >> 56) & 7 );
printf( " %d", (z >> 60) & 7 );
printf( "\n" );
}
// verification for 6-input function
static word If_Dec6ComposeLut4( int t, word f[4] )
{
int m, v;
word c, r = 0;
for ( m = 0; m < 16; m++ )
{
if ( !((t >> m) & 1) )
continue;
c = ~0;
for ( v = 0; v < 4; v++ )
c &= ((m >> v) & 1) ? f[v] : ~f[v];
r |= c;
}
return r;
}
static void If_Dec6Verify( word t, word z )
{
word r, q, f[4];
int i, v;
assert( z );
for ( i = 0; i < 4; i++ )
{
v = (z >> (16+(i<<2))) & 7;
assert( v != 7 );
f[i] = Truth6[v];
}
q = If_Dec6ComposeLut4( (int)(z & 0xffff), f );
for ( i = 0; i < 4; i++ )
{
v = (z >> (48+(i<<2))) & 7;
f[i] = (v == 7) ? q : Truth6[v];
}
r = If_Dec6ComposeLut4( (int)((z >> 32) & 0xffff), f );
if ( r != t )
{
If_DecPrintConfig( z );
Kit_DsdPrintFromTruth( (unsigned*)&t, 6 ); printf( "\n" );
Kit_DsdPrintFromTruth( (unsigned*)&q, 6 ); printf( "\n" );
Kit_DsdPrintFromTruth( (unsigned*)&r, 6 ); printf( "\n" );
printf( "Verification failed!\n" );
}
}
// verification for 7-input function
static void If_Dec7ComposeLut4( int t, word f[4][2], word r[2] )
{
int m, v;
word c[2];
r[0] = r[1] = 0;
for ( m = 0; m < 16; m++ )
{
if ( !((t >> m) & 1) )
continue;
c[0] = c[1] = ~0;
for ( v = 0; v < 4; v++ )
{
c[0] &= ((m >> v) & 1) ? f[v][0] : ~f[v][0];
c[1] &= ((m >> v) & 1) ? f[v][1] : ~f[v][1];
}
r[0] |= c[0];
r[1] |= c[1];
}
}
static void If_Dec7Verify( word t[2], word z )
{
word f[4][2], r[2];
int i, v;
assert( z );
for ( i = 0; i < 4; i++ )
{
v = (z >> (16+(i<<2))) & 7;
f[i][0] = Truth7[v][0];
f[i][1] = Truth7[v][1];
}
If_Dec7ComposeLut4( (int)(z & 0xffff), f, r );
f[3][0] = r[0];
f[3][1] = r[1];
for ( i = 0; i < 3; i++ )
{
v = (z >> (48+(i<<2))) & 7;
f[i][0] = Truth7[v][0];
f[i][1] = Truth7[v][1];
}
If_Dec7ComposeLut4( (int)((z >> 32) & 0xffff), f, r );
if ( r[0] != t[0] || r[1] != t[1] )
{
If_DecPrintConfig( z );
Kit_DsdPrintFromTruth( (unsigned*)t, 7 ); printf( "\n" );
Kit_DsdPrintFromTruth( (unsigned*)r, 7 ); printf( "\n" );
printf( "Verification failed!\n" );
}
}
// count the number of unique cofactors
static inline int If_Dec6CofCount2( word t )
{
int i, Mask = 0;
for ( i = 0; i < 16; i++ )
Mask |= (1 << ((t >> (i<<2)) & 15));
return BitCount8[((unsigned char*)&Mask)[0]] + BitCount8[((unsigned char*)&Mask)[1]];
}
// count the number of unique cofactors (up to 3)
static inline int If_Dec7CofCount3( word t[2] )
{
unsigned char * pTruth = (unsigned char *)t;
int i, iCof2 = 0;
for ( i = 1; i < 16; i++ )
{
if ( pTruth[i] == pTruth[0] )
continue;
if ( iCof2 == 0 )
iCof2 = i;
else if ( pTruth[i] != pTruth[iCof2] )
return 3;
}
assert( iCof2 );
return 2;
}
// permute 6-input function
static inline word If_Dec6SwapAdjacent( word t, int v )
{
assert( v < 5 );
return (t & PMasks[v][0]) | ((t & PMasks[v][1]) << (1 << v)) | ((t & PMasks[v][2]) >> (1 << v));
}
static inline word If_Dec6MoveTo( word t, int v, int p, int Pla2Var[6], int Var2Pla[6] )
{
int iPlace0, iPlace1;
assert( Var2Pla[v] >= p );
while ( Var2Pla[v] != p )
{
iPlace0 = Var2Pla[v]-1;
iPlace1 = Var2Pla[v];
t = If_Dec6SwapAdjacent( t, iPlace0 );
Var2Pla[Pla2Var[iPlace0]]++;
Var2Pla[Pla2Var[iPlace1]]--;
Pla2Var[iPlace0] ^= Pla2Var[iPlace1];
Pla2Var[iPlace1] ^= Pla2Var[iPlace0];
Pla2Var[iPlace0] ^= Pla2Var[iPlace1];
}
assert( Pla2Var[p] == v );
return t;
}
// permute 7-input function
static inline void If_Dec7SwapAdjacent( word t[2], int v )
{
if ( v == 5 )
{
unsigned Temp = (t[0] >> 32);
t[0] = (t[0] & 0xFFFFFFFF) | ((t[1] & 0xFFFFFFFF) << 32);
t[1] ^= (t[1] & 0xFFFFFFFF) ^ Temp;
return;
}
assert( v < 5 );
t[0] = If_Dec6SwapAdjacent( t[0], v );
t[1] = If_Dec6SwapAdjacent( t[1], v );
}
static inline void If_Dec7MoveTo( word t[2], int v, int p, int Pla2Var[7], int Var2Pla[7] )
{
int iPlace0, iPlace1;
assert( Var2Pla[v] >= p );
while ( Var2Pla[v] != p )
{
iPlace0 = Var2Pla[v]-1;
iPlace1 = Var2Pla[v];
If_Dec7SwapAdjacent( t, iPlace0 );
Var2Pla[Pla2Var[iPlace0]]++;
Var2Pla[Pla2Var[iPlace1]]--;
Pla2Var[iPlace0] ^= Pla2Var[iPlace1];
Pla2Var[iPlace1] ^= Pla2Var[iPlace0];
Pla2Var[iPlace0] ^= Pla2Var[iPlace1];
}
assert( Pla2Var[p] == v );
}
// derive binary function
static inline int If_Dec6DeriveCount2( word t, int * pCof0, int * pCof1 )
{
int i, Mask = 0;
*pCof0 = (t & 15);
*pCof1 = (t & 15);
for ( i = 1; i < 16; i++ )
if ( *pCof0 != ((t >> (i<<2)) & 15) )
{
*pCof1 = ((t >> (i<<2)) & 15);
Mask |= (1 << i);
}
return Mask;
}
static inline int If_Dec7DeriveCount3( word t[2], int * pCof0, int * pCof1 )
{
unsigned char * pTruth = (unsigned char *)t;
int i, Mask = 0;
*pCof0 = pTruth[0];
*pCof1 = pTruth[0];
for ( i = 1; i < 16; i++ )
if ( *pCof0 != pTruth[i] )
{
*pCof1 = pTruth[i];
Mask |= (1 << i);
}
return Mask;
}
// derives decomposition
static inline word If_Dec6Cofactor( word t, int iVar, int fCof1 )
{
assert( iVar >= 0 && iVar < 6 );
if ( fCof1 )
return (t & Truth6[iVar]) | ((t & Truth6[iVar]) >> (1<<iVar));
else
return (t &~Truth6[iVar]) | ((t &~Truth6[iVar]) << (1<<iVar));
}
static word If_Dec6DeriveDisjoint( word t, int Pla2Var[6], int Var2Pla[6] )
{
int i, Cof0, Cof1;
word z = If_Dec6DeriveCount2( t, &Cof0, &Cof1 );
for ( i = 0; i < 4; i++ )
z |= (((word)Pla2Var[i+2]) << (16 + 4*i));
z |= ((word)((Cof1 << 4) | Cof0) << 32);
z |= ((word)((Cof1 << 4) | Cof0) << 40);
for ( i = 0; i < 2; i++ )
z |= (((word)Pla2Var[i]) << (48 + 4*i));
z |= (((word)7) << (48 + 4*i++));
assert( i == 3 );
return z;
}
static word If_Dec6DeriveNonDisjoint( word t, int s, int Pla2Var0[6], int Var2Pla0[6] )
{
word z, c0, c1;
int Cof0[2], Cof1[2];
int Truth0, Truth1, i;
int Pla2Var[6], Var2Pla[6];
assert( s >= 2 && s <= 5 );
for ( i = 0; i < 6; i++ )
{
Pla2Var[i] = Pla2Var0[i];
Var2Pla[i] = Var2Pla0[i];
}
for ( i = s; i < 5; i++ )
{
t = If_Dec6SwapAdjacent( t, i );
Var2Pla[Pla2Var[i]]++;
Var2Pla[Pla2Var[i+1]]--;
Pla2Var[i] ^= Pla2Var[i+1];
Pla2Var[i+1] ^= Pla2Var[i];
Pla2Var[i] ^= Pla2Var[i+1];
}
c0 = If_Dec6Cofactor( t, 5, 0 );
c1 = If_Dec6Cofactor( t, 5, 1 );
assert( 2 >= If_Dec6CofCount2(c0) );
assert( 2 >= If_Dec6CofCount2(c1) );
Truth0 = If_Dec6DeriveCount2( c0, &Cof0[0], &Cof0[1] );
Truth1 = If_Dec6DeriveCount2( c1, &Cof1[0], &Cof1[1] );
z = ((Truth1 & 0xFF) << 8) | (Truth0 & 0xFF);
for ( i = 0; i < 4; i++ )
z |= (((word)Pla2Var[i+2]) << (16 + 4*i));
z |= ((word)((Cof0[1] << 4) | Cof0[0]) << 32);
z |= ((word)((Cof1[1] << 4) | Cof1[0]) << 40);
for ( i = 0; i < 2; i++ )
z |= (((word)Pla2Var[i]) << (48 + 4*i));
z |= (((word)7) << (48 + 4*i++));
z |= (((word)Pla2Var[5]) << (48 + 4*i++));
assert( i == 4 );
return z;
}
static word If_Dec7DeriveDisjoint( word t[2], int Pla2Var[7], int Var2Pla[7] )
{
int i, Cof0, Cof1;
word z = If_Dec7DeriveCount3( t, &Cof0, &Cof1 );
for ( i = 0; i < 4; i++ )
z |= (((word)Pla2Var[i+3]) << (16 + 4*i));
z |= ((word)((Cof1 << 8) | Cof0) << 32);
for ( i = 0; i < 3; i++ )
z |= (((word)Pla2Var[i]) << (48 + 4*i));
return z;
}
static inline int If_Dec6CountOnes( word t )
{
t = (t & 0x5555555555555555) + ((t>> 1) & 0x5555555555555555);
t = (t & 0x3333333333333333) + ((t>> 2) & 0x3333333333333333);
t = (t & 0x0F0F0F0F0F0F0F0F) + ((t>> 4) & 0x0F0F0F0F0F0F0F0F);
t = (t & 0x00FF00FF00FF00FF) + ((t>> 8) & 0x00FF00FF00FF00FF);
t = (t & 0x0000FFFF0000FFFF) + ((t>>16) & 0x0000FFFF0000FFFF);
return (t & 0x00000000FFFFFFFF) + (t>>32);
}
static inline int If_Dec6HasVar( word t, int v )
{
return ((t & Truth6[v]) >> (1<<v)) != (t & ~Truth6[v]);
}
static inline void If_DecVerifyPerm( int Pla2Var[6], int Var2Pla[6] )
{
int i;
for ( i = 0; i < 6; i++ )
assert( Pla2Var[Var2Pla[i]] == i );
}
static word If_Dec6Perform( word t, int fDerive )
{
word r = 0;
int i, v, u, x, Count, Pla2Var[6], Var2Pla[6];
// start arrays
for ( i = 0; i < 6; i++ )
{
assert( If_Dec6HasVar( t, i ) );
Pla2Var[i] = Var2Pla[i] = i;
}
// generate permutations
i = 0;
for ( v = 0; v < 6; v++ )
for ( u = v+1; u < 6; u++, i++ )
{
t = If_Dec6MoveTo( t, v, 0, Pla2Var, Var2Pla );
t = If_Dec6MoveTo( t, u, 1, Pla2Var, Var2Pla );
// If_DecVerifyPerm( Pla2Var, Var2Pla );
Count = If_Dec6CofCount2( t );
assert( Count > 1 );
if ( Count == 2 )
return !fDerive ? 1 : If_Dec6DeriveDisjoint( t, Pla2Var, Var2Pla );
// check non-disjoint decomposition
if ( !r && (Count == 3 || Count == 4) )
{
for ( x = 0; x < 4; x++ )
{
word c0 = If_Dec6Cofactor( t, x+2, 0 );
word c1 = If_Dec6Cofactor( t, x+2, 1 );
if ( If_Dec6CofCount2( c0 ) <= 2 && If_Dec6CofCount2( c1 ) <= 2 )
{
r = !fDerive ? 1 : If_Dec6DeriveNonDisjoint( t, x+2, Pla2Var, Var2Pla );
break;
}
}
}
}
assert( i == 15 );
return r;
}
static word If_Dec7Perform( word t0[2], int fDerive )
{
word t[2] = {t0[0], t0[1]};
int i, v, u, y, Pla2Var[7], Var2Pla[7];
// start arrays
for ( i = 0; i < 7; i++ )
{
if ( i < 6 )
assert( If_Dec6HasVar( t[0], i ) || If_Dec6HasVar( t[1], i ) );
else
assert( t[0] != t[1] );
Pla2Var[i] = Var2Pla[i] = i;
}
// generate permutations
for ( v = 0; v < 7; v++ )
for ( u = v+1; u < 7; u++ )
for ( y = u+1; y < 7; y++ )
{
If_Dec7MoveTo( t, v, 0, Pla2Var, Var2Pla );
If_Dec7MoveTo( t, u, 1, Pla2Var, Var2Pla );
If_Dec7MoveTo( t, y, 2, Pla2Var, Var2Pla );
// If_DecVerifyPerm( Pla2Var, Var2Pla );
if ( If_Dec7CofCount3( t ) == 2 )
{
return !fDerive ? 1 : If_Dec7DeriveDisjoint( t, Pla2Var, Var2Pla );
}
}
return 0;
}
/**Function*************************************************************
Synopsis [Performs additional check.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int If_CutPerformCheckInt( unsigned * pTruth, int nVars, int nLeaves )
{
int fDerive = 0;
if ( nLeaves < 6 )
return 1;
if ( nLeaves == 6 )
{
word t = ((word *)pTruth)[0];
word z = If_Dec6Perform( t, fDerive );
if ( fDerive && z )
If_Dec6Verify( t, z );
return z != 0;
}
if ( nLeaves == 7 )
{
word t[2], z;
t[0] = ((word *)pTruth)[0];
t[1] = ((word *)pTruth)[1];
z = If_Dec7Perform( t, fDerive );
if ( fDerive && z )
If_Dec7Verify( t, z );
return z != 0;
}
assert( 0 );
return 0;
}
int If_CutPerformCheck( unsigned * pTruth, int nVars, int nLeaves )
{
int RetValue = If_CutPerformCheckInt( pTruth, nVars, nLeaves );
/*
// if ( nLeaves == 6 || nLeaves == 7 )
if ( nLeaves == 7 )
{
if ( RetValue == 0 )
{
printf( "%d ", RetValue );
Kit_DsdPrintFromTruth( pTruth, nLeaves );
printf( "\n" );
If_CutPerformCheckInt( pTruth, nVars, nLeaves );
}
}
*/
return RetValue;
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
ABC_NAMESPACE_IMPL_END
|