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
|
/**CFile****************************************************************
FileName [extraUtilThresh.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [extra]
Synopsis [Dealing with threshold functions.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - October 7, 2014.]
Revision [$Id: extraUtilThresh.c,v 1.0 2014/10/07 00:00:00 alanmi Exp $]
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include "misc/vec/vec.h"
#include "misc/util/utilTruth.h"
ABC_NAMESPACE_IMPL_START
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
/**Function*************************************************************
Synopsis [Checks thresholdness of the function.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Extra_ThreshPrintChow( int Chow0, int * pChow, int nVars )
{
int i;
for ( i = 0; i < nVars; i++ )
printf( "%d ", pChow[i] );
printf( " %d\n", Chow0 );
}
int Extra_ThreshComputeChow( word * t, int nVars, int * pChow )
{
int i, k, Chow0 = 0, nMints = (1 << nVars);
memset( pChow, 0, sizeof(int) * nVars );
// compute Chow coefs
for ( i = 0; i < nMints; i++ )
if ( Abc_TtGetBit(t, i) )
for ( Chow0++, k = 0; k < nVars; k++ )
if ( (i >> k) & 1 )
pChow[k]++;
// compute modified Chow coefs
for ( k = 0; k < nVars; k++ )
pChow[k] = 2 * pChow[k] - Chow0;
return Chow0 - (1 << (nVars-1));
}
void Extra_ThreshSortByChow( word * t, int nVars, int * pChow )
{
int i, nWords = Abc_TtWordNum(nVars);
while ( 1 )
{
int fChange = 0;
for ( i = 0; i < nVars - 1; i++ )
{
if ( pChow[i] >= pChow[i+1] )
continue;
ABC_SWAP( int, pChow[i], pChow[i+1] );
Abc_TtSwapAdjacent( t, nWords, i );
fChange = 1;
}
if ( !fChange )
return;
}
}
static inline int Extra_ThreshWeightedSum( int * pW, int nVars, int m )
{
int i, Cost = 0;
for ( i = 0; i < nVars; i++ )
if ( (m >> i) & 1 )
Cost += pW[i];
return Cost;
}
int Extra_ThreshSelectWeights3( word * t, int nVars, int * pW )
{
int m, Lmin, Lmax, nMints = (1 << nVars);
assert( nVars == 3 );
for ( pW[2] = 1; pW[2] <= nVars; pW[2]++ )
for ( pW[1] = pW[2]; pW[1] <= nVars; pW[1]++ )
for ( pW[0] = pW[1]; pW[0] <= nVars; pW[0]++ )
{
Lmin = 10000; Lmax = 0;
for ( m = 0; m < nMints; m++ )
{
if ( Abc_TtGetBit(t, m) )
Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
else
Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
if ( Lmax >= Lmin )
break;
// printf( "%c%d ", Abc_TtGetBit(t, m) ? '+' : '-', Extra_ThreshWeightedSum(pW, nVars, m) );
}
// printf( " -%d +%d\n", Lmax, Lmin );
if ( m < nMints )
continue;
assert( Lmax < Lmin );
return Lmin;
}
return 0;
}
int Extra_ThreshSelectWeights4( word * t, int nVars, int * pW )
{
int m, Lmin, Lmax, nMints = (1 << nVars);
assert( nVars == 4 );
for ( pW[3] = 1; pW[3] <= nVars; pW[3]++ )
for ( pW[2] = pW[3]; pW[2] <= nVars; pW[2]++ )
for ( pW[1] = pW[2]; pW[1] <= nVars; pW[1]++ )
for ( pW[0] = pW[1]; pW[0] <= nVars; pW[0]++ )
{
Lmin = 10000; Lmax = 0;
for ( m = 0; m < nMints; m++ )
{
if ( Abc_TtGetBit(t, m) )
Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
else
Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
if ( Lmax >= Lmin )
break;
}
if ( m < nMints )
continue;
assert( Lmax < Lmin );
return Lmin;
}
return 0;
}
int Extra_ThreshSelectWeights5( word * t, int nVars, int * pW )
{
int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 0;
assert( nVars == 5 );
for ( pW[4] = 1; pW[4] <= Limit; pW[4]++ )
for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
{
Lmin = 10000; Lmax = 0;
for ( m = 0; m < nMints; m++ )
{
if ( Abc_TtGetBit(t, m) )
Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
else
Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
if ( Lmax >= Lmin )
break;
}
if ( m < nMints )
continue;
assert( Lmax < Lmin );
return Lmin;
}
return 0;
}
int Extra_ThreshSelectWeights6( word * t, int nVars, int * pW )
{
int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 3;
assert( nVars == 6 );
for ( pW[5] = 1; pW[5] <= Limit; pW[5]++ )
for ( pW[4] = pW[5]; pW[4] <= Limit; pW[4]++ )
for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
{
Lmin = 10000; Lmax = 0;
for ( m = 0; m < nMints; m++ )
{
if ( Abc_TtGetBit(t, m) )
Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
else
Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
if ( Lmax >= Lmin )
break;
}
if ( m < nMints )
continue;
assert( Lmax < Lmin );
return Lmin;
}
return 0;
}
int Extra_ThreshSelectWeights7( word * t, int nVars, int * pW )
{
int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 6;
assert( nVars == 7 );
for ( pW[6] = 1; pW[6] <= Limit; pW[6]++ )
for ( pW[5] = pW[6]; pW[5] <= Limit; pW[5]++ )
for ( pW[4] = pW[5]; pW[4] <= Limit; pW[4]++ )
for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
{
Lmin = 10000; Lmax = 0;
for ( m = 0; m < nMints; m++ )
{
if ( Abc_TtGetBit(t, m) )
Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
else
Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
if ( Lmax >= Lmin )
break;
}
if ( m < nMints )
continue;
assert( Lmax < Lmin );
return Lmin;
}
return 0;
}
int Extra_ThreshSelectWeights8( word * t, int nVars, int * pW )
{
int m, Lmin, Lmax, nMints = (1 << nVars), Limit = nVars + 1; // <<-- incomplete detection to save runtime!
assert( nVars == 8 );
for ( pW[7] = 1; pW[7] <= Limit; pW[7]++ )
for ( pW[6] = pW[7]; pW[6] <= Limit; pW[6]++ )
for ( pW[5] = pW[6]; pW[5] <= Limit; pW[5]++ )
for ( pW[4] = pW[5]; pW[4] <= Limit; pW[4]++ )
for ( pW[3] = pW[4]; pW[3] <= Limit; pW[3]++ )
for ( pW[2] = pW[3]; pW[2] <= Limit; pW[2]++ )
for ( pW[1] = pW[2]; pW[1] <= Limit; pW[1]++ )
for ( pW[0] = pW[1]; pW[0] <= Limit; pW[0]++ )
{
Lmin = 10000; Lmax = 0;
for ( m = 0; m < nMints; m++ )
{
if ( Abc_TtGetBit(t, m) )
Lmin = Abc_MinInt( Lmin, Extra_ThreshWeightedSum(pW, nVars, m) );
else
Lmax = Abc_MaxInt( Lmax, Extra_ThreshWeightedSum(pW, nVars, m) );
if ( Lmax >= Lmin )
break;
}
if ( m < nMints )
continue;
assert( Lmax < Lmin );
return Lmin;
}
return 0;
}
int Extra_ThreshSelectWeights( word * t, int nVars, int * pW )
{
if ( nVars <= 2 )
return (t[0] & 0xF) != 6 && (t[0] & 0xF) != 9;
if ( nVars == 3 )
return Extra_ThreshSelectWeights3( t, nVars, pW );
if ( nVars == 4 )
return Extra_ThreshSelectWeights4( t, nVars, pW );
if ( nVars == 5 )
return Extra_ThreshSelectWeights5( t, nVars, pW );
if ( nVars == 6 )
return Extra_ThreshSelectWeights6( t, nVars, pW );
if ( nVars == 7 )
return Extra_ThreshSelectWeights7( t, nVars, pW );
if ( nVars == 8 )
return Extra_ThreshSelectWeights8( t, nVars, pW );
return 0;
}
int Extra_ThreshCheck( word * t, int nVars, int * pW )
{
int Chow0, Chow[16];
if ( !Abc_TtIsUnate(t, nVars) )
return 0;
Abc_TtMakePosUnate( t, nVars );
Chow0 = Extra_ThreshComputeChow( t, nVars, Chow );
Extra_ThreshSortByChow( t, nVars, Chow );
return Extra_ThreshSelectWeights( t, nVars, pW );
}
/**Function*************************************************************
Synopsis [Checks unateness of a function.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Extra_ThreshCheckTest()
{
int nVars = 5;
int T, Chow0, Chow[16], Weights[16];
// word t = s_Truths6[0] & s_Truths6[1] & s_Truths6[2] & s_Truths6[3] & s_Truths6[4];
// word t = (s_Truths6[0] & s_Truths6[1]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[3]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[4]);
word t = (s_Truths6[2] & s_Truths6[1]) | (s_Truths6[2] & s_Truths6[0] & s_Truths6[3]) | (s_Truths6[2] & s_Truths6[0] & ~s_Truths6[4]);
// word t = (s_Truths6[0] & s_Truths6[1]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[3]) | (s_Truths6[0] & s_Truths6[2] & s_Truths6[4]) | (s_Truths6[1] & s_Truths6[2] & s_Truths6[3]);
// word t = (s_Truths6[0] & s_Truths6[1]) | (s_Truths6[0] & s_Truths6[2]) | (s_Truths6[0] & s_Truths6[3] & s_Truths6[4] & s_Truths6[5]) |
// (s_Truths6[1] & s_Truths6[2] & s_Truths6[3]) | (s_Truths6[1] & s_Truths6[2] & s_Truths6[4]) | (s_Truths6[1] & s_Truths6[2] & s_Truths6[5]);
int i;
assert( nVars <= 8 );
for ( i = 0; i < nVars; i++ )
printf( "%d %d %d\n", i, Abc_TtPosVar(&t, nVars, i), Abc_TtNegVar(&t, nVars, i) );
// word t = s_Truths6[0] & s_Truths6[1] & s_Truths6[2];
Chow0 = Extra_ThreshComputeChow( &t, nVars, Chow );
if ( (T = Extra_ThreshCheck(&t, nVars, Weights)) )
Extra_ThreshPrintChow( T, Weights, nVars );
else
printf( "No threshold\n" );
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
ABC_NAMESPACE_IMPL_END
|
