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
|
/**CFile***********************************************************************
FileName [cuddSolve.c]
PackageName [cudd]
Synopsis [Boolean equation solver and related functions.]
Description [External functions included in this modoule:
<ul>
<li> Cudd_SolveEqn()
<li> Cudd_VerifySol()
</ul>
Internal functions included in this module:
<ul>
<li> cuddSolveEqnRecur()
<li> cuddVerifySol()
</ul> ]
SeeAlso []
Author [Balakrishna Kumthekar]
Copyright [This file was created at the University of Colorado at
Boulder. The University of Colorado at Boulder makes no warranty
about the suitability of this software for any purpose. It is
presented on an AS IS basis.]
******************************************************************************/
#include "util.h"
#include "cuddInt.h"
/*---------------------------------------------------------------------------*/
/* Constant declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Type declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Structure declarations */
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* Variable declarations */
/*---------------------------------------------------------------------------*/
#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddSolve.c,v 1.1.1.1 2003/02/24 22:23:53 wjiang Exp $";
#endif
/*---------------------------------------------------------------------------*/
/* Macro declarations */
/*---------------------------------------------------------------------------*/
/**AutomaticStart*************************************************************/
/*---------------------------------------------------------------------------*/
/* Static function prototypes */
/*---------------------------------------------------------------------------*/
/**AutomaticEnd***************************************************************/
/*---------------------------------------------------------------------------*/
/* Definition of exported functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Implements the solution of F(x,y) = 0.]
Description [Implements the solution for F(x,y) = 0. The return
value is the consistency condition. The y variables are the unknowns
and the remaining variables are the parameters. Returns the
consistency condition if successful; NULL otherwise. Cudd_SolveEqn
allocates an array and fills it with the indices of the
unknowns. This array is used by Cudd_VerifySol.]
SideEffects [The solution is returned in G; the indices of the y
variables are returned in yIndex.]
SeeAlso [Cudd_VerifySol]
******************************************************************************/
DdNode *
Cudd_SolveEqn(
DdManager * bdd,
DdNode * F /* the left-hand side of the equation */,
DdNode * Y /* the cube of the y variables */,
DdNode ** G /* the array of solutions (return parameter) */,
int ** yIndex /* index of y variables */,
int n /* numbers of unknowns */)
{
DdNode *res;
int *temp;
*yIndex = temp = ALLOC(int, n);
if (temp == NULL) {
bdd->errorCode = CUDD_MEMORY_OUT;
(void) fprintf(bdd->out,
"Cudd_SolveEqn: Out of memory for yIndex\n");
return(NULL);
}
do {
bdd->reordered = 0;
res = cuddSolveEqnRecur(bdd, F, Y, G, n, temp, 0);
} while (bdd->reordered == 1);
return(res);
} /* end of Cudd_SolveEqn */
/**Function********************************************************************
Synopsis [Checks the solution of F(x,y) = 0.]
Description [Checks the solution of F(x,y) = 0. This procedure
substitutes the solution components for the unknowns of F and returns
the resulting BDD for F.]
SideEffects [Frees the memory pointed by yIndex.]
SeeAlso [Cudd_SolveEqn]
******************************************************************************/
DdNode *
Cudd_VerifySol(
DdManager * bdd,
DdNode * F /* the left-hand side of the equation */,
DdNode ** G /* the array of solutions */,
int * yIndex /* index of y variables */,
int n /* numbers of unknowns */)
{
DdNode *res;
do {
bdd->reordered = 0;
res = cuddVerifySol(bdd, F, G, yIndex, n);
} while (bdd->reordered == 1);
FREE(yIndex);
return(res);
} /* end of Cudd_VerifySol */
/*---------------------------------------------------------------------------*/
/* Definition of internal functions */
/*---------------------------------------------------------------------------*/
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_SolveEqn.]
Description [Implements the recursive step of Cudd_SolveEqn.
Returns NULL if the intermediate solution blows up
or reordering occurs. The parametric solutions are
stored in the array G.]
SideEffects [none]
SeeAlso [Cudd_SolveEqn, Cudd_VerifySol]
******************************************************************************/
DdNode *
cuddSolveEqnRecur(
DdManager * bdd,
DdNode * F /* the left-hand side of the equation */,
DdNode * Y /* the cube of remaining y variables */,
DdNode ** G /* the array of solutions */,
int n /* number of unknowns */,
int * yIndex /* array holding the y variable indices */,
int i /* level of recursion */)
{
DdNode *Fn, *Fm1, *Fv, *Fvbar, *T, *w, *nextY, *one;
DdNodePtr *variables;
int j;
statLine(bdd);
variables = bdd->vars;
one = DD_ONE(bdd);
/* Base condition. */
if (Y == one) {
return F;
}
/* Cofactor of Y. */
yIndex[i] = Y->index;
nextY = Cudd_T(Y);
/* Universal abstraction of F with respect to the top variable index. */
Fm1 = cuddBddExistAbstractRecur(bdd, Cudd_Not(F), variables[yIndex[i]]);
if (Fm1) {
Fm1 = Cudd_Not(Fm1);
cuddRef(Fm1);
} else {
return(NULL);
}
Fn = cuddSolveEqnRecur(bdd, Fm1, nextY, G, n, yIndex, i+1);
if (Fn) {
cuddRef(Fn);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
return(NULL);
}
Fv = cuddCofactorRecur(bdd, F, variables[yIndex[i]]);
if (Fv) {
cuddRef(Fv);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
return(NULL);
}
Fvbar = cuddCofactorRecur(bdd, F, Cudd_Not(variables[yIndex[i]]));
if (Fvbar) {
cuddRef(Fvbar);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, Fv);
return(NULL);
}
/* Build i-th component of the solution. */
w = cuddBddIteRecur(bdd, variables[yIndex[i]], Cudd_Not(Fv), Fvbar);
if (w) {
cuddRef(w);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, Fv);
Cudd_RecursiveDeref(bdd, Fvbar);
return(NULL);
}
T = cuddBddRestrictRecur(bdd, w, Cudd_Not(Fm1));
if(T) {
cuddRef(T);
} else {
Cudd_RecursiveDeref(bdd, Fm1);
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, Fv);
Cudd_RecursiveDeref(bdd, Fvbar);
Cudd_RecursiveDeref(bdd, w);
return(NULL);
}
Cudd_RecursiveDeref(bdd,Fm1);
Cudd_RecursiveDeref(bdd,w);
Cudd_RecursiveDeref(bdd,Fv);
Cudd_RecursiveDeref(bdd,Fvbar);
/* Substitute components of solution already found into solution. */
for (j = n-1; j > i; j--) {
w = cuddBddComposeRecur(bdd,T, G[j], variables[yIndex[j]]);
if(w) {
cuddRef(w);
} else {
Cudd_RecursiveDeref(bdd, Fn);
Cudd_RecursiveDeref(bdd, T);
return(NULL);
}
Cudd_RecursiveDeref(bdd,T);
T = w;
}
G[i] = T;
Cudd_Deref(Fn);
return(Fn);
} /* end of cuddSolveEqnRecur */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_VerifySol. ]
Description []
SideEffects [none]
SeeAlso [Cudd_VerifySol]
******************************************************************************/
DdNode *
cuddVerifySol(
DdManager * bdd,
DdNode * F /* the left-hand side of the equation */,
DdNode ** G /* the array of solutions */,
int * yIndex /* array holding the y variable indices */,
int n /* number of unknowns */)
{
DdNode *w, *R;
int j;
R = F;
cuddRef(R);
for(j = n - 1; j >= 0; j--) {
w = Cudd_bddCompose(bdd, R, G[j], yIndex[j]);
if (w) {
cuddRef(w);
} else {
return(NULL);
}
Cudd_RecursiveDeref(bdd,R);
R = w;
}
cuddDeref(R);
return(R);
} /* end of cuddVerifySol */
/*---------------------------------------------------------------------------*/
/* Definition of static functions */
/*---------------------------------------------------------------------------*/
|
