/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddWeakDivF.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddWeakDivF]
******************************************************************************/
DdNode *
cuddZddWeakDivF(
DdManager * dd,
DdNode * f,
DdNode * g)
{
int v, top_f, top_g, vf, vg;
DdNode *one = DD_ONE(dd);
DdNode *zero = DD_ZERO(dd);
DdNode *f0, *f1, *fd, *g0, *g1, *gd;
DdNode *q, *tmp;
DdNode *r;
DdNode *term1, *term0, *termd;
int flag;
int pv, nv;
statLine(dd);
if (g == one)
return(f);
if (f == zero || f == one)
return(zero);
if (f == g)
return(one);
/* Check cache. */
r = cuddCacheLookup2Zdd(dd, cuddZddWeakDivF, f, g);
if (r)
return(r);
top_f = dd->permZ[f->index];
top_g = dd->permZ[g->index];
vf = top_f >> 1;
vg = top_g >> 1;
v = ddMin(top_f, top_g);
if (v == top_f && vf < vg) {
v = f->index;
flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
pv = cuddZddGetPosVarIndex(dd, v);
nv = cuddZddGetNegVarIndex(dd, v);
term1 = cuddZddWeakDivF(dd, f1, g);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(term1);
Cudd_RecursiveDerefZdd(dd, f1);
term0 = cuddZddWeakDivF(dd, f0, g);
if (term0 == NULL) {
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, term1);
return(NULL);
}
Cudd_Ref(term0);
Cudd_RecursiveDerefZdd(dd, f0);
termd = cuddZddWeakDivF(dd, fd, g);
if (termd == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term0);
return(NULL);
}
Cudd_Ref(termd);
Cudd_RecursiveDerefZdd(dd, fd);
tmp = cuddZddGetNode(dd, nv, term0, termd); /* nv = zi */
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, term0);
Cudd_RecursiveDerefZdd(dd, termd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, term0);
Cudd_RecursiveDerefZdd(dd, termd);
q = cuddZddGetNode(dd, pv, term1, tmp); /* pv = yi */
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, term1);
Cudd_RecursiveDerefZdd(dd, tmp);
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, q);
Cudd_Deref(q);
return(q);
}
if (v == top_f)
v = f->index;
else
v = g->index;
flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
if (flag == 1)
return(NULL);
Cudd_Ref(f1);
Cudd_Ref(f0);
Cudd_Ref(fd);
flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
if (flag == 1) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
return(NULL);
}
Cudd_Ref(g1);
Cudd_Ref(g0);
Cudd_Ref(gd);
q = g;
if (g0 != zero) {
q = cuddZddWeakDivF(dd, f0, g0);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, g0);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(q);
}
else
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, f0);
Cudd_RecursiveDerefZdd(dd, g0);
if (q == zero) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, zero);
Cudd_Deref(q);
return(zero);
}
if (g1 != zero) {
Cudd_RecursiveDerefZdd(dd, q);
tmp = cuddZddWeakDivF(dd, f1, g1);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
if (q == g)
q = tmp;
else {
q = cuddZddIntersect(dd, q, tmp);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
}
else {
Cudd_RecursiveDerefZdd(dd, f1);
Cudd_RecursiveDerefZdd(dd, g1);
}
if (q == zero) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, zero);
Cudd_Deref(q);
return(zero);
}
if (gd != zero) {
Cudd_RecursiveDerefZdd(dd, q);
tmp = cuddZddWeakDivF(dd, fd, gd);
if (tmp == NULL) {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
return(NULL);
}
Cudd_Ref(tmp);
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
if (q == g)
q = tmp;
else {
q = cuddZddIntersect(dd, q, tmp);
if (q == NULL) {
Cudd_RecursiveDerefZdd(dd, tmp);
return(NULL);
}
Cudd_Ref(q);
Cudd_RecursiveDerefZdd(dd, tmp);
}
}
else {
Cudd_RecursiveDerefZdd(dd, fd);
Cudd_RecursiveDerefZdd(dd, gd);
}
cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, q);
Cudd_Deref(q);
return(q);
} /* end of cuddZddWeakDivF */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddIte.]
Description []
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddZddIte(
DdManager * dd,
DdNode * f,
DdNode * g,
DdNode * h)
{
DdNode *tautology, *empty;
DdNode *r,*Gv,*Gvn,*Hv,*Hvn,*t,*e;
unsigned int topf,topg,toph,v,top;
int index;
statLine(dd);
/* Trivial cases. */
/* One variable cases. */
if (f == (empty = DD_ZERO(dd))) { /* ITE(0,G,H) = H */
return(h);
}
topf = cuddIZ(dd,f->index);
topg = cuddIZ(dd,g->index);
toph = cuddIZ(dd,h->index);
v = ddMin(topg,toph);
top = ddMin(topf,v);
tautology = (top == CUDD_MAXINDEX) ? DD_ONE(dd) : dd->univ[top];
if (f == tautology) { /* ITE(1,G,H) = G */
return(g);
}
/* From now on, f is known to not be a constant. */
zddVarToConst(f,&g,&h,tautology,empty);
/* Check remaining one variable cases. */
if (g == h) { /* ITE(F,G,G) = G */
return(g);
}
if (g == tautology) { /* ITE(F,1,0) = F */
if (h == empty) return(f);
}
/* Check cache. */
r = cuddCacheLookupZdd(dd,DD_ZDD_ITE_TAG,f,g,h);
if (r != NULL) {
return(r);
}
/* Recompute these because they may have changed in zddVarToConst. */
topg = cuddIZ(dd,g->index);
toph = cuddIZ(dd,h->index);
v = ddMin(topg,toph);
if (topf < v) {
r = cuddZddIte(dd,cuddE(f),g,h);
if (r == NULL) return(NULL);
} else if (topf > v) {
if (topg > v) {
Gvn = g;
index = h->index;
} else {
Gvn = cuddE(g);
index = g->index;
}
if (toph > v) {
Hv = empty; Hvn = h;
} else {
Hv = cuddT(h); Hvn = cuddE(h);
}
e = cuddZddIte(dd,f,Gvn,Hvn);
if (e == NULL) return(NULL);
cuddRef(e);
r = cuddZddGetNode(dd,index,Hv,e);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd,e);
return(NULL);
}
cuddDeref(e);
} else {
index = f->index;
if (topg > v) {
Gv = empty; Gvn = g;
} else {
Gv = cuddT(g); Gvn = cuddE(g);
}
if (toph > v) {
Hv = empty; Hvn = h;
} else {
Hv = cuddT(h); Hvn = cuddE(h);
}
e = cuddZddIte(dd,cuddE(f),Gvn,Hvn);
if (e == NULL) return(NULL);
cuddRef(e);
t = cuddZddIte(dd,cuddT(f),Gv,Hv);
if (t == NULL) {
Cudd_RecursiveDerefZdd(dd,e);
return(NULL);
}
cuddRef(t);
r = cuddZddGetNode(dd,index,t,e);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd,e);
Cudd_RecursiveDerefZdd(dd,t);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
}
cuddCacheInsert(dd,DD_ZDD_ITE_TAG,f,g,h,r);
return(r);
} /* end of cuddZddIte */
/**Function********************************************************************
Synopsis [Implementation of the linear sifting algorithm for ZDDs.]
Description [Implementation of the linear sifting algorithm for ZDDs.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries
in each unique table.
<li> Sift the variable up and down and applies the XOR transformation,
remembering each time the total size of the DD heap.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
</ol>
Returns 1 if successful; 0 otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
int
cuddZddLinearSifting(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int size;
int x;
int result;
#ifdef DD_STATS
int previousSize;
#endif
size = table->sizeZ;
empty = table->zero;
/* Find order in which to sift variables. */
var = NULL;
zdd_entry = ALLOC(int, size);
if (zdd_entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSiftingOutOfMem;
}
var = ALLOC(int, size);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSiftingOutOfMem;
}
for (i = 0; i < size; i++) {
x = table->permZ[i];
zdd_entry[i] = table->subtableZ[x].keys;
var[i] = i;
}
qsort((void *)var, size, sizeof(int), (DD_QSFP)cuddZddUniqueCompare);
/* Now sift. */
for (i = 0; i < ddMin(table->siftMaxVar, size); i++) {
if (table->zddTotalNumberSwapping >= table->siftMaxSwap)
break;
if (util_cpu_time() - table->startTime > table->timeLimit) {
table->autoDynZ = 0; /* prevent further reordering */
break;
}
x = table->permZ[var[i]];
if (x < lower || x > upper) continue;
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
result = cuddZddLinearAux(table, x, lower, upper);
if (!result)
goto cuddZddSiftingOutOfMem;
#ifdef DD_STATS
if (table->keysZ < (unsigned) previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > (unsigned) previousSize) {
(void) fprintf(table->out,"+"); /* should never happen */
(void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ , var[i]);
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
FREE(var);
FREE(zdd_entry);
return(1);
cuddZddSiftingOutOfMem:
if (zdd_entry != NULL) FREE(zdd_entry);
if (var != NULL) FREE(var);
return(0);
} /* end of cuddZddLinearSifting */
/**
@brief Implementation of Rudell's sifting algorithm.
@details Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries
in each unique table.
<li> Sift the variable up and down, remembering each time the
total size of the %DD heap.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
</ol>
@return 1 if successful; 0 otherwise.
@sideeffect None
*/
int
cuddZddSifting(
DdManager * table,
int lower,
int upper)
{
int i;
IndexKey *var;
int size;
int x;
int result;
#ifdef DD_STATS
int previousSize;
#endif
size = table->sizeZ;
/* Find order in which to sift variables. */
var = ALLOC(IndexKey, size);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSiftingOutOfMem;
}
for (i = 0; i < size; i++) {
x = table->permZ[i];
var[i].index = i;
var[i].keys = table->subtableZ[x].keys;
}
util_qsort(var, size, sizeof(IndexKey), cuddZddUniqueCompare);
/* Now sift. */
for (i = 0; i < ddMin(table->siftMaxVar, size); i++) {
if (table->zddTotalNumberSwapping >= table->siftMaxSwap)
break;
if (util_cpu_time() - table->startTime > table->timeLimit) {
table->autoDynZ = 0; /* prevent further reordering */
break;
}
if (table->terminationCallback != NULL &&
table->terminationCallback(table->tcbArg)) {
table->autoDynZ = 0; /* prevent further reordering */
break;
}
x = table->permZ[var[i].index];
if (x < lower || x > upper) continue;
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
result = cuddZddSiftingAux(table, x, lower, upper);
if (!result)
goto cuddZddSiftingOutOfMem;
#ifdef DD_STATS
if (table->keysZ < (unsigned) previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > (unsigned) previousSize) {
(void) fprintf(table->out,"+"); /* should never happen */
(void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ , var[i].index);
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
FREE(var);
return(1);
cuddZddSiftingOutOfMem:
if (var != NULL) FREE(var);
return(0);
} /* end of cuddZddSifting */
/**Function********************************************************************
Synopsis [Symmetric sifting algorithm.]
Description [Symmetric sifting algorithm.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries in
each unique subtable.
<li> Sift the variable up and down, remembering each time the total
size of the DD heap and grouping variables that are symmetric.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
</ol>
Returns 1 plus the number of symmetric variables if successful; 0
otherwise.]
SideEffects [None]
SeeAlso [cuddSymmSiftingConv]
******************************************************************************/
int
cuddSymmSifting(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int size;
int x;
int result;
int symvars;
int symgroups;
#ifdef DD_STATS
int previousSize;
#endif
size = table->size;
/* Find order in which to sift variables. */
var = NULL;
entry = ALLOC(int,size);
if (entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingOutOfMem;
}
var = ALLOC(int,size);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingOutOfMem;
}
for (i = 0; i < size; i++) {
x = table->perm[i];
entry[i] = table->subtables[x].keys;
var[i] = i;
}
qsort((void *)var,size,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);
/* Initialize the symmetry of each subtable to itself. */
for (i = lower; i <= upper; i++) {
table->subtables[i].next = i;
}
for (i = 0; i < ddMin(table->siftMaxVar,size); i++) {
if (ddTotalNumberSwapping >= table->siftMaxSwap)
break;
if (util_cpu_time() - table->startTime > table->timeLimit) {
table->autoDyn = 0; /* prevent further reordering */
break;
}
x = table->perm[var[i]];
#ifdef DD_STATS
previousSize = table->keys - table->isolated;
#endif
if (x < lower || x > upper) continue;
if (table->subtables[x].next == (unsigned) x) {
result = ddSymmSiftingAux(table,x,lower,upper);
if (!result) goto ddSymmSiftingOutOfMem;
#ifdef DD_STATS
if (table->keys < (unsigned) previousSize + table->isolated) {
(void) fprintf(table->out,"-");
} else if (table->keys > (unsigned) previousSize +
table->isolated) {
(void) fprintf(table->out,"+"); /* should never happen */
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
}
FREE(var);
FREE(entry);
ddSymmSummary(table, lower, upper, &symvars, &symgroups);
#ifdef DD_STATS
(void) fprintf(table->out, "\n#:S_SIFTING %8d: symmetric variables\n",
symvars);
(void) fprintf(table->out, "#:G_SIFTING %8d: symmetric groups",
symgroups);
#endif
return(1+symvars);
ddSymmSiftingOutOfMem:
if (entry != NULL) FREE(entry);
if (var != NULL) FREE(var);
return(0);
} /* end of cuddSymmSifting */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_zddIsop.]
Description []
SideEffects [None]
SeeAlso [Cudd_zddIsop]
******************************************************************************/
DdNode *
cuddZddIsop(
DdManager * dd,
DdNode * L,
DdNode * U,
DdNode ** zdd_I)
{
DdNode *one = DD_ONE(dd);
DdNode *zero = Cudd_Not(one);
DdNode *zdd_one = DD_ONE(dd);
DdNode *zdd_zero = DD_ZERO(dd);
int v, top_l, top_u;
DdNode *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
DdNode *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
DdNode *Isub0, *Isub1, *Id;
DdNode *zdd_Isub0, *zdd_Isub1, *zdd_Id;
DdNode *x;
DdNode *term0, *term1, *sum;
DdNode *Lv, *Uv, *Lnv, *Unv;
DdNode *r, *y, *z;
int index;
DdNode *(*cacheOp)(DdManager *, DdNode *, DdNode *);
statLine(dd);
if (L == zero) {
*zdd_I = zdd_zero;
return(zero);
}
if (U == one) {
*zdd_I = zdd_one;
return(one);
}
if (U == zero || L == one) {
printf("*** ERROR : illegal condition for ISOP (U < L).\n");
exit(1);
}
/* Check the cache. We store two results for each recursive call.
** One is the BDD, and the other is the ZDD. Both are needed.
** Hence we need a double hit in the cache to terminate the
** recursion. Clearly, collisions may evict only one of the two
** results. */
cacheOp = (DdNode *(*)(DdManager *, DdNode *, DdNode *)) cuddZddIsop;
r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
if (r) {
*zdd_I = cuddCacheLookup2Zdd(dd, cacheOp, L, U);
if (*zdd_I)
return(r);
else {
/* The BDD result may have been dead. In that case
** cuddCacheLookup2 would have called cuddReclaim,
** whose effects we now have to undo. */
cuddRef(r);
Cudd_RecursiveDeref(dd, r);
}
}
top_l = dd->perm[Cudd_Regular(L)->index];
top_u = dd->perm[Cudd_Regular(U)->index];
v = ddMin(top_l, top_u);
/* Compute cofactors. */
if (top_l == v) {
index = Cudd_Regular(L)->index;
Lv = Cudd_T(L);
Lnv = Cudd_E(L);
if (Cudd_IsComplement(L)) {
Lv = Cudd_Not(Lv);
Lnv = Cudd_Not(Lnv);
}
}
else {
index = Cudd_Regular(U)->index;
Lv = Lnv = L;
}
if (top_u == v) {
Uv = Cudd_T(U);
Unv = Cudd_E(U);
if (Cudd_IsComplement(U)) {
Uv = Cudd_Not(Uv);
Unv = Cudd_Not(Unv);
}
}
else {
Uv = Unv = U;
}
Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
if (Lsub0 == NULL)
return(NULL);
Cudd_Ref(Lsub0);
Usub0 = Unv;
Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
if (Lsub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
return(NULL);
}
Cudd_Ref(Lsub1);
Usub1 = Uv;
Isub0 = cuddZddIsop(dd, Lsub0, Usub0, &zdd_Isub0);
if (Isub0 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
return(NULL);
}
/*
if ((!cuddIsConstant(Cudd_Regular(Isub0))) &&
(Cudd_Regular(Isub0)->index != zdd_Isub0->index / 2 ||
dd->permZ[index * 2] > dd->permZ[zdd_Isub0->index])) {
printf("*** ERROR : illegal permutation in ZDD. ***\n");
}
*/
Cudd_Ref(Isub0);
Cudd_Ref(zdd_Isub0);
Isub1 = cuddZddIsop(dd, Lsub1, Usub1, &zdd_Isub1);
if (Isub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
return(NULL);
}
/*
if ((!cuddIsConstant(Cudd_Regular(Isub1))) &&
(Cudd_Regular(Isub1)->index != zdd_Isub1->index / 2 ||
dd->permZ[index * 2] > dd->permZ[zdd_Isub1->index])) {
printf("*** ERROR : illegal permutation in ZDD. ***\n");
}
*/
Cudd_Ref(Isub1);
Cudd_Ref(zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
if (Lsuper0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
return(NULL);
}
Cudd_Ref(Lsuper0);
Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
if (Lsuper1 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
return(NULL);
}
Cudd_Ref(Lsuper1);
Usuper0 = Unv;
Usuper1 = Uv;
/* Ld = Lsuper0 + Lsuper1 */
Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
if (Ld == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
return(NULL);
}
Ld = Cudd_Not(Ld);
Cudd_Ref(Ld);
/* Ud = Usuper0 * Usuper1 */
Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
if (Ud == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Cudd_RecursiveDeref(dd, Ld);
return(NULL);
}
Cudd_Ref(Ud);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Id = cuddZddIsop(dd, Ld, Ud, &zdd_Id);
if (Id == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
return(NULL);
}
/*
if ((!cuddIsConstant(Cudd_Regular(Id))) &&
(Cudd_Regular(Id)->index != zdd_Id->index / 2 ||
dd->permZ[index * 2] > dd->permZ[zdd_Id->index])) {
printf("*** ERROR : illegal permutation in ZDD. ***\n");
}
*/
Cudd_Ref(Id);
Cudd_Ref(zdd_Id);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
x = cuddUniqueInter(dd, index, one, zero);
if (x == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
return(NULL);
}
Cudd_Ref(x);
/* term0 = x * Isub0 */
term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
if (term0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, x);
return(NULL);
}
Cudd_Ref(term0);
Cudd_RecursiveDeref(dd, Isub0);
/* term1 = x * Isub1 */
term1 = cuddBddAndRecur(dd, x, Isub1);
if (term1 == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, term0);
return(NULL);
}
Cudd_Ref(term1);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, Isub1);
/* sum = term0 + term1 */
sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
if (sum == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
return(NULL);
}
sum = Cudd_Not(sum);
Cudd_Ref(sum);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
/* r = sum + Id */
r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
r = Cudd_NotCond(r, r != NULL);
if (r == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, sum);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDeref(dd, sum);
Cudd_RecursiveDeref(dd, Id);
if (zdd_Isub0 != zdd_zero) {
z = cuddZddGetNodeIVO(dd, index * 2 + 1, zdd_Isub0, zdd_Id);
if (z == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, r);
return(NULL);
}
}
else {
z = zdd_Id;
}
Cudd_Ref(z);
if (zdd_Isub1 != zdd_zero) {
y = cuddZddGetNodeIVO(dd, index * 2, zdd_Isub1, z);
if (y == NULL) {
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDeref(dd, r);
Cudd_RecursiveDerefZdd(dd, z);
return(NULL);
}
}
else
y = z;
Cudd_Ref(y);
Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
Cudd_RecursiveDerefZdd(dd, zdd_Id);
Cudd_RecursiveDerefZdd(dd, z);
cuddCacheInsert2(dd, cuddBddIsop, L, U, r);
cuddCacheInsert2(dd, cacheOp, L, U, y);
Cudd_Deref(r);
Cudd_Deref(y);
*zdd_I = y;
/*
if (Cudd_Regular(r)->index != y->index / 2) {
printf("*** ERROR : mismatch in indices between BDD and ZDD. ***\n");
}
*/
return(r);
} /* end of cuddZddIsop */
/**Function********************************************************************
Synopsis [Sifts from treenode->low to treenode->high.]
Description [Sifts from treenode->low to treenode->high. If
croupcheck == CUDD_GROUP_CHECK7, it checks for group creation at the
end of the initial sifting. If a group is created, it is then sifted
again. After sifting one variable, the group that contains it is
dissolved. Returns 1 in case of success; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
zddGroupSifting(
DdManager * table,
int lower,
int upper)
{
int *var;
int i,j,x,xInit;
int nvars;
int classes;
int result;
int *sifted;
#ifdef DD_STATS
unsigned previousSize;
#endif
int xindex;
nvars = table->sizeZ;
/* Order variables to sift. */
entry = NULL;
sifted = NULL;
var = ALLOC(int,nvars);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto zddGroupSiftingOutOfMem;
}
entry = ALLOC(int,nvars);
if (entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto zddGroupSiftingOutOfMem;
}
sifted = ALLOC(int,nvars);
if (sifted == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto zddGroupSiftingOutOfMem;
}
/* Here we consider only one representative for each group. */
for (i = 0, classes = 0; i < nvars; i++) {
sifted[i] = 0;
x = table->permZ[i];
if ((unsigned) x >= table->subtableZ[x].next) {
entry[i] = table->subtableZ[x].keys;
var[classes] = i;
classes++;
}
}
qsort((void *)var,classes,sizeof(int),(int (*)(const void *, const void *))zddUniqueCompareGroup);
/* Now sift. */
for (i = 0; i < ddMin(table->siftMaxVar,classes); i++) {
if (zddTotalNumberSwapping >= table->siftMaxSwap)
break;
xindex = var[i];
if (sifted[xindex] == 1) /* variable already sifted as part of group */
continue;
x = table->permZ[xindex]; /* find current level of this variable */
if (x < lower || x > upper)
continue;
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
#ifdef DD_DEBUG
/* x is bottom of group */
assert((unsigned) x >= table->subtableZ[x].next);
#endif
result = zddGroupSiftingAux(table,x,lower,upper);
if (!result) goto zddGroupSiftingOutOfMem;
#ifdef DD_STATS
if (table->keysZ < previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > previousSize) {
(void) fprintf(table->out,"+");
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
/* Mark variables in the group just sifted. */
x = table->permZ[xindex];
if ((unsigned) x != table->subtableZ[x].next) {
xInit = x;
do {
j = table->invpermZ[x];
sifted[j] = 1;
x = table->subtableZ[x].next;
} while (x != xInit);
}
#ifdef DD_DEBUG
if (pr > 0) (void) fprintf(table->out,"zddGroupSifting:");
#endif
} /* for */
FREE(sifted);
FREE(var);
FREE(entry);
return(1);
zddGroupSiftingOutOfMem:
if (entry != NULL) FREE(entry);
if (var != NULL) FREE(var);
if (sifted != NULL) FREE(sifted);
return(0);
} /* end of zddGroupSifting */
/**Function********************************************************************
Synopsis [Symmetric sifting algorithm for ZDDs.]
Description [Symmetric sifting algorithm.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries in
each unique subtable.
<li> Sift the variable up and down, remembering each time the total
size of the ZDD heap and grouping variables that are symmetric.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
</ol>
Returns 1 plus the number of symmetric variables if successful; 0
otherwise.]
SideEffects [None]
SeeAlso [cuddZddSymmSiftingConv]
******************************************************************************/
int
cuddZddSymmSifting(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int nvars;
int x;
int result;
int symvars;
int symgroups;
int iteration;
#ifdef DD_STATS
int previousSize;
#endif
nvars = table->sizeZ;
/* Find order in which to sift variables. */
var = NULL;
zdd_entry = ALLOC(int, nvars);
if (zdd_entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSymmSiftingOutOfMem;
}
var = ALLOC(int, nvars);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSymmSiftingOutOfMem;
}
for (i = 0; i < nvars; i++) {
x = table->permZ[i];
zdd_entry[i] = table->subtableZ[x].keys;
var[i] = i;
}
qsort((void *)var, nvars, sizeof(int), (DD_QSFP)cuddZddUniqueCompare);
/* Initialize the symmetry of each subtable to itself. */
for (i = lower; i <= upper; i++)
table->subtableZ[i].next = i;
iteration = ddMin(table->siftMaxVar, nvars);
for (i = 0; i < iteration; i++) {
if (zddTotalNumberSwapping >= table->siftMaxSwap)
break;
x = table->permZ[var[i]];
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
if (x < lower || x > upper) continue;
if (table->subtableZ[x].next == (unsigned) x) {
result = cuddZddSymmSiftingAux(table, x, lower, upper);
if (!result)
goto cuddZddSymmSiftingOutOfMem;
#ifdef DD_STATS
if (table->keysZ < (unsigned) previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > (unsigned) previousSize) {
(void) fprintf(table->out,"+");
#ifdef DD_VERBOSE
(void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ, var[i]);
#endif
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
}
FREE(var);
FREE(zdd_entry);
cuddZddSymmSummary(table, lower, upper, &symvars, &symgroups);
#ifdef DD_STATS
(void) fprintf(table->out,"\n#:S_SIFTING %8d: symmetric variables\n",symvars);
(void) fprintf(table->out,"#:G_SIFTING %8d: symmetric groups\n",symgroups);
#endif
return(1+symvars);
cuddZddSymmSiftingOutOfMem:
if (zdd_entry != NULL)
FREE(zdd_entry);
if (var != NULL)
FREE(var);
return(0);
} /* end of cuddZddSymmSifting */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addNonSimCompose.]
Description []
SideEffects [None]
SeeAlso []
******************************************************************************/
static DdNode *
cuddAddNonSimComposeRecur(
DdManager * dd,
DdNode * f,
DdNode ** vector,
DdNode * key,
DdNode * cube,
int lastsub)
{
DdNode *f1, *f0, *key1, *key0, *cube1, *var;
DdNode *T,*E;
DdNode *r;
unsigned int top, topf, topk, topc;
unsigned int index;
int i;
DdNode **vect1;
DdNode **vect0;
statLine(dd);
/* If we are past the deepest substitution, return f. */
if (cube == DD_ONE(dd) || cuddIsConstant(f)) {
return(f);
}
/* If problem already solved, look up answer and return. */
r = cuddCacheLookup(dd,DD_ADD_NON_SIM_COMPOSE_TAG,f,key,cube);
if (r != NULL) {
return(r);
}
/* Find top variable. we just need to look at f, key, and cube,
** because all the varibles in the gi are in key.
*/
topf = cuddI(dd,f->index);
topk = cuddI(dd,key->index);
top = ddMin(topf,topk);
topc = cuddI(dd,cube->index);
top = ddMin(top,topc);
index = dd->invperm[top];
/* Compute the cofactors. */
if (topf == top) {
f1 = cuddT(f);
f0 = cuddE(f);
} else {
f1 = f0 = f;
}
if (topc == top) {
cube1 = cuddT(cube);
/* We want to eliminate vector[index] from key. Otherwise
** cache performance is severely affected. Hence we
** existentially quantify the variable with index "index" from key.
*/
var = Cudd_addIthVar(dd, (int) index);
if (var == NULL) {
return(NULL);
}
cuddRef(var);
key1 = cuddAddExistAbstractRecur(dd, key, var);
if (key1 == NULL) {
Cudd_RecursiveDeref(dd,var);
return(NULL);
}
cuddRef(key1);
Cudd_RecursiveDeref(dd,var);
key0 = key1;
} else {
cube1 = cube;
if (topk == top) {
key1 = cuddT(key);
key0 = cuddE(key);
} else {
key1 = key0 = key;
}
cuddRef(key1);
}
/* Allocate two new vectors for the cofactors of vector. */
vect1 = ALLOC(DdNode *,lastsub);
if (vect1 == NULL) {
dd->errorCode = CUDD_MEMORY_OUT;
Cudd_RecursiveDeref(dd,key1);
return(NULL);
}
vect0 = ALLOC(DdNode *,lastsub);
if (vect0 == NULL) {
dd->errorCode = CUDD_MEMORY_OUT;
Cudd_RecursiveDeref(dd,key1);
FREE(vect1);
return(NULL);
}
/* Cofactor the gi. Eliminate vect1[index] and vect0[index], because
** we do not need them.
*/
for (i = 0; i < lastsub; i++) {
DdNode *gi = vector[i];
if (gi == NULL) {
vect1[i] = vect0[i] = NULL;
} else if (gi->index == index) {
vect1[i] = cuddT(gi);
vect0[i] = cuddE(gi);
} else {
vect1[i] = vect0[i] = gi;
}
}
vect1[index] = vect0[index] = NULL;
/* Recur on children. */
T = cuddAddNonSimComposeRecur(dd,f1,vect1,key1,cube1,lastsub);
FREE(vect1);
if (T == NULL) {
Cudd_RecursiveDeref(dd,key1);
FREE(vect0);
return(NULL);
}
cuddRef(T);
E = cuddAddNonSimComposeRecur(dd,f0,vect0,key0,cube1,lastsub);
FREE(vect0);
if (E == NULL) {
Cudd_RecursiveDeref(dd,key1);
Cudd_RecursiveDeref(dd,T);
return(NULL);
}
cuddRef(E);
Cudd_RecursiveDeref(dd,key1);
/* Retrieve the 0-1 ADD for the current top variable from vector,
** and call cuddAddIteRecur with the T and E we just created.
*/
r = cuddAddIteRecur(dd,vector[index],T,E);
if (r == NULL) {
Cudd_RecursiveDeref(dd,T);
Cudd_RecursiveDeref(dd,E);
return(NULL);
}
cuddRef(r);
Cudd_RecursiveDeref(dd,T);
Cudd_RecursiveDeref(dd,E);
cuddDeref(r);
/* Store answer to trim recursion. */
cuddCacheInsert(dd,DD_ADD_NON_SIM_COMPOSE_TAG,f,key,cube,r);
return(r);
} /* end of cuddAddNonSimComposeRecur */
/**Function********************************************************************
Synopsis [Takes the exclusive OR of two BDDs and simultaneously abstracts the
variables in cube.]
Description [Takes the exclusive OR of two BDDs and simultaneously abstracts
the variables in cube. The variables are existentially abstracted. Returns a
pointer to the result is successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddAndAbstract]
******************************************************************************/
DdNode *
cuddBddXorExistAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * g,
DdNode * cube)
{
DdNode *F, *fv, *fnv, *G, *gv, *gnv;
DdNode *one, *zero, *r, *t, *e, *Cube;
unsigned int topf, topg, topcube, top, index;
statLine(manager);
one = DD_ONE(manager);
zero = Cudd_Not(one);
/* Terminal cases. */
if (f == g) {
return(zero);
}
if (f == Cudd_Not(g)) {
return(one);
}
if (cube == one) {
return(cuddBddXorRecur(manager, f, g));
}
if (f == one) {
return(cuddBddExistAbstractRecur(manager, Cudd_Not(g), cube));
}
if (g == one) {
return(cuddBddExistAbstractRecur(manager, Cudd_Not(f), cube));
}
if (f == zero) {
return(cuddBddExistAbstractRecur(manager, g, cube));
}
if (g == zero) {
return(cuddBddExistAbstractRecur(manager, f, cube));
}
/* At this point f, g, and cube are not constant. */
if (f > g) { /* Try to increase cache efficiency. */
DdNode *tmp = f;
f = g;
g = tmp;
}
/* Check cache. */
r = cuddCacheLookup(manager, DD_BDD_XOR_EXIST_ABSTRACT_TAG, f, g, cube);
if (r != NULL) {
return(r);
}
/* Here we can skip the use of cuddI, because the operands are known
** to be non-constant.
*/
F = Cudd_Regular(f);
topf = manager->perm[F->index];
G = Cudd_Regular(g);
topg = manager->perm[G->index];
top = ddMin(topf, topg);
topcube = manager->perm[cube->index];
if (topcube < top) {
return(cuddBddXorExistAbstractRecur(manager, f, g, cuddT(cube)));
}
/* Now, topcube >= top. */
if (topf == top) {
index = F->index;
fv = cuddT(F);
fnv = cuddE(F);
if (Cudd_IsComplement(f)) {
fv = Cudd_Not(fv);
fnv = Cudd_Not(fnv);
}
} else {
index = G->index;
fv = fnv = f;
}
if (topg == top) {
gv = cuddT(G);
gnv = cuddE(G);
if (Cudd_IsComplement(g)) {
gv = Cudd_Not(gv);
gnv = Cudd_Not(gnv);
}
} else {
gv = gnv = g;
}
if (topcube == top) {
Cube = cuddT(cube);
} else {
Cube = cube;
}
t = cuddBddXorExistAbstractRecur(manager, fv, gv, Cube);
if (t == NULL) return(NULL);
/* Special case: 1 OR anything = 1. Hence, no need to compute
** the else branch if t is 1.
*/
if (t == one && topcube == top) {
cuddCacheInsert(manager, DD_BDD_XOR_EXIST_ABSTRACT_TAG, f, g, cube, one);
return(one);
}
cuddRef(t);
e = cuddBddXorExistAbstractRecur(manager, fnv, gnv, Cube);
if (e == NULL) {
Cudd_IterDerefBdd(manager, t);
return(NULL);
}
cuddRef(e);
if (topcube == top) { /* abstract */
r = cuddBddAndRecur(manager, Cudd_Not(t), Cudd_Not(e));
if (r == NULL) {
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
return(NULL);
}
r = Cudd_Not(r);
cuddRef(r);
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
cuddDeref(r);
} else if (t == e) {
r = t;
cuddDeref(t);
cuddDeref(e);
} else {
if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(manager,(int)index,Cudd_Not(t),Cudd_Not(e));
if (r == NULL) {
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
return(NULL);
}
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(manager,(int)index,t,e);
if (r == NULL) {
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
return(NULL);
}
}
cuddDeref(e);
cuddDeref(t);
}
cuddCacheInsert(manager, DD_BDD_XOR_EXIST_ABSTRACT_TAG, f, g, cube, r);
return (r);
} /* end of cuddBddXorExistAbstractRecur */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_addIte(f,g,h).]
Description [Implements the recursive step of Cudd_addIte(f,g,h).
Returns a pointer to the resulting ADD if successful; NULL
otherwise.]
SideEffects [None]
SeeAlso [Cudd_addIte]
******************************************************************************/
DdNode *
cuddAddIteRecur(
DdManager * dd,
DdNode * f,
DdNode * g,
DdNode * h)
{
DdNode *one,*zero;
DdNode *r,*Fv,*Fnv,*Gv,*Gnv,*Hv,*Hnv,*t,*e;
unsigned int topf,topg,toph,v;
int index;
statLine(dd);
/* Trivial cases. */
/* One variable cases. */
if (f == (one = DD_ONE(dd))) { /* ITE(1,G,H) = G */
return(g);
}
if (f == (zero = DD_ZERO(dd))) { /* ITE(0,G,H) = H */
return(h);
}
/* From now on, f is known to not be a constant. */
addVarToConst(f,&g,&h,one,zero);
/* Check remaining one variable cases. */
if (g == h) { /* ITE(F,G,G) = G */
return(g);
}
if (g == one) { /* ITE(F,1,0) = F */
if (h == zero) return(f);
}
topf = cuddI(dd,f->index);
topg = cuddI(dd,g->index);
toph = cuddI(dd,h->index);
v = ddMin(topg,toph);
/* A shortcut: ITE(F,G,H) = (x,G,H) if F=(x,1,0), x < top(G,H). */
if (topf < v && cuddT(f) == one && cuddE(f) == zero) {
r = cuddUniqueInter(dd,(int)f->index,g,h);
return(r);
}
if (topf < v && cuddT(f) == zero && cuddE(f) == one) {
r = cuddUniqueInter(dd,(int)f->index,h,g);
return(r);
}
/* Check cache. */
r = cuddCacheLookup(dd,DD_ADD_ITE_TAG,f,g,h);
if (r != NULL) {
return(r);
}
/* Compute cofactors. */
if (topf <= v) {
v = ddMin(topf,v); /* v = top_var(F,G,H) */
index = f->index;
Fv = cuddT(f); Fnv = cuddE(f);
} else {
Fv = Fnv = f;
}
if (topg == v) {
index = g->index;
Gv = cuddT(g); Gnv = cuddE(g);
} else {
Gv = Gnv = g;
}
if (toph == v) {
index = h->index;
Hv = cuddT(h); Hnv = cuddE(h);
} else {
Hv = Hnv = h;
}
/* Recursive step. */
t = cuddAddIteRecur(dd,Fv,Gv,Hv);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddAddIteRecur(dd,Fnv,Gnv,Hnv);
if (e == NULL) {
Cudd_RecursiveDeref(dd,t);
return(NULL);
}
cuddRef(e);
r = (t == e) ? t : cuddUniqueInter(dd,index,t,e);
if (r == NULL) {
Cudd_RecursiveDeref(dd,t);
Cudd_RecursiveDeref(dd,e);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
cuddCacheInsert(dd,DD_ADD_ITE_TAG,f,g,h,r);
return(r);
} /* end of cuddAddIteRecur */
/**Function********************************************************************
Synopsis [Implements ITEconstant for ADDs.]
Description [Implements ITEconstant for ADDs. f must be a 0-1 ADD.
Returns a pointer to the resulting ADD (which may or may not be
constant) or DD_NON_CONSTANT. No new nodes are created. This function
can be used, for instance, to check that g has a constant value
(specified by h) whenever f is 1. If the constant value is unknown,
then one should use Cudd_addEvalConst.]
SideEffects [None]
SeeAlso [Cudd_addIte Cudd_addEvalConst Cudd_bddIteConstant]
******************************************************************************/
DdNode *
Cudd_addIteConstant(
DdManager * dd,
DdNode * f,
DdNode * g,
DdNode * h)
{
DdNode *one,*zero;
DdNode *Fv,*Fnv,*Gv,*Gnv,*Hv,*Hnv,*r,*t,*e;
unsigned int topf,topg,toph,v;
statLine(dd);
/* Trivial cases. */
if (f == (one = DD_ONE(dd))) { /* ITE(1,G,H) = G */
return(g);
}
if (f == (zero = DD_ZERO(dd))) { /* ITE(0,G,H) = H */
return(h);
}
/* From now on, f is known not to be a constant. */
addVarToConst(f,&g,&h,one,zero);
/* Check remaining one variable cases. */
if (g == h) { /* ITE(F,G,G) = G */
return(g);
}
if (cuddIsConstant(g) && cuddIsConstant(h)) {
return(DD_NON_CONSTANT);
}
topf = cuddI(dd,f->index);
topg = cuddI(dd,g->index);
toph = cuddI(dd,h->index);
v = ddMin(topg,toph);
/* ITE(F,G,H) = (x,G,H) (non constant) if F = (x,1,0), x < top(G,H). */
if (topf < v && cuddIsConstant(cuddT(f)) && cuddIsConstant(cuddE(f))) {
return(DD_NON_CONSTANT);
}
/* Check cache. */
r = cuddConstantLookup(dd,DD_ADD_ITE_CONSTANT_TAG,f,g,h);
if (r != NULL) {
return(r);
}
/* Compute cofactors. */
if (topf <= v) {
v = ddMin(topf,v); /* v = top_var(F,G,H) */
Fv = cuddT(f); Fnv = cuddE(f);
} else {
Fv = Fnv = f;
}
if (topg == v) {
Gv = cuddT(g); Gnv = cuddE(g);
} else {
Gv = Gnv = g;
}
if (toph == v) {
Hv = cuddT(h); Hnv = cuddE(h);
} else {
Hv = Hnv = h;
}
/* Recursive step. */
t = Cudd_addIteConstant(dd,Fv,Gv,Hv);
if (t == DD_NON_CONSTANT || !cuddIsConstant(t)) {
cuddCacheInsert(dd, DD_ADD_ITE_CONSTANT_TAG, f, g, h, DD_NON_CONSTANT);
return(DD_NON_CONSTANT);
}
e = Cudd_addIteConstant(dd,Fnv,Gnv,Hnv);
if (e == DD_NON_CONSTANT || !cuddIsConstant(e) || t != e) {
cuddCacheInsert(dd, DD_ADD_ITE_CONSTANT_TAG, f, g, h, DD_NON_CONSTANT);
return(DD_NON_CONSTANT);
}
cuddCacheInsert(dd, DD_ADD_ITE_CONSTANT_TAG, f, g, h, t);
return(t);
} /* end of Cudd_addIteConstant */
/**
@brief Sifts from treenode->low to treenode->high.
@details If croupcheck == CUDD_GROUP_CHECK7, it checks for group
creation at the end of the initial sifting. If a group is created,
it is then sifted again. After sifting one variable, the group that
contains it is dissolved.
@return 1 in case of success; 0 otherwise.
@sideeffect None
*/
static int
zddGroupSifting(
DdManager * table,
int lower,
int upper)
{
IndexKey *var;
int i,j,x,xInit;
int nvars;
int classes;
int result;
int *sifted;
#ifdef DD_STATS
unsigned previousSize;
#endif
int xindex;
nvars = table->sizeZ;
/* Order variables to sift. */
sifted = NULL;
var = ALLOC(IndexKey,nvars);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto zddGroupSiftingOutOfMem;
}
sifted = ALLOC(int,nvars);
if (sifted == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto zddGroupSiftingOutOfMem;
}
/* Here we consider only one representative for each group. */
for (i = 0, classes = 0; i < nvars; i++) {
sifted[i] = 0;
x = table->permZ[i];
if ((unsigned) x >= table->subtableZ[x].next) {
var[classes].index = i;
var[classes].keys = table->subtableZ[x].keys;
classes++;
}
}
util_qsort(var,classes,sizeof(IndexKey),zddUniqueCompareGroup);
/* Now sift. */
for (i = 0; i < ddMin(table->siftMaxVar,classes); i++) {
if (table->zddTotalNumberSwapping >= table->siftMaxSwap)
break;
if (util_cpu_time() - table->startTime > table->timeLimit) {
table->autoDynZ = 0; /* prevent further reordering */
break;
}
if (table->terminationCallback != NULL &&
table->terminationCallback(table->tcbArg)) {
table->autoDynZ = 0; /* prevent further reordering */
break;
}
xindex = var[i].index;
if (sifted[xindex] == 1) /* variable already sifted as part of group */
continue;
x = table->permZ[xindex]; /* find current level of this variable */
if (x < lower || x > upper)
continue;
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
#ifdef DD_DEBUG
/* x is bottom of group */
assert((unsigned) x >= table->subtableZ[x].next);
#endif
result = zddGroupSiftingAux(table,x,lower,upper);
if (!result) goto zddGroupSiftingOutOfMem;
#ifdef DD_STATS
if (table->keysZ < previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > previousSize) {
(void) fprintf(table->out,"+");
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
/* Mark variables in the group just sifted. */
x = table->permZ[xindex];
if ((unsigned) x != table->subtableZ[x].next) {
xInit = x;
do {
j = table->invpermZ[x];
sifted[j] = 1;
x = table->subtableZ[x].next;
} while (x != xInit);
}
#ifdef DD_DEBUG
if (table->enableExtraDebug > 0)
(void) fprintf(table->out,"zddGroupSifting:");
#endif
} /* for */
FREE(sifted);
FREE(var);
return(1);
zddGroupSiftingOutOfMem:
if (var != NULL) FREE(var);
if (sifted != NULL) FREE(sifted);
return(0);
} /* end of zddGroupSifting */
/**Function********************************************************************
Synopsis [Takes the AND of two BDDs and simultaneously abstracts the
variables in cube.]
Description [Takes the AND of two BDDs and simultaneously abstracts
the variables in cube. The variables are existentially abstracted.
Returns a pointer to the result is successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddAndAbstract]
******************************************************************************/
DdNode *
cuddBddAndAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * g,
DdNode * cube)
{
DdNode *F, *ft, *fe, *G, *gt, *ge;
DdNode *one, *zero, *r, *t, *e;
unsigned int topf, topg, topcube, top, index;
statLine(manager);
one = DD_ONE(manager);
zero = Cudd_Not(one);
/* Terminal cases. */
if (f == zero || g == zero || f == Cudd_Not(g)) return(zero);
if (f == one && g == one) return(one);
if (cube == one) {
return(cuddBddAndRecur(manager, f, g));
}
if (f == one || f == g) {
return(cuddBddExistAbstractRecur(manager, g, cube));
}
if (g == one) {
return(cuddBddExistAbstractRecur(manager, f, cube));
}
/* At this point f, g, and cube are not constant. */
if (f > g) { /* Try to increase cache efficiency. */
DdNode *tmp = f;
f = g;
g = tmp;
}
/* Here we can skip the use of cuddI, because the operands are known
** to be non-constant.
*/
F = Cudd_Regular(f);
G = Cudd_Regular(g);
topf = manager->perm[F->index];
topg = manager->perm[G->index];
top = ddMin(topf, topg);
topcube = manager->perm[cube->index];
while (topcube < top) {
cube = cuddT(cube);
if (cube == one) {
return(cuddBddAndRecur(manager, f, g));
}
topcube = manager->perm[cube->index];
}
/* Now, topcube >= top. */
/* Check cache. */
if (F->ref != 1 || G->ref != 1) {
r = cuddCacheLookup(manager, DD_BDD_AND_ABSTRACT_TAG, f, g, cube);
if (r != NULL) {
return(r);
}
}
if (topf == top) {
index = F->index;
ft = cuddT(F);
fe = cuddE(F);
if (Cudd_IsComplement(f)) {
ft = Cudd_Not(ft);
fe = Cudd_Not(fe);
}
} else {
index = G->index;
ft = fe = f;
}
if (topg == top) {
gt = cuddT(G);
ge = cuddE(G);
if (Cudd_IsComplement(g)) {
gt = Cudd_Not(gt);
ge = Cudd_Not(ge);
}
} else {
gt = ge = g;
}
if (topcube == top) { /* quantify */
DdNode *Cube = cuddT(cube);
t = cuddBddAndAbstractRecur(manager, ft, gt, Cube);
if (t == NULL) return(NULL);
/* Special case: 1 OR anything = 1. Hence, no need to compute
** the else branch if t is 1. Likewise t + t * anything == t.
** Notice that t == fe implies that fe does not depend on the
** variables in Cube. Likewise for t == ge.
*/
if (t == one || t == fe || t == ge) {
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert(manager, DD_BDD_AND_ABSTRACT_TAG,
f, g, cube, t);
return(t);
}
cuddRef(t);
/* Special case: t + !t * anything == t + anything. */
if (t == Cudd_Not(fe)) {
e = cuddBddExistAbstractRecur(manager, ge, Cube);
} else if (t == Cudd_Not(ge)) {
e = cuddBddExistAbstractRecur(manager, fe, Cube);
} else {
e = cuddBddAndAbstractRecur(manager, fe, ge, Cube);
}
if (e == NULL) {
Cudd_IterDerefBdd(manager, t);
return(NULL);
}
if (t == e) {
r = t;
cuddDeref(t);
} else {
cuddRef(e);
r = cuddBddAndRecur(manager, Cudd_Not(t), Cudd_Not(e));
if (r == NULL) {
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
return(NULL);
}
r = Cudd_Not(r);
cuddRef(r);
Cudd_DelayedDerefBdd(manager, t);
Cudd_DelayedDerefBdd(manager, e);
cuddDeref(r);
}
} else {
t = cuddBddAndAbstractRecur(manager, ft, gt, cube);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddAndAbstractRecur(manager, fe, ge, cube);
if (e == NULL) {
Cudd_IterDerefBdd(manager, t);
return(NULL);
}
if (t == e) {
r = t;
cuddDeref(t);
} else {
cuddRef(e);
if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(manager, (int) index,
Cudd_Not(t), Cudd_Not(e));
if (r == NULL) {
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
return(NULL);
}
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(manager,(int)index,t,e);
if (r == NULL) {
Cudd_IterDerefBdd(manager, t);
Cudd_IterDerefBdd(manager, e);
return(NULL);
}
}
cuddDeref(e);
cuddDeref(t);
}
}
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert(manager, DD_BDD_AND_ABSTRACT_TAG, f, g, cube, r);
return (r);
} /* end of cuddBddAndAbstractRecur */
/**Function********************************************************************
Synopsis [Shrinks almost empty ZDD subtables at the end of reordering
to guarantee that they have a reasonable load factor.]
Description [Shrinks almost empty subtables at the end of reordering to
guarantee that they have a reasonable load factor. However, if there many
nodes are being reclaimed, then no resizing occurs. Returns 1 in case of
success; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
zddReorderPostprocess(
DdManager * table)
{
int i, j, posn;
DdNodePtr *nodelist, *oldnodelist;
DdNode *node, *next;
unsigned int slots, oldslots;
extern DD_OOMFP MMoutOfMemory;
DD_OOMFP saveHandler;
#ifdef DD_VERBOSE
(void) fflush(table->out);
#endif
/* If we have very many reclaimed nodes, we do not want to shrink
** the subtables, because this will lead to more garbage
** collections. More garbage collections mean shorter mean life for
** nodes with zero reference count; hence lower probability of finding
** a result in the cache.
*/
if (table->reclaimed > table->allocated * 0.5) return(1);
/* Resize subtables. */
for (i = 0; i < table->sizeZ; i++) {
int shift;
oldslots = table->subtableZ[i].slots;
if (oldslots < table->subtableZ[i].keys * DD_MAX_SUBTABLE_SPARSITY ||
oldslots <= table->initSlots) continue;
oldnodelist = table->subtableZ[i].nodelist;
slots = oldslots >> 1;
saveHandler = MMoutOfMemory;
MMoutOfMemory = Cudd_OutOfMem;
nodelist = ALLOC(DdNodePtr, slots);
MMoutOfMemory = saveHandler;
if (nodelist == NULL) {
return(1);
}
table->subtableZ[i].nodelist = nodelist;
table->subtableZ[i].slots = slots;
table->subtableZ[i].shift++;
table->subtableZ[i].maxKeys = slots * DD_MAX_SUBTABLE_DENSITY;
#ifdef DD_VERBOSE
(void) fprintf(table->err,
"shrunk layer %d (%d keys) from %d to %d slots\n",
i, table->subtableZ[i].keys, oldslots, slots);
#endif
for (j = 0; (unsigned) j < slots; j++) {
nodelist[j] = NULL;
}
shift = table->subtableZ[i].shift;
for (j = 0; (unsigned) j < oldslots; j++) {
node = oldnodelist[j];
while (node != NULL) {
next = node->next;
posn = ddHash(cuddT(node), cuddE(node), shift);
node->next = nodelist[posn];
nodelist[posn] = node;
node = next;
}
}
FREE(oldnodelist);
table->memused += (slots - oldslots) * sizeof(DdNode *);
table->slots += slots - oldslots;
table->minDead = (unsigned) (table->gcFrac * (double) table->slots);
table->cacheSlack = (int) ddMin(table->maxCacheHard,
DD_MAX_CACHE_TO_SLOTS_RATIO*table->slots) -
2 * (int) table->cacheSlots;
}
/* We don't look at the constant subtable, because it is not
** affected by reordering.
*/
return(1);
} /* end of zddReorderPostprocess */
/**Function********************************************************************
Synopsis [Approximates the AND of two BDDs and simultaneously abstracts the
variables in cube.]
Description [Approximates the AND of two BDDs and simultaneously
abstracts the variables in cube. The variables are existentially
abstracted. Returns a pointer to the result is successful; NULL
otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddClippingAndAbstract]
******************************************************************************/
static DdNode *
cuddBddClipAndAbsRecur(
DdManager * manager,
DdNode * f,
DdNode * g,
DdNode * cube,
int distance,
int direction)
{
DdNode *F, *ft, *fe, *G, *gt, *ge;
DdNode *one, *zero, *r, *t, *e, *Cube;
unsigned int topf, topg, topcube, top, index;
ptruint cacheTag;
statLine(manager);
one = DD_ONE(manager);
zero = Cudd_Not(one);
/* Terminal cases. */
if (f == zero || g == zero || f == Cudd_Not(g)) return(zero);
if (f == one && g == one) return(one);
if (cube == one) {
return(cuddBddClippingAndRecur(manager, f, g, distance, direction));
}
if (f == one || f == g) {
return (cuddBddExistAbstractRecur(manager, g, cube));
}
if (g == one) {
return (cuddBddExistAbstractRecur(manager, f, cube));
}
if (distance == 0) return(Cudd_NotCond(one,(direction == 0)));
/* At this point f, g, and cube are not constant. */
distance--;
/* Check cache. */
if (f > g) { /* Try to increase cache efficiency. */
DdNode *tmp = f;
f = g; g = tmp;
}
F = Cudd_Regular(f);
G = Cudd_Regular(g);
cacheTag = direction ? DD_BDD_CLIPPING_AND_ABSTRACT_UP_TAG :
DD_BDD_CLIPPING_AND_ABSTRACT_DOWN_TAG;
if (F->ref != 1 || G->ref != 1) {
r = cuddCacheLookup(manager, cacheTag,
f, g, cube);
if (r != NULL) {
return(r);
}
}
/* Here we can skip the use of cuddI, because the operands are known
** to be non-constant.
*/
topf = manager->perm[F->index];
topg = manager->perm[G->index];
top = ddMin(topf, topg);
topcube = manager->perm[cube->index];
if (topcube < top) {
return(cuddBddClipAndAbsRecur(manager, f, g, cuddT(cube),
distance, direction));
}
/* Now, topcube >= top. */
if (topf == top) {
index = F->index;
ft = cuddT(F);
fe = cuddE(F);
if (Cudd_IsComplement(f)) {
ft = Cudd_Not(ft);
fe = Cudd_Not(fe);
}
} else {
index = G->index;
ft = fe = f;
}
if (topg == top) {
gt = cuddT(G);
ge = cuddE(G);
if (Cudd_IsComplement(g)) {
gt = Cudd_Not(gt);
ge = Cudd_Not(ge);
}
} else {
gt = ge = g;
}
if (topcube == top) {
Cube = cuddT(cube);
} else {
Cube = cube;
}
t = cuddBddClipAndAbsRecur(manager, ft, gt, Cube, distance, direction);
if (t == NULL) return(NULL);
/* Special case: 1 OR anything = 1. Hence, no need to compute
** the else branch if t is 1.
*/
if (t == one && topcube == top) {
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert(manager, cacheTag, f, g, cube, one);
return(one);
}
cuddRef(t);
e = cuddBddClipAndAbsRecur(manager, fe, ge, Cube, distance, direction);
if (e == NULL) {
Cudd_RecursiveDeref(manager, t);
return(NULL);
}
cuddRef(e);
if (topcube == top) { /* abstract */
r = cuddBddClippingAndRecur(manager, Cudd_Not(t), Cudd_Not(e),
distance, (direction == 0));
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
r = Cudd_Not(r);
cuddRef(r);
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
cuddDeref(r);
} else if (t == e) {
r = t;
cuddDeref(t);
cuddDeref(e);
} else {
if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(manager,(int)index,Cudd_Not(t),Cudd_Not(e));
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(manager,(int)index,t,e);
if (r == NULL) {
Cudd_RecursiveDeref(manager, t);
Cudd_RecursiveDeref(manager, e);
return(NULL);
}
}
cuddDeref(e);
cuddDeref(t);
}
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert(manager, cacheTag, f, g, cube, r);
return (r);
} /* end of cuddBddClipAndAbsRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addMatrixMultiply.]
Description [Performs the recursive step of Cudd_addMatrixMultiply.
Returns a pointer to the result if successful; NULL otherwise.]
SideEffects [None]
******************************************************************************/
static DdNode *
addMMRecur(
DdManager * dd,
DdNode * A,
DdNode * B,
int topP,
int * vars)
{
DdNode *zero,
*At, /* positive cofactor of first operand */
*Ae, /* negative cofactor of first operand */
*Bt, /* positive cofactor of second operand */
*Be, /* negative cofactor of second operand */
*t, /* positive cofactor of result */
*e, /* negative cofactor of result */
*scaled, /* scaled result */
*add_scale, /* ADD representing the scaling factor */
*res;
int i; /* loop index */
double scale; /* scaling factor */
int index; /* index of the top variable */
CUDD_VALUE_TYPE value;
unsigned int topA, topB, topV;
DD_CTFP cacheOp;
statLine(dd);
zero = DD_ZERO(dd);
if (A == zero || B == zero) {
return(zero);
}
if (cuddIsConstant(A) && cuddIsConstant(B)) {
/* Compute the scaling factor. It is 2^k, where k is the
** number of summation variables below the current variable.
** Indeed, these constants represent blocks of 2^k identical
** constant values in both A and B.
*/
value = cuddV(A) * cuddV(B);
for (i = 0; i < dd->size; i++) {
if (vars[i]) {
if (dd->perm[i] > topP) {
value *= (CUDD_VALUE_TYPE) 2;
}
}
}
res = cuddUniqueConst(dd, value);
return(res);
}
/* Standardize to increase cache efficiency. Clearly, A*B != B*A
** in matrix multiplication. However, which matrix is which is
** determined by the variables appearing in the ADDs and not by
** which one is passed as first argument.
*/
if (A > B) {
DdNode *tmp = A;
A = B;
B = tmp;
}
topA = cuddI(dd,A->index); topB = cuddI(dd,B->index);
topV = ddMin(topA,topB);
cacheOp = (DD_CTFP) addMMRecur;
res = cuddCacheLookup2(dd,cacheOp,A,B);
if (res != NULL) {
/* If the result is 0, there is no need to normalize.
** Otherwise we count the number of z variables between
** the current depth and the top of the ADDs. These are
** the missing variables that determine the size of the
** constant blocks.
*/
if (res == zero) return(res);
scale = 1.0;
for (i = 0; i < dd->size; i++) {
if (vars[i]) {
if (dd->perm[i] > topP && (unsigned) dd->perm[i] < topV) {
scale *= 2;
}
}
}
if (scale > 1.0) {
cuddRef(res);
add_scale = cuddUniqueConst(dd,(CUDD_VALUE_TYPE)scale);
if (add_scale == NULL) {
Cudd_RecursiveDeref(dd, res);
return(NULL);
}
cuddRef(add_scale);
scaled = cuddAddApplyRecur(dd,Cudd_addTimes,res,add_scale);
if (scaled == NULL) {
Cudd_RecursiveDeref(dd, add_scale);
Cudd_RecursiveDeref(dd, res);
return(NULL);
}
cuddRef(scaled);
Cudd_RecursiveDeref(dd, add_scale);
Cudd_RecursiveDeref(dd, res);
res = scaled;
cuddDeref(res);
}
return(res);
}
/* compute the cofactors */
if (topV == topA) {
At = cuddT(A);
Ae = cuddE(A);
} else {
At = Ae = A;
}
if (topV == topB) {
Bt = cuddT(B);
Be = cuddE(B);
} else {
Bt = Be = B;
}
t = addMMRecur(dd, At, Bt, (int)topV, vars);
if (t == NULL) return(NULL);
cuddRef(t);
e = addMMRecur(dd, Ae, Be, (int)topV, vars);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddRef(e);
index = dd->invperm[topV];
if (vars[index] == 0) {
/* We have split on either the rows of A or the columns
** of B. We just need to connect the two subresults,
** which correspond to two submatrices of the result.
*/
res = (t == e) ? t : cuddUniqueInter(dd,index,t,e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
return(NULL);
}
cuddRef(res);
cuddDeref(t);
cuddDeref(e);
} else {
/* we have simultaneously split on the columns of A and
** the rows of B. The two subresults must be added.
*/
res = cuddAddApplyRecur(dd,Cudd_addPlus,t,e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
}
cuddCacheInsert2(dd,cacheOp,A,B,res);
/* We have computed (and stored in the computed table) a minimal
** result; that is, a result that assumes no summation variables
** between the current depth of the recursion and its top
** variable. We now take into account the z variables by properly
** scaling the result.
*/
if (res != zero) {
scale = 1.0;
for (i = 0; i < dd->size; i++) {
if (vars[i]) {
if (dd->perm[i] > topP && (unsigned) dd->perm[i] < topV) {
scale *= 2;
}
}
}
if (scale > 1.0) {
add_scale = cuddUniqueConst(dd,(CUDD_VALUE_TYPE)scale);
if (add_scale == NULL) {
Cudd_RecursiveDeref(dd, res);
return(NULL);
}
cuddRef(add_scale);
scaled = cuddAddApplyRecur(dd,Cudd_addTimes,res,add_scale);
if (scaled == NULL) {
Cudd_RecursiveDeref(dd, res);
Cudd_RecursiveDeref(dd, add_scale);
return(NULL);
}
cuddRef(scaled);
Cudd_RecursiveDeref(dd, add_scale);
Cudd_RecursiveDeref(dd, res);
res = scaled;
}
}
cuddDeref(res);
return(res);
} /* end of addMMRecur */
/**Function********************************************************************
Synopsis [Symmetric sifting to convergence algorithm for ZDDs.]
Description [Symmetric sifting to convergence algorithm for ZDDs.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries in
each unique subtable.
<li> Sift the variable up and down, remembering each time the total
size of the ZDD heap and grouping variables that are symmetric.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
<li> Repeat 1-4 until no further improvement.
</ol>
Returns 1 plus the number of symmetric variables if successful; 0
otherwise.]
SideEffects [None]
SeeAlso [cuddZddSymmSifting]
******************************************************************************/
int
cuddZddSymmSiftingConv(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int nvars;
int initialSize;
int x;
int result;
int symvars;
int symgroups;
int classes;
int iteration;
#ifdef DD_STATS
int previousSize;
#endif
initialSize = table->keysZ;
nvars = table->sizeZ;
/* Find order in which to sift variables. */
var = NULL;
zdd_entry = ALLOC(int, nvars);
if (zdd_entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSymmSiftingConvOutOfMem;
}
var = ALLOC(int, nvars);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto cuddZddSymmSiftingConvOutOfMem;
}
for (i = 0; i < nvars; i++) {
x = table->permZ[i];
zdd_entry[i] = table->subtableZ[x].keys;
var[i] = i;
}
qsort((void *)var, nvars, sizeof(int), (DD_QSFP)cuddZddUniqueCompare);
/* Initialize the symmetry of each subtable to itself
** for first pass of converging symmetric sifting.
*/
for (i = lower; i <= upper; i++)
table->subtableZ[i].next = i;
iteration = ddMin(table->siftMaxVar, table->sizeZ);
for (i = 0; i < iteration; i++) {
if (zddTotalNumberSwapping >= table->siftMaxSwap)
break;
x = table->permZ[var[i]];
if (x < lower || x > upper) continue;
/* Only sift if not in symmetry group already. */
if (table->subtableZ[x].next == (unsigned) x) {
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
result = cuddZddSymmSiftingAux(table, x, lower, upper);
if (!result)
goto cuddZddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
if (table->keysZ < (unsigned) previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > (unsigned) previousSize) {
(void) fprintf(table->out,"+");
#ifdef DD_VERBOSE
(void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ, var[i]);
#endif
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
}
/* Sifting now until convergence. */
while ((unsigned) initialSize > table->keysZ) {
initialSize = table->keysZ;
#ifdef DD_STATS
(void) fprintf(table->out,"\n");
#endif
/* Here we consider only one representative for each symmetry class. */
for (x = lower, classes = 0; x <= upper; x++, classes++) {
while ((unsigned) x < table->subtableZ[x].next)
x = table->subtableZ[x].next;
/* Here x is the largest index in a group.
** Groups consists of adjacent variables.
** Hence, the next increment of x will move it to a new group.
*/
i = table->invpermZ[x];
zdd_entry[i] = table->subtableZ[x].keys;
var[classes] = i;
}
qsort((void *)var,classes,sizeof(int),(DD_QSFP)cuddZddUniqueCompare);
/* Now sift. */
iteration = ddMin(table->siftMaxVar, nvars);
for (i = 0; i < iteration; i++) {
if (zddTotalNumberSwapping >= table->siftMaxSwap)
break;
x = table->permZ[var[i]];
if ((unsigned) x >= table->subtableZ[x].next) {
#ifdef DD_STATS
previousSize = table->keysZ;
#endif
result = cuddZddSymmSiftingConvAux(table, x, lower, upper);
if (!result)
goto cuddZddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
if (table->keysZ < (unsigned) previousSize) {
(void) fprintf(table->out,"-");
} else if (table->keysZ > (unsigned) previousSize) {
(void) fprintf(table->out,"+");
#ifdef DD_VERBOSE
(void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ, var[i]);
#endif
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
} /* for */
}
cuddZddSymmSummary(table, lower, upper, &symvars, &symgroups);
#ifdef DD_STATS
(void) fprintf(table->out,"\n#:S_SIFTING %8d: symmetric variables\n",
symvars);
(void) fprintf(table->out,"#:G_SIFTING %8d: symmetric groups\n",
symgroups);
#endif
FREE(var);
FREE(zdd_entry);
return(1+symvars);
cuddZddSymmSiftingConvOutOfMem:
if (zdd_entry != NULL)
FREE(zdd_entry);
if (var != NULL)
FREE(var);
return(0);
} /* end of cuddZddSymmSiftingConv */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addTriangle.]
Description [Performs the recursive step of Cudd_addTriangle. Returns
a pointer to the result if successful; NULL otherwise.]
SideEffects [None]
******************************************************************************/
static DdNode *
addTriangleRecur(
DdManager * dd,
DdNode * f,
DdNode * g,
int * vars,
DdNode *cube)
{
DdNode *fv, *fvn, *gv, *gvn, *t, *e, *res;
CUDD_VALUE_TYPE value;
int top, topf, topg, index;
statLine(dd);
if (f == DD_PLUS_INFINITY(dd) || g == DD_PLUS_INFINITY(dd)) {
return(DD_PLUS_INFINITY(dd));
}
if (cuddIsConstant(f) && cuddIsConstant(g)) {
value = cuddV(f) + cuddV(g);
res = cuddUniqueConst(dd, value);
return(res);
}
if (f < g) {
DdNode *tmp = f;
f = g;
g = tmp;
}
if (f->ref != 1 || g->ref != 1) {
res = cuddCacheLookup(dd, DD_ADD_TRIANGLE_TAG, f, g, cube);
if (res != NULL) {
return(res);
}
}
topf = cuddI(dd,f->index); topg = cuddI(dd,g->index);
top = ddMin(topf,topg);
if (top == topf) {fv = cuddT(f); fvn = cuddE(f);} else {fv = fvn = f;}
if (top == topg) {gv = cuddT(g); gvn = cuddE(g);} else {gv = gvn = g;}
t = addTriangleRecur(dd, fv, gv, vars, cube);
if (t == NULL) return(NULL);
cuddRef(t);
e = addTriangleRecur(dd, fvn, gvn, vars, cube);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddRef(e);
index = dd->invperm[top];
if (vars[index] < 0) {
res = (t == e) ? t : cuddUniqueInter(dd,index,t,e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
} else {
res = cuddAddApplyRecur(dd,Cudd_addMinimum,t,e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
cuddDeref(res);
}
if (f->ref != 1 || g->ref != 1) {
cuddCacheInsert(dd, DD_ADD_TRIANGLE_TAG, f, g, cube, res);
}
return(res);
} /* end of addTriangleRecur */
/**Function********************************************************************
Synopsis [Symmetric sifting to convergence algorithm.]
Description [Symmetric sifting to convergence algorithm.
Assumes that no dead nodes are present.
<ol>
<li> Order all the variables according to the number of entries in
each unique subtable.
<li> Sift the variable up and down, remembering each time the total
size of the DD heap and grouping variables that are symmetric.
<li> Select the best permutation.
<li> Repeat 3 and 4 for all variables.
<li> Repeat 1-4 until no further improvement.
</ol>
Returns 1 plus the number of symmetric variables if successful; 0
otherwise.]
SideEffects [None]
SeeAlso [cuddSymmSifting]
******************************************************************************/
int
cuddSymmSiftingConv(
DdManager * table,
int lower,
int upper)
{
int i;
int *var;
int size;
int x;
int result;
int symvars;
int symgroups;
int classes;
int initialSize;
#ifdef DD_STATS
int previousSize;
#endif
initialSize = table->keys - table->isolated;
size = table->size;
/* Find order in which to sift variables. */
var = NULL;
entry = ALLOC(int,size);
if (entry == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingConvOutOfMem;
}
var = ALLOC(int,size);
if (var == NULL) {
table->errorCode = CUDD_MEMORY_OUT;
goto ddSymmSiftingConvOutOfMem;
}
for (i = 0; i < size; i++) {
x = table->perm[i];
entry[i] = table->subtables[x].keys;
var[i] = i;
}
qsort((void *)var,size,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);
/* Initialize the symmetry of each subtable to itself
** for first pass of converging symmetric sifting.
*/
for (i = lower; i <= upper; i++) {
table->subtables[i].next = i;
}
for (i = 0; i < ddMin(table->siftMaxVar, table->size); i++) {
if (ddTotalNumberSwapping >= table->siftMaxSwap)
break;
if (util_cpu_time() - table->startTime > table->timeLimit) {
table->autoDyn = 0; /* prevent further reordering */
break;
}
x = table->perm[var[i]];
if (x < lower || x > upper) continue;
/* Only sift if not in symmetry group already. */
if (table->subtables[x].next == (unsigned) x) {
#ifdef DD_STATS
previousSize = table->keys - table->isolated;
#endif
result = ddSymmSiftingAux(table,x,lower,upper);
if (!result) goto ddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
if (table->keys < (unsigned) previousSize + table->isolated) {
(void) fprintf(table->out,"-");
} else if (table->keys > (unsigned) previousSize +
table->isolated) {
(void) fprintf(table->out,"+");
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
}
/* Sifting now until convergence. */
while ((unsigned) initialSize > table->keys - table->isolated) {
initialSize = table->keys - table->isolated;
#ifdef DD_STATS
(void) fprintf(table->out,"\n");
#endif
/* Here we consider only one representative for each symmetry class. */
for (x = lower, classes = 0; x <= upper; x++, classes++) {
while ((unsigned) x < table->subtables[x].next) {
x = table->subtables[x].next;
}
/* Here x is the largest index in a group.
** Groups consist of adjacent variables.
** Hence, the next increment of x will move it to a new group.
*/
i = table->invperm[x];
entry[i] = table->subtables[x].keys;
var[classes] = i;
}
qsort((void *)var,classes,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);
/* Now sift. */
for (i = 0; i < ddMin(table->siftMaxVar,classes); i++) {
if (ddTotalNumberSwapping >= table->siftMaxSwap)
break;
if (util_cpu_time() - table->startTime > table->timeLimit) {
table->autoDyn = 0; /* prevent further reordering */
break;
}
x = table->perm[var[i]];
if ((unsigned) x >= table->subtables[x].next) {
#ifdef DD_STATS
previousSize = table->keys - table->isolated;
#endif
result = ddSymmSiftingConvAux(table,x,lower,upper);
if (!result ) goto ddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
if (table->keys < (unsigned) previousSize + table->isolated) {
(void) fprintf(table->out,"-");
} else if (table->keys > (unsigned) previousSize +
table->isolated) {
(void) fprintf(table->out,"+");
} else {
(void) fprintf(table->out,"=");
}
fflush(table->out);
#endif
}
} /* for */
}
ddSymmSummary(table, lower, upper, &symvars, &symgroups);
#ifdef DD_STATS
(void) fprintf(table->out, "\n#:S_SIFTING %8d: symmetric variables\n",
symvars);
(void) fprintf(table->out, "#:G_SIFTING %8d: symmetric groups",
symgroups);
#endif
FREE(var);
FREE(entry);
return(1+symvars);
ddSymmSiftingConvOutOfMem:
if (entry != NULL) FREE(entry);
if (var != NULL) FREE(var);
return(0);
} /* end of cuddSymmSiftingConv */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addOuterSum.]
Description [Performs the recursive step of Cudd_addOuterSum.
Returns a pointer to the result if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static DdNode *
cuddAddOuterSumRecur(
DdManager *dd,
DdNode *M,
DdNode *r,
DdNode *c)
{
DdNode *P, *R, *Mt, *Me, *rt, *re, *ct, *ce, *Rt, *Re;
int topM, topc, topr;
int v, index;
statLine(dd);
/* Check special cases. */
if (r == DD_PLUS_INFINITY(dd) || c == DD_PLUS_INFINITY(dd)) return(M);
if (cuddIsConstant(c) && cuddIsConstant(r)) {
R = cuddUniqueConst(dd,Cudd_V(c)+Cudd_V(r));
cuddRef(R);
if (cuddIsConstant(M)) {
if (cuddV(R) <= cuddV(M)) {
cuddDeref(R);
return(R);
} else {
Cudd_RecursiveDeref(dd,R);
return(M);
}
} else {
P = Cudd_addApply(dd,Cudd_addMinimum,R,M);
cuddRef(P);
Cudd_RecursiveDeref(dd,R);
cuddDeref(P);
return(P);
}
}
/* Check the cache. */
R = cuddCacheLookup(dd,DD_ADD_OUT_SUM_TAG,M,r,c);
if (R != NULL) return(R);
topM = cuddI(dd,M->index); topr = cuddI(dd,r->index);
topc = cuddI(dd,c->index);
v = ddMin(topM,ddMin(topr,topc));
/* Compute cofactors. */
if (topM == v) { Mt = cuddT(M); Me = cuddE(M); } else { Mt = Me = M; }
if (topr == v) { rt = cuddT(r); re = cuddE(r); } else { rt = re = r; }
if (topc == v) { ct = cuddT(c); ce = cuddE(c); } else { ct = ce = c; }
/* Recursively solve. */
Rt = cuddAddOuterSumRecur(dd,Mt,rt,ct);
if (Rt == NULL) return(NULL);
cuddRef(Rt);
Re = cuddAddOuterSumRecur(dd,Me,re,ce);
if (Re == NULL) {
Cudd_RecursiveDeref(dd, Rt);
return(NULL);
}
cuddRef(Re);
index = dd->invperm[v];
R = (Rt == Re) ? Rt : cuddUniqueInter(dd,index,Rt,Re);
if (R == NULL) {
Cudd_RecursiveDeref(dd, Rt);
Cudd_RecursiveDeref(dd, Re);
return(NULL);
}
cuddDeref(Rt);
cuddDeref(Re);
/* Store the result in the cache. */
cuddCacheInsert(dd,DD_ADD_OUT_SUM_TAG,M,r,c,R);
return(R);
} /* end of cuddAddOuterSumRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_bddIsop.]
Description []
SideEffects [None]
SeeAlso [Cudd_bddIsop]
******************************************************************************/
DdNode *
cuddBddIsop(
DdManager * dd,
DdNode * L,
DdNode * U)
{
DdNode *one = DD_ONE(dd);
DdNode *zero = Cudd_Not(one);
int v, top_l, top_u;
DdNode *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
DdNode *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
DdNode *Isub0, *Isub1, *Id;
DdNode *x;
DdNode *term0, *term1, *sum;
DdNode *Lv, *Uv, *Lnv, *Unv;
DdNode *r;
int index;
statLine(dd);
if (L == zero)
return(zero);
if (U == one)
return(one);
/* Check cache */
r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
if (r)
return(r);
top_l = dd->perm[Cudd_Regular(L)->index];
top_u = dd->perm[Cudd_Regular(U)->index];
v = ddMin(top_l, top_u);
/* Compute cofactors */
if (top_l == v) {
index = Cudd_Regular(L)->index;
Lv = Cudd_T(L);
Lnv = Cudd_E(L);
if (Cudd_IsComplement(L)) {
Lv = Cudd_Not(Lv);
Lnv = Cudd_Not(Lnv);
}
}
else {
index = Cudd_Regular(U)->index;
Lv = Lnv = L;
}
if (top_u == v) {
Uv = Cudd_T(U);
Unv = Cudd_E(U);
if (Cudd_IsComplement(U)) {
Uv = Cudd_Not(Uv);
Unv = Cudd_Not(Unv);
}
}
else {
Uv = Unv = U;
}
Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
if (Lsub0 == NULL)
return(NULL);
Cudd_Ref(Lsub0);
Usub0 = Unv;
Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
if (Lsub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
return(NULL);
}
Cudd_Ref(Lsub1);
Usub1 = Uv;
Isub0 = cuddBddIsop(dd, Lsub0, Usub0);
if (Isub0 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
return(NULL);
}
Cudd_Ref(Isub0);
Isub1 = cuddBddIsop(dd, Lsub1, Usub1);
if (Isub1 == NULL) {
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Cudd_RecursiveDeref(dd, Isub0);
return(NULL);
}
Cudd_Ref(Isub1);
Cudd_RecursiveDeref(dd, Lsub0);
Cudd_RecursiveDeref(dd, Lsub1);
Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
if (Lsuper0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
return(NULL);
}
Cudd_Ref(Lsuper0);
Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
if (Lsuper1 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
return(NULL);
}
Cudd_Ref(Lsuper1);
Usuper0 = Unv;
Usuper1 = Uv;
/* Ld = Lsuper0 + Lsuper1 */
Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
Ld = Cudd_NotCond(Ld, Ld != NULL);
if (Ld == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
return(NULL);
}
Cudd_Ref(Ld);
Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
if (Ud == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Cudd_RecursiveDeref(dd, Ld);
return(NULL);
}
Cudd_Ref(Ud);
Cudd_RecursiveDeref(dd, Lsuper0);
Cudd_RecursiveDeref(dd, Lsuper1);
Id = cuddBddIsop(dd, Ld, Ud);
if (Id == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
return(NULL);
}
Cudd_Ref(Id);
Cudd_RecursiveDeref(dd, Ld);
Cudd_RecursiveDeref(dd, Ud);
x = cuddUniqueInter(dd, index, one, zero);
if (x == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Id);
return(NULL);
}
Cudd_Ref(x);
term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
if (term0 == NULL) {
Cudd_RecursiveDeref(dd, Isub0);
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, x);
return(NULL);
}
Cudd_Ref(term0);
Cudd_RecursiveDeref(dd, Isub0);
term1 = cuddBddAndRecur(dd, x, Isub1);
if (term1 == NULL) {
Cudd_RecursiveDeref(dd, Isub1);
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, term0);
return(NULL);
}
Cudd_Ref(term1);
Cudd_RecursiveDeref(dd, x);
Cudd_RecursiveDeref(dd, Isub1);
/* sum = term0 + term1 */
sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
sum = Cudd_NotCond(sum, sum != NULL);
if (sum == NULL) {
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
return(NULL);
}
Cudd_Ref(sum);
Cudd_RecursiveDeref(dd, term0);
Cudd_RecursiveDeref(dd, term1);
/* r = sum + Id */
r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
r = Cudd_NotCond(r, r != NULL);
if (r == NULL) {
Cudd_RecursiveDeref(dd, Id);
Cudd_RecursiveDeref(dd, sum);
return(NULL);
}
Cudd_Ref(r);
Cudd_RecursiveDeref(dd, sum);
Cudd_RecursiveDeref(dd, Id);
cuddCacheInsert2(dd, cuddBddIsop, L, U, r);
Cudd_Deref(r);
return(r);
} /* end of cuddBddIsop */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_bddIte.]
Description [Implements the recursive step of Cudd_bddIte. Returns a
pointer to the resulting BDD. NULL if the intermediate result blows
up or if reordering occurs.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddBddIteRecur(
DdManager * dd,
DdNode * f,
DdNode * g,
DdNode * h)
{
DdNode *_true, *_false, *res;
DdNode *r, *Fv, *Fnv, *Gv, *Gnv, *H, *Hv, *Hnv, *t, *e;
unsigned int topf, topg, toph, v;
int index = 0;
int comple;
statLine(dd);
/* Terminal cases. */
/* _True variable cases. */
if (f == (_true = DD_TRUE(dd))) /* ITE(TRUE,G,H) = G */
return(g);
if (f == (_false = Cudd_Not(_true))) /* ITE(FALSE,G,H) = H */
return(h);
/* From now on, f is known not to be a constant. */
if (g == _true || f == g) { /* ITE(F,F,H) = ITE(F,TRUE,H) = F + H */
if (h == _false) { /* ITE(F,TRUE,FALSE) = F */
return(f);
} else {
res = cuddBddAndRecur(dd,Cudd_Not(f),Cudd_Not(h));
return(Cudd_NotCond(res,res != NULL));
}
} else if (g == _false || f == Cudd_Not(g)) { /* ITE(F,!F,H) = ITE(F,FALSE,H) = !F * H */
if (h == _true) { /* ITE(F,FALSE,TRUE) = !F */
return(Cudd_Not(f));
} else {
res = cuddBddAndRecur(dd,Cudd_Not(f),h);
return(res);
}
}
if (h == _false || f == h) { /* ITE(F,G,F) = ITE(F,G,FALSE) = F * G */
res = cuddBddAndRecur(dd,f,g);
return(res);
} else if (h == _true || f == Cudd_Not(h)) { /* ITE(F,G,!F) = ITE(F,G,TRUE) = !F + G */
res = cuddBddAndRecur(dd,f,Cudd_Not(g));
return(Cudd_NotCond(res,res != NULL));
}
/* Check remaining _true variable case. */
if (g == h) { /* ITE(F,G,G) = G */
return(g);
} else if (g == Cudd_Not(h)) { /* ITE(F,G,!G) = F <-> G */
res = cuddBddXorRecur(dd,f,h);
return(res);
}
/* From here, there are no constants. */
comple = bddVarToCanonicalSimple(dd, &f, &g, &h, &topf, &topg, &toph);
/* f & g are now regular pointers */
v = ddMin(topg, toph);
/* A shortcut: ITE(F,G,H) = (v,G,H) if F = (v,TRUE,FALSE), v < top(G,H). */
if (topf < v && cuddT(f) == _true && cuddE(f) == _false) {
r = cuddUniqueInter(dd, (int) f->index, g, h);
return(Cudd_NotCond(r,comple && r != NULL));
}
/* Check cache. */
r = cuddCacheLookup(dd, DD_BDD_ITE_TAG, f, g, h);
if (r != NULL) {
return(Cudd_NotCond(r,comple));
}
/* Compute cofactors. */
if (topf <= v) {
v = ddMin(topf, v); /* v = top_var(F,G,H) */
index = f->index;
Fv = cuddT(f); Fnv = cuddE(f);
} else {
Fv = Fnv = f;
}
if (topg == v) {
index = g->index;
Gv = cuddT(g); Gnv = cuddE(g);
} else {
Gv = Gnv = g;
}
if (toph == v) {
H = Cudd_Regular(h);
index = H->index;
Hv = cuddT(H); Hnv = cuddE(H);
if (Cudd_IsComplement(h)) {
Hv = Cudd_Not(Hv);
Hnv = Cudd_Not(Hnv);
}
} else {
Hv = Hnv = h;
}
/* Recursive step. */
t = cuddBddIteRecur(dd,Fv,Gv,Hv);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddIteRecur(dd,Fnv,Gnv,Hnv);
if (e == NULL) {
Cudd_IterDerefBdd(dd,t);
return(NULL);
}
cuddRef(e);
r = (t == e) ? t : cuddUniqueInter(dd,index,t,e);
if (r == NULL) {
Cudd_IterDerefBdd(dd,t);
Cudd_IterDerefBdd(dd,e);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
cuddCacheInsert(dd, DD_BDD_ITE_TAG, f, g, h, r);
return(Cudd_NotCond(r,comple));
} /* end of cuddBddIteRecur */
/**Function********************************************************************
Synopsis [Implements ITEconstant(f,g,h).]
Description [Implements ITEconstant(f,g,h). Returns a pointer to the
resulting BDD (which may or may not be constant) or DD_NON_CONSTANT.
No new nodes are created.]
SideEffects [None]
SeeAlso [Cudd_bddIte Cudd_bddIntersect Cudd_bddLeq Cudd_addIteConstant]
******************************************************************************/
DdNode *
Cudd_bddIteConstant(
DdManager * dd,
DdNode * f,
DdNode * g,
DdNode * h)
{
DdNode *r, *Fv, *Fnv, *Gv, *Gnv, *H, *Hv, *Hnv, *t, *e;
DdNode *one = DD_ONE(dd);
DdNode *zero = Cudd_Not(one);
int comple;
unsigned int topf, topg, toph, v;
statLine(dd);
/* Trivial cases. */
if (f == one) /* ITE(1,G,H) => G */
return(g);
if (f == zero) /* ITE(0,G,H) => H */
return(h);
/* f now not a constant. */
bddVarToConst(f, &g, &h, one); /* possibly convert g or h */
/* to constants */
if (g == h) /* ITE(F,G,G) => G */
return(g);
if (Cudd_IsConstant(g) && Cudd_IsConstant(h))
return(DD_NON_CONSTANT); /* ITE(F,1,0) or ITE(F,0,1) */
/* => DD_NON_CONSTANT */
if (g == Cudd_Not(h))
return(DD_NON_CONSTANT); /* ITE(F,G,G') => DD_NON_CONSTANT */
/* if F != G and F != G' */
comple = bddVarToCanonical(dd, &f, &g, &h, &topf, &topg, &toph);
/* Cache lookup. */
r = cuddConstantLookup(dd, DD_BDD_ITE_CONSTANT_TAG, f, g, h);
if (r != NULL) {
return(Cudd_NotCond(r,comple && r != DD_NON_CONSTANT));
}
v = ddMin(topg, toph);
/* ITE(F,G,H) = (v,G,H) (non constant) if F = (v,1,0), v < top(G,H). */
if (topf < v && cuddT(f) == one && cuddE(f) == zero) {
return(DD_NON_CONSTANT);
}
/* Compute cofactors. */
if (topf <= v) {
v = ddMin(topf, v); /* v = top_var(F,G,H) */
Fv = cuddT(f); Fnv = cuddE(f);
} else {
Fv = Fnv = f;
}
if (topg == v) {
Gv = cuddT(g); Gnv = cuddE(g);
} else {
Gv = Gnv = g;
}
if (toph == v) {
H = Cudd_Regular(h);
Hv = cuddT(H); Hnv = cuddE(H);
if (Cudd_IsComplement(h)) {
Hv = Cudd_Not(Hv);
Hnv = Cudd_Not(Hnv);
}
} else {
Hv = Hnv = h;
}
/* Recursion. */
t = Cudd_bddIteConstant(dd, Fv, Gv, Hv);
if (t == DD_NON_CONSTANT || !Cudd_IsConstant(t)) {
cuddCacheInsert(dd, DD_BDD_ITE_CONSTANT_TAG, f, g, h, DD_NON_CONSTANT);
return(DD_NON_CONSTANT);
}
e = Cudd_bddIteConstant(dd, Fnv, Gnv, Hnv);
if (e == DD_NON_CONSTANT || !Cudd_IsConstant(e) || t != e) {
cuddCacheInsert(dd, DD_BDD_ITE_CONSTANT_TAG, f, g, h, DD_NON_CONSTANT);
return(DD_NON_CONSTANT);
}
cuddCacheInsert(dd, DD_BDD_ITE_CONSTANT_TAG, f, g, h, t);
return(Cudd_NotCond(t,comple));
} /* end of Cudd_bddIteConstant */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_addIteGeneral(f,g,h).]
Description [Implements the recursive step of Cudd_addIteGeneral(f,g,h),
meaning that g and h are not supposed to be 0-1 ADDs but may have more terminals.
Applying arithmetic addition in the terminal case. Returns a pointer to the
resulting ADD if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_addIte]
******************************************************************************/
DdNode * extraAddIteRecurGeneral( DdManager * dd, DdNode * bX, DdNode * aF, DdNode * aG )
{
DdNode * aRes;
statLine( dd );
assert( !Cudd_IsConstant(bX) );
assert( cuddE(bX) == b0 && cuddT(bX) == b1 ); /* the elementary variable */
/* check cache */
if ( aRes = cuddCacheLookup(dd, DD_ADD_ITE_GENERAL_TAG, bX, aF, aG) )
return aRes;
else
{
DdNode * aF0, * aF1, * aG0, * aG1;
int LevelF, LevelG, LevelX, LevelTop;
LevelF = cuddI(dd,aF->index);
LevelG = cuddI(dd,aG->index);
LevelX = dd->perm[bX->index];
LevelTop = ddMin(LevelF, LevelG);
LevelTop = ddMin(LevelX, LevelTop);
if ( LevelF == LevelTop )
{
aF0 = cuddE(aF);
aF1 = cuddT(aF);
}
else
aF0 = aF1 = aF;
if ( LevelG == LevelTop )
{
aG0 = cuddE(aG);
aG1 = cuddT(aG);
}
else
aG0 = aG1 = aG;
if ( LevelX == LevelTop )
{
assert( LevelX < LevelF );
assert( LevelX < LevelG );
/* consider the case when Res0 and Res1 are the same node */
aRes = (aF == aG) ? aF : cuddUniqueInter( dd, bX->index, aF, aG );
if (aRes == NULL)
return NULL;
}
else
{
DdNode * aRes0, * aRes1; /* partial results to be composed by ITE */
aRes0 = extraAddIteRecurGeneral( dd, bX, aF0, aG0 );
if ( aRes0 == NULL )
return NULL;
cuddRef( aRes0 );
aRes1 = extraAddIteRecurGeneral( dd, bX, aF1, aG1 );
if ( aRes1 == NULL )
{
Cudd_RecursiveDeref(dd, aRes0);
return NULL;
}
cuddRef( aRes1 );
/* only aRes0 and aRes1 are referenced at this point */
/* consider the case when Res0 and Res1 are the same node */
aRes = (aRes1 == aRes0) ? aRes1 : cuddUniqueInter( dd, dd->invperm[LevelTop], aRes1, aRes0 );
if (aRes == NULL)
{
Cudd_RecursiveDeref(dd, aRes1);
Cudd_RecursiveDeref(dd, aRes0);
return NULL;
}
cuddDeref(aRes1);
cuddDeref(aRes0);
}
cuddCacheInsert( dd, DD_ADD_ITE_GENERAL_TAG, bX, aF, aG, aRes );
return aRes;
}
} /* end of extraAddIteRecurGeneral */
