/**Function********************************************************************
Synopsis [Substitutes g for x_v in the BDD for f.]
Description [Substitutes g for x_v in the BDD for f. v is the index of the
variable to be substituted. Cudd_bddCompose passes the corresponding
projection function to the recursive procedure, so that the cache may
be used. Returns the composed BDD if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_addCompose]
******************************************************************************/
DdNode *
Cudd_bddCompose(
DdManager * dd,
DdNode * f,
DdNode * g,
int v)
{
DdNode *proj, *res;
/* Sanity check. */
if (v < 0 || v > dd->size) return(NULL);
proj = dd->vars[v];
do {
dd->reordered = 0;
res = cuddBddComposeRecur(dd,f,g,proj);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_bddCompose */
/**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 [Performs the recursive step of Cudd_bddCompose.]
Description [Performs the recursive step of Cudd_bddCompose.
Exploits the fact that the composition of f' with g
produces the complement of the composition of f with g to better
utilize the cache. Returns the composed BDD if successful; NULL
otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddCompose]
******************************************************************************/
DdNode *
cuddBddComposeRecur(
DdManager * dd,
DdNode * f,
DdNode * g,
DdNode * proj)
{
DdNode *F, *G, *f1, *f0, *g1, *g0, *r, *t, *e;
unsigned int v, topf, topg, topindex;
int comple;
statLine(dd);
v = dd->perm[proj->index];
F = Cudd_Regular(f);
topf = cuddI(dd,F->index);
/* Terminal case. Subsumes the test for constant f. */
if (topf > v) return(f);
/* We solve the problem for a regular pointer, and then complement
** the result if the pointer was originally complemented.
*/
comple = Cudd_IsComplement(f);
/* Check cache. */
r = cuddCacheLookup(dd,DD_BDD_COMPOSE_RECUR_TAG,F,g,proj);
if (r != NULL) {
return(Cudd_NotCond(r,comple));
}
if (topf == v) {
/* Compose. */
f1 = cuddT(F);
f0 = cuddE(F);
r = cuddBddIteRecur(dd, g, f1, f0);
if (r == NULL) return(NULL);
} else {
/* Compute cofactors of f and g. Remember the index of the top
** variable.
*/
G = Cudd_Regular(g);
topg = cuddI(dd,G->index);
if (topf > topg) {
topindex = G->index;
f1 = f0 = F;
} else {
topindex = F->index;
f1 = cuddT(F);
f0 = cuddE(F);
}
if (topg > topf) {
g1 = g0 = g;
} else {
g1 = cuddT(G);
g0 = cuddE(G);
if (g != G) {
g1 = Cudd_Not(g1);
g0 = Cudd_Not(g0);
}
}
/* Recursive step. */
t = cuddBddComposeRecur(dd, f1, g1, proj);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddComposeRecur(dd, f0, g0, proj);
if (e == NULL) {
Cudd_IterDerefBdd(dd, t);
return(NULL);
}
cuddRef(e);
r = cuddBddIteRecur(dd, dd->vars[topindex], t, e);
if (r == NULL) {
Cudd_IterDerefBdd(dd, t);
Cudd_IterDerefBdd(dd, e);
return(NULL);
}
cuddRef(r);
Cudd_IterDerefBdd(dd, t); /* t & e not necessarily part of r */
Cudd_IterDerefBdd(dd, e);
cuddDeref(r);
}
cuddCacheInsert(dd,DD_BDD_COMPOSE_RECUR_TAG,F,g,proj,r);
return(Cudd_NotCond(r,comple));
} /* end of cuddBddComposeRecur */