/**Function********************************************************************
Synopsis [Computes the cofactor of f with respect to g.]
Description [Computes the cofactor of f with respect to g; g must be
the BDD or the ADD of a cube. Returns a pointer to the cofactor if
successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddConstrain Cudd_bddRestrict]
******************************************************************************/
DdNode *
Cudd_Cofactor(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res,*_false;
/* NuSMV: begin add */
abort(); /* NOT USED BY NUSMV */
/* NuSMV: begin end */
_false = Cudd_Not(DD_TRUE(dd));
if (g == _false || g == DD_FALSE(dd)) {
(void) fprintf(dd->err,"Cudd_Cofactor: Invalid restriction 1\n");
dd->errorCode = CUDD_INVALID_ARG;
return(NULL);
}
do {
dd->reordered = 0;
res = cuddCofactorRecur(dd,f,g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_Cofactor */
/**Function********************************************************************
Synopsis [Computes the cofactor of f with respect to g.]
Description [Computes the cofactor of f with respect to g; g must be
the BDD or the ADD of a cube. Returns a pointer to the cofactor if
successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddConstrain Cudd_bddRestrict]
******************************************************************************/
DdNode *
Cudd_Cofactor(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res,*zero;
zero = Cudd_Not(DD_ONE(dd));
if (g == zero || g == DD_ZERO(dd)) {
(void) fprintf(stdout,"Cudd_Cofactor: Invalid restriction 1\n");
return(NULL);
}
do {
dd->reordered = 0;
res = cuddCofactorRecur(dd,f,g);
} while (dd->reordered == 1);
return(res);
} /* end of Cudd_Cofactor */
/**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_Cofactor.]
Description [Performs the recursive step of Cudd_Cofactor. Returns a
pointer to the cofactor if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_Cofactor]
******************************************************************************/
DdNode *
cuddCofactorRecur(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *one,*zero,*F,*G,*g1,*g0,*f1,*f0,*t,*e,*r;
unsigned int topf,topg;
int comple;
F = Cudd_Regular(f);
if (cuddIsConstant(F)) return(f);
one = DD_ONE(dd);
/* The invariant g != 0 is true on entry to this procedure and is
** recursively maintained by it. Therefore it suffices to test g
** against one to make sure it is not constant.
*/
if (g == one) return(f);
/* From now on, f and g are known not to be constants. */
comple = f != F;
r = cuddCacheLookup2(dd,Cudd_Cofactor,F,g);
if (r != NULL) {
return(Cudd_NotCond(r,comple));
}
topf = dd->perm[F->index];
G = Cudd_Regular(g);
topg = dd->perm[G->index];
/* We take the cofactors of F because we are going to rely on
** the fact that the cofactors of the complement are the complements
** of the cofactors to better utilize the cache. Variable comple
** remembers whether we have to complement the result or not.
*/
if (topf <= topg) {
f1 = cuddT(F); f0 = cuddE(F);
} else {
f1 = f0 = F;
}
if (topg <= topf) {
g1 = cuddT(G); g0 = cuddE(G);
if (g != G) { g1 = Cudd_Not(g1); g0 = Cudd_Not(g0); }
} else {
g1 = g0 = g;
}
zero = Cudd_Not(one);
if (topf >= topg) {
if (g0 == zero || g0 == DD_ZERO(dd)) {
r = cuddCofactorRecur(dd, f1, g1);
} else if (g1 == zero || g1 == DD_ZERO(dd)) {
r = cuddCofactorRecur(dd, f0, g0);
} else {
(void) fprintf(stdout,"Cudd_Cofactor: Invalid restriction 2\n");
return(NULL);
}
if (r == NULL) return(NULL);
} else /* if (topf < topg) */ {
t = cuddCofactorRecur(dd, f1, g);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddCofactorRecur(dd, f0, g);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddRef(e);
if (t == e) {
r = t;
} else if (Cudd_IsComplement(t)) {
r = cuddUniqueInter(dd,(int)F->index,Cudd_Not(t),Cudd_Not(e));
if (r != NULL)
r = Cudd_Not(r);
} else {
r = cuddUniqueInter(dd,(int)F->index,t,e);
}
if (r == NULL) {
Cudd_RecursiveDeref(dd ,e);
Cudd_RecursiveDeref(dd ,t);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
}
cuddCacheInsert2(dd,Cudd_Cofactor,F,g,r);
return(Cudd_NotCond(r,comple));
} /* end of cuddCofactorRecur */
