/**Function********************************************************************
Synopsis [Performs a recursive step of Extra_zddGetSymmetricVars.]
Description [Returns the set of ZDD singletons, containing those positive
ZDD variables that correspond to BDD variables x, for which it is true
that bF(x=0) == bG(x=1).]
SideEffects []
SeeAlso []
******************************************************************************/
DdNode * extraZddGetSymmetricVars(
DdManager * dd, /* the DD manager */
DdNode * bF, /* the first function - originally, the positive cofactor */
DdNode * bG, /* the second function - originally, the negative cofactor */
DdNode * bVars) /* the set of variables, on which F and G depend */
{
DdNode * zRes;
DdNode * bFR = Cudd_Regular(bF);
DdNode * bGR = Cudd_Regular(bG);
if ( cuddIsConstant(bFR) && cuddIsConstant(bGR) )
{
if ( bF == bG )
return extraZddGetSingletons( dd, bVars );
else
return z0;
}
assert( bVars != b1 );
if ( (zRes = cuddCacheLookupZdd(dd, DD_GET_SYMM_VARS_TAG, bF, bG, bVars)) )
return zRes;
else
{
DdNode * zRes0, * zRes1;
DdNode * zPlus, * zTemp;
DdNode * bF0, * bF1;
DdNode * bG0, * bG1;
DdNode * bVarsNew;
int LevelF = cuddI(dd,bFR->index);
int LevelG = cuddI(dd,bGR->index);
int LevelFG;
if ( LevelF < LevelG )
LevelFG = LevelF;
else
LevelFG = LevelG;
// at least one of the arguments is not a constant
assert( LevelFG < dd->size );
// every variable in bF and bG should be also in bVars, therefore LevelFG cannot be above LevelV
// if LevelFG is below LevelV, scroll through the vars in bVars to the same level as LevelFG
for ( bVarsNew = bVars; LevelFG > dd->perm[bVarsNew->index]; bVarsNew = cuddT(bVarsNew) );
assert( LevelFG == dd->perm[bVarsNew->index] );
// cofactor the functions
if ( LevelF == LevelFG )
{
if ( bFR != bF ) // bF is complemented
{
bF0 = Cudd_Not( cuddE(bFR) );
bF1 = Cudd_Not( cuddT(bFR) );
}
else
{
bF0 = cuddE(bFR);
bF1 = cuddT(bFR);
}
}
else
bF0 = bF1 = bF;
if ( LevelG == LevelFG )
{
if ( bGR != bG ) // bG is complemented
{
bG0 = Cudd_Not( cuddE(bGR) );
bG1 = Cudd_Not( cuddT(bGR) );
}
else
{
bG0 = cuddE(bGR);
bG1 = cuddT(bGR);
}
}
else
bG0 = bG1 = bG;
// solve subproblems
zRes0 = extraZddGetSymmetricVars( dd, bF0, bG0, cuddT(bVarsNew) );
if ( zRes0 == NULL )
return NULL;
cuddRef( zRes0 );
// if there is not symmetries in the negative cofactor
// there is no need to test the positive cofactor
if ( zRes0 == z0 )
zRes = zRes0; // zRes takes reference
else
{
zRes1 = extraZddGetSymmetricVars( dd, bF1, bG1, cuddT(bVarsNew) );
if ( zRes1 == NULL )
{
Cudd_RecursiveDerefZdd( dd, zRes0 );
return NULL;
}
cuddRef( zRes1 );
// only those variables should belong to the resulting set
// for which the property is true for both cofactors
zRes = cuddZddIntersect( dd, zRes0, zRes1 );
if ( zRes == NULL )
{
Cudd_RecursiveDerefZdd( dd, zRes0 );
Cudd_RecursiveDerefZdd( dd, zRes1 );
return NULL;
}
cuddRef( zRes );
Cudd_RecursiveDerefZdd( dd, zRes0 );
Cudd_RecursiveDerefZdd( dd, zRes1 );
}
// add one more singleton if the property is true for this variable
if ( bF0 == bG1 )
{
zPlus = cuddZddGetNode( dd, 2*bVarsNew->index, z1, z0 );
if ( zPlus == NULL )
{
Cudd_RecursiveDerefZdd( dd, zRes );
return NULL;
}
cuddRef( zPlus );
// add these variable pairs to the result
zRes = cuddZddUnion( dd, zTemp = zRes, zPlus );
if ( zRes == NULL )
{
Cudd_RecursiveDerefZdd( dd, zTemp );
Cudd_RecursiveDerefZdd( dd, zPlus );
return NULL;
}
cuddRef( zRes );
Cudd_RecursiveDerefZdd( dd, zTemp );
Cudd_RecursiveDerefZdd( dd, zPlus );
}
if ( bF == bG && bVars != bVarsNew )
{
// if the functions are equal, so are their cofactors
// add those variables from V that are above F and G
DdNode * bVarsExtra;
assert( LevelFG > dd->perm[bVars->index] );
// create the BDD of the extra variables
bVarsExtra = cuddBddExistAbstractRecur( dd, bVars, bVarsNew );
if ( bVarsExtra == NULL )
{
Cudd_RecursiveDerefZdd( dd, zRes );
return NULL;
}
cuddRef( bVarsExtra );
zPlus = extraZddGetSingletons( dd, bVarsExtra );
if ( zPlus == NULL )
{
Cudd_RecursiveDeref( dd, bVarsExtra );
Cudd_RecursiveDerefZdd( dd, zRes );
return NULL;
}
cuddRef( zPlus );
Cudd_RecursiveDeref( dd, bVarsExtra );
// add these to the result
zRes = cuddZddUnion( dd, zTemp = zRes, zPlus );
if ( zRes == NULL )
{
Cudd_RecursiveDerefZdd( dd, zTemp );
Cudd_RecursiveDerefZdd( dd, zPlus );
return NULL;
}
cuddRef( zRes );
Cudd_RecursiveDerefZdd( dd, zTemp );
Cudd_RecursiveDerefZdd( dd, zPlus );
}
cuddDeref( zRes );
cuddCacheInsert( dd, DD_GET_SYMM_VARS_TAG, bF, bG, bVars, zRes );
return zRes;
}
} /* end of extraZddGetSymmetricVars */
/**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 */
