/**Function********************************************************************
Synopsis [Performs the recursive step of Cuddaux_IsVarIn.]
Description [Performs the recursive step of Cuddaux_IsVarIn. var is
supposed to be a BDD projection function. Returns the logical one or
zero.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode*
cuddauxIsVarInRecur(DdManager* manager, DdNode* f, DdNode* Var)
{
DdNode *zero,*one, *F, *res;
int topV,topF;
one = DD_ONE(manager);
zero = Cudd_Not(one);
F = Cudd_Regular(f);
if (cuddIsConstant(F)) return zero;
if (Var==F) return(one);
topV = Var->index;
topF = F->index;
if (topF == topV) return(one);
if (cuddI(manager,topV) < cuddI(manager,topF)) return(zero);
res = cuddCacheLookup2(manager,cuddauxIsVarInRecur, F, Var);
if (res != NULL) return(res);
res = cuddauxIsVarInRecur(manager,cuddT(F),Var);
if (res==zero){
res = cuddauxIsVarInRecur(manager,cuddE(F),Var);
}
cuddCacheInsert2(manager,cuddauxIsVarInRecur,F,Var,res);
return(res);
}
DdNode*
cuddauxAddGuardOfNodeRecur(DdManager* manager, DdNode* f, DdNode* h)
{
DdNode *one, *res, *T, *E;
int topf, toph;
/* Handle terminal cases */
one = DD_ONE(manager);
if (f==h){
return(one);
}
topf = cuddI(manager,f->index);
toph = cuddI(manager,h->index);
if (topf >= toph){
return Cudd_Not(one);
}
/* Look in the cache */
res = cuddCacheLookup2(manager,Cuddaux_addGuardOfNode,f,h);
if (res != NULL)
return(res);
T = cuddauxAddGuardOfNodeRecur(manager,cuddT(f),h);
if (T == NULL)
return(NULL);
cuddRef(T);
E = cuddauxAddGuardOfNodeRecur(manager,cuddE(f),h);
if (E == NULL){
Cudd_IterDerefBdd(manager, T);
return(NULL);
}
cuddRef(E);
if (T == E){
res = T;
}
else {
if (Cudd_IsComplement(T)){
res = cuddUniqueInter(manager,f->index,Cudd_Not(T),Cudd_Not(E));
if (res == NULL) {
Cudd_IterDerefBdd(manager, T);
Cudd_IterDerefBdd(manager, E);
return(NULL);
}
res = Cudd_Not(res);
}
else {
res = cuddUniqueInter(manager,f->index,T,E);
if (res == NULL) {
Cudd_IterDerefBdd(manager, T);
Cudd_IterDerefBdd(manager, E);
return(NULL);
}
}
}
cuddDeref(T);
cuddDeref(E);
cuddCacheInsert2(manager,Cuddaux_addGuardOfNode,f,h,res);
return(res);
}
/**Function********************************************************************
Synopsis [Performs the recursive step for Cudd_addBddStrictThreshold.]
Description [Performs the recursive step for Cudd_addBddStrictThreshold.
Returns a pointer to the BDD if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [addBddDoThreshold]
******************************************************************************/
static DdNode *
addBddDoStrictThreshold(
DdManager * dd,
DdNode * f,
DdNode * val)
{
DdNode *res, *T, *E;
DdNode *fv, *fvn;
int v;
statLine(dd);
/* Check terminal case. */
if (cuddIsConstant(f)) {
return(Cudd_NotCond(DD_TRUE(dd),cuddV(f) <= cuddV(val)));
}
/* Check cache. */
res = cuddCacheLookup2(dd,addBddDoStrictThreshold,f,val);
if (res != NULL) return(res);
/* Recursive step. */
v = f->index;
fv = cuddT(f); fvn = cuddE(f);
T = addBddDoStrictThreshold(dd,fv,val);
if (T == NULL) return(NULL);
cuddRef(T);
E = addBddDoStrictThreshold(dd,fvn,val);
if (E == NULL) {
Cudd_RecursiveDeref(dd, T);
return(NULL);
}
cuddRef(E);
if (Cudd_IsComplement(T)) {
res = (T == E) ? Cudd_Not(T) : cuddUniqueInter(dd,v,Cudd_Not(T),Cudd_Not(E));
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
res = Cudd_Not(res);
} else {
res = (T == E) ? T : cuddUniqueInter(dd,v,T,E);
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
}
cuddDeref(T);
cuddDeref(E);
/* Store result. */
cuddCacheInsert2(dd,addBddDoStrictThreshold,f,val,res);
return(res);
} /* end of addBddDoStrictThreshold */
/**Function********************************************************************
Synopsis [Performs the recursive steps of Cudd_bddBoleanDiff.]
Description [Performs the recursive steps of Cudd_bddBoleanDiff.
Returns the BDD obtained by XORing the cofactors of f with respect to
var if successful; NULL otherwise. Exploits the fact that dF/dx =
dF'/dx.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddBddBooleanDiffRecur(
DdManager * manager,
DdNode * f,
DdNode * var)
{
DdNode *T, *E, *res, *res1, *res2;
statLine(manager);
if (cuddI(manager,f->index) > manager->perm[var->index]) {
/* f does not depend on var. */
return(Cudd_Not(DD_ONE(manager)));
}
/* From now on, f is non-constant. */
/* If the two indices are the same, so are their levels. */
if (f->index == var->index) {
res = cuddBddXorRecur(manager, cuddT(f), cuddE(f));
return(res);
}
/* From now on, cuddI(manager,f->index) < cuddI(manager,cube->index). */
/* Check the cache. */
res = cuddCacheLookup2(manager, cuddBddBooleanDiffRecur, f, var);
if (res != NULL) {
return(res);
}
/* Compute the cofactors of f. */
T = cuddT(f); E = cuddE(f);
res1 = cuddBddBooleanDiffRecur(manager, T, var);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddBddBooleanDiffRecur(manager, Cudd_Regular(E), var);
if (res2 == NULL) {
Cudd_IterDerefBdd(manager, res1);
return(NULL);
}
cuddRef(res2);
/* ITE takes care of possible complementation of res1 and of the
** case in which res1 == res2. */
res = cuddBddIteRecur(manager, manager->vars[f->index], res1, res2);
if (res == NULL) {
Cudd_IterDerefBdd(manager, res1);
Cudd_IterDerefBdd(manager, res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
cuddCacheInsert2(manager, cuddBddBooleanDiffRecur, f, var, res);
return(res);
} /* end of cuddBddBooleanDiffRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step for Cudd_addIthBit.]
Description [Performs the recursive step for Cudd_addIthBit.
Returns a pointer to the BDD if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static DdNode *
addDoIthBit(
DdManager * dd,
DdNode * f,
DdNode * index)
{
DdNode *res, *T, *E;
DdNode *fv, *fvn;
int mask, value;
int v;
statLine(dd);
/* Check terminal case. */
if (cuddIsConstant(f)) {
mask = 1 << ((int) cuddV(index));
value = (int) cuddV(f);
return((value & mask) == 0 ? DD_ZERO(dd) : DD_ONE(dd));
}
/* Check cache. */
res = cuddCacheLookup2(dd,addDoIthBit,f,index);
if (res != NULL) return(res);
/* Recursive step. */
v = f->index;
fv = cuddT(f); fvn = cuddE(f);
T = addDoIthBit(dd,fv,index);
if (T == NULL) return(NULL);
cuddRef(T);
E = addDoIthBit(dd,fvn,index);
if (E == NULL) {
Cudd_RecursiveDeref(dd, T);
return(NULL);
}
cuddRef(E);
res = (T == E) ? T : cuddUniqueInter(dd,v,T,E);
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
cuddDeref(T);
cuddDeref(E);
/* Store result. */
cuddCacheInsert2(dd,addDoIthBit,f,index,res);
return(res);
} /* end of addDoIthBit */
/**Function********************************************************************
Synopsis [Checks whether a variable is dependent on others in a
function.]
Description [Checks whether a variable is dependent on others in a
function. Returns 1 if the variable is dependent; 0 otherwise. No
new nodes are created.]
SideEffects [None]
SeeAlso []
******************************************************************************/
int
Cudd_bddVarIsDependent(
DdManager *dd, /* manager */
DdNode *f, /* function */
DdNode *var /* variable */)
{
DdNode *F, *res, *zero, *ft, *fe;
unsigned topf, level;
DD_CTFP cacheOp;
int retval;
/* NuSMV: begin add */
abort(); /* NOT USED BY NUSMV */
/* NuSMV: begin end */
zero = Cudd_Not(DD_TRUE(dd));
if (Cudd_IsConstant(f)) return(f == zero);
/* From now on f is not constant. */
F = Cudd_Regular(f);
topf = (unsigned) dd->perm[F->index];
level = (unsigned) dd->perm[var->index];
/* Check terminal case. If topf > index of var, f does not depend on var.
** Therefore, var is not dependent in f. */
if (topf > level) {
return(0);
}
cacheOp = (DD_CTFP) Cudd_bddVarIsDependent;
res = cuddCacheLookup2(dd,cacheOp,f,var);
if (res != NULL) {
return(res != zero);
}
/* Compute cofactors. */
ft = Cudd_NotCond(cuddT(F), f != F);
fe = Cudd_NotCond(cuddE(F), f != F);
if (topf == level) {
retval = Cudd_bddLeq(dd,ft,Cudd_Not(fe));
} else {
retval = Cudd_bddVarIsDependent(dd,ft,var) &&
Cudd_bddVarIsDependent(dd,fe,var);
}
cuddCacheInsert2(dd,cacheOp,f,var,Cudd_NotCond(zero,retval));
return(retval);
} /* Cudd_bddVarIsDependent */
/**Function********************************************************************
Synopsis [Determines whether f is less than or equal to g.]
Description [Returns 1 if f is less than or equal to g; 0 otherwise.
No new nodes are created. This procedure works for arbitrary ADDs.
For 0-1 ADDs Cudd_addEvalConst is more efficient.]
SideEffects [None]
SeeAlso [Cudd_addIteConstant Cudd_addEvalConst Cudd_bddLeq]
******************************************************************************/
int
Cudd_addLeq(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *tmp, *fv, *fvn, *gv, *gvn;
unsigned int topf, topg, res;
/* Terminal cases. */
if (f == g) return(1);
statLine(dd);
if (cuddIsConstant(f)) {
if (cuddIsConstant(g)) return(cuddV(f) <= cuddV(g));
if (f == DD_MINUS_INFINITY(dd)) return(1);
if (f == DD_PLUS_INFINITY(dd)) return(0); /* since f != g */
}
if (g == DD_PLUS_INFINITY(dd)) return(1);
if (g == DD_MINUS_INFINITY(dd)) return(0); /* since f != g */
/* Check cache. */
tmp = cuddCacheLookup2(dd,(DD_CTFP)Cudd_addLeq,f,g);
if (tmp != NULL) {
return(tmp == DD_ONE(dd));
}
/* Compute cofactors. One of f and g is not constant. */
topf = cuddI(dd,f->index);
topg = cuddI(dd,g->index);
if (topf <= topg) {
fv = cuddT(f); fvn = cuddE(f);
} else {
fv = fvn = f;
}
if (topg <= topf) {
gv = cuddT(g); gvn = cuddE(g);
} else {
gv = gvn = g;
}
res = Cudd_addLeq(dd,fvn,gvn) && Cudd_addLeq(dd,fv,gv);
/* Store result in cache and return. */
cuddCacheInsert2(dd,(DD_CTFP) Cudd_addLeq,f,g,
Cudd_NotCond(DD_ONE(dd),res==0));
return(res);
} /* end of Cudd_addLeq */
/**
@brief Performs the recursive step of addScalarInverse.
@return a pointer to the resulting %ADD in case of success. Returns
NULL if any discriminants smaller than epsilon is encountered.
@sideeffect None
*/
DdNode *
cuddAddScalarInverseRecur(
DdManager * dd,
DdNode * f,
DdNode * epsilon)
{
DdNode *t, *e, *res;
CUDD_VALUE_TYPE value;
statLine(dd);
if (cuddIsConstant(f)) {
if (ddAbs(cuddV(f)) < cuddV(epsilon)) return(NULL);
value = 1.0 / cuddV(f);
res = cuddUniqueConst(dd,value);
return(res);
}
res = cuddCacheLookup2(dd,Cudd_addScalarInverse,f,epsilon);
if (res != NULL) return(res);
checkWhetherToGiveUp(dd);
t = cuddAddScalarInverseRecur(dd,cuddT(f),epsilon);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddAddScalarInverseRecur(dd,cuddE(f),epsilon);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddRef(e);
res = (t == e) ? t : cuddUniqueInter(dd,(int)f->index,t,e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, t);
Cudd_RecursiveDeref(dd, e);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
cuddCacheInsert2(dd,Cudd_addScalarInverse,f,epsilon,res);
return(res);
} /* end of cuddAddScalarInverseRecur */
/**
@brief Implements the recursive step of Cudd_bddClippingAnd.
@details Takes the conjunction of two BDDs.
@return a pointer to the result is successful; NULL otherwise.
@sideeffect None
@see cuddBddClippingAnd
*/
static DdNode *
cuddBddClippingAndRecur(
DdManager * manager,
DdNode * f,
DdNode * g,
int distance,
int direction)
{
DdNode *F, *ft, *fe, *G, *gt, *ge;
DdNode *one, *zero, *r, *t, *e;
int topf, topg;
unsigned int index;
DD_CTFP cacheOp;
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 == g || g == one) return(f);
if (f == one) return(g);
if (distance == 0) {
/* One last attempt at returning the right result. We sort of
** cheat by calling Cudd_bddLeq. */
if (Cudd_bddLeq(manager,f,g)) return(f);
if (Cudd_bddLeq(manager,g,f)) return(g);
if (direction == 1) {
if (Cudd_bddLeq(manager,f,Cudd_Not(g)) ||
Cudd_bddLeq(manager,g,Cudd_Not(f))) return(zero);
}
return(Cudd_NotCond(one,(direction == 0)));
}
/* At this point f and g are not constant. */
distance--;
/* Check cache. Try to increase cache efficiency by sorting the
** pointers. */
if (f > g) {
DdNode *tmp = f;
f = g; g = tmp;
}
F = Cudd_Regular(f);
G = Cudd_Regular(g);
cacheOp = (DD_CTFP)
(direction ? Cudd_bddClippingAnd : cuddBddClippingAnd);
if (F->ref != 1 || G->ref != 1) {
r = cuddCacheLookup2(manager, cacheOp, f, g);
if (r != NULL) return(r);
}
checkWhetherToGiveUp(manager);
/* 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];
/* Compute cofactors. */
if (topf <= topg) {
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 <= topf) {
gt = cuddT(G);
ge = cuddE(G);
if (Cudd_IsComplement(g)) {
gt = Cudd_Not(gt);
ge = Cudd_Not(ge);
}
} else {
gt = ge = g;
}
t = cuddBddClippingAndRecur(manager, ft, gt, distance, direction);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddClippingAndRecur(manager, fe, ge, distance, direction);
if (e == NULL) {
Cudd_RecursiveDeref(manager, t);
return(NULL);
}
cuddRef(e);
if (t == e) {
r = t;
} 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)
cuddCacheInsert2(manager, cacheOp, f, g, r);
return(r);
} /* end of cuddBddClippingAndRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addUnivAbstract.]
Description [Performs the recursive step of Cudd_addUnivAbstract.
Returns the ADD obtained by abstracting the variables of cube from f,
if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddAddUnivAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * cube)
{
DdNode *T, *E, *res, *res1, *res2, *one, *zero;
statLine(manager);
one = DD_ONE(manager);
zero = DD_ZERO(manager);
/* Cube is guaranteed to be a cube at this point.
** zero and one are the only constatnts c such that c*c=c.
*/
if (f == zero || f == one || cube == one) {
return(f);
}
/* Abstract a variable that does not appear in f. */
if (cuddI(manager,f->index) > cuddI(manager,cube->index)) {
res1 = cuddAddUnivAbstractRecur(manager, f, cuddT(cube));
if (res1 == NULL) return(NULL);
cuddRef(res1);
/* Use the "internal" procedure to be alerted in case of
** dynamic reordering. If dynamic reordering occurs, we
** have to abort the entire abstraction.
*/
res = cuddAddApplyRecur(manager, Cudd_addTimes, res1, res1);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(manager,res1);
cuddDeref(res);
return(res);
}
if ((res = cuddCacheLookup2(manager, Cudd_addUnivAbstract, f, cube)) != NULL) {
return(res);
}
T = cuddT(f);
E = cuddE(f);
/* If the two indices are the same, so are their levels. */
if (f->index == cube->index) {
res1 = cuddAddUnivAbstractRecur(manager, T, cuddT(cube));
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddAddUnivAbstractRecur(manager, E, cuddT(cube));
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = cuddAddApplyRecur(manager, Cudd_addTimes, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
cuddCacheInsert2(manager, Cudd_addUnivAbstract, f, cube, res);
cuddDeref(res);
return(res);
} else { /* if (cuddI(manager,f->index) < cuddI(manager,cube->index)) */
res1 = cuddAddUnivAbstractRecur(manager, T, cube);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddAddUnivAbstractRecur(manager, E, cube);
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = (res1 == res2) ? res1 :
cuddUniqueInter(manager, (int) f->index, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
cuddCacheInsert2(manager, Cudd_addUnivAbstract, f, cube, res);
return(res);
}
} /* end of cuddAddUnivAbstractRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_addOrAbstract.]
Description [Performs the recursive step of Cudd_addOrAbstract.
Returns the ADD obtained by abstracting the variables of cube from f,
if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
DdNode *
cuddAddOrAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * cube)
{
DdNode *T, *E, *res, *res1, *res2, *one;
statLine(manager);
one = DD_ONE(manager);
/* Cube is guaranteed to be a cube at this point. */
if (cuddIsConstant(f) || cube == one) {
return(f);
}
/* Abstract a variable that does not appear in f. */
if (cuddI(manager,f->index) > cuddI(manager,cube->index)) {
res = cuddAddOrAbstractRecur(manager, f, cuddT(cube));
return(res);
}
if ((res = cuddCacheLookup2(manager, Cudd_addOrAbstract, f, cube)) != NULL) {
return(res);
}
T = cuddT(f);
E = cuddE(f);
/* If the two indices are the same, so are their levels. */
if (f->index == cube->index) {
res1 = cuddAddOrAbstractRecur(manager, T, cuddT(cube));
if (res1 == NULL) return(NULL);
cuddRef(res1);
if (res1 != one) {
res2 = cuddAddOrAbstractRecur(manager, E, cuddT(cube));
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = cuddAddApplyRecur(manager, Cudd_addOr, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddRef(res);
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
} else {
res = res1;
}
cuddCacheInsert2(manager, Cudd_addOrAbstract, f, cube, res);
cuddDeref(res);
return(res);
} else { /* if (cuddI(manager,f->index) < cuddI(manager,cube->index)) */
res1 = cuddAddOrAbstractRecur(manager, T, cube);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddAddOrAbstractRecur(manager, E, cube);
if (res2 == NULL) {
Cudd_RecursiveDeref(manager,res1);
return(NULL);
}
cuddRef(res2);
res = (res1 == res2) ? res1 :
cuddUniqueInter(manager, (int) f->index, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(manager,res1);
Cudd_RecursiveDeref(manager,res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
cuddCacheInsert2(manager, Cudd_addOrAbstract, f, cube, res);
return(res);
}
} /* end of cuddAddOrAbstractRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step for Cudd_addBddIthBit.]
Description [Performs the recursive step for Cudd_addBddIthBit.
Returns a pointer to the BDD if successful; NULL otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static DdNode *
addBddDoIthBit(
DdManager * dd,
DdNode * f,
DdNode * index)
{
DdNode *res, *T, *E;
DdNode *fv, *fvn;
/* NuSMV: add begin */
ptrint mask, value;
/* WAS: long mask, value; */
/* NuSMV: add end */
int v;
statLine(dd);
/* Check terminal case. */
if (cuddIsConstant(f)) {
/* NuSMV: add begin */
mask = 1 << ((ptrint) cuddV(index));
value = (ptrint) cuddV(f);
/* WAS: mask = 1 << ((long) cuddV(index));
value = (long) cuddV(f); */
/* NuSMV: add end */
return(Cudd_NotCond(DD_TRUE(dd),(value & mask) == 0));
}
/* Check cache. */
res = cuddCacheLookup2(dd,addBddDoIthBit,f,index);
if (res != NULL) return(res);
/* Recursive step. */
v = f->index;
fv = cuddT(f); fvn = cuddE(f);
T = addBddDoIthBit(dd,fv,index);
if (T == NULL) return(NULL);
cuddRef(T);
E = addBddDoIthBit(dd,fvn,index);
if (E == NULL) {
Cudd_RecursiveDeref(dd, T);
return(NULL);
}
cuddRef(E);
if (Cudd_IsComplement(T)) {
res = (T == E) ? Cudd_Not(T) : cuddUniqueInter(dd,v,Cudd_Not(T),Cudd_Not(E));
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
res = Cudd_Not(res);
} else {
res = (T == E) ? T : cuddUniqueInter(dd,v,T,E);
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
}
cuddDeref(T);
cuddDeref(E);
/* Store result. */
cuddCacheInsert2(dd,addBddDoIthBit,f,index,res);
return(res);
} /* end of addBddDoIthBit */
/**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 */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_bddAnd.]
Description [Implements the recursive step of Cudd_bddAnd by taking
the conjunction of two BDDs. Returns a pointer to the result is
successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddAnd]
******************************************************************************/
DdNode *
cuddBddAndRecur(
DdManager * manager,
DdNode * f,
DdNode * g)
{
DdNode *F, *fv, *fnv, *G, *gv, *gnv;
DdNode *one, *r, *t, *e;
unsigned int topf, topg, index;
statLine(manager);
one = DD_ONE(manager);
/* Terminal cases. */
F = Cudd_Regular(f);
G = Cudd_Regular(g);
if (F == G) {
if (f == g) return(f);
else return(Cudd_Not(one));
}
if (F == one) {
if (f == one) return(g);
else return(f);
}
if (G == one) {
if (g == one) return(f);
else return(g);
}
/* At this point f and g are not constant. */
if (cuddF2L(f) > cuddF2L(g)) { /* Try to increase cache efficiency. */
DdNode *tmp = f;
f = g;
g = tmp;
F = Cudd_Regular(f);
G = Cudd_Regular(g);
}
/* Check cache. */
if (F->ref != 1 || G->ref != 1) {
r = cuddCacheLookup2(manager, Cudd_bddAnd, f, g);
if (r != NULL) return(r);
}
if ( manager->TimeStop && Abc_Clock() > manager->TimeStop )
return NULL;
/* 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];
/* Compute cofactors. */
if (topf <= topg) {
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 <= topf) {
gv = cuddT(G);
gnv = cuddE(G);
if (Cudd_IsComplement(g)) {
gv = Cudd_Not(gv);
gnv = Cudd_Not(gnv);
}
} else {
gv = gnv = g;
}
t = cuddBddAndRecur(manager, fv, gv);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddAndRecur(manager, fnv, gnv);
if (e == NULL) {
Cudd_IterDerefBdd(manager, t);
return(NULL);
}
cuddRef(e);
if (t == e) {
r = t;
} 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);
if (F->ref != 1 || G->ref != 1)
cuddCacheInsert2(manager, Cudd_bddAnd, f, g, r);
return(r);
} /* end of cuddBddAndRecur */
/**Function********************************************************************
Synopsis [Performs the recursive steps of Cudd_bddExistAbstract.]
Description [Performs the recursive steps of Cudd_bddExistAbstract.
Returns the BDD obtained by abstracting the variables
of cube from f if successful; NULL otherwise. It is also used by
Cudd_bddUnivAbstract.]
SideEffects [None]
SeeAlso [Cudd_bddExistAbstract Cudd_bddUnivAbstract]
******************************************************************************/
DdNode *
cuddBddExistAbstractRecur(
DdManager * manager,
DdNode * f,
DdNode * cube)
{
DdNode *F, *T, *E, *res, *res1, *res2, *one;
statLine(manager);
one = DD_ONE(manager);
F = Cudd_Regular(f);
/* Cube is guaranteed to be a cube at this point. */
if (cube == one || F == one) {
return(f);
}
/* From now on, f and cube are non-constant. */
/* Abstract a variable that does not appear in f. */
while (manager->perm[F->index] > manager->perm[cube->index]) {
cube = cuddT(cube);
if (cube == one) return(f);
}
/* Check the cache. */
if (F->ref != 1 && (res = cuddCacheLookup2(manager, Cudd_bddExistAbstract, f, cube)) != NULL) {
return(res);
}
/* Compute the cofactors of f. */
T = cuddT(F); E = cuddE(F);
if (f != F) {
T = Cudd_Not(T); E = Cudd_Not(E);
}
/* If the two indices are the same, so are their levels. */
if (F->index == cube->index) {
if (T == one || E == one || T == Cudd_Not(E)) {
return(one);
}
res1 = cuddBddExistAbstractRecur(manager, T, cuddT(cube));
if (res1 == NULL) return(NULL);
if (res1 == one) {
if (F->ref != 1)
cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, one);
return(one);
}
cuddRef(res1);
res2 = cuddBddExistAbstractRecur(manager, E, cuddT(cube));
if (res2 == NULL) {
Cudd_IterDerefBdd(manager,res1);
return(NULL);
}
cuddRef(res2);
res = cuddBddAndRecur(manager, Cudd_Not(res1), Cudd_Not(res2));
if (res == NULL) {
Cudd_IterDerefBdd(manager, res1);
Cudd_IterDerefBdd(manager, res2);
return(NULL);
}
res = Cudd_Not(res);
cuddRef(res);
Cudd_IterDerefBdd(manager, res1);
Cudd_IterDerefBdd(manager, res2);
if (F->ref != 1)
cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, res);
cuddDeref(res);
return(res);
} else { /* if (cuddI(manager,F->index) < cuddI(manager,cube->index)) */
res1 = cuddBddExistAbstractRecur(manager, T, cube);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddBddExistAbstractRecur(manager, E, cube);
if (res2 == NULL) {
Cudd_IterDerefBdd(manager, res1);
return(NULL);
}
cuddRef(res2);
/* ITE takes care of possible complementation of res1 and of the
** case in which res1 == res2. */
res = cuddBddIteRecur(manager, manager->vars[F->index], res1, res2);
if (res == NULL) {
Cudd_IterDerefBdd(manager, res1);
Cudd_IterDerefBdd(manager, res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
if (F->ref != 1)
cuddCacheInsert2(manager, Cudd_bddExistAbstract, f, cube, res);
return(res);
}
} /* end of cuddBddExistAbstractRecur */
/**Function********************************************************************
Synopsis [Performs the recursive steps of Extra_bddSpaceFromFunction.]
Description []
SideEffects []
SeeAlso []
******************************************************************************/
DdNode * extraBddSpaceFromFunction( DdManager * dd, DdNode * bF, DdNode * bG )
{
DdNode * bRes;
DdNode * bFR, * bGR;
bFR = Cudd_Regular( bF );
bGR = Cudd_Regular( bG );
if ( cuddIsConstant(bFR) )
{
if ( bF == bG )
return b1;
else
return b0;
}
if ( cuddIsConstant(bGR) )
return b0;
// both bFunc and bCore are not constants
// the operation is commutative - normalize the problem
if ( (unsigned)(ABC_PTRUINT_T)bF > (unsigned)(ABC_PTRUINT_T)bG )
return extraBddSpaceFromFunction(dd, bG, bF);
if ( (bRes = cuddCacheLookup2(dd, extraBddSpaceFromFunction, bF, bG)) )
return bRes;
else
{
DdNode * bF0, * bF1;
DdNode * bG0, * bG1;
DdNode * bTemp1, * bTemp2;
DdNode * bRes0, * bRes1;
int LevelF, LevelG;
int index;
LevelF = dd->perm[bFR->index];
LevelG = dd->perm[bGR->index];
if ( LevelF <= LevelG )
{
index = dd->invperm[LevelF];
if ( bFR != bF )
{
bF0 = Cudd_Not( cuddE(bFR) );
bF1 = Cudd_Not( cuddT(bFR) );
}
else
{
bF0 = cuddE(bFR);
bF1 = cuddT(bFR);
}
}
else
{
index = dd->invperm[LevelG];
bF0 = bF1 = bF;
}
if ( LevelG <= LevelF )
{
if ( bGR != bG )
{
bG0 = Cudd_Not( cuddE(bGR) );
bG1 = Cudd_Not( cuddT(bGR) );
}
else
{
bG0 = cuddE(bGR);
bG1 = cuddT(bGR);
}
}
else
bG0 = bG1 = bG;
bTemp1 = extraBddSpaceFromFunction( dd, bF0, bG0 );
if ( bTemp1 == NULL )
return NULL;
cuddRef( bTemp1 );
bTemp2 = extraBddSpaceFromFunction( dd, bF1, bG1 );
if ( bTemp2 == NULL )
{
Cudd_RecursiveDeref( dd, bTemp1 );
return NULL;
}
cuddRef( bTemp2 );
bRes0 = cuddBddAndRecur( dd, bTemp1, bTemp2 );
if ( bRes0 == NULL )
{
Cudd_RecursiveDeref( dd, bTemp1 );
Cudd_RecursiveDeref( dd, bTemp2 );
return NULL;
}
cuddRef( bRes0 );
Cudd_RecursiveDeref( dd, bTemp1 );
Cudd_RecursiveDeref( dd, bTemp2 );
bTemp1 = extraBddSpaceFromFunction( dd, bF0, bG1 );
if ( bTemp1 == NULL )
{
Cudd_RecursiveDeref( dd, bRes0 );
return NULL;
}
cuddRef( bTemp1 );
bTemp2 = extraBddSpaceFromFunction( dd, bF1, bG0 );
if ( bTemp2 == NULL )
{
Cudd_RecursiveDeref( dd, bRes0 );
Cudd_RecursiveDeref( dd, bTemp1 );
return NULL;
}
cuddRef( bTemp2 );
bRes1 = cuddBddAndRecur( dd, bTemp1, bTemp2 );
if ( bRes1 == NULL )
{
Cudd_RecursiveDeref( dd, bRes0 );
Cudd_RecursiveDeref( dd, bTemp1 );
Cudd_RecursiveDeref( dd, bTemp2 );
return NULL;
}
cuddRef( bRes1 );
Cudd_RecursiveDeref( dd, bTemp1 );
Cudd_RecursiveDeref( dd, bTemp2 );
// consider the case when Res0 and Res1 are the same node
if ( bRes0 == bRes1 )
bRes = bRes1;
// consider the case when Res1 is complemented
else if ( Cudd_IsComplement(bRes1) )
{
bRes = cuddUniqueInter(dd, index, Cudd_Not(bRes1), Cudd_Not(bRes0));
if ( bRes == NULL )
{
Cudd_RecursiveDeref(dd,bRes0);
Cudd_RecursiveDeref(dd,bRes1);
return NULL;
}
bRes = Cudd_Not(bRes);
}
else
{
bRes = cuddUniqueInter( dd, index, bRes1, bRes0 );
if ( bRes == NULL )
{
Cudd_RecursiveDeref(dd,bRes0);
Cudd_RecursiveDeref(dd,bRes1);
return NULL;
}
}
cuddDeref( bRes0 );
cuddDeref( bRes1 );
// insert the result into cache
cuddCacheInsert2(dd, extraBddSpaceFromFunction, bF, bG, bRes);
return bRes;
}
} /* end of extraBddSpaceFromFunction */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_bddIntersect.]
Description []
SideEffects [None]
SeeAlso [Cudd_bddIntersect]
******************************************************************************/
DdNode *
cuddBddIntersectRecur(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res;
DdNode *F, *G, *t, *e;
DdNode *fv, *fnv, *gv, *gnv;
DdNode *one, *zero;
unsigned int index, topf, topg;
statLine(dd);
one = DD_ONE(dd);
zero = Cudd_Not(one);
/* Terminal cases. */
if (f == zero || g == zero || f == Cudd_Not(g)) return(zero);
if (f == g || g == one) return(f);
if (f == one) return(g);
/* At this point f and g are not constant. */
if (cuddF2L(f) > cuddF2L(g)) { DdNode *tmp = f; f = g; g = tmp; }
res = cuddCacheLookup2(dd,Cudd_bddIntersect,f,g);
if (res != NULL) return(res);
/* Find splitting variable. Here we can skip the use of cuddI,
** because the operands are known to be non-constant.
*/
F = Cudd_Regular(f);
topf = dd->perm[F->index];
G = Cudd_Regular(g);
topg = dd->perm[G->index];
/* Compute cofactors. */
if (topf <= topg) {
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 <= topf) {
gv = cuddT(G);
gnv = cuddE(G);
if (Cudd_IsComplement(g)) {
gv = Cudd_Not(gv);
gnv = Cudd_Not(gnv);
}
} else {
gv = gnv = g;
}
/* Compute partial results. */
t = cuddBddIntersectRecur(dd,fv,gv);
if (t == NULL) return(NULL);
cuddRef(t);
if (t != zero) {
e = zero;
} else {
e = cuddBddIntersectRecur(dd,fnv,gnv);
if (e == NULL) {
Cudd_IterDerefBdd(dd, t);
return(NULL);
}
}
cuddRef(e);
if (t == e) { /* both equal zero */
res = t;
} else if (Cudd_IsComplement(t)) {
res = cuddUniqueInter(dd,(int)index,Cudd_Not(t),Cudd_Not(e));
if (res == NULL) {
Cudd_IterDerefBdd(dd, t);
Cudd_IterDerefBdd(dd, e);
return(NULL);
}
res = Cudd_Not(res);
} else {
res = cuddUniqueInter(dd,(int)index,t,e);
if (res == NULL) {
Cudd_IterDerefBdd(dd, t);
Cudd_IterDerefBdd(dd, e);
return(NULL);
}
}
cuddDeref(e);
cuddDeref(t);
cuddCacheInsert2(dd,Cudd_bddIntersect,f,g,res);
return(res);
} /* end of cuddBddIntersectRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cudd_CProjection.]
Description [Performs the recursive step of Cudd_CProjection. Returns
the projection if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_CProjection]
******************************************************************************/
DdNode *
cuddCProjectionRecur(
DdManager * dd,
DdNode * R,
DdNode * Y,
DdNode * Ysupp)
{
DdNode *res, *res1, *res2, *resA;
DdNode *r, *y, *RT, *RE, *YT, *YE, *Yrest, *Ra, *Ran, *Gamma, *Alpha;
unsigned int topR, topY, top, index;
DdNode *one = DD_ONE(dd);
statLine(dd);
if (Y == one) return(R);
#ifdef DD_DEBUG
assert(!Cudd_IsConstant(Y));
#endif
if (R == Cudd_Not(one)) return(R);
res = cuddCacheLookup2(dd, Cudd_CProjection, R, Y);
if (res != NULL) return(res);
r = Cudd_Regular(R);
topR = cuddI(dd,r->index);
y = Cudd_Regular(Y);
topY = cuddI(dd,y->index);
top = ddMin(topR, topY);
/* Compute the cofactors of R */
if (topR == top) {
index = r->index;
RT = cuddT(r);
RE = cuddE(r);
if (r != R) {
RT = Cudd_Not(RT); RE = Cudd_Not(RE);
}
} else {
RT = RE = R;
}
if (topY > top) {
/* Y does not depend on the current top variable.
** We just need to compute the results on the two cofactors of R
** and make them the children of a node labeled r->index.
*/
res1 = cuddCProjectionRecur(dd,RT,Y,Ysupp);
if (res1 == NULL) return(NULL);
cuddRef(res1);
res2 = cuddCProjectionRecur(dd,RE,Y,Ysupp);
if (res2 == NULL) {
Cudd_RecursiveDeref(dd,res1);
return(NULL);
}
cuddRef(res2);
res = cuddBddIteRecur(dd, dd->vars[index], res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
Cudd_RecursiveDeref(dd,res2);
return(NULL);
}
/* If we have reached this point, res1 and res2 are now
** incorporated in res. cuddDeref is therefore sufficient.
*/
cuddDeref(res1);
cuddDeref(res2);
} else {
/* Compute the cofactors of Y */
index = y->index;
YT = cuddT(y);
YE = cuddE(y);
if (y != Y) {
YT = Cudd_Not(YT); YE = Cudd_Not(YE);
}
if (YT == Cudd_Not(one)) {
Alpha = Cudd_Not(dd->vars[index]);
Yrest = YE;
Ra = RE;
Ran = RT;
} else {
Alpha = dd->vars[index];
Yrest = YT;
Ra = RT;
Ran = RE;
}
Gamma = cuddBddExistAbstractRecur(dd,Ra,cuddT(Ysupp));
if (Gamma == NULL) return(NULL);
if (Gamma == one) {
res1 = cuddCProjectionRecur(dd,Ra,Yrest,cuddT(Ysupp));
if (res1 == NULL) return(NULL);
cuddRef(res1);
res = cuddBddAndRecur(dd, Alpha, res1);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
return(NULL);
}
cuddDeref(res1);
} else if (Gamma == Cudd_Not(one)) {
res1 = cuddCProjectionRecur(dd,Ran,Yrest,cuddT(Ysupp));
if (res1 == NULL) return(NULL);
cuddRef(res1);
res = cuddBddAndRecur(dd, Cudd_Not(Alpha), res1);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
return(NULL);
}
cuddDeref(res1);
} else {
cuddRef(Gamma);
resA = cuddCProjectionRecur(dd,Ran,Yrest,cuddT(Ysupp));
if (resA == NULL) {
Cudd_RecursiveDeref(dd,Gamma);
return(NULL);
}
cuddRef(resA);
res2 = cuddBddAndRecur(dd, Cudd_Not(Gamma), resA);
if (res2 == NULL) {
Cudd_RecursiveDeref(dd,Gamma);
Cudd_RecursiveDeref(dd,resA);
return(NULL);
}
cuddRef(res2);
Cudd_RecursiveDeref(dd,Gamma);
Cudd_RecursiveDeref(dd,resA);
res1 = cuddCProjectionRecur(dd,Ra,Yrest,cuddT(Ysupp));
if (res1 == NULL) {
Cudd_RecursiveDeref(dd,res2);
return(NULL);
}
cuddRef(res1);
res = cuddBddIteRecur(dd, Alpha, res1, res2);
if (res == NULL) {
Cudd_RecursiveDeref(dd,res1);
Cudd_RecursiveDeref(dd,res2);
return(NULL);
}
cuddDeref(res1);
cuddDeref(res2);
}
}
cuddCacheInsert2(dd,Cudd_CProjection,R,Y,res);
return(res);
} /* end of cuddCProjectionRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Extra_bddCheckVarsSymmetric().]
Description [Returns b0 if the variables are not symmetric. Returns b1 if the
variables can be symmetric. The variables are represented in the form of a
two-variable cube. In case the cube contains one variable (below Var1 level),
the cube's pointer is complemented if the variable Var1 occurred on the
current path; otherwise, the cube's pointer is regular. Uses additional
complemented bit (Hash_Not) to mark the result if in the BDD rooted that this
node there is a branch passing though the node labeled with Var2.]
SideEffects []
SeeAlso []
******************************************************************************/
DdNode * extraBddCheckVarsSymmetric(
DdManager * dd, /* the DD manager */
DdNode * bF,
DdNode * bVars)
{
DdNode * bRes;
if ( bF == b0 )
return b1;
assert( bVars != b1 );
if ( (bRes = cuddCacheLookup2(dd, extraBddCheckVarsSymmetric, bF, bVars)) )
return bRes;
else
{
DdNode * bRes0, * bRes1;
DdNode * bF0, * bF1;
DdNode * bFR = Cudd_Regular(bF);
int LevelF = cuddI(dd,bFR->index);
DdNode * bVarsR = Cudd_Regular(bVars);
int fVar1Pres;
int iLev1;
int iLev2;
if ( bVarsR != bVars ) // cube's pointer is complemented
{
assert( cuddT(bVarsR) == b1 );
fVar1Pres = 1; // the first var is present on the path
iLev1 = -1; // we are already below the first var level
iLev2 = dd->perm[bVarsR->index]; // the level of the second var
}
else // cube's pointer is NOT complemented
{
fVar1Pres = 0; // the first var is absent on the path
if ( cuddT(bVars) == b1 )
{
iLev1 = -1; // we are already below the first var level
iLev2 = dd->perm[bVars->index]; // the level of the second var
}
else
{
assert( cuddT(cuddT(bVars)) == b1 );
iLev1 = dd->perm[bVars->index]; // the level of the first var
iLev2 = dd->perm[cuddT(bVars)->index]; // the level of the second var
}
}
// cofactor the function
// the cofactors are needed only if we are above the second level
if ( LevelF < iLev2 )
{
if ( bFR != bF ) // bFunc is complemented
{
bF0 = Cudd_Not( cuddE(bFR) );
bF1 = Cudd_Not( cuddT(bFR) );
}
else
{
bF0 = cuddE(bFR);
bF1 = cuddT(bFR);
}
}
else
bF0 = bF1 = NULL;
// consider five cases:
// (1) F is above iLev1
// (2) F is on the level iLev1
// (3) F is between iLev1 and iLev2
// (4) F is on the level iLev2
// (5) F is below iLev2
// (1) F is above iLev1
if ( LevelF < iLev1 )
{
// the returned result cannot have the hash attribute
// because we still did not reach the level of Var1;
// the attribute never travels above the level of Var1
bRes0 = extraBddCheckVarsSymmetric( dd, bF0, bVars );
// assert( !Hash_IsComplement( bRes0 ) );
assert( bRes0 != z0 );
if ( bRes0 == b0 )
bRes = b0;
else
bRes = extraBddCheckVarsSymmetric( dd, bF1, bVars );
// assert( !Hash_IsComplement( bRes ) );
assert( bRes != z0 );
}
// (2) F is on the level iLev1
else if ( LevelF == iLev1 )
{
bRes0 = extraBddCheckVarsSymmetric( dd, bF0, Cudd_Not( cuddT(bVars) ) );
if ( bRes0 == b0 )
bRes = b0;
else
{
bRes1 = extraBddCheckVarsSymmetric( dd, bF1, Cudd_Not( cuddT(bVars) ) );
if ( bRes1 == b0 )
bRes = b0;
else
{
// if ( Hash_IsComplement( bRes0 ) || Hash_IsComplement( bRes1 ) )
if ( bRes0 == z0 || bRes1 == z0 )
bRes = b1;
else
bRes = b0;
}
}
}
// (3) F is between iLev1 and iLev2
else if ( LevelF < iLev2 )
{
bRes0 = extraBddCheckVarsSymmetric( dd, bF0, bVars );
if ( bRes0 == b0 )
bRes = b0;
else
{
bRes1 = extraBddCheckVarsSymmetric( dd, bF1, bVars );
if ( bRes1 == b0 )
bRes = b0;
else
{
// if ( Hash_IsComplement( bRes0 ) || Hash_IsComplement( bRes1 ) )
// bRes = Hash_Not( b1 );
if ( bRes0 == z0 || bRes1 == z0 )
bRes = z0;
else
bRes = b1;
}
}
}
// (4) F is on the level iLev2
else if ( LevelF == iLev2 )
{
// this is the only place where the hash attribute (Hash_Not) can be added
// to the result; it can be added only if the path came through the node
// lebeled with Var1; therefore, the hash attribute cannot be returned
// to the caller function
if ( fVar1Pres )
// bRes = Hash_Not( b1 );
bRes = z0;
else
bRes = b0;
}
// (5) F is below iLev2
else // if ( LevelF > iLev2 )
{
// it is possible that the path goes through the node labeled by Var1
// and still everything is okay; we do not label with Hash_Not here
// because the path does not go through node labeled by Var2
bRes = b1;
}
cuddCacheInsert2(dd, extraBddCheckVarsSymmetric, bF, bVars, bRes);
return bRes;
}
} /* end of extraBddCheckVarsSymmetric */
/**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 [Performs the recursive step of
Cudd_bddLiteralSetIntersection.]
Description [Performs the recursive step of
Cudd_bddLiteralSetIntersection. Scans the cubes for common variables,
and checks whether they agree in phase. Returns a pointer to the
resulting cube if successful; NULL otherwise.]
SideEffects [None]
******************************************************************************/
DdNode *
cuddBddLiteralSetIntersectionRecur(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *res, *tmp;
DdNode *F, *G;
DdNode *fc, *gc;
DdNode *one;
DdNode *zero;
unsigned int topf, topg, comple;
int phasef, phaseg;
statLine(dd);
if (f == g) return(f);
F = Cudd_Regular(f);
G = Cudd_Regular(g);
one = DD_ONE(dd);
/* Here f != g. If F == G, then f and g are complementary.
** Since they are two cubes, this case only occurs when f == v,
** g == v', and v is a variable or its complement.
*/
if (F == G) return(one);
zero = Cudd_Not(one);
topf = cuddI(dd,F->index);
topg = cuddI(dd,G->index);
/* Look for a variable common to both cubes. If there are none, this
** loop will stop when the constant node is reached in both cubes.
*/
while (topf != topg) {
if (topf < topg) { /* move down on f */
comple = f != F;
f = cuddT(F);
if (comple) f = Cudd_Not(f);
if (f == zero) {
f = cuddE(F);
if (comple) f = Cudd_Not(f);
}
F = Cudd_Regular(f);
topf = cuddI(dd,F->index);
} else if (topg < topf) {
comple = g != G;
g = cuddT(G);
if (comple) g = Cudd_Not(g);
if (g == zero) {
g = cuddE(G);
if (comple) g = Cudd_Not(g);
}
G = Cudd_Regular(g);
topg = cuddI(dd,G->index);
}
}
/* At this point, f == one <=> g == 1. It suffices to test one of them. */
if (f == one) return(one);
res = cuddCacheLookup2(dd,Cudd_bddLiteralSetIntersection,f,g);
if (res != NULL) {
return(res);
}
/* Here f and g are both non constant and have the same top variable. */
comple = f != F;
fc = cuddT(F);
phasef = 1;
if (comple) fc = Cudd_Not(fc);
if (fc == zero) {
fc = cuddE(F);
phasef = 0;
if (comple) fc = Cudd_Not(fc);
}
comple = g != G;
gc = cuddT(G);
phaseg = 1;
if (comple) gc = Cudd_Not(gc);
if (gc == zero) {
gc = cuddE(G);
phaseg = 0;
if (comple) gc = Cudd_Not(gc);
}
tmp = cuddBddLiteralSetIntersectionRecur(dd,fc,gc);
if (tmp == NULL) {
return(NULL);
}
if (phasef != phaseg) {
res = tmp;
} else {
cuddRef(tmp);
if (phasef == 0) {
res = cuddBddAndRecur(dd,Cudd_Not(dd->vars[F->index]),tmp);
} else {
res = cuddBddAndRecur(dd,dd->vars[F->index],tmp);
}
if (res == NULL) {
Cudd_RecursiveDeref(dd,tmp);
return(NULL);
}
cuddDeref(tmp); /* Just cuddDeref, because it is included in result */
}
cuddCacheInsert2(dd,Cudd_bddLiteralSetIntersection,f,g,res);
return(res);
} /* end of cuddBddLiteralSetIntersectionRecur */
/**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 [Performs the recursive step of Cuddaux_addConstrain.]
Description [Performs the recursive step of Cuddaux_addConstrain.
Returns a pointer to the result if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cuddaux_addConstrain]
******************************************************************************/
DdNode *
cuddauxAddConstrainRecur(
DdManager * dd,
DdNode * f,
DdNode * c)
{
DdNode *Fv, *Fnv, *Cv, *Cnv, *t, *e, *res;
DdNode *one, *zero;
unsigned int topf, topc;
int index;
one = DD_ONE(dd);
zero = Cudd_Not(one);
/* Trivial cases. */
if (c == one) return(f);
if (c == zero){
fprintf(stderr,"CuddauxAddConstrainRecur: warning: false careset\n");
return(DD_BACKGROUND(dd));
}
if (Cudd_IsConstant(f)) return(f);
/* Now f and c are non-constant. */
/* Check the cache. */
res = cuddCacheLookup2(dd, Cuddaux_addConstrain, f, c);
if (res != NULL) {
return(res);
}
/* Recursive step. */
topf = dd->perm[f->index];
topc = dd->perm[Cudd_Regular(c)->index];
if (topf <= topc) {
index = f->index;
Fv = cuddT(f); Fnv = cuddE(f);
} else {
index = Cudd_Regular(c)->index;
Fv = Fnv = f;
}
if (topc <= topf) {
Cv = Cudd_T(c); Cnv = Cudd_E(c);
if (Cudd_IsComplement(c)) {
Cv = Cudd_Not(Cv); Cnv = Cudd_Not(Cnv);
}
} else {
Cv = Cnv = c;
}
if (!Cudd_IsConstant(Cv)) {
t = cuddauxAddConstrainRecur(dd, Fv, Cv);
if (t == NULL)
return(NULL);
}
else if (Cv == one) {
t = Fv;
}
else { /* Cv == zero: return Fnv @ Cnv */
if (Cnv == one) {
res = Fnv;
}
else {
res = cuddauxAddConstrainRecur(dd, Fnv, Cnv);
if (res == NULL)
return(NULL);
}
return(res);
}
cuddRef(t);
if (!Cudd_IsConstant(Cnv)) {
e = cuddauxAddConstrainRecur(dd, Fnv, Cnv);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
}
else if (Cnv == one) {
e = Fnv;
}
else { /* Cnv == zero: return Fv @ Cv previously computed */
cuddDeref(t);
return(t);
}
cuddRef(e);
res = (t == e) ? t : cuddUniqueInter(dd, index, t, e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, e);
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
cuddCacheInsert2(dd, Cuddaux_addConstrain, f, c, res);
return(res);
} /* end of cuddauxAddConstrainRecur */
/**Function********************************************************************
Synopsis [Performs the recursive step of Cuddaux_addRestrict.]
Description [Performs the recursive step of Cuddaux_addRestrict.
Returns the restricted ADD if successful; otherwise NULL.]
SideEffects [None]
SeeAlso [Cudd_addRestrict]
******************************************************************************/
DdNode *
cuddauxAddRestrictRecur(
DdManager * dd,
DdNode * f,
DdNode * c)
{
DdNode *Fv, *Fnv, *Cv, *Cnv, *t, *e, *res, *one, *zero;
unsigned int topf, topc;
int index;
one = DD_ONE(dd);
zero = Cudd_Not(one);
/* Trivial cases */
if (c == one) return(f);
if (c == zero){
fprintf(stderr,"CuddauxAddRestrictRecur: warning: false careset\n");
return(DD_BACKGROUND(dd));
}
if (Cudd_IsConstant(f)) return(f);
/* Now f and c are non-constant. */
/* Check the cache. */
res = cuddCacheLookup2(dd, Cuddaux_addRestrict, f, c);
if (res != NULL) {
return(res);
}
topf = dd->perm[f->index];
topc = dd->perm[Cudd_Regular(c)->index];
if (topc < topf) { /* abstract top variable from c */
DdNode *d, *s1, *s2;
/* Take the OR by applying DeMorgan. */
/* Find complements of cofactors of c. */
if (Cudd_IsComplement(c)) {
s1 = cuddT(Cudd_Regular(c));
s2 = cuddE(Cudd_Regular(c));
} else {
s1 = Cudd_Not(cuddT(c));
s2 = Cudd_Not(cuddE(c));
}
/* Take the AND and negate */
d = cuddBddAndRecur(dd, s1, s2);
if (d == NULL) return(NULL);
d = Cudd_Not(d);
cuddRef(d);
res = cuddauxAddRestrictRecur(dd, f, d);
if (res == NULL) {
Cudd_IterDerefBdd(dd, d);
return(NULL);
}
cuddRef(res);
Cudd_IterDerefBdd(dd, d);
cuddDeref(res);
cuddCacheInsert2(dd, Cuddaux_addRestrict, f, c, res);
return(res);
}
/* Recursive step. Here topf <= topc. */
index = f->index;
Fv = cuddT(f); Fnv = cuddE(f);
if (topc == topf) {
Cv = Cudd_T(c); Cnv = Cudd_E(c);
if (Cudd_IsComplement(c)) {
Cv = Cudd_Not(Cv); Cnv = Cudd_Not(Cnv);
}
} else {
Cv = Cnv = c;
}
if (!Cudd_IsConstant(Cv)) {
t = cuddauxAddRestrictRecur(dd, Fv, Cv);
if (t == NULL) return(NULL);
}
else if (Cv == one) {
t = Fv;
}
else { /* Cv == zero: return(Fnv @ Cnv) */
if (Cnv == one) {
res = Fnv;
}
else {
res = cuddauxAddRestrictRecur(dd, Fnv, Cnv);
if (res == NULL) return(NULL);
}
return(res);
}
cuddRef(t);
if (!Cudd_IsConstant(Cnv)) {
e = cuddauxAddRestrictRecur(dd, Fnv, Cnv);
if (e == NULL) {
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
} else if (Cnv == one) {
e = Fnv;
} else { /* Cnv == zero: return (Fv @ Cv) previously computed */
cuddDeref(t);
return(t);
}
cuddRef(e);
res = (t == e) ? t : cuddUniqueInter(dd, index, t, e);
if (res == NULL) {
Cudd_RecursiveDeref(dd, e);
Cudd_RecursiveDeref(dd, t);
return(NULL);
}
cuddDeref(t);
cuddDeref(e);
cuddCacheInsert2(dd, Cuddaux_addRestrict, f, c, res);
return(res);
} /* end of cuddauxAddRestrictRecur */
/**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 [Performs the recursive step of Cudd_addApply.]
Description [Performs the recursive step of Cudd_addApply. Returns a
pointer to the result if successful; NULL otherwise.]
SideEffects [None]
SeeAlso [cuddAddMonadicApplyRecur]
******************************************************************************/
DdNode *
cuddAddApplyRecur(
DdManager * dd,
DdNode * (*op)(DdManager *, DdNode **, DdNode **),
DdNode * f,
DdNode * g)
{
DdNode *res,
*fv, *fvn, *gv, *gvn,
*T, *E;
unsigned int ford, gord;
unsigned int index;
DdNode *(*cacheOp)(DdManager *, DdNode *, DdNode *);
/* Check terminal cases. Op may swap f and g to increase the
* cache hit rate.
*/
statLine(dd);
res = (*op)(dd,&f,&g);
if (res != NULL) return(res);
/* Check cache. */
cacheOp = (DdNode *(*)(DdManager *, DdNode *, DdNode *)) op;
res = cuddCacheLookup2(dd,cacheOp,f,g);
if (res != NULL) return(res);
/* Recursive step. */
ford = cuddI(dd,f->index);
gord = cuddI(dd,g->index);
if (ford <= gord) {
index = f->index;
fv = cuddT(f);
fvn = cuddE(f);
} else {
index = g->index;
fv = fvn = f;
}
if (gord <= ford) {
gv = cuddT(g);
gvn = cuddE(g);
} else {
gv = gvn = g;
}
T = cuddAddApplyRecur(dd,op,fv,gv);
if (T == NULL) return(NULL);
cuddRef(T);
E = cuddAddApplyRecur(dd,op,fvn,gvn);
if (E == NULL) {
Cudd_RecursiveDeref(dd,T);
return(NULL);
}
cuddRef(E);
res = (T == E) ? T : cuddUniqueInter(dd,(int)index,T,E);
if (res == NULL) {
Cudd_RecursiveDeref(dd, T);
Cudd_RecursiveDeref(dd, E);
return(NULL);
}
cuddDeref(T);
cuddDeref(E);
/* Store result. */
cuddCacheInsert2(dd,cacheOp,f,g,res);
return(res);
} /* end of cuddAddApplyRecur */
/**Function********************************************************************
Synopsis [Performs a recursive step of Extra_bddReduceVarSet.]
Description [Returns the set of all variables in the given set that are not in the
support of the given function.]
SideEffects []
SeeAlso []
******************************************************************************/
DdNode * extraBddReduceVarSet(
DdManager * dd, /* the DD manager */
DdNode * bVars, /* the set of variables to be reduced */
DdNode * bF) /* the function whose support is used for reduction */
{
DdNode * bRes;
DdNode * bFR = Cudd_Regular(bF);
if ( cuddIsConstant(bFR) || bVars == b1 )
return bVars;
if ( (bRes = cuddCacheLookup2(dd, extraBddReduceVarSet, bVars, bF)) )
return bRes;
else
{
DdNode * bF0, * bF1;
DdNode * bVarsThis, * bVarsLower, * bTemp;
int LevelF;
// if LevelF is below LevelV, scroll through the vars in bVars
LevelF = dd->perm[bFR->index];
for ( bVarsThis = bVars; LevelF > cuddI(dd,bVarsThis->index); bVarsThis = cuddT(bVarsThis) );
// scroll also through the current var, because it should be not be added
if ( LevelF == cuddI(dd,bVarsThis->index) )
bVarsLower = cuddT(bVarsThis);
else
bVarsLower = bVarsThis;
// cofactor the function
if ( bFR != bF ) // bFunc is complemented
{
bF0 = Cudd_Not( cuddE(bFR) );
bF1 = Cudd_Not( cuddT(bFR) );
}
else
{
bF0 = cuddE(bFR);
bF1 = cuddT(bFR);
}
// solve subproblems
bRes = extraBddReduceVarSet( dd, bVarsLower, bF0 );
if ( bRes == NULL )
return NULL;
cuddRef( bRes );
bRes = extraBddReduceVarSet( dd, bTemp = bRes, bF1 );
if ( bRes == NULL )
{
Cudd_RecursiveDeref( dd, bTemp );
return NULL;
}
cuddRef( bRes );
Cudd_RecursiveDeref( dd, bTemp );
// the current var should not be added
// add the skipped vars
if ( bVarsThis != bVars )
{
DdNode * bVarsExtra;
// extract the skipped variables
bVarsExtra = cuddBddExistAbstractRecur( dd, bVars, bVarsThis );
if ( bVarsExtra == NULL )
{
Cudd_RecursiveDeref( dd, bRes );
return NULL;
}
cuddRef( bVarsExtra );
// add these variables
bRes = cuddBddAndRecur( dd, bTemp = bRes, bVarsExtra );
if ( bRes == NULL )
{
Cudd_RecursiveDeref( dd, bTemp );
Cudd_RecursiveDeref( dd, bVarsExtra );
return NULL;
}
cuddRef( bRes );
Cudd_RecursiveDeref( dd, bTemp );
Cudd_RecursiveDeref( dd, bVarsExtra );
}
cuddDeref( bRes );
cuddCacheInsert2( dd, extraBddReduceVarSet, bVars, bF, bRes );
return bRes;
}
} /* end of extraBddReduceVarSet */
/**Function********************************************************************
Synopsis [Implements the recursive step of Cudd_bddXor.]
Description [Implements the recursive step of Cudd_bddXor by taking
the exclusive OR of two BDDs. Returns a pointer to the result is
successful; NULL otherwise.]
SideEffects [None]
SeeAlso [Cudd_bddXor]
******************************************************************************/
DdNode *
cuddBddXorRecur(
DdManager * manager,
DdNode * f,
DdNode * g)
{
DdNode *fv, *fnv, *G, *gv, *gnv;
DdNode *one, *zero, *r, *t, *e;
unsigned int topf, topg, 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 (cuddF2L(f) > cuddF2L(g)) { /* Try to increase cache efficiency and simplify tests. */
DdNode *tmp = f;
f = g;
g = tmp;
}
if (g == zero) return(f);
if (g == one) return(Cudd_Not(f));
if (Cudd_IsComplement(f)) {
f = Cudd_Not(f);
g = Cudd_Not(g);
}
/* Now the first argument is regular. */
if (f == one) return(Cudd_Not(g));
/* At this point f and g are not constant. */
/* Check cache. */
r = cuddCacheLookup2(manager, Cudd_bddXor, f, g);
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];
G = Cudd_Regular(g);
topg = manager->perm[G->index];
/* Compute cofactors. */
if (topf <= topg) {
index = f->index;
fv = cuddT(f);
fnv = cuddE(f);
} else {
index = G->index;
fv = fnv = f;
}
if (topg <= topf) {
gv = cuddT(G);
gnv = cuddE(G);
if (Cudd_IsComplement(g)) {
gv = Cudd_Not(gv);
gnv = Cudd_Not(gnv);
}
} else {
gv = gnv = g;
}
t = cuddBddXorRecur(manager, fv, gv);
if (t == NULL) return(NULL);
cuddRef(t);
e = cuddBddXorRecur(manager, fnv, gnv);
if (e == NULL) {
Cudd_IterDerefBdd(manager, t);
return(NULL);
}
cuddRef(e);
if (t == e) {
r = t;
} 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);
cuddCacheInsert2(manager, Cudd_bddXor, f, g, r);
return(r);
} /* end of cuddBddXorRecur */
/**Function********************************************************************
Synopsis [Determines whether f is less than or equal to g.]
Description [Returns 1 if f is less than or equal to g; 0 otherwise.
No new nodes are created.]
SideEffects [None]
SeeAlso [Cudd_bddIteConstant Cudd_addEvalConst]
******************************************************************************/
int
Cudd_bddLeq(
DdManager * dd,
DdNode * f,
DdNode * g)
{
DdNode *one, *zero, *tmp, *F, *fv, *fvn, *gv, *gvn;
unsigned int topf, topg, res;
statLine(dd);
/* Terminal cases and normalization. */
if (f == g) return(1);
if (Cudd_IsComplement(g)) {
/* Special case: if f is regular and g is complemented,
** f(1,...,1) = 1 > 0 = g(1,...,1).
*/
if (!Cudd_IsComplement(f)) return(0);
/* Both are complemented: Swap and complement because
** f <= g <=> g' <= f' and we want the second argument to be regular.
*/
tmp = g;
g = Cudd_Not(f);
f = Cudd_Not(tmp);
} else if (Cudd_IsComplement(f) && cuddF2L(g) < cuddF2L(f)) {
tmp = g;
g = Cudd_Not(f);
f = Cudd_Not(tmp);
}
/* Now g is regular and, if f is not regular, f < g. */
one = DD_ONE(dd);
if (g == one) return(1); /* no need to test against zero */
if (f == one) return(0); /* since at this point g != one */
if (Cudd_Not(f) == g) return(0); /* because neither is constant */
zero = Cudd_Not(one);
if (f == zero) return(1);
/* Here neither f nor g is constant. */
/* Check cache. */
tmp = cuddCacheLookup2(dd,(DD_CTFP)Cudd_bddLeq,f,g);
if (tmp != NULL) {
return(tmp == one);
}
/* Compute cofactors. */
F = Cudd_Regular(f);
topf = dd->perm[F->index];
topg = dd->perm[g->index];
if (topf <= topg) {
fv = cuddT(F); fvn = cuddE(F);
if (f != F) {
fv = Cudd_Not(fv);
fvn = Cudd_Not(fvn);
}
} else {
fv = fvn = f;
}
if (topg <= topf) {
gv = cuddT(g); gvn = cuddE(g);
} else {
gv = gvn = g;
}
/* Recursive calls. Since we want to maximize the probability of
** the special case f(1,...,1) > g(1,...,1), we consider the negative
** cofactors first. Indeed, the complementation parity of the positive
** cofactors is the same as the one of the parent functions.
*/
res = Cudd_bddLeq(dd,fvn,gvn) && Cudd_bddLeq(dd,fv,gv);
/* Store result in cache and return. */
cuddCacheInsert2(dd,(DD_CTFP)Cudd_bddLeq,f,g,(res ? one : zero));
return(res);
} /* end of Cudd_bddLeq */
/**Function********************************************************************
Synopsis [Performs the reordering-sensitive step of Extra_bddHaar().]
Description [Generates in a bottom-up fashion an ADD for all spectral
coefficients of the functions represented by a BDD.]
SideEffects []
SeeAlso []
******************************************************************************/
DdNode* extraBddHaar(
DdManager * dd, /* the manager */
DdNode * bFunc, /* the function whose spectrum is being computed */
DdNode * bVars) /* the variables on which the function depends */
{
DdNode * aRes;
statLine(dd);
/* terminal cases */
if ( bVars == b1 )
{
assert( Cudd_IsConstant(bFunc) );
if ( bFunc == b0 )
return a0;
else
return a1;
}
/* check cache */
// if ( bFunc->ref != 1 )
if ( aRes = cuddCacheLookup2(dd, extraBddHaar, bFunc, bVars) )
return aRes;
else
{
DdNode * bFunc0, * bFunc1; /* cofactors of the function */
DdNode * aHaar0, * aHaar1; /* partial solutions of the problem */
DdNode * aNode0, * aNode1; /* the special terminal nodes */
DdNode * aRes0, * aRes1; /* partial results to be composed by ITE */
DdNode * bFuncR = Cudd_Regular(bFunc); /* the regular pointer to the function */
DdNode * aTemp;
double dValue0, dValue1;
/* bFunc cannot depend on a variable that is not in bVars */
assert( cuddI(dd,bFuncR->index) >= cuddI(dd,bVars->index) );
/* cofactor the BDD */
if ( bFuncR->index == bVars->index )
{
if ( bFuncR != bFunc ) /* bFunc is complemented */
{
bFunc0 = Cudd_Not( cuddE(bFuncR) );
bFunc1 = Cudd_Not( cuddT(bFuncR) );
}
else
{
bFunc0 = cuddE(bFuncR);
bFunc1 = cuddT(bFuncR);
}
}
else /* bVars is higher in the variable order */
bFunc0 = bFunc1 = bFunc;
/* solve subproblems */
aHaar0 = extraBddHaar( dd, bFunc0, cuddT(bVars) );
if ( aHaar0 == NULL )
return NULL;
cuddRef( aHaar0 );
aHaar1 = extraBddHaar( dd, bFunc1, cuddT(bVars) );
if ( aHaar1 == NULL )
{
Cudd_RecursiveDeref( dd, aHaar0 );
return NULL;
}
cuddRef( aHaar1 );
/* retrieve the terminal values in aHaar0 and aHaar1 */
for ( aTemp = aHaar0; aTemp->index != CUDD_CONST_INDEX; aTemp = cuddE(aTemp) );
dValue0 = cuddV( aTemp );
for ( aTemp = aHaar1; aTemp->index != CUDD_CONST_INDEX; aTemp = cuddE(aTemp) );
dValue1 = cuddV( aTemp );
/* get the new terminal nodes */
aNode0 = cuddUniqueConst( dd, dValue0 + dValue1 );
if ( aNode0 == NULL )
{
Cudd_RecursiveDeref( dd, aHaar0 );
Cudd_RecursiveDeref( dd, aHaar1 );
return NULL;
}
cuddRef( aNode0 );
aNode1 = cuddUniqueConst( dd, dValue0 - dValue1 );
if ( aNode1 == NULL )
{
Cudd_RecursiveDeref( dd, aHaar0 );
Cudd_RecursiveDeref( dd, aHaar1 );
Cudd_RecursiveDeref( dd, aNode0 );
return NULL;
}
cuddRef( aNode1 );
/* replace the terminal nodes in the cofactor ADDs */
aRes0 = extraAddUpdateZeroCubeValue( dd, aHaar0, cuddT(bVars), aNode0 );
if ( aRes0 == NULL )
{
Cudd_RecursiveDeref( dd, aHaar0 );
Cudd_RecursiveDeref( dd, aHaar1 );
Cudd_RecursiveDeref( dd, aNode0 );
Cudd_RecursiveDeref( dd, aNode1 );
return NULL;
}
cuddRef( aRes0 );
aRes1 = extraAddUpdateZeroCubeValue( dd, aHaar1, cuddT(bVars), aNode1 );
if ( aRes1 == NULL )
{
Cudd_RecursiveDeref( dd, aHaar0 );
Cudd_RecursiveDeref( dd, aHaar1 );
Cudd_RecursiveDeref( dd, aNode0 );
Cudd_RecursiveDeref( dd, aNode1 );
Cudd_RecursiveDeref( dd, aRes0 );
return NULL;
}
cuddRef( aRes1 );
Cudd_RecursiveDeref(dd, aHaar0);
Cudd_RecursiveDeref(dd, aHaar1);
Cudd_RecursiveDeref(dd, aNode0);
Cudd_RecursiveDeref(dd, aNode1);
/* 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, bVars->index, aRes1, aRes0 );
if (aRes == NULL)
{
Cudd_RecursiveDeref(dd, aRes1);
Cudd_RecursiveDeref(dd, aRes0);
return NULL;
}
cuddDeref(aRes1);
cuddDeref(aRes0);
/* insert the result into cache */
// if ( bFunc->ref != 1 )
cuddCacheInsert2(dd, extraBddHaar, bFunc, bVars, aRes);
return aRes;
}
} /* end of extraBddHaar */
