C++ cuddCacheLookup2函数代码示例

/**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);
//.........这里部分代码省略.........

/**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);
//.........这里部分代码省略.........

/**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);
    }
//.........这里部分代码省略.........

/**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);
    }
//.........这里部分代码省略.........

/**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);
	}
//.........这里部分代码省略.........