C++ DD_ONE函数代码示例

/**Function********************************************************************

  Synopsis    [Integer and floating point multiplication.]

  Description [Integer and floating point multiplication. Returns NULL
  if not a terminal case; f * g otherwise.  This function can be used also
  to take the AND of two 0-1 ADDs.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

******************************************************************************/
DdNode *
Cudd_addTimes(
  DdManager * dd,
  DdNode ** f,
  DdNode ** g)
{
    DdNode *res;
    DdNode *F, *G;
    CUDD_VALUE_TYPE value;

    F = *f; G = *g;
    if (F == DD_ZERO(dd) || G == DD_ZERO(dd)) return(DD_ZERO(dd));
    if (F == DD_ONE(dd)) return(G);
    if (G == DD_ONE(dd)) return(F);
    if (cuddIsConstant(F) && cuddIsConstant(G)) {
	value = cuddV(F)*cuddV(G);
	res = cuddUniqueConst(dd,value);
	return(res);
    }
    if (F > G) { /* swap f and g */
	*f = G;
	*g = F;
    }
    return(NULL);

} /* end of Cudd_addTimes */

/**Function********************************************************************

  Synopsis    [Comparison of a pair of functions to the i-th ADD variable.]

  Description [Comparison of a pair of functions to the i-th ADD
  variable. Returns 1 if the functions are the i-th ADD variable and its
  complement; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
DD_INLINE
static int
ddIsIthAddVarPair(
  DdManager * dd,
  DdNode * f,
  DdNode * g,
  unsigned int  i)
{
    return(f->index == i && g->index == i && 
	   cuddT(f) == DD_ONE(dd) && cuddE(f) == DD_ZERO(dd) &&
	   cuddT(g) == DD_ZERO(dd) && cuddE(g) == DD_ONE(dd));

} /* end of ddIsIthAddVarPair */

/**Function********************************************************************

  Synopsis [Checks whether cube is an BDD representing the product of
  positive literals.]

  Description [Returns 1 in case of success; 0 otherwise.]

  SideEffects [None]

******************************************************************************/
static int
bddCheckPositiveCube(
  DdManager * manager,
  DdNode * cube)
{
    if (Cudd_IsComplement(cube)) return(0);
    if (cube == DD_ONE(manager)) return(1);
    if (cuddIsConstant(cube)) return(0);
    if (cuddE(cube) == Cudd_Not(DD_ONE(manager))) {
        return(bddCheckPositiveCube(manager, cuddT(cube)));
    }
    return(0);

} /* end of bddCheckPositiveCube */

/**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 */

/**Function********************************************************************

  Synopsis    [Performs the recursive step of Cuddaux_Support.]

  Description [Performs the recursive step of Cuddaux_Support.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
DdNode*
cuddauxSupportRecur(DdManager* dd,
		    DdNode * f)
{
  DdNode *one, *fv, *fvn, *T,*E, *res, *res1;

  one = DD_ONE(dd);
  if (cuddIsConstant(f)) {
    return one;
  }
  fv = cuddT(f);
  fvn = Cudd_Regular(cuddE(f));
  if (cuddIsConstant(fv) && cuddIsConstant(fvn)){
    return dd->vars[f->index];
  }
  /* Look in the cache */
  res = cuddCacheLookup1(dd,Cuddaux_Support,f);
  if (res != NULL)
    return(res);

  T = cuddIsConstant(fv) ? one : cuddauxSupportRecur(dd,fv);
  if (T == NULL)
    return(NULL);
  cuddRef(T);
  E = cuddIsConstant(fvn) ? one : cuddauxSupportRecur(dd,fvn);
  if (E == NULL){
    Cudd_IterDerefBdd(dd,T);
    return(NULL);
  }
  if (T==E){
    res = cuddUniqueInter(dd,f->index,T,Cudd_Not(one));
    if (res == NULL){
      Cudd_IterDerefBdd(dd,T);
      return NULL;
    }
    cuddDeref(T);
  }
  else {
    cuddRef(E);
    res1 = cuddBddAndRecur(dd,T,E);
    if (res1 == NULL){
      Cudd_IterDerefBdd(dd,T);
      Cudd_IterDerefBdd(dd,E);
      return(NULL);
    }
    cuddRef(res1);
    Cudd_IterDerefBdd(dd,T);
    Cudd_IterDerefBdd(dd,E);
    res = cuddUniqueInter(dd,f->index,res1,Cudd_Not(one));
    if (res == NULL){
      Cudd_IterDerefBdd(dd,T);
      Cudd_IterDerefBdd(dd,E);
      Cudd_IterDerefBdd(dd,res1);
      return(NULL);
    }
    cuddDeref(res1);
  }
  cuddCacheInsert1(dd,Cuddaux_Support,f,res);
  return(res);
} /* end of cuddauxSupportRecur */

/**Function********************************************************************

  Synopsis [Computes the negative cofactor of a ZDD w.r.t. a variable.]

  Description [Computes the negative cofactor of a ZDD w.r.t. a
  variable. In terms of combinations, the result is the set of all
  combinations in which the variable is negated. Returns a pointer to
  the result if successful; NULL otherwise. cuddZddSubset0 performs
  the same function as Cudd_zddSubset0, but does not restart if
  reordering has taken place. Therefore it can be called from within a
  recursive procedure.]

  SideEffects [None]

  SeeAlso     [cuddZddSubset1 Cudd_zddSubset0]

******************************************************************************/
DdNode *
cuddZddSubset0(
  DdManager * dd,
  DdNode * P,
  int  var)
{
    DdNode	*zvar, *r;
    DdNode	*base, *empty;

    base = DD_ONE(dd);
    empty = DD_ZERO(dd);

    zvar = cuddUniqueInterZdd(dd, var, base, empty);
    if (zvar == NULL) {
	return(NULL);
    } else {
	cuddRef(zvar);
	r = zdd_subset0_aux(dd, P, zvar);
	if (r == NULL) {
	    Cudd_RecursiveDerefZdd(dd, zvar);
	    return(NULL);
	}
	cuddRef(r);
	Cudd_RecursiveDerefZdd(dd, zvar);
    }

    cuddDeref(r);
    return(r);

} /* end of cuddZddSubset0 */

/**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);
}

/**
  @brief Computes the boolean difference of f with respect to x.

  @details Computes the boolean difference of f with respect to the
  variable with index x.

  @return the %BDD of the boolean difference if successful; NULL
  otherwise.

  @sideeffect None

*/
DdNode *
Cudd_bddBooleanDiff(
  DdManager * manager,
  DdNode * f,
  int  x)
{
    DdNode *res, *var;

    /* If the variable is not currently in the manager, f cannot
    ** depend on it.
    */
    if (x >= manager->size) return(Cudd_Not(DD_ONE(manager)));
    var = manager->vars[x];

    do {
	manager->reordered = 0;
	res = cuddBddBooleanDiffRecur(manager, Cudd_Regular(f), var);
    } while (manager->reordered == 1);
    if (manager->errorCode == CUDD_TIMEOUT_EXPIRED && manager->timeoutHandler) {
        manager->timeoutHandler(manager, manager->tohArg);
    }

    return(res);

} /* end of Cudd_bddBooleanDiff */

/**Function********************************************************************

  Synopsis    [Performs the recursive step of Cudd_zddPrintCover.]

  Description []

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static void
zddPrintCoverAux(
  DdManager * zdd /* manager */,
  DdNode * node /* current node */,
  int  level /* depth in the recursion */,
  int * list /* current recursion path */)
{
    DdNode	*Nv, *Nnv;
    int		i, v;
    DdNode	*base = DD_ONE(zdd);

    if (Cudd_IsConstant(node)) {
	if (node == base) {
	    /* Check for missing variable. */
	    if (level != zdd->sizeZ) {
		list[zdd->invpermZ[level]] = 0;
		zddPrintCoverAux(zdd, node, level + 1, list);
		return;
	    }
	    /* Terminal case: Print one cube based on the current recursion
	    ** path.
	    */
	    for (i = 0; i < zdd->sizeZ; i += 2) {
		v = list[i] * 4 + list[i+1];
		if (v == 0)
		    (void) fprintf(zdd->out,"-");
		else if (v == 4)
		    (void) fprintf(zdd->out,"1");
		else if (v == 1)
		    (void) fprintf(zdd->out,"0");
		else
		    (void) fprintf(zdd->out,"@"); /* should never happen */
	    }
	    (void) fprintf(zdd->out," 1\n");
	}
    } else {
	/* Check for missing variable. */
	if (level != cuddIZ(zdd,node->index)) {
	    list[zdd->invpermZ[level]] = 0;
	    zddPrintCoverAux(zdd, node, level + 1, list);
	    return;
	}

	Nnv = cuddE(node);
	Nv = cuddT(node);
	if (Nv == Nnv) {
	    list[node->index] = 2;
	    zddPrintCoverAux(zdd, Nnv, level + 1, list);
	    return;
	}

	list[node->index] = 1;
	zddPrintCoverAux(zdd, Nv, level + 1, list);
	list[node->index] = 0;
	zddPrintCoverAux(zdd, Nnv, level + 1, list);
    }
    return;

} /* end of zddPrintCoverAux */

/**Function********************************************************************

  Synopsis    [Annotates every node in the BDD node with its minterm count.]

  Description [Annotates every node in the BDD node with its minterm count.
  In this function, every node and the minterm count represented by it are
  stored in a hash table.]

  SideEffects [Fills up 'table' with the pair <node,minterm_count>.]

******************************************************************************/
static double
bddAnnotateMintermCount(
  DdManager * manager,
  DdNode * node,
  double  max,
  st_table * table)
{

    DdNode *N,*Nv,*Nnv;
    register double min_v,min_nv;
    register double min_N;
    double *pmin;
    double *dummy;

    statLine(manager);
    N = Cudd_Regular(node);
    if (cuddIsConstant(N)) {
	if (node == DD_ONE(manager)) {
	    return(max);
	} else {
	    return(0.0);
	}
    }

    if (st_lookup(table, node, &dummy)) {
	return(*dummy);
    }	
  
    Nv = cuddT(N);
    Nnv = cuddE(N);
    if (N != node) {
	Nv = Cudd_Not(Nv);
	Nnv = Cudd_Not(Nnv);
    }

    /* Recur on the two branches. */
    min_v  = bddAnnotateMintermCount(manager,Nv,max,table) / 2.0;
    if (min_v == (double)CUDD_OUT_OF_MEM)
	return ((double)CUDD_OUT_OF_MEM);
    min_nv = bddAnnotateMintermCount(manager,Nnv,max,table) / 2.0;
    if (min_nv == (double)CUDD_OUT_OF_MEM)
	return ((double)CUDD_OUT_OF_MEM);
    min_N  = min_v + min_nv;

    pmin = ALLOC(double,1);
    if (pmin == NULL) {
	manager->errorCode = CUDD_MEMORY_OUT;
	return((double)CUDD_OUT_OF_MEM);
    }
    *pmin = min_N;

    if (st_insert(table,(char *)node, (char *)pmin) == ST_OUT_OF_MEM) {
	FREE(pmin);
	return((double)CUDD_OUT_OF_MEM);
    }
    
    return(min_N);

} /* end of bddAnnotateMintermCount */

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    [Reads in a sparse matrix.]

  Description [Reads in a sparse matrix specified in a simple format.
  The first line of the input contains the numbers of rows and columns.
  The remaining lines contain the elements of the matrix, one per line.
  Given a background value
  (specified by the background field of the manager), only the values
  different from it are explicitly listed.  Each foreground element is
  described by two integers, i.e., the row and column number, and a
  real number, i.e., the value.<p>
  Cudd_addRead produces an ADD that depends on two sets of variables: x
  and y.  The x variables (x\[0\] ... x\[nx-1\]) encode the row index and
  the y variables (y\[0\] ... y\[ny-1\]) encode the column index.
  x\[0\] and y\[0\] are the most significant bits in the indices.
  The variables may already exist or may be created by the function.
  The index of x\[i\] is bx+i*sx, and the index of y\[i\] is by+i*sy.<p>
  On input, nx and ny hold the numbers
  of row and column variables already in existence. On output, they
  hold the numbers of row and column variables actually used by the
  matrix. When Cudd_addRead creates the variable arrays,
  the index of x\[i\] is bx+i*sx, and the index of y\[i\] is by+i*sy.
  When some variables already exist Cudd_addRead expects the indices
  of the existing x variables to be bx+i*sx, and the indices of the
  existing y variables to be by+i*sy.<p>
  m and n are set to the numbers of rows and columns of the
  matrix.  Their values on input are immaterial.
  The ADD for the
  sparse matrix is returned in E, and its reference count is > 0.
  Cudd_addRead returns 1 in case of success; 0 otherwise.]

  SideEffects [nx and ny are set to the numbers of row and column
  variables. m and n are set to the numbers of rows and columns. x and y
  are possibly extended to represent the array of row and column
  variables. Similarly for xn and yn_, which hold on return from
  Cudd_addRead the complements of the row and column variables.]

  SeeAlso     [Cudd_addHarwell Cudd_bddRead]

******************************************************************************/
int
Cudd_addRead(
  FILE * fp /* input file pointer */,
  DdManager * dd /* DD manager */,
  DdNode ** E /* characteristic function of the graph */,
  DdNode *** x /* array of row variables */,
  DdNode *** y /* array of column variables */,
  DdNode *** xn /* array of complemented row variables */,
  DdNode *** yn_ /* array of complemented column variables */,
  int * nx /* number or row variables */,
  int * ny /* number or column variables */,
  int * m /* number of rows */,
  int * n /* number of columns */,
  int  bx /* first index of row variables */,
  int  sx /* step of row variables */,
  int  by /* first index of column variables */,
  int  sy /* step of column variables */)
{
    DdNode *one, *zero;
    DdNode *w, *neW;
    DdNode *minterm1;
    int u, v, err, i, nv;
    int lnx, lny;
    CUDD_VALUE_TYPE val;
    DdNode **lx, **ly, **lxn, **lyn;

    one = DD_ONE(dd);
    zero = DD_ZERO(dd);

    err = fscanf(fp, "%d %d", &u, &v);
    if (err == EOF) {
	return(0);
    } else if (err != 2) {
	return(0);
    }

    *m = u;
    /* Compute the number of x variables. */
    lx = *x; lxn = *xn;
    u--; 	/* row and column numbers start from 0 */
    for (lnx=0; u > 0; lnx++) {
	u >>= 1;
    }
    /* Here we rely on the fact that REALLOC of a null pointer is
    ** translates to an ALLOC.
    */
    if (lnx > *nx) {
	*x = lx = REALLOC(DdNode *, *x, lnx);
	if (lx == NULL) {
	    dd->errorCode = CUDD_MEMORY_OUT;
	    return(0);
	}
	*xn = lxn =  REALLOC(DdNode *, *xn, lnx);
	if (lxn == NULL) {
	    dd->errorCode = CUDD_MEMORY_OUT;
	    return(0);
	}
    }

/**Function********************************************************************

  Synopsis    [Recursive procedure to extract n mintems from constant 1.]

  Description [Recursive procedure to extract n mintems from constant 1.]

  SideEffects [None]

******************************************************************************/
static DdNode *
mintermsFromUniverse(
  DdManager * manager,
  DdNode ** vars,
  int  numVars,
  double  n,
  int  index)
{
    DdNode *one, *zero;
    DdNode *q, *result;
    double max, max2;
    
    statLine(manager);
    one = DD_ONE(manager);
    zero = Cudd_Not(one);

    max = pow(2.0, (double)numVars);
    max2 = max / 2.0;

    if (n == max)
	return(one);
    if (n == 0.0)
	return(zero);
    /* if n == 2^(numVars-1), return a single variable */
    if (n == max2)
	return vars[index];
    else if (n > max2) {
	/* When n > 2^(numVars-1), a single variable vars[index]
	** contains 2^(numVars-1) minterms. The rest are extracted
	** from a constant with 1 less variable.
	*/
	q = mintermsFromUniverse(manager,vars,numVars-1,(n-max2),index+1);
	if (q == NULL)
	    return(NULL);
	cuddRef(q);
	result = cuddBddIteRecur(manager,vars[index],one,q);
    } else {
	/* When n < 2^(numVars-1), a literal of variable vars[index]
	** is selected. The required n minterms are extracted from a
	** constant with 1 less variable.
	*/
	q = mintermsFromUniverse(manager,vars,numVars-1,n,index+1);
	if (q == NULL)
	    return(NULL);
	cuddRef(q);
	result = cuddBddAndRecur(manager,vars[index],q);
    }
    
    if (result == NULL) {
	Cudd_RecursiveDeref(manager,q);
	return(NULL);
    }
    cuddRef(result);
    Cudd_RecursiveDeref(manager,q);
    cuddDeref(result);
    return(result);

} /* end of mintermsFromUniverse */

/**Function********************************************************************

  Synopsis    [NOR of two 0-1 ADDs.]

  Description [NOR of two 0-1 ADDs. Returns NULL
  if not a terminal case; f NOR g otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

******************************************************************************/
DdNode *
Cudd_addNor(
  DdManager * dd,
  DdNode ** f,
  DdNode ** g)
{
    DdNode *F, *G;

    F = *f; G = *g;
    if (F == DD_ONE(dd) || G == DD_ONE(dd)) return(DD_ZERO(dd));
    if (cuddIsConstant(F) && cuddIsConstant(G)) return(DD_ONE(dd));
    if (F > G) { /* swap f and g */
	*f = G;
	*g = F;
    }
    return(NULL);

} /* end of Cudd_addNor */

/**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 */