C++ DD_ZERO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 [Performs the recursive step of Cudd_zddChange.]

  Description []

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
DdNode *
cuddZddChangeAux(
  DdManager * zdd,
  DdNode * P,
  DdNode * zvar)
{
    int		top_var, level;
    DdNode	*res, *t, *e;
    DdNode	*base = DD_ONE(zdd);
    DdNode	*empty = DD_ZERO(zdd);

    statLine(zdd);
    if (P == empty)
	return(empty);
    if (P == base)
	return(zvar);

    /* Check cache. */
    res = cuddCacheLookup2Zdd(zdd, cuddZddChangeAux, P, zvar);
    if (res != NULL)
	return(res);

    top_var = zdd->permZ[P->index];
    level = zdd->permZ[zvar->index];

    if (top_var > level) {
	res = cuddZddGetNode(zdd, zvar->index, P, DD_ZERO(zdd));
	if (res == NULL) return(NULL);
    } else if (top_var == level) {
	res = cuddZddGetNode(zdd, zvar->index, cuddE(P), cuddT(P));
	if (res == NULL) return(NULL);
    } else {
	t = cuddZddChangeAux(zdd, cuddT(P), zvar);
	if (t == NULL) return(NULL);
	cuddRef(t);
	e = cuddZddChangeAux(zdd, cuddE(P), zvar);
	if (e == NULL) {
	    Cudd_RecursiveDerefZdd(zdd, t);
	    return(NULL);
	}
	cuddRef(e);
	res = cuddZddGetNode(zdd, P->index, t, e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(zdd, t);
	    Cudd_RecursiveDerefZdd(zdd, e);
	    return(NULL);
	}
	cuddDeref(t);
	cuddDeref(e);
    }

    cuddCacheInsert2(zdd, cuddZddChangeAux, P, zvar, res);

    return(res);

} /* end of cuddZddChangeAux */

/**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    [This operator sets f to the value of g wherever g != 0.]

  Description [This operator sets f to the value of g wherever g != 0.
  Returns NULL if not a terminal case; f op g otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

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

    F = *f; G = *g;
    if (F == DD_ZERO(dd)) return(G);
    if (G == DD_ZERO(dd)) return(F);
    if (cuddIsConstant(G)) return(G);
    return(NULL);

} /* end of Cudd_addSetNZ */

/**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    [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    [NAND of two 0-1 ADDs.]

  Description [NAND of two 0-1 ADDs. Returns NULL
  if not a terminal case; f NAND g otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

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

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

} /* end of Cudd_addNand */

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

  Synopsis [Performs the recursive step of Cudd_zddSubset1.]

  Description []

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static DdNode *
zdd_subset1_aux(
  DdManager * zdd,
  DdNode * P,
  DdNode * zvar)
{
    int		top_var, level;
    DdNode	*res, *t, *e;
    DdNode	*empty;

    statLine(zdd);
    empty = DD_ZERO(zdd);

    /* Check cache. */
    res = cuddCacheLookup2Zdd(zdd, zdd_subset1_aux, P, zvar);
    if (res != NULL)
	return(res);

    if (cuddIsConstant(P)) {
	res = empty;
	cuddCacheInsert2(zdd, zdd_subset1_aux, P, zvar, res);
	return(res);
    }

    top_var = zdd->permZ[P->index];
    level = zdd->permZ[zvar->index];

    if (top_var > level) {
        res = empty;
    } else if (top_var == level) {
	res = cuddT(P);
    } else {
        t = zdd_subset1_aux(zdd, cuddT(P), zvar);
	if (t == NULL) return(NULL);
	cuddRef(t);
        e = zdd_subset1_aux(zdd, cuddE(P), zvar);
	if (e == NULL) {
	    Cudd_RecursiveDerefZdd(zdd, t);
	    return(NULL);
	}
	cuddRef(e);
        res = cuddZddGetNode(zdd, P->index, t, e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(zdd, t);
	    Cudd_RecursiveDerefZdd(zdd, e);
	    return(NULL);
	}
	cuddDeref(t);
	cuddDeref(e);
    }

    cuddCacheInsert2(zdd, zdd_subset1_aux, P, zvar, res);

    return(res);

} /* end of zdd_subset1_aux */

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

  Synopsis    [Returns 1 if f &gt g and 0 otherwise.]

  Description [Returns 1 if f &gt g (both should be terminal cases) and 0 
  otherwise. Used in conjunction with Cudd_addApply. Returns NULL if not a 
  terminal case.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

******************************************************************************/
DdNode *
Cudd_addOneZeroMaximum(
  DdManager * dd,
  DdNode ** f,
  DdNode ** g)
{

    if (*g == DD_PLUS_INFINITY(dd))
	return DD_ZERO(dd);
    if (cuddIsConstant(*f) && cuddIsConstant(*g)) {
	if (cuddV(*f) > cuddV(*g)) {
	    return(DD_ONE(dd));
	} else {
	    return(DD_ZERO(dd));
	}
    }

    return(NULL);

} /* end of Cudd_addOneZeroMaximum */

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

  Synopsis    [Integer and floating point subtraction.]

  Description [Integer and floating point subtraction. Returns NULL if
  not a terminal case; f - g otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

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

    F = *f; G = *g;
    if (F == DD_ZERO(dd)) return(cuddAddNegateRecur(dd,G));
    if (G == DD_ZERO(dd)) return(F);
    if (cuddIsConstant(F) && cuddIsConstant(G)) {
	value = cuddV(F)-cuddV(G);
	res = cuddUniqueConst(dd,value);
	return(res);
    }
    return(NULL);

} /* end of Cudd_addMinus */

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

  Synopsis    [Integer and floating point division.]

  Description [Integer and floating point division. Returns NULL if not
  a terminal case; f / g otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

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

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

} /* end of Cudd_addDivide */

/**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    [Integer and floating point division.]

  Description [Integer and floating point division. Returns NULL if not
  a terminal case; f / g otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_addApply]

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

    F = *f; G = *g;
    /* We would like to use F == G -> F/G == 1, but F and G may
    ** contain zeroes. */
    if (F == DD_ZERO(dd)) return(DD_ZERO(dd));
    if (G == DD_ONE(dd)) return(F);
    if (cuddIsConstant(F) && cuddIsConstant(G)) {
	value = cuddV(F)/cuddV(G);
	res = cuddUniqueConst(dd,value);
	return(res);
    }
    return(NULL);

} /* end of Cudd_addDivide */

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

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

  Description [Checks whether cube is an ADD representing the product of
  positive literals. Returns 1 in case of success; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
addCheckPositiveCube(
  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) == DD_ZERO(manager)) {
        return(addCheckPositiveCube(manager, cuddT(cube)));
    }
    return(0);

} /* end of addCheckPositiveCube */

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

  Synopsis [Performs the inclusion test for ZDDs (P implies Q).]

  Description [Inclusion test for ZDDs (P implies Q). No new nodes are
  generated by this procedure. Returns empty if true;
  a valid pointer different from empty or DD_NON_CONSTANT otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_zddDiff]

******************************************************************************/
DdNode *
Cudd_zddDiffConst(
  DdManager * zdd,
  DdNode * P,
  DdNode * Q)
{
    int		p_top, q_top;
    DdNode	*empty = DD_ZERO(zdd), *t, *res;
    DdManager	*table = zdd;

    statLine(zdd);
    if (P == empty)
	return(empty);
    if (Q == empty)
	return(P);
    if (P == Q)
	return(empty);

    /* Check cache.  The cache is shared by cuddZddDiff(). */
    res = cuddCacheLookup2Zdd(table, cuddZddDiff, P, Q);
    if (res != NULL)
	return(res);

    if (cuddIsConstant(P))
	p_top = P->index;
    else
	p_top = zdd->permZ[P->index];
    if (cuddIsConstant(Q))
	q_top = Q->index;
    else
	q_top = zdd->permZ[Q->index];
    if (p_top < q_top) {
	res = DD_NON_CONSTANT;
    } else if (p_top > q_top) {
	res = Cudd_zddDiffConst(zdd, P, cuddE(Q));
    } else {
	t = Cudd_zddDiffConst(zdd, cuddT(P), cuddT(Q));
	if (t != empty)
	    res = DD_NON_CONSTANT;
	else
	    res = Cudd_zddDiffConst(zdd, cuddE(P), cuddE(Q));
    }

    cuddCacheInsert2(table, cuddZddDiff, P, Q, res);

    return(res);

} /* end of Cudd_zddDiffConst */