tempest/resources/3rdparty/cudd-3.0.0/cudd/cuddZddFuncs.c

/**
  @file

  @ingroup cudd

  @brief Functions to manipulate covers represented as ZDDs.

  @author In-Ho Moon

  @copyright@parblock
  Copyright (c) 1995-2015, Regents of the University of Colorado

  All rights reserved.

  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions
  are met:

  Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

  Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.

  Neither the name of the University of Colorado nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
  @endparblock

*/

#include "util.h"
#include "cuddInt.h"

/*---------------------------------------------------------------------------*/
/* Constant declarations                                                     */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Stucture declarations                                                     */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Type declarations                                                         */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Variable declarations                                                     */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Macro declarations                                                        */
/*---------------------------------------------------------------------------*/

/** \cond */

/*---------------------------------------------------------------------------*/
/* Static function prototypes                                                */
/*---------------------------------------------------------------------------*/

/** \endcond */


/*---------------------------------------------------------------------------*/
/* Definition of exported functions                                          */
/*---------------------------------------------------------------------------*/


/**
  @brief Computes the product of two covers represented by ZDDs.

  @details The result is also a %ZDD.  The covers on which
  Cudd_zddProduct operates use two %ZDD variables for each function
  variable (one %ZDD variable for each literal of the variable). Those
  two %ZDD variables should be adjacent in the order.

  @return a pointer to the result if successful; NULL otherwise.

  @sideeffect None

  @see Cudd_zddUnateProduct

*/
DdNode	*
Cudd_zddProduct(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode	*res;

    do {
	dd->reordered = 0;
	res = cuddZddProduct(dd, f, g);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddProduct */


/**
  @brief Computes the product of two unate covers represented as ZDDs.

  @details Unate covers use one %ZDD variable for each %BDD
  variable.

  @return a pointer to the result if successful; NULL otherwise.

  @sideeffect None

  @see Cudd_zddProduct

*/
DdNode	*
Cudd_zddUnateProduct(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode	*res;

    do {
	dd->reordered = 0;
	res = cuddZddUnateProduct(dd, f, g);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddUnateProduct */


/**
  @brief Applies weak division to two covers.

  @details Applies weak division to two ZDDs representing two covers.
  The result of weak division depends on the variable order. The
  covers on which Cudd_zddWeakDiv operates use two %ZDD variables for
  each function variable (one %ZDD variable for each literal of the
  variable). Those two %ZDD variables should be adjacent in the order.

  @return a pointer to the %ZDD representing the result if successful;
  NULL otherwise.

  @sideeffect None

  @see Cudd_zddDivide

*/
DdNode	*
Cudd_zddWeakDiv(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode	*res;

    do {
	dd->reordered = 0;
	res = cuddZddWeakDiv(dd, f, g);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddWeakDiv */


/**
  @brief Computes the quotient of two unate covers.

  @details Computes the quotient of two unate covers represented by
  ZDDs.  Unate covers use one %ZDD variable for each %BDD variable.

  @return a pointer to the resulting %ZDD if successful; NULL
  otherwise.

  @sideeffect None

  @see Cudd_zddWeakDiv

*/
DdNode	*
Cudd_zddDivide(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode	*res;

    do {
	dd->reordered = 0;
	res = cuddZddDivide(dd, f, g);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddDivide */


/**
  @brief Modified version of Cudd_zddWeakDiv.

  @details This function may disappear in future releases.

  @sideeffect None

  @see Cudd_zddWeakDiv

*/
DdNode	*
Cudd_zddWeakDivF(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode	*res;

    do {
	dd->reordered = 0;
	res = cuddZddWeakDivF(dd, f, g);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddWeakDivF */


/**
  @brief Modified version of Cudd_zddDivide.

  @details This function may disappear in future releases.

  @sideeffect None

*/
DdNode	*
Cudd_zddDivideF(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode	*res;

    do {
	dd->reordered = 0;
	res = cuddZddDivideF(dd, f, g);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddDivideF */


/**
  @brief Computes a complement cover for a %ZDD node.

  @details For lack of a better method, we first extract the function
  %BDD from the %ZDD cover, then make the complement of the %ZDD cover
  from the complement of the %BDD node by using ISOP.  The result
  depends on current variable order.

  @return a pointer to the resulting cover if successful; NULL
  otherwise.

  @sideeffect The result depends on current variable order.

*/
DdNode	*
Cudd_zddComplement(
  DdManager *dd,
  DdNode *node)
{
    DdNode	*b, *isop, *zdd_I;

    /* Check cache */
    zdd_I = cuddCacheLookup1Zdd(dd, cuddZddComplement, node);
    if (zdd_I)
	return(zdd_I);

    b = Cudd_MakeBddFromZddCover(dd, node);
    if (!b)
	return(NULL);
    Cudd_Ref(b);
    isop = Cudd_zddIsop(dd, Cudd_Not(b), Cudd_Not(b), &zdd_I);
    if (!isop) {
	Cudd_RecursiveDeref(dd, b);
	return(NULL);
    }
    Cudd_Ref(isop);
    Cudd_Ref(zdd_I);
    Cudd_RecursiveDeref(dd, b);
    Cudd_RecursiveDeref(dd, isop);

    cuddCacheInsert1(dd, cuddZddComplement, node, zdd_I);
    Cudd_Deref(zdd_I);
    return(zdd_I);
} /* end of Cudd_zddComplement */


/*---------------------------------------------------------------------------*/
/* Definition of internal functions                                          */
/*---------------------------------------------------------------------------*/


/**
  @brief Performs the recursive step of Cudd_zddProduct.

  @sideeffect None

  @see Cudd_zddProduct

*/
DdNode	*
cuddZddProduct(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    int		v;
    int		top_f, top_g;
    DdNode	*tmp, *term1, *term2, *term3;
    DdNode	*f0, *f1, *fd, *g0, *g1, *gd;
    DdNode	*R0, *R1, *Rd, *N0, *N1;
    DdNode	*r;
    DdNode	*one = DD_ONE(dd);
    DdNode	*zero = DD_ZERO(dd);
    int		flag;
    int		pv, nv;

    statLine(dd);
    if (f == zero || g == zero)
        return(zero);
    if (f == one)
        return(g);
    if (g == one)
        return(f);

    top_f = dd->permZ[f->index];
    top_g = dd->permZ[g->index];

    if (top_f > top_g)
	return(cuddZddProduct(dd, g, f));

    /* Check cache */
    r = cuddCacheLookup2Zdd(dd, cuddZddProduct, f, g);
    if (r)
	return(r);

    v = (int) f->index;	/* either yi or zi */
    flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
    if (flag == 1)
	return(NULL);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    Cudd_Ref(fd);
    flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
    if (flag == 1) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	return(NULL);
    }
    Cudd_Ref(g1);
    Cudd_Ref(g0);
    Cudd_Ref(gd);
    pv = cuddZddGetPosVarIndex(dd, v);
    nv = cuddZddGetNegVarIndex(dd, v);

    Rd = cuddZddProduct(dd, fd, gd);
    if (Rd == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, gd);
	return(NULL);
    }
    Cudd_Ref(Rd);

    term1 = cuddZddProduct(dd, f0, g0);
    if (term1 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, Rd);
	return(NULL);
    }
    Cudd_Ref(term1);
    term2 = cuddZddProduct(dd, f0, gd);
    if (term2 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, Rd);
	Cudd_RecursiveDerefZdd(dd, term1);
	return(NULL);
    }
    Cudd_Ref(term2);
    term3 = cuddZddProduct(dd, fd, g0);
    if (term3 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, Rd);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	return(NULL);
    }
    Cudd_Ref(term3);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, g0);
    tmp = cuddZddUnion(dd, term1, term2);
    if (tmp == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, Rd);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	Cudd_RecursiveDerefZdd(dd, term3);
	return(NULL);
    }
    Cudd_Ref(tmp);
    Cudd_RecursiveDerefZdd(dd, term1);
    Cudd_RecursiveDerefZdd(dd, term2);
    R0 = cuddZddUnion(dd, tmp, term3);
    if (R0 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, Rd);
	Cudd_RecursiveDerefZdd(dd, term3);
	Cudd_RecursiveDerefZdd(dd, tmp);
	return(NULL);
    }
    Cudd_Ref(R0);
    Cudd_RecursiveDerefZdd(dd, tmp);
    Cudd_RecursiveDerefZdd(dd, term3);
    N0 = cuddZddGetNode(dd, nv, R0, Rd); /* nv = zi */
    if (N0 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, Rd);
	Cudd_RecursiveDerefZdd(dd, R0);
	return(NULL);
    }
    Cudd_Ref(N0);
    Cudd_RecursiveDerefZdd(dd, R0);
    Cudd_RecursiveDerefZdd(dd, Rd);

    term1 = cuddZddProduct(dd, f1, g1);
    if (term1 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, N0);
	return(NULL);
    }
    Cudd_Ref(term1);
    term2 = cuddZddProduct(dd, f1, gd);
    if (term2 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, N0);
	Cudd_RecursiveDerefZdd(dd, term1);
	return(NULL);
    }
    Cudd_Ref(term2);
    term3 = cuddZddProduct(dd, fd, g1);
    if (term3 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, gd);
	Cudd_RecursiveDerefZdd(dd, N0);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	return(NULL);
    }
    Cudd_Ref(term3);
    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, g1);
    Cudd_RecursiveDerefZdd(dd, fd);
    Cudd_RecursiveDerefZdd(dd, gd);
    tmp = cuddZddUnion(dd, term1, term2);
    if (tmp == NULL) {
	Cudd_RecursiveDerefZdd(dd, N0);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	Cudd_RecursiveDerefZdd(dd, term3);
	return(NULL);
    }
    Cudd_Ref(tmp);
    Cudd_RecursiveDerefZdd(dd, term1);
    Cudd_RecursiveDerefZdd(dd, term2);
    R1 = cuddZddUnion(dd, tmp, term3);
    if (R1 == NULL) {
	Cudd_RecursiveDerefZdd(dd, N0);
	Cudd_RecursiveDerefZdd(dd, term3);
	Cudd_RecursiveDerefZdd(dd, tmp);
	return(NULL);
    }
    Cudd_Ref(R1);
    Cudd_RecursiveDerefZdd(dd, tmp);
    Cudd_RecursiveDerefZdd(dd, term3);
    N1 = cuddZddGetNode(dd, pv, R1, N0); /* pv = yi */
    if (N1 == NULL) {
	Cudd_RecursiveDerefZdd(dd, N0);
	Cudd_RecursiveDerefZdd(dd, R1);
	return(NULL);
    }
    Cudd_Ref(N1);
    Cudd_RecursiveDerefZdd(dd, R1);
    Cudd_RecursiveDerefZdd(dd, N0);

    cuddCacheInsert2(dd, cuddZddProduct, f, g, N1);
    Cudd_Deref(N1);
    return(N1);

} /* end of cuddZddProduct */


/**
  @brief Performs the recursive step of Cudd_zddUnateProduct.

  @sideeffect None

  @see Cudd_zddUnateProduct

*/
DdNode	*
cuddZddUnateProduct(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    int		v;
    int		top_f, top_g;
    DdNode	*term1, *term2, *term3, *term4;
    DdNode	*sum1, *sum2;
    DdNode	*f0, *f1, *g0, *g1;
    DdNode	*r;
    DdNode	*one = DD_ONE(dd);
    DdNode	*zero = DD_ZERO(dd);
    int		flag;

    statLine(dd);
    if (f == zero || g == zero)
        return(zero);
    if (f == one)
        return(g);
    if (g == one)
        return(f);

    top_f = dd->permZ[f->index];
    top_g = dd->permZ[g->index];

    if (top_f > top_g)
	return(cuddZddUnateProduct(dd, g, f));

    /* Check cache */
    r = cuddCacheLookup2Zdd(dd, cuddZddUnateProduct, f, g);
    if (r)
	return(r);

    v = (int) f->index;	/* either yi or zi */
    flag = cuddZddGetCofactors2(dd, f, v, &f1, &f0);
    if (flag == 1)
	return(NULL);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    flag = cuddZddGetCofactors2(dd, g, v, &g1, &g0);
    if (flag == 1) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	return(NULL);
    }
    Cudd_Ref(g1);
    Cudd_Ref(g0);

    term1 = cuddZddUnateProduct(dd, f1, g1);
    if (term1 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	return(NULL);
    }
    Cudd_Ref(term1);
    term2 = cuddZddUnateProduct(dd, f1, g0);
    if (term2 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, term1);
	return(NULL);
    }
    Cudd_Ref(term2);
    term3 = cuddZddUnateProduct(dd, f0, g1);
    if (term3 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	return(NULL);
    }
    Cudd_Ref(term3);
    term4 = cuddZddUnateProduct(dd, f0, g0);
    if (term4 == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	Cudd_RecursiveDerefZdd(dd, term3);
	return(NULL);
    }
    Cudd_Ref(term4);
    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, g1);
    Cudd_RecursiveDerefZdd(dd, g0);
    sum1 = cuddZddUnion(dd, term1, term2);
    if (sum1 == NULL) {
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, term2);
	Cudd_RecursiveDerefZdd(dd, term3);
	Cudd_RecursiveDerefZdd(dd, term4);
	return(NULL);
    }
    Cudd_Ref(sum1);
    Cudd_RecursiveDerefZdd(dd, term1);
    Cudd_RecursiveDerefZdd(dd, term2);
    sum2 = cuddZddUnion(dd, sum1, term3);
    if (sum2 == NULL) {
	Cudd_RecursiveDerefZdd(dd, term3);
	Cudd_RecursiveDerefZdd(dd, term4);
	Cudd_RecursiveDerefZdd(dd, sum1);
	return(NULL);
    }
    Cudd_Ref(sum2);
    Cudd_RecursiveDerefZdd(dd, sum1);
    Cudd_RecursiveDerefZdd(dd, term3);
    r = cuddZddGetNode(dd, v, sum2, term4);
    if (r == NULL) {
	Cudd_RecursiveDerefZdd(dd, term4);
	Cudd_RecursiveDerefZdd(dd, sum2);
	return(NULL);
    }
    Cudd_Ref(r);
    Cudd_RecursiveDerefZdd(dd, sum2);
    Cudd_RecursiveDerefZdd(dd, term4);

    cuddCacheInsert2(dd, cuddZddUnateProduct, f, g, r);
    Cudd_Deref(r);
    return(r);

} /* end of cuddZddUnateProduct */


/**
  @brief Performs the recursive step of Cudd_zddWeakDiv.

  @sideeffect None

  @see Cudd_zddWeakDiv

*/
DdNode	*
cuddZddWeakDiv(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    int		v;
    DdNode	*one = DD_ONE(dd);
    DdNode	*zero = DD_ZERO(dd);
    DdNode	*f0, *f1, *fd, *g0, *g1, *gd;
    DdNode	*q, *tmp;
    DdNode	*r;
    int		flag;

    statLine(dd);
    if (g == one)
	return(f);
    if (f == zero || f == one)
	return(zero);
    if (f == g)
	return(one);

    /* Check cache. */
    r = cuddCacheLookup2Zdd(dd, cuddZddWeakDiv, f, g);
    if (r)
	return(r);

    v = (int) g->index;

    flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
    if (flag == 1)
	return(NULL);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    Cudd_Ref(fd);
    flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
    if (flag == 1) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	return(NULL);
    }
    Cudd_Ref(g1);
    Cudd_Ref(g0);
    Cudd_Ref(gd);

    q = g;

    if (g0 != zero) {
	q = cuddZddWeakDiv(dd, f0, g0);
	if (q == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, g0);
	    Cudd_RecursiveDerefZdd(dd, gd);
	    return(NULL);
	}
	Cudd_Ref(q);
    }
    else
	Cudd_Ref(q);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, g0);

    if (q == zero) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
	cuddCacheInsert2(dd, cuddZddWeakDiv, f, g, zero);
	Cudd_Deref(q);
	return(zero);
    }

    if (g1 != zero) {
	Cudd_RecursiveDerefZdd(dd, q);
	tmp = cuddZddWeakDiv(dd, f1, g1);
	if (tmp == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, gd);
	    return(NULL);
	}
	Cudd_Ref(tmp);
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, g1);
	if (q == g)
	    q = tmp;
	else {
	    q = cuddZddIntersect(dd, q, tmp);
	    if (q == NULL) {
		Cudd_RecursiveDerefZdd(dd, fd);
		Cudd_RecursiveDerefZdd(dd, gd);
		return(NULL);
	    }
	    Cudd_Ref(q);
	    Cudd_RecursiveDerefZdd(dd, tmp);
	}
    }
    else {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, g1);
    }

    if (q == zero) {
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
	cuddCacheInsert2(dd, cuddZddWeakDiv, f, g, zero);
	Cudd_Deref(q);
	return(zero);
    }

    if (gd != zero) {
	Cudd_RecursiveDerefZdd(dd, q);
	tmp = cuddZddWeakDiv(dd, fd, gd);
	if (tmp == NULL) {
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, gd);
	    return(NULL);
	}
	Cudd_Ref(tmp);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
	if (q == g)
	    q = tmp;
	else {
	    q = cuddZddIntersect(dd, q, tmp);
	    if (q == NULL) {
		Cudd_RecursiveDerefZdd(dd, tmp);
		return(NULL);
	    }
	    Cudd_Ref(q);
	    Cudd_RecursiveDerefZdd(dd, tmp);
	}
    }
    else {
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
    }

    cuddCacheInsert2(dd, cuddZddWeakDiv, f, g, q);
    Cudd_Deref(q);
    return(q);

} /* end of cuddZddWeakDiv */


/**
  @brief Performs the recursive step of Cudd_zddWeakDivF.

  @sideeffect None

  @see Cudd_zddWeakDivF

*/
DdNode	*
cuddZddWeakDivF(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    int		v;
    int		top_f, top_g, vf, vg;
    DdNode	*one = DD_ONE(dd);
    DdNode	*zero = DD_ZERO(dd);
    DdNode	*f0, *f1, *fd, *g0, *g1, *gd;
    DdNode	*q, *tmp;
    DdNode	*r;
    DdNode	*term1, *term0, *termd;
    int		flag;
    int		pv, nv;

    statLine(dd);
    if (g == one)
	return(f);
    if (f == zero || f == one)
	return(zero);
    if (f == g)
	return(one);

    /* Check cache. */
    r = cuddCacheLookup2Zdd(dd, cuddZddWeakDivF, f, g);
    if (r)
	return(r);

    top_f = dd->permZ[f->index];
    top_g = dd->permZ[g->index];
    vf = top_f >> 1;
    vg = top_g >> 1;
    v = ddMin(top_f, top_g);

    if (v == top_f && vf < vg) {
	v = (int) f->index;
	flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
	if (flag == 1)
	    return(NULL);
	Cudd_Ref(f1);
	Cudd_Ref(f0);
	Cudd_Ref(fd);

	pv = cuddZddGetPosVarIndex(dd, v);
	nv = cuddZddGetNegVarIndex(dd, v);

	term1 = cuddZddWeakDivF(dd, f1, g);
	if (term1 == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, fd);
	    return(NULL);
	}
	Cudd_Ref(term1);
	Cudd_RecursiveDerefZdd(dd, f1);
	term0 = cuddZddWeakDivF(dd, f0, g);
	if (term0 == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, term1);
	    return(NULL);
	}
	Cudd_Ref(term0);
	Cudd_RecursiveDerefZdd(dd, f0);
	termd = cuddZddWeakDivF(dd, fd, g);
	if (termd == NULL) {
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, term1);
	    Cudd_RecursiveDerefZdd(dd, term0);
	    return(NULL);
	}
	Cudd_Ref(termd);
	Cudd_RecursiveDerefZdd(dd, fd);

	tmp = cuddZddGetNode(dd, nv, term0, termd); /* nv = zi */
	if (tmp == NULL) {
	    Cudd_RecursiveDerefZdd(dd, term1);
	    Cudd_RecursiveDerefZdd(dd, term0);
	    Cudd_RecursiveDerefZdd(dd, termd);
	    return(NULL);
	}
	Cudd_Ref(tmp);
	Cudd_RecursiveDerefZdd(dd, term0);
	Cudd_RecursiveDerefZdd(dd, termd);
	q = cuddZddGetNode(dd, pv, term1, tmp); /* pv = yi */
	if (q == NULL) {
	    Cudd_RecursiveDerefZdd(dd, term1);
	    Cudd_RecursiveDerefZdd(dd, tmp);
	    return(NULL);
	}
	Cudd_Ref(q);
	Cudd_RecursiveDerefZdd(dd, term1);
	Cudd_RecursiveDerefZdd(dd, tmp);

	cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, q);
	Cudd_Deref(q);
	return(q);
    }

    if (v == top_f)
	v = (int) f->index;
    else
	v = (int) g->index;

    flag = cuddZddGetCofactors3(dd, f, v, &f1, &f0, &fd);
    if (flag == 1)
	return(NULL);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    Cudd_Ref(fd);
    flag = cuddZddGetCofactors3(dd, g, v, &g1, &g0, &gd);
    if (flag == 1) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, fd);
	return(NULL);
    }
    Cudd_Ref(g1);
    Cudd_Ref(g0);
    Cudd_Ref(gd);

    q = g;

    if (g0 != zero) {
	q = cuddZddWeakDivF(dd, f0, g0);
	if (q == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, g0);
	    Cudd_RecursiveDerefZdd(dd, gd);
	    return(NULL);
	}
	Cudd_Ref(q);
    }
    else
	Cudd_Ref(q);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, g0);

    if (q == zero) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
	cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, zero);
	Cudd_Deref(q);
	return(zero);
    }

    if (g1 != zero) {
	Cudd_RecursiveDerefZdd(dd, q);
	tmp = cuddZddWeakDivF(dd, f1, g1);
	if (tmp == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, gd);
	    return(NULL);
	}
	Cudd_Ref(tmp);
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, g1);
	if (q == g)
	    q = tmp;
	else {
	    q = cuddZddIntersect(dd, q, tmp);
	    if (q == NULL) {
		Cudd_RecursiveDerefZdd(dd, fd);
		Cudd_RecursiveDerefZdd(dd, gd);
		return(NULL);
	    }
	    Cudd_Ref(q);
	    Cudd_RecursiveDerefZdd(dd, tmp);
	}
    }
    else {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, g1);
    }

    if (q == zero) {
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
	cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, zero);
	Cudd_Deref(q);
	return(zero);
    }

    if (gd != zero) {
	Cudd_RecursiveDerefZdd(dd, q);
	tmp = cuddZddWeakDivF(dd, fd, gd);
	if (tmp == NULL) {
	    Cudd_RecursiveDerefZdd(dd, fd);
	    Cudd_RecursiveDerefZdd(dd, gd);
	    return(NULL);
	}
	Cudd_Ref(tmp);
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
	if (q == g)
	    q = tmp;
	else {
	    q = cuddZddIntersect(dd, q, tmp);
	    if (q == NULL) {
		Cudd_RecursiveDerefZdd(dd, tmp);
		return(NULL);
	    }
	    Cudd_Ref(q);
	    Cudd_RecursiveDerefZdd(dd, tmp);
	}
    }
    else {
	Cudd_RecursiveDerefZdd(dd, fd);
	Cudd_RecursiveDerefZdd(dd, gd);
    }

    cuddCacheInsert2(dd, cuddZddWeakDivF, f, g, q);
    Cudd_Deref(q);
    return(q);

} /* end of cuddZddWeakDivF */


/**
  @brief Performs the recursive step of Cudd_zddDivide.

  @sideeffect None

  @see Cudd_zddDivide

*/
DdNode	*
cuddZddDivide(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    int		v;
    DdNode	*one = DD_ONE(dd);
    DdNode	*zero = DD_ZERO(dd);
    DdNode	*f0, *f1, *g0, *g1;
    DdNode	*q, *r, *tmp;
    int		flag;

    statLine(dd);
    if (g == one)
	return(f);
    if (f == zero || f == one)
	return(zero);
    if (f == g)
	return(one);

    /* Check cache. */
    r = cuddCacheLookup2Zdd(dd, cuddZddDivide, f, g);
    if (r)
	return(r);

    v = (int) g->index;

    flag = cuddZddGetCofactors2(dd, f, v, &f1, &f0);
    if (flag == 1)
	return(NULL);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    flag = cuddZddGetCofactors2(dd, g, v, &g1, &g0);	/* g1 != zero */
    if (flag == 1) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	return(NULL);
    }
    Cudd_Ref(g1);
    Cudd_Ref(g0);

    r = cuddZddDivide(dd, f1, g1);
    if (r == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	return(NULL);
    }
    Cudd_Ref(r);

    if (r != zero && g0 != zero) {
	tmp = r;
	q = cuddZddDivide(dd, f0, g0);
	if (q == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, g0);
	    return(NULL);
	}
	Cudd_Ref(q);
	r = cuddZddIntersect(dd, r, q);
	if (r == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, g0);
	    Cudd_RecursiveDerefZdd(dd, q);
	    return(NULL);
	}
	Cudd_Ref(r);
	Cudd_RecursiveDerefZdd(dd, q);
	Cudd_RecursiveDerefZdd(dd, tmp);
    }

    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, g1);
    Cudd_RecursiveDerefZdd(dd, g0);
    
    cuddCacheInsert2(dd, cuddZddDivide, f, g, r);
    Cudd_Deref(r);
    return(r);

} /* end of cuddZddDivide */


/**
  @brief Performs the recursive step of Cudd_zddDivideF.

  @sideeffect None

  @see Cudd_zddDivideF

*/
DdNode	*
cuddZddDivideF(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    int		v;
    DdNode	*one = DD_ONE(dd);
    DdNode	*zero = DD_ZERO(dd);
    DdNode	*f0, *f1, *g0, *g1;
    DdNode	*q, *r, *tmp;
    int		flag;

    statLine(dd);
    if (g == one)
	return(f);
    if (f == zero || f == one)
	return(zero);
    if (f == g)
	return(one);

    /* Check cache. */
    r = cuddCacheLookup2Zdd(dd, cuddZddDivideF, f, g);
    if (r)
	return(r);

    v = (int) g->index;

    flag = cuddZddGetCofactors2(dd, f, v, &f1, &f0);
    if (flag == 1)
	return(NULL);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    flag = cuddZddGetCofactors2(dd, g, v, &g1, &g0);	/* g1 != zero */
    if (flag == 1) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	return(NULL);
    }
    Cudd_Ref(g1);
    Cudd_Ref(g0);

    r = cuddZddDivideF(dd, f1, g1);
    if (r == NULL) {
	Cudd_RecursiveDerefZdd(dd, f1);
	Cudd_RecursiveDerefZdd(dd, f0);
	Cudd_RecursiveDerefZdd(dd, g1);
	Cudd_RecursiveDerefZdd(dd, g0);
	return(NULL);
    }
    Cudd_Ref(r);

    if (r != zero && g0 != zero) {
	tmp = r;
	q = cuddZddDivideF(dd, f0, g0);
	if (q == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, g0);
	    return(NULL);
	}
	Cudd_Ref(q);
	r = cuddZddIntersect(dd, r, q);
	if (r == NULL) {
	    Cudd_RecursiveDerefZdd(dd, f1);
	    Cudd_RecursiveDerefZdd(dd, f0);
	    Cudd_RecursiveDerefZdd(dd, g1);
	    Cudd_RecursiveDerefZdd(dd, g0);
	    Cudd_RecursiveDerefZdd(dd, q);
	    return(NULL);
	}
	Cudd_Ref(r);
	Cudd_RecursiveDerefZdd(dd, q);
	Cudd_RecursiveDerefZdd(dd, tmp);
    }

    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, g1);
    Cudd_RecursiveDerefZdd(dd, g0);
    
    cuddCacheInsert2(dd, cuddZddDivideF, f, g, r);
    Cudd_Deref(r);
    return(r);

} /* end of cuddZddDivideF */


/**
  @brief Computes the three-way decomposition of f w.r.t. v.

  @details Computes the three-way decomposition of function f
  (represented by a %ZDD) with respect to variable v.

  @return 0 if successful; 1 otherwise.

  @sideeffect The results are returned in f1, f0, and fd.

  @see cuddZddGetCofactors2

*/
int
cuddZddGetCofactors3(
  DdManager * dd,
  DdNode * f,
  int  v,
  DdNode ** f1,
  DdNode ** f0,
  DdNode ** fd)
{
    DdNode	*pc, *nc;
    DdNode	*zero = DD_ZERO(dd);
    int		top, hv, ht, pv, nv;
    int		level;

    top = dd->permZ[f->index];
    level = dd->permZ[v];
    hv = level >> 1;
    ht = top >> 1;

    if (hv < ht) {
	*f1 = zero;
	*f0 = zero;
	*fd = f;
    }
    else {
	pv = cuddZddGetPosVarIndex(dd, v);
	nv = cuddZddGetNegVarIndex(dd, v);

	/* not to create intermediate ZDD node */
	if (cuddZddGetPosVarLevel(dd, v) < cuddZddGetNegVarLevel(dd, v)) {
	    pc = cuddZddSubset1(dd, f, pv);
	    if (pc == NULL)
		return(1);
	    Cudd_Ref(pc);
	    nc = cuddZddSubset0(dd, f, pv);
	    if (nc == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		return(1);
	    }
	    Cudd_Ref(nc);

	    *f1 = cuddZddSubset0(dd, pc, nv);
	    if (*f1 == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		Cudd_RecursiveDerefZdd(dd, nc);
		return(1);
	    }
	    Cudd_Ref(*f1);
	    *f0 = cuddZddSubset1(dd, nc, nv);
	    if (*f0 == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		Cudd_RecursiveDerefZdd(dd, nc);
		Cudd_RecursiveDerefZdd(dd, *f1);
		return(1);
	    }
	    Cudd_Ref(*f0);

	    *fd = cuddZddSubset0(dd, nc, nv);
	    if (*fd == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		Cudd_RecursiveDerefZdd(dd, nc);
		Cudd_RecursiveDerefZdd(dd, *f1);
		Cudd_RecursiveDerefZdd(dd, *f0);
		return(1);
	    }
	    Cudd_Ref(*fd);
	} else {
	    pc = cuddZddSubset1(dd, f, nv);
	    if (pc == NULL)
		return(1);
	    Cudd_Ref(pc);
	    nc = cuddZddSubset0(dd, f, nv);
	    if (nc == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		return(1);
	    }
	    Cudd_Ref(nc);

	    *f0 = cuddZddSubset0(dd, pc, pv);
	    if (*f0 == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		Cudd_RecursiveDerefZdd(dd, nc);
		return(1);
	    }
	    Cudd_Ref(*f0);
	    *f1 = cuddZddSubset1(dd, nc, pv);
	    if (*f1 == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		Cudd_RecursiveDerefZdd(dd, nc);
		Cudd_RecursiveDerefZdd(dd, *f0);
		return(1);
	    }
	    Cudd_Ref(*f1);

	    *fd = cuddZddSubset0(dd, nc, pv);
	    if (*fd == NULL) {
		Cudd_RecursiveDerefZdd(dd, pc);
		Cudd_RecursiveDerefZdd(dd, nc);
		Cudd_RecursiveDerefZdd(dd, *f1);
		Cudd_RecursiveDerefZdd(dd, *f0);
		return(1);
	    }
	    Cudd_Ref(*fd);
	}

	Cudd_RecursiveDerefZdd(dd, pc);
	Cudd_RecursiveDerefZdd(dd, nc);
	Cudd_Deref(*f1);
	Cudd_Deref(*f0);
	Cudd_Deref(*fd);
    }
    return(0);

} /* end of cuddZddGetCofactors3 */


/**
  @brief Computes the two-way decomposition of f w.r.t. v.

  @sideeffect The results are returned in f1 and f0.

  @see cuddZddGetCofactors3

*/
int
cuddZddGetCofactors2(
  DdManager * dd,
  DdNode * f,
  int  v,
  DdNode ** f1,
  DdNode ** f0)
{
    *f1 = cuddZddSubset1(dd, f, v);
    if (*f1 == NULL)
	return(1);
    *f0 = cuddZddSubset0(dd, f, v);
    if (*f0 == NULL) {
	Cudd_RecursiveDerefZdd(dd, *f1);
	return(1);
    }
    return(0);

} /* end of cuddZddGetCofactors2 */


/**
  @brief Computes a complement of a %ZDD node.

  @details So far, since we couldn't find a direct way to get the
  complement of a %ZDD cover, we first convert a %ZDD cover to a %BDD,
  then make the complement of the %ZDD cover from the complement of the
  %BDD node by using ISOP.  The result depends on current variable order.

*/
DdNode	*
cuddZddComplement(
  DdManager * dd,
  DdNode *node)
{
    DdNode	*b, *isop, *zdd_I;

    /* Check cache */
    zdd_I = cuddCacheLookup1Zdd(dd, cuddZddComplement, node);
    if (zdd_I)
	return(zdd_I);

    b = cuddMakeBddFromZddCover(dd, node);
    if (!b)
	return(NULL);
    cuddRef(b);
    isop = cuddZddIsop(dd, Cudd_Not(b), Cudd_Not(b), &zdd_I);
    if (!isop) {
	Cudd_RecursiveDeref(dd, b);
	return(NULL);
    }
    cuddRef(isop);
    cuddRef(zdd_I);
    Cudd_RecursiveDeref(dd, b);
    Cudd_RecursiveDeref(dd, isop);

    cuddCacheInsert1(dd, cuddZddComplement, node, zdd_I);
    cuddDeref(zdd_I);
    return(zdd_I);
} /* end of cuddZddComplement */


/**
  @brief Returns the index of positive %ZDD variable.
*/
int
cuddZddGetPosVarIndex(
  DdManager * dd,
  int index)
{
    (void) dd; /* avoid warning */
    int	pv = index & ~0x1;
    return(pv);
} /* end of cuddZddGetPosVarIndex */


/**
  @brief Returns the index of negative %ZDD variable.
*/
int
cuddZddGetNegVarIndex(
  DdManager * dd,
  int index)
{
    (void) dd; /* avoid warning */
    int	nv = index | 0x1;
    return(nv);
} /* end of cuddZddGetPosVarIndex */


/**
  @brief Returns the level of positive %ZDD variable.
*/
int
cuddZddGetPosVarLevel(
  DdManager * dd,
  int index)
{
    int	pv = cuddZddGetPosVarIndex(dd, index);
    return(dd->permZ[pv]);
} /* end of cuddZddGetPosVarLevel */


/**
  @brief Returns the level of negative %ZDD variable.
*/
int
cuddZddGetNegVarLevel(
  DdManager * dd,
  int index)
{
    int	nv = cuddZddGetNegVarIndex(dd, index);
    return(dd->permZ[nv]);
} /* end of cuddZddGetNegVarLevel */