cuddZddIsop.c

/**CFile***********************************************************************

  FileName    [cuddZddIsop.c]

  PackageName [cudd]

  Synopsis    [Functions to find irredundant SOP covers as ZDDs from BDDs.]

  Description [External procedures included in this module:
            <ul>
            <li> Cudd_bddIsop()
            <li> Cudd_zddIsop()
            <li> Cudd_MakeBddFromZddCover()
            </ul>
           Internal procedures included in this module:
            <ul>
            <li> cuddBddIsop()
            <li> cuddZddIsop()
            <li> cuddMakeBddFromZddCover()
            </ul>
           Static procedures included in this module:
            <ul>
            </ul>
          ]

  SeeAlso     []

  Author      [In-Ho Moon]

  Copyright [ This file was created at the University of Colorado at
  Boulder.  The University of Colorado at Boulder makes no warranty
  about the suitability of this software for any purpose.  It is
  presented on an AS IS basis.]

******************************************************************************/

#include    "util_hack.h"
#include    "cuddInt.h"

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/* Constant declarations                                                     */
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/*---------------------------------------------------------------------------*/
/* Stucture declarations                                                     */
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/*---------------------------------------------------------------------------*/
/* Type declarations                                                         */
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/*---------------------------------------------------------------------------*/
/* Variable declarations                                                     */
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#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddZddIsop.c,v 1.1.1.1 2003/02/24 22:23:54 wjiang Exp $";
#endif

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/* Macro declarations                                                        */
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/**AutomaticStart*************************************************************/

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/* Static function prototypes                                                */
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/**AutomaticEnd***************************************************************/

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

  Synopsis    [Computes an ISOP in ZDD form from BDDs.]

  Description [Computes an irredundant sum of products (ISOP) in ZDD
  form from BDDs. The two BDDs L and U represent the lower bound and
  the upper bound, respectively, of the function. The ISOP uses two
  ZDD variables for each BDD variable: One for the positive literal,
  and one for the negative literal. These two variables should be
  adjacent in the ZDD order. The two ZDD variables corresponding to
  BDD variable <code>i</code> should have indices <code>2i</code> and
  <code>2i+1</code>.  The result of this procedure depends on the
  variable order. If successful, Cudd_zddIsop returns the BDD for
  the function chosen from the interval. The ZDD representing the
  irredundant cover is returned as a side effect in zdd_I. In case of
  failure, NULL is returned.]

  SideEffects [zdd_I holds the pointer to the ZDD for the ISOP on
  successful return.]

  SeeAlso     [Cudd_bddIsop Cudd_zddVarsFromBddVars]

******************************************************************************/
DdNode    *
Cudd_zddIsop(
  DdManager * dd,
  DdNode * L,
  DdNode * U,
  DdNode ** zdd_I)
{
    DdNode    *res;
    int        autoDynZ;

    autoDynZ = dd->autoDynZ;
    dd->autoDynZ = 0;

    do {
    dd->reordered = 0;
    res = cuddZddIsop(dd, L, U, zdd_I);
    } while (dd->reordered == 1);
    dd->autoDynZ = autoDynZ;
    return(res);

} /* end of Cudd_zddIsop */


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

  Synopsis    [Computes a BDD in the interval between L and U with a
  simple sum-of-produuct cover.]

  Description [Computes a BDD in the interval between L and U with a
  simple sum-of-produuct cover. This procedure is similar to
  Cudd_zddIsop, but it does not return the ZDD for the cover. Returns
  a pointer to the BDD if successful; NULL otherwise.]

  SideEffects [None]

  SeeAlso     [Cudd_zddIsop]

******************************************************************************/
DdNode    *
Cudd_bddIsop(
  DdManager * dd,
  DdNode * L,
  DdNode * U)
{
    DdNode    *res;

    do {
    dd->reordered = 0;
    res = cuddBddIsop(dd, L, U);
    } while (dd->reordered == 1);
    return(res);

} /* end of Cudd_bddIsop */


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

  Synopsis [Converts a ZDD cover to a BDD graph.]

  Description [Converts a ZDD cover to a BDD graph. If successful, it
  returns a BDD node, otherwise it returns NULL.]

  SideEffects []

  SeeAlso     [cuddMakeBddFromZddCover]

******************************************************************************/
DdNode    *
Cudd_MakeBddFromZddCover(
  DdManager * dd,
  DdNode * node)
{
    DdNode    *res;

    do {
    dd->reordered = 0;
    res = cuddMakeBddFromZddCover(dd, node);
    } while (dd->reordered == 1);
    return(res);
} /* end of Cudd_MakeBddFromZddCover */


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


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

  Synopsis [Performs the recursive step of Cudd_zddIsop.]

  Description []

  SideEffects [None]

  SeeAlso     [Cudd_zddIsop]

******************************************************************************/
DdNode    *
cuddZddIsop(
  DdManager * dd,
  DdNode * L,
  DdNode * U,
  DdNode ** zdd_I)
{
    DdNode    *one = DD_ONE(dd);
    DdNode    *zero = Cudd_Not(one);
    DdNode    *zdd_one = DD_ONE(dd);
    DdNode    *zdd_zero = DD_ZERO(dd);
    int        v, top_l, top_u;
    DdNode    *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
    DdNode    *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
    DdNode    *Isub0, *Isub1, *Id;
    DdNode    *zdd_Isub0, *zdd_Isub1, *zdd_Id;
    DdNode    *x;
    DdNode    *term0, *term1, *sum;
    DdNode    *Lv, *Uv, *Lnv, *Unv;
    DdNode    *r, *y, *z;
    int        index;
    DdNode *(*cacheOp)(DdManager *, DdNode *, DdNode *);

    statLine(dd);
    if (L == zero) {
    *zdd_I = zdd_zero;
        return(zero);
    }
    if (U == one) {
    *zdd_I = zdd_one;
        return(one);
    }

    if (U == zero || L == one) {
    printf("*** ERROR : illegal condition for ISOP (U < L).\n");
    exit(1);
    }

    /* Check the cache. We store two results for each recursive call.
    ** One is the BDD, and the other is the ZDD. Both are needed.
    ** Hence we need a double hit in the cache to terminate the
    ** recursion. Clearly, collisions may evict only one of the two
    ** results. */
    cacheOp = (DdNode *(*)(DdManager *, DdNode *, DdNode *)) cuddZddIsop;
    r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
    if (r) {
    *zdd_I = cuddCacheLookup2Zdd(dd, cacheOp, L, U);
    if (*zdd_I)
        return(r);
    else {
        /* The BDD result may have been dead. In that case
        ** cuddCacheLookup2 would have called cuddReclaim,
        ** whose effects we now have to undo. */
        cuddRef(r);
        Cudd_RecursiveDeref(dd, r);
    }
    }

    top_l = dd->perm[Cudd_Regular(L)->index];
    top_u = dd->perm[Cudd_Regular(U)->index];
    v = ddMin(top_l, top_u);

    /* Compute cofactors. */
    if (top_l == v) {
    index = Cudd_Regular(L)->index;
        Lv = Cudd_T(L);
        Lnv = Cudd_E(L);
        if (Cudd_IsComplement(L)) {
            Lv = Cudd_Not(Lv);
            Lnv = Cudd_Not(Lnv);
        }
    }
    else {
    index = Cudd_Regular(U)->index;
        Lv = Lnv = L;
    }

    if (top_u == v) {
        Uv = Cudd_T(U);
        Unv = Cudd_E(U);
        if (Cudd_IsComplement(U)) {
            Uv = Cudd_Not(Uv);
            Unv = Cudd_Not(Unv);
        }
    }
    else {
        Uv = Unv = U;
    }

    Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
    if (Lsub0 == NULL)
    return(NULL);
    Cudd_Ref(Lsub0);
    Usub0 = Unv;
    Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
    if (Lsub1 == NULL) {
    Cudd_RecursiveDeref(dd, Lsub0);
    return(NULL);
    }
    Cudd_Ref(Lsub1);
    Usub1 = Uv;

    Isub0 = cuddZddIsop(dd, Lsub0, Usub0, &zdd_Isub0);
    if (Isub0 == NULL) {
    Cudd_RecursiveDeref(dd, Lsub0);
    Cudd_RecursiveDeref(dd, Lsub1);
    return(NULL);
    }
    /*
    if ((!cuddIsConstant(Cudd_Regular(Isub0))) &&
    (Cudd_Regular(Isub0)->index != zdd_Isub0->index / 2 ||
    dd->permZ[index * 2] > dd->permZ[zdd_Isub0->index])) {
    printf("*** ERROR : illegal permutation in ZDD. ***\n");
    }
    */
    Cudd_Ref(Isub0);
    Cudd_Ref(zdd_Isub0);
    Isub1 = cuddZddIsop(dd, Lsub1, Usub1, &zdd_Isub1);
    if (Isub1 == NULL) {
    Cudd_RecursiveDeref(dd, Lsub0);
    Cudd_RecursiveDeref(dd, Lsub1);
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    return(NULL);
    }
    /*
    if ((!cuddIsConstant(Cudd_Regular(Isub1))) &&
    (Cudd_Regular(Isub1)->index != zdd_Isub1->index / 2 ||
    dd->permZ[index * 2] > dd->permZ[zdd_Isub1->index])) {
    printf("*** ERROR : illegal permutation in ZDD. ***\n");
    }
    */
    Cudd_Ref(Isub1);
    Cudd_Ref(zdd_Isub1);
    Cudd_RecursiveDeref(dd, Lsub0);
    Cudd_RecursiveDeref(dd, Lsub1);

    Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
    if (Lsuper0 == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    return(NULL);
    }
    Cudd_Ref(Lsuper0);
    Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
    if (Lsuper1 == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Lsuper0);
    return(NULL);
    }
    Cudd_Ref(Lsuper1);
    Usuper0 = Unv;
    Usuper1 = Uv;

    /* Ld = Lsuper0 + Lsuper1 */
    Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
    if (Ld == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Lsuper0);
    Cudd_RecursiveDeref(dd, Lsuper1);
    return(NULL);
    }
    Ld = Cudd_Not(Ld);
    Cudd_Ref(Ld);
    /* Ud = Usuper0 * Usuper1 */
    Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
    if (Ud == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Lsuper0);
    Cudd_RecursiveDeref(dd, Lsuper1);
    Cudd_RecursiveDeref(dd, Ld);
    return(NULL);
    }
    Cudd_Ref(Ud);
    Cudd_RecursiveDeref(dd, Lsuper0);
    Cudd_RecursiveDeref(dd, Lsuper1);

    Id = cuddZddIsop(dd, Ld, Ud, &zdd_Id);
    if (Id == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Ld);
    Cudd_RecursiveDeref(dd, Ud);
    return(NULL);
    }
    /*
    if ((!cuddIsConstant(Cudd_Regular(Id))) &&
    (Cudd_Regular(Id)->index != zdd_Id->index / 2 ||
    dd->permZ[index * 2] > dd->permZ[zdd_Id->index])) {
    printf("*** ERROR : illegal permutation in ZDD. ***\n");
    }
    */
    Cudd_Ref(Id);
    Cudd_Ref(zdd_Id);
    Cudd_RecursiveDeref(dd, Ld);
    Cudd_RecursiveDeref(dd, Ud);

    x = cuddUniqueInter(dd, index, one, zero);
    if (x == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDerefZdd(dd, zdd_Id);
    return(NULL);
    }
    Cudd_Ref(x);
    /* term0 = x * Isub0 */
    term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
    if (term0 == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDerefZdd(dd, zdd_Id);
    Cudd_RecursiveDeref(dd, x);
    return(NULL);
    }
    Cudd_Ref(term0);
    Cudd_RecursiveDeref(dd, Isub0);
    /* term1 = x * Isub1 */
    term1 = cuddBddAndRecur(dd, x, Isub1);
    if (term1 == NULL) {
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDerefZdd(dd, zdd_Id);
    Cudd_RecursiveDeref(dd, x);
    Cudd_RecursiveDeref(dd, term0);
    return(NULL);
    }
    Cudd_Ref(term1);
    Cudd_RecursiveDeref(dd, x);
    Cudd_RecursiveDeref(dd, Isub1);
    /* sum = term0 + term1 */
    sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
    if (sum == NULL) {
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDerefZdd(dd, zdd_Id);
    Cudd_RecursiveDeref(dd, term0);
    Cudd_RecursiveDeref(dd, term1);
    return(NULL);
    }
    sum = Cudd_Not(sum);
    Cudd_Ref(sum);
    Cudd_RecursiveDeref(dd, term0);
    Cudd_RecursiveDeref(dd, term1);
    /* r = sum + Id */
    r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
    r = Cudd_NotCond(r, r != NULL);
    if (r == NULL) {
    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDerefZdd(dd, zdd_Id);
    Cudd_RecursiveDeref(dd, sum);
    return(NULL);
    }
    Cudd_Ref(r);
    Cudd_RecursiveDeref(dd, sum);
    Cudd_RecursiveDeref(dd, Id);

    if (zdd_Isub0 != zdd_zero) {
    z = cuddZddGetNodeIVO(dd, index * 2 + 1, zdd_Isub0, zdd_Id);
    if (z == NULL) {
        Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
        Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
        Cudd_RecursiveDerefZdd(dd, zdd_Id);
        Cudd_RecursiveDeref(dd, r);
        return(NULL);
    }
    }
    else {
    z = zdd_Id;
    }
    Cudd_Ref(z);
    if (zdd_Isub1 != zdd_zero) {
    y = cuddZddGetNodeIVO(dd, index * 2, zdd_Isub1, z);
    if (y == NULL) {
        Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
        Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
        Cudd_RecursiveDerefZdd(dd, zdd_Id);
        Cudd_RecursiveDeref(dd, r);
        Cudd_RecursiveDerefZdd(dd, z);
        return(NULL);
    }
    }
    else
    y = z;
    Cudd_Ref(y);

    Cudd_RecursiveDerefZdd(dd, zdd_Isub0);
    Cudd_RecursiveDerefZdd(dd, zdd_Isub1);
    Cudd_RecursiveDerefZdd(dd, zdd_Id);
    Cudd_RecursiveDerefZdd(dd, z);

    cuddCacheInsert2(dd, cuddBddIsop, L, U, r);
    cuddCacheInsert2(dd, cacheOp, L, U, y);

    Cudd_Deref(r);
    Cudd_Deref(y);
    *zdd_I = y;
    /*
    if (Cudd_Regular(r)->index != y->index / 2) {
    printf("*** ERROR : mismatch in indices between BDD and ZDD. ***\n");
    }
    */
    return(r);

} /* end of cuddZddIsop */


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

  Synopsis [Performs the recursive step of Cudd_bddIsop.]

  Description []

  SideEffects [None]

  SeeAlso     [Cudd_bddIsop]

******************************************************************************/
DdNode    *
cuddBddIsop(
  DdManager * dd,
  DdNode * L,
  DdNode * U)
{
    DdNode    *one = DD_ONE(dd);
    DdNode    *zero = Cudd_Not(one);
    int        v, top_l, top_u;
    DdNode    *Lsub0, *Usub0, *Lsub1, *Usub1, *Ld, *Ud;
    DdNode    *Lsuper0, *Usuper0, *Lsuper1, *Usuper1;
    DdNode    *Isub0, *Isub1, *Id;
    DdNode    *x;
    DdNode    *term0, *term1, *sum;
    DdNode    *Lv, *Uv, *Lnv, *Unv;
    DdNode    *r;
    int        index;

    statLine(dd);
    if (L == zero)
        return(zero);
    if (U == one)
        return(one);

    /* Check cache */
    r = cuddCacheLookup2(dd, cuddBddIsop, L, U);
    if (r)
        return(r);

    top_l = dd->perm[Cudd_Regular(L)->index];
    top_u = dd->perm[Cudd_Regular(U)->index];
    v = ddMin(top_l, top_u);

    /* Compute cofactors */
    if (top_l == v) {
    index = Cudd_Regular(L)->index;
        Lv = Cudd_T(L);
        Lnv = Cudd_E(L);
        if (Cudd_IsComplement(L)) {
            Lv = Cudd_Not(Lv);
            Lnv = Cudd_Not(Lnv);
        }
    }
    else {
    index = Cudd_Regular(U)->index;
        Lv = Lnv = L;
    }

    if (top_u == v) {
        Uv = Cudd_T(U);
        Unv = Cudd_E(U);
        if (Cudd_IsComplement(U)) {
            Uv = Cudd_Not(Uv);
            Unv = Cudd_Not(Unv);
        }
    }
    else {
        Uv = Unv = U;
    }

    Lsub0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Uv));
    if (Lsub0 == NULL)
    return(NULL);
    Cudd_Ref(Lsub0);
    Usub0 = Unv;
    Lsub1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Unv));
    if (Lsub1 == NULL) {
    Cudd_RecursiveDeref(dd, Lsub0);
    return(NULL);
    }
    Cudd_Ref(Lsub1);
    Usub1 = Uv;

    Isub0 = cuddBddIsop(dd, Lsub0, Usub0);
    if (Isub0 == NULL) {
    Cudd_RecursiveDeref(dd, Lsub0);
    Cudd_RecursiveDeref(dd, Lsub1);
    return(NULL);
    }
    Cudd_Ref(Isub0);
    Isub1 = cuddBddIsop(dd, Lsub1, Usub1);
    if (Isub1 == NULL) {
    Cudd_RecursiveDeref(dd, Lsub0);
    Cudd_RecursiveDeref(dd, Lsub1);
    Cudd_RecursiveDeref(dd, Isub0);
    return(NULL);
    }
    Cudd_Ref(Isub1);
    Cudd_RecursiveDeref(dd, Lsub0);
    Cudd_RecursiveDeref(dd, Lsub1);

    Lsuper0 = cuddBddAndRecur(dd, Lnv, Cudd_Not(Isub0));
    if (Lsuper0 == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    return(NULL);
    }
    Cudd_Ref(Lsuper0);
    Lsuper1 = cuddBddAndRecur(dd, Lv, Cudd_Not(Isub1));
    if (Lsuper1 == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Lsuper0);
    return(NULL);
    }
    Cudd_Ref(Lsuper1);
    Usuper0 = Unv;
    Usuper1 = Uv;

    /* Ld = Lsuper0 + Lsuper1 */
    Ld = cuddBddAndRecur(dd, Cudd_Not(Lsuper0), Cudd_Not(Lsuper1));
    Ld = Cudd_NotCond(Ld, Ld != NULL);
    if (Ld == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Lsuper0);
    Cudd_RecursiveDeref(dd, Lsuper1);
    return(NULL);
    }
    Cudd_Ref(Ld);
    Ud = cuddBddAndRecur(dd, Usuper0, Usuper1);
    if (Ud == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Lsuper0);
    Cudd_RecursiveDeref(dd, Lsuper1);
    Cudd_RecursiveDeref(dd, Ld);
    return(NULL);
    }
    Cudd_Ref(Ud);
    Cudd_RecursiveDeref(dd, Lsuper0);
    Cudd_RecursiveDeref(dd, Lsuper1);

    Id = cuddBddIsop(dd, Ld, Ud);
    if (Id == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Ld);
    Cudd_RecursiveDeref(dd, Ud);
    return(NULL);
    }
    Cudd_Ref(Id);
    Cudd_RecursiveDeref(dd, Ld);
    Cudd_RecursiveDeref(dd, Ud);

    x = cuddUniqueInter(dd, index, one, zero);
    if (x == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Id);
    return(NULL);
    }
    Cudd_Ref(x);
    term0 = cuddBddAndRecur(dd, Cudd_Not(x), Isub0);
    if (term0 == NULL) {
    Cudd_RecursiveDeref(dd, Isub0);
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDeref(dd, x);
    return(NULL);
    }
    Cudd_Ref(term0);
    Cudd_RecursiveDeref(dd, Isub0);
    term1 = cuddBddAndRecur(dd, x, Isub1);
    if (term1 == NULL) {
    Cudd_RecursiveDeref(dd, Isub1);
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDeref(dd, x);
    Cudd_RecursiveDeref(dd, term0);
    return(NULL);
    }
    Cudd_Ref(term1);
    Cudd_RecursiveDeref(dd, x);
    Cudd_RecursiveDeref(dd, Isub1);
    /* sum = term0 + term1 */
    sum = cuddBddAndRecur(dd, Cudd_Not(term0), Cudd_Not(term1));
    sum = Cudd_NotCond(sum, sum != NULL);
    if (sum == NULL) {
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDeref(dd, term0);
    Cudd_RecursiveDeref(dd, term1);
    return(NULL);
    }
    Cudd_Ref(sum);
    Cudd_RecursiveDeref(dd, term0);
    Cudd_RecursiveDeref(dd, term1);
    /* r = sum + Id */
    r = cuddBddAndRecur(dd, Cudd_Not(sum), Cudd_Not(Id));
    r = Cudd_NotCond(r, r != NULL);
    if (r == NULL) {
    Cudd_RecursiveDeref(dd, Id);
    Cudd_RecursiveDeref(dd, sum);
    return(NULL);
    }
    Cudd_Ref(r);
    Cudd_RecursiveDeref(dd, sum);
    Cudd_RecursiveDeref(dd, Id);

    cuddCacheInsert2(dd, cuddBddIsop, L, U, r);

    Cudd_Deref(r);
    return(r);

} /* end of cuddBddIsop */


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

  Synopsis [Converts a ZDD cover to a BDD graph.]

  Description [Converts a ZDD cover to a BDD graph. If successful, it
  returns a BDD node, otherwise it returns NULL. It is a recursive
  algorithm as the following. First computes 3 cofactors of a ZDD cover;
  f1, f0 and fd. Second, compute BDDs(b1, b0 and bd) of f1, f0 and fd.
  Third, compute T=b1+bd and E=b0+bd. Fourth, compute ITE(v,T,E) where v
  is the variable which has the index of the top node of the ZDD cover.
  In this case, since the index of v can be larger than either one of T or
  one of E, cuddUniqueInterIVO is called, here IVO stands for
  independent variable ordering.]

  SideEffects []

  SeeAlso     [Cudd_MakeBddFromZddCover]

******************************************************************************/
DdNode    *
cuddMakeBddFromZddCover(
  DdManager * dd,
  DdNode * node)
{
    DdNode    *neW;
    int        v;
    DdNode    *f1, *f0, *fd;
    DdNode    *b1, *b0, *bd;
    DdNode    *T, *E;

    statLine(dd);
    if (node == dd->one)
    return(dd->one);
    if (node == dd->zero)
    return(Cudd_Not(dd->one));

    /* Check cache */
    neW = cuddCacheLookup1(dd, cuddMakeBddFromZddCover, node);
    if (neW)
    return(neW);

    v = Cudd_Regular(node)->index;    /* either yi or zi */
    cuddZddGetCofactors3(dd, node, v, &f1, &f0, &fd);
    Cudd_Ref(f1);
    Cudd_Ref(f0);
    Cudd_Ref(fd);

    b1 = cuddMakeBddFromZddCover(dd, f1);
    if (!b1) {
    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, fd);
    return(NULL);
    }
    Cudd_Ref(b1);
    b0 = cuddMakeBddFromZddCover(dd, f0);
    if (!b1) {
    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, f0);
    Cudd_RecursiveDerefZdd(dd, fd);
    Cudd_RecursiveDeref(dd, b1);
    return(NULL);
    }
    Cudd_Ref(b0);
    Cudd_RecursiveDerefZdd(dd, f1);
    Cudd_RecursiveDerefZdd(dd, f0);
    if (fd != dd->zero) {
    bd = cuddMakeBddFromZddCover(dd, fd);
    if (!bd) {
        Cudd_RecursiveDerefZdd(dd, fd);
        Cudd_RecursiveDeref(dd, b1);
        Cudd_RecursiveDeref(dd, b0);
        return(NULL);
    }
    Cudd_Ref(bd);
    Cudd_RecursiveDerefZdd(dd, fd);

    T = cuddBddAndRecur(dd, Cudd_Not(b1), Cudd_Not(bd));
    if (!T) {
        Cudd_RecursiveDeref(dd, b1);
        Cudd_RecursiveDeref(dd, b0);
        Cudd_RecursiveDeref(dd, bd);
        return(NULL);
    }
    T = Cudd_NotCond(T, T != NULL);
    Cudd_Ref(T);
    Cudd_RecursiveDeref(dd, b1);
    E = cuddBddAndRecur(dd, Cudd_Not(b0), Cudd_Not(bd));
    if (!E) {
        Cudd_RecursiveDeref(dd, b0);
        Cudd_RecursiveDeref(dd, bd);
        Cudd_RecursiveDeref(dd, T);
        return(NULL);
    }
    E = Cudd_NotCond(E, E != NULL);
    Cudd_Ref(E);
    Cudd_RecursiveDeref(dd, b0);
    Cudd_RecursiveDeref(dd, bd);
    }
    else {
    Cudd_RecursiveDerefZdd(dd, fd);
    T = b1;
    E = b0;
    }

    if (Cudd_IsComplement(T)) {
    neW = cuddUniqueInterIVO(dd, v / 2, Cudd_Not(T), Cudd_Not(E));
    if (!neW) {
        Cudd_RecursiveDeref(dd, T);
        Cudd_RecursiveDeref(dd, E);
        return(NULL);
    }
    neW = Cudd_Not(neW);
    }
    else {
    neW = cuddUniqueInterIVO(dd, v / 2, T, E);
    if (!neW) {
        Cudd_RecursiveDeref(dd, T);
        Cudd_RecursiveDeref(dd, E);
        return(NULL);
    }
    }
    Cudd_Ref(neW);
    Cudd_RecursiveDeref(dd, T);
    Cudd_RecursiveDeref(dd, E);

    cuddCacheInsert1(dd, cuddMakeBddFromZddCover, node, neW);
    Cudd_Deref(neW);
    return(neW);

} /* end of cuddMakeBddFromZddCover */


/*---------------------------------------------------------------------------*/
/* Definition of static functions                                            */
/*---------------------------------------------------------------------------*/