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

/**
  @file

  @ingroup cudd

  @brief Set operations on ZDDs.

  @author Hyong-Kyoon Shin, 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                                                */
/*---------------------------------------------------------------------------*/

static DdNode * zdd_subset1_aux (DdManager *zdd, DdNode *P, DdNode *zvar);
static DdNode * zdd_subset0_aux (DdManager *zdd, DdNode *P, DdNode *zvar);
static void zddVarToConst (DdNode *f, DdNode **gp, DdNode **hp, DdNode *base, DdNode *empty);

/** \endcond */

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


/**
  @brief Computes the ITE of three ZDDs.

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

  @sideeffect None

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

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

} /* end of Cudd_zddIte */


/**
  @brief Computes the union of two ZDDs.

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

  @sideeffect None

*/
DdNode *
Cudd_zddUnion(
  DdManager * dd,
  DdNode * P,
  DdNode * Q)
{
    DdNode *res;

    do {
	dd->reordered = 0;
	res = cuddZddUnion(dd, P, Q);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddUnion */


/**
  @brief Computes the intersection of two ZDDs.

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

  @sideeffect None

*/
DdNode *
Cudd_zddIntersect(
  DdManager * dd,
  DdNode * P,
  DdNode * Q)
{
    DdNode *res;

    do {
	dd->reordered = 0;
	res = cuddZddIntersect(dd, P, Q);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddIntersect */


/**
  @brief Computes the difference of two ZDDs.

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

  @sideeffect None

*/
DdNode *
Cudd_zddDiff(
  DdManager * dd,
  DdNode * P,
  DdNode * Q)
{
    DdNode *res;

    do {
	dd->reordered = 0;
	res = cuddZddDiff(dd, P, Q);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddDiff */


/**
  @brief Performs the inclusion test for ZDDs (P implies Q).

  @details No new nodes are generated by this procedure.

  @return empty if true; a valid pointer different from empty or
  DD_NON_CONSTANT otherwise.

  @sideeffect None

  @see 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 */


/**
  @brief Computes the positive cofactor of a %ZDD w.r.t. a variable.

  @details In terms of combinations, the result is the set of all
  combinations in which the variable is asserted.

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

  @sideeffect None

  @see Cudd_zddSubset0

*/
DdNode *
Cudd_zddSubset1(
  DdManager * dd,
  DdNode * P,
  int  var)
{
    DdNode	*r;

    do {
	dd->reordered = 0;
	r = cuddZddSubset1(dd, P, var);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }

    return(r);

} /* end of Cudd_zddSubset1 */


/**
  @brief Computes the negative cofactor of a %ZDD w.r.t. a variable.

  @details In terms of combinations, the result is the set of all
  combinations in which the variable is negated.

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

  @sideeffect None

  @see Cudd_zddSubset1

*/
DdNode *
Cudd_zddSubset0(
  DdManager * dd,
  DdNode * P,
  int  var)
{
    DdNode	*r;

    do {
	dd->reordered = 0;
	r = cuddZddSubset0(dd, P, var);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }

    return(r);

} /* end of Cudd_zddSubset0 */


/**
  @brief Substitutes a variable with its complement in a %ZDD.

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

  @sideeffect None

*/
DdNode *
Cudd_zddChange(
  DdManager * dd,
  DdNode * P,
  int  var)
{
    DdNode	*res;

    if ((unsigned int) var >= CUDD_MAXINDEX - 1) return(NULL);
    
    do {
	dd->reordered = 0;
	res = cuddZddChange(dd, P, var);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_zddChange */


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


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

  @sideeffect None

*/
DdNode *
cuddZddIte(
  DdManager * dd,
  DdNode * f,
  DdNode * g,
  DdNode * h)
{
    DdNode *tautology, *empty;
    DdNode *r,*Gv,*Gvn,*Hv,*Hvn,*t,*e;
    int topf,topg,toph,v,top;
    unsigned int index;

    statLine(dd);
    /* Trivial cases. */
    /* One variable cases. */
    if (f == (empty = DD_ZERO(dd))) {	/* ITE(0,G,H) = H */
	return(h);
    }
    topf = cuddIZ(dd,f->index);
    topg = cuddIZ(dd,g->index);
    toph = cuddIZ(dd,h->index);
    v = ddMin(topg,toph);
    top  = ddMin(topf,v);

    tautology = (top == CUDD_MAXINDEX) ? DD_ONE(dd) : dd->univ[top];
    if (f == tautology) {			/* ITE(1,G,H) = G */
    	return(g);
    }

    /* From now on, f is known to not be a constant. */
    zddVarToConst(f,&g,&h,tautology,empty);

    /* Check remaining one variable cases. */
    if (g == h) {			/* ITE(F,G,G) = G */
	return(g);
    }

    if (g == tautology) {			/* ITE(F,1,0) = F */
	if (h == empty) return(f);
    }

    /* Check cache. */
    r = cuddCacheLookupZdd(dd,DD_ZDD_ITE_TAG,f,g,h);
    if (r != NULL) {
	return(r);
    }

    /* Recompute these because they may have changed in zddVarToConst. */
    topg = cuddIZ(dd,g->index);
    toph = cuddIZ(dd,h->index);
    v = ddMin(topg,toph);

    if (topf < v) {
	r = cuddZddIte(dd,cuddE(f),g,h);
	if (r == NULL) return(NULL);
    } else if (topf > v) {
	if (topg > v) {
	    Gvn = g;
	    index = h->index;
	} else {
	    Gvn = cuddE(g);
	    index = g->index;
	}
	if (toph > v) {
	    Hv = empty; Hvn = h;
	} else {
	    Hv = cuddT(h); Hvn = cuddE(h);
	}
	e = cuddZddIte(dd,f,Gvn,Hvn);
	if (e == NULL) return(NULL);
	cuddRef(e);
	r = cuddZddGetNode(dd,index,Hv,e);
	if (r == NULL) {
	    Cudd_RecursiveDerefZdd(dd,e);
	    return(NULL);
	}
	cuddDeref(e);
    } else {
	index = f->index;
	if (topg > v) {
	    Gv = empty; Gvn = g;
	} else {
	    Gv = cuddT(g); Gvn = cuddE(g);
	}
	if (toph > v) {
	    Hv = empty; Hvn = h;
	} else {
	    Hv = cuddT(h); Hvn = cuddE(h);
	}
	e = cuddZddIte(dd,cuddE(f),Gvn,Hvn);
	if (e == NULL) return(NULL);
	cuddRef(e);
	t = cuddZddIte(dd,cuddT(f),Gv,Hv);
	if (t == NULL) {
	    Cudd_RecursiveDerefZdd(dd,e);
	    return(NULL);
	}
	cuddRef(t);
	r = cuddZddGetNode(dd,index,t,e);
	if (r == NULL) {
	    Cudd_RecursiveDerefZdd(dd,e);
	    Cudd_RecursiveDerefZdd(dd,t);
	    return(NULL);
	}
	cuddDeref(t);
	cuddDeref(e);
    }

    cuddCacheInsert(dd,DD_ZDD_ITE_TAG,f,g,h,r);

    return(r);

} /* end of cuddZddIte */


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

  @sideeffect None

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

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

    /* Check cache */
    res = cuddCacheLookup2Zdd(table, cuddZddUnion, 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) {
	e = cuddZddUnion(zdd, cuddE(P), Q);
	if (e == NULL) return (NULL);
	cuddRef(e);
	res = cuddZddGetNode(zdd, P->index, cuddT(P), e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(table, e);
	    return(NULL);
	}
	cuddDeref(e);
    } else if (p_top > q_top) {
	e = cuddZddUnion(zdd, P, cuddE(Q));
	if (e == NULL) return(NULL);
	cuddRef(e);
	res = cuddZddGetNode(zdd, Q->index, cuddT(Q), e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(table, e);
	    return(NULL);
	}
	cuddDeref(e);
    } else {
	t = cuddZddUnion(zdd, cuddT(P), cuddT(Q));
	if (t == NULL) return(NULL);
	cuddRef(t);
	e = cuddZddUnion(zdd, cuddE(P), cuddE(Q));
	if (e == NULL) {
	    Cudd_RecursiveDerefZdd(table, t);
	    return(NULL);
	}
	cuddRef(e);
	res = cuddZddGetNode(zdd, P->index, t, e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(table, t);
	    Cudd_RecursiveDerefZdd(table, e);
	    return(NULL);
	}
	cuddDeref(t);
	cuddDeref(e);
    }

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

    return(res);

} /* end of cuddZddUnion */


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

  @sideeffect None

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

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

    /* Check cache. */
    res = cuddCacheLookup2Zdd(table, cuddZddIntersect, 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 = cuddZddIntersect(zdd, cuddE(P), Q);
	if (res == NULL) return(NULL);
    } else if (p_top > q_top) {
	res = cuddZddIntersect(zdd, P, cuddE(Q));
	if (res == NULL) return(NULL);
    } else {
	t = cuddZddIntersect(zdd, cuddT(P), cuddT(Q));
	if (t == NULL) return(NULL);
	cuddRef(t);
	e = cuddZddIntersect(zdd, cuddE(P), cuddE(Q));
	if (e == NULL) {
	    Cudd_RecursiveDerefZdd(table, t);
	    return(NULL);
	}
	cuddRef(e);
	res = cuddZddGetNode(zdd, P->index, t, e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(table, t);
	    Cudd_RecursiveDerefZdd(table, e);
	    return(NULL);
	}
	cuddDeref(t);
	cuddDeref(e);
    }

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

    return(res);

} /* end of cuddZddIntersect */


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

  @sideeffect None

*/
DdNode *
cuddZddDiff(
  DdManager * zdd,
  DdNode * P,
  DdNode * Q)
{
    int		p_top, q_top;
    DdNode	*empty = DD_ZERO(zdd), *t, *e, *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 Cudd_zddDiffConst(). */
    res = cuddCacheLookup2Zdd(table, cuddZddDiff, P, Q);
    if (res != NULL && res != DD_NON_CONSTANT)
	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) {
	e = cuddZddDiff(zdd, cuddE(P), Q);
	if (e == NULL) return(NULL);
	cuddRef(e);
	res = cuddZddGetNode(zdd, P->index, cuddT(P), e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(table, e);
	    return(NULL);
	}
	cuddDeref(e);
    } else if (p_top > q_top) {
	res = cuddZddDiff(zdd, P, cuddE(Q));
	if (res == NULL) return(NULL);
    } else {
	t = cuddZddDiff(zdd, cuddT(P), cuddT(Q));
	if (t == NULL) return(NULL);
	cuddRef(t);
	e = cuddZddDiff(zdd, cuddE(P), cuddE(Q));
	if (e == NULL) {
	    Cudd_RecursiveDerefZdd(table, t);
	    return(NULL);
	}
	cuddRef(e);
	res = cuddZddGetNode(zdd, P->index, t, e);
	if (res == NULL) {
	    Cudd_RecursiveDerefZdd(table, t);
	    Cudd_RecursiveDerefZdd(table, e);
	    return(NULL);
	}
	cuddDeref(t);
	cuddDeref(e);
    }

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

    return(res);

} /* end of cuddZddDiff */


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

  @sideeffect None

*/
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 */


/**
  @brief Computes the positive cofactor of a %ZDD w.r.t. a variable.

  @details In terms of combinations, the result is the set of all
  combinations in which the variable is asserted.  cuddZddSubset1
  performs the same function as Cudd_zddSubset1, but does not restart
  if reordering has taken place. Therefore it can be called from
  within a recursive procedure.

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

  @sideeffect None

  @see cuddZddSubset0 Cudd_zddSubset1

*/
DdNode *
cuddZddSubset1(
  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_subset1_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 cuddZddSubset1 */


/**
  @brief Computes the negative cofactor of a %ZDD w.r.t. a variable.

  @details In terms of combinations, the result is the set of all
  combinations in which the variable is negated.  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.

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

  @sideeffect None

  @see 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 */


/**
  @brief Substitutes a variable with its complement in a %ZDD.

  @details cuddZddChange performs the same function as Cudd_zddChange,
  but does not restart if reordering has taken place. Therefore it can
  be called from within a recursive procedure.

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

  @sideeffect None

  @see Cudd_zddChange

*/
DdNode *
cuddZddChange(
  DdManager * dd,
  DdNode * P,
  int  var)
{
    DdNode	*zvar, *res;

    zvar = cuddUniqueInterZdd(dd, var, DD_ONE(dd), DD_ZERO(dd));
    if (zvar == NULL) return(NULL);
    cuddRef(zvar);

    res = cuddZddChangeAux(dd, P, zvar);
    if (res == NULL) {
	Cudd_RecursiveDerefZdd(dd,zvar);
	return(NULL);
    }
    cuddRef(res);
    Cudd_RecursiveDerefZdd(dd,zvar);
    cuddDeref(res);
    return(res);

} /* end of cuddZddChange */


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


/**
  @brief Performs the recursive step of Cudd_zddSubset1.

  @sideeffect None

*/
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 */


/**
  @brief Performs the recursive step of Cudd_zddSubset0.

  @sideeffect None

*/
static DdNode *
zdd_subset0_aux(
  DdManager * zdd,
  DdNode * P,
  DdNode * zvar)
{
    int		top_var, level;
    DdNode	*res, *t, *e;

    statLine(zdd);

    /* Check cache. */
    res = cuddCacheLookup2Zdd(zdd, zdd_subset0_aux, P, zvar);
    if (res != NULL)
	return(res);

    if (cuddIsConstant(P)) {
	res = P;
	cuddCacheInsert2(zdd, zdd_subset0_aux, P, zvar, res);
	return(res);
    }

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

    if (top_var > level) {
        res = P;
    }
    else if (top_var == level) {
        res = cuddE(P);
    }
    else {
        t = zdd_subset0_aux(zdd, cuddT(P), zvar);
	if (t == NULL) return(NULL);
	cuddRef(t);
        e = zdd_subset0_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_subset0_aux, P, zvar, res);

    return(res);

} /* end of zdd_subset0_aux */


/**
  @brief Replaces variables with constants if possible (part of
  canonical form).

  @sideeffect None

*/
static void
zddVarToConst(
  DdNode * f,
  DdNode ** gp,
  DdNode ** hp,
  DdNode * base,
  DdNode * empty)
{
    DdNode *g = *gp;
    DdNode *h = *hp;

    if (f == g) { /* ITE(F,F,H) = ITE(F,1,H) = F + H */
	*gp = base;
    }

    if (f == h) { /* ITE(F,G,F) = ITE(F,G,0) = F * G */
	*hp = empty;
    }

} /* end of zddVarToConst */