path: root/src/bdd/cudd/cuddZddLin.c

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

  FileName    [cuddZddLin.c]

  PackageName [cudd]

  Synopsis    [Procedures for dynamic variable ordering of ZDDs.]

  Description [Internal procedures included in this module:
                    <ul>
                    <li> cuddZddLinearSifting()
                    </ul>
               Static procedures included in this module:
                    <ul>
                    <li> cuddZddLinearInPlace()
                    <li> cuddZddLinerAux()
                    <li> cuddZddLinearUp()
                    <li> cuddZddLinearDown()
                    <li> cuddZddLinearBackward()
                    <li> cuddZddUndoMoves()
                    </ul>
              ]

  SeeAlso     [cuddLinear.c cuddZddReord.c]

  Author      [Fabio Somenzi]

  Copyright   [Copyright (c) 1995-2004, 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.]

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

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

ABC_NAMESPACE_IMPL_START



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

#define CUDD_SWAP_MOVE 0
#define CUDD_LINEAR_TRANSFORM_MOVE 1
#define CUDD_INVERSE_TRANSFORM_MOVE 2

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


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


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

#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddZddLin.c,v 1.14 2004/08/13 18:04:53 fabio Exp $";
#endif

extern  int     *zdd_entry;
extern  int     zddTotalNumberSwapping;
static  int     zddTotalNumberLinearTr;
static  DdNode  *empty;


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


/**AutomaticStart*************************************************************/

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

static int cuddZddLinearInPlace (DdManager * table, int x, int y);
static int cuddZddLinearAux (DdManager *table, int x, int xLow, int xHigh);
static Move * cuddZddLinearUp (DdManager *table, int y, int xLow, Move *prevMoves);
static Move * cuddZddLinearDown (DdManager *table, int x, int xHigh, Move *prevMoves);
static int cuddZddLinearBackward (DdManager *table, int size, Move *moves);
static Move* cuddZddUndoMoves (DdManager *table, Move *moves);

/**AutomaticEnd***************************************************************/


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


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




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

  Synopsis    [Implementation of the linear sifting algorithm for ZDDs.]

  Description [Implementation of the linear sifting algorithm for ZDDs.
  Assumes that no dead nodes are present.
    <ol>
    <li> Order all the variables according to the number of entries
    in each unique table.
    <li> Sift the variable up and down and applies the XOR transformation,
    remembering each time the total size of the DD heap.
    <li> Select the best permutation.
    <li> Repeat 3 and 4 for all variables.
    </ol>
  Returns 1 if successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
int
cuddZddLinearSifting(
  DdManager * table,
  int  lower,
  int  upper)
{
    int i;
    int *var;
    int size;
    int x;
    int result;
#ifdef DD_STATS
    int previousSize;
#endif

    size = table->sizeZ;
    empty = table->zero;

    /* Find order in which to sift variables. */
    var = NULL;
    zdd_entry = ABC_ALLOC(int, size);
    if (zdd_entry == NULL) {
        table->errorCode = CUDD_MEMORY_OUT;
        goto cuddZddSiftingOutOfMem;
    }
    var = ABC_ALLOC(int, size);
    if (var == NULL) {
        table->errorCode = CUDD_MEMORY_OUT;
        goto cuddZddSiftingOutOfMem;
    }

    for (i = 0; i < size; i++) {
        x = table->permZ[i];
        zdd_entry[i] = table->subtableZ[x].keys;
        var[i] = i;
    }

    qsort((void *)var, size, sizeof(int), (DD_QSFP)cuddZddUniqueCompare);

    /* Now sift. */
    for (i = 0; i < ddMin(table->siftMaxVar, size); i++) {
        if (zddTotalNumberSwapping >= table->siftMaxSwap)
            break;
        x = table->permZ[var[i]];
        if (x < lower || x > upper) continue;
#ifdef DD_STATS
        previousSize = table->keysZ;
#endif
        result = cuddZddLinearAux(table, x, lower, upper);
        if (!result)
            goto cuddZddSiftingOutOfMem;
#ifdef DD_STATS
        if (table->keysZ < (unsigned) previousSize) {
            (void) fprintf(table->out,"-");
        } else if (table->keysZ > (unsigned) previousSize) {
            (void) fprintf(table->out,"+");     /* should never happen */
            (void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ , var[i]);
        } else {
            (void) fprintf(table->out,"=");
        }
        fflush(table->out);
#endif
    }

    ABC_FREE(var);
    ABC_FREE(zdd_entry);

    return(1);

cuddZddSiftingOutOfMem:

    if (zdd_entry != NULL) ABC_FREE(zdd_entry);
    if (var != NULL) ABC_FREE(var);

    return(0);

} /* end of cuddZddLinearSifting */


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


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

  Synopsis    [Linearly combines two adjacent variables.]

  Description [Linearly combines two adjacent variables. It assumes
  that no dead nodes are present on entry to this procedure.  The
  procedure then guarantees that no dead nodes will be present when it
  terminates.  cuddZddLinearInPlace assumes that x &lt; y.  Returns the
  number of keys in the table if successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     [cuddZddSwapInPlace cuddLinearInPlace]

******************************************************************************/
static int
cuddZddLinearInPlace(
  DdManager * table,
  int  x,
  int  y)
{
    DdNodePtr *xlist, *ylist;
    int         xindex, yindex;
    int         xslots, yslots;
    int         xshift, yshift;
    int         oldxkeys, oldykeys;
    int         newxkeys, newykeys;
    int         i;
    int         posn;
    DdNode      *f, *f1, *f0, *f11, *f10, *f01, *f00;
    DdNode      *newf1, *newf0, *g, *next, *previous;
    DdNode      *special;

#ifdef DD_DEBUG
    assert(x < y);
    assert(cuddZddNextHigh(table,x) == y);
    assert(table->subtableZ[x].keys != 0);
    assert(table->subtableZ[y].keys != 0);
    assert(table->subtableZ[x].dead == 0);
    assert(table->subtableZ[y].dead == 0);
#endif

    zddTotalNumberLinearTr++;

    /* Get parameters of x subtable. */
    xindex   = table->invpermZ[x];
    xlist    = table->subtableZ[x].nodelist;
    oldxkeys = table->subtableZ[x].keys;
    xslots   = table->subtableZ[x].slots;
    xshift   = table->subtableZ[x].shift;
    newxkeys = 0;

    /* Get parameters of y subtable. */
    yindex   = table->invpermZ[y];
    ylist    = table->subtableZ[y].nodelist;
    oldykeys = table->subtableZ[y].keys;
    yslots   = table->subtableZ[y].slots;
    yshift   = table->subtableZ[y].shift;
    newykeys = oldykeys;

    /* The nodes in the x layer are put in two chains.  The chain
    ** pointed by g holds the normal nodes. When re-expressed they stay
    ** in the x list. The chain pointed by special holds the elements
    ** that will move to the y list.
    */
    g = special = NULL;
    for (i = 0; i < xslots; i++) {
        f = xlist[i];
        if (f == NULL) continue;
        xlist[i] = NULL;
        while (f != NULL) {
            next = f->next;
            f1 = cuddT(f);
            /* if (f1->index == yindex) */ cuddSatDec(f1->ref);
            f0 = cuddE(f);
            /* if (f0->index == yindex) */ cuddSatDec(f0->ref);
            if ((int) f1->index == yindex && cuddE(f1) == empty &&
                (int) f0->index != yindex) {
                f->next = special;
                special = f;
            } else {
                f->next = g;
                g = f;
            }
            f = next;
        } /* while there are elements in the collision chain */
    } /* for each slot of the x subtable */

    /* Mark y nodes with pointers from above x. We mark them by
    **  changing their index to x.
    */
    for (i = 0; i < yslots; i++) {
        f = ylist[i];
        while (f != NULL) {
            if (f->ref != 0) {
                f->index = xindex;
            }
            f = f->next;
        } /* while there are elements in the collision chain */
    } /* for each slot of the y subtable */

    /* Move special nodes to the y list. */
    f = special;
    while (f != NULL) {
        next = f->next;
        f1 = cuddT(f);
        f11 = cuddT(f1);
        cuddT(f) = f11;
        cuddSatInc(f11->ref);
        f0 = cuddE(f);
        cuddSatInc(f0->ref);
        f->index = yindex;
        /* Insert at the beginning of the list so that it will be
        ** found first if there is a duplicate. The duplicate will
        ** eventually be moved or garbage collected. No node
        ** re-expression will add a pointer to it.
        */
        posn = ddHash(cuddF2L(f11), cuddF2L(f0), yshift);
        f->next = ylist[posn];
        ylist[posn] = f;
        newykeys++;
        f = next;
    }

    /* Take care of the remaining x nodes that must be re-expressed.
    ** They form a linked list pointed by g.
    */
    f = g;
    while (f != NULL) {
#ifdef DD_COUNT
        table->swapSteps++;
#endif
        next = f->next;
        /* Find f1, f0, f11, f10, f01, f00. */
        f1 = cuddT(f);
        if ((int) f1->index == yindex || (int) f1->index == xindex) {
            f11 = cuddT(f1); f10 = cuddE(f1);
        } else {
            f11 = empty; f10 = f1;
        }
        f0 = cuddE(f);
        if ((int) f0->index == yindex || (int) f0->index == xindex) {
            f01 = cuddT(f0); f00 = cuddE(f0);
        } else {
            f01 = empty; f00 = f0;
        }
        /* Create the new T child. */
        if (f01 == empty) {
            newf1 = f10;
            cuddSatInc(newf1->ref);
        } else {
            /* Check ylist for triple (yindex, f01, f10). */
            posn = ddHash(cuddF2L(f01), cuddF2L(f10), yshift);
            /* For each element newf1 in collision list ylist[posn]. */
            newf1 = ylist[posn];
            /* Search the collision chain skipping the marked nodes. */
            while (newf1 != NULL) {
                if (cuddT(newf1) == f01 && cuddE(newf1) == f10 &&
                    (int) newf1->index == yindex) {
                    cuddSatInc(newf1->ref);
                    break; /* match */
                }
                newf1 = newf1->next;
            } /* while newf1 */
            if (newf1 == NULL) {        /* no match */
                newf1 = cuddDynamicAllocNode(table);
                if (newf1 == NULL)
                    goto zddSwapOutOfMem;
                newf1->index = yindex; newf1->ref = 1;
                cuddT(newf1) = f01;
                cuddE(newf1) = f10;
                /* Insert newf1 in the collision list ylist[pos];
                ** increase the ref counts of f01 and f10
                */
                newykeys++;
                newf1->next = ylist[posn];
                ylist[posn] = newf1;
                cuddSatInc(f01->ref);
                cuddSatInc(f10->ref);
            }
        }
        cuddT(f) = newf1;

        /* Do the same for f0. */
        /* Create the new E child. */
        if (f11 == empty) {
            newf0 = f00;
            cuddSatInc(newf0->ref);
        } else {
            /* Check ylist for triple (yindex, f11, f00). */
            posn = ddHash(cuddF2L(f11), cuddF2L(f00), yshift);
            /* For each element newf0 in collision list ylist[posn]. */
            newf0 = ylist[posn];
            while (newf0 != NULL) {
                if (cuddT(newf0) == f11 && cuddE(newf0) == f00 &&
                    (int) newf0->index == yindex) {
                    cuddSatInc(newf0->ref);
                    break; /* match */
                }
                newf0 = newf0->next;
            } /* while newf0 */
            if (newf0 == NULL) {        /* no match */
                newf0 = cuddDynamicAllocNode(table);
                if (newf0 == NULL)
                    goto zddSwapOutOfMem;
                newf0->index = yindex; newf0->ref = 1;
                cuddT(newf0) = f11; cuddE(newf0) = f00;
                /* Insert newf0 in the collision list ylist[posn];
                ** increase the ref counts of f11 and f00.
                */
                newykeys++;
                newf0->next = ylist[posn];
                ylist[posn] = newf0;
                cuddSatInc(f11->ref);
                cuddSatInc(f00->ref);
            }
        }
        cuddE(f) = newf0;

        /* Re-insert the modified f in xlist.
        ** The modified f does not already exists in xlist.
        ** (Because of the uniqueness of the cofactors.)
        */
        posn = ddHash(cuddF2L(newf1), cuddF2L(newf0), xshift);
        newxkeys++;
        f->next = xlist[posn];
        xlist[posn] = f;
        f = next;
    } /* while f != NULL */

    /* GC the y layer and move the marked nodes to the x list. */

    /* For each node f in ylist. */
    for (i = 0; i < yslots; i++) {
        previous = NULL;
        f = ylist[i];
        while (f != NULL) {
            next = f->next;
            if (f->ref == 0) {
                cuddSatDec(cuddT(f)->ref);
                cuddSatDec(cuddE(f)->ref);
                cuddDeallocNode(table, f);
                newykeys--;
                if (previous == NULL)
                    ylist[i] = next;
                else
                    previous->next = next;
            } else if ((int) f->index == xindex) { /* move marked node */
                if (previous == NULL)
                    ylist[i] = next;
                else
                    previous->next = next;
                f1 = cuddT(f);
                cuddSatDec(f1->ref);
                /* Check ylist for triple (yindex, f1, empty). */
                posn = ddHash(cuddF2L(f1), cuddF2L(empty), yshift);
                /* For each element newf1 in collision list ylist[posn]. */
                newf1 = ylist[posn];
                while (newf1 != NULL) {
                    if (cuddT(newf1) == f1 && cuddE(newf1) == empty &&
                        (int) newf1->index == yindex) {
                        cuddSatInc(newf1->ref);
                        break; /* match */
                    }
                    newf1 = newf1->next;
                } /* while newf1 */
                if (newf1 == NULL) {    /* no match */
                    newf1 = cuddDynamicAllocNode(table);
                    if (newf1 == NULL)
                        goto zddSwapOutOfMem;
                    newf1->index = yindex; newf1->ref = 1;
                    cuddT(newf1) = f1; cuddE(newf1) = empty;
                    /* Insert newf1 in the collision list ylist[posn];
                    ** increase the ref counts of f1 and empty.
                    */
                    newykeys++;
                    newf1->next = ylist[posn];
                    ylist[posn] = newf1;
                    if (posn == i && previous == NULL)
                        previous = newf1;
                    cuddSatInc(f1->ref);
                    cuddSatInc(empty->ref);
                }
                cuddT(f) = newf1;
                f0 = cuddE(f);
                /* Insert f in x list. */
                posn = ddHash(cuddF2L(newf1), cuddF2L(f0), xshift);
                newxkeys++;
                newykeys--;
                f->next = xlist[posn];
                xlist[posn] = f;
            } else {
                previous = f;
            }
            f = next;
        } /* while f */
    } /* for i */

    /* Set the appropriate fields in table. */
    table->subtableZ[x].keys     = newxkeys;
    table->subtableZ[y].keys     = newykeys;

    table->keysZ += newxkeys + newykeys - oldxkeys - oldykeys;

    /* Update univ section; univ[x] remains the same. */
    table->univ[y] = cuddT(table->univ[x]);

#if 0
    (void) fprintf(table->out,"x = %d  y = %d\n", x, y);
    (void) Cudd_DebugCheck(table);
    (void) Cudd_CheckKeys(table);
#endif

    return (table->keysZ);

zddSwapOutOfMem:
    (void) fprintf(table->err, "Error: cuddZddSwapInPlace out of memory\n");

    return (0);

} /* end of cuddZddLinearInPlace */


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

  Synopsis    [Given xLow <= x <= xHigh moves x up and down between the
  boundaries.]

  Description [Given xLow <= x <= xHigh moves x up and down between the
  boundaries. Finds the best position and does the required changes.
  Returns 1 if successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
cuddZddLinearAux(
  DdManager * table,
  int  x,
  int  xLow,
  int  xHigh)
{
    Move        *move;
    Move        *moveUp;        /* list of up move */
    Move        *moveDown;      /* list of down move */

    int         initial_size;
    int         result;

    initial_size = table->keysZ;

#ifdef DD_DEBUG
    assert(table->subtableZ[x].keys > 0);
#endif

    moveDown = NULL;
    moveUp = NULL;

    if (x == xLow) {
        moveDown = cuddZddLinearDown(table, x, xHigh, NULL);
        /* At this point x --> xHigh. */
        if (moveDown == (Move *) CUDD_OUT_OF_MEM)
            goto cuddZddLinearAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = cuddZddLinearBackward(table, initial_size, moveDown);
        if (!result)
            goto cuddZddLinearAuxOutOfMem;

    } else if (x == xHigh) {
        moveUp = cuddZddLinearUp(table, x, xLow, NULL);
        /* At this point x --> xLow. */
        if (moveUp == (Move *) CUDD_OUT_OF_MEM)
            goto cuddZddLinearAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = cuddZddLinearBackward(table, initial_size, moveUp);
        if (!result)
            goto cuddZddLinearAuxOutOfMem;

    } else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
        moveDown = cuddZddLinearDown(table, x, xHigh, NULL);
        /* At this point x --> xHigh. */
        if (moveDown == (Move *) CUDD_OUT_OF_MEM)
            goto cuddZddLinearAuxOutOfMem;
        moveUp = cuddZddUndoMoves(table,moveDown);
#ifdef DD_DEBUG
        assert(moveUp == NULL || moveUp->x == x);
#endif
        moveUp = cuddZddLinearUp(table, x, xLow, moveUp);
        if (moveUp == (Move *) CUDD_OUT_OF_MEM)
            goto cuddZddLinearAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = cuddZddLinearBackward(table, initial_size, moveUp);
        if (!result)
            goto cuddZddLinearAuxOutOfMem;

    } else {
        moveUp = cuddZddLinearUp(table, x, xLow, NULL);
        /* At this point x --> xHigh. */
        if (moveUp == (Move *) CUDD_OUT_OF_MEM)
            goto cuddZddLinearAuxOutOfMem;
        /* Then move up. */
        moveDown = cuddZddUndoMoves(table,moveUp);
#ifdef DD_DEBUG
        assert(moveDown == NULL || moveDown->y == x);
#endif
        moveDown = cuddZddLinearDown(table, x, xHigh, moveDown);
        if (moveDown == (Move *) CUDD_OUT_OF_MEM)
            goto cuddZddLinearAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = cuddZddLinearBackward(table, initial_size, moveDown);
        if (!result)
            goto cuddZddLinearAuxOutOfMem;
    }

    while (moveDown != NULL) {
        move = moveDown->next;
        cuddDeallocMove(table, moveDown);
        moveDown = move;
    }
    while (moveUp != NULL) {
        move = moveUp->next;
        cuddDeallocMove(table, moveUp);
        moveUp = move;
    }

    return(1);

cuddZddLinearAuxOutOfMem:
    if (moveDown != (Move *) CUDD_OUT_OF_MEM) {
        while (moveDown != NULL) {
            move = moveDown->next;
            cuddDeallocMove(table, moveDown);
            moveDown = move;
        }
    }
    if (moveUp != (Move *) CUDD_OUT_OF_MEM) {
        while (moveUp != NULL) {
            move = moveUp->next;
            cuddDeallocMove(table, moveUp);
            moveUp = move;
        }
    }

    return(0);

} /* end of cuddZddLinearAux */


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

  Synopsis    [Sifts a variable up applying the XOR transformation.]

  Description [Sifts a variable up applying the XOR
  transformation. Moves y up until either it reaches the bound (xLow)
  or the size of the ZDD heap increases too much.  Returns the set of
  moves in case of success; NULL if memory is full.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static Move *
cuddZddLinearUp(
  DdManager * table,
  int  y,
  int  xLow,
  Move * prevMoves)
{
    Move        *moves;
    Move        *move;
    int         x;
    int         size, newsize;
    int         limitSize;

    moves = prevMoves;
    limitSize = table->keysZ;

    x = cuddZddNextLow(table, y);
    while (x >= xLow) {
        size = cuddZddSwapInPlace(table, x, y);
        if (size == 0)
            goto cuddZddLinearUpOutOfMem;
        newsize = cuddZddLinearInPlace(table, x, y);
        if (newsize == 0)
            goto cuddZddLinearUpOutOfMem;
        move = (Move *) cuddDynamicAllocNode(table);
        if (move == NULL)
            goto cuddZddLinearUpOutOfMem;
        move->x = x;
        move->y = y;
        move->next = moves;
        moves = move;
        move->flags = CUDD_SWAP_MOVE;
        if (newsize > size) {
            /* Undo transformation. The transformation we apply is
            ** its own inverse. Hence, we just apply the transformation
            ** again.
            */
            newsize = cuddZddLinearInPlace(table,x,y);
            if (newsize == 0) goto cuddZddLinearUpOutOfMem;
#ifdef DD_DEBUG
            if (newsize != size) {
                (void) fprintf(table->err,"Change in size after identity transformation! From %d to %d\n",size,newsize);
            }
#endif
        } else {
            size = newsize;
            move->flags = CUDD_LINEAR_TRANSFORM_MOVE;
        }
        move->size = size;

        if ((double)size > (double)limitSize * table->maxGrowth)
            break;
        if (size < limitSize)
            limitSize = size;

        y = x;
        x = cuddZddNextLow(table, y);
    }
    return(moves);

cuddZddLinearUpOutOfMem:
    while (moves != NULL) {
        move = moves->next;
        cuddDeallocMove(table, moves);
        moves = move;
    }
    return((Move *) CUDD_OUT_OF_MEM);

} /* end of cuddZddLinearUp */


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

  Synopsis    [Sifts a variable down and applies the XOR transformation.]

  Description [Sifts a variable down. Moves x down until either it
  reaches the bound (xHigh) or the size of the ZDD heap increases too
  much. Returns the set of moves in case of success; NULL if memory is
  full.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static Move *
cuddZddLinearDown(
  DdManager * table,
  int  x,
  int  xHigh,
  Move * prevMoves)
{
    Move        *moves;
    Move        *move;
    int         y;
    int         size, newsize;
    int         limitSize;

    moves = prevMoves;
    limitSize = table->keysZ;

    y = cuddZddNextHigh(table, x);
    while (y <= xHigh) {
        size = cuddZddSwapInPlace(table, x, y);
        if (size == 0)
            goto cuddZddLinearDownOutOfMem;
        newsize = cuddZddLinearInPlace(table, x, y);
        if (newsize == 0)
            goto cuddZddLinearDownOutOfMem;
        move = (Move *) cuddDynamicAllocNode(table);
        if (move == NULL)
            goto cuddZddLinearDownOutOfMem;
        move->x = x;
        move->y = y;
        move->next = moves;
        moves = move;
        move->flags = CUDD_SWAP_MOVE;
        if (newsize > size) {
            /* Undo transformation. The transformation we apply is
            ** its own inverse. Hence, we just apply the transformation
            ** again.
            */
            newsize = cuddZddLinearInPlace(table,x,y);
            if (newsize == 0) goto cuddZddLinearDownOutOfMem;
            if (newsize != size) {
                (void) fprintf(table->err,"Change in size after identity transformation! From %d to %d\n",size,newsize);
            }
        } else {
            size = newsize;
            move->flags = CUDD_LINEAR_TRANSFORM_MOVE;
        }
        move->size = size;

        if ((double)size > (double)limitSize * table->maxGrowth)
            break;
        if (size < limitSize)
            limitSize = size;

        x = y;
        y = cuddZddNextHigh(table, x);
    }
    return(moves);

cuddZddLinearDownOutOfMem:
    while (moves != NULL) {
        move = moves->next;
        cuddDeallocMove(table, moves);
        moves = move;
    }
    return((Move *) CUDD_OUT_OF_MEM);

} /* end of cuddZddLinearDown */


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

  Synopsis    [Given a set of moves, returns the ZDD heap to the position
  giving the minimum size.]

  Description [Given a set of moves, returns the ZDD heap to the
  position giving the minimum size. In case of ties, returns to the
  closest position giving the minimum size. Returns 1 in case of
  success; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
cuddZddLinearBackward(
  DdManager * table,
  int  size,
  Move * moves)
{
    Move        *move;
    int         res;

    /* Find the minimum size among moves. */
    for (move = moves; move != NULL; move = move->next) {
        if (move->size < size) {
            size = move->size;
        }
    }

    for (move = moves; move != NULL; move = move->next) {
        if (move->size == size) return(1);
        if (move->flags == CUDD_LINEAR_TRANSFORM_MOVE) {
            res = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
            if (!res) return(0);
        }
        res = cuddZddSwapInPlace(table, move->x, move->y);
        if (!res)
            return(0);
        if (move->flags == CUDD_INVERSE_TRANSFORM_MOVE) {
            res = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
            if (!res) return(0);
        }
    }

    return(1);

} /* end of cuddZddLinearBackward */


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

  Synopsis    [Given a set of moves, returns the ZDD heap to the order
  in effect before the moves.]

  Description [Given a set of moves, returns the ZDD heap to the
  order in effect before the moves.  Returns 1 in case of success;
  0 otherwise.]

  SideEffects [None]

******************************************************************************/
static Move*
cuddZddUndoMoves(
  DdManager * table,
  Move * moves)
{
    Move *invmoves = NULL;
    Move *move;
    Move *invmove;
    int size;

    for (move = moves; move != NULL; move = move->next) {
        invmove = (Move *) cuddDynamicAllocNode(table);
        if (invmove == NULL) goto cuddZddUndoMovesOutOfMem;
        invmove->x = move->x;
        invmove->y = move->y;
        invmove->next = invmoves;
        invmoves = invmove;
        if (move->flags == CUDD_SWAP_MOVE) {
            invmove->flags = CUDD_SWAP_MOVE;
            size = cuddZddSwapInPlace(table,(int)move->x,(int)move->y);
            if (!size) goto cuddZddUndoMovesOutOfMem;
        } else if (move->flags == CUDD_LINEAR_TRANSFORM_MOVE) {
            invmove->flags = CUDD_INVERSE_TRANSFORM_MOVE;
            size = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
            if (!size) goto cuddZddUndoMovesOutOfMem;
            size = cuddZddSwapInPlace(table,(int)move->x,(int)move->y);
            if (!size) goto cuddZddUndoMovesOutOfMem;
        } else { /* must be CUDD_INVERSE_TRANSFORM_MOVE */
#ifdef DD_DEBUG
            (void) fprintf(table->err,"Unforseen event in ddUndoMoves!\n");
#endif
            invmove->flags = CUDD_LINEAR_TRANSFORM_MOVE;
            size = cuddZddSwapInPlace(table,(int)move->x,(int)move->y);
            if (!size) goto cuddZddUndoMovesOutOfMem;
            size = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
            if (!size) goto cuddZddUndoMovesOutOfMem;
        }
        invmove->size = size;
    }

    return(invmoves);

cuddZddUndoMovesOutOfMem:
    while (invmoves != NULL) {
        move = invmoves->next;
        cuddDeallocMove(table, invmoves);
        invmoves = move;
    }
    return((Move *) CUDD_OUT_OF_MEM);

} /* end of cuddZddUndoMoves */


ABC_NAMESPACE_IMPL_END