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

  FileName    [cuddZddSymm.c]

  PackageName [cudd]

  Synopsis    [Functions for symmetry-based ZDD variable reordering.]

  Description [External procedures included in this module:
            <ul>
            <li> Cudd_zddSymmProfile()
            </ul>
           Internal procedures included in this module:
            <ul>
            <li> cuddZddSymmCheck()
            <li> cuddZddSymmSifting()
            <li> cuddZddSymmSiftingConv()
            </ul>
           Static procedures included in this module:
            <ul>
            <li> cuddZddUniqueCompare()
            <li> cuddZddSymmSiftingAux()
            <li> cuddZddSymmSiftingConvAux()
            <li> cuddZddSymmSifting_up()
            <li> cuddZddSymmSifting_down()
            <li> zdd_group_move()
            <li> cuddZddSymmSiftingBackward()
            <li> zdd_group_move_backward()
            </ul>
          ]

  SeeAlso     [cuddSymmetry.c]

  Author      [Hyong-Kyoon Shin, 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"

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

#define ZDD_MV_OOM (Move *)1

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

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

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

#ifndef lint
static char rcsid[] DD_UNUSED = "$Id: cuddZddSymm.c,v 1.1.1.1 2003/02/24 22:23:54 wjiang Exp $";
#endif

extern int       *zdd_entry;

extern int    zddTotalNumberSwapping;

static DdNode    *empty;

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


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

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

static int cuddZddSymmSiftingAux ARGS((DdManager *table, int x, int x_low, int x_high));
static int cuddZddSymmSiftingConvAux ARGS((DdManager *table, int x, int x_low, int x_high));
static Move * cuddZddSymmSifting_up ARGS((DdManager *table, int x, int x_low, int initial_size));
static Move * cuddZddSymmSifting_down ARGS((DdManager *table, int x, int x_high, int initial_size));
static int cuddZddSymmSiftingBackward ARGS((DdManager *table, Move *moves, int size));
static int zdd_group_move ARGS((DdManager *table, int x, int y, Move **moves));
static int zdd_group_move_backward ARGS((DdManager *table, int x, int y));
static void cuddZddSymmSummary ARGS((DdManager *table, int lower, int upper, int *symvars, int *symgroups));

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


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


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

  Synopsis [Prints statistics on symmetric ZDD variables.]

  Description []

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
void
Cudd_zddSymmProfile(
  DdManager * table,
  int  lower,
  int  upper)
{
    int        i, x, gbot;
    int        TotalSymm = 0;
    int     TotalSymmGroups = 0;
    int     nvars;

    nvars = table->sizeZ;

    for (i = lower; i < upper; i++) {
    if (table->subtableZ[i].next != (unsigned) i) {
        x = i;
        (void) fprintf(table->out,"Group:");
        do {
        (void) fprintf(table->out,"  %d", table->invpermZ[x]);
        TotalSymm++;
        gbot = x;
        x = table->subtableZ[x].next;
        } while (x != i);
        TotalSymmGroups++;
#ifdef DD_DEBUG
        assert(table->subtableZ[gbot].next == (unsigned) i);
#endif
        i = gbot;
        (void) fprintf(table->out,"\n");
    }
    }
    (void) fprintf(table->out,"Total Symmetric = %d\n", TotalSymm);
    (void) fprintf(table->out,"Total Groups = %d\n", TotalSymmGroups);

} /* end of Cudd_zddSymmProfile */


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


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

  Synopsis [Checks for symmetry of x and y.]

  Description [Checks for symmetry of x and y. Ignores projection
  functions, unless they are isolated. Returns 1 in case of
  symmetry; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
int
cuddZddSymmCheck(
  DdManager * table,
  int  x,
  int  y)
{
    int        i;
    DdNode    *f, *f0, *f1, *f01, *f00, *f11, *f10;
    int        yindex;
    int     xsymmy = 1;
    int        xsymmyp = 1;
    int     arccount = 0;
    int     TotalRefCount = 0;
    int     symm_found;

    empty = table->zero;

    yindex = table->invpermZ[y];
    for (i = table->subtableZ[x].slots - 1; i >= 0; i--) {
    f = table->subtableZ[x].nodelist[i];
    while (f != NULL) {
        /* Find f1, f0, f11, f10, f01, f00 */
        f1 = cuddT(f);
        f0 = cuddE(f);
        if ((int) f1->index == yindex) {
        f11 = cuddT(f1);
        f10 = cuddE(f1);
        if (f10 != empty)
            arccount++;
        } else {
        if ((int) f0->index != yindex) {
            return(0); /* f bypasses layer y */
        }
        f11 = empty;
        f10 = f1;
        }
        if ((int) f0->index == yindex) {
        f01 = cuddT(f0);
        f00 = cuddE(f0);
        if (f00 != empty)
            arccount++;
        } else {
        f01 = empty;
        f00 = f0;
        }
        if (f01 != f10)
        xsymmy = 0;
        if (f11 != f00)
        xsymmyp = 0;
        if ((xsymmy == 0) && (xsymmyp == 0))
        return(0);

        f = f->next;
    } /* for each element of the collision list */
    } /* for each slot of the subtable */

    /* Calculate the total reference counts of y
    ** whose else arc is not empty.
    */
    for (i = table->subtableZ[y].slots - 1; i >= 0; i--) {
    f = table->subtableZ[y].nodelist[i];
    while (f != NIL(DdNode)) {
        if (cuddE(f) != empty)
        TotalRefCount += f->ref;
        f = f->next;
    }
    }

    symm_found = (arccount == TotalRefCount);
#if defined(DD_DEBUG) && defined(DD_VERBOSE)
    if (symm_found) {
    int xindex = table->invpermZ[x];
    (void) fprintf(table->out,
               "Found symmetry! x =%d\ty = %d\tPos(%d,%d)\n",
               xindex,yindex,x,y);
    }
#endif

    return(symm_found);

} /* end cuddZddSymmCheck */


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

  Synopsis [Symmetric sifting algorithm for ZDDs.]

  Description [Symmetric sifting algorithm.
  Assumes that no dead nodes are present.
    <ol>
    <li> Order all the variables according to the number of entries in
    each unique subtable.
    <li> Sift the variable up and down, remembering each time the total
    size of the ZDD heap and grouping variables that are symmetric.
    <li> Select the best permutation.
    <li> Repeat 3 and 4 for all variables.
    </ol>
  Returns 1 plus the number of symmetric variables if successful; 0
  otherwise.]

  SideEffects [None]

  SeeAlso     [cuddZddSymmSiftingConv]

******************************************************************************/
int
cuddZddSymmSifting(
  DdManager * table,
  int  lower,
  int  upper)
{
    int        i;
    int        *var;
    int        nvars;
    int        x;
    int        result;
    int        symvars;
    int        symgroups;
    int        iteration;
#ifdef DD_STATS
    int        previousSize;
#endif

    nvars = table->sizeZ;

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

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

    qsort((void *)var, nvars, sizeof(int), (int (*)(const void *, const void *))cuddZddUniqueCompare);

    /* Initialize the symmetry of each subtable to itself. */
    for (i = lower; i <= upper; i++)
    table->subtableZ[i].next = i;

    iteration = ddMin(table->siftMaxVar, nvars);
    for (i = 0; i < iteration; i++) {
    if (zddTotalNumberSwapping >= table->siftMaxSwap)
        break;
    x = table->permZ[var[i]];
#ifdef DD_STATS
    previousSize = table->keysZ;
#endif
    if (x < lower || x > upper) continue;
    if (table->subtableZ[x].next == (unsigned) x) {
        result = cuddZddSymmSiftingAux(table, x, lower, upper);
        if (!result)
        goto cuddZddSymmSiftingOutOfMem;
#ifdef DD_STATS
        if (table->keysZ < (unsigned) previousSize) {
        (void) fprintf(table->out,"-");
        } else if (table->keysZ > (unsigned) previousSize) {
        (void) fprintf(table->out,"+");
#ifdef DD_VERBOSE
        (void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ, var[i]);
#endif
        } else {
        (void) fprintf(table->out,"=");
        }
        fflush(table->out);
#endif
    }
    }

    FREE(var);
    FREE(zdd_entry);

    cuddZddSymmSummary(table, lower, upper, &symvars, &symgroups);

#ifdef DD_STATS
    (void) fprintf(table->out,"\n#:S_SIFTING %8d: symmetric variables\n",symvars);
    (void) fprintf(table->out,"#:G_SIFTING %8d: symmetric groups\n",symgroups);
#endif

    return(1+symvars);

cuddZddSymmSiftingOutOfMem:

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

    return(0);

} /* end of cuddZddSymmSifting */


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

  Synopsis [Symmetric sifting to convergence algorithm for ZDDs.]

  Description [Symmetric sifting to convergence 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 subtable.
    <li> Sift the variable up and down, remembering each time the total
    size of the ZDD heap and grouping variables that are symmetric.
    <li> Select the best permutation.
    <li> Repeat 3 and 4 for all variables.
    <li> Repeat 1-4 until no further improvement.
    </ol>
  Returns 1 plus the number of symmetric variables if successful; 0
  otherwise.]

  SideEffects [None]

  SeeAlso     [cuddZddSymmSifting]

******************************************************************************/
int
cuddZddSymmSiftingConv(
  DdManager * table,
  int  lower,
  int  upper)
{
    int        i;
    int        *var;
    int        nvars;
    int        initialSize;
    int        x;
    int        result;
    int        symvars;
    int        symgroups;
    int        classes;
    int        iteration;
#ifdef DD_STATS
    int         previousSize;
#endif

    initialSize = table->keysZ;

    nvars = table->sizeZ;

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

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

    qsort((void *)var, nvars, sizeof(int), (int (*)(const void *, const void *))cuddZddUniqueCompare);

    /* Initialize the symmetry of each subtable to itself
    ** for first pass of converging symmetric sifting.
    */
    for (i = lower; i <= upper; i++)
    table->subtableZ[i].next = i;

    iteration = ddMin(table->siftMaxVar, table->sizeZ);
    for (i = 0; i < iteration; i++) {
    if (zddTotalNumberSwapping >= table->siftMaxSwap)
        break;
    x = table->permZ[var[i]];
    if (x < lower || x > upper) continue;
    /* Only sift if not in symmetry group already. */
    if (table->subtableZ[x].next == (unsigned) x) {
#ifdef DD_STATS
        previousSize = table->keysZ;
#endif
        result = cuddZddSymmSiftingAux(table, x, lower, upper);
        if (!result)
        goto cuddZddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
        if (table->keysZ < (unsigned) previousSize) {
        (void) fprintf(table->out,"-");
        } else if (table->keysZ > (unsigned) previousSize) {
        (void) fprintf(table->out,"+");
#ifdef DD_VERBOSE
        (void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ, var[i]);
#endif
        } else {
        (void) fprintf(table->out,"=");
        }
        fflush(table->out);
#endif
    }
    }

    /* Sifting now until convergence. */
    while ((unsigned) initialSize > table->keysZ) {
    initialSize = table->keysZ;
#ifdef DD_STATS
    (void) fprintf(table->out,"\n");
#endif
    /* Here we consider only one representative for each symmetry class. */
    for (x = lower, classes = 0; x <= upper; x++, classes++) {
        while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
        /* Here x is the largest index in a group.
        ** Groups consists of adjacent variables.
        ** Hence, the next increment of x will move it to a new group.
        */
        i = table->invpermZ[x];
        zdd_entry[i] = table->subtableZ[x].keys;
        var[classes] = i;
    }

    qsort((void *)var,classes,sizeof(int),(int (*)(const void *, const void *))cuddZddUniqueCompare);

    /* Now sift. */
    iteration = ddMin(table->siftMaxVar, nvars);
    for (i = 0; i < iteration; i++) {
        if (zddTotalNumberSwapping >= table->siftMaxSwap)
        break;
        x = table->permZ[var[i]];
        if ((unsigned) x >= table->subtableZ[x].next) {
#ifdef DD_STATS
        previousSize = table->keysZ;
#endif
        result = cuddZddSymmSiftingConvAux(table, x, lower, upper);
        if (!result)
            goto cuddZddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
        if (table->keysZ < (unsigned) previousSize) {
            (void) fprintf(table->out,"-");
        } else if (table->keysZ > (unsigned) previousSize) {
            (void) fprintf(table->out,"+");
#ifdef DD_VERBOSE
        (void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ, var[i]);
#endif
        } else {
            (void) fprintf(table->out,"=");
        }
        fflush(table->out);
#endif
        }
    } /* for */
    }

    cuddZddSymmSummary(table, lower, upper, &symvars, &symgroups);

#ifdef DD_STATS
    (void) fprintf(table->out,"\n#:S_SIFTING %8d: symmetric variables\n",
           symvars);
    (void) fprintf(table->out,"#:G_SIFTING %8d: symmetric groups\n",
           symgroups);
#endif

    FREE(var);
    FREE(zdd_entry);

    return(1+symvars);

cuddZddSymmSiftingConvOutOfMem:

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

    return(0);

} /* end of cuddZddSymmSiftingConv */


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


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

  Synopsis [Given x_low <= x <= x_high moves x up and down between the
  boundaries.]

  Description [Given x_low <= x <= x_high moves x up and down between the
  boundaries. Finds the best position and does the required changes.
  Assumes that x is not part of a symmetry group. Returns 1 if
  successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
cuddZddSymmSiftingAux(
  DdManager * table,
  int  x,
  int  x_low,
  int  x_high)
{
    Move *move;
    Move *move_up;    /* list of up move */
    Move *move_down;    /* list of down move */
    int     initial_size;
    int     result;
    int     i;
    int  topbot;    /* index to either top or bottom of symmetry group */
    int     init_group_size, final_group_size;

    initial_size = table->keysZ;

    move_down = NULL;
    move_up = NULL;

    /* Look for consecutive symmetries above x. */
    for (i = x; i > x_low; i--) {
    if (!cuddZddSymmCheck(table, i - 1, i))
            break;
    /* find top of i-1's symmetry */
    topbot = table->subtableZ[i - 1].next;
    table->subtableZ[i - 1].next = i;
    table->subtableZ[x].next = topbot;
    /* x is bottom of group so its symmetry is top of i-1's
       group */
    i = topbot + 1; /* add 1 for i--, new i is top of symm group */
    }
    /* Look for consecutive symmetries below x. */
    for (i = x; i < x_high; i++) {
    if (!cuddZddSymmCheck(table, i, i + 1))
            break;
    /* find bottom of i+1's symm group */
    topbot = i + 1;
    while ((unsigned) topbot < table->subtableZ[topbot].next)
        topbot = table->subtableZ[topbot].next;

    table->subtableZ[topbot].next = table->subtableZ[i].next;
    table->subtableZ[i].next = i + 1;
    i = topbot - 1; /* add 1 for i++,
               new i is bottom of symm group */
    }

    /* Now x maybe in the middle of a symmetry group. */
    if (x == x_low) { /* Sift down */
    /* Find bottom of x's symm group */
    while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;

    i = table->subtableZ[x].next;
    init_group_size = x - i + 1;

    move_down = cuddZddSymmSifting_down(table, x, x_high,
        initial_size);
    /* after that point x --> x_high, unless early term */
    if (move_down == ZDD_MV_OOM)
        goto cuddZddSymmSiftingAuxOutOfMem;

    if (move_down == NULL ||
        table->subtableZ[move_down->y].next != move_down->y) {
        /* symmetry detected may have to make another complete
           pass */
            if (move_down != NULL)
        x = move_down->y;
        else
        x = table->subtableZ[x].next;
        i = x;
        while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
        }
        final_group_size = i - x + 1;

        if (init_group_size == final_group_size) {
        /* No new symmetry groups detected,
           return to best position */
        result = cuddZddSymmSiftingBackward(table,
            move_down, initial_size);
        }
        else {
        initial_size = table->keysZ;
        move_up = cuddZddSymmSifting_up(table, x, x_low,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_down,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingAuxOutOfMem;
    }
    else if (x == x_high) { /* Sift up */
    /* Find top of x's symm group */
    while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
    x = table->subtableZ[x].next;

    i = x;
    while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
    }
    init_group_size = i - x + 1;

    move_up = cuddZddSymmSifting_up(table, x, x_low, initial_size);
    /* after that point x --> x_low, unless early term */
    if (move_up == ZDD_MV_OOM)
        goto cuddZddSymmSiftingAuxOutOfMem;

    if (move_up == NULL ||
        table->subtableZ[move_up->x].next != move_up->x) {
        /* symmetry detected may have to make another complete
        pass */
            if (move_up != NULL)
        x = move_up->x;
        else {
        while ((unsigned) x < table->subtableZ[x].next)
            x = table->subtableZ[x].next;
        }
        i = table->subtableZ[x].next;
        final_group_size = x - i + 1;

        if (init_group_size == final_group_size) {
        /* No new symmetry groups detected,
           return to best position */
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
        else {
        initial_size = table->keysZ;
        move_down = cuddZddSymmSifting_down(table, x, x_high,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_up,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingAuxOutOfMem;
    }
    else if ((x - x_low) > (x_high - x)) { /* must go down first:
                        shorter */
    /* Find bottom of x's symm group */
    while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;

    move_down = cuddZddSymmSifting_down(table, x, x_high,
        initial_size);
    /* after that point x --> x_high, unless early term */
    if (move_down == ZDD_MV_OOM)
        goto cuddZddSymmSiftingAuxOutOfMem;

    if (move_down != NULL) {
        x = move_down->y;
    }
    else {
        x = table->subtableZ[x].next;
    }
    i = x;
    while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
    }
    init_group_size = i - x + 1;

    move_up = cuddZddSymmSifting_up(table, x, x_low, initial_size);
    if (move_up == ZDD_MV_OOM)
        goto cuddZddSymmSiftingAuxOutOfMem;

    if (move_up == NULL ||
        table->subtableZ[move_up->x].next != move_up->x) {
        /* symmetry detected may have to make another complete
           pass */
        if (move_up != NULL) {
        x = move_up->x;
        }
        else {
        while ((unsigned) x < table->subtableZ[x].next)
            x = table->subtableZ[x].next;
        }
        i = table->subtableZ[x].next;
        final_group_size = x - i + 1;

        if (init_group_size == final_group_size) {
        /* No new symmetry groups detected,
           return to best position */
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
        else {
        while (move_down != NULL) {
            move = move_down->next;
            cuddDeallocNode(table, (DdNode *)move_down);
            move_down = move;
        }
        initial_size = table->keysZ;
        move_down = cuddZddSymmSifting_down(table, x, x_high,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_up,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingAuxOutOfMem;
    }
    else { /* moving up first:shorter */
        /* Find top of x's symmetry group */
    while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
    x = table->subtableZ[x].next;

    move_up = cuddZddSymmSifting_up(table, x, x_low, initial_size);
    /* after that point x --> x_high, unless early term */
    if (move_up == ZDD_MV_OOM)
        goto cuddZddSymmSiftingAuxOutOfMem;

    if (move_up != NULL) {
        x = move_up->x;
    }
    else {
        while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
    }
    i = table->subtableZ[x].next;
    init_group_size = x - i + 1;

    move_down = cuddZddSymmSifting_down(table, x, x_high,
        initial_size);
    if (move_down == ZDD_MV_OOM)
        goto cuddZddSymmSiftingAuxOutOfMem;

    if (move_down == NULL ||
        table->subtableZ[move_down->y].next != move_down->y) {
        /* symmetry detected may have to make another complete
           pass */
            if (move_down != NULL) {
        x = move_down->y;
        }
        else {
        x = table->subtableZ[x].next;
        }
        i = x;
        while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
        }
        final_group_size = i - x + 1;

        if (init_group_size == final_group_size) {
        /* No new symmetries detected,
           go back to best position */
        result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
        }
        else {
        while (move_up != NULL) {
            move = move_up->next;
            cuddDeallocNode(table, (DdNode *)move_up);
            move_up = move;
        }
        initial_size = table->keysZ;
        move_up = cuddZddSymmSifting_up(table, x, x_low,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_down,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingAuxOutOfMem;
    }

    while (move_down != NULL) {
    move = move_down->next;
    cuddDeallocNode(table, (DdNode *)move_down);
    move_down = move;
    }
    while (move_up != NULL) {
    move = move_up->next;
    cuddDeallocNode(table, (DdNode *)move_up);
    move_up = move;
    }

    return(1);

cuddZddSymmSiftingAuxOutOfMem:
    if (move_down != ZDD_MV_OOM) {
    while (move_down != NULL) {
        move = move_down->next;
        cuddDeallocNode(table, (DdNode *)move_down);
        move_down = move;
    }
    }
    if (move_up != ZDD_MV_OOM) {
    while (move_up != NULL) {
        move = move_up->next;
        cuddDeallocNode(table, (DdNode *)move_up);
        move_up = move;
    }
    }

    return(0);

} /* end of cuddZddSymmSiftingAux */


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

  Synopsis [Given x_low <= x <= x_high moves x up and down between the
  boundaries.]

  Description [Given x_low <= x <= x_high moves x up and down between the
  boundaries. Finds the best position and does the required changes.
  Assumes that x is either an isolated variable, or it is the bottom of
  a symmetry group. All symmetries may not have been found, because of
  exceeded growth limit. Returns 1 if successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
cuddZddSymmSiftingConvAux(
  DdManager * table,
  int  x,
  int  x_low,
  int  x_high)
{
    Move    *move;
    Move    *move_up;    /* list of up move */
    Move    *move_down;    /* list of down move */
    int        initial_size;
    int        result;
    int        i;
    int        init_group_size, final_group_size;

    initial_size = table->keysZ;

    move_down = NULL;
    move_up = NULL;

    if (x == x_low) { /* Sift down */
        i = table->subtableZ[x].next;
    init_group_size = x - i + 1;

    move_down = cuddZddSymmSifting_down(table, x, x_high,
        initial_size);
    /* after that point x --> x_high, unless early term */
    if (move_down == ZDD_MV_OOM)
        goto cuddZddSymmSiftingConvAuxOutOfMem;

    if (move_down == NULL ||
        table->subtableZ[move_down->y].next != move_down->y) {
        /* symmetry detected may have to make another complete
        pass */
            if (move_down != NULL)
        x = move_down->y;
        else {
        while ((unsigned) x < table->subtableZ[x].next);
            x = table->subtableZ[x].next;
        x = table->subtableZ[x].next;
        }
        i = x;
        while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
        }
        final_group_size = i - x + 1;

        if (init_group_size == final_group_size) {
        /* No new symmetries detected,
           go back to best position */
        result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
        }
        else {
        initial_size = table->keysZ;
        move_up = cuddZddSymmSifting_up(table, x, x_low,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_down,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingConvAuxOutOfMem;
    }
    else if (x == x_high) { /* Sift up */
    /* Find top of x's symm group */
    while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
    x = table->subtableZ[x].next;

    i = x;
    while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
    }
    init_group_size = i - x + 1;

    move_up = cuddZddSymmSifting_up(table, x, x_low, initial_size);
    /* after that point x --> x_low, unless early term */
    if (move_up == ZDD_MV_OOM)
        goto cuddZddSymmSiftingConvAuxOutOfMem;

    if (move_up == NULL ||
        table->subtableZ[move_up->x].next != move_up->x) {
        /* symmetry detected may have to make another complete
           pass */
            if (move_up != NULL)
        x = move_up->x;
        else {
        while ((unsigned) x < table->subtableZ[x].next)
            x = table->subtableZ[x].next;
        }
        i = table->subtableZ[x].next;
        final_group_size = x - i + 1;

        if (init_group_size == final_group_size) {
        /* No new symmetry groups detected,
           return to best position */
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
        else {
        initial_size = table->keysZ;
        move_down = cuddZddSymmSifting_down(table, x, x_high,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_up,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingConvAuxOutOfMem;
    }
    else if ((x - x_low) > (x_high - x)) { /* must go down first:
                        shorter */
    move_down = cuddZddSymmSifting_down(table, x, x_high,
        initial_size);
    /* after that point x --> x_high */
    if (move_down == ZDD_MV_OOM)
        goto cuddZddSymmSiftingConvAuxOutOfMem;

    if (move_down != NULL) {
        x = move_down->y;
    }
    else {
        while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
        x = table->subtableZ[x].next;
    }
    i = x;
    while ((unsigned) i < table->subtableZ[i].next) {
        i = table->subtableZ[i].next;
    }
    init_group_size = i - x + 1;

    move_up = cuddZddSymmSifting_up(table, x, x_low, initial_size);
    if (move_up == ZDD_MV_OOM)
        goto cuddZddSymmSiftingConvAuxOutOfMem;

    if (move_up == NULL ||
        table->subtableZ[move_up->x].next != move_up->x) {
        /* symmetry detected may have to make another complete
           pass */
        if (move_up != NULL) {
        x = move_up->x;
        }
        else {
        while ((unsigned) x < table->subtableZ[x].next)
            x = table->subtableZ[x].next;
        }
            i = table->subtableZ[x].next;
            final_group_size = x - i + 1;

            if (init_group_size == final_group_size) {
        /* No new symmetry groups detected,
           return to best position */
                result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
            }
        else {
        while (move_down != NULL) {
            move = move_down->next;
            cuddDeallocNode(table, (DdNode *)move_down);
            move_down = move;
        }
        initial_size = table->keysZ;
        move_down = cuddZddSymmSifting_down(table, x, x_high,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_up,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingConvAuxOutOfMem;
    }
    else { /* moving up first:shorter */
    /* Find top of x's symmetry group */
    x = table->subtableZ[x].next;

    move_up = cuddZddSymmSifting_up(table, x, x_low, initial_size);
    /* after that point x --> x_high, unless early term */
    if (move_up == ZDD_MV_OOM)
        goto cuddZddSymmSiftingConvAuxOutOfMem;

    if (move_up != NULL) {
        x = move_up->x;
    }
    else {
        while ((unsigned) x < table->subtableZ[x].next)
        x = table->subtableZ[x].next;
    }
        i = table->subtableZ[x].next;
        init_group_size = x - i + 1;

    move_down = cuddZddSymmSifting_down(table, x, x_high,
        initial_size);
    if (move_down == ZDD_MV_OOM)
        goto cuddZddSymmSiftingConvAuxOutOfMem;

    if (move_down == NULL ||
        table->subtableZ[move_down->y].next != move_down->y) {
        /* symmetry detected may have to make another complete
           pass */
            if (move_down != NULL) {
        x = move_down->y;
        }
        else {
        while ((unsigned) x < table->subtableZ[x].next)
            x = table->subtableZ[x].next;
        x = table->subtableZ[x].next;
        }
            i = x;
            while ((unsigned) i < table->subtableZ[i].next) {
                i = table->subtableZ[i].next;
            }
        final_group_size = i - x + 1;

            if (init_group_size == final_group_size) {
        /* No new symmetries detected,
           go back to best position */
                result = cuddZddSymmSiftingBackward(table, move_down,
            initial_size);
            }
        else {
        while (move_up != NULL) {
            move = move_up->next;
            cuddDeallocNode(table, (DdNode *)move_up);
            move_up = move;
        }
        initial_size = table->keysZ;
        move_up = cuddZddSymmSifting_up(table, x, x_low,
            initial_size);
        result = cuddZddSymmSiftingBackward(table, move_up,
            initial_size);
        }
    }
    else {
        result = cuddZddSymmSiftingBackward(table, move_down,
        initial_size);
        /* move backward and stop at best position */
    }
    if (!result)
        goto cuddZddSymmSiftingConvAuxOutOfMem;
    }

    while (move_down != NULL) {
    move = move_down->next;
    cuddDeallocNode(table, (DdNode *)move_down);
    move_down = move;
    }
    while (move_up != NULL) {
    move = move_up->next;
    cuddDeallocNode(table, (DdNode *)move_up);
    move_up = move;
    }

    return(1);

cuddZddSymmSiftingConvAuxOutOfMem:
    if (move_down != ZDD_MV_OOM) {
    while (move_down != NULL) {
        move = move_down->next;
        cuddDeallocNode(table, (DdNode *)move_down);
        move_down = move;
    }
    }
    if (move_up != ZDD_MV_OOM) {
    while (move_up != NULL) {
        move = move_up->next;
        cuddDeallocNode(table, (DdNode *)move_up);
        move_up = move;
    }
    }

    return(0);

} /* end of cuddZddSymmSiftingConvAux */


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

  Synopsis [Moves x up until either it reaches the bound (x_low) or
  the size of the ZDD heap increases too much.]

  Description [Moves x up until either it reaches the bound (x_low) or
  the size of the ZDD heap increases too much. Assumes that x is the top
  of a symmetry group.  Checks x for symmetry to the adjacent
  variables. If symmetry is found, the symmetry group of x is merged
  with the symmetry group of the other variable. Returns the set of
  moves in case of success; ZDD_MV_OOM if memory is full.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static Move *
cuddZddSymmSifting_up(
  DdManager * table,
  int  x,
  int  x_low,
  int  initial_size)
{
    Move    *moves;
    Move    *move;
    int        y;
    int        size;
    int        limit_size = initial_size;
    int        i, gytop;

    moves = NULL;
    y = cuddZddNextLow(table, x);
    while (y >= x_low) {
    gytop = table->subtableZ[y].next;
    if (cuddZddSymmCheck(table, y, x)) {
        /* Symmetry found, attach symm groups */
        table->subtableZ[y].next = x;
        i = table->subtableZ[x].next;
        while (table->subtableZ[i].next != (unsigned) x)
        i = table->subtableZ[i].next;
        table->subtableZ[i].next = gytop;
    }
    else if ((table->subtableZ[x].next == (unsigned) x) &&
        (table->subtableZ[y].next == (unsigned) y)) {
        /* x and y have self symmetry */
        size = cuddZddSwapInPlace(table, y, x);
        if (size == 0)
        goto cuddZddSymmSifting_upOutOfMem;
        move = (Move *)cuddDynamicAllocNode(table);
        if (move == NULL)
        goto cuddZddSymmSifting_upOutOfMem;
        move->x = y;
        move->y = x;
        move->size = size;
        move->next = moves;
        moves = move;
        if ((double)size >
        (double)limit_size * table->maxGrowth)
        return(moves);
        if (size < limit_size)
        limit_size = size;
    }
    else { /* Group move */
        size = zdd_group_move(table, y, x, &moves);
        if ((double)size >
        (double)limit_size * table->maxGrowth)
        return(moves);
        if (size < limit_size)
        limit_size = size;
    }
    x = gytop;
    y = cuddZddNextLow(table, x);
    }

    return(moves);

cuddZddSymmSifting_upOutOfMem:
    while (moves != NULL) {
    move = moves->next;
    cuddDeallocNode(table, (DdNode *)moves);
    moves = move;
    }
    return(ZDD_MV_OOM);

} /* end of cuddZddSymmSifting_up */


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

  Synopsis [Moves x down until either it reaches the bound (x_high) or
  the size of the ZDD heap increases too much.]

  Description [Moves x down until either it reaches the bound (x_high)
  or the size of the ZDD heap increases too much. Assumes that x is the
  bottom of a symmetry group. Checks x for symmetry to the adjacent
  variables. If symmetry is found, the symmetry group of x is merged
  with the symmetry group of the other variable. Returns the set of
  moves in case of success; ZDD_MV_OOM if memory is full.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static Move *
cuddZddSymmSifting_down(
  DdManager * table,
  int  x,
  int  x_high,
  int  initial_size)
{
    Move    *moves;
    Move    *move;
    int        y;
    int        size;
    int        limit_size = initial_size;
    int        i, gxtop, gybot;

    moves = NULL;
    y = cuddZddNextHigh(table, x);
    while (y <= x_high) {
    gybot = table->subtableZ[y].next;
    while (table->subtableZ[gybot].next != (unsigned) y)
        gybot = table->subtableZ[gybot].next;
    if (cuddZddSymmCheck(table, x, y)) {
        /* Symmetry found, attach symm groups */
        gxtop = table->subtableZ[x].next;
        table->subtableZ[x].next = y;
        i = table->subtableZ[y].next;
        while (table->subtableZ[i].next != (unsigned) y)
        i = table->subtableZ[i].next;
        table->subtableZ[i].next = gxtop;
    }
    else if ((table->subtableZ[x].next == (unsigned) x) &&
        (table->subtableZ[y].next == (unsigned) y)) {
        /* x and y have self symmetry */
        size = cuddZddSwapInPlace(table, x, y);
        if (size == 0)
        goto cuddZddSymmSifting_downOutOfMem;
        move = (Move *)cuddDynamicAllocNode(table);
        if (move == NULL)
        goto cuddZddSymmSifting_downOutOfMem;
        move->x = x;
        move->y = y;
        move->size = size;
        move->next = moves;
        moves = move;
        if ((double)size >
        (double)limit_size * table->maxGrowth)
        return(moves);
        if (size < limit_size)
        limit_size = size;
        x = y;
        y = cuddZddNextHigh(table, x);
    }
    else { /* Group move */
        size = zdd_group_move(table, x, y, &moves);
        if ((double)size >
        (double)limit_size * table->maxGrowth)
        return(moves);
        if (size < limit_size)
        limit_size = size;
    }
    x = gybot;
    y = cuddZddNextHigh(table, x);
    }

    return(moves);

cuddZddSymmSifting_downOutOfMem:
    while (moves != NULL) {
    move = moves->next;
    cuddDeallocNode(table, (DdNode *)moves);
    moves = move;
    }
    return(ZDD_MV_OOM);

} /* end of cuddZddSymmSifting_down */


/**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
cuddZddSymmSiftingBackward(
  DdManager * table,
  Move * moves,
  int  size)
{
    int        i;
    int        i_best;
    Move    *move;
    int        res;

    i_best = -1;
    for (move = moves, i = 0; move != NULL; move = move->next, i++) {
    if (move->size < size) {
        i_best = i;
        size = move->size;
    }
    }

    for (move = moves, i = 0; move != NULL; move = move->next, i++) {
    if (i == i_best) break;
    if ((table->subtableZ[move->x].next == move->x) &&
        (table->subtableZ[move->y].next == move->y)) {
        res = cuddZddSwapInPlace(table, move->x, move->y);
        if (!res) return(0);
    }
    else { /* Group move necessary */
        res = zdd_group_move_backward(table, move->x, move->y);
    }
    if (i_best == -1 && res == size)
        break;
    }

    return(1);

} /* end of cuddZddSymmSiftingBackward */


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

  Synopsis [Swaps two groups.]

  Description [Swaps two groups. x is assumed to be the bottom variable
  of the first group. y is assumed to be the top variable of the second
  group.  Updates the list of moves. Returns the number of keys in the
  table if successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
zdd_group_move(
  DdManager * table,
  int  x,
  int  y,
  Move ** moves)
{
    Move    *move;
    int        size;
    int        i, temp, gxtop, gxbot, gytop, gybot, yprev;
    int        swapx, swapy;

#ifdef DD_DEBUG
    assert(x < y);    /* we assume that x < y */
#endif
    /* Find top and bottom for the two groups. */
    gxtop = table->subtableZ[x].next;
    gytop = y;
    gxbot = x;
    gybot = table->subtableZ[y].next;
    while (table->subtableZ[gybot].next != (unsigned) y)
    gybot = table->subtableZ[gybot].next;
    yprev = gybot;

    while (x <= y) {
    while (y > gxtop) {
        /* Set correct symmetries. */
        temp = table->subtableZ[x].next;
        if (temp == x)
        temp = y;
        i = gxtop;
        for (;;) {
        if (table->subtableZ[i].next == (unsigned) x) {
            table->subtableZ[i].next = y;
            break;
        } else {
            i = table->subtableZ[i].next;
        }
        }
        if (table->subtableZ[y].next != (unsigned) y) {
        table->subtableZ[x].next = table->subtableZ[y].next;
        } else {
        table->subtableZ[x].next = x;
        }

        if (yprev != y) {
        table->subtableZ[yprev].next = x;
        } else {
        yprev = x;
        }
        table->subtableZ[y].next = temp;

        size = cuddZddSwapInPlace(table, x, y);
        if (size == 0)
        goto zdd_group_moveOutOfMem;
            swapx = x;
        swapy = y;
        y = x;
        x--;
    } /* while y > gxtop */

    /* Trying to find the next y. */
    if (table->subtableZ[y].next <= (unsigned) y) {
        gybot = y;
    } else {
        y = table->subtableZ[y].next;
    }

    yprev = gxtop;
    gxtop++;
    gxbot++;
    x = gxbot;
    } /* while x <= y, end of group movement */
    move = (Move *)cuddDynamicAllocNode(table);
    if (move == NULL)
    goto zdd_group_moveOutOfMem;
    move->x = swapx;
    move->y = swapy;
    move->size = table->keysZ;
    move->next = *moves;
    *moves = move;

    return(table->keysZ);

zdd_group_moveOutOfMem:
    while (*moves != NULL) {
    move = (*moves)->next;
    cuddDeallocNode(table, (DdNode *)(*moves));
    *moves = move;
    }
    return(0);

} /* end of zdd_group_move */


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

  Synopsis [Undoes the swap of two groups.]

  Description [Undoes the swap of two groups. x is assumed to be the
  bottom variable of the first group. y is assumed to be the top
  variable of the second group.  Returns 1 if successful; 0 otherwise.]

  SideEffects [None]

  SeeAlso     []

******************************************************************************/
static int
zdd_group_move_backward(
  DdManager * table,
  int  x,
  int  y)
{
    int           size;
    int        i, temp, gxtop, gxbot, gytop, gybot, yprev;

#ifdef DD_DEBUG
    assert(x < y);    /* we assume that x < y */
#endif
    /* Find top and bottom of the two groups. */
    gxtop = table->subtableZ[x].next;
    gytop = y;
    gxbot = x;
    gybot = table->subtableZ[y].next;
    while (table->subtableZ[gybot].next != (unsigned) y)
    gybot = table->subtableZ[gybot].next;
    yprev = gybot;

    while (x <= y) {
    while (y > gxtop) {
        /* Set correct symmetries. */
        temp = table->subtableZ[x].next;
        if (temp == x)
        temp = y;
        i = gxtop;
        for (;;) {
        if (table->subtableZ[i].next == (unsigned) x) {
            table->subtableZ[i].next = y;
            break;
        } else {
            i = table->subtableZ[i].next;
        }
        }
        if (table->subtableZ[y].next != (unsigned) y) {
        table->subtableZ[x].next = table->subtableZ[y].next;
        } else {
        table->subtableZ[x].next = x;
        }

        if (yprev != y) {
        table->subtableZ[yprev].next = x;
        } else {
        yprev = x;
        }
        table->subtableZ[y].next = temp;

        size = cuddZddSwapInPlace(table, x, y);
        if (size == 0)
        return(0);
        y = x;
        x--;
    } /* while y > gxtop */

    /* Trying to find the next y. */
    if (table->subtableZ[y].next <= (unsigned) y) {
        gybot = y;
    } else {
        y = table->subtableZ[y].next;
    }

    yprev = gxtop;
    gxtop++;
    gxbot++;
    x = gxbot;
    } /* while x <= y, end of group movement backward */

    return(size);

} /* end of zdd_group_move_backward */


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

  Synopsis    [Counts numbers of symmetric variables and symmetry
  groups.]

  Description []

  SideEffects [None]

******************************************************************************/
static void
cuddZddSymmSummary(
  DdManager * table,
  int  lower,
  int  upper,
  int * symvars,
  int * symgroups)
{
    int i,x,gbot;
    int TotalSymm = 0;
    int TotalSymmGroups = 0;

    for (i = lower; i <= upper; i++) {
    if (table->subtableZ[i].next != (unsigned) i) {
        TotalSymmGroups++;
        x = i;
        do {
        TotalSymm++;
        gbot = x;
        x = table->subtableZ[x].next;
        } while (x != i);
#ifdef DD_DEBUG
        assert(table->subtableZ[gbot].next == (unsigned) i);
#endif
        i = gbot;
    }
    }
    *symvars = TotalSymm;
    *symgroups = TotalSymmGroups;

    return;

} /* end of cuddZddSymmSummary */

