src/bdd/cudd/cuddZddSymm.c File Reference

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

Include dependency graph for cuddZddSymm.c:

Go to the source code of this file.

Defines
#define	ZDD_MV_OOM   (Move *)1
Functions
static int cuddZddSymmSiftingAux	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))
void	Cudd_zddSymmProfile (DdManager *table, int lower, int upper)
int	cuddZddSymmCheck (DdManager *table, int x, int y)
int	cuddZddSymmSifting (DdManager *table, int lower, int upper)
int	cuddZddSymmSiftingConv (DdManager *table, int lower, int upper)
static int	cuddZddSymmSiftingAux (DdManager *table, int x, int x_low, int x_high)
static int	cuddZddSymmSiftingConvAux (DdManager *table, int x, int x_low, int x_high)
static Move *	cuddZddSymmSifting_up (DdManager *table, int x, int x_low, int initial_size)
static Move *	cuddZddSymmSifting_down (DdManager *table, int x, int x_high, int initial_size)
static int	cuddZddSymmSiftingBackward (DdManager *table, Move *moves, int size)
static int	zdd_group_move (DdManager *table, int x, int y, Move **moves)
static int	zdd_group_move_backward (DdManager *table, int x, int y)
static void	cuddZddSymmSummary (DdManager *table, int lower, int upper, int *symvars, int *symgroups)
Variables
static char rcsid[]	DD_UNUSED = "$Id: cuddZddSymm.c,v 1.1.1.1 2003/02/24 22:23:54 wjiang Exp $"
int *	zdd_entry
int	zddTotalNumberSwapping
static DdNode *	empty

---

Define Documentation

#define ZDD_MV_OOM   (Move *)1

CFile***********************************************************************

FileName [cuddZddSymm.c]

PackageName [cudd]

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

Description [External procedures included in this module:

• Cudd_zddSymmProfile()

Internal procedures included in this module:

• cuddZddSymmCheck()
• cuddZddSymmSifting()
• cuddZddSymmSiftingConv()

Static procedures included in this module:

• cuddZddUniqueCompare()
• cuddZddSymmSiftingAux()
• cuddZddSymmSiftingConvAux()
• cuddZddSymmSifting_up()
• cuddZddSymmSifting_down()
• zdd_group_move()
• cuddZddSymmSiftingBackward()
• zdd_group_move_backward()

]

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.]

Definition at line 50 of file cuddZddSymm.c.

---

Function Documentation

static void cuddZddSymmSummary ARGS

(

(DdManager *table, int lower, int upper, int *symvars, int *symgroups)

)

[static]

static int zdd_group_move_backward ARGS

(

(DdManager *table, int x, int y)

)

[static]

static int zdd_group_move ARGS

(

(DdManager *table, int x, int y, Move **moves)

)

[static]

static int cuddZddSymmSiftingBackward ARGS

(

(DdManager *table, Move *moves, int size)

)

[static]

static Move* cuddZddSymmSifting_down ARGS

(

(DdManager *table, int x, int x_high, int initial_size)

)

[static]

static Move* cuddZddSymmSifting_up ARGS

(

(DdManager *table, int x, int x_low, int initial_size)

)

[static]

static int cuddZddSymmSiftingConvAux ARGS

(

(DdManager *table, int x, int x_low, int x_high)

)

[static]

AutomaticStart

void Cudd_zddSymmProfile	(	DdManager *	table,
		int	lower,
		int	upper
	)

AutomaticEnd Function********************************************************************

Synopsis [Prints statistics on symmetric ZDD variables.]

Description []

SideEffects [None]

SeeAlso []

Definition at line 114 of file cuddZddSymm.c.

{
    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 */

int cuddZddSymmCheck	(	DdManager *	table,
		int	x,
		int	y
	)

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 []

Definition at line 169 of file cuddZddSymm.c.

{
    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 */

int cuddZddSymmSifting	(	DdManager *	table,
		int	lower,
		int	upper
	)

Function********************************************************************

Synopsis [Symmetric sifting algorithm for ZDDs.]

Description [Symmetric sifting algorithm. Assumes that no dead nodes are present.

1. Order all the variables according to the number of entries in each unique subtable.
2. Sift the variable up and down, remembering each time the total size of the ZDD heap and grouping variables that are symmetric.
3. Select the best permutation.
4. Repeat 3 and 4 for all variables.

Returns 1 plus the number of symmetric variables if successful; 0 otherwise.]

SideEffects [None]

SeeAlso [cuddZddSymmSiftingConv]

Definition at line 274 of file cuddZddSymm.c.

{
    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 */

static Move* cuddZddSymmSifting_down	(	DdManager *	table,
		int	x,
		int	x_high,
		int	initial_size
	)			[static]

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 []

Definition at line 1310 of file cuddZddSymm.c.

{
    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 */

static Move* cuddZddSymmSifting_up	(	DdManager *	table,
		int	x,
		int	x_low,
		int	initial_size
	)			[static]

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 []

Definition at line 1222 of file cuddZddSymm.c.

{
    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 */

static int cuddZddSymmSiftingAux	(	DdManager *	table,
		int	x,
		int	x_low,
		int	x_high
	)			[static]

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 []

Definition at line 573 of file cuddZddSymm.c.

{
    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 */

static int cuddZddSymmSiftingBackward	(	DdManager *	table,
		Move *	moves,
		int	size
	)			[static]

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 []

Definition at line 1401 of file cuddZddSymm.c.

{
    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 */

int cuddZddSymmSiftingConv	(	DdManager *	table,
		int	lower,
		int	upper
	)

Function********************************************************************

Synopsis [Symmetric sifting to convergence algorithm for ZDDs.]

Description [Symmetric sifting to convergence algorithm for ZDDs. Assumes that no dead nodes are present.

1. Order all the variables according to the number of entries in each unique subtable.
2. Sift the variable up and down, remembering each time the total size of the ZDD heap and grouping variables that are symmetric.
3. Select the best permutation.
4. Repeat 3 and 4 for all variables.
5. Repeat 1-4 until no further improvement.

Returns 1 plus the number of symmetric variables if successful; 0 otherwise.]

SideEffects [None]

SeeAlso [cuddZddSymmSifting]

Definition at line 395 of file cuddZddSymm.c.

{
    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 */

static int cuddZddSymmSiftingConvAux	(	DdManager *	table,
		int	x,
		int	x_low,
		int	x_high
	)			[static]

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 []

Definition at line 913 of file cuddZddSymm.c.

{
    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 */

static void cuddZddSymmSummary	(	DdManager *	table,
		int	lower,
		int	upper,
		int *	symvars,
		int *	symgroups
	)			[static]

Function********************************************************************

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

Description []

SideEffects [None]

Definition at line 1645 of file cuddZddSymm.c.

{
    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 */

static int zdd_group_move	(	DdManager *	table,
		int	x,
		int	y,
		Move **	moves
	)			[static]

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 []

Definition at line 1453 of file cuddZddSymm.c.

{
    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 */

static int zdd_group_move_backward	(	DdManager *	table,
		int	x,
		int	y
	)			[static]

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 []

Definition at line 1561 of file cuddZddSymm.c.

{
    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 */

---

Variable Documentation

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

Definition at line 65 of file cuddZddSymm.c.

DdNode* empty [static]

Definition at line 72 of file cuddZddSymm.c.

int* zdd_entry

Definition at line 77 of file cuddZddReord.c.

int zddTotalNumberSwapping

Definition at line 79 of file cuddZddReord.c.