src/cuBdd/cuddSymmetry.c File Reference

#include "util.h"
#include "cuddInt.h"

Include dependency graph for cuddSymmetry.c:

Go to the source code of this file.

Defines
#define	MV_OOM   (Move *)1
Functions
static int	ddSymmUniqueCompare (int *ptrX, int *ptrY)
static int	ddSymmSiftingAux (DdManager *table, int x, int xLow, int xHigh)
static int	ddSymmSiftingConvAux (DdManager *table, int x, int xLow, int xHigh)
static Move *	ddSymmSiftingUp (DdManager *table, int y, int xLow)
static Move *	ddSymmSiftingDown (DdManager *table, int x, int xHigh)
static int	ddSymmGroupMove (DdManager *table, int x, int y, Move **moves)
static int	ddSymmGroupMoveBackward (DdManager *table, int x, int y)
static int	ddSymmSiftingBackward (DdManager *table, Move *moves, int size)
static void	ddSymmSummary (DdManager *table, int lower, int upper, int *symvars, int *symgroups)
void	Cudd_SymmProfile (DdManager *table, int lower, int upper)
int	cuddSymmCheck (DdManager *table, int x, int y)
int	cuddSymmSifting (DdManager *table, int lower, int upper)
int	cuddSymmSiftingConv (DdManager *table, int lower, int upper)
Variables
static char rcsid[]	DD_UNUSED = "$Id: cuddSymmetry.c,v 1.26 2009/02/19 16:23:54 fabio Exp $"
static int *	entry
int	ddTotalNumberSwapping

---

Define Documentation

#define MV_OOM   (Move *)1

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

FileName [cuddSymmetry.c]

PackageName [cudd]

Synopsis [Functions for symmetry-based variable reordering.]

Description [External procedures included in this file:

• Cudd_SymmProfile()

Internal procedures included in this module:

• cuddSymmCheck()
• cuddSymmSifting()
• cuddSymmSiftingConv()

Static procedures included in this module:

• ddSymmUniqueCompare()
• ddSymmSiftingAux()
• ddSymmSiftingConvAux()
• ddSymmSiftingUp()
• ddSymmSiftingDown()
• ddSymmGroupMove()
• ddSymmGroupMoveBackward()
• ddSymmSiftingBackward()
• ddSymmSummary()

]

Author [Shipra Panda, Fabio Somenzi]

Copyright [Copyright (c) 1995-2004, Regents of the University of Colorado

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

Neither the name of the University of Colorado nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.]

Definition at line 75 of file cuddSymmetry.c.

---

Function Documentation

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

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

Synopsis [Prints statistics on symmetric variables.]

Description []

SideEffects [None]

Definition at line 138 of file cuddSymmetry.c.

{
    int i,x,gbot;
    int TotalSymm = 0;
    int TotalSymmGroups = 0;

    for (i = lower; i <= upper; i++) {
        if (table->subtables[i].next != (unsigned) i) {
            x = i;
            (void) fprintf(table->out,"Group:");
            do {
                (void) fprintf(table->out,"  %d",table->invperm[x]);
                TotalSymm++;
                gbot = x;
                x = table->subtables[x].next;
            } while (x != i);
            TotalSymmGroups++;
#ifdef DD_DEBUG
            assert(table->subtables[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_SymmProfile */

int cuddSymmCheck	(	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]

Definition at line 188 of file cuddSymmetry.c.

{
    DdNode *f,*f0,*f1,*f01,*f00,*f11,*f10;
    int comple;         /* f0 is complemented */
    int xsymmy;         /* x and y may be positively symmetric */
    int xsymmyp;        /* x and y may be negatively symmetric */
    int arccount;       /* number of arcs from layer x to layer y */
    int TotalRefCount;  /* total reference count of layer y minus 1 */
    int yindex;
    int i;
    DdNodePtr *list;
    int slots;
    DdNode *sentinel = &(table->sentinel);
#ifdef DD_DEBUG
    int xindex;
#endif

    /* Checks that x and y are not the projection functions.
    ** For x it is sufficient to check whether there is only one
    ** node; indeed, if there is one node, it is the projection function
    ** and it cannot point to y. Hence, if y isn't just the projection
    ** function, it has one arc coming from a layer different from x.
    */
    if (table->subtables[x].keys == 1) {
        return(0);
    }
    yindex = table->invperm[y];
    if (table->subtables[y].keys == 1) {
        if (table->vars[yindex]->ref == 1)
            return(0);
    }

    xsymmy = xsymmyp = 1;
    arccount = 0;
    slots = table->subtables[x].slots;
    list = table->subtables[x].nodelist;
    for (i = 0; i < slots; i++) {
        f = list[i];
        while (f != sentinel) {
            /* Find f1, f0, f11, f10, f01, f00. */
            f1 = cuddT(f);
            f0 = Cudd_Regular(cuddE(f));
            comple = Cudd_IsComplement(cuddE(f));
            if ((int) f1->index == yindex) {
                arccount++;
                f11 = cuddT(f1); f10 = cuddE(f1);
            } else {
                if ((int) f0->index != yindex) {
                    /* If f is an isolated projection function it is
                    ** allowed to bypass layer y.
                    */
                    if (f1 != DD_ONE(table) || f0 != DD_ONE(table) || f->ref != 1)
                        return(0); /* f bypasses layer y */
                }
                f11 = f10 = f1;
            }
            if ((int) f0->index == yindex) {
                arccount++;
                f01 = cuddT(f0); f00 = cuddE(f0);
            } else {
                f01 = f00 = f0;
            }
            if (comple) {
                f01 = Cudd_Not(f01);
                f00 = Cudd_Not(f00);
            }

            if (f1 != DD_ONE(table) || f0 != DD_ONE(table) || f->ref != 1) {
                xsymmy &= f01 == f10;
                xsymmyp &= f11 == f00;
                if ((xsymmy == 0) && (xsymmyp == 0))
                    return(0);
            }

            f = f->next;
        } /* while */
    } /* for */

    /* Calculate the total reference counts of y */
    TotalRefCount = -1; /* -1 for projection function */
    slots = table->subtables[y].slots;
    list = table->subtables[y].nodelist;
    for (i = 0; i < slots; i++) {
        f = list[i];
        while (f != sentinel) {
            TotalRefCount += f->ref;
            f = f->next;
        }
    }

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

    return(arccount == TotalRefCount);

} /* end of cuddSymmCheck */

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

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

Synopsis [Symmetric sifting algorithm.]

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 DD 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 [cuddSymmSiftingConv]

Definition at line 318 of file cuddSymmetry.c.

{
    int         i;
    int         *var;
    int         size;
    int         x;
    int         result;
    int         symvars;
    int         symgroups;
#ifdef DD_STATS
    int         previousSize;
#endif

    size = table->size;

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

    for (i = 0; i < size; i++) {
        x = table->perm[i];
        entry[i] = table->subtables[x].keys;
        var[i] = i;
    }

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

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

    for (i = 0; i < ddMin(table->siftMaxVar,size); i++) {
        if (ddTotalNumberSwapping >= table->siftMaxSwap)
            break;
        x = table->perm[var[i]];
#ifdef DD_STATS
        previousSize = table->keys - table->isolated;
#endif
        if (x < lower || x > upper) continue;
        if (table->subtables[x].next == (unsigned) x) {
            result = ddSymmSiftingAux(table,x,lower,upper);
            if (!result) goto ddSymmSiftingOutOfMem;
#ifdef DD_STATS
            if (table->keys < (unsigned) previousSize + table->isolated) {
                (void) fprintf(table->out,"-");
            } else if (table->keys > (unsigned) previousSize +
                       table->isolated) {
                (void) fprintf(table->out,"+"); /* should never happen */
            } else {
                (void) fprintf(table->out,"=");
            }
            fflush(table->out);
#endif
        }
    }

    FREE(var);
    FREE(entry);

    ddSymmSummary(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",
                   symgroups);
#endif

    return(1+symvars);

ddSymmSiftingOutOfMem:

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

    return(0);

} /* end of cuddSymmSifting */

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

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

Synopsis [Symmetric sifting to convergence algorithm.]

Description [Symmetric sifting to convergence 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 DD 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 [cuddSymmSifting]

Definition at line 435 of file cuddSymmetry.c.

{
    int         i;
    int         *var;
    int         size;
    int         x;
    int         result;
    int         symvars;
    int         symgroups;
    int         classes;
    int         initialSize;
#ifdef DD_STATS
    int         previousSize;
#endif

    initialSize = table->keys - table->isolated;

    size = table->size;

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

    for (i = 0; i < size; i++) {
        x = table->perm[i];
        entry[i] = table->subtables[x].keys;
        var[i] = i;
    }

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

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

    for (i = 0; i < ddMin(table->siftMaxVar, table->size); i++) {
        if (ddTotalNumberSwapping >= table->siftMaxSwap)
            break;
        x = table->perm[var[i]];
        if (x < lower || x > upper) continue;
        /* Only sift if not in symmetry group already. */
        if (table->subtables[x].next == (unsigned) x) {
#ifdef DD_STATS
            previousSize = table->keys - table->isolated;
#endif
            result = ddSymmSiftingAux(table,x,lower,upper);
            if (!result) goto ddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
            if (table->keys < (unsigned) previousSize + table->isolated) {
                (void) fprintf(table->out,"-");
            } else if (table->keys > (unsigned) previousSize +
                       table->isolated) {
                (void) fprintf(table->out,"+");
            } else {
                (void) fprintf(table->out,"=");
            }
            fflush(table->out);
#endif
        }
    }

    /* Sifting now until convergence. */
    while ((unsigned) initialSize > table->keys - table->isolated) {
        initialSize = table->keys - table->isolated;
#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->subtables[x].next) {
                x = table->subtables[x].next;
            }
            /* Here x is the largest index in a group.
            ** Groups consist of adjacent variables.
            ** Hence, the next increment of x will move it to a new group.
            */
            i = table->invperm[x];
            entry[i] = table->subtables[x].keys;
            var[classes] = i;
        }

        qsort((void *)var,classes,sizeof(int),(DD_QSFP)ddSymmUniqueCompare);

        /* Now sift. */
        for (i = 0; i < ddMin(table->siftMaxVar,classes); i++) {
            if (ddTotalNumberSwapping >= table->siftMaxSwap)
                break;
            x = table->perm[var[i]];
            if ((unsigned) x >= table->subtables[x].next) {
#ifdef DD_STATS
                previousSize = table->keys - table->isolated;
#endif
                result = ddSymmSiftingConvAux(table,x,lower,upper);
                if (!result ) goto ddSymmSiftingConvOutOfMem;
#ifdef DD_STATS
                if (table->keys < (unsigned) previousSize + table->isolated) {
                    (void) fprintf(table->out,"-");
                } else if (table->keys > (unsigned) previousSize +
                           table->isolated) {
                    (void) fprintf(table->out,"+");
                } else {
                    (void) fprintf(table->out,"=");
                }
                fflush(table->out);
#endif
            }
        } /* for */
    }

    ddSymmSummary(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",
                   symgroups);
#endif

    FREE(var);
    FREE(entry);

    return(1+symvars);

ddSymmSiftingConvOutOfMem:

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

    return(0);

} /* end of cuddSymmSiftingConv */

static int ddSymmGroupMove	(	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]

Definition at line 1468 of file cuddSymmetry.c.

{
    Move *move;
    int  size;
    int  i,j;
    int  xtop,xbot,xsize,ytop,ybot,ysize,newxtop;
    int  swapx,swapy;

#ifdef DD_DEBUG
    assert(x < y);      /* we assume that x < y */
#endif
    /* Find top, bottom, and size for the two groups. */
    xbot = x;
    xtop = table->subtables[x].next;
    xsize = xbot - xtop + 1;
    ybot = y;
    while ((unsigned) ybot < table->subtables[ybot].next)
        ybot = table->subtables[ybot].next;
    ytop = y;
    ysize = ybot - ytop + 1;

    /* Sift the variables of the second group up through the first group. */
    for (i = 1; i <= ysize; i++) {
        for (j = 1; j <= xsize; j++) {
            size = cuddSwapInPlace(table,x,y);
            if (size == 0) return(0);
            swapx = x; swapy = y;
            y = x;
            x = y - 1;
        }
        y = ytop + i;
        x = y - 1;
    }

    /* fix symmetries */
    y = xtop; /* ytop is now where xtop used to be */
    for (i = 0; i < ysize-1 ; i++) {
        table->subtables[y].next = y + 1;
        y = y + 1;
    }
    table->subtables[y].next = xtop; /* y is bottom of its group, join */
                                     /* its symmetry to top of its group */
    x = y + 1;
    newxtop = x;
    for (i = 0; i < xsize - 1 ; i++) {
        table->subtables[x].next = x + 1;
        x = x + 1;
    }
    table->subtables[x].next = newxtop; /* x is bottom of its group, join */
                                        /* its symmetry to top of its group */
    /* Store group move */
    move = (Move *) cuddDynamicAllocNode(table);
    if (move == NULL) return(0);
    move->x = swapx;
    move->y = swapy;
    move->size = size;
    move->next = *moves;
    *moves = move;

    return(size);

} /* end of ddSymmGroupMove */

static int ddSymmGroupMoveBackward	(	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 the number of keys in the table if successful; 0 otherwise.]

SideEffects [None]

Definition at line 1549 of file cuddSymmetry.c.

{
    int size;
    int i,j;
    int xtop,xbot,xsize,ytop,ybot,ysize,newxtop;

#ifdef DD_DEBUG
    assert(x < y); /* We assume that x < y */
#endif

    /* Find top, bottom, and size for the two groups. */
    xbot = x;
    xtop = table->subtables[x].next;
    xsize = xbot - xtop + 1;
    ybot = y;
    while ((unsigned) ybot < table->subtables[ybot].next)
        ybot = table->subtables[ybot].next;
    ytop = y;
    ysize = ybot - ytop + 1;

    /* Sift the variables of the second group up through the first group. */
    for (i = 1; i <= ysize; i++) {
        for (j = 1; j <= xsize; j++) {
            size = cuddSwapInPlace(table,x,y);
            if (size == 0) return(0);
            y = x;
            x = cuddNextLow(table,y);
        }
        y = ytop + i;
        x = y - 1;
    }

    /* Fix symmetries. */
    y = xtop;
    for (i = 0; i < ysize-1 ; i++) {
        table->subtables[y].next = y + 1;
        y = y + 1;
    }
    table->subtables[y].next = xtop; /* y is bottom of its group, join */
                                     /* its symmetry to top of its group */
    x = y + 1;
    newxtop = x;
    for (i = 0; i < xsize-1 ; i++) {
        table->subtables[x].next = x + 1;
        x = x + 1;
    }
    table->subtables[x].next = newxtop; /* x is bottom of its group, join */
                                        /* its symmetry to top of its group */

    return(size);

} /* end of ddSymmGroupMoveBackward */

static int ddSymmSiftingAux	(	DdManager *	table,
		int	x,
		int	xLow,
		int	xHigh
	)			[static]

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

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

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

SideEffects [None]

Definition at line 629 of file cuddSymmetry.c.

{
    Move *move;
    Move *moveUp;       /* list of up moves */
    Move *moveDown;     /* list of down moves */
    int  initialSize;
    int  result;
    int  i;
    int  topbot;        /* index to either top or bottom of symmetry group */
    int  initGroupSize, finalGroupSize;


#ifdef DD_DEBUG
    /* check for previously detected symmetry */
    assert(table->subtables[x].next == (unsigned) x);
#endif

    initialSize = table->keys - table->isolated;

    moveDown = NULL;
    moveUp = NULL;

    if ((x - xLow) > (xHigh - x)) {
        /* Will go down first, unless x == xHigh:
        ** Look for consecutive symmetries above x.
        */
        for (i = x; i > xLow; i--) {
            if (!cuddSymmCheck(table,i-1,i))
                break;
            topbot = table->subtables[i-1].next; /* find top of i-1's group */
            table->subtables[i-1].next = i;
            table->subtables[x].next = topbot; /* x is bottom of group so its */
                                               /* next is top of i-1's group */
            i = topbot + 1; /* add 1 for i--; new i is top of symm group */
        }
    } else {
        /* Will go up first unless x == xlow:
        ** Look for consecutive symmetries below x.
        */
        for (i = x; i < xHigh; i++) {
            if (!cuddSymmCheck(table,i,i+1))
                break;
            /* find bottom of i+1's symm group */
            topbot = i + 1;
            while ((unsigned) topbot < table->subtables[topbot].next) {
                topbot = table->subtables[topbot].next;
            }
            table->subtables[topbot].next = table->subtables[i].next;
            table->subtables[i].next = i + 1;
            i = topbot - 1; /* subtract 1 for i++; new i is bottom of group */
        }
    }

    /* Now x may be in the middle of a symmetry group.
    ** Find bottom of x's symm group.
    */
    while ((unsigned) x < table->subtables[x].next)
        x = table->subtables[x].next;

    if (x == xLow) { /* Sift down */

#ifdef DD_DEBUG
        /* x must be a singleton */
        assert((unsigned) x == table->subtables[x].next);
#endif
        if (x == xHigh) return(1);      /* just one variable */

        initGroupSize = 1;

        moveDown = ddSymmSiftingDown(table,x,xHigh);
            /* after this point x --> xHigh, unless early term */
        if (moveDown == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
        if (moveDown == NULL) return(1);

        x = moveDown->y;
        /* Find bottom of x's group */
        i = x;
        while ((unsigned) i < table->subtables[i].next) {
            i = table->subtables[i].next;
        }
#ifdef DD_DEBUG
        /* x should be the top of the symmetry group and i the bottom */
        assert((unsigned) i >= table->subtables[i].next);
        assert((unsigned) x == table->subtables[i].next);
#endif
        finalGroupSize = i - x + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetry groups detected, return to best position */
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        } else {
            initialSize = table->keys - table->isolated;
            moveUp = ddSymmSiftingUp(table,x,xLow);
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        }
        if (!result) goto ddSymmSiftingAuxOutOfMem;

    } else if (cuddNextHigh(table,x) > xHigh) { /* Sift up */
        /* Find top of x's symm group */
        i = x;                          /* bottom */
        x = table->subtables[x].next;   /* top */

        if (x == xLow) return(1); /* just one big group */

        initGroupSize = i - x + 1;

        moveUp = ddSymmSiftingUp(table,x,xLow);
            /* after this point x --> xLow, unless early term */
        if (moveUp == MV_OOM) goto ddSymmSiftingAuxOutOfMem;
        if (moveUp == NULL) return(1);

        x = moveUp->x;
        /* Find top of x's group */
        i = table->subtables[x].next;
#ifdef DD_DEBUG
        /* x should be the bottom of the symmetry group and i the top */
        assert((unsigned) x >= table->subtables[x].next);
        assert((unsigned) i == table->subtables[x].next);
#endif
        finalGroupSize = x - i + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetry groups detected, return to best position */
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        } else {
            initialSize = table->keys - table->isolated;
            moveDown = ddSymmSiftingDown(table,x,xHigh);
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        }
        if (!result) goto ddSymmSiftingAuxOutOfMem;

    } else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */

        moveDown = ddSymmSiftingDown(table,x,xHigh);
        /* at this point x == xHigh, unless early term */
        if (moveDown == MV_OOM) goto ddSymmSiftingAuxOutOfMem;

        if (moveDown != NULL) {
            x = moveDown->y;    /* x is top here */
            i = x;
            while ((unsigned) i < table->subtables[i].next) {
                i = table->subtables[i].next;
            }
        } else {
            i = x;
            while ((unsigned) i < table->subtables[i].next) {
                i = table->subtables[i].next;
            }
            x = table->subtables[i].next;
        }
#ifdef DD_DEBUG
        /* x should be the top of the symmetry group and i the bottom */
        assert((unsigned) i >= table->subtables[i].next);
        assert((unsigned) x == table->subtables[i].next);
#endif
        initGroupSize = i - x + 1;

        moveUp = ddSymmSiftingUp(table,x,xLow);
        if (moveUp == MV_OOM) goto ddSymmSiftingAuxOutOfMem;

        if (moveUp != NULL) {
            x = moveUp->x;
            i = table->subtables[x].next;
        } else {
            i = x;
            while ((unsigned) x < table->subtables[x].next)
                x = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x should be the bottom of the symmetry group and i the top */
        assert((unsigned) x >= table->subtables[x].next);
        assert((unsigned) i == table->subtables[x].next);
#endif
        finalGroupSize = x - i + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetry groups detected, return to best position */
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        } else {
            while (moveDown != NULL) {
                move = moveDown->next;
                cuddDeallocMove(table, moveDown);
                moveDown = move;
            }
            initialSize = table->keys - table->isolated;
            moveDown = ddSymmSiftingDown(table,x,xHigh);
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        }
        if (!result) goto ddSymmSiftingAuxOutOfMem;

    } else { /* moving up first: shorter */
        /* Find top of x's symmetry group */
        x = table->subtables[x].next;

        moveUp = ddSymmSiftingUp(table,x,xLow);
        /* at this point x == xHigh, unless early term */
        if (moveUp == MV_OOM) goto ddSymmSiftingAuxOutOfMem;

        if (moveUp != NULL) {
            x = moveUp->x;
            i = table->subtables[x].next;
        } else {
            while ((unsigned) x < table->subtables[x].next)
                x = table->subtables[x].next;
            i = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x is bottom of the symmetry group and i is top */
        assert((unsigned) x >= table->subtables[x].next);
        assert((unsigned) i == table->subtables[x].next);
#endif
        initGroupSize = x - i + 1;

        moveDown = ddSymmSiftingDown(table,x,xHigh);
        if (moveDown == MV_OOM) goto ddSymmSiftingAuxOutOfMem;

        if (moveDown != NULL) {
            x = moveDown->y;
            i = x;
            while ((unsigned) i < table->subtables[i].next) {
                i = table->subtables[i].next;
            }
        } else {
            i = x;
            x = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x should be the top of the symmetry group and i the bottom */
        assert((unsigned) i >= table->subtables[i].next);
        assert((unsigned) x == table->subtables[i].next);
#endif
        finalGroupSize = i - x + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetries detected, go back to best position */
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        } else {
            while (moveUp != NULL) {
                move = moveUp->next;
                cuddDeallocMove(table, moveUp);
                moveUp = move;
            }
            initialSize = table->keys - table->isolated;
            moveUp = ddSymmSiftingUp(table,x,xLow);
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        }
        if (!result) goto ddSymmSiftingAuxOutOfMem;
    }

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

    return(1);

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

    return(0);

} /* end of ddSymmSiftingAux */

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

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

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

Description [Given a set of moves, returns the DD 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]

Definition at line 1620 of file cuddSymmetry.c.

{
    Move *move;
    int  res;

    for (move = moves; move != NULL; move = move->next) {
        if (move->size < size) {
            size = move->size;
        }
    }

    for (move = moves; move != NULL; move = move->next) {
        if (move->size == size) return(1);
        if (table->subtables[move->x].next == move->x && table->subtables[move->y].next == move->y) {
            res = cuddSwapInPlace(table,(int)move->x,(int)move->y);
#ifdef DD_DEBUG
            assert(table->subtables[move->x].next == move->x);
            assert(table->subtables[move->y].next == move->y);
#endif
        } else { /* Group move necessary */
            res = ddSymmGroupMoveBackward(table,(int)move->x,(int)move->y);
        }
        if (!res) return(0);
    }

    return(1);

} /* end of ddSymmSiftingBackward */

static int ddSymmSiftingConvAux	(	DdManager *	table,
		int	x,
		int	xLow,
		int	xHigh
	)			[static]

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

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

Description [Given xLow <= x <= xHigh moves x up and down between the boundaries. Finds the best position and does the required changes. 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]

Definition at line 931 of file cuddSymmetry.c.

{
    Move *move;
    Move *moveUp;       /* list of up moves */
    Move *moveDown;     /* list of down moves */
    int  initialSize;
    int  result;
    int  i;
    int  initGroupSize, finalGroupSize;


    initialSize = table->keys - table->isolated;

    moveDown = NULL;
    moveUp = NULL;

    if (x == xLow) { /* Sift down */
#ifdef DD_DEBUG
        /* x is bottom of symmetry group */
        assert((unsigned) x >= table->subtables[x].next);
#endif
        i = table->subtables[x].next;
        initGroupSize = x - i + 1;

        moveDown = ddSymmSiftingDown(table,x,xHigh);
        /* at this point x == xHigh, unless early term */
        if (moveDown == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
        if (moveDown == NULL) return(1);

        x = moveDown->y;
        i = x;
        while ((unsigned) i < table->subtables[i].next) {
            i = table->subtables[i].next;
        }
#ifdef DD_DEBUG
        /* x should be the top of the symmetric group and i the bottom */
        assert((unsigned) i >= table->subtables[i].next);
        assert((unsigned) x == table->subtables[i].next);
#endif
        finalGroupSize = i - x + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetries detected, go back to best position */
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        } else {
            initialSize = table->keys - table->isolated;
            moveUp = ddSymmSiftingUp(table,x,xLow);
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        }
        if (!result) goto ddSymmSiftingConvAuxOutOfMem;

    } else if (cuddNextHigh(table,x) > xHigh) { /* Sift up */
        /* Find top of x's symm group */
        while ((unsigned) x < table->subtables[x].next)
            x = table->subtables[x].next;
        i = x;                          /* bottom */
        x = table->subtables[x].next;   /* top */

        if (x == xLow) return(1);

        initGroupSize = i - x + 1;

        moveUp = ddSymmSiftingUp(table,x,xLow);
            /* at this point x == xLow, unless early term */
        if (moveUp == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;
        if (moveUp == NULL) return(1);

        x = moveUp->x;
        i = table->subtables[x].next;
#ifdef DD_DEBUG
        /* x should be the bottom of the symmetry group and i the top */
        assert((unsigned) x >= table->subtables[x].next);
        assert((unsigned) i == table->subtables[x].next);
#endif
        finalGroupSize = x - i + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetry groups detected, return to best position */
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        } else {
            initialSize = table->keys - table->isolated;
            moveDown = ddSymmSiftingDown(table,x,xHigh);
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        }
        if (!result)
            goto ddSymmSiftingConvAuxOutOfMem;

    } else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
        moveDown = ddSymmSiftingDown(table,x,xHigh);
            /* at this point x == xHigh, unless early term */
        if (moveDown == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;

        if (moveDown != NULL) {
            x = moveDown->y;
            i = x;
            while ((unsigned) i < table->subtables[i].next) {
                i = table->subtables[i].next;
            }
        } else {
            while ((unsigned) x < table->subtables[x].next)
                x = table->subtables[x].next;
            i = x;
            x = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x should be the top of the symmetry group and i the bottom */
        assert((unsigned) i >= table->subtables[i].next);
        assert((unsigned) x == table->subtables[i].next);
#endif
        initGroupSize = i - x + 1;

        moveUp = ddSymmSiftingUp(table,x,xLow);
        if (moveUp == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;

        if (moveUp != NULL) {
            x = moveUp->x;
            i = table->subtables[x].next;
        } else {
            i = x;
            while ((unsigned) x < table->subtables[x].next)
                x = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x should be the bottom of the symmetry group and i the top */
        assert((unsigned) x >= table->subtables[x].next);
        assert((unsigned) i == table->subtables[x].next);
#endif
        finalGroupSize = x - i + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetry groups detected, return to best position */
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        } else {
            while (moveDown != NULL) {
                move = moveDown->next;
                cuddDeallocMove(table, moveDown);
                moveDown = move;
            }
            initialSize = table->keys - table->isolated;
            moveDown = ddSymmSiftingDown(table,x,xHigh);
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        }
        if (!result) goto ddSymmSiftingConvAuxOutOfMem;

    } else { /* moving up first: shorter */
        /* Find top of x's symmetry group */
        x = table->subtables[x].next;

        moveUp = ddSymmSiftingUp(table,x,xLow);
        /* at this point x == xHigh, unless early term */
        if (moveUp == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;

        if (moveUp != NULL) {
            x = moveUp->x;
            i = table->subtables[x].next;
        } else {
            i = x;
            while ((unsigned) x < table->subtables[x].next)
                x = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x is bottom of the symmetry group and i is top */
        assert((unsigned) x >= table->subtables[x].next);
        assert((unsigned) i == table->subtables[x].next);
#endif
        initGroupSize = x - i + 1;

        moveDown = ddSymmSiftingDown(table,x,xHigh);
        if (moveDown == MV_OOM) goto ddSymmSiftingConvAuxOutOfMem;

        if (moveDown != NULL) {
            x = moveDown->y;
            i = x;
            while ((unsigned) i < table->subtables[i].next) {
                i = table->subtables[i].next;
            }
        } else {
            i = x;
            x = table->subtables[x].next;
        }
#ifdef DD_DEBUG
        /* x should be the top of the symmetry group and i the bottom */
        assert((unsigned) i >= table->subtables[i].next);
        assert((unsigned) x == table->subtables[i].next);
#endif
        finalGroupSize = i - x + 1;

        if (initGroupSize == finalGroupSize) {
            /* No new symmetries detected, go back to best position */
            result = ddSymmSiftingBackward(table,moveDown,initialSize);
        } else {
            while (moveUp != NULL) {
                move = moveUp->next;
                cuddDeallocMove(table, moveUp);
                moveUp = move;
            }
            initialSize = table->keys - table->isolated;
            moveUp = ddSymmSiftingUp(table,x,xLow);
            result = ddSymmSiftingBackward(table,moveUp,initialSize);
        }
        if (!result) goto ddSymmSiftingConvAuxOutOfMem;
    }

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

    return(1);

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

    return(0);

} /* end of ddSymmSiftingConvAux */

static Move * ddSymmSiftingDown	(	DdManager *	table,
		int	x,
		int	xHigh
	)			[static]

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

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

Description [Moves x down until either it reaches the bound (xHigh) or the size of the DD 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; MV_OOM if memory is full.]

SideEffects [None]

Definition at line 1330 of file cuddSymmetry.c.

{
    Move *moves;
    Move *move;
    int  y;
    int  size;
    int  limitSize;
    int  gxtop,gybot;
    int  R;     /* upper bound on node decrease */
    int  xindex, yindex;
    int  isolated;
    int  z;
    int  zindex;
#ifdef DD_DEBUG
    int  checkR;
#endif

    moves = NULL;
    /* Initialize R */
    xindex = table->invperm[x];
    gxtop = table->subtables[x].next;
    limitSize = size = table->keys - table->isolated;
    R = 0;
    for (z = xHigh; z > gxtop; z--) {
        zindex = table->invperm[z];
        if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
            isolated = table->vars[zindex]->ref == 1;
            R += table->subtables[z].keys - isolated;
        }
    }

    y = cuddNextHigh(table,x);
    while (y <= xHigh && size - R < limitSize) {
#ifdef DD_DEBUG
        gxtop = table->subtables[x].next;
        checkR = 0;
        for (z = xHigh; z > gxtop; z--) {
            zindex = table->invperm[z];
            if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
                isolated = table->vars[zindex]->ref == 1;
                checkR += table->subtables[z].keys - isolated;
            }
        }
        assert(R == checkR);
#endif
        gybot = table->subtables[y].next;
        while (table->subtables[gybot].next != (unsigned) y)
            gybot = table->subtables[gybot].next;
        if (cuddSymmCheck(table,x,y)) {
            /* Symmetry found, attach symm groups */
            gxtop = table->subtables[x].next;
            table->subtables[x].next = y;
            table->subtables[gybot].next = gxtop;
        } else if (table->subtables[x].next == (unsigned) x &&
                   table->subtables[y].next == (unsigned) y) {
            /* x and y have self symmetry */
            /* Update upper bound on node decrease. */
            yindex = table->invperm[y];
            if (cuddTestInteract(table,xindex,yindex)) {
                isolated = table->vars[yindex]->ref == 1;
                R -= table->subtables[y].keys - isolated;
            }
            size = cuddSwapInPlace(table,x,y);
#ifdef DD_DEBUG
            assert(table->subtables[x].next == (unsigned) x);
            assert(table->subtables[y].next == (unsigned) y);
#endif
            if (size == 0) goto ddSymmSiftingDownOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSymmSiftingDownOutOfMem;
            move->x = x;
            move->y = y;
            move->size = size;
            move->next = moves;
            moves = move;
            if ((double) size > (double) limitSize * table->maxGrowth)
                return(moves);
            if (size < limitSize) limitSize = size;
        } else { /* Group move */
            /* Update upper bound on node decrease: first phase. */
            gxtop = table->subtables[x].next;
            z = gxtop + 1;
            do {
                zindex = table->invperm[z];
                if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
                    isolated = table->vars[zindex]->ref == 1;
                    R -= table->subtables[z].keys - isolated;
                }
                z++;
            } while (z <= gybot);
            size = ddSymmGroupMove(table,x,y,&moves);
            if (size == 0) goto ddSymmSiftingDownOutOfMem;
            if ((double) size > (double) limitSize * table->maxGrowth)
                return(moves);
            if (size < limitSize) limitSize = size;
            /* Update upper bound on node decrease: second phase. */
            gxtop = table->subtables[gybot].next;
            for (z = gxtop + 1; z <= gybot; z++) {
                zindex = table->invperm[z];
                if (zindex == xindex || cuddTestInteract(table,xindex,zindex)) {
                    isolated = table->vars[zindex]->ref == 1;
                    R += table->subtables[z].keys - isolated;
                }
            }
        }
        x = gybot;
        y = cuddNextHigh(table,x);
    }

    return(moves);

ddSymmSiftingDownOutOfMem:
    while (moves != NULL) {
        move = moves->next;
        cuddDeallocMove(table, moves);
        moves = move;
    }
    return(MV_OOM);

} /* end of ddSymmSiftingDown */

static Move * ddSymmSiftingUp	(	DdManager *	table,
		int	y,
		int	xLow
	)			[static]

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

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

Description [Moves x up until either it reaches the bound (xLow) or the size of the DD 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; MV_OOM if memory is full.]

SideEffects [None]

Definition at line 1188 of file cuddSymmetry.c.

{
    Move *moves;
    Move *move;
    int  x;
    int  size;
    int  i;
    int  gxtop,gybot;
    int  limitSize;
    int  xindex, yindex;
    int  zindex;
    int  z;
    int  isolated;
    int  L;     /* lower bound on DD size */
#ifdef DD_DEBUG
    int  checkL;
#endif


    moves = NULL;
    yindex = table->invperm[y];

    /* Initialize the lower bound.
    ** The part of the DD below the bottom of y' group will not change.
    ** The part of the DD above y that does not interact with y will not
    ** change. The rest may vanish in the best case, except for
    ** the nodes at level xLow, which will not vanish, regardless.
    */
    limitSize = L = table->keys - table->isolated;
    gybot = y;
    while ((unsigned) gybot < table->subtables[gybot].next)
        gybot = table->subtables[gybot].next;
    for (z = xLow + 1; z <= gybot; z++) {
        zindex = table->invperm[z];
        if (zindex == yindex || cuddTestInteract(table,zindex,yindex)) {
            isolated = table->vars[zindex]->ref == 1;
            L -= table->subtables[z].keys - isolated;
        }
    }

    x = cuddNextLow(table,y);
    while (x >= xLow && L <= limitSize) {
#ifdef DD_DEBUG
        gybot = y;
        while ((unsigned) gybot < table->subtables[gybot].next)
            gybot = table->subtables[gybot].next;
        checkL = table->keys - table->isolated;
        for (z = xLow + 1; z <= gybot; z++) {
            zindex = table->invperm[z];
            if (zindex == yindex || cuddTestInteract(table,zindex,yindex)) {
                isolated = table->vars[zindex]->ref == 1;
                checkL -= table->subtables[z].keys - isolated;
            }
        }
        assert(L == checkL);
#endif
        gxtop = table->subtables[x].next;
        if (cuddSymmCheck(table,x,y)) {
            /* Symmetry found, attach symm groups */
            table->subtables[x].next = y;
            i = table->subtables[y].next;
            while (table->subtables[i].next != (unsigned) y)
                i = table->subtables[i].next;
            table->subtables[i].next = gxtop;
        } else if (table->subtables[x].next == (unsigned) x &&
                   table->subtables[y].next == (unsigned) y) {
            /* x and y have self symmetry */
            xindex = table->invperm[x];
            size = cuddSwapInPlace(table,x,y);
#ifdef DD_DEBUG
            assert(table->subtables[x].next == (unsigned) x);
            assert(table->subtables[y].next == (unsigned) y);
#endif
            if (size == 0) goto ddSymmSiftingUpOutOfMem;
            /* Update the lower bound. */
            if (cuddTestInteract(table,xindex,yindex)) {
                isolated = table->vars[xindex]->ref == 1;
                L += table->subtables[y].keys - isolated;
            }
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSymmSiftingUpOutOfMem;
            move->x = x;
            move->y = y;
            move->size = size;
            move->next = moves;
            moves = move;
            if ((double) size > (double) limitSize * table->maxGrowth)
                return(moves);
            if (size < limitSize) limitSize = size;
        } else { /* Group move */
            size = ddSymmGroupMove(table,x,y,&moves);
            if (size == 0) goto ddSymmSiftingUpOutOfMem;
            /* Update the lower bound. */
            z = moves->y;
            do {
                zindex = table->invperm[z];
                if (cuddTestInteract(table,zindex,yindex)) {
                    isolated = table->vars[zindex]->ref == 1;
                    L += table->subtables[z].keys - isolated;
                }
                z = table->subtables[z].next;
            } while (z != (int) moves->y);
            if ((double) size > (double) limitSize * table->maxGrowth)
                return(moves);
            if (size < limitSize) limitSize = size;
        }
        y = gxtop;
        x = cuddNextLow(table,y);
    }

    return(moves);

ddSymmSiftingUpOutOfMem:
    while (moves != NULL) {
        move = moves->next;
        cuddDeallocMove(table, moves);
        moves = move;
    }
    return(MV_OOM);

} /* end of ddSymmSiftingUp */

static void ddSymmSummary	(	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 1664 of file cuddSymmetry.c.

{
    int i,x,gbot;
    int TotalSymm = 0;
    int TotalSymmGroups = 0;

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

    return;

} /* end of ddSymmSummary */

static int ddSymmUniqueCompare	(	int *	ptrX,
		int *	ptrY
	)			[static]

AutomaticStart

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

Synopsis [Comparison function used by qsort.]

Description [Comparison function used by qsort to order the variables according to the number of keys in the subtables. Returns the difference in number of keys between the two variables being compared.]

SideEffects [None]

Definition at line 601 of file cuddSymmetry.c.

{
#if 0
    if (entry[*ptrY] == entry[*ptrX]) {
        return((*ptrX) - (*ptrY));
    }
#endif
    return(entry[*ptrY] - entry[*ptrX]);

} /* end of ddSymmUniqueCompare */

---

Variable Documentation

char rcsid [] DD_UNUSED = "$Id: cuddSymmetry.c,v 1.26 2009/02/19 16:23:54 fabio Exp $" [static]

Definition at line 90 of file cuddSymmetry.c.

int ddTotalNumberSwapping

Definition at line 103 of file cuddReorder.c.

int* entry [static]

Definition at line 93 of file cuddSymmetry.c.