cuddReorder.c File Reference

#include "misc/util/util_hack.h"
#include "cuddInt.h"

Go to the source code of this file.

Macros
#define	DD_MAX_SUBTABLE_SPARSITY   8
#define	DD_SHRINK_FACTOR   2

Functions
static int	ddUniqueCompare (int *ptrX, int *ptrY)
static Move *	ddSwapAny (DdManager *table, int x, int y)
static int	ddSiftingAux (DdManager *table, int x, int xLow, int xHigh)
static Move *	ddSiftingUp (DdManager *table, int y, int xLow)
static Move *	ddSiftingDown (DdManager *table, int x, int xHigh)
static int	ddSiftingBackward (DdManager *table, int size, Move *moves)
static int	ddReorderPreprocess (DdManager *table)
static int	ddReorderPostprocess (DdManager *table)
static int	ddShuffle (DdManager *table, int *permutation)
static int	ddSiftUp (DdManager *table, int x, int xLow)
static void	bddFixTree (DdManager *table, MtrNode *treenode)
static int	ddUpdateMtrTree (DdManager *table, MtrNode *treenode, int *perm, int *invperm)
static int	ddCheckPermuation (DdManager *table, MtrNode *treenode, int *perm, int *invperm)
int	Cudd_ReduceHeap (DdManager *table, Cudd_ReorderingType heuristic, int minsize)
int	Cudd_ShuffleHeap (DdManager *table, int *permutation)
DdNode *	cuddDynamicAllocNode (DdManager *table)
int	cuddSifting (DdManager *table, int lower, int upper)
int	cuddSwapping (DdManager *table, int lower, int upper, Cudd_ReorderingType heuristic)
int	cuddNextHigh (DdManager *table, int x)
int	cuddNextLow (DdManager *table, int x)
int	cuddSwapInPlace (DdManager *table, int x, int y)
int	cuddBddAlignToZdd (DdManager *table)

Variables
static char rcsid[]	DD_UNUSED = "$Id: cuddReorder.c,v 1.69 2009/02/21 18:24:10 fabio Exp $"
static int *	entry
int	ddTotalNumberSwapping

Macro Definition Documentation

#define DD_MAX_SUBTABLE_SPARSITY   8

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

FileName [cuddReorder.c]

PackageName [cudd]

Synopsis [Functions for dynamic variable reordering.]

Description [External procedures included in this file:

• Cudd_ReduceHeap()
• Cudd_ShuffleHeap()

Internal procedures included in this module:

• cuddDynamicAllocNode()
• cuddSifting()
• cuddSwapping()
• cuddNextHigh()
• cuddNextLow()
• cuddSwapInPlace()
• cuddBddAlignToZdd()

Static procedures included in this module:

• ddUniqueCompare()
• ddSwapAny()
• ddSiftingAux()
• ddSiftingUp()
• ddSiftingDown()
• ddSiftingBackward()
• ddReorderPreprocess()
• ddReorderPostprocess()
• ddShuffle()
• ddSiftUp()
• bddFixTree()

]

Author [Shipra Panda, Bernard Plessier, 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 86 of file cuddReorder.c.

#define DD_SHRINK_FACTOR   2

Definition at line 87 of file cuddReorder.c.

Function Documentation

static void bddFixTree ( DdManager *  table, MtrNode *  treenode  )

static

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

Synopsis [Fixes the BDD variable group tree after a shuffle.]

Description [Fixes the BDD variable group tree after a shuffle. Assumes that the order of the variables in a terminal node has not been changed.]

SideEffects [Changes the BDD variable group tree.]

SeeAlso []

Definition at line 2010 of file cuddReorder.c.

{
    if (treenode == NULL) return;
    treenode->low = ((int) treenode->index < table->size) ?
        table->perm[treenode->index] : treenode->index;
    if (treenode->child != NULL) {
        bddFixTree(table, treenode->child);
    }
    if (treenode->younger != NULL)
        bddFixTree(table, treenode->younger);
    if (treenode->parent != NULL && treenode->low < treenode->parent->low) {
        treenode->parent->low = treenode->low;
        treenode->parent->index = treenode->index;
    }
    return;

} /* end of bddFixTree */

int Cudd_ReduceHeap	(	DdManager *	table,
		Cudd_ReorderingType	heuristic,
		int	minsize
	)

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

Synopsis [Main dynamic reordering routine.]

Description [Main dynamic reordering routine. Calls one of the possible reordering procedures:

• Swapping
• Sifting
• Symmetric Sifting
• Group Sifting
• Window Permutation
• Simulated Annealing
• Genetic Algorithm
• Dynamic Programming (exact)

For sifting, symmetric sifting, group sifting, and window permutation it is possible to request reordering to convergence.

The core of all methods is the reordering procedure cuddSwapInPlace() which swaps two adjacent variables and is based on Rudell's paper. Returns 1 in case of success; 0 otherwise. In the case of symmetric sifting (with and without convergence) returns 1 plus the number of symmetric variables, in case of success.]

SideEffects [Changes the variable order for all diagrams and clears the cache.]

Definition at line 176 of file cuddReorder.c.

{
    DdHook *hook;
    int result;
    unsigned int nextDyn;
#ifdef DD_STATS
    unsigned int initialSize;
    unsigned int finalSize;
#endif
    long localTime;

    /* Don't reorder if there are too many dead nodes. */
    if (table->keys - table->dead < (unsigned) minsize)
        return(1);

    if (heuristic == CUDD_REORDER_SAME) {
        heuristic = table->autoMethod;
    }
    if (heuristic == CUDD_REORDER_NONE) {
        return(1);
    }

    /* This call to Cudd_ReduceHeap does initiate reordering. Therefore
    ** we count it.
    */
    table->reorderings++;

    localTime = util_cpu_time();

    /* Run the hook functions. */
    hook = table->preReorderingHook;
    while (hook != NULL) {
        int res = (hook->f)(table, "BDD", (void *)heuristic);
        if (res == 0) return(0);
        hook = hook->next;
    }

    if (!ddReorderPreprocess(table)) return(0);
    ddTotalNumberSwapping = 0;

    if (table->keys > table->peakLiveNodes) {
        table->peakLiveNodes = table->keys;
    }
#ifdef DD_STATS
    initialSize = table->keys - table->isolated;
    ddTotalNISwaps = 0;

    switch(heuristic) {
    case CUDD_REORDER_RANDOM:
    case CUDD_REORDER_RANDOM_PIVOT:
        (void) fprintf(table->out,"#:I_RANDOM  ");
        break;
    case CUDD_REORDER_SIFT:
    case CUDD_REORDER_SIFT_CONVERGE:
    case CUDD_REORDER_SYMM_SIFT:
    case CUDD_REORDER_SYMM_SIFT_CONV:
    case CUDD_REORDER_GROUP_SIFT:
    case CUDD_REORDER_GROUP_SIFT_CONV:
        (void) fprintf(table->out,"#:I_SIFTING ");
        break;
    case CUDD_REORDER_WINDOW2:
    case CUDD_REORDER_WINDOW3:
    case CUDD_REORDER_WINDOW4:
    case CUDD_REORDER_WINDOW2_CONV:
    case CUDD_REORDER_WINDOW3_CONV:
    case CUDD_REORDER_WINDOW4_CONV:
        (void) fprintf(table->out,"#:I_WINDOW  ");
        break;
    case CUDD_REORDER_ANNEALING:
        (void) fprintf(table->out,"#:I_ANNEAL  ");
        break;
    case CUDD_REORDER_GENETIC:
        (void) fprintf(table->out,"#:I_GENETIC ");
        break;
    case CUDD_REORDER_LINEAR:
    case CUDD_REORDER_LINEAR_CONVERGE:
        (void) fprintf(table->out,"#:I_LINSIFT ");
        break;
    case CUDD_REORDER_EXACT:
        (void) fprintf(table->out,"#:I_EXACT   ");
        break;
    default:
        return(0);
    }
    (void) fprintf(table->out,"%8d: initial size",initialSize);
#endif

    /* See if we should use alternate threshold for maximum growth. */
    if (table->reordCycle && table->reorderings % table->reordCycle == 0) {
        double saveGrowth = table->maxGrowth;
        table->maxGrowth = table->maxGrowthAlt;
        result = cuddTreeSifting(table,heuristic);
        table->maxGrowth = saveGrowth;
    } else {
        result = cuddTreeSifting(table,heuristic);
    }

#ifdef DD_STATS
    (void) fprintf(table->out,"\n");
    finalSize = table->keys - table->isolated;
    (void) fprintf(table->out,"#:F_REORDER %8d: final size\n",finalSize);
    (void) fprintf(table->out,"#:T_REORDER %8g: total time (sec)\n",
                   ((double)(util_cpu_time() - localTime)/1000.0));
    (void) fprintf(table->out,"#:N_REORDER %8d: total swaps\n",
                   ddTotalNumberSwapping);
    (void) fprintf(table->out,"#:M_REORDER %8d: NI swaps\n",ddTotalNISwaps);
#endif

    if (result == 0)
        return(0);

    if (!ddReorderPostprocess(table))
        return(0);

    if (table->realign) {
        if (!cuddZddAlignToBdd(table))
            return(0);
    }

    nextDyn = (table->keys - table->constants.keys + 1) *
              DD_DYN_RATIO + table->constants.keys;
    if (table->reorderings < 20 || nextDyn > table->nextDyn)
        table->nextDyn = nextDyn;
    else
        table->nextDyn += 20;
    table->reordered = 1;

    /* Run hook functions. */
    hook = table->postReorderingHook;
    while (hook != NULL) {
        int res = (hook->f)(table, "BDD", (void *)localTime);
        if (res == 0) return(0);
        hook = hook->next;
    }
    /* Update cumulative reordering time. */
    table->reordTime += util_cpu_time() - localTime;

    return(result);

} /* end of Cudd_ReduceHeap */

int Cudd_ShuffleHeap	(	DdManager *	table,
		int *	permutation
	)

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

Synopsis [Reorders variables according to given permutation.]

Description [Reorders variables according to given permutation. The i-th entry of the permutation array contains the index of the variable that should be brought to the i-th level. The size of the array should be equal or greater to the number of variables currently in use. Returns 1 in case of success; 0 otherwise.]

SideEffects [Changes the variable order for all diagrams and clears the cache.]

SeeAlso [Cudd_ReduceHeap]

Definition at line 338 of file cuddReorder.c.

{

    int result;
    int i;
    int identity = 1;
    int *perm;

    /* Don't waste time in case of identity permutation. */
    for (i = 0; i < table->size; i++) {
        if (permutation[i] != table->invperm[i]) {
            identity = 0;
            break;
        }
    }
    if (identity == 1) {
        return(1);
    }
    if (!ddReorderPreprocess(table)) return(0);
    if (table->keys > table->peakLiveNodes) {
        table->peakLiveNodes = table->keys;
    }

    perm = ABC_ALLOC(int, table->size);
    for (i = 0; i < table->size; i++)
        perm[permutation[i]] = i;
    if (!ddCheckPermuation(table,table->tree,perm,permutation)) {
        ABC_FREE(perm);
        return(0);
    }
    if (!ddUpdateMtrTree(table,table->tree,perm,permutation)) {
        ABC_FREE(perm);
        return(0);
    }
    ABC_FREE(perm);

    result = ddShuffle(table,permutation);

    if (!ddReorderPostprocess(table)) return(0);

    return(result);

} /* end of Cudd_ShuffleHeap */

int cuddBddAlignToZdd

(

DdManager *

table

)

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

Synopsis [Reorders BDD variables according to the order of the ZDD variables.]

Description [Reorders BDD variables according to the order of the ZDD variables. This function can be called at the end of ZDD reordering to insure that the order of the BDD variables is consistent with the order of the ZDD variables. The number of ZDD variables must be a multiple of the number of BDD variables. Let M be the ratio of the two numbers. cuddBddAlignToZdd then considers the ZDD variables from M*i to (M+1)*i-1 as corresponding to BDD variable i. This function should be normally called from Cudd_zddReduceHeap, which clears the cache. Returns 1 in case of success; 0 otherwise.]

SideEffects [Changes the BDD variable order for all diagrams and performs garbage collection of the BDD unique table.]

SeeAlso [Cudd_ShuffleHeap Cudd_zddReduceHeap]

Definition at line 1251 of file cuddReorder.c.

{
    int *invperm;               /* permutation array */
    int M;                      /* ratio of ZDD variables to BDD variables */
    int i;                      /* loop index */
    int result;                 /* return value */

    /* We assume that a ratio of 0 is OK. */
    if (table->size == 0)
        return(1);

    M = table->sizeZ / table->size;
    /* Check whether the number of ZDD variables is a multiple of the
    ** number of BDD variables.
    */
    if (M * table->size != table->sizeZ)
        return(0);
    /* Create and initialize the inverse permutation array. */
    invperm = ABC_ALLOC(int,table->size);
    if (invperm == NULL) {
        table->errorCode = CUDD_MEMORY_OUT;
        return(0);
    }
    for (i = 0; i < table->sizeZ; i += M) {
        int indexZ = table->invpermZ[i];
        int index  = indexZ / M;
        invperm[i / M] = index;
    }
    /* Eliminate dead nodes. Do not scan the cache again, because we
    ** assume that Cudd_zddReduceHeap has already cleared it.
    */
    cuddGarbageCollect(table,0);

    /* Initialize number of isolated projection functions. */
    table->isolated = 0;
    for (i = 0; i < table->size; i++) {
        if (table->vars[i]->ref == 1) table->isolated++;
    }

    /* Initialize the interaction matrix. */
    result = cuddInitInteract(table);
    if (result == 0) return(0);

    result = ddShuffle(table, invperm);
    ABC_FREE(invperm);
    /* Free interaction matrix. */
    ABC_FREE(table->interact);
    /* Fix the BDD variable group tree. */
    bddFixTree(table,table->tree);
    return(result);

} /* end of cuddBddAlignToZdd */

DdNode* cuddDynamicAllocNode

(

DdManager *

table

)

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

Synopsis [Dynamically allocates a Node.]

Description [Dynamically allocates a Node. This procedure is similar to cuddAllocNode in Cudd_Table.c, but it does not attempt garbage collection, because during reordering there are no dead nodes. Returns a pointer to a new node if successful; NULL is memory is full.]

SideEffects [None]

SeeAlso [cuddAllocNode]

Definition at line 406 of file cuddReorder.c.

{
    int     i;
    DdNodePtr *mem;
    DdNode *list, *node;
    extern DD_OOMFP MMoutOfMemory;
    DD_OOMFP saveHandler;

    if (table->nextFree == NULL) {        /* free list is empty */
        /* Try to allocate a new block. */
        saveHandler = MMoutOfMemory;
        MMoutOfMemory = Cudd_OutOfMem;
//        mem = (DdNodePtr *) ABC_ALLOC(DdNode, DD_MEM_CHUNK + 1);
        mem = (DdNodePtr *) ABC_ALLOC(DdNode, DD_MEM_CHUNK + 2);
        MMoutOfMemory = saveHandler;
        if (mem == NULL && table->stash != NULL) {
            ABC_FREE(table->stash);
            table->stash = NULL;
            /* Inhibit resizing of tables. */
            table->maxCacheHard = table->cacheSlots - 1;
            table->cacheSlack = - (int) (table->cacheSlots + 1);
            for (i = 0; i < table->size; i++) {
                table->subtables[i].maxKeys <<= 2;
            }
//            mem = (DdNodePtr *) ABC_ALLOC(DdNode,DD_MEM_CHUNK + 1);
            mem = (DdNodePtr *) ABC_ALLOC(DdNode,DD_MEM_CHUNK + 2);
        }
        if (mem == NULL) {
            /* Out of luck. Call the default handler to do
            ** whatever it specifies for a failed malloc.  If this
            ** handler returns, then set error code, print
            ** warning, and return. */
            (*MMoutOfMemory)(sizeof(DdNode)*(DD_MEM_CHUNK + 1));
            table->errorCode = CUDD_MEMORY_OUT;
#ifdef DD_VERBOSE
            (void) fprintf(table->err,
                           "cuddDynamicAllocNode: out of memory");
            (void) fprintf(table->err,"Memory in use = %lu\n",
                           table->memused);
#endif
            return(NULL);
        } else {        /* successful allocation; slice memory */
            unsigned long offset;
            table->memused += (DD_MEM_CHUNK + 1) * sizeof(DdNode);
            mem[0] = (DdNode *) table->memoryList;
            table->memoryList = mem;

            /* Here we rely on the fact that the size of a DdNode is a
            ** power of 2 and a multiple of the size of a pointer.
            ** If we align one node, all the others will be aligned
            ** as well. */
//            offset = (unsigned long) mem & (sizeof(DdNode) - 1);
//            mem += (sizeof(DdNode) - offset) / sizeof(DdNodePtr);
            offset = (unsigned long) mem & (32 - 1);
            mem += (32 - offset) / sizeof(DdNodePtr);
#ifdef DD_DEBUG
//            assert(((unsigned long) mem & (sizeof(DdNode) - 1)) == 0);
            assert(((unsigned long) mem & (32 - 1)) == 0);
#endif
            list = (DdNode *) mem;

            i = 1;
            do {
                list[i - 1].ref = 0;
                list[i - 1].next = &list[i];
            } while (++i < DD_MEM_CHUNK);

            list[DD_MEM_CHUNK-1].ref = 0;
            list[DD_MEM_CHUNK - 1].next = NULL;

            table->nextFree = &list[0];
        }
    } /* if free list empty */

    node = table->nextFree;
    table->nextFree = node->next;
    return (node);

} /* end of cuddDynamicAllocNode */

int cuddNextHigh	(	DdManager *	table,
		int	x
	)

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

Synopsis [Finds the next subtable with a larger index.]

Description [Finds the next subtable with a larger index. Returns the index.]

SideEffects [None]

SeeAlso [cuddNextLow]

Definition at line 716 of file cuddReorder.c.

{
    return(x+1);

} /* end of cuddNextHigh */

int cuddNextLow	(	DdManager *	table,
		int	x
	)

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

Synopsis [Finds the next subtable with a smaller index.]

Description [Finds the next subtable with a smaller index. Returns the index.]

SideEffects [None]

SeeAlso [cuddNextHigh]

Definition at line 738 of file cuddReorder.c.

{
    return(x-1);

} /* end of cuddNextLow */

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

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

Synopsis [Implementation of Rudell's sifting algorithm.]

Description [Implementation of Rudell's sifting algorithm. Assumes that no dead nodes are present.

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

Returns 1 if successful; 0 otherwise.]

SideEffects [None]

Definition at line 508 of file cuddReorder.c.

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

    size = table->size;

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

    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)ddUniqueCompare);

    /* Now sift. */
    for (i = 0; i < ddMin(table->siftMaxVar,size); i++) {
        if (ddTotalNumberSwapping >= table->siftMaxSwap)
            break;
        x = table->perm[var[i]];

        if (x < lower || x > upper || table->subtables[x].bindVar == 1)
            continue;
#ifdef DD_STATS
        previousSize = table->keys - table->isolated;
#endif
        result = ddSiftingAux(table, x, lower, upper);
        if (!result) goto cuddSiftingOutOfMem;
#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 */
            (void) fprintf(table->err,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keys - table->isolated, var[i]);
        } else {
            (void) fprintf(table->out,"=");
        }
        fflush(table->out);
#endif
    }

    ABC_FREE(var);
    ABC_FREE(entry);

    return(1);

cuddSiftingOutOfMem:

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

    return(0);

} /* end of cuddSifting */

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

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

Synopsis [Swaps two adjacent variables.]

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

SideEffects [None]

Definition at line 761 of file cuddReorder.c.

{
    DdNodePtr *xlist, *ylist;
    int    xindex, yindex;
    int    xslots, yslots;
    int    xshift, yshift;
    int    oldxkeys, oldykeys;
    int    newxkeys, newykeys;
    int    comple, newcomplement;
    int    i;
    Cudd_VariableType varType;
    Cudd_LazyGroupType groupType;
    int    posn;
    int    isolated;
    DdNode *f,*f0,*f1,*f01,*f00,*f11,*f10,*newf1,*newf0;
    DdNode *g,*next;
    DdNodePtr *previousP;
    DdNode *tmp;
    DdNode *sentinel = &(table->sentinel);
    extern DD_OOMFP MMoutOfMemory;
    DD_OOMFP saveHandler;

#ifdef DD_DEBUG
    int    count,idcheck;
#endif

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

    ddTotalNumberSwapping++;

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

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

    if (!cuddTestInteract(table,xindex,yindex)) {
#ifdef DD_STATS
        ddTotalNISwaps++;
#endif
        newxkeys = oldxkeys;
        newykeys = oldykeys;
    } else {
        newxkeys = 0;
        newykeys = oldykeys;

        /* Check whether the two projection functions involved in this
        ** swap are isolated. At the end, we'll be able to tell how many
        ** isolated projection functions are there by checking only these
        ** two functions again. This is done to eliminate the isolated
        ** projection functions from the node count.
        */
        isolated = - ((table->vars[xindex]->ref == 1) +
                     (table->vars[yindex]->ref == 1));

        /* The nodes in the x layer that do not depend on
        ** y will stay there; the others are put in a chain.
        ** The chain is handled as a LIFO; g points to the beginning.
        */
        g = NULL;
        if ((oldxkeys >= xslots || (unsigned) xslots == table->initSlots) &&
            oldxkeys <= DD_MAX_SUBTABLE_DENSITY * xslots) {
            for (i = 0; i < xslots; i++) {
                previousP = &(xlist[i]);
                f = *previousP;
                while (f != sentinel) {
                    next = f->next;
                    f1 = cuddT(f); f0 = cuddE(f);
                    if (f1->index != (DdHalfWord) yindex &&
                        Cudd_Regular(f0)->index != (DdHalfWord) yindex) {
                        /* stays */
                        newxkeys++;
                        *previousP = f;
                        previousP = &(f->next);
                    } else {
                        f->index = yindex;
                        f->next = g;
                        g = f;
                    }
                    f = next;
                } /* while there are elements in the collision chain */
                *previousP = sentinel;
            } /* for each slot of the x subtable */
        } else {                /* resize xlist */
            DdNode *h = NULL;
            DdNodePtr *newxlist;
            unsigned int newxslots;
            int newxshift;
            /* Empty current xlist. Nodes that stay go to list h;
            ** nodes that move go to list g. */
            for (i = 0; i < xslots; i++) {
                f = xlist[i];
                while (f != sentinel) {
                    next = f->next;
                    f1 = cuddT(f); f0 = cuddE(f);
                    if (f1->index != (DdHalfWord) yindex &&
                        Cudd_Regular(f0)->index != (DdHalfWord) yindex) {
                        /* stays */
                        f->next = h;
                        h = f;
                        newxkeys++;
                    } else {
                        f->index = yindex;
                        f->next = g;
                        g = f;
                    }
                    f = next;
                } /* while there are elements in the collision chain */
            } /* for each slot of the x subtable */
            /* Decide size of new subtable. */
            newxshift = xshift;
            newxslots = xslots;
            while ((unsigned) oldxkeys > DD_MAX_SUBTABLE_DENSITY * newxslots) {
                newxshift--;
                newxslots <<= 1;
            }
            while ((unsigned) oldxkeys < newxslots &&
                   newxslots > table->initSlots) {
                newxshift++;
                newxslots >>= 1;
            }
            /* Try to allocate new table. Be ready to back off. */
            saveHandler = MMoutOfMemory;
            MMoutOfMemory = Cudd_OutOfMem;
            newxlist = ABC_ALLOC(DdNodePtr, newxslots);
            MMoutOfMemory = saveHandler;
            if (newxlist == NULL) {
                (void) fprintf(table->err, "Unable to resize subtable %d for lack of memory\n", i);
                newxlist = xlist;
                newxslots = xslots;
                newxshift = xshift;
            } else {
                table->slots += ((int) newxslots - xslots);
                table->minDead = (unsigned)
                    (table->gcFrac * (double) table->slots);
                table->cacheSlack = (int)
                    ddMin(table->maxCacheHard, DD_MAX_CACHE_TO_SLOTS_RATIO
                          * table->slots) - 2 * (int) table->cacheSlots;
                table->memused +=
                    ((int) newxslots - xslots) * sizeof(DdNodePtr);
                ABC_FREE(xlist);
                xslots =  newxslots;
                xshift = newxshift;
                xlist = newxlist;
            }
            /* Initialize new subtable. */
            for (i = 0; i < xslots; i++) {
                xlist[i] = sentinel;
            }
            /* Move nodes that were parked in list h to their new home. */
            f = h;
            while (f != NULL) {
                next = f->next;
                f1 = cuddT(f);
                f0 = cuddE(f);
                /* Check xlist for pair (f11,f01). */
                posn = ddHash(cuddF2L(f1), cuddF2L(f0), xshift);
                /* For each element tmp in collision list xlist[posn]. */
                previousP = &(xlist[posn]);
                tmp = *previousP;
                while (f1 < cuddT(tmp)) {
                    previousP = &(tmp->next);
                    tmp = *previousP;
                }
                while (f1 == cuddT(tmp) && f0 < cuddE(tmp)) {
                    previousP = &(tmp->next);
                    tmp = *previousP;
                }
                f->next = *previousP;
                *previousP = f;
                f = next;
            }
        }

#ifdef DD_COUNT
        table->swapSteps += oldxkeys - newxkeys;
#endif
        /* Take care of the x nodes that must be re-expressed.
        ** They form a linked list pointed by g. Their index has been
        ** already changed to yindex.
        */
        f = g;
        while (f != NULL) {
            next = f->next;
            /* Find f1, f0, f11, f10, f01, f00. */
            f1 = cuddT(f);
#ifdef DD_DEBUG
            assert(!(Cudd_IsComplement(f1)));
#endif
            if ((int) f1->index == yindex) {
                f11 = cuddT(f1); f10 = cuddE(f1);
            } else {
                f11 = f10 = f1;
            }
#ifdef DD_DEBUG
            assert(!(Cudd_IsComplement(f11)));
#endif
            f0 = cuddE(f);
            comple = Cudd_IsComplement(f0);
            f0 = Cudd_Regular(f0);
            if ((int) f0->index == yindex) {
                f01 = cuddT(f0); f00 = cuddE(f0);
            } else {
                f01 = f00 = f0;
            }
            if (comple) {
                f01 = Cudd_Not(f01);
                f00 = Cudd_Not(f00);
            }
            /* Decrease ref count of f1. */
            cuddSatDec(f1->ref);
            /* Create the new T child. */
            if (f11 == f01) {
                newf1 = f11;
                cuddSatInc(newf1->ref);
            } else {
                /* Check xlist for triple (xindex,f11,f01). */
                posn = ddHash(cuddF2L(f11), cuddF2L(f01), xshift);
                /* For each element newf1 in collision list xlist[posn]. */
                previousP = &(xlist[posn]);
                newf1 = *previousP;
                while (f11 < cuddT(newf1)) {
                    previousP = &(newf1->next);
                    newf1 = *previousP;
                }
                while (f11 == cuddT(newf1) && f01 < cuddE(newf1)) {
                    previousP = &(newf1->next);
                    newf1 = *previousP;
                }
                if (cuddT(newf1) == f11 && cuddE(newf1) == f01) {
                    cuddSatInc(newf1->ref);
                } else { /* no match */
                    newf1 = cuddDynamicAllocNode(table);
                    if (newf1 == NULL)
                        goto cuddSwapOutOfMem;
                    newf1->index = xindex; newf1->ref = 1;
                    cuddT(newf1) = f11;
                    cuddE(newf1) = f01;
                    /* Insert newf1 in the collision list xlist[posn];
                    ** increase the ref counts of f11 and f01.
                    */
                    newxkeys++;
                    newf1->next = *previousP;
                    *previousP = newf1;
                    cuddSatInc(f11->ref);
                    tmp = Cudd_Regular(f01);
                    cuddSatInc(tmp->ref);
                }
            }
            cuddT(f) = newf1;
#ifdef DD_DEBUG
            assert(!(Cudd_IsComplement(newf1)));
#endif

            /* Do the same for f0, keeping complement dots into account. */
            /* Decrease ref count of f0. */
            tmp = Cudd_Regular(f0);
            cuddSatDec(tmp->ref);
            /* Create the new E child. */
            if (f10 == f00) {
                newf0 = f00;
                tmp = Cudd_Regular(newf0);
                cuddSatInc(tmp->ref);
            } else {
                /* make sure f10 is regular */
                newcomplement = Cudd_IsComplement(f10);
                if (newcomplement) {
                    f10 = Cudd_Not(f10);
                    f00 = Cudd_Not(f00);
                }
                /* Check xlist for triple (xindex,f10,f00). */
                posn = ddHash(cuddF2L(f10), cuddF2L(f00), xshift);
                /* For each element newf0 in collision list xlist[posn]. */
                previousP = &(xlist[posn]);
                newf0 = *previousP;
                while (f10 < cuddT(newf0)) {
                    previousP = &(newf0->next);
                    newf0 = *previousP;
                }
                while (f10 == cuddT(newf0) && f00 < cuddE(newf0)) {
                    previousP = &(newf0->next);
                    newf0 = *previousP;
                }
                if (cuddT(newf0) == f10 && cuddE(newf0) == f00) {
                    cuddSatInc(newf0->ref);
                } else { /* no match */
                    newf0 = cuddDynamicAllocNode(table);
                    if (newf0 == NULL)
                        goto cuddSwapOutOfMem;
                    newf0->index = xindex; newf0->ref = 1;
                    cuddT(newf0) = f10;
                    cuddE(newf0) = f00;
                    /* Insert newf0 in the collision list xlist[posn];
                    ** increase the ref counts of f10 and f00.
                    */
                    newxkeys++;
                    newf0->next = *previousP;
                    *previousP = newf0;
                    cuddSatInc(f10->ref);
                    tmp = Cudd_Regular(f00);
                    cuddSatInc(tmp->ref);
                }
                if (newcomplement) {
                    newf0 = Cudd_Not(newf0);
                }
            }
            cuddE(f) = newf0;

            /* Insert the modified f in ylist.
            ** The modified f does not already exists in ylist.
            ** (Because of the uniqueness of the cofactors.)
            */
            posn = ddHash(cuddF2L(newf1), cuddF2L(newf0), yshift);
            newykeys++;
            previousP = &(ylist[posn]);
            tmp = *previousP;
            while (newf1 < cuddT(tmp)) {
                previousP = &(tmp->next);
                tmp = *previousP;
            }
            while (newf1 == cuddT(tmp) && newf0 < cuddE(tmp)) {
                previousP = &(tmp->next);
                tmp = *previousP;
            }
            f->next = *previousP;
            *previousP = f;
            f = next;
        } /* while f != NULL */

        /* GC the y layer. */

        /* For each node f in ylist. */
        for (i = 0; i < yslots; i++) {
            previousP = &(ylist[i]);
            f = *previousP;
            while (f != sentinel) {
                next = f->next;
                if (f->ref == 0) {
                    tmp = cuddT(f);
                    cuddSatDec(tmp->ref);
                    tmp = Cudd_Regular(cuddE(f));
                    cuddSatDec(tmp->ref);
                    cuddDeallocNode(table,f);
                    newykeys--;
                } else {
                    *previousP = f;
                    previousP = &(f->next);
                }
                f = next;
            } /* while f */
            *previousP = sentinel;
        } /* for i */

#ifdef DD_DEBUG
#if 0
        (void) fprintf(table->out,"Swapping %d and %d\n",x,y);
#endif
        count = 0;
        idcheck = 0;
        for (i = 0; i < yslots; i++) {
            f = ylist[i];
            while (f != sentinel) {
                count++;
                if (f->index != (DdHalfWord) yindex)
                    idcheck++;
                f = f->next;
            }
        }
        if (count != newykeys) {
            (void) fprintf(table->out,
                           "Error in finding newykeys\toldykeys = %d\tnewykeys = %d\tactual = %d\n",
                           oldykeys,newykeys,count);
        }
        if (idcheck != 0)
            (void) fprintf(table->out,
                           "Error in id's of ylist\twrong id's = %d\n",
                           idcheck);
        count = 0;
        idcheck = 0;
        for (i = 0; i < xslots; i++) {
            f = xlist[i];
            while (f != sentinel) {
                count++;
                if (f->index != (DdHalfWord) xindex)
                    idcheck++;
                f = f->next;
            }
        }
        if (count != newxkeys) {
            (void) fprintf(table->out,
                           "Error in finding newxkeys\toldxkeys = %d \tnewxkeys = %d \tactual = %d\n",
                           oldxkeys,newxkeys,count);
        }
        if (idcheck != 0)
            (void) fprintf(table->out,
                           "Error in id's of xlist\twrong id's = %d\n",
                           idcheck);
#endif

        isolated += (table->vars[xindex]->ref == 1) +
                    (table->vars[yindex]->ref == 1);
        table->isolated += isolated;
    }

    /* Set the appropriate fields in table. */
    table->subtables[x].nodelist = ylist;
    table->subtables[x].slots = yslots;
    table->subtables[x].shift = yshift;
    table->subtables[x].keys = newykeys;
    table->subtables[x].maxKeys = yslots * DD_MAX_SUBTABLE_DENSITY;
    i = table->subtables[x].bindVar;
    table->subtables[x].bindVar = table->subtables[y].bindVar;
    table->subtables[y].bindVar = i;
    /* Adjust filds for lazy sifting. */
    varType = table->subtables[x].varType;
    table->subtables[x].varType = table->subtables[y].varType;
    table->subtables[y].varType = varType;
    i = table->subtables[x].pairIndex;
    table->subtables[x].pairIndex = table->subtables[y].pairIndex;
    table->subtables[y].pairIndex = i;
    i = table->subtables[x].varHandled;
    table->subtables[x].varHandled = table->subtables[y].varHandled;
    table->subtables[y].varHandled = i;
    groupType = table->subtables[x].varToBeGrouped;
    table->subtables[x].varToBeGrouped = table->subtables[y].varToBeGrouped;
    table->subtables[y].varToBeGrouped = groupType;

    table->subtables[y].nodelist = xlist;
    table->subtables[y].slots = xslots;
    table->subtables[y].shift = xshift;
    table->subtables[y].keys = newxkeys;
    table->subtables[y].maxKeys = xslots * DD_MAX_SUBTABLE_DENSITY;

    table->perm[xindex] = y; table->perm[yindex] = x;
    table->invperm[x] = yindex; table->invperm[y] = xindex;

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

    return(table->keys - table->isolated);

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

    return (0);

} /* end of cuddSwapInPlace */

int cuddSwapping	(	DdManager *	table,
		int	lower,
		int	upper,
		Cudd_ReorderingType	heuristic
	)

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

Synopsis [Reorders variables by a sequence of (non-adjacent) swaps.]

Description [Implementation of Plessier's algorithm that reorders variables by a sequence of (non-adjacent) swaps.

1. Select two variables (RANDOM or HEURISTIC).
2. Permute these variables.
3. If the nodes have decreased accept the permutation.
4. Otherwise reconstruct the original heap.
5. Loop.

Returns 1 in case of success; 0 otherwise.]

SideEffects [None]

Definition at line 605 of file cuddReorder.c.

{
    int i, j;
    int max, keys;
    int nvars;
    int x, y;
    int iterate;
    int previousSize;
    Move *moves, *move;
    int pivot = -1;
    int modulo;
    int result;

#ifdef DD_DEBUG
    /* Sanity check */
    assert(lower >= 0 && upper < table->size && lower <= upper);
#endif

    nvars = upper - lower + 1;
    iterate = nvars;

    for (i = 0; i < iterate; i++) {
        if (ddTotalNumberSwapping >= table->siftMaxSwap)
            break;
        if (heuristic == CUDD_REORDER_RANDOM_PIVOT) {
            max = -1;
            for (j = lower; j <= upper; j++) {
                if ((keys = table->subtables[j].keys) > max) {
                    max = keys;
                    pivot = j;
                }
            }

            modulo = upper - pivot;
            if (modulo == 0) {
                y = pivot;
            } else{
                y = pivot + 1 + ((int) Cudd_Random() % modulo);
            }

            modulo = pivot - lower - 1;
            if (modulo < 1) {
                x = lower;
            } else{
                do {
                    x = (int) Cudd_Random() % modulo;
                } while (x == y);
            }
        } else {
            x = ((int) Cudd_Random() % nvars) + lower;
            do {
                y = ((int) Cudd_Random() % nvars) + lower;
            } while (x == y);
        }
        previousSize = table->keys - table->isolated;
        moves = ddSwapAny(table,x,y);
        if (moves == NULL) goto cuddSwappingOutOfMem;
        result = ddSiftingBackward(table,previousSize,moves);
        if (!result) goto cuddSwappingOutOfMem;
        while (moves != NULL) {
            move = moves->next;
            cuddDeallocMove(table, moves);
            moves = move;
        }
#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
#if 0
        (void) fprintf(table->out,"#:t_SWAPPING %8d: tmp size\n",
                       table->keys - table->isolated);
#endif
    }

    return(1);

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

    return(0);

} /* end of cuddSwapping */

static int ddCheckPermuation ( DdManager *  table, MtrNode *  treenode, int *  perm, int *  invperm  )

static

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

Synopsis [Checks the BDD variable group tree before a shuffle.]

Description [Checks the BDD variable group tree before a shuffle. Returns 1 if successful; 0 otherwise.]

SideEffects [Changes the BDD variable group tree.]

SeeAlso []

Definition at line 2103 of file cuddReorder.c.

{
    int i, size;
    int index, level, minLevel, maxLevel;

    if (treenode == NULL) return(1);

    minLevel = table->size;
    maxLevel = 0;
    /* i : level */
    for (i = treenode->low; i < treenode->low + treenode->size; i++) {
        index = table->invperm[i];
        level = perm[index];
        if (level < minLevel)
            minLevel = level;
        if (level > maxLevel)
            maxLevel = level;
    }
    size = maxLevel - minLevel + 1;
    if (size != treenode->size)
        return(0);

    if (treenode->child != NULL) {
        if (!ddCheckPermuation(table, treenode->child, perm, invperm))
            return(0);
    }
    if (treenode->younger != NULL) {
        if (!ddCheckPermuation(table, treenode->younger, perm, invperm))
            return(0);
    }
    return(1);
}

static int ddReorderPostprocess ( DdManager *  table )

static

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

Synopsis [Cleans up at the end of reordering.]

Description []

SideEffects [None]

Definition at line 1864 of file cuddReorder.c.

{

#ifdef DD_VERBOSE
    (void) fflush(table->out);
#endif

    /* Free interaction matrix. */
    ABC_FREE(table->interact);

    return(1);

} /* end of ddReorderPostprocess */

static int ddReorderPreprocess ( DdManager *  table )

static

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

Synopsis [Prepares the DD heap for dynamic reordering.]

Description [Prepares the DD heap for dynamic reordering. Does garbage collection, to guarantee that there are no dead nodes; clears the cache, which is invalidated by dynamic reordering; initializes the number of isolated projection functions; and initializes the interaction matrix. Returns 1 in case of success; 0 otherwise.]

SideEffects [None]

Definition at line 1826 of file cuddReorder.c.

{
    int i;
    int res;

    /* Clear the cache. */
    cuddCacheFlush(table);
    cuddLocalCacheClearAll(table);

    /* Eliminate dead nodes. Do not scan the cache again. */
    cuddGarbageCollect(table,0);

    /* Initialize number of isolated projection functions. */
    table->isolated = 0;
    for (i = 0; i < table->size; i++) {
        if (table->vars[i]->ref == 1) table->isolated++;
    }

    /* Initialize the interaction matrix. */
    res = cuddInitInteract(table);
    if (res == 0) return(0);

    return(1);

} /* end of ddReorderPreprocess */

static int ddShuffle ( DdManager *  table, int *  permutation  )

static

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

Synopsis [Reorders variables according to a given permutation.]

Description [Reorders variables according to a given permutation. The i-th permutation array contains the index of the variable that should be brought to the i-th level. ddShuffle assumes that no dead nodes are present and that the interaction matrix is properly initialized. The reordering is achieved by a series of upward sifts. Returns 1 if successful; 0 otherwise.]

SideEffects [None]

SeeAlso []

Definition at line 1897 of file cuddReorder.c.

{
    int         index;
    int         level;
    int         position;
    int         numvars;
    int         result;
#ifdef DD_STATS
    long        localTime;
    int         initialSize;
    int         finalSize;
    int         previousSize;
#endif

    ddTotalNumberSwapping = 0;
#ifdef DD_STATS
    localTime = util_cpu_time();
    initialSize = table->keys - table->isolated;
    (void) fprintf(table->out,"#:I_SHUFFLE %8d: initial size\n",
                   initialSize);
    ddTotalNISwaps = 0;
#endif

    numvars = table->size;

    for (level = 0; level < numvars; level++) {
        index = permutation[level];
        position = table->perm[index];
#ifdef DD_STATS
        previousSize = table->keys - table->isolated;
#endif
        result = ddSiftUp(table,position,level);
        if (!result) return(0);
#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
    }

#ifdef DD_STATS
    (void) fprintf(table->out,"\n");
    finalSize = table->keys - table->isolated;
    (void) fprintf(table->out,"#:F_SHUFFLE %8d: final size\n",finalSize);
    (void) fprintf(table->out,"#:T_SHUFFLE %8g: total time (sec)\n",
        ((double)(util_cpu_time() - localTime)/1000.0));
    (void) fprintf(table->out,"#:N_SHUFFLE %8d: total swaps\n",
                   ddTotalNumberSwapping);
    (void) fprintf(table->out,"#:M_SHUFFLE %8d: NI swaps\n",ddTotalNISwaps);
#endif

    return(1);

} /* end of ddShuffle */

static int ddSiftingAux ( 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. Returns 1 if successful; 0 otherwise.]

SideEffects [None]

Definition at line 1488 of file cuddReorder.c.

{

    Move        *move;
    Move        *moveUp;                /* list of up moves */
    Move        *moveDown;              /* list of down moves */
    int         initialSize;
    int         result;

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

    moveDown = NULL;
    moveUp = NULL;

    if (x == xLow) {
        moveDown = ddSiftingDown(table,x,xHigh);
        /* At this point x --> xHigh unless bounding occurred. */
        if (moveDown == (Move *) CUDD_OUT_OF_MEM) goto ddSiftingAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = ddSiftingBackward(table,initialSize,moveDown);
        if (!result) goto ddSiftingAuxOutOfMem;

    } else if (x == xHigh) {
        moveUp = ddSiftingUp(table,x,xLow);
        /* At this point x --> xLow unless bounding occurred. */
        if (moveUp == (Move *) CUDD_OUT_OF_MEM) goto ddSiftingAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = ddSiftingBackward(table,initialSize,moveUp);
        if (!result) goto ddSiftingAuxOutOfMem;

    } else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
        moveDown = ddSiftingDown(table,x,xHigh);
        /* At this point x --> xHigh unless bounding occurred. */
        if (moveDown == (Move *) CUDD_OUT_OF_MEM) goto ddSiftingAuxOutOfMem;
        if (moveDown != NULL) {
            x = moveDown->y;
        }
        moveUp = ddSiftingUp(table,x,xLow);
        if (moveUp == (Move *) CUDD_OUT_OF_MEM) goto ddSiftingAuxOutOfMem;
        /* Move backward and stop at best position */
        result = ddSiftingBackward(table,initialSize,moveUp);
        if (!result) goto ddSiftingAuxOutOfMem;

    } else { /* must go up first: shorter */
        moveUp = ddSiftingUp(table,x,xLow);
        /* At this point x --> xLow unless bounding occurred. */
        if (moveUp == (Move *) CUDD_OUT_OF_MEM) goto ddSiftingAuxOutOfMem;
        if (moveUp != NULL) {
            x = moveUp->x;
        }
        moveDown = ddSiftingDown(table,x,xHigh);
        if (moveDown == (Move *) CUDD_OUT_OF_MEM) goto ddSiftingAuxOutOfMem;
        /* Move backward and stop at best position. */
        result = ddSiftingBackward(table,initialSize,moveDown);
        if (!result) goto ddSiftingAuxOutOfMem;
    }

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

    return(1);

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

    return(0);

} /* end of ddSiftingAux */

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

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 1787 of file cuddReorder.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);
        res = cuddSwapInPlace(table,(int)move->x,(int)move->y);
        if (!res) return(0);
    }

    return(1);

} /* end of ddSiftingBackward */

static Move * ddSiftingDown ( DdManager *  table, int  x, int  xHigh  )

static

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

Synopsis [Sifts a variable down.]

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

SideEffects [None]

Definition at line 1695 of file cuddReorder.c.

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

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

    y = cuddNextHigh(table,x);
    while (y <= xHigh && size - R < limitSize) {
#ifdef DD_DEBUG
        checkR = 0;
        for (z = xHigh; z > x; z--) {
            zindex = table->invperm[z];
            if (cuddTestInteract(table,xindex,zindex)) {
                isolated = table->vars[zindex]->ref == 1;
                checkR += table->subtables[z].keys - isolated;
            }
        }
        assert(R == checkR);
#endif
        /* 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);
        if (size == 0) goto ddSiftingDownOutOfMem;
        move = (Move *) cuddDynamicAllocNode(table);
        if (move == NULL) goto ddSiftingDownOutOfMem;
        move->x = x;
        move->y = y;
        move->size = size;
        move->next = moves;
        moves = move;
        if ((double) size > (double) limitSize * table->maxGrowth) break;
        if (size < limitSize) limitSize = size;
        x = y;
        y = cuddNextHigh(table,x);
    }
    return(moves);

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

} /* end of ddSiftingDown */

static Move * ddSiftingUp ( DdManager *  table, int  y, int  xLow  )

static

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

Synopsis [Sifts a variable up.]

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

SideEffects [None]

Definition at line 1595 of file cuddReorder.c.

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

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

    /* Initialize the lower bound.
    ** The part of the DD below y 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;
    for (x = xLow + 1; x < y; x++) {
        xindex = table->invperm[x];
        if (cuddTestInteract(table,xindex,yindex)) {
            isolated = table->vars[xindex]->ref == 1;
            L -= table->subtables[x].keys - isolated;
        }
    }
    isolated = table->vars[yindex]->ref == 1;
    L -= table->subtables[y].keys - isolated;

    x = cuddNextLow(table,y);
    while (x >= xLow && L <= limitSize) {
        xindex = table->invperm[x];
#ifdef DD_DEBUG
        checkL = table->keys - table->isolated;
        for (z = xLow + 1; z < y; z++) {
            zindex = table->invperm[z];
            if (cuddTestInteract(table,zindex,yindex)) {
                isolated = table->vars[zindex]->ref == 1;
                checkL -= table->subtables[z].keys - isolated;
            }
        }
        isolated = table->vars[yindex]->ref == 1;
        checkL -= table->subtables[y].keys - isolated;
        assert(L == checkL);
#endif
        size = cuddSwapInPlace(table,x,y);
        if (size == 0) goto ddSiftingUpOutOfMem;
        /* 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 ddSiftingUpOutOfMem;
        move->x = x;
        move->y = y;
        move->size = size;
        move->next = moves;
        moves = move;
        if ((double) size > (double) limitSize * table->maxGrowth) break;
        if (size < limitSize) limitSize = size;
        y = x;
        x = cuddNextLow(table,y);
    }
    return(moves);

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

} /* end of ddSiftingUp */

static int ddSiftUp ( DdManager *  table, int  x, int  xLow  )

static

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

Synopsis [Moves one variable up.]

Description [Takes a variable from position x and sifts it up to position xLow; xLow should be less than or equal to x. Returns 1 if successful; 0 otherwise]

SideEffects [None]

SeeAlso []

Definition at line 1974 of file cuddReorder.c.

{
    int        y;
    int        size;

    y = cuddNextLow(table,x);
    while (y >= xLow) {
        size = cuddSwapInPlace(table,y,x);
        if (size == 0) {
            return(0);
        }
        x = y;
        y = cuddNextLow(table,x);
    }
    return(1);

} /* end of ddSiftUp */

static Move * ddSwapAny ( DdManager *  table, int  x, int  y  )

static

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

Synopsis [Swaps any two variables.]

Description [Swaps any two variables. Returns the set of moves.]

SideEffects [None]

Definition at line 1347 of file cuddReorder.c.

{
    Move        *move, *moves;
    int         xRef,yRef;
    int         xNext,yNext;
    int         size;
    int         limitSize;
    int         tmp;

    if (x >y) {
        tmp = x; x = y; y = tmp;
    }

    xRef = x; yRef = y;

    xNext = cuddNextHigh(table,x);
    yNext = cuddNextLow(table,y);
    moves = NULL;
    limitSize = table->keys - table->isolated;

    for (;;) {
        if ( xNext == yNext) {
            size = cuddSwapInPlace(table,x,xNext);
            if (size == 0) goto ddSwapAnyOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSwapAnyOutOfMem;
            move->x = x;
            move->y = xNext;
            move->size = size;
            move->next = moves;
            moves = move;

            size = cuddSwapInPlace(table,yNext,y);
            if (size == 0) goto ddSwapAnyOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSwapAnyOutOfMem;
            move->x = yNext;
            move->y = y;
            move->size = size;
            move->next = moves;
            moves = move;

            size = cuddSwapInPlace(table,x,xNext);
            if (size == 0) goto ddSwapAnyOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSwapAnyOutOfMem;
            move->x = x;
            move->y = xNext;
            move->size = size;
            move->next = moves;
            moves = move;

            tmp = x; x = y; y = tmp;

        } else if (x == yNext) {

            size = cuddSwapInPlace(table,x,xNext);
            if (size == 0) goto ddSwapAnyOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSwapAnyOutOfMem;
            move->x = x;
            move->y = xNext;
            move->size = size;
            move->next = moves;
            moves = move;

            tmp = x; x = y; y = tmp;

        } else {
            size = cuddSwapInPlace(table,x,xNext);
            if (size == 0) goto ddSwapAnyOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSwapAnyOutOfMem;
            move->x = x;
            move->y = xNext;
            move->size = size;
            move->next = moves;
            moves = move;

            size = cuddSwapInPlace(table,yNext,y);
            if (size == 0) goto ddSwapAnyOutOfMem;
            move = (Move *) cuddDynamicAllocNode(table);
            if (move == NULL) goto ddSwapAnyOutOfMem;
            move->x = yNext;
            move->y = y;
            move->size = size;
            move->next = moves;
            moves = move;

            x = xNext;
            y = yNext;
        }

        xNext = cuddNextHigh(table,x);
        yNext = cuddNextLow(table,y);
        if (xNext > yRef) break;

        if ((double) size > table->maxGrowth * (double) limitSize) break;
        if (size < limitSize) limitSize = size;
    }
    if (yNext>=xRef) {
        size = cuddSwapInPlace(table,yNext,y);
        if (size == 0) goto ddSwapAnyOutOfMem;
        move = (Move *) cuddDynamicAllocNode(table);
        if (move == NULL) goto ddSwapAnyOutOfMem;
        move->x = yNext;
        move->y = y;
        move->size = size;
        move->next = moves;
        moves = move;
    }

    return(moves);

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

} /* end of ddSwapAny */

static int ddUniqueCompare ( 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 1323 of file cuddReorder.c.

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

} /* end of ddUniqueCompare */

static int ddUpdateMtrTree ( DdManager *  table, MtrNode *  treenode, int *  perm, int *  invperm  )

static

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

Synopsis [Updates the BDD variable group tree before a shuffle.]

Description [Updates the BDD variable group tree before a shuffle. Returns 1 if successful; 0 otherwise.]

SideEffects [Changes the BDD variable group tree.]

SeeAlso []

Definition at line 2044 of file cuddReorder.c.

{
    int i, size;
    int index, level, minLevel, maxLevel, minIndex;

    if (treenode == NULL) return(1);

    minLevel = CUDD_MAXINDEX;
    maxLevel = 0;
    minIndex = -1;
    /* i : level */
    for (i = treenode->low; i < treenode->low + treenode->size; i++) {
        index = table->invperm[i];
        level = perm[index];
        if (level < minLevel) {
            minLevel = level;
            minIndex = index;
        }
        if (level > maxLevel)
            maxLevel = level;
    }
    size = maxLevel - minLevel + 1;
    if (minIndex == -1) return(0);
    if (size == treenode->size) {
        treenode->low = minLevel;
        treenode->index = minIndex;
    } else {
        return(0);
    }

    if (treenode->child != NULL) {
        if (!ddUpdateMtrTree(table, treenode->child, perm, invperm))
            return(0);
    }
    if (treenode->younger != NULL) {
        if (!ddUpdateMtrTree(table, treenode->younger, perm, invperm))
            return(0);
    }
    return(1);
}

Variable Documentation

char rcsid [] DD_UNUSED = "$Id: cuddReorder.c,v 1.69 2009/02/21 18:24:10 fabio Exp $"

static

Definition at line 102 of file cuddReorder.c.

int ddTotalNumberSwapping

Definition at line 107 of file cuddReorder.c.

int* entry

static

Definition at line 105 of file cuddReorder.c.