src/bdd/cudd/cuddLinear.c File Reference

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

Include dependency graph for cuddLinear.c:

Go to the source code of this file.

Defines
#define	CUDD_SWAP_MOVE   0
#define	CUDD_LINEAR_TRANSFORM_MOVE   1
#define	CUDD_INVERSE_TRANSFORM_MOVE   2
#define	BPL   32
#define	LOGBPL   5
Functions
static int ddLinearUniqueCompare	ARGS ((int *ptrX, int *ptrY))
static int ddLinearAndSiftingAux	ARGS ((DdManager *table, int x, int xLow, int xHigh))
static Move *ddLinearAndSiftingUp	ARGS ((DdManager *table, int y, int xLow, Move *prevMoves))
static Move *ddLinearAndSiftingDown	ARGS ((DdManager *table, int x, int xHigh, Move *prevMoves))
static int ddLinearAndSiftingBackward	ARGS ((DdManager *table, int size, Move *moves))
static Move *ddUndoMoves	ARGS ((DdManager *table, Move *moves))
static int cuddLinearInPlace	ARGS ((DdManager *table, int x, int y))
static void ddUpdateInteractionMatrix	ARGS ((DdManager *table, int xindex, int yindex))
static int cuddInitLinear	ARGS ((DdManager *table))
int	Cudd_PrintLinear (DdManager *table)
int	Cudd_ReadLinear (DdManager *table, int x, int y)
int	cuddLinearAndSifting (DdManager *table, int lower, int upper)
static int	ddLinearUniqueCompare (int *ptrX, int *ptrY)
static int	ddLinearAndSiftingAux (DdManager *table, int x, int xLow, int xHigh)
static Move *	ddLinearAndSiftingUp (DdManager *table, int y, int xLow, Move *prevMoves)
static Move *	ddLinearAndSiftingDown (DdManager *table, int x, int xHigh, Move *prevMoves)
static int	ddLinearAndSiftingBackward (DdManager *table, int size, Move *moves)
static Move *	ddUndoMoves (DdManager *table, Move *moves)
static int	cuddLinearInPlace (DdManager *table, int x, int y)
static void	ddUpdateInteractionMatrix (DdManager *table, int xindex, int yindex)
static int	cuddInitLinear (DdManager *table)
static int	cuddResizeLinear (DdManager *table)
static void	cuddXorLinear (DdManager *table, int x, int y)
Variables
static char rcsid[]	DD_UNUSED = "$Id: cuddLinear.c,v 1.1.1.1 2003/02/24 22:23:52 wjiang Exp $"
static int *	entry

---

Define Documentation

#define BPL   32

Definition at line 51 of file cuddLinear.c.

#define CUDD_INVERSE_TRANSFORM_MOVE   2

Definition at line 46 of file cuddLinear.c.

#define CUDD_LINEAR_TRANSFORM_MOVE   1

Definition at line 45 of file cuddLinear.c.

#define CUDD_SWAP_MOVE   0

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

FileName [cuddLinear.c]

PackageName [cudd]

Synopsis [Functions for DD reduction by linear transformations.]

Description [ Internal procedures included in this module:

• cuddLinearAndSifting()

Static procedures included in this module:

• ddLinearUniqueCompare()
• ddLinearAndSiftingAux()
• ddLinearAndSiftingUp()
• ddLinearAndSiftingDown()
• ddLinearAndSiftingBackward()
• ddUndoMoves()
• ddUpdateInteractionMatrix()
• cuddLinearInPlace()
• cuddInitLinear()
• cuddResizeLinear()
• cuddXorLinear()

]

Author [Fabio Somenzi]

Copyright [This file was created at the University of Colorado at Boulder. The University of Colorado at Boulder makes no warranty about the suitability of this software for any purpose. It is presented on an AS IS basis.]

Definition at line 44 of file cuddLinear.c.

#define LOGBPL   5

Definition at line 52 of file cuddLinear.c.

---

Function Documentation

static int cuddInitLinear ARGS

(

(DdManager *table)

)

[static]

static void ddUpdateInteractionMatrix ARGS

(

(DdManager *table, int xindex, int yindex)

)

[static]

static int cuddLinearInPlace ARGS

(

(DdManager *table, int x, int y)

)

[static]

static Move* ddUndoMoves ARGS

(

(DdManager *table, Move *moves)

)

[static]

static int ddLinearAndSiftingBackward ARGS

(

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

)

[static]

static Move* ddLinearAndSiftingDown ARGS

(

(DdManager *table, int x, int xHigh, Move *prevMoves)

)

[static]

static Move* ddLinearAndSiftingUp ARGS

(

(DdManager *table, int y, int xLow, Move *prevMoves)

)

[static]

static int ddLinearAndSiftingAux ARGS

(

(DdManager *table, int x, int xLow, int xHigh)

)

[static]

static int ddLinearUniqueCompare ARGS

(

(int *ptrX, int *ptrY)

)

[static]

AutomaticStart

int Cudd_PrintLinear

(

DdManager *

table

)

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

Synopsis [Prints the linear transform matrix.]

Description [Prints the linear transform matrix. Returns 1 in case of success; 0 otherwise.]

SideEffects [none]

SeeAlso []

Definition at line 126 of file cuddLinear.c.

{
    int i,j,k;
    int retval;
    int nvars = table->linearSize;
    int wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    long word;

    for (i = 0; i < nvars; i++) {
        for (j = 0; j < wordsPerRow; j++) {
            word = table->linear[i*wordsPerRow + j];
            for (k = 0; k < BPL; k++) {
                retval = fprintf(table->out,"%ld",word & 1);
                if (retval == 0) return(0);
                word >>= 1;
            }
        }
        retval = fprintf(table->out,"\n");
        if (retval == 0) return(0);
    }
    return(1);

} /* end of Cudd_PrintLinear */

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

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

Synopsis [Reads an entry of the linear transform matrix.]

Description [Reads an entry of the linear transform matrix.]

SideEffects [none]

SeeAlso []

Definition at line 164 of file cuddLinear.c.

{
    int nvars = table->size;
    int wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    long word;
    int bit;
    int result;

    assert(table->size == table->linearSize);

    word = wordsPerRow * x + (y >> LOGBPL);
    bit  = y & (BPL-1);
    result = (int) ((table->linear[word] >> bit) & 1);
    return(result);

} /* end of Cudd_ReadLinear */

static int cuddInitLinear

(

DdManager *

table

)

[static]

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

Synopsis [Initializes the linear transform matrix.]

Description []

SideEffects [none]

SeeAlso []

Definition at line 1209 of file cuddLinear.c.

{
    int words;
    int wordsPerRow;
    int nvars;
    int word;
    int bit;
    int i;
    long *linear;

    nvars = table->size;
    wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    words = wordsPerRow * nvars;
    table->linear = linear = ALLOC(long,words);
    if (linear == NULL) {
        table->errorCode = CUDD_MEMORY_OUT;
        return(0);
    }
    table->memused += words * sizeof(long);
    table->linearSize = nvars;
    for (i = 0; i < words; i++) linear[i] = 0;
    for (i = 0; i < nvars; i++) {
        word = wordsPerRow * i + (i >> LOGBPL);
        bit  = i & (BPL-1);
        linear[word] = 1 << bit;
    }
    return(1);

} /* end of cuddInitLinear */

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

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

Synopsis [BDD reduction based on combination of sifting and linear transformations.]

Description [BDD reduction based on combination of sifting and linear transformations. 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. At each position, linear transformation of the two adjacent variables is tried and is accepted if it reduces the size of the DD.
3. Select the best permutation.
4. Repeat 3 and 4 for all variables.

Returns 1 if successful; 0 otherwise.]

SideEffects [None]

Definition at line 213 of file cuddLinear.c.

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

#ifdef DD_STATS
    ddTotalNumberLinearTr = 0;
#endif

    size = table->size;

    var = NULL;
    entry = NULL;
    if (table->linear == NULL) {
        result = cuddInitLinear(table);
        if (result == 0) goto cuddLinearAndSiftingOutOfMem; 
#if 0
        (void) fprintf(table->out,"\n");
        result = Cudd_PrintLinear(table);
        if (result == 0) goto cuddLinearAndSiftingOutOfMem; 
#endif
    } else if (table->size != table->linearSize) {
        result = cuddResizeLinear(table);
        if (result == 0) goto cuddLinearAndSiftingOutOfMem; 
#if 0
        (void) fprintf(table->out,"\n");
        result = Cudd_PrintLinear(table);
        if (result == 0) goto cuddLinearAndSiftingOutOfMem; 
#endif
    }

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

    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),(int (*)(const void *, const void *))ddLinearUniqueCompare);

    /* Now sift. */
    for (i = 0; i < ddMin(table->siftMaxVar,size); i++) {
        x = table->perm[var[i]];
        if (x < lower || x > upper) continue;
#ifdef DD_STATS
        previousSize = table->keys - table->isolated;
#endif
        result = ddLinearAndSiftingAux(table,x,lower,upper);
        if (!result) goto cuddLinearAndSiftingOutOfMem; 
#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->out,"\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
#ifdef DD_DEBUG
        (void) Cudd_DebugCheck(table);
#endif
    }

    FREE(var);
    FREE(entry);

#ifdef DD_STATS
    (void) fprintf(table->out,"\n#:L_LINSIFT %8d: linear trans.",
                   ddTotalNumberLinearTr);
#endif

    return(1);

cuddLinearAndSiftingOutOfMem:

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

    return(0); 

} /* end of cuddLinearAndSifting */

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

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

Synopsis [Linearly combines two adjacent variables.]

Description [Linearly combines two adjacent variables. Specifically, replaces the top variable with the exclusive nor of the two 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. cuddLinearInPlace assumes that x < y. Returns the number of keys in the table if successful; 0 otherwise.]

SideEffects [The two subtables corrresponding to variables x and y are modified. The global counters of the unique table are also affected.]

SeeAlso [cuddSwapInPlace]

Definition at line 823 of file cuddLinear.c.

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

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

    if (cuddTestInteract(table,xindex,yindex)) {
#ifdef DD_STATS
        ddTotalNumberLinearTr++;
#endif
        /* Get parameters of x subtable. */
        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. */
        ylist = table->subtables[y].nodelist;
        oldykeys = table->subtables[y].keys;
        yslots = table->subtables[y].slots;
        yshift = table->subtables[y].shift;

        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 are put in a chain.
        ** The chain is handled as a FIFO; g points to the beginning and
        ** last points to the end.
        */
        g = NULL;
        for (i = 0; i < xslots; i++) {
            f = xlist[i];
            if (f == sentinel) continue;
            xlist[i] = sentinel;
            if (g == NULL) {
                g = f;
            } else {
                last->next = f;
            }
            while ((next = f->next) != sentinel) {
                f = next;
            } /* while there are elements in the collision chain */
            last = f;
        } /* for each slot of the x subtable */
        last->next = NULL;

#ifdef DD_COUNT
        table->swapSteps += oldxkeys;
#endif
        /* Take care of the x nodes that must be re-expressed.
        ** They form a linked list pointed by g.
        */
        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 == f00) {
                newf1 = f11;
                cuddSatInc(newf1->ref);
            } else {
                /* Check ylist for triple (yindex,f11,f00). */
                posn = ddHash(f11, f00, yshift);
                /* For each element newf1 in collision list ylist[posn]. */
                previousP = &(ylist[posn]);
                newf1 = *previousP;
                while (f11 < cuddT(newf1)) {
                    previousP = &(newf1->next);
                    newf1 = *previousP;
                }
                while (f11 == cuddT(newf1) && f00 < cuddE(newf1)) {
                    previousP = &(newf1->next);
                    newf1 = *previousP;
                }
                if (cuddT(newf1) == f11 && cuddE(newf1) == f00) {
                    cuddSatInc(newf1->ref);
                } else { /* no match */
                    newf1 = cuddDynamicAllocNode(table);
                    if (newf1 == NULL)
                        goto cuddLinearOutOfMem;
                    newf1->index = yindex; newf1->ref = 1;
                    cuddT(newf1) = f11;
                    cuddE(newf1) = f00;
                    /* Insert newf1 in the collision list ylist[posn];
                    ** increase the ref counts of f11 and f00.
                    */
                    newykeys++;
                    newf1->next = *previousP;
                    *previousP = newf1;
                    cuddSatInc(f11->ref);
                    tmp = Cudd_Regular(f00);
                    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 (f01 == f10) {
                newf0 = f01;
                tmp = Cudd_Regular(newf0);
                cuddSatInc(tmp->ref); 
            } else {
                /* make sure f01 is regular */
                newcomplement = Cudd_IsComplement(f01);
                if (newcomplement) {
                    f01 = Cudd_Not(f01);
                    f10 = Cudd_Not(f10);
                }
                /* Check ylist for triple (yindex,f01,f10). */
                posn = ddHash(f01, f10, yshift);
                /* For each element newf0 in collision list ylist[posn]. */
                previousP = &(ylist[posn]);
                newf0 = *previousP;
                while (f01 < cuddT(newf0)) {
                    previousP = &(newf0->next);
                    newf0 = *previousP;
                }
                while (f01 == cuddT(newf0) && f10 < cuddE(newf0)) {
                    previousP = &(newf0->next);
                    newf0 = *previousP;
                }
                if (cuddT(newf0) == f01 && cuddE(newf0) == f10) {
                    cuddSatInc(newf0->ref); 
                } else { /* no match */
                    newf0 = cuddDynamicAllocNode(table);
                    if (newf0 == NULL)
                        goto cuddLinearOutOfMem;
                    newf0->index = yindex; newf0->ref = 1;
                    cuddT(newf0) = f01;
                    cuddE(newf0) = f10;
                    /* Insert newf0 in the collision list ylist[posn];
                    ** increase the ref counts of f01 and f10.
                    */
                    newykeys++;
                    newf0->next = *previousP;
                    *previousP = newf0;
                    cuddSatInc(f01->ref);
                    tmp = Cudd_Regular(f10);
                    cuddSatInc(tmp->ref);
                }
                if (newcomplement) {
                    newf0 = Cudd_Not(newf0);
                }
            }
            cuddE(f) = newf0;

            /* Re-insert the modified f in xlist.
            ** The modified f does not already exists in xlist.
            ** (Because of the uniqueness of the cofactors.)
            */
            posn = ddHash(newf1, newf0, xshift);
            newxkeys++;
            previousP = &(xlist[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 every collision list */

#if DD_DEBUG
#if 0
        (void) fprintf(table->out,"Linearly combining %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) {
            fprintf(table->err,"Error in finding newykeys\toldykeys = %d\tnewykeys = %d\tactual = %d\n",oldykeys,newykeys,count);
        }
        if (idcheck != 0)
            fprintf(table->err,"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 || newxkeys != oldxkeys) {
            fprintf(table->err,"Error in finding newxkeys\toldxkeys = %d \tnewxkeys = %d \tactual = %d\n",oldxkeys,newxkeys,count);
        }
        if (idcheck != 0)
            fprintf(table->err,"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[y].keys = newykeys;

        /* Here we should update the linear combination table
        ** to record that x <- x EXNOR y. This is done by complementing
        ** the (x,y) entry of the table.
        */

        table->keys += newykeys - oldykeys;

        cuddXorLinear(table,xindex,yindex);
    }

#ifdef DD_DEBUG
    if (zero) {
        (void) Cudd_DebugCheck(table);
    }
#endif

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

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

    return (0);

} /* end of cuddLinearInPlace */

static int cuddResizeLinear

(

DdManager *

table

)

[static]

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

Synopsis [Resizes the linear transform matrix.]

Description []

SideEffects [none]

SeeAlso []

Definition at line 1253 of file cuddLinear.c.

{
    int words,oldWords;
    int wordsPerRow,oldWordsPerRow;
    int nvars,oldNvars;
    int word,oldWord;
    int bit;
    int i,j;
    long *linear,*oldLinear;

    oldNvars = table->linearSize;
    oldWordsPerRow = ((oldNvars - 1) >> LOGBPL) + 1;
    oldWords = oldWordsPerRow * oldNvars;
    oldLinear = table->linear;

    nvars = table->size;
    wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    words = wordsPerRow * nvars;
    table->linear = linear = ALLOC(long,words);
    if (linear == NULL) {
        table->errorCode = CUDD_MEMORY_OUT;
        return(0);
    }
    table->memused += (words - oldWords) * sizeof(long);
    for (i = 0; i < words; i++) linear[i] = 0;

    /* Copy old matrix. */
    for (i = 0; i < oldNvars; i++) {
        for (j = 0; j < oldWordsPerRow; j++) {
            oldWord = oldWordsPerRow * i + j;
            word = wordsPerRow * i + j;
            linear[word] = oldLinear[oldWord];
        }
    }
    FREE(oldLinear);

    /* Add elements to the diagonal. */
    for (i = oldNvars; i < nvars; i++) {
        word = wordsPerRow * i + (i >> LOGBPL);
        bit  = i & (BPL-1);
        linear[word] = 1 << bit;
    }
    table->linearSize = nvars;

    return(1);

} /* end of cuddResizeLinear */

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

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

Synopsis [XORs two rows of the linear transform matrix.]

Description [XORs two rows of the linear transform matrix and replaces the first row with the result.]

SideEffects [none]

SeeAlso []

Definition at line 1316 of file cuddLinear.c.

{
    int i;
    int nvars = table->size;
    int wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    int xstart = wordsPerRow * x;
    int ystart = wordsPerRow * y;
    long *linear = table->linear;

    for (i = 0; i < wordsPerRow; i++) {
        linear[xstart+i] ^= linear[ystart+i];
    }

} /* end of cuddXorLinear */

static int ddLinearAndSiftingAux	(	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. At each step a linear transformation is tried, and, if it decreases the size of the DD, it is accepted. Finds the best position and does the required changes. Returns 1 if successful; 0 otherwise.]

SideEffects [None]

Definition at line 364 of file cuddLinear.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 = ddLinearAndSiftingDown(table,x,xHigh,NULL);
        /* At this point x --> xHigh unless bounding occurred. */
        if (moveDown == (Move *) CUDD_OUT_OF_MEM) goto ddLinearAndSiftingAuxOutOfMem;
        /* Move backward and stop at best position. */  
        result = ddLinearAndSiftingBackward(table,initialSize,moveDown);
        if (!result) goto ddLinearAndSiftingAuxOutOfMem;

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

    } else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
        moveDown = ddLinearAndSiftingDown(table,x,xHigh,NULL);
        /* At this point x --> xHigh unless bounding occurred. */
        if (moveDown == (Move *) CUDD_OUT_OF_MEM) goto ddLinearAndSiftingAuxOutOfMem;
        moveUp = ddUndoMoves(table,moveDown);
#ifdef DD_DEBUG
        assert(moveUp == NULL || moveUp->x == x);
#endif
        moveUp = ddLinearAndSiftingUp(table,x,xLow,moveUp);
        if (moveUp == (Move *) CUDD_OUT_OF_MEM) goto ddLinearAndSiftingAuxOutOfMem;
        /* Move backward and stop at best position. */  
        result = ddLinearAndSiftingBackward(table,initialSize,moveUp);
        if (!result) goto ddLinearAndSiftingAuxOutOfMem;

    } else { /* must go up first: shorter */
        moveUp = ddLinearAndSiftingUp(table,x,xLow,NULL);
        /* At this point x --> xLow unless bounding occurred. */
        if (moveUp == (Move *) CUDD_OUT_OF_MEM) goto ddLinearAndSiftingAuxOutOfMem;
        moveDown = ddUndoMoves(table,moveUp);
#ifdef DD_DEBUG
        assert(moveDown == NULL || moveDown->y == x);
#endif
        moveDown = ddLinearAndSiftingDown(table,x,xHigh,moveDown);
        if (moveDown == (Move *) CUDD_OUT_OF_MEM) goto ddLinearAndSiftingAuxOutOfMem;
        /* Move backward and stop at best position. */  
        result = ddLinearAndSiftingBackward(table,initialSize,moveDown);
        if (!result) goto ddLinearAndSiftingAuxOutOfMem;
    }

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

    return(1);

ddLinearAndSiftingAuxOutOfMem:
    while (moveDown != NULL) {
        move = moveDown->next;
        cuddDeallocNode(table, (DdNode *) moveDown);
        moveDown = move;
    }
    while (moveUp != NULL) {
        move = moveUp->next;
        cuddDeallocNode(table, (DdNode *) moveUp);
        moveUp = move;
    }

    return(0);

} /* end of ddLinearAndSiftingAux */

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

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

Synopsis [Given a set of moves, returns the DD heap to the order 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 706 of file cuddLinear.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 (move->flags == CUDD_LINEAR_TRANSFORM_MOVE) {
            res = cuddLinearInPlace(table,(int)move->x,(int)move->y);
            if (!res) return(0);
        }
        res = cuddSwapInPlace(table,(int)move->x,(int)move->y);
        if (!res) return(0);
        if (move->flags == CUDD_INVERSE_TRANSFORM_MOVE) {
            res = cuddLinearInPlace(table,(int)move->x,(int)move->y);
            if (!res) return(0);
        }
    }

    return(1);

} /* end of ddLinearAndSiftingBackward */

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

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

Synopsis [Sifts a variable down and applies linear transformations.]

Description [Sifts a variable down and applies linear transformations. 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 593 of file cuddLinear.c.

{
    Move        *moves;
    Move        *move;
    int         y;
    int         size, newsize;
    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 = prevMoves;
    /* 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;
            }
        }
        if (R != checkR) {
            (void) fprintf(table->out, "checkR(%d) != R(%d)\n",checkR,R);
        }
#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 ddLinearAndSiftingDownOutOfMem; 
        newsize = cuddLinearInPlace(table,x,y);
        if (newsize == 0) goto ddLinearAndSiftingDownOutOfMem;
        move = (Move *) cuddDynamicAllocNode(table);
        if (move == NULL) goto ddLinearAndSiftingDownOutOfMem;
        move->x = x;
        move->y = y;
        move->next = moves;
        moves = move;
        move->flags = CUDD_SWAP_MOVE;
        if (newsize >= size) {
            /* Undo transformation. The transformation we apply is
            ** its own inverse. Hence, we just apply the transformation
            ** again.
            */
            newsize = cuddLinearInPlace(table,x,y);
            if (newsize == 0) goto ddLinearAndSiftingDownOutOfMem;
            if (newsize != size) {
                (void) fprintf(table->out,"Change in size after identity transformation! From %d to %d\n",size,newsize);
            }
        } else if (cuddTestInteract(table,xindex,yindex)) {
            size = newsize;
            move->flags = CUDD_LINEAR_TRANSFORM_MOVE;
            ddUpdateInteractionMatrix(table,xindex,yindex);
        }
        move->size = size;
        if ((double) size > (double) limitSize * table->maxGrowth) break;
        if (size < limitSize) limitSize = size;
        x = y;
        y = cuddNextHigh(table,x);
    }
    return(moves);

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

} /* end of ddLinearAndSiftingDown */

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

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

Synopsis [Sifts a variable up and applies linear transformations.]

Description [Sifts a variable up and applies linear transformations. 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 470 of file cuddLinear.c.

{
    Move        *moves;
    Move        *move;
    int         x;
    int         size, newsize;
    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 = prevMoves;
    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;
        if (L != checkL) {
            (void) fprintf(table->out, "checkL(%d) != L(%d)\n",checkL,L);
        }
#endif
        size = cuddSwapInPlace(table,x,y);
        if (size == 0) goto ddLinearAndSiftingUpOutOfMem;
        newsize = cuddLinearInPlace(table,x,y);
        if (newsize == 0) goto ddLinearAndSiftingUpOutOfMem;
        move = (Move *) cuddDynamicAllocNode(table);
        if (move == NULL) goto ddLinearAndSiftingUpOutOfMem;
        move->x = x;
        move->y = y;
        move->next = moves;
        moves = move;
        move->flags = CUDD_SWAP_MOVE;
        if (newsize >= size) {
            /* Undo transformation. The transformation we apply is
            ** its own inverse. Hence, we just apply the transformation
            ** again.
            */
            newsize = cuddLinearInPlace(table,x,y);
            if (newsize == 0) goto ddLinearAndSiftingUpOutOfMem;
#ifdef DD_DEBUG
            if (newsize != size) {
                (void) fprintf(table->out,"Change in size after identity transformation! From %d to %d\n",size,newsize);
            }
#endif
        } else if (cuddTestInteract(table,xindex,yindex)) {
            size = newsize;
            move->flags = CUDD_LINEAR_TRANSFORM_MOVE;
            ddUpdateInteractionMatrix(table,xindex,yindex);
        }
        move->size = size;
        /* Update the lower bound. */
        if (cuddTestInteract(table,xindex,yindex)) {
            isolated = table->vars[xindex]->ref == 1;
            L += table->subtables[y].keys - isolated;
        }
        if ((double) size > (double) limitSize * table->maxGrowth) break;
        if (size < limitSize) limitSize = size;
        y = x;
        x = cuddNextLow(table,y);
    }
    return(moves);

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

} /* end of ddLinearAndSiftingUp */

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

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 336 of file cuddLinear.c.

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

} /* end of ddLinearUniqueCompare */

static Move* ddUndoMoves	(	DdManager *	table,
		Move *	moves
	)			[static]

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

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

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

SideEffects [None]

Definition at line 752 of file cuddLinear.c.

{
    Move *invmoves = NULL;
    Move *move;
    Move *invmove;
    int size;

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

    return(invmoves);

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

} /* end of ddUndoMoves */

static void ddUpdateInteractionMatrix	(	DdManager *	table,
		int	xindex,
		int	yindex
	)			[static]

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

Synopsis [Updates the interaction matrix.]

Description []

SideEffects [none]

SeeAlso []

Definition at line 1169 of file cuddLinear.c.

{
    int i;
    for (i = 0; i < yindex; i++) {
        if (i != xindex && cuddTestInteract(table,i,yindex)) {
            if (i < xindex) {
                cuddSetInteract(table,i,xindex);
            } else {
                cuddSetInteract(table,xindex,i);
            }
        }
    }
    for (i = yindex+1; i < table->size; i++) {
        if (i != xindex && cuddTestInteract(table,yindex,i)) {
            if (i < xindex) {
                cuddSetInteract(table,i,xindex);
            } else {
                cuddSetInteract(table,xindex,i);
            }
        }
    }

} /* end of ddUpdateInteractionMatrix */

---

Variable Documentation

char rcsid [] DD_UNUSED = "$Id: cuddLinear.c,v 1.1.1.1 2003/02/24 22:23:52 wjiang Exp $" [static]

Definition at line 68 of file cuddLinear.c.

int* entry [static]

Definition at line 71 of file cuddLinear.c.