tempest/resources/3rdparty/cudd-3.0.0/cudd/cuddZddLin.c

/**
  @file

  @ingroup cudd

  @brief Procedures for dynamic variable ordering of ZDDs.

  @see cuddLinear.c cuddZddReord.c

  @author Fabio Somenzi

  @copyright@parblock
  Copyright (c) 1995-2015, 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.
  @endparblock

*/

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

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

#define CUDD_SWAP_MOVE 0
#define CUDD_LINEAR_TRANSFORM_MOVE 1
#define CUDD_INVERSE_TRANSFORM_MOVE 2

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


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


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


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

/** \cond */

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

static int cuddZddLinearInPlace (DdManager * table, int x, int y);
static int cuddZddLinearAux (DdManager *table, int x, int xLow, int xHigh);
static Move * cuddZddLinearUp (DdManager *table, int y, int xLow, Move *prevMoves);
static Move * cuddZddLinearDown (DdManager *table, int x, int xHigh, Move *prevMoves);
static int cuddZddLinearBackward (DdManager *table, int size, Move *moves);
static Move* cuddZddUndoMoves (DdManager *table, Move *moves);

/** \endcond */


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


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




/**
  @brief Implementation of the linear sifting algorithm for ZDDs.

  @details Assumes that no dead nodes are present.
    <ol>
    <li> Order all the variables according to the number of entries
    in each unique table.
    <li> Sift the variable up and down and applies the XOR transformation,
    remembering each time the total size of the %DD heap.
    <li> Select the best permutation.
    <li> Repeat 3 and 4 for all variables.
    </ol>

  @return 1 if successful; 0 otherwise.

  @sideeffect None

*/
int
cuddZddLinearSifting(
  DdManager * table,
  int  lower,
  int  upper)
{
    int	i;
    IndexKey *var;
    int	size;
    int	x;
    int	result;
#ifdef DD_STATS
    int	previousSize;
#endif

    size = table->sizeZ;

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

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

    util_qsort(var, size, sizeof(IndexKey), cuddZddUniqueCompare);

    /* Now sift. */
    for (i = 0; i < ddMin(table->siftMaxVar, size); i++) {
	if (table->zddTotalNumberSwapping >= table->siftMaxSwap)
	    break;
        if (util_cpu_time() - table->startTime > table->timeLimit) {
            table->autoDynZ = 0; /* prevent further reordering */
            break;
        }
        if (table->terminationCallback != NULL &&
            table->terminationCallback(table->tcbArg)) {
            table->autoDynZ = 0; /* prevent further reordering */
            break;
        }
	x = table->permZ[var[i].index];
	if (x < lower || x > upper) continue;
#ifdef DD_STATS
	previousSize = table->keysZ;
#endif
	result = cuddZddLinearAux(table, x, lower, upper);
	if (!result)
	    goto cuddZddSiftingOutOfMem;
#ifdef DD_STATS
	if (table->keysZ < (unsigned) previousSize) {
	    (void) fprintf(table->out,"-");
	} else if (table->keysZ > (unsigned) previousSize) {
	    (void) fprintf(table->out,"+");	/* should never happen */
	    (void) fprintf(table->out,"\nSize increased from %d to %d while sifting variable %d\n", previousSize, table->keysZ , var[i].index);
	} else {
	    (void) fprintf(table->out,"=");
	}
	fflush(table->out);
#endif
    }

    FREE(var);

    return(1);

cuddZddSiftingOutOfMem:

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

    return(0);

} /* end of cuddZddLinearSifting */


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


/**
  @brief Linearly combines two adjacent variables.

  @details 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.  cuddZddLinearInPlace assumes that x
  &lt; y.

  @return the number of keys in the table if successful; 0 otherwise.

  @sideeffect None

  @see cuddZddSwapInPlace cuddLinearInPlace

*/
static int
cuddZddLinearInPlace(
  DdManager * table,
  int  x,
  int  y)
{
    DdNodePtr *xlist, *ylist;
    int		xindex, yindex;
    int		xslots, yslots;
    int		xshift, yshift;
    int         oldxkeys, oldykeys;
    int         newxkeys, newykeys;
    int		i;
    int		posn;
    DdNode	*f, *f1, *f0, *f11, *f10, *f01, *f00;
    DdNode	*newf1, *newf0, *g, *next, *previous;
    DdNode	*special;
    DdNode	*empty = table->zero;

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

    /* Get parameters of x subtable. */
    xindex   = table->invpermZ[x];
    xlist    = table->subtableZ[x].nodelist;
    oldxkeys = table->subtableZ[x].keys;
    xslots   = table->subtableZ[x].slots;
    xshift   = table->subtableZ[x].shift;
    newxkeys = 0;

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

    /* The nodes in the x layer are put in two chains.  The chain
    ** pointed by g holds the normal nodes. When re-expressed they stay
    ** in the x list. The chain pointed by special holds the elements
    ** that will move to the y list.
    */
    g = special = NULL;
    for (i = 0; i < xslots; i++) {
	f = xlist[i];
	if (f == NULL) continue;
	xlist[i] = NULL;
	while (f != NULL) {
	    next = f->next;
	    f1 = cuddT(f);
	    /* if (f1->index == yindex) */ cuddSatDec(f1->ref);
	    f0 = cuddE(f);
	    /* if (f0->index == yindex) */ cuddSatDec(f0->ref);
	    if ((int) f1->index == yindex && cuddE(f1) == empty &&
		(int) f0->index != yindex) {
		f->next = special;
		special = f;
	    } else {
		f->next = g;
		g = f;
	    }
	    f = next;
	} /* while there are elements in the collision chain */
    } /* for each slot of the x subtable */

    /* Mark y nodes with pointers from above x. We mark them by
    **  changing their index to x.
    */
    for (i = 0; i < yslots; i++) {
	f = ylist[i];
	while (f != NULL) {
	    if (f->ref != 0) {
		f->index = xindex;
	    }
	    f = f->next;
	} /* while there are elements in the collision chain */
    } /* for each slot of the y subtable */

    /* Move special nodes to the y list. */
    f = special;
    while (f != NULL) {
	next = f->next;
	f1 = cuddT(f);
	f11 = cuddT(f1);
	cuddT(f) = f11;
	cuddSatInc(f11->ref);
	f0 = cuddE(f);
	cuddSatInc(f0->ref);
	f->index = yindex;
	/* Insert at the beginning of the list so that it will be
	** found first if there is a duplicate. The duplicate will
	** eventually be moved or garbage collected. No node
	** re-expression will add a pointer to it.
	*/
	posn = ddHash(f11, f0, yshift);
	f->next = ylist[posn];
	ylist[posn] = f;
	newykeys++;
	f = next;
    }

    /* Take care of the remaining x nodes that must be re-expressed.
    ** They form a linked list pointed by g.
    */
    f = g;
    while (f != NULL) {
#ifdef DD_COUNT
	table->swapSteps++;
#endif
	next = f->next;
	/* Find f1, f0, f11, f10, f01, f00. */
	f1 = cuddT(f);
	if ((int) f1->index == yindex || (int) f1->index == xindex) {
	    f11 = cuddT(f1); f10 = cuddE(f1);
	} else {
	    f11 = empty; f10 = f1;
	}
	f0 = cuddE(f);
	if ((int) f0->index == yindex || (int) f0->index == xindex) {
	    f01 = cuddT(f0); f00 = cuddE(f0);
	} else {
	    f01 = empty; f00 = f0;
	}
	/* Create the new T child. */
	if (f01 == empty) {
	    newf1 = f10;
	    cuddSatInc(newf1->ref);
	} else {
	    /* Check ylist for triple (yindex, f01, f10). */
	    posn = ddHash(f01, f10, yshift);
	    /* For each element newf1 in collision list ylist[posn]. */
	    newf1 = ylist[posn];
	    /* Search the collision chain skipping the marked nodes. */
	    while (newf1 != NULL) {
		if (cuddT(newf1) == f01 && cuddE(newf1) == f10 &&
		    (int) newf1->index == yindex) {
		    cuddSatInc(newf1->ref);
		    break; /* match */
		}
		newf1 = newf1->next;
	    } /* while newf1 */
	    if (newf1 == NULL) {	/* no match */
		newf1 = cuddDynamicAllocNode(table);
		if (newf1 == NULL)
		    goto zddSwapOutOfMem;
		newf1->index = yindex; newf1->ref = 1;
		cuddT(newf1) = f01;
		cuddE(newf1) = f10;
		/* Insert newf1 in the collision list ylist[pos];
		** increase the ref counts of f01 and f10
		*/
		newykeys++;
		newf1->next = ylist[posn];
		ylist[posn] = newf1;
		cuddSatInc(f01->ref);
		cuddSatInc(f10->ref);
	    }
	}
	cuddT(f) = newf1;

	/* Do the same for f0. */
	/* Create the new E child. */
	if (f11 == empty) {
	    newf0 = f00;
	    cuddSatInc(newf0->ref);
	} else {
	    /* Check ylist for triple (yindex, f11, f00). */
	    posn = ddHash(f11, f00, yshift);
	    /* For each element newf0 in collision list ylist[posn]. */
	    newf0 = ylist[posn];
	    while (newf0 != NULL) {
		if (cuddT(newf0) == f11 && cuddE(newf0) == f00 &&
		    (int) newf0->index == yindex) {
		    cuddSatInc(newf0->ref);
		    break; /* match */
		}
		newf0 = newf0->next;
	    } /* while newf0 */
	    if (newf0 == NULL) {	/* no match */
		newf0 = cuddDynamicAllocNode(table);
		if (newf0 == NULL)
		    goto zddSwapOutOfMem;
		newf0->index = yindex; newf0->ref = 1;
		cuddT(newf0) = f11; cuddE(newf0) = f00;
		/* Insert newf0 in the collision list ylist[posn];
		** increase the ref counts of f11 and f00.
		*/
		newykeys++;
		newf0->next = ylist[posn];
		ylist[posn] = newf0;
		cuddSatInc(f11->ref);
		cuddSatInc(f00->ref);
	    }
	}
	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++;
	f->next = xlist[posn];
	xlist[posn] = f;
	f = next;
    } /* while f != NULL */

    /* GC the y layer and move the marked nodes to the x list. */

    /* For each node f in ylist. */
    for (i = 0; i < yslots; i++) {
	previous = NULL;
	f = ylist[i];
	while (f != NULL) {
	    next = f->next;
	    if (f->ref == 0) {
		cuddSatDec(cuddT(f)->ref);
		cuddSatDec(cuddE(f)->ref);
		cuddDeallocNode(table, f);
		newykeys--;
		if (previous == NULL)
		    ylist[i] = next;
		else
		    previous->next = next;
	    } else if ((int) f->index == xindex) { /* move marked node */
		if (previous == NULL)
		    ylist[i] = next;
		else
		    previous->next = next;
		f1 = cuddT(f);
		cuddSatDec(f1->ref);
		/* Check ylist for triple (yindex, f1, empty). */
		posn = ddHash(f1, empty, yshift);
		/* For each element newf1 in collision list ylist[posn]. */
		newf1 = ylist[posn];
		while (newf1 != NULL) {
		    if (cuddT(newf1) == f1 && cuddE(newf1) == empty &&
			(int) newf1->index == yindex) {
			cuddSatInc(newf1->ref);
			break; /* match */
		    }
		    newf1 = newf1->next;
		} /* while newf1 */
		if (newf1 == NULL) {	/* no match */
		    newf1 = cuddDynamicAllocNode(table);
		    if (newf1 == NULL)
			goto zddSwapOutOfMem;
		    newf1->index = yindex; newf1->ref = 1;
		    cuddT(newf1) = f1; cuddE(newf1) = empty;
		    /* Insert newf1 in the collision list ylist[posn];
		    ** increase the ref counts of f1 and empty.
		    */
		    newykeys++;
		    newf1->next = ylist[posn];
		    ylist[posn] = newf1;
		    if (posn == i && previous == NULL)
			previous = newf1;
		    cuddSatInc(f1->ref);
		    cuddSatInc(empty->ref);
		}
		cuddT(f) = newf1;
		f0 = cuddE(f);
		/* Insert f in x list. */
		posn = ddHash(newf1, f0, xshift);
		newxkeys++;
		newykeys--;
		f->next = xlist[posn];
		xlist[posn] = f;
	    } else {
		previous = f;
	    }
	    f = next;
	} /* while f */
    } /* for i */

    /* Set the appropriate fields in table. */
    table->subtableZ[x].keys     = newxkeys;
    table->subtableZ[y].keys     = newykeys;

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

    /* Update univ section; univ[x] remains the same. */
    table->univ[y] = cuddT(table->univ[x]);

#if 0
    (void) fprintf(table->out,"x = %d  y = %d\n", x, y);
    (void) Cudd_DebugCheck(table);
    (void) Cudd_CheckKeys(table);
#endif

    return (table->keysZ);

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

    return (0);

} /* end of cuddZddLinearInPlace */


/**
  @brief Given xLow <= x <= xHigh moves x up and down between the
  boundaries.

  @details Finds the best position and does the required changes.

  @return 1 if successful; 0 otherwise.

  @sideeffect None

*/
static int
cuddZddLinearAux(
  DdManager * table,
  int  x,
  int  xLow,
  int  xHigh)
{
    Move	*move;
    Move	*moveUp;	/* list of up move */
    Move	*moveDown;	/* list of down move */

    int		initial_size;
    int		result;

    initial_size = table->keysZ;

#ifdef DD_DEBUG
    assert(table->subtableZ[x].keys > 0);
#endif

    moveDown = NULL;
    moveUp = NULL;

    if (x == xLow) {
	moveDown = cuddZddLinearDown(table, x, xHigh, NULL);
	/* At this point x --> xHigh. */
	if (moveDown == (Move *) CUDD_OUT_OF_MEM)
	    goto cuddZddLinearAuxOutOfMem;
	/* Move backward and stop at best position. */
	result = cuddZddLinearBackward(table, initial_size, moveDown);
	if (!result)
	    goto cuddZddLinearAuxOutOfMem;

    } else if (x == xHigh) {
	moveUp = cuddZddLinearUp(table, x, xLow, NULL);
	/* At this point x --> xLow. */
	if (moveUp == (Move *) CUDD_OUT_OF_MEM)
	    goto cuddZddLinearAuxOutOfMem;
	/* Move backward and stop at best position. */
	result = cuddZddLinearBackward(table, initial_size, moveUp);
	if (!result)
	    goto cuddZddLinearAuxOutOfMem;

    } else if ((x - xLow) > (xHigh - x)) { /* must go down first: shorter */
	moveDown = cuddZddLinearDown(table, x, xHigh, NULL);
	/* At this point x --> xHigh. */
	if (moveDown == (Move *) CUDD_OUT_OF_MEM)
	    goto cuddZddLinearAuxOutOfMem;
	moveUp = cuddZddUndoMoves(table,moveDown);
#ifdef DD_DEBUG
	assert(moveUp == NULL || moveUp->x == (DdHalfWord) x);
#endif
	moveUp = cuddZddLinearUp(table, x, xLow, moveUp);
	if (moveUp == (Move *) CUDD_OUT_OF_MEM)
	    goto cuddZddLinearAuxOutOfMem;
	/* Move backward and stop at best position. */
	result = cuddZddLinearBackward(table, initial_size, moveUp);
	if (!result)
	    goto cuddZddLinearAuxOutOfMem;

    } else {
	moveUp = cuddZddLinearUp(table, x, xLow, NULL);
	/* At this point x --> xHigh. */
	if (moveUp == (Move *) CUDD_OUT_OF_MEM)
	    goto cuddZddLinearAuxOutOfMem;
	/* Then move up. */
	moveDown = cuddZddUndoMoves(table,moveUp);
#ifdef DD_DEBUG
	assert(moveDown == NULL || moveDown->y == (DdHalfWord) x);
#endif
	moveDown = cuddZddLinearDown(table, x, xHigh, moveDown);
	if (moveDown == (Move *) CUDD_OUT_OF_MEM)
	    goto cuddZddLinearAuxOutOfMem;
	/* Move backward and stop at best position. */
	result = cuddZddLinearBackward(table, initial_size, moveDown);
	if (!result)
	    goto cuddZddLinearAuxOutOfMem;
    }

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

    return(1);

cuddZddLinearAuxOutOfMem:
    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 cuddZddLinearAux */


/**
  @brief Sifts a variable up applying the XOR transformation.

  @details Moves y up until either it reaches the bound (xLow) or the
  size of the %ZDD heap increases too much.

  @return the set of moves in case of success; NULL if memory is full.

  @sideeffect None

*/
static Move *
cuddZddLinearUp(
  DdManager * table,
  int  y,
  int  xLow,
  Move * prevMoves)
{
    Move	*moves;
    Move	*move;
    int		x;
    int		size, newsize;
    int		limitSize;

    moves = prevMoves;
    limitSize = table->keysZ;

    x = cuddZddNextLow(table, y);
    while (x >= xLow) {
	size = cuddZddSwapInPlace(table, x, y);
	if (size == 0)
	    goto cuddZddLinearUpOutOfMem;
	newsize = cuddZddLinearInPlace(table, x, y);
	if (newsize == 0)
	    goto cuddZddLinearUpOutOfMem;
	move = (Move *) cuddDynamicAllocNode(table);
	if (move == NULL)
	    goto cuddZddLinearUpOutOfMem;
	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 = cuddZddLinearInPlace(table,x,y);
	    if (newsize == 0) goto cuddZddLinearUpOutOfMem;
#ifdef DD_DEBUG
	    if (newsize != size) {
		(void) fprintf(table->err,"Change in size after identity transformation! From %d to %d\n",size,newsize);
	    }
#endif
	} else {
	    size = newsize;
	    move->flags = CUDD_LINEAR_TRANSFORM_MOVE;
	}
	move->size = size;

	if ((double)size > (double)limitSize * table->maxGrowth)
	    break;
        if (size < limitSize)
	    limitSize = size;

	y = x;
	x = cuddZddNextLow(table, y);
    }
    return(moves);

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

} /* end of cuddZddLinearUp */


/**
  @brief Sifts a variable down and applies the XOR transformation.

  @details Sifts a variable down. Moves x down until either it
  reaches the bound (xHigh) or the size of the %ZDD heap increases too
  much.

  @return the set of moves in case of success; NULL if memory is full.

  @sideeffect None

*/
static Move *
cuddZddLinearDown(
  DdManager * table,
  int  x,
  int  xHigh,
  Move * prevMoves)
{
    Move	*moves;
    Move	*move;
    int		y;
    int		size, newsize;
    int		limitSize;

    moves = prevMoves;
    limitSize = table->keysZ;

    y = cuddZddNextHigh(table, x);
    while (y <= xHigh) {
	size = cuddZddSwapInPlace(table, x, y);
	if (size == 0)
	    goto cuddZddLinearDownOutOfMem;
	newsize = cuddZddLinearInPlace(table, x, y);
	if (newsize == 0)
	    goto cuddZddLinearDownOutOfMem;
	move = (Move *) cuddDynamicAllocNode(table);
	if (move == NULL)
	    goto cuddZddLinearDownOutOfMem;
	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 = cuddZddLinearInPlace(table,x,y);
	    if (newsize == 0) goto cuddZddLinearDownOutOfMem;
	    if (newsize != size) {
		(void) fprintf(table->err,"Change in size after identity transformation! From %d to %d\n",size,newsize);
	    }
	} else {
	    size = newsize;
	    move->flags = CUDD_LINEAR_TRANSFORM_MOVE;
	}
	move->size = size;

	if ((double)size > (double)limitSize * table->maxGrowth)
	    break;
        if (size < limitSize)
	    limitSize = size;

	x = y;
	y = cuddZddNextHigh(table, x);
    }
    return(moves);

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

} /* end of cuddZddLinearDown */


/**
  @brief Given a set of moves, returns the %ZDD heap to the position
  giving the minimum size.

  @details In case of ties, returns to the closest position giving the
  minimum size.

  @return 1 in case of success; 0 otherwise.

  @sideeffect None

*/
static int
cuddZddLinearBackward(
  DdManager * table,
  int  size,
  Move * moves)
{
    Move	*move;
    int		res;

    /* Find the minimum size among moves. */
    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 = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
	    if (!res) return(0);
	}
	res = cuddZddSwapInPlace(table, move->x, move->y);
	if (!res)
	    return(0);
	if (move->flags == CUDD_INVERSE_TRANSFORM_MOVE) {
	    res = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
	    if (!res) return(0);
	}
    }

    return(1);

} /* end of cuddZddLinearBackward */


/**
  @brief Given a set of moves, returns the %ZDD heap to the order
  in effect before the moves.

  @return 1 in case of success; 0 otherwise.

  @sideeffect None

*/
static Move*
cuddZddUndoMoves(
  DdManager * table,
  Move * moves)
{
    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 cuddZddUndoMovesOutOfMem;
	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 = cuddZddSwapInPlace(table,(int)move->x,(int)move->y);
	    if (!size) goto cuddZddUndoMovesOutOfMem;
	} else if (move->flags == CUDD_LINEAR_TRANSFORM_MOVE) {
	    invmove->flags = CUDD_INVERSE_TRANSFORM_MOVE;
	    size = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
	    if (!size) goto cuddZddUndoMovesOutOfMem;
	    size = cuddZddSwapInPlace(table,(int)move->x,(int)move->y);
	    if (!size) goto cuddZddUndoMovesOutOfMem;
	} 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 = cuddZddSwapInPlace(table,(int)move->x,(int)move->y);
	    if (!size) goto cuddZddUndoMovesOutOfMem;
	    size = cuddZddLinearInPlace(table,(int)move->x,(int)move->y);
	    if (!size) goto cuddZddUndoMovesOutOfMem;
	}
	invmove->size = size;
    }

    return(invmoves);

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

} /* end of cuddZddUndoMoves */