GSW_AI_LAB/tempest-devel/resources/3rdparty/cudd-3.0.0/cudd/cuddLinear.c

/**
  @file

  @ingroup cudd

  @brief Functions for %BDD and %ADD reduction by linear
  transformations.

  @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
#if SIZEOF_VOID_P == 8
#define BPL 64
#define LOGBPL 6
#else
#define BPL 32
#define LOGBPL 5
#endif

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

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

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

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

/** \cond */

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

static int ddLinearUniqueCompare (void const *ptrX, void const *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 void cuddXorLinear (DdManager *table, int x, int y);

/** \endcond */


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


/**
  @brief Prints the linear transform matrix.

  @return 1 in case of success; 0 otherwise.

  @sideeffect none

*/
int
Cudd_PrintLinear(
  DdManager * table)
{
    int i,j,k;
    int retval;
    int nvars = table->linearSize;
    int wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    ptruint 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,"%" PRIuPTR,word & (ptruint) 1);
		if (retval == 0) return(0);
		word >>= 1;
	    }
	}
	retval = fprintf(table->out,"\n");
	if (retval == 0) return(0);
    }
    return(1);

} /* end of Cudd_PrintLinear */


/**
  @brief Reads an entry of the linear transform matrix.

  @sideeffect none

*/
int
Cudd_ReadLinear(
  DdManager * table /**< CUDD manager */,
  int  x /**< row index */,
  int  y /**< column index */)
{
    int nvars = table->size;
    ptruint wordsPerRow = ((ptruint)(nvars - 1) >> LOGBPL) + 1;
    ptruint word;
    int bit;
    int result;

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

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

} /* end of Cudd_ReadLinear */


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


/**
  @brief %BDD reduction based on combination of sifting and linear
  transformations.

  @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, 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.
    <li> Select the best permutation.
    <li> Repeat 3 and 4 for all variables.
    </ol>

  @return 1 if successful; 0 otherwise.

  @sideeffect None

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

#ifdef DD_STATS
    table->totalNumberLinearTr = 0;
#endif

    size = table->size;

    var = 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. */
    var = ALLOC(IndexKey,size);
    if (var == NULL) {
	table->errorCode = CUDD_MEMORY_OUT;
	goto cuddLinearAndSiftingOutOfMem;
    }

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

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

    /* Now sift. */
    for (i = 0; i < ddMin(table->siftMaxVar,size); i++) {
	x = table->perm[var[i].index];
	if (x < lower || x > upper) continue;
#ifdef DD_STATS
	previousSize = (int) (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 %u while sifting variable %d\n", previousSize, table->keys - table->isolated, var[i].index);
	} else {
	    (void) fprintf(table->out,"=");
	}
	fflush(table->out);
#endif
#ifdef DD_DEBUG
	(void) Cudd_DebugCheck(table);
#endif
    }

    FREE(var);

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

    return(1);

cuddLinearAndSiftingOutOfMem:

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

    return(0);

} /* end of cuddLinearAndSifting */


/**
  @brief Linearly combines two adjacent variables.

  @details 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 &lt; y.

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

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

  @see cuddSwapInPlace

*/
int
cuddLinearInPlace(
  DdManager * table,
  int  x,
  int  y)
{
    DdNodePtr *xlist, *ylist;
    int    xindex, yindex;
    int    xslots, yslots;
    int    xshift, yshift;
#if defined(DD_COUNT) || defined(DD_DEBUG)
    int    oldxkeys;
#endif
    int 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=NULL;
    DdNodePtr *previousP;
    DdNode *tmp;
    DdNode *sentinel = &(table->sentinel);
#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

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

    if (cuddTestInteract(table,xindex,yindex)) {
#ifdef DD_STATS
	table->totalNumberLinearTr++;
#endif
	/* Get parameters of x subtable. */
	xlist = table->subtables[x].nodelist;
#if defined(DD_COUNT) || defined(DD_DEBUG)
	oldxkeys = table->subtables[x].keys;
#endif
	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;
#ifdef DD_DEBUG
	last = NULL;
#endif
	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 */
#ifdef DD_DEBUG
	/* last is always assigned in the for loop because there is at
	** least one key */
	assert(last != NULL);
#endif
	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 */

#ifdef 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 += (unsigned int) 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 (table->enableExtraDebug) {
	(void) Cudd_DebugCheck(table);
    }
#endif

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

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

    return (0);

} /* end of cuddLinearInPlace */


/**
  @brief Updates the interaction matrix.

  @sideeffect none

*/
void
cuddUpdateInteractionMatrix(
  DdManager * table,
  int  xindex,
  int  yindex)
{
    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 cuddUpdateInteractionMatrix */


/**
  @brief Initializes the linear transform matrix.

  @return 1 if successful; 0 otherwise.

  @sideeffect none

*/
int
cuddInitLinear(
  DdManager * table)
{
    int words;
    int wordsPerRow;
    int nvars;
    int word;
    int bit;
    int i;
    ptruint *linear;

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

} /* end of cuddInitLinear */


/**
  @brief Resizes the linear transform matrix.

  @return 1 if successful; 0 otherwise.

  @sideeffect none

*/
int
cuddResizeLinear(
  DdManager * table)
{
    int words,oldWords;
    int wordsPerRow,oldWordsPerRow;
    int nvars,oldNvars;
    int word,oldWord;
    int bit;
    int i,j;
    ptruint *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(ptruint,words);
    if (linear == NULL) {
	table->errorCode = CUDD_MEMORY_OUT;
	return(0);
    }
    table->memused += (words - oldWords) * sizeof(ptruint);
    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] = (ptruint) 1 << bit;
    }
    table->linearSize = nvars;

    return(1);

} /* end of cuddResizeLinear */


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


/**
  @brief Comparison function used by qsort.

  @details Comparison function used by qsort to order the
  variables according to the number of keys in the subtables.

  @return the difference in number of keys between the two variables
  being compared.

  @sideeffect None

*/
static int
ddLinearUniqueCompare(
  void const * ptrX,
  void const * ptrY)
{
    IndexKey const * pX = (IndexKey const *) ptrX;
    IndexKey const * pY = (IndexKey const *) ptrY;
#if 0
    if (pY->keys == pX->keys) {
	return(pX->index - pY->index);
    }
#endif
    return(pY->keys - pX->keys);

} /* end of ddLinearUniqueCompare */


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

  @details 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.

  @return 1 if successful; 0 otherwise.

  @sideeffect None

*/
static int
ddLinearAndSiftingAux(
  DdManager * table,
  int  x,
  int  xLow,
  int  xHigh)
{

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

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

    return(1);

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

    return(0);

} /* end of ddLinearAndSiftingAux */


/**
  @brief Sifts a variable up and applies linear transformations.

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

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

  @sideeffect None

*/
static Move *
ddLinearAndSiftingUp(
  DdManager * table,
  int  y,
  int  xLow,
  Move * prevMoves)
{
    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 = (int) (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 -= (int) table->subtables[x].keys - isolated;
	}
    }
    isolated = table->vars[yindex]->ref == 1;
    L -= (int) 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;
	    cuddUpdateInteractionMatrix(table,xindex,yindex);
	}
	move->size = size;
	/* Update the lower bound. */
	if (cuddTestInteract(table,xindex,yindex)) {
	    isolated = table->vars[xindex]->ref == 1;
	    L += (int) 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;
	cuddDeallocMove(table, moves);
	moves = move;
    }
    return((Move *) CUDD_OUT_OF_MEM);

} /* end of ddLinearAndSiftingUp */


/**
  @brief Sifts a variable down and applies linear transformations.

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

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

  @sideeffect None

*/
static Move *
ddLinearAndSiftingDown(
  DdManager * table,
  int  x,
  int  xHigh,
  Move * prevMoves)
{
    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 += (int) 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 -= (int) 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;
	    cuddUpdateInteractionMatrix(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;
	cuddDeallocMove(table, moves);
	moves = move;
    }
    return((Move *) CUDD_OUT_OF_MEM);

} /* end of ddLinearAndSiftingDown */


/**
  @brief Given a set of moves, returns the %DD heap to the order
  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
ddLinearAndSiftingBackward(
  DdManager * table,
  int  size,
  Move * moves)
{
    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 */


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

  @return 1 in case of success; 0 otherwise.

  @sideeffect None

*/
static Move*
ddUndoMoves(
  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 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;
	cuddDeallocMove(table, invmoves);
	invmoves = move;
    }
    return((Move *) CUDD_OUT_OF_MEM);

} /* end of ddUndoMoves */


/**
  @brief XORs two rows of the linear transform matrix.

  @details Replaces the first row with the result.

  @sideeffect none

*/
static void
cuddXorLinear(
  DdManager * table,
  int  x,
  int  y)
{
    int i;
    int nvars = table->size;
    int wordsPerRow = ((nvars - 1) >> LOGBPL) + 1;
    int xstart = wordsPerRow * x;
    int ystart = wordsPerRow * y;
    ptruint *linear = table->linear;

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

} /* end of cuddXorLinear */