/**Function********************************************************************
Synopsis [Sifts a variable down.]
Description [Sifts a variable down. Moves x down until either it
reaches the bound (x_high) or the size of the ZDD heap increases too
much. Returns the set of moves in case of success; NULL if memory is
full.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static Move *
cuddZddSiftingDown(
DdManager * table,
int x,
int x_high,
int initial_size)
{
Move *moves;
Move *move;
int y;
int size;
int limit_size = initial_size;
moves = NULL;
y = cuddZddNextHigh(table, x);
while (y <= x_high) {
size = cuddZddSwapInPlace(table, x, y);
if (size == 0)
goto cuddZddSiftingDownOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto cuddZddSiftingDownOutOfMem;
move->x = x;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
if ((double)size > (double)limit_size * table->maxGrowth)
break;
if (size < limit_size)
limit_size = size;
x = y;
y = cuddZddNextHigh(table, x);
}
return(moves);
cuddZddSiftingDownOutOfMem:
while (moves != NULL) {
move = moves->next;
cuddDeallocNode(table, (DdNode *)moves);
moves = move;
}
return(NULL);
} /* end of cuddZddSiftingDown */
/**Function********************************************************************
Synopsis [Moves x down until either it reaches the bound (x_high) or
the size of the ZDD heap increases too much.]
Description [Moves x down until either it reaches the bound (x_high)
or the size of the ZDD heap increases too much. Assumes that x is the
bottom of a symmetry group. Checks x for symmetry to the adjacent
variables. If symmetry is found, the symmetry group of x is merged
with the symmetry group of the other variable. Returns the set of
moves in case of success; ZDD_MV_OOM if memory is full.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static Move *
cuddZddSymmSifting_down(
DdManager * table,
int x,
int x_high,
int initial_size)
{
Move *moves;
Move *move;
int y;
int size;
int limit_size = initial_size;
int i, gxtop, gybot;
moves = NULL;
y = cuddZddNextHigh(table, x);
while (y <= x_high) {
gybot = table->subtableZ[y].next;
while (table->subtableZ[gybot].next != (unsigned) y)
gybot = table->subtableZ[gybot].next;
if (cuddZddSymmCheck(table, x, y)) {
/* Symmetry found, attach symm groups */
gxtop = table->subtableZ[x].next;
table->subtableZ[x].next = y;
i = table->subtableZ[y].next;
while (table->subtableZ[i].next != (unsigned) y)
i = table->subtableZ[i].next;
table->subtableZ[i].next = gxtop;
}
else if ((table->subtableZ[x].next == (unsigned) x) &&
(table->subtableZ[y].next == (unsigned) y)) {
/* x and y have self symmetry */
size = cuddZddSwapInPlace(table, x, y);
if (size == 0)
goto cuddZddSymmSifting_downOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto cuddZddSymmSifting_downOutOfMem;
move->x = x;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
if ((double)size >
(double)limit_size * table->maxGrowth)
return(moves);
if (size < limit_size)
limit_size = size;
x = y;
y = cuddZddNextHigh(table, x);
}
else { /* Group move */
size = zdd_group_move(table, x, y, &moves);
if ((double)size >
(double)limit_size * table->maxGrowth)
return(moves);
if (size < limit_size)
limit_size = size;
}
x = gybot;
y = cuddZddNextHigh(table, x);
}
return(moves);
cuddZddSymmSifting_downOutOfMem:
while (moves != NULL) {
move = moves->next;
cuddDeallocMove(table, moves);
moves = move;
}
return(ZDD_MV_OOM);
} /* end of cuddZddSymmSifting_down */
/**Function********************************************************************
Synopsis [Swaps any two variables.]
Description [Swaps any two variables. Returns the set of moves.]
SideEffects [None]
SeeAlso []
******************************************************************************/
static Move *
zddSwapAny(
DdManager * table,
int x,
int y)
{
Move *move, *moves;
int tmp, size;
int x_ref, y_ref;
int x_next, y_next;
int limit_size;
if (x > y) { /* make x precede y */
tmp = x; x = y; y = tmp;
}
x_ref = x; y_ref = y;
x_next = cuddZddNextHigh(table, x);
y_next = cuddZddNextLow(table, y);
moves = NULL;
limit_size = table->keysZ;
for (;;) {
if (x_next == y_next) { /* x < x_next = y_next < y */
size = cuddZddSwapInPlace(table, x, x_next);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *) cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = x;
move->y = x_next;
move->size = size;
move->next = moves;
moves = move;
size = cuddZddSwapInPlace(table, y_next, y);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = y_next;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
size = cuddZddSwapInPlace(table, x, x_next);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = x;
move->y = x_next;
move->size = size;
move->next = moves;
moves = move;
tmp = x; x = y; y = tmp;
} else if (x == y_next) { /* x = y_next < y = x_next */
size = cuddZddSwapInPlace(table, x, x_next);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = x;
move->y = x_next;
move->size = size;
move->next = moves;
moves = move;
tmp = x; x = y; y = tmp;
} else {
size = cuddZddSwapInPlace(table, x, x_next);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = x;
move->y = x_next;
move->size = size;
move->next = moves;
moves = move;
size = cuddZddSwapInPlace(table, y_next, y);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = y_next;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
x = x_next; y = y_next;
}
x_next = cuddZddNextHigh(table, x);
y_next = cuddZddNextLow(table, y);
if (x_next > y_ref)
break; /* if x == y_ref */
if ((double) size > table->maxGrowth * (double) limit_size)
break;
if (size < limit_size)
limit_size = size;
}
if (y_next >= x_ref) {
size = cuddZddSwapInPlace(table, y_next, y);
if (size == 0)
goto zddSwapAnyOutOfMem;
move = (Move *)cuddDynamicAllocNode(table);
if (move == NULL)
goto zddSwapAnyOutOfMem;
move->x = y_next;
move->y = y;
move->size = size;
move->next = moves;
moves = move;
}
return(moves);
zddSwapAnyOutOfMem:
while (moves != NULL) {
move = moves->next;
cuddDeallocNode(table, (DdNode *)moves);
moves = move;
}
return(NULL);
} /* end of zddSwapAny */
/**Function********************************************************************
Synopsis [Swaps two adjacent variables.]
Description [Swaps two adjacent variables. It assumes that no dead
nodes are present on entry to this procedure. The procedure then
guarantees that no dead nodes will be present when it terminates.
cuddZddSwapInPlace assumes that x < y. Returns the number of keys in
the table if successful; 0 otherwise.]
SideEffects [None]
SeeAlso []
******************************************************************************/
int
cuddZddSwapInPlace(
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, *next;
DdNodePtr g, *lastP, *previousP;
#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
zddTotalNumberSwapping++;
/* 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;
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 that don't depend on y directly
** will stay there; the others 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;
lastP = &g;
for (i = 0; i < xslots; i++) {
previousP = &(xlist[i]);
f = *previousP;
while (f != NULL) {
next = f->next;
f1 = cuddT(f); f0 = cuddE(f);
if ((f1->index != (DdHalfWord) yindex) &&
(f0->index != (DdHalfWord) yindex)) { /* stays */
newxkeys++;
*previousP = f;
previousP = &(f->next);
} else {
f->index = yindex;
*lastP = f;
lastP = &(f->next);
}
f = next;
} /* while there are elements in the collision chain */
*previousP = NULL;
} /* for each slot of the x subtable */
*lastP = NULL;
#ifdef DD_COUNT
table->swapSteps += oldxkeys - newxkeys;
#endif
/* Take care of the x nodes that must be re-expressed.
** They form a linked list pointed by g. Their index has been
** changed to yindex already.
*/
f = g;
while (f != NULL) {
next = f->next;
/* Find f1, f0, f11, f10, f01, f00. */
f1 = cuddT(f);
if ((int) f1->index == yindex) {
f11 = cuddT(f1); f10 = cuddE(f1);
} else {
f11 = empty; f10 = f1;
}
f0 = cuddE(f);
if ((int) f0->index == yindex) {
f01 = cuddT(f0); f00 = cuddE(f0);
} else {
f01 = empty; f00 = f0;
}
/* Decrease ref count of f1. */
cuddSatDec(f1->ref);
/* Create the new T child. */
if (f11 == empty) {
if (f01 != empty) {
newf1 = f01;
cuddSatInc(newf1->ref);
}
/* else case was already handled when finding nodes
** with both children below level y
*/
} else {
/* Check xlist for triple (xindex, f11, f01). */
posn = ddHash(f11, f01, xshift);
/* For each element newf1 in collision list xlist[posn]. */
newf1 = xlist[posn];
while (newf1 != NULL) {
if (cuddT(newf1) == f11 && cuddE(newf1) == f01) {
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 = xindex; newf1->ref = 1;
cuddT(newf1) = f11;
cuddE(newf1) = f01;
/* Insert newf1 in the collision list xlist[pos];
** increase the ref counts of f11 and f01
*/
newxkeys++;
newf1->next = xlist[posn];
xlist[posn] = newf1;
cuddSatInc(f11->ref);
cuddSatInc(f01->ref);
}
}
cuddT(f) = newf1;
/* Do the same for f0. */
/* Decrease ref count of f0. */
cuddSatDec(f0->ref);
/* Create the new E child. */
if (f10 == empty) {
newf0 = f00;
cuddSatInc(newf0->ref);
} else {
/* Check xlist for triple (xindex, f10, f00). */
posn = ddHash(f10, f00, xshift);
/* For each element newf0 in collision list xlist[posn]. */
newf0 = xlist[posn];
while (newf0 != NULL) {
if (cuddT(newf0) == f10 && cuddE(newf0) == f00) {
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 = xindex; newf0->ref = 1;
cuddT(newf0) = f10; cuddE(newf0) = f00;
/* Insert newf0 in the collision list xlist[posn];
** increase the ref counts of f10 and f00.
*/
newxkeys++;
newf0->next = xlist[posn];
xlist[posn] = newf0;
cuddSatInc(f10->ref);
cuddSatInc(f00->ref);
}
}
cuddE(f) = newf0;
/* Insert the modified f in ylist.
** The modified f does not already exists in ylist.
** (Because of the uniqueness of the cofactors.)
*/
posn = ddHash(newf1, newf0, yshift);
newykeys++;
f->next = ylist[posn];
ylist[posn] = 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 != NULL) {
next = f->next;
if (f->ref == 0) {
cuddSatDec(cuddT(f)->ref);
cuddSatDec(cuddE(f)->ref);
cuddDeallocNode(table, f);
newykeys--;
} else {
*previousP = f;
previousP = &(f->next);
}
f = next;
} /* while f */
*previousP = NULL;
} /* for i */
/* Set the appropriate fields in table. */
table->subtableZ[x].nodelist = ylist;
table->subtableZ[x].slots = yslots;
table->subtableZ[x].shift = yshift;
table->subtableZ[x].keys = newykeys;
table->subtableZ[x].maxKeys = yslots * DD_MAX_SUBTABLE_DENSITY;
table->subtableZ[y].nodelist = xlist;
table->subtableZ[y].slots = xslots;
table->subtableZ[y].shift = xshift;
table->subtableZ[y].keys = newxkeys;
table->subtableZ[y].maxKeys = xslots * DD_MAX_SUBTABLE_DENSITY;
table->permZ[xindex] = y; table->permZ[yindex] = x;
table->invpermZ[x] = yindex; table->invpermZ[y] = xindex;
table->keysZ += newxkeys + newykeys - oldxkeys - oldykeys;
/* Update univ section; univ[x] remains the same. */
table->univ[y] = cuddT(table->univ[x]);
return (table->keysZ);
zddSwapOutOfMem:
(void) fprintf(table->err, "Error: cuddZddSwapInPlace out of memory\n");
return (0);
} /* end of cuddZddSwapInPlace */
/**Function********************************************************************
Synopsis [Sifts down a variable until it reaches position xHigh.]
Description [Sifts down a variable until it reaches position xHigh.
Assumes that x is the bottom of a group (or a singleton). Records
all the moves. Returns 1 in case of success; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
zddGroupSiftingDown(
DdManager * table,
int x,
int xHigh,
Move ** moves)
{
Move *move;
int y;
int size;
int limitSize;
int gxtop,gybot;
int xindex;
/* Initialize R */
xindex = table->invpermZ[x];
gxtop = table->subtableZ[x].next;
limitSize = size = table->keysZ;
y = cuddZddNextHigh(table,x);
while (y <= xHigh) {
/* Find bottom of y group. */
gybot = table->subtableZ[y].next;
while (table->subtableZ[gybot].next != (unsigned) y)
gybot = table->subtableZ[gybot].next;
if (table->subtableZ[x].next == (unsigned) x &&
table->subtableZ[y].next == (unsigned) y) {
/* x and y are self groups */
size = cuddZddSwapInPlace(table,x,y);
#ifdef DD_DEBUG
assert(table->subtableZ[x].next == (unsigned) x);
assert(table->subtableZ[y].next == (unsigned) y);
#endif
if (size == 0) goto zddGroupSiftingDownOutOfMem;
/* Record move. */
move = (Move *) cuddDynamicAllocNode(table);
if (move == NULL) goto zddGroupSiftingDownOutOfMem;
move->x = x;
move->y = y;
move->flags = MTR_DEFAULT;
move->size = size;
move->next = *moves;
*moves = move;
#ifdef DD_DEBUG
if (pr > 0) (void) fprintf(table->out,"zddGroupSiftingDown (2 single groups):\n");
#endif
if ((double) size > (double) limitSize * table->maxGrowth)
return(1);
if (size < limitSize) limitSize = size;
x = y;
y = cuddZddNextHigh(table,x);
} else { /* Group move */
size = zddGroupMove(table,x,y,moves);
if (size == 0) goto zddGroupSiftingDownOutOfMem;
if ((double) size > (double) limitSize * table->maxGrowth)
return(1);
if (size < limitSize) limitSize = size;
}
x = gybot;
y = cuddZddNextHigh(table,x);
}
return(1);
zddGroupSiftingDownOutOfMem:
while (*moves != NULL) {
move = (*moves)->next;
cuddDeallocNode(table, (DdNode *) *moves);
*moves = move;
}
return(0);
} /* end of zddGroupSiftingDown */
/**Function********************************************************************
Synopsis [Sifts one variable up and down until it has taken all
positions. Checks for aggregation.]
Description [Sifts one variable up and down until it has taken all
positions. Checks for aggregation. There may be at most two sweeps,
even if the group grows. Assumes that x is either an isolated
variable, or it is the bottom of a group. All groups may not have
been found. The variable being moved is returned to the best position
seen during sifting. Returns 1 in case of success; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
zddGroupSiftingAux(
DdManager * table,
int x,
int xLow,
int xHigh)
{
Move *move;
Move *moves; /* list of moves */
int initialSize;
int result;
#ifdef DD_DEBUG
if (pr > 0) (void) fprintf(table->out,"zddGroupSiftingAux from %d to %d\n",xLow,xHigh);
assert((unsigned) x >= table->subtableZ[x].next); /* x is bottom of group */
#endif
initialSize = table->keysZ;
moves = NULL;
if (x == xLow) { /* Sift down */
#ifdef DD_DEBUG
/* x must be a singleton */
assert((unsigned) x == table->subtableZ[x].next);
#endif
if (x == xHigh) return(1); /* just one variable */
if (!zddGroupSiftingDown(table,x,xHigh,&moves))
goto zddGroupSiftingAuxOutOfMem;
/* at this point x == xHigh, unless early term */
/* move backward and stop at best position */
result = zddGroupSiftingBackward(table,moves,initialSize);
#ifdef DD_DEBUG
assert(table->keysZ <= (unsigned) initialSize);
#endif
if (!result) goto zddGroupSiftingAuxOutOfMem;
} else if (cuddZddNextHigh(table,x) > xHigh) { /* Sift up */
#ifdef DD_DEBUG
/* x is bottom of group */
assert((unsigned) x >= table->subtableZ[x].next);
#endif
/* Find top of x's group */
x = table->subtableZ[x].next;
if (!zddGroupSiftingUp(table,x,xLow,&moves))
goto zddGroupSiftingAuxOutOfMem;
/* at this point x == xLow, unless early term */
/* move backward and stop at best position */
result = zddGroupSiftingBackward(table,moves,initialSize);
#ifdef DD_DEBUG
assert(table->keysZ <= (unsigned) initialSize);
#endif
if (!result) goto zddGroupSiftingAuxOutOfMem;
} else if (x - xLow > xHigh - x) { /* must go down first: shorter */
if (!zddGroupSiftingDown(table,x,xHigh,&moves))
goto zddGroupSiftingAuxOutOfMem;
/* at this point x == xHigh, unless early term */
/* Find top of group */
if (moves) {
x = moves->y;
}
while ((unsigned) x < table->subtableZ[x].next)
x = table->subtableZ[x].next;
x = table->subtableZ[x].next;
#ifdef DD_DEBUG
/* x should be the top of a group */
assert((unsigned) x <= table->subtableZ[x].next);
#endif
if (!zddGroupSiftingUp(table,x,xLow,&moves))
goto zddGroupSiftingAuxOutOfMem;
/* move backward and stop at best position */
result = zddGroupSiftingBackward(table,moves,initialSize);
#ifdef DD_DEBUG
assert(table->keysZ <= (unsigned) initialSize);
#endif
if (!result) goto zddGroupSiftingAuxOutOfMem;
} else { /* moving up first: shorter */
/* Find top of x's group */
x = table->subtableZ[x].next;
if (!zddGroupSiftingUp(table,x,xLow,&moves))
goto zddGroupSiftingAuxOutOfMem;
/* at this point x == xHigh, unless early term */
if (moves) {
x = moves->x;
}
while ((unsigned) x < table->subtableZ[x].next)
x = table->subtableZ[x].next;
#ifdef DD_DEBUG
/* x is bottom of a group */
assert((unsigned) x >= table->subtableZ[x].next);
#endif
if (!zddGroupSiftingDown(table,x,xHigh,&moves))
goto zddGroupSiftingAuxOutOfMem;
/* move backward and stop at best position */
result = zddGroupSiftingBackward(table,moves,initialSize);
#ifdef DD_DEBUG
assert(table->keysZ <= (unsigned) initialSize);
#endif
if (!result) goto zddGroupSiftingAuxOutOfMem;
}
while (moves != NULL) {
move = moves->next;
cuddDeallocNode(table, (DdNode *) moves);
moves = move;
}
return(1);
zddGroupSiftingAuxOutOfMem:
while (moves != NULL) {
move = moves->next;
cuddDeallocNode(table, (DdNode *) moves);
moves = move;
}
return(0);
} /* end of zddGroupSiftingAux */
/**Function********************************************************************
Synopsis [Undoes the swap two groups.]
Description [Undoes the swap two groups. Returns 1 in case of
success; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
zddGroupMoveBackward(
DdManager * table,
int x,
int y)
{
int size;
int i,j,xtop,xbot,xsize,ytop,ybot,ysize,newxtop;
#if DD_DEBUG
/* We assume that x < y */
assert(x < y);
#endif
/* Find top, bottom, and size for the two groups. */
xbot = x;
xtop = table->subtableZ[x].next;
xsize = xbot - xtop + 1;
ybot = y;
while ((unsigned) ybot < table->subtableZ[ybot].next)
ybot = table->subtableZ[ybot].next;
ytop = y;
ysize = ybot - ytop + 1;
/* Sift the variables of the second group up through the first group */
for (i = 1; i <= ysize; i++) {
for (j = 1; j <= xsize; j++) {
size = cuddZddSwapInPlace(table,x,y);
if (size == 0)
return(0);
y = x;
x = cuddZddNextLow(table,y);
}
y = ytop + i;
x = cuddZddNextLow(table,y);
}
/* fix groups */
y = xtop;
for (i = 0; i < ysize - 1; i++) {
table->subtableZ[y].next = cuddZddNextHigh(table,y);
y = cuddZddNextHigh(table,y);
}
table->subtableZ[y].next = xtop; /* y is bottom of its group, join */
/* to its top */
x = cuddZddNextHigh(table,y);
newxtop = x;
for (i = 0; i < xsize - 1; i++) {
table->subtableZ[x].next = cuddZddNextHigh(table,x);
x = cuddZddNextHigh(table,x);
}
table->subtableZ[x].next = newxtop; /* x is bottom of its group, join */
/* to its top */
#ifdef DD_DEBUG
if (pr > 0) (void) fprintf(table->out,"zddGroupMoveBackward:\n");
#endif
return(1);
} /* end of zddGroupMoveBackward */
/**Function********************************************************************
Synopsis [Swaps two groups and records the move.]
Description [Swaps two groups and records the move. Returns the
number of keys in the DD table in case of success; 0 otherwise.]
SideEffects [None]
******************************************************************************/
static int
zddGroupMove(
DdManager * table,
int x,
int y,
Move ** moves)
{
Move *move;
int size;
int i,j,xtop,xbot,xsize,ytop,ybot,ysize,newxtop;
int swapx = x, swapy = y;
#if defined(DD_DEBUG) && defined(DD_VERBOSE)
int initialSize,bestSize;
#endif
#if DD_DEBUG
/* We assume that x < y */
assert(x < y);
#endif
/* Find top, bottom, and size for the two groups. */
xbot = x;
xtop = table->subtableZ[x].next;
xsize = xbot - xtop + 1;
ybot = y;
while ((unsigned) ybot < table->subtableZ[ybot].next)
ybot = table->subtableZ[ybot].next;
ytop = y;
ysize = ybot - ytop + 1;
#if defined(DD_DEBUG) && defined(DD_VERBOSE)
initialSize = bestSize = table->keysZ;
#endif
/* Sift the variables of the second group up through the first group */
for (i = 1; i <= ysize; i++) {
for (j = 1; j <= xsize; j++) {
size = cuddZddSwapInPlace(table,x,y);
if (size == 0) goto zddGroupMoveOutOfMem;
#if defined(DD_DEBUG) && defined(DD_VERBOSE)
if (size < bestSize)
bestSize = size;
#endif
swapx = x; swapy = y;
y = x;
x = cuddZddNextLow(table,y);
}
y = ytop + i;
x = cuddZddNextLow(table,y);
}
#if defined(DD_DEBUG) && defined(DD_VERBOSE)
if ((bestSize < initialSize) && (bestSize < size))
(void) fprintf(table->out,"Missed local minimum: initialSize:%d bestSize:%d finalSize:%d\n",initialSize,bestSize,size);
#endif
/* fix groups */
y = xtop; /* ytop is now where xtop used to be */
for (i = 0; i < ysize - 1; i++) {
table->subtableZ[y].next = cuddZddNextHigh(table,y);
y = cuddZddNextHigh(table,y);
}
table->subtableZ[y].next = xtop; /* y is bottom of its group, join */
/* it to top of its group */
x = cuddZddNextHigh(table,y);
newxtop = x;
for (i = 0; i < xsize - 1; i++) {
table->subtableZ[x].next = cuddZddNextHigh(table,x);
x = cuddZddNextHigh(table,x);
}
table->subtableZ[x].next = newxtop; /* x is bottom of its group, join */
/* it to top of its group */
#ifdef DD_DEBUG
if (pr > 0) (void) fprintf(table->out,"zddGroupMove:\n");
#endif
/* Store group move */
move = (Move *) cuddDynamicAllocNode(table);
if (move == NULL) goto zddGroupMoveOutOfMem;
move->x = swapx;
move->y = swapy;
move->flags = MTR_DEFAULT;
move->size = table->keysZ;
move->next = *moves;
*moves = move;
return(table->keysZ);
zddGroupMoveOutOfMem:
while (*moves != NULL) {
move = (*moves)->next;
cuddDeallocNode(table, (DdNode *) *moves);
*moves = move;
}
return(0);
} /* end of zddGroupMove */
/**Function********************************************************************
Synopsis [Sifts a variable down and applies the XOR transformation.]
Description [Sifts a variable down. Moves x down until either it
reaches the bound (xHigh) or the size of the ZDD heap increases too
much. Returns the set of moves in case of success; NULL if memory is
full.]
SideEffects [None]
SeeAlso []
******************************************************************************/
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 */
/**Function********************************************************************
Synopsis [Linearly combines two adjacent variables.]
Description [Linearly combines two adjacent variables. It assumes
that no dead nodes are present on entry to this procedure. The
procedure then guarantees that no dead nodes will be present when it
terminates. cuddZddLinearInPlace assumes that x < y. Returns the
number of keys in the table if successful; 0 otherwise.]
SideEffects [None]
SeeAlso [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;
#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
zddTotalNumberLinearTr++;
/* 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 */