Beispiel #1
0
/*
 * The GiST Penalty method for boxes (also used for points)
 *
 * As in the R-tree paper, we use change in area as our penalty metric
 */
datum_t gist_box_penalty(PG_FUNC_ARGS)
{
	struct gist_entry* origentry = (struct gist_entry*) ARG_POINTER(0);
	struct gist_entry* newentry = (struct gist_entry*) ARG_POINTER(1);
	float* result = (float*) ARG_POINTER(2);
	datum_t ud;

	ud = DIRECT_FC2(rt_box_union, origentry->key, newentry->key);
	*result = (float)(size_box(ud) - size_box(origentry->key));
	RET_POINTER(result);
}
Beispiel #2
0
/*
 * The GiST Penalty method for boxes (also used for points)
 *
 * As in the R-tree paper, we use change in area as our penalty metric
 */
Datum
gist_box_penalty(PG_FUNCTION_ARGS)
{
	GISTENTRY  *origentry = (GISTENTRY *) PG_GETARG_POINTER(0);
	GISTENTRY  *newentry = (GISTENTRY *) PG_GETARG_POINTER(1);
	float	   *result = (float *) PG_GETARG_POINTER(2);
	Datum		ud;

	ud = DirectFunctionCall2(rt_box_union, origentry->key, newentry->key);
	*result = (float) (size_box(ud) - size_box(origentry->key));
	PG_RETURN_POINTER(result);
}
Beispiel #3
0
/*
 * The GiST Penalty method for boxes (also used for points)
 *
 * As in the R-tree paper, we use change in area as our penalty metric
 */
Datum
gist_box_penalty(PG_FUNCTION_ARGS)
{
	GISTENTRY  *origentry = (GISTENTRY *) PG_GETARG_POINTER(0);
	GISTENTRY  *newentry = (GISTENTRY *) PG_GETARG_POINTER(1);
	float	   *result = (float *) PG_GETARG_POINTER(2);
	BOX		   *origbox = DatumGetBoxP(origentry->key);
	BOX		   *newbox = DatumGetBoxP(newentry->key);
	BOX			unionbox;

	rt_box_union(&unionbox, origbox, newbox);
	*result = (float) (size_box(&unionbox) - size_box(origbox));
	PG_RETURN_POINTER(result);
}
Beispiel #4
0
/*
** The GiST Penalty method for boxes
** As in the R-tree paper, we use change in area as our penalty metric
*/
Datum
gbox_penalty(PG_FUNCTION_ARGS)
{
	GISTENTRY  *origentry = (GISTENTRY *) PG_GETARG_POINTER(0);
	GISTENTRY  *newentry = (GISTENTRY *) PG_GETARG_POINTER(1);
	float	   *result = (float *) PG_GETARG_POINTER(2);
	Datum		ud;
	float		tmp1;

	ud = DirectFunctionCall2(rt_box_union, origentry->key, newentry->key);
	tmp1 = size_box(ud);
	if (DatumGetPointer(ud) != NULL)
		pfree(DatumGetPointer(ud));

	*result = tmp1 - size_box(origentry->key);
	PG_RETURN_POINTER(result);
}
Beispiel #5
0
/*
 * The GiST PickSplit method
 *
 * New linear algorithm, see 'New Linear Node Splitting Algorithm for R-tree',
 * C.H.Ang and T.C.Tan
 *
 * This is used for both boxes and points.
 */
Datum
gist_box_picksplit(PG_FUNCTION_ARGS)
{
	GistEntryVector *entryvec = (GistEntryVector *) PG_GETARG_POINTER(0);
	GIST_SPLITVEC *v = (GIST_SPLITVEC *) PG_GETARG_POINTER(1);
	OffsetNumber i;
	OffsetNumber *listL,
			   *listR,
			   *listB,
			   *listT;
	BOX		   *unionL,
			   *unionR,
			   *unionB,
			   *unionT;
	int			posL,
				posR,
				posB,
				posT;
	BOX			pageunion;
	BOX		   *cur;
	char		direction = ' ';
	bool		allisequal = true;
	OffsetNumber maxoff;
	int			nbytes;

	posL = posR = posB = posT = 0;
	maxoff = entryvec->n - 1;

	cur = DatumGetBoxP(entryvec->vector[FirstOffsetNumber].key);
	memcpy((void *) &pageunion, (void *) cur, sizeof(BOX));

	/* find MBR */
	for (i = OffsetNumberNext(FirstOffsetNumber); i <= maxoff; i = OffsetNumberNext(i))
	{
		cur = DatumGetBoxP(entryvec->vector[i].key);
		if (allisequal && (
						   pageunion.high.x != cur->high.x ||
						   pageunion.high.y != cur->high.y ||
						   pageunion.low.x != cur->low.x ||
						   pageunion.low.y != cur->low.y
						   ))
			allisequal = false;

		adjustBox(&pageunion, cur);
	}

	if (allisequal)
	{
		/*
		 * All entries are the same
		 */
		fallbackSplit(entryvec, v);
		PG_RETURN_POINTER(v);
	}

	nbytes = (maxoff + 2) * sizeof(OffsetNumber);
	listL = (OffsetNumber *) palloc(nbytes);
	listR = (OffsetNumber *) palloc(nbytes);
	listB = (OffsetNumber *) palloc(nbytes);
	listT = (OffsetNumber *) palloc(nbytes);
	unionL = (BOX *) palloc(sizeof(BOX));
	unionR = (BOX *) palloc(sizeof(BOX));
	unionB = (BOX *) palloc(sizeof(BOX));
	unionT = (BOX *) palloc(sizeof(BOX));

#define ADDLIST( list, unionD, pos, num ) do { \
	if ( pos ) { \
		if ( (unionD)->high.x < cur->high.x ) (unionD)->high.x	= cur->high.x; \
		if ( (unionD)->low.x  > cur->low.x	) (unionD)->low.x	= cur->low.x; \
		if ( (unionD)->high.y < cur->high.y ) (unionD)->high.y	= cur->high.y; \
		if ( (unionD)->low.y  > cur->low.y	) (unionD)->low.y	= cur->low.y; \
	} else { \
			memcpy( (void*)(unionD), (void*) cur, sizeof( BOX ) );	\
	} \
	(list)[pos] = num; \
	(pos)++; \
} while(0)

	for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
	{
		cur = DatumGetBoxP(entryvec->vector[i].key);
		if (cur->low.x - pageunion.low.x < pageunion.high.x - cur->high.x)
			ADDLIST(listL, unionL, posL, i);
		else
			ADDLIST(listR, unionR, posR, i);
		if (cur->low.y - pageunion.low.y < pageunion.high.y - cur->high.y)
			ADDLIST(listB, unionB, posB, i);
		else
			ADDLIST(listT, unionT, posT, i);
	}

#define LIMIT_RATIO 0.1
#define _IS_BADRATIO(x,y)	( (y) == 0 || (float)(x)/(float)(y) < LIMIT_RATIO )
#define IS_BADRATIO(x,y) ( _IS_BADRATIO((x),(y)) || _IS_BADRATIO((y),(x)) )
	/* bad disposition, try to split by centers of boxes  */
	if (IS_BADRATIO(posR, posL) && IS_BADRATIO(posT, posB))
	{
		double		avgCenterX = 0.0,
					avgCenterY = 0.0;
		double		CenterX,
					CenterY;

		for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
		{
			cur = DatumGetBoxP(entryvec->vector[i].key);
			avgCenterX += ((double) cur->high.x + (double) cur->low.x) / 2.0;
			avgCenterY += ((double) cur->high.y + (double) cur->low.y) / 2.0;
		}

		avgCenterX /= maxoff;
		avgCenterY /= maxoff;

		posL = posR = posB = posT = 0;
		for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
		{
			cur = DatumGetBoxP(entryvec->vector[i].key);

			CenterX = ((double) cur->high.x + (double) cur->low.x) / 2.0;
			CenterY = ((double) cur->high.y + (double) cur->low.y) / 2.0;

			if (CenterX < avgCenterX)
				ADDLIST(listL, unionL, posL, i);
			else if (CenterX == avgCenterX)
			{
				if (posL > posR)
					ADDLIST(listR, unionR, posR, i);
				else
					ADDLIST(listL, unionL, posL, i);
			}
			else
				ADDLIST(listR, unionR, posR, i);

			if (CenterY < avgCenterY)
				ADDLIST(listB, unionB, posB, i);
			else if (CenterY == avgCenterY)
			{
				if (posB > posT)
					ADDLIST(listT, unionT, posT, i);
				else
					ADDLIST(listB, unionB, posB, i);
			}
			else
				ADDLIST(listT, unionT, posT, i);
		}

		if (IS_BADRATIO(posR, posL) && IS_BADRATIO(posT, posB))
		{
			fallbackSplit(entryvec, v);
			PG_RETURN_POINTER(v);
		}
	}

	/* which split more optimal? */
	if (Max(posL, posR) < Max(posB, posT))
		direction = 'x';
	else if (Max(posL, posR) > Max(posB, posT))
		direction = 'y';
	else
	{
		Datum		interLR = DirectFunctionCall2(rt_box_inter,
												  BoxPGetDatum(unionL),
												  BoxPGetDatum(unionR));
		Datum		interBT = DirectFunctionCall2(rt_box_inter,
												  BoxPGetDatum(unionB),
												  BoxPGetDatum(unionT));
		double		sizeLR,
					sizeBT;

		sizeLR = size_box(interLR);
		sizeBT = size_box(interBT);

		if (sizeLR < sizeBT)
			direction = 'x';
		else
			direction = 'y';
	}

	if (direction == 'x')
		chooseLR(v,
				 listL, posL, unionL,
				 listR, posR, unionR);
	else
		chooseLR(v,
				 listB, posB, unionB,
				 listT, posT, unionT);

	PG_RETURN_POINTER(v);
}
Beispiel #6
0
static void
chooseLR(GIST_SPLITVEC *v,
		 OffsetNumber *list1, int nlist1, BOX *union1,
		 OffsetNumber *list2, int nlist2, BOX *union2)
{
	bool		firstToLeft = true;

	if (v->spl_ldatum_exists || v->spl_rdatum_exists)
	{
		if (v->spl_ldatum_exists && v->spl_rdatum_exists)
		{
			BOX			LRl = *union1,
						LRr = *union2;
			BOX			RLl = *union2,
						RLr = *union1;
			double		sizeLR,
						sizeRL;

			adjustBox(&LRl, DatumGetBoxP(v->spl_ldatum));
			adjustBox(&LRr, DatumGetBoxP(v->spl_rdatum));
			adjustBox(&RLl, DatumGetBoxP(v->spl_ldatum));
			adjustBox(&RLr, DatumGetBoxP(v->spl_rdatum));

			sizeLR = size_box(DirectFunctionCall2(rt_box_inter, BoxPGetDatum(&LRl), BoxPGetDatum(&LRr)));
			sizeRL = size_box(DirectFunctionCall2(rt_box_inter, BoxPGetDatum(&RLl), BoxPGetDatum(&RLr)));

			if (sizeLR > sizeRL)
				firstToLeft = false;

		}
		else
		{
			float		p1,
						p2;
			GISTENTRY	oldUnion,
						addon;

			gistentryinit(oldUnion, (v->spl_ldatum_exists) ? v->spl_ldatum : v->spl_rdatum,
						  NULL, NULL, InvalidOffsetNumber, FALSE);

			gistentryinit(addon, BoxPGetDatum(union1), NULL, NULL, InvalidOffsetNumber, FALSE);
			DirectFunctionCall3(gist_box_penalty, PointerGetDatum(&oldUnion), PointerGetDatum(&addon), PointerGetDatum(&p1));
			gistentryinit(addon, BoxPGetDatum(union2), NULL, NULL, InvalidOffsetNumber, FALSE);
			DirectFunctionCall3(gist_box_penalty, PointerGetDatum(&oldUnion), PointerGetDatum(&addon), PointerGetDatum(&p2));

			if ((v->spl_ldatum_exists && p1 > p2) || (v->spl_rdatum_exists && p1 < p2))
				firstToLeft = false;
		}
	}

	if (firstToLeft)
	{
		v->spl_left = list1;
		v->spl_right = list2;
		v->spl_nleft = nlist1;
		v->spl_nright = nlist2;
		if (v->spl_ldatum_exists)
			adjustBox(union1, DatumGetBoxP(v->spl_ldatum));
		v->spl_ldatum = BoxPGetDatum(union1);
		if (v->spl_rdatum_exists)
			adjustBox(union2, DatumGetBoxP(v->spl_rdatum));
		v->spl_rdatum = BoxPGetDatum(union2);
	}
	else
	{
		v->spl_left = list2;
		v->spl_right = list1;
		v->spl_nleft = nlist2;
		v->spl_nright = nlist1;
		if (v->spl_ldatum_exists)
			adjustBox(union2, DatumGetBoxP(v->spl_ldatum));
		v->spl_ldatum = BoxPGetDatum(union2);
		if (v->spl_rdatum_exists)
			adjustBox(union1, DatumGetBoxP(v->spl_rdatum));
		v->spl_rdatum = BoxPGetDatum(union1);
	}

	v->spl_ldatum_exists = v->spl_rdatum_exists = false;
}
Beispiel #7
0
/*
 * The GiST PickSplit method
 *
 * New linear algorithm, see 'New Linear node_n Splitting Algorithm for R-tree',
 * C.H.Ang and T.C.Tan
 *
 * This is used for both boxes and points.
 */
datum_t gist_box_picksplit(PG_FUNC_ARGS)
{
	struct gist_entry_vector *entryvec = (struct gist_entry_vector *)ARG_POINTER(0);
	struct gist_splitvec *v = (struct gist_splitvec *)ARG_POINTER(1);
	item_id_t i;
	item_id_t *listL;
	item_id_t *listR;
	item_id_t *listB;
	item_id_t *listT;
	BOX *unionL;
	BOX *unionR;
	BOX *unionB;
	BOX *unionT;
	int posL, posR, posB, posT;
	BOX pageunion;
	BOX *cur;
	char direction = ' ';
	bool allisequal = true;
	item_id_t maxoff;
	int nbytes;

	posL = posR = posB = posT = 0;
	maxoff = entryvec->n - 1;

	cur = D_TO_BOX_P(entryvec->vector[FIRST_ITEM_ID].key);
	memcpy((void*) &pageunion, (void*) cur, sizeof(BOX));

	/* find MBR */
	for (i = ITEM_ID_NEXT(FIRST_ITEM_ID); i <= maxoff; i = ITEM_ID_NEXT(i)) {
		cur = D_TO_BOX_P(entryvec->vector[i].key);
		if (allisequal
			&& (pageunion.high.x != cur->high.x
				|| pageunion.high.y != cur->high.y
				|| pageunion.low.x != cur->low.x
				|| pageunion.low.y != cur->low.y))
			allisequal = false;

		adjustBox(&pageunion, cur);
	}

	if (allisequal) {
		/*
		 * All entries are the same
		 */
		fallbackSplit(entryvec, v);
		RET_POINTER(v);
	}

	nbytes = (maxoff + 2) * sizeof(item_id_t);
	listL = (item_id_t *) palloc(nbytes);
	listR = (item_id_t *) palloc(nbytes);
	listB = (item_id_t *) palloc(nbytes);
	listT = (item_id_t *) palloc(nbytes);
	unionL = (BOX *) palloc(sizeof(BOX));
	unionR = (BOX *) palloc(sizeof(BOX));
	unionB = (BOX *) palloc(sizeof(BOX));
	unionT = (BOX *) palloc(sizeof(BOX));

#define ADDLIST( list, unionD, pos, num ) do { \
	if ( pos ) { \
		if ( (unionD)->high.x < cur->high.x ) (unionD)->high.x	= cur->high.x; \
		if ( (unionD)->low.x  > cur->low.x	) (unionD)->low.x	= cur->low.x; \
		if ( (unionD)->high.y < cur->high.y ) (unionD)->high.y	= cur->high.y; \
		if ( (unionD)->low.y  > cur->low.y	) (unionD)->low.y	= cur->low.y; \
	} else { \
			memcpy( (void*)(unionD), (void*) cur, sizeof( BOX ) );	\
	} \
		\
	(list)[pos] = num; \
	(pos)++; \
} while(0)

	for (i = FIRST_ITEM_ID; i <= maxoff; i = ITEM_ID_NEXT(i)) {
		cur = D_TO_BOX_P(entryvec->vector[i].key);
		if (cur->low.x - pageunion.low.x < pageunion.high.x - cur->high.x)
			ADDLIST(listL, unionL, posL, i);
		else
			ADDLIST(listR, unionR, posR, i);

		if (cur->low.y - pageunion.low.y < pageunion.high.y - cur->high.y)
			ADDLIST(listB, unionB, posB, i);
		else
			ADDLIST(listT, unionT, posT, i);
	}

#define LIMIT_RATIO 0.1
#define _IS_BADRATIO(x,y)	( (y) == 0 || (float)(x)/(float)(y) < LIMIT_RATIO )
#define IS_BADRATIO(x,y) 	( _IS_BADRATIO((x),(y)) || _IS_BADRATIO((y),(x)) )

	/* bad disposition, try to split by centers of boxes  */
	if (IS_BADRATIO(posR, posL) && IS_BADRATIO(posT, posB)) {
		double avgCenterX = 0.0;
		double avgCenterY = 0.0;
		double CenterX;
		double CenterY;

		for (i = FIRST_ITEM_ID; i <= maxoff; i = ITEM_ID_NEXT(i)) {
			cur = D_TO_BOX_P(entryvec->vector[i].key);
			avgCenterX += ((double)cur->high.x + (double)cur->low.x) / 2.0;
			avgCenterY += ((double)cur->high.y + (double)cur->low.y) / 2.0;
		}

		avgCenterX /= maxoff;
		avgCenterY /= maxoff;

		posL = posR = posB = posT = 0;
		for (i = FIRST_ITEM_ID; i <= maxoff; i = ITEM_ID_NEXT(i)) {
			cur = D_TO_BOX_P(entryvec->vector[i].key);

			CenterX = ((double)cur->high.x + (double)cur->low.x) / 2.0;
			CenterY = ((double)cur->high.y + (double)cur->low.y) / 2.0;

			if (CenterX < avgCenterX)
				ADDLIST(listL, unionL, posL, i);
			else if (CenterX == avgCenterX) {
				if (posL > posR)
					ADDLIST(listR, unionR, posR, i);
				else
					ADDLIST(listL, unionL, posL, i);
			} else
				ADDLIST(listR, unionR, posR, i);

			if (CenterY < avgCenterY)
				ADDLIST(listB, unionB, posB, i);
			else if (CenterY == avgCenterY) {
				if (posB > posT)
					ADDLIST(listT, unionT, posT, i);
				else
					ADDLIST(listB, unionB, posB, i);
			} else
				ADDLIST(listT, unionT, posT, i);
		}

		if (IS_BADRATIO(posR, posL) && IS_BADRATIO(posT, posB)) {
			fallbackSplit(entryvec, v);
			RET_POINTER(v);
		}
	}

	/* which split more optimal? */
	if (Max(posL, posR) < Max(posB, posT))
		direction = 'x';
	else if (Max(posL, posR) > Max(posB, posT))
		direction = 'y';
	else {
		datum_t interLR = DIRECT_FC2(rt_box_inter, BOX_P_TO_D(unionL), BOX_P_TO_D(unionR));
		datum_t interBT = DIRECT_FC2(rt_box_inter, BOX_P_TO_D(unionB), BOX_P_TO_D(unionT));
		double sizeLR;
		double sizeBT;

		sizeLR = size_box(interLR);
		sizeBT = size_box(interBT);
		if (sizeLR < sizeBT)
			direction = 'x';
		else
			direction = 'y';
	}

	if (direction == 'x')
		chooseLR(v, listL, posL, unionL, listR, posR, unionR);
	else
		chooseLR(v, listB, posB, unionB, listT, posT, unionT);

	RET_POINTER(v);
}
Beispiel #8
0
static void
chooseLR(
	struct gist_splitvec *v,
	item_id_t* list1,
	int nlist1,
	BOX* union1,
	item_id_t* list2,
	int nlist2,
	BOX* union2)
{
	bool firstToLeft = true;

	if (v->spl_ldatum_exists || v->spl_rdatum_exists) {
		if (v->spl_ldatum_exists && v->spl_rdatum_exists) {
			BOX LRl = *union1;
			BOX LRr = *union2;
			BOX RLl = *union2;
			BOX RLr = *union1;
			double sizeLR;
			double sizeRL;

			adjustBox(&LRl, D_TO_BOX_P(v->spl_ldatum));
			adjustBox(&LRr, D_TO_BOX_P(v->spl_rdatum));
			adjustBox(&RLl, D_TO_BOX_P(v->spl_ldatum));
			adjustBox(&RLr, D_TO_BOX_P(v->spl_rdatum));

			sizeLR = size_box(DIRECT_FC2(
				rt_box_inter,
				BOX_P_TO_D(&LRl), 
				BOX_P_TO_D(&LRr)));
			sizeRL = size_box(DIRECT_FC2(
				rt_box_inter,
				BOX_P_TO_D(&RLl),
				BOX_P_TO_D(&RLr)));

			if (sizeLR > sizeRL)
				firstToLeft = false;

		} else {
			float p1;
			float p2;
			struct gist_entry oldUnion;
			struct gist_entry addon;

			gistentryinit(
				oldUnion,
				(v->spl_ldatum_exists) ? v->spl_ldatum : v->spl_rdatum,
				NULL,
				NULL,
				INVALID_ITEM_ID,
				FALSE);

			gistentryinit(addon, BOX_P_TO_D(union1), NULL, NULL, INVALID_ITEM_ID, FALSE);
			DIRECT_FC3(gist_box_penalty,
					    PTR_TO_D(&oldUnion),
					    PTR_TO_D(&addon),
					    PTR_TO_D(&p1));
			gistentryinit(addon, BOX_P_TO_D(union2), NULL, NULL, INVALID_ITEM_ID, FALSE);
			DIRECT_FC3(
				gist_box_penalty,
				PTR_TO_D(&oldUnion),
				PTR_TO_D(&addon),
				PTR_TO_D(&p2));

			if ((v->spl_ldatum_exists && p1 > p2)
				|| (v->spl_rdatum_exists && p1 < p2))
				firstToLeft = false;
		}
	}

	if (firstToLeft) {
		v->spl_left = list1;
		v->spl_right = list2;
		v->spl_nleft = nlist1;
		v->spl_nright = nlist2;
		if (v->spl_ldatum_exists)
			adjustBox(union1, D_TO_BOX_P(v->spl_ldatum));

		v->spl_ldatum = BOX_P_TO_D(union1);
		if (v->spl_rdatum_exists)
			adjustBox(union2, D_TO_BOX_P(v->spl_rdatum));

		v->spl_rdatum = BOX_P_TO_D(union2);
	} else {
		v->spl_left = list2;
		v->spl_right = list1;
		v->spl_nleft = nlist2;
		v->spl_nright = nlist1;
		if (v->spl_ldatum_exists)
			adjustBox(union2, D_TO_BOX_P(v->spl_ldatum));

		v->spl_ldatum = BOX_P_TO_D(union2);
		if (v->spl_rdatum_exists)
			adjustBox(union1, D_TO_BOX_P(v->spl_rdatum));

		v->spl_rdatum = BOX_P_TO_D(union1);
	}

	v->spl_ldatum_exists = v->spl_rdatum_exists = false;
}
Beispiel #9
0
/*
** The GiST PickSplit method
** New linear algorithm, see 'New Linear Node Splitting Algorithm for R-tree',
** C.H.Ang and T.C.Tan
*/
Datum
gbox_picksplit(PG_FUNCTION_ARGS)
{
	bytea	   *entryvec = (bytea *) PG_GETARG_POINTER(0);
	GIST_SPLITVEC *v = (GIST_SPLITVEC *) PG_GETARG_POINTER(1);
	OffsetNumber i;
	OffsetNumber *listL,
			   *listR,
			   *listB,
			   *listT;
	BOX		   *unionL,
			   *unionR,
			   *unionB,
			   *unionT;
	int			posL,
				posR,
				posB,
				posT;
	BOX			pageunion;
	BOX		   *cur;
	char		direction = ' ';
	bool		allisequal = true;
	OffsetNumber maxoff;
	int			nbytes;

	posL = posR = posB = posT = 0;
	maxoff = ((VARSIZE(entryvec) - VARHDRSZ) / sizeof(GISTENTRY)) - 1;

	cur = DatumGetBoxP(((GISTENTRY *) VARDATA(entryvec))[FirstOffsetNumber].key);
	memcpy((void *) &pageunion, (void *) cur, sizeof(BOX));

	/* find MBR */
	for (i = OffsetNumberNext(FirstOffsetNumber); i <= maxoff; i = OffsetNumberNext(i))
	{
		cur = DatumGetBoxP(((GISTENTRY *) VARDATA(entryvec))[i].key);
		if (allisequal == true && (
								   pageunion.high.x != cur->high.x ||
								   pageunion.high.y != cur->high.y ||
								   pageunion.low.x != cur->low.x ||
								   pageunion.low.y != cur->low.y
								   ))
			allisequal = false;

		if (pageunion.high.x < cur->high.x)
			pageunion.high.x = cur->high.x;
		if (pageunion.low.x > cur->low.x)
			pageunion.low.x = cur->low.x;
		if (pageunion.high.y < cur->high.y)
			pageunion.high.y = cur->high.y;
		if (pageunion.low.y > cur->low.y)
			pageunion.low.y = cur->low.y;
	}

	nbytes = (maxoff + 2) * sizeof(OffsetNumber);
	listL = (OffsetNumber *) palloc(nbytes);
	listR = (OffsetNumber *) palloc(nbytes);
	unionL = (BOX *) palloc(sizeof(BOX));
	unionR = (BOX *) palloc(sizeof(BOX));
	if (allisequal)
	{
		cur = DatumGetBoxP(((GISTENTRY *) VARDATA(entryvec))[OffsetNumberNext(FirstOffsetNumber)].key);
		if (memcmp((void *) cur, (void *) &pageunion, sizeof(BOX)) == 0)
		{
			v->spl_left = listL;
			v->spl_right = listR;
			v->spl_nleft = v->spl_nright = 0;
			memcpy((void *) unionL, (void *) &pageunion, sizeof(BOX));
			memcpy((void *) unionR, (void *) &pageunion, sizeof(BOX));

			for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
			{
				if (i <= (maxoff - FirstOffsetNumber + 1) / 2)
				{
					v->spl_left[v->spl_nleft] = i;
					v->spl_nleft++;
				}
				else
				{
					v->spl_right[v->spl_nright] = i;
					v->spl_nright++;
				}
			}
			v->spl_ldatum = BoxPGetDatum(unionL);
			v->spl_rdatum = BoxPGetDatum(unionR);

			PG_RETURN_POINTER(v);
		}
	}

	listB = (OffsetNumber *) palloc(nbytes);
	listT = (OffsetNumber *) palloc(nbytes);
	unionB = (BOX *) palloc(sizeof(BOX));
	unionT = (BOX *) palloc(sizeof(BOX));

#define ADDLIST( list, unionD, pos, num ) do { \
	if ( pos ) { \
		if ( unionD->high.x < cur->high.x ) unionD->high.x	= cur->high.x; \
		if ( unionD->low.x	> cur->low.x  ) unionD->low.x	= cur->low.x; \
		if ( unionD->high.y < cur->high.y ) unionD->high.y	= cur->high.y; \
		if ( unionD->low.y	> cur->low.y  ) unionD->low.y	= cur->low.y; \
	} else { \
			memcpy( (void*)unionD, (void*) cur, sizeof( BOX ) );  \
	} \
	list[pos] = num; \
	(pos)++; \
} while(0)

	for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
	{
		cur = DatumGetBoxP(((GISTENTRY *) VARDATA(entryvec))[i].key);
		if (cur->low.x - pageunion.low.x < pageunion.high.x - cur->high.x)
			ADDLIST(listL, unionL, posL, i);
		else
			ADDLIST(listR, unionR, posR, i);
		if (cur->low.y - pageunion.low.y < pageunion.high.y - cur->high.y)
			ADDLIST(listB, unionB, posB, i);
		else
			ADDLIST(listT, unionT, posT, i);
	}

	/* bad disposition, sort by ascending and resplit */
	if ((posR == 0 || posL == 0) && (posT == 0 || posB == 0))
	{
		KBsort	   *arr = (KBsort *) palloc(sizeof(KBsort) * maxoff);

		posL = posR = posB = posT = 0;
		for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
		{
			arr[i - 1].key = DatumGetBoxP(((GISTENTRY *) VARDATA(entryvec))[i].key);
			arr[i - 1].pos = i;
		}
		qsort(arr, maxoff, sizeof(KBsort), compare_KB);
		for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
		{
			cur = arr[i - 1].key;
			if (cur->low.x - pageunion.low.x < pageunion.high.x - cur->high.x)
				ADDLIST(listL, unionL, posL, arr[i - 1].pos);
			else if (cur->low.x - pageunion.low.x == pageunion.high.x - cur->high.x)
			{
				if (posL > posR)
					ADDLIST(listR, unionR, posR, arr[i - 1].pos);
				else
					ADDLIST(listL, unionL, posL, arr[i - 1].pos);
			}
			else
				ADDLIST(listR, unionR, posR, arr[i - 1].pos);

			if (cur->low.y - pageunion.low.y < pageunion.high.y - cur->high.y)
				ADDLIST(listB, unionB, posB, arr[i - 1].pos);
			else if (cur->low.y - pageunion.low.y == pageunion.high.y - cur->high.y)
			{
				if (posB > posT)
					ADDLIST(listT, unionT, posT, arr[i - 1].pos);
				else
					ADDLIST(listB, unionB, posB, arr[i - 1].pos);
			}
			else
				ADDLIST(listT, unionT, posT, arr[i - 1].pos);
		}
		pfree(arr);
	}

	/* which split more optimal? */
	if (Max(posL, posR) < Max(posB, posT))
		direction = 'x';
	else if (Max(posL, posR) > Max(posB, posT))
		direction = 'y';
	else
	{
		Datum		interLR = DirectFunctionCall2(rt_box_inter,
												  BoxPGetDatum(unionL),
												  BoxPGetDatum(unionR));
		Datum		interBT = DirectFunctionCall2(rt_box_inter,
												  BoxPGetDatum(unionB),
												  BoxPGetDatum(unionT));
		float		sizeLR,
					sizeBT;

		sizeLR = size_box(interLR);
		sizeBT = size_box(interBT);

		if (sizeLR < sizeBT)
			direction = 'x';
		else
			direction = 'y';
	}

	if (direction == 'x')
	{
		pfree(unionB);
		pfree(listB);
		pfree(unionT);
		pfree(listT);

		v->spl_left = listL;
		v->spl_right = listR;
		v->spl_nleft = posL;
		v->spl_nright = posR;
		v->spl_ldatum = BoxPGetDatum(unionL);
		v->spl_rdatum = BoxPGetDatum(unionR);
	}
	else
	{
		pfree(unionR);
		pfree(listR);
		pfree(unionL);
		pfree(listL);

		v->spl_left = listB;
		v->spl_right = listT;
		v->spl_nleft = posB;
		v->spl_nright = posT;
		v->spl_ldatum = BoxPGetDatum(unionB);
		v->spl_rdatum = BoxPGetDatum(unionT);
	}

	PG_RETURN_POINTER(v);
}