/*
* 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);
}
/*
* 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);
}
/*
* --------------------------------------------------------------------------
* Double sorting split algorithm. This is used for both boxes and points.
*
* The algorithm finds split of boxes by considering splits along each axis.
* Each entry is first projected as an interval on the X-axis, and different
* ways to split the intervals into two groups are considered, trying to
* minimize the overlap of the groups. Then the same is repeated for the
* Y-axis, and the overall best split is chosen. The quality of a split is
* determined by overlap along that axis and some other criteria (see
* g_box_consider_split).
*
* After that, all the entries are divided into three groups:
*
* 1) Entries which should be placed to the left group
* 2) Entries which should be placed to the right group
* 3) "Common entries" which can be placed to any of groups without affecting
* of overlap along selected axis.
*
* The common entries are distributed by minimizing penalty.
*
* For details see:
* "A new___ double sorting-based node splitting algorithm for R-tree", A. Korotkov
* http://syrcose.ispras.ru/2011/files/SYRCoSE2011_Proceedings.pdf#page=36
* --------------------------------------------------------------------------
*/
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,
maxoff;
ConsiderSplitContext context;
BOX *box,
*leftBox,
*rightBox;
int dim,
commonEntriesCount;
SplitInterval *intervalsLower,
*intervalsUpper;
CommonEntry *commonEntries;
int nentries;
memset(&context, 0, sizeof(ConsiderSplitContext));
maxoff = entryvec->n - 1;
nentries = context.entriesCount = maxoff - FirstOffsetNumber + 1;
/* Allocate arrays for intervals along axes */
intervalsLower = (SplitInterval *) palloc(nentries * sizeof(SplitInterval));
intervalsUpper = (SplitInterval *) palloc(nentries * sizeof(SplitInterval));
/*
* Calculate the overall minimum bounding box over all the entries.
*/
for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
{
box = DatumGetBoxP(entryvec->vector[i].key);
if (i == FirstOffsetNumber)
context.boundingBox = *box;
else
adjustBox(&context.boundingBox, box);
}
/*
* Iterate over axes for optimal split searching.
*/
context.first = true; /* nothing selected yet */
for (dim = 0; dim < 2; dim++)
{
double leftUpper,
rightLower;
int i1,
i2;
/* Project each entry as an interval on the selected axis. */
for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
{
box = DatumGetBoxP(entryvec->vector[i].key);
if (dim == 0)
{
intervalsLower[i - FirstOffsetNumber].lower = box->low.x;
intervalsLower[i - FirstOffsetNumber].upper = box->high.x;
}
else
{
intervalsLower[i - FirstOffsetNumber].lower = box->low.y;
intervalsLower[i - FirstOffsetNumber].upper = box->high.y;
}
}
/*
* Make two arrays of intervals: one sorted by lower bound and another
* sorted by upper bound.
*/
memcpy(intervalsUpper, intervalsLower,
sizeof(SplitInterval) * nentries);
qsort(intervalsLower, nentries, sizeof(SplitInterval),
interval_cmp_lower);
qsort(intervalsUpper, nentries, sizeof(SplitInterval),
interval_cmp_upper);
/*----
* The goal is to form a left and right interval, so that every entry
* interval is contained by either left or right interval (or both).
*
* For example, with the intervals (0,1), (1,3), (2,3), (2,4):
*
* 0 1 2 3 4
* +-+
* +---+
* +-+
* +---+
*
* The left and right intervals are of the form (0,a) and (b,4).
* We first consider splits where b is the lower bound of an entry.
* We iterate through all entries, and for each b, calculate the
* smallest possible a. Then we consider splits where a is the
* uppper bound of an entry, and for each a, calculate the greatest
* possible b.
*
* In the above example, the first loop would consider splits:
* b=0: (0,1)-(0,4)
* b=1: (0,1)-(1,4)
* b=2: (0,3)-(2,4)
*
* And the second loop:
* a=1: (0,1)-(1,4)
* a=3: (0,3)-(2,4)
* a=4: (0,4)-(2,4)
*/
/*
* Iterate over lower bound of right group, finding smallest possible
* upper bound of left group.
*/
i1 = 0;
i2 = 0;
rightLower = intervalsLower[i1].lower;
leftUpper = intervalsUpper[i2].lower;
while (true)
{
/*
* Find next lower bound of right group.
*/
while (i1 < nentries && rightLower == intervalsLower[i1].lower)
{
leftUpper = Max(leftUpper, intervalsLower[i1].upper);
i1++;
}
if (i1 >= nentries)
break;
rightLower = intervalsLower[i1].lower;
/*
* Find count of intervals which anyway should be placed to the
* left group.
*/
while (i2 < nentries && intervalsUpper[i2].upper <= leftUpper)
i2++;
/*
* Consider found split.
*/
g_box_consider_split(&context, dim, rightLower, i1, leftUpper, i2);
}
/*
* Iterate over upper bound of left group finding greates possible
* lower bound of right group.
*/
i1 = nentries - 1;
i2 = nentries - 1;
rightLower = intervalsLower[i1].upper;
leftUpper = intervalsUpper[i2].upper;
while (true)
{
/*
* Find next upper bound of left group.
*/
while (i2 >= 0 && leftUpper == intervalsUpper[i2].upper)
{
rightLower = Min(rightLower, intervalsUpper[i2].lower);
i2--;
}
if (i2 < 0)
break;
leftUpper = intervalsUpper[i2].upper;
/*
* Find count of intervals which anyway should be placed to the
* right group.
*/
while (i1 >= 0 && intervalsLower[i1].lower >= rightLower)
i1--;
/*
* Consider found split.
*/
g_box_consider_split(&context, dim,
rightLower, i1 + 1, leftUpper, i2 + 1);
}
}
/*
* If we failed to find any acceptable splits, use trivial split.
*/
if (context.first)
{
fallbackSplit(entryvec, v);
PG_RETURN_POINTER(v);
}
/*
* Ok, we have now selected the split across one axis.
*
* While considering the splits, we already determined that there will be
* enough entries in both groups to reach the desired ratio, but we did
* not memorize which entries go to which group. So determine that now.
*/
/* Allocate vectors for results */
v->spl_left = (OffsetNumber *) palloc(nentries * sizeof(OffsetNumber));
v->spl_right = (OffsetNumber *) palloc(nentries * sizeof(OffsetNumber));
v->spl_nleft = 0;
v->spl_nright = 0;
/* Allocate bounding boxes of left and right groups */
leftBox = static_cast<BOX *>(palloc0(sizeof(BOX)));
rightBox = static_cast<BOX *>(palloc0(sizeof(BOX)));
/*
* Allocate an array for "common entries" - entries which can be placed to
* either group without affecting overlap along selected axis.
*/
commonEntriesCount = 0;
commonEntries = (CommonEntry *) palloc(nentries * sizeof(CommonEntry));
/* Helper macros to place an entry in the left or right group */
#define PLACE_LEFT(box, off) \
do { \
if (v->spl_nleft > 0) \
adjustBox(leftBox, box); \
else \
*leftBox = *(box); \
v->spl_left[v->spl_nleft++] = off; \
} while(0)
#define PLACE_RIGHT(box, off) \
do { \
if (v->spl_nright > 0) \
adjustBox(rightBox, box); \
else \
*rightBox = *(box); \
v->spl_right[v->spl_nright++] = off; \
} while(0)
/*
* Distribute entries which can be distributed unambiguously, and collect
* common entries.
*/
for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
{
double lower,
upper;
/*
* Get upper and lower bounds along selected axis.
*/
box = DatumGetBoxP(entryvec->vector[i].key);
if (context.dim == 0)
{
lower = box->low.x;
upper = box->high.x;
}
else
{
lower = box->low.y;
upper = box->high.y;
}
if (upper <= context.leftUpper)
{
/* Fits to the left group */
if (lower >= context.rightLower)
{
/* Fits also to the right group, so "common entry" */
commonEntries[commonEntriesCount++].index = i;
}
else
{
/* Doesn't fit to the right group, so join to the left group */
PLACE_LEFT(box, i);
}
}
else
{
/*
* Each entry should fit on either left or right group. Since this
* entry didn't fit on the left group, it better fit in the right
* group.
*/
Assert(lower >= context.rightLower);
/* Doesn't fit to the left group, so join to the right group */
PLACE_RIGHT(box, i);
}
}
/*
* Distribute "common entries", if any.
*/
if (commonEntriesCount > 0)
{
/*
* Calculate minimum number of entries that must be placed in both
* groups, to reach LIMIT_RATIO.
*/
int m = ceil(LIMIT_RATIO * (double) nentries);
/*
* Calculate delta between penalties of join "common entries" to
* different groups.
*/
for (i = 0; i < commonEntriesCount; i++)
{
box = DatumGetBoxP(entryvec->vector[commonEntries[i].index].key);
commonEntries[i].delta = Abs(box_penalty(leftBox, box) -
box_penalty(rightBox, box));
}
/*
* Sort "common entries" by calculated deltas in order to distribute
* the most ambiguous entries first.
*/
qsort(commonEntries, commonEntriesCount, sizeof(CommonEntry), common_entry_cmp);
/*
* Distribute "common entries" between groups.
*/
for (i = 0; i < commonEntriesCount; i++)
{
box = DatumGetBoxP(entryvec->vector[commonEntries[i].index].key);
/*
* Check if we have to place this entry in either group to achieve
* LIMIT_RATIO.
*/
if (v->spl_nleft + (commonEntriesCount - i) <= m)
PLACE_LEFT(box, commonEntries[i].index);
else if (v->spl_nright + (commonEntriesCount - i) <= m)
PLACE_RIGHT(box, commonEntries[i].index);
else
{
/* Otherwise select the group by minimal penalty */
if (box_penalty(leftBox, box) < box_penalty(rightBox, box))
PLACE_LEFT(box, commonEntries[i].index);
else
PLACE_RIGHT(box, commonEntries[i].index);
}
}
}
v->spl_ldatum = PointerGetDatum(leftBox);
v->spl_rdatum = PointerGetDatum(rightBox);
PG_RETURN_POINTER(v);
}
