/*-------------------------------------------------------------------------
*
* gistproc.c
* Support procedures for GiSTs over 2-D objects (boxes, polygons, circles,
* points).
*
* This gives R-tree behavior, with Guttman's poly-time split algorithm.
*
*
* Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
* IDENTIFICATION
* src/backend/access/gist/gistproc.c
*
*-------------------------------------------------------------------------
*/
#include "postgres.h"
#include <math.h>
#include "access/gist.h"
#include "access/stratnum.h"
#include "utils/builtins.h"
#include "utils/float.h"
#include "utils/geo_decls.h"
static bool gist_box_leaf_consistent(BOX *key, BOX *query,
StrategyNumber strategy);
static bool rtree_internal_consistent(BOX *key, BOX *query,
StrategyNumber strategy);
/* Minimum accepted ratio of split */
#define LIMIT_RATIO 0.3
/**************************************************
* Box ops
**************************************************/
/*
* Calculates union of two boxes, a and b. The result is stored in *n.
*/
static void
rt_box_union(BOX *n, const BOX *a, const BOX *b)
{
n->high.x = float8_max(a->high.x, b->high.x);
n->high.y = float8_max(a->high.y, b->high.y);
n->low.x = float8_min(a->low.x, b->low.x);
n->low.y = float8_min(a->low.y, b->low.y);
}
/*
* Size of a BOX for penalty-calculation purposes.
* The result can be +Infinity, but not NaN.
*/
static float8
size_box(const BOX *box)
{
/*
* Check for zero-width cases. Note that we define the size of a zero-
* by-infinity box as zero. It's important to special-case this somehow,
* as naively multiplying infinity by zero will produce NaN.
*
* The less-than cases should not happen, but if they do, say "zero".
*/
if (float8_le(box->high.x, box->low.x) ||
float8_le(box->high.y, box->low.y))
return 0.0;
/*
* We treat NaN as larger than +Infinity, so any distance involving a NaN
* and a non-NaN is infinite. Note the previous check eliminated the
* possibility that the low fields are NaNs.
*/
if (isnan(box->high.x) || isnan(box->high.y))
return get_float8_infinity();
return float8_mul(float8_mi(box->high.x, box->low.x),
float8_mi(box->high.y, box->low.y));
}
/*
* Return amount by which the union of the two boxes is larger than
* the original BOX's area. The result can be +Infinity, but not NaN.
*/
static float8
box_penalty(const BOX *original, const BOX *new)
{
BOX unionbox;
rt_box_union(&unionbox, original, new);
return float8_mi(size_box(&unionbox), size_box(original));
}
/*
* The GiST Consistent method for boxes
*
* Should return false if for all data items x below entry,
* the predicate x op query must be false, where op is the oper
* corresponding to strategy in the pg_amop table.
*/
Datum
gist_box_consistent(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
BOX *query = PG_GETARG_BOX_P(1);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
/* Oid subtype = PG_GETARG_OID(3); */
bool *recheck = (bool *) PG_GETARG_POINTER(4);
/* All cases served by this function are exact */
*recheck = false;
if (DatumGetBoxP(entry->key) == NULL || query == NULL)
PG_RETURN_BOOL(false);
/*
* if entry is not leaf, use rtree_internal_consistent, else use
* gist_box_leaf_consistent
*/
if (GIST_LEAF(entry))
PG_RETURN_BOOL(gist_box_leaf_consistent(DatumGetBoxP(entry->key),
query,
strategy));
else
PG_RETURN_BOOL(rtree_internal_consistent(DatumGetBoxP(entry->key),
query,
strategy));
}
/*
* Increase BOX b to include addon.
*/
static void
adjustBox(BOX *b, const BOX *addon)
{
if (float8_lt(b->high.x, addon->high.x))
b->high.x = addon->high.x;
if (float8_gt(b->low.x, addon->low.x))
b->low.x = addon->low.x;
if (float8_lt(b->high.y, addon->high.y))
b->high.y = addon->high.y;
if (float8_gt(b->low.y, addon->low.y))
b->low.y = addon->low.y;
}
/*
* The GiST Union method for boxes
*
* returns the minimal bounding box that encloses all the entries in entryvec
*/
Datum
gist_box_union(PG_FUNCTION_ARGS)
{
GistEntryVector *entryvec = (GistEntryVector *) PG_GETARG_POINTER(0);
int *sizep = (int *) PG_GETARG_POINTER(1);
int numranges,
i;
BOX *cur,
*pageunion;
numranges = entryvec->n;
pageunion = (BOX *) palloc(sizeof(BOX));
cur = DatumGetBoxP(entryvec->vector[0].key);
memcpy((void *) pageunion, (void *) cur, sizeof(BOX));
for (i = 1; i < numranges; i++)
{
cur = DatumGetBoxP(entryvec->vector[i].key);
adjustBox(pageunion, cur);
}
*sizep = sizeof(BOX);
PG_RETURN_POINTER(pageunion);
}
/*
* We store boxes as boxes in GiST indexes, so we do not need
* compress, decompress, or fetch functions.
*/
/*
* 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);
*result = (float) box_penalty(origbox, newbox);
PG_RETURN_POINTER(result);
}
/*
* Trivial split: half of entries will be placed on one page
* and another half - to another
*/
static void
fallbackSplit(GistEntryVector *entryvec, GIST_SPLITVEC *v)
{
OffsetNumber i,
maxoff;
BOX *unionL = NULL,
*unionR = NULL;
int nbytes;
maxoff = entryvec->n - 1;
nbytes = (maxoff + 2) * sizeof(OffsetNumber);
v->spl_left = (OffsetNumber *) palloc(nbytes);
v->spl_right = (OffsetNumber *) palloc(nbytes);
v->spl_nleft = v->spl_nright = 0;
for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
{
BOX *cur = DatumGetBoxP(entryvec->vector[i].key);
if (i <= (maxoff - FirstOffsetNumber + 1) / 2)
{
v->spl_left[v->spl_nleft] = i;
if (unionL == NULL)
{
unionL = (BOX *) palloc(sizeof(BOX));
*unionL = *cur;
}
else
adjustBox(unionL, cur);
v->spl_nleft++;
}
else
{
v->spl_right[v->spl_nright] = i;
if (unionR == NULL)
{
unionR = (BOX *) palloc(sizeof(BOX));
*unionR = *cur;
}
else
adjustBox(unionR, cur);
v->spl_nright++;
}
}
v->spl_ldatum = BoxPGetDatum(unionL);
v->spl_rdatum = BoxPGetDatum(unionR);
}
/*
* Represents information about an entry that can be placed to either group
* without affecting overlap over selected axis ("common entry").
*/
typedef struct
{
/* Index of entry in the initial array */
int index;
/* Delta between penalties of entry insertion into different groups */
float8 delta;
} CommonEntry;
/*
* Context for g_box_consider_split. Contains information about currently
* selected split and some general information.
*/
typedef struct
{
int entriesCount; /* total number of entries being split */
BOX boundingBox; /* minimum bounding box across all entries */
/* Information about currently selected split follows */
bool first; /* true if no split was selected yet */
float8 leftUpper; /* upper bound of left interval */
float8 rightLower; /* lower bound of right interval */
float4 ratio;
float4 overlap;
int dim; /* axis of this split */
float8 range; /* width of general MBR projection to the
* selected axis */
} ConsiderSplitContext;
/*
* Interval represents projection of box to axis.
*/
typedef struct
{
float8 lower,
upper;
} SplitInterval;
/*
* Interval comparison function by lower bound of the interval;
*/
static int
interval_cmp_lower(const void *i1, const void *i2)
{
float8 lower1 = ((const SplitInterval *) i1)->lower,
lower2 = ((const SplitInterval *) i2)->lower;
return float8_cmp_internal(lower1, lower2);
}
/*
* Interval comparison function by upper bound of the interval;
*/
static int
interval_cmp_upper(const void *i1, const void *i2)
{
float8 upper1 = ((const SplitInterval *) i1)->upper,
upper2 = ((const SplitInterval *) i2)->upper;
return float8_cmp_internal(upper1, upper2);
}
/*
* Replace negative (or NaN) value with zero.
*/
static inline float
non_negative(float val)
{
if (val >= 0.0f)
return val;
else
return 0.0f;
}
/*
* Consider replacement of currently selected split with the better one.
*/
static inline void
g_box_consider_split(ConsiderSplitContext *context, int dimNum,
float8 rightLower, int minLeftCount,
float8 leftUpper, int maxLeftCount)
{
int leftCount,
rightCount;
float4 ratio,
overlap;
float8 range;
/*
* Calculate entries distribution ratio assuming most uniform distribution
* of common entries.
*/
if (minLeftCount >= (context->entriesCount + 1) / 2)
{
leftCount = minLeftCount;
}
else
{
if (maxLeftCount <= context->entriesCount / 2)
leftCount = maxLeftCount;
else
leftCount = context->entriesCount / 2;
}
rightCount = context->entriesCount - leftCount;
/*
* Ratio of split - quotient between size of lesser group and total
* entries count.
*/
ratio = float4_div(Min(leftCount, rightCount), context->entriesCount);
if (ratio > LIMIT_RATIO)
{
bool selectthis = false;
/*
* The ratio is acceptable, so compare current split with previously
* selected one. Between splits of one dimension we search for minimal
* overlap (allowing negative values) and minimal ration (between same
* overlaps. We switch dimension if find less overlap (non-negative)
* or less range with same overlap.
*/
if (dimNum == 0)
range = float8_mi(context->boundingBox.high.x,
context->boundingBox.low.x);
else
range = float8_mi(context->boundingBox.high.y,
context->boundingBox.low.y);
overlap = float8_div(float8_mi(leftUpper, rightLower), range);
/* If there is no previous selection, select this */
if (context->first)
selectthis = true;
else if (context->dim == dimNum)
{
/*
* Within the same dimension, choose the new split if it has a
* smaller overlap, or same overlap but better ratio.
*/
if (overlap < context->overlap ||
(overlap == context->overlap && ratio > context->ratio))
selectthis = true;
}
else
{
/*
* Across dimensions, choose the new split if it has a smaller
* *non-negative* overlap, or same *non-negative* overlap but
* bigger range. This condition differs from the one described in
* the article. On the datasets where leaf MBRs don't overlap
* themselves, non-overlapping splits (i.e. splits which have zero
* *non-negative* overlap) are frequently possible. In this case
* splits tends to be along one dimension, because most distant
* non-overlapping splits (i.e. having lowest negative overlap)
* appears to be in the same dimension as in the previous split.
* Therefore MBRs appear to be very prolonged along another
* dimension, which leads to bad search performance. Using range
* as the second split criteria makes MBRs more quadratic. Using
* *non-negative* overlap instead of overlap as the first split
* criteria gives to range criteria a chance to matter, because
* non-overlapping splits are equivalent in this criteria.
*/
if (non_negative(overlap) < non_negative(context->overlap) ||
(range > context->range &&
non_negative(overlap) <= non_negative(context->overlap)))
selectthis = true;
}
if (selectthis)
{
/* save information about selected split */
context->first = false;
context->ratio = ratio;
context->range = range;
context->overlap = overlap;
context->rightLower = rightLower;
context->leftUpper = leftUpper;
context->dim = dimNum;
}
}
}
/*
* Compare common entries by their deltas.
*/
static int
common_entry_cmp(const void *i1, const void *i2)
{
float8 delta1 = ((const CommonEntry *) i1)->delta,
delta2 = ((const CommonEntry *) i2)->delta;
return float8_cmp_internal(delta1, delta2);
}
/*
* --------------------------------------------------------------------------
* 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++)
{
float8 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
* upper 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 &&
float8_eq(rightLower, intervalsLower[i1].lower))
{
if (float8_lt(leftUpper, intervalsLower[i1].upper))
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 &&
float8_le(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 greatest 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 && float8_eq(leftUpper, intervalsUpper[i2].upper))
{
if (float8_gt(rightLower, intervalsUpper[i2].lower))
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 && float8_ge(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 = palloc0(sizeof(BOX));
rightBox = 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))
{
float8 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 (float8_le(upper, context.leftUpper))
{
/* Fits to the left group */
if (float8_ge(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(float8_ge(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 * 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(float8_mi(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);
}
/*
* Equality method
*
* This is used for boxes, points, circles, and polygons, all of which store
* boxes as GiST index entries.
*
* Returns true only when boxes are exactly the same. We can't use fuzzy
* comparisons here without breaking index consistency; therefore, this isn't
* equivalent to box_same().
*/
Datum
gist_box_same(PG_FUNCTION_ARGS)
{
BOX *b1 = PG_GETARG_BOX_P(0);
BOX *b2 = PG_GETARG_BOX_P(1);
bool *result = (bool *) PG_GETARG_POINTER(2);
if (b1 && b2)
*result = (float8_eq(b1->low.x, b2->low.x) &&
float8_eq(b1->low.y, b2->low.y) &&
float8_eq(b1->high.x, b2->high.x) &&
float8_eq(b1->high.y, b2->high.y));
else
*result = (b1 == NULL && b2 == NULL);
PG_RETURN_POINTER(result);
}
/*
* Leaf-level consistency for boxes: just apply the query operator
*/
static bool
gist_box_leaf_consistent(BOX *key, BOX *query, StrategyNumber strategy)
{
bool retval;
switch (strategy)
{
case RTLeftStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_left,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverLeftStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overleft,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverlapStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overlap,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverRightStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overright,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTRightStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_right,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTSameStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_same,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTContainsStrategyNumber:
case RTOldContainsStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_contain,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTContainedByStrategyNumber:
case RTOldContainedByStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_contained,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverBelowStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overbelow,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTBelowStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_below,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTAboveStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_above,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverAboveStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overabove,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
default:
elog(ERROR, "unrecognized strategy number: %d", strategy);
retval = false; /* keep compiler quiet */
break;
}
return retval;
}
/*****************************************
* Common rtree functions (for boxes, polygons, and circles)
*****************************************/
/*
* Internal-page consistency for all these types
*
* We can use the same function since all types use bounding boxes as the
* internal-page representation.
*/
static bool
rtree_internal_consistent(BOX *key, BOX *query, StrategyNumber strategy)
{
bool retval;
switch (strategy)
{
case RTLeftStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_overright,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverLeftStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_right,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverlapStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overlap,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverRightStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_left,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTRightStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_overleft,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTSameStrategyNumber:
case RTContainsStrategyNumber:
case RTOldContainsStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_contain,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTContainedByStrategyNumber:
case RTOldContainedByStrategyNumber:
retval = DatumGetBool(DirectFunctionCall2(box_overlap,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverBelowStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_above,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTBelowStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_overabove,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTAboveStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_overbelow,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
case RTOverAboveStrategyNumber:
retval = !DatumGetBool(DirectFunctionCall2(box_below,
PointerGetDatum(key),
PointerGetDatum(query)));
break;
default:
elog(ERROR, "unrecognized strategy number: %d", strategy);
retval = false; /* keep compiler quiet */
break;
}
return retval;
}
/**************************************************
* Polygon ops
**************************************************/
/*
* GiST compress for polygons: represent a polygon by its bounding box
*/
Datum
gist_poly_compress(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
GISTENTRY *retval;
if (entry->leafkey)
{
POLYGON *in = DatumGetPolygonP(entry->key);
BOX *r;
r = (BOX *) palloc(sizeof(BOX));
memcpy((void *) r, (void *) &(in->boundbox), sizeof(BOX));
retval = (GISTENTRY *) palloc(sizeof(GISTENTRY));
gistentryinit(*retval, PointerGetDatum(r),
entry->rel, entry->page,
entry->offset, false);
}
else
retval = entry;
PG_RETURN_POINTER(retval);
}
/*
* The GiST Consistent method for polygons
*/
Datum
gist_poly_consistent(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
POLYGON *query = PG_GETARG_POLYGON_P(1);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
/* Oid subtype = PG_GETARG_OID(3); */
bool *recheck = (bool *) PG_GETARG_POINTER(4);
bool result;
/* All cases served by this function are inexact */
*recheck = true;
if (DatumGetBoxP(entry->key) == NULL || query == NULL)
PG_RETURN_BOOL(false);
/*
* Since the operators require recheck anyway, we can just use
* rtree_internal_consistent even at leaf nodes. (This works in part
* because the index entries are bounding boxes not polygons.)
*/
result = rtree_internal_consistent(DatumGetBoxP(entry->key),
&(query->boundbox), strategy);
/* Avoid memory leak if supplied poly is toasted */
PG_FREE_IF_COPY(query, 1);
PG_RETURN_BOOL(result);
}
/**************************************************
* Circle ops
**************************************************/
/*
* GiST compress for circles: represent a circle by its bounding box
*/
Datum
gist_circle_compress(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
GISTENTRY *retval;
if (entry->leafkey)
{
CIRCLE *in = DatumGetCircleP(entry->key);
BOX *r;
r = (BOX *) palloc(sizeof(BOX));
r->high.x = float8_pl(in->center.x, in->radius);
r->low.x = float8_mi(in->center.x, in->radius);
r->high.y = float8_pl(in->center.y, in->radius);
r->low.y = float8_mi(in->center.y, in->radius);
retval = (GISTENTRY *) palloc(sizeof(GISTENTRY));
gistentryinit(*retval, PointerGetDatum(r),
entry->rel, entry->page,
entry->offset, false);
}
else
retval = entry;
PG_RETURN_POINTER(retval);
}
/*
* The GiST Consistent method for circles
*/
Datum
gist_circle_consistent(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
CIRCLE *query = PG_GETARG_CIRCLE_P(1);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
/* Oid subtype = PG_GETARG_OID(3); */
bool *recheck = (bool *) PG_GETARG_POINTER(4);
BOX bbox;
bool result;
/* All cases served by this function are inexact */
*recheck = true;
if (DatumGetBoxP(entry->key) == NULL || query == NULL)
PG_RETURN_BOOL(false);
/*
* Since the operators require recheck anyway, we can just use
* rtree_internal_consistent even at leaf nodes. (This works in part
* because the index entries are bounding boxes not circles.)
*/
bbox.high.x = float8_pl(query->center.x, query->radius);
bbox.low.x = float8_mi(query->center.x, query->radius);
bbox.high.y = float8_pl(query->center.y, query->radius);
bbox.low.y = float8_mi(query->center.y, query->radius);
result = rtree_internal_consistent(DatumGetBoxP(entry->key),
&bbox, strategy);
PG_RETURN_BOOL(result);
}
/**************************************************
* Point ops
**************************************************/
Datum
gist_point_compress(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
if (entry->leafkey) /* Point, actually */
{
BOX *box = palloc(sizeof(BOX));
Point *point = DatumGetPointP(entry->key);
GISTENTRY *retval = palloc(sizeof(GISTENTRY));
box->high = box->low = *point;
gistentryinit(*retval, BoxPGetDatum(box),
entry->rel, entry->page, entry->offset, false);
PG_RETURN_POINTER(retval);
}
PG_RETURN_POINTER(entry);
}
/*
* GiST Fetch method for point
*
* Get point coordinates from its bounding box coordinates and form new
* gistentry.
*/
Datum
gist_point_fetch(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
BOX *in = DatumGetBoxP(entry->key);
Point *r;
GISTENTRY *retval;
retval = palloc(sizeof(GISTENTRY));
r = (Point *) palloc(sizeof(Point));
r->x = in->high.x;
r->y = in->high.y;
gistentryinit(*retval, PointerGetDatum(r),
entry->rel, entry->page,
entry->offset, false);
PG_RETURN_POINTER(retval);
}
#define point_point_distance(p1,p2) \
DatumGetFloat8(DirectFunctionCall2(point_distance, \
PointPGetDatum(p1), PointPGetDatum(p2)))
static float8
computeDistance(bool isLeaf, BOX *box, Point *point)
{
float8 result = 0.0;
if (isLeaf)
{
/* simple point to point distance */
result = point_point_distance(point, &box->low);
}
else if (point->x <= box->high.x && point->x >= box->low.x &&
point->y <= box->high.y && point->y >= box->low.y)
{
/* point inside the box */
result = 0.0;
}
else if (point->x <= box->high.x && point->x >= box->low.x)
{
/* point is over or below box */
Assert(box->low.y <= box->high.y);
if (point->y > box->high.y)
result = float8_mi(point->y, box->high.y);
else if (point->y < box->low.y)
result = float8_mi(box->low.y, point->y);
else
elog(ERROR, "inconsistent point values");
}
else if (point->y <= box->high.y && point->y >= box->low.y)
{
/* point is to left or right of box */
Assert(box->low.x <= box->high.x);
if (point->x > box->high.x)
result = float8_mi(point->x, box->high.x);
else if (point->x < box->low.x)
result = float8_mi(box->low.x, point->x);
else
elog(ERROR, "inconsistent point values");
}
else
{
/* closest point will be a vertex */
Point p;
float8 subresult;
result = point_point_distance(point, &box->low);
subresult = point_point_distance(point, &box->high);
if (result > subresult)
result = subresult;
p.x = box->low.x;
p.y = box->high.y;
subresult = point_point_distance(point, &p);
if (result > subresult)
result = subresult;
p.x = box->high.x;
p.y = box->low.y;
subresult = point_point_distance(point, &p);
if (result > subresult)
result = subresult;
}
return result;
}
static bool
gist_point_consistent_internal(StrategyNumber strategy,
bool isLeaf, BOX *key, Point *query)
{
bool result = false;
switch (strategy)
{
case RTLeftStrategyNumber:
result = FPlt(key->low.x, query->x);
break;
case RTRightStrategyNumber:
result = FPgt(key->high.x, query->x);
break;
case RTAboveStrategyNumber:
result = FPgt(key->high.y, query->y);
break;
case RTBelowStrategyNumber:
result = FPlt(key->low.y, query->y);
break;
case RTSameStrategyNumber:
if (isLeaf)
{
/* key.high must equal key.low, so we can disregard it */
result = (FPeq(key->low.x, query->x) &&
FPeq(key->low.y, query->y));
}
else
{
result = (FPle(query->x, key->high.x) &&
FPge(query->x, key->low.x) &&
FPle(query->y, key->high.y) &&
FPge(query->y, key->low.y));
}
break;
default:
elog(ERROR, "unrecognized strategy number: %d", strategy);
result = false; /* keep compiler quiet */
break;
}
return result;
}
#define GeoStrategyNumberOffset 20
#define PointStrategyNumberGroup 0
#define BoxStrategyNumberGroup 1
#define PolygonStrategyNumberGroup 2
#define CircleStrategyNumberGroup 3
Datum
gist_point_consistent(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
bool *recheck = (bool *) PG_GETARG_POINTER(4);
bool result;
StrategyNumber strategyGroup = strategy / GeoStrategyNumberOffset;
switch (strategyGroup)
{
case PointStrategyNumberGroup:
result = gist_point_consistent_internal(strategy % GeoStrategyNumberOffset,
GIST_LEAF(entry),
DatumGetBoxP(entry->key),
PG_GETARG_POINT_P(1));
*recheck = false;
break;
case BoxStrategyNumberGroup:
{
/*
* The only operator in this group is point <@ box (on_pb), so
* we needn't examine strategy again.
*
* For historical reasons, on_pb uses exact rather than fuzzy
* comparisons. We could use box_overlap when at an internal
* page, but that would lead to possibly visiting child pages
* uselessly, because box_overlap uses fuzzy comparisons.
* Instead we write a non-fuzzy overlap test. The same code
* will also serve for leaf-page tests, since leaf keys have
* high == low.
*/
BOX *query,
*key;
query = PG_GETARG_BOX_P(1);
key = DatumGetBoxP(entry->key);
result = (key->high.x >= query->low.x &&
key->low.x <= query->high.x &&
key->high.y >= query->low.y &&
key->low.y <= query->high.y);
*recheck = false;
}
break;
case PolygonStrategyNumberGroup:
{
POLYGON *query = PG_GETARG_POLYGON_P(1);
result = DatumGetBool(DirectFunctionCall5(
gist_poly_consistent,
PointerGetDatum(entry),
PolygonPGetDatum(query),
Int16GetDatum(RTOverlapStrategyNumber),
0, PointerGetDatum(recheck)));
if (GIST_LEAF(entry) && result)
{
/*
* We are on leaf page and quick check shows overlapping
* of polygon's bounding box and point
*/
BOX *box = DatumGetBoxP(entry->key);
Assert(box->high.x == box->low.x
&& box->high.y == box->low.y);
result = DatumGetBool(DirectFunctionCall2(
poly_contain_pt,
PolygonPGetDatum(query),
PointPGetDatum(&box->high)));
*recheck = false;
}
}
break;
case CircleStrategyNumberGroup:
{
CIRCLE *query = PG_GETARG_CIRCLE_P(1);
result = DatumGetBool(DirectFunctionCall5(
gist_circle_consistent,
PointerGetDatum(entry),
CirclePGetDatum(query),
Int16GetDatum(RTOverlapStrategyNumber),
0, PointerGetDatum(recheck)));
if (GIST_LEAF(entry) && result)
{
/*
* We are on leaf page and quick check shows overlapping
* of polygon's bounding box and point
*/
BOX *box = DatumGetBoxP(entry->key);
Assert(box->high.x == box->low.x
&& box->high.y == box->low.y);
result = DatumGetBool(DirectFunctionCall2(
circle_contain_pt,
CirclePGetDatum(query),
PointPGetDatum(&box->high)));
*recheck = false;
}
}
break;
default:
elog(ERROR, "unrecognized strategy number: %d", strategy);
result = false; /* keep compiler quiet */
break;
}
PG_RETURN_BOOL(result);
}
Datum
gist_point_distance(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
float8 distance;
StrategyNumber strategyGroup = strategy / GeoStrategyNumberOffset;
switch (strategyGroup)
{
case PointStrategyNumberGroup:
distance = computeDistance(GIST_LEAF(entry),
DatumGetBoxP(entry->key),
PG_GETARG_POINT_P(1));
break;
default:
elog(ERROR, "unrecognized strategy number: %d", strategy);
distance = 0.0; /* keep compiler quiet */
break;
}
PG_RETURN_FLOAT8(distance);
}
static float8
gist_bbox_distance(GISTENTRY *entry, Datum query, StrategyNumber strategy)
{
float8 distance;
StrategyNumber strategyGroup = strategy / GeoStrategyNumberOffset;
switch (strategyGroup)
{
case PointStrategyNumberGroup:
distance = computeDistance(false,
DatumGetBoxP(entry->key),
DatumGetPointP(query));
break;
default:
elog(ERROR, "unrecognized strategy number: %d", strategy);
distance = 0.0; /* keep compiler quiet */
}
return distance;
}
Datum
gist_box_distance(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
Datum query = PG_GETARG_DATUM(1);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
/* Oid subtype = PG_GETARG_OID(3); */
/* bool *recheck = (bool *) PG_GETARG_POINTER(4); */
float8 distance;
distance = gist_bbox_distance(entry, query, strategy);
PG_RETURN_FLOAT8(distance);
}
/*
* The inexact GiST distance methods for geometric types that store bounding
* boxes.
*
* Compute lossy distance from point to index entries. The result is inexact
* because index entries are bounding boxes, not the exact shapes of the
* indexed geometric types. We use distance from point to MBR of index entry.
* This is a lower bound estimate of distance from point to indexed geometric
* type.
*/
Datum
gist_circle_distance(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
Datum query = PG_GETARG_DATUM(1);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
/* Oid subtype = PG_GETARG_OID(3); */
bool *recheck = (bool *) PG_GETARG_POINTER(4);
float8 distance;
distance = gist_bbox_distance(entry, query, strategy);
*recheck = true;
PG_RETURN_FLOAT8(distance);
}
Datum
gist_poly_distance(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
Datum query = PG_GETARG_DATUM(1);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
/* Oid subtype = PG_GETARG_OID(3); */
bool *recheck = (bool *) PG_GETARG_POINTER(4);
float8 distance;
distance = gist_bbox_distance(entry, query, strategy);
*recheck = true;
PG_RETURN_FLOAT8(distance);
}