geo_spgist.c

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/*-------------------------------------------------------------------------
 *
 * geo_spgist.c
 *    SP-GiST implementation of 4-dimensional quad tree over boxes
 *
 * This module provides SP-GiST implementation for boxes using quad tree
 * analogy in 4-dimensional space.  SP-GiST doesn't allow indexing of
 * overlapping objects.  We are making 2D objects never-overlapping in
 * 4D space.  This technique has some benefits compared to traditional
 * R-Tree which is implemented as GiST.  The performance tests reveal
 * that this technique especially beneficial with too much overlapping
 * objects, so called "spaghetti data".
 *
 * Unlike the original quad tree, we are splitting the tree into 16
 * quadrants in 4D space.  It is easier to imagine it as splitting space
 * two times into 4:
 *
 *              |      |
 *              |      |
 *              | -----+-----
 *              |      |
 *              |      |
 * -------------+-------------
 *              |
 *              |
 *              |
 *              |
 *              |
 *
 * We are using box datatype as the prefix, but we are treating them
 * as points in 4-dimensional space, because 2D boxes are not enough
 * to represent the quadrant boundaries in 4D space.  They however are
 * sufficient to point out the additional boundaries of the next
 * quadrant.
 *
 * We are using traversal values provided by SP-GiST to calculate and
 * to store the bounds of the quadrants, while traversing into the tree.
 * Traversal value has all the boundaries in the 4D space, and is capable
 * of transferring the required boundaries to the following traversal
 * values.  In conclusion, three things are necessary to calculate the
 * next traversal value:
 *
 *  (1) the traversal value of the parent
 *  (2) the quadrant of the current node
 *  (3) the prefix of the current node
 *
 * If we visualize them on our simplified drawing (see the drawing above);
 * transferred boundaries of (1) would be the outer axis, relevant part
 * of (2) would be the up right part of the other axis, and (3) would be
 * the inner axis.
 *
 * For example, consider the case of overlapping.  When recursion
 * descends deeper and deeper down the tree, all quadrants in
 * the current node will be checked for overlapping.  The boundaries
 * will be re-calculated for all quadrants.  Overlap check answers
 * the question: can any box from this quadrant overlap with the given
 * box?  If yes, then this quadrant will be walked.  If no, then this
 * quadrant will be skipped.
 *
 * This method provides restrictions for minimum and maximum values of
 * every dimension of every corner of the box on every level of the tree
 * except the root.  For the root node, we are setting the boundaries
 * that we don't yet have as infinity.
 *
 * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *          src/backend/utils/adt/geo_spgist.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include "access/spgist.h"
#include "access/spgist_private.h"
#include "access/stratnum.h"
#include "catalog/pg_type.h"
#include "utils/float.h"
#include "utils/fmgroids.h"
#include "utils/fmgrprotos.h"
#include "utils/geo_decls.h"
 
/*
 * Comparator for qsort
 *
 * We don't need to use the floating point macros in here, because this
 * is only going to be used in a place to effect the performance
 * of the index, not the correctness.
 */
static int
compareDoubles(const void *a, const void *b)
{
    float8      x = *(float8 *) a;
    float8      y = *(float8 *) b;
 
    if (x == y)
        return 0;
    return (x > y) ? 1 : -1;
}
 
typedef struct
{
    float8      low;
    float8      high;
} Range;
 
typedef struct
{
    Range       left;
    Range       right;
} RangeBox;
 
typedef struct
{
    RangeBox    range_box_x;
    RangeBox    range_box_y;
} RectBox;
 
/*
 * Calculate the quadrant
 *
 * The quadrant is 8 bit unsigned integer with 4 least bits in use.
 * This function accepts BOXes as input.  They are not casted to
 * RangeBoxes, yet.  All 4 bits are set by comparing a corner of the box.
 * This makes 16 quadrants in total.
 */
static uint8
getQuadrant(BOX *centroid, BOX *inBox)
{
    uint8       quadrant = 0;
 
    if (inBox->low.x > centroid->low.x)
        quadrant |= 0x8;
 
    if (inBox->high.x > centroid->high.x)
        quadrant |= 0x4;
 
    if (inBox->low.y > centroid->low.y)
        quadrant |= 0x2;
 
    if (inBox->high.y > centroid->high.y)
        quadrant |= 0x1;
 
    return quadrant;
}
 
/*
 * Get RangeBox using BOX
 *
 * We are turning the BOX to our structures to emphasize their function
 * of representing points in 4D space.  It also is more convenient to
 * access the values with this structure.
 */
static RangeBox *
getRangeBox(BOX *box)
{
    RangeBox   *range_box = (RangeBox *) palloc(sizeof(RangeBox));
 
    range_box->left.low = box->low.x;
    range_box->left.high = box->high.x;
 
    range_box->right.low = box->low.y;
    range_box->right.high = box->high.y;
 
    return range_box;
}
 
/*
 * Initialize the traversal value
 *
 * In the beginning, we don't have any restrictions.  We have to
 * initialize the struct to cover the whole 4D space.
 */
static RectBox *
initRectBox(void)
{
    RectBox    *rect_box = (RectBox *) palloc(sizeof(RectBox));
    float8      infinity = get_float8_infinity();
 
    rect_box->range_box_x.left.low = -infinity;
    rect_box->range_box_x.left.high = infinity;
 
    rect_box->range_box_x.right.low = -infinity;
    rect_box->range_box_x.right.high = infinity;
 
    rect_box->range_box_y.left.low = -infinity;
    rect_box->range_box_y.left.high = infinity;
 
    rect_box->range_box_y.right.low = -infinity;
    rect_box->range_box_y.right.high = infinity;
 
    return rect_box;
}
 
/*
 * Calculate the next traversal value
 *
 * All centroids are bounded by RectBox, but SP-GiST only keeps
 * boxes.  When we are traversing the tree, we must calculate RectBox,
 * using centroid and quadrant.
 */
static RectBox *
nextRectBox(RectBox *rect_box, RangeBox *centroid, uint8 quadrant)
{
    RectBox    *next_rect_box = (RectBox *) palloc(sizeof(RectBox));
 
    memcpy(next_rect_box, rect_box, sizeof(RectBox));
 
    if (quadrant & 0x8)
        next_rect_box->range_box_x.left.low = centroid->left.low;
    else
        next_rect_box->range_box_x.left.high = centroid->left.low;
 
    if (quadrant & 0x4)
        next_rect_box->range_box_x.right.low = centroid->left.high;
    else
        next_rect_box->range_box_x.right.high = centroid->left.high;
 
    if (quadrant & 0x2)
        next_rect_box->range_box_y.left.low = centroid->right.low;
    else
        next_rect_box->range_box_y.left.high = centroid->right.low;
 
    if (quadrant & 0x1)
        next_rect_box->range_box_y.right.low = centroid->right.high;
    else
        next_rect_box->range_box_y.right.high = centroid->right.high;
 
    return next_rect_box;
}
 
/* Can any range from range_box overlap with this argument? */
static bool
overlap2D(RangeBox *range_box, Range *query)
{
    return FPge(range_box->right.high, query->low) &&
        FPle(range_box->left.low, query->high);
}
 
/* Can any rectangle from rect_box overlap with this argument? */
static bool
overlap4D(RectBox *rect_box, RangeBox *query)
{
    return overlap2D(&rect_box->range_box_x, &query->left) &&
        overlap2D(&rect_box->range_box_y, &query->right);
}
 
/* Can any range from range_box contain this argument? */
static bool
contain2D(RangeBox *range_box, Range *query)
{
    return FPge(range_box->right.high, query->high) &&
        FPle(range_box->left.low, query->low);
}
 
/* Can any rectangle from rect_box contain this argument? */
static bool
contain4D(RectBox *rect_box, RangeBox *query)
{
    return contain2D(&rect_box->range_box_x, &query->left) &&
        contain2D(&rect_box->range_box_y, &query->right);
}
 
/* Can any range from range_box be contained by this argument? */
static bool
contained2D(RangeBox *range_box, Range *query)
{
    return FPle(range_box->left.low, query->high) &&
        FPge(range_box->left.high, query->low) &&
        FPle(range_box->right.low, query->high) &&
        FPge(range_box->right.high, query->low);
}
 
/* Can any rectangle from rect_box be contained by this argument? */
static bool
contained4D(RectBox *rect_box, RangeBox *query)
{
    return contained2D(&rect_box->range_box_x, &query->left) &&
        contained2D(&rect_box->range_box_y, &query->right);
}
 
/* Can any range from range_box to be lower than this argument? */
static bool
lower2D(RangeBox *range_box, Range *query)
{
    return FPlt(range_box->left.low, query->low) &&
        FPlt(range_box->right.low, query->low);
}
 
/* Can any range from range_box not extend to the right side of the query? */
static bool
overLower2D(RangeBox *range_box, Range *query)
{
    return FPle(range_box->left.low, query->high) &&
        FPle(range_box->right.low, query->high);
}
 
/* Can any range from range_box to be higher than this argument? */
static bool
higher2D(RangeBox *range_box, Range *query)
{
    return FPgt(range_box->left.high, query->high) &&
        FPgt(range_box->right.high, query->high);
}
 
/* Can any range from range_box not extend to the left side of the query? */
static bool
overHigher2D(RangeBox *range_box, Range *query)
{
    return FPge(range_box->left.high, query->low) &&
        FPge(range_box->right.high, query->low);
}
 
/* Can any rectangle from rect_box be left of this argument? */
static bool
left4D(RectBox *rect_box, RangeBox *query)
{
    return lower2D(&rect_box->range_box_x, &query->left);
}
 
/* Can any rectangle from rect_box does not extend the right of this argument? */
static bool
overLeft4D(RectBox *rect_box, RangeBox *query)
{
    return overLower2D(&rect_box->range_box_x, &query->left);
}
 
/* Can any rectangle from rect_box be right of this argument? */
static bool
right4D(RectBox *rect_box, RangeBox *query)
{
    return higher2D(&rect_box->range_box_x, &query->left);
}
 
/* Can any rectangle from rect_box does not extend the left of this argument? */
static bool
overRight4D(RectBox *rect_box, RangeBox *query)
{
    return overHigher2D(&rect_box->range_box_x, &query->left);
}
 
/* Can any rectangle from rect_box be below of this argument? */
static bool
below4D(RectBox *rect_box, RangeBox *query)
{
    return lower2D(&rect_box->range_box_y, &query->right);
}
 
/* Can any rectangle from rect_box does not extend above this argument? */
static bool
overBelow4D(RectBox *rect_box, RangeBox *query)
{
    return overLower2D(&rect_box->range_box_y, &query->right);
}
 
/* Can any rectangle from rect_box be above of this argument? */
static bool
above4D(RectBox *rect_box, RangeBox *query)
{
    return higher2D(&rect_box->range_box_y, &query->right);
}
 
/* Can any rectangle from rect_box does not extend below of this argument? */
static bool
overAbove4D(RectBox *rect_box, RangeBox *query)
{
    return overHigher2D(&rect_box->range_box_y, &query->right);
}
 
/* Lower bound for the distance between point and rect_box */
static double
pointToRectBoxDistance(Point *point, RectBox *rect_box)
{
    double      dx;
    double      dy;
 
    if (point->x < rect_box->range_box_x.left.low)
        dx = rect_box->range_box_x.left.low - point->x;
    else if (point->x > rect_box->range_box_x.right.high)
        dx = point->x - rect_box->range_box_x.right.high;
    else
        dx = 0;
 
    if (point->y < rect_box->range_box_y.left.low)
        dy = rect_box->range_box_y.left.low - point->y;
    else if (point->y > rect_box->range_box_y.right.high)
        dy = point->y - rect_box->range_box_y.right.high;
    else
        dy = 0;
 
    return HYPOT(dx, dy);
}
 
 
/*
 * SP-GiST config function
 */
Datum
spg_box_quad_config(PG_FUNCTION_ARGS)
{
    spgConfigOut *cfg = (spgConfigOut *) PG_GETARG_POINTER(1);
 
    cfg->prefixType = BOXOID;
    cfg->labelType = VOIDOID;   /* We don't need node labels. */
    cfg->canReturnData = true;
    cfg->longValuesOK = false;
 
    PG_RETURN_VOID();
}
 
/*
 * SP-GiST choose function
 */
Datum
spg_box_quad_choose(PG_FUNCTION_ARGS)
{
    spgChooseIn *in = (spgChooseIn *) PG_GETARG_POINTER(0);
    spgChooseOut *out = (spgChooseOut *) PG_GETARG_POINTER(1);
    BOX        *centroid = DatumGetBoxP(in->prefixDatum),
               *box = DatumGetBoxP(in->leafDatum);
 
    out->resultType = spgMatchNode;
    out->result.matchNode.restDatum = BoxPGetDatum(box);
 
    /* nodeN will be set by core, when allTheSame. */
    if (!in->allTheSame)
        out->result.matchNode.nodeN = getQuadrant(centroid, box);
 
    PG_RETURN_VOID();
}
 
/*
 * SP-GiST pick-split function
 *
 * It splits a list of boxes into quadrants by choosing a central 4D
 * point as the median of the coordinates of the boxes.
 */
Datum
spg_box_quad_picksplit(PG_FUNCTION_ARGS)
{
    spgPickSplitIn *in = (spgPickSplitIn *) PG_GETARG_POINTER(0);
    spgPickSplitOut *out = (spgPickSplitOut *) PG_GETARG_POINTER(1);
    BOX        *centroid;
    int         median,
                i;
    float8     *lowXs = palloc(sizeof(float8) * in->nTuples);
    float8     *highXs = palloc(sizeof(float8) * in->nTuples);
    float8     *lowYs = palloc(sizeof(float8) * in->nTuples);
    float8     *highYs = palloc(sizeof(float8) * in->nTuples);
 
    /* Calculate median of all 4D coordinates */
    for (i = 0; i < in->nTuples; i++)
    {
        BOX        *box = DatumGetBoxP(in->datums[i]);
 
        lowXs[i] = box->low.x;
        highXs[i] = box->high.x;
        lowYs[i] = box->low.y;
        highYs[i] = box->high.y;
    }
 
    qsort(lowXs, in->nTuples, sizeof(float8), compareDoubles);
    qsort(highXs, in->nTuples, sizeof(float8), compareDoubles);
    qsort(lowYs, in->nTuples, sizeof(float8), compareDoubles);
    qsort(highYs, in->nTuples, sizeof(float8), compareDoubles);
 
    median = in->nTuples / 2;
 
    centroid = palloc(sizeof(BOX));
 
    centroid->low.x = lowXs[median];
    centroid->high.x = highXs[median];
    centroid->low.y = lowYs[median];
    centroid->high.y = highYs[median];
 
    /* Fill the output */
    out->hasPrefix = true;
    out->prefixDatum = BoxPGetDatum(centroid);
 
    out->nNodes = 16;
    out->nodeLabels = NULL;     /* We don't need node labels. */
 
    out->mapTuplesToNodes = palloc(sizeof(int) * in->nTuples);
    out->leafTupleDatums = palloc(sizeof(Datum) * in->nTuples);
 
    /*
     * Assign ranges to corresponding nodes according to quadrants relative to
     * the "centroid" range
     */
    for (i = 0; i < in->nTuples; i++)
    {
        BOX        *box = DatumGetBoxP(in->datums[i]);
        uint8       quadrant = getQuadrant(centroid, box);
 
        out->leafTupleDatums[i] = BoxPGetDatum(box);
        out->mapTuplesToNodes[i] = quadrant;
    }
 
    PG_RETURN_VOID();
}
 
/*
 * Check if result of consistent method based on bounding box is exact.
 */
static bool
is_bounding_box_test_exact(StrategyNumber strategy)
{
    switch (strategy)
    {
        case RTLeftStrategyNumber:
        case RTOverLeftStrategyNumber:
        case RTOverRightStrategyNumber:
        case RTRightStrategyNumber:
        case RTOverBelowStrategyNumber:
        case RTBelowStrategyNumber:
        case RTAboveStrategyNumber:
        case RTOverAboveStrategyNumber:
            return true;
 
        default:
            return false;
    }
}
 
/*
 * Get bounding box for ScanKey.
 */
static BOX *
spg_box_quad_get_scankey_bbox(ScanKey sk, bool *recheck)
{
    switch (sk->sk_subtype)
    {
        case BOXOID:
            return DatumGetBoxP(sk->sk_argument);
 
        case POLYGONOID:
            if (recheck && !is_bounding_box_test_exact(sk->sk_strategy))
                *recheck = true;
            return &DatumGetPolygonP(sk->sk_argument)->boundbox;
 
        default:
            elog(ERROR, "unrecognized scankey subtype: %d", sk->sk_subtype);
            return NULL;
    }
}
 
/*
 * SP-GiST inner consistent function
 */
Datum
spg_box_quad_inner_consistent(PG_FUNCTION_ARGS)
{
    spgInnerConsistentIn *in = (spgInnerConsistentIn *) PG_GETARG_POINTER(0);
    spgInnerConsistentOut *out = (spgInnerConsistentOut *) PG_GETARG_POINTER(1);
    int         i;
    MemoryContext old_ctx;
    RectBox    *rect_box;
    uint8       quadrant;
    RangeBox   *centroid,
              **queries;
 
    /*
     * We are saving the traversal value or initialize it an unbounded one, if
     * we have just begun to walk the tree.
     */
    if (in->traversalValue)
        rect_box = in->traversalValue;
    else
        rect_box = initRectBox();
 
    if (in->allTheSame)
    {
        /* Report that all nodes should be visited */
        out->nNodes = in->nNodes;
        out->nodeNumbers = (int *) palloc(sizeof(int) * in->nNodes);
        for (i = 0; i < in->nNodes; i++)
            out->nodeNumbers[i] = i;
 
        if (in->norderbys > 0 && in->nNodes > 0)
        {
            double     *distances = palloc(sizeof(double) * in->norderbys);
            int         j;
 
            for (j = 0; j < in->norderbys; j++)
            {
                Point      *pt = DatumGetPointP(in->orderbys[j].sk_argument);
 
                distances[j] = pointToRectBoxDistance(pt, rect_box);
            }
 
            out->distances = (double **) palloc(sizeof(double *) * in->nNodes);
            out->distances[0] = distances;
 
            for (i = 1; i < in->nNodes; i++)
            {
                out->distances[i] = palloc(sizeof(double) * in->norderbys);
                memcpy(out->distances[i], distances,
                       sizeof(double) * in->norderbys);
            }
        }
 
        PG_RETURN_VOID();
    }
 
    /*
     * We are casting the prefix and queries to RangeBoxes for ease of the
     * following operations.
     */
    centroid = getRangeBox(DatumGetBoxP(in->prefixDatum));
    queries = (RangeBox **) palloc(in->nkeys * sizeof(RangeBox *));
    for (i = 0; i < in->nkeys; i++)
    {
        BOX        *box = spg_box_quad_get_scankey_bbox(&in->scankeys[i], NULL);
 
        queries[i] = getRangeBox(box);
    }
 
    /* Allocate enough memory for nodes */
    out->nNodes = 0;
    out->nodeNumbers = (int *) palloc(sizeof(int) * in->nNodes);
    out->traversalValues = (void **) palloc(sizeof(void *) * in->nNodes);
    if (in->norderbys > 0)
        out->distances = (double **) palloc(sizeof(double *) * in->nNodes);
 
    /*
     * We switch memory context, because we want to allocate memory for new
     * traversal values (next_rect_box) and pass these pieces of memory to
     * further call of this function.
     */
    old_ctx = MemoryContextSwitchTo(in->traversalMemoryContext);
 
    for (quadrant = 0; quadrant < in->nNodes; quadrant++)
    {
        RectBox    *next_rect_box = nextRectBox(rect_box, centroid, quadrant);
        bool        flag = true;
 
        for (i = 0; i < in->nkeys; i++)
        {
            StrategyNumber strategy = in->scankeys[i].sk_strategy;
 
            switch (strategy)
            {
                case RTOverlapStrategyNumber:
                    flag = overlap4D(next_rect_box, queries[i]);
                    break;
 
                case RTContainsStrategyNumber:
                    flag = contain4D(next_rect_box, queries[i]);
                    break;
 
                case RTSameStrategyNumber:
                case RTContainedByStrategyNumber:
                    flag = contained4D(next_rect_box, queries[i]);
                    break;
 
                case RTLeftStrategyNumber:
                    flag = left4D(next_rect_box, queries[i]);
                    break;
 
                case RTOverLeftStrategyNumber:
                    flag = overLeft4D(next_rect_box, queries[i]);
                    break;
 
                case RTRightStrategyNumber:
                    flag = right4D(next_rect_box, queries[i]);
                    break;
 
                case RTOverRightStrategyNumber:
                    flag = overRight4D(next_rect_box, queries[i]);
                    break;
 
                case RTAboveStrategyNumber:
                    flag = above4D(next_rect_box, queries[i]);
                    break;
 
                case RTOverAboveStrategyNumber:
                    flag = overAbove4D(next_rect_box, queries[i]);
                    break;
 
                case RTBelowStrategyNumber:
                    flag = below4D(next_rect_box, queries[i]);
                    break;
 
                case RTOverBelowStrategyNumber:
                    flag = overBelow4D(next_rect_box, queries[i]);
                    break;
 
                default:
                    elog(ERROR, "unrecognized strategy: %d", strategy);
            }
 
            /* If any check is failed, we have found our answer. */
            if (!flag)
                break;
        }
 
        if (flag)
        {
            out->traversalValues[out->nNodes] = next_rect_box;
            out->nodeNumbers[out->nNodes] = quadrant;
 
            if (in->norderbys > 0)
            {
                double     *distances = palloc(sizeof(double) * in->norderbys);
                int         j;
 
                out->distances[out->nNodes] = distances;
 
                for (j = 0; j < in->norderbys; j++)
                {
                    Point      *pt = DatumGetPointP(in->orderbys[j].sk_argument);
 
                    distances[j] = pointToRectBoxDistance(pt, next_rect_box);
                }
            }
 
            out->nNodes++;
        }
        else
        {
            /*
             * If this node is not selected, we don't need to keep the next
             * traversal value in the memory context.
             */
            pfree(next_rect_box);
        }
    }
 
    /* Switch back */
    MemoryContextSwitchTo(old_ctx);
 
    PG_RETURN_VOID();
}
 
/*
 * SP-GiST inner consistent function
 */
Datum
spg_box_quad_leaf_consistent(PG_FUNCTION_ARGS)
{
    spgLeafConsistentIn *in = (spgLeafConsistentIn *) PG_GETARG_POINTER(0);
    spgLeafConsistentOut *out = (spgLeafConsistentOut *) PG_GETARG_POINTER(1);
    Datum       leaf = in->leafDatum;
    bool        flag = true;
    int         i;
 
    /* All tests are exact. */
    out->recheck = false;
 
    /*
     * Don't return leafValue unless told to; this is used for both box and
     * polygon opclasses, and in the latter case the leaf datum is not even of
     * the right type to return.
     */
    if (in->returnData)
        out->leafValue = leaf;
 
    /* Perform the required comparison(s) */
    for (i = 0; i < in->nkeys; i++)
    {
        StrategyNumber strategy = in->scankeys[i].sk_strategy;
        BOX        *box = spg_box_quad_get_scankey_bbox(&in->scankeys[i],
                                                        &out->recheck);
        Datum       query = BoxPGetDatum(box);
 
        switch (strategy)
        {
            case RTOverlapStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_overlap, leaf,
                                                        query));
                break;
 
            case RTContainsStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_contain, leaf,
                                                        query));
                break;
 
            case RTContainedByStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_contained, leaf,
                                                        query));
                break;
 
            case RTSameStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_same, leaf,
                                                        query));
                break;
 
            case RTLeftStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_left, leaf,
                                                        query));
                break;
 
            case RTOverLeftStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_overleft, leaf,
                                                        query));
                break;
 
            case RTRightStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_right, leaf,
                                                        query));
                break;
 
            case RTOverRightStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_overright, leaf,
                                                        query));
                break;
 
            case RTAboveStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_above, leaf,
                                                        query));
                break;
 
            case RTOverAboveStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_overabove, leaf,
                                                        query));
                break;
 
            case RTBelowStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_below, leaf,
                                                        query));
                break;
 
            case RTOverBelowStrategyNumber:
                flag = DatumGetBool(DirectFunctionCall2(box_overbelow, leaf,
                                                        query));
                break;
 
            default:
                elog(ERROR, "unrecognized strategy: %d", strategy);
        }
 
        /* If any check is failed, we have found our answer. */
        if (!flag)
            break;
    }
 
    if (flag && in->norderbys > 0)
    {
        Oid         distfnoid = in->orderbys[0].sk_func.fn_oid;
 
        out->distances = spg_key_orderbys_distances(leaf, false,
                                                    in->orderbys, in->norderbys);
 
        /* Recheck is necessary when computing distance to polygon */
        out->recheckDistances = distfnoid == F_DIST_POLYP;
    }
 
    PG_RETURN_BOOL(flag);
}
 
 
/*
 * SP-GiST config function for 2-D types that are lossy represented by their
 * bounding boxes
 */
Datum
spg_bbox_quad_config(PG_FUNCTION_ARGS)
{
    spgConfigOut *cfg = (spgConfigOut *) PG_GETARG_POINTER(1);
 
    cfg->prefixType = BOXOID;   /* A type represented by its bounding box */
    cfg->labelType = VOIDOID;   /* We don't need node labels. */
    cfg->leafType = BOXOID;
    cfg->canReturnData = false;
    cfg->longValuesOK = false;
 
    PG_RETURN_VOID();
}
 
/*
 * SP-GiST compress function for polygons
 */
Datum
spg_poly_quad_compress(PG_FUNCTION_ARGS)
{
    POLYGON    *polygon = PG_GETARG_POLYGON_P(0);
    BOX        *box;
 
    box = (BOX *) palloc(sizeof(BOX));
    *box = polygon->boundbox;
 
    PG_RETURN_BOX_P(box);
}