gserialized_spgist_2d.c

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/*****************************************************************************
 *
 * gserialized_spgist_2d.c
 *        SP-GiST implementation of 4-dimensional quad-tree over box2df
 *
 * 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 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 2:
 *
 *                              |          |
 *                              |          |
 *                              | -----+-----
 *                              |          |
 *                              |          |
 * -------------+-------------
 *                              |
 *                              |
 *                              |
 *                              |
 *                              |
 *                        FRONT
 *
 * We are using box data type as the prefix, but we are treating them
 * as points in 4-dimensional space, because  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 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 range_y 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) 2018, Esteban Zimanyi, Arthur Lesuisse,
 *              Université Libre de Bruxelles
 * Portions Copyright (c) 1996-2016, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *****************************************************************************/
 
#include <postgres.h>
#include <utils/builtins.h>    /* For float manipulation */
#include "access/spgist.h"     /* For SP-GiST */
#include "catalog/pg_type_d.h" /* For VOIDOID */
 
#include "../postgis_config.h"
 
#include "liblwgeom.h"        /* For standard geometry types. */
#include "lwgeom_pg.h"        /* For debugging macros. */
#include <gserialized_gist.h> /* For utility functions. */
#include <lwgeom_pg.h>        /* For debugging macros. */
#include <math.h>
 
/*
** SP-GiST 2D index function prototypes
*/
 
Datum gserialized_spgist_config_2d(PG_FUNCTION_ARGS);
Datum gserialized_spgist_choose_2d(PG_FUNCTION_ARGS);
Datum gserialized_spgist_picksplit_2d(PG_FUNCTION_ARGS);
Datum gserialized_spgist_inner_consistent_2d(PG_FUNCTION_ARGS);
Datum gserialized_spgist_leaf_consistent_2d(PG_FUNCTION_ARGS);
Datum gserialized_spgist_compress_2d(PG_FUNCTION_ARGS);
 
/*
 * 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)
{
        double x = *(double *)a;
        double y = *(double *)b;
 
        if (x == y)
                return 0;
        return (x > y) ? 1 : -1;
}
 
typedef struct
{
        BOX2DF left;
        BOX2DF right;
} RectBox;
 
/*
 * Calculate the quadrant
 *
 * The quadrant is 4 bit unsigned integer with 4 least bits in use.
 * This function accepts 2 BOX2DF as input.  All 4 bits are set by comparing
 * a corner of the box. This makes 16 quadrants in total.
 */
static uint8
getQuadrant4D(BOX2DF *centroid, BOX2DF *inBox)
{
        uint8 quadrant = 0;
 
        if (inBox->xmin > centroid->xmin)
                quadrant |= 0x8;
 
        if (inBox->xmax > centroid->xmax)
                quadrant |= 0x4;
 
        if (inBox->ymin > centroid->ymin)
                quadrant |= 0x2;
 
        if (inBox->ymax > centroid->ymax)
                quadrant |= 0x1;
 
        return quadrant;
}
 
/*
 * 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));
        float infinity = FLT_MAX;
 
        rect_box->left.xmin = -infinity;
        rect_box->left.xmax = infinity;
 
        rect_box->left.ymin = -infinity;
        rect_box->left.ymax = infinity;
 
        rect_box->right.xmin = -infinity;
        rect_box->right.xmax = infinity;
 
        rect_box->right.ymin = -infinity;
        rect_box->right.ymax = 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, BOX2DF *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->left.xmin = centroid->xmin;
        else
                next_rect_box->left.xmax = centroid->xmin;
 
        if (quadrant & 0x4)
                next_rect_box->right.xmin = centroid->xmax;
        else
                next_rect_box->right.xmax = centroid->xmax;
 
        if (quadrant & 0x2)
                next_rect_box->left.ymin = centroid->ymin;
        else
                next_rect_box->left.ymax = centroid->ymin;
 
        if (quadrant & 0x1)
                next_rect_box->right.ymin = centroid->ymax;
        else
                next_rect_box->right.ymax = centroid->ymax;
 
        return next_rect_box;
}
 
/* Can any cube from rect_box overlap with query? */
static bool
overlap4D(RectBox *rect_box, BOX2DF *query)
{
        return (rect_box->left.xmin <= query->xmax && rect_box->right.xmax >= query->xmin) &&
               (rect_box->left.ymin <= query->ymax && rect_box->right.ymax >= query->ymin);
}
 
/* Can any cube from rect_box contain query? */
static bool
contain4D(RectBox *rect_box, BOX2DF *query)
{
        return (rect_box->right.xmax >= query->xmax && rect_box->left.xmin <= query->xmin) &&
               (rect_box->right.ymax >= query->ymax && rect_box->left.ymin <= query->ymin);
}
 
/* Can any cube from rect_box be left of query? */
static bool
left4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->right.xmax <= query->xmin;
}
 
/* Can any cube from rect_box does not extend the right of query? */
static bool
overLeft4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->right.xmax <= query->xmax;
}
 
/* Can any cube from rect_box be right of query? */
static bool
right4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->left.xmin >= query->xmax;
}
 
/* Can any cube from rect_box does not extend the left of query? */
static bool
overRight4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->left.xmin >= query->xmin;
}
 
/* Can any cube from rect_box be below of query? */
static bool
below4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->right.ymax <= query->ymin;
}
 
/* Can any cube from rect_box does not extend above query? */
static bool
overBelow4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->right.ymax <= query->ymax;
}
 
/* Can any cube from rect_box be above of query? */
static bool
above4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->left.ymin >= query->ymax;
}
 
/* Can any cube from rect_box does not extend below of query? */
static bool
overAbove4D(RectBox *rect_box, BOX2DF *query)
{
        return rect_box->left.ymin >= query->ymin;
}
 
/*
 * SP-GiST config function
 */
 
PG_FUNCTION_INFO_V1(gserialized_spgist_config_2d);
 
PGDLLEXPORT Datum gserialized_spgist_config_2d(PG_FUNCTION_ARGS)
{
        spgConfigOut *cfg = (spgConfigOut *)PG_GETARG_POINTER(1);
        Oid boxoid = InvalidOid;
        /* We need to initialize the internal cache to access it later via postgis_oid() */
        postgis_initialize_cache();
        boxoid = postgis_oid(BOX2DFOID);
 
        cfg->prefixType = boxoid;
        cfg->labelType = VOIDOID; /* We don't need node labels. */
        cfg->leafType = boxoid;
        cfg->canReturnData = false;
        cfg->longValuesOK = false;
 
        PG_RETURN_VOID();
}
 
/*
 * SP-GiST choose function
 */
 
PG_FUNCTION_INFO_V1(gserialized_spgist_choose_2d);
 
PGDLLEXPORT Datum gserialized_spgist_choose_2d(PG_FUNCTION_ARGS)
{
        spgChooseIn *in = (spgChooseIn *)PG_GETARG_POINTER(0);
        spgChooseOut *out = (spgChooseOut *)PG_GETARG_POINTER(1);
        BOX2DF *centroid = (BOX2DF *)DatumGetPointer(in->prefixDatum), *box = (BOX2DF *)DatumGetPointer(in->leafDatum);
 
        out->resultType = spgMatchNode;
        out->result.matchNode.restDatum = PointerGetDatum(box);
 
        /* nodeN will be set by core, when allTheSame. */
        if (!in->allTheSame)
                out->result.matchNode.nodeN = getQuadrant4D(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.
 */
PG_FUNCTION_INFO_V1(gserialized_spgist_picksplit_2d);
 
PGDLLEXPORT Datum gserialized_spgist_picksplit_2d(PG_FUNCTION_ARGS)
{
        spgPickSplitIn *in = (spgPickSplitIn *)PG_GETARG_POINTER(0);
        spgPickSplitOut *out = (spgPickSplitOut *)PG_GETARG_POINTER(1);
        BOX2DF *centroid;
        int median, i;
        double *lowXs = palloc(sizeof(double) * in->nTuples);
        double *highXs = palloc(sizeof(double) * in->nTuples);
        double *lowYs = palloc(sizeof(double) * in->nTuples);
        double *highYs = palloc(sizeof(double) * in->nTuples);
 
        /* Calculate median of all 4D coordinates */
        for (i = 0; i < in->nTuples; i++)
        {
                BOX2DF *box = (BOX2DF *)DatumGetPointer(in->datums[i]);
 
                lowXs[i] = (double)box->xmin;
                highXs[i] = (double)box->xmax;
                lowYs[i] = (double)box->ymin;
                highYs[i] = (double)box->ymax;
        }
 
        qsort(lowXs, in->nTuples, sizeof(double), compareDoubles);
        qsort(highXs, in->nTuples, sizeof(double), compareDoubles);
        qsort(lowYs, in->nTuples, sizeof(double), compareDoubles);
        qsort(highYs, in->nTuples, sizeof(double), compareDoubles);
 
        median = in->nTuples / 2;
 
        centroid = palloc(sizeof(BOX2DF));
 
        centroid->xmin = (float)lowXs[median];
        centroid->xmax = (float)highXs[median];
        centroid->ymin = (float)lowYs[median];
        centroid->ymax = (float)highYs[median];
 
        /* Fill the output */
        out->hasPrefix = true;
        out->prefixDatum = PointerGetDatum(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++)
        {
                BOX2DF *box = (BOX2DF *)DatumGetPointer(in->datums[i]);
                uint8 quadrant = getQuadrant4D(centroid, box);
 
                out->leafTupleDatums[i] = PointerGetDatum(box);
                out->mapTuplesToNodes[i] = quadrant;
        }
 
        pfree(lowXs);
        pfree(highXs);
        pfree(lowYs);
        pfree(highYs);
 
        PG_RETURN_VOID();
}
 
/*
 * SP-GiST inner consistent function
 */
PG_FUNCTION_INFO_V1(gserialized_spgist_inner_consistent_2d);
 
PGDLLEXPORT Datum gserialized_spgist_inner_consistent_2d(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;
        BOX2DF *centroid;
 
        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;
 
                PG_RETURN_VOID();
        }
 
        /*
         * 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();
 
        centroid = (BOX2DF *)DatumGetPointer(in->prefixDatum);
 
        /* Allocate enough memory for nodes */
        out->nNodes = 0;
        out->nodeNumbers = (int *)palloc(sizeof(int) * in->nNodes);
        out->traversalValues = (void **)palloc(sizeof(void *) * 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 < (uint8)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;
 
                        Datum query = in->scankeys[i].sk_argument;
                        BOX2DF query_gbox_index;
 
                        /* Quick sanity check on query argument. */
                        if (DatumGetPointer(query) == NULL)
                        {
                                POSTGIS_DEBUG(4, "[SPGIST] null query pointer (!?!), returning false");
                                PG_RETURN_BOOL(false); /* NULL query! This is screwy! */
                        }
 
                        if (gserialized_datum_get_box2df_p(query, &query_gbox_index) == LW_FAILURE)
                        {
                                POSTGIS_DEBUG(4, "[SPGIST] null query_gbox_index!");
                                PG_RETURN_BOOL(false);
                        }
 
                        switch (strategy)
                        {
                        case RTOverlapStrategyNumber:
                        case RTContainedByStrategyNumber:
                        case RTOldContainedByStrategyNumber:
                                flag = overlap4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTContainsStrategyNumber:
                        case RTSameStrategyNumber:
                                flag = contain4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTLeftStrategyNumber:
                                flag = !overRight4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTOverLeftStrategyNumber:
                                flag = !right4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTRightStrategyNumber:
                                flag = !overLeft4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTOverRightStrategyNumber:
                                flag = !left4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTAboveStrategyNumber:
                                flag = !overBelow4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTOverAboveStrategyNumber:
                                flag = !below4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTBelowStrategyNumber:
                                flag = !overAbove4D(next_rect_box, &query_gbox_index);
                                break;
 
                        case RTOverBelowStrategyNumber:
                                flag = !above4D(next_rect_box, &query_gbox_index);
                                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;
                        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 after */
        MemoryContextSwitchTo(old_ctx);
 
        PG_RETURN_VOID();
}
 
/*
 * SP-GiST inner consistent function
 */
PG_FUNCTION_INFO_V1(gserialized_spgist_leaf_consistent_2d);
 
PGDLLEXPORT Datum gserialized_spgist_leaf_consistent_2d(PG_FUNCTION_ARGS)
{
        spgLeafConsistentIn *in = (spgLeafConsistentIn *)PG_GETARG_POINTER(0);
        spgLeafConsistentOut *out = (spgLeafConsistentOut *)PG_GETARG_POINTER(1);
        BOX2DF *key = (BOX2DF *)DatumGetPointer(in->leafDatum);
        bool flag = true;
        int i;
 
        /* Quick sanity check on entry key. */
        if (key == NULL)
        {
                POSTGIS_DEBUG(4, "[SPGIST] null index entry, returning false");
                PG_RETURN_BOOL(false); /* NULL entry! */
        }
 
        /* All tests are exact. */
        out->recheck = false;
 
        /* leafDatum is what it is... */
        out->leafValue = in->leafDatum;
 
        /* Perform the required comparison(s) */
        for (i = 0; i < in->nkeys; i++)
        {
                StrategyNumber strategy = in->scankeys[i].sk_strategy;
                Datum query = in->scankeys[i].sk_argument;
                BOX2DF query_gbox_index;
 
                /* Quick sanity check on query argument. */
                if (DatumGetPointer(query) == NULL)
                {
                        POSTGIS_DEBUG(4, "[SPGIST] null query pointer (!?!), returning false");
                        PG_RETURN_BOOL(false); /* NULL query! This is screwy! */
                }
 
                if (gserialized_datum_get_box2df_p(query, &query_gbox_index) == LW_FAILURE)
                {
                        POSTGIS_DEBUG(4, "[SPGIST] null query_gbox_index!");
                        PG_RETURN_BOOL(false);
                }
 
                switch (strategy)
                {
                case RTOverlapStrategyNumber:
                        flag = box2df_overlaps(key, &query_gbox_index);
                        break;
 
                case RTContainsStrategyNumber:
                case RTOldContainsStrategyNumber:
                        flag = box2df_contains(key, &query_gbox_index);
                        break;
 
                case RTContainedByStrategyNumber:
                case RTOldContainedByStrategyNumber:
                        flag = box2df_contains(&query_gbox_index, key);
                        break;
 
                case RTSameStrategyNumber:
                        flag = box2df_equals(key, &query_gbox_index);
                        break;
 
                case RTLeftStrategyNumber:
                        flag = box2df_left(key, &query_gbox_index);
                        break;
 
                case RTOverLeftStrategyNumber:
                        flag = box2df_overleft(key, &query_gbox_index);
                        break;
 
                case RTRightStrategyNumber:
                        flag = box2df_right(key, &query_gbox_index);
                        break;
 
                case RTOverRightStrategyNumber:
                        flag = box2df_overright(key, &query_gbox_index);
                        break;
 
                case RTAboveStrategyNumber:
                        flag = box2df_above(key, &query_gbox_index);
                        break;
 
                case RTOverAboveStrategyNumber:
                        flag = box2df_overabove(key, &query_gbox_index);
                        break;
 
                case RTBelowStrategyNumber:
                        flag = box2df_below(key, &query_gbox_index);
                        break;
 
                case RTOverBelowStrategyNumber:
                        flag = box2df_overbelow(key, &query_gbox_index);
                        break;
 
                default:
                        elog(ERROR, "unrecognized strategy: %d", strategy);
                }
 
                /* If any check is failed, we have found our answer. */
                if (!flag)
                        break;
        }
 
        PG_RETURN_BOOL(flag);
}
 
PG_FUNCTION_INFO_V1(gserialized_spgist_compress_2d);
 
PGDLLEXPORT Datum gserialized_spgist_compress_2d(PG_FUNCTION_ARGS)
{
        Datum gsdatum = PG_GETARG_DATUM(0);
        BOX2DF *bbox_out = palloc(sizeof(BOX2DF));
        int result = LW_SUCCESS;
 
        POSTGIS_DEBUG(4, "[SPGIST] 'compress' function called");
 
        /* Extract the index key from the argument. */
        result = gserialized_datum_get_box2df_p(gsdatum, bbox_out);
 
        /* Is the bounding box valid (non-empty, non-infinite)? If not, return input uncompressed. */
        if (result == LW_FAILURE)
        {
                box2df_set_empty(bbox_out);
 
                POSTGIS_DEBUG(4, "[SPGIST] empty geometry!");
                PG_RETURN_POINTER(bbox_out);
        }
 
        /* Check all the dimensions for finite values */
        if ((!isfinite(bbox_out->xmax) || !isfinite(bbox_out->xmin)) ||
            (!isfinite(bbox_out->ymax) || !isfinite(bbox_out->ymin)))
        {
                box2df_set_finite(bbox_out);
 
                POSTGIS_DEBUG(4, "[SPGIST] infinite geometry!");
                PG_RETURN_POINTER(bbox_out);
        }
 
        /* Ensure bounding box has minimums below maximums. */
        box2df_validate(bbox_out);
 
        /* Return BOX2DF. */
        POSTGIS_DEBUG(4, "[SPGIST] 'compress' function complete");
        PG_RETURN_POINTER(bbox_out);
}
 
/*****************************************************************************/