cube.c

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/******************************************************************************
  contrib/cube/cube.c

  This file contains routines that can be bound to a Postgres backend and
  called by the backend in the process of processing queries.  The calling
  format for these routines is dictated by Postgres architecture.
******************************************************************************/

#include "postgres.h"

#include <math.h>

#include "access/gist.h"
#include "access/stratnum.h"
#include "cubedata.h"
#include "utils/array.h"
#include "utils/float.h"

PG_MODULE_MAGIC;

/*
 * Taken from the intarray contrib header
 */
#define ARRPTR(x)  ( (double *) ARR_DATA_PTR(x) )
#define ARRNELEMS(x)  ArrayGetNItems( ARR_NDIM(x), ARR_DIMS(x))

/*
** Input/Output routines
*/
PG_FUNCTION_INFO_V1(cube_in);
PG_FUNCTION_INFO_V1(cube_a_f8_f8);
PG_FUNCTION_INFO_V1(cube_a_f8);
PG_FUNCTION_INFO_V1(cube_out);
PG_FUNCTION_INFO_V1(cube_f8);
PG_FUNCTION_INFO_V1(cube_f8_f8);
PG_FUNCTION_INFO_V1(cube_c_f8);
PG_FUNCTION_INFO_V1(cube_c_f8_f8);
PG_FUNCTION_INFO_V1(cube_dim);
PG_FUNCTION_INFO_V1(cube_ll_coord);
PG_FUNCTION_INFO_V1(cube_ur_coord);
PG_FUNCTION_INFO_V1(cube_coord);
PG_FUNCTION_INFO_V1(cube_coord_llur);
PG_FUNCTION_INFO_V1(cube_subset);

/*
** GiST support methods
*/

PG_FUNCTION_INFO_V1(g_cube_consistent);
PG_FUNCTION_INFO_V1(g_cube_compress);
PG_FUNCTION_INFO_V1(g_cube_decompress);
PG_FUNCTION_INFO_V1(g_cube_penalty);
PG_FUNCTION_INFO_V1(g_cube_picksplit);
PG_FUNCTION_INFO_V1(g_cube_union);
PG_FUNCTION_INFO_V1(g_cube_same);
PG_FUNCTION_INFO_V1(g_cube_distance);

/*
** B-tree support functions
*/
PG_FUNCTION_INFO_V1(cube_eq);
PG_FUNCTION_INFO_V1(cube_ne);
PG_FUNCTION_INFO_V1(cube_lt);
PG_FUNCTION_INFO_V1(cube_gt);
PG_FUNCTION_INFO_V1(cube_le);
PG_FUNCTION_INFO_V1(cube_ge);
PG_FUNCTION_INFO_V1(cube_cmp);

/*
** R-tree support functions
*/

PG_FUNCTION_INFO_V1(cube_contains);
PG_FUNCTION_INFO_V1(cube_contained);
PG_FUNCTION_INFO_V1(cube_overlap);
PG_FUNCTION_INFO_V1(cube_union);
PG_FUNCTION_INFO_V1(cube_inter);
PG_FUNCTION_INFO_V1(cube_size);

/*
** miscellaneous
*/
PG_FUNCTION_INFO_V1(distance_taxicab);
PG_FUNCTION_INFO_V1(cube_distance);
PG_FUNCTION_INFO_V1(distance_chebyshev);
PG_FUNCTION_INFO_V1(cube_is_point);
PG_FUNCTION_INFO_V1(cube_enlarge);

/*
** For internal use only
*/
int32       cube_cmp_v0(NDBOX *a, NDBOX *b);
bool        cube_contains_v0(NDBOX *a, NDBOX *b);
bool        cube_overlap_v0(NDBOX *a, NDBOX *b);
NDBOX      *cube_union_v0(NDBOX *a, NDBOX *b);
void        rt_cube_size(NDBOX *a, double *sz);
NDBOX      *g_cube_binary_union(NDBOX *r1, NDBOX *r2, int *sizep);
bool        g_cube_leaf_consistent(NDBOX *key, NDBOX *query, StrategyNumber strategy);
bool        g_cube_internal_consistent(NDBOX *key, NDBOX *query, StrategyNumber strategy);

/*
** Auxiliary functions
*/
static double distance_1D(double a1, double a2, double b1, double b2);
static bool cube_is_point_internal(NDBOX *cube);


/*****************************************************************************
 * Input/Output functions
 *****************************************************************************/

/* NdBox = [(lowerleft),(upperright)] */
/* [(xLL(1)...xLL(N)),(xUR(1)...xUR(n))] */
Datum
cube_in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    NDBOX      *result;

    cube_scanner_init(str);

    if (cube_yyparse(&result) != 0)
        cube_yyerror(&result, "cube parser failed");

    cube_scanner_finish();

    PG_RETURN_NDBOX_P(result);
}


/*
** Allows the construction of a cube from 2 float[]'s
*/
Datum
cube_a_f8_f8(PG_FUNCTION_ARGS)
{
    ArrayType  *ur = PG_GETARG_ARRAYTYPE_P(0);
    ArrayType  *ll = PG_GETARG_ARRAYTYPE_P(1);
    NDBOX      *result;
    int         i;
    int         dim;
    int         size;
    bool        point;
    double     *dur,
               *dll;

    if (array_contains_nulls(ur) || array_contains_nulls(ll))
        ereport(ERROR,
                (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                 errmsg("cannot work with arrays containing NULLs")));

    dim = ARRNELEMS(ur);
    if (dim > CUBE_MAX_DIM)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("can't extend cube"),
                 errdetail("A cube cannot have more than %d dimensions.",
                           CUBE_MAX_DIM)));

    if (ARRNELEMS(ll) != dim)
        ereport(ERROR,
                (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                 errmsg("UR and LL arrays must be of same length")));

    dur = ARRPTR(ur);
    dll = ARRPTR(ll);

    /* Check if it's a point */
    point = true;
    for (i = 0; i < dim; i++)
    {
        if (dur[i] != dll[i])
        {
            point = false;
            break;
        }
    }

    size = point ? POINT_SIZE(dim) : CUBE_SIZE(dim);
    result = (NDBOX *) palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, dim);

    for (i = 0; i < dim; i++)
        result->x[i] = dur[i];

    if (!point)
    {
        for (i = 0; i < dim; i++)
            result->x[i + dim] = dll[i];
    }
    else
        SET_POINT_BIT(result);

    PG_RETURN_NDBOX_P(result);
}

/*
** Allows the construction of a zero-volume cube from a float[]
*/
Datum
cube_a_f8(PG_FUNCTION_ARGS)
{
    ArrayType  *ur = PG_GETARG_ARRAYTYPE_P(0);
    NDBOX      *result;
    int         i;
    int         dim;
    int         size;
    double     *dur;

    if (array_contains_nulls(ur))
        ereport(ERROR,
                (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                 errmsg("cannot work with arrays containing NULLs")));

    dim = ARRNELEMS(ur);
    if (dim > CUBE_MAX_DIM)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("array is too long"),
                 errdetail("A cube cannot have more than %d dimensions.",
                           CUBE_MAX_DIM)));

    dur = ARRPTR(ur);

    size = POINT_SIZE(dim);
    result = (NDBOX *) palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, dim);
    SET_POINT_BIT(result);

    for (i = 0; i < dim; i++)
        result->x[i] = dur[i];

    PG_RETURN_NDBOX_P(result);
}

Datum
cube_subset(PG_FUNCTION_ARGS)
{
    NDBOX      *c = PG_GETARG_NDBOX_P(0);
    ArrayType  *idx = PG_GETARG_ARRAYTYPE_P(1);
    NDBOX      *result;
    int         size,
                dim,
                i;
    int        *dx;

    if (array_contains_nulls(idx))
        ereport(ERROR,
                (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                 errmsg("cannot work with arrays containing NULLs")));

    dx = (int32 *) ARR_DATA_PTR(idx);

    dim = ARRNELEMS(idx);
    if (dim > CUBE_MAX_DIM)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("array is too long"),
                 errdetail("A cube cannot have more than %d dimensions.",
                           CUBE_MAX_DIM)));

    size = IS_POINT(c) ? POINT_SIZE(dim) : CUBE_SIZE(dim);
    result = (NDBOX *) palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, dim);

    if (IS_POINT(c))
        SET_POINT_BIT(result);

    for (i = 0; i < dim; i++)
    {
        if ((dx[i] <= 0) || (dx[i] > DIM(c)))
            ereport(ERROR,
                    (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                     errmsg("Index out of bounds")));
        result->x[i] = c->x[dx[i] - 1];
        if (!IS_POINT(c))
            result->x[i + dim] = c->x[dx[i] + DIM(c) - 1];
    }

    PG_FREE_IF_COPY(c, 0);
    PG_RETURN_NDBOX_P(result);
}

Datum
cube_out(PG_FUNCTION_ARGS)
{
    NDBOX      *cube = PG_GETARG_NDBOX_P(0);
    StringInfoData buf;
    int         dim = DIM(cube);
    int         i;

    initStringInfo(&buf);

    appendStringInfoChar(&buf, '(');
    for (i = 0; i < dim; i++)
    {
        if (i > 0)
            appendStringInfoString(&buf, ", ");
        appendStringInfoString(&buf, float8out_internal(LL_COORD(cube, i)));
    }
    appendStringInfoChar(&buf, ')');

    if (!cube_is_point_internal(cube))
    {
        appendStringInfoString(&buf, ",(");
        for (i = 0; i < dim; i++)
        {
            if (i > 0)
                appendStringInfoString(&buf, ", ");
            appendStringInfoString(&buf, float8out_internal(UR_COORD(cube, i)));
        }
        appendStringInfoChar(&buf, ')');
    }

    PG_FREE_IF_COPY(cube, 0);
    PG_RETURN_CSTRING(buf.data);
}


/*****************************************************************************
 *                         GiST functions
 *****************************************************************************/

/*
** The GiST Consistent method for boxes
** Should return false if for all data items x below entry,
** the predicate x op query == false, where op is the oper
** corresponding to strategy in the pg_amop table.
*/
Datum
g_cube_consistent(PG_FUNCTION_ARGS)
{
    GISTENTRY  *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
    NDBOX      *query = PG_GETARG_NDBOX_P(1);
    StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);

    /* Oid      subtype = PG_GETARG_OID(3); */
    bool       *recheck = (bool *) PG_GETARG_POINTER(4);
    bool        res;

    /* All cases served by this function are exact */
    *recheck = false;

    /*
     * if entry is not leaf, use g_cube_internal_consistent, else use
     * g_cube_leaf_consistent
     */
    if (GIST_LEAF(entry))
        res = g_cube_leaf_consistent(DatumGetNDBOXP(entry->key),
                                     query, strategy);
    else
        res = g_cube_internal_consistent(DatumGetNDBOXP(entry->key),
                                         query, strategy);

    PG_FREE_IF_COPY(query, 1);
    PG_RETURN_BOOL(res);
}


/*
** The GiST Union method for boxes
** returns the minimal bounding box that encloses all the entries in entryvec
*/
Datum
g_cube_union(PG_FUNCTION_ARGS)
{
    GistEntryVector *entryvec = (GistEntryVector *) PG_GETARG_POINTER(0);
    int        *sizep = (int *) PG_GETARG_POINTER(1);
    NDBOX      *out = (NDBOX *) NULL;
    NDBOX      *tmp;
    int         i;

    tmp = DatumGetNDBOXP(entryvec->vector[0].key);

    /*
     * sizep = sizeof(NDBOX); -- NDBOX has variable size
     */
    *sizep = VARSIZE(tmp);

    for (i = 1; i < entryvec->n; i++)
    {
        out = g_cube_binary_union(tmp,
                                  DatumGetNDBOXP(entryvec->vector[i].key),
                                  sizep);
        tmp = out;
    }

    PG_RETURN_POINTER(out);
}

/*
** GiST Compress and Decompress methods for boxes
** do not do anything.
*/

Datum
g_cube_compress(PG_FUNCTION_ARGS)
{
    PG_RETURN_DATUM(PG_GETARG_DATUM(0));
}

Datum
g_cube_decompress(PG_FUNCTION_ARGS)
{
    GISTENTRY  *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
    NDBOX      *key = DatumGetNDBOXP(entry->key);

    if (key != DatumGetNDBOXP(entry->key))
    {
        GISTENTRY  *retval = (GISTENTRY *) palloc(sizeof(GISTENTRY));

        gistentryinit(*retval, PointerGetDatum(key),
                      entry->rel, entry->page,
                      entry->offset, false);
        PG_RETURN_POINTER(retval);
    }
    PG_RETURN_POINTER(entry);
}


/*
** The GiST Penalty method for boxes
** As in the R-tree paper, we use change in area as our penalty metric
*/
Datum
g_cube_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);
    NDBOX      *ud;
    double      tmp1,
                tmp2;

    ud = cube_union_v0(DatumGetNDBOXP(origentry->key),
                       DatumGetNDBOXP(newentry->key));
    rt_cube_size(ud, &tmp1);
    rt_cube_size(DatumGetNDBOXP(origentry->key), &tmp2);
    *result = (float) (tmp1 - tmp2);

    PG_RETURN_FLOAT8(*result);
}



/*
** The GiST PickSplit method for boxes
** We use Guttman's poly time split algorithm
*/
Datum
g_cube_picksplit(PG_FUNCTION_ARGS)
{
    GistEntryVector *entryvec = (GistEntryVector *) PG_GETARG_POINTER(0);
    GIST_SPLITVEC *v = (GIST_SPLITVEC *) PG_GETARG_POINTER(1);
    OffsetNumber i,
                j;
    NDBOX      *datum_alpha,
               *datum_beta;
    NDBOX      *datum_l,
               *datum_r;
    NDBOX      *union_d,
               *union_dl,
               *union_dr;
    NDBOX      *inter_d;
    bool        firsttime;
    double      size_alpha,
                size_beta,
                size_union,
                size_inter;
    double      size_waste,
                waste;
    double      size_l,
                size_r;
    int         nbytes;
    OffsetNumber seed_1 = 1,
                seed_2 = 2;
    OffsetNumber *left,
               *right;
    OffsetNumber maxoff;

    maxoff = entryvec->n - 2;
    nbytes = (maxoff + 2) * sizeof(OffsetNumber);
    v->spl_left = (OffsetNumber *) palloc(nbytes);
    v->spl_right = (OffsetNumber *) palloc(nbytes);

    firsttime = true;
    waste = 0.0;

    for (i = FirstOffsetNumber; i < maxoff; i = OffsetNumberNext(i))
    {
        datum_alpha = DatumGetNDBOXP(entryvec->vector[i].key);
        for (j = OffsetNumberNext(i); j <= maxoff; j = OffsetNumberNext(j))
        {
            datum_beta = DatumGetNDBOXP(entryvec->vector[j].key);

            /* compute the wasted space by unioning these guys */
            /* size_waste = size_union - size_inter; */
            union_d = cube_union_v0(datum_alpha, datum_beta);
            rt_cube_size(union_d, &size_union);
            inter_d = DatumGetNDBOXP(DirectFunctionCall2(cube_inter,
                                                         entryvec->vector[i].key,
                                                         entryvec->vector[j].key));
            rt_cube_size(inter_d, &size_inter);
            size_waste = size_union - size_inter;

            /*
             * are these a more promising split than what we've already seen?
             */

            if (size_waste > waste || firsttime)
            {
                waste = size_waste;
                seed_1 = i;
                seed_2 = j;
                firsttime = false;
            }
        }
    }

    left = v->spl_left;
    v->spl_nleft = 0;
    right = v->spl_right;
    v->spl_nright = 0;

    datum_alpha = DatumGetNDBOXP(entryvec->vector[seed_1].key);
    datum_l = cube_union_v0(datum_alpha, datum_alpha);
    rt_cube_size(datum_l, &size_l);
    datum_beta = DatumGetNDBOXP(entryvec->vector[seed_2].key);
    datum_r = cube_union_v0(datum_beta, datum_beta);
    rt_cube_size(datum_r, &size_r);

    /*
     * Now split up the regions between the two seeds.  An important property
     * of this split algorithm is that the split vector v has the indices of
     * items to be split in order in its left and right vectors.  We exploit
     * this property by doing a merge in the code that actually splits the
     * page.
     *
     * For efficiency, we also place the new index tuple in this loop. This is
     * handled at the very end, when we have placed all the existing tuples
     * and i == maxoff + 1.
     */

    maxoff = OffsetNumberNext(maxoff);
    for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
    {
        /*
         * If we've already decided where to place this item, just put it on
         * the right list.  Otherwise, we need to figure out which page needs
         * the least enlargement in order to store the item.
         */

        if (i == seed_1)
        {
            *left++ = i;
            v->spl_nleft++;
            continue;
        }
        else if (i == seed_2)
        {
            *right++ = i;
            v->spl_nright++;
            continue;
        }

        /* okay, which page needs least enlargement? */
        datum_alpha = DatumGetNDBOXP(entryvec->vector[i].key);
        union_dl = cube_union_v0(datum_l, datum_alpha);
        union_dr = cube_union_v0(datum_r, datum_alpha);
        rt_cube_size(union_dl, &size_alpha);
        rt_cube_size(union_dr, &size_beta);

        /* pick which page to add it to */
        if (size_alpha - size_l < size_beta - size_r)
        {
            datum_l = union_dl;
            size_l = size_alpha;
            *left++ = i;
            v->spl_nleft++;
        }
        else
        {
            datum_r = union_dr;
            size_r = size_beta;
            *right++ = i;
            v->spl_nright++;
        }
    }
    *left = *right = FirstOffsetNumber; /* sentinel value */

    v->spl_ldatum = PointerGetDatum(datum_l);
    v->spl_rdatum = PointerGetDatum(datum_r);

    PG_RETURN_POINTER(v);
}

/*
** Equality method
*/
Datum
g_cube_same(PG_FUNCTION_ARGS)
{
    NDBOX      *b1 = PG_GETARG_NDBOX_P(0);
    NDBOX      *b2 = PG_GETARG_NDBOX_P(1);
    bool       *result = (bool *) PG_GETARG_POINTER(2);

    if (cube_cmp_v0(b1, b2) == 0)
        *result = true;
    else
        *result = false;

    PG_RETURN_NDBOX_P(result);
}

/*
** SUPPORT ROUTINES
*/
bool
g_cube_leaf_consistent(NDBOX *key,
                       NDBOX *query,
                       StrategyNumber strategy)
{
    bool        retval;

    switch (strategy)
    {
        case RTOverlapStrategyNumber:
            retval = cube_overlap_v0(key, query);
            break;
        case RTSameStrategyNumber:
            retval = (cube_cmp_v0(key, query) == 0);
            break;
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval = cube_contains_v0(key, query);
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval = cube_contains_v0(query, key);
            break;
        default:
            retval = false;
    }
    return retval;
}

bool
g_cube_internal_consistent(NDBOX *key,
                           NDBOX *query,
                           StrategyNumber strategy)
{
    bool        retval;

    switch (strategy)
    {
        case RTOverlapStrategyNumber:
            retval = (bool) cube_overlap_v0(key, query);
            break;
        case RTSameStrategyNumber:
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval = (bool) cube_contains_v0(key, query);
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval = (bool) cube_overlap_v0(key, query);
            break;
        default:
            retval = false;
    }
    return retval;
}

NDBOX *
g_cube_binary_union(NDBOX *r1, NDBOX *r2, int *sizep)
{
    NDBOX      *retval;

    retval = cube_union_v0(r1, r2);
    *sizep = VARSIZE(retval);

    return retval;
}


/* cube_union_v0 */
NDBOX *
cube_union_v0(NDBOX *a, NDBOX *b)
{
    int         i;
    NDBOX      *result;
    int         dim;
    int         size;

    /* trivial case */
    if (a == b)
        return a;

    /* swap the arguments if needed, so that 'a' is always larger than 'b' */
    if (DIM(a) < DIM(b))
    {
        NDBOX      *tmp = b;

        b = a;
        a = tmp;
    }
    dim = DIM(a);

    size = CUBE_SIZE(dim);
    result = palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, dim);

    /* First compute the union of the dimensions present in both args */
    for (i = 0; i < DIM(b); i++)
    {
        result->x[i] = Min(Min(LL_COORD(a, i), UR_COORD(a, i)),
                           Min(LL_COORD(b, i), UR_COORD(b, i)));
        result->x[i + DIM(a)] = Max(Max(LL_COORD(a, i), UR_COORD(a, i)),
                                    Max(LL_COORD(b, i), UR_COORD(b, i)));
    }
    /* continue on the higher dimensions only present in 'a' */
    for (; i < DIM(a); i++)
    {
        result->x[i] = Min(0,
                           Min(LL_COORD(a, i), UR_COORD(a, i))
            );
        result->x[i + dim] = Max(0,
                                 Max(LL_COORD(a, i), UR_COORD(a, i))
            );
    }

    /*
     * Check if the result was in fact a point, and set the flag in the datum
     * accordingly. (we don't bother to repalloc it smaller)
     */
    if (cube_is_point_internal(result))
    {
        size = POINT_SIZE(dim);
        SET_VARSIZE(result, size);
        SET_POINT_BIT(result);
    }

    return result;
}

Datum
cube_union(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0);
    NDBOX      *b = PG_GETARG_NDBOX_P(1);
    NDBOX      *res;

    res = cube_union_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_NDBOX_P(res);
}

/* cube_inter */
Datum
cube_inter(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0);
    NDBOX      *b = PG_GETARG_NDBOX_P(1);
    NDBOX      *result;
    bool        swapped = false;
    int         i;
    int         dim;
    int         size;

    /* swap the arguments if needed, so that 'a' is always larger than 'b' */
    if (DIM(a) < DIM(b))
    {
        NDBOX      *tmp = b;

        b = a;
        a = tmp;
        swapped = true;
    }
    dim = DIM(a);

    size = CUBE_SIZE(dim);
    result = (NDBOX *) palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, dim);

    /* First compute intersection of the dimensions present in both args */
    for (i = 0; i < DIM(b); i++)
    {
        result->x[i] = Max(Min(LL_COORD(a, i), UR_COORD(a, i)),
                           Min(LL_COORD(b, i), UR_COORD(b, i)));
        result->x[i + DIM(a)] = Min(Max(LL_COORD(a, i), UR_COORD(a, i)),
                                    Max(LL_COORD(b, i), UR_COORD(b, i)));
    }
    /* continue on the higher dimensions only present in 'a' */
    for (; i < DIM(a); i++)
    {
        result->x[i] = Max(0,
                           Min(LL_COORD(a, i), UR_COORD(a, i))
            );
        result->x[i + DIM(a)] = Min(0,
                                    Max(LL_COORD(a, i), UR_COORD(a, i))
            );
    }

    /*
     * Check if the result was in fact a point, and set the flag in the datum
     * accordingly. (we don't bother to repalloc it smaller)
     */
    if (cube_is_point_internal(result))
    {
        size = POINT_SIZE(dim);
        result = repalloc(result, size);
        SET_VARSIZE(result, size);
        SET_POINT_BIT(result);
    }

    if (swapped)
    {
        PG_FREE_IF_COPY(b, 0);
        PG_FREE_IF_COPY(a, 1);
    }
    else
    {
        PG_FREE_IF_COPY(a, 0);
        PG_FREE_IF_COPY(b, 1);
    }

    /*
     * Is it OK to return a non-null intersection for non-overlapping boxes?
     */
    PG_RETURN_NDBOX_P(result);
}

/* cube_size */
Datum
cube_size(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0);
    double      result;

    rt_cube_size(a, &result);
    PG_FREE_IF_COPY(a, 0);
    PG_RETURN_FLOAT8(result);
}

void
rt_cube_size(NDBOX *a, double *size)
{
    double      result;
    int         i;

    if (a == (NDBOX *) NULL)
    {
        /* special case for GiST */
        result = 0.0;
    }
    else if (IS_POINT(a) || DIM(a) == 0)
    {
        /* necessarily has zero size */
        result = 0.0;
    }
    else
    {
        result = 1.0;
        for (i = 0; i < DIM(a); i++)
            result *= Abs(UR_COORD(a, i) - LL_COORD(a, i));
    }
    *size = result;
}

/* make up a metric in which one box will be 'lower' than the other
   -- this can be useful for sorting and to determine uniqueness */
int32
cube_cmp_v0(NDBOX *a, NDBOX *b)
{
    int         i;
    int         dim;

    dim = Min(DIM(a), DIM(b));

    /* compare the common dimensions */
    for (i = 0; i < dim; i++)
    {
        if (Min(LL_COORD(a, i), UR_COORD(a, i)) >
            Min(LL_COORD(b, i), UR_COORD(b, i)))
            return 1;
        if (Min(LL_COORD(a, i), UR_COORD(a, i)) <
            Min(LL_COORD(b, i), UR_COORD(b, i)))
            return -1;
    }
    for (i = 0; i < dim; i++)
    {
        if (Max(LL_COORD(a, i), UR_COORD(a, i)) >
            Max(LL_COORD(b, i), UR_COORD(b, i)))
            return 1;
        if (Max(LL_COORD(a, i), UR_COORD(a, i)) <
            Max(LL_COORD(b, i), UR_COORD(b, i)))
            return -1;
    }

    /* compare extra dimensions to zero */
    if (DIM(a) > DIM(b))
    {
        for (i = dim; i < DIM(a); i++)
        {
            if (Min(LL_COORD(a, i), UR_COORD(a, i)) > 0)
                return 1;
            if (Min(LL_COORD(a, i), UR_COORD(a, i)) < 0)
                return -1;
        }
        for (i = dim; i < DIM(a); i++)
        {
            if (Max(LL_COORD(a, i), UR_COORD(a, i)) > 0)
                return 1;
            if (Max(LL_COORD(a, i), UR_COORD(a, i)) < 0)
                return -1;
        }

        /*
         * if all common dimensions are equal, the cube with more dimensions
         * wins
         */
        return 1;
    }
    if (DIM(a) < DIM(b))
    {
        for (i = dim; i < DIM(b); i++)
        {
            if (Min(LL_COORD(b, i), UR_COORD(b, i)) > 0)
                return -1;
            if (Min(LL_COORD(b, i), UR_COORD(b, i)) < 0)
                return 1;
        }
        for (i = dim; i < DIM(b); i++)
        {
            if (Max(LL_COORD(b, i), UR_COORD(b, i)) > 0)
                return -1;
            if (Max(LL_COORD(b, i), UR_COORD(b, i)) < 0)
                return 1;
        }

        /*
         * if all common dimensions are equal, the cube with more dimensions
         * wins
         */
        return -1;
    }

    /* They're really equal */
    return 0;
}

Datum
cube_cmp(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_INT32(res);
}


Datum
cube_eq(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res == 0);
}


Datum
cube_ne(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res != 0);
}


Datum
cube_lt(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res < 0);
}


Datum
cube_gt(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res > 0);
}


Datum
cube_le(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res <= 0);
}


Datum
cube_ge(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    int32       res;

    res = cube_cmp_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res >= 0);
}


/* Contains */
/* Box(A) CONTAINS Box(B) IFF pt(A) < pt(B) */
bool
cube_contains_v0(NDBOX *a, NDBOX *b)
{
    int         i;

    if ((a == NULL) || (b == NULL))
        return false;

    if (DIM(a) < DIM(b))
    {
        /*
         * the further comparisons will make sense if the excess dimensions of
         * (b) were zeroes Since both UL and UR coordinates must be zero, we
         * can check them all without worrying about which is which.
         */
        for (i = DIM(a); i < DIM(b); i++)
        {
            if (LL_COORD(b, i) != 0)
                return false;
            if (UR_COORD(b, i) != 0)
                return false;
        }
    }

    /* Can't care less about the excess dimensions of (a), if any */
    for (i = 0; i < Min(DIM(a), DIM(b)); i++)
    {
        if (Min(LL_COORD(a, i), UR_COORD(a, i)) >
            Min(LL_COORD(b, i), UR_COORD(b, i)))
            return false;
        if (Max(LL_COORD(a, i), UR_COORD(a, i)) <
            Max(LL_COORD(b, i), UR_COORD(b, i)))
            return false;
    }

    return true;
}

Datum
cube_contains(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    bool        res;

    res = cube_contains_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res);
}

/* Contained */
/* Box(A) Contained by Box(B) IFF Box(B) Contains Box(A) */
Datum
cube_contained(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    bool        res;

    res = cube_contains_v0(b, a);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res);
}

/* Overlap */
/* Box(A) Overlap Box(B) IFF (pt(a)LL < pt(B)UR) && (pt(b)LL < pt(a)UR) */
bool
cube_overlap_v0(NDBOX *a, NDBOX *b)
{
    int         i;

    if ((a == NULL) || (b == NULL))
        return false;

    /* swap the box pointers if needed */
    if (DIM(a) < DIM(b))
    {
        NDBOX      *tmp = b;

        b = a;
        a = tmp;
    }

    /* compare within the dimensions of (b) */
    for (i = 0; i < DIM(b); i++)
    {
        if (Min(LL_COORD(a, i), UR_COORD(a, i)) > Max(LL_COORD(b, i), UR_COORD(b, i)))
            return false;
        if (Max(LL_COORD(a, i), UR_COORD(a, i)) < Min(LL_COORD(b, i), UR_COORD(b, i)))
            return false;
    }

    /* compare to zero those dimensions in (a) absent in (b) */
    for (i = DIM(b); i < DIM(a); i++)
    {
        if (Min(LL_COORD(a, i), UR_COORD(a, i)) > 0)
            return false;
        if (Max(LL_COORD(a, i), UR_COORD(a, i)) < 0)
            return false;
    }

    return true;
}


Datum
cube_overlap(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    bool        res;

    res = cube_overlap_v0(a, b);

    PG_FREE_IF_COPY(a, 0);
    PG_FREE_IF_COPY(b, 1);
    PG_RETURN_BOOL(res);
}


/* Distance */
/* The distance is computed as a per axis sum of the squared distances
   between 1D projections of the boxes onto Cartesian axes. Assuming zero
   distance between overlapping projections, this metric coincides with the
   "common sense" geometric distance */
Datum
cube_distance(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    bool        swapped = false;
    double      d,
                distance;
    int         i;

    /* swap the box pointers if needed */
    if (DIM(a) < DIM(b))
    {
        NDBOX      *tmp = b;

        b = a;
        a = tmp;
        swapped = true;
    }

    distance = 0.0;
    /* compute within the dimensions of (b) */
    for (i = 0; i < DIM(b); i++)
    {
        d = distance_1D(LL_COORD(a, i), UR_COORD(a, i), LL_COORD(b, i), UR_COORD(b, i));
        distance += d * d;
    }

    /* compute distance to zero for those dimensions in (a) absent in (b) */
    for (i = DIM(b); i < DIM(a); i++)
    {
        d = distance_1D(LL_COORD(a, i), UR_COORD(a, i), 0.0, 0.0);
        distance += d * d;
    }

    if (swapped)
    {
        PG_FREE_IF_COPY(b, 0);
        PG_FREE_IF_COPY(a, 1);
    }
    else
    {
        PG_FREE_IF_COPY(a, 0);
        PG_FREE_IF_COPY(b, 1);
    }

    PG_RETURN_FLOAT8(sqrt(distance));
}

Datum
distance_taxicab(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    bool        swapped = false;
    double      distance;
    int         i;

    /* swap the box pointers if needed */
    if (DIM(a) < DIM(b))
    {
        NDBOX      *tmp = b;

        b = a;
        a = tmp;
        swapped = true;
    }

    distance = 0.0;
    /* compute within the dimensions of (b) */
    for (i = 0; i < DIM(b); i++)
        distance += fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i),
                                     LL_COORD(b, i), UR_COORD(b, i)));

    /* compute distance to zero for those dimensions in (a) absent in (b) */
    for (i = DIM(b); i < DIM(a); i++)
        distance += fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i),
                                     0.0, 0.0));

    if (swapped)
    {
        PG_FREE_IF_COPY(b, 0);
        PG_FREE_IF_COPY(a, 1);
    }
    else
    {
        PG_FREE_IF_COPY(a, 0);
        PG_FREE_IF_COPY(b, 1);
    }

    PG_RETURN_FLOAT8(distance);
}

Datum
distance_chebyshev(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0),
               *b = PG_GETARG_NDBOX_P(1);
    bool        swapped = false;
    double      d,
                distance;
    int         i;

    /* swap the box pointers if needed */
    if (DIM(a) < DIM(b))
    {
        NDBOX      *tmp = b;

        b = a;
        a = tmp;
        swapped = true;
    }

    distance = 0.0;
    /* compute within the dimensions of (b) */
    for (i = 0; i < DIM(b); i++)
    {
        d = fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i),
                             LL_COORD(b, i), UR_COORD(b, i)));
        if (d > distance)
            distance = d;
    }

    /* compute distance to zero for those dimensions in (a) absent in (b) */
    for (i = DIM(b); i < DIM(a); i++)
    {
        d = fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i), 0.0, 0.0));
        if (d > distance)
            distance = d;
    }

    if (swapped)
    {
        PG_FREE_IF_COPY(b, 0);
        PG_FREE_IF_COPY(a, 1);
    }
    else
    {
        PG_FREE_IF_COPY(a, 0);
        PG_FREE_IF_COPY(b, 1);
    }

    PG_RETURN_FLOAT8(distance);
}

Datum
g_cube_distance(PG_FUNCTION_ARGS)
{
    GISTENTRY  *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
    StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
    NDBOX      *cube = DatumGetNDBOXP(entry->key);
    double      retval;

    if (strategy == CubeKNNDistanceCoord)
    {
        /*
         * Handle ordering by ~> operator.  See comments of cube_coord_llur()
         * for details
         */
        int         coord = PG_GETARG_INT32(1);
        bool        isLeaf = GistPageIsLeaf(entry->page);
        bool        inverse = false;

        /* 0 is the only unsupported coordinate value */
        if (coord == 0)
            ereport(ERROR,
                    (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                     errmsg("zero cube index is not defined")));

        /* Return inversed value for negative coordinate */
        if (coord < 0)
        {
            coord = -coord;
            inverse = true;
        }

        if (coord <= 2 * DIM(cube))
        {
            /* dimension index */
            int         index = (coord - 1) / 2;

            /* whether this is upper bound (lower bound otherwise) */
            bool        upper = ((coord - 1) % 2 == 1);

            if (IS_POINT(cube))
            {
                retval = cube->x[index];
            }
            else
            {
                if (isLeaf)
                {
                    /* For leaf just return required upper/lower bound */
                    if (upper)
                        retval = Max(cube->x[index], cube->x[index + DIM(cube)]);
                    else
                        retval = Min(cube->x[index], cube->x[index + DIM(cube)]);
                }
                else
                {
                    /*
                     * For non-leaf we should always return lower bound,
                     * because even upper bound of a child in the subtree can
                     * be as small as our lower bound.  For inversed case we
                     * return upper bound because it becomes lower bound for
                     * inversed value.
                     */
                    if (!inverse)
                        retval = Min(cube->x[index], cube->x[index + DIM(cube)]);
                    else
                        retval = Max(cube->x[index], cube->x[index + DIM(cube)]);
                }
            }
        }
        else
        {
            retval = 0.0;
        }

        /* Inverse return value if needed */
        if (inverse)
            retval = -retval;
    }
    else
    {
        NDBOX      *query = PG_GETARG_NDBOX_P(1);

        switch (strategy)
        {
            case CubeKNNDistanceTaxicab:
                retval = DatumGetFloat8(DirectFunctionCall2(distance_taxicab,
                                                            PointerGetDatum(cube), PointerGetDatum(query)));
                break;
            case CubeKNNDistanceEuclid:
                retval = DatumGetFloat8(DirectFunctionCall2(cube_distance,
                                                            PointerGetDatum(cube), PointerGetDatum(query)));
                break;
            case CubeKNNDistanceChebyshev:
                retval = DatumGetFloat8(DirectFunctionCall2(distance_chebyshev,
                                                            PointerGetDatum(cube), PointerGetDatum(query)));
                break;
            default:
                elog(ERROR, "unrecognized cube strategy number: %d", strategy);
                retval = 0;     /* keep compiler quiet */
                break;
        }
    }
    PG_RETURN_FLOAT8(retval);
}

static double
distance_1D(double a1, double a2, double b1, double b2)
{
    /* interval (a) is entirely on the left of (b) */
    if ((a1 <= b1) && (a2 <= b1) && (a1 <= b2) && (a2 <= b2))
        return (Min(b1, b2) - Max(a1, a2));

    /* interval (a) is entirely on the right of (b) */
    if ((a1 > b1) && (a2 > b1) && (a1 > b2) && (a2 > b2))
        return (Min(a1, a2) - Max(b1, b2));

    /* the rest are all sorts of intersections */
    return 0.0;
}

/* Test if a box is also a point */
Datum
cube_is_point(PG_FUNCTION_ARGS)
{
    NDBOX      *cube = PG_GETARG_NDBOX_P(0);
    bool        result;

    result = cube_is_point_internal(cube);
    PG_FREE_IF_COPY(cube, 0);
    PG_RETURN_BOOL(result);
}

static bool
cube_is_point_internal(NDBOX *cube)
{
    int         i;

    if (IS_POINT(cube))
        return true;

    /*
     * Even if the point-flag is not set, all the lower-left coordinates might
     * match the upper-right coordinates, so that the value is in fact a
     * point. Such values don't arise with current code - the point flag is
     * always set if appropriate - but they might be present on-disk in
     * clusters upgraded from pre-9.4 versions.
     */
    for (i = 0; i < DIM(cube); i++)
    {
        if (LL_COORD(cube, i) != UR_COORD(cube, i))
            return false;
    }
    return true;
}

/* Return dimensions in use in the data structure */
Datum
cube_dim(PG_FUNCTION_ARGS)
{
    NDBOX      *c = PG_GETARG_NDBOX_P(0);
    int         dim = DIM(c);

    PG_FREE_IF_COPY(c, 0);
    PG_RETURN_INT32(dim);
}

/* Return a specific normalized LL coordinate */
Datum
cube_ll_coord(PG_FUNCTION_ARGS)
{
    NDBOX      *c = PG_GETARG_NDBOX_P(0);
    int         n = PG_GETARG_INT32(1);
    double      result;

    if (DIM(c) >= n && n > 0)
        result = Min(LL_COORD(c, n - 1), UR_COORD(c, n - 1));
    else
        result = 0;

    PG_FREE_IF_COPY(c, 0);
    PG_RETURN_FLOAT8(result);
}

/* Return a specific normalized UR coordinate */
Datum
cube_ur_coord(PG_FUNCTION_ARGS)
{
    NDBOX      *c = PG_GETARG_NDBOX_P(0);
    int         n = PG_GETARG_INT32(1);
    double      result;

    if (DIM(c) >= n && n > 0)
        result = Max(LL_COORD(c, n - 1), UR_COORD(c, n - 1));
    else
        result = 0;

    PG_FREE_IF_COPY(c, 0);
    PG_RETURN_FLOAT8(result);
}

/*
 * Function returns cube coordinate.
 * Numbers from 1 to DIM denotes first corner coordinates.
 * Numbers from DIM+1 to 2*DIM denotes second corner coordinates.
 */
Datum
cube_coord(PG_FUNCTION_ARGS)
{
    NDBOX      *cube = PG_GETARG_NDBOX_P(0);
    int         coord = PG_GETARG_INT32(1);

    if (coord <= 0 || coord > 2 * DIM(cube))
        ereport(ERROR,
                (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                 errmsg("cube index %d is out of bounds", coord)));

    if (IS_POINT(cube))
        PG_RETURN_FLOAT8(cube->x[(coord - 1) % DIM(cube)]);
    else
        PG_RETURN_FLOAT8(cube->x[coord - 1]);
}


/*----
 * This function works like cube_coord(), but rearranges coordinates in the
 * way suitable to support coordinate ordering using KNN-GiST.  For historical
 * reasons this extension allows us to create cubes in form ((2,1),(1,2)) and
 * instead of normalizing such cube to ((1,1),(2,2)) it stores cube in original
 * way.  But in order to get cubes ordered by one of dimensions from the index
 * without explicit sort step we need this representation-independent coordinate
 * getter.  Moreover, indexed dataset may contain cubes of different dimensions
 * number.  Accordingly, this coordinate getter should be able to return
 * lower/upper bound for particular dimension independently on number of cube
 * dimensions.  Also, KNN-GiST supports only ascending sorting.  In order to
 * support descending sorting, this function returns inverse of value when
 * negative coordinate is given.
 *
 * Long story short, this function uses following meaning of coordinates:
 * # (2 * N - 1) -- lower bound of Nth dimension,
 * # (2 * N) -- upper bound of Nth dimension,
 * # - (2 * N - 1) -- negative of lower bound of Nth dimension,
 * # - (2 * N) -- negative of upper bound of Nth dimension.
 *
 * When given coordinate exceeds number of cube dimensions, then 0 returned
 * (reproducing logic of GiST indexing of variable-length cubes).
 */
Datum
cube_coord_llur(PG_FUNCTION_ARGS)
{
    NDBOX      *cube = PG_GETARG_NDBOX_P(0);
    int         coord = PG_GETARG_INT32(1);
    bool        inverse = false;
    float8      result;

    /* 0 is the only unsupported coordinate value */
    if (coord == 0)
        ereport(ERROR,
                (errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
                 errmsg("zero cube index is not defined")));

    /* Return inversed value for negative coordinate */
    if (coord < 0)
    {
        coord = -coord;
        inverse = true;
    }

    if (coord <= 2 * DIM(cube))
    {
        /* dimension index */
        int         index = (coord - 1) / 2;

        /* whether this is upper bound (lower bound otherwise) */
        bool        upper = ((coord - 1) % 2 == 1);

        if (IS_POINT(cube))
        {
            result = cube->x[index];
        }
        else
        {
            if (upper)
                result = Max(cube->x[index], cube->x[index + DIM(cube)]);
            else
                result = Min(cube->x[index], cube->x[index + DIM(cube)]);
        }
    }
    else
    {
        /*
         * Return zero if coordinate is out of bound.  That reproduces logic
         * of how cubes with low dimension number are expanded during GiST
         * indexing.
         */
        result = 0.0;
    }

    /* Inverse value if needed */
    if (inverse)
        result = -result;

    PG_RETURN_FLOAT8(result);
}

/* Increase or decrease box size by a radius in at least n dimensions. */
Datum
cube_enlarge(PG_FUNCTION_ARGS)
{
    NDBOX      *a = PG_GETARG_NDBOX_P(0);
    double      r = PG_GETARG_FLOAT8(1);
    int32       n = PG_GETARG_INT32(2);
    NDBOX      *result;
    int         dim = 0;
    int         size;
    int         i,
                j;

    if (n > CUBE_MAX_DIM)
        n = CUBE_MAX_DIM;
    if (r > 0 && n > 0)
        dim = n;
    if (DIM(a) > dim)
        dim = DIM(a);

    size = CUBE_SIZE(dim);
    result = (NDBOX *) palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, dim);

    for (i = 0, j = dim; i < DIM(a); i++, j++)
    {
        if (LL_COORD(a, i) >= UR_COORD(a, i))
        {
            result->x[i] = UR_COORD(a, i) - r;
            result->x[j] = LL_COORD(a, i) + r;
        }
        else
        {
            result->x[i] = LL_COORD(a, i) - r;
            result->x[j] = UR_COORD(a, i) + r;
        }
        if (result->x[i] > result->x[j])
        {
            result->x[i] = (result->x[i] + result->x[j]) / 2;
            result->x[j] = result->x[i];
        }
    }
    /* dim > a->dim only if r > 0 */
    for (; i < dim; i++, j++)
    {
        result->x[i] = -r;
        result->x[j] = r;
    }

    /*
     * Check if the result was in fact a point, and set the flag in the datum
     * accordingly. (we don't bother to repalloc it smaller)
     */
    if (cube_is_point_internal(result))
    {
        size = POINT_SIZE(dim);
        SET_VARSIZE(result, size);
        SET_POINT_BIT(result);
    }

    PG_FREE_IF_COPY(a, 0);
    PG_RETURN_NDBOX_P(result);
}

/* Create a one dimensional box with identical upper and lower coordinates */
Datum
cube_f8(PG_FUNCTION_ARGS)
{
    double      x = PG_GETARG_FLOAT8(0);
    NDBOX      *result;
    int         size;

    size = POINT_SIZE(1);
    result = (NDBOX *) palloc0(size);
    SET_VARSIZE(result, size);
    SET_DIM(result, 1);
    SET_POINT_BIT(result);
    result->x[0] = x;

    PG_RETURN_NDBOX_P(result);
}

/* Create a one dimensional box */
Datum
cube_f8_f8(PG_FUNCTION_ARGS)
{
    double      x0 = PG_GETARG_FLOAT8(0);
    double      x1 = PG_GETARG_FLOAT8(1);
    NDBOX      *result;
    int         size;

    if (x0 == x1)
    {
        size = POINT_SIZE(1);
        result = (NDBOX *) palloc0(size);
        SET_VARSIZE(result, size);
        SET_DIM(result, 1);
        SET_POINT_BIT(result);
        result->x[0] = x0;
    }
    else
    {
        size = CUBE_SIZE(1);
        result = (NDBOX *) palloc0(size);
        SET_VARSIZE(result, size);
        SET_DIM(result, 1);
        result->x[0] = x0;
        result->x[1] = x1;
    }

    PG_RETURN_NDBOX_P(result);
}

/* Add a dimension to an existing cube with the same values for the new
   coordinate */
Datum
cube_c_f8(PG_FUNCTION_ARGS)
{
    NDBOX      *cube = PG_GETARG_NDBOX_P(0);
    double      x = PG_GETARG_FLOAT8(1);
    NDBOX      *result;
    int         size;
    int         i;

    if (DIM(cube) + 1 > CUBE_MAX_DIM)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("can't extend cube"),
                 errdetail("A cube cannot have more than %d dimensions.",
                           CUBE_MAX_DIM)));

    if (IS_POINT(cube))
    {
        size = POINT_SIZE((DIM(cube) + 1));
        result = (NDBOX *) palloc0(size);
        SET_VARSIZE(result, size);
        SET_DIM(result, DIM(cube) + 1);
        SET_POINT_BIT(result);
        for (i = 0; i < DIM(cube); i++)
            result->x[i] = cube->x[i];
        result->x[DIM(result) - 1] = x;
    }
    else
    {
        size = CUBE_SIZE((DIM(cube) + 1));
        result = (NDBOX *) palloc0(size);
        SET_VARSIZE(result, size);
        SET_DIM(result, DIM(cube) + 1);
        for (i = 0; i < DIM(cube); i++)
        {
            result->x[i] = cube->x[i];
            result->x[DIM(result) + i] = cube->x[DIM(cube) + i];
        }
        result->x[DIM(result) - 1] = x;
        result->x[2 * DIM(result) - 1] = x;
    }

    PG_FREE_IF_COPY(cube, 0);
    PG_RETURN_NDBOX_P(result);
}

/* Add a dimension to an existing cube */
Datum
cube_c_f8_f8(PG_FUNCTION_ARGS)
{
    NDBOX      *cube = PG_GETARG_NDBOX_P(0);
    double      x1 = PG_GETARG_FLOAT8(1);
    double      x2 = PG_GETARG_FLOAT8(2);
    NDBOX      *result;
    int         size;
    int         i;

    if (DIM(cube) + 1 > CUBE_MAX_DIM)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("can't extend cube"),
                 errdetail("A cube cannot have more than %d dimensions.",
                           CUBE_MAX_DIM)));

    if (IS_POINT(cube) && (x1 == x2))
    {
        size = POINT_SIZE((DIM(cube) + 1));
        result = (NDBOX *) palloc0(size);
        SET_VARSIZE(result, size);
        SET_DIM(result, DIM(cube) + 1);
        SET_POINT_BIT(result);
        for (i = 0; i < DIM(cube); i++)
            result->x[i] = cube->x[i];
        result->x[DIM(result) - 1] = x1;
    }
    else
    {
        size = CUBE_SIZE((DIM(cube) + 1));
        result = (NDBOX *) palloc0(size);
        SET_VARSIZE(result, size);
        SET_DIM(result, DIM(cube) + 1);
        for (i = 0; i < DIM(cube); i++)
        {
            result->x[i] = LL_COORD(cube, i);
            result->x[DIM(result) + i] = UR_COORD(cube, i);
        }
        result->x[DIM(result) - 1] = x1;
        result->x[2 * DIM(result) - 1] = x2;
    }

    PG_FREE_IF_COPY(cube, 0);
    PG_RETURN_NDBOX_P(result);
}