openGauss-server/contrib/cube/cube.cpp

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

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

#include "postgres.h"
#include "knl/knl_variable.h"

#include <float.h>
#include <math.h>

#include "access/gist.h"
#include "access/skey.h"
#include "utils/array.h"
#include "utils/builtins.h"

#include "cubedata.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))

extern int cube_yyparse(void*);
extern void cube_yyerror(const char* message);
extern void cube_scanner_init(const char* str);
extern void cube_scanner_finish(void);

/*
** Input/Output routines
*/
PG_FUNCTION_INFO_V1(cube_in);
PG_FUNCTION_INFO_V1(cube);
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_subset);

extern "C" Datum cube_in(PG_FUNCTION_ARGS);
extern "C" Datum cube(PG_FUNCTION_ARGS);
extern "C" Datum cube_a_f8_f8(PG_FUNCTION_ARGS);
extern "C" Datum cube_a_f8(PG_FUNCTION_ARGS);
extern "C" Datum cube_out(PG_FUNCTION_ARGS);
extern "C" Datum cube_f8(PG_FUNCTION_ARGS);
extern "C" Datum cube_f8_f8(PG_FUNCTION_ARGS);
extern "C" Datum cube_c_f8(PG_FUNCTION_ARGS);
extern "C" Datum cube_c_f8_f8(PG_FUNCTION_ARGS);
extern "C" Datum cube_dim(PG_FUNCTION_ARGS);
extern "C" Datum cube_ll_coord(PG_FUNCTION_ARGS);
extern "C" Datum cube_ur_coord(PG_FUNCTION_ARGS);
extern "C" Datum cube_subset(PG_FUNCTION_ARGS);

/*
** 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);

extern "C" Datum g_cube_consistent(PG_FUNCTION_ARGS);
extern "C" Datum g_cube_compress(PG_FUNCTION_ARGS);
extern "C" Datum g_cube_decompress(PG_FUNCTION_ARGS);
extern "C" Datum g_cube_penalty(PG_FUNCTION_ARGS);
extern "C" Datum g_cube_picksplit(PG_FUNCTION_ARGS);
extern "C" Datum g_cube_union(PG_FUNCTION_ARGS);
extern "C" Datum g_cube_same(PG_FUNCTION_ARGS);

/*
** 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);

extern "C" Datum cube_eq(PG_FUNCTION_ARGS);
extern "C" Datum cube_ne(PG_FUNCTION_ARGS);
extern "C" Datum cube_lt(PG_FUNCTION_ARGS);
extern "C" Datum cube_gt(PG_FUNCTION_ARGS);
extern "C" Datum cube_le(PG_FUNCTION_ARGS);
extern "C" Datum cube_ge(PG_FUNCTION_ARGS);
extern "C" Datum cube_cmp(PG_FUNCTION_ARGS);

/*
** 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);

extern "C" Datum cube_contains(PG_FUNCTION_ARGS);
extern "C" Datum cube_contained(PG_FUNCTION_ARGS);
extern "C" Datum cube_overlap(PG_FUNCTION_ARGS);
extern "C" Datum cube_union(PG_FUNCTION_ARGS);
extern "C" Datum cube_inter(PG_FUNCTION_ARGS);
extern "C" Datum cube_size(PG_FUNCTION_ARGS);

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

extern "C" Datum cube_distance(PG_FUNCTION_ARGS);
extern "C" Datum cube_is_point(PG_FUNCTION_ARGS);
extern "C" Datum cube_enlarge(PG_FUNCTION_ARGS);

/*
** 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 funxtions
*/
static double distance_1D(double a1, double a2, double b1, double b2);

/*****************************************************************************
 * 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);
    void* result = NULL;

    cube_scanner_init(str);

    if (cube_yyparse(&result) != 0)
        cube_yyerror("bogus input");

    cube_scanner_finish();

    PG_RETURN_NDBOX(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 = NULL;
    int i;
    int dim;
    int size;
    double *dur = NULL;
    double *dll = NULL;

    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 (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);

    size = offsetof(NDBOX, x[0]) + sizeof(double) * 2 * dim;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = dim;

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

    PG_RETURN_NDBOX(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 = NULL;
    int i;
    int dim;
    int size;
    double* dur = NULL;

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

    dim = ARRNELEMS(ur);

    dur = ARRPTR(ur);

    size = offsetof(NDBOX, x[0]) + sizeof(double) * 2 * dim;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = dim;

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

    PG_RETURN_NDBOX(result);
}

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

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

    dx = (int4*)ARR_DATA_PTR(idx);

    dim = ARRNELEMS(idx);
    size = offsetof(NDBOX, x[0]) + sizeof(double) * 2 * dim;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = dim;

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

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

Datum cube_out(PG_FUNCTION_ARGS)
{
    NDBOX* cube = PG_GETARG_NDBOX(0);
    StringInfoData buf;
    int dim = cube->dim;
    bool equal = true;
    int i;
    int ndig;

    initStringInfo(&buf);

    /*
     * Get the number of digits to display.
     */
    ndig = DBL_DIG + u_sess->attr.attr_common.extra_float_digits;
    if (ndig < 1)
        ndig = 1;

    /*
     * while printing the first (LL) corner, check if it is equal to the
     * second one
     */
    appendStringInfoChar(&buf, '(');
    for (i = 0; i < dim; i++) {
        if (i > 0)
            appendStringInfo(&buf, ", ");
        appendStringInfo(&buf, "%.*g", ndig, cube->x[i]);
        if (cube->x[i] != cube->x[i + dim]) {
            equal = false;
        }
    }
    appendStringInfoChar(&buf, ')');

    if (!equal) {
        appendStringInfo(&buf, ",(");
        for (i = 0; i < dim; i++) {
            if (i > 0)
                appendStringInfo(&buf, ", ");
            appendStringInfo(&buf, "%.*g", ndig, cube->x[i + dim]);
        }
        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(1);
    StrategyNumber strategy = (StrategyNumber)PG_GETARG_UINT16(2);

    bool* recheck = (bool*)PG_GETARG_POINTER(4);
    bool res = false;

    /* 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(DatumGetNDBOX(entry->key), query, strategy);
    else
        res = g_cube_internal_consistent(DatumGetNDBOX(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 = NULL;
    int i;

    /*
     * fprintf(stderr, "union\n");
     */
    tmp = DatumGetNDBOX(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, DatumGetNDBOX(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 = DatumGetNDBOX(PG_DETOAST_DATUM(entry->key));

    if (key != DatumGetNDBOX(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 = NULL;
    double tmp1, tmp2;

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

    /*
     * fprintf(stderr, "penalty\n"); fprintf(stderr, "\t%g\n", *result);
     */
    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 = NULL;
    NDBOX* datum_beta = NULL;
    NDBOX* datum_l = NULL;
    NDBOX* datum_r = NULL;
    NDBOX* union_d = NULL;
    NDBOX* union_dl = NULL;
    NDBOX* union_dr = NULL;
    NDBOX* inter_d = NULL;
    bool firsttime = false;
    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 = NULL;
    OffsetNumber* right = NULL;
    OffsetNumber maxoff;

    /*
     * fprintf(stderr, "picksplit\n");
     */
    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 = DatumGetNDBOX(entryvec->vector[i].key);
        for (j = OffsetNumberNext(i); j <= maxoff; j = OffsetNumberNext(j)) {
            datum_beta = DatumGetNDBOX(entryvec->vector[j].key);

            /* compute the wasted space by unioning these guys */
            union_d = cube_union_v0(datum_alpha, datum_beta);
            rt_cube_size(union_d, &size_union);
            inter_d = DatumGetNDBOX(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 = DatumGetNDBOX(entryvec->vector[seed_1].key);
    datum_l = cube_union_v0(datum_alpha, datum_alpha);
    rt_cube_size(datum_l, &size_l);
    datum_beta = DatumGetNDBOX(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 = DatumGetNDBOX(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, see dosplit() */

    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(0);
    NDBOX* b2 = PG_GETARG_NDBOX(1);
    bool* result = (bool*)PG_GETARG_POINTER(2);

    if (cube_cmp_v0(b1, b2) == 0)
        *result = TRUE;
    else
        *result = FALSE;

    /*
     * fprintf(stderr, "same: %s\n", (*result ? "TRUE" : "FALSE" ));
     */
    PG_RETURN_NDBOX(result);
}

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

    /*
     * fprintf(stderr, "leaf_consistent, %d\n", strategy);
     */
    switch (strategy) {
        case RTOverlapStrategyNumber:
            retval = (bool)cube_overlap_v0(key, query);
            break;
        case RTSameStrategyNumber:
            retval = (bool)(cube_cmp_v0(key, query) == 0);
            break;
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval = (bool)cube_contains_v0(key, query);
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval = (bool)cube_contains_v0(query, key);
            break;
        default:
            retval = FALSE;
    }
    return (retval);
}

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

    /*
     * fprintf(stderr, "internal_consistent, %d\n", strategy);
     */
    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 = NULL;

    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 = NULL;

    if (a->dim >= b->dim) {
        result = (NDBOX*)palloc0(VARSIZE(a));
        SET_VARSIZE(result, VARSIZE(a));
        result->dim = a->dim;
    } else {
        result = (NDBOX*)palloc0(VARSIZE(b));
        SET_VARSIZE(result, VARSIZE(b));
        result->dim = b->dim;
    }

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

        b = a;
        a = tmp;
    }

    /*
     * use the potentially smaller of the two boxes (b) to fill in the result,
     * padding absent dimensions with zeroes
     */
    for (i = 0; i < b->dim; i++) {
        result->x[i] = Min(b->x[i], b->x[i + b->dim]);
        result->x[i + a->dim] = Max(b->x[i], b->x[i + b->dim]);
    }
    for (i = b->dim; i < a->dim; i++) {
        result->x[i] = 0;
        result->x[i + a->dim] = 0;
    }

    /* compute the union */
    for (i = 0; i < a->dim; i++) {
        result->x[i] = Min(Min(a->x[i], a->x[i + a->dim]), result->x[i]);
        result->x[i + a->dim] = Max(Max(a->x[i], a->x[i + a->dim]), result->x[i + a->dim]);
    }

    return (result);
}

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

    res = cube_union_v0(a, b);

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

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

    if (a->dim >= b->dim) {
        result = (NDBOX*)palloc0(VARSIZE(a));
        SET_VARSIZE(result, VARSIZE(a));
        result->dim = a->dim;
    } else {
        result = (NDBOX*)palloc0(VARSIZE(b));
        SET_VARSIZE(result, VARSIZE(b));
        result->dim = b->dim;
    }

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

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

    /*
     * use the potentially	smaller of the two boxes (b) to fill in the
     * result, padding absent dimensions with zeroes
     */
    for (i = 0; i < b->dim; i++) {
        result->x[i] = Min(b->x[i], b->x[i + b->dim]);
        result->x[i + a->dim] = Max(b->x[i], b->x[i + b->dim]);
    }
    for (i = b->dim; i < a->dim; i++) {
        result->x[i] = 0;
        result->x[i + a->dim] = 0;
    }

    /* compute the intersection */
    for (i = 0; i < a->dim; i++) {
        result->x[i] = Max(Min(a->x[i], a->x[i + a->dim]), result->x[i]);
        result->x[i + a->dim] = Min(Max(a->x[i], a->x[i + a->dim]), result->x[i + a->dim]);
    }

    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(result);
}

/* cube_size */
Datum cube_size(PG_FUNCTION_ARGS)
{
    NDBOX* a = PG_GETARG_NDBOX(0);
    double result;
    int i, j;

    result = 1.0;
    for (i = 0, j = a->dim; i < a->dim; i++, j++)
        result = result * Abs((a->x[j] - a->x[i]));

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

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

    if (a == (NDBOX*)NULL)
        *size = 0.0;
    else {
        *size = 1.0;
        for (i = 0, j = a->dim; i < a->dim; i++, j++)
            *size = (*size) * Abs((a->x[j] - a->x[i]));
    }
    return;
}

/* 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(a->dim, b->dim);

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

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

        /*
         * if all common dimensions are equal, the cube with more dimensions
         * wins
         */
        return 1;
    }
    if (a->dim < b->dim) {
        for (i = dim; i < b->dim; i++) {
            if (Min(b->x[i], b->x[b->dim + i]) > 0)
                return -1;
            if (Min(b->x[i], b->x[b->dim + i]) < 0)
                return 1;
        }
        for (i = dim; i < b->dim; i++) {
            if (Max(b->x[i], b->x[b->dim + i]) > 0)
                return -1;
            if (Max(b->x[i], b->x[b->dim + 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(0), *b = PG_GETARG_NDBOX(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(0), *b = PG_GETARG_NDBOX(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(0), *b = PG_GETARG_NDBOX(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(0), *b = PG_GETARG_NDBOX(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(0), *b = PG_GETARG_NDBOX(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(0), *b = PG_GETARG_NDBOX(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(0), *b = PG_GETARG_NDBOX(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 (a->dim < b->dim) {
        /*
         * 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 = a->dim; i < b->dim; i++) {
            if (b->x[i] != 0)
                return (FALSE);
            if (b->x[i + b->dim] != 0)
                return (FALSE);
        }
    }

    /* Can't care less about the excess dimensions of (a), if any */
    for (i = 0; i < Min(a->dim, b->dim); i++) {
        if (Min(a->x[i], a->x[a->dim + i]) > Min(b->x[i], b->x[b->dim + i]))
            return (FALSE);
        if (Max(a->x[i], a->x[a->dim + i]) < Max(b->x[i], b->x[b->dim + i]))
            return (FALSE);
    }

    return (TRUE);
}

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

    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(0), *b = PG_GETARG_NDBOX(1);
    bool res = false;

    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;

    /*
     * This *very bad* error was found in the source: if ( (a==NULL) ||
     * (b=NULL) ) return(FALSE);
     */
    if ((a == NULL) || (b == NULL))
        return (FALSE);

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

        b = a;
        a = tmp;
    }

    /* compare within the dimensions of (b) */
    for (i = 0; i < b->dim; i++) {
        if (Min(a->x[i], a->x[a->dim + i]) > Max(b->x[i], b->x[b->dim + i]))
            return (FALSE);
        if (Max(a->x[i], a->x[a->dim + i]) < Min(b->x[i], b->x[b->dim + i]))
            return (FALSE);
    }

    /* compare to zero those dimensions in (a) absent in (b) */
    for (i = b->dim; i < a->dim; i++) {
        if (Min(a->x[i], a->x[a->dim + i]) > 0)
            return (FALSE);
        if (Max(a->x[i], a->x[a->dim + i]) < 0)
            return (FALSE);
    }

    return (TRUE);
}

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

    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(0), *b = PG_GETARG_NDBOX(1);
    bool swapped = false;
    double d, distance;
    int i;

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

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

    distance = 0.0;
    /* compute within the dimensions of (b) */
    for (i = 0; i < b->dim; i++) {
        d = distance_1D(a->x[i], a->x[i + a->dim], b->x[i], b->x[i + b->dim]);
        distance += d * d;
    }

    /* compute distance to zero for those dimensions in (a) absent in (b) */
    for (i = b->dim; i < a->dim; i++) {
        d = distance_1D(a->x[i], a->x[i + a->dim], 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));
}

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* a = PG_GETARG_NDBOX(0);
    int i, j;

    for (i = 0, j = a->dim; i < a->dim; i++, j++) {
        if (a->x[i] != a->x[j])
            PG_RETURN_BOOL(FALSE);
    }

    PG_FREE_IF_COPY(a, 0);
    PG_RETURN_BOOL(TRUE);
}

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

    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(0);
    int n = PG_GETARG_INT16(1);
    double result;

    if (c->dim >= n && n > 0) {
        result = Min(c->x[n - 1], c->x[c->dim + 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(0);
    int n = PG_GETARG_INT16(1);
    double result;

    if (c->dim >= n && n > 0) {
        result = Max(c->x[n - 1], c->x[c->dim + n - 1]);
    } else {
        result = 0;
    }

    PG_FREE_IF_COPY(c, 0);
    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(0);
    double r = PG_GETARG_FLOAT8(1);
    int4 n = PG_GETARG_INT32(2);
    NDBOX* result = NULL;
    int dim = 0;
    int size;
    int i, j, k;

    if (n > CUBE_MAX_DIM)
        n = CUBE_MAX_DIM;
    if (r > 0 && n > 0)
        dim = n;
    if (a->dim > dim) {
        dim = a->dim;
    }
    size = offsetof(NDBOX, x[0]) + sizeof(double) * dim * 2;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = dim;
    for (i = 0, j = dim, k = a->dim; i < a->dim; i++, j++, k++) {
        if (a->x[i] >= a->x[k]) {
            result->x[i] = a->x[k] - r;
            result->x[j] = a->x[i] + r;
        } else {
            result->x[i] = a->x[i] - r;
            result->x[j] = a->x[k] + 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;
    }

    PG_FREE_IF_COPY(a, 0);
    PG_RETURN_NDBOX(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 = NULL;
    int size;

    size = offsetof(NDBOX, x[0]) + sizeof(double) * 2;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = 1;
    result->x[0] = result->x[1] = x;

    PG_RETURN_NDBOX(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 = NULL;
    int size;

    size = offsetof(NDBOX, x[0]) + sizeof(double) * 2;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = 1;
    result->x[0] = x0;
    result->x[1] = x1;

    PG_RETURN_NDBOX(result);
}

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

    size = offsetof(NDBOX, x[0]) + sizeof(double) * (c->dim + 1) * 2;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = c->dim + 1;
    for (i = 0; i < c->dim; i++) {
        result->x[i] = c->x[i];
        result->x[result->dim + i] = c->x[c->dim + i];
    }
    result->x[result->dim - 1] = x;
    result->x[2 * result->dim - 1] = x;

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

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

    size = offsetof(NDBOX, x[0]) + sizeof(double) * (c->dim + 1) * 2;
    result = (NDBOX*)palloc0(size);
    SET_VARSIZE(result, size);
    result->dim = c->dim + 1;
    for (i = 0; i < c->dim; i++) {
        result->x[i] = c->x[i];
        result->x[result->dim + i] = c->x[c->dim + i];
    }
    result->x[result->dim - 1] = x1;
    result->x[2 * result->dim - 1] = x2;

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