seg.c

Go to the documentation of this file.

/*
 * contrib/seg/seg.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 <float.h>
#include <math.h>
 
#include "access/gist.h"
#include "access/stratnum.h"
#include "fmgr.h"
 
#include "segdata.h"
 
 
#define DatumGetSegP(X) ((SEG *) DatumGetPointer(X))
#define PG_GETARG_SEG_P(n) DatumGetSegP(PG_GETARG_DATUM(n))
 
 
/*
 * #define GIST_DEBUG
 * #define GIST_QUERY_DEBUG
 */
 
PG_MODULE_MAGIC_EXT(
                    .name = "seg",
                    .version = PG_VERSION
);
 
/*
 * Auxiliary data structure for picksplit method.
 */
typedef struct
{
    float       center;
    OffsetNumber index;
    SEG        *data;
} gseg_picksplit_item;
 
/*
 * Input/Output routines
 */
PG_FUNCTION_INFO_V1(seg_in);
PG_FUNCTION_INFO_V1(seg_out);
PG_FUNCTION_INFO_V1(seg_size);
PG_FUNCTION_INFO_V1(seg_lower);
PG_FUNCTION_INFO_V1(seg_upper);
PG_FUNCTION_INFO_V1(seg_center);
 
/*
 * GiST support methods
 */
PG_FUNCTION_INFO_V1(gseg_consistent);
PG_FUNCTION_INFO_V1(gseg_compress);
PG_FUNCTION_INFO_V1(gseg_decompress);
PG_FUNCTION_INFO_V1(gseg_picksplit);
PG_FUNCTION_INFO_V1(gseg_penalty);
PG_FUNCTION_INFO_V1(gseg_union);
PG_FUNCTION_INFO_V1(gseg_same);
static Datum gseg_leaf_consistent(Datum key, Datum query, StrategyNumber strategy);
static Datum gseg_internal_consistent(Datum key, Datum query, StrategyNumber strategy);
static Datum gseg_binary_union(Datum r1, Datum r2, int *sizep);
 
 
/*
 * R-tree support functions
 */
PG_FUNCTION_INFO_V1(seg_same);
PG_FUNCTION_INFO_V1(seg_contains);
PG_FUNCTION_INFO_V1(seg_contained);
PG_FUNCTION_INFO_V1(seg_overlap);
PG_FUNCTION_INFO_V1(seg_left);
PG_FUNCTION_INFO_V1(seg_over_left);
PG_FUNCTION_INFO_V1(seg_right);
PG_FUNCTION_INFO_V1(seg_over_right);
PG_FUNCTION_INFO_V1(seg_union);
PG_FUNCTION_INFO_V1(seg_inter);
static void rt_seg_size(SEG *a, float *size);
 
/*
 * Various operators
 */
PG_FUNCTION_INFO_V1(seg_cmp);
PG_FUNCTION_INFO_V1(seg_lt);
PG_FUNCTION_INFO_V1(seg_le);
PG_FUNCTION_INFO_V1(seg_gt);
PG_FUNCTION_INFO_V1(seg_ge);
PG_FUNCTION_INFO_V1(seg_different);
 
/*
 * Auxiliary functions
 */
static int  restore(char *result, float val, int n);
 
 
/*****************************************************************************
 * Input/Output functions
 *****************************************************************************/
 
Datum
seg_in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    SEG        *result = palloc_object(SEG);
    yyscan_t    scanner;
 
    seg_scanner_init(str, &scanner);
 
    if (seg_yyparse(result, fcinfo->context, scanner) != 0)
        seg_yyerror(result, fcinfo->context, scanner, "bogus input");
 
    seg_scanner_finish(scanner);
 
    PG_RETURN_POINTER(result);
}
 
Datum
seg_out(PG_FUNCTION_ARGS)
{
    SEG        *seg = PG_GETARG_SEG_P(0);
    char       *result;
    char       *p;
 
    p = result = (char *) palloc(40);
 
    if (seg->l_ext == '>' || seg->l_ext == '<' || seg->l_ext == '~')
        p += sprintf(p, "%c", seg->l_ext);
 
    if (seg->lower == seg->upper && seg->l_ext == seg->u_ext)
    {
        /*
         * indicates that this interval was built by seg_in off a single point
         */
        p += restore(p, seg->lower, seg->l_sigd);
    }
    else
    {
        if (seg->l_ext != '-')
        {
            /* print the lower boundary if exists */
            p += restore(p, seg->lower, seg->l_sigd);
            p += sprintf(p, " ");
        }
        p += sprintf(p, "..");
        if (seg->u_ext != '-')
        {
            /* print the upper boundary if exists */
            p += sprintf(p, " ");
            if (seg->u_ext == '>' || seg->u_ext == '<' || seg->l_ext == '~')
                p += sprintf(p, "%c", seg->u_ext);
            p += restore(p, seg->upper, seg->u_sigd);
        }
    }
 
    PG_RETURN_CSTRING(result);
}
 
Datum
seg_center(PG_FUNCTION_ARGS)
{
    SEG        *seg = PG_GETARG_SEG_P(0);
 
    PG_RETURN_FLOAT4(((float) seg->lower + (float) seg->upper) / 2.0);
}
 
Datum
seg_lower(PG_FUNCTION_ARGS)
{
    SEG        *seg = PG_GETARG_SEG_P(0);
 
    PG_RETURN_FLOAT4(seg->lower);
}
 
Datum
seg_upper(PG_FUNCTION_ARGS)
{
    SEG        *seg = PG_GETARG_SEG_P(0);
 
    PG_RETURN_FLOAT4(seg->upper);
}
 
 
/*****************************************************************************
 *                         GiST functions
 *****************************************************************************/
 
/*
 * The GiST Consistent method for segments
 * 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
gseg_consistent(PG_FUNCTION_ARGS)
{
    GISTENTRY  *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
    Datum       query = PG_GETARG_DATUM(1);
    StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
#ifdef NOT_USED
    Oid         subtype = PG_GETARG_OID(3);
#endif
    bool       *recheck = (bool *) PG_GETARG_POINTER(4);
 
    /* All cases served by this function are exact */
    *recheck = false;
 
    /*
     * if entry is not leaf, use gseg_internal_consistent, else use
     * gseg_leaf_consistent
     */
    if (GIST_LEAF(entry))
        return gseg_leaf_consistent(entry->key, query, strategy);
    else
        return gseg_internal_consistent(entry->key, query, strategy);
}
 
/*
 * The GiST Union method for segments
 * returns the minimal bounding seg that encloses all the entries in entryvec
 */
Datum
gseg_union(PG_FUNCTION_ARGS)
{
    GistEntryVector *entryvec = (GistEntryVector *) PG_GETARG_POINTER(0);
    int        *sizep = (int *) PG_GETARG_POINTER(1);
    int         numranges,
                i;
    Datum       out = 0;
    Datum       tmp;
 
#ifdef GIST_DEBUG
    fprintf(stderr, "union\n");
#endif
 
    numranges = entryvec->n;
    tmp = entryvec->vector[0].key;
    *sizep = sizeof(SEG);
 
    for (i = 1; i < numranges; i++)
    {
        out = gseg_binary_union(tmp, entryvec->vector[i].key, sizep);
        tmp = out;
    }
 
    PG_RETURN_DATUM(out);
}
 
/*
 * GiST Compress and Decompress methods for segments
 * do not do anything.
 */
Datum
gseg_compress(PG_FUNCTION_ARGS)
{
    PG_RETURN_POINTER(PG_GETARG_POINTER(0));
}
 
Datum
gseg_decompress(PG_FUNCTION_ARGS)
{
    PG_RETURN_POINTER(PG_GETARG_POINTER(0));
}
 
/*
 * The GiST Penalty method for segments
 * As in the R-tree paper, we use change in area as our penalty metric
 */
Datum
gseg_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);
    SEG        *ud;
    float       tmp1,
                tmp2;
 
    ud = DatumGetSegP(DirectFunctionCall2(seg_union,
                                          origentry->key,
                                          newentry->key));
    rt_seg_size(ud, &tmp1);
    rt_seg_size(DatumGetSegP(origentry->key), &tmp2);
    *result = tmp1 - tmp2;
 
#ifdef GIST_DEBUG
    fprintf(stderr, "penalty\n");
    fprintf(stderr, "\t%g\n", *result);
#endif
 
    PG_RETURN_POINTER(result);
}
 
/*
 * Compare function for gseg_picksplit_item: sort by center.
 */
static int
gseg_picksplit_item_cmp(const void *a, const void *b)
{
    const gseg_picksplit_item *i1 = (const gseg_picksplit_item *) a;
    const gseg_picksplit_item *i2 = (const gseg_picksplit_item *) b;
 
    if (i1->center < i2->center)
        return -1;
    else if (i1->center == i2->center)
        return 0;
    else
        return 1;
}
 
/*
 * The GiST PickSplit method for segments
 *
 * We used to use Guttman's split algorithm here, but since the data is 1-D
 * it's easier and more robust to just sort the segments by center-point and
 * split at the middle.
 */
Datum
gseg_picksplit(PG_FUNCTION_ARGS)
{
    GistEntryVector *entryvec = (GistEntryVector *) PG_GETARG_POINTER(0);
    GIST_SPLITVEC *v = (GIST_SPLITVEC *) PG_GETARG_POINTER(1);
    int         i;
    SEG        *seg,
               *seg_l,
               *seg_r;
    gseg_picksplit_item *sort_items;
    OffsetNumber *left,
               *right;
    OffsetNumber maxoff;
    OffsetNumber firstright;
 
#ifdef GIST_DEBUG
    fprintf(stderr, "picksplit\n");
#endif
 
    /* Valid items in entryvec->vector[] are indexed 1..maxoff */
    maxoff = entryvec->n - 1;
 
    /*
     * Prepare the auxiliary array and sort it.
     */
    sort_items = (gseg_picksplit_item *)
        palloc(maxoff * sizeof(gseg_picksplit_item));
    for (i = 1; i <= maxoff; i++)
    {
        seg = DatumGetSegP(entryvec->vector[i].key);
        /* center calculation is done this way to avoid possible overflow */
        sort_items[i - 1].center = seg->lower * 0.5f + seg->upper * 0.5f;
        sort_items[i - 1].index = i;
        sort_items[i - 1].data = seg;
    }
    qsort(sort_items, maxoff, sizeof(gseg_picksplit_item),
          gseg_picksplit_item_cmp);
 
    /* sort items below "firstright" will go into the left side */
    firstright = maxoff / 2;
 
    v->spl_left = (OffsetNumber *) palloc(maxoff * sizeof(OffsetNumber));
    v->spl_right = (OffsetNumber *) palloc(maxoff * sizeof(OffsetNumber));
    left = v->spl_left;
    v->spl_nleft = 0;
    right = v->spl_right;
    v->spl_nright = 0;
 
    /*
     * Emit segments to the left output page, and compute its bounding box.
     */
    seg_l = palloc_object(SEG);
    memcpy(seg_l, sort_items[0].data, sizeof(SEG));
    *left++ = sort_items[0].index;
    v->spl_nleft++;
    for (i = 1; i < firstright; i++)
    {
        Datum       sortitem = PointerGetDatum(sort_items[i].data);
 
        seg_l = DatumGetSegP(DirectFunctionCall2(seg_union,
                                                 PointerGetDatum(seg_l),
                                                 sortitem));
        *left++ = sort_items[i].index;
        v->spl_nleft++;
    }
 
    /*
     * Likewise for the right page.
     */
    seg_r = palloc_object(SEG);
    memcpy(seg_r, sort_items[firstright].data, sizeof(SEG));
    *right++ = sort_items[firstright].index;
    v->spl_nright++;
    for (i = firstright + 1; i < maxoff; i++)
    {
        Datum       sortitem = PointerGetDatum(sort_items[i].data);
 
        seg_r = DatumGetSegP(DirectFunctionCall2(seg_union,
                                                 PointerGetDatum(seg_r),
                                                 sortitem));
        *right++ = sort_items[i].index;
        v->spl_nright++;
    }
 
    v->spl_ldatum = PointerGetDatum(seg_l);
    v->spl_rdatum = PointerGetDatum(seg_r);
 
    PG_RETURN_POINTER(v);
}
 
/*
 * Equality methods
 */
Datum
gseg_same(PG_FUNCTION_ARGS)
{
    bool       *result = (bool *) PG_GETARG_POINTER(2);
 
    if (DatumGetBool(DirectFunctionCall2(seg_same, PG_GETARG_DATUM(0), PG_GETARG_DATUM(1))))
        *result = true;
    else
        *result = false;
 
#ifdef GIST_DEBUG
    fprintf(stderr, "same: %s\n", (*result ? "TRUE" : "FALSE"));
#endif
 
    PG_RETURN_POINTER(result);
}
 
/*
 * SUPPORT ROUTINES
 */
static Datum
gseg_leaf_consistent(Datum key, Datum query, StrategyNumber strategy)
{
    Datum       retval;
 
#ifdef GIST_QUERY_DEBUG
    fprintf(stderr, "leaf_consistent, %d\n", strategy);
#endif
 
    switch (strategy)
    {
        case RTLeftStrategyNumber:
            retval = DirectFunctionCall2(seg_left, key, query);
            break;
        case RTOverLeftStrategyNumber:
            retval = DirectFunctionCall2(seg_over_left, key, query);
            break;
        case RTOverlapStrategyNumber:
            retval = DirectFunctionCall2(seg_overlap, key, query);
            break;
        case RTOverRightStrategyNumber:
            retval = DirectFunctionCall2(seg_over_right, key, query);
            break;
        case RTRightStrategyNumber:
            retval = DirectFunctionCall2(seg_right, key, query);
            break;
        case RTSameStrategyNumber:
            retval = DirectFunctionCall2(seg_same, key, query);
            break;
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval = DirectFunctionCall2(seg_contains, key, query);
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval = DirectFunctionCall2(seg_contained, key, query);
            break;
        default:
            retval = BoolGetDatum(false);
    }
 
    PG_RETURN_DATUM(retval);
}
 
static Datum
gseg_internal_consistent(Datum key, Datum query, StrategyNumber strategy)
{
    bool        retval;
 
#ifdef GIST_QUERY_DEBUG
    fprintf(stderr, "internal_consistent, %d\n", strategy);
#endif
 
    switch (strategy)
    {
        case RTLeftStrategyNumber:
            retval =
                !DatumGetBool(DirectFunctionCall2(seg_over_right, key, query));
            break;
        case RTOverLeftStrategyNumber:
            retval =
                !DatumGetBool(DirectFunctionCall2(seg_right, key, query));
            break;
        case RTOverlapStrategyNumber:
            retval =
                DatumGetBool(DirectFunctionCall2(seg_overlap, key, query));
            break;
        case RTOverRightStrategyNumber:
            retval =
                !DatumGetBool(DirectFunctionCall2(seg_left, key, query));
            break;
        case RTRightStrategyNumber:
            retval =
                !DatumGetBool(DirectFunctionCall2(seg_over_left, key, query));
            break;
        case RTSameStrategyNumber:
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval =
                DatumGetBool(DirectFunctionCall2(seg_contains, key, query));
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval =
                DatumGetBool(DirectFunctionCall2(seg_overlap, key, query));
            break;
        default:
            retval = false;
    }
 
    PG_RETURN_BOOL(retval);
}
 
static Datum
gseg_binary_union(Datum r1, Datum r2, int *sizep)
{
    Datum       retval;
 
    retval = DirectFunctionCall2(seg_union, r1, r2);
    *sizep = sizeof(SEG);
 
    return retval;
}
 
 
Datum
seg_contains(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    PG_RETURN_BOOL((a->lower <= b->lower) && (a->upper >= b->upper));
}
 
Datum
seg_contained(PG_FUNCTION_ARGS)
{
    Datum       a = PG_GETARG_DATUM(0);
    Datum       b = PG_GETARG_DATUM(1);
 
    PG_RETURN_DATUM(DirectFunctionCall2(seg_contains, b, a));
}
 
/*****************************************************************************
 * Operator class for R-tree indexing
 *****************************************************************************/
 
Datum
seg_same(PG_FUNCTION_ARGS)
{
    int         cmp = DatumGetInt32(DirectFunctionCall2(seg_cmp,
                                                        PG_GETARG_DATUM(0),
                                                        PG_GETARG_DATUM(1)));
 
    PG_RETURN_BOOL(cmp == 0);
}
 
/*
 * seg_overlap -- does a overlap b?
 */
Datum
seg_overlap(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    PG_RETURN_BOOL(((a->upper >= b->upper) && (a->lower <= b->upper)) ||
                   ((b->upper >= a->upper) && (b->lower <= a->upper)));
}
 
/*
 * seg_over_left -- is the right edge of (a) located at or left of the right edge of (b)?
 */
Datum
seg_over_left(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    PG_RETURN_BOOL(a->upper <= b->upper);
}
 
/*
 * seg_left -- is (a) entirely on the left of (b)?
 */
Datum
seg_left(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    PG_RETURN_BOOL(a->upper < b->lower);
}
 
/*
 * seg_right -- is (a) entirely on the right of (b)?
 */
Datum
seg_right(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    PG_RETURN_BOOL(a->lower > b->upper);
}
 
/*
 * seg_over_right -- is the left edge of (a) located at or right of the left edge of (b)?
 */
Datum
seg_over_right(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    PG_RETURN_BOOL(a->lower >= b->lower);
}
 
Datum
seg_union(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
    SEG        *n;
 
    n = palloc_object(SEG);
 
    /* take max of upper endpoints */
    if (a->upper > b->upper)
    {
        n->upper = a->upper;
        n->u_sigd = a->u_sigd;
        n->u_ext = a->u_ext;
    }
    else
    {
        n->upper = b->upper;
        n->u_sigd = b->u_sigd;
        n->u_ext = b->u_ext;
    }
 
    /* take min of lower endpoints */
    if (a->lower < b->lower)
    {
        n->lower = a->lower;
        n->l_sigd = a->l_sigd;
        n->l_ext = a->l_ext;
    }
    else
    {
        n->lower = b->lower;
        n->l_sigd = b->l_sigd;
        n->l_ext = b->l_ext;
    }
 
    PG_RETURN_POINTER(n);
}
 
Datum
seg_inter(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
    SEG        *n;
 
    n = palloc_object(SEG);
 
    /* take min of upper endpoints */
    if (a->upper < b->upper)
    {
        n->upper = a->upper;
        n->u_sigd = a->u_sigd;
        n->u_ext = a->u_ext;
    }
    else
    {
        n->upper = b->upper;
        n->u_sigd = b->u_sigd;
        n->u_ext = b->u_ext;
    }
 
    /* take max of lower endpoints */
    if (a->lower > b->lower)
    {
        n->lower = a->lower;
        n->l_sigd = a->l_sigd;
        n->l_ext = a->l_ext;
    }
    else
    {
        n->lower = b->lower;
        n->l_sigd = b->l_sigd;
        n->l_ext = b->l_ext;
    }
 
    PG_RETURN_POINTER(n);
}
 
static void
rt_seg_size(SEG *a, float *size)
{
    if (a == (SEG *) NULL || a->upper <= a->lower)
        *size = 0.0;
    else
        *size = fabsf(a->upper - a->lower);
}
 
Datum
seg_size(PG_FUNCTION_ARGS)
{
    SEG        *seg = PG_GETARG_SEG_P(0);
 
    PG_RETURN_FLOAT4(fabsf(seg->upper - seg->lower));
}
 
 
/*****************************************************************************
 *                 Miscellaneous operators
 *****************************************************************************/
Datum
seg_cmp(PG_FUNCTION_ARGS)
{
    SEG        *a = PG_GETARG_SEG_P(0);
    SEG        *b = PG_GETARG_SEG_P(1);
 
    /*
     * First compare on lower boundary position
     */
    if (a->lower < b->lower)
        PG_RETURN_INT32(-1);
    if (a->lower > b->lower)
        PG_RETURN_INT32(1);
 
    /*
     * a->lower == b->lower, so consider type of boundary.
     *
     * A '-' lower bound is < any other kind (this could only be relevant if
     * -HUGE_VAL is used as a regular data value). A '<' lower bound is < any
     * other kind except '-'. A '>' lower bound is > any other kind.
     */
    if (a->l_ext != b->l_ext)
    {
        if (a->l_ext == '-')
            PG_RETURN_INT32(-1);
        if (b->l_ext == '-')
            PG_RETURN_INT32(1);
        if (a->l_ext == '<')
            PG_RETURN_INT32(-1);
        if (b->l_ext == '<')
            PG_RETURN_INT32(1);
        if (a->l_ext == '>')
            PG_RETURN_INT32(1);
        if (b->l_ext == '>')
            PG_RETURN_INT32(-1);
    }
 
    /*
     * For other boundary types, consider # of significant digits first.
     */
    if (a->l_sigd < b->l_sigd)  /* (a) is blurred and is likely to include (b) */
        PG_RETURN_INT32(-1);
    if (a->l_sigd > b->l_sigd)  /* (a) is less blurred and is likely to be
                                 * included in (b) */
        PG_RETURN_INT32(1);
 
    /*
     * For same # of digits, an approximate boundary is more blurred than
     * exact.
     */
    if (a->l_ext != b->l_ext)
    {
        if (a->l_ext == '~')    /* (a) is approximate, while (b) is exact */
            PG_RETURN_INT32(-1);
        if (b->l_ext == '~')
            PG_RETURN_INT32(1);
        /* can't get here unless data is corrupt */
        elog(ERROR, "bogus lower boundary types %d %d",
             (int) a->l_ext, (int) b->l_ext);
    }
 
    /* at this point, the lower boundaries are identical */
 
    /*
     * First compare on upper boundary position
     */
    if (a->upper < b->upper)
        PG_RETURN_INT32(-1);
    if (a->upper > b->upper)
        PG_RETURN_INT32(1);
 
    /*
     * a->upper == b->upper, so consider type of boundary.
     *
     * A '-' upper bound is > any other kind (this could only be relevant if
     * HUGE_VAL is used as a regular data value). A '<' upper bound is < any
     * other kind. A '>' upper bound is > any other kind except '-'.
     */
    if (a->u_ext != b->u_ext)
    {
        if (a->u_ext == '-')
            PG_RETURN_INT32(1);
        if (b->u_ext == '-')
            PG_RETURN_INT32(-1);
        if (a->u_ext == '<')
            PG_RETURN_INT32(-1);
        if (b->u_ext == '<')
            PG_RETURN_INT32(1);
        if (a->u_ext == '>')
            PG_RETURN_INT32(1);
        if (b->u_ext == '>')
            PG_RETURN_INT32(-1);
    }
 
    /*
     * For other boundary types, consider # of significant digits first. Note
     * result here is converse of the lower-boundary case.
     */
    if (a->u_sigd < b->u_sigd)  /* (a) is blurred and is likely to include (b) */
        PG_RETURN_INT32(1);
    if (a->u_sigd > b->u_sigd)  /* (a) is less blurred and is likely to be
                                 * included in (b) */
        PG_RETURN_INT32(-1);
 
    /*
     * For same # of digits, an approximate boundary is more blurred than
     * exact.  Again, result is converse of lower-boundary case.
     */
    if (a->u_ext != b->u_ext)
    {
        if (a->u_ext == '~')    /* (a) is approximate, while (b) is exact */
            PG_RETURN_INT32(1);
        if (b->u_ext == '~')
            PG_RETURN_INT32(-1);
        /* can't get here unless data is corrupt */
        elog(ERROR, "bogus upper boundary types %d %d",
             (int) a->u_ext, (int) b->u_ext);
    }
 
    PG_RETURN_INT32(0);
}
 
Datum
seg_lt(PG_FUNCTION_ARGS)
{
    int         cmp = DatumGetInt32(DirectFunctionCall2(seg_cmp,
                                                        PG_GETARG_DATUM(0),
                                                        PG_GETARG_DATUM(1)));
 
    PG_RETURN_BOOL(cmp < 0);
}
 
Datum
seg_le(PG_FUNCTION_ARGS)
{
    int         cmp = DatumGetInt32(DirectFunctionCall2(seg_cmp,
                                                        PG_GETARG_DATUM(0),
                                                        PG_GETARG_DATUM(1)));
 
    PG_RETURN_BOOL(cmp <= 0);
}
 
Datum
seg_gt(PG_FUNCTION_ARGS)
{
    int         cmp = DatumGetInt32(DirectFunctionCall2(seg_cmp,
                                                        PG_GETARG_DATUM(0),
                                                        PG_GETARG_DATUM(1)));
 
    PG_RETURN_BOOL(cmp > 0);
}
 
Datum
seg_ge(PG_FUNCTION_ARGS)
{
    int         cmp = DatumGetInt32(DirectFunctionCall2(seg_cmp,
                                                        PG_GETARG_DATUM(0),
                                                        PG_GETARG_DATUM(1)));
 
    PG_RETURN_BOOL(cmp >= 0);
}
 
 
Datum
seg_different(PG_FUNCTION_ARGS)
{
    int         cmp = DatumGetInt32(DirectFunctionCall2(seg_cmp,
                                                        PG_GETARG_DATUM(0),
                                                        PG_GETARG_DATUM(1)));
 
    PG_RETURN_BOOL(cmp != 0);
}
 
 
 
/*****************************************************************************
 *                 Auxiliary functions
 *****************************************************************************/
 
/*
 * The purpose of this routine is to print the given floating point
 * value with exactly n significant digits.  Its behaviour
 * is similar to %.ng except it prints 8.00 where %.ng would
 * print 8.  Returns the length of the string written at "result".
 *
 * Caller must provide a sufficiently large result buffer; 16 bytes
 * should be enough for all known float implementations.
 */
static int
restore(char *result, float val, int n)
{
    char        buf[25] = {
        '0', '0', '0', '0', '0',
        '0', '0', '0', '0', '0',
        '0', '0', '0', '0', '0',
        '0', '0', '0', '0', '0',
        '0', '0', '0', '0', '\0'
    };
    char       *p;
    int         exp;
    int         i,
                dp,
                sign;
 
    /*
     * Put a cap on the number of significant digits to avoid garbage in the
     * output and ensure we don't overrun the result buffer.  (n should not be
     * negative, but check to protect ourselves against corrupted data.)
     */
    if (n <= 0)
        n = FLT_DIG;
    else
        n = Min(n, FLT_DIG);
 
    /* remember the sign */
    sign = (val < 0 ? 1 : 0);
 
    /* print, in %e style to start with */
    sprintf(result, "%.*e", n - 1, val);
 
    /* find the exponent */
    p = strchr(result, 'e');
 
    /* punt if we have 'inf' or similar */
    if (p == NULL)
        return strlen(result);
 
    exp = atoi(p + 1);
    if (exp == 0)
    {
        /* just truncate off the 'e+00' */
        *p = '\0';
    }
    else
    {
        if (abs(exp) <= 4)
        {
            /*
             * remove the decimal point from the mantissa and write the digits
             * to the buf array
             */
            for (p = result + sign, i = 10, dp = 0; *p != 'e'; p++, i++)
            {
                buf[i] = *p;
                if (*p == '.')
                {
                    dp = i--;   /* skip the decimal point */
                }
            }
            if (dp == 0)
                dp = i--;       /* no decimal point was found in the above
                                 * for() loop */
 
            if (exp > 0)
            {
                if (dp - 10 + exp >= n)
                {
                    /*
                     * the decimal point is behind the last significant digit;
                     * the digits in between must be converted to the exponent
                     * and the decimal point placed after the first digit
                     */
                    exp = dp - 10 + exp - n;
                    buf[10 + n] = '\0';
 
                    /* insert the decimal point */
                    if (n > 1)
                    {
                        dp = 11;
                        for (i = 23; i > dp; i--)
                            buf[i] = buf[i - 1];
                        buf[dp] = '.';
                    }
 
                    /*
                     * adjust the exponent by the number of digits after the
                     * decimal point
                     */
                    if (n > 1)
                        sprintf(&buf[11 + n], "e%d", exp + n - 1);
                    else
                        sprintf(&buf[11], "e%d", exp + n - 1);
 
                    if (sign)
                    {
                        buf[9] = '-';
                        strcpy(result, &buf[9]);
                    }
                    else
                        strcpy(result, &buf[10]);
                }
                else
                {               /* insert the decimal point */
                    dp += exp;
                    for (i = 23; i > dp; i--)
                        buf[i] = buf[i - 1];
                    buf[11 + n] = '\0';
                    buf[dp] = '.';
                    if (sign)
                    {
                        buf[9] = '-';
                        strcpy(result, &buf[9]);
                    }
                    else
                        strcpy(result, &buf[10]);
                }
            }
            else
            {                   /* exp <= 0 */
                dp += exp - 1;
                buf[10 + n] = '\0';
                buf[dp] = '.';
                if (sign)
                {
                    buf[dp - 2] = '-';
                    strcpy(result, &buf[dp - 2]);
                }
                else
                    strcpy(result, &buf[dp - 1]);
            }
        }
 
        /* do nothing for abs(exp) > 4; %e must be OK */
        /* just get rid of zeroes after [eE]- and +zeroes after [Ee]. */
 
        /* ... this is not done yet. */
    }
    return strlen(result);
}
 
 
/*
 * Miscellany
 */
 
/*
 * find out the number of significant digits in a string representing
 * a floating point number
 */
int
significant_digits(const char *s)
{
    const char *p = s;
    int         n,
                c,
                zeroes;
 
    zeroes = 1;
    /* skip leading zeroes and sign */
    for (c = *p; (c == '0' || c == '+' || c == '-') && c != 0; c = *(++p));
 
    /* skip decimal point and following zeroes */
    for (c = *p; (c == '0' || c == '.') && c != 0; c = *(++p))
    {
        if (c != '.')
            zeroes++;
    }
 
    /* count significant digits (n) */
    for (c = *p, n = 0; c != 0; c = *(++p))
    {
        if (!((c >= '0' && c <= '9') || (c == '.')))
            break;
        if (c != '.')
            n++;
    }
 
    if (!n)
        return zeroes;
 
    return n;
}