seg.c

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/*
 * 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 "access/gist.h"
#include "access/skey.h"

#include "segdata.h"

/*
#define GIST_DEBUG
#define GIST_QUERY_DEBUG
*/

PG_MODULE_MAGIC;

extern int  seg_yyparse();
extern void seg_yyerror(const char *message);
extern void seg_scanner_init(const char *str);
extern void seg_scanner_finish(void);

/*
extern int   seg_yydebug;
*/

/*
 * 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);

Datum       seg_in(PG_FUNCTION_ARGS);
Datum       seg_out(PG_FUNCTION_ARGS);
Datum       seg_size(PG_FUNCTION_ARGS);
Datum       seg_lower(PG_FUNCTION_ARGS);
Datum       seg_upper(PG_FUNCTION_ARGS);
Datum       seg_center(PG_FUNCTION_ARGS);

/*
** GiST support methods
*/
bool gseg_consistent(GISTENTRY *entry,
                SEG *query,
                StrategyNumber strategy,
                Oid subtype,
                bool *recheck);
GISTENTRY  *gseg_compress(GISTENTRY *entry);
GISTENTRY  *gseg_decompress(GISTENTRY *entry);
float      *gseg_penalty(GISTENTRY *origentry, GISTENTRY *newentry, float *result);
GIST_SPLITVEC *gseg_picksplit(GistEntryVector *entryvec, GIST_SPLITVEC *v);
bool        gseg_leaf_consistent(SEG *key, SEG *query, StrategyNumber strategy);
bool        gseg_internal_consistent(SEG *key, SEG *query, StrategyNumber strategy);
SEG        *gseg_union(GistEntryVector *entryvec, int *sizep);
SEG        *gseg_binary_union(SEG *r1, SEG *r2, int *sizep);
bool       *gseg_same(SEG *b1, SEG *b2, bool *result);


/*
** R-tree support functions
*/
bool        seg_same(SEG *a, SEG *b);
bool        seg_contains_int(SEG *a, int *b);
bool        seg_contains_float4(SEG *a, float4 *b);
bool        seg_contains_float8(SEG *a, float8 *b);
bool        seg_contains(SEG *a, SEG *b);
bool        seg_contained(SEG *a, SEG *b);
bool        seg_overlap(SEG *a, SEG *b);
bool        seg_left(SEG *a, SEG *b);
bool        seg_over_left(SEG *a, SEG *b);
bool        seg_right(SEG *a, SEG *b);
bool        seg_over_right(SEG *a, SEG *b);
SEG        *seg_union(SEG *a, SEG *b);
SEG        *seg_inter(SEG *a, SEG *b);
void        rt_seg_size(SEG *a, float *sz);

/*
** Various operators
*/
int32       seg_cmp(SEG *a, SEG *b);
bool        seg_lt(SEG *a, SEG *b);
bool        seg_le(SEG *a, SEG *b);
bool        seg_gt(SEG *a, SEG *b);
bool        seg_ge(SEG *a, SEG *b);
bool        seg_different(SEG *a, SEG *b);

/*
** Auxiliary funxtions
*/
static int  restore(char *s, float val, int n);
int         significant_digits(char *s);


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

Datum
seg_in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    SEG        *result = palloc(sizeof(SEG));

    seg_scanner_init(str);

    if (seg_yyparse(result) != 0)
        seg_yyerror("bogus input");

    seg_scanner_finish();

    PG_RETURN_POINTER(result);
}

Datum
seg_out(PG_FUNCTION_ARGS)
{
    SEG        *seg = (SEG *) PG_GETARG_POINTER(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 = (SEG *) PG_GETARG_POINTER(0);

    PG_RETURN_FLOAT4(((float) seg->lower + (float) seg->upper) / 2.0);
}

Datum
seg_lower(PG_FUNCTION_ARGS)
{
    SEG        *seg = (SEG *) PG_GETARG_POINTER(0);

    PG_RETURN_FLOAT4(seg->lower);
}

Datum
seg_upper(PG_FUNCTION_ARGS)
{
    SEG        *seg = (SEG *) PG_GETARG_POINTER(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.
*/
bool
gseg_consistent(GISTENTRY *entry,
                SEG *query,
                StrategyNumber strategy,
                Oid subtype,
                bool *recheck)
{
    /* 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((SEG *) DatumGetPointer(entry->key), query, strategy));
    else
        return (gseg_internal_consistent((SEG *) DatumGetPointer(entry->key), query, strategy));
}

/*
** The GiST Union method for segments
** returns the minimal bounding seg that encloses all the entries in entryvec
*/
SEG *
gseg_union(GistEntryVector *entryvec, int *sizep)
{
    int         numranges,
                i;
    SEG        *out = (SEG *) NULL;
    SEG        *tmp;

#ifdef GIST_DEBUG
    fprintf(stderr, "union\n");
#endif

    numranges = entryvec->n;
    tmp = (SEG *) DatumGetPointer(entryvec->vector[0].key);
    *sizep = sizeof(SEG);

    for (i = 1; i < numranges; i++)
    {
        out = gseg_binary_union(tmp, (SEG *)
                                DatumGetPointer(entryvec->vector[i].key),
                                sizep);
        tmp = out;
    }

    return (out);
}

/*
** GiST Compress and Decompress methods for segments
** do not do anything.
*/
GISTENTRY *
gseg_compress(GISTENTRY *entry)
{
    return (entry);
}

GISTENTRY *
gseg_decompress(GISTENTRY *entry)
{
    return (entry);
}

/*
** The GiST Penalty method for segments
** As in the R-tree paper, we use change in area as our penalty metric
*/
float *
gseg_penalty(GISTENTRY *origentry, GISTENTRY *newentry, float *result)
{
    SEG        *ud;
    float       tmp1,
                tmp2;

    ud = seg_union((SEG *) DatumGetPointer(origentry->key),
                   (SEG *) DatumGetPointer(newentry->key));
    rt_seg_size(ud, &tmp1);
    rt_seg_size((SEG *) DatumGetPointer(origentry->key), &tmp2);
    *result = tmp1 - tmp2;

#ifdef GIST_DEBUG
    fprintf(stderr, "penalty\n");
    fprintf(stderr, "\t%g\n", *result);
#endif

    return (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.
 */
GIST_SPLITVEC *
gseg_picksplit(GistEntryVector *entryvec,
               GIST_SPLITVEC *v)
{
    int         i;
    SEG        *datum_l,
               *datum_r,
               *seg;
    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 = (SEG *) DatumGetPointer(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.
     */
    datum_l = (SEG *) palloc(sizeof(SEG));
    memcpy(datum_l, sort_items[0].data, sizeof(SEG));
    *left++ = sort_items[0].index;
    v->spl_nleft++;
    for (i = 1; i < firstright; i++)
    {
        datum_l = seg_union(datum_l, sort_items[i].data);
        *left++ = sort_items[i].index;
        v->spl_nleft++;
    }

    /*
     * Likewise for the right page.
     */
    datum_r = (SEG *) palloc(sizeof(SEG));
    memcpy(datum_r, sort_items[firstright].data, sizeof(SEG));
    *right++ = sort_items[firstright].index;
    v->spl_nright++;
    for (i = firstright + 1; i < maxoff; i++)
    {
        datum_r = seg_union(datum_r, sort_items[i].data);
        *right++ = sort_items[i].index;
        v->spl_nright++;
    }

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

    return v;
}

/*
** Equality methods
*/
bool *
gseg_same(SEG *b1, SEG *b2, bool *result)
{
    if (seg_same(b1, b2))
        *result = TRUE;
    else
        *result = FALSE;

#ifdef GIST_DEBUG
    fprintf(stderr, "same: %s\n", (*result ? "TRUE" : "FALSE"));
#endif

    return (result);
}

/*
** SUPPORT ROUTINES
*/
bool
gseg_leaf_consistent(SEG *key,
                     SEG *query,
                     StrategyNumber strategy)
{
    bool        retval;

#ifdef GIST_QUERY_DEBUG
    fprintf(stderr, "leaf_consistent, %d\n", strategy);
#endif

    switch (strategy)
    {
        case RTLeftStrategyNumber:
            retval = (bool) seg_left(key, query);
            break;
        case RTOverLeftStrategyNumber:
            retval = (bool) seg_over_left(key, query);
            break;
        case RTOverlapStrategyNumber:
            retval = (bool) seg_overlap(key, query);
            break;
        case RTOverRightStrategyNumber:
            retval = (bool) seg_over_right(key, query);
            break;
        case RTRightStrategyNumber:
            retval = (bool) seg_right(key, query);
            break;
        case RTSameStrategyNumber:
            retval = (bool) seg_same(key, query);
            break;
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval = (bool) seg_contains(key, query);
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval = (bool) seg_contained(key, query);
            break;
        default:
            retval = FALSE;
    }
    return (retval);
}

bool
gseg_internal_consistent(SEG *key,
                         SEG *query,
                         StrategyNumber strategy)
{
    bool        retval;

#ifdef GIST_QUERY_DEBUG
    fprintf(stderr, "internal_consistent, %d\n", strategy);
#endif

    switch (strategy)
    {
        case RTLeftStrategyNumber:
            retval = (bool) !seg_over_right(key, query);
            break;
        case RTOverLeftStrategyNumber:
            retval = (bool) !seg_right(key, query);
            break;
        case RTOverlapStrategyNumber:
            retval = (bool) seg_overlap(key, query);
            break;
        case RTOverRightStrategyNumber:
            retval = (bool) !seg_left(key, query);
            break;
        case RTRightStrategyNumber:
            retval = (bool) !seg_over_left(key, query);
            break;
        case RTSameStrategyNumber:
        case RTContainsStrategyNumber:
        case RTOldContainsStrategyNumber:
            retval = (bool) seg_contains(key, query);
            break;
        case RTContainedByStrategyNumber:
        case RTOldContainedByStrategyNumber:
            retval = (bool) seg_overlap(key, query);
            break;
        default:
            retval = FALSE;
    }
    return (retval);
}

SEG *
gseg_binary_union(SEG *r1, SEG *r2, int *sizep)
{
    SEG        *retval;

    retval = seg_union(r1, r2);
    *sizep = sizeof(SEG);

    return (retval);
}


bool
seg_contains(SEG *a, SEG *b)
{
    return ((a->lower <= b->lower) && (a->upper >= b->upper));
}

bool
seg_contained(SEG *a, SEG *b)
{
    return (seg_contains(b, a));
}

/*****************************************************************************
 * Operator class for R-tree indexing
 *****************************************************************************/

bool
seg_same(SEG *a, SEG *b)
{
    return seg_cmp(a, b) == 0;
}

/*  seg_overlap -- does a overlap b?
 */
bool
seg_overlap(SEG *a, SEG *b)
{
    return (
            ((a->upper >= b->upper) && (a->lower <= b->upper))
            ||
            ((b->upper >= a->upper) && (b->lower <= a->upper))
        );
}

/*  seg_overleft -- is the right edge of (a) located at or left of the right edge of (b)?
 */
bool
seg_over_left(SEG *a, SEG *b)
{
    return (a->upper <= b->upper);
}

/*  seg_left -- is (a) entirely on the left of (b)?
 */
bool
seg_left(SEG *a, SEG *b)
{
    return (a->upper < b->lower);
}

/*  seg_right -- is (a) entirely on the right of (b)?
 */
bool
seg_right(SEG *a, SEG *b)
{
    return (a->lower > b->upper);
}

/*  seg_overright -- is the left edge of (a) located at or right of the left edge of (b)?
 */
bool
seg_over_right(SEG *a, SEG *b)
{
    return (a->lower >= b->lower);
}


SEG *
seg_union(SEG *a, SEG *b)
{
    SEG        *n;

    n = (SEG *) palloc(sizeof(*n));

    /* 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;
    }

    return (n);
}


SEG *
seg_inter(SEG *a, SEG *b)
{
    SEG        *n;

    n = (SEG *) palloc(sizeof(*n));

    /* 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;
    }

    return (n);
}

void
rt_seg_size(SEG *a, float *size)
{
    if (a == (SEG *) NULL || a->upper <= a->lower)
        *size = 0.0;
    else
        *size = (float) Abs(a->upper - a->lower);

    return;
}

Datum
seg_size(PG_FUNCTION_ARGS)
{
    SEG        *seg = (SEG *) PG_GETARG_POINTER(0);

    PG_RETURN_FLOAT4((float) Abs(seg->upper - seg->lower));
}


/*****************************************************************************
 *                 Miscellaneous operators
 *****************************************************************************/
int32
seg_cmp(SEG *a, SEG *b)
{
    /*
     * First compare on lower boundary position
     */
    if (a->lower < b->lower)
        return -1;
    if (a->lower > b->lower)
        return 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 == '-')
            return -1;
        if (b->l_ext == '-')
            return 1;
        if (a->l_ext == '<')
            return -1;
        if (b->l_ext == '<')
            return 1;
        if (a->l_ext == '>')
            return 1;
        if (b->l_ext == '>')
            return -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) */
        return -1;
    if (a->l_sigd > b->l_sigd)  /* (a) is less blurred and is likely to be
                                 * included in (b) */
        return 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 */
            return -1;
        if (b->l_ext == '~')
            return 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)
        return -1;
    if (a->upper > b->upper)
        return 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 == '-')
            return 1;
        if (b->u_ext == '-')
            return -1;
        if (a->u_ext == '<')
            return -1;
        if (b->u_ext == '<')
            return 1;
        if (a->u_ext == '>')
            return 1;
        if (b->u_ext == '>')
            return -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) */
        return 1;
    if (a->u_sigd > b->u_sigd)  /* (a) is less blurred and is likely to be
                                 * included in (b) */
        return -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 */
            return 1;
        if (b->u_ext == '~')
            return -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);
    }

    return 0;
}

bool
seg_lt(SEG *a, SEG *b)
{
    return seg_cmp(a, b) < 0;
}

bool
seg_le(SEG *a, SEG *b)
{
    return seg_cmp(a, b) <= 0;
}

bool
seg_gt(SEG *a, SEG *b)
{
    return seg_cmp(a, b) > 0;
}

bool
seg_ge(SEG *a, SEG *b)
{
    return seg_cmp(a, b) >= 0;
}

bool
seg_different(SEG *a, SEG *b)
{
    return seg_cmp(a, b) != 0;
}



/*****************************************************************************
 *                 Auxiliary functions
 *****************************************************************************/

/* The purpose of this routine is to print the floating point
 * value with exact number of significant digits. Its behaviour
 * is similar to %.ng except it prints 8.00 where %.ng would
 * print 8
 */
static int
restore(char *result, float val, int n)
{
    static char efmt[8] = {'%', '-', '1', '5', '.', '#', 'e', 0};
    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 siugnificant digits to avoid nonsense in the
     * output
     */
    n = Min(n, FLT_DIG);

    /* remember the sign */
    sign = (val < 0 ? 1 : 0);

    efmt[5] = '0' + (n - 1) % 10;       /* makes %-15.(n-1)e -- this format
                                         * guarantees that the exponent is
                                         * always present */

    sprintf(result, efmt, val);

    /* trim the spaces left by the %e */
    for (p = result; *p != ' '; p++);
    *p = '\0';

    /* get the exponent */
    strtok(pstrdup(result), "e");
    exp = atoi(strtok(NULL, "e"));

    if (exp == 0)
    {
        /* use the supplied mantyssa with sign */
        strcpy((char *) strchr(result, 'e'), "");
    }
    else
    {
        if (Abs(exp) <= 4)
        {
            /*
             * remove the decimal point from the mantyssa 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
*/

bool
seg_contains_int(SEG *a, int *b)
{
    return ((a->lower <= *b) && (a->upper >= *b));
}

bool
seg_contains_float4(SEG *a, float4 *b)
{
    return ((a->lower <= *b) && (a->upper >= *b));
}

bool
seg_contains_float8(SEG *a, float8 *b)
{
    return ((a->lower <= *b) && (a->upper >= *b));
}

/* find out the number of significant digits in a string representing
 * a floating point number
 */
int
significant_digits(char *s)
{
    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);
}