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postgres/contrib/seg/seg.c
Tom Lane 2a8d3d83ef R-tree is dead ... long live GiST.
2005-11-07 17:36:47 +00:00

1090 lines
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/******************************************************************************
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 "utils/builtins.h"
#include "segdata.h"
/*
#define GIST_DEBUG
#define GIST_QUERY_DEBUG
*/
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;
*/
/*
** Input/Output routines
*/
SEG *seg_in(char *str);
char *seg_out(SEG * seg);
float32 seg_lower(SEG * seg);
float32 seg_upper(SEG * seg);
float32 seg_center(SEG * seg);
/*
** GiST support methods
*/
bool gseg_consistent(GISTENTRY *entry, SEG * query, StrategyNumber strategy);
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);
float *seg_size(SEG * a);
/*
** 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
*****************************************************************************/
SEG *
seg_in(char *str)
{
SEG *result = palloc(sizeof(SEG));
seg_scanner_init(str);
if (seg_yyparse(result) != 0)
seg_yyerror("bogus input");
seg_scanner_finish();
return (result);
}
char *
seg_out(SEG * seg)
{
char *result;
char *p;
if (seg == NULL)
return (NULL);
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 boudary if exists */
p += restore(p, seg->lower, seg->l_sigd);
p += sprintf(p, " ");
}
p += sprintf(p, "..");
if (seg->u_ext != '-')
{
/* print the upper boudary 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);
}
}
return (result);
}
float32
seg_center(SEG * seg)
{
float32 result = (float32) palloc(sizeof(float32data));
if (!seg)
return (float32) NULL;
*result = ((float) seg->lower + (float) seg->upper) / 2.0;
return (result);
}
float32
seg_lower(SEG * seg)
{
float32 result = (float32) palloc(sizeof(float32data));
if (!seg)
return (float32) NULL;
*result = (float) seg->lower;
return (result);
}
float32
seg_upper(SEG * seg)
{
float32 result = (float32) palloc(sizeof(float32data));
if (!seg)
return (float32) NULL;
*result = (float) seg->upper;
return (result);
}
/*****************************************************************************
* 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)
{
/*
* 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);
}
/*
** The GiST PickSplit method for segments
** We use Guttman's poly time split algorithm
*/
GIST_SPLITVEC *
gseg_picksplit(GistEntryVector *entryvec,
GIST_SPLITVEC *v)
{
OffsetNumber i,
j;
SEG *datum_alpha,
*datum_beta;
SEG *datum_l,
*datum_r;
SEG *union_d,
*union_dl,
*union_dr;
SEG *inter_d;
bool firsttime;
float size_alpha,
size_beta,
size_union,
size_inter;
float size_waste,
waste;
float size_l,
size_r;
int nbytes;
OffsetNumber seed_1 = 0,
seed_2 = 0;
OffsetNumber *left,
*right;
OffsetNumber maxoff;
#ifdef GIST_DEBUG
fprintf(stderr, "picksplit\n");
#endif
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 = (SEG *) DatumGetPointer(entryvec->vector[i].key);
for (j = OffsetNumberNext(i); j <= maxoff; j = OffsetNumberNext(j))
{
datum_beta = (SEG *) DatumGetPointer(entryvec->vector[j].key);
/* compute the wasted space by unioning these guys */
/* size_waste = size_union - size_inter; */
union_d = seg_union(datum_alpha, datum_beta);
rt_seg_size(union_d, &size_union);
inter_d = seg_inter(datum_alpha, datum_beta);
rt_seg_size(inter_d, &size_inter);
size_waste = size_union - size_inter;
/*
* are these a more promising split that 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 = (SEG *) DatumGetPointer(entryvec->vector[seed_1].key);
datum_l = seg_union(datum_alpha, datum_alpha);
rt_seg_size(datum_l, &size_l);
datum_beta = (SEG *) DatumGetPointer(entryvec->vector[seed_2].key);
datum_r = seg_union(datum_beta, datum_beta);
rt_seg_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 = (SEG *) DatumGetPointer(entryvec->vector[i].key);
union_dl = seg_union(datum_l, datum_alpha);
union_dr = seg_union(datum_r, datum_alpha);
rt_seg_size(union_dl, &size_alpha);
rt_seg_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_alpha;
*right++ = i;
v->spl_nright++;
}
}
*left = *right = FirstOffsetNumber; /* sentinel value, see dosplit() */
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:
retval = (bool) seg_contains(key, query);
break;
case RTContainedByStrategyNumber:
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:
retval = (bool) seg_contains(key, query);
break;
case RTContainedByStrategyNumber:
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;
}
float *
seg_size(SEG * a)
{
float *result;
result = (float *) palloc(sizeof(float));
*result = (float) Abs(a->upper - a->lower);
return (result);
}
/*****************************************************************************
* 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;
char *mant;
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 */
mant = (char *) strtok(strdup(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);
}
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