/* Enlarge b_union to contain b_new. If b_new contains more
dimensions than b_union, expand b_union to contain those dimensions. */
static void gidx_merge(GIDX **b_union, GIDX *b_new)
{
int i, dims_union, dims_new;
Assert(b_union);
Assert(*b_union);
Assert(b_new);
dims_union = GIDX_NDIMS(*b_union);
dims_new = GIDX_NDIMS(b_new);
POSTGIS_DEBUGF(4, "merging gidx (%s) into gidx (%s)", gidx_to_string(b_new), gidx_to_string(*b_union));
if ( dims_new > dims_union )
{
POSTGIS_DEBUGF(5, "reallocating b_union from %d dims to %d dims", dims_union, dims_new);
*b_union = (GIDX*)repalloc(*b_union, GIDX_SIZE(dims_new));
SET_VARSIZE(*b_union, VARSIZE(b_new));
dims_union = dims_new;
}
for ( i = 0; i < dims_new; i++ )
{
/* Adjust minimums */
GIDX_SET_MIN(*b_union, i, Min(GIDX_GET_MIN(*b_union,i),GIDX_GET_MIN(b_new,i)));
/* Adjust maximums */
GIDX_SET_MAX(*b_union, i, Max(GIDX_GET_MAX(*b_union,i),GIDX_GET_MAX(b_new,i)));
}
POSTGIS_DEBUGF(5, "merge complete (%s)", gidx_to_string(*b_union));
return;
}
/*
** Equality GIDX test.
**
** Box(A) EQUALS Box(B) IFF (pt(A)LL == pt(B)LL) && (pt(A)UR == pt(B)UR)
*/
static bool gidx_equals(GIDX *a, GIDX *b)
{
int i;
POSTGIS_DEBUG(5, "entered function");
if ( (a == NULL) && (b == NULL) ) return TRUE;
if ( (a == NULL) || (b == NULL) ) return FALSE;
/* Ensure 'a' has the most dimensions. */
gidx_dimensionality_check(&a, &b);
/* For all shared dimensions min(a) == min(b), max(a) == max(b) */
for (i = 0; i < GIDX_NDIMS(b); i++)
{
if ( GIDX_GET_MIN(a,i) != GIDX_GET_MIN(b,i) )
return FALSE;
if ( GIDX_GET_MAX(a,i) != GIDX_GET_MAX(b,i) )
return FALSE;
}
/* For all unshared dimensions min(a) == 0.0, max(a) == 0.0 */
for (i = GIDX_NDIMS(b); i < GIDX_NDIMS(a); i++)
{
if ( GIDX_GET_MIN(a,i) != 0.0 )
return FALSE;
if ( GIDX_GET_MAX(a,i) != 0.0 )
return FALSE;
}
return TRUE;
}
/*
** Overlapping GIDX box test.
**
** Box(A) Overlap Box(B) IFF (pt(a)LL < pt(B)UR) && (pt(b)LL < pt(a)UR)
*/
static bool gidx_overlaps(GIDX *a, GIDX *b)
{
int i;
int ndims_b;
POSTGIS_DEBUG(5, "entered function");
if ( (a == NULL) || (b == NULL) ) return FALSE;
/* Ensure 'a' has the most dimensions. */
gidx_dimensionality_check(&a, &b);
ndims_b = GIDX_NDIMS(b);
/* compare within the dimensions of (b) */
for ( i = 0; i < ndims_b; i++ )
{
if ( GIDX_GET_MIN(a,i) > GIDX_GET_MAX(b,i) )
return FALSE;
if ( GIDX_GET_MIN(b,i) > GIDX_GET_MAX(a,i) )
return FALSE;
}
/* compare to zero those dimensions in (a) absent in (b) */
for ( i = ndims_b; i < GIDX_NDIMS(a); i++ )
{
if ( GIDX_GET_MIN(a,i) > 0.0 )
return FALSE;
if ( GIDX_GET_MAX(a,i) < 0.0 )
return FALSE;
}
return TRUE;
}
/* Ensure the first argument has the higher dimensionality. */
static void gidx_dimensionality_check(GIDX **a, GIDX **b)
{
if ( GIDX_NDIMS(*a) < GIDX_NDIMS(*b) )
{
GIDX *tmp = *b;
*b = *a;
*a = tmp;
}
}
/* Calculate the volume of the intersection of the boxes. */
static float gidx_inter_volume(GIDX *a, GIDX *b)
{
int i;
float result;
POSTGIS_DEBUG(5,"entered function");
if ( a == NULL || b == NULL )
{
elog(ERROR, "gidx_inter_volume received a null argument");
return 0.0;
}
/* Ensure 'a' has the most dimensions. */
gidx_dimensionality_check(&a, &b);
/* Initialize with minimal length of first dimension. */
result = Min(GIDX_GET_MAX(a,0),GIDX_GET_MAX(b,0)) - Max(GIDX_GET_MIN(a,0),GIDX_GET_MIN(b,0));
/* If they are disjoint (max < min) then return zero. */
if ( result < 0.0 ) return 0.0;
/* Continue for remaining dimensions. */
for ( i = 1; i < GIDX_NDIMS(b); i++ )
{
float width = Min(GIDX_GET_MAX(a,i),GIDX_GET_MAX(b,i)) - Max(GIDX_GET_MIN(a,i),GIDX_GET_MIN(b,i));
if ( width < 0.0 ) return 0.0;
/* Multiply by minimal length of remaining dimensions. */
result *= width;
}
POSTGIS_DEBUGF(5, "volume( %s intersection %s ) = %.12g", gidx_to_string(a), gidx_to_string(b), result);
return result;
}
/* Calculate the volume of the union of the boxes. Avoids creating an intermediate box. */
static float gidx_union_volume(GIDX *a, GIDX *b)
{
float result;
int i;
int ndims_a, ndims_b;
POSTGIS_DEBUG(5,"entered function");
if ( a == NULL && b == NULL )
{
elog(ERROR, "gidx_union_volume received two null arguments");
return 0.0;
}
if ( a == NULL )
return gidx_volume(b);
if ( b == NULL )
return gidx_volume(a);
/* Ensure 'a' has the most dimensions. */
gidx_dimensionality_check(&a, &b);
ndims_a = GIDX_NDIMS(a);
ndims_b = GIDX_NDIMS(b);
/* Initialize with maximal length of first dimension. */
result = Max(GIDX_GET_MAX(a,0),GIDX_GET_MAX(b,0)) - Min(GIDX_GET_MIN(a,0),GIDX_GET_MIN(b,0));
/* Multiply by maximal length of remaining dimensions. */
for ( i = 1; i < ndims_b; i++ )
{
result *= (Max(GIDX_GET_MAX(a,i),GIDX_GET_MAX(b,i)) - Min(GIDX_GET_MIN(a,i),GIDX_GET_MIN(b,i)));
}
/* Add in dimensions of higher dimensional box. */
for ( i = ndims_b; i < ndims_a; i++ )
{
result *= (GIDX_GET_MAX(a,i) - GIDX_GET_MIN(a,i));
}
POSTGIS_DEBUGF(5, "volume( %s union %s ) = %.12g", gidx_to_string(a), gidx_to_string(b), result);
return result;
}
/*
** GIDX expansion, make d units bigger in all dimensions.
*/
void gidx_expand(GIDX *a, float d)
{
int i;
POSTGIS_DEBUG(5, "entered function");
if ( a == NULL ) return;
for (i = 0; i < GIDX_NDIMS(a); i++)
{
GIDX_SET_MIN(a, i, GIDX_GET_MIN(a, i) - d);
GIDX_SET_MAX(a, i, GIDX_GET_MAX(a, i) + d);
}
}
/*
** Containment GIDX test.
**
** Box(A) CONTAINS Box(B) IFF (pt(A)LL < pt(B)LL) && (pt(A)UR > pt(B)UR)
*/
static bool gidx_contains(GIDX *a, GIDX *b)
{
int i, dims_a, dims_b;
POSTGIS_DEBUG(5, "entered function");
if ( (a == NULL) || (b == NULL) ) return FALSE;
dims_a = GIDX_NDIMS(a);
dims_b = GIDX_NDIMS(b);
if ( dims_a < dims_b )
{
/*
** If (b) is of higher dimensionality than (a) it can only be contained
** if those higher dimensions are zeroes.
*/
for (i = dims_a; i < dims_b; i++)
{
if ( GIDX_GET_MIN(b,i) != 0 )
return FALSE;
if ( GIDX_GET_MAX(b,i) != 0 )
return FALSE;
}
}
/* Excess dimensions of (a), don't matter, it just has to contain (b) in (b)'s dimensions */
for (i = 0; i < Min(dims_a, dims_b); i++)
{
if ( GIDX_GET_MIN(a,i) > GIDX_GET_MIN(b,i) )
return FALSE;
if ( GIDX_GET_MAX(a,i) < GIDX_GET_MAX(b,i) )
return FALSE;
}
return TRUE;
}
/* Calculate the volume (in n-d units) of the GIDX */
static float gidx_volume(GIDX *a)
{
float result;
int i;
if ( a == NULL )
{
/* elog(ERROR, "gidx_volume received a null argument"); */
return 0.0;
}
result = GIDX_GET_MAX(a,0) - GIDX_GET_MIN(a,0);
for ( i = 1; i < GIDX_NDIMS(a); i++ )
result *= (GIDX_GET_MAX(a,i) - GIDX_GET_MIN(a,i));
POSTGIS_DEBUGF(5, "calculated volume of %s as %.12g", gidx_to_string(a), result);
return result;
}
/* Ensure all minimums are below maximums. */
static inline void gidx_validate(GIDX *b)
{
int i;
Assert(b);
POSTGIS_DEBUGF(5,"validating gidx (%s)", gidx_to_string(b));
for ( i = 0; i < GIDX_NDIMS(b); i++ )
{
if ( GIDX_GET_MIN(b,i) > GIDX_GET_MAX(b,i) )
{
float tmp;
tmp = GIDX_GET_MIN(b,i);
GIDX_SET_MIN(b,i,GIDX_GET_MAX(b,i));
GIDX_SET_MAX(b,i,tmp);
}
}
return;
}
/*
** Make a copy of a GSERIALIZED, with a new bounding box value embedded.
*/
GSERIALIZED* gidx_insert_into_gserialized(GSERIALIZED *g, GIDX *gidx)
{
int g_ndims = (FLAGS_GET_GEODETIC(g->flags) ? 3 : FLAGS_NDIMS(g->flags));
int box_ndims = GIDX_NDIMS(gidx);
GSERIALIZED *g_out = NULL;
size_t box_size = 2 * g_ndims * sizeof(float);
/* The dimensionality of the inputs has to match or we are SOL. */
if ( g_ndims != box_ndims )
{
return NULL;
}
/* Serialized already has room for a box. We just need to copy it and
write the new values into place. */
if ( FLAGS_GET_BBOX(g->flags) )
{
g_out = palloc(VARSIZE(g));
memcpy(g_out, g, VARSIZE(g));
}
/* Serialized has no box. We need to allocate enough space for the old
data plus the box, and leave a gap in the memory segment to write
the new values into.
*/
else
{
size_t varsize_new = VARSIZE(g) + box_size;
uchar *ptr;
g_out = palloc(varsize_new);
/* Copy the head of g into place */
memcpy(g_out, g, 8);
/* Copy the body of g into place after leaving space for the box */
ptr = g_out->data;
ptr += box_size;
memcpy(ptr, g->data, VARSIZE(g) - 8);
FLAGS_SET_BBOX(g_out->flags, 1);
SET_VARSIZE(g_out, varsize_new);
}
/* Now write the gidx values into the memory segement */
memcpy(g_out->data, gidx->c, box_size);
return g_out;
}
static char* gidx_to_string(GIDX *a)
{
char *str, *rv;
int i, ndims;
if ( a == NULL )
return pstrdup("<NULLPTR>");
str = (char*)palloc(128);
rv = str;
ndims = GIDX_NDIMS(a);
str += sprintf(str, "GIDX(");
for ( i = 0; i < ndims; i++ )
str += sprintf(str, " %.12g", GIDX_GET_MIN(a,i));
str += sprintf(str, ",");
for ( i = 0; i < ndims; i++ )
str += sprintf(str, " %.12g", GIDX_GET_MAX(a,i));
str += sprintf(str, " )");
return rv;
}
Datum geography_gist_compress(PG_FUNCTION_ARGS)
{
GISTENTRY *entry_in = (GISTENTRY*)PG_GETARG_POINTER(0);
GISTENTRY *entry_out = NULL;
char gidxmem[GIDX_MAX_SIZE];
GIDX *bbox_out = (GIDX*)gidxmem;
int result = G_SUCCESS;
int i;
POSTGIS_DEBUG(4, "[GIST] 'compress' function called");
/*
** Not a leaf key? There's nothing to do.
** Return the input unchanged.
*/
if ( ! entry_in->leafkey )
{
POSTGIS_DEBUG(4, "[GIST] non-leafkey entry, returning input unaltered");
PG_RETURN_POINTER(entry_in);
}
POSTGIS_DEBUG(4, "[GIST] processing leafkey input");
entry_out = palloc(sizeof(GISTENTRY));
/*
** Null key? Make a copy of the input entry and
** return.
*/
if ( DatumGetPointer(entry_in->key) == NULL )
{
POSTGIS_DEBUG(4, "[GIST] leafkey is null");
gistentryinit(*entry_out, (Datum) 0, entry_in->rel,
entry_in->page, entry_in->offset, FALSE);
POSTGIS_DEBUG(4, "[GIST] returning copy of input");
PG_RETURN_POINTER(entry_out);
}
/* Extract our index key from the GiST entry. */
result = geography_datum_gidx(entry_in->key, bbox_out);
/* Is the bounding box valid (non-empty, non-infinite)? If not, return input uncompressed. */
if ( result == G_FAILURE )
{
POSTGIS_DEBUG(4, "[GIST] empty geometry!");
PG_RETURN_POINTER(entry_in);
}
POSTGIS_DEBUGF(4, "[GIST] got entry_in->key: %s", gidx_to_string(bbox_out));
/* Check all the dimensions for finite values */
for ( i = 0; i < GIDX_NDIMS(bbox_out); i++ )
{
if ( ! finite(GIDX_GET_MAX(bbox_out, i)) || ! finite(GIDX_GET_MIN(bbox_out, i)) )
{
POSTGIS_DEBUG(4, "[GIST] infinite geometry!");
PG_RETURN_POINTER(entry_in);
}
}
/* Enure bounding box has minimums below maximums. */
gidx_validate(bbox_out);
/* Prepare GISTENTRY for return. */
gistentryinit(*entry_out, PointerGetDatum(gidx_copy(bbox_out)),
entry_in->rel, entry_in->page, entry_in->offset, FALSE);
/* Return GISTENTRY. */
POSTGIS_DEBUG(4, "[GIST] 'compress' function complete");
PG_RETURN_POINTER(entry_out);
}
Datum geography_gist_picksplit(PG_FUNCTION_ARGS)
{
GistEntryVector *entryvec = (GistEntryVector*) PG_GETARG_POINTER(0);
GIST_SPLITVEC *v = (GIST_SPLITVEC*) PG_GETARG_POINTER(1);
OffsetNumber i;
/* One union box for each half of the space. */
GIDX **box_union;
/* One offset number list for each half of the space. */
OffsetNumber **list;
/* One position index for each half of the space. */
int *pos;
GIDX *box_pageunion;
GIDX *box_current;
int direction = -1;
bool all_entries_equal = true;
OffsetNumber max_offset;
int nbytes, ndims_pageunion, d;
int posmax = -1;
POSTGIS_DEBUG(4, "[GIST] 'picksplit' function called");
/*
** First calculate the bounding box and maximum number of dimensions in this page.
*/
max_offset = entryvec->n - 1;
box_current = (GIDX*) DatumGetPointer(entryvec->vector[FirstOffsetNumber].key);
box_pageunion = gidx_copy(box_current);
/* Calculate the containing box (box_pageunion) for the whole page we are going to split. */
for ( i = OffsetNumberNext(FirstOffsetNumber); i <= max_offset; i = OffsetNumberNext(i) )
{
box_current = (GIDX*) DatumGetPointer(entryvec->vector[i].key);
if ( all_entries_equal == true && ! gidx_equals (box_pageunion, box_current) )
all_entries_equal = false;
gidx_merge( &box_pageunion, box_current );
}
POSTGIS_DEBUGF(3, "[GIST] box_pageunion: %s", gidx_to_string(box_pageunion));
/* Every box in the page is the same! So, we split and just put half the boxes in each child. */
if ( all_entries_equal )
{
POSTGIS_DEBUG(4, "[GIST] picksplit finds all entries equal!");
geography_gist_picksplit_fallback(entryvec, v);
PG_RETURN_POINTER(v);
}
/* Initialize memory structures. */
nbytes = (max_offset + 2) * sizeof(OffsetNumber);
ndims_pageunion = GIDX_NDIMS(box_pageunion);
POSTGIS_DEBUGF(4, "[GIST] ndims_pageunion == %d", ndims_pageunion);
pos = palloc(2*ndims_pageunion * sizeof(int));
list = palloc(2*ndims_pageunion * sizeof(OffsetNumber*));
box_union = palloc(2*ndims_pageunion * sizeof(GIDX*));
for ( d = 0; d < ndims_pageunion; d++ )
{
list[BELOW(d)] = (OffsetNumber*) palloc(nbytes);
list[ABOVE(d)] = (OffsetNumber*) palloc(nbytes);
box_union[BELOW(d)] = gidx_new(ndims_pageunion);
box_union[ABOVE(d)] = gidx_new(ndims_pageunion);
pos[BELOW(d)] = 0;
pos[ABOVE(d)] = 0;
}
/*
** Assign each entry in the node to the volume partitions it belongs to,
** such as "above the x/y plane, left of the y/z plane, below the x/z plane".
** Each entry thereby ends up in three of the six partitions.
*/
POSTGIS_DEBUG(4, "[GIST] 'picksplit' calculating best split axis");
for ( i = FirstOffsetNumber; i <= max_offset; i = OffsetNumberNext(i) )
{
box_current = (GIDX*) DatumGetPointer(entryvec->vector[i].key);
for ( d = 0; d < ndims_pageunion; d++ )
{
if ( GIDX_GET_MIN(box_current,d)-GIDX_GET_MIN(box_pageunion,d) < GIDX_GET_MAX(box_pageunion,d)-GIDX_GET_MAX(box_current,d) )
{
geography_gist_picksplit_addlist(list[BELOW(d)], &(box_union[BELOW(d)]), box_current, &(pos[BELOW(d)]), i);
}
else
{
geography_gist_picksplit_addlist(list[ABOVE(d)], &(box_union[ABOVE(d)]), box_current, &(pos[ABOVE(d)]), i);
}
}
}
/*
** "Bad disposition", too many entries fell into one octant of the space, so no matter which
** plane we choose to split on, we're going to end up with a mostly full node. Where the
** data is pretty homogeneous (lots of duplicates) entries that are equidistant from the
** sides of the page union box can occasionally all end up in one place, leading
** to this condition.
*/
if ( geography_gist_picksplit_badratios(pos,ndims_pageunion) == TRUE )
{
/*
** Instead we split on center points and see if we do better.
** First calculate the average center point for each axis.
*/
double *avgCenter = palloc(ndims_pageunion * sizeof(double));
for ( d = 0; d < ndims_pageunion; d++ )
{
avgCenter[d] = 0.0;
}
POSTGIS_DEBUG(4, "[GIST] picksplit can't find good split axis, trying center point method");
for ( i = FirstOffsetNumber; i <= max_offset; i = OffsetNumberNext(i) )
{
box_current = (GIDX*) DatumGetPointer(entryvec->vector[i].key);
for ( d = 0; d < ndims_pageunion; d++ )
{
avgCenter[d] += (GIDX_GET_MAX(box_current,d) + GIDX_GET_MIN(box_current,d)) / 2.0;
}
}
for ( d = 0; d < ndims_pageunion; d++ )
{
avgCenter[d] /= max_offset;
pos[BELOW(d)] = pos[ABOVE(d)] = 0; /* Re-initialize our counters. */
POSTGIS_DEBUGF(4, "[GIST] picksplit average center point[%d] = %.12g", d, avgCenter[d]);
}
/* For each of our entries... */
for ( i = FirstOffsetNumber; i <= max_offset; i = OffsetNumberNext(i) )
{
double center;
box_current = (GIDX*) DatumGetPointer(entryvec->vector[i].key);
for ( d = 0; d < ndims_pageunion; d++ )
{
center = (GIDX_GET_MIN(box_current,d)+GIDX_GET_MAX(box_current,d))/2.0;
if ( center < avgCenter[d] )
geography_gist_picksplit_addlist(list[BELOW(d)], &(box_union[BELOW(d)]), box_current, &(pos[BELOW(d)]), i);
else if ( FPeq(center, avgCenter[d]) )
if ( pos[BELOW(d)] > pos[ABOVE(d)] )
geography_gist_picksplit_addlist(list[ABOVE(d)], &(box_union[ABOVE(d)]), box_current, &(pos[ABOVE(d)]), i);
else
geography_gist_picksplit_addlist(list[BELOW(d)], &(box_union[BELOW(d)]), box_current, &(pos[BELOW(d)]), i);
else
geography_gist_picksplit_addlist(list[ABOVE(d)], &(box_union[ABOVE(d)]), box_current, &(pos[ABOVE(d)]), i);
}
}
/* Do we have a good disposition now? If not, screw it, just cut the node in half. */
if ( geography_gist_picksplit_badratios(pos,ndims_pageunion) == TRUE )
{
POSTGIS_DEBUG(4, "[GIST] picksplit still cannot find a good split! just cutting the node in half");
geography_gist_picksplit_fallback(entryvec, v);
PG_RETURN_POINTER(v);
}
}
/*
** Now, what splitting plane gives us the most even ratio of
** entries in our child pages? Since each split region has been apportioned entries
** against the same number of total entries, the axis that has the smallest maximum
** number of entries in its regions is the most evenly distributed.
** TODO: what if the distributions are equal in two or more axes?
*/
for ( d = 0; d < ndims_pageunion; d++ )
{
int posd = Max(pos[ABOVE(d)],pos[BELOW(d)]);
if ( posd > posmax )
{
direction = d;
posmax = posd;
}
}
if ( direction == -1 || posmax == -1 )
{
/* ERROR OUT HERE */
elog(ERROR, "Error in building split, unable to determine split direction.");
}
POSTGIS_DEBUGF(3, "[GIST] 'picksplit' splitting on axis %d", direction);
geography_gist_picksplit_constructsplit(v, list[BELOW(direction)],
pos[BELOW(direction)],
&(box_union[BELOW(direction)]),
list[ABOVE(direction)],
pos[ABOVE(direction)],
&(box_union[ABOVE(direction)]) );
POSTGIS_DEBUGF(4, "[GIST] spl_ldatum: %s", gidx_to_string((GIDX*)v->spl_ldatum));
POSTGIS_DEBUGF(4, "[GIST] spl_rdatum: %s", gidx_to_string((GIDX*)v->spl_rdatum));
POSTGIS_DEBUGF(4, "[GIST] axis %d: parent range (%.12g, %.12g) left range (%.12g, %.12g), right range (%.12g, %.12g)",
direction,
GIDX_GET_MIN(box_pageunion, direction), GIDX_GET_MAX(box_pageunion, direction),
GIDX_GET_MIN((GIDX*)v->spl_ldatum, direction), GIDX_GET_MAX((GIDX*)v->spl_ldatum, direction),
GIDX_GET_MIN((GIDX*)v->spl_rdatum, direction), GIDX_GET_MAX((GIDX*)v->spl_rdatum, direction) );
PG_RETURN_POINTER(v);
}