Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * multirangetypes_selfuncs.c
4 : * Functions for selectivity estimation of multirange operators
5 : *
6 : * Estimates are based on histograms of lower and upper bounds, and the
7 : * fraction of empty multiranges.
8 : *
9 : * Portions Copyright (c) 1996-2025, PostgreSQL Global Development Group
10 : * Portions Copyright (c) 1994, Regents of the University of California
11 : *
12 : *
13 : * IDENTIFICATION
14 : * src/backend/utils/adt/multirangetypes_selfuncs.c
15 : *
16 : *-------------------------------------------------------------------------
17 : */
18 : #include "postgres.h"
19 :
20 : #include <math.h>
21 :
22 : #include "access/htup_details.h"
23 : #include "catalog/pg_operator.h"
24 : #include "catalog/pg_statistic.h"
25 : #include "utils/float.h"
26 : #include "utils/fmgrprotos.h"
27 : #include "utils/lsyscache.h"
28 : #include "utils/multirangetypes.h"
29 : #include "utils/rangetypes.h"
30 : #include "utils/selfuncs.h"
31 : #include "utils/typcache.h"
32 :
33 : static double calc_multirangesel(TypeCacheEntry *typcache,
34 : VariableStatData *vardata,
35 : const MultirangeType *constval, Oid operator);
36 : static double default_multirange_selectivity(Oid operator);
37 : static double calc_hist_selectivity(TypeCacheEntry *typcache,
38 : VariableStatData *vardata,
39 : const MultirangeType *constval,
40 : Oid operator);
41 : static double calc_hist_selectivity_scalar(TypeCacheEntry *typcache,
42 : const RangeBound *constbound,
43 : const RangeBound *hist,
44 : int hist_nvalues, bool equal);
45 : static int rbound_bsearch(TypeCacheEntry *typcache, const RangeBound *value,
46 : const RangeBound *hist, int hist_length, bool equal);
47 : static float8 get_position(TypeCacheEntry *typcache, const RangeBound *value,
48 : const RangeBound *hist1, const RangeBound *hist2);
49 : static float8 get_len_position(double value, double hist1, double hist2);
50 : static float8 get_distance(TypeCacheEntry *typcache, const RangeBound *bound1,
51 : const RangeBound *bound2);
52 : static int length_hist_bsearch(Datum *length_hist_values,
53 : int length_hist_nvalues, double value,
54 : bool equal);
55 : static double calc_length_hist_frac(Datum *length_hist_values,
56 : int length_hist_nvalues, double length1,
57 : double length2, bool equal);
58 : static double calc_hist_selectivity_contained(TypeCacheEntry *typcache,
59 : const RangeBound *lower,
60 : RangeBound *upper,
61 : const RangeBound *hist_lower,
62 : int hist_nvalues,
63 : Datum *length_hist_values,
64 : int length_hist_nvalues);
65 : static double calc_hist_selectivity_contains(TypeCacheEntry *typcache,
66 : const RangeBound *lower,
67 : const RangeBound *upper,
68 : const RangeBound *hist_lower,
69 : int hist_nvalues,
70 : Datum *length_hist_values,
71 : int length_hist_nvalues);
72 :
73 : /*
74 : * Returns a default selectivity estimate for given operator, when we don't
75 : * have statistics or cannot use them for some reason.
76 : */
77 : static double
78 950 : default_multirange_selectivity(Oid operator)
79 : {
80 950 : switch (operator)
81 : {
82 422 : case OID_MULTIRANGE_OVERLAPS_MULTIRANGE_OP:
83 : case OID_MULTIRANGE_OVERLAPS_RANGE_OP:
84 : case OID_RANGE_OVERLAPS_MULTIRANGE_OP:
85 422 : return 0.01;
86 :
87 342 : case OID_RANGE_CONTAINS_MULTIRANGE_OP:
88 : case OID_RANGE_MULTIRANGE_CONTAINED_OP:
89 : case OID_MULTIRANGE_CONTAINS_RANGE_OP:
90 : case OID_MULTIRANGE_CONTAINS_MULTIRANGE_OP:
91 : case OID_MULTIRANGE_RANGE_CONTAINED_OP:
92 : case OID_MULTIRANGE_MULTIRANGE_CONTAINED_OP:
93 342 : return 0.005;
94 :
95 66 : case OID_MULTIRANGE_CONTAINS_ELEM_OP:
96 : case OID_MULTIRANGE_ELEM_CONTAINED_OP:
97 :
98 : /*
99 : * "multirange @> elem" is more or less identical to a scalar
100 : * inequality "A >= b AND A <= c".
101 : */
102 66 : return DEFAULT_MULTIRANGE_INEQ_SEL;
103 :
104 120 : case OID_MULTIRANGE_LESS_OP:
105 : case OID_MULTIRANGE_LESS_EQUAL_OP:
106 : case OID_MULTIRANGE_GREATER_OP:
107 : case OID_MULTIRANGE_GREATER_EQUAL_OP:
108 : case OID_MULTIRANGE_LEFT_RANGE_OP:
109 : case OID_MULTIRANGE_LEFT_MULTIRANGE_OP:
110 : case OID_RANGE_LEFT_MULTIRANGE_OP:
111 : case OID_MULTIRANGE_RIGHT_RANGE_OP:
112 : case OID_MULTIRANGE_RIGHT_MULTIRANGE_OP:
113 : case OID_RANGE_RIGHT_MULTIRANGE_OP:
114 : case OID_MULTIRANGE_OVERLAPS_LEFT_RANGE_OP:
115 : case OID_RANGE_OVERLAPS_LEFT_MULTIRANGE_OP:
116 : case OID_MULTIRANGE_OVERLAPS_LEFT_MULTIRANGE_OP:
117 : case OID_MULTIRANGE_OVERLAPS_RIGHT_RANGE_OP:
118 : case OID_RANGE_OVERLAPS_RIGHT_MULTIRANGE_OP:
119 : case OID_MULTIRANGE_OVERLAPS_RIGHT_MULTIRANGE_OP:
120 : /* these are similar to regular scalar inequalities */
121 120 : return DEFAULT_INEQ_SEL;
122 :
123 0 : default:
124 :
125 : /*
126 : * all multirange operators should be handled above, but just in
127 : * case
128 : */
129 0 : return 0.01;
130 : }
131 : }
132 :
133 : /*
134 : * multirangesel -- restriction selectivity for multirange operators
135 : */
136 : Datum
137 1424 : multirangesel(PG_FUNCTION_ARGS)
138 : {
139 1424 : PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
140 1424 : Oid operator = PG_GETARG_OID(1);
141 1424 : List *args = (List *) PG_GETARG_POINTER(2);
142 1424 : int varRelid = PG_GETARG_INT32(3);
143 : VariableStatData vardata;
144 : Node *other;
145 : bool varonleft;
146 : Selectivity selec;
147 1424 : TypeCacheEntry *typcache = NULL;
148 1424 : MultirangeType *constmultirange = NULL;
149 1424 : RangeType *constrange = NULL;
150 :
151 : /*
152 : * If expression is not (variable op something) or (something op
153 : * variable), then punt and return a default estimate.
154 : */
155 1424 : if (!get_restriction_variable(root, args, varRelid,
156 : &vardata, &other, &varonleft))
157 0 : PG_RETURN_FLOAT8(default_multirange_selectivity(operator));
158 :
159 : /*
160 : * Can't do anything useful if the something is not a constant, either.
161 : */
162 1424 : if (!IsA(other, Const))
163 : {
164 102 : ReleaseVariableStats(vardata);
165 102 : PG_RETURN_FLOAT8(default_multirange_selectivity(operator));
166 : }
167 :
168 : /*
169 : * All the multirange operators are strict, so we can cope with a NULL
170 : * constant right away.
171 : */
172 1322 : if (((Const *) other)->constisnull)
173 : {
174 0 : ReleaseVariableStats(vardata);
175 0 : PG_RETURN_FLOAT8(0.0);
176 : }
177 :
178 : /*
179 : * If var is on the right, commute the operator, so that we can assume the
180 : * var is on the left in what follows.
181 : */
182 1322 : if (!varonleft)
183 : {
184 : /* we have other Op var, commute to make var Op other */
185 498 : operator = get_commutator(operator);
186 498 : if (!operator)
187 : {
188 : /* Use default selectivity (should we raise an error instead?) */
189 0 : ReleaseVariableStats(vardata);
190 0 : PG_RETURN_FLOAT8(default_multirange_selectivity(operator));
191 : }
192 : }
193 :
194 : /*
195 : * OK, there's a Var and a Const we're dealing with here. We need the
196 : * Const to be of same multirange type as the column, else we can't do
197 : * anything useful. (Such cases will likely fail at runtime, but here we'd
198 : * rather just return a default estimate.)
199 : *
200 : * If the operator is "multirange @> element", the constant should be of
201 : * the element type of the multirange column. Convert it to a multirange
202 : * that includes only that single point, so that we don't need special
203 : * handling for that in what follows.
204 : */
205 1322 : if (operator == OID_MULTIRANGE_CONTAINS_ELEM_OP)
206 : {
207 96 : typcache = multirange_get_typcache(fcinfo, vardata.vartype);
208 :
209 96 : if (((Const *) other)->consttype == typcache->rngtype->rngelemtype->type_id)
210 : {
211 : RangeBound lower,
212 : upper;
213 :
214 96 : lower.inclusive = true;
215 96 : lower.val = ((Const *) other)->constvalue;
216 96 : lower.infinite = false;
217 96 : lower.lower = true;
218 96 : upper.inclusive = true;
219 96 : upper.val = ((Const *) other)->constvalue;
220 96 : upper.infinite = false;
221 96 : upper.lower = false;
222 96 : constrange = range_serialize(typcache->rngtype, &lower, &upper,
223 : false, NULL);
224 96 : constmultirange = make_multirange(typcache->type_id, typcache->rngtype,
225 : 1, &constrange);
226 : }
227 : }
228 1226 : else if (operator == OID_RANGE_MULTIRANGE_CONTAINED_OP ||
229 1036 : operator == OID_MULTIRANGE_CONTAINS_RANGE_OP ||
230 1000 : operator == OID_MULTIRANGE_OVERLAPS_RANGE_OP ||
231 976 : operator == OID_MULTIRANGE_OVERLAPS_LEFT_RANGE_OP ||
232 952 : operator == OID_MULTIRANGE_OVERLAPS_RIGHT_RANGE_OP ||
233 928 : operator == OID_MULTIRANGE_LEFT_RANGE_OP ||
234 : operator == OID_MULTIRANGE_RIGHT_RANGE_OP)
235 : {
236 : /*
237 : * Promote a range in "multirange OP range" just like we do an element
238 : * in "multirange OP element".
239 : */
240 322 : typcache = multirange_get_typcache(fcinfo, vardata.vartype);
241 322 : if (((Const *) other)->consttype == typcache->rngtype->type_id)
242 : {
243 322 : constrange = DatumGetRangeTypeP(((Const *) other)->constvalue);
244 322 : constmultirange = make_multirange(typcache->type_id, typcache->rngtype,
245 : 1, &constrange);
246 : }
247 : }
248 904 : else if (operator == OID_RANGE_OVERLAPS_MULTIRANGE_OP ||
249 868 : operator == OID_RANGE_OVERLAPS_LEFT_MULTIRANGE_OP ||
250 850 : operator == OID_RANGE_OVERLAPS_RIGHT_MULTIRANGE_OP ||
251 832 : operator == OID_RANGE_LEFT_MULTIRANGE_OP ||
252 814 : operator == OID_RANGE_RIGHT_MULTIRANGE_OP ||
253 778 : operator == OID_RANGE_CONTAINS_MULTIRANGE_OP ||
254 778 : operator == OID_MULTIRANGE_ELEM_CONTAINED_OP ||
255 : operator == OID_MULTIRANGE_RANGE_CONTAINED_OP)
256 : {
257 : /*
258 : * Here, the Var is the elem/range, not the multirange. For now we
259 : * just punt and return the default estimate. In future we could
260 : * disassemble the multirange constant to do something more
261 : * intelligent.
262 : */
263 : }
264 760 : else if (((Const *) other)->consttype == vardata.vartype)
265 : {
266 : /* Both sides are the same multirange type */
267 760 : typcache = multirange_get_typcache(fcinfo, vardata.vartype);
268 :
269 760 : constmultirange = DatumGetMultirangeTypeP(((Const *) other)->constvalue);
270 : }
271 :
272 : /*
273 : * If we got a valid constant on one side of the operator, proceed to
274 : * estimate using statistics. Otherwise punt and return a default constant
275 : * estimate. Note that calc_multirangesel need not handle
276 : * OID_MULTIRANGE_*_CONTAINED_OP.
277 : */
278 1322 : if (constmultirange)
279 1178 : selec = calc_multirangesel(typcache, &vardata, constmultirange, operator);
280 : else
281 144 : selec = default_multirange_selectivity(operator);
282 :
283 1322 : ReleaseVariableStats(vardata);
284 :
285 1322 : CLAMP_PROBABILITY(selec);
286 :
287 1322 : PG_RETURN_FLOAT8((float8) selec);
288 : }
289 :
290 : static double
291 1178 : calc_multirangesel(TypeCacheEntry *typcache, VariableStatData *vardata,
292 : const MultirangeType *constval, Oid operator)
293 : {
294 : double hist_selec;
295 : double selec;
296 : float4 empty_frac,
297 : null_frac;
298 :
299 : /*
300 : * First look up the fraction of NULLs and empty multiranges from
301 : * pg_statistic.
302 : */
303 1178 : if (HeapTupleIsValid(vardata->statsTuple))
304 : {
305 : Form_pg_statistic stats;
306 : AttStatsSlot sslot;
307 :
308 450 : stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
309 450 : null_frac = stats->stanullfrac;
310 :
311 : /* Try to get fraction of empty multiranges */
312 450 : if (get_attstatsslot(&sslot, vardata->statsTuple,
313 : STATISTIC_KIND_RANGE_LENGTH_HISTOGRAM,
314 : InvalidOid,
315 : ATTSTATSSLOT_NUMBERS))
316 : {
317 450 : if (sslot.nnumbers != 1)
318 0 : elog(ERROR, "invalid empty fraction statistic"); /* shouldn't happen */
319 450 : empty_frac = sslot.numbers[0];
320 450 : free_attstatsslot(&sslot);
321 : }
322 : else
323 : {
324 : /* No empty fraction statistic. Assume no empty ranges. */
325 0 : empty_frac = 0.0;
326 : }
327 : }
328 : else
329 : {
330 : /*
331 : * No stats are available. Follow through the calculations below
332 : * anyway, assuming no NULLs and no empty multiranges. This still
333 : * allows us to give a better-than-nothing estimate based on whether
334 : * the constant is an empty multirange or not.
335 : */
336 728 : null_frac = 0.0;
337 728 : empty_frac = 0.0;
338 : }
339 :
340 1178 : if (MultirangeIsEmpty(constval))
341 : {
342 : /*
343 : * An empty multirange matches all multiranges, all empty multiranges,
344 : * or nothing, depending on the operator
345 : */
346 222 : switch (operator)
347 : {
348 : /* these return false if either argument is empty */
349 126 : case OID_MULTIRANGE_OVERLAPS_RANGE_OP:
350 : case OID_MULTIRANGE_OVERLAPS_MULTIRANGE_OP:
351 : case OID_MULTIRANGE_OVERLAPS_LEFT_RANGE_OP:
352 : case OID_MULTIRANGE_OVERLAPS_LEFT_MULTIRANGE_OP:
353 : case OID_MULTIRANGE_OVERLAPS_RIGHT_RANGE_OP:
354 : case OID_MULTIRANGE_OVERLAPS_RIGHT_MULTIRANGE_OP:
355 : case OID_MULTIRANGE_LEFT_RANGE_OP:
356 : case OID_MULTIRANGE_LEFT_MULTIRANGE_OP:
357 : case OID_MULTIRANGE_RIGHT_RANGE_OP:
358 : case OID_MULTIRANGE_RIGHT_MULTIRANGE_OP:
359 : /* nothing is less than an empty multirange */
360 : case OID_MULTIRANGE_LESS_OP:
361 126 : selec = 0.0;
362 126 : break;
363 :
364 : /*
365 : * only empty multiranges can be contained by an empty
366 : * multirange
367 : */
368 30 : case OID_RANGE_MULTIRANGE_CONTAINED_OP:
369 : case OID_MULTIRANGE_MULTIRANGE_CONTAINED_OP:
370 : /* only empty ranges are <= an empty multirange */
371 : case OID_MULTIRANGE_LESS_EQUAL_OP:
372 30 : selec = empty_frac;
373 30 : break;
374 :
375 : /* everything contains an empty multirange */
376 60 : case OID_MULTIRANGE_CONTAINS_RANGE_OP:
377 : case OID_MULTIRANGE_CONTAINS_MULTIRANGE_OP:
378 : /* everything is >= an empty multirange */
379 : case OID_MULTIRANGE_GREATER_EQUAL_OP:
380 60 : selec = 1.0;
381 60 : break;
382 :
383 : /* all non-empty multiranges are > an empty multirange */
384 6 : case OID_MULTIRANGE_GREATER_OP:
385 6 : selec = 1.0 - empty_frac;
386 6 : break;
387 :
388 : /* an element cannot be empty */
389 0 : case OID_MULTIRANGE_CONTAINS_ELEM_OP:
390 :
391 : /* filtered out by multirangesel() */
392 : case OID_RANGE_OVERLAPS_MULTIRANGE_OP:
393 : case OID_RANGE_OVERLAPS_LEFT_MULTIRANGE_OP:
394 : case OID_RANGE_OVERLAPS_RIGHT_MULTIRANGE_OP:
395 : case OID_RANGE_LEFT_MULTIRANGE_OP:
396 : case OID_RANGE_RIGHT_MULTIRANGE_OP:
397 : case OID_RANGE_CONTAINS_MULTIRANGE_OP:
398 : case OID_MULTIRANGE_ELEM_CONTAINED_OP:
399 : case OID_MULTIRANGE_RANGE_CONTAINED_OP:
400 :
401 : default:
402 0 : elog(ERROR, "unexpected operator %u", operator);
403 : selec = 0.0; /* keep compiler quiet */
404 : break;
405 : }
406 : }
407 : else
408 : {
409 : /*
410 : * Calculate selectivity using bound histograms. If that fails for
411 : * some reason, e.g no histogram in pg_statistic, use the default
412 : * constant estimate for the fraction of non-empty values. This is
413 : * still somewhat better than just returning the default estimate,
414 : * because this still takes into account the fraction of empty and
415 : * NULL tuples, if we had statistics for them.
416 : */
417 956 : hist_selec = calc_hist_selectivity(typcache, vardata, constval,
418 : operator);
419 956 : if (hist_selec < 0.0)
420 704 : hist_selec = default_multirange_selectivity(operator);
421 :
422 : /*
423 : * Now merge the results for the empty multiranges and histogram
424 : * calculations, realizing that the histogram covers only the
425 : * non-null, non-empty values.
426 : */
427 956 : if (operator == OID_RANGE_MULTIRANGE_CONTAINED_OP ||
428 : operator == OID_MULTIRANGE_MULTIRANGE_CONTAINED_OP)
429 : {
430 : /* empty is contained by anything non-empty */
431 24 : selec = (1.0 - empty_frac) * hist_selec + empty_frac;
432 : }
433 : else
434 : {
435 : /* with any other operator, empty Op non-empty matches nothing */
436 932 : selec = (1.0 - empty_frac) * hist_selec;
437 : }
438 : }
439 :
440 : /* all multirange operators are strict */
441 1178 : selec *= (1.0 - null_frac);
442 :
443 : /* result should be in range, but make sure... */
444 1178 : CLAMP_PROBABILITY(selec);
445 :
446 1178 : return selec;
447 : }
448 :
449 : /*
450 : * Calculate multirange operator selectivity using histograms of multirange bounds.
451 : *
452 : * This estimate is for the portion of values that are not empty and not
453 : * NULL.
454 : */
455 : static double
456 956 : calc_hist_selectivity(TypeCacheEntry *typcache, VariableStatData *vardata,
457 : const MultirangeType *constval, Oid operator)
458 : {
459 956 : TypeCacheEntry *rng_typcache = typcache->rngtype;
460 : AttStatsSlot hslot;
461 : AttStatsSlot lslot;
462 : int nhist;
463 : RangeBound *hist_lower;
464 : RangeBound *hist_upper;
465 : int i;
466 : RangeBound const_lower;
467 : RangeBound const_upper;
468 : RangeBound tmp;
469 : double hist_selec;
470 :
471 : /* Can't use the histogram with insecure multirange support functions */
472 956 : if (!statistic_proc_security_check(vardata,
473 : rng_typcache->rng_cmp_proc_finfo.fn_oid))
474 0 : return -1;
475 956 : if (OidIsValid(rng_typcache->rng_subdiff_finfo.fn_oid) &&
476 956 : !statistic_proc_security_check(vardata,
477 : rng_typcache->rng_subdiff_finfo.fn_oid))
478 240 : return -1;
479 :
480 : /* Try to get histogram of ranges */
481 968 : if (!(HeapTupleIsValid(vardata->statsTuple) &&
482 252 : get_attstatsslot(&hslot, vardata->statsTuple,
483 : STATISTIC_KIND_BOUNDS_HISTOGRAM, InvalidOid,
484 : ATTSTATSSLOT_VALUES)))
485 464 : return -1.0;
486 :
487 : /* check that it's a histogram, not just a dummy entry */
488 252 : if (hslot.nvalues < 2)
489 : {
490 0 : free_attstatsslot(&hslot);
491 0 : return -1.0;
492 : }
493 :
494 : /*
495 : * Convert histogram of ranges into histograms of its lower and upper
496 : * bounds.
497 : */
498 252 : nhist = hslot.nvalues;
499 252 : hist_lower = (RangeBound *) palloc(sizeof(RangeBound) * nhist);
500 252 : hist_upper = (RangeBound *) palloc(sizeof(RangeBound) * nhist);
501 18936 : for (i = 0; i < nhist; i++)
502 : {
503 : bool empty;
504 :
505 18684 : range_deserialize(rng_typcache, DatumGetRangeTypeP(hslot.values[i]),
506 18684 : &hist_lower[i], &hist_upper[i], &empty);
507 : /* The histogram should not contain any empty ranges */
508 18684 : if (empty)
509 0 : elog(ERROR, "bounds histogram contains an empty range");
510 : }
511 :
512 : /* @> and @< also need a histogram of range lengths */
513 252 : if (operator == OID_MULTIRANGE_CONTAINS_RANGE_OP ||
514 204 : operator == OID_MULTIRANGE_CONTAINS_MULTIRANGE_OP ||
515 204 : operator == OID_MULTIRANGE_RANGE_CONTAINED_OP ||
516 : operator == OID_MULTIRANGE_MULTIRANGE_CONTAINED_OP)
517 : {
518 120 : if (!(HeapTupleIsValid(vardata->statsTuple) &&
519 60 : get_attstatsslot(&lslot, vardata->statsTuple,
520 : STATISTIC_KIND_RANGE_LENGTH_HISTOGRAM,
521 : InvalidOid,
522 : ATTSTATSSLOT_VALUES)))
523 : {
524 0 : free_attstatsslot(&hslot);
525 0 : return -1.0;
526 : }
527 :
528 : /* check that it's a histogram, not just a dummy entry */
529 60 : if (lslot.nvalues < 2)
530 : {
531 0 : free_attstatsslot(&lslot);
532 0 : free_attstatsslot(&hslot);
533 0 : return -1.0;
534 : }
535 : }
536 : else
537 192 : memset(&lslot, 0, sizeof(lslot));
538 :
539 : /* Extract the bounds of the constant value. */
540 : Assert(constval->rangeCount > 0);
541 252 : multirange_get_bounds(rng_typcache, constval, 0,
542 : &const_lower, &tmp);
543 252 : multirange_get_bounds(rng_typcache, constval, constval->rangeCount - 1,
544 : &tmp, &const_upper);
545 :
546 : /*
547 : * Calculate selectivity comparing the lower or upper bound of the
548 : * constant with the histogram of lower or upper bounds.
549 : */
550 252 : switch (operator)
551 : {
552 0 : case OID_MULTIRANGE_LESS_OP:
553 :
554 : /*
555 : * The regular b-tree comparison operators (<, <=, >, >=) compare
556 : * the lower bounds first, and the upper bounds for values with
557 : * equal lower bounds. Estimate that by comparing the lower bounds
558 : * only. This gives a fairly accurate estimate assuming there
559 : * aren't many rows with a lower bound equal to the constant's
560 : * lower bound.
561 : */
562 : hist_selec =
563 0 : calc_hist_selectivity_scalar(rng_typcache, &const_lower,
564 : hist_lower, nhist, false);
565 0 : break;
566 :
567 0 : case OID_MULTIRANGE_LESS_EQUAL_OP:
568 : hist_selec =
569 0 : calc_hist_selectivity_scalar(rng_typcache, &const_lower,
570 : hist_lower, nhist, true);
571 0 : break;
572 :
573 0 : case OID_MULTIRANGE_GREATER_OP:
574 0 : hist_selec =
575 0 : 1 - calc_hist_selectivity_scalar(rng_typcache, &const_lower,
576 : hist_lower, nhist, false);
577 0 : break;
578 :
579 0 : case OID_MULTIRANGE_GREATER_EQUAL_OP:
580 0 : hist_selec =
581 0 : 1 - calc_hist_selectivity_scalar(rng_typcache, &const_lower,
582 : hist_lower, nhist, true);
583 0 : break;
584 :
585 24 : case OID_MULTIRANGE_LEFT_RANGE_OP:
586 : case OID_MULTIRANGE_LEFT_MULTIRANGE_OP:
587 : /* var << const when upper(var) < lower(const) */
588 : hist_selec =
589 24 : calc_hist_selectivity_scalar(rng_typcache, &const_lower,
590 : hist_upper, nhist, false);
591 24 : break;
592 :
593 24 : case OID_MULTIRANGE_RIGHT_RANGE_OP:
594 : case OID_MULTIRANGE_RIGHT_MULTIRANGE_OP:
595 : /* var >> const when lower(var) > upper(const) */
596 24 : hist_selec =
597 24 : 1 - calc_hist_selectivity_scalar(rng_typcache, &const_upper,
598 : hist_lower, nhist, true);
599 24 : break;
600 :
601 24 : case OID_MULTIRANGE_OVERLAPS_RIGHT_RANGE_OP:
602 : case OID_MULTIRANGE_OVERLAPS_RIGHT_MULTIRANGE_OP:
603 : /* compare lower bounds */
604 24 : hist_selec =
605 24 : 1 - calc_hist_selectivity_scalar(rng_typcache, &const_lower,
606 : hist_lower, nhist, false);
607 24 : break;
608 :
609 24 : case OID_MULTIRANGE_OVERLAPS_LEFT_RANGE_OP:
610 : case OID_MULTIRANGE_OVERLAPS_LEFT_MULTIRANGE_OP:
611 : /* compare upper bounds */
612 : hist_selec =
613 24 : calc_hist_selectivity_scalar(rng_typcache, &const_upper,
614 : hist_upper, nhist, true);
615 24 : break;
616 :
617 84 : case OID_MULTIRANGE_OVERLAPS_RANGE_OP:
618 : case OID_MULTIRANGE_OVERLAPS_MULTIRANGE_OP:
619 : case OID_MULTIRANGE_CONTAINS_ELEM_OP:
620 :
621 : /*
622 : * A && B <=> NOT (A << B OR A >> B).
623 : *
624 : * Since A << B and A >> B are mutually exclusive events we can
625 : * sum their probabilities to find probability of (A << B OR A >>
626 : * B).
627 : *
628 : * "multirange @> elem" is equivalent to "multirange &&
629 : * {[elem,elem]}". The caller already constructed the singular
630 : * range from the element constant, so just treat it the same as
631 : * &&.
632 : */
633 : hist_selec =
634 84 : calc_hist_selectivity_scalar(rng_typcache,
635 : &const_lower, hist_upper,
636 : nhist, false);
637 84 : hist_selec +=
638 84 : (1.0 - calc_hist_selectivity_scalar(rng_typcache,
639 : &const_upper, hist_lower,
640 : nhist, true));
641 84 : hist_selec = 1.0 - hist_selec;
642 84 : break;
643 :
644 48 : case OID_MULTIRANGE_CONTAINS_RANGE_OP:
645 : case OID_MULTIRANGE_CONTAINS_MULTIRANGE_OP:
646 : hist_selec =
647 48 : calc_hist_selectivity_contains(rng_typcache, &const_lower,
648 : &const_upper, hist_lower, nhist,
649 : lslot.values, lslot.nvalues);
650 48 : break;
651 :
652 24 : case OID_MULTIRANGE_MULTIRANGE_CONTAINED_OP:
653 : case OID_RANGE_MULTIRANGE_CONTAINED_OP:
654 24 : if (const_lower.infinite)
655 : {
656 : /*
657 : * Lower bound no longer matters. Just estimate the fraction
658 : * with an upper bound <= const upper bound
659 : */
660 : hist_selec =
661 0 : calc_hist_selectivity_scalar(rng_typcache, &const_upper,
662 : hist_upper, nhist, true);
663 : }
664 24 : else if (const_upper.infinite)
665 : {
666 0 : hist_selec =
667 0 : 1.0 - calc_hist_selectivity_scalar(rng_typcache, &const_lower,
668 : hist_lower, nhist, false);
669 : }
670 : else
671 : {
672 : hist_selec =
673 24 : calc_hist_selectivity_contained(rng_typcache, &const_lower,
674 : &const_upper, hist_lower, nhist,
675 : lslot.values, lslot.nvalues);
676 : }
677 24 : break;
678 :
679 : /* filtered out by multirangesel() */
680 0 : case OID_RANGE_OVERLAPS_MULTIRANGE_OP:
681 : case OID_RANGE_OVERLAPS_LEFT_MULTIRANGE_OP:
682 : case OID_RANGE_OVERLAPS_RIGHT_MULTIRANGE_OP:
683 : case OID_RANGE_LEFT_MULTIRANGE_OP:
684 : case OID_RANGE_RIGHT_MULTIRANGE_OP:
685 : case OID_RANGE_CONTAINS_MULTIRANGE_OP:
686 : case OID_MULTIRANGE_ELEM_CONTAINED_OP:
687 : case OID_MULTIRANGE_RANGE_CONTAINED_OP:
688 :
689 : default:
690 0 : elog(ERROR, "unknown multirange operator %u", operator);
691 : hist_selec = -1.0; /* keep compiler quiet */
692 : break;
693 : }
694 :
695 252 : free_attstatsslot(&lslot);
696 252 : free_attstatsslot(&hslot);
697 :
698 252 : return hist_selec;
699 : }
700 :
701 :
702 : /*
703 : * Look up the fraction of values less than (or equal, if 'equal' argument
704 : * is true) a given const in a histogram of range bounds.
705 : */
706 : static double
707 264 : calc_hist_selectivity_scalar(TypeCacheEntry *typcache, const RangeBound *constbound,
708 : const RangeBound *hist, int hist_nvalues, bool equal)
709 : {
710 : Selectivity selec;
711 : int index;
712 :
713 : /*
714 : * Find the histogram bin the given constant falls into. Estimate
715 : * selectivity as the number of preceding whole bins.
716 : */
717 264 : index = rbound_bsearch(typcache, constbound, hist, hist_nvalues, equal);
718 264 : selec = (Selectivity) (Max(index, 0)) / (Selectivity) (hist_nvalues - 1);
719 :
720 : /* Adjust using linear interpolation within the bin */
721 264 : if (index >= 0 && index < hist_nvalues - 1)
722 360 : selec += get_position(typcache, constbound, &hist[index],
723 180 : &hist[index + 1]) / (Selectivity) (hist_nvalues - 1);
724 :
725 264 : return selec;
726 : }
727 :
728 : /*
729 : * Binary search on an array of range bounds. Returns greatest index of range
730 : * bound in array which is less(less or equal) than given range bound. If all
731 : * range bounds in array are greater or equal(greater) than given range bound,
732 : * return -1. When "equal" flag is set conditions in brackets are used.
733 : *
734 : * This function is used in scalar operator selectivity estimation. Another
735 : * goal of this function is to find a histogram bin where to stop
736 : * interpolation of portion of bounds which are less than or equal to given bound.
737 : */
738 : static int
739 336 : rbound_bsearch(TypeCacheEntry *typcache, const RangeBound *value, const RangeBound *hist,
740 : int hist_length, bool equal)
741 : {
742 336 : int lower = -1,
743 336 : upper = hist_length - 1,
744 : cmp,
745 : middle;
746 :
747 2136 : while (lower < upper)
748 : {
749 1800 : middle = (lower + upper + 1) / 2;
750 1800 : cmp = range_cmp_bounds(typcache, &hist[middle], value);
751 :
752 1800 : if (cmp < 0 || (equal && cmp == 0))
753 744 : lower = middle;
754 : else
755 1056 : upper = middle - 1;
756 : }
757 336 : return lower;
758 : }
759 :
760 :
761 : /*
762 : * Binary search on length histogram. Returns greatest index of range length in
763 : * histogram which is less than (less than or equal) the given length value. If
764 : * all lengths in the histogram are greater than (greater than or equal) the
765 : * given length, returns -1.
766 : */
767 : static int
768 360 : length_hist_bsearch(Datum *length_hist_values, int length_hist_nvalues,
769 : double value, bool equal)
770 : {
771 360 : int lower = -1,
772 360 : upper = length_hist_nvalues - 1,
773 : middle;
774 :
775 1872 : while (lower < upper)
776 : {
777 : double middleval;
778 :
779 1512 : middle = (lower + upper + 1) / 2;
780 :
781 1512 : middleval = DatumGetFloat8(length_hist_values[middle]);
782 1512 : if (middleval < value || (equal && middleval <= value))
783 744 : lower = middle;
784 : else
785 768 : upper = middle - 1;
786 : }
787 360 : return lower;
788 : }
789 :
790 : /*
791 : * Get relative position of value in histogram bin in [0,1] range.
792 : */
793 : static float8
794 276 : get_position(TypeCacheEntry *typcache, const RangeBound *value, const RangeBound *hist1,
795 : const RangeBound *hist2)
796 : {
797 276 : bool has_subdiff = OidIsValid(typcache->rng_subdiff_finfo.fn_oid);
798 : float8 position;
799 :
800 276 : if (!hist1->infinite && !hist2->infinite)
801 : {
802 : float8 bin_width;
803 :
804 : /*
805 : * Both bounds are finite. Assuming the subtype's comparison function
806 : * works sanely, the value must be finite, too, because it lies
807 : * somewhere between the bounds. If it doesn't, arbitrarily return
808 : * 0.5.
809 : */
810 204 : if (value->infinite)
811 0 : return 0.5;
812 :
813 : /* Can't interpolate without subdiff function */
814 204 : if (!has_subdiff)
815 0 : return 0.5;
816 :
817 : /* Calculate relative position using subdiff function. */
818 204 : bin_width = DatumGetFloat8(FunctionCall2Coll(&typcache->rng_subdiff_finfo,
819 : typcache->rng_collation,
820 : hist2->val,
821 : hist1->val));
822 204 : if (isnan(bin_width) || bin_width <= 0.0)
823 0 : return 0.5; /* punt for NaN or zero-width bin */
824 :
825 204 : position = DatumGetFloat8(FunctionCall2Coll(&typcache->rng_subdiff_finfo,
826 : typcache->rng_collation,
827 : value->val,
828 : hist1->val))
829 : / bin_width;
830 :
831 204 : if (isnan(position))
832 0 : return 0.5; /* punt for NaN from subdiff, Inf/Inf, etc */
833 :
834 : /* Relative position must be in [0,1] range */
835 204 : position = Max(position, 0.0);
836 204 : position = Min(position, 1.0);
837 204 : return position;
838 : }
839 72 : else if (hist1->infinite && !hist2->infinite)
840 : {
841 : /*
842 : * Lower bin boundary is -infinite, upper is finite. If the value is
843 : * -infinite, return 0.0 to indicate it's equal to the lower bound.
844 : * Otherwise return 1.0 to indicate it's infinitely far from the lower
845 : * bound.
846 : */
847 60 : return ((value->infinite && value->lower) ? 0.0 : 1.0);
848 : }
849 12 : else if (!hist1->infinite && hist2->infinite)
850 : {
851 : /* same as above, but in reverse */
852 12 : return ((value->infinite && !value->lower) ? 1.0 : 0.0);
853 : }
854 : else
855 : {
856 : /*
857 : * If both bin boundaries are infinite, they should be equal to each
858 : * other, and the value should also be infinite and equal to both
859 : * bounds. (But don't Assert that, to avoid crashing if a user creates
860 : * a datatype with a broken comparison function).
861 : *
862 : * Assume the value to lie in the middle of the infinite bounds.
863 : */
864 0 : return 0.5;
865 : }
866 : }
867 :
868 :
869 : /*
870 : * Get relative position of value in a length histogram bin in [0,1] range.
871 : */
872 : static double
873 360 : get_len_position(double value, double hist1, double hist2)
874 : {
875 360 : if (!isinf(hist1) && !isinf(hist2))
876 : {
877 : /*
878 : * Both bounds are finite. The value should be finite too, because it
879 : * lies somewhere between the bounds. If it doesn't, just return
880 : * something.
881 : */
882 60 : if (isinf(value))
883 0 : return 0.5;
884 :
885 60 : return 1.0 - (hist2 - value) / (hist2 - hist1);
886 : }
887 300 : else if (isinf(hist1) && !isinf(hist2))
888 : {
889 : /*
890 : * Lower bin boundary is -infinite, upper is finite. Return 1.0 to
891 : * indicate the value is infinitely far from the lower bound.
892 : */
893 0 : return 1.0;
894 : }
895 300 : else if (isinf(hist1) && isinf(hist2))
896 : {
897 : /* same as above, but in reverse */
898 0 : return 0.0;
899 : }
900 : else
901 : {
902 : /*
903 : * If both bin boundaries are infinite, they should be equal to each
904 : * other, and the value should also be infinite and equal to both
905 : * bounds. (But don't Assert that, to avoid crashing unnecessarily if
906 : * the caller messes up)
907 : *
908 : * Assume the value to lie in the middle of the infinite bounds.
909 : */
910 300 : return 0.5;
911 : }
912 : }
913 :
914 : /*
915 : * Measure distance between two range bounds.
916 : */
917 : static float8
918 408 : get_distance(TypeCacheEntry *typcache, const RangeBound *bound1, const RangeBound *bound2)
919 : {
920 408 : bool has_subdiff = OidIsValid(typcache->rng_subdiff_finfo.fn_oid);
921 :
922 408 : if (!bound1->infinite && !bound2->infinite)
923 : {
924 : /*
925 : * Neither bound is infinite, use subdiff function or return default
926 : * value of 1.0 if no subdiff is available.
927 : */
928 240 : if (has_subdiff)
929 : {
930 : float8 res;
931 :
932 240 : res = DatumGetFloat8(FunctionCall2Coll(&typcache->rng_subdiff_finfo,
933 : typcache->rng_collation,
934 : bound2->val,
935 : bound1->val));
936 : /* Reject possible NaN result, also negative result */
937 240 : if (isnan(res) || res < 0.0)
938 0 : return 1.0;
939 : else
940 240 : return res;
941 : }
942 : else
943 0 : return 1.0;
944 : }
945 168 : else if (bound1->infinite && bound2->infinite)
946 : {
947 : /* Both bounds are infinite */
948 0 : if (bound1->lower == bound2->lower)
949 0 : return 0.0;
950 : else
951 0 : return get_float8_infinity();
952 : }
953 : else
954 : {
955 : /* One bound is infinite, the other is not */
956 168 : return get_float8_infinity();
957 : }
958 : }
959 :
960 : /*
961 : * Calculate the average of function P(x), in the interval [length1, length2],
962 : * where P(x) is the fraction of tuples with length < x (or length <= x if
963 : * 'equal' is true).
964 : */
965 : static double
966 360 : calc_length_hist_frac(Datum *length_hist_values, int length_hist_nvalues,
967 : double length1, double length2, bool equal)
968 : {
969 : double frac;
970 : double A,
971 : B,
972 : PA,
973 : PB;
974 : double pos;
975 : int i;
976 : double area;
977 :
978 : Assert(length2 >= length1);
979 :
980 360 : if (length2 < 0.0)
981 0 : return 0.0; /* shouldn't happen, but doesn't hurt to check */
982 :
983 : /* All lengths in the table are <= infinite. */
984 360 : if (isinf(length2) && equal)
985 0 : return 1.0;
986 :
987 : /*----------
988 : * The average of a function between A and B can be calculated by the
989 : * formula:
990 : *
991 : * B
992 : * 1 /
993 : * ------- | P(x)dx
994 : * B - A /
995 : * A
996 : *
997 : * The geometrical interpretation of the integral is the area under the
998 : * graph of P(x). P(x) is defined by the length histogram. We calculate
999 : * the area in a piecewise fashion, iterating through the length histogram
1000 : * bins. Each bin is a trapezoid:
1001 : *
1002 : * P(x2)
1003 : * /|
1004 : * / |
1005 : * P(x1)/ |
1006 : * | |
1007 : * | |
1008 : * ---+---+--
1009 : * x1 x2
1010 : *
1011 : * where x1 and x2 are the boundaries of the current histogram, and P(x1)
1012 : * and P(x1) are the cumulative fraction of tuples at the boundaries.
1013 : *
1014 : * The area of each trapezoid is 1/2 * (P(x2) + P(x1)) * (x2 - x1)
1015 : *
1016 : * The first bin contains the lower bound passed by the caller, so we
1017 : * use linear interpolation between the previous and next histogram bin
1018 : * boundary to calculate P(x1). Likewise for the last bin: we use linear
1019 : * interpolation to calculate P(x2). For the bins in between, x1 and x2
1020 : * lie on histogram bin boundaries, so P(x1) and P(x2) are simply:
1021 : * P(x1) = (bin index) / (number of bins)
1022 : * P(x2) = (bin index + 1 / (number of bins)
1023 : */
1024 :
1025 : /* First bin, the one that contains lower bound */
1026 360 : i = length_hist_bsearch(length_hist_values, length_hist_nvalues, length1, equal);
1027 360 : if (i >= length_hist_nvalues - 1)
1028 48 : return 1.0;
1029 :
1030 312 : if (i < 0)
1031 : {
1032 84 : i = 0;
1033 84 : pos = 0.0;
1034 : }
1035 : else
1036 : {
1037 : /* interpolate length1's position in the bin */
1038 228 : pos = get_len_position(length1,
1039 228 : DatumGetFloat8(length_hist_values[i]),
1040 228 : DatumGetFloat8(length_hist_values[i + 1]));
1041 : }
1042 312 : PB = (((double) i) + pos) / (double) (length_hist_nvalues - 1);
1043 312 : B = length1;
1044 :
1045 : /*
1046 : * In the degenerate case that length1 == length2, simply return
1047 : * P(length1). This is not merely an optimization: if length1 == length2,
1048 : * we'd divide by zero later on.
1049 : */
1050 312 : if (length2 == length1)
1051 144 : return PB;
1052 :
1053 : /*
1054 : * Loop through all the bins, until we hit the last bin, the one that
1055 : * contains the upper bound. (if lower and upper bounds are in the same
1056 : * bin, this falls out immediately)
1057 : */
1058 168 : area = 0.0;
1059 3168 : for (; i < length_hist_nvalues - 1; i++)
1060 : {
1061 3168 : double bin_upper = DatumGetFloat8(length_hist_values[i + 1]);
1062 :
1063 : /* check if we've reached the last bin */
1064 3168 : if (!(bin_upper < length2 || (equal && bin_upper <= length2)))
1065 : break;
1066 :
1067 : /* the upper bound of previous bin is the lower bound of this bin */
1068 3000 : A = B;
1069 3000 : PA = PB;
1070 :
1071 3000 : B = bin_upper;
1072 3000 : PB = (double) i / (double) (length_hist_nvalues - 1);
1073 :
1074 : /*
1075 : * Add the area of this trapezoid to the total. The point of the
1076 : * if-check is to avoid NaN, in the corner case that PA == PB == 0,
1077 : * and B - A == Inf. The area of a zero-height trapezoid (PA == PB ==
1078 : * 0) is zero, regardless of the width (B - A).
1079 : */
1080 3000 : if (PA > 0 || PB > 0)
1081 2952 : area += 0.5 * (PB + PA) * (B - A);
1082 : }
1083 :
1084 : /* Last bin */
1085 168 : A = B;
1086 168 : PA = PB;
1087 :
1088 168 : B = length2; /* last bin ends at the query upper bound */
1089 168 : if (i >= length_hist_nvalues - 1)
1090 0 : pos = 0.0;
1091 : else
1092 : {
1093 168 : if (DatumGetFloat8(length_hist_values[i]) == DatumGetFloat8(length_hist_values[i + 1]))
1094 36 : pos = 0.0;
1095 : else
1096 132 : pos = get_len_position(length2,
1097 132 : DatumGetFloat8(length_hist_values[i]),
1098 132 : DatumGetFloat8(length_hist_values[i + 1]));
1099 : }
1100 168 : PB = (((double) i) + pos) / (double) (length_hist_nvalues - 1);
1101 :
1102 168 : if (PA > 0 || PB > 0)
1103 132 : area += 0.5 * (PB + PA) * (B - A);
1104 :
1105 : /*
1106 : * Ok, we have calculated the area, ie. the integral. Divide by width to
1107 : * get the requested average.
1108 : *
1109 : * Avoid NaN arising from infinite / infinite. This happens at least if
1110 : * length2 is infinite. It's not clear what the correct value would be in
1111 : * that case, so 0.5 seems as good as any value.
1112 : */
1113 168 : if (isinf(area) && isinf(length2))
1114 48 : frac = 0.5;
1115 : else
1116 120 : frac = area / (length2 - length1);
1117 :
1118 168 : return frac;
1119 : }
1120 :
1121 : /*
1122 : * Calculate selectivity of "var <@ const" operator, ie. estimate the fraction
1123 : * of multiranges that fall within the constant lower and upper bounds. This uses
1124 : * the histograms of range lower bounds and range lengths, on the assumption
1125 : * that the range lengths are independent of the lower bounds.
1126 : *
1127 : * The caller has already checked that constant lower and upper bounds are
1128 : * finite.
1129 : */
1130 : static double
1131 24 : calc_hist_selectivity_contained(TypeCacheEntry *typcache,
1132 : const RangeBound *lower, RangeBound *upper,
1133 : const RangeBound *hist_lower, int hist_nvalues,
1134 : Datum *length_hist_values, int length_hist_nvalues)
1135 : {
1136 : int i,
1137 : upper_index;
1138 : float8 prev_dist;
1139 : double bin_width;
1140 : double upper_bin_width;
1141 : double sum_frac;
1142 :
1143 : /*
1144 : * Begin by finding the bin containing the upper bound, in the lower bound
1145 : * histogram. Any range with a lower bound > constant upper bound can't
1146 : * match, ie. there are no matches in bins greater than upper_index.
1147 : */
1148 24 : upper->inclusive = !upper->inclusive;
1149 24 : upper->lower = true;
1150 24 : upper_index = rbound_bsearch(typcache, upper, hist_lower, hist_nvalues,
1151 : false);
1152 :
1153 : /*
1154 : * If the upper bound value is below the histogram's lower limit, there
1155 : * are no matches.
1156 : */
1157 24 : if (upper_index < 0)
1158 0 : return 0.0;
1159 :
1160 : /*
1161 : * If the upper bound value is at or beyond the histogram's upper limit,
1162 : * start our loop at the last actual bin, as though the upper bound were
1163 : * within that bin; get_position will clamp its result to 1.0 anyway.
1164 : * (This corresponds to assuming that the data population above the
1165 : * histogram's upper limit is empty, exactly like what we just assumed for
1166 : * the lower limit.)
1167 : */
1168 24 : upper_index = Min(upper_index, hist_nvalues - 2);
1169 :
1170 : /*
1171 : * Calculate upper_bin_width, ie. the fraction of the (upper_index,
1172 : * upper_index + 1) bin which is greater than upper bound of query range
1173 : * using linear interpolation of subdiff function.
1174 : */
1175 24 : upper_bin_width = get_position(typcache, upper,
1176 24 : &hist_lower[upper_index],
1177 24 : &hist_lower[upper_index + 1]);
1178 :
1179 : /*
1180 : * In the loop, dist and prev_dist are the distance of the "current" bin's
1181 : * lower and upper bounds from the constant upper bound.
1182 : *
1183 : * bin_width represents the width of the current bin. Normally it is 1.0,
1184 : * meaning a full width bin, but can be less in the corner cases: start
1185 : * and end of the loop. We start with bin_width = upper_bin_width, because
1186 : * we begin at the bin containing the upper bound.
1187 : */
1188 24 : prev_dist = 0.0;
1189 24 : bin_width = upper_bin_width;
1190 :
1191 24 : sum_frac = 0.0;
1192 120 : for (i = upper_index; i >= 0; i--)
1193 : {
1194 : double dist;
1195 : double length_hist_frac;
1196 120 : bool final_bin = false;
1197 :
1198 : /*
1199 : * dist -- distance from upper bound of query range to lower bound of
1200 : * the current bin in the lower bound histogram. Or to the lower bound
1201 : * of the constant range, if this is the final bin, containing the
1202 : * constant lower bound.
1203 : */
1204 120 : if (range_cmp_bounds(typcache, &hist_lower[i], lower) < 0)
1205 : {
1206 24 : dist = get_distance(typcache, lower, upper);
1207 :
1208 : /*
1209 : * Subtract from bin_width the portion of this bin that we want to
1210 : * ignore.
1211 : */
1212 48 : bin_width -= get_position(typcache, lower, &hist_lower[i],
1213 24 : &hist_lower[i + 1]);
1214 24 : if (bin_width < 0.0)
1215 0 : bin_width = 0.0;
1216 24 : final_bin = true;
1217 : }
1218 : else
1219 96 : dist = get_distance(typcache, &hist_lower[i], upper);
1220 :
1221 : /*
1222 : * Estimate the fraction of tuples in this bin that are narrow enough
1223 : * to not exceed the distance to the upper bound of the query range.
1224 : */
1225 120 : length_hist_frac = calc_length_hist_frac(length_hist_values,
1226 : length_hist_nvalues,
1227 : prev_dist, dist, true);
1228 :
1229 : /*
1230 : * Add the fraction of tuples in this bin, with a suitable length, to
1231 : * the total.
1232 : */
1233 120 : sum_frac += length_hist_frac * bin_width / (double) (hist_nvalues - 1);
1234 :
1235 120 : if (final_bin)
1236 24 : break;
1237 :
1238 96 : bin_width = 1.0;
1239 96 : prev_dist = dist;
1240 : }
1241 :
1242 24 : return sum_frac;
1243 : }
1244 :
1245 : /*
1246 : * Calculate selectivity of "var @> const" operator, ie. estimate the fraction
1247 : * of multiranges that contain the constant lower and upper bounds. This uses
1248 : * the histograms of range lower bounds and range lengths, on the assumption
1249 : * that the range lengths are independent of the lower bounds.
1250 : */
1251 : static double
1252 48 : calc_hist_selectivity_contains(TypeCacheEntry *typcache,
1253 : const RangeBound *lower, const RangeBound *upper,
1254 : const RangeBound *hist_lower, int hist_nvalues,
1255 : Datum *length_hist_values, int length_hist_nvalues)
1256 : {
1257 : int i,
1258 : lower_index;
1259 : double bin_width,
1260 : lower_bin_width;
1261 : double sum_frac;
1262 : float8 prev_dist;
1263 :
1264 : /* Find the bin containing the lower bound of query range. */
1265 48 : lower_index = rbound_bsearch(typcache, lower, hist_lower, hist_nvalues,
1266 : true);
1267 :
1268 : /*
1269 : * If the lower bound value is below the histogram's lower limit, there
1270 : * are no matches.
1271 : */
1272 48 : if (lower_index < 0)
1273 0 : return 0.0;
1274 :
1275 : /*
1276 : * If the lower bound value is at or beyond the histogram's upper limit,
1277 : * start our loop at the last actual bin, as though the upper bound were
1278 : * within that bin; get_position will clamp its result to 1.0 anyway.
1279 : * (This corresponds to assuming that the data population above the
1280 : * histogram's upper limit is empty, exactly like what we just assumed for
1281 : * the lower limit.)
1282 : */
1283 48 : lower_index = Min(lower_index, hist_nvalues - 2);
1284 :
1285 : /*
1286 : * Calculate lower_bin_width, ie. the fraction of the of (lower_index,
1287 : * lower_index + 1) bin which is greater than lower bound of query range
1288 : * using linear interpolation of subdiff function.
1289 : */
1290 48 : lower_bin_width = get_position(typcache, lower, &hist_lower[lower_index],
1291 48 : &hist_lower[lower_index + 1]);
1292 :
1293 : /*
1294 : * Loop through all the lower bound bins, smaller than the query lower
1295 : * bound. In the loop, dist and prev_dist are the distance of the
1296 : * "current" bin's lower and upper bounds from the constant upper bound.
1297 : * We begin from query lower bound, and walk backwards, so the first bin's
1298 : * upper bound is the query lower bound, and its distance to the query
1299 : * upper bound is the length of the query range.
1300 : *
1301 : * bin_width represents the width of the current bin. Normally it is 1.0,
1302 : * meaning a full width bin, except for the first bin, which is only
1303 : * counted up to the constant lower bound.
1304 : */
1305 48 : prev_dist = get_distance(typcache, lower, upper);
1306 48 : sum_frac = 0.0;
1307 48 : bin_width = lower_bin_width;
1308 288 : for (i = lower_index; i >= 0; i--)
1309 : {
1310 : float8 dist;
1311 : double length_hist_frac;
1312 :
1313 : /*
1314 : * dist -- distance from upper bound of query range to current value
1315 : * of lower bound histogram or lower bound of query range (if we've
1316 : * reach it).
1317 : */
1318 240 : dist = get_distance(typcache, &hist_lower[i], upper);
1319 :
1320 : /*
1321 : * Get average fraction of length histogram which covers intervals
1322 : * longer than (or equal to) distance to upper bound of query range.
1323 : */
1324 240 : length_hist_frac =
1325 240 : 1.0 - calc_length_hist_frac(length_hist_values,
1326 : length_hist_nvalues,
1327 : prev_dist, dist, false);
1328 :
1329 240 : sum_frac += length_hist_frac * bin_width / (double) (hist_nvalues - 1);
1330 :
1331 240 : bin_width = 1.0;
1332 240 : prev_dist = dist;
1333 : }
1334 :
1335 48 : return sum_frac;
1336 : }
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