TLA Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * rangetypes_selfuncs.c
4 : * Functions for selectivity estimation of range operators
5 : *
6 : * Estimates are based on histograms of lower and upper bounds, and the
7 : * fraction of empty ranges.
8 : *
9 : * Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
10 : * Portions Copyright (c) 1994, Regents of the University of California
11 : *
12 : *
13 : * IDENTIFICATION
14 : * src/backend/utils/adt/rangetypes_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 "catalog/pg_type.h"
26 : #include "utils/float.h"
27 : #include "utils/fmgrprotos.h"
28 : #include "utils/lsyscache.h"
29 : #include "utils/rangetypes.h"
30 : #include "utils/selfuncs.h"
31 : #include "utils/typcache.h"
32 :
33 : static double calc_rangesel(TypeCacheEntry *typcache, VariableStatData *vardata,
34 : const RangeType *constval, Oid operator);
35 : static double default_range_selectivity(Oid operator);
36 : static double calc_hist_selectivity(TypeCacheEntry *typcache,
37 : VariableStatData *vardata, const RangeType *constval,
38 : Oid operator);
39 : static double calc_hist_selectivity_scalar(TypeCacheEntry *typcache,
40 : const RangeBound *constbound,
41 : const RangeBound *hist, int hist_nvalues,
42 : bool equal);
43 : static int rbound_bsearch(TypeCacheEntry *typcache, const RangeBound *value,
44 : const RangeBound *hist, int hist_length, bool equal);
45 : static float8 get_position(TypeCacheEntry *typcache, const RangeBound *value,
46 : const RangeBound *hist1, const RangeBound *hist2);
47 : static float8 get_len_position(double value, double hist1, double hist2);
48 : static float8 get_distance(TypeCacheEntry *typcache, const RangeBound *bound1,
49 : const RangeBound *bound2);
50 : static int length_hist_bsearch(Datum *length_hist_values,
51 : int length_hist_nvalues, double value, bool equal);
52 : static double calc_length_hist_frac(Datum *length_hist_values,
53 : int length_hist_nvalues, double length1, double length2, bool equal);
54 : static double calc_hist_selectivity_contained(TypeCacheEntry *typcache,
55 : const RangeBound *lower, RangeBound *upper,
56 : const RangeBound *hist_lower, int hist_nvalues,
57 : Datum *length_hist_values, int length_hist_nvalues);
58 : static double calc_hist_selectivity_contains(TypeCacheEntry *typcache,
59 : const RangeBound *lower, const RangeBound *upper,
60 : const RangeBound *hist_lower, int hist_nvalues,
61 : Datum *length_hist_values, int length_hist_nvalues);
62 :
63 : /*
64 : * Returns a default selectivity estimate for given operator, when we don't
65 : * have statistics or cannot use them for some reason.
66 : */
67 : static double
68 CBC 260 : default_range_selectivity(Oid operator)
69 : {
70 260 : switch (operator)
71 : {
72 23 : case OID_RANGE_OVERLAP_OP:
73 23 : return 0.01;
74 :
75 54 : case OID_RANGE_CONTAINS_OP:
76 : case OID_RANGE_CONTAINED_OP:
77 54 : return 0.005;
78 :
79 33 : case OID_RANGE_CONTAINS_ELEM_OP:
80 : case OID_RANGE_ELEM_CONTAINED_OP:
81 :
82 : /*
83 : * "range @> elem" is more or less identical to a scalar
84 : * inequality "A >= b AND A <= c".
85 : */
86 33 : return DEFAULT_RANGE_INEQ_SEL;
87 :
88 150 : case OID_RANGE_LESS_OP:
89 : case OID_RANGE_LESS_EQUAL_OP:
90 : case OID_RANGE_GREATER_OP:
91 : case OID_RANGE_GREATER_EQUAL_OP:
92 : case OID_RANGE_LEFT_OP:
93 : case OID_RANGE_RIGHT_OP:
94 : case OID_RANGE_OVERLAPS_LEFT_OP:
95 : case OID_RANGE_OVERLAPS_RIGHT_OP:
96 : /* these are similar to regular scalar inequalities */
97 150 : return DEFAULT_INEQ_SEL;
98 :
99 UBC 0 : default:
100 : /* all range operators should be handled above, but just in case */
101 0 : return 0.01;
102 : }
103 : }
104 :
105 : /*
106 : * rangesel -- restriction selectivity for range operators
107 : */
108 : Datum
109 CBC 425 : rangesel(PG_FUNCTION_ARGS)
110 : {
111 425 : PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
112 425 : Oid operator = PG_GETARG_OID(1);
113 425 : List *args = (List *) PG_GETARG_POINTER(2);
114 425 : int varRelid = PG_GETARG_INT32(3);
115 : VariableStatData vardata;
116 : Node *other;
117 : bool varonleft;
118 : Selectivity selec;
119 425 : TypeCacheEntry *typcache = NULL;
120 425 : RangeType *constrange = NULL;
121 :
122 : /*
123 : * If expression is not (variable op something) or (something op
124 : * variable), then punt and return a default estimate.
125 : */
126 425 : if (!get_restriction_variable(root, args, varRelid,
127 : &vardata, &other, &varonleft))
128 UBC 0 : PG_RETURN_FLOAT8(default_range_selectivity(operator));
129 :
130 : /*
131 : * Can't do anything useful if the something is not a constant, either.
132 : */
133 CBC 425 : if (!IsA(other, Const))
134 : {
135 UBC 0 : ReleaseVariableStats(vardata);
136 0 : PG_RETURN_FLOAT8(default_range_selectivity(operator));
137 : }
138 :
139 : /*
140 : * All the range operators are strict, so we can cope with a NULL constant
141 : * right away.
142 : */
143 CBC 425 : if (((Const *) other)->constisnull)
144 : {
145 UBC 0 : ReleaseVariableStats(vardata);
146 0 : PG_RETURN_FLOAT8(0.0);
147 : }
148 :
149 : /*
150 : * If var is on the right, commute the operator, so that we can assume the
151 : * var is on the left in what follows.
152 : */
153 CBC 425 : if (!varonleft)
154 : {
155 : /* we have other Op var, commute to make var Op other */
156 8 : operator = get_commutator(operator);
157 8 : if (!operator)
158 : {
159 : /* Use default selectivity (should we raise an error instead?) */
160 UBC 0 : ReleaseVariableStats(vardata);
161 0 : PG_RETURN_FLOAT8(default_range_selectivity(operator));
162 : }
163 : }
164 :
165 : /*
166 : * OK, there's a Var and a Const we're dealing with here. We need the
167 : * Const to be of same range type as the column, else we can't do anything
168 : * useful. (Such cases will likely fail at runtime, but here we'd rather
169 : * just return a default estimate.)
170 : *
171 : * If the operator is "range @> element", the constant should be of the
172 : * element type of the range column. Convert it to a range that includes
173 : * only that single point, so that we don't need special handling for that
174 : * in what follows.
175 : */
176 CBC 425 : if (operator == OID_RANGE_CONTAINS_ELEM_OP)
177 : {
178 39 : typcache = range_get_typcache(fcinfo, vardata.vartype);
179 :
180 39 : if (((Const *) other)->consttype == typcache->rngelemtype->type_id)
181 : {
182 : RangeBound lower,
183 : upper;
184 :
185 39 : lower.inclusive = true;
186 39 : lower.val = ((Const *) other)->constvalue;
187 39 : lower.infinite = false;
188 39 : lower.lower = true;
189 39 : upper.inclusive = true;
190 39 : upper.val = ((Const *) other)->constvalue;
191 39 : upper.infinite = false;
192 39 : upper.lower = false;
193 GNC 39 : constrange = range_serialize(typcache, &lower, &upper, false, NULL);
194 : }
195 : }
196 CBC 386 : else if (operator == OID_RANGE_ELEM_CONTAINED_OP)
197 : {
198 : /*
199 : * Here, the Var is the elem, not the range. For now we just punt and
200 : * return the default estimate. In future we could disassemble the
201 : * range constant and apply scalarineqsel ...
202 : */
203 : }
204 383 : else if (((Const *) other)->consttype == vardata.vartype)
205 : {
206 : /* Both sides are the same range type */
207 383 : typcache = range_get_typcache(fcinfo, vardata.vartype);
208 :
209 383 : constrange = DatumGetRangeTypeP(((Const *) other)->constvalue);
210 : }
211 :
212 : /*
213 : * If we got a valid constant on one side of the operator, proceed to
214 : * estimate using statistics. Otherwise punt and return a default constant
215 : * estimate. Note that calc_rangesel need not handle
216 : * OID_RANGE_ELEM_CONTAINED_OP.
217 : */
218 425 : if (constrange)
219 422 : selec = calc_rangesel(typcache, &vardata, constrange, operator);
220 : else
221 3 : selec = default_range_selectivity(operator);
222 :
223 425 : ReleaseVariableStats(vardata);
224 :
225 425 : CLAMP_PROBABILITY(selec);
226 :
227 425 : PG_RETURN_FLOAT8((float8) selec);
228 : }
229 :
230 : static double
231 422 : calc_rangesel(TypeCacheEntry *typcache, VariableStatData *vardata,
232 : const RangeType *constval, Oid operator)
233 : {
234 : double hist_selec;
235 : double selec;
236 : float4 empty_frac,
237 : null_frac;
238 :
239 : /*
240 : * First look up the fraction of NULLs and empty ranges from pg_statistic.
241 : */
242 422 : if (HeapTupleIsValid(vardata->statsTuple))
243 : {
244 : Form_pg_statistic stats;
245 : AttStatsSlot sslot;
246 :
247 81 : stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
248 81 : null_frac = stats->stanullfrac;
249 :
250 : /* Try to get fraction of empty ranges */
251 81 : if (get_attstatsslot(&sslot, vardata->statsTuple,
252 : STATISTIC_KIND_RANGE_LENGTH_HISTOGRAM,
253 : InvalidOid,
254 : ATTSTATSSLOT_NUMBERS))
255 : {
256 81 : if (sslot.nnumbers != 1)
257 UBC 0 : elog(ERROR, "invalid empty fraction statistic"); /* shouldn't happen */
258 CBC 81 : empty_frac = sslot.numbers[0];
259 81 : free_attstatsslot(&sslot);
260 : }
261 : else
262 : {
263 : /* No empty fraction statistic. Assume no empty ranges. */
264 UBC 0 : empty_frac = 0.0;
265 : }
266 : }
267 : else
268 : {
269 : /*
270 : * No stats are available. Follow through the calculations below
271 : * anyway, assuming no NULLs and no empty ranges. This still allows us
272 : * to give a better-than-nothing estimate based on whether the
273 : * constant is an empty range or not.
274 : */
275 CBC 341 : null_frac = 0.0;
276 341 : empty_frac = 0.0;
277 : }
278 :
279 422 : if (RangeIsEmpty(constval))
280 : {
281 : /*
282 : * An empty range matches all ranges, all empty ranges, or nothing,
283 : * depending on the operator
284 : */
285 93 : switch (operator)
286 : {
287 : /* these return false if either argument is empty */
288 6 : case OID_RANGE_OVERLAP_OP:
289 : case OID_RANGE_OVERLAPS_LEFT_OP:
290 : case OID_RANGE_OVERLAPS_RIGHT_OP:
291 : case OID_RANGE_LEFT_OP:
292 : case OID_RANGE_RIGHT_OP:
293 : /* nothing is less than an empty range */
294 : case OID_RANGE_LESS_OP:
295 6 : selec = 0.0;
296 6 : break;
297 :
298 : /* only empty ranges can be contained by an empty range */
299 27 : case OID_RANGE_CONTAINED_OP:
300 : /* only empty ranges are <= an empty range */
301 : case OID_RANGE_LESS_EQUAL_OP:
302 27 : selec = empty_frac;
303 27 : break;
304 :
305 : /* everything contains an empty range */
306 45 : case OID_RANGE_CONTAINS_OP:
307 : /* everything is >= an empty range */
308 : case OID_RANGE_GREATER_EQUAL_OP:
309 45 : selec = 1.0;
310 45 : break;
311 :
312 : /* all non-empty ranges are > an empty range */
313 15 : case OID_RANGE_GREATER_OP:
314 15 : selec = 1.0 - empty_frac;
315 15 : break;
316 :
317 : /* an element cannot be empty */
318 UBC 0 : case OID_RANGE_CONTAINS_ELEM_OP:
319 : default:
320 0 : elog(ERROR, "unexpected operator %u", operator);
321 : selec = 0.0; /* keep compiler quiet */
322 : break;
323 : }
324 : }
325 : else
326 : {
327 : /*
328 : * Calculate selectivity using bound histograms. If that fails for
329 : * some reason, e.g no histogram in pg_statistic, use the default
330 : * constant estimate for the fraction of non-empty values. This is
331 : * still somewhat better than just returning the default estimate,
332 : * because this still takes into account the fraction of empty and
333 : * NULL tuples, if we had statistics for them.
334 : */
335 CBC 329 : hist_selec = calc_hist_selectivity(typcache, vardata, constval,
336 : operator);
337 329 : if (hist_selec < 0.0)
338 257 : hist_selec = default_range_selectivity(operator);
339 :
340 : /*
341 : * Now merge the results for the empty ranges and histogram
342 : * calculations, realizing that the histogram covers only the
343 : * non-null, non-empty values.
344 : */
345 329 : if (operator == OID_RANGE_CONTAINED_OP)
346 : {
347 : /* empty is contained by anything non-empty */
348 36 : selec = (1.0 - empty_frac) * hist_selec + empty_frac;
349 : }
350 : else
351 : {
352 : /* with any other operator, empty Op non-empty matches nothing */
353 293 : selec = (1.0 - empty_frac) * hist_selec;
354 : }
355 : }
356 :
357 : /* all range operators are strict */
358 422 : selec *= (1.0 - null_frac);
359 :
360 : /* result should be in range, but make sure... */
361 422 : CLAMP_PROBABILITY(selec);
362 :
363 422 : return selec;
364 : }
365 :
366 : /*
367 : * Calculate range operator selectivity using histograms of range bounds.
368 : *
369 : * This estimate is for the portion of values that are not empty and not
370 : * NULL.
371 : */
372 : static double
373 329 : calc_hist_selectivity(TypeCacheEntry *typcache, VariableStatData *vardata,
374 : const RangeType *constval, Oid operator)
375 : {
376 : AttStatsSlot hslot;
377 : AttStatsSlot lslot;
378 : int nhist;
379 : RangeBound *hist_lower;
380 : RangeBound *hist_upper;
381 : int i;
382 : RangeBound const_lower;
383 : RangeBound const_upper;
384 : bool empty;
385 : double hist_selec;
386 :
387 : /* Can't use the histogram with insecure range support functions */
388 329 : if (!statistic_proc_security_check(vardata,
389 : typcache->rng_cmp_proc_finfo.fn_oid))
390 UBC 0 : return -1;
391 CBC 329 : if (OidIsValid(typcache->rng_subdiff_finfo.fn_oid) &&
392 323 : !statistic_proc_security_check(vardata,
393 : typcache->rng_subdiff_finfo.fn_oid))
394 UBC 0 : return -1;
395 :
396 : /* Try to get histogram of ranges */
397 CBC 401 : if (!(HeapTupleIsValid(vardata->statsTuple) &&
398 72 : get_attstatsslot(&hslot, vardata->statsTuple,
399 : STATISTIC_KIND_BOUNDS_HISTOGRAM, InvalidOid,
400 : ATTSTATSSLOT_VALUES)))
401 257 : return -1.0;
402 :
403 : /* check that it's a histogram, not just a dummy entry */
404 72 : if (hslot.nvalues < 2)
405 : {
406 UBC 0 : free_attstatsslot(&hslot);
407 0 : return -1.0;
408 : }
409 :
410 : /*
411 : * Convert histogram of ranges into histograms of its lower and upper
412 : * bounds.
413 : */
414 CBC 72 : nhist = hslot.nvalues;
415 72 : hist_lower = (RangeBound *) palloc(sizeof(RangeBound) * nhist);
416 72 : hist_upper = (RangeBound *) palloc(sizeof(RangeBound) * nhist);
417 7344 : for (i = 0; i < nhist; i++)
418 : {
419 7272 : range_deserialize(typcache, DatumGetRangeTypeP(hslot.values[i]),
420 7272 : &hist_lower[i], &hist_upper[i], &empty);
421 : /* The histogram should not contain any empty ranges */
422 7272 : if (empty)
423 UBC 0 : elog(ERROR, "bounds histogram contains an empty range");
424 : }
425 :
426 : /* @> and @< also need a histogram of range lengths */
427 CBC 72 : if (operator == OID_RANGE_CONTAINS_OP ||
428 : operator == OID_RANGE_CONTAINED_OP)
429 : {
430 36 : if (!(HeapTupleIsValid(vardata->statsTuple) &&
431 18 : get_attstatsslot(&lslot, vardata->statsTuple,
432 : STATISTIC_KIND_RANGE_LENGTH_HISTOGRAM,
433 : InvalidOid,
434 : ATTSTATSSLOT_VALUES)))
435 : {
436 UBC 0 : free_attstatsslot(&hslot);
437 0 : return -1.0;
438 : }
439 :
440 : /* check that it's a histogram, not just a dummy entry */
441 CBC 18 : if (lslot.nvalues < 2)
442 : {
443 UBC 0 : free_attstatsslot(&lslot);
444 0 : free_attstatsslot(&hslot);
445 0 : return -1.0;
446 : }
447 : }
448 : else
449 CBC 54 : memset(&lslot, 0, sizeof(lslot));
450 :
451 : /* Extract the bounds of the constant value. */
452 72 : range_deserialize(typcache, constval, &const_lower, &const_upper, &empty);
453 72 : Assert(!empty);
454 :
455 : /*
456 : * Calculate selectivity comparing the lower or upper bound of the
457 : * constant with the histogram of lower or upper bounds.
458 : */
459 72 : switch (operator)
460 : {
461 UBC 0 : case OID_RANGE_LESS_OP:
462 :
463 : /*
464 : * The regular b-tree comparison operators (<, <=, >, >=) compare
465 : * the lower bounds first, and the upper bounds for values with
466 : * equal lower bounds. Estimate that by comparing the lower bounds
467 : * only. This gives a fairly accurate estimate assuming there
468 : * aren't many rows with a lower bound equal to the constant's
469 : * lower bound.
470 : */
471 : hist_selec =
472 0 : calc_hist_selectivity_scalar(typcache, &const_lower,
473 : hist_lower, nhist, false);
474 0 : break;
475 :
476 0 : case OID_RANGE_LESS_EQUAL_OP:
477 : hist_selec =
478 0 : calc_hist_selectivity_scalar(typcache, &const_lower,
479 : hist_lower, nhist, true);
480 0 : break;
481 :
482 0 : case OID_RANGE_GREATER_OP:
483 0 : hist_selec =
484 0 : 1 - calc_hist_selectivity_scalar(typcache, &const_lower,
485 : hist_lower, nhist, false);
486 0 : break;
487 :
488 0 : case OID_RANGE_GREATER_EQUAL_OP:
489 0 : hist_selec =
490 0 : 1 - calc_hist_selectivity_scalar(typcache, &const_lower,
491 : hist_lower, nhist, true);
492 0 : break;
493 :
494 CBC 9 : case OID_RANGE_LEFT_OP:
495 : /* var << const when upper(var) < lower(const) */
496 : hist_selec =
497 9 : calc_hist_selectivity_scalar(typcache, &const_lower,
498 : hist_upper, nhist, false);
499 9 : break;
500 :
501 9 : case OID_RANGE_RIGHT_OP:
502 : /* var >> const when lower(var) > upper(const) */
503 9 : hist_selec =
504 9 : 1 - calc_hist_selectivity_scalar(typcache, &const_upper,
505 : hist_lower, nhist, true);
506 9 : break;
507 :
508 9 : case OID_RANGE_OVERLAPS_RIGHT_OP:
509 : /* compare lower bounds */
510 9 : hist_selec =
511 9 : 1 - calc_hist_selectivity_scalar(typcache, &const_lower,
512 : hist_lower, nhist, false);
513 9 : break;
514 :
515 9 : case OID_RANGE_OVERLAPS_LEFT_OP:
516 : /* compare upper bounds */
517 : hist_selec =
518 9 : calc_hist_selectivity_scalar(typcache, &const_upper,
519 : hist_upper, nhist, true);
520 9 : break;
521 :
522 18 : case OID_RANGE_OVERLAP_OP:
523 : case OID_RANGE_CONTAINS_ELEM_OP:
524 :
525 : /*
526 : * A && B <=> NOT (A << B OR A >> B).
527 : *
528 : * Since A << B and A >> B are mutually exclusive events we can
529 : * sum their probabilities to find probability of (A << B OR A >>
530 : * B).
531 : *
532 : * "range @> elem" is equivalent to "range && [elem,elem]". The
533 : * caller already constructed the singular range from the element
534 : * constant, so just treat it the same as &&.
535 : */
536 : hist_selec =
537 18 : calc_hist_selectivity_scalar(typcache, &const_lower, hist_upper,
538 : nhist, false);
539 18 : hist_selec +=
540 18 : (1.0 - calc_hist_selectivity_scalar(typcache, &const_upper, hist_lower,
541 : nhist, true));
542 18 : hist_selec = 1.0 - hist_selec;
543 18 : break;
544 :
545 9 : case OID_RANGE_CONTAINS_OP:
546 : hist_selec =
547 9 : calc_hist_selectivity_contains(typcache, &const_lower,
548 : &const_upper, hist_lower, nhist,
549 : lslot.values, lslot.nvalues);
550 9 : break;
551 :
552 9 : case OID_RANGE_CONTAINED_OP:
553 9 : if (const_lower.infinite)
554 : {
555 : /*
556 : * Lower bound no longer matters. Just estimate the fraction
557 : * with an upper bound <= const upper bound
558 : */
559 : hist_selec =
560 UBC 0 : calc_hist_selectivity_scalar(typcache, &const_upper,
561 : hist_upper, nhist, true);
562 : }
563 CBC 9 : else if (const_upper.infinite)
564 : {
565 UBC 0 : hist_selec =
566 0 : 1.0 - calc_hist_selectivity_scalar(typcache, &const_lower,
567 : hist_lower, nhist, false);
568 : }
569 : else
570 : {
571 : hist_selec =
572 CBC 9 : calc_hist_selectivity_contained(typcache, &const_lower,
573 : &const_upper, hist_lower, nhist,
574 : lslot.values, lslot.nvalues);
575 : }
576 9 : break;
577 :
578 UBC 0 : default:
579 0 : elog(ERROR, "unknown range operator %u", operator);
580 : hist_selec = -1.0; /* keep compiler quiet */
581 : break;
582 : }
583 :
584 CBC 72 : free_attstatsslot(&lslot);
585 72 : free_attstatsslot(&hslot);
586 :
587 72 : return hist_selec;
588 : }
589 :
590 :
591 : /*
592 : * Look up the fraction of values less than (or equal, if 'equal' argument
593 : * is true) a given const in a histogram of range bounds.
594 : */
595 : static double
596 72 : calc_hist_selectivity_scalar(TypeCacheEntry *typcache, const RangeBound *constbound,
597 : const RangeBound *hist, int hist_nvalues, bool equal)
598 : {
599 : Selectivity selec;
600 : int index;
601 :
602 : /*
603 : * Find the histogram bin the given constant falls into. Estimate
604 : * selectivity as the number of preceding whole bins.
605 : */
606 72 : index = rbound_bsearch(typcache, constbound, hist, hist_nvalues, equal);
607 72 : selec = (Selectivity) (Max(index, 0)) / (Selectivity) (hist_nvalues - 1);
608 :
609 : /* Adjust using linear interpolation within the bin */
610 72 : if (index >= 0 && index < hist_nvalues - 1)
611 108 : selec += get_position(typcache, constbound, &hist[index],
612 54 : &hist[index + 1]) / (Selectivity) (hist_nvalues - 1);
613 :
614 72 : return selec;
615 : }
616 :
617 : /*
618 : * Binary search on an array of range bounds. Returns greatest index of range
619 : * bound in array which is less(less or equal) than given range bound. If all
620 : * range bounds in array are greater or equal(greater) than given range bound,
621 : * return -1. When "equal" flag is set conditions in brackets are used.
622 : *
623 : * This function is used in scalar operator selectivity estimation. Another
624 : * goal of this function is to find a histogram bin where to stop
625 : * interpolation of portion of bounds which are less than or equal to given bound.
626 : */
627 : static int
628 90 : rbound_bsearch(TypeCacheEntry *typcache, const RangeBound *value, const RangeBound *hist,
629 : int hist_length, bool equal)
630 : {
631 90 : int lower = -1,
632 90 : upper = hist_length - 1,
633 : cmp,
634 : middle;
635 :
636 684 : while (lower < upper)
637 : {
638 594 : middle = (lower + upper + 1) / 2;
639 594 : cmp = range_cmp_bounds(typcache, &hist[middle], value);
640 :
641 594 : if (cmp < 0 || (equal && cmp == 0))
642 171 : lower = middle;
643 : else
644 423 : upper = middle - 1;
645 : }
646 90 : return lower;
647 : }
648 :
649 :
650 : /*
651 : * Binary search on length histogram. Returns greatest index of range length in
652 : * histogram which is less than (less than or equal) the given length value. If
653 : * all lengths in the histogram are greater than (greater than or equal) the
654 : * given length, returns -1.
655 : */
656 : static int
657 54 : length_hist_bsearch(Datum *length_hist_values, int length_hist_nvalues,
658 : double value, bool equal)
659 : {
660 54 : int lower = -1,
661 54 : upper = length_hist_nvalues - 1,
662 : middle;
663 :
664 414 : while (lower < upper)
665 : {
666 : double middleval;
667 :
668 360 : middle = (lower + upper + 1) / 2;
669 :
670 360 : middleval = DatumGetFloat8(length_hist_values[middle]);
671 360 : if (middleval < value || (equal && middleval <= value))
672 135 : lower = middle;
673 : else
674 225 : upper = middle - 1;
675 : }
676 54 : return lower;
677 : }
678 :
679 : /*
680 : * Get relative position of value in histogram bin in [0,1] range.
681 : */
682 : static float8
683 81 : get_position(TypeCacheEntry *typcache, const RangeBound *value, const RangeBound *hist1,
684 : const RangeBound *hist2)
685 : {
686 81 : bool has_subdiff = OidIsValid(typcache->rng_subdiff_finfo.fn_oid);
687 : float8 position;
688 :
689 81 : if (!hist1->infinite && !hist2->infinite)
690 : {
691 : float8 bin_width;
692 :
693 : /*
694 : * Both bounds are finite. Assuming the subtype's comparison function
695 : * works sanely, the value must be finite, too, because it lies
696 : * somewhere between the bounds. If it doesn't, arbitrarily return
697 : * 0.5.
698 : */
699 81 : if (value->infinite)
700 UBC 0 : return 0.5;
701 :
702 : /* Can't interpolate without subdiff function */
703 CBC 81 : if (!has_subdiff)
704 UBC 0 : return 0.5;
705 :
706 : /* Calculate relative position using subdiff function. */
707 CBC 81 : bin_width = DatumGetFloat8(FunctionCall2Coll(&typcache->rng_subdiff_finfo,
708 : typcache->rng_collation,
709 81 : hist2->val,
710 81 : hist1->val));
711 81 : if (isnan(bin_width) || bin_width <= 0.0)
712 UBC 0 : return 0.5; /* punt for NaN or zero-width bin */
713 :
714 CBC 81 : position = DatumGetFloat8(FunctionCall2Coll(&typcache->rng_subdiff_finfo,
715 : typcache->rng_collation,
716 81 : value->val,
717 81 : hist1->val))
718 : / bin_width;
719 :
720 81 : if (isnan(position))
721 UBC 0 : return 0.5; /* punt for NaN from subdiff, Inf/Inf, etc */
722 :
723 : /* Relative position must be in [0,1] range */
724 CBC 81 : position = Max(position, 0.0);
725 81 : position = Min(position, 1.0);
726 81 : return position;
727 : }
728 UBC 0 : else if (hist1->infinite && !hist2->infinite)
729 : {
730 : /*
731 : * Lower bin boundary is -infinite, upper is finite. If the value is
732 : * -infinite, return 0.0 to indicate it's equal to the lower bound.
733 : * Otherwise return 1.0 to indicate it's infinitely far from the lower
734 : * bound.
735 : */
736 0 : return ((value->infinite && value->lower) ? 0.0 : 1.0);
737 : }
738 0 : else if (!hist1->infinite && hist2->infinite)
739 : {
740 : /* same as above, but in reverse */
741 0 : return ((value->infinite && !value->lower) ? 1.0 : 0.0);
742 : }
743 : else
744 : {
745 : /*
746 : * If both bin boundaries are infinite, they should be equal to each
747 : * other, and the value should also be infinite and equal to both
748 : * bounds. (But don't Assert that, to avoid crashing if a user creates
749 : * a datatype with a broken comparison function).
750 : *
751 : * Assume the value to lie in the middle of the infinite bounds.
752 : */
753 0 : return 0.5;
754 : }
755 : }
756 :
757 :
758 : /*
759 : * Get relative position of value in a length histogram bin in [0,1] range.
760 : */
761 : static double
762 CBC 81 : get_len_position(double value, double hist1, double hist2)
763 : {
764 81 : if (!isinf(hist1) && !isinf(hist2))
765 : {
766 : /*
767 : * Both bounds are finite. The value should be finite too, because it
768 : * lies somewhere between the bounds. If it doesn't, just return
769 : * something.
770 : */
771 63 : if (isinf(value))
772 UBC 0 : return 0.5;
773 :
774 CBC 63 : return 1.0 - (hist2 - value) / (hist2 - hist1);
775 : }
776 18 : else if (isinf(hist1) && !isinf(hist2))
777 : {
778 : /*
779 : * Lower bin boundary is -infinite, upper is finite. Return 1.0 to
780 : * indicate the value is infinitely far from the lower bound.
781 : */
782 UBC 0 : return 1.0;
783 : }
784 CBC 18 : else if (isinf(hist1) && isinf(hist2))
785 : {
786 : /* same as above, but in reverse */
787 UBC 0 : return 0.0;
788 : }
789 : else
790 : {
791 : /*
792 : * If both bin boundaries are infinite, they should be equal to each
793 : * other, and the value should also be infinite and equal to both
794 : * bounds. (But don't Assert that, to avoid crashing unnecessarily if
795 : * the caller messes up)
796 : *
797 : * Assume the value to lie in the middle of the infinite bounds.
798 : */
799 CBC 18 : return 0.5;
800 : }
801 : }
802 :
803 : /*
804 : * Measure distance between two range bounds.
805 : */
806 : static float8
807 63 : get_distance(TypeCacheEntry *typcache, const RangeBound *bound1, const RangeBound *bound2)
808 : {
809 63 : bool has_subdiff = OidIsValid(typcache->rng_subdiff_finfo.fn_oid);
810 :
811 63 : if (!bound1->infinite && !bound2->infinite)
812 : {
813 : /*
814 : * Neither bound is infinite, use subdiff function or return default
815 : * value of 1.0 if no subdiff is available.
816 : */
817 45 : if (has_subdiff)
818 : {
819 : float8 res;
820 :
821 45 : res = DatumGetFloat8(FunctionCall2Coll(&typcache->rng_subdiff_finfo,
822 : typcache->rng_collation,
823 45 : bound2->val,
824 45 : bound1->val));
825 : /* Reject possible NaN result, also negative result */
826 45 : if (isnan(res) || res < 0.0)
827 UBC 0 : return 1.0;
828 : else
829 CBC 45 : return res;
830 : }
831 : else
832 UBC 0 : return 1.0;
833 : }
834 CBC 18 : else if (bound1->infinite && bound2->infinite)
835 : {
836 : /* Both bounds are infinite */
837 UBC 0 : if (bound1->lower == bound2->lower)
838 0 : return 0.0;
839 : else
840 0 : return get_float8_infinity();
841 : }
842 : else
843 : {
844 : /* One bound is infinite, the other is not */
845 CBC 18 : return get_float8_infinity();
846 : }
847 : }
848 :
849 : /*
850 : * Calculate the average of function P(x), in the interval [length1, length2],
851 : * where P(x) is the fraction of tuples with length < x (or length <= x if
852 : * 'equal' is true).
853 : */
854 : static double
855 54 : calc_length_hist_frac(Datum *length_hist_values, int length_hist_nvalues,
856 : double length1, double length2, bool equal)
857 : {
858 : double frac;
859 : double A,
860 : B,
861 : PA,
862 : PB;
863 : double pos;
864 : int i;
865 : double area;
866 :
867 54 : Assert(length2 >= length1);
868 :
869 54 : if (length2 < 0.0)
870 UBC 0 : return 0.0; /* shouldn't happen, but doesn't hurt to check */
871 :
872 : /* All lengths in the table are <= infinite. */
873 CBC 54 : if (isinf(length2) && equal)
874 UBC 0 : return 1.0;
875 :
876 : /*----------
877 : * The average of a function between A and B can be calculated by the
878 : * formula:
879 : *
880 : * B
881 : * 1 /
882 : * ------- | P(x)dx
883 : * B - A /
884 : * A
885 : *
886 : * The geometrical interpretation of the integral is the area under the
887 : * graph of P(x). P(x) is defined by the length histogram. We calculate
888 : * the area in a piecewise fashion, iterating through the length histogram
889 : * bins. Each bin is a trapezoid:
890 : *
891 : * P(x2)
892 : * /|
893 : * / |
894 : * P(x1)/ |
895 : * | |
896 : * | |
897 : * ---+---+--
898 : * x1 x2
899 : *
900 : * where x1 and x2 are the boundaries of the current histogram, and P(x1)
901 : * and P(x1) are the cumulative fraction of tuples at the boundaries.
902 : *
903 : * The area of each trapezoid is 1/2 * (P(x2) + P(x1)) * (x2 - x1)
904 : *
905 : * The first bin contains the lower bound passed by the caller, so we
906 : * use linear interpolation between the previous and next histogram bin
907 : * boundary to calculate P(x1). Likewise for the last bin: we use linear
908 : * interpolation to calculate P(x2). For the bins in between, x1 and x2
909 : * lie on histogram bin boundaries, so P(x1) and P(x2) are simply:
910 : * P(x1) = (bin index) / (number of bins)
911 : * P(x2) = (bin index + 1 / (number of bins)
912 : */
913 :
914 : /* First bin, the one that contains lower bound */
915 CBC 54 : i = length_hist_bsearch(length_hist_values, length_hist_nvalues, length1, equal);
916 54 : if (i >= length_hist_nvalues - 1)
917 UBC 0 : return 1.0;
918 :
919 CBC 54 : if (i < 0)
920 : {
921 18 : i = 0;
922 18 : pos = 0.0;
923 : }
924 : else
925 : {
926 : /* interpolate length1's position in the bin */
927 36 : pos = get_len_position(length1,
928 36 : DatumGetFloat8(length_hist_values[i]),
929 36 : DatumGetFloat8(length_hist_values[i + 1]));
930 : }
931 54 : PB = (((double) i) + pos) / (double) (length_hist_nvalues - 1);
932 54 : B = length1;
933 :
934 : /*
935 : * In the degenerate case that length1 == length2, simply return
936 : * P(length1). This is not merely an optimization: if length1 == length2,
937 : * we'd divide by zero later on.
938 : */
939 54 : if (length2 == length1)
940 9 : return PB;
941 :
942 : /*
943 : * Loop through all the bins, until we hit the last bin, the one that
944 : * contains the upper bound. (if lower and upper bounds are in the same
945 : * bin, this falls out immediately)
946 : */
947 45 : area = 0.0;
948 1593 : for (; i < length_hist_nvalues - 1; i++)
949 : {
950 1593 : double bin_upper = DatumGetFloat8(length_hist_values[i + 1]);
951 :
952 : /* check if we've reached the last bin */
953 1593 : if (!(bin_upper < length2 || (equal && bin_upper <= length2)))
954 : break;
955 :
956 : /* the upper bound of previous bin is the lower bound of this bin */
957 1548 : A = B;
958 1548 : PA = PB;
959 :
960 1548 : B = bin_upper;
961 1548 : PB = (double) i / (double) (length_hist_nvalues - 1);
962 :
963 : /*
964 : * Add the area of this trapezoid to the total. The point of the
965 : * if-check is to avoid NaN, in the corner case that PA == PB == 0,
966 : * and B - A == Inf. The area of a zero-height trapezoid (PA == PB ==
967 : * 0) is zero, regardless of the width (B - A).
968 : */
969 1548 : if (PA > 0 || PB > 0)
970 1530 : area += 0.5 * (PB + PA) * (B - A);
971 : }
972 :
973 : /* Last bin */
974 45 : A = B;
975 45 : PA = PB;
976 :
977 45 : B = length2; /* last bin ends at the query upper bound */
978 45 : if (i >= length_hist_nvalues - 1)
979 UBC 0 : pos = 0.0;
980 : else
981 : {
982 CBC 45 : if (DatumGetFloat8(length_hist_values[i]) == DatumGetFloat8(length_hist_values[i + 1]))
983 UBC 0 : pos = 0.0;
984 : else
985 CBC 45 : pos = get_len_position(length2, DatumGetFloat8(length_hist_values[i]), DatumGetFloat8(length_hist_values[i + 1]));
986 : }
987 45 : PB = (((double) i) + pos) / (double) (length_hist_nvalues - 1);
988 :
989 45 : if (PA > 0 || PB > 0)
990 45 : area += 0.5 * (PB + PA) * (B - A);
991 :
992 : /*
993 : * Ok, we have calculated the area, ie. the integral. Divide by width to
994 : * get the requested average.
995 : *
996 : * Avoid NaN arising from infinite / infinite. This happens at least if
997 : * length2 is infinite. It's not clear what the correct value would be in
998 : * that case, so 0.5 seems as good as any value.
999 : */
1000 45 : if (isinf(area) && isinf(length2))
1001 9 : frac = 0.5;
1002 : else
1003 36 : frac = area / (length2 - length1);
1004 :
1005 45 : return frac;
1006 : }
1007 :
1008 : /*
1009 : * Calculate selectivity of "var <@ const" operator, ie. estimate the fraction
1010 : * of ranges that fall within the constant lower and upper bounds. This uses
1011 : * the histograms of range lower bounds and range lengths, on the assumption
1012 : * that the range lengths are independent of the lower bounds.
1013 : *
1014 : * The caller has already checked that constant lower and upper bounds are
1015 : * finite.
1016 : */
1017 : static double
1018 9 : calc_hist_selectivity_contained(TypeCacheEntry *typcache,
1019 : const RangeBound *lower, RangeBound *upper,
1020 : const RangeBound *hist_lower, int hist_nvalues,
1021 : Datum *length_hist_values, int length_hist_nvalues)
1022 : {
1023 : int i,
1024 : upper_index;
1025 : float8 prev_dist;
1026 : double bin_width;
1027 : double upper_bin_width;
1028 : double sum_frac;
1029 :
1030 : /*
1031 : * Begin by finding the bin containing the upper bound, in the lower bound
1032 : * histogram. Any range with a lower bound > constant upper bound can't
1033 : * match, ie. there are no matches in bins greater than upper_index.
1034 : */
1035 9 : upper->inclusive = !upper->inclusive;
1036 9 : upper->lower = true;
1037 9 : upper_index = rbound_bsearch(typcache, upper, hist_lower, hist_nvalues,
1038 : false);
1039 :
1040 : /*
1041 : * If the upper bound value is below the histogram's lower limit, there
1042 : * are no matches.
1043 : */
1044 9 : if (upper_index < 0)
1045 UBC 0 : return 0.0;
1046 :
1047 : /*
1048 : * If the upper bound value is at or beyond the histogram's upper limit,
1049 : * start our loop at the last actual bin, as though the upper bound were
1050 : * within that bin; get_position will clamp its result to 1.0 anyway.
1051 : * (This corresponds to assuming that the data population above the
1052 : * histogram's upper limit is empty, exactly like what we just assumed for
1053 : * the lower limit.)
1054 : */
1055 CBC 9 : upper_index = Min(upper_index, hist_nvalues - 2);
1056 :
1057 : /*
1058 : * Calculate upper_bin_width, ie. the fraction of the (upper_index,
1059 : * upper_index + 1) bin which is greater than upper bound of query range
1060 : * using linear interpolation of subdiff function.
1061 : */
1062 9 : upper_bin_width = get_position(typcache, upper,
1063 9 : &hist_lower[upper_index],
1064 9 : &hist_lower[upper_index + 1]);
1065 :
1066 : /*
1067 : * In the loop, dist and prev_dist are the distance of the "current" bin's
1068 : * lower and upper bounds from the constant upper bound.
1069 : *
1070 : * bin_width represents the width of the current bin. Normally it is 1.0,
1071 : * meaning a full width bin, but can be less in the corner cases: start
1072 : * and end of the loop. We start with bin_width = upper_bin_width, because
1073 : * we begin at the bin containing the upper bound.
1074 : */
1075 9 : prev_dist = 0.0;
1076 9 : bin_width = upper_bin_width;
1077 :
1078 9 : sum_frac = 0.0;
1079 27 : for (i = upper_index; i >= 0; i--)
1080 : {
1081 : double dist;
1082 : double length_hist_frac;
1083 27 : bool final_bin = false;
1084 :
1085 : /*
1086 : * dist -- distance from upper bound of query range to lower bound of
1087 : * the current bin in the lower bound histogram. Or to the lower bound
1088 : * of the constant range, if this is the final bin, containing the
1089 : * constant lower bound.
1090 : */
1091 27 : if (range_cmp_bounds(typcache, &hist_lower[i], lower) < 0)
1092 : {
1093 9 : dist = get_distance(typcache, lower, upper);
1094 :
1095 : /*
1096 : * Subtract from bin_width the portion of this bin that we want to
1097 : * ignore.
1098 : */
1099 18 : bin_width -= get_position(typcache, lower, &hist_lower[i],
1100 9 : &hist_lower[i + 1]);
1101 9 : if (bin_width < 0.0)
1102 UBC 0 : bin_width = 0.0;
1103 CBC 9 : final_bin = true;
1104 : }
1105 : else
1106 18 : dist = get_distance(typcache, &hist_lower[i], upper);
1107 :
1108 : /*
1109 : * Estimate the fraction of tuples in this bin that are narrow enough
1110 : * to not exceed the distance to the upper bound of the query range.
1111 : */
1112 27 : length_hist_frac = calc_length_hist_frac(length_hist_values,
1113 : length_hist_nvalues,
1114 : prev_dist, dist, true);
1115 :
1116 : /*
1117 : * Add the fraction of tuples in this bin, with a suitable length, to
1118 : * the total.
1119 : */
1120 27 : sum_frac += length_hist_frac * bin_width / (double) (hist_nvalues - 1);
1121 :
1122 27 : if (final_bin)
1123 9 : break;
1124 :
1125 18 : bin_width = 1.0;
1126 18 : prev_dist = dist;
1127 : }
1128 :
1129 9 : return sum_frac;
1130 : }
1131 :
1132 : /*
1133 : * Calculate selectivity of "var @> const" operator, ie. estimate the fraction
1134 : * of ranges that contain the constant lower and upper bounds. This uses
1135 : * the histograms of range lower bounds and range lengths, on the assumption
1136 : * that the range lengths are independent of the lower bounds.
1137 : */
1138 : static double
1139 9 : calc_hist_selectivity_contains(TypeCacheEntry *typcache,
1140 : const RangeBound *lower, const RangeBound *upper,
1141 : const RangeBound *hist_lower, int hist_nvalues,
1142 : Datum *length_hist_values, int length_hist_nvalues)
1143 : {
1144 : int i,
1145 : lower_index;
1146 : double bin_width,
1147 : lower_bin_width;
1148 : double sum_frac;
1149 : float8 prev_dist;
1150 :
1151 : /* Find the bin containing the lower bound of query range. */
1152 9 : lower_index = rbound_bsearch(typcache, lower, hist_lower, hist_nvalues,
1153 : true);
1154 :
1155 : /*
1156 : * If the lower bound value is below the histogram's lower limit, there
1157 : * are no matches.
1158 : */
1159 9 : if (lower_index < 0)
1160 UBC 0 : return 0.0;
1161 :
1162 : /*
1163 : * If the lower bound value is at or beyond the histogram's upper limit,
1164 : * start our loop at the last actual bin, as though the upper bound were
1165 : * within that bin; get_position will clamp its result to 1.0 anyway.
1166 : * (This corresponds to assuming that the data population above the
1167 : * histogram's upper limit is empty, exactly like what we just assumed for
1168 : * the lower limit.)
1169 : */
1170 CBC 9 : lower_index = Min(lower_index, hist_nvalues - 2);
1171 :
1172 : /*
1173 : * Calculate lower_bin_width, ie. the fraction of the of (lower_index,
1174 : * lower_index + 1) bin which is greater than lower bound of query range
1175 : * using linear interpolation of subdiff function.
1176 : */
1177 9 : lower_bin_width = get_position(typcache, lower, &hist_lower[lower_index],
1178 9 : &hist_lower[lower_index + 1]);
1179 :
1180 : /*
1181 : * Loop through all the lower bound bins, smaller than the query lower
1182 : * bound. In the loop, dist and prev_dist are the distance of the
1183 : * "current" bin's lower and upper bounds from the constant upper bound.
1184 : * We begin from query lower bound, and walk backwards, so the first bin's
1185 : * upper bound is the query lower bound, and its distance to the query
1186 : * upper bound is the length of the query range.
1187 : *
1188 : * bin_width represents the width of the current bin. Normally it is 1.0,
1189 : * meaning a full width bin, except for the first bin, which is only
1190 : * counted up to the constant lower bound.
1191 : */
1192 9 : prev_dist = get_distance(typcache, lower, upper);
1193 9 : sum_frac = 0.0;
1194 9 : bin_width = lower_bin_width;
1195 36 : for (i = lower_index; i >= 0; i--)
1196 : {
1197 : float8 dist;
1198 : double length_hist_frac;
1199 :
1200 : /*
1201 : * dist -- distance from upper bound of query range to current value
1202 : * of lower bound histogram or lower bound of query range (if we've
1203 : * reach it).
1204 : */
1205 27 : dist = get_distance(typcache, &hist_lower[i], upper);
1206 :
1207 : /*
1208 : * Get average fraction of length histogram which covers intervals
1209 : * longer than (or equal to) distance to upper bound of query range.
1210 : */
1211 27 : length_hist_frac =
1212 27 : 1.0 - calc_length_hist_frac(length_hist_values,
1213 : length_hist_nvalues,
1214 : prev_dist, dist, false);
1215 :
1216 27 : sum_frac += length_hist_frac * bin_width / (double) (hist_nvalues - 1);
1217 :
1218 27 : bin_width = 1.0;
1219 27 : prev_dist = dist;
1220 : }
1221 :
1222 9 : return sum_frac;
1223 : }
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