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selfuncs.c
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1 /*-------------------------------------------------------------------------
2  *
3  * selfuncs.c
4  * Selectivity functions and index cost estimation functions for
5  * standard operators and index access methods.
6  *
7  * Selectivity routines are registered in the pg_operator catalog
8  * in the "oprrest" and "oprjoin" attributes.
9  *
10  * Index cost functions are located via the index AM's API struct,
11  * which is obtained from the handler function registered in pg_am.
12  *
13  * Portions Copyright (c) 1996-2017, PostgreSQL Global Development Group
14  * Portions Copyright (c) 1994, Regents of the University of California
15  *
16  *
17  * IDENTIFICATION
18  * src/backend/utils/adt/selfuncs.c
19  *
20  *-------------------------------------------------------------------------
21  */
22 
23 /*----------
24  * Operator selectivity estimation functions are called to estimate the
25  * selectivity of WHERE clauses whose top-level operator is their operator.
26  * We divide the problem into two cases:
27  * Restriction clause estimation: the clause involves vars of just
28  * one relation.
29  * Join clause estimation: the clause involves vars of multiple rels.
30  * Join selectivity estimation is far more difficult and usually less accurate
31  * than restriction estimation.
32  *
33  * When dealing with the inner scan of a nestloop join, we consider the
34  * join's joinclauses as restriction clauses for the inner relation, and
35  * treat vars of the outer relation as parameters (a/k/a constants of unknown
36  * values). So, restriction estimators need to be able to accept an argument
37  * telling which relation is to be treated as the variable.
38  *
39  * The call convention for a restriction estimator (oprrest function) is
40  *
41  * Selectivity oprrest (PlannerInfo *root,
42  * Oid operator,
43  * List *args,
44  * int varRelid);
45  *
46  * root: general information about the query (rtable and RelOptInfo lists
47  * are particularly important for the estimator).
48  * operator: OID of the specific operator in question.
49  * args: argument list from the operator clause.
50  * varRelid: if not zero, the relid (rtable index) of the relation to
51  * be treated as the variable relation. May be zero if the args list
52  * is known to contain vars of only one relation.
53  *
54  * This is represented at the SQL level (in pg_proc) as
55  *
56  * float8 oprrest (internal, oid, internal, int4);
57  *
58  * The result is a selectivity, that is, a fraction (0 to 1) of the rows
59  * of the relation that are expected to produce a TRUE result for the
60  * given operator.
61  *
62  * The call convention for a join estimator (oprjoin function) is similar
63  * except that varRelid is not needed, and instead join information is
64  * supplied:
65  *
66  * Selectivity oprjoin (PlannerInfo *root,
67  * Oid operator,
68  * List *args,
69  * JoinType jointype,
70  * SpecialJoinInfo *sjinfo);
71  *
72  * float8 oprjoin (internal, oid, internal, int2, internal);
73  *
74  * (Before Postgres 8.4, join estimators had only the first four of these
75  * parameters. That signature is still allowed, but deprecated.) The
76  * relationship between jointype and sjinfo is explained in the comments for
77  * clause_selectivity() --- the short version is that jointype is usually
78  * best ignored in favor of examining sjinfo.
79  *
80  * Join selectivity for regular inner and outer joins is defined as the
81  * fraction (0 to 1) of the cross product of the relations that is expected
82  * to produce a TRUE result for the given operator. For both semi and anti
83  * joins, however, the selectivity is defined as the fraction of the left-hand
84  * side relation's rows that are expected to have a match (ie, at least one
85  * row with a TRUE result) in the right-hand side.
86  *
87  * For both oprrest and oprjoin functions, the operator's input collation OID
88  * (if any) is passed using the standard fmgr mechanism, so that the estimator
89  * function can fetch it with PG_GET_COLLATION(). Note, however, that all
90  * statistics in pg_statistic are currently built using the database's default
91  * collation. Thus, in most cases where we are looking at statistics, we
92  * should ignore the actual operator collation and use DEFAULT_COLLATION_OID.
93  * We expect that the error induced by doing this is usually not large enough
94  * to justify complicating matters.
95  *----------
96  */
97 
98 #include "postgres.h"
99 
100 #include <ctype.h>
101 #include <float.h>
102 #include <math.h>
103 
104 #include "access/brin.h"
105 #include "access/gin.h"
106 #include "access/htup_details.h"
107 #include "access/sysattr.h"
108 #include "catalog/index.h"
109 #include "catalog/pg_am.h"
110 #include "catalog/pg_collation.h"
111 #include "catalog/pg_operator.h"
112 #include "catalog/pg_opfamily.h"
113 #include "catalog/pg_statistic.h"
115 #include "catalog/pg_type.h"
116 #include "executor/executor.h"
117 #include "mb/pg_wchar.h"
118 #include "nodes/makefuncs.h"
119 #include "nodes/nodeFuncs.h"
120 #include "optimizer/clauses.h"
121 #include "optimizer/cost.h"
122 #include "optimizer/pathnode.h"
123 #include "optimizer/paths.h"
124 #include "optimizer/plancat.h"
125 #include "optimizer/predtest.h"
126 #include "optimizer/restrictinfo.h"
127 #include "optimizer/var.h"
128 #include "parser/parse_clause.h"
129 #include "parser/parse_coerce.h"
130 #include "parser/parsetree.h"
131 #include "statistics/statistics.h"
132 #include "utils/builtins.h"
133 #include "utils/bytea.h"
134 #include "utils/date.h"
135 #include "utils/datum.h"
136 #include "utils/fmgroids.h"
137 #include "utils/index_selfuncs.h"
138 #include "utils/lsyscache.h"
139 #include "utils/nabstime.h"
140 #include "utils/pg_locale.h"
141 #include "utils/rel.h"
142 #include "utils/selfuncs.h"
143 #include "utils/spccache.h"
144 #include "utils/syscache.h"
145 #include "utils/timestamp.h"
146 #include "utils/tqual.h"
147 #include "utils/typcache.h"
148 #include "utils/varlena.h"
149 
150 
151 /* Hooks for plugins to get control when we ask for stats */
154 
155 static double var_eq_const(VariableStatData *vardata, Oid operator,
156  Datum constval, bool constisnull,
157  bool varonleft);
158 static double var_eq_non_const(VariableStatData *vardata, Oid operator,
159  Node *other,
160  bool varonleft);
161 static double ineq_histogram_selectivity(PlannerInfo *root,
162  VariableStatData *vardata,
163  FmgrInfo *opproc, bool isgt,
164  Datum constval, Oid consttype);
165 static double eqjoinsel_inner(Oid operator,
166  VariableStatData *vardata1, VariableStatData *vardata2);
167 static double eqjoinsel_semi(Oid operator,
168  VariableStatData *vardata1, VariableStatData *vardata2,
169  RelOptInfo *inner_rel);
171  RelOptInfo *rel, List **varinfos, double *ndistinct);
172 static bool convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
173  Datum lobound, Datum hibound, Oid boundstypid,
174  double *scaledlobound, double *scaledhibound);
175 static double convert_numeric_to_scalar(Datum value, Oid typid);
176 static void convert_string_to_scalar(char *value,
177  double *scaledvalue,
178  char *lobound,
179  double *scaledlobound,
180  char *hibound,
181  double *scaledhibound);
183  double *scaledvalue,
184  Datum lobound,
185  double *scaledlobound,
186  Datum hibound,
187  double *scaledhibound);
188 static double convert_one_string_to_scalar(char *value,
189  int rangelo, int rangehi);
190 static double convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
191  int rangelo, int rangehi);
192 static char *convert_string_datum(Datum value, Oid typid);
193 static double convert_timevalue_to_scalar(Datum value, Oid typid);
194 static void examine_simple_variable(PlannerInfo *root, Var *var,
195  VariableStatData *vardata);
196 static bool get_variable_range(PlannerInfo *root, VariableStatData *vardata,
197  Oid sortop, Datum *min, Datum *max);
198 static bool get_actual_variable_range(PlannerInfo *root,
199  VariableStatData *vardata,
200  Oid sortop,
201  Datum *min, Datum *max);
202 static RelOptInfo *find_join_input_rel(PlannerInfo *root, Relids relids);
204  VariableStatData *vardata,
205  Oid vartype, Oid opfamily, Const *prefixcon);
206 static Selectivity like_selectivity(const char *patt, int pattlen,
207  bool case_insensitive);
208 static Selectivity regex_selectivity(const char *patt, int pattlen,
209  bool case_insensitive,
210  int fixed_prefix_len);
211 static Datum string_to_datum(const char *str, Oid datatype);
212 static Const *string_to_const(const char *str, Oid datatype);
213 static Const *string_to_bytea_const(const char *str, size_t str_len);
214 static List *add_predicate_to_quals(IndexOptInfo *index, List *indexQuals);
215 
216 
217 /*
218  * eqsel - Selectivity of "=" for any data types.
219  *
220  * Note: this routine is also used to estimate selectivity for some
221  * operators that are not "=" but have comparable selectivity behavior,
222  * such as "~=" (geometric approximate-match). Even for "=", we must
223  * keep in mind that the left and right datatypes may differ.
224  */
225 Datum
227 {
229  Oid operator = PG_GETARG_OID(1);
230  List *args = (List *) PG_GETARG_POINTER(2);
231  int varRelid = PG_GETARG_INT32(3);
232  VariableStatData vardata;
233  Node *other;
234  bool varonleft;
235  double selec;
236 
237  /*
238  * If expression is not variable = something or something = variable, then
239  * punt and return a default estimate.
240  */
241  if (!get_restriction_variable(root, args, varRelid,
242  &vardata, &other, &varonleft))
244 
245  /*
246  * We can do a lot better if the something is a constant. (Note: the
247  * Const might result from estimation rather than being a simple constant
248  * in the query.)
249  */
250  if (IsA(other, Const))
251  selec = var_eq_const(&vardata, operator,
252  ((Const *) other)->constvalue,
253  ((Const *) other)->constisnull,
254  varonleft);
255  else
256  selec = var_eq_non_const(&vardata, operator, other,
257  varonleft);
258 
259  ReleaseVariableStats(vardata);
260 
261  PG_RETURN_FLOAT8((float8) selec);
262 }
263 
264 /*
265  * var_eq_const --- eqsel for var = const case
266  *
267  * This is split out so that some other estimation functions can use it.
268  */
269 static double
270 var_eq_const(VariableStatData *vardata, Oid operator,
271  Datum constval, bool constisnull,
272  bool varonleft)
273 {
274  double selec;
275  bool isdefault;
276 
277  /*
278  * If the constant is NULL, assume operator is strict and return zero, ie,
279  * operator will never return TRUE.
280  */
281  if (constisnull)
282  return 0.0;
283 
284  /*
285  * If we matched the var to a unique index or DISTINCT clause, assume
286  * there is exactly one match regardless of anything else. (This is
287  * slightly bogus, since the index or clause's equality operator might be
288  * different from ours, but it's much more likely to be right than
289  * ignoring the information.)
290  */
291  if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
292  return 1.0 / vardata->rel->tuples;
293 
294  if (HeapTupleIsValid(vardata->statsTuple))
295  {
296  Form_pg_statistic stats;
297  Datum *values;
298  int nvalues;
299  float4 *numbers;
300  int nnumbers;
301  bool match = false;
302  int i;
303 
304  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
305 
306  /*
307  * Is the constant "=" to any of the column's most common values?
308  * (Although the given operator may not really be "=", we will assume
309  * that seeing whether it returns TRUE is an appropriate test. If you
310  * don't like this, maybe you shouldn't be using eqsel for your
311  * operator...)
312  */
313  if (get_attstatsslot(vardata->statsTuple,
314  vardata->atttype, vardata->atttypmod,
316  NULL,
317  &values, &nvalues,
318  &numbers, &nnumbers))
319  {
320  FmgrInfo eqproc;
321 
322  fmgr_info(get_opcode(operator), &eqproc);
323 
324  for (i = 0; i < nvalues; i++)
325  {
326  /* be careful to apply operator right way 'round */
327  if (varonleft)
328  match = DatumGetBool(FunctionCall2Coll(&eqproc,
330  values[i],
331  constval));
332  else
333  match = DatumGetBool(FunctionCall2Coll(&eqproc,
335  constval,
336  values[i]));
337  if (match)
338  break;
339  }
340  }
341  else
342  {
343  /* no most-common-value info available */
344  values = NULL;
345  numbers = NULL;
346  i = nvalues = nnumbers = 0;
347  }
348 
349  if (match)
350  {
351  /*
352  * Constant is "=" to this common value. We know selectivity
353  * exactly (or as exactly as ANALYZE could calculate it, anyway).
354  */
355  selec = numbers[i];
356  }
357  else
358  {
359  /*
360  * Comparison is against a constant that is neither NULL nor any
361  * of the common values. Its selectivity cannot be more than
362  * this:
363  */
364  double sumcommon = 0.0;
365  double otherdistinct;
366 
367  for (i = 0; i < nnumbers; i++)
368  sumcommon += numbers[i];
369  selec = 1.0 - sumcommon - stats->stanullfrac;
370  CLAMP_PROBABILITY(selec);
371 
372  /*
373  * and in fact it's probably a good deal less. We approximate that
374  * all the not-common values share this remaining fraction
375  * equally, so we divide by the number of other distinct values.
376  */
377  otherdistinct = get_variable_numdistinct(vardata, &isdefault) - nnumbers;
378  if (otherdistinct > 1)
379  selec /= otherdistinct;
380 
381  /*
382  * Another cross-check: selectivity shouldn't be estimated as more
383  * than the least common "most common value".
384  */
385  if (nnumbers > 0 && selec > numbers[nnumbers - 1])
386  selec = numbers[nnumbers - 1];
387  }
388 
389  free_attstatsslot(vardata->atttype, values, nvalues,
390  numbers, nnumbers);
391  }
392  else
393  {
394  /*
395  * No ANALYZE stats available, so make a guess using estimated number
396  * of distinct values and assuming they are equally common. (The guess
397  * is unlikely to be very good, but we do know a few special cases.)
398  */
399  selec = 1.0 / get_variable_numdistinct(vardata, &isdefault);
400  }
401 
402  /* result should be in range, but make sure... */
403  CLAMP_PROBABILITY(selec);
404 
405  return selec;
406 }
407 
408 /*
409  * var_eq_non_const --- eqsel for var = something-other-than-const case
410  */
411 static double
413  Node *other,
414  bool varonleft)
415 {
416  double selec;
417  bool isdefault;
418 
419  /*
420  * If we matched the var to a unique index or DISTINCT clause, assume
421  * there is exactly one match regardless of anything else. (This is
422  * slightly bogus, since the index or clause's equality operator might be
423  * different from ours, but it's much more likely to be right than
424  * ignoring the information.)
425  */
426  if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
427  return 1.0 / vardata->rel->tuples;
428 
429  if (HeapTupleIsValid(vardata->statsTuple))
430  {
431  Form_pg_statistic stats;
432  double ndistinct;
433  float4 *numbers;
434  int nnumbers;
435 
436  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
437 
438  /*
439  * Search is for a value that we do not know a priori, but we will
440  * assume it is not NULL. Estimate the selectivity as non-null
441  * fraction divided by number of distinct values, so that we get a
442  * result averaged over all possible values whether common or
443  * uncommon. (Essentially, we are assuming that the not-yet-known
444  * comparison value is equally likely to be any of the possible
445  * values, regardless of their frequency in the table. Is that a good
446  * idea?)
447  */
448  selec = 1.0 - stats->stanullfrac;
449  ndistinct = get_variable_numdistinct(vardata, &isdefault);
450  if (ndistinct > 1)
451  selec /= ndistinct;
452 
453  /*
454  * Cross-check: selectivity should never be estimated as more than the
455  * most common value's.
456  */
457  if (get_attstatsslot(vardata->statsTuple,
458  vardata->atttype, vardata->atttypmod,
460  NULL,
461  NULL, NULL,
462  &numbers, &nnumbers))
463  {
464  if (nnumbers > 0 && selec > numbers[0])
465  selec = numbers[0];
466  free_attstatsslot(vardata->atttype, NULL, 0, numbers, nnumbers);
467  }
468  }
469  else
470  {
471  /*
472  * No ANALYZE stats available, so make a guess using estimated number
473  * of distinct values and assuming they are equally common. (The guess
474  * is unlikely to be very good, but we do know a few special cases.)
475  */
476  selec = 1.0 / get_variable_numdistinct(vardata, &isdefault);
477  }
478 
479  /* result should be in range, but make sure... */
480  CLAMP_PROBABILITY(selec);
481 
482  return selec;
483 }
484 
485 /*
486  * neqsel - Selectivity of "!=" for any data types.
487  *
488  * This routine is also used for some operators that are not "!="
489  * but have comparable selectivity behavior. See above comments
490  * for eqsel().
491  */
492 Datum
494 {
496  Oid operator = PG_GETARG_OID(1);
497  List *args = (List *) PG_GETARG_POINTER(2);
498  int varRelid = PG_GETARG_INT32(3);
499  Oid eqop;
500  float8 result;
501 
502  /*
503  * We want 1 - eqsel() where the equality operator is the one associated
504  * with this != operator, that is, its negator.
505  */
506  eqop = get_negator(operator);
507  if (eqop)
508  {
510  PointerGetDatum(root),
511  ObjectIdGetDatum(eqop),
512  PointerGetDatum(args),
513  Int32GetDatum(varRelid)));
514  }
515  else
516  {
517  /* Use default selectivity (should we raise an error instead?) */
518  result = DEFAULT_EQ_SEL;
519  }
520  result = 1.0 - result;
521  PG_RETURN_FLOAT8(result);
522 }
523 
524 /*
525  * scalarineqsel - Selectivity of "<", "<=", ">", ">=" for scalars.
526  *
527  * This is the guts of both scalarltsel and scalargtsel. The caller has
528  * commuted the clause, if necessary, so that we can treat the variable as
529  * being on the left. The caller must also make sure that the other side
530  * of the clause is a non-null Const, and dissect same into a value and
531  * datatype.
532  *
533  * This routine works for any datatype (or pair of datatypes) known to
534  * convert_to_scalar(). If it is applied to some other datatype,
535  * it will return a default estimate.
536  */
537 static double
538 scalarineqsel(PlannerInfo *root, Oid operator, bool isgt,
539  VariableStatData *vardata, Datum constval, Oid consttype)
540 {
541  Form_pg_statistic stats;
542  FmgrInfo opproc;
543  double mcv_selec,
544  hist_selec,
545  sumcommon;
546  double selec;
547 
548  if (!HeapTupleIsValid(vardata->statsTuple))
549  {
550  /* no stats available, so default result */
551  return DEFAULT_INEQ_SEL;
552  }
553  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
554 
555  fmgr_info(get_opcode(operator), &opproc);
556 
557  /*
558  * If we have most-common-values info, add up the fractions of the MCV
559  * entries that satisfy MCV OP CONST. These fractions contribute directly
560  * to the result selectivity. Also add up the total fraction represented
561  * by MCV entries.
562  */
563  mcv_selec = mcv_selectivity(vardata, &opproc, constval, true,
564  &sumcommon);
565 
566  /*
567  * If there is a histogram, determine which bin the constant falls in, and
568  * compute the resulting contribution to selectivity.
569  */
570  hist_selec = ineq_histogram_selectivity(root, vardata, &opproc, isgt,
571  constval, consttype);
572 
573  /*
574  * Now merge the results from the MCV and histogram calculations,
575  * realizing that the histogram covers only the non-null values that are
576  * not listed in MCV.
577  */
578  selec = 1.0 - stats->stanullfrac - sumcommon;
579 
580  if (hist_selec >= 0.0)
581  selec *= hist_selec;
582  else
583  {
584  /*
585  * If no histogram but there are values not accounted for by MCV,
586  * arbitrarily assume half of them will match.
587  */
588  selec *= 0.5;
589  }
590 
591  selec += mcv_selec;
592 
593  /* result should be in range, but make sure... */
594  CLAMP_PROBABILITY(selec);
595 
596  return selec;
597 }
598 
599 /*
600  * mcv_selectivity - Examine the MCV list for selectivity estimates
601  *
602  * Determine the fraction of the variable's MCV population that satisfies
603  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft. Also
604  * compute the fraction of the total column population represented by the MCV
605  * list. This code will work for any boolean-returning predicate operator.
606  *
607  * The function result is the MCV selectivity, and the fraction of the
608  * total population is returned into *sumcommonp. Zeroes are returned
609  * if there is no MCV list.
610  */
611 double
613  Datum constval, bool varonleft,
614  double *sumcommonp)
615 {
616  double mcv_selec,
617  sumcommon;
618  Datum *values;
619  int nvalues;
620  float4 *numbers;
621  int nnumbers;
622  int i;
623 
624  mcv_selec = 0.0;
625  sumcommon = 0.0;
626 
627  if (HeapTupleIsValid(vardata->statsTuple) &&
628  get_attstatsslot(vardata->statsTuple,
629  vardata->atttype, vardata->atttypmod,
631  NULL,
632  &values, &nvalues,
633  &numbers, &nnumbers))
634  {
635  for (i = 0; i < nvalues; i++)
636  {
637  if (varonleft ?
640  values[i],
641  constval)) :
644  constval,
645  values[i])))
646  mcv_selec += numbers[i];
647  sumcommon += numbers[i];
648  }
649  free_attstatsslot(vardata->atttype, values, nvalues,
650  numbers, nnumbers);
651  }
652 
653  *sumcommonp = sumcommon;
654  return mcv_selec;
655 }
656 
657 /*
658  * histogram_selectivity - Examine the histogram for selectivity estimates
659  *
660  * Determine the fraction of the variable's histogram entries that satisfy
661  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft.
662  *
663  * This code will work for any boolean-returning predicate operator, whether
664  * or not it has anything to do with the histogram sort operator. We are
665  * essentially using the histogram just as a representative sample. However,
666  * small histograms are unlikely to be all that representative, so the caller
667  * should be prepared to fall back on some other estimation approach when the
668  * histogram is missing or very small. It may also be prudent to combine this
669  * approach with another one when the histogram is small.
670  *
671  * If the actual histogram size is not at least min_hist_size, we won't bother
672  * to do the calculation at all. Also, if the n_skip parameter is > 0, we
673  * ignore the first and last n_skip histogram elements, on the grounds that
674  * they are outliers and hence not very representative. Typical values for
675  * these parameters are 10 and 1.
676  *
677  * The function result is the selectivity, or -1 if there is no histogram
678  * or it's smaller than min_hist_size.
679  *
680  * The output parameter *hist_size receives the actual histogram size,
681  * or zero if no histogram. Callers may use this number to decide how
682  * much faith to put in the function result.
683  *
684  * Note that the result disregards both the most-common-values (if any) and
685  * null entries. The caller is expected to combine this result with
686  * statistics for those portions of the column population. It may also be
687  * prudent to clamp the result range, ie, disbelieve exact 0 or 1 outputs.
688  */
689 double
691  Datum constval, bool varonleft,
692  int min_hist_size, int n_skip,
693  int *hist_size)
694 {
695  double result;
696  Datum *values;
697  int nvalues;
698 
699  /* check sanity of parameters */
700  Assert(n_skip >= 0);
701  Assert(min_hist_size > 2 * n_skip);
702 
703  if (HeapTupleIsValid(vardata->statsTuple) &&
704  get_attstatsslot(vardata->statsTuple,
705  vardata->atttype, vardata->atttypmod,
707  NULL,
708  &values, &nvalues,
709  NULL, NULL))
710  {
711  *hist_size = nvalues;
712  if (nvalues >= min_hist_size)
713  {
714  int nmatch = 0;
715  int i;
716 
717  for (i = n_skip; i < nvalues - n_skip; i++)
718  {
719  if (varonleft ?
722  values[i],
723  constval)) :
726  constval,
727  values[i])))
728  nmatch++;
729  }
730  result = ((double) nmatch) / ((double) (nvalues - 2 * n_skip));
731  }
732  else
733  result = -1;
734  free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
735  }
736  else
737  {
738  *hist_size = 0;
739  result = -1;
740  }
741 
742  return result;
743 }
744 
745 /*
746  * ineq_histogram_selectivity - Examine the histogram for scalarineqsel
747  *
748  * Determine the fraction of the variable's histogram population that
749  * satisfies the inequality condition, ie, VAR < CONST or VAR > CONST.
750  *
751  * Returns -1 if there is no histogram (valid results will always be >= 0).
752  *
753  * Note that the result disregards both the most-common-values (if any) and
754  * null entries. The caller is expected to combine this result with
755  * statistics for those portions of the column population.
756  */
757 static double
759  VariableStatData *vardata,
760  FmgrInfo *opproc, bool isgt,
761  Datum constval, Oid consttype)
762 {
763  double hist_selec;
764  Oid hist_op;
765  Datum *values;
766  int nvalues;
767 
768  hist_selec = -1.0;
769 
770  /*
771  * Someday, ANALYZE might store more than one histogram per rel/att,
772  * corresponding to more than one possible sort ordering defined for the
773  * column type. However, to make that work we will need to figure out
774  * which staop to search for --- it's not necessarily the one we have at
775  * hand! (For example, we might have a '<=' operator rather than the '<'
776  * operator that will appear in staop.) For now, assume that whatever
777  * appears in pg_statistic is sorted the same way our operator sorts, or
778  * the reverse way if isgt is TRUE.
779  */
780  if (HeapTupleIsValid(vardata->statsTuple) &&
781  get_attstatsslot(vardata->statsTuple,
782  vardata->atttype, vardata->atttypmod,
784  &hist_op,
785  &values, &nvalues,
786  NULL, NULL))
787  {
788  if (nvalues > 1)
789  {
790  /*
791  * Use binary search to find proper location, ie, the first slot
792  * at which the comparison fails. (If the given operator isn't
793  * actually sort-compatible with the histogram, you'll get garbage
794  * results ... but probably not any more garbage-y than you would
795  * from the old linear search.)
796  *
797  * If the binary search accesses the first or last histogram
798  * entry, we try to replace that endpoint with the true column min
799  * or max as found by get_actual_variable_range(). This
800  * ameliorates misestimates when the min or max is moving as a
801  * result of changes since the last ANALYZE. Note that this could
802  * result in effectively including MCVs into the histogram that
803  * weren't there before, but we don't try to correct for that.
804  */
805  double histfrac;
806  int lobound = 0; /* first possible slot to search */
807  int hibound = nvalues; /* last+1 slot to search */
808  bool have_end = false;
809 
810  /*
811  * If there are only two histogram entries, we'll want up-to-date
812  * values for both. (If there are more than two, we need at most
813  * one of them to be updated, so we deal with that within the
814  * loop.)
815  */
816  if (nvalues == 2)
817  have_end = get_actual_variable_range(root,
818  vardata,
819  hist_op,
820  &values[0],
821  &values[1]);
822 
823  while (lobound < hibound)
824  {
825  int probe = (lobound + hibound) / 2;
826  bool ltcmp;
827 
828  /*
829  * If we find ourselves about to compare to the first or last
830  * histogram entry, first try to replace it with the actual
831  * current min or max (unless we already did so above).
832  */
833  if (probe == 0 && nvalues > 2)
834  have_end = get_actual_variable_range(root,
835  vardata,
836  hist_op,
837  &values[0],
838  NULL);
839  else if (probe == nvalues - 1 && nvalues > 2)
840  have_end = get_actual_variable_range(root,
841  vardata,
842  hist_op,
843  NULL,
844  &values[probe]);
845 
846  ltcmp = DatumGetBool(FunctionCall2Coll(opproc,
848  values[probe],
849  constval));
850  if (isgt)
851  ltcmp = !ltcmp;
852  if (ltcmp)
853  lobound = probe + 1;
854  else
855  hibound = probe;
856  }
857 
858  if (lobound <= 0)
859  {
860  /* Constant is below lower histogram boundary. */
861  histfrac = 0.0;
862  }
863  else if (lobound >= nvalues)
864  {
865  /* Constant is above upper histogram boundary. */
866  histfrac = 1.0;
867  }
868  else
869  {
870  int i = lobound;
871  double val,
872  high,
873  low;
874  double binfrac;
875 
876  /*
877  * We have values[i-1] <= constant <= values[i].
878  *
879  * Convert the constant and the two nearest bin boundary
880  * values to a uniform comparison scale, and do a linear
881  * interpolation within this bin.
882  */
883  if (convert_to_scalar(constval, consttype, &val,
884  values[i - 1], values[i],
885  vardata->vartype,
886  &low, &high))
887  {
888  if (high <= low)
889  {
890  /* cope if bin boundaries appear identical */
891  binfrac = 0.5;
892  }
893  else if (val <= low)
894  binfrac = 0.0;
895  else if (val >= high)
896  binfrac = 1.0;
897  else
898  {
899  binfrac = (val - low) / (high - low);
900 
901  /*
902  * Watch out for the possibility that we got a NaN or
903  * Infinity from the division. This can happen
904  * despite the previous checks, if for example "low"
905  * is -Infinity.
906  */
907  if (isnan(binfrac) ||
908  binfrac < 0.0 || binfrac > 1.0)
909  binfrac = 0.5;
910  }
911  }
912  else
913  {
914  /*
915  * Ideally we'd produce an error here, on the grounds that
916  * the given operator shouldn't have scalarXXsel
917  * registered as its selectivity func unless we can deal
918  * with its operand types. But currently, all manner of
919  * stuff is invoking scalarXXsel, so give a default
920  * estimate until that can be fixed.
921  */
922  binfrac = 0.5;
923  }
924 
925  /*
926  * Now, compute the overall selectivity across the values
927  * represented by the histogram. We have i-1 full bins and
928  * binfrac partial bin below the constant.
929  */
930  histfrac = (double) (i - 1) + binfrac;
931  histfrac /= (double) (nvalues - 1);
932  }
933 
934  /*
935  * Now histfrac = fraction of histogram entries below the
936  * constant.
937  *
938  * Account for "<" vs ">"
939  */
940  hist_selec = isgt ? (1.0 - histfrac) : histfrac;
941 
942  /*
943  * The histogram boundaries are only approximate to begin with,
944  * and may well be out of date anyway. Therefore, don't believe
945  * extremely small or large selectivity estimates --- unless we
946  * got actual current endpoint values from the table.
947  */
948  if (have_end)
949  CLAMP_PROBABILITY(hist_selec);
950  else
951  {
952  if (hist_selec < 0.0001)
953  hist_selec = 0.0001;
954  else if (hist_selec > 0.9999)
955  hist_selec = 0.9999;
956  }
957  }
958 
959  free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
960  }
961 
962  return hist_selec;
963 }
964 
965 /*
966  * scalarltsel - Selectivity of "<" (also "<=") for scalars.
967  */
968 Datum
970 {
972  Oid operator = PG_GETARG_OID(1);
973  List *args = (List *) PG_GETARG_POINTER(2);
974  int varRelid = PG_GETARG_INT32(3);
975  VariableStatData vardata;
976  Node *other;
977  bool varonleft;
978  Datum constval;
979  Oid consttype;
980  bool isgt;
981  double selec;
982 
983  /*
984  * If expression is not variable op something or something op variable,
985  * then punt and return a default estimate.
986  */
987  if (!get_restriction_variable(root, args, varRelid,
988  &vardata, &other, &varonleft))
990 
991  /*
992  * Can't do anything useful if the something is not a constant, either.
993  */
994  if (!IsA(other, Const))
995  {
996  ReleaseVariableStats(vardata);
998  }
999 
1000  /*
1001  * If the constant is NULL, assume operator is strict and return zero, ie,
1002  * operator will never return TRUE.
1003  */
1004  if (((Const *) other)->constisnull)
1005  {
1006  ReleaseVariableStats(vardata);
1007  PG_RETURN_FLOAT8(0.0);
1008  }
1009  constval = ((Const *) other)->constvalue;
1010  consttype = ((Const *) other)->consttype;
1011 
1012  /*
1013  * Force the var to be on the left to simplify logic in scalarineqsel.
1014  */
1015  if (varonleft)
1016  {
1017  /* we have var < other */
1018  isgt = false;
1019  }
1020  else
1021  {
1022  /* we have other < var, commute to make var > other */
1023  operator = get_commutator(operator);
1024  if (!operator)
1025  {
1026  /* Use default selectivity (should we raise an error instead?) */
1027  ReleaseVariableStats(vardata);
1029  }
1030  isgt = true;
1031  }
1032 
1033  selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
1034 
1035  ReleaseVariableStats(vardata);
1036 
1037  PG_RETURN_FLOAT8((float8) selec);
1038 }
1039 
1040 /*
1041  * scalargtsel - Selectivity of ">" (also ">=") for integers.
1042  */
1043 Datum
1045 {
1046  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1047  Oid operator = PG_GETARG_OID(1);
1048  List *args = (List *) PG_GETARG_POINTER(2);
1049  int varRelid = PG_GETARG_INT32(3);
1050  VariableStatData vardata;
1051  Node *other;
1052  bool varonleft;
1053  Datum constval;
1054  Oid consttype;
1055  bool isgt;
1056  double selec;
1057 
1058  /*
1059  * If expression is not variable op something or something op variable,
1060  * then punt and return a default estimate.
1061  */
1062  if (!get_restriction_variable(root, args, varRelid,
1063  &vardata, &other, &varonleft))
1065 
1066  /*
1067  * Can't do anything useful if the something is not a constant, either.
1068  */
1069  if (!IsA(other, Const))
1070  {
1071  ReleaseVariableStats(vardata);
1073  }
1074 
1075  /*
1076  * If the constant is NULL, assume operator is strict and return zero, ie,
1077  * operator will never return TRUE.
1078  */
1079  if (((Const *) other)->constisnull)
1080  {
1081  ReleaseVariableStats(vardata);
1082  PG_RETURN_FLOAT8(0.0);
1083  }
1084  constval = ((Const *) other)->constvalue;
1085  consttype = ((Const *) other)->consttype;
1086 
1087  /*
1088  * Force the var to be on the left to simplify logic in scalarineqsel.
1089  */
1090  if (varonleft)
1091  {
1092  /* we have var > other */
1093  isgt = true;
1094  }
1095  else
1096  {
1097  /* we have other > var, commute to make var < other */
1098  operator = get_commutator(operator);
1099  if (!operator)
1100  {
1101  /* Use default selectivity (should we raise an error instead?) */
1102  ReleaseVariableStats(vardata);
1104  }
1105  isgt = false;
1106  }
1107 
1108  selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
1109 
1110  ReleaseVariableStats(vardata);
1111 
1112  PG_RETURN_FLOAT8((float8) selec);
1113 }
1114 
1115 /*
1116  * patternsel - Generic code for pattern-match selectivity.
1117  */
1118 static double
1120 {
1121  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1122  Oid operator = PG_GETARG_OID(1);
1123  List *args = (List *) PG_GETARG_POINTER(2);
1124  int varRelid = PG_GETARG_INT32(3);
1125  Oid collation = PG_GET_COLLATION();
1126  VariableStatData vardata;
1127  Node *other;
1128  bool varonleft;
1129  Datum constval;
1130  Oid consttype;
1131  Oid vartype;
1132  Oid opfamily;
1133  Pattern_Prefix_Status pstatus;
1134  Const *patt;
1135  Const *prefix = NULL;
1136  Selectivity rest_selec = 0;
1137  double result;
1138 
1139  /*
1140  * If this is for a NOT LIKE or similar operator, get the corresponding
1141  * positive-match operator and work with that. Set result to the correct
1142  * default estimate, too.
1143  */
1144  if (negate)
1145  {
1146  operator = get_negator(operator);
1147  if (!OidIsValid(operator))
1148  elog(ERROR, "patternsel called for operator without a negator");
1149  result = 1.0 - DEFAULT_MATCH_SEL;
1150  }
1151  else
1152  {
1153  result = DEFAULT_MATCH_SEL;
1154  }
1155 
1156  /*
1157  * If expression is not variable op constant, then punt and return a
1158  * default estimate.
1159  */
1160  if (!get_restriction_variable(root, args, varRelid,
1161  &vardata, &other, &varonleft))
1162  return result;
1163  if (!varonleft || !IsA(other, Const))
1164  {
1165  ReleaseVariableStats(vardata);
1166  return result;
1167  }
1168 
1169  /*
1170  * If the constant is NULL, assume operator is strict and return zero, ie,
1171  * operator will never return TRUE. (It's zero even for a negator op.)
1172  */
1173  if (((Const *) other)->constisnull)
1174  {
1175  ReleaseVariableStats(vardata);
1176  return 0.0;
1177  }
1178  constval = ((Const *) other)->constvalue;
1179  consttype = ((Const *) other)->consttype;
1180 
1181  /*
1182  * The right-hand const is type text or bytea for all supported operators.
1183  * We do not expect to see binary-compatible types here, since
1184  * const-folding should have relabeled the const to exactly match the
1185  * operator's declared type.
1186  */
1187  if (consttype != TEXTOID && consttype != BYTEAOID)
1188  {
1189  ReleaseVariableStats(vardata);
1190  return result;
1191  }
1192 
1193  /*
1194  * Similarly, the exposed type of the left-hand side should be one of
1195  * those we know. (Do not look at vardata.atttype, which might be
1196  * something binary-compatible but different.) We can use it to choose
1197  * the index opfamily from which we must draw the comparison operators.
1198  *
1199  * NOTE: It would be more correct to use the PATTERN opfamilies than the
1200  * simple ones, but at the moment ANALYZE will not generate statistics for
1201  * the PATTERN operators. But our results are so approximate anyway that
1202  * it probably hardly matters.
1203  */
1204  vartype = vardata.vartype;
1205 
1206  switch (vartype)
1207  {
1208  case TEXTOID:
1209  opfamily = TEXT_BTREE_FAM_OID;
1210  break;
1211  case BPCHAROID:
1212  opfamily = BPCHAR_BTREE_FAM_OID;
1213  break;
1214  case NAMEOID:
1215  opfamily = NAME_BTREE_FAM_OID;
1216  break;
1217  case BYTEAOID:
1218  opfamily = BYTEA_BTREE_FAM_OID;
1219  break;
1220  default:
1221  ReleaseVariableStats(vardata);
1222  return result;
1223  }
1224 
1225  /*
1226  * Pull out any fixed prefix implied by the pattern, and estimate the
1227  * fractional selectivity of the remainder of the pattern. Unlike many of
1228  * the other functions in this file, we use the pattern operator's actual
1229  * collation for this step. This is not because we expect the collation
1230  * to make a big difference in the selectivity estimate (it seldom would),
1231  * but because we want to be sure we cache compiled regexps under the
1232  * right cache key, so that they can be re-used at runtime.
1233  */
1234  patt = (Const *) other;
1235  pstatus = pattern_fixed_prefix(patt, ptype, collation,
1236  &prefix, &rest_selec);
1237 
1238  /*
1239  * If necessary, coerce the prefix constant to the right type.
1240  */
1241  if (prefix && prefix->consttype != vartype)
1242  {
1243  char *prefixstr;
1244 
1245  switch (prefix->consttype)
1246  {
1247  case TEXTOID:
1248  prefixstr = TextDatumGetCString(prefix->constvalue);
1249  break;
1250  case BYTEAOID:
1252  prefix->constvalue));
1253  break;
1254  default:
1255  elog(ERROR, "unrecognized consttype: %u",
1256  prefix->consttype);
1257  ReleaseVariableStats(vardata);
1258  return result;
1259  }
1260  prefix = string_to_const(prefixstr, vartype);
1261  pfree(prefixstr);
1262  }
1263 
1264  if (pstatus == Pattern_Prefix_Exact)
1265  {
1266  /*
1267  * Pattern specifies an exact match, so pretend operator is '='
1268  */
1269  Oid eqopr = get_opfamily_member(opfamily, vartype, vartype,
1271 
1272  if (eqopr == InvalidOid)
1273  elog(ERROR, "no = operator for opfamily %u", opfamily);
1274  result = var_eq_const(&vardata, eqopr, prefix->constvalue,
1275  false, true);
1276  }
1277  else
1278  {
1279  /*
1280  * Not exact-match pattern. If we have a sufficiently large
1281  * histogram, estimate selectivity for the histogram part of the
1282  * population by counting matches in the histogram. If not, estimate
1283  * selectivity of the fixed prefix and remainder of pattern
1284  * separately, then combine the two to get an estimate of the
1285  * selectivity for the part of the column population represented by
1286  * the histogram. (For small histograms, we combine these
1287  * approaches.)
1288  *
1289  * We then add up data for any most-common-values values; these are
1290  * not in the histogram population, and we can get exact answers for
1291  * them by applying the pattern operator, so there's no reason to
1292  * approximate. (If the MCVs cover a significant part of the total
1293  * population, this gives us a big leg up in accuracy.)
1294  */
1295  Selectivity selec;
1296  int hist_size;
1297  FmgrInfo opproc;
1298  double nullfrac,
1299  mcv_selec,
1300  sumcommon;
1301 
1302  /* Try to use the histogram entries to get selectivity */
1303  fmgr_info(get_opcode(operator), &opproc);
1304 
1305  selec = histogram_selectivity(&vardata, &opproc, constval, true,
1306  10, 1, &hist_size);
1307 
1308  /* If not at least 100 entries, use the heuristic method */
1309  if (hist_size < 100)
1310  {
1311  Selectivity heursel;
1312  Selectivity prefixsel;
1313 
1314  if (pstatus == Pattern_Prefix_Partial)
1315  prefixsel = prefix_selectivity(root, &vardata, vartype,
1316  opfamily, prefix);
1317  else
1318  prefixsel = 1.0;
1319  heursel = prefixsel * rest_selec;
1320 
1321  if (selec < 0) /* fewer than 10 histogram entries? */
1322  selec = heursel;
1323  else
1324  {
1325  /*
1326  * For histogram sizes from 10 to 100, we combine the
1327  * histogram and heuristic selectivities, putting increasingly
1328  * more trust in the histogram for larger sizes.
1329  */
1330  double hist_weight = hist_size / 100.0;
1331 
1332  selec = selec * hist_weight + heursel * (1.0 - hist_weight);
1333  }
1334  }
1335 
1336  /* In any case, don't believe extremely small or large estimates. */
1337  if (selec < 0.0001)
1338  selec = 0.0001;
1339  else if (selec > 0.9999)
1340  selec = 0.9999;
1341 
1342  /*
1343  * If we have most-common-values info, add up the fractions of the MCV
1344  * entries that satisfy MCV OP PATTERN. These fractions contribute
1345  * directly to the result selectivity. Also add up the total fraction
1346  * represented by MCV entries.
1347  */
1348  mcv_selec = mcv_selectivity(&vardata, &opproc, constval, true,
1349  &sumcommon);
1350 
1351  if (HeapTupleIsValid(vardata.statsTuple))
1352  nullfrac = ((Form_pg_statistic) GETSTRUCT(vardata.statsTuple))->stanullfrac;
1353  else
1354  nullfrac = 0.0;
1355 
1356  /*
1357  * Now merge the results from the MCV and histogram calculations,
1358  * realizing that the histogram covers only the non-null values that
1359  * are not listed in MCV.
1360  */
1361  selec *= 1.0 - nullfrac - sumcommon;
1362  selec += mcv_selec;
1363 
1364  /* result should be in range, but make sure... */
1365  CLAMP_PROBABILITY(selec);
1366  result = selec;
1367  }
1368 
1369  if (prefix)
1370  {
1371  pfree(DatumGetPointer(prefix->constvalue));
1372  pfree(prefix);
1373  }
1374 
1375  ReleaseVariableStats(vardata);
1376 
1377  return negate ? (1.0 - result) : result;
1378 }
1379 
1380 /*
1381  * regexeqsel - Selectivity of regular-expression pattern match.
1382  */
1383 Datum
1385 {
1387 }
1388 
1389 /*
1390  * icregexeqsel - Selectivity of case-insensitive regex match.
1391  */
1392 Datum
1394 {
1396 }
1397 
1398 /*
1399  * likesel - Selectivity of LIKE pattern match.
1400  */
1401 Datum
1403 {
1405 }
1406 
1407 /*
1408  * iclikesel - Selectivity of ILIKE pattern match.
1409  */
1410 Datum
1412 {
1414 }
1415 
1416 /*
1417  * regexnesel - Selectivity of regular-expression pattern non-match.
1418  */
1419 Datum
1421 {
1423 }
1424 
1425 /*
1426  * icregexnesel - Selectivity of case-insensitive regex non-match.
1427  */
1428 Datum
1430 {
1432 }
1433 
1434 /*
1435  * nlikesel - Selectivity of LIKE pattern non-match.
1436  */
1437 Datum
1439 {
1441 }
1442 
1443 /*
1444  * icnlikesel - Selectivity of ILIKE pattern non-match.
1445  */
1446 Datum
1448 {
1450 }
1451 
1452 /*
1453  * boolvarsel - Selectivity of Boolean variable.
1454  *
1455  * This can actually be called on any boolean-valued expression. If it
1456  * involves only Vars of the specified relation, and if there are statistics
1457  * about the Var or expression (the latter is possible if it's indexed) then
1458  * we'll produce a real estimate; otherwise it's just a default.
1459  */
1461 boolvarsel(PlannerInfo *root, Node *arg, int varRelid)
1462 {
1463  VariableStatData vardata;
1464  double selec;
1465 
1466  examine_variable(root, arg, varRelid, &vardata);
1467  if (HeapTupleIsValid(vardata.statsTuple))
1468  {
1469  /*
1470  * A boolean variable V is equivalent to the clause V = 't', so we
1471  * compute the selectivity as if that is what we have.
1472  */
1473  selec = var_eq_const(&vardata, BooleanEqualOperator,
1474  BoolGetDatum(true), false, true);
1475  }
1476  else if (is_funcclause(arg))
1477  {
1478  /*
1479  * If we have no stats and it's a function call, estimate 0.3333333.
1480  * This seems a pretty unprincipled choice, but Postgres has been
1481  * using that estimate for function calls since 1992. The hoariness
1482  * of this behavior suggests that we should not be in too much hurry
1483  * to use another value.
1484  */
1485  selec = 0.3333333;
1486  }
1487  else
1488  {
1489  /* Otherwise, the default estimate is 0.5 */
1490  selec = 0.5;
1491  }
1492  ReleaseVariableStats(vardata);
1493  return selec;
1494 }
1495 
1496 /*
1497  * booltestsel - Selectivity of BooleanTest Node.
1498  */
1501  int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1502 {
1503  VariableStatData vardata;
1504  double selec;
1505 
1506  examine_variable(root, arg, varRelid, &vardata);
1507 
1508  if (HeapTupleIsValid(vardata.statsTuple))
1509  {
1510  Form_pg_statistic stats;
1511  double freq_null;
1512  Datum *values;
1513  int nvalues;
1514  float4 *numbers;
1515  int nnumbers;
1516 
1517  stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
1518  freq_null = stats->stanullfrac;
1519 
1520  if (get_attstatsslot(vardata.statsTuple,
1521  vardata.atttype, vardata.atttypmod,
1523  NULL,
1524  &values, &nvalues,
1525  &numbers, &nnumbers)
1526  && nnumbers > 0)
1527  {
1528  double freq_true;
1529  double freq_false;
1530 
1531  /*
1532  * Get first MCV frequency and derive frequency for true.
1533  */
1534  if (DatumGetBool(values[0]))
1535  freq_true = numbers[0];
1536  else
1537  freq_true = 1.0 - numbers[0] - freq_null;
1538 
1539  /*
1540  * Next derive frequency for false. Then use these as appropriate
1541  * to derive frequency for each case.
1542  */
1543  freq_false = 1.0 - freq_true - freq_null;
1544 
1545  switch (booltesttype)
1546  {
1547  case IS_UNKNOWN:
1548  /* select only NULL values */
1549  selec = freq_null;
1550  break;
1551  case IS_NOT_UNKNOWN:
1552  /* select non-NULL values */
1553  selec = 1.0 - freq_null;
1554  break;
1555  case IS_TRUE:
1556  /* select only TRUE values */
1557  selec = freq_true;
1558  break;
1559  case IS_NOT_TRUE:
1560  /* select non-TRUE values */
1561  selec = 1.0 - freq_true;
1562  break;
1563  case IS_FALSE:
1564  /* select only FALSE values */
1565  selec = freq_false;
1566  break;
1567  case IS_NOT_FALSE:
1568  /* select non-FALSE values */
1569  selec = 1.0 - freq_false;
1570  break;
1571  default:
1572  elog(ERROR, "unrecognized booltesttype: %d",
1573  (int) booltesttype);
1574  selec = 0.0; /* Keep compiler quiet */
1575  break;
1576  }
1577 
1578  free_attstatsslot(vardata.atttype, values, nvalues,
1579  numbers, nnumbers);
1580  }
1581  else
1582  {
1583  /*
1584  * No most-common-value info available. Still have null fraction
1585  * information, so use it for IS [NOT] UNKNOWN. Otherwise adjust
1586  * for null fraction and assume a 50-50 split of TRUE and FALSE.
1587  */
1588  switch (booltesttype)
1589  {
1590  case IS_UNKNOWN:
1591  /* select only NULL values */
1592  selec = freq_null;
1593  break;
1594  case IS_NOT_UNKNOWN:
1595  /* select non-NULL values */
1596  selec = 1.0 - freq_null;
1597  break;
1598  case IS_TRUE:
1599  case IS_FALSE:
1600  /* Assume we select half of the non-NULL values */
1601  selec = (1.0 - freq_null) / 2.0;
1602  break;
1603  case IS_NOT_TRUE:
1604  case IS_NOT_FALSE:
1605  /* Assume we select NULLs plus half of the non-NULLs */
1606  /* equiv. to freq_null + (1.0 - freq_null) / 2.0 */
1607  selec = (freq_null + 1.0) / 2.0;
1608  break;
1609  default:
1610  elog(ERROR, "unrecognized booltesttype: %d",
1611  (int) booltesttype);
1612  selec = 0.0; /* Keep compiler quiet */
1613  break;
1614  }
1615  }
1616  }
1617  else
1618  {
1619  /*
1620  * If we can't get variable statistics for the argument, perhaps
1621  * clause_selectivity can do something with it. We ignore the
1622  * possibility of a NULL value when using clause_selectivity, and just
1623  * assume the value is either TRUE or FALSE.
1624  */
1625  switch (booltesttype)
1626  {
1627  case IS_UNKNOWN:
1628  selec = DEFAULT_UNK_SEL;
1629  break;
1630  case IS_NOT_UNKNOWN:
1631  selec = DEFAULT_NOT_UNK_SEL;
1632  break;
1633  case IS_TRUE:
1634  case IS_NOT_FALSE:
1635  selec = (double) clause_selectivity(root, arg,
1636  varRelid,
1637  jointype, sjinfo);
1638  break;
1639  case IS_FALSE:
1640  case IS_NOT_TRUE:
1641  selec = 1.0 - (double) clause_selectivity(root, arg,
1642  varRelid,
1643  jointype, sjinfo);
1644  break;
1645  default:
1646  elog(ERROR, "unrecognized booltesttype: %d",
1647  (int) booltesttype);
1648  selec = 0.0; /* Keep compiler quiet */
1649  break;
1650  }
1651  }
1652 
1653  ReleaseVariableStats(vardata);
1654 
1655  /* result should be in range, but make sure... */
1656  CLAMP_PROBABILITY(selec);
1657 
1658  return (Selectivity) selec;
1659 }
1660 
1661 /*
1662  * nulltestsel - Selectivity of NullTest Node.
1663  */
1666  int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1667 {
1668  VariableStatData vardata;
1669  double selec;
1670 
1671  examine_variable(root, arg, varRelid, &vardata);
1672 
1673  if (HeapTupleIsValid(vardata.statsTuple))
1674  {
1675  Form_pg_statistic stats;
1676  double freq_null;
1677 
1678  stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
1679  freq_null = stats->stanullfrac;
1680 
1681  switch (nulltesttype)
1682  {
1683  case IS_NULL:
1684 
1685  /*
1686  * Use freq_null directly.
1687  */
1688  selec = freq_null;
1689  break;
1690  case IS_NOT_NULL:
1691 
1692  /*
1693  * Select not unknown (not null) values. Calculate from
1694  * freq_null.
1695  */
1696  selec = 1.0 - freq_null;
1697  break;
1698  default:
1699  elog(ERROR, "unrecognized nulltesttype: %d",
1700  (int) nulltesttype);
1701  return (Selectivity) 0; /* keep compiler quiet */
1702  }
1703  }
1704  else
1705  {
1706  /*
1707  * No ANALYZE stats available, so make a guess
1708  */
1709  switch (nulltesttype)
1710  {
1711  case IS_NULL:
1712  selec = DEFAULT_UNK_SEL;
1713  break;
1714  case IS_NOT_NULL:
1715  selec = DEFAULT_NOT_UNK_SEL;
1716  break;
1717  default:
1718  elog(ERROR, "unrecognized nulltesttype: %d",
1719  (int) nulltesttype);
1720  return (Selectivity) 0; /* keep compiler quiet */
1721  }
1722  }
1723 
1724  ReleaseVariableStats(vardata);
1725 
1726  /* result should be in range, but make sure... */
1727  CLAMP_PROBABILITY(selec);
1728 
1729  return (Selectivity) selec;
1730 }
1731 
1732 /*
1733  * strip_array_coercion - strip binary-compatible relabeling from an array expr
1734  *
1735  * For array values, the parser normally generates ArrayCoerceExpr conversions,
1736  * but it seems possible that RelabelType might show up. Also, the planner
1737  * is not currently tense about collapsing stacked ArrayCoerceExpr nodes,
1738  * so we need to be ready to deal with more than one level.
1739  */
1740 static Node *
1742 {
1743  for (;;)
1744  {
1745  if (node && IsA(node, ArrayCoerceExpr) &&
1746  ((ArrayCoerceExpr *) node)->elemfuncid == InvalidOid)
1747  {
1748  node = (Node *) ((ArrayCoerceExpr *) node)->arg;
1749  }
1750  else if (node && IsA(node, RelabelType))
1751  {
1752  /* We don't really expect this case, but may as well cope */
1753  node = (Node *) ((RelabelType *) node)->arg;
1754  }
1755  else
1756  break;
1757  }
1758  return node;
1759 }
1760 
1761 /*
1762  * scalararraysel - Selectivity of ScalarArrayOpExpr Node.
1763  */
1766  ScalarArrayOpExpr *clause,
1767  bool is_join_clause,
1768  int varRelid,
1769  JoinType jointype,
1770  SpecialJoinInfo *sjinfo)
1771 {
1772  Oid operator = clause->opno;
1773  bool useOr = clause->useOr;
1774  bool isEquality = false;
1775  bool isInequality = false;
1776  Node *leftop;
1777  Node *rightop;
1778  Oid nominal_element_type;
1779  Oid nominal_element_collation;
1780  TypeCacheEntry *typentry;
1781  RegProcedure oprsel;
1782  FmgrInfo oprselproc;
1783  Selectivity s1;
1784  Selectivity s1disjoint;
1785 
1786  /* First, deconstruct the expression */
1787  Assert(list_length(clause->args) == 2);
1788  leftop = (Node *) linitial(clause->args);
1789  rightop = (Node *) lsecond(clause->args);
1790 
1791  /* aggressively reduce both sides to constants */
1792  leftop = estimate_expression_value(root, leftop);
1793  rightop = estimate_expression_value(root, rightop);
1794 
1795  /* get nominal (after relabeling) element type of rightop */
1796  nominal_element_type = get_base_element_type(exprType(rightop));
1797  if (!OidIsValid(nominal_element_type))
1798  return (Selectivity) 0.5; /* probably shouldn't happen */
1799  /* get nominal collation, too, for generating constants */
1800  nominal_element_collation = exprCollation(rightop);
1801 
1802  /* look through any binary-compatible relabeling of rightop */
1803  rightop = strip_array_coercion(rightop);
1804 
1805  /*
1806  * Detect whether the operator is the default equality or inequality
1807  * operator of the array element type.
1808  */
1809  typentry = lookup_type_cache(nominal_element_type, TYPECACHE_EQ_OPR);
1810  if (OidIsValid(typentry->eq_opr))
1811  {
1812  if (operator == typentry->eq_opr)
1813  isEquality = true;
1814  else if (get_negator(operator) == typentry->eq_opr)
1815  isInequality = true;
1816  }
1817 
1818  /*
1819  * If it is equality or inequality, we might be able to estimate this as a
1820  * form of array containment; for instance "const = ANY(column)" can be
1821  * treated as "ARRAY[const] <@ column". scalararraysel_containment tries
1822  * that, and returns the selectivity estimate if successful, or -1 if not.
1823  */
1824  if ((isEquality || isInequality) && !is_join_clause)
1825  {
1826  s1 = scalararraysel_containment(root, leftop, rightop,
1827  nominal_element_type,
1828  isEquality, useOr, varRelid);
1829  if (s1 >= 0.0)
1830  return s1;
1831  }
1832 
1833  /*
1834  * Look up the underlying operator's selectivity estimator. Punt if it
1835  * hasn't got one.
1836  */
1837  if (is_join_clause)
1838  oprsel = get_oprjoin(operator);
1839  else
1840  oprsel = get_oprrest(operator);
1841  if (!oprsel)
1842  return (Selectivity) 0.5;
1843  fmgr_info(oprsel, &oprselproc);
1844 
1845  /*
1846  * In the array-containment check above, we must only believe that an
1847  * operator is equality or inequality if it is the default btree equality
1848  * operator (or its negator) for the element type, since those are the
1849  * operators that array containment will use. But in what follows, we can
1850  * be a little laxer, and also believe that any operators using eqsel() or
1851  * neqsel() as selectivity estimator act like equality or inequality.
1852  */
1853  if (oprsel == F_EQSEL || oprsel == F_EQJOINSEL)
1854  isEquality = true;
1855  else if (oprsel == F_NEQSEL || oprsel == F_NEQJOINSEL)
1856  isInequality = true;
1857 
1858  /*
1859  * We consider three cases:
1860  *
1861  * 1. rightop is an Array constant: deconstruct the array, apply the
1862  * operator's selectivity function for each array element, and merge the
1863  * results in the same way that clausesel.c does for AND/OR combinations.
1864  *
1865  * 2. rightop is an ARRAY[] construct: apply the operator's selectivity
1866  * function for each element of the ARRAY[] construct, and merge.
1867  *
1868  * 3. otherwise, make a guess ...
1869  */
1870  if (rightop && IsA(rightop, Const))
1871  {
1872  Datum arraydatum = ((Const *) rightop)->constvalue;
1873  bool arrayisnull = ((Const *) rightop)->constisnull;
1874  ArrayType *arrayval;
1875  int16 elmlen;
1876  bool elmbyval;
1877  char elmalign;
1878  int num_elems;
1879  Datum *elem_values;
1880  bool *elem_nulls;
1881  int i;
1882 
1883  if (arrayisnull) /* qual can't succeed if null array */
1884  return (Selectivity) 0.0;
1885  arrayval = DatumGetArrayTypeP(arraydatum);
1887  &elmlen, &elmbyval, &elmalign);
1888  deconstruct_array(arrayval,
1889  ARR_ELEMTYPE(arrayval),
1890  elmlen, elmbyval, elmalign,
1891  &elem_values, &elem_nulls, &num_elems);
1892 
1893  /*
1894  * For generic operators, we assume the probability of success is
1895  * independent for each array element. But for "= ANY" or "<> ALL",
1896  * if the array elements are distinct (which'd typically be the case)
1897  * then the probabilities are disjoint, and we should just sum them.
1898  *
1899  * If we were being really tense we would try to confirm that the
1900  * elements are all distinct, but that would be expensive and it
1901  * doesn't seem to be worth the cycles; it would amount to penalizing
1902  * well-written queries in favor of poorly-written ones. However, we
1903  * do protect ourselves a little bit by checking whether the
1904  * disjointness assumption leads to an impossible (out of range)
1905  * probability; if so, we fall back to the normal calculation.
1906  */
1907  s1 = s1disjoint = (useOr ? 0.0 : 1.0);
1908 
1909  for (i = 0; i < num_elems; i++)
1910  {
1911  List *args;
1912  Selectivity s2;
1913 
1914  args = list_make2(leftop,
1915  makeConst(nominal_element_type,
1916  -1,
1917  nominal_element_collation,
1918  elmlen,
1919  elem_values[i],
1920  elem_nulls[i],
1921  elmbyval));
1922  if (is_join_clause)
1923  s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
1924  clause->inputcollid,
1925  PointerGetDatum(root),
1926  ObjectIdGetDatum(operator),
1927  PointerGetDatum(args),
1928  Int16GetDatum(jointype),
1929  PointerGetDatum(sjinfo)));
1930  else
1931  s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
1932  clause->inputcollid,
1933  PointerGetDatum(root),
1934  ObjectIdGetDatum(operator),
1935  PointerGetDatum(args),
1936  Int32GetDatum(varRelid)));
1937 
1938  if (useOr)
1939  {
1940  s1 = s1 + s2 - s1 * s2;
1941  if (isEquality)
1942  s1disjoint += s2;
1943  }
1944  else
1945  {
1946  s1 = s1 * s2;
1947  if (isInequality)
1948  s1disjoint += s2 - 1.0;
1949  }
1950  }
1951 
1952  /* accept disjoint-probability estimate if in range */
1953  if ((useOr ? isEquality : isInequality) &&
1954  s1disjoint >= 0.0 && s1disjoint <= 1.0)
1955  s1 = s1disjoint;
1956  }
1957  else if (rightop && IsA(rightop, ArrayExpr) &&
1958  !((ArrayExpr *) rightop)->multidims)
1959  {
1960  ArrayExpr *arrayexpr = (ArrayExpr *) rightop;
1961  int16 elmlen;
1962  bool elmbyval;
1963  ListCell *l;
1964 
1965  get_typlenbyval(arrayexpr->element_typeid,
1966  &elmlen, &elmbyval);
1967 
1968  /*
1969  * We use the assumption of disjoint probabilities here too, although
1970  * the odds of equal array elements are rather higher if the elements
1971  * are not all constants (which they won't be, else constant folding
1972  * would have reduced the ArrayExpr to a Const). In this path it's
1973  * critical to have the sanity check on the s1disjoint estimate.
1974  */
1975  s1 = s1disjoint = (useOr ? 0.0 : 1.0);
1976 
1977  foreach(l, arrayexpr->elements)
1978  {
1979  Node *elem = (Node *) lfirst(l);
1980  List *args;
1981  Selectivity s2;
1982 
1983  /*
1984  * Theoretically, if elem isn't of nominal_element_type we should
1985  * insert a RelabelType, but it seems unlikely that any operator
1986  * estimation function would really care ...
1987  */
1988  args = list_make2(leftop, elem);
1989  if (is_join_clause)
1990  s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
1991  clause->inputcollid,
1992  PointerGetDatum(root),
1993  ObjectIdGetDatum(operator),
1994  PointerGetDatum(args),
1995  Int16GetDatum(jointype),
1996  PointerGetDatum(sjinfo)));
1997  else
1998  s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
1999  clause->inputcollid,
2000  PointerGetDatum(root),
2001  ObjectIdGetDatum(operator),
2002  PointerGetDatum(args),
2003  Int32GetDatum(varRelid)));
2004 
2005  if (useOr)
2006  {
2007  s1 = s1 + s2 - s1 * s2;
2008  if (isEquality)
2009  s1disjoint += s2;
2010  }
2011  else
2012  {
2013  s1 = s1 * s2;
2014  if (isInequality)
2015  s1disjoint += s2 - 1.0;
2016  }
2017  }
2018 
2019  /* accept disjoint-probability estimate if in range */
2020  if ((useOr ? isEquality : isInequality) &&
2021  s1disjoint >= 0.0 && s1disjoint <= 1.0)
2022  s1 = s1disjoint;
2023  }
2024  else
2025  {
2026  CaseTestExpr *dummyexpr;
2027  List *args;
2028  Selectivity s2;
2029  int i;
2030 
2031  /*
2032  * We need a dummy rightop to pass to the operator selectivity
2033  * routine. It can be pretty much anything that doesn't look like a
2034  * constant; CaseTestExpr is a convenient choice.
2035  */
2036  dummyexpr = makeNode(CaseTestExpr);
2037  dummyexpr->typeId = nominal_element_type;
2038  dummyexpr->typeMod = -1;
2039  dummyexpr->collation = clause->inputcollid;
2040  args = list_make2(leftop, dummyexpr);
2041  if (is_join_clause)
2042  s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
2043  clause->inputcollid,
2044  PointerGetDatum(root),
2045  ObjectIdGetDatum(operator),
2046  PointerGetDatum(args),
2047  Int16GetDatum(jointype),
2048  PointerGetDatum(sjinfo)));
2049  else
2050  s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
2051  clause->inputcollid,
2052  PointerGetDatum(root),
2053  ObjectIdGetDatum(operator),
2054  PointerGetDatum(args),
2055  Int32GetDatum(varRelid)));
2056  s1 = useOr ? 0.0 : 1.0;
2057 
2058  /*
2059  * Arbitrarily assume 10 elements in the eventual array value (see
2060  * also estimate_array_length). We don't risk an assumption of
2061  * disjoint probabilities here.
2062  */
2063  for (i = 0; i < 10; i++)
2064  {
2065  if (useOr)
2066  s1 = s1 + s2 - s1 * s2;
2067  else
2068  s1 = s1 * s2;
2069  }
2070  }
2071 
2072  /* result should be in range, but make sure... */
2073  CLAMP_PROBABILITY(s1);
2074 
2075  return s1;
2076 }
2077 
2078 /*
2079  * Estimate number of elements in the array yielded by an expression.
2080  *
2081  * It's important that this agree with scalararraysel.
2082  */
2083 int
2085 {
2086  /* look through any binary-compatible relabeling of arrayexpr */
2087  arrayexpr = strip_array_coercion(arrayexpr);
2088 
2089  if (arrayexpr && IsA(arrayexpr, Const))
2090  {
2091  Datum arraydatum = ((Const *) arrayexpr)->constvalue;
2092  bool arrayisnull = ((Const *) arrayexpr)->constisnull;
2093  ArrayType *arrayval;
2094 
2095  if (arrayisnull)
2096  return 0;
2097  arrayval = DatumGetArrayTypeP(arraydatum);
2098  return ArrayGetNItems(ARR_NDIM(arrayval), ARR_DIMS(arrayval));
2099  }
2100  else if (arrayexpr && IsA(arrayexpr, ArrayExpr) &&
2101  !((ArrayExpr *) arrayexpr)->multidims)
2102  {
2103  return list_length(((ArrayExpr *) arrayexpr)->elements);
2104  }
2105  else
2106  {
2107  /* default guess --- see also scalararraysel */
2108  return 10;
2109  }
2110 }
2111 
2112 /*
2113  * rowcomparesel - Selectivity of RowCompareExpr Node.
2114  *
2115  * We estimate RowCompare selectivity by considering just the first (high
2116  * order) columns, which makes it equivalent to an ordinary OpExpr. While
2117  * this estimate could be refined by considering additional columns, it
2118  * seems unlikely that we could do a lot better without multi-column
2119  * statistics.
2120  */
2123  RowCompareExpr *clause,
2124  int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
2125 {
2126  Selectivity s1;
2127  Oid opno = linitial_oid(clause->opnos);
2128  Oid inputcollid = linitial_oid(clause->inputcollids);
2129  List *opargs;
2130  bool is_join_clause;
2131 
2132  /* Build equivalent arg list for single operator */
2133  opargs = list_make2(linitial(clause->largs), linitial(clause->rargs));
2134 
2135  /*
2136  * Decide if it's a join clause. This should match clausesel.c's
2137  * treat_as_join_clause(), except that we intentionally consider only the
2138  * leading columns and not the rest of the clause.
2139  */
2140  if (varRelid != 0)
2141  {
2142  /*
2143  * Caller is forcing restriction mode (eg, because we are examining an
2144  * inner indexscan qual).
2145  */
2146  is_join_clause = false;
2147  }
2148  else if (sjinfo == NULL)
2149  {
2150  /*
2151  * It must be a restriction clause, since it's being evaluated at a
2152  * scan node.
2153  */
2154  is_join_clause = false;
2155  }
2156  else
2157  {
2158  /*
2159  * Otherwise, it's a join if there's more than one relation used.
2160  */
2161  is_join_clause = (NumRelids((Node *) opargs) > 1);
2162  }
2163 
2164  if (is_join_clause)
2165  {
2166  /* Estimate selectivity for a join clause. */
2167  s1 = join_selectivity(root, opno,
2168  opargs,
2169  inputcollid,
2170  jointype,
2171  sjinfo);
2172  }
2173  else
2174  {
2175  /* Estimate selectivity for a restriction clause. */
2176  s1 = restriction_selectivity(root, opno,
2177  opargs,
2178  inputcollid,
2179  varRelid);
2180  }
2181 
2182  return s1;
2183 }
2184 
2185 /*
2186  * eqjoinsel - Join selectivity of "="
2187  */
2188 Datum
2190 {
2191  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
2192  Oid operator = PG_GETARG_OID(1);
2193  List *args = (List *) PG_GETARG_POINTER(2);
2194 
2195 #ifdef NOT_USED
2196  JoinType jointype = (JoinType) PG_GETARG_INT16(3);
2197 #endif
2199  double selec;
2200  VariableStatData vardata1;
2201  VariableStatData vardata2;
2202  bool join_is_reversed;
2203  RelOptInfo *inner_rel;
2204 
2205  get_join_variables(root, args, sjinfo,
2206  &vardata1, &vardata2, &join_is_reversed);
2207 
2208  switch (sjinfo->jointype)
2209  {
2210  case JOIN_INNER:
2211  case JOIN_LEFT:
2212  case JOIN_FULL:
2213  selec = eqjoinsel_inner(operator, &vardata1, &vardata2);
2214  break;
2215  case JOIN_SEMI:
2216  case JOIN_ANTI:
2217 
2218  /*
2219  * Look up the join's inner relation. min_righthand is sufficient
2220  * information because neither SEMI nor ANTI joins permit any
2221  * reassociation into or out of their RHS, so the righthand will
2222  * always be exactly that set of rels.
2223  */
2224  inner_rel = find_join_input_rel(root, sjinfo->min_righthand);
2225 
2226  if (!join_is_reversed)
2227  selec = eqjoinsel_semi(operator, &vardata1, &vardata2,
2228  inner_rel);
2229  else
2230  selec = eqjoinsel_semi(get_commutator(operator),
2231  &vardata2, &vardata1,
2232  inner_rel);
2233  break;
2234  default:
2235  /* other values not expected here */
2236  elog(ERROR, "unrecognized join type: %d",
2237  (int) sjinfo->jointype);
2238  selec = 0; /* keep compiler quiet */
2239  break;
2240  }
2241 
2242  ReleaseVariableStats(vardata1);
2243  ReleaseVariableStats(vardata2);
2244 
2245  CLAMP_PROBABILITY(selec);
2246 
2247  PG_RETURN_FLOAT8((float8) selec);
2248 }
2249 
2250 /*
2251  * eqjoinsel_inner --- eqjoinsel for normal inner join
2252  *
2253  * We also use this for LEFT/FULL outer joins; it's not presently clear
2254  * that it's worth trying to distinguish them here.
2255  */
2256 static double
2258  VariableStatData *vardata1, VariableStatData *vardata2)
2259 {
2260  double selec;
2261  double nd1;
2262  double nd2;
2263  bool isdefault1;
2264  bool isdefault2;
2265  Form_pg_statistic stats1 = NULL;
2266  Form_pg_statistic stats2 = NULL;
2267  bool have_mcvs1 = false;
2268  Datum *values1 = NULL;
2269  int nvalues1 = 0;
2270  float4 *numbers1 = NULL;
2271  int nnumbers1 = 0;
2272  bool have_mcvs2 = false;
2273  Datum *values2 = NULL;
2274  int nvalues2 = 0;
2275  float4 *numbers2 = NULL;
2276  int nnumbers2 = 0;
2277 
2278  nd1 = get_variable_numdistinct(vardata1, &isdefault1);
2279  nd2 = get_variable_numdistinct(vardata2, &isdefault2);
2280 
2281  if (HeapTupleIsValid(vardata1->statsTuple))
2282  {
2283  stats1 = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
2284  have_mcvs1 = get_attstatsslot(vardata1->statsTuple,
2285  vardata1->atttype,
2286  vardata1->atttypmod,
2288  InvalidOid,
2289  NULL,
2290  &values1, &nvalues1,
2291  &numbers1, &nnumbers1);
2292  }
2293 
2294  if (HeapTupleIsValid(vardata2->statsTuple))
2295  {
2296  stats2 = (Form_pg_statistic) GETSTRUCT(vardata2->statsTuple);
2297  have_mcvs2 = get_attstatsslot(vardata2->statsTuple,
2298  vardata2->atttype,
2299  vardata2->atttypmod,
2301  InvalidOid,
2302  NULL,
2303  &values2, &nvalues2,
2304  &numbers2, &nnumbers2);
2305  }
2306 
2307  if (have_mcvs1 && have_mcvs2)
2308  {
2309  /*
2310  * We have most-common-value lists for both relations. Run through
2311  * the lists to see which MCVs actually join to each other with the
2312  * given operator. This allows us to determine the exact join
2313  * selectivity for the portion of the relations represented by the MCV
2314  * lists. We still have to estimate for the remaining population, but
2315  * in a skewed distribution this gives us a big leg up in accuracy.
2316  * For motivation see the analysis in Y. Ioannidis and S.
2317  * Christodoulakis, "On the propagation of errors in the size of join
2318  * results", Technical Report 1018, Computer Science Dept., University
2319  * of Wisconsin, Madison, March 1991 (available from ftp.cs.wisc.edu).
2320  */
2321  FmgrInfo eqproc;
2322  bool *hasmatch1;
2323  bool *hasmatch2;
2324  double nullfrac1 = stats1->stanullfrac;
2325  double nullfrac2 = stats2->stanullfrac;
2326  double matchprodfreq,
2327  matchfreq1,
2328  matchfreq2,
2329  unmatchfreq1,
2330  unmatchfreq2,
2331  otherfreq1,
2332  otherfreq2,
2333  totalsel1,
2334  totalsel2;
2335  int i,
2336  nmatches;
2337 
2338  fmgr_info(get_opcode(operator), &eqproc);
2339  hasmatch1 = (bool *) palloc0(nvalues1 * sizeof(bool));
2340  hasmatch2 = (bool *) palloc0(nvalues2 * sizeof(bool));
2341 
2342  /*
2343  * Note we assume that each MCV will match at most one member of the
2344  * other MCV list. If the operator isn't really equality, there could
2345  * be multiple matches --- but we don't look for them, both for speed
2346  * and because the math wouldn't add up...
2347  */
2348  matchprodfreq = 0.0;
2349  nmatches = 0;
2350  for (i = 0; i < nvalues1; i++)
2351  {
2352  int j;
2353 
2354  for (j = 0; j < nvalues2; j++)
2355  {
2356  if (hasmatch2[j])
2357  continue;
2358  if (DatumGetBool(FunctionCall2Coll(&eqproc,
2360  values1[i],
2361  values2[j])))
2362  {
2363  hasmatch1[i] = hasmatch2[j] = true;
2364  matchprodfreq += numbers1[i] * numbers2[j];
2365  nmatches++;
2366  break;
2367  }
2368  }
2369  }
2370  CLAMP_PROBABILITY(matchprodfreq);
2371  /* Sum up frequencies of matched and unmatched MCVs */
2372  matchfreq1 = unmatchfreq1 = 0.0;
2373  for (i = 0; i < nvalues1; i++)
2374  {
2375  if (hasmatch1[i])
2376  matchfreq1 += numbers1[i];
2377  else
2378  unmatchfreq1 += numbers1[i];
2379  }
2380  CLAMP_PROBABILITY(matchfreq1);
2381  CLAMP_PROBABILITY(unmatchfreq1);
2382  matchfreq2 = unmatchfreq2 = 0.0;
2383  for (i = 0; i < nvalues2; i++)
2384  {
2385  if (hasmatch2[i])
2386  matchfreq2 += numbers2[i];
2387  else
2388  unmatchfreq2 += numbers2[i];
2389  }
2390  CLAMP_PROBABILITY(matchfreq2);
2391  CLAMP_PROBABILITY(unmatchfreq2);
2392  pfree(hasmatch1);
2393  pfree(hasmatch2);
2394 
2395  /*
2396  * Compute total frequency of non-null values that are not in the MCV
2397  * lists.
2398  */
2399  otherfreq1 = 1.0 - nullfrac1 - matchfreq1 - unmatchfreq1;
2400  otherfreq2 = 1.0 - nullfrac2 - matchfreq2 - unmatchfreq2;
2401  CLAMP_PROBABILITY(otherfreq1);
2402  CLAMP_PROBABILITY(otherfreq2);
2403 
2404  /*
2405  * We can estimate the total selectivity from the point of view of
2406  * relation 1 as: the known selectivity for matched MCVs, plus
2407  * unmatched MCVs that are assumed to match against random members of
2408  * relation 2's non-MCV population, plus non-MCV values that are
2409  * assumed to match against random members of relation 2's unmatched
2410  * MCVs plus non-MCV values.
2411  */
2412  totalsel1 = matchprodfreq;
2413  if (nd2 > nvalues2)
2414  totalsel1 += unmatchfreq1 * otherfreq2 / (nd2 - nvalues2);
2415  if (nd2 > nmatches)
2416  totalsel1 += otherfreq1 * (otherfreq2 + unmatchfreq2) /
2417  (nd2 - nmatches);
2418  /* Same estimate from the point of view of relation 2. */
2419  totalsel2 = matchprodfreq;
2420  if (nd1 > nvalues1)
2421  totalsel2 += unmatchfreq2 * otherfreq1 / (nd1 - nvalues1);
2422  if (nd1 > nmatches)
2423  totalsel2 += otherfreq2 * (otherfreq1 + unmatchfreq1) /
2424  (nd1 - nmatches);
2425 
2426  /*
2427  * Use the smaller of the two estimates. This can be justified in
2428  * essentially the same terms as given below for the no-stats case: to
2429  * a first approximation, we are estimating from the point of view of
2430  * the relation with smaller nd.
2431  */
2432  selec = (totalsel1 < totalsel2) ? totalsel1 : totalsel2;
2433  }
2434  else
2435  {
2436  /*
2437  * We do not have MCV lists for both sides. Estimate the join
2438  * selectivity as MIN(1/nd1,1/nd2)*(1-nullfrac1)*(1-nullfrac2). This
2439  * is plausible if we assume that the join operator is strict and the
2440  * non-null values are about equally distributed: a given non-null
2441  * tuple of rel1 will join to either zero or N2*(1-nullfrac2)/nd2 rows
2442  * of rel2, so total join rows are at most
2443  * N1*(1-nullfrac1)*N2*(1-nullfrac2)/nd2 giving a join selectivity of
2444  * not more than (1-nullfrac1)*(1-nullfrac2)/nd2. By the same logic it
2445  * is not more than (1-nullfrac1)*(1-nullfrac2)/nd1, so the expression
2446  * with MIN() is an upper bound. Using the MIN() means we estimate
2447  * from the point of view of the relation with smaller nd (since the
2448  * larger nd is determining the MIN). It is reasonable to assume that
2449  * most tuples in this rel will have join partners, so the bound is
2450  * probably reasonably tight and should be taken as-is.
2451  *
2452  * XXX Can we be smarter if we have an MCV list for just one side? It
2453  * seems that if we assume equal distribution for the other side, we
2454  * end up with the same answer anyway.
2455  */
2456  double nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
2457  double nullfrac2 = stats2 ? stats2->stanullfrac : 0.0;
2458 
2459  selec = (1.0 - nullfrac1) * (1.0 - nullfrac2);
2460  if (nd1 > nd2)
2461  selec /= nd1;
2462  else
2463  selec /= nd2;
2464  }
2465 
2466  if (have_mcvs1)
2467  free_attstatsslot(vardata1->atttype, values1, nvalues1,
2468  numbers1, nnumbers1);
2469  if (have_mcvs2)
2470  free_attstatsslot(vardata2->atttype, values2, nvalues2,
2471  numbers2, nnumbers2);
2472 
2473  return selec;
2474 }
2475 
2476 /*
2477  * eqjoinsel_semi --- eqjoinsel for semi join
2478  *
2479  * (Also used for anti join, which we are supposed to estimate the same way.)
2480  * Caller has ensured that vardata1 is the LHS variable.
2481  */
2482 static double
2484  VariableStatData *vardata1, VariableStatData *vardata2,
2485  RelOptInfo *inner_rel)
2486 {
2487  double selec;
2488  double nd1;
2489  double nd2;
2490  bool isdefault1;
2491  bool isdefault2;
2492  Form_pg_statistic stats1 = NULL;
2493  bool have_mcvs1 = false;
2494  Datum *values1 = NULL;
2495  int nvalues1 = 0;
2496  float4 *numbers1 = NULL;
2497  int nnumbers1 = 0;
2498  bool have_mcvs2 = false;
2499  Datum *values2 = NULL;
2500  int nvalues2 = 0;
2501  float4 *numbers2 = NULL;
2502  int nnumbers2 = 0;
2503 
2504  nd1 = get_variable_numdistinct(vardata1, &isdefault1);
2505  nd2 = get_variable_numdistinct(vardata2, &isdefault2);
2506 
2507  /*
2508  * We clamp nd2 to be not more than what we estimate the inner relation's
2509  * size to be. This is intuitively somewhat reasonable since obviously
2510  * there can't be more than that many distinct values coming from the
2511  * inner rel. The reason for the asymmetry (ie, that we don't clamp nd1
2512  * likewise) is that this is the only pathway by which restriction clauses
2513  * applied to the inner rel will affect the join result size estimate,
2514  * since set_joinrel_size_estimates will multiply SEMI/ANTI selectivity by
2515  * only the outer rel's size. If we clamped nd1 we'd be double-counting
2516  * the selectivity of outer-rel restrictions.
2517  *
2518  * We can apply this clamping both with respect to the base relation from
2519  * which the join variable comes (if there is just one), and to the
2520  * immediate inner input relation of the current join.
2521  *
2522  * If we clamp, we can treat nd2 as being a non-default estimate; it's not
2523  * great, maybe, but it didn't come out of nowhere either. This is most
2524  * helpful when the inner relation is empty and consequently has no stats.
2525  */
2526  if (vardata2->rel)
2527  {
2528  if (nd2 >= vardata2->rel->rows)
2529  {
2530  nd2 = vardata2->rel->rows;
2531  isdefault2 = false;
2532  }
2533  }
2534  if (nd2 >= inner_rel->rows)
2535  {
2536  nd2 = inner_rel->rows;
2537  isdefault2 = false;
2538  }
2539 
2540  if (HeapTupleIsValid(vardata1->statsTuple))
2541  {
2542  stats1 = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
2543  have_mcvs1 = get_attstatsslot(vardata1->statsTuple,
2544  vardata1->atttype,
2545  vardata1->atttypmod,
2547  InvalidOid,
2548  NULL,
2549  &values1, &nvalues1,
2550  &numbers1, &nnumbers1);
2551  }
2552 
2553  if (HeapTupleIsValid(vardata2->statsTuple))
2554  {
2555  have_mcvs2 = get_attstatsslot(vardata2->statsTuple,
2556  vardata2->atttype,
2557  vardata2->atttypmod,
2559  InvalidOid,
2560  NULL,
2561  &values2, &nvalues2,
2562  &numbers2, &nnumbers2);
2563  }
2564 
2565  if (have_mcvs1 && have_mcvs2 && OidIsValid(operator))
2566  {
2567  /*
2568  * We have most-common-value lists for both relations. Run through
2569  * the lists to see which MCVs actually join to each other with the
2570  * given operator. This allows us to determine the exact join
2571  * selectivity for the portion of the relations represented by the MCV
2572  * lists. We still have to estimate for the remaining population, but
2573  * in a skewed distribution this gives us a big leg up in accuracy.
2574  */
2575  FmgrInfo eqproc;
2576  bool *hasmatch1;
2577  bool *hasmatch2;
2578  double nullfrac1 = stats1->stanullfrac;
2579  double matchfreq1,
2580  uncertainfrac,
2581  uncertain;
2582  int i,
2583  nmatches,
2584  clamped_nvalues2;
2585 
2586  /*
2587  * The clamping above could have resulted in nd2 being less than
2588  * nvalues2; in which case, we assume that precisely the nd2 most
2589  * common values in the relation will appear in the join input, and so
2590  * compare to only the first nd2 members of the MCV list. Of course
2591  * this is frequently wrong, but it's the best bet we can make.
2592  */
2593  clamped_nvalues2 = Min(nvalues2, nd2);
2594 
2595  fmgr_info(get_opcode(operator), &eqproc);
2596  hasmatch1 = (bool *) palloc0(nvalues1 * sizeof(bool));
2597  hasmatch2 = (bool *) palloc0(clamped_nvalues2 * sizeof(bool));
2598 
2599  /*
2600  * Note we assume that each MCV will match at most one member of the
2601  * other MCV list. If the operator isn't really equality, there could
2602  * be multiple matches --- but we don't look for them, both for speed
2603  * and because the math wouldn't add up...
2604  */
2605  nmatches = 0;
2606  for (i = 0; i < nvalues1; i++)
2607  {
2608  int j;
2609 
2610  for (j = 0; j < clamped_nvalues2; j++)
2611  {
2612  if (hasmatch2[j])
2613  continue;
2614  if (DatumGetBool(FunctionCall2Coll(&eqproc,
2616  values1[i],
2617  values2[j])))
2618  {
2619  hasmatch1[i] = hasmatch2[j] = true;
2620  nmatches++;
2621  break;
2622  }
2623  }
2624  }
2625  /* Sum up frequencies of matched MCVs */
2626  matchfreq1 = 0.0;
2627  for (i = 0; i < nvalues1; i++)
2628  {
2629  if (hasmatch1[i])
2630  matchfreq1 += numbers1[i];
2631  }
2632  CLAMP_PROBABILITY(matchfreq1);
2633  pfree(hasmatch1);
2634  pfree(hasmatch2);
2635 
2636  /*
2637  * Now we need to estimate the fraction of relation 1 that has at
2638  * least one join partner. We know for certain that the matched MCVs
2639  * do, so that gives us a lower bound, but we're really in the dark
2640  * about everything else. Our crude approach is: if nd1 <= nd2 then
2641  * assume all non-null rel1 rows have join partners, else assume for
2642  * the uncertain rows that a fraction nd2/nd1 have join partners. We
2643  * can discount the known-matched MCVs from the distinct-values counts
2644  * before doing the division.
2645  *
2646  * Crude as the above is, it's completely useless if we don't have
2647  * reliable ndistinct values for both sides. Hence, if either nd1 or
2648  * nd2 is default, punt and assume half of the uncertain rows have
2649  * join partners.
2650  */
2651  if (!isdefault1 && !isdefault2)
2652  {
2653  nd1 -= nmatches;
2654  nd2 -= nmatches;
2655  if (nd1 <= nd2 || nd2 < 0)
2656  uncertainfrac = 1.0;
2657  else
2658  uncertainfrac = nd2 / nd1;
2659  }
2660  else
2661  uncertainfrac = 0.5;
2662  uncertain = 1.0 - matchfreq1 - nullfrac1;
2663  CLAMP_PROBABILITY(uncertain);
2664  selec = matchfreq1 + uncertainfrac * uncertain;
2665  }
2666  else
2667  {
2668  /*
2669  * Without MCV lists for both sides, we can only use the heuristic
2670  * about nd1 vs nd2.
2671  */
2672  double nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
2673 
2674  if (!isdefault1 && !isdefault2)
2675  {
2676  if (nd1 <= nd2 || nd2 < 0)
2677  selec = 1.0 - nullfrac1;
2678  else
2679  selec = (nd2 / nd1) * (1.0 - nullfrac1);
2680  }
2681  else
2682  selec = 0.5 * (1.0 - nullfrac1);
2683  }
2684 
2685  if (have_mcvs1)
2686  free_attstatsslot(vardata1->atttype, values1, nvalues1,
2687  numbers1, nnumbers1);
2688  if (have_mcvs2)
2689  free_attstatsslot(vardata2->atttype, values2, nvalues2,
2690  numbers2, nnumbers2);
2691 
2692  return selec;
2693 }
2694 
2695 /*
2696  * neqjoinsel - Join selectivity of "!="
2697  */
2698 Datum
2700 {
2701  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
2702  Oid operator = PG_GETARG_OID(1);
2703  List *args = (List *) PG_GETARG_POINTER(2);
2704  JoinType jointype = (JoinType) PG_GETARG_INT16(3);
2706  Oid eqop;
2707  float8 result;
2708 
2709  /*
2710  * We want 1 - eqjoinsel() where the equality operator is the one
2711  * associated with this != operator, that is, its negator.
2712  */
2713  eqop = get_negator(operator);
2714  if (eqop)
2715  {
2717  PointerGetDatum(root),
2718  ObjectIdGetDatum(eqop),
2719  PointerGetDatum(args),
2720  Int16GetDatum(jointype),
2721  PointerGetDatum(sjinfo)));
2722  }
2723  else
2724  {
2725  /* Use default selectivity (should we raise an error instead?) */
2726  result = DEFAULT_EQ_SEL;
2727  }
2728  result = 1.0 - result;
2729  PG_RETURN_FLOAT8(result);
2730 }
2731 
2732 /*
2733  * scalarltjoinsel - Join selectivity of "<" and "<=" for scalars
2734  */
2735 Datum
2737 {
2739 }
2740 
2741 /*
2742  * scalargtjoinsel - Join selectivity of ">" and ">=" for scalars
2743  */
2744 Datum
2746 {
2748 }
2749 
2750 /*
2751  * patternjoinsel - Generic code for pattern-match join selectivity.
2752  */
2753 static double
2755 {
2756  /* For the moment we just punt. */
2757  return negate ? (1.0 - DEFAULT_MATCH_SEL) : DEFAULT_MATCH_SEL;
2758 }
2759 
2760 /*
2761  * regexeqjoinsel - Join selectivity of regular-expression pattern match.
2762  */
2763 Datum
2765 {
2767 }
2768 
2769 /*
2770  * icregexeqjoinsel - Join selectivity of case-insensitive regex match.
2771  */
2772 Datum
2774 {
2776 }
2777 
2778 /*
2779  * likejoinsel - Join selectivity of LIKE pattern match.
2780  */
2781 Datum
2783 {
2785 }
2786 
2787 /*
2788  * iclikejoinsel - Join selectivity of ILIKE pattern match.
2789  */
2790 Datum
2792 {
2794 }
2795 
2796 /*
2797  * regexnejoinsel - Join selectivity of regex non-match.
2798  */
2799 Datum
2801 {
2803 }
2804 
2805 /*
2806  * icregexnejoinsel - Join selectivity of case-insensitive regex non-match.
2807  */
2808 Datum
2810 {
2812 }
2813 
2814 /*
2815  * nlikejoinsel - Join selectivity of LIKE pattern non-match.
2816  */
2817 Datum
2819 {
2821 }
2822 
2823 /*
2824  * icnlikejoinsel - Join selectivity of ILIKE pattern non-match.
2825  */
2826 Datum
2828 {
2830 }
2831 
2832 /*
2833  * mergejoinscansel - Scan selectivity of merge join.
2834  *
2835  * A merge join will stop as soon as it exhausts either input stream.
2836  * Therefore, if we can estimate the ranges of both input variables,
2837  * we can estimate how much of the input will actually be read. This
2838  * can have a considerable impact on the cost when using indexscans.
2839  *
2840  * Also, we can estimate how much of each input has to be read before the
2841  * first join pair is found, which will affect the join's startup time.
2842  *
2843  * clause should be a clause already known to be mergejoinable. opfamily,
2844  * strategy, and nulls_first specify the sort ordering being used.
2845  *
2846  * The outputs are:
2847  * *leftstart is set to the fraction of the left-hand variable expected
2848  * to be scanned before the first join pair is found (0 to 1).
2849  * *leftend is set to the fraction of the left-hand variable expected
2850  * to be scanned before the join terminates (0 to 1).
2851  * *rightstart, *rightend similarly for the right-hand variable.
2852  */
2853 void
2855  Oid opfamily, int strategy, bool nulls_first,
2856  Selectivity *leftstart, Selectivity *leftend,
2857  Selectivity *rightstart, Selectivity *rightend)
2858 {
2859  Node *left,
2860  *right;
2861  VariableStatData leftvar,
2862  rightvar;
2863  int op_strategy;
2864  Oid op_lefttype;
2865  Oid op_righttype;
2866  Oid opno,
2867  lsortop,
2868  rsortop,
2869  lstatop,
2870  rstatop,
2871  ltop,
2872  leop,
2873  revltop,
2874  revleop;
2875  bool isgt;
2876  Datum leftmin,
2877  leftmax,
2878  rightmin,
2879  rightmax;
2880  double selec;
2881 
2882  /* Set default results if we can't figure anything out. */
2883  /* XXX should default "start" fraction be a bit more than 0? */
2884  *leftstart = *rightstart = 0.0;
2885  *leftend = *rightend = 1.0;
2886 
2887  /* Deconstruct the merge clause */
2888  if (!is_opclause(clause))
2889  return; /* shouldn't happen */
2890  opno = ((OpExpr *) clause)->opno;
2891  left = get_leftop((Expr *) clause);
2892  right = get_rightop((Expr *) clause);
2893  if (!right)
2894  return; /* shouldn't happen */
2895 
2896  /* Look for stats for the inputs */
2897  examine_variable(root, left, 0, &leftvar);
2898  examine_variable(root, right, 0, &rightvar);
2899 
2900  /* Extract the operator's declared left/right datatypes */
2901  get_op_opfamily_properties(opno, opfamily, false,
2902  &op_strategy,
2903  &op_lefttype,
2904  &op_righttype);
2905  Assert(op_strategy == BTEqualStrategyNumber);
2906 
2907  /*
2908  * Look up the various operators we need. If we don't find them all, it
2909  * probably means the opfamily is broken, but we just fail silently.
2910  *
2911  * Note: we expect that pg_statistic histograms will be sorted by the '<'
2912  * operator, regardless of which sort direction we are considering.
2913  */
2914  switch (strategy)
2915  {
2916  case BTLessStrategyNumber:
2917  isgt = false;
2918  if (op_lefttype == op_righttype)
2919  {
2920  /* easy case */
2921  ltop = get_opfamily_member(opfamily,
2922  op_lefttype, op_righttype,
2924  leop = get_opfamily_member(opfamily,
2925  op_lefttype, op_righttype,
2927  lsortop = ltop;
2928  rsortop = ltop;
2929  lstatop = lsortop;
2930  rstatop = rsortop;
2931  revltop = ltop;
2932  revleop = leop;
2933  }
2934  else
2935  {
2936  ltop = get_opfamily_member(opfamily,
2937  op_lefttype, op_righttype,
2939  leop = get_opfamily_member(opfamily,
2940  op_lefttype, op_righttype,
2942  lsortop = get_opfamily_member(opfamily,
2943  op_lefttype, op_lefttype,
2945  rsortop = get_opfamily_member(opfamily,
2946  op_righttype, op_righttype,
2948  lstatop = lsortop;
2949  rstatop = rsortop;
2950  revltop = get_opfamily_member(opfamily,
2951  op_righttype, op_lefttype,
2953  revleop = get_opfamily_member(opfamily,
2954  op_righttype, op_lefttype,
2956  }
2957  break;
2959  /* descending-order case */
2960  isgt = true;
2961  if (op_lefttype == op_righttype)
2962  {
2963  /* easy case */
2964  ltop = get_opfamily_member(opfamily,
2965  op_lefttype, op_righttype,
2967  leop = get_opfamily_member(opfamily,
2968  op_lefttype, op_righttype,
2970  lsortop = ltop;
2971  rsortop = ltop;
2972  lstatop = get_opfamily_member(opfamily,
2973  op_lefttype, op_lefttype,
2975  rstatop = lstatop;
2976  revltop = ltop;
2977  revleop = leop;
2978  }
2979  else
2980  {
2981  ltop = get_opfamily_member(opfamily,
2982  op_lefttype, op_righttype,
2984  leop = get_opfamily_member(opfamily,
2985  op_lefttype, op_righttype,
2987  lsortop = get_opfamily_member(opfamily,
2988  op_lefttype, op_lefttype,
2990  rsortop = get_opfamily_member(opfamily,
2991  op_righttype, op_righttype,
2993  lstatop = get_opfamily_member(opfamily,
2994  op_lefttype, op_lefttype,
2996  rstatop = get_opfamily_member(opfamily,
2997  op_righttype, op_righttype,
2999  revltop = get_opfamily_member(opfamily,
3000  op_righttype, op_lefttype,
3002  revleop = get_opfamily_member(opfamily,
3003  op_righttype, op_lefttype,
3005  }
3006  break;
3007  default:
3008  goto fail; /* shouldn't get here */
3009  }
3010 
3011  if (!OidIsValid(lsortop) ||
3012  !OidIsValid(rsortop) ||
3013  !OidIsValid(lstatop) ||
3014  !OidIsValid(rstatop) ||
3015  !OidIsValid(ltop) ||
3016  !OidIsValid(leop) ||
3017  !OidIsValid(revltop) ||
3018  !OidIsValid(revleop))
3019  goto fail; /* insufficient info in catalogs */
3020 
3021  /* Try to get ranges of both inputs */
3022  if (!isgt)
3023  {
3024  if (!get_variable_range(root, &leftvar, lstatop,
3025  &leftmin, &leftmax))
3026  goto fail; /* no range available from stats */
3027  if (!get_variable_range(root, &rightvar, rstatop,
3028  &rightmin, &rightmax))
3029  goto fail; /* no range available from stats */
3030  }
3031  else
3032  {
3033  /* need to swap the max and min */
3034  if (!get_variable_range(root, &leftvar, lstatop,
3035  &leftmax, &leftmin))
3036  goto fail; /* no range available from stats */
3037  if (!get_variable_range(root, &rightvar, rstatop,
3038  &rightmax, &rightmin))
3039  goto fail; /* no range available from stats */
3040  }
3041 
3042  /*
3043  * Now, the fraction of the left variable that will be scanned is the
3044  * fraction that's <= the right-side maximum value. But only believe
3045  * non-default estimates, else stick with our 1.0.
3046  */
3047  selec = scalarineqsel(root, leop, isgt, &leftvar,
3048  rightmax, op_righttype);
3049  if (selec != DEFAULT_INEQ_SEL)
3050  *leftend = selec;
3051 
3052  /* And similarly for the right variable. */
3053  selec = scalarineqsel(root, revleop, isgt, &rightvar,
3054  leftmax, op_lefttype);
3055  if (selec != DEFAULT_INEQ_SEL)
3056  *rightend = selec;
3057 
3058  /*
3059  * Only one of the two "end" fractions can really be less than 1.0;
3060  * believe the smaller estimate and reset the other one to exactly 1.0. If
3061  * we get exactly equal estimates (as can easily happen with self-joins),
3062  * believe neither.
3063  */
3064  if (*leftend > *rightend)
3065  *leftend = 1.0;
3066  else if (*leftend < *rightend)
3067  *rightend = 1.0;
3068  else
3069  *leftend = *rightend = 1.0;
3070 
3071  /*
3072  * Also, the fraction of the left variable that will be scanned before the
3073  * first join pair is found is the fraction that's < the right-side
3074  * minimum value. But only believe non-default estimates, else stick with
3075  * our own default.
3076  */
3077  selec = scalarineqsel(root, ltop, isgt, &leftvar,
3078  rightmin, op_righttype);
3079  if (selec != DEFAULT_INEQ_SEL)
3080  *leftstart = selec;
3081 
3082  /* And similarly for the right variable. */
3083  selec = scalarineqsel(root, revltop, isgt, &rightvar,
3084  leftmin, op_lefttype);
3085  if (selec != DEFAULT_INEQ_SEL)
3086  *rightstart = selec;
3087 
3088  /*
3089  * Only one of the two "start" fractions can really be more than zero;
3090  * believe the larger estimate and reset the other one to exactly 0.0. If
3091  * we get exactly equal estimates (as can easily happen with self-joins),
3092  * believe neither.
3093  */
3094  if (*leftstart < *rightstart)
3095  *leftstart = 0.0;
3096  else if (*leftstart > *rightstart)
3097  *rightstart = 0.0;
3098  else
3099  *leftstart = *rightstart = 0.0;
3100 
3101  /*
3102  * If the sort order is nulls-first, we're going to have to skip over any
3103  * nulls too. These would not have been counted by scalarineqsel, and we
3104  * can safely add in this fraction regardless of whether we believe
3105  * scalarineqsel's results or not. But be sure to clamp the sum to 1.0!
3106  */
3107  if (nulls_first)
3108  {
3109  Form_pg_statistic stats;
3110 
3111  if (HeapTupleIsValid(leftvar.statsTuple))
3112  {
3113  stats = (Form_pg_statistic) GETSTRUCT(leftvar.statsTuple);
3114  *leftstart += stats->stanullfrac;
3115  CLAMP_PROBABILITY(*leftstart);
3116  *leftend += stats->stanullfrac;
3117  CLAMP_PROBABILITY(*leftend);
3118  }
3119  if (HeapTupleIsValid(rightvar.statsTuple))
3120  {
3121  stats = (Form_pg_statistic) GETSTRUCT(rightvar.statsTuple);
3122  *rightstart += stats->stanullfrac;
3123  CLAMP_PROBABILITY(*rightstart);
3124  *rightend += stats->stanullfrac;
3125  CLAMP_PROBABILITY(*rightend);
3126  }
3127  }
3128 
3129  /* Disbelieve start >= end, just in case that can happen */
3130  if (*leftstart >= *leftend)
3131  {
3132  *leftstart = 0.0;
3133  *leftend = 1.0;
3134  }
3135  if (*rightstart >= *rightend)
3136  {
3137  *rightstart = 0.0;
3138  *rightend = 1.0;
3139  }
3140 
3141 fail:
3142  ReleaseVariableStats(leftvar);
3143  ReleaseVariableStats(rightvar);
3144 }
3145 
3146 
3147 /*
3148  * Helper routine for estimate_num_groups: add an item to a list of
3149  * GroupVarInfos, but only if it's not known equal to any of the existing
3150  * entries.
3151  */
3152 typedef struct
3153 {
3154  Node *var; /* might be an expression, not just a Var */
3155  RelOptInfo *rel; /* relation it belongs to */
3156  double ndistinct; /* # distinct values */
3157 } GroupVarInfo;
3158 
3159 static List *
3161  Node *var, VariableStatData *vardata)
3162 {
3163  GroupVarInfo *varinfo;
3164  double ndistinct;
3165  bool isdefault;
3166  ListCell *lc;
3167 
3168  ndistinct = get_variable_numdistinct(vardata, &isdefault);
3169 
3170  /* cannot use foreach here because of possible list_delete */
3171  lc = list_head(varinfos);
3172  while (lc)
3173  {
3174  varinfo = (GroupVarInfo *) lfirst(lc);
3175 
3176  /* must advance lc before list_delete possibly pfree's it */
3177  lc = lnext(lc);
3178 
3179  /* Drop exact duplicates */
3180  if (equal(var, varinfo->var))
3181  return varinfos;
3182 
3183  /*
3184  * Drop known-equal vars, but only if they belong to different
3185  * relations (see comments for estimate_num_groups)
3186  */
3187  if (vardata->rel != varinfo->rel &&
3188  exprs_known_equal(root, var, varinfo->var))
3189  {
3190  if (varinfo->ndistinct <= ndistinct)
3191  {
3192  /* Keep older item, forget new one */
3193  return varinfos;
3194  }
3195  else
3196  {
3197  /* Delete the older item */
3198  varinfos = list_delete_ptr(varinfos, varinfo);
3199  }
3200  }
3201  }
3202 
3203  varinfo = (GroupVarInfo *) palloc(sizeof(GroupVarInfo));
3204 
3205  varinfo->var = var;
3206  varinfo->rel = vardata->rel;
3207  varinfo->ndistinct = ndistinct;
3208  varinfos = lappend(varinfos, varinfo);
3209  return varinfos;
3210 }
3211 
3212 /*
3213  * estimate_num_groups - Estimate number of groups in a grouped query
3214  *
3215  * Given a query having a GROUP BY clause, estimate how many groups there
3216  * will be --- ie, the number of distinct combinations of the GROUP BY
3217  * expressions.
3218  *
3219  * This routine is also used to estimate the number of rows emitted by
3220  * a DISTINCT filtering step; that is an isomorphic problem. (Note:
3221  * actually, we only use it for DISTINCT when there's no grouping or
3222  * aggregation ahead of the DISTINCT.)
3223  *
3224  * Inputs:
3225  * root - the query
3226  * groupExprs - list of expressions being grouped by
3227  * input_rows - number of rows estimated to arrive at the group/unique
3228  * filter step
3229  * pgset - NULL, or a List** pointing to a grouping set to filter the
3230  * groupExprs against
3231  *
3232  * Given the lack of any cross-correlation statistics in the system, it's
3233  * impossible to do anything really trustworthy with GROUP BY conditions
3234  * involving multiple Vars. We should however avoid assuming the worst
3235  * case (all possible cross-product terms actually appear as groups) since
3236  * very often the grouped-by Vars are highly correlated. Our current approach
3237  * is as follows:
3238  * 1. Expressions yielding boolean are assumed to contribute two groups,
3239  * independently of their content, and are ignored in the subsequent
3240  * steps. This is mainly because tests like "col IS NULL" break the
3241  * heuristic used in step 2 especially badly.
3242  * 2. Reduce the given expressions to a list of unique Vars used. For
3243  * example, GROUP BY a, a + b is treated the same as GROUP BY a, b.
3244  * It is clearly correct not to count the same Var more than once.
3245  * It is also reasonable to treat f(x) the same as x: f() cannot
3246  * increase the number of distinct values (unless it is volatile,
3247  * which we consider unlikely for grouping), but it probably won't
3248  * reduce the number of distinct values much either.
3249  * As a special case, if a GROUP BY expression can be matched to an
3250  * expressional index for which we have statistics, then we treat the
3251  * whole expression as though it were just a Var.
3252  * 3. If the list contains Vars of different relations that are known equal
3253  * due to equivalence classes, then drop all but one of the Vars from each
3254  * known-equal set, keeping the one with smallest estimated # of values
3255  * (since the extra values of the others can't appear in joined rows).
3256  * Note the reason we only consider Vars of different relations is that
3257  * if we considered ones of the same rel, we'd be double-counting the
3258  * restriction selectivity of the equality in the next step.
3259  * 4. For Vars within a single source rel, we multiply together the numbers
3260  * of values, clamp to the number of rows in the rel (divided by 10 if
3261  * more than one Var), and then multiply by a factor based on the
3262  * selectivity of the restriction clauses for that rel. When there's
3263  * more than one Var, the initial product is probably too high (it's the
3264  * worst case) but clamping to a fraction of the rel's rows seems to be a
3265  * helpful heuristic for not letting the estimate get out of hand. (The
3266  * factor of 10 is derived from pre-Postgres-7.4 practice.) The factor
3267  * we multiply by to adjust for the restriction selectivity assumes that
3268  * the restriction clauses are independent of the grouping, which may not
3269  * be a valid assumption, but it's hard to do better.
3270  * 5. If there are Vars from multiple rels, we repeat step 4 for each such
3271  * rel, and multiply the results together.
3272  * Note that rels not containing grouped Vars are ignored completely, as are
3273  * join clauses. Such rels cannot increase the number of groups, and we
3274  * assume such clauses do not reduce the number either (somewhat bogus,
3275  * but we don't have the info to do better).
3276  */
3277 double
3278 estimate_num_groups(PlannerInfo *root, List *groupExprs, double input_rows,
3279  List **pgset)
3280 {
3281  List *varinfos = NIL;
3282  double numdistinct;
3283  ListCell *l;
3284  int i;
3285 
3286  /*
3287  * We don't ever want to return an estimate of zero groups, as that tends
3288  * to lead to division-by-zero and other unpleasantness. The input_rows
3289  * estimate is usually already at least 1, but clamp it just in case it
3290  * isn't.
3291  */
3292  input_rows = clamp_row_est(input_rows);
3293 
3294  /*
3295  * If no grouping columns, there's exactly one group. (This can't happen
3296  * for normal cases with GROUP BY or DISTINCT, but it is possible for
3297  * corner cases with set operations.)
3298  */
3299  if (groupExprs == NIL || (pgset && list_length(*pgset) < 1))
3300  return 1.0;
3301 
3302  /*
3303  * Count groups derived from boolean grouping expressions. For other
3304  * expressions, find the unique Vars used, treating an expression as a Var
3305  * if we can find stats for it. For each one, record the statistical
3306  * estimate of number of distinct values (total in its table, without
3307  * regard for filtering).
3308  */
3309  numdistinct = 1.0;
3310 
3311  i = 0;
3312  foreach(l, groupExprs)
3313  {
3314  Node *groupexpr = (Node *) lfirst(l);
3315  VariableStatData vardata;
3316  List *varshere;
3317  ListCell *l2;
3318 
3319  /* is expression in this grouping set? */
3320  if (pgset && !list_member_int(*pgset, i++))
3321  continue;
3322 
3323  /* Short-circuit for expressions returning boolean */
3324  if (exprType(groupexpr) == BOOLOID)
3325  {
3326  numdistinct *= 2.0;
3327  continue;
3328  }
3329 
3330  /*
3331  * If examine_variable is able to deduce anything about the GROUP BY
3332  * expression, treat it as a single variable even if it's really more
3333  * complicated.
3334  */
3335  examine_variable(root, groupexpr, 0, &vardata);
3336  if (HeapTupleIsValid(vardata.statsTuple) || vardata.isunique)
3337  {
3338  varinfos = add_unique_group_var(root, varinfos,
3339  groupexpr, &vardata);
3340  ReleaseVariableStats(vardata);
3341  continue;
3342  }
3343  ReleaseVariableStats(vardata);
3344 
3345  /*
3346  * Else pull out the component Vars. Handle PlaceHolderVars by
3347  * recursing into their arguments (effectively assuming that the
3348  * PlaceHolderVar doesn't change the number of groups, which boils
3349  * down to ignoring the possible addition of nulls to the result set).
3350  */
3351  varshere = pull_var_clause(groupexpr,
3355 
3356  /*
3357  * If we find any variable-free GROUP BY item, then either it is a
3358  * constant (and we can ignore it) or it contains a volatile function;
3359  * in the latter case we punt and assume that each input row will
3360  * yield a distinct group.
3361  */
3362  if (varshere == NIL)
3363  {
3364  if (contain_volatile_functions(groupexpr))
3365  return input_rows;
3366  continue;
3367  }
3368 
3369  /*
3370  * Else add variables to varinfos list
3371  */
3372  foreach(l2, varshere)
3373  {
3374  Node *var = (Node *) lfirst(l2);
3375 
3376  examine_variable(root, var, 0, &vardata);
3377  varinfos = add_unique_group_var(root, varinfos, var, &vardata);
3378  ReleaseVariableStats(vardata);
3379  }
3380  }
3381 
3382  /*
3383  * If now no Vars, we must have an all-constant or all-boolean GROUP BY
3384  * list.
3385  */
3386  if (varinfos == NIL)
3387  {
3388  /* Guard against out-of-range answers */
3389  if (numdistinct > input_rows)
3390  numdistinct = input_rows;
3391  return numdistinct;
3392  }
3393 
3394  /*
3395  * Group Vars by relation and estimate total numdistinct.
3396  *
3397  * For each iteration of the outer loop, we process the frontmost Var in
3398  * varinfos, plus all other Vars in the same relation. We remove these
3399  * Vars from the newvarinfos list for the next iteration. This is the
3400  * easiest way to group Vars of same rel together.
3401  */
3402  do
3403  {
3404  GroupVarInfo *varinfo1 = (GroupVarInfo *) linitial(varinfos);
3405  RelOptInfo *rel = varinfo1->rel;
3406  double reldistinct = 1;
3407  double relmaxndistinct = reldistinct;
3408  int relvarcount = 0;
3409  List *newvarinfos = NIL;
3410  List *relvarinfos = NIL;
3411 
3412  /*
3413  * Split the list of varinfos in two - one for the current rel,
3414  * one for remaining Vars on other rels.
3415  */
3416  relvarinfos = lcons(varinfo1, relvarinfos);
3417  for_each_cell(l, lnext(list_head(varinfos)))
3418  {
3419  GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
3420 
3421  if (varinfo2->rel == varinfo1->rel)
3422  {
3423  /* varinfos on current rel */
3424  relvarinfos = lcons(varinfo2, relvarinfos);
3425  }
3426  else
3427  {
3428  /* not time to process varinfo2 yet */
3429  newvarinfos = lcons(varinfo2, newvarinfos);
3430  }
3431  }
3432 
3433  /*
3434  * Get the numdistinct estimate for the Vars of this rel. We
3435  * iteratively search for multivariate n-distinct with maximum number
3436  * of vars; assuming that each var group is independent of the others,
3437  * we multiply them together. Any remaining relvarinfos after
3438  * no more multivariate matches are found are assumed independent too,
3439  * so their individual ndistinct estimates are multiplied also.
3440  *
3441  * While iterating, count how many separate numdistinct values we
3442  * apply. We apply a fudge factor below, but only if we multiplied
3443  * more than one such values.
3444  */
3445  while (relvarinfos)
3446  {
3447  double mvndistinct;
3448 
3449  if (estimate_multivariate_ndistinct(root, rel, &relvarinfos,
3450  &mvndistinct))
3451  {
3452  reldistinct *= mvndistinct;
3453  if (relmaxndistinct < mvndistinct)
3454  relmaxndistinct = mvndistinct;
3455  relvarcount++;
3456  }
3457  else
3458  {
3459  foreach (l, relvarinfos)
3460  {
3461  GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
3462 
3463  reldistinct *= varinfo2->ndistinct;
3464  if (relmaxndistinct < varinfo2->ndistinct)
3465  relmaxndistinct = varinfo2->ndistinct;
3466  relvarcount++;
3467  }
3468 
3469  /* we're done with this relation */
3470  relvarinfos = NIL;
3471  }
3472  }
3473 
3474  /*
3475  * Sanity check --- don't divide by zero if empty relation.
3476  */
3477  Assert(IS_SIMPLE_REL(rel));
3478  if (rel->tuples > 0)
3479  {
3480  /*
3481  * Clamp to size of rel, or size of rel / 10 if multiple Vars. The
3482  * fudge factor is because the Vars are probably correlated but we
3483  * don't know by how much. We should never clamp to less than the
3484  * largest ndistinct value for any of the Vars, though, since
3485  * there will surely be at least that many groups.
3486  */
3487  double clamp = rel->tuples;
3488 
3489  if (relvarcount > 1)
3490  {
3491  clamp *= 0.1;
3492  if (clamp < relmaxndistinct)
3493  {
3494  clamp = relmaxndistinct;
3495  /* for sanity in case some ndistinct is too large: */
3496  if (clamp > rel->tuples)
3497  clamp = rel->tuples;
3498  }
3499  }
3500  if (reldistinct > clamp)
3501  reldistinct = clamp;
3502 
3503  /*
3504  * Update the estimate based on the restriction selectivity,
3505  * guarding against division by zero when reldistinct is zero.
3506  * Also skip this if we know that we are returning all rows.
3507  */
3508  if (reldistinct > 0 && rel->rows < rel->tuples)
3509  {
3510  /*
3511  * Given a table containing N rows with n distinct values in a
3512  * uniform distribution, if we select p rows at random then
3513  * the expected number of distinct values selected is
3514  *
3515  * n * (1 - product((N-N/n-i)/(N-i), i=0..p-1))
3516  *
3517  * = n * (1 - (N-N/n)! / (N-N/n-p)! * (N-p)! / N!)
3518  *
3519  * See "Approximating block accesses in database
3520  * organizations", S. B. Yao, Communications of the ACM,
3521  * Volume 20 Issue 4, April 1977 Pages 260-261.
3522  *
3523  * Alternatively, re-arranging the terms from the factorials,
3524  * this may be written as
3525  *
3526  * n * (1 - product((N-p-i)/(N-i), i=0..N/n-1))
3527  *
3528  * This form of the formula is more efficient to compute in
3529  * the common case where p is larger than N/n. Additionally,
3530  * as pointed out by Dell'Era, if i << N for all terms in the
3531  * product, it can be approximated by
3532  *
3533  * n * (1 - ((N-p)/N)^(N/n))
3534  *
3535  * See "Expected distinct values when selecting from a bag
3536  * without replacement", Alberto Dell'Era,
3537  * http://www.adellera.it/investigations/distinct_balls/.
3538  *
3539  * The condition i << N is equivalent to n >> 1, so this is a
3540  * good approximation when the number of distinct values in
3541  * the table is large. It turns out that this formula also
3542  * works well even when n is small.
3543  */
3544  reldistinct *=
3545  (1 - pow((rel->tuples - rel->rows) / rel->tuples,
3546  rel->tuples / reldistinct));
3547  }
3548  reldistinct = clamp_row_est(reldistinct);
3549 
3550  /*
3551  * Update estimate of total distinct groups.
3552  */
3553  numdistinct *= reldistinct;
3554  }
3555 
3556  varinfos = newvarinfos;
3557  } while (varinfos != NIL);
3558 
3559  numdistinct = ceil(numdistinct);
3560 
3561  /* Guard against out-of-range answers */
3562  if (numdistinct > input_rows)
3563  numdistinct = input_rows;
3564  if (numdistinct < 1.0)
3565  numdistinct = 1.0;
3566 
3567  return numdistinct;
3568 }
3569 
3570 /*
3571  * Estimate hash bucketsize fraction (ie, number of entries in a bucket
3572  * divided by total tuples in relation) if the specified expression is used
3573  * as a hash key.
3574  *
3575  * XXX This is really pretty bogus since we're effectively assuming that the
3576  * distribution of hash keys will be the same after applying restriction
3577  * clauses as it was in the underlying relation. However, we are not nearly
3578  * smart enough to figure out how the restrict clauses might change the
3579  * distribution, so this will have to do for now.
3580  *
3581  * We are passed the number of buckets the executor will use for the given
3582  * input relation. If the data were perfectly distributed, with the same
3583  * number of tuples going into each available bucket, then the bucketsize
3584  * fraction would be 1/nbuckets. But this happy state of affairs will occur
3585  * only if (a) there are at least nbuckets distinct data values, and (b)
3586  * we have a not-too-skewed data distribution. Otherwise the buckets will
3587  * be nonuniformly occupied. If the other relation in the join has a key
3588  * distribution similar to this one's, then the most-loaded buckets are
3589  * exactly those that will be probed most often. Therefore, the "average"
3590  * bucket size for costing purposes should really be taken as something close
3591  * to the "worst case" bucket size. We try to estimate this by adjusting the
3592  * fraction if there are too few distinct data values, and then scaling up
3593  * by the ratio of the most common value's frequency to the average frequency.
3594  *
3595  * If no statistics are available, use a default estimate of 0.1. This will
3596  * discourage use of a hash rather strongly if the inner relation is large,
3597  * which is what we want. We do not want to hash unless we know that the
3598  * inner rel is well-dispersed (or the alternatives seem much worse).
3599  */
3601 estimate_hash_bucketsize(PlannerInfo *root, Node *hashkey, double nbuckets)
3602 {
3603  VariableStatData vardata;
3604  double estfract,
3605  ndistinct,
3606  stanullfrac,
3607  mcvfreq,
3608  avgfreq;
3609  bool isdefault;
3610  float4 *numbers;
3611  int nnumbers;
3612 
3613  examine_variable(root, hashkey, 0, &vardata);
3614 
3615  /* Get number of distinct values */
3616  ndistinct = get_variable_numdistinct(&vardata, &isdefault);
3617 
3618  /* If ndistinct isn't real, punt and return 0.1, per comments above */
3619  if (isdefault)
3620  {
3621  ReleaseVariableStats(vardata);
3622  return (Selectivity) 0.1;
3623  }
3624 
3625  /* Get fraction that are null */
3626  if (HeapTupleIsValid(vardata.statsTuple))
3627  {
3628  Form_pg_statistic stats;
3629 
3630  stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
3631  stanullfrac = stats->stanullfrac;
3632  }
3633  else
3634  stanullfrac = 0.0;
3635 
3636  /* Compute avg freq of all distinct data values in raw relation */
3637  avgfreq = (1.0 - stanullfrac) / ndistinct;
3638 
3639  /*
3640  * Adjust ndistinct to account for restriction clauses. Observe we are
3641  * assuming that the data distribution is affected uniformly by the
3642  * restriction clauses!
3643  *
3644  * XXX Possibly better way, but much more expensive: multiply by
3645  * selectivity of rel's restriction clauses that mention the target Var.
3646  */
3647  if (vardata.rel && vardata.rel->tuples > 0)
3648  {
3649  ndistinct *= vardata.rel->rows / vardata.rel->tuples;
3650  ndistinct = clamp_row_est(ndistinct);
3651  }
3652 
3653  /*
3654  * Initial estimate of bucketsize fraction is 1/nbuckets as long as the
3655  * number of buckets is less than the expected number of distinct values;
3656  * otherwise it is 1/ndistinct.
3657  */
3658  if (ndistinct > nbuckets)
3659  estfract = 1.0 / nbuckets;
3660  else
3661  estfract = 1.0 / ndistinct;
3662 
3663  /*
3664  * Look up the frequency of the most common value, if available.
3665  */
3666  mcvfreq = 0.0;
3667 
3668  if (HeapTupleIsValid(vardata.statsTuple))
3669  {
3670  if (get_attstatsslot(vardata.statsTuple,
3671  vardata.atttype, vardata.atttypmod,
3673  NULL,
3674  NULL, NULL,
3675  &numbers, &nnumbers))
3676  {
3677  /*
3678  * The first MCV stat is for the most common value.
3679  */
3680  if (nnumbers > 0)
3681  mcvfreq = numbers[0];
3682  free_attstatsslot(vardata.atttype, NULL, 0,
3683  numbers, nnumbers);
3684  }
3685  }
3686 
3687  /*
3688  * Adjust estimated bucketsize upward to account for skewed distribution.
3689  */
3690  if (avgfreq > 0.0 && mcvfreq > avgfreq)
3691  estfract *= mcvfreq / avgfreq;
3692 
3693  /*
3694  * Clamp bucketsize to sane range (the above adjustment could easily
3695  * produce an out-of-range result). We set the lower bound a little above
3696  * zero, since zero isn't a very sane result.
3697  */
3698  if (estfract < 1.0e-6)
3699  estfract = 1.0e-6;
3700  else if (estfract > 1.0)
3701  estfract = 1.0;
3702 
3703  ReleaseVariableStats(vardata);
3704 
3705  return (Selectivity) estfract;
3706 }
3707 
3708 
3709 /*-------------------------------------------------------------------------
3710  *
3711  * Support routines
3712  *
3713  *-------------------------------------------------------------------------
3714  */
3715 
3716 /*
3717  * Find applicable ndistinct statistics for the given list of VarInfos (which
3718  * must all belong to the given rel), and update *ndistinct to the estimate of
3719  * the MVNDistinctItem that best matches. If a match it found, *varinfos is
3720  * updated to remove the list of matched varinfos.
3721  *
3722  * Varinfos that aren't for simple Vars are ignored.
3723  *
3724  * Return TRUE if we're able to find a match, FALSE otherwise.
3725  */
3726 static bool
3728  List **varinfos, double *ndistinct)
3729 {
3730  ListCell *lc;
3731  Bitmapset *attnums = NULL;
3732  int nmatches;
3733  Oid statOid = InvalidOid;
3734  MVNDistinct *stats;
3735  Bitmapset *matched = NULL;
3736 
3737  /* bail out immediately if the table has no extended statistics */
3738  if (!rel->statlist)
3739  return false;
3740 
3741  /* Determine the attnums we're looking for */
3742  foreach(lc, *varinfos)
3743  {
3744  GroupVarInfo *varinfo = (GroupVarInfo *) lfirst(lc);
3745 
3746  Assert(varinfo->rel == rel);
3747 
3748  if (IsA(varinfo->var, Var))
3749  {
3750  attnums = bms_add_member(attnums,
3751  ((Var *) varinfo->var)->varattno);
3752  }
3753  }
3754 
3755  /* look for the ndistinct statistics matching the most vars */
3756  nmatches = 1; /* we require at least two matches */
3757  foreach(lc, rel->statlist)
3758  {
3759  StatisticExtInfo *info = (StatisticExtInfo *) lfirst(lc);
3760  Bitmapset *shared;
3761 
3762  /* skip statistics of other kinds */
3763  if (info->kind != STATS_EXT_NDISTINCT)
3764  continue;
3765 
3766  /* compute attnums shared by the vars and the statistic */
3767  shared = bms_intersect(info->keys, attnums);
3768 
3769  /*
3770  * Does this statistics matches more columns than the currently
3771  * best statistic? If so, use this one instead.
3772  *
3773  * XXX This should break ties using name of the statistic, or
3774  * something like that, to make the outcome stable.
3775  */
3776  if (bms_num_members(shared) > nmatches)
3777  {
3778  statOid = info->statOid;
3779  nmatches = bms_num_members(shared);
3780  matched = shared;
3781  }
3782  }
3783 
3784  /* No match? */
3785  if (statOid == InvalidOid)
3786  return false;
3787  Assert(nmatches > 1 && matched != NULL);
3788 
3789  stats = statext_ndistinct_load(statOid);
3790 
3791  /*
3792  * If we have a match, search it for the specific item that matches (there
3793  * must be one), and construct the output values.
3794  */
3795  if (stats)
3796  {
3797  int i;
3798  List *newlist = NIL;
3799  MVNDistinctItem *item = NULL;
3800 
3801  /* Find the specific item that exactly matches the combination */
3802  for (i = 0; i < stats->nitems; i++)
3803  {
3804  MVNDistinctItem *tmpitem = &stats->items[i];
3805 
3806  if (bms_subset_compare(tmpitem->attrs, matched) == BMS_EQUAL)
3807  {
3808  item = tmpitem;
3809  break;
3810  }
3811  }
3812 
3813  /* make sure we found an item */
3814  if (!item)
3815  elog(ERROR, "corrupt MVNDistinct entry");
3816 
3817  /* Form the output varinfo list, keeping only unmatched ones */
3818  foreach(lc, *varinfos)
3819  {
3820  GroupVarInfo *varinfo = (GroupVarInfo *) lfirst(lc);
3821  AttrNumber attnum;
3822 
3823  if (!IsA(varinfo->var, Var))
3824  {
3825  newlist = lappend(newlist, varinfo);
3826  continue;
3827  }
3828 
3829  attnum = ((Var *) varinfo->var)->varattno;
3830  if (!bms_is_member(attnum, matched))
3831  newlist = lappend(newlist, varinfo);
3832  }
3833 
3834  *varinfos = newlist;
3835  *ndistinct = item->ndistinct;
3836  return true;
3837  }
3838 
3839  return false;
3840 }
3841 
3842 /*
3843  * convert_to_scalar
3844  * Convert non-NULL values of the indicated types to the comparison
3845  * scale needed by scalarineqsel().
3846  * Returns "true" if successful.
3847  *
3848  * XXX this routine is a hack: ideally we should look up the conversion
3849  * subroutines in pg_type.
3850  *
3851  * All numeric datatypes are simply converted to their equivalent
3852  * "double" values. (NUMERIC values that are outside the range of "double"
3853  * are clamped to +/- HUGE_VAL.)
3854  *
3855  * String datatypes are converted by convert_string_to_scalar(),
3856  * which is explained below. The reason why this routine deals with
3857  * three values at a time, not just one, is that we need it for strings.
3858  *
3859  * The bytea datatype is just enough different from strings that it has
3860  * to be treated separately.
3861  *
3862  * The several datatypes representing absolute times are all converted
3863  * to Timestamp, which is actually a double, and then we just use that
3864  * double value. Note this will give correct results even for the "special"
3865  * values of Timestamp, since those are chosen to compare correctly;
3866  * see timestamp_cmp.
3867  *
3868  * The several datatypes representing relative times (intervals) are all
3869  * converted to measurements expressed in seconds.
3870  */
3871 static bool
3872 convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
3873  Datum lobound, Datum hibound, Oid boundstypid,
3874  double *scaledlobound, double *scaledhibound)
3875 {
3876  /*
3877  * Both the valuetypid and the boundstypid should exactly match the
3878  * declared input type(s) of the operator we are invoked for, so we just
3879  * error out if either is not recognized.
3880  *
3881  * XXX The histogram we are interpolating between points of could belong
3882  * to a column that's only binary-compatible with the declared type. In
3883  * essence we are assuming that the semantics of binary-compatible types
3884  * are enough alike that we can use a histogram generated with one type's
3885  * operators to estimate selectivity for the other's. This is outright
3886  * wrong in some cases --- in particular signed versus unsigned
3887  * interpretation could trip us up. But it's useful enough in the
3888  * majority of cases that we do it anyway. Should think about more
3889  * rigorous ways to do it.
3890  */
3891  switch (valuetypid)
3892  {
3893  /*
3894  * Built-in numeric types
3895  */
3896  case BOOLOID:
3897  case INT2OID:
3898  case INT4OID:
3899  case INT8OID:
3900  case FLOAT4OID:
3901  case FLOAT8OID:
3902  case NUMERICOID:
3903  case OIDOID:
3904  case REGPROCOID:
3905  case REGPROCEDUREOID:
3906  case REGOPEROID:
3907  case REGOPERATOROID:
3908  case REGCLASSOID:
3909  case REGTYPEOID:
3910  case REGCONFIGOID:
3911  case REGDICTIONARYOID:
3912  case REGROLEOID:
3913  case REGNAMESPACEOID:
3914  *scaledvalue = convert_numeric_to_scalar(value, valuetypid);
3915  *scaledlobound = convert_numeric_to_scalar(lobound, boundstypid);
3916  *scaledhibound = convert_numeric_to_scalar(hibound, boundstypid);
3917  return true;
3918 
3919  /*
3920  * Built-in string types
3921  */
3922  case CHAROID:
3923  case BPCHAROID:
3924  case VARCHAROID:
3925  case TEXTOID:
3926  case NAMEOID:
3927  {
3928  char *valstr = convert_string_datum(value, valuetypid);
3929  char *lostr = convert_string_datum(lobound, boundstypid);
3930  char *histr = convert_string_datum(hibound, boundstypid);
3931 
3932  convert_string_to_scalar(valstr, scaledvalue,
3933  lostr, scaledlobound,
3934  histr, scaledhibound);
3935  pfree(valstr);
3936  pfree(lostr);
3937  pfree(histr);
3938  return true;
3939  }
3940 
3941  /*
3942  * Built-in bytea type
3943  */
3944  case BYTEAOID:
3945  {
3946  convert_bytea_to_scalar(value, scaledvalue,
3947  lobound, scaledlobound,
3948  hibound, scaledhibound);
3949  return true;
3950  }
3951 
3952  /*
3953  * Built-in time types
3954  */
3955  case TIMESTAMPOID:
3956  case TIMESTAMPTZOID:
3957  case ABSTIMEOID:
3958  case DATEOID:
3959  case INTERVALOID:
3960  case RELTIMEOID:
3961  case TINTERVALOID:
3962  case TIMEOID:
3963  case TIMETZOID:
3964  *scaledvalue = convert_timevalue_to_scalar(value, valuetypid);
3965  *scaledlobound = convert_timevalue_to_scalar(lobound, boundstypid);
3966  *scaledhibound = convert_timevalue_to_scalar(hibound, boundstypid);
3967  return true;
3968 
3969  /*
3970  * Built-in network types
3971  */
3972  case INETOID:
3973  case CIDROID:
3974  case MACADDROID:
3975  case MACADDR8OID:
3976  *scaledvalue = convert_network_to_scalar(value, valuetypid);
3977  *scaledlobound = convert_network_to_scalar(lobound, boundstypid);
3978  *scaledhibound = convert_network_to_scalar(hibound, boundstypid);
3979  return true;
3980  }
3981  /* Don't know how to convert */
3982  *scaledvalue = *scaledlobound = *scaledhibound = 0;
3983  return false;
3984 }
3985 
3986 /*
3987  * Do convert_to_scalar()'s work for any numeric data type.
3988  */
3989 static double
3991 {
3992  switch (typid)
3993  {
3994  case BOOLOID:
3995  return (double) DatumGetBool(value);
3996  case INT2OID:
3997  return (double) DatumGetInt16(value);
3998  case INT4OID:
3999  return (double) DatumGetInt32(value);
4000  case INT8OID:
4001  return (double) DatumGetInt64(value);
4002  case FLOAT4OID:
4003  return (double) DatumGetFloat4(value);
4004  case FLOAT8OID:
4005  return (double) DatumGetFloat8(value);
4006  case NUMERICOID:
4007  /* Note: out-of-range values will be clamped to +-HUGE_VAL */
4008  return (double)
4010  value));
4011  case OIDOID:
4012  case REGPROCOID:
4013  case REGPROCEDUREOID:
4014  case REGOPEROID:
4015  case REGOPERATOROID:
4016  case REGCLASSOID:
4017  case REGTYPEOID:
4018  case REGCONFIGOID:
4019  case REGDICTIONARYOID:
4020  case REGROLEOID:
4021  case REGNAMESPACEOID:
4022  /* we can treat OIDs as integers... */
4023  return (double) DatumGetObjectId(value);
4024  }
4025 
4026  /*
4027  * Can't get here unless someone tries to use scalarltsel/scalargtsel on
4028  * an operator with one numeric and one non-numeric operand.
4029  */
4030  elog(ERROR, "unsupported type: %u", typid);
4031  return 0;
4032 }
4033 
4034 /*
4035  * Do convert_to_scalar()'s work for any character-string data type.
4036  *
4037  * String datatypes are converted to a scale that ranges from 0 to 1,
4038  * where we visualize the bytes of the string as fractional digits.
4039  *
4040  * We do not want the base to be 256, however, since that tends to
4041  * generate inflated selectivity estimates; few databases will have
4042  * occurrences of all 256 possible byte values at each position.
4043  * Instead, use the smallest and largest byte values seen in the bounds
4044  * as the estimated range for each byte, after some fudging to deal with
4045  * the fact that we probably aren't going to see the full range that way.
4046  *
4047  * An additional refinement is that we discard any common prefix of the
4048  * three strings before computing the scaled values. This allows us to
4049  * "zoom in" when we encounter a narrow data range. An example is a phone
4050  * number database where all the values begin with the same area code.
4051  * (Actually, the bounds will be adjacent histogram-bin-boundary values,
4052  * so this is more likely to happen than you might think.)
4053  */
4054 static void
4056  double *scaledvalue,
4057  char *lobound,
4058  double *scaledlobound,
4059  char *hibound,
4060  double *scaledhibound)
4061 {
4062  int rangelo,
4063  rangehi;
4064  char *sptr;
4065 
4066  rangelo = rangehi = (unsigned char) hibound[0];
4067  for (sptr = lobound; *sptr; sptr++)
4068  {
4069  if (rangelo > (unsigned char) *sptr)
4070  rangelo = (unsigned char) *sptr;
4071  if (rangehi < (unsigned char) *sptr)
4072  rangehi = (unsigned char) *sptr;
4073  }
4074  for (sptr = hibound; *sptr; sptr++)
4075  {
4076  if (rangelo > (unsigned char) *sptr)
4077  rangelo = (unsigned char) *sptr;
4078  if (rangehi < (unsigned char) *sptr)
4079  rangehi = (unsigned char) *sptr;
4080  }
4081  /* If range includes any upper-case ASCII chars, make it include all */
4082  if (rangelo <= 'Z' && rangehi >= 'A')
4083  {
4084  if (rangelo > 'A')
4085  rangelo = 'A';
4086  if (rangehi < 'Z')
4087  rangehi = 'Z';
4088  }
4089  /* Ditto lower-case */
4090  if (rangelo <= 'z' && rangehi >= 'a')
4091  {
4092  if (rangelo > 'a')
4093  rangelo = 'a';
4094  if (rangehi < 'z')
4095  rangehi = 'z';
4096  }
4097  /* Ditto digits */
4098  if (rangelo <= '9' && rangehi >= '0')
4099  {
4100  if (rangelo > '0')
4101  rangelo = '0';
4102  if (rangehi < '9')
4103  rangehi = '9';
4104  }
4105 
4106  /*
4107  * If range includes less than 10 chars, assume we have not got enough
4108  * data, and make it include regular ASCII set.
4109  */
4110  if (rangehi - rangelo < 9)
4111  {
4112  rangelo = ' ';
4113  rangehi = 127;
4114  }
4115 
4116  /*
4117  * Now strip any common prefix of the three strings.
4118  */
4119  while (*lobound)
4120  {
4121  if (*lobound != *hibound || *lobound != *value)
4122  break;
4123  lobound++, hibound++, value++;
4124  }
4125 
4126  /*
4127  * Now we can do the conversions.
4128  */
4129  *scaledvalue = convert_one_string_to_scalar(value, rangelo, rangehi);
4130  *scaledlobound = convert_one_string_to_scalar(lobound, rangelo, rangehi);
4131  *scaledhibound = convert_one_string_to_scalar(hibound, rangelo, rangehi);
4132 }
4133 
4134 static double
4135 convert_one_string_to_scalar(char *value, int rangelo, int rangehi)
4136 {
4137  int slen = strlen(value);
4138  double num,
4139  denom,
4140  base;
4141 
4142  if (slen <= 0)
4143  return 0.0; /* empty string has scalar value 0 */
4144 
4145  /*
4146  * There seems little point in considering more than a dozen bytes from
4147  * the string. Since base is at least 10, that will give us nominal
4148  * resolution of at least 12 decimal digits, which is surely far more
4149  * precision than this estimation technique has got anyway (especially in
4150  * non-C locales). Also, even with the maximum possible base of 256, this
4151  * ensures denom cannot grow larger than 256^13 = 2.03e31, which will not
4152  * overflow on any known machine.
4153  */
4154  if (slen > 12)
4155  slen = 12;
4156 
4157  /* Convert initial characters to fraction */
4158  base = rangehi - rangelo + 1;
4159  num = 0.0;
4160  denom = base;
4161  while (slen-- > 0)
4162  {
4163  int ch = (unsigned char) *value++;
4164 
4165  if (ch < rangelo)
4166  ch = rangelo - 1;
4167  else if (ch > rangehi)
4168  ch = rangehi + 1;
4169  num += ((double) (ch - rangelo)) / denom;
4170  denom *= base;
4171  }
4172 
4173  return num;
4174 }
4175 
4176 /*
4177  * Convert a string-type Datum into a palloc'd, null-terminated string.
4178  *
4179  * When using a non-C locale, we must pass the string through strxfrm()
4180  * before continuing, so as to generate correct locale-specific results.
4181  */
4182 static char *
4184 {
4185  char *val;
4186 
4187  switch (typid)
4188  {
4189  case CHAROID:
4190  val = (char *) palloc(2);
4191  val[0] = DatumGetChar(value);
4192  val[1] = '\0';
4193  break;
4194  case BPCHAROID:
4195  case VARCHAROID:
4196  case TEXTOID:
4197  val = TextDatumGetCString(value);
4198  break;
4199  case NAMEOID:
4200  {
4201  NameData *nm = (NameData *) DatumGetPointer(value);
4202 
4203  val = pstrdup(NameStr(*nm));
4204  break;
4205  }
4206  default:
4207 
4208  /*
4209  * Can't get here unless someone tries to use scalarltsel on an
4210  * operator with one string and one non-string operand.
4211  */
4212  elog(ERROR, "unsupported type: %u", typid);
4213  return NULL;
4214  }
4215 
4217  {
4218  char *xfrmstr;
4219  size_t xfrmlen;
4220  size_t xfrmlen2 PG_USED_FOR_ASSERTS_ONLY;
4221 
4222  /*
4223  * XXX: We could guess at a suitable output buffer size and only call
4224  * strxfrm twice if our guess is too small.
4225  *
4226  * XXX: strxfrm doesn't support UTF-8 encoding on Win32, it can return
4227  * bogus data or set an error. This is not really a problem unless it
4228  * crashes since it will only give an estimation error and nothing
4229  * fatal.
4230  */
4231 #if _MSC_VER == 1400 /* VS.Net 2005 */
4232 
4233  /*
4234  *
4235  * http://connect.microsoft.com/VisualStudio/feedback/ViewFeedback.aspx?
4236  * FeedbackID=99694 */
4237  {
4238  char x[1];
4239 
4240  xfrmlen = strxfrm(x, val, 0);
4241  }
4242 #else
4243  xfrmlen = strxfrm(NULL, val, 0);
4244 #endif
4245 #ifdef WIN32
4246 
4247  /*
4248  * On Windows, strxfrm returns INT_MAX when an error occurs. Instead
4249  * of trying to allocate this much memory (and fail), just return the
4250  * original string unmodified as if we were in the C locale.
4251  */
4252  if (xfrmlen == INT_MAX)
4253  return val;
4254 #endif
4255  xfrmstr = (char *) palloc(xfrmlen + 1);
4256  xfrmlen2 = strxfrm(xfrmstr, val, xfrmlen + 1);
4257 
4258  /*
4259  * Some systems (e.g., glibc) can return a smaller value from the
4260  * second call than the first; thus the Assert must be <= not ==.
4261  */
4262  Assert(xfrmlen2 <= xfrmlen);
4263  pfree(val);
4264  val = xfrmstr;
4265  }
4266 
4267  return val;
4268 }
4269 
4270 /*
4271  * Do convert_to_scalar()'s work for any bytea data type.
4272  *
4273  * Very similar to convert_string_to_scalar except we can't assume
4274  * null-termination and therefore pass explicit lengths around.
4275  *
4276  * Also, assumptions about likely "normal" ranges of characters have been
4277  * removed - a data range of 0..255 is always used, for now. (Perhaps
4278  * someday we will add information about actual byte data range to
4279  * pg_statistic.)
4280  */
4281 static void
4283  double *scaledvalue,
4284  Datum lobound,
4285  double *scaledlobound,
4286  Datum hibound,
4287  double *scaledhibound)
4288 {
4289  int rangelo,
4290  rangehi,
4291  valuelen = VARSIZE(DatumGetPointer(value)) - VARHDRSZ,
4292  loboundlen = VARSIZE(DatumGetPointer(lobound)) - VARHDRSZ,
4293  hiboundlen = VARSIZE(DatumGetPointer(hibound)) - VARHDRSZ,
4294  i,
4295  minlen;
4296  unsigned char *valstr = (unsigned char *) VARDATA(DatumGetPointer(value)),
4297  *lostr = (unsigned char *) VARDATA(DatumGetPointer(lobound)),
4298  *histr = (unsigned char *) VARDATA(DatumGetPointer(hibound));
4299 
4300  /*
4301  * Assume bytea data is uniformly distributed across all byte values.
4302  */
4303  rangelo = 0;
4304  rangehi = 255;
4305 
4306  /*
4307  * Now strip any common prefix of the three strings.
4308  */
4309  minlen = Min(Min(valuelen, loboundlen), hiboundlen);
4310  for (i = 0; i < minlen; i++)
4311  {
4312  if (*lostr != *histr || *lostr != *valstr)
4313  break;
4314  lostr++, histr++, valstr++;
4315  loboundlen--, hiboundlen--, valuelen--;
4316  }
4317 
4318  /*
4319  * Now we can do the conversions.
4320  */
4321  *scaledvalue = convert_one_bytea_to_scalar(valstr, valuelen, rangelo, rangehi);
4322  *scaledlobound = convert_one_bytea_to_scalar(lostr, loboundlen, rangelo, rangehi);
4323  *scaledhibound = convert_one_bytea_to_scalar(histr, hiboundlen, rangelo, rangehi);
4324 }
4325 
4326 static double
4327 convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
4328  int rangelo, int rangehi)
4329 {
4330  double num,
4331  denom,
4332  base;
4333 
4334  if (valuelen <= 0)
4335  return 0.0; /* empty string has scalar value 0 */
4336 
4337  /*
4338  * Since base is 256, need not consider more than about 10 chars (even
4339  * this many seems like overkill)
4340  */
4341  if (valuelen > 10)
4342  valuelen = 10;
4343 
4344  /* Convert initial characters to fraction */
4345  base = rangehi - rangelo + 1;
4346  num = 0.0;
4347  denom = base;
4348  while (valuelen-- > 0)
4349  {
4350  int ch = *value++;
4351 
4352  if (ch < rangelo)
4353  ch = rangelo - 1;
4354  else if (ch > rangehi)
4355  ch = rangehi + 1;
4356  num += ((double) (ch - rangelo)) / denom;
4357  denom *= base;
4358  }
4359 
4360  return num;
4361 }
4362 
4363 /*
4364  * Do convert_to_scalar()'s work for any timevalue data type.
4365  */
4366 static double
4368 {
4369  switch (typid)
4370  {
4371  case TIMESTAMPOID:
4372  return DatumGetTimestamp(value);
4373  case TIMESTAMPTZOID:
4374  return DatumGetTimestampTz(value);
4375  case ABSTIMEOID:
4377  value));
4378  case DATEOID:
4380  case INTERVALOID:
4381  {
4383 
4384  /*
4385  * Convert the month part of Interval to days using assumed
4386  * average month length of 365.25/12.0 days. Not too
4387  * accurate, but plenty good enough for our purposes.
4388  */
4389  return interval->time + interval->day * (double) USECS_PER_DAY +
4390  interval->month * ((DAYS_PER_YEAR / (double) MONTHS_PER_YEAR) * USECS_PER_DAY);
4391  }
4392  case RELTIMEOID:
4393  return (DatumGetRelativeTime(value) * 1000000.0);
4394  case TINTERVALOID:
4395  {
4396  TimeInterval tinterval = DatumGetTimeInterval(value);
4397 
4398  if (tinterval->status != 0)
4399  return ((tinterval->data[1] - tinterval->data[0]) * 1000000.0);
4400  return 0; /* for lack of a better idea */
4401  }
4402  case TIMEOID:
4403  return DatumGetTimeADT(value);
4404  case TIMETZOID:
4405  {
4406  TimeTzADT *timetz = DatumGetTimeTzADTP(value);
4407 
4408  /* use GMT-equivalent time */
4409  return (double) (timetz->time + (timetz->zone * 1000000.0));
4410  }
4411  }
4412 
4413  /*
4414  * Can't get here unless someone tries to use scalarltsel/scalargtsel on
4415  * an operator with one timevalue and one non-timevalue operand.
4416  */
4417  elog(ERROR, "unsupported type: %u", typid);
4418  return 0;
4419 }
4420 
4421 
4422 /*
4423  * get_restriction_variable
4424  * Examine the args of a restriction clause to see if it's of the
4425  * form (variable op pseudoconstant) or (pseudoconstant op variable),
4426  * where "variable" could be either a Var or an expression in vars of a
4427  * single relation. If so, extract information about the variable,
4428  * and also indicate which side it was on and the other argument.
4429  *
4430  * Inputs:
4431  * root: the planner info
4432  * args: clause argument list
4433  * varRelid: see specs for restriction selectivity functions
4434  *
4435  * Outputs: (these are valid only if TRUE is returned)
4436  * *vardata: gets information about variable (see examine_variable)
4437  * *other: gets other clause argument, aggressively reduced to a constant
4438  * *varonleft: set TRUE if variable is on the left, FALSE if on the right
4439  *
4440  * Returns TRUE if a variable is identified, otherwise FALSE.
4441  *
4442  * Note: if there are Vars on both sides of the clause, we must fail, because
4443  * callers are expecting that the other side will act like a pseudoconstant.
4444  */
4445 bool
4447  VariableStatData *vardata, Node **other,
4448  bool *varonleft)
4449 {
4450  Node *left,
4451  *right;
4452  VariableStatData rdata;
4453 
4454  /* Fail if not a binary opclause (probably shouldn't happen) */
4455  if (list_length(args) != 2)
4456  return false;
4457 
4458  left = (Node *) linitial(args);
4459  right = (Node *) lsecond(args);
4460 
4461  /*
4462  * Examine both sides. Note that when varRelid is nonzero, Vars of other
4463  * relations will be treated as pseudoconstants.
4464  */
4465  examine_variable(root, left, varRelid, vardata);
4466  examine_variable(root, right, varRelid, &rdata);
4467 
4468  /*
4469  * If one side is a variable and the other not, we win.
4470  */
4471  if (vardata->rel && rdata.rel == NULL)
4472  {
4473  *varonleft = true;
4474  *other = estimate_expression_value(root, rdata.var);
4475  /* Assume we need no ReleaseVariableStats(rdata) here */
4476  return true;
4477  }
4478 
4479  if (vardata->rel == NULL && rdata.rel)
4480  {
4481  *varonleft = false;
4482  *other = estimate_expression_value(root, vardata->var);
4483  /* Assume we need no ReleaseVariableStats(*vardata) here */
4484  *vardata = rdata;
4485  return true;
4486  }
4487 
4488  /* Oops, clause has wrong structure (probably var op var) */
4489  ReleaseVariableStats(*vardata);
4490  ReleaseVariableStats(rdata);
4491 
4492  return false;
4493 }
4494 
4495 /*
4496  * get_join_variables
4497  * Apply examine_variable() to each side of a join clause.
4498  * Also, attempt to identify whether the join clause has the same
4499  * or reversed sense compared to the SpecialJoinInfo.
4500  *
4501  * We consider the join clause "normal" if it is "lhs_var OP rhs_var",
4502  * or "reversed" if it is "rhs_var OP lhs_var". In complicated cases
4503  * where we can't tell for sure, we default to assuming it's normal.
4504  */
4505 void
4507  VariableStatData *vardata1, VariableStatData *vardata2,
4508  bool *join_is_reversed)
4509 {
4510  Node *left,
4511  *right;
4512 
4513  if (list_length(args) != 2)
4514  elog(ERROR, "join operator should take two arguments");
4515 
4516  left = (Node *) linitial(args);
4517  right = (Node *) lsecond(args);
4518 
4519  examine_variable(root, left, 0, vardata1);
4520  examine_variable(root, right, 0, vardata2);
4521 
4522  if (vardata1->rel &&
4523  bms_is_subset(vardata1->rel->relids, sjinfo->syn_righthand))
4524  *join_is_reversed = true; /* var1 is on RHS */
4525  else if (vardata2->rel &&
4526  bms_is_subset(vardata2->rel->relids, sjinfo->syn_lefthand))
4527  *join_is_reversed = true; /* var2 is on LHS */
4528  else
4529  *join_is_reversed = false;
4530 }
4531 
4532 /*
4533  * examine_variable
4534  * Try to look up statistical data about an expression.
4535  * Fill in a VariableStatData struct to describe the expression.
4536  *
4537  * Inputs:
4538  * root: the planner info
4539  * node: the expression tree to examine
4540  * varRelid: see specs for restriction selectivity functions
4541  *
4542  * Outputs: *vardata is filled as follows:
4543  * var: the input expression (with any binary relabeling stripped, if
4544  * it is or contains a variable; but otherwise the type is preserved)
4545  * rel: RelOptInfo for relation containing variable; NULL if expression
4546  * contains no Vars (NOTE this could point to a RelOptInfo of a
4547  * subquery, not one in the current query).
4548  * statsTuple: the pg_statistic entry for the variable, if one exists;
4549  * otherwise NULL.
4550  * freefunc: pointer to a function to release statsTuple with.
4551  * vartype: exposed type of the expression; this should always match
4552  * the declared input type of the operator we are estimating for.
4553  * atttype, atttypmod: type data to pass to get_attstatsslot(). This is
4554  * commonly the same as the exposed type of the variable argument,
4555  * but can be different in binary-compatible-type cases.
4556  * isunique: TRUE if we were able to match the var to a unique index or a
4557  * single-column DISTINCT clause, implying its values are unique for
4558  * this query. (Caution: this should be trusted for statistical
4559  * purposes only, since we do not check indimmediate nor verify that
4560  * the exact same definition of equality applies.)
4561  *
4562  * Caller is responsible for doing ReleaseVariableStats() before exiting.
4563  */
4564 void
4565 examine_variable(PlannerInfo *root, Node *node, int varRelid,
4566  VariableStatData *vardata)
4567 {
4568  Node *basenode;
4569  Relids varnos;
4570  RelOptInfo *onerel;
4571 
4572  /* Make sure we don't return dangling pointers in vardata */
4573  MemSet(vardata, 0, sizeof(VariableStatData));
4574 
4575  /* Save the exposed type of the expression */
4576  vardata->vartype = exprType(node);
4577 
4578  /* Look inside any binary-compatible relabeling */
4579 
4580  if (IsA(node, RelabelType))
4581  basenode = (Node *) ((RelabelType *) node)->arg;
4582  else
4583  basenode = node;
4584 
4585  /* Fast path for a simple Var */
4586 
4587  if (IsA(basenode, Var) &&
4588  (varRelid == 0 || varRelid == ((Var *) basenode)->varno))
4589  {
4590  Var *var = (Var *) basenode;
4591 
4592  /* Set up result fields other than the stats tuple */
4593  vardata->var = basenode; /* return Var without relabeling */
4594  vardata->rel = find_base_rel(root, var->varno);
4595  vardata->atttype = var->vartype;
4596  vardata->atttypmod = var->vartypmod;
4597  vardata->isunique = has_unique_index(vardata->rel, var->varattno);
4598 
4599  /* Try to locate some stats */
4600  examine_simple_variable(root, var, vardata);
4601 
4602  return;
4603  }
4604 
4605  /*
4606  * Okay, it's a more complicated expression. Determine variable
4607  * membership. Note that when varRelid isn't zero, only vars of that
4608  * relation are considered "real" vars.
4609  */
4610  varnos = pull_varnos(basenode);
4611 
4612  onerel = NULL;
4613 
4614  switch (bms_membership(varnos))
4615  {
4616  case BMS_EMPTY_SET:
4617  /* No Vars at all ... must be pseudo-constant clause */
4618  break;
4619  case BMS_SINGLETON:
4620  if (varRelid == 0 || bms_is_member(varRelid, varnos))
4621  {
4622  onerel = find_base_rel(root,
4623  (varRelid ? varRelid : bms_singleton_member(varnos)));
4624  vardata->rel = onerel;
4625  node = basenode; /* strip any relabeling */
4626  }
4627  /* else treat it as a constant */
4628  break;
4629  case BMS_MULTIPLE:
4630  if (varRelid == 0)
4631  {
4632  /* treat it as a variable of a join relation */
4633  vardata->rel = find_join_rel(root, varnos);
4634  node = basenode; /* strip any relabeling */
4635  }
4636  else if (bms_is_member(varRelid, varnos))
4637  {
4638  /* ignore the vars belonging to other relations */
4639  vardata->rel = find_base_rel(root, varRelid);
4640  node = basenode; /* strip any relabeling */
4641  /* note: no point in expressional-index search here */
4642  }
4643  /* else treat it as a constant */
4644  break;
4645  }
4646 
4647  bms_free(varnos);
4648 
4649  vardata->var = node;
4650  vardata->atttype = exprType(node);
4651  vardata->atttypmod = exprTypmod(node);
4652 
4653  if (onerel)
4654  {
4655  /*
4656  * We have an expression in vars of a single relation. Try to match
4657  * it to expressional index columns, in hopes of finding some
4658  * statistics.
4659  *
4660  * XXX it's conceivable that there are multiple matches with different
4661  * index opfamilies; if so, we need to pick one that matches the
4662  * operator we are estimating for. FIXME later.
4663  */
4664  ListCell *ilist;
4665 
4666  foreach(ilist, onerel->indexlist)
4667  {
4668  IndexOptInfo *index = (IndexOptInfo *) lfirst(ilist);
4669  ListCell *indexpr_item;
4670  int pos;
4671 
4672  indexpr_item = list_head(index->indexprs);
4673  if (indexpr_item == NULL)
4674  continue; /* no expressions here... */
4675 
4676  for (pos = 0; pos < index->ncolumns; pos++)
4677  {
4678  if (index->indexkeys[pos] == 0)
4679  {
4680  Node *indexkey;
4681 
4682  if (indexpr_item == NULL)
4683  elog(ERROR, "too few entries in indexprs list");
4684  indexkey = (Node *) lfirst(indexpr_item);
4685  if (indexkey && IsA(indexkey, RelabelType))
4686  indexkey = (Node *) ((RelabelType *) indexkey)->arg;
4687  if (equal(node, indexkey))
4688  {
4689  /*
4690  * Found a match ... is it a unique index? Tests here
4691  * should match has_unique_index().
4692  */
4693  if (index->unique &&
4694  index->ncolumns == 1 &&
4695  (index->indpred == NIL || index->predOK))
4696  vardata->isunique = true;
4697 
4698  /*
4699  * Has it got stats? We only consider stats for
4700  * non-partial indexes, since partial indexes probably
4701  * don't reflect whole-relation statistics; the above
4702  * check for uniqueness is the only info we take from
4703  * a partial index.
4704  *
4705  * An index stats hook, however, must make its own
4706  * decisions about what to do with partial indexes.
4707  */
4708  if (get_index_stats_hook &&
4709  (*get_index_stats_hook) (root, index->indexoid,
4710  pos + 1, vardata))
4711  {
4712  /*
4713  * The hook took control of acquiring a stats
4714  * tuple. If it did supply a tuple, it'd better
4715  * have supplied a freefunc.
4716  */
4717  if (HeapTupleIsValid(vardata->statsTuple) &&
4718  !vardata->freefunc)
4719  elog(ERROR, "no function provided to release variable stats with");
4720  }
4721  else if (index->indpred == NIL)
4722  {
4723  vardata->statsTuple =
4725  ObjectIdGetDatum(index->indexoid),
4726  Int16GetDatum(pos + 1),
4727  BoolGetDatum(false));
4728  vardata->freefunc = ReleaseSysCache;
4729  }
4730  if (vardata->statsTuple)
4731  break;
4732  }
4733  indexpr_item = lnext(indexpr_item);
4734  }
4735  }
4736  if (vardata->statsTuple)
4737  break;
4738  }
4739  }
4740 }
4741 
4742 /*
4743  * examine_simple_variable
4744  * Handle a simple Var for examine_variable
4745  *
4746  * This is split out as a subroutine so that we can recurse to deal with
4747  * Vars referencing subqueries.
4748  *
4749  * We already filled in all the fields of *vardata except for the stats tuple.
4750  */
4751 static void
4753  VariableStatData *vardata)
4754 {
4755  RangeTblEntry *rte = root->simple_rte_array[var->varno];
4756 
4757  Assert(IsA(rte, RangeTblEntry));
4758 
4760  (*get_relation_stats_hook) (root, rte, var->varattno, vardata))
4761  {
4762  /*
4763  * The hook took control of acquiring a stats tuple. If it did supply
4764  * a tuple, it'd better have supplied a freefunc.
4765  */
4766  if (HeapTupleIsValid(vardata->statsTuple) &&
4767  !vardata->freefunc)
4768  elog(ERROR, "no function provided to release variable stats with");
4769  }
4770  else if (rte->rtekind == RTE_RELATION)
4771  {
4772  /*
4773  * Plain table or parent of an inheritance appendrel, so look up the
4774  * column in pg_statistic
4775  */
4777  ObjectIdGetDatum(rte->relid),
4778  Int16GetDatum(var->varattno),
4779  BoolGetDatum(rte->inh));
4780  vardata->freefunc = ReleaseSysCache;
4781  }
4782  else if (rte->rtekind == RTE_SUBQUERY && !rte->inh)
4783  {
4784  /*
4785  * Plain subquery (not one that was converted to an appendrel).
4786  */
4787  Query *subquery = rte->subquery;
4788  RelOptInfo *rel;
4789  TargetEntry *ste;
4790 
4791  /*
4792  * Punt if it's a whole-row var rather than a plain column reference.
4793  */
4794  if (var->varattno == InvalidAttrNumber)
4795  return;
4796 
4797  /*
4798  * Punt if subquery uses set operations or GROUP BY, as these will
4799  * mash underlying columns' stats beyond recognition. (Set ops are
4800  * particularly nasty; if we forged ahead, we would return stats
4801  * relevant to only the leftmost subselect...) DISTINCT is also
4802  * problematic, but we check that later because there is a possibility
4803  * of learning something even with it.
4804  */
4805  if (subquery->setOperations ||
4806  subquery->groupClause)
4807  return;
4808 
4809  /*
4810  * OK, fetch RelOptInfo for subquery. Note that we don't change the
4811  * rel returned in vardata, since caller expects it to be a rel of the
4812  * caller's query level. Because we might already be recursing, we
4813  * can't use that rel pointer either, but have to look up the Var's
4814  * rel afresh.
4815  */
4816  rel = find_base_rel(root, var->varno);
4817 
4818  /* If the subquery hasn't been planned yet, we have to punt */
4819  if (rel->subroot == NULL)
4820  return;
4821  Assert(IsA(rel->subroot, PlannerInfo));
4822 
4823  /*
4824  * Switch our attention to the subquery as mangled by the planner. It
4825  * was okay to look at the pre-planning version for the tests above,
4826  * but now we need a Var that will refer to the subroot's live
4827  * RelOptInfos. For instance, if any subquery pullup happened during
4828  * planning, Vars in the targetlist might have gotten replaced, and we
4829  * need to see the replacement expressions.
4830  */
4831  subquery = rel->subroot->parse;
4832  Assert(IsA(subquery, Query));
4833 
4834  /* Get the subquery output expression referenced by the upper Var */
4835  ste = get_tle_by_resno(subquery->targetList, var->varattno);
4836  if (ste == NULL || ste->resjunk)
4837  elog(ERROR, "subquery %s does not have attribute %d",
4838  rte->eref->aliasname, var->varattno);
4839  var = (Var *) ste->expr;
4840 
4841  /*
4842  * If subquery uses DISTINCT, we can't make use of any stats for the
4843  * variable ... but, if it's the only DISTINCT column, we are entitled
4844  * to consider it unique. We do the test this way so that it works
4845  * for cases involving DISTINCT ON.
4846  */
4847  if (subquery->distinctClause)
4848  {
4849  if (list_length(subquery->distinctClause) == 1 &&
4850  targetIsInSortList(ste, InvalidOid, subquery->distinctClause))
4851  vardata->isunique = true;
4852  /* cannot go further */
4853  return;
4854  }
4855 
4856  /*
4857  * If the sub-query originated from a view with the security_barrier
4858  * attribute, we must not look at the variable's statistics, though it
4859  * seems all right to notice the existence of a DISTINCT clause. So
4860  * stop here.
4861  *
4862  * This is probably a harsher restriction than necessary; it's
4863  * certainly OK for the selectivity estimator (which is a C function,
4864  * and therefore omnipotent anyway) to look at the statistics. But
4865  * many selectivity estimators will happily *invoke the operator
4866  * function* to try to work out a good estimate - and that's not OK.
4867  * So for now, don't dig down for stats.
4868  */
4869  if (rte->security_barrier)
4870  return;
4871 
4872  /* Can only handle a simple Var of subquery's query level */
4873  if (var && IsA(var, Var) &&
4874  var->varlevelsup == 0)
4875  {
4876  /*
4877  * OK, recurse into the subquery. Note that the original setting
4878  * of vardata->isunique (which will surely be false) is left
4879  * unchanged in this situation. That's what we want, since even
4880  * if the underlying column is unique, the subquery may have
4881  * joined to other tables in a way that creates duplicates.
4882  */
4883  examine_simple_variable(rel->subroot, var, vardata);
4884  }
4885  }
4886  else
4887  {
4888  /*
4889  * Otherwise, the Var comes from a FUNCTION, VALUES, or CTE RTE. (We
4890  * won't see RTE_JOIN here because join alias Vars have already been
4891  * flattened.) There's not much we can do with function outputs, but
4892  * maybe someday try to be smarter about VALUES and/or CTEs.
4893  */
4894  }
4895 }
4896 
4897 /*
4898  * get_variable_numdistinct
4899  * Estimate the number of distinct values of a variable.
4900  *
4901  * vardata: results of examine_variable
4902  * *isdefault: set to TRUE if the result is a default rather than based on
4903  * anything meaningful.
4904  *
4905  * NB: be careful to produce a positive integral result, since callers may
4906  * compare the result to exact integer counts, or might divide by it.
4907  */
4908 double
4909 get_variable_numdistinct(VariableStatData *vardata, bool *isdefault)
4910 {
4911  double stadistinct;
4912  double stanullfrac = 0.0;
4913  double ntuples;
4914 
4915  *isdefault = false;
4916 
4917  /*
4918  * Determine the stadistinct value to use. There are cases where we can
4919  * get an estimate even without a pg_statistic entry, or can get a better
4920  * value than is in pg_statistic. Grab stanullfrac too if we can find it
4921  * (otherwise, assume no nulls, for lack of any better idea).
4922  */
4923  if (HeapTupleIsValid(vardata->statsTuple))
4924  {
4925  /* Use the pg_statistic entry */
4926  Form_pg_statistic stats;
4927 
4928  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
4929  stadistinct = stats->stadistinct;
4930  stanullfrac = stats->stanullfrac;
4931  }
4932  else if (vardata->vartype == BOOLOID)
4933  {
4934  /*
4935  * Special-case boolean columns: presumably, two distinct values.
4936  *
4937  * Are there any other datatypes we should wire in special estimates
4938  * for?
4939  */
4940  stadistinct = 2.0;
4941  }
4942  else
4943  {
4944  /*
4945  * We don't keep statistics for system columns, but in some cases we
4946  * can infer distinctness anyway.
4947  */
4948  if (vardata->var && IsA(vardata->var, Var))
4949  {
4950  switch (((Var *) vardata->var)->varattno)
4951  {
4954  stadistinct = -1.0; /* unique (and all non null) */
4955  break;
4957  stadistinct = 1.0; /* only 1 value */
4958  break;
4959  default:
4960  stadistinct = 0.0; /* means "unknown" */
4961  break;
4962  }
4963  }
4964  else
4965  stadistinct = 0.0; /* means "unknown" */
4966 
4967  /*
4968  * XXX consider using estimate_num_groups on expressions?
4969  */
4970  }
4971 
4972  /*
4973  * If there is a unique index or DISTINCT clause for the variable, assume
4974  * it is unique no matter what pg_statistic says; the statistics could be
4975  * out of date, or we might have found a partial unique index that proves
4976  * the var is unique for this query. However, we'd better still believe
4977  * the null-fraction statistic.
4978  */
4979  if (vardata->isunique)
4980  stadistinct = -1.0 * (1.0 - stanullfrac);
4981 
4982  /*
4983  * If we had an absolute estimate, use that.
4984  */
4985  if (stadistinct > 0.0)
4986  return clamp_row_est(stadistinct);
4987 
4988  /*
4989  * Otherwise we need to get the relation size; punt if not available.
4990  */
4991  if (vardata->rel == NULL)
4992  {
4993  *isdefault = true;
4994  return DEFAULT_NUM_DISTINCT;
4995  }
4996  ntuples = vardata->rel->tuples;
4997  if (ntuples <= 0.0)
4998  {
4999  *isdefault = true;
5000  return DEFAULT_NUM_DISTINCT;
5001  }
5002 
5003  /*
5004  * If we had a relative estimate, use that.
5005  */
5006  if (stadistinct < 0.0)
5007  return clamp_row_est(-stadistinct * ntuples);
5008 
5009  /*
5010  * With no data, estimate ndistinct = ntuples if the table is small, else
5011  * use default. We use DEFAULT_NUM_DISTINCT as the cutoff for "small" so
5012  * that the behavior isn't discontinuous.
5013  */
5014  if (ntuples < DEFAULT_NUM_DISTINCT)
5015  return clamp_row_est(ntuples);
5016 
5017  *isdefault = true;
5018  return DEFAULT_NUM_DISTINCT;
5019 }
5020 
5021 /*
5022  * get_variable_range
5023  * Estimate the minimum and maximum value of the specified variable.
5024  * If successful, store values in *min and *max, and return TRUE.
5025  * If no data available, return FALSE.
5026  *
5027  * sortop is the "<" comparison operator to use. This should generally
5028  * be "<" not ">", as only the former is likely to be found in pg_statistic.
5029  */
5030 static bool
5032  Datum *min, Datum *max)
5033 {
5034  Datum tmin = 0;
5035  Datum tmax = 0;
5036  bool have_data = false;
5037  int16 typLen;
5038  bool typByVal;
5039  Datum *values;
5040  int nvalues;
5041  int i;
5042 
5043  /*
5044  * XXX It's very tempting to try to use the actual column min and max, if
5045  * we can get them relatively-cheaply with an index probe. However, since
5046  * this function is called many times during join planning, that could
5047  * have unpleasant effects on planning speed. Need more investigation
5048  * before enabling this.
5049  */
5050 #ifdef NOT_USED
5051  if (get_actual_variable_range(root, vardata, sortop, min, max))
5052  return true;
5053 #endif
5054 
5055  if (!HeapTupleIsValid(vardata->statsTuple))
5056  {
5057  /* no stats available, so default result */
5058  return false;
5059  }
5060 
5061  get_typlenbyval(vardata->atttype, &typLen, &typByVal);
5062 
5063  /*
5064  * If there is a histogram, grab the first and last values.
5065  *
5066  * If there is a histogram that is sorted with some other operator than
5067  * the one we want, fail --- this suggests that there is data we can't
5068  * use.
5069  */
5070  if (get_attstatsslot(vardata->statsTuple,
5071  vardata->atttype, vardata->atttypmod,
5072  STATISTIC_KIND_HISTOGRAM, sortop,
5073  NULL,
5074  &values, &nvalues,
5075  NULL, NULL))
5076  {
5077  if (nvalues > 0)
5078  {
5079  tmin = datumCopy(values[0], typByVal, typLen);
5080  tmax = datumCopy(values[nvalues - 1], typByVal, typLen);
5081  have_data = true;
5082  }
5083  free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
5084  }
5085  else if (get_attstatsslot(vardata->statsTuple,
5086  vardata->atttype, vardata->atttypmod,
5088  NULL,
5089  &values, &nvalues,
5090  NULL, NULL))
5091  {
5092  free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
5093  return false;
5094  }
5095 
5096  /*
5097  * If we have most-common-values info, look for extreme MCVs. This is
5098  * needed even if we also have a histogram, since the histogram excludes
5099  * the MCVs. However, usually the MCVs will not be the extreme values, so
5100  * avoid unnecessary data copying.
5101  */
5102  if (get_attstatsslot(vardata->statsTuple,
5103  vardata->atttype, vardata->atttypmod,
5105  NULL,
5106  &values, &nvalues,
5107  NULL, NULL))
5108  {
5109  bool tmin_is_mcv = false;
5110  bool tmax_is_mcv = false;
5111  FmgrInfo opproc;
5112 
5113  fmgr_info(get_opcode(sortop), &opproc);
5114 
5115  for (i = 0; i < nvalues; i++)
5116  {
5117  if (!have_data)
5118  {
5119  tmin = tmax = values[i];
5120  tmin_is_mcv = tmax_is_mcv = have_data = true;
5121  continue;
5122  }
5123  if (DatumGetBool(FunctionCall2Coll(&opproc,
5125  values[i], tmin)))
5126  {
5127  tmin = values[i];
5128  tmin_is_mcv = true;
5129  }
5130  if (DatumGetBool(FunctionCall2Coll(&opproc,
5132  tmax, values[i])))
5133  {
5134  tmax = values[i];
5135  tmax_is_mcv = true;
5136  }
5137  }
5138  if (tmin_is_mcv)
5139  tmin = datumCopy(tmin, typByVal, typLen);
5140  if (tmax_is_mcv)
5141  tmax = datumCopy(tmax, typByVal, typLen);
5142  free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
5143  }
5144 
5145  *min = tmin;
5146  *max = tmax;
5147  return have_data;
5148 }
5149 
5150 
5151 /*
5152  * get_actual_variable_range
5153  * Attempt to identify the current *actual* minimum and/or maximum
5154  * of the specified variable, by looking for a suitable btree index
5155  * and fetching its low and/or high values.
5156  * If successful, store values in *min and *max, and return TRUE.
5157  * (Either pointer can be NULL if that endpoint isn't needed.)
5158  * If no data available, return FALSE.
5159  *
5160  * sortop is the "<" comparison operator to use.
5161  */
5162 static bool
5164  Oid sortop,
5165  Datum *min, Datum *max)
5166 {
5167  bool have_data = false;
5168  RelOptInfo *rel = vardata->rel;
5169  RangeTblEntry *rte;
5170  ListCell *lc;
5171 
5172  /* No hope if no relation or it doesn't have indexes */
5173  if (rel == NULL || rel->indexlist == NIL)
5174  return false;
5175  /* If it has indexes it must be a plain relation */
5176  rte = root->simple_rte_array[rel->relid];
5177  Assert(rte->rtekind == RTE_RELATION);
5178 
5179  /* Search through the indexes to see if any match our problem */
5180  foreach(lc, rel->indexlist)
5181  {
5183  ScanDirection indexscandir;
5184 
5185  /* Ignore non-btree indexes */
5186  if (index->relam != BTREE_AM_OID)
5187  continue;
5188 
5189  /*
5190  * Ignore partial indexes --- we only want stats that cover the entire
5191  * relation.
5192  */
5193  if (index->indpred != NIL)
5194  continue;
5195 
5196  /*
5197  * The index list might include hypothetical indexes inserted by a
5198  * get_relation_info hook --- don't try to access them.
5199  */
5200  if (index->hypothetical)
5201  continue;
5202 
5203  /*
5204  * The first index column must match the desired variable and sort
5205  * operator --- but we can use a descending-order index.
5206  */
5207  if (!match_index_to_operand(vardata->var, 0, index))
5208  continue;
5209  switch (get_op_opfamily_strategy(sortop, index->sortopfamily[0]))
5210  {
5211  case BTLessStrategyNumber:
5212  if (index->reverse_sort[0])
5213  indexscandir = BackwardScanDirection;
5214  else
5215  indexscandir = ForwardScanDirection;
5216  break;
5218  if (index->reverse_sort[0])
5219  indexscandir = ForwardScanDirection;
5220  else
5221  indexscandir = BackwardScanDirection;
5222  break;
5223  default:
5224  /* index doesn't match the sortop */
5225  continue;
5226  }
5227 
5228  /*
5229  * Found a suitable index to extract data from. We'll need an EState
5230  * and a bunch of other infrastructure.
5231  */
5232  {
5233  EState *estate;
5234  ExprContext *econtext;
5235  MemoryContext tmpcontext;
5236  MemoryContext oldcontext;
5237  Relation heapRel;
5238  Relation indexRel;
5239  IndexInfo *indexInfo;
5240  TupleTableSlot *slot;
5241  int16 typLen;
5242  bool typByVal;
5243  ScanKeyData scankeys[1];
5244  IndexScanDesc index_scan;
5245  HeapTuple tup;
5247  bool isnull[INDEX_MAX_KEYS];
5248  SnapshotData SnapshotDirty;
5249 
5250  estate = CreateExecutorState();
5251  econtext = GetPerTupleExprContext(estate);
5252  /* Make sure any cruft is generated in the econtext's memory */
5253  tmpcontext = econtext->ecxt_per_tuple_memory;
5254  oldcontext = MemoryContextSwitchTo(tmpcontext);
5255 
5256  /*
5257  * Open the table and index so we can read from them. We should
5258  * already have at least AccessShareLock on the table, but not
5259  * necessarily on the index.
5260  */
5261  heapRel = heap_open(rte->relid, NoLock);
5262  indexRel = index_open(index->indexoid, AccessShareLock);
5263 
5264  /* extract index key information from the index's pg_index info */
5265  indexInfo = BuildIndexInfo(indexRel);
5266 
5267  /* some other stuff */
5268  slot = MakeSingleTupleTableSlot(RelationGetDescr(heapRel));
5269  econtext->ecxt_scantuple = slot;
5270  get_typlenbyval(vardata->atttype, &typLen, &typByVal);
5271  InitDirtySnapshot(SnapshotDirty);
5272 
5273  /* set up an IS NOT NULL scan key so that we ignore nulls */
5274  ScanKeyEntryInitialize(&scankeys[0],
5276  1, /* index col to scan */
5277  InvalidStrategy, /* no strategy */
5278  InvalidOid, /* no strategy subtype */
5279  InvalidOid, /* no collation */
5280  InvalidOid, /* no reg proc for this */
5281  (Datum) 0); /* constant */
5282 
5283  have_data = true;
5284 
5285  /* If min is requested ... */
5286  if (min)
5287  {
5288  /*
5289  * In principle, we should scan the index with our current
5290  * active snapshot, which is the best approximation we've got
5291  * to what the query will see when executed. But that won't
5292  * be exact if a new snap is taken before running the query,
5293  * and it can be very expensive if a lot of uncommitted rows
5294  * exist at the end of the index (because we'll laboriously
5295  * fetch each one and reject it). What seems like a good
5296  * compromise is to use SnapshotDirty. That will accept
5297  * uncommitted rows, and thus avoid fetching multiple heap
5298  * tuples in this scenario. On the other hand, it will reject
5299  * known-dead rows, and thus not give a bogus answer when the
5300  * extreme value has been deleted; that case motivates not
5301  * using SnapshotAny here.
5302  */
5303  index_scan = index_beginscan(heapRel, indexRel, &SnapshotDirty,
5304  1, 0);
5305  index_rescan(index_scan, scankeys, 1, NULL, 0);
5306 
5307  /* Fetch first tuple in sortop's direction */
5308  if ((tup = index_getnext(index_scan,
5309  indexscandir)) != NULL)
5310  {
5311  /* Extract the index column values from the heap tuple */
5312  ExecStoreTuple(tup, slot, InvalidBuffer, false);
5313  FormIndexDatum(indexInfo, slot, estate,
5314  values, isnull);
5315 
5316  /* Shouldn't have got a null, but be careful */
5317  if (isnull[0])
5318  elog(ERROR, "found unexpected null value in index \"%s\"",
5319  RelationGetRelationName(indexRel));
5320 
5321  /* Copy the index column value out to caller's context */
5322  MemoryContextSwitchTo(oldcontext);
5323  *min = datumCopy(values[0], typByVal, typLen);
5324  MemoryContextSwitchTo(tmpcontext);
5325  }
5326  else
5327  have_data = false;
5328 
5329  index_endscan(index_scan);
5330  }
5331 
5332  /* If max is requested, and we didn't find the index is empty */
5333  if (max && have_data)
5334  {
5335  index_scan = index_beginscan(heapRel, indexRel, &SnapshotDirty,
5336  1, 0);
5337  index_rescan(index_scan, scankeys, 1, NULL, 0);
5338 
5339  /* Fetch first tuple in reverse direction */
5340  if ((tup = index_getnext(index_scan,
5341  -indexscandir)) != NULL)
5342  {
5343  /* Extract the index column values from the heap tuple */
5344  ExecStoreTuple(tup, slot, InvalidBuffer, false);
5345  FormIndexDatum(indexInfo, slot, estate,
5346  values, isnull);
5347 
5348  /* Shouldn't have got a null, but be careful */
5349  if (isnull[0])
5350  elog(ERROR, "found unexpected null value in index \"%s\"",
5351  RelationGetRelationName(indexRel));
5352 
5353  /* Copy the index column value out to caller's context */
5354  MemoryContextSwitchTo(oldcontext);
5355  *max = datumCopy(values[0], typByVal, typLen);
5356  MemoryContextSwitchTo(tmpcontext);
5357  }
5358  else
5359  have_data = false;
5360 
5361  index_endscan(index_scan);
5362  }
5363 
5364  /* Clean everything up */
5366 
5367  index_close(indexRel, AccessShareLock);
5368  heap_close(heapRel, NoLock);
5369 
5370  MemoryContextSwitchTo(oldcontext);
5371  FreeExecutorState(estate);
5372 
5373  /* And we're done */
5374  break;
5375  }
5376  }
5377 
5378  return have_data;
5379 }
5380 
5381 /*
5382  * find_join_input_rel
5383  * Look up the input relation for a join.
5384  *
5385  * We assume that the input relation's RelOptInfo must have been constructed
5386  * already.
5387  */
5388 static RelOptInfo *
5390 {
5391  RelOptInfo *rel = NULL;
5392 
5393  switch (bms_membership(relids))
5394  {
5395  case BMS_EMPTY_SET:
5396  /* should not happen */
5397  break;
5398  case BMS_SINGLETON:
5399  rel = find_base_rel(root, bms_singleton_member(relids));
5400  break;
5401  case BMS_MULTIPLE:
5402  rel = find_join_rel(root, relids);
5403  break;
5404  }
5405 
5406  if (rel == NULL)
5407  elog(ERROR, "could not find RelOptInfo for given relids");
5408 
5409  return rel;
5410 }
5411 
5412 
5413 /*-------------------------------------------------------------------------
5414  *
5415  * Pattern analysis functions
5416  *
5417  * These routines support analysis of LIKE and regular-expression patterns
5418  * by the planner/optimizer. It's important that they agree with the
5419  * regular-expression code in backend/regex/ and the LIKE code in
5420  * backend/utils/adt/like.c. Also, the computation of the fixed prefix
5421  * must be conservative: if we report a string longer than the true fixed
5422  * prefix, the query may produce actually wrong answers, rather than just
5423  * getting a bad selectivity estimate!
5424  *
5425  * Note that the prefix-analysis functions are called from
5426  * backend/optimizer/path/indxpath.c as well as from routines in this file.
5427  *
5428  *-------------------------------------------------------------------------
5429  */
5430 
5431 /*
5432  * Check whether char is a letter (and, hence, subject to case-folding)
5433  *
5434  * In multibyte character sets or with ICU, we can't use isalpha, and it does not seem
5435  * worth trying to convert to wchar_t to use iswalpha. Instead, just assume
5436  * any multibyte char is potentially case-varying.
5437  */
5438 static int
5439 pattern_char_isalpha(char c, bool is_multibyte,
5440  pg_locale_t locale, bool locale_is_c)
5441 {
5442  if (locale_is_c)
5443  return (c >= 'A' && c <= 'Z') || (c >= 'a' && c <= 'z');
5444  else if (is_multibyte && IS_HIGHBIT_SET(c))
5445  return true;
5446  else if (locale && locale->provider == COLLPROVIDER_ICU)
5447  return IS_HIGHBIT_SET(c) ? true : false;
5448 #ifdef HAVE_LOCALE_T
5449  else if (locale && locale->provider == COLLPROVIDER_LIBC)
5450  return isalpha_l((unsigned char) c, locale->info.lt);
5451 #endif
5452  else
5453  return isalpha((unsigned char) c);
5454 }
5455 
5456 /*
5457  * Extract the fixed prefix, if any, for a pattern.
5458  *
5459  * *prefix is set to a palloc'd prefix string (in the form of a Const node),
5460  * or to NULL if no fixed prefix exists for the pattern.
5461  * If rest_selec is not NULL, *rest_selec is set to an estimate of the
5462  * selectivity of the remainder of the pattern (without any fixed prefix).
5463  * The prefix Const has the same type (TEXT or BYTEA) as the input pattern.
5464  *
5465  * The return value distinguishes no fixed prefix, a partial prefix,
5466  * or an exact-match-only pattern.
5467  */
5468 
5469 static Pattern_Prefix_Status
5470 like_fixed_prefix(Const *patt_const, bool case_insensitive, Oid collation,
5471  Const **prefix_const, Selectivity *rest_selec)
5472 {
5473  char *match;
5474  char *patt;
5475  int pattlen;
5476  Oid typeid = patt_const->consttype;
5477  int pos,
5478  match_pos;
5479  bool is_multibyte = (pg_database_encoding_max_length() > 1);
5480  pg_locale_t locale = 0;
5481  bool locale_is_c = false;
5482 
5483  /* the right-hand const is type text or bytea */
5484  Assert(typeid == BYTEAOID || typeid == TEXTOID);
5485 
5486  if (case_insensitive)
5487  {
5488  if (typeid == BYTEAOID)
5489  ereport(ERROR,
5490  (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5491  errmsg("case insensitive matching not supported on type bytea")));
5492 
5493  /* If case-insensitive, we need locale info */
5494  if (lc_ctype_is_c(collation))
5495  locale_is_c = true;
5496  else if (collation != DEFAULT_COLLATION_OID)
5497  {
5498  if (!OidIsValid(collation))
5499  {
5500  /*
5501  * This typically means that the parser could not resolve a
5502  * conflict of implicit collations, so report it that way.
5503  */
5504  ereport(ERROR,
5505  (errcode(ERRCODE_INDETERMINATE_COLLATION),
5506  errmsg("could not determine which collation to use for ILIKE"),
5507  errhint("Use the COLLATE clause to set the collation explicitly.")));
5508  }
5509  locale = pg_newlocale_from_collation(collation);
5510  }
5511  }
5512 
5513  if (typeid != BYTEAOID)
5514  {
5515  patt = TextDatumGetCString(patt_const->constvalue);
5516  pattlen = strlen(patt);
5517  }
5518  else
5519  {
5520  bytea *bstr = DatumGetByteaPP(patt_const->constvalue);
5521 
5522  pattlen = VARSIZE_ANY_EXHDR(bstr);
5523  patt = (char *) palloc(pattlen);
5524  memcpy(patt, VARDATA_ANY(bstr), pattlen);
5525  Assert((Pointer) bstr == DatumGetPointer(patt_const->constvalue));
5526  }
5527 
5528  match = palloc(pattlen + 1);
5529  match_pos = 0;
5530  for (pos = 0; pos < pattlen; pos++)
5531  {
5532  /* % and _ are wildcard characters in LIKE */
5533  if (patt[pos] == '%' ||
5534  patt[pos] == '_')
5535  break;
5536 
5537  /* Backslash escapes the next character */
5538  if (patt[pos] == '\\')
5539  {
5540  pos++;
5541  if (pos >= pattlen)
5542  break;
5543  }
5544 
5545  /* Stop if case-varying character (it's sort of a wildcard) */
5546  if (case_insensitive &&
5547  pattern_char_isalpha(patt[pos], is_multibyte, locale, locale_is_c))
5548  break;
5549 
5550  match[match_pos++] = patt[pos];
5551  }
5552 
5553  match[match_pos] = '\0';
5554 
5555  if (typeid != BYTEAOID)
5556  *prefix_const = string_to_const(match, typeid);
5557  else
5558  *prefix_const = string_to_bytea_const(match, match_pos);
5559 
5560  if (rest_selec != NULL)
5561  *rest_selec = like_selectivity(&patt[pos], pattlen - pos,
5562  case_insensitive);
5563 
5564  pfree(patt);
5565  pfree(match);
5566 
5567  /* in LIKE, an empty pattern is an exact match! */
5568  if (pos == pattlen)
5569  return Pattern_Prefix_Exact; /* reached end of pattern, so exact */
5570 
5571  if (match_pos > 0)
5572  return Pattern_Prefix_Partial;
5573 
5574  return Pattern_Prefix_None;
5575 }
5576 
5577 static Pattern_Prefix_Status
5578 regex_fixed_prefix(Const *patt_const, bool case_insensitive, Oid collation,
5579  Const **prefix_const, Selectivity *rest_selec)
5580 {
5581  Oid typeid = patt_const->consttype;
5582  char *prefix;
5583  bool exact;
5584 
5585  /*
5586  * Should be unnecessary, there are no bytea regex operators defined. As
5587  * such, it should be noted that the rest of this function has *not* been
5588  * made safe for binary (possibly NULL containing) strings.
5589  */
5590  if (typeid == BYTEAOID)
5591  ereport(ERROR,
5592  (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5593  errmsg("regular-expression matching not supported on type bytea")));
5594 
5595  /* Use the regexp machinery to extract the prefix, if any */
5596  prefix = regexp_fixed_prefix(DatumGetTextPP(patt_const->constvalue),
5597  case_insensitive, collation,
5598  &exact);
5599 
5600  if (prefix == NULL)
5601  {
5602  *prefix_const = NULL;
5603 
5604  if (rest_selec != NULL)
5605  {
5606  char *patt = TextDatumGetCString(patt_const->constvalue);
5607 
5608  *rest_selec = regex_selectivity(patt, strlen(patt),
5609  case_insensitive,
5610  0);
5611  pfree(patt);
5612  }
5613 
5614  return Pattern_Prefix_None;
5615  }
5616 
5617  *prefix_const = string_to_const(prefix, typeid);
5618 
5619  if (rest_selec != NULL)
5620  {
5621  if (exact)
5622  {
5623  /* Exact match, so there's no additional selectivity */
5624  *rest_selec = 1.0;
5625  }
5626  else
5627  {
5628  char *patt = TextDatumGetCString(patt_const->constvalue);
5629 
5630  *rest_selec = regex_selectivity(patt, strlen(patt),
5631  case_insensitive,
5632  strlen(prefix));
5633  pfree(patt);
5634  }
5635  }
5636 
5637  pfree(prefix);
5638 
5639  if (exact)
5640  return Pattern_Prefix_Exact; /* pattern specifies exact match */
5641  else
5642  return Pattern_Prefix_Partial;
5643 }
5644 
5646 pattern_fixed_prefix(Const *patt, Pattern_Type ptype, Oid collation,
5647  Const **prefix, Selectivity *rest_selec)
5648 {
5650 
5651  switch (ptype)
5652  {
5653  case Pattern_Type_Like:
5654  result = like_fixed_prefix(patt, false, collation,
5655  prefix, rest_selec);
5656  break;
5657  case Pattern_Type_Like_IC:
5658  result = like_fixed_prefix(patt, true, collation,
5659  prefix, rest_selec);
5660  break;
5661  case Pattern_Type_Regex:
5662  result = regex_fixed_prefix(patt, false, collation,
5663  prefix, rest_selec);
5664  break;
5665  case Pattern_Type_Regex_IC:
5666  result = regex_fixed_prefix(patt, true, collation,
5667  prefix, rest_selec);
5668  break;
5669  default:
5670  elog(ERROR, "unrecognized ptype: %d", (int) ptype);
5671  result = Pattern_Prefix_None; /* keep compiler quiet */
5672  break;
5673  }
5674  return result;
5675 }
5676 
5677 /*
5678  * Estimate the selectivity of a fixed prefix for a pattern match.
5679  *
5680  * A fixed prefix "foo" is estimated as the selectivity of the expression
5681  * "variable >= 'foo' AND variable < 'fop'" (see also indxpath.c).
5682  *
5683  * The selectivity estimate is with respect to the portion of the column
5684  * population represented by the histogram --- the caller must fold this
5685  * together with info about MCVs and NULLs.
5686  *
5687  * We use the >= and < operators from the specified btree opfamily to do the
5688  * estimation. The given variable and Const must be of the associated
5689  * datatype.
5690  *
5691  * XXX Note: we make use of the upper bound to estimate operator selectivity
5692  * even if the locale is such that we cannot rely on the upper-bound string.
5693  * The selectivity only needs to be approximately right anyway, so it seems
5694  * more useful to use the upper-bound code than not.
5695  */
5696 static Selectivity
5698  Oid vartype, Oid opfamily, Const *prefixcon)
5699 {
5700  Selectivity prefixsel;
5701  Oid cmpopr;
5702  FmgrInfo opproc;
5703  Const *greaterstrcon;
5704  Selectivity eq_sel;
5705 
5706  cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5708  if (cmpopr == InvalidOid)
5709  elog(ERROR, "no >= operator for opfamily %u", opfamily);
5710  fmgr_info(get_opcode(cmpopr), &opproc);
5711 
5712  prefixsel = ineq_histogram_selectivity(root, vardata, &opproc, true,
5713  prefixcon->constvalue,
5714  prefixcon->consttype);
5715 
5716  if (prefixsel < 0.0)
5717  {
5718  /* No histogram is present ... return a suitable default estimate */
5719  return DEFAULT_MATCH_SEL;
5720  }
5721 
5722  /*-------
5723  * If we can create a string larger than the prefix, say
5724  * "x < greaterstr".
5725  *-------
5726  */
5727  cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5729  if (cmpopr == InvalidOid)
5730  elog(ERROR, "no < operator for opfamily %u", opfamily);
5731  fmgr_info(get_opcode(cmpopr), &opproc);
5732  greaterstrcon = make_greater_string(prefixcon, &opproc,
5734  if (greaterstrcon)
5735  {
5736  Selectivity topsel;
5737 
5738  topsel = ineq_histogram_selectivity(root, vardata, &opproc, false,
5739  greaterstrcon->constvalue,
5740  greaterstrcon->consttype);
5741 
5742  /* ineq_histogram_selectivity worked before, it shouldn't fail now */
5743  Assert(topsel >= 0.0);
5744 
5745  /*
5746  * Merge the two selectivities in the same way as for a range query
5747  * (see clauselist_selectivity()). Note that we don't need to worry
5748  * about double-exclusion of nulls, since ineq_histogram_selectivity
5749  * doesn't count those anyway.
5750  */
5751  prefixsel = topsel + prefixsel - 1.0;
5752  }
5753 
5754  /*
5755  * If the prefix is long then the two bounding values might be too close
5756  * together for the histogram to distinguish them usefully, resulting in a
5757  * zero estimate (plus or minus roundoff error). To avoid returning a
5758  * ridiculously small estimate, compute the estimated selectivity for
5759  * "variable = 'foo'", and clamp to that. (Obviously, the resultant
5760  * estimate should be at least that.)
5761  *
5762  * We apply this even if we couldn't make a greater string. That case
5763  * suggests that the prefix is near the maximum possible, and thus
5764  * probably off the end of the histogram, and thus we probably got a very
5765  * small estimate from the >= condition; so we still need to clamp.
5766  */
5767  cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5769  if (cmpopr == InvalidOid)
5770  elog(ERROR, "no = operator for opfamily %u", opfamily);
5771  eq_sel = var_eq_const(vardata, cmpopr, prefixcon->constvalue,
5772  false, true);
5773 
5774  prefixsel = Max(prefixsel, eq_sel);
5775 
5776  return prefixsel;
5777 }
5778 
5779 
5780 /*
5781  * Estimate the selectivity of a pattern of the specified type.
5782  * Note that any fixed prefix of the pattern will have been removed already,
5783  * so actually we may be looking at just a fragment of the pattern.
5784  *
5785  * For now, we use a very simplistic approach: fixed characters reduce the
5786  * selectivity a good deal, character ranges reduce it a little,
5787  * wildcards (such as % for LIKE or .* for regex) increase it.
5788  */
5789 
5790 #define FIXED_CHAR_SEL 0.20 /* about 1/5 */
5791 #define CHAR_RANGE_SEL 0.25
5792 #define ANY_CHAR_SEL 0.9 /* not 1, since it won't match end-of-string */
5793 #define FULL_WILDCARD_SEL 5.0
5794 #define PARTIAL_WILDCARD_SEL 2.0
5795 
5796 static Selectivity
5797 like_selectivity(const char *patt, int pattlen, bool case_insensitive)
5798 {
5799  Selectivity sel = 1.0;
5800  int pos;
5801 
5802  /* Skip any leading wildcard; it's already factored into initial sel */
5803  for (pos = 0; pos < pattlen; pos++)
5804  {
5805  if (patt[pos] != '%' && patt[pos] != '_')
5806  break;
5807  }
5808 
5809  for (; pos < pattlen; pos++)
5810  {
5811  /* % and _ are wildcard characters in LIKE */
5812  if (patt[pos] == '%')
5813  sel *= FULL_WILDCARD_SEL;
5814  else if (patt[pos] == '_')
5815  sel *= ANY_CHAR_SEL;
5816  else if (patt[pos] == '\\')
5817  {
5818  /* Backslash quotes the next character */
5819  pos++;
5820  if (pos >= pattlen)
5821  break;
5822  sel *= FIXED_CHAR_SEL;
5823  }
5824  else
5825  sel *= FIXED_CHAR_SEL;
5826  }
5827  /* Could get sel > 1 if multiple wildcards */
5828  if (sel > 1.0)
5829  sel = 1.0;
5830  return sel;
5831 }
5832 
5833 static Selectivity
5834 regex_selectivity_sub(const char *patt, int pattlen, bool case_insensitive)
5835 {
5836  Selectivity sel = 1.0;
5837  int paren_depth = 0;
5838  int paren_pos = 0; /* dummy init to keep compiler quiet */
5839  int pos;
5840 
5841  for (pos = 0; pos < pattlen; pos++)
5842  {
5843  if (patt[pos] == '(')
5844  {
5845  if (paren_depth == 0)
5846  paren_pos = pos; /* remember start of parenthesized item */
5847  paren_depth++;
5848  }
5849  else if (patt[pos] == ')' && paren_depth > 0)
5850  {
5851  paren_depth--;
5852  if (paren_depth == 0)
5853  sel *= regex_selectivity_sub(patt + (paren_pos + 1),
5854  pos - (paren_pos + 1),
5855  case_insensitive);
5856  }
5857  else if (patt[pos] == '|' && paren_depth == 0)
5858  {
5859  /*
5860  * If unquoted | is present at paren level 0 in pattern, we have
5861  * multiple alternatives; sum their probabilities.
5862  */
5863  sel += regex_selectivity_sub(patt + (pos + 1),
5864  pattlen - (pos + 1),
5865  case_insensitive);
5866  break; /* rest of pattern is now processed */
5867  }
5868  else if (patt[pos] == '[')
5869  {
5870  bool negclass = false;
5871 
5872  if (patt[++pos] == '^')
5873  {
5874  negclass = true;
5875  pos++;
5876  }
5877  if (patt[pos] == ']') /* ']' at start of class is not
5878  * special */
5879  pos++;
5880  while (pos < pattlen && patt[pos] != ']')
5881  pos++;
5882  if (paren_depth == 0)
5883  sel *= (negclass ? (1.0 - CHAR_RANGE_SEL) : CHAR_RANGE_SEL);
5884  }
5885  else if (patt[pos] == '.')
5886  {
5887  if (paren_depth == 0)
5888  sel *= ANY_CHAR_SEL;
5889  }
5890  else if (patt[pos] == '*' ||
5891  patt[pos] == '?' ||
5892  patt[pos] == '+')
5893  {
5894  /* Ought to be smarter about quantifiers... */
5895  if (paren_depth == 0)
5896  sel *= PARTIAL_WILDCARD_SEL;
5897  }
5898  else if (patt[pos] == '{')
5899  {
5900  while (pos < pattlen && patt[pos] != '}')
5901  pos++;
5902  if (paren_depth == 0)
5903  sel *= PARTIAL_WILDCARD_SEL;
5904  }
5905  else if (patt[pos] == '\\')
5906  {
5907  /* backslash quotes the next character */
5908  pos++;
5909  if (pos >= pattlen)
5910  break;
5911  if (paren_depth == 0)
5912  sel *= FIXED_CHAR_SEL;
5913  }
5914  else
5915  {
5916  if (paren_depth == 0)
5917  sel *= FIXED_CHAR_SEL;
5918  }
5919  }
5920  /* Could get sel > 1 if multiple wildcards */
5921  if (sel > 1.0)
5922  sel = 1.0;
5923  return sel;
5924 }
5925 
5926 static Selectivity
5927 regex_selectivity(const char *patt, int pattlen, bool case_insensitive,
5928  int fixed_prefix_len)
5929 {
5930  Selectivity sel;
5931 
5932  /* If patt doesn't end with $, consider it to have a trailing wildcard */
5933  if (pattlen > 0 && patt[pattlen - 1] == '$' &&
5934  (pattlen == 1 || patt[pattlen - 2] != '\\'))
5935  {
5936  /* has trailing $ */
5937  sel = regex_selectivity_sub(patt, pattlen - 1, case_insensitive);
5938  }
5939  else
5940  {
5941  /* no trailing $ */
5942  sel = regex_selectivity_sub(patt, pattlen, case_insensitive);
5943  sel *= FULL_WILDCARD_SEL;
5944  }
5945 
5946  /* If there's a fixed prefix, discount its selectivity */
5947  if (fixed_prefix_len > 0)
5948  sel /= pow(FIXED_CHAR_SEL, fixed_prefix_len);
5949 
5950  /* Make sure result stays in range */
5951  CLAMP_PROBABILITY(sel);
5952  return sel;
5953 }
5954 
5955 
5956 /*
5957  * For bytea, the increment function need only increment the current byte
5958  * (there are no multibyte characters to worry about).
5959  */
5960 static bool
5961 byte_increment(unsigned char *ptr, int len)
5962 {
5963  if (*ptr >= 255)
5964  return false;
5965  (*ptr)++;
5966  return true;
5967 }
5968 
5969 /*
5970  * Try to generate a string greater than the given string or any
5971  * string it is a prefix of. If successful, return a palloc'd string
5972  * in the form of a Const node; else return NULL.
5973  *
5974  * The caller must provide the appropriate "less than" comparison function
5975  * for testing the strings, along with the collation to use.
5976  *
5977  * The key requirement here is that given a prefix string, say "foo",
5978  * we must be able to generate another string "fop" that is greater than
5979  * all strings "foobar" starting with "foo". We can test that we have
5980  * generated a string greater than the prefix string, but in non-C collations
5981  * that is not a bulletproof guarantee that an extension of the string might
5982  * not sort after it; an example is that "foo " is less than "foo!", but it
5983  * is not clear that a "dictionary" sort ordering will consider "foo!" less
5984  * than "foo bar". CAUTION: Therefore, this function should be used only for
5985  * estimation purposes when working in a non-C collation.
5986  *
5987  * To try to catch most cases where an extended string might otherwise sort
5988  * before the result value, we determine which of the strings "Z", "z", "y",
5989  * and "9" is seen as largest by the collation, and append that to the given
5990  * prefix before trying to find a string that compares as larger.
5991  *
5992  * To search for a greater string, we repeatedly "increment" the rightmost
5993  * character, using an encoding-specific character incrementer function.
5994  * When it's no longer possible to increment the last character, we truncate
5995  * off that character and start incrementing the next-to-rightmost.
5996  * For example, if "z" were the last character in the sort order, then we
5997  * could produce "foo" as a string greater than "fonz".
5998  *
5999  * This could be rather slow in the worst case, but in most cases we
6000  * won't have to try more than one or two strings before succeeding.
6001  *
6002  * Note that it's important for the character incrementer not to be too anal
6003  * about producing every possible character code, since in some cases the only
6004  * way to get a larger string is to increment a previous character position.
6005  * So we don't want to spend too much time trying every possible character
6006  * code at the last position. A good rule of thumb is to be sure that we
6007  * don't try more than 256*K values for a K-byte character (and definitely
6008  * not 256^K, which is what an exhaustive search would approach).
6009  */
6010 Const *
6011 make_greater_string(const Const *str_const, FmgrInfo *ltproc, Oid collation)
6012 {
6013  Oid datatype = str_const->consttype;
6014  char *workstr;
6015  int len;
6016  Datum cmpstr;
6017  text *cmptxt = NULL;
6018  mbcharacter_incrementer charinc;
6019 
6020  /*
6021  * Get a modifiable copy of the prefix string in C-string format, and set
6022  * up the string we will compare to as a Datum. In C locale this can just
6023  * be the given prefix string, otherwise we need to add a suffix. Types
6024  * NAME and BYTEA sort bytewise so they don't need a suffix either.
6025  */
6026  if (datatype == NAMEOID)
6027  {
6029  str_const->constvalue));
6030  len = strlen(workstr);
6031  cmpstr = str_const->constvalue;
6032  }
6033  else if (datatype == BYTEAOID)
6034  {
6035  bytea *bstr = DatumGetByteaPP(str_const->constvalue);
6036 
6037  len = VARSIZE_ANY_EXHDR(bstr);
6038  workstr = (char *) palloc(len);
6039  memcpy(workstr, VARDATA_ANY(bstr), len);
6040  Assert((Pointer) bstr == DatumGetPointer(str_const->constvalue));
6041  cmpstr = str_const->constvalue;
6042  }
6043  else
6044  {
6045  workstr = TextDatumGetCString(str_const->constvalue);
6046  len = strlen(workstr);
6047  if (lc_collate_is_c(collation) || len == 0)
6048  cmpstr = str_const->constvalue;
6049  else
6050  {
6051  /* If first time through, determine the suffix to use */
6052  static char suffixchar = 0;
6053  static Oid suffixcollation = 0;
6054 
6055  if (!suffixchar || suffixcollation != collation)
6056  {
6057  char *best;
6058 
6059  best = "Z";
6060  if (varstr_cmp(best, 1, "z", 1, collation) < 0)
6061  best = "z";
6062  if (varstr_cmp(best, 1, "y", 1, collation) < 0)
6063  best = "y";
6064  if (varstr_cmp(best, 1, "9", 1, collation) < 0)
6065  best = "9";
6066  suffixchar = *best;
6067  suffixcollation = collation;
6068  }
6069 
6070  /* And build the string to compare to */
6071  cmptxt = (text *) palloc(VARHDRSZ + len + 1);
6072  SET_VARSIZE(cmptxt, VARHDRSZ + len + 1);
6073  memcpy(VARDATA(cmptxt), workstr, len);
6074  *(VARDATA(cmptxt) + len) = suffixchar;
6075  cmpstr = PointerGetDatum(cmptxt);
6076  }
6077  }
6078 
6079  /* Select appropriate character-incrementer function */
6080  if (datatype == BYTEAOID)
6081  charinc = byte_increment;
6082  else
6084 
6085  /* And search ... */
6086  while (len > 0)
6087  {
6088  int charlen;
6089  unsigned char *lastchar;
6090 
6091  /* Identify the last character --- for bytea, just the last byte */
6092  if (datatype ==