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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 "miscadmin.h"
119 #include "nodes/makefuncs.h"
120 #include "nodes/nodeFuncs.h"
121 #include "optimizer/clauses.h"
122 #include "optimizer/cost.h"
123 #include "optimizer/pathnode.h"
124 #include "optimizer/paths.h"
125 #include "optimizer/plancat.h"
126 #include "optimizer/predtest.h"
127 #include "optimizer/restrictinfo.h"
128 #include "optimizer/var.h"
129 #include "parser/parse_clause.h"
130 #include "parser/parse_coerce.h"
131 #include "parser/parsetree.h"
132 #include "statistics/statistics.h"
133 #include "utils/acl.h"
134 #include "utils/builtins.h"
135 #include "utils/bytea.h"
136 #include "utils/date.h"
137 #include "utils/datum.h"
138 #include "utils/fmgroids.h"
139 #include "utils/index_selfuncs.h"
140 #include "utils/lsyscache.h"
141 #include "utils/nabstime.h"
142 #include "utils/pg_locale.h"
143 #include "utils/rel.h"
144 #include "utils/selfuncs.h"
145 #include "utils/spccache.h"
146 #include "utils/syscache.h"
147 #include "utils/timestamp.h"
148 #include "utils/tqual.h"
149 #include "utils/typcache.h"
150 #include "utils/varlena.h"
151 
152 
153 /* Hooks for plugins to get control when we ask for stats */
156 
157 static double var_eq_const(VariableStatData *vardata, Oid operator,
158  Datum constval, bool constisnull,
159  bool varonleft);
160 static double var_eq_non_const(VariableStatData *vardata, Oid operator,
161  Node *other,
162  bool varonleft);
163 static double ineq_histogram_selectivity(PlannerInfo *root,
164  VariableStatData *vardata,
165  FmgrInfo *opproc, bool isgt,
166  Datum constval, Oid consttype);
167 static double eqjoinsel_inner(Oid operator,
168  VariableStatData *vardata1, VariableStatData *vardata2);
169 static double eqjoinsel_semi(Oid operator,
170  VariableStatData *vardata1, VariableStatData *vardata2,
171  RelOptInfo *inner_rel);
173  RelOptInfo *rel, List **varinfos, double *ndistinct);
174 static bool convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
175  Datum lobound, Datum hibound, Oid boundstypid,
176  double *scaledlobound, double *scaledhibound);
177 static double convert_numeric_to_scalar(Datum value, Oid typid);
178 static void convert_string_to_scalar(char *value,
179  double *scaledvalue,
180  char *lobound,
181  double *scaledlobound,
182  char *hibound,
183  double *scaledhibound);
185  double *scaledvalue,
186  Datum lobound,
187  double *scaledlobound,
188  Datum hibound,
189  double *scaledhibound);
190 static double convert_one_string_to_scalar(char *value,
191  int rangelo, int rangehi);
192 static double convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
193  int rangelo, int rangehi);
194 static char *convert_string_datum(Datum value, Oid typid);
195 static double convert_timevalue_to_scalar(Datum value, Oid typid);
196 static void examine_simple_variable(PlannerInfo *root, Var *var,
197  VariableStatData *vardata);
198 static bool get_variable_range(PlannerInfo *root, VariableStatData *vardata,
199  Oid sortop, Datum *min, Datum *max);
200 static bool get_actual_variable_range(PlannerInfo *root,
201  VariableStatData *vardata,
202  Oid sortop,
203  Datum *min, Datum *max);
204 static RelOptInfo *find_join_input_rel(PlannerInfo *root, Relids relids);
206  VariableStatData *vardata,
207  Oid vartype, Oid opfamily, Const *prefixcon);
208 static Selectivity like_selectivity(const char *patt, int pattlen,
209  bool case_insensitive);
210 static Selectivity regex_selectivity(const char *patt, int pattlen,
211  bool case_insensitive,
212  int fixed_prefix_len);
213 static Datum string_to_datum(const char *str, Oid datatype);
214 static Const *string_to_const(const char *str, Oid datatype);
215 static Const *string_to_bytea_const(const char *str, size_t str_len);
216 static List *add_predicate_to_quals(IndexOptInfo *index, List *indexQuals);
217 
218 
219 /*
220  * eqsel - Selectivity of "=" for any data types.
221  *
222  * Note: this routine is also used to estimate selectivity for some
223  * operators that are not "=" but have comparable selectivity behavior,
224  * such as "~=" (geometric approximate-match). Even for "=", we must
225  * keep in mind that the left and right datatypes may differ.
226  */
227 Datum
229 {
231  Oid operator = PG_GETARG_OID(1);
232  List *args = (List *) PG_GETARG_POINTER(2);
233  int varRelid = PG_GETARG_INT32(3);
234  VariableStatData vardata;
235  Node *other;
236  bool varonleft;
237  double selec;
238 
239  /*
240  * If expression is not variable = something or something = variable, then
241  * punt and return a default estimate.
242  */
243  if (!get_restriction_variable(root, args, varRelid,
244  &vardata, &other, &varonleft))
246 
247  /*
248  * We can do a lot better if the something is a constant. (Note: the
249  * Const might result from estimation rather than being a simple constant
250  * in the query.)
251  */
252  if (IsA(other, Const))
253  selec = var_eq_const(&vardata, operator,
254  ((Const *) other)->constvalue,
255  ((Const *) other)->constisnull,
256  varonleft);
257  else
258  selec = var_eq_non_const(&vardata, operator, other,
259  varonleft);
260 
261  ReleaseVariableStats(vardata);
262 
263  PG_RETURN_FLOAT8((float8) selec);
264 }
265 
266 /*
267  * var_eq_const --- eqsel for var = const case
268  *
269  * This is split out so that some other estimation functions can use it.
270  */
271 static double
272 var_eq_const(VariableStatData *vardata, Oid operator,
273  Datum constval, bool constisnull,
274  bool varonleft)
275 {
276  double selec;
277  bool isdefault;
278  Oid opfuncoid;
279 
280  /*
281  * If the constant is NULL, assume operator is strict and return zero, ie,
282  * operator will never return TRUE.
283  */
284  if (constisnull)
285  return 0.0;
286 
287  /*
288  * If we matched the var to a unique index or DISTINCT clause, assume
289  * there is exactly one match regardless of anything else. (This is
290  * slightly bogus, since the index or clause's equality operator might be
291  * different from ours, but it's much more likely to be right than
292  * ignoring the information.)
293  */
294  if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
295  return 1.0 / vardata->rel->tuples;
296 
297  if (HeapTupleIsValid(vardata->statsTuple) &&
299  (opfuncoid = get_opcode(operator))))
300  {
301  Form_pg_statistic stats;
302  AttStatsSlot sslot;
303  bool match = false;
304  int i;
305 
306  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
307 
308  /*
309  * Is the constant "=" to any of the column's most common values?
310  * (Although the given operator may not really be "=", we will assume
311  * that seeing whether it returns TRUE is an appropriate test. If you
312  * don't like this, maybe you shouldn't be using eqsel for your
313  * operator...)
314  */
315  if (get_attstatsslot(&sslot, vardata->statsTuple,
318  {
319  FmgrInfo eqproc;
320 
321  fmgr_info(opfuncoid, &eqproc);
322 
323  for (i = 0; i < sslot.nvalues; i++)
324  {
325  /* be careful to apply operator right way 'round */
326  if (varonleft)
327  match = DatumGetBool(FunctionCall2Coll(&eqproc,
329  sslot.values[i],
330  constval));
331  else
332  match = DatumGetBool(FunctionCall2Coll(&eqproc,
334  constval,
335  sslot.values[i]));
336  if (match)
337  break;
338  }
339  }
340  else
341  {
342  /* no most-common-value info available */
343  i = 0; /* keep compiler quiet */
344  }
345 
346  if (match)
347  {
348  /*
349  * Constant is "=" to this common value. We know selectivity
350  * exactly (or as exactly as ANALYZE could calculate it, anyway).
351  */
352  selec = sslot.numbers[i];
353  }
354  else
355  {
356  /*
357  * Comparison is against a constant that is neither NULL nor any
358  * of the common values. Its selectivity cannot be more than
359  * this:
360  */
361  double sumcommon = 0.0;
362  double otherdistinct;
363 
364  for (i = 0; i < sslot.nnumbers; i++)
365  sumcommon += sslot.numbers[i];
366  selec = 1.0 - sumcommon - stats->stanullfrac;
367  CLAMP_PROBABILITY(selec);
368 
369  /*
370  * and in fact it's probably a good deal less. We approximate that
371  * all the not-common values share this remaining fraction
372  * equally, so we divide by the number of other distinct values.
373  */
374  otherdistinct = get_variable_numdistinct(vardata, &isdefault) -
375  sslot.nnumbers;
376  if (otherdistinct > 1)
377  selec /= otherdistinct;
378 
379  /*
380  * Another cross-check: selectivity shouldn't be estimated as more
381  * than the least common "most common value".
382  */
383  if (sslot.nnumbers > 0 && selec > sslot.numbers[sslot.nnumbers - 1])
384  selec = sslot.numbers[sslot.nnumbers - 1];
385  }
386 
387  free_attstatsslot(&sslot);
388  }
389  else
390  {
391  /*
392  * No ANALYZE stats available, so make a guess using estimated number
393  * of distinct values and assuming they are equally common. (The guess
394  * is unlikely to be very good, but we do know a few special cases.)
395  */
396  selec = 1.0 / get_variable_numdistinct(vardata, &isdefault);
397  }
398 
399  /* result should be in range, but make sure... */
400  CLAMP_PROBABILITY(selec);
401 
402  return selec;
403 }
404 
405 /*
406  * var_eq_non_const --- eqsel for var = something-other-than-const case
407  */
408 static double
410  Node *other,
411  bool varonleft)
412 {
413  double selec;
414  bool isdefault;
415 
416  /*
417  * If we matched the var to a unique index or DISTINCT clause, assume
418  * there is exactly one match regardless of anything else. (This is
419  * slightly bogus, since the index or clause's equality operator might be
420  * different from ours, but it's much more likely to be right than
421  * ignoring the information.)
422  */
423  if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
424  return 1.0 / vardata->rel->tuples;
425 
426  if (HeapTupleIsValid(vardata->statsTuple))
427  {
428  Form_pg_statistic stats;
429  double ndistinct;
430  AttStatsSlot sslot;
431 
432  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
433 
434  /*
435  * Search is for a value that we do not know a priori, but we will
436  * assume it is not NULL. Estimate the selectivity as non-null
437  * fraction divided by number of distinct values, so that we get a
438  * result averaged over all possible values whether common or
439  * uncommon. (Essentially, we are assuming that the not-yet-known
440  * comparison value is equally likely to be any of the possible
441  * values, regardless of their frequency in the table. Is that a good
442  * idea?)
443  */
444  selec = 1.0 - stats->stanullfrac;
445  ndistinct = get_variable_numdistinct(vardata, &isdefault);
446  if (ndistinct > 1)
447  selec /= ndistinct;
448 
449  /*
450  * Cross-check: selectivity should never be estimated as more than the
451  * most common value's.
452  */
453  if (get_attstatsslot(&sslot, vardata->statsTuple,
456  {
457  if (sslot.nnumbers > 0 && selec > sslot.numbers[0])
458  selec = sslot.numbers[0];
459  free_attstatsslot(&sslot);
460  }
461  }
462  else
463  {
464  /*
465  * No ANALYZE stats available, so make a guess using estimated number
466  * of distinct values and assuming they are equally common. (The guess
467  * is unlikely to be very good, but we do know a few special cases.)
468  */
469  selec = 1.0 / get_variable_numdistinct(vardata, &isdefault);
470  }
471 
472  /* result should be in range, but make sure... */
473  CLAMP_PROBABILITY(selec);
474 
475  return selec;
476 }
477 
478 /*
479  * neqsel - Selectivity of "!=" for any data types.
480  *
481  * This routine is also used for some operators that are not "!="
482  * but have comparable selectivity behavior. See above comments
483  * for eqsel().
484  */
485 Datum
487 {
489  Oid operator = PG_GETARG_OID(1);
490  List *args = (List *) PG_GETARG_POINTER(2);
491  int varRelid = PG_GETARG_INT32(3);
492  Oid eqop;
493  float8 result;
494 
495  /*
496  * We want 1 - eqsel() where the equality operator is the one associated
497  * with this != operator, that is, its negator.
498  */
499  eqop = get_negator(operator);
500  if (eqop)
501  {
503  PointerGetDatum(root),
504  ObjectIdGetDatum(eqop),
505  PointerGetDatum(args),
506  Int32GetDatum(varRelid)));
507  }
508  else
509  {
510  /* Use default selectivity (should we raise an error instead?) */
511  result = DEFAULT_EQ_SEL;
512  }
513  result = 1.0 - result;
514  PG_RETURN_FLOAT8(result);
515 }
516 
517 /*
518  * scalarineqsel - Selectivity of "<", "<=", ">", ">=" for scalars.
519  *
520  * This is the guts of both scalarltsel and scalargtsel. The caller has
521  * commuted the clause, if necessary, so that we can treat the variable as
522  * being on the left. The caller must also make sure that the other side
523  * of the clause is a non-null Const, and dissect same into a value and
524  * datatype.
525  *
526  * This routine works for any datatype (or pair of datatypes) known to
527  * convert_to_scalar(). If it is applied to some other datatype,
528  * it will return a default estimate.
529  */
530 static double
531 scalarineqsel(PlannerInfo *root, Oid operator, bool isgt,
532  VariableStatData *vardata, Datum constval, Oid consttype)
533 {
534  Form_pg_statistic stats;
535  FmgrInfo opproc;
536  double mcv_selec,
537  hist_selec,
538  sumcommon;
539  double selec;
540 
541  if (!HeapTupleIsValid(vardata->statsTuple))
542  {
543  /* no stats available, so default result */
544  return DEFAULT_INEQ_SEL;
545  }
546  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
547 
548  fmgr_info(get_opcode(operator), &opproc);
549 
550  /*
551  * If we have most-common-values info, add up the fractions of the MCV
552  * entries that satisfy MCV OP CONST. These fractions contribute directly
553  * to the result selectivity. Also add up the total fraction represented
554  * by MCV entries.
555  */
556  mcv_selec = mcv_selectivity(vardata, &opproc, constval, true,
557  &sumcommon);
558 
559  /*
560  * If there is a histogram, determine which bin the constant falls in, and
561  * compute the resulting contribution to selectivity.
562  */
563  hist_selec = ineq_histogram_selectivity(root, vardata, &opproc, isgt,
564  constval, consttype);
565 
566  /*
567  * Now merge the results from the MCV and histogram calculations,
568  * realizing that the histogram covers only the non-null values that are
569  * not listed in MCV.
570  */
571  selec = 1.0 - stats->stanullfrac - sumcommon;
572 
573  if (hist_selec >= 0.0)
574  selec *= hist_selec;
575  else
576  {
577  /*
578  * If no histogram but there are values not accounted for by MCV,
579  * arbitrarily assume half of them will match.
580  */
581  selec *= 0.5;
582  }
583 
584  selec += mcv_selec;
585 
586  /* result should be in range, but make sure... */
587  CLAMP_PROBABILITY(selec);
588 
589  return selec;
590 }
591 
592 /*
593  * mcv_selectivity - Examine the MCV list for selectivity estimates
594  *
595  * Determine the fraction of the variable's MCV population that satisfies
596  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft. Also
597  * compute the fraction of the total column population represented by the MCV
598  * list. This code will work for any boolean-returning predicate operator.
599  *
600  * The function result is the MCV selectivity, and the fraction of the
601  * total population is returned into *sumcommonp. Zeroes are returned
602  * if there is no MCV list.
603  */
604 double
606  Datum constval, bool varonleft,
607  double *sumcommonp)
608 {
609  double mcv_selec,
610  sumcommon;
611  AttStatsSlot sslot;
612  int i;
613 
614  mcv_selec = 0.0;
615  sumcommon = 0.0;
616 
617  if (HeapTupleIsValid(vardata->statsTuple) &&
618  statistic_proc_security_check(vardata, opproc->fn_oid) &&
619  get_attstatsslot(&sslot, vardata->statsTuple,
622  {
623  for (i = 0; i < sslot.nvalues; i++)
624  {
625  if (varonleft ?
628  sslot.values[i],
629  constval)) :
632  constval,
633  sslot.values[i])))
634  mcv_selec += sslot.numbers[i];
635  sumcommon += sslot.numbers[i];
636  }
637  free_attstatsslot(&sslot);
638  }
639 
640  *sumcommonp = sumcommon;
641  return mcv_selec;
642 }
643 
644 /*
645  * histogram_selectivity - Examine the histogram for selectivity estimates
646  *
647  * Determine the fraction of the variable's histogram entries that satisfy
648  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft.
649  *
650  * This code will work for any boolean-returning predicate operator, whether
651  * or not it has anything to do with the histogram sort operator. We are
652  * essentially using the histogram just as a representative sample. However,
653  * small histograms are unlikely to be all that representative, so the caller
654  * should be prepared to fall back on some other estimation approach when the
655  * histogram is missing or very small. It may also be prudent to combine this
656  * approach with another one when the histogram is small.
657  *
658  * If the actual histogram size is not at least min_hist_size, we won't bother
659  * to do the calculation at all. Also, if the n_skip parameter is > 0, we
660  * ignore the first and last n_skip histogram elements, on the grounds that
661  * they are outliers and hence not very representative. Typical values for
662  * these parameters are 10 and 1.
663  *
664  * The function result is the selectivity, or -1 if there is no histogram
665  * or it's smaller than min_hist_size.
666  *
667  * The output parameter *hist_size receives the actual histogram size,
668  * or zero if no histogram. Callers may use this number to decide how
669  * much faith to put in the function result.
670  *
671  * Note that the result disregards both the most-common-values (if any) and
672  * null entries. The caller is expected to combine this result with
673  * statistics for those portions of the column population. It may also be
674  * prudent to clamp the result range, ie, disbelieve exact 0 or 1 outputs.
675  */
676 double
678  Datum constval, bool varonleft,
679  int min_hist_size, int n_skip,
680  int *hist_size)
681 {
682  double result;
683  AttStatsSlot sslot;
684 
685  /* check sanity of parameters */
686  Assert(n_skip >= 0);
687  Assert(min_hist_size > 2 * n_skip);
688 
689  if (HeapTupleIsValid(vardata->statsTuple) &&
690  statistic_proc_security_check(vardata, opproc->fn_oid) &&
691  get_attstatsslot(&sslot, vardata->statsTuple,
694  {
695  *hist_size = sslot.nvalues;
696  if (sslot.nvalues >= min_hist_size)
697  {
698  int nmatch = 0;
699  int i;
700 
701  for (i = n_skip; i < sslot.nvalues - n_skip; i++)
702  {
703  if (varonleft ?
706  sslot.values[i],
707  constval)) :
710  constval,
711  sslot.values[i])))
712  nmatch++;
713  }
714  result = ((double) nmatch) / ((double) (sslot.nvalues - 2 * n_skip));
715  }
716  else
717  result = -1;
718  free_attstatsslot(&sslot);
719  }
720  else
721  {
722  *hist_size = 0;
723  result = -1;
724  }
725 
726  return result;
727 }
728 
729 /*
730  * ineq_histogram_selectivity - Examine the histogram for scalarineqsel
731  *
732  * Determine the fraction of the variable's histogram population that
733  * satisfies the inequality condition, ie, VAR < CONST or VAR > CONST.
734  *
735  * Returns -1 if there is no histogram (valid results will always be >= 0).
736  *
737  * Note that the result disregards both the most-common-values (if any) and
738  * null entries. The caller is expected to combine this result with
739  * statistics for those portions of the column population.
740  */
741 static double
743  VariableStatData *vardata,
744  FmgrInfo *opproc, bool isgt,
745  Datum constval, Oid consttype)
746 {
747  double hist_selec;
748  AttStatsSlot sslot;
749 
750  hist_selec = -1.0;
751 
752  /*
753  * Someday, ANALYZE might store more than one histogram per rel/att,
754  * corresponding to more than one possible sort ordering defined for the
755  * column type. However, to make that work we will need to figure out
756  * which staop to search for --- it's not necessarily the one we have at
757  * hand! (For example, we might have a '<=' operator rather than the '<'
758  * operator that will appear in staop.) For now, assume that whatever
759  * appears in pg_statistic is sorted the same way our operator sorts, or
760  * the reverse way if isgt is TRUE.
761  */
762  if (HeapTupleIsValid(vardata->statsTuple) &&
763  statistic_proc_security_check(vardata, opproc->fn_oid) &&
764  get_attstatsslot(&sslot, vardata->statsTuple,
767  {
768  if (sslot.nvalues > 1)
769  {
770  /*
771  * Use binary search to find proper location, ie, the first slot
772  * at which the comparison fails. (If the given operator isn't
773  * actually sort-compatible with the histogram, you'll get garbage
774  * results ... but probably not any more garbage-y than you would
775  * from the old linear search.)
776  *
777  * If the binary search accesses the first or last histogram
778  * entry, we try to replace that endpoint with the true column min
779  * or max as found by get_actual_variable_range(). This
780  * ameliorates misestimates when the min or max is moving as a
781  * result of changes since the last ANALYZE. Note that this could
782  * result in effectively including MCVs into the histogram that
783  * weren't there before, but we don't try to correct for that.
784  */
785  double histfrac;
786  int lobound = 0; /* first possible slot to search */
787  int hibound = sslot.nvalues; /* last+1 slot to search */
788  bool have_end = false;
789 
790  /*
791  * If there are only two histogram entries, we'll want up-to-date
792  * values for both. (If there are more than two, we need at most
793  * one of them to be updated, so we deal with that within the
794  * loop.)
795  */
796  if (sslot.nvalues == 2)
797  have_end = get_actual_variable_range(root,
798  vardata,
799  sslot.staop,
800  &sslot.values[0],
801  &sslot.values[1]);
802 
803  while (lobound < hibound)
804  {
805  int probe = (lobound + hibound) / 2;
806  bool ltcmp;
807 
808  /*
809  * If we find ourselves about to compare to the first or last
810  * histogram entry, first try to replace it with the actual
811  * current min or max (unless we already did so above).
812  */
813  if (probe == 0 && sslot.nvalues > 2)
814  have_end = get_actual_variable_range(root,
815  vardata,
816  sslot.staop,
817  &sslot.values[0],
818  NULL);
819  else if (probe == sslot.nvalues - 1 && sslot.nvalues > 2)
820  have_end = get_actual_variable_range(root,
821  vardata,
822  sslot.staop,
823  NULL,
824  &sslot.values[probe]);
825 
826  ltcmp = DatumGetBool(FunctionCall2Coll(opproc,
828  sslot.values[probe],
829  constval));
830  if (isgt)
831  ltcmp = !ltcmp;
832  if (ltcmp)
833  lobound = probe + 1;
834  else
835  hibound = probe;
836  }
837 
838  if (lobound <= 0)
839  {
840  /* Constant is below lower histogram boundary. */
841  histfrac = 0.0;
842  }
843  else if (lobound >= sslot.nvalues)
844  {
845  /* Constant is above upper histogram boundary. */
846  histfrac = 1.0;
847  }
848  else
849  {
850  int i = lobound;
851  double val,
852  high,
853  low;
854  double binfrac;
855 
856  /*
857  * We have values[i-1] <= constant <= values[i].
858  *
859  * Convert the constant and the two nearest bin boundary
860  * values to a uniform comparison scale, and do a linear
861  * interpolation within this bin.
862  */
863  if (convert_to_scalar(constval, consttype, &val,
864  sslot.values[i - 1], sslot.values[i],
865  vardata->vartype,
866  &low, &high))
867  {
868  if (high <= low)
869  {
870  /* cope if bin boundaries appear identical */
871  binfrac = 0.5;
872  }
873  else if (val <= low)
874  binfrac = 0.0;
875  else if (val >= high)
876  binfrac = 1.0;
877  else
878  {
879  binfrac = (val - low) / (high - low);
880 
881  /*
882  * Watch out for the possibility that we got a NaN or
883  * Infinity from the division. This can happen
884  * despite the previous checks, if for example "low"
885  * is -Infinity.
886  */
887  if (isnan(binfrac) ||
888  binfrac < 0.0 || binfrac > 1.0)
889  binfrac = 0.5;
890  }
891  }
892  else
893  {
894  /*
895  * Ideally we'd produce an error here, on the grounds that
896  * the given operator shouldn't have scalarXXsel
897  * registered as its selectivity func unless we can deal
898  * with its operand types. But currently, all manner of
899  * stuff is invoking scalarXXsel, so give a default
900  * estimate until that can be fixed.
901  */
902  binfrac = 0.5;
903  }
904 
905  /*
906  * Now, compute the overall selectivity across the values
907  * represented by the histogram. We have i-1 full bins and
908  * binfrac partial bin below the constant.
909  */
910  histfrac = (double) (i - 1) + binfrac;
911  histfrac /= (double) (sslot.nvalues - 1);
912  }
913 
914  /*
915  * Now histfrac = fraction of histogram entries below the
916  * constant.
917  *
918  * Account for "<" vs ">"
919  */
920  hist_selec = isgt ? (1.0 - histfrac) : histfrac;
921 
922  /*
923  * The histogram boundaries are only approximate to begin with,
924  * and may well be out of date anyway. Therefore, don't believe
925  * extremely small or large selectivity estimates --- unless we
926  * got actual current endpoint values from the table.
927  */
928  if (have_end)
929  CLAMP_PROBABILITY(hist_selec);
930  else
931  {
932  if (hist_selec < 0.0001)
933  hist_selec = 0.0001;
934  else if (hist_selec > 0.9999)
935  hist_selec = 0.9999;
936  }
937  }
938 
939  free_attstatsslot(&sslot);
940  }
941 
942  return hist_selec;
943 }
944 
945 /*
946  * scalarltsel - Selectivity of "<" (also "<=") for scalars.
947  */
948 Datum
950 {
952  Oid operator = PG_GETARG_OID(1);
953  List *args = (List *) PG_GETARG_POINTER(2);
954  int varRelid = PG_GETARG_INT32(3);
955  VariableStatData vardata;
956  Node *other;
957  bool varonleft;
958  Datum constval;
959  Oid consttype;
960  bool isgt;
961  double selec;
962 
963  /*
964  * If expression is not variable op something or something op variable,
965  * then punt and return a default estimate.
966  */
967  if (!get_restriction_variable(root, args, varRelid,
968  &vardata, &other, &varonleft))
970 
971  /*
972  * Can't do anything useful if the something is not a constant, either.
973  */
974  if (!IsA(other, Const))
975  {
976  ReleaseVariableStats(vardata);
978  }
979 
980  /*
981  * If the constant is NULL, assume operator is strict and return zero, ie,
982  * operator will never return TRUE.
983  */
984  if (((Const *) other)->constisnull)
985  {
986  ReleaseVariableStats(vardata);
987  PG_RETURN_FLOAT8(0.0);
988  }
989  constval = ((Const *) other)->constvalue;
990  consttype = ((Const *) other)->consttype;
991 
992  /*
993  * Force the var to be on the left to simplify logic in scalarineqsel.
994  */
995  if (varonleft)
996  {
997  /* we have var < other */
998  isgt = false;
999  }
1000  else
1001  {
1002  /* we have other < var, commute to make var > other */
1003  operator = get_commutator(operator);
1004  if (!operator)
1005  {
1006  /* Use default selectivity (should we raise an error instead?) */
1007  ReleaseVariableStats(vardata);
1009  }
1010  isgt = true;
1011  }
1012 
1013  selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
1014 
1015  ReleaseVariableStats(vardata);
1016 
1017  PG_RETURN_FLOAT8((float8) selec);
1018 }
1019 
1020 /*
1021  * scalargtsel - Selectivity of ">" (also ">=") for integers.
1022  */
1023 Datum
1025 {
1026  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1027  Oid operator = PG_GETARG_OID(1);
1028  List *args = (List *) PG_GETARG_POINTER(2);
1029  int varRelid = PG_GETARG_INT32(3);
1030  VariableStatData vardata;
1031  Node *other;
1032  bool varonleft;
1033  Datum constval;
1034  Oid consttype;
1035  bool isgt;
1036  double selec;
1037 
1038  /*
1039  * If expression is not variable op something or something op variable,
1040  * then punt and return a default estimate.
1041  */
1042  if (!get_restriction_variable(root, args, varRelid,
1043  &vardata, &other, &varonleft))
1045 
1046  /*
1047  * Can't do anything useful if the something is not a constant, either.
1048  */
1049  if (!IsA(other, Const))
1050  {
1051  ReleaseVariableStats(vardata);
1053  }
1054 
1055  /*
1056  * If the constant is NULL, assume operator is strict and return zero, ie,
1057  * operator will never return TRUE.
1058  */
1059  if (((Const *) other)->constisnull)
1060  {
1061  ReleaseVariableStats(vardata);
1062  PG_RETURN_FLOAT8(0.0);
1063  }
1064  constval = ((Const *) other)->constvalue;
1065  consttype = ((Const *) other)->consttype;
1066 
1067  /*
1068  * Force the var to be on the left to simplify logic in scalarineqsel.
1069  */
1070  if (varonleft)
1071  {
1072  /* we have var > other */
1073  isgt = true;
1074  }
1075  else
1076  {
1077  /* we have other > var, commute to make var < other */
1078  operator = get_commutator(operator);
1079  if (!operator)
1080  {
1081  /* Use default selectivity (should we raise an error instead?) */
1082  ReleaseVariableStats(vardata);
1084  }
1085  isgt = false;
1086  }
1087 
1088  selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
1089 
1090  ReleaseVariableStats(vardata);
1091 
1092  PG_RETURN_FLOAT8((float8) selec);
1093 }
1094 
1095 /*
1096  * patternsel - Generic code for pattern-match selectivity.
1097  */
1098 static double
1100 {
1101  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1102  Oid operator = PG_GETARG_OID(1);
1103  List *args = (List *) PG_GETARG_POINTER(2);
1104  int varRelid = PG_GETARG_INT32(3);
1105  Oid collation = PG_GET_COLLATION();
1106  VariableStatData vardata;
1107  Node *other;
1108  bool varonleft;
1109  Datum constval;
1110  Oid consttype;
1111  Oid vartype;
1112  Oid opfamily;
1113  Pattern_Prefix_Status pstatus;
1114  Const *patt;
1115  Const *prefix = NULL;
1116  Selectivity rest_selec = 0;
1117  double result;
1118 
1119  /*
1120  * If this is for a NOT LIKE or similar operator, get the corresponding
1121  * positive-match operator and work with that. Set result to the correct
1122  * default estimate, too.
1123  */
1124  if (negate)
1125  {
1126  operator = get_negator(operator);
1127  if (!OidIsValid(operator))
1128  elog(ERROR, "patternsel called for operator without a negator");
1129  result = 1.0 - DEFAULT_MATCH_SEL;
1130  }
1131  else
1132  {
1133  result = DEFAULT_MATCH_SEL;
1134  }
1135 
1136  /*
1137  * If expression is not variable op constant, then punt and return a
1138  * default estimate.
1139  */
1140  if (!get_restriction_variable(root, args, varRelid,
1141  &vardata, &other, &varonleft))
1142  return result;
1143  if (!varonleft || !IsA(other, Const))
1144  {
1145  ReleaseVariableStats(vardata);
1146  return result;
1147  }
1148 
1149  /*
1150  * If the constant is NULL, assume operator is strict and return zero, ie,
1151  * operator will never return TRUE. (It's zero even for a negator op.)
1152  */
1153  if (((Const *) other)->constisnull)
1154  {
1155  ReleaseVariableStats(vardata);
1156  return 0.0;
1157  }
1158  constval = ((Const *) other)->constvalue;
1159  consttype = ((Const *) other)->consttype;
1160 
1161  /*
1162  * The right-hand const is type text or bytea for all supported operators.
1163  * We do not expect to see binary-compatible types here, since
1164  * const-folding should have relabeled the const to exactly match the
1165  * operator's declared type.
1166  */
1167  if (consttype != TEXTOID && consttype != BYTEAOID)
1168  {
1169  ReleaseVariableStats(vardata);
1170  return result;
1171  }
1172 
1173  /*
1174  * Similarly, the exposed type of the left-hand side should be one of
1175  * those we know. (Do not look at vardata.atttype, which might be
1176  * something binary-compatible but different.) We can use it to choose
1177  * the index opfamily from which we must draw the comparison operators.
1178  *
1179  * NOTE: It would be more correct to use the PATTERN opfamilies than the
1180  * simple ones, but at the moment ANALYZE will not generate statistics for
1181  * the PATTERN operators. But our results are so approximate anyway that
1182  * it probably hardly matters.
1183  */
1184  vartype = vardata.vartype;
1185 
1186  switch (vartype)
1187  {
1188  case TEXTOID:
1189  opfamily = TEXT_BTREE_FAM_OID;
1190  break;
1191  case BPCHAROID:
1192  opfamily = BPCHAR_BTREE_FAM_OID;
1193  break;
1194  case NAMEOID:
1195  opfamily = NAME_BTREE_FAM_OID;
1196  break;
1197  case BYTEAOID:
1198  opfamily = BYTEA_BTREE_FAM_OID;
1199  break;
1200  default:
1201  ReleaseVariableStats(vardata);
1202  return result;
1203  }
1204 
1205  /*
1206  * Pull out any fixed prefix implied by the pattern, and estimate the
1207  * fractional selectivity of the remainder of the pattern. Unlike many of
1208  * the other functions in this file, we use the pattern operator's actual
1209  * collation for this step. This is not because we expect the collation
1210  * to make a big difference in the selectivity estimate (it seldom would),
1211  * but because we want to be sure we cache compiled regexps under the
1212  * right cache key, so that they can be re-used at runtime.
1213  */
1214  patt = (Const *) other;
1215  pstatus = pattern_fixed_prefix(patt, ptype, collation,
1216  &prefix, &rest_selec);
1217 
1218  /*
1219  * If necessary, coerce the prefix constant to the right type.
1220  */
1221  if (prefix && prefix->consttype != vartype)
1222  {
1223  char *prefixstr;
1224 
1225  switch (prefix->consttype)
1226  {
1227  case TEXTOID:
1228  prefixstr = TextDatumGetCString(prefix->constvalue);
1229  break;
1230  case BYTEAOID:
1232  prefix->constvalue));
1233  break;
1234  default:
1235  elog(ERROR, "unrecognized consttype: %u",
1236  prefix->consttype);
1237  ReleaseVariableStats(vardata);
1238  return result;
1239  }
1240  prefix = string_to_const(prefixstr, vartype);
1241  pfree(prefixstr);
1242  }
1243 
1244  if (pstatus == Pattern_Prefix_Exact)
1245  {
1246  /*
1247  * Pattern specifies an exact match, so pretend operator is '='
1248  */
1249  Oid eqopr = get_opfamily_member(opfamily, vartype, vartype,
1251 
1252  if (eqopr == InvalidOid)
1253  elog(ERROR, "no = operator for opfamily %u", opfamily);
1254  result = var_eq_const(&vardata, eqopr, prefix->constvalue,
1255  false, true);
1256  }
1257  else
1258  {
1259  /*
1260  * Not exact-match pattern. If we have a sufficiently large
1261  * histogram, estimate selectivity for the histogram part of the
1262  * population by counting matches in the histogram. If not, estimate
1263  * selectivity of the fixed prefix and remainder of pattern
1264  * separately, then combine the two to get an estimate of the
1265  * selectivity for the part of the column population represented by
1266  * the histogram. (For small histograms, we combine these
1267  * approaches.)
1268  *
1269  * We then add up data for any most-common-values values; these are
1270  * not in the histogram population, and we can get exact answers for
1271  * them by applying the pattern operator, so there's no reason to
1272  * approximate. (If the MCVs cover a significant part of the total
1273  * population, this gives us a big leg up in accuracy.)
1274  */
1275  Selectivity selec;
1276  int hist_size;
1277  FmgrInfo opproc;
1278  double nullfrac,
1279  mcv_selec,
1280  sumcommon;
1281 
1282  /* Try to use the histogram entries to get selectivity */
1283  fmgr_info(get_opcode(operator), &opproc);
1284 
1285  selec = histogram_selectivity(&vardata, &opproc, constval, true,
1286  10, 1, &hist_size);
1287 
1288  /* If not at least 100 entries, use the heuristic method */
1289  if (hist_size < 100)
1290  {
1291  Selectivity heursel;
1292  Selectivity prefixsel;
1293 
1294  if (pstatus == Pattern_Prefix_Partial)
1295  prefixsel = prefix_selectivity(root, &vardata, vartype,
1296  opfamily, prefix);
1297  else
1298  prefixsel = 1.0;
1299  heursel = prefixsel * rest_selec;
1300 
1301  if (selec < 0) /* fewer than 10 histogram entries? */
1302  selec = heursel;
1303  else
1304  {
1305  /*
1306  * For histogram sizes from 10 to 100, we combine the
1307  * histogram and heuristic selectivities, putting increasingly
1308  * more trust in the histogram for larger sizes.
1309  */
1310  double hist_weight = hist_size / 100.0;
1311 
1312  selec = selec * hist_weight + heursel * (1.0 - hist_weight);
1313  }
1314  }
1315 
1316  /* In any case, don't believe extremely small or large estimates. */
1317  if (selec < 0.0001)
1318  selec = 0.0001;
1319  else if (selec > 0.9999)
1320  selec = 0.9999;
1321 
1322  /*
1323  * If we have most-common-values info, add up the fractions of the MCV
1324  * entries that satisfy MCV OP PATTERN. These fractions contribute
1325  * directly to the result selectivity. Also add up the total fraction
1326  * represented by MCV entries.
1327  */
1328  mcv_selec = mcv_selectivity(&vardata, &opproc, constval, true,
1329  &sumcommon);
1330 
1331  if (HeapTupleIsValid(vardata.statsTuple))
1332  nullfrac = ((Form_pg_statistic) GETSTRUCT(vardata.statsTuple))->stanullfrac;
1333  else
1334  nullfrac = 0.0;
1335 
1336  /*
1337  * Now merge the results from the MCV and histogram calculations,
1338  * realizing that the histogram covers only the non-null values that
1339  * are not listed in MCV.
1340  */
1341  selec *= 1.0 - nullfrac - sumcommon;
1342  selec += mcv_selec;
1343 
1344  /* result should be in range, but make sure... */
1345  CLAMP_PROBABILITY(selec);
1346  result = selec;
1347  }
1348 
1349  if (prefix)
1350  {
1351  pfree(DatumGetPointer(prefix->constvalue));
1352  pfree(prefix);
1353  }
1354 
1355  ReleaseVariableStats(vardata);
1356 
1357  return negate ? (1.0 - result) : result;
1358 }
1359 
1360 /*
1361  * regexeqsel - Selectivity of regular-expression pattern match.
1362  */
1363 Datum
1365 {
1367 }
1368 
1369 /*
1370  * icregexeqsel - Selectivity of case-insensitive regex match.
1371  */
1372 Datum
1374 {
1376 }
1377 
1378 /*
1379  * likesel - Selectivity of LIKE pattern match.
1380  */
1381 Datum
1383 {
1385 }
1386 
1387 /*
1388  * iclikesel - Selectivity of ILIKE pattern match.
1389  */
1390 Datum
1392 {
1394 }
1395 
1396 /*
1397  * regexnesel - Selectivity of regular-expression pattern non-match.
1398  */
1399 Datum
1401 {
1403 }
1404 
1405 /*
1406  * icregexnesel - Selectivity of case-insensitive regex non-match.
1407  */
1408 Datum
1410 {
1412 }
1413 
1414 /*
1415  * nlikesel - Selectivity of LIKE pattern non-match.
1416  */
1417 Datum
1419 {
1421 }
1422 
1423 /*
1424  * icnlikesel - Selectivity of ILIKE pattern non-match.
1425  */
1426 Datum
1428 {
1430 }
1431 
1432 /*
1433  * boolvarsel - Selectivity of Boolean variable.
1434  *
1435  * This can actually be called on any boolean-valued expression. If it
1436  * involves only Vars of the specified relation, and if there are statistics
1437  * about the Var or expression (the latter is possible if it's indexed) then
1438  * we'll produce a real estimate; otherwise it's just a default.
1439  */
1441 boolvarsel(PlannerInfo *root, Node *arg, int varRelid)
1442 {
1443  VariableStatData vardata;
1444  double selec;
1445 
1446  examine_variable(root, arg, varRelid, &vardata);
1447  if (HeapTupleIsValid(vardata.statsTuple))
1448  {
1449  /*
1450  * A boolean variable V is equivalent to the clause V = 't', so we
1451  * compute the selectivity as if that is what we have.
1452  */
1453  selec = var_eq_const(&vardata, BooleanEqualOperator,
1454  BoolGetDatum(true), false, true);
1455  }
1456  else if (is_funcclause(arg))
1457  {
1458  /*
1459  * If we have no stats and it's a function call, estimate 0.3333333.
1460  * This seems a pretty unprincipled choice, but Postgres has been
1461  * using that estimate for function calls since 1992. The hoariness
1462  * of this behavior suggests that we should not be in too much hurry
1463  * to use another value.
1464  */
1465  selec = 0.3333333;
1466  }
1467  else
1468  {
1469  /* Otherwise, the default estimate is 0.5 */
1470  selec = 0.5;
1471  }
1472  ReleaseVariableStats(vardata);
1473  return selec;
1474 }
1475 
1476 /*
1477  * booltestsel - Selectivity of BooleanTest Node.
1478  */
1481  int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1482 {
1483  VariableStatData vardata;
1484  double selec;
1485 
1486  examine_variable(root, arg, varRelid, &vardata);
1487 
1488  if (HeapTupleIsValid(vardata.statsTuple))
1489  {
1490  Form_pg_statistic stats;
1491  double freq_null;
1492  AttStatsSlot sslot;
1493 
1494  stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
1495  freq_null = stats->stanullfrac;
1496 
1497  if (get_attstatsslot(&sslot, vardata.statsTuple,
1500  && sslot.nnumbers > 0)
1501  {
1502  double freq_true;
1503  double freq_false;
1504 
1505  /*
1506  * Get first MCV frequency and derive frequency for true.
1507  */
1508  if (DatumGetBool(sslot.values[0]))
1509  freq_true = sslot.numbers[0];
1510  else
1511  freq_true = 1.0 - sslot.numbers[0] - freq_null;
1512 
1513  /*
1514  * Next derive frequency for false. Then use these as appropriate
1515  * to derive frequency for each case.
1516  */
1517  freq_false = 1.0 - freq_true - freq_null;
1518 
1519  switch (booltesttype)
1520  {
1521  case IS_UNKNOWN:
1522  /* select only NULL values */
1523  selec = freq_null;
1524  break;
1525  case IS_NOT_UNKNOWN:
1526  /* select non-NULL values */
1527  selec = 1.0 - freq_null;
1528  break;
1529  case IS_TRUE:
1530  /* select only TRUE values */
1531  selec = freq_true;
1532  break;
1533  case IS_NOT_TRUE:
1534  /* select non-TRUE values */
1535  selec = 1.0 - freq_true;
1536  break;
1537  case IS_FALSE:
1538  /* select only FALSE values */
1539  selec = freq_false;
1540  break;
1541  case IS_NOT_FALSE:
1542  /* select non-FALSE values */
1543  selec = 1.0 - freq_false;
1544  break;
1545  default:
1546  elog(ERROR, "unrecognized booltesttype: %d",
1547  (int) booltesttype);
1548  selec = 0.0; /* Keep compiler quiet */
1549  break;
1550  }
1551 
1552  free_attstatsslot(&sslot);
1553  }
1554  else
1555  {
1556  /*
1557  * No most-common-value info available. Still have null fraction
1558  * information, so use it for IS [NOT] UNKNOWN. Otherwise adjust
1559  * for null fraction and assume a 50-50 split of TRUE and FALSE.
1560  */
1561  switch (booltesttype)
1562  {
1563  case IS_UNKNOWN:
1564  /* select only NULL values */
1565  selec = freq_null;
1566  break;
1567  case IS_NOT_UNKNOWN:
1568  /* select non-NULL values */
1569  selec = 1.0 - freq_null;
1570  break;
1571  case IS_TRUE:
1572  case IS_FALSE:
1573  /* Assume we select half of the non-NULL values */
1574  selec = (1.0 - freq_null) / 2.0;
1575  break;
1576  case IS_NOT_TRUE:
1577  case IS_NOT_FALSE:
1578  /* Assume we select NULLs plus half of the non-NULLs */
1579  /* equiv. to freq_null + (1.0 - freq_null) / 2.0 */
1580  selec = (freq_null + 1.0) / 2.0;
1581  break;
1582  default:
1583  elog(ERROR, "unrecognized booltesttype: %d",
1584  (int) booltesttype);
1585  selec = 0.0; /* Keep compiler quiet */
1586  break;
1587  }
1588  }
1589  }
1590  else
1591  {
1592  /*
1593  * If we can't get variable statistics for the argument, perhaps
1594  * clause_selectivity can do something with it. We ignore the
1595  * possibility of a NULL value when using clause_selectivity, and just
1596  * assume the value is either TRUE or FALSE.
1597  */
1598  switch (booltesttype)
1599  {
1600  case IS_UNKNOWN:
1601  selec = DEFAULT_UNK_SEL;
1602  break;
1603  case IS_NOT_UNKNOWN:
1604  selec = DEFAULT_NOT_UNK_SEL;
1605  break;
1606  case IS_TRUE:
1607  case IS_NOT_FALSE:
1608  selec = (double) clause_selectivity(root, arg,
1609  varRelid,
1610  jointype, sjinfo);
1611  break;
1612  case IS_FALSE:
1613  case IS_NOT_TRUE:
1614  selec = 1.0 - (double) clause_selectivity(root, arg,
1615  varRelid,
1616  jointype, sjinfo);
1617  break;
1618  default:
1619  elog(ERROR, "unrecognized booltesttype: %d",
1620  (int) booltesttype);
1621  selec = 0.0; /* Keep compiler quiet */
1622  break;
1623  }
1624  }
1625 
1626  ReleaseVariableStats(vardata);
1627 
1628  /* result should be in range, but make sure... */
1629  CLAMP_PROBABILITY(selec);
1630 
1631  return (Selectivity) selec;
1632 }
1633 
1634 /*
1635  * nulltestsel - Selectivity of NullTest Node.
1636  */
1639  int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1640 {
1641  VariableStatData vardata;
1642  double selec;
1643 
1644  examine_variable(root, arg, varRelid, &vardata);
1645 
1646  if (HeapTupleIsValid(vardata.statsTuple))
1647  {
1648  Form_pg_statistic stats;
1649  double freq_null;
1650 
1651  stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
1652  freq_null = stats->stanullfrac;
1653 
1654  switch (nulltesttype)
1655  {
1656  case IS_NULL:
1657 
1658  /*
1659  * Use freq_null directly.
1660  */
1661  selec = freq_null;
1662  break;
1663  case IS_NOT_NULL:
1664 
1665  /*
1666  * Select not unknown (not null) values. Calculate from
1667  * freq_null.
1668  */
1669  selec = 1.0 - freq_null;
1670  break;
1671  default:
1672  elog(ERROR, "unrecognized nulltesttype: %d",
1673  (int) nulltesttype);
1674  return (Selectivity) 0; /* keep compiler quiet */
1675  }
1676  }
1677  else
1678  {
1679  /*
1680  * No ANALYZE stats available, so make a guess
1681  */
1682  switch (nulltesttype)
1683  {
1684  case IS_NULL:
1685  selec = DEFAULT_UNK_SEL;
1686  break;
1687  case IS_NOT_NULL:
1688  selec = DEFAULT_NOT_UNK_SEL;
1689  break;
1690  default:
1691  elog(ERROR, "unrecognized nulltesttype: %d",
1692  (int) nulltesttype);
1693  return (Selectivity) 0; /* keep compiler quiet */
1694  }
1695  }
1696 
1697  ReleaseVariableStats(vardata);
1698 
1699  /* result should be in range, but make sure... */
1700  CLAMP_PROBABILITY(selec);
1701 
1702  return (Selectivity) selec;
1703 }
1704 
1705 /*
1706  * strip_array_coercion - strip binary-compatible relabeling from an array expr
1707  *
1708  * For array values, the parser normally generates ArrayCoerceExpr conversions,
1709  * but it seems possible that RelabelType might show up. Also, the planner
1710  * is not currently tense about collapsing stacked ArrayCoerceExpr nodes,
1711  * so we need to be ready to deal with more than one level.
1712  */
1713 static Node *
1715 {
1716  for (;;)
1717  {
1718  if (node && IsA(node, ArrayCoerceExpr) &&
1719  ((ArrayCoerceExpr *) node)->elemfuncid == InvalidOid)
1720  {
1721  node = (Node *) ((ArrayCoerceExpr *) node)->arg;
1722  }
1723  else if (node && IsA(node, RelabelType))
1724  {
1725  /* We don't really expect this case, but may as well cope */
1726  node = (Node *) ((RelabelType *) node)->arg;
1727  }
1728  else
1729  break;
1730  }
1731  return node;
1732 }
1733 
1734 /*
1735  * scalararraysel - Selectivity of ScalarArrayOpExpr Node.
1736  */
1739  ScalarArrayOpExpr *clause,
1740  bool is_join_clause,
1741  int varRelid,
1742  JoinType jointype,
1743  SpecialJoinInfo *sjinfo)
1744 {
1745  Oid operator = clause->opno;
1746  bool useOr = clause->useOr;
1747  bool isEquality = false;
1748  bool isInequality = false;
1749  Node *leftop;
1750  Node *rightop;
1751  Oid nominal_element_type;
1752  Oid nominal_element_collation;
1753  TypeCacheEntry *typentry;
1754  RegProcedure oprsel;
1755  FmgrInfo oprselproc;
1756  Selectivity s1;
1757  Selectivity s1disjoint;
1758 
1759  /* First, deconstruct the expression */
1760  Assert(list_length(clause->args) == 2);
1761  leftop = (Node *) linitial(clause->args);
1762  rightop = (Node *) lsecond(clause->args);
1763 
1764  /* aggressively reduce both sides to constants */
1765  leftop = estimate_expression_value(root, leftop);
1766  rightop = estimate_expression_value(root, rightop);
1767 
1768  /* get nominal (after relabeling) element type of rightop */
1769  nominal_element_type = get_base_element_type(exprType(rightop));
1770  if (!OidIsValid(nominal_element_type))
1771  return (Selectivity) 0.5; /* probably shouldn't happen */
1772  /* get nominal collation, too, for generating constants */
1773  nominal_element_collation = exprCollation(rightop);
1774 
1775  /* look through any binary-compatible relabeling of rightop */
1776  rightop = strip_array_coercion(rightop);
1777 
1778  /*
1779  * Detect whether the operator is the default equality or inequality
1780  * operator of the array element type.
1781  */
1782  typentry = lookup_type_cache(nominal_element_type, TYPECACHE_EQ_OPR);
1783  if (OidIsValid(typentry->eq_opr))
1784  {
1785  if (operator == typentry->eq_opr)
1786  isEquality = true;
1787  else if (get_negator(operator) == typentry->eq_opr)
1788  isInequality = true;
1789  }
1790 
1791  /*
1792  * If it is equality or inequality, we might be able to estimate this as a
1793  * form of array containment; for instance "const = ANY(column)" can be
1794  * treated as "ARRAY[const] <@ column". scalararraysel_containment tries
1795  * that, and returns the selectivity estimate if successful, or -1 if not.
1796  */
1797  if ((isEquality || isInequality) && !is_join_clause)
1798  {
1799  s1 = scalararraysel_containment(root, leftop, rightop,
1800  nominal_element_type,
1801  isEquality, useOr, varRelid);
1802  if (s1 >= 0.0)
1803  return s1;
1804  }
1805 
1806  /*
1807  * Look up the underlying operator's selectivity estimator. Punt if it
1808  * hasn't got one.
1809  */
1810  if (is_join_clause)
1811  oprsel = get_oprjoin(operator);
1812  else
1813  oprsel = get_oprrest(operator);
1814  if (!oprsel)
1815  return (Selectivity) 0.5;
1816  fmgr_info(oprsel, &oprselproc);
1817 
1818  /*
1819  * In the array-containment check above, we must only believe that an
1820  * operator is equality or inequality if it is the default btree equality
1821  * operator (or its negator) for the element type, since those are the
1822  * operators that array containment will use. But in what follows, we can
1823  * be a little laxer, and also believe that any operators using eqsel() or
1824  * neqsel() as selectivity estimator act like equality or inequality.
1825  */
1826  if (oprsel == F_EQSEL || oprsel == F_EQJOINSEL)
1827  isEquality = true;
1828  else if (oprsel == F_NEQSEL || oprsel == F_NEQJOINSEL)
1829  isInequality = true;
1830 
1831  /*
1832  * We consider three cases:
1833  *
1834  * 1. rightop is an Array constant: deconstruct the array, apply the
1835  * operator's selectivity function for each array element, and merge the
1836  * results in the same way that clausesel.c does for AND/OR combinations.
1837  *
1838  * 2. rightop is an ARRAY[] construct: apply the operator's selectivity
1839  * function for each element of the ARRAY[] construct, and merge.
1840  *
1841  * 3. otherwise, make a guess ...
1842  */
1843  if (rightop && IsA(rightop, Const))
1844  {
1845  Datum arraydatum = ((Const *) rightop)->constvalue;
1846  bool arrayisnull = ((Const *) rightop)->constisnull;
1847  ArrayType *arrayval;
1848  int16 elmlen;
1849  bool elmbyval;
1850  char elmalign;
1851  int num_elems;
1852  Datum *elem_values;
1853  bool *elem_nulls;
1854  int i;
1855 
1856  if (arrayisnull) /* qual can't succeed if null array */
1857  return (Selectivity) 0.0;
1858  arrayval = DatumGetArrayTypeP(arraydatum);
1860  &elmlen, &elmbyval, &elmalign);
1861  deconstruct_array(arrayval,
1862  ARR_ELEMTYPE(arrayval),
1863  elmlen, elmbyval, elmalign,
1864  &elem_values, &elem_nulls, &num_elems);
1865 
1866  /*
1867  * For generic operators, we assume the probability of success is
1868  * independent for each array element. But for "= ANY" or "<> ALL",
1869  * if the array elements are distinct (which'd typically be the case)
1870  * then the probabilities are disjoint, and we should just sum them.
1871  *
1872  * If we were being really tense we would try to confirm that the
1873  * elements are all distinct, but that would be expensive and it
1874  * doesn't seem to be worth the cycles; it would amount to penalizing
1875  * well-written queries in favor of poorly-written ones. However, we
1876  * do protect ourselves a little bit by checking whether the
1877  * disjointness assumption leads to an impossible (out of range)
1878  * probability; if so, we fall back to the normal calculation.
1879  */
1880  s1 = s1disjoint = (useOr ? 0.0 : 1.0);
1881 
1882  for (i = 0; i < num_elems; i++)
1883  {
1884  List *args;
1885  Selectivity s2;
1886 
1887  args = list_make2(leftop,
1888  makeConst(nominal_element_type,
1889  -1,
1890  nominal_element_collation,
1891  elmlen,
1892  elem_values[i],
1893  elem_nulls[i],
1894  elmbyval));
1895  if (is_join_clause)
1896  s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
1897  clause->inputcollid,
1898  PointerGetDatum(root),
1899  ObjectIdGetDatum(operator),
1900  PointerGetDatum(args),
1901  Int16GetDatum(jointype),
1902  PointerGetDatum(sjinfo)));
1903  else
1904  s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
1905  clause->inputcollid,
1906  PointerGetDatum(root),
1907  ObjectIdGetDatum(operator),
1908  PointerGetDatum(args),
1909  Int32GetDatum(varRelid)));
1910 
1911  if (useOr)
1912  {
1913  s1 = s1 + s2 - s1 * s2;
1914  if (isEquality)
1915  s1disjoint += s2;
1916  }
1917  else
1918  {
1919  s1 = s1 * s2;
1920  if (isInequality)
1921  s1disjoint += s2 - 1.0;
1922  }
1923  }
1924 
1925  /* accept disjoint-probability estimate if in range */
1926  if ((useOr ? isEquality : isInequality) &&
1927  s1disjoint >= 0.0 && s1disjoint <= 1.0)
1928  s1 = s1disjoint;
1929  }
1930  else if (rightop && IsA(rightop, ArrayExpr) &&
1931  !((ArrayExpr *) rightop)->multidims)
1932  {
1933  ArrayExpr *arrayexpr = (ArrayExpr *) rightop;
1934  int16 elmlen;
1935  bool elmbyval;
1936  ListCell *l;
1937 
1938  get_typlenbyval(arrayexpr->element_typeid,
1939  &elmlen, &elmbyval);
1940 
1941  /*
1942  * We use the assumption of disjoint probabilities here too, although
1943  * the odds of equal array elements are rather higher if the elements
1944  * are not all constants (which they won't be, else constant folding
1945  * would have reduced the ArrayExpr to a Const). In this path it's
1946  * critical to have the sanity check on the s1disjoint estimate.
1947  */
1948  s1 = s1disjoint = (useOr ? 0.0 : 1.0);
1949 
1950  foreach(l, arrayexpr->elements)
1951  {
1952  Node *elem = (Node *) lfirst(l);
1953  List *args;
1954  Selectivity s2;
1955 
1956  /*
1957  * Theoretically, if elem isn't of nominal_element_type we should
1958  * insert a RelabelType, but it seems unlikely that any operator
1959  * estimation function would really care ...
1960  */
1961  args = list_make2(leftop, elem);
1962  if (is_join_clause)
1963  s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
1964  clause->inputcollid,
1965  PointerGetDatum(root),
1966  ObjectIdGetDatum(operator),
1967  PointerGetDatum(args),
1968  Int16GetDatum(jointype),
1969  PointerGetDatum(sjinfo)));
1970  else
1971  s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
1972  clause->inputcollid,
1973  PointerGetDatum(root),
1974  ObjectIdGetDatum(operator),
1975  PointerGetDatum(args),
1976  Int32GetDatum(varRelid)));
1977 
1978  if (useOr)
1979  {
1980  s1 = s1 + s2 - s1 * s2;
1981  if (isEquality)
1982  s1disjoint += s2;
1983  }
1984  else
1985  {
1986  s1 = s1 * s2;
1987  if (isInequality)
1988  s1disjoint += s2 - 1.0;
1989  }
1990  }
1991 
1992  /* accept disjoint-probability estimate if in range */
1993  if ((useOr ? isEquality : isInequality) &&
1994  s1disjoint >= 0.0 && s1disjoint <= 1.0)
1995  s1 = s1disjoint;
1996  }
1997  else
1998  {
1999  CaseTestExpr *dummyexpr;
2000  List *args;
2001  Selectivity s2;
2002  int i;
2003 
2004  /*
2005  * We need a dummy rightop to pass to the operator selectivity
2006  * routine. It can be pretty much anything that doesn't look like a
2007  * constant; CaseTestExpr is a convenient choice.
2008  */
2009  dummyexpr = makeNode(CaseTestExpr);
2010  dummyexpr->typeId = nominal_element_type;
2011  dummyexpr->typeMod = -1;
2012  dummyexpr->collation = clause->inputcollid;
2013  args = list_make2(leftop, dummyexpr);
2014  if (is_join_clause)
2015  s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
2016  clause->inputcollid,
2017  PointerGetDatum(root),
2018  ObjectIdGetDatum(operator),
2019  PointerGetDatum(args),
2020  Int16GetDatum(jointype),
2021  PointerGetDatum(sjinfo)));
2022  else
2023  s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
2024  clause->inputcollid,
2025  PointerGetDatum(root),
2026  ObjectIdGetDatum(operator),
2027  PointerGetDatum(args),
2028  Int32GetDatum(varRelid)));
2029  s1 = useOr ? 0.0 : 1.0;
2030 
2031  /*
2032  * Arbitrarily assume 10 elements in the eventual array value (see
2033  * also estimate_array_length). We don't risk an assumption of
2034  * disjoint probabilities here.
2035  */
2036  for (i = 0; i < 10; i++)
2037  {
2038  if (useOr)
2039  s1 = s1 + s2 - s1 * s2;
2040  else
2041  s1 = s1 * s2;
2042  }
2043  }
2044 
2045  /* result should be in range, but make sure... */
2046  CLAMP_PROBABILITY(s1);
2047 
2048  return s1;
2049 }
2050 
2051 /*
2052  * Estimate number of elements in the array yielded by an expression.
2053  *
2054  * It's important that this agree with scalararraysel.
2055  */
2056 int
2058 {
2059  /* look through any binary-compatible relabeling of arrayexpr */
2060  arrayexpr = strip_array_coercion(arrayexpr);
2061 
2062  if (arrayexpr && IsA(arrayexpr, Const))
2063  {
2064  Datum arraydatum = ((Const *) arrayexpr)->constvalue;
2065  bool arrayisnull = ((Const *) arrayexpr)->constisnull;
2066  ArrayType *arrayval;
2067 
2068  if (arrayisnull)
2069  return 0;
2070  arrayval = DatumGetArrayTypeP(arraydatum);
2071  return ArrayGetNItems(ARR_NDIM(arrayval), ARR_DIMS(arrayval));
2072  }
2073  else if (arrayexpr && IsA(arrayexpr, ArrayExpr) &&
2074  !((ArrayExpr *) arrayexpr)->multidims)
2075  {
2076  return list_length(((ArrayExpr *) arrayexpr)->elements);
2077  }
2078  else
2079  {
2080  /* default guess --- see also scalararraysel */
2081  return 10;
2082  }
2083 }
2084 
2085 /*
2086  * rowcomparesel - Selectivity of RowCompareExpr Node.
2087  *
2088  * We estimate RowCompare selectivity by considering just the first (high
2089  * order) columns, which makes it equivalent to an ordinary OpExpr. While
2090  * this estimate could be refined by considering additional columns, it
2091  * seems unlikely that we could do a lot better without multi-column
2092  * statistics.
2093  */
2096  RowCompareExpr *clause,
2097  int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
2098 {
2099  Selectivity s1;
2100  Oid opno = linitial_oid(clause->opnos);
2101  Oid inputcollid = linitial_oid(clause->inputcollids);
2102  List *opargs;
2103  bool is_join_clause;
2104 
2105  /* Build equivalent arg list for single operator */
2106  opargs = list_make2(linitial(clause->largs), linitial(clause->rargs));
2107 
2108  /*
2109  * Decide if it's a join clause. This should match clausesel.c's
2110  * treat_as_join_clause(), except that we intentionally consider only the
2111  * leading columns and not the rest of the clause.
2112  */
2113  if (varRelid != 0)
2114  {
2115  /*
2116  * Caller is forcing restriction mode (eg, because we are examining an
2117  * inner indexscan qual).
2118  */
2119  is_join_clause = false;
2120  }
2121  else if (sjinfo == NULL)
2122  {
2123  /*
2124  * It must be a restriction clause, since it's being evaluated at a
2125  * scan node.
2126  */
2127  is_join_clause = false;
2128  }
2129  else
2130  {
2131  /*
2132  * Otherwise, it's a join if there's more than one relation used.
2133  */
2134  is_join_clause = (NumRelids((Node *) opargs) > 1);
2135  }
2136 
2137  if (is_join_clause)
2138  {
2139  /* Estimate selectivity for a join clause. */
2140  s1 = join_selectivity(root, opno,
2141  opargs,
2142  inputcollid,
2143  jointype,
2144  sjinfo);
2145  }
2146  else
2147  {
2148  /* Estimate selectivity for a restriction clause. */
2149  s1 = restriction_selectivity(root, opno,
2150  opargs,
2151  inputcollid,
2152  varRelid);
2153  }
2154 
2155  return s1;
2156 }
2157 
2158 /*
2159  * eqjoinsel - Join selectivity of "="
2160  */
2161 Datum
2163 {
2164  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
2165  Oid operator = PG_GETARG_OID(1);
2166  List *args = (List *) PG_GETARG_POINTER(2);
2167 
2168 #ifdef NOT_USED
2169  JoinType jointype = (JoinType) PG_GETARG_INT16(3);
2170 #endif
2172  double selec;
2173  VariableStatData vardata1;
2174  VariableStatData vardata2;
2175  bool join_is_reversed;
2176  RelOptInfo *inner_rel;
2177 
2178  get_join_variables(root, args, sjinfo,
2179  &vardata1, &vardata2, &join_is_reversed);
2180 
2181  switch (sjinfo->jointype)
2182  {
2183  case JOIN_INNER:
2184  case JOIN_LEFT:
2185  case JOIN_FULL:
2186  selec = eqjoinsel_inner(operator, &vardata1, &vardata2);
2187  break;
2188  case JOIN_SEMI:
2189  case JOIN_ANTI:
2190 
2191  /*
2192  * Look up the join's inner relation. min_righthand is sufficient
2193  * information because neither SEMI nor ANTI joins permit any
2194  * reassociation into or out of their RHS, so the righthand will
2195  * always be exactly that set of rels.
2196  */
2197  inner_rel = find_join_input_rel(root, sjinfo->min_righthand);
2198 
2199  if (!join_is_reversed)
2200  selec = eqjoinsel_semi(operator, &vardata1, &vardata2,
2201  inner_rel);
2202  else
2203  selec = eqjoinsel_semi(get_commutator(operator),
2204  &vardata2, &vardata1,
2205  inner_rel);
2206  break;
2207  default:
2208  /* other values not expected here */
2209  elog(ERROR, "unrecognized join type: %d",
2210  (int) sjinfo->jointype);
2211  selec = 0; /* keep compiler quiet */
2212  break;
2213  }
2214 
2215  ReleaseVariableStats(vardata1);
2216  ReleaseVariableStats(vardata2);
2217 
2218  CLAMP_PROBABILITY(selec);
2219 
2220  PG_RETURN_FLOAT8((float8) selec);
2221 }
2222 
2223 /*
2224  * eqjoinsel_inner --- eqjoinsel for normal inner join
2225  *
2226  * We also use this for LEFT/FULL outer joins; it's not presently clear
2227  * that it's worth trying to distinguish them here.
2228  */
2229 static double
2231  VariableStatData *vardata1, VariableStatData *vardata2)
2232 {
2233  double selec;
2234  double nd1;
2235  double nd2;
2236  bool isdefault1;
2237  bool isdefault2;
2238  Oid opfuncoid;
2239  Form_pg_statistic stats1 = NULL;
2240  Form_pg_statistic stats2 = NULL;
2241  bool have_mcvs1 = false;
2242  bool have_mcvs2 = false;
2243  AttStatsSlot sslot1;
2244  AttStatsSlot sslot2;
2245 
2246  nd1 = get_variable_numdistinct(vardata1, &isdefault1);
2247  nd2 = get_variable_numdistinct(vardata2, &isdefault2);
2248 
2249  opfuncoid = get_opcode(operator);
2250 
2251  memset(&sslot1, 0, sizeof(sslot1));
2252  memset(&sslot2, 0, sizeof(sslot2));
2253 
2254  if (HeapTupleIsValid(vardata1->statsTuple))
2255  {
2256  /* note we allow use of nullfrac regardless of security check */
2257  stats1 = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
2258  if (statistic_proc_security_check(vardata1, opfuncoid))
2259  have_mcvs1 = get_attstatsslot(&sslot1, vardata1->statsTuple,
2262  }
2263 
2264  if (HeapTupleIsValid(vardata2->statsTuple))
2265  {
2266  /* note we allow use of nullfrac regardless of security check */
2267  stats2 = (Form_pg_statistic) GETSTRUCT(vardata2->statsTuple);
2268  if (statistic_proc_security_check(vardata2, opfuncoid))
2269  have_mcvs2 = get_attstatsslot(&sslot2, vardata2->statsTuple,
2272  }
2273 
2274  if (have_mcvs1 && have_mcvs2)
2275  {
2276  /*
2277  * We have most-common-value lists for both relations. Run through
2278  * the lists to see which MCVs actually join to each other with the
2279  * given operator. This allows us to determine the exact join
2280  * selectivity for the portion of the relations represented by the MCV
2281  * lists. We still have to estimate for the remaining population, but
2282  * in a skewed distribution this gives us a big leg up in accuracy.
2283  * For motivation see the analysis in Y. Ioannidis and S.
2284  * Christodoulakis, "On the propagation of errors in the size of join
2285  * results", Technical Report 1018, Computer Science Dept., University
2286  * of Wisconsin, Madison, March 1991 (available from ftp.cs.wisc.edu).
2287  */
2288  FmgrInfo eqproc;
2289  bool *hasmatch1;
2290  bool *hasmatch2;
2291  double nullfrac1 = stats1->stanullfrac;
2292  double nullfrac2 = stats2->stanullfrac;
2293  double matchprodfreq,
2294  matchfreq1,
2295  matchfreq2,
2296  unmatchfreq1,
2297  unmatchfreq2,
2298  otherfreq1,
2299  otherfreq2,
2300  totalsel1,
2301  totalsel2;
2302  int i,
2303  nmatches;
2304 
2305  fmgr_info(opfuncoid, &eqproc);
2306  hasmatch1 = (bool *) palloc0(sslot1.nvalues * sizeof(bool));
2307  hasmatch2 = (bool *) palloc0(sslot2.nvalues * sizeof(bool));
2308 
2309  /*
2310  * Note we assume that each MCV will match at most one member of the
2311  * other MCV list. If the operator isn't really equality, there could
2312  * be multiple matches --- but we don't look for them, both for speed
2313  * and because the math wouldn't add up...
2314  */
2315  matchprodfreq = 0.0;
2316  nmatches = 0;
2317  for (i = 0; i < sslot1.nvalues; i++)
2318  {
2319  int j;
2320 
2321  for (j = 0; j < sslot2.nvalues; j++)
2322  {
2323  if (hasmatch2[j])
2324  continue;
2325  if (DatumGetBool(FunctionCall2Coll(&eqproc,
2327  sslot1.values[i],
2328  sslot2.values[j])))
2329  {
2330  hasmatch1[i] = hasmatch2[j] = true;
2331  matchprodfreq += sslot1.numbers[i] * sslot2.numbers[j];
2332  nmatches++;
2333  break;
2334  }
2335  }
2336  }
2337  CLAMP_PROBABILITY(matchprodfreq);
2338  /* Sum up frequencies of matched and unmatched MCVs */
2339  matchfreq1 = unmatchfreq1 = 0.0;
2340  for (i = 0; i < sslot1.nvalues; i++)
2341  {
2342  if (hasmatch1[i])
2343  matchfreq1 += sslot1.numbers[i];
2344  else
2345  unmatchfreq1 += sslot1.numbers[i];
2346  }
2347  CLAMP_PROBABILITY(matchfreq1);
2348  CLAMP_PROBABILITY(unmatchfreq1);
2349  matchfreq2 = unmatchfreq2 = 0.0;
2350  for (i = 0; i < sslot2.nvalues; i++)
2351  {
2352  if (hasmatch2[i])
2353  matchfreq2 += sslot2.numbers[i];
2354  else
2355  unmatchfreq2 += sslot2.numbers[i];
2356  }
2357  CLAMP_PROBABILITY(matchfreq2);
2358  CLAMP_PROBABILITY(unmatchfreq2);
2359  pfree(hasmatch1);
2360  pfree(hasmatch2);
2361 
2362  /*
2363  * Compute total frequency of non-null values that are not in the MCV
2364  * lists.
2365  */
2366  otherfreq1 = 1.0 - nullfrac1 - matchfreq1 - unmatchfreq1;
2367  otherfreq2 = 1.0 - nullfrac2 - matchfreq2 - unmatchfreq2;
2368  CLAMP_PROBABILITY(otherfreq1);
2369  CLAMP_PROBABILITY(otherfreq2);
2370 
2371  /*
2372  * We can estimate the total selectivity from the point of view of
2373  * relation 1 as: the known selectivity for matched MCVs, plus
2374  * unmatched MCVs that are assumed to match against random members of
2375  * relation 2's non-MCV population, plus non-MCV values that are
2376  * assumed to match against random members of relation 2's unmatched
2377  * MCVs plus non-MCV values.
2378  */
2379  totalsel1 = matchprodfreq;
2380  if (nd2 > sslot2.nvalues)
2381  totalsel1 += unmatchfreq1 * otherfreq2 / (nd2 - sslot2.nvalues);
2382  if (nd2 > nmatches)
2383  totalsel1 += otherfreq1 * (otherfreq2 + unmatchfreq2) /
2384  (nd2 - nmatches);
2385  /* Same estimate from the point of view of relation 2. */
2386  totalsel2 = matchprodfreq;
2387  if (nd1 > sslot1.nvalues)
2388  totalsel2 += unmatchfreq2 * otherfreq1 / (nd1 - sslot1.nvalues);
2389  if (nd1 > nmatches)
2390  totalsel2 += otherfreq2 * (otherfreq1 + unmatchfreq1) /
2391  (nd1 - nmatches);
2392 
2393  /*
2394  * Use the smaller of the two estimates. This can be justified in
2395  * essentially the same terms as given below for the no-stats case: to
2396  * a first approximation, we are estimating from the point of view of
2397  * the relation with smaller nd.
2398  */
2399  selec = (totalsel1 < totalsel2) ? totalsel1 : totalsel2;
2400  }
2401  else
2402  {
2403  /*
2404  * We do not have MCV lists for both sides. Estimate the join
2405  * selectivity as MIN(1/nd1,1/nd2)*(1-nullfrac1)*(1-nullfrac2). This
2406  * is plausible if we assume that the join operator is strict and the
2407  * non-null values are about equally distributed: a given non-null
2408  * tuple of rel1 will join to either zero or N2*(1-nullfrac2)/nd2 rows
2409  * of rel2, so total join rows are at most
2410  * N1*(1-nullfrac1)*N2*(1-nullfrac2)/nd2 giving a join selectivity of
2411  * not more than (1-nullfrac1)*(1-nullfrac2)/nd2. By the same logic it
2412  * is not more than (1-nullfrac1)*(1-nullfrac2)/nd1, so the expression
2413  * with MIN() is an upper bound. Using the MIN() means we estimate
2414  * from the point of view of the relation with smaller nd (since the
2415  * larger nd is determining the MIN). It is reasonable to assume that
2416  * most tuples in this rel will have join partners, so the bound is
2417  * probably reasonably tight and should be taken as-is.
2418  *
2419  * XXX Can we be smarter if we have an MCV list for just one side? It
2420  * seems that if we assume equal distribution for the other side, we
2421  * end up with the same answer anyway.
2422  */
2423  double nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
2424  double nullfrac2 = stats2 ? stats2->stanullfrac : 0.0;
2425 
2426  selec = (1.0 - nullfrac1) * (1.0 - nullfrac2);
2427  if (nd1 > nd2)
2428  selec /= nd1;
2429  else
2430  selec /= nd2;
2431  }
2432 
2433  free_attstatsslot(&sslot1);
2434  free_attstatsslot(&sslot2);
2435 
2436  return selec;
2437 }
2438 
2439 /*
2440  * eqjoinsel_semi --- eqjoinsel for semi join
2441  *
2442  * (Also used for anti join, which we are supposed to estimate the same way.)
2443  * Caller has ensured that vardata1 is the LHS variable.
2444  * Unlike eqjoinsel_inner, we have to cope with operator being InvalidOid.
2445  */
2446 static double
2448  VariableStatData *vardata1, VariableStatData *vardata2,
2449  RelOptInfo *inner_rel)
2450 {
2451  double selec;
2452  double nd1;
2453  double nd2;
2454  bool isdefault1;
2455  bool isdefault2;
2456  Oid opfuncoid;
2457  Form_pg_statistic stats1 = NULL;
2458  bool have_mcvs1 = false;
2459  bool have_mcvs2 = false;
2460  AttStatsSlot sslot1;
2461  AttStatsSlot sslot2;
2462 
2463  nd1 = get_variable_numdistinct(vardata1, &isdefault1);
2464  nd2 = get_variable_numdistinct(vardata2, &isdefault2);
2465 
2466  opfuncoid = OidIsValid(operator) ? get_opcode(operator) : InvalidOid;
2467 
2468  memset(&sslot1, 0, sizeof(sslot1));
2469  memset(&sslot2, 0, sizeof(sslot2));
2470 
2471  /*
2472  * We clamp nd2 to be not more than what we estimate the inner relation's
2473  * size to be. This is intuitively somewhat reasonable since obviously
2474  * there can't be more than that many distinct values coming from the
2475  * inner rel. The reason for the asymmetry (ie, that we don't clamp nd1
2476  * likewise) is that this is the only pathway by which restriction clauses
2477  * applied to the inner rel will affect the join result size estimate,
2478  * since set_joinrel_size_estimates will multiply SEMI/ANTI selectivity by
2479  * only the outer rel's size. If we clamped nd1 we'd be double-counting
2480  * the selectivity of outer-rel restrictions.
2481  *
2482  * We can apply this clamping both with respect to the base relation from
2483  * which the join variable comes (if there is just one), and to the
2484  * immediate inner input relation of the current join.
2485  *
2486  * If we clamp, we can treat nd2 as being a non-default estimate; it's not
2487  * great, maybe, but it didn't come out of nowhere either. This is most
2488  * helpful when the inner relation is empty and consequently has no stats.
2489  */
2490  if (vardata2->rel)
2491  {
2492  if (nd2 >= vardata2->rel->rows)
2493  {
2494  nd2 = vardata2->rel->rows;
2495  isdefault2 = false;
2496  }
2497  }
2498  if (nd2 >= inner_rel->rows)
2499  {
2500  nd2 = inner_rel->rows;
2501  isdefault2 = false;
2502  }
2503 
2504  if (HeapTupleIsValid(vardata1->statsTuple))
2505  {
2506  /* note we allow use of nullfrac regardless of security check */
2507  stats1 = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
2508  if (statistic_proc_security_check(vardata1, opfuncoid))
2509  have_mcvs1 = get_attstatsslot(&sslot1, vardata1->statsTuple,
2512  }
2513 
2514  if (HeapTupleIsValid(vardata2->statsTuple) &&
2515  statistic_proc_security_check(vardata2, opfuncoid))
2516  {
2517  have_mcvs2 = get_attstatsslot(&sslot2, vardata2->statsTuple,
2520  /* note: currently don't need stanumbers from RHS */
2521  }
2522 
2523  if (have_mcvs1 && have_mcvs2 && OidIsValid(operator))
2524  {
2525  /*
2526  * We have most-common-value lists for both relations. Run through
2527  * the lists to see which MCVs actually join to each other with the
2528  * given operator. This allows us to determine the exact join
2529  * selectivity for the portion of the relations represented by the MCV
2530  * lists. We still have to estimate for the remaining population, but
2531  * in a skewed distribution this gives us a big leg up in accuracy.
2532  */
2533  FmgrInfo eqproc;
2534  bool *hasmatch1;
2535  bool *hasmatch2;
2536  double nullfrac1 = stats1->stanullfrac;
2537  double matchfreq1,
2538  uncertainfrac,
2539  uncertain;
2540  int i,
2541  nmatches,
2542  clamped_nvalues2;
2543 
2544  /*
2545  * The clamping above could have resulted in nd2 being less than
2546  * sslot2.nvalues; in which case, we assume that precisely the nd2
2547  * most common values in the relation will appear in the join input,
2548  * and so compare to only the first nd2 members of the MCV list. Of
2549  * course this is frequently wrong, but it's the best bet we can make.
2550  */
2551  clamped_nvalues2 = Min(sslot2.nvalues, nd2);
2552 
2553  fmgr_info(opfuncoid, &eqproc);
2554  hasmatch1 = (bool *) palloc0(sslot1.nvalues * sizeof(bool));
2555  hasmatch2 = (bool *) palloc0(clamped_nvalues2 * sizeof(bool));
2556 
2557  /*
2558  * Note we assume that each MCV will match at most one member of the
2559  * other MCV list. If the operator isn't really equality, there could
2560  * be multiple matches --- but we don't look for them, both for speed
2561  * and because the math wouldn't add up...
2562  */
2563  nmatches = 0;
2564  for (i = 0; i < sslot1.nvalues; i++)
2565  {
2566  int j;
2567 
2568  for (j = 0; j < clamped_nvalues2; j++)
2569  {
2570  if (hasmatch2[j])
2571  continue;
2572  if (DatumGetBool(FunctionCall2Coll(&eqproc,
2574  sslot1.values[i],
2575  sslot2.values[j])))
2576  {
2577  hasmatch1[i] = hasmatch2[j] = true;
2578  nmatches++;
2579  break;
2580  }
2581  }
2582  }
2583  /* Sum up frequencies of matched MCVs */
2584  matchfreq1 = 0.0;
2585  for (i = 0; i < sslot1.nvalues; i++)
2586  {
2587  if (hasmatch1[i])
2588  matchfreq1 += sslot1.numbers[i];
2589  }
2590  CLAMP_PROBABILITY(matchfreq1);
2591  pfree(hasmatch1);
2592  pfree(hasmatch2);
2593 
2594  /*
2595  * Now we need to estimate the fraction of relation 1 that has at
2596  * least one join partner. We know for certain that the matched MCVs
2597  * do, so that gives us a lower bound, but we're really in the dark
2598  * about everything else. Our crude approach is: if nd1 <= nd2 then
2599  * assume all non-null rel1 rows have join partners, else assume for
2600  * the uncertain rows that a fraction nd2/nd1 have join partners. We
2601  * can discount the known-matched MCVs from the distinct-values counts
2602  * before doing the division.
2603  *
2604  * Crude as the above is, it's completely useless if we don't have
2605  * reliable ndistinct values for both sides. Hence, if either nd1 or
2606  * nd2 is default, punt and assume half of the uncertain rows have
2607  * join partners.
2608  */
2609  if (!isdefault1 && !isdefault2)
2610  {
2611  nd1 -= nmatches;
2612  nd2 -= nmatches;
2613  if (nd1 <= nd2 || nd2 < 0)
2614  uncertainfrac = 1.0;
2615  else
2616  uncertainfrac = nd2 / nd1;
2617  }
2618  else
2619  uncertainfrac = 0.5;
2620  uncertain = 1.0 - matchfreq1 - nullfrac1;
2621  CLAMP_PROBABILITY(uncertain);
2622  selec = matchfreq1 + uncertainfrac * uncertain;
2623  }
2624  else
2625  {
2626  /*
2627  * Without MCV lists for both sides, we can only use the heuristic
2628  * about nd1 vs nd2.
2629  */
2630  double nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
2631 
2632  if (!isdefault1 && !isdefault2)
2633  {
2634  if (nd1 <= nd2 || nd2 < 0)
2635  selec = 1.0 - nullfrac1;
2636  else
2637  selec = (nd2 / nd1) * (1.0 - nullfrac1);
2638  }
2639  else
2640  selec = 0.5 * (1.0 - nullfrac1);
2641  }
2642 
2643  free_attstatsslot(&sslot1);
2644  free_attstatsslot(&sslot2);
2645 
2646  return selec;
2647 }
2648 
2649 /*
2650  * neqjoinsel - Join selectivity of "!="
2651  */
2652 Datum
2654 {
2655  PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
2656  Oid operator = PG_GETARG_OID(1);
2657  List *args = (List *) PG_GETARG_POINTER(2);
2658  JoinType jointype = (JoinType) PG_GETARG_INT16(3);
2660  Oid eqop;
2661  float8 result;
2662 
2663  /*
2664  * We want 1 - eqjoinsel() where the equality operator is the one
2665  * associated with this != operator, that is, its negator.
2666  */
2667  eqop = get_negator(operator);
2668  if (eqop)
2669  {
2671  PointerGetDatum(root),
2672  ObjectIdGetDatum(eqop),
2673  PointerGetDatum(args),
2674  Int16GetDatum(jointype),
2675  PointerGetDatum(sjinfo)));
2676  }
2677  else
2678  {
2679  /* Use default selectivity (should we raise an error instead?) */
2680  result = DEFAULT_EQ_SEL;
2681  }
2682  result = 1.0 - result;
2683  PG_RETURN_FLOAT8(result);
2684 }
2685 
2686 /*
2687  * scalarltjoinsel - Join selectivity of "<" and "<=" for scalars
2688  */
2689 Datum
2691 {
2693 }
2694 
2695 /*
2696  * scalargtjoinsel - Join selectivity of ">" and ">=" for scalars
2697  */
2698 Datum
2700 {
2702 }
2703 
2704 /*
2705  * patternjoinsel - Generic code for pattern-match join selectivity.
2706  */
2707 static double
2709 {
2710  /* For the moment we just punt. */
2711  return negate ? (1.0 - DEFAULT_MATCH_SEL) : DEFAULT_MATCH_SEL;
2712 }
2713 
2714 /*
2715  * regexeqjoinsel - Join selectivity of regular-expression pattern match.
2716  */
2717 Datum
2719 {
2721 }
2722 
2723 /*
2724  * icregexeqjoinsel - Join selectivity of case-insensitive regex match.
2725  */
2726 Datum
2728 {
2730 }
2731 
2732 /*
2733  * likejoinsel - Join selectivity of LIKE pattern match.
2734  */
2735 Datum
2737 {
2739 }
2740 
2741 /*
2742  * iclikejoinsel - Join selectivity of ILIKE pattern match.
2743  */
2744 Datum
2746 {
2748 }
2749 
2750 /*
2751  * regexnejoinsel - Join selectivity of regex non-match.
2752  */
2753 Datum
2755 {
2757 }
2758 
2759 /*
2760  * icregexnejoinsel - Join selectivity of case-insensitive regex non-match.
2761  */
2762 Datum
2764 {
2766 }
2767 
2768 /*
2769  * nlikejoinsel - Join selectivity of LIKE pattern non-match.
2770  */
2771 Datum
2773 {
2775 }
2776 
2777 /*
2778  * icnlikejoinsel - Join selectivity of ILIKE pattern non-match.
2779  */
2780 Datum
2782 {
2784 }
2785 
2786 /*
2787  * mergejoinscansel - Scan selectivity of merge join.
2788  *
2789  * A merge join will stop as soon as it exhausts either input stream.
2790  * Therefore, if we can estimate the ranges of both input variables,
2791  * we can estimate how much of the input will actually be read. This
2792  * can have a considerable impact on the cost when using indexscans.
2793  *
2794  * Also, we can estimate how much of each input has to be read before the
2795  * first join pair is found, which will affect the join's startup time.
2796  *
2797  * clause should be a clause already known to be mergejoinable. opfamily,
2798  * strategy, and nulls_first specify the sort ordering being used.
2799  *
2800  * The outputs are:
2801  * *leftstart is set to the fraction of the left-hand variable expected
2802  * to be scanned before the first join pair is found (0 to 1).
2803  * *leftend is set to the fraction of the left-hand variable expected
2804  * to be scanned before the join terminates (0 to 1).
2805  * *rightstart, *rightend similarly for the right-hand variable.
2806  */
2807 void
2809  Oid opfamily, int strategy, bool nulls_first,
2810  Selectivity *leftstart, Selectivity *leftend,
2811  Selectivity *rightstart, Selectivity *rightend)
2812 {
2813  Node *left,
2814  *right;
2815  VariableStatData leftvar,
2816  rightvar;
2817  int op_strategy;
2818  Oid op_lefttype;
2819  Oid op_righttype;
2820  Oid opno,
2821  lsortop,
2822  rsortop,
2823  lstatop,
2824  rstatop,
2825  ltop,
2826  leop,
2827  revltop,
2828  revleop;
2829  bool isgt;
2830  Datum leftmin,
2831  leftmax,
2832  rightmin,
2833  rightmax;
2834  double selec;
2835 
2836  /* Set default results if we can't figure anything out. */
2837  /* XXX should default "start" fraction be a bit more than 0? */
2838  *leftstart = *rightstart = 0.0;
2839  *leftend = *rightend = 1.0;
2840 
2841  /* Deconstruct the merge clause */
2842  if (!is_opclause(clause))
2843  return; /* shouldn't happen */
2844  opno = ((OpExpr *) clause)->opno;
2845  left = get_leftop((Expr *) clause);
2846  right = get_rightop((Expr *) clause);
2847  if (!right)
2848  return; /* shouldn't happen */
2849 
2850  /* Look for stats for the inputs */
2851  examine_variable(root, left, 0, &leftvar);
2852  examine_variable(root, right, 0, &rightvar);
2853 
2854  /* Extract the operator's declared left/right datatypes */
2855  get_op_opfamily_properties(opno, opfamily, false,
2856  &op_strategy,
2857  &op_lefttype,
2858  &op_righttype);
2859  Assert(op_strategy == BTEqualStrategyNumber);
2860 
2861  /*
2862  * Look up the various operators we need. If we don't find them all, it
2863  * probably means the opfamily is broken, but we just fail silently.
2864  *
2865  * Note: we expect that pg_statistic histograms will be sorted by the '<'
2866  * operator, regardless of which sort direction we are considering.
2867  */
2868  switch (strategy)
2869  {
2870  case BTLessStrategyNumber:
2871  isgt = false;
2872  if (op_lefttype == op_righttype)
2873  {
2874  /* easy case */
2875  ltop = get_opfamily_member(opfamily,
2876  op_lefttype, op_righttype,
2878  leop = get_opfamily_member(opfamily,
2879  op_lefttype, op_righttype,
2881  lsortop = ltop;
2882  rsortop = ltop;
2883  lstatop = lsortop;
2884  rstatop = rsortop;
2885  revltop = ltop;
2886  revleop = leop;
2887  }
2888  else
2889  {
2890  ltop = get_opfamily_member(opfamily,
2891  op_lefttype, op_righttype,
2893  leop = get_opfamily_member(opfamily,
2894  op_lefttype, op_righttype,
2896  lsortop = get_opfamily_member(opfamily,
2897  op_lefttype, op_lefttype,
2899  rsortop = get_opfamily_member(opfamily,
2900  op_righttype, op_righttype,
2902  lstatop = lsortop;
2903  rstatop = rsortop;
2904  revltop = get_opfamily_member(opfamily,
2905  op_righttype, op_lefttype,
2907  revleop = get_opfamily_member(opfamily,
2908  op_righttype, op_lefttype,
2910  }
2911  break;
2913  /* descending-order case */
2914  isgt = true;
2915  if (op_lefttype == op_righttype)
2916  {
2917  /* easy case */
2918  ltop = get_opfamily_member(opfamily,
2919  op_lefttype, op_righttype,
2921  leop = get_opfamily_member(opfamily,
2922  op_lefttype, op_righttype,
2924  lsortop = ltop;
2925  rsortop = ltop;
2926  lstatop = get_opfamily_member(opfamily,
2927  op_lefttype, op_lefttype,
2929  rstatop = lstatop;
2930  revltop = ltop;
2931  revleop = leop;
2932  }
2933  else
2934  {
2935  ltop = get_opfamily_member(opfamily,
2936  op_lefttype, op_righttype,
2938  leop = get_opfamily_member(opfamily,
2939  op_lefttype, op_righttype,
2941  lsortop = get_opfamily_member(opfamily,
2942  op_lefttype, op_lefttype,
2944  rsortop = get_opfamily_member(opfamily,
2945  op_righttype, op_righttype,
2947  lstatop = get_opfamily_member(opfamily,
2948  op_lefttype, op_lefttype,
2950  rstatop = get_opfamily_member(opfamily,
2951  op_righttype, op_righttype,
2953  revltop = get_opfamily_member(opfamily,
2954  op_righttype, op_lefttype,
2956  revleop = get_opfamily_member(opfamily,
2957  op_righttype, op_lefttype,
2959  }
2960  break;
2961  default:
2962  goto fail; /* shouldn't get here */
2963  }
2964 
2965  if (!OidIsValid(lsortop) ||
2966  !OidIsValid(rsortop) ||
2967  !OidIsValid(lstatop) ||
2968  !OidIsValid(rstatop) ||
2969  !OidIsValid(ltop) ||
2970  !OidIsValid(leop) ||
2971  !OidIsValid(revltop) ||
2972  !OidIsValid(revleop))
2973  goto fail; /* insufficient info in catalogs */
2974 
2975  /* Try to get ranges of both inputs */
2976  if (!isgt)
2977  {
2978  if (!get_variable_range(root, &leftvar, lstatop,
2979  &leftmin, &leftmax))
2980  goto fail; /* no range available from stats */
2981  if (!get_variable_range(root, &rightvar, rstatop,
2982  &rightmin, &rightmax))
2983  goto fail; /* no range available from stats */
2984  }
2985  else
2986  {
2987  /* need to swap the max and min */
2988  if (!get_variable_range(root, &leftvar, lstatop,
2989  &leftmax, &leftmin))
2990  goto fail; /* no range available from stats */
2991  if (!get_variable_range(root, &rightvar, rstatop,
2992  &rightmax, &rightmin))
2993  goto fail; /* no range available from stats */
2994  }
2995 
2996  /*
2997  * Now, the fraction of the left variable that will be scanned is the
2998  * fraction that's <= the right-side maximum value. But only believe
2999  * non-default estimates, else stick with our 1.0.
3000  */
3001  selec = scalarineqsel(root, leop, isgt, &leftvar,
3002  rightmax, op_righttype);
3003  if (selec != DEFAULT_INEQ_SEL)
3004  *leftend = selec;
3005 
3006  /* And similarly for the right variable. */
3007  selec = scalarineqsel(root, revleop, isgt, &rightvar,
3008  leftmax, op_lefttype);
3009  if (selec != DEFAULT_INEQ_SEL)
3010  *rightend = selec;
3011 
3012  /*
3013  * Only one of the two "end" fractions can really be less than 1.0;
3014  * believe the smaller estimate and reset the other one to exactly 1.0. If
3015  * we get exactly equal estimates (as can easily happen with self-joins),
3016  * believe neither.
3017  */
3018  if (*leftend > *rightend)
3019  *leftend = 1.0;
3020  else if (*leftend < *rightend)
3021  *rightend = 1.0;
3022  else
3023  *leftend = *rightend = 1.0;
3024 
3025  /*
3026  * Also, the fraction of the left variable that will be scanned before the
3027  * first join pair is found is the fraction that's < the right-side
3028  * minimum value. But only believe non-default estimates, else stick with
3029  * our own default.
3030  */
3031  selec = scalarineqsel(root, ltop, isgt, &leftvar,
3032  rightmin, op_righttype);
3033  if (selec != DEFAULT_INEQ_SEL)
3034  *leftstart = selec;
3035 
3036  /* And similarly for the right variable. */
3037  selec = scalarineqsel(root, revltop, isgt, &rightvar,
3038  leftmin, op_lefttype);
3039  if (selec != DEFAULT_INEQ_SEL)
3040  *rightstart = selec;
3041 
3042  /*
3043  * Only one of the two "start" fractions can really be more than zero;
3044  * believe the larger estimate and reset the other one to exactly 0.0. If
3045  * we get exactly equal estimates (as can easily happen with self-joins),
3046  * believe neither.
3047  */
3048  if (*leftstart < *rightstart)
3049  *leftstart = 0.0;
3050  else if (*leftstart > *rightstart)
3051  *rightstart = 0.0;
3052  else
3053  *leftstart = *rightstart = 0.0;
3054 
3055  /*
3056  * If the sort order is nulls-first, we're going to have to skip over any
3057  * nulls too. These would not have been counted by scalarineqsel, and we
3058  * can safely add in this fraction regardless of whether we believe
3059  * scalarineqsel's results or not. But be sure to clamp the sum to 1.0!
3060  */
3061  if (nulls_first)
3062  {
3063  Form_pg_statistic stats;
3064 
3065  if (HeapTupleIsValid(leftvar.statsTuple))
3066  {
3067  stats = (Form_pg_statistic) GETSTRUCT(leftvar.statsTuple);
3068  *leftstart += stats->stanullfrac;
3069  CLAMP_PROBABILITY(*leftstart);
3070  *leftend += stats->stanullfrac;
3071  CLAMP_PROBABILITY(*leftend);
3072  }
3073  if (HeapTupleIsValid(rightvar.statsTuple))
3074  {
3075  stats = (Form_pg_statistic) GETSTRUCT(rightvar.statsTuple);
3076  *rightstart += stats->stanullfrac;
3077  CLAMP_PROBABILITY(*rightstart);
3078  *rightend += stats->stanullfrac;
3079  CLAMP_PROBABILITY(*rightend);
3080  }
3081  }
3082 
3083  /* Disbelieve start >= end, just in case that can happen */
3084  if (*leftstart >= *leftend)
3085  {
3086  *leftstart = 0.0;
3087  *leftend = 1.0;
3088  }
3089  if (*rightstart >= *rightend)
3090  {
3091  *rightstart = 0.0;
3092  *rightend = 1.0;
3093  }
3094 
3095 fail:
3096  ReleaseVariableStats(leftvar);
3097  ReleaseVariableStats(rightvar);
3098 }
3099 
3100 
3101 /*
3102  * Helper routine for estimate_num_groups: add an item to a list of
3103  * GroupVarInfos, but only if it's not known equal to any of the existing
3104  * entries.
3105  */
3106 typedef struct
3107 {
3108  Node *var; /* might be an expression, not just a Var */
3109  RelOptInfo *rel; /* relation it belongs to */
3110  double ndistinct; /* # distinct values */
3111 } GroupVarInfo;
3112 
3113 static List *
3115  Node *var, VariableStatData *vardata)
3116 {
3117  GroupVarInfo *varinfo;
3118  double ndistinct;
3119  bool isdefault;
3120  ListCell *lc;
3121 
3122  ndistinct = get_variable_numdistinct(vardata, &isdefault);
3123 
3124  /* cannot use foreach here because of possible list_delete */
3125  lc = list_head(varinfos);
3126  while (lc)
3127  {
3128  varinfo = (GroupVarInfo *) lfirst(lc);
3129 
3130  /* must advance lc before list_delete possibly pfree's it */
3131  lc = lnext(lc);
3132 
3133  /* Drop exact duplicates */
3134  if (equal(var, varinfo->var))
3135  return varinfos;
3136 
3137  /*
3138  * Drop known-equal vars, but only if they belong to different
3139  * relations (see comments for estimate_num_groups)
3140  */
3141  if (vardata->rel != varinfo->rel &&
3142  exprs_known_equal(root, var, varinfo->var))
3143  {
3144  if (varinfo->ndistinct <= ndistinct)
3145  {
3146  /* Keep older item, forget new one */
3147  return varinfos;
3148  }
3149  else
3150  {
3151  /* Delete the older item */
3152  varinfos = list_delete_ptr(varinfos, varinfo);
3153  }
3154  }
3155  }
3156 
3157  varinfo = (GroupVarInfo *) palloc(sizeof(GroupVarInfo));
3158 
3159  varinfo->var = var;
3160  varinfo->rel = vardata->rel;
3161  varinfo->ndistinct = ndistinct;
3162  varinfos = lappend(varinfos, varinfo);
3163  return varinfos;
3164 }
3165 
3166 /*
3167  * estimate_num_groups - Estimate number of groups in a grouped query
3168  *
3169  * Given a query having a GROUP BY clause, estimate how many groups there
3170  * will be --- ie, the number of distinct combinations of the GROUP BY
3171  * expressions.
3172  *
3173  * This routine is also used to estimate the number of rows emitted by
3174  * a DISTINCT filtering step; that is an isomorphic problem. (Note:
3175  * actually, we only use it for DISTINCT when there's no grouping or
3176  * aggregation ahead of the DISTINCT.)
3177  *
3178  * Inputs:
3179  * root - the query
3180  * groupExprs - list of expressions being grouped by
3181  * input_rows - number of rows estimated to arrive at the group/unique
3182  * filter step
3183  * pgset - NULL, or a List** pointing to a grouping set to filter the
3184  * groupExprs against
3185  *
3186  * Given the lack of any cross-correlation statistics in the system, it's
3187  * impossible to do anything really trustworthy with GROUP BY conditions
3188  * involving multiple Vars. We should however avoid assuming the worst
3189  * case (all possible cross-product terms actually appear as groups) since
3190  * very often the grouped-by Vars are highly correlated. Our current approach
3191  * is as follows:
3192  * 1. Expressions yielding boolean are assumed to contribute two groups,
3193  * independently of their content, and are ignored in the subsequent
3194  * steps. This is mainly because tests like "col IS NULL" break the
3195  * heuristic used in step 2 especially badly.
3196  * 2. Reduce the given expressions to a list of unique Vars used. For
3197  * example, GROUP BY a, a + b is treated the same as GROUP BY a, b.
3198  * It is clearly correct not to count the same Var more than once.
3199  * It is also reasonable to treat f(x) the same as x: f() cannot
3200  * increase the number of distinct values (unless it is volatile,
3201  * which we consider unlikely for grouping), but it probably won't
3202  * reduce the number of distinct values much either.
3203  * As a special case, if a GROUP BY expression can be matched to an
3204  * expressional index for which we have statistics, then we treat the
3205  * whole expression as though it were just a Var.
3206  * 3. If the list contains Vars of different relations that are known equal
3207  * due to equivalence classes, then drop all but one of the Vars from each
3208  * known-equal set, keeping the one with smallest estimated # of values
3209  * (since the extra values of the others can't appear in joined rows).
3210  * Note the reason we only consider Vars of different relations is that
3211  * if we considered ones of the same rel, we'd be double-counting the
3212  * restriction selectivity of the equality in the next step.
3213  * 4. For Vars within a single source rel, we multiply together the numbers
3214  * of values, clamp to the number of rows in the rel (divided by 10 if
3215  * more than one Var), and then multiply by a factor based on the
3216  * selectivity of the restriction clauses for that rel. When there's
3217  * more than one Var, the initial product is probably too high (it's the
3218  * worst case) but clamping to a fraction of the rel's rows seems to be a
3219  * helpful heuristic for not letting the estimate get out of hand. (The
3220  * factor of 10 is derived from pre-Postgres-7.4 practice.) The factor
3221  * we multiply by to adjust for the restriction selectivity assumes that
3222  * the restriction clauses are independent of the grouping, which may not
3223  * be a valid assumption, but it's hard to do better.
3224  * 5. If there are Vars from multiple rels, we repeat step 4 for each such
3225  * rel, and multiply the results together.
3226  * Note that rels not containing grouped Vars are ignored completely, as are
3227  * join clauses. Such rels cannot increase the number of groups, and we
3228  * assume such clauses do not reduce the number either (somewhat bogus,
3229  * but we don't have the info to do better).
3230  */
3231 double
3232 estimate_num_groups(PlannerInfo *root, List *groupExprs, double input_rows,
3233  List **pgset)
3234 {
3235  List *varinfos = NIL;
3236  double numdistinct;
3237  ListCell *l;
3238  int i;
3239 
3240  /*
3241  * We don't ever want to return an estimate of zero groups, as that tends
3242  * to lead to division-by-zero and other unpleasantness. The input_rows
3243  * estimate is usually already at least 1, but clamp it just in case it
3244  * isn't.
3245  */
3246  input_rows = clamp_row_est(input_rows);
3247 
3248  /*
3249  * If no grouping columns, there's exactly one group. (This can't happen
3250  * for normal cases with GROUP BY or DISTINCT, but it is possible for
3251  * corner cases with set operations.)
3252  */
3253  if (groupExprs == NIL || (pgset && list_length(*pgset) < 1))
3254  return 1.0;
3255 
3256  /*
3257  * Count groups derived from boolean grouping expressions. For other
3258  * expressions, find the unique Vars used, treating an expression as a Var
3259  * if we can find stats for it. For each one, record the statistical
3260  * estimate of number of distinct values (total in its table, without
3261  * regard for filtering).
3262  */
3263  numdistinct = 1.0;
3264 
3265  i = 0;
3266  foreach(l, groupExprs)
3267  {
3268  Node *groupexpr = (Node *) lfirst(l);
3269  VariableStatData vardata;
3270  List *varshere;
3271  ListCell *l2;
3272 
3273  /* is expression in this grouping set? */
3274  if (pgset && !list_member_int(*pgset, i++))
3275  continue;
3276 
3277  /* Short-circuit for expressions returning boolean */
3278  if (exprType(groupexpr) == BOOLOID)
3279  {
3280  numdistinct *= 2.0;
3281  continue;
3282  }
3283 
3284  /*
3285  * If examine_variable is able to deduce anything about the GROUP BY
3286  * expression, treat it as a single variable even if it's really more
3287  * complicated.
3288  */
3289  examine_variable(root, groupexpr, 0, &vardata);
3290  if (HeapTupleIsValid(vardata.statsTuple) || vardata.isunique)
3291  {
3292  varinfos = add_unique_group_var(root, varinfos,
3293  groupexpr, &vardata);
3294  ReleaseVariableStats(vardata);
3295  continue;
3296  }
3297  ReleaseVariableStats(vardata);
3298 
3299  /*
3300  * Else pull out the component Vars. Handle PlaceHolderVars by
3301  * recursing into their arguments (effectively assuming that the
3302  * PlaceHolderVar doesn't change the number of groups, which boils
3303  * down to ignoring the possible addition of nulls to the result set).
3304  */
3305  varshere = pull_var_clause(groupexpr,
3309 
3310  /*
3311  * If we find any variable-free GROUP BY item, then either it is a
3312  * constant (and we can ignore it) or it contains a volatile function;
3313  * in the latter case we punt and assume that each input row will
3314  * yield a distinct group.
3315  */
3316  if (varshere == NIL)
3317  {
3318  if (contain_volatile_functions(groupexpr))
3319  return input_rows;
3320  continue;
3321  }
3322 
3323  /*
3324  * Else add variables to varinfos list
3325  */
3326  foreach(l2, varshere)
3327  {
3328  Node *var = (Node *) lfirst(l2);
3329 
3330  examine_variable(root, var, 0, &vardata);
3331  varinfos = add_unique_group_var(root, varinfos, var, &vardata);
3332  ReleaseVariableStats(vardata);
3333  }
3334  }
3335 
3336  /*
3337  * If now no Vars, we must have an all-constant or all-boolean GROUP BY
3338  * list.
3339  */
3340  if (varinfos == NIL)
3341  {
3342  /* Guard against out-of-range answers */
3343  if (numdistinct > input_rows)
3344  numdistinct = input_rows;
3345  return numdistinct;
3346  }
3347 
3348  /*
3349  * Group Vars by relation and estimate total numdistinct.
3350  *
3351  * For each iteration of the outer loop, we process the frontmost Var in
3352  * varinfos, plus all other Vars in the same relation. We remove these
3353  * Vars from the newvarinfos list for the next iteration. This is the
3354  * easiest way to group Vars of same rel together.
3355  */
3356  do
3357  {
3358  GroupVarInfo *varinfo1 = (GroupVarInfo *) linitial(varinfos);
3359  RelOptInfo *rel = varinfo1->rel;
3360  double reldistinct = 1;
3361  double relmaxndistinct = reldistinct;
3362  int relvarcount = 0;
3363  List *newvarinfos = NIL;
3364  List *relvarinfos = NIL;
3365 
3366  /*
3367  * Split the list of varinfos in two - one for the current rel, one
3368  * for remaining Vars on other rels.
3369  */
3370  relvarinfos = lcons(varinfo1, relvarinfos);
3371  for_each_cell(l, lnext(list_head(varinfos)))
3372  {
3373  GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
3374 
3375  if (varinfo2->rel == varinfo1->rel)
3376  {
3377  /* varinfos on current rel */
3378  relvarinfos = lcons(varinfo2, relvarinfos);
3379  }
3380  else
3381  {
3382  /* not time to process varinfo2 yet */
3383  newvarinfos = lcons(varinfo2, newvarinfos);
3384  }
3385  }
3386 
3387  /*
3388  * Get the numdistinct estimate for the Vars of this rel. We
3389  * iteratively search for multivariate n-distinct with maximum number
3390  * of vars; assuming that each var group is independent of the others,
3391  * we multiply them together. Any remaining relvarinfos after no more
3392  * multivariate matches are found are assumed independent too, so
3393  * their individual ndistinct estimates are multiplied also.
3394  *
3395  * While iterating, count how many separate numdistinct values we
3396  * apply. We apply a fudge factor below, but only if we multiplied
3397  * more than one such values.
3398  */
3399  while (relvarinfos)
3400  {
3401  double mvndistinct;
3402 
3403  if (estimate_multivariate_ndistinct(root, rel, &relvarinfos,
3404  &mvndistinct))
3405  {
3406  reldistinct *= mvndistinct;
3407  if (relmaxndistinct < mvndistinct)
3408  relmaxndistinct = mvndistinct;
3409  relvarcount++;
3410  }
3411  else
3412  {
3413  foreach(l, relvarinfos)
3414  {
3415  GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
3416 
3417  reldistinct *= varinfo2->ndistinct;
3418  if (relmaxndistinct < varinfo2->ndistinct)
3419  relmaxndistinct = varinfo2->ndistinct;
3420  relvarcount++;
3421  }
3422 
3423  /* we're done with this relation */
3424  relvarinfos = NIL;
3425  }
3426  }
3427 
3428  /*
3429  * Sanity check --- don't divide by zero if empty relation.
3430  */
3431  Assert(IS_SIMPLE_REL(rel));
3432  if (rel->tuples > 0)
3433  {
3434  /*
3435  * Clamp to size of rel, or size of rel / 10 if multiple Vars. The
3436  * fudge factor is because the Vars are probably correlated but we
3437  * don't know by how much. We should never clamp to less than the
3438  * largest ndistinct value for any of the Vars, though, since
3439  * there will surely be at least that many groups.
3440  */
3441  double clamp = rel->tuples;
3442 
3443  if (relvarcount > 1)
3444  {
3445  clamp *= 0.1;
3446  if (clamp < relmaxndistinct)
3447  {
3448  clamp = relmaxndistinct;
3449  /* for sanity in case some ndistinct is too large: */
3450  if (clamp > rel->tuples)
3451  clamp = rel->tuples;
3452  }
3453  }
3454  if (reldistinct > clamp)
3455  reldistinct = clamp;
3456 
3457  /*
3458  * Update the estimate based on the restriction selectivity,
3459  * guarding against division by zero when reldistinct is zero.
3460  * Also skip this if we know that we are returning all rows.
3461  */
3462  if (reldistinct > 0 && rel->rows < rel->tuples)
3463  {
3464  /*
3465  * Given a table containing N rows with n distinct values in a
3466  * uniform distribution, if we select p rows at random then
3467  * the expected number of distinct values selected is
3468  *
3469  * n * (1 - product((N-N/n-i)/(N-i), i=0..p-1))
3470  *
3471  * = n * (1 - (N-N/n)! / (N-N/n-p)! * (N-p)! / N!)
3472  *
3473  * See "Approximating block accesses in database
3474  * organizations", S. B. Yao, Communications of the ACM,
3475  * Volume 20 Issue 4, April 1977 Pages 260-261.
3476  *
3477  * Alternatively, re-arranging the terms from the factorials,
3478  * this may be written as
3479  *
3480  * n * (1 - product((N-p-i)/(N-i), i=0..N/n-1))
3481  *
3482  * This form of the formula is more efficient to compute in
3483  * the common case where p is larger than N/n. Additionally,
3484  * as pointed out by Dell'Era, if i << N for all terms in the
3485  * product, it can be approximated by
3486  *
3487  * n * (1 - ((N-p)/N)^(N/n))
3488  *
3489  * See "Expected distinct values when selecting from a bag
3490  * without replacement", Alberto Dell'Era,
3491  * http://www.adellera.it/investigations/distinct_balls/.
3492  *
3493  * The condition i << N is equivalent to n >> 1, so this is a
3494  * good approximation when the number of distinct values in
3495  * the table is large. It turns out that this formula also
3496  * works well even when n is small.
3497  */
3498  reldistinct *=
3499  (1 - pow((rel->tuples - rel->rows) / rel->tuples,
3500  rel->tuples / reldistinct));
3501  }
3502  reldistinct = clamp_row_est(reldistinct);
3503 
3504  /*
3505  * Update estimate of total distinct groups.
3506  */
3507  numdistinct *= reldistinct;
3508  }
3509 
3510  varinfos = newvarinfos;
3511  } while (varinfos != NIL);
3512 
3513  numdistinct = ceil(numdistinct);
3514 
3515  /* Guard against out-of-range answers */
3516  if (numdistinct > input_rows)
3517  numdistinct = input_rows;
3518  if (numdistinct < 1.0)
3519  numdistinct = 1.0;
3520 
3521  return numdistinct;
3522 }
3523 
3524 /*
3525  * Estimate hash bucketsize fraction (ie, number of entries in a bucket
3526  * divided by total tuples in relation) if the specified expression is used
3527  * as a hash key.
3528  *
3529  * XXX This is really pretty bogus since we're effectively assuming that the
3530  * distribution of hash keys will be the same after applying restriction
3531  * clauses as it was in the underlying relation. However, we are not nearly
3532  * smart enough to figure out how the restrict clauses might change the
3533  * distribution, so this will have to do for now.
3534  *
3535  * We are passed the number of buckets the executor will use for the given
3536  * input relation. If the data were perfectly distributed, with the same
3537  * number of tuples going into each available bucket, then the bucketsize
3538  * fraction would be 1/nbuckets. But this happy state of affairs will occur
3539  * only if (a) there are at least nbuckets distinct data values, and (b)
3540  * we have a not-too-skewed data distribution. Otherwise the buckets will
3541  * be nonuniformly occupied. If the other relation in the join has a key
3542  * distribution similar to this one's, then the most-loaded buckets are
3543  * exactly those that will be probed most often. Therefore, the "average"
3544  * bucket size for costing purposes should really be taken as something close
3545  * to the "worst case" bucket size. We try to estimate this by adjusting the
3546  * fraction if there are too few distinct data values, and then scaling up
3547  * by the ratio of the most common value's frequency to the average frequency.
3548  *
3549  * If no statistics are available, use a default estimate of 0.1. This will
3550  * discourage use of a hash rather strongly if the inner relation is large,
3551  * which is what we want. We do not want to hash unless we know that the
3552  * inner rel is well-dispersed (or the alternatives seem much worse).
3553  */
3555 estimate_hash_bucketsize(PlannerInfo *root, Node *hashkey, double nbuckets)
3556 {
3557  VariableStatData vardata;
3558  double estfract,
3559  ndistinct,
3560  stanullfrac,
3561  mcvfreq,
3562  avgfreq;
3563  bool isdefault;
3564  AttStatsSlot sslot;
3565 
3566  examine_variable(root, hashkey, 0, &vardata);
3567 
3568  /* Get number of distinct values */
3569  ndistinct = get_variable_numdistinct(&vardata, &isdefault);
3570 
3571  /* If ndistinct isn't real, punt and return 0.1, per comments above */
3572  if (isdefault)
3573  {
3574  ReleaseVariableStats(vardata);
3575  return (Selectivity) 0.1;
3576  }
3577 
3578  /* Get fraction that are null */
3579  if (HeapTupleIsValid(vardata.statsTuple))
3580  {
3581  Form_pg_statistic stats;
3582 
3583  stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
3584  stanullfrac = stats->stanullfrac;
3585  }
3586  else
3587  stanullfrac = 0.0;
3588 
3589  /* Compute avg freq of all distinct data values in raw relation */
3590  avgfreq = (1.0 - stanullfrac) / ndistinct;
3591 
3592  /*
3593  * Adjust ndistinct to account for restriction clauses. Observe we are
3594  * assuming that the data distribution is affected uniformly by the
3595  * restriction clauses!
3596  *
3597  * XXX Possibly better way, but much more expensive: multiply by
3598  * selectivity of rel's restriction clauses that mention the target Var.
3599  */
3600  if (vardata.rel && vardata.rel->tuples > 0)
3601  {
3602  ndistinct *= vardata.rel->rows / vardata.rel->tuples;
3603  ndistinct = clamp_row_est(ndistinct);
3604  }
3605 
3606  /*
3607  * Initial estimate of bucketsize fraction is 1/nbuckets as long as the
3608  * number of buckets is less than the expected number of distinct values;
3609  * otherwise it is 1/ndistinct.
3610  */
3611  if (ndistinct > nbuckets)
3612  estfract = 1.0 / nbuckets;
3613  else
3614  estfract = 1.0 / ndistinct;
3615 
3616  /*
3617  * Look up the frequency of the most common value, if available.
3618  */
3619  mcvfreq = 0.0;
3620 
3621  if (HeapTupleIsValid(vardata.statsTuple))
3622  {
3623  if (get_attstatsslot(&sslot, vardata.statsTuple,
3626  {
3627  /*
3628  * The first MCV stat is for the most common value.
3629  */
3630  if (sslot.nnumbers > 0)
3631  mcvfreq = sslot.numbers[0];
3632  free_attstatsslot(&sslot);
3633  }
3634  }
3635 
3636  /*
3637  * Adjust estimated bucketsize upward to account for skewed distribution.
3638  */
3639  if (avgfreq > 0.0 && mcvfreq > avgfreq)
3640  estfract *= mcvfreq / avgfreq;
3641 
3642  /*
3643  * Clamp bucketsize to sane range (the above adjustment could easily
3644  * produce an out-of-range result). We set the lower bound a little above
3645  * zero, since zero isn't a very sane result.
3646  */
3647  if (estfract < 1.0e-6)
3648  estfract = 1.0e-6;
3649  else if (estfract > 1.0)
3650  estfract = 1.0;
3651 
3652  ReleaseVariableStats(vardata);
3653 
3654  return (Selectivity) estfract;
3655 }
3656 
3657 
3658 /*-------------------------------------------------------------------------
3659  *
3660  * Support routines
3661  *
3662  *-------------------------------------------------------------------------
3663  */
3664 
3665 /*
3666  * Find applicable ndistinct statistics for the given list of VarInfos (which
3667  * must all belong to the given rel), and update *ndistinct to the estimate of
3668  * the MVNDistinctItem that best matches. If a match it found, *varinfos is
3669  * updated to remove the list of matched varinfos.
3670  *
3671  * Varinfos that aren't for simple Vars are ignored.
3672  *
3673  * Return TRUE if we're able to find a match, FALSE otherwise.
3674  */
3675 static bool
3677  List **varinfos, double *ndistinct)
3678 {
3679  ListCell *lc;
3680  Bitmapset *attnums = NULL;
3681  int nmatches;
3682  Oid statOid = InvalidOid;
3683  MVNDistinct *stats;
3684  Bitmapset *matched = NULL;
3685 
3686  /* bail out immediately if the table has no extended statistics */
3687  if (!rel->statlist)
3688  return false;
3689 
3690  /* Determine the attnums we're looking for */
3691  foreach(lc, *varinfos)
3692  {
3693  GroupVarInfo *varinfo = (GroupVarInfo *) lfirst(lc);
3694 
3695  Assert(varinfo->rel == rel);
3696 
3697  if (IsA(varinfo->var, Var))
3698  {
3699  attnums = bms_add_member(attnums,
3700  ((Var *) varinfo->var)->varattno);
3701  }
3702  }
3703 
3704  /* look for the ndistinct statistics matching the most vars */
3705  nmatches = 1; /* we require at least two matches */
3706  foreach(lc, rel->statlist)
3707  {
3708  StatisticExtInfo *info = (StatisticExtInfo *) lfirst(lc);
3709  Bitmapset *shared;
3710  int nshared;
3711 
3712  /* skip statistics of other kinds */
3713  if (info->kind != STATS_EXT_NDISTINCT)
3714  continue;
3715 
3716  /* compute attnums shared by the vars and the statistics object */
3717  shared = bms_intersect(info->keys, attnums);
3718  nshared = bms_num_members(shared);
3719 
3720  /*
3721  * Does this statistics object match more columns than the currently
3722  * best object? If so, use this one instead.
3723  *
3724  * XXX This should break ties using name of the object, or something
3725  * like that, to make the outcome stable.
3726  */
3727  if (nshared > nmatches)
3728  {
3729  statOid = info->statOid;
3730  nmatches = nshared;
3731  matched = shared;
3732  }
3733  }
3734 
3735  /* No match? */
3736  if (statOid == InvalidOid)
3737  return false;
3738  Assert(nmatches > 1 && matched != NULL);
3739 
3740  stats = statext_ndistinct_load(statOid);
3741 
3742  /*
3743  * If we have a match, search it for the specific item that matches (there
3744  * must be one), and construct the output values.
3745  */
3746  if (stats)
3747  {
3748  int i;
3749  List *newlist = NIL;
3750  MVNDistinctItem *item = NULL;
3751 
3752  /* Find the specific item that exactly matches the combination */
3753  for (i = 0; i < stats->nitems; i++)
3754  {
3755  MVNDistinctItem *tmpitem = &stats->items[i];
3756 
3757  if (bms_subset_compare(tmpitem->attrs, matched) == BMS_EQUAL)
3758  {
3759  item = tmpitem;
3760  break;
3761  }
3762  }
3763 
3764  /* make sure we found an item */
3765  if (!item)
3766  elog(ERROR, "corrupt MVNDistinct entry");
3767 
3768  /* Form the output varinfo list, keeping only unmatched ones */
3769  foreach(lc, *varinfos)
3770  {
3771  GroupVarInfo *varinfo = (GroupVarInfo *) lfirst(lc);
3772  AttrNumber attnum;
3773 
3774  if (!IsA(varinfo->var, Var))
3775  {
3776  newlist = lappend(newlist, varinfo);
3777  continue;
3778  }
3779 
3780  attnum = ((Var *) varinfo->var)->varattno;
3781  if (!bms_is_member(attnum, matched))
3782  newlist = lappend(newlist, varinfo);
3783  }
3784 
3785  *varinfos = newlist;
3786  *ndistinct = item->ndistinct;
3787  return true;
3788  }
3789 
3790  return false;
3791 }
3792 
3793 /*
3794  * convert_to_scalar
3795  * Convert non-NULL values of the indicated types to the comparison
3796  * scale needed by scalarineqsel().
3797  * Returns "true" if successful.
3798  *
3799  * XXX this routine is a hack: ideally we should look up the conversion
3800  * subroutines in pg_type.
3801  *
3802  * All numeric datatypes are simply converted to their equivalent
3803  * "double" values. (NUMERIC values that are outside the range of "double"
3804  * are clamped to +/- HUGE_VAL.)
3805  *
3806  * String datatypes are converted by convert_string_to_scalar(),
3807  * which is explained below. The reason why this routine deals with
3808  * three values at a time, not just one, is that we need it for strings.
3809  *
3810  * The bytea datatype is just enough different from strings that it has
3811  * to be treated separately.
3812  *
3813  * The several datatypes representing absolute times are all converted
3814  * to Timestamp, which is actually a double, and then we just use that
3815  * double value. Note this will give correct results even for the "special"
3816  * values of Timestamp, since those are chosen to compare correctly;
3817  * see timestamp_cmp.
3818  *
3819  * The several datatypes representing relative times (intervals) are all
3820  * converted to measurements expressed in seconds.
3821  */
3822 static bool
3823 convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
3824  Datum lobound, Datum hibound, Oid boundstypid,
3825  double *scaledlobound, double *scaledhibound)
3826 {
3827  /*
3828  * Both the valuetypid and the boundstypid should exactly match the
3829  * declared input type(s) of the operator we are invoked for, so we just
3830  * error out if either is not recognized.
3831  *
3832  * XXX The histogram we are interpolating between points of could belong
3833  * to a column that's only binary-compatible with the declared type. In
3834  * essence we are assuming that the semantics of binary-compatible types
3835  * are enough alike that we can use a histogram generated with one type's
3836  * operators to estimate selectivity for the other's. This is outright
3837  * wrong in some cases --- in particular signed versus unsigned
3838  * interpretation could trip us up. But it's useful enough in the
3839  * majority of cases that we do it anyway. Should think about more
3840  * rigorous ways to do it.
3841  */
3842  switch (valuetypid)
3843  {
3844  /*
3845  * Built-in numeric types
3846  */
3847  case BOOLOID:
3848  case INT2OID:
3849  case INT4OID:
3850  case INT8OID:
3851  case FLOAT4OID:
3852  case FLOAT8OID:
3853  case NUMERICOID:
3854  case OIDOID:
3855  case REGPROCOID:
3856  case REGPROCEDUREOID:
3857  case REGOPEROID:
3858  case REGOPERATOROID:
3859  case REGCLASSOID:
3860  case REGTYPEOID:
3861  case REGCONFIGOID:
3862  case REGDICTIONARYOID:
3863  case REGROLEOID:
3864  case REGNAMESPACEOID:
3865  *scaledvalue = convert_numeric_to_scalar(value, valuetypid);
3866  *scaledlobound = convert_numeric_to_scalar(lobound, boundstypid);
3867  *scaledhibound = convert_numeric_to_scalar(hibound, boundstypid);
3868  return true;
3869 
3870  /*
3871  * Built-in string types
3872  */
3873  case CHAROID:
3874  case BPCHAROID:
3875  case VARCHAROID:
3876  case TEXTOID:
3877  case NAMEOID:
3878  {
3879  char *valstr = convert_string_datum(value, valuetypid);
3880  char *lostr = convert_string_datum(lobound, boundstypid);
3881  char *histr = convert_string_datum(hibound, boundstypid);
3882 
3883  convert_string_to_scalar(valstr, scaledvalue,
3884  lostr, scaledlobound,
3885  histr, scaledhibound);
3886  pfree(valstr);
3887  pfree(lostr);
3888  pfree(histr);
3889  return true;
3890  }
3891 
3892  /*
3893  * Built-in bytea type
3894  */
3895  case BYTEAOID:
3896  {
3897  convert_bytea_to_scalar(value, scaledvalue,
3898  lobound, scaledlobound,
3899  hibound, scaledhibound);
3900  return true;
3901  }
3902 
3903  /*
3904  * Built-in time types
3905  */
3906  case TIMESTAMPOID:
3907  case TIMESTAMPTZOID:
3908  case ABSTIMEOID:
3909  case DATEOID:
3910  case INTERVALOID:
3911  case RELTIMEOID:
3912  case TINTERVALOID:
3913  case TIMEOID:
3914  case TIMETZOID:
3915  *scaledvalue = convert_timevalue_to_scalar(value, valuetypid);
3916  *scaledlobound = convert_timevalue_to_scalar(lobound, boundstypid);
3917  *scaledhibound = convert_timevalue_to_scalar(hibound, boundstypid);
3918  return true;
3919 
3920  /*
3921  * Built-in network types
3922  */
3923  case INETOID:
3924  case CIDROID:
3925  case MACADDROID:
3926  case MACADDR8OID:
3927  *scaledvalue = convert_network_to_scalar(value, valuetypid);
3928  *scaledlobound = convert_network_to_scalar(lobound, boundstypid);
3929  *scaledhibound = convert_network_to_scalar(hibound, boundstypid);
3930  return true;
3931  }
3932  /* Don't know how to convert */
3933  *scaledvalue = *scaledlobound = *scaledhibound = 0;
3934  return false;
3935 }
3936 
3937 /*
3938  * Do convert_to_scalar()'s work for any numeric data type.
3939  */
3940 static double
3942 {
3943  switch (typid)
3944  {
3945  case BOOLOID:
3946  return (double) DatumGetBool(value);
3947  case INT2OID:
3948  return (double) DatumGetInt16(value);
3949  case INT4OID:
3950  return (double) DatumGetInt32(value);
3951  case INT8OID:
3952  return (double) DatumGetInt64(value);
3953  case FLOAT4OID:
3954  return (double) DatumGetFloat4(value);
3955  case FLOAT8OID:
3956  return (double) DatumGetFloat8(value);
3957  case NUMERICOID:
3958  /* Note: out-of-range values will be clamped to +-HUGE_VAL */
3959  return (double)
3961  value));
3962  case OIDOID:
3963  case REGPROCOID:
3964  case REGPROCEDUREOID:
3965  case REGOPEROID:
3966  case REGOPERATOROID:
3967  case REGCLASSOID:
3968  case REGTYPEOID:
3969  case REGCONFIGOID:
3970  case REGDICTIONARYOID:
3971  case REGROLEOID:
3972  case REGNAMESPACEOID:
3973  /* we can treat OIDs as integers... */
3974  return (double) DatumGetObjectId(value);
3975  }
3976 
3977  /*
3978  * Can't get here unless someone tries to use scalarltsel/scalargtsel on
3979  * an operator with one numeric and one non-numeric operand.
3980  */
3981  elog(ERROR, "unsupported type: %u", typid);
3982  return 0;
3983 }
3984 
3985 /*
3986  * Do convert_to_scalar()'s work for any character-string data type.
3987  *
3988  * String datatypes are converted to a scale that ranges from 0 to 1,
3989  * where we visualize the bytes of the string as fractional digits.
3990  *
3991  * We do not want the base to be 256, however, since that tends to
3992  * generate inflated selectivity estimates; few databases will have
3993  * occurrences of all 256 possible byte values at each position.
3994  * Instead, use the smallest and largest byte values seen in the bounds
3995  * as the estimated range for each byte, after some fudging to deal with
3996  * the fact that we probably aren't going to see the full range that way.
3997  *
3998  * An additional refinement is that we discard any common prefix of the
3999  * three strings before computing the scaled values. This allows us to
4000  * "zoom in" when we encounter a narrow data range. An example is a phone
4001  * number database where all the values begin with the same area code.
4002  * (Actually, the bounds will be adjacent histogram-bin-boundary values,
4003  * so this is more likely to happen than you might think.)
4004  */
4005 static void
4007  double *scaledvalue,
4008  char *lobound,
4009  double *scaledlobound,
4010  char *hibound,
4011  double *scaledhibound)
4012 {
4013  int rangelo,
4014  rangehi;
4015  char *sptr;
4016 
4017  rangelo = rangehi = (unsigned char) hibound[0];
4018  for (sptr = lobound; *sptr; sptr++)
4019  {
4020  if (rangelo > (unsigned char) *sptr)
4021  rangelo = (unsigned char) *sptr;
4022  if (rangehi < (unsigned char) *sptr)
4023  rangehi = (unsigned char) *sptr;
4024  }
4025  for (sptr = hibound; *sptr; sptr++)
4026  {
4027  if (rangelo > (unsigned char) *sptr)
4028  rangelo = (unsigned char) *sptr;
4029  if (rangehi < (unsigned char) *sptr)
4030  rangehi = (unsigned char) *sptr;
4031  }
4032  /* If range includes any upper-case ASCII chars, make it include all */
4033  if (rangelo <= 'Z' && rangehi >= 'A')
4034  {
4035  if (rangelo > 'A')
4036  rangelo = 'A';
4037  if (rangehi < 'Z')
4038  rangehi = 'Z';
4039  }
4040  /* Ditto lower-case */
4041  if (rangelo <= 'z' && rangehi >= 'a')
4042  {
4043  if (rangelo > 'a')
4044  rangelo = 'a';
4045  if (rangehi < 'z')
4046  rangehi = 'z';
4047  }
4048  /* Ditto digits */
4049  if (rangelo <= '9' && rangehi >= '0')
4050  {
4051  if (rangelo > '0')
4052  rangelo = '0';
4053  if (rangehi < '9')
4054  rangehi = '9';
4055  }
4056 
4057  /*
4058  * If range includes less than 10 chars, assume we have not got enough
4059  * data, and make it include regular ASCII set.
4060  */
4061  if (rangehi - rangelo < 9)
4062  {
4063  rangelo = ' ';
4064  rangehi = 127;
4065  }
4066 
4067  /*
4068  * Now strip any common prefix of the three strings.
4069  */
4070  while (*lobound)
4071  {
4072  if (*lobound != *hibound || *lobound != *value)
4073  break;
4074  lobound++, hibound++, value++;
4075  }
4076 
4077  /*
4078  * Now we can do the conversions.
4079  */
4080  *scaledvalue = convert_one_string_to_scalar(value, rangelo, rangehi);
4081  *scaledlobound = convert_one_string_to_scalar(lobound, rangelo, rangehi);
4082  *scaledhibound = convert_one_string_to_scalar(hibound, rangelo, rangehi);
4083 }
4084 
4085 static double
4086 convert_one_string_to_scalar(char *value, int rangelo, int rangehi)
4087 {
4088  int slen = strlen(value);
4089  double num,
4090  denom,
4091  base;
4092 
4093  if (slen <= 0)
4094  return 0.0; /* empty string has scalar value 0 */
4095 
4096  /*
4097  * There seems little point in considering more than a dozen bytes from
4098  * the string. Since base is at least 10, that will give us nominal
4099  * resolution of at least 12 decimal digits, which is surely far more
4100  * precision than this estimation technique has got anyway (especially in
4101  * non-C locales). Also, even with the maximum possible base of 256, this
4102  * ensures denom cannot grow larger than 256^13 = 2.03e31, which will not
4103  * overflow on any known machine.
4104  */
4105  if (slen > 12)
4106  slen = 12;
4107 
4108  /* Convert initial characters to fraction */
4109  base = rangehi - rangelo + 1;
4110  num = 0.0;
4111  denom = base;
4112  while (slen-- > 0)
4113  {
4114  int ch = (unsigned char) *value++;
4115 
4116  if (ch < rangelo)
4117  ch = rangelo - 1;
4118  else if (ch > rangehi)
4119  ch = rangehi + 1;
4120  num += ((double) (ch - rangelo)) / denom;
4121  denom *= base;
4122  }
4123 
4124  return num;
4125 }
4126 
4127 /*
4128  * Convert a string-type Datum into a palloc'd, null-terminated string.
4129  *
4130  * When using a non-C locale, we must pass the string through strxfrm()
4131  * before continuing, so as to generate correct locale-specific results.
4132  */
4133 static char *
4135 {
4136  char *val;
4137 
4138  switch (typid)
4139  {
4140  case CHAROID:
4141  val = (char *) palloc(2);
4142  val[0] = DatumGetChar(value);
4143  val[1] = '\0';
4144  break;
4145  case BPCHAROID:
4146  case VARCHAROID:
4147  case TEXTOID:
4148  val = TextDatumGetCString(value);
4149  break;
4150  case NAMEOID:
4151  {
4152  NameData *nm = (NameData *) DatumGetPointer(value);
4153 
4154  val = pstrdup(NameStr(*nm));
4155  break;
4156  }
4157  default:
4158 
4159  /*
4160  * Can't get here unless someone tries to use scalarltsel on an
4161  * operator with one string and one non-string operand.
4162  */
4163  elog(ERROR, "unsupported type: %u", typid);
4164  return NULL;
4165  }
4166 
4168  {
4169  char *xfrmstr;
4170  size_t xfrmlen;
4171  size_t xfrmlen2 PG_USED_FOR_ASSERTS_ONLY;
4172 
4173  /*
4174  * XXX: We could guess at a suitable output buffer size and only call
4175  * strxfrm twice if our guess is too small.
4176  *
4177  * XXX: strxfrm doesn't support UTF-8 encoding on Win32, it can return
4178  * bogus data or set an error. This is not really a problem unless it
4179  * crashes since it will only give an estimation error and nothing
4180  * fatal.
4181  */
4182 #if _MSC_VER == 1400 /* VS.Net 2005 */
4183 
4184  /*
4185  *
4186  * http://connect.microsoft.com/VisualStudio/feedback/ViewFeedback.aspx?
4187  * FeedbackID=99694 */
4188  {
4189  char x[1];
4190 
4191  xfrmlen = strxfrm(x, val, 0);
4192  }
4193 #else
4194  xfrmlen = strxfrm(NULL, val, 0);
4195 #endif
4196 #ifdef WIN32
4197 
4198  /*
4199  * On Windows, strxfrm returns INT_MAX when an error occurs. Instead
4200  * of trying to allocate this much memory (and fail), just return the
4201  * original string unmodified as if we were in the C locale.
4202  */
4203  if (xfrmlen == INT_MAX)
4204  return val;
4205 #endif
4206  xfrmstr = (char *) palloc(xfrmlen + 1);
4207  xfrmlen2 = strxfrm(xfrmstr, val, xfrmlen + 1);
4208 
4209  /*
4210  * Some systems (e.g., glibc) can return a smaller value from the
4211  * second call than the first; thus the Assert must be <= not ==.
4212  */
4213  Assert(xfrmlen2 <= xfrmlen);
4214  pfree(val);
4215  val = xfrmstr;
4216  }
4217 
4218  return val;
4219 }
4220 
4221 /*
4222  * Do convert_to_scalar()'s work for any bytea data type.
4223  *
4224  * Very similar to convert_string_to_scalar except we can't assume
4225  * null-termination and therefore pass explicit lengths around.
4226  *
4227  * Also, assumptions about likely "normal" ranges of characters have been
4228  * removed - a data range of 0..255 is always used, for now. (Perhaps
4229  * someday we will add information about actual byte data range to
4230  * pg_statistic.)
4231  */
4232 static void
4234  double *scaledvalue,
4235  Datum lobound,
4236  double *scaledlobound,
4237  Datum hibound,
4238  double *scaledhibound)
4239 {
4240  int rangelo,
4241  rangehi,
4242  valuelen = VARSIZE(DatumGetPointer(value)) - VARHDRSZ,
4243  loboundlen = VARSIZE(DatumGetPointer(lobound)) - VARHDRSZ,
4244  hiboundlen = VARSIZE(DatumGetPointer(hibound)) - VARHDRSZ,
4245  i,
4246  minlen;
4247  unsigned char *valstr = (unsigned char *) VARDATA(DatumGetPointer(value)),
4248  *lostr = (unsigned char *) VARDATA(DatumGetPointer(lobound)),
4249  *histr = (unsigned char *) VARDATA(DatumGetPointer(hibound));
4250 
4251  /*
4252  * Assume bytea data is uniformly distributed across all byte values.
4253  */
4254  rangelo = 0;
4255  rangehi = 255;
4256 
4257  /*
4258  * Now strip any common prefix of the three strings.
4259  */
4260  minlen = Min(Min(valuelen, loboundlen), hiboundlen);
4261  for (i = 0; i < minlen; i++)
4262  {
4263  if (*lostr != *histr || *lostr != *valstr)
4264  break;
4265  lostr++, histr++, valstr++;
4266  loboundlen--, hiboundlen--, valuelen--;
4267  }
4268 
4269  /*
4270  * Now we can do the conversions.
4271  */
4272  *scaledvalue = convert_one_bytea_to_scalar(valstr, valuelen, rangelo, rangehi);
4273  *scaledlobound = convert_one_bytea_to_scalar(lostr, loboundlen, rangelo, rangehi);
4274  *scaledhibound = convert_one_bytea_to_scalar(histr, hiboundlen, rangelo, rangehi);
4275 }
4276 
4277 static double
4278 convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
4279  int rangelo, int rangehi)
4280 {
4281  double num,
4282  denom,
4283  base;
4284 
4285  if (valuelen <= 0)
4286  return 0.0; /* empty string has scalar value 0 */
4287 
4288  /*
4289  * Since base is 256, need not consider more than about 10 chars (even
4290  * this many seems like overkill)
4291  */
4292  if (valuelen > 10)
4293  valuelen = 10;
4294 
4295  /* Convert initial characters to fraction */
4296  base = rangehi - rangelo + 1;
4297  num = 0.0;
4298  denom = base;
4299  while (valuelen-- > 0)
4300  {
4301  int ch = *value++;
4302 
4303  if (ch < rangelo)
4304  ch = rangelo - 1;
4305  else if (ch > rangehi)
4306  ch = rangehi + 1;
4307  num += ((double) (ch - rangelo)) / denom;
4308  denom *= base;
4309  }
4310 
4311  return num;
4312 }
4313 
4314 /*
4315  * Do convert_to_scalar()'s work for any timevalue data type.
4316  */
4317 static double
4319 {
4320  switch (typid)
4321  {
4322  case TIMESTAMPOID:
4323  return DatumGetTimestamp(value);
4324  case TIMESTAMPTZOID:
4325  return DatumGetTimestampTz(value);
4326  case ABSTIMEOID:
4328  value));
4329  case DATEOID:
4331  case INTERVALOID:
4332  {
4334 
4335  /*
4336  * Convert the month part of Interval to days using assumed
4337  * average month length of 365.25/12.0 days. Not too
4338  * accurate, but plenty good enough for our purposes.
4339  */
4340  return interval->time + interval->day * (double) USECS_PER_DAY +
4341  interval->month * ((DAYS_PER_YEAR / (double) MONTHS_PER_YEAR) * USECS_PER_DAY);
4342  }
4343  case RELTIMEOID:
4344  return (DatumGetRelativeTime(value) * 1000000.0);
4345  case TINTERVALOID:
4346  {
4347  TimeInterval tinterval = DatumGetTimeInterval(value);
4348 
4349  if (tinterval->status != 0)
4350  return ((tinterval->data[1] - tinterval->data[0]) * 1000000.0);
4351  return 0; /* for lack of a better idea */
4352  }
4353  case TIMEOID:
4354  return DatumGetTimeADT(value);
4355  case TIMETZOID:
4356  {
4357  TimeTzADT *timetz = DatumGetTimeTzADTP(value);
4358 
4359  /* use GMT-equivalent time */
4360  return (double) (timetz->time + (timetz->zone * 1000000.0));
4361  }
4362  }
4363 
4364  /*
4365  * Can't get here unless someone tries to use scalarltsel/scalargtsel on
4366  * an operator with one timevalue and one non-timevalue operand.
4367  */
4368  elog(ERROR, "unsupported type: %u", typid);
4369  return 0;
4370 }
4371 
4372 
4373 /*
4374  * get_restriction_variable
4375  * Examine the args of a restriction clause to see if it's of the
4376  * form (variable op pseudoconstant) or (pseudoconstant op variable),
4377  * where "variable" could be either a Var or an expression in vars of a
4378  * single relation. If so, extract information about the variable,
4379  * and also indicate which side it was on and the other argument.
4380  *
4381  * Inputs:
4382  * root: the planner info
4383  * args: clause argument list
4384  * varRelid: see specs for restriction selectivity functions
4385  *
4386  * Outputs: (these are valid only if TRUE is returned)
4387  * *vardata: gets information about variable (see examine_variable)
4388  * *other: gets other clause argument, aggressively reduced to a constant
4389  * *varonleft: set TRUE if variable is on the left, FALSE if on the right
4390  *
4391  * Returns TRUE if a variable is identified, otherwise FALSE.
4392  *
4393  * Note: if there are Vars on both sides of the clause, we must fail, because
4394  * callers are expecting that the other side will act like a pseudoconstant.
4395  */
4396 bool
4398  VariableStatData *vardata, Node **other,
4399  bool *varonleft)
4400 {
4401  Node *left,
4402  *right;
4403  VariableStatData rdata;
4404 
4405  /* Fail if not a binary opclause (probably shouldn't happen) */
4406  if (list_length(args) != 2)
4407  return false;
4408 
4409  left = (Node *) linitial(args);
4410  right = (Node *) lsecond(args);
4411 
4412  /*
4413  * Examine both sides. Note that when varRelid is nonzero, Vars of other
4414  * relations will be treated as pseudoconstants.
4415  */
4416  examine_variable(root, left, varRelid, vardata);
4417  examine_variable(root, right, varRelid, &rdata);
4418 
4419  /*
4420  * If one side is a variable and the other not, we win.
4421  */
4422  if (vardata->rel && rdata.rel == NULL)
4423  {
4424  *varonleft = true;
4425  *other = estimate_expression_value(root, rdata.var);
4426  /* Assume we need no ReleaseVariableStats(rdata) here */
4427  return true;
4428  }
4429 
4430  if (vardata->rel == NULL && rdata.rel)
4431  {
4432  *varonleft = false;
4433  *other = estimate_expression_value(root, vardata->var);
4434  /* Assume we need no ReleaseVariableStats(*vardata) here */
4435  *vardata = rdata;
4436  return true;
4437  }
4438 
4439  /* Oops, clause has wrong structure (probably var op var) */
4440  ReleaseVariableStats(*vardata);
4441  ReleaseVariableStats(rdata);
4442 
4443  return false;
4444 }
4445 
4446 /*
4447  * get_join_variables
4448  * Apply examine_variable() to each side of a join clause.
4449  * Also, attempt to identify whether the join clause has the same
4450  * or reversed sense compared to the SpecialJoinInfo.
4451  *
4452  * We consider the join clause "normal" if it is "lhs_var OP rhs_var",
4453  * or "reversed" if it is "rhs_var OP lhs_var". In complicated cases
4454  * where we can't tell for sure, we default to assuming it's normal.
4455  */
4456 void
4458  VariableStatData *vardata1, VariableStatData *vardata2,
4459  bool *join_is_reversed)
4460 {
4461  Node *left,
4462  *right;
4463 
4464  if (list_length(args) != 2)
4465  elog(ERROR, "join operator should take two arguments");
4466 
4467  left = (Node *) linitial(args);
4468  right = (Node *) lsecond(args);
4469 
4470  examine_variable(root, left, 0, vardata1);
4471  examine_variable(root, right, 0, vardata2);
4472 
4473  if (vardata1->rel &&
4474  bms_is_subset(vardata1->rel->relids, sjinfo->syn_righthand))
4475  *join_is_reversed = true; /* var1 is on RHS */
4476  else if (vardata2->rel &&
4477  bms_is_subset(vardata2->rel->relids, sjinfo->syn_lefthand))
4478  *join_is_reversed = true; /* var2 is on LHS */
4479  else
4480  *join_is_reversed = false;
4481 }
4482 
4483 /*
4484  * examine_variable
4485  * Try to look up statistical data about an expression.
4486  * Fill in a VariableStatData struct to describe the expression.
4487  *
4488  * Inputs:
4489  * root: the planner info
4490  * node: the expression tree to examine
4491  * varRelid: see specs for restriction selectivity functions
4492  *
4493  * Outputs: *vardata is filled as follows:
4494  * var: the input expression (with any binary relabeling stripped, if
4495  * it is or contains a variable; but otherwise the type is preserved)
4496  * rel: RelOptInfo for relation containing variable; NULL if expression
4497  * contains no Vars (NOTE this could point to a RelOptInfo of a
4498  * subquery, not one in the current query).
4499  * statsTuple: the pg_statistic entry for the variable, if one exists;
4500  * otherwise NULL.
4501  * freefunc: pointer to a function to release statsTuple with.
4502  * vartype: exposed type of the expression; this should always match
4503  * the declared input type of the operator we are estimating for.
4504  * atttype, atttypmod: actual type/typmod of the "var" expression. This is
4505  * commonly the same as the exposed type of the variable argument,
4506  * but can be different in binary-compatible-type cases.
4507  * isunique: TRUE if we were able to match the var to a unique index or a
4508  * single-column DISTINCT clause, implying its values are unique for
4509  * this query. (Caution: this should be trusted for statistical
4510  * purposes only, since we do not check indimmediate nor verify that
4511  * the exact same definition of equality applies.)
4512  * acl_ok: TRUE if current user has permission to read the column(s)
4513  * underlying the pg_statistic entry. This is consulted by
4514  * statistic_proc_security_check().
4515  *
4516  * Caller is responsible for doing ReleaseVariableStats() before exiting.
4517  */
4518 void
4519 examine_variable(PlannerInfo *root, Node *node, int varRelid,
4520  VariableStatData *vardata)
4521 {
4522  Node *basenode;
4523  Relids varnos;
4524  RelOptInfo *onerel;
4525 
4526  /* Make sure we don't return dangling pointers in vardata */
4527  MemSet(vardata, 0, sizeof(VariableStatData));
4528 
4529  /* Save the exposed type of the expression */
4530  vardata->vartype = exprType(node);
4531 
4532  /* Look inside any binary-compatible relabeling */
4533 
4534  if (IsA(node, RelabelType))
4535  basenode = (Node *) ((RelabelType *) node)->arg;
4536  else
4537  basenode = node;
4538 
4539  /* Fast path for a simple Var */
4540 
4541  if (IsA(basenode, Var) &&
4542  (varRelid == 0 || varRelid == ((Var *) basenode)->varno))
4543  {
4544  Var *var = (Var *) basenode;
4545 
4546  /* Set up result fields other than the stats tuple */
4547  vardata->var = basenode; /* return Var without relabeling */
4548  vardata->rel = find_base_rel(root, var->varno);
4549  vardata->atttype = var->vartype;
4550  vardata->atttypmod = var->vartypmod;
4551  vardata->isunique = has_unique_index(vardata->rel, var->varattno);
4552 
4553  /* Try to locate some stats */
4554  examine_simple_variable(root, var, vardata);
4555 
4556  return;
4557  }
4558 
4559  /*
4560  * Okay, it's a more complicated expression. Determine variable
4561  * membership. Note that when varRelid isn't zero, only vars of that
4562  * relation are considered "real" vars.
4563  */
4564  varnos = pull_varnos(basenode);
4565 
4566  onerel = NULL;
4567 
4568  switch (bms_membership(varnos))
4569  {
4570  case BMS_EMPTY_SET:
4571  /* No Vars at all ... must be pseudo-constant clause */
4572  break;
4573  case BMS_SINGLETON:
4574  if (varRelid == 0 || bms_is_member(varRelid, varnos))
4575  {
4576  onerel = find_base_rel(root,
4577  (varRelid ? varRelid : bms_singleton_member(varnos)));
4578  vardata->rel = onerel;
4579  node = basenode; /* strip any relabeling */
4580  }
4581  /* else treat it as a constant */
4582  break;
4583  case BMS_MULTIPLE:
4584  if (varRelid == 0)
4585  {
4586  /* treat it as a variable of a join relation */
4587  vardata->rel = find_join_rel(root, varnos);
4588  node = basenode; /* strip any relabeling */
4589  }
4590  else if (bms_is_member(varRelid, varnos))
4591  {
4592  /* ignore the vars belonging to other relations */
4593  vardata->rel = find_base_rel(root, varRelid);
4594  node = basenode; /* strip any relabeling */
4595  /* note: no point in expressional-index search here */
4596  }
4597  /* else treat it as a constant */
4598  break;
4599  }
4600 
4601  bms_free(varnos);
4602 
4603  vardata->var = node;
4604  vardata->atttype = exprType(node);
4605  vardata->atttypmod = exprTypmod(node);
4606 
4607  if (onerel)
4608  {
4609  /*
4610  * We have an expression in vars of a single relation. Try to match
4611  * it to expressional index columns, in hopes of finding some
4612  * statistics.
4613  *
4614  * XXX it's conceivable that there are multiple matches with different
4615  * index opfamilies; if so, we need to pick one that matches the
4616  * operator we are estimating for. FIXME later.
4617  */
4618  ListCell *ilist;
4619 
4620  foreach(ilist, onerel->indexlist)
4621  {
4622  IndexOptInfo *index = (IndexOptInfo *) lfirst(ilist);
4623  ListCell *indexpr_item;
4624  int pos;
4625 
4626  indexpr_item = list_head(index->indexprs);
4627  if (indexpr_item == NULL)
4628  continue; /* no expressions here... */
4629 
4630  for (pos = 0; pos < index->ncolumns; pos++)
4631  {
4632  if (index->indexkeys[pos] == 0)
4633  {
4634  Node *indexkey;
4635 
4636  if (indexpr_item == NULL)
4637  elog(ERROR, "too few entries in indexprs list");
4638  indexkey = (Node *) lfirst(indexpr_item);
4639  if (indexkey && IsA(indexkey, RelabelType))
4640  indexkey = (Node *) ((RelabelType *) indexkey)->arg;
4641  if (equal(node, indexkey))
4642  {
4643  /*
4644  * Found a match ... is it a unique index? Tests here
4645  * should match has_unique_index().
4646  */
4647  if (index->unique &&
4648  index->ncolumns == 1 &&
4649  (index->indpred == NIL || index->predOK))
4650  vardata->isunique = true;
4651 
4652  /*
4653  * Has it got stats? We only consider stats for
4654  * non-partial indexes, since partial indexes probably
4655  * don't reflect whole-relation statistics; the above
4656  * check for uniqueness is the only info we take from
4657  * a partial index.
4658  *
4659  * An index stats hook, however, must make its own
4660  * decisions about what to do with partial indexes.
4661  */
4662  if (get_index_stats_hook &&
4663  (*get_index_stats_hook) (root, index->indexoid,
4664  pos + 1, vardata))
4665  {
4666  /*
4667  * The hook took control of acquiring a stats
4668  * tuple. If it did supply a tuple, it'd better
4669  * have supplied a freefunc.
4670  */
4671  if (HeapTupleIsValid(vardata->statsTuple) &&
4672  !vardata->freefunc)
4673  elog(ERROR, "no function provided to release variable stats with");
4674  }
4675  else if (index->indpred == NIL)
4676  {
4677  vardata->statsTuple =
4679  ObjectIdGetDatum(index->indexoid),
4680  Int16GetDatum(pos + 1),
4681  BoolGetDatum(false));
4682  vardata->freefunc = ReleaseSysCache;
4683 
4684  if (HeapTupleIsValid(vardata->statsTuple))
4685  {
4686  /* Get index's table for permission check */
4687  RangeTblEntry *rte;
4688 
4689  rte = planner_rt_fetch(index->rel->relid, root);
4690  Assert(rte->rtekind == RTE_RELATION);
4691 
4692  /*
4693  * For simplicity, we insist on the whole
4694  * table being selectable, rather than trying
4695  * to identify which column(s) the index
4696  * depends on.
4697  */
4698  vardata->acl_ok =
4700  ACL_SELECT) == ACLCHECK_OK);
4701  }
4702  else
4703  {
4704  /* suppress leakproofness checks later */
4705  vardata->acl_ok = true;
4706  }
4707  }
4708  if (vardata->statsTuple)
4709  break;
4710  }
4711  indexpr_item = lnext(indexpr_item);
4712  }
4713  }
4714  if (vardata->statsTuple)
4715  break;
4716  }
4717  }
4718 }
4719 
4720 /*
4721  * examine_simple_variable
4722  * Handle a simple Var for examine_variable
4723  *
4724  * This is split out as a subroutine so that we can recurse to deal with
4725  * Vars referencing subqueries.
4726  *
4727  * We already filled in all the fields of *vardata except for the stats tuple.
4728  */
4729 static void
4731  VariableStatData *vardata)
4732 {
4733  RangeTblEntry *rte = root->simple_rte_array[var->varno];
4734 
4735  Assert(IsA(rte, RangeTblEntry));
4736 
4738  (*get_relation_stats_hook) (root, rte, var->varattno, vardata))
4739  {
4740  /*
4741  * The hook took control of acquiring a stats tuple. If it did supply
4742  * a tuple, it'd better have supplied a freefunc.
4743  */
4744  if (HeapTupleIsValid(vardata->statsTuple) &&
4745  !vardata->freefunc)
4746  elog(ERROR, "no function provided to release variable stats with");
4747  }
4748  else if (rte->rtekind == RTE_RELATION)
4749  {
4750  /*
4751  * Plain table or parent of an inheritance appendrel, so look up the
4752  * column in pg_statistic
4753  */
4755  ObjectIdGetDatum(rte->relid),
4756  Int16GetDatum(var->varattno),
4757  BoolGetDatum(rte->inh));
4758  vardata->freefunc = ReleaseSysCache;
4759 
4760  if (HeapTupleIsValid(vardata->statsTuple))
4761  {
4762  /* check if user has permission to read this column */
4763  vardata->acl_ok =
4765  ACL_SELECT) == ACLCHECK_OK) ||
4767  ACL_SELECT) == ACLCHECK_OK);
4768  }
4769  else
4770  {
4771  /* suppress any possible leakproofness checks later */
4772  vardata->acl_ok = true;
4773  }
4774  }
4775  else if (rte->rtekind == RTE_SUBQUERY && !rte->inh)
4776  {
4777  /*
4778  * Plain subquery (not one that was converted to an appendrel).
4779  */
4780  Query *subquery = rte->subquery;
4781  RelOptInfo *rel;
4782  TargetEntry *ste;
4783 
4784  /*
4785  * Punt if it's a whole-row var rather than a plain column reference.
4786  */
4787  if (var->varattno == InvalidAttrNumber)
4788  return;
4789 
4790  /*
4791  * Punt if subquery uses set operations or GROUP BY, as these will
4792  * mash underlying columns' stats beyond recognition. (Set ops are
4793  * particularly nasty; if we forged ahead, we would return stats
4794  * relevant to only the leftmost subselect...) DISTINCT is also
4795  * problematic, but we check that later because there is a possibility
4796  * of learning something even with it.
4797  */
4798  if (subquery->setOperations ||
4799  subquery->groupClause)
4800  return;
4801 
4802  /*
4803  * OK, fetch RelOptInfo for subquery. Note that we don't change the
4804  * rel returned in vardata, since caller expects it to be a rel of the
4805  * caller's query level. Because we might already be recursing, we
4806  * can't use that rel pointer either, but have to look up the Var's
4807  * rel afresh.
4808  */
4809  rel = find_base_rel(root, var->varno);
4810 
4811  /* If the subquery hasn't been planned yet, we have to punt */
4812  if (rel->subroot == NULL)
4813  return;
4814  Assert(IsA(rel->subroot, PlannerInfo));
4815 
4816  /*
4817  * Switch our attention to the subquery as mangled by the planner. It
4818  * was okay to look at the pre-planning version for the tests above,
4819  * but now we need a Var that will refer to the subroot's live
4820  * RelOptInfos. For instance, if any subquery pullup happened during
4821  * planning, Vars in the targetlist might have gotten replaced, and we
4822  * need to see the replacement expressions.
4823  */
4824  subquery = rel->subroot->parse;
4825  Assert(IsA(subquery, Query));
4826 
4827  /* Get the subquery output expression referenced by the upper Var */
4828  ste = get_tle_by_resno(subquery->targetList, var->varattno);
4829  if (ste == NULL || ste->resjunk)
4830  elog(ERROR, "subquery %s does not have attribute %d",
4831  rte->eref->aliasname, var->varattno);
4832  var = (Var *) ste->expr;
4833 
4834  /*
4835  * If subquery uses DISTINCT, we can't make use of any stats for the
4836  * variable ... but, if it's the only DISTINCT column, we are entitled
4837  * to consider it unique. We do the test this way so that it works
4838  * for cases involving DISTINCT ON.
4839  */
4840  if (subquery->distinctClause)
4841  {
4842  if (list_length(subquery->distinctClause) == 1 &&
4843  targetIsInSortList(ste, InvalidOid, subquery->distinctClause))
4844  vardata->isunique = true;
4845  /* cannot go further */
4846  return;
4847  }
4848 
4849  /*
4850  * If the sub-query originated from a view with the security_barrier
4851  * attribute, we must not look at the variable's statistics, though it
4852  * seems all right to notice the existence of a DISTINCT clause. So
4853  * stop here.
4854  *
4855  * This is probably a harsher restriction than necessary; it's
4856  * certainly OK for the selectivity estimator (which is a C function,
4857  * and therefore omnipotent anyway) to look at the statistics. But
4858  * many selectivity estimators will happily *invoke the operator
4859  * function* to try to work out a good estimate - and that's not OK.
4860  * So for now, don't dig down for stats.
4861  */
4862  if (rte->security_barrier)
4863  return;
4864 
4865  /* Can only handle a simple Var of subquery's query level */
4866  if (var && IsA(var, Var) &&
4867  var->varlevelsup == 0)
4868  {
4869  /*
4870  * OK, recurse into the subquery. Note that the original setting
4871  * of vardata->isunique (which will surely be false) is left
4872  * unchanged in this situation. That's what we want, since even
4873  * if the underlying column is unique, the subquery may have
4874  * joined to other tables in a way that creates duplicates.
4875  */
4876  examine_simple_variable(rel->subroot, var, vardata);
4877  }
4878  }
4879  else
4880  {
4881  /*
4882  * Otherwise, the Var comes from a FUNCTION, VALUES, or CTE RTE. (We
4883  * won't see RTE_JOIN here because join alias Vars have already been
4884  * flattened.) There's not much we can do with function outputs, but
4885  * maybe someday try to be smarter about VALUES and/or CTEs.
4886  */
4887  }
4888 }
4889 
4890 /*
4891  * Check whether it is permitted to call func_oid passing some of the
4892  * pg_statistic data in vardata. We allow this either if the user has SELECT
4893  * privileges on the table or column underlying the pg_statistic data or if
4894  * the function is marked leak-proof.
4895  */
4896 bool
4898 {
4899  if (vardata->acl_ok)
4900  return true;
4901 
4902  if (!OidIsValid(func_oid))
4903  return false;
4904 
4905  if (get_func_leakproof(func_oid))
4906  return true;
4907 
4908  ereport(DEBUG2,
4909  (errmsg_internal("not using statistics because function \"%s\" is not leak-proof",
4910  get_func_name(func_oid))));
4911  return false;
4912 }
4913 
4914 /*
4915  * get_variable_numdistinct
4916  * Estimate the number of distinct values of a variable.
4917  *
4918  * vardata: results of examine_variable
4919  * *isdefault: set to TRUE if the result is a default rather than based on
4920  * anything meaningful.
4921  *
4922  * NB: be careful to produce a positive integral result, since callers may
4923  * compare the result to exact integer counts, or might divide by it.
4924  */
4925 double
4926 get_variable_numdistinct(VariableStatData *vardata, bool *isdefault)
4927 {
4928  double stadistinct;
4929  double stanullfrac = 0.0;
4930  double ntuples;
4931 
4932  *isdefault = false;
4933 
4934  /*
4935  * Determine the stadistinct value to use. There are cases where we can
4936  * get an estimate even without a pg_statistic entry, or can get a better
4937  * value than is in pg_statistic. Grab stanullfrac too if we can find it
4938  * (otherwise, assume no nulls, for lack of any better idea).
4939  */
4940  if (HeapTupleIsValid(vardata->statsTuple))
4941  {
4942  /* Use the pg_statistic entry */
4943  Form_pg_statistic stats;
4944 
4945  stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
4946  stadistinct = stats->stadistinct;
4947  stanullfrac = stats->stanullfrac;
4948  }
4949  else if (vardata->vartype == BOOLOID)
4950  {
4951  /*
4952  * Special-case boolean columns: presumably, two distinct values.
4953  *
4954  * Are there any other datatypes we should wire in special estimates
4955  * for?
4956  */
4957  stadistinct = 2.0;
4958  }
4959  else
4960  {
4961  /*
4962  * We don't keep statistics for system columns, but in some cases we
4963  * can infer distinctness anyway.
4964  */
4965  if (vardata->var && IsA(vardata->var, Var))
4966  {
4967  switch (((Var *) vardata->var)->varattno)
4968  {
4971  stadistinct = -1.0; /* unique (and all non null) */
4972  break;
4974  stadistinct = 1.0; /* only 1 value */
4975  break;
4976  default:
4977  stadistinct = 0.0; /* means "unknown" */
4978  break;
4979  }
4980  }
4981  else
4982  stadistinct = 0.0; /* means "unknown" */
4983 
4984  /*
4985  * XXX consider using estimate_num_groups on expressions?
4986  */
4987  }
4988 
4989  /*
4990  * If there is a unique index or DISTINCT clause for the variable, assume
4991  * it is unique no matter what pg_statistic says; the statistics could be
4992  * out of date, or we might have found a partial unique index that proves
4993  * the var is unique for this query. However, we'd better still believe
4994  * the null-fraction statistic.
4995  */
4996  if (vardata->isunique)
4997  stadistinct = -1.0 * (1.0 - stanullfrac);
4998 
4999  /*
5000  * If we had an absolute estimate, use that.
5001  */
5002  if (stadistinct > 0.0)
5003  return clamp_row_est(stadistinct);
5004 
5005  /*
5006  * Otherwise we need to get the relation size; punt if not available.
5007  */
5008  if (vardata->rel == NULL)
5009  {
5010  *isdefault = true;
5011  return DEFAULT_NUM_DISTINCT;
5012  }
5013  ntuples = vardata->rel->tuples;
5014  if (ntuples <= 0.0)
5015  {
5016  *isdefault = true;
5017  return DEFAULT_NUM_DISTINCT;
5018  }
5019 
5020  /*
5021  * If we had a relative estimate, use that.
5022  */
5023  if (stadistinct < 0.0)
5024  return clamp_row_est(-stadistinct * ntuples);
5025 
5026  /*
5027  * With no data, estimate ndistinct = ntuples if the table is small, else
5028  * use default. We use DEFAULT_NUM_DISTINCT as the cutoff for "small" so
5029  * that the behavior isn't discontinuous.
5030  */
5031  if (ntuples < DEFAULT_NUM_DISTINCT)
5032  return clamp_row_est(ntuples);
5033 
5034  *isdefault = true;
5035  return DEFAULT_NUM_DISTINCT;
5036 }
5037 
5038 /*
5039  * get_variable_range
5040  * Estimate the minimum and maximum value of the specified variable.
5041  * If successful, store values in *min and *max, and return TRUE.
5042  * If no data available, return FALSE.
5043  *
5044  * sortop is the "<" comparison operator to use. This should generally
5045  * be "<" not ">", as only the former is likely to be found in pg_statistic.
5046  */
5047 static bool
5049  Datum *min, Datum *max)
5050 {
5051  Datum tmin = 0;
5052  Datum tmax = 0;
5053  bool have_data = false;
5054  int16 typLen;
5055  bool typByVal;
5056  Oid opfuncoid;
5057  AttStatsSlot sslot;
5058  int i;
5059 
5060  /*
5061  * XXX It's very tempting to try to use the actual column min and max, if
5062  * we can get them relatively-cheaply with an index probe. However, since
5063  * this function is called many times during join planning, that could
5064  * have unpleasant effects on planning speed. Need more investigation
5065  * before enabling this.
5066  */
5067 #ifdef NOT_USED
5068  if (get_actual_variable_range(root, vardata, sortop, min, max))
5069  return true;
5070 #endif
5071 
5072  if (!HeapTupleIsValid(vardata->statsTuple))
5073  {
5074  /* no stats available, so default result */
5075  return false;
5076  }
5077 
5078  /*
5079  * If we can't apply the sortop to the stats data, just fail. In
5080  * principle, if there's a histogram and no MCVs, we could return the
5081  * histogram endpoints without ever applying the sortop ... but it's
5082  * probably not worth trying, because whatever the caller wants to do with
5083  * the endpoints would likely fail the security check too.
5084  */
5085  if (!statistic_proc_security_check(vardata,
5086  (opfuncoid = get_opcode(sortop))))
5087  return false;
5088 
5089  get_typlenbyval(vardata->atttype, &typLen, &typByVal);
5090 
5091  /*
5092  * If there is a histogram, grab the first and last values.
5093  *
5094  * If there is a histogram that is sorted with some other operator than
5095  * the one we want, fail --- this suggests that there is data we can't
5096  * use.
5097  */
5098  if (get_attstatsslot(&sslot, vardata->statsTuple,
5099  STATISTIC_KIND_HISTOGRAM, sortop,
5101  {
5102  if (sslot.nvalues > 0)
5103  {
5104  tmin = datumCopy(sslot.values[0], typByVal, typLen);
5105  tmax = datumCopy(sslot.values[sslot.nvalues - 1], typByVal, typLen);
5106  have_data = true;
5107  }
5108  free_attstatsslot(&sslot);
5109  }
5110  else if (get_attstatsslot(&sslot, vardata->statsTuple,
5112  0))
5113  {
5114  free_attstatsslot(&sslot);
5115  return false;
5116  }
5117 
5118  /*
5119  * If we have most-common-values info, look for extreme MCVs. This is
5120  * needed even if we also have a histogram, since the histogram excludes
5121  * the MCVs. However, usually the MCVs will not be the extreme values, so
5122  * avoid unnecessary data copying.
5123  */
5124  if (get_attstatsslot(&sslot, vardata->statsTuple,
5127  {
5128  bool tmin_is_mcv = false;
5129  bool tmax_is_mcv = false;
5130  FmgrInfo opproc;
5131 
5132  fmgr_info(opfuncoid, &opproc);
5133 
5134  for (i = 0; i < sslot.nvalues; i++)
5135  {
5136  if (!have_data)
5137  {
5138  tmin = tmax = sslot.values[i];
5139  tmin_is_mcv = tmax_is_mcv = have_data = true;
5140  continue;
5141  }
5142  if (DatumGetBool(FunctionCall2Coll(&opproc,
5144  sslot.values[i], tmin)))
5145  {
5146  tmin = sslot.values[i];
5147  tmin_is_mcv = true;
5148  }
5149  if (DatumGetBool(FunctionCall2Coll(&opproc,
5151  tmax, sslot.values[i])))
5152  {
5153  tmax = sslot.values[i];
5154  tmax_is_mcv = true;
5155  }
5156  }
5157  if (tmin_is_mcv)
5158  tmin = datumCopy(tmin, typByVal, typLen);
5159  if (tmax_is_mcv)
5160  tmax = datumCopy(tmax, typByVal, typLen);
5161  free_attstatsslot(&sslot);
5162  }
5163 
5164  *min = tmin;
5165  *max = tmax;
5166  return have_data;
5167 }
5168 
5169 
5170 /*
5171  * get_actual_variable_range
5172  * Attempt to identify the current *actual* minimum and/or maximum
5173  * of the specified variable, by looking for a suitable btree index
5174  * and fetching its low and/or high values.
5175  * If successful, store values in *min and *max, and return TRUE.
5176  * (Either pointer can be NULL if that endpoint isn't needed.)
5177  * If no data available, return FALSE.
5178  *
5179  * sortop is the "<" comparison operator to use.
5180  */
5181 static bool
5183  Oid sortop,
5184  Datum *min, Datum *max)
5185 {
5186  bool have_data = false;
5187  RelOptInfo *rel = vardata->rel;
5188  RangeTblEntry *rte;
5189  ListCell *lc;
5190 
5191  /* No hope if no relation or it doesn't have indexes */
5192  if (rel == NULL || rel->indexlist == NIL)
5193  return false;
5194  /* If it has indexes it must be a plain relation */
5195  rte = root->simple_rte_array[rel->relid];
5196  Assert(rte->rtekind == RTE_RELATION);
5197 
5198  /* Search through the indexes to see if any match our problem */
5199  foreach(lc, rel->indexlist)
5200  {
5202  ScanDirection indexscandir;
5203 
5204  /* Ignore non-btree indexes */
5205  if (index->relam != BTREE_AM_OID)
5206  continue;
5207 
5208  /*
5209  * Ignore partial indexes --- we only want stats that cover the entire
5210  * relation.
5211  */
5212  if (index->indpred != NIL)
5213  continue;
5214 
5215  /*
5216  * The index list might include hypothetical indexes inserted by a
5217  * get_relation_info hook --- don't try to access them.
5218  */
5219  if (index->hypothetical)
5220  continue;
5221 
5222  /*
5223  * The first index column must match the desired variable and sort
5224  * operator --- but we can use a descending-order index.
5225  */
5226  if (!match_index_to_operand(vardata->var, 0, index))
5227  continue;
5228  switch (get_op_opfamily_strategy(sortop, index->sortopfamily[0]))
5229  {
5230  case BTLessStrategyNumber:
5231  if (index->reverse_sort[0])
5232  indexscandir = BackwardScanDirection;
5233  else
5234  indexscandir = ForwardScanDirection;
5235  break;
5237  if (index->reverse_sort[0])
5238  indexscandir = ForwardScanDirection;
5239  else
5240  indexscandir = BackwardScanDirection;
5241  break;
5242  default:
5243  /* index doesn't match the sortop */
5244  continue;
5245  }
5246 
5247  /*
5248  * Found a suitable index to extract data from. We'll need an EState
5249  * and a bunch of other infrastructure.
5250  */
5251  {
5252  EState *estate;
5253  ExprContext *econtext;
5254  MemoryContext tmpcontext;
5255  MemoryContext oldcontext;
5256  Relation heapRel;
5257  Relation indexRel;
5258  IndexInfo *indexInfo;
5259  TupleTableSlot *slot;
5260  int16 typLen;
5261  bool typByVal;
5262  ScanKeyData scankeys[1];
5263  IndexScanDesc index_scan;
5264  HeapTuple tup;
5266  bool isnull[INDEX_MAX_KEYS];
5267  SnapshotData SnapshotDirty;
5268 
5269  estate = CreateExecutorState();
5270  econtext = GetPerTupleExprContext(estate);
5271  /* Make sure any cruft is generated in the econtext's memory */
5272  tmpcontext = econtext->ecxt_per_tuple_memory;
5273  oldcontext = MemoryContextSwitchTo(tmpcontext);
5274 
5275  /*
5276  * Open the table and index so we can read from them. We should
5277  * already have at least AccessShareLock on the table, but not
5278  * necessarily on the index.
5279  */
5280  heapRel = heap_open(rte->relid, NoLock);
5281  indexRel = index_open(index->indexoid, AccessShareLock);
5282 
5283  /* extract index key information from the index's pg_index info */
5284  indexInfo = BuildIndexInfo(indexRel);
5285 
5286  /* some other stuff */
5287  slot = MakeSingleTupleTableSlot(RelationGetDescr(heapRel));
5288  econtext->ecxt_scantuple = slot;
5289  get_typlenbyval(vardata->atttype, &typLen, &typByVal);
5290  InitDirtySnapshot(SnapshotDirty);
5291 
5292  /* set up an IS NOT NULL scan key so that we ignore nulls */
5293  ScanKeyEntryInitialize(&scankeys[0],
5295  1, /* index col to scan */
5296  InvalidStrategy, /* no strategy */
5297  InvalidOid, /* no strategy subtype */
5298  InvalidOid, /* no collation */
5299  InvalidOid, /* no reg proc for this */
5300  (Datum) 0); /* constant */
5301 
5302  have_data = true;
5303 
5304  /* If min is requested ... */
5305  if (min)
5306  {
5307  /*
5308  * In principle, we should scan the index with our current
5309  * active snapshot, which is the best approximation we've got
5310  * to what the query will see when executed. But that won't
5311  * be exact if a new snap is taken before running the query,
5312  * and it can be very expensive if a lot of uncommitted rows
5313  * exist at the end of the index (because we'll laboriously
5314  * fetch each one and reject it). What seems like a good
5315  * compromise is to use SnapshotDirty. That will accept
5316  * uncommitted rows, and thus avoid fetching multiple heap
5317  * tuples in this scenario. On the other hand, it will reject
5318  * known-dead rows, and thus not give a bogus answer when the
5319  * extreme value has been deleted; that case motivates not
5320  * using SnapshotAny here.
5321  */
5322  index_scan = index_beginscan(heapRel, indexRel, &SnapshotDirty,
5323  1, 0);
5324  index_rescan(index_scan, scankeys, 1, NULL, 0);
5325 
5326  /* Fetch first tuple in sortop's direction */
5327  if ((tup = index_getnext(index_scan,
5328  indexscandir)) != NULL)
5329  {
5330  /* Extract the index column values from the heap tuple */
5331  ExecStoreTuple(tup, slot, InvalidBuffer, false);
5332  FormIndexDatum(indexInfo, slot, estate,
5333  values, isnull);
5334 
5335  /* Shouldn't have got a null, but be careful */
5336  if (isnull[0])
5337  elog(ERROR, "found unexpected null value in index \"%s\"",
5338  RelationGetRelationName(indexRel));
5339 
5340  /* Copy the index column value out to caller's context */
5341  MemoryContextSwitchTo(oldcontext);
5342  *min = datumCopy(values[0], typByVal, typLen);
5343  MemoryContextSwitchTo(tmpcontext);
5344  }
5345  else
5346  have_data = false;
5347 
5348  index_endscan(index_scan);
5349  }
5350 
5351  /* If max is requested, and we didn't find the index is empty */
5352  if (max && have_data)
5353  {
5354  index_scan = index_beginscan(heapRel, indexRel, &SnapshotDirty,
5355  1, 0);
5356  index_rescan(index_scan, scankeys, 1, NULL, 0);
5357 
5358  /* Fetch first tuple in reverse direction */
5359  if ((tup = index_getnext(index_scan,
5360  -indexscandir)) != NULL)
5361  {
5362  /* Extract the index column values from the heap tuple */
5363  ExecStoreTuple(tup, slot, InvalidBuffer, false);
5364  FormIndexDatum(indexInfo, slot, estate,
5365  values, isnull);
5366 
5367  /* Shouldn't have got a null, but be careful */
5368  if (isnull[0])
5369  elog(ERROR, "found unexpected null value in index \"%s\"",
5370  RelationGetRelationName(indexRel));
5371 
5372  /* Copy the index column value out to caller's context */
5373  MemoryContextSwitchTo(oldcontext);
5374  *max = datumCopy(values[0], typByVal, typLen);
5375  MemoryContextSwitchTo(tmpcontext);
5376  }
5377  else
5378  have_data = false;
5379 
5380  index_endscan(index_scan);
5381  }
5382 
5383  /* Clean everything up */
5385 
5386  index_close(indexRel, AccessShareLock);
5387  heap_close(heapRel, NoLock);
5388 
5389  MemoryContextSwitchTo(oldcontext);
5390  FreeExecutorState(estate);
5391 
5392  /* And we're done */
5393  break;
5394  }
5395  }
5396 
5397  return have_data;
5398 }
5399 
5400 /*
5401  * find_join_input_rel
5402  * Look up the input relation for a join.
5403  *
5404  * We assume that the input relation's RelOptInfo must have been constructed
5405  * already.
5406  */
5407 static RelOptInfo *
5409 {
5410  RelOptInfo *rel = NULL;
5411 
5412  switch (bms_membership(relids))
5413  {
5414  case BMS_EMPTY_SET:
5415  /* should not happen */
5416  break;
5417  case BMS_SINGLETON:
5418  rel = find_base_rel(root, bms_singleton_member(relids));
5419  break;
5420  case BMS_MULTIPLE:
5421  rel = find_join_rel(root, relids);
5422  break;
5423  }
5424 
5425  if (rel == NULL)
5426  elog(ERROR, "could not find RelOptInfo for given relids");
5427 
5428  return rel;
5429 }
5430 
5431 
5432 /*-------------------------------------------------------------------------
5433  *
5434  * Pattern analysis functions
5435  *
5436  * These routines support analysis of LIKE and regular-expression patterns
5437  * by the planner/optimizer. It's important that they agree with the
5438  * regular-expression code in backend/regex/ and the LIKE code in
5439  * backend/utils/adt/like.c. Also, the computation of the fixed prefix
5440  * must be conservative: if we report a string longer than the true fixed
5441  * prefix, the query may produce actually wrong answers, rather than just
5442  * getting a bad selectivity estimate!
5443  *
5444  * Note that the prefix-analysis functions are called from
5445  * backend/optimizer/path/indxpath.c as well as from routines in this file.
5446  *
5447  *-------------------------------------------------------------------------
5448  */
5449 
5450 /*
5451  * Check whether char is a letter (and, hence, subject to case-folding)
5452  *
5453  * In multibyte character sets or with ICU, we can't use isalpha, and it does not seem
5454  * worth trying to convert to wchar_t to use iswalpha. Instead, just assume
5455  * any multibyte char is potentially case-varying.
5456  */
5457 static int
5458 pattern_char_isalpha(char c, bool is_multibyte,
5459  pg_locale_t locale, bool locale_is_c)
5460 {
5461  if (locale_is_c)
5462  return (c >= 'A' && c <= 'Z') || (c >= 'a' && c <= 'z');
5463  else if (is_multibyte && IS_HIGHBIT_SET(c))
5464  return true;
5465  else if (locale && locale->provider == COLLPROVIDER_ICU)
5466  return IS_HIGHBIT_SET(c) ? true : false;
5467 #ifdef HAVE_LOCALE_T
5468  else if (locale && locale->provider == COLLPROVIDER_LIBC)
5469  return isalpha_l((unsigned char) c, locale->info.lt);
5470 #endif
5471  else
5472  return isalpha((unsigned char) c);
5473 }
5474 
5475 /*
5476  * Extract the fixed prefix, if any, for a pattern.
5477  *
5478  * *prefix is set to a palloc'd prefix string (in the form of a Const node),
5479  * or to NULL if no fixed prefix exists for the pattern.
5480  * If rest_selec is not NULL, *rest_selec is set to an estimate of the
5481  * selectivity of the remainder of the pattern (without any fixed prefix).
5482  * The prefix Const has the same type (TEXT or BYTEA) as the input pattern.
5483  *
5484  * The return value distinguishes no fixed prefix, a partial prefix,
5485  * or an exact-match-only pattern.
5486  */
5487 
5488 static Pattern_Prefix_Status
5489 like_fixed_prefix(Const *patt_const, bool case_insensitive, Oid collation,
5490  Const **prefix_const, Selectivity *rest_selec)
5491 {
5492  char *match;
5493  char *patt;
5494  int pattlen;
5495  Oid typeid = patt_const->consttype;
5496  int pos,
5497  match_pos;
5498  bool is_multibyte = (pg_database_encoding_max_length() > 1);
5499  pg_locale_t locale = 0;
5500  bool locale_is_c = false;
5501 
5502  /* the right-hand const is type text or bytea */
5503  Assert(typeid == BYTEAOID || typeid == TEXTOID);
5504 
5505  if (case_insensitive)
5506  {
5507  if (typeid == BYTEAOID)
5508  ereport(ERROR,
5509  (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5510  errmsg("case insensitive matching not supported on type bytea")));
5511 
5512  /* If case-insensitive, we need locale info */
5513  if (lc_ctype_is_c(collation))
5514  locale_is_c = true;
5515  else if (collation != DEFAULT_COLLATION_OID)
5516  {
5517  if (!OidIsValid(collation))
5518  {
5519  /*
5520  * This typically means that the parser could not resolve a
5521  * conflict of implicit collations, so report it that way.
5522  */
5523  ereport(ERROR,
5524  (errcode(ERRCODE_INDETERMINATE_COLLATION),
5525  errmsg("could not determine which collation to use for ILIKE"),
5526  errhint("Use the COLLATE clause to set the collation explicitly.")));
5527  }
5528  locale = pg_newlocale_from_collation(collation);
5529  }
5530  }
5531 
5532  if (typeid != BYTEAOID)
5533  {
5534  patt = TextDatumGetCString(patt_const->constvalue);
5535  pattlen = strlen(patt);
5536  }
5537  else
5538  {
5539  bytea *bstr = DatumGetByteaPP(patt_const->constvalue);
5540 
5541  pattlen = VARSIZE_ANY_EXHDR(bstr);
5542  patt = (char *) palloc(pattlen);
5543  memcpy(patt, VARDATA_ANY(bstr), pattlen);
5544  Assert((Pointer) bstr == DatumGetPointer(patt_const->constvalue));
5545  }
5546 
5547  match = palloc(pattlen + 1);
5548  match_pos = 0;
5549  for (pos = 0; pos < pattlen; pos++)
5550  {
5551  /* % and _ are wildcard characters in LIKE */
5552  if (patt[pos] == '%' ||
5553  patt[pos] == '_')
5554  break;
5555 
5556  /* Backslash escapes the next character */
5557  if (patt[pos] == '\\')
5558  {
5559  pos++;
5560  if (pos >= pattlen)
5561  break;
5562  }
5563 
5564  /* Stop if case-varying character (it's sort of a wildcard) */
5565  if (case_insensitive &&
5566  pattern_char_isalpha(patt[pos], is_multibyte, locale, locale_is_c))
5567  break;
5568 
5569  match[match_pos++] = patt[pos];
5570  }
5571 
5572  match[match_pos] = '\0';
5573 
5574  if (typeid != BYTEAOID)
5575  *prefix_const = string_to_const(match, typeid);
5576  else
5577  *prefix_const = string_to_bytea_const(match, match_pos);
5578 
5579  if (rest_selec != NULL)
5580  *rest_selec = like_selectivity(&patt[pos], pattlen - pos,
5581  case_insensitive);
5582 
5583  pfree(patt);
5584  pfree(match);
5585 
5586  /* in LIKE, an empty pattern is an exact match! */
5587  if (pos == pattlen)
5588  return Pattern_Prefix_Exact; /* reached end of pattern, so exact */
5589 
5590  if (match_pos > 0)
5591  return Pattern_Prefix_Partial;
5592 
5593  return Pattern_Prefix_None;
5594 }
5595 
5596 static Pattern_Prefix_Status
5597 regex_fixed_prefix(Const *patt_const, bool case_insensitive, Oid collation,
5598  Const **prefix_const, Selectivity *rest_selec)
5599 {
5600  Oid typeid = patt_const->consttype;
5601  char *prefix;
5602  bool exact;
5603 
5604  /*
5605  * Should be unnecessary, there are no bytea regex operators defined. As
5606  * such, it should be noted that the rest of this function has *not* been
5607  * made safe for binary (possibly NULL containing) strings.
5608  */
5609  if (typeid == BYTEAOID)
5610  ereport(ERROR,
5611  (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5612  errmsg("regular-expression matching not supported on type bytea")));
5613 
5614  /* Use the regexp machinery to extract the prefix, if any */
5615  prefix = regexp_fixed_prefix(DatumGetTextPP(patt_const->constvalue),
5616  case_insensitive, collation,
5617  &exact);
5618 
5619  if (prefix == NULL)
5620  {
5621  *prefix_const = NULL;
5622 
5623  if (rest_selec != NULL)
5624  {
5625  char *patt = TextDatumGetCString(patt_const->constvalue);
5626 
5627  *rest_selec = regex_selectivity(patt, strlen(patt),
5628  case_insensitive,
5629  0);
5630  pfree(patt);
5631  }
5632 
5633  return Pattern_Prefix_None;
5634  }
5635 
5636  *prefix_const = string_to_const(prefix, typeid);
5637 
5638  if (rest_selec != NULL)
5639  {
5640  if (exact)
5641  {
5642  /* Exact match, so there's no additional selectivity */
5643  *rest_selec = 1.0;
5644  }
5645  else
5646  {
5647  char *patt = TextDatumGetCString(patt_const->constvalue);
5648 
5649  *rest_selec = regex_selectivity(patt, strlen(patt),
5650  case_insensitive,
5651  strlen(prefix));
5652  pfree(patt);
5653  }
5654  }
5655 
5656  pfree(prefix);
5657 
5658  if (exact)
5659  return Pattern_Prefix_Exact; /* pattern specifies exact match */
5660  else
5661  return Pattern_Prefix_Partial;
5662 }
5663 
5665 pattern_fixed_prefix(Const *patt, Pattern_Type ptype, Oid collation,
5666  Const **prefix, Selectivity *rest_selec)
5667 {
5669 
5670  switch (ptype)
5671  {
5672  case Pattern_Type_Like:
5673  result = like_fixed_prefix(patt, false, collation,
5674  prefix, rest_selec);
5675  break;
5676  case Pattern_Type_Like_IC:
5677  result = like_fixed_prefix(patt, true, collation,
5678  prefix, rest_selec);
5679  break;
5680  case Pattern_Type_Regex:
5681  result = regex_fixed_prefix(patt, false, collation,
5682  prefix, rest_selec);
5683  break;
5684  case Pattern_Type_Regex_IC:
5685  result = regex_fixed_prefix(patt, true, collation,
5686  prefix, rest_selec);
5687  break;
5688  default:
5689  elog(ERROR, "unrecognized ptype: %d", (int) ptype);
5690  result = Pattern_Prefix_None; /* keep compiler quiet */
5691  break;
5692  }
5693  return result;
5694 }
5695 
5696 /*
5697  * Estimate the selectivity of a fixed prefix for a pattern match.
5698  *
5699  * A fixed prefix "foo" is estimated as the selectivity of the expression
5700  * "variable >= 'foo' AND variable < 'fop'" (see also indxpath.c).
5701  *
5702  * The selectivity estimate is with respect to the portion of the column
5703  * population represented by the histogram --- the caller must fold this
5704  * together with info about MCVs and NULLs.
5705  *
5706  * We use the >= and < operators from the specified btree opfamily to do the
5707  * estimation. The given variable and Const must be of the associated
5708  * datatype.
5709  *
5710  * XXX Note: we make use of the upper bound to estimate operator selectivity
5711  * even if the locale is such that we cannot rely on the upper-bound string.
5712  * The selectivity only needs to be approximately right anyway, so it seems
5713  * more useful to use the upper-bound code than not.
5714  */
5715 static Selectivity
5717  Oid vartype, Oid opfamily, Const *prefixcon)
5718 {
5719  Selectivity prefixsel;
5720  Oid cmpopr;
5721  FmgrInfo opproc;
5722  Const *greaterstrcon;
5723  Selectivity eq_sel;
5724 
5725  cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5727  if (cmpopr == InvalidOid)
5728  elog(ERROR, "no >= operator for opfamily %u", opfamily);
5729  fmgr_info(get_opcode(cmpopr), &opproc);
5730 
5731  prefixsel = ineq_histogram_selectivity(root, vardata, &opproc, true,
5732  prefixcon->constvalue,
5733  prefixcon->consttype);
5734 
5735  if (prefixsel < 0.0)
5736  {
5737  /* No histogram is present ... return a suitable default estimate */
5738  return DEFAULT_MATCH_SEL;
5739  }
5740 
5741  /*-------
5742  * If we can create a string larger than the prefix, say
5743  * "x < greaterstr".
5744  *-------
5745  */
5746  cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5748  if (cmpopr == InvalidOid)
5749  elog(ERROR, "no < operator for opfamily %u", opfamily);
5750  fmgr_info(get_opcode(cmpopr), &opproc);
5751  greaterstrcon = make_greater_string(prefixcon, &opproc,
5753  if (greaterstrcon)
5754  {
5755  Selectivity topsel;
5756 
5757  topsel = ineq_histogram_selectivity(root, vardata, &opproc, false,
5758  greaterstrcon->constvalue,
5759  greaterstrcon->consttype);
5760 
5761  /* ineq_histogram_selectivity worked before, it shouldn't fail now */
5762  Assert(topsel >= 0.0);
5763 
5764  /*
5765  * Merge the two selectivities in the same way as for a range query
5766  * (see clauselist_selectivity()). Note that we don't need to worry
5767  * about double-exclusion of nulls, since ineq_histogram_selectivity
5768  * doesn't count those anyway.
5769  */
5770  prefixsel = topsel + prefixsel - 1.0;
5771  }
5772 
5773  /*
5774  * If the prefix is long then the two bounding values might be too close
5775  * together for the histogram to distinguish them usefully, resulting in a
5776  * zero estimate (plus or minus roundoff error). To avoid returning a
5777  * ridiculously small estimate, compute the estimated selectivity for
5778  * "variable = 'foo'", and clamp to that. (Obviously, the resultant
5779  * estimate should be at least that.)
5780  *
5781  * We apply this even if we couldn't make a greater string. That case
5782  * suggests that the prefix is near the maximum possible, and thus
5783  * probably off the end of the histogram, and thus we probably got a very
5784  * small estimate from the >= condition; so we still need to clamp.
5785  */
5786  cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5788  if (cmpopr == InvalidOid)
5789  elog(ERROR, "no = operator for opfamily %u", opfamily);
5790  eq_sel = var_eq_const(vardata, cmpopr, prefixcon->constvalue,
5791  false, true);
5792 
5793  prefixsel = Max(prefixsel, eq_sel);
5794 
5795  return prefixsel;
5796 }
5797 
5798 
5799 /*
5800  * Estimate the selectivity of a pattern of the specified type.
5801  * Note that any fixed prefix of the pattern will have been removed already,
5802  * so actually we may be looking at just a fragment of the pattern.
5803  *
5804  * For now, we use a very simplistic approach: fixed characters reduce the
5805  * selectivity a good deal, character ranges reduce it a little,
5806  * wildcards (such as % for LIKE or .* for regex) increase it.
5807  */
5808 
5809 #define FIXED_CHAR_SEL 0.20 /* about 1/5 */
5810 #define CHAR_RANGE_SEL 0.25
5811 #define ANY_CHAR_SEL 0.9 /* not 1, since it won't match end-of-string */
5812 #define FULL_WILDCARD_SEL 5.0
5813 #define PARTIAL_WILDCARD_SEL 2.0
5814 
5815 static Selectivity
5816 like_selectivity(const char *patt, int pattlen, bool case_insensitive)
5817 {
5818  Selectivity sel = 1.0;
5819  int pos;
5820 
5821  /* Skip any leading wildcard; it's already factored into initial sel */
5822  for (pos = 0; pos < pattlen; pos++)
5823  {
5824  if (patt[pos] != '%' && patt[pos] != '_')
5825  break;
5826  }
5827 
5828  for (; pos < pattlen; pos++)
5829  {
5830  /* % and _ are wildcard characters in LIKE */
5831  if (patt[pos] == '%')
5832  sel *= FULL_WILDCARD_SEL;
5833  else if (patt[pos] == '_')
5834  sel *= ANY_CHAR_SEL;
5835  else if (patt[pos] == '\\')
5836  {
5837  /* Backslash quotes the next character */
5838  pos++;
5839  if (pos >= pattlen)
5840  break;
5841  sel *= FIXED_CHAR_SEL;
5842  }
5843  else
5844  sel *= FIXED_CHAR_SEL;
5845  }
5846  /* Could get sel > 1 if multiple wildcards */
5847  if (sel > 1.0)
5848  sel = 1.0;
5849  return sel;
5850 }
5851 
5852 static Selectivity
5853 regex_selectivity_sub(const char *patt, int pattlen, bool case_insensitive)
5854 {
5855  Selectivity sel = 1.0;
5856  int paren_depth = 0;
5857  int paren_pos = 0; /* dummy init to keep compiler quiet */
5858  int pos;
5859 
5860  for (pos = 0; pos < pattlen; pos++)
5861  {
5862  if (patt[pos] == '(')
5863  {
5864  if (paren_depth == 0)
5865  paren_pos = pos; /* remember start of parenthesized item */
5866  paren_depth++;
5867  }
5868  else if (patt[pos] == ')' && paren_depth > 0)
5869  {
5870  paren_depth--;
5871  if (paren_depth == 0)
5872  sel *= regex_selectivity_sub(patt + (paren_pos + 1),
5873  pos - (paren_pos + 1),
5874  case_insensitive);
5875  }
5876  else if (patt[pos] == '|' && paren_depth == 0)
5877  {
5878  /*
5879  * If unquoted | is present at paren level 0 in pattern, we have
5880  * multiple alternatives; sum their probabilities.
5881  */
5882  sel += regex_selectivity_sub(patt + (pos + 1),
5883  pattlen - (pos + 1),
5884  case_insensitive);
5885  break; /* rest of pattern is now processed */
5886  }
5887  else if (patt[pos] == '[')
5888  {
5889  bool negclass = false;
5890 
5891  if (patt[++pos] == '^')
5892  {
5893  negclass = true;
5894  pos++;
5895  }
5896  if (patt[pos] == ']') /* ']' at start of class is not
5897  * special */
5898  pos++;
5899  while (pos < pattlen && patt[pos] != ']')
5900  pos++;
5901  if (paren_depth == 0)
5902  sel *= (negclass ? (1.0 - CHAR_RANGE_SEL) : CHAR_RANGE_SEL);
5903  }
5904  else if (patt[pos] == '.')
5905  {
5906  if (paren_depth == 0)
5907  sel *= ANY_CHAR_SEL;
5908  }
5909  else if (patt[pos] == '*' ||
5910  patt[pos] == '?' ||
5911  patt[pos] == '+')
5912  {
5913  /* Ought to be smarter about quantifiers... */
5914  if (paren_depth == 0)
5915  sel *= PARTIAL_WILDCARD_SEL;
5916  }
5917  else if (patt[pos] == '{')
5918  {
5919  while (pos < pattlen && patt[pos] != '}')
5920  pos++;
5921  if (paren_depth == 0)
5922  sel *= PARTIAL_WILDCARD_SEL;
5923  }
5924  else if (patt[pos] == '\\')
5925  {
5926  /* backslash quotes the next character */
5927  pos++;
5928  if (pos >= pattlen)
5929  break;
5930  if (paren_depth == 0)
5931  sel *= FIXED_CHAR_SEL;
5932  }
5933  else
5934  {
5935  if (paren_depth == 0)
5936  sel *= FIXED_CHAR_SEL;
5937  }
5938  }
5939  /* Could get sel > 1 if multiple wildcards */
5940  if (sel > 1.0)
5941  sel = 1.0;
5942  return sel;
5943 }
5944 
5945 static Selectivity
5946 regex_selectivity(const char *patt, int pattlen, bool case_insensitive,
5947  int fixed_prefix_len)
5948 {
5949  Selectivity sel;
5950 
5951  /* If patt doesn't end with $, consider it to have a trailing wildcard */
5952  if (pattlen > 0 && patt[pattlen - 1] == '$' &&
5953  (pattlen == 1 || patt[pattlen - 2] != '\\'))
5954  {
5955  /* has trailing $ */
5956  sel = regex_selectivity_sub(patt, pattlen - 1, case_insensitive);
5957  }
5958  else
5959  {
5960  /* no trailing $ */
5961  sel = regex_selectivity_sub(patt, pattlen, case_insensitive);
5962  sel *= FULL_WILDCARD_SEL;
5963  }
5964 
5965  /* If there's a fixed prefix, discount its selectivity */
5966  if (fixed_prefix_len > 0)
5967  sel /= pow(FIXED_CHAR_SEL, fixed_prefix_len);
5968 
5969  /* Make sure result stays in range */
5970  CLAMP_PROBABILITY(sel);
5971  return sel;
5972 }
5973 
5974 
5975 /*
5976  * For bytea, the increment function need only increment the current byte
5977  * (there are no multibyte characters to worry about).
5978  */
5979 static bool
5980 byte_increment(unsigned char *ptr, int len)
5981 {
5982  if (*ptr >= 255)
5983  return false;
5984  (*ptr)++;
5985  return true;
5986 }
5987 
5988 /*
5989  * Try to generate a string greater than the given string or any
5990  * string it is a prefix of. If successful, return a palloc'd string
5991  * in the form of a Const node; else return NULL.
5992  *
5993  * The caller must provide the appropriate "less than" comparison function
5994  * for testing the strings, along with the collation to use.
5995  *
5996  * The key requirement here is that given a prefix string, say "foo",
5997  * we must be able to generate another string "fop" that is greater than
5998  * all strings "foobar" starting with "foo". We can test that we have
5999  * generated a string greater than the prefix string, but in non-C collations
6000  * that is not a bulletproof guarantee that an extension of the string might
6001  * not sort after it; an example is that "foo " is less than "foo!", but it
6002  * is not clear that a "dictionary" sort ordering will consider "foo!" less
6003  * than "foo bar". CAUTION: Therefore, this function should be used only for
6004  * estimation purposes when working in a non-C collation.
6005  *
6006  * To try to catch most cases where an extended string might otherwise sort
6007  * before the result value, we determine which of the strings "Z", "z", "y",
6008  * and "9" is seen as largest by the collation, and append that to the given
6009  * prefix before trying to find a string that compares as larger.
6010  *
6011  * To search for a greater string, we repeatedly "increment" the rightmost
6012  * character, using an encoding-specific character incrementer function.
6013  * When it's no longer possible to increment the last character, we truncate
6014  * off that character and start incrementing the next-to-rightmost.
6015  * For example, if "z" were the last character in the sort order, then we
6016  * could produce "foo" as a string greater than "fonz".
6017  *
6018  * This could be rather slow in the worst case, but in most cases we
6019  * won't have to try more than one or two strings before succeeding.
6020  *
6021  * Note that it's important for the character incrementer not to be too anal
6022  * about producing every possible character code, since in some cases the only
6023  * way to get a larger string is to increment a previous character position.
6024  * So we don't want to spend too much time trying every possible character
6025  * code at the last position. A good rule of thumb is to be sure that we
6026  * don't try more than 256*K values for a K-byte character (and definitely
6027  * not 256^K, which is what an exhaustive search would approach).
6028  */
6029 Const *
6030 make_greater_string(const Const *str_const, FmgrInfo *ltproc, Oid collation)
6031 {
6032  Oid datatype = str_const->consttype;
6033  char *workstr;
6034  int len;
6035  Datum cmpstr;
6036  text *cmptxt = NULL;
6037  mbcharacter_incrementer charinc;
6038 
6039  /*
6040  * Get a modifiable copy of the prefix string in C-string format, and set
6041  * up the string we will compare to as a Datum. In C locale this can just
6042  * be the given prefix string, otherwise we need to add a suffix. Types
6043  * NAME and BYTEA sort bytewise so they don't need a suffix either.
6044  */
6045  if (datatype == NAMEOID)
6046  {
6048  str_const->constvalue));
6049  len = strlen(workstr);
6050  cmpstr = str_const->constvalue;
6051  }
6052  else if (datatype == BYTEAOID)
6053  {
6054  bytea *bstr = DatumGetByteaPP(str_const->constvalue);
6055 
6056  len = VARSIZE_ANY_EXHDR(bstr);
6057  workstr = (char *) palloc(len);