LCOV - code coverage report
Current view: top level - src/backend/utils/adt - selfuncs.c (source / functions) Hit Total Coverage
Test: PostgreSQL 14devel Lines: 1881 2190 85.9 %
Date: 2021-01-26 03:06:49 Functions: 67 70 95.7 %
Legend: Lines: hit not hit

          Line data    Source code
       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) 1996-2021, 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 relevant column's
      91             :  * collation.
      92             :  *----------
      93             :  */
      94             : 
      95             : #include "postgres.h"
      96             : 
      97             : #include <ctype.h>
      98             : #include <math.h>
      99             : 
     100             : #include "access/brin.h"
     101             : #include "access/brin_page.h"
     102             : #include "access/gin.h"
     103             : #include "access/table.h"
     104             : #include "access/tableam.h"
     105             : #include "access/visibilitymap.h"
     106             : #include "catalog/pg_am.h"
     107             : #include "catalog/pg_collation.h"
     108             : #include "catalog/pg_operator.h"
     109             : #include "catalog/pg_statistic.h"
     110             : #include "catalog/pg_statistic_ext.h"
     111             : #include "executor/nodeAgg.h"
     112             : #include "miscadmin.h"
     113             : #include "nodes/makefuncs.h"
     114             : #include "nodes/nodeFuncs.h"
     115             : #include "optimizer/clauses.h"
     116             : #include "optimizer/cost.h"
     117             : #include "optimizer/optimizer.h"
     118             : #include "optimizer/pathnode.h"
     119             : #include "optimizer/paths.h"
     120             : #include "optimizer/plancat.h"
     121             : #include "parser/parse_clause.h"
     122             : #include "parser/parsetree.h"
     123             : #include "statistics/statistics.h"
     124             : #include "storage/bufmgr.h"
     125             : #include "utils/acl.h"
     126             : #include "utils/builtins.h"
     127             : #include "utils/date.h"
     128             : #include "utils/datum.h"
     129             : #include "utils/fmgroids.h"
     130             : #include "utils/index_selfuncs.h"
     131             : #include "utils/lsyscache.h"
     132             : #include "utils/memutils.h"
     133             : #include "utils/pg_locale.h"
     134             : #include "utils/rel.h"
     135             : #include "utils/selfuncs.h"
     136             : #include "utils/snapmgr.h"
     137             : #include "utils/spccache.h"
     138             : #include "utils/syscache.h"
     139             : #include "utils/timestamp.h"
     140             : #include "utils/typcache.h"
     141             : 
     142             : 
     143             : /* Hooks for plugins to get control when we ask for stats */
     144             : get_relation_stats_hook_type get_relation_stats_hook = NULL;
     145             : get_index_stats_hook_type get_index_stats_hook = NULL;
     146             : 
     147             : static double eqsel_internal(PG_FUNCTION_ARGS, bool negate);
     148             : static double eqjoinsel_inner(Oid opfuncoid, Oid collation,
     149             :                               VariableStatData *vardata1, VariableStatData *vardata2,
     150             :                               double nd1, double nd2,
     151             :                               bool isdefault1, bool isdefault2,
     152             :                               AttStatsSlot *sslot1, AttStatsSlot *sslot2,
     153             :                               Form_pg_statistic stats1, Form_pg_statistic stats2,
     154             :                               bool have_mcvs1, bool have_mcvs2);
     155             : static double eqjoinsel_semi(Oid opfuncoid, Oid collation,
     156             :                              VariableStatData *vardata1, VariableStatData *vardata2,
     157             :                              double nd1, double nd2,
     158             :                              bool isdefault1, bool isdefault2,
     159             :                              AttStatsSlot *sslot1, AttStatsSlot *sslot2,
     160             :                              Form_pg_statistic stats1, Form_pg_statistic stats2,
     161             :                              bool have_mcvs1, bool have_mcvs2,
     162             :                              RelOptInfo *inner_rel);
     163             : static bool estimate_multivariate_ndistinct(PlannerInfo *root,
     164             :                                             RelOptInfo *rel, List **varinfos, double *ndistinct);
     165             : static bool convert_to_scalar(Datum value, Oid valuetypid, Oid collid,
     166             :                               double *scaledvalue,
     167             :                               Datum lobound, Datum hibound, Oid boundstypid,
     168             :                               double *scaledlobound, double *scaledhibound);
     169             : static double convert_numeric_to_scalar(Datum value, Oid typid, bool *failure);
     170             : static void convert_string_to_scalar(char *value,
     171             :                                      double *scaledvalue,
     172             :                                      char *lobound,
     173             :                                      double *scaledlobound,
     174             :                                      char *hibound,
     175             :                                      double *scaledhibound);
     176             : static void convert_bytea_to_scalar(Datum value,
     177             :                                     double *scaledvalue,
     178             :                                     Datum lobound,
     179             :                                     double *scaledlobound,
     180             :                                     Datum hibound,
     181             :                                     double *scaledhibound);
     182             : static double convert_one_string_to_scalar(char *value,
     183             :                                            int rangelo, int rangehi);
     184             : static double convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
     185             :                                           int rangelo, int rangehi);
     186             : static char *convert_string_datum(Datum value, Oid typid, Oid collid,
     187             :                                   bool *failure);
     188             : static double convert_timevalue_to_scalar(Datum value, Oid typid,
     189             :                                           bool *failure);
     190             : static void examine_simple_variable(PlannerInfo *root, Var *var,
     191             :                                     VariableStatData *vardata);
     192             : static bool get_variable_range(PlannerInfo *root, VariableStatData *vardata,
     193             :                                Oid sortop, Oid collation,
     194             :                                Datum *min, Datum *max);
     195             : static void get_stats_slot_range(AttStatsSlot *sslot,
     196             :                                  Oid opfuncoid, FmgrInfo *opproc,
     197             :                                  Oid collation, int16 typLen, bool typByVal,
     198             :                                  Datum *min, Datum *max, bool *p_have_data);
     199             : static bool get_actual_variable_range(PlannerInfo *root,
     200             :                                       VariableStatData *vardata,
     201             :                                       Oid sortop, Oid collation,
     202             :                                       Datum *min, Datum *max);
     203             : static bool get_actual_variable_endpoint(Relation heapRel,
     204             :                                          Relation indexRel,
     205             :                                          ScanDirection indexscandir,
     206             :                                          ScanKey scankeys,
     207             :                                          int16 typLen,
     208             :                                          bool typByVal,
     209             :                                          TupleTableSlot *tableslot,
     210             :                                          MemoryContext outercontext,
     211             :                                          Datum *endpointDatum);
     212             : static RelOptInfo *find_join_input_rel(PlannerInfo *root, Relids relids);
     213             : 
     214             : 
     215             : /*
     216             :  *      eqsel           - Selectivity of "=" for any data types.
     217             :  *
     218             :  * Note: this routine is also used to estimate selectivity for some
     219             :  * operators that are not "=" but have comparable selectivity behavior,
     220             :  * such as "~=" (geometric approximate-match).  Even for "=", we must
     221             :  * keep in mind that the left and right datatypes may differ.
     222             :  */
     223             : Datum
     224      332524 : eqsel(PG_FUNCTION_ARGS)
     225             : {
     226      332524 :     PG_RETURN_FLOAT8((float8) eqsel_internal(fcinfo, false));
     227             : }
     228             : 
     229             : /*
     230             :  * Common code for eqsel() and neqsel()
     231             :  */
     232             : static double
     233      345756 : eqsel_internal(PG_FUNCTION_ARGS, bool negate)
     234             : {
     235      345756 :     PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
     236      345756 :     Oid         operator = PG_GETARG_OID(1);
     237      345756 :     List       *args = (List *) PG_GETARG_POINTER(2);
     238      345756 :     int         varRelid = PG_GETARG_INT32(3);
     239      345756 :     Oid         collation = PG_GET_COLLATION();
     240             :     VariableStatData vardata;
     241             :     Node       *other;
     242             :     bool        varonleft;
     243             :     double      selec;
     244             : 
     245             :     /*
     246             :      * When asked about <>, we do the estimation using the corresponding =
     247             :      * operator, then convert to <> via "1.0 - eq_selectivity - nullfrac".
     248             :      */
     249      345756 :     if (negate)
     250             :     {
     251       13232 :         operator = get_negator(operator);
     252       13232 :         if (!OidIsValid(operator))
     253             :         {
     254             :             /* Use default selectivity (should we raise an error instead?) */
     255           0 :             return 1.0 - DEFAULT_EQ_SEL;
     256             :         }
     257             :     }
     258             : 
     259             :     /*
     260             :      * If expression is not variable = something or something = variable, then
     261             :      * punt and return a default estimate.
     262             :      */
     263      345756 :     if (!get_restriction_variable(root, args, varRelid,
     264             :                                   &vardata, &other, &varonleft))
     265        1686 :         return negate ? (1.0 - DEFAULT_EQ_SEL) : DEFAULT_EQ_SEL;
     266             : 
     267             :     /*
     268             :      * We can do a lot better if the something is a constant.  (Note: the
     269             :      * Const might result from estimation rather than being a simple constant
     270             :      * in the query.)
     271             :      */
     272      344070 :     if (IsA(other, Const))
     273      477972 :         selec = var_eq_const(&vardata, operator, collation,
     274      159324 :                              ((Const *) other)->constvalue,
     275      159324 :                              ((Const *) other)->constisnull,
     276             :                              varonleft, negate);
     277             :     else
     278      184746 :         selec = var_eq_non_const(&vardata, operator, collation, other,
     279             :                                  varonleft, negate);
     280             : 
     281      344070 :     ReleaseVariableStats(vardata);
     282             : 
     283      344070 :     return selec;
     284             : }
     285             : 
     286             : /*
     287             :  * var_eq_const --- eqsel for var = const case
     288             :  *
     289             :  * This is exported so that some other estimation functions can use it.
     290             :  */
     291             : double
     292      174114 : var_eq_const(VariableStatData *vardata, Oid operator, Oid collation,
     293             :              Datum constval, bool constisnull,
     294             :              bool varonleft, bool negate)
     295             : {
     296             :     double      selec;
     297      174114 :     double      nullfrac = 0.0;
     298             :     bool        isdefault;
     299             :     Oid         opfuncoid;
     300             : 
     301             :     /*
     302             :      * If the constant is NULL, assume operator is strict and return zero, ie,
     303             :      * operator will never return TRUE.  (It's zero even for a negator op.)
     304             :      */
     305      174114 :     if (constisnull)
     306          86 :         return 0.0;
     307             : 
     308             :     /*
     309             :      * Grab the nullfrac for use below.  Note we allow use of nullfrac
     310             :      * regardless of security check.
     311             :      */
     312      174028 :     if (HeapTupleIsValid(vardata->statsTuple))
     313             :     {
     314             :         Form_pg_statistic stats;
     315             : 
     316      121172 :         stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
     317      121172 :         nullfrac = stats->stanullfrac;
     318             :     }
     319             : 
     320             :     /*
     321             :      * If we matched the var to a unique index or DISTINCT clause, assume
     322             :      * there is exactly one match regardless of anything else.  (This is
     323             :      * slightly bogus, since the index or clause's equality operator might be
     324             :      * different from ours, but it's much more likely to be right than
     325             :      * ignoring the information.)
     326             :      */
     327      174028 :     if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
     328             :     {
     329       33106 :         selec = 1.0 / vardata->rel->tuples;
     330             :     }
     331      241202 :     else if (HeapTupleIsValid(vardata->statsTuple) &&
     332      100280 :              statistic_proc_security_check(vardata,
     333      100280 :                                            (opfuncoid = get_opcode(operator))))
     334      100280 :     {
     335             :         AttStatsSlot sslot;
     336      100280 :         bool        match = false;
     337             :         int         i;
     338             : 
     339             :         /*
     340             :          * Is the constant "=" to any of the column's most common values?
     341             :          * (Although the given operator may not really be "=", we will assume
     342             :          * that seeing whether it returns TRUE is an appropriate test.  If you
     343             :          * don't like this, maybe you shouldn't be using eqsel for your
     344             :          * operator...)
     345             :          */
     346      100280 :         if (get_attstatsslot(&sslot, vardata->statsTuple,
     347             :                              STATISTIC_KIND_MCV, InvalidOid,
     348             :                              ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS))
     349             :         {
     350       90664 :             LOCAL_FCINFO(fcinfo, 2);
     351             :             FmgrInfo    eqproc;
     352             : 
     353       90664 :             fmgr_info(opfuncoid, &eqproc);
     354             : 
     355             :             /*
     356             :              * Save a few cycles by setting up the fcinfo struct just once.
     357             :              * Using FunctionCallInvoke directly also avoids failure if the
     358             :              * eqproc returns NULL, though really equality functions should
     359             :              * never do that.
     360             :              */
     361       90664 :             InitFunctionCallInfoData(*fcinfo, &eqproc, 2, collation,
     362             :                                      NULL, NULL);
     363       90664 :             fcinfo->args[0].isnull = false;
     364       90664 :             fcinfo->args[1].isnull = false;
     365             :             /* be careful to apply operator right way 'round */
     366       90664 :             if (varonleft)
     367       90648 :                 fcinfo->args[1].value = constval;
     368             :             else
     369          16 :                 fcinfo->args[0].value = constval;
     370             : 
     371     1686236 :             for (i = 0; i < sslot.nvalues; i++)
     372             :             {
     373             :                 Datum       fresult;
     374             : 
     375     1641490 :                 if (varonleft)
     376     1641458 :                     fcinfo->args[0].value = sslot.values[i];
     377             :                 else
     378          32 :                     fcinfo->args[1].value = sslot.values[i];
     379     1641490 :                 fcinfo->isnull = false;
     380     1641490 :                 fresult = FunctionCallInvoke(fcinfo);
     381     1641490 :                 if (!fcinfo->isnull && DatumGetBool(fresult))
     382             :                 {
     383       45918 :                     match = true;
     384       45918 :                     break;
     385             :                 }
     386             :             }
     387             :         }
     388             :         else
     389             :         {
     390             :             /* no most-common-value info available */
     391        9616 :             i = 0;              /* keep compiler quiet */
     392             :         }
     393             : 
     394      100280 :         if (match)
     395             :         {
     396             :             /*
     397             :              * Constant is "=" to this common value.  We know selectivity
     398             :              * exactly (or as exactly as ANALYZE could calculate it, anyway).
     399             :              */
     400       45918 :             selec = sslot.numbers[i];
     401             :         }
     402             :         else
     403             :         {
     404             :             /*
     405             :              * Comparison is against a constant that is neither NULL nor any
     406             :              * of the common values.  Its selectivity cannot be more than
     407             :              * this:
     408             :              */
     409       54362 :             double      sumcommon = 0.0;
     410             :             double      otherdistinct;
     411             : 
     412     1488962 :             for (i = 0; i < sslot.nnumbers; i++)
     413     1434600 :                 sumcommon += sslot.numbers[i];
     414       54362 :             selec = 1.0 - sumcommon - nullfrac;
     415       54362 :             CLAMP_PROBABILITY(selec);
     416             : 
     417             :             /*
     418             :              * and in fact it's probably a good deal less. We approximate that
     419             :              * all the not-common values share this remaining fraction
     420             :              * equally, so we divide by the number of other distinct values.
     421             :              */
     422       54362 :             otherdistinct = get_variable_numdistinct(vardata, &isdefault) -
     423       54362 :                 sslot.nnumbers;
     424       54362 :             if (otherdistinct > 1)
     425       32754 :                 selec /= otherdistinct;
     426             : 
     427             :             /*
     428             :              * Another cross-check: selectivity shouldn't be estimated as more
     429             :              * than the least common "most common value".
     430             :              */
     431       54362 :             if (sslot.nnumbers > 0 && selec > sslot.numbers[sslot.nnumbers - 1])
     432           0 :                 selec = sslot.numbers[sslot.nnumbers - 1];
     433             :         }
     434             : 
     435      100280 :         free_attstatsslot(&sslot);
     436             :     }
     437             :     else
     438             :     {
     439             :         /*
     440             :          * No ANALYZE stats available, so make a guess using estimated number
     441             :          * of distinct values and assuming they are equally common. (The guess
     442             :          * is unlikely to be very good, but we do know a few special cases.)
     443             :          */
     444       40642 :         selec = 1.0 / get_variable_numdistinct(vardata, &isdefault);
     445             :     }
     446             : 
     447             :     /* now adjust if we wanted <> rather than = */
     448      174028 :     if (negate)
     449        9378 :         selec = 1.0 - selec - nullfrac;
     450             : 
     451             :     /* result should be in range, but make sure... */
     452      174028 :     CLAMP_PROBABILITY(selec);
     453             : 
     454      174028 :     return selec;
     455             : }
     456             : 
     457             : /*
     458             :  * var_eq_non_const --- eqsel for var = something-other-than-const case
     459             :  *
     460             :  * This is exported so that some other estimation functions can use it.
     461             :  */
     462             : double
     463      184746 : var_eq_non_const(VariableStatData *vardata, Oid operator, Oid collation,
     464             :                  Node *other,
     465             :                  bool varonleft, bool negate)
     466             : {
     467             :     double      selec;
     468      184746 :     double      nullfrac = 0.0;
     469             :     bool        isdefault;
     470             : 
     471             :     /*
     472             :      * Grab the nullfrac for use below.
     473             :      */
     474      184746 :     if (HeapTupleIsValid(vardata->statsTuple))
     475             :     {
     476             :         Form_pg_statistic stats;
     477             : 
     478      154454 :         stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
     479      154454 :         nullfrac = stats->stanullfrac;
     480             :     }
     481             : 
     482             :     /*
     483             :      * If we matched the var to a unique index or DISTINCT clause, assume
     484             :      * there is exactly one match regardless of anything else.  (This is
     485             :      * slightly bogus, since the index or clause's equality operator might be
     486             :      * different from ours, but it's much more likely to be right than
     487             :      * ignoring the information.)
     488             :      */
     489      184746 :     if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
     490             :     {
     491       86856 :         selec = 1.0 / vardata->rel->tuples;
     492             :     }
     493       97890 :     else if (HeapTupleIsValid(vardata->statsTuple))
     494             :     {
     495             :         double      ndistinct;
     496             :         AttStatsSlot sslot;
     497             : 
     498             :         /*
     499             :          * Search is for a value that we do not know a priori, but we will
     500             :          * assume it is not NULL.  Estimate the selectivity as non-null
     501             :          * fraction divided by number of distinct values, so that we get a
     502             :          * result averaged over all possible values whether common or
     503             :          * uncommon.  (Essentially, we are assuming that the not-yet-known
     504             :          * comparison value is equally likely to be any of the possible
     505             :          * values, regardless of their frequency in the table.  Is that a good
     506             :          * idea?)
     507             :          */
     508       75634 :         selec = 1.0 - nullfrac;
     509       75634 :         ndistinct = get_variable_numdistinct(vardata, &isdefault);
     510       75634 :         if (ndistinct > 1)
     511       69798 :             selec /= ndistinct;
     512             : 
     513             :         /*
     514             :          * Cross-check: selectivity should never be estimated as more than the
     515             :          * most common value's.
     516             :          */
     517       75634 :         if (get_attstatsslot(&sslot, vardata->statsTuple,
     518             :                              STATISTIC_KIND_MCV, InvalidOid,
     519             :                              ATTSTATSSLOT_NUMBERS))
     520             :         {
     521       65110 :             if (sslot.nnumbers > 0 && selec > sslot.numbers[0])
     522         140 :                 selec = sslot.numbers[0];
     523       65110 :             free_attstatsslot(&sslot);
     524             :         }
     525             :     }
     526             :     else
     527             :     {
     528             :         /*
     529             :          * No ANALYZE stats available, so make a guess using estimated number
     530             :          * of distinct values and assuming they are equally common. (The guess
     531             :          * is unlikely to be very good, but we do know a few special cases.)
     532             :          */
     533       22256 :         selec = 1.0 / get_variable_numdistinct(vardata, &isdefault);
     534             :     }
     535             : 
     536             :     /* now adjust if we wanted <> rather than = */
     537      184746 :     if (negate)
     538        2902 :         selec = 1.0 - selec - nullfrac;
     539             : 
     540             :     /* result should be in range, but make sure... */
     541      184746 :     CLAMP_PROBABILITY(selec);
     542             : 
     543      184746 :     return selec;
     544             : }
     545             : 
     546             : /*
     547             :  *      neqsel          - Selectivity of "!=" for any data types.
     548             :  *
     549             :  * This routine is also used for some operators that are not "!="
     550             :  * but have comparable selectivity behavior.  See above comments
     551             :  * for eqsel().
     552             :  */
     553             : Datum
     554       13232 : neqsel(PG_FUNCTION_ARGS)
     555             : {
     556       13232 :     PG_RETURN_FLOAT8((float8) eqsel_internal(fcinfo, true));
     557             : }
     558             : 
     559             : /*
     560             :  *  scalarineqsel       - Selectivity of "<", "<=", ">", ">=" for scalars.
     561             :  *
     562             :  * This is the guts of scalarltsel/scalarlesel/scalargtsel/scalargesel.
     563             :  * The isgt and iseq flags distinguish which of the four cases apply.
     564             :  *
     565             :  * The caller has commuted the clause, if necessary, so that we can treat
     566             :  * the variable as being on the left.  The caller must also make sure that
     567             :  * the other side of the clause is a non-null Const, and dissect that into
     568             :  * a value and datatype.  (This definition simplifies some callers that
     569             :  * want to estimate against a computed value instead of a Const node.)
     570             :  *
     571             :  * This routine works for any datatype (or pair of datatypes) known to
     572             :  * convert_to_scalar().  If it is applied to some other datatype,
     573             :  * it will return an approximate estimate based on assuming that the constant
     574             :  * value falls in the middle of the bin identified by binary search.
     575             :  */
     576             : static double
     577      194762 : scalarineqsel(PlannerInfo *root, Oid operator, bool isgt, bool iseq,
     578             :               Oid collation,
     579             :               VariableStatData *vardata, Datum constval, Oid consttype)
     580             : {
     581             :     Form_pg_statistic stats;
     582             :     FmgrInfo    opproc;
     583             :     double      mcv_selec,
     584             :                 hist_selec,
     585             :                 sumcommon;
     586             :     double      selec;
     587             : 
     588      194762 :     if (!HeapTupleIsValid(vardata->statsTuple))
     589             :     {
     590             :         /*
     591             :          * No stats are available.  Typically this means we have to fall back
     592             :          * on the default estimate; but if the variable is CTID then we can
     593             :          * make an estimate based on comparing the constant to the table size.
     594             :          */
     595       11896 :         if (vardata->var && IsA(vardata->var, Var) &&
     596        8796 :             ((Var *) vardata->var)->varattno == SelfItemPointerAttributeNumber)
     597             :         {
     598             :             ItemPointer itemptr;
     599             :             double      block;
     600             :             double      density;
     601             : 
     602             :             /*
     603             :              * If the relation's empty, we're going to include all of it.
     604             :              * (This is mostly to avoid divide-by-zero below.)
     605             :              */
     606           4 :             if (vardata->rel->pages == 0)
     607           0 :                 return 1.0;
     608             : 
     609           4 :             itemptr = (ItemPointer) DatumGetPointer(constval);
     610           4 :             block = ItemPointerGetBlockNumberNoCheck(itemptr);
     611             : 
     612             :             /*
     613             :              * Determine the average number of tuples per page (density).
     614             :              *
     615             :              * Since the last page will, on average, be only half full, we can
     616             :              * estimate it to have half as many tuples as earlier pages.  So
     617             :              * give it half the weight of a regular page.
     618             :              */
     619           4 :             density = vardata->rel->tuples / (vardata->rel->pages - 0.5);
     620             : 
     621             :             /* If target is the last page, use half the density. */
     622           4 :             if (block >= vardata->rel->pages - 1)
     623           0 :                 density *= 0.5;
     624             : 
     625             :             /*
     626             :              * Using the average tuples per page, calculate how far into the
     627             :              * page the itemptr is likely to be and adjust block accordingly,
     628             :              * by adding that fraction of a whole block (but never more than a
     629             :              * whole block, no matter how high the itemptr's offset is).  Here
     630             :              * we are ignoring the possibility of dead-tuple line pointers,
     631             :              * which is fairly bogus, but we lack the info to do better.
     632             :              */
     633           4 :             if (density > 0.0)
     634             :             {
     635           4 :                 OffsetNumber offset = ItemPointerGetOffsetNumberNoCheck(itemptr);
     636             : 
     637           4 :                 block += Min(offset / density, 1.0);
     638             :             }
     639             : 
     640             :             /*
     641             :              * Convert relative block number to selectivity.  Again, the last
     642             :              * page has only half weight.
     643             :              */
     644           4 :             selec = block / (vardata->rel->pages - 0.5);
     645             : 
     646             :             /*
     647             :              * The calculation so far gave us a selectivity for the "<=" case.
     648             :              * We'll have one less tuple for "<" and one additional tuple for
     649             :              * ">=", the latter of which we'll reverse the selectivity for
     650             :              * below, so we can simply subtract one tuple for both cases.  The
     651             :              * cases that need this adjustment can be identified by iseq being
     652             :              * equal to isgt.
     653             :              */
     654           4 :             if (iseq == isgt && vardata->rel->tuples >= 1.0)
     655           0 :                 selec -= (1.0 / vardata->rel->tuples);
     656             : 
     657             :             /* Finally, reverse the selectivity for the ">", ">=" cases. */
     658           4 :             if (isgt)
     659           4 :                 selec = 1.0 - selec;
     660             : 
     661           4 :             CLAMP_PROBABILITY(selec);
     662           4 :             return selec;
     663             :         }
     664             : 
     665             :         /* no stats available, so default result */
     666       11892 :         return DEFAULT_INEQ_SEL;
     667             :     }
     668      182866 :     stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
     669             : 
     670      182866 :     fmgr_info(get_opcode(operator), &opproc);
     671             : 
     672             :     /*
     673             :      * If we have most-common-values info, add up the fractions of the MCV
     674             :      * entries that satisfy MCV OP CONST.  These fractions contribute directly
     675             :      * to the result selectivity.  Also add up the total fraction represented
     676             :      * by MCV entries.
     677             :      */
     678      182866 :     mcv_selec = mcv_selectivity(vardata, &opproc, collation, constval, true,
     679             :                                 &sumcommon);
     680             : 
     681             :     /*
     682             :      * If there is a histogram, determine which bin the constant falls in, and
     683             :      * compute the resulting contribution to selectivity.
     684             :      */
     685      182866 :     hist_selec = ineq_histogram_selectivity(root, vardata,
     686             :                                             operator, &opproc, isgt, iseq,
     687             :                                             collation,
     688             :                                             constval, consttype);
     689             : 
     690             :     /*
     691             :      * Now merge the results from the MCV and histogram calculations,
     692             :      * realizing that the histogram covers only the non-null values that are
     693             :      * not listed in MCV.
     694             :      */
     695      182866 :     selec = 1.0 - stats->stanullfrac - sumcommon;
     696             : 
     697      182866 :     if (hist_selec >= 0.0)
     698      150816 :         selec *= hist_selec;
     699             :     else
     700             :     {
     701             :         /*
     702             :          * If no histogram but there are values not accounted for by MCV,
     703             :          * arbitrarily assume half of them will match.
     704             :          */
     705       32050 :         selec *= 0.5;
     706             :     }
     707             : 
     708      182866 :     selec += mcv_selec;
     709             : 
     710             :     /* result should be in range, but make sure... */
     711      182866 :     CLAMP_PROBABILITY(selec);
     712             : 
     713      182866 :     return selec;
     714             : }
     715             : 
     716             : /*
     717             :  *  mcv_selectivity         - Examine the MCV list for selectivity estimates
     718             :  *
     719             :  * Determine the fraction of the variable's MCV population that satisfies
     720             :  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft.  Also
     721             :  * compute the fraction of the total column population represented by the MCV
     722             :  * list.  This code will work for any boolean-returning predicate operator.
     723             :  *
     724             :  * The function result is the MCV selectivity, and the fraction of the
     725             :  * total population is returned into *sumcommonp.  Zeroes are returned
     726             :  * if there is no MCV list.
     727             :  */
     728             : double
     729      186318 : mcv_selectivity(VariableStatData *vardata, FmgrInfo *opproc, Oid collation,
     730             :                 Datum constval, bool varonleft,
     731             :                 double *sumcommonp)
     732             : {
     733             :     double      mcv_selec,
     734             :                 sumcommon;
     735             :     AttStatsSlot sslot;
     736             :     int         i;
     737             : 
     738      186318 :     mcv_selec = 0.0;
     739      186318 :     sumcommon = 0.0;
     740             : 
     741      370778 :     if (HeapTupleIsValid(vardata->statsTuple) &&
     742      368864 :         statistic_proc_security_check(vardata, opproc->fn_oid) &&
     743      184404 :         get_attstatsslot(&sslot, vardata->statsTuple,
     744             :                          STATISTIC_KIND_MCV, InvalidOid,
     745             :                          ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS))
     746             :     {
     747       92136 :         LOCAL_FCINFO(fcinfo, 2);
     748             : 
     749             :         /*
     750             :          * We invoke the opproc "by hand" so that we won't fail on NULL
     751             :          * results.  Such cases won't arise for normal comparison functions,
     752             :          * but generic_restriction_selectivity could perhaps be used with
     753             :          * operators that can return NULL.  A small side benefit is to not
     754             :          * need to re-initialize the fcinfo struct from scratch each time.
     755             :          */
     756       92136 :         InitFunctionCallInfoData(*fcinfo, opproc, 2, collation,
     757             :                                  NULL, NULL);
     758       92136 :         fcinfo->args[0].isnull = false;
     759       92136 :         fcinfo->args[1].isnull = false;
     760             :         /* be careful to apply operator right way 'round */
     761       92136 :         if (varonleft)
     762       92136 :             fcinfo->args[1].value = constval;
     763             :         else
     764           0 :             fcinfo->args[0].value = constval;
     765             : 
     766     3331372 :         for (i = 0; i < sslot.nvalues; i++)
     767             :         {
     768             :             Datum       fresult;
     769             : 
     770     3239236 :             if (varonleft)
     771     3239236 :                 fcinfo->args[0].value = sslot.values[i];
     772             :             else
     773           0 :                 fcinfo->args[1].value = sslot.values[i];
     774     3239236 :             fcinfo->isnull = false;
     775     3239236 :             fresult = FunctionCallInvoke(fcinfo);
     776     3239236 :             if (!fcinfo->isnull && DatumGetBool(fresult))
     777     1508406 :                 mcv_selec += sslot.numbers[i];
     778     3239236 :             sumcommon += sslot.numbers[i];
     779             :         }
     780       92136 :         free_attstatsslot(&sslot);
     781             :     }
     782             : 
     783      186318 :     *sumcommonp = sumcommon;
     784      186318 :     return mcv_selec;
     785             : }
     786             : 
     787             : /*
     788             :  *  histogram_selectivity   - Examine the histogram for selectivity estimates
     789             :  *
     790             :  * Determine the fraction of the variable's histogram entries that satisfy
     791             :  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft.
     792             :  *
     793             :  * This code will work for any boolean-returning predicate operator, whether
     794             :  * or not it has anything to do with the histogram sort operator.  We are
     795             :  * essentially using the histogram just as a representative sample.  However,
     796             :  * small histograms are unlikely to be all that representative, so the caller
     797             :  * should be prepared to fall back on some other estimation approach when the
     798             :  * histogram is missing or very small.  It may also be prudent to combine this
     799             :  * approach with another one when the histogram is small.
     800             :  *
     801             :  * If the actual histogram size is not at least min_hist_size, we won't bother
     802             :  * to do the calculation at all.  Also, if the n_skip parameter is > 0, we
     803             :  * ignore the first and last n_skip histogram elements, on the grounds that
     804             :  * they are outliers and hence not very representative.  Typical values for
     805             :  * these parameters are 10 and 1.
     806             :  *
     807             :  * The function result is the selectivity, or -1 if there is no histogram
     808             :  * or it's smaller than min_hist_size.
     809             :  *
     810             :  * The output parameter *hist_size receives the actual histogram size,
     811             :  * or zero if no histogram.  Callers may use this number to decide how
     812             :  * much faith to put in the function result.
     813             :  *
     814             :  * Note that the result disregards both the most-common-values (if any) and
     815             :  * null entries.  The caller is expected to combine this result with
     816             :  * statistics for those portions of the column population.  It may also be
     817             :  * prudent to clamp the result range, ie, disbelieve exact 0 or 1 outputs.
     818             :  */
     819             : double
     820        3452 : histogram_selectivity(VariableStatData *vardata,
     821             :                       FmgrInfo *opproc, Oid collation,
     822             :                       Datum constval, bool varonleft,
     823             :                       int min_hist_size, int n_skip,
     824             :                       int *hist_size)
     825             : {
     826             :     double      result;
     827             :     AttStatsSlot sslot;
     828             : 
     829             :     /* check sanity of parameters */
     830             :     Assert(n_skip >= 0);
     831             :     Assert(min_hist_size > 2 * n_skip);
     832             : 
     833        5046 :     if (HeapTupleIsValid(vardata->statsTuple) &&
     834        3184 :         statistic_proc_security_check(vardata, opproc->fn_oid) &&
     835        1590 :         get_attstatsslot(&sslot, vardata->statsTuple,
     836             :                          STATISTIC_KIND_HISTOGRAM, InvalidOid,
     837             :                          ATTSTATSSLOT_VALUES))
     838             :     {
     839        1546 :         *hist_size = sslot.nvalues;
     840        1546 :         if (sslot.nvalues >= min_hist_size)
     841             :         {
     842        1106 :             LOCAL_FCINFO(fcinfo, 2);
     843        1106 :             int         nmatch = 0;
     844             :             int         i;
     845             : 
     846             :             /*
     847             :              * We invoke the opproc "by hand" so that we won't fail on NULL
     848             :              * results.  Such cases won't arise for normal comparison
     849             :              * functions, but generic_restriction_selectivity could perhaps be
     850             :              * used with operators that can return NULL.  A small side benefit
     851             :              * is to not need to re-initialize the fcinfo struct from scratch
     852             :              * each time.
     853             :              */
     854        1106 :             InitFunctionCallInfoData(*fcinfo, opproc, 2, collation,
     855             :                                      NULL, NULL);
     856        1106 :             fcinfo->args[0].isnull = false;
     857        1106 :             fcinfo->args[1].isnull = false;
     858             :             /* be careful to apply operator right way 'round */
     859        1106 :             if (varonleft)
     860        1106 :                 fcinfo->args[1].value = constval;
     861             :             else
     862           0 :                 fcinfo->args[0].value = constval;
     863             : 
     864      106228 :             for (i = n_skip; i < sslot.nvalues - n_skip; i++)
     865             :             {
     866             :                 Datum       fresult;
     867             : 
     868      105122 :                 if (varonleft)
     869      105122 :                     fcinfo->args[0].value = sslot.values[i];
     870             :                 else
     871           0 :                     fcinfo->args[1].value = sslot.values[i];
     872      105122 :                 fcinfo->isnull = false;
     873      105122 :                 fresult = FunctionCallInvoke(fcinfo);
     874      105122 :                 if (!fcinfo->isnull && DatumGetBool(fresult))
     875        5602 :                     nmatch++;
     876             :             }
     877        1106 :             result = ((double) nmatch) / ((double) (sslot.nvalues - 2 * n_skip));
     878             :         }
     879             :         else
     880         440 :             result = -1;
     881        1546 :         free_attstatsslot(&sslot);
     882             :     }
     883             :     else
     884             :     {
     885        1906 :         *hist_size = 0;
     886        1906 :         result = -1;
     887             :     }
     888             : 
     889        3452 :     return result;
     890             : }
     891             : 
     892             : /*
     893             :  *  generic_restriction_selectivity     - Selectivity for almost anything
     894             :  *
     895             :  * This function estimates selectivity for operators that we don't have any
     896             :  * special knowledge about, but are on data types that we collect standard
     897             :  * MCV and/or histogram statistics for.  (Additional assumptions are that
     898             :  * the operator is strict and immutable, or at least stable.)
     899             :  *
     900             :  * If we have "VAR OP CONST" or "CONST OP VAR", selectivity is estimated by
     901             :  * applying the operator to each element of the column's MCV and/or histogram
     902             :  * stats, and merging the results using the assumption that the histogram is
     903             :  * a reasonable random sample of the column's non-MCV population.  Note that
     904             :  * if the operator's semantics are related to the histogram ordering, this
     905             :  * might not be such a great assumption; other functions such as
     906             :  * scalarineqsel() are probably a better match in such cases.
     907             :  *
     908             :  * Otherwise, fall back to the default selectivity provided by the caller.
     909             :  */
     910             : double
     911         810 : generic_restriction_selectivity(PlannerInfo *root, Oid oproid, Oid collation,
     912             :                                 List *args, int varRelid,
     913             :                                 double default_selectivity)
     914             : {
     915             :     double      selec;
     916             :     VariableStatData vardata;
     917             :     Node       *other;
     918             :     bool        varonleft;
     919             : 
     920             :     /*
     921             :      * If expression is not variable OP something or something OP variable,
     922             :      * then punt and return the default estimate.
     923             :      */
     924         810 :     if (!get_restriction_variable(root, args, varRelid,
     925             :                                   &vardata, &other, &varonleft))
     926           0 :         return default_selectivity;
     927             : 
     928             :     /*
     929             :      * If the something is a NULL constant, assume operator is strict and
     930             :      * return zero, ie, operator will never return TRUE.
     931             :      */
     932         810 :     if (IsA(other, Const) &&
     933         810 :         ((Const *) other)->constisnull)
     934             :     {
     935           0 :         ReleaseVariableStats(vardata);
     936           0 :         return 0.0;
     937             :     }
     938             : 
     939         810 :     if (IsA(other, Const))
     940             :     {
     941             :         /* Variable is being compared to a known non-null constant */
     942         810 :         Datum       constval = ((Const *) other)->constvalue;
     943             :         FmgrInfo    opproc;
     944             :         double      mcvsum;
     945             :         double      mcvsel;
     946             :         double      nullfrac;
     947             :         int         hist_size;
     948             : 
     949         810 :         fmgr_info(get_opcode(oproid), &opproc);
     950             : 
     951             :         /*
     952             :          * Calculate the selectivity for the column's most common values.
     953             :          */
     954         810 :         mcvsel = mcv_selectivity(&vardata, &opproc, collation,
     955             :                                  constval, varonleft,
     956             :                                  &mcvsum);
     957             : 
     958             :         /*
     959             :          * If the histogram is large enough, see what fraction of it matches
     960             :          * the query, and assume that's representative of the non-MCV
     961             :          * population.  Otherwise use the default selectivity for the non-MCV
     962             :          * population.
     963             :          */
     964         810 :         selec = histogram_selectivity(&vardata, &opproc, collation,
     965             :                                       constval, varonleft,
     966             :                                       10, 1, &hist_size);
     967         810 :         if (selec < 0)
     968             :         {
     969             :             /* Nope, fall back on default */
     970         410 :             selec = default_selectivity;
     971             :         }
     972         400 :         else if (hist_size < 100)
     973             :         {
     974             :             /*
     975             :              * For histogram sizes from 10 to 100, we combine the histogram
     976             :              * and default selectivities, putting increasingly more trust in
     977             :              * the histogram for larger sizes.
     978             :              */
     979           0 :             double      hist_weight = hist_size / 100.0;
     980             : 
     981           0 :             selec = selec * hist_weight +
     982           0 :                 default_selectivity * (1.0 - hist_weight);
     983             :         }
     984             : 
     985             :         /* In any case, don't believe extremely small or large estimates. */
     986         810 :         if (selec < 0.0001)
     987         236 :             selec = 0.0001;
     988         574 :         else if (selec > 0.9999)
     989          32 :             selec = 0.9999;
     990             : 
     991             :         /* Don't forget to account for nulls. */
     992         810 :         if (HeapTupleIsValid(vardata.statsTuple))
     993         440 :             nullfrac = ((Form_pg_statistic) GETSTRUCT(vardata.statsTuple))->stanullfrac;
     994             :         else
     995         370 :             nullfrac = 0.0;
     996             : 
     997             :         /*
     998             :          * Now merge the results from the MCV and histogram calculations,
     999             :          * realizing that the histogram covers only the non-null values that
    1000             :          * are not listed in MCV.
    1001             :          */
    1002         810 :         selec *= 1.0 - nullfrac - mcvsum;
    1003         810 :         selec += mcvsel;
    1004             :     }
    1005             :     else
    1006             :     {
    1007             :         /* Comparison value is not constant, so we can't do anything */
    1008           0 :         selec = default_selectivity;
    1009             :     }
    1010             : 
    1011         810 :     ReleaseVariableStats(vardata);
    1012             : 
    1013             :     /* result should be in range, but make sure... */
    1014         810 :     CLAMP_PROBABILITY(selec);
    1015             : 
    1016         810 :     return selec;
    1017             : }
    1018             : 
    1019             : /*
    1020             :  *  ineq_histogram_selectivity  - Examine the histogram for scalarineqsel
    1021             :  *
    1022             :  * Determine the fraction of the variable's histogram population that
    1023             :  * satisfies the inequality condition, ie, VAR < (or <=, >, >=) CONST.
    1024             :  * The isgt and iseq flags distinguish which of the four cases apply.
    1025             :  *
    1026             :  * While opproc could be looked up from the operator OID, common callers
    1027             :  * also need to call it separately, so we make the caller pass both.
    1028             :  *
    1029             :  * Returns -1 if there is no histogram (valid results will always be >= 0).
    1030             :  *
    1031             :  * Note that the result disregards both the most-common-values (if any) and
    1032             :  * null entries.  The caller is expected to combine this result with
    1033             :  * statistics for those portions of the column population.
    1034             :  *
    1035             :  * This is exported so that some other estimation functions can use it.
    1036             :  */
    1037             : double
    1038      184854 : ineq_histogram_selectivity(PlannerInfo *root,
    1039             :                            VariableStatData *vardata,
    1040             :                            Oid opoid, FmgrInfo *opproc, bool isgt, bool iseq,
    1041             :                            Oid collation,
    1042             :                            Datum constval, Oid consttype)
    1043             : {
    1044             :     double      hist_selec;
    1045             :     AttStatsSlot sslot;
    1046             : 
    1047      184854 :     hist_selec = -1.0;
    1048             : 
    1049             :     /*
    1050             :      * Someday, ANALYZE might store more than one histogram per rel/att,
    1051             :      * corresponding to more than one possible sort ordering defined for the
    1052             :      * column type.  Right now, we know there is only one, so just grab it and
    1053             :      * see if it matches the query.
    1054             :      *
    1055             :      * Note that we can't use opoid as search argument; the staop appearing in
    1056             :      * pg_statistic will be for the relevant '<' operator, but what we have
    1057             :      * might be some other inequality operator such as '>='.  (Even if opoid
    1058             :      * is a '<' operator, it could be cross-type.)  Hence we must use
    1059             :      * comparison_ops_are_compatible() to see if the operators match.
    1060             :      */
    1061      368690 :     if (HeapTupleIsValid(vardata->statsTuple) &&
    1062      367620 :         statistic_proc_security_check(vardata, opproc->fn_oid) &&
    1063      183784 :         get_attstatsslot(&sslot, vardata->statsTuple,
    1064             :                          STATISTIC_KIND_HISTOGRAM, InvalidOid,
    1065             :                          ATTSTATSSLOT_VALUES))
    1066             :     {
    1067      151784 :         if (sslot.nvalues > 1 &&
    1068      303540 :             sslot.stacoll == collation &&
    1069      151756 :             comparison_ops_are_compatible(sslot.staop, opoid))
    1070      151684 :         {
    1071             :             /*
    1072             :              * Use binary search to find the desired location, namely the
    1073             :              * right end of the histogram bin containing the comparison value,
    1074             :              * which is the leftmost entry for which the comparison operator
    1075             :              * succeeds (if isgt) or fails (if !isgt).
    1076             :              *
    1077             :              * In this loop, we pay no attention to whether the operator iseq
    1078             :              * or not; that detail will be mopped up below.  (We cannot tell,
    1079             :              * anyway, whether the operator thinks the values are equal.)
    1080             :              *
    1081             :              * If the binary search accesses the first or last histogram
    1082             :              * entry, we try to replace that endpoint with the true column min
    1083             :              * or max as found by get_actual_variable_range().  This
    1084             :              * ameliorates misestimates when the min or max is moving as a
    1085             :              * result of changes since the last ANALYZE.  Note that this could
    1086             :              * result in effectively including MCVs into the histogram that
    1087             :              * weren't there before, but we don't try to correct for that.
    1088             :              */
    1089             :             double      histfrac;
    1090      151684 :             int         lobound = 0;    /* first possible slot to search */
    1091      151684 :             int         hibound = sslot.nvalues;    /* last+1 slot to search */
    1092      151684 :             bool        have_end = false;
    1093             : 
    1094             :             /*
    1095             :              * If there are only two histogram entries, we'll want up-to-date
    1096             :              * values for both.  (If there are more than two, we need at most
    1097             :              * one of them to be updated, so we deal with that within the
    1098             :              * loop.)
    1099             :              */
    1100      151684 :             if (sslot.nvalues == 2)
    1101         568 :                 have_end = get_actual_variable_range(root,
    1102             :                                                      vardata,
    1103             :                                                      sslot.staop,
    1104             :                                                      collation,
    1105             :                                                      &sslot.values[0],
    1106         568 :                                                      &sslot.values[1]);
    1107             : 
    1108     1008648 :             while (lobound < hibound)
    1109             :             {
    1110      856964 :                 int         probe = (lobound + hibound) / 2;
    1111             :                 bool        ltcmp;
    1112             : 
    1113             :                 /*
    1114             :                  * If we find ourselves about to compare to the first or last
    1115             :                  * histogram entry, first try to replace it with the actual
    1116             :                  * current min or max (unless we already did so above).
    1117             :                  */
    1118      856964 :                 if (probe == 0 && sslot.nvalues > 2)
    1119       75510 :                     have_end = get_actual_variable_range(root,
    1120             :                                                          vardata,
    1121             :                                                          sslot.staop,
    1122             :                                                          collation,
    1123             :                                                          &sslot.values[0],
    1124             :                                                          NULL);
    1125      781454 :                 else if (probe == sslot.nvalues - 1 && sslot.nvalues > 2)
    1126       49158 :                     have_end = get_actual_variable_range(root,
    1127             :                                                          vardata,
    1128             :                                                          sslot.staop,
    1129             :                                                          collation,
    1130             :                                                          NULL,
    1131       49158 :                                                          &sslot.values[probe]);
    1132             : 
    1133      856964 :                 ltcmp = DatumGetBool(FunctionCall2Coll(opproc,
    1134             :                                                        collation,
    1135             :                                                        sslot.values[probe],
    1136             :                                                        constval));
    1137      856964 :                 if (isgt)
    1138       61002 :                     ltcmp = !ltcmp;
    1139      856964 :                 if (ltcmp)
    1140      309450 :                     lobound = probe + 1;
    1141             :                 else
    1142      547514 :                     hibound = probe;
    1143             :             }
    1144             : 
    1145      151684 :             if (lobound <= 0)
    1146             :             {
    1147             :                 /*
    1148             :                  * Constant is below lower histogram boundary.  More
    1149             :                  * precisely, we have found that no entry in the histogram
    1150             :                  * satisfies the inequality clause (if !isgt) or they all do
    1151             :                  * (if isgt).  We estimate that that's true of the entire
    1152             :                  * table, so set histfrac to 0.0 (which we'll flip to 1.0
    1153             :                  * below, if isgt).
    1154             :                  */
    1155       69364 :                 histfrac = 0.0;
    1156             :             }
    1157       82320 :             else if (lobound >= sslot.nvalues)
    1158             :             {
    1159             :                 /*
    1160             :                  * Inverse case: constant is above upper histogram boundary.
    1161             :                  */
    1162       25568 :                 histfrac = 1.0;
    1163             :             }
    1164             :             else
    1165             :             {
    1166             :                 /* We have values[i-1] <= constant <= values[i]. */
    1167       56752 :                 int         i = lobound;
    1168       56752 :                 double      eq_selec = 0;
    1169             :                 double      val,
    1170             :                             high,
    1171             :                             low;
    1172             :                 double      binfrac;
    1173             : 
    1174             :                 /*
    1175             :                  * In the cases where we'll need it below, obtain an estimate
    1176             :                  * of the selectivity of "x = constval".  We use a calculation
    1177             :                  * similar to what var_eq_const() does for a non-MCV constant,
    1178             :                  * ie, estimate that all distinct non-MCV values occur equally
    1179             :                  * often.  But multiplication by "1.0 - sumcommon - nullfrac"
    1180             :                  * will be done by our caller, so we shouldn't do that here.
    1181             :                  * Therefore we can't try to clamp the estimate by reference
    1182             :                  * to the least common MCV; the result would be too small.
    1183             :                  *
    1184             :                  * Note: since this is effectively assuming that constval
    1185             :                  * isn't an MCV, it's logically dubious if constval in fact is
    1186             :                  * one.  But we have to apply *some* correction for equality,
    1187             :                  * and anyway we cannot tell if constval is an MCV, since we
    1188             :                  * don't have a suitable equality operator at hand.
    1189             :                  */
    1190       56752 :                 if (i == 1 || isgt == iseq)
    1191             :                 {
    1192             :                     double      otherdistinct;
    1193             :                     bool        isdefault;
    1194             :                     AttStatsSlot mcvslot;
    1195             : 
    1196             :                     /* Get estimated number of distinct values */
    1197       17322 :                     otherdistinct = get_variable_numdistinct(vardata,
    1198             :                                                              &isdefault);
    1199             : 
    1200             :                     /* Subtract off the number of known MCVs */
    1201       17322 :                     if (get_attstatsslot(&mcvslot, vardata->statsTuple,
    1202             :                                          STATISTIC_KIND_MCV, InvalidOid,
    1203             :                                          ATTSTATSSLOT_NUMBERS))
    1204             :                     {
    1205        5646 :                         otherdistinct -= mcvslot.nnumbers;
    1206        5646 :                         free_attstatsslot(&mcvslot);
    1207             :                     }
    1208             : 
    1209             :                     /* If result doesn't seem sane, leave eq_selec at 0 */
    1210       17322 :                     if (otherdistinct > 1)
    1211       17322 :                         eq_selec = 1.0 / otherdistinct;
    1212             :                 }
    1213             : 
    1214             :                 /*
    1215             :                  * Convert the constant and the two nearest bin boundary
    1216             :                  * values to a uniform comparison scale, and do a linear
    1217             :                  * interpolation within this bin.
    1218             :                  */
    1219       56752 :                 if (convert_to_scalar(constval, consttype, collation,
    1220             :                                       &val,
    1221       56752 :                                       sslot.values[i - 1], sslot.values[i],
    1222             :                                       vardata->vartype,
    1223             :                                       &low, &high))
    1224             :                 {
    1225       56748 :                     if (high <= low)
    1226             :                     {
    1227             :                         /* cope if bin boundaries appear identical */
    1228           0 :                         binfrac = 0.5;
    1229             :                     }
    1230       56748 :                     else if (val <= low)
    1231        7530 :                         binfrac = 0.0;
    1232       49218 :                     else if (val >= high)
    1233        1404 :                         binfrac = 1.0;
    1234             :                     else
    1235             :                     {
    1236       47814 :                         binfrac = (val - low) / (high - low);
    1237             : 
    1238             :                         /*
    1239             :                          * Watch out for the possibility that we got a NaN or
    1240             :                          * Infinity from the division.  This can happen
    1241             :                          * despite the previous checks, if for example "low"
    1242             :                          * is -Infinity.
    1243             :                          */
    1244       47814 :                         if (isnan(binfrac) ||
    1245       47814 :                             binfrac < 0.0 || binfrac > 1.0)
    1246           0 :                             binfrac = 0.5;
    1247             :                     }
    1248             :                 }
    1249             :                 else
    1250             :                 {
    1251             :                     /*
    1252             :                      * Ideally we'd produce an error here, on the grounds that
    1253             :                      * the given operator shouldn't have scalarXXsel
    1254             :                      * registered as its selectivity func unless we can deal
    1255             :                      * with its operand types.  But currently, all manner of
    1256             :                      * stuff is invoking scalarXXsel, so give a default
    1257             :                      * estimate until that can be fixed.
    1258             :                      */
    1259           4 :                     binfrac = 0.5;
    1260             :                 }
    1261             : 
    1262             :                 /*
    1263             :                  * Now, compute the overall selectivity across the values
    1264             :                  * represented by the histogram.  We have i-1 full bins and
    1265             :                  * binfrac partial bin below the constant.
    1266             :                  */
    1267       56752 :                 histfrac = (double) (i - 1) + binfrac;
    1268       56752 :                 histfrac /= (double) (sslot.nvalues - 1);
    1269             : 
    1270             :                 /*
    1271             :                  * At this point, histfrac is an estimate of the fraction of
    1272             :                  * the population represented by the histogram that satisfies
    1273             :                  * "x <= constval".  Somewhat remarkably, this statement is
    1274             :                  * true regardless of which operator we were doing the probes
    1275             :                  * with, so long as convert_to_scalar() delivers reasonable
    1276             :                  * results.  If the probe constant is equal to some histogram
    1277             :                  * entry, we would have considered the bin to the left of that
    1278             :                  * entry if probing with "<" or ">=", or the bin to the right
    1279             :                  * if probing with "<=" or ">"; but binfrac would have come
    1280             :                  * out as 1.0 in the first case and 0.0 in the second, leading
    1281             :                  * to the same histfrac in either case.  For probe constants
    1282             :                  * between histogram entries, we find the same bin and get the
    1283             :                  * same estimate with any operator.
    1284             :                  *
    1285             :                  * The fact that the estimate corresponds to "x <= constval"
    1286             :                  * and not "x < constval" is because of the way that ANALYZE
    1287             :                  * constructs the histogram: each entry is, effectively, the
    1288             :                  * rightmost value in its sample bucket.  So selectivity
    1289             :                  * values that are exact multiples of 1/(histogram_size-1)
    1290             :                  * should be understood as estimates including a histogram
    1291             :                  * entry plus everything to its left.
    1292             :                  *
    1293             :                  * However, that breaks down for the first histogram entry,
    1294             :                  * which necessarily is the leftmost value in its sample
    1295             :                  * bucket.  That means the first histogram bin is slightly
    1296             :                  * narrower than the rest, by an amount equal to eq_selec.
    1297             :                  * Another way to say that is that we want "x <= leftmost" to
    1298             :                  * be estimated as eq_selec not zero.  So, if we're dealing
    1299             :                  * with the first bin (i==1), rescale to make that true while
    1300             :                  * adjusting the rest of that bin linearly.
    1301             :                  */
    1302       56752 :                 if (i == 1)
    1303        6496 :                     histfrac += eq_selec * (1.0 - binfrac);
    1304             : 
    1305             :                 /*
    1306             :                  * "x <= constval" is good if we want an estimate for "<=" or
    1307             :                  * ">", but if we are estimating for "<" or ">=", we now need
    1308             :                  * to decrease the estimate by eq_selec.
    1309             :                  */
    1310       56752 :                 if (isgt == iseq)
    1311       14868 :                     histfrac -= eq_selec;
    1312             :             }
    1313             : 
    1314             :             /*
    1315             :              * Now the estimate is finished for "<" and "<=" cases.  If we are
    1316             :              * estimating for ">" or ">=", flip it.
    1317             :              */
    1318      151684 :             hist_selec = isgt ? (1.0 - histfrac) : histfrac;
    1319             : 
    1320             :             /*
    1321             :              * The histogram boundaries are only approximate to begin with,
    1322             :              * and may well be out of date anyway.  Therefore, don't believe
    1323             :              * extremely small or large selectivity estimates --- unless we
    1324             :              * got actual current endpoint values from the table, in which
    1325             :              * case just do the usual sanity clamp.  Somewhat arbitrarily, we
    1326             :              * set the cutoff for other cases at a hundredth of the histogram
    1327             :              * resolution.
    1328             :              */
    1329      151684 :             if (have_end)
    1330       78256 :                 CLAMP_PROBABILITY(hist_selec);
    1331             :             else
    1332             :             {
    1333       73428 :                 double      cutoff = 0.01 / (double) (sslot.nvalues - 1);
    1334             : 
    1335       73428 :                 if (hist_selec < cutoff)
    1336       21096 :                     hist_selec = cutoff;
    1337       52332 :                 else if (hist_selec > 1.0 - cutoff)
    1338       23178 :                     hist_selec = 1.0 - cutoff;
    1339             :             }
    1340             :         }
    1341         100 :         else if (sslot.nvalues > 1)
    1342             :         {
    1343             :             /*
    1344             :              * If we get here, we have a histogram but it's not sorted the way
    1345             :              * we want.  Do a brute-force search to see how many of the
    1346             :              * entries satisfy the comparison condition, and take that
    1347             :              * fraction as our estimate.  (This is identical to the inner loop
    1348             :              * of histogram_selectivity; maybe share code?)
    1349             :              */
    1350         100 :             LOCAL_FCINFO(fcinfo, 2);
    1351         100 :             int         nmatch = 0;
    1352             : 
    1353         100 :             InitFunctionCallInfoData(*fcinfo, opproc, 2, collation,
    1354             :                                      NULL, NULL);
    1355         100 :             fcinfo->args[0].isnull = false;
    1356         100 :             fcinfo->args[1].isnull = false;
    1357         100 :             fcinfo->args[1].value = constval;
    1358      641148 :             for (int i = 0; i < sslot.nvalues; i++)
    1359             :             {
    1360             :                 Datum       fresult;
    1361             : 
    1362      641048 :                 fcinfo->args[0].value = sslot.values[i];
    1363      641048 :                 fcinfo->isnull = false;
    1364      641048 :                 fresult = FunctionCallInvoke(fcinfo);
    1365      641048 :                 if (!fcinfo->isnull && DatumGetBool(fresult))
    1366        1204 :                     nmatch++;
    1367             :             }
    1368         100 :             hist_selec = ((double) nmatch) / ((double) sslot.nvalues);
    1369             : 
    1370             :             /*
    1371             :              * As above, clamp to a hundredth of the histogram resolution.
    1372             :              * This case is surely even less trustworthy than the normal one,
    1373             :              * so we shouldn't believe exact 0 or 1 selectivity.  (Maybe the
    1374             :              * clamp should be more restrictive in this case?)
    1375             :              */
    1376             :             {
    1377         100 :                 double      cutoff = 0.01 / (double) (sslot.nvalues - 1);
    1378             : 
    1379         100 :                 if (hist_selec < cutoff)
    1380           0 :                     hist_selec = cutoff;
    1381         100 :                 else if (hist_selec > 1.0 - cutoff)
    1382           0 :                     hist_selec = 1.0 - cutoff;
    1383             :             }
    1384             :         }
    1385             : 
    1386      151784 :         free_attstatsslot(&sslot);
    1387             :     }
    1388             : 
    1389      184854 :     return hist_selec;
    1390             : }
    1391             : 
    1392             : /*
    1393             :  * Common wrapper function for the selectivity estimators that simply
    1394             :  * invoke scalarineqsel().
    1395             :  */
    1396             : static Datum
    1397       30382 : scalarineqsel_wrapper(PG_FUNCTION_ARGS, bool isgt, bool iseq)
    1398             : {
    1399       30382 :     PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    1400       30382 :     Oid         operator = PG_GETARG_OID(1);
    1401       30382 :     List       *args = (List *) PG_GETARG_POINTER(2);
    1402       30382 :     int         varRelid = PG_GETARG_INT32(3);
    1403       30382 :     Oid         collation = PG_GET_COLLATION();
    1404             :     VariableStatData vardata;
    1405             :     Node       *other;
    1406             :     bool        varonleft;
    1407             :     Datum       constval;
    1408             :     Oid         consttype;
    1409             :     double      selec;
    1410             : 
    1411             :     /*
    1412             :      * If expression is not variable op something or something op variable,
    1413             :      * then punt and return a default estimate.
    1414             :      */
    1415       30382 :     if (!get_restriction_variable(root, args, varRelid,
    1416             :                                   &vardata, &other, &varonleft))
    1417         200 :         PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    1418             : 
    1419             :     /*
    1420             :      * Can't do anything useful if the something is not a constant, either.
    1421             :      */
    1422       30182 :     if (!IsA(other, Const))
    1423             :     {
    1424        1428 :         ReleaseVariableStats(vardata);
    1425        1428 :         PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    1426             :     }
    1427             : 
    1428             :     /*
    1429             :      * If the constant is NULL, assume operator is strict and return zero, ie,
    1430             :      * operator will never return TRUE.
    1431             :      */
    1432       28754 :     if (((Const *) other)->constisnull)
    1433             :     {
    1434          24 :         ReleaseVariableStats(vardata);
    1435          24 :         PG_RETURN_FLOAT8(0.0);
    1436             :     }
    1437       28730 :     constval = ((Const *) other)->constvalue;
    1438       28730 :     consttype = ((Const *) other)->consttype;
    1439             : 
    1440             :     /*
    1441             :      * Force the var to be on the left to simplify logic in scalarineqsel.
    1442             :      */
    1443       28730 :     if (!varonleft)
    1444             :     {
    1445         168 :         operator = get_commutator(operator);
    1446         168 :         if (!operator)
    1447             :         {
    1448             :             /* Use default selectivity (should we raise an error instead?) */
    1449           0 :             ReleaseVariableStats(vardata);
    1450           0 :             PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    1451             :         }
    1452         168 :         isgt = !isgt;
    1453             :     }
    1454             : 
    1455             :     /* The rest of the work is done by scalarineqsel(). */
    1456       28730 :     selec = scalarineqsel(root, operator, isgt, iseq, collation,
    1457             :                           &vardata, constval, consttype);
    1458             : 
    1459       28730 :     ReleaseVariableStats(vardata);
    1460             : 
    1461       28730 :     PG_RETURN_FLOAT8((float8) selec);
    1462             : }
    1463             : 
    1464             : /*
    1465             :  *      scalarltsel     - Selectivity of "<" for scalars.
    1466             :  */
    1467             : Datum
    1468        8658 : scalarltsel(PG_FUNCTION_ARGS)
    1469             : {
    1470        8658 :     return scalarineqsel_wrapper(fcinfo, false, false);
    1471             : }
    1472             : 
    1473             : /*
    1474             :  *      scalarlesel     - Selectivity of "<=" for scalars.
    1475             :  */
    1476             : Datum
    1477        2232 : scalarlesel(PG_FUNCTION_ARGS)
    1478             : {
    1479        2232 :     return scalarineqsel_wrapper(fcinfo, false, true);
    1480             : }
    1481             : 
    1482             : /*
    1483             :  *      scalargtsel     - Selectivity of ">" for scalars.
    1484             :  */
    1485             : Datum
    1486       12656 : scalargtsel(PG_FUNCTION_ARGS)
    1487             : {
    1488       12656 :     return scalarineqsel_wrapper(fcinfo, true, false);
    1489             : }
    1490             : 
    1491             : /*
    1492             :  *      scalargesel     - Selectivity of ">=" for scalars.
    1493             :  */
    1494             : Datum
    1495        6836 : scalargesel(PG_FUNCTION_ARGS)
    1496             : {
    1497        6836 :     return scalarineqsel_wrapper(fcinfo, true, true);
    1498             : }
    1499             : 
    1500             : /*
    1501             :  *      boolvarsel      - Selectivity of Boolean variable.
    1502             :  *
    1503             :  * This can actually be called on any boolean-valued expression.  If it
    1504             :  * involves only Vars of the specified relation, and if there are statistics
    1505             :  * about the Var or expression (the latter is possible if it's indexed) then
    1506             :  * we'll produce a real estimate; otherwise it's just a default.
    1507             :  */
    1508             : Selectivity
    1509       15202 : boolvarsel(PlannerInfo *root, Node *arg, int varRelid)
    1510             : {
    1511             :     VariableStatData vardata;
    1512             :     double      selec;
    1513             : 
    1514       15202 :     examine_variable(root, arg, varRelid, &vardata);
    1515       15202 :     if (HeapTupleIsValid(vardata.statsTuple))
    1516             :     {
    1517             :         /*
    1518             :          * A boolean variable V is equivalent to the clause V = 't', so we
    1519             :          * compute the selectivity as if that is what we have.
    1520             :          */
    1521       11886 :         selec = var_eq_const(&vardata, BooleanEqualOperator, InvalidOid,
    1522             :                              BoolGetDatum(true), false, true, false);
    1523             :     }
    1524             :     else
    1525             :     {
    1526             :         /* Otherwise, the default estimate is 0.5 */
    1527        3316 :         selec = 0.5;
    1528             :     }
    1529       15202 :     ReleaseVariableStats(vardata);
    1530       15202 :     return selec;
    1531             : }
    1532             : 
    1533             : /*
    1534             :  *      booltestsel     - Selectivity of BooleanTest Node.
    1535             :  */
    1536             : Selectivity
    1537         132 : booltestsel(PlannerInfo *root, BoolTestType booltesttype, Node *arg,
    1538             :             int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
    1539             : {
    1540             :     VariableStatData vardata;
    1541             :     double      selec;
    1542             : 
    1543         132 :     examine_variable(root, arg, varRelid, &vardata);
    1544             : 
    1545         132 :     if (HeapTupleIsValid(vardata.statsTuple))
    1546             :     {
    1547             :         Form_pg_statistic stats;
    1548             :         double      freq_null;
    1549             :         AttStatsSlot sslot;
    1550             : 
    1551           0 :         stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
    1552           0 :         freq_null = stats->stanullfrac;
    1553             : 
    1554           0 :         if (get_attstatsslot(&sslot, vardata.statsTuple,
    1555             :                              STATISTIC_KIND_MCV, InvalidOid,
    1556             :                              ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS)
    1557           0 :             && sslot.nnumbers > 0)
    1558           0 :         {
    1559             :             double      freq_true;
    1560             :             double      freq_false;
    1561             : 
    1562             :             /*
    1563             :              * Get first MCV frequency and derive frequency for true.
    1564             :              */
    1565           0 :             if (DatumGetBool(sslot.values[0]))
    1566           0 :                 freq_true = sslot.numbers[0];
    1567             :             else
    1568           0 :                 freq_true = 1.0 - sslot.numbers[0] - freq_null;
    1569             : 
    1570             :             /*
    1571             :              * Next derive frequency for false. Then use these as appropriate
    1572             :              * to derive frequency for each case.
    1573             :              */
    1574           0 :             freq_false = 1.0 - freq_true - freq_null;
    1575             : 
    1576           0 :             switch (booltesttype)
    1577             :             {
    1578           0 :                 case IS_UNKNOWN:
    1579             :                     /* select only NULL values */
    1580           0 :                     selec = freq_null;
    1581           0 :                     break;
    1582           0 :                 case IS_NOT_UNKNOWN:
    1583             :                     /* select non-NULL values */
    1584           0 :                     selec = 1.0 - freq_null;
    1585           0 :                     break;
    1586           0 :                 case IS_TRUE:
    1587             :                     /* select only TRUE values */
    1588           0 :                     selec = freq_true;
    1589           0 :                     break;
    1590           0 :                 case IS_NOT_TRUE:
    1591             :                     /* select non-TRUE values */
    1592           0 :                     selec = 1.0 - freq_true;
    1593           0 :                     break;
    1594           0 :                 case IS_FALSE:
    1595             :                     /* select only FALSE values */
    1596           0 :                     selec = freq_false;
    1597           0 :                     break;
    1598           0 :                 case IS_NOT_FALSE:
    1599             :                     /* select non-FALSE values */
    1600           0 :                     selec = 1.0 - freq_false;
    1601           0 :                     break;
    1602           0 :                 default:
    1603           0 :                     elog(ERROR, "unrecognized booltesttype: %d",
    1604             :                          (int) booltesttype);
    1605             :                     selec = 0.0;    /* Keep compiler quiet */
    1606             :                     break;
    1607             :             }
    1608             : 
    1609           0 :             free_attstatsslot(&sslot);
    1610             :         }
    1611             :         else
    1612             :         {
    1613             :             /*
    1614             :              * No most-common-value info available. Still have null fraction
    1615             :              * information, so use it for IS [NOT] UNKNOWN. Otherwise adjust
    1616             :              * for null fraction and assume a 50-50 split of TRUE and FALSE.
    1617             :              */
    1618           0 :             switch (booltesttype)
    1619             :             {
    1620           0 :                 case IS_UNKNOWN:
    1621             :                     /* select only NULL values */
    1622           0 :                     selec = freq_null;
    1623           0 :                     break;
    1624           0 :                 case IS_NOT_UNKNOWN:
    1625             :                     /* select non-NULL values */
    1626           0 :                     selec = 1.0 - freq_null;
    1627           0 :                     break;
    1628           0 :                 case IS_TRUE:
    1629             :                 case IS_FALSE:
    1630             :                     /* Assume we select half of the non-NULL values */
    1631           0 :                     selec = (1.0 - freq_null) / 2.0;
    1632           0 :                     break;
    1633           0 :                 case IS_NOT_TRUE:
    1634             :                 case IS_NOT_FALSE:
    1635             :                     /* Assume we select NULLs plus half of the non-NULLs */
    1636             :                     /* equiv. to freq_null + (1.0 - freq_null) / 2.0 */
    1637           0 :                     selec = (freq_null + 1.0) / 2.0;
    1638           0 :                     break;
    1639           0 :                 default:
    1640           0 :                     elog(ERROR, "unrecognized booltesttype: %d",
    1641             :                          (int) booltesttype);
    1642             :                     selec = 0.0;    /* Keep compiler quiet */
    1643             :                     break;
    1644             :             }
    1645             :         }
    1646             :     }
    1647             :     else
    1648             :     {
    1649             :         /*
    1650             :          * If we can't get variable statistics for the argument, perhaps
    1651             :          * clause_selectivity can do something with it.  We ignore the
    1652             :          * possibility of a NULL value when using clause_selectivity, and just
    1653             :          * assume the value is either TRUE or FALSE.
    1654             :          */
    1655         132 :         switch (booltesttype)
    1656             :         {
    1657          12 :             case IS_UNKNOWN:
    1658          12 :                 selec = DEFAULT_UNK_SEL;
    1659          12 :                 break;
    1660          12 :             case IS_NOT_UNKNOWN:
    1661          12 :                 selec = DEFAULT_NOT_UNK_SEL;
    1662          12 :                 break;
    1663          32 :             case IS_TRUE:
    1664             :             case IS_NOT_FALSE:
    1665          32 :                 selec = (double) clause_selectivity(root, arg,
    1666             :                                                     varRelid,
    1667             :                                                     jointype, sjinfo);
    1668          32 :                 break;
    1669          76 :             case IS_FALSE:
    1670             :             case IS_NOT_TRUE:
    1671          76 :                 selec = 1.0 - (double) clause_selectivity(root, arg,
    1672             :                                                           varRelid,
    1673             :                                                           jointype, sjinfo);
    1674          76 :                 break;
    1675           0 :             default:
    1676           0 :                 elog(ERROR, "unrecognized booltesttype: %d",
    1677             :                      (int) booltesttype);
    1678             :                 selec = 0.0;    /* Keep compiler quiet */
    1679             :                 break;
    1680             :         }
    1681             :     }
    1682             : 
    1683         132 :     ReleaseVariableStats(vardata);
    1684             : 
    1685             :     /* result should be in range, but make sure... */
    1686         132 :     CLAMP_PROBABILITY(selec);
    1687             : 
    1688         132 :     return (Selectivity) selec;
    1689             : }
    1690             : 
    1691             : /*
    1692             :  *      nulltestsel     - Selectivity of NullTest Node.
    1693             :  */
    1694             : Selectivity
    1695       17064 : nulltestsel(PlannerInfo *root, NullTestType nulltesttype, Node *arg,
    1696             :             int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
    1697             : {
    1698             :     VariableStatData vardata;
    1699             :     double      selec;
    1700             : 
    1701       17064 :     examine_variable(root, arg, varRelid, &vardata);
    1702             : 
    1703       17064 :     if (HeapTupleIsValid(vardata.statsTuple))
    1704             :     {
    1705             :         Form_pg_statistic stats;
    1706             :         double      freq_null;
    1707             : 
    1708        7474 :         stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
    1709        7474 :         freq_null = stats->stanullfrac;
    1710             : 
    1711        7474 :         switch (nulltesttype)
    1712             :         {
    1713        3862 :             case IS_NULL:
    1714             : 
    1715             :                 /*
    1716             :                  * Use freq_null directly.
    1717             :                  */
    1718        3862 :                 selec = freq_null;
    1719        3862 :                 break;
    1720        3612 :             case IS_NOT_NULL:
    1721             : 
    1722             :                 /*
    1723             :                  * Select not unknown (not null) values. Calculate from
    1724             :                  * freq_null.
    1725             :                  */
    1726        3612 :                 selec = 1.0 - freq_null;
    1727        3612 :                 break;
    1728           0 :             default:
    1729           0 :                 elog(ERROR, "unrecognized nulltesttype: %d",
    1730             :                      (int) nulltesttype);
    1731             :                 return (Selectivity) 0; /* keep compiler quiet */
    1732             :         }
    1733             :     }
    1734        9590 :     else if (vardata.var && IsA(vardata.var, Var) &&
    1735        6790 :              ((Var *) vardata.var)->varattno < 0)
    1736             :     {
    1737             :         /*
    1738             :          * There are no stats for system columns, but we know they are never
    1739             :          * NULL.
    1740             :          */
    1741          16 :         selec = (nulltesttype == IS_NULL) ? 0.0 : 1.0;
    1742             :     }
    1743             :     else
    1744             :     {
    1745             :         /*
    1746             :          * No ANALYZE stats available, so make a guess
    1747             :          */
    1748        9574 :         switch (nulltesttype)
    1749             :         {
    1750        1032 :             case IS_NULL:
    1751        1032 :                 selec = DEFAULT_UNK_SEL;
    1752        1032 :                 break;
    1753        8542 :             case IS_NOT_NULL:
    1754        8542 :                 selec = DEFAULT_NOT_UNK_SEL;
    1755        8542 :                 break;
    1756           0 :             default:
    1757           0 :                 elog(ERROR, "unrecognized nulltesttype: %d",
    1758             :                      (int) nulltesttype);
    1759             :                 return (Selectivity) 0; /* keep compiler quiet */
    1760             :         }
    1761             :     }
    1762             : 
    1763       17064 :     ReleaseVariableStats(vardata);
    1764             : 
    1765             :     /* result should be in range, but make sure... */
    1766       17064 :     CLAMP_PROBABILITY(selec);
    1767             : 
    1768       17064 :     return (Selectivity) selec;
    1769             : }
    1770             : 
    1771             : /*
    1772             :  * strip_array_coercion - strip binary-compatible relabeling from an array expr
    1773             :  *
    1774             :  * For array values, the parser normally generates ArrayCoerceExpr conversions,
    1775             :  * but it seems possible that RelabelType might show up.  Also, the planner
    1776             :  * is not currently tense about collapsing stacked ArrayCoerceExpr nodes,
    1777             :  * so we need to be ready to deal with more than one level.
    1778             :  */
    1779             : static Node *
    1780       73516 : strip_array_coercion(Node *node)
    1781             : {
    1782             :     for (;;)
    1783             :     {
    1784       73516 :         if (node && IsA(node, ArrayCoerceExpr))
    1785          12 :         {
    1786         388 :             ArrayCoerceExpr *acoerce = (ArrayCoerceExpr *) node;
    1787             : 
    1788             :             /*
    1789             :              * If the per-element expression is just a RelabelType on top of
    1790             :              * CaseTestExpr, then we know it's a binary-compatible relabeling.
    1791             :              */
    1792         388 :             if (IsA(acoerce->elemexpr, RelabelType) &&
    1793          12 :                 IsA(((RelabelType *) acoerce->elemexpr)->arg, CaseTestExpr))
    1794          12 :                 node = (Node *) acoerce->arg;
    1795             :             else
    1796             :                 break;
    1797             :         }
    1798       73128 :         else if (node && IsA(node, RelabelType))
    1799             :         {
    1800             :             /* We don't really expect this case, but may as well cope */
    1801           0 :             node = (Node *) ((RelabelType *) node)->arg;
    1802             :         }
    1803             :         else
    1804             :             break;
    1805             :     }
    1806       73504 :     return node;
    1807             : }
    1808             : 
    1809             : /*
    1810             :  *      scalararraysel      - Selectivity of ScalarArrayOpExpr Node.
    1811             :  */
    1812             : Selectivity
    1813       14934 : scalararraysel(PlannerInfo *root,
    1814             :                ScalarArrayOpExpr *clause,
    1815             :                bool is_join_clause,
    1816             :                int varRelid,
    1817             :                JoinType jointype,
    1818             :                SpecialJoinInfo *sjinfo)
    1819             : {
    1820       14934 :     Oid         operator = clause->opno;
    1821       14934 :     bool        useOr = clause->useOr;
    1822       14934 :     bool        isEquality = false;
    1823       14934 :     bool        isInequality = false;
    1824             :     Node       *leftop;
    1825             :     Node       *rightop;
    1826             :     Oid         nominal_element_type;
    1827             :     Oid         nominal_element_collation;
    1828             :     TypeCacheEntry *typentry;
    1829             :     RegProcedure oprsel;
    1830             :     FmgrInfo    oprselproc;
    1831             :     Selectivity s1;
    1832             :     Selectivity s1disjoint;
    1833             : 
    1834             :     /* First, deconstruct the expression */
    1835             :     Assert(list_length(clause->args) == 2);
    1836       14934 :     leftop = (Node *) linitial(clause->args);
    1837       14934 :     rightop = (Node *) lsecond(clause->args);
    1838             : 
    1839             :     /* aggressively reduce both sides to constants */
    1840       14934 :     leftop = estimate_expression_value(root, leftop);
    1841       14934 :     rightop = estimate_expression_value(root, rightop);
    1842             : 
    1843             :     /* get nominal (after relabeling) element type of rightop */
    1844       14934 :     nominal_element_type = get_base_element_type(exprType(rightop));
    1845       14934 :     if (!OidIsValid(nominal_element_type))
    1846           0 :         return (Selectivity) 0.5;   /* probably shouldn't happen */
    1847             :     /* get nominal collation, too, for generating constants */
    1848       14934 :     nominal_element_collation = exprCollation(rightop);
    1849             : 
    1850             :     /* look through any binary-compatible relabeling of rightop */
    1851       14934 :     rightop = strip_array_coercion(rightop);
    1852             : 
    1853             :     /*
    1854             :      * Detect whether the operator is the default equality or inequality
    1855             :      * operator of the array element type.
    1856             :      */
    1857       14934 :     typentry = lookup_type_cache(nominal_element_type, TYPECACHE_EQ_OPR);
    1858       14934 :     if (OidIsValid(typentry->eq_opr))
    1859             :     {
    1860       14934 :         if (operator == typentry->eq_opr)
    1861       13858 :             isEquality = true;
    1862        1076 :         else if (get_negator(operator) == typentry->eq_opr)
    1863         832 :             isInequality = true;
    1864             :     }
    1865             : 
    1866             :     /*
    1867             :      * If it is equality or inequality, we might be able to estimate this as a
    1868             :      * form of array containment; for instance "const = ANY(column)" can be
    1869             :      * treated as "ARRAY[const] <@ column".  scalararraysel_containment tries
    1870             :      * that, and returns the selectivity estimate if successful, or -1 if not.
    1871             :      */
    1872       14934 :     if ((isEquality || isInequality) && !is_join_clause)
    1873             :     {
    1874       14690 :         s1 = scalararraysel_containment(root, leftop, rightop,
    1875             :                                         nominal_element_type,
    1876             :                                         isEquality, useOr, varRelid);
    1877       14690 :         if (s1 >= 0.0)
    1878          70 :             return s1;
    1879             :     }
    1880             : 
    1881             :     /*
    1882             :      * Look up the underlying operator's selectivity estimator. Punt if it
    1883             :      * hasn't got one.
    1884             :      */
    1885       14864 :     if (is_join_clause)
    1886           0 :         oprsel = get_oprjoin(operator);
    1887             :     else
    1888       14864 :         oprsel = get_oprrest(operator);
    1889       14864 :     if (!oprsel)
    1890           0 :         return (Selectivity) 0.5;
    1891       14864 :     fmgr_info(oprsel, &oprselproc);
    1892             : 
    1893             :     /*
    1894             :      * In the array-containment check above, we must only believe that an
    1895             :      * operator is equality or inequality if it is the default btree equality
    1896             :      * operator (or its negator) for the element type, since those are the
    1897             :      * operators that array containment will use.  But in what follows, we can
    1898             :      * be a little laxer, and also believe that any operators using eqsel() or
    1899             :      * neqsel() as selectivity estimator act like equality or inequality.
    1900             :      */
    1901       14864 :     if (oprsel == F_EQSEL || oprsel == F_EQJOINSEL)
    1902       13880 :         isEquality = true;
    1903         984 :     else if (oprsel == F_NEQSEL || oprsel == F_NEQJOINSEL)
    1904         776 :         isInequality = true;
    1905             : 
    1906             :     /*
    1907             :      * We consider three cases:
    1908             :      *
    1909             :      * 1. rightop is an Array constant: deconstruct the array, apply the
    1910             :      * operator's selectivity function for each array element, and merge the
    1911             :      * results in the same way that clausesel.c does for AND/OR combinations.
    1912             :      *
    1913             :      * 2. rightop is an ARRAY[] construct: apply the operator's selectivity
    1914             :      * function for each element of the ARRAY[] construct, and merge.
    1915             :      *
    1916             :      * 3. otherwise, make a guess ...
    1917             :      */
    1918       14864 :     if (rightop && IsA(rightop, Const))
    1919        7800 :     {
    1920        7812 :         Datum       arraydatum = ((Const *) rightop)->constvalue;
    1921        7812 :         bool        arrayisnull = ((Const *) rightop)->constisnull;
    1922             :         ArrayType  *arrayval;
    1923             :         int16       elmlen;
    1924             :         bool        elmbyval;
    1925             :         char        elmalign;
    1926             :         int         num_elems;
    1927             :         Datum      *elem_values;
    1928             :         bool       *elem_nulls;
    1929             :         int         i;
    1930             : 
    1931        7812 :         if (arrayisnull)        /* qual can't succeed if null array */
    1932          12 :             return (Selectivity) 0.0;
    1933        7800 :         arrayval = DatumGetArrayTypeP(arraydatum);
    1934        7800 :         get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
    1935             :                              &elmlen, &elmbyval, &elmalign);
    1936        7800 :         deconstruct_array(arrayval,
    1937             :                           ARR_ELEMTYPE(arrayval),
    1938             :                           elmlen, elmbyval, elmalign,
    1939             :                           &elem_values, &elem_nulls, &num_elems);
    1940             : 
    1941             :         /*
    1942             :          * For generic operators, we assume the probability of success is
    1943             :          * independent for each array element.  But for "= ANY" or "<> ALL",
    1944             :          * if the array elements are distinct (which'd typically be the case)
    1945             :          * then the probabilities are disjoint, and we should just sum them.
    1946             :          *
    1947             :          * If we were being really tense we would try to confirm that the
    1948             :          * elements are all distinct, but that would be expensive and it
    1949             :          * doesn't seem to be worth the cycles; it would amount to penalizing
    1950             :          * well-written queries in favor of poorly-written ones.  However, we
    1951             :          * do protect ourselves a little bit by checking whether the
    1952             :          * disjointness assumption leads to an impossible (out of range)
    1953             :          * probability; if so, we fall back to the normal calculation.
    1954             :          */
    1955        7800 :         s1 = s1disjoint = (useOr ? 0.0 : 1.0);
    1956             : 
    1957       32808 :         for (i = 0; i < num_elems; i++)
    1958             :         {
    1959             :             List       *args;
    1960             :             Selectivity s2;
    1961             : 
    1962       25008 :             args = list_make2(leftop,
    1963             :                               makeConst(nominal_element_type,
    1964             :                                         -1,
    1965             :                                         nominal_element_collation,
    1966             :                                         elmlen,
    1967             :                                         elem_values[i],
    1968             :                                         elem_nulls[i],
    1969             :                                         elmbyval));
    1970       25008 :             if (is_join_clause)
    1971           0 :                 s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
    1972             :                                                       clause->inputcollid,
    1973             :                                                       PointerGetDatum(root),
    1974             :                                                       ObjectIdGetDatum(operator),
    1975             :                                                       PointerGetDatum(args),
    1976             :                                                       Int16GetDatum(jointype),
    1977             :                                                       PointerGetDatum(sjinfo)));
    1978             :             else
    1979       25008 :                 s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
    1980             :                                                       clause->inputcollid,
    1981             :                                                       PointerGetDatum(root),
    1982             :                                                       ObjectIdGetDatum(operator),
    1983             :                                                       PointerGetDatum(args),
    1984             :                                                       Int32GetDatum(varRelid)));
    1985             : 
    1986       25008 :             if (useOr)
    1987             :             {
    1988       22622 :                 s1 = s1 + s2 - s1 * s2;
    1989       22622 :                 if (isEquality)
    1990       22226 :                     s1disjoint += s2;
    1991             :             }
    1992             :             else
    1993             :             {
    1994        2386 :                 s1 = s1 * s2;
    1995        2386 :                 if (isInequality)
    1996        2242 :                     s1disjoint += s2 - 1.0;
    1997             :             }
    1998             :         }
    1999             : 
    2000             :         /* accept disjoint-probability estimate if in range */
    2001        7800 :         if ((useOr ? isEquality : isInequality) &&
    2002        7524 :             s1disjoint >= 0.0 && s1disjoint <= 1.0)
    2003        7504 :             s1 = s1disjoint;
    2004             :     }
    2005        7052 :     else if (rightop && IsA(rightop, ArrayExpr) &&
    2006          70 :              !((ArrayExpr *) rightop)->multidims)
    2007          70 :     {
    2008          70 :         ArrayExpr  *arrayexpr = (ArrayExpr *) rightop;
    2009             :         int16       elmlen;
    2010             :         bool        elmbyval;
    2011             :         ListCell   *l;
    2012             : 
    2013          70 :         get_typlenbyval(arrayexpr->element_typeid,
    2014             :                         &elmlen, &elmbyval);
    2015             : 
    2016             :         /*
    2017             :          * We use the assumption of disjoint probabilities here too, although
    2018             :          * the odds of equal array elements are rather higher if the elements
    2019             :          * are not all constants (which they won't be, else constant folding
    2020             :          * would have reduced the ArrayExpr to a Const).  In this path it's
    2021             :          * critical to have the sanity check on the s1disjoint estimate.
    2022             :          */
    2023          70 :         s1 = s1disjoint = (useOr ? 0.0 : 1.0);
    2024             : 
    2025         248 :         foreach(l, arrayexpr->elements)
    2026             :         {
    2027         178 :             Node       *elem = (Node *) lfirst(l);
    2028             :             List       *args;
    2029             :             Selectivity s2;
    2030             : 
    2031             :             /*
    2032             :              * Theoretically, if elem isn't of nominal_element_type we should
    2033             :              * insert a RelabelType, but it seems unlikely that any operator
    2034             :              * estimation function would really care ...
    2035             :              */
    2036         178 :             args = list_make2(leftop, elem);
    2037         178 :             if (is_join_clause)
    2038           0 :                 s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
    2039             :                                                       clause->inputcollid,
    2040             :                                                       PointerGetDatum(root),
    2041             :                                                       ObjectIdGetDatum(operator),
    2042             :                                                       PointerGetDatum(args),
    2043             :                                                       Int16GetDatum(jointype),
    2044             :                                                       PointerGetDatum(sjinfo)));
    2045             :             else
    2046         178 :                 s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
    2047             :                                                       clause->inputcollid,
    2048             :                                                       PointerGetDatum(root),
    2049             :                                                       ObjectIdGetDatum(operator),
    2050             :                                                       PointerGetDatum(args),
    2051             :                                                       Int32GetDatum(varRelid)));
    2052             : 
    2053         178 :             if (useOr)
    2054             :             {
    2055         178 :                 s1 = s1 + s2 - s1 * s2;
    2056         178 :                 if (isEquality)
    2057         178 :                     s1disjoint += s2;
    2058             :             }
    2059             :             else
    2060             :             {
    2061           0 :                 s1 = s1 * s2;
    2062           0 :                 if (isInequality)
    2063           0 :                     s1disjoint += s2 - 1.0;
    2064             :             }
    2065             :         }
    2066             : 
    2067             :         /* accept disjoint-probability estimate if in range */
    2068          70 :         if ((useOr ? isEquality : isInequality) &&
    2069          70 :             s1disjoint >= 0.0 && s1disjoint <= 1.0)
    2070          70 :             s1 = s1disjoint;
    2071             :     }
    2072             :     else
    2073             :     {
    2074             :         CaseTestExpr *dummyexpr;
    2075             :         List       *args;
    2076             :         Selectivity s2;
    2077             :         int         i;
    2078             : 
    2079             :         /*
    2080             :          * We need a dummy rightop to pass to the operator selectivity
    2081             :          * routine.  It can be pretty much anything that doesn't look like a
    2082             :          * constant; CaseTestExpr is a convenient choice.
    2083             :          */
    2084        6982 :         dummyexpr = makeNode(CaseTestExpr);
    2085        6982 :         dummyexpr->typeId = nominal_element_type;
    2086        6982 :         dummyexpr->typeMod = -1;
    2087        6982 :         dummyexpr->collation = clause->inputcollid;
    2088        6982 :         args = list_make2(leftop, dummyexpr);
    2089        6982 :         if (is_join_clause)
    2090           0 :             s2 = DatumGetFloat8(FunctionCall5Coll(&oprselproc,
    2091             :                                                   clause->inputcollid,
    2092             :                                                   PointerGetDatum(root),
    2093             :                                                   ObjectIdGetDatum(operator),
    2094             :                                                   PointerGetDatum(args),
    2095             :                                                   Int16GetDatum(jointype),
    2096             :                                                   PointerGetDatum(sjinfo)));
    2097             :         else
    2098        6982 :             s2 = DatumGetFloat8(FunctionCall4Coll(&oprselproc,
    2099             :                                                   clause->inputcollid,
    2100             :                                                   PointerGetDatum(root),
    2101             :                                                   ObjectIdGetDatum(operator),
    2102             :                                                   PointerGetDatum(args),
    2103             :                                                   Int32GetDatum(varRelid)));
    2104        6982 :         s1 = useOr ? 0.0 : 1.0;
    2105             : 
    2106             :         /*
    2107             :          * Arbitrarily assume 10 elements in the eventual array value (see
    2108             :          * also estimate_array_length).  We don't risk an assumption of
    2109             :          * disjoint probabilities here.
    2110             :          */
    2111       76802 :         for (i = 0; i < 10; i++)
    2112             :         {
    2113       69820 :             if (useOr)
    2114       69820 :                 s1 = s1 + s2 - s1 * s2;
    2115             :             else
    2116           0 :                 s1 = s1 * s2;
    2117             :         }
    2118             :     }
    2119             : 
    2120             :     /* result should be in range, but make sure... */
    2121       14852 :     CLAMP_PROBABILITY(s1);
    2122             : 
    2123       14852 :     return s1;
    2124             : }
    2125             : 
    2126             : /*
    2127             :  * Estimate number of elements in the array yielded by an expression.
    2128             :  *
    2129             :  * It's important that this agree with scalararraysel.
    2130             :  */
    2131             : int
    2132       58570 : estimate_array_length(Node *arrayexpr)
    2133             : {
    2134             :     /* look through any binary-compatible relabeling of arrayexpr */
    2135       58570 :     arrayexpr = strip_array_coercion(arrayexpr);
    2136             : 
    2137       58570 :     if (arrayexpr && IsA(arrayexpr, Const))
    2138             :     {
    2139       13568 :         Datum       arraydatum = ((Const *) arrayexpr)->constvalue;
    2140       13568 :         bool        arrayisnull = ((Const *) arrayexpr)->constisnull;
    2141             :         ArrayType  *arrayval;
    2142             : 
    2143       13568 :         if (arrayisnull)
    2144          12 :             return 0;
    2145       13556 :         arrayval = DatumGetArrayTypeP(arraydatum);
    2146       13556 :         return ArrayGetNItems(ARR_NDIM(arrayval), ARR_DIMS(arrayval));
    2147             :     }
    2148       45002 :     else if (arrayexpr && IsA(arrayexpr, ArrayExpr) &&
    2149         112 :              !((ArrayExpr *) arrayexpr)->multidims)
    2150             :     {
    2151         112 :         return list_length(((ArrayExpr *) arrayexpr)->elements);
    2152             :     }
    2153             :     else
    2154             :     {
    2155             :         /* default guess --- see also scalararraysel */
    2156       44890 :         return 10;
    2157             :     }
    2158             : }
    2159             : 
    2160             : /*
    2161             :  *      rowcomparesel       - Selectivity of RowCompareExpr Node.
    2162             :  *
    2163             :  * We estimate RowCompare selectivity by considering just the first (high
    2164             :  * order) columns, which makes it equivalent to an ordinary OpExpr.  While
    2165             :  * this estimate could be refined by considering additional columns, it
    2166             :  * seems unlikely that we could do a lot better without multi-column
    2167             :  * statistics.
    2168             :  */
    2169             : Selectivity
    2170         104 : rowcomparesel(PlannerInfo *root,
    2171             :               RowCompareExpr *clause,
    2172             :               int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
    2173             : {
    2174             :     Selectivity s1;
    2175         104 :     Oid         opno = linitial_oid(clause->opnos);
    2176         104 :     Oid         inputcollid = linitial_oid(clause->inputcollids);
    2177             :     List       *opargs;
    2178             :     bool        is_join_clause;
    2179             : 
    2180             :     /* Build equivalent arg list for single operator */
    2181         104 :     opargs = list_make2(linitial(clause->largs), linitial(clause->rargs));
    2182             : 
    2183             :     /*
    2184             :      * Decide if it's a join clause.  This should match clausesel.c's
    2185             :      * treat_as_join_clause(), except that we intentionally consider only the
    2186             :      * leading columns and not the rest of the clause.
    2187             :      */
    2188         104 :     if (varRelid != 0)
    2189             :     {
    2190             :         /*
    2191             :          * Caller is forcing restriction mode (eg, because we are examining an
    2192             :          * inner indexscan qual).
    2193             :          */
    2194          36 :         is_join_clause = false;
    2195             :     }
    2196          68 :     else if (sjinfo == NULL)
    2197             :     {
    2198             :         /*
    2199             :          * It must be a restriction clause, since it's being evaluated at a
    2200             :          * scan node.
    2201             :          */
    2202          60 :         is_join_clause = false;
    2203             :     }
    2204             :     else
    2205             :     {
    2206             :         /*
    2207             :          * Otherwise, it's a join if there's more than one relation used.
    2208             :          */
    2209           8 :         is_join_clause = (NumRelids(root, (Node *) opargs) > 1);
    2210             :     }
    2211             : 
    2212         104 :     if (is_join_clause)
    2213             :     {
    2214             :         /* Estimate selectivity for a join clause. */
    2215           8 :         s1 = join_selectivity(root, opno,
    2216             :                               opargs,
    2217             :                               inputcollid,
    2218             :                               jointype,
    2219             :                               sjinfo);
    2220             :     }
    2221             :     else
    2222             :     {
    2223             :         /* Estimate selectivity for a restriction clause. */
    2224          96 :         s1 = restriction_selectivity(root, opno,
    2225             :                                      opargs,
    2226             :                                      inputcollid,
    2227             :                                      varRelid);
    2228             :     }
    2229             : 
    2230         104 :     return s1;
    2231             : }
    2232             : 
    2233             : /*
    2234             :  *      eqjoinsel       - Join selectivity of "="
    2235             :  */
    2236             : Datum
    2237      125196 : eqjoinsel(PG_FUNCTION_ARGS)
    2238             : {
    2239      125196 :     PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    2240      125196 :     Oid         operator = PG_GETARG_OID(1);
    2241      125196 :     List       *args = (List *) PG_GETARG_POINTER(2);
    2242             : 
    2243             : #ifdef NOT_USED
    2244             :     JoinType    jointype = (JoinType) PG_GETARG_INT16(3);
    2245             : #endif
    2246      125196 :     SpecialJoinInfo *sjinfo = (SpecialJoinInfo *) PG_GETARG_POINTER(4);
    2247      125196 :     Oid         collation = PG_GET_COLLATION();
    2248             :     double      selec;
    2249             :     double      selec_inner;
    2250             :     VariableStatData vardata1;
    2251             :     VariableStatData vardata2;
    2252             :     double      nd1;
    2253             :     double      nd2;
    2254             :     bool        isdefault1;
    2255             :     bool        isdefault2;
    2256             :     Oid         opfuncoid;
    2257             :     AttStatsSlot sslot1;
    2258             :     AttStatsSlot sslot2;
    2259      125196 :     Form_pg_statistic stats1 = NULL;
    2260      125196 :     Form_pg_statistic stats2 = NULL;
    2261      125196 :     bool        have_mcvs1 = false;
    2262      125196 :     bool        have_mcvs2 = false;
    2263             :     bool        join_is_reversed;
    2264             :     RelOptInfo *inner_rel;
    2265             : 
    2266      125196 :     get_join_variables(root, args, sjinfo,
    2267             :                        &vardata1, &vardata2, &join_is_reversed);
    2268             : 
    2269      125196 :     nd1 = get_variable_numdistinct(&vardata1, &isdefault1);
    2270      125196 :     nd2 = get_variable_numdistinct(&vardata2, &isdefault2);
    2271             : 
    2272      125196 :     opfuncoid = get_opcode(operator);
    2273             : 
    2274      125196 :     memset(&sslot1, 0, sizeof(sslot1));
    2275      125196 :     memset(&sslot2, 0, sizeof(sslot2));
    2276             : 
    2277      125196 :     if (HeapTupleIsValid(vardata1.statsTuple))
    2278             :     {
    2279             :         /* note we allow use of nullfrac regardless of security check */
    2280       87296 :         stats1 = (Form_pg_statistic) GETSTRUCT(vardata1.statsTuple);
    2281       87296 :         if (statistic_proc_security_check(&vardata1, opfuncoid))
    2282       87296 :             have_mcvs1 = get_attstatsslot(&sslot1, vardata1.statsTuple,
    2283             :                                           STATISTIC_KIND_MCV, InvalidOid,
    2284             :                                           ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
    2285             :     }
    2286             : 
    2287      125196 :     if (HeapTupleIsValid(vardata2.statsTuple))
    2288             :     {
    2289             :         /* note we allow use of nullfrac regardless of security check */
    2290       88830 :         stats2 = (Form_pg_statistic) GETSTRUCT(vardata2.statsTuple);
    2291       88830 :         if (statistic_proc_security_check(&vardata2, opfuncoid))
    2292       88830 :             have_mcvs2 = get_attstatsslot(&sslot2, vardata2.statsTuple,
    2293             :                                           STATISTIC_KIND_MCV, InvalidOid,
    2294             :                                           ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
    2295             :     }
    2296             : 
    2297             :     /* We need to compute the inner-join selectivity in all cases */
    2298      125196 :     selec_inner = eqjoinsel_inner(opfuncoid, collation,
    2299             :                                   &vardata1, &vardata2,
    2300             :                                   nd1, nd2,
    2301             :                                   isdefault1, isdefault2,
    2302             :                                   &sslot1, &sslot2,
    2303             :                                   stats1, stats2,
    2304             :                                   have_mcvs1, have_mcvs2);
    2305             : 
    2306      125196 :     switch (sjinfo->jointype)
    2307             :     {
    2308      114430 :         case JOIN_INNER:
    2309             :         case JOIN_LEFT:
    2310             :         case JOIN_FULL:
    2311      114430 :             selec = selec_inner;
    2312      114430 :             break;
    2313       10766 :         case JOIN_SEMI:
    2314             :         case JOIN_ANTI:
    2315             : 
    2316             :             /*
    2317             :              * Look up the join's inner relation.  min_righthand is sufficient
    2318             :              * information because neither SEMI nor ANTI joins permit any
    2319             :              * reassociation into or out of their RHS, so the righthand will
    2320             :              * always be exactly that set of rels.
    2321             :              */
    2322       10766 :             inner_rel = find_join_input_rel(root, sjinfo->min_righthand);
    2323             : 
    2324       10766 :             if (!join_is_reversed)
    2325        8002 :                 selec = eqjoinsel_semi(opfuncoid, collation,
    2326             :                                        &vardata1, &vardata2,
    2327             :                                        nd1, nd2,
    2328             :                                        isdefault1, isdefault2,
    2329             :                                        &sslot1, &sslot2,
    2330             :                                        stats1, stats2,
    2331             :                                        have_mcvs1, have_mcvs2,
    2332             :                                        inner_rel);
    2333             :             else
    2334             :             {
    2335        2764 :                 Oid         commop = get_commutator(operator);
    2336        2764 :                 Oid         commopfuncoid = OidIsValid(commop) ? get_opcode(commop) : InvalidOid;
    2337             : 
    2338        2764 :                 selec = eqjoinsel_semi(commopfuncoid, collation,
    2339             :                                        &vardata2, &vardata1,
    2340             :                                        nd2, nd1,
    2341             :                                        isdefault2, isdefault1,
    2342             :                                        &sslot2, &sslot1,
    2343             :                                        stats2, stats1,
    2344             :                                        have_mcvs2, have_mcvs1,
    2345             :                                        inner_rel);
    2346             :             }
    2347             : 
    2348             :             /*
    2349             :              * We should never estimate the output of a semijoin to be more
    2350             :              * rows than we estimate for an inner join with the same input
    2351             :              * rels and join condition; it's obviously impossible for that to
    2352             :              * happen.  The former estimate is N1 * Ssemi while the latter is
    2353             :              * N1 * N2 * Sinner, so we may clamp Ssemi <= N2 * Sinner.  Doing
    2354             :              * this is worthwhile because of the shakier estimation rules we
    2355             :              * use in eqjoinsel_semi, particularly in cases where it has to
    2356             :              * punt entirely.
    2357             :              */
    2358       10766 :             selec = Min(selec, inner_rel->rows * selec_inner);
    2359       10766 :             break;
    2360           0 :         default:
    2361             :             /* other values not expected here */
    2362           0 :             elog(ERROR, "unrecognized join type: %d",
    2363             :                  (int) sjinfo->jointype);
    2364             :             selec = 0;          /* keep compiler quiet */
    2365             :             break;
    2366             :     }
    2367             : 
    2368      125196 :     free_attstatsslot(&sslot1);
    2369      125196 :     free_attstatsslot(&sslot2);
    2370             : 
    2371      125196 :     ReleaseVariableStats(vardata1);
    2372      125196 :     ReleaseVariableStats(vardata2);
    2373             : 
    2374      125196 :     CLAMP_PROBABILITY(selec);
    2375             : 
    2376      125196 :     PG_RETURN_FLOAT8((float8) selec);
    2377             : }
    2378             : 
    2379             : /*
    2380             :  * eqjoinsel_inner --- eqjoinsel for normal inner join
    2381             :  *
    2382             :  * We also use this for LEFT/FULL outer joins; it's not presently clear
    2383             :  * that it's worth trying to distinguish them here.
    2384             :  */
    2385             : static double
    2386      125196 : eqjoinsel_inner(Oid opfuncoid, Oid collation,
    2387             :                 VariableStatData *vardata1, VariableStatData *vardata2,
    2388             :                 double nd1, double nd2,
    2389             :                 bool isdefault1, bool isdefault2,
    2390             :                 AttStatsSlot *sslot1, AttStatsSlot *sslot2,
    2391             :                 Form_pg_statistic stats1, Form_pg_statistic stats2,
    2392             :                 bool have_mcvs1, bool have_mcvs2)
    2393             : {
    2394             :     double      selec;
    2395             : 
    2396      125196 :     if (have_mcvs1 && have_mcvs2)
    2397       10656 :     {
    2398             :         /*
    2399             :          * We have most-common-value lists for both relations.  Run through
    2400             :          * the lists to see which MCVs actually join to each other with the
    2401             :          * given operator.  This allows us to determine the exact join
    2402             :          * selectivity for the portion of the relations represented by the MCV
    2403             :          * lists.  We still have to estimate for the remaining population, but
    2404             :          * in a skewed distribution this gives us a big leg up in accuracy.
    2405             :          * For motivation see the analysis in Y. Ioannidis and S.
    2406             :          * Christodoulakis, "On the propagation of errors in the size of join
    2407             :          * results", Technical Report 1018, Computer Science Dept., University
    2408             :          * of Wisconsin, Madison, March 1991 (available from ftp.cs.wisc.edu).
    2409             :          */
    2410       10656 :         LOCAL_FCINFO(fcinfo, 2);
    2411             :         FmgrInfo    eqproc;
    2412             :         bool       *hasmatch1;
    2413             :         bool       *hasmatch2;
    2414       10656 :         double      nullfrac1 = stats1->stanullfrac;
    2415       10656 :         double      nullfrac2 = stats2->stanullfrac;
    2416             :         double      matchprodfreq,
    2417             :                     matchfreq1,
    2418             :                     matchfreq2,
    2419             :                     unmatchfreq1,
    2420             :                     unmatchfreq2,
    2421             :                     otherfreq1,
    2422             :                     otherfreq2,
    2423             :                     totalsel1,
    2424             :                     totalsel2;
    2425             :         int         i,
    2426             :                     nmatches;
    2427             : 
    2428       10656 :         fmgr_info(opfuncoid, &eqproc);
    2429             : 
    2430             :         /*
    2431             :          * Save a few cycles by setting up the fcinfo struct just once. Using
    2432             :          * FunctionCallInvoke directly also avoids failure if the eqproc
    2433             :          * returns NULL, though really equality functions should never do
    2434             :          * that.
    2435             :          */
    2436       10656 :         InitFunctionCallInfoData(*fcinfo, &eqproc, 2, collation,
    2437             :                                  NULL, NULL);
    2438       10656 :         fcinfo->args[0].isnull = false;
    2439       10656 :         fcinfo->args[1].isnull = false;
    2440             : 
    2441       10656 :         hasmatch1 = (bool *) palloc0(sslot1->nvalues * sizeof(bool));
    2442       10656 :         hasmatch2 = (bool *) palloc0(sslot2->nvalues * sizeof(bool));
    2443             : 
    2444             :         /*
    2445             :          * Note we assume that each MCV will match at most one member of the
    2446             :          * other MCV list.  If the operator isn't really equality, there could
    2447             :          * be multiple matches --- but we don't look for them, both for speed
    2448             :          * and because the math wouldn't add up...
    2449             :          */
    2450       10656 :         matchprodfreq = 0.0;
    2451       10656 :         nmatches = 0;
    2452      258576 :         for (i = 0; i < sslot1->nvalues; i++)
    2453             :         {
    2454             :             int         j;
    2455             : 
    2456      247920 :             fcinfo->args[0].value = sslot1->values[i];
    2457             : 
    2458     8714624 :             for (j = 0; j < sslot2->nvalues; j++)
    2459             :             {
    2460             :                 Datum       fresult;
    2461             : 
    2462     8529048 :                 if (hasmatch2[j])
    2463     1971344 :                     continue;
    2464     6557704 :                 fcinfo->args[1].value = sslot2->values[j];
    2465     6557704 :                 fcinfo->isnull = false;
    2466     6557704 :                 fresult = FunctionCallInvoke(fcinfo);
    2467     6557704 :                 if (!fcinfo->isnull && DatumGetBool(fresult))
    2468             :                 {
    2469       62344 :                     hasmatch1[i] = hasmatch2[j] = true;
    2470       62344 :                     matchprodfreq += sslot1->numbers[i] * sslot2->numbers[j];
    2471       62344 :                     nmatches++;
    2472       62344 :                     break;
    2473             :                 }
    2474             :             }
    2475             :         }
    2476       10656 :         CLAMP_PROBABILITY(matchprodfreq);
    2477             :         /* Sum up frequencies of matched and unmatched MCVs */
    2478       10656 :         matchfreq1 = unmatchfreq1 = 0.0;
    2479      258576 :         for (i = 0; i < sslot1->nvalues; i++)
    2480             :         {
    2481      247920 :             if (hasmatch1[i])
    2482       62344 :                 matchfreq1 += sslot1->numbers[i];
    2483             :             else
    2484      185576 :                 unmatchfreq1 += sslot1->numbers[i];
    2485             :         }
    2486       10656 :         CLAMP_PROBABILITY(matchfreq1);
    2487       10656 :         CLAMP_PROBABILITY(unmatchfreq1);
    2488       10656 :         matchfreq2 = unmatchfreq2 = 0.0;
    2489      424332 :         for (i = 0; i < sslot2->nvalues; i++)
    2490             :         {
    2491      413676 :             if (hasmatch2[i])
    2492       62344 :                 matchfreq2 += sslot2->numbers[i];
    2493             :             else
    2494      351332 :                 unmatchfreq2 += sslot2->numbers[i];
    2495             :         }
    2496       10656 :         CLAMP_PROBABILITY(matchfreq2);
    2497       10656 :         CLAMP_PROBABILITY(unmatchfreq2);
    2498       10656 :         pfree(hasmatch1);
    2499       10656 :         pfree(hasmatch2);
    2500             : 
    2501             :         /*
    2502             :          * Compute total frequency of non-null values that are not in the MCV
    2503             :          * lists.
    2504             :          */
    2505       10656 :         otherfreq1 = 1.0 - nullfrac1 - matchfreq1 - unmatchfreq1;
    2506       10656 :         otherfreq2 = 1.0 - nullfrac2 - matchfreq2 - unmatchfreq2;
    2507       10656 :         CLAMP_PROBABILITY(otherfreq1);
    2508       10656 :         CLAMP_PROBABILITY(otherfreq2);
    2509             : 
    2510             :         /*
    2511             :          * We can estimate the total selectivity from the point of view of
    2512             :          * relation 1 as: the known selectivity for matched MCVs, plus
    2513             :          * unmatched MCVs that are assumed to match against random members of
    2514             :          * relation 2's non-MCV population, plus non-MCV values that are
    2515             :          * assumed to match against random members of relation 2's unmatched
    2516             :          * MCVs plus non-MCV values.
    2517             :          */
    2518       10656 :         totalsel1 = matchprodfreq;
    2519       10656 :         if (nd2 > sslot2->nvalues)
    2520        7052 :             totalsel1 += unmatchfreq1 * otherfreq2 / (nd2 - sslot2->nvalues);
    2521       10656 :         if (nd2 > nmatches)
    2522       18128 :             totalsel1 += otherfreq1 * (otherfreq2 + unmatchfreq2) /
    2523        9064 :                 (nd2 - nmatches);
    2524             :         /* Same estimate from the point of view of relation 2. */
    2525       10656 :         totalsel2 = matchprodfreq;
    2526       10656 :         if (nd1 > sslot1->nvalues)
    2527        6836 :             totalsel2 += unmatchfreq2 * otherfreq1 / (nd1 - sslot1->nvalues);
    2528       10656 :         if (nd1 > nmatches)
    2529       16808 :             totalsel2 += otherfreq2 * (otherfreq1 + unmatchfreq1) /
    2530        8404 :                 (nd1 - nmatches);
    2531             : 
    2532             :         /*
    2533             :          * Use the smaller of the two estimates.  This can be justified in
    2534             :          * essentially the same terms as given below for the no-stats case: to
    2535             :          * a first approximation, we are estimating from the point of view of
    2536             :          * the relation with smaller nd.
    2537             :          */
    2538       10656 :         selec = (totalsel1 < totalsel2) ? totalsel1 : totalsel2;
    2539             :     }
    2540             :     else
    2541             :     {
    2542             :         /*
    2543             :          * We do not have MCV lists for both sides.  Estimate the join
    2544             :          * selectivity as MIN(1/nd1,1/nd2)*(1-nullfrac1)*(1-nullfrac2). This
    2545             :          * is plausible if we assume that the join operator is strict and the
    2546             :          * non-null values are about equally distributed: a given non-null
    2547             :          * tuple of rel1 will join to either zero or N2*(1-nullfrac2)/nd2 rows
    2548             :          * of rel2, so total join rows are at most
    2549             :          * N1*(1-nullfrac1)*N2*(1-nullfrac2)/nd2 giving a join selectivity of
    2550             :          * not more than (1-nullfrac1)*(1-nullfrac2)/nd2. By the same logic it
    2551             :          * is not more than (1-nullfrac1)*(1-nullfrac2)/nd1, so the expression
    2552             :          * with MIN() is an upper bound.  Using the MIN() means we estimate
    2553             :          * from the point of view of the relation with smaller nd (since the
    2554             :          * larger nd is determining the MIN).  It is reasonable to assume that
    2555             :          * most tuples in this rel will have join partners, so the bound is
    2556             :          * probably reasonably tight and should be taken as-is.
    2557             :          *
    2558             :          * XXX Can we be smarter if we have an MCV list for just one side? It
    2559             :          * seems that if we assume equal distribution for the other side, we
    2560             :          * end up with the same answer anyway.
    2561             :          */
    2562      114540 :         double      nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
    2563      114540 :         double      nullfrac2 = stats2 ? stats2->stanullfrac : 0.0;
    2564             : 
    2565      114540 :         selec = (1.0 - nullfrac1) * (1.0 - nullfrac2);
    2566      114540 :         if (nd1 > nd2)
    2567       41094 :             selec /= nd1;
    2568             :         else
    2569       73446 :             selec /= nd2;
    2570             :     }
    2571             : 
    2572      125196 :     return selec;
    2573             : }
    2574             : 
    2575             : /*
    2576             :  * eqjoinsel_semi --- eqjoinsel for semi join
    2577             :  *
    2578             :  * (Also used for anti join, which we are supposed to estimate the same way.)
    2579             :  * Caller has ensured that vardata1 is the LHS variable.
    2580             :  * Unlike eqjoinsel_inner, we have to cope with opfuncoid being InvalidOid.
    2581             :  */
    2582             : static double
    2583       10766 : eqjoinsel_semi(Oid opfuncoid, Oid collation,
    2584             :                VariableStatData *vardata1, VariableStatData *vardata2,
    2585             :                double nd1, double nd2,
    2586             :                bool isdefault1, bool isdefault2,
    2587             :                AttStatsSlot *sslot1, AttStatsSlot *sslot2,
    2588             :                Form_pg_statistic stats1, Form_pg_statistic stats2,
    2589             :                bool have_mcvs1, bool have_mcvs2,
    2590             :                RelOptInfo *inner_rel)
    2591             : {
    2592             :     double      selec;
    2593             : 
    2594             :     /*
    2595             :      * We clamp nd2 to be not more than what we estimate the inner relation's
    2596             :      * size to be.  This is intuitively somewhat reasonable since obviously
    2597             :      * there can't be more than that many distinct values coming from the
    2598             :      * inner rel.  The reason for the asymmetry (ie, that we don't clamp nd1
    2599             :      * likewise) is that this is the only pathway by which restriction clauses
    2600             :      * applied to the inner rel will affect the join result size estimate,
    2601             :      * since set_joinrel_size_estimates will multiply SEMI/ANTI selectivity by
    2602             :      * only the outer rel's size.  If we clamped nd1 we'd be double-counting
    2603             :      * the selectivity of outer-rel restrictions.
    2604             :      *
    2605             :      * We can apply this clamping both with respect to the base relation from
    2606             :      * which the join variable comes (if there is just one), and to the
    2607             :      * immediate inner input relation of the current join.
    2608             :      *
    2609             :      * If we clamp, we can treat nd2 as being a non-default estimate; it's not
    2610             :      * great, maybe, but it didn't come out of nowhere either.  This is most
    2611             :      * helpful when the inner relation is empty and consequently has no stats.
    2612             :      */
    2613       10766 :     if (vardata2->rel)
    2614             :     {
    2615       10766 :         if (nd2 >= vardata2->rel->rows)
    2616             :         {
    2617        9890 :             nd2 = vardata2->rel->rows;
    2618        9890 :             isdefault2 = false;
    2619             :         }
    2620             :     }
    2621       10766 :     if (nd2 >= inner_rel->rows)
    2622             :     {
    2623        9862 :         nd2 = inner_rel->rows;
    2624        9862 :         isdefault2 = false;
    2625             :     }
    2626             : 
    2627       10766 :     if (have_mcvs1 && have_mcvs2 && OidIsValid(opfuncoid))
    2628         304 :     {
    2629             :         /*
    2630             :          * We have most-common-value lists for both relations.  Run through
    2631             :          * the lists to see which MCVs actually join to each other with the
    2632             :          * given operator.  This allows us to determine the exact join
    2633             :          * selectivity for the portion of the relations represented by the MCV
    2634             :          * lists.  We still have to estimate for the remaining population, but
    2635             :          * in a skewed distribution this gives us a big leg up in accuracy.
    2636             :          */
    2637         304 :         LOCAL_FCINFO(fcinfo, 2);
    2638             :         FmgrInfo    eqproc;
    2639             :         bool       *hasmatch1;
    2640             :         bool       *hasmatch2;
    2641         304 :         double      nullfrac1 = stats1->stanullfrac;
    2642             :         double      matchfreq1,
    2643             :                     uncertainfrac,
    2644             :                     uncertain;
    2645             :         int         i,
    2646             :                     nmatches,
    2647             :                     clamped_nvalues2;
    2648             : 
    2649             :         /*
    2650             :          * The clamping above could have resulted in nd2 being less than
    2651             :          * sslot2->nvalues; in which case, we assume that precisely the nd2
    2652             :          * most common values in the relation will appear in the join input,
    2653             :          * and so compare to only the first nd2 members of the MCV list.  Of
    2654             :          * course this is frequently wrong, but it's the best bet we can make.
    2655             :          */
    2656         304 :         clamped_nvalues2 = Min(sslot2->nvalues, nd2);
    2657             : 
    2658         304 :         fmgr_info(opfuncoid, &eqproc);
    2659             : 
    2660             :         /*
    2661             :          * Save a few cycles by setting up the fcinfo struct just once. Using
    2662             :          * FunctionCallInvoke directly also avoids failure if the eqproc
    2663             :          * returns NULL, though really equality functions should never do
    2664             :          * that.
    2665             :          */
    2666         304 :         InitFunctionCallInfoData(*fcinfo, &eqproc, 2, collation,
    2667             :                                  NULL, NULL);
    2668         304 :         fcinfo->args[0].isnull = false;
    2669         304 :         fcinfo->args[1].isnull = false;
    2670             : 
    2671         304 :         hasmatch1 = (bool *) palloc0(sslot1->nvalues * sizeof(bool));
    2672         304 :         hasmatch2 = (bool *) palloc0(clamped_nvalues2 * sizeof(bool));
    2673             : 
    2674             :         /*
    2675             :          * Note we assume that each MCV will match at most one member of the
    2676             :          * other MCV list.  If the operator isn't really equality, there could
    2677             :          * be multiple matches --- but we don't look for them, both for speed
    2678             :          * and because the math wouldn't add up...
    2679             :          */
    2680         304 :         nmatches = 0;
    2681        4916 :         for (i = 0; i < sslot1->nvalues; i++)
    2682             :         {
    2683             :             int         j;
    2684             : 
    2685        4612 :             fcinfo->args[0].value = sslot1->values[i];
    2686             : 
    2687      136888 :             for (j = 0; j < clamped_nvalues2; j++)
    2688             :             {
    2689             :                 Datum       fresult;
    2690             : 
    2691      136288 :                 if (hasmatch2[j])
    2692      123564 :                     continue;
    2693       12724 :                 fcinfo->args[1].value = sslot2->values[j];
    2694       12724 :                 fcinfo->isnull = false;
    2695       12724 :                 fresult = FunctionCallInvoke(fcinfo);
    2696       12724 :                 if (!fcinfo->isnull && DatumGetBool(fresult))
    2697             :                 {
    2698        4012 :                     hasmatch1[i] = hasmatch2[j] = true;
    2699        4012 :                     nmatches++;
    2700        4012 :                     break;
    2701             :                 }
    2702             :             }
    2703             :         }
    2704             :         /* Sum up frequencies of matched MCVs */
    2705         304 :         matchfreq1 = 0.0;
    2706        4916 :         for (i = 0; i < sslot1->nvalues; i++)
    2707             :         {
    2708        4612 :             if (hasmatch1[i])
    2709        4012 :                 matchfreq1 += sslot1->numbers[i];
    2710             :         }
    2711         304 :         CLAMP_PROBABILITY(matchfreq1);
    2712         304 :         pfree(hasmatch1);
    2713         304 :         pfree(hasmatch2);
    2714             : 
    2715             :         /*
    2716             :          * Now we need to estimate the fraction of relation 1 that has at
    2717             :          * least one join partner.  We know for certain that the matched MCVs
    2718             :          * do, so that gives us a lower bound, but we're really in the dark
    2719             :          * about everything else.  Our crude approach is: if nd1 <= nd2 then
    2720             :          * assume all non-null rel1 rows have join partners, else assume for
    2721             :          * the uncertain rows that a fraction nd2/nd1 have join partners. We
    2722             :          * can discount the known-matched MCVs from the distinct-values counts
    2723             :          * before doing the division.
    2724             :          *
    2725             :          * Crude as the above is, it's completely useless if we don't have
    2726             :          * reliable ndistinct values for both sides.  Hence, if either nd1 or
    2727             :          * nd2 is default, punt and assume half of the uncertain rows have
    2728             :          * join partners.
    2729             :          */
    2730         304 :         if (!isdefault1 && !isdefault2)
    2731             :         {
    2732         304 :             nd1 -= nmatches;
    2733         304 :             nd2 -= nmatches;
    2734         608 :             if (nd1 <= nd2 || nd2 < 0)
    2735         288 :                 uncertainfrac = 1.0;
    2736             :             else
    2737          16 :                 uncertainfrac = nd2 / nd1;
    2738             :         }
    2739             :         else
    2740           0 :             uncertainfrac = 0.5;
    2741         304 :         uncertain = 1.0 - matchfreq1 - nullfrac1;
    2742         304 :         CLAMP_PROBABILITY(uncertain);
    2743         304 :         selec = matchfreq1 + uncertainfrac * uncertain;
    2744             :     }
    2745             :     else
    2746             :     {
    2747             :         /*
    2748             :          * Without MCV lists for both sides, we can only use the heuristic
    2749             :          * about nd1 vs nd2.
    2750             :          */
    2751       10462 :         double      nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
    2752             : 
    2753       10462 :         if (!isdefault1 && !isdefault2)
    2754             :         {
    2755       18692 :             if (nd1 <= nd2 || nd2 < 0)
    2756        7556 :                 selec = 1.0 - nullfrac1;
    2757             :             else
    2758        1790 :                 selec = (nd2 / nd1) * (1.0 - nullfrac1);
    2759             :         }
    2760             :         else
    2761        1116 :             selec = 0.5 * (1.0 - nullfrac1);
    2762             :     }
    2763             : 
    2764       10766 :     return selec;
    2765             : }
    2766             : 
    2767             : /*
    2768             :  *      neqjoinsel      - Join selectivity of "!="
    2769             :  */
    2770             : Datum
    2771        1654 : neqjoinsel(PG_FUNCTION_ARGS)
    2772             : {
    2773        1654 :     PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    2774        1654 :     Oid         operator = PG_GETARG_OID(1);
    2775        1654 :     List       *args = (List *) PG_GETARG_POINTER(2);
    2776        1654 :     JoinType    jointype = (JoinType) PG_GETARG_INT16(3);
    2777        1654 :     SpecialJoinInfo *sjinfo = (SpecialJoinInfo *) PG_GETARG_POINTER(4);
    2778        1654 :     Oid         collation = PG_GET_COLLATION();
    2779             :     float8      result;
    2780             : 
    2781        1654 :     if (jointype == JOIN_SEMI || jointype == JOIN_ANTI)
    2782         602 :     {
    2783             :         /*
    2784             :          * For semi-joins, if there is more than one distinct value in the RHS
    2785             :          * relation then every non-null LHS row must find a row to join since
    2786             :          * it can only be equal to one of them.  We'll assume that there is
    2787             :          * always more than one distinct RHS value for the sake of stability,
    2788             :          * though in theory we could have special cases for empty RHS
    2789             :          * (selectivity = 0) and single-distinct-value RHS (selectivity =
    2790             :          * fraction of LHS that has the same value as the single RHS value).
    2791             :          *
    2792             :          * For anti-joins, if we use the same assumption that there is more
    2793             :          * than one distinct key in the RHS relation, then every non-null LHS
    2794             :          * row must be suppressed by the anti-join.
    2795             :          *
    2796             :          * So either way, the selectivity estimate should be 1 - nullfrac.
    2797             :          */
    2798             :         VariableStatData leftvar;
    2799             :         VariableStatData rightvar;
    2800             :         bool        reversed;
    2801             :         HeapTuple   statsTuple;
    2802             :         double      nullfrac;
    2803             : 
    2804         602 :         get_join_variables(root, args, sjinfo, &leftvar, &rightvar, &reversed);
    2805         602 :         statsTuple = reversed ? rightvar.statsTuple : leftvar.statsTuple;
    2806         602 :         if (HeapTupleIsValid(statsTuple))
    2807         508 :             nullfrac = ((Form_pg_statistic) GETSTRUCT(statsTuple))->stanullfrac;
    2808             :         else
    2809          94 :             nullfrac = 0.0;
    2810         602 :         ReleaseVariableStats(leftvar);
    2811         602 :         ReleaseVariableStats(rightvar);
    2812             : 
    2813         602 :         result = 1.0 - nullfrac;
    2814             :     }
    2815             :     else
    2816             :     {
    2817             :         /*
    2818             :          * We want 1 - eqjoinsel() where the equality operator is the one
    2819             :          * associated with this != operator, that is, its negator.
    2820             :          */
    2821        1052 :         Oid         eqop = get_negator(operator);
    2822             : 
    2823        1052 :         if (eqop)
    2824             :         {
    2825             :             result =
    2826        1052 :                 DatumGetFloat8(DirectFunctionCall5Coll(eqjoinsel,
    2827             :                                                        collation,
    2828             :                                                        PointerGetDatum(root),
    2829             :                                                        ObjectIdGetDatum(eqop),
    2830             :                                                        PointerGetDatum(args),
    2831             :                                                        Int16GetDatum(jointype),
    2832             :                                                        PointerGetDatum(sjinfo)));
    2833             :         }
    2834             :         else
    2835             :         {
    2836             :             /* Use default selectivity (should we raise an error instead?) */
    2837           0 :             result = DEFAULT_EQ_SEL;
    2838             :         }
    2839        1052 :         result = 1.0 - result;
    2840             :     }
    2841             : 
    2842        1654 :     PG_RETURN_FLOAT8(result);
    2843             : }
    2844             : 
    2845             : /*
    2846             :  *      scalarltjoinsel - Join selectivity of "<" for scalars
    2847             :  */
    2848             : Datum
    2849         200 : scalarltjoinsel(PG_FUNCTION_ARGS)
    2850             : {
    2851         200 :     PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    2852             : }
    2853             : 
    2854             : /*
    2855             :  *      scalarlejoinsel - Join selectivity of "<=" for scalars
    2856             :  */
    2857             : Datum
    2858         130 : scalarlejoinsel(PG_FUNCTION_ARGS)
    2859             : {
    2860         130 :     PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    2861             : }
    2862             : 
    2863             : /*
    2864             :  *      scalargtjoinsel - Join selectivity of ">" for scalars
    2865             :  */
    2866             : Datum
    2867         140 : scalargtjoinsel(PG_FUNCTION_ARGS)
    2868             : {
    2869         140 :     PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    2870             : }
    2871             : 
    2872             : /*
    2873             :  *      scalargejoinsel - Join selectivity of ">=" for scalars
    2874             :  */
    2875             : Datum
    2876         108 : scalargejoinsel(PG_FUNCTION_ARGS)
    2877             : {
    2878         108 :     PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
    2879             : }
    2880             : 
    2881             : 
    2882             : /*
    2883             :  * mergejoinscansel         - Scan selectivity of merge join.
    2884             :  *
    2885             :  * A merge join will stop as soon as it exhausts either input stream.
    2886             :  * Therefore, if we can estimate the ranges of both input variables,
    2887             :  * we can estimate how much of the input will actually be read.  This
    2888             :  * can have a considerable impact on the cost when using indexscans.
    2889             :  *
    2890             :  * Also, we can estimate how much of each input has to be read before the
    2891             :  * first join pair is found, which will affect the join's startup time.
    2892             :  *
    2893             :  * clause should be a clause already known to be mergejoinable.  opfamily,
    2894             :  * strategy, and nulls_first specify the sort ordering being used.
    2895             :  *
    2896             :  * The outputs are:
    2897             :  *      *leftstart is set to the fraction of the left-hand variable expected
    2898             :  *       to be scanned before the first join pair is found (0 to 1).
    2899             :  *      *leftend is set to the fraction of the left-hand variable expected
    2900             :  *       to be scanned before the join terminates (0 to 1).
    2901             :  *      *rightstart, *rightend similarly for the right-hand variable.
    2902             :  */
    2903             : void
    2904       58908 : mergejoinscansel(PlannerInfo *root, Node *clause,
    2905             :                  Oid opfamily, int strategy, bool nulls_first,
    2906             :                  Selectivity *leftstart, Selectivity *leftend,
    2907             :                  Selectivity *rightstart, Selectivity *rightend)
    2908             : {
    2909             :     Node       *left,
    2910             :                *right;
    2911             :     VariableStatData leftvar,
    2912             :                 rightvar;
    2913             :     int         op_strategy;
    2914             :     Oid         op_lefttype;
    2915             :     Oid         op_righttype;
    2916             :     Oid         opno,
    2917             :                 collation,
    2918             :                 lsortop,
    2919             :                 rsortop,
    2920             :                 lstatop,
    2921             :                 rstatop,
    2922             :                 ltop,
    2923             :                 leop,
    2924             :                 revltop,
    2925             :                 revleop;
    2926             :     bool        isgt;
    2927             :     Datum       leftmin,
    2928             :                 leftmax,
    2929             :                 rightmin,
    2930             :                 rightmax;
    2931             :     double      selec;
    2932             : 
    2933             :     /* Set default results if we can't figure anything out. */
    2934             :     /* XXX should default "start" fraction be a bit more than 0? */
    2935       58908 :     *leftstart = *rightstart = 0.0;
    2936       58908 :     *leftend = *rightend = 1.0;
    2937             : 
    2938             :     /* Deconstruct the merge clause */
    2939       58908 :     if (!is_opclause(clause))
    2940           0 :         return;                 /* shouldn't happen */
    2941       58908 :     opno = ((OpExpr *) clause)->opno;
    2942       58908 :     collation = ((OpExpr *) clause)->inputcollid;
    2943       58908 :     left = get_leftop((Expr *) clause);
    2944       58908 :     right = get_rightop((Expr *) clause);
    2945       58908 :     if (!right)
    2946           0 :         return;                 /* shouldn't happen */
    2947             : 
    2948             :     /* Look for stats for the inputs */
    2949       58908 :     examine_variable(root, left, 0, &leftvar);
    2950       58908 :     examine_variable(root, right, 0, &rightvar);
    2951             : 
    2952             :     /* Extract the operator's declared left/right datatypes */
    2953       58908 :     get_op_opfamily_properties(opno, opfamily, false,
    2954             :                                &op_strategy,
    2955             :                                &op_lefttype,
    2956             :                                &op_righttype);
    2957             :     Assert(op_strategy == BTEqualStrategyNumber);
    2958             : 
    2959             :     /*
    2960             :      * Look up the various operators we need.  If we don't find them all, it
    2961             :      * probably means the opfamily is broken, but we just fail silently.
    2962             :      *
    2963             :      * Note: we expect that pg_statistic histograms will be sorted by the '<'
    2964             :      * operator, regardless of which sort direction we are considering.
    2965             :      */
    2966       58908 :     switch (strategy)
    2967             :     {
    2968       58888 :         case BTLessStrategyNumber:
    2969       58888 :             isgt = false;
    2970       58888 :             if (op_lefttype == op_righttype)
    2971             :             {
    2972             :                 /* easy case */
    2973       57680 :                 ltop = get_opfamily_member(opfamily,
    2974             :                                            op_lefttype, op_righttype,
    2975             :                                            BTLessStrategyNumber);
    2976       57680 :                 leop = get_opfamily_member(opfamily,
    2977             :                                            op_lefttype, op_righttype,
    2978             :                                            BTLessEqualStrategyNumber);
    2979       57680 :                 lsortop = ltop;
    2980       57680 :                 rsortop = ltop;
    2981       57680 :                 lstatop = lsortop;
    2982       57680 :                 rstatop = rsortop;
    2983       57680 :                 revltop = ltop;
    2984       57680 :                 revleop = leop;
    2985             :             }
    2986             :             else
    2987             :             {
    2988        1208 :                 ltop = get_opfamily_member(opfamily,
    2989             :                                            op_lefttype, op_righttype,
    2990             :                                            BTLessStrategyNumber);
    2991        1208 :                 leop = get_opfamily_member(opfamily,
    2992             :                                            op_lefttype, op_righttype,
    2993             :                                            BTLessEqualStrategyNumber);
    2994        1208 :                 lsortop = get_opfamily_member(opfamily,
    2995             :                                               op_lefttype, op_lefttype,
    2996             :                                               BTLessStrategyNumber);
    2997        1208 :                 rsortop = get_opfamily_member(opfamily,
    2998             :                                               op_righttype, op_righttype,
    2999             :                                               BTLessStrategyNumber);
    3000        1208 :                 lstatop = lsortop;
    3001        1208 :                 rstatop = rsortop;
    3002        1208 :                 revltop = get_opfamily_member(opfamily,
    3003             :                                               op_righttype, op_lefttype,
    3004             :                                               BTLessStrategyNumber);
    3005        1208 :                 revleop = get_opfamily_member(opfamily,
    3006             :                                               op_righttype, op_lefttype,
    3007             :                                               BTLessEqualStrategyNumber);
    3008             :             }
    3009       58888 :             break;
    3010          20 :         case BTGreaterStrategyNumber:
    3011             :             /* descending-order case */
    3012          20 :             isgt = true;
    3013          20 :             if (op_lefttype == op_righttype)
    3014             :             {
    3015             :                 /* easy case */
    3016          20 :                 ltop = get_opfamily_member(opfamily,
    3017             :                                            op_lefttype, op_righttype,
    3018             :                                            BTGreaterStrategyNumber);
    3019          20 :                 leop = get_opfamily_member(opfamily,
    3020             :                                            op_lefttype, op_righttype,
    3021             :                                            BTGreaterEqualStrategyNumber);
    3022          20 :                 lsortop = ltop;
    3023          20 :                 rsortop = ltop;
    3024          20 :                 lstatop = get_opfamily_member(opfamily,
    3025             :                                               op_lefttype, op_lefttype,
    3026             :                                               BTLessStrategyNumber);
    3027          20 :                 rstatop = lstatop;
    3028          20 :                 revltop = ltop;
    3029          20 :                 revleop = leop;
    3030             :             }
    3031             :             else
    3032             :             {
    3033           0 :                 ltop = get_opfamily_member(opfamily,
    3034             :                                            op_lefttype, op_righttype,
    3035             :                                            BTGreaterStrategyNumber);
    3036           0 :                 leop = get_opfamily_member(opfamily,
    3037             :                                            op_lefttype, op_righttype,
    3038             :                                            BTGreaterEqualStrategyNumber);
    3039           0 :                 lsortop = get_opfamily_member(opfamily,
    3040             :                                               op_lefttype, op_lefttype,
    3041             :                                               BTGreaterStrategyNumber);
    3042           0 :                 rsortop = get_opfamily_member(opfamily,
    3043             :                                               op_righttype, op_righttype,
    3044             :                                               BTGreaterStrategyNumber);
    3045           0 :                 lstatop = get_opfamily_member(opfamily,
    3046             :                                               op_lefttype, op_lefttype,
    3047             :                                               BTLessStrategyNumber);
    3048           0 :                 rstatop = get_opfamily_member(opfamily,
    3049             :                                               op_righttype, op_righttype,
    3050             :                                               BTLessStrategyNumber);
    3051           0 :                 revltop = get_opfamily_member(opfamily,
    3052             :                                               op_righttype, op_lefttype,
    3053             :                                               BTGreaterStrategyNumber);
    3054           0 :                 revleop = get_opfamily_member(opfamily,
    3055             :                                               op_righttype, op_lefttype,
    3056             :                                               BTGreaterEqualStrategyNumber);
    3057             :             }
    3058          20 :             break;
    3059           0 :         default:
    3060           0 :             goto fail;          /* shouldn't get here */
    3061             :     }
    3062             : 
    3063       58908 :     if (!OidIsValid(lsortop) ||
    3064       58908 :         !OidIsValid(rsortop) ||
    3065       58908 :         !OidIsValid(lstatop) ||
    3066       58908 :         !OidIsValid(rstatop) ||
    3067       58900 :         !OidIsValid(ltop) ||
    3068       58900 :         !OidIsValid(leop) ||
    3069       58900 :         !OidIsValid(revltop) ||
    3070             :         !OidIsValid(revleop))
    3071           8 :         goto fail;              /* insufficient info in catalogs */
    3072             : 
    3073             :     /* Try to get ranges of both inputs */
    3074       58900 :     if (!isgt)
    3075             :     {
    3076       58880 :         if (!get_variable_range(root, &leftvar, lstatop, collation,
    3077             :                                 &leftmin, &leftmax))
    3078       13504 :             goto fail;          /* no range available from stats */
    3079       45376 :         if (!get_variable_range(root, &rightvar, rstatop, collation,
    3080             :                                 &rightmin, &rightmax))
    3081        3868 :             goto fail;          /* no range available from stats */
    3082             :     }
    3083             :     else
    3084             :     {
    3085             :         /* need to swap the max and min */
    3086          20 :         if (!get_variable_range(root, &leftvar, lstatop, collation,
    3087             :                                 &leftmax, &leftmin))
    3088          20 :             goto fail;          /* no range available from stats */
    3089           0 :         if (!get_variable_range(root, &rightvar, rstatop, collation,
    3090             :                                 &rightmax, &rightmin))
    3091           0 :             goto fail;          /* no range available from stats */
    3092             :     }
    3093             : 
    3094             :     /*
    3095             :      * Now, the fraction of the left variable that will be scanned is the
    3096             :      * fraction that's <= the right-side maximum value.  But only believe
    3097             :      * non-default estimates, else stick with our 1.0.
    3098             :      */
    3099       41508 :     selec = scalarineqsel(root, leop, isgt, true, collation, &leftvar,
    3100             :                           rightmax, op_righttype);
    3101       41508 :     if (selec != DEFAULT_INEQ_SEL)
    3102       41504 :         *leftend = selec;
    3103             : 
    3104             :     /* And similarly for the right variable. */
    3105       41508 :     selec = scalarineqsel(root, revleop, isgt, true, collation, &rightvar,
    3106             :                           leftmax, op_lefttype);
    3107       41508 :     if (selec != DEFAULT_INEQ_SEL)
    3108       41508 :         *rightend = selec;
    3109             : 
    3110             :     /*
    3111             :      * Only one of the two "end" fractions can really be less than 1.0;
    3112             :      * believe the smaller estimate and reset the other one to exactly 1.0. If
    3113             :      * we get exactly equal estimates (as can easily happen with self-joins),
    3114             :      * believe neither.
    3115             :      */
    3116       41508 :     if (*leftend > *rightend)
    3117       23356 :         *leftend = 1.0;
    3118       18152 :     else if (*leftend < *rightend)
    3119       14386 :         *rightend = 1.0;
    3120             :     else
    3121        3766 :         *leftend = *rightend = 1.0;
    3122             : 
    3123             :     /*
    3124             :      * Also, the fraction of the left variable that will be scanned before the
    3125             :      * first join pair is found is the fraction that's < the right-side
    3126             :      * minimum value.  But only believe non-default estimates, else stick with
    3127             :      * our own default.
    3128             :      */
    3129       41508 :     selec = scalarineqsel(root, ltop, isgt, false, collation, &leftvar,
    3130             :                           rightmin, op_righttype);
    3131       41508 :     if (selec != DEFAULT_INEQ_SEL)
    3132       41508 :         *leftstart = selec;
    3133             : 
    3134             :     /* And similarly for the right variable. */
    3135       41508 :     selec = scalarineqsel(root, revltop, isgt, false, collation, &rightvar,
    3136             :                           leftmin, op_lefttype);
    3137       41508 :     if (selec != DEFAULT_INEQ_SEL)
    3138       41508 :         *rightstart = selec;
    3139             : 
    3140             :     /*
    3141             :      * Only one of the two "start" fractions can really be more than zero;
    3142             :      * believe the larger estimate and reset the other one to exactly 0.0. If
    3143             :      * we get exactly equal estimates (as can easily happen with self-joins),
    3144             :      * believe neither.
    3145             :      */
    3146       41508 :     if (*leftstart < *rightstart)
    3147       10952 :         *leftstart = 0.0;
    3148       30556 :     else if (*leftstart > *rightstart)
    3149       20772 :         *rightstart = 0.0;
    3150             :     else
    3151        9784 :         *leftstart = *rightstart = 0.0;
    3152             : 
    3153             :     /*
    3154             :      * If the sort order is nulls-first, we're going to have to skip over any
    3155             :      * nulls too.  These would not have been counted by scalarineqsel, and we
    3156             :      * can safely add in this fraction regardless of whether we believe
    3157             :      * scalarineqsel's results or not.  But be sure to clamp the sum to 1.0!
    3158             :      */
    3159       41508 :     if (nulls_first)
    3160             :     {
    3161             :         Form_pg_statistic stats;
    3162             : 
    3163           0 :         if (HeapTupleIsValid(leftvar.statsTuple))
    3164             :         {
    3165           0 :             stats = (Form_pg_statistic) GETSTRUCT(leftvar.statsTuple);
    3166           0 :             *leftstart += stats->stanullfrac;
    3167           0 :             CLAMP_PROBABILITY(*leftstart);
    3168           0 :             *leftend += stats->stanullfrac;
    3169           0 :             CLAMP_PROBABILITY(*leftend);
    3170             :         }
    3171           0 :         if (HeapTupleIsValid(rightvar.statsTuple))
    3172             :         {
    3173           0 :             stats = (Form_pg_statistic) GETSTRUCT(rightvar.statsTuple);
    3174           0 :             *rightstart += stats->stanullfrac;
    3175           0 :             CLAMP_PROBABILITY(*rightstart);
    3176           0 :             *rightend += stats->stanullfrac;
    3177           0 :             CLAMP_PROBABILITY(*rightend);
    3178             :         }
    3179             :     }
    3180             : 
    3181             :     /* Disbelieve start >= end, just in case that can happen */
    3182       41508 :     if (*leftstart >= *leftend)
    3183             :     {
    3184        1466 :         *leftstart = 0.0;
    3185        1466 :         *leftend = 1.0;
    3186             :     }
    3187       41508 :     if (*rightstart >= *rightend)
    3188             :     {
    3189        1666 :         *rightstart = 0.0;
    3190        1666 :         *rightend = 1.0;
    3191             :     }
    3192             : 
    3193       39842 : fail:
    3194       58908 :     ReleaseVariableStats(leftvar);
    3195       58908 :     ReleaseVariableStats(rightvar);
    3196             : }
    3197             : 
    3198             : 
    3199             : /*
    3200             :  *  matchingsel -- generic matching-operator selectivity support
    3201             :  *
    3202             :  * Use these for any operators that (a) are on data types for which we collect
    3203             :  * standard statistics, and (b) have behavior for which the default estimate
    3204             :  * (twice DEFAULT_EQ_SEL) is sane.  Typically that is good for match-like
    3205             :  * operators.
    3206             :  */
    3207             : 
    3208             : Datum
    3209         810 : matchingsel(PG_FUNCTION_ARGS)
    3210             : {
    3211         810 :     PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
    3212         810 :     Oid         operator = PG_GETARG_OID(1);
    3213         810 :     List       *args = (List *) PG_GETARG_POINTER(2);
    3214         810 :     int         varRelid = PG_GETARG_INT32(3);
    3215         810 :     Oid         collation = PG_GET_COLLATION();
    3216             :     double      selec;
    3217             : 
    3218             :     /* Use generic restriction selectivity logic. */
    3219         810 :     selec = generic_restriction_selectivity(root, operator, collation,
    3220             :                                             args, varRelid,
    3221             :                                             DEFAULT_MATCHING_SEL);
    3222             : 
    3223         810 :     PG_RETURN_FLOAT8((float8) selec);
    3224             : }
    3225             : 
    3226             : Datum
    3227           4 : matchingjoinsel(PG_FUNCTION_ARGS)
    3228             : {
    3229             :     /* Just punt, for the moment. */
    3230           4 :     PG_RETURN_FLOAT8(DEFAULT_MATCHING_SEL);
    3231             : }
    3232             : 
    3233             : 
    3234             : /*
    3235             :  * Helper routine for estimate_num_groups: add an item to a list of
    3236             :  * GroupVarInfos, but only if it's not known equal to any of the existing
    3237             :  * entries.
    3238             :  */
    3239             : typedef struct
    3240             : {
    3241             :     Node       *var;            /* might be an expression, not just a Var */
    3242             :     RelOptInfo *rel;            /* relation it belongs to */
    3243             :     double      ndistinct;      /* # distinct values */
    3244             : } GroupVarInfo;
    3245             : 
    3246             : static List *
    3247       12188 : add_unique_group_var(PlannerInfo *root, List *varinfos,
    3248             :                      Node *var, VariableStatData *vardata)
    3249             : {
    3250             :     GroupVarInfo *varinfo;
    3251             :     double      ndistinct;
    3252             :     bool        isdefault;
    3253             :     ListCell   *lc;
    3254             : 
    3255       12188 :     ndistinct = get_variable_numdistinct(vardata, &isdefault);
    3256             : 
    3257       17674 :     foreach(lc, varinfos)
    3258             :     {
    3259        5682 :         varinfo = (GroupVarInfo *) lfirst(lc);
    3260             : 
    3261             :         /* Drop exact duplicates */
    3262        5682 :         if (equal(var, varinfo->var))
    3263         196 :             return varinfos;
    3264             : 
    3265             :         /*
    3266             :          * Drop known-equal vars, but only if they belong to different
    3267             :          * relations (see comments for estimate_num_groups)
    3268             :          */
    3269        6104 :         if (vardata->rel != varinfo->rel &&
    3270         566 :             exprs_known_equal(root, var, varinfo->var))
    3271             :         {
    3272          56 :             if (varinfo->ndistinct <= ndistinct)
    3273             :             {
    3274             :                 /* Keep older item, forget new one */
    3275          52 :                 return varinfos;
    3276             :             }
    3277             :             else
    3278             :             {
    3279             :                 /* Delete the older item */
    3280           4 :                 varinfos = foreach_delete_current(varinfos, lc);
    3281             :             }
    3282             :         }
    3283             :     }
    3284             : 
    3285       11992 :     varinfo = (GroupVarInfo *) palloc(sizeof(GroupVarInfo));
    3286             : 
    3287       11992 :     varinfo->var = var;
    3288       11992 :     varinfo->rel = vardata->rel;
    3289       11992 :     varinfo->ndistinct = ndistinct;
    3290       11992 :     varinfos = lappend(varinfos, varinfo);
    3291       11992 :     return varinfos;
    3292             : }
    3293             : 
    3294             : /*
    3295             :  * estimate_num_groups      - Estimate number of groups in a grouped query
    3296             :  *
    3297             :  * Given a query having a GROUP BY clause, estimate how many groups there
    3298             :  * will be --- ie, the number of distinct combinations of the GROUP BY
    3299             :  * expressions.
    3300             :  *
    3301             :  * This routine is also used to estimate the number of rows emitted by
    3302             :  * a DISTINCT filtering step; that is an isomorphic problem.  (Note:
    3303             :  * actually, we only use it for DISTINCT when there's no grouping or
    3304             :  * aggregation ahead of the DISTINCT.)
    3305             :  *
    3306             :  * Inputs:
    3307             :  *  root - the query
    3308             :  *  groupExprs - list of expressions being grouped by
    3309             :  *  input_rows - number of rows estimated to arrive at the group/unique
    3310             :  *      filter step
    3311             :  *  pgset - NULL, or a List** pointing to a grouping set to filter the
    3312             :  *      groupExprs against
    3313             :  *
    3314             :  * Given the lack of any cross-correlation statistics in the system, it's
    3315             :  * impossible to do anything really trustworthy with GROUP BY conditions
    3316             :  * involving multiple Vars.  We should however avoid assuming the worst
    3317             :  * case (all possible cross-product terms actually appear as groups) since
    3318             :  * very often the grouped-by Vars are highly correlated.  Our current approach
    3319             :  * is as follows:
    3320             :  *  1.  Expressions yielding boolean are assumed to contribute two groups,
    3321             :  *      independently of their content, and are ignored in the subsequent
    3322             :  *      steps.  This is mainly because tests like "col IS NULL" break the
    3323             :  *      heuristic used in step 2 especially badly.
    3324             :  *  2.  Reduce the given expressions to a list of unique Vars used.  For
    3325             :  *      example, GROUP BY a, a + b is treated the same as GROUP BY a, b.
    3326             :  *      It is clearly correct not to count the same Var more than once.
    3327             :  *      It is also reasonable to treat f(x) the same as x: f() cannot
    3328             :  *      increase the number of distinct values (unless it is volatile,
    3329             :  *      which we consider unlikely for grouping), but it probably won't
    3330             :  *      reduce the number of distinct values much either.
    3331             :  *      As a special case, if a GROUP BY expression can be matched to an
    3332             :  *      expressional index for which we have statistics, then we treat the
    3333             :  *      whole expression as though it were just a Var.
    3334             :  *  3.  If the list contains Vars of different relations that are known equal
    3335             :  *      due to equivalence classes, then drop all but one of the Vars from each
    3336             :  *      known-equal set, keeping the one with smallest estimated # of values
    3337             :  *      (since the extra values of the others can't appear in joined rows).
    3338             :  *      Note the reason we only consider Vars of different relations is that
    3339             :  *      if we considered ones of the same rel, we'd be double-counting the
    3340             :  *      restriction selectivity of the equality in the next step.
    3341             :  *  4.  For Vars within a single source rel, we multiply together the numbers
    3342             :  *      of values, clamp to the number of rows in the rel (divided by 10 if
    3343             :  *      more than one Var), and then multiply by a factor based on the
    3344             :  *      selectivity of the restriction clauses for that rel.  When there's
    3345             :  *      more than one Var, the initial product is probably too high (it's the
    3346             :  *      worst case) but clamping to a fraction of the rel's rows seems to be a
    3347             :  *      helpful heuristic for not letting the estimate get out of hand.  (The
    3348             :  *      factor of 10 is derived from pre-Postgres-7.4 practice.)  The factor
    3349             :  *      we multiply by to adjust for the restriction selectivity assumes that
    3350             :  *      the restriction clauses are independent of the grouping, which may not
    3351             :  *      be a valid assumption, but it's hard to do better.
    3352             :  *  5.  If there are Vars from multiple rels, we repeat step 4 for each such
    3353             :  *      rel, and multiply the results together.
    3354             :  * Note that rels not containing grouped Vars are ignored completely, as are
    3355             :  * join clauses.  Such rels cannot increase the number of groups, and we
    3356             :  * assume such clauses do not reduce the number either (somewhat bogus,
    3357             :  * but we don't have the info to do better).
    3358             :  */
    3359             : double
    3360        9838 : estimate_num_groups(PlannerInfo *root, List *groupExprs, double input_rows,
    3361             :                     List **pgset)
    3362             : {
    3363        9838 :     List       *varinfos = NIL;
    3364        9838 :     double      srf_multiplier = 1.0;
    3365             :     double      numdistinct;
    3366             :     ListCell   *l;
    3367             :     int         i;
    3368             : 
    3369             :     /*
    3370             :      * We don't ever want to return an estimate of zero groups, as that tends
    3371             :      * to lead to division-by-zero and other unpleasantness.  The input_rows
    3372             :      * estimate is usually already at least 1, but clamp it just in case it
    3373             :      * isn't.
    3374             :      */
    3375        9838 :     input_rows = clamp_row_est(input_rows);
    3376             : 
    3377             :     /*
    3378             :      * If no grouping columns, there's exactly one group.  (This can't happen
    3379             :      * for normal cases with GROUP BY or DISTINCT, but it is possible for
    3380             :      * corner cases with set operations.)
    3381             :      */
    3382        9838 :     if (groupExprs == NIL || (pgset && list_length(*pgset) < 1))
    3383         458 :         return 1.0;
    3384             : 
    3385             :     /*
    3386             :      * Count groups derived from boolean grouping expressions.  For other
    3387             :      * expressions, find the unique Vars used, treating an expression as a Var
    3388             :      * if we can find stats for it.  For each one, record the statistical
    3389             :      * estimate of number of distinct values (total in its table, without
    3390             :      * regard for filtering).
    3391             :      */
    3392        9380 :     numdistinct = 1.0;
    3393             : 
    3394        9380 :     i = 0;
    3395       22082 :     foreach(l, groupExprs)
    3396             :     {
    3397       12706 :         Node       *groupexpr = (Node *) lfirst(l);
    3398             :         double      this_srf_multiplier;
    3399             :         VariableStatData vardata;
    3400             :         List       *varshere;
    3401             :         ListCell   *l2;
    3402             : 
    3403             :         /* is expression in this grouping set? */
    3404       12706 :         if (pgset && !list_member_int(*pgset, i++))
    3405        7620 :             continue;
    3406             : 
    3407             :         /*
    3408             :          * Set-returning functions in grouping columns are a bit problematic.
    3409             :          * The code below will effectively ignore their SRF nature and come up
    3410             :          * with a numdistinct estimate as though they were scalar functions.
    3411             :          * We compensate by scaling up the end result by the largest SRF
    3412             :          * rowcount estimate.  (This will be an overestimate if the SRF
    3413             :          * produces multiple copies of any output value, but it seems best to
    3414             :          * assume the SRF's outputs are distinct.  In any case, it's probably
    3415             :          * pointless to worry too much about this without much better
    3416             :          * estimates for SRF output rowcounts than we have today.)
    3417             :          */
    3418       12346 :         this_srf_multiplier = expression_returns_set_rows(root, groupexpr);
    3419       12346 :         if (srf_multiplier < this_srf_multiplier)
    3420          72 :             srf_multiplier = this_srf_multiplier;
    3421             : 
    3422             :         /* Short-circuit for expressions returning boolean */
    3423       12346 :         if (exprType(groupexpr) == BOOLOID)
    3424             :         {
    3425          24 :             numdistinct *= 2.0;
    3426          24 :             continue;
    3427             :         }
    3428             : 
    3429             :         /*
    3430             :          * If examine_variable is able to deduce anything about the GROUP BY
    3431             :          * expression, treat it as a single variable even if it's really more
    3432             :          * complicated.
    3433             :          */
    3434       12322 :         examine_variable(root, groupexpr, 0, &vardata);
    3435       12322 :         if (HeapTupleIsValid(vardata.statsTuple) || vardata.isunique)
    3436             :         {
    3437        6930 :             varinfos = add_unique_group_var(root, varinfos,
    3438             :                                             groupexpr, &vardata);
    3439        6930 :             ReleaseVariableStats(vardata);
    3440        6930 :             continue;
    3441             :         }
    3442        5392 :         ReleaseVariableStats(vardata);
    3443             : 
    3444             :         /*
    3445             :          * Else pull out the component Vars.  Handle PlaceHolderVars by
    3446             :          * recursing into their arguments (effectively assuming that the
    3447             :          * PlaceHolderVar doesn't change the number of groups, which boils
    3448             :          * down to ignoring the possible addition of nulls to the result set).
    3449             :          */
    3450        5392 :         varshere = pull_var_clause(groupexpr,
    3451             :                                    PVC_RECURSE_AGGREGATES |
    3452             :                                    PVC_RECURSE_WINDOWFUNCS |
    3453             :                                    PVC_RECURSE_PLACEHOLDERS);
    3454             : 
    3455             :         /*
    3456             :          * If we find any variable-free GROUP BY item, then either it is a
    3457             :          * constant (and we can ignore it) or it contains a volatile function;
    3458             :          * in the latter case we punt and assume that each input row will
    3459             :          * yield a distinct group.
    3460             :          */
    3461        5392 :         if (varshere == NIL)
    3462             :         {
    3463         310 :             if (contain_volatile_functions(groupexpr))
    3464           4 :                 return input_rows;
    3465         306 :             continue;
    3466             :         }
    3467             : 
    3468             :         /*
    3469             :          * Else add variables to varinfos list
    3470             :          */
    3471       10340 :         foreach(l2, varshere)
    3472             :         {
    3473        5258 :             Node       *var = (Node *) lfirst(l2);
    3474             : 
    3475        5258 :             examine_variable(root, var, 0, &vardata);
    3476        5258 :             varinfos = add_unique_group_var(root, varinfos, var, &vardata);
    3477        5258 :             ReleaseVariableStats(vardata);
    3478             :         }
    3479             :     }
    3480             : 
    3481             :     /*
    3482             :      * If now no Vars, we must have an all-constant or all-boolean GROUP BY
    3483             :      * list.
    3484             :      */
    3485        9376 :     if (varinfos == NIL)
    3486             :     {
    3487             :         /* Apply SRF multiplier as we would do in the long path */
    3488         168 :         numdistinct *= srf_multiplier;
    3489             :         /* Round off */
    3490         168 :         numdistinct = ceil(numdistinct);
    3491             :         /* Guard against out-of-range answers */
    3492         168 :         if (numdistinct > input_rows)
    3493           0 :             numdistinct = input_rows;
    3494         168 :         if (numdistinct < 1.0)
    3495           0 :             numdistinct = 1.0;
    3496         168 :         return numdistinct;
    3497             :     }
    3498             : 
    3499             :     /*
    3500             :      * Group Vars by relation and estimate total numdistinct.
    3501             :      *
    3502             :      * For each iteration of the outer loop, we process the frontmost Var in
    3503             :      * varinfos, plus all other Vars in the same relation.  We remove these
    3504             :      * Vars from the newvarinfos list for the next iteration. This is the
    3505             :      * easiest way to group Vars of same rel together.
    3506             :      */
    3507             :     do
    3508             :     {
    3509        9510 :         GroupVarInfo *varinfo1 = (GroupVarInfo *) linitial(varinfos);
    3510        9510 :         RelOptInfo *rel = varinfo1->rel;
    3511        9510 :         double      reldistinct = 1;
    3512        9510 :         double      relmaxndistinct = reldistinct;
    3513        9510 :         int         relvarcount = 0;
    3514        9510 :         List       *newvarinfos = NIL;
    3515        9510 :         List       *relvarinfos = NIL;
    3516             : 
    3517             :         /*
    3518             :          * Split the list of varinfos in two - one for the current rel, one
    3519             :          * for remaining Vars on other rels.
    3520             :          */
    3521        9510 :         relvarinfos = lappend(relvarinfos, varinfo1);
    3522       12358 :         for_each_from(l, varinfos, 1)
    3523             :         {
    3524        2848 :             GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
    3525             : 
    3526        2848 :             if (varinfo2->rel == varinfo1->rel)
    3527             :             {
    3528             :                 /* varinfos on current rel */
    3529        2478 :                 relvarinfos = lappend(relvarinfos, varinfo2);
    3530             :             }
    3531             :             else
    3532             :             {
    3533             :                 /* not time to process varinfo2 yet */
    3534         370 :                 newvarinfos = lappend(newvarinfos, varinfo2);
    3535             :             }
    3536             :         }
    3537             : 
    3538             :         /*
    3539             :          * Get the numdistinct estimate for the Vars of this rel.  We
    3540             :          * iteratively search for multivariate n-distinct with maximum number
    3541             :          * of vars; assuming that each var group is independent of the others,
    3542             :          * we multiply them together.  Any remaining relvarinfos after no more
    3543             :          * multivariate matches are found are assumed independent too, so
    3544             :          * their individual ndistinct estimates are multiplied also.
    3545             :          *
    3546             :          * While iterating, count how many separate numdistinct values we
    3547             :          * apply.  We apply a fudge factor below, but only if we multiplied
    3548             :          * more than one such values.
    3549             :          */
    3550       19036 :         while (relvarinfos)
    3551             :         {
    3552             :             double      mvndistinct;
    3553             : 
    3554        9526 :             if (estimate_multivariate_ndistinct(root, rel, &relvarinfos,
    3555             :                                                 &mvndistinct))
    3556             :             {
    3557          40 :                 reldistinct *= mvndistinct;
    3558          40 :                 if (relmaxndistinct < mvndistinct)
    3559          40 :                     relmaxndistinct = mvndistinct;
    3560          40 :                 relvarcount++;
    3561             :             }
    3562             :             else
    3563             :             {
    3564       21374 :                 foreach(l, relvarinfos)
    3565             :                 {
    3566       11888 :                     GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
    3567             : 
    3568       11888 :                     reldistinct *= varinfo2->ndistinct;
    3569       11888 :                     if (relmaxndistinct < varinfo2->ndistinct)
    3570        9752 :                         relmaxndistinct = varinfo2->ndistinct;
    3571       11888 :                     relvarcount++;
    3572             :                 }
    3573             : 
    3574             :                 /* we're done with this relation */
    3575        9486 :                 relvarinfos = NIL;
    3576             :             }
    3577             :         }
    3578             : 
    3579             :         /*
    3580             :          * Sanity check --- don't divide by zero if empty relation.
    3581             :          */
    3582             :         Assert(IS_SIMPLE_REL(rel));
    3583        9510 :         if (rel->tuples > 0)
    3584             :         {
    3585             :             /*
    3586             :              * Clamp to size of rel, or size of rel / 10 if multiple Vars. The
    3587             :              * fudge factor is because the Vars are probably correlated but we
    3588             :              * don't know by how much.  We should never clamp to less than the
    3589             :              * largest ndistinct value for any of the Vars, though, since
    3590             :              * there will surely be at least that many groups.
    3591             :              */
    3592        9482 :             double      clamp = rel->tuples;
    3593             : 
    3594        9482 :             if (relvarcount > 1)
    3595             :             {
    3596        1596 :                 clamp *= 0.1;
    3597        1596 :                 if (clamp < relmaxndistinct)
    3598             :                 {
    3599         966 :                     clamp = relmaxndistinct;
    3600             :                     /* for sanity in case some ndistinct is too large: */
    3601         966 :                     if (clamp > rel->tuples)
    3602          56 :                         clamp = rel->tuples;
    3603             :                 }
    3604             :             }
    3605        9482 :             if (reldistinct > clamp)
    3606        1192 :                 reldistinct = clamp;
    3607             : 
    3608             :             /*
    3609             :              * Update the estimate based on the restriction selectivity,
    3610             :              * guarding against division by zero when reldistinct is zero.
    3611             :              * Also skip this if we know that we are returning all rows.
    3612             :              */
    3613        9482 :             if (reldistinct > 0 && rel->rows < rel->tuples)
    3614             :             {
    3615             :                 /*
    3616             :                  * Given a table containing N rows with n distinct values in a
    3617             :                  * uniform distribution, if we select p rows at random then
    3618             :                  * the expected number of distinct values selected is
    3619             :                  *
    3620             :                  * n * (1 - product((N-N/n-i)/(N-i), i=0..p-1))
    3621             :                  *
    3622             :                  * = n * (1 - (N-N/n)! / (N-N/n-p)! * (N-p)! / N!)
    3623             :                  *
    3624             :                  * See "Approximating block accesses in database
    3625             :                  * organizations", S. B. Yao, Communications of the ACM,
    3626             :                  * Volume 20 Issue 4, April 1977 Pages 260-261.
    3627             :                  *
    3628             :                  * Alternatively, re-arranging the terms from the factorials,
    3629             :                  * this may be written as
    3630             :                  *
    3631             :                  * n * (1 - product((N-p-i)/(N-i), i=0..N/n-1))
    3632             :                  *
    3633             :                  * This form of the formula is more efficient to compute in
    3634             :                  * the common case where p is larger than N/n.  Additionally,
    3635             :                  * as pointed out by Dell'Era, if i << N for all terms in the
    3636             :                  * product, it can be approximated by
    3637             :                  *
    3638             :                  * n * (1 - ((N-p)/N)^(N/n))
    3639             :                  *
    3640             :                  * See "Expected distinct values when selecting from a bag
    3641             :                  * without replacement", Alberto Dell'Era,
    3642             :                  * http://www.adellera.it/investigations/distinct_balls/.
    3643             :                  *
    3644             :                  * The condition i << N is equivalent to n >> 1, so this is a
    3645             :                  * good approximation when the number of distinct values in
    3646             :                  * the table is large.  It turns out that this formula also
    3647             :                  * works well even when n is small.
    3648             :                  */
    3649        2484 :                 reldistinct *=
    3650        2484 :                     (1 - pow((rel->tuples - rel->rows) / rel->tuples,
    3651        2484 :                              rel->tuples / reldistinct));
    3652             :             }
    3653        9482 :             reldistinct = clamp_row_est(reldistinct);
    3654             : 
    3655             :             /*
    3656             :              * Update estimate of total distinct groups.
    3657             :              */
    3658        9482 :             numdistinct *= reldistinct;
    3659             :         }
    3660             : 
    3661        9510 :         varinfos = newvarinfos;
    3662        9510 :     } while (varinfos != NIL);
    3663             : 
    3664             :     /* Now we can account for the effects of any SRFs */
    3665        9208 :     numdistinct *= srf_multiplier;
    3666             : 
    3667             :     /* Round off */
    3668        9208 :     numdistinct = ceil(numdistinct);
    3669             : 
    3670             :     /* Guard against out-of-range answers */
    3671        9208 :     if (numdistinct > input_rows)
    3672         742 :         numdistinct = input_rows;
    3673        9208 :     if (numdistinct < 1.0)
    3674           0 :         numdistinct = 1.0;
    3675             : 
    3676        9208 :     return numdistinct;
    3677             : }
    3678             : 
    3679             : /*
    3680             :  * Estimate hash bucket statistics when the specified expression is used
    3681             :  * as a hash key for the given number of buckets.
    3682             :  *
    3683             :  * This attempts to determine two values:
    3684             :  *
    3685             :  * 1. The frequency of the most common value of the expression (returns
    3686             :  * zero into *mcv_freq if we can't get that).
    3687             :  *
    3688             :  * 2. The "bucketsize fraction", ie, average number of entries in a bucket
    3689             :  * divided by total tuples in relation.
    3690             :  *
    3691             :  * XXX This is really pretty bogus since we're effectively assuming that the
    3692             :  * distribution of hash keys will be the same after applying restriction
    3693             :  * clauses as it was in the underlying relation.  However, we are not nearly
    3694             :  * smart enough to figure out how the restrict clauses might change the
    3695             :  * distribution, so this will have to do for now.
    3696             :  *
    3697             :  * We are passed the number of buckets the executor will use for the given
    3698             :  * input relation.  If the data were perfectly distributed, with the same
    3699             :  * number of tuples going into each available bucket, then the bucketsize
    3700             :  * fraction would be 1/nbuckets.  But this happy state of affairs will occur
    3701             :  * only if (a) there are at least nbuckets distinct data values, and (b)
    3702             :  * we have a not-too-skewed data distribution.  Otherwise the buckets will
    3703             :  * be nonuniformly occupied.  If the other relation in the join has a key
    3704             :  * distribution similar to this one's, then the most-loaded buckets are
    3705             :  * exactly those that will be probed most often.  Therefore, the "average"
    3706             :  * bucket size for costing purposes should really be taken as something close
    3707             :  * to the "worst case" bucket size.  We try to estimate this by adjusting the
    3708             :  * fraction if there are too few distinct data values, and then scaling up
    3709             :  * by the ratio of the most common value's frequency to the average frequency.
    3710             :  *
    3711             :  * If no statistics are available, use a default estimate of 0.1.  This will
    3712             :  * discourage use of a hash rather strongly if the inner relation is large,
    3713             :  * which is what we want.  We do not want to hash unless we know that the
    3714             :  * inner rel is well-dispersed (or the alternatives seem much worse).
    3715             :  *
    3716             :  * The caller should also check that the mcv_freq is not so large that the
    3717             :  * most common value would by itself require an impractically large bucket.
    3718             :  * In a hash join, the executor can split buckets if they get too big, but
    3719             :  * obviously that doesn't help for a bucket that contains many duplicates of
    3720             :  * the same value.
    3721             :  */
    3722             : void
    3723       87808 : estimate_hash_bucket_stats(PlannerInfo *root, Node *hashkey, double nbuckets,
    3724             :                            Selectivity *mcv_freq,
    3725             :                            Selectivity *bucketsize_frac)
    3726             : {
    3727             :     VariableStatData vardata;
    3728             :     double      estfract,
    3729             :                 ndistinct,
    3730             :                 stanullfrac,
    3731             :                 avgfreq;
    3732             :     bool        isdefault;
    3733             :     AttStatsSlot sslot;
    3734             : 
    3735       87808 :     examine_variable(root, hashkey, 0, &vardata);
    3736             : 
    3737             :     /* Look up the frequency of the most common value, if available */
    3738       87808 :     *mcv_freq = 0.0;
    3739             : 
    3740       87808 :     if (HeapTupleIsValid(vardata.statsTuple))
    3741             :     {
    3742       61146 :         if (get_attstatsslot(&sslot, vardata.statsTuple,
    3743             :                              STATISTIC_KIND_MCV, InvalidOid,
    3744             :                              ATTSTATSSLOT_NUMBERS))
    3745             :         {
    3746             :             /*
    3747             :              * The first MCV stat is for the most common value.
    3748             :              */
    3749       32458 :             if (sslot.nnumbers > 0)
    3750       32458 :                 *mcv_freq = sslot.numbers[0];
    3751       32458 :             free_attstatsslot(&sslot);
    3752             :         }
    3753             :     }
    3754             : 
    3755             :     /* Get number of distinct values */
    3756       87808 :     ndistinct = get_variable_numdistinct(&vardata, &isdefault);
    3757             : 
    3758             :     /*
    3759             :      * If ndistinct isn't real, punt.  We normally return 0.1, but if the
    3760             :      * mcv_freq is known to be even higher than that, use it instead.
    3761             :      */
    3762       87808 :     if (isdefault)
    3763             :     {
    3764        8340 :         *bucketsize_frac = (Selectivity) Max(0.1, *mcv_freq);
    3765        8340 :         ReleaseVariableStats(vardata);
    3766        8340 :         return;
    3767             :     }
    3768             : 
    3769             :     /* Get fraction that are null */
    3770       79468 :     if (HeapTupleIsValid(vardata.statsTuple))
    3771             :     {
    3772             :         Form_pg_statistic stats;
    3773             : 
    3774       61134 :         stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
    3775       61134 :         stanullfrac = stats->stanullfrac;
    3776             :     }
    3777             :     else
    3778       18334 :         stanullfrac = 0.0;
    3779             : 
    3780             :     /* Compute avg freq of all distinct data values in raw relation */
    3781       79468 :     avgfreq = (1.0 - stanullfrac) / ndistinct;
    3782             : 
    3783             :     /*
    3784             :      * Adjust ndistinct to account for restriction clauses.  Observe we are
    3785             :      * assuming that the data distribution is affected uniformly by the
    3786             :      * restriction clauses!
    3787             :      *
    3788             :      * XXX Possibly better way, but much more expensive: multiply by
    3789             :      * selectivity of rel's restriction clauses that mention the target Var.
    3790             :      */
    3791       79468 :     if (vardata.rel && vardata.rel->tuples > 0)
    3792             :     {
    3793       79458 :         ndistinct *= vardata.rel->rows / vardata.rel->tuples;
    3794       79458 :         ndistinct = clamp_row_est(ndistinct);
    3795             :     }
    3796             : 
    3797             :     /*
    3798             :      * Initial estimate of bucketsize fraction is 1/nbuckets as long as the
    3799             :      * number of buckets is less than the expected number of distinct values;
    3800             :      * otherwise it is 1/ndistinct.
    3801             :      */
    3802       79468 :     if (ndistinct > nbuckets)
    3803          36 :         estfract = 1.0 / nbuckets;
    3804             :     else
    3805       79432 :         estfract = 1.0 / ndistinct;
    3806             : 
    3807             :     /*
    3808             :      * Adjust estimated bucketsize upward to account for skewed distribution.
    3809             :      */
    3810       79468 :     if (avgfreq > 0.0 && *mcv_freq > avgfreq)
    3811       28716 :         estfract *= *mcv_freq / avgfreq;
    3812             : 
    3813             :     /*
    3814             :      * Clamp bucketsize to sane range (the above adjustment could easily
    3815             :      * produce an out-of-range result).  We set the lower bound a little above
    3816             :      * zero, since zero isn't a very sane result.
    3817             :      */
    3818       79468 :     if (estfract < 1.0e-6)
    3819           0 :         estfract = 1.0e-6;
    3820       79468 :     else if (estfract > 1.0)
    3821       23494 :         estfract = 1.0;
    3822             : 
    3823       79468 :     *bucketsize_frac = (Selectivity) estfract;
    3824             : 
    3825       79468 :     ReleaseVariableStats(vardata);
    3826             : }
    3827             : 
    3828             : /*
    3829             :  * estimate_hashagg_tablesize
    3830             :  *    estimate the number of bytes that a hash aggregate hashtable will
    3831             :  *    require based on the agg_costs, path width and number of groups.
    3832             :  *
    3833             :  * We return the result as "double" to forestall any possible overflow
    3834             :  * problem in the multiplication by dNumGroups.
    3835             :  *
    3836             :  * XXX this may be over-estimating the size now that hashagg knows to omit
    3837             :  * unneeded columns from the hashtable.  Also for mixed-mode grouping sets,
    3838             :  * grouping columns not in the hashed set are counted here even though hashagg
    3839             :  * won't store them.  Is this a problem?
    3840             :  */
    3841             : double
    3842        1256 : estimate_hashagg_tablesize(PlannerInfo *root, Path *path,
    3843             :                            const AggClauseCosts *agg_costs, double dNumGroups)
    3844             : {
    3845             :     Size        hashentrysize;
    3846             : 
    3847        1256 :     hashentrysize = hash_agg_entry_size(list_length(root->aggtransinfos),
    3848        1256 :                                         path->pathtarget->width,
    3849             :                                         agg_costs->transitionSpace);
    3850             : 
    3851             :     /*
    3852             :      * Note that this disregards the effect of fill-factor and growth policy
    3853             :      * of the hash table.  That's probably ok, given that the default
    3854             :      * fill-factor is relatively high.  It'd be hard to meaningfully factor in
    3855             :      * "double-in-size" growth policies here.
    3856             :      */
    3857        1256 :     return hashentrysize * dNumGroups;
    3858             : }
    3859             : 
    3860             : 
    3861             : /*-------------------------------------------------------------------------
    3862             :  *
    3863             :  * Support routines
    3864             :  *
    3865             :  *-------------------------------------------------------------------------
    3866             :  */
    3867             : 
    3868             : /*
    3869             :  * Find applicable ndistinct statistics for the given list of VarInfos (which
    3870             :  * must all belong to the given rel), and update *ndistinct to the estimate of
    3871             :  * the MVNDistinctItem that best matches.  If a match it found, *varinfos is
    3872             :  * updated to remove the list of matched varinfos.
    3873             :  *
    3874             :  * Varinfos that aren't for simple Vars are ignored.
    3875             :  *
    3876             :  * Return true if we're able to find a match, false otherwise.
    3877             :  */
    3878             : static bool
    3879        9526 : estimate_multivariate_ndistinct(PlannerInfo *root, RelOptInfo *rel,
    3880             :                                 List **varinfos, double *ndistinct)
    3881             : {
    3882             :     ListCell   *lc;
    3883        9526 :     Bitmapset  *attnums = NULL;
    3884             :     int         nmatches;
    3885        9526 :     Oid         statOid = InvalidOid;
    3886             :     MVNDistinct *stats;
    3887        9526 :     Bitmapset  *matched = NULL;
    3888             : 
    3889             :     /* bail out immediately if the table has no extended statistics */
    3890        9526 :     if (!rel->statlist)
    3891        9466 :         return false;
    3892             : 
    3893             :     /* Determine the attnums we're looking for */
    3894         200 :     foreach(lc, *varinfos)
    3895             :     {
    3896         140 :         GroupVarInfo *varinfo = (GroupVarInfo *) lfirst(lc);
    3897             :         AttrNumber  attnum;
    3898             : 
    3899             :         Assert(varinfo->rel == rel);
    3900             : 
    3901         140 :         if (!IsA(varinfo->var, Var))
    3902           0 :             continue;
    3903             : 
    3904         140 :         attnum = ((Var *) varinfo->var)->varattno;
    3905             : 
    3906         140 :         if (!AttrNumberIsForUserDefinedAttr(attnum))
    3907           4 :             continue;
    3908             : 
    3909         136 :         attnums = bms_add_member(attnums, attnum);
    3910             :     }
    3911             : 
    3912             :     /* look for the ndistinct statistics matching the most vars */
    3913          60 :     nmatches = 1;               /* we require at least two matches */
    3914         240 :     foreach(lc, rel->statlist)
    3915             :     {
    3916         180 :         StatisticExtInfo *info = (StatisticExtInfo *) lfirst(lc);
    3917             :         Bitmapset  *shared;
    3918             :         int         nshared;
    3919             : 
    3920             :         /* skip statistics of other kinds */
    3921         180 :         if (info->kind != STATS_EXT_NDISTINCT)
    3922         120 :             continue;
    3923             : 
    3924             :         /* compute attnums shared by the vars and the statistics object */
    3925          60 :         shared = bms_intersect(info->keys, attnums);
    3926          60 :         nshared = bms_num_members(shared);
    3927             : 
    3928             :         /*
    3929             :          * Does this statistics object match more columns than the currently
    3930             :          * best object?  If so, use this one instead.
    3931             :          *
    3932             :          * XXX This should break ties using name of the object, or something
    3933             :          * like that, to make the outcome stable.
    3934             :          */
    3935          60 :         if (nshared > nmatches)
    3936             :         {
    3937          40 :             statOid = info->statOid;
    3938          40 :             nmatches = nshared;
    3939          40 :             matched = shared;
    3940             :         }
    3941             :     }
    3942             : 
    3943             :     /* No match? */
    3944          60 :     if (statOid == InvalidOid)
    3945          20 :         return false;
    3946             :     Assert(nmatches > 1 && matched != NULL);
    3947             : 
    3948          40 :     stats = statext_ndistinct_load(statOid);
    3949             : 
    3950             :     /*
    3951             :      * If we have a match, search it for the specific item that matches (there
    3952             :      * must be one), and construct the output values.
    3953             :      */
    3954          40 :     if (stats)
    3955             :     {
    3956             :         int         i;
    3957          40 :         List       *newlist = NIL;
    3958          40 :         MVNDistinctItem *item = NULL;
    3959             : 
    3960             :         /* Find the specific item that exactly matches the combination */
    3961         112 :         for (i = 0; i < stats->nitems; i++)
    3962             :         {
    3963         112 :             MVNDistinctItem *tmpitem = &stats->items[i];
    3964             : 
    3965         112 :             if (bms_subset_compare(tmpitem->attrs, matched) == BMS_EQUAL)
    3966             :             {
    3967          40 :                 item = tmpitem;
    3968          40 :                 break;
    3969             :             }
    3970             :         }
    3971             : 
    3972             :         /* make sure we found an item */
    3973          40 :         if (!item)
    3974           0 :             elog(ERROR, "corrupt MVNDistinct entry");
    3975             : 
    3976             :         /* Form the output varinfo list, keeping only unmatched ones */
    3977         156 :         foreach(lc, *varinfos)
    3978             :         {
    3979         116 :             GroupVarInfo *varinfo = (GroupVarInfo *) lfirst(lc);
    3980             :             AttrNumber  attnum;
    3981             : 
    3982         116 :             if (!IsA(varinfo->var, Var))
    3983             :             {
    3984           0 :                 newlist = lappend(newlist, varinfo);
    3985           0 :                 continue;
    3986             :             }
    3987             : 
    3988         116 :             attnum = ((Var *) varinfo->var)->varattno;
    3989             : 
    3990         116 :             if (!AttrNumberIsForUserDefinedAttr(attnum))
    3991           4 :                 continue;
    3992             : 
    3993         112 :             if (!bms_is_member(attnum, matched))
    3994          16 :                 newlist = lappend(newlist, varinfo);
    3995             :         }
    3996             : 
    3997          40 :         *varinfos = newlist;
    3998          40 :         *ndistinct = item->ndistinct;
    3999          40 :         return true;
    4000             :     }
    4001             : 
    4002           0 :     return false;
    4003             : }
    4004             : 
    4005             : /*
    4006             :  * convert_to_scalar
    4007             :  *    Convert non-NULL values of the indicated types to the comparison
    4008             :  *    scale needed by scalarineqsel().
    4009             :  *    Returns "true" if successful.
    4010             :  *
    4011             :  * XXX this routine is a hack: ideally we should look up the conversion
    4012             :  * subroutines in pg_type.
    4013             :  *
    4014             :  * All numeric datatypes are simply converted to their equivalent
    4015             :  * "double" values.  (NUMERIC values that are outside the range of "double"
    4016             :  * are clamped to +/- HUGE_VAL.)
    4017             :  *
    4018             :  * String datatypes are converted by convert_string_to_scalar(),
    4019             :  * which is explained below.  The reason why this routine deals with
    4020             :  * three values at a time, not just one, is that we need it for strings.
    4021             :  *
    4022             :  * The bytea datatype is just enough different from strings that it has
    4023             :  * to be treated separately.
    4024             :  *
    4025             :  * The several datatypes representing absolute times are all converted
    4026             :  * to Timestamp, which is actually an int64, and then we promote that to
    4027             :  * a double.  Note this will give correct results even for the "special"
    4028             :  * values of Timestamp, since those are chosen to compare correctly;
    4029             :  * see timestamp_cmp.
    4030             :  *
    4031             :  * The several datatypes representing relative times (intervals) are all
    4032             :  * converted to measurements expressed in seconds.
    4033             :  */
    4034             : static bool
    4035       56752 : convert_to_scalar(Datum value, Oid valuetypid, Oid collid, double *scaledvalue,
    4036             :                   Datum lobound, Datum hibound, Oid boundstypid,
    4037             :                   double *scaledlobound, double *scaledhibound)
    4038             : {
    4039       56752 :     bool        failure = false;
    4040             : 
    4041             :     /*
    4042             :      * Both the valuetypid and the boundstypid should exactly match the
    4043             :      * declared input type(s) of the operator we are invoked for.  However,
    4044             :      * extensions might try to use scalarineqsel as estimator for operators
    4045             :      * with input type(s) we don't handle here; in such cases, we want to
    4046             :      * return false, not fail.  In any case, we mustn't assume that valuetypid
    4047             :      * and boundstypid are identical.
    4048             :      *
    4049             :      * XXX The histogram we are interpolating between points of could belong
    4050             :      * to a column that's only binary-compatible with the declared type. In
    4051             :      * essence we are assuming that the semantics of binary-compatible types
    4052             :      * are enough alike that we can use a histogram generated with one type's
    4053             :      * operators to estimate selectivity for the other's.  This is outright
    4054             :      * wrong in some cases --- in particular signed versus unsigned
    4055             :      * interpretation could trip us up.  But it's useful enough in the
    4056             :      * majority of cases that we do it anyway.  Should think about more
    4057             :      * rigorous ways to do it.
    4058             :      */
    4059       56752 :     switch (valuetypid)
    4060             :     {
    4061             :             /*
    4062             :              * Built-in numeric types
    4063             :              */
    4064       54524 :         case BOOLOID:
    4065             :         case INT2OID:
    4066             :         case INT4OID:
    4067             :         case INT8OID:
    4068             :         case FLOAT4OID:
    4069             :         case FLOAT8OID:
    4070             :         case NUMERICOID:
    4071             :         case OIDOID:
    4072             :         case REGPROCOID:
    4073             :         case REGPROCEDUREOID:
    4074             :         case REGOPEROID:
    4075             :         case REGOPERATOROID:
    4076             :         case REGCLASSOID:
    4077             :         case REGTYPEOID:
    4078             :         case REGCONFIGOID:
    4079             :         case REGDICTIONARYOID:
    4080             :         case REGROLEOID:
    4081             :         case REGNAMESPACEOID:
    4082       54524 :             *scaledvalue = convert_numeric_to_scalar(value, valuetypid,
    4083             :                                                      &failure);
    4084       54524 :             *scaledlobound = convert_numeric_to_scalar(lobound, boundstypid,
    4085             :                                                        &failure);
    4086       54524 :             *scaledhibound = convert_numeric_to_scalar(hibound, boundstypid,
    4087             :                                                        &failure);
    4088       54524 :             return !failure;
    4089             : 
    4090             :             /*
    4091             :              * Built-in string types
    4092             :              */
    4093        2224 :         case CHAROID:
    4094             :         case BPCHAROID:
    4095             :         case VARCHAROID:
    4096             :         case TEXTOID:
    4097             :         case NAMEOID:
    4098             :             {
    4099        2224 :                 char       *valstr = convert_string_datum(value, valuetypid,
    4100             :                                                           collid, &failure);
    4101        2224 :                 char       *lostr = convert_string_datum(lobound, boundstypid,
    4102             :                                                          collid, &failure);
    4103        2224 :                 char       *histr = convert_string_datum(hibound, boundstypid,
    4104             :                                                          collid, &failure);
    4105             : 
    4106             :                 /*
    4107             :                  * Bail out if any of the values is not of string type.  We
    4108             :                  * might leak converted strings for the other value(s), but
    4109             :                  * that's not worth troubling over.
    4110             :                  */
    4111        2224 :                 if (failure)
    4112           0 :                     return false;
    4113             : 
    4114        2224 :                 convert_string_to_scalar(valstr, scaledvalue,
    4115             :                                          lostr, scaledlobound,
    4116             :                                          histr, scaledhibound);
    4117        2224 :                 pfree(valstr);
    4118        2224 :                 pfree(lostr);
    4119        2224 :                 pfree(histr);
    4120        2224 :                 return true;
    4121             :             }
    4122             : 
    4123             :             /*
    4124             :              * Built-in bytea type
    4125             :              */
    4126           0 :         case BYTEAOID:
    4127             :             {
    4128             :                 /* We only support bytea vs bytea comparison */
    4129           0 :                 if (boundstypid != BYTEAOID)
    4130           0 :                     return false;
    4131           0 :                 convert_bytea_to_scalar(value, scaledvalue,
    4132             :                                         lobound, scaledlobound,
    4133             :                                         hibound, scaledhibound);
    4134           0 :                 return true;
    4135             :             }
    4136             : 
    4137             :             /*
    4138             :              * Built-in time types
    4139             :              */
    4140           0 :         case TIMESTAMPOID:
    4141             :         case TIMESTAMPTZOID:
    4142             :         case DATEOID:
    4143             :         case INTERVALOID:
    4144             :         case TIMEOID:
    4145             :         case TIMETZOID:
    4146           0 :             *scaledvalue = convert_timevalue_to_scalar(value, valuetypid,
    4147             :                                                        &failure);
    4148           0 :             *scaledlobound = convert_timevalue_to_scalar(lobound, boundstypid,
    4149             :                                                          &failure);
    4150           0 :             *scaledhibound = convert_timevalue_to_scalar(hibound, boundstypid,
    4151             :                                                          &failure);
    4152           0 :             return !failure;
    4153             : 
    4154             :             /*
    4155             :              * Built-in network types
    4156             :              */
    4157           0 :         case INETOID:
    4158             :         case CIDROID:
    4159             :         case MACADDROID:
    4160             :         case MACADDR8OID:
    4161           0 :             *scaledvalue = convert_network_to_scalar(value, valuetypid,
    4162             :                                                      &failure);
    4163           0 :             *scaledlobound = convert_network_to_scalar(lobound, boundstypid,
    4164             :                                                        &failure);
    4165           0 :             *scaledhibound = convert_network_to_scalar(hibound, boundstypid,
    4166             :                                                        &failure);
    4167           0 :             return !failure;
    4168             :     }
    4169             :     /* Don't know how to convert */
    4170           4 :     *scaledvalue = *scaledlobound = *scaledhibound = 0;
    4171           4 :     return false;
    4172             : }
    4173             : 
    4174             : /*
    4175             :  * Do convert_to_scalar()'s work for any numeric data type.
    4176             :  *
    4177             :  * On failure (e.g., unsupported typid), set *failure to true;
    4178             :  * otherwise, that variable is not changed.
    4179             :  */
    4180             : static double
    4181      163572 : convert_numeric_to_scalar(Datum value, Oid typid, bool *failure)
    4182             : {
    4183      163572 :     switch (typid)
    4184             :     {
    4185           0 :         case BOOLOID:
    4186           0 :             return (double) DatumGetBool(value);
    4187           8 :         case INT2OID:
    4188           8 :             return (double) DatumGetInt16(value);
    4189       18472 :         case INT4OID:
    4190       18472 :             return (double) DatumGetInt32(value);
    4191           0 :         case INT8OID:
    4192           0 :             return (double) DatumGetInt64(value);
    4193           0 :         case FLOAT4OID:
    4194           0 :             return (double) DatumGetFloat4(value);
    4195          24 :         case FLOAT8OID:
    4196          24 :             return (double) DatumGetFloat8(value);
    4197           0 :         case NUMERICOID:
    4198             :             /* Note: out-of-range values will be clamped to +-HUGE_VAL */
    4199           0 :             return (double)
    4200           0 :                 DatumGetFloat8(DirectFunctionCall1(numeric_float8_no_overflow,
    4201             :                                                    value));
    4202      145068 :         case OIDOID:
    4203             :         case REGPROCOID:
    4204             :         case REGPROCEDUREOID:
    4205             :         case REGOPEROID:
    4206             :         case REGOPERATOROID:
    4207             :         case REGCLASSOID:
    4208             :         case REGTYPEOID:
    4209             :         case REGCONFIGOID:
    4210             :         case REGDICTIONARYOID:
    4211             :         case REGROLEOID:
    4212             :         case REGNAMESPACEOID:
    4213             :             /* we can treat OIDs as integers... */
    4214      145068 :             return (double) DatumGetObjectId(value);
    4215             :     }
    4216             : 
    4217           0 :     *failure = true;
    4218           0 :     return 0;
    4219             : }
    4220             : 
    4221             : /*
    4222             :  * Do convert_to_scalar()'s work for any character-string data type.
    4223             :  *
    4224             :  * String datatypes are converted to a scale that ranges from 0 to 1,
    4225             :  * where we visualize the bytes of the string as fractional digits.
    4226             :  *
    4227             :  * We do not want the base to be 256, however, since that tends to
    4228             :  * generate inflated selectivity estimates; few databases will have
    4229             :  * occurrences of all 256 possible byte values at each position.
    4230             :  * Instead, use the smallest and largest byte values seen in the bounds
    4231             :  * as the estimated range for each byte, after some fudging to deal with
    4232             :  * the fact that we probably aren't going to see the full range that way.
    4233             :  *
    4234             :  * An additional refinement is that we discard any common prefix of the
    4235             :  * three strings before computing the scaled values.  This allows us to
    4236             :  * "zoom in" when we encounter a narrow data range.  An example is a phone
    4237             :  * number database where all the values begin with the same area code.
    4238             :  * (Actually, the bounds will be adjacent histogram-bin-boundary values,
    4239             :  * so this is more likely to happen than you might think.)
    4240             :  */
    4241             : static void
    4242        2224 : convert_string_to_scalar(char *value,
    4243             :                          double *scaledvalue,
    4244             :                          char *lobound,
    4245             :                          double *scaledlobound,
    4246             :                          char *hibound,
    4247             :                          double *scaledhibound)
    4248             : {
    4249             :     int         rangelo,
    4250             :                 rangehi;
    4251             :     char       *sptr;
    4252             : 
    4253        2224 :     rangelo = rangehi = (unsigned char) hibound[0];
    4254       32296 :     for (sptr = lobound; *sptr; sptr++)
    4255             :     {
    4256       30072 :         if (rangelo > (unsigned char) *sptr)
    4257        6088 :             rangelo = (unsigned char) *sptr;
    4258       30072 :         if (rangehi < (unsigned char) *sptr)
    4259        2716 :             rangehi = (unsigned char) *sptr;
    4260             :     }
    4261       27960 :     for (sptr = hibound; *sptr; sptr++)
    4262             :     {
    4263       25736 :         if (rangelo > (unsigned char) *sptr)
    4264         274 :             rangelo = (unsigned char) *sptr;
    4265       25736 :         if (rangehi < (unsigned char) *sptr)
    4266        2864 :             rangehi = (unsigned char) *sptr;
    4267             :     }
    4268             :     /* If range includes any upper-case ASCII chars, make it include all */
    4269        2224 :     if (rangelo <= 'Z' && rangehi >= 'A')
    4270             :     {
    4271         846 :         if (rangelo > 'A')
    4272          56 :             rangelo = 'A';
    4273         846 :         if (rangehi < 'Z')
    4274         320 :             rangehi = 'Z';
    4275             :     }
    4276             :     /* Ditto lower-case */
    4277        2224 :     if (rangelo <= 'z' && rangehi >= 'a')
    4278             :     {
    4279        1896 :         if (rangelo > 'a')
    4280           0 :             rangelo = 'a';
    4281        1896 :         if (rangehi < 'z')
    4282        1782 :             rangehi = 'z';
    4283             :     }
    4284             :     /* Ditto digits */
    4285        2224 :     if (rangelo <= '9' && rangehi >= '0')
    4286             :     {
    4287         478 :         if (rangelo > '0')
    4288         446 :             rangelo = '0';
    4289         478 :         if (rangehi < '9')
    4290           4 :             rangehi = '9';
    4291             :     }
    4292             : 
    4293             :     /*
    4294             :      * If range includes less than 10 chars, assume we have not got enough
    4295             :      * data, and make it include regular ASCII set.
    4296             :      */
    4297        2224 :     if (rangehi - rangelo < 9)
    4298             :     {
    4299           0 :         rangelo = ' ';
    4300           0 :         rangehi = 127;
    4301             :     }
    4302             : 
    4303             :     /*
    4304             :      * Now strip any common prefix of the three strings.
    4305             :      */
    4306        3510 :     while (*lobound)
    4307             :     {
    4308        3510 :         if (*lobound != *hibound || *lobound != *value)
    4309             :             break;
    4310        1286 :         lobound++, hibound++, value++;
    4311             :     }
    4312             : 
    4313             :     /*
    4314             :      * Now we can do the conversions.
    4315             :      */
    4316        2224 :     *scaledvalue = convert_one_string_to_scalar(value, rangelo, rangehi);
    4317        2224 :     *scaledlobound = convert_one_string_to_scalar(lobound, rangelo, rangehi);
    4318        2224 :     *scaledhibound = convert_one_string_to_scalar(hibound, rangelo, rangehi);
    4319        2224 : }
    4320             : 
    4321             : static double
    4322        6672 : convert_one_string_to_scalar(char *value, int rangelo, int rangehi)
    4323             : {
    4324        6672 :     int         slen = strlen(value);
    4325             :     double      num,
    4326             :                 denom,
    4327             :                 base;
    4328             : 
    4329        6672 :     if (slen <= 0)
    4330           0 :         return 0.0;             /* empty string has scalar value 0 */
    4331             : 
    4332             :     /*
    4333             :      * There seems little point in considering more than a dozen bytes from
    4334             :      * the string.  Since base is at least 10, that will give us nominal
    4335             :      * resolution of at least 12 decimal digits, which is surely far more
    4336             :      * precision than this estimation technique has got anyway (especially in
    4337             :      * non-C locales).  Also, even with the maximum possible base of 256, this
    4338             :      * ensures denom cannot grow larger than 256^13 = 2.03e31, which will not
    4339             :      * overflow on any known machine.
    4340             :      */
    4341        6672 :     if (slen > 12)
    4342        1956 :         slen = 12;
    4343             : 
    4344             :     /* Convert initial characters to fraction */
    4345        6672 :     base = rangehi - rangelo + 1;
    4346        6672 :     num = 0.0;
    4347        6672 :     denom = base;
    4348       57834 :     while (slen-- > 0)
    4349             :     {
    4350       51162 :         int         ch = (unsigned char) *value++;
    4351             : 
    4352       51162 :         if (ch < rangelo)
    4353          24 :             ch = rangelo - 1;
    4354       51138 :         else if (ch > rangehi)
    4355           0 :             ch = rangehi + 1;
    4356       51162 :         num += ((double) (ch - rangelo)) / denom;
    4357       51162 :         denom *= base;
    4358             :     }
    4359             : 
    4360        6672 :     return num;
    4361             : }
    4362             : 
    4363             : /*
    4364             :  * Convert a string-type Datum into a palloc'd, null-terminated string.
    4365             :  *
    4366             :  * On failure (e.g., unsupported typid), set *failure to true;
    4367             :  * otherwise, that variable is not changed.  (We'll return NULL on failure.)
    4368             :  *
    4369             :  * When using a non-C locale, we must pass the string through strxfrm()
    4370             :  * before continuing, so as to generate correct locale-specific results.
    4371             :  */
    4372             : static char *
    4373        6672 : convert_string_datum(Datum value, Oid typid, Oid collid, bool *failure)
    4374             : {
    4375             :     char       *val;
    4376             : 
    4377        6672 :     switch (typid)
    4378             :     {
    4379           0 :         case CHAROID:
    4380           0 :             val = (char *) palloc(2);
    4381           0 :             val[0] = DatumGetChar(value);
    4382           0 :             val[1] = '\0';
    4383           0 :             break;
    4384        1968 :         case BPCHAROID:
    4385             :         case VARCHAROID:
    4386             :         case TEXTOID:
    4387        1968 :             val = TextDatumGetCString(value);
    4388        1968 :             break;
    4389        4704 :         case NAMEOID:
    4390             :             {
    4391        4704 :                 NameData   *nm = (NameData *) DatumGetPointer(value);
    4392             : 
    4393        4704 :                 val = pstrdup(NameStr(*nm));
    4394        4704 :                 break;
    4395             :             }
    4396           0 :         default:
    4397           0 :             *failure = true;
    4398           0 :             return NULL;
    4399             :     }
    4400             : 
    4401        6672 :     if (!lc_collate_is_c(collid))
    4402             :     {
    4403             :         char       *xfrmstr;
    4404             :         size_t      xfrmlen;
    4405             :         size_t      xfrmlen2 PG_USED_FOR_ASSERTS_ONLY;
    4406             : 
    4407             :         /*
    4408             :          * XXX: We could guess at a suitable output buffer size and only call
    4409             :          * strxfrm twice if our guess is too small.
    4410             :          *
    4411             :          * XXX: strxfrm doesn't support UTF-8 encoding on Win32, it can return
    4412             :          * bogus data or set an error. This is not really a problem unless it
    4413             :          * crashes since it will only give an estimation error and nothing
    4414             :          * fatal.
    4415             :          */
    4416          72 :         xfrmlen = strxfrm(NULL, val, 0);
    4417             : #ifdef WIN32
    4418             : 
    4419             :         /*
    4420             :          * On Windows, strxfrm returns INT_MAX when an error occurs. Instead
    4421             :          * of trying to allocate this much memory (and fail), just return the
    4422             :          * original string unmodified as if we were in the C locale.
    4423             :          */
    4424             :         if (xfrmlen == INT_MAX)
    4425             :             return val;
    4426             : #endif
    4427          72 :         xfrmstr = (char *) palloc(xfrmlen + 1);
    4428          72 :         xfrmlen2 = strxfrm(xfrmstr, val, xfrmlen + 1);
    4429             : 
    4430             :         /*
    4431             :          * Some systems (e.g., glibc) can return a smaller value from the
    4432             :          * second call than the first; thus the Assert must be <= not ==.
    4433             :          */
    4434             :         Assert(xfrmlen2 <= xfrmlen);
    4435          72 :         pfree(val);
    4436          72 :         val = xfrmstr;
    4437             :     }
    4438             : 
    4439        6672 :     return val;
    4440             : }
    4441             : 
    4442             : /*
    4443             :  * Do convert_to_scalar()'s work for any bytea data type.
    4444             :  *
    4445             :  * Very similar to convert_string_to_scalar except we can't assume
    4446             :  * null-termination and therefore pass explicit lengths around.
    4447             :  *
    4448             :  * Also, assumptions about likely "normal" ranges of characters have been
    4449             :  * removed - a data range of 0..255 is always used, for now.  (Perhaps
    4450             :  * someday we will add information about actual byte data range to
    4451             :  * pg_statistic.)
    4452             :  */
    4453             : static void
    4454           0 : convert_bytea_to_scalar(Datum value,
    4455             :                         double *scaledvalue,
    4456             :                         Datum lobound,
    4457             :                         double *scaledlobound,
    4458             :                         Datum hibound,
    4459             :                         double *scaledhibound)
    4460             : {
    4461           0 :     bytea      *valuep = DatumGetByteaPP(value);
    4462           0 :     bytea      *loboundp = DatumGetByteaPP(lobound);
    4463           0 :     bytea      *hiboundp = DatumGetByteaPP(hibound);
    4464             :     int         rangelo,
    4465             :                 rangehi,
    4466           0 :                 valuelen = VARSIZE_ANY_EXHDR(valuep),
    4467           0 :                 loboundlen = VARSIZE_ANY_EXHDR(loboundp),
    4468           0 :                 hiboundlen = VARSIZE_ANY_EXHDR(hiboundp),
    4469             :                 i,
    4470             :                 minlen;
    4471           0 :     unsigned char *valstr = (unsigned char *) VARDATA_ANY(valuep);
    4472           0 :     unsigned char *lostr = (unsigned char *) VARDATA_ANY(loboundp);
    4473           0 :     unsigned char *histr = (unsigned char *) VARDATA_ANY(hiboundp);
    4474             : 
    4475             :     /*
    4476             :      * Assume bytea data is uniformly distributed across all byte values.
    4477             :      */
    4478           0 :     rangelo = 0;
    4479           0 :     rangehi = 255;
    4480             : 
    4481             :     /*
    4482             :      * Now strip any common prefix of the three strings.
    4483             :      */
    4484           0 :     minlen = Min(Min(valuelen, loboundlen), hiboundlen);
    4485           0 :     for (i = 0; i < minlen; i++)
    4486             :     {
    4487           0 :         if (*lostr != *histr || *lostr != *valstr)
    4488             :             break;
    4489           0 :         lostr++, histr++, valstr++;
    4490           0 :         loboundlen--, hiboundlen--, valuelen--;
    4491             :     }
    4492             : 
    4493             :     /*
    4494             :      * Now we can do the conversions.
    4495             :      */
    4496           0 :     *scaledvalue = convert_one_bytea_to_scalar(valstr, valuelen, rangelo, rangehi);
    4497           0 :     *scaledlobound = convert_one_bytea_to_scalar(lostr, loboundlen, rangelo, rangehi);
    4498           0 :     *scaledhibound = convert_one_bytea_to_scalar(histr, hiboundlen, rangelo, rangehi);
    4499           0 : }
    4500             : 
    4501             : static double
    4502           0 : convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
    4503             :                             int rangelo, int rangehi)
    4504             : {
    4505             :     double      num,
    4506             :                 denom,
    4507             :                 base;
    4508             : 
    4509           0 :     if (valuelen <= 0)
    4510           0 :         return 0.0;             /* empty string has scalar value 0 */
    4511             : 
    4512             :     /*
    4513             :      * Since base is 256, need not consider more than about 10 chars (even
    4514             :      * this many seems like overkill)
    4515             :      */
    4516           0 :     if (valuelen > 10)
    4517           0 :         valuelen = 10;
    4518             : 
    4519             :     /* Convert initial characters to fraction */
    4520           0 :     base = rangehi - rangelo + 1;
    4521           0 :     num = 0.0;
    4522           0 :     denom = base;
    4523           0 :     while (valuelen-- > 0)
    4524             :     {
    4525           0 :         int         ch = *value++;
    4526             : 
    4527           0 :         if (ch < rangelo)
    4528           0 :             ch = rangelo - 1;
    4529           0 :         else if (ch > rangehi)
    4530           0 :             ch = rangehi + 1;
    4531           0 :         num += ((double) (ch - rangelo)) / denom;
    4532           0 :         denom *= base;
    4533             :     }
    4534             : 
    4535           0 :     return num;
    4536             : }
    4537             : 
    4538             : /*
    4539             :  * Do convert_to_scalar()'s work for any timevalue data type.
    4540             :  *
    4541             :  * On failure (e.g., unsupported typid), set *failure to true;
    4542             :  * otherwise, that variable is not changed.
    4543             :  */
    4544             : static double
    4545           0 : convert_timevalue_to_scalar(Datum value, Oid typid, bool *failure)
    4546             : {
    4547           0 :     switch (typid)
    4548             :     {
    4549           0 :         case TIMESTAMPOID:
    4550           0 :             return DatumGetTimestamp(value);
    4551           0 :         case TIMESTAMPTZOID:
    4552           0 :             return DatumGetTimestampTz(value);
    4553           0 :         case DATEOID:
    4554           0 :             return date2timestamp_no_overflow(DatumGetDateADT(value));
    4555           0 :         case INTERVALOID:
    4556             :             {
    4557           0 :                 Interval   *interval = DatumGetIntervalP(value);
    4558             : 
    4559             :                 /*
    4560             :                  * Convert the month part of Interval to days using assumed
    4561             :                  * average month length of 365.25/12.0 days.  Not too
    4562             :                  * accurate, but plenty good enough for our purposes.
    4563             :                  */
    4564           0 :                 return interval->time + interval->day * (double) USECS_PER_DAY +
    4565           0 :                     interval->month * ((DAYS_PER_YEAR / (double) MONTHS_PER_YEAR) * USECS_PER_DAY);
    4566             :             }
    4567           0 :         case TIMEOID:
    4568           0 :             return DatumGetTimeADT(value);
    4569           0 :         case TIMETZOID:
    4570             :             {
    4571           0 :                 TimeTzADT  *timetz = DatumGetTimeTzADTP(value);
    4572             : 
    4573             :                 /* use GMT-equivalent time */
    4574           0 :                 return (double) (timetz->time + (timetz->zone * 1000000.0));
    4575             :             }
    4576             :     }
    4577             : 
    4578           0 :     *failure = true;
    4579           0 :     return 0;
    4580             : }
    4581             : 
    4582             : 
    4583             : /*
    4584             :  * get_restriction_variable
    4585             :  *      Examine the args of a restriction clause to see if it's of the
    4586             :  *      form (variable op pseudoconstant) or (pseudoconstant op variable),
    4587             :  *      where "variable" could be either a Var or an expression in vars of a
    4588             :  *      single relation.  If so, extract information about the variable,
    4589             :  *      and also indicate which side it was on and the other argument.
    4590             :  *
    4591             :  * Inputs:
    4592             :  *  root: the planner info
    4593             :  *  args: clause argument list
    4594             :  *  varRelid: see specs for restriction selectivity functions
    4595             :  *
    4596             :  * Outputs: (these are valid only if true is returned)
    4597             :  *  *vardata: gets information about variable (see examine_variable)
    4598             :  *  *other: gets other clause argument, aggressively reduced to a constant
    4599             :  *  *varonleft: set true if variable is on the left, false if on the right
    4600             :  *
    4601             :  * Returns true if a variable is identified, otherwise false.
    4602             :  *
    4603             :  * Note: if there are Vars on both sides of the clause, we must fail, because
    4604             :  * callers are expecting that the other side will act like a pseudoconstant.
    4605             :  */
    4606             : bool
    4607      385040 : get_restriction_variable(PlannerInfo *root, List *args, int varRelid,
    4608             :                          VariableStatData *vardata, Node **other,
    4609             :                          bool *varonleft)
    4610             : {
    4611             :     Node       *left,
    4612             :                *right;
    4613             :     VariableStatData rdata;
    4614             : 
    4615             :     /* Fail if not a binary opclause (probably shouldn't happen) */
    4616      385040 :     if (list_length(args) != 2)
    4617           0 :         return false;
    4618             : 
    4619      385040 :     left = (Node *) linitial(args);
    4620      385040 :     right = (Node *) lsecond(args);
    4621             : 
    4622             :     /*
    4623             :      * Examine both sides.  Note that when varRelid is nonzero, Vars of other
    4624             :      * relations will be treated as pseudoconstants.
    4625             :      */
    4626      385040 :     examine_variable(root, left, varRelid, vardata);
    4627      385040 :     examine_variable(root, right, varRelid, &rdata);
    4628             : 
    4629             :     /*
    4630             :      * If one side is a variable and the other not, we win.
    4631             :      */
    4632      385040 :     if (vardata->rel && rdata.rel == NULL)
    4633             :     {
    4634      321336 :         *varonleft = true;
    4635      321336 :         *other = estimate_expression_value(root, rdata.var);
    4636             :         /* Assume we need no ReleaseVariableStats(rdata) here */
    4637      321336 :         return true;
    4638             :     }
    4639             : 
    4640       63704 :     if (vardata->rel == NULL && rdata.rel)
    4641             :     {
    4642       61754 :         *varonleft = false;
    4643       61754 :         *other = estimate_expression_value(root, vardata->var);
    4644             :         /* Assume we need no ReleaseVariableStats(*vardata) here */
    4645       61754 :         *vardata = rdata;
    4646       61754 :         return true;
    4647             :     }
    4648             : 
    4649             :     /* Oops, clause has wrong structure (probably var op var) */
    4650        1950 :     ReleaseVariableStats(*vardata);
    4651        1950 :     ReleaseVariableStats(rdata);
    4652             : 
    4653        1950 :     return false;
    4654             : }
    4655             : 
    4656             : /*
    4657             :  * get_join_variables
    4658             :  *      Apply examine_variable() to each side of a join clause.
    4659             :  *      Also, attempt to identify whether the join clause has the same
    4660             :  *      or reversed sense compared to the SpecialJoinInfo.
    4661             :  *
    4662             :  * We consider the join clause "normal" if it is "lhs_var OP rhs_var",
    4663             :  * or "reversed" if it is "rhs_var OP lhs_var".  In complicated cases
    4664             :  * where we can't tell for sure, we default to assuming it's normal.
    4665             :  */
    4666             : void
    4667      125798 : get_join_variables(PlannerInfo *root, List *args, SpecialJoinInfo *sjinfo,
    4668             :                    VariableStatData *vardata1, VariableStatData *vardata2,
    4669             :                    bool *join_is_reversed)
    4670             : {
    4671             :     Node       *left,
    4672             :                *right;
    4673             : 
    4674      125798 :     if (list_length(args) != 2)
    4675           0 :         elog(ERROR, "join operator should take two arguments");
    4676             : 
    4677      125798 :     left = (Node *) linitial(args);
    4678      125798 :     right = (Node *) lsecond(args);
    4679             : 
    4680      125798 :     examine_variable(root, left, 0, vardata1);
    4681      125798 :     examine_variable(root, right, 0, vardata2);
    4682             : 
    4683      251506 :     if (vardata1->rel &&
    4684      125708 :         bms_is_subset(vardata1->rel->relids, sjinfo->syn_righthand))
    4685       20674 :         *join_is_reversed = true;   /* var1 is on RHS */
    4686      210176 :     else if (vardata2->rel &&
    4687      105052 :              bms_is_subset(vardata2->rel->relids, sjinfo->syn_lefthand))
    4688          80 :         *join_is_reversed = true;   /* var2 is on LHS */
    4689             :     else
    4690      105044 :         *join_is_reversed = false;
    4691      125798 : }
    4692             : 
    4693             : /*
    4694             :  * examine_variable
    4695             :  *      Try to look up statistical data about an expression.
    4696             :  *      Fill in a VariableStatData struct to describe the expression.
    4697             :  *
    4698             :  * Inputs:
    4699             :  *  root: the planner info
    4700             :  *  node: the expression tree to examine
    4701             :  *  varRelid: see specs for restriction selectivity functions
    4702             :  *
    4703             :  * Outputs: *vardata is filled as follows:
    4704             :  *  var: the input expression (with any binary relabeling stripped, if
    4705             :  *      it is or contains a variable; but otherwise the type is preserved)
    4706             :  *  rel: RelOptInfo for relation containing variable; NULL if expression
    4707             :  *      contains no Vars (NOTE this could point to a RelOptInfo of a
    4708             :  *      subquery, not one in the current query).
    4709             :  *  statsTuple: the pg_statistic entry for the variable, if one exists;
    4710             :  *      otherwise NULL.
    4711             :  *  freefunc: pointer to a function to release statsTuple with.
    4712             :  *  vartype: exposed type of the expression; this should always match
    4713             :  *      the declared input type of the operator we are estimating for.
    4714             :  *  atttype, atttypmod: actual type/typmod of the "var" expression.  This is
    4715             :  *      commonly the same as the exposed type of the variable argument,
    4716             :  *      but can be different in binary-compatible-type cases.
    4717             :  *  isunique: true if we were able to match the var to a unique index or a
    4718             :  *      single-column DISTINCT clause, implying its values are unique for
    4719             :  *      this query.  (Caution: this should be trusted for statistical
    4720             :  *      purposes only, since we do not check indimmediate nor verify that
    4721             :  *      the exact same definition of equality applies.)
    4722             :  *  acl_ok: true if current user has permission to read the column(s)
    4723             :  *      underlying the pg_statistic entry.  This is consulted by
    4724             :  *      statistic_proc_security_check().
    4725             :  *
    4726             :  * Caller is responsible for doing ReleaseVariableStats() before exiting.
    4727             :  */
    4728             : void
    4729     1291968 : examine_variable(PlannerInfo *root, Node *node, int varRelid,
    4730             :                  VariableStatData *vardata)
    4731             : {
    4732             :     Node       *basenode;
    4733             :     Relids      varnos;
    4734             :     RelOptInfo *onerel;
    4735             : 
    4736             :     /* Make sure we don't return dangling pointers in vardata */
    4737     9043776 :     MemSet(vardata, 0, sizeof(VariableStatData));
    4738             : 
    4739             :     /* Save the exposed type of the expression */
    4740     1291968 :     vardata->vartype = exprType(node);
    4741             : 
    4742             :     /* Look inside any binary-compatible relabeling */
    4743             : 
    4744     1291968 :     if (IsA(node, RelabelType))
    4745       16374 :         basenode = (Node *) ((RelabelType *) node)->arg;
    4746             :     else
    4747     1275594 :         basenode = node;
    4748             : 
    4749             :     /* Fast path for a simple Var */
    4750             : 
    4751     1291968 :     if (IsA(basenode, Var) &&
    4752      303218 :         (varRelid == 0 || varRelid == ((Var *) basenode)->varno))
    4753             :     {
    4754      873254 :         Var        *var = (Var *) basenode;
    4755             : 
    4756             :         /* Set up result fields other than the stats tuple */
    4757      873254 :         vardata->var = basenode; /* return Var without relabeling */
    4758      873254 :         vardata->rel = find_base_rel(root, var->varno);
    4759      873254 :         vardata->atttype = var->vartype;
    4760      873254 :         vardata->atttypmod = var->vartypmod;
    4761      873254 :         vardata->isunique = has_unique_index(vardata->rel, var->varattno);
    4762             : 
    4763             :         /* Try to locate some stats */
    4764      873254 :         examine_simple_variable(root, var, vardata);
    4765             : 
    4766      873254 :         return;
    4767             :     }
    4768             : 
    4769             :     /*
    4770             :      * Okay, it's a more complicated expression.  Determine variable
    4771             :      * membership.  Note that when varRelid isn't zero, only vars of that
    4772             :      * relation are considered "real" vars.
    4773             :      */
    4774      418714 :     varnos = pull_varnos(root, basenode);
    4775             : 
    4776      418714 :     onerel = NULL;
    4777             : 
    4778      418714 :     switch (bms_membership(varnos))
    4779             :     {
    4780      251388 :         case BMS_EMPTY_SET:
    4781             :             /* No Vars at all ... must be pseudo-constant clause */
    4782      251388 :             break;
    4783      163578 :         case BMS_SINGLETON:
    4784      163578 :             if (varRelid == 0 || bms_is_member(varRelid, varnos))
    4785             :             {
    4786       28668 :                 onerel = find_base_rel(root,
    4787       13532 :                                        (varRelid ? varRelid : bms_singleton_member(varnos)));
    4788       15136 :                 vardata->rel = onerel;
    4789       15136 :                 node = basenode;    /* strip any relabeling */
    4790             :             }
    4791             :             /* else treat it as a constant */
    4792      163578 :             break;
    4793        3748 :         case BMS_MULTIPLE:
    4794        3748 :             if (varRelid == 0)
    4795             :             {
    4796             :                 /* treat it as a variable of a join relation */
    4797        3584 :                 vardata->rel = find_join_rel(root, varnos);
    4798        3584 :                 node = basenode;    /* strip any relabeling */
    4799             :             }
    4800         164 :             else if (bms_is_member(varRelid, varnos))
    4801             :             {
    4802             :                 /* ignore the vars belonging to other relations */
    4803          48 :                 vardata->rel = find_base_rel(root, varRelid);
    4804          48 :                 node = basenode;    /* strip any relabeling */
    4805             :                 /* note: no point in expressional-index search here */
    4806             :             }
    4807             :             /* else treat it as a constant */
    4808        3748 :             break;
    4809             :     }
    4810             : 
    4811      418714 :     bms_free(varnos);
    4812             : 
    4813      418714 :     vardata->var = node;
    4814      418714 :     vardata->atttype = exprType(node);
    4815      418714 :     vardata->atttypmod = exprTypmod(node);
    4816             : 
    4817      418714 :     if (onerel)
    4818             :     {
    4819             :         /*
    4820             :          * We have an expression in vars of a single relation.  Try to match
    4821             :          * it to expressional index columns, in hopes of finding some
    4822             :          * statistics.
    4823             :          *
    4824             :          * Note that we consider all index columns including INCLUDE columns,
    4825             :          * since there could be stats for such columns.  But the test for
    4826             :          * uniqueness needs to be warier.
    4827             :          *
    4828             :          * XXX it's conceivable that there are multiple matches with different
    4829             :          * index opfamilies; if so, we need to pick one that matches the
    4830             :          * operator we are estimating for.  FIXME later.
    4831             :          */
    4832             :         ListCell   *ilist;
    4833             : 
    4834       24538 :         foreach(ilist, onerel->indexlist)
    4835             :         {
    4836       11270 :             IndexOptInfo *index = (IndexOptInfo *) lfirst(ilist);
    4837             :             ListCell   *indexpr_item;
    4838             :             int         pos;
    4839             : 
    4840       11270 :             indexpr_item = list_head(index->indexprs);
    4841       11270 :             if (indexpr_item == NULL)
    4842        8198 :                 continue;       /* no expressions here... */
    4843             : 
    4844        4324 :             for (pos = 0; pos < index->ncolumns; pos++)
    4845             :             {
    4846        3120 :                 if (index->indexkeys[pos] == 0)
    4847             :                 {
    4848             :                     Node       *indexkey;
    4849             : 
    4850        3072 :                     if (indexpr_item == NULL)
    4851           0 :                         elog(ERROR, "too few entries in indexprs list");
    4852        3072 :                     indexkey = (Node *) lfirst(indexpr_item);
    4853        3072 :                     if (indexkey && IsA(indexkey, RelabelType))
    4854           0 :                         indexkey = (Node *) ((RelabelType *) indexkey)->arg;
    4855        3072 :                     if (equal(node, indexkey))
    4856             :                     {
    4857             :                         /*
    4858             :                          * Found a match ... is it a unique index? Tests here
    4859             :                          * should match has_unique_index().
    4860             :                          */
    4861        2252 :                         if (index->unique &&
    4862         260 :                             index->nkeycolumns == 1 &&
    4863         260 :                             pos == 0 &&
    4864         260 :                             (index->indpred == NIL || index->predOK))
    4865         260 :                             vardata->isunique = true;
    4866             : 
    4867             :                         /*
    4868             :                          * Has it got stats?  We only consider stats for
    4869             :                          * non-partial indexes, since partial indexes probably
    4870             :                          * don't reflect whole-relation statistics; the above
    4871             :                          * check for uniqueness is the only info we take from
    4872             :                          * a partial index.
    4873             :                          *
    4874             :                          * An index stats hook, however, must make its own
    4875             :                          * decisions about what to do with partial indexes.
    4876             :                          */
    4877        2252 :                         if (get_index_stats_hook &&
    4878           0 :                             (*get_index_stats_hook) (root, index->indexoid,
    4879           0 :                                                      pos + 1, vardata))
    4880             :                         {
    4881             :                             /*
    4882             :                              * The hook took control of acquiring a stats
    4883             :                              * tuple.  If it did supply a tuple, it'd better
    4884             :                              * have supplied a freefunc.
    4885             :                              */
    4886           0 :                             if (HeapTupleIsValid(vardata->statsTuple) &&
    4887           0 :                                 !vardata->freefunc)
    4888           0 :                                 elog(ERROR, "no function provided to release variable stats with");
    4889             :                         }
    4890        2252 :                         else if (index->indpred == NIL)
    4891             :                         {
    4892        2252 :                             vardata->statsTuple =
    4893        4504 :                                 SearchSysCache3(STATRELATTINH,
    4894        2252 :                                                 ObjectIdGetDatum(index->indexoid),
    4895        2252 :                                                 Int16GetDatum(pos + 1),
    4896             :                                                 BoolGetDatum(false));
    4897        2252 :                             vardata->freefunc = ReleaseSysCache;
    4898             : 
    4899        2252 :                             if (HeapTupleIsValid(vardata->statsTuple))
    4900             :                             {
    4901             :                                 /* Get index's table for permission check */
    4902             :                                 RangeTblEntry *rte;
    4903             :                                 Oid         userid;
    4904             : 
    4905        1868 :                                 rte = planner_rt_fetch(index->rel->relid, root);
    4906             :                                 Assert(rte->rtekind == RTE_RELATION);
    4907             : 
    4908             :                                 /*
    4909             :                                  * Use checkAsUser if it's set, in case we're
    4910             :                                  * accessing the table via a view.
    4911             :                                  */
    4912        1868 :                                 userid = rte->checkAsUser ? rte->checkAsUser : GetUserId();
    4913             : 
    4914             :                                 /*
    4915             :                                  * For simplicity, we insist on the whole
    4916             :                                  * table being selectable, rather than trying
    4917             :                                  * to identify which column(s) the index
    4918             :                                  * depends on.  Also require all rows to be
    4919             :                                  * selectable --- there must be no
    4920             :                                  * securityQuals from security barrier views
    4921             :                                  * or RLS policies.
    4922             :                                  */
    4923        1868 :                                 vardata->acl_ok =
    4924        3736 :                                     rte->securityQuals == NIL &&
    4925        1868 :                                     (pg_class_aclcheck(rte->relid, userid,
    4926             :                                                        ACL_SELECT) == ACLCHECK_OK);
    4927             : 
    4928             :                                 /*
    4929             :                                  * If the user doesn't have permissions to
    4930             :                                  * access an inheritance child relation, check
    4931             :                                  * the permissions of the table actually
    4932             :                                  * mentioned in the query, since most likely
    4933             :                                  * the user does have that permission.  Note
    4934             :                                  * that whole-table select privilege on the
    4935             :                                  * parent doesn't quite guarantee that the
    4936             :                                  * user could read all columns of the child.
    4937             :                                  * But in practice it's unlikely that any
    4938             :                                  * interesting security violation could result
    4939             :                                  * from allowing access to the expression
    4940             :                                  * index's stats, so we allow it anyway.  See
    4941             :                                  * similar code in examine_simple_variable()
    4942             :                                  * for additional comments.
    4943             :                                  */
    4944        1868 :                                 if (!vardata->acl_ok &&
    4945          12 :                                     root->append_rel_array != NULL)
    4946             :                                 {
    4947             :                                     AppendRelInfo *appinfo;
    4948           8 :                                     Index       varno = index->rel->relid;
    4949             : 
    4950           8 :                                     appinfo = root->append_rel_array[varno];
    4951          24 :                                     while (appinfo &&
    4952          16 :                                            planner_rt_fetch(appinfo->parent_relid,
    4953          16 :                                                             root)->rtekind == RTE_RELATION)
    4954             :                                     {
    4955          16 :                                         varno = appinfo->parent_relid;
    4956          16 :                                         appinfo = root->append_rel_array[varno];
    4957             :                                     }
    4958           8 :                                     if (varno != index->rel->relid)
    4959             :                                     {
    4960             :                                         /* Repeat access check on this rel */
    4961           8 :                                         rte = planner_rt_fetch(varno, root);
    4962             :                                         Assert(rte->rtekind == RTE_RELATION);
    4963             : 
    4964           8 :                                         userid = rte->checkAsUser ? rte->checkAsUser : GetUserId();
    4965             : 
    4966           8 :                                         vardata->acl_ok =
    4967          16 :                                             rte->securityQuals == NIL &&
    4968           8 :                                             (pg_class_aclcheck(rte->relid,
    4969             :                                                                userid,
    4970             :                                                                ACL_SELECT) == ACLCHECK_OK);
    4971             :                                     }
    4972             :                                 }
    4973             :                             }
    4974             :                             else
    4975             :                             {
    4976             :                                 /* suppress leakproofness checks later */
    4977         384 :                                 vardata->acl_ok = true;
    4978             :                             }
    4979             :                         }
    4980        2252 :                         if (vardata->statsTuple)
    4981        1868 :                             break;
    4982             :                     }
    4983        1204 :                     indexpr_item = lnext(index->indexprs, indexpr_item);
    4984             :                 }
    4985             :             }
    4986        3072 :             if (vardata->statsTuple)
    4987        1868 :                 break;
    4988             :         }
    4989             :     }
    4990             : }
    4991             : 
    4992             : /*
    4993             :  * examine_simple_variable
    4994             :  *      Handle a simple Var for examine_variable
    4995             :  *
    4996             :  * This is split out as a subroutine so that we can recurse to deal with
    4997             :  * Vars referencing subqueries.
    4998             :  *
    4999             :  * We already filled in all the fields of *vardata except for the stats tuple.
    5000             :  */
    5001             : static void
    5002      873998 : examine_simple_variable(PlannerInfo *root, Var *var,
    5003             :                         VariableStatData *vardata)
    5004             : {
    5005      873998 :     RangeTblEntry *rte = root->simple_rte_array[var->varno];
    5006             : 
    5007             :     Assert(IsA(rte, RangeTblEntry));
    5008             : 
    5009      873998 :     if (get_relation_stats_hook &&
    5010           0 :         (*get_relation_stats_hook) (root, rte, var->varattno, vardata))
    5011             :     {
    5012             :         /*
    5013             :          * The hook took control of acquiring a stats tuple.  If it did supply
    5014             :          * a tuple, it'd better have supplied a freefunc.
    5015             :          */
    5016           0 :         if (HeapTupleIsValid(vardata->statsTuple) &&
    5017           0 :             !vardata->freefunc)
    5018           0 :             elog(ERROR, "no function provided to release variable stats with");
    5019             :     }
    5020      873998 :     else if (rte->rtekind == RTE_RELATION)
    5021             :     {
    5022             :         /*
    5023             :          * Plain table or parent of an inheritance appendrel, so look up the
    5024             :          * column in pg_statistic
    5025             :          */
    5026      820212 :         vardata->statsTuple = SearchSysCache3(STATRELATTINH,
    5027      820212 :                                               ObjectIdGetDatum(rte->relid),
    5028      820212 :                                               Int16GetDatum(var->varattno),
    5029      820212 :                                               BoolGetDatum(rte->inh));
    5030      820212 :         vardata->freefunc = ReleaseSysCache;
    5031             : 
    5032      820212 :         if (HeapTupleIsValid(vardata->statsTuple))
    5033             :         {
    5034             :             Oid         userid;
    5035             : 
    5036             :             /*
    5037             :              * Check if user has permission to read this column.  We require
    5038             :              * all rows to be accessible, so there must be no securityQuals
    5039             :              * from security barrier views or RLS policies.  Use checkAsUser
    5040             :              * if it's set, in case we're accessing the table via a view.
    5041             :              */
    5042      638908 :             userid = rte->checkAsUser ? rte->checkAsUser : GetUserId();
    5043             : 
    5044      638908 :             vardata->acl_ok =
    5045     1277692 :                 rte->securityQuals == NIL &&
    5046      638608 :                 ((pg_class_aclcheck(rte->relid, userid,
    5047         176 :                                     ACL_SELECT) == ACLCHECK_OK) ||
    5048         176 :                  (pg_attribute_aclcheck(rte->relid, var->varattno, userid,
    5049             :                                         ACL_SELECT) == ACLCHECK_OK));
    5050             : 
    5051             :             /*
    5052             :              * If the user doesn't have permissions to access an inheritance
    5053             :              * child relation or specifically this attribute, check the
    5054             :              * permissions of the table/column actually mentioned in the
    5055             :              * query, since most likely the user does have that permission
    5056             :              * (else the query will fail at runtime), and if the user can read
    5057             :              * the column there then he can get the values of the child table
    5058             :              * too.  To do that, we must find out which of the root parent's
    5059             :              * attributes the child relation's attribute corresponds to.
    5060             :              */
    5061      638908 :             if (!vardata->acl_ok && var->varattno > 0 &&
    5062         328 :                 root->append_rel_array != NULL)
    5063             :             {
    5064             :                 AppendRelInfo *appinfo;
    5065           8 :                 Index       varno = var->varno;
    5066           8 :                 int         varattno = var->varattno;
    5067           8 :                 bool        found = false;
    5068             : 
    5069           8 :                 appinfo = root->append_rel_array[varno];
    5070             : 
    5071             :                 /*
    5072             :                  * Partitions are mapped to their immediate parent, not the
    5073             :                  * root parent, so must be ready to walk up multiple
    5074             :                  * AppendRelInfos.  But stop if we hit a parent that is not
    5075             :                  * RTE_RELATION --- that's a flattened UNION ALL subquery, not
    5076             :                  * an inheritance parent.
    5077             :                  */
    5078          24 :                 while (appinfo &&
    5079          16 :                        planner_rt_fetch(appinfo->parent_relid,
    5080          16 :                                         root)->rtekind == RTE_RELATION)
    5081             :                 {
    5082             :                     int         parent_varattno;
    5083             : 
    5084          16 :                     found = false;
    5085          16 :                     if (varattno <= 0 || varattno > appinfo->num_child_cols)
    5086             :                         break;  /* safety check */
    5087          16 :                     parent_varattno = appinfo->parent_colnos[varattno - 1];
    5088          16 :                     if (parent_varattno == 0)
    5089           0 :                         break;  /* Var is local to child */
    5090             : 
    5091          16 :                     varno = appinfo->parent_relid;
    5092          16 :                     varattno = parent_varattno;
    5093          16 :                     found = true;
    5094             : 
    5095             :                     /* If the parent is itself a child, continue up. */
    5096          16 :                     appinfo = root->append_rel_array[varno];
    5097             :                 }
    5098             : 
    5099             :                 /*
    5100             :                  * In rare cases, the Var may be local to the child table, in
    5101             :                  * which case, we've got to live with having no access to this
    5102             :                  * column's stats.
    5103             :                  */
    5104           8 :                 if (!found)
    5105           0 :                     return;
    5106             : 
    5107             :                 /* Repeat the access check on this parent rel & column */
    5108           8 :                 rte = planner_rt_fetch(varno, root);
    5109             :                 Assert(rte->rtekind == RTE_RELATION);
    5110             : 
    5111           8 :                 userid = rte->checkAsUser ? rte->checkAsUser : GetUserId();
    5112             : 
    5113           8 :                 vardata->acl_ok =
    5114          20 :                     rte->securityQuals == NIL &&
    5115           8 :                     ((pg_class_aclcheck(rte->relid, userid,
    5116           4 :                                         ACL_SELECT) == ACLCHECK_OK) ||
    5117           4 :                      (pg_attribute_aclcheck(rte->relid, varattno, userid,
    5118             :                                             ACL_SELECT) == ACLCHECK_OK));
    5119             :             }
    5120             :         }
    5121             :         else
    5122             :         {
    5123             :             /* suppress any possible leakproofness checks later */
    5124      181304 :             vardata->acl_ok = true;
    5125             :         }
    5126             :     }
    5127       53786 :     else if (rte->rtekind == RTE_SUBQUERY && !rte->inh)
    5128             :     {
    5129             :         /*
    5130             :          * Plain subquery (not one that was converted to an appendrel).
    5131             :          */
    5132        2504 :         Query      *subquery = rte->subquery;
    5133             :         RelOptInfo *rel;
    5134             :         TargetEntry *ste;
    5135             : 
    5136             :         /*
    5137             :          * Punt if it's a whole-row var rather than a plain column reference.
    5138             :          */
    5139        2504 :         if (var->varattno == InvalidAttrNumber)
    5140           0 :             return;
    5141             : 
    5142             :         /*
    5143             :          * Punt if subquery uses set operations or GROUP BY, as these will
    5144             :          * mash underlying columns' stats beyond recognition.  (Set ops are
    5145             :          * particularly nasty; if we forged ahead, we would return stats
    5146             :          * relevant to only the leftmost subselect...)  DISTINCT is also
    5147             :          * problematic, but we check that later because there is a possibility
    5148             :          * of learning something even with it.
    5149             :          */
    5150        2504 :         if (subquery->setOperations ||
    5151        2396 :             subquery->groupClause)
    5152         372 :             return;
    5153             : 
    5154             :         /*
    5155             :          * OK, fetch RelOptInfo for subquery.  Note that we don't change the
    5156             :          * rel returned in vardata, since caller expects it to be a rel of the
    5157             :          * caller's query level.  Because we might already be recursing, we
    5158             :          * can't use that rel pointer either, but have to look up the Var's
    5159             :          * rel afresh.
    5160             :          */
    5161        2132 :         rel = find_base_rel(root, var->varno);
    5162             : 
    5163             :         /* If the subquery hasn't been planned yet, we have to punt */
    5164        2132 :         if (rel->subroot == NULL)
    5165           0 :             return;
    5166             :         Assert(IsA(rel->subroot, PlannerInfo));
    5167             : 
    5168             :         /*
    5169             :          * Switch our attention to the subquery as mangled by the planner. It
    5170             :          * was okay to look at the pre-planning version for the tests above,
    5171             :          * but now we need a Var that will refer to the subroot's live
    5172             :          * RelOptInfos.  For instance, if any subquery pullup happened during
    5173             :          * planning, Vars in the targetlist might have gotten replaced, and we
    5174             :          * need to see the replacement expressions.
    5175             :          */
    5176        2132 :         subquery = rel->subroot->parse;
    5177             :         Assert(IsA(subquery, Query));
    5178             : 
    5179             :         /* Get the subquery output expression referenced by the upper Var */
    5180        2132 :         ste = get_tle_by_resno(subquery->targetList, var->varattno);
    5181        2132 :         if (ste == NULL || ste->resjunk)
    5182           0 :             elog(ERROR, "subquery %s does not have attribute %d",
    5183             :                  rte->eref->aliasname, var->varattno);
    5184        2132 :         var = (Var *) ste->expr;
    5185             : 
    5186             :         /*
    5187             :          * If subquery uses DISTINCT, we can't make use of any stats for the
    5188             :          * variable ... but, if it's the only DISTINCT column, we are entitled
    5189             :          * to consider it unique.  We do the test this way so that it works
    5190             :          * for cases involving DISTINCT ON.
    5191             :          */
    5192        2132 :         if (subquery->distinctClause)
    5193             :         {
    5194         200 :             if (list_length(subquery->distinctClause) == 1 &&
    5195          68 :                 targetIsInSortList(ste, InvalidOid, subquery->distinctClause))
    5196          68 :                 vardata->isunique = true;
    5197             :             /* cannot go further */
    5198         132 :             return;
    5199             :         }
    5200             : 
    5201             :         /*
    5202             :          * If the sub-query originated from a view with the security_barrier
    5203             :          * attribute, we must not look at the variable's statistics, though it
    5204             :          * seems all right to notice the existence of a DISTINCT clause. So
    5205             :          * stop here.
    5206             :          *
    5207             :          * This is probably a harsher restriction than necessary; it's
    5208             :          * certainly OK for the selectivity estimator (which is a C function,
    5209             :          * and therefore omnipotent anyway) to look at the statistics.  But
    5210             :          * many selectivity estimators will happily *invoke the operator
    5211             :          * function* to try to work out a good estimate - and that's not OK.
    5212             :          * So for now, don't dig down for stats.
    5213             :          */
    5214        2000 :         if (rte->security_barrier)
    5215         140 :             return;
    5216             : 
    5217             :         /* Can only handle a simple Var of subquery's query level */
    5218        1860 :         if (var && IsA(var, Var) &&
    5219         744 :             var->varlevelsup == 0)
    5220             :         {
    5221             :             /*
    5222             :              * OK, recurse into the subquery.  Note that the original setting
    5223             :              * of vardata->isunique (which will surely be false) is left
    5224             :              * unchanged in this situation.  That's what we want, since even
    5225             :              * if the underlying column is unique, the subquery may have
    5226             :              * joined to other tables in a way that creates duplicates.
    5227             :              */
    5228         744 :             examine_simple_variable(rel->subroot, var, vardata);
    5229             :         }
    5230             :     }
    5231             :     else
    5232             :     {
    5233             :         /*
    5234             :          * Otherwise, the Var comes from a FUNCTION, VALUES, or CTE RTE.  (We
    5235             :          * won't see RTE_JOIN here because join alias Vars have already been
    5236             :          * flattened.)  There's not much we can do with function outputs, but
    5237             :          * maybe someday try to be smarter about VALUES and/or CTEs.
    5238             :          */
    5239             :     }
    5240             : }
    5241             : 
    5242             : /*
    5243             :  * Check whether it is permitted to call func_oid passing some of the
    5244             :  * pg_statistic data in vardata.  We allow this either if the user has SELECT
    5245             :  * privileges on the table or column underlying the pg_statistic data or if
    5246             :  * the function is marked leak-proof.
    5247             :  */
    5248             : bool
    5249      735264 : statistic_proc_security_check(VariableStatData *vardata, Oid func_oid)
    5250             : {
    5251      735264 :     if (vardata->acl_ok)
    5252      734864 :         return true;
    5253             : 
    5254         400 :     if (!OidIsValid(func_oid))
    5255           0 :         return false;
    5256             : 
    5257         400 :     if (get_func_leakproof(func_oid))
    5258         288 :         return true;
    5259             : 
    5260         112 :     ereport(DEBUG2,
    5261             :             (errmsg_internal("not using statistics because function \"%s\" is not leak-proof",
    5262             :                              get_func_name(func_oid))));
    5263         112 :     return false;
    5264             : }
    5265             : 
    5266             : /*
    5267             :  * get_variable_numdistinct
    5268             :  *    Estimate the number of distinct values of a variable.
    5269             :  *
    5270             :  * vardata: results of examine_variable
    5271             :  * *isdefault: set to true if the result is a default rather than based on
    5272             :  * anything meaningful.
    5273             :  *
    5274             :  * NB: be careful to produce a positive integral result, since callers may
    5275             :  * compare the result to exact integer counts, or might divide by it.
    5276             :  */
    5277             : double
    5278      560604 : get_variable_numdistinct(VariableStatData *vardata, bool *isdefault)
    5279             : {
    5280             :     double      stadistinct;
    5281      560604 :     double      stanullfrac = 0.0;
    5282             :     double      ntuples;
    5283             : 
    5284      560604 :     *isdefault = false;
    5285             : 
    5286             :     /*
    5287             :      * Determine the stadistinct value to use.  There are cases where we can
    5288             :      * get an estimate even without a pg_statistic entry, or can get a better
    5289             :      * value than is in pg_statistic.  Grab stanullfrac too if we can find it
    5290             :      * (otherwise, assume no nulls, for lack of any better idea).
    5291             :      */
    5292      560604 :     if (HeapTupleIsValid(vardata->statsTuple))
    5293             :     {
    5294             :         /* Use the pg_statistic entry */
    5295             :         Form_pg_statistic stats;
    5296             : 
    5297      391916 :         stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
    5298      391916 :         stadistinct = stats->stadistinct;
    5299      391916 :         stanullfrac = stats->stanullfrac;
    5300             :     }
    5301      168688 :     else if (vardata->vartype == BOOLOID)
    5302             :     {
    5303             :         /*
    5304             :          * Special-case boolean columns: presumably, two distinct values.
    5305             :          *
    5306             :          * Are there any other datatypes we should wire in special estimates
    5307             :          * for?
    5308             :          */
    5309         140 :         stadistinct = 2.0;
    5310             :     }
    5311      168548 :     else if (vardata->rel && vardata->rel->rtekind == RTE_VALUES)
    5312             :     {
    5313             :         /*
    5314             :          * If the Var represents a column of a VALUES RTE, assume it's unique.
    5315             :          * This could of course be very wrong, but it should tend to be true
    5316             :          * in well-written queries.  We could consider examining the VALUES'
    5317             :          * contents to get some real statistics; but that only works if the
    5318             :          * entries are all constants, and it would be pretty expensive anyway.
    5319             :          */
    5320         858 :         stadistinct = -1.0;     /* unique (and all non null) */
    5321             :     }
    5322             :     else
    5323             :     {
    5324             :         /*
    5325             :          * We don't keep statistics for system columns, but in some cases we
    5326             :          * can infer distinctness anyway.
    5327             :          */
    5328      167690 :         if (vardata->var && IsA(vardata->var, Var))
    5329             :         {
    5330      321964 :             switch (((Var *) vardata->var)->varattno)
    5331             :             {
    5332         496 :                 case SelfItemPointerAttributeNumber:
    5333         496 :                     stadistinct = -1.0; /* unique (and all non null) */
    5334         496 :                     break;
    5335        1986 :                 case TableOidAttributeNumber:
    5336        1986 :                     stadistinct = 1.0;  /* only 1 value */
    5337        1986 :                     break;
    5338      158500 :                 default:
    5339      158500 :                     stadistinct = 0.0;  /* means "unknown" */
    5340      158500 :                     break;
    5341             :             }
    5342             :         }
    5343             :         else
    5344        6708 :             stadistinct = 0.0;  /* means "unknown" */
    5345             : 
    5346             :         /*
    5347             :          * XXX consider using estimate_num_groups on expressions?
    5348             :          */
    5349             :     }
    5350             : 
    5351             :     /*
    5352             :      * If there is a unique index or DISTINCT clause for the variable, assume
    5353             :      * it is unique no matter what pg_statistic says; the statistics could be
    5354             :      * out of date, or we might have found a partial unique index that proves
    5355             :      * the var is unique for this query.  However, we'd better still believe
    5356             :      * the null-fraction statistic.
    5357             :      */
    5358      560604 :     if (vardata->isunique)
    5359      123528 :         stadistinct = -1.0 * (1.0 - stanullfrac);
    5360             : 
    5361             :     /*
    5362             :      * If we had an absolute estimate, use that.
    5363             :      */
    5364      560604 :     if (stadistinct > 0.0)
    5365       99778 :         return clamp_row_est(stadistinct);
    5366             : 
    5367             :     /*
    5368             :      * Otherwise we need to get the relation size; punt if not available.
    5369             :      */
    5370      460826 :     if (vardata->rel == NULL)
    5371             :     {
    5372         162 :         *isdefault = true;
    5373         162 :         return DEFAULT_NUM_DISTINCT;
    5374             :     }
    5375      460664 :     ntuples = vardata->rel->tuples;
    5376      460664 :     if (ntuples <= 0.0)
    5377             :     {
    5378        8956 :         *isdefault = true;
    5379        8956 :         return DEFAULT_NUM_DISTINCT;
    5380             :     }
    5381             : 
    5382             :     /*
    5383             :      * If we had a relative estimate, use that.
    5384             :      */
    5385      451708 :     if (stadistinct < 0.0)
    5386      309154 :         return clamp_row_est(-stadistinct * ntuples);
    5387             : 
    5388             :     /*
    5389             :      * With no data, estimate ndistinct = ntuples if the table is small, else
    5390             :      * use default.  We use DEFAULT_NUM_DISTINCT as the cutoff for "small" so
    5391             :      * that the behavior isn't discontinuous.
    5392             :      */
    5393      142554 :     if (ntuples < DEFAULT_NUM_DISTINCT)
    5394       71282 :         return clamp_row_est(ntuples);
    5395             : 
    5396       71272 :     *isdefault = true;
    5397       71272 :     return DEFAULT_NUM_DISTINCT;
    5398             : }
    5399             : 
    5400             : /*
    5401             :  * get_variable_range
    5402             :  *      Estimate the minimum and maximum value of the specified variable.
    5403             :  *      If successful, store values in *min and *max, and return true.
    5404             :  *      If no data available, return false.
    5405             :  *
    5406             :  * sortop is the "<" comparison operator to use.  This should generally
    5407             :  * be "<" not ">", as only the former is likely to be found in pg_statistic.
    5408             :  * The collation must be specified too.
    5409             :  */
    5410             : static bool
    5411      104276 : get_variable_range(PlannerInfo *root, VariableStatData *vardata,
    5412             :                    Oid sortop, Oid collation,
    5413             :                    Datum *min, Datum *max)
    5414             : {
    5415      104276 :     Datum       tmin = 0;
    5416      104276 :     Datum       tmax = 0;
    5417      104276 :     bool        have_data = false;
    5418             :     int16       typLen;
    5419             :     bool        typByVal;
    5420             :     Oid         opfuncoid;
    5421             :     FmgrInfo    opproc;
    5422             :     AttStatsSlot sslot;
    5423             : 
    5424             :     /*
    5425             :      * XXX It's very tempting to try to use the actual column min and max, if
    5426             :      * we can get them relatively-cheaply with an index probe.  However, since
    5427             :      * this function is called many times during join planning, that could
    5428             :      * have unpleasant effects on planning speed.  Need more investigation
    5429             :      * before enabling this.
    5430             :      */
    5431             : #ifdef NOT_USED
    5432             :     if (get_actual_variable_range(root, vardata, sortop, collation, min, max))
    5433             :         return true;
    5434             : #endif
    5435             : 
    5436      104276 :     if (!HeapTupleIsValid(vardata->statsTuple))
    5437             :     {
    5438             :         /* no stats available, so default result */
    5439       16904 :         return false;
    5440             :     }
    5441             : 
    5442             :     /*
    5443             :      * If we can't apply the sortop to the stats data, just fail.  In
    5444             :      * principle, if there's a histogram and no MCVs, we could return the
    5445             :      * histogram endpoints without ever applying the sortop ... but it's
    5446             :      * probably not worth trying, because whatever the caller wants to do with
    5447             :      * the endpoints would likely fail the security check too.
    5448             :      */
    5449       87372 :     if (!statistic_proc_security_check(vardata,
    5450       87372 :                                        (opfuncoid = get_opcode(sortop))))
    5451           0 :         return false;
    5452             : 
    5453       87372 :     opproc.fn_oid = InvalidOid; /* mark this as not looked up yet */
    5454             : 
    5455       87372 :     get_typlenbyval(vardata->atttype, &typLen, &typByVal);
    5456             : 
    5457             :     /*
    5458             :      * If there is a histogram with the ordering we want, grab the first and
    5459             :      * last values.
    5460             :      */
    5461       87372 :     if (get_attstatsslot(&sslot, vardata->statsTuple,
    5462             :                          STATISTIC_KIND_HISTOGRAM, sortop,
    5463             :                          ATTSTATSSLOT_VALUES))
    5464             :     {
    5465       72312 :         if (sslot.stacoll == collation && sslot.nvalues > 0)
    5466             :         {
    5467       72312 :             tmin = datumCopy(sslot.values[0], typByVal, typLen);
    5468       72312 :             tmax = datumCopy(sslot.values[sslot.nvalues - 1], typByVal, typLen);
    5469       72312 :             have_data = true;
    5470             :         }
    5471       72312 :         free_attstatsslot(&sslot);
    5472             :     }
    5473             : 
    5474             :     /*
    5475             :      * Otherwise, if there is a histogram with some other ordering, scan it
    5476             :      * and get the min and max values according to the ordering we want.  This
    5477             :      * of course may not find values that are really extremal according to our
    5478             :      * ordering, but it beats ignoring available data.
    5479             :      */
    5480      102432 :     if (!have_data &&
    5481       15060 :         get_attstatsslot(&sslot, vardata->statsTuple,
    5482             :                          STATISTIC_KIND_HISTOGRAM, InvalidOid,
    5483             :                          ATTSTATSSLOT_VALUES))
    5484             :     {
    5485           0 :         get_stats_slot_range(&sslot, opfuncoid, &opproc,
    5486             :                              collation, typLen, typByVal,
    5487             :                              &tmin, &tmax, &have_data);
    5488           0 :         free_attstatsslot(&sslot);
    5489             :     }
    5490             : 
    5491             :     /*
    5492             :      * If we have most-common-values info, look for extreme MCVs.  This is
    5493             :      * needed even if we also have a histogram, since the histogram excludes
    5494             :      * the MCVs.
    5495             :      */
    5496       87372 :     if (get_attstatsslot(&sslot, vardata->statsTuple,
    5497             :                          STATISTIC_KIND_MCV, InvalidOid,
    5498             :                          ATTSTATSSLOT_VALUES))
    5499             :     {
    5500       41190 :         get_stats_slot_range(&sslot, opfuncoid, &opproc,
    5501             :                              collation, typLen, typByVal,
    5502             :                              &tmin, &tmax, &have_data);
    5503       41190 :         free_attstatsslot(&sslot);
    5504             :     }
    5505             : 
    5506       87372 :     *min = tmin;
    5507       87372 :     *max = tmax;
    5508       87372 :     return have_data;
    5509             : }
    5510             : 
    5511             : /*
    5512             :  * get_stats_slot_range: scan sslot for min/max values
    5513             :  *
    5514             :  * Subroutine for get_variable_range: update min/max/have_data according
    5515             :  * to what we find in the statistics array.
    5516             :  */
    5517             : static void
    5518       41190 : get_stats_slot_range(AttStatsSlot *sslot, Oid opfuncoid, FmgrInfo *opproc,
    5519             :                      Oid collation, int16 typLen, bool typByVal,
    5520             :                      Datum *min, Datum *max, bool *p_have_data)
    5521             : {
    5522       41190 :     Datum       tmin = *min;
    5523       41190 :     Datum       tmax = *max;
    5524       41190 :     bool        have_data = *p_have_data;
    5525       41190 :     bool        found_tmin = false;
    5526       41190 :     bool        found_tmax = false;
    5527             : 
    5528             :     /* Look up the comparison function, if we didn't already do so */
    5529       41190 :     if (opproc->fn_oid != opfuncoid)
    5530       41190 :         fmgr_info(opfuncoid, opproc);
    5531             : 
    5532             :     /* Scan all the slot's values */
    5533     1387170 :     for (int i = 0; i < sslot->nvalues; i++)
    5534             :     {
    5535     1345980 :         if (!have_data)
    5536             :         {
    5537       14572 :             tmin = tmax = sslot->values[i];
    5538       14572 :             found_tmin = found_tmax = true;
    5539       14572 :             *p_have_data = have_data = true;
    5540       14572 :             continue;
    5541             :         }
    5542     1331408 :         if (DatumGetBool(FunctionCall2Coll(opproc,
    5543             :                                            collation,
    5544             :                                            sslot->values[i], tmin)))
    5545             :         {
    5546       38028 :             tmin = sslot->values[i];
    5547       38028 :             found_tmin = true;
    5548             :         }
    5549     1331408 :         if (DatumGetBool(FunctionCall2Coll(opproc,
    5550             :                                            collation,
    5551             :                                            tmax, sslot->values[i])))
    5552             :         {
    5553       43808 :             tmax = sslot->values[i];
    5554       43808 :             found_tmax = true;
    5555             :         }
    5556             :     }
    5557             : 
    5558             :     /*
    5559             :      * Copy the slot's values, if we found new extreme values.
    5560             :      */
    5561       41190 :     if (found_tmin)
    5562       32658 :         *min = datumCopy(tmin, typByVal, typLen);
    5563       41190 :     if (found_tmax)
    5564       17984 :         *max = datumCopy(tmax, typByVal, typLen);
    5565       41190 : }
    5566             : 
    5567             : 
    5568             : /*
    5569             :  * get_actual_variable_range
    5570             :  *      Attempt to identify the current *actual* minimum and/or maximum
    5571             :  *      of the specified variable, by looking for a suitable btree index
    5572             :  *      and fetching its low and/or high values.
    5573             :  *      If successful, store values in *min and *max, and return true.
    5574             :  *      (Either pointer can be NULL if that endpoint isn't needed.)
    5575             :  *      If no data available, return false.
    5576             :  *
    5577             :  * sortop is the "<" comparison operator to use.
    5578             :  * collation is the required collation.
    5579             :  */
    5580             : static bool
    5581      125236 : get_actual_variable_range(PlannerInfo *root, VariableStatData *vardata,
    5582             :                           Oid sortop, Oid collation,
    5583             :                           Datum *min, Datum *max)
    5584             : {
    5585      125236 :     bool        have_data = false;
    5586      125236 :     RelOptInfo *rel = vardata->rel;
    5587             :     RangeTblEntry *rte;
    5588             :     ListCell   *lc;
    5589             : 
    5590             :     /* No hope if no relation or it doesn't have indexes */
    5591      125236 :     if (rel == NULL || rel->indexlist == NIL)
    5592        9054 :         return false;
    5593             :     /* If it has indexes it must be a plain relation */
    5594      116182 :     rte = root->simple_rte_array[rel->relid];
    5595             :     Assert(rte->rtekind == RTE_RELATION);
    5596             : 
    5597             :     /* Search through the indexes to see if any match our problem */
    5598      247500 :     foreach(lc, rel->indexlist)
    5599             :     {
    5600      209574 :         IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);
    5601             :         ScanDirection indexscandir;
    5602             : 
    5603             :         /* Ignore non-btree indexes */
    5604      209574 :         if (index->relam != BTREE_AM_OID)
    5605           0 :             continue;
    5606             : 
    5607             :         /*
    5608             :          * Ignore partial indexes --- we only want stats that cover the entire
    5609             :          * relation.
    5610             :          */
    5611      209574 :         if (index->indpred != NIL)
    5612         132 :             continue;
    5613             : 
    5614             :         /*
    5615             :          * The index list might include hypothetical indexes inserted by a
    5616             :          * get_relation_info hook --- don't try to access them.
    5617             :          */
    5618      209442 :         if (index->hypothetical)
    5619           0 :             continue;
    5620             : 
    5621             :         /*
    5622             :          * The first index column must match the desired variable, sortop, and
    5623             :          * collation --- but we can use a descending-order index.
    5624             :          */
    5625      209442 :         if (collation != index->indexcollations[0])
    5626       34930 :             continue;           /* test first 'cause it's cheapest */
    5627      174512 :         if (!match_index_to_operand(vardata->var, 0, index))
    5628       96256 :             continue;
    5629       78256 :         switch (get_op_opfamily_strategy(sortop, index->sortopfamily[0]))
    5630             :         {
    5631       78256 :             case BTLessStrategyNumber:
    5632       78256 :                 if (index->reverse_sort[0])
    5633           0 :                     indexscandir = BackwardScanDirection;
    5634             :                 else
    5635       78256 :                     indexscandir = ForwardScanDirection;
    5636       78256 :                 break;
    5637           0 :             case BTGreaterStrategyNumber:
    5638           0 :                 if (index->reverse_sort[0])
    5639           0 :                     indexscandir = ForwardScanDirection;
    5640             :                 else
    5641           0 :                     indexscandir = BackwardScanDirection;
    5642           0 :                 break;
    5643           0 :             default:
    5644             :                 /* index doesn't match the sortop */
    5645           0 :                 continue;
    5646             :         }
    5647             : 
    5648             :         /*
    5649             :          * Found a suitable index to extract data from.  Set up some data that
    5650             :          * can be used by both invocations of get_actual_variable_endpoint.
    5651             :          */
    5652             :         {
    5653             :             MemoryContext tmpcontext;
    5654             :             MemoryContext oldcontext;
    5655             :             Relation    heapRel;
    5656             :             Relation    indexRel;
    5657             :             TupleTableSlot *slot;
    5658             :             int16       typLen;
    5659             :             bool        typByVal;
    5660             :             ScanKeyData scankeys[1];
    5661             : 
    5662             :             /* Make sure any cruft gets recycled when we're done */
    5663       78256 :             tmpcontext = AllocSetContextCreate(CurrentMemoryContext,
    5664             :                                                "get_actual_variable_range workspace",
    5665             :                                                ALLOCSET_DEFAULT_SIZES);
    5666       78256 :             oldcontext = MemoryContextSwitchTo(tmpcontext);
    5667             : 
    5668             :             /*
    5669             :              * Open the table and index so we can read from them.  We should
    5670             :              * already have some type of lock on each.
    5671             :              */
    5672       78256 :             heapRel = table_open(rte->relid, NoLock);
    5673       78256 :             indexRel = index_open(index->indexoid, NoLock);
    5674             : 
    5675             :             /* build some stuff needed for indexscan execution */
    5676       78256 :             slot = table_slot_create(heapRel, NULL);
    5677       78256 :             get_typlenbyval(vardata->atttype, &typLen, &typByVal);
    5678             : 
    5679             :             /* set up an IS NOT NULL scan key so that we ignore nulls */
    5680       78256 :             ScanKeyEntryInitialize(&scankeys[0],
    5681             :                                    SK_ISNULL | SK_SEARCHNOTNULL,
    5682             :                                    1,   /* index col to scan */
    5683             :                                    InvalidStrategy, /* no strategy */
    5684             :                                    InvalidOid,  /* no strategy subtype */
    5685             :                                    InvalidOid,  /* no collation */
    5686             :                                    InvalidOid,  /* no reg proc for this */
    5687             :                                    (Datum) 0);  /* constant */
    5688             : 
    5689             :             /* If min is requested ... */
    5690       78256 :             if (min)
    5691             :             {
    5692       46652 :                 have_data = get_actual_variable_endpoint(heapRel,
    5693             :                                                          indexRel,
    5694             :                                                          indexscandir,
    5695             :                                                          scankeys,
    5696             :                                                          typLen,
    5697             :                                                          typByVal,
    5698             :                                                          slot,
    5699             :                                                          oldcontext,
    5700             :                                                          min);
    5701             :             }
    5702             :             else
    5703             :             {
    5704             :                 /* If min not requested, assume index is nonempty */
    5705       31604 :                 have_data = true;
    5706             :             }
    5707             : 
    5708             :             /* If max is requested, and we didn't find the index is empty */
    5709       78256 :             if (max && have_data)
    5710             :             {
    5711             :                 /* scan in the opposite direction; all else is the same */
    5712       63736 :                 have_data = get_actual_variable_endpoint(heapRel,
    5713             :                                                          indexRel,
    5714       31868 :                                                          -indexscandir,
    5715             :                                                          scankeys,
    5716             :                                                          typLen,
    5717             :                                                          typByVal,
    5718             :                                                          slot,
    5719             :                                                          oldcontext,
    5720             :                                                          max);
    5721             :             }
    5722             : 
    5723             :             /* Clean everything up */
    5724       78256 :             ExecDropSingleTupleTableSlot(slot);
    5725             : 
    5726       78256 :             index_close(indexRel, NoLock);
    5727       78256 :             table_close(heapRel, NoLock);
    5728             : 
    5729       78256 :             MemoryContextSwitchTo(oldcontext);
    5730       78256 :             MemoryContextDelete(tmpcontext);
    5731             : 
    5732             :             /* And we're done */
    5733       78256 :             break;
    5734             :         }
    5735             :     }
    5736             : 
    5737      116182 :     return have_data;
    5738             : }
    5739             : 
    5740             : /*
    5741             :  * Get one endpoint datum (min or max depending on indexscandir) from the
    5742             :  * specified index.  Return true if successful, false if index is empty.
    5743             :  * On success, endpoint value is stored to *endpointDatum (and copied into
    5744             :  * outercontext).
    5745             :  *
    5746             :  * scankeys is a 1-element scankey array set up to reject nulls.
    5747             :  * typLen/typByVal describe the datatype of the index's first column.
    5748             :  * tableslot is a slot suitable to hold table tuples, in case we need
    5749             :  * to probe the heap.
    5750             :  * (We could compute these values locally, but that would mean computing them
    5751             :  * twice when get_actual_variable_range needs both the min and the max.)
    5752             :  */
    5753             : static bool
    5754       78520 : get_actual_variable_endpoint(Relation heapRel,
    5755             :                              Relation indexRel,
    5756             :                              ScanDirection indexscandir,
    5757             :                              ScanKey scankeys,
    5758             :                              int16 typLen,
    5759             :                              bool typByVal,
    5760             :                              TupleTableSlot *tableslot,
    5761             :                              MemoryContext outercontext,
    5762             :                              Datum *endpointDatum)
    5763             : {
    5764       78520 :     bool        have_data = false;
    5765             :     SnapshotData SnapshotNonVacuumable;
    5766             :     IndexScanDesc index_scan;
    5767       78520 :     Buffer      vmbuffer = InvalidBuffer;
    5768             :     ItemPointer tid;
    5769             :     Datum       values[INDEX_MAX_KEYS];
    5770             :     bool        isnull[INDEX_MAX_KEYS];
    5771             :     MemoryContext oldcontext;
    5772             : 
    5773             :     /*
    5774             :      * We use the index-only-scan machinery for this.  With mostly-static
    5775             :      * tables that's a win because it avoids a heap visit.  It's also a win
    5776             :      * for dynamic data, but the reason is less obvious; read on for details.
    5777             :      *
    5778             :      * In principle, we should scan the index with our current active
    5779             :      * snapshot, which is the best approximation we've got to what the query
    5780             :      * will see when executed.  But that won't be exact if a new snap is taken
    5781             :      * before running the query, and it can be very expensive if a lot of
    5782             :      * recently-dead or uncommitted rows exist at the beginning or end of the
    5783             :      * index (because we'll laboriously fetch each one and reject it).
    5784             :      * Instead, we use SnapshotNonVacuumable.  That will accept recently-dead
    5785             :      * and uncommitted rows as well as normal visible rows.  On the other
    5786             :      * hand, it will reject known-dead rows, and thus not give a bogus answer
    5787             :      * when the extreme value has been deleted (unless the deletion was quite
    5788             :      * recent); that case motivates not using SnapshotAny here.
    5789             :      *
    5790             :      * A crucial point here is that SnapshotNonVacuumable, with
    5791             :      * GlobalVisTestFor(heapRel) as horizon, yields the inverse of the
    5792             :      * condition that the indexscan will use to decide that index entries are
    5793             :      * killable (see heap_hot_search_buffer()).  Therefore, if the snapshot
    5794             :      * rejects a tuple (or more precisely, all tuples of a HOT chain) and we
    5795             :      * have to continue scanning past it, we know that the indexscan will mark
    5796             :      * that index entry killed.  That means that the next
    5797             :      * get_actual_variable_endpoint() call will not have to re-consider that
    5798             :      * index entry.  In this way we avoid repetitive work when this function
    5799             :      * is used a lot during planning.
    5800             :      *
    5801             :      * But using SnapshotNonVacuumable creates a hazard of its own.  In a
    5802             :      * recently-created index, some index entries may point at "broken" HOT
    5803             :      * chains in which not all the tuple versions contain data matching the
    5804             :      * index entry.  The live tuple version(s) certainly do match the index,
    5805             :      * but SnapshotNonVacuumable can accept recently-dead tuple versions that
    5806             :      * don't match.  Hence, if we took data from the selected heap tuple, we
    5807             :      * might get a bogus answer that's not close to the index extremal value,
    5808             :      * or could even be NULL.  We avoid this hazard because we take the data
    5809             :      * from the index entry not the heap.
    5810             :      */
    5811       78520 :     InitNonVacuumableSnapshot(SnapshotNonVacuumable,
    5812             :                               GlobalVisTestFor(heapRel));
    5813             : 
    5814       78520 :     index_scan = index_beginscan(heapRel, indexRel,
    5815             :                                  &SnapshotNonVacuumable,
    5816             :                                  1, 0);
    5817             :     /* Set it up for index-only scan */
    5818       78520 :     index_scan->xs_want_itup = true;
    5819       78520 :     index_rescan(index_scan, scankeys, 1, NULL, 0);
    5820             : 
    5821             :     /* Fetch first/next tuple in specified direction */
    5822       82282 :     while ((tid = index_getnext_tid(index_scan, indexscandir)) != NULL)
    5823             :     {
    5824       82282 :         if (!VM_ALL_VISIBLE(heapRel,
    5825             :                             ItemPointerGetBlockNumber(tid),
    5826             :                             &vmbuffer))
    5827             :         {
    5828             :             /* Rats, we have to visit the heap to check visibility */
    5829       48594 :             if (!index_fetch_heap(index_scan, tableslot))
    5830        3762 :                 continue;       /* no visible tuple, try next index entry */
    5831             : 
    5832             :             /* We don't actually need the heap tuple for anything */
    5833       44832 :             ExecClearTuple(tableslot);
    5834             : 
    5835             :             /*
    5836             :              * We don't care whether there's more than one visible tuple in
    5837             :              * the HOT chain; if any are visible, that's good enough.
    5838             :              */
    5839             :         }
    5840             : 
    5841             :         /*
    5842             :          * We expect that btree will return data in IndexTuple not HeapTuple
    5843             :          * format.  It's not lossy either.
    5844             :          */
    5845       78520 :         if (!index_scan->xs_itup)
    5846           0 :             elog(ERROR, "no data returned for index-only scan");
    5847       78520 :         if (index_scan->xs_recheck)
    5848           0 :             elog(ERROR, "unexpected recheck indication from btree");
    5849             : 
    5850             :         /* OK to deconstruct the index tuple */
    5851       78520 :         index_deform_tuple(index_scan->xs_itup,
    5852             :                            index_scan->xs_itupdesc,
    5853             :                            values, isnull);
    5854             : 
    5855             :         /* Shouldn't have got a null, but be careful */
    5856       78520 :         if (isnull[0])
    5857           0 :             elog(ERROR, "found unexpected null value in index \"%s\"",
    5858             :                  RelationGetRelationName(indexRel));
    5859             : 
    5860             :         /* Copy the index column value out to caller's context */
    5861       78520 :         oldcontext = MemoryContextSwitchTo(outercontext);
    5862       78520 :         *endpointDatum = datumCopy(values[0], typByVal, typLen);
    5863       78520 :         MemoryContextSwitchTo(oldcontext);
    5864       78520 :         have_data = true;
    5865       78520 :         break;
    5866             :     }
    5867             : 
    5868       78520 :     if (vmbuffer != InvalidBuffer)
    5869       70932 :         ReleaseBuffer(vmbuffer);
    5870       78520 :     index_endscan(index_scan);
    5871             : 
    5872       78520 :     return have_data;
    5873             : }
    5874             : 
    5875             : /*
    5876             :  * find_join_input_rel
    5877             :  *      Look up the input relation for a join.
    5878             :  *
    5879             :  * We assume that the input relation's RelOptInfo must have been constructed
    5880             :  * already.
    5881             :  */
    5882             : static RelOptInfo *
    5883       10766 : find_join_input_rel(PlannerInfo *root, Relids relids)
    5884             : {
    5885       10766 :     RelOptInfo *rel = NULL;
    5886             : 
    5887       10766 :     switch (bms_membership(relids))
    5888             :     {
    5889           0 :         case BMS_EMPTY_SET:
    5890             :             /* should not happen */
    5891           0 :             break;
    5892       10610 :         case BMS_SINGLETON:
    5893       10610 :             rel = find_base_rel(root, bms_singleton_member(relids));
    5894       10610 :             break;
    5895         156 :         case BMS_MULTIPLE:
    5896         156 :             rel = find_join_rel(root, relids);
    5897         156 :             break;
    5898             :     }
    5899             : 
    5900       10766 :     if (rel == NULL)
    5901           0 :         elog(ERROR, "could not find RelOptInfo for given relids");
    5902             : 
    5903       10766 :     return rel;
    5904             : }
    5905             : 
    5906             : 
    5907             : /*-------------------------------------------------------------------------
    5908             :  *
    5909             :  * Index cost estimation functions
    5910             :  *
    5911             :  *-------------------------------------------------------------------------
    5912             :  */
    5913             : 
    5914             : /*
    5915             :  * Extract the actual indexquals (as RestrictInfos) from an IndexClause list
    5916             :  */
    5917             : List *
    5918      404980 : get_quals_from_indexclauses(List *indexclauses)
    5919             : {
    5920      404980 :     List       *result = NIL;
    5921             :     ListCell   *lc;
    5922             : 
    5923      747590 :     foreach(lc, indexclauses)
    5924             :     {
    5925      342610 :         IndexClause *iclause = lfirst_node(IndexClause, lc);
    5926             :         ListCell   *lc2;
    5927             : 
    5928      687086 :         foreach(lc2, iclause->indexquals)
    5929             :         {
    5930      344476 :             RestrictInfo *rinfo = lfirst_node(RestrictInfo, lc2);
    5931             : 
    5932      344476 :             result = lappend(result, rinfo);
    5933             :         }
    5934             :     }
    5935      404980 :     return result;
    5936             : }
    5937             : 
    5938             : /*
    5939             :  * Compute the total evaluation cost of the comparison operands in a list
    5940             :  * of index qual expressions.  Since we know these will be evaluated just
    5941             :  * once per scan, there's no need to distinguish startup from per-row cost.
    5942             :  *
    5943             :  * This can be used either on the result of get_quals_from_indexclauses(),
    5944             :  * or directly on an indexorderbys list.  In both cases, we expect that the
    5945             :  * index key expression is on the left side of binary clauses.
    5946             :  */
    5947             : Cost
    5948      804526 : index_other_operands_eval_cost(PlannerInfo *root, List *indexquals)
    5949             : {
    5950      804526 :     Cost        qual_arg_cost = 0;
    5951             :     ListCell   *lc;
    5952             : 
    5953     1149314 :     foreach(lc, indexquals)
    5954             :     {
    5955      344788 :         Expr       *clause = (Expr *) lfirst(lc);
    5956             :         Node       *other_operand;
    5957             :         QualCost    index_qual_cost;
    5958             : 
    5959             :         /*
    5960             :          * Index quals will have RestrictInfos, indexorderbys won't.  Look
    5961             :          * through RestrictInfo if present.
    5962             :          */
    5963      344788 :         if (IsA(clause, RestrictInfo))
    5964      344468 :             clause = ((RestrictInfo *) clause)->clause;
    5965             : 
    5966      344788 :         if (IsA(clause, OpExpr))
    5967             :         {
    5968      333466 :             OpExpr     *op = (OpExpr *) clause;
    5969             : 
    5970      333466 :             other_operand = (Node *) lsecond(op->args);
    5971             :         }
    5972       11322 :         else if (IsA(clause, RowCompareExpr))
    5973             :         {
    5974          88 :             RowCompareExpr *rc = (RowCompareExpr *) clause;
    5975             : 
    5976          88 :             other_operand = (Node *) rc->rargs;
    5977             :         }
    5978       11234 :         else if (IsA(clause, ScalarArrayOpExpr))
    5979             :         {
    5980        9320 :             ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
    5981             : 
    5982        9320 :             other_operand = (Node *) lsecond(saop->args);
    5983             :         }
    5984        1914 :         else if (IsA(clause, NullTest))
    5985             :         {
    5986        1914 :             other_operand = NULL;
    5987             :         }
    5988             :         else
    5989             :         {
    5990           0 :             elog(ERROR, "unsupported indexqual type: %d",
    5991             :                  (int) nodeTag(clause));
    5992             :             other_operand = NULL;   /* keep compiler quiet */
    5993             :         }
    5994             : 
    5995      344788 :         cost_qual_eval_node(&index_qual_cost, other_operand, root);
    5996      344788 :         qual_arg_cost += index_qual_cost.startup + index_qual_cost.per_tuple;
    5997             :     }
    5998      804526 :     return qual_arg_cost;
    5999             : }
    6000             : 
    6001             : void
    6002      399554 : genericcostestimate(PlannerInfo *root,
    6003             :                     IndexPath *path,
    6004             :                     double loop_count,
    6005             :                     GenericCosts *costs)
    6006             : {
    6007      399554 :     IndexOptInfo *index = path->indexinfo;
    6008      399554 :     List       *indexQuals = get_quals_from_indexclauses(path->indexclauses);
    6009      399554 :     List       *indexOrderBys = path->indexorderbys;
    6010             :     Cost        indexStartupCost;
    6011             :     Cost        indexTotalCost;
    6012             :     Selectivity indexSelectivity;
    6013             :     double      indexCorrelation;
    6014             :     double      numIndexPages;
    6015             :     double      numIndexTuples;
    6016             :     double      spc_random_page_cost;
    6017             :     double      num_sa_scans;
    6018             :     double      num_outer_scans;
    6019             :     double      num_scans;
    6020             :     double      qual_op_cost;
    6021             :     double      qual_arg_cost;
    6022             :     List       *selectivityQuals;
    6023             :     ListCell   *l;
    6024             : 
    6025             :     /*
    6026             :      * If the index is partial, AND the index predicate with the explicitly
    6027             :      * given indexquals to produce a more accurate idea of the index
    6028             :      * selectivity.
    6029             :      */
    6030      399554 :     selectivityQuals = add_predicate_to_index_quals(index, indexQuals);
    6031             : 
    6032             :     /*
    6033             :      * Check for ScalarArrayOpExpr index quals, and estimate the number of
    6034             :      * index scans that will be performed.
    6035             :      */
    6036      399554 :     num_sa_scans = 1;
    6037      738464 :     foreach(l, indexQuals)
    6038             :     {
    6039      338910 :         RestrictInfo *rinfo = (RestrictInfo *) lfirst(l);
    6040             : 
    6041      338910 :         if (IsA(rinfo->clause, ScalarArrayOpExpr))
    6042             :         {
    6043        9316 :             ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) rinfo->clause;
    6044        9316 :             int         alength = estimate_array_length(lsecond(saop->args));
    6045             : 
    6046        9316 :             if (alength > 1)
    6047        9252 :                 num_sa_scans *= alength;
    6048             :         }
    6049             :     }
    6050             : 
    6051             :     /* Estimate the fraction of main-table tuples that will be visited */
    6052      399554 :     indexSelectivity = clauselist_selectivity(root, selectivityQuals,
    6053      399554 :                                               index->rel->relid,
    6054             :                                               JOIN_INNER,
    6055             :                                               NULL);
    6056             : 
    6057             :     /*
    6058             :      * If caller didn't give us an estimate, estimate the number of index
    6059             :      * tuples that will be visited.  We do it in this rather peculiar-looking
    6060             :      * way in order to get the right answer for partial indexes.
    6061             :      */
    6062      399554 :     numIndexTuples = costs->numIndexTuples;
    6063      399554 :     if (numIndexTuples <= 0.0)
    6064             :     {
    6065       33046 :         numIndexTuples = indexSelectivity * index->rel->tuples;
    6066             : 
    6067             :         /*
    6068             :          * The above calculation counts all the tuples visited across all
    6069             :          * scans induced by ScalarArrayOpExpr nodes.  We want to consider the
    6070             :          * average per-indexscan number, so adjust.  This is a handy place to
    6071             :          * round to integer, too.  (If caller supplied tuple estimate, it's
    6072             :          * responsible for handling these considerations.)
    6073             :          */
    6074       33046 :         numIndexTuples = rint(numIndexTuples / num_sa_scans);
    6075             :     }
    6076             : 
    6077             :     /*
    6078             :      * We can bound the number of tuples by the index size in any case. Also,
    6079             :      * always estimate at least one tuple is touched, even when
    6080             :      * indexSelectivity estimate is tiny.
    6081             :      */
    6082      399554 :     if (numIndexTuples > index->tuples)
    6083        1418 :         numIndexTuples = index->tuples;
    6084      399554 :     if (numIndexTuples < 1.0)
    6085       30856 :         numIndexTuples = 1.0;
    6086             : 
    6087             :     /*
    6088             :      * Estimate the number of index pages that will be retrieved.
    6089             :      *
    6090             :      * We use the simplistic method of taking a pro-rata fraction of the total
    6091             :      * number of index pages.  In effect, this counts only leaf pages and not
    6092             :      * any overhead such as index metapage or upper tree levels.
    6093             :      *
    6094             :      * In practice access to upper index levels is often nearly free because
    6095             :      * those tend to stay in cache under load; moreover, the cost involved is
    6096             :      * highly dependent on index type.  We therefore ignore such costs here
    6097             :      * and leave it to the caller to add a suitable charge if needed.
    6098             :      */
    6099      399554 :     if (index->pages > 1 && index->tuples > 1)
    6100      385298 :         numIndexPages = ceil(numIndexTuples * index->pages / index->tuples);
    6101             :     else
    6102       14256 :         numIndexPages = 1.0;
    6103             : 
    6104             :     /* fetch estimated page cost for tablespace containing index */
    6105      399554 :     get_tablespace_page_costs(index->reltablespace,
    6106             :                               &spc_random_page_cost,
    6107             :                               NULL);
    6108             : 
    6109             :     /*
    6110             :      * Now compute the disk access costs.
    6111             :      *
    6112             :      * The above calculations are all per-index-scan.  However, if we are in a
    6113             :      * nestloop inner scan, we can expect the scan to be repeated (with
    6114             :      * different search keys) for each row of the outer relation.  Likewise,
    6115             :      * ScalarArrayOpExpr quals result in multiple index scans.  This creates
    6116             :      * the potential for cache effects to reduce the number of disk page
    6117             :      * fetches needed.  We want to estimate the average per-scan I/O cost in
    6118             :      * the presence of caching.
    6119             :      *
    6120             :      * We use the Mackert-Lohman formula (see costsize.c for details) to
    6121             :      * estimate the total number of page fetches that occur.  While this
    6122             :      * wasn't what it was designed for, it seems a reasonable model anyway.
    6123             :      * Note that we are counting pages not tuples anymore, so we take N = T =
    6124             :      * index size, as if there were one "tuple" per page.
    6125             :      */
    6126      399554 :     num_outer_scans = loop_count;
    6127      399554 :     num_scans = num_sa_scans * num_outer_scans;
    6128             : 
    6129      399554 :     if (num_scans > 1)
    6130             :     {
    6131             :         double      pages_fetched;
    6132             : 
    6133             :         /* total page fetches ignoring cache effects */
    6134       48082 :         pages_fetched = numIndexPages * num_scans;
    6135             : 
    6136             :         /* use Mackert and Lohman formula to adjust for cache effects */
    6137       48082 :         pages_fetched = index_pages_fetched(pages_fetched,
    6138             :                                             index->pages,
    6139       48082 :                                             (double) index->pages,
    6140             :                                             root);
    6141             : 
    6142             :         /*
    6143             :          * Now compute the total disk access cost, and then report a pro-rated
    6144             :          * share for each outer scan.  (Don't pro-rate for ScalarArrayOpExpr,
    6145             :          * since that's internal to the indexscan.)
    6146             :          */
    6147       48082 :         indexTotalCost = (pages_fetched * spc_random_page_cost)
    6148             :             / num_outer_scans;
    6149             :     }
    6150             :     else
    6151             :     {
    6152             :         /*
    6153             :          * For a single index scan, we just charge spc_random_page_cost per
    6154             :          * page touched.
    6155             :          */
    6156      351472 :         indexTotalCost = numIndexPages * spc_random_page_cost;
    6157             :     }
    6158             : 
    6159             :     /*
    6160             :      * CPU cost: any complex expressions in the indexquals will need to be
    6161             :      * evaluated once at the start of the scan to reduce them to runtime keys
    6162             :      * to pass to the index AM (see nodeIndexscan.c).  We model the per-tuple
    6163             :      * CPU costs as cpu_index_tuple_cost plus one cpu_operator_cost per
    6164             :      * indexqual operator.  Because we have numIndexTuples as a per-scan
    6165             :      * number, we have to multiply by num_sa_scans to get the correct result
    6166             :      * for ScalarArrayOpExpr cases.  Similarly add in costs for any index
    6167             :      * ORDER BY expressions.
    6168             :      *
    6169             :      * Note: this neglects the possible costs of rechecking lossy operators.
    6170             :      * Detecting that that might be needed seems more expensive than it's
    6171             :      * worth, though, considering all the other inaccuracies here ...
    6172             :      */
    6173      399554 :     qual_arg_cost = index_other_operands_eval_cost(root, indexQuals) +
    6174      399554 :         index_other_operands_eval_cost(root, indexOrderBys);
    6175      399554 :     qual_op_cost = cpu_operator_cost *
    6176      399554 :         (list_length(indexQuals) + list_length(indexOrderBys));
    6177             : 
    6178      399554 :     indexStartupCost = qual_arg_cost;
    6179      399554 :     indexTotalCost += qual_arg_cost;
    6180      399554 :     indexTotalCost += numIndexTuples * num_sa_scans * (cpu_index_tuple_cost + qual_op_cost);
    6181             : 
    6182             :     /*
    6183             :      * Generic assumption about index correlation: there isn't any.
    6184             :      */
    6185      399554 :     indexCorrelation = 0.0;
    6186             : 
    6187             :     /*
    6188             :      * Return everything to caller.
    6189             :      */
    6190      399554 :     costs->indexStartupCost = indexStartupCost;
    6191      399554 :     costs->indexTotalCost = indexTotalCost;
    6192      399554 :     costs->indexSelectivity = indexSelectivity;
    6193      399554 :     costs->indexCorrelation = indexCorrelation;
    6194      399554 :     costs->numIndexPages = numIndexPages;
    6195      399554 :     costs->numIndexTuples = numIndexTuples;
    6196      399554 :     costs->spc_random_page_cost = spc_random_page_cost;
    6197      399554 :     costs->num_sa_scans = num_sa_scans;
    6198      399554 : }
    6199             : 
    6200             : /*
    6201             :  * If the index is partial, add its predicate to the given qual list.
    6202             :  *
    6203             :  * ANDing the index predicate with the explicitly given indexquals produces
    6204             :  * a more accurate idea of the index's selectivity.  However, we need to be
    6205             :  * careful not to insert redundant clauses, because clauselist_selectivity()
    6206             :  * is easily fooled into computing a too-low selectivity estimate.  Our
    6207             :  * approach is to add only the predicate clause(s) that cannot be proven to
    6208             :  * be implied by the given indexquals.  This successfully handles cases such
    6209             :  * as a qual "x = 42" used with a partial index "WHERE x >= 40 AND x < 50".
    6210             :  * There are many other cases where we won't detect redundancy, leading to a
    6211             :  * too-low selectivity estimate, which will bias the system in favor of using
    6212             :  * partial indexes where possible.  That is not necessarily bad though.
    6213             :  *
    6214             :  * Note that indexQuals contains RestrictInfo nodes while the indpred
    6215             :  * does not, so the output list will be mixed.  This is OK for both
    6216             :  * predicate_implied_by() and clauselist_selectivity(), but might be
    6217             :  * problematic if the result were passed to other things.
    6218             :  */
    6219             : List *
    6220      685974 : add_predicate_to_index_quals(IndexOptInfo *index, List *indexQuals)
    6221             : {
    6222      685974 :     List       *predExtraQuals = NIL;
    6223             :     ListCell   *lc;
    6224             : 
    6225      685974 :     if (index->indpred == NIL)
    6226      684546 :         return indexQuals;
    6227             : 
    6228        2864 :     foreach(lc, index->indpred)
    6229             :     {
    6230        1436 :         Node       *predQual = (Node *) lfirst(lc);
    6231        1436 :         List       *oneQual = list_make1(predQual);
    6232             : 
    6233        1436 :         if (!predicate_implied_by(oneQual, indexQuals, false))
    6234        1288 :             predExtraQuals = list_concat(predExtraQuals, oneQual);
    6235             :     }
    6236        1428 :     return list_concat(predExtraQuals, indexQuals);
    6237             : }
    6238             : 
    6239             : 
    6240             : void
    6241      395764 : btcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
    6242             :                Cost *indexStartupCost, Cost *indexTotalCost,
    6243             :                Selectivity *indexSelectivity, double *indexCorrelation,
    6244             :                double *indexPages)
    6245             : {
    6246      395764 :     IndexOptInfo *index = path->indexinfo;
    6247             :     GenericCosts costs;
    6248             :     Oid         relid;
    6249             :     AttrNumber  colnum;
    6250             :     VariableStatData vardata;
    6251             :     double      numIndexTuples;
    6252             :     Cost        descentCost;
    6253             :     List       *indexBoundQuals;
    6254             :     int         indexcol;
    6255             :     bool        eqQualHere;
    6256             :     bool        found_saop;
    6257             :     bool        found_is_null_op;
    6258             :     double      num_sa_scans;
    6259             :     ListCell   *lc;
    6260             : 
    6261             :     /*
    6262             :      * For a btree scan, only leading '=' quals plus inequality quals for the
    6263             :      * immediately next attribute contribute to index selectivity (these are
    6264             :      * the "boundary quals" that determine the starting and stopping points of
    6265             :      * the index scan).  Additional quals can suppress visits to the heap, so
    6266             :      * it's OK to count them in indexSelectivity, but they should not count
    6267             :      * for estimating numIndexTuples.  So we must examine the given indexquals
    6268             :      * to find out which ones count as boundary quals.  We rely on the
    6269             :      * knowledge that they are given in index column order.
    6270             :      *
    6271             :      * For a RowCompareExpr, we consider only the first column, just as
    6272             :      * rowcomparesel() does.
    6273             :      *
    6274             :      * If there's a ScalarArrayOpExpr in the quals, we'll actually perform N
    6275             :      * index scans not one, but the ScalarArrayOpExpr's operator can be
    6276             :      * considered to act the same as it normally does.
    6277             :      */
    6278      395764 :     indexBoundQuals = NIL;
    6279      395764 :     indexcol = 0;
    6280      395764 :     eqQualHere = false;
    6281      395764 :     found_saop = false;
    6282      395764 :     found_is_null_op = false;
    6283      395764 :     num_sa_scans = 1;
    6284      713984 :     foreach(lc, path->indexclauses)
    6285             :     {
    6286      330072 :         IndexClause *iclause = lfirst_node(IndexClause, lc);
    6287             :         ListCell   *lc2;
    6288             : 
    6289      330072 :         if (indexcol != iclause->indexcol)
    6290             :         {
    6291             :             /* Beginning of a new column's quals */
    6292       59452 :             if (!eqQualHere)
    6293       11212 :                 break;          /* done if no '=' qual for indexcol */
    6294       48240 :             eqQualHere = false;
    6295       48240 :             indexcol++;
    6296       48240 :             if (indexcol != iclause->indexcol)
    6297         640 :                 break;          /* no quals at all for indexcol */
    6298             :         }
    6299             : 
    6300             :         /* Examine each indexqual associated with this index clause */
    6301      638258 :         foreach(lc2, iclause->indexquals)
    6302             :         {
    6303      320038 :             RestrictInfo *rinfo = lfirst_node(RestrictInfo, lc2);
    6304      320038 :             Expr       *clause = rinfo->clause;
    6305      320038 :             Oid         clause_op = InvalidOid;
    6306             :             int         op_strategy;
    6307             : 
    6308      320038 :             if (IsA(clause, OpExpr))
    6309             :             {
    6310      309180 :                 OpExpr     *op = (OpExpr *) clause;
    6311             : 
    6312      309180 :                 clause_op = op->opno;
    6313             :             }
    6314       10858 :             else if (IsA(clause, RowCompareExpr))
    6315             :             {
    6316          88 :                 RowCompareExpr *rc = (RowCompareExpr *) clause;
    6317             : 
    6318          88 :                 clause_op = linitial_oid(rc->opnos);
    6319             :             }
    6320       10770 :             else if (IsA(clause, ScalarArrayOpExpr))
    6321             :             {
    6322        9184 :                 ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
    6323        9184 :                 Node       *other_operand = (Node *) lsecond(saop->args);
    6324        9184 :                 int         alength = estimate_array_length(other_operand);
    6325             : 
    6326        9184 :                 clause_op = saop->opno;
    6327        9184 :                 found_saop = true;
    6328             :                 /* count number of SA scans induced by indexBoundQuals only */
    6329        9184 :                 if (alength > 1)
    6330        9120 :                     num_sa_scans *= alength;
    6331             :             }
    6332        1586 :             else if (IsA(clause, NullTest))
    6333             :             {
    6334        1586 :                 NullTest   *nt = (NullTest *) clause;
    6335             : 
    6336        1586 :                 if (nt->nulltesttype == IS_NULL)
    6337             :                 {
    6338          92 :                     found_is_null_op = true;
    6339             :                     /* IS NULL is like = for selectivity purposes */
    6340          92 :                     eqQualHere = true;
    6341             :                 }
    6342             :             }
    6343             :             else
    6344           0 :                 elog(ERROR, "unsupported indexqual type: %d",
    6345             :                      (int) nodeTag(clause));
    6346             : 
    6347             :             /* check for equality operator */
    6348      320038 :             if (OidIsValid(clause_op))
    6349             :             {
    6350      318452 :                 op_strategy = get_op_opfamily_strategy(clause_op,
    6351      318452 :                                                        index->opfamily[indexcol]);
    6352             :                 Assert(op_strategy != 0);   /* not a member of opfamily?? */
    6353      318452 :                 if (op_strategy == BTEqualStrategyNumber)
    6354      294984 :                     eqQualHere = true;
    6355             :             }
    6356             : 
    6357      320038 :             indexBoundQuals = lappend(indexBoundQuals, rinfo);
    6358             :         }
    6359             :     }
    6360             : 
    6361             :     /*
    6362             :      * If index is unique and we found an '=' clause for each column, we can
    6363             :      * just assume numIndexTuples = 1 and skip the expensive
    6364             :      * clauselist_selectivity calculations.  However, a ScalarArrayOp or
    6365             :      * NullTest invalidates that theory, even though it sets eqQualHere.
    6366             :      */
    6367      395764 :     if (index->unique &&
    6368      331370 :         indexcol == index->nkeycolumns - 1 &&
    6369      118190 :         eqQualHere &&
    6370      118190 :         !found_saop &&
    6371      110818 :         !found_is_null_op)
    6372      110774 :         numIndexTuples = 1.0;
    6373             :     else
    6374             :     {
    6375             :         List       *selectivityQuals;
    6376             :         Selectivity btreeSelectivity;
    6377             : 
    6378             :         /*
    6379             :          * If the index is partial, AND the index predicate with the
    6380             :          * index-bound quals to produce a more accurate idea of the number of
    6381             :          * rows covered by the bound conditions.
    6382             :          */
    6383      284990 :         selectivityQuals = add_predicate_to_index_quals(index, indexBoundQuals);
    6384             : 
    6385      284990 :         btreeSelectivity = clauselist_selectivity(root, selectivityQuals,
    6386      284990 :                                                   index->rel->relid,
    6387             :                                                   JOIN_INNER,
    6388             :                                                   NULL);
    6389      284990 :         numIndexTuples = btreeSelectivity * index->rel->tuples;
    6390             : 
    6391             :         /*
    6392             :          * As in genericcostestimate(), we have to adjust for any
    6393             :          * ScalarArrayOpExpr quals included in indexBoundQuals, and then round
    6394             :          * to integer.
    6395             :          */
    6396      284990 :         numIndexTuples = rint(numIndexTuples / num_sa_scans);
    6397             :     }
    6398             : 
    6399             :     /*
    6400             :      * Now do generic index cost estimation.
    6401             :      */
    6402     3561876 :     MemSet(&costs, 0, sizeof(costs));
    6403      395764 :     costs.numIndexTuples = numIndexTuples;
    6404             : 
    6405      395764 :     genericcostestimate(root, path, loop_count, &costs);
    6406             : 
    6407             :     /*
    6408             :      * Add a CPU-cost component to represent the costs of initial btree
    6409             :      * descent.  We don't charge any I/O cost for touching upper btree levels,
    6410             :      * since they tend to stay in cache, but we still have to do about log2(N)
    6411             :      * comparisons to descend a btree of N leaf tuples.  We charge one
    6412             :      * cpu_operator_cost per comparison.
    6413             :      *
    6414             :      * If there are ScalarArrayOpExprs, charge this once per SA scan.  The
    6415             :      * ones after the first one are not startup cost so far as the overall
    6416             :      * plan is concerned, so add them only to "total" cost.
    6417             :      */
    6418      395764 :     if (index->tuples > 1)        /* avoid computing log(0) */
    6419             :     {
    6420      385294 :         descentCost = ceil(log(index->tuples) / log(2.0)) * cpu_operator_cost;
    6421      385294 :         costs.indexStartupCost += descentCost;
    6422      385294 :         costs.indexTotalCost += costs.num_sa_scans * descentCost;
    6423             :     }
    6424             : 
    6425             :     /*
    6426             :      * Even though we're not charging I/O cost for touching upper btree pages,
    6427             :      * it's still reasonable to charge some CPU cost per page descended
    6428             :      * through.  Moreover, if we had no such charge at all, bloated indexes
    6429             :      * would appear to have the same search cost as unbloated ones, at least
    6430             :      * in cases where only a single leaf page is expected to be visited.  This
    6431             :      * cost is somewhat arbitrarily set at 50x cpu_operator_cost per page
    6432             :      * touched.  The number of such pages is btree tree height plus one (ie,
    6433             :      * we charge for the leaf page too).  As above, charge once per SA scan.
    6434             :      */
    6435      395764 :     descentCost = (index->tree_height + 1) * 50.0 * cpu_operator_cost;
    6436      395764 :     costs.indexStartupCost += descentCost;
    6437      395764 :     costs.indexTotalCost += costs.num_sa_scans * descentCost;
    6438             : 
    6439             :     /*
    6440             :      * If we can get an estimate of the first column's ordering correlation C
    6441             :      * from pg_statistic, estimate the index correlation as C for a
    6442             :      * single-column index, or C * 0.75 for multiple columns. (The idea here
    6443             :      * is that multiple columns dilute the importance of the first column's
    6444             :      * ordering, but don't negate it entirely.  Before 8.0 we divided the
    6445             :      * correlation by the number of columns, but that seems too strong.)
    6446             :      */
    6447     2770348 :     MemSet(&vardata, 0, sizeof(vardata));
    6448             : 
    6449      395764 :     if (index->indexkeys[0] != 0)
    6450             :     {
    6451             :         /* Simple variable --- look to stats for the underlying table */
    6452      394456 :         RangeTblEntry *rte = planner_rt_fetch(index->rel->relid, root);
    6453             : 
    6454             :         Assert(rte->rtekind == RTE_RELATION);
    6455      394456 :         relid = rte->relid;
    6456             :         Assert(relid != InvalidOid);
    6457      394456 :         colnum = index->indexkeys[0];
    6458             : 
    6459      394456 :         if (get_relation_stats_hook &&
    6460           0 :             (*get_relation_stats_hook) (root, rte, colnum, &vardata))
    6461             :         {
    6462             :             /*
    6463             :              * The hook took control of acquiring a stats tuple.  If it did
    6464             :              * supply a tuple, it'd better have supplied a freefunc.
    6465             :              */
    6466           0 :             if (HeapTupleIsValid(vardata.statsTuple) &&
    6467           0 :                 !vardata.freefunc)
    6468           0 :                 elog(ERROR, "no function provided to release variable stats with");
    6469             :         }
    6470             :         else
    6471             :         {
    6472      394456 :             vardata.statsTuple = SearchSysCache3(STATRELATTINH,
    6473             :                                                  ObjectIdGetDatum(relid),
    6474             :                                                  Int16GetDatum(colnum),
    6475      394456 :                                                  BoolGetDatum(rte->inh));
    6476      394456 :             vardata.freefunc = ReleaseSysCache;
    6477             :         }
    6478             :     }
    6479             :     else
    6480             :     {
    6481             :         /* Expression --- maybe there are stats for the index itself */
    6482        1308 :         relid = index->indexoid;
    6483        1308 :         colnum = 1;
    6484             : 
    6485        1308 :         if (get_index_stats_hook &&
    6486           0 :             (*get_index_stats_hook) (root, relid, colnum, &vardata))
    6487             :         {
    6488             :             /*
    6489             :              * The hook took control of acquiring a stats tuple.  If it did
    6490             :              * supply a tuple, it'd better have supplied a freefunc.
    6491             :              */
    6492           0 :             if (HeapTupleIsValid(vardata.statsTuple) &&
    6493           0 :                 !vardata.freefunc)
    6494           0 :                 elog(ERROR, "no function provided to release variable stats with");
    6495             :         }
    6496             :         else
    6497             :         {
    6498        1308 :             vardata.statsTuple = SearchSysCache3(STATRELATTINH,
    6499             :                                                  ObjectIdGetDatum(relid),
    6500             :                                                  Int16GetDatum(colnum),
    6501             :                                                  BoolGetDatum(false));
    6502        1308 :             vardata.freefunc = ReleaseSysCache;
    6503             :         }
    6504             :     }
    6505             : 
    6506      395764 :     if (HeapTupleIsValid(vardata.statsTuple))
    6507             :     {
    6508             :         Oid         sortop;
    6509             :         AttStatsSlot sslot;
    6510             : 
    6511      632480 :         sortop = get_opfamily_member(index->opfamily[0],
    6512      316240 :                                      index->opcintype[0],
    6513      316240 :                                      index->opcintype[0],
    6514             :                                      BTLessStrategyNumber);
    6515      632480 :         if (OidIsValid(sortop) &&
    6516      316240 :             get_attstatsslot(&sslot, vardata.statsTuple,
    6517             :                              STATISTIC_KIND_CORRELATION, sortop,
    6518             :                              ATTSTATSSLOT_NUMBERS))
    6519             :         {
    6520             :             double      varCorrelation;
    6521             : 
    6522             :             Assert(sslot.nnumbers == 1);
    6523      313958 :             varCorrelation = sslot.numbers[0];
    6524             : 
    6525      313958 :             if (index->reverse_sort[0])
    6526           0 :                 varCorrelation = -varCorrelation;
    6527             : 
    6528      313958 :             if (index->nkeycolumns > 1)
    6529      131704 :                 costs.indexCorrelation = varCorrelation * 0.75;
    6530             :             else
    6531      182254 :                 costs.indexCorrelation = varCorrelation;
    6532             : 
    6533      313958 :             free_attstatsslot(&sslot);
    6534             :         }
    6535             :     }
    6536             : 
    6537      395764 :     ReleaseVariableStats(vardata);
    6538             : 
    6539      395764 :     *indexStartupCost = costs.indexStartupCost;
    6540      395764 :     *indexTotalCost = costs.indexTotalCost;
    6541      395764 :     *indexSelectivity = costs.indexSelectivity;
    6542      395764 :     *indexCorrelation = costs.indexCorrelation;
    6543      395764 :     *indexPages = costs.numIndexPages;
    6544      395764 : }
    6545             : 
    6546             : void
    6547         318 : hashcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
    6548             :                  Cost *indexStartupCost, Cost *indexTotalCost,
    6549             :                  Selectivity *indexSelectivity, double *indexCorrelation,
    6550             :                  double *indexPages)
    6551             : {
    6552             :     GenericCosts costs;
    6553             : 
    6554        2862 :     MemSet(&costs, 0, sizeof(costs));
    6555             : 
    6556         318 :     genericcostestimate(root, path, loop_count, &costs);
    6557             : 
    6558             :     /*
    6559             :      * A hash index has no descent costs as such, since the index AM can go
    6560             :      * directly to the target bucket after computing the hash value.  There
    6561             :      * are a couple of other hash-specific costs that we could conceivably add
    6562             :      * here, though:
    6563             :      *
    6564             :      * Ideally we'd charge spc_random_page_cost for each page in the target
    6565             :      * bucket, not just the numIndexPages pages that genericcostestimate
    6566             :      * thought we'd visit.  However in most cases we don't know which bucket
    6567             :      * that will be.  There's no point in considering the average bucket size
    6568             :      * because the hash AM makes sure that's always one page.
    6569             :      *
    6570             :      * Likewise, we could consider charging some CPU for each index tuple in
    6571             :      * the bucket, if we knew how many there were.  But the per-tuple cost is
    6572             :      * just a hash value comparison, not a general datatype-dependent
    6573             :      * comparison, so any such charge ought to be quite a bit less than
    6574             :      * cpu_operator_cost; which makes it probably not worth worrying about.
    6575             :      *
    6576             :      * A bigger issue is that chance hash-value collisions will result in
    6577             :      * wasted probes into the heap.  We don't currently attempt to model this
    6578             :      * cost on the grounds that it's rare, but maybe it's not rare enough.
    6579             :      * (Any fix for this ought to consider the generic lossy-operator problem,
    6580             :      * though; it's not entirely hash-specific.)
    6581             :      */
    6582             : 
    6583         318 :     *indexStartupCost = costs.indexStartupCost;
    6584         318 :     *indexTotalCost = costs.indexTotalCost;
    6585         318 :     *indexSelectivity = costs.indexSelectivity;
    6586         318 :     *indexCorrelation = costs.indexCorrelation;
    6587         318 :     *indexPages = costs.numIndexPages;
    6588         318 : }
    6589             : 
    6590             : void
    6591        2284 : gistcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
    6592             :                  Cost *indexStartupCost, Cost *indexTotalCost,
    6593             :                  Selectivity *indexSelectivity, double *indexCorrelation,
    6594             :                  double *indexPages)
    6595             : {
    6596        2284 :     IndexOptInfo *index = path->indexinfo;
    6597             :     GenericCosts costs;
    6598             :     Cost        descentCost;
    6599             : 
    6600       20556 :     MemSet(&costs, 0, sizeof(costs));
    6601             : 
    6602        2284 :     genericcostestimate(root, path, loop_count, &costs);
    6603             : 
    6604             :     /*
    6605             :      * We model index descent costs similarly to those for btree, but to do
    6606             :      * that we first need an idea of the tree height.  We somewhat arbitrarily
    6607             :      * assume that the fanout is 100, meaning the tree height is at most
    6608             :      * log100(index->pages).
    6609             :      *
    6610             :      * Although this computation isn't really expensive enough to require
    6611             :      * caching, we might as well use index->tree_height to cache it.
    6612             :      */
    6613        2284 :     if (index->tree_height < 0) /* unknown? */
    6614             :     {
    6615        2272 :         if (index->pages > 1) /* avoid computing log(0) */
    6616        1904 :             index->tree_height = (int) (log(index->pages) / log(100.0));
    6617             :         else
    6618         368 :             index->tree_height = 0;
    6619             :     }
    6620             : 
    6621             :     /*
    6622             :      * Add a CPU-cost component to represent the costs of initial descent. We
    6623             :      * just use log(N) here not log2(N) since the branching factor isn't
    6624             :      * necessarily two anyway.  As for btree, charge once per SA scan.
    6625             :      */
    6626        2284 :     if (index->tuples > 1)        /* avoid computing log(0) */
    6627             :     {
    6628        2284 :         descentCost = ceil(log(index->tuples)) * cpu_operator_cost;
    6629        2284 :         costs.indexStartupCost += descentCost;
    6630        2284 :         costs.indexTotalCost += costs.num_sa_scans * descentCost;
    6631             :     }
    6632             : 
    6633             :     /*
    6634             :      * Likewise add a per-page charge, calculated the same as for btrees.
    6635             :      */
    6636        2284 :     descentCost = (index->tree_height + 1) * 50.0 * cpu_operator_cost;
    6637        2284 :     costs.indexStartupCost += descentCost;
    6638        2284 :     costs.indexTotalCost += costs.num_sa_scans * descentCost;
    6639             : 
    6640        2284 :     *indexStartupCost = costs.indexStartupCost;
    6641        2284 :     *indexTotalCost = costs.indexTotalCost;
    6642        2284 :     *indexSelectivity = costs.indexSelectivity;
    6643        2284 :     *indexCorrelation = costs.indexCorrelation;
    6644        2284 :     *indexPages = costs.numIndexPages;
    6645        2284 : }
    6646             : 
    6647             : void
    6648        1140 : spgcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
    6649             :                 Cost *indexStartupCost, Cost *indexTotalCost,
    6650             :                 Selectivity *indexSelectivity, double *indexCorrelation,
    6651             :                 double *indexPages)
    6652             : {
    6653        1140 :     IndexOptInfo *index = path->indexinfo;
    6654             :     GenericCosts costs;
    6655             :     Cost        descentCost;
    6656             : 
    6657       10260 :     MemSet(&costs, 0, sizeof(costs));
    6658             : 
    6659        1140 :     genericcostestimate(root, path, loop_count, &costs);
    6660             : 
    6661             :     /*
    6662             :      * We model index descent costs similarly to those for btree, but to do
    6663             :      * that we first need an idea of the tree height.  We somewhat arbitrarily
    6664             :      * assume that the fanout is 100, meaning the tree height is at most
    6665             :      * log100(index->pages).
    6666             :      *
    6667             :      * Although this computation isn't really expensive enough to require
    6668             :      * caching, we might as well use index->tree_height to cache it.
    6669             :      */
    6670        1140 :     if (index->tree_height < 0) /* unknown? */
    6671             :     {
    6672        1136 :         if (index->pages > 1) /* avoid computing log(0) */
    6673        1136 :             index->tree_height = (int) (log(index->pages) / log(100.0));
    6674             :         else
    6675           0 :             index->tree_height = 0;
    6676             :     }
    6677             : 
    6678             :     /*
    6679             :      * Add a CPU-cost component to represent the costs of initial descent. We
    6680             :      * just use log(N) here not log2(N) since the branching factor isn't
    6681             :      * necessarily two anyway.  As for btree, charge once per SA scan.
    6682             :      */
    6683        1140 :     if (index->tuples > 1)        /* avoid computing log(0) */
    6684             :     {
    6685        1140 :         descentCost = ceil(log(index->tuples)) * cpu_operator_cost;
    6686        1140 :         costs.indexStartupCost += descentCost;
    6687        1140 :         costs.indexTotalCost += costs.num_sa_scans * descentCost;
    6688             :     }
    6689             : 
    6690             :     /*
    6691             :      * Likewise add a per-page charge, calculated the same as for btrees.
    6692             :      */
    6693        1140 :     descentCost = (index->tree_height + 1) * 50.0 * cpu_operator_cost;
    6694        1140 :     costs.indexStartupCost += descentCost;
    6695        1140 :     costs.indexTotalCost += costs.num_sa_scans * descentCost;
    6696             : 
    6697        1140 :     *indexStartupCost = costs.indexStartupCost;
    6698        1140 :     *indexTotalCost = costs.indexTotalCost;
    6699        1140 :     *indexSelectivity = costs.indexSelectivity;
    6700        1140 :     *indexCorrelation = costs.indexCorrelation;
    6701        1140 :     *indexPages = costs.numIndexPages;
    6702        1140 : }
    6703             : 
    6704             : 
    6705             : /*
    6706             :  * Support routines for gincostestimate
    6707             :  */
    6708             : 
    6709             : typedef struct
    6710             : {
    6711             :     bool        attHasFullScan[INDEX_MAX_KEYS];
    6712             :     bool        attHasNormalScan[INDEX_MAX_KEYS];
    6713             :     double      partialEntries;
    6714             :     double      exactEntries;
    6715             :     double      searchEntries;
    6716             :     double      arrayScans;
    6717             : } GinQualCounts;
    6718             : 
    6719             : /*
    6720             :  * Estimate the number of index terms that need to be searched for while
    6721             :  * testing the given GIN query, and increment the counts in *counts
    6722             :  * appropriately.  If the query is unsatisfiable, return false.
    6723             :  */
    6724             : static bool
    6725        1574 : gincost_pattern(IndexOptInfo *index, int indexcol,
    6726             :                 Oid clause_op, Datum query,
    6727             :                 GinQualCounts *counts)
    6728             : {
    6729             :     FmgrInfo    flinfo;
    6730             :     Oid         extractProcOid;
    6731             :     Oid         collation;
    6732             :     int         strategy_op;
    6733             :     Oid         lefttype,
    6734             :                 righttype;
    6735        1574 :     int32       nentries = 0;
    6736        1574 :     bool       *partial_matches = NULL;
    6737        1574 :     Pointer    *extra_data = NULL;
    6738        1574 :     bool       *nullFlags = NULL;
    6739        1574 :     int32       searchMode = GIN_SEARCH_MODE_DEFAULT;
    6740             :     int32       i;
    6741             : 
    6742             :     Assert(indexcol < index->nkeycolumns);
    6743             : 
    6744             :     /*
    6745             :      * Get the operator's strategy number and declared input data types within
    6746             :      * the index opfamily.  (We don't need the latter, but we use
    6747             :      * get_op_opfamily_properties because it will throw error if it fails to
    6748             :      * find a matching pg_amop entry.)
    6749             :      */
    6750        1574 :     get_op_opfamily_properties(clause_op, index->opfamily[indexcol], false,
    6751             :                                &strategy_op, &lefttype, &righttype);
    6752             : 
    6753             :     /*
    6754             :      * GIN always uses the "default" support functions, which are those with
    6755             :      * lefttype == righttype == the opclass' opcintype (see
    6756             :      * IndexSupportInitialize in relcache.c).
    6757             :      */
    6758        3148 :     extractProcOid = get_opfamily_proc(index->opfamily[indexcol],
    6759        1574 :                                        index->opcintype[indexcol],
    6760        1574 :                                        index->opcintype[indexcol],
    6761             :                                        GIN_EXTRACTQUERY_PROC);
    6762             : 
    6763        1574 :     if (!OidIsValid(extractProcOid))
    6764             :     {
    6765             :         /* should not happen; throw same error as index_getprocinfo */
    6766           0 :         elog(ERROR, "missing support function %d for attribute %d of index \"%s\"",
    6767             :              GIN_EXTRACTQUERY_PROC, indexcol + 1,
    6768             :              get_rel_name(index->indexoid));
    6769             :     }
    6770             : 
    6771             :     /*
    6772             :      * Choose collation to pass to extractProc (should match initGinState).
    6773             :      */
    6774        1574 :     if (OidIsValid(index->indexcollations[indexcol]))
    6775         326 :         collation = index->indexcollations[indexcol];
    6776             :     else
    6777        1248 :         collation = DEFAULT_COLLATION_OID;
    6778             : 
    6779        1574 :     fmgr_info(extractProcOid, &flinfo);
    6780             : 
    6781        1574 :     set_fn_opclass_options(&flinfo, index->opclassoptions[indexcol]);
    6782             : 
    6783        1574 :     FunctionCall7Coll(&flinfo,
    6784             :                       collation,
    6785             :                       query,
    6786             :                       PointerGetDatum(&nentries),
    6787             :                       UInt16GetDatum(strategy_op),
    6788             :                       PointerGetDatum(&partial_matches),
    6789             :                       PointerGetDatum(&extra_data),
    6790             :                       PointerGetDatum(&nullFlags),
    6791             :                       PointerGetDatum(&searchMode));
    6792             : 
    6793        1574 :     if (nentries <= 0 && searchMode == GIN_SEARCH_MODE_DEFAULT)
    6794             :     {
    6795             :         /* No match is possible */
    6796           8 :         return false;
    6797             :     }
    6798             : 
    6799        4744 :     for (i = 0; i < nentries; i++)
    6800             :     {
    6801             :         /*
    6802             :          * For partial match we haven't any information to estimate number of
    6803             :          * matched entries in index, so, we just estimate it as 100
    6804             :          */
    6805        3178 :         if (partial_matches && partial_matches[i])
    6806         302 :             counts->partialEntries += 100;
    6807             :         else
    6808        2876 :             counts->exactEntries++;
    6809             : 
    6810        3178 :         counts->searchEntries++;
    6811             :     }
    6812             : 
    6813        1566 :     if (searchMode == GIN_SEARCH_MODE_DEFAULT)
    6814             :     {
    6815        1236 :         counts->attHasNormalScan[indexcol] = true;
    6816             :     }
    6817         330 :     else if (searchMode == GIN_SEARCH_MODE_INCLUDE_EMPTY)
    6818             :     {
    6819             :         /* Treat "include empty" like an exact-match item */
    6820          30 :         counts->attHasNormalScan[indexcol] = true;
    6821          30 :         counts->exactEntries++;
    6822          30 :         counts->searchEntries++;
    6823             :     }
    6824             :     else
    6825             :     {
    6826             :         /* It's GIN_SEARCH_MODE_ALL */
    6827         300 :         counts->attHasFullScan[indexcol] = true;
    6828             :     }
    6829             : 
    6830        1566 :     return true;
    6831             : }
    6832             : 
    6833             : /*
    6834             :  * Estimate the number of index terms that need to be searched for while
    6835             :  * testing the given GIN index clause, and increment the counts in *counts
    6836             :  * appropriately.  If the query is unsatisfiable, return false.
    6837             :  */
    6838             : static bool
    6839        1566 : gincost_opexpr(PlannerInfo *root,
    6840             :                IndexOptInfo *index,
    6841             :                int indexcol,
    6842             :                OpExpr *clause,
    6843             :                GinQualCounts *counts)
    6844             : {
    6845        1566 :     Oid         clause_op = clause->opno;
    6846        1566 :     Node       *operand = (Node *) lsecond(clause->args);
    6847             : 
    6848             :     /* aggressively reduce to a constant, and look through relabeling */
    6849        1566 :     operand = estimate_expression_value(root, operand);
    6850             : 
    6851        1566 :     if (IsA(operand, RelabelType))
    6852           0 :         operand = (Node *) ((RelabelType *) operand)->arg;
    6853             : 
    6854             :     /*
    6855             :      * It's impossible to call extractQuery method for unknown operand. So
    6856             :      * unless operand is a Const we can't do much; just assume there will be
    6857             :      * one ordinary search entry from the operand at runtime.
    6858             :      */
    6859        1566 :     if (!IsA(operand, Const))
    6860             :     {
    6861           0 :         counts->exactEntries++;
    6862           0 :         counts->searchEntries++;
    6863           0 :         return true;
    6864             :     }
    6865             : 
    6866             :     /* If Const is null, there can be no matches */
    6867        1566 :     if (((Const *) operand)->constisnull)
    6868           0 :         return false;
    6869             : 
    6870             :     /* Otherwise, apply extractQuery and get the actual term counts */
    6871        1566 :     return gincost_pattern(index, indexcol, clause_op,
    6872             :                            ((Const *) operand)->constvalue,
    6873             :                            counts);
    6874             : }
    6875             : 
    6876             : /*
    6877             :  * Estimate the number of index terms that need to be searched for while
    6878             :  * testing the given GIN index clause, and increment the counts in *counts
    6879             :  * appropriately.  If the query is unsatisfiable, return false.
    6880             :  *
    6881             :  * A ScalarArrayOpExpr will give rise to N separate indexscans at runtime,
    6882             :  * each of which involves one value from the RHS array, plus all the
    6883             :  * non-array quals (if any).  To model this, we average the counts across
    6884             :  * the RHS elements, and add the averages to the counts in *counts (which
    6885             :  * correspond to per-indexscan costs).  We also multiply counts->arrayScans
    6886             :  * by N, causing gincostestimate to scale up its estimates accordingly.
    6887             :  */
    6888             : static bool
    6889           4 : gincost_scalararrayopexpr(PlannerInfo *root,
    6890             :                           IndexOptInfo *index,
    6891             :                           int indexcol,
    6892             :                           ScalarArrayOpExpr *clause,
    6893             :                           double numIndexEntries,
    6894             :                           GinQualCounts *counts)
    6895             : {
    6896           4 :     Oid         clause_op = clause->opno;
    6897           4 :     Node       *rightop = (Node *) lsecond(clause->args);
    6898             :     ArrayType  *arrayval;
    6899             :     int16       elmlen;
    6900             :     bool        elmbyval;
    6901             :     char        elmalign;
    6902             :     int         numElems;
    6903             :     Datum      *elemValues;
    6904             :     bool       *elemNulls;
    6905             :     GinQualCounts arraycounts;
    6906           4 :     int         numPossible = 0;
    6907             :     int         i;
    6908             : 
    6909             :     Assert(clause->useOr);
    6910             : 
    6911             :     /* aggressively reduce to a constant, and look through relabeling */
    6912           4 :     rightop = estimate_expression_value(root, rightop);
    6913             : 
    6914           4 :     if (IsA(rightop, RelabelType))
    6915           0 :         rightop = (Node *) ((RelabelType *) rightop)->arg;
    6916             : 
    6917             :     /*
    6918             :      * It's impossible to call extractQuery method for unknown operand. So
    6919             :      * unless operand is a Const we can't do much; just assume there will be
    6920             :      * one ordinary search entry from each array entry at runtime, and fall
    6921             :      * back on a probably-bad estimate of the number of array entries.
    6922             :      */
    6923           4 :     if (!IsA(rightop, Const))
    6924             :     {
    6925           0 :         counts->exactEntries++;
    6926           0 :         counts->searchEntries++;
    6927           0 :         counts->arrayScans *= estimate_array_length(rightop);
    6928           0 :         return true;
    6929             :     }
    6930             : 
    6931             :     /* If Const is null, there can be no matches */
    6932           4 :     if (((Const *) rightop)->constisnull)
    6933           0 :         return false;
    6934             : 
    6935             :     /* Otherwise, extract the array elements and iterate over them */
    6936           4 :     arrayval = DatumGetArrayTypeP(((Const *) rightop)->constvalue);
    6937           4 :     get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
    6938             :                          &elmlen, &elmbyval, &elmalign);
    6939           4 :     deconstruct_array(arrayval,
    6940             :                       ARR_ELEMTYPE(arrayval),
    6941             :                       elmlen, elmbyval, elmalign,
    6942             :                       &elemValues, &elemNulls, &numElems);
    6943             : 
    6944           4 :     memset(&arraycounts, 0, sizeof(arraycounts));
    6945             : 
    6946          12 :     for (i = 0; i < numElems; i++)
    6947             :     {
    6948             :         GinQualCounts elemcounts;
    6949             : 
    6950             :         /* NULL can't match anything, so ignore, as the executor will */
    6951           8 :         if (elemNulls[i])
    6952           0 :             continue;
    6953             : 
    6954             :         /* Otherwise, apply extractQuery and get the actual term counts */
    6955           8 :         memset(&elemcounts, 0, sizeof(elemcounts));
    6956             : 
    6957           8 :         if (gincost_pattern(index, indexcol, clause_op, elemValues[i],
    6958             :                             &elemcounts))
    6959             :         {
    6960             :             /* We ignore array elements that are unsatisfiable patterns */
    6961           8 :             numPossible++;
    6962             : 
    6963           8 :             if (elemcounts.attHasFullScan[indexcol] &&
    6964           0 :                 !elemcounts.attHasNormalScan[indexcol])
    6965             :             {
    6966             :                 /*
    6967             :                  * Full index scan will be required.  We treat this as if
    6968             :                  * every key in the index had been listed in the query; is
    6969             :                  * that reasonable?
    6970             :                  */
    6971           0 :                 elemcounts.partialEntries = 0;
    6972           0 :                 elemcounts.exactEntries = numIndexEntries;
    6973           0 :                 elemcounts.searchEntries = numIndexEntries;
    6974             :             }
    6975           8 :             arraycounts.partialEntries += elemcounts.partialEntries;
    6976           8 :             arraycounts.exactEntries += elemcounts.exactEntries;
    6977           8 :             arraycounts.searchEntries += elemcounts.searchEntries;
    6978             :         }
    6979             :     }
    6980             : 
    6981           4 :     if (numPossible == 0)
    6982             :     {
    6983             :         /* No satisfiable patterns in the array */
    6984           0 :         return false;
    6985             :     }
    6986             : 
    6987             :     /*
    6988             :      * Now add the averages to the global counts.  This will give us an
    6989             :      * estimate of the average number of terms searched for in each indexscan,
    6990             :      * including contributions from both array and non-array quals.
    6991             :      */
    6992           4 :     counts->partialEntries += arraycounts.partialEntries / numPossible;
    6993           4 :     counts->exactEntries += arraycounts.exactEntries / numPossible;
    6994           4 :     counts->searchEntries += arraycounts.searchEntries / numPossible;
    6995             : 
    6996           4 :     counts->arrayScans *= numPossible;
    6997             : 
    6998           4 :     return true;
    6999             : }
    7000             : 
    7001             : /*
    7002             :  * GIN has search behavior completely different from other index types
    7003             :  */
    7004             : void
    7005        1430 : gincostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
    7006             :                 Cost *indexStartupCost, Cost *indexTotalCost,
    7007             :                 Selectivity *indexSelectivity, double *indexCorrelation,
    7008             :                 double *indexPages)
    7009             : {
    7010        1430 :     IndexOptInfo *index = path->indexinfo;
    7011        1430 :     List       *indexQuals = get_quals_from_indexclauses(path->indexclauses);
    7012             :     List       *selectivityQuals;
    7013        1430 :     double      numPages = index->pages,
    7014        1430 :                 numTuples = index->tuples;
    7015             :     double      numEntryPages,
    7016             :                 numDataPages,
    7017             :                 numPendingPages,
    7018             :                 numEntries;
    7019             :     GinQualCounts counts;
    7020             :     bool        matchPossible;
    7021             :     bool        fullIndexScan;
    7022             :     double      partialScale;
    7023             :     double      entryPagesFetched,
    7024             :                 dataPagesFetched,
    7025             :                 dataPagesFetchedBySel;
    7026             :     double      qual_op_cost,
    7027             :                 qual_arg_cost,
    7028             :                 spc_random_page_cost,
    7029             :                 outer_scans;
    7030             :     Relation    indexRel;
    7031             :     GinStatsData ginStats;
    7032             :     ListCell   *lc;
    7033             :     int         i;
    7034             : 
    7035             :     /*
    7036             :      * Obtain statistical information from the meta page, if possible.  Else
    7037             :      * set ginStats to zeroes, and we'll cope below.
    7038             :      */
    7039        1430 :     if (!index->hypothetical)
    7040             :     {
    7041             :         /* Lock should have already been obtained in plancat.c */
    7042        1430 :         indexRel = index_open(index->indexoid, NoLock);
    7043        1430 :         ginGetStats(indexRel, &ginStats);
    7044        1430 :         index_close(indexRel, NoLock);
    7045             :     }
    7046             :     else
    7047             :     {
    7048           0 :         memset(&ginStats, 0, sizeof(ginStats));
    7049             :     }
    7050             : 
    7051             :     /*
    7052             :      * Assuming we got valid (nonzero) stats at all, nPendingPages can be
    7053             :      * trusted, but the other fields are data as of the last VACUUM.  We can
    7054             :      * scale them up to account for growth since then, but that method only
    7055             :      * goes so far; in the worst case, the stats might be for a completely
    7056             :      * empty index, and scaling them will produce pretty bogus numbers.
    7057             :      * Somewhat arbitrarily, set the cutoff for doing scaling at 4X growth; if
    7058             :      * it's grown more than that, fall back to estimating things only from the
    7059             :      * assumed-accurate index size.  But we'll trust nPendingPages in any case
    7060             :      * so long as it's not clearly insane, ie, more than the index size.
    7061             :      */
    7062        1430 :     if (ginStats.nPendingPages < numPages)
    7063        1430 :         numPendingPages = ginStats.nPendingPages;
    7064             :     else
    7065           0 :         numPendingPages = 0;
    7066             : 
    7067        1430 :     if (numPages > 0 && ginStats.nTotalPages <= numPages &&
    7068        1430 :         ginStats.nTotalPages > numPages / 4 &&
    7069        1402 :         ginStats.nEntryPages > 0 && ginStats.nEntries > 0)
    7070        1230 :     {
    7071             :         /*
    7072             :          * OK, the stats seem close enough to sane to be trusted.  But we
    7073             :          * still need to scale them by the ratio numPages / nTotalPages to
    7074             :          * account for growth since the last VACUUM.
    7075             :          */
    7076        1230 :         double      scale = numPages / ginStats.nTotalPages;
    7077             : 
    7078        1230 :         numEntryPages = ceil(ginStats.nEntryPages * scale);
    7079        1230 :         numDataPages = ceil(ginStats.nDataPages * scale);
    7080        1230 :         numEntries = ceil(ginStats.nEntries * scale);
    7081             :         /* ensure we didn't round up too much */
    7082        1230 :         numEntryPages = Min(numEntryPages, numPages - numPendingPages);
    7083        1230 :         numDataPages = Min(numDataPages,
    7084             :                            numPages - numPendingPages - numEntryPages);
    7085             :     }
    7086             :     else
    7087             :     {
    7088             :         /*
    7089             :          * We might get here because it's a hypothetical index, or an index
    7090             :          * created pre-9.1 and never vacuumed since upgrading (in which case
    7091             :          * its stats would read as zeroes), or just because it's grown too
    7092             :          * much since the last VACUUM for us to put our faith in scaling.
    7093             :          *
    7094             :          * Invent some plausible internal statistics based on the index page
    7095             :          * count (and clamp that to at least 10 pages, just in case).  We
    7096             :          * estimate that 90% of the index is entry pages, and the rest is data
    7097             :          * pages.  Estimate 100 entries per entry page; this is rather bogus
    7098             :          * since it'll depend on the size of the keys, but it's more robust
    7099             :          * than trying to predict the number of entries per heap tuple.
    7100             :          */
    7101         200 :         numPages = Max(numPages, 10);
    7102         200 :         numEntryPages = floor((numPages - numPendingPages) * 0.90);
    7103         200 :         numDataPages = numPages - numPendingPages - numEntryPages;
    7104         200 :         numEntries = floor(numEntryPages * 100);
    7105             :     }
    7106             : 
    7107             :     /* In an empty index, numEntries could be zero.  Avoid divide-by-zero */
    7108        1430 :     if (numEntries < 1)
    7109           0 :         numEntries = 1;
    7110             : 
    7111             :     /*
    7112             :      * If the index is partial, AND the index predicate with the index-bound
    7113             :      * quals to produce a more accurate idea of the number of rows covered by
    7114             :      * the bound conditions.
    7115             :      */
    7116        1430 :     selectivityQuals = add_predicate_to_index_quals(index, indexQuals);
    7117             : 
    7118             :     /* Estimate the fraction of main-table tuples that will be visited */
    7119        2860 :     *indexSelectivity = clauselist_selectivity(root, selectivityQuals,
    7120        1430 :                                                index->rel->relid,
    7121             :                                                JOIN_INNER,
    7122             :                                                NULL);
    7123             : 
    7124             :     /* fetch estimated page cost for tablespace containing index */
    7125        1430 :     get_tablespace_page_costs(index->reltablespace,
    7126             :                               &spc_random_page_cost,
    7127             :                               NULL);
    7128             : 
    7129             :     /*
    7130             :      * Generic assumption about index correlation: there isn't any.
    7131             :      */
    7132        1430 :     *indexCorrelation = 0.0;
    7133             : 
    7134             :     /*
    7135             :      * Examine quals to estimate number of search entries & partial matches
    7136             :      */
    7137        1430 :     memset(&counts, 0, sizeof(counts));
    7138        1430 :     counts.arrayScans = 1;
    7139        1430 :     matchPossible = true;
    7140             : 
    7141        3000 :     foreach(lc, path->indexclauses)
    7142             :     {
    7143        1570 :         IndexClause *iclause = lfirst_node(IndexClause, lc);
    7144             :         ListCell   *lc2;
    7145             : 
    7146        3132 :         foreach(lc2, iclause->indexquals)
    7147             :         {
    7148        1570 :             RestrictInfo *rinfo = lfirst_node(RestrictInfo, lc2);
    7149        1570 :             Expr       *clause = rinfo->clause;
    7150             : 
    7151        1570 :             if (IsA(clause, OpExpr))
    7152             :             {
    7153        1566 :                 matchPossible = gincost_opexpr(root,
    7154             :                                                index,
    7155        1566 :                                                iclause->indexcol,
    7156             :                                                (OpExpr *) clause,
    7157             :                                                &counts);
    7158        1566 :                 if (!matchPossible)
    7159           8 :                     break;
    7160             :             }
    7161           4 :             else if (IsA(clause, ScalarArrayOpExpr))
    7162             :             {
    7163           4 :                 matchPossible = gincost_scalararrayopexpr(root,
    7164             :                                                           index,
    7165           4 :                                                           iclause->indexcol,
    7166             :                                                           (ScalarArrayOpExpr *) clause,
    7167             :                                                           numEntries,
    7168             :                                                           &counts);
    7169           4 :                 if (!matchPossible)
    7170           0 :                     break;
    7171             :             }
    7172             :             else
    7173             :             {
    7174             :                 /* shouldn't be anything else for a GIN index */
    7175           0 :                 elog(ERROR, "unsupported GIN indexqual type: %d",
    7176             :                      (int) nodeTag(clause));
    7177             :             }
    7178             :         }
    7179             :     }
    7180             : 
    7181             :     /* Fall out if there were any provably-unsatisfiable quals */
    7182        1430 :     if (!matchPossible)
    7183             :     {
    7184           8 :         *indexStartupCost = 0;
    7185           8 :         *indexTotalCost = 0;
    7186           8 :         *indexSelectivity = 0;
    7187           8 :         return;
    7188             :     }
    7189             : 
    7190             :     /*
    7191             :      * If attribute has a full scan and at the same time doesn't have normal
    7192             :      * scan, then we'll have to scan all non-null entries of that attribute.
    7193             :      * Currently, we don't have per-attribute statistics for GIN.  Thus, we
    7194             :      * must assume the whole GIN index has to be scanned in this case.
    7195             :      */
    7196        1422 :     fullIndexScan = false;
    7197        2764 :     for (i = 0; i < index->nkeycolumns; i++)
    7198             :     {
    7199        1574 :         if (counts.attHasFullScan[i] && !counts.attHasNormalScan[i])
    7200             :         {
    7201         232 :             fullIndexScan = true;
    7202         232 :             break;
    7203             :         }
    7204             :     }
    7205             : 
    7206        1422 :     if (fullIndexScan || indexQuals == NIL)
    7207             :     {
    7208             :         /*
    7209             :          * Full index scan will be required.  We treat this as if every key in
    7210             :          * the index had been listed in the query; is that reasonable?
    7211             :          */
    7212         232 :         counts.partialEntries = 0;
    7213         232 :         counts.exactEntries = numEntries;
    7214         232 :         counts.searchEntries = numEntries;
    7215             :     }
    7216             : 
    7217             :     /* Will we have more than one iteration of a nestloop scan? */
    7218        1422 :     outer_scans = loop_count;
    7219             : 
    7220             :     /*
    7221             :      * Compute cost to begin scan, first of all, pay attention to pending
    7222             :      * list.
    7223             :      */
    7224        1422 :     entryPagesFetched = numPendingPages;
    7225             : 
    7226             :     /*
    7227             :      * Estimate number of entry pages read.  We need to do
    7228             :      * counts.searchEntries searches.  Use a power function as it should be,
    7229             :      * but tuples on leaf pages usually is much greater. Here we include all
    7230             :      * searches in entry tree, including search of first entry in partial
    7231             :      * match algorithm
    7232             :      */
    7233        1422 :     entryPagesFetched += ceil(counts.searchEntries * rint(pow(numEntryPages, 0.15)));
    7234             : 
    7235             :     /*
    7236             :      * Add an estimate of entry pages read by partial match algorithm. It's a
    7237             :      * scan over leaf pages in entry tree.  We haven't any useful stats here,
    7238             :      * so estimate it as proportion.  Because counts.partialEntries is really
    7239             :      * pretty bogus (see code above), it's possible that it is more than
    7240             :      * numEntries; clamp the proportion to ensure sanity.
    7241             :      */
    7242        1422 :     partialScale = counts.partialEntries / numEntries;
    7243        1422 :     partialScale = Min(partialScale, 1.0);
    7244             : 
    7245        1422 :     entryPagesFetched += ceil(numEntryPages * partialScale);
    7246             : 
    7247             :     /*
    7248             :      * Partial match algorithm reads all data pages before doing actual scan,
    7249             :      * so it's a startup cost.  Again, we haven't any useful stats here, so
    7250             :      * estimate it as proportion.
    7251             :      */
    7252        1422 :     dataPagesFetched = ceil(numDataPages * partialScale);
    7253             : 
    7254             :     /*
    7255             :      * Calculate cache effects if more than one scan due to nestloops or array
    7256             :      * quals.  The result is pro-rated per nestloop scan, but the array qual
    7257             :      * factor shouldn't be pro-rated (compare genericcostestimate).
    7258             :      */
    7259        1422 :     if (outer_scans > 1 || counts.arrayScans > 1)
    7260             :     {
    7261           4 :         entryPagesFetched *= outer_scans * counts.arrayScans;
    7262           4 :         entryPagesFetched = index_pages_fetched(entryPagesFetched,
    7263             :                                                 (BlockNumber) numEntryPages,
    7264             :                                                 numEntryPages, root);
    7265           4 :         entryPagesFetched /= outer_scans;
    7266           4 :         dataPagesFetched *= outer_scans * counts.arrayScans;
    7267           4 :         dataPagesFetched = index_pages_fetched(dataPagesFetched,
    7268             :                                                (BlockNumber) numDataPages,
    7269             :                                                numDataPages, root);
    7270           4 :         dataPagesFetched /= outer_scans;
    7271             :     }
    7272             : 
    7273             :     /*
    7274             :      * Here we use random page cost because logically-close pages could be far
    7275             :      * apart on disk.
    7276             :      */
    7277        1422 :     *indexStartupCost = (entryPagesFetched + dataPagesFetched) * spc_random_page_cost;
    7278             : 
    7279             :     /*
    7280             :      * Now compute the number of data pages fetched during the scan.
    7281             :      *
    7282             :      * We assume every entry to have the same number of items, and that there
    7283             :      * is no overlap between them. (XXX: tsvector and array opclasses collect
    7284             :      * statistics on the frequency of individual keys; it would be nice to use
    7285             :      * those here.)
    7286             :      */
    7287        1422 :     dataPagesFetched = ceil(numDataPages * counts.exactEntries / numEntries);
    7288             : 
    7289             :     /*
    7290             :      * If there is a lot of overlap among the entries, in particular if one of
    7291             :      * the entries is very frequent, the above calculation can grossly
    7292             :      * under-estimate.  As a simple cross-check, calculate a lower bound based
    7293             :      * on the overall selectivity of the quals.  At a minimum, we must read
    7294             :      * one item pointer for each matching entry.
    7295             :      *
    7296             :      * The width of each item pointer varies, based on the level of
    7297             :      * compression.  We don't have statistics on that, but an average of
    7298             :      * around 3 bytes per item is fairly typical.
    7299             :      */
    7300        2844 :     dataPagesFetchedBySel = ceil(*indexSelectivity *
    7301        1422 :                                  (numTuples / (BLCKSZ / 3)));
    7302        1422 :     if (dataPagesFetchedBySel > dataPagesFetched)
    7303        1152 :         dataPagesFetched = dataPagesFetchedBySel;
    7304             : 
    7305             :     /* Account for cache effects, the same as above */
    7306        1422 :     if (outer_scans > 1 || counts.arrayScans > 1)
    7307             :     {
    7308           4 :         dataPagesFetched *= outer_scans * counts.arrayScans;
    7309           4 :         dataPagesFetched = index_pages_fetched(dataPagesFetched,
    7310             :                                                (BlockNumber) numDataPages,
    7311             :                                                numDataPages, root);
    7312           4 :         dataPagesFetched /= outer_scans;
    7313             :     }
    7314             : 
    7315             :     /* And apply random_page_cost as the cost per page */
    7316        2844 :     *indexTotalCost = *indexStartupCost +
    7317        1422 :         dataPagesFetched * spc_random_page_cost;
    7318             : 
    7319             :     /*
    7320             :      * Add on index qual eval costs, much as in genericcostestimate.  But we
    7321             :      * can disregard indexorderbys, since GIN doesn't support those.
    7322             :      */
    7323        1422 :     qual_arg_cost = index_other_operands_eval_cost(root, indexQuals);
    7324        1422 :     qual_op_cost = cpu_operator_cost * list_length(indexQuals);
    7325             : 
    7326        1422 :     *indexStartupCost += qual_arg_cost;
    7327        1422 :     *indexTotalCost += qual_arg_cost;
    7328        1422 :     *indexTotalCost += (numTuples * *indexSelectivity) * (cpu_index_tuple_cost + qual_op_cost);
    7329        1422 :     *indexPages = dataPagesFetched;
    7330             : }
    7331             : 
    7332             : /*
    7333             :  * BRIN has search behavior completely different from other index types
    7334             :  */
    7335             : void
    7336        3996 : brincostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
    7337             :                  Cost *indexStartupCost, Cost *indexTotalCost,
    7338             :                  Selectivity *indexSelectivity, double *indexCorrelation,
    7339             :                  double *indexPages)
    7340             : {
    7341        3996 :     IndexOptInfo *index = path->indexinfo;
    7342        3996 :     List       *indexQuals = get_quals_from_indexclauses(path->indexclauses);
    7343        3996 :     double      numPages = index->pages;
    7344        3996 :     RelOptInfo *baserel = index->rel;
    7345        3996 :     RangeTblEntry *rte = planner_rt_fetch(baserel->relid, root);
    7346             :     Cost        spc_seq_page_cost;
    7347             :     Cost        spc_random_page_cost;
    7348             :     double      qual_arg_cost;
    7349             :     double      qualSelectivity;
    7350             :     BrinStatsData statsData;
    7351             :     double      indexRanges;
    7352             :     double      minimalRanges;
    7353             :     double      estimatedRanges;
    7354             :     double      selec;
    7355             :     Relation    indexRel;
    7356             :     ListCell   *l;
    7357             :     VariableStatData vardata;
    7358             : 
    7359             :     Assert(rte->rtekind == RTE_RELATION);
    7360             : 
    7361             :     /* fetch estimated page cost for the tablespace containing the index */
    7362        3996 :     get_tablespace_page_costs(index->reltablespace,
    7363             :                               &spc_random_page_cost,
    7364             :                               &spc_seq_page_cost);
    7365             : 
    7366             :     /*
    7367             :      * Obtain some data from the index itself, if possible.  Otherwise invent
    7368             :      * some plausible internal statistics based on the relation page count.
    7369             :      */
    7370        3996 :     if (!index->hypothetical)
    7371             :     {
    7372             :         /*
    7373             :          * A lock should have already been obtained on the index in plancat.c.
    7374             :          */
    7375        3996 :         indexRel = index_open(index->indexoid, NoLock);
    7376        3996 :         brinGetStats(indexRel, &statsData);
    7377        3996 :         index_close(indexRel, NoLock);
    7378             : 
    7379             :         /* work out the actual number of ranges in the index */
    7380        3996 :         indexRanges = Max(ceil((double) baserel->pages /
    7381             :                                statsData.pagesPerRange), 1.0);
    7382             :     }
    7383             :     else
    7384             :     {
    7385             :         /*
    7386             :          * Assume default number of pages per range, and estimate the number
    7387             :          * of ranges based on that.
    7388             :          */
    7389           0 :         indexRanges = Max(ceil((double) baserel->pages /
    7390             :                                BRIN_DEFAULT_PAGES_PER_RANGE), 1.0);
    7391             : 
    7392           0 :         statsData.pagesPerRange = BRIN_DEFAULT_PAGES_PER_RANGE;
    7393           0 :         statsData.revmapNumPages = (indexRanges / REVMAP_PAGE_MAXITEMS) + 1;
    7394             :     }
    7395             : 
    7396             :     /*
    7397             :      * Compute index correlation
    7398             :      *
    7399             :      * Because we can use all index quals equally when scanning, we can use
    7400             :      * the largest correlation (in absolute value) among columns used by the
    7401             :      * query.  Start at zero, the worst possible case.  If we cannot find any
    7402             :      * correlation statistics, we will keep it as 0.
    7403             :      */
    7404        3996 :     *indexCorrelation = 0;
    7405             : 
    7406        7992 :     foreach(l, path->indexclauses)
    7407             :     {
    7408        3996 :         IndexClause *iclause = lfirst_node(IndexClause, l);
    7409        3996 :         AttrNumber  attnum = index->indexkeys[iclause->indexcol];
    7410             : 
    7411             :         /* attempt to lookup stats in relation for this index column */
    7412        3996 :         if (attnum != 0)
    7413             :         {
    7414             :             /* Simple variable -- look to stats for the underlying table */
    7415        3996 :             if (get_relation_stats_hook &&
    7416           0 :                 (*get_relation_stats_hook) (root, rte, attnum, &vardata))
    7417             :             {
    7418             :                 /*
    7419             :                  * The hook took control of acquiring a stats tuple.  If it
    7420             :                  * did supply a tuple, it'd better have supplied a freefunc.
    7421             :                  */
    7422           0 :                 if (HeapTupleIsValid(vardata.statsTuple) && !vardata.freefunc)
    7423           0 :                     elog(ERROR,
    7424             :                          "no function provided to release variable stats with");
    7425             :             }
    7426             :             else
    7427             :             {
    7428        3996 :                 vardata.statsTuple =
    7429        7992 :                     SearchSysCache3(STATRELATTINH,
    7430        3996 :                                     ObjectIdGetDatum(rte->relid),
    7431             :                                     Int16GetDatum(attnum),
    7432             :                                     BoolGetDatum(false));
    7433        3996 :                 vardata.freefunc = ReleaseSysCache;
    7434             :             }
    7435             :         }
    7436             :         else
    7437             :         {
    7438             :             /*
    7439             :              * Looks like we've found an expression column in the index. Let's
    7440             :              * see if there's any stats for it.
    7441             :              */
    7442             : 
    7443             :             /* get the attnum from the 0-based index. */
    7444           0 :             attnum = iclause->indexcol + 1;
    7445             : 
    7446           0 :             if (get_index_stats_hook &&
    7447           0 :                 (*get_index_stats_hook) (root, index->indexoid, attnum, &vardata))
    7448             :             {
    7449             :                 /*
    7450             :                  * The hook took control of acquiring a stats tuple.  If it
    7451             :                  * did supply a tuple, it'd better have supplied a freefunc.
    7452             :                  */
    7453           0 :                 if (HeapTupleIsValid(vardata.statsTuple) &&
    7454           0 :                     !vardata.freefunc)
    7455           0 :                     elog(ERROR, "no function provided to release variable stats with");
    7456             :             }
    7457             :             else
    7458             :             {
    7459           0 :                 vardata.statsTuple = SearchSysCache3(STATRELATTINH,
    7460           0 :                                                      ObjectIdGetDatum(index->indexoid),
    7461             :                                                      Int16GetDatum(attnum),
    7462             :                                                      BoolGetDatum(false));
    7463           0 :                 vardata.freefunc = ReleaseSysCache;
    7464             :             }
    7465             :         }
    7466             : 
    7467        3996 :         if (HeapTupleIsValid(vardata.statsTuple))
    7468             :         {
    7469             :             AttStatsSlot sslot;
    7470             : 
    7471           8 :             if (get_attstatsslot(&sslot, vardata.statsTuple,
    7472             :                                  STATISTIC_KIND_CORRELATION, InvalidOid,
    7473             :                                  ATTSTATSSLOT_NUMBERS))
    7474             :             {
    7475           8 :                 double      varCorrelation = 0.0;
    7476             : 
    7477           8 :                 if (sslot.nnumbers > 0)
    7478           8 :                     varCorrelation = Abs(sslot.numbers[0]);
    7479             : 
    7480           8 :                 if (varCorrelation > *indexCorrelation)
    7481           8 :                     *indexCorrelation = varCorrelation;
    7482             : 
    7483           8 :                 free_attstatsslot(&sslot);
    7484             :             }
    7485             :         }
    7486             : 
    7487        3996 :         ReleaseVariableStats(vardata);
    7488             :     }
    7489             : 
    7490        3996 :     qualSelectivity = clauselist_selectivity(root, indexQuals,
    7491        3996 :                                              baserel->relid,
    7492             :                                              JOIN_INNER, NULL);
    7493             : 
    7494             :     /*
    7495             :      * Now calculate the minimum possible ranges we could match with if all of
    7496             :      * the rows were in the perfect order in the table's heap.
    7497             :      */
    7498        3996 :     minimalRanges = ceil(indexRanges * qualSelectivity);
    7499             : 
    7500             :     /*
    7501             :      * Now estimate the number of ranges that we'll touch by using the
    7502             :      * indexCorrelation from the stats. Careful not to divide by zero (note
    7503             :      * we're using the absolute value of the correlation).
    7504             :      */
    7505        3996 :     if (*indexCorrelation < 1.0e-10)
    7506        3988 :         estimatedRanges = indexRanges;
    7507             :     else
    7508           8 :         estimatedRanges = Min(minimalRanges / *indexCorrelation, indexRanges);
    7509             : 
    7510             :     /* we expect to visit this portion of the table */
    7511        3996 :     selec = estimatedRanges / indexRanges;
    7512             : 
    7513        3996 :     CLAMP_PROBABILITY(selec);
    7514             : 
    7515        3996 :     *indexSelectivity = selec;
    7516             : 
    7517             :     /*
    7518             :      * Compute the index qual costs, much as in genericcostestimate, to add to
    7519             :      * the index costs.  We can disregard indexorderbys, since BRIN doesn't
    7520             :      * support those.
    7521             :      */
    7522        3996 :     qual_arg_cost = index_other_operands_eval_cost(root, indexQuals);
    7523             : 
    7524             :     /*
    7525             :      * Compute the startup cost as the cost to read the whole revmap
    7526             :      * sequentially, including the cost to execute the index quals.
    7527             :      */
    7528        3996 :     *indexStartupCost =
    7529        3996 :         spc_seq_page_cost * statsData.revmapNumPages * loop_count;
    7530        3996 :     *indexStartupCost += qual_arg_cost;
    7531             : 
    7532             :     /*
    7533             :      * To read a BRIN index there might be a bit of back and forth over
    7534             :      * regular pages, as revmap might point to them out of sequential order;
    7535             :      * calculate the total cost as reading the whole index in random order.
    7536             :      */
    7537        7992 :     *indexTotalCost = *indexStartupCost +
    7538        3996 :         spc_random_page_cost * (numPages - statsData.revmapNumPages) * loop_count;
    7539             : 
    7540             :     /*
    7541             :      * Charge a small amount per range tuple which we expect to match to. This
    7542             :      * is meant to reflect the costs of manipulating the bitmap. The BRIN scan
    7543             :      * will set a bit for each page in the range when we find a matching
    7544             :      * range, so we must multiply the charge by the number of pages in the
    7545             :      * range.
    7546             :      */
    7547        7992 :     *indexTotalCost += 0.1 * cpu_operator_cost * estimatedRanges *
    7548        3996 :         statsData.pagesPerRange;
    7549             : 
    7550        3996 :     *indexPages = index->pages;
    7551        3996 : }

Generated by: LCOV version 1.13