LCOV - code coverage report
Current view: top level - src/backend/utils/adt - array_selfuncs.c (source / functions) Hit Total Coverage
Test: PostgreSQL 12beta2 Lines: 239 319 74.9 %
Date: 2019-06-19 16:07:09 Functions: 11 13 84.6 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /*-------------------------------------------------------------------------
       2             :  *
       3             :  * array_selfuncs.c
       4             :  *    Functions for selectivity estimation of array operators
       5             :  *
       6             :  * Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
       7             :  * Portions Copyright (c) 1994, Regents of the University of California
       8             :  *
       9             :  *
      10             :  * IDENTIFICATION
      11             :  *    src/backend/utils/adt/array_selfuncs.c
      12             :  *
      13             :  *-------------------------------------------------------------------------
      14             :  */
      15             : #include "postgres.h"
      16             : 
      17             : #include <math.h>
      18             : 
      19             : #include "access/htup_details.h"
      20             : #include "catalog/pg_collation.h"
      21             : #include "catalog/pg_operator.h"
      22             : #include "catalog/pg_statistic.h"
      23             : #include "utils/array.h"
      24             : #include "utils/builtins.h"
      25             : #include "utils/lsyscache.h"
      26             : #include "utils/selfuncs.h"
      27             : #include "utils/typcache.h"
      28             : 
      29             : 
      30             : /* Default selectivity constant for "@>" and "<@" operators */
      31             : #define DEFAULT_CONTAIN_SEL 0.005
      32             : 
      33             : /* Default selectivity constant for "&&" operator */
      34             : #define DEFAULT_OVERLAP_SEL 0.01
      35             : 
      36             : /* Default selectivity for given operator */
      37             : #define DEFAULT_SEL(operator) \
      38             :     ((operator) == OID_ARRAY_OVERLAP_OP ? \
      39             :         DEFAULT_OVERLAP_SEL : DEFAULT_CONTAIN_SEL)
      40             : 
      41             : static Selectivity calc_arraycontsel(VariableStatData *vardata, Datum constval,
      42             :                                      Oid elemtype, Oid operator);
      43             : static Selectivity mcelem_array_selec(ArrayType *array,
      44             :                                       TypeCacheEntry *typentry,
      45             :                                       Datum *mcelem, int nmcelem,
      46             :                                       float4 *numbers, int nnumbers,
      47             :                                       float4 *hist, int nhist,
      48             :                                       Oid operator);
      49             : static Selectivity mcelem_array_contain_overlap_selec(Datum *mcelem, int nmcelem,
      50             :                                                       float4 *numbers, int nnumbers,
      51             :                                                       Datum *array_data, int nitems,
      52             :                                                       Oid operator, TypeCacheEntry *typentry);
      53             : static Selectivity mcelem_array_contained_selec(Datum *mcelem, int nmcelem,
      54             :                                                 float4 *numbers, int nnumbers,
      55             :                                                 Datum *array_data, int nitems,
      56             :                                                 float4 *hist, int nhist,
      57             :                                                 Oid operator, TypeCacheEntry *typentry);
      58             : static float *calc_hist(const float4 *hist, int nhist, int n);
      59             : static float *calc_distr(const float *p, int n, int m, float rest);
      60             : static int  floor_log2(uint32 n);
      61             : static bool find_next_mcelem(Datum *mcelem, int nmcelem, Datum value,
      62             :                              int *index, TypeCacheEntry *typentry);
      63             : static int  element_compare(const void *key1, const void *key2, void *arg);
      64             : static int  float_compare_desc(const void *key1, const void *key2);
      65             : 
      66             : 
      67             : /*
      68             :  * scalararraysel_containment
      69             :  *      Estimate selectivity of ScalarArrayOpExpr via array containment.
      70             :  *
      71             :  * If we have const =/<> ANY/ALL (array_var) then we can estimate the
      72             :  * selectivity as though this were an array containment operator,
      73             :  * array_var op ARRAY[const].
      74             :  *
      75             :  * scalararraysel() has already verified that the ScalarArrayOpExpr's operator
      76             :  * is the array element type's default equality or inequality operator, and
      77             :  * has aggressively simplified both inputs to constants.
      78             :  *
      79             :  * Returns selectivity (0..1), or -1 if we fail to estimate selectivity.
      80             :  */
      81             : Selectivity
      82       12624 : scalararraysel_containment(PlannerInfo *root,
      83             :                            Node *leftop, Node *rightop,
      84             :                            Oid elemtype, bool isEquality, bool useOr,
      85             :                            int varRelid)
      86             : {
      87             :     Selectivity selec;
      88             :     VariableStatData vardata;
      89             :     Datum       constval;
      90             :     TypeCacheEntry *typentry;
      91             :     FmgrInfo   *cmpfunc;
      92             : 
      93             :     /*
      94             :      * rightop must be a variable, else punt.
      95             :      */
      96       12624 :     examine_variable(root, rightop, varRelid, &vardata);
      97       12624 :     if (!vardata.rel)
      98             :     {
      99       12576 :         ReleaseVariableStats(vardata);
     100       12576 :         return -1.0;
     101             :     }
     102             : 
     103             :     /*
     104             :      * leftop must be a constant, else punt.
     105             :      */
     106          48 :     if (!IsA(leftop, Const))
     107             :     {
     108          10 :         ReleaseVariableStats(vardata);
     109          10 :         return -1.0;
     110             :     }
     111          38 :     if (((Const *) leftop)->constisnull)
     112             :     {
     113             :         /* qual can't succeed if null on left */
     114           0 :         ReleaseVariableStats(vardata);
     115           0 :         return (Selectivity) 0.0;
     116             :     }
     117          38 :     constval = ((Const *) leftop)->constvalue;
     118             : 
     119             :     /* Get element type's default comparison function */
     120          38 :     typentry = lookup_type_cache(elemtype, TYPECACHE_CMP_PROC_FINFO);
     121          38 :     if (!OidIsValid(typentry->cmp_proc_finfo.fn_oid))
     122             :     {
     123           0 :         ReleaseVariableStats(vardata);
     124           0 :         return -1.0;
     125             :     }
     126          38 :     cmpfunc = &typentry->cmp_proc_finfo;
     127             : 
     128             :     /*
     129             :      * If the operator is <>, swap ANY/ALL, then invert the result later.
     130             :      */
     131          38 :     if (!isEquality)
     132          24 :         useOr = !useOr;
     133             : 
     134             :     /* Get array element stats for var, if available */
     135          38 :     if (HeapTupleIsValid(vardata.statsTuple) &&
     136           0 :         statistic_proc_security_check(&vardata, cmpfunc->fn_oid))
     137           0 :     {
     138             :         Form_pg_statistic stats;
     139             :         AttStatsSlot sslot;
     140             :         AttStatsSlot hslot;
     141             : 
     142           0 :         stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
     143             : 
     144             :         /* MCELEM will be an array of same type as element */
     145           0 :         if (get_attstatsslot(&sslot, vardata.statsTuple,
     146             :                              STATISTIC_KIND_MCELEM, InvalidOid,
     147             :                              ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS))
     148             :         {
     149             :             /* For ALL case, also get histogram of distinct-element counts */
     150           0 :             if (useOr ||
     151           0 :                 !get_attstatsslot(&hslot, vardata.statsTuple,
     152             :                                   STATISTIC_KIND_DECHIST, InvalidOid,
     153             :                                   ATTSTATSSLOT_NUMBERS))
     154           0 :                 memset(&hslot, 0, sizeof(hslot));
     155             : 
     156             :             /*
     157             :              * For = ANY, estimate as var @> ARRAY[const].
     158             :              *
     159             :              * For = ALL, estimate as var <@ ARRAY[const].
     160             :              */
     161           0 :             if (useOr)
     162           0 :                 selec = mcelem_array_contain_overlap_selec(sslot.values,
     163             :                                                            sslot.nvalues,
     164             :                                                            sslot.numbers,
     165             :                                                            sslot.nnumbers,
     166             :                                                            &constval, 1,
     167             :                                                            OID_ARRAY_CONTAINS_OP,
     168             :                                                            typentry);
     169             :             else
     170           0 :                 selec = mcelem_array_contained_selec(sslot.values,
     171             :                                                      sslot.nvalues,
     172             :                                                      sslot.numbers,
     173             :                                                      sslot.nnumbers,
     174             :                                                      &constval, 1,
     175             :                                                      hslot.numbers,
     176             :                                                      hslot.nnumbers,
     177             :                                                      OID_ARRAY_CONTAINED_OP,
     178             :                                                      typentry);
     179             : 
     180           0 :             free_attstatsslot(&hslot);
     181           0 :             free_attstatsslot(&sslot);
     182             :         }
     183             :         else
     184             :         {
     185             :             /* No most-common-elements info, so do without */
     186           0 :             if (useOr)
     187           0 :                 selec = mcelem_array_contain_overlap_selec(NULL, 0,
     188             :                                                            NULL, 0,
     189             :                                                            &constval, 1,
     190             :                                                            OID_ARRAY_CONTAINS_OP,
     191             :                                                            typentry);
     192             :             else
     193           0 :                 selec = mcelem_array_contained_selec(NULL, 0,
     194             :                                                      NULL, 0,
     195             :                                                      &constval, 1,
     196             :                                                      NULL, 0,
     197             :                                                      OID_ARRAY_CONTAINED_OP,
     198             :                                                      typentry);
     199             :         }
     200             : 
     201             :         /*
     202             :          * MCE stats count only non-null rows, so adjust for null rows.
     203             :          */
     204           0 :         selec *= (1.0 - stats->stanullfrac);
     205             :     }
     206             :     else
     207             :     {
     208             :         /* No stats at all, so do without */
     209          38 :         if (useOr)
     210          38 :             selec = mcelem_array_contain_overlap_selec(NULL, 0,
     211             :                                                        NULL, 0,
     212             :                                                        &constval, 1,
     213             :                                                        OID_ARRAY_CONTAINS_OP,
     214             :                                                        typentry);
     215             :         else
     216           0 :             selec = mcelem_array_contained_selec(NULL, 0,
     217             :                                                  NULL, 0,
     218             :                                                  &constval, 1,
     219             :                                                  NULL, 0,
     220             :                                                  OID_ARRAY_CONTAINED_OP,
     221             :                                                  typentry);
     222             :         /* we assume no nulls here, so no stanullfrac correction */
     223             :     }
     224             : 
     225          38 :     ReleaseVariableStats(vardata);
     226             : 
     227             :     /*
     228             :      * If the operator is <>, invert the results.
     229             :      */
     230          38 :     if (!isEquality)
     231          24 :         selec = 1.0 - selec;
     232             : 
     233          38 :     CLAMP_PROBABILITY(selec);
     234             : 
     235          38 :     return selec;
     236             : }
     237             : 
     238             : /*
     239             :  * arraycontsel -- restriction selectivity for array @>, &&, <@ operators
     240             :  */
     241             : Datum
     242         354 : arraycontsel(PG_FUNCTION_ARGS)
     243             : {
     244         354 :     PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
     245         354 :     Oid         operator = PG_GETARG_OID(1);
     246         354 :     List       *args = (List *) PG_GETARG_POINTER(2);
     247         354 :     int         varRelid = PG_GETARG_INT32(3);
     248             :     VariableStatData vardata;
     249             :     Node       *other;
     250             :     bool        varonleft;
     251             :     Selectivity selec;
     252             :     Oid         element_typeid;
     253             : 
     254             :     /*
     255             :      * If expression is not (variable op something) or (something op
     256             :      * variable), then punt and return a default estimate.
     257             :      */
     258         354 :     if (!get_restriction_variable(root, args, varRelid,
     259             :                                   &vardata, &other, &varonleft))
     260           0 :         PG_RETURN_FLOAT8(DEFAULT_SEL(operator));
     261             : 
     262             :     /*
     263             :      * Can't do anything useful if the something is not a constant, either.
     264             :      */
     265         354 :     if (!IsA(other, Const))
     266             :     {
     267           0 :         ReleaseVariableStats(vardata);
     268           0 :         PG_RETURN_FLOAT8(DEFAULT_SEL(operator));
     269             :     }
     270             : 
     271             :     /*
     272             :      * The "&&", "@>" and "<@" operators are strict, so we can cope with a
     273             :      * NULL constant right away.
     274             :      */
     275         354 :     if (((Const *) other)->constisnull)
     276             :     {
     277           0 :         ReleaseVariableStats(vardata);
     278           0 :         PG_RETURN_FLOAT8(0.0);
     279             :     }
     280             : 
     281             :     /*
     282             :      * If var is on the right, commute the operator, so that we can assume the
     283             :      * var is on the left in what follows.
     284             :      */
     285         354 :     if (!varonleft)
     286             :     {
     287           0 :         if (operator == OID_ARRAY_CONTAINS_OP)
     288           0 :             operator = OID_ARRAY_CONTAINED_OP;
     289           0 :         else if (operator == OID_ARRAY_CONTAINED_OP)
     290           0 :             operator = OID_ARRAY_CONTAINS_OP;
     291             :     }
     292             : 
     293             :     /*
     294             :      * OK, there's a Var and a Const we're dealing with here.  We need the
     295             :      * Const to be an array with same element type as column, else we can't do
     296             :      * anything useful.  (Such cases will likely fail at runtime, but here
     297             :      * we'd rather just return a default estimate.)
     298             :      */
     299         354 :     element_typeid = get_base_element_type(((Const *) other)->consttype);
     300         708 :     if (element_typeid != InvalidOid &&
     301         354 :         element_typeid == get_base_element_type(vardata.vartype))
     302             :     {
     303         354 :         selec = calc_arraycontsel(&vardata, ((Const *) other)->constvalue,
     304             :                                   element_typeid, operator);
     305             :     }
     306             :     else
     307             :     {
     308           0 :         selec = DEFAULT_SEL(operator);
     309             :     }
     310             : 
     311         354 :     ReleaseVariableStats(vardata);
     312             : 
     313         354 :     CLAMP_PROBABILITY(selec);
     314             : 
     315         354 :     PG_RETURN_FLOAT8((float8) selec);
     316             : }
     317             : 
     318             : /*
     319             :  * arraycontjoinsel -- join selectivity for array @>, &&, <@ operators
     320             :  */
     321             : Datum
     322           0 : arraycontjoinsel(PG_FUNCTION_ARGS)
     323             : {
     324             :     /* For the moment this is just a stub */
     325           0 :     Oid         operator = PG_GETARG_OID(1);
     326             : 
     327           0 :     PG_RETURN_FLOAT8(DEFAULT_SEL(operator));
     328             : }
     329             : 
     330             : /*
     331             :  * Calculate selectivity for "arraycolumn @> const", "arraycolumn && const"
     332             :  * or "arraycolumn <@ const" based on the statistics
     333             :  *
     334             :  * This function is mainly responsible for extracting the pg_statistic data
     335             :  * to be used; we then pass the problem on to mcelem_array_selec().
     336             :  */
     337             : static Selectivity
     338         354 : calc_arraycontsel(VariableStatData *vardata, Datum constval,
     339             :                   Oid elemtype, Oid operator)
     340             : {
     341             :     Selectivity selec;
     342             :     TypeCacheEntry *typentry;
     343             :     FmgrInfo   *cmpfunc;
     344             :     ArrayType  *array;
     345             : 
     346             :     /* Get element type's default comparison function */
     347         354 :     typentry = lookup_type_cache(elemtype, TYPECACHE_CMP_PROC_FINFO);
     348         354 :     if (!OidIsValid(typentry->cmp_proc_finfo.fn_oid))
     349           0 :         return DEFAULT_SEL(operator);
     350         354 :     cmpfunc = &typentry->cmp_proc_finfo;
     351             : 
     352             :     /*
     353             :      * The caller made sure the const is an array with same element type, so
     354             :      * get it now
     355             :      */
     356         354 :     array = DatumGetArrayTypeP(constval);
     357             : 
     358         622 :     if (HeapTupleIsValid(vardata->statsTuple) &&
     359         268 :         statistic_proc_security_check(vardata, cmpfunc->fn_oid))
     360         268 :     {
     361             :         Form_pg_statistic stats;
     362             :         AttStatsSlot sslot;
     363             :         AttStatsSlot hslot;
     364             : 
     365         268 :         stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
     366             : 
     367             :         /* MCELEM will be an array of same type as column */
     368         268 :         if (get_attstatsslot(&sslot, vardata->statsTuple,
     369             :                              STATISTIC_KIND_MCELEM, InvalidOid,
     370             :                              ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS))
     371             :         {
     372             :             /*
     373             :              * For "array <@ const" case we also need histogram of distinct
     374             :              * element counts.
     375             :              */
     376         312 :             if (operator != OID_ARRAY_CONTAINED_OP ||
     377          44 :                 !get_attstatsslot(&hslot, vardata->statsTuple,
     378             :                                   STATISTIC_KIND_DECHIST, InvalidOid,
     379             :                                   ATTSTATSSLOT_NUMBERS))
     380         224 :                 memset(&hslot, 0, sizeof(hslot));
     381             : 
     382             :             /* Use the most-common-elements slot for the array Var. */
     383         268 :             selec = mcelem_array_selec(array, typentry,
     384             :                                        sslot.values, sslot.nvalues,
     385             :                                        sslot.numbers, sslot.nnumbers,
     386             :                                        hslot.numbers, hslot.nnumbers,
     387             :                                        operator);
     388             : 
     389         268 :             free_attstatsslot(&hslot);
     390         268 :             free_attstatsslot(&sslot);
     391             :         }
     392             :         else
     393             :         {
     394             :             /* No most-common-elements info, so do without */
     395           0 :             selec = mcelem_array_selec(array, typentry,
     396             :                                        NULL, 0, NULL, 0, NULL, 0,
     397             :                                        operator);
     398             :         }
     399             : 
     400             :         /*
     401             :          * MCE stats count only non-null rows, so adjust for null rows.
     402             :          */
     403         268 :         selec *= (1.0 - stats->stanullfrac);
     404             :     }
     405             :     else
     406             :     {
     407             :         /* No stats at all, so do without */
     408          86 :         selec = mcelem_array_selec(array, typentry,
     409             :                                    NULL, 0, NULL, 0, NULL, 0,
     410             :                                    operator);
     411             :         /* we assume no nulls here, so no stanullfrac correction */
     412             :     }
     413             : 
     414             :     /* If constant was toasted, release the copy we made */
     415         354 :     if (PointerGetDatum(array) != constval)
     416           0 :         pfree(array);
     417             : 
     418         354 :     return selec;
     419             : }
     420             : 
     421             : /*
     422             :  * Array selectivity estimation based on most common elements statistics
     423             :  *
     424             :  * This function just deconstructs and sorts the array constant's contents,
     425             :  * and then passes the problem on to mcelem_array_contain_overlap_selec or
     426             :  * mcelem_array_contained_selec depending on the operator.
     427             :  */
     428             : static Selectivity
     429         354 : mcelem_array_selec(ArrayType *array, TypeCacheEntry *typentry,
     430             :                    Datum *mcelem, int nmcelem,
     431             :                    float4 *numbers, int nnumbers,
     432             :                    float4 *hist, int nhist,
     433             :                    Oid operator)
     434             : {
     435             :     Selectivity selec;
     436             :     int         num_elems;
     437             :     Datum      *elem_values;
     438             :     bool       *elem_nulls;
     439             :     bool        null_present;
     440             :     int         nonnull_nitems;
     441             :     int         i;
     442             : 
     443             :     /*
     444             :      * Prepare constant array data for sorting.  Sorting lets us find unique
     445             :      * elements and efficiently merge with the MCELEM array.
     446             :      */
     447        1062 :     deconstruct_array(array,
     448             :                       typentry->type_id,
     449         354 :                       typentry->typlen,
     450         354 :                       typentry->typbyval,
     451         354 :                       typentry->typalign,
     452             :                       &elem_values, &elem_nulls, &num_elems);
     453             : 
     454             :     /* Collapse out any null elements */
     455         354 :     nonnull_nitems = 0;
     456         354 :     null_present = false;
     457         796 :     for (i = 0; i < num_elems; i++)
     458             :     {
     459         442 :         if (elem_nulls[i])
     460          28 :             null_present = true;
     461             :         else
     462         414 :             elem_values[nonnull_nitems++] = elem_values[i];
     463             :     }
     464             : 
     465             :     /*
     466             :      * Query "column @> '{anything, null}'" matches nothing.  For the other
     467             :      * two operators, presence of a null in the constant can be ignored.
     468             :      */
     469         354 :     if (null_present && operator == OID_ARRAY_CONTAINS_OP)
     470             :     {
     471           8 :         pfree(elem_values);
     472           8 :         pfree(elem_nulls);
     473           8 :         return (Selectivity) 0.0;
     474             :     }
     475             : 
     476             :     /* Sort extracted elements using their default comparison function. */
     477         346 :     qsort_arg(elem_values, nonnull_nitems, sizeof(Datum),
     478             :               element_compare, typentry);
     479             : 
     480             :     /* Separate cases according to operator */
     481         346 :     if (operator == OID_ARRAY_CONTAINS_OP || operator == OID_ARRAY_OVERLAP_OP)
     482         302 :         selec = mcelem_array_contain_overlap_selec(mcelem, nmcelem,
     483             :                                                    numbers, nnumbers,
     484             :                                                    elem_values, nonnull_nitems,
     485             :                                                    operator, typentry);
     486          44 :     else if (operator == OID_ARRAY_CONTAINED_OP)
     487          44 :         selec = mcelem_array_contained_selec(mcelem, nmcelem,
     488             :                                              numbers, nnumbers,
     489             :                                              elem_values, nonnull_nitems,
     490             :                                              hist, nhist,
     491             :                                              operator, typentry);
     492             :     else
     493             :     {
     494           0 :         elog(ERROR, "arraycontsel called for unrecognized operator %u",
     495             :              operator);
     496             :         selec = 0.0;            /* keep compiler quiet */
     497             :     }
     498             : 
     499         346 :     pfree(elem_values);
     500         346 :     pfree(elem_nulls);
     501         346 :     return selec;
     502             : }
     503             : 
     504             : /*
     505             :  * Estimate selectivity of "column @> const" and "column && const" based on
     506             :  * most common element statistics.  This estimation assumes element
     507             :  * occurrences are independent.
     508             :  *
     509             :  * mcelem (of length nmcelem) and numbers (of length nnumbers) are from
     510             :  * the array column's MCELEM statistics slot, or are NULL/0 if stats are
     511             :  * not available.  array_data (of length nitems) is the constant's elements.
     512             :  *
     513             :  * Both the mcelem and array_data arrays are assumed presorted according
     514             :  * to the element type's cmpfunc.  Null elements are not present.
     515             :  *
     516             :  * TODO: this estimate probably could be improved by using the distinct
     517             :  * elements count histogram.  For example, excepting the special case of
     518             :  * "column @> '{}'", we can multiply the calculated selectivity by the
     519             :  * fraction of nonempty arrays in the column.
     520             :  */
     521             : static Selectivity
     522         340 : mcelem_array_contain_overlap_selec(Datum *mcelem, int nmcelem,
     523             :                                    float4 *numbers, int nnumbers,
     524             :                                    Datum *array_data, int nitems,
     525             :                                    Oid operator, TypeCacheEntry *typentry)
     526             : {
     527             :     Selectivity selec,
     528             :                 elem_selec;
     529             :     int         mcelem_index,
     530             :                 i;
     531             :     bool        use_bsearch;
     532             :     float4      minfreq;
     533             : 
     534             :     /*
     535             :      * There should be three more Numbers than Values, because the last three
     536             :      * cells should hold minimal and maximal frequency among the non-null
     537             :      * elements, and then the frequency of null elements.  Ignore the Numbers
     538             :      * if not right.
     539             :      */
     540         340 :     if (nnumbers != nmcelem + 3)
     541             :     {
     542         124 :         numbers = NULL;
     543         124 :         nnumbers = 0;
     544             :     }
     545             : 
     546         340 :     if (numbers)
     547             :     {
     548             :         /* Grab the lowest observed frequency */
     549         216 :         minfreq = numbers[nmcelem];
     550             :     }
     551             :     else
     552             :     {
     553             :         /* Without statistics make some default assumptions */
     554         124 :         minfreq = 2 * (float4) DEFAULT_CONTAIN_SEL;
     555             :     }
     556             : 
     557             :     /* Decide whether it is faster to use binary search or not. */
     558         340 :     if (nitems * floor_log2((uint32) nmcelem) < nmcelem + nitems)
     559         340 :         use_bsearch = true;
     560             :     else
     561           0 :         use_bsearch = false;
     562             : 
     563         340 :     if (operator == OID_ARRAY_CONTAINS_OP)
     564             :     {
     565             :         /*
     566             :          * Initial selectivity for "column @> const" query is 1.0, and it will
     567             :          * be decreased with each element of constant array.
     568             :          */
     569         244 :         selec = 1.0;
     570             :     }
     571             :     else
     572             :     {
     573             :         /*
     574             :          * Initial selectivity for "column && const" query is 0.0, and it will
     575             :          * be increased with each element of constant array.
     576             :          */
     577          96 :         selec = 0.0;
     578             :     }
     579             : 
     580             :     /* Scan mcelem and array in parallel. */
     581         340 :     mcelem_index = 0;
     582         712 :     for (i = 0; i < nitems; i++)
     583             :     {
     584         372 :         bool        match = false;
     585             : 
     586             :         /* Ignore any duplicates in the array data. */
     587         444 :         if (i > 0 &&
     588          72 :             element_compare(&array_data[i - 1], &array_data[i], typentry) == 0)
     589           0 :             continue;
     590             : 
     591             :         /* Find the smallest MCELEM >= this array item. */
     592         372 :         if (use_bsearch)
     593             :         {
     594         372 :             match = find_next_mcelem(mcelem, nmcelem, array_data[i],
     595             :                                      &mcelem_index, typentry);
     596             :         }
     597             :         else
     598             :         {
     599           0 :             while (mcelem_index < nmcelem)
     600             :             {
     601           0 :                 int         cmp = element_compare(&mcelem[mcelem_index],
     602           0 :                                                   &array_data[i],
     603             :                                                   typentry);
     604             : 
     605           0 :                 if (cmp < 0)
     606           0 :                     mcelem_index++;
     607             :                 else
     608             :                 {
     609           0 :                     if (cmp == 0)
     610           0 :                         match = true;   /* mcelem is found */
     611           0 :                     break;
     612             :                 }
     613             :             }
     614             :         }
     615             : 
     616         372 :         if (match && numbers)
     617             :         {
     618             :             /* MCELEM matches the array item; use its frequency. */
     619         248 :             elem_selec = numbers[mcelem_index];
     620         248 :             mcelem_index++;
     621             :         }
     622             :         else
     623             :         {
     624             :             /*
     625             :              * The element is not in MCELEM.  Punt, but assume that the
     626             :              * selectivity cannot be more than minfreq / 2.
     627             :              */
     628         124 :             elem_selec = Min(DEFAULT_CONTAIN_SEL, minfreq / 2);
     629             :         }
     630             : 
     631             :         /*
     632             :          * Update overall selectivity using the current element's selectivity
     633             :          * and an assumption of element occurrence independence.
     634             :          */
     635         372 :         if (operator == OID_ARRAY_CONTAINS_OP)
     636         276 :             selec *= elem_selec;
     637             :         else
     638          96 :             selec = selec + elem_selec - selec * elem_selec;
     639             : 
     640             :         /* Clamp intermediate results to stay sane despite roundoff error */
     641         372 :         CLAMP_PROBABILITY(selec);
     642             :     }
     643             : 
     644         340 :     return selec;
     645             : }
     646             : 
     647             : /*
     648             :  * Estimate selectivity of "column <@ const" based on most common element
     649             :  * statistics.
     650             :  *
     651             :  * mcelem (of length nmcelem) and numbers (of length nnumbers) are from
     652             :  * the array column's MCELEM statistics slot, or are NULL/0 if stats are
     653             :  * not available.  array_data (of length nitems) is the constant's elements.
     654             :  * hist (of length nhist) is from the array column's DECHIST statistics slot,
     655             :  * or is NULL/0 if those stats are not available.
     656             :  *
     657             :  * Both the mcelem and array_data arrays are assumed presorted according
     658             :  * to the element type's cmpfunc.  Null elements are not present.
     659             :  *
     660             :  * Independent element occurrence would imply a particular distribution of
     661             :  * distinct element counts among matching rows.  Real data usually falsifies
     662             :  * that assumption.  For example, in a set of 11-element integer arrays having
     663             :  * elements in the range [0..10], element occurrences are typically not
     664             :  * independent.  If they were, a sufficiently-large set would include all
     665             :  * distinct element counts 0 through 11.  We correct for this using the
     666             :  * histogram of distinct element counts.
     667             :  *
     668             :  * In the "column @> const" and "column && const" cases, we usually have a
     669             :  * "const" with low number of elements (otherwise we have selectivity close
     670             :  * to 0 or 1 respectively).  That's why the effect of dependence related
     671             :  * to distinct element count distribution is negligible there.  In the
     672             :  * "column <@ const" case, number of elements is usually high (otherwise we
     673             :  * have selectivity close to 0).  That's why we should do a correction with
     674             :  * the array distinct element count distribution here.
     675             :  *
     676             :  * Using the histogram of distinct element counts produces a different
     677             :  * distribution law than independent occurrences of elements.  This
     678             :  * distribution law can be described as follows:
     679             :  *
     680             :  * P(o1, o2, ..., on) = f1^o1 * (1 - f1)^(1 - o1) * f2^o2 *
     681             :  *    (1 - f2)^(1 - o2) * ... * fn^on * (1 - fn)^(1 - on) * hist[m] / ind[m]
     682             :  *
     683             :  * where:
     684             :  * o1, o2, ..., on - occurrences of elements 1, 2, ..., n
     685             :  *      (1 - occurrence, 0 - no occurrence) in row
     686             :  * f1, f2, ..., fn - frequencies of elements 1, 2, ..., n
     687             :  *      (scalar values in [0..1]) according to collected statistics
     688             :  * m = o1 + o2 + ... + on = total number of distinct elements in row
     689             :  * hist[m] - histogram data for occurrence of m elements.
     690             :  * ind[m] - probability of m occurrences from n events assuming their
     691             :  *    probabilities to be equal to frequencies of array elements.
     692             :  *
     693             :  * ind[m] = sum(f1^o1 * (1 - f1)^(1 - o1) * f2^o2 * (1 - f2)^(1 - o2) *
     694             :  * ... * fn^on * (1 - fn)^(1 - on), o1, o2, ..., on) | o1 + o2 + .. on = m
     695             :  */
     696             : static Selectivity
     697          44 : mcelem_array_contained_selec(Datum *mcelem, int nmcelem,
     698             :                              float4 *numbers, int nnumbers,
     699             :                              Datum *array_data, int nitems,
     700             :                              float4 *hist, int nhist,
     701             :                              Oid operator, TypeCacheEntry *typentry)
     702             : {
     703             :     int         mcelem_index,
     704             :                 i,
     705          44 :                 unique_nitems = 0;
     706             :     float       selec,
     707             :                 minfreq,
     708             :                 nullelem_freq;
     709             :     float      *dist,
     710             :                *mcelem_dist,
     711             :                *hist_part;
     712             :     float       avg_count,
     713             :                 mult,
     714             :                 rest;
     715             :     float      *elem_selec;
     716             : 
     717             :     /*
     718             :      * There should be three more Numbers than Values in the MCELEM slot,
     719             :      * because the last three cells should hold minimal and maximal frequency
     720             :      * among the non-null elements, and then the frequency of null elements.
     721             :      * Punt if not right, because we can't do much without the element freqs.
     722             :      */
     723          44 :     if (numbers == NULL || nnumbers != nmcelem + 3)
     724           0 :         return DEFAULT_CONTAIN_SEL;
     725             : 
     726             :     /* Can't do much without a count histogram, either */
     727          44 :     if (hist == NULL || nhist < 3)
     728           0 :         return DEFAULT_CONTAIN_SEL;
     729             : 
     730             :     /*
     731             :      * Grab some of the summary statistics that compute_array_stats() stores:
     732             :      * lowest frequency, frequency of null elements, and average distinct
     733             :      * element count.
     734             :      */
     735          44 :     minfreq = numbers[nmcelem];
     736          44 :     nullelem_freq = numbers[nmcelem + 2];
     737          44 :     avg_count = hist[nhist - 1];
     738             : 
     739             :     /*
     740             :      * "rest" will be the sum of the frequencies of all elements not
     741             :      * represented in MCELEM.  The average distinct element count is the sum
     742             :      * of the frequencies of *all* elements.  Begin with that; we will proceed
     743             :      * to subtract the MCELEM frequencies.
     744             :      */
     745          44 :     rest = avg_count;
     746             : 
     747             :     /*
     748             :      * mult is a multiplier representing estimate of probability that each
     749             :      * mcelem that is not present in constant doesn't occur.
     750             :      */
     751          44 :     mult = 1.0f;
     752             : 
     753             :     /*
     754             :      * elem_selec is array of estimated frequencies for elements in the
     755             :      * constant.
     756             :      */
     757          44 :     elem_selec = (float *) palloc(sizeof(float) * nitems);
     758             : 
     759             :     /* Scan mcelem and array in parallel. */
     760          44 :     mcelem_index = 0;
     761         124 :     for (i = 0; i < nitems; i++)
     762             :     {
     763          80 :         bool        match = false;
     764             : 
     765             :         /* Ignore any duplicates in the array data. */
     766         144 :         if (i > 0 &&
     767          64 :             element_compare(&array_data[i - 1], &array_data[i], typentry) == 0)
     768           0 :             continue;
     769             : 
     770             :         /*
     771             :          * Iterate over MCELEM until we find an entry greater than or equal to
     772             :          * this element of the constant.  Update "rest" and "mult" for mcelem
     773             :          * entries skipped over.
     774             :          */
     775        2240 :         while (mcelem_index < nmcelem)
     776             :         {
     777        2160 :             int         cmp = element_compare(&mcelem[mcelem_index],
     778        2160 :                                               &array_data[i],
     779             :                                               typentry);
     780             : 
     781        2160 :             if (cmp < 0)
     782             :             {
     783        2080 :                 mult *= (1.0f - numbers[mcelem_index]);
     784        2080 :                 rest -= numbers[mcelem_index];
     785        2080 :                 mcelem_index++;
     786             :             }
     787             :             else
     788             :             {
     789          80 :                 if (cmp == 0)
     790          80 :                     match = true;   /* mcelem is found */
     791          80 :                 break;
     792             :             }
     793             :         }
     794             : 
     795          80 :         if (match)
     796             :         {
     797             :             /* MCELEM matches the array item. */
     798          80 :             elem_selec[unique_nitems] = numbers[mcelem_index];
     799             :             /* "rest" is decremented for all mcelems, matched or not */
     800          80 :             rest -= numbers[mcelem_index];
     801          80 :             mcelem_index++;
     802             :         }
     803             :         else
     804             :         {
     805             :             /*
     806             :              * The element is not in MCELEM.  Punt, but assume that the
     807             :              * selectivity cannot be more than minfreq / 2.
     808             :              */
     809           0 :             elem_selec[unique_nitems] = Min(DEFAULT_CONTAIN_SEL,
     810             :                                             minfreq / 2);
     811             :         }
     812             : 
     813          80 :         unique_nitems++;
     814             :     }
     815             : 
     816             :     /*
     817             :      * If we handled all constant elements without exhausting the MCELEM
     818             :      * array, finish walking it to complete calculation of "rest" and "mult".
     819             :      */
     820        3740 :     while (mcelem_index < nmcelem)
     821             :     {
     822        3652 :         mult *= (1.0f - numbers[mcelem_index]);
     823        3652 :         rest -= numbers[mcelem_index];
     824        3652 :         mcelem_index++;
     825             :     }
     826             : 
     827             :     /*
     828             :      * The presence of many distinct rare elements materially decreases
     829             :      * selectivity.  Use the Poisson distribution to estimate the probability
     830             :      * of a column value having zero occurrences of such elements.  See above
     831             :      * for the definition of "rest".
     832             :      */
     833          44 :     mult *= exp(-rest);
     834             : 
     835             :     /*----------
     836             :      * Using the distinct element count histogram requires
     837             :      *      O(unique_nitems * (nmcelem + unique_nitems))
     838             :      * operations.  Beyond a certain computational cost threshold, it's
     839             :      * reasonable to sacrifice accuracy for decreased planning time.  We limit
     840             :      * the number of operations to EFFORT * nmcelem; since nmcelem is limited
     841             :      * by the column's statistics target, the work done is user-controllable.
     842             :      *
     843             :      * If the number of operations would be too large, we can reduce it
     844             :      * without losing all accuracy by reducing unique_nitems and considering
     845             :      * only the most-common elements of the constant array.  To make the
     846             :      * results exactly match what we would have gotten with only those
     847             :      * elements to start with, we'd have to remove any discarded elements'
     848             :      * frequencies from "mult", but since this is only an approximation
     849             :      * anyway, we don't bother with that.  Therefore it's sufficient to qsort
     850             :      * elem_selec[] and take the largest elements.  (They will no longer match
     851             :      * up with the elements of array_data[], but we don't care.)
     852             :      *----------
     853             :      */
     854             : #define EFFORT 100
     855             : 
     856          88 :     if ((nmcelem + unique_nitems) > 0 &&
     857          44 :         unique_nitems > EFFORT * nmcelem / (nmcelem + unique_nitems))
     858             :     {
     859             :         /*
     860             :          * Use the quadratic formula to solve for largest allowable N.  We
     861             :          * have A = 1, B = nmcelem, C = - EFFORT * nmcelem.
     862             :          */
     863           0 :         double      b = (double) nmcelem;
     864             :         int         n;
     865             : 
     866           0 :         n = (int) ((sqrt(b * b + 4 * EFFORT * b) - b) / 2);
     867             : 
     868             :         /* Sort, then take just the first n elements */
     869           0 :         qsort(elem_selec, unique_nitems, sizeof(float),
     870             :               float_compare_desc);
     871           0 :         unique_nitems = n;
     872             :     }
     873             : 
     874             :     /*
     875             :      * Calculate probabilities of each distinct element count for both mcelems
     876             :      * and constant elements.  At this point, assume independent element
     877             :      * occurrence.
     878             :      */
     879          44 :     dist = calc_distr(elem_selec, unique_nitems, unique_nitems, 0.0f);
     880          44 :     mcelem_dist = calc_distr(numbers, nmcelem, unique_nitems, rest);
     881             : 
     882             :     /* ignore hist[nhist-1], which is the average not a histogram member */
     883          44 :     hist_part = calc_hist(hist, nhist - 1, unique_nitems);
     884             : 
     885          44 :     selec = 0.0f;
     886         168 :     for (i = 0; i <= unique_nitems; i++)
     887             :     {
     888             :         /*
     889             :          * mult * dist[i] / mcelem_dist[i] gives us probability of qual
     890             :          * matching from assumption of independent element occurrence with the
     891             :          * condition that distinct element count = i.
     892             :          */
     893         124 :         if (mcelem_dist[i] > 0)
     894         124 :             selec += hist_part[i] * mult * dist[i] / mcelem_dist[i];
     895             :     }
     896             : 
     897          44 :     pfree(dist);
     898          44 :     pfree(mcelem_dist);
     899          44 :     pfree(hist_part);
     900          44 :     pfree(elem_selec);
     901             : 
     902             :     /* Take into account occurrence of NULL element. */
     903          44 :     selec *= (1.0f - nullelem_freq);
     904             : 
     905          44 :     CLAMP_PROBABILITY(selec);
     906             : 
     907          44 :     return selec;
     908             : }
     909             : 
     910             : /*
     911             :  * Calculate the first n distinct element count probabilities from a
     912             :  * histogram of distinct element counts.
     913             :  *
     914             :  * Returns a palloc'd array of n+1 entries, with array[k] being the
     915             :  * probability of element count k, k in [0..n].
     916             :  *
     917             :  * We assume that a histogram box with bounds a and b gives 1 / ((b - a + 1) *
     918             :  * (nhist - 1)) probability to each value in (a,b) and an additional half of
     919             :  * that to a and b themselves.
     920             :  */
     921             : static float *
     922          44 : calc_hist(const float4 *hist, int nhist, int n)
     923             : {
     924             :     float      *hist_part;
     925             :     int         k,
     926          44 :                 i = 0;
     927          44 :     float       prev_interval = 0,
     928             :                 next_interval;
     929             :     float       frac;
     930             : 
     931          44 :     hist_part = (float *) palloc((n + 1) * sizeof(float));
     932             : 
     933             :     /*
     934             :      * frac is a probability contribution for each interval between histogram
     935             :      * values.  We have nhist - 1 intervals, so contribution of each one will
     936             :      * be 1 / (nhist - 1).
     937             :      */
     938          44 :     frac = 1.0f / ((float) (nhist - 1));
     939             : 
     940         168 :     for (k = 0; k <= n; k++)
     941             :     {
     942         124 :         int         count = 0;
     943             : 
     944             :         /*
     945             :          * Count the histogram boundaries equal to k.  (Although the histogram
     946             :          * should theoretically contain only exact integers, entries are
     947             :          * floats so there could be roundoff error in large values.  Treat any
     948             :          * fractional value as equal to the next larger k.)
     949             :          */
     950        1120 :         while (i < nhist && hist[i] <= k)
     951             :         {
     952         872 :             count++;
     953         872 :             i++;
     954             :         }
     955             : 
     956         124 :         if (count > 0)
     957             :         {
     958             :             /* k is an exact bound for at least one histogram box. */
     959             :             float       val;
     960             : 
     961             :             /* Find length between current histogram value and the next one */
     962         124 :             if (i < nhist)
     963         124 :                 next_interval = hist[i] - hist[i - 1];
     964             :             else
     965           0 :                 next_interval = 0;
     966             : 
     967             :             /*
     968             :              * count - 1 histogram boxes contain k exclusively.  They
     969             :              * contribute a total of (count - 1) * frac probability.  Also
     970             :              * factor in the partial histogram boxes on either side.
     971             :              */
     972         124 :             val = (float) (count - 1);
     973         124 :             if (next_interval > 0)
     974         124 :                 val += 0.5f / next_interval;
     975         124 :             if (prev_interval > 0)
     976          80 :                 val += 0.5f / prev_interval;
     977         124 :             hist_part[k] = frac * val;
     978             : 
     979         124 :             prev_interval = next_interval;
     980             :         }
     981             :         else
     982             :         {
     983             :             /* k does not appear as an exact histogram bound. */
     984           0 :             if (prev_interval > 0)
     985           0 :                 hist_part[k] = frac / prev_interval;
     986             :             else
     987           0 :                 hist_part[k] = 0.0f;
     988             :         }
     989             :     }
     990             : 
     991          44 :     return hist_part;
     992             : }
     993             : 
     994             : /*
     995             :  * Consider n independent events with probabilities p[].  This function
     996             :  * calculates probabilities of exact k of events occurrence for k in [0..m].
     997             :  * Returns a palloc'd array of size m+1.
     998             :  *
     999             :  * "rest" is the sum of the probabilities of all low-probability events not
    1000             :  * included in p.
    1001             :  *
    1002             :  * Imagine matrix M of size (n + 1) x (m + 1).  Element M[i,j] denotes the
    1003             :  * probability that exactly j of first i events occur.  Obviously M[0,0] = 1.
    1004             :  * For any constant j, each increment of i increases the probability iff the
    1005             :  * event occurs.  So, by the law of total probability:
    1006             :  *  M[i,j] = M[i - 1, j] * (1 - p[i]) + M[i - 1, j - 1] * p[i]
    1007             :  *      for i > 0, j > 0.
    1008             :  *  M[i,0] = M[i - 1, 0] * (1 - p[i]) for i > 0.
    1009             :  */
    1010             : static float *
    1011          88 : calc_distr(const float *p, int n, int m, float rest)
    1012             : {
    1013             :     float      *row,
    1014             :                *prev_row,
    1015             :                *tmp;
    1016             :     int         i,
    1017             :                 j;
    1018             : 
    1019             :     /*
    1020             :      * Since we return only the last row of the matrix and need only the
    1021             :      * current and previous row for calculations, allocate two rows.
    1022             :      */
    1023          88 :     row = (float *) palloc((m + 1) * sizeof(float));
    1024          88 :     prev_row = (float *) palloc((m + 1) * sizeof(float));
    1025             : 
    1026             :     /* M[0,0] = 1 */
    1027          88 :     row[0] = 1.0f;
    1028        5980 :     for (i = 1; i <= n; i++)
    1029             :     {
    1030        5892 :         float       t = p[i - 1];
    1031             : 
    1032             :         /* Swap rows */
    1033        5892 :         tmp = row;
    1034        5892 :         row = prev_row;
    1035        5892 :         prev_row = tmp;
    1036             : 
    1037             :         /* Calculate next row */
    1038       24152 :         for (j = 0; j <= i && j <= m; j++)
    1039             :         {
    1040       18260 :             float       val = 0.0f;
    1041             : 
    1042       18260 :             if (j < i)
    1043       18100 :                 val += prev_row[j] * (1.0f - t);
    1044       18260 :             if (j > 0)
    1045       12368 :                 val += prev_row[j - 1] * t;
    1046       18260 :             row[j] = val;
    1047             :         }
    1048             :     }
    1049             : 
    1050             :     /*
    1051             :      * The presence of many distinct rare (not in "p") elements materially
    1052             :      * decreases selectivity.  Model their collective occurrence with the
    1053             :      * Poisson distribution.
    1054             :      */
    1055          88 :     if (rest > DEFAULT_CONTAIN_SEL)
    1056             :     {
    1057             :         float       t;
    1058             : 
    1059             :         /* Swap rows */
    1060           0 :         tmp = row;
    1061           0 :         row = prev_row;
    1062           0 :         prev_row = tmp;
    1063             : 
    1064           0 :         for (i = 0; i <= m; i++)
    1065           0 :             row[i] = 0.0f;
    1066             : 
    1067             :         /* Value of Poisson distribution for 0 occurrences */
    1068           0 :         t = exp(-rest);
    1069             : 
    1070             :         /*
    1071             :          * Calculate convolution of previously computed distribution and the
    1072             :          * Poisson distribution.
    1073             :          */
    1074           0 :         for (i = 0; i <= m; i++)
    1075             :         {
    1076           0 :             for (j = 0; j <= m - i; j++)
    1077           0 :                 row[j + i] += prev_row[j] * t;
    1078             : 
    1079             :             /* Get Poisson distribution value for (i + 1) occurrences */
    1080           0 :             t *= rest / (float) (i + 1);
    1081             :         }
    1082             :     }
    1083             : 
    1084          88 :     pfree(prev_row);
    1085          88 :     return row;
    1086             : }
    1087             : 
    1088             : /* Fast function for floor value of 2 based logarithm calculation. */
    1089             : static int
    1090         340 : floor_log2(uint32 n)
    1091             : {
    1092         340 :     int         logval = 0;
    1093             : 
    1094         340 :     if (n == 0)
    1095         124 :         return -1;
    1096         216 :     if (n >= (1 << 16))
    1097             :     {
    1098           0 :         n >>= 16;
    1099           0 :         logval += 16;
    1100             :     }
    1101         216 :     if (n >= (1 << 8))
    1102             :     {
    1103          40 :         n >>= 8;
    1104          40 :         logval += 8;
    1105             :     }
    1106         216 :     if (n >= (1 << 4))
    1107             :     {
    1108         176 :         n >>= 4;
    1109         176 :         logval += 4;
    1110             :     }
    1111         216 :     if (n >= (1 << 2))
    1112             :     {
    1113         176 :         n >>= 2;
    1114         176 :         logval += 2;
    1115             :     }
    1116         216 :     if (n >= (1 << 1))
    1117             :     {
    1118          84 :         logval += 1;
    1119             :     }
    1120         216 :     return logval;
    1121             : }
    1122             : 
    1123             : /*
    1124             :  * find_next_mcelem binary-searches a most common elements array, starting
    1125             :  * from *index, for the first member >= value.  It saves the position of the
    1126             :  * match into *index and returns true if it's an exact match.  (Note: we
    1127             :  * assume the mcelem elements are distinct so there can't be more than one
    1128             :  * exact match.)
    1129             :  */
    1130             : static bool
    1131         372 : find_next_mcelem(Datum *mcelem, int nmcelem, Datum value, int *index,
    1132             :                  TypeCacheEntry *typentry)
    1133             : {
    1134         372 :     int         l = *index,
    1135         372 :                 r = nmcelem - 1,
    1136             :                 i,
    1137             :                 res;
    1138             : 
    1139        2104 :     while (l <= r)
    1140             :     {
    1141        1608 :         i = (l + r) / 2;
    1142        1608 :         res = element_compare(&mcelem[i], &value, typentry);
    1143        1608 :         if (res == 0)
    1144             :         {
    1145         248 :             *index = i;
    1146         248 :             return true;
    1147             :         }
    1148        1360 :         else if (res < 0)
    1149         520 :             l = i + 1;
    1150             :         else
    1151         840 :             r = i - 1;
    1152             :     }
    1153         124 :     *index = l;
    1154         124 :     return false;
    1155             : }
    1156             : 
    1157             : /*
    1158             :  * Comparison function for elements.
    1159             :  *
    1160             :  * We use the element type's default btree opclass, and its default collation
    1161             :  * if the type is collation-sensitive.
    1162             :  *
    1163             :  * XXX consider using SortSupport infrastructure
    1164             :  */
    1165             : static int
    1166        4104 : element_compare(const void *key1, const void *key2, void *arg)
    1167             : {
    1168        4104 :     Datum       d1 = *((const Datum *) key1);
    1169        4104 :     Datum       d2 = *((const Datum *) key2);
    1170        4104 :     TypeCacheEntry *typentry = (TypeCacheEntry *) arg;
    1171        4104 :     FmgrInfo   *cmpfunc = &typentry->cmp_proc_finfo;
    1172             :     Datum       c;
    1173             : 
    1174        4104 :     c = FunctionCall2Coll(cmpfunc, typentry->typcollation, d1, d2);
    1175        4104 :     return DatumGetInt32(c);
    1176             : }
    1177             : 
    1178             : /*
    1179             :  * Comparison function for sorting floats into descending order.
    1180             :  */
    1181             : static int
    1182           0 : float_compare_desc(const void *key1, const void *key2)
    1183             : {
    1184           0 :     float       d1 = *((const float *) key1);
    1185           0 :     float       d2 = *((const float *) key2);
    1186             : 
    1187           0 :     if (d1 > d2)
    1188           0 :         return -1;
    1189           0 :     else if (d1 < d2)
    1190           0 :         return 1;
    1191             :     else
    1192           0 :         return 0;
    1193             : }

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