extended_stats.c

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/*-------------------------------------------------------------------------
 *
 * extended_stats.c
 *    POSTGRES extended statistics
 *
 * Generic code supporting statistics objects created via CREATE STATISTICS.
 *
 *
 * Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/statistics/extended_stats.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/detoast.h"
#include "access/genam.h"
#include "access/htup_details.h"
#include "access/table.h"
#include "catalog/indexing.h"
#include "catalog/pg_collation.h"
#include "catalog/pg_statistic_ext.h"
#include "catalog/pg_statistic_ext_data.h"
#include "executor/executor.h"
#include "commands/progress.h"
#include "miscadmin.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/optimizer.h"
#include "pgstat.h"
#include "postmaster/autovacuum.h"
#include "statistics/extended_stats_internal.h"
#include "statistics/statistics.h"
#include "utils/acl.h"
#include "utils/array.h"
#include "utils/attoptcache.h"
#include "utils/builtins.h"
#include "utils/datum.h"
#include "utils/fmgroids.h"
#include "utils/lsyscache.h"
#include "utils/memutils.h"
#include "utils/rel.h"
#include "utils/selfuncs.h"
#include "utils/syscache.h"
#include "utils/typcache.h"

/*
 * To avoid consuming too much memory during analysis and/or too much space
 * in the resulting pg_statistic rows, we ignore varlena datums that are wider
 * than WIDTH_THRESHOLD (after detoasting!).  This is legitimate for MCV
 * and distinct-value calculations since a wide value is unlikely to be
 * duplicated at all, much less be a most-common value.  For the same reason,
 * ignoring wide values will not affect our estimates of histogram bin
 * boundaries very much.
 */
#define WIDTH_THRESHOLD  1024

/*
 * Used internally to refer to an individual statistics object, i.e.,
 * a pg_statistic_ext entry.
 */
typedef struct StatExtEntry
{
    Oid         statOid;        /* OID of pg_statistic_ext entry */
    char       *schema;         /* statistics object's schema */
    char       *name;           /* statistics object's name */
    Bitmapset  *columns;        /* attribute numbers covered by the object */
    List       *types;          /* 'char' list of enabled statistics kinds */
    int         stattarget;     /* statistics target (-1 for default) */
    List       *exprs;          /* expressions */
} StatExtEntry;


static List *fetch_statentries_for_relation(Relation pg_statext, Oid relid);
static VacAttrStats **lookup_var_attr_stats(Relation rel, Bitmapset *attrs, List *exprs,
                                            int nvacatts, VacAttrStats **vacatts);
static void statext_store(Oid statOid,
                          MVNDistinct *ndistinct, MVDependencies *dependencies,
                          MCVList *mcv, Datum exprs, VacAttrStats **stats);
static int  statext_compute_stattarget(int stattarget,
                                       int natts, VacAttrStats **stats);

/* Information needed to analyze a single simple expression. */
typedef struct AnlExprData
{
    Node       *expr;           /* expression to analyze */
    VacAttrStats *vacattrstat;  /* statistics attrs to analyze */
} AnlExprData;

static void compute_expr_stats(Relation onerel, double totalrows,
                               AnlExprData * exprdata, int nexprs,
                               HeapTuple *rows, int numrows);
static Datum serialize_expr_stats(AnlExprData * exprdata, int nexprs);
static Datum expr_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull);
static AnlExprData *build_expr_data(List *exprs, int stattarget);

static StatsBuildData *make_build_data(Relation onerel, StatExtEntry *stat,
                                       int numrows, HeapTuple *rows,
                                       VacAttrStats **stats, int stattarget);


/*
 * Compute requested extended stats, using the rows sampled for the plain
 * (single-column) stats.
 *
 * This fetches a list of stats types from pg_statistic_ext, computes the
 * requested stats, and serializes them back into the catalog.
 */
void
BuildRelationExtStatistics(Relation onerel, double totalrows,
                           int numrows, HeapTuple *rows,
                           int natts, VacAttrStats **vacattrstats)
{
    Relation    pg_stext;
    ListCell   *lc;
    List       *statslist;
    MemoryContext cxt;
    MemoryContext oldcxt;
    int64       ext_cnt;

    /* Do nothing if there are no columns to analyze. */
    if (!natts)
        return;

    cxt = AllocSetContextCreate(CurrentMemoryContext,
                                "BuildRelationExtStatistics",
                                ALLOCSET_DEFAULT_SIZES);
    oldcxt = MemoryContextSwitchTo(cxt);

    pg_stext = table_open(StatisticExtRelationId, RowExclusiveLock);
    statslist = fetch_statentries_for_relation(pg_stext, RelationGetRelid(onerel));

    /* report this phase */
    if (statslist != NIL)
    {
        const int   index[] = {
            PROGRESS_ANALYZE_PHASE,
            PROGRESS_ANALYZE_EXT_STATS_TOTAL
        };
        const int64 val[] = {
            PROGRESS_ANALYZE_PHASE_COMPUTE_EXT_STATS,
            list_length(statslist)
        };

        pgstat_progress_update_multi_param(2, index, val);
    }

    ext_cnt = 0;
    foreach(lc, statslist)
    {
        StatExtEntry *stat = (StatExtEntry *) lfirst(lc);
        MVNDistinct *ndistinct = NULL;
        MVDependencies *dependencies = NULL;
        MCVList    *mcv = NULL;
        Datum       exprstats = (Datum) 0;
        VacAttrStats **stats;
        ListCell   *lc2;
        int         stattarget;
        StatsBuildData *data;

        /*
         * Check if we can build these stats based on the column analyzed. If
         * not, report this fact (except in autovacuum) and move on.
         */
        stats = lookup_var_attr_stats(onerel, stat->columns, stat->exprs,
                                      natts, vacattrstats);
        if (!stats)
        {
            if (!IsAutoVacuumWorkerProcess())
                ereport(WARNING,
                        (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                         errmsg("statistics object \"%s.%s\" could not be computed for relation \"%s.%s\"",
                                stat->schema, stat->name,
                                get_namespace_name(onerel->rd_rel->relnamespace),
                                RelationGetRelationName(onerel)),
                         errtable(onerel)));
            continue;
        }

        /* compute statistics target for this statistics */
        stattarget = statext_compute_stattarget(stat->stattarget,
                                                bms_num_members(stat->columns),
                                                stats);

        /*
         * Don't rebuild statistics objects with statistics target set to 0
         * (we just leave the existing values around, just like we do for
         * regular per-column statistics).
         */
        if (stattarget == 0)
            continue;

        /* evaluate expressions (if the statistics has any) */
        data = make_build_data(onerel, stat, numrows, rows, stats, stattarget);

        /* compute statistic of each requested type */
        foreach(lc2, stat->types)
        {
            char        t = (char) lfirst_int(lc2);

            if (t == STATS_EXT_NDISTINCT)
                ndistinct = statext_ndistinct_build(totalrows, data);
            else if (t == STATS_EXT_DEPENDENCIES)
                dependencies = statext_dependencies_build(data);
            else if (t == STATS_EXT_MCV)
                mcv = statext_mcv_build(data, totalrows, stattarget);
            else if (t == STATS_EXT_EXPRESSIONS)
            {
                AnlExprData *exprdata;
                int         nexprs;

                /* should not happen, thanks to checks when defining stats */
                if (!stat->exprs)
                    elog(ERROR, "requested expression stats, but there are no expressions");

                exprdata = build_expr_data(stat->exprs, stattarget);
                nexprs = list_length(stat->exprs);

                compute_expr_stats(onerel, totalrows,
                                   exprdata, nexprs,
                                   rows, numrows);

                exprstats = serialize_expr_stats(exprdata, nexprs);
            }
        }

        /* store the statistics in the catalog */
        statext_store(stat->statOid, ndistinct, dependencies, mcv, exprstats, stats);

        /* for reporting progress */
        pgstat_progress_update_param(PROGRESS_ANALYZE_EXT_STATS_COMPUTED,
                                     ++ext_cnt);

        /* free the build data (allocated as a single chunk) */
        pfree(data);
    }

    table_close(pg_stext, RowExclusiveLock);

    MemoryContextSwitchTo(oldcxt);
    MemoryContextDelete(cxt);
}

/*
 * ComputeExtStatisticsRows
 *      Compute number of rows required by extended statistics on a table.
 *
 * Computes number of rows we need to sample to build extended statistics on a
 * table. This only looks at statistics we can actually build - for example
 * when analyzing only some of the columns, this will skip statistics objects
 * that would require additional columns.
 *
 * See statext_compute_stattarget for details about how we compute statistics
 * target for a statistics object (from the object target, attribute targets
 * and default statistics target).
 */
int
ComputeExtStatisticsRows(Relation onerel,
                         int natts, VacAttrStats **vacattrstats)
{
    Relation    pg_stext;
    ListCell   *lc;
    List       *lstats;
    MemoryContext cxt;
    MemoryContext oldcxt;
    int         result = 0;

    /* If there are no columns to analyze, just return 0. */
    if (!natts)
        return 0;

    cxt = AllocSetContextCreate(CurrentMemoryContext,
                                "ComputeExtStatisticsRows",
                                ALLOCSET_DEFAULT_SIZES);
    oldcxt = MemoryContextSwitchTo(cxt);

    pg_stext = table_open(StatisticExtRelationId, RowExclusiveLock);
    lstats = fetch_statentries_for_relation(pg_stext, RelationGetRelid(onerel));

    foreach(lc, lstats)
    {
        StatExtEntry *stat = (StatExtEntry *) lfirst(lc);
        int         stattarget;
        VacAttrStats **stats;
        int         nattrs = bms_num_members(stat->columns);

        /*
         * Check if we can build this statistics object based on the columns
         * analyzed. If not, ignore it (don't report anything, we'll do that
         * during the actual build BuildRelationExtStatistics).
         */
        stats = lookup_var_attr_stats(onerel, stat->columns, stat->exprs,
                                      natts, vacattrstats);

        if (!stats)
            continue;

        /*
         * Compute statistics target, based on what's set for the statistic
         * object itself, and for its attributes.
         */
        stattarget = statext_compute_stattarget(stat->stattarget,
                                                nattrs, stats);

        /* Use the largest value for all statistics objects. */
        if (stattarget > result)
            result = stattarget;
    }

    table_close(pg_stext, RowExclusiveLock);

    MemoryContextSwitchTo(oldcxt);
    MemoryContextDelete(cxt);

    /* compute sample size based on the statistics target */
    return (300 * result);
}

/*
 * statext_compute_stattarget
 *      compute statistics target for an extended statistic
 *
 * When computing target for extended statistics objects, we consider three
 * places where the target may be set - the statistics object itself,
 * attributes the statistics is defined on, and then the default statistics
 * target.
 *
 * First we look at what's set for the statistics object itself, using the
 * ALTER STATISTICS ... SET STATISTICS command. If we find a valid value
 * there (i.e. not -1) we're done. Otherwise we look at targets set for any
 * of the attributes the statistic is defined on, and if there are columns
 * with defined target, we use the maximum value. We do this mostly for
 * backwards compatibility, because this is what we did before having
 * statistics target for extended statistics.
 *
 * And finally, if we still don't have a statistics target, we use the value
 * set in default_statistics_target.
 */
static int
statext_compute_stattarget(int stattarget, int nattrs, VacAttrStats **stats)
{
    int         i;

    /*
     * If there's statistics target set for the statistics object, use it. It
     * may be set to 0 which disables building of that statistic.
     */
    if (stattarget >= 0)
        return stattarget;

    /*
     * The target for the statistics object is set to -1, in which case we
     * look at the maximum target set for any of the attributes the object is
     * defined on.
     */
    for (i = 0; i < nattrs; i++)
    {
        /* keep the maximum statistics target */
        if (stats[i]->attr->attstattarget > stattarget)
            stattarget = stats[i]->attr->attstattarget;
    }

    /*
     * If the value is still negative (so neither the statistics object nor
     * any of the columns have custom statistics target set), use the global
     * default target.
     */
    if (stattarget < 0)
        stattarget = default_statistics_target;

    /* As this point we should have a valid statistics target. */
    Assert((stattarget >= 0) && (stattarget <= 10000));

    return stattarget;
}

/*
 * statext_is_kind_built
 *      Is this stat kind built in the given pg_statistic_ext_data tuple?
 */
bool
statext_is_kind_built(HeapTuple htup, char type)
{
    AttrNumber  attnum;

    switch (type)
    {
        case STATS_EXT_NDISTINCT:
            attnum = Anum_pg_statistic_ext_data_stxdndistinct;
            break;

        case STATS_EXT_DEPENDENCIES:
            attnum = Anum_pg_statistic_ext_data_stxddependencies;
            break;

        case STATS_EXT_MCV:
            attnum = Anum_pg_statistic_ext_data_stxdmcv;
            break;

        case STATS_EXT_EXPRESSIONS:
            attnum = Anum_pg_statistic_ext_data_stxdexpr;
            break;

        default:
            elog(ERROR, "unexpected statistics type requested: %d", type);
    }

    return !heap_attisnull(htup, attnum, NULL);
}

/*
 * Return a list (of StatExtEntry) of statistics objects for the given relation.
 */
static List *
fetch_statentries_for_relation(Relation pg_statext, Oid relid)
{
    SysScanDesc scan;
    ScanKeyData skey;
    HeapTuple   htup;
    List       *result = NIL;

    /*
     * Prepare to scan pg_statistic_ext for entries having stxrelid = this
     * rel.
     */
    ScanKeyInit(&skey,
                Anum_pg_statistic_ext_stxrelid,
                BTEqualStrategyNumber, F_OIDEQ,
                ObjectIdGetDatum(relid));

    scan = systable_beginscan(pg_statext, StatisticExtRelidIndexId, true,
                              NULL, 1, &skey);

    while (HeapTupleIsValid(htup = systable_getnext(scan)))
    {
        StatExtEntry *entry;
        Datum       datum;
        bool        isnull;
        int         i;
        ArrayType  *arr;
        char       *enabled;
        Form_pg_statistic_ext staForm;
        List       *exprs = NIL;

        entry = palloc0(sizeof(StatExtEntry));
        staForm = (Form_pg_statistic_ext) GETSTRUCT(htup);
        entry->statOid = staForm->oid;
        entry->schema = get_namespace_name(staForm->stxnamespace);
        entry->name = pstrdup(NameStr(staForm->stxname));
        entry->stattarget = staForm->stxstattarget;
        for (i = 0; i < staForm->stxkeys.dim1; i++)
        {
            entry->columns = bms_add_member(entry->columns,
                                            staForm->stxkeys.values[i]);
        }

        /* decode the stxkind char array into a list of chars */
        datum = SysCacheGetAttr(STATEXTOID, htup,
                                Anum_pg_statistic_ext_stxkind, &isnull);
        Assert(!isnull);
        arr = DatumGetArrayTypeP(datum);
        if (ARR_NDIM(arr) != 1 ||
            ARR_HASNULL(arr) ||
            ARR_ELEMTYPE(arr) != CHAROID)
            elog(ERROR, "stxkind is not a 1-D char array");
        enabled = (char *) ARR_DATA_PTR(arr);
        for (i = 0; i < ARR_DIMS(arr)[0]; i++)
        {
            Assert((enabled[i] == STATS_EXT_NDISTINCT) ||
                   (enabled[i] == STATS_EXT_DEPENDENCIES) ||
                   (enabled[i] == STATS_EXT_MCV) ||
                   (enabled[i] == STATS_EXT_EXPRESSIONS));
            entry->types = lappend_int(entry->types, (int) enabled[i]);
        }

        /* decode expression (if any) */
        datum = SysCacheGetAttr(STATEXTOID, htup,
                                Anum_pg_statistic_ext_stxexprs, &isnull);

        if (!isnull)
        {
            char       *exprsString;

            exprsString = TextDatumGetCString(datum);
            exprs = (List *) stringToNode(exprsString);

            pfree(exprsString);

            /*
             * Run the expressions through eval_const_expressions. This is not
             * just an optimization, but is necessary, because the planner
             * will be comparing them to similarly-processed qual clauses, and
             * may fail to detect valid matches without this.  We must not use
             * canonicalize_qual, however, since these aren't qual
             * expressions.
             */
            exprs = (List *) eval_const_expressions(NULL, (Node *) exprs);

            /* May as well fix opfuncids too */
            fix_opfuncids((Node *) exprs);
        }

        entry->exprs = exprs;

        result = lappend(result, entry);
    }

    systable_endscan(scan);

    return result;
}

/*
 * examine_attribute -- pre-analysis of a single column
 *
 * Determine whether the column is analyzable; if so, create and initialize
 * a VacAttrStats struct for it.  If not, return NULL.
 */
static VacAttrStats *
examine_attribute(Node *expr)
{
    HeapTuple   typtuple;
    VacAttrStats *stats;
    int         i;
    bool        ok;

    /*
     * Create the VacAttrStats struct.  Note that we only have a copy of the
     * fixed fields of the pg_attribute tuple.
     */
    stats = (VacAttrStats *) palloc0(sizeof(VacAttrStats));

    /* fake the attribute */
    stats->attr = (Form_pg_attribute) palloc0(ATTRIBUTE_FIXED_PART_SIZE);
    stats->attr->attstattarget = -1;

    /*
     * When analyzing an expression, believe the expression tree's type not
     * the column datatype --- the latter might be the opckeytype storage
     * type of the opclass, which is not interesting for our purposes.  (Note:
     * if we did anything with non-expression statistics columns, we'd need to
     * figure out where to get the correct type info from, but for now that's
     * not a problem.)  It's not clear whether anyone will care about the
     * typmod, but we store that too just in case.
     */
    stats->attrtypid = exprType(expr);
    stats->attrtypmod = exprTypmod(expr);
    stats->attrcollid = exprCollation(expr);

    typtuple = SearchSysCacheCopy1(TYPEOID,
                                   ObjectIdGetDatum(stats->attrtypid));
    if (!HeapTupleIsValid(typtuple))
        elog(ERROR, "cache lookup failed for type %u", stats->attrtypid);
    stats->attrtype = (Form_pg_type) GETSTRUCT(typtuple);

    /*
     * We don't actually analyze individual attributes, so no need to set the
     * memory context.
     */
    stats->anl_context = NULL;
    stats->tupattnum = InvalidAttrNumber;

    /*
     * The fields describing the stats->stavalues[n] element types default to
     * the type of the data being analyzed, but the type-specific typanalyze
     * function can change them if it wants to store something else.
     */
    for (i = 0; i < STATISTIC_NUM_SLOTS; i++)
    {
        stats->statypid[i] = stats->attrtypid;
        stats->statyplen[i] = stats->attrtype->typlen;
        stats->statypbyval[i] = stats->attrtype->typbyval;
        stats->statypalign[i] = stats->attrtype->typalign;
    }

    /*
     * Call the type-specific typanalyze function.  If none is specified, use
     * std_typanalyze().
     */
    if (OidIsValid(stats->attrtype->typanalyze))
        ok = DatumGetBool(OidFunctionCall1(stats->attrtype->typanalyze,
                                           PointerGetDatum(stats)));
    else
        ok = std_typanalyze(stats);

    if (!ok || stats->compute_stats == NULL || stats->minrows <= 0)
    {
        heap_freetuple(typtuple);
        pfree(stats->attr);
        pfree(stats);
        return NULL;
    }

    return stats;
}

/*
 * examine_expression -- pre-analysis of a single expression
 *
 * Determine whether the expression is analyzable; if so, create and initialize
 * a VacAttrStats struct for it.  If not, return NULL.
 */
static VacAttrStats *
examine_expression(Node *expr, int stattarget)
{
    HeapTuple   typtuple;
    VacAttrStats *stats;
    int         i;
    bool        ok;

    Assert(expr != NULL);

    /*
     * Create the VacAttrStats struct.
     */
    stats = (VacAttrStats *) palloc0(sizeof(VacAttrStats));

    /*
     * When analyzing an expression, believe the expression tree's type.
     */
    stats->attrtypid = exprType(expr);
    stats->attrtypmod = exprTypmod(expr);

    /*
     * We don't allow collation to be specified in CREATE STATISTICS, so we
     * have to use the collation specified for the expression. It's possible
     * to specify the collation in the expression "(col COLLATE "en_US")" in
     * which case exprCollation() does the right thing.
     */
    stats->attrcollid = exprCollation(expr);

    /*
     * We don't have any pg_attribute for expressions, so let's fake something
     * reasonable into attstattarget, which is the only thing std_typanalyze
     * needs.
     */
    stats->attr = (Form_pg_attribute) palloc(ATTRIBUTE_FIXED_PART_SIZE);

    /*
     * We can't have statistics target specified for the expression, so we
     * could use either the default_statistics_target, or the target computed
     * for the extended statistics. The second option seems more reasonable.
     */
    stats->attr->attstattarget = stattarget;

    /* initialize some basic fields */
    stats->attr->attrelid = InvalidOid;
    stats->attr->attnum = InvalidAttrNumber;
    stats->attr->atttypid = stats->attrtypid;

    typtuple = SearchSysCacheCopy1(TYPEOID,
                                   ObjectIdGetDatum(stats->attrtypid));
    if (!HeapTupleIsValid(typtuple))
        elog(ERROR, "cache lookup failed for type %u", stats->attrtypid);

    stats->attrtype = (Form_pg_type) GETSTRUCT(typtuple);
    stats->anl_context = CurrentMemoryContext;  /* XXX should be using
                                                 * something else? */
    stats->tupattnum = InvalidAttrNumber;

    /*
     * The fields describing the stats->stavalues[n] element types default to
     * the type of the data being analyzed, but the type-specific typanalyze
     * function can change them if it wants to store something else.
     */
    for (i = 0; i < STATISTIC_NUM_SLOTS; i++)
    {
        stats->statypid[i] = stats->attrtypid;
        stats->statyplen[i] = stats->attrtype->typlen;
        stats->statypbyval[i] = stats->attrtype->typbyval;
        stats->statypalign[i] = stats->attrtype->typalign;
    }

    /*
     * Call the type-specific typanalyze function.  If none is specified, use
     * std_typanalyze().
     */
    if (OidIsValid(stats->attrtype->typanalyze))
        ok = DatumGetBool(OidFunctionCall1(stats->attrtype->typanalyze,
                                           PointerGetDatum(stats)));
    else
        ok = std_typanalyze(stats);

    if (!ok || stats->compute_stats == NULL || stats->minrows <= 0)
    {
        heap_freetuple(typtuple);
        pfree(stats);
        return NULL;
    }

    return stats;
}

/*
 * Using 'vacatts' of size 'nvacatts' as input data, return a newly built
 * VacAttrStats array which includes only the items corresponding to
 * attributes indicated by 'stxkeys'. If we don't have all of the per column
 * stats available to compute the extended stats, then we return NULL to indicate
 * to the caller that the stats should not be built.
 */
static VacAttrStats **
lookup_var_attr_stats(Relation rel, Bitmapset *attrs, List *exprs,
                      int nvacatts, VacAttrStats **vacatts)
{
    int         i = 0;
    int         x = -1;
    int         natts;
    VacAttrStats **stats;
    ListCell   *lc;

    natts = bms_num_members(attrs) + list_length(exprs);

    stats = (VacAttrStats **) palloc(natts * sizeof(VacAttrStats *));

    /* lookup VacAttrStats info for the requested columns (same attnum) */
    while ((x = bms_next_member(attrs, x)) >= 0)
    {
        int         j;

        stats[i] = NULL;
        for (j = 0; j < nvacatts; j++)
        {
            if (x == vacatts[j]->tupattnum)
            {
                stats[i] = vacatts[j];
                break;
            }
        }

        if (!stats[i])
        {
            /*
             * Looks like stats were not gathered for one of the columns
             * required. We'll be unable to build the extended stats without
             * this column.
             */
            pfree(stats);
            return NULL;
        }

        /*
         * Sanity check that the column is not dropped - stats should have
         * been removed in this case.
         */
        Assert(!stats[i]->attr->attisdropped);

        i++;
    }

    /* also add info for expressions */
    foreach(lc, exprs)
    {
        Node       *expr = (Node *) lfirst(lc);

        stats[i] = examine_attribute(expr);

        /*
         * XXX We need tuple descriptor later, and we just grab it from
         * stats[0]->tupDesc (see e.g. statext_mcv_build). But as coded
         * examine_attribute does not set that, so just grab it from the first
         * vacatts element.
         */
        stats[i]->tupDesc = vacatts[0]->tupDesc;

        i++;
    }

    return stats;
}

/*
 * statext_store
 *  Serializes the statistics and stores them into the pg_statistic_ext_data
 *  tuple.
 */
static void
statext_store(Oid statOid,
              MVNDistinct *ndistinct, MVDependencies *dependencies,
              MCVList *mcv, Datum exprs, VacAttrStats **stats)
{
    Relation    pg_stextdata;
    HeapTuple   stup,
                oldtup;
    Datum       values[Natts_pg_statistic_ext_data];
    bool        nulls[Natts_pg_statistic_ext_data];
    bool        replaces[Natts_pg_statistic_ext_data];

    pg_stextdata = table_open(StatisticExtDataRelationId, RowExclusiveLock);

    memset(nulls, true, sizeof(nulls));
    memset(replaces, false, sizeof(replaces));
    memset(values, 0, sizeof(values));

    /*
     * Construct a new pg_statistic_ext_data tuple, replacing the calculated
     * stats.
     */
    if (ndistinct != NULL)
    {
        bytea      *data = statext_ndistinct_serialize(ndistinct);

        nulls[Anum_pg_statistic_ext_data_stxdndistinct - 1] = (data == NULL);
        values[Anum_pg_statistic_ext_data_stxdndistinct - 1] = PointerGetDatum(data);
    }

    if (dependencies != NULL)
    {
        bytea      *data = statext_dependencies_serialize(dependencies);

        nulls[Anum_pg_statistic_ext_data_stxddependencies - 1] = (data == NULL);
        values[Anum_pg_statistic_ext_data_stxddependencies - 1] = PointerGetDatum(data);
    }
    if (mcv != NULL)
    {
        bytea      *data = statext_mcv_serialize(mcv, stats);

        nulls[Anum_pg_statistic_ext_data_stxdmcv - 1] = (data == NULL);
        values[Anum_pg_statistic_ext_data_stxdmcv - 1] = PointerGetDatum(data);
    }
    if (exprs != (Datum) 0)
    {
        nulls[Anum_pg_statistic_ext_data_stxdexpr - 1] = false;
        values[Anum_pg_statistic_ext_data_stxdexpr - 1] = exprs;
    }

    /* always replace the value (either by bytea or NULL) */
    replaces[Anum_pg_statistic_ext_data_stxdndistinct - 1] = true;
    replaces[Anum_pg_statistic_ext_data_stxddependencies - 1] = true;
    replaces[Anum_pg_statistic_ext_data_stxdmcv - 1] = true;
    replaces[Anum_pg_statistic_ext_data_stxdexpr - 1] = true;

    /* there should already be a pg_statistic_ext_data tuple */
    oldtup = SearchSysCache1(STATEXTDATASTXOID, ObjectIdGetDatum(statOid));
    if (!HeapTupleIsValid(oldtup))
        elog(ERROR, "cache lookup failed for statistics object %u", statOid);

    /* replace it */
    stup = heap_modify_tuple(oldtup,
                             RelationGetDescr(pg_stextdata),
                             values,
                             nulls,
                             replaces);
    ReleaseSysCache(oldtup);
    CatalogTupleUpdate(pg_stextdata, &stup->t_self, stup);

    heap_freetuple(stup);

    table_close(pg_stextdata, RowExclusiveLock);
}

/* initialize multi-dimensional sort */
MultiSortSupport
multi_sort_init(int ndims)
{
    MultiSortSupport mss;

    Assert(ndims >= 2);

    mss = (MultiSortSupport) palloc0(offsetof(MultiSortSupportData, ssup)
                                     + sizeof(SortSupportData) * ndims);

    mss->ndims = ndims;

    return mss;
}

/*
 * Prepare sort support info using the given sort operator and collation
 * at the position 'sortdim'
 */
void
multi_sort_add_dimension(MultiSortSupport mss, int sortdim,
                         Oid oper, Oid collation)
{
    SortSupport ssup = &mss->ssup[sortdim];

    ssup->ssup_cxt = CurrentMemoryContext;
    ssup->ssup_collation = collation;
    ssup->ssup_nulls_first = false;

    PrepareSortSupportFromOrderingOp(oper, ssup);
}

/* compare all the dimensions in the selected order */
int
multi_sort_compare(const void *a, const void *b, void *arg)
{
    MultiSortSupport mss = (MultiSortSupport) arg;
    SortItem   *ia = (SortItem *) a;
    SortItem   *ib = (SortItem *) b;
    int         i;

    for (i = 0; i < mss->ndims; i++)
    {
        int         compare;

        compare = ApplySortComparator(ia->values[i], ia->isnull[i],
                                      ib->values[i], ib->isnull[i],
                                      &mss->ssup[i]);

        if (compare != 0)
            return compare;
    }

    /* equal by default */
    return 0;
}

/* compare selected dimension */
int
multi_sort_compare_dim(int dim, const SortItem *a, const SortItem *b,
                       MultiSortSupport mss)
{
    return ApplySortComparator(a->values[dim], a->isnull[dim],
                               b->values[dim], b->isnull[dim],
                               &mss->ssup[dim]);
}

int
multi_sort_compare_dims(int start, int end,
                        const SortItem *a, const SortItem *b,
                        MultiSortSupport mss)
{
    int         dim;

    for (dim = start; dim <= end; dim++)
    {
        int         r = ApplySortComparator(a->values[dim], a->isnull[dim],
                                            b->values[dim], b->isnull[dim],
                                            &mss->ssup[dim]);

        if (r != 0)
            return r;
    }

    return 0;
}

int
compare_scalars_simple(const void *a, const void *b, void *arg)
{
    return compare_datums_simple(*(Datum *) a,
                                 *(Datum *) b,
                                 (SortSupport) arg);
}

int
compare_datums_simple(Datum a, Datum b, SortSupport ssup)
{
    return ApplySortComparator(a, false, b, false, ssup);
}

/*
 * build_attnums_array
 *      Transforms a bitmap into an array of AttrNumber values.
 *
 * This is used for extended statistics only, so all the attribute must be
 * user-defined. That means offsetting by FirstLowInvalidHeapAttributeNumber
 * is not necessary here (and when querying the bitmap).
 */
AttrNumber *
build_attnums_array(Bitmapset *attrs, int nexprs, int *numattrs)
{
    int         i,
                j;
    AttrNumber *attnums;
    int         num = bms_num_members(attrs);

    if (numattrs)
        *numattrs = num;

    /* build attnums from the bitmapset */
    attnums = (AttrNumber *) palloc(sizeof(AttrNumber) * num);
    i = 0;
    j = -1;
    while ((j = bms_next_member(attrs, j)) >= 0)
    {
        int         attnum = (j - nexprs);

        /*
         * Make sure the bitmap contains only user-defined attributes. As
         * bitmaps can't contain negative values, this can be violated in two
         * ways. Firstly, the bitmap might contain 0 as a member, and secondly
         * the integer value might be larger than MaxAttrNumber.
         */
        Assert(AttributeNumberIsValid(attnum));
        Assert(attnum <= MaxAttrNumber);
        Assert(attnum >= (-nexprs));

        attnums[i++] = (AttrNumber) attnum;

        /* protect against overflows */
        Assert(i <= num);
    }

    return attnums;
}

/*
 * build_sorted_items
 *      build a sorted array of SortItem with values from rows
 *
 * Note: All the memory is allocated in a single chunk, so that the caller
 * can simply pfree the return value to release all of it.
 */
SortItem *
build_sorted_items(StatsBuildData *data, int *nitems,
                   MultiSortSupport mss,
                   int numattrs, AttrNumber *attnums)
{
    int         i,
                j,
                len,
                nrows;
    int         nvalues = data->numrows * numattrs;

    SortItem   *items;
    Datum      *values;
    bool       *isnull;
    char       *ptr;
    int        *typlen;

    /* Compute the total amount of memory we need (both items and values). */
    len = data->numrows * sizeof(SortItem) + nvalues * (sizeof(Datum) + sizeof(bool));

    /* Allocate the memory and split it into the pieces. */
    ptr = palloc0(len);

    /* items to sort */
    items = (SortItem *) ptr;
    ptr += data->numrows * sizeof(SortItem);

    /* values and null flags */
    values = (Datum *) ptr;
    ptr += nvalues * sizeof(Datum);

    isnull = (bool *) ptr;
    ptr += nvalues * sizeof(bool);

    /* make sure we consumed the whole buffer exactly */
    Assert((ptr - (char *) items) == len);

    /* fix the pointers to Datum and bool arrays */
    nrows = 0;
    for (i = 0; i < data->numrows; i++)
    {
        items[nrows].values = &values[nrows * numattrs];
        items[nrows].isnull = &isnull[nrows * numattrs];

        nrows++;
    }

    /* build a local cache of typlen for all attributes */
    typlen = (int *) palloc(sizeof(int) * data->nattnums);
    for (i = 0; i < data->nattnums; i++)
        typlen[i] = get_typlen(data->stats[i]->attrtypid);

    nrows = 0;
    for (i = 0; i < data->numrows; i++)
    {
        bool        toowide = false;

        /* load the values/null flags from sample rows */
        for (j = 0; j < numattrs; j++)
        {
            Datum       value;
            bool        isnull;
            int         attlen;
            AttrNumber  attnum = attnums[j];

            int         idx;

            /* match attnum to the pre-calculated data */
            for (idx = 0; idx < data->nattnums; idx++)
            {
                if (attnum == data->attnums[idx])
                    break;
            }

            Assert(idx < data->nattnums);

            value = data->values[idx][i];
            isnull = data->nulls[idx][i];
            attlen = typlen[idx];

            /*
             * If this is a varlena value, check if it's too wide and if yes
             * then skip the whole item. Otherwise detoast the value.
             *
             * XXX It may happen that we've already detoasted some preceding
             * values for the current item. We don't bother to cleanup those
             * on the assumption that those are small (below WIDTH_THRESHOLD)
             * and will be discarded at the end of analyze.
             */
            if ((!isnull) && (attlen == -1))
            {
                if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
                {
                    toowide = true;
                    break;
                }

                value = PointerGetDatum(PG_DETOAST_DATUM(value));
            }

            items[nrows].values[j] = value;
            items[nrows].isnull[j] = isnull;
        }

        if (toowide)
            continue;

        nrows++;
    }

    /* store the actual number of items (ignoring the too-wide ones) */
    *nitems = nrows;

    /* all items were too wide */
    if (nrows == 0)
    {
        /* everything is allocated as a single chunk */
        pfree(items);
        return NULL;
    }

    /* do the sort, using the multi-sort */
    qsort_arg((void *) items, nrows, sizeof(SortItem),
              multi_sort_compare, mss);

    return items;
}

/*
 * has_stats_of_kind
 *      Check whether the list contains statistic of a given kind
 */
bool
has_stats_of_kind(List *stats, char requiredkind)
{
    ListCell   *l;

    foreach(l, stats)
    {
        StatisticExtInfo *stat = (StatisticExtInfo *) lfirst(l);

        if (stat->kind == requiredkind)
            return true;
    }

    return false;
}

/*
 * stat_find_expression
 *      Search for an expression in statistics object's list of expressions.
 *
 * Returns the index of the expression in the statistics object's list of
 * expressions, or -1 if not found.
 */
static int
stat_find_expression(StatisticExtInfo *stat, Node *expr)
{
    ListCell   *lc;
    int         idx;

    idx = 0;
    foreach(lc, stat->exprs)
    {
        Node       *stat_expr = (Node *) lfirst(lc);

        if (equal(stat_expr, expr))
            return idx;
        idx++;
    }

    /* Expression not found */
    return -1;
}

/*
 * stat_covers_expressions
 *      Test whether a statistics object covers all expressions in a list.
 *
 * Returns true if all expressions are covered.  If expr_idxs is non-NULL, it
 * is populated with the indexes of the expressions found.
 */
static bool
stat_covers_expressions(StatisticExtInfo *stat, List *exprs,
                        Bitmapset **expr_idxs)
{
    ListCell   *lc;

    foreach(lc, exprs)
    {
        Node       *expr = (Node *) lfirst(lc);
        int         expr_idx;

        expr_idx = stat_find_expression(stat, expr);
        if (expr_idx == -1)
            return false;

        if (expr_idxs != NULL)
            *expr_idxs = bms_add_member(*expr_idxs, expr_idx);
    }

    /* If we reach here, all expressions are covered */
    return true;
}

/*
 * choose_best_statistics
 *      Look for and return statistics with the specified 'requiredkind' which
 *      have keys that match at least two of the given attnums.  Return NULL if
 *      there's no match.
 *
 * The current selection criteria is very simple - we choose the statistics
 * object referencing the most attributes in covered (and still unestimated
 * clauses), breaking ties in favor of objects with fewer keys overall.
 *
 * The clause_attnums is an array of bitmaps, storing attnums for individual
 * clauses. A NULL element means the clause is either incompatible or already
 * estimated.
 *
 * XXX If multiple statistics objects tie on both criteria, then which object
 * is chosen depends on the order that they appear in the stats list. Perhaps
 * further tiebreakers are needed.
 */
StatisticExtInfo *
choose_best_statistics(List *stats, char requiredkind,
                       Bitmapset **clause_attnums, List **clause_exprs,
                       int nclauses)
{
    ListCell   *lc;
    StatisticExtInfo *best_match = NULL;
    int         best_num_matched = 2;   /* goal #1: maximize */
    int         best_match_keys = (STATS_MAX_DIMENSIONS + 1);   /* goal #2: minimize */

    foreach(lc, stats)
    {
        int         i;
        StatisticExtInfo *info = (StatisticExtInfo *) lfirst(lc);
        Bitmapset  *matched_attnums = NULL;
        Bitmapset  *matched_exprs = NULL;
        int         num_matched;
        int         numkeys;

        /* skip statistics that are not of the correct type */
        if (info->kind != requiredkind)
            continue;

        /*
         * Collect attributes and expressions in remaining (unestimated)
         * clauses fully covered by this statistic object.
         *
         * We know already estimated clauses have both clause_attnums and
         * clause_exprs set to NULL. We leave the pointers NULL if already
         * estimated, or we reset them to NULL after estimating the clause.
         */
        for (i = 0; i < nclauses; i++)
        {
            Bitmapset  *expr_idxs = NULL;

            /* ignore incompatible/estimated clauses */
            if (!clause_attnums[i] && !clause_exprs[i])
                continue;

            /* ignore clauses that are not covered by this object */
            if (!bms_is_subset(clause_attnums[i], info->keys) ||
                !stat_covers_expressions(info, clause_exprs[i], &expr_idxs))
                continue;

            /* record attnums and indexes of expressions covered */
            matched_attnums = bms_add_members(matched_attnums, clause_attnums[i]);
            matched_exprs = bms_add_members(matched_exprs, expr_idxs);
        }

        num_matched = bms_num_members(matched_attnums) + bms_num_members(matched_exprs);

        bms_free(matched_attnums);
        bms_free(matched_exprs);

        /*
         * save the actual number of keys in the stats so that we can choose
         * the narrowest stats with the most matching keys.
         */
        numkeys = bms_num_members(info->keys) + list_length(info->exprs);

        /*
         * Use this object when it increases the number of matched attributes
         * and expressions or when it matches the same number of attributes
         * and expressions but these stats have fewer keys than any previous
         * match.
         */
        if (num_matched > best_num_matched ||
            (num_matched == best_num_matched && numkeys < best_match_keys))
        {
            best_match = info;
            best_num_matched = num_matched;
            best_match_keys = numkeys;
        }
    }

    return best_match;
}

/*
 * statext_is_compatible_clause_internal
 *      Determines if the clause is compatible with MCV lists.
 *
 * Does the heavy lifting of actually inspecting the clauses for
 * statext_is_compatible_clause. It needs to be split like this because
 * of recursion.  The attnums bitmap is an input/output parameter collecting
 * attribute numbers from all compatible clauses (recursively).
 */
static bool
statext_is_compatible_clause_internal(PlannerInfo *root, Node *clause,
                                      Index relid, Bitmapset **attnums,
                                      List **exprs)
{
    /* Look inside any binary-compatible relabeling (as in examine_variable) */
    if (IsA(clause, RelabelType))
        clause = (Node *) ((RelabelType *) clause)->arg;

    /* plain Var references (boolean Vars or recursive checks) */
    if (IsA(clause, Var))
    {
        Var        *var = (Var *) clause;

        /* Ensure var is from the correct relation */
        if (var->varno != relid)
            return false;

        /* we also better ensure the Var is from the current level */
        if (var->varlevelsup > 0)
            return false;

        /* Also skip system attributes (we don't allow stats on those). */
        if (!AttrNumberIsForUserDefinedAttr(var->varattno))
            return false;

        *attnums = bms_add_member(*attnums, var->varattno);

        return true;
    }

    /* (Var/Expr op Const) or (Const op Var/Expr) */
    if (is_opclause(clause))
    {
        RangeTblEntry *rte = root->simple_rte_array[relid];
        OpExpr     *expr = (OpExpr *) clause;
        Node       *clause_expr;

        /* Only expressions with two arguments are considered compatible. */
        if (list_length(expr->args) != 2)
            return false;

        /* Check if the expression has the right shape */
        if (!examine_opclause_args(expr->args, &clause_expr, NULL, NULL))
            return false;

        /*
         * If it's not one of the supported operators ("=", "<", ">", etc.),
         * just ignore the clause, as it's not compatible with MCV lists.
         *
         * This uses the function for estimating selectivity, not the operator
         * directly (a bit awkward, but well ...).
         */
        switch (get_oprrest(expr->opno))
        {
            case F_EQSEL:
            case F_NEQSEL:
            case F_SCALARLTSEL:
            case F_SCALARLESEL:
            case F_SCALARGTSEL:
            case F_SCALARGESEL:
                /* supported, will continue with inspection of the Var/Expr */
                break;

            default:
                /* other estimators are considered unknown/unsupported */
                return false;
        }

        /*
         * If there are any securityQuals on the RTE from security barrier
         * views or RLS policies, then the user may not have access to all the
         * table's data, and we must check that the operator is leak-proof.
         *
         * If the operator is leaky, then we must ignore this clause for the
         * purposes of estimating with MCV lists, otherwise the operator might
         * reveal values from the MCV list that the user doesn't have
         * permission to see.
         */
        if (rte->securityQuals != NIL &&
            !get_func_leakproof(get_opcode(expr->opno)))
            return false;

        /* Check (Var op Const) or (Const op Var) clauses by recursing. */
        if (IsA(clause_expr, Var))
            return statext_is_compatible_clause_internal(root, clause_expr,
                                                         relid, attnums, exprs);

        /* Otherwise we have (Expr op Const) or (Const op Expr). */
        *exprs = lappend(*exprs, clause_expr);
        return true;
    }

    /* Var/Expr IN Array */
    if (IsA(clause, ScalarArrayOpExpr))
    {
        RangeTblEntry *rte = root->simple_rte_array[relid];
        ScalarArrayOpExpr *expr = (ScalarArrayOpExpr *) clause;
        Node       *clause_expr;

        /* Only expressions with two arguments are considered compatible. */
        if (list_length(expr->args) != 2)
            return false;

        /* Check if the expression has the right shape (one Var, one Const) */
        if (!examine_opclause_args(expr->args, &clause_expr, NULL, NULL))
            return false;

        /*
         * If it's not one of the supported operators ("=", "<", ">", etc.),
         * just ignore the clause, as it's not compatible with MCV lists.
         *
         * This uses the function for estimating selectivity, not the operator
         * directly (a bit awkward, but well ...).
         */
        switch (get_oprrest(expr->opno))
        {
            case F_EQSEL:
            case F_NEQSEL:
            case F_SCALARLTSEL:
            case F_SCALARLESEL:
            case F_SCALARGTSEL:
            case F_SCALARGESEL:
                /* supported, will continue with inspection of the Var/Expr */
                break;

            default:
                /* other estimators are considered unknown/unsupported */
                return false;
        }

        /*
         * If there are any securityQuals on the RTE from security barrier
         * views or RLS policies, then the user may not have access to all the
         * table's data, and we must check that the operator is leak-proof.
         *
         * If the operator is leaky, then we must ignore this clause for the
         * purposes of estimating with MCV lists, otherwise the operator might
         * reveal values from the MCV list that the user doesn't have
         * permission to see.
         */
        if (rte->securityQuals != NIL &&
            !get_func_leakproof(get_opcode(expr->opno)))
            return false;

        /* Check Var IN Array clauses by recursing. */
        if (IsA(clause_expr, Var))
            return statext_is_compatible_clause_internal(root, clause_expr,
                                                         relid, attnums, exprs);

        /* Otherwise we have Expr IN Array. */
        *exprs = lappend(*exprs, clause_expr);
        return true;
    }

    /* AND/OR/NOT clause */
    if (is_andclause(clause) ||
        is_orclause(clause) ||
        is_notclause(clause))
    {
        /*
         * AND/OR/NOT-clauses are supported if all sub-clauses are supported
         *
         * Perhaps we could improve this by handling mixed cases, when some of
         * the clauses are supported and some are not. Selectivity for the
         * supported subclauses would be computed using extended statistics,
         * and the remaining clauses would be estimated using the traditional
         * algorithm (product of selectivities).
         *
         * It however seems overly complex, and in a way we already do that
         * because if we reject the whole clause as unsupported here, it will
         * be eventually passed to clauselist_selectivity() which does exactly
         * this (split into supported/unsupported clauses etc).
         */
        BoolExpr   *expr = (BoolExpr *) clause;
        ListCell   *lc;

        foreach(lc, expr->args)
        {
            /*
             * Had we found incompatible clause in the arguments, treat the
             * whole clause as incompatible.
             */
            if (!statext_is_compatible_clause_internal(root,
                                                       (Node *) lfirst(lc),
                                                       relid, attnums, exprs))
                return false;
        }

        return true;
    }

    /* Var/Expr IS NULL */
    if (IsA(clause, NullTest))
    {
        NullTest   *nt = (NullTest *) clause;

        /* Check Var IS NULL clauses by recursing. */
        if (IsA(nt->arg, Var))
            return statext_is_compatible_clause_internal(root, (Node *) (nt->arg),
                                                         relid, attnums, exprs);

        /* Otherwise we have Expr IS NULL. */
        *exprs = lappend(*exprs, nt->arg);
        return true;
    }

    /*
     * Treat any other expressions as bare expressions to be matched against
     * expressions in statistics objects.
     */
    *exprs = lappend(*exprs, clause);
    return true;
}

/*
 * statext_is_compatible_clause
 *      Determines if the clause is compatible with MCV lists.
 *
 * Currently, we only support the following types of clauses:
 *
 * (a) OpExprs of the form (Var/Expr op Const), or (Const op Var/Expr), where
 * the op is one of ("=", "<", ">", ">=", "<=")
 *
 * (b) (Var/Expr IS [NOT] NULL)
 *
 * (c) combinations using AND/OR/NOT
 *
 * (d) ScalarArrayOpExprs of the form (Var/Expr op ANY (array)) or (Var/Expr
 * op ALL (array))
 *
 * In the future, the range of supported clauses may be expanded to more
 * complex cases, for example (Var op Var).
 */
static bool
statext_is_compatible_clause(PlannerInfo *root, Node *clause, Index relid,
                             Bitmapset **attnums, List **exprs)
{
    RangeTblEntry *rte = root->simple_rte_array[relid];
    RestrictInfo *rinfo = (RestrictInfo *) clause;
    int         clause_relid;
    Oid         userid;

    /*
     * Special-case handling for bare BoolExpr AND clauses, because the
     * restrictinfo machinery doesn't build RestrictInfos on top of AND
     * clauses.
     */
    if (is_andclause(clause))
    {
        BoolExpr   *expr = (BoolExpr *) clause;
        ListCell   *lc;

        /*
         * Check that each sub-clause is compatible.  We expect these to be
         * RestrictInfos.
         */
        foreach(lc, expr->args)
        {
            if (!statext_is_compatible_clause(root, (Node *) lfirst(lc),
                                              relid, attnums, exprs))
                return false;
        }

        return true;
    }

    /* Otherwise it must be a RestrictInfo. */
    if (!IsA(rinfo, RestrictInfo))
        return false;

    /* Pseudoconstants are not really interesting here. */
    if (rinfo->pseudoconstant)
        return false;

    /* Clauses referencing other varnos are incompatible. */
    if (!bms_get_singleton_member(rinfo->clause_relids, &clause_relid) ||
        clause_relid != relid)
        return false;

    /* Check the clause and determine what attributes it references. */
    if (!statext_is_compatible_clause_internal(root, (Node *) rinfo->clause,
                                               relid, attnums, exprs))
        return false;

    /*
     * Check that the user has permission to read all required attributes. Use
     * checkAsUser if it's set, in case we're accessing the table via a view.
     */
    userid = rte->checkAsUser ? rte->checkAsUser : GetUserId();

    if (pg_class_aclcheck(rte->relid, userid, ACL_SELECT) != ACLCHECK_OK)
    {
        Bitmapset  *clause_attnums = NULL;

        /* Don't have table privilege, must check individual columns */
        if (*exprs != NIL)
        {
            pull_varattnos((Node *) exprs, relid, &clause_attnums);
            clause_attnums = bms_add_members(clause_attnums, *attnums);
        }
        else
            clause_attnums = *attnums;

        if (bms_is_member(InvalidAttrNumber, clause_attnums))
        {
            /* Have a whole-row reference, must have access to all columns */
            if (pg_attribute_aclcheck_all(rte->relid, userid, ACL_SELECT,
                                          ACLMASK_ALL) != ACLCHECK_OK)
                return false;
        }
        else
        {
            /* Check the columns referenced by the clause */
            int         attnum = -1;

            while ((attnum = bms_next_member(clause_attnums, attnum)) >= 0)
            {
                if (pg_attribute_aclcheck(rte->relid, attnum, userid,
                                          ACL_SELECT) != ACLCHECK_OK)
                    return false;
            }
        }
    }

    /* If we reach here, the clause is OK */
    return true;
}

/*
 * statext_mcv_clauselist_selectivity
 *      Estimate clauses using the best multi-column statistics.
 *
 * Applies available extended (multi-column) statistics on a table. There may
 * be multiple applicable statistics (with respect to the clauses), in which
 * case we use greedy approach. In each round we select the best statistic on
 * a table (measured by the number of attributes extracted from the clauses
 * and covered by it), and compute the selectivity for the supplied clauses.
 * We repeat this process with the remaining clauses (if any), until none of
 * the available statistics can be used.
 *
 * One of the main challenges with using MCV lists is how to extrapolate the
 * estimate to the data not covered by the MCV list. To do that, we compute
 * not only the "MCV selectivity" (selectivities for MCV items matching the
 * supplied clauses), but also the following related selectivities:
 *
 * - simple selectivity:  Computed without extended statistics, i.e. as if the
 * columns/clauses were independent.
 *
 * - base selectivity:  Similar to simple selectivity, but is computed using
 * the extended statistic by adding up the base frequencies (that we compute
 * and store for each MCV item) of matching MCV items.
 *
 * - total selectivity: Selectivity covered by the whole MCV list.
 *
 * These are passed to mcv_combine_selectivities() which combines them to
 * produce a selectivity estimate that makes use of both per-column statistics
 * and the multi-column MCV statistics.
 *
 * 'estimatedclauses' is an input/output parameter.  We set bits for the
 * 0-based 'clauses' indexes we estimate for and also skip clause items that
 * already have a bit set.
 */
static Selectivity
statext_mcv_clauselist_selectivity(PlannerInfo *root, List *clauses, int varRelid,
                                   JoinType jointype, SpecialJoinInfo *sjinfo,
                                   RelOptInfo *rel, Bitmapset **estimatedclauses,
                                   bool is_or)
{
    ListCell   *l;
    Bitmapset **list_attnums;   /* attnums extracted from the clause */
    List      **list_exprs;     /* expressions matched to any statistic */
    int         listidx;
    Selectivity sel = (is_or) ? 0.0 : 1.0;

    /* check if there's any stats that might be useful for us. */
    if (!has_stats_of_kind(rel->statlist, STATS_EXT_MCV))
        return sel;

    list_attnums = (Bitmapset **) palloc(sizeof(Bitmapset *) *
                                         list_length(clauses));

    /* expressions extracted from complex expressions */
    list_exprs = (List **) palloc(sizeof(Node *) * list_length(clauses));

    /*
     * Pre-process the clauses list to extract the attnums and expressions
     * seen in each item.  We need to determine if there are any clauses which
     * will be useful for selectivity estimations with extended stats.  Along
     * the way we'll record all of the attnums and expressions for each clause
     * in lists which we'll reference later so we don't need to repeat the
     * same work again.
     *
     * We also skip clauses that we already estimated using different types of
     * statistics (we treat them as incompatible).
     */
    listidx = 0;
    foreach(l, clauses)
    {
        Node       *clause = (Node *) lfirst(l);
        Bitmapset  *attnums = NULL;
        List       *exprs = NIL;

        if (!bms_is_member(listidx, *estimatedclauses) &&
            statext_is_compatible_clause(root, clause, rel->relid, &attnums, &exprs))
        {
            list_attnums[listidx] = attnums;
            list_exprs[listidx] = exprs;
        }
        else
        {
            list_attnums[listidx] = NULL;
            list_exprs[listidx] = NIL;
        }

        listidx++;
    }

    /* apply as many extended statistics as possible */
    while (true)
    {
        StatisticExtInfo *stat;
        List       *stat_clauses;
        Bitmapset  *simple_clauses;

        /* find the best suited statistics object for these attnums */
        stat = choose_best_statistics(rel->statlist, STATS_EXT_MCV,
                                      list_attnums, list_exprs,
                                      list_length(clauses));

        /*
         * if no (additional) matching stats could be found then we've nothing
         * to do
         */
        if (!stat)
            break;

        /* Ensure choose_best_statistics produced an expected stats type. */
        Assert(stat->kind == STATS_EXT_MCV);

        /* now filter the clauses to be estimated using the selected MCV */
        stat_clauses = NIL;

        /* record which clauses are simple (single column or expression) */
        simple_clauses = NULL;

        listidx = -1;
        foreach(l, clauses)
        {
            /* Increment the index before we decide if to skip the clause. */
            listidx++;

            /*
             * Ignore clauses from which we did not extract any attnums or
             * expressions (this needs to be consistent with what we do in
             * choose_best_statistics).
             *
             * This also eliminates already estimated clauses - both those
             * estimated before and during applying extended statistics.
             *
             * XXX This check is needed because both bms_is_subset and
             * stat_covers_expressions return true for empty attnums and
             * expressions.
             */
            if (!list_attnums[listidx] && !list_exprs[listidx])
                continue;

            /*
             * The clause was not estimated yet, and we've extracted either
             * attnums of expressions from it. Ignore it if it's not fully
             * covered by the chosen statistics.
             *
             * We need to check both attributes and expressions, and reject
             * if either is not covered.
             */
            if (!bms_is_subset(list_attnums[listidx], stat->keys) ||
                !stat_covers_expressions(stat, list_exprs[listidx], NULL))
                continue;

            /*
             * Now we know the clause is compatible (we have either atttnums
             * or expressions extracted from it), and was not estimated yet.
             */

            /* record simple clauses (single column or expression) */
            if ((list_attnums[listidx] == NULL &&
                 list_length(list_exprs[listidx]) == 1) ||
                (list_exprs[listidx] == NIL &&
                 bms_membership(list_attnums[listidx]) == BMS_SINGLETON))
                simple_clauses = bms_add_member(simple_clauses,
                                                list_length(stat_clauses));

            /* add clause to list and mark it as estimated */
            stat_clauses = lappend(stat_clauses, (Node *) lfirst(l));
            *estimatedclauses = bms_add_member(*estimatedclauses, listidx);

            /*
             * Reset the pointers, so that choose_best_statistics knows this
             * clause was estimated and does not consider it again.
             */
            bms_free(list_attnums[listidx]);
            list_attnums[listidx] = NULL;

            list_free(list_exprs[listidx]);
            list_exprs[listidx] = NULL;
        }

        if (is_or)
        {
            bool       *or_matches = NULL;
            Selectivity simple_or_sel = 0.0,
                        stat_sel = 0.0;
            MCVList    *mcv_list;

            /* Load the MCV list stored in the statistics object */
            mcv_list = statext_mcv_load(stat->statOid);

            /*
             * Compute the selectivity of the ORed list of clauses covered by
             * this statistics object by estimating each in turn and combining
             * them using the formula P(A OR B) = P(A) + P(B) - P(A AND B).
             * This allows us to use the multivariate MCV stats to better
             * estimate the individual terms and their overlap.
             *
             * Each time we iterate this formula, the clause "A" above is
             * equal to all the clauses processed so far, combined with "OR".
             */
            listidx = 0;
            foreach(l, stat_clauses)
            {
                Node       *clause = (Node *) lfirst(l);
                Selectivity simple_sel,
                            overlap_simple_sel,
                            mcv_sel,
                            mcv_basesel,
                            overlap_mcvsel,
                            overlap_basesel,
                            mcv_totalsel,
                            clause_sel,
                            overlap_sel;

                /*
                 * "Simple" selectivity of the next clause and its overlap
                 * with any of the previous clauses.  These are our initial
                 * estimates of P(B) and P(A AND B), assuming independence of
                 * columns/clauses.
                 */
                simple_sel = clause_selectivity_ext(root, clause, varRelid,
                                                    jointype, sjinfo, false);

                overlap_simple_sel = simple_or_sel * simple_sel;

                /*
                 * New "simple" selectivity of all clauses seen so far,
                 * assuming independence.
                 */
                simple_or_sel += simple_sel - overlap_simple_sel;
                CLAMP_PROBABILITY(simple_or_sel);

                /*
                 * Multi-column estimate of this clause using MCV statistics,
                 * along with base and total selectivities, and corresponding
                 * selectivities for the overlap term P(A AND B).
                 */
                mcv_sel = mcv_clause_selectivity_or(root, stat, mcv_list,
                                                    clause, &or_matches,
                                                    &mcv_basesel,
                                                    &overlap_mcvsel,
                                                    &overlap_basesel,
                                                    &mcv_totalsel);

                /*
                 * Combine the simple and multi-column estimates.
                 *
                 * If this clause is a simple single-column clause, then we
                 * just use the simple selectivity estimate for it, since the
                 * multi-column statistics are unlikely to improve on that
                 * (and in fact could make it worse).  For the overlap, we
                 * always make use of the multi-column statistics.
                 */
                if (bms_is_member(listidx, simple_clauses))
                    clause_sel = simple_sel;
                else
                    clause_sel = mcv_combine_selectivities(simple_sel,
                                                           mcv_sel,
                                                           mcv_basesel,
                                                           mcv_totalsel);

                overlap_sel = mcv_combine_selectivities(overlap_simple_sel,
                                                        overlap_mcvsel,
                                                        overlap_basesel,
                                                        mcv_totalsel);

                /* Factor these into the result for this statistics object */
                stat_sel += clause_sel - overlap_sel;
                CLAMP_PROBABILITY(stat_sel);

                listidx++;
            }

            /*
             * Factor the result for this statistics object into the overall
             * result.  We treat the results from each separate statistics
             * object as independent of one another.
             */
            sel = sel + stat_sel - sel * stat_sel;
        }
        else                    /* Implicitly-ANDed list of clauses */
        {
            Selectivity simple_sel,
                        mcv_sel,
                        mcv_basesel,
                        mcv_totalsel,
                        stat_sel;

            /*
             * "Simple" selectivity, i.e. without any extended statistics,
             * essentially assuming independence of the columns/clauses.
             */
            simple_sel = clauselist_selectivity_ext(root, stat_clauses,
                                                    varRelid, jointype,
                                                    sjinfo, false);

            /*
             * Multi-column estimate using MCV statistics, along with base and
             * total selectivities.
             */
            mcv_sel = mcv_clauselist_selectivity(root, stat, stat_clauses,
                                                 varRelid, jointype, sjinfo,
                                                 rel, &mcv_basesel,
                                                 &mcv_totalsel);

            /* Combine the simple and multi-column estimates. */
            stat_sel = mcv_combine_selectivities(simple_sel,
                                                 mcv_sel,
                                                 mcv_basesel,
                                                 mcv_totalsel);

            /* Factor this into the overall result */
            sel *= stat_sel;
        }
    }

    return sel;
}

/*
 * statext_clauselist_selectivity
 *      Estimate clauses using the best multi-column statistics.
 */
Selectivity
statext_clauselist_selectivity(PlannerInfo *root, List *clauses, int varRelid,
                               JoinType jointype, SpecialJoinInfo *sjinfo,
                               RelOptInfo *rel, Bitmapset **estimatedclauses,
                               bool is_or)
{
    Selectivity sel;

    /* First, try estimating clauses using a multivariate MCV list. */
    sel = statext_mcv_clauselist_selectivity(root, clauses, varRelid, jointype,
                                             sjinfo, rel, estimatedclauses, is_or);

    /*
     * Functional dependencies only work for clauses connected by AND, so for
     * OR clauses we're done.
     */
    if (is_or)
        return sel;

    /*
     * Then, apply functional dependencies on the remaining clauses by calling
     * dependencies_clauselist_selectivity.  Pass 'estimatedclauses' so the
     * function can properly skip clauses already estimated above.
     *
     * The reasoning for applying dependencies last is that the more complex
     * stats can track more complex correlations between the attributes, and
     * so may be considered more reliable.
     *
     * For example, MCV list can give us an exact selectivity for values in
     * two columns, while functional dependencies can only provide information
     * about the overall strength of the dependency.
     */
    sel *= dependencies_clauselist_selectivity(root, clauses, varRelid,
                                               jointype, sjinfo, rel,
                                               estimatedclauses);

    return sel;
}

/*
 * examine_opclause_args
 *      Split an operator expression's arguments into Expr and Const parts.
 *
 * Attempts to match the arguments to either (Expr op Const) or (Const op
 * Expr), possibly with a RelabelType on top. When the expression matches this
 * form, returns true, otherwise returns false.
 *
 * Optionally returns pointers to the extracted Expr/Const nodes, when passed
 * non-null pointers (exprp, cstp and expronleftp). The expronleftp flag
 * specifies on which side of the operator we found the expression node.
 */
bool
examine_opclause_args(List *args, Node **exprp, Const **cstp,
                      bool *expronleftp)
{
    Node       *expr;
    Const      *cst;
    bool        expronleft;
    Node       *leftop,
               *rightop;

    /* enforced by statext_is_compatible_clause_internal */
    Assert(list_length(args) == 2);

    leftop = linitial(args);
    rightop = lsecond(args);

    /* strip RelabelType from either side of the expression */
    if (IsA(leftop, RelabelType))
        leftop = (Node *) ((RelabelType *) leftop)->arg;

    if (IsA(rightop, RelabelType))
        rightop = (Node *) ((RelabelType *) rightop)->arg;

    if (IsA(rightop, Const))
    {
        expr = (Node *) leftop;
        cst = (Const *) rightop;
        expronleft = true;
    }
    else if (IsA(leftop, Const))
    {
        expr = (Node *) rightop;
        cst = (Const *) leftop;
        expronleft = false;
    }
    else
        return false;

    /* return pointers to the extracted parts if requested */
    if (exprp)
        *exprp = expr;

    if (cstp)
        *cstp = cst;

    if (expronleftp)
        *expronleftp = expronleft;

    return true;
}


/*
 * Compute statistics about expressions of a relation.
 */
static void
compute_expr_stats(Relation onerel, double totalrows,
                   AnlExprData *exprdata, int nexprs,
                   HeapTuple *rows, int numrows)
{
    MemoryContext expr_context,
                old_context;
    int         ind,
                i;

    expr_context = AllocSetContextCreate(CurrentMemoryContext,
                                         "Analyze Expression",
                                         ALLOCSET_DEFAULT_SIZES);
    old_context = MemoryContextSwitchTo(expr_context);

    for (ind = 0; ind < nexprs; ind++)
    {
        AnlExprData *thisdata = &exprdata[ind];
        VacAttrStats *stats = thisdata->vacattrstat;
        Node       *expr = thisdata->expr;
        TupleTableSlot *slot;
        EState     *estate;
        ExprContext *econtext;
        Datum      *exprvals;
        bool       *exprnulls;
        ExprState  *exprstate;
        int         tcnt;

        /* Are we still in the main context? */
        Assert(CurrentMemoryContext == expr_context);

        /*
         * Need an EState for evaluation of expressions.  Create it in the
         * per-expression context to be sure it gets cleaned up at the bottom
         * of the loop.
         */
        estate = CreateExecutorState();
        econtext = GetPerTupleExprContext(estate);

        /* Set up expression evaluation state */
        exprstate = ExecPrepareExpr((Expr *) expr, estate);

        /* Need a slot to hold the current heap tuple, too */
        slot = MakeSingleTupleTableSlot(RelationGetDescr(onerel),
                                        &TTSOpsHeapTuple);

        /* Arrange for econtext's scan tuple to be the tuple under test */
        econtext->ecxt_scantuple = slot;

        /* Compute and save expression values */
        exprvals = (Datum *) palloc(numrows * sizeof(Datum));
        exprnulls = (bool *) palloc(numrows * sizeof(bool));

        tcnt = 0;
        for (i = 0; i < numrows; i++)
        {
            Datum       datum;
            bool        isnull;

            /*
             * Reset the per-tuple context each time, to reclaim any cruft
             * left behind by evaluating the statistics expressions.
             */
            ResetExprContext(econtext);

            /* Set up for expression evaluation */
            ExecStoreHeapTuple(rows[i], slot, false);

            /*
             * Evaluate the expression. We do this in the per-tuple context so
             * as not to leak memory, and then copy the result into the
             * context created at the beginning of this function.
             */
            datum = ExecEvalExprSwitchContext(exprstate,
                                              GetPerTupleExprContext(estate),
                                              &isnull);
            if (isnull)
            {
                exprvals[tcnt] = (Datum) 0;
                exprnulls[tcnt] = true;
            }
            else
            {
                /* Make sure we copy the data into the context. */
                Assert(CurrentMemoryContext == expr_context);

                exprvals[tcnt] = datumCopy(datum,
                                           stats->attrtype->typbyval,
                                           stats->attrtype->typlen);
                exprnulls[tcnt] = false;
            }

            tcnt++;
        }

        /*
         * Now we can compute the statistics for the expression columns.
         *
         * XXX Unlike compute_index_stats we don't need to switch and reset
         * memory contexts here, because we're only computing stats for a
         * single expression (and not iterating over many indexes), so we just
         * do it in expr_context. Note that compute_stats copies the result
         * into stats->anl_context, so it does not disappear.
         */
        if (tcnt > 0)
        {
            AttributeOpts *aopt =
            get_attribute_options(stats->attr->attrelid,
                                  stats->attr->attnum);

            stats->exprvals = exprvals;
            stats->exprnulls = exprnulls;
            stats->rowstride = 1;
            stats->compute_stats(stats,
                                 expr_fetch_func,
                                 tcnt,
                                 tcnt);

            /*
             * If the n_distinct option is specified, it overrides the above
             * computation.
             */
            if (aopt != NULL && aopt->n_distinct != 0.0)
                stats->stadistinct = aopt->n_distinct;
        }

        /* And clean up */
        MemoryContextSwitchTo(expr_context);

        ExecDropSingleTupleTableSlot(slot);
        FreeExecutorState(estate);
        MemoryContextResetAndDeleteChildren(expr_context);
    }

    MemoryContextSwitchTo(old_context);
    MemoryContextDelete(expr_context);
}


/*
 * Fetch function for analyzing statistics object expressions.
 *
 * We have not bothered to construct tuples from the data, instead the data
 * is just in Datum arrays.
 */
static Datum
expr_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull)
{
    int         i;

    /* exprvals and exprnulls are already offset for proper column */
    i = rownum * stats->rowstride;
    *isNull = stats->exprnulls[i];
    return stats->exprvals[i];
}

/*
 * Build analyze data for a list of expressions. As this is not tied
 * directly to a relation (table or index), we have to fake some of
 * the fields in examine_expression().
 */
static AnlExprData *
build_expr_data(List *exprs, int stattarget)
{
    int         idx;
    int         nexprs = list_length(exprs);
    AnlExprData *exprdata;
    ListCell   *lc;

    exprdata = (AnlExprData *) palloc0(nexprs * sizeof(AnlExprData));

    idx = 0;
    foreach(lc, exprs)
    {
        Node       *expr = (Node *) lfirst(lc);
        AnlExprData *thisdata = &exprdata[idx];

        thisdata->expr = expr;
        thisdata->vacattrstat = examine_expression(expr, stattarget);
        idx++;
    }

    return exprdata;
}

/* form an array of pg_statistic rows (per update_attstats) */
static Datum
serialize_expr_stats(AnlExprData *exprdata, int nexprs)
{
    int         exprno;
    Oid         typOid;
    Relation    sd;

    ArrayBuildState *astate = NULL;

    sd = table_open(StatisticRelationId, RowExclusiveLock);

    /* lookup OID of composite type for pg_statistic */
    typOid = get_rel_type_id(StatisticRelationId);
    if (!OidIsValid(typOid))
        ereport(ERROR,
                (errcode(ERRCODE_WRONG_OBJECT_TYPE),
                 errmsg("relation \"pg_statistic\" does not have a composite type")));

    for (exprno = 0; exprno < nexprs; exprno++)
    {
        int         i,
                    k;
        VacAttrStats *stats = exprdata[exprno].vacattrstat;

        Datum       values[Natts_pg_statistic];
        bool        nulls[Natts_pg_statistic];
        HeapTuple   stup;

        if (!stats->stats_valid)
        {
            astate = accumArrayResult(astate,
                                      (Datum) 0,
                                      true,
                                      typOid,
                                      CurrentMemoryContext);
            continue;
        }

        /*
         * Construct a new pg_statistic tuple
         */
        for (i = 0; i < Natts_pg_statistic; ++i)
        {
            nulls[i] = false;
        }

        values[Anum_pg_statistic_starelid - 1] = ObjectIdGetDatum(InvalidOid);
        values[Anum_pg_statistic_staattnum - 1] = Int16GetDatum(InvalidAttrNumber);
        values[Anum_pg_statistic_stainherit - 1] = BoolGetDatum(false);
        values[Anum_pg_statistic_stanullfrac - 1] = Float4GetDatum(stats->stanullfrac);
        values[Anum_pg_statistic_stawidth - 1] = Int32GetDatum(stats->stawidth);
        values[Anum_pg_statistic_stadistinct - 1] = Float4GetDatum(stats->stadistinct);
        i = Anum_pg_statistic_stakind1 - 1;
        for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
        {
            values[i++] = Int16GetDatum(stats->stakind[k]); /* stakindN */
        }
        i = Anum_pg_statistic_staop1 - 1;
        for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
        {
            values[i++] = ObjectIdGetDatum(stats->staop[k]);    /* staopN */
        }
        i = Anum_pg_statistic_stacoll1 - 1;
        for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
        {
            values[i++] = ObjectIdGetDatum(stats->stacoll[k]);  /* stacollN */
        }
        i = Anum_pg_statistic_stanumbers1 - 1;
        for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
        {
            int         nnum = stats->numnumbers[k];

            if (nnum > 0)
            {
                int         n;
                Datum      *numdatums = (Datum *) palloc(nnum * sizeof(Datum));
                ArrayType  *arry;

                for (n = 0; n < nnum; n++)
                    numdatums[n] = Float4GetDatum(stats->stanumbers[k][n]);
                /* XXX knows more than it should about type float4: */
                arry = construct_array(numdatums, nnum,
                                       FLOAT4OID,
                                       sizeof(float4), true, TYPALIGN_INT);
                values[i++] = PointerGetDatum(arry);    /* stanumbersN */
            }
            else
            {
                nulls[i] = true;
                values[i++] = (Datum) 0;
            }
        }
        i = Anum_pg_statistic_stavalues1 - 1;
        for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
        {
            if (stats->numvalues[k] > 0)
            {
                ArrayType  *arry;

                arry = construct_array(stats->stavalues[k],
                                       stats->numvalues[k],
                                       stats->statypid[k],
                                       stats->statyplen[k],
                                       stats->statypbyval[k],
                                       stats->statypalign[k]);
                values[i++] = PointerGetDatum(arry);    /* stavaluesN */
            }
            else
            {
                nulls[i] = true;
                values[i++] = (Datum) 0;
            }
        }

        stup = heap_form_tuple(RelationGetDescr(sd), values, nulls);

        astate = accumArrayResult(astate,
                                  heap_copy_tuple_as_datum(stup, RelationGetDescr(sd)),
                                  false,
                                  typOid,
                                  CurrentMemoryContext);
    }

    table_close(sd, RowExclusiveLock);

    return makeArrayResult(astate, CurrentMemoryContext);
}

/*
 * Loads pg_statistic record from expression statistics for expression
 * identified by the supplied index.
 */
HeapTuple
statext_expressions_load(Oid stxoid, int idx)
{
    bool        isnull;
    Datum       value;
    HeapTuple   htup;
    ExpandedArrayHeader *eah;
    HeapTupleHeader td;
    HeapTupleData tmptup;
    HeapTuple   tup;

    htup = SearchSysCache1(STATEXTDATASTXOID, ObjectIdGetDatum(stxoid));
    if (!HeapTupleIsValid(htup))
        elog(ERROR, "cache lookup failed for statistics object %u", stxoid);

    value = SysCacheGetAttr(STATEXTDATASTXOID, htup,
                            Anum_pg_statistic_ext_data_stxdexpr, &isnull);
    if (isnull)
        elog(ERROR,
             "requested statistics kind \"%c\" is not yet built for statistics object %u",
             STATS_EXT_DEPENDENCIES, stxoid);

    eah = DatumGetExpandedArray(value);

    deconstruct_expanded_array(eah);

    td = DatumGetHeapTupleHeader(eah->dvalues[idx]);

    /* Build a temporary HeapTuple control structure */
    tmptup.t_len = HeapTupleHeaderGetDatumLength(td);
    ItemPointerSetInvalid(&(tmptup.t_self));
    tmptup.t_tableOid = InvalidOid;
    tmptup.t_data = td;

    tup = heap_copytuple(&tmptup);

    ReleaseSysCache(htup);

    return tup;
}

/*
 * Evaluate the expressions, so that we can use the results to build
 * all the requested statistics types. This matters especially for
 * expensive expressions, of course.
 */
static StatsBuildData *
make_build_data(Relation rel, StatExtEntry *stat, int numrows, HeapTuple *rows,
                VacAttrStats **stats, int stattarget)
{
    /* evaluated expressions */
    StatsBuildData *result;
    char       *ptr;
    Size        len;

    int         i;
    int         k;
    int         idx;
    TupleTableSlot *slot;
    EState     *estate;
    ExprContext *econtext;
    List       *exprstates = NIL;
    int         nkeys = bms_num_members(stat->columns) + list_length(stat->exprs);
    ListCell   *lc;

    /* allocate everything as a single chunk, so we can free it easily */
    len = MAXALIGN(sizeof(StatsBuildData));
    len += MAXALIGN(sizeof(AttrNumber) * nkeys);    /* attnums */
    len += MAXALIGN(sizeof(VacAttrStats *) * nkeys);    /* stats */

    /* values */
    len += MAXALIGN(sizeof(Datum *) * nkeys);
    len += nkeys * MAXALIGN(sizeof(Datum) * numrows);

    /* nulls */
    len += MAXALIGN(sizeof(bool *) * nkeys);
    len += nkeys * MAXALIGN(sizeof(bool) * numrows);

    ptr = palloc(len);

    /* set the pointers */
    result = (StatsBuildData *) ptr;
    ptr += MAXALIGN(sizeof(StatsBuildData));

    /* attnums */
    result->attnums = (AttrNumber *) ptr;
    ptr += MAXALIGN(sizeof(AttrNumber) * nkeys);

    /* stats */
    result->stats = (VacAttrStats **) ptr;
    ptr += MAXALIGN(sizeof(VacAttrStats *) * nkeys);

    /* values */
    result->values = (Datum **) ptr;
    ptr += MAXALIGN(sizeof(Datum *) * nkeys);

    /* nulls */
    result->nulls = (bool **) ptr;
    ptr += MAXALIGN(sizeof(bool *) * nkeys);

    for (i = 0; i < nkeys; i++)
    {
        result->values[i] = (Datum *) ptr;
        ptr += MAXALIGN(sizeof(Datum) * numrows);

        result->nulls[i] = (bool *) ptr;
        ptr += MAXALIGN(sizeof(bool) * numrows);
    }

    Assert((ptr - (char *) result) == len);

    /* we have it allocated, so let's fill the values */
    result->nattnums = nkeys;
    result->numrows = numrows;

    /* fill the attribute info - first attributes, then expressions */
    idx = 0;
    k = -1;
    while ((k = bms_next_member(stat->columns, k)) >= 0)
    {
        result->attnums[idx] = k;
        result->stats[idx] = stats[idx];

        idx++;
    }

    k = -1;
    foreach(lc, stat->exprs)
    {
        Node       *expr = (Node *) lfirst(lc);

        result->attnums[idx] = k;
        result->stats[idx] = examine_expression(expr, stattarget);

        idx++;
        k--;
    }

    /* first extract values for all the regular attributes */
    for (i = 0; i < numrows; i++)
    {
        idx = 0;
        k = -1;
        while ((k = bms_next_member(stat->columns, k)) >= 0)
        {
            result->values[idx][i] = heap_getattr(rows[i], k,
                                                  result->stats[idx]->tupDesc,
                                                  &result->nulls[idx][i]);

            idx++;
        }
    }

    /* Need an EState for evaluation expressions. */
    estate = CreateExecutorState();
    econtext = GetPerTupleExprContext(estate);

    /* Need a slot to hold the current heap tuple, too */
    slot = MakeSingleTupleTableSlot(RelationGetDescr(rel),
                                    &TTSOpsHeapTuple);

    /* Arrange for econtext's scan tuple to be the tuple under test */
    econtext->ecxt_scantuple = slot;

    /* Set up expression evaluation state */
    exprstates = ExecPrepareExprList(stat->exprs, estate);

    for (i = 0; i < numrows; i++)
    {
        /*
         * Reset the per-tuple context each time, to reclaim any cruft left
         * behind by evaluating the statistics object expressions.
         */
        ResetExprContext(econtext);

        /* Set up for expression evaluation */
        ExecStoreHeapTuple(rows[i], slot, false);

        idx = bms_num_members(stat->columns);
        foreach(lc, exprstates)
        {
            Datum       datum;
            bool        isnull;
            ExprState  *exprstate = (ExprState *) lfirst(lc);

            /*
             * XXX This probably leaks memory. Maybe we should use
             * ExecEvalExprSwitchContext but then we need to copy the result
             * somewhere else.
             */
            datum = ExecEvalExpr(exprstate,
                                 GetPerTupleExprContext(estate),
                                 &isnull);
            if (isnull)
            {
                result->values[idx][i] = (Datum) 0;
                result->nulls[idx][i] = true;
            }
            else
            {
                result->values[idx][i] = (Datum) datum;
                result->nulls[idx][i] = false;
            }

            idx++;
        }
    }

    ExecDropSingleTupleTableSlot(slot);
    FreeExecutorState(estate);

    return result;
}