extended_stats.c

Go to the documentation of this file.

/*-------------------------------------------------------------------------
 *
 * extended_stats.c
 *    POSTGRES extended statistics
 *
 * Generic code supporting statistics objects created via CREATE STATISTICS.
 *
 *
 * Portions Copyright (c) 1996-2020, 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 "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/builtins.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"

/*
 * 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 statistic kinds */
    int         stattarget;     /* statistics target (-1 for default) */
} StatExtEntry;


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

/*
 * 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       *stats;
    MemoryContext cxt;
    MemoryContext oldcxt;
    int64       ext_cnt;

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

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

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

        pgstat_progress_update_multi_param(2, index, val);
    }

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

        /*
         * 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,
                                      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;
        }

        /* check allowed number of dimensions */
        Assert(bms_num_members(stat->columns) >= 2 &&
               bms_num_members(stat->columns) <= STATS_MAX_DIMENSIONS);

        /* 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;

        /* 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, numrows, rows,
                                                    stat->columns, stats);
            else if (t == STATS_EXT_DEPENDENCIES)
                dependencies = statext_dependencies_build(numrows, rows,
                                                          stat->columns, stats);
            else if (t == STATS_EXT_MCV)
                mcv = statext_mcv_build(numrows, rows, stat->columns, stats,
                                        totalrows, stattarget);
        }

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

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

    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 objects (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;

    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 = stat->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,
                                      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 maximmum 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;

        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;

        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));
            entry->types = lappend_int(entry->types, (int) enabled[i]);
        }

        result = lappend(result, entry);
    }

    systable_endscan(scan);

    return result;
}

/*
 * 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,
                      int nvacatts, VacAttrStats **vacatts)
{
    int         i = 0;
    int         x = -1;
    VacAttrStats **stats;

    stats = (VacAttrStats **)
        palloc(bms_num_members(attrs) * 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++;
    }

    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, 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);
    }

    /* 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;

    /* 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);
}

/* simple counterpart to qsort_arg */
void *
bsearch_arg(const void *key, const void *base, size_t nmemb, size_t size,
            int (*compar) (const void *, const void *, void *),
            void *arg)
{
    size_t      l,
                u,
                idx;
    const void *p;
    int         comparison;

    l = 0;
    u = nmemb;
    while (l < u)
    {
        idx = (l + u) / 2;
        p = (void *) (((const char *) base) + (idx * size));
        comparison = (*compar) (key, p, arg);

        if (comparison < 0)
            u = idx;
        else if (comparison > 0)
            l = idx + 1;
        else
            return (void *) p;
    }

    return NULL;
}

/*
 * 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 *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)
    {
        /*
         * 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(AttrNumberIsForUserDefinedAttr(j));
        Assert(j <= MaxAttrNumber);

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

        /* 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(int numrows, int *nitems, HeapTuple *rows, TupleDesc tdesc,
                   MultiSortSupport mss, int numattrs, AttrNumber *attnums)
{
    int         i,
                j,
                len,
                idx;
    int         nvalues = numrows * numattrs;

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

    /* Compute the total amount of memory we need (both items and values). */
    len = 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 += 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 */
    idx = 0;
    for (i = 0; i < numrows; i++)
    {
        bool        toowide = false;

        items[idx].values = &values[idx * numattrs];
        items[idx].isnull = &isnull[idx * numattrs];

        /* load the values/null flags from sample rows */
        for (j = 0; j < numattrs; j++)
        {
            Datum       value;
            bool        isnull;

            value = heap_getattr(rows[i], attnums[j], tdesc, &isnull);

            /*
             * 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) &&
                (TupleDescAttr(tdesc, attnums[j] - 1)->attlen == -1))
            {
                if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
                {
                    toowide = true;
                    break;
                }

                value = PointerGetDatum(PG_DETOAST_DATUM(value));
            }

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

        if (toowide)
            continue;

        idx++;
    }

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

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

    /* do the sort, using the multi-sort */
    qsort_arg((void *) items, idx, 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;
}

/*
 * 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, 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 = NULL;
        int         num_matched;
        int         numkeys;

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

        /*
         * Collect attributes in remaining (unestimated) clauses fully covered
         * by this statistic object.
         */
        for (i = 0; i < nclauses; i++)
        {
            /* ignore incompatible/estimated clauses */
            if (!clause_attnums[i])
                continue;

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

            matched = bms_add_members(matched, clause_attnums[i]);
        }

        num_matched = bms_num_members(matched);
        bms_free(matched);

        /*
         * 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);

        /*
         * Use this object when it increases the number of matched clauses or
         * when it matches the same number of attributes 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)
{
    /* 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 op Const) or (Const op Var) */
    if (is_opclause(clause))
    {
        RangeTblEntry *rte = root->simple_rte_array[relid];
        OpExpr     *expr = (OpExpr *) clause;
        Var        *var;

        /* 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_clause_args(expr->args, &var, 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 */
                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;

        return statext_is_compatible_clause_internal(root, (Node *) var,
                                                     relid, attnums);
    }

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

        /* 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_clause_args(expr->args, &var, 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 */
                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;

        return statext_is_compatible_clause_internal(root, (Node *) var,
                                                     relid, attnums);
    }

    /* 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))
                return false;
        }

        return true;
    }

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

        /*
         * Only simple (Var IS NULL) expressions supported for now. Maybe we
         * could use examine_variable to fix this?
         */
        if (!IsA(nt->arg, Var))
            return false;

        return statext_is_compatible_clause_internal(root, (Node *) (nt->arg),
                                                     relid, attnums);
    }

    return false;
}

/*
 * statext_is_compatible_clause
 *      Determines if the clause is compatible with MCV lists.
 *
 * Currently, we only support three types of clauses:
 *
 * (a) OpExprs of the form (Var op Const), or (Const op Var), where the op
 * is one of ("=", "<", ">", ">=", "<=")
 *
 * (b) (Var IS [NOT] NULL)
 *
 * (c) combinations using AND/OR/NOT
 *
 * 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)
{
    RangeTblEntry *rte = root->simple_rte_array[relid];
    RestrictInfo *rinfo = (RestrictInfo *) clause;
    Oid         userid;

    if (!IsA(rinfo, RestrictInfo))
        return false;

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

    /* clauses referencing multiple varnos are incompatible */
    if (bms_membership(rinfo->clause_relids) != BMS_SINGLETON)
        return false;

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

    /*
     * Check that the user has permission to read all these 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)
    {
        /* Don't have table privilege, must check individual columns */
        if (bms_is_member(InvalidAttrNumber, *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(*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 a couple of derived selectivities:
 *
 * - simple selectivity:  Computed without extended statistic, 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.
 *
 * - other selectivity: A selectivity estimate for data not covered by the MCV
 * list (i.e. satisfying the clauses, but not common enough to make it into
 * the MCV list)
 *
 * Note: While simple and base selectivities are defined in a quite similar
 * way, the values are computed differently and are not therefore equal. The
 * simple selectivity is computed as a product of per-clause estimates, while
 * the base selectivity is computed by adding up base frequencies of matching
 * items of the multi-column MCV list. So the values may differ for two main
 * reasons - (a) the MCV list may not cover 100% of the data and (b) some of
 * the MCV items did not match the estimated clauses.
 *
 * As both (a) and (b) reduce the base selectivity value, it generally holds
 * that (simple_selectivity >= base_selectivity). If the MCV list covers all
 * the data, the values may be equal.
 *
 * So, (simple_selectivity - base_selectivity) is an estimate for the part
 * not covered by the MCV list, and (mcv_selectivity - base_selectivity) may
 * be seen as a correction for the part covered by the MCV list. Those two
 * statements are actually equivalent.
 *
 * Note: Due to rounding errors and minor differences in how the estimates
 * are computed, the inequality may not always hold. Which is why we clamp
 * the selectivities to prevent strange estimate (negative etc.).
 *
 * '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)
{
    ListCell   *l;
    Bitmapset **list_attnums;
    int         listidx;
    Selectivity sel = 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 1.0;

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

    /*
     * Pre-process the clauses list to extract the attnums seen in each item.
     * We need to determine if there's any clauses which will be useful for
     * selectivity estimations with extended stats. Along the way we'll record
     * all of the attnums for each clause in a list which we'll reference
     * later so we don't need to repeat the same work again. We'll also keep
     * track of all attnums seen.
     *
     * 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;

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

        listidx++;
    }

    /* apply as many extended statistics as possible */
    while (true)
    {
        StatisticExtInfo *stat;
        List       *stat_clauses;
        Selectivity simple_sel,
                    mcv_sel,
                    mcv_basesel,
                    mcv_totalsel,
                    other_sel,
                    stat_sel;

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

        listidx = 0;
        foreach(l, clauses)
        {
            /*
             * If the clause is compatible with the selected statistics, mark it
             * as estimated and add it to the list to estimate.
             */
            if (list_attnums[listidx] != NULL &&
                bms_is_subset(list_attnums[listidx], stat->keys))
            {
                stat_clauses = lappend(stat_clauses, (Node *) lfirst(l));
                *estimatedclauses = bms_add_member(*estimatedclauses, listidx);

                bms_free(list_attnums[listidx]);
                list_attnums[listidx] = NULL;
            }

            listidx++;
        }

        /*
         * First compute "simple" selectivity, i.e. without the extended
         * statistics, and essentially assuming independence of the
         * columns/clauses. We'll then use the various selectivities computed from
         * MCV list to improve it.
         */
        simple_sel = clauselist_selectivity_simple(root, stat_clauses, varRelid,
                                                jointype, sjinfo, NULL);

        /*
         * Now compute the multi-column estimate from the MCV list, along with the
         * other selectivities (base & total selectivity).
         */
        mcv_sel = mcv_clauselist_selectivity(root, stat, stat_clauses, varRelid,
                                             jointype, sjinfo, rel,
                                             &mcv_basesel, &mcv_totalsel);

        /* Estimated selectivity of values not covered by MCV matches */
        other_sel = simple_sel - mcv_basesel;
        CLAMP_PROBABILITY(other_sel);

        /* The non-MCV selectivity can't exceed the 1 - mcv_totalsel. */
        if (other_sel > 1.0 - mcv_totalsel)
            other_sel = 1.0 - mcv_totalsel;

        /* Overall selectivity is the combination of MCV and non-MCV estimates. */
        stat_sel = mcv_sel + other_sel;
        CLAMP_PROBABILITY(stat_sel);

        /* Factor the estimate from this MCV to the oveall estimate. */
        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)
{
    Selectivity sel;

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

    /*
     * 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_expression
 *      Split expression into Var and Const parts.
 *
 * Attempts to match the arguments to either (Var op Const) or (Const op Var),
 * possibly with a RelabelType on top. When the expression matches this form,
 * returns true, otherwise returns false.
 *
 * Optionally returns pointers to the extracted Var/Const nodes, when passed
 * non-null pointers (varp, cstp and varonleftp). The varonleftp flag specifies
 * on which side of the operator we found the Var node.
 */
bool
examine_clause_args(List *args, Var **varp, Const **cstp, bool *varonleftp)
{
    Var    *var;
    Const  *cst;
    bool    varonleft;
    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(leftop, Var) && IsA(rightop, Const))
    {
        var = (Var *) leftop;
        cst = (Const *) rightop;
        varonleft = true;
    }
    else if (IsA(leftop, Const) && IsA(rightop, Var))
    {
        var = (Var *) rightop;
        cst = (Const *) leftop;
        varonleft = false;
    }
    else
        return false;

    /* return pointers to the extracted parts if requested */
    if (varp)
        *varp = var;

    if (cstp)
        *cstp = cst;

    if (varonleftp)
        *varonleftp = varonleft;

    return true;
}