/src/postgres/src/backend/commands/analyze.c

Source
/*-------------------------------------------------------------------------
 *
 * analyze.c
 *    the Postgres statistics generator
 *
 * Portions Copyright (c) 1996-2026, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/commands/analyze.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <math.h>

#include "access/detoast.h"
#include "access/genam.h"
#include "access/multixact.h"
#include "access/relation.h"
#include "access/table.h"
#include "access/tableam.h"
#include "access/transam.h"
#include "access/tupconvert.h"
#include "access/visibilitymap.h"
#include "access/xact.h"
#include "catalog/index.h"
#include "catalog/indexing.h"
#include "catalog/pg_inherits.h"
#include "commands/progress.h"
#include "commands/tablecmds.h"
#include "commands/vacuum.h"
#include "common/pg_prng.h"
#include "executor/executor.h"
#include "executor/instrument.h"
#include "foreign/fdwapi.h"
#include "miscadmin.h"
#include "nodes/nodeFuncs.h"
#include "parser/parse_oper.h"
#include "parser/parse_relation.h"
#include "pgstat.h"
#include "statistics/extended_stats_internal.h"
#include "statistics/statistics.h"
#include "storage/bufmgr.h"
#include "storage/procarray.h"
#include "utils/attoptcache.h"
#include "utils/datum.h"
#include "utils/guc.h"
#include "utils/lsyscache.h"
#include "utils/memutils.h"
#include "utils/pg_rusage.h"
#include "utils/sampling.h"
#include "utils/sortsupport.h"
#include "utils/syscache.h"
#include "utils/timestamp.h"


/* Per-index data for ANALYZE */
typedef struct AnlIndexData
{
  IndexInfo  *indexInfo;    /* BuildIndexInfo result */
  double    tupleFract;   /* fraction of rows for partial index */
  VacAttrStats **vacattrstats;  /* index attrs to analyze */
  int     attr_cnt;
} AnlIndexData;


/* Default statistics target (GUC parameter) */
int     default_statistics_target = 100;

/* A few variables that don't seem worth passing around as parameters */
static MemoryContext anl_context = NULL;
static BufferAccessStrategy vac_strategy;


static void do_analyze_rel(Relation onerel,
               const VacuumParams *params, List *va_cols,
               AcquireSampleRowsFunc acquirefunc, BlockNumber relpages,
               bool inh, bool in_outer_xact, int elevel);
static void compute_index_stats(Relation onerel, double totalrows,
                AnlIndexData *indexdata, int nindexes,
                HeapTuple *rows, int numrows,
                MemoryContext col_context);
static void validate_va_cols_list(Relation onerel, List *va_cols);
static VacAttrStats *examine_attribute(Relation onerel, int attnum,
                     Node *index_expr);
static int  acquire_sample_rows(Relation onerel, int elevel,
                HeapTuple *rows, int targrows,
                double *totalrows, double *totaldeadrows);
static int  compare_rows(const void *a, const void *b, void *arg);
static int  acquire_inherited_sample_rows(Relation onerel, int elevel,
                      HeapTuple *rows, int targrows,
                      double *totalrows, double *totaldeadrows);
static void update_attstats(Oid relid, bool inh,
              int natts, VacAttrStats **vacattrstats);
static Datum std_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull);
static Datum ind_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull);


/*
 *  analyze_rel() -- analyze one relation
 *
 * relid identifies the relation to analyze.  If relation is supplied, use
 * the name therein for reporting any failure to open/lock the rel; do not
 * use it once we've successfully opened the rel, since it might be stale.
 */
void
analyze_rel(Oid relid, RangeVar *relation,
      const VacuumParams *params, List *va_cols, bool in_outer_xact,
      BufferAccessStrategy bstrategy)
{
  Relation  onerel;
  int     elevel;
  AcquireSampleRowsFunc acquirefunc = NULL;
  BlockNumber relpages = 0;
  bool    stats_imported = false;

  /* Select logging level */
  if (params->options & VACOPT_VERBOSE)
    elevel = INFO;
  else
    elevel = DEBUG2;

  /* Set up static variables */
  vac_strategy = bstrategy;

  /*
   * Check for user-requested abort.
   */
  CHECK_FOR_INTERRUPTS();

  /*
   * Open the relation, getting ShareUpdateExclusiveLock to ensure that two
   * ANALYZEs don't run on it concurrently.  (This also locks out a
   * concurrent VACUUM, which doesn't matter much at the moment but might
   * matter if we ever try to accumulate stats on dead tuples.) If the rel
   * has been dropped since we last saw it, we don't need to process it.
   *
   * Make sure to generate only logs for ANALYZE in this case.
   */
  onerel = vacuum_open_relation(relid, relation, params->options & ~(VACOPT_VACUUM),
                  params->log_analyze_min_duration >= 0,
                  ShareUpdateExclusiveLock);

  /* leave if relation could not be opened or locked */
  if (!onerel)
    return;

  /*
   * Check if relation needs to be skipped based on privileges.  This check
   * happens also when building the relation list to analyze for a manual
   * operation, and needs to be done additionally here as ANALYZE could
   * happen across multiple transactions where privileges could have changed
   * in-between.  Make sure to generate only logs for ANALYZE in this case.
   */
  if (!vacuum_is_permitted_for_relation(RelationGetRelid(onerel),
                      onerel->rd_rel,
                      params->options & ~VACOPT_VACUUM,
                      false))
  {
    relation_close(onerel, ShareUpdateExclusiveLock);
    return;
  }

  /*
   * Silently ignore tables that are temp tables of other backends ---
   * trying to analyze these is rather pointless, since their contents are
   * probably not up-to-date on disk.  (We don't throw a warning here; it
   * would just lead to chatter during a database-wide ANALYZE.)
   */
  if (RELATION_IS_OTHER_TEMP(onerel))
  {
    relation_close(onerel, ShareUpdateExclusiveLock);
    return;
  }

  /*
   * We can ANALYZE any table except pg_statistic. See update_attstats
   */
  if (RelationGetRelid(onerel) == StatisticRelationId)
  {
    relation_close(onerel, ShareUpdateExclusiveLock);
    return;
  }

  /*
   * Check the given list of columns
   */
  if (va_cols != NIL)
    validate_va_cols_list(onerel, va_cols);

  /*
   * Initialize progress reporting before setup for regular/foreign tables.
   * (For the former, the time spent on it would be negligible, but for the
   * latter, if FDWs support statistics import or analysis, they'd do some
   * work that needs the remote access, so the time might be
   * non-negligible.)
   */
  pgstat_progress_start_command(PROGRESS_COMMAND_ANALYZE,
                  RelationGetRelid(onerel));
  if (AmAutoVacuumWorkerProcess())
    pgstat_progress_update_param(PROGRESS_ANALYZE_STARTED_BY,
                   PROGRESS_ANALYZE_STARTED_BY_AUTOVACUUM);
  else
    pgstat_progress_update_param(PROGRESS_ANALYZE_STARTED_BY,
                   PROGRESS_ANALYZE_STARTED_BY_MANUAL);

  /*
   * Check that it's of an analyzable relkind, and set up appropriately.
   */
  if (onerel->rd_rel->relkind == RELKIND_RELATION ||
    onerel->rd_rel->relkind == RELKIND_MATVIEW)
  {
    /* Regular table, so we'll use the regular row acquisition function */
    acquirefunc = acquire_sample_rows;
    /* Also get regular table's size */
    relpages = RelationGetNumberOfBlocks(onerel);
  }
  else if (onerel->rd_rel->relkind == RELKIND_FOREIGN_TABLE)
  {
    /*
     * For a foreign table, call the FDW's hook functions to see whether
     * it supports statistics import or analysis.
     */
    FdwRoutine *fdwroutine;

    fdwroutine = GetFdwRoutineForRelation(onerel, false);

    if (fdwroutine->ImportForeignStatistics != NULL)
    {
      Oid     save_userid;
      int     save_sec_context;
      int     save_nestlevel;

      /*
       * Switch to the table owner's userid, as in the sampling path.
       * Also lock down security-restricted operations and arrange to
       * make GUC variable changes local to this command.
       */
      GetUserIdAndSecContext(&save_userid, &save_sec_context);
      SetUserIdAndSecContext(onerel->rd_rel->relowner,
                   save_sec_context | SECURITY_RESTRICTED_OPERATION);
      save_nestlevel = NewGUCNestLevel();
      RestrictSearchPath();

      stats_imported = fdwroutine->ImportForeignStatistics(onerel,
                                 va_cols,
                                 elevel);

      AtEOXact_GUC(false, save_nestlevel);
      SetUserIdAndSecContext(save_userid, save_sec_context);
    }

    if (!stats_imported)
    {
      bool    ok = false;

      if (fdwroutine->AnalyzeForeignTable != NULL)
        ok = fdwroutine->AnalyzeForeignTable(onerel,
                           &acquirefunc,
                           &relpages);

      if (!ok)
      {
        ereport(WARNING,
            errmsg("skipping \"%s\" --- cannot analyze this foreign table",
                 RelationGetRelationName(onerel)));
        relation_close(onerel, ShareUpdateExclusiveLock);
        goto out;
      }
    }
  }
  else if (onerel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
  {
    /*
     * For partitioned tables, we want to do the recursive ANALYZE below.
     */
  }
  else
  {
    /* No need for a WARNING if we already complained during VACUUM */
    if (!(params->options & VACOPT_VACUUM))
      ereport(WARNING,
          (errmsg("skipping \"%s\" --- cannot analyze non-tables or special system tables",
              RelationGetRelationName(onerel))));
    relation_close(onerel, ShareUpdateExclusiveLock);
    goto out;
  }

  /*
   * Do the normal non-recursive ANALYZE.  We can skip this for partitioned
   * tables, which don't contain any rows, and foreign tables that
   * successfully imported statistics.
   */
  if ((onerel->rd_rel->relkind != RELKIND_PARTITIONED_TABLE)
    && !stats_imported)
    do_analyze_rel(onerel, params, va_cols, acquirefunc,
             relpages, false, in_outer_xact, elevel);

  /*
   * If there are child tables, do recursive ANALYZE.
   */
  if (onerel->rd_rel->relhassubclass)
    do_analyze_rel(onerel, params, va_cols, acquirefunc, relpages,
             true, in_outer_xact, elevel);

  /*
   * Close source relation now, but keep lock so that no one deletes it
   * before we commit.  (If someone did, they'd fail to clean up the entries
   * we made in pg_statistic.  Also, releasing the lock before commit would
   * expose us to concurrent-update failures in update_attstats.)
   */
  relation_close(onerel, NoLock);

out:
  pgstat_progress_end_command();
}

/*
 *  do_analyze_rel() -- analyze one relation, recursively or not
 *
 * Note that "acquirefunc" is only relevant for the non-inherited case.
 * For the inherited case, acquire_inherited_sample_rows() determines the
 * appropriate acquirefunc for each child table.
 */
static void
do_analyze_rel(Relation onerel, const VacuumParams *params,
         List *va_cols, AcquireSampleRowsFunc acquirefunc,
         BlockNumber relpages, bool inh, bool in_outer_xact,
         int elevel)
{
  int     attr_cnt,
        tcnt,
        i,
        ind;
  Relation   *Irel;
  int     nindexes;
  bool    verbose,
        instrument,
        hasindex;
  VacAttrStats **vacattrstats;
  AnlIndexData *indexdata;
  int     targrows,
        numrows,
        minrows;
  double    totalrows,
        totaldeadrows;
  HeapTuple  *rows;
  PGRUsage  ru0;
  TimestampTz starttime = 0;
  MemoryContext caller_context;
  Oid     save_userid;
  int     save_sec_context;
  int     save_nestlevel;
  WalUsage  startwalusage = pgWalUsage;
  BufferUsage startbufferusage = pgBufferUsage;
  BufferUsage bufferusage;
  PgStat_Counter startreadtime = 0;
  PgStat_Counter startwritetime = 0;

  verbose = (params->options & VACOPT_VERBOSE) != 0;
  instrument = (verbose || (AmAutoVacuumWorkerProcess() &&
                params->log_analyze_min_duration >= 0));
  if (inh)
    ereport(elevel,
        (errmsg("analyzing \"%s.%s\" inheritance tree",
            get_namespace_name(RelationGetNamespace(onerel)),
            RelationGetRelationName(onerel))));
  else
    ereport(elevel,
        (errmsg("analyzing \"%s.%s\"",
            get_namespace_name(RelationGetNamespace(onerel)),
            RelationGetRelationName(onerel))));

  /*
   * Set up a working context so that we can easily free whatever junk gets
   * created.
   */
  anl_context = AllocSetContextCreate(CurrentMemoryContext,
                    "Analyze",
                    ALLOCSET_DEFAULT_SIZES);
  caller_context = MemoryContextSwitchTo(anl_context);

  /*
   * Switch to the table owner's userid, so that any index functions are run
   * as that user.  Also lock down security-restricted operations and
   * arrange to make GUC variable changes local to this command.
   */
  GetUserIdAndSecContext(&save_userid, &save_sec_context);
  SetUserIdAndSecContext(onerel->rd_rel->relowner,
               save_sec_context | SECURITY_RESTRICTED_OPERATION);
  save_nestlevel = NewGUCNestLevel();
  RestrictSearchPath();

  /*
   * When verbose or autovacuum logging is used, initialize a resource usage
   * snapshot and optionally track I/O timing.
   */
  if (instrument)
  {
    if (track_io_timing)
    {
      startreadtime = pgStatBlockReadTime;
      startwritetime = pgStatBlockWriteTime;
    }

    pg_rusage_init(&ru0);
  }

  /* Used for instrumentation and stats report */
  starttime = GetCurrentTimestamp();

  /*
   * Determine which columns to analyze.
   */
  if (va_cols != NIL)
  {
    ListCell   *le;

    vacattrstats = palloc_array(VacAttrStats *, list_length(va_cols));
    tcnt = 0;
    foreach(le, va_cols)
    {
      char     *col = strVal(lfirst(le));

      i = attnameAttNum(onerel, col, false);
      Assert(i != InvalidAttrNumber);
      vacattrstats[tcnt] = examine_attribute(onerel, i, NULL);
      if (vacattrstats[tcnt] != NULL)
        tcnt++;
    }
    attr_cnt = tcnt;
  }
  else
  {
    attr_cnt = onerel->rd_att->natts;
    vacattrstats = palloc_array(VacAttrStats *, attr_cnt);
    tcnt = 0;
    for (i = 1; i <= attr_cnt; i++)
    {
      vacattrstats[tcnt] = examine_attribute(onerel, i, NULL);
      if (vacattrstats[tcnt] != NULL)
        tcnt++;
    }
    attr_cnt = tcnt;
  }

  /*
   * Open all indexes of the relation, and see if there are any analyzable
   * columns in the indexes.  We do not analyze index columns if there was
   * an explicit column list in the ANALYZE command, however.
   *
   * If we are doing a recursive scan, we don't want to touch the parent's
   * indexes at all.  If we're processing a partitioned table, we need to
   * know if there are any indexes, but we don't want to process them.
   */
  if (onerel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
  {
    List     *idxs = RelationGetIndexList(onerel);

    Irel = NULL;
    nindexes = 0;
    hasindex = idxs != NIL;
    list_free(idxs);
  }
  else if (!inh)
  {
    vac_open_indexes(onerel, AccessShareLock, &nindexes, &Irel);
    hasindex = nindexes > 0;
  }
  else
  {
    Irel = NULL;
    nindexes = 0;
    hasindex = false;
  }
  indexdata = NULL;
  if (nindexes > 0)
  {
    indexdata = palloc0_array(AnlIndexData, nindexes);
    for (ind = 0; ind < nindexes; ind++)
    {
      AnlIndexData *thisdata = &indexdata[ind];
      IndexInfo  *indexInfo;

      thisdata->indexInfo = indexInfo = BuildIndexInfo(Irel[ind]);
      thisdata->tupleFract = 1.0; /* fix later if partial */
      if (indexInfo->ii_Expressions != NIL && va_cols == NIL)
      {
        ListCell   *indexpr_item = list_head(indexInfo->ii_Expressions);

        thisdata->vacattrstats = palloc_array(VacAttrStats *,
                            indexInfo->ii_NumIndexAttrs);
        tcnt = 0;
        for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
        {
          int     keycol = indexInfo->ii_IndexAttrNumbers[i];

          if (keycol == 0)
          {
            /* Found an index expression */
            Node     *indexkey;

            if (indexpr_item == NULL) /* shouldn't happen */
              elog(ERROR, "too few entries in indexprs list");
            indexkey = (Node *) lfirst(indexpr_item);
            indexpr_item = lnext(indexInfo->ii_Expressions,
                       indexpr_item);
            thisdata->vacattrstats[tcnt] =
              examine_attribute(Irel[ind], i + 1, indexkey);
            if (thisdata->vacattrstats[tcnt] != NULL)
              tcnt++;
          }
        }
        thisdata->attr_cnt = tcnt;
      }
    }
  }

  /*
   * Determine how many rows we need to sample, using the worst case from
   * all analyzable columns.  We use a lower bound of 100 rows to avoid
   * possible overflow in Vitter's algorithm.  (Note: that will also be the
   * target in the corner case where there are no analyzable columns.)
   */
  targrows = 100;
  for (i = 0; i < attr_cnt; i++)
  {
    if (targrows < vacattrstats[i]->minrows)
      targrows = vacattrstats[i]->minrows;
  }
  for (ind = 0; ind < nindexes; ind++)
  {
    AnlIndexData *thisdata = &indexdata[ind];

    for (i = 0; i < thisdata->attr_cnt; i++)
    {
      if (targrows < thisdata->vacattrstats[i]->minrows)
        targrows = thisdata->vacattrstats[i]->minrows;
    }
  }

  /*
   * Look at extended statistics objects too, as those may define custom
   * statistics target. So we may need to sample more rows and then build
   * the statistics with enough detail.
   */
  minrows = ComputeExtStatisticsRows(onerel, attr_cnt, vacattrstats);

  if (targrows < minrows)
    targrows = minrows;

  /*
   * Acquire the sample rows
   */
  rows = palloc_array(HeapTuple, targrows);
  pgstat_progress_update_param(PROGRESS_ANALYZE_PHASE,
                 inh ? PROGRESS_ANALYZE_PHASE_ACQUIRE_SAMPLE_ROWS_INH :
                 PROGRESS_ANALYZE_PHASE_ACQUIRE_SAMPLE_ROWS);
  if (inh)
    numrows = acquire_inherited_sample_rows(onerel, elevel,
                        rows, targrows,
                        &totalrows, &totaldeadrows);
  else
    numrows = (*acquirefunc) (onerel, elevel,
                  rows, targrows,
                  &totalrows, &totaldeadrows);

  /*
   * Compute the statistics.  Temporary results during the calculations for
   * each column are stored in a child context.  The calc routines are
   * responsible to make sure that whatever they store into the VacAttrStats
   * structure is allocated in anl_context.
   */
  if (numrows > 0)
  {
    MemoryContext col_context,
          old_context;

    pgstat_progress_update_param(PROGRESS_ANALYZE_PHASE,
                   PROGRESS_ANALYZE_PHASE_COMPUTE_STATS);

    col_context = AllocSetContextCreate(anl_context,
                      "Analyze Column",
                      ALLOCSET_DEFAULT_SIZES);
    old_context = MemoryContextSwitchTo(col_context);

    for (i = 0; i < attr_cnt; i++)
    {
      VacAttrStats *stats = vacattrstats[i];
      AttributeOpts *aopt;

      stats->rows = rows;
      stats->tupDesc = onerel->rd_att;
      stats->compute_stats(stats,
                 std_fetch_func,
                 numrows,
                 totalrows);

      /*
       * If the appropriate flavor of the n_distinct option is
       * specified, override with the corresponding value.
       */
      aopt = get_attribute_options(onerel->rd_id, stats->tupattnum);
      if (aopt != NULL)
      {
        float8    n_distinct;

        n_distinct = inh ? aopt->n_distinct_inherited : aopt->n_distinct;
        if (n_distinct != 0.0)
          stats->stadistinct = n_distinct;
      }

      MemoryContextReset(col_context);
    }

    if (nindexes > 0)
      compute_index_stats(onerel, totalrows,
                indexdata, nindexes,
                rows, numrows,
                col_context);

    MemoryContextSwitchTo(old_context);
    MemoryContextDelete(col_context);

    /*
     * Emit the completed stats rows into pg_statistic, replacing any
     * previous statistics for the target columns.  (If there are stats in
     * pg_statistic for columns we didn't process, we leave them alone.)
     */
    update_attstats(RelationGetRelid(onerel), inh,
            attr_cnt, vacattrstats);

    for (ind = 0; ind < nindexes; ind++)
    {
      AnlIndexData *thisdata = &indexdata[ind];

      update_attstats(RelationGetRelid(Irel[ind]), false,
              thisdata->attr_cnt, thisdata->vacattrstats);
    }

    /* Build extended statistics (if there are any). */
    BuildRelationExtStatistics(onerel, inh, totalrows, numrows, rows,
                   attr_cnt, vacattrstats);
  }

  pgstat_progress_update_param(PROGRESS_ANALYZE_PHASE,
                 PROGRESS_ANALYZE_PHASE_FINALIZE_ANALYZE);

  /*
   * Update pages/tuples stats in pg_class ... but not if we're doing
   * inherited stats.
   *
   * We assume that VACUUM hasn't set pg_class.reltuples already, even
   * during a VACUUM ANALYZE.  Although VACUUM often updates pg_class,
   * exceptions exist.  A "VACUUM (ANALYZE, INDEX_CLEANUP OFF)" command will
   * never update pg_class entries for index relations.  It's also possible
   * that an individual index's pg_class entry won't be updated during
   * VACUUM if the index AM returns NULL from its amvacuumcleanup() routine.
   */
  if (!inh)
  {
    BlockNumber relallvisible = 0;
    BlockNumber relallfrozen = 0;

    if (RELKIND_HAS_STORAGE(onerel->rd_rel->relkind))
      visibilitymap_count(onerel, &relallvisible, &relallfrozen);

    /*
     * Update pg_class for table relation.  CCI first, in case acquirefunc
     * updated pg_class.
     */
    CommandCounterIncrement();
    vac_update_relstats(onerel,
              relpages,
              totalrows,
              relallvisible,
              relallfrozen,
              hasindex,
              InvalidTransactionId,
              InvalidMultiXactId,
              NULL, NULL,
              in_outer_xact);

    /* Same for indexes */
    for (ind = 0; ind < nindexes; ind++)
    {
      AnlIndexData *thisdata = &indexdata[ind];
      double    totalindexrows;

      totalindexrows = ceil(thisdata->tupleFract * totalrows);
      vac_update_relstats(Irel[ind],
                RelationGetNumberOfBlocks(Irel[ind]),
                totalindexrows,
                0, 0,
                false,
                InvalidTransactionId,
                InvalidMultiXactId,
                NULL, NULL,
                in_outer_xact);
    }
  }
  else if (onerel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
  {
    /*
     * Partitioned tables don't have storage, so we don't set any fields
     * in their pg_class entries except for reltuples and relhasindex.
     */
    CommandCounterIncrement();
    vac_update_relstats(onerel, -1, totalrows,
              0, 0, hasindex, InvalidTransactionId,
              InvalidMultiXactId,
              NULL, NULL,
              in_outer_xact);
  }

  /*
   * Now report ANALYZE to the cumulative stats system.  For regular tables,
   * we do it only if not doing inherited stats.  For partitioned tables, we
   * only do it for inherited stats. (We're never called for not-inherited
   * stats on partitioned tables anyway.)
   *
   * Reset the mod_since_analyze counter only if we analyzed all columns;
   * otherwise, there is still work for auto-analyze to do.
   */
  if (!inh)
    pgstat_report_analyze(onerel, totalrows, totaldeadrows,
                (va_cols == NIL), starttime);
  else if (onerel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
    pgstat_report_analyze(onerel, 0, 0, (va_cols == NIL), starttime);

  /*
   * If this isn't part of VACUUM ANALYZE, let index AMs do cleanup.
   *
   * Note that most index AMs perform a no-op as a matter of policy for
   * amvacuumcleanup() when called in ANALYZE-only mode.  The only exception
   * among core index AMs is GIN/ginvacuumcleanup().
   */
  if (!(params->options & VACOPT_VACUUM))
  {
    for (ind = 0; ind < nindexes; ind++)
    {
      IndexBulkDeleteResult *stats;
      IndexVacuumInfo ivinfo;

      ivinfo.index = Irel[ind];
      ivinfo.heaprel = onerel;
      ivinfo.analyze_only = true;
      ivinfo.is_autovacuum = AmAutoVacuumWorkerProcess();
      ivinfo.estimated_count = true;
      ivinfo.message_level = elevel;
      ivinfo.num_heap_tuples = onerel->rd_rel->reltuples;
      ivinfo.strategy = vac_strategy;

      stats = index_vacuum_cleanup(&ivinfo, NULL);

      if (stats)
        pfree(stats);
    }
  }

  /* Done with indexes */
  vac_close_indexes(nindexes, Irel, NoLock);

  /* Log the action if appropriate */
  if (instrument)
  {
    TimestampTz endtime = GetCurrentTimestamp();

    if (verbose || params->log_analyze_min_duration == 0 ||
      TimestampDifferenceExceeds(starttime, endtime,
                     params->log_analyze_min_duration))
    {
      long    delay_in_ms;
      WalUsage  walusage;
      double    read_rate = 0;
      double    write_rate = 0;
      char     *msgfmt;
      StringInfoData buf;
      int64   total_blks_hit;
      int64   total_blks_read;
      int64   total_blks_dirtied;

      memset(&bufferusage, 0, sizeof(BufferUsage));
      BufferUsageAccumDiff(&bufferusage, &pgBufferUsage, &startbufferusage);
      memset(&walusage, 0, sizeof(WalUsage));
      WalUsageAccumDiff(&walusage, &pgWalUsage, &startwalusage);

      total_blks_hit = bufferusage.shared_blks_hit +
        bufferusage.local_blks_hit;
      total_blks_read = bufferusage.shared_blks_read +
        bufferusage.local_blks_read;
      total_blks_dirtied = bufferusage.shared_blks_dirtied +
        bufferusage.local_blks_dirtied;

      /*
       * We do not expect an analyze to take > 25 days and it simplifies
       * things a bit to use TimestampDifferenceMilliseconds.
       */
      delay_in_ms = TimestampDifferenceMilliseconds(starttime, endtime);

      /*
       * Note that we are reporting these read/write rates in the same
       * manner as VACUUM does, which means that while the 'average read
       * rate' here actually corresponds to page misses and resulting
       * reads which are also picked up by track_io_timing, if enabled,
       * the 'average write rate' is actually talking about the rate of
       * pages being dirtied, not being written out, so it's typical to
       * have a non-zero 'avg write rate' while I/O timings only reports
       * reads.
       *
       * It's not clear that an ANALYZE will ever result in
       * FlushBuffer() being called, but we track and support reporting
       * on I/O write time in case that changes as it's practically free
       * to do so anyway.
       */

      if (delay_in_ms > 0)
      {
        read_rate = (double) BLCKSZ * total_blks_read /
          (1024 * 1024) / (delay_in_ms / 1000.0);
        write_rate = (double) BLCKSZ * total_blks_dirtied /
          (1024 * 1024) / (delay_in_ms / 1000.0);
      }

      /*
       * We split this up so we don't emit empty I/O timing values when
       * track_io_timing isn't enabled.
       */

      initStringInfo(&buf);

      if (AmAutoVacuumWorkerProcess())
        msgfmt = _("automatic analyze of table \"%s.%s.%s\"\n");
      else
        msgfmt = _("finished analyzing table \"%s.%s.%s\"\n");

      appendStringInfo(&buf, msgfmt,
               get_database_name(MyDatabaseId),
               get_namespace_name(RelationGetNamespace(onerel)),
               RelationGetRelationName(onerel));
      if (track_cost_delay_timing)
      {
        /*
         * We bypass the changecount mechanism because this value is
         * only updated by the calling process.
         */
        appendStringInfo(&buf, _("delay time: %.3f ms\n"),
                 (double) MyBEEntry->st_progress_param[PROGRESS_ANALYZE_DELAY_TIME] / 1000000.0);
      }
      if (track_io_timing)
      {
        double    read_ms = (double) (pgStatBlockReadTime - startreadtime) / 1000;
        double    write_ms = (double) (pgStatBlockWriteTime - startwritetime) / 1000;

        appendStringInfo(&buf, _("I/O timings: read: %.3f ms, write: %.3f ms\n"),
                 read_ms, write_ms);
      }
      appendStringInfo(&buf, _("avg read rate: %.3f MB/s, avg write rate: %.3f MB/s\n"),
               read_rate, write_rate);
      appendStringInfo(&buf, _("buffer usage: %" PRId64 " hits, %" PRId64 " reads, %" PRId64 " dirtied\n"),
               total_blks_hit,
               total_blks_read,
               total_blks_dirtied);
      appendStringInfo(&buf,
               _("WAL usage: %" PRId64 " records, %" PRId64 " full page images, %" PRIu64 " bytes, %" PRIu64 " full page image bytes, %" PRId64 " buffers full\n"),
               walusage.wal_records,
               walusage.wal_fpi,
               walusage.wal_bytes,
               walusage.wal_fpi_bytes,
               walusage.wal_buffers_full);
      appendStringInfo(&buf, _("system usage: %s"), pg_rusage_show(&ru0));

      ereport(verbose ? INFO : LOG,
          (errmsg_internal("%s", buf.data)));

      pfree(buf.data);
    }
  }

  /* Roll back any GUC changes executed by index functions */
  AtEOXact_GUC(false, save_nestlevel);

  /* Restore userid and security context */
  SetUserIdAndSecContext(save_userid, save_sec_context);

  /* Restore current context and release memory */
  MemoryContextSwitchTo(caller_context);
  MemoryContextDelete(anl_context);
  anl_context = NULL;
}

/*
 * Compute statistics about indexes of a relation
 */
static void
compute_index_stats(Relation onerel, double totalrows,
          AnlIndexData *indexdata, int nindexes,
          HeapTuple *rows, int numrows,
          MemoryContext col_context)
{
  MemoryContext ind_context,
        old_context;
  Datum   values[INDEX_MAX_KEYS];
  bool    isnull[INDEX_MAX_KEYS];
  int     ind,
        i;

  ind_context = AllocSetContextCreate(anl_context,
                    "Analyze Index",
                    ALLOCSET_DEFAULT_SIZES);
  old_context = MemoryContextSwitchTo(ind_context);

  for (ind = 0; ind < nindexes; ind++)
  {
    AnlIndexData *thisdata = &indexdata[ind];
    IndexInfo  *indexInfo = thisdata->indexInfo;
    int     attr_cnt = thisdata->attr_cnt;
    TupleTableSlot *slot;
    EState     *estate;
    ExprContext *econtext;
    ExprState  *predicate;
    Datum    *exprvals;
    bool     *exprnulls;
    int     numindexrows,
          tcnt,
          rowno;
    double    totalindexrows;

    /* Ignore index if no columns to analyze and not partial */
    if (attr_cnt == 0 && indexInfo->ii_Predicate == NIL)
      continue;

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

    /* Set up execution state for predicate. */
    predicate = ExecPrepareQual(indexInfo->ii_Predicate, estate);

    /* Compute and save index expression values */
    exprvals = palloc_array(Datum, numrows * attr_cnt);
    exprnulls = palloc_array(bool, numrows * attr_cnt);
    numindexrows = 0;
    tcnt = 0;
    for (rowno = 0; rowno < numrows; rowno++)
    {
      HeapTuple heapTuple = rows[rowno];

      vacuum_delay_point(true);

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

      /* Set up for predicate or expression evaluation */
      ExecStoreHeapTuple(heapTuple, slot, false);

      /* If index is partial, check predicate */
      if (predicate != NULL)
      {
        if (!ExecQual(predicate, econtext))
          continue;
      }
      numindexrows++;

      if (attr_cnt > 0)
      {
        /*
         * Evaluate the index row to compute expression values. We
         * could do this by hand, but FormIndexDatum is convenient.
         */
        FormIndexDatum(indexInfo,
                 slot,
                 estate,
                 values,
                 isnull);

        /*
         * Save just the columns we care about.  We copy the values
         * into ind_context from the estate's per-tuple context.
         */
        for (i = 0; i < attr_cnt; i++)
        {
          VacAttrStats *stats = thisdata->vacattrstats[i];
          int     attnum = stats->tupattnum;

          if (isnull[attnum - 1])
          {
            exprvals[tcnt] = (Datum) 0;
            exprnulls[tcnt] = true;
          }
          else
          {
            exprvals[tcnt] = datumCopy(values[attnum - 1],
                           stats->attrtype->typbyval,
                           stats->attrtype->typlen);
            exprnulls[tcnt] = false;
          }
          tcnt++;
        }
      }
    }

    /*
     * Having counted the number of rows that pass the predicate in the
     * sample, we can estimate the total number of rows in the index.
     */
    thisdata->tupleFract = (double) numindexrows / (double) numrows;
    totalindexrows = ceil(thisdata->tupleFract * totalrows);

    /*
     * Now we can compute the statistics for the expression columns.
     */
    if (numindexrows > 0)
    {
      MemoryContextSwitchTo(col_context);
      for (i = 0; i < attr_cnt; i++)
      {
        VacAttrStats *stats = thisdata->vacattrstats[i];

        stats->exprvals = exprvals + i;
        stats->exprnulls = exprnulls + i;
        stats->rowstride = attr_cnt;
        stats->compute_stats(stats,
                   ind_fetch_func,
                   numindexrows,
                   totalindexrows);

        MemoryContextReset(col_context);
      }
    }

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

    ExecDropSingleTupleTableSlot(slot);
    FreeExecutorState(estate);
    MemoryContextReset(ind_context);
  }

  MemoryContextSwitchTo(old_context);
  MemoryContextDelete(ind_context);
}

/*
 * validate_va_cols_list -- validate the columns list given to analyze_rel
 *
 * Note that system attributes are never analyzed, so we just reject them at
 * the lookup stage.  We also reject duplicate column mentions.  (We could
 * alternatively ignore duplicates, but analyzing a column twice won't work;
 * we'd end up making a conflicting update in pg_statistic.)
 */
static void
validate_va_cols_list(Relation onerel, List *va_cols)
{
  Bitmapset  *unique_cols = NULL;
  ListCell   *le;

  Assert(va_cols != NIL);
  foreach(le, va_cols)
  {
    char     *col = strVal(lfirst(le));
    int     i = attnameAttNum(onerel, col, false);

    if (i == InvalidAttrNumber)
      ereport(ERROR,
          (errcode(ERRCODE_UNDEFINED_COLUMN),
           errmsg("column \"%s\" of relation \"%s\" does not exist",
              col, RelationGetRelationName(onerel))));
    if (bms_is_member(i, unique_cols))
      ereport(ERROR,
          (errcode(ERRCODE_DUPLICATE_COLUMN),
           errmsg("column \"%s\" of relation \"%s\" appears more than once",
              col, RelationGetRelationName(onerel))));
    unique_cols = bms_add_member(unique_cols, i);
  }
}

/*
 * 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.
 *
 * If index_expr isn't NULL, then we're trying to analyze an expression index,
 * and index_expr is the expression tree representing the column's data.
 */
static VacAttrStats *
examine_attribute(Relation onerel, int attnum, Node *index_expr)
{
  Form_pg_attribute attr = TupleDescAttr(onerel->rd_att, attnum - 1);
  int     attstattarget;
  HeapTuple typtuple;
  VacAttrStats *stats;
  int     i;
  bool    ok;

  /*
   * Check if the column is analyzable.
   */
  if (!attribute_is_analyzable(onerel, attnum, attr, &attstattarget))
    return NULL;

  /*
   * Create the VacAttrStats struct.
   */
  stats = palloc0_object(VacAttrStats);
  stats->attstattarget = attstattarget;

  /*
   * When analyzing an expression index, 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 index 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.
   */
  if (index_expr)
  {
    stats->attrtypid = exprType(index_expr);
    stats->attrtypmod = exprTypmod(index_expr);

    /*
     * If a collation has been specified for the index column, use that in
     * preference to anything else; but if not, fall back to whatever we
     * can get from the expression.
     */
    if (OidIsValid(onerel->rd_indcollation[attnum - 1]))
      stats->attrcollid = onerel->rd_indcollation[attnum - 1];
    else
      stats->attrcollid = exprCollation(index_expr);
  }
  else
  {
    stats->attrtypid = attr->atttypid;
    stats->attrtypmod = attr->atttypmod;
    stats->attrcollid = attr->attcollation;
  }

  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 = anl_context;
  stats->tupattnum = attnum;

  /*
   * 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;
}

/*
 * Determine whether the column is analyzable.
 *
 * If the column is analyzable, return its attstattarget value, if asked to.
 */
bool
attribute_is_analyzable(Relation onerel, int attnum, Form_pg_attribute attr,
            int *p_attstattarget)
{
  int     attstattarget;
  HeapTuple atttuple;
  Datum   dat;
  bool    isnull;

  /* Never analyze dropped columns */
  if (attr->attisdropped)
    return false;

  /* Don't analyze virtual generated columns */
  if (attr->attgenerated == ATTRIBUTE_GENERATED_VIRTUAL)
    return false;

  /*
   * Get attstattarget value.  Set to -1 if null.  (Analyze functions expect
   * -1 to mean use default_statistics_target; see for example
   * std_typanalyze.)
   */
  atttuple = SearchSysCache2(ATTNUM, ObjectIdGetDatum(RelationGetRelid(onerel)), Int16GetDatum(attnum));
  if (!HeapTupleIsValid(atttuple))
    elog(ERROR, "cache lookup failed for attribute %d of relation %u",
       attnum, RelationGetRelid(onerel));
  dat = SysCacheGetAttr(ATTNUM, atttuple, Anum_pg_attribute_attstattarget, &isnull);
  attstattarget = isnull ? -1 : DatumGetInt16(dat);
  ReleaseSysCache(atttuple);

  /* Don't analyze column if user has specified not to */
  if (attstattarget == 0)
    return false;

  if (p_attstattarget)
    *p_attstattarget = attstattarget;
  return true;
}

/*
 * Read stream callback returning the next BlockNumber as chosen by the
 * BlockSampling algorithm.
 */
static BlockNumber
block_sampling_read_stream_next(ReadStream *stream,
                void *callback_private_data,
                void *per_buffer_data)
{
  BlockSamplerData *bs = callback_private_data;

  return BlockSampler_HasMore(bs) ? BlockSampler_Next(bs) : InvalidBlockNumber;
}

/*
 * acquire_sample_rows -- acquire a random sample of rows from the table
 *
 * Selected rows are returned in the caller-allocated array rows[], which
 * must have at least targrows entries.
 * The actual number of rows selected is returned as the function result.
 * We also estimate the total numbers of live and dead rows in the table,
 * and return them into *totalrows and *totaldeadrows, respectively.
 *
 * The returned list of tuples is in order by physical position in the table.
 * (We will rely on this later to derive correlation estimates.)
 *
 * As of May 2004 we use a new two-stage method:  Stage one selects up
 * to targrows random blocks (or all blocks, if there aren't so many).
 * Stage two scans these blocks and uses the Vitter algorithm to create
 * a random sample of targrows rows (or less, if there are less in the
 * sample of blocks).  The two stages are executed simultaneously: each
 * block is processed as soon as stage one returns its number and while
 * the rows are read stage two controls which ones are to be inserted
 * into the sample.
 *
 * Although every row has an equal chance of ending up in the final
 * sample, this sampling method is not perfect: not every possible
 * sample has an equal chance of being selected.  For large relations
 * the number of different blocks represented by the sample tends to be
 * too small.  We can live with that for now.  Improvements are welcome.
 *
 * An important property of this sampling method is that because we do
 * look at a statistically unbiased set of blocks, we should get
 * unbiased estimates of the average numbers of live and dead rows per
 * block.  The previous sampling method put too much credence in the row
 * density near the start of the table.
 */
static int
acquire_sample_rows(Relation onerel, int elevel,
          HeapTuple *rows, int targrows,
          double *totalrows, double *totaldeadrows)
{
  int     numrows = 0;  /* # rows now in reservoir */
  double    samplerows = 0; /* total # rows collected */
  double    liverows = 0; /* # live rows seen */
  double    deadrows = 0; /* # dead rows seen */
  double    rowstoskip = -1;  /* -1 means not set yet */
  uint32    randseed;   /* Seed for block sampler(s) */
  BlockNumber totalblocks;
  BlockSamplerData bs;
  ReservoirStateData rstate;
  TupleTableSlot *slot;
  TableScanDesc scan;
  BlockNumber nblocks;
  BlockNumber blksdone = 0;
  ReadStream *stream;

  Assert(targrows > 0);

  totalblocks = RelationGetNumberOfBlocks(onerel);

  /* Prepare for sampling block numbers */
  randseed = pg_prng_uint32(&pg_global_prng_state);
  nblocks = BlockSampler_Init(&bs, totalblocks, targrows, randseed);

  /* Report sampling block numbers */
  pgstat_progress_update_param(PROGRESS_ANALYZE_BLOCKS_TOTAL,
                 nblocks);

  /* Prepare for sampling rows */
  reservoir_init_selection_state(&rstate, targrows);

  scan = table_beginscan_analyze(onerel);
  slot = table_slot_create(onerel, NULL);

  /*
   * It is safe to use batching, as block_sampling_read_stream_next never
   * blocks.
   */
  stream = read_stream_begin_relation(READ_STREAM_MAINTENANCE |
                    READ_STREAM_USE_BATCHING,
                    vac_strategy,
                    scan->rs_rd,
                    MAIN_FORKNUM,
                    block_sampling_read_stream_next,
                    &bs,
                    0);

  /* Outer loop over blocks to sample */
  while (table_scan_analyze_next_block(scan, stream))
  {
    while (table_scan_analyze_next_tuple(scan, &liverows, &deadrows, slot))
    {
      /*
       * The first targrows sample rows are simply copied into the
       * reservoir. Then we start replacing tuples in the sample until
       * we reach the end of the relation.  This algorithm is from Jeff
       * Vitter's paper (see full citation in utils/misc/sampling.c). It
       * works by repeatedly computing the number of tuples to skip
       * before selecting a tuple, which replaces a randomly chosen
       * element of the reservoir (current set of tuples).  At all times
       * the reservoir is a true random sample of the tuples we've
       * passed over so far, so when we fall off the end of the relation
       * we're done.
       */
      if (numrows < targrows)
        rows[numrows++] = ExecCopySlotHeapTuple(slot);
      else
      {
        /*
         * t in Vitter's paper is the number of records already
         * processed.  If we need to compute a new S value, we must
         * use the not-yet-incremented value of samplerows as t.
         */
        if (rowstoskip < 0)
          rowstoskip = reservoir_get_next_S(&rstate, samplerows, targrows);

        if (rowstoskip <= 0)
        {
          /*
           * Found a suitable tuple, so save it, replacing one old
           * tuple at random
           */
          int     k = (int) (targrows * sampler_random_fract(&rstate.randstate));

          Assert(k >= 0 && k < targrows);
          heap_freetuple(rows[k]);
          rows[k] = ExecCopySlotHeapTuple(slot);
        }

        rowstoskip -= 1;
      }

      samplerows += 1;
    }

    pgstat_progress_update_param(PROGRESS_ANALYZE_BLOCKS_DONE,
                   ++blksdone);
    vacuum_delay_point(true);
  }

  read_stream_end(stream);

  ExecDropSingleTupleTableSlot(slot);
  table_endscan(scan);

  /*
   * If we didn't find as many tuples as we wanted then we're done. No sort
   * is needed, since they're already in order.
   *
   * Otherwise we need to sort the collected tuples by position
   * (itempointer). It's not worth worrying about corner cases where the
   * tuples are already sorted.
   */
  if (numrows == targrows)
    qsort_interruptible(rows, numrows, sizeof(HeapTuple),
              compare_rows, NULL);

  /*
   * Estimate total numbers of live and dead rows in relation, extrapolating
   * on the assumption that the average tuple density in pages we didn't
   * scan is the same as in the pages we did scan.  Since what we scanned is
   * a random sample of the pages in the relation, this should be a good
   * assumption.
   */
  if (bs.m > 0)
  {
    *totalrows = floor((liverows / bs.m) * totalblocks + 0.5);
    *totaldeadrows = floor((deadrows / bs.m) * totalblocks + 0.5);
  }
  else
  {
    *totalrows = 0.0;
    *totaldeadrows = 0.0;
  }

  /*
   * Emit some interesting relation info
   */
  ereport(elevel,
      (errmsg("\"%s\": scanned %d of %u pages, "
          "containing %.0f live rows and %.0f dead rows; "
          "%d rows in sample, %.0f estimated total rows",
          RelationGetRelationName(onerel),
          bs.m, totalblocks,
          liverows, deadrows,
          numrows, *totalrows)));

  return numrows;
}

/*
 * Comparator for sorting rows[] array
 */
static int
compare_rows(const void *a, const void *b, void *arg)
{
  HeapTuple ha = *(const HeapTuple *) a;
  HeapTuple hb = *(const HeapTuple *) b;
  BlockNumber ba = ItemPointerGetBlockNumber(&ha->t_self);
  OffsetNumber oa = ItemPointerGetOffsetNumber(&ha->t_self);
  BlockNumber bb = ItemPointerGetBlockNumber(&hb->t_self);
  OffsetNumber ob = ItemPointerGetOffsetNumber(&hb->t_self);

  if (ba < bb)
    return -1;
  if (ba > bb)
    return 1;
  if (oa < ob)
    return -1;
  if (oa > ob)
    return 1;
  return 0;
}


/*
 * acquire_inherited_sample_rows -- acquire sample rows from inheritance tree
 *
 * This has the same API as acquire_sample_rows, except that rows are
 * collected from all inheritance children as well as the specified table.
 * We fail and return zero if there are no inheritance children, or if all
 * children are foreign tables that don't support ANALYZE.
 */
static int
acquire_inherited_sample_rows(Relation onerel, int elevel,
                HeapTuple *rows, int targrows,
                double *totalrows, double *totaldeadrows)
{
  List     *tableOIDs;
  Relation   *rels;
  AcquireSampleRowsFunc *acquirefuncs;
  double     *relblocks;
  double    totalblocks;
  int     numrows,
        nrels,
        i;
  ListCell   *lc;
  bool    has_child;

  /* Initialize output parameters to zero now, in case we exit early */
  *totalrows = 0;
  *totaldeadrows = 0;

  /*
   * Find all members of inheritance set.  We only need AccessShareLock on
   * the children.
   */
  tableOIDs =
    find_all_inheritors(RelationGetRelid(onerel), AccessShareLock, NULL);

  /*
   * Check that there's at least one descendant, else fail.  This could
   * happen despite analyze_rel's relhassubclass check, if table once had a
   * child but no longer does.  In that case, we can clear the
   * relhassubclass field so as not to make the same mistake again later.
   * (This is safe because we hold ShareUpdateExclusiveLock.)
   */
  if (list_length(tableOIDs) < 2)
  {
    /* CCI because we already updated the pg_class row in this command */
    CommandCounterIncrement();
    SetRelationHasSubclass(RelationGetRelid(onerel), false);
    ereport(elevel,
        (errmsg("skipping analyze of \"%s.%s\" inheritance tree --- this inheritance tree contains no child tables",
            get_namespace_name(RelationGetNamespace(onerel)),
            RelationGetRelationName(onerel))));
    return 0;
  }

  /*
   * Identify acquirefuncs to use, and count blocks in all the relations.
   * The result could overflow BlockNumber, so we use double arithmetic.
   */
  rels = palloc_array(Relation, list_length(tableOIDs));
  acquirefuncs = palloc_array(AcquireSampleRowsFunc, list_length(tableOIDs));
  relblocks = palloc_array(double, list_length(tableOIDs));
  totalblocks = 0;
  nrels = 0;
  has_child = false;
  foreach(lc, tableOIDs)
  {
    Oid     childOID = lfirst_oid(lc);
    Relation  childrel;
    AcquireSampleRowsFunc acquirefunc = NULL;
    BlockNumber relpages = 0;

    /* We already got the needed lock */
    childrel = table_open(childOID, NoLock);

    /* Ignore if temp table of another backend */
    if (RELATION_IS_OTHER_TEMP(childrel))
    {
      /* ... but release the lock on it */
      Assert(childrel != onerel);
      table_close(childrel, AccessShareLock);
      continue;
    }

    /* Check table type (MATVIEW can't happen, but might as well allow) */
    if (childrel->rd_rel->relkind == RELKIND_RELATION ||
      childrel->rd_rel->relkind == RELKIND_MATVIEW)
    {
      /* Regular table, so use the regular row acquisition function */
      acquirefunc = acquire_sample_rows;
      relpages = RelationGetNumberOfBlocks(childrel);
    }
    else if (childrel->rd_rel->relkind == RELKIND_FOREIGN_TABLE)
    {
      /*
       * For a foreign table, call the FDW's hook function to see
       * whether it supports analysis.
       */
      FdwRoutine *fdwroutine;
      bool    ok = false;

      fdwroutine = GetFdwRoutineForRelation(childrel, false);

      if (fdwroutine->AnalyzeForeignTable != NULL)
        ok = fdwroutine->AnalyzeForeignTable(childrel,
                           &acquirefunc,
                           &relpages);

      if (!ok)
      {
        /* ignore, but release the lock on it */
        Assert(childrel != onerel);
        table_close(childrel, AccessShareLock);
        continue;
      }
    }
    else
    {
      /*
       * ignore, but release the lock on it.  don't try to unlock the
       * passed-in relation
       */
      Assert(childrel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE);
      if (childrel != onerel)
        table_close(childrel, AccessShareLock);
      else
        table_close(childrel, NoLock);
      continue;
    }

    /* OK, we'll process this child */
    has_child = true;
    rels[nrels] = childrel;
    acquirefuncs[nrels] = acquirefunc;
    relblocks[nrels] = (double) relpages;
    totalblocks += (double) relpages;
    nrels++;
  }

  /*
   * If we don't have at least one child table to consider, fail.  If the
   * relation is a partitioned table, it's not counted as a child table.
   */
  if (!has_child)
  {
    ereport(elevel,
        (errmsg("skipping analyze of \"%s.%s\" inheritance tree --- this inheritance tree contains no analyzable child tables",
            get_namespace_name(RelationGetNamespace(onerel)),
            RelationGetRelationName(onerel))));
    return 0;
  }

  /*
   * Now sample rows from each relation, proportionally to its fraction of
   * the total block count.  (This might be less than desirable if the child
   * rels have radically different free-space percentages, but it's not
   * clear that it's worth working harder.)
   */
  pgstat_progress_update_param(PROGRESS_ANALYZE_CHILD_TABLES_TOTAL,
                 nrels);
  numrows = 0;
  for (i = 0; i < nrels; i++)
  {
    Relation  childrel = rels[i];
    AcquireSampleRowsFunc acquirefunc = acquirefuncs[i];
    double    childblocks = relblocks[i];

    /*
     * Report progress.  The sampling function will normally report blocks
     * done/total, but we need to reset them to 0 here, so that they don't
     * show an old value until that.
     */
    {
      const int progress_index[] = {
        PROGRESS_ANALYZE_CURRENT_CHILD_TABLE_RELID,
        PROGRESS_ANALYZE_BLOCKS_DONE,
        PROGRESS_ANALYZE_BLOCKS_TOTAL
      };
      const int64 progress_vals[] = {
        RelationGetRelid(childrel),
        0,
        0,
      };

      pgstat_progress_update_multi_param(3, progress_index, progress_vals);
    }

    if (childblocks > 0)
    {
      int     childtargrows;

      childtargrows = (int) rint(targrows * childblocks / totalblocks);
      /* Make sure we don't overrun due to roundoff error */
      childtargrows = Min(childtargrows, targrows - numrows);
      if (childtargrows > 0)
      {
        int     childrows;
        double    trows,
              tdrows;

        /* Fetch a random sample of the child's rows */
        childrows = (*acquirefunc) (childrel, elevel,
                      rows + numrows, childtargrows,
                      &trows, &tdrows);

        /* We may need to convert from child's rowtype to parent's */
        if (childrows > 0 &&
          !equalRowTypes(RelationGetDescr(childrel),
                   RelationGetDescr(onerel)))
        {
          TupleConversionMap *map;

          map = convert_tuples_by_name(RelationGetDescr(childrel),
                         RelationGetDescr(onerel));
          if (map != NULL)
          {
            int     j;

            for (j = 0; j < childrows; j++)
            {
              HeapTuple newtup;

              newtup = execute_attr_map_tuple(rows[numrows + j], map);
              heap_freetuple(rows[numrows + j]);
              rows[numrows + j] = newtup;
            }
            free_conversion_map(map);
          }
        }

        /* And add to counts */
        numrows += childrows;
        *totalrows += trows;
        *totaldeadrows += tdrows;
      }
    }

    /*
     * Note: we cannot release the child-table locks, since we may have
     * pointers to their TOAST tables in the sampled rows.
     */
    table_close(childrel, NoLock);
    pgstat_progress_update_param(PROGRESS_ANALYZE_CHILD_TABLES_DONE,
                   i + 1);
  }

  return numrows;
}


/*
 *  update_attstats() -- update attribute statistics for one relation
 *
 *    Statistics are stored in several places: the pg_class row for the
 *    relation has stats about the whole relation, and there is a
 *    pg_statistic row for each (non-system) attribute that has ever
 *    been analyzed.  The pg_class values are updated by VACUUM, not here.
 *
 *    pg_statistic rows are just added or updated normally.  This means
 *    that pg_statistic will probably contain some deleted rows at the
 *    completion of a vacuum cycle, unless it happens to get vacuumed last.
 *
 *    To keep things simple, we punt for pg_statistic, and don't try
 *    to compute or store rows for pg_statistic itself in pg_statistic.
 *    This could possibly be made to work, but it's not worth the trouble.
 *    Note analyze_rel() has seen to it that we won't come here when
 *    vacuuming pg_statistic itself.
 *
 *    Note: there would be a race condition here if two backends could
 *    ANALYZE the same table concurrently.  Presently, we lock that out
 *    by taking a self-exclusive lock on the relation in analyze_rel().
 */
static void
update_attstats(Oid relid, bool inh, int natts, VacAttrStats **vacattrstats)
{
  Relation  sd;
  int     attno;
  CatalogIndexState indstate = NULL;

  if (natts <= 0)
    return;         /* nothing to do */

  sd = table_open(StatisticRelationId, RowExclusiveLock);

  for (attno = 0; attno < natts; attno++)
  {
    VacAttrStats *stats = vacattrstats[attno];
    HeapTuple stup,
          oldtup;
    int     i,
          k,
          n;
    Datum   values[Natts_pg_statistic];
    bool    nulls[Natts_pg_statistic];
    bool    replaces[Natts_pg_statistic];

    /* Ignore attr if we weren't able to collect stats */
    if (!stats->stats_valid)
      continue;

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

    values[Anum_pg_statistic_starelid - 1] = ObjectIdGetDatum(relid);
    values[Anum_pg_statistic_staattnum - 1] = Int16GetDatum(stats->tupattnum);
    values[Anum_pg_statistic_stainherit - 1] = BoolGetDatum(inh);
    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++)
    {
      if (stats->stanumbers[k] != NULL)
      {
        int     nnum = stats->numnumbers[k];
        Datum    *numdatums = palloc_array(Datum, nnum);
        ArrayType  *arry;

        for (n = 0; n < nnum; n++)
          numdatums[n] = Float4GetDatum(stats->stanumbers[k][n]);
        arry = construct_array_builtin(numdatums, nnum, FLOAT4OID);
        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->stavalues[k] != NULL)
      {
        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;
      }
    }

    /* Is there already a pg_statistic tuple for this attribute? */
    oldtup = SearchSysCache3(STATRELATTINH,
                 ObjectIdGetDatum(relid),
                 Int16GetDatum(stats->tupattnum),
                 BoolGetDatum(inh));

    /* Open index information when we know we need it */
    if (indstate == NULL)
      indstate = CatalogOpenIndexes(sd);

    if (HeapTupleIsValid(oldtup))
    {
      /* Yes, replace it */
      stup = heap_modify_tuple(oldtup,
                   RelationGetDescr(sd),
                   values,
                   nulls,
                   replaces);
      ReleaseSysCache(oldtup);
      CatalogTupleUpdateWithInfo(sd, &stup->t_self, stup, indstate);
    }
    else
    {
      /* No, insert new tuple */
      stup = heap_form_tuple(RelationGetDescr(sd), values, nulls);
      CatalogTupleInsertWithInfo(sd, stup, indstate);
    }

    heap_freetuple(stup);
  }

  if (indstate != NULL)
    CatalogCloseIndexes(indstate);
  table_close(sd, RowExclusiveLock);
}

/*
 * Standard fetch function for use by compute_stats subroutines.
 *
 * This exists to provide some insulation between compute_stats routines
 * and the actual storage of the sample data.
 */
static Datum
std_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull)
{
  int     attnum = stats->tupattnum;
  HeapTuple tuple = stats->rows[rownum];
  TupleDesc tupDesc = stats->tupDesc;

  return heap_getattr(tuple, attnum, tupDesc, isNull);
}

/*
 * Fetch function for analyzing index expressions.
 *
 * We have not bothered to construct index tuples, instead the data is
 * just in Datum arrays.
 */
static Datum
ind_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];
}


/*
 * ==========================================================================
 *
 * Code below this point represents the "standard" type-specific statistics
 * analysis algorithms.  This code can be replaced on a per-data-type basis
 * by setting a nonzero value in pg_type.typanalyze.
 *
 *==========================================================================
 */


/*
 * 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

#define swapInt(a,b)  do {int _tmp; _tmp=a; a=b; b=_tmp;} while(0)
#define swapDatum(a,b)  do {Datum _tmp; _tmp=a; a=b; b=_tmp;} while(0)

/*
 * Extra information used by the default analysis routines
 */
typedef struct
{
  int     count;      /* # of duplicates */
  int     first;      /* values[] index of first occurrence */
} ScalarMCVItem;

typedef struct
{
  SortSupport ssup;
  int      *tupnoLink;
} CompareScalarsContext;


static void compute_trivial_stats(VacAttrStatsP stats,
                  AnalyzeAttrFetchFunc fetchfunc,
                  int samplerows,
                  double totalrows);
static void compute_distinct_stats(VacAttrStatsP stats,
                   AnalyzeAttrFetchFunc fetchfunc,
                   int samplerows,
                   double totalrows);
static void compute_scalar_stats(VacAttrStatsP stats,
                 AnalyzeAttrFetchFunc fetchfunc,
                 int samplerows,
                 double totalrows);
static int  compare_scalars(const void *a, const void *b, void *arg);
static int  compare_mcvs(const void *a, const void *b, void *arg);
static int  analyze_mcv_list(int *mcv_counts,
               int num_mcv,
               double stadistinct,
               double stanullfrac,
               int samplerows,
               double totalrows);


/*
 * std_typanalyze -- the default type-specific typanalyze function
 */
bool
std_typanalyze(VacAttrStats *stats)
{
  Oid     ltopr;
  Oid     eqopr;
  StdAnalyzeData *mystats;

  /* If the attstattarget column is negative, use the default value */
  if (stats->attstattarget < 0)
    stats->attstattarget = default_statistics_target;

  /* Look for default "<" and "=" operators for column's type */
  get_sort_group_operators(stats->attrtypid,
               false, false, false,
               &ltopr, &eqopr, NULL,
               NULL);

  /* Save the operator info for compute_stats routines */
  mystats = palloc_object(StdAnalyzeData);
  mystats->eqopr = eqopr;
  mystats->eqfunc = OidIsValid(eqopr) ? get_opcode(eqopr) : InvalidOid;
  mystats->ltopr = ltopr;
  stats->extra_data = mystats;

  /*
   * Determine which standard statistics algorithm to use
   */
  if (OidIsValid(eqopr) && OidIsValid(ltopr))
  {
    /* Seems to be a scalar datatype */
    stats->compute_stats = compute_scalar_stats;
    /*--------------------
     * The following choice of minrows is based on the paper
     * "Random sampling for histogram construction: how much is enough?"
     * by Surajit Chaudhuri, Rajeev Motwani and Vivek Narasayya, in
     * Proceedings of ACM SIGMOD International Conference on Management
     * of Data, 1998, Pages 436-447.  Their Corollary 1 to Theorem 5
     * says that for table size n, histogram size k, maximum relative
     * error in bin size f, and error probability gamma, the minimum
     * random sample size is
     *    r = 4 * k * ln(2*n/gamma) / f^2
     * Taking f = 0.5, gamma = 0.01, n = 10^6 rows, we obtain
     *    r = 305.82 * k
     * Note that because of the log function, the dependence on n is
     * quite weak; even at n = 10^12, a 300*k sample gives <= 0.66
     * bin size error with probability 0.99.  So there's no real need to
     * scale for n, which is a good thing because we don't necessarily
     * know it at this point.
     *--------------------
     */
    stats->minrows = 300 * stats->attstattarget;
  }
  else if (OidIsValid(eqopr))
  {
    /* We can still recognize distinct values */
    stats->compute_stats = compute_distinct_stats;
    /* Might as well use the same minrows as above */
    stats->minrows = 300 * stats->attstattarget;
  }
  else
  {
    /* Can't do much but the trivial stuff */
    stats->compute_stats = compute_trivial_stats;
    /* Might as well use the same minrows as above */
    stats->minrows = 300 * stats->attstattarget;
  }

  return true;
}


/*
 *  compute_trivial_stats() -- compute very basic column statistics
 *
 *  We use this when we cannot find a hash "=" operator for the datatype.
 *
 *  We determine the fraction of non-null rows and the average datum width.
 */
static void
compute_trivial_stats(VacAttrStatsP stats,
            AnalyzeAttrFetchFunc fetchfunc,
            int samplerows,
            double totalrows)
{
  int     i;
  int     null_cnt = 0;
  int     nonnull_cnt = 0;
  double    total_width = 0;
  bool    is_varlena = (!stats->attrtype->typbyval &&
                stats->attrtype->typlen == -1);
  bool    is_varwidth = (!stats->attrtype->typbyval &&
                 stats->attrtype->typlen < 0);

  for (i = 0; i < samplerows; i++)
  {
    Datum   value;
    bool    isnull;

    vacuum_delay_point(true);

    value = fetchfunc(stats, i, &isnull);

    /* Check for null/nonnull */
    if (isnull)
    {
      null_cnt++;
      continue;
    }
    nonnull_cnt++;

    /*
     * If it's a variable-width field, add up widths for average width
     * calculation.  Note that if the value is toasted, we use the toasted
     * width.  We don't bother with this calculation if it's a fixed-width
     * type.
     */
    if (is_varlena)
    {
      total_width += VARSIZE_ANY(DatumGetPointer(value));
    }
    else if (is_varwidth)
    {
      /* must be cstring */
      total_width += strlen(DatumGetCString(value)) + 1;
    }
  }

  /* We can only compute average width if we found some non-null values. */
  if (nonnull_cnt > 0)
  {
    stats->stats_valid = true;
    /* Do the simple null-frac and width stats */
    stats->stanullfrac = (double) null_cnt / (double) samplerows;
    if (is_varwidth)
      stats->stawidth = total_width / (double) nonnull_cnt;
    else
      stats->stawidth = stats->attrtype->typlen;
    stats->stadistinct = 0.0; /* "unknown" */
  }
  else if (null_cnt > 0)
  {
    /* We found only nulls; assume the column is entirely null */
    stats->stats_valid = true;
    stats->stanullfrac = 1.0;
    if (is_varwidth)
      stats->stawidth = 0; /* "unknown" */
    else
      stats->stawidth = stats->attrtype->typlen;
    stats->stadistinct = 0.0; /* "unknown" */
  }
}


/*
 *  compute_distinct_stats() -- compute column statistics including ndistinct
 *
 *  We use this when we can find only an "=" operator for the datatype.
 *
 *  We determine the fraction of non-null rows, the average width, the
 *  most common values, and the (estimated) number of distinct values.
 *
 *  The most common values are determined by brute force: we keep a list
 *  of previously seen values, ordered by number of times seen, as we scan
 *  the samples.  A newly seen value is inserted just after the last
 *  multiply-seen value, causing the bottommost (oldest) singly-seen value
 *  to drop off the list.  The accuracy of this method, and also its cost,
 *  depend mainly on the length of the list we are willing to keep.
 */
static void
compute_distinct_stats(VacAttrStatsP stats,
             AnalyzeAttrFetchFunc fetchfunc,
             int samplerows,
             double totalrows)
{
  int     i;
  int     null_cnt = 0;
  int     nonnull_cnt = 0;
  int     toowide_cnt = 0;
  double    total_width = 0;
  bool    is_varlena = (!stats->attrtype->typbyval &&
                stats->attrtype->typlen == -1);
  bool    is_varwidth = (!stats->attrtype->typbyval &&
                 stats->attrtype->typlen < 0);
  FmgrInfo  f_cmpeq;
  typedef struct
  {
    Datum   value;
    int     count;
  } TrackItem;
  TrackItem  *track;
  int     track_cnt,
        track_max;
  int     num_mcv = stats->attstattarget;
  StdAnalyzeData *mystats = (StdAnalyzeData *) stats->extra_data;

  /*
   * We track up to 2*n values for an n-element MCV list; but at least 10
   */
  track_max = 2 * num_mcv;
  if (track_max < 10)
    track_max = 10;
  track = palloc_array(TrackItem, track_max);
  track_cnt = 0;

  fmgr_info(mystats->eqfunc, &f_cmpeq);

  for (i = 0; i < samplerows; i++)
  {
    Datum   value;
    bool    isnull;
    bool    match;
    int     firstcount1,
          j;

    vacuum_delay_point(true);

    value = fetchfunc(stats, i, &isnull);

    /* Check for null/nonnull */
    if (isnull)
    {
      null_cnt++;
      continue;
    }
    nonnull_cnt++;

    /*
     * If it's a variable-width field, add up widths for average width
     * calculation.  Note that if the value is toasted, we use the toasted
     * width.  We don't bother with this calculation if it's a fixed-width
     * type.
     */
    if (is_varlena)
    {
      total_width += VARSIZE_ANY(DatumGetPointer(value));

      /*
       * If the value is toasted, we want to detoast it just once to
       * avoid repeated detoastings and resultant excess memory usage
       * during the comparisons.  Also, check to see if the value is
       * excessively wide, and if so don't detoast at all --- just
       * ignore the value.
       */
      if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
      {
        toowide_cnt++;
        continue;
      }
      value = PointerGetDatum(PG_DETOAST_DATUM(value));
    }
    else if (is_varwidth)
    {
      /* must be cstring */
      total_width += strlen(DatumGetCString(value)) + 1;
    }

    /*
     * See if the value matches anything we're already tracking.
     */
    match = false;
    firstcount1 = track_cnt;
    for (j = 0; j < track_cnt; j++)
    {
      if (DatumGetBool(FunctionCall2Coll(&f_cmpeq,
                         stats->attrcollid,
                         value, track[j].value)))
      {
        match = true;
        break;
      }
      if (j < firstcount1 && track[j].count == 1)
        firstcount1 = j;
    }

    if (match)
    {
      /* Found a match */
      track[j].count++;
      /* This value may now need to "bubble up" in the track list */
      while (j > 0 && track[j].count > track[j - 1].count)
      {
        swapDatum(track[j].value, track[j - 1].value);
        swapInt(track[j].count, track[j - 1].count);
        j--;
      }
    }
    else
    {
      /* No match.  Insert at head of count-1 list */
      if (track_cnt < track_max)
        track_cnt++;
      for (j = track_cnt - 1; j > firstcount1; j--)
      {
        track[j].value = track[j - 1].value;
        track[j].count = track[j - 1].count;
      }
      if (firstcount1 < track_cnt)
      {
        track[firstcount1].value = value;
        track[firstcount1].count = 1;
      }
    }
  }

  /* We can only compute real stats if we found some non-null values. */
  if (nonnull_cnt > 0)
  {
    int     nmultiple,
          summultiple;

    stats->stats_valid = true;
    /* Do the simple null-frac and width stats */
    stats->stanullfrac = (double) null_cnt / (double) samplerows;
    if (is_varwidth)
      stats->stawidth = total_width / (double) nonnull_cnt;
    else
      stats->stawidth = stats->attrtype->typlen;

    /* Count the number of values we found multiple times */
    summultiple = 0;
    for (nmultiple = 0; nmultiple < track_cnt; nmultiple++)
    {
      if (track[nmultiple].count == 1)
        break;
      summultiple += track[nmultiple].count;
    }

    if (nmultiple == 0)
    {
      /*
       * If we found no repeated non-null values, assume it's a unique
       * column; but be sure to discount for any nulls we found.
       */
      stats->stadistinct = -1.0 * (1.0 - stats->stanullfrac);
    }
    else if (track_cnt < track_max && toowide_cnt == 0 &&
         nmultiple == track_cnt)
    {
      /*
       * Our track list includes every value in the sample, and every
       * value appeared more than once.  Assume the column has just
       * these values.  (This case is meant to address columns with
       * small, fixed sets of possible values, such as boolean or enum
       * columns.  If there are any values that appear just once in the
       * sample, including too-wide values, we should assume that that's
       * not what we're dealing with.)
       */
      stats->stadistinct = track_cnt;
    }
    else
    {
      /*----------
       * Estimate the number of distinct values using the estimator
       * proposed by Haas and Stokes in IBM Research Report RJ 10025:
       *    n*d / (n - f1 + f1*n/N)
       * where f1 is the number of distinct values that occurred
       * exactly once in our sample of n rows (from a total of N),
       * and d is the total number of distinct values in the sample.
       * This is their Duj1 estimator; the other estimators they
       * recommend are considerably more complex, and are numerically
       * very unstable when n is much smaller than N.
       *
       * In this calculation, we consider only non-nulls.  We used to
       * include rows with null values in the n and N counts, but that
       * leads to inaccurate answers in columns with many nulls, and
       * it's intuitively bogus anyway considering the desired result is
       * the number of distinct non-null values.
       *
       * We assume (not very reliably!) that all the multiply-occurring
       * values are reflected in the final track[] list, and the other
       * nonnull values all appeared but once.  (XXX this usually
       * results in a drastic overestimate of ndistinct.  Can we do
       * any better?)
       *----------
       */
      int     f1 = nonnull_cnt - summultiple;
      int     d = f1 + nmultiple;
      double    n = samplerows - null_cnt;
      double    N = totalrows * (1.0 - stats->stanullfrac);
      double    stadistinct;

      /* N == 0 shouldn't happen, but just in case ... */
      if (N > 0)
        stadistinct = (n * d) / ((n - f1) + f1 * n / N);
      else
        stadistinct = 0;

      /* Clamp to sane range in case of roundoff error */
      if (stadistinct < d)
        stadistinct = d;
      if (stadistinct > N)
        stadistinct = N;
      /* And round to integer */
      stats->stadistinct = floor(stadistinct + 0.5);
    }

    /*
     * If we estimated the number of distinct values at more than 10% of
     * the total row count (a very arbitrary limit), then assume that
     * stadistinct should scale with the row count rather than be a fixed
     * value.
     */
    if (stats->stadistinct > 0.1 * totalrows)
      stats->stadistinct = -(stats->stadistinct / totalrows);

    /*
     * Decide how many values are worth storing as most-common values. If
     * we are able to generate a complete MCV list (all the values in the
     * sample will fit, and we think these are all the ones in the table),
     * then do so.  Otherwise, store only those values that are
     * significantly more common than the values not in the list.
     *
     * Note: the first of these cases is meant to address columns with
     * small, fixed sets of possible values, such as boolean or enum
     * columns.  If we can *completely* represent the column population by
     * an MCV list that will fit into the stats target, then we should do
     * so and thus provide the planner with complete information.  But if
     * the MCV list is not complete, it's generally worth being more
     * selective, and not just filling it all the way up to the stats
     * target.
     */
    if (track_cnt < track_max && toowide_cnt == 0 &&
      stats->stadistinct > 0 &&
      track_cnt <= num_mcv)
    {
      /* Track list includes all values seen, and all will fit */
      num_mcv = track_cnt;
    }
    else
    {
      int      *mcv_counts;

      /* Incomplete list; decide how many values are worth keeping */
      if (num_mcv > track_cnt)
        num_mcv = track_cnt;

      if (num_mcv > 0)
      {
        mcv_counts = palloc_array(int, num_mcv);
        for (i = 0; i < num_mcv; i++)
          mcv_counts[i] = track[i].count;

        num_mcv = analyze_mcv_list(mcv_counts, num_mcv,
                       stats->stadistinct,
                       stats->stanullfrac,
                       samplerows, totalrows);
      }
    }

    /* Generate MCV slot entry */
    if (num_mcv > 0)
    {
      MemoryContext old_context;
      Datum    *mcv_values;
      float4     *mcv_freqs;

      /* Must copy the target values into anl_context */
      old_context = MemoryContextSwitchTo(stats->anl_context);
      mcv_values = palloc_array(Datum, num_mcv);
      mcv_freqs = palloc_array(float4, num_mcv);
      for (i = 0; i < num_mcv; i++)
      {
        mcv_values[i] = datumCopy(track[i].value,
                      stats->attrtype->typbyval,
                      stats->attrtype->typlen);
        mcv_freqs[i] = (double) track[i].count / (double) samplerows;
      }
      MemoryContextSwitchTo(old_context);

      stats->stakind[0] = STATISTIC_KIND_MCV;
      stats->staop[0] = mystats->eqopr;
      stats->stacoll[0] = stats->attrcollid;
      stats->stanumbers[0] = mcv_freqs;
      stats->numnumbers[0] = num_mcv;
      stats->stavalues[0] = mcv_values;
      stats->numvalues[0] = num_mcv;

      /*
       * Accept the defaults for stats->statypid and others. They have
       * been set before we were called (see vacuum.h)
       */
    }
  }
  else if (null_cnt > 0)
  {
    /* We found only nulls; assume the column is entirely null */
    stats->stats_valid = true;
    stats->stanullfrac = 1.0;
    if (is_varwidth)
      stats->stawidth = 0; /* "unknown" */
    else
      stats->stawidth = stats->attrtype->typlen;
    stats->stadistinct = 0.0; /* "unknown" */
  }

  /* We don't need to bother cleaning up any of our temporary palloc's */
}


/*
 *  compute_scalar_stats() -- compute column statistics
 *
 *  We use this when we can find "=" and "<" operators for the datatype.
 *
 *  We determine the fraction of non-null rows, the average width, the
 *  most common values, the (estimated) number of distinct values, the
 *  distribution histogram, and the correlation of physical to logical order.
 *
 *  The desired stats can be determined fairly easily after sorting the
 *  data values into order.
 */
static void
compute_scalar_stats(VacAttrStatsP stats,
           AnalyzeAttrFetchFunc fetchfunc,
           int samplerows,
           double totalrows)
{
  int     i;
  int     null_cnt = 0;
  int     nonnull_cnt = 0;
  int     toowide_cnt = 0;
  double    total_width = 0;
  bool    is_varlena = (!stats->attrtype->typbyval &&
                stats->attrtype->typlen == -1);
  bool    is_varwidth = (!stats->attrtype->typbyval &&
                 stats->attrtype->typlen < 0);
  double    corr_xysum;
  SortSupportData ssup;
  ScalarItem *values;
  int     values_cnt = 0;
  int      *tupnoLink;
  ScalarMCVItem *track;
  int     track_cnt = 0;
  int     num_mcv = stats->attstattarget;
  int     num_bins = stats->attstattarget;
  StdAnalyzeData *mystats = (StdAnalyzeData *) stats->extra_data;

  values = palloc_array(ScalarItem, samplerows);
  tupnoLink = palloc_array(int, samplerows);
  track = palloc_array(ScalarMCVItem, num_mcv);

  memset(&ssup, 0, sizeof(ssup));
  ssup.ssup_cxt = CurrentMemoryContext;
  ssup.ssup_collation = stats->attrcollid;
  ssup.ssup_nulls_first = false;

  /*
   * For now, don't perform abbreviated key conversion, because full values
   * are required for MCV slot generation.  Supporting that optimization
   * would necessitate teaching compare_scalars() to call a tie-breaker.
   */
  ssup.abbreviate = false;

  PrepareSortSupportFromOrderingOp(mystats->ltopr, &ssup);

  /* Initial scan to find sortable values */
  for (i = 0; i < samplerows; i++)
  {
    Datum   value;
    bool    isnull;

    vacuum_delay_point(true);

    value = fetchfunc(stats, i, &isnull);

    /* Check for null/nonnull */
    if (isnull)
    {
      null_cnt++;
      continue;
    }
    nonnull_cnt++;

    /*
     * If it's a variable-width field, add up widths for average width
     * calculation.  Note that if the value is toasted, we use the toasted
     * width.  We don't bother with this calculation if it's a fixed-width
     * type.
     */
    if (is_varlena)
    {
      total_width += VARSIZE_ANY(DatumGetPointer(value));

      /*
       * If the value is toasted, we want to detoast it just once to
       * avoid repeated detoastings and resultant excess memory usage
       * during the comparisons.  Also, check to see if the value is
       * excessively wide, and if so don't detoast at all --- just
       * ignore the value.
       */
      if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
      {
        toowide_cnt++;
        continue;
      }
      value = PointerGetDatum(PG_DETOAST_DATUM(value));
    }
    else if (is_varwidth)
    {
      /* must be cstring */
      total_width += strlen(DatumGetCString(value)) + 1;
    }

    /* Add it to the list to be sorted */
    values[values_cnt].value = value;
    values[values_cnt].tupno = values_cnt;
    tupnoLink[values_cnt] = values_cnt;
    values_cnt++;
  }

  /* We can only compute real stats if we found some sortable values. */
  if (values_cnt > 0)
  {
    int     ndistinct,  /* # distinct values in sample */
          nmultiple,  /* # that appear multiple times */
          num_hist,
          dups_cnt;
    int     slot_idx = 0;
    CompareScalarsContext cxt;

    /* Sort the collected values */
    cxt.ssup = &ssup;
    cxt.tupnoLink = tupnoLink;
    qsort_interruptible(values, values_cnt, sizeof(ScalarItem),
              compare_scalars, &cxt);

    /*
     * Now scan the values in order, find the most common ones, and also
     * accumulate ordering-correlation statistics.
     *
     * To determine which are most common, we first have to count the
     * number of duplicates of each value.  The duplicates are adjacent in
     * the sorted list, so a brute-force approach is to compare successive
     * datum values until we find two that are not equal. However, that
     * requires N-1 invocations of the datum comparison routine, which are
     * completely redundant with work that was done during the sort.  (The
     * sort algorithm must at some point have compared each pair of items
     * that are adjacent in the sorted order; otherwise it could not know
     * that it's ordered the pair correctly.) We exploit this by having
     * compare_scalars remember the highest tupno index that each
     * ScalarItem has been found equal to.  At the end of the sort, a
     * ScalarItem's tupnoLink will still point to itself if and only if it
     * is the last item of its group of duplicates (since the group will
     * be ordered by tupno).
     */
    corr_xysum = 0;
    ndistinct = 0;
    nmultiple = 0;
    dups_cnt = 0;
    for (i = 0; i < values_cnt; i++)
    {
      int     tupno = values[i].tupno;

      corr_xysum += ((double) i) * ((double) tupno);
      dups_cnt++;
      if (tupnoLink[tupno] == tupno)
      {
        /* Reached end of duplicates of this value */
        ndistinct++;
        if (dups_cnt > 1)
        {
          nmultiple++;
          if (track_cnt < num_mcv ||
            dups_cnt > track[track_cnt - 1].count)
          {
            /*
             * Found a new item for the mcv list; find its
             * position, bubbling down old items if needed. Loop
             * invariant is that j points at an empty/ replaceable
             * slot.
             */
            int     j;

            if (track_cnt < num_mcv)
              track_cnt++;
            for (j = track_cnt - 1; j > 0; j--)
            {
              if (dups_cnt <= track[j - 1].count)
                break;
              track[j].count = track[j - 1].count;
              track[j].first = track[j - 1].first;
            }
            track[j].count = dups_cnt;
            track[j].first = i + 1 - dups_cnt;
          }
        }
        dups_cnt = 0;
      }
    }

    stats->stats_valid = true;
    /* Do the simple null-frac and width stats */
    stats->stanullfrac = (double) null_cnt / (double) samplerows;
    if (is_varwidth)
      stats->stawidth = total_width / (double) nonnull_cnt;
    else
      stats->stawidth = stats->attrtype->typlen;

    if (nmultiple == 0)
    {
      /*
       * If we found no repeated non-null values, assume it's a unique
       * column; but be sure to discount for any nulls we found.
       */
      stats->stadistinct = -1.0 * (1.0 - stats->stanullfrac);
    }
    else if (toowide_cnt == 0 && nmultiple == ndistinct)
    {
      /*
       * Every value in the sample appeared more than once.  Assume the
       * column has just these values.  (This case is meant to address
       * columns with small, fixed sets of possible values, such as
       * boolean or enum columns.  If there are any values that appear
       * just once in the sample, including too-wide values, we should
       * assume that that's not what we're dealing with.)
       */
      stats->stadistinct = ndistinct;
    }
    else
    {
      /*----------
       * Estimate the number of distinct values using the estimator
       * proposed by Haas and Stokes in IBM Research Report RJ 10025:
       *    n*d / (n - f1 + f1*n/N)
       * where f1 is the number of distinct values that occurred
       * exactly once in our sample of n rows (from a total of N),
       * and d is the total number of distinct values in the sample.
       * This is their Duj1 estimator; the other estimators they
       * recommend are considerably more complex, and are numerically
       * very unstable when n is much smaller than N.
       *
       * In this calculation, we consider only non-nulls.  We used to
       * include rows with null values in the n and N counts, but that
       * leads to inaccurate answers in columns with many nulls, and
       * it's intuitively bogus anyway considering the desired result is
       * the number of distinct non-null values.
       *
       * Overwidth values are assumed to have been distinct.
       *----------
       */
      int     f1 = ndistinct - nmultiple + toowide_cnt;
      int     d = f1 + nmultiple;
      double    n = samplerows - null_cnt;
      double    N = totalrows * (1.0 - stats->stanullfrac);
      double    stadistinct;

      /* N == 0 shouldn't happen, but just in case ... */
      if (N > 0)
        stadistinct = (n * d) / ((n - f1) + f1 * n / N);
      else
        stadistinct = 0;

      /* Clamp to sane range in case of roundoff error */
      if (stadistinct < d)
        stadistinct = d;
      if (stadistinct > N)
        stadistinct = N;
      /* And round to integer */
      stats->stadistinct = floor(stadistinct + 0.5);
    }

    /*
     * If we estimated the number of distinct values at more than 10% of
     * the total row count (a very arbitrary limit), then assume that
     * stadistinct should scale with the row count rather than be a fixed
     * value.
     */
    if (stats->stadistinct > 0.1 * totalrows)
      stats->stadistinct = -(stats->stadistinct / totalrows);

    /*
     * Decide how many values are worth storing as most-common values. If
     * we are able to generate a complete MCV list (all the values in the
     * sample will fit, and we think these are all the ones in the table),
     * then do so.  Otherwise, store only those values that are
     * significantly more common than the values not in the list.
     *
     * Note: the first of these cases is meant to address columns with
     * small, fixed sets of possible values, such as boolean or enum
     * columns.  If we can *completely* represent the column population by
     * an MCV list that will fit into the stats target, then we should do
     * so and thus provide the planner with complete information.  But if
     * the MCV list is not complete, it's generally worth being more
     * selective, and not just filling it all the way up to the stats
     * target.
     */
    if (track_cnt == ndistinct && toowide_cnt == 0 &&
      stats->stadistinct > 0 &&
      track_cnt <= num_mcv)
    {
      /* Track list includes all values seen, and all will fit */
      num_mcv = track_cnt;
    }
    else
    {
      int      *mcv_counts;

      /* Incomplete list; decide how many values are worth keeping */
      if (num_mcv > track_cnt)
        num_mcv = track_cnt;

      if (num_mcv > 0)
      {
        mcv_counts = palloc_array(int, num_mcv);
        for (i = 0; i < num_mcv; i++)
          mcv_counts[i] = track[i].count;

        num_mcv = analyze_mcv_list(mcv_counts, num_mcv,
                       stats->stadistinct,
                       stats->stanullfrac,
                       samplerows, totalrows);
      }
    }

    /* Generate MCV slot entry */
    if (num_mcv > 0)
    {
      MemoryContext old_context;
      Datum    *mcv_values;
      float4     *mcv_freqs;

      /* Must copy the target values into anl_context */
      old_context = MemoryContextSwitchTo(stats->anl_context);
      mcv_values = palloc_array(Datum, num_mcv);
      mcv_freqs = palloc_array(float4, num_mcv);
      for (i = 0; i < num_mcv; i++)
      {
        mcv_values[i] = datumCopy(values[track[i].first].value,
                      stats->attrtype->typbyval,
                      stats->attrtype->typlen);
        mcv_freqs[i] = (double) track[i].count / (double) samplerows;
      }
      MemoryContextSwitchTo(old_context);

      stats->stakind[slot_idx] = STATISTIC_KIND_MCV;
      stats->staop[slot_idx] = mystats->eqopr;
      stats->stacoll[slot_idx] = stats->attrcollid;
      stats->stanumbers[slot_idx] = mcv_freqs;
      stats->numnumbers[slot_idx] = num_mcv;
      stats->stavalues[slot_idx] = mcv_values;
      stats->numvalues[slot_idx] = num_mcv;

      /*
       * Accept the defaults for stats->statypid and others. They have
       * been set before we were called (see vacuum.h)
       */
      slot_idx++;
    }

    /*
     * Generate a histogram slot entry if there are at least two distinct
     * values not accounted for in the MCV list.  (This ensures the
     * histogram won't collapse to empty or a singleton.)
     */
    num_hist = ndistinct - num_mcv;
    if (num_hist > num_bins)
      num_hist = num_bins + 1;
    if (num_hist >= 2)
    {
      MemoryContext old_context;
      Datum    *hist_values;
      int     nvals;
      int     pos,
            posfrac,
            delta,
            deltafrac;

      /* Sort the MCV items into position order to speed next loop */
      qsort_interruptible(track, num_mcv, sizeof(ScalarMCVItem),
                compare_mcvs, NULL);

      /*
       * Collapse out the MCV items from the values[] array.
       *
       * Note we destroy the values[] array here... but we don't need it
       * for anything more.  We do, however, still need values_cnt.
       * nvals will be the number of remaining entries in values[].
       */
      if (num_mcv > 0)
      {
        int     src,
              dest;
        int     j;

        src = dest = 0;
        j = 0;      /* index of next interesting MCV item */
        while (src < values_cnt)
        {
          int     ncopy;

          if (j < num_mcv)
          {
            int     first = track[j].first;

            if (src >= first)
            {
              /* advance past this MCV item */
              src = first + track[j].count;
              j++;
              continue;
            }
            ncopy = first - src;
          }
          else
            ncopy = values_cnt - src;
          memmove(&values[dest], &values[src],
              ncopy * sizeof(ScalarItem));
          src += ncopy;
          dest += ncopy;
        }
        nvals = dest;
      }
      else
        nvals = values_cnt;
      Assert(nvals >= num_hist);

      /* Must copy the target values into anl_context */
      old_context = MemoryContextSwitchTo(stats->anl_context);
      hist_values = palloc_array(Datum, num_hist);

      /*
       * The object of this loop is to copy the first and last values[]
       * entries along with evenly-spaced values in between.  So the
       * i'th value is values[(i * (nvals - 1)) / (num_hist - 1)].  But
       * computing that subscript directly risks integer overflow when
       * the stats target is more than a couple thousand.  Instead we
       * add (nvals - 1) / (num_hist - 1) to pos at each step, tracking
       * the integral and fractional parts of the sum separately.
       */
      delta = (nvals - 1) / (num_hist - 1);
      deltafrac = (nvals - 1) % (num_hist - 1);
      pos = posfrac = 0;

      for (i = 0; i < num_hist; i++)
      {
        hist_values[i] = datumCopy(values[pos].value,
                       stats->attrtype->typbyval,
                       stats->attrtype->typlen);
        pos += delta;
        posfrac += deltafrac;
        if (posfrac >= (num_hist - 1))
        {
          /* fractional part exceeds 1, carry to integer part */
          pos++;
          posfrac -= (num_hist - 1);
        }
      }

      MemoryContextSwitchTo(old_context);

      stats->stakind[slot_idx] = STATISTIC_KIND_HISTOGRAM;
      stats->staop[slot_idx] = mystats->ltopr;
      stats->stacoll[slot_idx] = stats->attrcollid;
      stats->stavalues[slot_idx] = hist_values;
      stats->numvalues[slot_idx] = num_hist;

      /*
       * Accept the defaults for stats->statypid and others. They have
       * been set before we were called (see vacuum.h)
       */
      slot_idx++;
    }

    /* Generate a correlation entry if there are multiple values */
    if (values_cnt > 1)
    {
      MemoryContext old_context;
      float4     *corrs;
      double    corr_xsum,
            corr_x2sum;

      /* Must copy the target values into anl_context */
      old_context = MemoryContextSwitchTo(stats->anl_context);
      corrs = palloc_object(float4);
      MemoryContextSwitchTo(old_context);

      /*----------
       * Since we know the x and y value sets are both
       *    0, 1, ..., values_cnt-1
       * we have sum(x) = sum(y) =
       *    (values_cnt-1)*values_cnt / 2
       * and sum(x^2) = sum(y^2) =
       *    (values_cnt-1)*values_cnt*(2*values_cnt-1) / 6.
       *----------
       */
      corr_xsum = ((double) (values_cnt - 1)) *
        ((double) values_cnt) / 2.0;
      corr_x2sum = ((double) (values_cnt - 1)) *
        ((double) values_cnt) * (double) (2 * values_cnt - 1) / 6.0;

      /* And the correlation coefficient reduces to */
      corrs[0] = (values_cnt * corr_xysum - corr_xsum * corr_xsum) /
        (values_cnt * corr_x2sum - corr_xsum * corr_xsum);

      stats->stakind[slot_idx] = STATISTIC_KIND_CORRELATION;
      stats->staop[slot_idx] = mystats->ltopr;
      stats->stacoll[slot_idx] = stats->attrcollid;
      stats->stanumbers[slot_idx] = corrs;
      stats->numnumbers[slot_idx] = 1;
      slot_idx++;
    }
  }
  else if (nonnull_cnt > 0)
  {
    /* We found some non-null values, but they were all too wide */
    Assert(nonnull_cnt == toowide_cnt);
    stats->stats_valid = true;
    /* Do the simple null-frac and width stats */
    stats->stanullfrac = (double) null_cnt / (double) samplerows;
    if (is_varwidth)
      stats->stawidth = total_width / (double) nonnull_cnt;
    else
      stats->stawidth = stats->attrtype->typlen;
    /* Assume all too-wide values are distinct, so it's a unique column */
    stats->stadistinct = -1.0 * (1.0 - stats->stanullfrac);
  }
  else if (null_cnt > 0)
  {
    /* We found only nulls; assume the column is entirely null */
    stats->stats_valid = true;
    stats->stanullfrac = 1.0;
    if (is_varwidth)
      stats->stawidth = 0; /* "unknown" */
    else
      stats->stawidth = stats->attrtype->typlen;
    stats->stadistinct = 0.0; /* "unknown" */
  }

  /* We don't need to bother cleaning up any of our temporary palloc's */
}

/*
 * Comparator for sorting ScalarItems
 *
 * Aside from sorting the items, we update the tupnoLink[] array
 * whenever two ScalarItems are found to contain equal datums.  The array
 * is indexed by tupno; for each ScalarItem, it contains the highest
 * tupno that that item's datum has been found to be equal to.  This allows
 * us to avoid additional comparisons in compute_scalar_stats().
 */
static int
compare_scalars(const void *a, const void *b, void *arg)
{
  Datum   da = ((const ScalarItem *) a)->value;
  int     ta = ((const ScalarItem *) a)->tupno;
  Datum   db = ((const ScalarItem *) b)->value;
  int     tb = ((const ScalarItem *) b)->tupno;
  CompareScalarsContext *cxt = (CompareScalarsContext *) arg;
  int     compare;

  compare = ApplySortComparator(da, false, db, false, cxt->ssup);
  if (compare != 0)
    return compare;

  /*
   * The two datums are equal, so update cxt->tupnoLink[].
   */
  if (cxt->tupnoLink[ta] < tb)
    cxt->tupnoLink[ta] = tb;
  if (cxt->tupnoLink[tb] < ta)
    cxt->tupnoLink[tb] = ta;

  /*
   * For equal datums, sort by tupno
   */
  return ta - tb;
}

/*
 * Comparator for sorting ScalarMCVItems by position
 */
static int
compare_mcvs(const void *a, const void *b, void *arg)
{
  int     da = ((const ScalarMCVItem *) a)->first;
  int     db = ((const ScalarMCVItem *) b)->first;

  return da - db;
}

/*
 * Analyze the list of common values in the sample and decide how many are
 * worth storing in the table's MCV list.
 *
 * mcv_counts is assumed to be a list of the counts of the most common values
 * seen in the sample, starting with the most common.  The return value is the
 * number that are significantly more common than the values not in the list,
 * and which are therefore deemed worth storing in the table's MCV list.
 */
static int
analyze_mcv_list(int *mcv_counts,
         int num_mcv,
         double stadistinct,
         double stanullfrac,
         int samplerows,
         double totalrows)
{
  double    ndistinct_table;
  double    sumcount;
  int     i;

  /*
   * If the entire table was sampled, keep the whole list.  This also
   * protects us against division by zero in the code below.
   */
  if (samplerows == totalrows || totalrows <= 1.0)
    return num_mcv;

  /* Re-extract the estimated number of distinct nonnull values in table */
  ndistinct_table = stadistinct;
  if (ndistinct_table < 0)
    ndistinct_table = -ndistinct_table * totalrows;

  /*
   * Exclude the least common values from the MCV list, if they are not
   * significantly more common than the estimated selectivity they would
   * have if they weren't in the list.  All non-MCV values are assumed to be
   * equally common, after taking into account the frequencies of all the
   * values in the MCV list and the number of nulls (c.f. eqsel()).
   *
   * Here sumcount tracks the total count of all but the last (least common)
   * value in the MCV list, allowing us to determine the effect of excluding
   * that value from the list.
   *
   * Note that we deliberately do this by removing values from the full
   * list, rather than starting with an empty list and adding values,
   * because the latter approach can fail to add any values if all the most
   * common values have around the same frequency and make up the majority
   * of the table, so that the overall average frequency of all values is
   * roughly the same as that of the common values.  This would lead to any
   * uncommon values being significantly overestimated.
   */
  sumcount = 0.0;
  for (i = 0; i < num_mcv - 1; i++)
    sumcount += mcv_counts[i];

  while (num_mcv > 0)
  {
    double    selec,
          otherdistinct,
          N,
          n,
          K,
          variance,
          stddev;

    /*
     * Estimated selectivity the least common value would have if it
     * wasn't in the MCV list (c.f. eqsel()).
     */
    selec = 1.0 - sumcount / samplerows - stanullfrac;
    if (selec < 0.0)
      selec = 0.0;
    if (selec > 1.0)
      selec = 1.0;
    otherdistinct = ndistinct_table - (num_mcv - 1);
    if (otherdistinct > 1)
      selec /= otherdistinct;

    /*
     * If the value is kept in the MCV list, its population frequency is
     * assumed to equal its sample frequency.  We use the lower end of a
     * textbook continuity-corrected Wald-type confidence interval to
     * determine if that is significantly more common than the non-MCV
     * frequency --- specifically we assume the population frequency is
     * highly likely to be within around 2 standard errors of the sample
     * frequency, which equates to an interval of 2 standard deviations
     * either side of the sample count, plus an additional 0.5 for the
     * continuity correction.  Since we are sampling without replacement,
     * this is a hypergeometric distribution.
     *
     * XXX: Empirically, this approach seems to work quite well, but it
     * may be worth considering more advanced techniques for estimating
     * the confidence interval of the hypergeometric distribution.
     */
    N = totalrows;
    n = samplerows;
    K = N * mcv_counts[num_mcv - 1] / n;
    variance = n * K * (N - K) * (N - n) / (N * N * (N - 1));
    stddev = sqrt(variance);

    if (mcv_counts[num_mcv - 1] > selec * samplerows + 2 * stddev + 0.5)
    {
      /*
       * The value is significantly more common than the non-MCV
       * selectivity would suggest.  Keep it, and all the other more
       * common values in the list.
       */
      break;
    }
    else
    {
      /* Discard this value and consider the next least common value */
      num_mcv--;
      if (num_mcv == 0)
        break;
      sumcount -= mcv_counts[num_mcv - 1];
    }
  }
  return num_mcv;
}

Coverage Report

Created: 2026-11-09 07:20