text: /*-------------------------------------------------------------------------
   *
   * analyze.c
   *	  the Postgres statistics generator
   *
   * Portions Copyright (c) 1996-2016, 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/multixact.h"
  #include "access/transam.h"
  #include "access/tupconvert.h"
  #include "access/tuptoaster.h"
  #include "access/visibilitymap.h"
  #include "access/xact.h"
  #include "catalog/catalog.h"
  #include "catalog/index.h"
  #include "catalog/indexing.h"
  #include "catalog/pg_collation.h"
  #include "catalog/pg_inherits_fn.h"
  #include "catalog/pg_namespace.h"
  #include "commands/dbcommands.h"
  #include "commands/tablecmds.h"
  #include "commands/vacuum.h"
  #include "executor/executor.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 "postmaster/autovacuum.h"
  #include "storage/bufmgr.h"
  #include "storage/lmgr.h"
  #include "storage/proc.h"
  #include "storage/procarray.h"
  #include "utils/acl.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"
  #include "utils/tqual.h"
  
  #ifdef ADB
  #include "catalog/pg_operator.h"
  #include "intercomm/inter-comm.h"
  #include "nodes/makefuncs.h"
  #include "pgxc/execRemote.h"
  #include "pgxc/pgxc.h"
  #include "utils/snapmgr.h"
  #endif
  
  /* 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, int options,
  			   VacuumParams *params, List *va_cols,
  			   AcquireSampleRowsFunc acquirefunc, BlockNumber relpages, ADB_ONLY_ARG(uint64 reltuples)
  			   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 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);
  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);
  
  #ifdef ADB
  static void node_analyze_rel(Relation relation,
  							 AcquireSampleRowsFunc *func,
  							 BlockNumber *totalpages,
  							 uint64 *totalrows);
  #endif
  
  /*
   *	analyze_rel() -- analyze one relation
   */
  void
  analyze_rel(Oid relid, RangeVar *relation, int options,
  			VacuumParams *params, List *va_cols, bool in_outer_xact,
  			BufferAccessStrategy bstrategy)
  {
  	Relation	onerel;
  	int			elevel;
  	AcquireSampleRowsFunc acquirefunc = NULL;
  	BlockNumber relpages = 0;
  #ifdef ADB
  	uint64		reltuples = 0;
  #endif
  
  	/* Select logging level */
  	if (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.
  	 */
  	if (!(options & VACOPT_NOWAIT))
  		onerel = try_relation_open(relid, ShareUpdateExclusiveLock);
  	else if (ConditionalLockRelationOid(relid, ShareUpdateExclusiveLock))
  		onerel = try_relation_open(relid, NoLock);
  	else
  	{
  		onerel = NULL;
  		if (IsAutoVacuumWorkerProcess() && params->log_min_duration >= 0)
  			ereport(LOG,
  					(errcode(ERRCODE_LOCK_NOT_AVAILABLE),
  				  errmsg("skipping analyze of \"%s\" --- lock not available",
  						 relation->relname)));
  	}
  	if (!onerel)
  		return;
  
  	/*
  	 * Check permissions --- this should match vacuum's check!
  	 */
  	if (!(pg_class_ownercheck(RelationGetRelid(onerel), GetUserId()) ||
  		  (pg_database_ownercheck(MyDatabaseId, GetUserId()) && !onerel->rd_rel->relisshared)))
  	{
  		/* No need for a WARNING if we already complained during VACUUM */
  		if (!(options & VACOPT_VACUUM))
  		{
  			if (onerel->rd_rel->relisshared)
  				ereport(WARNING,
  				 (errmsg("skipping \"%s\" --- only superuser can analyze it",
  						 RelationGetRelationName(onerel))));
  			else if (onerel->rd_rel->relnamespace == PG_CATALOG_NAMESPACE)
  				ereport(WARNING,
  						(errmsg("skipping \"%s\" --- only superuser or database owner can analyze it",
  								RelationGetRelationName(onerel))));
  			else
  				ereport(WARNING,
  						(errmsg("skipping \"%s\" --- only table or database owner can analyze it",
  								RelationGetRelationName(onerel))));
  		}
  		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 that it's a plain table, materialized view, or foreign table; we
  	 * used to do this in get_rel_oids() but seems safer to check after we've
  	 * locked the relation.
  	 */
  	if (onerel->rd_rel->relkind == RELKIND_RELATION ||
  		onerel->rd_rel->relkind == RELKIND_MATVIEW)
  	{
  #ifdef ADB
  		node_analyze_rel(onerel, &acquirefunc, &relpages, &reltuples);
  #else
  		/* Regular table, so we'll use the regular row acquisition function */
  		acquirefunc = acquire_sample_rows;
  		/* Also get regular table's size */
  		relpages = RelationGetNumberOfBlocks(onerel);
  #endif
  	}
  	else if (onerel->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(onerel, 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);
  			return;
  		}
  	}
  	else
  	{
  		/* No need for a WARNING if we already complained during VACUUM */
  		if (!(options & VACOPT_VACUUM))
  			ereport(WARNING,
  					(errmsg("skipping \"%s\" --- cannot analyze non-tables or special system tables",
  							RelationGetRelationName(onerel))));
  		relation_close(onerel, ShareUpdateExclusiveLock);
  		return;
  	}
  
  	/*
  	 * OK, let's do it.  First let other backends know I'm in ANALYZE.
  	 */
  	LWLockAcquire(ProcArrayLock, LW_EXCLUSIVE);
  	MyPgXact->vacuumFlags |= PROC_IN_ANALYZE;
  	LWLockRelease(ProcArrayLock);
  
  	/*
  	 * Do the normal non-recursive ANALYZE.
  	 */
  	do_analyze_rel(onerel, options, params, va_cols, acquirefunc, relpages,
  				   ADB_ONLY_ARG(reltuples) false, in_outer_xact, elevel);
  
  	/*
  	 * If there are child tables, do recursive ANALYZE.
  	 */
  	if (onerel->rd_rel->relhassubclass)
  		do_analyze_rel(onerel, options, params, va_cols, acquirefunc,
  					   relpages, ADB_ONLY_ARG(0) 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);
  
  	/*
  	 * Reset my PGXACT flag.  Note: we need this here, and not in vacuum_rel,
  	 * because the vacuum flag is cleared by the end-of-xact code.
  	 */
  	LWLockAcquire(ProcArrayLock, LW_EXCLUSIVE);
  	MyPgXact->vacuumFlags &= ~PROC_IN_ANALYZE;
  	LWLockRelease(ProcArrayLock);
  }
  
  #ifdef ADB
  static void
  node_analyze_rel(Relation relation,
  				AcquireSampleRowsFunc *func,
  				BlockNumber *totalpages,
  				uint64 *totalrows)
  {
  	if (IsCnNode() && RelationGetLocInfo(relation))
  	{
  		/* Return the row-analysis function pointer for Coordinator */
  		*func = CnAcquireSampleRowsFunc;
  		/* Also get regular table's size by Coordinator */
  		*totalpages = CnGetRelationNumberOfBlocks(relation, totalrows);
  	} else
  	{
  		/* Regular table, so we'll use the regular row acquisition function */
  		*func = acquire_sample_rows;
  		/* Also get regular table's size */
  		*totalpages = RelationGetNumberOfBlocks(relation);
  		*totalrows = 0;
  	}
  }
  #endif
  
  /*
   *	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, int options, VacuumParams *params,
  			   List *va_cols, AcquireSampleRowsFunc acquirefunc,
  			   BlockNumber relpages, ADB_ONLY_ARG(uint64 reltuples)
  			   bool inh, bool in_outer_xact, int elevel)
  {
  	int			attr_cnt,
  				tcnt,
  				i,
  				ind;
  	Relation   *Irel;
  	int			nindexes;
  	bool		hasindex;
  	VacAttrStats **vacattrstats;
  	AnlIndexData *indexdata;
  	int			targrows,
  				numrows;
  	double		totalrows,
  				totaldeadrows;
  	HeapTuple  *rows;
  	PGRUsage	ru0;
  	TimestampTz starttime = 0;
  	MemoryContext caller_context;
  	Oid			save_userid;
  	int			save_sec_context;
  	int			save_nestlevel;
  
  	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();
  
  	/* measure elapsed time iff autovacuum logging requires it */
  	if (IsAutoVacuumWorkerProcess() && params->log_min_duration >= 0)
  	{
  		pg_rusage_init(&ru0);
  		if (params->log_min_duration > 0)
  			starttime = GetCurrentTimestamp();
  	}
  
  	/*
  	 * Determine which columns to analyze
  	 *
  	 * 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.)
  	 */
  	if (va_cols != NIL)
  	{
  		Bitmapset  *unique_cols = NULL;
  		ListCell   *le;
  
  		vacattrstats = (VacAttrStats **) palloc(list_length(va_cols) *
  												sizeof(VacAttrStats *));
  		tcnt = 0;
  		foreach(le, va_cols)
  		{
  			char	   *col = strVal(lfirst(le));
  
  			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);
  
  			vacattrstats[tcnt] = examine_attribute(onerel, i, NULL);
  			if (vacattrstats[tcnt] != NULL)
  				tcnt++;
  		}
  		attr_cnt = tcnt;
  	}
  	else
  	{
  		attr_cnt = onerel->rd_att->natts;
  		vacattrstats = (VacAttrStats **)
  			palloc(attr_cnt * sizeof(VacAttrStats *));
  		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 (!inh)
  		vac_open_indexes(onerel, AccessShareLock, &nindexes, &Irel);
  	else
  	{
  		Irel = NULL;
  		nindexes = 0;
  	}
  	hasindex = (nindexes > 0);
  	indexdata = NULL;
  	if (hasindex)
  	{
  		indexdata = (AnlIndexData *) palloc0(nindexes * sizeof(AnlIndexData));
  		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 = (VacAttrStats **)
  					palloc(indexInfo->ii_NumIndexAttrs * sizeof(VacAttrStats *));
  				tcnt = 0;
  				for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
  				{
  					int			keycol = indexInfo->ii_KeyAttrNumbers[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(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;
  		}
  	}
  
  #ifdef ADB
  	if (IsCnNode())
  		totalrows = reltuples;
  	else
  		totalrows = 0.0;
  #endif
  
  	/*
  	 * Acquire the sample rows
  	 */
  	rows = (HeapTuple *) palloc(targrows * sizeof(HeapTuple));
  	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;
  
  		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->attr->attnum);
  			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;
  			}
  
  			MemoryContextResetAndDeleteChildren(col_context);
  		}
  
  		if (hasindex)
  			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);
  		}
  	}
  
  	/*
  	 * Update pages/tuples stats in pg_class ... but not if we're doing
  	 * inherited stats.
  	 */
  	if (!inh)
  	{
  		BlockNumber relallvisible;
  
  		visibilitymap_count(onerel, &relallvisible, NULL);
  
  		vac_update_relstats(onerel,
  							relpages,
  							totalrows,
  							relallvisible,
  							hasindex,
  							InvalidTransactionId,
  							InvalidMultiXactId,
  							in_outer_xact);
  	}
  
  	/*
  	 * Same for indexes. Vacuum always scans all indexes, so if we're part of
  	 * VACUUM ANALYZE, don't overwrite the accurate count already inserted by
  	 * VACUUM.
  	 */
  	if (!inh && !(options & VACOPT_VACUUM))
  	{
  		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,
  								false,
  								InvalidTransactionId,
  								InvalidMultiXactId,
  								in_outer_xact);
  		}
  	}
  
  	/*
  	 * Report ANALYZE to the stats collector, too.  However, if doing
  	 * inherited stats we shouldn't report, because the stats collector only
  	 * tracks per-table stats.  Reset the changes_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));
  
  	/* If this isn't part of VACUUM ANALYZE, let index AMs do cleanup */
  	if (!(options & VACOPT_VACUUM))
  	{
  		for (ind = 0; ind < nindexes; ind++)
  		{
  			IndexBulkDeleteResult *stats;
  			IndexVacuumInfo ivinfo;
  
  			ivinfo.index = Irel[ind];
  			ivinfo.analyze_only = true;
  			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 (IsAutoVacuumWorkerProcess() && params->log_min_duration >= 0)
  	{
  		if (params->log_min_duration == 0 ||
  			TimestampDifferenceExceeds(starttime, GetCurrentTimestamp(),
  									   params->log_min_duration))
  			ereport(LOG,
  					(errmsg("automatic analyze of table \"%s.%s.%s\" system usage: %s",
  							get_database_name(MyDatabaseId),
  							get_namespace_name(RelationGetNamespace(onerel)),
  							RelationGetRelationName(onerel),
  							pg_rusage_show(&ru0))));
  	}
  
  	/* 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;
  		List	   *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));
  
  		/* Arrange for econtext's scan tuple to be the tuple under test */
  		econtext->ecxt_scantuple = slot;
  
  		/* Set up execution state for predicate. */
  		predicate = (List *)
  			ExecPrepareExpr((Expr *) indexInfo->ii_Predicate,
  							estate);
  
  		/* Compute and save index expression values */
  		exprvals = (Datum *) palloc(numrows * attr_cnt * sizeof(Datum));
  		exprnulls = (bool *) palloc(numrows * attr_cnt * sizeof(bool));
  		numindexrows = 0;
  		tcnt = 0;
  		for (rowno = 0; rowno < numrows; rowno++)
  		{
  			HeapTuple	heapTuple = rows[rowno];
  
  			vacuum_delay_point();
  
  			/*
  			 * 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 */
  			ExecStoreTuple(heapTuple, slot, InvalidBuffer, false);
  
  			/* If index is partial, check predicate */
  			if (predicate != NIL)
  			{
  				if (!ExecQual(predicate, econtext, false))
  					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->attr->attnum;
  
  					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];
  				AttributeOpts *aopt =
  				get_attribute_options(stats->attr->attrelid,
  									  stats->attr->attnum);
  
  				stats->exprvals = exprvals + i;
  				stats->exprnulls = exprnulls + i;
  				stats->rowstride = attr_cnt;
  				(*stats->compute_stats) (stats,
  										 ind_fetch_func,
  										 numindexrows,
  										 totalindexrows);
  
  				/*
  				 * If the n_distinct option is specified, it overrides the
  				 * above computation.  For indices, we always use just
  				 * n_distinct, not n_distinct_inherited.
  				 */
  				if (aopt != NULL && aopt->n_distinct != 0.0)
  					stats->stadistinct = aopt->n_distinct;
  
  				MemoryContextResetAndDeleteChildren(col_context);
  			}
  		}
  
  		/* And clean up */
  		MemoryContextSwitchTo(ind_context);
  
  		ExecDropSingleTupleTableSlot(slot);
  		FreeExecutorState(estate);
  		MemoryContextResetAndDeleteChildren(ind_context);
  	}
  
  	MemoryContextSwitchTo(old_context);
  	MemoryContextDelete(ind_context);
  }
  
  /*
   * 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 = onerel->rd_att->attrs[attnum - 1];
  	HeapTuple	typtuple;
  	VacAttrStats *stats;
  	int			i;
  	bool		ok;
  
  	/* Never analyze dropped columns */
  	if (attr->attisdropped)
  		return NULL;
  
  	/* Don't analyze column if user has specified not to */
  	if (attr->attstattarget == 0)
  		return NULL;
  
  	/*
  	 * Create the VacAttrStats struct.  Note that we only have a copy of the
  	 * fixed fields of the pg_attribute tuple.
  	 */
  	stats = (VacAttrStats *) palloc0(sizeof(VacAttrStats));
  	stats->attr = (Form_pg_attribute) palloc(ATTRIBUTE_FIXED_PART_SIZE);
  	memcpy(stats->attr, attr, ATTRIBUTE_FIXED_PART_SIZE);
  
  	/*
  	 * 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);
  	}
  	else
  	{
  		stats->attrtypid = attr->atttypid;
  		stats->attrtypmod = attr->atttypmod;
  	}
  
  	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->attr);
  		pfree(stats);
  		return NULL;
  	}
  
  	return stats;
  }
  
  /*
   * 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 */
  	BlockNumber totalblocks;
  	TransactionId OldestXmin;
  	BlockSamplerData bs;
  	ReservoirStateData rstate;
  
  	Assert(targrows > 0);
  
  	totalblocks = RelationGetNumberOfBlocks(onerel);
  
  	/* Need a cutoff xmin for HeapTupleSatisfiesVacuum */
  	OldestXmin = GetOldestXmin(onerel, true);
  
  	/* Prepare for sampling block numbers */
  	BlockSampler_Init(&bs, totalblocks, targrows, random());
  	/* Prepare for sampling rows */
  	reservoir_init_selection_state(&rstate, targrows);
  
  	/* Outer loop over blocks to sample */
  	while (BlockSampler_HasMore(&bs))
  	{
  		BlockNumber targblock = BlockSampler_Next(&bs);
  		Buffer		targbuffer;
  		Page		targpage;
  		OffsetNumber targoffset,
  					maxoffset;
  
  		vacuum_delay_point();
  
  		/*
  		 * We must maintain a pin on the target page's buffer to ensure that
  		 * the maxoffset value stays good (else concurrent VACUUM might delete
  		 * tuples out from under us).  Hence, pin the page until we are done
  		 * looking at it.  We also choose to hold sharelock on the buffer
  		 * throughout --- we could release and re-acquire sharelock for each
  		 * tuple, but since we aren't doing much work per tuple, the extra
  		 * lock traffic is probably better avoided.
  		 */
  		targbuffer = ReadBufferExtended(onerel, MAIN_FORKNUM, targblock,
  										RBM_NORMAL, vac_strategy);
  		LockBuffer(targbuffer, BUFFER_LOCK_SHARE);
  		targpage = BufferGetPage(targbuffer);
  		maxoffset = PageGetMaxOffsetNumber(targpage);
  
  		/* Inner loop over all tuples on the selected page */
  		for (targoffset = FirstOffsetNumber; targoffset <= maxoffset; targoffset++)
  		{
  			ItemId		itemid;
  			HeapTupleData targtuple;
  			bool		sample_it = false;
  
  			itemid = PageGetItemId(targpage, targoffset);
  
  			/*
  			 * We ignore unused and redirect line pointers.  DEAD line
  			 * pointers should be counted as dead, because we need vacuum to
  			 * run to get rid of them.  Note that this rule agrees with the
  			 * way that heap_page_prune() counts things.
  			 */
  			if (!ItemIdIsNormal(itemid))
  			{
  				if (ItemIdIsDead(itemid))
  					deadrows += 1;
  				continue;
  			}
  
  			ItemPointerSet(&targtuple.t_self, targblock, targoffset);
  
  			targtuple.t_tableOid = RelationGetRelid(onerel);
  			targtuple.t_data = (HeapTupleHeader) PageGetItem(targpage, itemid);
  			targtuple.t_len = ItemIdGetLength(itemid);
  
  			switch (HeapTupleSatisfiesVacuum(&targtuple,
  											 OldestXmin,
  											 targbuffer))
  			{
  				case HEAPTUPLE_LIVE:
  					sample_it = true;
  					liverows += 1;
  					break;
  
  				case HEAPTUPLE_DEAD:
  				case HEAPTUPLE_RECENTLY_DEAD:
  					/* Count dead and recently-dead rows */
  					deadrows += 1;
  					break;
  
  				case HEAPTUPLE_INSERT_IN_PROGRESS:
  
  					/*
  					 * Insert-in-progress rows are not counted.  We assume
  					 * that when the inserting transaction commits or aborts,
  					 * it will send a stats message to increment the proper
  					 * count.  This works right only if that transaction ends
  					 * after we finish analyzing the table; if things happen
  					 * in the other order, its stats update will be
  					 * overwritten by ours.  However, the error will be large
  					 * only if the other transaction runs long enough to
  					 * insert many tuples, so assuming it will finish after us
  					 * is the safer option.
  					 *
  					 * A special case is that the inserting transaction might
  					 * be our own.  In this case we should count and sample
  					 * the row, to accommodate users who load a table and
  					 * analyze it in one transaction.  (pgstat_report_analyze
  					 * has to adjust the numbers we send to the stats
  					 * collector to make this come out right.)
  					 */
  					if (TransactionIdIsCurrentTransactionId(HeapTupleHeaderGetXmin(targtuple.t_data)))
  					{
  						sample_it = true;
  						liverows += 1;
  					}
  					break;
  
  				case HEAPTUPLE_DELETE_IN_PROGRESS:
  
  					/*
  					 * We count delete-in-progress rows as still live, using
  					 * the same reasoning given above; but we don't bother to
  					 * include them in the sample.
  					 *
  					 * If the delete was done by our own transaction, however,
  					 * we must count the row as dead to make
  					 * pgstat_report_analyze's stats adjustments come out
  					 * right.  (Note: this works out properly when the row was
  					 * both inserted and deleted in our xact.)
  					 */
  					if (TransactionIdIsCurrentTransactionId(HeapTupleHeaderGetUpdateXid(targtuple.t_data)))
  						deadrows += 1;
  					else
  						liverows += 1;
  					break;
  
  				default:
  					elog(ERROR, "unexpected HeapTupleSatisfiesVacuum result");
  					break;
  			}
  
  			if (sample_it)
  			{
  				/*
  				 * 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 below). 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++] = heap_copytuple(&targtuple);
  				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] = heap_copytuple(&targtuple);
  					}
  
  					rowstoskip -= 1;
  				}
  
  				samplerows += 1;
  			}
  		}
  
  		/* Now release the lock and pin on the page */
  		UnlockReleaseBuffer(targbuffer);
  	}
  
  	/*
  	 * 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((void *) rows, numrows, sizeof(HeapTuple), compare_rows);
  
  	/*
  	 * 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;
  }
  
  /*
   * qsort comparator for sorting rows[] array
   */
  static int
  compare_rows(const void *a, const void *b)
  {
  	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;
  
  	/*
  	 * 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 = (Relation *) palloc(list_length(tableOIDs) * sizeof(Relation));
  	acquirefuncs = (AcquireSampleRowsFunc *)
  		palloc(list_length(tableOIDs) * sizeof(AcquireSampleRowsFunc));
  	relblocks = (double *) palloc(list_length(tableOIDs) * sizeof(double));
  	totalblocks = 0;
  	nrels = 0;
  	foreach(lc, tableOIDs)
  	{
  		Oid			childOID = lfirst_oid(lc);
  		Relation	childrel;
  		AcquireSampleRowsFunc acquirefunc = NULL;
  		BlockNumber relpages = 0;
  
  		/* We already got the needed lock */
  		childrel = heap_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);
  			heap_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);
  				heap_close(childrel, AccessShareLock);
  				continue;
  			}
  		}
  		else
  		{
  			/* ignore, but release the lock on it */
  			Assert(childrel != onerel);
  			heap_close(childrel, AccessShareLock);
  			continue;
  		}
  
  		/* OK, we'll process this child */
  		rels[nrels] = childrel;
  		acquirefuncs[nrels] = acquirefunc;
  		relblocks[nrels] = (double) relpages;
  		totalblocks += (double) relpages;
  		nrels++;
  	}
  
  	/*
  	 * If we don't have at least two tables to consider, fail.
  	 */
  	if (nrels < 2)
  	{
  		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.)
  	 */
  	numrows = 0;
  	*totalrows = 0;
  	*totaldeadrows = 0;
  	for (i = 0; i < nrels; i++)
  	{
  		Relation	childrel = rels[i];
  		AcquireSampleRowsFunc acquirefunc = acquirefuncs[i];
  		double		childblocks = relblocks[i];
  
  		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 &&
  					!equalTupleDescs(RelationGetDescr(childrel),
  									 RelationGetDescr(onerel)))
  				{
  					TupleConversionMap *map;
  
  					map = convert_tuples_by_name(RelationGetDescr(childrel),
  												 RelationGetDescr(onerel),
  								 gettext_noop("could not convert row type"));
  					if (map != NULL)
  					{
  						int			j;
  
  						for (j = 0; j < childrows; j++)
  						{
  							HeapTuple	newtup;
  
  							newtup = do_convert_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.
  		 */
  		heap_close(childrel, NoLock);
  	}
  
  	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;
  
  	if (natts <= 0)
  		return;					/* nothing to do */
  
  	sd = heap_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->attr->attnum);
  		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_stanumbers1 - 1;
  		for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
  		{
  			int			nnum = stats->numnumbers[k];
  
  			if (nnum > 0)
  			{
  				Datum	   *numdatums = (Datum *) palloc(nnum * sizeof(Datum));
  				ArrayType  *arry;
  
  				for (n = 0; n < nnum; n++)
  					numdatums[n] = Float4GetDatum(stats->stanumbers[k][n]);
  				/* XXX knows more than it should about type float4: */
  				arry = construct_array(numdatums, nnum,
  									   FLOAT4OID,
  									   sizeof(float4), FLOAT4PASSBYVAL, 'i');
  				values[i++] = PointerGetDatum(arry);	/* stanumbersN */
  			}
  			else
  			{
  				nulls[i] = true;
  				values[i++] = (Datum) 0;
  			}
  		}
  		i = Anum_pg_statistic_stavalues1 - 1;
  		for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
  		{
  			if (stats->numvalues[k] > 0)
  			{
  				ArrayType  *arry;
  
  				arry = construct_array(stats->stavalues[k],
  									   stats->numvalues[k],
  									   stats->statypid[k],
  									   stats->statyplen[k],
  									   stats->statypbyval[k],
  									   stats->statypalign[k]);
  				values[i++] = PointerGetDatum(arry);	/* stavaluesN */
  			}
  			else
  			{
  				nulls[i] = true;
  				values[i++] = (Datum) 0;
  			}
  		}
  
  		/* Is there already a pg_statistic tuple for this attribute? */
  		oldtup = SearchSysCache3(STATRELATTINH,
  								 ObjectIdGetDatum(relid),
  								 Int16GetDatum(stats->attr->attnum),
  								 BoolGetDatum(inh));
  
  		if (HeapTupleIsValid(oldtup))
  		{
  			/* Yes, replace it */
  			stup = heap_modify_tuple(oldtup,
  									 RelationGetDescr(sd),
  									 values,
  									 nulls,
  									 replaces);
  			ReleaseSysCache(oldtup);
  			simple_heap_update(sd, &stup->t_self, stup);
  		}
  		else
  		{
  			/* No, insert new tuple */
  			stup = heap_form_tuple(RelationGetDescr(sd), values, nulls);
  			simple_heap_insert(sd, stup);
  		}
  
  		/* update indexes too */
  		CatalogUpdateIndexes(sd, stup);
  
  		heap_freetuple(stup);
  	}
  
  	heap_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
  {
  	Oid			eqopr;			/* '=' operator for datatype, if any */
  	Oid			eqfunc;			/* and associated function */
  	Oid			ltopr;			/* '<' operator for datatype, if any */
  } StdAnalyzeData;
  
  typedef struct
  {
  	Datum		value;			/* a data value */
  	int			tupno;			/* position index for tuple it came from */
  } ScalarItem;
  
  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);
  
  
  /*
   * std_typanalyze -- the default type-specific typanalyze function
   */
  bool
  std_typanalyze(VacAttrStats *stats)
  {
  	Form_pg_attribute attr = stats->attr;
  	Oid			ltopr;
  	Oid			eqopr;
  	StdAnalyzeData *mystats;
  
  	/* If the attstattarget column is negative, use the default value */
  	/* NB: it is okay to scribble on stats->attr since it's a copy */
  	if (attr->attstattarget < 0)
  		attr->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 = (StdAnalyzeData *) palloc(sizeof(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 * attr->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 * attr->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 * attr->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();
  
  		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->attr->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 = (TrackItem *) palloc(track_max * sizeof(TrackItem));
  	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();
  
  		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++)
  		{
  			/* We always use the default collation for statistics */
  			if (DatumGetBool(FunctionCall2Coll(&f_cmpeq,
  											   DEFAULT_COLLATION_OID,
  											   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 (estimated) average. We set the
  		 * threshold rather arbitrarily at 25% more than average, with at
  		 * least 2 instances in the sample.
  		 *
  		 * 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.  So for an incomplete list, we try to take only MCVs that
  		 * are significantly more common than average.
  		 */
  		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
  		{
  			double		ndistinct_table = stats->stadistinct;
  			double		avgcount,
  						mincount;
  
  			/* Re-extract estimate of # distinct nonnull values in table */
  			if (ndistinct_table < 0)
  				ndistinct_table = -ndistinct_table * totalrows;
  			/* estimate # occurrences in sample of a typical nonnull value */
  			avgcount = (double) nonnull_cnt / ndistinct_table;
  			/* set minimum threshold count to store a value */
  			mincount = avgcount * 1.25;
  			if (mincount < 2)
  				mincount = 2;
  			if (num_mcv > track_cnt)
  				num_mcv = track_cnt;
  			for (i = 0; i < num_mcv; i++)
  			{
  				if (track[i].count < mincount)
  				{
  					num_mcv = i;
  					break;
  				}
  			}
  		}
  
  		/* 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 = (Datum *) palloc(num_mcv * sizeof(Datum));
  			mcv_freqs = (float4 *) palloc(num_mcv * sizeof(float4));
  			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->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->attr->attstattarget;
  	int			num_bins = stats->attr->attstattarget;
  	StdAnalyzeData *mystats = (StdAnalyzeData *) stats->extra_data;
  
  	values = (ScalarItem *) palloc(samplerows * sizeof(ScalarItem));
  	tupnoLink = (int *) palloc(samplerows * sizeof(int));
  	track = (ScalarMCVItem *) palloc(num_mcv * sizeof(ScalarMCVItem));
  
  	memset(&ssup, 0, sizeof(ssup));
  	ssup.ssup_cxt = CurrentMemoryContext;
  	/* We always use the default collation for statistics */
  	ssup.ssup_collation = DEFAULT_COLLATION_OID;
  	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();
  
  		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_arg((void *) values, values_cnt, sizeof(ScalarItem),
  				  compare_scalars, (void *) &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 (estimated) average. We set the
  		 * threshold rather arbitrarily at 25% more than average, with at
  		 * least 2 instances in the sample.  Also, we won't suppress values
  		 * that have a frequency of at least 1/K where K is the intended
  		 * number of histogram bins; such values might otherwise cause us to
  		 * emit duplicate histogram bin boundaries.  (We might end up with
  		 * duplicate histogram entries anyway, if the distribution is skewed;
  		 * but we prefer to treat such values as MCVs if at all possible.)
  		 *
  		 * 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.  So for an incomplete list, we try to take only MCVs that
  		 * are significantly more common than average.
  		 */
  		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
  		{
  			double		ndistinct_table = stats->stadistinct;
  			double		avgcount,
  						mincount,
  						maxmincount;
  
  			/* Re-extract estimate of # distinct nonnull values in table */
  			if (ndistinct_table < 0)
  				ndistinct_table = -ndistinct_table * totalrows;
  			/* estimate # occurrences in sample of a typical nonnull value */
  			avgcount = (double) nonnull_cnt / ndistinct_table;
  			/* set minimum threshold count to store a value */
  			mincount = avgcount * 1.25;
  			if (mincount < 2)
  				mincount = 2;
  			/* don't let threshold exceed 1/K, however */
  			maxmincount = (double) values_cnt / (double) num_bins;
  			if (mincount > maxmincount)
  				mincount = maxmincount;
  			if (num_mcv > track_cnt)
  				num_mcv = track_cnt;
  			for (i = 0; i < num_mcv; i++)
  			{
  				if (track[i].count < mincount)
  				{
  					num_mcv = i;
  					break;
  				}
  			}
  		}
  
  		/* 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 = (Datum *) palloc(num_mcv * sizeof(Datum));
  			mcv_freqs = (float4 *) palloc(num_mcv * sizeof(float4));
  			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->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((void *) track, num_mcv,
  				  sizeof(ScalarMCVItem), compare_mcvs);
  
  			/*
  			 * 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 = (Datum *) palloc(num_hist * sizeof(Datum));
  
  			/*
  			 * 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->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 = (float4 *) palloc(sizeof(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->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 */
  }
  
  /*
   * qsort_arg 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;
  }
  
  /*
   * qsort comparator for sorting ScalarMCVItems by position
   */
  static int
  compare_mcvs(const void *a, const void *b)
  {
  	int			da = ((const ScalarMCVItem *) a)->first;
  	int			db = ((const ScalarMCVItem *) b)->first;
  
  	return da - db;
  }
  