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analyze.c

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    Peter Eisentraut authored
    This adds collation support for columns and domains, a COLLATE clause
    to override it per expression, and B-tree index support.
    
    Peter Eisentraut
    reviewed by Pavel Stehule, Itagaki Takahiro, Robert Haas, Noah Misch
    414c5a2e
    History
    analyze.c 79.50 KiB
    /*-------------------------------------------------------------------------
     *
     * analyze.c
     *	  the Postgres statistics generator
     *
     * Portions Copyright (c) 1996-2011, 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/heapam.h"
    #include "access/transam.h"
    #include "access/tupconvert.h"
    #include "access/tuptoaster.h"
    #include "access/xact.h"
    #include "catalog/index.h"
    #include "catalog/indexing.h"
    #include "catalog/namespace.h"
    #include "catalog/pg_inherits_fn.h"
    #include "catalog/pg_namespace.h"
    #include "commands/dbcommands.h"
    #include "commands/vacuum.h"
    #include "executor/executor.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/syscache.h"
    #include "utils/tuplesort.h"
    #include "utils/tqual.h"
    
    
    /* Data structure for Algorithm S from Knuth 3.4.2 */
    typedef struct
    {
    	BlockNumber N;				/* number of blocks, known in advance */
    	int			n;				/* desired sample size */
    	BlockNumber t;				/* current block number */
    	int			m;				/* blocks selected so far */
    } BlockSamplerData;
    
    typedef BlockSamplerData *BlockSampler;
    
    /* 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 int	elevel = -1;
    
    static MemoryContext anl_context = NULL;
    
    static BufferAccessStrategy vac_strategy;
    
    
    static void do_analyze_rel(Relation onerel, VacuumStmt *vacstmt,
    			   bool update_reltuples, bool inh);
    static void BlockSampler_Init(BlockSampler bs, BlockNumber nblocks,
    				  int samplesize);
    static bool BlockSampler_HasMore(BlockSampler bs);
    static BlockNumber BlockSampler_Next(BlockSampler bs);
    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, HeapTuple *rows,
    					int targrows, double *totalrows, double *totaldeadrows);
    static double random_fract(void);
    static double init_selection_state(int n);
    static double get_next_S(double t, int n, double *stateptr);
    static int	compare_rows(const void *a, const void *b);
    static int acquire_inherited_sample_rows(Relation onerel,
    							  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);
    
    static bool std_typanalyze(VacAttrStats *stats);
    
    
    /*
     *	analyze_rel() -- analyze one relation
     *
     * If update_reltuples is true, we update reltuples and relpages columns
     * in pg_class.  Caller should pass false if we're part of VACUUM ANALYZE,
     * and the VACUUM didn't skip any pages.  We only have an approximate count,
     * so we don't want to overwrite the accurate values already inserted by the
     * VACUUM in that case.  VACUUM always scans all indexes, however, so the
     * pg_class entries for indexes are never updated if we're part of VACUUM
     * ANALYZE.
     */
    void
    analyze_rel(Oid relid, VacuumStmt *vacstmt,
    			BufferAccessStrategy bstrategy, bool update_reltuples)
    {
    	Relation	onerel;
    
    	/* Set up static variables */
    	if (vacstmt->options & VACOPT_VERBOSE)
    		elevel = INFO;
    	else
    		elevel = DEBUG2;
    
    	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 (!(vacstmt->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() && Log_autovacuum_min_duration >= 0)
    			ereport(LOG,
    					(errcode(ERRCODE_LOCK_NOT_AVAILABLE),
    					 errmsg("skipping analyze of \"%s\" --- lock not available",
    						vacstmt->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 (!(vacstmt->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;
    	}
    
    	/*
    	 * Check that it's a plain 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)
    	{
    		/* No need for a WARNING if we already complained during VACUUM */
    		if (!(vacstmt->options & VACOPT_VACUUM))
    			ereport(WARNING,
    					(errmsg("skipping \"%s\" --- cannot analyze non-tables or special system tables",
    							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;
    	}
    
    	/*
    	 * OK, let's do it.  First let other backends know I'm in ANALYZE.
    	 */
    	LWLockAcquire(ProcArrayLock, LW_EXCLUSIVE);
    	MyProc->vacuumFlags |= PROC_IN_ANALYZE;
    	LWLockRelease(ProcArrayLock);
    
    	/*
    	 * Do the normal non-recursive ANALYZE.
    	 */
    	do_analyze_rel(onerel, vacstmt, update_reltuples, false);
    
    	/*
    	 * If there are child tables, do recursive ANALYZE.
    	 */
    	if (onerel->rd_rel->relhassubclass)
    		do_analyze_rel(onerel, vacstmt, false, true);
    
    	/*
    	 * 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 PGPROC 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);
    	MyProc->vacuumFlags &= ~PROC_IN_ANALYZE;
    	LWLockRelease(ProcArrayLock);
    }
    
    /*
     *	do_analyze_rel() -- analyze one relation, recursively or not
     */
    static void
    do_analyze_rel(Relation onerel, VacuumStmt *vacstmt,
    			   bool update_reltuples, bool inh)
    {
    	int			attr_cnt,
    				tcnt,
    				i,
    				ind;
    	Relation   *Irel;
    	int			nindexes;
    	bool		hasindex;
    	bool		analyzableindex;
    	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_MINSIZE,
    										ALLOCSET_DEFAULT_INITSIZE,
    										ALLOCSET_DEFAULT_MAXSIZE);
    	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() && Log_autovacuum_min_duration >= 0)
    	{
    		pg_rusage_init(&ru0);
    		if (Log_autovacuum_min_duration > 0)
    			starttime = GetCurrentTimestamp();
    	}
    
    	/*
    	 * Determine which columns to analyze
    	 *
    	 * Note that system attributes are never analyzed.
    	 */
    	if (vacstmt->va_cols != NIL)
    	{
    		ListCell   *le;
    
    		vacattrstats = (VacAttrStats **) palloc(list_length(vacstmt->va_cols) *
    												sizeof(VacAttrStats *));
    		tcnt = 0;
    		foreach(le, vacstmt->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))));
    			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;
    	analyzableindex = false;
    	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 && vacstmt->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++;
    							analyzableindex = true;
    						}
    					}
    				}
    				thisdata->attr_cnt = tcnt;
    			}
    		}
    	}
    
    	/*
    	 * Quit if no analyzable columns and no pg_class update needed.
    	 */
    	if (attr_cnt <= 0 && !analyzableindex && !update_reltuples)
    		goto cleanup;
    
    	/*
    	 * 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.
    	 */
    	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;
    		}
    	}
    
    	/*
    	 * Acquire the sample rows
    	 */
    	rows = (HeapTuple *) palloc(targrows * sizeof(HeapTuple));
    	if (inh)
    		numrows = acquire_inherited_sample_rows(onerel, rows, targrows,
    												&totalrows, &totaldeadrows);
    	else
    		numrows = acquire_sample_rows(onerel, 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_MINSIZE,
    											ALLOCSET_DEFAULT_INITSIZE,
    											ALLOCSET_DEFAULT_MAXSIZE);
    		old_context = MemoryContextSwitchTo(col_context);
    
    		for (i = 0; i < attr_cnt; i++)
    		{
    			VacAttrStats *stats = vacattrstats[i];
    			AttributeOpts *aopt =
    			get_attribute_options(onerel->rd_id, stats->attr->attnum);
    
    			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.
    			 */
    			if (aopt != NULL)
    			{
    				float8		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 inside a VACUUM
    	 * that got a more precise number.
    	 */
    	if (update_reltuples)
    		vac_update_relstats(onerel,
    							RelationGetNumberOfBlocks(onerel),
    							totalrows, hasindex, InvalidTransactionId);
    
    	/*
    	 * 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 (!(vacstmt->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, false, InvalidTransactionId);
    		}
    	}
    
    	/*
    	 * Report ANALYZE to the stats collector, too; likewise, tell it to adopt
    	 * these numbers only if we're not inside a VACUUM that got a better
    	 * number.	However, a call with inh = true shouldn't reset the stats.
    	 */
    	if (!inh)
    		pgstat_report_analyze(onerel, update_reltuples,
    							  totalrows, totaldeadrows);
    
    	/* We skip to here if there were no analyzable columns */
    cleanup:
    
    	/* If this isn't part of VACUUM ANALYZE, let index AMs do cleanup */
    	if (!(vacstmt->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() && Log_autovacuum_min_duration >= 0)
    	{
    		if (Log_autovacuum_min_duration == 0 ||
    			TimestampDifferenceExceeds(starttime, GetCurrentTimestamp(),
    									   Log_autovacuum_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_MINSIZE,
    										ALLOCSET_DEFAULT_INITSIZE,
    										ALLOCSET_DEFAULT_MAXSIZE);
    	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];
    
    			/*
    			 * 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);
    		stats->attrcollation = exprCollation(index_expr);
    	}
    	else
    	{
    		stats->attrtypid = attr->atttypid;
    		stats->attrtypmod = attr->atttypmod;
    		stats->attrcollation = attr->attcollation;
    	}
    
    	typtuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(stats->attrtypid));
    	if (!HeapTupleIsValid(typtuple))
    		elog(ERROR, "cache lookup failed for type %u", stats->attrtypid);
    	stats->attrtype = (Form_pg_type) palloc(sizeof(FormData_pg_type));
    	memcpy(stats->attrtype, GETSTRUCT(typtuple), sizeof(FormData_pg_type));
    	ReleaseSysCache(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)
    	{
    		pfree(stats->attrtype);
    		pfree(stats->attr);
    		pfree(stats);
    		return NULL;
    	}
    
    	return stats;
    }
    
    /*
     * BlockSampler_Init -- prepare for random sampling of blocknumbers
     *
     * BlockSampler is used for stage one of our new two-stage tuple
     * sampling mechanism as discussed on pgsql-hackers 2004-04-02 (subject
     * "Large DB").  It selects a random sample of samplesize blocks out of
     * the nblocks blocks in the table.  If the table has less than
     * samplesize blocks, all blocks are selected.
     *
     * Since we know the total number of blocks in advance, we can use the
     * straightforward Algorithm S from Knuth 3.4.2, rather than Vitter's
     * algorithm.
     */
    static void
    BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, int samplesize)
    {
    	bs->N = nblocks;			/* measured table size */
    
    	/*
    	 * If we decide to reduce samplesize for tables that have less or not much
    	 * more than samplesize blocks, here is the place to do it.
    	 */
    	bs->n = samplesize;
    	bs->t = 0;					/* blocks scanned so far */
    	bs->m = 0;					/* blocks selected so far */
    }
    
    static bool
    BlockSampler_HasMore(BlockSampler bs)
    {
    	return (bs->t < bs->N) && (bs->m < bs->n);
    }
    
    static BlockNumber
    BlockSampler_Next(BlockSampler bs)
    {
    	BlockNumber K = bs->N - bs->t;		/* remaining blocks */
    	int			k = bs->n - bs->m;		/* blocks still to sample */
    	double		p;				/* probability to skip block */
    	double		V;				/* random */
    
    	Assert(BlockSampler_HasMore(bs));	/* hence K > 0 and k > 0 */
    
    	if ((BlockNumber) k >= K)
    	{
    		/* need all the rest */
    		bs->m++;
    		return bs->t++;
    	}
    
    	/*----------
    	 * It is not obvious that this code matches Knuth's Algorithm S.
    	 * Knuth says to skip the current block with probability 1 - k/K.
    	 * If we are to skip, we should advance t (hence decrease K), and
    	 * repeat the same probabilistic test for the next block.  The naive
    	 * implementation thus requires a random_fract() call for each block
    	 * number.	But we can reduce this to one random_fract() call per
    	 * selected block, by noting that each time the while-test succeeds,
    	 * we can reinterpret V as a uniform random number in the range 0 to p.
    	 * Therefore, instead of choosing a new V, we just adjust p to be
    	 * the appropriate fraction of its former value, and our next loop
    	 * makes the appropriate probabilistic test.
    	 *
    	 * We have initially K > k > 0.  If the loop reduces K to equal k,
    	 * the next while-test must fail since p will become exactly zero
    	 * (we assume there will not be roundoff error in the division).
    	 * (Note: Knuth suggests a "<=" loop condition, but we use "<" just
    	 * to be doubly sure about roundoff error.)  Therefore K cannot become
    	 * less than k, which means that we cannot fail to select enough blocks.
    	 *----------
    	 */
    	V = random_fract();
    	p = 1.0 - (double) k / (double) K;
    	while (V < p)
    	{
    		/* skip */
    		bs->t++;
    		K--;					/* keep K == N - t */
    
    		/* adjust p to be new cutoff point in reduced range */
    		p *= 1.0 - (double) k / (double) K;
    	}
    
    	/* select */
    	bs->m++;
    	return bs->t++;
    }
    
    /*
     * 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, 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;
    	double		rstate;
    
    	Assert(targrows > 0);
    
    	totalblocks = RelationGetNumberOfBlocks(onerel);
    
    	/* Need a cutoff xmin for HeapTupleSatisfiesVacuum */
    	OldestXmin = GetOldestXmin(onerel->rd_rel->relisshared, true);
    
    	/* Prepare for sampling block numbers */
    	BlockSampler_Init(&bs, totalblocks, targrows);
    	/* Prepare for sampling rows */
    	rstate = init_selection_state(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_data = (HeapTupleHeader) PageGetItem(targpage, itemid);
    			targtuple.t_len = ItemIdGetLength(itemid);
    
    			switch (HeapTupleSatisfiesVacuum(targtuple.t_data,
    											 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(HeapTupleHeaderGetXmax(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 = get_next_S(samplerows, targrows, &rstate);
    
    					if (rowstoskip <= 0)
    					{
    						/*
    						 * Found a suitable tuple, so save it, replacing one
    						 * old tuple at random
    						 */
    						int			k = (int) (targrows * random_fract());
    
    						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 rows in relation.
    	 */
    	if (bs.m > 0)
    	{
    		*totalrows = floor((liverows * totalblocks) / bs.m + 0.5);
    		*totaldeadrows = floor((deadrows * totalblocks) / bs.m + 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;
    }
    
    /* Select a random value R uniformly distributed in (0 - 1) */
    static double
    random_fract(void)
    {
    	return ((double) random() + 1) / ((double) MAX_RANDOM_VALUE + 2);
    }
    
    /*
     * These two routines embody Algorithm Z from "Random sampling with a
     * reservoir" by Jeffrey S. Vitter, in ACM Trans. Math. Softw. 11, 1
     * (Mar. 1985), Pages 37-57.  Vitter describes his algorithm in terms
     * of the count S of records to skip before processing another record.
     * It is computed primarily based on t, the number of records already read.
     * The only extra state needed between calls is W, a random state variable.
     *
     * init_selection_state computes the initial W value.
     *
     * Given that we've already read t records (t >= n), get_next_S
     * determines the number of records to skip before the next record is
     * processed.
     */
    static double
    init_selection_state(int n)
    {
    	/* Initial value of W (for use when Algorithm Z is first applied) */
    	return exp(-log(random_fract()) / n);
    }
    
    static double
    get_next_S(double t, int n, double *stateptr)
    {
    	double		S;
    
    	/* The magic constant here is T from Vitter's paper */
    	if (t <= (22.0 * n))
    	{
    		/* Process records using Algorithm X until t is large enough */
    		double		V,
    					quot;
    
    		V = random_fract();		/* Generate V */
    		S = 0;
    		t += 1;
    		/* Note: "num" in Vitter's code is always equal to t - n */
    		quot = (t - (double) n) / t;
    		/* Find min S satisfying (4.1) */
    		while (quot > V)
    		{
    			S += 1;
    			t += 1;
    			quot *= (t - (double) n) / t;
    		}
    	}
    	else
    	{
    		/* Now apply Algorithm Z */
    		double		W = *stateptr;
    		double		term = t - (double) n + 1;
    
    		for (;;)
    		{
    			double		numer,
    						numer_lim,
    						denom;
    			double		U,
    						X,
    						lhs,
    						rhs,
    						y,
    						tmp;
    
    			/* Generate U and X */
    			U = random_fract();
    			X = t * (W - 1.0);
    			S = floor(X);		/* S is tentatively set to floor(X) */
    			/* Test if U <= h(S)/cg(X) in the manner of (6.3) */
    			tmp = (t + 1) / term;
    			lhs = exp(log(((U * tmp * tmp) * (term + S)) / (t + X)) / n);
    			rhs = (((t + X) / (term + S)) * term) / t;
    			if (lhs <= rhs)
    			{
    				W = rhs / lhs;
    				break;
    			}
    			/* Test if U <= f(S)/cg(X) */
    			y = (((U * (t + 1)) / term) * (t + S + 1)) / (t + X);
    			if ((double) n < S)
    			{
    				denom = t;
    				numer_lim = term + S;
    			}
    			else
    			{
    				denom = t - (double) n + S;
    				numer_lim = t + 1;
    			}
    			for (numer = t + S; numer >= numer_lim; numer -= 1)
    			{
    				y *= numer / denom;
    				denom -= 1;
    			}
    			W = exp(-log(random_fract()) / n);	/* Generate W in advance */
    			if (exp(log(y) / n) <= (t + X) / t)
    				break;
    		}
    		*stateptr = W;
    	}
    	return S;
    }
    
    /*
     * qsort comparator for sorting rows[] array
     */
    static int
    compare_rows(const void *a, const void *b)
    {
    	HeapTuple	ha = *(HeapTuple *) a;
    	HeapTuple	hb = *(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.
     */
    static int
    acquire_inherited_sample_rows(Relation onerel, HeapTuple *rows, int targrows,
    							  double *totalrows, double *totaldeadrows)
    {
    	List	   *tableOIDs;
    	Relation   *rels;
    	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.
    	 */
    	if (list_length(tableOIDs) < 2)
    	{
    		/*
    		 * XXX It would be desirable to clear relhassubclass here, but we
    		 * don't have adequate lock to do that safely.
    		 */
    		return 0;
    	}
    
    	/*
    	 * Count the blocks in all the relations.  The result could overflow
    	 * BlockNumber, so we use double arithmetic.
    	 */
    	rels = (Relation *) palloc(list_length(tableOIDs) * sizeof(Relation));
    	relblocks = (double *) palloc(list_length(tableOIDs) * sizeof(double));
    	totalblocks = 0;
    	nrels = 0;
    	foreach(lc, tableOIDs)
    	{
    		Oid			childOID = lfirst_oid(lc);
    		Relation	childrel;
    
    		/* 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;
    		}
    
    		rels[nrels] = childrel;
    		relblocks[nrels] = (double) RelationGetNumberOfBlocks(childrel);
    		totalblocks += relblocks[nrels];
    		nrels++;
    	}
    
    	/*
    	 * 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];
    		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 = acquire_sample_rows(childrel,
    												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;
    		}
    
    		i = 0;
    		values[i++] = ObjectIdGetDatum(relid);	/* starelid */
    		values[i++] = Int16GetDatum(stats->attr->attnum);		/* staattnum */
    		values[i++] = BoolGetDatum(inh);		/* stainherit */
    		values[i++] = Float4GetDatum(stats->stanullfrac);		/* stanullfrac */
    		values[i++] = Int32GetDatum(stats->stawidth);	/* stawidth */
    		values[i++] = Float4GetDatum(stats->stadistinct);		/* stadistinct */
    		for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
    		{
    			values[i++] = Int16GetDatum(stats->stakind[k]);		/* stakindN */
    		}
    		for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
    		{
    			values[i++] = ObjectIdGetDatum(stats->staop[k]);	/* staopN */
    		}
    		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;
    			}
    		}
    		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
    {
    	FmgrInfo   *cmpFn;
    	int			cmpFlags;
    	int		   *tupnoLink;
    } CompareScalarsContext;
    
    
    static void compute_minimal_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
     */
    static 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);
    
    	/* If column has no "=" operator, we can't do much of anything */
    	if (!OidIsValid(eqopr))
    		return false;
    
    	/* Save the operator info for compute_stats routines */
    	mystats = (StdAnalyzeData *) palloc(sizeof(StdAnalyzeData));
    	mystats->eqopr = eqopr;
    	mystats->eqfunc = get_opcode(eqopr);
    	mystats->ltopr = ltopr;
    	stats->extra_data = mystats;
    
    	/*
    	 * Determine which standard statistics algorithm to use
    	 */
    	if (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
    	{
    		/* Can't do much but the minimal stuff */
    		stats->compute_stats = compute_minimal_stats;
    		/* Might as well use the same minrows as above */
    		stats->minrows = 300 * attr->attstattarget;
    	}
    
    	return true;
    }
    
    /*
     *	compute_minimal_stats() -- compute minimal column statistics
     *
     *	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_minimal_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);
    	fmgr_info_collation(stats->attrcollation, &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++)
    		{
    			if (DatumGetBool(FunctionCall2(&f_cmpeq, 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 values, assume it's a unique column */
    			stats->stadistinct = -1.0;
    		}
    		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.
    			 */
    			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.
    			 *
    			 * 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		numer,
    						denom,
    						stadistinct;
    
    			numer = (double) samplerows *(double) d;
    
    			denom = (double) (samplerows - f1) +
    				(double) f1 *(double) samplerows / totalrows;
    
    			stadistinct = numer / denom;
    			/* Clamp to sane range in case of roundoff error */
    			if (stadistinct < (double) d)
    				stadistinct = (double) d;
    			if (stadistinct > totalrows)
    				stadistinct = totalrows;
    			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.
    		 */
    		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 = stats->stadistinct;
    			double		avgcount,
    						mincount;
    
    			if (ndistinct < 0)
    				ndistinct = -ndistinct * totalrows;
    			/* estimate # of occurrences in sample of a typical value */
    			avgcount = (double) samplerows / ndistinct;
    			/* 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;
    	Oid			cmpFn;
    	int			cmpFlags;
    	FmgrInfo	f_cmpfn;
    	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));
    
    	SelectSortFunction(mystats->ltopr, false, &cmpFn, &cmpFlags);
    	fmgr_info(cmpFn, &f_cmpfn);
    	fmgr_info_collation(stats->attrcollation, &f_cmpfn);
    
    	/* 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.cmpFn = &f_cmpfn;
    		cxt.cmpFlags = cmpFlags;
    		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 values, assume it's a unique column */
    			stats->stadistinct = -1.0;
    		}
    		else if (toowide_cnt == 0 && nmultiple == ndistinct)
    		{
    			/*
    			 * Every value in the sample appeared more than once.  Assume the
    			 * column has just these values.
    			 */
    			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.
    			 *
    			 * Overwidth values are assumed to have been distinct.
    			 *----------
    			 */
    			int			f1 = ndistinct - nmultiple + toowide_cnt;
    			int			d = f1 + nmultiple;
    			double		numer,
    						denom,
    						stadistinct;
    
    			numer = (double) samplerows *(double) d;
    
    			denom = (double) (samplerows - f1) +
    				(double) f1 *(double) samplerows / totalrows;
    
    			stadistinct = numer / denom;
    			/* Clamp to sane range in case of roundoff error */
    			if (stadistinct < (double) d)
    				stadistinct = (double) d;
    			if (stadistinct > totalrows)
    				stadistinct = totalrows;
    			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.)
    		 */
    		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 = stats->stadistinct;
    			double		avgcount,
    						mincount,
    						maxmincount;
    
    			if (ndistinct < 0)
    				ndistinct = -ndistinct * totalrows;
    			/* estimate # of occurrences in sample of a typical value */
    			avgcount = (double) samplerows / ndistinct;
    			/* 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) samplerows / (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 && 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 = ((ScalarItem *) a)->value;
    	int			ta = ((ScalarItem *) a)->tupno;
    	Datum		db = ((ScalarItem *) b)->value;
    	int			tb = ((ScalarItem *) b)->tupno;
    	CompareScalarsContext *cxt = (CompareScalarsContext *) arg;
    	int32		compare;
    
    	compare = ApplySortFunction(cxt->cmpFn, cxt->cmpFlags,
    								da, false, db, false);
    	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 = ((ScalarMCVItem *) a)->first;
    	int			db = ((ScalarMCVItem *) b)->first;
    
    	return da - db;
    }