When updating reltuples after ANALYZE, just extrapolate from our sample.

The existing logic for updating pg_class.reltuples trusted the sampling
results only for the pages ANALYZE actually visited, preferring to
believe the previous tuple density estimate for all the unvisited pages.
While there's some rationale for doing that for VACUUM (first that
VACUUM is likely to visit a very nonrandom subset of pages, and second
that we know for sure that the unvisited pages did not change), there's
no such rationale for ANALYZE: by assumption, it's looked at an unbiased
random sample of the table's pages.  Furthermore, in a very large table
ANALYZE will have examined only a tiny fraction of the table's pages,
meaning it cannot slew the overall density estimate very far at all.
In a table that is physically growing, this causes reltuples to increase
nearly proportionally to the change in relpages, regardless of what is
actually happening in the table.  This has been observed to cause reltuples
to become so much larger than reality that it effectively shuts off
autovacuum, whose threshold for doing anything is a fraction of reltuples.
(Getting to the point where that would happen seems to require some
additional, not well understood, conditions.  But it's undeniable that if
reltuples is seriously off in a large table, ANALYZE alone will not fix it
in any reasonable number of iterations, especially not if the table is
continuing to grow.)

Hence, restrict the use of vac_estimate_reltuples() to VACUUM alone,
and in ANALYZE, just extrapolate from the sample pages on the assumption
that they provide an accurate model of the whole table.  If, by very bad
luck, they don't, at least another ANALYZE will fix it; in the old logic
a single bad estimate could cause problems indefinitely.

In HEAD, let's remove vac_estimate_reltuples' is_analyze argument
altogether; it was never used for anything and now it's totally pointless.
But keep it in the back branches, in case any third-party code is calling
this function.

Per bug #15005.  Back-patch to all supported branches.

David Gould, reviewed by Alexander Kuzmenkov, cosmetic changes by me

Discussion: https://postgr.es/m/20180117164916.3fdcf2e9@engels

contrib/pgstattuple/pgstatapprox.c

@@ -184,7 +184,7 @@ statapprox_heap(Relation rel, output_type *stat)
 
 	stat->table_len = (uint64) nblocks * BLCKSZ;
 
-	stat->tuple_count = vac_estimate_reltuples(rel, false, nblocks, scanned,
+	stat->tuple_count = vac_estimate_reltuples(rel, nblocks, scanned,
 											   stat->tuple_count + misc_count);
 
 	/*

src/backend/commands/analyze.c

@@ -1249,19 +1249,22 @@ acquire_sample_rows(Relation onerel, int elevel,
 		qsort((void *) rows, numrows, sizeof(HeapTuple), compare_rows);
 
 	/*
-	 * Estimate total numbers of rows in relation.  For live rows, use
-	 * vac_estimate_reltuples; for dead rows, we have no source of old
-	 * information, so we have to assume the density is the same in unseen
-	 * pages as in the pages we scanned.
+	 * Estimate total numbers of live and dead rows in relation, extrapolating
+	 * on the assumption that the average tuple density in pages we didn't
+	 * scan is the same as in the pages we did scan.  Since what we scanned is
+	 * a random sample of the pages in the relation, this should be a good
+	 * assumption.
 	 */
-	*totalrows = vac_estimate_reltuples(onerel, true,
-										totalblocks,
-										bs.m,
-										liverows);
 	if (bs.m > 0)
+	{
+		*totalrows = floor((liverows / bs.m) * totalblocks + 0.5);
 		*totaldeadrows = floor((deadrows / bs.m) * totalblocks + 0.5);
+	}
 	else
+	{
+		*totalrows = 0.0;
 		*totaldeadrows = 0.0;
+	}
 
 	/*
 	 * Emit some interesting relation info

src/backend/commands/vacuum.c

@@ -766,16 +766,14 @@ vacuum_set_xid_limits(Relation rel,
  * vac_estimate_reltuples() -- estimate the new value for pg_class.reltuples
  *
  *		If we scanned the whole relation then we should just use the count of
- *		live tuples seen; but if we did not, we should not trust the count
- *		unreservedly, especially not in VACUUM, which may have scanned a quite
- *		nonrandom subset of the table.  When we have only partial information,
- *		we take the old value of pg_class.reltuples as a measurement of the
+ *		live tuples seen; but if we did not, we should not blindly extrapolate
+ *		from that number, since VACUUM may have scanned a quite nonrandom
+ *		subset of the table.  When we have only partial information, we take
+ *		the old value of pg_class.reltuples as a measurement of the
  *		tuple density in the unscanned pages.
- *
- *		This routine is shared by VACUUM and ANALYZE.
  */
 double
-vac_estimate_reltuples(Relation relation, bool is_analyze,
+vac_estimate_reltuples(Relation relation,
 					   BlockNumber total_pages,
 					   BlockNumber scanned_pages,
 					   double scanned_tuples)
@@ -783,9 +781,8 @@ vac_estimate_reltuples(Relation relation, bool is_analyze,
 	BlockNumber old_rel_pages = relation->rd_rel->relpages;
 	double		old_rel_tuples = relation->rd_rel->reltuples;
 	double		old_density;
-	double		new_density;
-	double		multiplier;
-	double		updated_density;
+	double		unscanned_pages;
+	double		total_tuples;
 
 	/* If we did scan the whole table, just use the count as-is */
 	if (scanned_pages >= total_pages)
@@ -809,31 +806,14 @@ vac_estimate_reltuples(Relation relation, bool is_analyze,
 
 	/*
 	 * Okay, we've covered the corner cases.  The normal calculation is to
-	 * convert the old measurement to a density (tuples per page), then update
-	 * the density using an exponential-moving-average approach, and finally
-	 * compute reltuples as updated_density * total_pages.
-	 *
-	 * For ANALYZE, the moving average multiplier is just the fraction of the
-	 * table's pages we scanned.  This is equivalent to assuming that the
-	 * tuple density in the unscanned pages didn't change.  Of course, it
-	 * probably did, if the new density measurement is different. But over
-	 * repeated cycles, the value of reltuples will converge towards the
-	 * correct value, if repeated measurements show the same new density.
-	 *
-	 * For VACUUM, the situation is a bit different: we have looked at a
-	 * nonrandom sample of pages, but we know for certain that the pages we
-	 * didn't look at are precisely the ones that haven't changed lately.
-	 * Thus, there is a reasonable argument for doing exactly the same thing
-	 * as for the ANALYZE case, that is use the old density measurement as the
-	 * value for the unscanned pages.
-	 *
-	 * This logic could probably use further refinement.
+	 * convert the old measurement to a density (tuples per page), then
+	 * estimate the number of tuples in the unscanned pages using that figure,
+	 * and finally add on the number of tuples in the scanned pages.
 	 */
 	old_density = old_rel_tuples / old_rel_pages;
-	new_density = scanned_tuples / scanned_pages;
-	multiplier = (double) scanned_pages / (double) total_pages;
-	updated_density = old_density + (new_density - old_density) * multiplier;
-	return floor(updated_density * total_pages + 0.5);
+	unscanned_pages = (double) total_pages - (double) scanned_pages;
+	total_tuples = old_density * unscanned_pages + scanned_tuples;
+	return floor(total_tuples + 0.5);
 }
 
 

src/backend/commands/vacuumlazy.c

@@ -1286,7 +1286,7 @@ lazy_scan_heap(Relation onerel, int options, LVRelStats *vacrelstats,
 	vacrelstats->new_dead_tuples = nkeep;
 
 	/* now we can compute the new value for pg_class.reltuples */
-	vacrelstats->new_rel_tuples = vac_estimate_reltuples(onerel, false,
+	vacrelstats->new_rel_tuples = vac_estimate_reltuples(onerel,
 														 nblocks,
 														 vacrelstats->tupcount_pages,
 														 num_tuples);

src/include/commands/vacuum.h

@@ -162,7 +162,7 @@ extern void vacuum(int options, List *relations, VacuumParams *params,
 extern void vac_open_indexes(Relation relation, LOCKMODE lockmode,
 				 int *nindexes, Relation **Irel);
 extern void vac_close_indexes(int nindexes, Relation *Irel, LOCKMODE lockmode);
-extern double vac_estimate_reltuples(Relation relation, bool is_analyze,
+extern double vac_estimate_reltuples(Relation relation,
 					   BlockNumber total_pages,
 					   BlockNumber scanned_pages,
 					   double scanned_tuples);