Use extended statistics for precise estimation of bucket size in hash join.

Recognizing the real-life complexity where columns in the table often have
functional dependencies, PostgreSQL's estimation of the number of distinct
values over a set of columns can be underestimated (or much rarely,
overestimated) when dealing with multi-clause JOIN.
In the case of hash join, it can end up with a small number of predicted hash
buckets and, as a result, picking non-optimal merge join.

To improve the situation, we introduce one additional stage of bucket size
estimation - having two or more join clauses estimator lookup for extended
statistics and use it for multicolumn estimation.
Clauses are grouped into lists, each containing expressions referencing the
same relation. The result of the multicolumn estimation made over such a list
is combined with others according to the caller's logic.
Clauses that are not estimated are returned to the caller for further
estimation.

Author: danolivo

src/backend/optimizer/path/costsize.c

@@ -4250,9 +4250,19 @@ final_cost_hashjoin(PlannerInfo *root, HashPath *path,
 	}
 	else
 	{
+		List *otherclauses;
+
 		innerbucketsize = 1.0;
 		innermcvfreq = 1.0;
-		foreach(hcl, hashclauses)
+
+		/* At first, try to estimate bucket size using extended statistics. */
+		otherclauses = estimate_multivariate_bucketsize(root,
+														inner_path->parent,
+														hashclauses,
+														&innerbucketsize);
+
+		/* Pass through the remaining clauses */
+		foreach(hcl, otherclauses)
 		{
 			RestrictInfo *restrictinfo = lfirst_node(RestrictInfo, hcl);
 			Selectivity thisbucketsize;

src/backend/utils/adt/selfuncs.c

@@ -3751,6 +3751,177 @@ estimate_num_groups(PlannerInfo *root, List *groupExprs, double input_rows,
 	return numdistinct;
 }
 
+/*
+ * Try to estimate the bucket size of the hash join inner side when the join
+ * condition contains two or more clauses by employing extended statistics.
+ *
+ * The main idea of this approach is that the distinct value generated by
+ * multivariate estimation on two or more columns would provide less bucket size
+ * than estimation on one separate column.
+ *
+ * IMPORTANT: It is crucial to synchronise the approach of combining different
+ * estimations with the caller's method.
+ * Return a list of clauses that didn't fetch any extended statistics.
+ */
+List *
+estimate_multivariate_bucketsize(PlannerInfo *root, RelOptInfo *inner,
+								 List *hashclauses,
+								 Selectivity *innerbucketsize)
+{
+	List   *clauses = list_copy(hashclauses);
+	List   *otherclauses = NIL;
+	double	ndistinct = 1.0;
+
+	if (list_length(hashclauses) <= 1)
+		/*
+		 * Nothing to do for a single clause. Could we employ univariate
+		 * extended stat here?
+		 */
+		return hashclauses;
+
+	while (clauses != NIL)
+	{
+		ListCell   *lc;
+		int			relid = -1;
+		List	   *varinfos = NIL;
+		List	   *saveList = NIL;
+		double		mvndistinct;
+		List	   *origin_varinfos;
+		int			group_relid = -1;
+		RelOptInfo *group_rel;
+		ListCell   *lc1, *lc2;
+
+		/*
+		 * Find clauses, referencing the same single base relation and try to
+		 * estimate such a group with extended statistics.
+		 * Create varinfo for an approved clause, push it to otherclauses, if it
+		 * can't be estimated here or ignore to process at the next iteration.
+		 */
+		foreach(lc, clauses)
+		{
+			RestrictInfo   *rinfo = lfirst_node(RestrictInfo, lc);
+			Node		   *expr;
+			Relids			relids;
+			GroupVarInfo   *varinfo;
+
+			/*
+			 * Find the inner side of the join which we need to estimate the
+			 * number of buckets. Use outer_is_left because the
+			 * clause_sides_match_join routine has called on hash clauses.
+			 */
+			relids = rinfo->outer_is_left ?
+						rinfo->right_relids : rinfo->left_relids;
+			expr = rinfo->outer_is_left ?
+						get_rightop(rinfo->clause) : get_leftop(rinfo->clause);
+
+			if (bms_get_singleton_member(relids, &relid) &&
+				root->simple_rel_array[relid]->statlist != NIL)
+			{
+				/*
+				 * This inner-side expression references only one relation.
+				 * Extended statistics on this clause can exist.
+				 */
+
+				if (group_relid < 0)
+				{
+					RangeTblEntry *rte = root->simple_rte_array[relid];
+
+					if (!rte || (rte->relkind != RELKIND_RELATION &&
+						rte->relkind != RELKIND_MATVIEW &&
+						rte->relkind != RELKIND_FOREIGN_TABLE &&
+						rte->relkind != RELKIND_PARTITIONED_TABLE))
+					{
+						/* Extended statistics can't exist in principle */
+						otherclauses = lappend(otherclauses, rinfo);
+						clauses = foreach_delete_current(clauses, lc);
+						continue;
+					}
+
+					group_relid = relid;
+					group_rel = root->simple_rel_array[relid];
+					Assert(group_rel != NULL);
+				}
+				else if (group_relid != relid)
+					/*
+					 * Being in the group forming state we don't
+					 * need other clauses.
+					 */
+					continue;
+
+				varinfo = (GroupVarInfo *) palloc(sizeof(GroupVarInfo));
+				varinfo->var = expr;
+				varinfo->rel = root->simple_rel_array[relid];
+				varinfo->ndistinct = 0.0;
+				varinfo->isdefault = false;
+				varinfos = lappend(varinfos, varinfo);
+
+				/*
+				 * Remember the link to RestrictInfo for the case the clause is
+				 * failed to be estimated.
+				 */
+				saveList = lappend(saveList, rinfo);
+			}
+			else
+				/* This clause can't be estimated with extended statistics */
+				otherclauses = lappend(otherclauses, rinfo);
+
+			clauses = foreach_delete_current(clauses, lc);
+		}
+
+		if (list_length(varinfos) < 2)
+		{
+			/*
+			 * Multivariate statistics doesn't apply to single column except
+			 * expressions, but it has not implemented yet.
+			 */
+			otherclauses = list_concat(otherclauses, saveList);
+			list_free_deep(varinfos);
+			list_free(saveList);
+			continue;
+		}
+
+		/* Let's employ extended statistics. */
+		origin_varinfos = varinfos;
+		for (;;)
+		{
+			bool	estimated = estimate_multivariate_ndistinct(root,
+																group_rel,
+																&varinfos,
+																&mvndistinct);
+			if (!estimated)
+				break;
+
+			/*
+			 * We've got an estimation. Use ndistinct value in consistent way -
+			 * according to the caller's logic (see final_cost_hashjoin).
+			 */
+			if (ndistinct < mvndistinct)
+				ndistinct = mvndistinct;
+			Assert(ndistinct >= 1.0);
+		}
+
+		Assert(list_length(origin_varinfos) == list_length(saveList));
+
+		/*
+		 * Remove already estimated clauses from the saveList
+		 */
+		forboth(lc1, origin_varinfos, lc2, saveList)
+		{
+			GroupVarInfo *vinfo = lfirst(lc1);
+
+			if (!list_member_ptr(varinfos, vinfo))
+				/* Already estimated */
+				continue;
+
+			/* Can't be estimated here - push to the returning list */
+			otherclauses = lappend(otherclauses, lfirst(lc2));
+		}
+	}
+
+	*innerbucketsize = 1.0 / ndistinct;
+	return otherclauses;
+}
+
 /*
  * Estimate hash bucket statistics when the specified expression is used
  * as a hash key for the given number of buckets.

src/include/utils/selfuncs.h

@@ -217,6 +217,10 @@ extern double estimate_num_groups(PlannerInfo *root, List *groupExprs,
 								  double input_rows, List **pgset,
 								  EstimationInfo *estinfo);
 
+extern List *estimate_multivariate_bucketsize(PlannerInfo *root,
+											  RelOptInfo *inner,
+											  List *hashclauses,
+											  Selectivity *innerbucketsize);
 extern void estimate_hash_bucket_stats(PlannerInfo *root,
 									   Node *hashkey, double nbuckets,
 									   Selectivity *mcv_freq,