From f302c867126d1b29c0e2a5c1562c0d9a63cef55d Mon Sep 17 00:00:00 2001
From: David Rowley <dgrowley@gmail.com>
Date: Sun, 4 Dec 2022 11:09:21 +1300
Subject: [PATCH v18 2/5] Add Bitmapset indexes for faster lookup of
 EquivalenceMembers

For queries containing a large number of joins or for queries to
partitioned tables, the looking up of EquivalenceMembers in an
EquivalenceClass can become slow due to the large number of members.
Until now, the searching for EquivalenceMembers has been done using a
linear search over the EquivalenceClass's list of members. Here we
effectively add an index to allow faster lookups of these members.  This
is done by way of adding all members to all classes into a List in
PlannerInfo, then we have a Bitmapset in each EquivalenceClass with
members for each index in PlannerInfo's list which belong to this class.
Additionally, each RelOptInfo also maintains another Bitmapset which
stores each index in PlannerInfo's list of EquivalenceMember for all
members, in all classes, which mention this relation.  This allows us to
quickly find all EquivalenceMembers for a given RelOptInfo and a given
EquivalenceClass by intersecting these two lists.

When searching for members belonging to join rels, we must either
intersect or union all base RelOptInfo's member indexes then intersect the
result to the EquivalenceClass's indexes.  Whether we intersect or union
depends on if we need members that mention all relations or members that
mention any of the base relations making up the join relation.

This method of indexing can significantly speed up the planner when
querying a partitioned table with a large number of partitions when the
query contains a few joins.  Tests have shown around a x10 increase in
performance with 1000 partitions.
---
 contrib/postgres_fdw/postgres_fdw.c       |   50 +-
 src/backend/nodes/list.c                  |   16 +
 src/backend/nodes/outfuncs.c              |    7 +-
 src/backend/optimizer/path/costsize.c     |    3 +-
 src/backend/optimizer/path/equivclass.c   | 1173 +++++++++++++++++----
 src/backend/optimizer/path/indxpath.c     |   22 +-
 src/backend/optimizer/path/pathkeys.c     |   26 +-
 src/backend/optimizer/plan/createplan.c   |   66 +-
 src/backend/optimizer/plan/planagg.c      |    1 +
 src/backend/optimizer/plan/planner.c      |    3 +
 src/backend/optimizer/prep/prepjointree.c |    3 +
 src/backend/optimizer/prep/prepunion.c    |   25 +-
 src/backend/optimizer/util/relnode.c      |    9 +
 src/include/nodes/pathnodes.h             |   81 +-
 src/include/nodes/pg_list.h               |    1 +
 src/include/optimizer/paths.h             |   67 +-
 src/tools/pgindent/typedefs.list          |    1 +
 17 files changed, 1285 insertions(+), 269 deletions(-)

diff --git a/contrib/postgres_fdw/postgres_fdw.c b/contrib/postgres_fdw/postgres_fdw.c
index f5926ab89d..8c48b7e479 100644
--- a/contrib/postgres_fdw/postgres_fdw.c
+++ b/contrib/postgres_fdw/postgres_fdw.c
@@ -7617,6 +7617,10 @@ conversion_error_callback(void *arg)
 				varno = var->varno;
 				colno = var->varattno;
 			}
+			/*
+			 * XXX why don't we break here? Surely there can't be another
+			 * equal EquivalenceMember?
+			 */
 		}
 
 		if (varno > 0)
@@ -7675,23 +7679,27 @@ conversion_error_callback(void *arg)
 EquivalenceMember *
 find_em_for_rel(PlannerInfo *root, EquivalenceClass *ec, RelOptInfo *rel)
 {
-	ListCell   *lc;
+	EquivalenceMemberIterator iter;
+	EquivalenceMember *em;
 
-	foreach(lc, ec->ec_members)
-	{
-		EquivalenceMember *em = (EquivalenceMember *) lfirst(lc);
+	setup_eclass_member_iterator(&iter, root, ec, rel->relids, true, false);
 
+	while ((em = eclass_member_iterator_next(&iter)) != NULL)
+	{
 		/*
 		 * Note we require !bms_is_empty, else we'd accept constant
 		 * expressions which are not suitable for the purpose.
 		 */
+		Assert(!bms_is_empty(em->em_relids));
+
 		if (bms_is_subset(em->em_relids, rel->relids) &&
-			!bms_is_empty(em->em_relids) &&
 			is_foreign_expr(root, rel, em->em_expr))
-			return em;
+			break;
 	}
 
-	return NULL;
+	eclass_member_iterator_dispose(&iter);
+
+	return em;
 }
 
 /*
@@ -7718,7 +7726,9 @@ find_em_for_rel_target(PlannerInfo *root, EquivalenceClass *ec,
 	{
 		Expr	   *expr = (Expr *) lfirst(lc1);
 		Index		sgref = get_pathtarget_sortgroupref(target, i);
-		ListCell   *lc2;
+		EquivalenceMemberIterator iter;
+		EquivalenceMember *em;
+		Relids		expr_relids;
 
 		/* Ignore non-sort expressions */
 		if (sgref == 0 ||
@@ -7733,19 +7743,20 @@ find_em_for_rel_target(PlannerInfo *root, EquivalenceClass *ec,
 		while (expr && IsA(expr, RelabelType))
 			expr = ((RelabelType *) expr)->arg;
 
+		expr_relids = pull_varnos(root, (Node *) expr);
+		setup_eclass_member_strict_iterator(&iter, root, ec, expr_relids,
+											false, false);
+
 		/* Locate an EquivalenceClass member matching this expr, if any */
-		foreach(lc2, ec->ec_members)
+		while ((em = eclass_member_iterator_strict_next(&iter)) != NULL)
 		{
-			EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
 			Expr	   *em_expr;
 
-			/* Don't match constants */
-			if (em->em_is_const)
-				continue;
+			/* don't expect constants */
+			Assert(!em->em_is_const);
 
-			/* Ignore child members */
-			if (em->em_is_child)
-				continue;
+			/* don't expect child members */
+			Assert(!em->em_is_child);
 
 			/* Match if same expression (after stripping relabel) */
 			em_expr = em->em_expr;
@@ -7757,10 +7768,15 @@ find_em_for_rel_target(PlannerInfo *root, EquivalenceClass *ec,
 
 			/* Check that expression (including relabels!) is shippable */
 			if (is_foreign_expr(root, rel, em->em_expr))
+			{
+				bms_free(expr_relids);
+				eclass_member_iterator_dispose(&iter);
 				return em;
+			}
 		}
-
 		i++;
+		bms_free(expr_relids);
+		eclass_member_iterator_dispose(&iter);
 	}
 
 	return NULL;
diff --git a/src/backend/nodes/list.c b/src/backend/nodes/list.c
index a709d23ef1..b8972bbe5a 100644
--- a/src/backend/nodes/list.c
+++ b/src/backend/nodes/list.c
@@ -1683,6 +1683,22 @@ list_sort(List *list, list_sort_comparator cmp)
 		qsort(list->elements, len, sizeof(ListCell), (qsort_comparator) cmp);
 }
 
+/*
+ * list_sort comparator for sorting a list into ascending ptr order.
+ */
+int
+list_ptr_cmp(const ListCell *p1, const ListCell *p2)
+{
+	void	   *v1 = lfirst(p1);
+	void	   *v2 = lfirst(p2);
+
+	if (v1 < v2)
+		return -1;
+	if (v1 > v2)
+		return 1;
+	return 0;
+}
+
 /*
  * list_sort comparator for sorting a list into ascending int order.
  */
diff --git a/src/backend/nodes/outfuncs.c b/src/backend/nodes/outfuncs.c
index ba00b99249..416c972b4e 100644
--- a/src/backend/nodes/outfuncs.c
+++ b/src/backend/nodes/outfuncs.c
@@ -463,8 +463,11 @@ _outEquivalenceClass(StringInfo str, const EquivalenceClass *node)
 	WRITE_NODE_FIELD(ec_opfamilies);
 	WRITE_OID_FIELD(ec_collation);
 	WRITE_NODE_FIELD(ec_members);
-	WRITE_NODE_FIELD(ec_sources);
-	WRITE_NODE_FIELD(ec_derives);
+	WRITE_BITMAPSET_FIELD(ec_member_indexes);
+	WRITE_BITMAPSET_FIELD(ec_nonchild_indexes);
+	WRITE_BITMAPSET_FIELD(ec_norel_indexes);
+	WRITE_BITMAPSET_FIELD(ec_source_indexes);
+	WRITE_BITMAPSET_FIELD(ec_derive_indexes);
 	WRITE_BITMAPSET_FIELD(ec_relids);
 	WRITE_BOOL_FIELD(ec_has_const);
 	WRITE_BOOL_FIELD(ec_has_volatile);
diff --git a/src/backend/optimizer/path/costsize.c b/src/backend/optimizer/path/costsize.c
index 7918bb6f0d..361de60cb5 100644
--- a/src/backend/optimizer/path/costsize.c
+++ b/src/backend/optimizer/path/costsize.c
@@ -5507,7 +5507,8 @@ get_foreign_key_join_selectivity(PlannerInfo *root,
 				if (ec && ec->ec_has_const)
 				{
 					EquivalenceMember *em = fkinfo->fk_eclass_member[i];
-					RestrictInfo *rinfo = find_derived_clause_for_ec_member(ec,
+					RestrictInfo *rinfo = find_derived_clause_for_ec_member(root,
+																			ec,
 																			em);
 
 					if (rinfo)
diff --git a/src/backend/optimizer/path/equivclass.c b/src/backend/optimizer/path/equivclass.c
index 9949d5b1d3..9205e4093f 100644
--- a/src/backend/optimizer/path/equivclass.c
+++ b/src/backend/optimizer/path/equivclass.c
@@ -32,8 +32,12 @@
 #include "rewrite/rewriteManip.h"
 #include "utils/lsyscache.h"
 
-
-static EquivalenceMember *add_eq_member(EquivalenceClass *ec,
+static void add_eq_source(PlannerInfo *root, EquivalenceClass *ec,
+						  RestrictInfo *rinfo);
+static void add_eq_derive(PlannerInfo *root, EquivalenceClass *ec,
+						  RestrictInfo *rinfo);
+static EquivalenceMember *add_eq_member(PlannerInfo *root,
+										EquivalenceClass *ec,
 										Expr *expr, Relids relids,
 										JoinDomain *jdomain,
 										EquivalenceMember *parent,
@@ -308,7 +312,6 @@ process_equivalence(PlannerInfo *root,
 		/* If case 1, nothing to do, except add to sources */
 		if (ec1 == ec2)
 		{
-			ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
 			ec1->ec_min_security = Min(ec1->ec_min_security,
 									   restrictinfo->security_level);
 			ec1->ec_max_security = Max(ec1->ec_max_security,
@@ -319,6 +322,8 @@ process_equivalence(PlannerInfo *root,
 			/* mark the RI as usable with this pair of EMs */
 			restrictinfo->left_em = em1;
 			restrictinfo->right_em = em2;
+
+			add_eq_source(root, ec1, restrictinfo);
 			return true;
 		}
 
@@ -339,8 +344,16 @@ process_equivalence(PlannerInfo *root,
 		 * be found.
 		 */
 		ec1->ec_members = list_concat(ec1->ec_members, ec2->ec_members);
-		ec1->ec_sources = list_concat(ec1->ec_sources, ec2->ec_sources);
-		ec1->ec_derives = list_concat(ec1->ec_derives, ec2->ec_derives);
+		ec1->ec_member_indexes = bms_add_members(ec1->ec_member_indexes,
+												 ec2->ec_member_indexes);
+		ec1->ec_nonchild_indexes = bms_add_members(ec1->ec_nonchild_indexes,
+												   ec2->ec_nonchild_indexes);
+		ec1->ec_norel_indexes = bms_add_members(ec1->ec_norel_indexes,
+												ec2->ec_norel_indexes);
+		ec1->ec_source_indexes = bms_join(ec1->ec_source_indexes,
+										  ec2->ec_source_indexes);
+		ec1->ec_derive_indexes = bms_join(ec1->ec_derive_indexes,
+										  ec2->ec_derive_indexes);
 		ec1->ec_relids = bms_join(ec1->ec_relids, ec2->ec_relids);
 		ec1->ec_has_const |= ec2->ec_has_const;
 		/* can't need to set has_volatile */
@@ -352,10 +365,12 @@ process_equivalence(PlannerInfo *root,
 		root->eq_classes = list_delete_nth_cell(root->eq_classes, ec2_idx);
 		/* just to avoid debugging confusion w/ dangling pointers: */
 		ec2->ec_members = NIL;
-		ec2->ec_sources = NIL;
-		ec2->ec_derives = NIL;
+		ec2->ec_member_indexes = NULL;
+		ec2->ec_nonchild_indexes = NULL;
+		ec2->ec_norel_indexes = NULL;
+		ec2->ec_source_indexes = NULL;
+		ec2->ec_derive_indexes = NULL;
 		ec2->ec_relids = NULL;
-		ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
 		ec1->ec_min_security = Min(ec1->ec_min_security,
 								   restrictinfo->security_level);
 		ec1->ec_max_security = Max(ec1->ec_max_security,
@@ -366,13 +381,14 @@ process_equivalence(PlannerInfo *root,
 		/* mark the RI as usable with this pair of EMs */
 		restrictinfo->left_em = em1;
 		restrictinfo->right_em = em2;
+
+		add_eq_source(root, ec1, restrictinfo);
 	}
 	else if (ec1)
 	{
 		/* Case 3: add item2 to ec1 */
-		em2 = add_eq_member(ec1, item2, item2_relids,
+		em2 = add_eq_member(root, ec1, item2, item2_relids,
 							jdomain, NULL, item2_type);
-		ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
 		ec1->ec_min_security = Min(ec1->ec_min_security,
 								   restrictinfo->security_level);
 		ec1->ec_max_security = Max(ec1->ec_max_security,
@@ -383,13 +399,14 @@ process_equivalence(PlannerInfo *root,
 		/* mark the RI as usable with this pair of EMs */
 		restrictinfo->left_em = em1;
 		restrictinfo->right_em = em2;
+
+		add_eq_source(root, ec1, restrictinfo);
 	}
 	else if (ec2)
 	{
 		/* Case 3: add item1 to ec2 */
-		em1 = add_eq_member(ec2, item1, item1_relids,
+		em1 = add_eq_member(root, ec2, item1, item1_relids,
 							jdomain, NULL, item1_type);
-		ec2->ec_sources = lappend(ec2->ec_sources, restrictinfo);
 		ec2->ec_min_security = Min(ec2->ec_min_security,
 								   restrictinfo->security_level);
 		ec2->ec_max_security = Max(ec2->ec_max_security,
@@ -400,6 +417,8 @@ process_equivalence(PlannerInfo *root,
 		/* mark the RI as usable with this pair of EMs */
 		restrictinfo->left_em = em1;
 		restrictinfo->right_em = em2;
+
+		add_eq_source(root, ec2, restrictinfo);
 	}
 	else
 	{
@@ -409,8 +428,11 @@ process_equivalence(PlannerInfo *root,
 		ec->ec_opfamilies = opfamilies;
 		ec->ec_collation = collation;
 		ec->ec_members = NIL;
-		ec->ec_sources = list_make1(restrictinfo);
-		ec->ec_derives = NIL;
+		ec->ec_member_indexes = NULL;
+		ec->ec_nonchild_indexes = NULL;
+		ec->ec_norel_indexes = NULL;
+		ec->ec_source_indexes = NULL;
+		ec->ec_derive_indexes = NULL;
 		ec->ec_relids = NULL;
 		ec->ec_has_const = false;
 		ec->ec_has_volatile = false;
@@ -419,9 +441,9 @@ process_equivalence(PlannerInfo *root,
 		ec->ec_min_security = restrictinfo->security_level;
 		ec->ec_max_security = restrictinfo->security_level;
 		ec->ec_merged = NULL;
-		em1 = add_eq_member(ec, item1, item1_relids,
+		em1 = add_eq_member(root, ec, item1, item1_relids,
 							jdomain, NULL, item1_type);
-		em2 = add_eq_member(ec, item2, item2_relids,
+		em2 = add_eq_member(root, ec, item2, item2_relids,
 							jdomain, NULL, item2_type);
 
 		root->eq_classes = lappend(root->eq_classes, ec);
@@ -432,6 +454,8 @@ process_equivalence(PlannerInfo *root,
 		/* mark the RI as usable with this pair of EMs */
 		restrictinfo->left_em = em1;
 		restrictinfo->right_em = em2;
+
+		add_eq_source(root, ec, restrictinfo);
 	}
 
 	return true;
@@ -507,14 +531,61 @@ canonicalize_ec_expression(Expr *expr, Oid req_type, Oid req_collation)
 	return expr;
 }
 
+/*
+ * add_eq_source - add 'rinfo' in eq_sources for this 'ec'
+ */
+static void
+add_eq_source(PlannerInfo *root, EquivalenceClass *ec, RestrictInfo *rinfo)
+{
+	int			source_idx = list_length(root->eq_sources);
+	int			i;
+
+	ec->ec_source_indexes = bms_add_member(ec->ec_source_indexes, source_idx);
+	root->eq_sources = lappend(root->eq_sources, rinfo);
+
+	i = -1;
+	while ((i = bms_next_member(rinfo->clause_relids, i)) >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		rel->eclass_source_indexes = bms_add_member(rel->eclass_source_indexes,
+													source_idx);
+	}
+}
+
+/*
+ * add_eq_derive - add 'rinfo' in eq_derives for this 'ec'
+ */
+static void
+add_eq_derive(PlannerInfo *root, EquivalenceClass *ec, RestrictInfo *rinfo)
+{
+	int			derive_idx = list_length(root->eq_derives);
+	int			i;
+
+	ec->ec_derive_indexes = bms_add_member(ec->ec_derive_indexes, derive_idx);
+	root->eq_derives = lappend(root->eq_derives, rinfo);
+
+	i = -1;
+	while ((i = bms_next_member(rinfo->clause_relids, i)) >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		rel->eclass_derive_indexes = bms_add_member(rel->eclass_derive_indexes,
+													derive_idx);
+	}
+}
+
 /*
  * add_eq_member - build a new EquivalenceMember and add it to an EC
  */
 static EquivalenceMember *
-add_eq_member(EquivalenceClass *ec, Expr *expr, Relids relids,
+add_eq_member(PlannerInfo *root, EquivalenceClass *ec, Expr *expr, Relids relids,
 			  JoinDomain *jdomain, EquivalenceMember *parent, Oid datatype)
 {
 	EquivalenceMember *em = makeNode(EquivalenceMember);
+	Relids		expr_relids;
+	int			em_index = list_length(root->eq_members);
+	int			i;
 
 	em->em_expr = expr;
 	em->em_relids = relids;
@@ -524,6 +595,23 @@ add_eq_member(EquivalenceClass *ec, Expr *expr, Relids relids,
 	em->em_jdomain = jdomain;
 	em->em_parent = parent;
 
+	/*
+	 * We must determine the exact set of relids in the expr for child
+	 * EquivalenceMembers as what is given to us in 'relids' may differ from
+	 * the relids mentioned in the expression.  See add_child_rel_equivalences
+	 */
+	if (parent != NULL)
+		expr_relids = pull_varnos(root, (Node *) expr);
+	else
+	{
+		expr_relids = relids;
+		/* We expect the relids to match for non-child members */
+		Assert(bms_equal(pull_varnos(root, (Node *) expr), relids));
+	}
+
+	/* record the actual relids from 'expr' */
+	em->em_norel_expr = bms_is_empty(expr_relids);
+
 	if (bms_is_empty(relids))
 	{
 		/*
@@ -542,9 +630,31 @@ add_eq_member(EquivalenceClass *ec, Expr *expr, Relids relids,
 	else if (!parent)			/* child members don't add to ec_relids */
 	{
 		ec->ec_relids = bms_add_members(ec->ec_relids, relids);
+		ec->ec_nonchild_indexes = bms_add_member(ec->ec_nonchild_indexes, em_index);
 	}
+
+	/* add the new member to the list */
 	ec->ec_members = lappend(ec->ec_members, em);
 
+	/* and add it to the index and PlannerInfo's list */
+	ec->ec_member_indexes = bms_add_member(ec->ec_member_indexes, em_index);
+	root->eq_members = lappend(root->eq_members, em);
+
+	/* record exprs with no relids */
+	if (bms_is_empty(expr_relids))
+		ec->ec_norel_indexes = bms_add_member(ec->ec_norel_indexes, em_index);
+
+	if (parent != NULL)
+		expr_relids = bms_add_members(expr_relids, relids);
+
+	i = -1;
+	while ((i = bms_next_member(expr_relids, i)) >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		rel->eclass_member_indexes = bms_add_member(rel->eclass_member_indexes, em_index);
+	}
+
 	return em;
 }
 
@@ -601,6 +711,7 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 	 * Ensure the expression exposes the correct type and collation.
 	 */
 	expr = canonicalize_ec_expression(expr, opcintype, collation);
+	expr_relids = pull_varnos(root, (Node *) expr);
 
 	/*
 	 * Since SortGroupClause nodes are top-level expressions (GROUP BY, ORDER
@@ -614,7 +725,8 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 	foreach(lc1, root->eq_classes)
 	{
 		EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
-		ListCell   *lc2;
+		EquivalenceMemberIterator iter;
+		EquivalenceMember *cur_em;
 
 		/*
 		 * Never match to a volatile EC, except when we are looking at another
@@ -629,10 +741,11 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 		if (!equal(opfamilies, cur_ec->ec_opfamilies))
 			continue;
 
-		foreach(lc2, cur_ec->ec_members)
-		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
+		setup_eclass_member_strict_iterator(&iter, root, cur_ec, expr_relids,
+											true, true);
 
+		while ((cur_em = eclass_member_iterator_strict_next(&iter)) != NULL)
+		{
 			/*
 			 * Ignore child members unless they match the request.
 			 */
@@ -651,6 +764,8 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 				equal(expr, cur_em->em_expr))
 				return cur_ec;	/* Match! */
 		}
+
+		eclass_member_iterator_dispose(&iter);
 	}
 
 	/* No match; does caller want a NULL result? */
@@ -668,8 +783,11 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 	newec->ec_opfamilies = list_copy(opfamilies);
 	newec->ec_collation = collation;
 	newec->ec_members = NIL;
-	newec->ec_sources = NIL;
-	newec->ec_derives = NIL;
+	newec->ec_member_indexes = NULL;
+	newec->ec_nonchild_indexes = NULL;
+	newec->ec_norel_indexes = NULL;
+	newec->ec_source_indexes = NULL;
+	newec->ec_derive_indexes = NULL;
 	newec->ec_relids = NULL;
 	newec->ec_has_const = false;
 	newec->ec_has_volatile = contain_volatile_functions((Node *) expr);
@@ -682,12 +800,7 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 	if (newec->ec_has_volatile && sortref == 0) /* should not happen */
 		elog(ERROR, "volatile EquivalenceClass has no sortref");
 
-	/*
-	 * Get the precise set of relids appearing in the expression.
-	 */
-	expr_relids = pull_varnos(root, (Node *) expr);
-
-	newem = add_eq_member(newec, copyObject(expr), expr_relids,
+	newem = add_eq_member(root, newec, copyObject(expr), expr_relids,
 						  jdomain, NULL, opcintype);
 
 	/*
@@ -719,7 +832,7 @@ get_eclass_for_sort_expr(PlannerInfo *root,
 		int			ec_index = list_length(root->eq_classes) - 1;
 		int			i = -1;
 
-		while ((i = bms_next_member(newec->ec_relids, i)) > 0)
+		while ((i = bms_next_member(newec->ec_relids, i)) >= 0)
 		{
 			RelOptInfo *rel = root->simple_rel_array[i];
 
@@ -754,19 +867,25 @@ get_eclass_for_sort_expr(PlannerInfo *root,
  * Child EC members are ignored unless they belong to given 'relids'.
  */
 EquivalenceMember *
-find_ec_member_matching_expr(EquivalenceClass *ec,
+find_ec_member_matching_expr(PlannerInfo *root,
+							 EquivalenceClass *ec,
 							 Expr *expr,
 							 Relids relids)
 {
-	ListCell   *lc;
+	EquivalenceMemberIterator iter;
+	Relids		expr_relids;
+	EquivalenceMember *em;
 
 	/* We ignore binary-compatible relabeling on both ends */
 	while (expr && IsA(expr, RelabelType))
 		expr = ((RelabelType *) expr)->arg;
 
-	foreach(lc, ec->ec_members)
+	expr_relids = pull_varnos(root, (Node *) expr);
+	setup_eclass_member_strict_iterator(&iter, root, ec, expr_relids, true,
+										true);
+
+	while ((em = eclass_member_iterator_strict_next(&iter)) != NULL)
 	{
-		EquivalenceMember *em = (EquivalenceMember *) lfirst(lc);
 		Expr	   *emexpr;
 
 		/*
@@ -791,10 +910,13 @@ find_ec_member_matching_expr(EquivalenceClass *ec,
 			emexpr = ((RelabelType *) emexpr)->arg;
 
 		if (equal(emexpr, expr))
-			return em;
+			break;
 	}
 
-	return NULL;
+	bms_free(expr_relids);
+	eclass_member_iterator_dispose(&iter);
+
+	return em;
 }
 
 /*
@@ -936,7 +1058,7 @@ relation_can_be_sorted_early(PlannerInfo *root, RelOptInfo *rel,
 	{
 		Expr	   *targetexpr = (Expr *) lfirst(lc);
 
-		em = find_ec_member_matching_expr(ec, targetexpr, rel->relids);
+		em = find_ec_member_matching_expr(root, ec, targetexpr, rel->relids);
 		if (!em)
 			continue;
 
@@ -1023,7 +1145,7 @@ relation_can_be_sorted_early(PlannerInfo *root, RelOptInfo *rel,
  * scanning of the quals and before Path construction begins.
  *
  * We make no attempt to avoid generating duplicate RestrictInfos here: we
- * don't search ec_sources or ec_derives for matches.  It doesn't really
+ * don't search eq_sources or eq_derives for matches.  It doesn't really
  * seem worth the trouble to do so.
  */
 void
@@ -1080,7 +1202,7 @@ generate_base_implied_equalities(PlannerInfo *root)
 		 * this is a cheap version of has_relevant_eclass_joinclause().
 		 */
 		i = -1;
-		while ((i = bms_next_member(ec->ec_relids, i)) > 0)
+		while ((i = bms_next_member(ec->ec_relids, i)) >= 0)
 		{
 			RelOptInfo *rel = root->simple_rel_array[i];
 
@@ -1112,6 +1234,7 @@ generate_base_implied_equalities_const(PlannerInfo *root,
 {
 	EquivalenceMember *const_em = NULL;
 	ListCell   *lc;
+	int			i;
 
 	/*
 	 * In the trivial case where we just had one "var = const" clause, push
@@ -1121,9 +1244,9 @@ generate_base_implied_equalities_const(PlannerInfo *root,
 	 * equivalent to the old one.
 	 */
 	if (list_length(ec->ec_members) == 2 &&
-		list_length(ec->ec_sources) == 1)
+		bms_get_singleton_member(ec->ec_source_indexes, &i))
 	{
-		RestrictInfo *restrictinfo = (RestrictInfo *) linitial(ec->ec_sources);
+		RestrictInfo *restrictinfo = list_nth_node(RestrictInfo, root->eq_sources, i);
 
 		distribute_restrictinfo_to_rels(root, restrictinfo);
 		return;
@@ -1135,9 +1258,11 @@ generate_base_implied_equalities_const(PlannerInfo *root,
 	 * machinery might be able to exclude relations on the basis of generated
 	 * "var = const" equalities, but "var = param" won't work for that.
 	 */
-	foreach(lc, ec->ec_members)
+	i = -1;
+	while ((i = bms_next_member(ec->ec_norel_indexes, i)) >= 0)
 	{
-		EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
+		EquivalenceMember *cur_em = list_nth_node(EquivalenceMember,
+												  root->eq_members, i);
 
 		if (cur_em->em_is_const)
 		{
@@ -1181,9 +1306,9 @@ generate_base_implied_equalities_const(PlannerInfo *root,
 
 		/*
 		 * If the clause didn't degenerate to a constant, fill in the correct
-		 * markings for a mergejoinable clause, and save it in ec_derives. (We
+		 * markings for a mergejoinable clause, and save it in eq_derives. (We
 		 * will not re-use such clauses directly, but selectivity estimation
-		 * may consult the list later.  Note that this use of ec_derives does
+		 * may consult the list later.  Note that this use of eq_derives does
 		 * not overlap with its use for join clauses, since we never generate
 		 * join clauses from an ec_has_const eclass.)
 		 */
@@ -1193,7 +1318,8 @@ generate_base_implied_equalities_const(PlannerInfo *root,
 			rinfo->left_ec = rinfo->right_ec = ec;
 			rinfo->left_em = cur_em;
 			rinfo->right_em = const_em;
-			ec->ec_derives = lappend(ec->ec_derives, rinfo);
+
+			add_eq_derive(root, ec, rinfo);
 		}
 	}
 }
@@ -1206,7 +1332,8 @@ generate_base_implied_equalities_no_const(PlannerInfo *root,
 										  EquivalenceClass *ec)
 {
 	EquivalenceMember **prev_ems;
-	ListCell   *lc;
+	Bitmapset  *matching_ems;
+	int			i;
 
 	/*
 	 * We scan the EC members once and track the last-seen member for each
@@ -1219,9 +1346,12 @@ generate_base_implied_equalities_no_const(PlannerInfo *root,
 	prev_ems = (EquivalenceMember **)
 		palloc0(root->simple_rel_array_size * sizeof(EquivalenceMember *));
 
-	foreach(lc, ec->ec_members)
+	matching_ems = bms_difference(ec->ec_member_indexes, ec->ec_norel_indexes);
+	i = -1;
+	while ((i = bms_next_member(matching_ems, i)) >= 0)
 	{
-		EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
+		EquivalenceMember *cur_em = list_nth_node(EquivalenceMember,
+												  root->eq_members, i);
 		int			relid;
 
 		Assert(!cur_em->em_is_child);	/* no children yet */
@@ -1259,7 +1389,7 @@ generate_base_implied_equalities_no_const(PlannerInfo *root,
 			/*
 			 * If the clause didn't degenerate to a constant, fill in the
 			 * correct markings for a mergejoinable clause.  We don't put it
-			 * in ec_derives however; we don't currently need to re-find such
+			 * in eq_derives however; we don't currently need to re-find such
 			 * clauses, and we don't want to clutter that list with non-join
 			 * clauses.
 			 */
@@ -1282,11 +1412,15 @@ generate_base_implied_equalities_no_const(PlannerInfo *root,
 	 * For the moment we force all the Vars to be available at all join nodes
 	 * for this eclass.  Perhaps this could be improved by doing some
 	 * pre-analysis of which members we prefer to join, but it's no worse than
-	 * what happened in the pre-8.3 code.
+	 * what happened in the pre-8.3 code.  We're able to make use of
+	 * matching_ems from above.  We're not going to find Vars in
+	 * em_const_indexes.
 	 */
-	foreach(lc, ec->ec_members)
+	i = -1;
+	while ((i = bms_next_member(matching_ems, i)) >= 0)
 	{
-		EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
+		EquivalenceMember *cur_em = list_nth_node(EquivalenceMember,
+												  root->eq_members, i);
 		List	   *vars = pull_var_clause((Node *) cur_em->em_expr,
 										   PVC_RECURSE_AGGREGATES |
 										   PVC_RECURSE_WINDOWFUNCS |
@@ -1295,6 +1429,7 @@ generate_base_implied_equalities_no_const(PlannerInfo *root,
 		add_vars_to_targetlist(root, vars, ec->ec_relids);
 		list_free(vars);
 	}
+	bms_free(matching_ems);
 }
 
 /*
@@ -1315,11 +1450,12 @@ static void
 generate_base_implied_equalities_broken(PlannerInfo *root,
 										EquivalenceClass *ec)
 {
-	ListCell   *lc;
+	int			i = -1;
 
-	foreach(lc, ec->ec_sources)
+	while ((i = bms_next_member(ec->ec_source_indexes, i)) >= 0)
 	{
-		RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(lc);
+		RestrictInfo *restrictinfo = list_nth_node(RestrictInfo,
+												   root->eq_sources, i);
 
 		if (ec->ec_has_const ||
 			bms_membership(restrictinfo->required_relids) != BMS_MULTIPLE)
@@ -1360,11 +1496,11 @@ generate_base_implied_equalities_broken(PlannerInfo *root,
  * Because the same join clauses are likely to be needed multiple times as
  * we consider different join paths, we avoid generating multiple copies:
  * whenever we select a particular pair of EquivalenceMembers to join,
- * we check to see if the pair matches any original clause (in ec_sources)
- * or previously-built clause (in ec_derives).  This saves memory and allows
- * re-use of information cached in RestrictInfos.  We also avoid generating
- * commutative duplicates, i.e. if the algorithm selects "a.x = b.y" but
- * we already have "b.y = a.x", we return the existing clause.
+ * we check to see if the pair matches any original clause in root's
+ * eq_sources or previously-built clause (in root's eq_derives).  This saves
+ * memory and allows re-use of information cached in RestrictInfos.  We also
+ * avoid generating commutative duplicates, i.e. if the algorithm selects
+ * "a.x = b.y" but we already have "b.y = a.x", we return the existing clause.
  *
  * If we are considering an outer join, ojrelid is the associated OJ relid,
  * otherwise it's zero.
@@ -1549,6 +1685,8 @@ generate_join_implied_equalities_normal(PlannerInfo *root,
 										Relids outer_relids,
 										Relids inner_relids)
 {
+	EquivalenceMemberIterator iter;
+	EquivalenceMember *cur_em;
 	List	   *result = NIL;
 	List	   *new_members = NIL;
 	List	   *outer_members = NIL;
@@ -1564,10 +1702,10 @@ generate_join_implied_equalities_normal(PlannerInfo *root,
 	 * as well as to at least one input member, plus enforce at least one
 	 * outer-rel member equal to at least one inner-rel member.
 	 */
-	foreach(lc1, ec->ec_members)
-	{
-		EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc1);
+	setup_eclass_member_iterator(&iter, root, ec, join_relids, true, false);
 
+	while ((cur_em = eclass_member_iterator_next(&iter)) != NULL)
+	{
 		/*
 		 * We don't need to check explicitly for child EC members.  This test
 		 * against join_relids will cause them to be ignored except when
@@ -1584,6 +1722,8 @@ generate_join_implied_equalities_normal(PlannerInfo *root,
 			new_members = lappend(new_members, cur_em);
 	}
 
+	eclass_member_iterator_dispose(&iter);
+
 	/*
 	 * First, select the joinclause if needed.  We can equate any one outer
 	 * member to any one inner member, but we have to find a datatype
@@ -1681,7 +1821,7 @@ generate_join_implied_equalities_normal(PlannerInfo *root,
 
 		foreach(lc1, new_members)
 		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc1);
+			cur_em = (EquivalenceMember *) lfirst(lc1);
 
 			if (prev_em != NULL)
 			{
@@ -1726,12 +1866,16 @@ generate_join_implied_equalities_broken(PlannerInfo *root,
 										Relids nominal_inner_relids,
 										RelOptInfo *inner_rel)
 {
+	Bitmapset  *matching_es;
 	List	   *result = NIL;
-	ListCell   *lc;
+	int			i;
 
-	foreach(lc, ec->ec_sources)
+	matching_es = get_ec_source_indexes(root, ec, nominal_join_relids);
+	i = -1;
+	while ((i = bms_next_member(matching_es, i)) >= 0)
 	{
-		RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(lc);
+		RestrictInfo *restrictinfo = list_nth_node(RestrictInfo,
+												   root->eq_sources, i);
 		Relids		clause_relids = restrictinfo->required_relids;
 
 		if (bms_is_subset(clause_relids, nominal_join_relids) &&
@@ -1743,12 +1887,12 @@ generate_join_implied_equalities_broken(PlannerInfo *root,
 	/*
 	 * If we have to translate, just brute-force apply adjust_appendrel_attrs
 	 * to all the RestrictInfos at once.  This will result in returning
-	 * RestrictInfos that are not listed in ec_derives, but there shouldn't be
+	 * RestrictInfos that are not listed in eq_derives, but there shouldn't be
 	 * any duplication, and it's a sufficiently narrow corner case that we
 	 * shouldn't sweat too much over it anyway.
 	 *
 	 * Since inner_rel might be an indirect descendant of the baserel
-	 * mentioned in the ec_sources clauses, we have to be prepared to apply
+	 * mentioned in the eq_sources clauses, we have to be prepared to apply
 	 * multiple levels of Var translation.
 	 */
 	if (IS_OTHER_REL(inner_rel) && result != NIL)
@@ -1810,10 +1954,11 @@ create_join_clause(PlannerInfo *root,
 				   EquivalenceMember *rightem,
 				   EquivalenceClass *parent_ec)
 {
+	Bitmapset  *matches;
 	RestrictInfo *rinfo;
 	RestrictInfo *parent_rinfo = NULL;
-	ListCell   *lc;
 	MemoryContext oldcontext;
+	int			i;
 
 	/*
 	 * Search to see if we already built a RestrictInfo for this pair of
@@ -1824,9 +1969,12 @@ create_join_clause(PlannerInfo *root,
 	 * it's not identical, it'd better have the same effects, or the operator
 	 * families we're using are broken.
 	 */
-	foreach(lc, ec->ec_sources)
+	matches = bms_int_members(get_ec_source_indexes_strict(root, ec, leftem->em_relids),
+							  get_ec_source_indexes_strict(root, ec, rightem->em_relids));
+	i = -1;
+	while ((i = bms_next_member(matches, i)) >= 0)
 	{
-		rinfo = (RestrictInfo *) lfirst(lc);
+		rinfo = list_nth_node(RestrictInfo, root->eq_sources, i);
 		if (rinfo->left_em == leftem &&
 			rinfo->right_em == rightem &&
 			rinfo->parent_ec == parent_ec)
@@ -1837,9 +1985,13 @@ create_join_clause(PlannerInfo *root,
 			return rinfo;
 	}
 
-	foreach(lc, ec->ec_derives)
+	matches = bms_int_members(get_ec_derive_indexes_strict(root, ec, leftem->em_relids),
+							  get_ec_derive_indexes_strict(root, ec, rightem->em_relids));
+
+	i = -1;
+	while ((i = bms_next_member(matches, i)) >= 0)
 	{
-		rinfo = (RestrictInfo *) lfirst(lc);
+		rinfo = list_nth_node(RestrictInfo, root->eq_derives, i);
 		if (rinfo->left_em == leftem &&
 			rinfo->right_em == rightem &&
 			rinfo->parent_ec == parent_ec)
@@ -1897,7 +2049,7 @@ create_join_clause(PlannerInfo *root,
 	rinfo->left_em = leftem;
 	rinfo->right_em = rightem;
 	/* and save it for possible re-use */
-	ec->ec_derives = lappend(ec->ec_derives, rinfo);
+	add_eq_derive(root, ec, rinfo);
 
 	MemoryContextSwitchTo(oldcontext);
 
@@ -2097,7 +2249,8 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 				left_type,
 				right_type,
 				inner_datatype;
-	Relids		inner_relids;
+	Relids		outer_relids,
+				inner_relids;
 	ListCell   *lc1;
 
 	Assert(is_opclause(rinfo->clause));
@@ -2111,6 +2264,7 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 		outervar = (Expr *) get_leftop(rinfo->clause);
 		innervar = (Expr *) get_rightop(rinfo->clause);
 		inner_datatype = right_type;
+		outer_relids = rinfo->left_relids;
 		inner_relids = rinfo->right_relids;
 	}
 	else
@@ -2118,6 +2272,7 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 		outervar = (Expr *) get_rightop(rinfo->clause);
 		innervar = (Expr *) get_leftop(rinfo->clause);
 		inner_datatype = left_type;
+		outer_relids = rinfo->right_relids;
 		inner_relids = rinfo->left_relids;
 	}
 
@@ -2125,8 +2280,10 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 	foreach(lc1, root->eq_classes)
 	{
 		EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
+		EquivalenceMemberIterator iter;
+		EquivalenceMember *cur_em;
 		bool		match;
-		ListCell   *lc2;
+		int			i;
 
 		/* Ignore EC unless it contains pseudoconstants */
 		if (!cur_ec->ec_has_const)
@@ -2141,10 +2298,12 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 			continue;
 		/* Does it contain a match to outervar? */
 		match = false;
-		foreach(lc2, cur_ec->ec_members)
-		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
 
+		setup_eclass_member_strict_iterator(&iter, root, cur_ec, outer_relids,
+											false, true);
+
+		while ((cur_em = eclass_member_iterator_strict_next(&iter)) != NULL)
+		{
 			Assert(!cur_em->em_is_child);	/* no children yet */
 			if (equal(outervar, cur_em->em_expr))
 			{
@@ -2152,6 +2311,8 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 				break;
 			}
 		}
+		eclass_member_iterator_dispose(&iter);
+
 		if (!match)
 			continue;			/* no match, so ignore this EC */
 
@@ -2161,13 +2322,15 @@ reconsider_outer_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo,
 		 * constant before we can decide to throw away the outer-join clause.
 		 */
 		match = false;
-		foreach(lc2, cur_ec->ec_members)
+		i = -1;
+		while ((i = bms_next_member(cur_ec->ec_norel_indexes, i)) >= 0)
 		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
 			Oid			eq_op;
 			RestrictInfo *newrinfo;
 			JoinDomain *jdomain;
 
+			cur_em = list_nth_node(EquivalenceMember, root->eq_members, i);
+
 			if (!cur_em->em_is_const)
 				continue;		/* ignore non-const members */
 			eq_op = select_equality_operator(cur_ec,
@@ -2237,11 +2400,12 @@ reconsider_full_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo)
 	{
 		EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
 		EquivalenceMember *coal_em = NULL;
+		Bitmapset  *matching_ems;
 		bool		match;
 		bool		matchleft;
 		bool		matchright;
-		ListCell   *lc2;
 		int			coal_idx = -1;
+		int			i;
 
 		/* Ignore EC unless it contains pseudoconstants */
 		if (!cur_ec->ec_has_const)
@@ -2268,10 +2432,14 @@ reconsider_full_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo)
 		 * the two column types). Is it OK to strip implicit coercions from
 		 * the COALESCE arguments?
 		 */
+		matching_ems = get_ecmember_indexes_strict(root, cur_ec,
+												   rinfo->clause_relids, true,
+												   false);
 		match = false;
-		foreach(lc2, cur_ec->ec_members)
+		i = -1;
+		while ((i = bms_next_member(matching_ems, i)) >= 0)
 		{
-			coal_em = (EquivalenceMember *) lfirst(lc2);
+			coal_em = list_nth_node(EquivalenceMember, root->eq_members, i);
 			Assert(!coal_em->em_is_child);	/* no children yet */
 			if (IsA(coal_em->em_expr, CoalesceExpr))
 			{
@@ -2298,7 +2466,7 @@ reconsider_full_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo)
 
 				if (equal(leftvar, cfirst) && equal(rightvar, csecond))
 				{
-					coal_idx = foreach_current_index(lc2);
+					coal_idx = i;
 					match = true;
 					break;
 				}
@@ -2314,9 +2482,11 @@ reconsider_full_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo)
 		 * decide to throw away the outer-join clause.
 		 */
 		matchleft = matchright = false;
-		foreach(lc2, cur_ec->ec_members)
+		i = -1;
+		while ((i = bms_next_member(cur_ec->ec_norel_indexes, i)) >= 0)
 		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
+			EquivalenceMember *cur_em = list_nth_node(EquivalenceMember,
+													  root->eq_members, i);
 			Oid			eq_op;
 			RestrictInfo *newrinfo;
 			JoinDomain *jdomain;
@@ -2364,11 +2534,28 @@ reconsider_full_join_clause(PlannerInfo *root, OuterJoinClauseInfo *ojcinfo)
 		 * we can throw away the full-join clause as redundant.  Moreover, we
 		 * can remove the COALESCE entry from the EC, since the added
 		 * restrictions ensure it will always have the expected value. (We
-		 * don't bother trying to update ec_relids or ec_sources.)
+		 * don't bother trying to update ec_relids or root's eq_sources.)
 		 */
 		if (matchleft && matchright)
 		{
-			cur_ec->ec_members = list_delete_nth_cell(cur_ec->ec_members, coal_idx);
+			/* XXX performance of list_delete()?? */
+			cur_ec->ec_members = list_delete(cur_ec->ec_members, coal_em);
+			cur_ec->ec_member_indexes = bms_del_member(cur_ec->ec_member_indexes,
+													   coal_idx);
+			cur_ec->ec_nonchild_indexes = bms_del_member(cur_ec->ec_nonchild_indexes,
+														 coal_idx);
+			/* no need to adjust ec_norel_indexes */
+
+			/* Remove the member from each of the relations */
+			i = -1;
+			while ((i = bms_next_member(coal_em->em_relids, i)) >= 0)
+			{
+				RelOptInfo *rel = root->simple_rel_array[i];
+
+				rel->eclass_member_indexes = bms_del_member(rel->eclass_member_indexes,
+															coal_idx);
+			}
+
 			return true;
 		}
 
@@ -2423,21 +2610,28 @@ bool
 exprs_known_equal(PlannerInfo *root, Node *item1, Node *item2)
 {
 	ListCell   *lc1;
+	Relids		item1_relids = pull_varnos(root, item1);
+	Relids		item2_relids = pull_varnos(root, item2);
 
 	foreach(lc1, root->eq_classes)
 	{
 		EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);
 		bool		item1member = false;
 		bool		item2member = false;
-		ListCell   *lc2;
+		Bitmapset  *matching_ems;
+		int			i;
 
 		/* Never match to a volatile EC */
 		if (ec->ec_has_volatile)
 			continue;
 
-		foreach(lc2, ec->ec_members)
+		matching_ems = bms_join(get_ecmember_indexes_strict(root, ec, item1_relids, false, true),
+								get_ecmember_indexes_strict(root, ec, item2_relids, false, true));
+		i = -1;
+		while ((i = bms_next_member(matching_ems, i)) >= 0)
 		{
-			EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
+			EquivalenceMember *em = list_nth_node(EquivalenceMember,
+												  root->eq_members, i);
 
 			if (em->em_is_child)
 				continue;		/* ignore children here */
@@ -2500,16 +2694,21 @@ match_eclasses_to_foreign_key_col(PlannerInfo *root,
 															 i);
 		EquivalenceMember *item1_em = NULL;
 		EquivalenceMember *item2_em = NULL;
-		ListCell   *lc2;
+		Bitmapset  *matching_ems;
+		int			j;
 
 		/* Never match to a volatile EC */
 		if (ec->ec_has_volatile)
 			continue;
 		/* Note: it seems okay to match to "broken" eclasses here */
+		matching_ems = bms_join(get_ecmember_indexes_strict(root, ec, rel1->relids, false, false),
+								get_ecmember_indexes_strict(root, ec, rel2->relids, false, false));
 
-		foreach(lc2, ec->ec_members)
+		j = -1;
+		while ((j = bms_next_member(matching_ems, j)) >= 0)
 		{
-			EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
+			EquivalenceMember *em = list_nth_node(EquivalenceMember,
+												  root->eq_members, j);
 			Var		   *var;
 
 			if (em->em_is_child)
@@ -2562,16 +2761,19 @@ match_eclasses_to_foreign_key_col(PlannerInfo *root,
  * Returns NULL if no such clause can be found.
  */
 RestrictInfo *
-find_derived_clause_for_ec_member(EquivalenceClass *ec,
+find_derived_clause_for_ec_member(PlannerInfo *root, EquivalenceClass *ec,
 								  EquivalenceMember *em)
 {
-	ListCell   *lc;
+	int			i;
 
 	Assert(ec->ec_has_const);
 	Assert(!em->em_is_const);
-	foreach(lc, ec->ec_derives)
+
+	i = -1;
+	while ((i = bms_next_member(ec->ec_derive_indexes, i)) >= 0)
 	{
-		RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
+		RestrictInfo *rinfo = list_nth_node(RestrictInfo, root->eq_derives,
+											i);
 
 		/*
 		 * generate_base_implied_equalities_const will have put non-const
@@ -2622,7 +2824,8 @@ add_child_rel_equivalences(PlannerInfo *root,
 	while ((i = bms_next_member(parent_rel->eclass_indexes, i)) >= 0)
 	{
 		EquivalenceClass *cur_ec = (EquivalenceClass *) list_nth(root->eq_classes, i);
-		int			num_members;
+		EquivalenceMemberIterator iter;
+		EquivalenceMember *cur_em;
 
 		/*
 		 * If this EC contains a volatile expression, then generating child
@@ -2636,29 +2839,15 @@ add_child_rel_equivalences(PlannerInfo *root,
 		Assert(bms_is_subset(top_parent_relids, cur_ec->ec_relids));
 
 		/*
-		 * We don't use foreach() here because there's no point in scanning
-		 * newly-added child members, so we can stop after the last
-		 * pre-existing EC member.
+		 * Looping using the EquivalenceMemberIterator means we only loop over
+		 * the members which existed when we set up the iterator, not newly
+		 * added ones.
 		 */
-		num_members = list_length(cur_ec->ec_members);
-		for (int pos = 0; pos < num_members; pos++)
-		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) list_nth(cur_ec->ec_members, pos);
-
-			if (cur_em->em_is_const)
-				continue;		/* ignore consts here */
-
-			/*
-			 * We consider only original EC members here, not
-			 * already-transformed child members.  Otherwise, if some original
-			 * member expression references more than one appendrel, we'd get
-			 * an O(N^2) explosion of useless derived expressions for
-			 * combinations of children.  (But add_child_join_rel_equivalences
-			 * may add targeted combinations for partitionwise-join purposes.)
-			 */
-			if (cur_em->em_is_child)
-				continue;		/* ignore children here */
+		setup_eclass_member_iterator(&iter, root, cur_ec, top_parent_relids,
+									 false, false);
 
+		while ((cur_em = eclass_member_iterator_next(&iter)) != NULL)
+		{
 			/*
 			 * Consider only members that reference and can be computed at
 			 * child's topmost parent rel.  In particular we want to exclude
@@ -2667,13 +2856,16 @@ add_child_rel_equivalences(PlannerInfo *root,
 			 * simple Var; and in any case it wouldn't produce a member that
 			 * has any use in creating plans for the child rel.
 			 */
-			if (bms_is_subset(cur_em->em_relids, top_parent_relids) &&
-				!bms_is_empty(cur_em->em_relids))
+			if (bms_is_subset(cur_em->em_relids, top_parent_relids))
 			{
 				/* OK, generate transformed child version */
 				Expr	   *child_expr;
 				Relids		new_relids;
 
+				Assert(!cur_em->em_is_const);
+				Assert(!cur_em->em_is_child);
+				Assert(!bms_is_empty(cur_em->em_relids));
+
 				if (parent_rel->reloptkind == RELOPT_BASEREL)
 				{
 					/* Simple single-level transformation */
@@ -2702,7 +2894,7 @@ add_child_rel_equivalences(PlannerInfo *root,
 											top_parent_relids);
 				new_relids = bms_add_members(new_relids, child_relids);
 
-				(void) add_eq_member(cur_ec, child_expr, new_relids,
+				(void) add_eq_member(root, cur_ec, child_expr, new_relids,
 									 cur_em->em_jdomain,
 									 cur_em, cur_em->em_datatype);
 
@@ -2710,6 +2902,7 @@ add_child_rel_equivalences(PlannerInfo *root,
 				child_rel->eclass_indexes = bms_add_member(child_rel->eclass_indexes, i);
 			}
 		}
+		eclass_member_iterator_dispose(&iter);
 	}
 }
 
@@ -2754,7 +2947,8 @@ add_child_join_rel_equivalences(PlannerInfo *root,
 	while ((i = bms_next_member(matching_ecs, i)) >= 0)
 	{
 		EquivalenceClass *cur_ec = (EquivalenceClass *) list_nth(root->eq_classes, i);
-		int			num_members;
+		EquivalenceMemberIterator iter;
+		EquivalenceMember *cur_em;
 
 		/*
 		 * If this EC contains a volatile expression, then generating child
@@ -2768,24 +2962,21 @@ add_child_join_rel_equivalences(PlannerInfo *root,
 		Assert(bms_overlap(top_parent_relids, cur_ec->ec_relids));
 
 		/*
-		 * We don't use foreach() here because there's no point in scanning
-		 * newly-added child members, so we can stop after the last
-		 * pre-existing EC member.
+		 * Looping using the EquivalenceMemberIterator means we only loop over
+		 * the members which existed when we set up the iterator, not newly
+		 * added ones.
 		 */
-		num_members = list_length(cur_ec->ec_members);
-		for (int pos = 0; pos < num_members; pos++)
+		setup_eclass_member_iterator(&iter, root, cur_ec, top_parent_relids,
+									 false, false);
+
+		while ((cur_em = eclass_member_iterator_next(&iter)) != NULL)
 		{
-			EquivalenceMember *cur_em = (EquivalenceMember *) list_nth(cur_ec->ec_members, pos);
+			Expr	   *child_expr;
+			Relids		new_relids;
 
-			if (cur_em->em_is_const)
-				continue;		/* ignore consts here */
-
-			/*
-			 * We consider only original EC members here, not
-			 * already-transformed child members.
-			 */
-			if (cur_em->em_is_child)
-				continue;		/* ignore children here */
+			Assert(!cur_em->em_is_const);
+			Assert(!cur_em->em_is_child);
+			Assert(bms_overlap(cur_em->em_relids, top_parent_relids));
 
 			/*
 			 * We may ignore expressions that reference a single baserel,
@@ -2794,47 +2985,40 @@ add_child_join_rel_equivalences(PlannerInfo *root,
 			if (bms_membership(cur_em->em_relids) != BMS_MULTIPLE)
 				continue;
 
-			/* Does this member reference child's topmost parent rel? */
-			if (bms_overlap(cur_em->em_relids, top_parent_relids))
+			if (parent_joinrel->reloptkind == RELOPT_JOINREL)
 			{
-				/* Yes, generate transformed child version */
-				Expr	   *child_expr;
-				Relids		new_relids;
-
-				if (parent_joinrel->reloptkind == RELOPT_JOINREL)
-				{
-					/* Simple single-level transformation */
-					child_expr = (Expr *)
-						adjust_appendrel_attrs(root,
-											   (Node *) cur_em->em_expr,
-											   nappinfos, appinfos);
-				}
-				else
-				{
-					/* Must do multi-level transformation */
-					Assert(parent_joinrel->reloptkind == RELOPT_OTHER_JOINREL);
-					child_expr = (Expr *)
-						adjust_appendrel_attrs_multilevel(root,
-														  (Node *) cur_em->em_expr,
-														  child_joinrel,
-														  child_joinrel->top_parent);
-				}
+				/* Simple single-level transformation */
+				child_expr = (Expr *)
+					adjust_appendrel_attrs(root,
+										   (Node *) cur_em->em_expr,
+										   nappinfos, appinfos);
+			}
+			else
+			{
+				/* Must do multi-level transformation */
+				Assert(parent_joinrel->reloptkind == RELOPT_OTHER_JOINREL);
+				child_expr = (Expr *)
+					adjust_appendrel_attrs_multilevel(root,
+													  (Node *) cur_em->em_expr,
+													  child_joinrel,
+													  child_joinrel->top_parent);
+			}
 
-				/*
-				 * Transform em_relids to match.  Note we do *not* do
-				 * pull_varnos(child_expr) here, as for example the
-				 * transformation might have substituted a constant, but we
-				 * don't want the child member to be marked as constant.
-				 */
-				new_relids = bms_difference(cur_em->em_relids,
-											top_parent_relids);
-				new_relids = bms_add_members(new_relids, child_relids);
+			/*
+			 * Transform em_relids to match.  Note we do *not* do
+			 * pull_varnos(child_expr) here, as for example the
+			 * transformation might have substituted a constant, but we
+			 * don't want the child member to be marked as constant.
+			 */
+			new_relids = bms_difference(cur_em->em_relids,
+										top_parent_relids);
+			new_relids = bms_add_members(new_relids, child_relids);
 
-				(void) add_eq_member(cur_ec, child_expr, new_relids,
-									 cur_em->em_jdomain,
-									 cur_em, cur_em->em_datatype);
-			}
+			(void) add_eq_member(root, cur_ec, child_expr, new_relids,
+								 cur_em->em_jdomain,
+								 cur_em, cur_em->em_datatype);
 		}
+		eclass_member_iterator_dispose(&iter);
 	}
 
 	MemoryContextSwitchTo(oldcontext);
@@ -2893,7 +3077,8 @@ generate_implied_equalities_for_column(PlannerInfo *root,
 	{
 		EquivalenceClass *cur_ec = (EquivalenceClass *) list_nth(root->eq_classes, i);
 		EquivalenceMember *cur_em;
-		ListCell   *lc2;
+		EquivalenceMemberIterator iter;
+		int			j;
 
 		/* Sanity check eclass_indexes only contain ECs for rel */
 		Assert(is_child_rel || bms_is_subset(rel->relids, cur_ec->ec_relids));
@@ -2915,16 +3100,19 @@ generate_implied_equalities_for_column(PlannerInfo *root,
 		 * corner cases, so for now we live with just reporting the first
 		 * match.  See also get_eclass_for_sort_expr.)
 		 */
-		cur_em = NULL;
-		foreach(lc2, cur_ec->ec_members)
+		setup_eclass_member_iterator(&iter, root, cur_ec, rel->relids, true,
+									 false);
+
+		while ((cur_em = eclass_member_iterator_next(&iter)) != NULL)
 		{
-			cur_em = (EquivalenceMember *) lfirst(lc2);
 			if (bms_equal(cur_em->em_relids, rel->relids) &&
 				callback(root, rel, cur_ec, cur_em, callback_arg))
 				break;
 			cur_em = NULL;
 		}
 
+		eclass_member_iterator_dispose(&iter);
+
 		if (!cur_em)
 			continue;
 
@@ -2932,14 +3120,15 @@ generate_implied_equalities_for_column(PlannerInfo *root,
 		 * Found our match.  Scan the other EC members and attempt to generate
 		 * joinclauses.
 		 */
-		foreach(lc2, cur_ec->ec_members)
+		j = -1;
+		while ((j = bms_next_member(cur_ec->ec_nonchild_indexes, j)) >= 0)
 		{
-			EquivalenceMember *other_em = (EquivalenceMember *) lfirst(lc2);
+			EquivalenceMember *other_em = list_nth_node(EquivalenceMember,
+														root->eq_members, j);
 			Oid			eq_op;
 			RestrictInfo *rinfo;
 
-			if (other_em->em_is_child)
-				continue;		/* ignore children here */
+			Assert(!other_em->em_is_child);
 
 			/* Make sure it'll be a join to a different rel */
 			if (other_em == cur_em ||
@@ -3047,7 +3236,7 @@ have_relevant_eclass_joinclause(PlannerInfo *root,
 		 * surely be true if both of them overlap ec_relids.)
 		 *
 		 * Note we don't test ec_broken; if we did, we'd need a separate code
-		 * path to look through ec_sources.  Checking the membership anyway is
+		 * path to look through eq_sources.  Checking the membership anyway is
 		 * OK as a possibly-overoptimistic heuristic.
 		 *
 		 * We don't test ec_has_const either, even though a const eclass won't
@@ -3122,7 +3311,7 @@ eclass_useful_for_merging(PlannerInfo *root,
 						  RelOptInfo *rel)
 {
 	Relids		relids;
-	ListCell   *lc;
+	int			i;
 
 	Assert(!eclass->ec_merged);
 
@@ -3135,7 +3324,7 @@ eclass_useful_for_merging(PlannerInfo *root,
 
 	/*
 	 * Note we don't test ec_broken; if we did, we'd need a separate code path
-	 * to look through ec_sources.  Checking the members anyway is OK as a
+	 * to look through eq_sources.  Checking the members anyway is OK as a
 	 * possibly-overoptimistic heuristic.
 	 */
 
@@ -3153,12 +3342,14 @@ eclass_useful_for_merging(PlannerInfo *root,
 		return false;
 
 	/* To join, we need a member not in the given rel */
-	foreach(lc, eclass->ec_members)
+	i = -1;
+	while ((i = bms_next_member(eclass->ec_nonchild_indexes, i)) >= 0)
 	{
-		EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
+		EquivalenceMember *cur_em =
+		list_nth_node(EquivalenceMember, root->eq_members, i);
 
-		if (cur_em->em_is_child)
-			continue;			/* ignore children here */
+		/* we don't expect child members here */
+		Assert(!cur_em->em_is_child);
 
 		if (!bms_overlap(cur_em->em_relids, relids))
 			return true;
@@ -3246,7 +3437,7 @@ get_eclass_indexes_for_relids(PlannerInfo *root, Relids relids)
 	/* Should be OK to rely on eclass_indexes */
 	Assert(root->ec_merging_done);
 
-	while ((i = bms_next_member(relids, i)) > 0)
+	while ((i = bms_next_member(relids, i)) >= 0)
 	{
 		RelOptInfo *rel = root->simple_rel_array[i];
 
@@ -3288,3 +3479,595 @@ get_common_eclass_indexes(PlannerInfo *root, Relids relids1, Relids relids2)
 	/* Calculate and return the common EC indexes, recycling the left input. */
 	return bms_int_members(rel1ecs, rel2ecs);
 }
+
+/*
+ * get_ecmember_indexes
+ *		Returns a Bitmapset with indexes into root->eq_members for all
+ *		EquivalenceMembers in 'ec' that have
+ *		bms_overlap(em->em_relids, relids) as true.  The returned indexes
+ *		may reference EquivalenceMembers with em_relids containing members
+ *		not mentioned in 'relids'.
+ *
+ * Returns a newly allocated Bitmapset which the caller is free to modify.
+ */
+Bitmapset *
+get_ecmember_indexes(PlannerInfo *root, EquivalenceClass *ec, Relids relids,
+					 bool with_children, bool with_norel_members)
+{
+	Bitmapset  *matching_ems;
+	Bitmapset  *rel_ems = NULL;
+	int			i = -1;
+
+	while ((i = bms_next_member(relids, i)) >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		rel_ems = bms_add_members(rel_ems, rel->eclass_member_indexes);
+	}
+
+#ifdef USE_ASSERT_CHECKING
+	/* verify the results look sane */
+	i = -1;
+	while ((i = bms_next_member(rel_ems, i)) >= 0)
+	{
+		EquivalenceMember *em = list_nth_node(EquivalenceMember,
+											  root->eq_members, i);
+
+		Assert(bms_overlap(em->em_relids, relids));
+	}
+#endif
+
+	/* remove EC members not mentioning the required rels. */
+	if (!with_children)
+		matching_ems = bms_int_members(rel_ems, ec->ec_nonchild_indexes);
+	else
+		matching_ems = bms_int_members(rel_ems, ec->ec_member_indexes);
+
+	/* now add any members with that are not mentioned by any relation */
+	if (with_norel_members)
+		matching_ems = bms_add_members(matching_ems, ec->ec_norel_indexes);
+
+	return matching_ems;
+}
+
+/*
+ * get_ecmember_indexes_strict
+ *		Returns a Bitmapset with indexes into root->eq_members for all
+ *		EquivalenceMembers in 'ec' that have
+ *		bms_is_subset(relids, em->em_relids) as true.
+ *
+ * Returns a newly allocated Bitmapset which the caller is free to modify.
+ */
+Bitmapset *
+get_ecmember_indexes_strict(PlannerInfo *root, EquivalenceClass *ec,
+							Relids relids, bool with_children,
+							bool with_norel_members)
+{
+	Bitmapset  *matching_ems = NULL;
+	int			i = bms_next_member(relids, -1);
+
+	if (i >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		/*
+		 * bms_intersect to the first relation to try to keep the resulting
+		 * Bitmapset as small as possible.  This saves having to make a
+		 * complete bms_copy() of one of them.  One may contain significantly
+		 * more words than the other.
+		 */
+		if (!with_children)
+			matching_ems = bms_intersect(rel->eclass_member_indexes,
+										 ec->ec_nonchild_indexes);
+		else
+			matching_ems = bms_intersect(rel->eclass_member_indexes,
+										 ec->ec_member_indexes);
+
+		while ((i = bms_next_member(relids, i)) >= 0)
+		{
+			rel = root->simple_rel_array[i];
+			matching_ems = bms_int_members(matching_ems,
+										   rel->eclass_member_indexes);
+		}
+	}
+
+#ifdef USE_ASSERT_CHECKING
+	/* verify the results look sane */
+	i = -1;
+	while ((i = bms_next_member(matching_ems, i)) >= 0)
+	{
+		EquivalenceMember *em = list_nth_node(EquivalenceMember,
+											  root->eq_members, i);
+
+		Assert(bms_is_subset(relids, em->em_relids));
+	}
+#endif
+
+	/* optionally add members with that are not mentioned by any relation */
+	if (with_norel_members)
+		matching_ems = bms_add_members(matching_ems, ec->ec_norel_indexes);
+
+	return matching_ems;
+}
+
+/*
+ * The threshold for the number of members that must be in an EquivalenceClass
+ * before we switch to searching for EquivalenceMember by using the Bitmapset
+ * indexes stored in EquivalenceClass and RelOptInfo.  We don't want to make
+ * this too low as the manipulation of Bitmapsets slows this down for
+ * EquivalenceClasses with just a few members.  The linear search becomes very
+ * slow when an EquivalenceClass has a large number of members, as can happen
+ * when planning queries to partitioned tables.
+ */
+#define ECMEMBER_INDEX_THRESHOLD 16
+
+/*
+ * setup_eclass_member_iterator
+ *		Setup 'iter' so it's ready for eclass_member_iterator_next to start
+ *		searching for EquivalenceMembers matching the specified parameters.
+ *
+ * Once used, the iterator must be disposed of using
+ * eclass_member_iterator_dispose.
+ */
+void
+setup_eclass_member_iterator(EquivalenceMemberIterator *iter,
+							 PlannerInfo *root, EquivalenceClass *ec,
+							 Relids relids, bool with_children,
+							 bool with_norel_members)
+{
+	iter->orig_length = list_length(ec->ec_members);
+	iter->use_index = iter->orig_length >= ECMEMBER_INDEX_THRESHOLD;
+	iter->with_children = with_children;
+	iter->with_norel_members = with_norel_members;
+	iter->relids_empty = bms_is_empty(relids);
+#ifdef USE_ASSERT_CHECKING
+	iter->isstrict = false;
+#endif
+	iter->with_relids = relids;
+	iter->root = root;
+	iter->eclass = ec;
+
+#ifdef USE_ASSERT_CHECKING
+	if (1)
+#else
+	if (iter->use_index)
+#endif
+		iter->matching_ems = get_ecmember_indexes(root, ec, relids,
+												  with_children,
+												  with_norel_members);
+	else
+		iter->matching_ems = NULL;
+
+	iter->current_index = -1;
+
+#ifdef USE_ASSERT_CHECKING
+
+	/*
+	 * Verify that an iterator that uses the index and one that does not both
+	 * return the same EquivalenceMembers
+	 */
+	{
+		EquivalenceMemberIterator idx_iter;
+		EquivalenceMemberIterator noidx_iter;
+		EquivalenceMember *em;
+		List	   *list1 = NIL;
+		List	   *list2 = NIL;
+		ListCell   *lc1,
+				   *lc2;
+
+		memcpy(&idx_iter, iter, sizeof(EquivalenceMemberIterator));
+		memcpy(&noidx_iter, iter, sizeof(EquivalenceMemberIterator));
+
+		idx_iter.use_index = true;
+		noidx_iter.use_index = false;
+
+		while ((em = eclass_member_iterator_next(&idx_iter)) != NULL)
+			list1 = lappend(list1, em);
+
+		while ((em = eclass_member_iterator_next(&noidx_iter)) != NULL)
+			list2 = lappend(list2, em);
+
+		list_sort(list1, list_ptr_cmp);
+		list_sort(list2, list_ptr_cmp);
+
+		Assert(list_length(list1) == list_length(list2));
+
+		forboth(lc1, list1, lc2, list2)
+			Assert(lfirst(lc1) == lfirst(lc2));
+	}
+#endif
+
+}
+
+/*
+ * setup_eclass_member_strict_iterator
+ *		Setup 'iter' so it's ready for eclass_member_iterator_strict_next to
+ *		start searching for EquivalenceMembers matching the specified
+ *		parameters.
+ *
+ * Once used, the iterator must be disposed of using
+ * eclass_member_iterator_dispose.
+ */
+void
+setup_eclass_member_strict_iterator(EquivalenceMemberIterator *iter,
+									PlannerInfo *root, EquivalenceClass *ec,
+									Relids relids, bool with_children,
+									bool with_norel_members)
+{
+	iter->orig_length = list_length(ec->ec_members);
+	iter->use_index = iter->orig_length >= ECMEMBER_INDEX_THRESHOLD;
+	iter->with_children = with_children;
+	iter->with_norel_members = with_norel_members;
+	iter->relids_empty = bms_is_empty(relids);
+#ifdef USE_ASSERT_CHECKING
+	iter->isstrict = true;
+#endif
+	iter->with_relids = relids;
+	iter->root = root;
+	iter->eclass = ec;
+
+#ifdef USE_ASSERT_CHECKING
+	if (1)
+#else
+	if (iter->use_index)
+#endif
+		iter->matching_ems = get_ecmember_indexes_strict(root, ec, relids,
+														 with_children,
+														 with_norel_members);
+	else
+		iter->matching_ems = NULL;
+
+	iter->current_index = -1;
+
+#ifdef USE_ASSERT_CHECKING
+
+	/*
+	 * Verify that an iterator that uses the index and one that does not both
+	 * return the same EquivalenceMembers
+	 */
+	{
+		EquivalenceMemberIterator idx_iter;
+		EquivalenceMemberIterator noidx_iter;
+		EquivalenceMember *em;
+		List	   *list1 = NIL;
+		List	   *list2 = NIL;
+		ListCell   *lc1,
+				   *lc2;
+
+		memcpy(&idx_iter, iter, sizeof(EquivalenceMemberIterator));
+		memcpy(&noidx_iter, iter, sizeof(EquivalenceMemberIterator));
+
+		idx_iter.use_index = true;
+		noidx_iter.use_index = false;
+
+		while ((em = eclass_member_iterator_strict_next(&idx_iter)) != NULL)
+			list1 = lappend(list1, em);
+
+		while ((em = eclass_member_iterator_strict_next(&noidx_iter)) != NULL)
+			list2 = lappend(list2, em);
+
+		list_sort(list1, list_ptr_cmp);
+		list_sort(list2, list_ptr_cmp);
+
+		Assert(list_length(list1) == list_length(list2));
+
+		forboth(lc1, list1, lc2, list2)
+			Assert(lfirst(lc1) == lfirst(lc2));
+	}
+#endif
+}
+
+/*
+ * eclass_member_iterator_next
+ *		Fetch the next EquivalenceMember from an EquivalenceMemberIterator
+ *		which was set up by setup_eclass_member_iterator().  Returns NULL when
+ *		there are no more matching EquivalenceMembers.
+ */
+EquivalenceMember *
+eclass_member_iterator_next(EquivalenceMemberIterator *iter)
+{
+	/* Fail if this was used instead of eclass_member_iterator_strict_next */
+	Assert(!iter->isstrict);
+
+	if (iter->use_index)
+	{
+		iter->current_index = bms_next_member(iter->matching_ems,
+											  iter->current_index);
+		if (iter->current_index >= 0)
+			return list_nth_node(EquivalenceMember, iter->root->eq_members,
+								 iter->current_index);
+		return NULL;
+	}
+	else
+	{
+		ListCell   *lc;
+
+		for_each_from(lc, iter->eclass->ec_members, iter->current_index + 1)
+		{
+			EquivalenceMember *em = lfirst_node(EquivalenceMember, lc);
+
+			iter->current_index = foreach_current_index(lc);
+
+			/*
+			 * Some users of this iterator will be adding new
+			 * EquivalenceMember during the loop.  We must ensure we don't
+			 * return those, so here we return NULL when the loop index goes
+			 * beyond the original length of the ec_members list.
+			 */
+			if (iter->current_index >= iter->orig_length)
+				return NULL;
+
+			/* don't return child members when with_children==false */
+			if (!iter->with_children && em->em_is_child)
+				continue;
+
+			/*
+			 * When with_norel_members==true, make sure we return all members
+			 * without Vars.
+			 */
+			if (iter->with_norel_members && em->em_norel_expr)
+				return em;
+
+			/*
+			 * Don't return members which have no common rels with with_relids
+			 */
+			if (!bms_overlap(em->em_relids, iter->with_relids))
+				continue;
+
+			return em;
+		}
+		return NULL;
+	}
+}
+
+/*
+ * eclass_member_iterator_strict_next
+ *		Fetch the next EquivalenceMember from an EquivalenceMemberIterator
+ *		which was set up by setup_eclass_member_strict_iterator().  Returns
+ *		NULL when there are no more matching EquivalenceMembers.
+ */
+EquivalenceMember *
+eclass_member_iterator_strict_next(EquivalenceMemberIterator *iter)
+{
+	/* Fail if this was used instead of eclass_member_iterator_next */
+	Assert(iter->isstrict);
+
+	if (iter->use_index)
+	{
+		iter->current_index = bms_next_member(iter->matching_ems,
+											  iter->current_index);
+		if (iter->current_index >= 0)
+			return list_nth_node(EquivalenceMember, iter->root->eq_members,
+								 iter->current_index);
+		return NULL;
+	}
+	else
+	{
+		ListCell   *lc;
+
+		for_each_from(lc, iter->eclass->ec_members, iter->current_index + 1)
+		{
+			EquivalenceMember *em = lfirst_node(EquivalenceMember, lc);
+
+			iter->current_index = foreach_current_index(lc);
+
+			/*
+			 * Some users of this iterator will be adding new
+			 * EquivalenceMember during the loop.  We must ensure we don't
+			 * return those, so here we return NULL when the loop index goes
+			 * beyond the original length of the ec_members list.
+			 */
+			if (iter->current_index >= iter->orig_length)
+				return NULL;
+
+			/* don't return child members when with_children==false */
+			if (!iter->with_children && em->em_is_child)
+				continue;
+
+			/*
+			 * When with_norel_members==true, make sure we return all members
+			 * without Vars.
+			 */
+			if (iter->with_norel_members && em->em_norel_expr)
+				return em;
+
+			/*
+			 * Don't match members where em_relids that don't contain all rels
+			 * mentioned in with_relids.
+			 */
+			if (iter->relids_empty ||
+				!bms_is_subset(iter->with_relids, em->em_relids))
+				continue;
+
+			return em;
+		}
+		return NULL;
+	}
+}
+
+/*
+ * eclass_member_iterator_dispose
+ *		Free any memory allocated by the iterator
+ */
+void
+eclass_member_iterator_dispose(EquivalenceMemberIterator *iter)
+{
+	bms_free(iter->matching_ems);
+}
+
+
+/*
+ * get_ec_source_indexes
+ *		Returns a Bitmapset with indexes into root->eq_sources for all
+ *		RestrictInfos in 'ec' that have
+ *		bms_overlap(relids, rinfo->clause_relids) as true.
+ *
+ * Returns a newly allocated Bitmapset which the caller is free to modify.
+ */
+Bitmapset *
+get_ec_source_indexes(PlannerInfo *root, EquivalenceClass *ec, Relids relids)
+{
+	Bitmapset  *rel_esis = NULL;
+	int			i = -1;
+
+	while ((i = bms_next_member(relids, i)) >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		rel_esis = bms_add_members(rel_esis, rel->eclass_source_indexes);
+	}
+
+#ifdef USE_ASSERT_CHECKING
+	/* verify the results look sane */
+	i = -1;
+	while ((i = bms_next_member(rel_esis, i)) >= 0)
+	{
+		RestrictInfo *rinfo = list_nth_node(RestrictInfo, root->eq_sources,
+											i);
+
+		Assert(bms_overlap(relids, rinfo->clause_relids));
+	}
+#endif
+
+	/* bitwise-AND to leave only the ones for this EquivalenceClass */
+	return bms_int_members(rel_esis, ec->ec_source_indexes);
+}
+
+/*
+ * get_ec_source_indexes_strict
+ *		Returns a Bitmapset with indexes into root->eq_sources for all
+ *		RestrictInfos in 'ec' that have
+ *		bms_is_subset(relids, rinfo->clause_relids) as true.
+ *
+ * Returns a newly allocated Bitmapset which the caller is free to modify.
+ */
+Bitmapset *
+get_ec_source_indexes_strict(PlannerInfo *root, EquivalenceClass *ec,
+							 Relids relids)
+{
+	Bitmapset  *esis = NULL;
+	int			i = bms_next_member(relids, -1);
+
+	if (i >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		/*
+		 * bms_intersect to the first relation to try to keep the resulting
+		 * Bitmapset as small as possible.  This saves having to make a
+		 * complete bms_copy() of one of them.  One may contain significantly
+		 * more words than the other.
+		 */
+		esis = bms_intersect(ec->ec_source_indexes,
+							 rel->eclass_source_indexes);
+
+		while ((i = bms_next_member(relids, i)) >= 0)
+		{
+			rel = root->simple_rel_array[i];
+			esis = bms_int_members(esis, rel->eclass_source_indexes);
+		}
+	}
+
+#ifdef USE_ASSERT_CHECKING
+	/* verify the results look sane */
+	i = -1;
+	while ((i = bms_next_member(esis, i)) >= 0)
+	{
+		RestrictInfo *rinfo = list_nth_node(RestrictInfo, root->eq_sources,
+											i);
+
+		Assert(bms_is_subset(relids, rinfo->clause_relids));
+	}
+#endif
+
+	return esis;
+}
+
+/*
+ * get_ec_derive_indexes
+ *		Returns a Bitmapset with indexes into root->eq_derives for all
+ *		RestrictInfos in 'ec' that have
+ *		bms_overlap(relids, rinfo->clause_relids) as true.
+ *
+ * Returns a newly allocated Bitmapset which the caller is free to modify.
+ *
+ * XXX is this function even needed?
+ */
+Bitmapset *
+get_ec_derive_indexes(PlannerInfo *root, EquivalenceClass *ec, Relids relids)
+{
+	Bitmapset  *rel_edis = NULL;
+	int			i = -1;
+
+	while ((i = bms_next_member(relids, i)) >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		rel_edis = bms_add_members(rel_edis, rel->eclass_derive_indexes);
+	}
+
+#ifdef USE_ASSERT_CHECKING
+	/* verify the results look sane */
+	i = -1;
+	while ((i = bms_next_member(rel_edis, i)) >= 0)
+	{
+		RestrictInfo *rinfo = list_nth_node(RestrictInfo, root->eq_derives,
+											i);
+
+		Assert(bms_overlap(relids, rinfo->clause_relids));
+	}
+#endif
+
+	/* bitwise-AND to leave only the ones for this EquivalenceClass */
+	return bms_int_members(rel_edis, ec->ec_derive_indexes);
+}
+
+/*
+ * get_ec_derive_indexes_strict
+ *		Returns a Bitmapset with indexes into root->eq_derives for all
+ *		RestrictInfos in 'ec' that have
+ *		bms_is_subset(relids, rinfo->clause_relids) as true.
+ *
+ * Returns a newly allocated Bitmapset which the caller is free to modify.
+ */
+Bitmapset *
+get_ec_derive_indexes_strict(PlannerInfo *root, EquivalenceClass *ec,
+							 Relids relids)
+{
+	Bitmapset  *edis = NULL;
+	int			i = bms_next_member(relids, -1);
+
+	if (i >= 0)
+	{
+		RelOptInfo *rel = root->simple_rel_array[i];
+
+		/*
+		 * bms_intersect to the first relation to try to keep the resulting
+		 * Bitmapset as small as possible.  This saves having to make a
+		 * complete bms_copy() of one of them.  One may contain significantly
+		 * more words than the other.
+		 */
+		edis = bms_intersect(ec->ec_derive_indexes,
+							 rel->eclass_derive_indexes);
+
+		while ((i = bms_next_member(relids, i)) >= 0)
+		{
+			rel = root->simple_rel_array[i];
+			edis = bms_int_members(edis, rel->eclass_derive_indexes);
+		}
+	}
+
+#ifdef USE_ASSERT_CHECKING
+	/* verify the results look sane */
+	i = -1;
+	while ((i = bms_next_member(edis, i)) >= 0)
+	{
+		RestrictInfo *rinfo = list_nth_node(RestrictInfo, root->eq_derives,
+											i);
+
+		Assert(bms_is_subset(relids, rinfo->clause_relids));
+	}
+#endif
+
+	return edis;
+}
diff --git a/src/backend/optimizer/path/indxpath.c b/src/backend/optimizer/path/indxpath.c
index 9f4698f2a2..e63ddad305 100644
--- a/src/backend/optimizer/path/indxpath.c
+++ b/src/backend/optimizer/path/indxpath.c
@@ -184,8 +184,8 @@ static IndexClause *expand_indexqual_rowcompare(PlannerInfo *root,
 												IndexOptInfo *index,
 												Oid expr_op,
 												bool var_on_left);
-static void match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
-									List **orderby_clauses_p,
+static void match_pathkeys_to_index(PlannerInfo *root, IndexOptInfo *index,
+									List *pathkeys, List **orderby_clauses_p,
 									List **clause_columns_p);
 static Expr *match_clause_to_ordering_op(IndexOptInfo *index,
 										 int indexcol, Expr *clause, Oid pk_opfamily);
@@ -975,7 +975,7 @@ build_index_paths(PlannerInfo *root, RelOptInfo *rel,
 	else if (index->amcanorderbyop && pathkeys_possibly_useful)
 	{
 		/* see if we can generate ordering operators for query_pathkeys */
-		match_pathkeys_to_index(index, root->query_pathkeys,
+		match_pathkeys_to_index(root, index, root->query_pathkeys,
 								&orderbyclauses,
 								&orderbyclausecols);
 		if (orderbyclauses)
@@ -3063,8 +3063,8 @@ expand_indexqual_rowcompare(PlannerInfo *root,
  * one-to-one with the requested pathkeys.
  */
 static void
-match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
-						List **orderby_clauses_p,
+match_pathkeys_to_index(PlannerInfo *root, IndexOptInfo *index,
+						List *pathkeys, List **orderby_clauses_p,
 						List **clause_columns_p)
 {
 	List	   *orderby_clauses = NIL;
@@ -3081,8 +3081,9 @@ match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
 	foreach(lc1, pathkeys)
 	{
 		PathKey    *pathkey = (PathKey *) lfirst(lc1);
+		Bitmapset  *matching_ems;
 		bool		found = false;
-		ListCell   *lc2;
+		int			i;
 
 		/*
 		 * Note: for any failure to match, we just return NIL immediately.
@@ -3106,9 +3107,14 @@ match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
 		 * be considered to match more than one pathkey list, which is OK
 		 * here.  See also get_eclass_for_sort_expr.)
 		 */
-		foreach(lc2, pathkey->pk_eclass->ec_members)
+		matching_ems = bms_intersect(pathkey->pk_eclass->ec_member_indexes,
+									 index->rel->eclass_member_indexes);
+
+		i = -1;
+		while ((i = bms_next_member(matching_ems, i)) >= 0)
 		{
-			EquivalenceMember *member = (EquivalenceMember *) lfirst(lc2);
+			EquivalenceMember *member = list_nth_node(EquivalenceMember,
+													  root->eq_members, i);
 			int			indexcol;
 
 			/* No possibility of match if it references other relations */
diff --git a/src/backend/optimizer/path/pathkeys.c b/src/backend/optimizer/path/pathkeys.c
index c4e7f97f68..0596532db4 100644
--- a/src/backend/optimizer/path/pathkeys.c
+++ b/src/backend/optimizer/path/pathkeys.c
@@ -940,18 +940,19 @@ convert_subquery_pathkeys(PlannerInfo *root, RelOptInfo *rel,
 			 * outer query.
 			 */
 			int			best_score = -1;
-			ListCell   *j;
+			int			j = -1;
 
-			foreach(j, sub_eclass->ec_members)
+			while ((j = bms_next_member(sub_eclass->ec_nonchild_indexes, j)) >= 0)
 			{
-				EquivalenceMember *sub_member = (EquivalenceMember *) lfirst(j);
+				EquivalenceMember *sub_member = list_nth_node(EquivalenceMember,
+															  rel->subroot->eq_members,
+															  j);
 				Expr	   *sub_expr = sub_member->em_expr;
 				Oid			sub_expr_type = sub_member->em_datatype;
 				Oid			sub_expr_coll = sub_eclass->ec_collation;
 				ListCell   *k;
 
-				if (sub_member->em_is_child)
-					continue;	/* ignore children here */
+				Assert(!sub_member->em_is_child);
 
 				foreach(k, subquery_tlist)
 				{
@@ -1450,7 +1451,7 @@ select_outer_pathkeys_for_merge(PlannerInfo *root,
 		RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
 		EquivalenceClass *oeclass;
 		int			score;
-		ListCell   *lc2;
+		int			i;
 
 		/* get the outer eclass */
 		update_mergeclause_eclasses(root, rinfo);
@@ -1471,13 +1472,16 @@ select_outer_pathkeys_for_merge(PlannerInfo *root,
 
 		/* compute score */
 		score = 0;
-		foreach(lc2, oeclass->ec_members)
+		i = -1;
+		while ((i = bms_next_member(oeclass->ec_nonchild_indexes, i)) >= 0)
 		{
-			EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
+			EquivalenceMember *em = list_nth_node(EquivalenceMember,
+												  root->eq_members, i);
 
-			/* Potential future join partner? */
-			if (!em->em_is_const && !em->em_is_child &&
-				!bms_overlap(em->em_relids, joinrel->relids))
+			/* shouldn't be consts or child members in ec_nonchild_indexes */
+			Assert(!em->em_is_const && !em->em_is_child);
+
+			if (!bms_overlap(em->em_relids, joinrel->relids))
 				score++;
 		}
 
diff --git a/src/backend/optimizer/plan/createplan.c b/src/backend/optimizer/plan/createplan.c
index fa09a6103b..7d0fab0354 100644
--- a/src/backend/optimizer/plan/createplan.c
+++ b/src/backend/optimizer/plan/createplan.c
@@ -260,8 +260,8 @@ static IncrementalSort *make_incrementalsort(Plan *lefttree,
 											 int numCols, int nPresortedCols,
 											 AttrNumber *sortColIdx, Oid *sortOperators,
 											 Oid *collations, bool *nullsFirst);
-static Plan *prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
-										Relids relids,
+static Plan *prepare_sort_from_pathkeys(PlannerInfo *root, Plan *lefttree,
+										List *pathkeys, Relids relids,
 										const AttrNumber *reqColIdx,
 										bool adjust_tlist_in_place,
 										int *p_numsortkeys,
@@ -269,10 +269,13 @@ static Plan *prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
 										Oid **p_sortOperators,
 										Oid **p_collations,
 										bool **p_nullsFirst);
-static Sort *make_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
-									 Relids relids);
-static IncrementalSort *make_incrementalsort_from_pathkeys(Plan *lefttree,
-														   List *pathkeys, Relids relids, int nPresortedCols);
+static Sort *make_sort_from_pathkeys(PlannerInfo *root, Plan *lefttree,
+									 List *pathkeys, Relids relids);
+static IncrementalSort *make_incrementalsort_from_pathkeys(PlannerInfo *root,
+														   Plan *lefttree,
+														   List *pathkeys,
+														   Relids relids,
+														   int nPresortedCols);
 static Sort *make_sort_from_groupcols(List *groupcls,
 									  AttrNumber *grpColIdx,
 									  Plan *lefttree);
@@ -293,7 +296,7 @@ static Group *make_group(List *tlist, List *qual, int numGroupCols,
 						 AttrNumber *grpColIdx, Oid *grpOperators, Oid *grpCollations,
 						 Plan *lefttree);
 static Unique *make_unique_from_sortclauses(Plan *lefttree, List *distinctList);
-static Unique *make_unique_from_pathkeys(Plan *lefttree,
+static Unique *make_unique_from_pathkeys(PlannerInfo *root, Plan *lefttree,
 										 List *pathkeys, int numCols);
 static Gather *make_gather(List *qptlist, List *qpqual,
 						   int nworkers, int rescan_param, bool single_copy, Plan *subplan);
@@ -1260,7 +1263,8 @@ create_append_plan(PlannerInfo *root, AppendPath *best_path, int flags)
 		 * function result; it must be the same plan node.  However, we then
 		 * need to detect whether any tlist entries were added.
 		 */
-		(void) prepare_sort_from_pathkeys((Plan *) plan, pathkeys,
+		(void) prepare_sort_from_pathkeys(root,
+										  (Plan *) plan, pathkeys,
 										  best_path->path.parent->relids,
 										  NULL,
 										  true,
@@ -1304,7 +1308,7 @@ create_append_plan(PlannerInfo *root, AppendPath *best_path, int flags)
 			 * don't need an explicit sort, to make sure they are returning
 			 * the same sort key columns the Append expects.
 			 */
-			subplan = prepare_sort_from_pathkeys(subplan, pathkeys,
+			subplan = prepare_sort_from_pathkeys(root, subplan, pathkeys,
 												 subpath->parent->relids,
 												 nodeSortColIdx,
 												 false,
@@ -1445,7 +1449,7 @@ create_merge_append_plan(PlannerInfo *root, MergeAppendPath *best_path,
 	 * function result; it must be the same plan node.  However, we then need
 	 * to detect whether any tlist entries were added.
 	 */
-	(void) prepare_sort_from_pathkeys(plan, pathkeys,
+	(void) prepare_sort_from_pathkeys(root, plan, pathkeys,
 									  best_path->path.parent->relids,
 									  NULL,
 									  true,
@@ -1476,7 +1480,7 @@ create_merge_append_plan(PlannerInfo *root, MergeAppendPath *best_path,
 		subplan = create_plan_recurse(root, subpath, CP_EXACT_TLIST);
 
 		/* Compute sort column info, and adjust subplan's tlist as needed */
-		subplan = prepare_sort_from_pathkeys(subplan, pathkeys,
+		subplan = prepare_sort_from_pathkeys(root, subplan, pathkeys,
 											 subpath->parent->relids,
 											 node->sortColIdx,
 											 false,
@@ -1966,7 +1970,7 @@ create_gather_merge_plan(PlannerInfo *root, GatherMergePath *best_path)
 	Assert(pathkeys != NIL);
 
 	/* Compute sort column info, and adjust subplan's tlist as needed */
-	subplan = prepare_sort_from_pathkeys(subplan, pathkeys,
+	subplan = prepare_sort_from_pathkeys(root, subplan, pathkeys,
 										 best_path->subpath->parent->relids,
 										 gm_plan->sortColIdx,
 										 false,
@@ -2185,7 +2189,7 @@ create_sort_plan(PlannerInfo *root, SortPath *best_path, int flags)
 	 * relids. Thus, if this sort path is based on a child relation, we must
 	 * pass its relids.
 	 */
-	plan = make_sort_from_pathkeys(subplan, best_path->path.pathkeys,
+	plan = make_sort_from_pathkeys(root, subplan, best_path->path.pathkeys,
 								   IS_OTHER_REL(best_path->subpath->parent) ?
 								   best_path->path.parent->relids : NULL);
 
@@ -2209,7 +2213,7 @@ create_incrementalsort_plan(PlannerInfo *root, IncrementalSortPath *best_path,
 	/* See comments in create_sort_plan() above */
 	subplan = create_plan_recurse(root, best_path->spath.subpath,
 								  flags | CP_SMALL_TLIST);
-	plan = make_incrementalsort_from_pathkeys(subplan,
+	plan = make_incrementalsort_from_pathkeys(root, subplan,
 											  best_path->spath.path.pathkeys,
 											  IS_OTHER_REL(best_path->spath.subpath->parent) ?
 											  best_path->spath.path.parent->relids : NULL,
@@ -2278,7 +2282,7 @@ create_upper_unique_plan(PlannerInfo *root, UpperUniquePath *best_path, int flag
 	subplan = create_plan_recurse(root, best_path->subpath,
 								  flags | CP_LABEL_TLIST);
 
-	plan = make_unique_from_pathkeys(subplan,
+	plan = make_unique_from_pathkeys(root, subplan,
 									 best_path->path.pathkeys,
 									 best_path->numkeys);
 
@@ -4494,7 +4498,7 @@ create_mergejoin_plan(PlannerInfo *root,
 	if (best_path->outersortkeys)
 	{
 		Relids		outer_relids = outer_path->parent->relids;
-		Sort	   *sort = make_sort_from_pathkeys(outer_plan,
+		Sort	   *sort = make_sort_from_pathkeys(root, outer_plan,
 												   best_path->outersortkeys,
 												   outer_relids);
 
@@ -4508,7 +4512,7 @@ create_mergejoin_plan(PlannerInfo *root,
 	if (best_path->innersortkeys)
 	{
 		Relids		inner_relids = inner_path->parent->relids;
-		Sort	   *sort = make_sort_from_pathkeys(inner_plan,
+		Sort	   *sort = make_sort_from_pathkeys(root, inner_plan,
 												   best_path->innersortkeys,
 												   inner_relids);
 
@@ -6129,7 +6133,8 @@ make_incrementalsort(Plan *lefttree, int numCols, int nPresortedCols,
  * or a Result stacked atop lefttree).
  */
 static Plan *
-prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
+prepare_sort_from_pathkeys(PlannerInfo *root,
+						   Plan *lefttree, List *pathkeys,
 						   Relids relids,
 						   const AttrNumber *reqColIdx,
 						   bool adjust_tlist_in_place,
@@ -6196,7 +6201,7 @@ prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
 			tle = get_tle_by_resno(tlist, reqColIdx[numsortkeys]);
 			if (tle)
 			{
-				em = find_ec_member_matching_expr(ec, tle->expr, relids);
+				em = find_ec_member_matching_expr(root, ec, tle->expr, relids);
 				if (em)
 				{
 					/* found expr at right place in tlist */
@@ -6224,7 +6229,7 @@ prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
 			foreach(j, tlist)
 			{
 				tle = (TargetEntry *) lfirst(j);
-				em = find_ec_member_matching_expr(ec, tle->expr, relids);
+				em = find_ec_member_matching_expr(root, ec, tle->expr, relids);
 				if (em)
 				{
 					/* found expr already in tlist */
@@ -6240,7 +6245,7 @@ prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
 			/*
 			 * No matching tlist item; look for a computable expression.
 			 */
-			em = find_computable_ec_member(NULL, ec, tlist, relids, false);
+			em = find_computable_ec_member(root, ec, tlist, relids, false);
 			if (!em)
 				elog(ERROR, "could not find pathkey item to sort");
 			pk_datatype = em->em_datatype;
@@ -6311,7 +6316,8 @@ prepare_sort_from_pathkeys(Plan *lefttree, List *pathkeys,
  *	  'relids' is the set of relations required by prepare_sort_from_pathkeys()
  */
 static Sort *
-make_sort_from_pathkeys(Plan *lefttree, List *pathkeys, Relids relids)
+make_sort_from_pathkeys(PlannerInfo *root, Plan *lefttree, List *pathkeys,
+						Relids relids)
 {
 	int			numsortkeys;
 	AttrNumber *sortColIdx;
@@ -6320,7 +6326,9 @@ make_sort_from_pathkeys(Plan *lefttree, List *pathkeys, Relids relids)
 	bool	   *nullsFirst;
 
 	/* Compute sort column info, and adjust lefttree as needed */
-	lefttree = prepare_sort_from_pathkeys(lefttree, pathkeys,
+	lefttree = prepare_sort_from_pathkeys(root,
+										  lefttree,
+										  pathkeys,
 										  relids,
 										  NULL,
 										  false,
@@ -6346,7 +6354,8 @@ make_sort_from_pathkeys(Plan *lefttree, List *pathkeys, Relids relids)
  *	  'nPresortedCols' is the number of presorted columns in input tuples
  */
 static IncrementalSort *
-make_incrementalsort_from_pathkeys(Plan *lefttree, List *pathkeys,
+make_incrementalsort_from_pathkeys(PlannerInfo *root,
+								   Plan *lefttree, List *pathkeys,
 								   Relids relids, int nPresortedCols)
 {
 	int			numsortkeys;
@@ -6356,7 +6365,9 @@ make_incrementalsort_from_pathkeys(Plan *lefttree, List *pathkeys,
 	bool	   *nullsFirst;
 
 	/* Compute sort column info, and adjust lefttree as needed */
-	lefttree = prepare_sort_from_pathkeys(lefttree, pathkeys,
+	lefttree = prepare_sort_from_pathkeys(root,
+										  lefttree,
+										  pathkeys,
 										  relids,
 										  NULL,
 										  false,
@@ -6706,7 +6717,8 @@ make_unique_from_sortclauses(Plan *lefttree, List *distinctList)
  * as above, but use pathkeys to identify the sort columns and semantics
  */
 static Unique *
-make_unique_from_pathkeys(Plan *lefttree, List *pathkeys, int numCols)
+make_unique_from_pathkeys(PlannerInfo *root, Plan *lefttree, List *pathkeys,
+						  int numCols)
 {
 	Unique	   *node = makeNode(Unique);
 	Plan	   *plan = &node->plan;
@@ -6769,7 +6781,7 @@ make_unique_from_pathkeys(Plan *lefttree, List *pathkeys, int numCols)
 			foreach(j, plan->targetlist)
 			{
 				tle = (TargetEntry *) lfirst(j);
-				em = find_ec_member_matching_expr(ec, tle->expr, NULL);
+				em = find_ec_member_matching_expr(root, ec, tle->expr, NULL);
 				if (em)
 				{
 					/* found expr already in tlist */
diff --git a/src/backend/optimizer/plan/planagg.c b/src/backend/optimizer/plan/planagg.c
index d168620665..9f0fa42045 100644
--- a/src/backend/optimizer/plan/planagg.c
+++ b/src/backend/optimizer/plan/planagg.c
@@ -356,6 +356,7 @@ build_minmax_path(PlannerInfo *root, MinMaxAggInfo *mminfo,
 	Assert(subroot->join_info_list == NIL);
 	/* and we haven't made equivalence classes, either */
 	Assert(subroot->eq_classes == NIL);
+	Assert(root->eq_members == NIL);
 	/* and we haven't created PlaceHolderInfos, either */
 	Assert(subroot->placeholder_list == NIL);
 
diff --git a/src/backend/optimizer/plan/planner.c b/src/backend/optimizer/plan/planner.c
index a1873ce26d..c8275e704a 100644
--- a/src/backend/optimizer/plan/planner.c
+++ b/src/backend/optimizer/plan/planner.c
@@ -627,6 +627,9 @@ subquery_planner(PlannerGlobal *glob, Query *parse,
 	root->multiexpr_params = NIL;
 	root->join_domains = NIL;
 	root->eq_classes = NIL;
+	root->eq_members = NIL;
+	root->eq_sources = NIL;
+	root->eq_derives = NIL;
 	root->ec_merging_done = false;
 	root->last_rinfo_serial = 0;
 	root->all_result_relids =
diff --git a/src/backend/optimizer/prep/prepjointree.c b/src/backend/optimizer/prep/prepjointree.c
index 870d84b29d..804ede97b1 100644
--- a/src/backend/optimizer/prep/prepjointree.c
+++ b/src/backend/optimizer/prep/prepjointree.c
@@ -993,6 +993,9 @@ pull_up_simple_subquery(PlannerInfo *root, Node *jtnode, RangeTblEntry *rte,
 	subroot->multiexpr_params = NIL;
 	subroot->join_domains = NIL;
 	subroot->eq_classes = NIL;
+	subroot->eq_members = NIL;
+	subroot->eq_sources = NIL;
+	subroot->eq_derives = NIL;
 	subroot->ec_merging_done = false;
 	subroot->last_rinfo_serial = 0;
 	subroot->all_result_relids = NULL;
diff --git a/src/backend/optimizer/prep/prepunion.c b/src/backend/optimizer/prep/prepunion.c
index 0c68ec011b..4c7d66311f 100644
--- a/src/backend/optimizer/prep/prepunion.c
+++ b/src/backend/optimizer/prep/prepunion.c
@@ -45,7 +45,7 @@
 #include "utils/selfuncs.h"
 #include "utils/syscache.h"
 
-
+static void setup_append_rel_entry(PlannerInfo *root);
 static RelOptInfo *recurse_set_operations(Node *setOp, PlannerInfo *root,
 										  List *colTypes, List *colCollations,
 										  bool junkOK,
@@ -128,6 +128,7 @@ plan_set_operations(PlannerInfo *root)
 	 * so that pathkeys.c won't complain.
 	 */
 	Assert(root->eq_classes == NIL);
+	Assert(root->eq_members == NIL);
 	root->ec_merging_done = true;
 
 	/*
@@ -149,6 +150,8 @@ plan_set_operations(PlannerInfo *root)
 	leftmostQuery = leftmostRTE->subquery;
 	Assert(leftmostQuery != NULL);
 
+	setup_append_rel_entry(root);
+
 	/*
 	 * If the topmost node is a recursive union, it needs special processing.
 	 */
@@ -180,6 +183,26 @@ plan_set_operations(PlannerInfo *root)
 	return setop_rel;
 }
 
+/*
+ * setup_append_rel_entry
+ *		Add entry into root's simple_rel_array at element 0.  This is required
+ *		because generate_append_tlist() makes Vars with varno=0.  In
+ *		add_eq_member() we need to index EquivalenceMembers belonging to this
+ *		relation.
+ */
+static void
+setup_append_rel_entry(PlannerInfo *root)
+{
+	RelOptInfo *rel = makeNode(RelOptInfo);
+
+	memset(rel, 0, sizeof(RelOptInfo));
+	rel->eclass_member_indexes = NULL;
+
+	/* make sure nothing else has made use of this element */
+	Assert(root->simple_rel_array[0] == NULL);
+	root->simple_rel_array[0] = rel;
+}
+
 /*
  * recurse_set_operations
  *	  Recursively handle one step in a tree of set operations
diff --git a/src/backend/optimizer/util/relnode.c b/src/backend/optimizer/util/relnode.c
index 68fd033595..f2f9a350ce 100644
--- a/src/backend/optimizer/util/relnode.c
+++ b/src/backend/optimizer/util/relnode.c
@@ -227,6 +227,9 @@ build_simple_rel(PlannerInfo *root, int relid, RelOptInfo *parent)
 	rel->tuples = 0;
 	rel->allvisfrac = 0;
 	rel->eclass_indexes = NULL;
+	rel->eclass_member_indexes = NULL;
+	rel->eclass_source_indexes = NULL;
+	rel->eclass_derive_indexes = NULL;
 	rel->subroot = NULL;
 	rel->subplan_params = NIL;
 	rel->rel_parallel_workers = -1; /* set up in get_relation_info */
@@ -713,6 +716,9 @@ build_join_rel(PlannerInfo *root,
 	joinrel->tuples = 0;
 	joinrel->allvisfrac = 0;
 	joinrel->eclass_indexes = NULL;
+	joinrel->eclass_member_indexes = NULL;
+	joinrel->eclass_source_indexes = NULL;
+	joinrel->eclass_derive_indexes = NULL;
 	joinrel->subroot = NULL;
 	joinrel->subplan_params = NIL;
 	joinrel->rel_parallel_workers = -1;
@@ -901,6 +907,9 @@ build_child_join_rel(PlannerInfo *root, RelOptInfo *outer_rel,
 	joinrel->tuples = 0;
 	joinrel->allvisfrac = 0;
 	joinrel->eclass_indexes = NULL;
+	joinrel->eclass_member_indexes = NULL;
+	joinrel->eclass_source_indexes = NULL;
+	joinrel->eclass_derive_indexes = NULL;
 	joinrel->subroot = NULL;
 	joinrel->subplan_params = NIL;
 	joinrel->amflags = 0;
diff --git a/src/include/nodes/pathnodes.h b/src/include/nodes/pathnodes.h
index d61a62da19..40c86e6c4b 100644
--- a/src/include/nodes/pathnodes.h
+++ b/src/include/nodes/pathnodes.h
@@ -313,6 +313,15 @@ struct PlannerInfo
 	/* list of active EquivalenceClasses */
 	List	   *eq_classes;
 
+	/* list of each EquivalenceMember */
+	List	   *eq_members;
+
+	/* list of source RestrictInfos used to build EquivalenceClasses */
+	List	   *eq_sources;
+
+	/* list of RestrictInfos derived from EquivalenceClasses */
+	List	   *eq_derives;
+
 	/* set true once ECs are canonical */
 	bool		ec_merging_done;
 
@@ -935,6 +944,24 @@ typedef struct RelOptInfo
 	double		allvisfrac;
 	/* indexes in PlannerInfo's eq_classes list of ECs that mention this rel */
 	Bitmapset  *eclass_indexes;
+
+	/*
+	 * Indexes in PlannerInfo's eq_members list of EMs that mention this rel
+	 */
+	Bitmapset  *eclass_member_indexes;
+
+	/*
+	 * Indexes in PlannerInfo's eq_sources list for RestrictInfos that mention
+	 * this relation.
+	 */
+	Bitmapset  *eclass_source_indexes;
+
+	/*
+	 * Indexes in PlannerInfo's eq_derives list for RestrictInfos that mention
+	 * this relation.
+	 */
+	Bitmapset  *eclass_derive_indexes;
+
 	PlannerInfo *subroot;		/* if subquery */
 	List	   *subplan_params; /* if subquery */
 	/* wanted number of parallel workers */
@@ -1356,6 +1383,39 @@ typedef struct JoinDomain
  * entry: consider SELECT random() AS a, random() AS b ... ORDER BY b,a.
  * So we record the SortGroupRef of the originating sort clause.
  *
+ * At various locations in the query planner, we must search for
+ * EquivalenceMembers within a given EquivalenceClass.  For the common case,
+ * an EquivalenceClass does not have a large number of EquivalenceMembers,
+ * however, in cases such as planning queries to partitioned tables, the number
+ * of members can become large.  To maintain planning performance, we make use
+ * of a bitmap index to allow us to quickly find EquivalenceMembers in a given
+ * EquivalenceClass belonging to a given relation or set of relations.  This
+ * is done by storing a list of EquivalenceMembers belonging to all
+ * EquivalenceClasses in PlannerInfo and storing a Bitmapset for each
+ * RelOptInfo which has a bit set for each EquivalenceMember in that list
+ * which relates to the given relation.  We also store a Bitmapset to mark all
+ * of the indexes in the PlannerInfo's list of EquivalenceMembers in the
+ * EquivalenceClass.  We can quickly find the interesting indexes into the
+ * PlannerInfo's list by performing a bit-wise AND on the RelOptInfo's
+ * Bitmapset and the EquivalenceClasses.
+ *
+ * To further speed up the lookup of EquivalenceMembers we also record the
+ * non-child indexes.  This allows us to deal with fewer bits for searches
+ * that don't require "is_child" EquivalenceMembers.  We must also store the
+ * indexes into EquivalenceMembers which have no relids mentioned as some
+ * searches require that.
+ *
+ * Additionally, we also store the EquivalenceMembers of a given
+ * EquivalenceClass in the ec_members list.  Technically, we could obtain this
+ * from looking at the bits in ec_member_indexes, however, finding all members
+ * of a given EquivalenceClass is common enough that it pays to have fast
+ * access to a dense list containing all members.
+ *
+ * The source and derived RestrictInfos are indexed in a similar method,
+ * although we don't maintain a List in the EquivalenceClass for these.  These
+ * must be looked up in PlannerInfo using the ec_source_indexes and
+ * ec_derive_indexes Bitmapsets.
+ *
  * NB: if ec_merged isn't NULL, this class has been merged into another, and
  * should be ignored in favor of using the pointed-to class.
  *
@@ -1373,9 +1433,19 @@ typedef struct EquivalenceClass
 
 	List	   *ec_opfamilies;	/* btree operator family OIDs */
 	Oid			ec_collation;	/* collation, if datatypes are collatable */
-	List	   *ec_members;		/* list of EquivalenceMembers */
-	List	   *ec_sources;		/* list of generating RestrictInfos */
-	List	   *ec_derives;		/* list of derived RestrictInfos */
+	List	   *ec_members;		/* list of EquivalenceMembers in the class */
+	Bitmapset  *ec_member_indexes;	/* Indexes into all PlannerInfos
+									 * eq_members for this EquivalenceClass */
+	Bitmapset  *ec_nonchild_indexes;	/* Indexes into PlannerInfo's
+										 * eq_members with em_is_child ==
+										 * false */
+	Bitmapset  *ec_norel_indexes;	/* Indexes into PlannerInfo's eq_members
+									 * for members where pull_varno on the
+									 * em_expr is an empty set */
+	Bitmapset  *ec_source_indexes;	/* indexes into PlannerInfo's eq_sources
+									 * list of generating RestrictInfos */
+	Bitmapset  *ec_derive_indexes;	/* indexes into PlannerInfo's eq_derives
+									 * list of derived RestrictInfos */
 	Relids		ec_relids;		/* all relids appearing in ec_members, except
 								 * for child members (see below) */
 	bool		ec_has_const;	/* any pseudoconstants in ec_members? */
@@ -1423,8 +1493,9 @@ typedef struct EquivalenceMember
 	NodeTag		type;
 
 	Expr	   *em_expr;		/* the expression represented */
-	Relids		em_relids;		/* all relids appearing in em_expr */
-	bool		em_is_const;	/* expression is pseudoconstant? */
+	Relids		em_relids;		/* relids for this member */
+	bool		em_is_const;	/* is em_relids empty? */
+	bool		em_norel_expr;	/* true if em_expr contains no Vars */
 	bool		em_is_child;	/* derived version for a child relation? */
 	Oid			em_datatype;	/* the "nominal type" used by the opfamily */
 	JoinDomain *em_jdomain;		/* join domain containing the source clause */
diff --git a/src/include/nodes/pg_list.h b/src/include/nodes/pg_list.h
index 529a382d28..77f26edf22 100644
--- a/src/include/nodes/pg_list.h
+++ b/src/include/nodes/pg_list.h
@@ -629,6 +629,7 @@ extern pg_nodiscard List *list_copy_deep(const List *oldlist);
 typedef int (*list_sort_comparator) (const ListCell *a, const ListCell *b);
 extern void list_sort(List *list, list_sort_comparator cmp);
 
+extern int	list_ptr_cmp(const ListCell *p1, const ListCell *p2);
 extern int	list_int_cmp(const ListCell *p1, const ListCell *p2);
 extern int	list_oid_cmp(const ListCell *p1, const ListCell *p2);
 
diff --git a/src/include/optimizer/paths.h b/src/include/optimizer/paths.h
index 5b9db7733d..cc5b8701a7 100644
--- a/src/include/optimizer/paths.h
+++ b/src/include/optimizer/paths.h
@@ -114,6 +114,31 @@ extern void mark_dummy_rel(RelOptInfo *rel);
  * equivclass.c
  *	  routines for managing EquivalenceClasses
  */
+
+/*
+ * EquivalenceMemberIterator
+ *		Data structure used for iteration over an EquivalenceClass's
+ *		EquivalenceMember in order to quickly find the members matching our
+ *		search pattern.
+ */
+typedef struct EquivalenceMemberIterator
+{
+	bool		use_index;		/* use matching_ems index? */
+	bool		relids_empty;	/* is with_relids empty? */
+	bool		with_children;	/* include em_is_child members? */
+	bool		with_norel_members; /* include members with empty em_relids */
+#ifdef USE_ASSERT_CHECKING
+	bool		isstrict;		/* ensure the correct next function is used */
+#endif
+	int			orig_length;	/* elements in eclass->ec_members at the start */
+	int			current_index;	/* current iterator position, or -1. */
+	Relids		with_relids;	/* relids to match in em_relids */
+	PlannerInfo *root;			/* PlannerInfo the eclass belongs to */
+	EquivalenceClass *eclass;	/* the EquivalenceClass we're looking at */
+	Bitmapset  *matching_ems;	/* when use_index == true, these are the
+								 * matching indexes in root eq_members */
+} EquivalenceMemberIterator;
+
 typedef bool (*ec_matches_callback_type) (PlannerInfo *root,
 										  RelOptInfo *rel,
 										  EquivalenceClass *ec,
@@ -134,7 +159,8 @@ extern EquivalenceClass *get_eclass_for_sort_expr(PlannerInfo *root,
 												  Index sortref,
 												  Relids rel,
 												  bool create_it);
-extern EquivalenceMember *find_ec_member_matching_expr(EquivalenceClass *ec,
+extern EquivalenceMember *find_ec_member_matching_expr(PlannerInfo *root,
+													   EquivalenceClass *ec,
 													   Expr *expr,
 													   Relids relids);
 extern EquivalenceMember *find_computable_ec_member(PlannerInfo *root,
@@ -160,7 +186,8 @@ extern bool exprs_known_equal(PlannerInfo *root, Node *item1, Node *item2);
 extern EquivalenceClass *match_eclasses_to_foreign_key_col(PlannerInfo *root,
 														   ForeignKeyOptInfo *fkinfo,
 														   int colno);
-extern RestrictInfo *find_derived_clause_for_ec_member(EquivalenceClass *ec,
+extern RestrictInfo *find_derived_clause_for_ec_member(PlannerInfo *root,
+													   EquivalenceClass *ec,
 													   EquivalenceMember *em);
 extern void add_child_rel_equivalences(PlannerInfo *root,
 									   AppendRelInfo *appinfo,
@@ -186,6 +213,42 @@ extern bool eclass_useful_for_merging(PlannerInfo *root,
 extern bool is_redundant_derived_clause(RestrictInfo *rinfo, List *clauselist);
 extern bool is_redundant_with_indexclauses(RestrictInfo *rinfo,
 										   List *indexclauses);
+extern Bitmapset *get_ecmember_indexes(PlannerInfo *root,
+									   EquivalenceClass *ec,
+									   Relids relids,
+									   bool with_children,
+									   bool with_norel_members);
+extern Bitmapset *get_ecmember_indexes_strict(PlannerInfo *root,
+											  EquivalenceClass *ec,
+											  Relids relids,
+											  bool with_children,
+											  bool with_norel_members);
+extern void setup_eclass_member_iterator(EquivalenceMemberIterator *iter,
+										 PlannerInfo *root,
+										 EquivalenceClass *ec, Relids relids,
+										 bool with_children,
+										 bool with_norel_members);
+extern void setup_eclass_member_strict_iterator(EquivalenceMemberIterator *iter,
+												PlannerInfo *root,
+												EquivalenceClass *ec,
+												Relids relids,
+												bool with_children,
+												bool with_norel_members);
+extern EquivalenceMember *eclass_member_iterator_next(EquivalenceMemberIterator *iter);
+extern EquivalenceMember *eclass_member_iterator_strict_next(EquivalenceMemberIterator *iter);
+extern void eclass_member_iterator_dispose(EquivalenceMemberIterator *iter);
+extern Bitmapset *get_ec_source_indexes(PlannerInfo *root,
+										EquivalenceClass *ec,
+										Relids relids);
+extern Bitmapset *get_ec_source_indexes_strict(PlannerInfo *root,
+											   EquivalenceClass *ec,
+											   Relids relids);
+extern Bitmapset *get_ec_derive_indexes(PlannerInfo *root,
+										EquivalenceClass *ec,
+										Relids relids);
+extern Bitmapset *get_ec_derive_indexes_strict(PlannerInfo *root,
+											   EquivalenceClass *ec,
+											   Relids relids);
 
 /*
  * pathkeys.c
diff --git a/src/tools/pgindent/typedefs.list b/src/tools/pgindent/typedefs.list
index 86a9303bf5..36b65025ed 100644
--- a/src/tools/pgindent/typedefs.list
+++ b/src/tools/pgindent/typedefs.list
@@ -643,6 +643,7 @@ EphemeralNamedRelationMetadata
 EphemeralNamedRelationMetadataData
 EquivalenceClass
 EquivalenceMember
+EquivalenceMemberIterator
 ErrorContextCallback
 ErrorData
 ErrorSaveContext
-- 
2.39.2.windows.1

