Adding upstream version 15.5.upstream/15.5

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1917 insertions, 0 deletions

diff --git a/src/backend/optimizer/path/pathkeys.c b/src/backend/optimizer/path/pathkeys.c
new file mode 100644
index 0000000..86a35cd
--- /dev/null
+++ b/src/backend/optimizer/path/pathkeys.c
@@ -0,0 +1,1917 @@
+/*-------------------------------------------------------------------------
+ *
+ * pathkeys.c
+ *	  Utilities for matching and building path keys
+ *
+ * See src/backend/optimizer/README for a great deal of information about
+ * the nature and use of path keys.
+ *
+ *
+ * Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1994, Regents of the University of California
+ *
+ * IDENTIFICATION
+ *	  src/backend/optimizer/path/pathkeys.c
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include "access/stratnum.h"
+#include "catalog/pg_opfamily.h"
+#include "nodes/makefuncs.h"
+#include "nodes/nodeFuncs.h"
+#include "nodes/plannodes.h"
+#include "optimizer/optimizer.h"
+#include "optimizer/pathnode.h"
+#include "optimizer/paths.h"
+#include "partitioning/partbounds.h"
+#include "utils/lsyscache.h"
+
+
+static bool pathkey_is_redundant(PathKey *new_pathkey, List *pathkeys);
+static bool matches_boolean_partition_clause(RestrictInfo *rinfo,
+											 RelOptInfo *partrel,
+											 int partkeycol);
+static Var *find_var_for_subquery_tle(RelOptInfo *rel, TargetEntry *tle);
+static bool right_merge_direction(PlannerInfo *root, PathKey *pathkey);
+
+
+/****************************************************************************
+ *		PATHKEY CONSTRUCTION AND REDUNDANCY TESTING
+ ****************************************************************************/
+
+/*
+ * make_canonical_pathkey
+ *	  Given the parameters for a PathKey, find any pre-existing matching
+ *	  pathkey in the query's list of "canonical" pathkeys.  Make a new
+ *	  entry if there's not one already.
+ *
+ * Note that this function must not be used until after we have completed
+ * merging EquivalenceClasses.
+ */
+PathKey *
+make_canonical_pathkey(PlannerInfo *root,
+					   EquivalenceClass *eclass, Oid opfamily,
+					   int strategy, bool nulls_first)
+{
+	PathKey    *pk;
+	ListCell   *lc;
+	MemoryContext oldcontext;
+
+	/* Can't make canonical pathkeys if the set of ECs might still change */
+	if (!root->ec_merging_done)
+		elog(ERROR, "too soon to build canonical pathkeys");
+
+	/* The passed eclass might be non-canonical, so chase up to the top */
+	while (eclass->ec_merged)
+		eclass = eclass->ec_merged;
+
+	foreach(lc, root->canon_pathkeys)
+	{
+		pk = (PathKey *) lfirst(lc);
+		if (eclass == pk->pk_eclass &&
+			opfamily == pk->pk_opfamily &&
+			strategy == pk->pk_strategy &&
+			nulls_first == pk->pk_nulls_first)
+			return pk;
+	}
+
+	/*
+	 * Be sure canonical pathkeys are allocated in the main planning context.
+	 * Not an issue in normal planning, but it is for GEQO.
+	 */
+	oldcontext = MemoryContextSwitchTo(root->planner_cxt);
+
+	pk = makeNode(PathKey);
+	pk->pk_eclass = eclass;
+	pk->pk_opfamily = opfamily;
+	pk->pk_strategy = strategy;
+	pk->pk_nulls_first = nulls_first;
+
+	root->canon_pathkeys = lappend(root->canon_pathkeys, pk);
+
+	MemoryContextSwitchTo(oldcontext);
+
+	return pk;
+}
+
+/*
+ * pathkey_is_redundant
+ *	   Is a pathkey redundant with one already in the given list?
+ *
+ * We detect two cases:
+ *
+ * 1. If the new pathkey's equivalence class contains a constant, and isn't
+ * below an outer join, then we can disregard it as a sort key.  An example:
+ *			SELECT ... WHERE x = 42 ORDER BY x, y;
+ * We may as well just sort by y.  Note that because of opfamily matching,
+ * this is semantically correct: we know that the equality constraint is one
+ * that actually binds the variable to a single value in the terms of any
+ * ordering operator that might go with the eclass.  This rule not only lets
+ * us simplify (or even skip) explicit sorts, but also allows matching index
+ * sort orders to a query when there are don't-care index columns.
+ *
+ * 2. If the new pathkey's equivalence class is the same as that of any
+ * existing member of the pathkey list, then it is redundant.  Some examples:
+ *			SELECT ... ORDER BY x, x;
+ *			SELECT ... ORDER BY x, x DESC;
+ *			SELECT ... WHERE x = y ORDER BY x, y;
+ * In all these cases the second sort key cannot distinguish values that are
+ * considered equal by the first, and so there's no point in using it.
+ * Note in particular that we need not compare opfamily (all the opfamilies
+ * of the EC have the same notion of equality) nor sort direction.
+ *
+ * Both the given pathkey and the list members must be canonical for this
+ * to work properly, but that's okay since we no longer ever construct any
+ * non-canonical pathkeys.  (Note: the notion of a pathkey *list* being
+ * canonical includes the additional requirement of no redundant entries,
+ * which is exactly what we are checking for here.)
+ *
+ * Because the equivclass.c machinery forms only one copy of any EC per query,
+ * pointer comparison is enough to decide whether canonical ECs are the same.
+ */
+static bool
+pathkey_is_redundant(PathKey *new_pathkey, List *pathkeys)
+{
+	EquivalenceClass *new_ec = new_pathkey->pk_eclass;
+	ListCell   *lc;
+
+	/* Check for EC containing a constant --- unconditionally redundant */
+	if (EC_MUST_BE_REDUNDANT(new_ec))
+		return true;
+
+	/* If same EC already used in list, then redundant */
+	foreach(lc, pathkeys)
+	{
+		PathKey    *old_pathkey = (PathKey *) lfirst(lc);
+
+		if (new_ec == old_pathkey->pk_eclass)
+			return true;
+	}
+
+	return false;
+}
+
+/*
+ * make_pathkey_from_sortinfo
+ *	  Given an expression and sort-order information, create a PathKey.
+ *	  The result is always a "canonical" PathKey, but it might be redundant.
+ *
+ * expr is the expression, and nullable_relids is the set of base relids
+ * that are potentially nullable below it.
+ *
+ * If the PathKey is being generated from a SortGroupClause, sortref should be
+ * the SortGroupClause's SortGroupRef; otherwise zero.
+ *
+ * If rel is not NULL, it identifies a specific relation we're considering
+ * a path for, and indicates that child EC members for that relation can be
+ * considered.  Otherwise child members are ignored.  (See the comments for
+ * get_eclass_for_sort_expr.)
+ *
+ * create_it is true if we should create any missing EquivalenceClass
+ * needed to represent the sort key.  If it's false, we return NULL if the
+ * sort key isn't already present in any EquivalenceClass.
+ */
+static PathKey *
+make_pathkey_from_sortinfo(PlannerInfo *root,
+						   Expr *expr,
+						   Relids nullable_relids,
+						   Oid opfamily,
+						   Oid opcintype,
+						   Oid collation,
+						   bool reverse_sort,
+						   bool nulls_first,
+						   Index sortref,
+						   Relids rel,
+						   bool create_it)
+{
+	int16		strategy;
+	Oid			equality_op;
+	List	   *opfamilies;
+	EquivalenceClass *eclass;
+
+	strategy = reverse_sort ? BTGreaterStrategyNumber : BTLessStrategyNumber;
+
+	/*
+	 * EquivalenceClasses need to contain opfamily lists based on the family
+	 * membership of mergejoinable equality operators, which could belong to
+	 * more than one opfamily.  So we have to look up the opfamily's equality
+	 * operator and get its membership.
+	 */
+	equality_op = get_opfamily_member(opfamily,
+									  opcintype,
+									  opcintype,
+									  BTEqualStrategyNumber);
+	if (!OidIsValid(equality_op))	/* shouldn't happen */
+		elog(ERROR, "missing operator %d(%u,%u) in opfamily %u",
+			 BTEqualStrategyNumber, opcintype, opcintype, opfamily);
+	opfamilies = get_mergejoin_opfamilies(equality_op);
+	if (!opfamilies)			/* certainly should find some */
+		elog(ERROR, "could not find opfamilies for equality operator %u",
+			 equality_op);
+
+	/* Now find or (optionally) create a matching EquivalenceClass */
+	eclass = get_eclass_for_sort_expr(root, expr, nullable_relids,
+									  opfamilies, opcintype, collation,
+									  sortref, rel, create_it);
+
+	/* Fail if no EC and !create_it */
+	if (!eclass)
+		return NULL;
+
+	/* And finally we can find or create a PathKey node */
+	return make_canonical_pathkey(root, eclass, opfamily,
+								  strategy, nulls_first);
+}
+
+/*
+ * make_pathkey_from_sortop
+ *	  Like make_pathkey_from_sortinfo, but work from a sort operator.
+ *
+ * This should eventually go away, but we need to restructure SortGroupClause
+ * first.
+ */
+static PathKey *
+make_pathkey_from_sortop(PlannerInfo *root,
+						 Expr *expr,
+						 Relids nullable_relids,
+						 Oid ordering_op,
+						 bool nulls_first,
+						 Index sortref,
+						 bool create_it)
+{
+	Oid			opfamily,
+				opcintype,
+				collation;
+	int16		strategy;
+
+	/* Find the operator in pg_amop --- failure shouldn't happen */
+	if (!get_ordering_op_properties(ordering_op,
+									&opfamily, &opcintype, &strategy))
+		elog(ERROR, "operator %u is not a valid ordering operator",
+			 ordering_op);
+
+	/* Because SortGroupClause doesn't carry collation, consult the expr */
+	collation = exprCollation((Node *) expr);
+
+	return make_pathkey_from_sortinfo(root,
+									  expr,
+									  nullable_relids,
+									  opfamily,
+									  opcintype,
+									  collation,
+									  (strategy == BTGreaterStrategyNumber),
+									  nulls_first,
+									  sortref,
+									  NULL,
+									  create_it);
+}
+
+
+/****************************************************************************
+ *		PATHKEY COMPARISONS
+ ****************************************************************************/
+
+/*
+ * compare_pathkeys
+ *	  Compare two pathkeys to see if they are equivalent, and if not whether
+ *	  one is "better" than the other.
+ *
+ *	  We assume the pathkeys are canonical, and so they can be checked for
+ *	  equality by simple pointer comparison.
+ */
+PathKeysComparison
+compare_pathkeys(List *keys1, List *keys2)
+{
+	ListCell   *key1,
+			   *key2;
+
+	/*
+	 * Fall out quickly if we are passed two identical lists.  This mostly
+	 * catches the case where both are NIL, but that's common enough to
+	 * warrant the test.
+	 */
+	if (keys1 == keys2)
+		return PATHKEYS_EQUAL;
+
+	forboth(key1, keys1, key2, keys2)
+	{
+		PathKey    *pathkey1 = (PathKey *) lfirst(key1);
+		PathKey    *pathkey2 = (PathKey *) lfirst(key2);
+
+		if (pathkey1 != pathkey2)
+			return PATHKEYS_DIFFERENT;	/* no need to keep looking */
+	}
+
+	/*
+	 * If we reached the end of only one list, the other is longer and
+	 * therefore not a subset.
+	 */
+	if (key1 != NULL)
+		return PATHKEYS_BETTER1;	/* key1 is longer */
+	if (key2 != NULL)
+		return PATHKEYS_BETTER2;	/* key2 is longer */
+	return PATHKEYS_EQUAL;
+}
+
+/*
+ * pathkeys_contained_in
+ *	  Common special case of compare_pathkeys: we just want to know
+ *	  if keys2 are at least as well sorted as keys1.
+ */
+bool
+pathkeys_contained_in(List *keys1, List *keys2)
+{
+	switch (compare_pathkeys(keys1, keys2))
+	{
+		case PATHKEYS_EQUAL:
+		case PATHKEYS_BETTER2:
+			return true;
+		default:
+			break;
+	}
+	return false;
+}
+
+/*
+ * pathkeys_count_contained_in
+ *    Same as pathkeys_contained_in, but also sets length of longest
+ *    common prefix of keys1 and keys2.
+ */
+bool
+pathkeys_count_contained_in(List *keys1, List *keys2, int *n_common)
+{
+	int			n = 0;
+	ListCell   *key1,
+			   *key2;
+
+	/*
+	 * See if we can avoiding looping through both lists. This optimization
+	 * gains us several percent in planning time in a worst-case test.
+	 */
+	if (keys1 == keys2)
+	{
+		*n_common = list_length(keys1);
+		return true;
+	}
+	else if (keys1 == NIL)
+	{
+		*n_common = 0;
+		return true;
+	}
+	else if (keys2 == NIL)
+	{
+		*n_common = 0;
+		return false;
+	}
+
+	/*
+	 * If both lists are non-empty, iterate through both to find out how many
+	 * items are shared.
+	 */
+	forboth(key1, keys1, key2, keys2)
+	{
+		PathKey    *pathkey1 = (PathKey *) lfirst(key1);
+		PathKey    *pathkey2 = (PathKey *) lfirst(key2);
+
+		if (pathkey1 != pathkey2)
+		{
+			*n_common = n;
+			return false;
+		}
+		n++;
+	}
+
+	/* If we ended with a null value, then we've processed the whole list. */
+	*n_common = n;
+	return (key1 == NULL);
+}
+
+/*
+ * get_cheapest_path_for_pathkeys
+ *	  Find the cheapest path (according to the specified criterion) that
+ *	  satisfies the given pathkeys and parameterization.
+ *	  Return NULL if no such path.
+ *
+ * 'paths' is a list of possible paths that all generate the same relation
+ * 'pathkeys' represents a required ordering (in canonical form!)
+ * 'required_outer' denotes allowable outer relations for parameterized paths
+ * 'cost_criterion' is STARTUP_COST or TOTAL_COST
+ * 'require_parallel_safe' causes us to consider only parallel-safe paths
+ */
+Path *
+get_cheapest_path_for_pathkeys(List *paths, List *pathkeys,
+							   Relids required_outer,
+							   CostSelector cost_criterion,
+							   bool require_parallel_safe)
+{
+	Path	   *matched_path = NULL;
+	ListCell   *l;
+
+	foreach(l, paths)
+	{
+		Path	   *path = (Path *) lfirst(l);
+
+		/*
+		 * Since cost comparison is a lot cheaper than pathkey comparison, do
+		 * that first.  (XXX is that still true?)
+		 */
+		if (matched_path != NULL &&
+			compare_path_costs(matched_path, path, cost_criterion) <= 0)
+			continue;
+
+		if (require_parallel_safe && !path->parallel_safe)
+			continue;
+
+		if (pathkeys_contained_in(pathkeys, path->pathkeys) &&
+			bms_is_subset(PATH_REQ_OUTER(path), required_outer))
+			matched_path = path;
+	}
+	return matched_path;
+}
+
+/*
+ * get_cheapest_fractional_path_for_pathkeys
+ *	  Find the cheapest path (for retrieving a specified fraction of all
+ *	  the tuples) that satisfies the given pathkeys and parameterization.
+ *	  Return NULL if no such path.
+ *
+ * See compare_fractional_path_costs() for the interpretation of the fraction
+ * parameter.
+ *
+ * 'paths' is a list of possible paths that all generate the same relation
+ * 'pathkeys' represents a required ordering (in canonical form!)
+ * 'required_outer' denotes allowable outer relations for parameterized paths
+ * 'fraction' is the fraction of the total tuples expected to be retrieved
+ */
+Path *
+get_cheapest_fractional_path_for_pathkeys(List *paths,
+										  List *pathkeys,
+										  Relids required_outer,
+										  double fraction)
+{
+	Path	   *matched_path = NULL;
+	ListCell   *l;
+
+	foreach(l, paths)
+	{
+		Path	   *path = (Path *) lfirst(l);
+
+		/*
+		 * Since cost comparison is a lot cheaper than pathkey comparison, do
+		 * that first.  (XXX is that still true?)
+		 */
+		if (matched_path != NULL &&
+			compare_fractional_path_costs(matched_path, path, fraction) <= 0)
+			continue;
+
+		if (pathkeys_contained_in(pathkeys, path->pathkeys) &&
+			bms_is_subset(PATH_REQ_OUTER(path), required_outer))
+			matched_path = path;
+	}
+	return matched_path;
+}
+
+
+/*
+ * get_cheapest_parallel_safe_total_inner
+ *	  Find the unparameterized parallel-safe path with the least total cost.
+ */
+Path *
+get_cheapest_parallel_safe_total_inner(List *paths)
+{
+	ListCell   *l;
+
+	foreach(l, paths)
+	{
+		Path	   *innerpath = (Path *) lfirst(l);
+
+		if (innerpath->parallel_safe &&
+			bms_is_empty(PATH_REQ_OUTER(innerpath)))
+			return innerpath;
+	}
+
+	return NULL;
+}
+
+/****************************************************************************
+ *		NEW PATHKEY FORMATION
+ ****************************************************************************/
+
+/*
+ * build_index_pathkeys
+ *	  Build a pathkeys list that describes the ordering induced by an index
+ *	  scan using the given index.  (Note that an unordered index doesn't
+ *	  induce any ordering, so we return NIL.)
+ *
+ * If 'scandir' is BackwardScanDirection, build pathkeys representing a
+ * backwards scan of the index.
+ *
+ * We iterate only key columns of covering indexes, since non-key columns
+ * don't influence index ordering.  The result is canonical, meaning that
+ * redundant pathkeys are removed; it may therefore have fewer entries than
+ * there are key columns in the index.
+ *
+ * Another reason for stopping early is that we may be able to tell that
+ * an index column's sort order is uninteresting for this query.  However,
+ * that test is just based on the existence of an EquivalenceClass and not
+ * on position in pathkey lists, so it's not complete.  Caller should call
+ * truncate_useless_pathkeys() to possibly remove more pathkeys.
+ */
+List *
+build_index_pathkeys(PlannerInfo *root,
+					 IndexOptInfo *index,
+					 ScanDirection scandir)
+{
+	List	   *retval = NIL;
+	ListCell   *lc;
+	int			i;
+
+	if (index->sortopfamily == NULL)
+		return NIL;				/* non-orderable index */
+
+	i = 0;
+	foreach(lc, index->indextlist)
+	{
+		TargetEntry *indextle = (TargetEntry *) lfirst(lc);
+		Expr	   *indexkey;
+		bool		reverse_sort;
+		bool		nulls_first;
+		PathKey    *cpathkey;
+
+		/*
+		 * INCLUDE columns are stored in index unordered, so they don't
+		 * support ordered index scan.
+		 */
+		if (i >= index->nkeycolumns)
+			break;
+
+		/* We assume we don't need to make a copy of the tlist item */
+		indexkey = indextle->expr;
+
+		if (ScanDirectionIsBackward(scandir))
+		{
+			reverse_sort = !index->reverse_sort[i];
+			nulls_first = !index->nulls_first[i];
+		}
+		else
+		{
+			reverse_sort = index->reverse_sort[i];
+			nulls_first = index->nulls_first[i];
+		}
+
+		/*
+		 * OK, try to make a canonical pathkey for this sort key.  Note we're
+		 * underneath any outer joins, so nullable_relids should be NULL.
+		 */
+		cpathkey = make_pathkey_from_sortinfo(root,
+											  indexkey,
+											  NULL,
+											  index->sortopfamily[i],
+											  index->opcintype[i],
+											  index->indexcollations[i],
+											  reverse_sort,
+											  nulls_first,
+											  0,
+											  index->rel->relids,
+											  false);
+
+		if (cpathkey)
+		{
+			/*
+			 * We found the sort key in an EquivalenceClass, so it's relevant
+			 * for this query.  Add it to list, unless it's redundant.
+			 */
+			if (!pathkey_is_redundant(cpathkey, retval))
+				retval = lappend(retval, cpathkey);
+		}
+		else
+		{
+			/*
+			 * Boolean index keys might be redundant even if they do not
+			 * appear in an EquivalenceClass, because of our special treatment
+			 * of boolean equality conditions --- see the comment for
+			 * indexcol_is_bool_constant_for_query().  If that applies, we can
+			 * continue to examine lower-order index columns.  Otherwise, the
+			 * sort key is not an interesting sort order for this query, so we
+			 * should stop considering index columns; any lower-order sort
+			 * keys won't be useful either.
+			 */
+			if (!indexcol_is_bool_constant_for_query(root, index, i))
+				break;
+		}
+
+		i++;
+	}
+
+	return retval;
+}
+
+/*
+ * partkey_is_bool_constant_for_query
+ *
+ * If a partition key column is constrained to have a constant value by the
+ * query's WHERE conditions, then it's irrelevant for sort-order
+ * considerations.  Usually that means we have a restriction clause
+ * WHERE partkeycol = constant, which gets turned into an EquivalenceClass
+ * containing a constant, which is recognized as redundant by
+ * build_partition_pathkeys().  But if the partition key column is a
+ * boolean variable (or expression), then we are not going to see such a
+ * WHERE clause, because expression preprocessing will have simplified it
+ * to "WHERE partkeycol" or "WHERE NOT partkeycol".  So we are not going
+ * to have a matching EquivalenceClass (unless the query also contains
+ * "ORDER BY partkeycol").  To allow such cases to work the same as they would
+ * for non-boolean values, this function is provided to detect whether the
+ * specified partition key column matches a boolean restriction clause.
+ */
+static bool
+partkey_is_bool_constant_for_query(RelOptInfo *partrel, int partkeycol)
+{
+	PartitionScheme partscheme = partrel->part_scheme;
+	ListCell   *lc;
+
+	/* If the partkey isn't boolean, we can't possibly get a match */
+	if (!IsBooleanOpfamily(partscheme->partopfamily[partkeycol]))
+		return false;
+
+	/* Check each restriction clause for the partitioned rel */
+	foreach(lc, partrel->baserestrictinfo)
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
+
+		/* Ignore pseudoconstant quals, they won't match */
+		if (rinfo->pseudoconstant)
+			continue;
+
+		/* See if we can match the clause's expression to the partkey column */
+		if (matches_boolean_partition_clause(rinfo, partrel, partkeycol))
+			return true;
+	}
+
+	return false;
+}
+
+/*
+ * matches_boolean_partition_clause
+ *		Determine if the boolean clause described by rinfo matches
+ *		partrel's partkeycol-th partition key column.
+ *
+ * "Matches" can be either an exact match (equivalent to partkey = true),
+ * or a NOT above an exact match (equivalent to partkey = false).
+ */
+static bool
+matches_boolean_partition_clause(RestrictInfo *rinfo,
+								 RelOptInfo *partrel, int partkeycol)
+{
+	Node	   *clause = (Node *) rinfo->clause;
+	Node	   *partexpr = (Node *) linitial(partrel->partexprs[partkeycol]);
+
+	/* Direct match? */
+	if (equal(partexpr, clause))
+		return true;
+	/* NOT clause? */
+	else if (is_notclause(clause))
+	{
+		Node	   *arg = (Node *) get_notclausearg((Expr *) clause);
+
+		if (equal(partexpr, arg))
+			return true;
+	}
+
+	return false;
+}
+
+/*
+ * build_partition_pathkeys
+ *	  Build a pathkeys list that describes the ordering induced by the
+ *	  partitions of partrel, under either forward or backward scan
+ *	  as per scandir.
+ *
+ * Caller must have checked that the partitions are properly ordered,
+ * as detected by partitions_are_ordered().
+ *
+ * Sets *partialkeys to true if pathkeys were only built for a prefix of the
+ * partition key, or false if the pathkeys include all columns of the
+ * partition key.
+ */
+List *
+build_partition_pathkeys(PlannerInfo *root, RelOptInfo *partrel,
+						 ScanDirection scandir, bool *partialkeys)
+{
+	List	   *retval = NIL;
+	PartitionScheme partscheme = partrel->part_scheme;
+	int			i;
+
+	Assert(partscheme != NULL);
+	Assert(partitions_are_ordered(partrel->boundinfo, partrel->live_parts));
+	/* For now, we can only cope with baserels */
+	Assert(IS_SIMPLE_REL(partrel));
+
+	for (i = 0; i < partscheme->partnatts; i++)
+	{
+		PathKey    *cpathkey;
+		Expr	   *keyCol = (Expr *) linitial(partrel->partexprs[i]);
+
+		/*
+		 * Try to make a canonical pathkey for this partkey.
+		 *
+		 * We're considering a baserel scan, so nullable_relids should be
+		 * NULL.  Also, we assume the PartitionDesc lists any NULL partition
+		 * last, so we treat the scan like a NULLS LAST index: we have
+		 * nulls_first for backwards scan only.
+		 */
+		cpathkey = make_pathkey_from_sortinfo(root,
+											  keyCol,
+											  NULL,
+											  partscheme->partopfamily[i],
+											  partscheme->partopcintype[i],
+											  partscheme->partcollation[i],
+											  ScanDirectionIsBackward(scandir),
+											  ScanDirectionIsBackward(scandir),
+											  0,
+											  partrel->relids,
+											  false);
+
+
+		if (cpathkey)
+		{
+			/*
+			 * We found the sort key in an EquivalenceClass, so it's relevant
+			 * for this query.  Add it to list, unless it's redundant.
+			 */
+			if (!pathkey_is_redundant(cpathkey, retval))
+				retval = lappend(retval, cpathkey);
+		}
+		else
+		{
+			/*
+			 * Boolean partition keys might be redundant even if they do not
+			 * appear in an EquivalenceClass, because of our special treatment
+			 * of boolean equality conditions --- see the comment for
+			 * partkey_is_bool_constant_for_query().  If that applies, we can
+			 * continue to examine lower-order partition keys.  Otherwise, the
+			 * sort key is not an interesting sort order for this query, so we
+			 * should stop considering partition columns; any lower-order sort
+			 * keys won't be useful either.
+			 */
+			if (!partkey_is_bool_constant_for_query(partrel, i))
+			{
+				*partialkeys = true;
+				return retval;
+			}
+		}
+	}
+
+	*partialkeys = false;
+	return retval;
+}
+
+/*
+ * build_expression_pathkey
+ *	  Build a pathkeys list that describes an ordering by a single expression
+ *	  using the given sort operator.
+ *
+ * expr, nullable_relids, and rel are as for make_pathkey_from_sortinfo.
+ * We induce the other arguments assuming default sort order for the operator.
+ *
+ * Similarly to make_pathkey_from_sortinfo, the result is NIL if create_it
+ * is false and the expression isn't already in some EquivalenceClass.
+ */
+List *
+build_expression_pathkey(PlannerInfo *root,
+						 Expr *expr,
+						 Relids nullable_relids,
+						 Oid opno,
+						 Relids rel,
+						 bool create_it)
+{
+	List	   *pathkeys;
+	Oid			opfamily,
+				opcintype;
+	int16		strategy;
+	PathKey    *cpathkey;
+
+	/* Find the operator in pg_amop --- failure shouldn't happen */
+	if (!get_ordering_op_properties(opno,
+									&opfamily, &opcintype, &strategy))
+		elog(ERROR, "operator %u is not a valid ordering operator",
+			 opno);
+
+	cpathkey = make_pathkey_from_sortinfo(root,
+										  expr,
+										  nullable_relids,
+										  opfamily,
+										  opcintype,
+										  exprCollation((Node *) expr),
+										  (strategy == BTGreaterStrategyNumber),
+										  (strategy == BTGreaterStrategyNumber),
+										  0,
+										  rel,
+										  create_it);
+
+	if (cpathkey)
+		pathkeys = list_make1(cpathkey);
+	else
+		pathkeys = NIL;
+
+	return pathkeys;
+}
+
+/*
+ * convert_subquery_pathkeys
+ *	  Build a pathkeys list that describes the ordering of a subquery's
+ *	  result, in the terms of the outer query.  This is essentially a
+ *	  task of conversion.
+ *
+ * 'rel': outer query's RelOptInfo for the subquery relation.
+ * 'subquery_pathkeys': the subquery's output pathkeys, in its terms.
+ * 'subquery_tlist': the subquery's output targetlist, in its terms.
+ *
+ * We intentionally don't do truncate_useless_pathkeys() here, because there
+ * are situations where seeing the raw ordering of the subquery is helpful.
+ * For example, if it returns ORDER BY x DESC, that may prompt us to
+ * construct a mergejoin using DESC order rather than ASC order; but the
+ * right_merge_direction heuristic would have us throw the knowledge away.
+ */
+List *
+convert_subquery_pathkeys(PlannerInfo *root, RelOptInfo *rel,
+						  List *subquery_pathkeys,
+						  List *subquery_tlist)
+{
+	List	   *retval = NIL;
+	int			retvallen = 0;
+	int			outer_query_keys = list_length(root->query_pathkeys);
+	ListCell   *i;
+
+	foreach(i, subquery_pathkeys)
+	{
+		PathKey    *sub_pathkey = (PathKey *) lfirst(i);
+		EquivalenceClass *sub_eclass = sub_pathkey->pk_eclass;
+		PathKey    *best_pathkey = NULL;
+
+		if (sub_eclass->ec_has_volatile)
+		{
+			/*
+			 * If the sub_pathkey's EquivalenceClass is volatile, then it must
+			 * have come from an ORDER BY clause, and we have to match it to
+			 * that same targetlist entry.
+			 */
+			TargetEntry *tle;
+			Var		   *outer_var;
+
+			if (sub_eclass->ec_sortref == 0)	/* can't happen */
+				elog(ERROR, "volatile EquivalenceClass has no sortref");
+			tle = get_sortgroupref_tle(sub_eclass->ec_sortref, subquery_tlist);
+			Assert(tle);
+			/* Is TLE actually available to the outer query? */
+			outer_var = find_var_for_subquery_tle(rel, tle);
+			if (outer_var)
+			{
+				/* We can represent this sub_pathkey */
+				EquivalenceMember *sub_member;
+				EquivalenceClass *outer_ec;
+
+				Assert(list_length(sub_eclass->ec_members) == 1);
+				sub_member = (EquivalenceMember *) linitial(sub_eclass->ec_members);
+
+				/*
+				 * Note: it might look funny to be setting sortref = 0 for a
+				 * reference to a volatile sub_eclass.  However, the
+				 * expression is *not* volatile in the outer query: it's just
+				 * a Var referencing whatever the subquery emitted. (IOW, the
+				 * outer query isn't going to re-execute the volatile
+				 * expression itself.)	So this is okay.  Likewise, it's
+				 * correct to pass nullable_relids = NULL, because we're
+				 * underneath any outer joins appearing in the outer query.
+				 */
+				outer_ec =
+					get_eclass_for_sort_expr(root,
+											 (Expr *) outer_var,
+											 NULL,
+											 sub_eclass->ec_opfamilies,
+											 sub_member->em_datatype,
+											 sub_eclass->ec_collation,
+											 0,
+											 rel->relids,
+											 false);
+
+				/*
+				 * If we don't find a matching EC, sub-pathkey isn't
+				 * interesting to the outer query
+				 */
+				if (outer_ec)
+					best_pathkey =
+						make_canonical_pathkey(root,
+											   outer_ec,
+											   sub_pathkey->pk_opfamily,
+											   sub_pathkey->pk_strategy,
+											   sub_pathkey->pk_nulls_first);
+			}
+		}
+		else
+		{
+			/*
+			 * Otherwise, the sub_pathkey's EquivalenceClass could contain
+			 * multiple elements (representing knowledge that multiple items
+			 * are effectively equal).  Each element might match none, one, or
+			 * more of the output columns that are visible to the outer query.
+			 * This means we may have multiple possible representations of the
+			 * sub_pathkey in the context of the outer query.  Ideally we
+			 * would generate them all and put them all into an EC of the
+			 * outer query, thereby propagating equality knowledge up to the
+			 * outer query.  Right now we cannot do so, because the outer
+			 * query's EquivalenceClasses are already frozen when this is
+			 * called. Instead we prefer the one that has the highest "score"
+			 * (number of EC peers, plus one if it matches the outer
+			 * query_pathkeys). This is the most likely to be useful in the
+			 * outer query.
+			 */
+			int			best_score = -1;
+			ListCell   *j;
+
+			foreach(j, sub_eclass->ec_members)
+			{
+				EquivalenceMember *sub_member = (EquivalenceMember *) lfirst(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 */
+
+				foreach(k, subquery_tlist)
+				{
+					TargetEntry *tle = (TargetEntry *) lfirst(k);
+					Var		   *outer_var;
+					Expr	   *tle_expr;
+					EquivalenceClass *outer_ec;
+					PathKey    *outer_pk;
+					int			score;
+
+					/* Is TLE actually available to the outer query? */
+					outer_var = find_var_for_subquery_tle(rel, tle);
+					if (!outer_var)
+						continue;
+
+					/*
+					 * The targetlist entry is considered to match if it
+					 * matches after sort-key canonicalization.  That is
+					 * needed since the sub_expr has been through the same
+					 * process.
+					 */
+					tle_expr = canonicalize_ec_expression(tle->expr,
+														  sub_expr_type,
+														  sub_expr_coll);
+					if (!equal(tle_expr, sub_expr))
+						continue;
+
+					/* See if we have a matching EC for the TLE */
+					outer_ec = get_eclass_for_sort_expr(root,
+														(Expr *) outer_var,
+														NULL,
+														sub_eclass->ec_opfamilies,
+														sub_expr_type,
+														sub_expr_coll,
+														0,
+														rel->relids,
+														false);
+
+					/*
+					 * If we don't find a matching EC, this sub-pathkey isn't
+					 * interesting to the outer query
+					 */
+					if (!outer_ec)
+						continue;
+
+					outer_pk = make_canonical_pathkey(root,
+													  outer_ec,
+													  sub_pathkey->pk_opfamily,
+													  sub_pathkey->pk_strategy,
+													  sub_pathkey->pk_nulls_first);
+					/* score = # of equivalence peers */
+					score = list_length(outer_ec->ec_members) - 1;
+					/* +1 if it matches the proper query_pathkeys item */
+					if (retvallen < outer_query_keys &&
+						list_nth(root->query_pathkeys, retvallen) == outer_pk)
+						score++;
+					if (score > best_score)
+					{
+						best_pathkey = outer_pk;
+						best_score = score;
+					}
+				}
+			}
+		}
+
+		/*
+		 * If we couldn't find a representation of this sub_pathkey, we're
+		 * done (we can't use the ones to its right, either).
+		 */
+		if (!best_pathkey)
+			break;
+
+		/*
+		 * Eliminate redundant ordering info; could happen if outer query
+		 * equivalences subquery keys...
+		 */
+		if (!pathkey_is_redundant(best_pathkey, retval))
+		{
+			retval = lappend(retval, best_pathkey);
+			retvallen++;
+		}
+	}
+
+	return retval;
+}
+
+/*
+ * find_var_for_subquery_tle
+ *
+ * If the given subquery tlist entry is due to be emitted by the subquery's
+ * scan node, return a Var for it, else return NULL.
+ *
+ * We need this to ensure that we don't return pathkeys describing values
+ * that are unavailable above the level of the subquery scan.
+ */
+static Var *
+find_var_for_subquery_tle(RelOptInfo *rel, TargetEntry *tle)
+{
+	ListCell   *lc;
+
+	/* If the TLE is resjunk, it's certainly not visible to the outer query */
+	if (tle->resjunk)
+		return NULL;
+
+	/* Search the rel's targetlist to see what it will return */
+	foreach(lc, rel->reltarget->exprs)
+	{
+		Var		   *var = (Var *) lfirst(lc);
+
+		/* Ignore placeholders */
+		if (!IsA(var, Var))
+			continue;
+		Assert(var->varno == rel->relid);
+
+		/* If we find a Var referencing this TLE, we're good */
+		if (var->varattno == tle->resno)
+			return copyObject(var); /* Make a copy for safety */
+	}
+	return NULL;
+}
+
+/*
+ * build_join_pathkeys
+ *	  Build the path keys for a join relation constructed by mergejoin or
+ *	  nestloop join.  This is normally the same as the outer path's keys.
+ *
+ *	  EXCEPTION: in a FULL or RIGHT join, we cannot treat the result as
+ *	  having the outer path's path keys, because null lefthand rows may be
+ *	  inserted at random points.  It must be treated as unsorted.
+ *
+ *	  We truncate away any pathkeys that are uninteresting for higher joins.
+ *
+ * 'joinrel' is the join relation that paths are being formed for
+ * 'jointype' is the join type (inner, left, full, etc)
+ * 'outer_pathkeys' is the list of the current outer path's path keys
+ *
+ * Returns the list of new path keys.
+ */
+List *
+build_join_pathkeys(PlannerInfo *root,
+					RelOptInfo *joinrel,
+					JoinType jointype,
+					List *outer_pathkeys)
+{
+	if (jointype == JOIN_FULL || jointype == JOIN_RIGHT)
+		return NIL;
+
+	/*
+	 * This used to be quite a complex bit of code, but now that all pathkey
+	 * sublists start out life canonicalized, we don't have to do a darn thing
+	 * here!
+	 *
+	 * We do, however, need to truncate the pathkeys list, since it may
+	 * contain pathkeys that were useful for forming this joinrel but are
+	 * uninteresting to higher levels.
+	 */
+	return truncate_useless_pathkeys(root, joinrel, outer_pathkeys);
+}
+
+/****************************************************************************
+ *		PATHKEYS AND SORT CLAUSES
+ ****************************************************************************/
+
+/*
+ * make_pathkeys_for_sortclauses
+ *		Generate a pathkeys list that represents the sort order specified
+ *		by a list of SortGroupClauses
+ *
+ * The resulting PathKeys are always in canonical form.  (Actually, there
+ * is no longer any code anywhere that creates non-canonical PathKeys.)
+ *
+ * We assume that root->nullable_baserels is the set of base relids that could
+ * have gone to NULL below the SortGroupClause expressions.  This is okay if
+ * the expressions came from the query's top level (ORDER BY, DISTINCT, etc)
+ * and if this function is only invoked after deconstruct_jointree.  In the
+ * future we might have to make callers pass in the appropriate
+ * nullable-relids set, but for now it seems unnecessary.
+ *
+ * 'sortclauses' is a list of SortGroupClause nodes
+ * 'tlist' is the targetlist to find the referenced tlist entries in
+ */
+List *
+make_pathkeys_for_sortclauses(PlannerInfo *root,
+							  List *sortclauses,
+							  List *tlist)
+{
+	List	   *pathkeys = NIL;
+	ListCell   *l;
+
+	foreach(l, sortclauses)
+	{
+		SortGroupClause *sortcl = (SortGroupClause *) lfirst(l);
+		Expr	   *sortkey;
+		PathKey    *pathkey;
+
+		sortkey = (Expr *) get_sortgroupclause_expr(sortcl, tlist);
+		Assert(OidIsValid(sortcl->sortop));
+		pathkey = make_pathkey_from_sortop(root,
+										   sortkey,
+										   root->nullable_baserels,
+										   sortcl->sortop,
+										   sortcl->nulls_first,
+										   sortcl->tleSortGroupRef,
+										   true);
+
+		/* Canonical form eliminates redundant ordering keys */
+		if (!pathkey_is_redundant(pathkey, pathkeys))
+			pathkeys = lappend(pathkeys, pathkey);
+	}
+	return pathkeys;
+}
+
+/****************************************************************************
+ *		PATHKEYS AND MERGECLAUSES
+ ****************************************************************************/
+
+/*
+ * initialize_mergeclause_eclasses
+ *		Set the EquivalenceClass links in a mergeclause restrictinfo.
+ *
+ * RestrictInfo contains fields in which we may cache pointers to
+ * EquivalenceClasses for the left and right inputs of the mergeclause.
+ * (If the mergeclause is a true equivalence clause these will be the
+ * same EquivalenceClass, otherwise not.)  If the mergeclause is either
+ * used to generate an EquivalenceClass, or derived from an EquivalenceClass,
+ * then it's easy to set up the left_ec and right_ec members --- otherwise,
+ * this function should be called to set them up.  We will generate new
+ * EquivalenceClauses if necessary to represent the mergeclause's left and
+ * right sides.
+ *
+ * Note this is called before EC merging is complete, so the links won't
+ * necessarily point to canonical ECs.  Before they are actually used for
+ * anything, update_mergeclause_eclasses must be called to ensure that
+ * they've been updated to point to canonical ECs.
+ */
+void
+initialize_mergeclause_eclasses(PlannerInfo *root, RestrictInfo *restrictinfo)
+{
+	Expr	   *clause = restrictinfo->clause;
+	Oid			lefttype,
+				righttype;
+
+	/* Should be a mergeclause ... */
+	Assert(restrictinfo->mergeopfamilies != NIL);
+	/* ... with links not yet set */
+	Assert(restrictinfo->left_ec == NULL);
+	Assert(restrictinfo->right_ec == NULL);
+
+	/* Need the declared input types of the operator */
+	op_input_types(((OpExpr *) clause)->opno, &lefttype, &righttype);
+
+	/* Find or create a matching EquivalenceClass for each side */
+	restrictinfo->left_ec =
+		get_eclass_for_sort_expr(root,
+								 (Expr *) get_leftop(clause),
+								 restrictinfo->nullable_relids,
+								 restrictinfo->mergeopfamilies,
+								 lefttype,
+								 ((OpExpr *) clause)->inputcollid,
+								 0,
+								 NULL,
+								 true);
+	restrictinfo->right_ec =
+		get_eclass_for_sort_expr(root,
+								 (Expr *) get_rightop(clause),
+								 restrictinfo->nullable_relids,
+								 restrictinfo->mergeopfamilies,
+								 righttype,
+								 ((OpExpr *) clause)->inputcollid,
+								 0,
+								 NULL,
+								 true);
+}
+
+/*
+ * update_mergeclause_eclasses
+ *		Make the cached EquivalenceClass links valid in a mergeclause
+ *		restrictinfo.
+ *
+ * These pointers should have been set by process_equivalence or
+ * initialize_mergeclause_eclasses, but they might have been set to
+ * non-canonical ECs that got merged later.  Chase up to the canonical
+ * merged parent if so.
+ */
+void
+update_mergeclause_eclasses(PlannerInfo *root, RestrictInfo *restrictinfo)
+{
+	/* Should be a merge clause ... */
+	Assert(restrictinfo->mergeopfamilies != NIL);
+	/* ... with pointers already set */
+	Assert(restrictinfo->left_ec != NULL);
+	Assert(restrictinfo->right_ec != NULL);
+
+	/* Chase up to the top as needed */
+	while (restrictinfo->left_ec->ec_merged)
+		restrictinfo->left_ec = restrictinfo->left_ec->ec_merged;
+	while (restrictinfo->right_ec->ec_merged)
+		restrictinfo->right_ec = restrictinfo->right_ec->ec_merged;
+}
+
+/*
+ * find_mergeclauses_for_outer_pathkeys
+ *	  This routine attempts to find a list of mergeclauses that can be
+ *	  used with a specified ordering for the join's outer relation.
+ *	  If successful, it returns a list of mergeclauses.
+ *
+ * 'pathkeys' is a pathkeys list showing the ordering of an outer-rel path.
+ * 'restrictinfos' is a list of mergejoinable restriction clauses for the
+ *			join relation being formed, in no particular order.
+ *
+ * The restrictinfos must be marked (via outer_is_left) to show which side
+ * of each clause is associated with the current outer path.  (See
+ * select_mergejoin_clauses())
+ *
+ * The result is NIL if no merge can be done, else a maximal list of
+ * usable mergeclauses (represented as a list of their restrictinfo nodes).
+ * The list is ordered to match the pathkeys, as required for execution.
+ */
+List *
+find_mergeclauses_for_outer_pathkeys(PlannerInfo *root,
+									 List *pathkeys,
+									 List *restrictinfos)
+{
+	List	   *mergeclauses = NIL;
+	ListCell   *i;
+
+	/* make sure we have eclasses cached in the clauses */
+	foreach(i, restrictinfos)
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) lfirst(i);
+
+		update_mergeclause_eclasses(root, rinfo);
+	}
+
+	foreach(i, pathkeys)
+	{
+		PathKey    *pathkey = (PathKey *) lfirst(i);
+		EquivalenceClass *pathkey_ec = pathkey->pk_eclass;
+		List	   *matched_restrictinfos = NIL;
+		ListCell   *j;
+
+		/*----------
+		 * A mergejoin clause matches a pathkey if it has the same EC.
+		 * If there are multiple matching clauses, take them all.  In plain
+		 * inner-join scenarios we expect only one match, because
+		 * equivalence-class processing will have removed any redundant
+		 * mergeclauses.  However, in outer-join scenarios there might be
+		 * multiple matches.  An example is
+		 *
+		 *	select * from a full join b
+		 *		on a.v1 = b.v1 and a.v2 = b.v2 and a.v1 = b.v2;
+		 *
+		 * Given the pathkeys ({a.v1}, {a.v2}) it is okay to return all three
+		 * clauses (in the order a.v1=b.v1, a.v1=b.v2, a.v2=b.v2) and indeed
+		 * we *must* do so or we will be unable to form a valid plan.
+		 *
+		 * We expect that the given pathkeys list is canonical, which means
+		 * no two members have the same EC, so it's not possible for this
+		 * code to enter the same mergeclause into the result list twice.
+		 *
+		 * It's possible that multiple matching clauses might have different
+		 * ECs on the other side, in which case the order we put them into our
+		 * result makes a difference in the pathkeys required for the inner
+		 * input rel.  However this routine hasn't got any info about which
+		 * order would be best, so we don't worry about that.
+		 *
+		 * It's also possible that the selected mergejoin clauses produce
+		 * a noncanonical ordering of pathkeys for the inner side, ie, we
+		 * might select clauses that reference b.v1, b.v2, b.v1 in that
+		 * order.  This is not harmful in itself, though it suggests that
+		 * the clauses are partially redundant.  Since the alternative is
+		 * to omit mergejoin clauses and thereby possibly fail to generate a
+		 * plan altogether, we live with it.  make_inner_pathkeys_for_merge()
+		 * has to delete duplicates when it constructs the inner pathkeys
+		 * list, and we also have to deal with such cases specially in
+		 * create_mergejoin_plan().
+		 *----------
+		 */
+		foreach(j, restrictinfos)
+		{
+			RestrictInfo *rinfo = (RestrictInfo *) lfirst(j);
+			EquivalenceClass *clause_ec;
+
+			clause_ec = rinfo->outer_is_left ?
+				rinfo->left_ec : rinfo->right_ec;
+			if (clause_ec == pathkey_ec)
+				matched_restrictinfos = lappend(matched_restrictinfos, rinfo);
+		}
+
+		/*
+		 * If we didn't find a mergeclause, we're done --- any additional
+		 * sort-key positions in the pathkeys are useless.  (But we can still
+		 * mergejoin if we found at least one mergeclause.)
+		 */
+		if (matched_restrictinfos == NIL)
+			break;
+
+		/*
+		 * If we did find usable mergeclause(s) for this sort-key position,
+		 * add them to result list.
+		 */
+		mergeclauses = list_concat(mergeclauses, matched_restrictinfos);
+	}
+
+	return mergeclauses;
+}
+
+/*
+ * select_outer_pathkeys_for_merge
+ *	  Builds a pathkey list representing a possible sort ordering
+ *	  that can be used with the given mergeclauses.
+ *
+ * 'mergeclauses' is a list of RestrictInfos for mergejoin clauses
+ *			that will be used in a merge join.
+ * 'joinrel' is the join relation we are trying to construct.
+ *
+ * The restrictinfos must be marked (via outer_is_left) to show which side
+ * of each clause is associated with the current outer path.  (See
+ * select_mergejoin_clauses())
+ *
+ * Returns a pathkeys list that can be applied to the outer relation.
+ *
+ * Since we assume here that a sort is required, there is no particular use
+ * in matching any available ordering of the outerrel.  (joinpath.c has an
+ * entirely separate code path for considering sort-free mergejoins.)  Rather,
+ * it's interesting to try to match the requested query_pathkeys so that a
+ * second output sort may be avoided; and failing that, we try to list "more
+ * popular" keys (those with the most unmatched EquivalenceClass peers)
+ * earlier, in hopes of making the resulting ordering useful for as many
+ * higher-level mergejoins as possible.
+ */
+List *
+select_outer_pathkeys_for_merge(PlannerInfo *root,
+								List *mergeclauses,
+								RelOptInfo *joinrel)
+{
+	List	   *pathkeys = NIL;
+	int			nClauses = list_length(mergeclauses);
+	EquivalenceClass **ecs;
+	int		   *scores;
+	int			necs;
+	ListCell   *lc;
+	int			j;
+
+	/* Might have no mergeclauses */
+	if (nClauses == 0)
+		return NIL;
+
+	/*
+	 * Make arrays of the ECs used by the mergeclauses (dropping any
+	 * duplicates) and their "popularity" scores.
+	 */
+	ecs = (EquivalenceClass **) palloc(nClauses * sizeof(EquivalenceClass *));
+	scores = (int *) palloc(nClauses * sizeof(int));
+	necs = 0;
+
+	foreach(lc, mergeclauses)
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
+		EquivalenceClass *oeclass;
+		int			score;
+		ListCell   *lc2;
+
+		/* get the outer eclass */
+		update_mergeclause_eclasses(root, rinfo);
+
+		if (rinfo->outer_is_left)
+			oeclass = rinfo->left_ec;
+		else
+			oeclass = rinfo->right_ec;
+
+		/* reject duplicates */
+		for (j = 0; j < necs; j++)
+		{
+			if (ecs[j] == oeclass)
+				break;
+		}
+		if (j < necs)
+			continue;
+
+		/* compute score */
+		score = 0;
+		foreach(lc2, oeclass->ec_members)
+		{
+			EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
+
+			/* Potential future join partner? */
+			if (!em->em_is_const && !em->em_is_child &&
+				!bms_overlap(em->em_relids, joinrel->relids))
+				score++;
+		}
+
+		ecs[necs] = oeclass;
+		scores[necs] = score;
+		necs++;
+	}
+
+	/*
+	 * Find out if we have all the ECs mentioned in query_pathkeys; if so we
+	 * can generate a sort order that's also useful for final output. There is
+	 * no percentage in a partial match, though, so we have to have 'em all.
+	 */
+	if (root->query_pathkeys)
+	{
+		foreach(lc, root->query_pathkeys)
+		{
+			PathKey    *query_pathkey = (PathKey *) lfirst(lc);
+			EquivalenceClass *query_ec = query_pathkey->pk_eclass;
+
+			for (j = 0; j < necs; j++)
+			{
+				if (ecs[j] == query_ec)
+					break;		/* found match */
+			}
+			if (j >= necs)
+				break;			/* didn't find match */
+		}
+		/* if we got to the end of the list, we have them all */
+		if (lc == NULL)
+		{
+			/* copy query_pathkeys as starting point for our output */
+			pathkeys = list_copy(root->query_pathkeys);
+			/* mark their ECs as already-emitted */
+			foreach(lc, root->query_pathkeys)
+			{
+				PathKey    *query_pathkey = (PathKey *) lfirst(lc);
+				EquivalenceClass *query_ec = query_pathkey->pk_eclass;
+
+				for (j = 0; j < necs; j++)
+				{
+					if (ecs[j] == query_ec)
+					{
+						scores[j] = -1;
+						break;
+					}
+				}
+			}
+		}
+	}
+
+	/*
+	 * Add remaining ECs to the list in popularity order, using a default sort
+	 * ordering.  (We could use qsort() here, but the list length is usually
+	 * so small it's not worth it.)
+	 */
+	for (;;)
+	{
+		int			best_j;
+		int			best_score;
+		EquivalenceClass *ec;
+		PathKey    *pathkey;
+
+		best_j = 0;
+		best_score = scores[0];
+		for (j = 1; j < necs; j++)
+		{
+			if (scores[j] > best_score)
+			{
+				best_j = j;
+				best_score = scores[j];
+			}
+		}
+		if (best_score < 0)
+			break;				/* all done */
+		ec = ecs[best_j];
+		scores[best_j] = -1;
+		pathkey = make_canonical_pathkey(root,
+										 ec,
+										 linitial_oid(ec->ec_opfamilies),
+										 BTLessStrategyNumber,
+										 false);
+		/* can't be redundant because no duplicate ECs */
+		Assert(!pathkey_is_redundant(pathkey, pathkeys));
+		pathkeys = lappend(pathkeys, pathkey);
+	}
+
+	pfree(ecs);
+	pfree(scores);
+
+	return pathkeys;
+}
+
+/*
+ * make_inner_pathkeys_for_merge
+ *	  Builds a pathkey list representing the explicit sort order that
+ *	  must be applied to an inner path to make it usable with the
+ *	  given mergeclauses.
+ *
+ * 'mergeclauses' is a list of RestrictInfos for the mergejoin clauses
+ *			that will be used in a merge join, in order.
+ * 'outer_pathkeys' are the already-known canonical pathkeys for the outer
+ *			side of the join.
+ *
+ * The restrictinfos must be marked (via outer_is_left) to show which side
+ * of each clause is associated with the current outer path.  (See
+ * select_mergejoin_clauses())
+ *
+ * Returns a pathkeys list that can be applied to the inner relation.
+ *
+ * Note that it is not this routine's job to decide whether sorting is
+ * actually needed for a particular input path.  Assume a sort is necessary;
+ * just make the keys, eh?
+ */
+List *
+make_inner_pathkeys_for_merge(PlannerInfo *root,
+							  List *mergeclauses,
+							  List *outer_pathkeys)
+{
+	List	   *pathkeys = NIL;
+	EquivalenceClass *lastoeclass;
+	PathKey    *opathkey;
+	ListCell   *lc;
+	ListCell   *lop;
+
+	lastoeclass = NULL;
+	opathkey = NULL;
+	lop = list_head(outer_pathkeys);
+
+	foreach(lc, mergeclauses)
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
+		EquivalenceClass *oeclass;
+		EquivalenceClass *ieclass;
+		PathKey    *pathkey;
+
+		update_mergeclause_eclasses(root, rinfo);
+
+		if (rinfo->outer_is_left)
+		{
+			oeclass = rinfo->left_ec;
+			ieclass = rinfo->right_ec;
+		}
+		else
+		{
+			oeclass = rinfo->right_ec;
+			ieclass = rinfo->left_ec;
+		}
+
+		/* outer eclass should match current or next pathkeys */
+		/* we check this carefully for debugging reasons */
+		if (oeclass != lastoeclass)
+		{
+			if (!lop)
+				elog(ERROR, "too few pathkeys for mergeclauses");
+			opathkey = (PathKey *) lfirst(lop);
+			lop = lnext(outer_pathkeys, lop);
+			lastoeclass = opathkey->pk_eclass;
+			if (oeclass != lastoeclass)
+				elog(ERROR, "outer pathkeys do not match mergeclause");
+		}
+
+		/*
+		 * Often, we'll have same EC on both sides, in which case the outer
+		 * pathkey is also canonical for the inner side, and we can skip a
+		 * useless search.
+		 */
+		if (ieclass == oeclass)
+			pathkey = opathkey;
+		else
+			pathkey = make_canonical_pathkey(root,
+											 ieclass,
+											 opathkey->pk_opfamily,
+											 opathkey->pk_strategy,
+											 opathkey->pk_nulls_first);
+
+		/*
+		 * Don't generate redundant pathkeys (which can happen if multiple
+		 * mergeclauses refer to the same EC).  Because we do this, the output
+		 * pathkey list isn't necessarily ordered like the mergeclauses, which
+		 * complicates life for create_mergejoin_plan().  But if we didn't,
+		 * we'd have a noncanonical sort key list, which would be bad; for one
+		 * reason, it certainly wouldn't match any available sort order for
+		 * the input relation.
+		 */
+		if (!pathkey_is_redundant(pathkey, pathkeys))
+			pathkeys = lappend(pathkeys, pathkey);
+	}
+
+	return pathkeys;
+}
+
+/*
+ * trim_mergeclauses_for_inner_pathkeys
+ *	  This routine trims a list of mergeclauses to include just those that
+ *	  work with a specified ordering for the join's inner relation.
+ *
+ * 'mergeclauses' is a list of RestrictInfos for mergejoin clauses for the
+ *			join relation being formed, in an order known to work for the
+ *			currently-considered sort ordering of the join's outer rel.
+ * 'pathkeys' is a pathkeys list showing the ordering of an inner-rel path;
+ *			it should be equal to, or a truncation of, the result of
+ *			make_inner_pathkeys_for_merge for these mergeclauses.
+ *
+ * What we return will be a prefix of the given mergeclauses list.
+ *
+ * We need this logic because make_inner_pathkeys_for_merge's result isn't
+ * necessarily in the same order as the mergeclauses.  That means that if we
+ * consider an inner-rel pathkey list that is a truncation of that result,
+ * we might need to drop mergeclauses even though they match a surviving inner
+ * pathkey.  This happens when they are to the right of a mergeclause that
+ * matches a removed inner pathkey.
+ *
+ * The mergeclauses must be marked (via outer_is_left) to show which side
+ * of each clause is associated with the current outer path.  (See
+ * select_mergejoin_clauses())
+ */
+List *
+trim_mergeclauses_for_inner_pathkeys(PlannerInfo *root,
+									 List *mergeclauses,
+									 List *pathkeys)
+{
+	List	   *new_mergeclauses = NIL;
+	PathKey    *pathkey;
+	EquivalenceClass *pathkey_ec;
+	bool		matched_pathkey;
+	ListCell   *lip;
+	ListCell   *i;
+
+	/* No pathkeys => no mergeclauses (though we don't expect this case) */
+	if (pathkeys == NIL)
+		return NIL;
+	/* Initialize to consider first pathkey */
+	lip = list_head(pathkeys);
+	pathkey = (PathKey *) lfirst(lip);
+	pathkey_ec = pathkey->pk_eclass;
+	lip = lnext(pathkeys, lip);
+	matched_pathkey = false;
+
+	/* Scan mergeclauses to see how many we can use */
+	foreach(i, mergeclauses)
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) lfirst(i);
+		EquivalenceClass *clause_ec;
+
+		/* Assume we needn't do update_mergeclause_eclasses again here */
+
+		/* Check clause's inner-rel EC against current pathkey */
+		clause_ec = rinfo->outer_is_left ?
+			rinfo->right_ec : rinfo->left_ec;
+
+		/* If we don't have a match, attempt to advance to next pathkey */
+		if (clause_ec != pathkey_ec)
+		{
+			/* If we had no clauses matching this inner pathkey, must stop */
+			if (!matched_pathkey)
+				break;
+
+			/* Advance to next inner pathkey, if any */
+			if (lip == NULL)
+				break;
+			pathkey = (PathKey *) lfirst(lip);
+			pathkey_ec = pathkey->pk_eclass;
+			lip = lnext(pathkeys, lip);
+			matched_pathkey = false;
+		}
+
+		/* If mergeclause matches current inner pathkey, we can use it */
+		if (clause_ec == pathkey_ec)
+		{
+			new_mergeclauses = lappend(new_mergeclauses, rinfo);
+			matched_pathkey = true;
+		}
+		else
+		{
+			/* Else, no hope of adding any more mergeclauses */
+			break;
+		}
+	}
+
+	return new_mergeclauses;
+}
+
+
+/****************************************************************************
+ *		PATHKEY USEFULNESS CHECKS
+ *
+ * We only want to remember as many of the pathkeys of a path as have some
+ * potential use, either for subsequent mergejoins or for meeting the query's
+ * requested output ordering.  This ensures that add_path() won't consider
+ * a path to have a usefully different ordering unless it really is useful.
+ * These routines check for usefulness of given pathkeys.
+ ****************************************************************************/
+
+/*
+ * pathkeys_useful_for_merging
+ *		Count the number of pathkeys that may be useful for mergejoins
+ *		above the given relation.
+ *
+ * We consider a pathkey potentially useful if it corresponds to the merge
+ * ordering of either side of any joinclause for the rel.  This might be
+ * overoptimistic, since joinclauses that require different other relations
+ * might never be usable at the same time, but trying to be exact is likely
+ * to be more trouble than it's worth.
+ *
+ * To avoid doubling the number of mergejoin paths considered, we would like
+ * to consider only one of the two scan directions (ASC or DESC) as useful
+ * for merging for any given target column.  The choice is arbitrary unless
+ * one of the directions happens to match an ORDER BY key, in which case
+ * that direction should be preferred, in hopes of avoiding a final sort step.
+ * right_merge_direction() implements this heuristic.
+ */
+static int
+pathkeys_useful_for_merging(PlannerInfo *root, RelOptInfo *rel, List *pathkeys)
+{
+	int			useful = 0;
+	ListCell   *i;
+
+	foreach(i, pathkeys)
+	{
+		PathKey    *pathkey = (PathKey *) lfirst(i);
+		bool		matched = false;
+		ListCell   *j;
+
+		/* If "wrong" direction, not useful for merging */
+		if (!right_merge_direction(root, pathkey))
+			break;
+
+		/*
+		 * First look into the EquivalenceClass of the pathkey, to see if
+		 * there are any members not yet joined to the rel.  If so, it's
+		 * surely possible to generate a mergejoin clause using them.
+		 */
+		if (rel->has_eclass_joins &&
+			eclass_useful_for_merging(root, pathkey->pk_eclass, rel))
+			matched = true;
+		else
+		{
+			/*
+			 * Otherwise search the rel's joininfo list, which contains
+			 * non-EquivalenceClass-derivable join clauses that might
+			 * nonetheless be mergejoinable.
+			 */
+			foreach(j, rel->joininfo)
+			{
+				RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(j);
+
+				if (restrictinfo->mergeopfamilies == NIL)
+					continue;
+				update_mergeclause_eclasses(root, restrictinfo);
+
+				if (pathkey->pk_eclass == restrictinfo->left_ec ||
+					pathkey->pk_eclass == restrictinfo->right_ec)
+				{
+					matched = true;
+					break;
+				}
+			}
+		}
+
+		/*
+		 * If we didn't find a mergeclause, we're done --- any additional
+		 * sort-key positions in the pathkeys are useless.  (But we can still
+		 * mergejoin if we found at least one mergeclause.)
+		 */
+		if (matched)
+			useful++;
+		else
+			break;
+	}
+
+	return useful;
+}
+
+/*
+ * right_merge_direction
+ *		Check whether the pathkey embodies the preferred sort direction
+ *		for merging its target column.
+ */
+static bool
+right_merge_direction(PlannerInfo *root, PathKey *pathkey)
+{
+	ListCell   *l;
+
+	foreach(l, root->query_pathkeys)
+	{
+		PathKey    *query_pathkey = (PathKey *) lfirst(l);
+
+		if (pathkey->pk_eclass == query_pathkey->pk_eclass &&
+			pathkey->pk_opfamily == query_pathkey->pk_opfamily)
+		{
+			/*
+			 * Found a matching query sort column.  Prefer this pathkey's
+			 * direction iff it matches.  Note that we ignore pk_nulls_first,
+			 * which means that a sort might be needed anyway ... but we still
+			 * want to prefer only one of the two possible directions, and we
+			 * might as well use this one.
+			 */
+			return (pathkey->pk_strategy == query_pathkey->pk_strategy);
+		}
+	}
+
+	/* If no matching ORDER BY request, prefer the ASC direction */
+	return (pathkey->pk_strategy == BTLessStrategyNumber);
+}
+
+/*
+ * pathkeys_useful_for_ordering
+ *		Count the number of pathkeys that are useful for meeting the
+ *		query's requested output ordering.
+ *
+ * Because we the have the possibility of incremental sort, a prefix list of
+ * keys is potentially useful for improving the performance of the requested
+ * ordering. Thus we return 0, if no valuable keys are found, or the number
+ * of leading keys shared by the list and the requested ordering..
+ */
+static int
+pathkeys_useful_for_ordering(PlannerInfo *root, List *pathkeys)
+{
+	int			n_common_pathkeys;
+
+	if (root->query_pathkeys == NIL)
+		return 0;				/* no special ordering requested */
+
+	if (pathkeys == NIL)
+		return 0;				/* unordered path */
+
+	(void) pathkeys_count_contained_in(root->query_pathkeys, pathkeys,
+									   &n_common_pathkeys);
+
+	return n_common_pathkeys;
+}
+
+/*
+ * truncate_useless_pathkeys
+ *		Shorten the given pathkey list to just the useful pathkeys.
+ */
+List *
+truncate_useless_pathkeys(PlannerInfo *root,
+						  RelOptInfo *rel,
+						  List *pathkeys)
+{
+	int			nuseful;
+	int			nuseful2;
+
+	nuseful = pathkeys_useful_for_merging(root, rel, pathkeys);
+	nuseful2 = pathkeys_useful_for_ordering(root, pathkeys);
+	if (nuseful2 > nuseful)
+		nuseful = nuseful2;
+
+	/*
+	 * Note: not safe to modify input list destructively, but we can avoid
+	 * copying the list if we're not actually going to change it
+	 */
+	if (nuseful == 0)
+		return NIL;
+	else if (nuseful == list_length(pathkeys))
+		return pathkeys;
+	else
+		return list_truncate(list_copy(pathkeys), nuseful);
+}
+
+/*
+ * has_useful_pathkeys
+ *		Detect whether the specified rel could have any pathkeys that are
+ *		useful according to truncate_useless_pathkeys().
+ *
+ * This is a cheap test that lets us skip building pathkeys at all in very
+ * simple queries.  It's OK to err in the direction of returning "true" when
+ * there really aren't any usable pathkeys, but erring in the other direction
+ * is bad --- so keep this in sync with the routines above!
+ *
+ * We could make the test more complex, for example checking to see if any of
+ * the joinclauses are really mergejoinable, but that likely wouldn't win
+ * often enough to repay the extra cycles.  Queries with neither a join nor
+ * a sort are reasonably common, though, so this much work seems worthwhile.
+ */
+bool
+has_useful_pathkeys(PlannerInfo *root, RelOptInfo *rel)
+{
+	if (rel->joininfo != NIL || rel->has_eclass_joins)
+		return true;			/* might be able to use pathkeys for merging */
+	if (root->query_pathkeys != NIL)
+		return true;			/* might be able to use them for ordering */
+	return false;				/* definitely useless */
+}