pgindent run.

[postgresql] / src / backend / optimizer / path / pathkeys.c

/*-------------------------------------------------------------------------
 *
 * 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) 1996-2002, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *        $Header: /cvsroot/pgsql/src/backend/optimizer/path/pathkeys.c,v 1.40 2002/09/04 20:31:20 momjian Exp $
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "nodes/makefuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/planmain.h"
#include "optimizer/tlist.h"
#include "parser/parsetree.h"
#include "parser/parse_func.h"
#include "utils/lsyscache.h"


static PathKeyItem *makePathKeyItem(Node *key, Oid sortop);
static List *make_canonical_pathkey(Query *root, PathKeyItem *item);
static Var *find_indexkey_var(Query *root, RelOptInfo *rel,
                                  AttrNumber varattno);


/*
 * makePathKeyItem
 *              create a PathKeyItem node
 */
static PathKeyItem *
makePathKeyItem(Node *key, Oid sortop)
{
        PathKeyItem *item = makeNode(PathKeyItem);

        item->key = key;
        item->sortop = sortop;
        return item;
}

/*
 * add_equijoined_keys
 *        The given clause has a mergejoinable operator, so its two sides
 *        can be considered equal after restriction clause application; in
 *        particular, any pathkey mentioning one side (with the correct sortop)
 *        can be expanded to include the other as well.  Record the vars and
 *        associated sortops in the query's equi_key_list for future use.
 *
 * The query's equi_key_list field points to a list of sublists of PathKeyItem
 * nodes, where each sublist is a set of two or more vars+sortops that have
 * been identified as logically equivalent (and, therefore, we may consider
 * any two in a set to be equal).  As described above, we will subsequently
 * use direct pointers to one of these sublists to represent any pathkey
 * that involves an equijoined variable.
 *
 * This code would actually work fine with expressions more complex than
 * a single Var, but currently it won't see any because check_mergejoinable
 * won't accept such clauses as mergejoinable.
 */
void
add_equijoined_keys(Query *root, RestrictInfo *restrictinfo)
{
        Expr       *clause = restrictinfo->clause;
        PathKeyItem *item1 = makePathKeyItem((Node *) get_leftop(clause),
                                                                                 restrictinfo->left_sortop);
        PathKeyItem *item2 = makePathKeyItem((Node *) get_rightop(clause),
                                                                                 restrictinfo->right_sortop);
        List       *newset,
                           *cursetlink;

        /* We might see a clause X=X; don't make a single-element list from it */
        if (equal(item1, item2))
                return;

        /*
         * Our plan is to make a two-element set, then sweep through the
         * existing equijoin sets looking for matches to item1 or item2.  When
         * we find one, we remove that set from equi_key_list and union it
         * into our new set. When done, we add the new set to the front of
         * equi_key_list.
         *
         * It may well be that the two items we're given are already known to be
         * equijoin-equivalent, in which case we don't need to change our data
         * structure.  If we find both of them in the same equivalence set to
         * start with, we can quit immediately.
         *
         * This is a standard UNION-FIND problem, for which there exist better
         * data structures than simple lists.  If this code ever proves to be
         * a bottleneck then it could be sped up --- but for now, simple is
         * beautiful.
         */
        newset = NIL;

        foreach(cursetlink, root->equi_key_list)
        {
                List       *curset = lfirst(cursetlink);
                bool            item1here = member(item1, curset);
                bool            item2here = member(item2, curset);

                if (item1here || item2here)
                {
                        /*
                         * If find both in same equivalence set, no need to do any
                         * more
                         */
                        if (item1here && item2here)
                        {
                                /* Better not have seen only one in an earlier set... */
                                Assert(newset == NIL);
                                return;
                        }

                        /* Build the new set only when we know we must */
                        if (newset == NIL)
                                newset = makeList2(item1, item2);

                        /* Found a set to merge into our new set */
                        newset = set_union(newset, curset);

                        /*
                         * Remove old set from equi_key_list.  NOTE this does not
                         * change lnext(cursetlink), so the foreach loop doesn't
                         * break.
                         */
                        root->equi_key_list = lremove(curset, root->equi_key_list);
                        freeList(curset);       /* might as well recycle old cons cells */
                }
        }

        /* Build the new set only when we know we must */
        if (newset == NIL)
                newset = makeList2(item1, item2);

        root->equi_key_list = lcons(newset, root->equi_key_list);
}

/*
 * generate_implied_equalities
 *        Scan the completed equi_key_list for the query, and generate explicit
 *        qualifications (WHERE clauses) for all the pairwise equalities not
 *        already mentioned in the quals.  This is useful because the additional
 *        clauses help the selectivity-estimation code, and in fact it's
 *        *necessary* to ensure that sort keys we think are equivalent really
 *        are (see src/backend/optimizer/README for more info).
 *
 * This routine just walks the equi_key_list to find all pairwise equalities.
 * We call process_implied_equality (in plan/initsplan.c) to determine whether
 * each is already known and add it to the proper restrictinfo list if not.
 */
void
generate_implied_equalities(Query *root)
{
        List       *cursetlink;

        foreach(cursetlink, root->equi_key_list)
        {
                List       *curset = lfirst(cursetlink);
                List       *ptr1;

                /*
                 * A set containing only two items cannot imply any equalities
                 * beyond the one that created the set, so we can skip it.
                 */
                if (length(curset) < 3)
                        continue;

                /*
                 * Match each item in the set with all that appear after it (it's
                 * sufficient to generate A=B, need not process B=A too).
                 */
                foreach(ptr1, curset)
                {
                        PathKeyItem *item1 = (PathKeyItem *) lfirst(ptr1);
                        List       *ptr2;

                        foreach(ptr2, lnext(ptr1))
                        {
                                PathKeyItem *item2 = (PathKeyItem *) lfirst(ptr2);

                                process_implied_equality(root, item1->key, item2->key,
                                                                                 item1->sortop, item2->sortop);
                        }
                }
        }
}

/*
 * make_canonical_pathkey
 *        Given a PathKeyItem, find the equi_key_list subset it is a member of,
 *        if any.  If so, return a pointer to that sublist, which is the
 *        canonical representation (for this query) of that PathKeyItem's
 *        equivalence set.      If it is not found, add a singleton "equivalence set"
 *        to the equi_key_list and return that --- see compare_pathkeys.
 *
 * Note that this function must not be used until after we have completed
 * scanning the WHERE clause for equijoin operators.
 */
static List *
make_canonical_pathkey(Query *root, PathKeyItem *item)
{
        List       *cursetlink;
        List       *newset;

        foreach(cursetlink, root->equi_key_list)
        {
                List       *curset = lfirst(cursetlink);

                if (member(item, curset))
                        return curset;
        }
        newset = makeList1(item);
        root->equi_key_list = lcons(newset, root->equi_key_list);
        return newset;
}

/*
 * canonicalize_pathkeys
 *         Convert a not-necessarily-canonical pathkeys list to canonical form.
 *
 * Note that this function must not be used until after we have completed
 * scanning the WHERE clause for equijoin operators.
 */
List *
canonicalize_pathkeys(Query *root, List *pathkeys)
{
        List       *new_pathkeys = NIL;
        List       *i;

        foreach(i, pathkeys)
        {
                List       *pathkey = (List *) lfirst(i);
                PathKeyItem *item;
                List       *cpathkey;

                /*
                 * It's sufficient to look at the first entry in the sublist; if
                 * there are more entries, they're already part of an equivalence
                 * set by definition.
                 */
                Assert(pathkey != NIL);
                item = (PathKeyItem *) lfirst(pathkey);
                cpathkey = make_canonical_pathkey(root, item);

                /*
                 * Eliminate redundant ordering requests --- ORDER BY A,A is the
                 * same as ORDER BY A.  We want to check this only after we have
                 * canonicalized the keys, so that equivalent-key knowledge is
                 * used when deciding if an item is redundant.
                 */
                if (!ptrMember(cpathkey, new_pathkeys))
                        new_pathkeys = lappend(new_pathkeys, cpathkey);
        }
        return new_pathkeys;
}

/****************************************************************************
 *              PATHKEY COMPARISONS
 ****************************************************************************/

/*
 * compare_pathkeys
 *        Compare two pathkeys to see if they are equivalent, and if not whether
 *        one is "better" than the other.
 *
 *        This function may only be applied to canonicalized pathkey lists.
 *        In the canonical representation, sublists can be checked for equality
 *        by simple pointer comparison.
 */
PathKeysComparison
compare_pathkeys(List *keys1, List *keys2)
{
        List       *key1,
                           *key2;

        for (key1 = keys1, key2 = keys2;
                 key1 != NIL && key2 != NIL;
                 key1 = lnext(key1), key2 = lnext(key2))
        {
                List       *subkey1 = lfirst(key1);
                List       *subkey2 = lfirst(key2);

                /*
                 * XXX would like to check that we've been given canonicalized
                 * input, but query root not accessible here...
                 */
#ifdef NOT_USED
                Assert(ptrMember(subkey1, root->equi_key_list));
                Assert(ptrMember(subkey2, root->equi_key_list));
#endif

                /*
                 * We will never have two subkeys where one is a subset of the
                 * other, because of the canonicalization process.      Either they
                 * are equal or they ain't.  Furthermore, we only need pointer
                 * comparison to detect equality.
                 */
                if (subkey1 != subkey2)
                        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.      (We assume the additional sublist(s) of
         * the other list are not NIL --- no pathkey list should ever have a
         * NIL sublist.)
         */
        if (key1 == NIL && key2 == NIL)
                return PATHKEYS_EQUAL;
        if (key1 != NIL)
                return PATHKEYS_BETTER1;        /* key1 is longer */
        return PATHKEYS_BETTER2;        /* key2 is longer */
}

/*
 * compare_noncanonical_pathkeys
 *        Compare two pathkeys to see if they are equivalent, and if not whether
 *        one is "better" than the other.  This is used when we must compare
 *        non-canonicalized pathkeys.
 *
 *        A pathkey can be considered better than another if it is a superset:
 *        it contains all the keys of the other plus more.      For example, either
 *        ((A) (B)) or ((A B)) is better than ((A)).
 *
 *        Currently, the only user of this routine is grouping_planner(),
 *        and it will only pass single-element sublists (from
 *        make_pathkeys_for_sortclauses).  Therefore we don't have to do the
 *        full two-way-subset-inclusion test on each pair of sublists that is
 *        implied by the above statement.  Instead we just verify they are
 *        singleton lists and then do an equal().  This could be improved if
 *        necessary.
 */
PathKeysComparison
compare_noncanonical_pathkeys(List *keys1, List *keys2)
{
        List       *key1,
                           *key2;

        for (key1 = keys1, key2 = keys2;
                 key1 != NIL && key2 != NIL;
                 key1 = lnext(key1), key2 = lnext(key2))
        {
                List       *subkey1 = lfirst(key1);
                List       *subkey2 = lfirst(key2);

                Assert(length(subkey1) == 1);
                Assert(length(subkey2) == 1);
                if (!equal(subkey1, subkey2))
                        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.      (We assume the additional sublist(s) of
         * the other list are not NIL --- no pathkey list should ever have a
         * NIL sublist.)
         */
        if (key1 == NIL && key2 == NIL)
                return PATHKEYS_EQUAL;
        if (key1 != NIL)
                return PATHKEYS_BETTER1;        /* key1 is longer */
        return PATHKEYS_BETTER2;        /* key2 is longer */
}

/*
 * 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;
}

/*
 * noncanonical_pathkeys_contained_in
 *        The same, when we don't have canonical pathkeys.
 */
bool
noncanonical_pathkeys_contained_in(List *keys1, List *keys2)
{
        switch (compare_noncanonical_pathkeys(keys1, keys2))
        {
                case PATHKEYS_EQUAL:
                case PATHKEYS_BETTER2:
                        return true;
                default:
                        break;
        }
        return false;
}

/*
 * get_cheapest_path_for_pathkeys
 *        Find the cheapest path (according to the specified criterion) that
 *        satisfies the given pathkeys.  Return NULL if no such path.
 *
 * 'paths' is a list of possible paths that all generate the same relation
 * 'pathkeys' represents a required ordering (already canonicalized!)
 * 'cost_criterion' is STARTUP_COST or TOTAL_COST
 */
Path *
get_cheapest_path_for_pathkeys(List *paths, List *pathkeys,
                                                           CostSelector cost_criterion)
{
        Path       *matched_path = NULL;
        List       *i;

        foreach(i, paths)
        {
                Path       *path = (Path *) lfirst(i);

                /*
                 * 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 (pathkeys_contained_in(pathkeys, path->pathkeys))
                        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.
 *        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 (already canonicalized!)
 * 'fraction' is the fraction of the total tuples expected to be retrieved
 */
Path *
get_cheapest_fractional_path_for_pathkeys(List *paths,
                                                                                  List *pathkeys,
                                                                                  double fraction)
{
        Path       *matched_path = NULL;
        List       *i;

        foreach(i, paths)
        {
                Path       *path = (Path *) lfirst(i);

                /*
                 * Since cost comparison is a lot cheaper than pathkey comparison,
                 * do that first.
                 */
                if (matched_path != NULL &&
                compare_fractional_path_costs(matched_path, path, fraction) <= 0)
                        continue;

                if (pathkeys_contained_in(pathkeys, path->pathkeys))
                        matched_path = path;
        }
        return matched_path;
}

/****************************************************************************
 *              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; such an index will have no sortop OIDS in
 *        its "ordering" field, and we will return NIL.)
 *
 * If 'scandir' is BackwardScanDirection, attempt to build pathkeys
 * representing a backwards scan of the index.  Return NIL if can't do it.
 */
List *
build_index_pathkeys(Query *root,
                                         RelOptInfo *rel,
                                         IndexOptInfo *index,
                                         ScanDirection scandir)
{
        List       *retval = NIL;
        int                *indexkeys = index->indexkeys;
        Oid                *ordering = index->ordering;
        PathKeyItem *item;
        Oid                     sortop;

        if (!indexkeys || indexkeys[0] == 0 ||
                !ordering || ordering[0] == InvalidOid)
                return NIL;                             /* unordered index? */

        if (index->indproc)
        {
                /* Functional index: build a representation of the function call */
                Func       *funcnode = makeNode(Func);
                List       *funcargs = NIL;

                funcnode->funcid = index->indproc;
                funcnode->funcresulttype = get_func_rettype(index->indproc);
                funcnode->funcretset = false;   /* can never be a set */
                funcnode->func_fcache = NULL;

                while (*indexkeys != 0)
                {
                        funcargs = lappend(funcargs,
                                                           find_indexkey_var(root, rel, *indexkeys));
                        indexkeys++;
                }

                sortop = *ordering;
                if (ScanDirectionIsBackward(scandir))
                {
                        sortop = get_commutator(sortop);
                        if (sortop == InvalidOid)
                                return NIL;             /* oops, no reverse sort operator? */
                }

                /* Make a one-sublist pathkeys list for the function expression */
                item = makePathKeyItem((Node *) make_funcclause(funcnode, funcargs),
                                                           sortop);
                retval = makeList1(make_canonical_pathkey(root, item));
        }
        else
        {
                /* Normal non-functional index */
                while (*indexkeys != 0 && *ordering != InvalidOid)
                {
                        Var                *relvar = find_indexkey_var(root, rel, *indexkeys);
                        List       *cpathkey;

                        sortop = *ordering;
                        if (ScanDirectionIsBackward(scandir))
                        {
                                sortop = get_commutator(sortop);
                                if (sortop == InvalidOid)
                                        break;          /* oops, no reverse sort operator? */
                        }

                        /* OK, make a sublist for this sort key */
                        item = makePathKeyItem((Node *) relvar, sortop);
                        cpathkey = make_canonical_pathkey(root, item);

                        /*
                         * Eliminate redundant ordering info; could happen if query is
                         * such that index keys are equijoined...
                         */
                        if (!ptrMember(cpathkey, retval))
                                retval = lappend(retval, cpathkey);
                        indexkeys++;
                        ordering++;
                }
        }

        return retval;
}

/*
 * Find or make a Var node for the specified attribute of the rel.
 *
 * We first look for the var in the rel's target list, because that's
 * easy and fast.  But the var might not be there (this should normally
 * only happen for vars that are used in WHERE restriction clauses,
 * but not in join clauses or in the SELECT target list).  In that case,
 * gin up a Var node the hard way.
 */
static Var *
find_indexkey_var(Query *root, RelOptInfo *rel, AttrNumber varattno)
{
        List       *temp;
        int                     relid;
        Oid                     reloid,
                                vartypeid;
        int32           type_mod;

        foreach(temp, rel->targetlist)
        {
                Var                *tle_var = get_expr(lfirst(temp));

                if (IsA(tle_var, Var) &&tle_var->varattno == varattno)
                        return tle_var;
        }

        relid = lfirsti(rel->relids);
        reloid = getrelid(relid, root->rtable);
        vartypeid = get_atttype(reloid, varattno);
        type_mod = get_atttypmod(reloid, varattno);

        return makeVar(relid, varattno, vartypeid, type_mod, 0);
}

/*
 * build_join_pathkeys
 *        Build the path keys for a join relation constructed by mergejoin or
 *        nestloop join.  These keys should include all the path key vars of the
 *        outer path (since the join will retain the ordering of the outer path)
 *        plus any vars of the inner path that are equijoined to the outer vars.
 *
 *        Per the discussion in backend/optimizer/README, equijoined inner vars
 *        can be considered path keys of the result, just the same as the outer
 *        vars they were joined with; furthermore, it doesn't matter what kind
 *        of join algorithm is actually used.
 *
 * 'joinrel' is the join relation that paths are being formed for
 * 'outer_pathkeys' is the list of the current outer path's path keys
 *
 * Returns the list of new path keys.
 */
List *
build_join_pathkeys(Query *root,
                                        RelOptInfo *joinrel,
                                        List *outer_pathkeys)
{
        /*
         * 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!  The inner-rel vars we used to need to add are
         * *already* part of the outer pathkey!
         *
         * 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 SortClauses (GroupClauses will work too!)
 *
 * NB: the result is NOT in canonical form, but must be passed through
 * canonicalize_pathkeys() before it can be used for comparisons or
 * labeling relation sort orders.  (We do things this way because
 * grouping_planner needs to be able to construct requested pathkeys
 * before the pathkey equivalence sets have been created for the query.)
 *
 * 'sortclauses' is a list of SortClause or GroupClause nodes
 * 'tlist' is the targetlist to find the referenced tlist entries in
 */
List *
make_pathkeys_for_sortclauses(List *sortclauses,
                                                          List *tlist)
{
        List       *pathkeys = NIL;
        List       *i;

        foreach(i, sortclauses)
        {
                SortClause *sortcl = (SortClause *) lfirst(i);
                Node       *sortkey;
                PathKeyItem *pathkey;

                sortkey = get_sortgroupclause_expr(sortcl, tlist);
                pathkey = makePathKeyItem(sortkey, sortcl->sortop);

                /*
                 * The pathkey becomes a one-element sublist, for now;
                 * canonicalize_pathkeys() might replace it with a longer sublist
                 * later.
                 */
                pathkeys = lappend(pathkeys, makeList1(pathkey));
        }
        return pathkeys;
}

/****************************************************************************
 *              PATHKEYS AND MERGECLAUSES
 ****************************************************************************/

/*
 * cache_mergeclause_pathkeys
 *              Make the cached pathkeys valid in a mergeclause restrictinfo.
 *
 * RestrictInfo contains fields in which we may cache the result
 * of looking up the canonical pathkeys for the left and right sides
 * of the mergeclause.  (Note that in normal cases they will be the
 * same, but not if the mergeclause appears above an OUTER JOIN.)
 * This is a worthwhile savings because these routines will be invoked
 * many times when dealing with a many-relation query.
 */
void
cache_mergeclause_pathkeys(Query *root, RestrictInfo *restrictinfo)
{
        Node       *key;
        PathKeyItem *item;

        Assert(restrictinfo->mergejoinoperator != InvalidOid);

        if (restrictinfo->left_pathkey == NIL)
        {
                key = (Node *) get_leftop(restrictinfo->clause);
                item = makePathKeyItem(key, restrictinfo->left_sortop);
                restrictinfo->left_pathkey = make_canonical_pathkey(root, item);
        }
        if (restrictinfo->right_pathkey == NIL)
        {
                key = (Node *) get_rightop(restrictinfo->clause);
                item = makePathKeyItem(key, restrictinfo->right_sortop);
                restrictinfo->right_pathkey = make_canonical_pathkey(root, item);
        }
}

/*
 * find_mergeclauses_for_pathkeys
 *        This routine attempts to find a set of mergeclauses that can be
 *        used with a specified ordering for one of the input relations.
 *        If successful, it returns a list of mergeclauses.
 *
 * 'pathkeys' is a pathkeys list showing the ordering of an input path.
 *                      It doesn't matter whether it is for the inner or outer path.
 * 'restrictinfos' is a list of mergejoinable restriction clauses for the
 *                      join relation being formed.
 *
 * 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).
 *
 * XXX Ideally we ought to be considering context, ie what path orderings
 * are available on the other side of the join, rather than just making
 * an arbitrary choice among the mergeclauses that will work for this side
 * of the join.
 */
List *
find_mergeclauses_for_pathkeys(Query *root,
                                                           List *pathkeys,
                                                           List *restrictinfos)
{
        List       *mergeclauses = NIL;
        List       *i;

        /* make sure we have pathkeys cached in the clauses */
        foreach(i, restrictinfos)
        {
                RestrictInfo *restrictinfo = lfirst(i);

                cache_mergeclause_pathkeys(root, restrictinfo);
        }

        foreach(i, pathkeys)
        {
                List       *pathkey = lfirst(i);
                List       *matched_restrictinfos = NIL;
                List       *j;

                /*
                 * We can match a pathkey against either left or right side of any
                 * mergejoin clause.  (We examine both sides since we aren't told
                 * if the given pathkeys are for inner or outer input path; no
                 * confusion is possible.)      Furthermore, if there are multiple
                 * matching clauses, take them all.  In plain inner-join scenarios
                 * we expect only one match, because redundant-mergeclause
                 * elimination will have removed any redundant mergeclauses from
                 * the input list. 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.
                 */
                foreach(j, restrictinfos)
                {
                        RestrictInfo *restrictinfo = lfirst(j);

                        /*
                         * We can compare canonical pathkey sublists by simple pointer
                         * equality; see compare_pathkeys.
                         */
                        if ((pathkey == restrictinfo->left_pathkey ||
                                 pathkey == restrictinfo->right_pathkey) &&
                                !ptrMember(restrictinfo, mergeclauses))
                        {
                                matched_restrictinfos = lappend(matched_restrictinfos,
                                                                                                restrictinfo);
                        }
                }

                /*
                 * 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 = nconc(mergeclauses, matched_restrictinfos);
        }

        return mergeclauses;
}

/*
 * make_pathkeys_for_mergeclauses
 *        Builds a pathkey list representing the explicit sort order that
 *        must be applied to a path in order to make it usable for the
 *        given mergeclauses.
 *
 * 'mergeclauses' is a list of RestrictInfos for mergejoin clauses
 *                      that will be used in a merge join.
 * 'rel' is the relation the pathkeys will apply to (ie, either the inner
 *                      or outer side of the proposed join rel).
 *
 * Returns a pathkeys list that can be applied to the indicated 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_pathkeys_for_mergeclauses(Query *root,
                                                           List *mergeclauses,
                                                           RelOptInfo *rel)
{
        List       *pathkeys = NIL;
        List       *i;

        foreach(i, mergeclauses)
        {
                RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(i);
                Node       *key;
                List       *pathkey;

                cache_mergeclause_pathkeys(root, restrictinfo);

                key = (Node *) get_leftop(restrictinfo->clause);
                if (IsA(key, Var) &&
                        VARISRELMEMBER(((Var *) key)->varno, rel))
                {
                        /* Rel is left side of mergeclause */
                        pathkey = restrictinfo->left_pathkey;
                }
                else
                {
                        key = (Node *) get_rightop(restrictinfo->clause);
                        if (IsA(key, Var) &&
                                VARISRELMEMBER(((Var *) key)->varno, rel))
                        {
                                /* Rel is right side of mergeclause */
                                pathkey = restrictinfo->right_pathkey;
                        }
                        else
                        {
                                elog(ERROR, "make_pathkeys_for_mergeclauses: can't identify which side of mergeclause to use");
                                pathkey = NIL;  /* keep compiler quiet */
                        }
                }

                /*
                 * When we are given multiple merge clauses, it's possible that
                 * some clauses refer to the same vars as earlier clauses. There's
                 * no reason for us to specify sort keys like (A,B,A) when (A,B)
                 * will do --- and adding redundant sort keys makes add_path think
                 * that this sort order is different from ones that are really the
                 * same, so don't do it.  Since we now have a canonicalized
                 * pathkey, a simple ptrMember test is sufficient to detect
                 * redundant keys.
                 */
                if (!ptrMember(pathkey, pathkeys))
                        pathkeys = lappend(pathkeys, pathkey);
        }

        return pathkeys;
}

/****************************************************************************
 *              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 (by looking at its joininfo lists).
 *
 * 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 appear in different join lists
 * might never be usable at the same time, but trying to be exact is likely
 * to be more trouble than it's worth.
 */
int
pathkeys_useful_for_merging(Query *root, RelOptInfo *rel, List *pathkeys)
{
        int                     useful = 0;
        List       *i;

        foreach(i, pathkeys)
        {
                List       *pathkey = lfirst(i);
                bool            matched = false;
                List       *j;

                foreach(j, rel->joininfo)
                {
                        JoinInfo   *joininfo = (JoinInfo *) lfirst(j);
                        List       *k;

                        foreach(k, joininfo->jinfo_restrictinfo)
                        {
                                RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(k);

                                if (restrictinfo->mergejoinoperator == InvalidOid)
                                        continue;
                                cache_mergeclause_pathkeys(root, restrictinfo);

                                /*
                                 * We can compare canonical pathkey sublists by simple
                                 * pointer equality; see compare_pathkeys.
                                 */
                                if (pathkey == restrictinfo->left_pathkey ||
                                        pathkey == restrictinfo->right_pathkey)
                                {
                                        matched = true;
                                        break;
                                }
                        }

                        if (matched)
                                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;
}

/*
 * pathkeys_useful_for_ordering
 *              Count the number of pathkeys that are useful for meeting the
 *              query's requested output ordering.
 *
 * Unlike merge pathkeys, this is an all-or-nothing affair: it does us
 * no good to order by just the first key(s) of the requested ordering.
 * So the result is always either 0 or length(root->query_pathkeys).
 */
int
pathkeys_useful_for_ordering(Query *root, List *pathkeys)
{
        if (root->query_pathkeys == NIL)
                return 0;                               /* no special ordering requested */

        if (pathkeys == NIL)
                return 0;                               /* unordered path */

        if (pathkeys_contained_in(root->query_pathkeys, pathkeys))
        {
                /* It's useful ... or at least the first N keys are */
                return length(root->query_pathkeys);
        }

        return 0;                                       /* path ordering not useful */
}

/*
 * truncate_useless_pathkeys
 *              Shorten the given pathkey list to just the useful pathkeys.
 */
List *
truncate_useless_pathkeys(Query *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 == length(pathkeys))
                return pathkeys;
        else
                return ltruncate(nuseful, listCopy(pathkeys));
}