pathnode.c

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/*-------------------------------------------------------------------------
 *
 * pathnode.c
 *    Routines to manipulate pathlists and create path nodes
 *
 * Portions Copyright (c) 1996-2013, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/optimizer/util/pathnode.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <math.h>

#include "miscadmin.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/restrictinfo.h"
#include "optimizer/tlist.h"
#include "parser/parsetree.h"
#include "utils/lsyscache.h"
#include "utils/selfuncs.h"


typedef enum
{
    COSTS_EQUAL,                /* path costs are fuzzily equal */
    COSTS_BETTER1,              /* first path is cheaper than second */
    COSTS_BETTER2,              /* second path is cheaper than first */
    COSTS_DIFFERENT             /* neither path dominates the other on cost */
} PathCostComparison;

static List *translate_sub_tlist(List *tlist, int relid);
static bool query_is_distinct_for(Query *query, List *colnos, List *opids);
static Oid  distinct_col_search(int colno, List *colnos, List *opids);


/*****************************************************************************
 *      MISC. PATH UTILITIES
 *****************************************************************************/

/*
 * compare_path_costs
 *    Return -1, 0, or +1 according as path1 is cheaper, the same cost,
 *    or more expensive than path2 for the specified criterion.
 */
int
compare_path_costs(Path *path1, Path *path2, CostSelector criterion)
{
    if (criterion == STARTUP_COST)
    {
        if (path1->startup_cost < path2->startup_cost)
            return -1;
        if (path1->startup_cost > path2->startup_cost)
            return +1;

        /*
         * If paths have the same startup cost (not at all unlikely), order
         * them by total cost.
         */
        if (path1->total_cost < path2->total_cost)
            return -1;
        if (path1->total_cost > path2->total_cost)
            return +1;
    }
    else
    {
        if (path1->total_cost < path2->total_cost)
            return -1;
        if (path1->total_cost > path2->total_cost)
            return +1;

        /*
         * If paths have the same total cost, order them by startup cost.
         */
        if (path1->startup_cost < path2->startup_cost)
            return -1;
        if (path1->startup_cost > path2->startup_cost)
            return +1;
    }
    return 0;
}

/*
 * compare_path_fractional_costs
 *    Return -1, 0, or +1 according as path1 is cheaper, the same cost,
 *    or more expensive than path2 for fetching the specified fraction
 *    of the total tuples.
 *
 * If fraction is <= 0 or > 1, we interpret it as 1, ie, we select the
 * path with the cheaper total_cost.
 */
int
compare_fractional_path_costs(Path *path1, Path *path2,
                              double fraction)
{
    Cost        cost1,
                cost2;

    if (fraction <= 0.0 || fraction >= 1.0)
        return compare_path_costs(path1, path2, TOTAL_COST);
    cost1 = path1->startup_cost +
        fraction * (path1->total_cost - path1->startup_cost);
    cost2 = path2->startup_cost +
        fraction * (path2->total_cost - path2->startup_cost);
    if (cost1 < cost2)
        return -1;
    if (cost1 > cost2)
        return +1;
    return 0;
}

/*
 * compare_path_costs_fuzzily
 *    Compare the costs of two paths to see if either can be said to
 *    dominate the other.
 *
 * We use fuzzy comparisons so that add_path() can avoid keeping both of
 * a pair of paths that really have insignificantly different cost.
 *
 * The fuzz_factor argument must be 1.0 plus delta, where delta is the
 * fraction of the smaller cost that is considered to be a significant
 * difference.  For example, fuzz_factor = 1.01 makes the fuzziness limit
 * be 1% of the smaller cost.
 *
 * The two paths are said to have "equal" costs if both startup and total
 * costs are fuzzily the same.  Path1 is said to be better than path2 if
 * it has fuzzily better startup cost and fuzzily no worse total cost,
 * or if it has fuzzily better total cost and fuzzily no worse startup cost.
 * Path2 is better than path1 if the reverse holds.  Finally, if one path
 * is fuzzily better than the other on startup cost and fuzzily worse on
 * total cost, we just say that their costs are "different", since neither
 * dominates the other across the whole performance spectrum.
 *
 * If consider_startup is false, then we don't care about keeping paths with
 * good startup cost, so we'll never return COSTS_DIFFERENT.
 *
 * This function also includes special hacks to support a policy enforced
 * by its sole caller, add_path(): paths that have any parameterization
 * cannot win comparisons on the grounds of having cheaper startup cost,
 * since we deem only total cost to be of interest for a parameterized path.
 * (Unparameterized paths are more common, so we check for this case last.)
 */
static PathCostComparison
compare_path_costs_fuzzily(Path *path1, Path *path2, double fuzz_factor,
                           bool consider_startup)
{
    /*
     * Check total cost first since it's more likely to be different; many
     * paths have zero startup cost.
     */
    if (path1->total_cost > path2->total_cost * fuzz_factor)
    {
        /* path1 fuzzily worse on total cost */
        if (consider_startup &&
            path2->startup_cost > path1->startup_cost * fuzz_factor &&
            path1->param_info == NULL)
        {
            /* ... but path2 fuzzily worse on startup, so DIFFERENT */
            return COSTS_DIFFERENT;
        }
        /* else path2 dominates */
        return COSTS_BETTER2;
    }
    if (path2->total_cost > path1->total_cost * fuzz_factor)
    {
        /* path2 fuzzily worse on total cost */
        if (consider_startup &&
            path1->startup_cost > path2->startup_cost * fuzz_factor &&
            path2->param_info == NULL)
        {
            /* ... but path1 fuzzily worse on startup, so DIFFERENT */
            return COSTS_DIFFERENT;
        }
        /* else path1 dominates */
        return COSTS_BETTER1;
    }
    /* fuzzily the same on total cost */
    /* (so we may as well compare startup cost, even if !consider_startup) */
    if (path1->startup_cost > path2->startup_cost * fuzz_factor &&
        path2->param_info == NULL)
    {
        /* ... but path1 fuzzily worse on startup, so path2 wins */
        return COSTS_BETTER2;
    }
    if (path2->startup_cost > path1->startup_cost * fuzz_factor &&
        path1->param_info == NULL)
    {
        /* ... but path2 fuzzily worse on startup, so path1 wins */
        return COSTS_BETTER1;
    }
    /* fuzzily the same on both costs */
    return COSTS_EQUAL;
}

/*
 * set_cheapest
 *    Find the minimum-cost paths from among a relation's paths,
 *    and save them in the rel's cheapest-path fields.
 *
 * cheapest_total_path is normally the cheapest-total-cost unparameterized
 * path; but if there are no unparameterized paths, we assign it to be the
 * best (cheapest least-parameterized) parameterized path.  However, only
 * unparameterized paths are considered candidates for cheapest_startup_path,
 * so that will be NULL if there are no unparameterized paths.
 *
 * The cheapest_parameterized_paths list collects all parameterized paths
 * that have survived the add_path() tournament for this relation.  (Since
 * add_path ignores pathkeys and startup cost for a parameterized path,
 * these will be paths that have best total cost or best row count for their
 * parameterization.)  cheapest_parameterized_paths always includes the
 * cheapest-total unparameterized path, too, if there is one; the users of
 * that list find it more convenient if that's included.
 *
 * This is normally called only after we've finished constructing the path
 * list for the rel node.
 */
void
set_cheapest(RelOptInfo *parent_rel)
{
    Path       *cheapest_startup_path;
    Path       *cheapest_total_path;
    Path       *best_param_path;
    List       *parameterized_paths;
    ListCell   *p;

    Assert(IsA(parent_rel, RelOptInfo));

    if (parent_rel->pathlist == NIL)
        elog(ERROR, "could not devise a query plan for the given query");

    cheapest_startup_path = cheapest_total_path = best_param_path = NULL;
    parameterized_paths = NIL;

    foreach(p, parent_rel->pathlist)
    {
        Path       *path = (Path *) lfirst(p);
        int         cmp;

        if (path->param_info)
        {
            /* Parameterized path, so add it to parameterized_paths */
            parameterized_paths = lappend(parameterized_paths, path);

            /*
             * If we have an unparameterized cheapest-total, we no longer care
             * about finding the best parameterized path, so move on.
             */
            if (cheapest_total_path)
                continue;

            /*
             * Otherwise, track the best parameterized path, which is the one
             * with least total cost among those of the minimum
             * parameterization.
             */
            if (best_param_path == NULL)
                best_param_path = path;
            else
            {
                switch (bms_subset_compare(PATH_REQ_OUTER(path),
                                           PATH_REQ_OUTER(best_param_path)))
                {
                    case BMS_EQUAL:
                        /* keep the cheaper one */
                        if (compare_path_costs(path, best_param_path,
                                               TOTAL_COST) < 0)
                            best_param_path = path;
                        break;
                    case BMS_SUBSET1:
                        /* new path is less-parameterized */
                        best_param_path = path;
                        break;
                    case BMS_SUBSET2:
                        /* old path is less-parameterized, keep it */
                        break;
                    case BMS_DIFFERENT:
                        /*
                         * This means that neither path has the least possible
                         * parameterization for the rel.  We'll sit on the old
                         * path until something better comes along.
                         */
                        break;
                }
            }
        }
        else
        {
            /* Unparameterized path, so consider it for cheapest slots */
            if (cheapest_total_path == NULL)
            {
                cheapest_startup_path = cheapest_total_path = path;
                continue;
            }

            /*
             * If we find two paths of identical costs, try to keep the
             * better-sorted one.  The paths might have unrelated sort
             * orderings, in which case we can only guess which might be
             * better to keep, but if one is superior then we definitely
             * should keep that one.
             */
            cmp = compare_path_costs(cheapest_startup_path, path, STARTUP_COST);
            if (cmp > 0 ||
                (cmp == 0 &&
                 compare_pathkeys(cheapest_startup_path->pathkeys,
                                  path->pathkeys) == PATHKEYS_BETTER2))
                cheapest_startup_path = path;

            cmp = compare_path_costs(cheapest_total_path, path, TOTAL_COST);
            if (cmp > 0 ||
                (cmp == 0 &&
                 compare_pathkeys(cheapest_total_path->pathkeys,
                                  path->pathkeys) == PATHKEYS_BETTER2))
                cheapest_total_path = path;
        }
    }

    /* Add cheapest unparameterized path, if any, to parameterized_paths */
    if (cheapest_total_path)
        parameterized_paths = lcons(cheapest_total_path, parameterized_paths);

    /*
     * If there is no unparameterized path, use the best parameterized path
     * as cheapest_total_path (but not as cheapest_startup_path).
     */
    if (cheapest_total_path == NULL)
        cheapest_total_path = best_param_path;
    Assert(cheapest_total_path != NULL);

    parent_rel->cheapest_startup_path = cheapest_startup_path;
    parent_rel->cheapest_total_path = cheapest_total_path;
    parent_rel->cheapest_unique_path = NULL;    /* computed only if needed */
    parent_rel->cheapest_parameterized_paths = parameterized_paths;
}

/*
 * add_path
 *    Consider a potential implementation path for the specified parent rel,
 *    and add it to the rel's pathlist if it is worthy of consideration.
 *    A path is worthy if it has a better sort order (better pathkeys) or
 *    cheaper cost (on either dimension), or generates fewer rows, than any
 *    existing path that has the same or superset parameterization rels.
 *
 *    We also remove from the rel's pathlist any old paths that are dominated
 *    by new_path --- that is, new_path is cheaper, at least as well ordered,
 *    generates no more rows, and requires no outer rels not required by the
 *    old path.
 *
 *    In most cases, a path with a superset parameterization will generate
 *    fewer rows (since it has more join clauses to apply), so that those two
 *    figures of merit move in opposite directions; this means that a path of
 *    one parameterization can seldom dominate a path of another.  But such
 *    cases do arise, so we make the full set of checks anyway.
 *
 *    There are two policy decisions embedded in this function, along with
 *    its sibling add_path_precheck: we treat all parameterized paths as
 *    having NIL pathkeys, and we ignore their startup costs, so that they
 *    compete only on parameterization, total cost and rowcount.  This is to
 *    reduce the number of parameterized paths that are kept.  See discussion
 *    in src/backend/optimizer/README.
 *
 *    Another policy that is enforced here is that we only consider cheap
 *    startup cost to be interesting if parent_rel->consider_startup is true.
 *
 *    The pathlist is kept sorted by total_cost, with cheaper paths
 *    at the front.  Within this routine, that's simply a speed hack:
 *    doing it that way makes it more likely that we will reject an inferior
 *    path after a few comparisons, rather than many comparisons.
 *    However, add_path_precheck relies on this ordering to exit early
 *    when possible.
 *
 *    NOTE: discarded Path objects are immediately pfree'd to reduce planner
 *    memory consumption.  We dare not try to free the substructure of a Path,
 *    since much of it may be shared with other Paths or the query tree itself;
 *    but just recycling discarded Path nodes is a very useful savings in
 *    a large join tree.  We can recycle the List nodes of pathlist, too.
 *
 *    BUT: we do not pfree IndexPath objects, since they may be referenced as
 *    children of BitmapHeapPaths as well as being paths in their own right.
 *
 * 'parent_rel' is the relation entry to which the path corresponds.
 * 'new_path' is a potential path for parent_rel.
 *
 * Returns nothing, but modifies parent_rel->pathlist.
 */
void
add_path(RelOptInfo *parent_rel, Path *new_path)
{
    bool        accept_new = true;      /* unless we find a superior old path */
    ListCell   *insert_after = NULL;    /* where to insert new item */
    List       *new_path_pathkeys;
    ListCell   *p1;
    ListCell   *p1_prev;
    ListCell   *p1_next;

    /*
     * This is a convenient place to check for query cancel --- no part of the
     * planner goes very long without calling add_path().
     */
    CHECK_FOR_INTERRUPTS();

    /* Pretend parameterized paths have no pathkeys, per comment above */
    new_path_pathkeys = new_path->param_info ? NIL : new_path->pathkeys;

    /*
     * Loop to check proposed new path against old paths.  Note it is possible
     * for more than one old path to be tossed out because new_path dominates
     * it.
     *
     * We can't use foreach here because the loop body may delete the current
     * list cell.
     */
    p1_prev = NULL;
    for (p1 = list_head(parent_rel->pathlist); p1 != NULL; p1 = p1_next)
    {
        Path       *old_path = (Path *) lfirst(p1);
        bool        remove_old = false; /* unless new proves superior */
        PathCostComparison costcmp;
        PathKeysComparison keyscmp;
        BMS_Comparison outercmp;

        p1_next = lnext(p1);

        /*
         * Do a fuzzy cost comparison with 1% fuzziness limit.  (XXX does this
         * percentage need to be user-configurable?)
         */
        costcmp = compare_path_costs_fuzzily(new_path, old_path, 1.01,
                                             parent_rel->consider_startup);

        /*
         * If the two paths compare differently for startup and total cost,
         * then we want to keep both, and we can skip comparing pathkeys and
         * required_outer rels.  If they compare the same, proceed with the
         * other comparisons.  Row count is checked last.  (We make the tests
         * in this order because the cost comparison is most likely to turn
         * out "different", and the pathkeys comparison next most likely.  As
         * explained above, row count very seldom makes a difference, so even
         * though it's cheap to compare there's not much point in checking it
         * earlier.)
         */
        if (costcmp != COSTS_DIFFERENT)
        {
            /* Similarly check to see if either dominates on pathkeys */
            List       *old_path_pathkeys;

            old_path_pathkeys = old_path->param_info ? NIL : old_path->pathkeys;
            keyscmp = compare_pathkeys(new_path_pathkeys,
                                       old_path_pathkeys);
            if (keyscmp != PATHKEYS_DIFFERENT)
            {
                switch (costcmp)
                {
                    case COSTS_EQUAL:
                        outercmp = bms_subset_compare(PATH_REQ_OUTER(new_path),
                                                   PATH_REQ_OUTER(old_path));
                        if (keyscmp == PATHKEYS_BETTER1)
                        {
                            if ((outercmp == BMS_EQUAL ||
                                 outercmp == BMS_SUBSET1) &&
                                new_path->rows <= old_path->rows)
                                remove_old = true;      /* new dominates old */
                        }
                        else if (keyscmp == PATHKEYS_BETTER2)
                        {
                            if ((outercmp == BMS_EQUAL ||
                                 outercmp == BMS_SUBSET2) &&
                                new_path->rows >= old_path->rows)
                                accept_new = false;     /* old dominates new */
                        }
                        else    /* keyscmp == PATHKEYS_EQUAL */
                        {
                            if (outercmp == BMS_EQUAL)
                            {
                                /*
                                 * Same pathkeys and outer rels, and fuzzily
                                 * the same cost, so keep just one; to decide
                                 * which, first check rows and then do a fuzzy
                                 * cost comparison with very small fuzz limit.
                                 * (We used to do an exact cost comparison,
                                 * but that results in annoying
                                 * platform-specific plan variations due to
                                 * roundoff in the cost estimates.)  If things
                                 * are still tied, arbitrarily keep only the
                                 * old path.  Notice that we will keep only
                                 * the old path even if the less-fuzzy
                                 * comparison decides the startup and total
                                 * costs compare differently.
                                 */
                                if (new_path->rows < old_path->rows)
                                    remove_old = true;  /* new dominates old */
                                else if (new_path->rows > old_path->rows)
                                    accept_new = false; /* old dominates new */
                                else if (compare_path_costs_fuzzily(new_path,
                                                                    old_path,
                                                                    1.0000000001,
                                                                    parent_rel->consider_startup) == COSTS_BETTER1)
                                    remove_old = true;  /* new dominates old */
                                else
                                    accept_new = false; /* old equals or
                                                         * dominates new */
                            }
                            else if (outercmp == BMS_SUBSET1 &&
                                     new_path->rows <= old_path->rows)
                                remove_old = true;      /* new dominates old */
                            else if (outercmp == BMS_SUBSET2 &&
                                     new_path->rows >= old_path->rows)
                                accept_new = false;     /* old dominates new */
                            /* else different parameterizations, keep both */
                        }
                        break;
                    case COSTS_BETTER1:
                        if (keyscmp != PATHKEYS_BETTER2)
                        {
                            outercmp = bms_subset_compare(PATH_REQ_OUTER(new_path),
                                                   PATH_REQ_OUTER(old_path));
                            if ((outercmp == BMS_EQUAL ||
                                 outercmp == BMS_SUBSET1) &&
                                new_path->rows <= old_path->rows)
                                remove_old = true;      /* new dominates old */
                        }
                        break;
                    case COSTS_BETTER2:
                        if (keyscmp != PATHKEYS_BETTER1)
                        {
                            outercmp = bms_subset_compare(PATH_REQ_OUTER(new_path),
                                                   PATH_REQ_OUTER(old_path));
                            if ((outercmp == BMS_EQUAL ||
                                 outercmp == BMS_SUBSET2) &&
                                new_path->rows >= old_path->rows)
                                accept_new = false;     /* old dominates new */
                        }
                        break;
                    case COSTS_DIFFERENT:

                        /*
                         * can't get here, but keep this case to keep compiler
                         * quiet
                         */
                        break;
                }
            }
        }

        /*
         * Remove current element from pathlist if dominated by new.
         */
        if (remove_old)
        {
            parent_rel->pathlist = list_delete_cell(parent_rel->pathlist,
                                                    p1, p1_prev);

            /*
             * Delete the data pointed-to by the deleted cell, if possible
             */
            if (!IsA(old_path, IndexPath))
                pfree(old_path);
            /* p1_prev does not advance */
        }
        else
        {
            /* new belongs after this old path if it has cost >= old's */
            if (new_path->total_cost >= old_path->total_cost)
                insert_after = p1;
            /* p1_prev advances */
            p1_prev = p1;
        }

        /*
         * If we found an old path that dominates new_path, we can quit
         * scanning the pathlist; we will not add new_path, and we assume
         * new_path cannot dominate any other elements of the pathlist.
         */
        if (!accept_new)
            break;
    }

    if (accept_new)
    {
        /* Accept the new path: insert it at proper place in pathlist */
        if (insert_after)
            lappend_cell(parent_rel->pathlist, insert_after, new_path);
        else
            parent_rel->pathlist = lcons(new_path, parent_rel->pathlist);
    }
    else
    {
        /* Reject and recycle the new path */
        if (!IsA(new_path, IndexPath))
            pfree(new_path);
    }
}

/*
 * add_path_precheck
 *    Check whether a proposed new path could possibly get accepted.
 *    We assume we know the path's pathkeys and parameterization accurately,
 *    and have lower bounds for its costs.
 *
 * Note that we do not know the path's rowcount, since getting an estimate for
 * that is too expensive to do before prechecking.  We assume here that paths
 * of a superset parameterization will generate fewer rows; if that holds,
 * then paths with different parameterizations cannot dominate each other
 * and so we can simply ignore existing paths of another parameterization.
 * (In the infrequent cases where that rule of thumb fails, add_path will
 * get rid of the inferior path.)
 *
 * At the time this is called, we haven't actually built a Path structure,
 * so the required information has to be passed piecemeal.
 */
bool
add_path_precheck(RelOptInfo *parent_rel,
                  Cost startup_cost, Cost total_cost,
                  List *pathkeys, Relids required_outer)
{
    List       *new_path_pathkeys;
    ListCell   *p1;

    /* Pretend parameterized paths have no pathkeys, per add_path policy */
    new_path_pathkeys = required_outer ? NIL : pathkeys;

    foreach(p1, parent_rel->pathlist)
    {
        Path       *old_path = (Path *) lfirst(p1);
        PathKeysComparison keyscmp;

        /*
         * We are looking for an old_path with the same parameterization (and
         * by assumption the same rowcount) that dominates the new path on
         * pathkeys as well as both cost metrics.  If we find one, we can
         * reject the new path.
         *
         * For speed, we make exact rather than fuzzy cost comparisons. If an
         * old path dominates the new path exactly on both costs, it will
         * surely do so fuzzily.
         */
        if (total_cost >= old_path->total_cost)
        {
            /* can win on startup cost only if unparameterized */
            if (startup_cost >= old_path->startup_cost || required_outer)
            {
                /* new path does not win on cost, so check pathkeys... */
                List       *old_path_pathkeys;

                old_path_pathkeys = old_path->param_info ? NIL : old_path->pathkeys;
                keyscmp = compare_pathkeys(new_path_pathkeys,
                                           old_path_pathkeys);
                if (keyscmp == PATHKEYS_EQUAL ||
                    keyscmp == PATHKEYS_BETTER2)
                {
                    /* new path does not win on pathkeys... */
                    if (bms_equal(required_outer, PATH_REQ_OUTER(old_path)))
                    {
                        /* Found an old path that dominates the new one */
                        return false;
                    }
                }
            }
        }
        else
        {
            /*
             * Since the pathlist is sorted by total_cost, we can stop looking
             * once we reach a path with a total_cost larger than the new
             * path's.
             */
            break;
        }
    }

    return true;
}


/*****************************************************************************
 *      PATH NODE CREATION ROUTINES
 *****************************************************************************/

/*
 * create_seqscan_path
 *    Creates a path corresponding to a sequential scan, returning the
 *    pathnode.
 */
Path *
create_seqscan_path(PlannerInfo *root, RelOptInfo *rel, Relids required_outer)
{
    Path       *pathnode = makeNode(Path);

    pathnode->pathtype = T_SeqScan;
    pathnode->parent = rel;
    pathnode->param_info = get_baserel_parampathinfo(root, rel,
                                                     required_outer);
    pathnode->pathkeys = NIL;   /* seqscan has unordered result */

    cost_seqscan(pathnode, root, rel, pathnode->param_info);

    return pathnode;
}

/*
 * create_index_path
 *    Creates a path node for an index scan.
 *
 * 'index' is a usable index.
 * 'indexclauses' is a list of RestrictInfo nodes representing clauses
 *          to be used as index qual conditions in the scan.
 * 'indexclausecols' is an integer list of index column numbers (zero based)
 *          the indexclauses can be used with.
 * 'indexorderbys' is a list of bare expressions (no RestrictInfos)
 *          to be used as index ordering operators in the scan.
 * 'indexorderbycols' is an integer list of index column numbers (zero based)
 *          the ordering operators can be used with.
 * 'pathkeys' describes the ordering of the path.
 * 'indexscandir' is ForwardScanDirection or BackwardScanDirection
 *          for an ordered index, or NoMovementScanDirection for
 *          an unordered index.
 * 'indexonly' is true if an index-only scan is wanted.
 * 'required_outer' is the set of outer relids for a parameterized path.
 * 'loop_count' is the number of repetitions of the indexscan to factor into
 *      estimates of caching behavior.
 *
 * Returns the new path node.
 */
IndexPath *
create_index_path(PlannerInfo *root,
                  IndexOptInfo *index,
                  List *indexclauses,
                  List *indexclausecols,
                  List *indexorderbys,
                  List *indexorderbycols,
                  List *pathkeys,
                  ScanDirection indexscandir,
                  bool indexonly,
                  Relids required_outer,
                  double loop_count)
{
    IndexPath  *pathnode = makeNode(IndexPath);
    RelOptInfo *rel = index->rel;
    List       *indexquals,
               *indexqualcols;

    pathnode->path.pathtype = indexonly ? T_IndexOnlyScan : T_IndexScan;
    pathnode->path.parent = rel;
    pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
                                                          required_outer);
    pathnode->path.pathkeys = pathkeys;

    /* Convert clauses to indexquals the executor can handle */
    expand_indexqual_conditions(index, indexclauses, indexclausecols,
                                &indexquals, &indexqualcols);

    /* Fill in the pathnode */
    pathnode->indexinfo = index;
    pathnode->indexclauses = indexclauses;
    pathnode->indexquals = indexquals;
    pathnode->indexqualcols = indexqualcols;
    pathnode->indexorderbys = indexorderbys;
    pathnode->indexorderbycols = indexorderbycols;
    pathnode->indexscandir = indexscandir;

    cost_index(pathnode, root, loop_count);

    return pathnode;
}

/*
 * create_bitmap_heap_path
 *    Creates a path node for a bitmap scan.
 *
 * 'bitmapqual' is a tree of IndexPath, BitmapAndPath, and BitmapOrPath nodes.
 * 'required_outer' is the set of outer relids for a parameterized path.
 * 'loop_count' is the number of repetitions of the indexscan to factor into
 *      estimates of caching behavior.
 *
 * loop_count should match the value used when creating the component
 * IndexPaths.
 */
BitmapHeapPath *
create_bitmap_heap_path(PlannerInfo *root,
                        RelOptInfo *rel,
                        Path *bitmapqual,
                        Relids required_outer,
                        double loop_count)
{
    BitmapHeapPath *pathnode = makeNode(BitmapHeapPath);

    pathnode->path.pathtype = T_BitmapHeapScan;
    pathnode->path.parent = rel;
    pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
                                                          required_outer);
    pathnode->path.pathkeys = NIL;      /* always unordered */

    pathnode->bitmapqual = bitmapqual;

    cost_bitmap_heap_scan(&pathnode->path, root, rel,
                          pathnode->path.param_info,
                          bitmapqual, loop_count);

    return pathnode;
}

/*
 * create_bitmap_and_path
 *    Creates a path node representing a BitmapAnd.
 */
BitmapAndPath *
create_bitmap_and_path(PlannerInfo *root,
                       RelOptInfo *rel,
                       List *bitmapquals)
{
    BitmapAndPath *pathnode = makeNode(BitmapAndPath);

    pathnode->path.pathtype = T_BitmapAnd;
    pathnode->path.parent = rel;
    pathnode->path.param_info = NULL;   /* not used in bitmap trees */
    pathnode->path.pathkeys = NIL;      /* always unordered */

    pathnode->bitmapquals = bitmapquals;

    /* this sets bitmapselectivity as well as the regular cost fields: */
    cost_bitmap_and_node(pathnode, root);

    return pathnode;
}

/*
 * create_bitmap_or_path
 *    Creates a path node representing a BitmapOr.
 */
BitmapOrPath *
create_bitmap_or_path(PlannerInfo *root,
                      RelOptInfo *rel,
                      List *bitmapquals)
{
    BitmapOrPath *pathnode = makeNode(BitmapOrPath);

    pathnode->path.pathtype = T_BitmapOr;
    pathnode->path.parent = rel;
    pathnode->path.param_info = NULL;   /* not used in bitmap trees */
    pathnode->path.pathkeys = NIL;      /* always unordered */

    pathnode->bitmapquals = bitmapquals;

    /* this sets bitmapselectivity as well as the regular cost fields: */
    cost_bitmap_or_node(pathnode, root);

    return pathnode;
}

/*
 * create_tidscan_path
 *    Creates a path corresponding to a scan by TID, returning the pathnode.
 */
TidPath *
create_tidscan_path(PlannerInfo *root, RelOptInfo *rel, List *tidquals,
                    Relids required_outer)
{
    TidPath    *pathnode = makeNode(TidPath);

    pathnode->path.pathtype = T_TidScan;
    pathnode->path.parent = rel;
    pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
                                                          required_outer);
    pathnode->path.pathkeys = NIL;      /* always unordered */

    pathnode->tidquals = tidquals;

    cost_tidscan(&pathnode->path, root, rel, tidquals,
                 pathnode->path.param_info);

    return pathnode;
}

/*
 * create_append_path
 *    Creates a path corresponding to an Append plan, returning the
 *    pathnode.
 *
 * Note that we must handle subpaths = NIL, representing a dummy access path.
 */
AppendPath *
create_append_path(RelOptInfo *rel, List *subpaths, Relids required_outer)
{
    AppendPath *pathnode = makeNode(AppendPath);
    ListCell   *l;

    pathnode->path.pathtype = T_Append;
    pathnode->path.parent = rel;
    pathnode->path.param_info = get_appendrel_parampathinfo(rel,
                                                            required_outer);
    pathnode->path.pathkeys = NIL;      /* result is always considered
                                         * unsorted */
    pathnode->subpaths = subpaths;

    /*
     * We don't bother with inventing a cost_append(), but just do it here.
     *
     * Compute rows and costs as sums of subplan rows and costs.  We charge
     * nothing extra for the Append itself, which perhaps is too optimistic,
     * but since it doesn't do any selection or projection, it is a pretty
     * cheap node.  If you change this, see also make_append().
     */
    pathnode->path.rows = 0;
    pathnode->path.startup_cost = 0;
    pathnode->path.total_cost = 0;
    foreach(l, subpaths)
    {
        Path       *subpath = (Path *) lfirst(l);

        pathnode->path.rows += subpath->rows;

        if (l == list_head(subpaths))   /* first node? */
            pathnode->path.startup_cost = subpath->startup_cost;
        pathnode->path.total_cost += subpath->total_cost;

        /* All child paths must have same parameterization */
        Assert(bms_equal(PATH_REQ_OUTER(subpath), required_outer));
    }

    return pathnode;
}

/*
 * create_merge_append_path
 *    Creates a path corresponding to a MergeAppend plan, returning the
 *    pathnode.
 */
MergeAppendPath *
create_merge_append_path(PlannerInfo *root,
                         RelOptInfo *rel,
                         List *subpaths,
                         List *pathkeys,
                         Relids required_outer)
{
    MergeAppendPath *pathnode = makeNode(MergeAppendPath);
    Cost        input_startup_cost;
    Cost        input_total_cost;
    ListCell   *l;

    pathnode->path.pathtype = T_MergeAppend;
    pathnode->path.parent = rel;
    pathnode->path.param_info = get_appendrel_parampathinfo(rel,
                                                            required_outer);
    pathnode->path.pathkeys = pathkeys;
    pathnode->subpaths = subpaths;

    /*
     * Apply query-wide LIMIT if known and path is for sole base relation.
     * (Handling this at this low level is a bit klugy.)
     */
    if (bms_equal(rel->relids, root->all_baserels))
        pathnode->limit_tuples = root->limit_tuples;
    else
        pathnode->limit_tuples = -1.0;

    /*
     * Add up the sizes and costs of the input paths.
     */
    pathnode->path.rows = 0;
    input_startup_cost = 0;
    input_total_cost = 0;
    foreach(l, subpaths)
    {
        Path       *subpath = (Path *) lfirst(l);

        pathnode->path.rows += subpath->rows;

        if (pathkeys_contained_in(pathkeys, subpath->pathkeys))
        {
            /* Subpath is adequately ordered, we won't need to sort it */
            input_startup_cost += subpath->startup_cost;
            input_total_cost += subpath->total_cost;
        }
        else
        {
            /* We'll need to insert a Sort node, so include cost for that */
            Path        sort_path;      /* dummy for result of cost_sort */

            cost_sort(&sort_path,
                      root,
                      pathkeys,
                      subpath->total_cost,
                      subpath->parent->tuples,
                      subpath->parent->width,
                      0.0,
                      work_mem,
                      pathnode->limit_tuples);
            input_startup_cost += sort_path.startup_cost;
            input_total_cost += sort_path.total_cost;
        }

        /* All child paths must have same parameterization */
        Assert(bms_equal(PATH_REQ_OUTER(subpath), required_outer));
    }

    /* Now we can compute total costs of the MergeAppend */
    cost_merge_append(&pathnode->path, root,
                      pathkeys, list_length(subpaths),
                      input_startup_cost, input_total_cost,
                      rel->tuples);

    return pathnode;
}

/*
 * create_result_path
 *    Creates a path representing a Result-and-nothing-else plan.
 *    This is only used for the case of a query with an empty jointree.
 */
ResultPath *
create_result_path(List *quals)
{
    ResultPath *pathnode = makeNode(ResultPath);

    pathnode->path.pathtype = T_Result;
    pathnode->path.parent = NULL;
    pathnode->path.param_info = NULL;       /* there are no other rels... */
    pathnode->path.pathkeys = NIL;
    pathnode->quals = quals;

    /* Hardly worth defining a cost_result() function ... just do it */
    pathnode->path.rows = 1;
    pathnode->path.startup_cost = 0;
    pathnode->path.total_cost = cpu_tuple_cost;

    /*
     * In theory we should include the qual eval cost as well, but at present
     * that doesn't accomplish much except duplicate work that will be done
     * again in make_result; since this is only used for degenerate cases,
     * nothing interesting will be done with the path cost values...
     */

    return pathnode;
}

/*
 * create_material_path
 *    Creates a path corresponding to a Material plan, returning the
 *    pathnode.
 */
MaterialPath *
create_material_path(RelOptInfo *rel, Path *subpath)
{
    MaterialPath *pathnode = makeNode(MaterialPath);

    Assert(subpath->parent == rel);

    pathnode->path.pathtype = T_Material;
    pathnode->path.parent = rel;
    pathnode->path.param_info = subpath->param_info;
    pathnode->path.pathkeys = subpath->pathkeys;

    pathnode->subpath = subpath;

    cost_material(&pathnode->path,
                  subpath->startup_cost,
                  subpath->total_cost,
                  subpath->rows,
                  rel->width);

    return pathnode;
}

/*
 * create_unique_path
 *    Creates a path representing elimination of distinct rows from the
 *    input data.  Distinct-ness is defined according to the needs of the
 *    semijoin represented by sjinfo.  If it is not possible to identify
 *    how to make the data unique, NULL is returned.
 *
 * If used at all, this is likely to be called repeatedly on the same rel;
 * and the input subpath should always be the same (the cheapest_total path
 * for the rel).  So we cache the result.
 */
UniquePath *
create_unique_path(PlannerInfo *root, RelOptInfo *rel, Path *subpath,
                   SpecialJoinInfo *sjinfo)
{
    UniquePath *pathnode;
    Path        sort_path;      /* dummy for result of cost_sort */
    Path        agg_path;       /* dummy for result of cost_agg */
    MemoryContext oldcontext;
    List       *in_operators;
    List       *uniq_exprs;
    bool        all_btree;
    bool        all_hash;
    int         numCols;
    ListCell   *lc;

    /* Caller made a mistake if subpath isn't cheapest_total ... */
    Assert(subpath == rel->cheapest_total_path);
    Assert(subpath->parent == rel);
    /* ... or if SpecialJoinInfo is the wrong one */
    Assert(sjinfo->jointype == JOIN_SEMI);
    Assert(bms_equal(rel->relids, sjinfo->syn_righthand));

    /* If result already cached, return it */
    if (rel->cheapest_unique_path)
        return (UniquePath *) rel->cheapest_unique_path;

    /* If we previously failed, return NULL quickly */
    if (sjinfo->join_quals == NIL)
        return NULL;

    /*
     * We must ensure path struct and subsidiary data are allocated in main
     * planning context; otherwise GEQO memory management causes trouble.
     */
    oldcontext = MemoryContextSwitchTo(root->planner_cxt);

    /*----------
     * Look to see whether the semijoin's join quals consist of AND'ed
     * equality operators, with (only) RHS variables on only one side of
     * each one.  If so, we can figure out how to enforce uniqueness for
     * the RHS.
     *
     * Note that the input join_quals list is the list of quals that are
     * *syntactically* associated with the semijoin, which in practice means
     * the synthesized comparison list for an IN or the WHERE of an EXISTS.
     * Particularly in the latter case, it might contain clauses that aren't
     * *semantically* associated with the join, but refer to just one side or
     * the other.  We can ignore such clauses here, as they will just drop
     * down to be processed within one side or the other.  (It is okay to
     * consider only the syntactically-associated clauses here because for a
     * semijoin, no higher-level quals could refer to the RHS, and so there
     * can be no other quals that are semantically associated with this join.
     * We do things this way because it is useful to be able to run this test
     * before we have extracted the list of quals that are actually
     * semantically associated with the particular join.)
     *
     * Note that the in_operators list consists of the joinqual operators
     * themselves (but commuted if needed to put the RHS value on the right).
     * These could be cross-type operators, in which case the operator
     * actually needed for uniqueness is a related single-type operator.
     * We assume here that that operator will be available from the btree
     * or hash opclass when the time comes ... if not, create_unique_plan()
     * will fail.
     *----------
     */
    in_operators = NIL;
    uniq_exprs = NIL;
    all_btree = true;
    all_hash = enable_hashagg;  /* don't consider hash if not enabled */
    foreach(lc, sjinfo->join_quals)
    {
        OpExpr     *op = (OpExpr *) lfirst(lc);
        Oid         opno;
        Node       *left_expr;
        Node       *right_expr;
        Relids      left_varnos;
        Relids      right_varnos;
        Relids      all_varnos;
        Oid         opinputtype;

        /* Is it a binary opclause? */
        if (!IsA(op, OpExpr) ||
            list_length(op->args) != 2)
        {
            /* No, but does it reference both sides? */
            all_varnos = pull_varnos((Node *) op);
            if (!bms_overlap(all_varnos, sjinfo->syn_righthand) ||
                bms_is_subset(all_varnos, sjinfo->syn_righthand))
            {
                /*
                 * Clause refers to only one rel, so ignore it --- unless it
                 * contains volatile functions, in which case we'd better
                 * punt.
                 */
                if (contain_volatile_functions((Node *) op))
                    goto no_unique_path;
                continue;
            }
            /* Non-operator clause referencing both sides, must punt */
            goto no_unique_path;
        }

        /* Extract data from binary opclause */
        opno = op->opno;
        left_expr = linitial(op->args);
        right_expr = lsecond(op->args);
        left_varnos = pull_varnos(left_expr);
        right_varnos = pull_varnos(right_expr);
        all_varnos = bms_union(left_varnos, right_varnos);
        opinputtype = exprType(left_expr);

        /* Does it reference both sides? */
        if (!bms_overlap(all_varnos, sjinfo->syn_righthand) ||
            bms_is_subset(all_varnos, sjinfo->syn_righthand))
        {
            /*
             * Clause refers to only one rel, so ignore it --- unless it
             * contains volatile functions, in which case we'd better punt.
             */
            if (contain_volatile_functions((Node *) op))
                goto no_unique_path;
            continue;
        }

        /* check rel membership of arguments */
        if (!bms_is_empty(right_varnos) &&
            bms_is_subset(right_varnos, sjinfo->syn_righthand) &&
            !bms_overlap(left_varnos, sjinfo->syn_righthand))
        {
            /* typical case, right_expr is RHS variable */
        }
        else if (!bms_is_empty(left_varnos) &&
                 bms_is_subset(left_varnos, sjinfo->syn_righthand) &&
                 !bms_overlap(right_varnos, sjinfo->syn_righthand))
        {
            /* flipped case, left_expr is RHS variable */
            opno = get_commutator(opno);
            if (!OidIsValid(opno))
                goto no_unique_path;
            right_expr = left_expr;
        }
        else
            goto no_unique_path;

        /* all operators must be btree equality or hash equality */
        if (all_btree)
        {
            /* oprcanmerge is considered a hint... */
            if (!op_mergejoinable(opno, opinputtype) ||
                get_mergejoin_opfamilies(opno) == NIL)
                all_btree = false;
        }
        if (all_hash)
        {
            /* ... but oprcanhash had better be correct */
            if (!op_hashjoinable(opno, opinputtype))
                all_hash = false;
        }
        if (!(all_btree || all_hash))
            goto no_unique_path;

        /* so far so good, keep building lists */
        in_operators = lappend_oid(in_operators, opno);
        uniq_exprs = lappend(uniq_exprs, copyObject(right_expr));
    }

    /* Punt if we didn't find at least one column to unique-ify */
    if (uniq_exprs == NIL)
        goto no_unique_path;

    /*
     * The expressions we'd need to unique-ify mustn't be volatile.
     */
    if (contain_volatile_functions((Node *) uniq_exprs))
        goto no_unique_path;

    /*
     * If we get here, we can unique-ify using at least one of sorting and
     * hashing.  Start building the result Path object.
     */
    pathnode = makeNode(UniquePath);

    pathnode->path.pathtype = T_Unique;
    pathnode->path.parent = rel;
    pathnode->path.param_info = subpath->param_info;

    /*
     * Assume the output is unsorted, since we don't necessarily have pathkeys
     * to represent it.  (This might get overridden below.)
     */
    pathnode->path.pathkeys = NIL;

    pathnode->subpath = subpath;
    pathnode->in_operators = in_operators;
    pathnode->uniq_exprs = uniq_exprs;

    /*
     * If the input is a relation and it has a unique index that proves the
     * uniq_exprs are unique, then we don't need to do anything.  Note that
     * relation_has_unique_index_for automatically considers restriction
     * clauses for the rel, as well.
     */
    if (rel->rtekind == RTE_RELATION && all_btree &&
        relation_has_unique_index_for(root, rel, NIL,
                                      uniq_exprs, in_operators))
    {
        pathnode->umethod = UNIQUE_PATH_NOOP;
        pathnode->path.rows = rel->rows;
        pathnode->path.startup_cost = subpath->startup_cost;
        pathnode->path.total_cost = subpath->total_cost;
        pathnode->path.pathkeys = subpath->pathkeys;

        rel->cheapest_unique_path = (Path *) pathnode;

        MemoryContextSwitchTo(oldcontext);

        return pathnode;
    }

    /*
     * If the input is a subquery whose output must be unique already, then we
     * don't need to do anything.  The test for uniqueness has to consider
     * exactly which columns we are extracting; for example "SELECT DISTINCT
     * x,y" doesn't guarantee that x alone is distinct. So we cannot check for
     * this optimization unless uniq_exprs consists only of simple Vars
     * referencing subquery outputs.  (Possibly we could do something with
     * expressions in the subquery outputs, too, but for now keep it simple.)
     */
    if (rel->rtekind == RTE_SUBQUERY)
    {
        RangeTblEntry *rte = planner_rt_fetch(rel->relid, root);
        List       *sub_tlist_colnos;

        sub_tlist_colnos = translate_sub_tlist(uniq_exprs, rel->relid);

        if (sub_tlist_colnos &&
            query_is_distinct_for(rte->subquery,
                                  sub_tlist_colnos, in_operators))
        {
            pathnode->umethod = UNIQUE_PATH_NOOP;
            pathnode->path.rows = rel->rows;
            pathnode->path.startup_cost = subpath->startup_cost;
            pathnode->path.total_cost = subpath->total_cost;
            pathnode->path.pathkeys = subpath->pathkeys;

            rel->cheapest_unique_path = (Path *) pathnode;

            MemoryContextSwitchTo(oldcontext);

            return pathnode;
        }
    }

    /* Estimate number of output rows */
    pathnode->path.rows = estimate_num_groups(root, uniq_exprs, rel->rows);
    numCols = list_length(uniq_exprs);

    if (all_btree)
    {
        /*
         * Estimate cost for sort+unique implementation
         */
        cost_sort(&sort_path, root, NIL,
                  subpath->total_cost,
                  rel->rows,
                  rel->width,
                  0.0,
                  work_mem,
                  -1.0);

        /*
         * Charge one cpu_operator_cost per comparison per input tuple. We
         * assume all columns get compared at most of the tuples. (XXX
         * probably this is an overestimate.)  This should agree with
         * make_unique.
         */
        sort_path.total_cost += cpu_operator_cost * rel->rows * numCols;
    }

    if (all_hash)
    {
        /*
         * Estimate the overhead per hashtable entry at 64 bytes (same as in
         * planner.c).
         */
        int         hashentrysize = rel->width + 64;

        if (hashentrysize * pathnode->path.rows > work_mem * 1024L)
            all_hash = false;   /* don't try to hash */
        else
            cost_agg(&agg_path, root,
                     AGG_HASHED, NULL,
                     numCols, pathnode->path.rows,
                     subpath->startup_cost,
                     subpath->total_cost,
                     rel->rows);
    }

    if (all_btree && all_hash)
    {
        if (agg_path.total_cost < sort_path.total_cost)
            pathnode->umethod = UNIQUE_PATH_HASH;
        else
            pathnode->umethod = UNIQUE_PATH_SORT;
    }
    else if (all_btree)
        pathnode->umethod = UNIQUE_PATH_SORT;
    else if (all_hash)
        pathnode->umethod = UNIQUE_PATH_HASH;
    else
        goto no_unique_path;

    if (pathnode->umethod == UNIQUE_PATH_HASH)
    {
        pathnode->path.startup_cost = agg_path.startup_cost;
        pathnode->path.total_cost = agg_path.total_cost;
    }
    else
    {
        pathnode->path.startup_cost = sort_path.startup_cost;
        pathnode->path.total_cost = sort_path.total_cost;
    }

    rel->cheapest_unique_path = (Path *) pathnode;

    MemoryContextSwitchTo(oldcontext);

    return pathnode;

no_unique_path:         /* failure exit */

    /* Mark the SpecialJoinInfo as not unique-able */
    sjinfo->join_quals = NIL;

    MemoryContextSwitchTo(oldcontext);

    return NULL;
}

/*
 * translate_sub_tlist - get subquery column numbers represented by tlist
 *
 * The given targetlist usually contains only Vars referencing the given relid.
 * Extract their varattnos (ie, the column numbers of the subquery) and return
 * as an integer List.
 *
 * If any of the tlist items is not a simple Var, we cannot determine whether
 * the subquery's uniqueness condition (if any) matches ours, so punt and
 * return NIL.
 */
static List *
translate_sub_tlist(List *tlist, int relid)
{
    List       *result = NIL;
    ListCell   *l;

    foreach(l, tlist)
    {
        Var        *var = (Var *) lfirst(l);

        if (!var || !IsA(var, Var) ||
            var->varno != relid)
            return NIL;         /* punt */

        result = lappend_int(result, var->varattno);
    }
    return result;
}

/*
 * query_is_distinct_for - does query never return duplicates of the
 *      specified columns?
 *
 * colnos is an integer list of output column numbers (resno's).  We are
 * interested in whether rows consisting of just these columns are certain
 * to be distinct.  "Distinctness" is defined according to whether the
 * corresponding upper-level equality operators listed in opids would think
 * the values are distinct.  (Note: the opids entries could be cross-type
 * operators, and thus not exactly the equality operators that the subquery
 * would use itself.  We use equality_ops_are_compatible() to check
 * compatibility.  That looks at btree or hash opfamily membership, and so
 * should give trustworthy answers for all operators that we might need
 * to deal with here.)
 */
static bool
query_is_distinct_for(Query *query, List *colnos, List *opids)
{
    ListCell   *l;
    Oid         opid;

    Assert(list_length(colnos) == list_length(opids));

    /*
     * DISTINCT (including DISTINCT ON) guarantees uniqueness if all the
     * columns in the DISTINCT clause appear in colnos and operator semantics
     * match.
     */
    if (query->distinctClause)
    {
        foreach(l, query->distinctClause)
        {
            SortGroupClause *sgc = (SortGroupClause *) lfirst(l);
            TargetEntry *tle = get_sortgroupclause_tle(sgc,
                                                       query->targetList);

            opid = distinct_col_search(tle->resno, colnos, opids);
            if (!OidIsValid(opid) ||
                !equality_ops_are_compatible(opid, sgc->eqop))
                break;          /* exit early if no match */
        }
        if (l == NULL)          /* had matches for all? */
            return true;
    }

    /*
     * Similarly, GROUP BY guarantees uniqueness if all the grouped columns
     * appear in colnos and operator semantics match.
     */
    if (query->groupClause)
    {
        foreach(l, query->groupClause)
        {
            SortGroupClause *sgc = (SortGroupClause *) lfirst(l);
            TargetEntry *tle = get_sortgroupclause_tle(sgc,
                                                       query->targetList);

            opid = distinct_col_search(tle->resno, colnos, opids);
            if (!OidIsValid(opid) ||
                !equality_ops_are_compatible(opid, sgc->eqop))
                break;          /* exit early if no match */
        }
        if (l == NULL)          /* had matches for all? */
            return true;
    }
    else
    {
        /*
         * If we have no GROUP BY, but do have aggregates or HAVING, then the
         * result is at most one row so it's surely unique, for any operators.
         */
        if (query->hasAggs || query->havingQual)
            return true;
    }

    /*
     * UNION, INTERSECT, EXCEPT guarantee uniqueness of the whole output row,
     * except with ALL.
     */
    if (query->setOperations)
    {
        SetOperationStmt *topop = (SetOperationStmt *) query->setOperations;

        Assert(IsA(topop, SetOperationStmt));
        Assert(topop->op != SETOP_NONE);

        if (!topop->all)
        {
            ListCell   *lg;

            /* We're good if all the nonjunk output columns are in colnos */
            lg = list_head(topop->groupClauses);
            foreach(l, query->targetList)
            {
                TargetEntry *tle = (TargetEntry *) lfirst(l);
                SortGroupClause *sgc;

                if (tle->resjunk)
                    continue;   /* ignore resjunk columns */

                /* non-resjunk columns should have grouping clauses */
                Assert(lg != NULL);
                sgc = (SortGroupClause *) lfirst(lg);
                lg = lnext(lg);

                opid = distinct_col_search(tle->resno, colnos, opids);
                if (!OidIsValid(opid) ||
                    !equality_ops_are_compatible(opid, sgc->eqop))
                    break;      /* exit early if no match */
            }
            if (l == NULL)      /* had matches for all? */
                return true;
        }
    }

    /*
     * XXX Are there any other cases in which we can easily see the result
     * must be distinct?
     */

    return false;
}

/*
 * distinct_col_search - subroutine for query_is_distinct_for
 *
 * If colno is in colnos, return the corresponding element of opids,
 * else return InvalidOid.  (We expect colnos does not contain duplicates,
 * so the result is well-defined.)
 */
static Oid
distinct_col_search(int colno, List *colnos, List *opids)
{
    ListCell   *lc1,
               *lc2;

    forboth(lc1, colnos, lc2, opids)
    {
        if (colno == lfirst_int(lc1))
            return lfirst_oid(lc2);
    }
    return InvalidOid;
}

/*
 * create_subqueryscan_path
 *    Creates a path corresponding to a sequential scan of a subquery,
 *    returning the pathnode.
 */
Path *
create_subqueryscan_path(PlannerInfo *root, RelOptInfo *rel,
                         List *pathkeys, Relids required_outer)
{
    Path       *pathnode = makeNode(Path);

    pathnode->pathtype = T_SubqueryScan;
    pathnode->parent = rel;
    pathnode->param_info = get_baserel_parampathinfo(root, rel,
                                                     required_outer);
    pathnode->pathkeys = pathkeys;

    cost_subqueryscan(pathnode, root, rel, pathnode->param_info);

    return pathnode;
}

/*
 * create_functionscan_path
 *    Creates a path corresponding to a sequential scan of a function,
 *    returning the pathnode.
 */
Path *
create_functionscan_path(PlannerInfo *root, RelOptInfo *rel,
                         Relids required_outer)
{
    Path       *pathnode = makeNode(Path);

    pathnode->pathtype = T_FunctionScan;
    pathnode->parent = rel;
    pathnode->param_info = get_baserel_parampathinfo(root, rel,
                                                     required_outer);
    pathnode->pathkeys = NIL;   /* for now, assume unordered result */

    cost_functionscan(pathnode, root, rel, pathnode->param_info);

    return pathnode;
}

/*
 * create_valuesscan_path
 *    Creates a path corresponding to a scan of a VALUES list,
 *    returning the pathnode.
 */
Path *
create_valuesscan_path(PlannerInfo *root, RelOptInfo *rel,
                       Relids required_outer)
{
    Path       *pathnode = makeNode(Path);

    pathnode->pathtype = T_ValuesScan;
    pathnode->parent = rel;
    pathnode->param_info = get_baserel_parampathinfo(root, rel,
                                                     required_outer);
    pathnode->pathkeys = NIL;   /* result is always unordered */

    cost_valuesscan(pathnode, root, rel, pathnode->param_info);

    return pathnode;
}

/*
 * create_ctescan_path
 *    Creates a path corresponding to a scan of a non-self-reference CTE,
 *    returning the pathnode.
 */
Path *
create_ctescan_path(PlannerInfo *root, RelOptInfo *rel, Relids required_outer)
{
    Path       *pathnode = makeNode(Path);

    pathnode->pathtype = T_CteScan;
    pathnode->parent = rel;
    pathnode->param_info = get_baserel_parampathinfo(root, rel,
                                                     required_outer);
    pathnode->pathkeys = NIL;   /* XXX for now, result is always unordered */

    cost_ctescan(pathnode, root, rel, pathnode->param_info);

    return pathnode;
}

/*
 * create_worktablescan_path
 *    Creates a path corresponding to a scan of a self-reference CTE,
 *    returning the pathnode.
 */
Path *
create_worktablescan_path(PlannerInfo *root, RelOptInfo *rel,
                          Relids required_outer)
{
    Path       *pathnode = makeNode(Path);

    pathnode->pathtype = T_WorkTableScan;
    pathnode->parent = rel;
    pathnode->param_info = get_baserel_parampathinfo(root, rel,
                                                     required_outer);
    pathnode->pathkeys = NIL;   /* result is always unordered */

    /* Cost is the same as for a regular CTE scan */
    cost_ctescan(pathnode, root, rel, pathnode->param_info);

    return pathnode;
}

/*
 * create_foreignscan_path
 *    Creates a path corresponding to a scan of a foreign table,
 *    returning the pathnode.
 *
 * This function is never called from core Postgres; rather, it's expected
 * to be called by the GetForeignPaths function of a foreign data wrapper.
 * We make the FDW supply all fields of the path, since we do not have any
 * way to calculate them in core.
 */
ForeignPath *
create_foreignscan_path(PlannerInfo *root, RelOptInfo *rel,
                        double rows, Cost startup_cost, Cost total_cost,
                        List *pathkeys,
                        Relids required_outer,
                        List *fdw_private)
{
    ForeignPath *pathnode = makeNode(ForeignPath);

    pathnode->path.pathtype = T_ForeignScan;
    pathnode->path.parent = rel;
    pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
                                                          required_outer);
    pathnode->path.rows = rows;
    pathnode->path.startup_cost = startup_cost;
    pathnode->path.total_cost = total_cost;
    pathnode->path.pathkeys = pathkeys;

    pathnode->fdw_private = fdw_private;

    return pathnode;
}

/*
 * calc_nestloop_required_outer
 *    Compute the required_outer set for a nestloop join path
 *
 * Note: result must not share storage with either input
 */
Relids
calc_nestloop_required_outer(Path *outer_path, Path *inner_path)
{
    Relids      outer_paramrels = PATH_REQ_OUTER(outer_path);
    Relids      inner_paramrels = PATH_REQ_OUTER(inner_path);
    Relids      required_outer;

    /* inner_path can require rels from outer path, but not vice versa */
    Assert(!bms_overlap(outer_paramrels, inner_path->parent->relids));
    /* easy case if inner path is not parameterized */
    if (!inner_paramrels)
        return bms_copy(outer_paramrels);
    /* else, form the union ... */
    required_outer = bms_union(outer_paramrels, inner_paramrels);
    /* ... and remove any mention of now-satisfied outer rels */
    required_outer = bms_del_members(required_outer,
                                     outer_path->parent->relids);
    /* maintain invariant that required_outer is exactly NULL if empty */
    if (bms_is_empty(required_outer))
    {
        bms_free(required_outer);
        required_outer = NULL;
    }
    return required_outer;
}

/*
 * calc_non_nestloop_required_outer
 *    Compute the required_outer set for a merge or hash join path
 *
 * Note: result must not share storage with either input
 */
Relids
calc_non_nestloop_required_outer(Path *outer_path, Path *inner_path)
{
    Relids      outer_paramrels = PATH_REQ_OUTER(outer_path);
    Relids      inner_paramrels = PATH_REQ_OUTER(inner_path);
    Relids      required_outer;

    /* neither path can require rels from the other */
    Assert(!bms_overlap(outer_paramrels, inner_path->parent->relids));
    Assert(!bms_overlap(inner_paramrels, outer_path->parent->relids));
    /* form the union ... */
    required_outer = bms_union(outer_paramrels, inner_paramrels);
    /* we do not need an explicit test for empty; bms_union gets it right */
    return required_outer;
}

/*
 * create_nestloop_path
 *    Creates a pathnode corresponding to a nestloop join between two
 *    relations.
 *
 * 'joinrel' is the join relation.
 * 'jointype' is the type of join required
 * 'workspace' is the result from initial_cost_nestloop
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'semifactors' contains valid data if jointype is SEMI or ANTI
 * 'outer_path' is the outer path
 * 'inner_path' is the inner path
 * 'restrict_clauses' are the RestrictInfo nodes to apply at the join
 * 'pathkeys' are the path keys of the new join path
 * 'required_outer' is the set of required outer rels
 *
 * Returns the resulting path node.
 */
NestPath *
create_nestloop_path(PlannerInfo *root,
                     RelOptInfo *joinrel,
                     JoinType jointype,
                     JoinCostWorkspace *workspace,
                     SpecialJoinInfo *sjinfo,
                     SemiAntiJoinFactors *semifactors,
                     Path *outer_path,
                     Path *inner_path,
                     List *restrict_clauses,
                     List *pathkeys,
                     Relids required_outer)
{
    NestPath   *pathnode = makeNode(NestPath);
    Relids      inner_req_outer = PATH_REQ_OUTER(inner_path);

    /*
     * If the inner path is parameterized by the outer, we must drop any
     * restrict_clauses that are due to be moved into the inner path.  We have
     * to do this now, rather than postpone the work till createplan time,
     * because the restrict_clauses list can affect the size and cost
     * estimates for this path.
     */
    if (bms_overlap(inner_req_outer, outer_path->parent->relids))
    {
        Relids      inner_and_outer = bms_union(inner_path->parent->relids,
                                                inner_req_outer);
        List       *jclauses = NIL;
        ListCell   *lc;

        foreach(lc, restrict_clauses)
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

            if (!join_clause_is_movable_into(rinfo,
                                             inner_path->parent->relids,
                                             inner_and_outer))
                jclauses = lappend(jclauses, rinfo);
        }
        restrict_clauses = jclauses;
    }

    pathnode->path.pathtype = T_NestLoop;
    pathnode->path.parent = joinrel;
    pathnode->path.param_info =
        get_joinrel_parampathinfo(root,
                                  joinrel,
                                  outer_path,
                                  inner_path,
                                  sjinfo,
                                  required_outer,
                                  &restrict_clauses);
    pathnode->path.pathkeys = pathkeys;
    pathnode->jointype = jointype;
    pathnode->outerjoinpath = outer_path;
    pathnode->innerjoinpath = inner_path;
    pathnode->joinrestrictinfo = restrict_clauses;

    final_cost_nestloop(root, pathnode, workspace, sjinfo, semifactors);

    return pathnode;
}

/*
 * create_mergejoin_path
 *    Creates a pathnode corresponding to a mergejoin join between
 *    two relations
 *
 * 'joinrel' is the join relation
 * 'jointype' is the type of join required
 * 'workspace' is the result from initial_cost_mergejoin
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'outer_path' is the outer path
 * 'inner_path' is the inner path
 * 'restrict_clauses' are the RestrictInfo nodes to apply at the join
 * 'pathkeys' are the path keys of the new join path
 * 'required_outer' is the set of required outer rels
 * 'mergeclauses' are the RestrictInfo nodes to use as merge clauses
 *      (this should be a subset of the restrict_clauses list)
 * 'outersortkeys' are the sort varkeys for the outer relation
 * 'innersortkeys' are the sort varkeys for the inner relation
 */
MergePath *
create_mergejoin_path(PlannerInfo *root,
                      RelOptInfo *joinrel,
                      JoinType jointype,
                      JoinCostWorkspace *workspace,
                      SpecialJoinInfo *sjinfo,
                      Path *outer_path,
                      Path *inner_path,
                      List *restrict_clauses,
                      List *pathkeys,
                      Relids required_outer,
                      List *mergeclauses,
                      List *outersortkeys,
                      List *innersortkeys)
{
    MergePath  *pathnode = makeNode(MergePath);

    pathnode->jpath.path.pathtype = T_MergeJoin;
    pathnode->jpath.path.parent = joinrel;
    pathnode->jpath.path.param_info =
        get_joinrel_parampathinfo(root,
                                  joinrel,
                                  outer_path,
                                  inner_path,
                                  sjinfo,
                                  required_outer,
                                  &restrict_clauses);
    pathnode->jpath.path.pathkeys = pathkeys;
    pathnode->jpath.jointype = jointype;
    pathnode->jpath.outerjoinpath = outer_path;
    pathnode->jpath.innerjoinpath = inner_path;
    pathnode->jpath.joinrestrictinfo = restrict_clauses;
    pathnode->path_mergeclauses = mergeclauses;
    pathnode->outersortkeys = outersortkeys;
    pathnode->innersortkeys = innersortkeys;
    /* pathnode->materialize_inner will be set by final_cost_mergejoin */

    final_cost_mergejoin(root, pathnode, workspace, sjinfo);

    return pathnode;
}

/*
 * create_hashjoin_path
 *    Creates a pathnode corresponding to a hash join between two relations.
 *
 * 'joinrel' is the join relation
 * 'jointype' is the type of join required
 * 'workspace' is the result from initial_cost_hashjoin
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'semifactors' contains valid data if jointype is SEMI or ANTI
 * 'outer_path' is the cheapest outer path
 * 'inner_path' is the cheapest inner path
 * 'restrict_clauses' are the RestrictInfo nodes to apply at the join
 * 'required_outer' is the set of required outer rels
 * 'hashclauses' are the RestrictInfo nodes to use as hash clauses
 *      (this should be a subset of the restrict_clauses list)
 */
HashPath *
create_hashjoin_path(PlannerInfo *root,
                     RelOptInfo *joinrel,
                     JoinType jointype,
                     JoinCostWorkspace *workspace,
                     SpecialJoinInfo *sjinfo,
                     SemiAntiJoinFactors *semifactors,
                     Path *outer_path,
                     Path *inner_path,
                     List *restrict_clauses,
                     Relids required_outer,
                     List *hashclauses)
{
    HashPath   *pathnode = makeNode(HashPath);

    pathnode->jpath.path.pathtype = T_HashJoin;
    pathnode->jpath.path.parent = joinrel;
    pathnode->jpath.path.param_info =
        get_joinrel_parampathinfo(root,
                                  joinrel,
                                  outer_path,
                                  inner_path,
                                  sjinfo,
                                  required_outer,
                                  &restrict_clauses);

    /*
     * A hashjoin never has pathkeys, since its output ordering is
     * unpredictable due to possible batching.  XXX If the inner relation is
     * small enough, we could instruct the executor that it must not batch,
     * and then we could assume that the output inherits the outer relation's
     * ordering, which might save a sort step.  However there is considerable
     * downside if our estimate of the inner relation size is badly off. For
     * the moment we don't risk it.  (Note also that if we wanted to take this
     * seriously, joinpath.c would have to consider many more paths for the
     * outer rel than it does now.)
     */
    pathnode->jpath.path.pathkeys = NIL;
    pathnode->jpath.jointype = jointype;
    pathnode->jpath.outerjoinpath = outer_path;
    pathnode->jpath.innerjoinpath = inner_path;
    pathnode->jpath.joinrestrictinfo = restrict_clauses;
    pathnode->path_hashclauses = hashclauses;
    /* final_cost_hashjoin will fill in pathnode->num_batches */

    final_cost_hashjoin(root, pathnode, workspace, sjinfo, semifactors);

    return pathnode;
}

/*
 * reparameterize_path
 *      Attempt to modify a Path to have greater parameterization
 *
 * We use this to attempt to bring all child paths of an appendrel to the
 * same parameterization level, ensuring that they all enforce the same set
 * of join quals (and thus that that parameterization can be attributed to
 * an append path built from such paths).  Currently, only a few path types
 * are supported here, though more could be added at need.  We return NULL
 * if we can't reparameterize the given path.
 *
 * Note: we intentionally do not pass created paths to add_path(); it would
 * possibly try to delete them on the grounds of being cost-inferior to the
 * paths they were made from, and we don't want that.  Paths made here are
 * not necessarily of general-purpose usefulness, but they can be useful
 * as members of an append path.
 */
Path *
reparameterize_path(PlannerInfo *root, Path *path,
                    Relids required_outer,
                    double loop_count)
{
    RelOptInfo *rel = path->parent;

    /* Can only increase, not decrease, path's parameterization */
    if (!bms_is_subset(PATH_REQ_OUTER(path), required_outer))
        return NULL;
    switch (path->pathtype)
    {
        case T_SeqScan:
            return create_seqscan_path(root, rel, required_outer);
        case T_IndexScan:
        case T_IndexOnlyScan:
            {
                IndexPath  *ipath = (IndexPath *) path;
                IndexPath  *newpath = makeNode(IndexPath);

                /*
                 * We can't use create_index_path directly, and would not want
                 * to because it would re-compute the indexqual conditions
                 * which is wasted effort.  Instead we hack things a bit:
                 * flat-copy the path node, revise its param_info, and redo
                 * the cost estimate.
                 */
                memcpy(newpath, ipath, sizeof(IndexPath));
                newpath->path.param_info =
                    get_baserel_parampathinfo(root, rel, required_outer);
                cost_index(newpath, root, loop_count);
                return (Path *) newpath;
            }
        case T_BitmapHeapScan:
            {
                BitmapHeapPath *bpath = (BitmapHeapPath *) path;

                return (Path *) create_bitmap_heap_path(root,
                                                        rel,
                                                        bpath->bitmapqual,
                                                        required_outer,
                                                        loop_count);
            }
        case T_SubqueryScan:
            return create_subqueryscan_path(root, rel, path->pathkeys,
                                            required_outer);
        default:
            break;
    }
    return NULL;
}