indxpath.c

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/*-------------------------------------------------------------------------
 *
 * indxpath.c
 *    Routines to determine which indexes are usable for scanning a
 *    given relation, and create Paths accordingly.
 *
 * Portions Copyright (c) 1996-2013, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/optimizer/path/indxpath.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <math.h>

#include "access/skey.h"
#include "access/sysattr.h"
#include "catalog/pg_am.h"
#include "catalog/pg_collation.h"
#include "catalog/pg_operator.h"
#include "catalog/pg_opfamily.h"
#include "catalog/pg_type.h"
#include "nodes/makefuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/predtest.h"
#include "optimizer/restrictinfo.h"
#include "optimizer/var.h"
#include "utils/builtins.h"
#include "utils/bytea.h"
#include "utils/lsyscache.h"
#include "utils/pg_locale.h"
#include "utils/selfuncs.h"


#define IsBooleanOpfamily(opfamily) \
    ((opfamily) == BOOL_BTREE_FAM_OID || (opfamily) == BOOL_HASH_FAM_OID)

#define IndexCollMatchesExprColl(idxcollation, exprcollation) \
    ((idxcollation) == InvalidOid || (idxcollation) == (exprcollation))

/* Whether to use ScalarArrayOpExpr to build index qualifications */
typedef enum
{
    SAOP_PER_AM,                /* Use ScalarArrayOpExpr if amsearcharray */
    SAOP_ALLOW,                 /* Use ScalarArrayOpExpr for all indexes */
    SAOP_REQUIRE                /* Require ScalarArrayOpExpr to be used */
} SaOpControl;

/* Whether we are looking for plain indexscan, bitmap scan, or either */
typedef enum
{
    ST_INDEXSCAN,               /* must support amgettuple */
    ST_BITMAPSCAN,              /* must support amgetbitmap */
    ST_ANYSCAN                  /* either is okay */
} ScanTypeControl;

/* Data structure for collecting qual clauses that match an index */
typedef struct
{
    bool        nonempty;       /* True if lists are not all empty */
    /* Lists of RestrictInfos, one per index column */
    List       *indexclauses[INDEX_MAX_KEYS];
} IndexClauseSet;

/* Per-path data used within choose_bitmap_and() */
typedef struct
{
    Path       *path;           /* IndexPath, BitmapAndPath, or BitmapOrPath */
    List       *quals;          /* the WHERE clauses it uses */
    List       *preds;          /* predicates of its partial index(es) */
    Bitmapset  *clauseids;      /* quals+preds represented as a bitmapset */
} PathClauseUsage;

/* Callback argument for ec_member_matches_indexcol */
typedef struct
{
    IndexOptInfo *index;        /* index we're considering */
    int         indexcol;       /* index column we want to match to */
} ec_member_matches_arg;


static void consider_index_join_clauses(PlannerInfo *root, RelOptInfo *rel,
                            IndexOptInfo *index,
                            IndexClauseSet *rclauseset,
                            IndexClauseSet *jclauseset,
                            IndexClauseSet *eclauseset,
                            List **bitindexpaths);
static void consider_index_join_outer_rels(PlannerInfo *root, RelOptInfo *rel,
                               IndexOptInfo *index,
                               IndexClauseSet *rclauseset,
                               IndexClauseSet *jclauseset,
                               IndexClauseSet *eclauseset,
                               List **bitindexpaths,
                               List *indexjoinclauses,
                               int considered_clauses,
                               List **considered_relids);
static void get_join_index_paths(PlannerInfo *root, RelOptInfo *rel,
                     IndexOptInfo *index,
                     IndexClauseSet *rclauseset,
                     IndexClauseSet *jclauseset,
                     IndexClauseSet *eclauseset,
                     List **bitindexpaths,
                     Relids relids,
                     List **considered_relids);
static bool eclass_already_used(EquivalenceClass *parent_ec, Relids oldrelids,
                    List *indexjoinclauses);
static bool bms_equal_any(Relids relids, List *relids_list);
static void get_index_paths(PlannerInfo *root, RelOptInfo *rel,
                IndexOptInfo *index, IndexClauseSet *clauses,
                List **bitindexpaths);
static List *build_index_paths(PlannerInfo *root, RelOptInfo *rel,
                  IndexOptInfo *index, IndexClauseSet *clauses,
                  bool useful_predicate,
                  SaOpControl saop_control, ScanTypeControl scantype);
static List *build_paths_for_OR(PlannerInfo *root, RelOptInfo *rel,
                   List *clauses, List *other_clauses);
static List *drop_indexable_join_clauses(RelOptInfo *rel, List *clauses);
static Path *choose_bitmap_and(PlannerInfo *root, RelOptInfo *rel,
                  List *paths);
static int  path_usage_comparator(const void *a, const void *b);
static Cost bitmap_scan_cost_est(PlannerInfo *root, RelOptInfo *rel,
                     Path *ipath);
static Cost bitmap_and_cost_est(PlannerInfo *root, RelOptInfo *rel,
                    List *paths);
static PathClauseUsage *classify_index_clause_usage(Path *path,
                            List **clauselist);
static Relids get_bitmap_tree_required_outer(Path *bitmapqual);
static void find_indexpath_quals(Path *bitmapqual, List **quals, List **preds);
static int  find_list_position(Node *node, List **nodelist);
static bool check_index_only(RelOptInfo *rel, IndexOptInfo *index);
static double get_loop_count(PlannerInfo *root, Relids outer_relids);
static void match_restriction_clauses_to_index(RelOptInfo *rel,
                                   IndexOptInfo *index,
                                   IndexClauseSet *clauseset);
static void match_join_clauses_to_index(PlannerInfo *root,
                            RelOptInfo *rel, IndexOptInfo *index,
                            Relids lateral_referencers,
                            IndexClauseSet *clauseset,
                            List **joinorclauses);
static void match_eclass_clauses_to_index(PlannerInfo *root,
                              IndexOptInfo *index,
                              Relids lateral_referencers,
                              IndexClauseSet *clauseset);
static void match_clauses_to_index(IndexOptInfo *index,
                       List *clauses,
                       IndexClauseSet *clauseset);
static void match_clause_to_index(IndexOptInfo *index,
                      RestrictInfo *rinfo,
                      IndexClauseSet *clauseset);
static bool match_clause_to_indexcol(IndexOptInfo *index,
                         int indexcol,
                         RestrictInfo *rinfo);
static bool is_indexable_operator(Oid expr_op, Oid opfamily,
                      bool indexkey_on_left);
static bool match_rowcompare_to_indexcol(IndexOptInfo *index,
                             int indexcol,
                             Oid opfamily,
                             Oid idxcollation,
                             RowCompareExpr *clause);
static void match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
                        List **orderby_clauses_p,
                        List **clause_columns_p);
static Expr *match_clause_to_ordering_op(IndexOptInfo *index,
                            int indexcol, Expr *clause, Oid pk_opfamily);
static bool ec_member_matches_indexcol(PlannerInfo *root, RelOptInfo *rel,
                           EquivalenceClass *ec, EquivalenceMember *em,
                           void *arg);
static bool match_boolean_index_clause(Node *clause, int indexcol,
                           IndexOptInfo *index);
static bool match_special_index_operator(Expr *clause,
                             Oid opfamily, Oid idxcollation,
                             bool indexkey_on_left);
static Expr *expand_boolean_index_clause(Node *clause, int indexcol,
                            IndexOptInfo *index);
static List *expand_indexqual_opclause(RestrictInfo *rinfo,
                          Oid opfamily, Oid idxcollation);
static RestrictInfo *expand_indexqual_rowcompare(RestrictInfo *rinfo,
                            IndexOptInfo *index,
                            int indexcol);
static List *prefix_quals(Node *leftop, Oid opfamily, Oid collation,
             Const *prefix, Pattern_Prefix_Status pstatus);
static List *network_prefix_quals(Node *leftop, Oid expr_op, Oid opfamily,
                     Datum rightop);
static Datum string_to_datum(const char *str, Oid datatype);
static Const *string_to_const(const char *str, Oid datatype);


/*
 * create_index_paths()
 *    Generate all interesting index paths for the given relation.
 *    Candidate paths are added to the rel's pathlist (using add_path).
 *
 * To be considered for an index scan, an index must match one or more
 * restriction clauses or join clauses from the query's qual condition,
 * or match the query's ORDER BY condition, or have a predicate that
 * matches the query's qual condition.
 *
 * There are two basic kinds of index scans.  A "plain" index scan uses
 * only restriction clauses (possibly none at all) in its indexqual,
 * so it can be applied in any context.  A "parameterized" index scan uses
 * join clauses (plus restriction clauses, if available) in its indexqual.
 * When joining such a scan to one of the relations supplying the other
 * variables used in its indexqual, the parameterized scan must appear as
 * the inner relation of a nestloop join; it can't be used on the outer side,
 * nor in a merge or hash join.  In that context, values for the other rels'
 * attributes are available and fixed during any one scan of the indexpath.
 *
 * An IndexPath is generated and submitted to add_path() for each plain or
 * parameterized index scan this routine deems potentially interesting for
 * the current query.
 *
 * 'rel' is the relation for which we want to generate index paths
 *
 * Note: check_partial_indexes() must have been run previously for this rel.
 *
 * Note: in corner cases involving LATERAL appendrel children, it's possible
 * that rel->lateral_relids is nonempty.  Currently, we include lateral_relids
 * into the parameterization reported for each path, but don't take it into
 * account otherwise.  The fact that any such rels *must* be available as
 * parameter sources perhaps should influence our choices of index quals ...
 * but for now, it doesn't seem worth troubling over.  In particular, comments
 * below about "unparameterized" paths should be read as meaning
 * "unparameterized so far as the indexquals are concerned".
 */
void
create_index_paths(PlannerInfo *root, RelOptInfo *rel)
{
    List       *indexpaths;
    List       *bitindexpaths;
    List       *bitjoinpaths;
    List       *joinorclauses;
    Relids      lateral_referencers;
    IndexClauseSet rclauseset;
    IndexClauseSet jclauseset;
    IndexClauseSet eclauseset;
    ListCell   *lc;

    /* Skip the whole mess if no indexes */
    if (rel->indexlist == NIL)
        return;

    /*
     * If there are any rels that have LATERAL references to this one, we
     * cannot use join quals referencing them as index quals for this one,
     * since such rels would have to be on the inside not the outside of a
     * nestloop join relative to this one.  Create a Relids set listing all
     * such rels, for use in checks of potential join clauses.
     */
    lateral_referencers = NULL;
    foreach(lc, root->lateral_info_list)
    {
        LateralJoinInfo *ljinfo = (LateralJoinInfo *) lfirst(lc);

        if (bms_is_member(rel->relid, ljinfo->lateral_lhs))
            lateral_referencers = bms_add_member(lateral_referencers,
                                                 ljinfo->lateral_rhs);
    }

    /* Bitmap paths are collected and then dealt with at the end */
    bitindexpaths = bitjoinpaths = joinorclauses = NIL;

    /* Examine each index in turn */
    foreach(lc, rel->indexlist)
    {
        IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);

        /* Protect limited-size array in IndexClauseSets */
        Assert(index->ncolumns <= INDEX_MAX_KEYS);

        /*
         * Ignore partial indexes that do not match the query.
         * (generate_bitmap_or_paths() might be able to do something with
         * them, but that's of no concern here.)
         */
        if (index->indpred != NIL && !index->predOK)
            continue;

        /*
         * Identify the restriction clauses that can match the index.
         */
        MemSet(&rclauseset, 0, sizeof(rclauseset));
        match_restriction_clauses_to_index(rel, index, &rclauseset);

        /*
         * Build index paths from the restriction clauses.  These will be
         * non-parameterized paths.  Plain paths go directly to add_path(),
         * bitmap paths are added to bitindexpaths to be handled below.
         */
        get_index_paths(root, rel, index, &rclauseset,
                        &bitindexpaths);

        /*
         * Identify the join clauses that can match the index.  For the moment
         * we keep them separate from the restriction clauses.  Note that this
         * step finds only "loose" join clauses that have not been merged into
         * EquivalenceClasses.  Also, collect join OR clauses for later.
         */
        MemSet(&jclauseset, 0, sizeof(jclauseset));
        match_join_clauses_to_index(root, rel, index, lateral_referencers,
                                    &jclauseset, &joinorclauses);

        /*
         * Look for EquivalenceClasses that can generate joinclauses matching
         * the index.
         */
        MemSet(&eclauseset, 0, sizeof(eclauseset));
        match_eclass_clauses_to_index(root, index, lateral_referencers,
                                      &eclauseset);

        /*
         * If we found any plain or eclass join clauses, build parameterized
         * index paths using them.
         */
        if (jclauseset.nonempty || eclauseset.nonempty)
            consider_index_join_clauses(root, rel, index,
                                        &rclauseset,
                                        &jclauseset,
                                        &eclauseset,
                                        &bitjoinpaths);
    }

    /*
     * Generate BitmapOrPaths for any suitable OR-clauses present in the
     * restriction list.  Add these to bitindexpaths.
     */
    indexpaths = generate_bitmap_or_paths(root, rel,
                                          rel->baserestrictinfo, NIL,
                                          false);
    bitindexpaths = list_concat(bitindexpaths, indexpaths);

    /*
     * Likewise, generate BitmapOrPaths for any suitable OR-clauses present in
     * the joinclause list.  Add these to bitjoinpaths.
     */
    indexpaths = generate_bitmap_or_paths(root, rel,
                                        joinorclauses, rel->baserestrictinfo,
                                          false);
    bitjoinpaths = list_concat(bitjoinpaths, indexpaths);

    /*
     * If we found anything usable, generate a BitmapHeapPath for the most
     * promising combination of restriction bitmap index paths.  Note there
     * will be only one such path no matter how many indexes exist.  This
     * should be sufficient since there's basically only one figure of merit
     * (total cost) for such a path.
     */
    if (bitindexpaths != NIL)
    {
        Path       *bitmapqual;
        BitmapHeapPath *bpath;

        bitmapqual = choose_bitmap_and(root, rel, bitindexpaths);
        bpath = create_bitmap_heap_path(root, rel, bitmapqual,
                                        rel->lateral_relids, 1.0);
        add_path(rel, (Path *) bpath);
    }

    /*
     * Likewise, if we found anything usable, generate BitmapHeapPaths for the
     * most promising combinations of join bitmap index paths.  Our strategy
     * is to generate one such path for each distinct parameterization seen
     * among the available bitmap index paths.  This may look pretty
     * expensive, but usually there won't be very many distinct
     * parameterizations.  (This logic is quite similar to that in
     * consider_index_join_clauses, but we're working with whole paths not
     * individual clauses.)
     */
    if (bitjoinpaths != NIL)
    {
        List       *path_outer;
        List       *all_path_outers;
        ListCell   *lc;

        /*
         * path_outer holds the parameterization of each path in bitjoinpaths
         * (to save recalculating that several times), while all_path_outers
         * holds all distinct parameterization sets.
         */
        path_outer = all_path_outers = NIL;
        foreach(lc, bitjoinpaths)
        {
            Path       *path = (Path *) lfirst(lc);
            Relids      required_outer;

            required_outer = get_bitmap_tree_required_outer(path);
            path_outer = lappend(path_outer, required_outer);
            if (!bms_equal_any(required_outer, all_path_outers))
                all_path_outers = lappend(all_path_outers, required_outer);
        }

        /* Now, for each distinct parameterization set ... */
        foreach(lc, all_path_outers)
        {
            Relids      max_outers = (Relids) lfirst(lc);
            List       *this_path_set;
            Path       *bitmapqual;
            Relids      required_outer;
            double      loop_count;
            BitmapHeapPath *bpath;
            ListCell   *lcp;
            ListCell   *lco;

            /* Identify all the bitmap join paths needing no more than that */
            this_path_set = NIL;
            forboth(lcp, bitjoinpaths, lco, path_outer)
            {
                Path       *path = (Path *) lfirst(lcp);
                Relids      p_outers = (Relids) lfirst(lco);

                if (bms_is_subset(p_outers, max_outers))
                    this_path_set = lappend(this_path_set, path);
            }

            /*
             * Add in restriction bitmap paths, since they can be used
             * together with any join paths.
             */
            this_path_set = list_concat(this_path_set, bitindexpaths);

            /* Select best AND combination for this parameterization */
            bitmapqual = choose_bitmap_and(root, rel, this_path_set);

            /* And push that path into the mix */
            required_outer = get_bitmap_tree_required_outer(bitmapqual);
            loop_count = get_loop_count(root, required_outer);
            bpath = create_bitmap_heap_path(root, rel, bitmapqual,
                                            required_outer, loop_count);
            add_path(rel, (Path *) bpath);
        }
    }
}

/*
 * consider_index_join_clauses
 *    Given sets of join clauses for an index, decide which parameterized
 *    index paths to build.
 *
 * Plain indexpaths are sent directly to add_path, while potential
 * bitmap indexpaths are added to *bitindexpaths for later processing.
 *
 * 'rel' is the index's heap relation
 * 'index' is the index for which we want to generate paths
 * 'rclauseset' is the collection of indexable restriction clauses
 * 'jclauseset' is the collection of indexable simple join clauses
 * 'eclauseset' is the collection of indexable clauses from EquivalenceClasses
 * '*bitindexpaths' is the list to add bitmap paths to
 */
static void
consider_index_join_clauses(PlannerInfo *root, RelOptInfo *rel,
                            IndexOptInfo *index,
                            IndexClauseSet *rclauseset,
                            IndexClauseSet *jclauseset,
                            IndexClauseSet *eclauseset,
                            List **bitindexpaths)
{
    int         considered_clauses = 0;
    List       *considered_relids = NIL;
    int         indexcol;

    /*
     * The strategy here is to identify every potentially useful set of outer
     * rels that can provide indexable join clauses.  For each such set,
     * select all the join clauses available from those outer rels, add on all
     * the indexable restriction clauses, and generate plain and/or bitmap
     * index paths for that set of clauses.  This is based on the assumption
     * that it's always better to apply a clause as an indexqual than as a
     * filter (qpqual); which is where an available clause would end up being
     * applied if we omit it from the indexquals.
     *
     * This looks expensive, but in most practical cases there won't be very
     * many distinct sets of outer rels to consider.  As a safety valve when
     * that's not true, we use a heuristic: limit the number of outer rel sets
     * considered to a multiple of the number of clauses considered.  (We'll
     * always consider using each individual join clause, though.)
     *
     * For simplicity in selecting relevant clauses, we represent each set of
     * outer rels as a maximum set of clause_relids --- that is, the indexed
     * relation itself is also included in the relids set.  considered_relids
     * lists all relids sets we've already tried.
     */
    for (indexcol = 0; indexcol < index->ncolumns; indexcol++)
    {
        /* Consider each applicable simple join clause */
        considered_clauses += list_length(jclauseset->indexclauses[indexcol]);
        consider_index_join_outer_rels(root, rel, index,
                                       rclauseset, jclauseset, eclauseset,
                                       bitindexpaths,
                                       jclauseset->indexclauses[indexcol],
                                       considered_clauses,
                                       &considered_relids);
        /* Consider each applicable eclass join clause */
        considered_clauses += list_length(eclauseset->indexclauses[indexcol]);
        consider_index_join_outer_rels(root, rel, index,
                                       rclauseset, jclauseset, eclauseset,
                                       bitindexpaths,
                                       eclauseset->indexclauses[indexcol],
                                       considered_clauses,
                                       &considered_relids);
    }
}

/*
 * consider_index_join_outer_rels
 *    Generate parameterized paths based on clause relids in the clause list.
 *
 * Workhorse for consider_index_join_clauses; see notes therein for rationale.
 *
 * 'rel', 'index', 'rclauseset', 'jclauseset', 'eclauseset', and
 *      'bitindexpaths' as above
 * 'indexjoinclauses' is a list of RestrictInfos for join clauses
 * 'considered_clauses' is the total number of clauses considered (so far)
 * '*considered_relids' is a list of all relids sets already considered
 */
static void
consider_index_join_outer_rels(PlannerInfo *root, RelOptInfo *rel,
                               IndexOptInfo *index,
                               IndexClauseSet *rclauseset,
                               IndexClauseSet *jclauseset,
                               IndexClauseSet *eclauseset,
                               List **bitindexpaths,
                               List *indexjoinclauses,
                               int considered_clauses,
                               List **considered_relids)
{
    ListCell   *lc;

    /* Examine relids of each joinclause in the given list */
    foreach(lc, indexjoinclauses)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
        Relids      clause_relids = rinfo->clause_relids;
        ListCell   *lc2;

        /* If we already tried its relids set, no need to do so again */
        if (bms_equal_any(clause_relids, *considered_relids))
            continue;

        /*
         * Generate the union of this clause's relids set with each
         * previously-tried set.  This ensures we try this clause along with
         * every interesting subset of previous clauses.  However, to avoid
         * exponential growth of planning time when there are many clauses,
         * limit the number of relid sets accepted to 10 * considered_clauses.
         *
         * Note: get_join_index_paths adds entries to *considered_relids, but
         * it prepends them to the list, so that we won't visit new entries
         * during the inner foreach loop.  No real harm would be done if we
         * did, since the subset check would reject them; but it would waste
         * some cycles.
         */
        foreach(lc2, *considered_relids)
        {
            Relids  oldrelids = (Relids) lfirst(lc2);

            /*
             * If either is a subset of the other, no new set is possible.
             * This isn't a complete test for redundancy, but it's easy and
             * cheap.  get_join_index_paths will check more carefully if we
             * already generated the same relids set.
             */
            if (bms_subset_compare(clause_relids, oldrelids) != BMS_DIFFERENT)
                continue;

            /*
             * If this clause was derived from an equivalence class, the
             * clause list may contain other clauses derived from the same
             * eclass.  We should not consider that combining this clause with
             * one of those clauses generates a usefully different
             * parameterization; so skip if any clause derived from the same
             * eclass would already have been included when using oldrelids.
             */
            if (rinfo->parent_ec &&
                eclass_already_used(rinfo->parent_ec, oldrelids,
                                    indexjoinclauses))
                continue;

            /*
             * If the number of relid sets considered exceeds our heuristic
             * limit, stop considering combinations of clauses.  We'll still
             * consider the current clause alone, though (below this loop).
             */
            if (list_length(*considered_relids) >= 10 * considered_clauses)
                break;

            /* OK, try the union set */
            get_join_index_paths(root, rel, index,
                                 rclauseset, jclauseset, eclauseset,
                                 bitindexpaths,
                                 bms_union(clause_relids, oldrelids),
                                 considered_relids);
        }

        /* Also try this set of relids by itself */
        get_join_index_paths(root, rel, index,
                             rclauseset, jclauseset, eclauseset,
                             bitindexpaths,
                             clause_relids,
                             considered_relids);
    }
}

/*
 * get_join_index_paths
 *    Generate index paths using clauses from the specified outer relations.
 *    In addition to generating paths, relids is added to *considered_relids
 *    if not already present.
 *
 * Workhorse for consider_index_join_clauses; see notes therein for rationale.
 *
 * 'rel', 'index', 'rclauseset', 'jclauseset', 'eclauseset',
 *      'bitindexpaths', 'considered_relids' as above
 * 'relids' is the current set of relids to consider (the target rel plus
 *      one or more outer rels)
 */
static void
get_join_index_paths(PlannerInfo *root, RelOptInfo *rel,
                     IndexOptInfo *index,
                     IndexClauseSet *rclauseset,
                     IndexClauseSet *jclauseset,
                     IndexClauseSet *eclauseset,
                     List **bitindexpaths,
                     Relids relids,
                     List **considered_relids)
{
    IndexClauseSet clauseset;
    int         indexcol;

    /* If we already considered this relids set, don't repeat the work */
    if (bms_equal_any(relids, *considered_relids))
        return;

    /* Identify indexclauses usable with this relids set */
    MemSet(&clauseset, 0, sizeof(clauseset));

    for (indexcol = 0; indexcol < index->ncolumns; indexcol++)
    {
        ListCell   *lc;

        /* First find applicable simple join clauses */
        foreach(lc, jclauseset->indexclauses[indexcol])
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

            if (bms_is_subset(rinfo->clause_relids, relids))
                clauseset.indexclauses[indexcol] =
                    lappend(clauseset.indexclauses[indexcol], rinfo);
        }

        /*
         * Add applicable eclass join clauses.  The clauses generated for each
         * column are redundant (cf generate_implied_equalities_for_column),
         * so we need at most one.  This is the only exception to the general
         * rule of using all available index clauses.
         */
        foreach(lc, eclauseset->indexclauses[indexcol])
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

            if (bms_is_subset(rinfo->clause_relids, relids))
            {
                clauseset.indexclauses[indexcol] =
                    lappend(clauseset.indexclauses[indexcol], rinfo);
                break;
            }
        }

        /* Add restriction clauses (this is nondestructive to rclauseset) */
        clauseset.indexclauses[indexcol] =
            list_concat(clauseset.indexclauses[indexcol],
                        rclauseset->indexclauses[indexcol]);

        if (clauseset.indexclauses[indexcol] != NIL)
            clauseset.nonempty = true;
    }

    /* We should have found something, else caller passed silly relids */
    Assert(clauseset.nonempty);

    /* Build index path(s) using the collected set of clauses */
    get_index_paths(root, rel, index, &clauseset, bitindexpaths);

    /*
     * Remember we considered paths for this set of relids.  We use lcons not
     * lappend to avoid confusing the loop in consider_index_join_outer_rels.
     */
    *considered_relids = lcons(relids, *considered_relids);
}

/*
 * eclass_already_used
 *      True if any join clause usable with oldrelids was generated from
 *      the specified equivalence class.
 */
static bool
eclass_already_used(EquivalenceClass *parent_ec, Relids oldrelids,
                    List *indexjoinclauses)
{
    ListCell   *lc;

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

        if (rinfo->parent_ec == parent_ec &&
            bms_is_subset(rinfo->clause_relids, oldrelids))
            return true;
    }
    return false;
}

/*
 * bms_equal_any
 *      True if relids is bms_equal to any member of relids_list
 *
 * Perhaps this should be in bitmapset.c someday.
 */
static bool
bms_equal_any(Relids relids, List *relids_list)
{
    ListCell   *lc;

    foreach(lc, relids_list)
    {
        if (bms_equal(relids, (Relids) lfirst(lc)))
            return true;
    }
    return false;
}


/*
 * get_index_paths
 *    Given an index and a set of index clauses for it, construct IndexPaths.
 *
 * Plain indexpaths are sent directly to add_path, while potential
 * bitmap indexpaths are added to *bitindexpaths for later processing.
 *
 * This is a fairly simple frontend to build_index_paths().  Its reason for
 * existence is mainly to handle ScalarArrayOpExpr quals properly.  If the
 * index AM supports them natively, we should just include them in simple
 * index paths.  If not, we should exclude them while building simple index
 * paths, and then make a separate attempt to include them in bitmap paths.
 */
static void
get_index_paths(PlannerInfo *root, RelOptInfo *rel,
                IndexOptInfo *index, IndexClauseSet *clauses,
                List **bitindexpaths)
{
    List       *indexpaths;
    ListCell   *lc;

    /*
     * Build simple index paths using the clauses.  Allow ScalarArrayOpExpr
     * clauses only if the index AM supports them natively.
     */
    indexpaths = build_index_paths(root, rel,
                                   index, clauses,
                                   index->predOK,
                                   SAOP_PER_AM, ST_ANYSCAN);

    /*
     * Submit all the ones that can form plain IndexScan plans to add_path. (A
     * plain IndexPath can represent either a plain IndexScan or an
     * IndexOnlyScan, but for our purposes here that distinction does not
     * matter.  However, some of the indexes might support only bitmap scans,
     * and those we mustn't submit to add_path here.)
     *
     * Also, pick out the ones that are usable as bitmap scans.  For that, we
     * must discard indexes that don't support bitmap scans, and we also are
     * only interested in paths that have some selectivity; we should discard
     * anything that was generated solely for ordering purposes.
     */
    foreach(lc, indexpaths)
    {
        IndexPath  *ipath = (IndexPath *) lfirst(lc);

        if (index->amhasgettuple)
            add_path(rel, (Path *) ipath);

        if (index->amhasgetbitmap &&
            (ipath->path.pathkeys == NIL ||
             ipath->indexselectivity < 1.0))
            *bitindexpaths = lappend(*bitindexpaths, ipath);
    }

    /*
     * If the index doesn't handle ScalarArrayOpExpr clauses natively, check
     * to see if there are any such clauses, and if so generate bitmap scan
     * paths relying on executor-managed ScalarArrayOpExpr.
     */
    if (!index->amsearcharray)
    {
        indexpaths = build_index_paths(root, rel,
                                       index, clauses,
                                       false,
                                       SAOP_REQUIRE, ST_BITMAPSCAN);
        *bitindexpaths = list_concat(*bitindexpaths, indexpaths);
    }
}

/*
 * build_index_paths
 *    Given an index and a set of index clauses for it, construct zero
 *    or more IndexPaths.
 *
 * We return a list of paths because (1) this routine checks some cases
 * that should cause us to not generate any IndexPath, and (2) in some
 * cases we want to consider both a forward and a backward scan, so as
 * to obtain both sort orders.  Note that the paths are just returned
 * to the caller and not immediately fed to add_path().
 *
 * At top level, useful_predicate should be exactly the index's predOK flag
 * (ie, true if it has a predicate that was proven from the restriction
 * clauses).  When working on an arm of an OR clause, useful_predicate
 * should be true if the predicate required the current OR list to be proven.
 * Note that this routine should never be called at all if the index has an
 * unprovable predicate.
 *
 * saop_control indicates whether ScalarArrayOpExpr clauses can be used.
 * When it's SAOP_REQUIRE, index paths are created only if we found at least
 * one ScalarArrayOpExpr clause.
 *
 * scantype indicates whether we want to create plain indexscans, bitmap
 * indexscans, or both.  When it's ST_BITMAPSCAN, we will not consider
 * index ordering while deciding if a Path is worth generating.
 *
 * 'rel' is the index's heap relation
 * 'index' is the index for which we want to generate paths
 * 'clauses' is the collection of indexable clauses (RestrictInfo nodes)
 * 'useful_predicate' indicates whether the index has a useful predicate
 * 'saop_control' indicates whether ScalarArrayOpExpr clauses can be used
 * 'scantype' indicates whether we need plain or bitmap scan support
 */
static List *
build_index_paths(PlannerInfo *root, RelOptInfo *rel,
                  IndexOptInfo *index, IndexClauseSet *clauses,
                  bool useful_predicate,
                  SaOpControl saop_control, ScanTypeControl scantype)
{
    List       *result = NIL;
    IndexPath  *ipath;
    List       *index_clauses;
    List       *clause_columns;
    Relids      outer_relids;
    double      loop_count;
    List       *orderbyclauses;
    List       *orderbyclausecols;
    List       *index_pathkeys;
    List       *useful_pathkeys;
    bool        found_clause;
    bool        found_lower_saop_clause;
    bool        pathkeys_possibly_useful;
    bool        index_is_ordered;
    bool        index_only_scan;
    int         indexcol;

    /*
     * Check that index supports the desired scan type(s)
     */
    switch (scantype)
    {
        case ST_INDEXSCAN:
            if (!index->amhasgettuple)
                return NIL;
            break;
        case ST_BITMAPSCAN:
            if (!index->amhasgetbitmap)
                return NIL;
            break;
        case ST_ANYSCAN:
            /* either or both are OK */
            break;
    }

    /*
     * 1. Collect the index clauses into a single list.
     *
     * We build a list of RestrictInfo nodes for clauses to be used with this
     * index, along with an integer list of the index column numbers (zero
     * based) that each clause should be used with.  The clauses are ordered
     * by index key, so that the column numbers form a nondecreasing sequence.
     * (This order is depended on by btree and possibly other places.)  The
     * lists can be empty, if the index AM allows that.
     *
     * found_clause is set true only if there's at least one index clause; and
     * if saop_control is SAOP_REQUIRE, it has to be a ScalarArrayOpExpr
     * clause.
     *
     * found_lower_saop_clause is set true if there's a ScalarArrayOpExpr
     * index clause for a non-first index column.  This prevents us from
     * assuming that the scan result is ordered.  (Actually, the result is
     * still ordered if there are equality constraints for all earlier
     * columns, but it seems too expensive and non-modular for this code to be
     * aware of that refinement.)
     *
     * We also build a Relids set showing which outer rels are required by the
     * selected clauses.  Any lateral_relids are included in that, but not
     * otherwise accounted for.
     */
    index_clauses = NIL;
    clause_columns = NIL;
    found_clause = false;
    found_lower_saop_clause = false;
    outer_relids = bms_copy(rel->lateral_relids);
    for (indexcol = 0; indexcol < index->ncolumns; indexcol++)
    {
        ListCell   *lc;

        foreach(lc, clauses->indexclauses[indexcol])
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

            if (IsA(rinfo->clause, ScalarArrayOpExpr))
            {
                /* Ignore if not supported by index */
                if (saop_control == SAOP_PER_AM && !index->amsearcharray)
                    continue;
                found_clause = true;
                if (indexcol > 0)
                    found_lower_saop_clause = true;
            }
            else
            {
                if (saop_control != SAOP_REQUIRE)
                    found_clause = true;
            }
            index_clauses = lappend(index_clauses, rinfo);
            clause_columns = lappend_int(clause_columns, indexcol);
            outer_relids = bms_add_members(outer_relids,
                                           rinfo->clause_relids);
        }

        /*
         * If no clauses match the first index column, check for amoptionalkey
         * restriction.  We can't generate a scan over an index with
         * amoptionalkey = false unless there's at least one index clause.
         * (When working on columns after the first, this test cannot fail. It
         * is always okay for columns after the first to not have any
         * clauses.)
         */
        if (index_clauses == NIL && !index->amoptionalkey)
            return NIL;
    }

    /* We do not want the index's rel itself listed in outer_relids */
    outer_relids = bms_del_member(outer_relids, rel->relid);
    /* Enforce convention that outer_relids is exactly NULL if empty */
    if (bms_is_empty(outer_relids))
        outer_relids = NULL;

    /* Compute loop_count for cost estimation purposes */
    loop_count = get_loop_count(root, outer_relids);

    /*
     * 2. Compute pathkeys describing index's ordering, if any, then see how
     * many of them are actually useful for this query.  This is not relevant
     * if we are only trying to build bitmap indexscans, nor if we have to
     * assume the scan is unordered.
     */
    pathkeys_possibly_useful = (scantype != ST_BITMAPSCAN &&
                                !found_lower_saop_clause &&
                                has_useful_pathkeys(root, rel));
    index_is_ordered = (index->sortopfamily != NULL);
    if (index_is_ordered && pathkeys_possibly_useful)
    {
        index_pathkeys = build_index_pathkeys(root, index,
                                              ForwardScanDirection);
        useful_pathkeys = truncate_useless_pathkeys(root, rel,
                                                    index_pathkeys);
        orderbyclauses = NIL;
        orderbyclausecols = NIL;
    }
    else if (index->amcanorderbyop && pathkeys_possibly_useful)
    {
        /* see if we can generate ordering operators for query_pathkeys */
        match_pathkeys_to_index(index, root->query_pathkeys,
                                &orderbyclauses,
                                &orderbyclausecols);
        if (orderbyclauses)
            useful_pathkeys = root->query_pathkeys;
        else
            useful_pathkeys = NIL;
    }
    else
    {
        useful_pathkeys = NIL;
        orderbyclauses = NIL;
        orderbyclausecols = NIL;
    }

    /*
     * 3. Check if an index-only scan is possible.  If we're not building
     * plain indexscans, this isn't relevant since bitmap scans don't support
     * index data retrieval anyway.
     */
    index_only_scan = (scantype != ST_BITMAPSCAN &&
                       check_index_only(rel, index));

    /*
     * 4. Generate an indexscan path if there are relevant restriction clauses
     * in the current clauses, OR the index ordering is potentially useful for
     * later merging or final output ordering, OR the index has a useful
     * predicate, OR an index-only scan is possible.
     */
    if (found_clause || useful_pathkeys != NIL || useful_predicate ||
        index_only_scan)
    {
        ipath = create_index_path(root, index,
                                  index_clauses,
                                  clause_columns,
                                  orderbyclauses,
                                  orderbyclausecols,
                                  useful_pathkeys,
                                  index_is_ordered ?
                                  ForwardScanDirection :
                                  NoMovementScanDirection,
                                  index_only_scan,
                                  outer_relids,
                                  loop_count);
        result = lappend(result, ipath);
    }

    /*
     * 5. If the index is ordered, a backwards scan might be interesting.
     */
    if (index_is_ordered && pathkeys_possibly_useful)
    {
        index_pathkeys = build_index_pathkeys(root, index,
                                              BackwardScanDirection);
        useful_pathkeys = truncate_useless_pathkeys(root, rel,
                                                    index_pathkeys);
        if (useful_pathkeys != NIL)
        {
            ipath = create_index_path(root, index,
                                      index_clauses,
                                      clause_columns,
                                      NIL,
                                      NIL,
                                      useful_pathkeys,
                                      BackwardScanDirection,
                                      index_only_scan,
                                      outer_relids,
                                      loop_count);
            result = lappend(result, ipath);
        }
    }

    return result;
}

/*
 * build_paths_for_OR
 *    Given a list of restriction clauses from one arm of an OR clause,
 *    construct all matching IndexPaths for the relation.
 *
 * Here we must scan all indexes of the relation, since a bitmap OR tree
 * can use multiple indexes.
 *
 * The caller actually supplies two lists of restriction clauses: some
 * "current" ones and some "other" ones.  Both lists can be used freely
 * to match keys of the index, but an index must use at least one of the
 * "current" clauses to be considered usable.  The motivation for this is
 * examples like
 *      WHERE (x = 42) AND (... OR (y = 52 AND z = 77) OR ....)
 * While we are considering the y/z subclause of the OR, we can use "x = 42"
 * as one of the available index conditions; but we shouldn't match the
 * subclause to any index on x alone, because such a Path would already have
 * been generated at the upper level.  So we could use an index on x,y,z
 * or an index on x,y for the OR subclause, but not an index on just x.
 * When dealing with a partial index, a match of the index predicate to
 * one of the "current" clauses also makes the index usable.
 *
 * 'rel' is the relation for which we want to generate index paths
 * 'clauses' is the current list of clauses (RestrictInfo nodes)
 * 'other_clauses' is the list of additional upper-level clauses
 */
static List *
build_paths_for_OR(PlannerInfo *root, RelOptInfo *rel,
                   List *clauses, List *other_clauses)
{
    List       *result = NIL;
    List       *all_clauses = NIL;      /* not computed till needed */
    ListCell   *lc;

    foreach(lc, rel->indexlist)
    {
        IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);
        IndexClauseSet clauseset;
        List       *indexpaths;
        bool        useful_predicate;

        /* Ignore index if it doesn't support bitmap scans */
        if (!index->amhasgetbitmap)
            continue;

        /*
         * Ignore partial indexes that do not match the query.  If a partial
         * index is marked predOK then we know it's OK.  Otherwise, we have to
         * test whether the added clauses are sufficient to imply the
         * predicate. If so, we can use the index in the current context.
         *
         * We set useful_predicate to true iff the predicate was proven using
         * the current set of clauses.  This is needed to prevent matching a
         * predOK index to an arm of an OR, which would be a legal but
         * pointlessly inefficient plan.  (A better plan will be generated by
         * just scanning the predOK index alone, no OR.)
         */
        useful_predicate = false;
        if (index->indpred != NIL)
        {
            if (index->predOK)
            {
                /* Usable, but don't set useful_predicate */
            }
            else
            {
                /* Form all_clauses if not done already */
                if (all_clauses == NIL)
                    all_clauses = list_concat(list_copy(clauses),
                                              other_clauses);

                if (!predicate_implied_by(index->indpred, all_clauses))
                    continue;   /* can't use it at all */

                if (!predicate_implied_by(index->indpred, other_clauses))
                    useful_predicate = true;
            }
        }

        /*
         * Identify the restriction clauses that can match the index.
         */
        MemSet(&clauseset, 0, sizeof(clauseset));
        match_clauses_to_index(index, clauses, &clauseset);

        /*
         * If no matches so far, and the index predicate isn't useful, we
         * don't want it.
         */
        if (!clauseset.nonempty && !useful_predicate)
            continue;

        /*
         * Add "other" restriction clauses to the clauseset.
         */
        match_clauses_to_index(index, other_clauses, &clauseset);

        /*
         * Construct paths if possible.
         */
        indexpaths = build_index_paths(root, rel,
                                       index, &clauseset,
                                       useful_predicate,
                                       SAOP_ALLOW, ST_BITMAPSCAN);
        result = list_concat(result, indexpaths);
    }

    return result;
}

/*
 * generate_bitmap_or_paths
 *      Look through the list of clauses to find OR clauses, and generate
 *      a BitmapOrPath for each one we can handle that way.  Return a list
 *      of the generated BitmapOrPaths.
 *
 * other_clauses is a list of additional clauses that can be assumed true
 * for the purpose of generating indexquals, but are not to be searched for
 * ORs.  (See build_paths_for_OR() for motivation.)
 *
 * If restriction_only is true, ignore OR elements that are join clauses.
 * When using this feature it is caller's responsibility that neither clauses
 * nor other_clauses contain any join clauses that are not ORs, as we do not
 * re-filter those lists.
 */
List *
generate_bitmap_or_paths(PlannerInfo *root, RelOptInfo *rel,
                         List *clauses, List *other_clauses,
                         bool restriction_only)
{
    List       *result = NIL;
    List       *all_clauses;
    ListCell   *lc;

    /*
     * We can use both the current and other clauses as context for
     * build_paths_for_OR; no need to remove ORs from the lists.
     */
    all_clauses = list_concat(list_copy(clauses), other_clauses);

    foreach(lc, clauses)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
        List       *pathlist;
        Path       *bitmapqual;
        ListCell   *j;

        Assert(IsA(rinfo, RestrictInfo));
        /* Ignore RestrictInfos that aren't ORs */
        if (!restriction_is_or_clause(rinfo))
            continue;

        /*
         * We must be able to match at least one index to each of the arms of
         * the OR, else we can't use it.
         */
        pathlist = NIL;
        foreach(j, ((BoolExpr *) rinfo->orclause)->args)
        {
            Node       *orarg = (Node *) lfirst(j);
            List       *indlist;

            /* OR arguments should be ANDs or sub-RestrictInfos */
            if (and_clause(orarg))
            {
                List       *andargs = ((BoolExpr *) orarg)->args;

                if (restriction_only)
                    andargs = drop_indexable_join_clauses(rel, andargs);

                indlist = build_paths_for_OR(root, rel,
                                             andargs,
                                             all_clauses);

                /* Recurse in case there are sub-ORs */
                indlist = list_concat(indlist,
                                      generate_bitmap_or_paths(root, rel,
                                                               andargs,
                                                               all_clauses,
                                                          restriction_only));
            }
            else
            {
                List       *orargs;

                Assert(IsA(orarg, RestrictInfo));
                Assert(!restriction_is_or_clause((RestrictInfo *) orarg));
                orargs = list_make1(orarg);

                if (restriction_only)
                    orargs = drop_indexable_join_clauses(rel, orargs);

                indlist = build_paths_for_OR(root, rel,
                                             orargs,
                                             all_clauses);
            }

            /*
             * If nothing matched this arm, we can't do anything with this OR
             * clause.
             */
            if (indlist == NIL)
            {
                pathlist = NIL;
                break;
            }

            /*
             * OK, pick the most promising AND combination, and add it to
             * pathlist.
             */
            bitmapqual = choose_bitmap_and(root, rel, indlist);
            pathlist = lappend(pathlist, bitmapqual);
        }

        /*
         * If we have a match for every arm, then turn them into a
         * BitmapOrPath, and add to result list.
         */
        if (pathlist != NIL)
        {
            bitmapqual = (Path *) create_bitmap_or_path(root, rel, pathlist);
            result = lappend(result, bitmapqual);
        }
    }

    return result;
}

/*
 * drop_indexable_join_clauses
 *      Remove any indexable join clauses from the list.
 *
 * This is a helper for generate_bitmap_or_paths().  We leave OR clauses
 * in the list whether they are joins or not, since we might be able to
 * extract a restriction item from an OR list.  It's safe to leave such
 * clauses in the list because match_clauses_to_index() will ignore them,
 * so there's no harm in passing such clauses to build_paths_for_OR().
 */
static List *
drop_indexable_join_clauses(RelOptInfo *rel, List *clauses)
{
    List       *result = NIL;
    ListCell   *lc;

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

        Assert(IsA(rinfo, RestrictInfo));
        if (restriction_is_or_clause(rinfo) ||
            bms_is_subset(rinfo->clause_relids, rel->relids))
            result = lappend(result, rinfo);
    }
    return result;
}


/*
 * choose_bitmap_and
 *      Given a nonempty list of bitmap paths, AND them into one path.
 *
 * This is a nontrivial decision since we can legally use any subset of the
 * given path set.  We want to choose a good tradeoff between selectivity
 * and cost of computing the bitmap.
 *
 * The result is either a single one of the inputs, or a BitmapAndPath
 * combining multiple inputs.
 */
static Path *
choose_bitmap_and(PlannerInfo *root, RelOptInfo *rel, List *paths)
{
    int         npaths = list_length(paths);
    PathClauseUsage **pathinfoarray;
    PathClauseUsage *pathinfo;
    List       *clauselist;
    List       *bestpaths = NIL;
    Cost        bestcost = 0;
    int         i,
                j;
    ListCell   *l;

    Assert(npaths > 0);         /* else caller error */
    if (npaths == 1)
        return (Path *) linitial(paths);        /* easy case */

    /*
     * In theory we should consider every nonempty subset of the given paths.
     * In practice that seems like overkill, given the crude nature of the
     * estimates, not to mention the possible effects of higher-level AND and
     * OR clauses.  Moreover, it's completely impractical if there are a large
     * number of paths, since the work would grow as O(2^N).
     *
     * As a heuristic, we first check for paths using exactly the same sets of
     * WHERE clauses + index predicate conditions, and reject all but the
     * cheapest-to-scan in any such group.  This primarily gets rid of indexes
     * that include the interesting columns but also irrelevant columns.  (In
     * situations where the DBA has gone overboard on creating variant
     * indexes, this can make for a very large reduction in the number of
     * paths considered further.)
     *
     * We then sort the surviving paths with the cheapest-to-scan first, and
     * for each path, consider using that path alone as the basis for a bitmap
     * scan.  Then we consider bitmap AND scans formed from that path plus
     * each subsequent (higher-cost) path, adding on a subsequent path if it
     * results in a reduction in the estimated total scan cost. This means we
     * consider about O(N^2) rather than O(2^N) path combinations, which is
     * quite tolerable, especially given than N is usually reasonably small
     * because of the prefiltering step.  The cheapest of these is returned.
     *
     * We will only consider AND combinations in which no two indexes use the
     * same WHERE clause.  This is a bit of a kluge: it's needed because
     * costsize.c and clausesel.c aren't very smart about redundant clauses.
     * They will usually double-count the redundant clauses, producing a
     * too-small selectivity that makes a redundant AND step look like it
     * reduces the total cost.  Perhaps someday that code will be smarter and
     * we can remove this limitation.  (But note that this also defends
     * against flat-out duplicate input paths, which can happen because
     * match_join_clauses_to_index will find the same OR join clauses that
     * create_or_index_quals has pulled OR restriction clauses out of.)
     *
     * For the same reason, we reject AND combinations in which an index
     * predicate clause duplicates another clause.  Here we find it necessary
     * to be even stricter: we'll reject a partial index if any of its
     * predicate clauses are implied by the set of WHERE clauses and predicate
     * clauses used so far.  This covers cases such as a condition "x = 42"
     * used with a plain index, followed by a clauseless scan of a partial
     * index "WHERE x >= 40 AND x < 50".  The partial index has been accepted
     * only because "x = 42" was present, and so allowing it would partially
     * double-count selectivity.  (We could use predicate_implied_by on
     * regular qual clauses too, to have a more intelligent, but much more
     * expensive, check for redundancy --- but in most cases simple equality
     * seems to suffice.)
     */

    /*
     * Extract clause usage info and detect any paths that use exactly the
     * same set of clauses; keep only the cheapest-to-scan of any such groups.
     * The surviving paths are put into an array for qsort'ing.
     */
    pathinfoarray = (PathClauseUsage **)
        palloc(npaths * sizeof(PathClauseUsage *));
    clauselist = NIL;
    npaths = 0;
    foreach(l, paths)
    {
        Path       *ipath = (Path *) lfirst(l);

        pathinfo = classify_index_clause_usage(ipath, &clauselist);
        for (i = 0; i < npaths; i++)
        {
            if (bms_equal(pathinfo->clauseids, pathinfoarray[i]->clauseids))
                break;
        }
        if (i < npaths)
        {
            /* duplicate clauseids, keep the cheaper one */
            Cost        ncost;
            Cost        ocost;
            Selectivity nselec;
            Selectivity oselec;

            cost_bitmap_tree_node(pathinfo->path, &ncost, &nselec);
            cost_bitmap_tree_node(pathinfoarray[i]->path, &ocost, &oselec);
            if (ncost < ocost)
                pathinfoarray[i] = pathinfo;
        }
        else
        {
            /* not duplicate clauseids, add to array */
            pathinfoarray[npaths++] = pathinfo;
        }
    }

    /* If only one surviving path, we're done */
    if (npaths == 1)
        return pathinfoarray[0]->path;

    /* Sort the surviving paths by index access cost */
    qsort(pathinfoarray, npaths, sizeof(PathClauseUsage *),
          path_usage_comparator);

    /*
     * For each surviving index, consider it as an "AND group leader", and see
     * whether adding on any of the later indexes results in an AND path with
     * cheaper total cost than before.  Then take the cheapest AND group.
     */
    for (i = 0; i < npaths; i++)
    {
        Cost        costsofar;
        List       *qualsofar;
        Bitmapset  *clauseidsofar;
        ListCell   *lastcell;

        pathinfo = pathinfoarray[i];
        paths = list_make1(pathinfo->path);
        costsofar = bitmap_scan_cost_est(root, rel, pathinfo->path);
        qualsofar = list_concat(list_copy(pathinfo->quals),
                                list_copy(pathinfo->preds));
        clauseidsofar = bms_copy(pathinfo->clauseids);
        lastcell = list_head(paths);    /* for quick deletions */

        for (j = i + 1; j < npaths; j++)
        {
            Cost        newcost;

            pathinfo = pathinfoarray[j];
            /* Check for redundancy */
            if (bms_overlap(pathinfo->clauseids, clauseidsofar))
                continue;       /* consider it redundant */
            if (pathinfo->preds)
            {
                bool        redundant = false;

                /* we check each predicate clause separately */
                foreach(l, pathinfo->preds)
                {
                    Node       *np = (Node *) lfirst(l);

                    if (predicate_implied_by(list_make1(np), qualsofar))
                    {
                        redundant = true;
                        break;  /* out of inner foreach loop */
                    }
                }
                if (redundant)
                    continue;
            }
            /* tentatively add new path to paths, so we can estimate cost */
            paths = lappend(paths, pathinfo->path);
            newcost = bitmap_and_cost_est(root, rel, paths);
            if (newcost < costsofar)
            {
                /* keep new path in paths, update subsidiary variables */
                costsofar = newcost;
                qualsofar = list_concat(qualsofar,
                                        list_copy(pathinfo->quals));
                qualsofar = list_concat(qualsofar,
                                        list_copy(pathinfo->preds));
                clauseidsofar = bms_add_members(clauseidsofar,
                                                pathinfo->clauseids);
                lastcell = lnext(lastcell);
            }
            else
            {
                /* reject new path, remove it from paths list */
                paths = list_delete_cell(paths, lnext(lastcell), lastcell);
            }
            Assert(lnext(lastcell) == NULL);
        }

        /* Keep the cheapest AND-group (or singleton) */
        if (i == 0 || costsofar < bestcost)
        {
            bestpaths = paths;
            bestcost = costsofar;
        }

        /* some easy cleanup (we don't try real hard though) */
        list_free(qualsofar);
    }

    if (list_length(bestpaths) == 1)
        return (Path *) linitial(bestpaths);    /* no need for AND */
    return (Path *) create_bitmap_and_path(root, rel, bestpaths);
}

/* qsort comparator to sort in increasing index access cost order */
static int
path_usage_comparator(const void *a, const void *b)
{
    PathClauseUsage *pa = *(PathClauseUsage *const *) a;
    PathClauseUsage *pb = *(PathClauseUsage *const *) b;
    Cost        acost;
    Cost        bcost;
    Selectivity aselec;
    Selectivity bselec;

    cost_bitmap_tree_node(pa->path, &acost, &aselec);
    cost_bitmap_tree_node(pb->path, &bcost, &bselec);

    /*
     * If costs are the same, sort by selectivity.
     */
    if (acost < bcost)
        return -1;
    if (acost > bcost)
        return 1;

    if (aselec < bselec)
        return -1;
    if (aselec > bselec)
        return 1;

    return 0;
}

/*
 * Estimate the cost of actually executing a bitmap scan with a single
 * index path (no BitmapAnd, at least not at this level; but it could be
 * a BitmapOr).
 */
static Cost
bitmap_scan_cost_est(PlannerInfo *root, RelOptInfo *rel, Path *ipath)
{
    BitmapHeapPath bpath;
    Relids      required_outer;

    /* Identify required outer rels, in case it's a parameterized scan */
    required_outer = get_bitmap_tree_required_outer(ipath);

    /* Set up a dummy BitmapHeapPath */
    bpath.path.type = T_BitmapHeapPath;
    bpath.path.pathtype = T_BitmapHeapScan;
    bpath.path.parent = rel;
    bpath.path.param_info = get_baserel_parampathinfo(root, rel,
                                                      required_outer);
    bpath.path.pathkeys = NIL;
    bpath.bitmapqual = ipath;

    cost_bitmap_heap_scan(&bpath.path, root, rel,
                          bpath.path.param_info,
                          ipath,
                          get_loop_count(root, required_outer));

    return bpath.path.total_cost;
}

/*
 * Estimate the cost of actually executing a BitmapAnd scan with the given
 * inputs.
 */
static Cost
bitmap_and_cost_est(PlannerInfo *root, RelOptInfo *rel, List *paths)
{
    BitmapAndPath apath;
    BitmapHeapPath bpath;
    Relids      required_outer;

    /* Set up a dummy BitmapAndPath */
    apath.path.type = T_BitmapAndPath;
    apath.path.pathtype = T_BitmapAnd;
    apath.path.parent = rel;
    apath.path.param_info = NULL;       /* not used in bitmap trees */
    apath.path.pathkeys = NIL;
    apath.bitmapquals = paths;
    cost_bitmap_and_node(&apath, root);

    /* Identify required outer rels, in case it's a parameterized scan */
    required_outer = get_bitmap_tree_required_outer((Path *) &apath);

    /* Set up a dummy BitmapHeapPath */
    bpath.path.type = T_BitmapHeapPath;
    bpath.path.pathtype = T_BitmapHeapScan;
    bpath.path.parent = rel;
    bpath.path.param_info = get_baserel_parampathinfo(root, rel,
                                                      required_outer);
    bpath.path.pathkeys = NIL;
    bpath.bitmapqual = (Path *) &apath;

    /* Now we can do cost_bitmap_heap_scan */
    cost_bitmap_heap_scan(&bpath.path, root, rel,
                          bpath.path.param_info,
                          (Path *) &apath,
                          get_loop_count(root, required_outer));

    return bpath.path.total_cost;
}


/*
 * classify_index_clause_usage
 *      Construct a PathClauseUsage struct describing the WHERE clauses and
 *      index predicate clauses used by the given indexscan path.
 *      We consider two clauses the same if they are equal().
 *
 * At some point we might want to migrate this info into the Path data
 * structure proper, but for the moment it's only needed within
 * choose_bitmap_and().
 *
 * *clauselist is used and expanded as needed to identify all the distinct
 * clauses seen across successive calls.  Caller must initialize it to NIL
 * before first call of a set.
 */
static PathClauseUsage *
classify_index_clause_usage(Path *path, List **clauselist)
{
    PathClauseUsage *result;
    Bitmapset  *clauseids;
    ListCell   *lc;

    result = (PathClauseUsage *) palloc(sizeof(PathClauseUsage));
    result->path = path;

    /* Recursively find the quals and preds used by the path */
    result->quals = NIL;
    result->preds = NIL;
    find_indexpath_quals(path, &result->quals, &result->preds);

    /* Build up a bitmapset representing the quals and preds */
    clauseids = NULL;
    foreach(lc, result->quals)
    {
        Node       *node = (Node *) lfirst(lc);

        clauseids = bms_add_member(clauseids,
                                   find_list_position(node, clauselist));
    }
    foreach(lc, result->preds)
    {
        Node       *node = (Node *) lfirst(lc);

        clauseids = bms_add_member(clauseids,
                                   find_list_position(node, clauselist));
    }
    result->clauseids = clauseids;

    return result;
}


/*
 * get_bitmap_tree_required_outer
 *      Find the required outer rels for a bitmap tree (index/and/or)
 *
 * We don't associate any particular parameterization with a BitmapAnd or
 * BitmapOr node; however, the IndexPaths have parameterization info, in
 * their capacity as standalone access paths.  The parameterization required
 * for the bitmap heap scan node is the union of rels referenced in the
 * child IndexPaths.
 */
static Relids
get_bitmap_tree_required_outer(Path *bitmapqual)
{
    Relids      result = NULL;
    ListCell   *lc;

    if (IsA(bitmapqual, IndexPath))
    {
        return bms_copy(PATH_REQ_OUTER(bitmapqual));
    }
    else if (IsA(bitmapqual, BitmapAndPath))
    {
        foreach(lc, ((BitmapAndPath *) bitmapqual)->bitmapquals)
        {
            result = bms_join(result,
                        get_bitmap_tree_required_outer((Path *) lfirst(lc)));
        }
    }
    else if (IsA(bitmapqual, BitmapOrPath))
    {
        foreach(lc, ((BitmapOrPath *) bitmapqual)->bitmapquals)
        {
            result = bms_join(result,
                        get_bitmap_tree_required_outer((Path *) lfirst(lc)));
        }
    }
    else
        elog(ERROR, "unrecognized node type: %d", nodeTag(bitmapqual));

    return result;
}


/*
 * find_indexpath_quals
 *
 * Given the Path structure for a plain or bitmap indexscan, extract lists
 * of all the indexquals and index predicate conditions used in the Path.
 * These are appended to the initial contents of *quals and *preds (hence
 * caller should initialize those to NIL).
 *
 * This is sort of a simplified version of make_restrictinfo_from_bitmapqual;
 * here, we are not trying to produce an accurate representation of the AND/OR
 * semantics of the Path, but just find out all the base conditions used.
 *
 * The result lists contain pointers to the expressions used in the Path,
 * but all the list cells are freshly built, so it's safe to destructively
 * modify the lists (eg, by concat'ing with other lists).
 */
static void
find_indexpath_quals(Path *bitmapqual, List **quals, List **preds)
{
    if (IsA(bitmapqual, BitmapAndPath))
    {
        BitmapAndPath *apath = (BitmapAndPath *) bitmapqual;
        ListCell   *l;

        foreach(l, apath->bitmapquals)
        {
            find_indexpath_quals((Path *) lfirst(l), quals, preds);
        }
    }
    else if (IsA(bitmapqual, BitmapOrPath))
    {
        BitmapOrPath *opath = (BitmapOrPath *) bitmapqual;
        ListCell   *l;

        foreach(l, opath->bitmapquals)
        {
            find_indexpath_quals((Path *) lfirst(l), quals, preds);
        }
    }
    else if (IsA(bitmapqual, IndexPath))
    {
        IndexPath  *ipath = (IndexPath *) bitmapqual;

        *quals = list_concat(*quals, get_actual_clauses(ipath->indexclauses));
        *preds = list_concat(*preds, list_copy(ipath->indexinfo->indpred));
    }
    else
        elog(ERROR, "unrecognized node type: %d", nodeTag(bitmapqual));
}


/*
 * find_list_position
 *      Return the given node's position (counting from 0) in the given
 *      list of nodes.  If it's not equal() to any existing list member,
 *      add it at the end, and return that position.
 */
static int
find_list_position(Node *node, List **nodelist)
{
    int         i;
    ListCell   *lc;

    i = 0;
    foreach(lc, *nodelist)
    {
        Node       *oldnode = (Node *) lfirst(lc);

        if (equal(node, oldnode))
            return i;
        i++;
    }

    *nodelist = lappend(*nodelist, node);

    return i;
}


/*
 * check_index_only
 *      Determine whether an index-only scan is possible for this index.
 */
static bool
check_index_only(RelOptInfo *rel, IndexOptInfo *index)
{
    bool        result;
    Bitmapset  *attrs_used = NULL;
    Bitmapset  *index_attrs = NULL;
    ListCell   *lc;
    int         i;

    /* Index-only scans must be enabled, and index must be capable of them */
    if (!enable_indexonlyscan)
        return false;
    if (!index->canreturn)
        return false;

    /*
     * Check that all needed attributes of the relation are available from the
     * index.
     *
     * XXX this is overly conservative for partial indexes, since we will
     * consider attributes involved in the index predicate as required even
     * though the predicate won't need to be checked at runtime.  (The same is
     * true for attributes used only in index quals, if we are certain that
     * the index is not lossy.)  However, it would be quite expensive to
     * determine that accurately at this point, so for now we take the easy
     * way out.
     */

    /*
     * Add all the attributes needed for joins or final output.  Note: we must
     * look at reltargetlist, not the attr_needed data, because attr_needed
     * isn't computed for inheritance child rels.
     */
    pull_varattnos((Node *) rel->reltargetlist, rel->relid, &attrs_used);

    /* Add all the attributes used by restriction clauses. */
    foreach(lc, rel->baserestrictinfo)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

        pull_varattnos((Node *) rinfo->clause, rel->relid, &attrs_used);
    }

    /* Construct a bitmapset of columns stored in the index. */
    for (i = 0; i < index->ncolumns; i++)
    {
        int         attno = index->indexkeys[i];

        /*
         * For the moment, we just ignore index expressions.  It might be nice
         * to do something with them, later.
         */
        if (attno == 0)
            continue;

        index_attrs =
            bms_add_member(index_attrs,
                           attno - FirstLowInvalidHeapAttributeNumber);
    }

    /* Do we have all the necessary attributes? */
    result = bms_is_subset(attrs_used, index_attrs);

    bms_free(attrs_used);
    bms_free(index_attrs);

    return result;
}

/*
 * get_loop_count
 *      Choose the loop count estimate to use for costing a parameterized path
 *      with the given set of outer relids.
 *
 * Since we produce parameterized paths before we've begun to generate join
 * relations, it's impossible to predict exactly how many times a parameterized
 * path will be iterated; we don't know the size of the relation that will be
 * on the outside of the nestloop.  However, we should try to account for
 * multiple iterations somehow in costing the path.  The heuristic embodied
 * here is to use the rowcount of the smallest other base relation needed in
 * the join clauses used by the path.  (We could alternatively consider the
 * largest one, but that seems too optimistic.)  This is of course the right
 * answer for single-other-relation cases, and it seems like a reasonable
 * zero-order approximation for multiway-join cases.
 *
 * Note: for this to work, allpaths.c must establish all baserel size
 * estimates before it begins to compute paths, or at least before it
 * calls create_index_paths().
 */
static double
get_loop_count(PlannerInfo *root, Relids outer_relids)
{
    double      result = 1.0;

    /* For a non-parameterized path, just return 1.0 quickly */
    if (outer_relids != NULL)
    {
        int         relid;

        /* Need a working copy since bms_first_member is destructive */
        outer_relids = bms_copy(outer_relids);
        while ((relid = bms_first_member(outer_relids)) >= 0)
        {
            RelOptInfo *outer_rel;

            /* Paranoia: ignore bogus relid indexes */
            if (relid >= root->simple_rel_array_size)
                continue;
            outer_rel = root->simple_rel_array[relid];
            if (outer_rel == NULL)
                continue;
            Assert(outer_rel->relid == relid);  /* sanity check on array */

            /* Other relation could be proven empty, if so ignore */
            if (IS_DUMMY_REL(outer_rel))
                continue;

            /* Otherwise, rel's rows estimate should be valid by now */
            Assert(outer_rel->rows > 0);

            /* Remember smallest row count estimate among the outer rels */
            if (result == 1.0 || result > outer_rel->rows)
                result = outer_rel->rows;
        }
        bms_free(outer_relids);
    }
    return result;
}


/****************************************************************************
 *              ----  ROUTINES TO CHECK QUERY CLAUSES  ----
 ****************************************************************************/

/*
 * match_restriction_clauses_to_index
 *    Identify restriction clauses for the rel that match the index.
 *    Matching clauses are added to *clauseset.
 */
static void
match_restriction_clauses_to_index(RelOptInfo *rel, IndexOptInfo *index,
                                   IndexClauseSet *clauseset)
{
    match_clauses_to_index(index, rel->baserestrictinfo, clauseset);
}

/*
 * match_join_clauses_to_index
 *    Identify join clauses for the rel that match the index.
 *    Matching clauses are added to *clauseset.
 *    Also, add any potentially usable join OR clauses to *joinorclauses.
 */
static void
match_join_clauses_to_index(PlannerInfo *root,
                            RelOptInfo *rel, IndexOptInfo *index,
                            Relids lateral_referencers,
                            IndexClauseSet *clauseset,
                            List **joinorclauses)
{
    ListCell   *lc;

    /* Scan the rel's join clauses */
    foreach(lc, rel->joininfo)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

        /* Check if clause can be moved to this rel */
        if (!join_clause_is_movable_to(rinfo, rel->relid))
            continue;

        /* Not useful if it conflicts with any LATERAL references */
        if (bms_overlap(rinfo->clause_relids, lateral_referencers))
            continue;

        /* Potentially usable, so see if it matches the index or is an OR */
        if (restriction_is_or_clause(rinfo))
            *joinorclauses = lappend(*joinorclauses, rinfo);
        else
            match_clause_to_index(index, rinfo, clauseset);
    }
}

/*
 * match_eclass_clauses_to_index
 *    Identify EquivalenceClass join clauses for the rel that match the index.
 *    Matching clauses are added to *clauseset.
 */
static void
match_eclass_clauses_to_index(PlannerInfo *root, IndexOptInfo *index,
                              Relids lateral_referencers,
                              IndexClauseSet *clauseset)
{
    int         indexcol;

    /* No work if rel is not in any such ECs */
    if (!index->rel->has_eclass_joins)
        return;

    for (indexcol = 0; indexcol < index->ncolumns; indexcol++)
    {
        ec_member_matches_arg arg;
        List       *clauses;

        /* Generate clauses, skipping any that join to lateral_referencers */
        arg.index = index;
        arg.indexcol = indexcol;
        clauses = generate_implied_equalities_for_column(root,
                                                         index->rel,
                                                  ec_member_matches_indexcol,
                                                         (void *) &arg,
                                                         lateral_referencers);

        /*
         * We have to check whether the results actually do match the index,
         * since for non-btree indexes the EC's equality operators might not
         * be in the index opclass (cf ec_member_matches_indexcol).
         */
        match_clauses_to_index(index, clauses, clauseset);
    }
}

/*
 * match_clauses_to_index
 *    Perform match_clause_to_index() for each clause in a list.
 *    Matching clauses are added to *clauseset.
 */
static void
match_clauses_to_index(IndexOptInfo *index,
                       List *clauses,
                       IndexClauseSet *clauseset)
{
    ListCell   *lc;

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

        Assert(IsA(rinfo, RestrictInfo));
        match_clause_to_index(index, rinfo, clauseset);
    }
}

/*
 * match_clause_to_index
 *    Test whether a qual clause can be used with an index.
 *
 * If the clause is usable, add it to the appropriate list in *clauseset.
 * *clauseset must be initialized to zeroes before first call.
 *
 * Note: in some circumstances we may find the same RestrictInfos coming from
 * multiple places.  Defend against redundant outputs by refusing to add a
 * clause twice (pointer equality should be a good enough check for this).
 *
 * Note: it's possible that a badly-defined index could have multiple matching
 * columns.  We always select the first match if so; this avoids scenarios
 * wherein we get an inflated idea of the index's selectivity by using the
 * same clause multiple times with different index columns.
 */
static void
match_clause_to_index(IndexOptInfo *index,
                      RestrictInfo *rinfo,
                      IndexClauseSet *clauseset)
{
    int         indexcol;

    for (indexcol = 0; indexcol < index->ncolumns; indexcol++)
    {
        if (match_clause_to_indexcol(index,
                                     indexcol,
                                     rinfo))
        {
            clauseset->indexclauses[indexcol] =
                list_append_unique_ptr(clauseset->indexclauses[indexcol],
                                       rinfo);
            clauseset->nonempty = true;
            return;
        }
    }
}

/*
 * match_clause_to_indexcol()
 *    Determines whether a restriction clause matches a column of an index.
 *
 *    To match an index normally, the clause:
 *
 *    (1)  must be in the form (indexkey op const) or (const op indexkey);
 *         and
 *    (2)  must contain an operator which is in the same family as the index
 *         operator for this column, or is a "special" operator as recognized
 *         by match_special_index_operator();
 *         and
 *    (3)  must match the collation of the index, if collation is relevant.
 *
 *    Our definition of "const" is exceedingly liberal: we allow anything that
 *    doesn't involve a volatile function or a Var of the index's relation.
 *    In particular, Vars belonging to other relations of the query are
 *    accepted here, since a clause of that form can be used in a
 *    parameterized indexscan.  It's the responsibility of higher code levels
 *    to manage restriction and join clauses appropriately.
 *
 *    Note: we do need to check for Vars of the index's relation on the
 *    "const" side of the clause, since clauses like (a.f1 OP (b.f2 OP a.f3))
 *    are not processable by a parameterized indexscan on a.f1, whereas
 *    something like (a.f1 OP (b.f2 OP c.f3)) is.
 *
 *    Presently, the executor can only deal with indexquals that have the
 *    indexkey on the left, so we can only use clauses that have the indexkey
 *    on the right if we can commute the clause to put the key on the left.
 *    We do not actually do the commuting here, but we check whether a
 *    suitable commutator operator is available.
 *
 *    If the index has a collation, the clause must have the same collation.
 *    For collation-less indexes, we assume it doesn't matter; this is
 *    necessary for cases like "hstore ? text", wherein hstore's operators
 *    don't care about collation but the clause will get marked with a
 *    collation anyway because of the text argument.  (This logic is
 *    embodied in the macro IndexCollMatchesExprColl.)
 *
 *    It is also possible to match RowCompareExpr clauses to indexes (but
 *    currently, only btree indexes handle this).  In this routine we will
 *    report a match if the first column of the row comparison matches the
 *    target index column.  This is sufficient to guarantee that some index
 *    condition can be constructed from the RowCompareExpr --- whether the
 *    remaining columns match the index too is considered in
 *    adjust_rowcompare_for_index().
 *
 *    It is also possible to match ScalarArrayOpExpr clauses to indexes, when
 *    the clause is of the form "indexkey op ANY (arrayconst)".
 *
 *    For boolean indexes, it is also possible to match the clause directly
 *    to the indexkey; or perhaps the clause is (NOT indexkey).
 *
 * 'index' is the index of interest.
 * 'indexcol' is a column number of 'index' (counting from 0).
 * 'rinfo' is the clause to be tested (as a RestrictInfo node).
 *
 * Returns true if the clause can be used with this index key.
 *
 * NOTE:  returns false if clause is an OR or AND clause; it is the
 * responsibility of higher-level routines to cope with those.
 */
static bool
match_clause_to_indexcol(IndexOptInfo *index,
                         int indexcol,
                         RestrictInfo *rinfo)
{
    Expr       *clause = rinfo->clause;
    Index       index_relid = index->rel->relid;
    Oid         opfamily = index->opfamily[indexcol];
    Oid         idxcollation = index->indexcollations[indexcol];
    Node       *leftop,
               *rightop;
    Relids      left_relids;
    Relids      right_relids;
    Oid         expr_op;
    Oid         expr_coll;
    bool        plain_op;

    /*
     * Never match pseudoconstants to indexes.  (Normally this could not
     * happen anyway, since a pseudoconstant clause couldn't contain a Var,
     * but what if someone builds an expression index on a constant? It's not
     * totally unreasonable to do so with a partial index, either.)
     */
    if (rinfo->pseudoconstant)
        return false;

    /* First check for boolean-index cases. */
    if (IsBooleanOpfamily(opfamily))
    {
        if (match_boolean_index_clause((Node *) clause, indexcol, index))
            return true;
    }

    /*
     * Clause must be a binary opclause, or possibly a ScalarArrayOpExpr
     * (which is always binary, by definition).  Or it could be a
     * RowCompareExpr, which we pass off to match_rowcompare_to_indexcol().
     * Or, if the index supports it, we can handle IS NULL/NOT NULL clauses.
     */
    if (is_opclause(clause))
    {
        leftop = get_leftop(clause);
        rightop = get_rightop(clause);
        if (!leftop || !rightop)
            return false;
        left_relids = rinfo->left_relids;
        right_relids = rinfo->right_relids;
        expr_op = ((OpExpr *) clause)->opno;
        expr_coll = ((OpExpr *) clause)->inputcollid;
        plain_op = true;
    }
    else if (clause && IsA(clause, ScalarArrayOpExpr))
    {
        ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;

        /* We only accept ANY clauses, not ALL */
        if (!saop->useOr)
            return false;
        leftop = (Node *) linitial(saop->args);
        rightop = (Node *) lsecond(saop->args);
        left_relids = NULL;     /* not actually needed */
        right_relids = pull_varnos(rightop);
        expr_op = saop->opno;
        expr_coll = saop->inputcollid;
        plain_op = false;
    }
    else if (clause && IsA(clause, RowCompareExpr))
    {
        return match_rowcompare_to_indexcol(index, indexcol,
                                            opfamily, idxcollation,
                                            (RowCompareExpr *) clause);
    }
    else if (index->amsearchnulls && IsA(clause, NullTest))
    {
        NullTest   *nt = (NullTest *) clause;

        if (!nt->argisrow &&
            match_index_to_operand((Node *) nt->arg, indexcol, index))
            return true;
        return false;
    }
    else
        return false;

    /*
     * Check for clauses of the form: (indexkey operator constant) or
     * (constant operator indexkey).  See above notes about const-ness.
     */
    if (match_index_to_operand(leftop, indexcol, index) &&
        !bms_is_member(index_relid, right_relids) &&
        !contain_volatile_functions(rightop))
    {
        if (IndexCollMatchesExprColl(idxcollation, expr_coll) &&
            is_indexable_operator(expr_op, opfamily, true))
            return true;

        /*
         * If we didn't find a member of the index's opfamily, see whether it
         * is a "special" indexable operator.
         */
        if (plain_op &&
            match_special_index_operator(clause, opfamily,
                                         idxcollation, true))
            return true;
        return false;
    }

    if (plain_op &&
        match_index_to_operand(rightop, indexcol, index) &&
        !bms_is_member(index_relid, left_relids) &&
        !contain_volatile_functions(leftop))
    {
        if (IndexCollMatchesExprColl(idxcollation, expr_coll) &&
            is_indexable_operator(expr_op, opfamily, false))
            return true;

        /*
         * If we didn't find a member of the index's opfamily, see whether it
         * is a "special" indexable operator.
         */
        if (match_special_index_operator(clause, opfamily,
                                         idxcollation, false))
            return true;
        return false;
    }

    return false;
}

/*
 * is_indexable_operator
 *    Does the operator match the specified index opfamily?
 *
 * If the indexkey is on the right, what we actually want to know
 * is whether the operator has a commutator operator that matches
 * the opfamily.
 */
static bool
is_indexable_operator(Oid expr_op, Oid opfamily, bool indexkey_on_left)
{
    /* Get the commuted operator if necessary */
    if (!indexkey_on_left)
    {
        expr_op = get_commutator(expr_op);
        if (expr_op == InvalidOid)
            return false;
    }

    /* OK if the (commuted) operator is a member of the index's opfamily */
    return op_in_opfamily(expr_op, opfamily);
}

/*
 * match_rowcompare_to_indexcol()
 *    Handles the RowCompareExpr case for match_clause_to_indexcol(),
 *    which see for comments.
 */
static bool
match_rowcompare_to_indexcol(IndexOptInfo *index,
                             int indexcol,
                             Oid opfamily,
                             Oid idxcollation,
                             RowCompareExpr *clause)
{
    Index       index_relid = index->rel->relid;
    Node       *leftop,
               *rightop;
    Oid         expr_op;
    Oid         expr_coll;

    /* Forget it if we're not dealing with a btree index */
    if (index->relam != BTREE_AM_OID)
        return false;

    /*
     * We could do the matching on the basis of insisting that the opfamily
     * shown in the RowCompareExpr be the same as the index column's opfamily,
     * but that could fail in the presence of reverse-sort opfamilies: it'd be
     * a matter of chance whether RowCompareExpr had picked the forward or
     * reverse-sort family.  So look only at the operator, and match if it is
     * a member of the index's opfamily (after commutation, if the indexkey is
     * on the right).  We'll worry later about whether any additional
     * operators are matchable to the index.
     */
    leftop = (Node *) linitial(clause->largs);
    rightop = (Node *) linitial(clause->rargs);
    expr_op = linitial_oid(clause->opnos);
    expr_coll = linitial_oid(clause->inputcollids);

    /* Collations must match, if relevant */
    if (!IndexCollMatchesExprColl(idxcollation, expr_coll))
        return false;

    /*
     * These syntactic tests are the same as in match_clause_to_indexcol()
     */
    if (match_index_to_operand(leftop, indexcol, index) &&
        !bms_is_member(index_relid, pull_varnos(rightop)) &&
        !contain_volatile_functions(rightop))
    {
        /* OK, indexkey is on left */
    }
    else if (match_index_to_operand(rightop, indexcol, index) &&
             !bms_is_member(index_relid, pull_varnos(leftop)) &&
             !contain_volatile_functions(leftop))
    {
        /* indexkey is on right, so commute the operator */
        expr_op = get_commutator(expr_op);
        if (expr_op == InvalidOid)
            return false;
    }
    else
        return false;

    /* We're good if the operator is the right type of opfamily member */
    switch (get_op_opfamily_strategy(expr_op, opfamily))
    {
        case BTLessStrategyNumber:
        case BTLessEqualStrategyNumber:
        case BTGreaterEqualStrategyNumber:
        case BTGreaterStrategyNumber:
            return true;
    }

    return false;
}


/****************************************************************************
 *              ----  ROUTINES TO CHECK ORDERING OPERATORS  ----
 ****************************************************************************/

/*
 * match_pathkeys_to_index
 *      Test whether an index can produce output ordered according to the
 *      given pathkeys using "ordering operators".
 *
 * If it can, return a list of suitable ORDER BY expressions, each of the form
 * "indexedcol operator pseudoconstant", along with an integer list of the
 * index column numbers (zero based) that each clause would be used with.
 * NIL lists are returned if the ordering is not achievable this way.
 *
 * On success, the result list is ordered by pathkeys, and in fact is
 * one-to-one with the requested pathkeys.
 */
static void
match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
                        List **orderby_clauses_p,
                        List **clause_columns_p)
{
    List       *orderby_clauses = NIL;
    List       *clause_columns = NIL;
    ListCell   *lc1;

    *orderby_clauses_p = NIL;   /* set default results */
    *clause_columns_p = NIL;

    /* Only indexes with the amcanorderbyop property are interesting here */
    if (!index->amcanorderbyop)
        return;

    foreach(lc1, pathkeys)
    {
        PathKey    *pathkey = (PathKey *) lfirst(lc1);
        bool        found = false;
        ListCell   *lc2;

        /*
         * Note: for any failure to match, we just return NIL immediately.
         * There is no value in matching just some of the pathkeys.
         */

        /* Pathkey must request default sort order for the target opfamily */
        if (pathkey->pk_strategy != BTLessStrategyNumber ||
            pathkey->pk_nulls_first)
            return;

        /* If eclass is volatile, no hope of using an indexscan */
        if (pathkey->pk_eclass->ec_has_volatile)
            return;

        /*
         * Try to match eclass member expression(s) to index.  Note that child
         * EC members are considered, but only when they belong to the target
         * relation.  (Unlike regular members, the same expression could be a
         * child member of more than one EC.  Therefore, the same index could
         * be considered to match more than one pathkey list, which is OK
         * here.  See also get_eclass_for_sort_expr.)
         */
        foreach(lc2, pathkey->pk_eclass->ec_members)
        {
            EquivalenceMember *member = (EquivalenceMember *) lfirst(lc2);
            int         indexcol;

            /* No possibility of match if it references other relations */
            if (!bms_equal(member->em_relids, index->rel->relids))
                continue;

            /*
             * We allow any column of the index to match each pathkey; they
             * don't have to match left-to-right as you might expect.  This is
             * correct for GiST, which is the sole existing AM supporting
             * amcanorderbyop.  We might need different logic in future for
             * other implementations.
             */
            for (indexcol = 0; indexcol < index->ncolumns; indexcol++)
            {
                Expr       *expr;

                expr = match_clause_to_ordering_op(index,
                                                   indexcol,
                                                   member->em_expr,
                                                   pathkey->pk_opfamily);
                if (expr)
                {
                    orderby_clauses = lappend(orderby_clauses, expr);
                    clause_columns = lappend_int(clause_columns, indexcol);
                    found = true;
                    break;
                }
            }

            if (found)          /* don't want to look at remaining members */
                break;
        }

        if (!found)             /* fail if no match for this pathkey */
            return;
    }

    *orderby_clauses_p = orderby_clauses;       /* success! */
    *clause_columns_p = clause_columns;
}

/*
 * match_clause_to_ordering_op
 *    Determines whether an ordering operator expression matches an
 *    index column.
 *
 *    This is similar to, but simpler than, match_clause_to_indexcol.
 *    We only care about simple OpExpr cases.  The input is a bare
 *    expression that is being ordered by, which must be of the form
 *    (indexkey op const) or (const op indexkey) where op is an ordering
 *    operator for the column's opfamily.
 *
 * 'index' is the index of interest.
 * 'indexcol' is a column number of 'index' (counting from 0).
 * 'clause' is the ordering expression to be tested.
 * 'pk_opfamily' is the btree opfamily describing the required sort order.
 *
 * Note that we currently do not consider the collation of the ordering
 * operator's result.  In practical cases the result type will be numeric
 * and thus have no collation, and it's not very clear what to match to
 * if it did have a collation.  The index's collation should match the
 * ordering operator's input collation, not its result.
 *
 * If successful, return 'clause' as-is if the indexkey is on the left,
 * otherwise a commuted copy of 'clause'.  If no match, return NULL.
 */
static Expr *
match_clause_to_ordering_op(IndexOptInfo *index,
                            int indexcol,
                            Expr *clause,
                            Oid pk_opfamily)
{
    Oid         opfamily = index->opfamily[indexcol];
    Oid         idxcollation = index->indexcollations[indexcol];
    Node       *leftop,
               *rightop;
    Oid         expr_op;
    Oid         expr_coll;
    Oid         sortfamily;
    bool        commuted;

    /*
     * Clause must be a binary opclause.
     */
    if (!is_opclause(clause))
        return NULL;
    leftop = get_leftop(clause);
    rightop = get_rightop(clause);
    if (!leftop || !rightop)
        return NULL;
    expr_op = ((OpExpr *) clause)->opno;
    expr_coll = ((OpExpr *) clause)->inputcollid;

    /*
     * We can forget the whole thing right away if wrong collation.
     */
    if (!IndexCollMatchesExprColl(idxcollation, expr_coll))
        return NULL;

    /*
     * Check for clauses of the form: (indexkey operator constant) or
     * (constant operator indexkey).
     */
    if (match_index_to_operand(leftop, indexcol, index) &&
        !contain_var_clause(rightop) &&
        !contain_volatile_functions(rightop))
    {
        commuted = false;
    }
    else if (match_index_to_operand(rightop, indexcol, index) &&
             !contain_var_clause(leftop) &&
             !contain_volatile_functions(leftop))
    {
        /* Might match, but we need a commuted operator */
        expr_op = get_commutator(expr_op);
        if (expr_op == InvalidOid)
            return NULL;
        commuted = true;
    }
    else
        return NULL;

    /*
     * Is the (commuted) operator an ordering operator for the opfamily? And
     * if so, does it yield the right sorting semantics?
     */
    sortfamily = get_op_opfamily_sortfamily(expr_op, opfamily);
    if (sortfamily != pk_opfamily)
        return NULL;

    /* We have a match.  Return clause or a commuted version thereof. */
    if (commuted)
    {
        OpExpr     *newclause = makeNode(OpExpr);

        /* flat-copy all the fields of clause */
        memcpy(newclause, clause, sizeof(OpExpr));

        /* commute it */
        newclause->opno = expr_op;
        newclause->opfuncid = InvalidOid;
        newclause->args = list_make2(rightop, leftop);

        clause = (Expr *) newclause;
    }

    return clause;
}


/****************************************************************************
 *              ----  ROUTINES TO DO PARTIAL INDEX PREDICATE TESTS  ----
 ****************************************************************************/

/*
 * check_partial_indexes
 *      Check each partial index of the relation, and mark it predOK if
 *      the index's predicate is satisfied for this query.
 *
 * Note: it is possible for this to get re-run after adding more restrictions
 * to the rel; so we might be able to prove more indexes OK.  We assume that
 * adding more restrictions can't make an index not OK.
 */
void
check_partial_indexes(PlannerInfo *root, RelOptInfo *rel)
{
    List       *clauselist;
    bool        have_partial;
    Relids      otherrels;
    ListCell   *lc;

    /*
     * Frequently, there will be no partial indexes, so first check to make
     * sure there's something useful to do here.
     */
    have_partial = false;
    foreach(lc, rel->indexlist)
    {
        IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);

        if (index->indpred == NIL)
            continue;           /* ignore non-partial indexes */

        if (index->predOK)
            continue;           /* don't repeat work if already proven OK */

        have_partial = true;
        break;
    }
    if (!have_partial)
        return;

    /*
     * Construct a list of clauses that we can assume true for the purpose
     * of proving the index(es) usable.  Restriction clauses for the rel are
     * always usable, and so are any join clauses that are "movable to" this
     * rel.  Also, we can consider any EC-derivable join clauses (which must
     * be "movable to" this rel, by definition).
     */
    clauselist = list_copy(rel->baserestrictinfo);

    /* Scan the rel's join clauses */
    foreach(lc, rel->joininfo)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

        /* Check if clause can be moved to this rel */
        if (!join_clause_is_movable_to(rinfo, rel->relid))
            continue;

        clauselist = lappend(clauselist, rinfo);
    }

    /*
     * Add on any equivalence-derivable join clauses.  Computing the correct
     * relid sets for generate_join_implied_equalities is slightly tricky
     * because the rel could be a child rel rather than a true baserel, and
     * in that case we must remove its parent's relid from all_baserels.
     */
    if (rel->reloptkind == RELOPT_OTHER_MEMBER_REL)
    {
        /* Lookup parent->child translation data */
        AppendRelInfo *appinfo = find_childrel_appendrelinfo(root, rel);

        otherrels = bms_difference(root->all_baserels,
                                   bms_make_singleton(appinfo->parent_relid));
    }
    else
        otherrels = bms_difference(root->all_baserels, rel->relids);

    if (!bms_is_empty(otherrels))
        clauselist =
            list_concat(clauselist,
                        generate_join_implied_equalities(root,
                                                         bms_union(rel->relids,
                                                                   otherrels),
                                                         otherrels,
                                                         rel));

    /* Now try to prove each index predicate true */
    foreach(lc, rel->indexlist)
    {
        IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);

        if (index->indpred == NIL)
            continue;           /* ignore non-partial indexes */

        if (index->predOK)
            continue;           /* don't repeat work if already proven OK */

        index->predOK = predicate_implied_by(index->indpred, clauselist);
    }
}

/****************************************************************************
 *              ----  ROUTINES TO CHECK EXTERNALLY-VISIBLE CONDITIONS  ----
 ****************************************************************************/

/*
 * ec_member_matches_indexcol
 *    Test whether an EquivalenceClass member matches an index column.
 *
 * This is a callback for use by generate_implied_equalities_for_column.
 */
static bool
ec_member_matches_indexcol(PlannerInfo *root, RelOptInfo *rel,
                           EquivalenceClass *ec, EquivalenceMember *em,
                           void *arg)
{
    IndexOptInfo *index = ((ec_member_matches_arg *) arg)->index;
    int         indexcol = ((ec_member_matches_arg *) arg)->indexcol;
    Oid         curFamily = index->opfamily[indexcol];
    Oid         curCollation = index->indexcollations[indexcol];

    /*
     * If it's a btree index, we can reject it if its opfamily isn't
     * compatible with the EC, since no clause generated from the EC could be
     * used with the index.  For non-btree indexes, we can't easily tell
     * whether clauses generated from the EC could be used with the index, so
     * don't check the opfamily.  This might mean we return "true" for a
     * useless EC, so we have to recheck the results of
     * generate_implied_equalities_for_column; see
     * match_eclass_clauses_to_index.
     */
    if (index->relam == BTREE_AM_OID &&
        !list_member_oid(ec->ec_opfamilies, curFamily))
        return false;

    /* We insist on collation match for all index types, though */
    if (!IndexCollMatchesExprColl(curCollation, ec->ec_collation))
        return false;

    return match_index_to_operand((Node *) em->em_expr, indexcol, index);
}

/*
 * relation_has_unique_index_for
 *    Determine whether the relation provably has at most one row satisfying
 *    a set of equality conditions, because the conditions constrain all
 *    columns of some unique index.
 *
 * The conditions can be represented in either or both of two ways:
 * 1. A list of RestrictInfo nodes, where the caller has already determined
 * that each condition is a mergejoinable equality with an expression in
 * this relation on one side, and an expression not involving this relation
 * on the other.  The transient outer_is_left flag is used to identify which
 * side we should look at: left side if outer_is_left is false, right side
 * if it is true.
 * 2. A list of expressions in this relation, and a corresponding list of
 * equality operators. The caller must have already checked that the operators
 * represent equality.  (Note: the operators could be cross-type; the
 * expressions should correspond to their RHS inputs.)
 *
 * The caller need only supply equality conditions arising from joins;
 * this routine automatically adds in any usable baserestrictinfo clauses.
 * (Note that the passed-in restrictlist will be destructively modified!)
 */
bool
relation_has_unique_index_for(PlannerInfo *root, RelOptInfo *rel,
                              List *restrictlist,
                              List *exprlist, List *oprlist)
{
    ListCell   *ic;

    Assert(list_length(exprlist) == list_length(oprlist));

    /* Short-circuit if no indexes... */
    if (rel->indexlist == NIL)
        return false;

    /*
     * Examine the rel's restriction clauses for usable var = const clauses
     * that we can add to the restrictlist.
     */
    foreach(ic, rel->baserestrictinfo)
    {
        RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(ic);

        /*
         * Note: can_join won't be set for a restriction clause, but
         * mergeopfamilies will be if it has a mergejoinable operator and
         * doesn't contain volatile functions.
         */
        if (restrictinfo->mergeopfamilies == NIL)
            continue;           /* not mergejoinable */

        /*
         * The clause certainly doesn't refer to anything but the given rel.
         * If either side is pseudoconstant then we can use it.
         */
        if (bms_is_empty(restrictinfo->left_relids))
        {
            /* righthand side is inner */
            restrictinfo->outer_is_left = true;
        }
        else if (bms_is_empty(restrictinfo->right_relids))
        {
            /* lefthand side is inner */
            restrictinfo->outer_is_left = false;
        }
        else
            continue;

        /* OK, add to list */
        restrictlist = lappend(restrictlist, restrictinfo);
    }

    /* Short-circuit the easy case */
    if (restrictlist == NIL && exprlist == NIL)
        return false;

    /* Examine each index of the relation ... */
    foreach(ic, rel->indexlist)
    {
        IndexOptInfo *ind = (IndexOptInfo *) lfirst(ic);
        int         c;

        /*
         * If the index is not unique, or not immediately enforced, or if it's
         * a partial index that doesn't match the query, it's useless here.
         */
        if (!ind->unique || !ind->immediate ||
            (ind->indpred != NIL && !ind->predOK))
            continue;

        /*
         * Try to find each index column in the lists of conditions.  This is
         * O(N^2) or worse, but we expect all the lists to be short.
         */
        for (c = 0; c < ind->ncolumns; c++)
        {
            bool        matched = false;
            ListCell   *lc;
            ListCell   *lc2;

            foreach(lc, restrictlist)
            {
                RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
                Node       *rexpr;

                /*
                 * The condition's equality operator must be a member of the
                 * index opfamily, else it is not asserting the right kind of
                 * equality behavior for this index.  We check this first
                 * since it's probably cheaper than match_index_to_operand().
                 */
                if (!list_member_oid(rinfo->mergeopfamilies, ind->opfamily[c]))
                    continue;

                /*
                 * XXX at some point we may need to check collations here too.
                 * For the moment we assume all collations reduce to the same
                 * notion of equality.
                 */

                /* OK, see if the condition operand matches the index key */
                if (rinfo->outer_is_left)
                    rexpr = get_rightop(rinfo->clause);
                else
                    rexpr = get_leftop(rinfo->clause);

                if (match_index_to_operand(rexpr, c, ind))
                {
                    matched = true;     /* column is unique */
                    break;
                }
            }

            if (matched)
                continue;

            forboth(lc, exprlist, lc2, oprlist)
            {
                Node       *expr = (Node *) lfirst(lc);
                Oid         opr = lfirst_oid(lc2);

                /* See if the expression matches the index key */
                if (!match_index_to_operand(expr, c, ind))
                    continue;

                /*
                 * The equality operator must be a member of the index
                 * opfamily, else it is not asserting the right kind of
                 * equality behavior for this index.  We assume the caller
                 * determined it is an equality operator, so we don't need to
                 * check any more tightly than this.
                 */
                if (!op_in_opfamily(opr, ind->opfamily[c]))
                    continue;

                /*
                 * XXX at some point we may need to check collations here too.
                 * For the moment we assume all collations reduce to the same
                 * notion of equality.
                 */

                matched = true; /* column is unique */
                break;
            }

            if (!matched)
                break;          /* no match; this index doesn't help us */
        }

        /* Matched all columns of this index? */
        if (c == ind->ncolumns)
            return true;
    }

    return false;
}


/****************************************************************************
 *              ----  ROUTINES TO CHECK OPERANDS  ----
 ****************************************************************************/

/*
 * match_index_to_operand()
 *    Generalized test for a match between an index's key
 *    and the operand on one side of a restriction or join clause.
 *
 * operand: the nodetree to be compared to the index
 * indexcol: the column number of the index (counting from 0)
 * index: the index of interest
 *
 * Note that we aren't interested in collations here; the caller must check
 * for a collation match, if it's dealing with an operator where that matters.
 *
 * This is exported for use in selfuncs.c.
 */
bool
match_index_to_operand(Node *operand,
                       int indexcol,
                       IndexOptInfo *index)
{
    int         indkey;

    /*
     * Ignore any RelabelType node above the operand.   This is needed to be
     * able to apply indexscanning in binary-compatible-operator cases. Note:
     * we can assume there is at most one RelabelType node;
     * eval_const_expressions() will have simplified if more than one.
     */
    if (operand && IsA(operand, RelabelType))
        operand = (Node *) ((RelabelType *) operand)->arg;

    indkey = index->indexkeys[indexcol];
    if (indkey != 0)
    {
        /*
         * Simple index column; operand must be a matching Var.
         */
        if (operand && IsA(operand, Var) &&
            index->rel->relid == ((Var *) operand)->varno &&
            indkey == ((Var *) operand)->varattno)
            return true;
    }
    else
    {
        /*
         * Index expression; find the correct expression.  (This search could
         * be avoided, at the cost of complicating all the callers of this
         * routine; doesn't seem worth it.)
         */
        ListCell   *indexpr_item;
        int         i;
        Node       *indexkey;

        indexpr_item = list_head(index->indexprs);
        for (i = 0; i < indexcol; i++)
        {
            if (index->indexkeys[i] == 0)
            {
                if (indexpr_item == NULL)
                    elog(ERROR, "wrong number of index expressions");
                indexpr_item = lnext(indexpr_item);
            }
        }
        if (indexpr_item == NULL)
            elog(ERROR, "wrong number of index expressions");
        indexkey = (Node *) lfirst(indexpr_item);

        /*
         * Does it match the operand?  Again, strip any relabeling.
         */
        if (indexkey && IsA(indexkey, RelabelType))
            indexkey = (Node *) ((RelabelType *) indexkey)->arg;

        if (equal(indexkey, operand))
            return true;
    }

    return false;
}

/****************************************************************************
 *          ----  ROUTINES FOR "SPECIAL" INDEXABLE OPERATORS  ----
 ****************************************************************************/

/*
 * These routines handle special optimization of operators that can be
 * used with index scans even though they are not known to the executor's
 * indexscan machinery.  The key idea is that these operators allow us
 * to derive approximate indexscan qual clauses, such that any tuples
 * that pass the operator clause itself must also satisfy the simpler
 * indexscan condition(s).  Then we can use the indexscan machinery
 * to avoid scanning as much of the table as we'd otherwise have to,
 * while applying the original operator as a qpqual condition to ensure
 * we deliver only the tuples we want.  (In essence, we're using a regular
 * index as if it were a lossy index.)
 *
 * An example of what we're doing is
 *          textfield LIKE 'abc%'
 * from which we can generate the indexscanable conditions
 *          textfield >= 'abc' AND textfield < 'abd'
 * which allow efficient scanning of an index on textfield.
 * (In reality, character set and collation issues make the transformation
 * from LIKE to indexscan limits rather harder than one might think ...
 * but that's the basic idea.)
 *
 * Another thing that we do with this machinery is to provide special
 * smarts for "boolean" indexes (that is, indexes on boolean columns
 * that support boolean equality).  We can transform a plain reference
 * to the indexkey into "indexkey = true", or "NOT indexkey" into
 * "indexkey = false", so as to make the expression indexable using the
 * regular index operators.  (As of Postgres 8.1, we must do this here
 * because constant simplification does the reverse transformation;
 * without this code there'd be no way to use such an index at all.)
 *
 * Three routines are provided here:
 *
 * match_special_index_operator() is just an auxiliary function for
 * match_clause_to_indexcol(); after the latter fails to recognize a
 * restriction opclause's operator as a member of an index's opfamily,
 * it asks match_special_index_operator() whether the clause should be
 * considered an indexqual anyway.
 *
 * match_boolean_index_clause() similarly detects clauses that can be
 * converted into boolean equality operators.
 *
 * expand_indexqual_conditions() converts a list of RestrictInfo nodes
 * (with implicit AND semantics across list elements) into a list of clauses
 * that the executor can actually handle.  For operators that are members of
 * the index's opfamily this transformation is a no-op, but clauses recognized
 * by match_special_index_operator() or match_boolean_index_clause() must be
 * converted into one or more "regular" indexqual conditions.
 */

/*
 * match_boolean_index_clause
 *    Recognize restriction clauses that can be matched to a boolean index.
 *
 * This should be called only when IsBooleanOpfamily() recognizes the
 * index's operator family.  We check to see if the clause matches the
 * index's key.
 */
static bool
match_boolean_index_clause(Node *clause,
                           int indexcol,
                           IndexOptInfo *index)
{
    /* Direct match? */
    if (match_index_to_operand(clause, indexcol, index))
        return true;
    /* NOT clause? */
    if (not_clause(clause))
    {
        if (match_index_to_operand((Node *) get_notclausearg((Expr *) clause),
                                   indexcol, index))
            return true;
    }

    /*
     * Since we only consider clauses at top level of WHERE, we can convert
     * indexkey IS TRUE and indexkey IS FALSE to index searches as well. The
     * different meaning for NULL isn't important.
     */
    else if (clause && IsA(clause, BooleanTest))
    {
        BooleanTest *btest = (BooleanTest *) clause;

        if (btest->booltesttype == IS_TRUE ||
            btest->booltesttype == IS_FALSE)
            if (match_index_to_operand((Node *) btest->arg,
                                       indexcol, index))
                return true;
    }
    return false;
}

/*
 * match_special_index_operator
 *    Recognize restriction clauses that can be used to generate
 *    additional indexscanable qualifications.
 *
 * The given clause is already known to be a binary opclause having
 * the form (indexkey OP pseudoconst) or (pseudoconst OP indexkey),
 * but the OP proved not to be one of the index's opfamily operators.
 * Return 'true' if we can do something with it anyway.
 */
static bool
match_special_index_operator(Expr *clause, Oid opfamily, Oid idxcollation,
                             bool indexkey_on_left)
{
    bool        isIndexable = false;
    Node       *rightop;
    Oid         expr_op;
    Oid         expr_coll;
    Const      *patt;
    Const      *prefix = NULL;
    Pattern_Prefix_Status pstatus = Pattern_Prefix_None;

    /*
     * Currently, all known special operators require the indexkey on the
     * left, but this test could be pushed into the switch statement if some
     * are added that do not...
     */
    if (!indexkey_on_left)
        return false;

    /* we know these will succeed */
    rightop = get_rightop(clause);
    expr_op = ((OpExpr *) clause)->opno;
    expr_coll = ((OpExpr *) clause)->inputcollid;

    /* again, required for all current special ops: */
    if (!IsA(rightop, Const) ||
        ((Const *) rightop)->constisnull)
        return false;
    patt = (Const *) rightop;

    switch (expr_op)
    {
        case OID_TEXT_LIKE_OP:
        case OID_BPCHAR_LIKE_OP:
        case OID_NAME_LIKE_OP:
            /* the right-hand const is type text for all of these */
            pstatus = pattern_fixed_prefix(patt, Pattern_Type_Like, expr_coll,
                                           &prefix, NULL);
            isIndexable = (pstatus != Pattern_Prefix_None);
            break;

        case OID_BYTEA_LIKE_OP:
            pstatus = pattern_fixed_prefix(patt, Pattern_Type_Like, expr_coll,
                                           &prefix, NULL);
            isIndexable = (pstatus != Pattern_Prefix_None);
            break;

        case OID_TEXT_ICLIKE_OP:
        case OID_BPCHAR_ICLIKE_OP:
        case OID_NAME_ICLIKE_OP:
            /* the right-hand const is type text for all of these */
            pstatus = pattern_fixed_prefix(patt, Pattern_Type_Like_IC, expr_coll,
                                           &prefix, NULL);
            isIndexable = (pstatus != Pattern_Prefix_None);
            break;

        case OID_TEXT_REGEXEQ_OP:
        case OID_BPCHAR_REGEXEQ_OP:
        case OID_NAME_REGEXEQ_OP:
            /* the right-hand const is type text for all of these */
            pstatus = pattern_fixed_prefix(patt, Pattern_Type_Regex, expr_coll,
                                           &prefix, NULL);
            isIndexable = (pstatus != Pattern_Prefix_None);
            break;

        case OID_TEXT_ICREGEXEQ_OP:
        case OID_BPCHAR_ICREGEXEQ_OP:
        case OID_NAME_ICREGEXEQ_OP:
            /* the right-hand const is type text for all of these */
            pstatus = pattern_fixed_prefix(patt, Pattern_Type_Regex_IC, expr_coll,
                                           &prefix, NULL);
            isIndexable = (pstatus != Pattern_Prefix_None);
            break;

        case OID_INET_SUB_OP:
        case OID_INET_SUBEQ_OP:
            isIndexable = true;
            break;
    }

    if (prefix)
    {
        pfree(DatumGetPointer(prefix->constvalue));
        pfree(prefix);
    }

    /* done if the expression doesn't look indexable */
    if (!isIndexable)
        return false;

    /*
     * Must also check that index's opfamily supports the operators we will
     * want to apply.  (A hash index, for example, will not support ">=".)
     * Currently, only btree and spgist support the operators we need.
     *
     * Note: actually, in the Pattern_Prefix_Exact case, we only need "=" so a
     * hash index would work.  Currently it doesn't seem worth checking for
     * that, however.
     *
     * We insist on the opfamily being the specific one we expect, else we'd
     * do the wrong thing if someone were to make a reverse-sort opfamily with
     * the same operators.
     *
     * The non-pattern opclasses will not sort the way we need in most non-C
     * locales.  We can use such an index anyway for an exact match (simple
     * equality), but not for prefix-match cases.  Note that here we are
     * looking at the index's collation, not the expression's collation --
     * this test is *not* dependent on the LIKE/regex operator's collation.
     */
    switch (expr_op)
    {
        case OID_TEXT_LIKE_OP:
        case OID_TEXT_ICLIKE_OP:
        case OID_TEXT_REGEXEQ_OP:
        case OID_TEXT_ICREGEXEQ_OP:
            isIndexable =
                (opfamily == TEXT_PATTERN_BTREE_FAM_OID) ||
                (opfamily == TEXT_SPGIST_FAM_OID) ||
                (opfamily == TEXT_BTREE_FAM_OID &&
                 (pstatus == Pattern_Prefix_Exact ||
                  lc_collate_is_c(idxcollation)));
            break;

        case OID_BPCHAR_LIKE_OP:
        case OID_BPCHAR_ICLIKE_OP:
        case OID_BPCHAR_REGEXEQ_OP:
        case OID_BPCHAR_ICREGEXEQ_OP:
            isIndexable =
                (opfamily == BPCHAR_PATTERN_BTREE_FAM_OID) ||
                (opfamily == BPCHAR_BTREE_FAM_OID &&
                 (pstatus == Pattern_Prefix_Exact ||
                  lc_collate_is_c(idxcollation)));
            break;

        case OID_NAME_LIKE_OP:
        case OID_NAME_ICLIKE_OP:
        case OID_NAME_REGEXEQ_OP:
        case OID_NAME_ICREGEXEQ_OP:
            /* name uses locale-insensitive sorting */
            isIndexable = (opfamily == NAME_BTREE_FAM_OID);
            break;

        case OID_BYTEA_LIKE_OP:
            isIndexable = (opfamily == BYTEA_BTREE_FAM_OID);
            break;

        case OID_INET_SUB_OP:
        case OID_INET_SUBEQ_OP:
            isIndexable = (opfamily == NETWORK_BTREE_FAM_OID);
            break;
    }

    return isIndexable;
}

/*
 * expand_indexqual_conditions
 *    Given a list of RestrictInfo nodes, produce a list of directly usable
 *    index qual clauses.
 *
 * Standard qual clauses (those in the index's opfamily) are passed through
 * unchanged.  Boolean clauses and "special" index operators are expanded
 * into clauses that the indexscan machinery will know what to do with.
 * RowCompare clauses are simplified if necessary to create a clause that is
 * fully checkable by the index.
 *
 * In addition to the expressions themselves, there are auxiliary lists
 * of the index column numbers that the clauses are meant to be used with;
 * we generate an updated column number list for the result.  (This is not
 * the identical list because one input clause sometimes produces more than
 * one output clause.)
 *
 * The input clauses are sorted by column number, and so the output is too.
 * (This is depended on in various places in both planner and executor.)
 */
void
expand_indexqual_conditions(IndexOptInfo *index,
                            List *indexclauses, List *indexclausecols,
                            List **indexquals_p, List **indexqualcols_p)
{
    List       *indexquals = NIL;
    List       *indexqualcols = NIL;
    ListCell   *lcc,
               *lci;

    forboth(lcc, indexclauses, lci, indexclausecols)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lcc);
        int         indexcol = lfirst_int(lci);
        Expr       *clause = rinfo->clause;
        Oid         curFamily = index->opfamily[indexcol];
        Oid         curCollation = index->indexcollations[indexcol];

        /* First check for boolean cases */
        if (IsBooleanOpfamily(curFamily))
        {
            Expr       *boolqual;

            boolqual = expand_boolean_index_clause((Node *) clause,
                                                   indexcol,
                                                   index);
            if (boolqual)
            {
                indexquals = lappend(indexquals,
                                     make_simple_restrictinfo(boolqual));
                indexqualcols = lappend_int(indexqualcols, indexcol);
                continue;
            }
        }

        /*
         * Else it must be an opclause (usual case), ScalarArrayOp,
         * RowCompare, or NullTest
         */
        if (is_opclause(clause))
        {
            indexquals = list_concat(indexquals,
                                     expand_indexqual_opclause(rinfo,
                                                               curFamily,
                                                               curCollation));
            /* expand_indexqual_opclause can produce multiple clauses */
            while (list_length(indexqualcols) < list_length(indexquals))
                indexqualcols = lappend_int(indexqualcols, indexcol);
        }
        else if (IsA(clause, ScalarArrayOpExpr))
        {
            /* no extra work at this time */
            indexquals = lappend(indexquals, rinfo);
            indexqualcols = lappend_int(indexqualcols, indexcol);
        }
        else if (IsA(clause, RowCompareExpr))
        {
            indexquals = lappend(indexquals,
                                 expand_indexqual_rowcompare(rinfo,
                                                             index,
                                                             indexcol));
            indexqualcols = lappend_int(indexqualcols, indexcol);
        }
        else if (IsA(clause, NullTest))
        {
            Assert(index->amsearchnulls);
            indexquals = lappend(indexquals, rinfo);
            indexqualcols = lappend_int(indexqualcols, indexcol);
        }
        else
            elog(ERROR, "unsupported indexqual type: %d",
                 (int) nodeTag(clause));
    }

    *indexquals_p = indexquals;
    *indexqualcols_p = indexqualcols;
}

/*
 * expand_boolean_index_clause
 *    Convert a clause recognized by match_boolean_index_clause into
 *    a boolean equality operator clause.
 *
 * Returns NULL if the clause isn't a boolean index qual.
 */
static Expr *
expand_boolean_index_clause(Node *clause,
                            int indexcol,
                            IndexOptInfo *index)
{
    /* Direct match? */
    if (match_index_to_operand(clause, indexcol, index))
    {
        /* convert to indexkey = TRUE */
        return make_opclause(BooleanEqualOperator, BOOLOID, false,
                             (Expr *) clause,
                             (Expr *) makeBoolConst(true, false),
                             InvalidOid, InvalidOid);
    }
    /* NOT clause? */
    if (not_clause(clause))
    {
        Node       *arg = (Node *) get_notclausearg((Expr *) clause);

        /* It must have matched the indexkey */
        Assert(match_index_to_operand(arg, indexcol, index));
        /* convert to indexkey = FALSE */
        return make_opclause(BooleanEqualOperator, BOOLOID, false,
                             (Expr *) arg,
                             (Expr *) makeBoolConst(false, false),
                             InvalidOid, InvalidOid);
    }
    if (clause && IsA(clause, BooleanTest))
    {
        BooleanTest *btest = (BooleanTest *) clause;
        Node       *arg = (Node *) btest->arg;

        /* It must have matched the indexkey */
        Assert(match_index_to_operand(arg, indexcol, index));
        if (btest->booltesttype == IS_TRUE)
        {
            /* convert to indexkey = TRUE */
            return make_opclause(BooleanEqualOperator, BOOLOID, false,
                                 (Expr *) arg,
                                 (Expr *) makeBoolConst(true, false),
                                 InvalidOid, InvalidOid);
        }
        if (btest->booltesttype == IS_FALSE)
        {
            /* convert to indexkey = FALSE */
            return make_opclause(BooleanEqualOperator, BOOLOID, false,
                                 (Expr *) arg,
                                 (Expr *) makeBoolConst(false, false),
                                 InvalidOid, InvalidOid);
        }
        /* Oops */
        Assert(false);
    }

    return NULL;
}

/*
 * expand_indexqual_opclause --- expand a single indexqual condition
 *      that is an operator clause
 *
 * The input is a single RestrictInfo, the output a list of RestrictInfos.
 *
 * In the base case this is just list_make1(), but we have to be prepared to
 * expand special cases that were accepted by match_special_index_operator().
 */
static List *
expand_indexqual_opclause(RestrictInfo *rinfo, Oid opfamily, Oid idxcollation)
{
    Expr       *clause = rinfo->clause;

    /* we know these will succeed */
    Node       *leftop = get_leftop(clause);
    Node       *rightop = get_rightop(clause);
    Oid         expr_op = ((OpExpr *) clause)->opno;
    Oid         expr_coll = ((OpExpr *) clause)->inputcollid;
    Const      *patt = (Const *) rightop;
    Const      *prefix = NULL;
    Pattern_Prefix_Status pstatus;

    /*
     * LIKE and regex operators are not members of any btree index opfamily,
     * but they can be members of opfamilies for more exotic index types such
     * as GIN.  Therefore, we should only do expansion if the operator is
     * actually not in the opfamily.  But checking that requires a syscache
     * lookup, so it's best to first see if the operator is one we are
     * interested in.
     */
    switch (expr_op)
    {
        case OID_TEXT_LIKE_OP:
        case OID_BPCHAR_LIKE_OP:
        case OID_NAME_LIKE_OP:
        case OID_BYTEA_LIKE_OP:
            if (!op_in_opfamily(expr_op, opfamily))
            {
                pstatus = pattern_fixed_prefix(patt, Pattern_Type_Like, expr_coll,
                                               &prefix, NULL);
                return prefix_quals(leftop, opfamily, idxcollation, prefix, pstatus);
            }
            break;

        case OID_TEXT_ICLIKE_OP:
        case OID_BPCHAR_ICLIKE_OP:
        case OID_NAME_ICLIKE_OP:
            if (!op_in_opfamily(expr_op, opfamily))
            {
                /* the right-hand const is type text for all of these */
                pstatus = pattern_fixed_prefix(patt, Pattern_Type_Like_IC, expr_coll,
                                               &prefix, NULL);
                return prefix_quals(leftop, opfamily, idxcollation, prefix, pstatus);
            }
            break;

        case OID_TEXT_REGEXEQ_OP:
        case OID_BPCHAR_REGEXEQ_OP:
        case OID_NAME_REGEXEQ_OP:
            if (!op_in_opfamily(expr_op, opfamily))
            {
                /* the right-hand const is type text for all of these */
                pstatus = pattern_fixed_prefix(patt, Pattern_Type_Regex, expr_coll,
                                               &prefix, NULL);
                return prefix_quals(leftop, opfamily, idxcollation, prefix, pstatus);
            }
            break;

        case OID_TEXT_ICREGEXEQ_OP:
        case OID_BPCHAR_ICREGEXEQ_OP:
        case OID_NAME_ICREGEXEQ_OP:
            if (!op_in_opfamily(expr_op, opfamily))
            {
                /* the right-hand const is type text for all of these */
                pstatus = pattern_fixed_prefix(patt, Pattern_Type_Regex_IC, expr_coll,
                                               &prefix, NULL);
                return prefix_quals(leftop, opfamily, idxcollation, prefix, pstatus);
            }
            break;

        case OID_INET_SUB_OP:
        case OID_INET_SUBEQ_OP:
            if (!op_in_opfamily(expr_op, opfamily))
            {
                return network_prefix_quals(leftop, expr_op, opfamily,
                                            patt->constvalue);
            }
            break;
    }

    /* Default case: just make a list of the unmodified indexqual */
    return list_make1(rinfo);
}

/*
 * expand_indexqual_rowcompare --- expand a single indexqual condition
 *      that is a RowCompareExpr
 *
 * This is a thin wrapper around adjust_rowcompare_for_index; we export the
 * latter so that createplan.c can use it to re-discover which columns of the
 * index are used by a row comparison indexqual.
 */
static RestrictInfo *
expand_indexqual_rowcompare(RestrictInfo *rinfo,
                            IndexOptInfo *index,
                            int indexcol)
{
    RowCompareExpr *clause = (RowCompareExpr *) rinfo->clause;
    Expr       *newclause;
    List       *indexcolnos;
    bool        var_on_left;

    newclause = adjust_rowcompare_for_index(clause,
                                            index,
                                            indexcol,
                                            &indexcolnos,
                                            &var_on_left);

    /*
     * If we didn't have to change the RowCompareExpr, return the original
     * RestrictInfo.
     */
    if (newclause == (Expr *) clause)
        return rinfo;

    /* Else we need a new RestrictInfo */
    return make_simple_restrictinfo(newclause);
}

/*
 * adjust_rowcompare_for_index --- expand a single indexqual condition
 *      that is a RowCompareExpr
 *
 * It's already known that the first column of the row comparison matches
 * the specified column of the index.  We can use additional columns of the
 * row comparison as index qualifications, so long as they match the index
 * in the "same direction", ie, the indexkeys are all on the same side of the
 * clause and the operators are all the same-type members of the opfamilies.
 * If all the columns of the RowCompareExpr match in this way, we just use it
 * as-is.  Otherwise, we build a shortened RowCompareExpr (if more than one
 * column matches) or a simple OpExpr (if the first-column match is all
 * there is).  In these cases the modified clause is always "<=" or ">="
 * even when the original was "<" or ">" --- this is necessary to match all
 * the rows that could match the original.  (We are essentially building a
 * lossy version of the row comparison when we do this.)
 *
 * *indexcolnos receives an integer list of the index column numbers (zero
 * based) used in the resulting expression.  The reason we need to return
 * that is that if the index is selected for use, createplan.c will need to
 * call this again to extract that list.  (This is a bit grotty, but row
 * comparison indexquals aren't used enough to justify finding someplace to
 * keep the information in the Path representation.)  Since createplan.c
 * also needs to know which side of the RowCompareExpr is the index side,
 * we also return *var_on_left_p rather than re-deducing that there.
 */
Expr *
adjust_rowcompare_for_index(RowCompareExpr *clause,
                            IndexOptInfo *index,
                            int indexcol,
                            List **indexcolnos,
                            bool *var_on_left_p)
{
    bool        var_on_left;
    int         op_strategy;
    Oid         op_lefttype;
    Oid         op_righttype;
    int         matching_cols;
    Oid         expr_op;
    List       *opfamilies;
    List       *lefttypes;
    List       *righttypes;
    List       *new_ops;
    ListCell   *largs_cell;
    ListCell   *rargs_cell;
    ListCell   *opnos_cell;
    ListCell   *collids_cell;

    /* We have to figure out (again) how the first col matches */
    var_on_left = match_index_to_operand((Node *) linitial(clause->largs),
                                         indexcol, index);
    Assert(var_on_left ||
           match_index_to_operand((Node *) linitial(clause->rargs),
                                  indexcol, index));
    *var_on_left_p = var_on_left;

    expr_op = linitial_oid(clause->opnos);
    if (!var_on_left)
        expr_op = get_commutator(expr_op);
    get_op_opfamily_properties(expr_op, index->opfamily[indexcol], false,
                               &op_strategy,
                               &op_lefttype,
                               &op_righttype);

    /* Initialize returned list of which index columns are used */
    *indexcolnos = list_make1_int(indexcol);

    /* Build lists of the opfamilies and operator datatypes in case needed */
    opfamilies = list_make1_oid(index->opfamily[indexcol]);
    lefttypes = list_make1_oid(op_lefttype);
    righttypes = list_make1_oid(op_righttype);

    /*
     * See how many of the remaining columns match some index column in the
     * same way.  As in match_clause_to_indexcol(), the "other" side of any
     * potential index condition is OK as long as it doesn't use Vars from the
     * indexed relation.
     */
    matching_cols = 1;
    largs_cell = lnext(list_head(clause->largs));
    rargs_cell = lnext(list_head(clause->rargs));
    opnos_cell = lnext(list_head(clause->opnos));
    collids_cell = lnext(list_head(clause->inputcollids));

    while (largs_cell != NULL)
    {
        Node       *varop;
        Node       *constop;
        int         i;

        expr_op = lfirst_oid(opnos_cell);
        if (var_on_left)
        {
            varop = (Node *) lfirst(largs_cell);
            constop = (Node *) lfirst(rargs_cell);
        }
        else
        {
            varop = (Node *) lfirst(rargs_cell);
            constop = (Node *) lfirst(largs_cell);
            /* indexkey is on right, so commute the operator */
            expr_op = get_commutator(expr_op);
            if (expr_op == InvalidOid)
                break;          /* operator is not usable */
        }
        if (bms_is_member(index->rel->relid, pull_varnos(constop)))
            break;              /* no good, Var on wrong side */
        if (contain_volatile_functions(constop))
            break;              /* no good, volatile comparison value */

        /*
         * The Var side can match any column of the index.
         */
        for (i = 0; i < index->ncolumns; i++)
        {
            if (match_index_to_operand(varop, i, index) &&
                get_op_opfamily_strategy(expr_op,
                                         index->opfamily[i]) == op_strategy &&
                IndexCollMatchesExprColl(index->indexcollations[i],
                                         lfirst_oid(collids_cell)))
                break;
        }
        if (i >= index->ncolumns)
            break;              /* no match found */

        /* Add column number to returned list */
        *indexcolnos = lappend_int(*indexcolnos, i);

        /* Add opfamily and datatypes to lists */
        get_op_opfamily_properties(expr_op, index->opfamily[i], false,
                                   &op_strategy,
                                   &op_lefttype,
                                   &op_righttype);
        opfamilies = lappend_oid(opfamilies, index->opfamily[i]);
        lefttypes = lappend_oid(lefttypes, op_lefttype);
        righttypes = lappend_oid(righttypes, op_righttype);

        /* This column matches, keep scanning */
        matching_cols++;
        largs_cell = lnext(largs_cell);
        rargs_cell = lnext(rargs_cell);
        opnos_cell = lnext(opnos_cell);
        collids_cell = lnext(collids_cell);
    }

    /* Return clause as-is if it's all usable as index quals */
    if (matching_cols == list_length(clause->opnos))
        return (Expr *) clause;

    /*
     * We have to generate a subset rowcompare (possibly just one OpExpr). The
     * painful part of this is changing < to <= or > to >=, so deal with that
     * first.
     */
    if (op_strategy == BTLessEqualStrategyNumber ||
        op_strategy == BTGreaterEqualStrategyNumber)
    {
        /* easy, just use the same operators */
        new_ops = list_truncate(list_copy(clause->opnos), matching_cols);
    }
    else
    {
        ListCell   *opfamilies_cell;
        ListCell   *lefttypes_cell;
        ListCell   *righttypes_cell;

        if (op_strategy == BTLessStrategyNumber)
            op_strategy = BTLessEqualStrategyNumber;
        else if (op_strategy == BTGreaterStrategyNumber)
            op_strategy = BTGreaterEqualStrategyNumber;
        else
            elog(ERROR, "unexpected strategy number %d", op_strategy);
        new_ops = NIL;
        lefttypes_cell = list_head(lefttypes);
        righttypes_cell = list_head(righttypes);
        foreach(opfamilies_cell, opfamilies)
        {
            Oid         opfam = lfirst_oid(opfamilies_cell);
            Oid         lefttype = lfirst_oid(lefttypes_cell);
            Oid         righttype = lfirst_oid(righttypes_cell);

            expr_op = get_opfamily_member(opfam, lefttype, righttype,
                                          op_strategy);
            if (!OidIsValid(expr_op))   /* should not happen */
                elog(ERROR, "could not find member %d(%u,%u) of opfamily %u",
                     op_strategy, lefttype, righttype, opfam);
            if (!var_on_left)
            {
                expr_op = get_commutator(expr_op);
                if (!OidIsValid(expr_op))       /* should not happen */
                    elog(ERROR, "could not find commutator of member %d(%u,%u) of opfamily %u",
                         op_strategy, lefttype, righttype, opfam);
            }
            new_ops = lappend_oid(new_ops, expr_op);
            lefttypes_cell = lnext(lefttypes_cell);
            righttypes_cell = lnext(righttypes_cell);
        }
    }

    /* If we have more than one matching col, create a subset rowcompare */
    if (matching_cols > 1)
    {
        RowCompareExpr *rc = makeNode(RowCompareExpr);

        if (var_on_left)
            rc->rctype = (RowCompareType) op_strategy;
        else
            rc->rctype = (op_strategy == BTLessEqualStrategyNumber) ?
                ROWCOMPARE_GE : ROWCOMPARE_LE;
        rc->opnos = new_ops;
        rc->opfamilies = list_truncate(list_copy(clause->opfamilies),
                                       matching_cols);
        rc->inputcollids = list_truncate(list_copy(clause->inputcollids),
                                         matching_cols);
        rc->largs = list_truncate((List *) copyObject(clause->largs),
                                  matching_cols);
        rc->rargs = list_truncate((List *) copyObject(clause->rargs),
                                  matching_cols);
        return (Expr *) rc;
    }
    else
    {
        return make_opclause(linitial_oid(new_ops), BOOLOID, false,
                             copyObject(linitial(clause->largs)),
                             copyObject(linitial(clause->rargs)),
                             InvalidOid,
                             linitial_oid(clause->inputcollids));
    }
}

/*
 * Given a fixed prefix that all the "leftop" values must have,
 * generate suitable indexqual condition(s).  opfamily is the index
 * operator family; we use it to deduce the appropriate comparison
 * operators and operand datatypes.  collation is the input collation to use.
 */
static List *
prefix_quals(Node *leftop, Oid opfamily, Oid collation,
             Const *prefix_const, Pattern_Prefix_Status pstatus)
{
    List       *result;
    Oid         datatype;
    Oid         oproid;
    Expr       *expr;
    FmgrInfo    ltproc;
    Const      *greaterstr;

    Assert(pstatus != Pattern_Prefix_None);

    switch (opfamily)
    {
        case TEXT_BTREE_FAM_OID:
        case TEXT_PATTERN_BTREE_FAM_OID:
        case TEXT_SPGIST_FAM_OID:
            datatype = TEXTOID;
            break;

        case BPCHAR_BTREE_FAM_OID:
        case BPCHAR_PATTERN_BTREE_FAM_OID:
            datatype = BPCHAROID;
            break;

        case NAME_BTREE_FAM_OID:
            datatype = NAMEOID;
            break;

        case BYTEA_BTREE_FAM_OID:
            datatype = BYTEAOID;
            break;

        default:
            /* shouldn't get here */
            elog(ERROR, "unexpected opfamily: %u", opfamily);
            return NIL;
    }

    /*
     * If necessary, coerce the prefix constant to the right type. The given
     * prefix constant is either text or bytea type.
     */
    if (prefix_const->consttype != datatype)
    {
        char       *prefix;

        switch (prefix_const->consttype)
        {
            case TEXTOID:
                prefix = TextDatumGetCString(prefix_const->constvalue);
                break;
            case BYTEAOID:
                prefix = DatumGetCString(DirectFunctionCall1(byteaout,
                                                  prefix_const->constvalue));
                break;
            default:
                elog(ERROR, "unexpected const type: %u",
                     prefix_const->consttype);
                return NIL;
        }
        prefix_const = string_to_const(prefix, datatype);
        pfree(prefix);
    }

    /*
     * If we found an exact-match pattern, generate an "=" indexqual.
     */
    if (pstatus == Pattern_Prefix_Exact)
    {
        oproid = get_opfamily_member(opfamily, datatype, datatype,
                                     BTEqualStrategyNumber);
        if (oproid == InvalidOid)
            elog(ERROR, "no = operator for opfamily %u", opfamily);
        expr = make_opclause(oproid, BOOLOID, false,
                             (Expr *) leftop, (Expr *) prefix_const,
                             InvalidOid, collation);
        result = list_make1(make_simple_restrictinfo(expr));
        return result;
    }

    /*
     * Otherwise, we have a nonempty required prefix of the values.
     *
     * We can always say "x >= prefix".
     */
    oproid = get_opfamily_member(opfamily, datatype, datatype,
                                 BTGreaterEqualStrategyNumber);
    if (oproid == InvalidOid)
        elog(ERROR, "no >= operator for opfamily %u", opfamily);
    expr = make_opclause(oproid, BOOLOID, false,
                         (Expr *) leftop, (Expr *) prefix_const,
                         InvalidOid, collation);
    result = list_make1(make_simple_restrictinfo(expr));

    /*-------
     * If we can create a string larger than the prefix, we can say
     * "x < greaterstr".  NB: we rely on make_greater_string() to generate
     * a guaranteed-greater string, not just a probably-greater string.
     * In general this is only guaranteed in C locale, so we'd better be
     * using a C-locale index collation.
     *-------
     */
    oproid = get_opfamily_member(opfamily, datatype, datatype,
                                 BTLessStrategyNumber);
    if (oproid == InvalidOid)
        elog(ERROR, "no < operator for opfamily %u", opfamily);
    fmgr_info(get_opcode(oproid), &ltproc);
    greaterstr = make_greater_string(prefix_const, &ltproc, collation);
    if (greaterstr)
    {
        expr = make_opclause(oproid, BOOLOID, false,
                             (Expr *) leftop, (Expr *) greaterstr,
                             InvalidOid, collation);
        result = lappend(result, make_simple_restrictinfo(expr));
    }

    return result;
}

/*
 * Given a leftop and a rightop, and a inet-family sup/sub operator,
 * generate suitable indexqual condition(s).  expr_op is the original
 * operator, and opfamily is the index opfamily.
 */
static List *
network_prefix_quals(Node *leftop, Oid expr_op, Oid opfamily, Datum rightop)
{
    bool        is_eq;
    Oid         datatype;
    Oid         opr1oid;
    Oid         opr2oid;
    Datum       opr1right;
    Datum       opr2right;
    List       *result;
    Expr       *expr;

    switch (expr_op)
    {
        case OID_INET_SUB_OP:
            datatype = INETOID;
            is_eq = false;
            break;
        case OID_INET_SUBEQ_OP:
            datatype = INETOID;
            is_eq = true;
            break;
        default:
            elog(ERROR, "unexpected operator: %u", expr_op);
            return NIL;
    }

    /*
     * create clause "key >= network_scan_first( rightop )", or ">" if the
     * operator disallows equality.
     */
    if (is_eq)
    {
        opr1oid = get_opfamily_member(opfamily, datatype, datatype,
                                      BTGreaterEqualStrategyNumber);
        if (opr1oid == InvalidOid)
            elog(ERROR, "no >= operator for opfamily %u", opfamily);
    }
    else
    {
        opr1oid = get_opfamily_member(opfamily, datatype, datatype,
                                      BTGreaterStrategyNumber);
        if (opr1oid == InvalidOid)
            elog(ERROR, "no > operator for opfamily %u", opfamily);
    }

    opr1right = network_scan_first(rightop);

    expr = make_opclause(opr1oid, BOOLOID, false,
                         (Expr *) leftop,
                         (Expr *) makeConst(datatype, -1,
                                            InvalidOid, /* not collatable */
                                            -1, opr1right,
                                            false, false),
                         InvalidOid, InvalidOid);
    result = list_make1(make_simple_restrictinfo(expr));

    /* create clause "key <= network_scan_last( rightop )" */

    opr2oid = get_opfamily_member(opfamily, datatype, datatype,
                                  BTLessEqualStrategyNumber);
    if (opr2oid == InvalidOid)
        elog(ERROR, "no <= operator for opfamily %u", opfamily);

    opr2right = network_scan_last(rightop);

    expr = make_opclause(opr2oid, BOOLOID, false,
                         (Expr *) leftop,
                         (Expr *) makeConst(datatype, -1,
                                            InvalidOid, /* not collatable */
                                            -1, opr2right,
                                            false, false),
                         InvalidOid, InvalidOid);
    result = lappend(result, make_simple_restrictinfo(expr));

    return result;
}

/*
 * Handy subroutines for match_special_index_operator() and friends.
 */

/*
 * Generate a Datum of the appropriate type from a C string.
 * Note that all of the supported types are pass-by-ref, so the
 * returned value should be pfree'd if no longer needed.
 */
static Datum
string_to_datum(const char *str, Oid datatype)
{
    /*
     * We cheat a little by assuming that CStringGetTextDatum() will do for
     * bpchar and varchar constants too...
     */
    if (datatype == NAMEOID)
        return DirectFunctionCall1(namein, CStringGetDatum(str));
    else if (datatype == BYTEAOID)
        return DirectFunctionCall1(byteain, CStringGetDatum(str));
    else
        return CStringGetTextDatum(str);
}

/*
 * Generate a Const node of the appropriate type from a C string.
 */
static Const *
string_to_const(const char *str, Oid datatype)
{
    Datum       conval = string_to_datum(str, datatype);
    Oid         collation;
    int         constlen;

    /*
     * We only need to support a few datatypes here, so hard-wire properties
     * instead of incurring the expense of catalog lookups.
     */
    switch (datatype)
    {
        case TEXTOID:
        case VARCHAROID:
        case BPCHAROID:
            collation = DEFAULT_COLLATION_OID;
            constlen = -1;
            break;

        case NAMEOID:
            collation = InvalidOid;
            constlen = NAMEDATALEN;
            break;

        case BYTEAOID:
            collation = InvalidOid;
            constlen = -1;
            break;

        default:
            elog(ERROR, "unexpected datatype in string_to_const: %u",
                 datatype);
            return NULL;
    }

    return makeConst(datatype, -1, collation, constlen,
                     conval, false, false);
}