/src/postgres/src/backend/optimizer/path/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) 1996-2025, 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/stratnum.h"
#include "access/sysattr.h"
#include "catalog/pg_am.h"
#include "catalog/pg_amop.h"
#include "catalog/pg_operator.h"
#include "catalog/pg_opfamily.h"
#include "catalog/pg_type.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "nodes/supportnodes.h"
#include "optimizer/cost.h"
#include "optimizer/optimizer.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/prep.h"
#include "optimizer/restrictinfo.h"
#include "utils/lsyscache.h"
#include "utils/selfuncs.h"


/* XXX see PartCollMatchesExprColl */
#define IndexCollMatchesExprColl(idxcollation, exprcollation) \
  ((idxcollation) == InvalidOid || (idxcollation) == (exprcollation))

/* 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 IndexClause nodes, one list 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 */
  bool    unclassifiable; /* has too many quals+preds to process? */
} 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 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,
                 ScanTypeControl scantype,
                 bool *skip_nonnative_saop);
static List *build_paths_for_OR(PlannerInfo *root, RelOptInfo *rel,
                List *clauses, List *other_clauses);
static List *generate_bitmap_or_paths(PlannerInfo *root, RelOptInfo *rel,
                    List *clauses, List *other_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 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, Index cur_relid, Relids outer_relids);
static double adjust_rowcount_for_semijoins(PlannerInfo *root,
                      Index cur_relid,
                      Index outer_relid,
                      double rowcount);
static double approximate_joinrel_size(PlannerInfo *root, Relids relids);
static void match_restriction_clauses_to_index(PlannerInfo *root,
                         IndexOptInfo *index,
                         IndexClauseSet *clauseset);
static void match_join_clauses_to_index(PlannerInfo *root,
                    RelOptInfo *rel, IndexOptInfo *index,
                    IndexClauseSet *clauseset,
                    List **joinorclauses);
static void match_eclass_clauses_to_index(PlannerInfo *root,
                      IndexOptInfo *index,
                      IndexClauseSet *clauseset);
static void match_clauses_to_index(PlannerInfo *root,
                   List *clauses,
                   IndexOptInfo *index,
                   IndexClauseSet *clauseset);
static void match_clause_to_index(PlannerInfo *root,
                  RestrictInfo *rinfo,
                  IndexOptInfo *index,
                  IndexClauseSet *clauseset);
static IndexClause *match_clause_to_indexcol(PlannerInfo *root,
                       RestrictInfo *rinfo,
                       int indexcol,
                       IndexOptInfo *index);
static bool IsBooleanOpfamily(Oid opfamily);
static IndexClause *match_boolean_index_clause(PlannerInfo *root,
                         RestrictInfo *rinfo,
                         int indexcol, IndexOptInfo *index);
static IndexClause *match_opclause_to_indexcol(PlannerInfo *root,
                         RestrictInfo *rinfo,
                         int indexcol,
                         IndexOptInfo *index);
static IndexClause *match_funcclause_to_indexcol(PlannerInfo *root,
                         RestrictInfo *rinfo,
                         int indexcol,
                         IndexOptInfo *index);
static IndexClause *get_index_clause_from_support(PlannerInfo *root,
                          RestrictInfo *rinfo,
                          Oid funcid,
                          int indexarg,
                          int indexcol,
                          IndexOptInfo *index);
static IndexClause *match_saopclause_to_indexcol(PlannerInfo *root,
                         RestrictInfo *rinfo,
                         int indexcol,
                         IndexOptInfo *index);
static IndexClause *match_rowcompare_to_indexcol(PlannerInfo *root,
                         RestrictInfo *rinfo,
                         int indexcol,
                         IndexOptInfo *index);
static IndexClause *match_orclause_to_indexcol(PlannerInfo *root,
                         RestrictInfo *rinfo,
                         int indexcol,
                         IndexOptInfo *index);
static IndexClause *expand_indexqual_rowcompare(PlannerInfo *root,
                        RestrictInfo *rinfo,
                        int indexcol,
                        IndexOptInfo *index,
                        Oid expr_op,
                        bool var_on_left);
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);


/*
 * 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_index_predicates() must have been run previously for this rel.
 *
 * Note: in cases involving LATERAL references in the relation's tlist, 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;
  IndexClauseSet rclauseset;
  IndexClauseSet jclauseset;
  IndexClauseSet eclauseset;
  ListCell   *lc;

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

  /* 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->nkeycolumns <= 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(root, 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,
                  &jclauseset, &joinorclauses);

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

    /* create a partial bitmap heap path */
    if (rel->consider_parallel && rel->lateral_relids == NULL)
      create_partial_bitmap_paths(root, rel, bitmapqual);
  }

  /*
   * 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     *all_path_outers;

    /* Identify each distinct parameterization seen in bitjoinpaths */
    all_path_outers = NIL;
    foreach(lc, bitjoinpaths)
    {
      Path     *path = (Path *) lfirst(lc);
      Relids    required_outer = PATH_REQ_OUTER(path);

      all_path_outers = list_append_unique(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;

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

        if (bms_is_subset(PATH_REQ_OUTER(path), 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 = PATH_REQ_OUTER(bitmapqual);
      loop_count = get_loop_count(root, rel->relid, required_outer);
      bpath = create_bitmap_heap_path(root, rel, bitmapqual,
                      required_outer, loop_count, 0);
      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->nkeycolumns; 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 IndexClauses 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)
  {
    IndexClause *iclause = (IndexClause *) lfirst(lc);
    Relids    clause_relids = iclause->rinfo->clause_relids;
    EquivalenceClass *parent_ec = iclause->rinfo->parent_ec;
    int     num_considered_relids;

    /* If we already tried its relids set, no need to do so again */
    if (list_member(*considered_relids, clause_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 appends entries to *considered_relids,
     * but we do not need to visit such newly-added entries within this
     * loop, so we don't use foreach() here.  No real harm would be done
     * if we did visit them, since the subset check would reject them; but
     * it would waste some cycles.
     */
    num_considered_relids = list_length(*considered_relids);
    for (int pos = 0; pos < num_considered_relids; pos++)
    {
      Relids    oldrelids = (Relids) list_nth(*considered_relids, pos);

      /*
       * 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 (parent_ec &&
        eclass_already_used(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 (list_member(*considered_relids, relids))
    return;

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

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

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

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

    /*
     * 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])
    {
      IndexClause *iclause = (IndexClause *) lfirst(lc);

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

    /* Add restriction clauses */
    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.
   */
  *considered_relids = lappend(*considered_relids, 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)
  {
    IndexClause *iclause = (IndexClause *) lfirst(lc);
    RestrictInfo *rinfo = iclause->rinfo;

    if (rinfo->parent_ec == parent_ec &&
      bms_is_subset(rinfo->clause_relids, oldrelids))
      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;
  bool    skip_nonnative_saop = false;
  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,
                   ST_ANYSCAN,
                   &skip_nonnative_saop);

  /*
   * 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 there were ScalarArrayOpExpr clauses that the index can't handle
   * natively, generate bitmap scan paths relying on executor-managed
   * ScalarArrayOpExpr.
   */
  if (skip_nonnative_saop)
  {
    indexpaths = build_index_paths(root, rel,
                     index, clauses,
                     false,
                     ST_BITMAPSCAN,
                     NULL);
    *bitindexpaths = list_concat(*bitindexpaths, indexpaths);
  }
}

/*
 * build_index_paths
 *    Given an index and a set of index clauses for it, construct zero
 *    or more IndexPaths. It also constructs zero or more partial 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.
 *
 * 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.
 *
 * If skip_nonnative_saop is non-NULL, we ignore ScalarArrayOpExpr clauses
 * unless the index AM supports them directly, and we set *skip_nonnative_saop
 * to true if we found any such clauses (caller must initialize the variable
 * to false).  If it's NULL, we do not ignore ScalarArrayOpExpr clauses.
 *
 * '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 (IndexClause nodes)
 * 'useful_predicate' indicates whether the index has a useful predicate
 * 'scantype' indicates whether we need plain or bitmap scan support
 * 'skip_nonnative_saop' indicates whether to accept SAOP if index AM doesn't
 */
static List *
build_index_paths(PlannerInfo *root, RelOptInfo *rel,
          IndexOptInfo *index, IndexClauseSet *clauses,
          bool useful_predicate,
          ScanTypeControl scantype,
          bool *skip_nonnative_saop)
{
  List     *result = NIL;
  IndexPath  *ipath;
  List     *index_clauses;
  Relids    outer_relids;
  double    loop_count;
  List     *orderbyclauses;
  List     *orderbyclausecols;
  List     *index_pathkeys;
  List     *useful_pathkeys;
  bool    pathkeys_possibly_useful;
  bool    index_is_ordered;
  bool    index_only_scan;
  int     indexcol;

  Assert(skip_nonnative_saop != NULL || scantype == ST_BITMAPSCAN);

  /*
   * 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. Combine the per-column IndexClause lists into an overall list.
   *
   * In the resulting list, 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 list can be empty, if the
   * index AM allows that.
   *
   * 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;
  outer_relids = bms_copy(rel->lateral_relids);
  for (indexcol = 0; indexcol < index->nkeycolumns; indexcol++)
  {
    ListCell   *lc;

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

      if (skip_nonnative_saop && !index->amsearcharray &&
        IsA(rinfo->clause, ScalarArrayOpExpr))
      {
        /*
         * Caller asked us to generate IndexPaths that omit any
         * ScalarArrayOpExpr clauses when the underlying index AM
         * lacks native support.
         *
         * We must omit this clause (and tell caller about it).
         */
        *skip_nonnative_saop = true;
        continue;
      }

      /* OK to include this clause */
      index_clauses = lappend(index_clauses, iclause);
      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);

  /* Compute loop_count for cost estimation purposes */
  loop_count = get_loop_count(root, rel->relid, 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.
   */
  pathkeys_possibly_useful = (scantype != ST_BITMAPSCAN &&
                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 or at
     * least some prefix thereof.  Matching to just a prefix of the
     * query_pathkeys will allow an incremental sort to be considered on
     * the index's partially sorted results.
     */
    match_pathkeys_to_index(index, root->query_pathkeys,
                &orderbyclauses,
                &orderbyclausecols);
    if (list_length(root->query_pathkeys) == list_length(orderbyclauses))
      useful_pathkeys = root->query_pathkeys;
    else
      useful_pathkeys = list_copy_head(root->query_pathkeys,
                       list_length(orderbyclauses));
  }
  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 (index_clauses != NIL || useful_pathkeys != NIL || useful_predicate ||
    index_only_scan)
  {
    ipath = create_index_path(root, index,
                  index_clauses,
                  orderbyclauses,
                  orderbyclausecols,
                  useful_pathkeys,
                  ForwardScanDirection,
                  index_only_scan,
                  outer_relids,
                  loop_count,
                  false);
    result = lappend(result, ipath);

    /*
     * If appropriate, consider parallel index scan.  We don't allow
     * parallel index scan for bitmap index scans.
     */
    if (index->amcanparallel &&
      rel->consider_parallel && outer_relids == NULL &&
      scantype != ST_BITMAPSCAN)
    {
      ipath = create_index_path(root, index,
                    index_clauses,
                    orderbyclauses,
                    orderbyclausecols,
                    useful_pathkeys,
                    ForwardScanDirection,
                    index_only_scan,
                    outer_relids,
                    loop_count,
                    true);

      /*
       * if, after costing the path, we find that it's not worth using
       * parallel workers, just free it.
       */
      if (ipath->path.parallel_workers > 0)
        add_partial_path(rel, (Path *) ipath);
      else
        pfree(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,
                    NIL,
                    NIL,
                    useful_pathkeys,
                    BackwardScanDirection,
                    index_only_scan,
                    outer_relids,
                    loop_count,
                    false);
      result = lappend(result, ipath);

      /* If appropriate, consider parallel index scan */
      if (index->amcanparallel &&
        rel->consider_parallel && outer_relids == NULL &&
        scantype != ST_BITMAPSCAN)
      {
        ipath = create_index_path(root, index,
                      index_clauses,
                      NIL,
                      NIL,
                      useful_pathkeys,
                      BackwardScanDirection,
                      index_only_scan,
                      outer_relids,
                      loop_count,
                      true);

        /*
         * if, after costing the path, we find that it's not worth
         * using parallel workers, just free it.
         */
        if (ipath->path.parallel_workers > 0)
          add_partial_path(rel, (Path *) ipath);
        else
          pfree(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_copy(clauses, other_clauses);

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

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

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

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

  return result;
}

/*
 * Utility structure used to group similar OR-clause arguments in
 * group_similar_or_args().  It represents information about the OR-clause
 * argument and its matching index key.
 */
typedef struct
{
  int     indexnum;   /* index of the matching index, or -1 if no
                 * matching index */
  int     colnum;     /* index of the matching column, or -1 if no
                 * matching index */
  Oid     opno;     /* OID of the OpClause operator, or InvalidOid
                 * if not an OpExpr */
  Oid     inputcollid;  /* OID of the OpClause input collation */
  int     argindex;   /* index of the clause in the list of
                 * arguments */
  int     groupindex;   /* value of argindex for the fist clause in
                 * the group of similar clauses */
} OrArgIndexMatch;

/*
 * Comparison function for OrArgIndexMatch which provides sort order placing
 * similar OR-clause arguments together.
 */
static int
or_arg_index_match_cmp(const void *a, const void *b)
{
  const OrArgIndexMatch *match_a = (const OrArgIndexMatch *) a;
  const OrArgIndexMatch *match_b = (const OrArgIndexMatch *) b;

  if (match_a->indexnum < match_b->indexnum)
    return -1;
  else if (match_a->indexnum > match_b->indexnum)
    return 1;

  if (match_a->colnum < match_b->colnum)
    return -1;
  else if (match_a->colnum > match_b->colnum)
    return 1;

  if (match_a->opno < match_b->opno)
    return -1;
  else if (match_a->opno > match_b->opno)
    return 1;

  if (match_a->inputcollid < match_b->inputcollid)
    return -1;
  else if (match_a->inputcollid > match_b->inputcollid)
    return 1;

  if (match_a->argindex < match_b->argindex)
    return -1;
  else if (match_a->argindex > match_b->argindex)
    return 1;

  return 0;
}

/*
 * Another comparison function for OrArgIndexMatch.  It sorts groups together
 * using groupindex.  The group items are then sorted by argindex.
 */
static int
or_arg_index_match_cmp_group(const void *a, const void *b)
{
  const OrArgIndexMatch *match_a = (const OrArgIndexMatch *) a;
  const OrArgIndexMatch *match_b = (const OrArgIndexMatch *) b;

  if (match_a->groupindex < match_b->groupindex)
    return -1;
  else if (match_a->groupindex > match_b->groupindex)
    return 1;

  if (match_a->argindex < match_b->argindex)
    return -1;
  else if (match_a->argindex > match_b->argindex)
    return 1;

  return 0;
}

/*
 * group_similar_or_args
 *    Transform incoming OR-restrictinfo into a list of sub-restrictinfos,
 *    each of them containing a subset of similar OR-clause arguments from
 *    the source rinfo.
 *
 * Similar OR-clause arguments are of the form "indexkey op constant" having
 * the same indexkey, operator, and collation.  Constant may comprise either
 * Const or Param.  It may be employed later, during the
 * match_clause_to_indexcol() to transform the whole OR-sub-rinfo to an SAOP
 * clause.
 *
 * Returns the processed list of OR-clause arguments.
 */
static List *
group_similar_or_args(PlannerInfo *root, RelOptInfo *rel, RestrictInfo *rinfo)
{
  int     n;
  int     i;
  int     group_start;
  OrArgIndexMatch *matches;
  bool    matched = false;
  ListCell   *lc;
  ListCell   *lc2;
  List     *orargs;
  List     *result = NIL;
  Index   relid = rel->relid;

  Assert(IsA(rinfo->orclause, BoolExpr));
  orargs = ((BoolExpr *) rinfo->orclause)->args;
  n = list_length(orargs);

  /*
   * To avoid N^2 behavior, take utility pass along the list of OR-clause
   * arguments.  For each argument, fill the OrArgIndexMatch structure,
   * which will be used to sort these arguments at the next step.
   */
  i = -1;
  matches = (OrArgIndexMatch *) palloc(sizeof(OrArgIndexMatch) * n);
  foreach(lc, orargs)
  {
    Node     *arg = lfirst(lc);
    RestrictInfo *argrinfo;
    OpExpr     *clause;
    Oid     opno;
    Node     *leftop,
           *rightop;
    Node     *nonConstExpr;
    int     indexnum;
    int     colnum;

    i++;
    matches[i].argindex = i;
    matches[i].groupindex = i;
    matches[i].indexnum = -1;
    matches[i].colnum = -1;
    matches[i].opno = InvalidOid;
    matches[i].inputcollid = InvalidOid;

    if (!IsA(arg, RestrictInfo))
      continue;

    argrinfo = castNode(RestrictInfo, arg);

    /* Only operator clauses can match  */
    if (!IsA(argrinfo->clause, OpExpr))
      continue;

    clause = (OpExpr *) argrinfo->clause;
    opno = clause->opno;

    /* Only binary operators can match  */
    if (list_length(clause->args) != 2)
      continue;

    /*
     * Ignore any RelabelType node above the operands.  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.
     */
    leftop = get_leftop(clause);
    if (IsA(leftop, RelabelType))
      leftop = (Node *) ((RelabelType *) leftop)->arg;

    rightop = get_rightop(clause);
    if (IsA(rightop, RelabelType))
      rightop = (Node *) ((RelabelType *) rightop)->arg;

    /*
     * Check for clauses of the form: (indexkey operator constant) or
     * (constant operator indexkey).  But we don't know a particular index
     * yet.  Therefore, we try to distinguish the potential index key and
     * constant first, then search for a matching index key among all
     * indexes.
     */
    if (bms_is_member(relid, argrinfo->right_relids) &&
      !bms_is_member(relid, argrinfo->left_relids) &&
      !contain_volatile_functions(leftop))
    {
      opno = get_commutator(opno);

      if (!OidIsValid(opno))
      {
        /* commutator doesn't exist, we can't reverse the order */
        continue;
      }
      nonConstExpr = rightop;
    }
    else if (bms_is_member(relid, argrinfo->left_relids) &&
         !bms_is_member(relid, argrinfo->right_relids) &&
         !contain_volatile_functions(rightop))
    {
      nonConstExpr = leftop;
    }
    else
    {
      continue;
    }

    /*
     * Match non-constant part to the index key.  It's possible that a
     * single non-constant part matches multiple index keys.  It's OK, we
     * just stop with first matching index key.  Given that this choice is
     * determined the same for every clause, we will group similar clauses
     * together anyway.
     */
    indexnum = 0;
    foreach(lc2, rel->indexlist)
    {
      IndexOptInfo *index = (IndexOptInfo *) lfirst(lc2);

      /*
       * Ignore index if it doesn't support bitmap scans or SAOP
       * clauses.
       */
      if (!index->amhasgetbitmap || !index->amsearcharray)
        continue;

      for (colnum = 0; colnum < index->nkeycolumns; colnum++)
      {
        if (match_index_to_operand(nonConstExpr, colnum, index))
        {
          matches[i].indexnum = indexnum;
          matches[i].colnum = colnum;
          matches[i].opno = opno;
          matches[i].inputcollid = clause->inputcollid;
          matched = true;
          break;
        }
      }

      /*
       * Stop looping through the indexes, if we managed to match
       * nonConstExpr to any index column.
       */
      if (matches[i].indexnum >= 0)
        break;
      indexnum++;
    }
  }

  /*
   * Fast-path check: if no clause is matching to the index column, we can
   * just give up at this stage and return the clause list as-is.
   */
  if (!matched)
  {
    pfree(matches);
    return orargs;
  }

  /*
   * Sort clauses to make similar clauses go together.  But at the same
   * time, we would like to change the order of clauses as little as
   * possible.  To do so, we reorder each group of similar clauses so that
   * the first item of the group stays in place, and all the other items are
   * moved after it.  So, if there are no similar clauses, the order of
   * clauses stays the same.  When there are some groups, required
   * reordering happens while the rest of the clauses remain in their
   * places.  That is achieved by assigning a 'groupindex' to each clause:
   * the number of the first item in the group in the original clause list.
   */
  qsort(matches, n, sizeof(OrArgIndexMatch), or_arg_index_match_cmp);

  /* Assign groupindex to the sorted clauses */
  for (i = 1; i < n; i++)
  {
    /*
     * When two clauses are similar and should belong to the same group,
     * copy the 'groupindex' from the previous clause.  Given we are
     * considering clauses in direct order, all the clauses would have a
     * 'groupindex' equal to the 'groupindex' of the first clause in the
     * group.
     */
    if (matches[i].indexnum == matches[i - 1].indexnum &&
      matches[i].colnum == matches[i - 1].colnum &&
      matches[i].opno == matches[i - 1].opno &&
      matches[i].inputcollid == matches[i - 1].inputcollid &&
      matches[i].indexnum != -1)
      matches[i].groupindex = matches[i - 1].groupindex;
  }

  /* Re-sort clauses first by groupindex then by argindex */
  qsort(matches, n, sizeof(OrArgIndexMatch), or_arg_index_match_cmp_group);

  /*
   * Group similar clauses into single sub-restrictinfo. Side effect: the
   * resulting list of restrictions will be sorted by indexnum and colnum.
   */
  group_start = 0;
  for (i = 1; i <= n; i++)
  {
    /* Check if it's a group boundary */
    if (group_start >= 0 &&
      (i == n ||
       matches[i].indexnum != matches[group_start].indexnum ||
       matches[i].colnum != matches[group_start].colnum ||
       matches[i].opno != matches[group_start].opno ||
       matches[i].inputcollid != matches[group_start].inputcollid ||
       matches[i].indexnum == -1))
    {
      /*
       * One clause in group: add it "as is" to the upper-level OR.
       */
      if (i - group_start == 1)
      {
        result = lappend(result,
                 list_nth(orargs,
                      matches[group_start].argindex));
      }
      else
      {
        /*
         * Two or more clauses in a group: create a nested OR.
         */
        List     *args = NIL;
        List     *rargs = NIL;
        RestrictInfo *subrinfo;
        int     j;

        Assert(i - group_start >= 2);

        /* Construct the list of nested OR arguments */
        for (j = group_start; j < i; j++)
        {
          Node     *arg = list_nth(orargs, matches[j].argindex);

          rargs = lappend(rargs, arg);
          if (IsA(arg, RestrictInfo))
            args = lappend(args, ((RestrictInfo *) arg)->clause);
          else
            args = lappend(args, arg);
        }

        /* Construct the nested OR and wrap it with RestrictInfo */
        subrinfo = make_plain_restrictinfo(root,
                           make_orclause(args),
                           make_orclause(rargs),
                           rinfo->is_pushed_down,
                           rinfo->has_clone,
                           rinfo->is_clone,
                           rinfo->pseudoconstant,
                           rinfo->security_level,
                           rinfo->required_relids,
                           rinfo->incompatible_relids,
                           rinfo->outer_relids);
        result = lappend(result, subrinfo);
      }

      group_start = i;
    }
  }
  pfree(matches);
  return result;
}

/*
 * make_bitmap_paths_for_or_group
 *    Generate bitmap paths for a group of similar OR-clause arguments
 *    produced by group_similar_or_args().
 *
 * This function considers two cases: (1) matching a group of clauses to
 * the index as a whole, and (2) matching the individual clauses one-by-one.
 * (1) typically comprises an optimal solution.  If not, (2) typically
 * comprises fair alternative.
 *
 * Ideally, we could consider all arbitrary splits of arguments into
 * subgroups, but that could lead to unacceptable computational complexity.
 * This is why we only consider two cases of above.
 */
static List *
make_bitmap_paths_for_or_group(PlannerInfo *root, RelOptInfo *rel,
                 RestrictInfo *ri, List *other_clauses)
{
  List     *jointlist = NIL;
  List     *splitlist = NIL;
  ListCell   *lc;
  List     *orargs;
  List     *args = ((BoolExpr *) ri->orclause)->args;
  Cost    jointcost = 0.0,
        splitcost = 0.0;
  Path     *bitmapqual;
  List     *indlist;

  /*
   * First, try to match the whole group to the one index.
   */
  orargs = list_make1(ri);
  indlist = build_paths_for_OR(root, rel,
                 orargs,
                 other_clauses);
  if (indlist != NIL)
  {
    bitmapqual = choose_bitmap_and(root, rel, indlist);
    jointcost = bitmapqual->total_cost;
    jointlist = list_make1(bitmapqual);
  }

  /*
   * If we manage to find a bitmap scan, which uses the group of OR-clause
   * arguments as a whole, we can skip matching OR-clause arguments
   * one-by-one as long as there are no other clauses, which can bring more
   * efficiency to one-by-one case.
   */
  if (jointlist != NIL && other_clauses == NIL)
    return jointlist;

  /*
   * Also try to match all containing clauses one-by-one.
   */
  foreach(lc, args)
  {
    orargs = list_make1(lfirst(lc));

    indlist = build_paths_for_OR(root, rel,
                   orargs,
                   other_clauses);

    if (indlist == NIL)
    {
      splitlist = NIL;
      break;
    }

    bitmapqual = choose_bitmap_and(root, rel, indlist);
    splitcost += bitmapqual->total_cost;
    splitlist = lappend(splitlist, bitmapqual);
  }

  /*
   * Pick the best option.
   */
  if (splitlist == NIL)
    return jointlist;
  else if (jointlist == NIL)
    return splitlist;
  else
    return (jointcost < splitcost) ? jointlist : splitlist;
}


/*
 * 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.)
 */
static List *
generate_bitmap_or_paths(PlannerInfo *root, RelOptInfo *rel,
             List *clauses, List *other_clauses)
{
  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_copy(clauses, other_clauses);

  foreach(lc, clauses)
  {
    RestrictInfo *rinfo = lfirst_node(RestrictInfo, lc);
    List     *pathlist;
    Path     *bitmapqual;
    ListCell   *j;
    List     *groupedArgs;
    List     *inner_other_clauses = NIL;

    /* 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;

    /*
     * Group the similar OR-clause arguments into dedicated RestrictInfos,
     * because each of those RestrictInfos has a chance to match the index
     * as a whole.
     */
    groupedArgs = group_similar_or_args(root, rel, rinfo);

    if (groupedArgs != ((BoolExpr *) rinfo->orclause)->args)
    {
      /*
       * Some parts of the rinfo were probably grouped.  In this case,
       * we have a set of sub-rinfos that together are an exact
       * duplicate of rinfo.  Thus, we need to remove the rinfo from
       * other clauses. match_clauses_to_index detects duplicated
       * iclauses by comparing pointers to original rinfos that would be
       * different.  So, we must delete rinfo to avoid de-facto
       * duplicated clauses in the index clauses list.
       */
      inner_other_clauses = list_delete(list_copy(all_clauses), rinfo);
    }

    foreach(j, groupedArgs)
    {
      Node     *orarg = (Node *) lfirst(j);
      List     *indlist;

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

        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));
      }
      else if (restriction_is_or_clause(castNode(RestrictInfo, orarg)))
      {
        RestrictInfo *ri = castNode(RestrictInfo, orarg);

        /*
         * Generate bitmap paths for the group of similar OR-clause
         * arguments.
         */
        indlist = make_bitmap_paths_for_or_group(root,
                             rel, ri,
                             inner_other_clauses);

        if (indlist == NIL)
        {
          pathlist = NIL;
          break;
        }
        else
        {
          pathlist = list_concat(pathlist, indlist);
          continue;
        }
      }
      else
      {
        RestrictInfo *ri = castNode(RestrictInfo, orarg);
        List     *orargs;

        orargs = list_make1(ri);

        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 (inner_other_clauses != NIL)
      list_free(inner_other_clauses);

    /*
     * 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;
}


/*
 * 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
   * extract_restriction_or_clauses 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);

    /* If it's unclassifiable, treat it as distinct from all others */
    if (pathinfo->unclassifiable)
    {
      pathinfoarray[npaths++] = pathinfo;
      continue;
    }

    for (i = 0; i < npaths; i++)
    {
      if (!pathinfoarray[i]->unclassifiable &&
        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.
   *
   * Note: paths that are either clauseless or unclassifiable will have
   * empty clauseids, so that they will not be rejected by the clauseids
   * filter here, nor will they cause later paths to be rejected by it.
   */
  for (i = 0; i < npaths; i++)
  {
    Cost    costsofar;
    List     *qualsofar;
    Bitmapset  *clauseidsofar;

    pathinfo = pathinfoarray[i];
    paths = list_make1(pathinfo->path);
    costsofar = bitmap_scan_cost_est(root, rel, pathinfo->path);
    qualsofar = list_concat_copy(pathinfo->quals, pathinfo->preds);
    clauseidsofar = bms_copy(pathinfo->clauseids);

    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, false))
          {
            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, pathinfo->quals);
        qualsofar = list_concat(qualsofar, pathinfo->preds);
        clauseidsofar = bms_add_members(clauseidsofar,
                        pathinfo->clauseids);
      }
      else
      {
        /* reject new path, remove it from paths list */
        paths = list_truncate(paths, list_length(paths) - 1);
      }
    }

    /* 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 (which could be a BitmapAnd or BitmapOr node).
 */
static Cost
bitmap_scan_cost_est(PlannerInfo *root, RelOptInfo *rel, Path *ipath)
{
  BitmapHeapPath bpath;

  /* Set up a dummy BitmapHeapPath */
  bpath.path.type = T_BitmapHeapPath;
  bpath.path.pathtype = T_BitmapHeapScan;
  bpath.path.parent = rel;
  bpath.path.pathtarget = rel->reltarget;
  bpath.path.param_info = ipath->param_info;
  bpath.path.pathkeys = NIL;
  bpath.bitmapqual = ipath;

  /*
   * Check the cost of temporary path without considering parallelism.
   * Parallel bitmap heap path will be considered at later stage.
   */
  bpath.path.parallel_workers = 0;

  /* Now we can do cost_bitmap_heap_scan */
  cost_bitmap_heap_scan(&bpath.path, root, rel,
              bpath.path.param_info,
              ipath,
              get_loop_count(root, rel->relid,
                     PATH_REQ_OUTER(ipath)));

  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;

  /*
   * Might as well build a real BitmapAndPath here, as the work is slightly
   * too complicated to be worth repeating just to save one palloc.
   */
  apath = create_bitmap_and_path(root, rel, paths);

  return bitmap_scan_cost_est(root, rel, (Path *) apath);
}


/*
 * 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);

  /*
   * Some machine-generated queries have outlandish numbers of qual clauses.
   * To avoid getting into O(N^2) behavior even in this preliminary
   * classification step, we want to limit the number of entries we can
   * accumulate in *clauselist.  Treat any path with more than 100 quals +
   * preds as unclassifiable, which will cause calling code to consider it
   * distinct from all other paths.
   */
  if (list_length(result->quals) + list_length(result->preds) > 100)
  {
    result->clauseids = NULL;
    result->unclassifiable = true;
    return result;
  }

  /* 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;
  result->unclassifiable = false;

  return result;
}


/*
 * find_indexpath_quals
 *
 * Given the Path structure for a plain or bitmap indexscan, extract lists
 * of all the index clauses 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).
 *
 * Note 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;
    ListCell   *l;

    foreach(l, ipath->indexclauses)
    {
      IndexClause *iclause = (IndexClause *) lfirst(l);

      *quals = lappend(*quals, iclause->rinfo->clause);
    }
    *preds = list_concat(*preds, 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_canreturn_attrs = NULL;
  ListCell   *lc;
  int     i;

  /* Index-only scans must be enabled */
  if (!enable_indexonlyscan)
    return false;

  /*
   * Check that all needed attributes of the relation are available from the
   * index.
   */

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

  /*
   * Add all the attributes used by restriction clauses; but consider only
   * those clauses not implied by the index predicate, since ones that are
   * so implied don't need to be checked explicitly in the plan.
   *
   * Note: attributes used only in index quals would not be needed at
   * runtime either, if we are certain that the index is not lossy.  However
   * it'd be complicated to account for that accurately, and it doesn't
   * matter in most cases, since we'd conclude that such attributes are
   * available from the index anyway.
   */
  foreach(lc, index->indrestrictinfo)
  {
    RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

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

  /*
   * Construct a bitmapset of columns that the index can return back in an
   * index-only scan.
   */
  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;

    if (index->canreturn[i])
      index_canreturn_attrs =
        bms_add_member(index_canreturn_attrs,
                 attno - FirstLowInvalidHeapAttributeNumber);
  }

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

  bms_free(attrs_used);
  bms_free(index_canreturn_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.
 *
 * In addition, we check to see if the other side of each join clause is on
 * the inside of some semijoin that the current relation is on the outside of.
 * If so, the only way that a parameterized path could be used is if the
 * semijoin RHS has been unique-ified, so we should use the number of unique
 * RHS rows rather than using the relation's raw rowcount.
 *
 * 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, Index cur_relid, Relids outer_relids)
{
  double    result;
  int     outer_relid;

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

  result = 0.0;
  outer_relid = -1;
  while ((outer_relid = bms_next_member(outer_relids, outer_relid)) >= 0)
  {
    RelOptInfo *outer_rel;
    double    rowcount;

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

    /* Check to see if rel is on the inside of any semijoins */
    rowcount = adjust_rowcount_for_semijoins(root,
                         cur_relid,
                         outer_relid,
                         outer_rel->rows);

    /* Remember smallest row count estimate among the outer rels */
    if (result == 0.0 || result > rowcount)
      result = rowcount;
  }
  /* Return 1.0 if we found no valid relations (shouldn't happen) */
  return (result > 0.0) ? result : 1.0;
}

/*
 * Check to see if outer_relid is on the inside of any semijoin that cur_relid
 * is on the outside of.  If so, replace rowcount with the estimated number of
 * unique rows from the semijoin RHS (assuming that's smaller, which it might
 * not be).  The estimate is crude but it's the best we can do at this stage
 * of the proceedings.
 */
static double
adjust_rowcount_for_semijoins(PlannerInfo *root,
                Index cur_relid,
                Index outer_relid,
                double rowcount)
{
  ListCell   *lc;

  foreach(lc, root->join_info_list)
  {
    SpecialJoinInfo *sjinfo = (SpecialJoinInfo *) lfirst(lc);

    if (sjinfo->jointype == JOIN_SEMI &&
      bms_is_member(cur_relid, sjinfo->syn_lefthand) &&
      bms_is_member(outer_relid, sjinfo->syn_righthand))
    {
      /* Estimate number of unique-ified rows */
      double    nraw;
      double    nunique;

      nraw = approximate_joinrel_size(root, sjinfo->syn_righthand);
      nunique = estimate_num_groups(root,
                      sjinfo->semi_rhs_exprs,
                      nraw,
                      NULL,
                      NULL);
      if (rowcount > nunique)
        rowcount = nunique;
    }
  }
  return rowcount;
}

/*
 * Make an approximate estimate of the size of a joinrel.
 *
 * We don't have enough info at this point to get a good estimate, so we
 * just multiply the base relation sizes together.  Fortunately, this is
 * the right answer anyway for the most common case with a single relation
 * on the RHS of a semijoin.  Also, estimate_num_groups() has only a weak
 * dependency on its input_rows argument (it basically uses it as a clamp).
 * So we might be able to get a fairly decent end result even with a severe
 * overestimate of the RHS's raw size.
 */
static double
approximate_joinrel_size(PlannerInfo *root, Relids relids)
{
  double    rowcount = 1.0;
  int     relid;

  relid = -1;
  while ((relid = bms_next_member(relids, relid)) >= 0)
  {
    RelOptInfo *rel;

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

    /* Relation could be proven empty, if so ignore */
    if (IS_DUMMY_REL(rel))
      continue;

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

    /* Accumulate product */
    rowcount *= rel->rows;
  }
  return rowcount;
}


/****************************************************************************
 *        ----  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(PlannerInfo *root,
                   IndexOptInfo *index,
                   IndexClauseSet *clauseset)
{
  /* We can ignore clauses that are implied by the index predicate */
  match_clauses_to_index(root, index->indrestrictinfo, index, 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.
 *    They also might be processed by match_clause_to_index() as a whole.
 */
static void
match_join_clauses_to_index(PlannerInfo *root,
              RelOptInfo *rel, IndexOptInfo *index,
              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))
      continue;

    /*
     * Potentially usable, so see if it matches the index or is an OR. Use
     * list_append_unique_ptr() here to avoid possible duplicates when
     * processing the same clauses with different indexes.
     */
    if (restriction_is_or_clause(rinfo))
      *joinorclauses = list_append_unique_ptr(*joinorclauses, rinfo);

    match_clause_to_index(root, rinfo, index, 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,
                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->nkeycolumns; 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,
                             &arg,
                             index->rel->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(root, clauses, index, 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(PlannerInfo *root,
             List *clauses,
             IndexOptInfo *index,
             IndexClauseSet *clauseset)
{
  ListCell   *lc;

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

    match_clause_to_index(root, rinfo, index, clauseset);
  }
}

/*
 * match_clause_to_index
 *    Test whether a qual clause can be used with an index.
 *
 * If the clause is usable, add an IndexClause entry for 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(PlannerInfo *root,
            RestrictInfo *rinfo,
            IndexOptInfo *index,
            IndexClauseSet *clauseset)
{
  int     indexcol;

  /*
   * Never match pseudoconstants to indexes.  (Normally a match 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;

  /*
   * If clause can't be used as an indexqual because it must wait till after
   * some lower-security-level restriction clause, reject it.
   */
  if (!restriction_is_securely_promotable(rinfo, index->rel))
    return;

  /* OK, check each index key column for a match */
  for (indexcol = 0; indexcol < index->nkeycolumns; indexcol++)
  {
    IndexClause *iclause;
    ListCell   *lc;

    /* Ignore duplicates */
    foreach(lc, clauseset->indexclauses[indexcol])
    {
      iclause = (IndexClause *) lfirst(lc);

      if (iclause->rinfo == rinfo)
        return;
    }

    /* OK, try to match the clause to the index column */
    iclause = match_clause_to_indexcol(root,
                       rinfo,
                       indexcol,
                       index);
    if (iclause)
    {
      /* Success, so record it */
      clauseset->indexclauses[indexcol] =
        lappend(clauseset->indexclauses[indexcol], iclause);
      clauseset->nonempty = true;
      return;
    }
  }
}

/*
 * match_clause_to_indexcol()
 *    Determine whether a restriction clause matches a column of an index,
 *    and if so, build an IndexClause node describing the details.
 *
 *    To match an index normally, an operator clause:
 *
 *    (1)  must be in the form (indexkey op const) or (const op indexkey);
 *       and
 *    (2)  must contain an operator which is in the index's operator family
 *       for this column; 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 handle that by generating an IndexClause with the correctly-commuted
 *    opclause as a derived indexqual.
 *
 *    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).
 *
 *    It is also possible to match ScalarArrayOpExpr clauses to indexes, when
 *    the clause is of the form "indexkey op ANY (arrayconst)".
 *
 *    It is also possible to match a list of OR clauses if it might be
 *    transformed into a single ScalarArrayOpExpr clause.  On success,
 *    the returning index clause will contain a transformed clause.
 *
 *    For boolean indexes, it is also possible to match the clause directly
 *    to the indexkey; or perhaps the clause is (NOT indexkey).
 *
 *    And, last but not least, some operators and functions can be processed
 *    to derive (typically lossy) indexquals from a clause that isn't in
 *    itself indexable.  If we see that any operand of an OpExpr or FuncExpr
 *    matches the index key, and the function has a planner support function
 *    attached to it, we'll invoke the support function to see if such an
 *    indexqual can be built.
 *
 * 'rinfo' is the clause to be tested (as a RestrictInfo node).
 * 'indexcol' is a column number of 'index' (counting from 0).
 * 'index' is the index of interest.
 *
 * Returns an IndexClause if the clause can be used with this index key,
 * or NULL if not.
 *
 * NOTE:  This routine always returns NULL if the clause is an AND clause.
 * Higher-level routines deal with OR and AND clauses. OR clause can be
 * matched as a whole by match_orclause_to_indexcol() though.
 */
static IndexClause *
match_clause_to_indexcol(PlannerInfo *root,
             RestrictInfo *rinfo,
             int indexcol,
             IndexOptInfo *index)
{
  IndexClause *iclause;
  Expr     *clause = rinfo->clause;
  Oid     opfamily;

  Assert(indexcol < index->nkeycolumns);

  /*
   * Historically this code has coped with NULL clauses.  That's probably
   * not possible anymore, but we might as well continue to cope.
   */
  if (clause == NULL)
    return NULL;

  /* First check for boolean-index cases. */
  opfamily = index->opfamily[indexcol];
  if (IsBooleanOpfamily(opfamily))
  {
    iclause = match_boolean_index_clause(root, rinfo, indexcol, index);
    if (iclause)
      return iclause;
  }

  /*
   * Clause must be an opclause, funcclause, ScalarArrayOpExpr,
   * RowCompareExpr, or OR-clause that could be converted to SAOP.  Or, if
   * the index supports it, we can handle IS NULL/NOT NULL clauses.
   */
  if (IsA(clause, OpExpr))
  {
    return match_opclause_to_indexcol(root, rinfo, indexcol, index);
  }
  else if (IsA(clause, FuncExpr))
  {
    return match_funcclause_to_indexcol(root, rinfo, indexcol, index);
  }
  else if (IsA(clause, ScalarArrayOpExpr))
  {
    return match_saopclause_to_indexcol(root, rinfo, indexcol, index);
  }
  else if (IsA(clause, RowCompareExpr))
  {
    return match_rowcompare_to_indexcol(root, rinfo, indexcol, index);
  }
  else if (restriction_is_or_clause(rinfo))
  {
    return match_orclause_to_indexcol(root, rinfo, indexcol, index);
  }
  else if (index->amsearchnulls && IsA(clause, NullTest))
  {
    NullTest   *nt = (NullTest *) clause;

    if (!nt->argisrow &&
      match_index_to_operand((Node *) nt->arg, indexcol, index))
    {
      iclause = makeNode(IndexClause);
      iclause->rinfo = rinfo;
      iclause->indexquals = list_make1(rinfo);
      iclause->lossy = false;
      iclause->indexcol = indexcol;
      iclause->indexcols = NIL;
      return iclause;
    }
  }

  return NULL;
}

/*
 * IsBooleanOpfamily
 *    Detect whether an opfamily supports boolean equality as an operator.
 *
 * If the opfamily OID is in the range of built-in objects, we can rely
 * on hard-wired knowledge of which built-in opfamilies support this.
 * For extension opfamilies, there's no choice but to do a catcache lookup.
 */
static bool
IsBooleanOpfamily(Oid opfamily)
{
  if (opfamily < FirstNormalObjectId)
    return IsBuiltinBooleanOpfamily(opfamily);
  else
    return op_in_opfamily(BooleanEqualOperator, opfamily);
}

/*
 * match_boolean_index_clause
 *    Recognize restriction clauses that can be matched to a boolean index.
 *
 * The idea here is that, for an index on a boolean column that supports the
 * BooleanEqualOperator, we can transform a plain reference to the indexkey
 * into "indexkey = true", or "NOT indexkey" into "indexkey = false", etc,
 * so as to make the expression indexable using the index's "=" operator.
 * Since Postgres 8.1, we must do this because constant simplification does
 * the reverse transformation; without this code there'd be no way to use
 * such an index at all.
 *
 * 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, and if so, build a suitable IndexClause.
 */
static IndexClause *
match_boolean_index_clause(PlannerInfo *root,
               RestrictInfo *rinfo,
               int indexcol,
               IndexOptInfo *index)
{
  Node     *clause = (Node *) rinfo->clause;
  Expr     *op = NULL;

  /* Direct match? */
  if (match_index_to_operand(clause, indexcol, index))
  {
    /* convert to indexkey = TRUE */
    op = make_opclause(BooleanEqualOperator, BOOLOID, false,
               (Expr *) clause,
               (Expr *) makeBoolConst(true, false),
               InvalidOid, InvalidOid);
  }
  /* NOT clause? */
  else if (is_notclause(clause))
  {
    Node     *arg = (Node *) get_notclausearg((Expr *) clause);

    if (match_index_to_operand(arg, indexcol, index))
    {
      /* convert to indexkey = FALSE */
      op = make_opclause(BooleanEqualOperator, BOOLOID, false,
                 (Expr *) arg,
                 (Expr *) makeBoolConst(false, false),
                 InvalidOid, InvalidOid);
    }
  }

  /*
   * 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;
    Node     *arg = (Node *) btest->arg;

    if (btest->booltesttype == IS_TRUE &&
      match_index_to_operand(arg, indexcol, index))
    {
      /* convert to indexkey = TRUE */
      op = make_opclause(BooleanEqualOperator, BOOLOID, false,
                 (Expr *) arg,
                 (Expr *) makeBoolConst(true, false),
                 InvalidOid, InvalidOid);
    }
    else if (btest->booltesttype == IS_FALSE &&
         match_index_to_operand(arg, indexcol, index))
    {
      /* convert to indexkey = FALSE */
      op = make_opclause(BooleanEqualOperator, BOOLOID, false,
                 (Expr *) arg,
                 (Expr *) makeBoolConst(false, false),
                 InvalidOid, InvalidOid);
    }
  }

  /*
   * If we successfully made an operator clause from the given qual, we must
   * wrap it in an IndexClause.  It's not lossy.
   */
  if (op)
  {
    IndexClause *iclause = makeNode(IndexClause);

    iclause->rinfo = rinfo;
    iclause->indexquals = list_make1(make_simple_restrictinfo(root, op));
    iclause->lossy = false;
    iclause->indexcol = indexcol;
    iclause->indexcols = NIL;
    return iclause;
  }

  return NULL;
}

/*
 * match_opclause_to_indexcol()
 *    Handles the OpExpr case for match_clause_to_indexcol(),
 *    which see for comments.
 */
static IndexClause *
match_opclause_to_indexcol(PlannerInfo *root,
               RestrictInfo *rinfo,
               int indexcol,
               IndexOptInfo *index)
{
  IndexClause *iclause;
  OpExpr     *clause = (OpExpr *) rinfo->clause;
  Node     *leftop,
         *rightop;
  Oid     expr_op;
  Oid     expr_coll;
  Index   index_relid;
  Oid     opfamily;
  Oid     idxcollation;

  /*
   * Only binary operators need apply.  (In theory, a planner support
   * function could do something with a unary operator, but it seems
   * unlikely to be worth the cycles to check.)
   */
  if (list_length(clause->args) != 2)
    return NULL;

  leftop = (Node *) linitial(clause->args);
  rightop = (Node *) lsecond(clause->args);
  expr_op = clause->opno;
  expr_coll = clause->inputcollid;

  index_relid = index->rel->relid;
  opfamily = index->opfamily[indexcol];
  idxcollation = index->indexcollations[indexcol];

  /*
   * Check for clauses of the form: (indexkey operator constant) or
   * (constant operator indexkey).  See match_clause_to_indexcol's notes
   * about const-ness.
   *
   * Note that we don't ask the support function about clauses that don't
   * have one of these forms.  Again, in principle it might be possible to
   * do something, but it seems unlikely to be worth the cycles to check.
   */
  if (match_index_to_operand(leftop, indexcol, index) &&
    !bms_is_member(index_relid, rinfo->right_relids) &&
    !contain_volatile_functions(rightop))
  {
    if (IndexCollMatchesExprColl(idxcollation, expr_coll) &&
      op_in_opfamily(expr_op, opfamily))
    {
      iclause = makeNode(IndexClause);
      iclause->rinfo = rinfo;
      iclause->indexquals = list_make1(rinfo);
      iclause->lossy = false;
      iclause->indexcol = indexcol;
      iclause->indexcols = NIL;
      return iclause;
    }

    /*
     * If we didn't find a member of the index's opfamily, try the support
     * function for the operator's underlying function.
     */
    set_opfuncid(clause); /* make sure we have opfuncid */
    return get_index_clause_from_support(root,
                       rinfo,
                       clause->opfuncid,
                       0, /* indexarg on left */
                       indexcol,
                       index);
  }

  if (match_index_to_operand(rightop, indexcol, index) &&
    !bms_is_member(index_relid, rinfo->left_relids) &&
    !contain_volatile_functions(leftop))
  {
    if (IndexCollMatchesExprColl(idxcollation, expr_coll))
    {
      Oid     comm_op = get_commutator(expr_op);

      if (OidIsValid(comm_op) &&
        op_in_opfamily(comm_op, opfamily))
      {
        RestrictInfo *commrinfo;

        /* Build a commuted OpExpr and RestrictInfo */
        commrinfo = commute_restrictinfo(rinfo, comm_op);

        /* Make an IndexClause showing that as a derived qual */
        iclause = makeNode(IndexClause);
        iclause->rinfo = rinfo;
        iclause->indexquals = list_make1(commrinfo);
        iclause->lossy = false;
        iclause->indexcol = indexcol;
        iclause->indexcols = NIL;
        return iclause;
      }
    }

    /*
     * If we didn't find a member of the index's opfamily, try the support
     * function for the operator's underlying function.
     */
    set_opfuncid(clause); /* make sure we have opfuncid */
    return get_index_clause_from_support(root,
                       rinfo,
                       clause->opfuncid,
                       1, /* indexarg on right */
                       indexcol,
                       index);
  }

  return NULL;
}

/*
 * match_funcclause_to_indexcol()
 *    Handles the FuncExpr case for match_clause_to_indexcol(),
 *    which see for comments.
 */
static IndexClause *
match_funcclause_to_indexcol(PlannerInfo *root,
               RestrictInfo *rinfo,
               int indexcol,
               IndexOptInfo *index)
{
  FuncExpr   *clause = (FuncExpr *) rinfo->clause;
  int     indexarg;
  ListCell   *lc;

  /*
   * We have no built-in intelligence about function clauses, but if there's
   * a planner support function, it might be able to do something.  But, to
   * cut down on wasted planning cycles, only call the support function if
   * at least one argument matches the target index column.
   *
   * Note that we don't insist on the other arguments being pseudoconstants;
   * the support function has to check that.  This is to allow cases where
   * only some of the other arguments need to be included in the indexqual.
   */
  indexarg = 0;
  foreach(lc, clause->args)
  {
    Node     *op = (Node *) lfirst(lc);

    if (match_index_to_operand(op, indexcol, index))
    {
      return get_index_clause_from_support(root,
                         rinfo,
                         clause->funcid,
                         indexarg,
                         indexcol,
                         index);
    }

    indexarg++;
  }

  return NULL;
}

/*
 * get_index_clause_from_support()
 *    If the function has a planner support function, try to construct
 *    an IndexClause using indexquals created by the support function.
 */
static IndexClause *
get_index_clause_from_support(PlannerInfo *root,
                RestrictInfo *rinfo,
                Oid funcid,
                int indexarg,
                int indexcol,
                IndexOptInfo *index)
{
  Oid     prosupport = get_func_support(funcid);
  SupportRequestIndexCondition req;
  List     *sresult;

  if (!OidIsValid(prosupport))
    return NULL;

  req.type = T_SupportRequestIndexCondition;
  req.root = root;
  req.funcid = funcid;
  req.node = (Node *) rinfo->clause;
  req.indexarg = indexarg;
  req.index = index;
  req.indexcol = indexcol;
  req.opfamily = index->opfamily[indexcol];
  req.indexcollation = index->indexcollations[indexcol];

  req.lossy = true;     /* default assumption */

  sresult = (List *)
    DatumGetPointer(OidFunctionCall1(prosupport,
                     PointerGetDatum(&req)));

  if (sresult != NIL)
  {
    IndexClause *iclause = makeNode(IndexClause);
    List     *indexquals = NIL;
    ListCell   *lc;

    /*
     * The support function API says it should just give back bare
     * clauses, so here we must wrap each one in a RestrictInfo.
     */
    foreach(lc, sresult)
    {
      Expr     *clause = (Expr *) lfirst(lc);

      indexquals = lappend(indexquals,
                 make_simple_restrictinfo(root, clause));
    }

    iclause->rinfo = rinfo;
    iclause->indexquals = indexquals;
    iclause->lossy = req.lossy;
    iclause->indexcol = indexcol;
    iclause->indexcols = NIL;

    return iclause;
  }

  return NULL;
}

/*
 * match_saopclause_to_indexcol()
 *    Handles the ScalarArrayOpExpr case for match_clause_to_indexcol(),
 *    which see for comments.
 */
static IndexClause *
match_saopclause_to_indexcol(PlannerInfo *root,
               RestrictInfo *rinfo,
               int indexcol,
               IndexOptInfo *index)
{
  ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) rinfo->clause;
  Node     *leftop,
         *rightop;
  Relids    right_relids;
  Oid     expr_op;
  Oid     expr_coll;
  Index   index_relid;
  Oid     opfamily;
  Oid     idxcollation;

  /* We only accept ANY clauses, not ALL */
  if (!saop->useOr)
    return NULL;
  leftop = (Node *) linitial(saop->args);
  rightop = (Node *) lsecond(saop->args);
  right_relids = pull_varnos(root, rightop);
  expr_op = saop->opno;
  expr_coll = saop->inputcollid;

  index_relid = index->rel->relid;
  opfamily = index->opfamily[indexcol];
  idxcollation = index->indexcollations[indexcol];

  /*
   * We must have indexkey on the left and a pseudo-constant array argument.
   */
  if (match_index_to_operand(leftop, indexcol, index) &&
    !bms_is_member(index_relid, right_relids) &&
    !contain_volatile_functions(rightop))
  {
    if (IndexCollMatchesExprColl(idxcollation, expr_coll) &&
      op_in_opfamily(expr_op, opfamily))
    {
      IndexClause *iclause = makeNode(IndexClause);

      iclause->rinfo = rinfo;
      iclause->indexquals = list_make1(rinfo);
      iclause->lossy = false;
      iclause->indexcol = indexcol;
      iclause->indexcols = NIL;
      return iclause;
    }

    /*
     * We do not currently ask support functions about ScalarArrayOpExprs,
     * though in principle we could.
     */
  }

  return NULL;
}

/*
 * match_rowcompare_to_indexcol()
 *    Handles the RowCompareExpr case for match_clause_to_indexcol(),
 *    which see for comments.
 *
 * In this routine we check whether 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 --- the rest
 * is handled by expand_indexqual_rowcompare().
 */
static IndexClause *
match_rowcompare_to_indexcol(PlannerInfo *root,
               RestrictInfo *rinfo,
               int indexcol,
               IndexOptInfo *index)
{
  RowCompareExpr *clause = (RowCompareExpr *) rinfo->clause;
  Index   index_relid;
  Oid     opfamily;
  Oid     idxcollation;
  Node     *leftop,
         *rightop;
  bool    var_on_left;
  Oid     expr_op;
  Oid     expr_coll;

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

  index_relid = index->rel->relid;
  opfamily = index->opfamily[indexcol];
  idxcollation = index->indexcollations[indexcol];

  /*
   * 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 NULL;

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

  /* 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 expand_indexqual_rowcompare(root,
                         rinfo,
                         indexcol,
                         index,
                         expr_op,
                         var_on_left);
  }

  return NULL;
}

/*
 * match_orclause_to_indexcol()
 *    Handles the OR-expr case for match_clause_to_indexcol() in the case
 *    when it could be transformed to ScalarArrayOpExpr.
 *
 * In this routine, we attempt to transform a list of OR-clause args into a
 * single SAOP expression matching the target index column.  On success,
 * return an IndexClause, containing the transformed expression or NULL,
 * if failed.
 */
static IndexClause *
match_orclause_to_indexcol(PlannerInfo *root,
               RestrictInfo *rinfo,
               int indexcol,
               IndexOptInfo *index)
{
  ListCell   *lc;
  BoolExpr   *orclause = (BoolExpr *) rinfo->orclause;
  Node     *indexExpr = NULL;
  List     *consts = NIL;
  ScalarArrayOpExpr *saopexpr = NULL;
  Oid     matchOpno = InvalidOid;
  IndexClause *iclause;
  Oid     consttype = InvalidOid;
  Oid     arraytype = InvalidOid;
  Oid     inputcollid = InvalidOid;
  bool    firstTime = true;
  bool    haveNonConst = false;
  Index   indexRelid = index->rel->relid;

  Assert(IsA(orclause, BoolExpr));
  Assert(orclause->boolop == OR_EXPR);

  /* Ignore index if it doesn't support SAOP clauses */
  if (!index->amsearcharray)
    return NULL;

  /*
   * Try to convert a list of OR-clauses to a single SAOP expression. Each
   * OR entry must be in the form: (indexkey operator constant) or (constant
   * operator indexkey).  Operators of all the entries must match.  To be
   * effective, give up on the first non-matching entry.  Exit is
   * implemented as a break from the loop, which is catched afterwards.
   */
  foreach(lc, orclause->args)
  {
    RestrictInfo *subRinfo;
    OpExpr     *subClause;
    Oid     opno;
    Node     *leftop,
           *rightop;
    Node     *constExpr;

    if (!IsA(lfirst(lc), RestrictInfo))
      break;

    subRinfo = (RestrictInfo *) lfirst(lc);

    /* Only operator clauses can match  */
    if (!IsA(subRinfo->clause, OpExpr))
      break;

    subClause = (OpExpr *) subRinfo->clause;
    opno = subClause->opno;

    /* Only binary operators can match  */
    if (list_length(subClause->args) != 2)
      break;

    /*
     * The parameters below must match between sub-rinfo and its parent as
     * make_restrictinfo() fills them with the same values, and further
     * modifications are also the same for the whole subtree.  However,
     * still make a sanity check.
     */
    Assert(subRinfo->is_pushed_down == rinfo->is_pushed_down);
    Assert(subRinfo->is_clone == rinfo->is_clone);
    Assert(subRinfo->security_level == rinfo->security_level);
    Assert(bms_equal(subRinfo->incompatible_relids, rinfo->incompatible_relids));
    Assert(bms_equal(subRinfo->outer_relids, rinfo->outer_relids));

    /*
     * Also, check that required_relids in sub-rinfo is subset of parent's
     * required_relids.
     */
    Assert(bms_is_subset(subRinfo->required_relids, rinfo->required_relids));

    /* Only the operator returning a boolean suit the transformation. */
    if (get_op_rettype(opno) != BOOLOID)
      break;

    /*
     * Check for clauses of the form: (indexkey operator constant) or
     * (constant operator indexkey).  See match_clause_to_indexcol's notes
     * about const-ness.
     */
    leftop = (Node *) linitial(subClause->args);
    rightop = (Node *) lsecond(subClause->args);
    if (match_index_to_operand(leftop, indexcol, index) &&
      !bms_is_member(indexRelid, subRinfo->right_relids) &&
      !contain_volatile_functions(rightop))
    {
      indexExpr = leftop;
      constExpr = rightop;
    }
    else if (match_index_to_operand(rightop, indexcol, index) &&
         !bms_is_member(indexRelid, subRinfo->left_relids) &&
         !contain_volatile_functions(leftop))
    {
      opno = get_commutator(opno);
      if (!OidIsValid(opno))
      {
        /* commutator doesn't exist, we can't reverse the order */
        break;
      }
      indexExpr = rightop;
      constExpr = leftop;
    }
    else
    {
      break;
    }

    /*
     * Ignore any RelabelType node above the operands.  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 (IsA(constExpr, RelabelType))
      constExpr = (Node *) ((RelabelType *) constExpr)->arg;
    if (IsA(indexExpr, RelabelType))
      indexExpr = (Node *) ((RelabelType *) indexExpr)->arg;

    /* Forbid transformation for composite types, records. */
    if (type_is_rowtype(exprType(constExpr)) ||
      type_is_rowtype(exprType(indexExpr)))
      break;

    /*
     * Save information about the operator, type, and collation for the
     * first matching qual.  Then, check that subsequent quals match the
     * first.
     */
    if (firstTime)
    {
      matchOpno = opno;
      consttype = exprType(constExpr);
      arraytype = get_array_type(consttype);
      inputcollid = subClause->inputcollid;

      /*
       * Check that the operator is presented in the opfamily and that
       * the expression collation matches the index collation.  Also,
       * there must be an array type to construct an array later.
       */
      if (!IndexCollMatchesExprColl(index->indexcollations[indexcol], inputcollid) ||
        !op_in_opfamily(matchOpno, index->opfamily[indexcol]) ||
        !OidIsValid(arraytype))
        break;
      firstTime = false;
    }
    else
    {
      if (opno != matchOpno ||
        inputcollid != subClause->inputcollid ||
        consttype != exprType(constExpr))
        break;
    }

    /*
     * Check if our list of constants in match_clause_to_indexcol's
     * understanding of const-ness have something other than Const.
     */
    if (!IsA(constExpr, Const))
      haveNonConst = true;
    consts = lappend(consts, constExpr);
  }

  /*
   * Catch the break from the loop above.  Normally, a foreach() loop ends
   * up with a NULL list cell.  A non-NULL list cell indicates a break from
   * the foreach() loop.  Free the consts list and return NULL then.
   */
  if (lc != NULL)
  {
    list_free(consts);
    return NULL;
  }

  saopexpr = make_SAOP_expr(matchOpno, indexExpr, consttype, inputcollid,
                inputcollid, consts, haveNonConst);

  /*
   * Finally, build an IndexClause based on the SAOP node.  Use
   * make_simple_restrictinfo() to get RestrictInfo with clean selectivity
   * estimations, because they may differ from the estimation made for an OR
   * clause.  Although it is not a lossy expression, keep the original rinfo
   * in iclause->rinfo as prescribed.
   */
  iclause = makeNode(IndexClause);
  iclause->rinfo = rinfo;
  iclause->indexquals = list_make1(make_simple_restrictinfo(root,
                                &saopexpr->xpr));
  iclause->lossy = false;
  iclause->indexcol = indexcol;
  iclause->indexcols = NIL;
  return iclause;
}

/*
 * expand_indexqual_rowcompare --- 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, except for possibly commuting it to put the indexkeys on the left.
 *
 * 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 building a lossy version
 * of the row comparison when we do this, so we set lossy = true.)
 *
 * Note: this is really just the last half of match_rowcompare_to_indexcol,
 * but we split it out for comprehensibility.
 */
static IndexClause *
expand_indexqual_rowcompare(PlannerInfo *root,
              RestrictInfo *rinfo,
              int indexcol,
              IndexOptInfo *index,
              Oid expr_op,
              bool var_on_left)
{
  IndexClause *iclause = makeNode(IndexClause);
  RowCompareExpr *clause = (RowCompareExpr *) rinfo->clause;
  int     op_strategy;
  Oid     op_lefttype;
  Oid     op_righttype;
  int     matching_cols;
  List     *expr_ops;
  List     *opfamilies;
  List     *lefttypes;
  List     *righttypes;
  List     *new_ops;
  List     *var_args;
  List     *non_var_args;

  iclause->rinfo = rinfo;
  iclause->indexcol = indexcol;

  if (var_on_left)
  {
    var_args = clause->largs;
    non_var_args = clause->rargs;
  }
  else
  {
    var_args = clause->rargs;
    non_var_args = clause->largs;
  }

  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 */
  iclause->indexcols = list_make1_int(indexcol);

  /* Build lists of ops, opfamilies and operator datatypes in case needed */
  expr_ops = list_make1_oid(expr_op);
  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;

  while (matching_cols < list_length(var_args))
  {
    Node     *varop = (Node *) list_nth(var_args, matching_cols);
    Node     *constop = (Node *) list_nth(non_var_args, matching_cols);
    int     i;

    expr_op = list_nth_oid(clause->opnos, matching_cols);
    if (!var_on_left)
    {
      /* 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(root, 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 key column of the index.
     */
    for (i = 0; i < index->nkeycolumns; i++)
    {
      if (match_index_to_operand(varop, i, index) &&
        get_op_opfamily_strategy(expr_op,
                     index->opfamily[i]) == op_strategy &&
        IndexCollMatchesExprColl(index->indexcollations[i],
                     list_nth_oid(clause->inputcollids,
                            matching_cols)))
        break;
    }
    if (i >= index->nkeycolumns)
      break;       /* no match found */

    /* Add column number to returned list */
    iclause->indexcols = lappend_int(iclause->indexcols, i);

    /* Add operator info to lists */
    get_op_opfamily_properties(expr_op, index->opfamily[i], false,
                   &op_strategy,
                   &op_lefttype,
                   &op_righttype);
    expr_ops = lappend_oid(expr_ops, expr_op);
    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++;
  }

  /* Result is non-lossy if all columns are usable as index quals */
  iclause->lossy = (matching_cols != list_length(clause->opnos));

  /*
   * We can use rinfo->clause as-is if we have var on left and it's all
   * usable as index quals.
   */
  if (var_on_left && !iclause->lossy)
    iclause->indexquals = list_make1(rinfo);
  else
  {
    /*
     * We have to generate a modified rowcompare (possibly just one
     * OpExpr).  The painful part of this is changing < to <= or > to >=,
     * so deal with that first.
     */
    if (!iclause->lossy)
    {
      /* very easy, just use the commuted operators */
      new_ops = expr_ops;
    }
    else if (op_strategy == BTLessEqualStrategyNumber ||
         op_strategy == BTGreaterEqualStrategyNumber)
    {
      /* easy, just use the same (possibly commuted) operators */
      new_ops = list_truncate(expr_ops, 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;
      forthree(opfamilies_cell, opfamilies,
           lefttypes_cell, lefttypes,
           righttypes_cell, righttypes)
      {
        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, "missing operator %d(%u,%u) in opfamily %u",
             op_strategy, lefttype, righttype, opfam);
        new_ops = lappend_oid(new_ops, expr_op);
      }
    }

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

      rc->cmptype = (CompareType) op_strategy;
      rc->opnos = new_ops;
      rc->opfamilies = list_copy_head(clause->opfamilies,
                      matching_cols);
      rc->inputcollids = list_copy_head(clause->inputcollids,
                        matching_cols);
      rc->largs = list_copy_head(var_args, matching_cols);
      rc->rargs = list_copy_head(non_var_args, matching_cols);
      iclause->indexquals = list_make1(make_simple_restrictinfo(root,
                                    (Expr *) rc));
    }
    else
    {
      Expr     *op;

      /* We don't report an index column list in this case */
      iclause->indexcols = NIL;

      op = make_opclause(linitial_oid(new_ops), BOOLOID, false,
                 copyObject(linitial(var_args)),
                 copyObject(linitial(non_var_args)),
                 InvalidOid,
                 linitial_oid(clause->inputcollids));
      iclause->indexquals = list_make1(make_simple_restrictinfo(root, op));
    }
  }

  return iclause;
}


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

/*
 * match_pathkeys_to_index
 *    For the given 'index' and 'pathkeys', output 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.
 *
 * This attempts to find an ORDER BY and index column number for all items in
 * the pathkey list, however, if we're unable to match any given pathkey to an
 * index column, we return just the ones matched by the function so far.  This
 * allows callers who are interested in partial matches to get them.  Callers
 * can determine a partial match vs a full match by checking the outputted
 * list lengths.  A full match will have one item in the output lists for each
 * item in the given 'pathkeys' list.
 */
static void
match_pathkeys_to_index(IndexOptInfo *index, List *pathkeys,
            List **orderby_clauses_p,
            List **clause_columns_p)
{
  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;
    EquivalenceMemberIterator it;
    EquivalenceMember *member;


    /* Pathkey must request default sort order for the target opfamily */
    if (pathkey->pk_cmptype != COMPARE_LT || 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.)
     */
    setup_eclass_member_iterator(&it, pathkey->pk_eclass,
                   index->rel->relids);
    while ((member = eclass_member_iterator_next(&it)) != NULL)
    {
      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, and it doesn't matter for SP-GiST because
       * that doesn't handle multiple columns anyway, and no other
       * existing AMs support amcanorderbyop.  We might need different
       * logic in future for other implementations.
       */
      for (indexcol = 0; indexcol < index->nkeycolumns; indexcol++)
      {
        Expr     *expr;

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

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

    /*
     * Return the matches found so far when this pathkey couldn't be
     * matched to the index.
     */
    if (!found)
      return;
  }
}

/*
 * 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;
  Oid     idxcollation;
  Node     *leftop,
         *rightop;
  Oid     expr_op;
  Oid     expr_coll;
  Oid     sortfamily;
  bool    commuted;

  Assert(indexcol < index->nkeycolumns);

  opfamily = index->opfamily[indexcol];
  idxcollation = index->indexcollations[indexcol];

  /*
   * 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_index_predicates
 *    Set the predicate-derived IndexOptInfo fields for each index
 *    of the specified relation.
 *
 * predOK is set true if the index is partial and its predicate is satisfied
 * for this query, ie the query's WHERE clauses imply the predicate.
 *
 * indrestrictinfo is set to the relation's baserestrictinfo list less any
 * conditions that are implied by the index's predicate.  (Obviously, for a
 * non-partial index, this is the same as baserestrictinfo.)  Such conditions
 * can be dropped from the plan when using the index, in certain cases.
 *
 * At one time it was possible for this to get re-run after adding more
 * restrictions to the rel, thus possibly letting us prove more indexes OK.
 * That doesn't happen any more (at least not in the core code's usage),
 * but this code still supports it in case extensions want to mess with the
 * baserestrictinfo list.  We assume that adding more restrictions can't make
 * an index not predOK.  We must recompute indrestrictinfo each time, though,
 * to make sure any newly-added restrictions get into it if needed.
 */
void
check_index_predicates(PlannerInfo *root, RelOptInfo *rel)
{
  List     *clauselist;
  bool    have_partial;
  bool    is_target_rel;
  Relids    otherrels;
  ListCell   *lc;

  /* Indexes are available only on base or "other" member relations. */
  Assert(IS_SIMPLE_REL(rel));

  /*
   * Initialize the indrestrictinfo lists to be identical to
   * baserestrictinfo, and check whether there are any partial indexes.  If
   * not, this is all we need to do.
   */
  have_partial = false;
  foreach(lc, rel->indexlist)
  {
    IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);

    index->indrestrictinfo = rel->baserestrictinfo;
    if (index->indpred)
      have_partial = true;
  }
  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))
      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 subtract its parents' relid(s) from all_query_rels.
   * Additionally, we mustn't consider clauses that are only computable
   * after outer joins that can null the rel.
   */
  if (rel->reloptkind == RELOPT_OTHER_MEMBER_REL)
    otherrels = bms_difference(root->all_query_rels,
                   find_childrel_parents(root, rel));
  else
    otherrels = bms_difference(root->all_query_rels, rel->relids);
  otherrels = bms_del_members(otherrels, rel->nulling_relids);

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

  /*
   * Normally we remove quals that are implied by a partial index's
   * predicate from indrestrictinfo, indicating that they need not be
   * checked explicitly by an indexscan plan using this index.  However, if
   * the rel is a target relation of UPDATE/DELETE/MERGE/SELECT FOR UPDATE,
   * we cannot remove such quals from the plan, because they need to be in
   * the plan so that they will be properly rechecked by EvalPlanQual
   * testing.  Some day we might want to remove such quals from the main
   * plan anyway and pass them through to EvalPlanQual via a side channel;
   * but for now, we just don't remove implied quals at all for target
   * relations.
   */
  is_target_rel = (bms_is_member(rel->relid, root->all_result_relids) ||
           get_plan_rowmark(root->rowMarks, rel->relid) != NULL);

  /*
   * Now try to prove each index predicate true, and compute the
   * indrestrictinfo lists for partial indexes.  Note that we compute the
   * indrestrictinfo list even for non-predOK indexes; this might seem
   * wasteful, but we may be able to use such indexes in OR clauses, cf
   * generate_bitmap_or_paths().
   */
  foreach(lc, rel->indexlist)
  {
    IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);
    ListCell   *lcr;

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

    if (!index->predOK)   /* don't repeat work if already proven OK */
      index->predOK = predicate_implied_by(index->indpred, clauselist,
                         false);

    /* If rel is an update target, leave indrestrictinfo as set above */
    if (is_target_rel)
      continue;

    /* Else compute indrestrictinfo as the non-implied quals */
    index->indrestrictinfo = NIL;
    foreach(lcr, rel->baserestrictinfo)
    {
      RestrictInfo *rinfo = (RestrictInfo *) lfirst(lcr);

      /* predicate_implied_by() assumes first arg is immutable */
      if (contain_mutable_functions((Node *) rinfo->clause) ||
        !predicate_implied_by(list_make1(rinfo->clause),
                    index->indpred, false))
        index->indrestrictinfo = lappend(index->indrestrictinfo, rinfo);
    }
  }
}

/****************************************************************************
 *        ----  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;
  Oid     curCollation;

  Assert(indexcol < index->nkeycolumns);

  curFamily = index->opfamily[indexcol];
  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)
{
  return relation_has_unique_index_ext(root, rel, restrictlist,
                     exprlist, oprlist, NULL);
}

/*
 * relation_has_unique_index_ext
 *    Same as relation_has_unique_index_for(), but supports extra_clauses
 *    parameter.  If extra_clauses isn't NULL, return baserestrictinfo clauses
 *    which were used to derive uniqueness.
 */
bool
relation_has_unique_index_ext(PlannerInfo *root, RelOptInfo *rel,
                List *restrictlist,
                List *exprlist, List *oprlist,
                List **extra_clauses)
{
  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;
    List     *exprs = NIL;

    /*
     * If the index is not unique, or not immediately enforced, or if it's
     * a partial index, it's useless here.  We're unable to make use of
     * predOK partial unique indexes due to the fact that
     * check_index_predicates() also makes use of join predicates to
     * determine if the partial index is usable. Here we need proofs that
     * hold true before any joins are evaluated.
     */
    if (!ind->unique || !ind->immediate || ind->indpred != NIL)
      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->nkeycolumns; 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 */

          if (bms_membership(rinfo->clause_relids) == BMS_SINGLETON)
          {
            MemoryContext oldMemCtx =
              MemoryContextSwitchTo(root->planner_cxt);

            /*
             * Add filter clause into a list allowing caller to
             * know if uniqueness have made not only by join
             * clauses.
             */
            Assert(bms_is_empty(rinfo->left_relids) ||
                 bms_is_empty(rinfo->right_relids));
            if (extra_clauses)
              exprs = lappend(exprs, rinfo);
            MemoryContextSwitchTo(oldMemCtx);
          }

          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 key columns of this index? */
    if (c == ind->nkeycolumns)
    {
      if (extra_clauses)
        *extra_clauses = exprs;
      return true;
    }
  }

  return false;
}

/*
 * indexcol_is_bool_constant_for_query
 *
 * If an index column is constrained to have a constant value by the query's
 * WHERE conditions, then it's irrelevant for sort-order considerations.
 * Usually that means we have a restriction clause WHERE indexcol = constant,
 * which gets turned into an EquivalenceClass containing a constant, which
 * is recognized as redundant by build_index_pathkeys().  But if the index
 * column is a boolean variable (or expression), then we are not going to
 * see WHERE indexcol = constant, because expression preprocessing will have
 * simplified that to "WHERE indexcol" or "WHERE NOT indexcol".  So we are not
 * going to have a matching EquivalenceClass (unless the query also contains
 * "ORDER BY indexcol").  To allow such cases to work the same as they would
 * for non-boolean values, this function is provided to detect whether the
 * specified index column matches a boolean restriction clause.
 */
bool
indexcol_is_bool_constant_for_query(PlannerInfo *root,
                  IndexOptInfo *index,
                  int indexcol)
{
  ListCell   *lc;

  /* If the index isn't boolean, we can't possibly get a match */
  if (!IsBooleanOpfamily(index->opfamily[indexcol]))
    return false;

  /* Check each restriction clause for the index's rel */
  foreach(lc, index->rel->baserestrictinfo)
  {
    RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);

    /*
     * As in match_clause_to_indexcol, never match pseudoconstants to
     * indexes.  (It might be semantically okay to do so here, but the
     * odds of getting a match are negligible, so don't waste the cycles.)
     */
    if (rinfo->pseudoconstant)
      continue;

    /* See if we can match the clause's expression to the index column */
    if (match_boolean_index_clause(root, rinfo, indexcol, index))
      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 &&
      ((Var *) operand)->varnullingrels == NULL)
      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(index->indexprs, 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;
}

/*
 * is_pseudo_constant_for_index()
 *    Test whether the given expression can be used as an indexscan
 *    comparison value.
 *
 * An indexscan comparison value must not contain any volatile functions,
 * and it can't contain any Vars of the index's own table.  Vars of
 * other tables are okay, though; in that case we'd be producing an
 * indexqual usable in a parameterized indexscan.  This is, therefore,
 * a weaker condition than is_pseudo_constant_clause().
 *
 * This function is exported for use by planner support functions,
 * which will have available the IndexOptInfo, but not any RestrictInfo
 * infrastructure.  It is making the same test made by functions above
 * such as match_opclause_to_indexcol(), but those rely where possible
 * on RestrictInfo information about variable membership.
 *
 * expr: the nodetree to be checked
 * index: the index of interest
 */
bool
is_pseudo_constant_for_index(PlannerInfo *root, Node *expr, IndexOptInfo *index)
{
  /* pull_varnos is cheaper than volatility check, so do that first */
  if (bms_is_member(index->rel->relid, pull_varnos(root, expr)))
    return false;     /* no good, contains Var of table */
  if (contain_volatile_functions(expr))
    return false;     /* no good, volatile comparison value */
  return true;
}

Coverage Report

Created: 2025-06-15 06:31