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Sourcecode: postgresql-8.4 version File versions

equivclass.c

/*-------------------------------------------------------------------------
 *
 * equivclass.c
 *      Routines for managing EquivalenceClasses
 *
 * See src/backend/optimizer/README for discussion of EquivalenceClasses.
 *
 *
 * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *      $PostgreSQL: pgsql/src/backend/optimizer/path/equivclass.c,v 1.19 2009/06/11 14:48:58 momjian Exp $
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/skey.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/paths.h"
#include "optimizer/planmain.h"
#include "optimizer/prep.h"
#include "optimizer/var.h"
#include "utils/lsyscache.h"


static EquivalenceMember *add_eq_member(EquivalenceClass *ec,
                    Expr *expr, Relids relids,
                    bool is_child, Oid datatype);
static void generate_base_implied_equalities_const(PlannerInfo *root,
                                                         EquivalenceClass *ec);
static void generate_base_implied_equalities_no_const(PlannerInfo *root,
                                                              EquivalenceClass *ec);
static void generate_base_implied_equalities_broken(PlannerInfo *root,
                                                            EquivalenceClass *ec);
static List *generate_join_implied_equalities_normal(PlannerInfo *root,
                                                            EquivalenceClass *ec,
                                                            RelOptInfo *joinrel,
                                                            RelOptInfo *outer_rel,
                                                            RelOptInfo *inner_rel);
static List *generate_join_implied_equalities_broken(PlannerInfo *root,
                                                            EquivalenceClass *ec,
                                                            RelOptInfo *joinrel,
                                                            RelOptInfo *outer_rel,
                                                            RelOptInfo *inner_rel);
static Oid select_equality_operator(EquivalenceClass *ec,
                                     Oid lefttype, Oid righttype);
static RestrictInfo *create_join_clause(PlannerInfo *root,
                           EquivalenceClass *ec, Oid opno,
                           EquivalenceMember *leftem,
                           EquivalenceMember *rightem,
                           EquivalenceClass *parent_ec);
static bool reconsider_outer_join_clause(PlannerInfo *root,
                                           RestrictInfo *rinfo,
                                           bool outer_on_left);
static bool reconsider_full_join_clause(PlannerInfo *root,
                                          RestrictInfo *rinfo);


/*
 * process_equivalence
 *      The given clause has a mergejoinable operator and can be applied without
 *      any delay by an outer join, so its two sides can be considered equal
 *      anywhere they are both computable; moreover that equality can be
 *      extended transitively.  Record this knowledge in the EquivalenceClass
 *      data structure.  Returns TRUE if successful, FALSE if not (in which
 *      case caller should treat the clause as ordinary, not an equivalence).
 *
 * If below_outer_join is true, then the clause was found below the nullable
 * side of an outer join, so its sides might validly be both NULL rather than
 * strictly equal.      We can still deduce equalities in such cases, but we take
 * care to mark an EquivalenceClass if it came from any such clauses.  Also,
 * we have to check that both sides are either pseudo-constants or strict
 * functions of Vars, else they might not both go to NULL above the outer
 * join.  (This is the reason why we need a failure return.  It's more
 * convenient to check this case here than at the call sites...)
 *
 * Note: constructing merged EquivalenceClasses is a standard UNION-FIND
 * problem, for which there exist better data structures than simple lists.
 * If this code ever proves to be a bottleneck then it could be sped up ---
 * but for now, simple is beautiful.
 *
 * Note: this is only called during planner startup, not during GEQO
 * exploration, so we need not worry about whether we're in the right
 * memory context.
 */
bool
process_equivalence(PlannerInfo *root, RestrictInfo *restrictinfo,
                              bool below_outer_join)
{
      Expr     *clause = restrictinfo->clause;
      Oid               opno,
                        item1_type,
                        item2_type;
      Expr     *item1;
      Expr     *item2;
      Relids            item1_relids,
                        item2_relids;
      List     *opfamilies;
      EquivalenceClass *ec1,
                     *ec2;
      EquivalenceMember *em1,
                     *em2;
      ListCell   *lc1;

      /* Extract info from given clause */
      Assert(is_opclause(clause));
      opno = ((OpExpr *) clause)->opno;
      item1 = (Expr *) get_leftop(clause);
      item2 = (Expr *) get_rightop(clause);
      item1_relids = restrictinfo->left_relids;
      item2_relids = restrictinfo->right_relids;

      /*
       * If below outer join, check for strictness, else reject.
       */
      if (below_outer_join)
      {
            if (!bms_is_empty(item1_relids) &&
                  contain_nonstrict_functions((Node *) item1))
                  return false;           /* LHS is non-strict but not constant */
            if (!bms_is_empty(item2_relids) &&
                  contain_nonstrict_functions((Node *) item2))
                  return false;           /* RHS is non-strict but not constant */
      }

      /*
       * We use the declared input types of the operator, not exprType() of the
       * inputs, as the nominal datatypes for opfamily lookup.  This presumes
       * that btree operators are always registered with amoplefttype and
       * amoprighttype equal to their declared input types.  We will need this
       * info anyway to build EquivalenceMember nodes, and by extracting it now
       * we can use type comparisons to short-circuit some equal() tests.
       */
      op_input_types(opno, &item1_type, &item2_type);

      opfamilies = restrictinfo->mergeopfamilies;

      /*
       * Sweep through the existing EquivalenceClasses looking for matches to
       * item1 and item2.  These are the possible outcomes:
       *
       * 1. We find both in the same EC.  The equivalence is already known, so
       * there's nothing to do.
       *
       * 2. We find both in different ECs.  Merge the two ECs together.
       *
       * 3. We find just one.  Add the other to its EC.
       *
       * 4. We find neither.  Make a new, two-entry EC.
       *
       * Note: since all ECs are built through this process, it's impossible
       * that we'd match an item in more than one existing EC.  It is possible
       * to match more than once within an EC, if someone fed us something silly
       * like "WHERE X=X".  (However, we can't simply discard such clauses,
       * since they should fail when X is null; so we will build a 2-member EC
       * to ensure the correct restriction clause gets generated.  Hence there
       * is no shortcut here for item1 and item2 equal.)
       */
      ec1 = ec2 = NULL;
      em1 = em2 = NULL;
      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            ListCell   *lc2;

            /* Never match to a volatile EC */
            if (cur_ec->ec_has_volatile)
                  continue;

            /*
             * A "match" requires matching sets of btree opfamilies.  Use of
             * equal() for this test has implications discussed in the comments
             * for get_mergejoin_opfamilies().
             */
            if (!equal(opfamilies, cur_ec->ec_opfamilies))
                  continue;

            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  Assert(!cur_em->em_is_child);       /* no children yet */

                  /*
                   * If below an outer join, don't match constants: they're not as
                   * constant as they look.
                   */
                  if ((below_outer_join || cur_ec->ec_below_outer_join) &&
                        cur_em->em_is_const)
                        continue;

                  if (!ec1 &&
                        item1_type == cur_em->em_datatype &&
                        equal(item1, cur_em->em_expr))
                  {
                        ec1 = cur_ec;
                        em1 = cur_em;
                        if (ec2)
                              break;
                  }

                  if (!ec2 &&
                        item2_type == cur_em->em_datatype &&
                        equal(item2, cur_em->em_expr))
                  {
                        ec2 = cur_ec;
                        em2 = cur_em;
                        if (ec1)
                              break;
                  }
            }

            if (ec1 && ec2)
                  break;
      }

      /* Sweep finished, what did we find? */

      if (ec1 && ec2)
      {
            /* If case 1, nothing to do, except add to sources */
            if (ec1 == ec2)
            {
                  ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
                  ec1->ec_below_outer_join |= below_outer_join;
                  /* mark the RI as usable with this pair of EMs */
                  /* NB: can't set left_ec/right_ec until merging is finished */
                  restrictinfo->left_em = em1;
                  restrictinfo->right_em = em2;
                  return true;
            }

            /*
             * Case 2: need to merge ec1 and ec2.  We add ec2's items to ec1, then
             * set ec2's ec_merged link to point to ec1 and remove ec2 from the
             * eq_classes list.  We cannot simply delete ec2 because that could
             * leave dangling pointers in existing PathKeys.  We leave it behind
             * with a link so that the merged EC can be found.
             */
            ec1->ec_members = list_concat(ec1->ec_members, ec2->ec_members);
            ec1->ec_sources = list_concat(ec1->ec_sources, ec2->ec_sources);
            ec1->ec_derives = list_concat(ec1->ec_derives, ec2->ec_derives);
            ec1->ec_relids = bms_join(ec1->ec_relids, ec2->ec_relids);
            ec1->ec_has_const |= ec2->ec_has_const;
            /* can't need to set has_volatile */
            ec1->ec_below_outer_join |= ec2->ec_below_outer_join;
            ec2->ec_merged = ec1;
            root->eq_classes = list_delete_ptr(root->eq_classes, ec2);
            /* just to avoid debugging confusion w/ dangling pointers: */
            ec2->ec_members = NIL;
            ec2->ec_sources = NIL;
            ec2->ec_derives = NIL;
            ec2->ec_relids = NULL;
            ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
            ec1->ec_below_outer_join |= below_outer_join;
            /* mark the RI as usable with this pair of EMs */
            restrictinfo->left_em = em1;
            restrictinfo->right_em = em2;
      }
      else if (ec1)
      {
            /* Case 3: add item2 to ec1 */
            em2 = add_eq_member(ec1, item2, item2_relids, false, item2_type);
            ec1->ec_sources = lappend(ec1->ec_sources, restrictinfo);
            ec1->ec_below_outer_join |= below_outer_join;
            /* mark the RI as usable with this pair of EMs */
            restrictinfo->left_em = em1;
            restrictinfo->right_em = em2;
      }
      else if (ec2)
      {
            /* Case 3: add item1 to ec2 */
            em1 = add_eq_member(ec2, item1, item1_relids, false, item1_type);
            ec2->ec_sources = lappend(ec2->ec_sources, restrictinfo);
            ec2->ec_below_outer_join |= below_outer_join;
            /* mark the RI as usable with this pair of EMs */
            restrictinfo->left_em = em1;
            restrictinfo->right_em = em2;
      }
      else
      {
            /* Case 4: make a new, two-entry EC */
            EquivalenceClass *ec = makeNode(EquivalenceClass);

            ec->ec_opfamilies = opfamilies;
            ec->ec_members = NIL;
            ec->ec_sources = list_make1(restrictinfo);
            ec->ec_derives = NIL;
            ec->ec_relids = NULL;
            ec->ec_has_const = false;
            ec->ec_has_volatile = false;
            ec->ec_below_outer_join = below_outer_join;
            ec->ec_broken = false;
            ec->ec_sortref = 0;
            ec->ec_merged = NULL;
            em1 = add_eq_member(ec, item1, item1_relids, false, item1_type);
            em2 = add_eq_member(ec, item2, item2_relids, false, item2_type);

            root->eq_classes = lappend(root->eq_classes, ec);

            /* mark the RI as usable with this pair of EMs */
            restrictinfo->left_em = em1;
            restrictinfo->right_em = em2;
      }

      return true;
}

/*
 * add_eq_member - build a new EquivalenceMember and add it to an EC
 */
static EquivalenceMember *
add_eq_member(EquivalenceClass *ec, Expr *expr, Relids relids,
                    bool is_child, Oid datatype)
{
      EquivalenceMember *em = makeNode(EquivalenceMember);

      em->em_expr = expr;
      em->em_relids = relids;
      em->em_is_const = false;
      em->em_is_child = is_child;
      em->em_datatype = datatype;

      if (bms_is_empty(relids))
      {
            /*
             * No Vars, assume it's a pseudoconstant.  This is correct for entries
             * generated from process_equivalence(), because a WHERE clause can't
             * contain aggregates or SRFs, and non-volatility was checked before
             * process_equivalence() ever got called.  But
             * get_eclass_for_sort_expr() has to work harder.  We put the tests
             * there not here to save cycles in the equivalence case.
             */
            Assert(!is_child);
            em->em_is_const = true;
            ec->ec_has_const = true;
            /* it can't affect ec_relids */
      }
      else if (!is_child)                 /* child members don't add to ec_relids */
      {
            ec->ec_relids = bms_add_members(ec->ec_relids, relids);
      }
      ec->ec_members = lappend(ec->ec_members, em);

      return em;
}


/*
 * get_eclass_for_sort_expr
 *      Given an expression and opfamily info, find an existing equivalence
 *      class it is a member of; if none, build a new single-member
 *      EquivalenceClass for it.
 *
 * sortref is the SortGroupRef of the originating SortGroupClause, if any,
 * or zero if not.
 *
 * This can be used safely both before and after EquivalenceClass merging;
 * since it never causes merging it does not invalidate any existing ECs
 * or PathKeys.
 *
 * Note: opfamilies must be chosen consistently with the way
 * process_equivalence() would do; that is, generated from a mergejoinable
 * equality operator.  Else we might fail to detect valid equivalences,
 * generating poor (but not incorrect) plans.
 */
EquivalenceClass *
get_eclass_for_sort_expr(PlannerInfo *root,
                                     Expr *expr,
                                     Oid expr_datatype,
                                     List *opfamilies,
                                     Index sortref)
{
      EquivalenceClass *newec;
      EquivalenceMember *newem;
      ListCell   *lc1;
      MemoryContext oldcontext;

      /*
       * Scan through the existing EquivalenceClasses for a match
       */
      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            ListCell   *lc2;

            /* Never match to a volatile EC */
            if (cur_ec->ec_has_volatile)
                  continue;

            if (!equal(opfamilies, cur_ec->ec_opfamilies))
                  continue;

            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  /*
                   * If below an outer join, don't match constants: they're not as
                   * constant as they look.
                   */
                  if (cur_ec->ec_below_outer_join &&
                        cur_em->em_is_const)
                        continue;

                  if (expr_datatype == cur_em->em_datatype &&
                        equal(expr, cur_em->em_expr))
                        return cur_ec;    /* Match! */
            }
      }

      /*
       * No match, so build a new single-member EC
       *
       * Here, we must be sure that we construct the EC in the right context. We
       * can assume, however, that the passed expr is long-lived.
       */
      oldcontext = MemoryContextSwitchTo(root->planner_cxt);

      newec = makeNode(EquivalenceClass);
      newec->ec_opfamilies = list_copy(opfamilies);
      newec->ec_members = NIL;
      newec->ec_sources = NIL;
      newec->ec_derives = NIL;
      newec->ec_relids = NULL;
      newec->ec_has_const = false;
      newec->ec_has_volatile = contain_volatile_functions((Node *) expr);
      newec->ec_below_outer_join = false;
      newec->ec_broken = false;
      newec->ec_sortref = sortref;
      newec->ec_merged = NULL;
      newem = add_eq_member(newec, expr, pull_varnos((Node *) expr),
                                      false, expr_datatype);

      /*
       * add_eq_member doesn't check for volatile functions, set-returning
       * functions, aggregates, or window functions, but such could appear in
       * sort expressions; so we have to check whether its const-marking was
       * correct.
       */
      if (newec->ec_has_const)
      {
            if (newec->ec_has_volatile ||
                  expression_returns_set((Node *) expr) ||
                  contain_agg_clause((Node *) expr) ||
                  contain_window_function((Node *) expr))
            {
                  newec->ec_has_const = false;
                  newem->em_is_const = false;
            }
      }

      root->eq_classes = lappend(root->eq_classes, newec);

      MemoryContextSwitchTo(oldcontext);

      return newec;
}


/*
 * generate_base_implied_equalities
 *      Generate any restriction clauses that we can deduce from equivalence
 *      classes.
 *
 * When an EC contains pseudoconstants, our strategy is to generate
 * "member = const1" clauses where const1 is the first constant member, for
 * every other member (including other constants).    If we are able to do this
 * then we don't need any "var = var" comparisons because we've successfully
 * constrained all the vars at their points of creation.  If we fail to
 * generate any of these clauses due to lack of cross-type operators, we fall
 * back to the "ec_broken" strategy described below.  (XXX if there are
 * multiple constants of different types, it's possible that we might succeed
 * in forming all the required clauses if we started from a different const
 * member; but this seems a sufficiently hokey corner case to not be worth
 * spending lots of cycles on.)
 *
 * For ECs that contain no pseudoconstants, we generate derived clauses
 * "member1 = member2" for each pair of members belonging to the same base
 * relation (actually, if there are more than two for the same base relation,
 * we only need enough clauses to link each to each other).  This provides
 * the base case for the recursion: each row emitted by a base relation scan
 * will constrain all computable members of the EC to be equal.  As each
 * join path is formed, we'll add additional derived clauses on-the-fly
 * to maintain this invariant (see generate_join_implied_equalities).
 *
 * If the opfamilies used by the EC do not provide complete sets of cross-type
 * equality operators, it is possible that we will fail to generate a clause
 * that must be generated to maintain the invariant.  (An example: given
 * "WHERE a.x = b.y AND b.y = a.z", the scheme breaks down if we cannot
 * generate "a.x = a.z" as a restriction clause for A.)  In this case we mark
 * the EC "ec_broken" and fall back to regurgitating its original source
 * RestrictInfos at appropriate times.    We do not try to retract any derived
 * clauses already generated from the broken EC, so the resulting plan could
 * be poor due to bad selectivity estimates caused by redundant clauses.  But
 * the correct solution to that is to fix the opfamilies ...
 *
 * Equality clauses derived by this function are passed off to
 * process_implied_equality (in plan/initsplan.c) to be inserted into the
 * restrictinfo datastructures.  Note that this must be called after initial
 * scanning of the quals and before Path construction begins.
 *
 * We make no attempt to avoid generating duplicate RestrictInfos here: we
 * don't search ec_sources for matches, nor put the created RestrictInfos
 * into ec_derives.  Doing so would require some slightly ugly changes in
 * initsplan.c's API, and there's no real advantage, because the clauses
 * generated here can't duplicate anything we will generate for joins anyway.
 */
void
generate_base_implied_equalities(PlannerInfo *root)
{
      ListCell   *lc;
      Index       rti;

      foreach(lc, root->eq_classes)
      {
            EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc);

            Assert(ec->ec_merged == NULL);      /* else shouldn't be in list */
            Assert(!ec->ec_broken); /* not yet anyway... */

            /* Single-member ECs won't generate any deductions */
            if (list_length(ec->ec_members) <= 1)
                  continue;

            if (ec->ec_has_const)
                  generate_base_implied_equalities_const(root, ec);
            else
                  generate_base_implied_equalities_no_const(root, ec);

            /* Recover if we failed to generate required derived clauses */
            if (ec->ec_broken)
                  generate_base_implied_equalities_broken(root, ec);
      }

      /*
       * This is also a handy place to mark base rels (which should all exist by
       * now) with flags showing whether they have pending eclass joins.
       */
      for (rti = 1; rti < root->simple_rel_array_size; rti++)
      {
            RelOptInfo *brel = root->simple_rel_array[rti];

            if (brel == NULL)
                  continue;

            brel->has_eclass_joins = has_relevant_eclass_joinclause(root, brel);
      }
}

/*
 * generate_base_implied_equalities when EC contains pseudoconstant(s)
 */
static void
generate_base_implied_equalities_const(PlannerInfo *root,
                                                         EquivalenceClass *ec)
{
      EquivalenceMember *const_em = NULL;
      ListCell   *lc;

      /*
       * In the trivial case where we just had one "var = const" clause, push
       * the original clause back into the main planner machinery.  There is
       * nothing to be gained by doing it differently, and we save the effort to
       * re-build and re-analyze an equality clause that will be exactly
       * equivalent to the old one.
       */
      if (list_length(ec->ec_members) == 2 &&
            list_length(ec->ec_sources) == 1)
      {
            RestrictInfo *restrictinfo = (RestrictInfo *) linitial(ec->ec_sources);

            if (bms_membership(restrictinfo->required_relids) != BMS_MULTIPLE)
            {
                  distribute_restrictinfo_to_rels(root, restrictinfo);
                  return;
            }
      }

      /* Find the constant member to use */
      foreach(lc, ec->ec_members)
      {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);

            if (cur_em->em_is_const)
            {
                  const_em = cur_em;
                  break;
            }
      }
      Assert(const_em != NULL);

      /* Generate a derived equality against each other member */
      foreach(lc, ec->ec_members)
      {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
            Oid               eq_op;

            Assert(!cur_em->em_is_child); /* no children yet */
            if (cur_em == const_em)
                  continue;
            eq_op = select_equality_operator(ec,
                                                             cur_em->em_datatype,
                                                             const_em->em_datatype);
            if (!OidIsValid(eq_op))
            {
                  /* failed... */
                  ec->ec_broken = true;
                  break;
            }
            process_implied_equality(root, eq_op,
                                                 cur_em->em_expr, const_em->em_expr,
                                                 ec->ec_relids,
                                                 ec->ec_below_outer_join,
                                                 cur_em->em_is_const);
      }
}

/*
 * generate_base_implied_equalities when EC contains no pseudoconstants
 */
static void
generate_base_implied_equalities_no_const(PlannerInfo *root,
                                                              EquivalenceClass *ec)
{
      EquivalenceMember **prev_ems;
      ListCell   *lc;

      /*
       * We scan the EC members once and track the last-seen member for each
       * base relation.  When we see another member of the same base relation,
       * we generate "prev_mem = cur_mem".  This results in the minimum number
       * of derived clauses, but it's possible that it will fail when a
       * different ordering would succeed.  XXX FIXME: use a UNION-FIND
       * algorithm similar to the way we build merged ECs.  (Use a list-of-lists
       * for each rel.)
       */
      prev_ems = (EquivalenceMember **)
            palloc0(root->simple_rel_array_size * sizeof(EquivalenceMember *));

      foreach(lc, ec->ec_members)
      {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
            int               relid;

            Assert(!cur_em->em_is_child); /* no children yet */
            if (bms_membership(cur_em->em_relids) != BMS_SINGLETON)
                  continue;
            relid = bms_singleton_member(cur_em->em_relids);
            Assert(relid < root->simple_rel_array_size);

            if (prev_ems[relid] != NULL)
            {
                  EquivalenceMember *prev_em = prev_ems[relid];
                  Oid               eq_op;

                  eq_op = select_equality_operator(ec,
                                                                   prev_em->em_datatype,
                                                                   cur_em->em_datatype);
                  if (!OidIsValid(eq_op))
                  {
                        /* failed... */
                        ec->ec_broken = true;
                        break;
                  }
                  process_implied_equality(root, eq_op,
                                                       prev_em->em_expr, cur_em->em_expr,
                                                       ec->ec_relids,
                                                       ec->ec_below_outer_join,
                                                       false);
            }
            prev_ems[relid] = cur_em;
      }

      pfree(prev_ems);

      /*
       * We also have to make sure that all the Vars used in the member clauses
       * will be available at any join node we might try to reference them at.
       * For the moment we force all the Vars to be available at all join nodes
       * for this eclass.  Perhaps this could be improved by doing some
       * pre-analysis of which members we prefer to join, but it's no worse than
       * what happened in the pre-8.3 code.
       */
      foreach(lc, ec->ec_members)
      {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);
            List     *vars = pull_var_clause((Node *) cur_em->em_expr,
                                                               PVC_INCLUDE_PLACEHOLDERS);

            add_vars_to_targetlist(root, vars, ec->ec_relids);
            list_free(vars);
      }
}

/*
 * generate_base_implied_equalities cleanup after failure
 *
 * What we must do here is push any zero- or one-relation source RestrictInfos
 * of the EC back into the main restrictinfo datastructures.  Multi-relation
 * clauses will be regurgitated later by generate_join_implied_equalities().
 * (We do it this way to maintain continuity with the case that ec_broken
 * becomes set only after we've gone up a join level or two.)
 */
static void
generate_base_implied_equalities_broken(PlannerInfo *root,
                                                            EquivalenceClass *ec)
{
      ListCell   *lc;

      foreach(lc, ec->ec_sources)
      {
            RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(lc);

            if (bms_membership(restrictinfo->required_relids) != BMS_MULTIPLE)
                  distribute_restrictinfo_to_rels(root, restrictinfo);
      }
}


/*
 * generate_join_implied_equalities
 *      Generate any join clauses that we can deduce from equivalence classes.
 *
 * At a join node, we must enforce restriction clauses sufficient to ensure
 * that all equivalence-class members computable at that node are equal.
 * Since the set of clauses to enforce can vary depending on which subset
 * relations are the inputs, we have to compute this afresh for each join
 * path pair.  Hence a fresh List of RestrictInfo nodes is built and passed
 * back on each call.
 *
 * The results are sufficient for use in merge, hash, and plain nestloop join
 * methods.  We do not worry here about selecting clauses that are optimal
 * for use in a nestloop-with-inner-indexscan join, however.  indxpath.c makes
 * its own selections of clauses to use, and if the ones we pick here are
 * redundant with those, the extras will be eliminated in createplan.c.
 *
 * Because the same join clauses are likely to be needed multiple times as
 * we consider different join paths, we avoid generating multiple copies:
 * whenever we select a particular pair of EquivalenceMembers to join,
 * we check to see if the pair matches any original clause (in ec_sources)
 * or previously-built clause (in ec_derives).  This saves memory and allows
 * re-use of information cached in RestrictInfos.
 */
List *
generate_join_implied_equalities(PlannerInfo *root,
                                                 RelOptInfo *joinrel,
                                                 RelOptInfo *outer_rel,
                                                 RelOptInfo *inner_rel)
{
      List     *result = NIL;
      ListCell   *lc;

      foreach(lc, root->eq_classes)
      {
            EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc);
            List     *sublist = NIL;

            /* ECs containing consts do not need any further enforcement */
            if (ec->ec_has_const)
                  continue;

            /* Single-member ECs won't generate any deductions */
            if (list_length(ec->ec_members) <= 1)
                  continue;

            /* We can quickly ignore any that don't overlap the join, too */
            if (!bms_overlap(ec->ec_relids, joinrel->relids))
                  continue;

            if (!ec->ec_broken)
                  sublist = generate_join_implied_equalities_normal(root,
                                                                                            ec,
                                                                                            joinrel,
                                                                                            outer_rel,
                                                                                            inner_rel);

            /* Recover if we failed to generate required derived clauses */
            if (ec->ec_broken)
                  sublist = generate_join_implied_equalities_broken(root,
                                                                                            ec,
                                                                                            joinrel,
                                                                                            outer_rel,
                                                                                            inner_rel);

            result = list_concat(result, sublist);
      }

      return result;
}

/*
 * generate_join_implied_equalities for a still-valid EC
 */
static List *
generate_join_implied_equalities_normal(PlannerInfo *root,
                                                            EquivalenceClass *ec,
                                                            RelOptInfo *joinrel,
                                                            RelOptInfo *outer_rel,
                                                            RelOptInfo *inner_rel)
{
      List     *result = NIL;
      List     *new_members = NIL;
      List     *outer_members = NIL;
      List     *inner_members = NIL;
      ListCell   *lc1;

      /*
       * First, scan the EC to identify member values that are computable at the
       * outer rel, at the inner rel, or at this relation but not in either
       * input rel.  The outer-rel members should already be enforced equal,
       * likewise for the inner-rel members.    We'll need to create clauses to
       * enforce that any newly computable members are all equal to each other
       * as well as to at least one input member, plus enforce at least one
       * outer-rel member equal to at least one inner-rel member.
       */
      foreach(lc1, ec->ec_members)
      {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc1);

            if (cur_em->em_is_child)
                  continue;               /* ignore children here */
            if (!bms_is_subset(cur_em->em_relids, joinrel->relids))
                  continue;               /* ignore --- not computable yet */

            if (bms_is_subset(cur_em->em_relids, outer_rel->relids))
                  outer_members = lappend(outer_members, cur_em);
            else if (bms_is_subset(cur_em->em_relids, inner_rel->relids))
                  inner_members = lappend(inner_members, cur_em);
            else
                  new_members = lappend(new_members, cur_em);
      }

      /*
       * First, select the joinclause if needed.      We can equate any one outer
       * member to any one inner member, but we have to find a datatype
       * combination for which an opfamily member operator exists.  If we have
       * choices, we prefer simple Var members (possibly with RelabelType) since
       * these are (a) cheapest to compute at runtime and (b) most likely to
       * have useful statistics.    Also, if enable_hashjoin is on, we prefer
       * operators that are also hashjoinable.
       */
      if (outer_members && inner_members)
      {
            EquivalenceMember *best_outer_em = NULL;
            EquivalenceMember *best_inner_em = NULL;
            Oid               best_eq_op = InvalidOid;
            int               best_score = -1;
            RestrictInfo *rinfo;

            foreach(lc1, outer_members)
            {
                  EquivalenceMember *outer_em = (EquivalenceMember *) lfirst(lc1);
                  ListCell   *lc2;

                  foreach(lc2, inner_members)
                  {
                        EquivalenceMember *inner_em = (EquivalenceMember *) lfirst(lc2);
                        Oid               eq_op;
                        int               score;

                        eq_op = select_equality_operator(ec,
                                                                         outer_em->em_datatype,
                                                                         inner_em->em_datatype);
                        if (!OidIsValid(eq_op))
                              continue;
                        score = 0;
                        if (IsA(outer_em->em_expr, Var) ||
                              (IsA(outer_em->em_expr, RelabelType) &&
                               IsA(((RelabelType *) outer_em->em_expr)->arg, Var)))
                              score++;
                        if (IsA(inner_em->em_expr, Var) ||
                              (IsA(inner_em->em_expr, RelabelType) &&
                               IsA(((RelabelType *) inner_em->em_expr)->arg, Var)))
                              score++;
                        if (!enable_hashjoin || op_hashjoinable(eq_op))
                              score++;
                        if (score > best_score)
                        {
                              best_outer_em = outer_em;
                              best_inner_em = inner_em;
                              best_eq_op = eq_op;
                              best_score = score;
                              if (best_score == 3)
                                    break;      /* no need to look further */
                        }
                  }
                  if (best_score == 3)
                        break;                  /* no need to look further */
            }
            if (best_score < 0)
            {
                  /* failed... */
                  ec->ec_broken = true;
                  return NIL;
            }

            /*
             * Create clause, setting parent_ec to mark it as redundant with other
             * joinclauses
             */
            rinfo = create_join_clause(root, ec, best_eq_op,
                                                   best_outer_em, best_inner_em,
                                                   ec);

            result = lappend(result, rinfo);
      }

      /*
       * Now deal with building restrictions for any expressions that involve
       * Vars from both sides of the join.  We have to equate all of these to
       * each other as well as to at least one old member (if any).
       *
       * XXX as in generate_base_implied_equalities_no_const, we could be a lot
       * smarter here to avoid unnecessary failures in cross-type situations.
       * For now, use the same left-to-right method used there.
       */
      if (new_members)
      {
            List     *old_members = list_concat(outer_members, inner_members);
            EquivalenceMember *prev_em = NULL;
            RestrictInfo *rinfo;

            /* For now, arbitrarily take the first old_member as the one to use */
            if (old_members)
                  new_members = lappend(new_members, linitial(old_members));

            foreach(lc1, new_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc1);

                  if (prev_em != NULL)
                  {
                        Oid               eq_op;

                        eq_op = select_equality_operator(ec,
                                                                         prev_em->em_datatype,
                                                                         cur_em->em_datatype);
                        if (!OidIsValid(eq_op))
                        {
                              /* failed... */
                              ec->ec_broken = true;
                              return NIL;
                        }
                        /* do NOT set parent_ec, this qual is not redundant! */
                        rinfo = create_join_clause(root, ec, eq_op,
                                                               prev_em, cur_em,
                                                               NULL);

                        result = lappend(result, rinfo);
                  }
                  prev_em = cur_em;
            }
      }

      return result;
}

/*
 * generate_join_implied_equalities cleanup after failure
 *
 * Return any original RestrictInfos that are enforceable at this join.
 */
static List *
generate_join_implied_equalities_broken(PlannerInfo *root,
                                                            EquivalenceClass *ec,
                                                            RelOptInfo *joinrel,
                                                            RelOptInfo *outer_rel,
                                                            RelOptInfo *inner_rel)
{
      List     *result = NIL;
      ListCell   *lc;

      foreach(lc, ec->ec_sources)
      {
            RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(lc);

            if (bms_is_subset(restrictinfo->required_relids, joinrel->relids) &&
              !bms_is_subset(restrictinfo->required_relids, outer_rel->relids) &&
                  !bms_is_subset(restrictinfo->required_relids, inner_rel->relids))
                  result = lappend(result, restrictinfo);
      }

      return result;
}


/*
 * select_equality_operator
 *      Select a suitable equality operator for comparing two EC members
 *
 * Returns InvalidOid if no operator can be found for this datatype combination
 */
static Oid
select_equality_operator(EquivalenceClass *ec, Oid lefttype, Oid righttype)
{
      ListCell   *lc;

      foreach(lc, ec->ec_opfamilies)
      {
            Oid               opfamily = lfirst_oid(lc);
            Oid               opno;

            opno = get_opfamily_member(opfamily, lefttype, righttype,
                                                   BTEqualStrategyNumber);
            if (OidIsValid(opno))
                  return opno;
      }
      return InvalidOid;
}


/*
 * create_join_clause
 *      Find or make a RestrictInfo comparing the two given EC members
 *      with the given operator.
 *
 * parent_ec is either equal to ec (if the clause is a potentially-redundant
 * join clause) or NULL (if not).  We have to treat this as part of the
 * match requirements --- it's possible that a clause comparing the same two
 * EMs is a join clause in one join path and a restriction clause in another.
 */
static RestrictInfo *
create_join_clause(PlannerInfo *root,
                           EquivalenceClass *ec, Oid opno,
                           EquivalenceMember *leftem,
                           EquivalenceMember *rightem,
                           EquivalenceClass *parent_ec)
{
      RestrictInfo *rinfo;
      ListCell   *lc;
      MemoryContext oldcontext;

      /*
       * Search to see if we already built a RestrictInfo for this pair of
       * EquivalenceMembers.  We can use either original source clauses or
       * previously-derived clauses.      The check on opno is probably redundant,
       * but be safe ...
       */
      foreach(lc, ec->ec_sources)
      {
            rinfo = (RestrictInfo *) lfirst(lc);
            if (rinfo->left_em == leftem &&
                  rinfo->right_em == rightem &&
                  rinfo->parent_ec == parent_ec &&
                  opno == ((OpExpr *) rinfo->clause)->opno)
                  return rinfo;
      }

      foreach(lc, ec->ec_derives)
      {
            rinfo = (RestrictInfo *) lfirst(lc);
            if (rinfo->left_em == leftem &&
                  rinfo->right_em == rightem &&
                  rinfo->parent_ec == parent_ec &&
                  opno == ((OpExpr *) rinfo->clause)->opno)
                  return rinfo;
      }

      /*
       * Not there, so build it, in planner context so we can re-use it. (Not
       * important in normal planning, but definitely so in GEQO.)
       */
      oldcontext = MemoryContextSwitchTo(root->planner_cxt);

      rinfo = build_implied_join_equality(opno,
                                                            leftem->em_expr,
                                                            rightem->em_expr,
                                                            bms_union(leftem->em_relids,
                                                                          rightem->em_relids));

      /* Mark the clause as redundant, or not */
      rinfo->parent_ec = parent_ec;

      /*
       * We can set these now, rather than letting them be looked up later,
       * since this is only used after EC merging is complete.
       */
      rinfo->left_ec = ec;
      rinfo->right_ec = ec;

      /* Mark it as usable with these EMs */
      rinfo->left_em = leftem;
      rinfo->right_em = rightem;
      /* and save it for possible re-use */
      ec->ec_derives = lappend(ec->ec_derives, rinfo);

      MemoryContextSwitchTo(oldcontext);

      return rinfo;
}


/*
 * reconsider_outer_join_clauses
 *      Re-examine any outer-join clauses that were set aside by
 *      distribute_qual_to_rels(), and see if we can derive any
 *      EquivalenceClasses from them.  Then, if they were not made
 *      redundant, push them out into the regular join-clause lists.
 *
 * When we have mergejoinable clauses A = B that are outer-join clauses,
 * we can't blindly combine them with other clauses A = C to deduce B = C,
 * since in fact the "equality" A = B won't necessarily hold above the
 * outer join (one of the variables might be NULL instead).  Nonetheless
 * there are cases where we can add qual clauses using transitivity.
 *
 * One case that we look for here is an outer-join clause OUTERVAR = INNERVAR
 * for which there is also an equivalence clause OUTERVAR = CONSTANT.
 * It is safe and useful to push a clause INNERVAR = CONSTANT into the
 * evaluation of the inner (nullable) relation, because any inner rows not
 * meeting this condition will not contribute to the outer-join result anyway.
 * (Any outer rows they could join to will be eliminated by the pushed-down
 * equivalence clause.)
 *
 * Note that the above rule does not work for full outer joins; nor is it
 * very interesting to consider cases where the generated equivalence clause
 * would involve relations outside the outer join, since such clauses couldn't
 * be pushed into the inner side's scan anyway.  So the restriction to
 * outervar = pseudoconstant is not really giving up anything.
 *
 * For full-join cases, we can only do something useful if it's a FULL JOIN
 * USING and a merged column has an equivalence MERGEDVAR = CONSTANT.
 * By the time it gets here, the merged column will look like
 *          COALESCE(LEFTVAR, RIGHTVAR)
 * and we will have a full-join clause LEFTVAR = RIGHTVAR that we can match
 * the COALESCE expression to. In this situation we can push LEFTVAR = CONSTANT
 * and RIGHTVAR = CONSTANT into the input relations, since any rows not
 * meeting these conditions cannot contribute to the join result.
 *
 * Again, there isn't any traction to be gained by trying to deal with
 * clauses comparing a mergedvar to a non-pseudoconstant.  So we can make
 * use of the EquivalenceClasses to search for matching variables that were
 * equivalenced to constants.  The interesting outer-join clauses were
 * accumulated for us by distribute_qual_to_rels.
 *
 * When we find one of these cases, we implement the changes we want by
 * generating a new equivalence clause INNERVAR = CONSTANT (or LEFTVAR, etc)
 * and pushing it into the EquivalenceClass structures.  This is because we
 * may already know that INNERVAR is equivalenced to some other var(s), and
 * we'd like the constant to propagate to them too.  Note that it would be
 * unsafe to merge any existing EC for INNERVAR with the OUTERVAR's EC ---
 * that could result in propagating constant restrictions from
 * INNERVAR to OUTERVAR, which would be very wrong.
 *
 * It's possible that the INNERVAR is also an OUTERVAR for some other
 * outer-join clause, in which case the process can be repeated.  So we repeat
 * looping over the lists of clauses until no further deductions can be made.
 * Whenever we do make a deduction, we remove the generating clause from the
 * lists, since we don't want to make the same deduction twice.
 *
 * If we don't find any match for a set-aside outer join clause, we must
 * throw it back into the regular joinclause processing by passing it to
 * distribute_restrictinfo_to_rels().  If we do generate a derived clause,
 * however, the outer-join clause is redundant.  We still throw it back,
 * because otherwise the join will be seen as a clauseless join and avoided
 * during join order searching; but we mark it as redundant to keep from
 * messing up the joinrel's size estimate.  (This behavior means that the
 * API for this routine is uselessly complex: we could have just put all
 * the clauses into the regular processing initially.  We keep it because
 * someday we might want to do something else, such as inserting "dummy"
 * joinclauses instead of real ones.)
 *
 * Outer join clauses that are marked outerjoin_delayed are special: this
 * condition means that one or both VARs might go to null due to a lower
 * outer join.    We can still push a constant through the clause, but only
 * if its operator is strict; and we *have to* throw the clause back into
 * regular joinclause processing.  By keeping the strict join clause,
 * we ensure that any null-extended rows that are mistakenly generated due
 * to suppressing rows not matching the constant will be rejected at the
 * upper outer join.  (This doesn't work for full-join clauses.)
 */
void
reconsider_outer_join_clauses(PlannerInfo *root)
{
      bool        found;
      ListCell   *cell;
      ListCell   *prev;
      ListCell   *next;

      /* Outer loop repeats until we find no more deductions */
      do
      {
            found = false;

            /* Process the LEFT JOIN clauses */
            prev = NULL;
            for (cell = list_head(root->left_join_clauses); cell; cell = next)
            {
                  RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

                  next = lnext(cell);
                  if (reconsider_outer_join_clause(root, rinfo, true))
                  {
                        found = true;
                        /* remove it from the list */
                        root->left_join_clauses =
                              list_delete_cell(root->left_join_clauses, cell, prev);
                        /* we throw it back anyway (see notes above) */
                        /* but the thrown-back clause has no extra selectivity */
                        rinfo->norm_selec = 2.0;
                        rinfo->outer_selec = 1.0;
                        distribute_restrictinfo_to_rels(root, rinfo);
                  }
                  else
                        prev = cell;
            }

            /* Process the RIGHT JOIN clauses */
            prev = NULL;
            for (cell = list_head(root->right_join_clauses); cell; cell = next)
            {
                  RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

                  next = lnext(cell);
                  if (reconsider_outer_join_clause(root, rinfo, false))
                  {
                        found = true;
                        /* remove it from the list */
                        root->right_join_clauses =
                              list_delete_cell(root->right_join_clauses, cell, prev);
                        /* we throw it back anyway (see notes above) */
                        /* but the thrown-back clause has no extra selectivity */
                        rinfo->norm_selec = 2.0;
                        rinfo->outer_selec = 1.0;
                        distribute_restrictinfo_to_rels(root, rinfo);
                  }
                  else
                        prev = cell;
            }

            /* Process the FULL JOIN clauses */
            prev = NULL;
            for (cell = list_head(root->full_join_clauses); cell; cell = next)
            {
                  RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

                  next = lnext(cell);
                  if (reconsider_full_join_clause(root, rinfo))
                  {
                        found = true;
                        /* remove it from the list */
                        root->full_join_clauses =
                              list_delete_cell(root->full_join_clauses, cell, prev);
                        /* we throw it back anyway (see notes above) */
                        /* but the thrown-back clause has no extra selectivity */
                        rinfo->norm_selec = 2.0;
                        rinfo->outer_selec = 1.0;
                        distribute_restrictinfo_to_rels(root, rinfo);
                  }
                  else
                        prev = cell;
            }
      } while (found);

      /* Now, any remaining clauses have to be thrown back */
      foreach(cell, root->left_join_clauses)
      {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

            distribute_restrictinfo_to_rels(root, rinfo);
      }
      foreach(cell, root->right_join_clauses)
      {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

            distribute_restrictinfo_to_rels(root, rinfo);
      }
      foreach(cell, root->full_join_clauses)
      {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);

            distribute_restrictinfo_to_rels(root, rinfo);
      }
}

/*
 * reconsider_outer_join_clauses for a single LEFT/RIGHT JOIN clause
 *
 * Returns TRUE if we were able to propagate a constant through the clause.
 */
static bool
reconsider_outer_join_clause(PlannerInfo *root, RestrictInfo *rinfo,
                                           bool outer_on_left)
{
      Expr     *outervar,
                     *innervar;
      Oid               opno,
                        left_type,
                        right_type,
                        inner_datatype;
      Relids            inner_relids;
      ListCell   *lc1;

      Assert(is_opclause(rinfo->clause));
      opno = ((OpExpr *) rinfo->clause)->opno;

      /* If clause is outerjoin_delayed, operator must be strict */
      if (rinfo->outerjoin_delayed && !op_strict(opno))
            return false;

      /* Extract needed info from the clause */
      op_input_types(opno, &left_type, &right_type);
      if (outer_on_left)
      {
            outervar = (Expr *) get_leftop(rinfo->clause);
            innervar = (Expr *) get_rightop(rinfo->clause);
            inner_datatype = right_type;
            inner_relids = rinfo->right_relids;
      }
      else
      {
            outervar = (Expr *) get_rightop(rinfo->clause);
            innervar = (Expr *) get_leftop(rinfo->clause);
            inner_datatype = left_type;
            inner_relids = rinfo->left_relids;
      }

      /* Scan EquivalenceClasses for a match to outervar */
      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            bool        match;
            ListCell   *lc2;

            /* Ignore EC unless it contains pseudoconstants */
            if (!cur_ec->ec_has_const)
                  continue;
            /* Never match to a volatile EC */
            if (cur_ec->ec_has_volatile)
                  continue;
            /* It has to match the outer-join clause as to opfamilies, too */
            if (!equal(rinfo->mergeopfamilies, cur_ec->ec_opfamilies))
                  continue;
            /* Does it contain a match to outervar? */
            match = false;
            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  if (equal(outervar, cur_em->em_expr))
                  {
                        match = true;
                        break;
                  }
            }
            if (!match)
                  continue;               /* no match, so ignore this EC */

            /*
             * Yes it does!  Try to generate a clause INNERVAR = CONSTANT for each
             * CONSTANT in the EC.  Note that we must succeed with at least one
             * constant before we can decide to throw away the outer-join clause.
             */
            match = false;
            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
                  Oid               eq_op;
                  RestrictInfo *newrinfo;

                  if (!cur_em->em_is_const)
                        continue;         /* ignore non-const members */
                  eq_op = select_equality_operator(cur_ec,
                                                                   inner_datatype,
                                                                   cur_em->em_datatype);
                  if (!OidIsValid(eq_op))
                        continue;         /* can't generate equality */
                  newrinfo = build_implied_join_equality(eq_op,
                                                                           innervar,
                                                                           cur_em->em_expr,
                                                                           inner_relids);
                  if (process_equivalence(root, newrinfo, true))
                        match = true;
            }

            /*
             * If we were able to equate INNERVAR to any constant, report success.
             * Otherwise, fall out of the search loop, since we know the OUTERVAR
             * appears in at most one EC.
             */
            if (match)
                  return true;
            else
                  break;
      }

      return false;                       /* failed to make any deduction */
}

/*
 * reconsider_outer_join_clauses for a single FULL JOIN clause
 *
 * Returns TRUE if we were able to propagate a constant through the clause.
 */
static bool
reconsider_full_join_clause(PlannerInfo *root, RestrictInfo *rinfo)
{
      Expr     *leftvar;
      Expr     *rightvar;
      Oid               opno,
                        left_type,
                        right_type;
      Relids            left_relids,
                        right_relids;
      ListCell   *lc1;

      /* Can't use an outerjoin_delayed clause here */
      if (rinfo->outerjoin_delayed)
            return false;

      /* Extract needed info from the clause */
      Assert(is_opclause(rinfo->clause));
      opno = ((OpExpr *) rinfo->clause)->opno;
      op_input_types(opno, &left_type, &right_type);
      leftvar = (Expr *) get_leftop(rinfo->clause);
      rightvar = (Expr *) get_rightop(rinfo->clause);
      left_relids = rinfo->left_relids;
      right_relids = rinfo->right_relids;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            EquivalenceMember *coal_em = NULL;
            bool        match;
            bool        matchleft;
            bool        matchright;
            ListCell   *lc2;

            /* Ignore EC unless it contains pseudoconstants */
            if (!cur_ec->ec_has_const)
                  continue;
            /* Never match to a volatile EC */
            if (cur_ec->ec_has_volatile)
                  continue;
            /* It has to match the outer-join clause as to opfamilies, too */
            if (!equal(rinfo->mergeopfamilies, cur_ec->ec_opfamilies))
                  continue;

            /*
             * Does it contain a COALESCE(leftvar, rightvar) construct?
             *
             * We can assume the COALESCE() inputs are in the same order as the
             * join clause, since both were automatically generated in the cases
             * we care about.
             *
             * XXX currently this may fail to match in cross-type cases because
             * the COALESCE will contain typecast operations while the join clause
             * may not (if there is a cross-type mergejoin operator available for
             * the two column types). Is it OK to strip implicit coercions from
             * the COALESCE arguments?
             */
            match = false;
            foreach(lc2, cur_ec->ec_members)
            {
                  coal_em = (EquivalenceMember *) lfirst(lc2);
                  if (IsA(coal_em->em_expr, CoalesceExpr))
                  {
                        CoalesceExpr *cexpr = (CoalesceExpr *) coal_em->em_expr;
                        Node     *cfirst;
                        Node     *csecond;

                        if (list_length(cexpr->args) != 2)
                              continue;
                        cfirst = (Node *) linitial(cexpr->args);
                        csecond = (Node *) lsecond(cexpr->args);

                        if (equal(leftvar, cfirst) && equal(rightvar, csecond))
                        {
                              match = true;
                              break;
                        }
                  }
            }
            if (!match)
                  continue;               /* no match, so ignore this EC */

            /*
             * Yes it does!  Try to generate clauses LEFTVAR = CONSTANT and
             * RIGHTVAR = CONSTANT for each CONSTANT in the EC.  Note that we must
             * succeed with at least one constant for each var before we can
             * decide to throw away the outer-join clause.
             */
            matchleft = matchright = false;
            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
                  Oid               eq_op;
                  RestrictInfo *newrinfo;

                  if (!cur_em->em_is_const)
                        continue;         /* ignore non-const members */
                  eq_op = select_equality_operator(cur_ec,
                                                                   left_type,
                                                                   cur_em->em_datatype);
                  if (OidIsValid(eq_op))
                  {
                        newrinfo = build_implied_join_equality(eq_op,
                                                                                 leftvar,
                                                                                 cur_em->em_expr,
                                                                                 left_relids);
                        if (process_equivalence(root, newrinfo, true))
                              matchleft = true;
                  }
                  eq_op = select_equality_operator(cur_ec,
                                                                   right_type,
                                                                   cur_em->em_datatype);
                  if (OidIsValid(eq_op))
                  {
                        newrinfo = build_implied_join_equality(eq_op,
                                                                                 rightvar,
                                                                                 cur_em->em_expr,
                                                                                 right_relids);
                        if (process_equivalence(root, newrinfo, true))
                              matchright = true;
                  }
            }

            /*
             * If we were able to equate both vars to constants, we're done, and
             * we can throw away the full-join clause as redundant.  Moreover, we
             * can remove the COALESCE entry from the EC, since the added
             * restrictions ensure it will always have the expected value. (We
             * don't bother trying to update ec_relids or ec_sources.)
             */
            if (matchleft && matchright)
            {
                  cur_ec->ec_members = list_delete_ptr(cur_ec->ec_members, coal_em);
                  return true;
            }

            /*
             * Otherwise, fall out of the search loop, since we know the COALESCE
             * appears in at most one EC (XXX might stop being true if we allow
             * stripping of coercions above?)
             */
            break;
      }

      return false;                       /* failed to make any deduction */
}


/*
 * exprs_known_equal
 *      Detect whether two expressions are known equal due to equivalence
 *      relationships.
 *
 * Actually, this only shows that the expressions are equal according
 * to some opfamily's notion of equality --- but we only use it for
 * selectivity estimation, so a fuzzy idea of equality is OK.
 *
 * Note: does not bother to check for "equal(item1, item2)"; caller must
 * check that case if it's possible to pass identical items.
 */
bool
exprs_known_equal(PlannerInfo *root, Node *item1, Node *item2)
{
      ListCell   *lc1;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);
            bool        item1member = false;
            bool        item2member = false;
            ListCell   *lc2;

            /* Never match to a volatile EC */
            if (ec->ec_has_volatile)
                  continue;

            foreach(lc2, ec->ec_members)
            {
                  EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);

                  if (equal(item1, em->em_expr))
                        item1member = true;
                  else if (equal(item2, em->em_expr))
                        item2member = true;
                  /* Exit as soon as equality is proven */
                  if (item1member && item2member)
                        return true;
            }
      }
      return false;
}


/*
 * add_child_rel_equivalences
 *      Search for EC members that reference (only) the parent_rel, and
 *      add transformed members referencing the child_rel.
 *
 * We only need to do this for ECs that could generate join conditions,
 * since the child members are only used for creating inner-indexscan paths.
 *
 * parent_rel and child_rel could be derived from appinfo, but since the
 * caller has already computed them, we might as well just pass them in.
 */
void
add_child_rel_equivalences(PlannerInfo *root,
                                       AppendRelInfo *appinfo,
                                       RelOptInfo *parent_rel,
                                       RelOptInfo *child_rel)
{
      ListCell   *lc1;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            ListCell   *lc2;

            /*
             * Won't generate joinclauses if const or single-member (the latter
             * test covers the volatile case too)
             */
            if (cur_ec->ec_has_const || list_length(cur_ec->ec_members) <= 1)
                  continue;

            /* No point in searching if parent rel not mentioned in eclass */
            if (!bms_is_subset(parent_rel->relids, cur_ec->ec_relids))
                  continue;

            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  /* Does it reference (only) parent_rel? */
                  if (bms_equal(cur_em->em_relids, parent_rel->relids))
                  {
                        /* Yes, generate transformed child version */
                        Expr     *child_expr;

                        child_expr = (Expr *)
                              adjust_appendrel_attrs((Node *) cur_em->em_expr,
                                                               appinfo);
                        (void) add_eq_member(cur_ec, child_expr, child_rel->relids,
                                                       true, cur_em->em_datatype);
                  }
            }
      }
}


/*
 * mutate_eclass_expressions
 *      Apply an expression tree mutator to all expressions stored in
 *      equivalence classes.
 *
 * This is a bit of a hack ... it's currently needed only by planagg.c,
 * which needs to do a global search-and-replace of MIN/MAX Aggrefs
 * after eclasses are already set up.  Without changing the eclasses too,
 * subsequent matching of ORDER BY clauses would fail.
 *
 * Note that we assume the mutation won't affect relation membership or any
 * other properties we keep track of (which is a bit bogus, but by the time
 * planagg.c runs, it no longer matters).  Also we must be called in the
 * main planner memory context.
 */
void
mutate_eclass_expressions(PlannerInfo *root,
                                      Node *(*mutator) (),
                                      void *context)
{
      ListCell   *lc1;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            ListCell   *lc2;

            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  cur_em->em_expr = (Expr *)
                        mutator((Node *) cur_em->em_expr, context);
            }
      }
}


/*
 * find_eclass_clauses_for_index_join
 *      Create joinclauses usable for a nestloop-with-inner-indexscan
 *      scanning the given inner rel with the specified set of outer rels.
 */
List *
find_eclass_clauses_for_index_join(PlannerInfo *root, RelOptInfo *rel,
                                                   Relids outer_relids)
{
      List     *result = NIL;
      bool        is_child_rel = (rel->reloptkind == RELOPT_OTHER_MEMBER_REL);
      ListCell   *lc1;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *cur_ec = (EquivalenceClass *) lfirst(lc1);
            ListCell   *lc2;

            /*
             * Won't generate joinclauses if const or single-member (the latter
             * test covers the volatile case too)
             */
            if (cur_ec->ec_has_const || list_length(cur_ec->ec_members) <= 1)
                  continue;

            /*
             * No point in searching if rel not mentioned in eclass (but we can't
             * tell that for a child rel).
             */
            if (!is_child_rel &&
                  !bms_is_subset(rel->relids, cur_ec->ec_relids))
                  continue;
            /* ... nor if no overlap with outer_relids */
            if (!bms_overlap(outer_relids, cur_ec->ec_relids))
                  continue;

            /* Scan members, looking for indexable columns */
            foreach(lc2, cur_ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);
                  EquivalenceMember *best_outer_em = NULL;
                  Oid               best_eq_op = InvalidOid;
                  ListCell   *lc3;

                  if (!bms_equal(cur_em->em_relids, rel->relids) ||
                        !eclass_matches_any_index(cur_ec, cur_em, rel))
                        continue;

                  /*
                   * Found one, so try to generate a join clause.  This is like
                   * generate_join_implied_equalities_normal, except simpler since
                   * our only preference item is to pick a Var on the outer side. We
                   * only need one join clause per index col.
                   */
                  foreach(lc3, cur_ec->ec_members)
                  {
                        EquivalenceMember *outer_em = (EquivalenceMember *) lfirst(lc3);
                        Oid               eq_op;

                        if (!bms_is_subset(outer_em->em_relids, outer_relids))
                              continue;
                        eq_op = select_equality_operator(cur_ec,
                                                                         cur_em->em_datatype,
                                                                         outer_em->em_datatype);
                        if (!OidIsValid(eq_op))
                              continue;
                        best_outer_em = outer_em;
                        best_eq_op = eq_op;
                        if (IsA(outer_em->em_expr, Var) ||
                              (IsA(outer_em->em_expr, RelabelType) &&
                               IsA(((RelabelType *) outer_em->em_expr)->arg, Var)))
                              break;            /* no need to look further */
                  }

                  if (best_outer_em)
                  {
                        /* Found a suitable joinclause */
                        RestrictInfo *rinfo;

                        /* set parent_ec to mark as redundant with other joinclauses */
                        rinfo = create_join_clause(root, cur_ec, best_eq_op,
                                                               cur_em, best_outer_em,
                                                               cur_ec);

                        result = lappend(result, rinfo);

                        /*
                         * Note: we keep scanning here because we want to provide a
                         * clause for every possible indexcol.
                         */
                  }
            }
      }

      return result;
}


/*
 * have_relevant_eclass_joinclause
 *          Detect whether there is an EquivalenceClass that could produce
 *          a joinclause between the two given relations.
 *
 * This is essentially a very cut-down version of
 * generate_join_implied_equalities().    Note it's OK to occasionally say "yes"
 * incorrectly.  Hence we don't bother with details like whether the lack of a
 * cross-type operator might prevent the clause from actually being generated.
 */
bool
have_relevant_eclass_joinclause(PlannerInfo *root,
                                                RelOptInfo *rel1, RelOptInfo *rel2)
{
      ListCell   *lc1;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);
            bool        has_rel1;
            bool        has_rel2;
            ListCell   *lc2;

            /*
             * Won't generate joinclauses if single-member (this test covers the
             * volatile case too)
             */
            if (list_length(ec->ec_members) <= 1)
                  continue;

            /*
             * Note we don't test ec_broken; if we did, we'd need a separate code
             * path to look through ec_sources.  Checking the members anyway is OK
             * as a possibly-overoptimistic heuristic.
             *
             * We don't test ec_has_const either, even though a const eclass won't
             * generate real join clauses.      This is because if we had "WHERE a.x =
             * b.y and a.x = 42", it is worth considering a join between a and b,
             * since the join result is likely to be small even though it'll end
             * up being an unqualified nestloop.
             */

            /* Needn't scan if it couldn't contain members from each rel */
            if (!bms_overlap(rel1->relids, ec->ec_relids) ||
                  !bms_overlap(rel2->relids, ec->ec_relids))
                  continue;

            /* Scan the EC to see if it has member(s) in each rel */
            has_rel1 = has_rel2 = false;
            foreach(lc2, ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  if (cur_em->em_is_const || cur_em->em_is_child)
                        continue;         /* ignore consts and children here */
                  if (bms_is_subset(cur_em->em_relids, rel1->relids))
                  {
                        has_rel1 = true;
                        if (has_rel2)
                              break;
                  }
                  if (bms_is_subset(cur_em->em_relids, rel2->relids))
                  {
                        has_rel2 = true;
                        if (has_rel1)
                              break;
                  }
            }

            if (has_rel1 && has_rel2)
                  return true;
      }

      return false;
}


/*
 * has_relevant_eclass_joinclause
 *          Detect whether there is an EquivalenceClass that could produce
 *          a joinclause between the given relation and anything else.
 *
 * This is the same as have_relevant_eclass_joinclause with the other rel
 * implicitly defined as "everything else in the query".
 */
bool
has_relevant_eclass_joinclause(PlannerInfo *root, RelOptInfo *rel1)
{
      ListCell   *lc1;

      foreach(lc1, root->eq_classes)
      {
            EquivalenceClass *ec = (EquivalenceClass *) lfirst(lc1);
            bool        has_rel1;
            bool        has_rel2;
            ListCell   *lc2;

            /*
             * Won't generate joinclauses if single-member (this test covers the
             * volatile case too)
             */
            if (list_length(ec->ec_members) <= 1)
                  continue;

            /*
             * Note we don't test ec_broken; if we did, we'd need a separate code
             * path to look through ec_sources.  Checking the members anyway is OK
             * as a possibly-overoptimistic heuristic.
             *
             * We don't test ec_has_const either, even though a const eclass won't
             * generate real join clauses.      This is because if we had "WHERE a.x =
             * b.y and a.x = 42", it is worth considering a join between a and b,
             * since the join result is likely to be small even though it'll end
             * up being an unqualified nestloop.
             */

            /* Needn't scan if it couldn't contain members from each rel */
            if (!bms_overlap(rel1->relids, ec->ec_relids) ||
                  bms_is_subset(ec->ec_relids, rel1->relids))
                  continue;

            /* Scan the EC to see if it has member(s) in each rel */
            has_rel1 = has_rel2 = false;
            foreach(lc2, ec->ec_members)
            {
                  EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc2);

                  if (cur_em->em_is_const || cur_em->em_is_child)
                        continue;         /* ignore consts and children here */
                  if (bms_is_subset(cur_em->em_relids, rel1->relids))
                  {
                        has_rel1 = true;
                        if (has_rel2)
                              break;
                  }
                  if (!bms_overlap(cur_em->em_relids, rel1->relids))
                  {
                        has_rel2 = true;
                        if (has_rel1)
                              break;
                  }
            }

            if (has_rel1 && has_rel2)
                  return true;
      }

      return false;
}


/*
 * eclass_useful_for_merging
 *      Detect whether the EC could produce any mergejoinable join clauses
 *      against the specified relation.
 *
 * This is just a heuristic test and doesn't have to be exact; it's better
 * to say "yes" incorrectly than "no".    Hence we don't bother with details
 * like whether the lack of a cross-type operator might prevent the clause
 * from actually being generated.
 */
bool
eclass_useful_for_merging(EquivalenceClass *eclass,
                                      RelOptInfo *rel)
{
      ListCell   *lc;

      Assert(!eclass->ec_merged);

      /*
       * Won't generate joinclauses if const or single-member (the latter test
       * covers the volatile case too)
       */
      if (eclass->ec_has_const || list_length(eclass->ec_members) <= 1)
            return false;

      /*
       * Note we don't test ec_broken; if we did, we'd need a separate code path
       * to look through ec_sources.      Checking the members anyway is OK as a
       * possibly-overoptimistic heuristic.
       */

      /* If rel already includes all members of eclass, no point in searching */
      if (bms_is_subset(eclass->ec_relids, rel->relids))
            return false;

      /* To join, we need a member not in the given rel */
      foreach(lc, eclass->ec_members)
      {
            EquivalenceMember *cur_em = (EquivalenceMember *) lfirst(lc);

            if (!cur_em->em_is_child &&
                  !bms_overlap(cur_em->em_relids, rel->relids))
                  return true;
      }

      return false;
}

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