text: /*-------------------------------------------------------------------------
   *
   * pathnode.c
   *	  Routines to manipulate pathlists and create path nodes
   *
   * Portions Copyright (c) 1996-2014, PostgreSQL Global Development Group
   * Portions Copyright (c) 1994, Regents of the University of California
   *
   *
   * IDENTIFICATION
   *	  src/backend/optimizer/util/pathnode.c
   *
   *-------------------------------------------------------------------------
   */
  #include "postgres.h"
  
  #include <math.h>
  
  #include "miscadmin.h"
  #include "nodes/nodeFuncs.h"
  #include "optimizer/clauses.h"
  #include "optimizer/cost.h"
  #include "optimizer/pathnode.h"
  #include "optimizer/paths.h"
  #include "optimizer/restrictinfo.h"
  #include "optimizer/tlist.h"
  #include "parser/parsetree.h"
  #include "utils/lsyscache.h"
  #include "utils/selfuncs.h"
  
  
  typedef enum
  {
  	COSTS_EQUAL,				/* path costs are fuzzily equal */
  	COSTS_BETTER1,				/* first path is cheaper than second */
  	COSTS_BETTER2,				/* second path is cheaper than first */
  	COSTS_DIFFERENT				/* neither path dominates the other on cost */
  } PathCostComparison;
  
  static List *translate_sub_tlist(List *tlist, int relid);
  static bool query_is_distinct_for(Query *query, List *colnos, List *opids);
  static Oid	distinct_col_search(int colno, List *colnos, List *opids);
  
  
  /*****************************************************************************
   *		MISC. PATH UTILITIES
   *****************************************************************************/
  
  /*
   * compare_path_costs
   *	  Return -1, 0, or +1 according as path1 is cheaper, the same cost,
   *	  or more expensive than path2 for the specified criterion.
   */
  int
  compare_path_costs(Path *path1, Path *path2, CostSelector criterion)
  {
  	if (criterion == STARTUP_COST)
  	{
  		if (path1->startup_cost < path2->startup_cost)
  			return -1;
  		if (path1->startup_cost > path2->startup_cost)
  			return +1;
  
  		/*
  		 * If paths have the same startup cost (not at all unlikely), order
  		 * them by total cost.
  		 */
  		if (path1->total_cost < path2->total_cost)
  			return -1;
  		if (path1->total_cost > path2->total_cost)
  			return +1;
  	}
  	else
  	{
  		if (path1->total_cost < path2->total_cost)
  			return -1;
  		if (path1->total_cost > path2->total_cost)
  			return +1;
  
  		/*
  		 * If paths have the same total cost, order them by startup cost.
  		 */
  		if (path1->startup_cost < path2->startup_cost)
  			return -1;
  		if (path1->startup_cost > path2->startup_cost)
  			return +1;
  	}
  	return 0;
  }
  
  /*
   * compare_path_fractional_costs
   *	  Return -1, 0, or +1 according as path1 is cheaper, the same cost,
   *	  or more expensive than path2 for fetching the specified fraction
   *	  of the total tuples.
   *
   * If fraction is <= 0 or > 1, we interpret it as 1, ie, we select the
   * path with the cheaper total_cost.
   */
  int
  compare_fractional_path_costs(Path *path1, Path *path2,
  							  double fraction)
  {
  	Cost		cost1,
  				cost2;
  
  	if (fraction <= 0.0 || fraction >= 1.0)
  		return compare_path_costs(path1, path2, TOTAL_COST);
  	cost1 = path1->startup_cost +
  		fraction * (path1->total_cost - path1->startup_cost);
  	cost2 = path2->startup_cost +
  		fraction * (path2->total_cost - path2->startup_cost);
  	if (cost1 < cost2)
  		return -1;
  	if (cost1 > cost2)
  		return +1;
  	return 0;
  }
  
  /*
   * compare_path_costs_fuzzily
   *	  Compare the costs of two paths to see if either can be said to
   *	  dominate the other.
   *
   * We use fuzzy comparisons so that add_path() can avoid keeping both of
   * a pair of paths that really have insignificantly different cost.
   *
   * The fuzz_factor argument must be 1.0 plus delta, where delta is the
   * fraction of the smaller cost that is considered to be a significant
   * difference.	For example, fuzz_factor = 1.01 makes the fuzziness limit
   * be 1% of the smaller cost.
   *
   * The two paths are said to have "equal" costs if both startup and total
   * costs are fuzzily the same.	Path1 is said to be better than path2 if
   * it has fuzzily better startup cost and fuzzily no worse total cost,
   * or if it has fuzzily better total cost and fuzzily no worse startup cost.
   * Path2 is better than path1 if the reverse holds.  Finally, if one path
   * is fuzzily better than the other on startup cost and fuzzily worse on
   * total cost, we just say that their costs are "different", since neither
   * dominates the other across the whole performance spectrum.
   *
   * If consider_startup is false, then we don't care about keeping paths with
   * good startup cost, so we'll never return COSTS_DIFFERENT.
   *
   * This function also includes special hacks to support a policy enforced
   * by its sole caller, add_path(): paths that have any parameterization
   * cannot win comparisons on the grounds of having cheaper startup cost,
   * since we deem only total cost to be of interest for a parameterized path.
   * (Unparameterized paths are more common, so we check for this case last.)
   */
  static PathCostComparison
  compare_path_costs_fuzzily(Path *path1, Path *path2, double fuzz_factor,
  						   bool consider_startup)
  {
  	/*
  	 * Check total cost first since it's more likely to be different; many
  	 * paths have zero startup cost.
  	 */
  	if (path1->total_cost > path2->total_cost * fuzz_factor)
  	{
  		/* path1 fuzzily worse on total cost */
  		if (consider_startup &&
  			path2->startup_cost > path1->startup_cost * fuzz_factor &&
  			path1->param_info == NULL)
  		{
  			/* ... but path2 fuzzily worse on startup, so DIFFERENT */
  			return COSTS_DIFFERENT;
  		}
  		/* else path2 dominates */
  		return COSTS_BETTER2;
  	}
  	if (path2->total_cost > path1->total_cost * fuzz_factor)
  	{
  		/* path2 fuzzily worse on total cost */
  		if (consider_startup &&
  			path1->startup_cost > path2->startup_cost * fuzz_factor &&
  			path2->param_info == NULL)
  		{
  			/* ... but path1 fuzzily worse on startup, so DIFFERENT */
  			return COSTS_DIFFERENT;
  		}
  		/* else path1 dominates */
  		return COSTS_BETTER1;
  	}
  	/* fuzzily the same on total cost */
  	/* (so we may as well compare startup cost, even if !consider_startup) */
  	if (path1->startup_cost > path2->startup_cost * fuzz_factor &&
  		path2->param_info == NULL)
  	{
  		/* ... but path1 fuzzily worse on startup, so path2 wins */
  		return COSTS_BETTER2;
  	}
  	if (path2->startup_cost > path1->startup_cost * fuzz_factor &&
  		path1->param_info == NULL)
  	{
  		/* ... but path2 fuzzily worse on startup, so path1 wins */
  		return COSTS_BETTER1;
  	}
  	/* fuzzily the same on both costs */
  	return COSTS_EQUAL;
  }
  
  /*
   * set_cheapest
   *	  Find the minimum-cost paths from among a relation's paths,
   *	  and save them in the rel's cheapest-path fields.
   *
   * cheapest_total_path is normally the cheapest-total-cost unparameterized
   * path; but if there are no unparameterized paths, we assign it to be the
   * best (cheapest least-parameterized) parameterized path.	However, only
   * unparameterized paths are considered candidates for cheapest_startup_path,
   * so that will be NULL if there are no unparameterized paths.
   *
   * The cheapest_parameterized_paths list collects all parameterized paths
   * that have survived the add_path() tournament for this relation.	(Since
   * add_path ignores pathkeys and startup cost for a parameterized path,
   * these will be paths that have best total cost or best row count for their
   * parameterization.)  cheapest_parameterized_paths always includes the
   * cheapest-total unparameterized path, too, if there is one; the users of
   * that list find it more convenient if that's included.
   *
   * This is normally called only after we've finished constructing the path
   * list for the rel node.
   */
  void
  set_cheapest(RelOptInfo *parent_rel)
  {
  	Path	   *cheapest_startup_path;
  	Path	   *cheapest_total_path;
  	Path	   *best_param_path;
  	List	   *parameterized_paths;
  	ListCell   *p;
  
  	Assert(IsA(parent_rel, RelOptInfo));
  
  	if (parent_rel->pathlist == NIL)
  		elog(ERROR, "could not devise a query plan for the given query");
  
  	cheapest_startup_path = cheapest_total_path = best_param_path = NULL;
  	parameterized_paths = NIL;
  
  	foreach(p, parent_rel->pathlist)
  	{
  		Path	   *path = (Path *) lfirst(p);
  		int			cmp;
  
  		if (path->param_info)
  		{
  			/* Parameterized path, so add it to parameterized_paths */
  			parameterized_paths = lappend(parameterized_paths, path);
  
  			/*
  			 * If we have an unparameterized cheapest-total, we no longer care
  			 * about finding the best parameterized path, so move on.
  			 */
  			if (cheapest_total_path)
  				continue;
  
  			/*
  			 * Otherwise, track the best parameterized path, which is the one
  			 * with least total cost among those of the minimum
  			 * parameterization.
  			 */
  			if (best_param_path == NULL)
  				best_param_path = path;
  			else
  			{
  				switch (bms_subset_compare(PATH_REQ_OUTER(path),
  										   PATH_REQ_OUTER(best_param_path)))
  				{
  					case BMS_EQUAL:
  						/* keep the cheaper one */
  						if (compare_path_costs(path, best_param_path,
  											   TOTAL_COST) < 0)
  							best_param_path = path;
  						break;
  					case BMS_SUBSET1:
  						/* new path is less-parameterized */
  						best_param_path = path;
  						break;
  					case BMS_SUBSET2:
  						/* old path is less-parameterized, keep it */
  						break;
  					case BMS_DIFFERENT:
  
  						/*
  						 * This means that neither path has the least possible
  						 * parameterization for the rel.  We'll sit on the old
  						 * path until something better comes along.
  						 */
  						break;
  				}
  			}
  		}
  		else
  		{
  			/* Unparameterized path, so consider it for cheapest slots */
  			if (cheapest_total_path == NULL)
  			{
  				cheapest_startup_path = cheapest_total_path = path;
  				continue;
  			}
  
  			/*
  			 * If we find two paths of identical costs, try to keep the
  			 * better-sorted one.  The paths might have unrelated sort
  			 * orderings, in which case we can only guess which might be
  			 * better to keep, but if one is superior then we definitely
  			 * should keep that one.
  			 */
  			cmp = compare_path_costs(cheapest_startup_path, path, STARTUP_COST);
  			if (cmp > 0 ||
  				(cmp == 0 &&
  				 compare_pathkeys(cheapest_startup_path->pathkeys,
  								  path->pathkeys) == PATHKEYS_BETTER2))
  				cheapest_startup_path = path;
  
  			cmp = compare_path_costs(cheapest_total_path, path, TOTAL_COST);
  			if (cmp > 0 ||
  				(cmp == 0 &&
  				 compare_pathkeys(cheapest_total_path->pathkeys,
  								  path->pathkeys) == PATHKEYS_BETTER2))
  				cheapest_total_path = path;
  		}
  	}
  
  	/* Add cheapest unparameterized path, if any, to parameterized_paths */
  	if (cheapest_total_path)
  		parameterized_paths = lcons(cheapest_total_path, parameterized_paths);
  
  	/*
  	 * If there is no unparameterized path, use the best parameterized path as
  	 * cheapest_total_path (but not as cheapest_startup_path).
  	 */
  	if (cheapest_total_path == NULL)
  		cheapest_total_path = best_param_path;
  	Assert(cheapest_total_path != NULL);
  
  	parent_rel->cheapest_startup_path = cheapest_startup_path;
  	parent_rel->cheapest_total_path = cheapest_total_path;
  	parent_rel->cheapest_unique_path = NULL;	/* computed only if needed */
  	parent_rel->cheapest_parameterized_paths = parameterized_paths;
  }
  
  /*
   * add_path
   *	  Consider a potential implementation path for the specified parent rel,
   *	  and add it to the rel's pathlist if it is worthy of consideration.
   *	  A path is worthy if it has a better sort order (better pathkeys) or
   *	  cheaper cost (on either dimension), or generates fewer rows, than any
   *	  existing path that has the same or superset parameterization rels.
   *
   *	  We also remove from the rel's pathlist any old paths that are dominated
   *	  by new_path --- that is, new_path is cheaper, at least as well ordered,
   *	  generates no more rows, and requires no outer rels not required by the
   *	  old path.
   *
   *	  In most cases, a path with a superset parameterization will generate
   *	  fewer rows (since it has more join clauses to apply), so that those two
   *	  figures of merit move in opposite directions; this means that a path of
   *	  one parameterization can seldom dominate a path of another.  But such
   *	  cases do arise, so we make the full set of checks anyway.
   *
   *	  There are two policy decisions embedded in this function, along with
   *	  its sibling add_path_precheck: we treat all parameterized paths as
   *	  having NIL pathkeys, and we ignore their startup costs, so that they
   *	  compete only on parameterization, total cost and rowcount.  This is to
   *	  reduce the number of parameterized paths that are kept.  See discussion
   *	  in src/backend/optimizer/README.
   *
   *	  Another policy that is enforced here is that we only consider cheap
   *	  startup cost to be interesting if parent_rel->consider_startup is true.
   *
   *	  The pathlist is kept sorted by total_cost, with cheaper paths
   *	  at the front.  Within this routine, that's simply a speed hack:
   *	  doing it that way makes it more likely that we will reject an inferior
   *	  path after a few comparisons, rather than many comparisons.
   *	  However, add_path_precheck relies on this ordering to exit early
   *	  when possible.
   *
   *	  NOTE: discarded Path objects are immediately pfree'd to reduce planner
   *	  memory consumption.  We dare not try to free the substructure of a Path,
   *	  since much of it may be shared with other Paths or the query tree itself;
   *	  but just recycling discarded Path nodes is a very useful savings in
   *	  a large join tree.  We can recycle the List nodes of pathlist, too.
   *
   *	  BUT: we do not pfree IndexPath objects, since they may be referenced as
   *	  children of BitmapHeapPaths as well as being paths in their own right.
   *
   * 'parent_rel' is the relation entry to which the path corresponds.
   * 'new_path' is a potential path for parent_rel.
   *
   * Returns nothing, but modifies parent_rel->pathlist.
   */
  void
  add_path(RelOptInfo *parent_rel, Path *new_path)
  {
  	bool		accept_new = true;		/* unless we find a superior old path */
  	ListCell   *insert_after = NULL;	/* where to insert new item */
  	List	   *new_path_pathkeys;
  	ListCell   *p1;
  	ListCell   *p1_prev;
  	ListCell   *p1_next;
  
  	/*
  	 * This is a convenient place to check for query cancel --- no part of the
  	 * planner goes very long without calling add_path().
  	 */
  	CHECK_FOR_INTERRUPTS();
  
  	/* Pretend parameterized paths have no pathkeys, per comment above */
  	new_path_pathkeys = new_path->param_info ? NIL : new_path->pathkeys;
  
  	/*
  	 * Loop to check proposed new path against old paths.  Note it is possible
  	 * for more than one old path to be tossed out because new_path dominates
  	 * it.
  	 *
  	 * We can't use foreach here because the loop body may delete the current
  	 * list cell.
  	 */
  	p1_prev = NULL;
  	for (p1 = list_head(parent_rel->pathlist); p1 != NULL; p1 = p1_next)
  	{
  		Path	   *old_path = (Path *) lfirst(p1);
  		bool		remove_old = false; /* unless new proves superior */
  		PathCostComparison costcmp;
  		PathKeysComparison keyscmp;
  		BMS_Comparison outercmp;
  
  		p1_next = lnext(p1);
  
  		/*
  		 * Do a fuzzy cost comparison with 1% fuzziness limit.	(XXX does this
  		 * percentage need to be user-configurable?)
  		 */
  		costcmp = compare_path_costs_fuzzily(new_path, old_path, 1.01,
  											 parent_rel->consider_startup);
  
  		/*
  		 * If the two paths compare differently for startup and total cost,
  		 * then we want to keep both, and we can skip comparing pathkeys and
  		 * required_outer rels.  If they compare the same, proceed with the
  		 * other comparisons.  Row count is checked last.  (We make the tests
  		 * in this order because the cost comparison is most likely to turn
  		 * out "different", and the pathkeys comparison next most likely.  As
  		 * explained above, row count very seldom makes a difference, so even
  		 * though it's cheap to compare there's not much point in checking it
  		 * earlier.)
  		 */
  		if (costcmp != COSTS_DIFFERENT)
  		{
  			/* Similarly check to see if either dominates on pathkeys */
  			List	   *old_path_pathkeys;
  
  			old_path_pathkeys = old_path->param_info ? NIL : old_path->pathkeys;
  			keyscmp = compare_pathkeys(new_path_pathkeys,
  									   old_path_pathkeys);
  			if (keyscmp != PATHKEYS_DIFFERENT)
  			{
  				switch (costcmp)
  				{
  					case COSTS_EQUAL:
  						outercmp = bms_subset_compare(PATH_REQ_OUTER(new_path),
  												   PATH_REQ_OUTER(old_path));
  						if (keyscmp == PATHKEYS_BETTER1)
  						{
  							if ((outercmp == BMS_EQUAL ||
  								 outercmp == BMS_SUBSET1) &&
  								new_path->rows <= old_path->rows)
  								remove_old = true;		/* new dominates old */
  						}
  						else if (keyscmp == PATHKEYS_BETTER2)
  						{
  							if ((outercmp == BMS_EQUAL ||
  								 outercmp == BMS_SUBSET2) &&
  								new_path->rows >= old_path->rows)
  								accept_new = false;		/* old dominates new */
  						}
  						else	/* keyscmp == PATHKEYS_EQUAL */
  						{
  							if (outercmp == BMS_EQUAL)
  							{
  								/*
  								 * Same pathkeys and outer rels, and fuzzily
  								 * the same cost, so keep just one; to decide
  								 * which, first check rows and then do a fuzzy
  								 * cost comparison with very small fuzz limit.
  								 * (We used to do an exact cost comparison,
  								 * but that results in annoying
  								 * platform-specific plan variations due to
  								 * roundoff in the cost estimates.)  If things
  								 * are still tied, arbitrarily keep only the
  								 * old path.  Notice that we will keep only
  								 * the old path even if the less-fuzzy
  								 * comparison decides the startup and total
  								 * costs compare differently.
  								 */
  								if (new_path->rows < old_path->rows)
  									remove_old = true;	/* new dominates old */
  								else if (new_path->rows > old_path->rows)
  									accept_new = false; /* old dominates new */
  								else if (compare_path_costs_fuzzily(new_path,
  																	old_path,
  																1.0000000001,
  																	parent_rel->consider_startup) == COSTS_BETTER1)
  									remove_old = true;	/* new dominates old */
  								else
  									accept_new = false; /* old equals or
  														 * dominates new */
  							}
  							else if (outercmp == BMS_SUBSET1 &&
  									 new_path->rows <= old_path->rows)
  								remove_old = true;		/* new dominates old */
  							else if (outercmp == BMS_SUBSET2 &&
  									 new_path->rows >= old_path->rows)
  								accept_new = false;		/* old dominates new */
  							/* else different parameterizations, keep both */
  						}
  						break;
  					case COSTS_BETTER1:
  						if (keyscmp != PATHKEYS_BETTER2)
  						{
  							outercmp = bms_subset_compare(PATH_REQ_OUTER(new_path),
  												   PATH_REQ_OUTER(old_path));
  							if ((outercmp == BMS_EQUAL ||
  								 outercmp == BMS_SUBSET1) &&
  								new_path->rows <= old_path->rows)
  								remove_old = true;		/* new dominates old */
  						}
  						break;
  					case COSTS_BETTER2:
  						if (keyscmp != PATHKEYS_BETTER1)
  						{
  							outercmp = bms_subset_compare(PATH_REQ_OUTER(new_path),
  												   PATH_REQ_OUTER(old_path));
  							if ((outercmp == BMS_EQUAL ||
  								 outercmp == BMS_SUBSET2) &&
  								new_path->rows >= old_path->rows)
  								accept_new = false;		/* old dominates new */
  						}
  						break;
  					case COSTS_DIFFERENT:
  
  						/*
  						 * can't get here, but keep this case to keep compiler
  						 * quiet
  						 */
  						break;
  				}
  			}
  		}
  
  		/*
  		 * Remove current element from pathlist if dominated by new.
  		 */
  		if (remove_old)
  		{
  			parent_rel->pathlist = list_delete_cell(parent_rel->pathlist,
  													p1, p1_prev);
  
  			/*
  			 * Delete the data pointed-to by the deleted cell, if possible
  			 */
  			if (!IsA(old_path, IndexPath))
  				pfree(old_path);
  			/* p1_prev does not advance */
  		}
  		else
  		{
  			/* new belongs after this old path if it has cost >= old's */
  			if (new_path->total_cost >= old_path->total_cost)
  				insert_after = p1;
  			/* p1_prev advances */
  			p1_prev = p1;
  		}
  
  		/*
  		 * If we found an old path that dominates new_path, we can quit
  		 * scanning the pathlist; we will not add new_path, and we assume
  		 * new_path cannot dominate any other elements of the pathlist.
  		 */
  		if (!accept_new)
  			break;
  	}
  
  	if (accept_new)
  	{
  		/* Accept the new path: insert it at proper place in pathlist */
  		if (insert_after)
  			lappend_cell(parent_rel->pathlist, insert_after, new_path);
  		else
  			parent_rel->pathlist = lcons(new_path, parent_rel->pathlist);
  	}
  	else
  	{
  		/* Reject and recycle the new path */
  		if (!IsA(new_path, IndexPath))
  			pfree(new_path);
  	}
  }
  
  /*
   * add_path_precheck
   *	  Check whether a proposed new path could possibly get accepted.
   *	  We assume we know the path's pathkeys and parameterization accurately,
   *	  and have lower bounds for its costs.
   *
   * Note that we do not know the path's rowcount, since getting an estimate for
   * that is too expensive to do before prechecking.	We assume here that paths
   * of a superset parameterization will generate fewer rows; if that holds,
   * then paths with different parameterizations cannot dominate each other
   * and so we can simply ignore existing paths of another parameterization.
   * (In the infrequent cases where that rule of thumb fails, add_path will
   * get rid of the inferior path.)
   *
   * At the time this is called, we haven't actually built a Path structure,
   * so the required information has to be passed piecemeal.
   */
  bool
  add_path_precheck(RelOptInfo *parent_rel,
  				  Cost startup_cost, Cost total_cost,
  				  List *pathkeys, Relids required_outer)
  {
  	List	   *new_path_pathkeys;
  	ListCell   *p1;
  
  	/* Pretend parameterized paths have no pathkeys, per add_path policy */
  	new_path_pathkeys = required_outer ? NIL : pathkeys;
  
  	foreach(p1, parent_rel->pathlist)
  	{
  		Path	   *old_path = (Path *) lfirst(p1);
  		PathKeysComparison keyscmp;
  
  		/*
  		 * We are looking for an old_path with the same parameterization (and
  		 * by assumption the same rowcount) that dominates the new path on
  		 * pathkeys as well as both cost metrics.  If we find one, we can
  		 * reject the new path.
  		 *
  		 * For speed, we make exact rather than fuzzy cost comparisons. If an
  		 * old path dominates the new path exactly on both costs, it will
  		 * surely do so fuzzily.
  		 */
  		if (total_cost >= old_path->total_cost)
  		{
  			/* can win on startup cost only if unparameterized */
  			if (startup_cost >= old_path->startup_cost || required_outer)
  			{
  				/* new path does not win on cost, so check pathkeys... */
  				List	   *old_path_pathkeys;
  
  				old_path_pathkeys = old_path->param_info ? NIL : old_path->pathkeys;
  				keyscmp = compare_pathkeys(new_path_pathkeys,
  										   old_path_pathkeys);
  				if (keyscmp == PATHKEYS_EQUAL ||
  					keyscmp == PATHKEYS_BETTER2)
  				{
  					/* new path does not win on pathkeys... */
  					if (bms_equal(required_outer, PATH_REQ_OUTER(old_path)))
  					{
  						/* Found an old path that dominates the new one */
  						return false;
  					}
  				}
  			}
  		}
  		else
  		{
  			/*
  			 * Since the pathlist is sorted by total_cost, we can stop looking
  			 * once we reach a path with a total_cost larger than the new
  			 * path's.
  			 */
  			break;
  		}
  	}
  
  	return true;
  }
  
  
  /*****************************************************************************
   *		PATH NODE CREATION ROUTINES
   *****************************************************************************/
  
  /*
   * create_seqscan_path
   *	  Creates a path corresponding to a sequential scan, returning the
   *	  pathnode.
   */
  Path *
  create_seqscan_path(PlannerInfo *root, RelOptInfo *rel, Relids required_outer)
  {
  	Path	   *pathnode = makeNode(Path);
  
  	pathnode->pathtype = T_SeqScan;
  	pathnode->parent = rel;
  	pathnode->param_info = get_baserel_parampathinfo(root, rel,
  													 required_outer);
  	pathnode->pathkeys = NIL;	/* seqscan has unordered result */
  
  	cost_seqscan(pathnode, root, rel, pathnode->param_info);
  
  	return pathnode;
  }
  
  /*
   * create_index_path
   *	  Creates a path node for an index scan.
   *
   * 'index' is a usable index.
   * 'indexclauses' is a list of RestrictInfo nodes representing clauses
   *			to be used as index qual conditions in the scan.
   * 'indexclausecols' is an integer list of index column numbers (zero based)
   *			the indexclauses can be used with.
   * 'indexorderbys' is a list of bare expressions (no RestrictInfos)
   *			to be used as index ordering operators in the scan.
   * 'indexorderbycols' is an integer list of index column numbers (zero based)
   *			the ordering operators can be used with.
   * 'pathkeys' describes the ordering of the path.
   * 'indexscandir' is ForwardScanDirection or BackwardScanDirection
   *			for an ordered index, or NoMovementScanDirection for
   *			an unordered index.
   * 'indexonly' is true if an index-only scan is wanted.
   * 'required_outer' is the set of outer relids for a parameterized path.
   * 'loop_count' is the number of repetitions of the indexscan to factor into
   *		estimates of caching behavior.
   *
   * Returns the new path node.
   */
  IndexPath *
  create_index_path(PlannerInfo *root,
  				  IndexOptInfo *index,
  				  List *indexclauses,
  				  List *indexclausecols,
  				  List *indexorderbys,
  				  List *indexorderbycols,
  				  List *pathkeys,
  				  ScanDirection indexscandir,
  				  bool indexonly,
  				  Relids required_outer,
  				  double loop_count)
  {
  	IndexPath  *pathnode = makeNode(IndexPath);
  	RelOptInfo *rel = index->rel;
  	List	   *indexquals,
  			   *indexqualcols;
  
  	pathnode->path.pathtype = indexonly ? T_IndexOnlyScan : T_IndexScan;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
  														  required_outer);
  	pathnode->path.pathkeys = pathkeys;
  
  	/* Convert clauses to indexquals the executor can handle */
  	expand_indexqual_conditions(index, indexclauses, indexclausecols,
  								&indexquals, &indexqualcols);
  
  	/* Fill in the pathnode */
  	pathnode->indexinfo = index;
  	pathnode->indexclauses = indexclauses;
  	pathnode->indexquals = indexquals;
  	pathnode->indexqualcols = indexqualcols;
  	pathnode->indexorderbys = indexorderbys;
  	pathnode->indexorderbycols = indexorderbycols;
  	pathnode->indexscandir = indexscandir;
  
  	cost_index(pathnode, root, loop_count);
  
  	return pathnode;
  }
  
  /*
   * create_bitmap_heap_path
   *	  Creates a path node for a bitmap scan.
   *
   * 'bitmapqual' is a tree of IndexPath, BitmapAndPath, and BitmapOrPath nodes.
   * 'required_outer' is the set of outer relids for a parameterized path.
   * 'loop_count' is the number of repetitions of the indexscan to factor into
   *		estimates of caching behavior.
   *
   * loop_count should match the value used when creating the component
   * IndexPaths.
   */
  BitmapHeapPath *
  create_bitmap_heap_path(PlannerInfo *root,
  						RelOptInfo *rel,
  						Path *bitmapqual,
  						Relids required_outer,
  						double loop_count)
  {
  	BitmapHeapPath *pathnode = makeNode(BitmapHeapPath);
  
  	pathnode->path.pathtype = T_BitmapHeapScan;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
  														  required_outer);
  	pathnode->path.pathkeys = NIL;		/* always unordered */
  
  	pathnode->bitmapqual = bitmapqual;
  
  	cost_bitmap_heap_scan(&pathnode->path, root, rel,
  						  pathnode->path.param_info,
  						  bitmapqual, loop_count);
  
  	return pathnode;
  }
  
  /*
   * create_bitmap_and_path
   *	  Creates a path node representing a BitmapAnd.
   */
  BitmapAndPath *
  create_bitmap_and_path(PlannerInfo *root,
  					   RelOptInfo *rel,
  					   List *bitmapquals)
  {
  	BitmapAndPath *pathnode = makeNode(BitmapAndPath);
  
  	pathnode->path.pathtype = T_BitmapAnd;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = NULL;	/* not used in bitmap trees */
  	pathnode->path.pathkeys = NIL;		/* always unordered */
  
  	pathnode->bitmapquals = bitmapquals;
  
  	/* this sets bitmapselectivity as well as the regular cost fields: */
  	cost_bitmap_and_node(pathnode, root);
  
  	return pathnode;
  }
  
  /*
   * create_bitmap_or_path
   *	  Creates a path node representing a BitmapOr.
   */
  BitmapOrPath *
  create_bitmap_or_path(PlannerInfo *root,
  					  RelOptInfo *rel,
  					  List *bitmapquals)
  {
  	BitmapOrPath *pathnode = makeNode(BitmapOrPath);
  
  	pathnode->path.pathtype = T_BitmapOr;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = NULL;	/* not used in bitmap trees */
  	pathnode->path.pathkeys = NIL;		/* always unordered */
  
  	pathnode->bitmapquals = bitmapquals;
  
  	/* this sets bitmapselectivity as well as the regular cost fields: */
  	cost_bitmap_or_node(pathnode, root);
  
  	return pathnode;
  }
  
  /*
   * create_tidscan_path
   *	  Creates a path corresponding to a scan by TID, returning the pathnode.
   */
  TidPath *
  create_tidscan_path(PlannerInfo *root, RelOptInfo *rel, List *tidquals,
  					Relids required_outer)
  {
  	TidPath    *pathnode = makeNode(TidPath);
  
  	pathnode->path.pathtype = T_TidScan;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
  														  required_outer);
  	pathnode->path.pathkeys = NIL;		/* always unordered */
  
  	pathnode->tidquals = tidquals;
  
  	cost_tidscan(&pathnode->path, root, rel, tidquals,
  				 pathnode->path.param_info);
  
  	return pathnode;
  }
  
  /*
   * create_append_path
   *	  Creates a path corresponding to an Append plan, returning the
   *	  pathnode.
   *
   * Note that we must handle subpaths = NIL, representing a dummy access path.
   */
  AppendPath *
  create_append_path(RelOptInfo *rel, List *subpaths, Relids required_outer)
  {
  	AppendPath *pathnode = makeNode(AppendPath);
  	ListCell   *l;
  
  	pathnode->path.pathtype = T_Append;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = get_appendrel_parampathinfo(rel,
  															required_outer);
  	pathnode->path.pathkeys = NIL;		/* result is always considered
  										 * unsorted */
  	pathnode->subpaths = subpaths;
  
  	/*
  	 * We don't bother with inventing a cost_append(), but just do it here.
  	 *
  	 * Compute rows and costs as sums of subplan rows and costs.  We charge
  	 * nothing extra for the Append itself, which perhaps is too optimistic,
  	 * but since it doesn't do any selection or projection, it is a pretty
  	 * cheap node.	If you change this, see also make_append().
  	 */
  	pathnode->path.rows = 0;
  	pathnode->path.startup_cost = 0;
  	pathnode->path.total_cost = 0;
  	foreach(l, subpaths)
  	{
  		Path	   *subpath = (Path *) lfirst(l);
  
  		pathnode->path.rows += subpath->rows;
  
  		if (l == list_head(subpaths))	/* first node? */
  			pathnode->path.startup_cost = subpath->startup_cost;
  		pathnode->path.total_cost += subpath->total_cost;
  
  		/* All child paths must have same parameterization */
  		Assert(bms_equal(PATH_REQ_OUTER(subpath), required_outer));
  	}
  
  	return pathnode;
  }
  
  /*
   * create_merge_append_path
   *	  Creates a path corresponding to a MergeAppend plan, returning the
   *	  pathnode.
   */
  MergeAppendPath *
  create_merge_append_path(PlannerInfo *root,
  						 RelOptInfo *rel,
  						 List *subpaths,
  						 List *pathkeys,
  						 Relids required_outer)
  {
  	MergeAppendPath *pathnode = makeNode(MergeAppendPath);
  	Cost		input_startup_cost;
  	Cost		input_total_cost;
  	ListCell   *l;
  
  	pathnode->path.pathtype = T_MergeAppend;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = get_appendrel_parampathinfo(rel,
  															required_outer);
  	pathnode->path.pathkeys = pathkeys;
  	pathnode->subpaths = subpaths;
  
  	/*
  	 * Apply query-wide LIMIT if known and path is for sole base relation.
  	 * (Handling this at this low level is a bit klugy.)
  	 */
  	if (bms_equal(rel->relids, root->all_baserels))
  		pathnode->limit_tuples = root->limit_tuples;
  	else
  		pathnode->limit_tuples = -1.0;
  
  	/*
  	 * Add up the sizes and costs of the input paths.
  	 */
  	pathnode->path.rows = 0;
  	input_startup_cost = 0;
  	input_total_cost = 0;
  	foreach(l, subpaths)
  	{
  		Path	   *subpath = (Path *) lfirst(l);
  
  		pathnode->path.rows += subpath->rows;
  
  		if (pathkeys_contained_in(pathkeys, subpath->pathkeys))
  		{
  			/* Subpath is adequately ordered, we won't need to sort it */
  			input_startup_cost += subpath->startup_cost;
  			input_total_cost += subpath->total_cost;
  		}
  		else
  		{
  			/* We'll need to insert a Sort node, so include cost for that */
  			Path		sort_path;		/* dummy for result of cost_sort */
  
  			cost_sort(&sort_path,
  					  root,
  					  pathkeys,
  					  subpath->total_cost,
  					  subpath->parent->tuples,
  					  subpath->parent->width,
  					  0.0,
  					  work_mem,
  					  pathnode->limit_tuples);
  			input_startup_cost += sort_path.startup_cost;
  			input_total_cost += sort_path.total_cost;
  		}
  
  		/* All child paths must have same parameterization */
  		Assert(bms_equal(PATH_REQ_OUTER(subpath), required_outer));
  	}
  
  	/* Now we can compute total costs of the MergeAppend */
  	cost_merge_append(&pathnode->path, root,
  					  pathkeys, list_length(subpaths),
  					  input_startup_cost, input_total_cost,
  					  rel->tuples);
  
  	return pathnode;
  }
  
  /*
   * create_result_path
   *	  Creates a path representing a Result-and-nothing-else plan.
   *	  This is only used for the case of a query with an empty jointree.
   */
  ResultPath *
  create_result_path(List *quals)
  {
  	ResultPath *pathnode = makeNode(ResultPath);
  
  	pathnode->path.pathtype = T_Result;
  	pathnode->path.parent = NULL;
  	pathnode->path.param_info = NULL;	/* there are no other rels... */
  	pathnode->path.pathkeys = NIL;
  	pathnode->quals = quals;
  
  	/* Hardly worth defining a cost_result() function ... just do it */
  	pathnode->path.rows = 1;
  	pathnode->path.startup_cost = 0;
  	pathnode->path.total_cost = cpu_tuple_cost;
  
  	/*
  	 * In theory we should include the qual eval cost as well, but at present
  	 * that doesn't accomplish much except duplicate work that will be done
  	 * again in make_result; since this is only used for degenerate cases,
  	 * nothing interesting will be done with the path cost values...
  	 */
  
  	return pathnode;
  }
  
  /*
   * create_material_path
   *	  Creates a path corresponding to a Material plan, returning the
   *	  pathnode.
   */
  MaterialPath *
  create_material_path(RelOptInfo *rel, Path *subpath)
  {
  	MaterialPath *pathnode = makeNode(MaterialPath);
  
  	Assert(subpath->parent == rel);
  
  	pathnode->path.pathtype = T_Material;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = subpath->param_info;
  	pathnode->path.pathkeys = subpath->pathkeys;
  
  	pathnode->subpath = subpath;
  
  	cost_material(&pathnode->path,
  				  subpath->startup_cost,
  				  subpath->total_cost,
  				  subpath->rows,
  				  rel->width);
  
  	return pathnode;
  }
  
  /*
   * create_unique_path
   *	  Creates a path representing elimination of distinct rows from the
   *	  input data.  Distinct-ness is defined according to the needs of the
   *	  semijoin represented by sjinfo.  If it is not possible to identify
   *	  how to make the data unique, NULL is returned.
   *
   * If used at all, this is likely to be called repeatedly on the same rel;
   * and the input subpath should always be the same (the cheapest_total path
   * for the rel).  So we cache the result.
   */
  UniquePath *
  create_unique_path(PlannerInfo *root, RelOptInfo *rel, Path *subpath,
  				   SpecialJoinInfo *sjinfo)
  {
  	UniquePath *pathnode;
  	Path		sort_path;		/* dummy for result of cost_sort */
  	Path		agg_path;		/* dummy for result of cost_agg */
  	MemoryContext oldcontext;
  	List	   *in_operators;
  	List	   *uniq_exprs;
  	bool		all_btree;
  	bool		all_hash;
  	int			numCols;
  	ListCell   *lc;
  
  	/* Caller made a mistake if subpath isn't cheapest_total ... */
  	Assert(subpath == rel->cheapest_total_path);
  	Assert(subpath->parent == rel);
  	/* ... or if SpecialJoinInfo is the wrong one */
  	Assert(sjinfo->jointype == JOIN_SEMI);
  	Assert(bms_equal(rel->relids, sjinfo->syn_righthand));
  
  	/* If result already cached, return it */
  	if (rel->cheapest_unique_path)
  		return (UniquePath *) rel->cheapest_unique_path;
  
  	/* If we previously failed, return NULL quickly */
  	if (sjinfo->join_quals == NIL)
  		return NULL;
  
  	/*
  	 * We must ensure path struct and subsidiary data are allocated in main
  	 * planning context; otherwise GEQO memory management causes trouble.
  	 */
  	oldcontext = MemoryContextSwitchTo(root->planner_cxt);
  
  	/*----------
  	 * Look to see whether the semijoin's join quals consist of AND'ed
  	 * equality operators, with (only) RHS variables on only one side of
  	 * each one.  If so, we can figure out how to enforce uniqueness for
  	 * the RHS.
  	 *
  	 * Note that the input join_quals list is the list of quals that are
  	 * *syntactically* associated with the semijoin, which in practice means
  	 * the synthesized comparison list for an IN or the WHERE of an EXISTS.
  	 * Particularly in the latter case, it might contain clauses that aren't
  	 * *semantically* associated with the join, but refer to just one side or
  	 * the other.  We can ignore such clauses here, as they will just drop
  	 * down to be processed within one side or the other.  (It is okay to
  	 * consider only the syntactically-associated clauses here because for a
  	 * semijoin, no higher-level quals could refer to the RHS, and so there
  	 * can be no other quals that are semantically associated with this join.
  	 * We do things this way because it is useful to be able to run this test
  	 * before we have extracted the list of quals that are actually
  	 * semantically associated with the particular join.)
  	 *
  	 * Note that the in_operators list consists of the joinqual operators
  	 * themselves (but commuted if needed to put the RHS value on the right).
  	 * These could be cross-type operators, in which case the operator
  	 * actually needed for uniqueness is a related single-type operator.
  	 * We assume here that that operator will be available from the btree
  	 * or hash opclass when the time comes ... if not, create_unique_plan()
  	 * will fail.
  	 *----------
  	 */
  	in_operators = NIL;
  	uniq_exprs = NIL;
  	all_btree = true;
  	all_hash = enable_hashagg;	/* don't consider hash if not enabled */
  	foreach(lc, sjinfo->join_quals)
  	{
  		OpExpr	   *op = (OpExpr *) lfirst(lc);
  		Oid			opno;
  		Node	   *left_expr;
  		Node	   *right_expr;
  		Relids		left_varnos;
  		Relids		right_varnos;
  		Relids		all_varnos;
  		Oid			opinputtype;
  
  		/* Is it a binary opclause? */
  		if (!IsA(op, OpExpr) ||
  			list_length(op->args) != 2)
  		{
  			/* No, but does it reference both sides? */
  			all_varnos = pull_varnos((Node *) op);
  			if (!bms_overlap(all_varnos, sjinfo->syn_righthand) ||
  				bms_is_subset(all_varnos, sjinfo->syn_righthand))
  			{
  				/*
  				 * Clause refers to only one rel, so ignore it --- unless it
  				 * contains volatile functions, in which case we'd better
  				 * punt.
  				 */
  				if (contain_volatile_functions((Node *) op))
  					goto no_unique_path;
  				continue;
  			}
  			/* Non-operator clause referencing both sides, must punt */
  			goto no_unique_path;
  		}
  
  		/* Extract data from binary opclause */
  		opno = op->opno;
  		left_expr = linitial(op->args);
  		right_expr = lsecond(op->args);
  		left_varnos = pull_varnos(left_expr);
  		right_varnos = pull_varnos(right_expr);
  		all_varnos = bms_union(left_varnos, right_varnos);
  		opinputtype = exprType(left_expr);
  
  		/* Does it reference both sides? */
  		if (!bms_overlap(all_varnos, sjinfo->syn_righthand) ||
  			bms_is_subset(all_varnos, sjinfo->syn_righthand))
  		{
  			/*
  			 * Clause refers to only one rel, so ignore it --- unless it
  			 * contains volatile functions, in which case we'd better punt.
  			 */
  			if (contain_volatile_functions((Node *) op))
  				goto no_unique_path;
  			continue;
  		}
  
  		/* check rel membership of arguments */
  		if (!bms_is_empty(right_varnos) &&
  			bms_is_subset(right_varnos, sjinfo->syn_righthand) &&
  			!bms_overlap(left_varnos, sjinfo->syn_righthand))
  		{
  			/* typical case, right_expr is RHS variable */
  		}
  		else if (!bms_is_empty(left_varnos) &&
  				 bms_is_subset(left_varnos, sjinfo->syn_righthand) &&
  				 !bms_overlap(right_varnos, sjinfo->syn_righthand))
  		{
  			/* flipped case, left_expr is RHS variable */
  			opno = get_commutator(opno);
  			if (!OidIsValid(opno))
  				goto no_unique_path;
  			right_expr = left_expr;
  		}
  		else
  			goto no_unique_path;
  
  		/* all operators must be btree equality or hash equality */
  		if (all_btree)
  		{
  			/* oprcanmerge is considered a hint... */
  			if (!op_mergejoinable(opno, opinputtype) ||
  				get_mergejoin_opfamilies(opno) == NIL)
  				all_btree = false;
  		}
  		if (all_hash)
  		{
  			/* ... but oprcanhash had better be correct */
  			if (!op_hashjoinable(opno, opinputtype))
  				all_hash = false;
  		}
  		if (!(all_btree || all_hash))
  			goto no_unique_path;
  
  		/* so far so good, keep building lists */
  		in_operators = lappend_oid(in_operators, opno);
  		uniq_exprs = lappend(uniq_exprs, copyObject(right_expr));
  	}
  
  	/* Punt if we didn't find at least one column to unique-ify */
  	if (uniq_exprs == NIL)
  		goto no_unique_path;
  
  	/*
  	 * The expressions we'd need to unique-ify mustn't be volatile.
  	 */
  	if (contain_volatile_functions((Node *) uniq_exprs))
  		goto no_unique_path;
  
  	/*
  	 * If we get here, we can unique-ify using at least one of sorting and
  	 * hashing.  Start building the result Path object.
  	 */
  	pathnode = makeNode(UniquePath);
  
  	pathnode->path.pathtype = T_Unique;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = subpath->param_info;
  
  	/*
  	 * Assume the output is unsorted, since we don't necessarily have pathkeys
  	 * to represent it.  (This might get overridden below.)
  	 */
  	pathnode->path.pathkeys = NIL;
  
  	pathnode->subpath = subpath;
  	pathnode->in_operators = in_operators;
  	pathnode->uniq_exprs = uniq_exprs;
  
  	/*
  	 * If the input is a relation and it has a unique index that proves the
  	 * uniq_exprs are unique, then we don't need to do anything.  Note that
  	 * relation_has_unique_index_for automatically considers restriction
  	 * clauses for the rel, as well.
  	 */
  	if (rel->rtekind == RTE_RELATION && all_btree &&
  		relation_has_unique_index_for(root, rel, NIL,
  									  uniq_exprs, in_operators))
  	{
  		pathnode->umethod = UNIQUE_PATH_NOOP;
  		pathnode->path.rows = rel->rows;
  		pathnode->path.startup_cost = subpath->startup_cost;
  		pathnode->path.total_cost = subpath->total_cost;
  		pathnode->path.pathkeys = subpath->pathkeys;
  
  		rel->cheapest_unique_path = (Path *) pathnode;
  
  		MemoryContextSwitchTo(oldcontext);
  
  		return pathnode;
  	}
  
  	/*
  	 * If the input is a subquery whose output must be unique already, then we
  	 * don't need to do anything.  The test for uniqueness has to consider
  	 * exactly which columns we are extracting; for example "SELECT DISTINCT
  	 * x,y" doesn't guarantee that x alone is distinct. So we cannot check for
  	 * this optimization unless uniq_exprs consists only of simple Vars
  	 * referencing subquery outputs.  (Possibly we could do something with
  	 * expressions in the subquery outputs, too, but for now keep it simple.)
  	 */
  	if (rel->rtekind == RTE_SUBQUERY)
  	{
  		RangeTblEntry *rte = planner_rt_fetch(rel->relid, root);
  		List	   *sub_tlist_colnos;
  
  		sub_tlist_colnos = translate_sub_tlist(uniq_exprs, rel->relid);
  
  		if (sub_tlist_colnos &&
  			query_is_distinct_for(rte->subquery,
  								  sub_tlist_colnos, in_operators))
  		{
  			pathnode->umethod = UNIQUE_PATH_NOOP;
  			pathnode->path.rows = rel->rows;
  			pathnode->path.startup_cost = subpath->startup_cost;
  			pathnode->path.total_cost = subpath->total_cost;
  			pathnode->path.pathkeys = subpath->pathkeys;
  
  			rel->cheapest_unique_path = (Path *) pathnode;
  
  			MemoryContextSwitchTo(oldcontext);
  
  			return pathnode;
  		}
  	}
  
  	/* Estimate number of output rows */
  	pathnode->path.rows = estimate_num_groups(root, uniq_exprs, rel->rows);
  	numCols = list_length(uniq_exprs);
  
  	if (all_btree)
  	{
  		/*
  		 * Estimate cost for sort+unique implementation
  		 */
  		cost_sort(&sort_path, root, NIL,
  				  subpath->total_cost,
  				  rel->rows,
  				  rel->width,
  				  0.0,
  				  work_mem,
  				  -1.0);
  
  		/*
  		 * Charge one cpu_operator_cost per comparison per input tuple. We
  		 * assume all columns get compared at most of the tuples. (XXX
  		 * probably this is an overestimate.)  This should agree with
  		 * make_unique.
  		 */
  		sort_path.total_cost += cpu_operator_cost * rel->rows * numCols;
  	}
  
  	if (all_hash)
  	{
  		/*
  		 * Estimate the overhead per hashtable entry at 64 bytes (same as in
  		 * planner.c).
  		 */
  		int			hashentrysize = rel->width + 64;
  
  		if (hashentrysize * pathnode->path.rows > work_mem * 1024L)
  			all_hash = false;	/* don't try to hash */
  		else
  			cost_agg(&agg_path, root,
  					 AGG_HASHED, NULL,
  					 numCols, pathnode->path.rows,
  					 subpath->startup_cost,
  					 subpath->total_cost,
  					 rel->rows);
  	}
  
  	if (all_btree && all_hash)
  	{
  		if (agg_path.total_cost < sort_path.total_cost)
  			pathnode->umethod = UNIQUE_PATH_HASH;
  		else
  			pathnode->umethod = UNIQUE_PATH_SORT;
  	}
  	else if (all_btree)
  		pathnode->umethod = UNIQUE_PATH_SORT;
  	else if (all_hash)
  		pathnode->umethod = UNIQUE_PATH_HASH;
  	else
  		goto no_unique_path;
  
  	if (pathnode->umethod == UNIQUE_PATH_HASH)
  	{
  		pathnode->path.startup_cost = agg_path.startup_cost;
  		pathnode->path.total_cost = agg_path.total_cost;
  	}
  	else
  	{
  		pathnode->path.startup_cost = sort_path.startup_cost;
  		pathnode->path.total_cost = sort_path.total_cost;
  	}
  
  	rel->cheapest_unique_path = (Path *) pathnode;
  
  	MemoryContextSwitchTo(oldcontext);
  
  	return pathnode;
  
  no_unique_path:			/* failure exit */
  
  	/* Mark the SpecialJoinInfo as not unique-able */
  	sjinfo->join_quals = NIL;
  
  	MemoryContextSwitchTo(oldcontext);
  
  	return NULL;
  }
  
  /*
   * translate_sub_tlist - get subquery column numbers represented by tlist
   *
   * The given targetlist usually contains only Vars referencing the given relid.
   * Extract their varattnos (ie, the column numbers of the subquery) and return
   * as an integer List.
   *
   * If any of the tlist items is not a simple Var, we cannot determine whether
   * the subquery's uniqueness condition (if any) matches ours, so punt and
   * return NIL.
   */
  static List *
  translate_sub_tlist(List *tlist, int relid)
  {
  	List	   *result = NIL;
  	ListCell   *l;
  
  	foreach(l, tlist)
  	{
  		Var		   *var = (Var *) lfirst(l);
  
  		if (!var || !IsA(var, Var) ||
  			var->varno != relid)
  			return NIL;			/* punt */
  
  		result = lappend_int(result, var->varattno);
  	}
  	return result;
  }
  
  /*
   * query_is_distinct_for - does query never return duplicates of the
   *		specified columns?
   *
   * colnos is an integer list of output column numbers (resno's).  We are
   * interested in whether rows consisting of just these columns are certain
   * to be distinct.	"Distinctness" is defined according to whether the
   * corresponding upper-level equality operators listed in opids would think
   * the values are distinct.  (Note: the opids entries could be cross-type
   * operators, and thus not exactly the equality operators that the subquery
   * would use itself.  We use equality_ops_are_compatible() to check
   * compatibility.  That looks at btree or hash opfamily membership, and so
   * should give trustworthy answers for all operators that we might need
   * to deal with here.)
   */
  static bool
  query_is_distinct_for(Query *query, List *colnos, List *opids)
  {
  	ListCell   *l;
  	Oid			opid;
  
  	Assert(list_length(colnos) == list_length(opids));
  
  	/*
  	 * DISTINCT (including DISTINCT ON) guarantees uniqueness if all the
  	 * columns in the DISTINCT clause appear in colnos and operator semantics
  	 * match.
  	 */
  	if (query->distinctClause)
  	{
  		foreach(l, query->distinctClause)
  		{
  			SortGroupClause *sgc = (SortGroupClause *) lfirst(l);
  			TargetEntry *tle = get_sortgroupclause_tle(sgc,
  													   query->targetList);
  
  			opid = distinct_col_search(tle->resno, colnos, opids);
  			if (!OidIsValid(opid) ||
  				!equality_ops_are_compatible(opid, sgc->eqop))
  				break;			/* exit early if no match */
  		}
  		if (l == NULL)			/* had matches for all? */
  			return true;
  	}
  
  	/*
  	 * Similarly, GROUP BY guarantees uniqueness if all the grouped columns
  	 * appear in colnos and operator semantics match.
  	 */
  	if (query->groupClause)
  	{
  		foreach(l, query->groupClause)
  		{
  			SortGroupClause *sgc = (SortGroupClause *) lfirst(l);
  			TargetEntry *tle = get_sortgroupclause_tle(sgc,
  													   query->targetList);
  
  			opid = distinct_col_search(tle->resno, colnos, opids);
  			if (!OidIsValid(opid) ||
  				!equality_ops_are_compatible(opid, sgc->eqop))
  				break;			/* exit early if no match */
  		}
  		if (l == NULL)			/* had matches for all? */
  			return true;
  	}
  	else
  	{
  		/*
  		 * If we have no GROUP BY, but do have aggregates or HAVING, then the
  		 * result is at most one row so it's surely unique, for any operators.
  		 */
  		if (query->hasAggs || query->havingQual)
  			return true;
  	}
  
  	/*
  	 * UNION, INTERSECT, EXCEPT guarantee uniqueness of the whole output row,
  	 * except with ALL.
  	 */
  	if (query->setOperations)
  	{
  		SetOperationStmt *topop = (SetOperationStmt *) query->setOperations;
  
  		Assert(IsA(topop, SetOperationStmt));
  		Assert(topop->op != SETOP_NONE);
  
  		if (!topop->all)
  		{
  			ListCell   *lg;
  
  			/* We're good if all the nonjunk output columns are in colnos */
  			lg = list_head(topop->groupClauses);
  			foreach(l, query->targetList)
  			{
  				TargetEntry *tle = (TargetEntry *) lfirst(l);
  				SortGroupClause *sgc;
  
  				if (tle->resjunk)
  					continue;	/* ignore resjunk columns */
  
  				/* non-resjunk columns should have grouping clauses */
  				Assert(lg != NULL);
  				sgc = (SortGroupClause *) lfirst(lg);
  				lg = lnext(lg);
  
  				opid = distinct_col_search(tle->resno, colnos, opids);
  				if (!OidIsValid(opid) ||
  					!equality_ops_are_compatible(opid, sgc->eqop))
  					break;		/* exit early if no match */
  			}
  			if (l == NULL)		/* had matches for all? */
  				return true;
  		}
  	}
  
  	/*
  	 * XXX Are there any other cases in which we can easily see the result
  	 * must be distinct?
  	 */
  
  	return false;
  }
  
  /*
   * distinct_col_search - subroutine for query_is_distinct_for
   *
   * If colno is in colnos, return the corresponding element of opids,
   * else return InvalidOid.	(We expect colnos does not contain duplicates,
   * so the result is well-defined.)
   */
  static Oid
  distinct_col_search(int colno, List *colnos, List *opids)
  {
  	ListCell   *lc1,
  			   *lc2;
  
  	forboth(lc1, colnos, lc2, opids)
  	{
  		if (colno == lfirst_int(lc1))
  			return lfirst_oid(lc2);
  	}
  	return InvalidOid;
  }
  
  /*
   * create_subqueryscan_path
   *	  Creates a path corresponding to a sequential scan of a subquery,
   *	  returning the pathnode.
   */
  Path *
  create_subqueryscan_path(PlannerInfo *root, RelOptInfo *rel,
  						 List *pathkeys, Relids required_outer)
  {
  	Path	   *pathnode = makeNode(Path);
  
  	pathnode->pathtype = T_SubqueryScan;
  	pathnode->parent = rel;
  	pathnode->param_info = get_baserel_parampathinfo(root, rel,
  													 required_outer);
  	pathnode->pathkeys = pathkeys;
  
  	cost_subqueryscan(pathnode, root, rel, pathnode->param_info);
  
  	return pathnode;
  }
  
  /*
   * create_functionscan_path
   *	  Creates a path corresponding to a sequential scan of a function,
   *	  returning the pathnode.
   */
  Path *
  create_functionscan_path(PlannerInfo *root, RelOptInfo *rel,
  						 List *pathkeys, Relids required_outer)
  {
  	Path	   *pathnode = makeNode(Path);
  
  	pathnode->pathtype = T_FunctionScan;
  	pathnode->parent = rel;
  	pathnode->param_info = get_baserel_parampathinfo(root, rel,
  													 required_outer);
  	pathnode->pathkeys = pathkeys;
  
  	cost_functionscan(pathnode, root, rel, pathnode->param_info);
  
  	return pathnode;
  }
  
  /*
   * create_valuesscan_path
   *	  Creates a path corresponding to a scan of a VALUES list,
   *	  returning the pathnode.
   */
  Path *
  create_valuesscan_path(PlannerInfo *root, RelOptInfo *rel,
  					   Relids required_outer)
  {
  	Path	   *pathnode = makeNode(Path);
  
  	pathnode->pathtype = T_ValuesScan;
  	pathnode->parent = rel;
  	pathnode->param_info = get_baserel_parampathinfo(root, rel,
  													 required_outer);
  	pathnode->pathkeys = NIL;	/* result is always unordered */
  
  	cost_valuesscan(pathnode, root, rel, pathnode->param_info);
  
  	return pathnode;
  }
  
  /*
   * create_ctescan_path
   *	  Creates a path corresponding to a scan of a non-self-reference CTE,
   *	  returning the pathnode.
   */
  Path *
  create_ctescan_path(PlannerInfo *root, RelOptInfo *rel, Relids required_outer)
  {
  	Path	   *pathnode = makeNode(Path);
  
  	pathnode->pathtype = T_CteScan;
  	pathnode->parent = rel;
  	pathnode->param_info = get_baserel_parampathinfo(root, rel,
  													 required_outer);
  	pathnode->pathkeys = NIL;	/* XXX for now, result is always unordered */
  
  	cost_ctescan(pathnode, root, rel, pathnode->param_info);
  
  	return pathnode;
  }
  
  /*
   * create_worktablescan_path
   *	  Creates a path corresponding to a scan of a self-reference CTE,
   *	  returning the pathnode.
   */
  Path *
  create_worktablescan_path(PlannerInfo *root, RelOptInfo *rel,
  						  Relids required_outer)
  {
  	Path	   *pathnode = makeNode(Path);
  
  	pathnode->pathtype = T_WorkTableScan;
  	pathnode->parent = rel;
  	pathnode->param_info = get_baserel_parampathinfo(root, rel,
  													 required_outer);
  	pathnode->pathkeys = NIL;	/* result is always unordered */
  
  	/* Cost is the same as for a regular CTE scan */
  	cost_ctescan(pathnode, root, rel, pathnode->param_info);
  
  	return pathnode;
  }
  
  /*
   * create_foreignscan_path
   *	  Creates a path corresponding to a scan of a foreign table,
   *	  returning the pathnode.
   *
   * This function is never called from core Postgres; rather, it's expected
   * to be called by the GetForeignPaths function of a foreign data wrapper.
   * We make the FDW supply all fields of the path, since we do not have any
   * way to calculate them in core.
   */
  ForeignPath *
  create_foreignscan_path(PlannerInfo *root, RelOptInfo *rel,
  						double rows, Cost startup_cost, Cost total_cost,
  						List *pathkeys,
  						Relids required_outer,
  						List *fdw_private)
  {
  	ForeignPath *pathnode = makeNode(ForeignPath);
  
  	pathnode->path.pathtype = T_ForeignScan;
  	pathnode->path.parent = rel;
  	pathnode->path.param_info = get_baserel_parampathinfo(root, rel,
  														  required_outer);
  	pathnode->path.rows = rows;
  	pathnode->path.startup_cost = startup_cost;
  	pathnode->path.total_cost = total_cost;
  	pathnode->path.pathkeys = pathkeys;
  
  	pathnode->fdw_private = fdw_private;
  
  	return pathnode;
  }
  
  /*
   * calc_nestloop_required_outer
   *	  Compute the required_outer set for a nestloop join path
   *
   * Note: result must not share storage with either input
   */
  Relids
  calc_nestloop_required_outer(Path *outer_path, Path *inner_path)
  {
  	Relids		outer_paramrels = PATH_REQ_OUTER(outer_path);
  	Relids		inner_paramrels = PATH_REQ_OUTER(inner_path);
  	Relids		required_outer;
  
  	/* inner_path can require rels from outer path, but not vice versa */
  	Assert(!bms_overlap(outer_paramrels, inner_path->parent->relids));
  	/* easy case if inner path is not parameterized */
  	if (!inner_paramrels)
  		return bms_copy(outer_paramrels);
  	/* else, form the union ... */
  	required_outer = bms_union(outer_paramrels, inner_paramrels);
  	/* ... and remove any mention of now-satisfied outer rels */
  	required_outer = bms_del_members(required_outer,
  									 outer_path->parent->relids);
  	/* maintain invariant that required_outer is exactly NULL if empty */
  	if (bms_is_empty(required_outer))
  	{
  		bms_free(required_outer);
  		required_outer = NULL;
  	}
  	return required_outer;
  }
  
  /*
   * calc_non_nestloop_required_outer
   *	  Compute the required_outer set for a merge or hash join path
   *
   * Note: result must not share storage with either input
   */
  Relids
  calc_non_nestloop_required_outer(Path *outer_path, Path *inner_path)
  {
  	Relids		outer_paramrels = PATH_REQ_OUTER(outer_path);
  	Relids		inner_paramrels = PATH_REQ_OUTER(inner_path);
  	Relids		required_outer;
  
  	/* neither path can require rels from the other */
  	Assert(!bms_overlap(outer_paramrels, inner_path->parent->relids));
  	Assert(!bms_overlap(inner_paramrels, outer_path->parent->relids));
  	/* form the union ... */
  	required_outer = bms_union(outer_paramrels, inner_paramrels);
  	/* we do not need an explicit test for empty; bms_union gets it right */
  	return required_outer;
  }
  
  /*
   * create_nestloop_path
   *	  Creates a pathnode corresponding to a nestloop join between two
   *	  relations.
   *
   * 'joinrel' is the join relation.
   * 'jointype' is the type of join required
   * 'workspace' is the result from initial_cost_nestloop
   * 'sjinfo' is extra info about the join for selectivity estimation
   * 'semifactors' contains valid data if jointype is SEMI or ANTI
   * 'outer_path' is the outer path
   * 'inner_path' is the inner path
   * 'restrict_clauses' are the RestrictInfo nodes to apply at the join
   * 'pathkeys' are the path keys of the new join path
   * 'required_outer' is the set of required outer rels
   *
   * Returns the resulting path node.
   */
  NestPath *
  create_nestloop_path(PlannerInfo *root,
  					 RelOptInfo *joinrel,
  					 JoinType jointype,
  					 JoinCostWorkspace *workspace,
  					 SpecialJoinInfo *sjinfo,
  					 SemiAntiJoinFactors *semifactors,
  					 Path *outer_path,
  					 Path *inner_path,
  					 List *restrict_clauses,
  					 List *pathkeys,
  					 Relids required_outer)
  {
  	NestPath   *pathnode = makeNode(NestPath);
  	Relids		inner_req_outer = PATH_REQ_OUTER(inner_path);
  
  	/*
  	 * If the inner path is parameterized by the outer, we must drop any
  	 * restrict_clauses that are due to be moved into the inner path.  We have
  	 * to do this now, rather than postpone the work till createplan time,
  	 * because the restrict_clauses list can affect the size and cost
  	 * estimates for this path.
  	 */
  	if (bms_overlap(inner_req_outer, outer_path->parent->relids))
  	{
  		Relids		inner_and_outer = bms_union(inner_path->parent->relids,
  												inner_req_outer);
  		List	   *jclauses = NIL;
  		ListCell   *lc;
  
  		foreach(lc, restrict_clauses)
  		{
  			RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
  
  			if (!join_clause_is_movable_into(rinfo,
  											 inner_path->parent->relids,
  											 inner_and_outer))
  				jclauses = lappend(jclauses, rinfo);
  		}
  		restrict_clauses = jclauses;
  	}
  
  	pathnode->path.pathtype = T_NestLoop;
  	pathnode->path.parent = joinrel;
  	pathnode->path.param_info =
  		get_joinrel_parampathinfo(root,
  								  joinrel,
  								  outer_path,
  								  inner_path,
  								  sjinfo,
  								  required_outer,
  								  &restrict_clauses);
  	pathnode->path.pathkeys = pathkeys;
  	pathnode->jointype = jointype;
  	pathnode->outerjoinpath = outer_path;
  	pathnode->innerjoinpath = inner_path;
  	pathnode->joinrestrictinfo = restrict_clauses;
  
  	final_cost_nestloop(root, pathnode, workspace, sjinfo, semifactors);
  
  	return pathnode;
  }
  
  /*
   * create_mergejoin_path
   *	  Creates a pathnode corresponding to a mergejoin join between
   *	  two relations
   *
   * 'joinrel' is the join relation
   * 'jointype' is the type of join required
   * 'workspace' is the result from initial_cost_mergejoin
   * 'sjinfo' is extra info about the join for selectivity estimation
   * 'outer_path' is the outer path
   * 'inner_path' is the inner path
   * 'restrict_clauses' are the RestrictInfo nodes to apply at the join
   * 'pathkeys' are the path keys of the new join path
   * 'required_outer' is the set of required outer rels
   * 'mergeclauses' are the RestrictInfo nodes to use as merge clauses
   *		(this should be a subset of the restrict_clauses list)
   * 'outersortkeys' are the sort varkeys for the outer relation
   * 'innersortkeys' are the sort varkeys for the inner relation
   */
  MergePath *
  create_mergejoin_path(PlannerInfo *root,
  					  RelOptInfo *joinrel,
  					  JoinType jointype,
  					  JoinCostWorkspace *workspace,
  					  SpecialJoinInfo *sjinfo,
  					  Path *outer_path,
  					  Path *inner_path,
  					  List *restrict_clauses,
  					  List *pathkeys,
  					  Relids required_outer,
  					  List *mergeclauses,
  					  List *outersortkeys,
  					  List *innersortkeys)
  {
  	MergePath  *pathnode = makeNode(MergePath);
  
  	pathnode->jpath.path.pathtype = T_MergeJoin;
  	pathnode->jpath.path.parent = joinrel;
  	pathnode->jpath.path.param_info =
  		get_joinrel_parampathinfo(root,
  								  joinrel,
  								  outer_path,
  								  inner_path,
  								  sjinfo,
  								  required_outer,
  								  &restrict_clauses);
  	pathnode->jpath.path.pathkeys = pathkeys;
  	pathnode->jpath.jointype = jointype;
  	pathnode->jpath.outerjoinpath = outer_path;
  	pathnode->jpath.innerjoinpath = inner_path;
  	pathnode->jpath.joinrestrictinfo = restrict_clauses;
  	pathnode->path_mergeclauses = mergeclauses;
  	pathnode->outersortkeys = outersortkeys;
  	pathnode->innersortkeys = innersortkeys;
  	/* pathnode->materialize_inner will be set by final_cost_mergejoin */
  
  	final_cost_mergejoin(root, pathnode, workspace, sjinfo);
  
  	return pathnode;
  }
  
  /*
   * create_hashjoin_path
   *	  Creates a pathnode corresponding to a hash join between two relations.
   *
   * 'joinrel' is the join relation
   * 'jointype' is the type of join required
   * 'workspace' is the result from initial_cost_hashjoin
   * 'sjinfo' is extra info about the join for selectivity estimation
   * 'semifactors' contains valid data if jointype is SEMI or ANTI
   * 'outer_path' is the cheapest outer path
   * 'inner_path' is the cheapest inner path
   * 'restrict_clauses' are the RestrictInfo nodes to apply at the join
   * 'required_outer' is the set of required outer rels
   * 'hashclauses' are the RestrictInfo nodes to use as hash clauses
   *		(this should be a subset of the restrict_clauses list)
   */
  HashPath *
  create_hashjoin_path(PlannerInfo *root,
  					 RelOptInfo *joinrel,
  					 JoinType jointype,
  					 JoinCostWorkspace *workspace,
  					 SpecialJoinInfo *sjinfo,
  					 SemiAntiJoinFactors *semifactors,
  					 Path *outer_path,
  					 Path *inner_path,
  					 List *restrict_clauses,
  					 Relids required_outer,
  					 List *hashclauses)
  {
  	HashPath   *pathnode = makeNode(HashPath);
  
  	pathnode->jpath.path.pathtype = T_HashJoin;
  	pathnode->jpath.path.parent = joinrel;
  	pathnode->jpath.path.param_info =
  		get_joinrel_parampathinfo(root,
  								  joinrel,
  								  outer_path,
  								  inner_path,
  								  sjinfo,
  								  required_outer,
  								  &restrict_clauses);
  
  	/*
  	 * A hashjoin never has pathkeys, since its output ordering is
  	 * unpredictable due to possible batching.	XXX If the inner relation is
  	 * small enough, we could instruct the executor that it must not batch,
  	 * and then we could assume that the output inherits the outer relation's
  	 * ordering, which might save a sort step.	However there is considerable
  	 * downside if our estimate of the inner relation size is badly off. For
  	 * the moment we don't risk it.  (Note also that if we wanted to take this
  	 * seriously, joinpath.c would have to consider many more paths for the
  	 * outer rel than it does now.)
  	 */
  	pathnode->jpath.path.pathkeys = NIL;
  	pathnode->jpath.jointype = jointype;
  	pathnode->jpath.outerjoinpath = outer_path;
  	pathnode->jpath.innerjoinpath = inner_path;
  	pathnode->jpath.joinrestrictinfo = restrict_clauses;
  	pathnode->path_hashclauses = hashclauses;
  	/* final_cost_hashjoin will fill in pathnode->num_batches */
  
  	final_cost_hashjoin(root, pathnode, workspace, sjinfo, semifactors);
  
  	return pathnode;
  }
  
  /*
   * reparameterize_path
   *		Attempt to modify a Path to have greater parameterization
   *
   * We use this to attempt to bring all child paths of an appendrel to the
   * same parameterization level, ensuring that they all enforce the same set
   * of join quals (and thus that that parameterization can be attributed to
   * an append path built from such paths).  Currently, only a few path types
   * are supported here, though more could be added at need.	We return NULL
   * if we can't reparameterize the given path.
   *
   * Note: we intentionally do not pass created paths to add_path(); it would
   * possibly try to delete them on the grounds of being cost-inferior to the
   * paths they were made from, and we don't want that.  Paths made here are
   * not necessarily of general-purpose usefulness, but they can be useful
   * as members of an append path.
   */
  Path *
  reparameterize_path(PlannerInfo *root, Path *path,
  					Relids required_outer,
  					double loop_count)
  {
  	RelOptInfo *rel = path->parent;
  
  	/* Can only increase, not decrease, path's parameterization */
  	if (!bms_is_subset(PATH_REQ_OUTER(path), required_outer))
  		return NULL;
  	switch (path->pathtype)
  	{
  		case T_SeqScan:
  			return create_seqscan_path(root, rel, required_outer);
  		case T_IndexScan:
  		case T_IndexOnlyScan:
  			{
  				IndexPath  *ipath = (IndexPath *) path;
  				IndexPath  *newpath = makeNode(IndexPath);
  
  				/*
  				 * We can't use create_index_path directly, and would not want
  				 * to because it would re-compute the indexqual conditions
  				 * which is wasted effort.	Instead we hack things a bit:
  				 * flat-copy the path node, revise its param_info, and redo
  				 * the cost estimate.
  				 */
  				memcpy(newpath, ipath, sizeof(IndexPath));
  				newpath->path.param_info =
  					get_baserel_parampathinfo(root, rel, required_outer);
  				cost_index(newpath, root, loop_count);
  				return (Path *) newpath;
  			}
  		case T_BitmapHeapScan:
  			{
  				BitmapHeapPath *bpath = (BitmapHeapPath *) path;
  
  				return (Path *) create_bitmap_heap_path(root,
  														rel,
  														bpath->bitmapqual,
  														required_outer,
  														loop_count);
  			}
  		case T_SubqueryScan:
  			return create_subqueryscan_path(root, rel, path->pathkeys,
  											required_outer);
  		default:
  			break;
  	}
  	return NULL;
  }
  