Adding upstream version 15.5.upstream/15.5

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 6221 insertions, 0 deletions

diff --git a/src/backend/optimizer/path/costsize.c b/src/backend/optimizer/path/costsize.c
new file mode 100644
index 0000000..0ba26b2
--- /dev/null
+++ b/src/backend/optimizer/path/costsize.c
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+/*-------------------------------------------------------------------------
+ *
+ * costsize.c
+ *	  Routines to compute (and set) relation sizes and path costs
+ *
+ * Path costs are measured in arbitrary units established by these basic
+ * parameters:
+ *
+ *	seq_page_cost		Cost of a sequential page fetch
+ *	random_page_cost	Cost of a non-sequential page fetch
+ *	cpu_tuple_cost		Cost of typical CPU time to process a tuple
+ *	cpu_index_tuple_cost  Cost of typical CPU time to process an index tuple
+ *	cpu_operator_cost	Cost of CPU time to execute an operator or function
+ *	parallel_tuple_cost Cost of CPU time to pass a tuple from worker to leader backend
+ *	parallel_setup_cost Cost of setting up shared memory for parallelism
+ *
+ * We expect that the kernel will typically do some amount of read-ahead
+ * optimization; this in conjunction with seek costs means that seq_page_cost
+ * is normally considerably less than random_page_cost.  (However, if the
+ * database is fully cached in RAM, it is reasonable to set them equal.)
+ *
+ * We also use a rough estimate "effective_cache_size" of the number of
+ * disk pages in Postgres + OS-level disk cache.  (We can't simply use
+ * NBuffers for this purpose because that would ignore the effects of
+ * the kernel's disk cache.)
+ *
+ * Obviously, taking constants for these values is an oversimplification,
+ * but it's tough enough to get any useful estimates even at this level of
+ * detail.  Note that all of these parameters are user-settable, in case
+ * the default values are drastically off for a particular platform.
+ *
+ * seq_page_cost and random_page_cost can also be overridden for an individual
+ * tablespace, in case some data is on a fast disk and other data is on a slow
+ * disk.  Per-tablespace overrides never apply to temporary work files such as
+ * an external sort or a materialize node that overflows work_mem.
+ *
+ * We compute two separate costs for each path:
+ *		total_cost: total estimated cost to fetch all tuples
+ *		startup_cost: cost that is expended before first tuple is fetched
+ * In some scenarios, such as when there is a LIMIT or we are implementing
+ * an EXISTS(...) sub-select, it is not necessary to fetch all tuples of the
+ * path's result.  A caller can estimate the cost of fetching a partial
+ * result by interpolating between startup_cost and total_cost.  In detail:
+ *		actual_cost = startup_cost +
+ *			(total_cost - startup_cost) * tuples_to_fetch / path->rows;
+ * Note that a base relation's rows count (and, by extension, plan_rows for
+ * plan nodes below the LIMIT node) are set without regard to any LIMIT, so
+ * that this equation works properly.  (Note: while path->rows is never zero
+ * for ordinary relations, it is zero for paths for provably-empty relations,
+ * so beware of division-by-zero.)	The LIMIT is applied as a top-level
+ * plan node.
+ *
+ * For largely historical reasons, most of the routines in this module use
+ * the passed result Path only to store their results (rows, startup_cost and
+ * total_cost) into.  All the input data they need is passed as separate
+ * parameters, even though much of it could be extracted from the Path.
+ * An exception is made for the cost_XXXjoin() routines, which expect all
+ * the other fields of the passed XXXPath to be filled in, and similarly
+ * cost_index() assumes the passed IndexPath is valid except for its output
+ * values.
+ *
+ *
+ * Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1994, Regents of the University of California
+ *
+ * IDENTIFICATION
+ *	  src/backend/optimizer/path/costsize.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "postgres.h"
+
+#include <limits.h>
+#include <math.h>
+
+#include "access/amapi.h"
+#include "access/htup_details.h"
+#include "access/tsmapi.h"
+#include "executor/executor.h"
+#include "executor/nodeAgg.h"
+#include "executor/nodeHash.h"
+#include "executor/nodeMemoize.h"
+#include "miscadmin.h"
+#include "nodes/makefuncs.h"
+#include "nodes/nodeFuncs.h"
+#include "optimizer/clauses.h"
+#include "optimizer/cost.h"
+#include "optimizer/optimizer.h"
+#include "optimizer/pathnode.h"
+#include "optimizer/paths.h"
+#include "optimizer/placeholder.h"
+#include "optimizer/plancat.h"
+#include "optimizer/planmain.h"
+#include "optimizer/restrictinfo.h"
+#include "parser/parsetree.h"
+#include "utils/lsyscache.h"
+#include "utils/selfuncs.h"
+#include "utils/spccache.h"
+#include "utils/tuplesort.h"
+
+
+#define LOG2(x)  (log(x) / 0.693147180559945)
+
+/*
+ * Append and MergeAppend nodes are less expensive than some other operations
+ * which use cpu_tuple_cost; instead of adding a separate GUC, estimate the
+ * per-tuple cost as cpu_tuple_cost multiplied by this value.
+ */
+#define APPEND_CPU_COST_MULTIPLIER 0.5
+
+/*
+ * Maximum value for row estimates.  We cap row estimates to this to help
+ * ensure that costs based on these estimates remain within the range of what
+ * double can represent.  add_path() wouldn't act sanely given infinite or NaN
+ * cost values.
+ */
+#define MAXIMUM_ROWCOUNT 1e100
+
+double		seq_page_cost = DEFAULT_SEQ_PAGE_COST;
+double		random_page_cost = DEFAULT_RANDOM_PAGE_COST;
+double		cpu_tuple_cost = DEFAULT_CPU_TUPLE_COST;
+double		cpu_index_tuple_cost = DEFAULT_CPU_INDEX_TUPLE_COST;
+double		cpu_operator_cost = DEFAULT_CPU_OPERATOR_COST;
+double		parallel_tuple_cost = DEFAULT_PARALLEL_TUPLE_COST;
+double		parallel_setup_cost = DEFAULT_PARALLEL_SETUP_COST;
+double		recursive_worktable_factor = DEFAULT_RECURSIVE_WORKTABLE_FACTOR;
+
+int			effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;
+
+Cost		disable_cost = 1.0e10;
+
+int			max_parallel_workers_per_gather = 2;
+
+bool		enable_seqscan = true;
+bool		enable_indexscan = true;
+bool		enable_indexonlyscan = true;
+bool		enable_bitmapscan = true;
+bool		enable_tidscan = true;
+bool		enable_sort = true;
+bool		enable_incremental_sort = true;
+bool		enable_hashagg = true;
+bool		enable_nestloop = true;
+bool		enable_material = true;
+bool		enable_memoize = true;
+bool		enable_mergejoin = true;
+bool		enable_hashjoin = true;
+bool		enable_gathermerge = true;
+bool		enable_partitionwise_join = false;
+bool		enable_partitionwise_aggregate = false;
+bool		enable_parallel_append = true;
+bool		enable_parallel_hash = true;
+bool		enable_partition_pruning = true;
+bool		enable_async_append = true;
+
+typedef struct
+{
+	PlannerInfo *root;
+	QualCost	total;
+} cost_qual_eval_context;
+
+static List *extract_nonindex_conditions(List *qual_clauses, List *indexclauses);
+static MergeScanSelCache *cached_scansel(PlannerInfo *root,
+										 RestrictInfo *rinfo,
+										 PathKey *pathkey);
+static void cost_rescan(PlannerInfo *root, Path *path,
+						Cost *rescan_startup_cost, Cost *rescan_total_cost);
+static bool cost_qual_eval_walker(Node *node, cost_qual_eval_context *context);
+static void get_restriction_qual_cost(PlannerInfo *root, RelOptInfo *baserel,
+									  ParamPathInfo *param_info,
+									  QualCost *qpqual_cost);
+static bool has_indexed_join_quals(NestPath *path);
+static double approx_tuple_count(PlannerInfo *root, JoinPath *path,
+								 List *quals);
+static double calc_joinrel_size_estimate(PlannerInfo *root,
+										 RelOptInfo *joinrel,
+										 RelOptInfo *outer_rel,
+										 RelOptInfo *inner_rel,
+										 double outer_rows,
+										 double inner_rows,
+										 SpecialJoinInfo *sjinfo,
+										 List *restrictlist);
+static Selectivity get_foreign_key_join_selectivity(PlannerInfo *root,
+													Relids outer_relids,
+													Relids inner_relids,
+													SpecialJoinInfo *sjinfo,
+													List **restrictlist);
+static Cost append_nonpartial_cost(List *subpaths, int numpaths,
+								   int parallel_workers);
+static void set_rel_width(PlannerInfo *root, RelOptInfo *rel);
+static double relation_byte_size(double tuples, int width);
+static double page_size(double tuples, int width);
+static double get_parallel_divisor(Path *path);
+
+
+/*
+ * clamp_row_est
+ *		Force a row-count estimate to a sane value.
+ */
+double
+clamp_row_est(double nrows)
+{
+	/*
+	 * Avoid infinite and NaN row estimates.  Costs derived from such values
+	 * are going to be useless.  Also force the estimate to be at least one
+	 * row, to make explain output look better and to avoid possible
+	 * divide-by-zero when interpolating costs.  Make it an integer, too.
+	 */
+	if (nrows > MAXIMUM_ROWCOUNT || isnan(nrows))
+		nrows = MAXIMUM_ROWCOUNT;
+	else if (nrows <= 1.0)
+		nrows = 1.0;
+	else
+		nrows = rint(nrows);
+
+	return nrows;
+}
+
+/*
+ * clamp_cardinality_to_long
+ *		Cast a Cardinality value to a sane long value.
+ */
+long
+clamp_cardinality_to_long(Cardinality x)
+{
+	/*
+	 * Just for paranoia's sake, ensure we do something sane with negative or
+	 * NaN values.
+	 */
+	if (isnan(x))
+		return LONG_MAX;
+	if (x <= 0)
+		return 0;
+
+	/*
+	 * If "long" is 64 bits, then LONG_MAX cannot be represented exactly as a
+	 * double.  Casting it to double and back may well result in overflow due
+	 * to rounding, so avoid doing that.  We trust that any double value that
+	 * compares strictly less than "(double) LONG_MAX" will cast to a
+	 * representable "long" value.
+	 */
+	return (x < (double) LONG_MAX) ? (long) x : LONG_MAX;
+}
+
+
+/*
+ * cost_seqscan
+ *	  Determines and returns the cost of scanning a relation sequentially.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_seqscan(Path *path, PlannerInfo *root,
+			 RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		cpu_run_cost;
+	Cost		disk_run_cost;
+	double		spc_seq_page_cost;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to base relations */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_RELATION);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	if (!enable_seqscan)
+		startup_cost += disable_cost;
+
+	/* fetch estimated page cost for tablespace containing table */
+	get_tablespace_page_costs(baserel->reltablespace,
+							  NULL,
+							  &spc_seq_page_cost);
+
+	/*
+	 * disk costs
+	 */
+	disk_run_cost = spc_seq_page_cost * baserel->pages;
+
+	/* CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	cpu_run_cost = cpu_per_tuple * baserel->tuples;
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	cpu_run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	/* Adjust costing for parallelism, if used. */
+	if (path->parallel_workers > 0)
+	{
+		double		parallel_divisor = get_parallel_divisor(path);
+
+		/* The CPU cost is divided among all the workers. */
+		cpu_run_cost /= parallel_divisor;
+
+		/*
+		 * It may be possible to amortize some of the I/O cost, but probably
+		 * not very much, because most operating systems already do aggressive
+		 * prefetching.  For now, we assume that the disk run cost can't be
+		 * amortized at all.
+		 */
+
+		/*
+		 * In the case of a parallel plan, the row count needs to represent
+		 * the number of tuples processed per worker.
+		 */
+		path->rows = clamp_row_est(path->rows / parallel_divisor);
+	}
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + cpu_run_cost + disk_run_cost;
+}
+
+/*
+ * cost_samplescan
+ *	  Determines and returns the cost of scanning a relation using sampling.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_samplescan(Path *path, PlannerInfo *root,
+				RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	RangeTblEntry *rte;
+	TableSampleClause *tsc;
+	TsmRoutine *tsm;
+	double		spc_seq_page_cost,
+				spc_random_page_cost,
+				spc_page_cost;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to base relations with tablesample clauses */
+	Assert(baserel->relid > 0);
+	rte = planner_rt_fetch(baserel->relid, root);
+	Assert(rte->rtekind == RTE_RELATION);
+	tsc = rte->tablesample;
+	Assert(tsc != NULL);
+	tsm = GetTsmRoutine(tsc->tsmhandler);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/* fetch estimated page cost for tablespace containing table */
+	get_tablespace_page_costs(baserel->reltablespace,
+							  &spc_random_page_cost,
+							  &spc_seq_page_cost);
+
+	/* if NextSampleBlock is used, assume random access, else sequential */
+	spc_page_cost = (tsm->NextSampleBlock != NULL) ?
+		spc_random_page_cost : spc_seq_page_cost;
+
+	/*
+	 * disk costs (recall that baserel->pages has already been set to the
+	 * number of pages the sampling method will visit)
+	 */
+	run_cost += spc_page_cost * baserel->pages;
+
+	/*
+	 * CPU costs (recall that baserel->tuples has already been set to the
+	 * number of tuples the sampling method will select).  Note that we ignore
+	 * execution cost of the TABLESAMPLE parameter expressions; they will be
+	 * evaluated only once per scan, and in most usages they'll likely be
+	 * simple constants anyway.  We also don't charge anything for the
+	 * calculations the sampling method might do internally.
+	 */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_gather
+ *	  Determines and returns the cost of gather path.
+ *
+ * 'rel' is the relation to be operated upon
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ * 'rows' may be used to point to a row estimate; if non-NULL, it overrides
+ * both 'rel' and 'param_info'.  This is useful when the path doesn't exactly
+ * correspond to any particular RelOptInfo.
+ */
+void
+cost_gather(GatherPath *path, PlannerInfo *root,
+			RelOptInfo *rel, ParamPathInfo *param_info,
+			double *rows)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+
+	/* Mark the path with the correct row estimate */
+	if (rows)
+		path->path.rows = *rows;
+	else if (param_info)
+		path->path.rows = param_info->ppi_rows;
+	else
+		path->path.rows = rel->rows;
+
+	startup_cost = path->subpath->startup_cost;
+
+	run_cost = path->subpath->total_cost - path->subpath->startup_cost;
+
+	/* Parallel setup and communication cost. */
+	startup_cost += parallel_setup_cost;
+	run_cost += parallel_tuple_cost * path->path.rows;
+
+	path->path.startup_cost = startup_cost;
+	path->path.total_cost = (startup_cost + run_cost);
+}
+
+/*
+ * cost_gather_merge
+ *	  Determines and returns the cost of gather merge path.
+ *
+ * GatherMerge merges several pre-sorted input streams, using a heap that at
+ * any given instant holds the next tuple from each stream. If there are N
+ * streams, we need about N*log2(N) tuple comparisons to construct the heap at
+ * startup, and then for each output tuple, about log2(N) comparisons to
+ * replace the top heap entry with the next tuple from the same stream.
+ */
+void
+cost_gather_merge(GatherMergePath *path, PlannerInfo *root,
+				  RelOptInfo *rel, ParamPathInfo *param_info,
+				  Cost input_startup_cost, Cost input_total_cost,
+				  double *rows)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	Cost		comparison_cost;
+	double		N;
+	double		logN;
+
+	/* Mark the path with the correct row estimate */
+	if (rows)
+		path->path.rows = *rows;
+	else if (param_info)
+		path->path.rows = param_info->ppi_rows;
+	else
+		path->path.rows = rel->rows;
+
+	if (!enable_gathermerge)
+		startup_cost += disable_cost;
+
+	/*
+	 * Add one to the number of workers to account for the leader.  This might
+	 * be overgenerous since the leader will do less work than other workers
+	 * in typical cases, but we'll go with it for now.
+	 */
+	Assert(path->num_workers > 0);
+	N = (double) path->num_workers + 1;
+	logN = LOG2(N);
+
+	/* Assumed cost per tuple comparison */
+	comparison_cost = 2.0 * cpu_operator_cost;
+
+	/* Heap creation cost */
+	startup_cost += comparison_cost * N * logN;
+
+	/* Per-tuple heap maintenance cost */
+	run_cost += path->path.rows * comparison_cost * logN;
+
+	/* small cost for heap management, like cost_merge_append */
+	run_cost += cpu_operator_cost * path->path.rows;
+
+	/*
+	 * Parallel setup and communication cost.  Since Gather Merge, unlike
+	 * Gather, requires us to block until a tuple is available from every
+	 * worker, we bump the IPC cost up a little bit as compared with Gather.
+	 * For lack of a better idea, charge an extra 5%.
+	 */
+	startup_cost += parallel_setup_cost;
+	run_cost += parallel_tuple_cost * path->path.rows * 1.05;
+
+	path->path.startup_cost = startup_cost + input_startup_cost;
+	path->path.total_cost = (startup_cost + run_cost + input_total_cost);
+}
+
+/*
+ * cost_index
+ *	  Determines and returns the cost of scanning a relation using an index.
+ *
+ * 'path' describes the indexscan under consideration, and is complete
+ *		except for the fields to be set by this routine
+ * 'loop_count' is the number of repetitions of the indexscan to factor into
+ *		estimates of caching behavior
+ *
+ * In addition to rows, startup_cost and total_cost, cost_index() sets the
+ * path's indextotalcost and indexselectivity fields.  These values will be
+ * needed if the IndexPath is used in a BitmapIndexScan.
+ *
+ * NOTE: path->indexquals must contain only clauses usable as index
+ * restrictions.  Any additional quals evaluated as qpquals may reduce the
+ * number of returned tuples, but they won't reduce the number of tuples
+ * we have to fetch from the table, so they don't reduce the scan cost.
+ */
+void
+cost_index(IndexPath *path, PlannerInfo *root, double loop_count,
+		   bool partial_path)
+{
+	IndexOptInfo *index = path->indexinfo;
+	RelOptInfo *baserel = index->rel;
+	bool		indexonly = (path->path.pathtype == T_IndexOnlyScan);
+	amcostestimate_function amcostestimate;
+	List	   *qpquals;
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	Cost		cpu_run_cost = 0;
+	Cost		indexStartupCost;
+	Cost		indexTotalCost;
+	Selectivity indexSelectivity;
+	double		indexCorrelation,
+				csquared;
+	double		spc_seq_page_cost,
+				spc_random_page_cost;
+	Cost		min_IO_cost,
+				max_IO_cost;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+	double		tuples_fetched;
+	double		pages_fetched;
+	double		rand_heap_pages;
+	double		index_pages;
+
+	/* Should only be applied to base relations */
+	Assert(IsA(baserel, RelOptInfo) &&
+		   IsA(index, IndexOptInfo));
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_RELATION);
+
+	/*
+	 * Mark the path with the correct row estimate, and identify which quals
+	 * will need to be enforced as qpquals.  We need not check any quals that
+	 * are implied by the index's predicate, so we can use indrestrictinfo not
+	 * baserestrictinfo as the list of relevant restriction clauses for the
+	 * rel.
+	 */
+	if (path->path.param_info)
+	{
+		path->path.rows = path->path.param_info->ppi_rows;
+		/* qpquals come from the rel's restriction clauses and ppi_clauses */
+		qpquals = list_concat(extract_nonindex_conditions(path->indexinfo->indrestrictinfo,
+														  path->indexclauses),
+							  extract_nonindex_conditions(path->path.param_info->ppi_clauses,
+														  path->indexclauses));
+	}
+	else
+	{
+		path->path.rows = baserel->rows;
+		/* qpquals come from just the rel's restriction clauses */
+		qpquals = extract_nonindex_conditions(path->indexinfo->indrestrictinfo,
+											  path->indexclauses);
+	}
+
+	if (!enable_indexscan)
+		startup_cost += disable_cost;
+	/* we don't need to check enable_indexonlyscan; indxpath.c does that */
+
+	/*
+	 * Call index-access-method-specific code to estimate the processing cost
+	 * for scanning the index, as well as the selectivity of the index (ie,
+	 * the fraction of main-table tuples we will have to retrieve) and its
+	 * correlation to the main-table tuple order.  We need a cast here because
+	 * pathnodes.h uses a weak function type to avoid including amapi.h.
+	 */
+	amcostestimate = (amcostestimate_function) index->amcostestimate;
+	amcostestimate(root, path, loop_count,
+				   &indexStartupCost, &indexTotalCost,
+				   &indexSelectivity, &indexCorrelation,
+				   &index_pages);
+
+	/*
+	 * Save amcostestimate's results for possible use in bitmap scan planning.
+	 * We don't bother to save indexStartupCost or indexCorrelation, because a
+	 * bitmap scan doesn't care about either.
+	 */
+	path->indextotalcost = indexTotalCost;
+	path->indexselectivity = indexSelectivity;
+
+	/* all costs for touching index itself included here */
+	startup_cost += indexStartupCost;
+	run_cost += indexTotalCost - indexStartupCost;
+
+	/* estimate number of main-table tuples fetched */
+	tuples_fetched = clamp_row_est(indexSelectivity * baserel->tuples);
+
+	/* fetch estimated page costs for tablespace containing table */
+	get_tablespace_page_costs(baserel->reltablespace,
+							  &spc_random_page_cost,
+							  &spc_seq_page_cost);
+
+	/*----------
+	 * Estimate number of main-table pages fetched, and compute I/O cost.
+	 *
+	 * When the index ordering is uncorrelated with the table ordering,
+	 * we use an approximation proposed by Mackert and Lohman (see
+	 * index_pages_fetched() for details) to compute the number of pages
+	 * fetched, and then charge spc_random_page_cost per page fetched.
+	 *
+	 * When the index ordering is exactly correlated with the table ordering
+	 * (just after a CLUSTER, for example), the number of pages fetched should
+	 * be exactly selectivity * table_size.  What's more, all but the first
+	 * will be sequential fetches, not the random fetches that occur in the
+	 * uncorrelated case.  So if the number of pages is more than 1, we
+	 * ought to charge
+	 *		spc_random_page_cost + (pages_fetched - 1) * spc_seq_page_cost
+	 * For partially-correlated indexes, we ought to charge somewhere between
+	 * these two estimates.  We currently interpolate linearly between the
+	 * estimates based on the correlation squared (XXX is that appropriate?).
+	 *
+	 * If it's an index-only scan, then we will not need to fetch any heap
+	 * pages for which the visibility map shows all tuples are visible.
+	 * Hence, reduce the estimated number of heap fetches accordingly.
+	 * We use the measured fraction of the entire heap that is all-visible,
+	 * which might not be particularly relevant to the subset of the heap
+	 * that this query will fetch; but it's not clear how to do better.
+	 *----------
+	 */
+	if (loop_count > 1)
+	{
+		/*
+		 * For repeated indexscans, the appropriate estimate for the
+		 * uncorrelated case is to scale up the number of tuples fetched in
+		 * the Mackert and Lohman formula by the number of scans, so that we
+		 * estimate the number of pages fetched by all the scans; then
+		 * pro-rate the costs for one scan.  In this case we assume all the
+		 * fetches are random accesses.
+		 */
+		pages_fetched = index_pages_fetched(tuples_fetched * loop_count,
+											baserel->pages,
+											(double) index->pages,
+											root);
+
+		if (indexonly)
+			pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
+
+		rand_heap_pages = pages_fetched;
+
+		max_IO_cost = (pages_fetched * spc_random_page_cost) / loop_count;
+
+		/*
+		 * In the perfectly correlated case, the number of pages touched by
+		 * each scan is selectivity * table_size, and we can use the Mackert
+		 * and Lohman formula at the page level to estimate how much work is
+		 * saved by caching across scans.  We still assume all the fetches are
+		 * random, though, which is an overestimate that's hard to correct for
+		 * without double-counting the cache effects.  (But in most cases
+		 * where such a plan is actually interesting, only one page would get
+		 * fetched per scan anyway, so it shouldn't matter much.)
+		 */
+		pages_fetched = ceil(indexSelectivity * (double) baserel->pages);
+
+		pages_fetched = index_pages_fetched(pages_fetched * loop_count,
+											baserel->pages,
+											(double) index->pages,
+											root);
+
+		if (indexonly)
+			pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
+
+		min_IO_cost = (pages_fetched * spc_random_page_cost) / loop_count;
+	}
+	else
+	{
+		/*
+		 * Normal case: apply the Mackert and Lohman formula, and then
+		 * interpolate between that and the correlation-derived result.
+		 */
+		pages_fetched = index_pages_fetched(tuples_fetched,
+											baserel->pages,
+											(double) index->pages,
+											root);
+
+		if (indexonly)
+			pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
+
+		rand_heap_pages = pages_fetched;
+
+		/* max_IO_cost is for the perfectly uncorrelated case (csquared=0) */
+		max_IO_cost = pages_fetched * spc_random_page_cost;
+
+		/* min_IO_cost is for the perfectly correlated case (csquared=1) */
+		pages_fetched = ceil(indexSelectivity * (double) baserel->pages);
+
+		if (indexonly)
+			pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
+
+		if (pages_fetched > 0)
+		{
+			min_IO_cost = spc_random_page_cost;
+			if (pages_fetched > 1)
+				min_IO_cost += (pages_fetched - 1) * spc_seq_page_cost;
+		}
+		else
+			min_IO_cost = 0;
+	}
+
+	if (partial_path)
+	{
+		/*
+		 * For index only scans compute workers based on number of index pages
+		 * fetched; the number of heap pages we fetch might be so small as to
+		 * effectively rule out parallelism, which we don't want to do.
+		 */
+		if (indexonly)
+			rand_heap_pages = -1;
+
+		/*
+		 * Estimate the number of parallel workers required to scan index. Use
+		 * the number of heap pages computed considering heap fetches won't be
+		 * sequential as for parallel scans the pages are accessed in random
+		 * order.
+		 */
+		path->path.parallel_workers = compute_parallel_worker(baserel,
+															  rand_heap_pages,
+															  index_pages,
+															  max_parallel_workers_per_gather);
+
+		/*
+		 * Fall out if workers can't be assigned for parallel scan, because in
+		 * such a case this path will be rejected.  So there is no benefit in
+		 * doing extra computation.
+		 */
+		if (path->path.parallel_workers <= 0)
+			return;
+
+		path->path.parallel_aware = true;
+	}
+
+	/*
+	 * Now interpolate based on estimated index order correlation to get total
+	 * disk I/O cost for main table accesses.
+	 */
+	csquared = indexCorrelation * indexCorrelation;
+
+	run_cost += max_IO_cost + csquared * (min_IO_cost - max_IO_cost);
+
+	/*
+	 * Estimate CPU costs per tuple.
+	 *
+	 * What we want here is cpu_tuple_cost plus the evaluation costs of any
+	 * qual clauses that we have to evaluate as qpquals.
+	 */
+	cost_qual_eval(&qpqual_cost, qpquals, root);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+
+	cpu_run_cost += cpu_per_tuple * tuples_fetched;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->path.pathtarget->cost.startup;
+	cpu_run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;
+
+	/* Adjust costing for parallelism, if used. */
+	if (path->path.parallel_workers > 0)
+	{
+		double		parallel_divisor = get_parallel_divisor(&path->path);
+
+		path->path.rows = clamp_row_est(path->path.rows / parallel_divisor);
+
+		/* The CPU cost is divided among all the workers. */
+		cpu_run_cost /= parallel_divisor;
+	}
+
+	run_cost += cpu_run_cost;
+
+	path->path.startup_cost = startup_cost;
+	path->path.total_cost = startup_cost + run_cost;
+}
+
+/*
+ * extract_nonindex_conditions
+ *
+ * Given a list of quals to be enforced in an indexscan, extract the ones that
+ * will have to be applied as qpquals (ie, the index machinery won't handle
+ * them).  Here we detect only whether a qual clause is directly redundant
+ * with some indexclause.  If the index path is chosen for use, createplan.c
+ * will try a bit harder to get rid of redundant qual conditions; specifically
+ * it will see if quals can be proven to be implied by the indexquals.  But
+ * it does not seem worth the cycles to try to factor that in at this stage,
+ * since we're only trying to estimate qual eval costs.  Otherwise this must
+ * match the logic in create_indexscan_plan().
+ *
+ * qual_clauses, and the result, are lists of RestrictInfos.
+ * indexclauses is a list of IndexClauses.
+ */
+static List *
+extract_nonindex_conditions(List *qual_clauses, List *indexclauses)
+{
+	List	   *result = NIL;
+	ListCell   *lc;
+
+	foreach(lc, qual_clauses)
+	{
+		RestrictInfo *rinfo = lfirst_node(RestrictInfo, lc);
+
+		if (rinfo->pseudoconstant)
+			continue;			/* we may drop pseudoconstants here */
+		if (is_redundant_with_indexclauses(rinfo, indexclauses))
+			continue;			/* dup or derived from same EquivalenceClass */
+		/* ... skip the predicate proof attempt createplan.c will try ... */
+		result = lappend(result, rinfo);
+	}
+	return result;
+}
+
+/*
+ * index_pages_fetched
+ *	  Estimate the number of pages actually fetched after accounting for
+ *	  cache effects.
+ *
+ * We use an approximation proposed by Mackert and Lohman, "Index Scans
+ * Using a Finite LRU Buffer: A Validated I/O Model", ACM Transactions
+ * on Database Systems, Vol. 14, No. 3, September 1989, Pages 401-424.
+ * The Mackert and Lohman approximation is that the number of pages
+ * fetched is
+ *	PF =
+ *		min(2TNs/(2T+Ns), T)			when T <= b
+ *		2TNs/(2T+Ns)					when T > b and Ns <= 2Tb/(2T-b)
+ *		b + (Ns - 2Tb/(2T-b))*(T-b)/T	when T > b and Ns > 2Tb/(2T-b)
+ * where
+ *		T = # pages in table
+ *		N = # tuples in table
+ *		s = selectivity = fraction of table to be scanned
+ *		b = # buffer pages available (we include kernel space here)
+ *
+ * We assume that effective_cache_size is the total number of buffer pages
+ * available for the whole query, and pro-rate that space across all the
+ * tables in the query and the index currently under consideration.  (This
+ * ignores space needed for other indexes used by the query, but since we
+ * don't know which indexes will get used, we can't estimate that very well;
+ * and in any case counting all the tables may well be an overestimate, since
+ * depending on the join plan not all the tables may be scanned concurrently.)
+ *
+ * The product Ns is the number of tuples fetched; we pass in that
+ * product rather than calculating it here.  "pages" is the number of pages
+ * in the object under consideration (either an index or a table).
+ * "index_pages" is the amount to add to the total table space, which was
+ * computed for us by make_one_rel.
+ *
+ * Caller is expected to have ensured that tuples_fetched is greater than zero
+ * and rounded to integer (see clamp_row_est).  The result will likewise be
+ * greater than zero and integral.
+ */
+double
+index_pages_fetched(double tuples_fetched, BlockNumber pages,
+					double index_pages, PlannerInfo *root)
+{
+	double		pages_fetched;
+	double		total_pages;
+	double		T,
+				b;
+
+	/* T is # pages in table, but don't allow it to be zero */
+	T = (pages > 1) ? (double) pages : 1.0;
+
+	/* Compute number of pages assumed to be competing for cache space */
+	total_pages = root->total_table_pages + index_pages;
+	total_pages = Max(total_pages, 1.0);
+	Assert(T <= total_pages);
+
+	/* b is pro-rated share of effective_cache_size */
+	b = (double) effective_cache_size * T / total_pages;
+
+	/* force it positive and integral */
+	if (b <= 1.0)
+		b = 1.0;
+	else
+		b = ceil(b);
+
+	/* This part is the Mackert and Lohman formula */
+	if (T <= b)
+	{
+		pages_fetched =
+			(2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
+		if (pages_fetched >= T)
+			pages_fetched = T;
+		else
+			pages_fetched = ceil(pages_fetched);
+	}
+	else
+	{
+		double		lim;
+
+		lim = (2.0 * T * b) / (2.0 * T - b);
+		if (tuples_fetched <= lim)
+		{
+			pages_fetched =
+				(2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
+		}
+		else
+		{
+			pages_fetched =
+				b + (tuples_fetched - lim) * (T - b) / T;
+		}
+		pages_fetched = ceil(pages_fetched);
+	}
+	return pages_fetched;
+}
+
+/*
+ * get_indexpath_pages
+ *		Determine the total size of the indexes used in a bitmap index path.
+ *
+ * Note: if the same index is used more than once in a bitmap tree, we will
+ * count it multiple times, which perhaps is the wrong thing ... but it's
+ * not completely clear, and detecting duplicates is difficult, so ignore it
+ * for now.
+ */
+static double
+get_indexpath_pages(Path *bitmapqual)
+{
+	double		result = 0;
+	ListCell   *l;
+
+	if (IsA(bitmapqual, BitmapAndPath))
+	{
+		BitmapAndPath *apath = (BitmapAndPath *) bitmapqual;
+
+		foreach(l, apath->bitmapquals)
+		{
+			result += get_indexpath_pages((Path *) lfirst(l));
+		}
+	}
+	else if (IsA(bitmapqual, BitmapOrPath))
+	{
+		BitmapOrPath *opath = (BitmapOrPath *) bitmapqual;
+
+		foreach(l, opath->bitmapquals)
+		{
+			result += get_indexpath_pages((Path *) lfirst(l));
+		}
+	}
+	else if (IsA(bitmapqual, IndexPath))
+	{
+		IndexPath  *ipath = (IndexPath *) bitmapqual;
+
+		result = (double) ipath->indexinfo->pages;
+	}
+	else
+		elog(ERROR, "unrecognized node type: %d", nodeTag(bitmapqual));
+
+	return result;
+}
+
+/*
+ * cost_bitmap_heap_scan
+ *	  Determines and returns the cost of scanning a relation using a bitmap
+ *	  index-then-heap plan.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ * 'bitmapqual' is a tree of IndexPaths, BitmapAndPaths, and BitmapOrPaths
+ * 'loop_count' is the number of repetitions of the indexscan to factor into
+ *		estimates of caching behavior
+ *
+ * Note: the component IndexPaths in bitmapqual should have been costed
+ * using the same loop_count.
+ */
+void
+cost_bitmap_heap_scan(Path *path, PlannerInfo *root, RelOptInfo *baserel,
+					  ParamPathInfo *param_info,
+					  Path *bitmapqual, double loop_count)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	Cost		indexTotalCost;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+	Cost		cost_per_page;
+	Cost		cpu_run_cost;
+	double		tuples_fetched;
+	double		pages_fetched;
+	double		spc_seq_page_cost,
+				spc_random_page_cost;
+	double		T;
+
+	/* Should only be applied to base relations */
+	Assert(IsA(baserel, RelOptInfo));
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_RELATION);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	if (!enable_bitmapscan)
+		startup_cost += disable_cost;
+
+	pages_fetched = compute_bitmap_pages(root, baserel, bitmapqual,
+										 loop_count, &indexTotalCost,
+										 &tuples_fetched);
+
+	startup_cost += indexTotalCost;
+	T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
+
+	/* Fetch estimated page costs for tablespace containing table. */
+	get_tablespace_page_costs(baserel->reltablespace,
+							  &spc_random_page_cost,
+							  &spc_seq_page_cost);
+
+	/*
+	 * For small numbers of pages we should charge spc_random_page_cost
+	 * apiece, while if nearly all the table's pages are being read, it's more
+	 * appropriate to charge spc_seq_page_cost apiece.  The effect is
+	 * nonlinear, too. For lack of a better idea, interpolate like this to
+	 * determine the cost per page.
+	 */
+	if (pages_fetched >= 2.0)
+		cost_per_page = spc_random_page_cost -
+			(spc_random_page_cost - spc_seq_page_cost)
+			* sqrt(pages_fetched / T);
+	else
+		cost_per_page = spc_random_page_cost;
+
+	run_cost += pages_fetched * cost_per_page;
+
+	/*
+	 * Estimate CPU costs per tuple.
+	 *
+	 * Often the indexquals don't need to be rechecked at each tuple ... but
+	 * not always, especially not if there are enough tuples involved that the
+	 * bitmaps become lossy.  For the moment, just assume they will be
+	 * rechecked always.  This means we charge the full freight for all the
+	 * scan clauses.
+	 */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	cpu_run_cost = cpu_per_tuple * tuples_fetched;
+
+	/* Adjust costing for parallelism, if used. */
+	if (path->parallel_workers > 0)
+	{
+		double		parallel_divisor = get_parallel_divisor(path);
+
+		/* The CPU cost is divided among all the workers. */
+		cpu_run_cost /= parallel_divisor;
+
+		path->rows = clamp_row_est(path->rows / parallel_divisor);
+	}
+
+
+	run_cost += cpu_run_cost;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_bitmap_tree_node
+ *		Extract cost and selectivity from a bitmap tree node (index/and/or)
+ */
+void
+cost_bitmap_tree_node(Path *path, Cost *cost, Selectivity *selec)
+{
+	if (IsA(path, IndexPath))
+	{
+		*cost = ((IndexPath *) path)->indextotalcost;
+		*selec = ((IndexPath *) path)->indexselectivity;
+
+		/*
+		 * Charge a small amount per retrieved tuple to reflect the costs of
+		 * manipulating the bitmap.  This is mostly to make sure that a bitmap
+		 * scan doesn't look to be the same cost as an indexscan to retrieve a
+		 * single tuple.
+		 */
+		*cost += 0.1 * cpu_operator_cost * path->rows;
+	}
+	else if (IsA(path, BitmapAndPath))
+	{
+		*cost = path->total_cost;
+		*selec = ((BitmapAndPath *) path)->bitmapselectivity;
+	}
+	else if (IsA(path, BitmapOrPath))
+	{
+		*cost = path->total_cost;
+		*selec = ((BitmapOrPath *) path)->bitmapselectivity;
+	}
+	else
+	{
+		elog(ERROR, "unrecognized node type: %d", nodeTag(path));
+		*cost = *selec = 0;		/* keep compiler quiet */
+	}
+}
+
+/*
+ * cost_bitmap_and_node
+ *		Estimate the cost of a BitmapAnd node
+ *
+ * Note that this considers only the costs of index scanning and bitmap
+ * creation, not the eventual heap access.  In that sense the object isn't
+ * truly a Path, but it has enough path-like properties (costs in particular)
+ * to warrant treating it as one.  We don't bother to set the path rows field,
+ * however.
+ */
+void
+cost_bitmap_and_node(BitmapAndPath *path, PlannerInfo *root)
+{
+	Cost		totalCost;
+	Selectivity selec;
+	ListCell   *l;
+
+	/*
+	 * We estimate AND selectivity on the assumption that the inputs are
+	 * independent.  This is probably often wrong, but we don't have the info
+	 * to do better.
+	 *
+	 * The runtime cost of the BitmapAnd itself is estimated at 100x
+	 * cpu_operator_cost for each tbm_intersect needed.  Probably too small,
+	 * definitely too simplistic?
+	 */
+	totalCost = 0.0;
+	selec = 1.0;
+	foreach(l, path->bitmapquals)
+	{
+		Path	   *subpath = (Path *) lfirst(l);
+		Cost		subCost;
+		Selectivity subselec;
+
+		cost_bitmap_tree_node(subpath, &subCost, &subselec);
+
+		selec *= subselec;
+
+		totalCost += subCost;
+		if (l != list_head(path->bitmapquals))
+			totalCost += 100.0 * cpu_operator_cost;
+	}
+	path->bitmapselectivity = selec;
+	path->path.rows = 0;		/* per above, not used */
+	path->path.startup_cost = totalCost;
+	path->path.total_cost = totalCost;
+}
+
+/*
+ * cost_bitmap_or_node
+ *		Estimate the cost of a BitmapOr node
+ *
+ * See comments for cost_bitmap_and_node.
+ */
+void
+cost_bitmap_or_node(BitmapOrPath *path, PlannerInfo *root)
+{
+	Cost		totalCost;
+	Selectivity selec;
+	ListCell   *l;
+
+	/*
+	 * We estimate OR selectivity on the assumption that the inputs are
+	 * non-overlapping, since that's often the case in "x IN (list)" type
+	 * situations.  Of course, we clamp to 1.0 at the end.
+	 *
+	 * The runtime cost of the BitmapOr itself is estimated at 100x
+	 * cpu_operator_cost for each tbm_union needed.  Probably too small,
+	 * definitely too simplistic?  We are aware that the tbm_unions are
+	 * optimized out when the inputs are BitmapIndexScans.
+	 */
+	totalCost = 0.0;
+	selec = 0.0;
+	foreach(l, path->bitmapquals)
+	{
+		Path	   *subpath = (Path *) lfirst(l);
+		Cost		subCost;
+		Selectivity subselec;
+
+		cost_bitmap_tree_node(subpath, &subCost, &subselec);
+
+		selec += subselec;
+
+		totalCost += subCost;
+		if (l != list_head(path->bitmapquals) &&
+			!IsA(subpath, IndexPath))
+			totalCost += 100.0 * cpu_operator_cost;
+	}
+	path->bitmapselectivity = Min(selec, 1.0);
+	path->path.rows = 0;		/* per above, not used */
+	path->path.startup_cost = totalCost;
+	path->path.total_cost = totalCost;
+}
+
+/*
+ * cost_tidscan
+ *	  Determines and returns the cost of scanning a relation using TIDs.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'tidquals' is the list of TID-checkable quals
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_tidscan(Path *path, PlannerInfo *root,
+			 RelOptInfo *baserel, List *tidquals, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	bool		isCurrentOf = false;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+	QualCost	tid_qual_cost;
+	int			ntuples;
+	ListCell   *l;
+	double		spc_random_page_cost;
+
+	/* Should only be applied to base relations */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_RELATION);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/* Count how many tuples we expect to retrieve */
+	ntuples = 0;
+	foreach(l, tidquals)
+	{
+		RestrictInfo *rinfo = lfirst_node(RestrictInfo, l);
+		Expr	   *qual = rinfo->clause;
+
+		if (IsA(qual, ScalarArrayOpExpr))
+		{
+			/* Each element of the array yields 1 tuple */
+			ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) qual;
+			Node	   *arraynode = (Node *) lsecond(saop->args);
+
+			ntuples += estimate_array_length(arraynode);
+		}
+		else if (IsA(qual, CurrentOfExpr))
+		{
+			/* CURRENT OF yields 1 tuple */
+			isCurrentOf = true;
+			ntuples++;
+		}
+		else
+		{
+			/* It's just CTID = something, count 1 tuple */
+			ntuples++;
+		}
+	}
+
+	/*
+	 * We must force TID scan for WHERE CURRENT OF, because only nodeTidscan.c
+	 * understands how to do it correctly.  Therefore, honor enable_tidscan
+	 * only when CURRENT OF isn't present.  Also note that cost_qual_eval
+	 * counts a CurrentOfExpr as having startup cost disable_cost, which we
+	 * subtract off here; that's to prevent other plan types such as seqscan
+	 * from winning.
+	 */
+	if (isCurrentOf)
+	{
+		Assert(baserel->baserestrictcost.startup >= disable_cost);
+		startup_cost -= disable_cost;
+	}
+	else if (!enable_tidscan)
+		startup_cost += disable_cost;
+
+	/*
+	 * The TID qual expressions will be computed once, any other baserestrict
+	 * quals once per retrieved tuple.
+	 */
+	cost_qual_eval(&tid_qual_cost, tidquals, root);
+
+	/* fetch estimated page cost for tablespace containing table */
+	get_tablespace_page_costs(baserel->reltablespace,
+							  &spc_random_page_cost,
+							  NULL);
+
+	/* disk costs --- assume each tuple on a different page */
+	run_cost += spc_random_page_cost * ntuples;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	/* XXX currently we assume TID quals are a subset of qpquals */
+	startup_cost += qpqual_cost.startup + tid_qual_cost.per_tuple;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple -
+		tid_qual_cost.per_tuple;
+	run_cost += cpu_per_tuple * ntuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_tidrangescan
+ *	  Determines and sets the costs of scanning a relation using a range of
+ *	  TIDs for 'path'
+ *
+ * 'baserel' is the relation to be scanned
+ * 'tidrangequals' is the list of TID-checkable range quals
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_tidrangescan(Path *path, PlannerInfo *root,
+				  RelOptInfo *baserel, List *tidrangequals,
+				  ParamPathInfo *param_info)
+{
+	Selectivity selectivity;
+	double		pages;
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+	QualCost	tid_qual_cost;
+	double		ntuples;
+	double		nseqpages;
+	double		spc_random_page_cost;
+	double		spc_seq_page_cost;
+
+	/* Should only be applied to base relations */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_RELATION);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/* Count how many tuples and pages we expect to scan */
+	selectivity = clauselist_selectivity(root, tidrangequals, baserel->relid,
+										 JOIN_INNER, NULL);
+	pages = ceil(selectivity * baserel->pages);
+
+	if (pages <= 0.0)
+		pages = 1.0;
+
+	/*
+	 * The first page in a range requires a random seek, but each subsequent
+	 * page is just a normal sequential page read. NOTE: it's desirable for
+	 * TID Range Scans to cost more than the equivalent Sequential Scans,
+	 * because Seq Scans have some performance advantages such as scan
+	 * synchronization and parallelizability, and we'd prefer one of them to
+	 * be picked unless a TID Range Scan really is better.
+	 */
+	ntuples = selectivity * baserel->tuples;
+	nseqpages = pages - 1.0;
+
+	if (!enable_tidscan)
+		startup_cost += disable_cost;
+
+	/*
+	 * The TID qual expressions will be computed once, any other baserestrict
+	 * quals once per retrieved tuple.
+	 */
+	cost_qual_eval(&tid_qual_cost, tidrangequals, root);
+
+	/* fetch estimated page cost for tablespace containing table */
+	get_tablespace_page_costs(baserel->reltablespace,
+							  &spc_random_page_cost,
+							  &spc_seq_page_cost);
+
+	/* disk costs; 1 random page and the remainder as seq pages */
+	run_cost += spc_random_page_cost + spc_seq_page_cost * nseqpages;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	/*
+	 * XXX currently we assume TID quals are a subset of qpquals at this
+	 * point; they will be removed (if possible) when we create the plan, so
+	 * we subtract their cost from the total qpqual cost.  (If the TID quals
+	 * can't be removed, this is a mistake and we're going to underestimate
+	 * the CPU cost a bit.)
+	 */
+	startup_cost += qpqual_cost.startup + tid_qual_cost.per_tuple;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple -
+		tid_qual_cost.per_tuple;
+	run_cost += cpu_per_tuple * ntuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_subqueryscan
+ *	  Determines and returns the cost of scanning a subquery RTE.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_subqueryscan(SubqueryScanPath *path, PlannerInfo *root,
+				  RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost;
+	Cost		run_cost;
+	List	   *qpquals;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to base relations that are subqueries */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_SUBQUERY);
+
+	/*
+	 * We compute the rowcount estimate as the subplan's estimate times the
+	 * selectivity of relevant restriction clauses.  In simple cases this will
+	 * come out the same as baserel->rows; but when dealing with parallelized
+	 * paths we must do it like this to get the right answer.
+	 */
+	if (param_info)
+		qpquals = list_concat_copy(param_info->ppi_clauses,
+								   baserel->baserestrictinfo);
+	else
+		qpquals = baserel->baserestrictinfo;
+
+	path->path.rows = clamp_row_est(path->subpath->rows *
+									clauselist_selectivity(root,
+														   qpquals,
+														   0,
+														   JOIN_INNER,
+														   NULL));
+
+	/*
+	 * Cost of path is cost of evaluating the subplan, plus cost of evaluating
+	 * any restriction clauses and tlist that will be attached to the
+	 * SubqueryScan node, plus cpu_tuple_cost to account for selection and
+	 * projection overhead.
+	 */
+	path->path.startup_cost = path->subpath->startup_cost;
+	path->path.total_cost = path->subpath->total_cost;
+
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost = qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost = cpu_per_tuple * path->subpath->rows;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->path.pathtarget->cost.startup;
+	run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;
+
+	path->path.startup_cost += startup_cost;
+	path->path.total_cost += startup_cost + run_cost;
+}
+
+/*
+ * cost_functionscan
+ *	  Determines and returns the cost of scanning a function RTE.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_functionscan(Path *path, PlannerInfo *root,
+				  RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+	RangeTblEntry *rte;
+	QualCost	exprcost;
+
+	/* Should only be applied to base relations that are functions */
+	Assert(baserel->relid > 0);
+	rte = planner_rt_fetch(baserel->relid, root);
+	Assert(rte->rtekind == RTE_FUNCTION);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/*
+	 * Estimate costs of executing the function expression(s).
+	 *
+	 * Currently, nodeFunctionscan.c always executes the functions to
+	 * completion before returning any rows, and caches the results in a
+	 * tuplestore.  So the function eval cost is all startup cost, and per-row
+	 * costs are minimal.
+	 *
+	 * XXX in principle we ought to charge tuplestore spill costs if the
+	 * number of rows is large.  However, given how phony our rowcount
+	 * estimates for functions tend to be, there's not a lot of point in that
+	 * refinement right now.
+	 */
+	cost_qual_eval_node(&exprcost, (Node *) rte->functions, root);
+
+	startup_cost += exprcost.startup + exprcost.per_tuple;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_tablefuncscan
+ *	  Determines and returns the cost of scanning a table function.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_tablefuncscan(Path *path, PlannerInfo *root,
+				   RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+	RangeTblEntry *rte;
+	QualCost	exprcost;
+
+	/* Should only be applied to base relations that are functions */
+	Assert(baserel->relid > 0);
+	rte = planner_rt_fetch(baserel->relid, root);
+	Assert(rte->rtekind == RTE_TABLEFUNC);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/*
+	 * Estimate costs of executing the table func expression(s).
+	 *
+	 * XXX in principle we ought to charge tuplestore spill costs if the
+	 * number of rows is large.  However, given how phony our rowcount
+	 * estimates for tablefuncs tend to be, there's not a lot of point in that
+	 * refinement right now.
+	 */
+	cost_qual_eval_node(&exprcost, (Node *) rte->tablefunc, root);
+
+	startup_cost += exprcost.startup + exprcost.per_tuple;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_valuesscan
+ *	  Determines and returns the cost of scanning a VALUES RTE.
+ *
+ * 'baserel' is the relation to be scanned
+ * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
+ */
+void
+cost_valuesscan(Path *path, PlannerInfo *root,
+				RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to base relations that are values lists */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_VALUES);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/*
+	 * For now, estimate list evaluation cost at one operator eval per list
+	 * (probably pretty bogus, but is it worth being smarter?)
+	 */
+	cpu_per_tuple = cpu_operator_cost;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_ctescan
+ *	  Determines and returns the cost of scanning a CTE RTE.
+ *
+ * Note: this is used for both self-reference and regular CTEs; the
+ * possible cost differences are below the threshold of what we could
+ * estimate accurately anyway.  Note that the costs of evaluating the
+ * referenced CTE query are added into the final plan as initplan costs,
+ * and should NOT be counted here.
+ */
+void
+cost_ctescan(Path *path, PlannerInfo *root,
+			 RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to base relations that are CTEs */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_CTE);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/* Charge one CPU tuple cost per row for tuplestore manipulation */
+	cpu_per_tuple = cpu_tuple_cost;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->pathtarget->cost.startup;
+	run_cost += path->pathtarget->cost.per_tuple * path->rows;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_namedtuplestorescan
+ *	  Determines and returns the cost of scanning a named tuplestore.
+ */
+void
+cost_namedtuplestorescan(Path *path, PlannerInfo *root,
+						 RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to base relations that are Tuplestores */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_NAMEDTUPLESTORE);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/* Charge one CPU tuple cost per row for tuplestore manipulation */
+	cpu_per_tuple = cpu_tuple_cost;
+
+	/* Add scanning CPU costs */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_resultscan
+ *	  Determines and returns the cost of scanning an RTE_RESULT relation.
+ */
+void
+cost_resultscan(Path *path, PlannerInfo *root,
+				RelOptInfo *baserel, ParamPathInfo *param_info)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	QualCost	qpqual_cost;
+	Cost		cpu_per_tuple;
+
+	/* Should only be applied to RTE_RESULT base relations */
+	Assert(baserel->relid > 0);
+	Assert(baserel->rtekind == RTE_RESULT);
+
+	/* Mark the path with the correct row estimate */
+	if (param_info)
+		path->rows = param_info->ppi_rows;
+	else
+		path->rows = baserel->rows;
+
+	/* We charge qual cost plus cpu_tuple_cost */
+	get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
+
+	startup_cost += qpqual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
+	run_cost += cpu_per_tuple * baserel->tuples;
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_recursive_union
+ *	  Determines and returns the cost of performing a recursive union,
+ *	  and also the estimated output size.
+ *
+ * We are given Paths for the nonrecursive and recursive terms.
+ */
+void
+cost_recursive_union(Path *runion, Path *nrterm, Path *rterm)
+{
+	Cost		startup_cost;
+	Cost		total_cost;
+	double		total_rows;
+
+	/* We probably have decent estimates for the non-recursive term */
+	startup_cost = nrterm->startup_cost;
+	total_cost = nrterm->total_cost;
+	total_rows = nrterm->rows;
+
+	/*
+	 * We arbitrarily assume that about 10 recursive iterations will be
+	 * needed, and that we've managed to get a good fix on the cost and output
+	 * size of each one of them.  These are mighty shaky assumptions but it's
+	 * hard to see how to do better.
+	 */
+	total_cost += 10 * rterm->total_cost;
+	total_rows += 10 * rterm->rows;
+
+	/*
+	 * Also charge cpu_tuple_cost per row to account for the costs of
+	 * manipulating the tuplestores.  (We don't worry about possible
+	 * spill-to-disk costs.)
+	 */
+	total_cost += cpu_tuple_cost * total_rows;
+
+	runion->startup_cost = startup_cost;
+	runion->total_cost = total_cost;
+	runion->rows = total_rows;
+	runion->pathtarget->width = Max(nrterm->pathtarget->width,
+									rterm->pathtarget->width);
+}
+
+/*
+ * cost_tuplesort
+ *	  Determines and returns the cost of sorting a relation using tuplesort,
+ *    not including the cost of reading the input data.
+ *
+ * If the total volume of data to sort is less than sort_mem, we will do
+ * an in-memory sort, which requires no I/O and about t*log2(t) tuple
+ * comparisons for t tuples.
+ *
+ * If the total volume exceeds sort_mem, we switch to a tape-style merge
+ * algorithm.  There will still be about t*log2(t) tuple comparisons in
+ * total, but we will also need to write and read each tuple once per
+ * merge pass.  We expect about ceil(logM(r)) merge passes where r is the
+ * number of initial runs formed and M is the merge order used by tuplesort.c.
+ * Since the average initial run should be about sort_mem, we have
+ *		disk traffic = 2 * relsize * ceil(logM(p / sort_mem))
+ *		cpu = comparison_cost * t * log2(t)
+ *
+ * If the sort is bounded (i.e., only the first k result tuples are needed)
+ * and k tuples can fit into sort_mem, we use a heap method that keeps only
+ * k tuples in the heap; this will require about t*log2(k) tuple comparisons.
+ *
+ * The disk traffic is assumed to be 3/4ths sequential and 1/4th random
+ * accesses (XXX can't we refine that guess?)
+ *
+ * By default, we charge two operator evals per tuple comparison, which should
+ * be in the right ballpark in most cases.  The caller can tweak this by
+ * specifying nonzero comparison_cost; typically that's used for any extra
+ * work that has to be done to prepare the inputs to the comparison operators.
+ *
+ * 'tuples' is the number of tuples in the relation
+ * 'width' is the average tuple width in bytes
+ * 'comparison_cost' is the extra cost per comparison, if any
+ * 'sort_mem' is the number of kilobytes of work memory allowed for the sort
+ * 'limit_tuples' is the bound on the number of output tuples; -1 if no bound
+ */
+static void
+cost_tuplesort(Cost *startup_cost, Cost *run_cost,
+			   double tuples, int width,
+			   Cost comparison_cost, int sort_mem,
+			   double limit_tuples)
+{
+	double		input_bytes = relation_byte_size(tuples, width);
+	double		output_bytes;
+	double		output_tuples;
+	long		sort_mem_bytes = sort_mem * 1024L;
+
+	/*
+	 * We want to be sure the cost of a sort is never estimated as zero, even
+	 * if passed-in tuple count is zero.  Besides, mustn't do log(0)...
+	 */
+	if (tuples < 2.0)
+		tuples = 2.0;
+
+	/* Include the default cost-per-comparison */
+	comparison_cost += 2.0 * cpu_operator_cost;
+
+	/* Do we have a useful LIMIT? */
+	if (limit_tuples > 0 && limit_tuples < tuples)
+	{
+		output_tuples = limit_tuples;
+		output_bytes = relation_byte_size(output_tuples, width);
+	}
+	else
+	{
+		output_tuples = tuples;
+		output_bytes = input_bytes;
+	}
+
+	if (output_bytes > sort_mem_bytes)
+	{
+		/*
+		 * We'll have to use a disk-based sort of all the tuples
+		 */
+		double		npages = ceil(input_bytes / BLCKSZ);
+		double		nruns = input_bytes / sort_mem_bytes;
+		double		mergeorder = tuplesort_merge_order(sort_mem_bytes);
+		double		log_runs;
+		double		npageaccesses;
+
+		/*
+		 * CPU costs
+		 *
+		 * Assume about N log2 N comparisons
+		 */
+		*startup_cost = comparison_cost * tuples * LOG2(tuples);
+
+		/* Disk costs */
+
+		/* Compute logM(r) as log(r) / log(M) */
+		if (nruns > mergeorder)
+			log_runs = ceil(log(nruns) / log(mergeorder));
+		else
+			log_runs = 1.0;
+		npageaccesses = 2.0 * npages * log_runs;
+		/* Assume 3/4ths of accesses are sequential, 1/4th are not */
+		*startup_cost += npageaccesses *
+			(seq_page_cost * 0.75 + random_page_cost * 0.25);
+	}
+	else if (tuples > 2 * output_tuples || input_bytes > sort_mem_bytes)
+	{
+		/*
+		 * We'll use a bounded heap-sort keeping just K tuples in memory, for
+		 * a total number of tuple comparisons of N log2 K; but the constant
+		 * factor is a bit higher than for quicksort.  Tweak it so that the
+		 * cost curve is continuous at the crossover point.
+		 */
+		*startup_cost = comparison_cost * tuples * LOG2(2.0 * output_tuples);
+	}
+	else
+	{
+		/* We'll use plain quicksort on all the input tuples */
+		*startup_cost = comparison_cost * tuples * LOG2(tuples);
+	}
+
+	/*
+	 * Also charge a small amount (arbitrarily set equal to operator cost) per
+	 * extracted tuple.  We don't charge cpu_tuple_cost because a Sort node
+	 * doesn't do qual-checking or projection, so it has less overhead than
+	 * most plan nodes.  Note it's correct to use tuples not output_tuples
+	 * here --- the upper LIMIT will pro-rate the run cost so we'd be double
+	 * counting the LIMIT otherwise.
+	 */
+	*run_cost = cpu_operator_cost * tuples;
+}
+
+/*
+ * cost_incremental_sort
+ * 	Determines and returns the cost of sorting a relation incrementally, when
+ *  the input path is presorted by a prefix of the pathkeys.
+ *
+ * 'presorted_keys' is the number of leading pathkeys by which the input path
+ * is sorted.
+ *
+ * We estimate the number of groups into which the relation is divided by the
+ * leading pathkeys, and then calculate the cost of sorting a single group
+ * with tuplesort using cost_tuplesort().
+ */
+void
+cost_incremental_sort(Path *path,
+					  PlannerInfo *root, List *pathkeys, int presorted_keys,
+					  Cost input_startup_cost, Cost input_total_cost,
+					  double input_tuples, int width, Cost comparison_cost, int sort_mem,
+					  double limit_tuples)
+{
+	Cost		startup_cost = 0,
+				run_cost = 0,
+				input_run_cost = input_total_cost - input_startup_cost;
+	double		group_tuples,
+				input_groups;
+	Cost		group_startup_cost,
+				group_run_cost,
+				group_input_run_cost;
+	List	   *presortedExprs = NIL;
+	ListCell   *l;
+	int			i = 0;
+	bool		unknown_varno = false;
+
+	Assert(presorted_keys != 0);
+
+	/*
+	 * We want to be sure the cost of a sort is never estimated as zero, even
+	 * if passed-in tuple count is zero.  Besides, mustn't do log(0)...
+	 */
+	if (input_tuples < 2.0)
+		input_tuples = 2.0;
+
+	/* Default estimate of number of groups, capped to one group per row. */
+	input_groups = Min(input_tuples, DEFAULT_NUM_DISTINCT);
+
+	/*
+	 * Extract presorted keys as list of expressions.
+	 *
+	 * We need to be careful about Vars containing "varno 0" which might have
+	 * been introduced by generate_append_tlist, which would confuse
+	 * estimate_num_groups (in fact it'd fail for such expressions). See
+	 * recurse_set_operations which has to deal with the same issue.
+	 *
+	 * Unlike recurse_set_operations we can't access the original target list
+	 * here, and even if we could it's not very clear how useful would that be
+	 * for a set operation combining multiple tables. So we simply detect if
+	 * there are any expressions with "varno 0" and use the default
+	 * DEFAULT_NUM_DISTINCT in that case.
+	 *
+	 * We might also use either 1.0 (a single group) or input_tuples (each row
+	 * being a separate group), pretty much the worst and best case for
+	 * incremental sort. But those are extreme cases and using something in
+	 * between seems reasonable. Furthermore, generate_append_tlist is used
+	 * for set operations, which are likely to produce mostly unique output
+	 * anyway - from that standpoint the DEFAULT_NUM_DISTINCT is defensive
+	 * while maintaining lower startup cost.
+	 */
+	foreach(l, pathkeys)
+	{
+		PathKey    *key = (PathKey *) lfirst(l);
+		EquivalenceMember *member = (EquivalenceMember *)
+		linitial(key->pk_eclass->ec_members);
+
+		/*
+		 * Check if the expression contains Var with "varno 0" so that we
+		 * don't call estimate_num_groups in that case.
+		 */
+		if (bms_is_member(0, pull_varnos(root, (Node *) member->em_expr)))
+		{
+			unknown_varno = true;
+			break;
+		}
+
+		/* expression not containing any Vars with "varno 0" */
+		presortedExprs = lappend(presortedExprs, member->em_expr);
+
+		i++;
+		if (i >= presorted_keys)
+			break;
+	}
+
+	/* Estimate number of groups with equal presorted keys. */
+	if (!unknown_varno)
+		input_groups = estimate_num_groups(root, presortedExprs, input_tuples,
+										   NULL, NULL);
+
+	group_tuples = input_tuples / input_groups;
+	group_input_run_cost = input_run_cost / input_groups;
+
+	/*
+	 * Estimate average cost of sorting of one group where presorted keys are
+	 * equal.  Incremental sort is sensitive to distribution of tuples to the
+	 * groups, where we're relying on quite rough assumptions.  Thus, we're
+	 * pessimistic about incremental sort performance and increase its average
+	 * group size by half.
+	 */
+	cost_tuplesort(&group_startup_cost, &group_run_cost,
+				   1.5 * group_tuples, width, comparison_cost, sort_mem,
+				   limit_tuples);
+
+	/*
+	 * Startup cost of incremental sort is the startup cost of its first group
+	 * plus the cost of its input.
+	 */
+	startup_cost += group_startup_cost
+		+ input_startup_cost + group_input_run_cost;
+
+	/*
+	 * After we started producing tuples from the first group, the cost of
+	 * producing all the tuples is given by the cost to finish processing this
+	 * group, plus the total cost to process the remaining groups, plus the
+	 * remaining cost of input.
+	 */
+	run_cost += group_run_cost
+		+ (group_run_cost + group_startup_cost) * (input_groups - 1)
+		+ group_input_run_cost * (input_groups - 1);
+
+	/*
+	 * Incremental sort adds some overhead by itself. Firstly, it has to
+	 * detect the sort groups. This is roughly equal to one extra copy and
+	 * comparison per tuple. Secondly, it has to reset the tuplesort context
+	 * for every group.
+	 */
+	run_cost += (cpu_tuple_cost + comparison_cost) * input_tuples;
+	run_cost += 2.0 * cpu_tuple_cost * input_groups;
+
+	path->rows = input_tuples;
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_sort
+ *	  Determines and returns the cost of sorting a relation, including
+ *	  the cost of reading the input data.
+ *
+ * NOTE: some callers currently pass NIL for pathkeys because they
+ * can't conveniently supply the sort keys.  Since this routine doesn't
+ * currently do anything with pathkeys anyway, that doesn't matter...
+ * but if it ever does, it should react gracefully to lack of key data.
+ * (Actually, the thing we'd most likely be interested in is just the number
+ * of sort keys, which all callers *could* supply.)
+ */
+void
+cost_sort(Path *path, PlannerInfo *root,
+		  List *pathkeys, Cost input_cost, double tuples, int width,
+		  Cost comparison_cost, int sort_mem,
+		  double limit_tuples)
+
+{
+	Cost		startup_cost;
+	Cost		run_cost;
+
+	cost_tuplesort(&startup_cost, &run_cost,
+				   tuples, width,
+				   comparison_cost, sort_mem,
+				   limit_tuples);
+
+	if (!enable_sort)
+		startup_cost += disable_cost;
+
+	startup_cost += input_cost;
+
+	path->rows = tuples;
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * append_nonpartial_cost
+ *	  Estimate the cost of the non-partial paths in a Parallel Append.
+ *	  The non-partial paths are assumed to be the first "numpaths" paths
+ *	  from the subpaths list, and to be in order of decreasing cost.
+ */
+static Cost
+append_nonpartial_cost(List *subpaths, int numpaths, int parallel_workers)
+{
+	Cost	   *costarr;
+	int			arrlen;
+	ListCell   *l;
+	ListCell   *cell;
+	int			i;
+	int			path_index;
+	int			min_index;
+	int			max_index;
+
+	if (numpaths == 0)
+		return 0;
+
+	/*
+	 * Array length is number of workers or number of relevant paths,
+	 * whichever is less.
+	 */
+	arrlen = Min(parallel_workers, numpaths);
+	costarr = (Cost *) palloc(sizeof(Cost) * arrlen);
+
+	/* The first few paths will each be claimed by a different worker. */
+	path_index = 0;
+	foreach(cell, subpaths)
+	{
+		Path	   *subpath = (Path *) lfirst(cell);
+
+		if (path_index == arrlen)
+			break;
+		costarr[path_index++] = subpath->total_cost;
+	}
+
+	/*
+	 * Since subpaths are sorted by decreasing cost, the last one will have
+	 * the minimum cost.
+	 */
+	min_index = arrlen - 1;
+
+	/*
+	 * For each of the remaining subpaths, add its cost to the array element
+	 * with minimum cost.
+	 */
+	for_each_cell(l, subpaths, cell)
+	{
+		Path	   *subpath = (Path *) lfirst(l);
+		int			i;
+
+		/* Consider only the non-partial paths */
+		if (path_index++ == numpaths)
+			break;
+
+		costarr[min_index] += subpath->total_cost;
+
+		/* Update the new min cost array index */
+		for (min_index = i = 0; i < arrlen; i++)
+		{
+			if (costarr[i] < costarr[min_index])
+				min_index = i;
+		}
+	}
+
+	/* Return the highest cost from the array */
+	for (max_index = i = 0; i < arrlen; i++)
+	{
+		if (costarr[i] > costarr[max_index])
+			max_index = i;
+	}
+
+	return costarr[max_index];
+}
+
+/*
+ * cost_append
+ *	  Determines and returns the cost of an Append node.
+ */
+void
+cost_append(AppendPath *apath)
+{
+	ListCell   *l;
+
+	apath->path.startup_cost = 0;
+	apath->path.total_cost = 0;
+	apath->path.rows = 0;
+
+	if (apath->subpaths == NIL)
+		return;
+
+	if (!apath->path.parallel_aware)
+	{
+		List	   *pathkeys = apath->path.pathkeys;
+
+		if (pathkeys == NIL)
+		{
+			Path	   *subpath = (Path *) linitial(apath->subpaths);
+
+			/*
+			 * For an unordered, non-parallel-aware Append we take the startup
+			 * cost as the startup cost of the first subpath.
+			 */
+			apath->path.startup_cost = subpath->startup_cost;
+
+			/* Compute rows and costs as sums of subplan rows and costs. */
+			foreach(l, apath->subpaths)
+			{
+				Path	   *subpath = (Path *) lfirst(l);
+
+				apath->path.rows += subpath->rows;
+				apath->path.total_cost += subpath->total_cost;
+			}
+		}
+		else
+		{
+			/*
+			 * For an ordered, non-parallel-aware Append we take the startup
+			 * cost as the sum of the subpath startup costs.  This ensures
+			 * that we don't underestimate the startup cost when a query's
+			 * LIMIT is such that several of the children have to be run to
+			 * satisfy it.  This might be overkill --- another plausible hack
+			 * would be to take the Append's startup cost as the maximum of
+			 * the child startup costs.  But we don't want to risk believing
+			 * that an ORDER BY LIMIT query can be satisfied at small cost
+			 * when the first child has small startup cost but later ones
+			 * don't.  (If we had the ability to deal with nonlinear cost
+			 * interpolation for partial retrievals, we would not need to be
+			 * so conservative about this.)
+			 *
+			 * This case is also different from the above in that we have to
+			 * account for possibly injecting sorts into subpaths that aren't
+			 * natively ordered.
+			 */
+			foreach(l, apath->subpaths)
+			{
+				Path	   *subpath = (Path *) lfirst(l);
+				Path		sort_path;	/* dummy for result of cost_sort */
+
+				if (!pathkeys_contained_in(pathkeys, subpath->pathkeys))
+				{
+					/*
+					 * We'll need to insert a Sort node, so include costs for
+					 * that.  We can use the parent's LIMIT if any, since we
+					 * certainly won't pull more than that many tuples from
+					 * any child.
+					 */
+					cost_sort(&sort_path,
+							  NULL, /* doesn't currently need root */
+							  pathkeys,
+							  subpath->total_cost,
+							  subpath->rows,
+							  subpath->pathtarget->width,
+							  0.0,
+							  work_mem,
+							  apath->limit_tuples);
+					subpath = &sort_path;
+				}
+
+				apath->path.rows += subpath->rows;
+				apath->path.startup_cost += subpath->startup_cost;
+				apath->path.total_cost += subpath->total_cost;
+			}
+		}
+	}
+	else						/* parallel-aware */
+	{
+		int			i = 0;
+		double		parallel_divisor = get_parallel_divisor(&apath->path);
+
+		/* Parallel-aware Append never produces ordered output. */
+		Assert(apath->path.pathkeys == NIL);
+
+		/* Calculate startup cost. */
+		foreach(l, apath->subpaths)
+		{
+			Path	   *subpath = (Path *) lfirst(l);
+
+			/*
+			 * Append will start returning tuples when the child node having
+			 * lowest startup cost is done setting up. We consider only the
+			 * first few subplans that immediately get a worker assigned.
+			 */
+			if (i == 0)
+				apath->path.startup_cost = subpath->startup_cost;
+			else if (i < apath->path.parallel_workers)
+				apath->path.startup_cost = Min(apath->path.startup_cost,
+											   subpath->startup_cost);
+
+			/*
+			 * Apply parallel divisor to subpaths.  Scale the number of rows
+			 * for each partial subpath based on the ratio of the parallel
+			 * divisor originally used for the subpath to the one we adopted.
+			 * Also add the cost of partial paths to the total cost, but
+			 * ignore non-partial paths for now.
+			 */
+			if (i < apath->first_partial_path)
+				apath->path.rows += subpath->rows / parallel_divisor;
+			else
+			{
+				double		subpath_parallel_divisor;
+
+				subpath_parallel_divisor = get_parallel_divisor(subpath);
+				apath->path.rows += subpath->rows * (subpath_parallel_divisor /
+													 parallel_divisor);
+				apath->path.total_cost += subpath->total_cost;
+			}
+
+			apath->path.rows = clamp_row_est(apath->path.rows);
+
+			i++;
+		}
+
+		/* Add cost for non-partial subpaths. */
+		apath->path.total_cost +=
+			append_nonpartial_cost(apath->subpaths,
+								   apath->first_partial_path,
+								   apath->path.parallel_workers);
+	}
+
+	/*
+	 * Although Append does not do any selection or projection, it's not free;
+	 * add a small per-tuple overhead.
+	 */
+	apath->path.total_cost +=
+		cpu_tuple_cost * APPEND_CPU_COST_MULTIPLIER * apath->path.rows;
+}
+
+/*
+ * cost_merge_append
+ *	  Determines and returns the cost of a MergeAppend node.
+ *
+ * MergeAppend merges several pre-sorted input streams, using a heap that
+ * at any given instant holds the next tuple from each stream.  If there
+ * are N streams, we need about N*log2(N) tuple comparisons to construct
+ * the heap at startup, and then for each output tuple, about log2(N)
+ * comparisons to replace the top entry.
+ *
+ * (The effective value of N will drop once some of the input streams are
+ * exhausted, but it seems unlikely to be worth trying to account for that.)
+ *
+ * The heap is never spilled to disk, since we assume N is not very large.
+ * So this is much simpler than cost_sort.
+ *
+ * As in cost_sort, we charge two operator evals per tuple comparison.
+ *
+ * 'pathkeys' is a list of sort keys
+ * 'n_streams' is the number of input streams
+ * 'input_startup_cost' is the sum of the input streams' startup costs
+ * 'input_total_cost' is the sum of the input streams' total costs
+ * 'tuples' is the number of tuples in all the streams
+ */
+void
+cost_merge_append(Path *path, PlannerInfo *root,
+				  List *pathkeys, int n_streams,
+				  Cost input_startup_cost, Cost input_total_cost,
+				  double tuples)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	Cost		comparison_cost;
+	double		N;
+	double		logN;
+
+	/*
+	 * Avoid log(0)...
+	 */
+	N = (n_streams < 2) ? 2.0 : (double) n_streams;
+	logN = LOG2(N);
+
+	/* Assumed cost per tuple comparison */
+	comparison_cost = 2.0 * cpu_operator_cost;
+
+	/* Heap creation cost */
+	startup_cost += comparison_cost * N * logN;
+
+	/* Per-tuple heap maintenance cost */
+	run_cost += tuples * comparison_cost * logN;
+
+	/*
+	 * Although MergeAppend does not do any selection or projection, it's not
+	 * free; add a small per-tuple overhead.
+	 */
+	run_cost += cpu_tuple_cost * APPEND_CPU_COST_MULTIPLIER * tuples;
+
+	path->startup_cost = startup_cost + input_startup_cost;
+	path->total_cost = startup_cost + run_cost + input_total_cost;
+}
+
+/*
+ * cost_material
+ *	  Determines and returns the cost of materializing a relation, including
+ *	  the cost of reading the input data.
+ *
+ * If the total volume of data to materialize exceeds work_mem, we will need
+ * to write it to disk, so the cost is much higher in that case.
+ *
+ * Note that here we are estimating the costs for the first scan of the
+ * relation, so the materialization is all overhead --- any savings will
+ * occur only on rescan, which is estimated in cost_rescan.
+ */
+void
+cost_material(Path *path,
+			  Cost input_startup_cost, Cost input_total_cost,
+			  double tuples, int width)
+{
+	Cost		startup_cost = input_startup_cost;
+	Cost		run_cost = input_total_cost - input_startup_cost;
+	double		nbytes = relation_byte_size(tuples, width);
+	long		work_mem_bytes = work_mem * 1024L;
+
+	path->rows = tuples;
+
+	/*
+	 * Whether spilling or not, charge 2x cpu_operator_cost per tuple to
+	 * reflect bookkeeping overhead.  (This rate must be more than what
+	 * cost_rescan charges for materialize, ie, cpu_operator_cost per tuple;
+	 * if it is exactly the same then there will be a cost tie between
+	 * nestloop with A outer, materialized B inner and nestloop with B outer,
+	 * materialized A inner.  The extra cost ensures we'll prefer
+	 * materializing the smaller rel.)	Note that this is normally a good deal
+	 * less than cpu_tuple_cost; which is OK because a Material plan node
+	 * doesn't do qual-checking or projection, so it's got less overhead than
+	 * most plan nodes.
+	 */
+	run_cost += 2 * cpu_operator_cost * tuples;
+
+	/*
+	 * If we will spill to disk, charge at the rate of seq_page_cost per page.
+	 * This cost is assumed to be evenly spread through the plan run phase,
+	 * which isn't exactly accurate but our cost model doesn't allow for
+	 * nonuniform costs within the run phase.
+	 */
+	if (nbytes > work_mem_bytes)
+	{
+		double		npages = ceil(nbytes / BLCKSZ);
+
+		run_cost += seq_page_cost * npages;
+	}
+
+	path->startup_cost = startup_cost;
+	path->total_cost = startup_cost + run_cost;
+}
+
+/*
+ * cost_memoize_rescan
+ *	  Determines the estimated cost of rescanning a Memoize node.
+ *
+ * In order to estimate this, we must gain knowledge of how often we expect to
+ * be called and how many distinct sets of parameters we are likely to be
+ * called with. If we expect a good cache hit ratio, then we can set our
+ * costs to account for that hit ratio, plus a little bit of cost for the
+ * caching itself.  Caching will not work out well if we expect to be called
+ * with too many distinct parameter values.  The worst-case here is that we
+ * never see any parameter value twice, in which case we'd never get a cache
+ * hit and caching would be a complete waste of effort.
+ */
+static void
+cost_memoize_rescan(PlannerInfo *root, MemoizePath *mpath,
+					Cost *rescan_startup_cost, Cost *rescan_total_cost)
+{
+	EstimationInfo estinfo;
+	Cost		input_startup_cost = mpath->subpath->startup_cost;
+	Cost		input_total_cost = mpath->subpath->total_cost;
+	double		tuples = mpath->subpath->rows;
+	double		calls = mpath->calls;
+	int			width = mpath->subpath->pathtarget->width;
+
+	double		hash_mem_bytes;
+	double		est_entry_bytes;
+	double		est_cache_entries;
+	double		ndistinct;
+	double		evict_ratio;
+	double		hit_ratio;
+	Cost		startup_cost;
+	Cost		total_cost;
+
+	/* available cache space */
+	hash_mem_bytes = get_hash_memory_limit();
+
+	/*
+	 * Set the number of bytes each cache entry should consume in the cache.
+	 * To provide us with better estimations on how many cache entries we can
+	 * store at once, we make a call to the executor here to ask it what
+	 * memory overheads there are for a single cache entry.
+	 *
+	 * XXX we also store the cache key, but that's not accounted for here.
+	 */
+	est_entry_bytes = relation_byte_size(tuples, width) +
+		ExecEstimateCacheEntryOverheadBytes(tuples);
+
+	/* estimate on the upper limit of cache entries we can hold at once */
+	est_cache_entries = floor(hash_mem_bytes / est_entry_bytes);
+
+	/* estimate on the distinct number of parameter values */
+	ndistinct = estimate_num_groups(root, mpath->param_exprs, calls, NULL,
+									&estinfo);
+
+	/*
+	 * When the estimation fell back on using a default value, it's a bit too
+	 * risky to assume that it's ok to use a Memoize node.  The use of a
+	 * default could cause us to use a Memoize node when it's really
+	 * inappropriate to do so.  If we see that this has been done, then we'll
+	 * assume that every call will have unique parameters, which will almost
+	 * certainly mean a MemoizePath will never survive add_path().
+	 */
+	if ((estinfo.flags & SELFLAG_USED_DEFAULT) != 0)
+		ndistinct = calls;
+
+	/*
+	 * Since we've already estimated the maximum number of entries we can
+	 * store at once and know the estimated number of distinct values we'll be
+	 * called with, we'll take this opportunity to set the path's est_entries.
+	 * This will ultimately determine the hash table size that the executor
+	 * will use.  If we leave this at zero, the executor will just choose the
+	 * size itself.  Really this is not the right place to do this, but it's
+	 * convenient since everything is already calculated.
+	 */
+	mpath->est_entries = Min(Min(ndistinct, est_cache_entries),
+							 PG_UINT32_MAX);
+
+	/*
+	 * When the number of distinct parameter values is above the amount we can
+	 * store in the cache, then we'll have to evict some entries from the
+	 * cache.  This is not free. Here we estimate how often we'll incur the
+	 * cost of that eviction.
+	 */
+	evict_ratio = 1.0 - Min(est_cache_entries, ndistinct) / ndistinct;
+
+	/*
+	 * In order to estimate how costly a single scan will be, we need to
+	 * attempt to estimate what the cache hit ratio will be.  To do that we
+	 * must look at how many scans are estimated in total for this node and
+	 * how many of those scans we expect to get a cache hit.
+	 */
+	hit_ratio = 1.0 / ndistinct * Min(est_cache_entries, ndistinct) -
+		(ndistinct / calls);
+
+	/* Ensure we don't go negative */
+	hit_ratio = Max(hit_ratio, 0.0);
+
+	/*
+	 * Set the total_cost accounting for the expected cache hit ratio.  We
+	 * also add on a cpu_operator_cost to account for a cache lookup. This
+	 * will happen regardless of whether it's a cache hit or not.
+	 */
+	total_cost = input_total_cost * (1.0 - hit_ratio) + cpu_operator_cost;
+
+	/* Now adjust the total cost to account for cache evictions */
+
+	/* Charge a cpu_tuple_cost for evicting the actual cache entry */
+	total_cost += cpu_tuple_cost * evict_ratio;
+
+	/*
+	 * Charge a 10th of cpu_operator_cost to evict every tuple in that entry.
+	 * The per-tuple eviction is really just a pfree, so charging a whole
+	 * cpu_operator_cost seems a little excessive.
+	 */
+	total_cost += cpu_operator_cost / 10.0 * evict_ratio * tuples;
+
+	/*
+	 * Now adjust for storing things in the cache, since that's not free
+	 * either.  Everything must go in the cache.  We don't proportion this
+	 * over any ratio, just apply it once for the scan.  We charge a
+	 * cpu_tuple_cost for the creation of the cache entry and also a
+	 * cpu_operator_cost for each tuple we expect to cache.
+	 */
+	total_cost += cpu_tuple_cost + cpu_operator_cost * tuples;
+
+	/*
+	 * Getting the first row must be also be proportioned according to the
+	 * expected cache hit ratio.
+	 */
+	startup_cost = input_startup_cost * (1.0 - hit_ratio);
+
+	/*
+	 * Additionally we charge a cpu_tuple_cost to account for cache lookups,
+	 * which we'll do regardless of whether it was a cache hit or not.
+	 */
+	startup_cost += cpu_tuple_cost;
+
+	*rescan_startup_cost = startup_cost;
+	*rescan_total_cost = total_cost;
+}
+
+/*
+ * cost_agg
+ *		Determines and returns the cost of performing an Agg plan node,
+ *		including the cost of its input.
+ *
+ * aggcosts can be NULL when there are no actual aggregate functions (i.e.,
+ * we are using a hashed Agg node just to do grouping).
+ *
+ * Note: when aggstrategy == AGG_SORTED, caller must ensure that input costs
+ * are for appropriately-sorted input.
+ */
+void
+cost_agg(Path *path, PlannerInfo *root,
+		 AggStrategy aggstrategy, const AggClauseCosts *aggcosts,
+		 int numGroupCols, double numGroups,
+		 List *quals,
+		 Cost input_startup_cost, Cost input_total_cost,
+		 double input_tuples, double input_width)
+{
+	double		output_tuples;
+	Cost		startup_cost;
+	Cost		total_cost;
+	AggClauseCosts dummy_aggcosts;
+
+	/* Use all-zero per-aggregate costs if NULL is passed */
+	if (aggcosts == NULL)
+	{
+		Assert(aggstrategy == AGG_HASHED);
+		MemSet(&dummy_aggcosts, 0, sizeof(AggClauseCosts));
+		aggcosts = &dummy_aggcosts;
+	}
+
+	/*
+	 * The transCost.per_tuple component of aggcosts should be charged once
+	 * per input tuple, corresponding to the costs of evaluating the aggregate
+	 * transfns and their input expressions. The finalCost.per_tuple component
+	 * is charged once per output tuple, corresponding to the costs of
+	 * evaluating the finalfns.  Startup costs are of course charged but once.
+	 *
+	 * If we are grouping, we charge an additional cpu_operator_cost per
+	 * grouping column per input tuple for grouping comparisons.
+	 *
+	 * We will produce a single output tuple if not grouping, and a tuple per
+	 * group otherwise.  We charge cpu_tuple_cost for each output tuple.
+	 *
+	 * Note: in this cost model, AGG_SORTED and AGG_HASHED have exactly the
+	 * same total CPU cost, but AGG_SORTED has lower startup cost.  If the
+	 * input path is already sorted appropriately, AGG_SORTED should be
+	 * preferred (since it has no risk of memory overflow).  This will happen
+	 * as long as the computed total costs are indeed exactly equal --- but if
+	 * there's roundoff error we might do the wrong thing.  So be sure that
+	 * the computations below form the same intermediate values in the same
+	 * order.
+	 */
+	if (aggstrategy == AGG_PLAIN)
+	{
+		startup_cost = input_total_cost;
+		startup_cost += aggcosts->transCost.startup;
+		startup_cost += aggcosts->transCost.per_tuple * input_tuples;
+		startup_cost += aggcosts->finalCost.startup;
+		startup_cost += aggcosts->finalCost.per_tuple;
+		/* we aren't grouping */
+		total_cost = startup_cost + cpu_tuple_cost;
+		output_tuples = 1;
+	}
+	else if (aggstrategy == AGG_SORTED || aggstrategy == AGG_MIXED)
+	{
+		/* Here we are able to deliver output on-the-fly */
+		startup_cost = input_startup_cost;
+		total_cost = input_total_cost;
+		if (aggstrategy == AGG_MIXED && !enable_hashagg)
+		{
+			startup_cost += disable_cost;
+			total_cost += disable_cost;
+		}
+		/* calcs phrased this way to match HASHED case, see note above */
+		total_cost += aggcosts->transCost.startup;
+		total_cost += aggcosts->transCost.per_tuple * input_tuples;
+		total_cost += (cpu_operator_cost * numGroupCols) * input_tuples;
+		total_cost += aggcosts->finalCost.startup;
+		total_cost += aggcosts->finalCost.per_tuple * numGroups;
+		total_cost += cpu_tuple_cost * numGroups;
+		output_tuples = numGroups;
+	}
+	else
+	{
+		/* must be AGG_HASHED */
+		startup_cost = input_total_cost;
+		if (!enable_hashagg)
+			startup_cost += disable_cost;
+		startup_cost += aggcosts->transCost.startup;
+		startup_cost += aggcosts->transCost.per_tuple * input_tuples;
+		/* cost of computing hash value */
+		startup_cost += (cpu_operator_cost * numGroupCols) * input_tuples;
+		startup_cost += aggcosts->finalCost.startup;
+
+		total_cost = startup_cost;
+		total_cost += aggcosts->finalCost.per_tuple * numGroups;
+		/* cost of retrieving from hash table */
+		total_cost += cpu_tuple_cost * numGroups;
+		output_tuples = numGroups;
+	}
+
+	/*
+	 * Add the disk costs of hash aggregation that spills to disk.
+	 *
+	 * Groups that go into the hash table stay in memory until finalized, so
+	 * spilling and reprocessing tuples doesn't incur additional invocations
+	 * of transCost or finalCost. Furthermore, the computed hash value is
+	 * stored with the spilled tuples, so we don't incur extra invocations of
+	 * the hash function.
+	 *
+	 * Hash Agg begins returning tuples after the first batch is complete.
+	 * Accrue writes (spilled tuples) to startup_cost and to total_cost;
+	 * accrue reads only to total_cost.
+	 */
+	if (aggstrategy == AGG_HASHED || aggstrategy == AGG_MIXED)
+	{
+		double		pages;
+		double		pages_written = 0.0;
+		double		pages_read = 0.0;
+		double		spill_cost;
+		double		hashentrysize;
+		double		nbatches;
+		Size		mem_limit;
+		uint64		ngroups_limit;
+		int			num_partitions;
+		int			depth;
+
+		/*
+		 * Estimate number of batches based on the computed limits. If less
+		 * than or equal to one, all groups are expected to fit in memory;
+		 * otherwise we expect to spill.
+		 */
+		hashentrysize = hash_agg_entry_size(list_length(root->aggtransinfos),
+											input_width,
+											aggcosts->transitionSpace);
+		hash_agg_set_limits(hashentrysize, numGroups, 0, &mem_limit,
+							&ngroups_limit, &num_partitions);
+
+		nbatches = Max((numGroups * hashentrysize) / mem_limit,
+					   numGroups / ngroups_limit);
+
+		nbatches = Max(ceil(nbatches), 1.0);
+		num_partitions = Max(num_partitions, 2);
+
+		/*
+		 * The number of partitions can change at different levels of
+		 * recursion; but for the purposes of this calculation assume it stays
+		 * constant.
+		 */
+		depth = ceil(log(nbatches) / log(num_partitions));
+
+		/*
+		 * Estimate number of pages read and written. For each level of
+		 * recursion, a tuple must be written and then later read.
+		 */
+		pages = relation_byte_size(input_tuples, input_width) / BLCKSZ;
+		pages_written = pages_read = pages * depth;
+
+		/*
+		 * HashAgg has somewhat worse IO behavior than Sort on typical
+		 * hardware/OS combinations. Account for this with a generic penalty.
+		 */
+		pages_read *= 2.0;
+		pages_written *= 2.0;
+
+		startup_cost += pages_written * random_page_cost;
+		total_cost += pages_written * random_page_cost;
+		total_cost += pages_read * seq_page_cost;
+
+		/* account for CPU cost of spilling a tuple and reading it back */
+		spill_cost = depth * input_tuples * 2.0 * cpu_tuple_cost;
+		startup_cost += spill_cost;
+		total_cost += spill_cost;
+	}
+
+	/*
+	 * If there are quals (HAVING quals), account for their cost and
+	 * selectivity.
+	 */
+	if (quals)
+	{
+		QualCost	qual_cost;
+
+		cost_qual_eval(&qual_cost, quals, root);
+		startup_cost += qual_cost.startup;
+		total_cost += qual_cost.startup + output_tuples * qual_cost.per_tuple;
+
+		output_tuples = clamp_row_est(output_tuples *
+									  clauselist_selectivity(root,
+															 quals,
+															 0,
+															 JOIN_INNER,
+															 NULL));
+	}
+
+	path->rows = output_tuples;
+	path->startup_cost = startup_cost;
+	path->total_cost = total_cost;
+}
+
+/*
+ * cost_windowagg
+ *		Determines and returns the cost of performing a WindowAgg plan node,
+ *		including the cost of its input.
+ *
+ * Input is assumed already properly sorted.
+ */
+void
+cost_windowagg(Path *path, PlannerInfo *root,
+			   List *windowFuncs, int numPartCols, int numOrderCols,
+			   Cost input_startup_cost, Cost input_total_cost,
+			   double input_tuples)
+{
+	Cost		startup_cost;
+	Cost		total_cost;
+	ListCell   *lc;
+
+	startup_cost = input_startup_cost;
+	total_cost = input_total_cost;
+
+	/*
+	 * Window functions are assumed to cost their stated execution cost, plus
+	 * the cost of evaluating their input expressions, per tuple.  Since they
+	 * may in fact evaluate their inputs at multiple rows during each cycle,
+	 * this could be a drastic underestimate; but without a way to know how
+	 * many rows the window function will fetch, it's hard to do better.  In
+	 * any case, it's a good estimate for all the built-in window functions,
+	 * so we'll just do this for now.
+	 */
+	foreach(lc, windowFuncs)
+	{
+		WindowFunc *wfunc = lfirst_node(WindowFunc, lc);
+		Cost		wfunccost;
+		QualCost	argcosts;
+
+		argcosts.startup = argcosts.per_tuple = 0;
+		add_function_cost(root, wfunc->winfnoid, (Node *) wfunc,
+						  &argcosts);
+		startup_cost += argcosts.startup;
+		wfunccost = argcosts.per_tuple;
+
+		/* also add the input expressions' cost to per-input-row costs */
+		cost_qual_eval_node(&argcosts, (Node *) wfunc->args, root);
+		startup_cost += argcosts.startup;
+		wfunccost += argcosts.per_tuple;
+
+		/*
+		 * Add the filter's cost to per-input-row costs.  XXX We should reduce
+		 * input expression costs according to filter selectivity.
+		 */
+		cost_qual_eval_node(&argcosts, (Node *) wfunc->aggfilter, root);
+		startup_cost += argcosts.startup;
+		wfunccost += argcosts.per_tuple;
+
+		total_cost += wfunccost * input_tuples;
+	}
+
+	/*
+	 * We also charge cpu_operator_cost per grouping column per tuple for
+	 * grouping comparisons, plus cpu_tuple_cost per tuple for general
+	 * overhead.
+	 *
+	 * XXX this neglects costs of spooling the data to disk when it overflows
+	 * work_mem.  Sooner or later that should get accounted for.
+	 */
+	total_cost += cpu_operator_cost * (numPartCols + numOrderCols) * input_tuples;
+	total_cost += cpu_tuple_cost * input_tuples;
+
+	path->rows = input_tuples;
+	path->startup_cost = startup_cost;
+	path->total_cost = total_cost;
+}
+
+/*
+ * cost_group
+ *		Determines and returns the cost of performing a Group plan node,
+ *		including the cost of its input.
+ *
+ * Note: caller must ensure that input costs are for appropriately-sorted
+ * input.
+ */
+void
+cost_group(Path *path, PlannerInfo *root,
+		   int numGroupCols, double numGroups,
+		   List *quals,
+		   Cost input_startup_cost, Cost input_total_cost,
+		   double input_tuples)
+{
+	double		output_tuples;
+	Cost		startup_cost;
+	Cost		total_cost;
+
+	output_tuples = numGroups;
+	startup_cost = input_startup_cost;
+	total_cost = input_total_cost;
+
+	/*
+	 * Charge one cpu_operator_cost per comparison per input tuple. We assume
+	 * all columns get compared at most of the tuples.
+	 */
+	total_cost += cpu_operator_cost * input_tuples * numGroupCols;
+
+	/*
+	 * If there are quals (HAVING quals), account for their cost and
+	 * selectivity.
+	 */
+	if (quals)
+	{
+		QualCost	qual_cost;
+
+		cost_qual_eval(&qual_cost, quals, root);
+		startup_cost += qual_cost.startup;
+		total_cost += qual_cost.startup + output_tuples * qual_cost.per_tuple;
+
+		output_tuples = clamp_row_est(output_tuples *
+									  clauselist_selectivity(root,
+															 quals,
+															 0,
+															 JOIN_INNER,
+															 NULL));
+	}
+
+	path->rows = output_tuples;
+	path->startup_cost = startup_cost;
+	path->total_cost = total_cost;
+}
+
+/*
+ * initial_cost_nestloop
+ *	  Preliminary estimate of the cost of a nestloop join path.
+ *
+ * This must quickly produce lower-bound estimates of the path's startup and
+ * total costs.  If we are unable to eliminate the proposed path from
+ * consideration using the lower bounds, final_cost_nestloop will be called
+ * to obtain the final estimates.
+ *
+ * The exact division of labor between this function and final_cost_nestloop
+ * is private to them, and represents a tradeoff between speed of the initial
+ * estimate and getting a tight lower bound.  We choose to not examine the
+ * join quals here, since that's by far the most expensive part of the
+ * calculations.  The end result is that CPU-cost considerations must be
+ * left for the second phase; and for SEMI/ANTI joins, we must also postpone
+ * incorporation of the inner path's run cost.
+ *
+ * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
+ *		other data to be used by final_cost_nestloop
+ * 'jointype' is the type of join to be performed
+ * 'outer_path' is the outer input to the join
+ * 'inner_path' is the inner input to the join
+ * 'extra' contains miscellaneous information about the join
+ */
+void
+initial_cost_nestloop(PlannerInfo *root, JoinCostWorkspace *workspace,
+					  JoinType jointype,
+					  Path *outer_path, Path *inner_path,
+					  JoinPathExtraData *extra)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	double		outer_path_rows = outer_path->rows;
+	Cost		inner_rescan_start_cost;
+	Cost		inner_rescan_total_cost;
+	Cost		inner_run_cost;
+	Cost		inner_rescan_run_cost;
+
+	/* estimate costs to rescan the inner relation */
+	cost_rescan(root, inner_path,
+				&inner_rescan_start_cost,
+				&inner_rescan_total_cost);
+
+	/* cost of source data */
+
+	/*
+	 * NOTE: clearly, we must pay both outer and inner paths' startup_cost
+	 * before we can start returning tuples, so the join's startup cost is
+	 * their sum.  We'll also pay the inner path's rescan startup cost
+	 * multiple times.
+	 */
+	startup_cost += outer_path->startup_cost + inner_path->startup_cost;
+	run_cost += outer_path->total_cost - outer_path->startup_cost;
+	if (outer_path_rows > 1)
+		run_cost += (outer_path_rows - 1) * inner_rescan_start_cost;
+
+	inner_run_cost = inner_path->total_cost - inner_path->startup_cost;
+	inner_rescan_run_cost = inner_rescan_total_cost - inner_rescan_start_cost;
+
+	if (jointype == JOIN_SEMI || jointype == JOIN_ANTI ||
+		extra->inner_unique)
+	{
+		/*
+		 * With a SEMI or ANTI join, or if the innerrel is known unique, the
+		 * executor will stop after the first match.
+		 *
+		 * Getting decent estimates requires inspection of the join quals,
+		 * which we choose to postpone to final_cost_nestloop.
+		 */
+
+		/* Save private data for final_cost_nestloop */
+		workspace->inner_run_cost = inner_run_cost;
+		workspace->inner_rescan_run_cost = inner_rescan_run_cost;
+	}
+	else
+	{
+		/* Normal case; we'll scan whole input rel for each outer row */
+		run_cost += inner_run_cost;
+		if (outer_path_rows > 1)
+			run_cost += (outer_path_rows - 1) * inner_rescan_run_cost;
+	}
+
+	/* CPU costs left for later */
+
+	/* Public result fields */
+	workspace->startup_cost = startup_cost;
+	workspace->total_cost = startup_cost + run_cost;
+	/* Save private data for final_cost_nestloop */
+	workspace->run_cost = run_cost;
+}
+
+/*
+ * final_cost_nestloop
+ *	  Final estimate of the cost and result size of a nestloop join path.
+ *
+ * 'path' is already filled in except for the rows and cost fields
+ * 'workspace' is the result from initial_cost_nestloop
+ * 'extra' contains miscellaneous information about the join
+ */
+void
+final_cost_nestloop(PlannerInfo *root, NestPath *path,
+					JoinCostWorkspace *workspace,
+					JoinPathExtraData *extra)
+{
+	Path	   *outer_path = path->jpath.outerjoinpath;
+	Path	   *inner_path = path->jpath.innerjoinpath;
+	double		outer_path_rows = outer_path->rows;
+	double		inner_path_rows = inner_path->rows;
+	Cost		startup_cost = workspace->startup_cost;
+	Cost		run_cost = workspace->run_cost;
+	Cost		cpu_per_tuple;
+	QualCost	restrict_qual_cost;
+	double		ntuples;
+
+	/* Protect some assumptions below that rowcounts aren't zero */
+	if (outer_path_rows <= 0)
+		outer_path_rows = 1;
+	if (inner_path_rows <= 0)
+		inner_path_rows = 1;
+	/* Mark the path with the correct row estimate */
+	if (path->jpath.path.param_info)
+		path->jpath.path.rows = path->jpath.path.param_info->ppi_rows;
+	else
+		path->jpath.path.rows = path->jpath.path.parent->rows;
+
+	/* For partial paths, scale row estimate. */
+	if (path->jpath.path.parallel_workers > 0)
+	{
+		double		parallel_divisor = get_parallel_divisor(&path->jpath.path);
+
+		path->jpath.path.rows =
+			clamp_row_est(path->jpath.path.rows / parallel_divisor);
+	}
+
+	/*
+	 * We could include disable_cost in the preliminary estimate, but that
+	 * would amount to optimizing for the case where the join method is
+	 * disabled, which doesn't seem like the way to bet.
+	 */
+	if (!enable_nestloop)
+		startup_cost += disable_cost;
+
+	/* cost of inner-relation source data (we already dealt with outer rel) */
+
+	if (path->jpath.jointype == JOIN_SEMI || path->jpath.jointype == JOIN_ANTI ||
+		extra->inner_unique)
+	{
+		/*
+		 * With a SEMI or ANTI join, or if the innerrel is known unique, the
+		 * executor will stop after the first match.
+		 */
+		Cost		inner_run_cost = workspace->inner_run_cost;
+		Cost		inner_rescan_run_cost = workspace->inner_rescan_run_cost;
+		double		outer_matched_rows;
+		double		outer_unmatched_rows;
+		Selectivity inner_scan_frac;
+
+		/*
+		 * For an outer-rel row that has at least one match, we can expect the
+		 * inner scan to stop after a fraction 1/(match_count+1) of the inner
+		 * rows, if the matches are evenly distributed.  Since they probably
+		 * aren't quite evenly distributed, we apply a fuzz factor of 2.0 to
+		 * that fraction.  (If we used a larger fuzz factor, we'd have to
+		 * clamp inner_scan_frac to at most 1.0; but since match_count is at
+		 * least 1, no such clamp is needed now.)
+		 */
+		outer_matched_rows = rint(outer_path_rows * extra->semifactors.outer_match_frac);
+		outer_unmatched_rows = outer_path_rows - outer_matched_rows;
+		inner_scan_frac = 2.0 / (extra->semifactors.match_count + 1.0);
+
+		/*
+		 * Compute number of tuples processed (not number emitted!).  First,
+		 * account for successfully-matched outer rows.
+		 */
+		ntuples = outer_matched_rows * inner_path_rows * inner_scan_frac;
+
+		/*
+		 * Now we need to estimate the actual costs of scanning the inner
+		 * relation, which may be quite a bit less than N times inner_run_cost
+		 * due to early scan stops.  We consider two cases.  If the inner path
+		 * is an indexscan using all the joinquals as indexquals, then an
+		 * unmatched outer row results in an indexscan returning no rows,
+		 * which is probably quite cheap.  Otherwise, the executor will have
+		 * to scan the whole inner rel for an unmatched row; not so cheap.
+		 */
+		if (has_indexed_join_quals(path))
+		{
+			/*
+			 * Successfully-matched outer rows will only require scanning
+			 * inner_scan_frac of the inner relation.  In this case, we don't
+			 * need to charge the full inner_run_cost even when that's more
+			 * than inner_rescan_run_cost, because we can assume that none of
+			 * the inner scans ever scan the whole inner relation.  So it's
+			 * okay to assume that all the inner scan executions can be
+			 * fractions of the full cost, even if materialization is reducing
+			 * the rescan cost.  At this writing, it's impossible to get here
+			 * for a materialized inner scan, so inner_run_cost and
+			 * inner_rescan_run_cost will be the same anyway; but just in
+			 * case, use inner_run_cost for the first matched tuple and
+			 * inner_rescan_run_cost for additional ones.
+			 */
+			run_cost += inner_run_cost * inner_scan_frac;
+			if (outer_matched_rows > 1)
+				run_cost += (outer_matched_rows - 1) * inner_rescan_run_cost * inner_scan_frac;
+
+			/*
+			 * Add the cost of inner-scan executions for unmatched outer rows.
+			 * We estimate this as the same cost as returning the first tuple
+			 * of a nonempty scan.  We consider that these are all rescans,
+			 * since we used inner_run_cost once already.
+			 */
+			run_cost += outer_unmatched_rows *
+				inner_rescan_run_cost / inner_path_rows;
+
+			/*
+			 * We won't be evaluating any quals at all for unmatched rows, so
+			 * don't add them to ntuples.
+			 */
+		}
+		else
+		{
+			/*
+			 * Here, a complicating factor is that rescans may be cheaper than
+			 * first scans.  If we never scan all the way to the end of the
+			 * inner rel, it might be (depending on the plan type) that we'd
+			 * never pay the whole inner first-scan run cost.  However it is
+			 * difficult to estimate whether that will happen (and it could
+			 * not happen if there are any unmatched outer rows!), so be
+			 * conservative and always charge the whole first-scan cost once.
+			 * We consider this charge to correspond to the first unmatched
+			 * outer row, unless there isn't one in our estimate, in which
+			 * case blame it on the first matched row.
+			 */
+
+			/* First, count all unmatched join tuples as being processed */
+			ntuples += outer_unmatched_rows * inner_path_rows;
+
+			/* Now add the forced full scan, and decrement appropriate count */
+			run_cost += inner_run_cost;
+			if (outer_unmatched_rows >= 1)
+				outer_unmatched_rows -= 1;
+			else
+				outer_matched_rows -= 1;
+
+			/* Add inner run cost for additional outer tuples having matches */
+			if (outer_matched_rows > 0)
+				run_cost += outer_matched_rows * inner_rescan_run_cost * inner_scan_frac;
+
+			/* Add inner run cost for additional unmatched outer tuples */
+			if (outer_unmatched_rows > 0)
+				run_cost += outer_unmatched_rows * inner_rescan_run_cost;
+		}
+	}
+	else
+	{
+		/* Normal-case source costs were included in preliminary estimate */
+
+		/* Compute number of tuples processed (not number emitted!) */
+		ntuples = outer_path_rows * inner_path_rows;
+	}
+
+	/* CPU costs */
+	cost_qual_eval(&restrict_qual_cost, path->jpath.joinrestrictinfo, root);
+	startup_cost += restrict_qual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + restrict_qual_cost.per_tuple;
+	run_cost += cpu_per_tuple * ntuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->jpath.path.pathtarget->cost.startup;
+	run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;
+
+	path->jpath.path.startup_cost = startup_cost;
+	path->jpath.path.total_cost = startup_cost + run_cost;
+}
+
+/*
+ * initial_cost_mergejoin
+ *	  Preliminary estimate of the cost of a mergejoin path.
+ *
+ * This must quickly produce lower-bound estimates of the path's startup and
+ * total costs.  If we are unable to eliminate the proposed path from
+ * consideration using the lower bounds, final_cost_mergejoin will be called
+ * to obtain the final estimates.
+ *
+ * The exact division of labor between this function and final_cost_mergejoin
+ * is private to them, and represents a tradeoff between speed of the initial
+ * estimate and getting a tight lower bound.  We choose to not examine the
+ * join quals here, except for obtaining the scan selectivity estimate which
+ * is really essential (but fortunately, use of caching keeps the cost of
+ * getting that down to something reasonable).
+ * We also assume that cost_sort is cheap enough to use here.
+ *
+ * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
+ *		other data to be used by final_cost_mergejoin
+ * 'jointype' is the type of join to be performed
+ * 'mergeclauses' is the list of joinclauses to be used as merge clauses
+ * 'outer_path' is the outer input to the join
+ * 'inner_path' is the inner input to the join
+ * 'outersortkeys' is the list of sort keys for the outer path
+ * 'innersortkeys' is the list of sort keys for the inner path
+ * 'extra' contains miscellaneous information about the join
+ *
+ * Note: outersortkeys and innersortkeys should be NIL if no explicit
+ * sort is needed because the respective source path is already ordered.
+ */
+void
+initial_cost_mergejoin(PlannerInfo *root, JoinCostWorkspace *workspace,
+					   JoinType jointype,
+					   List *mergeclauses,
+					   Path *outer_path, Path *inner_path,
+					   List *outersortkeys, List *innersortkeys,
+					   JoinPathExtraData *extra)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	double		outer_path_rows = outer_path->rows;
+	double		inner_path_rows = inner_path->rows;
+	Cost		inner_run_cost;
+	double		outer_rows,
+				inner_rows,
+				outer_skip_rows,
+				inner_skip_rows;
+	Selectivity outerstartsel,
+				outerendsel,
+				innerstartsel,
+				innerendsel;
+	Path		sort_path;		/* dummy for result of cost_sort */
+
+	/* Protect some assumptions below that rowcounts aren't zero */
+	if (outer_path_rows <= 0)
+		outer_path_rows = 1;
+	if (inner_path_rows <= 0)
+		inner_path_rows = 1;
+
+	/*
+	 * A merge join will stop as soon as it exhausts either input stream
+	 * (unless it's an outer join, in which case the outer side has to be
+	 * scanned all the way anyway).  Estimate fraction of the left and right
+	 * inputs that will actually need to be scanned.  Likewise, we can
+	 * estimate the number of rows that will be skipped before the first join
+	 * pair is found, which should be factored into startup cost. We use only
+	 * the first (most significant) merge clause for this purpose. Since
+	 * mergejoinscansel() is a fairly expensive computation, we cache the
+	 * results in the merge clause RestrictInfo.
+	 */
+	if (mergeclauses && jointype != JOIN_FULL)
+	{
+		RestrictInfo *firstclause = (RestrictInfo *) linitial(mergeclauses);
+		List	   *opathkeys;
+		List	   *ipathkeys;
+		PathKey    *opathkey;
+		PathKey    *ipathkey;
+		MergeScanSelCache *cache;
+
+		/* Get the input pathkeys to determine the sort-order details */
+		opathkeys = outersortkeys ? outersortkeys : outer_path->pathkeys;
+		ipathkeys = innersortkeys ? innersortkeys : inner_path->pathkeys;
+		Assert(opathkeys);
+		Assert(ipathkeys);
+		opathkey = (PathKey *) linitial(opathkeys);
+		ipathkey = (PathKey *) linitial(ipathkeys);
+		/* debugging check */
+		if (opathkey->pk_opfamily != ipathkey->pk_opfamily ||
+			opathkey->pk_eclass->ec_collation != ipathkey->pk_eclass->ec_collation ||
+			opathkey->pk_strategy != ipathkey->pk_strategy ||
+			opathkey->pk_nulls_first != ipathkey->pk_nulls_first)
+			elog(ERROR, "left and right pathkeys do not match in mergejoin");
+
+		/* Get the selectivity with caching */
+		cache = cached_scansel(root, firstclause, opathkey);
+
+		if (bms_is_subset(firstclause->left_relids,
+						  outer_path->parent->relids))
+		{
+			/* left side of clause is outer */
+			outerstartsel = cache->leftstartsel;
+			outerendsel = cache->leftendsel;
+			innerstartsel = cache->rightstartsel;
+			innerendsel = cache->rightendsel;
+		}
+		else
+		{
+			/* left side of clause is inner */
+			outerstartsel = cache->rightstartsel;
+			outerendsel = cache->rightendsel;
+			innerstartsel = cache->leftstartsel;
+			innerendsel = cache->leftendsel;
+		}
+		if (jointype == JOIN_LEFT ||
+			jointype == JOIN_ANTI)
+		{
+			outerstartsel = 0.0;
+			outerendsel = 1.0;
+		}
+		else if (jointype == JOIN_RIGHT)
+		{
+			innerstartsel = 0.0;
+			innerendsel = 1.0;
+		}
+	}
+	else
+	{
+		/* cope with clauseless or full mergejoin */
+		outerstartsel = innerstartsel = 0.0;
+		outerendsel = innerendsel = 1.0;
+	}
+
+	/*
+	 * Convert selectivities to row counts.  We force outer_rows and
+	 * inner_rows to be at least 1, but the skip_rows estimates can be zero.
+	 */
+	outer_skip_rows = rint(outer_path_rows * outerstartsel);
+	inner_skip_rows = rint(inner_path_rows * innerstartsel);
+	outer_rows = clamp_row_est(outer_path_rows * outerendsel);
+	inner_rows = clamp_row_est(inner_path_rows * innerendsel);
+
+	Assert(outer_skip_rows <= outer_rows);
+	Assert(inner_skip_rows <= inner_rows);
+
+	/*
+	 * Readjust scan selectivities to account for above rounding.  This is
+	 * normally an insignificant effect, but when there are only a few rows in
+	 * the inputs, failing to do this makes for a large percentage error.
+	 */
+	outerstartsel = outer_skip_rows / outer_path_rows;
+	innerstartsel = inner_skip_rows / inner_path_rows;
+	outerendsel = outer_rows / outer_path_rows;
+	innerendsel = inner_rows / inner_path_rows;
+
+	Assert(outerstartsel <= outerendsel);
+	Assert(innerstartsel <= innerendsel);
+
+	/* cost of source data */
+
+	if (outersortkeys)			/* do we need to sort outer? */
+	{
+		cost_sort(&sort_path,
+				  root,
+				  outersortkeys,
+				  outer_path->total_cost,
+				  outer_path_rows,
+				  outer_path->pathtarget->width,
+				  0.0,
+				  work_mem,
+				  -1.0);
+		startup_cost += sort_path.startup_cost;
+		startup_cost += (sort_path.total_cost - sort_path.startup_cost)
+			* outerstartsel;
+		run_cost += (sort_path.total_cost - sort_path.startup_cost)
+			* (outerendsel - outerstartsel);
+	}
+	else
+	{
+		startup_cost += outer_path->startup_cost;
+		startup_cost += (outer_path->total_cost - outer_path->startup_cost)
+			* outerstartsel;
+		run_cost += (outer_path->total_cost - outer_path->startup_cost)
+			* (outerendsel - outerstartsel);
+	}
+
+	if (innersortkeys)			/* do we need to sort inner? */
+	{
+		cost_sort(&sort_path,
+				  root,
+				  innersortkeys,
+				  inner_path->total_cost,
+				  inner_path_rows,
+				  inner_path->pathtarget->width,
+				  0.0,
+				  work_mem,
+				  -1.0);
+		startup_cost += sort_path.startup_cost;
+		startup_cost += (sort_path.total_cost - sort_path.startup_cost)
+			* innerstartsel;
+		inner_run_cost = (sort_path.total_cost - sort_path.startup_cost)
+			* (innerendsel - innerstartsel);
+	}
+	else
+	{
+		startup_cost += inner_path->startup_cost;
+		startup_cost += (inner_path->total_cost - inner_path->startup_cost)
+			* innerstartsel;
+		inner_run_cost = (inner_path->total_cost - inner_path->startup_cost)
+			* (innerendsel - innerstartsel);
+	}
+
+	/*
+	 * We can't yet determine whether rescanning occurs, or whether
+	 * materialization of the inner input should be done.  The minimum
+	 * possible inner input cost, regardless of rescan and materialization
+	 * considerations, is inner_run_cost.  We include that in
+	 * workspace->total_cost, but not yet in run_cost.
+	 */
+
+	/* CPU costs left for later */
+
+	/* Public result fields */
+	workspace->startup_cost = startup_cost;
+	workspace->total_cost = startup_cost + run_cost + inner_run_cost;
+	/* Save private data for final_cost_mergejoin */
+	workspace->run_cost = run_cost;
+	workspace->inner_run_cost = inner_run_cost;
+	workspace->outer_rows = outer_rows;
+	workspace->inner_rows = inner_rows;
+	workspace->outer_skip_rows = outer_skip_rows;
+	workspace->inner_skip_rows = inner_skip_rows;
+}
+
+/*
+ * final_cost_mergejoin
+ *	  Final estimate of the cost and result size of a mergejoin path.
+ *
+ * Unlike other costsize functions, this routine makes two actual decisions:
+ * whether the executor will need to do mark/restore, and whether we should
+ * materialize the inner path.  It would be logically cleaner to build
+ * separate paths testing these alternatives, but that would require repeating
+ * most of the cost calculations, which are not all that cheap.  Since the
+ * choice will not affect output pathkeys or startup cost, only total cost,
+ * there is no possibility of wanting to keep more than one path.  So it seems
+ * best to make the decisions here and record them in the path's
+ * skip_mark_restore and materialize_inner fields.
+ *
+ * Mark/restore overhead is usually required, but can be skipped if we know
+ * that the executor need find only one match per outer tuple, and that the
+ * mergeclauses are sufficient to identify a match.
+ *
+ * We materialize the inner path if we need mark/restore and either the inner
+ * path can't support mark/restore, or it's cheaper to use an interposed
+ * Material node to handle mark/restore.
+ *
+ * 'path' is already filled in except for the rows and cost fields and
+ *		skip_mark_restore and materialize_inner
+ * 'workspace' is the result from initial_cost_mergejoin
+ * 'extra' contains miscellaneous information about the join
+ */
+void
+final_cost_mergejoin(PlannerInfo *root, MergePath *path,
+					 JoinCostWorkspace *workspace,
+					 JoinPathExtraData *extra)
+{
+	Path	   *outer_path = path->jpath.outerjoinpath;
+	Path	   *inner_path = path->jpath.innerjoinpath;
+	double		inner_path_rows = inner_path->rows;
+	List	   *mergeclauses = path->path_mergeclauses;
+	List	   *innersortkeys = path->innersortkeys;
+	Cost		startup_cost = workspace->startup_cost;
+	Cost		run_cost = workspace->run_cost;
+	Cost		inner_run_cost = workspace->inner_run_cost;
+	double		outer_rows = workspace->outer_rows;
+	double		inner_rows = workspace->inner_rows;
+	double		outer_skip_rows = workspace->outer_skip_rows;
+	double		inner_skip_rows = workspace->inner_skip_rows;
+	Cost		cpu_per_tuple,
+				bare_inner_cost,
+				mat_inner_cost;
+	QualCost	merge_qual_cost;
+	QualCost	qp_qual_cost;
+	double		mergejointuples,
+				rescannedtuples;
+	double		rescanratio;
+
+	/* Protect some assumptions below that rowcounts aren't zero */
+	if (inner_path_rows <= 0)
+		inner_path_rows = 1;
+
+	/* Mark the path with the correct row estimate */
+	if (path->jpath.path.param_info)
+		path->jpath.path.rows = path->jpath.path.param_info->ppi_rows;
+	else
+		path->jpath.path.rows = path->jpath.path.parent->rows;
+
+	/* For partial paths, scale row estimate. */
+	if (path->jpath.path.parallel_workers > 0)
+	{
+		double		parallel_divisor = get_parallel_divisor(&path->jpath.path);
+
+		path->jpath.path.rows =
+			clamp_row_est(path->jpath.path.rows / parallel_divisor);
+	}
+
+	/*
+	 * We could include disable_cost in the preliminary estimate, but that
+	 * would amount to optimizing for the case where the join method is
+	 * disabled, which doesn't seem like the way to bet.
+	 */
+	if (!enable_mergejoin)
+		startup_cost += disable_cost;
+
+	/*
+	 * Compute cost of the mergequals and qpquals (other restriction clauses)
+	 * separately.
+	 */
+	cost_qual_eval(&merge_qual_cost, mergeclauses, root);
+	cost_qual_eval(&qp_qual_cost, path->jpath.joinrestrictinfo, root);
+	qp_qual_cost.startup -= merge_qual_cost.startup;
+	qp_qual_cost.per_tuple -= merge_qual_cost.per_tuple;
+
+	/*
+	 * With a SEMI or ANTI join, or if the innerrel is known unique, the
+	 * executor will stop scanning for matches after the first match.  When
+	 * all the joinclauses are merge clauses, this means we don't ever need to
+	 * back up the merge, and so we can skip mark/restore overhead.
+	 */
+	if ((path->jpath.jointype == JOIN_SEMI ||
+		 path->jpath.jointype == JOIN_ANTI ||
+		 extra->inner_unique) &&
+		(list_length(path->jpath.joinrestrictinfo) ==
+		 list_length(path->path_mergeclauses)))
+		path->skip_mark_restore = true;
+	else
+		path->skip_mark_restore = false;
+
+	/*
+	 * Get approx # tuples passing the mergequals.  We use approx_tuple_count
+	 * here because we need an estimate done with JOIN_INNER semantics.
+	 */
+	mergejointuples = approx_tuple_count(root, &path->jpath, mergeclauses);
+
+	/*
+	 * When there are equal merge keys in the outer relation, the mergejoin
+	 * must rescan any matching tuples in the inner relation. This means
+	 * re-fetching inner tuples; we have to estimate how often that happens.
+	 *
+	 * For regular inner and outer joins, the number of re-fetches can be
+	 * estimated approximately as size of merge join output minus size of
+	 * inner relation. Assume that the distinct key values are 1, 2, ..., and
+	 * denote the number of values of each key in the outer relation as m1,
+	 * m2, ...; in the inner relation, n1, n2, ...  Then we have
+	 *
+	 * size of join = m1 * n1 + m2 * n2 + ...
+	 *
+	 * number of rescanned tuples = (m1 - 1) * n1 + (m2 - 1) * n2 + ... = m1 *
+	 * n1 + m2 * n2 + ... - (n1 + n2 + ...) = size of join - size of inner
+	 * relation
+	 *
+	 * This equation works correctly for outer tuples having no inner match
+	 * (nk = 0), but not for inner tuples having no outer match (mk = 0); we
+	 * are effectively subtracting those from the number of rescanned tuples,
+	 * when we should not.  Can we do better without expensive selectivity
+	 * computations?
+	 *
+	 * The whole issue is moot if we are working from a unique-ified outer
+	 * input, or if we know we don't need to mark/restore at all.
+	 */
+	if (IsA(outer_path, UniquePath) || path->skip_mark_restore)
+		rescannedtuples = 0;
+	else
+	{
+		rescannedtuples = mergejointuples - inner_path_rows;
+		/* Must clamp because of possible underestimate */
+		if (rescannedtuples < 0)
+			rescannedtuples = 0;
+	}
+
+	/*
+	 * We'll inflate various costs this much to account for rescanning.  Note
+	 * that this is to be multiplied by something involving inner_rows, or
+	 * another number related to the portion of the inner rel we'll scan.
+	 */
+	rescanratio = 1.0 + (rescannedtuples / inner_rows);
+
+	/*
+	 * Decide whether we want to materialize the inner input to shield it from
+	 * mark/restore and performing re-fetches.  Our cost model for regular
+	 * re-fetches is that a re-fetch costs the same as an original fetch,
+	 * which is probably an overestimate; but on the other hand we ignore the
+	 * bookkeeping costs of mark/restore.  Not clear if it's worth developing
+	 * a more refined model.  So we just need to inflate the inner run cost by
+	 * rescanratio.
+	 */
+	bare_inner_cost = inner_run_cost * rescanratio;
+
+	/*
+	 * When we interpose a Material node the re-fetch cost is assumed to be
+	 * just cpu_operator_cost per tuple, independently of the underlying
+	 * plan's cost; and we charge an extra cpu_operator_cost per original
+	 * fetch as well.  Note that we're assuming the materialize node will
+	 * never spill to disk, since it only has to remember tuples back to the
+	 * last mark.  (If there are a huge number of duplicates, our other cost
+	 * factors will make the path so expensive that it probably won't get
+	 * chosen anyway.)	So we don't use cost_rescan here.
+	 *
+	 * Note: keep this estimate in sync with create_mergejoin_plan's labeling
+	 * of the generated Material node.
+	 */
+	mat_inner_cost = inner_run_cost +
+		cpu_operator_cost * inner_rows * rescanratio;
+
+	/*
+	 * If we don't need mark/restore at all, we don't need materialization.
+	 */
+	if (path->skip_mark_restore)
+		path->materialize_inner = false;
+
+	/*
+	 * Prefer materializing if it looks cheaper, unless the user has asked to
+	 * suppress materialization.
+	 */
+	else if (enable_material && mat_inner_cost < bare_inner_cost)
+		path->materialize_inner = true;
+
+	/*
+	 * Even if materializing doesn't look cheaper, we *must* do it if the
+	 * inner path is to be used directly (without sorting) and it doesn't
+	 * support mark/restore.
+	 *
+	 * Since the inner side must be ordered, and only Sorts and IndexScans can
+	 * create order to begin with, and they both support mark/restore, you
+	 * might think there's no problem --- but you'd be wrong.  Nestloop and
+	 * merge joins can *preserve* the order of their inputs, so they can be
+	 * selected as the input of a mergejoin, and they don't support
+	 * mark/restore at present.
+	 *
+	 * We don't test the value of enable_material here, because
+	 * materialization is required for correctness in this case, and turning
+	 * it off does not entitle us to deliver an invalid plan.
+	 */
+	else if (innersortkeys == NIL &&
+			 !ExecSupportsMarkRestore(inner_path))
+		path->materialize_inner = true;
+
+	/*
+	 * Also, force materializing if the inner path is to be sorted and the
+	 * sort is expected to spill to disk.  This is because the final merge
+	 * pass can be done on-the-fly if it doesn't have to support mark/restore.
+	 * We don't try to adjust the cost estimates for this consideration,
+	 * though.
+	 *
+	 * Since materialization is a performance optimization in this case,
+	 * rather than necessary for correctness, we skip it if enable_material is
+	 * off.
+	 */
+	else if (enable_material && innersortkeys != NIL &&
+			 relation_byte_size(inner_path_rows,
+								inner_path->pathtarget->width) >
+			 (work_mem * 1024L))
+		path->materialize_inner = true;
+	else
+		path->materialize_inner = false;
+
+	/* Charge the right incremental cost for the chosen case */
+	if (path->materialize_inner)
+		run_cost += mat_inner_cost;
+	else
+		run_cost += bare_inner_cost;
+
+	/* CPU costs */
+
+	/*
+	 * The number of tuple comparisons needed is approximately number of outer
+	 * rows plus number of inner rows plus number of rescanned tuples (can we
+	 * refine this?).  At each one, we need to evaluate the mergejoin quals.
+	 */
+	startup_cost += merge_qual_cost.startup;
+	startup_cost += merge_qual_cost.per_tuple *
+		(outer_skip_rows + inner_skip_rows * rescanratio);
+	run_cost += merge_qual_cost.per_tuple *
+		((outer_rows - outer_skip_rows) +
+		 (inner_rows - inner_skip_rows) * rescanratio);
+
+	/*
+	 * For each tuple that gets through the mergejoin proper, we charge
+	 * cpu_tuple_cost plus the cost of evaluating additional restriction
+	 * clauses that are to be applied at the join.  (This is pessimistic since
+	 * not all of the quals may get evaluated at each tuple.)
+	 *
+	 * Note: we could adjust for SEMI/ANTI joins skipping some qual
+	 * evaluations here, but it's probably not worth the trouble.
+	 */
+	startup_cost += qp_qual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qp_qual_cost.per_tuple;
+	run_cost += cpu_per_tuple * mergejointuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->jpath.path.pathtarget->cost.startup;
+	run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;
+
+	path->jpath.path.startup_cost = startup_cost;
+	path->jpath.path.total_cost = startup_cost + run_cost;
+}
+
+/*
+ * run mergejoinscansel() with caching
+ */
+static MergeScanSelCache *
+cached_scansel(PlannerInfo *root, RestrictInfo *rinfo, PathKey *pathkey)
+{
+	MergeScanSelCache *cache;
+	ListCell   *lc;
+	Selectivity leftstartsel,
+				leftendsel,
+				rightstartsel,
+				rightendsel;
+	MemoryContext oldcontext;
+
+	/* Do we have this result already? */
+	foreach(lc, rinfo->scansel_cache)
+	{
+		cache = (MergeScanSelCache *) lfirst(lc);
+		if (cache->opfamily == pathkey->pk_opfamily &&
+			cache->collation == pathkey->pk_eclass->ec_collation &&
+			cache->strategy == pathkey->pk_strategy &&
+			cache->nulls_first == pathkey->pk_nulls_first)
+			return cache;
+	}
+
+	/* Nope, do the computation */
+	mergejoinscansel(root,
+					 (Node *) rinfo->clause,
+					 pathkey->pk_opfamily,
+					 pathkey->pk_strategy,
+					 pathkey->pk_nulls_first,
+					 &leftstartsel,
+					 &leftendsel,
+					 &rightstartsel,
+					 &rightendsel);
+
+	/* Cache the result in suitably long-lived workspace */
+	oldcontext = MemoryContextSwitchTo(root->planner_cxt);
+
+	cache = (MergeScanSelCache *) palloc(sizeof(MergeScanSelCache));
+	cache->opfamily = pathkey->pk_opfamily;
+	cache->collation = pathkey->pk_eclass->ec_collation;
+	cache->strategy = pathkey->pk_strategy;
+	cache->nulls_first = pathkey->pk_nulls_first;
+	cache->leftstartsel = leftstartsel;
+	cache->leftendsel = leftendsel;
+	cache->rightstartsel = rightstartsel;
+	cache->rightendsel = rightendsel;
+
+	rinfo->scansel_cache = lappend(rinfo->scansel_cache, cache);
+
+	MemoryContextSwitchTo(oldcontext);
+
+	return cache;
+}
+
+/*
+ * initial_cost_hashjoin
+ *	  Preliminary estimate of the cost of a hashjoin path.
+ *
+ * This must quickly produce lower-bound estimates of the path's startup and
+ * total costs.  If we are unable to eliminate the proposed path from
+ * consideration using the lower bounds, final_cost_hashjoin will be called
+ * to obtain the final estimates.
+ *
+ * The exact division of labor between this function and final_cost_hashjoin
+ * is private to them, and represents a tradeoff between speed of the initial
+ * estimate and getting a tight lower bound.  We choose to not examine the
+ * join quals here (other than by counting the number of hash clauses),
+ * so we can't do much with CPU costs.  We do assume that
+ * ExecChooseHashTableSize is cheap enough to use here.
+ *
+ * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
+ *		other data to be used by final_cost_hashjoin
+ * 'jointype' is the type of join to be performed
+ * 'hashclauses' is the list of joinclauses to be used as hash clauses
+ * 'outer_path' is the outer input to the join
+ * 'inner_path' is the inner input to the join
+ * 'extra' contains miscellaneous information about the join
+ * 'parallel_hash' indicates that inner_path is partial and that a shared
+ *		hash table will be built in parallel
+ */
+void
+initial_cost_hashjoin(PlannerInfo *root, JoinCostWorkspace *workspace,
+					  JoinType jointype,
+					  List *hashclauses,
+					  Path *outer_path, Path *inner_path,
+					  JoinPathExtraData *extra,
+					  bool parallel_hash)
+{
+	Cost		startup_cost = 0;
+	Cost		run_cost = 0;
+	double		outer_path_rows = outer_path->rows;
+	double		inner_path_rows = inner_path->rows;
+	double		inner_path_rows_total = inner_path_rows;
+	int			num_hashclauses = list_length(hashclauses);
+	int			numbuckets;
+	int			numbatches;
+	int			num_skew_mcvs;
+	size_t		space_allowed;	/* unused */
+
+	/* cost of source data */
+	startup_cost += outer_path->startup_cost;
+	run_cost += outer_path->total_cost - outer_path->startup_cost;
+	startup_cost += inner_path->total_cost;
+
+	/*
+	 * Cost of computing hash function: must do it once per input tuple. We
+	 * charge one cpu_operator_cost for each column's hash function.  Also,
+	 * tack on one cpu_tuple_cost per inner row, to model the costs of
+	 * inserting the row into the hashtable.
+	 *
+	 * XXX when a hashclause is more complex than a single operator, we really
+	 * should charge the extra eval costs of the left or right side, as
+	 * appropriate, here.  This seems more work than it's worth at the moment.
+	 */
+	startup_cost += (cpu_operator_cost * num_hashclauses + cpu_tuple_cost)
+		* inner_path_rows;
+	run_cost += cpu_operator_cost * num_hashclauses * outer_path_rows;
+
+	/*
+	 * If this is a parallel hash build, then the value we have for
+	 * inner_rows_total currently refers only to the rows returned by each
+	 * participant.  For shared hash table size estimation, we need the total
+	 * number, so we need to undo the division.
+	 */
+	if (parallel_hash)
+		inner_path_rows_total *= get_parallel_divisor(inner_path);
+
+	/*
+	 * Get hash table size that executor would use for inner relation.
+	 *
+	 * XXX for the moment, always assume that skew optimization will be
+	 * performed.  As long as SKEW_HASH_MEM_PERCENT is small, it's not worth
+	 * trying to determine that for sure.
+	 *
+	 * XXX at some point it might be interesting to try to account for skew
+	 * optimization in the cost estimate, but for now, we don't.
+	 */
+	ExecChooseHashTableSize(inner_path_rows_total,
+							inner_path->pathtarget->width,
+							true,	/* useskew */
+							parallel_hash,	/* try_combined_hash_mem */
+							outer_path->parallel_workers,
+							&space_allowed,
+							&numbuckets,
+							&numbatches,
+							&num_skew_mcvs);
+
+	/*
+	 * If inner relation is too big then we will need to "batch" the join,
+	 * which implies writing and reading most of the tuples to disk an extra
+	 * time.  Charge seq_page_cost per page, since the I/O should be nice and
+	 * sequential.  Writing the inner rel counts as startup cost, all the rest
+	 * as run cost.
+	 */
+	if (numbatches > 1)
+	{
+		double		outerpages = page_size(outer_path_rows,
+										   outer_path->pathtarget->width);
+		double		innerpages = page_size(inner_path_rows,
+										   inner_path->pathtarget->width);
+
+		startup_cost += seq_page_cost * innerpages;
+		run_cost += seq_page_cost * (innerpages + 2 * outerpages);
+	}
+
+	/* CPU costs left for later */
+
+	/* Public result fields */
+	workspace->startup_cost = startup_cost;
+	workspace->total_cost = startup_cost + run_cost;
+	/* Save private data for final_cost_hashjoin */
+	workspace->run_cost = run_cost;
+	workspace->numbuckets = numbuckets;
+	workspace->numbatches = numbatches;
+	workspace->inner_rows_total = inner_path_rows_total;
+}
+
+/*
+ * final_cost_hashjoin
+ *	  Final estimate of the cost and result size of a hashjoin path.
+ *
+ * Note: the numbatches estimate is also saved into 'path' for use later
+ *
+ * 'path' is already filled in except for the rows and cost fields and
+ *		num_batches
+ * 'workspace' is the result from initial_cost_hashjoin
+ * 'extra' contains miscellaneous information about the join
+ */
+void
+final_cost_hashjoin(PlannerInfo *root, HashPath *path,
+					JoinCostWorkspace *workspace,
+					JoinPathExtraData *extra)
+{
+	Path	   *outer_path = path->jpath.outerjoinpath;
+	Path	   *inner_path = path->jpath.innerjoinpath;
+	double		outer_path_rows = outer_path->rows;
+	double		inner_path_rows = inner_path->rows;
+	double		inner_path_rows_total = workspace->inner_rows_total;
+	List	   *hashclauses = path->path_hashclauses;
+	Cost		startup_cost = workspace->startup_cost;
+	Cost		run_cost = workspace->run_cost;
+	int			numbuckets = workspace->numbuckets;
+	int			numbatches = workspace->numbatches;
+	Cost		cpu_per_tuple;
+	QualCost	hash_qual_cost;
+	QualCost	qp_qual_cost;
+	double		hashjointuples;
+	double		virtualbuckets;
+	Selectivity innerbucketsize;
+	Selectivity innermcvfreq;
+	ListCell   *hcl;
+
+	/* Mark the path with the correct row estimate */
+	if (path->jpath.path.param_info)
+		path->jpath.path.rows = path->jpath.path.param_info->ppi_rows;
+	else
+		path->jpath.path.rows = path->jpath.path.parent->rows;
+
+	/* For partial paths, scale row estimate. */
+	if (path->jpath.path.parallel_workers > 0)
+	{
+		double		parallel_divisor = get_parallel_divisor(&path->jpath.path);
+
+		path->jpath.path.rows =
+			clamp_row_est(path->jpath.path.rows / parallel_divisor);
+	}
+
+	/*
+	 * We could include disable_cost in the preliminary estimate, but that
+	 * would amount to optimizing for the case where the join method is
+	 * disabled, which doesn't seem like the way to bet.
+	 */
+	if (!enable_hashjoin)
+		startup_cost += disable_cost;
+
+	/* mark the path with estimated # of batches */
+	path->num_batches = numbatches;
+
+	/* store the total number of tuples (sum of partial row estimates) */
+	path->inner_rows_total = inner_path_rows_total;
+
+	/* and compute the number of "virtual" buckets in the whole join */
+	virtualbuckets = (double) numbuckets * (double) numbatches;
+
+	/*
+	 * Determine bucketsize fraction and MCV frequency for the inner relation.
+	 * We use the smallest bucketsize or MCV frequency estimated for any
+	 * individual hashclause; this is undoubtedly conservative.
+	 *
+	 * BUT: if inner relation has been unique-ified, we can assume it's good
+	 * for hashing.  This is important both because it's the right answer, and
+	 * because we avoid contaminating the cache with a value that's wrong for
+	 * non-unique-ified paths.
+	 */
+	if (IsA(inner_path, UniquePath))
+	{
+		innerbucketsize = 1.0 / virtualbuckets;
+		innermcvfreq = 0.0;
+	}
+	else
+	{
+		innerbucketsize = 1.0;
+		innermcvfreq = 1.0;
+		foreach(hcl, hashclauses)
+		{
+			RestrictInfo *restrictinfo = lfirst_node(RestrictInfo, hcl);
+			Selectivity thisbucketsize;
+			Selectivity thismcvfreq;
+
+			/*
+			 * First we have to figure out which side of the hashjoin clause
+			 * is the inner side.
+			 *
+			 * Since we tend to visit the same clauses over and over when
+			 * planning a large query, we cache the bucket stats estimates in
+			 * the RestrictInfo node to avoid repeated lookups of statistics.
+			 */
+			if (bms_is_subset(restrictinfo->right_relids,
+							  inner_path->parent->relids))
+			{
+				/* righthand side is inner */
+				thisbucketsize = restrictinfo->right_bucketsize;
+				if (thisbucketsize < 0)
+				{
+					/* not cached yet */
+					estimate_hash_bucket_stats(root,
+											   get_rightop(restrictinfo->clause),
+											   virtualbuckets,
+											   &restrictinfo->right_mcvfreq,
+											   &restrictinfo->right_bucketsize);
+					thisbucketsize = restrictinfo->right_bucketsize;
+				}
+				thismcvfreq = restrictinfo->right_mcvfreq;
+			}
+			else
+			{
+				Assert(bms_is_subset(restrictinfo->left_relids,
+									 inner_path->parent->relids));
+				/* lefthand side is inner */
+				thisbucketsize = restrictinfo->left_bucketsize;
+				if (thisbucketsize < 0)
+				{
+					/* not cached yet */
+					estimate_hash_bucket_stats(root,
+											   get_leftop(restrictinfo->clause),
+											   virtualbuckets,
+											   &restrictinfo->left_mcvfreq,
+											   &restrictinfo->left_bucketsize);
+					thisbucketsize = restrictinfo->left_bucketsize;
+				}
+				thismcvfreq = restrictinfo->left_mcvfreq;
+			}
+
+			if (innerbucketsize > thisbucketsize)
+				innerbucketsize = thisbucketsize;
+			if (innermcvfreq > thismcvfreq)
+				innermcvfreq = thismcvfreq;
+		}
+	}
+
+	/*
+	 * If the bucket holding the inner MCV would exceed hash_mem, we don't
+	 * want to hash unless there is really no other alternative, so apply
+	 * disable_cost.  (The executor normally copes with excessive memory usage
+	 * by splitting batches, but obviously it cannot separate equal values
+	 * that way, so it will be unable to drive the batch size below hash_mem
+	 * when this is true.)
+	 */
+	if (relation_byte_size(clamp_row_est(inner_path_rows * innermcvfreq),
+						   inner_path->pathtarget->width) > get_hash_memory_limit())
+		startup_cost += disable_cost;
+
+	/*
+	 * Compute cost of the hashquals and qpquals (other restriction clauses)
+	 * separately.
+	 */
+	cost_qual_eval(&hash_qual_cost, hashclauses, root);
+	cost_qual_eval(&qp_qual_cost, path->jpath.joinrestrictinfo, root);
+	qp_qual_cost.startup -= hash_qual_cost.startup;
+	qp_qual_cost.per_tuple -= hash_qual_cost.per_tuple;
+
+	/* CPU costs */
+
+	if (path->jpath.jointype == JOIN_SEMI ||
+		path->jpath.jointype == JOIN_ANTI ||
+		extra->inner_unique)
+	{
+		double		outer_matched_rows;
+		Selectivity inner_scan_frac;
+
+		/*
+		 * With a SEMI or ANTI join, or if the innerrel is known unique, the
+		 * executor will stop after the first match.
+		 *
+		 * For an outer-rel row that has at least one match, we can expect the
+		 * bucket scan to stop after a fraction 1/(match_count+1) of the
+		 * bucket's rows, if the matches are evenly distributed.  Since they
+		 * probably aren't quite evenly distributed, we apply a fuzz factor of
+		 * 2.0 to that fraction.  (If we used a larger fuzz factor, we'd have
+		 * to clamp inner_scan_frac to at most 1.0; but since match_count is
+		 * at least 1, no such clamp is needed now.)
+		 */
+		outer_matched_rows = rint(outer_path_rows * extra->semifactors.outer_match_frac);
+		inner_scan_frac = 2.0 / (extra->semifactors.match_count + 1.0);
+
+		startup_cost += hash_qual_cost.startup;
+		run_cost += hash_qual_cost.per_tuple * outer_matched_rows *
+			clamp_row_est(inner_path_rows * innerbucketsize * inner_scan_frac) * 0.5;
+
+		/*
+		 * For unmatched outer-rel rows, the picture is quite a lot different.
+		 * In the first place, there is no reason to assume that these rows
+		 * preferentially hit heavily-populated buckets; instead assume they
+		 * are uncorrelated with the inner distribution and so they see an
+		 * average bucket size of inner_path_rows / virtualbuckets.  In the
+		 * second place, it seems likely that they will have few if any exact
+		 * hash-code matches and so very few of the tuples in the bucket will
+		 * actually require eval of the hash quals.  We don't have any good
+		 * way to estimate how many will, but for the moment assume that the
+		 * effective cost per bucket entry is one-tenth what it is for
+		 * matchable tuples.
+		 */
+		run_cost += hash_qual_cost.per_tuple *
+			(outer_path_rows - outer_matched_rows) *
+			clamp_row_est(inner_path_rows / virtualbuckets) * 0.05;
+
+		/* Get # of tuples that will pass the basic join */
+		if (path->jpath.jointype == JOIN_ANTI)
+			hashjointuples = outer_path_rows - outer_matched_rows;
+		else
+			hashjointuples = outer_matched_rows;
+	}
+	else
+	{
+		/*
+		 * The number of tuple comparisons needed is the number of outer
+		 * tuples times the typical number of tuples in a hash bucket, which
+		 * is the inner relation size times its bucketsize fraction.  At each
+		 * one, we need to evaluate the hashjoin quals.  But actually,
+		 * charging the full qual eval cost at each tuple is pessimistic,
+		 * since we don't evaluate the quals unless the hash values match
+		 * exactly.  For lack of a better idea, halve the cost estimate to
+		 * allow for that.
+		 */
+		startup_cost += hash_qual_cost.startup;
+		run_cost += hash_qual_cost.per_tuple * outer_path_rows *
+			clamp_row_est(inner_path_rows * innerbucketsize) * 0.5;
+
+		/*
+		 * Get approx # tuples passing the hashquals.  We use
+		 * approx_tuple_count here because we need an estimate done with
+		 * JOIN_INNER semantics.
+		 */
+		hashjointuples = approx_tuple_count(root, &path->jpath, hashclauses);
+	}
+
+	/*
+	 * For each tuple that gets through the hashjoin proper, we charge
+	 * cpu_tuple_cost plus the cost of evaluating additional restriction
+	 * clauses that are to be applied at the join.  (This is pessimistic since
+	 * not all of the quals may get evaluated at each tuple.)
+	 */
+	startup_cost += qp_qual_cost.startup;
+	cpu_per_tuple = cpu_tuple_cost + qp_qual_cost.per_tuple;
+	run_cost += cpu_per_tuple * hashjointuples;
+
+	/* tlist eval costs are paid per output row, not per tuple scanned */
+	startup_cost += path->jpath.path.pathtarget->cost.startup;
+	run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;
+
+	path->jpath.path.startup_cost = startup_cost;
+	path->jpath.path.total_cost = startup_cost + run_cost;
+}
+
+
+/*
+ * cost_subplan
+ *		Figure the costs for a SubPlan (or initplan).
+ *
+ * Note: we could dig the subplan's Plan out of the root list, but in practice
+ * all callers have it handy already, so we make them pass it.
+ */
+void
+cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
+{
+	QualCost	sp_cost;
+
+	/* Figure any cost for evaluating the testexpr */
+	cost_qual_eval(&sp_cost,
+				   make_ands_implicit((Expr *) subplan->testexpr),
+				   root);
+
+	if (subplan->useHashTable)
+	{
+		/*
+		 * If we are using a hash table for the subquery outputs, then the
+		 * cost of evaluating the query is a one-time cost.  We charge one
+		 * cpu_operator_cost per tuple for the work of loading the hashtable,
+		 * too.
+		 */
+		sp_cost.startup += plan->total_cost +
+			cpu_operator_cost * plan->plan_rows;
+
+		/*
+		 * The per-tuple costs include the cost of evaluating the lefthand
+		 * expressions, plus the cost of probing the hashtable.  We already
+		 * accounted for the lefthand expressions as part of the testexpr, and
+		 * will also have counted one cpu_operator_cost for each comparison
+		 * operator.  That is probably too low for the probing cost, but it's
+		 * hard to make a better estimate, so live with it for now.
+		 */
+	}
+	else
+	{
+		/*
+		 * Otherwise we will be rescanning the subplan output on each
+		 * evaluation.  We need to estimate how much of the output we will
+		 * actually need to scan.  NOTE: this logic should agree with the
+		 * tuple_fraction estimates used by make_subplan() in
+		 * plan/subselect.c.
+		 */
+		Cost		plan_run_cost = plan->total_cost - plan->startup_cost;
+
+		if (subplan->subLinkType == EXISTS_SUBLINK)
+		{
+			/* we only need to fetch 1 tuple; clamp to avoid zero divide */
+			sp_cost.per_tuple += plan_run_cost / clamp_row_est(plan->plan_rows);
+		}
+		else if (subplan->subLinkType == ALL_SUBLINK ||
+				 subplan->subLinkType == ANY_SUBLINK)
+		{
+			/* assume we need 50% of the tuples */
+			sp_cost.per_tuple += 0.50 * plan_run_cost;
+			/* also charge a cpu_operator_cost per row examined */
+			sp_cost.per_tuple += 0.50 * plan->plan_rows * cpu_operator_cost;
+		}
+		else
+		{
+			/* assume we need all tuples */
+			sp_cost.per_tuple += plan_run_cost;
+		}
+
+		/*
+		 * Also account for subplan's startup cost. If the subplan is
+		 * uncorrelated or undirect correlated, AND its topmost node is one
+		 * that materializes its output, assume that we'll only need to pay
+		 * its startup cost once; otherwise assume we pay the startup cost
+		 * every time.
+		 */
+		if (subplan->parParam == NIL &&
+			ExecMaterializesOutput(nodeTag(plan)))
+			sp_cost.startup += plan->startup_cost;
+		else
+			sp_cost.per_tuple += plan->startup_cost;
+	}
+
+	subplan->startup_cost = sp_cost.startup;
+	subplan->per_call_cost = sp_cost.per_tuple;
+}
+
+
+/*
+ * cost_rescan
+ *		Given a finished Path, estimate the costs of rescanning it after
+ *		having done so the first time.  For some Path types a rescan is
+ *		cheaper than an original scan (if no parameters change), and this
+ *		function embodies knowledge about that.  The default is to return
+ *		the same costs stored in the Path.  (Note that the cost estimates
+ *		actually stored in Paths are always for first scans.)
+ *
+ * This function is not currently intended to model effects such as rescans
+ * being cheaper due to disk block caching; what we are concerned with is
+ * plan types wherein the executor caches results explicitly, or doesn't
+ * redo startup calculations, etc.
+ */
+static void
+cost_rescan(PlannerInfo *root, Path *path,
+			Cost *rescan_startup_cost,	/* output parameters */
+			Cost *rescan_total_cost)
+{
+	switch (path->pathtype)
+	{
+		case T_FunctionScan:
+
+			/*
+			 * Currently, nodeFunctionscan.c always executes the function to
+			 * completion before returning any rows, and caches the results in
+			 * a tuplestore.  So the function eval cost is all startup cost
+			 * and isn't paid over again on rescans. However, all run costs
+			 * will be paid over again.
+			 */
+			*rescan_startup_cost = 0;
+			*rescan_total_cost = path->total_cost - path->startup_cost;
+			break;
+		case T_HashJoin:
+
+			/*
+			 * If it's a single-batch join, we don't need to rebuild the hash
+			 * table during a rescan.
+			 */
+			if (((HashPath *) path)->num_batches == 1)
+			{
+				/* Startup cost is exactly the cost of hash table building */
+				*rescan_startup_cost = 0;
+				*rescan_total_cost = path->total_cost - path->startup_cost;
+			}
+			else
+			{
+				/* Otherwise, no special treatment */
+				*rescan_startup_cost = path->startup_cost;
+				*rescan_total_cost = path->total_cost;
+			}
+			break;
+		case T_CteScan:
+		case T_WorkTableScan:
+			{
+				/*
+				 * These plan types materialize their final result in a
+				 * tuplestore or tuplesort object.  So the rescan cost is only
+				 * cpu_tuple_cost per tuple, unless the result is large enough
+				 * to spill to disk.
+				 */
+				Cost		run_cost = cpu_tuple_cost * path->rows;
+				double		nbytes = relation_byte_size(path->rows,
+														path->pathtarget->width);
+				long		work_mem_bytes = work_mem * 1024L;
+
+				if (nbytes > work_mem_bytes)
+				{
+					/* It will spill, so account for re-read cost */
+					double		npages = ceil(nbytes / BLCKSZ);
+
+					run_cost += seq_page_cost * npages;
+				}
+				*rescan_startup_cost = 0;
+				*rescan_total_cost = run_cost;
+			}
+			break;
+		case T_Material:
+		case T_Sort:
+			{
+				/*
+				 * These plan types not only materialize their results, but do
+				 * not implement qual filtering or projection.  So they are
+				 * even cheaper to rescan than the ones above.  We charge only
+				 * cpu_operator_cost per tuple.  (Note: keep that in sync with
+				 * the run_cost charge in cost_sort, and also see comments in
+				 * cost_material before you change it.)
+				 */
+				Cost		run_cost = cpu_operator_cost * path->rows;
+				double		nbytes = relation_byte_size(path->rows,
+														path->pathtarget->width);
+				long		work_mem_bytes = work_mem * 1024L;
+
+				if (nbytes > work_mem_bytes)
+				{
+					/* It will spill, so account for re-read cost */
+					double		npages = ceil(nbytes / BLCKSZ);
+
+					run_cost += seq_page_cost * npages;
+				}
+				*rescan_startup_cost = 0;
+				*rescan_total_cost = run_cost;
+			}
+			break;
+		case T_Memoize:
+			/* All the hard work is done by cost_memoize_rescan */
+			cost_memoize_rescan(root, (MemoizePath *) path,
+								rescan_startup_cost, rescan_total_cost);
+			break;
+		default:
+			*rescan_startup_cost = path->startup_cost;
+			*rescan_total_cost = path->total_cost;
+			break;
+	}
+}
+
+
+/*
+ * cost_qual_eval
+ *		Estimate the CPU costs of evaluating a WHERE clause.
+ *		The input can be either an implicitly-ANDed list of boolean
+ *		expressions, or a list of RestrictInfo nodes.  (The latter is
+ *		preferred since it allows caching of the results.)
+ *		The result includes both a one-time (startup) component,
+ *		and a per-evaluation component.
+ */
+void
+cost_qual_eval(QualCost *cost, List *quals, PlannerInfo *root)
+{
+	cost_qual_eval_context context;
+	ListCell   *l;
+
+	context.root = root;
+	context.total.startup = 0;
+	context.total.per_tuple = 0;
+
+	/* We don't charge any cost for the implicit ANDing at top level ... */
+
+	foreach(l, quals)
+	{
+		Node	   *qual = (Node *) lfirst(l);
+
+		cost_qual_eval_walker(qual, &context);
+	}
+
+	*cost = context.total;
+}
+
+/*
+ * cost_qual_eval_node
+ *		As above, for a single RestrictInfo or expression.
+ */
+void
+cost_qual_eval_node(QualCost *cost, Node *qual, PlannerInfo *root)
+{
+	cost_qual_eval_context context;
+
+	context.root = root;
+	context.total.startup = 0;
+	context.total.per_tuple = 0;
+
+	cost_qual_eval_walker(qual, &context);
+
+	*cost = context.total;
+}
+
+static bool
+cost_qual_eval_walker(Node *node, cost_qual_eval_context *context)
+{
+	if (node == NULL)
+		return false;
+
+	/*
+	 * RestrictInfo nodes contain an eval_cost field reserved for this
+	 * routine's use, so that it's not necessary to evaluate the qual clause's
+	 * cost more than once.  If the clause's cost hasn't been computed yet,
+	 * the field's startup value will contain -1.
+	 */
+	if (IsA(node, RestrictInfo))
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) node;
+
+		if (rinfo->eval_cost.startup < 0)
+		{
+			cost_qual_eval_context locContext;
+
+			locContext.root = context->root;
+			locContext.total.startup = 0;
+			locContext.total.per_tuple = 0;
+
+			/*
+			 * For an OR clause, recurse into the marked-up tree so that we
+			 * set the eval_cost for contained RestrictInfos too.
+			 */
+			if (rinfo->orclause)
+				cost_qual_eval_walker((Node *) rinfo->orclause, &locContext);
+			else
+				cost_qual_eval_walker((Node *) rinfo->clause, &locContext);
+
+			/*
+			 * If the RestrictInfo is marked pseudoconstant, it will be tested
+			 * only once, so treat its cost as all startup cost.
+			 */
+			if (rinfo->pseudoconstant)
+			{
+				/* count one execution during startup */
+				locContext.total.startup += locContext.total.per_tuple;
+				locContext.total.per_tuple = 0;
+			}
+			rinfo->eval_cost = locContext.total;
+		}
+		context->total.startup += rinfo->eval_cost.startup;
+		context->total.per_tuple += rinfo->eval_cost.per_tuple;
+		/* do NOT recurse into children */
+		return false;
+	}
+
+	/*
+	 * For each operator or function node in the given tree, we charge the
+	 * estimated execution cost given by pg_proc.procost (remember to multiply
+	 * this by cpu_operator_cost).
+	 *
+	 * Vars and Consts are charged zero, and so are boolean operators (AND,
+	 * OR, NOT). Simplistic, but a lot better than no model at all.
+	 *
+	 * Should we try to account for the possibility of short-circuit
+	 * evaluation of AND/OR?  Probably *not*, because that would make the
+	 * results depend on the clause ordering, and we are not in any position
+	 * to expect that the current ordering of the clauses is the one that's
+	 * going to end up being used.  The above per-RestrictInfo caching would
+	 * not mix well with trying to re-order clauses anyway.
+	 *
+	 * Another issue that is entirely ignored here is that if a set-returning
+	 * function is below top level in the tree, the functions/operators above
+	 * it will need to be evaluated multiple times.  In practical use, such
+	 * cases arise so seldom as to not be worth the added complexity needed;
+	 * moreover, since our rowcount estimates for functions tend to be pretty
+	 * phony, the results would also be pretty phony.
+	 */
+	if (IsA(node, FuncExpr))
+	{
+		add_function_cost(context->root, ((FuncExpr *) node)->funcid, node,
+						  &context->total);
+	}
+	else if (IsA(node, OpExpr) ||
+			 IsA(node, DistinctExpr) ||
+			 IsA(node, NullIfExpr))
+	{
+		/* rely on struct equivalence to treat these all alike */
+		set_opfuncid((OpExpr *) node);
+		add_function_cost(context->root, ((OpExpr *) node)->opfuncid, node,
+						  &context->total);
+	}
+	else if (IsA(node, ScalarArrayOpExpr))
+	{
+		ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) node;
+		Node	   *arraynode = (Node *) lsecond(saop->args);
+		QualCost	sacosts;
+		QualCost	hcosts;
+		int			estarraylen = estimate_array_length(arraynode);
+
+		set_sa_opfuncid(saop);
+		sacosts.startup = sacosts.per_tuple = 0;
+		add_function_cost(context->root, saop->opfuncid, NULL,
+						  &sacosts);
+
+		if (OidIsValid(saop->hashfuncid))
+		{
+			/* Handle costs for hashed ScalarArrayOpExpr */
+			hcosts.startup = hcosts.per_tuple = 0;
+
+			add_function_cost(context->root, saop->hashfuncid, NULL, &hcosts);
+			context->total.startup += sacosts.startup + hcosts.startup;
+
+			/* Estimate the cost of building the hashtable. */
+			context->total.startup += estarraylen * hcosts.per_tuple;
+
+			/*
+			 * XXX should we charge a little bit for sacosts.per_tuple when
+			 * building the table, or is it ok to assume there will be zero
+			 * hash collision?
+			 */
+
+			/*
+			 * Charge for hashtable lookups.  Charge a single hash and a
+			 * single comparison.
+			 */
+			context->total.per_tuple += hcosts.per_tuple + sacosts.per_tuple;
+		}
+		else
+		{
+			/*
+			 * Estimate that the operator will be applied to about half of the
+			 * array elements before the answer is determined.
+			 */
+			context->total.startup += sacosts.startup;
+			context->total.per_tuple += sacosts.per_tuple *
+				estimate_array_length(arraynode) * 0.5;
+		}
+	}
+	else if (IsA(node, Aggref) ||
+			 IsA(node, WindowFunc))
+	{
+		/*
+		 * Aggref and WindowFunc nodes are (and should be) treated like Vars,
+		 * ie, zero execution cost in the current model, because they behave
+		 * essentially like Vars at execution.  We disregard the costs of
+		 * their input expressions for the same reason.  The actual execution
+		 * costs of the aggregate/window functions and their arguments have to
+		 * be factored into plan-node-specific costing of the Agg or WindowAgg
+		 * plan node.
+		 */
+		return false;			/* don't recurse into children */
+	}
+	else if (IsA(node, GroupingFunc))
+	{
+		/* Treat this as having cost 1 */
+		context->total.per_tuple += cpu_operator_cost;
+		return false;			/* don't recurse into children */
+	}
+	else if (IsA(node, CoerceViaIO))
+	{
+		CoerceViaIO *iocoerce = (CoerceViaIO *) node;
+		Oid			iofunc;
+		Oid			typioparam;
+		bool		typisvarlena;
+
+		/* check the result type's input function */
+		getTypeInputInfo(iocoerce->resulttype,
+						 &iofunc, &typioparam);
+		add_function_cost(context->root, iofunc, NULL,
+						  &context->total);
+		/* check the input type's output function */
+		getTypeOutputInfo(exprType((Node *) iocoerce->arg),
+						  &iofunc, &typisvarlena);
+		add_function_cost(context->root, iofunc, NULL,
+						  &context->total);
+	}
+	else if (IsA(node, ArrayCoerceExpr))
+	{
+		ArrayCoerceExpr *acoerce = (ArrayCoerceExpr *) node;
+		QualCost	perelemcost;
+
+		cost_qual_eval_node(&perelemcost, (Node *) acoerce->elemexpr,
+							context->root);
+		context->total.startup += perelemcost.startup;
+		if (perelemcost.per_tuple > 0)
+			context->total.per_tuple += perelemcost.per_tuple *
+				estimate_array_length((Node *) acoerce->arg);
+	}
+	else if (IsA(node, RowCompareExpr))
+	{
+		/* Conservatively assume we will check all the columns */
+		RowCompareExpr *rcexpr = (RowCompareExpr *) node;
+		ListCell   *lc;
+
+		foreach(lc, rcexpr->opnos)
+		{
+			Oid			opid = lfirst_oid(lc);
+
+			add_function_cost(context->root, get_opcode(opid), NULL,
+							  &context->total);
+		}
+	}
+	else if (IsA(node, MinMaxExpr) ||
+			 IsA(node, SQLValueFunction) ||
+			 IsA(node, XmlExpr) ||
+			 IsA(node, CoerceToDomain) ||
+			 IsA(node, NextValueExpr))
+	{
+		/* Treat all these as having cost 1 */
+		context->total.per_tuple += cpu_operator_cost;
+	}
+	else if (IsA(node, CurrentOfExpr))
+	{
+		/* Report high cost to prevent selection of anything but TID scan */
+		context->total.startup += disable_cost;
+	}
+	else if (IsA(node, SubLink))
+	{
+		/* This routine should not be applied to un-planned expressions */
+		elog(ERROR, "cannot handle unplanned sub-select");
+	}
+	else if (IsA(node, SubPlan))
+	{
+		/*
+		 * A subplan node in an expression typically indicates that the
+		 * subplan will be executed on each evaluation, so charge accordingly.
+		 * (Sub-selects that can be executed as InitPlans have already been
+		 * removed from the expression.)
+		 */
+		SubPlan    *subplan = (SubPlan *) node;
+
+		context->total.startup += subplan->startup_cost;
+		context->total.per_tuple += subplan->per_call_cost;
+
+		/*
+		 * We don't want to recurse into the testexpr, because it was already
+		 * counted in the SubPlan node's costs.  So we're done.
+		 */
+		return false;
+	}
+	else if (IsA(node, AlternativeSubPlan))
+	{
+		/*
+		 * Arbitrarily use the first alternative plan for costing.  (We should
+		 * certainly only include one alternative, and we don't yet have
+		 * enough information to know which one the executor is most likely to
+		 * use.)
+		 */
+		AlternativeSubPlan *asplan = (AlternativeSubPlan *) node;
+
+		return cost_qual_eval_walker((Node *) linitial(asplan->subplans),
+									 context);
+	}
+	else if (IsA(node, PlaceHolderVar))
+	{
+		/*
+		 * A PlaceHolderVar should be given cost zero when considering general
+		 * expression evaluation costs.  The expense of doing the contained
+		 * expression is charged as part of the tlist eval costs of the scan
+		 * or join where the PHV is first computed (see set_rel_width and
+		 * add_placeholders_to_joinrel).  If we charged it again here, we'd be
+		 * double-counting the cost for each level of plan that the PHV
+		 * bubbles up through.  Hence, return without recursing into the
+		 * phexpr.
+		 */
+		return false;
+	}
+
+	/* recurse into children */
+	return expression_tree_walker(node, cost_qual_eval_walker,
+								  (void *) context);
+}
+
+/*
+ * get_restriction_qual_cost
+ *	  Compute evaluation costs of a baserel's restriction quals, plus any
+ *	  movable join quals that have been pushed down to the scan.
+ *	  Results are returned into *qpqual_cost.
+ *
+ * This is a convenience subroutine that works for seqscans and other cases
+ * where all the given quals will be evaluated the hard way.  It's not useful
+ * for cost_index(), for example, where the index machinery takes care of
+ * some of the quals.  We assume baserestrictcost was previously set by
+ * set_baserel_size_estimates().
+ */
+static void
+get_restriction_qual_cost(PlannerInfo *root, RelOptInfo *baserel,
+						  ParamPathInfo *param_info,
+						  QualCost *qpqual_cost)
+{
+	if (param_info)
+	{
+		/* Include costs of pushed-down clauses */
+		cost_qual_eval(qpqual_cost, param_info->ppi_clauses, root);
+
+		qpqual_cost->startup += baserel->baserestrictcost.startup;
+		qpqual_cost->per_tuple += baserel->baserestrictcost.per_tuple;
+	}
+	else
+		*qpqual_cost = baserel->baserestrictcost;
+}
+
+
+/*
+ * compute_semi_anti_join_factors
+ *	  Estimate how much of the inner input a SEMI, ANTI, or inner_unique join
+ *	  can be expected to scan.
+ *
+ * In a hash or nestloop SEMI/ANTI join, the executor will stop scanning
+ * inner rows as soon as it finds a match to the current outer row.
+ * The same happens if we have detected the inner rel is unique.
+ * We should therefore adjust some of the cost components for this effect.
+ * This function computes some estimates needed for these adjustments.
+ * These estimates will be the same regardless of the particular paths used
+ * for the outer and inner relation, so we compute these once and then pass
+ * them to all the join cost estimation functions.
+ *
+ * Input parameters:
+ *	joinrel: join relation under consideration
+ *	outerrel: outer relation under consideration
+ *	innerrel: inner relation under consideration
+ *	jointype: if not JOIN_SEMI or JOIN_ANTI, we assume it's inner_unique
+ *	sjinfo: SpecialJoinInfo relevant to this join
+ *	restrictlist: join quals
+ * Output parameters:
+ *	*semifactors is filled in (see pathnodes.h for field definitions)
+ */
+void
+compute_semi_anti_join_factors(PlannerInfo *root,
+							   RelOptInfo *joinrel,
+							   RelOptInfo *outerrel,
+							   RelOptInfo *innerrel,
+							   JoinType jointype,
+							   SpecialJoinInfo *sjinfo,
+							   List *restrictlist,
+							   SemiAntiJoinFactors *semifactors)
+{
+	Selectivity jselec;
+	Selectivity nselec;
+	Selectivity avgmatch;
+	SpecialJoinInfo norm_sjinfo;
+	List	   *joinquals;
+	ListCell   *l;
+
+	/*
+	 * In an ANTI join, we must ignore clauses that are "pushed down", since
+	 * those won't affect the match logic.  In a SEMI join, we do not
+	 * distinguish joinquals from "pushed down" quals, so just use the whole
+	 * restrictinfo list.  For other outer join types, we should consider only
+	 * non-pushed-down quals, so that this devolves to an IS_OUTER_JOIN check.
+	 */
+	if (IS_OUTER_JOIN(jointype))
+	{
+		joinquals = NIL;
+		foreach(l, restrictlist)
+		{
+			RestrictInfo *rinfo = lfirst_node(RestrictInfo, l);
+
+			if (!RINFO_IS_PUSHED_DOWN(rinfo, joinrel->relids))
+				joinquals = lappend(joinquals, rinfo);
+		}
+	}
+	else
+		joinquals = restrictlist;
+
+	/*
+	 * Get the JOIN_SEMI or JOIN_ANTI selectivity of the join clauses.
+	 */
+	jselec = clauselist_selectivity(root,
+									joinquals,
+									0,
+									(jointype == JOIN_ANTI) ? JOIN_ANTI : JOIN_SEMI,
+									sjinfo);
+
+	/*
+	 * Also get the normal inner-join selectivity of the join clauses.
+	 */
+	norm_sjinfo.type = T_SpecialJoinInfo;
+	norm_sjinfo.min_lefthand = outerrel->relids;
+	norm_sjinfo.min_righthand = innerrel->relids;
+	norm_sjinfo.syn_lefthand = outerrel->relids;
+	norm_sjinfo.syn_righthand = innerrel->relids;
+	norm_sjinfo.jointype = JOIN_INNER;
+	/* we don't bother trying to make the remaining fields valid */
+	norm_sjinfo.lhs_strict = false;
+	norm_sjinfo.delay_upper_joins = false;
+	norm_sjinfo.semi_can_btree = false;
+	norm_sjinfo.semi_can_hash = false;
+	norm_sjinfo.semi_operators = NIL;
+	norm_sjinfo.semi_rhs_exprs = NIL;
+
+	nselec = clauselist_selectivity(root,
+									joinquals,
+									0,
+									JOIN_INNER,
+									&norm_sjinfo);
+
+	/* Avoid leaking a lot of ListCells */
+	if (IS_OUTER_JOIN(jointype))
+		list_free(joinquals);
+
+	/*
+	 * jselec can be interpreted as the fraction of outer-rel rows that have
+	 * any matches (this is true for both SEMI and ANTI cases).  And nselec is
+	 * the fraction of the Cartesian product that matches.  So, the average
+	 * number of matches for each outer-rel row that has at least one match is
+	 * nselec * inner_rows / jselec.
+	 *
+	 * Note: it is correct to use the inner rel's "rows" count here, even
+	 * though we might later be considering a parameterized inner path with
+	 * fewer rows.  This is because we have included all the join clauses in
+	 * the selectivity estimate.
+	 */
+	if (jselec > 0)				/* protect against zero divide */
+	{
+		avgmatch = nselec * innerrel->rows / jselec;
+		/* Clamp to sane range */
+		avgmatch = Max(1.0, avgmatch);
+	}
+	else
+		avgmatch = 1.0;
+
+	semifactors->outer_match_frac = jselec;
+	semifactors->match_count = avgmatch;
+}
+
+/*
+ * has_indexed_join_quals
+ *	  Check whether all the joinquals of a nestloop join are used as
+ *	  inner index quals.
+ *
+ * If the inner path of a SEMI/ANTI join is an indexscan (including bitmap
+ * indexscan) that uses all the joinquals as indexquals, we can assume that an
+ * unmatched outer tuple is cheap to process, whereas otherwise it's probably
+ * expensive.
+ */
+static bool
+has_indexed_join_quals(NestPath *path)
+{
+	JoinPath   *joinpath = &path->jpath;
+	Relids		joinrelids = joinpath->path.parent->relids;
+	Path	   *innerpath = joinpath->innerjoinpath;
+	List	   *indexclauses;
+	bool		found_one;
+	ListCell   *lc;
+
+	/* If join still has quals to evaluate, it's not fast */
+	if (joinpath->joinrestrictinfo != NIL)
+		return false;
+	/* Nor if the inner path isn't parameterized at all */
+	if (innerpath->param_info == NULL)
+		return false;
+
+	/* Find the indexclauses list for the inner scan */
+	switch (innerpath->pathtype)
+	{
+		case T_IndexScan:
+		case T_IndexOnlyScan:
+			indexclauses = ((IndexPath *) innerpath)->indexclauses;
+			break;
+		case T_BitmapHeapScan:
+			{
+				/* Accept only a simple bitmap scan, not AND/OR cases */
+				Path	   *bmqual = ((BitmapHeapPath *) innerpath)->bitmapqual;
+
+				if (IsA(bmqual, IndexPath))
+					indexclauses = ((IndexPath *) bmqual)->indexclauses;
+				else
+					return false;
+				break;
+			}
+		default:
+
+			/*
+			 * If it's not a simple indexscan, it probably doesn't run quickly
+			 * for zero rows out, even if it's a parameterized path using all
+			 * the joinquals.
+			 */
+			return false;
+	}
+
+	/*
+	 * Examine the inner path's param clauses.  Any that are from the outer
+	 * path must be found in the indexclauses list, either exactly or in an
+	 * equivalent form generated by equivclass.c.  Also, we must find at least
+	 * one such clause, else it's a clauseless join which isn't fast.
+	 */
+	found_one = false;
+	foreach(lc, innerpath->param_info->ppi_clauses)
+	{
+		RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
+
+		if (join_clause_is_movable_into(rinfo,
+										innerpath->parent->relids,
+										joinrelids))
+		{
+			if (!is_redundant_with_indexclauses(rinfo, indexclauses))
+				return false;
+			found_one = true;
+		}
+	}
+	return found_one;
+}
+
+
+/*
+ * approx_tuple_count
+ *		Quick-and-dirty estimation of the number of join rows passing
+ *		a set of qual conditions.
+ *
+ * The quals can be either an implicitly-ANDed list of boolean expressions,
+ * or a list of RestrictInfo nodes (typically the latter).
+ *
+ * We intentionally compute the selectivity under JOIN_INNER rules, even
+ * if it's some type of outer join.  This is appropriate because we are
+ * trying to figure out how many tuples pass the initial merge or hash
+ * join step.
+ *
+ * This is quick-and-dirty because we bypass clauselist_selectivity, and
+ * simply multiply the independent clause selectivities together.  Now
+ * clauselist_selectivity often can't do any better than that anyhow, but
+ * for some situations (such as range constraints) it is smarter.  However,
+ * we can't effectively cache the results of clauselist_selectivity, whereas
+ * the individual clause selectivities can be and are cached.
+ *
+ * Since we are only using the results to estimate how many potential
+ * output tuples are generated and passed through qpqual checking, it
+ * seems OK to live with the approximation.
+ */
+static double
+approx_tuple_count(PlannerInfo *root, JoinPath *path, List *quals)
+{
+	double		tuples;
+	double		outer_tuples = path->outerjoinpath->rows;
+	double		inner_tuples = path->innerjoinpath->rows;
+	SpecialJoinInfo sjinfo;
+	Selectivity selec = 1.0;
+	ListCell   *l;
+
+	/*
+	 * Make up a SpecialJoinInfo for JOIN_INNER semantics.
+	 */
+	sjinfo.type = T_SpecialJoinInfo;
+	sjinfo.min_lefthand = path->outerjoinpath->parent->relids;
+	sjinfo.min_righthand = path->innerjoinpath->parent->relids;
+	sjinfo.syn_lefthand = path->outerjoinpath->parent->relids;
+	sjinfo.syn_righthand = path->innerjoinpath->parent->relids;
+	sjinfo.jointype = JOIN_INNER;
+	/* we don't bother trying to make the remaining fields valid */
+	sjinfo.lhs_strict = false;
+	sjinfo.delay_upper_joins = false;
+	sjinfo.semi_can_btree = false;
+	sjinfo.semi_can_hash = false;
+	sjinfo.semi_operators = NIL;
+	sjinfo.semi_rhs_exprs = NIL;
+
+	/* Get the approximate selectivity */
+	foreach(l, quals)
+	{
+		Node	   *qual = (Node *) lfirst(l);
+
+		/* Note that clause_selectivity will be able to cache its result */
+		selec *= clause_selectivity(root, qual, 0, JOIN_INNER, &sjinfo);
+	}
+
+	/* Apply it to the input relation sizes */
+	tuples = selec * outer_tuples * inner_tuples;
+
+	return clamp_row_est(tuples);
+}
+
+
+/*
+ * set_baserel_size_estimates
+ *		Set the size estimates for the given base relation.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already, and rel->tuples must be set.
+ *
+ * We set the following fields of the rel node:
+ *	rows: the estimated number of output tuples (after applying
+ *		  restriction clauses).
+ *	width: the estimated average output tuple width in bytes.
+ *	baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
+ */
+void
+set_baserel_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	double		nrows;
+
+	/* Should only be applied to base relations */
+	Assert(rel->relid > 0);
+
+	nrows = rel->tuples *
+		clauselist_selectivity(root,
+							   rel->baserestrictinfo,
+							   0,
+							   JOIN_INNER,
+							   NULL);
+
+	rel->rows = clamp_row_est(nrows);
+
+	cost_qual_eval(&rel->baserestrictcost, rel->baserestrictinfo, root);
+
+	set_rel_width(root, rel);
+}
+
+/*
+ * get_parameterized_baserel_size
+ *		Make a size estimate for a parameterized scan of a base relation.
+ *
+ * 'param_clauses' lists the additional join clauses to be used.
+ *
+ * set_baserel_size_estimates must have been applied already.
+ */
+double
+get_parameterized_baserel_size(PlannerInfo *root, RelOptInfo *rel,
+							   List *param_clauses)
+{
+	List	   *allclauses;
+	double		nrows;
+
+	/*
+	 * Estimate the number of rows returned by the parameterized scan, knowing
+	 * that it will apply all the extra join clauses as well as the rel's own
+	 * restriction clauses.  Note that we force the clauses to be treated as
+	 * non-join clauses during selectivity estimation.
+	 */
+	allclauses = list_concat_copy(param_clauses, rel->baserestrictinfo);
+	nrows = rel->tuples *
+		clauselist_selectivity(root,
+							   allclauses,
+							   rel->relid,	/* do not use 0! */
+							   JOIN_INNER,
+							   NULL);
+	nrows = clamp_row_est(nrows);
+	/* For safety, make sure result is not more than the base estimate */
+	if (nrows > rel->rows)
+		nrows = rel->rows;
+	return nrows;
+}
+
+/*
+ * set_joinrel_size_estimates
+ *		Set the size estimates for the given join relation.
+ *
+ * The rel's targetlist must have been constructed already, and a
+ * restriction clause list that matches the given component rels must
+ * be provided.
+ *
+ * Since there is more than one way to make a joinrel for more than two
+ * base relations, the results we get here could depend on which component
+ * rel pair is provided.  In theory we should get the same answers no matter
+ * which pair is provided; in practice, since the selectivity estimation
+ * routines don't handle all cases equally well, we might not.  But there's
+ * not much to be done about it.  (Would it make sense to repeat the
+ * calculations for each pair of input rels that's encountered, and somehow
+ * average the results?  Probably way more trouble than it's worth, and
+ * anyway we must keep the rowcount estimate the same for all paths for the
+ * joinrel.)
+ *
+ * We set only the rows field here.  The reltarget field was already set by
+ * build_joinrel_tlist, and baserestrictcost is not used for join rels.
+ */
+void
+set_joinrel_size_estimates(PlannerInfo *root, RelOptInfo *rel,
+						   RelOptInfo *outer_rel,
+						   RelOptInfo *inner_rel,
+						   SpecialJoinInfo *sjinfo,
+						   List *restrictlist)
+{
+	rel->rows = calc_joinrel_size_estimate(root,
+										   rel,
+										   outer_rel,
+										   inner_rel,
+										   outer_rel->rows,
+										   inner_rel->rows,
+										   sjinfo,
+										   restrictlist);
+}
+
+/*
+ * get_parameterized_joinrel_size
+ *		Make a size estimate for a parameterized scan of a join relation.
+ *
+ * 'rel' is the joinrel under consideration.
+ * 'outer_path', 'inner_path' are (probably also parameterized) Paths that
+ *		produce the relations being joined.
+ * 'sjinfo' is any SpecialJoinInfo relevant to this join.
+ * 'restrict_clauses' lists the join clauses that need to be applied at the
+ * join node (including any movable clauses that were moved down to this join,
+ * and not including any movable clauses that were pushed down into the
+ * child paths).
+ *
+ * set_joinrel_size_estimates must have been applied already.
+ */
+double
+get_parameterized_joinrel_size(PlannerInfo *root, RelOptInfo *rel,
+							   Path *outer_path,
+							   Path *inner_path,
+							   SpecialJoinInfo *sjinfo,
+							   List *restrict_clauses)
+{
+	double		nrows;
+
+	/*
+	 * Estimate the number of rows returned by the parameterized join as the
+	 * sizes of the input paths times the selectivity of the clauses that have
+	 * ended up at this join node.
+	 *
+	 * As with set_joinrel_size_estimates, the rowcount estimate could depend
+	 * on the pair of input paths provided, though ideally we'd get the same
+	 * estimate for any pair with the same parameterization.
+	 */
+	nrows = calc_joinrel_size_estimate(root,
+									   rel,
+									   outer_path->parent,
+									   inner_path->parent,
+									   outer_path->rows,
+									   inner_path->rows,
+									   sjinfo,
+									   restrict_clauses);
+	/* For safety, make sure result is not more than the base estimate */
+	if (nrows > rel->rows)
+		nrows = rel->rows;
+	return nrows;
+}
+
+/*
+ * calc_joinrel_size_estimate
+ *		Workhorse for set_joinrel_size_estimates and
+ *		get_parameterized_joinrel_size.
+ *
+ * outer_rel/inner_rel are the relations being joined, but they should be
+ * assumed to have sizes outer_rows/inner_rows; those numbers might be less
+ * than what rel->rows says, when we are considering parameterized paths.
+ */
+static double
+calc_joinrel_size_estimate(PlannerInfo *root,
+						   RelOptInfo *joinrel,
+						   RelOptInfo *outer_rel,
+						   RelOptInfo *inner_rel,
+						   double outer_rows,
+						   double inner_rows,
+						   SpecialJoinInfo *sjinfo,
+						   List *restrictlist_in)
+{
+	/* This apparently-useless variable dodges a compiler bug in VS2013: */
+	List	   *restrictlist = restrictlist_in;
+	JoinType	jointype = sjinfo->jointype;
+	Selectivity fkselec;
+	Selectivity jselec;
+	Selectivity pselec;
+	double		nrows;
+
+	/*
+	 * Compute joinclause selectivity.  Note that we are only considering
+	 * clauses that become restriction clauses at this join level; we are not
+	 * double-counting them because they were not considered in estimating the
+	 * sizes of the component rels.
+	 *
+	 * First, see whether any of the joinclauses can be matched to known FK
+	 * constraints.  If so, drop those clauses from the restrictlist, and
+	 * instead estimate their selectivity using FK semantics.  (We do this
+	 * without regard to whether said clauses are local or "pushed down".
+	 * Probably, an FK-matching clause could never be seen as pushed down at
+	 * an outer join, since it would be strict and hence would be grounds for
+	 * join strength reduction.)  fkselec gets the net selectivity for
+	 * FK-matching clauses, or 1.0 if there are none.
+	 */
+	fkselec = get_foreign_key_join_selectivity(root,
+											   outer_rel->relids,
+											   inner_rel->relids,
+											   sjinfo,
+											   &restrictlist);
+
+	/*
+	 * For an outer join, we have to distinguish the selectivity of the join's
+	 * own clauses (JOIN/ON conditions) from any clauses that were "pushed
+	 * down".  For inner joins we just count them all as joinclauses.
+	 */
+	if (IS_OUTER_JOIN(jointype))
+	{
+		List	   *joinquals = NIL;
+		List	   *pushedquals = NIL;
+		ListCell   *l;
+
+		/* Grovel through the clauses to separate into two lists */
+		foreach(l, restrictlist)
+		{
+			RestrictInfo *rinfo = lfirst_node(RestrictInfo, l);
+
+			if (RINFO_IS_PUSHED_DOWN(rinfo, joinrel->relids))
+				pushedquals = lappend(pushedquals, rinfo);
+			else
+				joinquals = lappend(joinquals, rinfo);
+		}
+
+		/* Get the separate selectivities */
+		jselec = clauselist_selectivity(root,
+										joinquals,
+										0,
+										jointype,
+										sjinfo);
+		pselec = clauselist_selectivity(root,
+										pushedquals,
+										0,
+										jointype,
+										sjinfo);
+
+		/* Avoid leaking a lot of ListCells */
+		list_free(joinquals);
+		list_free(pushedquals);
+	}
+	else
+	{
+		jselec = clauselist_selectivity(root,
+										restrictlist,
+										0,
+										jointype,
+										sjinfo);
+		pselec = 0.0;			/* not used, keep compiler quiet */
+	}
+
+	/*
+	 * Basically, we multiply size of Cartesian product by selectivity.
+	 *
+	 * If we are doing an outer join, take that into account: the joinqual
+	 * selectivity has to be clamped using the knowledge that the output must
+	 * be at least as large as the non-nullable input.  However, any
+	 * pushed-down quals are applied after the outer join, so their
+	 * selectivity applies fully.
+	 *
+	 * For JOIN_SEMI and JOIN_ANTI, the selectivity is defined as the fraction
+	 * of LHS rows that have matches, and we apply that straightforwardly.
+	 */
+	switch (jointype)
+	{
+		case JOIN_INNER:
+			nrows = outer_rows * inner_rows * fkselec * jselec;
+			/* pselec not used */
+			break;
+		case JOIN_LEFT:
+			nrows = outer_rows * inner_rows * fkselec * jselec;
+			if (nrows < outer_rows)
+				nrows = outer_rows;
+			nrows *= pselec;
+			break;
+		case JOIN_FULL:
+			nrows = outer_rows * inner_rows * fkselec * jselec;
+			if (nrows < outer_rows)
+				nrows = outer_rows;
+			if (nrows < inner_rows)
+				nrows = inner_rows;
+			nrows *= pselec;
+			break;
+		case JOIN_SEMI:
+			nrows = outer_rows * fkselec * jselec;
+			/* pselec not used */
+			break;
+		case JOIN_ANTI:
+			nrows = outer_rows * (1.0 - fkselec * jselec);
+			nrows *= pselec;
+			break;
+		default:
+			/* other values not expected here */
+			elog(ERROR, "unrecognized join type: %d", (int) jointype);
+			nrows = 0;			/* keep compiler quiet */
+			break;
+	}
+
+	return clamp_row_est(nrows);
+}
+
+/*
+ * get_foreign_key_join_selectivity
+ *		Estimate join selectivity for foreign-key-related clauses.
+ *
+ * Remove any clauses that can be matched to FK constraints from *restrictlist,
+ * and return a substitute estimate of their selectivity.  1.0 is returned
+ * when there are no such clauses.
+ *
+ * The reason for treating such clauses specially is that we can get better
+ * estimates this way than by relying on clauselist_selectivity(), especially
+ * for multi-column FKs where that function's assumption that the clauses are
+ * independent falls down badly.  But even with single-column FKs, we may be
+ * able to get a better answer when the pg_statistic stats are missing or out
+ * of date.
+ */
+static Selectivity
+get_foreign_key_join_selectivity(PlannerInfo *root,
+								 Relids outer_relids,
+								 Relids inner_relids,
+								 SpecialJoinInfo *sjinfo,
+								 List **restrictlist)
+{
+	Selectivity fkselec = 1.0;
+	JoinType	jointype = sjinfo->jointype;
+	List	   *worklist = *restrictlist;
+	ListCell   *lc;
+
+	/* Consider each FK constraint that is known to match the query */
+	foreach(lc, root->fkey_list)
+	{
+		ForeignKeyOptInfo *fkinfo = (ForeignKeyOptInfo *) lfirst(lc);
+		bool		ref_is_outer;
+		List	   *removedlist;
+		ListCell   *cell;
+
+		/*
+		 * This FK is not relevant unless it connects a baserel on one side of
+		 * this join to a baserel on the other side.
+		 */
+		if (bms_is_member(fkinfo->con_relid, outer_relids) &&
+			bms_is_member(fkinfo->ref_relid, inner_relids))
+			ref_is_outer = false;
+		else if (bms_is_member(fkinfo->ref_relid, outer_relids) &&
+				 bms_is_member(fkinfo->con_relid, inner_relids))
+			ref_is_outer = true;
+		else
+			continue;
+
+		/*
+		 * If we're dealing with a semi/anti join, and the FK's referenced
+		 * relation is on the outside, then knowledge of the FK doesn't help
+		 * us figure out what we need to know (which is the fraction of outer
+		 * rows that have matches).  On the other hand, if the referenced rel
+		 * is on the inside, then all outer rows must have matches in the
+		 * referenced table (ignoring nulls).  But any restriction or join
+		 * clauses that filter that table will reduce the fraction of matches.
+		 * We can account for restriction clauses, but it's too hard to guess
+		 * how many table rows would get through a join that's inside the RHS.
+		 * Hence, if either case applies, punt and ignore the FK.
+		 */
+		if ((jointype == JOIN_SEMI || jointype == JOIN_ANTI) &&
+			(ref_is_outer || bms_membership(inner_relids) != BMS_SINGLETON))
+			continue;
+
+		/*
+		 * Modify the restrictlist by removing clauses that match the FK (and
+		 * putting them into removedlist instead).  It seems unsafe to modify
+		 * the originally-passed List structure, so we make a shallow copy the
+		 * first time through.
+		 */
+		if (worklist == *restrictlist)
+			worklist = list_copy(worklist);
+
+		removedlist = NIL;
+		foreach(cell, worklist)
+		{
+			RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);
+			bool		remove_it = false;
+			int			i;
+
+			/* Drop this clause if it matches any column of the FK */
+			for (i = 0; i < fkinfo->nkeys; i++)
+			{
+				if (rinfo->parent_ec)
+				{
+					/*
+					 * EC-derived clauses can only match by EC.  It is okay to
+					 * consider any clause derived from the same EC as
+					 * matching the FK: even if equivclass.c chose to generate
+					 * a clause equating some other pair of Vars, it could
+					 * have generated one equating the FK's Vars.  So for
+					 * purposes of estimation, we can act as though it did so.
+					 *
+					 * Note: checking parent_ec is a bit of a cheat because
+					 * there are EC-derived clauses that don't have parent_ec
+					 * set; but such clauses must compare expressions that
+					 * aren't just Vars, so they cannot match the FK anyway.
+					 */
+					if (fkinfo->eclass[i] == rinfo->parent_ec)
+					{
+						remove_it = true;
+						break;
+					}
+				}
+				else
+				{
+					/*
+					 * Otherwise, see if rinfo was previously matched to FK as
+					 * a "loose" clause.
+					 */
+					if (list_member_ptr(fkinfo->rinfos[i], rinfo))
+					{
+						remove_it = true;
+						break;
+					}
+				}
+			}
+			if (remove_it)
+			{
+				worklist = foreach_delete_current(worklist, cell);
+				removedlist = lappend(removedlist, rinfo);
+			}
+		}
+
+		/*
+		 * If we failed to remove all the matching clauses we expected to
+		 * find, chicken out and ignore this FK; applying its selectivity
+		 * might result in double-counting.  Put any clauses we did manage to
+		 * remove back into the worklist.
+		 *
+		 * Since the matching clauses are known not outerjoin-delayed, they
+		 * would normally have appeared in the initial joinclause list.  If we
+		 * didn't find them, there are two possibilities:
+		 *
+		 * 1. If the FK match is based on an EC that is ec_has_const, it won't
+		 * have generated any join clauses at all.  We discount such ECs while
+		 * checking to see if we have "all" the clauses.  (Below, we'll adjust
+		 * the selectivity estimate for this case.)
+		 *
+		 * 2. The clauses were matched to some other FK in a previous
+		 * iteration of this loop, and thus removed from worklist.  (A likely
+		 * case is that two FKs are matched to the same EC; there will be only
+		 * one EC-derived clause in the initial list, so the first FK will
+		 * consume it.)  Applying both FKs' selectivity independently risks
+		 * underestimating the join size; in particular, this would undo one
+		 * of the main things that ECs were invented for, namely to avoid
+		 * double-counting the selectivity of redundant equality conditions.
+		 * Later we might think of a reasonable way to combine the estimates,
+		 * but for now, just punt, since this is a fairly uncommon situation.
+		 */
+		if (removedlist == NIL ||
+			list_length(removedlist) !=
+			(fkinfo->nmatched_ec - fkinfo->nconst_ec + fkinfo->nmatched_ri))
+		{
+			worklist = list_concat(worklist, removedlist);
+			continue;
+		}
+
+		/*
+		 * Finally we get to the payoff: estimate selectivity using the
+		 * knowledge that each referencing row will match exactly one row in
+		 * the referenced table.
+		 *
+		 * XXX that's not true in the presence of nulls in the referencing
+		 * column(s), so in principle we should derate the estimate for those.
+		 * However (1) if there are any strict restriction clauses for the
+		 * referencing column(s) elsewhere in the query, derating here would
+		 * be double-counting the null fraction, and (2) it's not very clear
+		 * how to combine null fractions for multiple referencing columns. So
+		 * we do nothing for now about correcting for nulls.
+		 *
+		 * XXX another point here is that if either side of an FK constraint
+		 * is an inheritance parent, we estimate as though the constraint
+		 * covers all its children as well.  This is not an unreasonable
+		 * assumption for a referencing table, ie the user probably applied
+		 * identical constraints to all child tables (though perhaps we ought
+		 * to check that).  But it's not possible to have done that for a
+		 * referenced table.  Fortunately, precisely because that doesn't
+		 * work, it is uncommon in practice to have an FK referencing a parent
+		 * table.  So, at least for now, disregard inheritance here.
+		 */
+		if (jointype == JOIN_SEMI || jointype == JOIN_ANTI)
+		{
+			/*
+			 * For JOIN_SEMI and JOIN_ANTI, we only get here when the FK's
+			 * referenced table is exactly the inside of the join.  The join
+			 * selectivity is defined as the fraction of LHS rows that have
+			 * matches.  The FK implies that every LHS row has a match *in the
+			 * referenced table*; but any restriction clauses on it will
+			 * reduce the number of matches.  Hence we take the join
+			 * selectivity as equal to the selectivity of the table's
+			 * restriction clauses, which is rows / tuples; but we must guard
+			 * against tuples == 0.
+			 */
+			RelOptInfo *ref_rel = find_base_rel(root, fkinfo->ref_relid);
+			double		ref_tuples = Max(ref_rel->tuples, 1.0);
+
+			fkselec *= ref_rel->rows / ref_tuples;
+		}
+		else
+		{
+			/*
+			 * Otherwise, selectivity is exactly 1/referenced-table-size; but
+			 * guard against tuples == 0.  Note we should use the raw table
+			 * tuple count, not any estimate of its filtered or joined size.
+			 */
+			RelOptInfo *ref_rel = find_base_rel(root, fkinfo->ref_relid);
+			double		ref_tuples = Max(ref_rel->tuples, 1.0);
+
+			fkselec *= 1.0 / ref_tuples;
+		}
+
+		/*
+		 * If any of the FK columns participated in ec_has_const ECs, then
+		 * equivclass.c will have generated "var = const" restrictions for
+		 * each side of the join, thus reducing the sizes of both input
+		 * relations.  Taking the fkselec at face value would amount to
+		 * double-counting the selectivity of the constant restriction for the
+		 * referencing Var.  Hence, look for the restriction clause(s) that
+		 * were applied to the referencing Var(s), and divide out their
+		 * selectivity to correct for this.
+		 */
+		if (fkinfo->nconst_ec > 0)
+		{
+			for (int i = 0; i < fkinfo->nkeys; i++)
+			{
+				EquivalenceClass *ec = fkinfo->eclass[i];
+
+				if (ec && ec->ec_has_const)
+				{
+					EquivalenceMember *em = fkinfo->fk_eclass_member[i];
+					RestrictInfo *rinfo = find_derived_clause_for_ec_member(ec,
+																			em);
+
+					if (rinfo)
+					{
+						Selectivity s0;
+
+						s0 = clause_selectivity(root,
+												(Node *) rinfo,
+												0,
+												jointype,
+												sjinfo);
+						if (s0 > 0)
+							fkselec /= s0;
+					}
+				}
+			}
+		}
+	}
+
+	*restrictlist = worklist;
+	CLAMP_PROBABILITY(fkselec);
+	return fkselec;
+}
+
+/*
+ * set_subquery_size_estimates
+ *		Set the size estimates for a base relation that is a subquery.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already, and the Paths for the subquery must have been completed.
+ * We look at the subquery's PlannerInfo to extract data.
+ *
+ * We set the same fields as set_baserel_size_estimates.
+ */
+void
+set_subquery_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	PlannerInfo *subroot = rel->subroot;
+	RelOptInfo *sub_final_rel;
+	ListCell   *lc;
+
+	/* Should only be applied to base relations that are subqueries */
+	Assert(rel->relid > 0);
+	Assert(planner_rt_fetch(rel->relid, root)->rtekind == RTE_SUBQUERY);
+
+	/*
+	 * Copy raw number of output rows from subquery.  All of its paths should
+	 * have the same output rowcount, so just look at cheapest-total.
+	 */
+	sub_final_rel = fetch_upper_rel(subroot, UPPERREL_FINAL, NULL);
+	rel->tuples = sub_final_rel->cheapest_total_path->rows;
+
+	/*
+	 * Compute per-output-column width estimates by examining the subquery's
+	 * targetlist.  For any output that is a plain Var, get the width estimate
+	 * that was made while planning the subquery.  Otherwise, we leave it to
+	 * set_rel_width to fill in a datatype-based default estimate.
+	 */
+	foreach(lc, subroot->parse->targetList)
+	{
+		TargetEntry *te = lfirst_node(TargetEntry, lc);
+		Node	   *texpr = (Node *) te->expr;
+		int32		item_width = 0;
+
+		/* junk columns aren't visible to upper query */
+		if (te->resjunk)
+			continue;
+
+		/*
+		 * The subquery could be an expansion of a view that's had columns
+		 * added to it since the current query was parsed, so that there are
+		 * non-junk tlist columns in it that don't correspond to any column
+		 * visible at our query level.  Ignore such columns.
+		 */
+		if (te->resno < rel->min_attr || te->resno > rel->max_attr)
+			continue;
+
+		/*
+		 * XXX This currently doesn't work for subqueries containing set
+		 * operations, because the Vars in their tlists are bogus references
+		 * to the first leaf subquery, which wouldn't give the right answer
+		 * even if we could still get to its PlannerInfo.
+		 *
+		 * Also, the subquery could be an appendrel for which all branches are
+		 * known empty due to constraint exclusion, in which case
+		 * set_append_rel_pathlist will have left the attr_widths set to zero.
+		 *
+		 * In either case, we just leave the width estimate zero until
+		 * set_rel_width fixes it.
+		 */
+		if (IsA(texpr, Var) &&
+			subroot->parse->setOperations == NULL)
+		{
+			Var		   *var = (Var *) texpr;
+			RelOptInfo *subrel = find_base_rel(subroot, var->varno);
+
+			item_width = subrel->attr_widths[var->varattno - subrel->min_attr];
+		}
+		rel->attr_widths[te->resno - rel->min_attr] = item_width;
+	}
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_function_size_estimates
+ *		Set the size estimates for a base relation that is a function call.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already.
+ *
+ * We set the same fields as set_baserel_size_estimates.
+ */
+void
+set_function_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	RangeTblEntry *rte;
+	ListCell   *lc;
+
+	/* Should only be applied to base relations that are functions */
+	Assert(rel->relid > 0);
+	rte = planner_rt_fetch(rel->relid, root);
+	Assert(rte->rtekind == RTE_FUNCTION);
+
+	/*
+	 * Estimate number of rows the functions will return. The rowcount of the
+	 * node is that of the largest function result.
+	 */
+	rel->tuples = 0;
+	foreach(lc, rte->functions)
+	{
+		RangeTblFunction *rtfunc = (RangeTblFunction *) lfirst(lc);
+		double		ntup = expression_returns_set_rows(root, rtfunc->funcexpr);
+
+		if (ntup > rel->tuples)
+			rel->tuples = ntup;
+	}
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_function_size_estimates
+ *		Set the size estimates for a base relation that is a function call.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already.
+ *
+ * We set the same fields as set_tablefunc_size_estimates.
+ */
+void
+set_tablefunc_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	/* Should only be applied to base relations that are functions */
+	Assert(rel->relid > 0);
+	Assert(planner_rt_fetch(rel->relid, root)->rtekind == RTE_TABLEFUNC);
+
+	rel->tuples = 100;
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_values_size_estimates
+ *		Set the size estimates for a base relation that is a values list.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already.
+ *
+ * We set the same fields as set_baserel_size_estimates.
+ */
+void
+set_values_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	RangeTblEntry *rte;
+
+	/* Should only be applied to base relations that are values lists */
+	Assert(rel->relid > 0);
+	rte = planner_rt_fetch(rel->relid, root);
+	Assert(rte->rtekind == RTE_VALUES);
+
+	/*
+	 * Estimate number of rows the values list will return. We know this
+	 * precisely based on the list length (well, barring set-returning
+	 * functions in list items, but that's a refinement not catered for
+	 * anywhere else either).
+	 */
+	rel->tuples = list_length(rte->values_lists);
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_cte_size_estimates
+ *		Set the size estimates for a base relation that is a CTE reference.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already, and we need an estimate of the number of rows returned by the CTE
+ * (if a regular CTE) or the non-recursive term (if a self-reference).
+ *
+ * We set the same fields as set_baserel_size_estimates.
+ */
+void
+set_cte_size_estimates(PlannerInfo *root, RelOptInfo *rel, double cte_rows)
+{
+	RangeTblEntry *rte;
+
+	/* Should only be applied to base relations that are CTE references */
+	Assert(rel->relid > 0);
+	rte = planner_rt_fetch(rel->relid, root);
+	Assert(rte->rtekind == RTE_CTE);
+
+	if (rte->self_reference)
+	{
+		/*
+		 * In a self-reference, we assume the average worktable size is a
+		 * multiple of the nonrecursive term's size.  The best multiplier will
+		 * vary depending on query "fan-out", so make its value adjustable.
+		 */
+		rel->tuples = clamp_row_est(recursive_worktable_factor * cte_rows);
+	}
+	else
+	{
+		/* Otherwise just believe the CTE's rowcount estimate */
+		rel->tuples = cte_rows;
+	}
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_namedtuplestore_size_estimates
+ *		Set the size estimates for a base relation that is a tuplestore reference.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already.
+ *
+ * We set the same fields as set_baserel_size_estimates.
+ */
+void
+set_namedtuplestore_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	RangeTblEntry *rte;
+
+	/* Should only be applied to base relations that are tuplestore references */
+	Assert(rel->relid > 0);
+	rte = planner_rt_fetch(rel->relid, root);
+	Assert(rte->rtekind == RTE_NAMEDTUPLESTORE);
+
+	/*
+	 * Use the estimate provided by the code which is generating the named
+	 * tuplestore.  In some cases, the actual number might be available; in
+	 * others the same plan will be re-used, so a "typical" value might be
+	 * estimated and used.
+	 */
+	rel->tuples = rte->enrtuples;
+	if (rel->tuples < 0)
+		rel->tuples = 1000;
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_result_size_estimates
+ *		Set the size estimates for an RTE_RESULT base relation
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already.
+ *
+ * We set the same fields as set_baserel_size_estimates.
+ */
+void
+set_result_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	/* Should only be applied to RTE_RESULT base relations */
+	Assert(rel->relid > 0);
+	Assert(planner_rt_fetch(rel->relid, root)->rtekind == RTE_RESULT);
+
+	/* RTE_RESULT always generates a single row, natively */
+	rel->tuples = 1;
+
+	/* Now estimate number of output rows, etc */
+	set_baserel_size_estimates(root, rel);
+}
+
+/*
+ * set_foreign_size_estimates
+ *		Set the size estimates for a base relation that is a foreign table.
+ *
+ * There is not a whole lot that we can do here; the foreign-data wrapper
+ * is responsible for producing useful estimates.  We can do a decent job
+ * of estimating baserestrictcost, so we set that, and we also set up width
+ * using what will be purely datatype-driven estimates from the targetlist.
+ * There is no way to do anything sane with the rows value, so we just put
+ * a default estimate and hope that the wrapper can improve on it.  The
+ * wrapper's GetForeignRelSize function will be called momentarily.
+ *
+ * The rel's targetlist and restrictinfo list must have been constructed
+ * already.
+ */
+void
+set_foreign_size_estimates(PlannerInfo *root, RelOptInfo *rel)
+{
+	/* Should only be applied to base relations */
+	Assert(rel->relid > 0);
+
+	rel->rows = 1000;			/* entirely bogus default estimate */
+
+	cost_qual_eval(&rel->baserestrictcost, rel->baserestrictinfo, root);
+
+	set_rel_width(root, rel);
+}
+
+
+/*
+ * set_rel_width
+ *		Set the estimated output width of a base relation.
+ *
+ * The estimated output width is the sum of the per-attribute width estimates
+ * for the actually-referenced columns, plus any PHVs or other expressions
+ * that have to be calculated at this relation.  This is the amount of data
+ * we'd need to pass upwards in case of a sort, hash, etc.
+ *
+ * This function also sets reltarget->cost, so it's a bit misnamed now.
+ *
+ * NB: this works best on plain relations because it prefers to look at
+ * real Vars.  For subqueries, set_subquery_size_estimates will already have
+ * copied up whatever per-column estimates were made within the subquery,
+ * and for other types of rels there isn't much we can do anyway.  We fall
+ * back on (fairly stupid) datatype-based width estimates if we can't get
+ * any better number.
+ *
+ * The per-attribute width estimates are cached for possible re-use while
+ * building join relations or post-scan/join pathtargets.
+ */
+static void
+set_rel_width(PlannerInfo *root, RelOptInfo *rel)
+{
+	Oid			reloid = planner_rt_fetch(rel->relid, root)->relid;
+	int32		tuple_width = 0;
+	bool		have_wholerow_var = false;
+	ListCell   *lc;
+
+	/* Vars are assumed to have cost zero, but other exprs do not */
+	rel->reltarget->cost.startup = 0;
+	rel->reltarget->cost.per_tuple = 0;
+
+	foreach(lc, rel->reltarget->exprs)
+	{
+		Node	   *node = (Node *) lfirst(lc);
+
+		/*
+		 * Ordinarily, a Var in a rel's targetlist must belong to that rel;
+		 * but there are corner cases involving LATERAL references where that
+		 * isn't so.  If the Var has the wrong varno, fall through to the
+		 * generic case (it doesn't seem worth the trouble to be any smarter).
+		 */
+		if (IsA(node, Var) &&
+			((Var *) node)->varno == rel->relid)
+		{
+			Var		   *var = (Var *) node;
+			int			ndx;
+			int32		item_width;
+
+			Assert(var->varattno >= rel->min_attr);
+			Assert(var->varattno <= rel->max_attr);
+
+			ndx = var->varattno - rel->min_attr;
+
+			/*
+			 * If it's a whole-row Var, we'll deal with it below after we have
+			 * already cached as many attr widths as possible.
+			 */
+			if (var->varattno == 0)
+			{
+				have_wholerow_var = true;
+				continue;
+			}
+
+			/*
+			 * The width may have been cached already (especially if it's a
+			 * subquery), so don't duplicate effort.
+			 */
+			if (rel->attr_widths[ndx] > 0)
+			{
+				tuple_width += rel->attr_widths[ndx];
+				continue;
+			}
+
+			/* Try to get column width from statistics */
+			if (reloid != InvalidOid && var->varattno > 0)
+			{
+				item_width = get_attavgwidth(reloid, var->varattno);
+				if (item_width > 0)
+				{
+					rel->attr_widths[ndx] = item_width;
+					tuple_width += item_width;
+					continue;
+				}
+			}
+
+			/*
+			 * Not a plain relation, or can't find statistics for it. Estimate
+			 * using just the type info.
+			 */
+			item_width = get_typavgwidth(var->vartype, var->vartypmod);
+			Assert(item_width > 0);
+			rel->attr_widths[ndx] = item_width;
+			tuple_width += item_width;
+		}
+		else if (IsA(node, PlaceHolderVar))
+		{
+			/*
+			 * We will need to evaluate the PHV's contained expression while
+			 * scanning this rel, so be sure to include it in reltarget->cost.
+			 */
+			PlaceHolderVar *phv = (PlaceHolderVar *) node;
+			PlaceHolderInfo *phinfo = find_placeholder_info(root, phv, false);
+			QualCost	cost;
+
+			tuple_width += phinfo->ph_width;
+			cost_qual_eval_node(&cost, (Node *) phv->phexpr, root);
+			rel->reltarget->cost.startup += cost.startup;
+			rel->reltarget->cost.per_tuple += cost.per_tuple;
+		}
+		else
+		{
+			/*
+			 * We could be looking at an expression pulled up from a subquery,
+			 * or a ROW() representing a whole-row child Var, etc.  Do what we
+			 * can using the expression type information.
+			 */
+			int32		item_width;
+			QualCost	cost;
+
+			item_width = get_typavgwidth(exprType(node), exprTypmod(node));
+			Assert(item_width > 0);
+			tuple_width += item_width;
+			/* Not entirely clear if we need to account for cost, but do so */
+			cost_qual_eval_node(&cost, node, root);
+			rel->reltarget->cost.startup += cost.startup;
+			rel->reltarget->cost.per_tuple += cost.per_tuple;
+		}
+	}
+
+	/*
+	 * If we have a whole-row reference, estimate its width as the sum of
+	 * per-column widths plus heap tuple header overhead.
+	 */
+	if (have_wholerow_var)
+	{
+		int32		wholerow_width = MAXALIGN(SizeofHeapTupleHeader);
+
+		if (reloid != InvalidOid)
+		{
+			/* Real relation, so estimate true tuple width */
+			wholerow_width += get_relation_data_width(reloid,
+													  rel->attr_widths - rel->min_attr);
+		}
+		else
+		{
+			/* Do what we can with info for a phony rel */
+			AttrNumber	i;
+
+			for (i = 1; i <= rel->max_attr; i++)
+				wholerow_width += rel->attr_widths[i - rel->min_attr];
+		}
+
+		rel->attr_widths[0 - rel->min_attr] = wholerow_width;
+
+		/*
+		 * Include the whole-row Var as part of the output tuple.  Yes, that
+		 * really is what happens at runtime.
+		 */
+		tuple_width += wholerow_width;
+	}
+
+	Assert(tuple_width >= 0);
+	rel->reltarget->width = tuple_width;
+}
+
+/*
+ * set_pathtarget_cost_width
+ *		Set the estimated eval cost and output width of a PathTarget tlist.
+ *
+ * As a notational convenience, returns the same PathTarget pointer passed in.
+ *
+ * Most, though not quite all, uses of this function occur after we've run
+ * set_rel_width() for base relations; so we can usually obtain cached width
+ * estimates for Vars.  If we can't, fall back on datatype-based width
+ * estimates.  Present early-planning uses of PathTargets don't need accurate
+ * widths badly enough to justify going to the catalogs for better data.
+ */
+PathTarget *
+set_pathtarget_cost_width(PlannerInfo *root, PathTarget *target)
+{
+	int32		tuple_width = 0;
+	ListCell   *lc;
+
+	/* Vars are assumed to have cost zero, but other exprs do not */
+	target->cost.startup = 0;
+	target->cost.per_tuple = 0;
+
+	foreach(lc, target->exprs)
+	{
+		Node	   *node = (Node *) lfirst(lc);
+
+		if (IsA(node, Var))
+		{
+			Var		   *var = (Var *) node;
+			int32		item_width;
+
+			/* We should not see any upper-level Vars here */
+			Assert(var->varlevelsup == 0);
+
+			/* Try to get data from RelOptInfo cache */
+			if (!IS_SPECIAL_VARNO(var->varno) &&
+				var->varno < root->simple_rel_array_size)
+			{
+				RelOptInfo *rel = root->simple_rel_array[var->varno];
+
+				if (rel != NULL &&
+					var->varattno >= rel->min_attr &&
+					var->varattno <= rel->max_attr)
+				{
+					int			ndx = var->varattno - rel->min_attr;
+
+					if (rel->attr_widths[ndx] > 0)
+					{
+						tuple_width += rel->attr_widths[ndx];
+						continue;
+					}
+				}
+			}
+
+			/*
+			 * No cached data available, so estimate using just the type info.
+			 */
+			item_width = get_typavgwidth(var->vartype, var->vartypmod);
+			Assert(item_width > 0);
+			tuple_width += item_width;
+		}
+		else
+		{
+			/*
+			 * Handle general expressions using type info.
+			 */
+			int32		item_width;
+			QualCost	cost;
+
+			item_width = get_typavgwidth(exprType(node), exprTypmod(node));
+			Assert(item_width > 0);
+			tuple_width += item_width;
+
+			/* Account for cost, too */
+			cost_qual_eval_node(&cost, node, root);
+			target->cost.startup += cost.startup;
+			target->cost.per_tuple += cost.per_tuple;
+		}
+	}
+
+	Assert(tuple_width >= 0);
+	target->width = tuple_width;
+
+	return target;
+}
+
+/*
+ * relation_byte_size
+ *	  Estimate the storage space in bytes for a given number of tuples
+ *	  of a given width (size in bytes).
+ */
+static double
+relation_byte_size(double tuples, int width)
+{
+	return tuples * (MAXALIGN(width) + MAXALIGN(SizeofHeapTupleHeader));
+}
+
+/*
+ * page_size
+ *	  Returns an estimate of the number of pages covered by a given
+ *	  number of tuples of a given width (size in bytes).
+ */
+static double
+page_size(double tuples, int width)
+{
+	return ceil(relation_byte_size(tuples, width) / BLCKSZ);
+}
+
+/*
+ * Estimate the fraction of the work that each worker will do given the
+ * number of workers budgeted for the path.
+ */
+static double
+get_parallel_divisor(Path *path)
+{
+	double		parallel_divisor = path->parallel_workers;
+
+	/*
+	 * Early experience with parallel query suggests that when there is only
+	 * one worker, the leader often makes a very substantial contribution to
+	 * executing the parallel portion of the plan, but as more workers are
+	 * added, it does less and less, because it's busy reading tuples from the
+	 * workers and doing whatever non-parallel post-processing is needed.  By
+	 * the time we reach 4 workers, the leader no longer makes a meaningful
+	 * contribution.  Thus, for now, estimate that the leader spends 30% of
+	 * its time servicing each worker, and the remainder executing the
+	 * parallel plan.
+	 */
+	if (parallel_leader_participation)
+	{
+		double		leader_contribution;
+
+		leader_contribution = 1.0 - (0.3 * path->parallel_workers);
+		if (leader_contribution > 0)
+			parallel_divisor += leader_contribution;
+	}
+
+	return parallel_divisor;
+}
+
+/*
+ * compute_bitmap_pages
+ *
+ * compute number of pages fetched from heap in bitmap heap scan.
+ */
+double
+compute_bitmap_pages(PlannerInfo *root, RelOptInfo *baserel, Path *bitmapqual,
+					 int loop_count, Cost *cost, double *tuple)
+{
+	Cost		indexTotalCost;
+	Selectivity indexSelectivity;
+	double		T;
+	double		pages_fetched;
+	double		tuples_fetched;
+	double		heap_pages;
+	long		maxentries;
+
+	/*
+	 * Fetch total cost of obtaining the bitmap, as well as its total
+	 * selectivity.
+	 */
+	cost_bitmap_tree_node(bitmapqual, &indexTotalCost, &indexSelectivity);
+
+	/*
+	 * Estimate number of main-table pages fetched.
+	 */
+	tuples_fetched = clamp_row_est(indexSelectivity * baserel->tuples);
+
+	T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
+
+	/*
+	 * For a single scan, the number of heap pages that need to be fetched is
+	 * the same as the Mackert and Lohman formula for the case T <= b (ie, no
+	 * re-reads needed).
+	 */
+	pages_fetched = (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
+
+	/*
+	 * Calculate the number of pages fetched from the heap.  Then based on
+	 * current work_mem estimate get the estimated maxentries in the bitmap.
+	 * (Note that we always do this calculation based on the number of pages
+	 * that would be fetched in a single iteration, even if loop_count > 1.
+	 * That's correct, because only that number of entries will be stored in
+	 * the bitmap at one time.)
+	 */
+	heap_pages = Min(pages_fetched, baserel->pages);
+	maxentries = tbm_calculate_entries(work_mem * 1024L);
+
+	if (loop_count > 1)
+	{
+		/*
+		 * For repeated bitmap scans, scale up the number of tuples fetched in
+		 * the Mackert and Lohman formula by the number of scans, so that we
+		 * estimate the number of pages fetched by all the scans. Then
+		 * pro-rate for one scan.
+		 */
+		pages_fetched = index_pages_fetched(tuples_fetched * loop_count,
+											baserel->pages,
+											get_indexpath_pages(bitmapqual),
+											root);
+		pages_fetched /= loop_count;
+	}
+
+	if (pages_fetched >= T)
+		pages_fetched = T;
+	else
+		pages_fetched = ceil(pages_fetched);
+
+	if (maxentries < heap_pages)
+	{
+		double		exact_pages;
+		double		lossy_pages;
+
+		/*
+		 * Crude approximation of the number of lossy pages.  Because of the
+		 * way tbm_lossify() is coded, the number of lossy pages increases
+		 * very sharply as soon as we run short of memory; this formula has
+		 * that property and seems to perform adequately in testing, but it's
+		 * possible we could do better somehow.
+		 */
+		lossy_pages = Max(0, heap_pages - maxentries / 2);
+		exact_pages = heap_pages - lossy_pages;
+
+		/*
+		 * If there are lossy pages then recompute the number of tuples
+		 * processed by the bitmap heap node.  We assume here that the chance
+		 * of a given tuple coming from an exact page is the same as the
+		 * chance that a given page is exact.  This might not be true, but
+		 * it's not clear how we can do any better.
+		 */
+		if (lossy_pages > 0)
+			tuples_fetched =
+				clamp_row_est(indexSelectivity *
+							  (exact_pages / heap_pages) * baserel->tuples +
+							  (lossy_pages / heap_pages) * baserel->tuples);
+	}
+
+	if (cost)
+		*cost = indexTotalCost;
+	if (tuple)
+		*tuple = tuples_fetched;
+
+	return pages_fetched;
+}