/*-------------------------------------------------------------------------
 *
 * 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 master 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.  (Also, these routines guarantee not to
 * set the rows count to zero, so there will be no zero divide.)  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) 1996-2016, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *	  src/backend/optimizer/path/costsize.c
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#ifdef _MSC_VER
#include <float.h>				/* for _isnan */
#endif
#include <math.h>

#include "access/amapi.h"
#include "access/htup_details.h"
#include "access/tsmapi.h"
#include "executor/executor.h"
#include "executor/nodeHash.h"
#include "miscadmin.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/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)


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;

int			effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;

Cost		disable_cost = 1.0e10;

int			max_parallel_degree = 0;

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_hashagg = true;
bool		enable_nestloop = true;
bool		enable_material = true;
bool		enable_mergejoin = true;
bool		enable_hashjoin = true;

typedef struct
{
	PlannerInfo *root;
	QualCost	total;
} cost_qual_eval_context;

static List *extract_nonindex_conditions(List *qual_clauses, List *indexquals);
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 *joinpath);
static double approx_tuple_count(PlannerInfo *root, JoinPath *path,
				   List *quals);
static double calc_joinrel_size_estimate(PlannerInfo *root,
						   double outer_rows,
						   double inner_rows,
						   SpecialJoinInfo *sjinfo,
						   List *restrictlist);
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);


/*
 * clamp_row_est
 *		Force a row-count estimate to a sane value.
 */
double
clamp_row_est(double nrows)
{
	/*
	 * Force 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 <= 1.0)
		nrows = 1.0;
	else
		nrows = rint(nrows);

	return nrows;
}


/*
 * 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
 * 'nworkers' are the number of workers among which the work will be
 *			distributed if the scan is parallel scan
 */
void
cost_seqscan(Path *path, PlannerInfo *root,
			 RelOptInfo *baserel, ParamPathInfo *param_info,
			 int nworkers)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	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
	 */
	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;
	run_cost += cpu_per_tuple * baserel->tuples;

	/*
	 * Primitive parallel cost model.  Assume the leader will do half as much
	 * work as a regular worker, because it will also need to read the tuples
	 * returned by the workers when they percolate up to the gather node. This
	 * is almost certainly not exactly the right way to model this, so this
	 * will probably need to be changed at some point...
	 */
	if (nworkers > 0)
		run_cost = run_cost / (nworkers + 0.5);

	path->startup_cost = startup_cost;
	path->total_cost = startup_cost + 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;

	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
 */
void
cost_gather(GatherPath *path, PlannerInfo *root,
			RelOptInfo *rel, ParamPathInfo *param_info)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;

	/* Mark the path with the correct row estimate */
	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_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)
{
	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		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;

	/* 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.
	 */
	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(baserel->baserestrictinfo,
												   path->indexquals),
			  extract_nonindex_conditions(path->path.param_info->ppi_clauses,
										  path->indexquals));
	}
	else
	{
		path->path.rows = baserel->rows;
		/* qpquals come from just the rel's restriction clauses */
		qpquals = extract_nonindex_conditions(baserel->baserestrictinfo,
											  path->indexquals);
	}

	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
	 * relation.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);

	/*
	 * 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));

		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));

		/* 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;
	}

	/*
	 * 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;

	run_cost += cpu_per_tuple * tuples_fetched;

	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).  The actual rules for this appear in create_indexscan_plan() in
 * createplan.c, but the full rules are fairly expensive and we don't want to
 * go to that much effort for index paths that don't get selected for the
 * final plan.  So we approximate it as quals that don't appear directly in
 * indexquals and also are not redundant children of the same EquivalenceClass
 * as some indexqual.  This method neglects some infrequently-relevant
 * considerations such as clauses that needn't be checked because they are
 * implied by a partial index's predicate.  It does not seem worth the cycles
 * to try to factor those things in at this stage, even though createplan.c
 * will take pains to remove such unnecessary clauses from the qpquals list if
 * this path is selected for use.
 */
static List *
extract_nonindex_conditions(List *qual_clauses, List *indexquals)
{
	List	   *result = NIL;
	ListCell   *lc;

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

		Assert(IsA(rinfo, RestrictInfo));
		if (rinfo->pseudoconstant)
			continue;			/* we may drop pseudoconstants here */
		if (list_member_ptr(indexquals, rinfo))
			continue;			/* simple duplicate */
		if (is_redundant_derived_clause(rinfo, indexquals))
			continue;			/* derived from same EquivalenceClass */
		/* ... skip the predicate proof attempts 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 query_planner.
 *
 * 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;
	Selectivity indexSelectivity;
	QualCost	qpqual_cost;
	Cost		cpu_per_tuple;
	Cost		cost_per_page;
	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;

	/*
	 * Fetch total cost of obtaining the bitmap, as well as its total
	 * selectivity.
	 */
	cost_bitmap_tree_node(bitmapqual, &indexTotalCost, &indexSelectivity);

	startup_cost += indexTotalCost;

	/* 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.
	 */
	tuples_fetched = clamp_row_est(indexSelectivity * baserel->tuples);

	T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;

	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;
	}
	else
	{
		/*
		 * 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);
	}
	if (pages_fetched >= T)
		pages_fetched = T;
	else
		pages_fetched = ceil(pages_fetched);

	/*
	 * 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;

	run_cost += cpu_per_tuple * tuples_fetched;

	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)
	{
		if (IsA(lfirst(l), ScalarArrayOpExpr))
		{
			/* Each element of the array yields 1 tuple */
			ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) lfirst(l);
			Node	   *arraynode = (Node *) lsecond(saop->args);

			ntuples += estimate_array_length(arraynode);
		}
		else if (IsA(lfirst(l), 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;

	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(Path *path, PlannerInfo *root,
				  RelOptInfo *baserel, ParamPathInfo *param_info)
{
	Cost		startup_cost;
	Cost		run_cost;
	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);

	/* Mark the path with the correct row estimate */
	if (param_info)
		path->rows = param_info->ppi_rows;
	else
		path->rows = baserel->rows;

	/*
	 * Cost of path is cost of evaluating the subplan, plus cost of evaluating
	 * any restriction clauses that will be attached to the SubqueryScan node,
	 * plus cpu_tuple_cost to account for selection and projection overhead.
	 */
	path->startup_cost = baserel->subplan->startup_cost;
	path->total_cost = baserel->subplan->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 * baserel->tuples;

	path->startup_cost += startup_cost;
	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;

	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;

	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;

	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 Plans for the nonrecursive and recursive terms.
 *
 * Note that the arguments and output are Plans, not Paths as in most of
 * the rest of this module.  That's because we don't bother setting up a
 * Path representation for recursive union --- we have only one way to do it.
 */
void
cost_recursive_union(Plan *runion, Plan *nrterm, Plan *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->plan_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->plan_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->plan_rows = total_rows;
	runion->plan_width = Max(nrterm->plan_width, rterm->plan_width);
}

/*
 * cost_sort
 *	  Determines and returns the cost of sorting a relation, 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 twice sort_mem, we have
 *		disk traffic = 2 * relsize * ceil(logM(p / (2*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.
 *
 * 'pathkeys' is a list of sort keys
 * 'input_cost' is the total cost for reading the input data
 * '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
 *
 * 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 = input_cost;
	Cost		run_cost = 0;
	double		input_bytes = relation_byte_size(tuples, width);
	double		output_bytes;
	double		output_tuples;
	long		sort_mem_bytes = sort_mem * 1024L;

	if (!enable_sort)
		startup_cost += disable_cost;

	path->rows = tuples;

	/*
	 * 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) * 0.5;
		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;

	path->startup_cost = startup_cost;
	path->total_cost = startup_cost + run_cost;
}

/*
 * 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 delete the top heap entry and another log2(N) comparisons
 * to insert its successor from the same stream.
 *
 * (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 * 2.0 * logN;

	/*
	 * Also charge a small amount (arbitrarily set equal to operator cost) per
	 * extracted tuple.  We don't charge cpu_tuple_cost because a MergeAppend
	 * node doesn't do qual-checking or projection, so it has less overhead
	 * than most plan nodes.
	 */
	run_cost += cpu_operator_cost * 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_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,
		 Cost input_startup_cost, Cost input_total_cost,
		 double input_tuples)
{
	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 (with any startup cost of course
	 * charged but once).  The finalCost component is charged once per output
	 * tuple, corresponding to the costs of evaluating the finalfns.
	 *
	 * 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;
		/* we aren't grouping */
		total_cost = startup_cost + cpu_tuple_cost;
		output_tuples = 1;
	}
	else if (aggstrategy == AGG_SORTED)
	{
		/* Here we are able to deliver output on-the-fly */
		startup_cost = input_startup_cost;
		total_cost = input_total_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 * numGroups;
		total_cost += cpu_tuple_cost * numGroups;
		output_tuples = numGroups;
	}
	else
	{
		/* must be AGG_HASHED */
		startup_cost = input_total_cost;
		startup_cost += aggcosts->transCost.startup;
		startup_cost += aggcosts->transCost.per_tuple * input_tuples;
		startup_cost += (cpu_operator_cost * numGroupCols) * input_tuples;
		total_cost = startup_cost;
		total_cost += aggcosts->finalCost * numGroups;
		total_cost += cpu_tuple_cost * numGroups;
		output_tuples = numGroups;
	}

	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 = (WindowFunc *) lfirst(lc);
		Cost		wfunccost;
		QualCost	argcosts;

		Assert(IsA(wfunc, WindowFunc));

		wfunccost = get_func_cost(wfunc->winfnoid) * cpu_operator_cost;

		/* 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,
		   Cost input_startup_cost, Cost input_total_cost,
		   double input_tuples)
{
	Cost		startup_cost;
	Cost		total_cost;

	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;

	path->rows = numGroups;
	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
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'semifactors' contains valid data if jointype is SEMI or ANTI
 */
void
initial_cost_nestloop(PlannerInfo *root, JoinCostWorkspace *workspace,
					  JoinType jointype,
					  Path *outer_path, Path *inner_path,
					  SpecialJoinInfo *sjinfo,
					  SemiAntiJoinFactors *semifactors)
{
	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)
	{
		/*
		 * SEMI or ANTI join: executor will stop after 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
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'semifactors' contains valid data if path->jointype is SEMI or ANTI
 */
void
final_cost_nestloop(PlannerInfo *root, NestPath *path,
					JoinCostWorkspace *workspace,
					SpecialJoinInfo *sjinfo,
					SemiAntiJoinFactors *semifactors)
{
	Path	   *outer_path = path->outerjoinpath;
	Path	   *inner_path = path->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;

	/* Mark the path with the correct row estimate */
	if (path->path.param_info)
		path->path.rows = path->path.param_info->ppi_rows;
	else
		path->path.rows = path->path.parent->rows;

	/*
	 * 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->jointype == JOIN_SEMI || path->jointype == JOIN_ANTI)
	{
		/*
		 * SEMI or ANTI join: executor will stop after first match.
		 */
		Cost		inner_run_cost = workspace->inner_run_cost;
		Cost		inner_rescan_run_cost = workspace->inner_rescan_run_cost;
		double		outer_matched_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 * semifactors->outer_match_frac);
		inner_scan_frac = 2.0 / (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_path_rows - outer_matched_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.
			 */
			run_cost += inner_run_cost;

			/* Add inner run cost for additional outer tuples having matches */
			if (outer_matched_rows > 1)
				run_cost += (outer_matched_rows - 1) * inner_rescan_run_cost * inner_scan_frac;

			/* Add inner run cost for unmatched outer tuples */
			run_cost += (outer_path_rows - outer_matched_rows) *
				inner_rescan_run_cost;

			/* And count the unmatched join tuples as being processed */
			ntuples += (outer_path_rows - outer_matched_rows) *
				inner_path_rows;
		}
	}
	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->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;

	path->path.startup_cost = startup_cost;
	path->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
 * 'sjinfo' is extra info about the join for selectivity estimation
 *
 * 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,
					   SpecialJoinInfo *sjinfo)
{
	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 or NaN */
	if (outer_path_rows <= 0 || isnan(outer_path_rows))
		outer_path_rows = 1;
	if (inner_path_rows <= 0 || isnan(inner_path_rows))
		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->parent->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->parent->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 one actual decision:
 * whether we should materialize the inner path.  We do that either because
 * the inner path can't support mark/restore, or because it's cheaper to
 * use an interposed Material node to handle mark/restore.  When the decision
 * is cost-based it would be logically cleaner to build and cost two separate
 * paths with and without that flag set; 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 both paths.  So it seems best to make
 * the decision here and record it in the path's materialize_inner field.
 *
 * 'path' is already filled in except for the rows and cost fields and
 *		materialize_inner
 * 'workspace' is the result from initial_cost_mergejoin
 * 'sjinfo' is extra info about the join for selectivity estimation
 */
void
final_cost_mergejoin(PlannerInfo *root, MergePath *path,
					 JoinCostWorkspace *workspace,
					 SpecialJoinInfo *sjinfo)
{
	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 or NaN */
	if (inner_path_rows <= 0 || isnan(inner_path_rows))
		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;

	/*
	 * 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;

	/*
	 * 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.
	 */
	if (IsA(outer_path, UniquePath))
		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 */
	rescanratio = 1.0 + (rescannedtuples / inner_path_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_path_rows * rescanratio;

	/*
	 * Prefer materializing if it looks cheaper, unless the user has asked to
	 * suppress materialization.
	 */
	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->parent->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;

	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
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'semifactors' contains valid data if jointype is SEMI or ANTI
 */
void
initial_cost_hashjoin(PlannerInfo *root, JoinCostWorkspace *workspace,
					  JoinType jointype,
					  List *hashclauses,
					  Path *outer_path, Path *inner_path,
					  SpecialJoinInfo *sjinfo,
					  SemiAntiJoinFactors *semifactors)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	double		outer_path_rows = outer_path->rows;
	double		inner_path_rows = inner_path->rows;
	int			num_hashclauses = list_length(hashclauses);
	int			numbuckets;
	int			numbatches;
	int			num_skew_mcvs;

	/* 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;

	/*
	 * 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_WORK_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,
							inner_path->parent->width,
							true,		/* useskew */
							&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->parent->width);
		double		innerpages = page_size(inner_path_rows,
										   inner_path->parent->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;
}

/*
 * 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
 * 'sjinfo' is extra info about the join for selectivity estimation
 * 'semifactors' contains valid data if path->jointype is SEMI or ANTI
 */
void
final_cost_hashjoin(PlannerInfo *root, HashPath *path,
					JoinCostWorkspace *workspace,
					SpecialJoinInfo *sjinfo,
					SemiAntiJoinFactors *semifactors)
{
	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;
	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;
	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;

	/*
	 * 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;

	/* and compute the number of "virtual" buckets in the whole join */
	virtualbuckets = (double) numbuckets *(double) numbatches;

	/*
	 * Determine bucketsize fraction for inner relation.  We use the smallest
	 * bucketsize 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;
	else
	{
		innerbucketsize = 1.0;
		foreach(hcl, hashclauses)
		{
			RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(hcl);
			Selectivity thisbucketsize;

			Assert(IsA(restrictinfo, RestrictInfo));

			/*
			 * 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 bucketsize estimate 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 */
					thisbucketsize =
						estimate_hash_bucketsize(root,
										   get_rightop(restrictinfo->clause),
												 virtualbuckets);
					restrictinfo->right_bucketsize = thisbucketsize;
				}
			}
			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 */
					thisbucketsize =
						estimate_hash_bucketsize(root,
											get_leftop(restrictinfo->clause),
												 virtualbuckets);
					restrictinfo->left_bucketsize = thisbucketsize;
				}
			}

			if (innerbucketsize > thisbucketsize)
				innerbucketsize = thisbucketsize;
		}
	}

	/*
	 * 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)
	{
		double		outer_matched_rows;
		Selectivity inner_scan_frac;

		/*
		 * SEMI or ANTI join: executor will stop after 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 * semifactors->outer_match_frac);
		inner_scan_frac = 2.0 / (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_SEMI)
			hashjointuples = outer_matched_rows;
		else
			hashjointuples = outer_path_rows - 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;

	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 */
			sp_cost.per_tuple += plan_run_cost / 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:

			/*
			 * Assume that all of the startup cost represents hash table
			 * building, which we won't have to do over.
			 */
			*rescan_startup_cost = 0;
			*rescan_total_cost = path->total_cost - path->startup_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->parent->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->parent->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;
		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))
	{
		context->total.per_tuple +=
			get_func_cost(((FuncExpr *) node)->funcid) * cpu_operator_cost;
	}
	else if (IsA(node, OpExpr) ||
			 IsA(node, DistinctExpr) ||
			 IsA(node, NullIfExpr))
	{
		/* rely on struct equivalence to treat these all alike */
		set_opfuncid((OpExpr *) node);
		context->total.per_tuple +=
			get_func_cost(((OpExpr *) node)->opfuncid) * cpu_operator_cost;
	}
	else if (IsA(node, ScalarArrayOpExpr))
	{
		/*
		 * Estimate that the operator will be applied to about half of the
		 * array elements before the answer is determined.
		 */
		ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) node;
		Node	   *arraynode = (Node *) lsecond(saop->args);

		set_sa_opfuncid(saop);
		context->total.per_tuple += get_func_cost(saop->opfuncid) *
			cpu_operator_cost * 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 in execQual.c.  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, CoerceViaIO))
	{
		CoerceViaIO *iocoerce = (CoerceViaIO *) node;
		Oid			iofunc;
		Oid			typioparam;
		bool		typisvarlena;

		/* check the result type's input function */
		getTypeInputInfo(iocoerce->resulttype,
						 &iofunc, &typioparam);
		context->total.per_tuple += get_func_cost(iofunc) * cpu_operator_cost;
		/* check the input type's output function */
		getTypeOutputInfo(exprType((Node *) iocoerce->arg),
						  &iofunc, &typisvarlena);
		context->total.per_tuple += get_func_cost(iofunc) * cpu_operator_cost;
	}
	else if (IsA(node, ArrayCoerceExpr))
	{
		ArrayCoerceExpr *acoerce = (ArrayCoerceExpr *) node;
		Node	   *arraynode = (Node *) acoerce->arg;

		if (OidIsValid(acoerce->elemfuncid))
			context->total.per_tuple += get_func_cost(acoerce->elemfuncid) *
				cpu_operator_cost * estimate_array_length(arraynode);
	}
	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);

			context->total.per_tuple += get_func_cost(get_opcode(opid)) *
				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);
	}

	/* 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 or ANTI 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.
 * 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:
 *	outerrel: outer relation under consideration
 *	innerrel: inner relation under consideration
 *	jointype: must be JOIN_SEMI or JOIN_ANTI
 *	sjinfo: SpecialJoinInfo relevant to this join
 *	restrictlist: join quals
 * Output parameters:
 *	*semifactors is filled in (see relation.h for field definitions)
 */
void
compute_semi_anti_join_factors(PlannerInfo *root,
							   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;

	/* Should only be called in these cases */
	Assert(jointype == JOIN_SEMI || jointype == JOIN_ANTI);

	/*
	 * 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.
	 */
	if (jointype == JOIN_ANTI)
	{
		joinquals = NIL;
		foreach(l, restrictlist)
		{
			RestrictInfo *rinfo = (RestrictInfo *) lfirst(l);

			Assert(IsA(rinfo, RestrictInfo));
			if (!rinfo->is_pushed_down)
				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,
									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 (jointype == JOIN_ANTI)
		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 *joinpath)
{
	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 (!(list_member_ptr(indexclauses, rinfo) ||
				  is_redundant_derived_clause(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(list_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 width 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,
										   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_rows', 'inner_rows' are the sizes of the (probably also
 *		parameterized) join inputs under consideration.
 * '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,
							   double outer_rows,
							   double inner_rows,
							   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,
									   outer_rows,
									   inner_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.
 */
static double
calc_joinrel_size_estimate(PlannerInfo *root,
						   double outer_rows,
						   double inner_rows,
						   SpecialJoinInfo *sjinfo,
						   List *restrictlist)
{
	JoinType	jointype = sjinfo->jointype;
	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.
	 *
	 * 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 = (RestrictInfo *) lfirst(l);

			Assert(IsA(rinfo, RestrictInfo));
			if (rinfo->is_pushed_down)
				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 * jselec;
			break;
		case JOIN_LEFT:
			nrows = outer_rows * inner_rows * jselec;
			if (nrows < outer_rows)
				nrows = outer_rows;
			nrows *= pselec;
			break;
		case JOIN_FULL:
			nrows = outer_rows * inner_rows * jselec;
			if (nrows < outer_rows)
				nrows = outer_rows;
			if (nrows < inner_rows)
				nrows = inner_rows;
			nrows *= pselec;
			break;
		case JOIN_SEMI:
			nrows = outer_rows * jselec;
			/* pselec not used */
			break;
		case JOIN_ANTI:
			nrows = outer_rows * (1.0 - 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);
}

/*
 * 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 plan for the subquery must have been completed.
 * We look at the subquery's plan and 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;
	RangeTblEntry *rte PG_USED_FOR_ASSERTS_ONLY;
	ListCell   *lc;

	/* Should only be applied to base relations that are subqueries */
	Assert(rel->relid > 0);
	rte = planner_rt_fetch(rel->relid, root);
	Assert(rte->rtekind == RTE_SUBQUERY);

	/* Copy raw number of output rows from subplan */
	rel->tuples = rel->subplan->plan_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 = (TargetEntry *) lfirst(lc);
		Node	   *texpr = (Node *) te->expr;
		int32		item_width = 0;

		Assert(IsA(te, TargetEntry));
		/* 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(rtfunc->funcexpr);

		if (ntup > rel->tuples)
			rel->tuples = ntup;
	}

	/* 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 the completed plan for 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, Plan *cteplan)
{
	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, arbitrarily assume the average worktable size
		 * is about 10 times the nonrecursive term's size.
		 */
		rel->tuples = 10 * cteplan->plan_rows;
	}
	else
	{
		/* Otherwise just believe the CTE plan's output estimate */
		rel->tuples = cteplan->plan_rows;
	}

	/* 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.
 *
 * 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.
 */
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;

	foreach(lc, rel->reltargetlist)
	{
		Node	   *node = (Node *) lfirst(lc);

		/*
		 * Ordinarily, a Var in a rel's reltargetlist 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))
		{
			PlaceHolderVar *phv = (PlaceHolderVar *) node;
			PlaceHolderInfo *phinfo = find_placeholder_info(root, phv, false);

			tuple_width += phinfo->ph_width;
		}
		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;

			item_width = get_typavgwidth(exprType(node), exprTypmod(node));
			Assert(item_width > 0);
			tuple_width += item_width;
		}
	}

	/*
	 * 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->width = tuple_width;
}

/*
 * 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);
}