/*-------------------------------------------------------------------------
 *
 * costsize.c
 *	  Routines to compute (and set) relation sizes and path costs
 *
 * Path costs are measured in units of disk accesses: one sequential page
 * fetch has cost 1.  All else is scaled relative to a page fetch, using
 * the scaling parameters
 *
 *	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 process a typical WHERE operator
 *
 * 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.
 *
 * 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->parent->rows;
 * Note that a relation's rows count (and, by extension, a Plan's plan_rows)
 * 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.)  RelOptInfos, Paths, and Plans themselves never
 * account for LIMIT.
 *
 * 
 * Portions Copyright (c) 1996-2000, PostgreSQL, Inc
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *	  $Header: /cvsroot/pgsql/src/backend/optimizer/path/costsize.c,v 1.55 2000/03/30 00:53:29 tgl Exp $
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#include <math.h>

#include "miscadmin.h"
#include "nodes/plannodes.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/internal.h"
#include "optimizer/tlist.h"
#include "utils/lsyscache.h"


#define LOG2(x)  (log(x) / 0.693147180559945)
#define LOG6(x)  (log(x) / 1.79175946922805)


double		effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;
Cost		random_page_cost = DEFAULT_RANDOM_PAGE_COST;
Cost		cpu_tuple_cost = DEFAULT_CPU_TUPLE_COST;
Cost		cpu_index_tuple_cost = DEFAULT_CPU_INDEX_TUPLE_COST;
Cost		cpu_operator_cost = DEFAULT_CPU_OPERATOR_COST;

Cost		disable_cost = 100000000.0;

bool		enable_seqscan = true;
bool		enable_indexscan = true;
bool		enable_tidscan = true;
bool		enable_sort = true;
bool		enable_nestloop = true;
bool		enable_mergejoin = true;
bool		enable_hashjoin = true;


static bool cost_qual_eval_walker(Node *node, Cost *total);
static void set_rel_width(Query *root, RelOptInfo *rel);
static int	compute_attribute_width(TargetEntry *tlistentry);
static double relation_byte_size(double tuples, int width);
static double page_size(double tuples, int width);


/*
 * cost_seqscan
 *	  Determines and returns the cost of scanning a relation sequentially.
 *
 * If the relation is a temporary to be materialized from a query
 * embedded within a data field (determined by 'relid' containing an
 * attribute reference), then a predetermined constant is returned (we
 * have NO IDEA how big the result of a POSTQUEL procedure is going to be).
 *
 * Note: for historical reasons, this routine and the others in this module
 * use the passed result Path only to store their startup_cost and total_cost
 * results into.  All the input data they need is passed as separate
 * parameters, even though much of it could be extracted from the result Path.
 */
void
cost_seqscan(Path *path, RelOptInfo *baserel)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	Cost		cpu_per_tuple;

	/* Should only be applied to base relations */
	Assert(length(baserel->relids) == 1);

	if (!enable_seqscan)
		startup_cost += disable_cost;

	/* disk costs */
	if (lfirsti(baserel->relids) < 0)
	{
		/*
		 * cost of sequentially scanning a materialized temporary relation
		 */
		run_cost += _NONAME_SCAN_COST_;
	}
	else
	{
		/*
		 * The cost of reading a page sequentially is 1.0, by definition.
		 * Note that the Unix kernel will typically do some amount of
		 * read-ahead optimization, so that this cost is less than the true
		 * cost of reading a page from disk.  We ignore that issue here,
		 * but must take it into account when estimating the cost of
		 * non-sequential accesses!
		 */
		run_cost += baserel->pages;	/* sequential fetches with cost 1.0 */
	}

	/* CPU costs */
	cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
	run_cost += cpu_per_tuple * baserel->tuples;

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

/*
 * cost_nonsequential_access
 *	  Estimate the cost of accessing one page at random from a relation
 *	  (or sort temp file) of the given size in pages.
 *
 * The simplistic model that the cost is random_page_cost is what we want
 * to use for large relations; but for small ones that is a serious
 * overestimate because of the effects of caching.  This routine tries to
 * account for that.
 *
 * Unfortunately we don't have any good way of estimating the effective cache
 * size we are working with --- we know that Postgres itself has NBuffers
 * internal buffers, but the size of the kernel's disk cache is uncertain,
 * and how much of it we get to use is even less certain.  We punt the problem
 * for now by assuming we are given an effective_cache_size parameter.
 *
 * Given a guesstimated cache size, we estimate the actual I/O cost per page
 * with the entirely ad-hoc equations:
 *	for rel_size <= effective_cache_size:
 *		1 + (random_page_cost/2-1) * (rel_size/effective_cache_size) ** 2
 *	for rel_size >= effective_cache_size:
 *		random_page_cost * (1 - (effective_cache_size/rel_size)/2)
 * These give the right asymptotic behavior (=> 1.0 as rel_size becomes
 * small, => random_page_cost as it becomes large) and meet in the middle
 * with the estimate that the cache is about 50% effective for a relation
 * of the same size as effective_cache_size.  (XXX this is probably all
 * wrong, but I haven't been able to find any theory about how effective
 * a disk cache should be presumed to be.)
 */
static Cost
cost_nonsequential_access(double relpages)
{
	double		relsize;

	/* don't crash on bad input data */
	if (relpages <= 0.0 || effective_cache_size <= 0.0)
		return random_page_cost;

	relsize = relpages / effective_cache_size;

	if (relsize >= 1.0)
		return random_page_cost * (1.0 - 0.5 / relsize);
	else
		return 1.0 + (random_page_cost * 0.5 - 1.0) * relsize * relsize;
}

/*
 * cost_index
 *	  Determines and returns the cost of scanning a relation using an index.
 *
 *	  NOTE: an indexscan plan node can actually represent several passes,
 *	  but here we consider the cost of just one pass.
 *
 * 'root' is the query root
 * 'baserel' is the base relation the index is for
 * 'index' is the index to be used
 * 'indexQuals' is the list of applicable qual clauses (implicit AND semantics)
 * 'is_injoin' is T if we are considering using the index scan as the inside
 *		of a nestloop join (hence, some of the indexQuals are join clauses)
 *
 * NOTE: '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(Path *path, Query *root,
		   RelOptInfo *baserel,
		   IndexOptInfo *index,
		   List *indexQuals,
		   bool is_injoin)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	Cost		cpu_per_tuple;
	Cost		indexStartupCost;
	Cost		indexTotalCost;
	Selectivity	indexSelectivity;
	double		tuples_fetched;
	double		pages_fetched;

	/* Should only be applied to base relations */
	Assert(IsA(baserel, RelOptInfo) && IsA(index, IndexOptInfo));
	Assert(length(baserel->relids) == 1);

	if (!enable_indexscan && !is_injoin)
		startup_cost += disable_cost;

	/*
	 * 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).
	 */
	fmgr(index->amcostestimate, root, baserel, index, indexQuals,
		 &indexStartupCost, &indexTotalCost, &indexSelectivity);

	/* all costs for touching index itself included here */
	startup_cost += indexStartupCost;
	run_cost += indexTotalCost - indexStartupCost;

	/*
	 * Estimate number of main-table tuples and pages fetched.
	 *
	 * If the number of tuples is much smaller than the number of pages in
	 * the relation, each tuple will cost a separate nonsequential fetch.
	 * If it is comparable or larger, then probably we will be able to avoid
	 * some fetches.  We use a growth rate of log(#tuples/#pages + 1) ---
	 * probably totally bogus, but intuitively it gives the right shape of
	 * curve at least.
	 *
	 * XXX if the relation has recently been "clustered" using this index,
	 * then in fact the target tuples will be highly nonuniformly distributed,
	 * and we will be seriously overestimating the scan cost!  Currently we
	 * have no way to know whether the relation has been clustered, nor how
	 * much it's been modified since the last clustering, so we ignore this
	 * effect.  Would be nice to do better someday.
	 */

	tuples_fetched = ceil(indexSelectivity * baserel->tuples);

	if (tuples_fetched > 0 && baserel->pages > 0)
		pages_fetched = ceil(baserel->pages *
							 log(tuples_fetched / baserel->pages + 1.0));
	else
		pages_fetched = tuples_fetched;

	/*
	 * Now estimate one nonsequential access per page fetched,
	 * plus appropriate CPU costs per tuple.
	 */

	/* disk costs for main table */
	run_cost += pages_fetched * cost_nonsequential_access(baserel->pages);

	/* CPU costs */
	cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
	/*
	 * Normally the indexquals will be removed from the list of restriction
	 * clauses that we have to evaluate as qpquals, so we should subtract
	 * their costs from baserestrictcost.  For a lossy index, however, we
	 * will have to recheck all the quals and so mustn't subtract anything.
	 * Also, if we are doing a join then some of the indexquals are join
	 * clauses and shouldn't be subtracted.  Rather than work out exactly
	 * how much to subtract, we don't subtract anything in that case either.
	 */
	if (! index->lossy && ! is_injoin)
		cpu_per_tuple -= cost_qual_eval(indexQuals);

	run_cost += cpu_per_tuple * tuples_fetched;

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

/*
 * cost_tidscan
 *	  Determines and returns the cost of scanning a relation using tid-s.
 */
void
cost_tidscan(Path *path, RelOptInfo *baserel, List *tideval)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	Cost		cpu_per_tuple;
	int			ntuples = length(tideval);

	if (!enable_tidscan)
		startup_cost += disable_cost;

	/* disk costs --- assume each tuple on a different page */
	run_cost += random_page_cost * ntuples;

	/* CPU costs */
	cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
	run_cost += cpu_per_tuple * ntuples;

	path->startup_cost = startup_cost;
	path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_sort
 *	  Determines and returns the cost of sorting a relation.
 *
 * The cost of supplying the input data is NOT included; the caller should
 * add that cost to both startup and total costs returned from this routine!
 *
 * If the total volume of data to sort is less than SortMem, 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 SortMem, 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(log6(r)) merge passes where r is the
 * number of initial runs formed (log6 because tuplesort.c uses six-tape
 * merging).  Since the average initial run should be about twice SortMem,
 * we have
 *		disk traffic = 2 * relsize * ceil(log6(p / (2*SortMem)))
 *		cpu = comparison_cost * t * log2(t)
 *
 * The disk traffic is assumed to be half sequential and half random
 * accesses (XXX can't we refine that guess?)
 *
 * We charge two operator evals per tuple comparison, which should be in
 * the right ballpark in most cases.
 *
 * 'pathkeys' is a list of sort keys
 * 'tuples' is the number of tuples in the relation
 * 'width' is the average tuple width in bytes
 *
 * 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.
 */
void
cost_sort(Path *path, List *pathkeys, double tuples, int width)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	double		nbytes = relation_byte_size(tuples, width);
	long		sortmembytes = SortMem * 1024L;

	if (!enable_sort)
		startup_cost += disable_cost;

	/*
	 * 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;

	/*
	 * CPU costs
	 *
	 * Assume about two operator evals per tuple comparison
	 * and N log2 N comparisons
	 */
	startup_cost += 2.0 * cpu_operator_cost * tuples * LOG2(tuples);

	/* disk costs */
	if (nbytes > sortmembytes)
	{
		double		npages = ceil(nbytes / BLCKSZ);
		double		nruns = nbytes / (sortmembytes * 2);
		double		log_runs = ceil(LOG6(nruns));
		double		npageaccesses;

		if (log_runs < 1.0)
			log_runs = 1.0;
		npageaccesses = 2.0 * npages * log_runs;
		/* Assume half are sequential (cost 1), half are not */
		startup_cost += npageaccesses *
			(1.0 + cost_nonsequential_access(npages)) * 0.5;
	}

	/*
	 * Note: should we bother to assign a nonzero run_cost to reflect the
	 * overhead of extracting tuples from the sort result?  Probably not
	 * worth worrying about.
	 */
	path->startup_cost = startup_cost;
	path->total_cost = startup_cost + run_cost;
}


/*
 * cost_nestloop
 *	  Determines and returns the cost of joining two relations using the
 *	  nested loop algorithm.
 *
 * 'outer_path' is the path for the outer relation
 * 'inner_path' is the path for the inner relation
 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
 */
void
cost_nestloop(Path *path,
			  Path *outer_path,
			  Path *inner_path,
			  List *restrictlist)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	Cost		cpu_per_tuple;
	double		ntuples;

	if (!enable_nestloop)
		startup_cost += disable_cost;

	/* cost of source data */
	/*
	 * NOTE: we assume that the inner path's startup_cost is paid once, not
	 * over again on each restart.  This is certainly correct if the inner
	 * path is materialized.  Are there any cases where it is wrong?
	 */
	startup_cost += outer_path->startup_cost + inner_path->startup_cost;
	run_cost += outer_path->total_cost - outer_path->startup_cost;
	run_cost += outer_path->parent->rows *
		(inner_path->total_cost - inner_path->startup_cost);

	/* Number of tuples processed (not number emitted!).  If inner path is
	 * an indexscan, be sure to use its estimated output row count, which
	 * may be lower than the restriction-clause-only row count of its parent.
	 */
	if (IsA(inner_path, IndexPath))
		ntuples = ((IndexPath *) inner_path)->rows;
	else
		ntuples = inner_path->parent->rows;
	ntuples *= outer_path->parent->rows;

	/* CPU costs */
	cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
	run_cost += cpu_per_tuple * ntuples;

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

/*
 * cost_mergejoin
 *	  Determines and returns the cost of joining two relations using the
 *	  merge join algorithm.
 *
 * 'outer_path' is the path for the outer relation
 * 'inner_path' is the path for the inner relation
 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
 * 'outersortkeys' and 'innersortkeys' are lists of the keys to be used
 *				to sort the outer and inner relations, or NIL if no explicit
 *				sort is needed because the source path is already ordered
 */
void
cost_mergejoin(Path *path,
			   Path *outer_path,
			   Path *inner_path,
			   List *restrictlist,
			   List *outersortkeys,
			   List *innersortkeys)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	Cost		cpu_per_tuple;
	double		ntuples;
	Path		sort_path;		/* dummy for result of cost_sort */

	if (!enable_mergejoin)
		startup_cost += disable_cost;

	/* cost of source data */
	/*
	 * Note we are assuming that each source tuple is fetched just once,
	 * which is not right in the presence of equal keys.  If we had a way of
	 * estimating the proportion of equal keys, we could apply a correction
	 * factor...
	 */
	if (outersortkeys)			/* do we need to sort outer? */
	{
		startup_cost += outer_path->total_cost;
		cost_sort(&sort_path,
				  outersortkeys,
				  outer_path->parent->rows,
				  outer_path->parent->width);
		startup_cost += sort_path.startup_cost;
		run_cost += sort_path.total_cost - sort_path.startup_cost;
	}
	else
	{
		startup_cost += outer_path->startup_cost;
		run_cost += outer_path->total_cost - outer_path->startup_cost;
	}

	if (innersortkeys)			/* do we need to sort inner? */
	{
		startup_cost += inner_path->total_cost;
		cost_sort(&sort_path,
				  innersortkeys,
				  inner_path->parent->rows,
				  inner_path->parent->width);
		startup_cost += sort_path.startup_cost;
		run_cost += sort_path.total_cost - sort_path.startup_cost;
	}
	else
	{
		startup_cost += inner_path->startup_cost;
		run_cost += inner_path->total_cost - inner_path->startup_cost;
	}

	/*
	 * Estimate the number of tuples to be processed in the mergejoin itself
	 * as one per tuple in the two source relations.  This could be a drastic
	 * underestimate if there are many equal-keyed tuples in either relation,
	 * but we have no good way of estimating that...
	 */
	ntuples = outer_path->parent->rows + inner_path->parent->rows;

	/* CPU costs */
	cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
	run_cost += cpu_per_tuple * ntuples;

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

/*
 * cost_hashjoin
 *	  Determines and returns the cost of joining two relations using the
 *	  hash join algorithm.
 *
 * 'outer_path' is the path for the outer relation
 * 'inner_path' is the path for the inner relation
 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
 * 'innerdisbursion' is an estimate of the disbursion statistic
 *				for the inner hash key.
 */
void
cost_hashjoin(Path *path,
			  Path *outer_path,
			  Path *inner_path,
			  List *restrictlist,
			  Selectivity innerdisbursion)
{
	Cost		startup_cost = 0;
	Cost		run_cost = 0;
	Cost		cpu_per_tuple;
	double		ntuples;
	double		outerbytes = relation_byte_size(outer_path->parent->rows,
												outer_path->parent->width);
	double		innerbytes = relation_byte_size(inner_path->parent->rows,
												inner_path->parent->width);
	long		hashtablebytes = SortMem * 1024L;

	if (!enable_hashjoin)
		startup_cost += disable_cost;

	/* 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 */
	startup_cost += cpu_operator_cost * inner_path->parent->rows;
	run_cost += cpu_operator_cost * outer_path->parent->rows;

	/* the number of tuple comparisons needed is the number of outer
	 * tuples times the typical hash bucket size, which we estimate
	 * conservatively as the inner disbursion times the inner tuple count.
	 */
	run_cost += cpu_operator_cost * outer_path->parent->rows *
		ceil(inner_path->parent->rows * innerdisbursion);

	/*
	 * Estimate the number of tuples that get through the hashing filter
	 * as one per tuple in the two source relations.  This could be a drastic
	 * underestimate if there are many equal-keyed tuples in either relation,
	 * but we have no good way of estimating that...
	 */
	ntuples = outer_path->parent->rows + inner_path->parent->rows;

	/* CPU costs */
	cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
	run_cost += cpu_per_tuple * ntuples;

	/*
	 * 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 one cost unit per page of I/O (correct since
	 * it should be nice and sequential...).  Writing the inner rel counts
	 * as startup cost, all the rest as run cost.
	 */
	if (innerbytes > hashtablebytes)
	{
		double	outerpages = page_size(outer_path->parent->rows,
									   outer_path->parent->width);
		double	innerpages = page_size(inner_path->parent->rows,
									   inner_path->parent->width);

		startup_cost += innerpages;
		run_cost += innerpages + 2 * outerpages;
	}

	/*
	 * Bias against putting larger relation on inside.  We don't want
	 * an absolute prohibition, though, since larger relation might have
	 * better disbursion --- and we can't trust the size estimates
	 * unreservedly, anyway.  Instead, inflate the startup cost by
	 * the square root of the size ratio.  (Why square root?  No real good
	 * reason, but it seems reasonable...)
	 */
	if (innerbytes > outerbytes && outerbytes > 0)
	{
		startup_cost *= sqrt(innerbytes / outerbytes);
	}

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


/*
 * cost_qual_eval
 *		Estimate the CPU cost of evaluating a WHERE clause (once).
 *		The input can be either an implicitly-ANDed list of boolean
 *		expressions, or a list of RestrictInfo nodes.
 */
Cost
cost_qual_eval(List *quals)
{
	Cost	total = 0;

	cost_qual_eval_walker((Node *) quals, &total);
	return total;
}

static bool
cost_qual_eval_walker(Node *node, Cost *total)
{
	if (node == NULL)
		return false;
	/*
	 * Our basic strategy is to charge one cpu_operator_cost for each
	 * operator or function node in the given tree.  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?
	 */
	if (IsA(node, Expr))
	{
		Expr   *expr = (Expr *) node;

		switch (expr->opType)
		{
			case OP_EXPR:
			case FUNC_EXPR:
				*total += cpu_operator_cost;
				break;
			case OR_EXPR:
			case AND_EXPR:
			case NOT_EXPR:
				break;
			case SUBPLAN_EXPR:
				/*
				 * A subplan node in an expression indicates that the subplan
				 * will be executed on each evaluation, so charge accordingly.
				 * (We assume that sub-selects that can be executed as
				 * InitPlans have already been removed from the expression.)
				 *
				 * NOTE: this logic should agree with the estimates used by
				 * make_subplan() in plan/subselect.c. 
				 */
				{
					SubPlan	   *subplan = (SubPlan *) expr->oper;
					Plan	   *plan = subplan->plan;
					Cost		subcost;

					if (subplan->sublink->subLinkType == EXISTS_SUBLINK)
					{
						/* we only need to fetch 1 tuple */
						subcost = plan->startup_cost +
							(plan->total_cost - plan->startup_cost) / plan->plan_rows;
					}
					else if (subplan->sublink->subLinkType == ALL_SUBLINK ||
							 subplan->sublink->subLinkType == ANY_SUBLINK)
					{
						/* assume we need 50% of the tuples */
						subcost = plan->startup_cost +
							0.50 * (plan->total_cost - plan->startup_cost);
						/* XXX what if subplan has been materialized? */
					}
					else
					{
						/* assume we need all tuples */
						subcost = plan->total_cost;
					}
					*total += subcost;
				}
				break;
		}
		/* fall through to examine args of Expr node */
	}
	/*
	 * expression_tree_walker doesn't know what to do with RestrictInfo nodes,
	 * but we just want to recurse through them.
	 */
	if (IsA(node, RestrictInfo))
	{
		RestrictInfo   *restrictinfo = (RestrictInfo *) node;

		return cost_qual_eval_walker((Node *) restrictinfo->clause, total);
	}
	/* Otherwise, recurse. */
	return expression_tree_walker(node, cost_qual_eval_walker,
								  (void *) total);
}


/*
 * 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.
 *
 * 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(Query *root, RelOptInfo *rel)
{
	/* Should only be applied to base relations */
	Assert(length(rel->relids) == 1);

	rel->rows = rel->tuples *
		restrictlist_selectivity(root,
								 rel->baserestrictinfo,
								 lfirsti(rel->relids));
	/*
	 * Force estimate to be at least one row, to make explain output look
	 * better and to avoid possible divide-by-zero when interpolating cost.
	 */
	if (rel->rows < 1.0)
		rel->rows = 1.0;

	rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);

	set_rel_width(root, rel);
}

/*
 * 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.)
 *
 * We set the same relnode fields as set_baserel_size_estimates() does.
 */
void
set_joinrel_size_estimates(Query *root, RelOptInfo *rel,
						   RelOptInfo *outer_rel,
						   RelOptInfo *inner_rel,
						   List *restrictlist)
{
	double		temp;

	/* cartesian product */
	temp = outer_rel->rows * inner_rel->rows;

	/*
	 * Apply join restrictivity.  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.
	 */
	temp *= restrictlist_selectivity(root,
									 restrictlist,
									 0);

	/*
	 * Force estimate to be at least one row, to make explain output look
	 * better and to avoid possible divide-by-zero when interpolating cost.
	 */
	if (temp < 1.0)
		temp = 1.0;
	rel->rows = temp;

	/*
	 * We could apply set_rel_width() to compute the output tuple width
	 * from scratch, but at present it's always just the sum of the input
	 * widths, so why work harder than necessary?  If relnode.c is ever
	 * taught to remove unneeded columns from join targetlists, go back
	 * to using set_rel_width here.
	 */
	rel->width = outer_rel->width + inner_rel->width;
}

/*
 * set_rel_width
 *		Set the estimated output width of the relation.
 */
static void
set_rel_width(Query *root, RelOptInfo *rel)
{
	int			tuple_width = 0;
	List	   *tle;

	foreach(tle, rel->targetlist)
		tuple_width += compute_attribute_width((TargetEntry *) lfirst(tle));
	Assert(tuple_width >= 0);
	rel->width = tuple_width;
}

/*
 * compute_attribute_width
 *	  Given a target list entry, find the size in bytes of the attribute.
 *
 *	  If a field is variable-length, we make a default assumption.  Would be
 *	  better if VACUUM recorded some stats about the average field width...
 *	  also, we have access to the atttypmod, but fail to use it...
 */
static int
compute_attribute_width(TargetEntry *tlistentry)
{
	int			width = get_typlen(tlistentry->resdom->restype);

	if (width < 0)
		return _DEFAULT_ATTRIBUTE_WIDTH_;
	else
		return 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 * ((double) (width + sizeof(HeapTupleData)));
}

/*
 * 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);
}
