Fix some bogosities in the code that deals with estimating the fraction

[postgresql] / src / backend / optimizer / path / costsize.c

/*-------------------------------------------------------------------------
 *
 * 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 1.53 2000/03/14 02:23:14 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.
 *
 * 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 = indexSelectivity * baserel->tuples;

        if (tuples_fetched > 0 && baserel->pages > 0)
                pages_fetched = 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;
        /*
         * Assume that the indexquals will be removed from the list of
         * restriction clauses that we actually have to evaluate as qpquals.
         * This is not completely right, but it's close.
         * For a lossy index, however, we will have to recheck all the quals.
         */
        if (! index->lossy)
                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
 * 'is_indexjoin' is true if we are using an indexscan for the inner relation
 *              (not currently needed here; the indexscan adjusts its cost...)
 */
void
cost_nestloop(Path *path,
                          Path *outer_path,
                          Path *inner_path,
                          List *restrictlist,
                          bool is_indexjoin)
{
        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!) */
        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_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 *
                (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);
}