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

/*-------------------------------------------------------------------------
 *
 * 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.  (Note: while path->rows is never zero
 * for ordinary relations, it is zero for paths for provably-empty relations,
 * so beware of division-by-zero.)      The LIMIT is applied as a top-level
 * plan node.
 *
 * For largely historical reasons, most of the routines in this module use
 * the passed result Path only to store their results (rows, startup_cost and
 * total_cost) into.  All the input data they need is passed as separate
 * parameters, even though much of it could be extracted from the Path.
 * An exception is made for the cost_XXXjoin() routines, which expect all
 * the other fields of the passed XXXPath to be filled in, and similarly
 * cost_index() assumes the passed IndexPath is valid except for its output
 * values.
 *
 *
 * Portions Copyright (c) 1996-2016, 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 = 2;

bool            enable_seqscan = true;
bool            enable_indexscan = true;
bool            enable_indexonlyscan = true;
bool            enable_bitmapscan = true;
bool            enable_tidscan = true;
bool            enable_sort = true;
bool            enable_hashagg = true;
bool            enable_nestloop = true;
bool            enable_material = true;
bool            enable_mergejoin = true;
bool            enable_hashjoin = true;
bool            enable_fkey_estimates = 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
 */
void
cost_seqscan(Path *path, PlannerInfo *root,
                         RelOptInfo *baserel, ParamPathInfo *param_info)
{
        Cost            startup_cost = 0;
        Cost            cpu_run_cost;
        Cost            disk_run_cost;
        double          spc_seq_page_cost;
        QualCost        qpqual_cost;
        Cost            cpu_per_tuple;

        /* Should only be applied to base relations */
        Assert(baserel->relid > 0);
        Assert(baserel->rtekind == RTE_RELATION);

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

        if (!enable_seqscan)
                startup_cost += disable_cost;

        /* fetch estimated page cost for tablespace containing table */
        get_tablespace_page_costs(baserel->reltablespace,
                                                          NULL,
                                                          &spc_seq_page_cost);

        /*
         * disk costs
         */
        disk_run_cost = spc_seq_page_cost * baserel->pages;

        /* CPU costs */
        get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);

        startup_cost += qpqual_cost.startup;
        cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
        cpu_run_cost = cpu_per_tuple * baserel->tuples;
        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        cpu_run_cost += path->pathtarget->cost.per_tuple * path->rows;

        /* Adjust costing for parallelism, if used. */
        if (path->parallel_degree > 0)
        {
                double          parallel_divisor = path->parallel_degree;
                double          leader_contribution;

                /*
                 * Early experience with parallel query suggests that when there is
                 * only one worker, the leader often makes a very substantial
                 * contribution to executing the parallel portion of the plan, but as
                 * more workers are added, it does less and less, because it's busy
                 * reading tuples from the workers and doing whatever non-parallel
                 * post-processing is needed.  By the time we reach 4 workers, the
                 * leader no longer makes a meaningful contribution.  Thus, for now,
                 * estimate that the leader spends 30% of its time servicing each
                 * worker, and the remainder executing the parallel plan.
                 */
                leader_contribution = 1.0 - (0.3 * path->parallel_degree);
                if (leader_contribution > 0)
                        parallel_divisor += leader_contribution;

                /*
                 * In the case of a parallel plan, the row count needs to represent
                 * the number of tuples processed per worker.  Otherwise, higher-level
                 * plan nodes that appear below the gather will be costed incorrectly,
                 * because they'll anticipate receiving more rows than any given copy
                 * will actually get.
                 */
                path->rows /= parallel_divisor;

                /* The CPU cost is divided among all the workers. */
                cpu_run_cost /= parallel_divisor;

                /*
                 * It may be possible to amortize some of the I/O cost, but probably
                 * not very much, because most operating systems already do aggressive
                 * prefetching.  For now, we assume that the disk run cost can't be
                 * amortized at all.
                 */
        }

        path->startup_cost = startup_cost;
        path->total_cost = startup_cost + cpu_run_cost + disk_run_cost;
}

/*
 * cost_samplescan
 *        Determines and returns the cost of scanning a relation using sampling.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_samplescan(Path *path, PlannerInfo *root,
                                RelOptInfo *baserel, ParamPathInfo *param_info)
{
        Cost            startup_cost = 0;
        Cost            run_cost = 0;
        RangeTblEntry *rte;
        TableSampleClause *tsc;
        TsmRoutine *tsm;
        double          spc_seq_page_cost,
                                spc_random_page_cost,
                                spc_page_cost;
        QualCost        qpqual_cost;
        Cost            cpu_per_tuple;

        /* Should only be applied to base relations with tablesample clauses */
        Assert(baserel->relid > 0);
        rte = planner_rt_fetch(baserel->relid, root);
        Assert(rte->rtekind == RTE_RELATION);
        tsc = rte->tablesample;
        Assert(tsc != NULL);
        tsm = GetTsmRoutine(tsc->tsmhandler);

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

        /* fetch estimated page cost for tablespace containing table */
        get_tablespace_page_costs(baserel->reltablespace,
                                                          &spc_random_page_cost,
                                                          &spc_seq_page_cost);

        /* if NextSampleBlock is used, assume random access, else sequential */
        spc_page_cost = (tsm->NextSampleBlock != NULL) ?
                spc_random_page_cost : spc_seq_page_cost;

        /*
         * disk costs (recall that baserel->pages has already been set to the
         * number of pages the sampling method will visit)
         */
        run_cost += spc_page_cost * baserel->pages;

        /*
         * CPU costs (recall that baserel->tuples has already been set to the
         * number of tuples the sampling method will select).  Note that we ignore
         * execution cost of the TABLESAMPLE parameter expressions; they will be
         * evaluated only once per scan, and in most usages they'll likely be
         * simple constants anyway.  We also don't charge anything for the
         * calculations the sampling method might do internally.
         */
        get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);

        startup_cost += qpqual_cost.startup;
        cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
        run_cost += cpu_per_tuple * baserel->tuples;
        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        run_cost += path->pathtarget->cost.per_tuple * path->rows;

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

/*
 * cost_gather
 *        Determines and returns the cost of gather path.
 *
 * 'rel' is the relation to be operated upon
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 * 'rows' may be used to point to a row estimate; if non-NULL, it overrides
 * both 'rel' and 'param_info'.  This is useful when the path doesn't exactly
 * correspond to any particular RelOptInfo.
 */
void
cost_gather(GatherPath *path, PlannerInfo *root,
                        RelOptInfo *rel, ParamPathInfo *param_info,
                        double *rows)
{
        Cost            startup_cost = 0;
        Cost            run_cost = 0;

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

        startup_cost = path->subpath->startup_cost;

        run_cost = path->subpath->total_cost - path->subpath->startup_cost;

        /* Parallel setup and communication cost. */
        startup_cost += parallel_setup_cost;
        run_cost += parallel_tuple_cost * path->path.rows;

        path->path.startup_cost = startup_cost;
        path->path.total_cost = (startup_cost + run_cost);
}

/*
 * cost_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.  We need not check any quals that
         * are implied by the index's predicate, so we can use indrestrictinfo not
         * baserestrictinfo as the list of relevant restriction clauses for the
         * rel.
         */
        if (path->path.param_info)
        {
                path->path.rows = path->path.param_info->ppi_rows;
                /* qpquals come from the rel's restriction clauses and ppi_clauses */
                qpquals = list_concat(
                                extract_nonindex_conditions(path->indexinfo->indrestrictinfo,
                                                                                        path->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(path->indexinfo->indrestrictinfo,
                                                                                          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;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->path.pathtarget->cost.startup;
        run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;

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

/*
 * 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, specifically clauses that needn't be checked because they
 * are implied by an indexqual.  It does not seem worth the cycles to try to
 * factor that 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 attempt createplan.c will try ... */
                result = lappend(result, rinfo);
        }
        return result;
}

/*
 * index_pages_fetched
 *        Estimate the number of pages actually fetched after accounting for
 *        cache effects.
 *
 * We use an approximation proposed by Mackert and Lohman, "Index Scans
 * Using a Finite LRU Buffer: A Validated I/O Model", ACM Transactions
 * on Database Systems, Vol. 14, No. 3, September 1989, Pages 401-424.
 * The Mackert and Lohman approximation is that the number of pages
 * fetched is
 *      PF =
 *              min(2TNs/(2T+Ns), T)                    when T <= b
 *              2TNs/(2T+Ns)                                    when T > b and Ns <= 2Tb/(2T-b)
 *              b + (Ns - 2Tb/(2T-b))*(T-b)/T   when T > b and Ns > 2Tb/(2T-b)
 * where
 *              T = # pages in table
 *              N = # tuples in table
 *              s = selectivity = fraction of table to be scanned
 *              b = # buffer pages available (we include kernel space here)
 *
 * We assume that effective_cache_size is the total number of buffer pages
 * available for the whole query, and pro-rate that space across all the
 * tables in the query and the index currently under consideration.  (This
 * ignores space needed for other indexes used by the query, but since we
 * don't know which indexes will get used, we can't estimate that very well;
 * and in any case counting all the tables may well be an overestimate, since
 * depending on the join plan not all the tables may be scanned concurrently.)
 *
 * The product Ns is the number of tuples fetched; we pass in that
 * product rather than calculating it here.  "pages" is the number of pages
 * in the object under consideration (either an index or a table).
 * "index_pages" is the amount to add to the total table space, which was
 * computed for us by 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;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        run_cost += path->pathtarget->cost.per_tuple * path->rows;

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

/*
 * cost_bitmap_tree_node
 *              Extract cost and selectivity from a bitmap tree node (index/and/or)
 */
void
cost_bitmap_tree_node(Path *path, Cost *cost, Selectivity *selec)
{
        if (IsA(path, IndexPath))
        {
                *cost = ((IndexPath *) path)->indextotalcost;
                *selec = ((IndexPath *) path)->indexselectivity;

                /*
                 * Charge a small amount per retrieved tuple to reflect the costs of
                 * manipulating the bitmap.  This is mostly to make sure that a bitmap
                 * scan doesn't look to be the same cost as an indexscan to retrieve a
                 * single tuple.
                 */
                *cost += 0.1 * cpu_operator_cost * path->rows;
        }
        else if (IsA(path, BitmapAndPath))
        {
                *cost = path->total_cost;
                *selec = ((BitmapAndPath *) path)->bitmapselectivity;
        }
        else if (IsA(path, BitmapOrPath))
        {
                *cost = path->total_cost;
                *selec = ((BitmapOrPath *) path)->bitmapselectivity;
        }
        else
        {
                elog(ERROR, "unrecognized node type: %d", nodeTag(path));
                *cost = *selec = 0;             /* keep compiler quiet */
        }
}

/*
 * cost_bitmap_and_node
 *              Estimate the cost of a BitmapAnd node
 *
 * Note that this considers only the costs of index scanning and bitmap
 * creation, not the eventual heap access.  In that sense the object isn't
 * truly a Path, but it has enough path-like properties (costs in particular)
 * to warrant treating it as one.  We don't bother to set the path rows field,
 * however.
 */
void
cost_bitmap_and_node(BitmapAndPath *path, PlannerInfo *root)
{
        Cost            totalCost;
        Selectivity selec;
        ListCell   *l;

        /*
         * We estimate AND selectivity on the assumption that the inputs are
         * independent.  This is probably often wrong, but we don't have the info
         * to do better.
         *
         * The runtime cost of the BitmapAnd itself is estimated at 100x
         * cpu_operator_cost for each tbm_intersect needed.  Probably too small,
         * definitely too simplistic?
         */
        totalCost = 0.0;
        selec = 1.0;
        foreach(l, path->bitmapquals)
        {
                Path       *subpath = (Path *) lfirst(l);
                Cost            subCost;
                Selectivity subselec;

                cost_bitmap_tree_node(subpath, &subCost, &subselec);

                selec *= subselec;

                totalCost += subCost;
                if (l != list_head(path->bitmapquals))
                        totalCost += 100.0 * cpu_operator_cost;
        }
        path->bitmapselectivity = selec;
        path->path.rows = 0;            /* per above, not used */
        path->path.startup_cost = totalCost;
        path->path.total_cost = totalCost;
}

/*
 * cost_bitmap_or_node
 *              Estimate the cost of a BitmapOr node
 *
 * See comments for cost_bitmap_and_node.
 */
void
cost_bitmap_or_node(BitmapOrPath *path, PlannerInfo *root)
{
        Cost            totalCost;
        Selectivity selec;
        ListCell   *l;

        /*
         * We estimate OR selectivity on the assumption that the inputs are
         * non-overlapping, since that's often the case in "x IN (list)" type
         * situations.  Of course, we clamp to 1.0 at the end.
         *
         * The runtime cost of the BitmapOr itself is estimated at 100x
         * cpu_operator_cost for each tbm_union needed.  Probably too small,
         * definitely too simplistic?  We are aware that the tbm_unions are
         * optimized out when the inputs are BitmapIndexScans.
         */
        totalCost = 0.0;
        selec = 0.0;
        foreach(l, path->bitmapquals)
        {
                Path       *subpath = (Path *) lfirst(l);
                Cost            subCost;
                Selectivity subselec;

                cost_bitmap_tree_node(subpath, &subCost, &subselec);

                selec += subselec;

                totalCost += subCost;
                if (l != list_head(path->bitmapquals) &&
                        !IsA(subpath, IndexPath))
                        totalCost += 100.0 * cpu_operator_cost;
        }
        path->bitmapselectivity = Min(selec, 1.0);
        path->path.rows = 0;            /* per above, not used */
        path->path.startup_cost = totalCost;
        path->path.total_cost = totalCost;
}

/*
 * cost_tidscan
 *        Determines and returns the cost of scanning a relation using TIDs.
 *
 * 'baserel' is the relation to be scanned
 * 'tidquals' is the list of TID-checkable quals
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_tidscan(Path *path, PlannerInfo *root,
                         RelOptInfo *baserel, List *tidquals, ParamPathInfo *param_info)
{
        Cost            startup_cost = 0;
        Cost            run_cost = 0;
        bool            isCurrentOf = false;
        QualCost        qpqual_cost;
        Cost            cpu_per_tuple;
        QualCost        tid_qual_cost;
        int                     ntuples;
        ListCell   *l;
        double          spc_random_page_cost;

        /* Should only be applied to base relations */
        Assert(baserel->relid > 0);
        Assert(baserel->rtekind == RTE_RELATION);

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

        /* Count how many tuples we expect to retrieve */
        ntuples = 0;
        foreach(l, tidquals)
        {
                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;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        run_cost += path->pathtarget->cost.per_tuple * path->rows;

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

/*
 * cost_subqueryscan
 *        Determines and returns the cost of scanning a subquery RTE.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_subqueryscan(SubqueryScanPath *path, PlannerInfo *root,
                                  RelOptInfo *baserel, ParamPathInfo *param_info)
{
        Cost            startup_cost;
        Cost            run_cost;
        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->path.rows = param_info->ppi_rows;
        else
                path->path.rows = baserel->rows;

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

        get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);

        startup_cost = qpqual_cost.startup;
        cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
        run_cost = cpu_per_tuple * baserel->tuples;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->path.pathtarget->cost.startup;
        run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;

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

/*
 * cost_functionscan
 *        Determines and returns the cost of scanning a function RTE.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_functionscan(Path *path, PlannerInfo *root,
                                  RelOptInfo *baserel, ParamPathInfo *param_info)
{
        Cost            startup_cost = 0;
        Cost            run_cost = 0;
        QualCost        qpqual_cost;
        Cost            cpu_per_tuple;
        RangeTblEntry *rte;
        QualCost        exprcost;

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

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

        /*
         * Estimate costs of executing the function expression(s).
         *
         * Currently, nodeFunctionscan.c always executes the functions to
         * completion before returning any rows, and caches the results in a
         * tuplestore.  So the function eval cost is all startup cost, and per-row
         * costs are minimal.
         *
         * XXX in principle we ought to charge tuplestore spill costs if the
         * number of rows is large.  However, given how phony our rowcount
         * estimates for functions tend to be, there's not a lot of point in that
         * refinement right now.
         */
        cost_qual_eval_node(&exprcost, (Node *) rte->functions, root);

        startup_cost += exprcost.startup + exprcost.per_tuple;

        /* Add scanning CPU costs */
        get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);

        startup_cost += qpqual_cost.startup;
        cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
        run_cost += cpu_per_tuple * baserel->tuples;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        run_cost += path->pathtarget->cost.per_tuple * path->rows;

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

/*
 * cost_valuesscan
 *        Determines and returns the cost of scanning a VALUES RTE.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_valuesscan(Path *path, PlannerInfo *root,
                                RelOptInfo *baserel, ParamPathInfo *param_info)
{
        Cost            startup_cost = 0;
        Cost            run_cost = 0;
        QualCost        qpqual_cost;
        Cost            cpu_per_tuple;

        /* Should only be applied to base relations that are values lists */
        Assert(baserel->relid > 0);
        Assert(baserel->rtekind == RTE_VALUES);

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

        /*
         * For now, estimate list evaluation cost at one operator eval per list
         * (probably pretty bogus, but is it worth being smarter?)
         */
        cpu_per_tuple = cpu_operator_cost;

        /* Add scanning CPU costs */
        get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);

        startup_cost += qpqual_cost.startup;
        cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
        run_cost += cpu_per_tuple * baserel->tuples;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        run_cost += path->pathtarget->cost.per_tuple * path->rows;

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

/*
 * cost_ctescan
 *        Determines and returns the cost of scanning a CTE RTE.
 *
 * Note: this is used for both self-reference and regular CTEs; the
 * possible cost differences are below the threshold of what we could
 * estimate accurately anyway.  Note that the costs of evaluating the
 * referenced CTE query are added into the final plan as initplan costs,
 * and should NOT be counted here.
 */
void
cost_ctescan(Path *path, PlannerInfo *root,
                         RelOptInfo *baserel, ParamPathInfo *param_info)
{
        Cost            startup_cost = 0;
        Cost            run_cost = 0;
        QualCost        qpqual_cost;
        Cost            cpu_per_tuple;

        /* Should only be applied to base relations that are CTEs */
        Assert(baserel->relid > 0);
        Assert(baserel->rtekind == RTE_CTE);

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

        /* Charge one CPU tuple cost per row for tuplestore manipulation */
        cpu_per_tuple = cpu_tuple_cost;

        /* Add scanning CPU costs */
        get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);

        startup_cost += qpqual_cost.startup;
        cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
        run_cost += cpu_per_tuple * baserel->tuples;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->pathtarget->cost.startup;
        run_cost += path->pathtarget->cost.per_tuple * path->rows;

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

/*
 * cost_recursive_union
 *        Determines and returns the cost of performing a recursive union,
 *        and also the estimated output size.
 *
 * We are given Paths for the nonrecursive and recursive terms.
 */
void
cost_recursive_union(Path *runion, Path *nrterm, Path *rterm)
{
        Cost            startup_cost;
        Cost            total_cost;
        double          total_rows;

        /* We probably have decent estimates for the non-recursive term */
        startup_cost = nrterm->startup_cost;
        total_cost = nrterm->total_cost;
        total_rows = nrterm->rows;

        /*
         * We arbitrarily assume that about 10 recursive iterations will be
         * needed, and that we've managed to get a good fix on the cost and output
         * size of each one of them.  These are mighty shaky assumptions but it's
         * hard to see how to do better.
         */
        total_cost += 10 * rterm->total_cost;
        total_rows += 10 * rterm->rows;

        /*
         * Also charge cpu_tuple_cost per row to account for the costs of
         * manipulating the tuplestores.  (We don't worry about possible
         * spill-to-disk costs.)
         */
        total_cost += cpu_tuple_cost * total_rows;

        runion->startup_cost = startup_cost;
        runion->total_cost = total_cost;
        runion->rows = total_rows;
        runion->pathtarget->width = Max(nrterm->pathtarget->width,
                                                                        rterm->pathtarget->width);
}

/*
 * cost_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 sort_mem, we have
 *              disk traffic = 2 * relsize * ceil(logM(p / sort_mem))
 *              cpu = comparison_cost * t * log2(t)
 *
 * If the sort is bounded (i.e., only the first k result tuples are needed)
 * and k tuples can fit into sort_mem, we use a heap method that keeps only
 * k tuples in the heap; this will require about t*log2(k) tuple comparisons.
 *
 * The disk traffic is assumed to be 3/4ths sequential and 1/4th random
 * accesses (XXX can't we refine that guess?)
 *
 * By default, we charge two operator evals per tuple comparison, which should
 * be in the right ballpark in most cases.  The caller can tweak this by
 * specifying nonzero comparison_cost; typically that's used for any extra
 * work that has to be done to prepare the inputs to the comparison operators.
 *
 * '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;
                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;
                if (!enable_hashagg)
                        startup_cost += disable_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;

        /* 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;

        /* 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;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->path.pathtarget->cost.startup;
        run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;

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

/*
 * 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->pathtarget->width,
                                  0.0,
                                  work_mem,
                                  -1.0);
                startup_cost += sort_path.startup_cost;
                startup_cost += (sort_path.total_cost - sort_path.startup_cost)
                        * outerstartsel;
                run_cost += (sort_path.total_cost - sort_path.startup_cost)
                        * (outerendsel - outerstartsel);
        }
        else
        {
                startup_cost += outer_path->startup_cost;
                startup_cost += (outer_path->total_cost - outer_path->startup_cost)
                        * outerstartsel;
                run_cost += (outer_path->total_cost - outer_path->startup_cost)
                        * (outerendsel - outerstartsel);
        }

        if (innersortkeys)                      /* do we need to sort inner? */
        {
                cost_sort(&sort_path,
                                  root,
                                  innersortkeys,
                                  inner_path->total_cost,
                                  inner_path_rows,
                                  inner_path->pathtarget->width,
                                  0.0,
                                  work_mem,
                                  -1.0);
                startup_cost += sort_path.startup_cost;
                startup_cost += (sort_path.total_cost - sort_path.startup_cost)
                        * innerstartsel;
                inner_run_cost = (sort_path.total_cost - sort_path.startup_cost)
                        * (innerendsel - innerstartsel);
        }
        else
        {
                startup_cost += inner_path->startup_cost;
                startup_cost += (inner_path->total_cost - inner_path->startup_cost)
                        * innerstartsel;
                inner_run_cost = (inner_path->total_cost - inner_path->startup_cost)
                        * (innerendsel - innerstartsel);
        }

        /*
         * We can't yet determine whether rescanning occurs, or whether
         * materialization of the inner input should be done.  The minimum
         * possible inner input cost, regardless of rescan and materialization
         * considerations, is inner_run_cost.  We include that in
         * workspace->total_cost, but not yet in run_cost.
         */

        /* CPU costs left for later */

        /* Public result fields */
        workspace->startup_cost = startup_cost;
        workspace->total_cost = startup_cost + run_cost + inner_run_cost;
        /* Save private data for final_cost_mergejoin */
        workspace->run_cost = run_cost;
        workspace->inner_run_cost = inner_run_cost;
        workspace->outer_rows = outer_rows;
        workspace->inner_rows = inner_rows;
        workspace->outer_skip_rows = outer_skip_rows;
        workspace->inner_skip_rows = inner_skip_rows;
}

/*
 * final_cost_mergejoin
 *        Final estimate of the cost and result size of a mergejoin path.
 *
 * Unlike other costsize functions, this routine makes 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->pathtarget->width) >
                         (work_mem * 1024L))
                path->materialize_inner = true;
        else
                path->materialize_inner = false;

        /* Charge the right incremental cost for the chosen case */
        if (path->materialize_inner)
                run_cost += mat_inner_cost;
        else
                run_cost += bare_inner_cost;

        /* CPU costs */

        /*
         * The number of tuple comparisons needed is approximately number of outer
         * rows plus number of inner rows plus number of rescanned tuples (can we
         * refine this?).  At each one, we need to evaluate the mergejoin quals.
         */
        startup_cost += merge_qual_cost.startup;
        startup_cost += merge_qual_cost.per_tuple *
                (outer_skip_rows + inner_skip_rows * rescanratio);
        run_cost += merge_qual_cost.per_tuple *
                ((outer_rows - outer_skip_rows) +
                 (inner_rows - inner_skip_rows) * rescanratio);

        /*
         * For each tuple that gets through the mergejoin proper, we charge
         * cpu_tuple_cost plus the cost of evaluating additional restriction
         * clauses that are to be applied at the join.  (This is pessimistic since
         * not all of the quals may get evaluated at each tuple.)
         *
         * Note: we could adjust for SEMI/ANTI joins skipping some qual
         * evaluations here, but it's probably not worth the trouble.
         */
        startup_cost += qp_qual_cost.startup;
        cpu_per_tuple = cpu_tuple_cost + qp_qual_cost.per_tuple;
        run_cost += cpu_per_tuple * mergejointuples;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->jpath.path.pathtarget->cost.startup;
        run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;

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

/*
 * run mergejoinscansel() with caching
 */
static MergeScanSelCache *
cached_scansel(PlannerInfo *root, RestrictInfo *rinfo, PathKey *pathkey)
{
        MergeScanSelCache *cache;
        ListCell   *lc;
        Selectivity leftstartsel,
                                leftendsel,
                                rightstartsel,
                                rightendsel;
        MemoryContext oldcontext;

        /* Do we have this result already? */
        foreach(lc, rinfo->scansel_cache)
        {
                cache = (MergeScanSelCache *) lfirst(lc);
                if (cache->opfamily == pathkey->pk_opfamily &&
                        cache->collation == pathkey->pk_eclass->ec_collation &&
                        cache->strategy == pathkey->pk_strategy &&
                        cache->nulls_first == pathkey->pk_nulls_first)
                        return cache;
        }

        /* Nope, do the computation */
        mergejoinscansel(root,
                                         (Node *) rinfo->clause,
                                         pathkey->pk_opfamily,
                                         pathkey->pk_strategy,
                                         pathkey->pk_nulls_first,
                                         &leftstartsel,
                                         &leftendsel,
                                         &rightstartsel,
                                         &rightendsel);

        /* Cache the result in suitably long-lived workspace */
        oldcontext = MemoryContextSwitchTo(root->planner_cxt);

        cache = (MergeScanSelCache *) palloc(sizeof(MergeScanSelCache));
        cache->opfamily = pathkey->pk_opfamily;
        cache->collation = pathkey->pk_eclass->ec_collation;
        cache->strategy = pathkey->pk_strategy;
        cache->nulls_first = pathkey->pk_nulls_first;
        cache->leftstartsel = leftstartsel;
        cache->leftendsel = leftendsel;
        cache->rightstartsel = rightstartsel;
        cache->rightendsel = rightendsel;

        rinfo->scansel_cache = lappend(rinfo->scansel_cache, cache);

        MemoryContextSwitchTo(oldcontext);

        return cache;
}

/*
 * initial_cost_hashjoin
 *        Preliminary estimate of the cost of a hashjoin path.
 *
 * This must quickly produce lower-bound estimates of the path's startup and
 * total costs.  If we are unable to eliminate the proposed path from
 * consideration using the lower bounds, final_cost_hashjoin will be called
 * to obtain the final estimates.
 *
 * The exact division of labor between this function and final_cost_hashjoin
 * is private to them, and represents a tradeoff between speed of the initial
 * estimate and getting a tight lower bound.  We choose to not examine the
 * join quals here (other than by counting the number of hash clauses),
 * so we can't do much with CPU costs.  We do assume that
 * ExecChooseHashTableSize is cheap enough to use here.
 *
 * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
 *              other data to be used by final_cost_hashjoin
 * 'jointype' is the type of join to be performed
 * 'hashclauses' is the list of joinclauses to be used as hash clauses
 * 'outer_path' is the outer input to the join
 * 'inner_path' is the inner input to the join
 * '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->pathtarget->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->pathtarget->width);
                double          innerpages = page_size(inner_path_rows,
                                                                                   inner_path->pathtarget->width);

                startup_cost += seq_page_cost * innerpages;
                run_cost += seq_page_cost * (innerpages + 2 * outerpages);
        }

        /* CPU costs left for later */

        /* Public result fields */
        workspace->startup_cost = startup_cost;
        workspace->total_cost = startup_cost + run_cost;
        /* Save private data for final_cost_hashjoin */
        workspace->run_cost = run_cost;
        workspace->numbuckets = numbuckets;
        workspace->numbatches = numbatches;
}

/*
 * 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;

        /* tlist eval costs are paid per output row, not per tuple scanned */
        startup_cost += path->jpath.path.pathtarget->cost.startup;
        run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;

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


/*
 * cost_subplan
 *              Figure the costs for a SubPlan (or initplan).
 *
 * Note: we could dig the subplan's Plan out of the root list, but in practice
 * all callers have it handy already, so we make them pass it.
 */
void
cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
{
        QualCost        sp_cost;

        /* Figure any cost for evaluating the testexpr */
        cost_qual_eval(&sp_cost,
                                   make_ands_implicit((Expr *) subplan->testexpr),
                                   root);

        if (subplan->useHashTable)
        {
                /*
                 * If we are using a hash table for the subquery outputs, then the
                 * cost of evaluating the query is a one-time cost.  We charge one
                 * cpu_operator_cost per tuple for the work of loading the hashtable,
                 * too.
                 */
                sp_cost.startup += plan->total_cost +
                        cpu_operator_cost * plan->plan_rows;

                /*
                 * The per-tuple costs include the cost of evaluating the lefthand
                 * expressions, plus the cost of probing the hashtable.  We already
                 * accounted for the lefthand expressions as part of the testexpr, and
                 * will also have counted one cpu_operator_cost for each comparison
                 * operator.  That is probably too low for the probing cost, but it's
                 * hard to make a better estimate, so live with it for now.
                 */
        }
        else
        {
                /*
                 * Otherwise we will be rescanning the subplan output on each
                 * evaluation.  We need to estimate how much of the output we will
                 * actually need to scan.  NOTE: this logic should agree with the
                 * tuple_fraction estimates used by make_subplan() in
                 * plan/subselect.c.
                 */
                Cost            plan_run_cost = plan->total_cost - plan->startup_cost;

                if (subplan->subLinkType == EXISTS_SUBLINK)
                {
                        /* we only need to fetch 1 tuple; clamp to avoid zero divide */
                        sp_cost.per_tuple += plan_run_cost / clamp_row_est(plan->plan_rows);
                }
                else if (subplan->subLinkType == ALL_SUBLINK ||
                                 subplan->subLinkType == ANY_SUBLINK)
                {
                        /* assume we need 50% of the tuples */
                        sp_cost.per_tuple += 0.50 * plan_run_cost;
                        /* also charge a cpu_operator_cost per row examined */
                        sp_cost.per_tuple += 0.50 * plan->plan_rows * cpu_operator_cost;
                }
                else
                {
                        /* assume we need all tuples */
                        sp_cost.per_tuple += plan_run_cost;
                }

                /*
                 * Also account for subplan's startup cost. If the subplan is
                 * uncorrelated or undirect correlated, AND its topmost node is one
                 * that materializes its output, assume that we'll only need to pay
                 * its startup cost once; otherwise assume we pay the startup cost
                 * every time.
                 */
                if (subplan->parParam == NIL &&
                        ExecMaterializesOutput(nodeTag(plan)))
                        sp_cost.startup += plan->startup_cost;
                else
                        sp_cost.per_tuple += plan->startup_cost;
        }

        subplan->startup_cost = sp_cost.startup;
        subplan->per_call_cost = sp_cost.per_tuple;
}


/*
 * cost_rescan
 *              Given a finished Path, estimate the costs of rescanning it after
 *              having done so the first time.  For some Path types a rescan is
 *              cheaper than an original scan (if no parameters change), and this
 *              function embodies knowledge about that.  The default is to return
 *              the same costs stored in the Path.  (Note that the cost estimates
 *              actually stored in Paths are always for first scans.)
 *
 * This function is not currently intended to model effects such as rescans
 * being cheaper due to disk block caching; what we are concerned with is
 * plan types wherein the executor caches results explicitly, or doesn't
 * redo startup calculations, etc.
 */
static void
cost_rescan(PlannerInfo *root, Path *path,
                        Cost *rescan_startup_cost,      /* output parameters */
                        Cost *rescan_total_cost)
{
        switch (path->pathtype)
        {
                case T_FunctionScan:

                        /*
                         * Currently, nodeFunctionscan.c always executes the function to
                         * completion before returning any rows, and caches the results in
                         * a tuplestore.  So the function eval cost is all startup cost
                         * and isn't paid over again on rescans. However, all run costs
                         * will be paid over again.
                         */
                        *rescan_startup_cost = 0;
                        *rescan_total_cost = path->total_cost - path->startup_cost;
                        break;
                case T_HashJoin:

                        /*
                         * 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->pathtarget->width);
                                long            work_mem_bytes = work_mem * 1024L;

                                if (nbytes > work_mem_bytes)
                                {
                                        /* It will spill, so account for re-read cost */
                                        double          npages = ceil(nbytes / BLCKSZ);

                                        run_cost += seq_page_cost * npages;
                                }
                                *rescan_startup_cost = 0;
                                *rescan_total_cost = run_cost;
                        }
                        break;
                case T_Material:
                case T_Sort:
                        {
                                /*
                                 * These plan types not only materialize their results, but do
                                 * not implement qual filtering or projection.  So they are
                                 * even cheaper to rescan than the ones above.  We charge only
                                 * cpu_operator_cost per tuple.  (Note: keep that in sync with
                                 * the run_cost charge in cost_sort, and also see comments in
                                 * cost_material before you change it.)
                                 */
                                Cost            run_cost = cpu_operator_cost * path->rows;
                                double          nbytes = relation_byte_size(path->rows,
                                                                                                        path->pathtarget->width);
                                long            work_mem_bytes = work_mem * 1024L;

                                if (nbytes > work_mem_bytes)
                                {
                                        /* It will spill, so account for re-read cost */
                                        double          npages = ceil(nbytes / BLCKSZ);

                                        run_cost += seq_page_cost * npages;
                                }
                                *rescan_startup_cost = 0;
                                *rescan_total_cost = run_cost;
                        }
                        break;
                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);
        }
        else if (IsA(node, PlaceHolderVar))
        {
                /*
                 * A PlaceHolderVar should be given cost zero when considering general
                 * expression evaluation costs.  The expense of doing the contained
                 * expression is charged as part of the tlist eval costs of the scan
                 * or join where the PHV is first computed (see set_rel_width and
                 * add_placeholders_to_joinrel).  If we charged it again here, we'd be
                 * double-counting the cost for each level of plan that the PHV
                 * bubbles up through.  Hence, return without recursing into the
                 * phexpr.
                 */
                return false;
        }

        /* recurse into children */
        return expression_tree_walker(node, cost_qual_eval_walker,
                                                                  (void *) context);
}

/*
 * get_restriction_qual_cost
 *        Compute evaluation costs of a baserel's restriction quals, plus any
 *        movable join quals that have been pushed down to the scan.
 *        Results are returned into *qpqual_cost.
 *
 * This is a convenience subroutine that works for seqscans and other cases
 * where all the given quals will be evaluated the hard way.  It's not useful
 * for cost_index(), for example, where the index machinery takes care of
 * some of the quals.  We assume baserestrictcost was previously set by
 * set_baserel_size_estimates().
 */
static void
get_restriction_qual_cost(PlannerInfo *root, RelOptInfo *baserel,
                                                  ParamPathInfo *param_info,
                                                  QualCost *qpqual_cost)
{
        if (param_info)
        {
                /* Include costs of pushed-down clauses */
                cost_qual_eval(qpqual_cost, param_info->ppi_clauses, root);

                qpqual_cost->startup += baserel->baserestrictcost.startup;
                qpqual_cost->per_tuple += baserel->baserestrictcost.per_tuple;
        }
        else
                *qpqual_cost = baserel->baserestrictcost;
}


/*
 * compute_semi_anti_join_factors
 *        Estimate how much of the inner input a SEMI 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 reltarget field was already set by
 * build_joinrel_tlist, and baserestrictcost is not used for join rels.
 */
void
set_joinrel_size_estimates(PlannerInfo *root, RelOptInfo *rel,
                                                   RelOptInfo *outer_rel,
                                                   RelOptInfo *inner_rel,
                                                   SpecialJoinInfo *sjinfo,
                                                   List *restrictlist)
{
        rel->rows = calc_joinrel_size_estimate(root,
                                                                                   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;
}

/*
 * quals_match_foreign_key
 *              Determines if the foreign key is matched by joinquals.
 *
 * Checks that there are conditions on all columns of the foreign key, matching
 * the operator used by the foreign key etc. If such complete match is found,
 * the function returns bitmap identifying the matching quals (0-based).
 *
 * Otherwise (no match at all or incomplete match), NULL is returned.
 *
 * XXX It seems possible in the future to do something useful when a
 * partial match occurs between join and FK, but that is less common
 * and that part isn't worked out yet.
 */
static Bitmapset *
quals_match_foreign_key(PlannerInfo *root, ForeignKeyOptInfo *fkinfo,
                                                RelOptInfo *fkrel, RelOptInfo *foreignrel,
                                                List *joinquals)
{
        int i;
        int nkeys = fkinfo->nkeys;
        Bitmapset *qualmatches = NULL;
        Bitmapset *fkmatches = NULL;

        /*
         * Loop over each column of the foreign key and build a bitmapset
         * of each joinqual which matches. Note that we don't stop when we find
         * the first match, as the expression could be duplicated in the
         * joinquals, and we want to generate a bitmapset which has bits set for
         * every matching join qual.
         */
        for (i = 0; i < nkeys; i++)
        {
                ListCell *lc;
                int quallstidx = -1;

                foreach(lc, joinquals)
                {
                        RestrictInfo   *rinfo;
                        OpExpr             *clause;
                        Var                        *leftvar;
                        Var                        *rightvar;

                        quallstidx++;

                        /*
                         * Technically we don't need to, but here we skip this qual if
                         * we've matched it to part of the foreign key already. This
                         * should prove to be a useful optimization when the quals appear
                         * in the same order as the foreign key's keys. We need only bother
                         * doing this when the foreign key is made up of more than 1 set
                         * of columns, and we're not testing the first column.
                         */
                        if (i > 0 && bms_is_member(quallstidx, qualmatches))
                                continue;

                        /*
                         * Here since 'usefulquals' only contains bitmap indexes for quals
                         * of type "var op var" we can safely skip checking this.
                         */
                        rinfo = (RestrictInfo *) lfirst(lc);
                        clause = (OpExpr *) rinfo->clause;

                        /*
                         * If the operator does not match then there's little point in
                         * checking the operands.
                         */
                        if (clause->opno != fkinfo->conpfeqop[i])
                                continue;

                        leftvar = (Var *) get_leftop((Expr *) clause);
                        rightvar = (Var *) get_rightop((Expr *) clause);

                        /* Foreign keys only support Vars, so ignore anything more complex */
                        if (!IsA(leftvar, Var) || !IsA(rightvar, Var))
                                continue;

                        /*
                         * For RestrictInfos built from an eclass we must consider each
                         * member of the eclass as rinfo's operands may not belong to the
                         * foreign key. For efficient tracking of which Vars we've found,
                         * since we're only tracking 2 Vars, we use a bitmask. We can
                         * safely finish searching when both of the least significant bits
                         * are set.
                         */
                        if (rinfo->parent_ec)
                        {
                                EquivalenceClass   *ec = rinfo->parent_ec;
                                ListCell                   *lc2;
                                int                                     foundvarmask = 0;

                                foreach(lc2, ec->ec_members)
                                {
                                        EquivalenceMember *em = (EquivalenceMember *) lfirst(lc2);
                                        Var *var = (Var *) em->em_expr;

                                        if (!IsA(var, Var))
                                                continue;

                                        if (foreignrel->relid == var->varno &&
                                                fkinfo->confkeys[i] == var->varattno)
                                                foundvarmask |= 1;

                                        else if (fkrel->relid == var->varno &&
                                                fkinfo->conkeys[i] == var->varattno)
                                                foundvarmask |= 2;

                                        /*
                                         * Check if we've found both matches. If found we add
                                         * this qual to the matched list and mark this key as
                                         * matched too.
                                         */
                                        if (foundvarmask == 3)
                                        {
                                                qualmatches = bms_add_member(qualmatches, quallstidx);
                                                fkmatches = bms_add_member(fkmatches, i);
                                                break;
                                        }
                                }
                        }
                        else
                        {
                                /*
                                 * In this non eclass RestrictInfo case we'll check if the left
                                 * and right Vars match to this part of the foreign key.
                                 * Remember that this could be written with the Vars in either
                                 * order, so we test both permutations of the expression.
                                 */
                                if ((foreignrel->relid == leftvar->varno) &&
                                        (fkrel->relid == rightvar->varno) &&
                                        (fkinfo->confkeys[i] == leftvar->varattno) &&
                                        (fkinfo->conkeys[i] == rightvar->varattno))
                                {
                                        qualmatches = bms_add_member(qualmatches, quallstidx);
                                        fkmatches = bms_add_member(fkmatches, i);
                                }
                                else if ((foreignrel->relid == rightvar->varno) &&
                                                 (fkrel->relid == leftvar->varno) &&
                                                 (fkinfo->confkeys[i] == rightvar->varattno) &&
                                                 (fkinfo->conkeys[i] == leftvar->varattno))
                                {
                                        qualmatches = bms_add_member(qualmatches, quallstidx);
                                        fkmatches = bms_add_member(fkmatches, i);
                                }
                        }
                }
        }

        /* can't find more matches than columns in the foreign key */
        Assert(bms_num_members(fkmatches) <= nkeys);

        /* Only return the matches if the foreign key is matched fully. */
        if (bms_num_members(fkmatches) == nkeys)
        {
                bms_free(fkmatches);
                return qualmatches;
        }

        bms_free(fkmatches);
        bms_free(qualmatches);

        return NULL;
}

/*
 * find_best_foreign_key_quals
 *              Finds the foreign key best matching the joinquals.
 *
 * Analyzes joinquals to determine if any quals match foreign keys defined the
 * two relations (fkrel referencing foreignrel). When multiple foreign keys
 * match, we choose the one with the most keys as the best one because of the
 * way estimation occurs in clauselist_join_selectivity().  We could choose
 * the FK matching the most quals, however we assume the quals may be duplicated.
 *
 * We also track which joinquals match the current foreign key, so that we can
 * easily skip then when computing the selectivity.
 *
 * When no matching foreign key is found we return 0, otherwise we return the
 * number of keys in the foreign key.
 *
 * Foreign keys matched only partially are currently ignored.
 */
static int
find_best_foreign_key_quals(PlannerInfo *root, RelOptInfo *fkrel,
                                                        RelOptInfo *foreignrel, List *joinquals,
                                                        Bitmapset **joinqualsbitmap)
{
        Bitmapset          *qualbestmatch;
        ListCell           *lc;
        int                             bestmatchnkeys;

        /*
         * fast path out when there's no foreign keys on fkrel, or when use of
         * foreign keys for estimation is disabled by GUC
         */
        if ((fkrel->fkeylist == NIL) || (!enable_fkey_estimates))
        {
                *joinqualsbitmap = NULL;
                return 0;
        }

        qualbestmatch = NULL;
        bestmatchnkeys = 0;

        /* now check the matches for each foreign key defined on the fkrel */
        foreach(lc, fkrel->fkeylist)
        {
                ForeignKeyOptInfo *fkinfo = (ForeignKeyOptInfo *) lfirst(lc);
                Bitmapset *qualsmatched;

                /*
                 * We make no attempt in checking that this foreign key actually
                 * references 'foreignrel', the reasoning here is that we may be able
                 * to match the foreign key to an eclass member Var of a RestrictInfo
                 * that's in qualslist, this Var may belong to some other relation.
                 *
                 * XXX Is this assumption safe in all cases? Maybe not, but does
                 * it lead to a worse estimate than the previous approach? Doubt it.
                 */
                qualsmatched = quals_match_foreign_key(root, fkinfo, fkrel, foreignrel,
                                                                                           joinquals);

                /* Did we get a match? And is that match better than a previous one? */
                if (qualsmatched != NULL && fkinfo->nkeys > bestmatchnkeys)
                {
                        /* save the new best match */
                        bms_free(qualbestmatch);
                        qualbestmatch = qualsmatched;
                        bestmatchnkeys = fkinfo->nkeys;
                }
        }

        *joinqualsbitmap = qualbestmatch;
        return bestmatchnkeys;
}

/*
 * clauselist_join_selectivity
 *              Estimate selectivity of join clauses either by using foreign key info
 *              or by using the regular clauselist_selectivity().
 *
 * Since selectivity estimates for each joinqual are multiplied together, this
 * can cause significant underestimates on the number of join tuples in cases
 * where there's more than 1 clause in the join condition. To help ease the
 * pain here we make use of foreign keys, and we assume that 1 row will match
 * when *all* of the foreign key columns are present in the join condition, any
 * additional clauses are estimated using clauselist_selectivity().
 *
 * Note this ignores whether the FK is invalid or currently deferred; we don't
 * rely on this assumption for correctness of the query, so it is a reasonable
 * and safe assumption for planning purposes.
 */
static Selectivity
clauselist_join_selectivity(PlannerInfo *root, List *joinquals,
                                                        JoinType jointype, SpecialJoinInfo *sjinfo)
{
        int                             outerid;
        int                             innerid;
        Selectivity             sel = 1.0;
        Bitmapset          *foundfkquals = NULL;

        innerid = -1;
        while ((innerid = bms_next_member(sjinfo->min_righthand, innerid)) >= 0)
        {
                RelOptInfo *innerrel = find_base_rel(root, innerid);

                outerid = -1;
                while ((outerid = bms_next_member(sjinfo->min_lefthand, outerid)) >= 0)
                {
                        RelOptInfo         *outerrel = find_base_rel(root, outerid);
                        Bitmapset          *outer2inner;
                        Bitmapset          *inner2outer;
                        int                             innermatches;
                        int                             outermatches;

                        /*
                         * check which quals are matched by a foreign key referencing the
                         * innerrel.
                         */
                        outermatches = find_best_foreign_key_quals(root, outerrel,
                                                                                        innerrel, joinquals, &outer2inner);

                        /* do the same, but with relations swapped */
                        innermatches = find_best_foreign_key_quals(root, innerrel,
                                                                                        outerrel, joinquals, &inner2outer);

                        /*
                         * did we find any matches at all? If so we need to see which one is
                         * the best/longest match
                         */
                        if (outermatches != 0 || innermatches != 0)
                        {
                                double  referenced_tuples;
                                bool overlap;

                                /* either could be zero, but not both. */
                                if (outermatches < innermatches)
                                {
                                        overlap = bms_overlap(foundfkquals, inner2outer);

                                        foundfkquals = bms_add_members(foundfkquals, inner2outer);
                                        referenced_tuples = Max(outerrel->tuples, 1.0);
                                }
                                else
                                {
                                        overlap = bms_overlap(foundfkquals, outer2inner);

                                        foundfkquals = bms_add_members(foundfkquals, outer2inner);
                                        referenced_tuples = Max(innerrel->tuples, 1.0);
                                }

                                /*
                                 * XXX should we ignore these overlapping matches?
                                 * Or perhaps take the Max() or Min()?
                                 */
                                if (overlap)
                                {
                                        if (jointype == JOIN_SEMI || jointype == JOIN_ANTI)
                                                sel = Min(sel,Min(1.0 / (outerrel->tuples / Max(innerrel->tuples, 1.0)), 1.0));
                                        else
                                                sel = Min(sel, 1.0 / referenced_tuples);
                                }
                                else
                                {
                                        if (jointype == JOIN_SEMI || jointype == JOIN_ANTI)
                                                sel *= Min(1.0 / (outerrel->tuples / Max(innerrel->tuples, 1.0)), 1.0);
                                        else
                                                sel *= 1.0 / referenced_tuples;
                                }
                        }
                }
        }

        /*
         * If any non matched quals exist then we build a list of the non-matches
         * and use clauselist_selectivity() to estimate the selectivity of these.
         */
        if (bms_num_members(foundfkquals) < list_length(joinquals))
        {
                ListCell *lc;
                int lstidx = 0;
                List *nonfkeyclauses = NIL;

                foreach (lc, joinquals)
                {
                        if (!bms_is_member(lstidx, foundfkquals))
                                nonfkeyclauses = lappend(nonfkeyclauses, lfirst(lc));
                        lstidx++;
                }
                sel *= clauselist_selectivity(root, nonfkeyclauses, 0, jointype, sjinfo);
        }

        return sel;
}

/*
 * 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_join_selectivity(root,
                                                                                         joinquals,
                                                                                         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_join_selectivity(root,
                                                                                         restrictlist,
                                                                                         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 Paths for the subquery must have been completed.
 * We look at the subquery's PlannerInfo to extract data.
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_subquery_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
        PlannerInfo *subroot = rel->subroot;
        RelOptInfo *sub_final_rel;
        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 subquery.  All of its paths should
         * have the same output rowcount, so just look at cheapest-total.
         */
        sub_final_rel = fetch_upper_rel(subroot, UPPERREL_FINAL, NULL);
        rel->tuples = sub_final_rel->cheapest_total_path->rows;

        /*
         * Compute per-output-column width estimates by examining the subquery's
         * targetlist.  For any output that is a plain Var, get the width estimate
         * that was made while planning the subquery.  Otherwise, we leave it to
         * set_rel_width to fill in a datatype-based default estimate.
         */
        foreach(lc, subroot->parse->targetList)
        {
                TargetEntry *te = (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 an estimate of the number of rows returned by the CTE
 * (if a regular CTE) or the non-recursive term (if a self-reference).
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_cte_size_estimates(PlannerInfo *root, RelOptInfo *rel, double cte_rows)
{
        RangeTblEntry *rte;

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

        if (rte->self_reference)
        {
                /*
                 * In a self-reference, arbitrarily assume the average worktable size
                 * is about 10 times the nonrecursive term's size.
                 */
                rel->tuples = 10 * cte_rows;
        }
        else
        {
                /* Otherwise just believe the CTE's rowcount estimate */
                rel->tuples = cte_rows;
        }

        /* Now estimate number of output rows, etc */
        set_baserel_size_estimates(root, rel);
}

/*
 * set_foreign_size_estimates
 *              Set the size estimates for a base relation that is a foreign table.
 *
 * There is not a whole lot that we can do here; the foreign-data wrapper
 * is responsible for producing useful estimates.  We can do a decent job
 * of estimating baserestrictcost, so we set that, and we also set up width
 * using what will be purely datatype-driven estimates from the targetlist.
 * There is no way to do anything sane with the rows value, so we just put
 * a default estimate and hope that the wrapper can improve on it.  The
 * wrapper's GetForeignRelSize function will be called momentarily.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 */
void
set_foreign_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
        /* Should only be applied to base relations */
        Assert(rel->relid > 0);

        rel->rows = 1000;                       /* entirely bogus default estimate */

        cost_qual_eval(&rel->baserestrictcost, rel->baserestrictinfo, root);

        set_rel_width(root, rel);
}


/*
 * set_rel_width
 *              Set the estimated output width of a base relation.
 *
 * The estimated output width is the sum of the per-attribute width estimates
 * for the actually-referenced columns, plus any PHVs or other expressions
 * that have to be calculated at this relation.  This is the amount of data
 * we'd need to pass upwards in case of a sort, hash, etc.
 *
 * This function also sets reltarget->cost, so it's a bit misnamed now.
 *
 * NB: this works best on plain relations because it prefers to look at
 * real Vars.  For subqueries, set_subquery_size_estimates will already have
 * copied up whatever per-column estimates were made within the subquery,
 * and for other types of rels there isn't much we can do anyway.  We fall
 * back on (fairly stupid) datatype-based width estimates if we can't get
 * any better number.
 *
 * The per-attribute width estimates are cached for possible re-use while
 * building join relations or post-scan/join pathtargets.
 */
static void
set_rel_width(PlannerInfo *root, RelOptInfo *rel)
{
        Oid                     reloid = planner_rt_fetch(rel->relid, root)->relid;
        int32           tuple_width = 0;
        bool            have_wholerow_var = false;
        ListCell   *lc;

        /* Vars are assumed to have cost zero, but other exprs do not */
        rel->reltarget->cost.startup = 0;
        rel->reltarget->cost.per_tuple = 0;

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

                /*
                 * Ordinarily, a Var in a rel's targetlist must belong to that rel;
                 * but there are corner cases involving LATERAL references where that
                 * isn't so.  If the Var has the wrong varno, fall through to the
                 * generic case (it doesn't seem worth the trouble to be any smarter).
                 */
                if (IsA(node, Var) &&
                        ((Var *) node)->varno == rel->relid)
                {
                        Var                *var = (Var *) node;
                        int                     ndx;
                        int32           item_width;

                        Assert(var->varattno >= rel->min_attr);
                        Assert(var->varattno <= rel->max_attr);

                        ndx = var->varattno - rel->min_attr;

                        /*
                         * If it's a whole-row Var, we'll deal with it below after we have
                         * already cached as many attr widths as possible.
                         */
                        if (var->varattno == 0)
                        {
                                have_wholerow_var = true;
                                continue;
                        }

                        /*
                         * The width may have been cached already (especially if it's a
                         * subquery), so don't duplicate effort.
                         */
                        if (rel->attr_widths[ndx] > 0)
                        {
                                tuple_width += rel->attr_widths[ndx];
                                continue;
                        }

                        /* Try to get column width from statistics */
                        if (reloid != InvalidOid && var->varattno > 0)
                        {
                                item_width = get_attavgwidth(reloid, var->varattno);
                                if (item_width > 0)
                                {
                                        rel->attr_widths[ndx] = item_width;
                                        tuple_width += item_width;
                                        continue;
                                }
                        }

                        /*
                         * Not a plain relation, or can't find statistics for it. Estimate
                         * using just the type info.
                         */
                        item_width = get_typavgwidth(var->vartype, var->vartypmod);
                        Assert(item_width > 0);
                        rel->attr_widths[ndx] = item_width;
                        tuple_width += item_width;
                }
                else if (IsA(node, PlaceHolderVar))
                {
                        /*
                         * We will need to evaluate the PHV's contained expression while
                         * scanning this rel, so be sure to include it in reltarget->cost.
                         */
                        PlaceHolderVar *phv = (PlaceHolderVar *) node;
                        PlaceHolderInfo *phinfo = find_placeholder_info(root, phv, false);
                        QualCost        cost;

                        tuple_width += phinfo->ph_width;
                        cost_qual_eval_node(&cost, (Node *) phv->phexpr, root);
                        rel->reltarget->cost.startup += cost.startup;
                        rel->reltarget->cost.per_tuple += cost.per_tuple;
                }
                else
                {
                        /*
                         * We could be looking at an expression pulled up from a subquery,
                         * or a ROW() representing a whole-row child Var, etc.  Do what we
                         * can using the expression type information.
                         */
                        int32           item_width;
                        QualCost        cost;

                        item_width = get_typavgwidth(exprType(node), exprTypmod(node));
                        Assert(item_width > 0);
                        tuple_width += item_width;
                        /* Not entirely clear if we need to account for cost, but do so */
                        cost_qual_eval_node(&cost, node, root);
                        rel->reltarget->cost.startup += cost.startup;
                        rel->reltarget->cost.per_tuple += cost.per_tuple;
                }
        }

        /*
         * If we have a whole-row reference, estimate its width as the sum of
         * per-column widths plus heap tuple header overhead.
         */
        if (have_wholerow_var)
        {
                int32           wholerow_width = MAXALIGN(SizeofHeapTupleHeader);

                if (reloid != InvalidOid)
                {
                        /* Real relation, so estimate true tuple width */
                        wholerow_width += get_relation_data_width(reloid,
                                                                                   rel->attr_widths - rel->min_attr);
                }
                else
                {
                        /* Do what we can with info for a phony rel */
                        AttrNumber      i;

                        for (i = 1; i <= rel->max_attr; i++)
                                wholerow_width += rel->attr_widths[i - rel->min_attr];
                }

                rel->attr_widths[0 - rel->min_attr] = wholerow_width;

                /*
                 * Include the whole-row Var as part of the output tuple.  Yes, that
                 * really is what happens at runtime.
                 */
                tuple_width += wholerow_width;
        }

        Assert(tuple_width >= 0);
        rel->reltarget->width = tuple_width;
}

/*
 * set_pathtarget_cost_width
 *              Set the estimated eval cost and output width of a PathTarget tlist.
 *
 * As a notational convenience, returns the same PathTarget pointer passed in.
 *
 * Most, though not quite all, uses of this function occur after we've run
 * set_rel_width() for base relations; so we can usually obtain cached width
 * estimates for Vars.  If we can't, fall back on datatype-based width
 * estimates.  Present early-planning uses of PathTargets don't need accurate
 * widths badly enough to justify going to the catalogs for better data.
 */
PathTarget *
set_pathtarget_cost_width(PlannerInfo *root, PathTarget *target)
{
        int32           tuple_width = 0;
        ListCell   *lc;

        /* Vars are assumed to have cost zero, but other exprs do not */
        target->cost.startup = 0;
        target->cost.per_tuple = 0;

        foreach(lc, target->exprs)
        {
                Node       *node = (Node *) lfirst(lc);

                if (IsA(node, Var))
                {
                        Var                *var = (Var *) node;
                        int32           item_width;

                        /* We should not see any upper-level Vars here */
                        Assert(var->varlevelsup == 0);

                        /* Try to get data from RelOptInfo cache */
                        if (var->varno < root->simple_rel_array_size)
                        {
                                RelOptInfo *rel = root->simple_rel_array[var->varno];

                                if (rel != NULL &&
                                        var->varattno >= rel->min_attr &&
                                        var->varattno <= rel->max_attr)
                                {
                                        int                     ndx = var->varattno - rel->min_attr;

                                        if (rel->attr_widths[ndx] > 0)
                                        {
                                                tuple_width += rel->attr_widths[ndx];
                                                continue;
                                        }
                                }
                        }

                        /*
                         * No cached data available, so estimate using just the type info.
                         */
                        item_width = get_typavgwidth(var->vartype, var->vartypmod);
                        Assert(item_width > 0);
                        tuple_width += item_width;
                }
                else
                {
                        /*
                         * Handle general expressions using type info.
                         */
                        int32           item_width;
                        QualCost        cost;

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

                        /* Account for cost, too */
                        cost_qual_eval_node(&cost, node, root);
                        target->cost.startup += cost.startup;
                        target->cost.per_tuple += cost.per_tuple;
                }
        }

        Assert(tuple_width >= 0);
        target->width = tuple_width;

        return target;
}

/*
 * relation_byte_size
 *        Estimate the storage space in bytes for a given number of tuples
 *        of a given width (size in bytes).
 */
static double
relation_byte_size(double tuples, int width)
{
        return tuples * (MAXALIGN(width) + MAXALIGN(SizeofHeapTupleHeader));
}

/*
 * page_size
 *        Returns an estimate of the number of pages covered by a given
 *        number of tuples of a given width (size in bytes).
 */
static double
page_size(double tuples, int width)
{
        return ceil(relation_byte_size(tuples, width) / BLCKSZ);
}