costsize.c

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/*-------------------------------------------------------------------------
 *
 * costsize.c
 *    Routines to compute (and set) relation sizes and path costs
 *
 * Path costs are measured in arbitrary units established by these basic
 * parameters:
 *
 *  seq_page_cost       Cost of a sequential page fetch
 *  random_page_cost    Cost of a non-sequential page fetch
 *  cpu_tuple_cost      Cost of typical CPU time to process a tuple
 *  cpu_index_tuple_cost  Cost of typical CPU time to process an index tuple
 *  cpu_operator_cost   Cost of CPU time to execute an operator or function
 *  parallel_tuple_cost Cost of CPU time to pass a tuple from worker to leader backend
 *  parallel_setup_cost Cost of setting up shared memory for parallelism
 *
 * We expect that the kernel will typically do some amount of read-ahead
 * optimization; this in conjunction with seek costs means that seq_page_cost
 * is normally considerably less than random_page_cost.  (However, if the
 * database is fully cached in RAM, it is reasonable to set them equal.)
 *
 * We also use a rough estimate "effective_cache_size" of the number of
 * disk pages in Postgres + OS-level disk cache.  (We can't simply use
 * NBuffers for this purpose because that would ignore the effects of
 * the kernel's disk cache.)
 *
 * Obviously, taking constants for these values is an oversimplification,
 * but it's tough enough to get any useful estimates even at this level of
 * detail.  Note that all of these parameters are user-settable, in case
 * the default values are drastically off for a particular platform.
 *
 * seq_page_cost and random_page_cost can also be overridden for an individual
 * tablespace, in case some data is on a fast disk and other data is on a slow
 * disk.  Per-tablespace overrides never apply to temporary work files such as
 * an external sort or a materialize node that overflows work_mem.
 *
 * We compute two separate costs for each path:
 *      total_cost: total estimated cost to fetch all tuples
 *      startup_cost: cost that is expended before first tuple is fetched
 * In some scenarios, such as when there is a LIMIT or we are implementing
 * an EXISTS(...) sub-select, it is not necessary to fetch all tuples of the
 * path's result.  A caller can estimate the cost of fetching a partial
 * result by interpolating between startup_cost and total_cost.  In detail:
 *      actual_cost = startup_cost +
 *          (total_cost - startup_cost) * tuples_to_fetch / path->rows;
 * Note that a base relation's rows count (and, by extension, plan_rows for
 * plan nodes below the LIMIT node) are set without regard to any LIMIT, so
 * that this equation works properly.  (Note: while path->rows is never zero
 * for ordinary relations, it is zero for paths for provably-empty relations,
 * so beware of division-by-zero.)  The LIMIT is applied as a top-level
 * plan node.
 *
 * For largely historical reasons, most of the routines in this module use
 * the passed result Path only to store their results (rows, startup_cost and
 * total_cost) into.  All the input data they need is passed as separate
 * parameters, even though much of it could be extracted from the Path.
 * An exception is made for the cost_XXXjoin() routines, which expect all
 * the other fields of the passed XXXPath to be filled in, and similarly
 * cost_index() assumes the passed IndexPath is valid except for its output
 * values.
 *
 *
 * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/optimizer/path/costsize.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include <limits.h>
#include <math.h>
 
#include "access/amapi.h"
#include "access/htup_details.h"
#include "access/tsmapi.h"
#include "executor/executor.h"
#include "executor/nodeAgg.h"
#include "executor/nodeHash.h"
#include "executor/nodeMemoize.h"
#include "miscadmin.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/optimizer.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/placeholder.h"
#include "optimizer/plancat.h"
#include "optimizer/restrictinfo.h"
#include "parser/parsetree.h"
#include "utils/lsyscache.h"
#include "utils/selfuncs.h"
#include "utils/spccache.h"
#include "utils/tuplesort.h"
 
 
#define LOG2(x)  (log(x) / 0.693147180559945)
 
/*
 * Append and MergeAppend nodes are less expensive than some other operations
 * which use cpu_tuple_cost; instead of adding a separate GUC, estimate the
 * per-tuple cost as cpu_tuple_cost multiplied by this value.
 */
#define APPEND_CPU_COST_MULTIPLIER 0.5
 
/*
 * Maximum value for row estimates.  We cap row estimates to this to help
 * ensure that costs based on these estimates remain within the range of what
 * double can represent.  add_path() wouldn't act sanely given infinite or NaN
 * cost values.
 */
#define MAXIMUM_ROWCOUNT 1e100
 
double      seq_page_cost = DEFAULT_SEQ_PAGE_COST;
double      random_page_cost = DEFAULT_RANDOM_PAGE_COST;
double      cpu_tuple_cost = DEFAULT_CPU_TUPLE_COST;
double      cpu_index_tuple_cost = DEFAULT_CPU_INDEX_TUPLE_COST;
double      cpu_operator_cost = DEFAULT_CPU_OPERATOR_COST;
double      parallel_tuple_cost = DEFAULT_PARALLEL_TUPLE_COST;
double      parallel_setup_cost = DEFAULT_PARALLEL_SETUP_COST;
double      recursive_worktable_factor = DEFAULT_RECURSIVE_WORKTABLE_FACTOR;
 
int         effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;
 
Cost        disable_cost = 1.0e10;
 
int         max_parallel_workers_per_gather = 2;
 
bool        enable_seqscan = true;
bool        enable_indexscan = true;
bool        enable_indexonlyscan = true;
bool        enable_bitmapscan = true;
bool        enable_tidscan = true;
bool        enable_sort = true;
bool        enable_incremental_sort = true;
bool        enable_hashagg = true;
bool        enable_nestloop = true;
bool        enable_material = true;
bool        enable_memoize = true;
bool        enable_mergejoin = true;
bool        enable_hashjoin = true;
bool        enable_gathermerge = true;
bool        enable_partitionwise_join = false;
bool        enable_partitionwise_aggregate = false;
bool        enable_parallel_append = true;
bool        enable_parallel_hash = true;
bool        enable_partition_pruning = true;
bool        enable_presorted_aggregate = true;
bool        enable_async_append = true;
 
typedef struct
{
    PlannerInfo *root;
    QualCost    total;
} cost_qual_eval_context;
 
static List *extract_nonindex_conditions(List *qual_clauses, List *indexclauses);
static MergeScanSelCache *cached_scansel(PlannerInfo *root,
                                         RestrictInfo *rinfo,
                                         PathKey *pathkey);
static void cost_rescan(PlannerInfo *root, Path *path,
                        Cost *rescan_startup_cost, Cost *rescan_total_cost);
static bool cost_qual_eval_walker(Node *node, cost_qual_eval_context *context);
static void get_restriction_qual_cost(PlannerInfo *root, RelOptInfo *baserel,
                                      ParamPathInfo *param_info,
                                      QualCost *qpqual_cost);
static bool has_indexed_join_quals(NestPath *path);
static double approx_tuple_count(PlannerInfo *root, JoinPath *path,
                                 List *quals);
static double calc_joinrel_size_estimate(PlannerInfo *root,
                                         RelOptInfo *joinrel,
                                         RelOptInfo *outer_rel,
                                         RelOptInfo *inner_rel,
                                         double outer_rows,
                                         double inner_rows,
                                         SpecialJoinInfo *sjinfo,
                                         List *restrictlist);
static Selectivity get_foreign_key_join_selectivity(PlannerInfo *root,
                                                    Relids outer_relids,
                                                    Relids inner_relids,
                                                    SpecialJoinInfo *sjinfo,
                                                    List **restrictlist);
static Cost append_nonpartial_cost(List *subpaths, int numpaths,
                                   int parallel_workers);
static void set_rel_width(PlannerInfo *root, RelOptInfo *rel);
static int32 get_expr_width(PlannerInfo *root, const Node *expr);
static double relation_byte_size(double tuples, int width);
static double page_size(double tuples, int width);
static double get_parallel_divisor(Path *path);
 
 
/*
 * clamp_row_est
 *      Force a row-count estimate to a sane value.
 */
double
clamp_row_est(double nrows)
{
    /*
     * Avoid infinite and NaN row estimates.  Costs derived from such values
     * are going to be useless.  Also force the estimate to be at least one
     * row, to make explain output look better and to avoid possible
     * divide-by-zero when interpolating costs.  Make it an integer, too.
     */
    if (nrows > MAXIMUM_ROWCOUNT || isnan(nrows))
        nrows = MAXIMUM_ROWCOUNT;
    else if (nrows <= 1.0)
        nrows = 1.0;
    else
        nrows = rint(nrows);
 
    return nrows;
}
 
/*
 * clamp_width_est
 *      Force a tuple-width estimate to a sane value.
 *
 * The planner represents datatype width and tuple width estimates as int32.
 * When summing column width estimates to create a tuple width estimate,
 * it's possible to reach integer overflow in edge cases.  To ensure sane
 * behavior, we form such sums in int64 arithmetic and then apply this routine
 * to clamp to int32 range.
 */
int32
clamp_width_est(int64 tuple_width)
{
    /*
     * Anything more than MaxAllocSize is clearly bogus, since we could not
     * create a tuple that large.
     */
    if (tuple_width > MaxAllocSize)
        return (int32) MaxAllocSize;
 
    /*
     * Unlike clamp_row_est, we just Assert that the value isn't negative,
     * rather than masking such errors.
     */
    Assert(tuple_width >= 0);
 
    return (int32) tuple_width;
}
 
/*
 * clamp_cardinality_to_long
 *      Cast a Cardinality value to a sane long value.
 */
long
clamp_cardinality_to_long(Cardinality x)
{
    /*
     * Just for paranoia's sake, ensure we do something sane with negative or
     * NaN values.
     */
    if (isnan(x))
        return LONG_MAX;
    if (x <= 0)
        return 0;
 
    /*
     * If "long" is 64 bits, then LONG_MAX cannot be represented exactly as a
     * double.  Casting it to double and back may well result in overflow due
     * to rounding, so avoid doing that.  We trust that any double value that
     * compares strictly less than "(double) LONG_MAX" will cast to a
     * representable "long" value.
     */
    return (x < (double) LONG_MAX) ? (long) x : LONG_MAX;
}
 
 
/*
 * cost_seqscan
 *    Determines and returns the cost of scanning a relation sequentially.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_seqscan(Path *path, PlannerInfo *root,
             RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        cpu_run_cost;
    Cost        disk_run_cost;
    double      spc_seq_page_cost;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to base relations */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_RELATION);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    if (!enable_seqscan)
        startup_cost += disable_cost;
 
    /* fetch estimated page cost for tablespace containing table */
    get_tablespace_page_costs(baserel->reltablespace,
                              NULL,
                              &spc_seq_page_cost);
 
    /*
     * disk costs
     */
    disk_run_cost = spc_seq_page_cost * baserel->pages;
 
    /* CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    cpu_run_cost = cpu_per_tuple * baserel->tuples;
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    cpu_run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    /* Adjust costing for parallelism, if used. */
    if (path->parallel_workers > 0)
    {
        double      parallel_divisor = get_parallel_divisor(path);
 
        /* The CPU cost is divided among all the workers. */
        cpu_run_cost /= parallel_divisor;
 
        /*
         * It may be possible to amortize some of the I/O cost, but probably
         * not very much, because most operating systems already do aggressive
         * prefetching.  For now, we assume that the disk run cost can't be
         * amortized at all.
         */
 
        /*
         * In the case of a parallel plan, the row count needs to represent
         * the number of tuples processed per worker.
         */
        path->rows = clamp_row_est(path->rows / parallel_divisor);
    }
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + cpu_run_cost + disk_run_cost;
}
 
/*
 * cost_samplescan
 *    Determines and returns the cost of scanning a relation using sampling.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_samplescan(Path *path, PlannerInfo *root,
                RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    RangeTblEntry *rte;
    TableSampleClause *tsc;
    TsmRoutine *tsm;
    double      spc_seq_page_cost,
                spc_random_page_cost,
                spc_page_cost;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to base relations with tablesample clauses */
    Assert(baserel->relid > 0);
    rte = planner_rt_fetch(baserel->relid, root);
    Assert(rte->rtekind == RTE_RELATION);
    tsc = rte->tablesample;
    Assert(tsc != NULL);
    tsm = GetTsmRoutine(tsc->tsmhandler);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /* fetch estimated page cost for tablespace containing table */
    get_tablespace_page_costs(baserel->reltablespace,
                              &spc_random_page_cost,
                              &spc_seq_page_cost);
 
    /* if NextSampleBlock is used, assume random access, else sequential */
    spc_page_cost = (tsm->NextSampleBlock != NULL) ?
        spc_random_page_cost : spc_seq_page_cost;
 
    /*
     * disk costs (recall that baserel->pages has already been set to the
     * number of pages the sampling method will visit)
     */
    run_cost += spc_page_cost * baserel->pages;
 
    /*
     * CPU costs (recall that baserel->tuples has already been set to the
     * number of tuples the sampling method will select).  Note that we ignore
     * execution cost of the TABLESAMPLE parameter expressions; they will be
     * evaluated only once per scan, and in most usages they'll likely be
     * simple constants anyway.  We also don't charge anything for the
     * calculations the sampling method might do internally.
     */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_gather
 *    Determines and returns the cost of gather path.
 *
 * 'rel' is the relation to be operated upon
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 * 'rows' may be used to point to a row estimate; if non-NULL, it overrides
 * both 'rel' and 'param_info'.  This is useful when the path doesn't exactly
 * correspond to any particular RelOptInfo.
 */
void
cost_gather(GatherPath *path, PlannerInfo *root,
            RelOptInfo *rel, ParamPathInfo *param_info,
            double *rows)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
 
    /* Mark the path with the correct row estimate */
    if (rows)
        path->path.rows = *rows;
    else if (param_info)
        path->path.rows = param_info->ppi_rows;
    else
        path->path.rows = rel->rows;
 
    startup_cost = path->subpath->startup_cost;
 
    run_cost = path->subpath->total_cost - path->subpath->startup_cost;
 
    /* Parallel setup and communication cost. */
    startup_cost += parallel_setup_cost;
    run_cost += parallel_tuple_cost * path->path.rows;
 
    path->path.startup_cost = startup_cost;
    path->path.total_cost = (startup_cost + run_cost);
}
 
/*
 * cost_gather_merge
 *    Determines and returns the cost of gather merge path.
 *
 * GatherMerge merges several pre-sorted input streams, using a heap that at
 * any given instant holds the next tuple from each stream. If there are N
 * streams, we need about N*log2(N) tuple comparisons to construct the heap at
 * startup, and then for each output tuple, about log2(N) comparisons to
 * replace the top heap entry with the next tuple from the same stream.
 */
void
cost_gather_merge(GatherMergePath *path, PlannerInfo *root,
                  RelOptInfo *rel, ParamPathInfo *param_info,
                  Cost input_startup_cost, Cost input_total_cost,
                  double *rows)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    Cost        comparison_cost;
    double      N;
    double      logN;
 
    /* Mark the path with the correct row estimate */
    if (rows)
        path->path.rows = *rows;
    else if (param_info)
        path->path.rows = param_info->ppi_rows;
    else
        path->path.rows = rel->rows;
 
    if (!enable_gathermerge)
        startup_cost += disable_cost;
 
    /*
     * Add one to the number of workers to account for the leader.  This might
     * be overgenerous since the leader will do less work than other workers
     * in typical cases, but we'll go with it for now.
     */
    Assert(path->num_workers > 0);
    N = (double) path->num_workers + 1;
    logN = LOG2(N);
 
    /* Assumed cost per tuple comparison */
    comparison_cost = 2.0 * cpu_operator_cost;
 
    /* Heap creation cost */
    startup_cost += comparison_cost * N * logN;
 
    /* Per-tuple heap maintenance cost */
    run_cost += path->path.rows * comparison_cost * logN;
 
    /* small cost for heap management, like cost_merge_append */
    run_cost += cpu_operator_cost * path->path.rows;
 
    /*
     * Parallel setup and communication cost.  Since Gather Merge, unlike
     * Gather, requires us to block until a tuple is available from every
     * worker, we bump the IPC cost up a little bit as compared with Gather.
     * For lack of a better idea, charge an extra 5%.
     */
    startup_cost += parallel_setup_cost;
    run_cost += parallel_tuple_cost * path->path.rows * 1.05;
 
    path->path.startup_cost = startup_cost + input_startup_cost;
    path->path.total_cost = (startup_cost + run_cost + input_total_cost);
}
 
/*
 * cost_index
 *    Determines and returns the cost of scanning a relation using an index.
 *
 * 'path' describes the indexscan under consideration, and is complete
 *      except for the fields to be set by this routine
 * 'loop_count' is the number of repetitions of the indexscan to factor into
 *      estimates of caching behavior
 *
 * In addition to rows, startup_cost and total_cost, cost_index() sets the
 * path's indextotalcost and indexselectivity fields.  These values will be
 * needed if the IndexPath is used in a BitmapIndexScan.
 *
 * NOTE: path->indexquals must contain only clauses usable as index
 * restrictions.  Any additional quals evaluated as qpquals may reduce the
 * number of returned tuples, but they won't reduce the number of tuples
 * we have to fetch from the table, so they don't reduce the scan cost.
 */
void
cost_index(IndexPath *path, PlannerInfo *root, double loop_count,
           bool partial_path)
{
    IndexOptInfo *index = path->indexinfo;
    RelOptInfo *baserel = index->rel;
    bool        indexonly = (path->path.pathtype == T_IndexOnlyScan);
    amcostestimate_function amcostestimate;
    List       *qpquals;
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    Cost        cpu_run_cost = 0;
    Cost        indexStartupCost;
    Cost        indexTotalCost;
    Selectivity indexSelectivity;
    double      indexCorrelation,
                csquared;
    double      spc_seq_page_cost,
                spc_random_page_cost;
    Cost        min_IO_cost,
                max_IO_cost;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
    double      tuples_fetched;
    double      pages_fetched;
    double      rand_heap_pages;
    double      index_pages;
 
    /* Should only be applied to base relations */
    Assert(IsA(baserel, RelOptInfo) &&
           IsA(index, IndexOptInfo));
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_RELATION);
 
    /*
     * Mark the path with the correct row estimate, and identify which quals
     * will need to be enforced as qpquals.  We need not check any quals that
     * are implied by the index's predicate, so we can use indrestrictinfo not
     * baserestrictinfo as the list of relevant restriction clauses for the
     * rel.
     */
    if (path->path.param_info)
    {
        path->path.rows = path->path.param_info->ppi_rows;
        /* qpquals come from the rel's restriction clauses and ppi_clauses */
        qpquals = list_concat(extract_nonindex_conditions(path->indexinfo->indrestrictinfo,
                                                          path->indexclauses),
                              extract_nonindex_conditions(path->path.param_info->ppi_clauses,
                                                          path->indexclauses));
    }
    else
    {
        path->path.rows = baserel->rows;
        /* qpquals come from just the rel's restriction clauses */
        qpquals = extract_nonindex_conditions(path->indexinfo->indrestrictinfo,
                                              path->indexclauses);
    }
 
    if (!enable_indexscan)
        startup_cost += disable_cost;
    /* we don't need to check enable_indexonlyscan; indxpath.c does that */
 
    /*
     * Call index-access-method-specific code to estimate the processing cost
     * for scanning the index, as well as the selectivity of the index (ie,
     * the fraction of main-table tuples we will have to retrieve) and its
     * correlation to the main-table tuple order.  We need a cast here because
     * pathnodes.h uses a weak function type to avoid including amapi.h.
     */
    amcostestimate = (amcostestimate_function) index->amcostestimate;
    amcostestimate(root, path, loop_count,
                   &indexStartupCost, &indexTotalCost,
                   &indexSelectivity, &indexCorrelation,
                   &index_pages);
 
    /*
     * Save amcostestimate's results for possible use in bitmap scan planning.
     * We don't bother to save indexStartupCost or indexCorrelation, because a
     * bitmap scan doesn't care about either.
     */
    path->indextotalcost = indexTotalCost;
    path->indexselectivity = indexSelectivity;
 
    /* all costs for touching index itself included here */
    startup_cost += indexStartupCost;
    run_cost += indexTotalCost - indexStartupCost;
 
    /* estimate number of main-table tuples fetched */
    tuples_fetched = clamp_row_est(indexSelectivity * baserel->tuples);
 
    /* fetch estimated page costs for tablespace containing table */
    get_tablespace_page_costs(baserel->reltablespace,
                              &spc_random_page_cost,
                              &spc_seq_page_cost);
 
    /*----------
     * Estimate number of main-table pages fetched, and compute I/O cost.
     *
     * When the index ordering is uncorrelated with the table ordering,
     * we use an approximation proposed by Mackert and Lohman (see
     * index_pages_fetched() for details) to compute the number of pages
     * fetched, and then charge spc_random_page_cost per page fetched.
     *
     * When the index ordering is exactly correlated with the table ordering
     * (just after a CLUSTER, for example), the number of pages fetched should
     * be exactly selectivity * table_size.  What's more, all but the first
     * will be sequential fetches, not the random fetches that occur in the
     * uncorrelated case.  So if the number of pages is more than 1, we
     * ought to charge
     *      spc_random_page_cost + (pages_fetched - 1) * spc_seq_page_cost
     * For partially-correlated indexes, we ought to charge somewhere between
     * these two estimates.  We currently interpolate linearly between the
     * estimates based on the correlation squared (XXX is that appropriate?).
     *
     * If it's an index-only scan, then we will not need to fetch any heap
     * pages for which the visibility map shows all tuples are visible.
     * Hence, reduce the estimated number of heap fetches accordingly.
     * We use the measured fraction of the entire heap that is all-visible,
     * which might not be particularly relevant to the subset of the heap
     * that this query will fetch; but it's not clear how to do better.
     *----------
     */
    if (loop_count > 1)
    {
        /*
         * For repeated indexscans, the appropriate estimate for the
         * uncorrelated case is to scale up the number of tuples fetched in
         * the Mackert and Lohman formula by the number of scans, so that we
         * estimate the number of pages fetched by all the scans; then
         * pro-rate the costs for one scan.  In this case we assume all the
         * fetches are random accesses.
         */
        pages_fetched = index_pages_fetched(tuples_fetched * loop_count,
                                            baserel->pages,
                                            (double) index->pages,
                                            root);
 
        if (indexonly)
            pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
 
        rand_heap_pages = pages_fetched;
 
        max_IO_cost = (pages_fetched * spc_random_page_cost) / loop_count;
 
        /*
         * In the perfectly correlated case, the number of pages touched by
         * each scan is selectivity * table_size, and we can use the Mackert
         * and Lohman formula at the page level to estimate how much work is
         * saved by caching across scans.  We still assume all the fetches are
         * random, though, which is an overestimate that's hard to correct for
         * without double-counting the cache effects.  (But in most cases
         * where such a plan is actually interesting, only one page would get
         * fetched per scan anyway, so it shouldn't matter much.)
         */
        pages_fetched = ceil(indexSelectivity * (double) baserel->pages);
 
        pages_fetched = index_pages_fetched(pages_fetched * loop_count,
                                            baserel->pages,
                                            (double) index->pages,
                                            root);
 
        if (indexonly)
            pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
 
        min_IO_cost = (pages_fetched * spc_random_page_cost) / loop_count;
    }
    else
    {
        /*
         * Normal case: apply the Mackert and Lohman formula, and then
         * interpolate between that and the correlation-derived result.
         */
        pages_fetched = index_pages_fetched(tuples_fetched,
                                            baserel->pages,
                                            (double) index->pages,
                                            root);
 
        if (indexonly)
            pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
 
        rand_heap_pages = pages_fetched;
 
        /* max_IO_cost is for the perfectly uncorrelated case (csquared=0) */
        max_IO_cost = pages_fetched * spc_random_page_cost;
 
        /* min_IO_cost is for the perfectly correlated case (csquared=1) */
        pages_fetched = ceil(indexSelectivity * (double) baserel->pages);
 
        if (indexonly)
            pages_fetched = ceil(pages_fetched * (1.0 - baserel->allvisfrac));
 
        if (pages_fetched > 0)
        {
            min_IO_cost = spc_random_page_cost;
            if (pages_fetched > 1)
                min_IO_cost += (pages_fetched - 1) * spc_seq_page_cost;
        }
        else
            min_IO_cost = 0;
    }
 
    if (partial_path)
    {
        /*
         * For index only scans compute workers based on number of index pages
         * fetched; the number of heap pages we fetch might be so small as to
         * effectively rule out parallelism, which we don't want to do.
         */
        if (indexonly)
            rand_heap_pages = -1;
 
        /*
         * Estimate the number of parallel workers required to scan index. Use
         * the number of heap pages computed considering heap fetches won't be
         * sequential as for parallel scans the pages are accessed in random
         * order.
         */
        path->path.parallel_workers = compute_parallel_worker(baserel,
                                                              rand_heap_pages,
                                                              index_pages,
                                                              max_parallel_workers_per_gather);
 
        /*
         * Fall out if workers can't be assigned for parallel scan, because in
         * such a case this path will be rejected.  So there is no benefit in
         * doing extra computation.
         */
        if (path->path.parallel_workers <= 0)
            return;
 
        path->path.parallel_aware = true;
    }
 
    /*
     * Now interpolate based on estimated index order correlation to get total
     * disk I/O cost for main table accesses.
     */
    csquared = indexCorrelation * indexCorrelation;
 
    run_cost += max_IO_cost + csquared * (min_IO_cost - max_IO_cost);
 
    /*
     * Estimate CPU costs per tuple.
     *
     * What we want here is cpu_tuple_cost plus the evaluation costs of any
     * qual clauses that we have to evaluate as qpquals.
     */
    cost_qual_eval(&qpqual_cost, qpquals, root);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
 
    cpu_run_cost += cpu_per_tuple * tuples_fetched;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->path.pathtarget->cost.startup;
    cpu_run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;
 
    /* Adjust costing for parallelism, if used. */
    if (path->path.parallel_workers > 0)
    {
        double      parallel_divisor = get_parallel_divisor(&path->path);
 
        path->path.rows = clamp_row_est(path->path.rows / parallel_divisor);
 
        /* The CPU cost is divided among all the workers. */
        cpu_run_cost /= parallel_divisor;
    }
 
    run_cost += cpu_run_cost;
 
    path->path.startup_cost = startup_cost;
    path->path.total_cost = startup_cost + run_cost;
}
 
/*
 * extract_nonindex_conditions
 *
 * Given a list of quals to be enforced in an indexscan, extract the ones that
 * will have to be applied as qpquals (ie, the index machinery won't handle
 * them).  Here we detect only whether a qual clause is directly redundant
 * with some indexclause.  If the index path is chosen for use, createplan.c
 * will try a bit harder to get rid of redundant qual conditions; specifically
 * it will see if quals can be proven to be implied by the indexquals.  But
 * it does not seem worth the cycles to try to factor that in at this stage,
 * since we're only trying to estimate qual eval costs.  Otherwise this must
 * match the logic in create_indexscan_plan().
 *
 * qual_clauses, and the result, are lists of RestrictInfos.
 * indexclauses is a list of IndexClauses.
 */
static List *
extract_nonindex_conditions(List *qual_clauses, List *indexclauses)
{
    List       *result = NIL;
    ListCell   *lc;
 
    foreach(lc, qual_clauses)
    {
        RestrictInfo *rinfo = lfirst_node(RestrictInfo, lc);
 
        if (rinfo->pseudoconstant)
            continue;           /* we may drop pseudoconstants here */
        if (is_redundant_with_indexclauses(rinfo, indexclauses))
            continue;           /* dup or derived from same EquivalenceClass */
        /* ... skip the predicate proof attempt createplan.c will try ... */
        result = lappend(result, rinfo);
    }
    return result;
}
 
/*
 * index_pages_fetched
 *    Estimate the number of pages actually fetched after accounting for
 *    cache effects.
 *
 * We use an approximation proposed by Mackert and Lohman, "Index Scans
 * Using a Finite LRU Buffer: A Validated I/O Model", ACM Transactions
 * on Database Systems, Vol. 14, No. 3, September 1989, Pages 401-424.
 * The Mackert and Lohman approximation is that the number of pages
 * fetched is
 *  PF =
 *      min(2TNs/(2T+Ns), T)            when T <= b
 *      2TNs/(2T+Ns)                    when T > b and Ns <= 2Tb/(2T-b)
 *      b + (Ns - 2Tb/(2T-b))*(T-b)/T   when T > b and Ns > 2Tb/(2T-b)
 * where
 *      T = # pages in table
 *      N = # tuples in table
 *      s = selectivity = fraction of table to be scanned
 *      b = # buffer pages available (we include kernel space here)
 *
 * We assume that effective_cache_size is the total number of buffer pages
 * available for the whole query, and pro-rate that space across all the
 * tables in the query and the index currently under consideration.  (This
 * ignores space needed for other indexes used by the query, but since we
 * don't know which indexes will get used, we can't estimate that very well;
 * and in any case counting all the tables may well be an overestimate, since
 * depending on the join plan not all the tables may be scanned concurrently.)
 *
 * The product Ns is the number of tuples fetched; we pass in that
 * product rather than calculating it here.  "pages" is the number of pages
 * in the object under consideration (either an index or a table).
 * "index_pages" is the amount to add to the total table space, which was
 * computed for us by make_one_rel.
 *
 * Caller is expected to have ensured that tuples_fetched is greater than zero
 * and rounded to integer (see clamp_row_est).  The result will likewise be
 * greater than zero and integral.
 */
double
index_pages_fetched(double tuples_fetched, BlockNumber pages,
                    double index_pages, PlannerInfo *root)
{
    double      pages_fetched;
    double      total_pages;
    double      T,
                b;
 
    /* T is # pages in table, but don't allow it to be zero */
    T = (pages > 1) ? (double) pages : 1.0;
 
    /* Compute number of pages assumed to be competing for cache space */
    total_pages = root->total_table_pages + index_pages;
    total_pages = Max(total_pages, 1.0);
    Assert(T <= total_pages);
 
    /* b is pro-rated share of effective_cache_size */
    b = (double) effective_cache_size * T / total_pages;
 
    /* force it positive and integral */
    if (b <= 1.0)
        b = 1.0;
    else
        b = ceil(b);
 
    /* This part is the Mackert and Lohman formula */
    if (T <= b)
    {
        pages_fetched =
            (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
        if (pages_fetched >= T)
            pages_fetched = T;
        else
            pages_fetched = ceil(pages_fetched);
    }
    else
    {
        double      lim;
 
        lim = (2.0 * T * b) / (2.0 * T - b);
        if (tuples_fetched <= lim)
        {
            pages_fetched =
                (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
        }
        else
        {
            pages_fetched =
                b + (tuples_fetched - lim) * (T - b) / T;
        }
        pages_fetched = ceil(pages_fetched);
    }
    return pages_fetched;
}
 
/*
 * get_indexpath_pages
 *      Determine the total size of the indexes used in a bitmap index path.
 *
 * Note: if the same index is used more than once in a bitmap tree, we will
 * count it multiple times, which perhaps is the wrong thing ... but it's
 * not completely clear, and detecting duplicates is difficult, so ignore it
 * for now.
 */
static double
get_indexpath_pages(Path *bitmapqual)
{
    double      result = 0;
    ListCell   *l;
 
    if (IsA(bitmapqual, BitmapAndPath))
    {
        BitmapAndPath *apath = (BitmapAndPath *) bitmapqual;
 
        foreach(l, apath->bitmapquals)
        {
            result += get_indexpath_pages((Path *) lfirst(l));
        }
    }
    else if (IsA(bitmapqual, BitmapOrPath))
    {
        BitmapOrPath *opath = (BitmapOrPath *) bitmapqual;
 
        foreach(l, opath->bitmapquals)
        {
            result += get_indexpath_pages((Path *) lfirst(l));
        }
    }
    else if (IsA(bitmapqual, IndexPath))
    {
        IndexPath  *ipath = (IndexPath *) bitmapqual;
 
        result = (double) ipath->indexinfo->pages;
    }
    else
        elog(ERROR, "unrecognized node type: %d", nodeTag(bitmapqual));
 
    return result;
}
 
/*
 * cost_bitmap_heap_scan
 *    Determines and returns the cost of scanning a relation using a bitmap
 *    index-then-heap plan.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 * 'bitmapqual' is a tree of IndexPaths, BitmapAndPaths, and BitmapOrPaths
 * 'loop_count' is the number of repetitions of the indexscan to factor into
 *      estimates of caching behavior
 *
 * Note: the component IndexPaths in bitmapqual should have been costed
 * using the same loop_count.
 */
void
cost_bitmap_heap_scan(Path *path, PlannerInfo *root, RelOptInfo *baserel,
                      ParamPathInfo *param_info,
                      Path *bitmapqual, double loop_count)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    Cost        indexTotalCost;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
    Cost        cost_per_page;
    Cost        cpu_run_cost;
    double      tuples_fetched;
    double      pages_fetched;
    double      spc_seq_page_cost,
                spc_random_page_cost;
    double      T;
 
    /* Should only be applied to base relations */
    Assert(IsA(baserel, RelOptInfo));
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_RELATION);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    if (!enable_bitmapscan)
        startup_cost += disable_cost;
 
    pages_fetched = compute_bitmap_pages(root, baserel, bitmapqual,
                                         loop_count, &indexTotalCost,
                                         &tuples_fetched);
 
    startup_cost += indexTotalCost;
    T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
 
    /* Fetch estimated page costs for tablespace containing table. */
    get_tablespace_page_costs(baserel->reltablespace,
                              &spc_random_page_cost,
                              &spc_seq_page_cost);
 
    /*
     * For small numbers of pages we should charge spc_random_page_cost
     * apiece, while if nearly all the table's pages are being read, it's more
     * appropriate to charge spc_seq_page_cost apiece.  The effect is
     * nonlinear, too. For lack of a better idea, interpolate like this to
     * determine the cost per page.
     */
    if (pages_fetched >= 2.0)
        cost_per_page = spc_random_page_cost -
            (spc_random_page_cost - spc_seq_page_cost)
            * sqrt(pages_fetched / T);
    else
        cost_per_page = spc_random_page_cost;
 
    run_cost += pages_fetched * cost_per_page;
 
    /*
     * Estimate CPU costs per tuple.
     *
     * Often the indexquals don't need to be rechecked at each tuple ... but
     * not always, especially not if there are enough tuples involved that the
     * bitmaps become lossy.  For the moment, just assume they will be
     * rechecked always.  This means we charge the full freight for all the
     * scan clauses.
     */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    cpu_run_cost = cpu_per_tuple * tuples_fetched;
 
    /* Adjust costing for parallelism, if used. */
    if (path->parallel_workers > 0)
    {
        double      parallel_divisor = get_parallel_divisor(path);
 
        /* The CPU cost is divided among all the workers. */
        cpu_run_cost /= parallel_divisor;
 
        path->rows = clamp_row_est(path->rows / parallel_divisor);
    }
 
 
    run_cost += cpu_run_cost;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_bitmap_tree_node
 *      Extract cost and selectivity from a bitmap tree node (index/and/or)
 */
void
cost_bitmap_tree_node(Path *path, Cost *cost, Selectivity *selec)
{
    if (IsA(path, IndexPath))
    {
        *cost = ((IndexPath *) path)->indextotalcost;
        *selec = ((IndexPath *) path)->indexselectivity;
 
        /*
         * Charge a small amount per retrieved tuple to reflect the costs of
         * manipulating the bitmap.  This is mostly to make sure that a bitmap
         * scan doesn't look to be the same cost as an indexscan to retrieve a
         * single tuple.
         */
        *cost += 0.1 * cpu_operator_cost * path->rows;
    }
    else if (IsA(path, BitmapAndPath))
    {
        *cost = path->total_cost;
        *selec = ((BitmapAndPath *) path)->bitmapselectivity;
    }
    else if (IsA(path, BitmapOrPath))
    {
        *cost = path->total_cost;
        *selec = ((BitmapOrPath *) path)->bitmapselectivity;
    }
    else
    {
        elog(ERROR, "unrecognized node type: %d", nodeTag(path));
        *cost = *selec = 0;     /* keep compiler quiet */
    }
}
 
/*
 * cost_bitmap_and_node
 *      Estimate the cost of a BitmapAnd node
 *
 * Note that this considers only the costs of index scanning and bitmap
 * creation, not the eventual heap access.  In that sense the object isn't
 * truly a Path, but it has enough path-like properties (costs in particular)
 * to warrant treating it as one.  We don't bother to set the path rows field,
 * however.
 */
void
cost_bitmap_and_node(BitmapAndPath *path, PlannerInfo *root)
{
    Cost        totalCost;
    Selectivity selec;
    ListCell   *l;
 
    /*
     * We estimate AND selectivity on the assumption that the inputs are
     * independent.  This is probably often wrong, but we don't have the info
     * to do better.
     *
     * The runtime cost of the BitmapAnd itself is estimated at 100x
     * cpu_operator_cost for each tbm_intersect needed.  Probably too small,
     * definitely too simplistic?
     */
    totalCost = 0.0;
    selec = 1.0;
    foreach(l, path->bitmapquals)
    {
        Path       *subpath = (Path *) lfirst(l);
        Cost        subCost;
        Selectivity subselec;
 
        cost_bitmap_tree_node(subpath, &subCost, &subselec);
 
        selec *= subselec;
 
        totalCost += subCost;
        if (l != list_head(path->bitmapquals))
            totalCost += 100.0 * cpu_operator_cost;
    }
    path->bitmapselectivity = selec;
    path->path.rows = 0;        /* per above, not used */
    path->path.startup_cost = totalCost;
    path->path.total_cost = totalCost;
}
 
/*
 * cost_bitmap_or_node
 *      Estimate the cost of a BitmapOr node
 *
 * See comments for cost_bitmap_and_node.
 */
void
cost_bitmap_or_node(BitmapOrPath *path, PlannerInfo *root)
{
    Cost        totalCost;
    Selectivity selec;
    ListCell   *l;
 
    /*
     * We estimate OR selectivity on the assumption that the inputs are
     * non-overlapping, since that's often the case in "x IN (list)" type
     * situations.  Of course, we clamp to 1.0 at the end.
     *
     * The runtime cost of the BitmapOr itself is estimated at 100x
     * cpu_operator_cost for each tbm_union needed.  Probably too small,
     * definitely too simplistic?  We are aware that the tbm_unions are
     * optimized out when the inputs are BitmapIndexScans.
     */
    totalCost = 0.0;
    selec = 0.0;
    foreach(l, path->bitmapquals)
    {
        Path       *subpath = (Path *) lfirst(l);
        Cost        subCost;
        Selectivity subselec;
 
        cost_bitmap_tree_node(subpath, &subCost, &subselec);
 
        selec += subselec;
 
        totalCost += subCost;
        if (l != list_head(path->bitmapquals) &&
            !IsA(subpath, IndexPath))
            totalCost += 100.0 * cpu_operator_cost;
    }
    path->bitmapselectivity = Min(selec, 1.0);
    path->path.rows = 0;        /* per above, not used */
    path->path.startup_cost = totalCost;
    path->path.total_cost = totalCost;
}
 
/*
 * cost_tidscan
 *    Determines and returns the cost of scanning a relation using TIDs.
 *
 * 'baserel' is the relation to be scanned
 * 'tidquals' is the list of TID-checkable quals
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_tidscan(Path *path, PlannerInfo *root,
             RelOptInfo *baserel, List *tidquals, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
    QualCost    tid_qual_cost;
    double      ntuples;
    ListCell   *l;
    double      spc_random_page_cost;
 
    /* Should only be applied to base relations */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_RELATION);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /* Count how many tuples we expect to retrieve */
    ntuples = 0;
    foreach(l, tidquals)
    {
        RestrictInfo *rinfo = lfirst_node(RestrictInfo, l);
        Expr       *qual = rinfo->clause;
 
        if (IsA(qual, ScalarArrayOpExpr))
        {
            /* Each element of the array yields 1 tuple */
            ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) qual;
            Node       *arraynode = (Node *) lsecond(saop->args);
 
            ntuples += estimate_array_length(root, arraynode);
        }
        else if (IsA(qual, CurrentOfExpr))
        {
            /* CURRENT OF yields 1 tuple */
            ntuples++;
        }
        else
        {
            /* It's just CTID = something, count 1 tuple */
            ntuples++;
        }
    }
 
    /*
     * The TID qual expressions will be computed once, any other baserestrict
     * quals once per retrieved tuple.
     */
    cost_qual_eval(&tid_qual_cost, tidquals, root);
 
    /* fetch estimated page cost for tablespace containing table */
    get_tablespace_page_costs(baserel->reltablespace,
                              &spc_random_page_cost,
                              NULL);
 
    /* disk costs --- assume each tuple on a different page */
    run_cost += spc_random_page_cost * ntuples;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    /* XXX currently we assume TID quals are a subset of qpquals */
    startup_cost += qpqual_cost.startup + tid_qual_cost.per_tuple;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple -
        tid_qual_cost.per_tuple;
    run_cost += cpu_per_tuple * ntuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_tidrangescan
 *    Determines and sets the costs of scanning a relation using a range of
 *    TIDs for 'path'
 *
 * 'baserel' is the relation to be scanned
 * 'tidrangequals' is the list of TID-checkable range quals
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_tidrangescan(Path *path, PlannerInfo *root,
                  RelOptInfo *baserel, List *tidrangequals,
                  ParamPathInfo *param_info)
{
    Selectivity selectivity;
    double      pages;
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
    QualCost    tid_qual_cost;
    double      ntuples;
    double      nseqpages;
    double      spc_random_page_cost;
    double      spc_seq_page_cost;
 
    /* Should only be applied to base relations */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_RELATION);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /* Count how many tuples and pages we expect to scan */
    selectivity = clauselist_selectivity(root, tidrangequals, baserel->relid,
                                         JOIN_INNER, NULL);
    pages = ceil(selectivity * baserel->pages);
 
    if (pages <= 0.0)
        pages = 1.0;
 
    /*
     * The first page in a range requires a random seek, but each subsequent
     * page is just a normal sequential page read. NOTE: it's desirable for
     * TID Range Scans to cost more than the equivalent Sequential Scans,
     * because Seq Scans have some performance advantages such as scan
     * synchronization and parallelizability, and we'd prefer one of them to
     * be picked unless a TID Range Scan really is better.
     */
    ntuples = selectivity * baserel->tuples;
    nseqpages = pages - 1.0;
 
    /*
     * The TID qual expressions will be computed once, any other baserestrict
     * quals once per retrieved tuple.
     */
    cost_qual_eval(&tid_qual_cost, tidrangequals, root);
 
    /* fetch estimated page cost for tablespace containing table */
    get_tablespace_page_costs(baserel->reltablespace,
                              &spc_random_page_cost,
                              &spc_seq_page_cost);
 
    /* disk costs; 1 random page and the remainder as seq pages */
    run_cost += spc_random_page_cost + spc_seq_page_cost * nseqpages;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    /*
     * XXX currently we assume TID quals are a subset of qpquals at this
     * point; they will be removed (if possible) when we create the plan, so
     * we subtract their cost from the total qpqual cost.  (If the TID quals
     * can't be removed, this is a mistake and we're going to underestimate
     * the CPU cost a bit.)
     */
    startup_cost += qpqual_cost.startup + tid_qual_cost.per_tuple;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple -
        tid_qual_cost.per_tuple;
    run_cost += cpu_per_tuple * ntuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_subqueryscan
 *    Determines and returns the cost of scanning a subquery RTE.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 * 'trivial_pathtarget' is true if the pathtarget is believed to be trivial.
 */
void
cost_subqueryscan(SubqueryScanPath *path, PlannerInfo *root,
                  RelOptInfo *baserel, ParamPathInfo *param_info,
                  bool trivial_pathtarget)
{
    Cost        startup_cost;
    Cost        run_cost;
    List       *qpquals;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to base relations that are subqueries */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_SUBQUERY);
 
    /*
     * We compute the rowcount estimate as the subplan's estimate times the
     * selectivity of relevant restriction clauses.  In simple cases this will
     * come out the same as baserel->rows; but when dealing with parallelized
     * paths we must do it like this to get the right answer.
     */
    if (param_info)
        qpquals = list_concat_copy(param_info->ppi_clauses,
                                   baserel->baserestrictinfo);
    else
        qpquals = baserel->baserestrictinfo;
 
    path->path.rows = clamp_row_est(path->subpath->rows *
                                    clauselist_selectivity(root,
                                                           qpquals,
                                                           0,
                                                           JOIN_INNER,
                                                           NULL));
 
    /*
     * Cost of path is cost of evaluating the subplan, plus cost of evaluating
     * any restriction clauses and tlist that will be attached to the
     * SubqueryScan node, plus cpu_tuple_cost to account for selection and
     * projection overhead.
     */
    path->path.startup_cost = path->subpath->startup_cost;
    path->path.total_cost = path->subpath->total_cost;
 
    /*
     * However, if there are no relevant restriction clauses and the
     * pathtarget is trivial, then we expect that setrefs.c will optimize away
     * the SubqueryScan plan node altogether, so we should just make its cost
     * and rowcount equal to the input path's.
     *
     * Note: there are some edge cases where createplan.c will apply a
     * different targetlist to the SubqueryScan node, thus falsifying our
     * current estimate of whether the target is trivial, and making the cost
     * estimate (though not the rowcount) wrong.  It does not seem worth the
     * extra complication to try to account for that exactly, especially since
     * that behavior falsifies other cost estimates as well.
     */
    if (qpquals == NIL && trivial_pathtarget)
        return;
 
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost = qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost = cpu_per_tuple * path->subpath->rows;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->path.pathtarget->cost.startup;
    run_cost += path->path.pathtarget->cost.per_tuple * path->path.rows;
 
    path->path.startup_cost += startup_cost;
    path->path.total_cost += startup_cost + run_cost;
}
 
/*
 * cost_functionscan
 *    Determines and returns the cost of scanning a function RTE.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_functionscan(Path *path, PlannerInfo *root,
                  RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
    RangeTblEntry *rte;
    QualCost    exprcost;
 
    /* Should only be applied to base relations that are functions */
    Assert(baserel->relid > 0);
    rte = planner_rt_fetch(baserel->relid, root);
    Assert(rte->rtekind == RTE_FUNCTION);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /*
     * Estimate costs of executing the function expression(s).
     *
     * Currently, nodeFunctionscan.c always executes the functions to
     * completion before returning any rows, and caches the results in a
     * tuplestore.  So the function eval cost is all startup cost, and per-row
     * costs are minimal.
     *
     * XXX in principle we ought to charge tuplestore spill costs if the
     * number of rows is large.  However, given how phony our rowcount
     * estimates for functions tend to be, there's not a lot of point in that
     * refinement right now.
     */
    cost_qual_eval_node(&exprcost, (Node *) rte->functions, root);
 
    startup_cost += exprcost.startup + exprcost.per_tuple;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_tablefuncscan
 *    Determines and returns the cost of scanning a table function.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_tablefuncscan(Path *path, PlannerInfo *root,
                   RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
    RangeTblEntry *rte;
    QualCost    exprcost;
 
    /* Should only be applied to base relations that are functions */
    Assert(baserel->relid > 0);
    rte = planner_rt_fetch(baserel->relid, root);
    Assert(rte->rtekind == RTE_TABLEFUNC);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /*
     * Estimate costs of executing the table func expression(s).
     *
     * XXX in principle we ought to charge tuplestore spill costs if the
     * number of rows is large.  However, given how phony our rowcount
     * estimates for tablefuncs tend to be, there's not a lot of point in that
     * refinement right now.
     */
    cost_qual_eval_node(&exprcost, (Node *) rte->tablefunc, root);
 
    startup_cost += exprcost.startup + exprcost.per_tuple;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_valuesscan
 *    Determines and returns the cost of scanning a VALUES RTE.
 *
 * 'baserel' is the relation to be scanned
 * 'param_info' is the ParamPathInfo if this is a parameterized path, else NULL
 */
void
cost_valuesscan(Path *path, PlannerInfo *root,
                RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to base relations that are values lists */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_VALUES);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /*
     * For now, estimate list evaluation cost at one operator eval per list
     * (probably pretty bogus, but is it worth being smarter?)
     */
    cpu_per_tuple = cpu_operator_cost;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_ctescan
 *    Determines and returns the cost of scanning a CTE RTE.
 *
 * Note: this is used for both self-reference and regular CTEs; the
 * possible cost differences are below the threshold of what we could
 * estimate accurately anyway.  Note that the costs of evaluating the
 * referenced CTE query are added into the final plan as initplan costs,
 * and should NOT be counted here.
 */
void
cost_ctescan(Path *path, PlannerInfo *root,
             RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to base relations that are CTEs */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_CTE);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /* Charge one CPU tuple cost per row for tuplestore manipulation */
    cpu_per_tuple = cpu_tuple_cost;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->pathtarget->cost.startup;
    run_cost += path->pathtarget->cost.per_tuple * path->rows;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_namedtuplestorescan
 *    Determines and returns the cost of scanning a named tuplestore.
 */
void
cost_namedtuplestorescan(Path *path, PlannerInfo *root,
                         RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to base relations that are Tuplestores */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_NAMEDTUPLESTORE);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /* Charge one CPU tuple cost per row for tuplestore manipulation */
    cpu_per_tuple = cpu_tuple_cost;
 
    /* Add scanning CPU costs */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple += cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_resultscan
 *    Determines and returns the cost of scanning an RTE_RESULT relation.
 */
void
cost_resultscan(Path *path, PlannerInfo *root,
                RelOptInfo *baserel, ParamPathInfo *param_info)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    QualCost    qpqual_cost;
    Cost        cpu_per_tuple;
 
    /* Should only be applied to RTE_RESULT base relations */
    Assert(baserel->relid > 0);
    Assert(baserel->rtekind == RTE_RESULT);
 
    /* Mark the path with the correct row estimate */
    if (param_info)
        path->rows = param_info->ppi_rows;
    else
        path->rows = baserel->rows;
 
    /* We charge qual cost plus cpu_tuple_cost */
    get_restriction_qual_cost(root, baserel, param_info, &qpqual_cost);
 
    startup_cost += qpqual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qpqual_cost.per_tuple;
    run_cost += cpu_per_tuple * baserel->tuples;
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_recursive_union
 *    Determines and returns the cost of performing a recursive union,
 *    and also the estimated output size.
 *
 * We are given Paths for the nonrecursive and recursive terms.
 */
void
cost_recursive_union(Path *runion, Path *nrterm, Path *rterm)
{
    Cost        startup_cost;
    Cost        total_cost;
    double      total_rows;
 
    /* We probably have decent estimates for the non-recursive term */
    startup_cost = nrterm->startup_cost;
    total_cost = nrterm->total_cost;
    total_rows = nrterm->rows;
 
    /*
     * We arbitrarily assume that about 10 recursive iterations will be
     * needed, and that we've managed to get a good fix on the cost and output
     * size of each one of them.  These are mighty shaky assumptions but it's
     * hard to see how to do better.
     */
    total_cost += 10 * rterm->total_cost;
    total_rows += 10 * rterm->rows;
 
    /*
     * Also charge cpu_tuple_cost per row to account for the costs of
     * manipulating the tuplestores.  (We don't worry about possible
     * spill-to-disk costs.)
     */
    total_cost += cpu_tuple_cost * total_rows;
 
    runion->startup_cost = startup_cost;
    runion->total_cost = total_cost;
    runion->rows = total_rows;
    runion->pathtarget->width = Max(nrterm->pathtarget->width,
                                    rterm->pathtarget->width);
}
 
/*
 * cost_tuplesort
 *    Determines and returns the cost of sorting a relation using tuplesort,
 *    not including the cost of reading the input data.
 *
 * If the total volume of data to sort is less than sort_mem, we will do
 * an in-memory sort, which requires no I/O and about t*log2(t) tuple
 * comparisons for t tuples.
 *
 * If the total volume exceeds sort_mem, we switch to a tape-style merge
 * algorithm.  There will still be about t*log2(t) tuple comparisons in
 * total, but we will also need to write and read each tuple once per
 * merge pass.  We expect about ceil(logM(r)) merge passes where r is the
 * number of initial runs formed and M is the merge order used by tuplesort.c.
 * Since the average initial run should be about sort_mem, we have
 *      disk traffic = 2 * relsize * ceil(logM(p / sort_mem))
 *      cpu = comparison_cost * t * log2(t)
 *
 * If the sort is bounded (i.e., only the first k result tuples are needed)
 * and k tuples can fit into sort_mem, we use a heap method that keeps only
 * k tuples in the heap; this will require about t*log2(k) tuple comparisons.
 *
 * The disk traffic is assumed to be 3/4ths sequential and 1/4th random
 * accesses (XXX can't we refine that guess?)
 *
 * By default, we charge two operator evals per tuple comparison, which should
 * be in the right ballpark in most cases.  The caller can tweak this by
 * specifying nonzero comparison_cost; typically that's used for any extra
 * work that has to be done to prepare the inputs to the comparison operators.
 *
 * 'tuples' is the number of tuples in the relation
 * 'width' is the average tuple width in bytes
 * 'comparison_cost' is the extra cost per comparison, if any
 * 'sort_mem' is the number of kilobytes of work memory allowed for the sort
 * 'limit_tuples' is the bound on the number of output tuples; -1 if no bound
 */
static void
cost_tuplesort(Cost *startup_cost, Cost *run_cost,
               double tuples, int width,
               Cost comparison_cost, int sort_mem,
               double limit_tuples)
{
    double      input_bytes = relation_byte_size(tuples, width);
    double      output_bytes;
    double      output_tuples;
    long        sort_mem_bytes = sort_mem * 1024L;
 
    /*
     * We want to be sure the cost of a sort is never estimated as zero, even
     * if passed-in tuple count is zero.  Besides, mustn't do log(0)...
     */
    if (tuples < 2.0)
        tuples = 2.0;
 
    /* Include the default cost-per-comparison */
    comparison_cost += 2.0 * cpu_operator_cost;
 
    /* Do we have a useful LIMIT? */
    if (limit_tuples > 0 && limit_tuples < tuples)
    {
        output_tuples = limit_tuples;
        output_bytes = relation_byte_size(output_tuples, width);
    }
    else
    {
        output_tuples = tuples;
        output_bytes = input_bytes;
    }
 
    if (output_bytes > sort_mem_bytes)
    {
        /*
         * We'll have to use a disk-based sort of all the tuples
         */
        double      npages = ceil(input_bytes / BLCKSZ);
        double      nruns = input_bytes / sort_mem_bytes;
        double      mergeorder = tuplesort_merge_order(sort_mem_bytes);
        double      log_runs;
        double      npageaccesses;
 
        /*
         * CPU costs
         *
         * Assume about N log2 N comparisons
         */
        *startup_cost = comparison_cost * tuples * LOG2(tuples);
 
        /* Disk costs */
 
        /* Compute logM(r) as log(r) / log(M) */
        if (nruns > mergeorder)
            log_runs = ceil(log(nruns) / log(mergeorder));
        else
            log_runs = 1.0;
        npageaccesses = 2.0 * npages * log_runs;
        /* Assume 3/4ths of accesses are sequential, 1/4th are not */
        *startup_cost += npageaccesses *
            (seq_page_cost * 0.75 + random_page_cost * 0.25);
    }
    else if (tuples > 2 * output_tuples || input_bytes > sort_mem_bytes)
    {
        /*
         * We'll use a bounded heap-sort keeping just K tuples in memory, for
         * a total number of tuple comparisons of N log2 K; but the constant
         * factor is a bit higher than for quicksort.  Tweak it so that the
         * cost curve is continuous at the crossover point.
         */
        *startup_cost = comparison_cost * tuples * LOG2(2.0 * output_tuples);
    }
    else
    {
        /* We'll use plain quicksort on all the input tuples */
        *startup_cost = comparison_cost * tuples * LOG2(tuples);
    }
 
    /*
     * Also charge a small amount (arbitrarily set equal to operator cost) per
     * extracted tuple.  We don't charge cpu_tuple_cost because a Sort node
     * doesn't do qual-checking or projection, so it has less overhead than
     * most plan nodes.  Note it's correct to use tuples not output_tuples
     * here --- the upper LIMIT will pro-rate the run cost so we'd be double
     * counting the LIMIT otherwise.
     */
    *run_cost = cpu_operator_cost * tuples;
}
 
/*
 * cost_incremental_sort
 *  Determines and returns the cost of sorting a relation incrementally, when
 *  the input path is presorted by a prefix of the pathkeys.
 *
 * 'presorted_keys' is the number of leading pathkeys by which the input path
 * is sorted.
 *
 * We estimate the number of groups into which the relation is divided by the
 * leading pathkeys, and then calculate the cost of sorting a single group
 * with tuplesort using cost_tuplesort().
 */
void
cost_incremental_sort(Path *path,
                      PlannerInfo *root, List *pathkeys, int presorted_keys,
                      Cost input_startup_cost, Cost input_total_cost,
                      double input_tuples, int width, Cost comparison_cost, int sort_mem,
                      double limit_tuples)
{
    Cost        startup_cost,
                run_cost,
                input_run_cost = input_total_cost - input_startup_cost;
    double      group_tuples,
                input_groups;
    Cost        group_startup_cost,
                group_run_cost,
                group_input_run_cost;
    List       *presortedExprs = NIL;
    ListCell   *l;
    bool        unknown_varno = false;
 
    Assert(presorted_keys > 0 && presorted_keys < list_length(pathkeys));
 
    /*
     * We want to be sure the cost of a sort is never estimated as zero, even
     * if passed-in tuple count is zero.  Besides, mustn't do log(0)...
     */
    if (input_tuples < 2.0)
        input_tuples = 2.0;
 
    /* Default estimate of number of groups, capped to one group per row. */
    input_groups = Min(input_tuples, DEFAULT_NUM_DISTINCT);
 
    /*
     * Extract presorted keys as list of expressions.
     *
     * We need to be careful about Vars containing "varno 0" which might have
     * been introduced by generate_append_tlist, which would confuse
     * estimate_num_groups (in fact it'd fail for such expressions). See
     * recurse_set_operations which has to deal with the same issue.
     *
     * Unlike recurse_set_operations we can't access the original target list
     * here, and even if we could it's not very clear how useful would that be
     * for a set operation combining multiple tables. So we simply detect if
     * there are any expressions with "varno 0" and use the default
     * DEFAULT_NUM_DISTINCT in that case.
     *
     * We might also use either 1.0 (a single group) or input_tuples (each row
     * being a separate group), pretty much the worst and best case for
     * incremental sort. But those are extreme cases and using something in
     * between seems reasonable. Furthermore, generate_append_tlist is used
     * for set operations, which are likely to produce mostly unique output
     * anyway - from that standpoint the DEFAULT_NUM_DISTINCT is defensive
     * while maintaining lower startup cost.
     */
    foreach(l, pathkeys)
    {
        PathKey    *key = (PathKey *) lfirst(l);
        EquivalenceMember *member = (EquivalenceMember *)
            linitial(key->pk_eclass->ec_members);
 
        /*
         * Check if the expression contains Var with "varno 0" so that we
         * don't call estimate_num_groups in that case.
         */
        if (bms_is_member(0, pull_varnos(root, (Node *) member->em_expr)))
        {
            unknown_varno = true;
            break;
        }
 
        /* expression not containing any Vars with "varno 0" */
        presortedExprs = lappend(presortedExprs, member->em_expr);
 
        if (foreach_current_index(l) + 1 >= presorted_keys)
            break;
    }
 
    /* Estimate the number of groups with equal presorted keys. */
    if (!unknown_varno)
        input_groups = estimate_num_groups(root, presortedExprs, input_tuples,
                                           NULL, NULL);
 
    group_tuples = input_tuples / input_groups;
    group_input_run_cost = input_run_cost / input_groups;
 
    /*
     * Estimate the average cost of sorting of one group where presorted keys
     * are equal.
     */
    cost_tuplesort(&group_startup_cost, &group_run_cost,
                   group_tuples, width, comparison_cost, sort_mem,
                   limit_tuples);
 
    /*
     * Startup cost of incremental sort is the startup cost of its first group
     * plus the cost of its input.
     */
    startup_cost = group_startup_cost + input_startup_cost +
        group_input_run_cost;
 
    /*
     * After we started producing tuples from the first group, the cost of
     * producing all the tuples is given by the cost to finish processing this
     * group, plus the total cost to process the remaining groups, plus the
     * remaining cost of input.
     */
    run_cost = group_run_cost + (group_run_cost + group_startup_cost) *
        (input_groups - 1) + group_input_run_cost * (input_groups - 1);
 
    /*
     * Incremental sort adds some overhead by itself. Firstly, it has to
     * detect the sort groups. This is roughly equal to one extra copy and
     * comparison per tuple.
     */
    run_cost += (cpu_tuple_cost + comparison_cost) * input_tuples;
 
    /*
     * Additionally, we charge double cpu_tuple_cost for each input group to
     * account for the tuplesort_reset that's performed after each group.
     */
    run_cost += 2.0 * cpu_tuple_cost * input_groups;
 
    path->rows = input_tuples;
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_sort
 *    Determines and returns the cost of sorting a relation, including
 *    the cost of reading the input data.
 *
 * NOTE: some callers currently pass NIL for pathkeys because they
 * can't conveniently supply the sort keys.  Since this routine doesn't
 * currently do anything with pathkeys anyway, that doesn't matter...
 * but if it ever does, it should react gracefully to lack of key data.
 * (Actually, the thing we'd most likely be interested in is just the number
 * of sort keys, which all callers *could* supply.)
 */
void
cost_sort(Path *path, PlannerInfo *root,
          List *pathkeys, Cost input_cost, double tuples, int width,
          Cost comparison_cost, int sort_mem,
          double limit_tuples)
 
{
    Cost        startup_cost;
    Cost        run_cost;
 
    cost_tuplesort(&startup_cost, &run_cost,
                   tuples, width,
                   comparison_cost, sort_mem,
                   limit_tuples);
 
    if (!enable_sort)
        startup_cost += disable_cost;
 
    startup_cost += input_cost;
 
    path->rows = tuples;
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * append_nonpartial_cost
 *    Estimate the cost of the non-partial paths in a Parallel Append.
 *    The non-partial paths are assumed to be the first "numpaths" paths
 *    from the subpaths list, and to be in order of decreasing cost.
 */
static Cost
append_nonpartial_cost(List *subpaths, int numpaths, int parallel_workers)
{
    Cost       *costarr;
    int         arrlen;
    ListCell   *l;
    ListCell   *cell;
    int         path_index;
    int         min_index;
    int         max_index;
 
    if (numpaths == 0)
        return 0;
 
    /*
     * Array length is number of workers or number of relevant paths,
     * whichever is less.
     */
    arrlen = Min(parallel_workers, numpaths);
    costarr = (Cost *) palloc(sizeof(Cost) * arrlen);
 
    /* The first few paths will each be claimed by a different worker. */
    path_index = 0;
    foreach(cell, subpaths)
    {
        Path       *subpath = (Path *) lfirst(cell);
 
        if (path_index == arrlen)
            break;
        costarr[path_index++] = subpath->total_cost;
    }
 
    /*
     * Since subpaths are sorted by decreasing cost, the last one will have
     * the minimum cost.
     */
    min_index = arrlen - 1;
 
    /*
     * For each of the remaining subpaths, add its cost to the array element
     * with minimum cost.
     */
    for_each_cell(l, subpaths, cell)
    {
        Path       *subpath = (Path *) lfirst(l);
 
        /* Consider only the non-partial paths */
        if (path_index++ == numpaths)
            break;
 
        costarr[min_index] += subpath->total_cost;
 
        /* Update the new min cost array index */
        min_index = 0;
        for (int i = 0; i < arrlen; i++)
        {
            if (costarr[i] < costarr[min_index])
                min_index = i;
        }
    }
 
    /* Return the highest cost from the array */
    max_index = 0;
    for (int i = 0; i < arrlen; i++)
    {
        if (costarr[i] > costarr[max_index])
            max_index = i;
    }
 
    return costarr[max_index];
}
 
/*
 * cost_append
 *    Determines and returns the cost of an Append node.
 */
void
cost_append(AppendPath *apath)
{
    ListCell   *l;
 
    apath->path.startup_cost = 0;
    apath->path.total_cost = 0;
    apath->path.rows = 0;
 
    if (apath->subpaths == NIL)
        return;
 
    if (!apath->path.parallel_aware)
    {
        List       *pathkeys = apath->path.pathkeys;
 
        if (pathkeys == NIL)
        {
            Path       *firstsubpath = (Path *) linitial(apath->subpaths);
 
            /*
             * For an unordered, non-parallel-aware Append we take the startup
             * cost as the startup cost of the first subpath.
             */
            apath->path.startup_cost = firstsubpath->startup_cost;
 
            /* Compute rows and costs as sums of subplan rows and costs. */
            foreach(l, apath->subpaths)
            {
                Path       *subpath = (Path *) lfirst(l);
 
                apath->path.rows += subpath->rows;
                apath->path.total_cost += subpath->total_cost;
            }
        }
        else
        {
            /*
             * For an ordered, non-parallel-aware Append we take the startup
             * cost as the sum of the subpath startup costs.  This ensures
             * that we don't underestimate the startup cost when a query's
             * LIMIT is such that several of the children have to be run to
             * satisfy it.  This might be overkill --- another plausible hack
             * would be to take the Append's startup cost as the maximum of
             * the child startup costs.  But we don't want to risk believing
             * that an ORDER BY LIMIT query can be satisfied at small cost
             * when the first child has small startup cost but later ones
             * don't.  (If we had the ability to deal with nonlinear cost
             * interpolation for partial retrievals, we would not need to be
             * so conservative about this.)
             *
             * This case is also different from the above in that we have to
             * account for possibly injecting sorts into subpaths that aren't
             * natively ordered.
             */
            foreach(l, apath->subpaths)
            {
                Path       *subpath = (Path *) lfirst(l);
                Path        sort_path;  /* dummy for result of cost_sort */
 
                if (!pathkeys_contained_in(pathkeys, subpath->pathkeys))
                {
                    /*
                     * We'll need to insert a Sort node, so include costs for
                     * that.  We can use the parent's LIMIT if any, since we
                     * certainly won't pull more than that many tuples from
                     * any child.
                     */
                    cost_sort(&sort_path,
                              NULL, /* doesn't currently need root */
                              pathkeys,
                              subpath->total_cost,
                              subpath->rows,
                              subpath->pathtarget->width,
                              0.0,
                              work_mem,
                              apath->limit_tuples);
                    subpath = &sort_path;
                }
 
                apath->path.rows += subpath->rows;
                apath->path.startup_cost += subpath->startup_cost;
                apath->path.total_cost += subpath->total_cost;
            }
        }
    }
    else                        /* parallel-aware */
    {
        int         i = 0;
        double      parallel_divisor = get_parallel_divisor(&apath->path);
 
        /* Parallel-aware Append never produces ordered output. */
        Assert(apath->path.pathkeys == NIL);
 
        /* Calculate startup cost. */
        foreach(l, apath->subpaths)
        {
            Path       *subpath = (Path *) lfirst(l);
 
            /*
             * Append will start returning tuples when the child node having
             * lowest startup cost is done setting up. We consider only the
             * first few subplans that immediately get a worker assigned.
             */
            if (i == 0)
                apath->path.startup_cost = subpath->startup_cost;
            else if (i < apath->path.parallel_workers)
                apath->path.startup_cost = Min(apath->path.startup_cost,
                                               subpath->startup_cost);
 
            /*
             * Apply parallel divisor to subpaths.  Scale the number of rows
             * for each partial subpath based on the ratio of the parallel
             * divisor originally used for the subpath to the one we adopted.
             * Also add the cost of partial paths to the total cost, but
             * ignore non-partial paths for now.
             */
            if (i < apath->first_partial_path)
                apath->path.rows += subpath->rows / parallel_divisor;
            else
            {
                double      subpath_parallel_divisor;
 
                subpath_parallel_divisor = get_parallel_divisor(subpath);
                apath->path.rows += subpath->rows * (subpath_parallel_divisor /
                                                     parallel_divisor);
                apath->path.total_cost += subpath->total_cost;
            }
 
            apath->path.rows = clamp_row_est(apath->path.rows);
 
            i++;
        }
 
        /* Add cost for non-partial subpaths. */
        apath->path.total_cost +=
            append_nonpartial_cost(apath->subpaths,
                                   apath->first_partial_path,
                                   apath->path.parallel_workers);
    }
 
    /*
     * Although Append does not do any selection or projection, it's not free;
     * add a small per-tuple overhead.
     */
    apath->path.total_cost +=
        cpu_tuple_cost * APPEND_CPU_COST_MULTIPLIER * apath->path.rows;
}
 
/*
 * cost_merge_append
 *    Determines and returns the cost of a MergeAppend node.
 *
 * MergeAppend merges several pre-sorted input streams, using a heap that
 * at any given instant holds the next tuple from each stream.  If there
 * are N streams, we need about N*log2(N) tuple comparisons to construct
 * the heap at startup, and then for each output tuple, about log2(N)
 * comparisons to replace the top entry.
 *
 * (The effective value of N will drop once some of the input streams are
 * exhausted, but it seems unlikely to be worth trying to account for that.)
 *
 * The heap is never spilled to disk, since we assume N is not very large.
 * So this is much simpler than cost_sort.
 *
 * As in cost_sort, we charge two operator evals per tuple comparison.
 *
 * 'pathkeys' is a list of sort keys
 * 'n_streams' is the number of input streams
 * 'input_startup_cost' is the sum of the input streams' startup costs
 * 'input_total_cost' is the sum of the input streams' total costs
 * 'tuples' is the number of tuples in all the streams
 */
void
cost_merge_append(Path *path, PlannerInfo *root,
                  List *pathkeys, int n_streams,
                  Cost input_startup_cost, Cost input_total_cost,
                  double tuples)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    Cost        comparison_cost;
    double      N;
    double      logN;
 
    /*
     * Avoid log(0)...
     */
    N = (n_streams < 2) ? 2.0 : (double) n_streams;
    logN = LOG2(N);
 
    /* Assumed cost per tuple comparison */
    comparison_cost = 2.0 * cpu_operator_cost;
 
    /* Heap creation cost */
    startup_cost += comparison_cost * N * logN;
 
    /* Per-tuple heap maintenance cost */
    run_cost += tuples * comparison_cost * logN;
 
    /*
     * Although MergeAppend does not do any selection or projection, it's not
     * free; add a small per-tuple overhead.
     */
    run_cost += cpu_tuple_cost * APPEND_CPU_COST_MULTIPLIER * tuples;
 
    path->startup_cost = startup_cost + input_startup_cost;
    path->total_cost = startup_cost + run_cost + input_total_cost;
}
 
/*
 * cost_material
 *    Determines and returns the cost of materializing a relation, including
 *    the cost of reading the input data.
 *
 * If the total volume of data to materialize exceeds work_mem, we will need
 * to write it to disk, so the cost is much higher in that case.
 *
 * Note that here we are estimating the costs for the first scan of the
 * relation, so the materialization is all overhead --- any savings will
 * occur only on rescan, which is estimated in cost_rescan.
 */
void
cost_material(Path *path,
              Cost input_startup_cost, Cost input_total_cost,
              double tuples, int width)
{
    Cost        startup_cost = input_startup_cost;
    Cost        run_cost = input_total_cost - input_startup_cost;
    double      nbytes = relation_byte_size(tuples, width);
    long        work_mem_bytes = work_mem * 1024L;
 
    path->rows = tuples;
 
    /*
     * Whether spilling or not, charge 2x cpu_operator_cost per tuple to
     * reflect bookkeeping overhead.  (This rate must be more than what
     * cost_rescan charges for materialize, ie, cpu_operator_cost per tuple;
     * if it is exactly the same then there will be a cost tie between
     * nestloop with A outer, materialized B inner and nestloop with B outer,
     * materialized A inner.  The extra cost ensures we'll prefer
     * materializing the smaller rel.)  Note that this is normally a good deal
     * less than cpu_tuple_cost; which is OK because a Material plan node
     * doesn't do qual-checking or projection, so it's got less overhead than
     * most plan nodes.
     */
    run_cost += 2 * cpu_operator_cost * tuples;
 
    /*
     * If we will spill to disk, charge at the rate of seq_page_cost per page.
     * This cost is assumed to be evenly spread through the plan run phase,
     * which isn't exactly accurate but our cost model doesn't allow for
     * nonuniform costs within the run phase.
     */
    if (nbytes > work_mem_bytes)
    {
        double      npages = ceil(nbytes / BLCKSZ);
 
        run_cost += seq_page_cost * npages;
    }
 
    path->startup_cost = startup_cost;
    path->total_cost = startup_cost + run_cost;
}
 
/*
 * cost_memoize_rescan
 *    Determines the estimated cost of rescanning a Memoize node.
 *
 * In order to estimate this, we must gain knowledge of how often we expect to
 * be called and how many distinct sets of parameters we are likely to be
 * called with. If we expect a good cache hit ratio, then we can set our
 * costs to account for that hit ratio, plus a little bit of cost for the
 * caching itself.  Caching will not work out well if we expect to be called
 * with too many distinct parameter values.  The worst-case here is that we
 * never see any parameter value twice, in which case we'd never get a cache
 * hit and caching would be a complete waste of effort.
 */
static void
cost_memoize_rescan(PlannerInfo *root, MemoizePath *mpath,
                    Cost *rescan_startup_cost, Cost *rescan_total_cost)
{
    EstimationInfo estinfo;
    ListCell   *lc;
    Cost        input_startup_cost = mpath->subpath->startup_cost;
    Cost        input_total_cost = mpath->subpath->total_cost;
    double      tuples = mpath->subpath->rows;
    double      calls = mpath->calls;
    int         width = mpath->subpath->pathtarget->width;
 
    double      hash_mem_bytes;
    double      est_entry_bytes;
    double      est_cache_entries;
    double      ndistinct;
    double      evict_ratio;
    double      hit_ratio;
    Cost        startup_cost;
    Cost        total_cost;
 
    /* available cache space */
    hash_mem_bytes = get_hash_memory_limit();
 
    /*
     * Set the number of bytes each cache entry should consume in the cache.
     * To provide us with better estimations on how many cache entries we can
     * store at once, we make a call to the executor here to ask it what
     * memory overheads there are for a single cache entry.
     */
    est_entry_bytes = relation_byte_size(tuples, width) +
        ExecEstimateCacheEntryOverheadBytes(tuples);
 
    /* include the estimated width for the cache keys */
    foreach(lc, mpath->param_exprs)
        est_entry_bytes += get_expr_width(root, (Node *) lfirst(lc));
 
    /* estimate on the upper limit of cache entries we can hold at once */
    est_cache_entries = floor(hash_mem_bytes / est_entry_bytes);
 
    /* estimate on the distinct number of parameter values */
    ndistinct = estimate_num_groups(root, mpath->param_exprs, calls, NULL,
                                    &estinfo);
 
    /*
     * When the estimation fell back on using a default value, it's a bit too
     * risky to assume that it's ok to use a Memoize node.  The use of a
     * default could cause us to use a Memoize node when it's really
     * inappropriate to do so.  If we see that this has been done, then we'll
     * assume that every call will have unique parameters, which will almost
     * certainly mean a MemoizePath will never survive add_path().
     */
    if ((estinfo.flags & SELFLAG_USED_DEFAULT) != 0)
        ndistinct = calls;
 
    /*
     * Since we've already estimated the maximum number of entries we can
     * store at once and know the estimated number of distinct values we'll be
     * called with, we'll take this opportunity to set the path's est_entries.
     * This will ultimately determine the hash table size that the executor
     * will use.  If we leave this at zero, the executor will just choose the
     * size itself.  Really this is not the right place to do this, but it's
     * convenient since everything is already calculated.
     */
    mpath->est_entries = Min(Min(ndistinct, est_cache_entries),
                             PG_UINT32_MAX);
 
    /*
     * When the number of distinct parameter values is above the amount we can
     * store in the cache, then we'll have to evict some entries from the
     * cache.  This is not free. Here we estimate how often we'll incur the
     * cost of that eviction.
     */
    evict_ratio = 1.0 - Min(est_cache_entries, ndistinct) / ndistinct;
 
    /*
     * In order to estimate how costly a single scan will be, we need to
     * attempt to estimate what the cache hit ratio will be.  To do that we
     * must look at how many scans are estimated in total for this node and
     * how many of those scans we expect to get a cache hit.
     */
    hit_ratio = ((calls - ndistinct) / calls) *
        (est_cache_entries / Max(ndistinct, est_cache_entries));
 
    Assert(hit_ratio >= 0 && hit_ratio <= 1.0);
 
    /*
     * Set the total_cost accounting for the expected cache hit ratio.  We
     * also add on a cpu_operator_cost to account for a cache lookup. This
     * will happen regardless of whether it's a cache hit or not.
     */
    total_cost = input_total_cost * (1.0 - hit_ratio) + cpu_operator_cost;
 
    /* Now adjust the total cost to account for cache evictions */
 
    /* Charge a cpu_tuple_cost for evicting the actual cache entry */
    total_cost += cpu_tuple_cost * evict_ratio;
 
    /*
     * Charge a 10th of cpu_operator_cost to evict every tuple in that entry.
     * The per-tuple eviction is really just a pfree, so charging a whole
     * cpu_operator_cost seems a little excessive.
     */
    total_cost += cpu_operator_cost / 10.0 * evict_ratio * tuples;
 
    /*
     * Now adjust for storing things in the cache, since that's not free
     * either.  Everything must go in the cache.  We don't proportion this
     * over any ratio, just apply it once for the scan.  We charge a
     * cpu_tuple_cost for the creation of the cache entry and also a
     * cpu_operator_cost for each tuple we expect to cache.
     */
    total_cost += cpu_tuple_cost + cpu_operator_cost * tuples;
 
    /*
     * Getting the first row must be also be proportioned according to the
     * expected cache hit ratio.
     */
    startup_cost = input_startup_cost * (1.0 - hit_ratio);
 
    /*
     * Additionally we charge a cpu_tuple_cost to account for cache lookups,
     * which we'll do regardless of whether it was a cache hit or not.
     */
    startup_cost += cpu_tuple_cost;
 
    *rescan_startup_cost = startup_cost;
    *rescan_total_cost = total_cost;
}
 
/*
 * cost_agg
 *      Determines and returns the cost of performing an Agg plan node,
 *      including the cost of its input.
 *
 * aggcosts can be NULL when there are no actual aggregate functions (i.e.,
 * we are using a hashed Agg node just to do grouping).
 *
 * Note: when aggstrategy == AGG_SORTED, caller must ensure that input costs
 * are for appropriately-sorted input.
 */
void
cost_agg(Path *path, PlannerInfo *root,
         AggStrategy aggstrategy, const AggClauseCosts *aggcosts,
         int numGroupCols, double numGroups,
         List *quals,
         Cost input_startup_cost, Cost input_total_cost,
         double input_tuples, double input_width)
{
    double      output_tuples;
    Cost        startup_cost;
    Cost        total_cost;
    AggClauseCosts dummy_aggcosts;
 
    /* Use all-zero per-aggregate costs if NULL is passed */
    if (aggcosts == NULL)
    {
        Assert(aggstrategy == AGG_HASHED);
        MemSet(&dummy_aggcosts, 0, sizeof(AggClauseCosts));
        aggcosts = &dummy_aggcosts;
    }
 
    /*
     * The transCost.per_tuple component of aggcosts should be charged once
     * per input tuple, corresponding to the costs of evaluating the aggregate
     * transfns and their input expressions. The finalCost.per_tuple component
     * is charged once per output tuple, corresponding to the costs of
     * evaluating the finalfns.  Startup costs are of course charged but once.
     *
     * If we are grouping, we charge an additional cpu_operator_cost per
     * grouping column per input tuple for grouping comparisons.
     *
     * We will produce a single output tuple if not grouping, and a tuple per
     * group otherwise.  We charge cpu_tuple_cost for each output tuple.
     *
     * Note: in this cost model, AGG_SORTED and AGG_HASHED have exactly the
     * same total CPU cost, but AGG_SORTED has lower startup cost.  If the
     * input path is already sorted appropriately, AGG_SORTED should be
     * preferred (since it has no risk of memory overflow).  This will happen
     * as long as the computed total costs are indeed exactly equal --- but if
     * there's roundoff error we might do the wrong thing.  So be sure that
     * the computations below form the same intermediate values in the same
     * order.
     */
    if (aggstrategy == AGG_PLAIN)
    {
        startup_cost = input_total_cost;
        startup_cost += aggcosts->transCost.startup;
        startup_cost += aggcosts->transCost.per_tuple * input_tuples;
        startup_cost += aggcosts->finalCost.startup;
        startup_cost += aggcosts->finalCost.per_tuple;
        /* we aren't grouping */
        total_cost = startup_cost + cpu_tuple_cost;
        output_tuples = 1;
    }
    else if (aggstrategy == AGG_SORTED || aggstrategy == AGG_MIXED)
    {
        /* Here we are able to deliver output on-the-fly */
        startup_cost = input_startup_cost;
        total_cost = input_total_cost;
        if (aggstrategy == AGG_MIXED && !enable_hashagg)
        {
            startup_cost += disable_cost;
            total_cost += disable_cost;
        }
        /* calcs phrased this way to match HASHED case, see note above */
        total_cost += aggcosts->transCost.startup;
        total_cost += aggcosts->transCost.per_tuple * input_tuples;
        total_cost += (cpu_operator_cost * numGroupCols) * input_tuples;
        total_cost += aggcosts->finalCost.startup;
        total_cost += aggcosts->finalCost.per_tuple * numGroups;
        total_cost += cpu_tuple_cost * numGroups;
        output_tuples = numGroups;
    }
    else
    {
        /* must be AGG_HASHED */
        startup_cost = input_total_cost;
        if (!enable_hashagg)
            startup_cost += disable_cost;
        startup_cost += aggcosts->transCost.startup;
        startup_cost += aggcosts->transCost.per_tuple * input_tuples;
        /* cost of computing hash value */
        startup_cost += (cpu_operator_cost * numGroupCols) * input_tuples;
        startup_cost += aggcosts->finalCost.startup;
 
        total_cost = startup_cost;
        total_cost += aggcosts->finalCost.per_tuple * numGroups;
        /* cost of retrieving from hash table */
        total_cost += cpu_tuple_cost * numGroups;
        output_tuples = numGroups;
    }
 
    /*
     * Add the disk costs of hash aggregation that spills to disk.
     *
     * Groups that go into the hash table stay in memory until finalized, so
     * spilling and reprocessing tuples doesn't incur additional invocations
     * of transCost or finalCost. Furthermore, the computed hash value is
     * stored with the spilled tuples, so we don't incur extra invocations of
     * the hash function.
     *
     * Hash Agg begins returning tuples after the first batch is complete.
     * Accrue writes (spilled tuples) to startup_cost and to total_cost;
     * accrue reads only to total_cost.
     */
    if (aggstrategy == AGG_HASHED || aggstrategy == AGG_MIXED)
    {
        double      pages;
        double      pages_written = 0.0;
        double      pages_read = 0.0;
        double      spill_cost;
        double      hashentrysize;
        double      nbatches;
        Size        mem_limit;
        uint64      ngroups_limit;
        int         num_partitions;
        int         depth;
 
        /*
         * Estimate number of batches based on the computed limits. If less
         * than or equal to one, all groups are expected to fit in memory;
         * otherwise we expect to spill.
         */
        hashentrysize = hash_agg_entry_size(list_length(root->aggtransinfos),
                                            input_width,
                                            aggcosts->transitionSpace);
        hash_agg_set_limits(hashentrysize, numGroups, 0, &mem_limit,
                            &ngroups_limit, &num_partitions);
 
        nbatches = Max((numGroups * hashentrysize) / mem_limit,
                       numGroups / ngroups_limit);
 
        nbatches = Max(ceil(nbatches), 1.0);
        num_partitions = Max(num_partitions, 2);
 
        /*
         * The number of partitions can change at different levels of
         * recursion; but for the purposes of this calculation assume it stays
         * constant.
         */
        depth = ceil(log(nbatches) / log(num_partitions));
 
        /*
         * Estimate number of pages read and written. For each level of
         * recursion, a tuple must be written and then later read.
         */
        pages = relation_byte_size(input_tuples, input_width) / BLCKSZ;
        pages_written = pages_read = pages * depth;
 
        /*
         * HashAgg has somewhat worse IO behavior than Sort on typical
         * hardware/OS combinations. Account for this with a generic penalty.
         */
        pages_read *= 2.0;
        pages_written *= 2.0;
 
        startup_cost += pages_written * random_page_cost;
        total_cost += pages_written * random_page_cost;
        total_cost += pages_read * seq_page_cost;
 
        /* account for CPU cost of spilling a tuple and reading it back */
        spill_cost = depth * input_tuples * 2.0 * cpu_tuple_cost;
        startup_cost += spill_cost;
        total_cost += spill_cost;
    }
 
    /*
     * If there are quals (HAVING quals), account for their cost and
     * selectivity.
     */
    if (quals)
    {
        QualCost    qual_cost;
 
        cost_qual_eval(&qual_cost, quals, root);
        startup_cost += qual_cost.startup;
        total_cost += qual_cost.startup + output_tuples * qual_cost.per_tuple;
 
        output_tuples = clamp_row_est(output_tuples *
                                      clauselist_selectivity(root,
                                                             quals,
                                                             0,
                                                             JOIN_INNER,
                                                             NULL));
    }
 
    path->rows = output_tuples;
    path->startup_cost = startup_cost;
    path->total_cost = total_cost;
}
 
/*
 * get_windowclause_startup_tuples
 *      Estimate how many tuples we'll need to fetch from a WindowAgg's
 *      subnode before we can output the first WindowAgg tuple.
 *
 * How many tuples need to be read depends on the WindowClause.  For example,
 * a WindowClause with no PARTITION BY and no ORDER BY requires that all
 * subnode tuples are read and aggregated before the WindowAgg can output
 * anything.  If there's a PARTITION BY, then we only need to look at tuples
 * in the first partition.  Here we attempt to estimate just how many
 * 'input_tuples' the WindowAgg will need to read for the given WindowClause
 * before the first tuple can be output.
 */
static double
get_windowclause_startup_tuples(PlannerInfo *root, WindowClause *wc,
                                double input_tuples)
{
    int         frameOptions = wc->frameOptions;
    double      partition_tuples;
    double      return_tuples;
    double      peer_tuples;
 
    /*
     * First, figure out how many partitions there are likely to be and set
     * partition_tuples according to that estimate.
     */
    if (wc->partitionClause != NIL)
    {
        double      num_partitions;
        List       *partexprs = get_sortgrouplist_exprs(wc->partitionClause,
                                                        root->parse->targetList);
 
        num_partitions = estimate_num_groups(root, partexprs, input_tuples,
                                             NULL, NULL);
        list_free(partexprs);
 
        partition_tuples = input_tuples / num_partitions;
    }
    else
    {
        /* all tuples belong to the same partition */
        partition_tuples = input_tuples;
    }
 
    /* estimate the number of tuples in each peer group */
    if (wc->orderClause != NIL)
    {
        double      num_groups;
        List       *orderexprs;
 
        orderexprs = get_sortgrouplist_exprs(wc->orderClause,
                                             root->parse->targetList);
 
        /* estimate out how many peer groups there are in the partition */
        num_groups = estimate_num_groups(root, orderexprs,
                                         partition_tuples, NULL,
                                         NULL);
        list_free(orderexprs);
        peer_tuples = partition_tuples / num_groups;
    }
    else
    {
        /* no ORDER BY so only 1 tuple belongs in each peer group */
        peer_tuples = 1.0;
    }
 
    if (frameOptions & FRAMEOPTION_END_UNBOUNDED_FOLLOWING)
    {
        /* include all partition rows */
        return_tuples = partition_tuples;
    }
    else if (frameOptions & FRAMEOPTION_END_CURRENT_ROW)
    {
        if (frameOptions & FRAMEOPTION_ROWS)
        {
            /* just count the current row */
            return_tuples = 1.0;
        }
        else if (frameOptions & (FRAMEOPTION_RANGE | FRAMEOPTION_GROUPS))
        {
            /*
             * When in RANGE/GROUPS mode, it's more complex.  If there's no
             * ORDER BY, then all rows in the partition are peers, otherwise
             * we'll need to read the first group of peers.
             */
            if (wc->orderClause == NIL)
                return_tuples = partition_tuples;
            else
                return_tuples = peer_tuples;
        }
        else
        {
            /*
             * Something new we don't support yet?  This needs attention.
             * We'll just return 1.0 in the meantime.
             */
            Assert(false);
            return_tuples = 1.0;
        }
    }
    else if (frameOptions & FRAMEOPTION_END_OFFSET_PRECEDING)
    {
        /*
         * BETWEEN ... AND N PRECEDING will only need to read the WindowAgg's
         * subnode after N ROWS/RANGES/GROUPS.  N can be 0, but not negative,
         * so we'll just assume only the current row needs to be read to fetch
         * the first WindowAgg row.
         */
        return_tuples = 1.0;
    }
    else if (frameOptions & FRAMEOPTION_END_OFFSET_FOLLOWING)
    {
        Const      *endOffset = (Const *) wc->endOffset;
        double      end_offset_value;
 
        /* try and figure out the value specified in the endOffset. */
        if (IsA(endOffset, Const))
        {
            if (endOffset->constisnull)
            {
                /*
                 * NULLs are not allowed, but currently, there's no code to
                 * error out if there's a NULL Const.  We'll only discover
                 * this during execution.  For now, just pretend everything is
                 * fine and assume that just the first row/range/group will be
                 * needed.
                 */
                end_offset_value = 1.0;
            }
            else
            {
                switch (endOffset->consttype)
                {
                    case INT2OID:
                        end_offset_value =
                            (double) DatumGetInt16(endOffset->constvalue);
                        break;
                    case INT4OID:
                        end_offset_value =
                            (double) DatumGetInt32(endOffset->constvalue);
                        break;
                    case INT8OID:
                        end_offset_value =
                            (double) DatumGetInt64(endOffset->constvalue);
                        break;
                    default:
                        end_offset_value =
                            partition_tuples / peer_tuples *
                            DEFAULT_INEQ_SEL;
                        break;
                }
            }
        }
        else
        {
            /*
             * When the end bound is not a Const, we'll just need to guess. We
             * just make use of DEFAULT_INEQ_SEL.
             */
            end_offset_value =
                partition_tuples / peer_tuples * DEFAULT_INEQ_SEL;
        }
 
        if (frameOptions & FRAMEOPTION_ROWS)
        {
            /* include the N FOLLOWING and the current row */
            return_tuples = end_offset_value + 1.0;
        }
        else if (frameOptions & (FRAMEOPTION_RANGE | FRAMEOPTION_GROUPS))
        {
            /* include N FOLLOWING ranges/group and the initial range/group */
            return_tuples = peer_tuples * (end_offset_value + 1.0);
        }
        else
        {
            /*
             * Something new we don't support yet?  This needs attention.
             * We'll just return 1.0 in the meantime.
             */
            Assert(false);
            return_tuples = 1.0;
        }
    }
    else
    {
        /*
         * Something new we don't support yet?  This needs attention.  We'll
         * just return 1.0 in the meantime.
         */
        Assert(false);
        return_tuples = 1.0;
    }
 
    if (wc->partitionClause != NIL || wc->orderClause != NIL)
    {
        /*
         * Cap the return value to the estimated partition tuples and account
         * for the extra tuple WindowAgg will need to read to confirm the next
         * tuple does not belong to the same partition or peer group.
         */
        return_tuples = Min(return_tuples + 1.0, partition_tuples);
    }
    else
    {
        /*
         * Cap the return value so it's never higher than the expected tuples
         * in the partition.
         */
        return_tuples = Min(return_tuples, partition_tuples);
    }
 
    /*
     * We needn't worry about any EXCLUDE options as those only exclude rows
     * from being aggregated, not from being read from the WindowAgg's
     * subnode.
     */
 
    return clamp_row_est(return_tuples);
}
 
/*
 * 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, WindowClause *winclause,
               Cost input_startup_cost, Cost input_total_cost,
               double input_tuples)
{
    Cost        startup_cost;
    Cost        total_cost;
    double      startup_tuples;
    int         numPartCols;
    int         numOrderCols;
    ListCell   *lc;
 
    numPartCols = list_length(winclause->partitionClause);
    numOrderCols = list_length(winclause->orderClause);
 
    startup_cost = input_startup_cost;
    total_cost = input_total_cost;
 
    /*
     * Window functions are assumed to cost their stated execution cost, plus
     * the cost of evaluating their input expressions, per tuple.  Since they
     * may in fact evaluate their inputs at multiple rows during each cycle,
     * this could be a drastic underestimate; but without a way to know how
     * many rows the window function will fetch, it's hard to do better.  In
     * any case, it's a good estimate for all the built-in window functions,
     * so we'll just do this for now.
     */
    foreach(lc, windowFuncs)
    {
        WindowFunc *wfunc = lfirst_node(WindowFunc, lc);
        Cost        wfunccost;
        QualCost    argcosts;
 
        argcosts.startup = argcosts.per_tuple = 0;
        add_function_cost(root, wfunc->winfnoid, (Node *) wfunc,
                          &argcosts);
        startup_cost += argcosts.startup;
        wfunccost = argcosts.per_tuple;
 
        /* also add the input expressions' cost to per-input-row costs */
        cost_qual_eval_node(&argcosts, (Node *) wfunc->args, root);
        startup_cost += argcosts.startup;
        wfunccost += argcosts.per_tuple;
 
        /*
         * Add the filter's cost to per-input-row costs.  XXX We should reduce
         * input expression costs according to filter selectivity.
         */
        cost_qual_eval_node(&argcosts, (Node *) wfunc->aggfilter, root);
        startup_cost += argcosts.startup;
        wfunccost += argcosts.per_tuple;
 
        total_cost += wfunccost * input_tuples;
    }
 
    /*
     * We also charge cpu_operator_cost per grouping column per tuple for
     * grouping comparisons, plus cpu_tuple_cost per tuple for general
     * overhead.
     *
     * XXX this neglects costs of spooling the data to disk when it overflows
     * work_mem.  Sooner or later that should get accounted for.
     */
    total_cost += cpu_operator_cost * (numPartCols + numOrderCols) * input_tuples;
    total_cost += cpu_tuple_cost * input_tuples;
 
    path->rows = input_tuples;
    path->startup_cost = startup_cost;
    path->total_cost = total_cost;
 
    /*
     * Also, take into account how many tuples we need to read from the
     * subnode in order to produce the first tuple from the WindowAgg.  To do
     * this we proportion the run cost (total cost not including startup cost)
     * over the estimated startup tuples.  We already included the startup
     * cost of the subnode, so we only need to do this when the estimated
     * startup tuples is above 1.0.
     */
    startup_tuples = get_windowclause_startup_tuples(root, winclause,
                                                     input_tuples);
 
    if (startup_tuples > 1.0)
        path->startup_cost += (total_cost - startup_cost) / input_tuples *
            (startup_tuples - 1.0);
}
 
/*
 * cost_group
 *      Determines and returns the cost of performing a Group plan node,
 *      including the cost of its input.
 *
 * Note: caller must ensure that input costs are for appropriately-sorted
 * input.
 */
void
cost_group(Path *path, PlannerInfo *root,
           int numGroupCols, double numGroups,
           List *quals,
           Cost input_startup_cost, Cost input_total_cost,
           double input_tuples)
{
    double      output_tuples;
    Cost        startup_cost;
    Cost        total_cost;
 
    output_tuples = numGroups;
    startup_cost = input_startup_cost;
    total_cost = input_total_cost;
 
    /*
     * Charge one cpu_operator_cost per comparison per input tuple. We assume
     * all columns get compared at most of the tuples.
     */
    total_cost += cpu_operator_cost * input_tuples * numGroupCols;
 
    /*
     * If there are quals (HAVING quals), account for their cost and
     * selectivity.
     */
    if (quals)
    {
        QualCost    qual_cost;
 
        cost_qual_eval(&qual_cost, quals, root);
        startup_cost += qual_cost.startup;
        total_cost += qual_cost.startup + output_tuples * qual_cost.per_tuple;
 
        output_tuples = clamp_row_est(output_tuples *
                                      clauselist_selectivity(root,
                                                             quals,
                                                             0,
                                                             JOIN_INNER,
                                                             NULL));
    }
 
    path->rows = output_tuples;
    path->startup_cost = startup_cost;
    path->total_cost = total_cost;
}
 
/*
 * initial_cost_nestloop
 *    Preliminary estimate of the cost of a nestloop join path.
 *
 * This must quickly produce lower-bound estimates of the path's startup and
 * total costs.  If we are unable to eliminate the proposed path from
 * consideration using the lower bounds, final_cost_nestloop will be called
 * to obtain the final estimates.
 *
 * The exact division of labor between this function and final_cost_nestloop
 * is private to them, and represents a tradeoff between speed of the initial
 * estimate and getting a tight lower bound.  We choose to not examine the
 * join quals here, since that's by far the most expensive part of the
 * calculations.  The end result is that CPU-cost considerations must be
 * left for the second phase; and for SEMI/ANTI joins, we must also postpone
 * incorporation of the inner path's run cost.
 *
 * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
 *      other data to be used by final_cost_nestloop
 * 'jointype' is the type of join to be performed
 * 'outer_path' is the outer input to the join
 * 'inner_path' is the inner input to the join
 * 'extra' contains miscellaneous information about the join
 */
void
initial_cost_nestloop(PlannerInfo *root, JoinCostWorkspace *workspace,
                      JoinType jointype,
                      Path *outer_path, Path *inner_path,
                      JoinPathExtraData *extra)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    double      outer_path_rows = outer_path->rows;
    Cost        inner_rescan_start_cost;
    Cost        inner_rescan_total_cost;
    Cost        inner_run_cost;
    Cost        inner_rescan_run_cost;
 
    /* estimate costs to rescan the inner relation */
    cost_rescan(root, inner_path,
                &inner_rescan_start_cost,
                &inner_rescan_total_cost);
 
    /* cost of source data */
 
    /*
     * NOTE: clearly, we must pay both outer and inner paths' startup_cost
     * before we can start returning tuples, so the join's startup cost is
     * their sum.  We'll also pay the inner path's rescan startup cost
     * multiple times.
     */
    startup_cost += outer_path->startup_cost + inner_path->startup_cost;
    run_cost += outer_path->total_cost - outer_path->startup_cost;
    if (outer_path_rows > 1)
        run_cost += (outer_path_rows - 1) * inner_rescan_start_cost;
 
    inner_run_cost = inner_path->total_cost - inner_path->startup_cost;
    inner_rescan_run_cost = inner_rescan_total_cost - inner_rescan_start_cost;
 
    if (jointype == JOIN_SEMI || jointype == JOIN_ANTI ||
        extra->inner_unique)
    {
        /*
         * With a SEMI or ANTI join, or if the innerrel is known unique, the
         * executor will stop after the first match.
         *
         * Getting decent estimates requires inspection of the join quals,
         * which we choose to postpone to final_cost_nestloop.
         */
 
        /* Save private data for final_cost_nestloop */
        workspace->inner_run_cost = inner_run_cost;
        workspace->inner_rescan_run_cost = inner_rescan_run_cost;
    }
    else
    {
        /* Normal case; we'll scan whole input rel for each outer row */
        run_cost += inner_run_cost;
        if (outer_path_rows > 1)
            run_cost += (outer_path_rows - 1) * inner_rescan_run_cost;
    }
 
    /* CPU costs left for later */
 
    /* Public result fields */
    workspace->startup_cost = startup_cost;
    workspace->total_cost = startup_cost + run_cost;
    /* Save private data for final_cost_nestloop */
    workspace->run_cost = run_cost;
}
 
/*
 * final_cost_nestloop
 *    Final estimate of the cost and result size of a nestloop join path.
 *
 * 'path' is already filled in except for the rows and cost fields
 * 'workspace' is the result from initial_cost_nestloop
 * 'extra' contains miscellaneous information about the join
 */
void
final_cost_nestloop(PlannerInfo *root, NestPath *path,
                    JoinCostWorkspace *workspace,
                    JoinPathExtraData *extra)
{
    Path       *outer_path = path->jpath.outerjoinpath;
    Path       *inner_path = path->jpath.innerjoinpath;
    double      outer_path_rows = outer_path->rows;
    double      inner_path_rows = inner_path->rows;
    Cost        startup_cost = workspace->startup_cost;
    Cost        run_cost = workspace->run_cost;
    Cost        cpu_per_tuple;
    QualCost    restrict_qual_cost;
    double      ntuples;
 
    /* Protect some assumptions below that rowcounts aren't zero */
    if (outer_path_rows <= 0)
        outer_path_rows = 1;
    if (inner_path_rows <= 0)
        inner_path_rows = 1;
    /* Mark the path with the correct row estimate */
    if (path->jpath.path.param_info)
        path->jpath.path.rows = path->jpath.path.param_info->ppi_rows;
    else
        path->jpath.path.rows = path->jpath.path.parent->rows;
 
    /* For partial paths, scale row estimate. */
    if (path->jpath.path.parallel_workers > 0)
    {
        double      parallel_divisor = get_parallel_divisor(&path->jpath.path);
 
        path->jpath.path.rows =
            clamp_row_est(path->jpath.path.rows / parallel_divisor);
    }
 
    /*
     * We could include disable_cost in the preliminary estimate, but that
     * would amount to optimizing for the case where the join method is
     * disabled, which doesn't seem like the way to bet.
     */
    if (!enable_nestloop)
        startup_cost += disable_cost;
 
    /* cost of inner-relation source data (we already dealt with outer rel) */
 
    if (path->jpath.jointype == JOIN_SEMI || path->jpath.jointype == JOIN_ANTI ||
        extra->inner_unique)
    {
        /*
         * With a SEMI or ANTI join, or if the innerrel is known unique, the
         * executor will stop after the first match.
         */
        Cost        inner_run_cost = workspace->inner_run_cost;
        Cost        inner_rescan_run_cost = workspace->inner_rescan_run_cost;
        double      outer_matched_rows;
        double      outer_unmatched_rows;
        Selectivity inner_scan_frac;
 
        /*
         * For an outer-rel row that has at least one match, we can expect the
         * inner scan to stop after a fraction 1/(match_count+1) of the inner
         * rows, if the matches are evenly distributed.  Since they probably
         * aren't quite evenly distributed, we apply a fuzz factor of 2.0 to
         * that fraction.  (If we used a larger fuzz factor, we'd have to
         * clamp inner_scan_frac to at most 1.0; but since match_count is at
         * least 1, no such clamp is needed now.)
         */
        outer_matched_rows = rint(outer_path_rows * extra->semifactors.outer_match_frac);
        outer_unmatched_rows = outer_path_rows - outer_matched_rows;
        inner_scan_frac = 2.0 / (extra->semifactors.match_count + 1.0);
 
        /*
         * Compute number of tuples processed (not number emitted!).  First,
         * account for successfully-matched outer rows.
         */
        ntuples = outer_matched_rows * inner_path_rows * inner_scan_frac;
 
        /*
         * Now we need to estimate the actual costs of scanning the inner
         * relation, which may be quite a bit less than N times inner_run_cost
         * due to early scan stops.  We consider two cases.  If the inner path
         * is an indexscan using all the joinquals as indexquals, then an
         * unmatched outer row results in an indexscan returning no rows,
         * which is probably quite cheap.  Otherwise, the executor will have
         * to scan the whole inner rel for an unmatched row; not so cheap.
         */
        if (has_indexed_join_quals(path))
        {
            /*
             * Successfully-matched outer rows will only require scanning
             * inner_scan_frac of the inner relation.  In this case, we don't
             * need to charge the full inner_run_cost even when that's more
             * than inner_rescan_run_cost, because we can assume that none of
             * the inner scans ever scan the whole inner relation.  So it's
             * okay to assume that all the inner scan executions can be
             * fractions of the full cost, even if materialization is reducing
             * the rescan cost.  At this writing, it's impossible to get here
             * for a materialized inner scan, so inner_run_cost and
             * inner_rescan_run_cost will be the same anyway; but just in
             * case, use inner_run_cost for the first matched tuple and
             * inner_rescan_run_cost for additional ones.
             */
            run_cost += inner_run_cost * inner_scan_frac;
            if (outer_matched_rows > 1)
                run_cost += (outer_matched_rows - 1) * inner_rescan_run_cost * inner_scan_frac;
 
            /*
             * Add the cost of inner-scan executions for unmatched outer rows.
             * We estimate this as the same cost as returning the first tuple
             * of a nonempty scan.  We consider that these are all rescans,
             * since we used inner_run_cost once already.
             */
            run_cost += outer_unmatched_rows *
                inner_rescan_run_cost / inner_path_rows;
 
            /*
             * We won't be evaluating any quals at all for unmatched rows, so
             * don't add them to ntuples.
             */
        }
        else
        {
            /*
             * Here, a complicating factor is that rescans may be cheaper than
             * first scans.  If we never scan all the way to the end of the
             * inner rel, it might be (depending on the plan type) that we'd
             * never pay the whole inner first-scan run cost.  However it is
             * difficult to estimate whether that will happen (and it could
             * not happen if there are any unmatched outer rows!), so be
             * conservative and always charge the whole first-scan cost once.
             * We consider this charge to correspond to the first unmatched
             * outer row, unless there isn't one in our estimate, in which
             * case blame it on the first matched row.
             */
 
            /* First, count all unmatched join tuples as being processed */
            ntuples += outer_unmatched_rows * inner_path_rows;
 
            /* Now add the forced full scan, and decrement appropriate count */
            run_cost += inner_run_cost;
            if (outer_unmatched_rows >= 1)
                outer_unmatched_rows -= 1;
            else
                outer_matched_rows -= 1;
 
            /* Add inner run cost for additional outer tuples having matches */
            if (outer_matched_rows > 0)
                run_cost += outer_matched_rows * inner_rescan_run_cost * inner_scan_frac;
 
            /* Add inner run cost for additional unmatched outer tuples */
            if (outer_unmatched_rows > 0)
                run_cost += outer_unmatched_rows * inner_rescan_run_cost;
        }
    }
    else
    {
        /* Normal-case source costs were included in preliminary estimate */
 
        /* Compute number of tuples processed (not number emitted!) */
        ntuples = outer_path_rows * inner_path_rows;
    }
 
    /* CPU costs */
    cost_qual_eval(&restrict_qual_cost, path->jpath.joinrestrictinfo, root);
    startup_cost += restrict_qual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + restrict_qual_cost.per_tuple;
    run_cost += cpu_per_tuple * ntuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->jpath.path.pathtarget->cost.startup;
    run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;
 
    path->jpath.path.startup_cost = startup_cost;
    path->jpath.path.total_cost = startup_cost + run_cost;
}
 
/*
 * initial_cost_mergejoin
 *    Preliminary estimate of the cost of a mergejoin path.
 *
 * This must quickly produce lower-bound estimates of the path's startup and
 * total costs.  If we are unable to eliminate the proposed path from
 * consideration using the lower bounds, final_cost_mergejoin will be called
 * to obtain the final estimates.
 *
 * The exact division of labor between this function and final_cost_mergejoin
 * is private to them, and represents a tradeoff between speed of the initial
 * estimate and getting a tight lower bound.  We choose to not examine the
 * join quals here, except for obtaining the scan selectivity estimate which
 * is really essential (but fortunately, use of caching keeps the cost of
 * getting that down to something reasonable).
 * We also assume that cost_sort is cheap enough to use here.
 *
 * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
 *      other data to be used by final_cost_mergejoin
 * 'jointype' is the type of join to be performed
 * 'mergeclauses' is the list of joinclauses to be used as merge clauses
 * 'outer_path' is the outer input to the join
 * 'inner_path' is the inner input to the join
 * 'outersortkeys' is the list of sort keys for the outer path
 * 'innersortkeys' is the list of sort keys for the inner path
 * 'extra' contains miscellaneous information about the join
 *
 * Note: outersortkeys and innersortkeys should be NIL if no explicit
 * sort is needed because the respective source path is already ordered.
 */
void
initial_cost_mergejoin(PlannerInfo *root, JoinCostWorkspace *workspace,
                       JoinType jointype,
                       List *mergeclauses,
                       Path *outer_path, Path *inner_path,
                       List *outersortkeys, List *innersortkeys,
                       JoinPathExtraData *extra)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    double      outer_path_rows = outer_path->rows;
    double      inner_path_rows = inner_path->rows;
    Cost        inner_run_cost;
    double      outer_rows,
                inner_rows,
                outer_skip_rows,
                inner_skip_rows;
    Selectivity outerstartsel,
                outerendsel,
                innerstartsel,
                innerendsel;
    Path        sort_path;      /* dummy for result of cost_sort */
 
    /* Protect some assumptions below that rowcounts aren't zero */
    if (outer_path_rows <= 0)
        outer_path_rows = 1;
    if (inner_path_rows <= 0)
        inner_path_rows = 1;
 
    /*
     * A merge join will stop as soon as it exhausts either input stream
     * (unless it's an outer join, in which case the outer side has to be
     * scanned all the way anyway).  Estimate fraction of the left and right
     * inputs that will actually need to be scanned.  Likewise, we can
     * estimate the number of rows that will be skipped before the first join
     * pair is found, which should be factored into startup cost. We use only
     * the first (most significant) merge clause for this purpose. Since
     * mergejoinscansel() is a fairly expensive computation, we cache the
     * results in the merge clause RestrictInfo.
     */
    if (mergeclauses && jointype != JOIN_FULL)
    {
        RestrictInfo *firstclause = (RestrictInfo *) linitial(mergeclauses);
        List       *opathkeys;
        List       *ipathkeys;
        PathKey    *opathkey;
        PathKey    *ipathkey;
        MergeScanSelCache *cache;
 
        /* Get the input pathkeys to determine the sort-order details */
        opathkeys = outersortkeys ? outersortkeys : outer_path->pathkeys;
        ipathkeys = innersortkeys ? innersortkeys : inner_path->pathkeys;
        Assert(opathkeys);
        Assert(ipathkeys);
        opathkey = (PathKey *) linitial(opathkeys);
        ipathkey = (PathKey *) linitial(ipathkeys);
        /* debugging check */
        if (opathkey->pk_opfamily != ipathkey->pk_opfamily ||
            opathkey->pk_eclass->ec_collation != ipathkey->pk_eclass->ec_collation ||
            opathkey->pk_strategy != ipathkey->pk_strategy ||
            opathkey->pk_nulls_first != ipathkey->pk_nulls_first)
            elog(ERROR, "left and right pathkeys do not match in mergejoin");
 
        /* Get the selectivity with caching */
        cache = cached_scansel(root, firstclause, opathkey);
 
        if (bms_is_subset(firstclause->left_relids,
                          outer_path->parent->relids))
        {
            /* left side of clause is outer */
            outerstartsel = cache->leftstartsel;
            outerendsel = cache->leftendsel;
            innerstartsel = cache->rightstartsel;
            innerendsel = cache->rightendsel;
        }
        else
        {
            /* left side of clause is inner */
            outerstartsel = cache->rightstartsel;
            outerendsel = cache->rightendsel;
            innerstartsel = cache->leftstartsel;
            innerendsel = cache->leftendsel;
        }
        if (jointype == JOIN_LEFT ||
            jointype == JOIN_ANTI)
        {
            outerstartsel = 0.0;
            outerendsel = 1.0;
        }
        else if (jointype == JOIN_RIGHT ||
                 jointype == JOIN_RIGHT_ANTI)
        {
            innerstartsel = 0.0;
            innerendsel = 1.0;
        }
    }
    else
    {
        /* cope with clauseless or full mergejoin */
        outerstartsel = innerstartsel = 0.0;
        outerendsel = innerendsel = 1.0;
    }
 
    /*
     * Convert selectivities to row counts.  We force outer_rows and
     * inner_rows to be at least 1, but the skip_rows estimates can be zero.
     */
    outer_skip_rows = rint(outer_path_rows * outerstartsel);
    inner_skip_rows = rint(inner_path_rows * innerstartsel);
    outer_rows = clamp_row_est(outer_path_rows * outerendsel);
    inner_rows = clamp_row_est(inner_path_rows * innerendsel);
 
    Assert(outer_skip_rows <= outer_rows);
    Assert(inner_skip_rows <= inner_rows);
 
    /*
     * Readjust scan selectivities to account for above rounding.  This is
     * normally an insignificant effect, but when there are only a few rows in
     * the inputs, failing to do this makes for a large percentage error.
     */
    outerstartsel = outer_skip_rows / outer_path_rows;
    innerstartsel = inner_skip_rows / inner_path_rows;
    outerendsel = outer_rows / outer_path_rows;
    innerendsel = inner_rows / inner_path_rows;
 
    Assert(outerstartsel <= outerendsel);
    Assert(innerstartsel <= innerendsel);
 
    /* cost of source data */
 
    if (outersortkeys)          /* do we need to sort outer? */
    {
        cost_sort(&sort_path,
                  root,
                  outersortkeys,
                  outer_path->total_cost,
                  outer_path_rows,
                  outer_path->pathtarget->width,
                  0.0,
                  work_mem,
                  -1.0);
        startup_cost += sort_path.startup_cost;
        startup_cost += (sort_path.total_cost - sort_path.startup_cost)
            * outerstartsel;
        run_cost += (sort_path.total_cost - sort_path.startup_cost)
            * (outerendsel - outerstartsel);
    }
    else
    {
        startup_cost += outer_path->startup_cost;
        startup_cost += (outer_path->total_cost - outer_path->startup_cost)
            * outerstartsel;
        run_cost += (outer_path->total_cost - outer_path->startup_cost)
            * (outerendsel - outerstartsel);
    }
 
    if (innersortkeys)          /* do we need to sort inner? */
    {
        cost_sort(&sort_path,
                  root,
                  innersortkeys,
                  inner_path->total_cost,
                  inner_path_rows,
                  inner_path->pathtarget->width,
                  0.0,
                  work_mem,
                  -1.0);
        startup_cost += sort_path.startup_cost;
        startup_cost += (sort_path.total_cost - sort_path.startup_cost)
            * innerstartsel;
        inner_run_cost = (sort_path.total_cost - sort_path.startup_cost)
            * (innerendsel - innerstartsel);
    }
    else
    {
        startup_cost += inner_path->startup_cost;
        startup_cost += (inner_path->total_cost - inner_path->startup_cost)
            * innerstartsel;
        inner_run_cost = (inner_path->total_cost - inner_path->startup_cost)
            * (innerendsel - innerstartsel);
    }
 
    /*
     * We can't yet determine whether rescanning occurs, or whether
     * materialization of the inner input should be done.  The minimum
     * possible inner input cost, regardless of rescan and materialization
     * considerations, is inner_run_cost.  We include that in
     * workspace->total_cost, but not yet in run_cost.
     */
 
    /* CPU costs left for later */
 
    /* Public result fields */
    workspace->startup_cost = startup_cost;
    workspace->total_cost = startup_cost + run_cost + inner_run_cost;
    /* Save private data for final_cost_mergejoin */
    workspace->run_cost = run_cost;
    workspace->inner_run_cost = inner_run_cost;
    workspace->outer_rows = outer_rows;
    workspace->inner_rows = inner_rows;
    workspace->outer_skip_rows = outer_skip_rows;
    workspace->inner_skip_rows = inner_skip_rows;
}
 
/*
 * final_cost_mergejoin
 *    Final estimate of the cost and result size of a mergejoin path.
 *
 * Unlike other costsize functions, this routine makes two actual decisions:
 * whether the executor will need to do mark/restore, and whether we should
 * materialize the inner path.  It would be logically cleaner to build
 * separate paths testing these alternatives, but that would require repeating
 * most of the cost calculations, which are not all that cheap.  Since the
 * choice will not affect output pathkeys or startup cost, only total cost,
 * there is no possibility of wanting to keep more than one path.  So it seems
 * best to make the decisions here and record them in the path's
 * skip_mark_restore and materialize_inner fields.
 *
 * Mark/restore overhead is usually required, but can be skipped if we know
 * that the executor need find only one match per outer tuple, and that the
 * mergeclauses are sufficient to identify a match.
 *
 * We materialize the inner path if we need mark/restore and either the inner
 * path can't support mark/restore, or it's cheaper to use an interposed
 * Material node to handle mark/restore.
 *
 * 'path' is already filled in except for the rows and cost fields and
 *      skip_mark_restore and materialize_inner
 * 'workspace' is the result from initial_cost_mergejoin
 * 'extra' contains miscellaneous information about the join
 */
void
final_cost_mergejoin(PlannerInfo *root, MergePath *path,
                     JoinCostWorkspace *workspace,
                     JoinPathExtraData *extra)
{
    Path       *outer_path = path->jpath.outerjoinpath;
    Path       *inner_path = path->jpath.innerjoinpath;
    double      inner_path_rows = inner_path->rows;
    List       *mergeclauses = path->path_mergeclauses;
    List       *innersortkeys = path->innersortkeys;
    Cost        startup_cost = workspace->startup_cost;
    Cost        run_cost = workspace->run_cost;
    Cost        inner_run_cost = workspace->inner_run_cost;
    double      outer_rows = workspace->outer_rows;
    double      inner_rows = workspace->inner_rows;
    double      outer_skip_rows = workspace->outer_skip_rows;
    double      inner_skip_rows = workspace->inner_skip_rows;
    Cost        cpu_per_tuple,
                bare_inner_cost,
                mat_inner_cost;
    QualCost    merge_qual_cost;
    QualCost    qp_qual_cost;
    double      mergejointuples,
                rescannedtuples;
    double      rescanratio;
 
    /* Protect some assumptions below that rowcounts aren't zero */
    if (inner_path_rows <= 0)
        inner_path_rows = 1;
 
    /* Mark the path with the correct row estimate */
    if (path->jpath.path.param_info)
        path->jpath.path.rows = path->jpath.path.param_info->ppi_rows;
    else
        path->jpath.path.rows = path->jpath.path.parent->rows;
 
    /* For partial paths, scale row estimate. */
    if (path->jpath.path.parallel_workers > 0)
    {
        double      parallel_divisor = get_parallel_divisor(&path->jpath.path);
 
        path->jpath.path.rows =
            clamp_row_est(path->jpath.path.rows / parallel_divisor);
    }
 
    /*
     * We could include disable_cost in the preliminary estimate, but that
     * would amount to optimizing for the case where the join method is
     * disabled, which doesn't seem like the way to bet.
     */
    if (!enable_mergejoin)
        startup_cost += disable_cost;
 
    /*
     * Compute cost of the mergequals and qpquals (other restriction clauses)
     * separately.
     */
    cost_qual_eval(&merge_qual_cost, mergeclauses, root);
    cost_qual_eval(&qp_qual_cost, path->jpath.joinrestrictinfo, root);
    qp_qual_cost.startup -= merge_qual_cost.startup;
    qp_qual_cost.per_tuple -= merge_qual_cost.per_tuple;
 
    /*
     * With a SEMI or ANTI join, or if the innerrel is known unique, the
     * executor will stop scanning for matches after the first match.  When
     * all the joinclauses are merge clauses, this means we don't ever need to
     * back up the merge, and so we can skip mark/restore overhead.
     */
    if ((path->jpath.jointype == JOIN_SEMI ||
         path->jpath.jointype == JOIN_ANTI ||
         extra->inner_unique) &&
        (list_length(path->jpath.joinrestrictinfo) ==
         list_length(path->path_mergeclauses)))
        path->skip_mark_restore = true;
    else
        path->skip_mark_restore = false;
 
    /*
     * Get approx # tuples passing the mergequals.  We use approx_tuple_count
     * here because we need an estimate done with JOIN_INNER semantics.
     */
    mergejointuples = approx_tuple_count(root, &path->jpath, mergeclauses);
 
    /*
     * When there are equal merge keys in the outer relation, the mergejoin
     * must rescan any matching tuples in the inner relation. This means
     * re-fetching inner tuples; we have to estimate how often that happens.
     *
     * For regular inner and outer joins, the number of re-fetches can be
     * estimated approximately as size of merge join output minus size of
     * inner relation. Assume that the distinct key values are 1, 2, ..., and
     * denote the number of values of each key in the outer relation as m1,
     * m2, ...; in the inner relation, n1, n2, ...  Then we have
     *
     * size of join = m1 * n1 + m2 * n2 + ...
     *
     * number of rescanned tuples = (m1 - 1) * n1 + (m2 - 1) * n2 + ... = m1 *
     * n1 + m2 * n2 + ... - (n1 + n2 + ...) = size of join - size of inner
     * relation
     *
     * This equation works correctly for outer tuples having no inner match
     * (nk = 0), but not for inner tuples having no outer match (mk = 0); we
     * are effectively subtracting those from the number of rescanned tuples,
     * when we should not.  Can we do better without expensive selectivity
     * computations?
     *
     * The whole issue is moot if we are working from a unique-ified outer
     * input, or if we know we don't need to mark/restore at all.
     */
    if (IsA(outer_path, UniquePath) || path->skip_mark_restore)
        rescannedtuples = 0;
    else
    {
        rescannedtuples = mergejointuples - inner_path_rows;
        /* Must clamp because of possible underestimate */
        if (rescannedtuples < 0)
            rescannedtuples = 0;
    }
 
    /*
     * We'll inflate various costs this much to account for rescanning.  Note
     * that this is to be multiplied by something involving inner_rows, or
     * another number related to the portion of the inner rel we'll scan.
     */
    rescanratio = 1.0 + (rescannedtuples / inner_rows);
 
    /*
     * Decide whether we want to materialize the inner input to shield it from
     * mark/restore and performing re-fetches.  Our cost model for regular
     * re-fetches is that a re-fetch costs the same as an original fetch,
     * which is probably an overestimate; but on the other hand we ignore the
     * bookkeeping costs of mark/restore.  Not clear if it's worth developing
     * a more refined model.  So we just need to inflate the inner run cost by
     * rescanratio.
     */
    bare_inner_cost = inner_run_cost * rescanratio;
 
    /*
     * When we interpose a Material node the re-fetch cost is assumed to be
     * just cpu_operator_cost per tuple, independently of the underlying
     * plan's cost; and we charge an extra cpu_operator_cost per original
     * fetch as well.  Note that we're assuming the materialize node will
     * never spill to disk, since it only has to remember tuples back to the
     * last mark.  (If there are a huge number of duplicates, our other cost
     * factors will make the path so expensive that it probably won't get
     * chosen anyway.)  So we don't use cost_rescan here.
     *
     * Note: keep this estimate in sync with create_mergejoin_plan's labeling
     * of the generated Material node.
     */
    mat_inner_cost = inner_run_cost +
        cpu_operator_cost * inner_rows * rescanratio;
 
    /*
     * If we don't need mark/restore at all, we don't need materialization.
     */
    if (path->skip_mark_restore)
        path->materialize_inner = false;
 
    /*
     * Prefer materializing if it looks cheaper, unless the user has asked to
     * suppress materialization.
     */
    else if (enable_material && mat_inner_cost < bare_inner_cost)
        path->materialize_inner = true;
 
    /*
     * Even if materializing doesn't look cheaper, we *must* do it if the
     * inner path is to be used directly (without sorting) and it doesn't
     * support mark/restore.
     *
     * Since the inner side must be ordered, and only Sorts and IndexScans can
     * create order to begin with, and they both support mark/restore, you
     * might think there's no problem --- but you'd be wrong.  Nestloop and
     * merge joins can *preserve* the order of their inputs, so they can be
     * selected as the input of a mergejoin, and they don't support
     * mark/restore at present.
     *
     * We don't test the value of enable_material here, because
     * materialization is required for correctness in this case, and turning
     * it off does not entitle us to deliver an invalid plan.
     */
    else if (innersortkeys == NIL &&
             !ExecSupportsMarkRestore(inner_path))
        path->materialize_inner = true;
 
    /*
     * Also, force materializing if the inner path is to be sorted and the
     * sort is expected to spill to disk.  This is because the final merge
     * pass can be done on-the-fly if it doesn't have to support mark/restore.
     * We don't try to adjust the cost estimates for this consideration,
     * though.
     *
     * Since materialization is a performance optimization in this case,
     * rather than necessary for correctness, we skip it if enable_material is
     * off.
     */
    else if (enable_material && innersortkeys != NIL &&
             relation_byte_size(inner_path_rows,
                                inner_path->pathtarget->width) >
             (work_mem * 1024L))
        path->materialize_inner = true;
    else
        path->materialize_inner = false;
 
    /* Charge the right incremental cost for the chosen case */
    if (path->materialize_inner)
        run_cost += mat_inner_cost;
    else
        run_cost += bare_inner_cost;
 
    /* CPU costs */
 
    /*
     * The number of tuple comparisons needed is approximately number of outer
     * rows plus number of inner rows plus number of rescanned tuples (can we
     * refine this?).  At each one, we need to evaluate the mergejoin quals.
     */
    startup_cost += merge_qual_cost.startup;
    startup_cost += merge_qual_cost.per_tuple *
        (outer_skip_rows + inner_skip_rows * rescanratio);
    run_cost += merge_qual_cost.per_tuple *
        ((outer_rows - outer_skip_rows) +
         (inner_rows - inner_skip_rows) * rescanratio);
 
    /*
     * For each tuple that gets through the mergejoin proper, we charge
     * cpu_tuple_cost plus the cost of evaluating additional restriction
     * clauses that are to be applied at the join.  (This is pessimistic since
     * not all of the quals may get evaluated at each tuple.)
     *
     * Note: we could adjust for SEMI/ANTI joins skipping some qual
     * evaluations here, but it's probably not worth the trouble.
     */
    startup_cost += qp_qual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qp_qual_cost.per_tuple;
    run_cost += cpu_per_tuple * mergejointuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->jpath.path.pathtarget->cost.startup;
    run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;
 
    path->jpath.path.startup_cost = startup_cost;
    path->jpath.path.total_cost = startup_cost + run_cost;
}
 
/*
 * run mergejoinscansel() with caching
 */
static MergeScanSelCache *
cached_scansel(PlannerInfo *root, RestrictInfo *rinfo, PathKey *pathkey)
{
    MergeScanSelCache *cache;
    ListCell   *lc;
    Selectivity leftstartsel,
                leftendsel,
                rightstartsel,
                rightendsel;
    MemoryContext oldcontext;
 
    /* Do we have this result already? */
    foreach(lc, rinfo->scansel_cache)
    {
        cache = (MergeScanSelCache *) lfirst(lc);
        if (cache->opfamily == pathkey->pk_opfamily &&
            cache->collation == pathkey->pk_eclass->ec_collation &&
            cache->strategy == pathkey->pk_strategy &&
            cache->nulls_first == pathkey->pk_nulls_first)
            return cache;
    }
 
    /* Nope, do the computation */
    mergejoinscansel(root,
                     (Node *) rinfo->clause,
                     pathkey->pk_opfamily,
                     pathkey->pk_strategy,
                     pathkey->pk_nulls_first,
                     &leftstartsel,
                     &leftendsel,
                     &rightstartsel,
                     &rightendsel);
 
    /* Cache the result in suitably long-lived workspace */
    oldcontext = MemoryContextSwitchTo(root->planner_cxt);
 
    cache = (MergeScanSelCache *) palloc(sizeof(MergeScanSelCache));
    cache->opfamily = pathkey->pk_opfamily;
    cache->collation = pathkey->pk_eclass->ec_collation;
    cache->strategy = pathkey->pk_strategy;
    cache->nulls_first = pathkey->pk_nulls_first;
    cache->leftstartsel = leftstartsel;
    cache->leftendsel = leftendsel;
    cache->rightstartsel = rightstartsel;
    cache->rightendsel = rightendsel;
 
    rinfo->scansel_cache = lappend(rinfo->scansel_cache, cache);
 
    MemoryContextSwitchTo(oldcontext);
 
    return cache;
}
 
/*
 * initial_cost_hashjoin
 *    Preliminary estimate of the cost of a hashjoin path.
 *
 * This must quickly produce lower-bound estimates of the path's startup and
 * total costs.  If we are unable to eliminate the proposed path from
 * consideration using the lower bounds, final_cost_hashjoin will be called
 * to obtain the final estimates.
 *
 * The exact division of labor between this function and final_cost_hashjoin
 * is private to them, and represents a tradeoff between speed of the initial
 * estimate and getting a tight lower bound.  We choose to not examine the
 * join quals here (other than by counting the number of hash clauses),
 * so we can't do much with CPU costs.  We do assume that
 * ExecChooseHashTableSize is cheap enough to use here.
 *
 * 'workspace' is to be filled with startup_cost, total_cost, and perhaps
 *      other data to be used by final_cost_hashjoin
 * 'jointype' is the type of join to be performed
 * 'hashclauses' is the list of joinclauses to be used as hash clauses
 * 'outer_path' is the outer input to the join
 * 'inner_path' is the inner input to the join
 * 'extra' contains miscellaneous information about the join
 * 'parallel_hash' indicates that inner_path is partial and that a shared
 *      hash table will be built in parallel
 */
void
initial_cost_hashjoin(PlannerInfo *root, JoinCostWorkspace *workspace,
                      JoinType jointype,
                      List *hashclauses,
                      Path *outer_path, Path *inner_path,
                      JoinPathExtraData *extra,
                      bool parallel_hash)
{
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
    double      outer_path_rows = outer_path->rows;
    double      inner_path_rows = inner_path->rows;
    double      inner_path_rows_total = inner_path_rows;
    int         num_hashclauses = list_length(hashclauses);
    int         numbuckets;
    int         numbatches;
    int         num_skew_mcvs;
    size_t      space_allowed;  /* unused */
 
    /* cost of source data */
    startup_cost += outer_path->startup_cost;
    run_cost += outer_path->total_cost - outer_path->startup_cost;
    startup_cost += inner_path->total_cost;
 
    /*
     * Cost of computing hash function: must do it once per input tuple. We
     * charge one cpu_operator_cost for each column's hash function.  Also,
     * tack on one cpu_tuple_cost per inner row, to model the costs of
     * inserting the row into the hashtable.
     *
     * XXX when a hashclause is more complex than a single operator, we really
     * should charge the extra eval costs of the left or right side, as
     * appropriate, here.  This seems more work than it's worth at the moment.
     */
    startup_cost += (cpu_operator_cost * num_hashclauses + cpu_tuple_cost)
        * inner_path_rows;
    run_cost += cpu_operator_cost * num_hashclauses * outer_path_rows;
 
    /*
     * If this is a parallel hash build, then the value we have for
     * inner_rows_total currently refers only to the rows returned by each
     * participant.  For shared hash table size estimation, we need the total
     * number, so we need to undo the division.
     */
    if (parallel_hash)
        inner_path_rows_total *= get_parallel_divisor(inner_path);
 
    /*
     * Get hash table size that executor would use for inner relation.
     *
     * XXX for the moment, always assume that skew optimization will be
     * performed.  As long as SKEW_HASH_MEM_PERCENT is small, it's not worth
     * trying to determine that for sure.
     *
     * XXX at some point it might be interesting to try to account for skew
     * optimization in the cost estimate, but for now, we don't.
     */
    ExecChooseHashTableSize(inner_path_rows_total,
                            inner_path->pathtarget->width,
                            true,   /* useskew */
                            parallel_hash,  /* try_combined_hash_mem */
                            outer_path->parallel_workers,
                            &space_allowed,
                            &numbuckets,
                            &numbatches,
                            &num_skew_mcvs);
 
    /*
     * If inner relation is too big then we will need to "batch" the join,
     * which implies writing and reading most of the tuples to disk an extra
     * time.  Charge seq_page_cost per page, since the I/O should be nice and
     * sequential.  Writing the inner rel counts as startup cost, all the rest
     * as run cost.
     */
    if (numbatches > 1)
    {
        double      outerpages = page_size(outer_path_rows,
                                           outer_path->pathtarget->width);
        double      innerpages = page_size(inner_path_rows,
                                           inner_path->pathtarget->width);
 
        startup_cost += seq_page_cost * innerpages;
        run_cost += seq_page_cost * (innerpages + 2 * outerpages);
    }
 
    /* CPU costs left for later */
 
    /* Public result fields */
    workspace->startup_cost = startup_cost;
    workspace->total_cost = startup_cost + run_cost;
    /* Save private data for final_cost_hashjoin */
    workspace->run_cost = run_cost;
    workspace->numbuckets = numbuckets;
    workspace->numbatches = numbatches;
    workspace->inner_rows_total = inner_path_rows_total;
}
 
/*
 * final_cost_hashjoin
 *    Final estimate of the cost and result size of a hashjoin path.
 *
 * Note: the numbatches estimate is also saved into 'path' for use later
 *
 * 'path' is already filled in except for the rows and cost fields and
 *      num_batches
 * 'workspace' is the result from initial_cost_hashjoin
 * 'extra' contains miscellaneous information about the join
 */
void
final_cost_hashjoin(PlannerInfo *root, HashPath *path,
                    JoinCostWorkspace *workspace,
                    JoinPathExtraData *extra)
{
    Path       *outer_path = path->jpath.outerjoinpath;
    Path       *inner_path = path->jpath.innerjoinpath;
    double      outer_path_rows = outer_path->rows;
    double      inner_path_rows = inner_path->rows;
    double      inner_path_rows_total = workspace->inner_rows_total;
    List       *hashclauses = path->path_hashclauses;
    Cost        startup_cost = workspace->startup_cost;
    Cost        run_cost = workspace->run_cost;
    int         numbuckets = workspace->numbuckets;
    int         numbatches = workspace->numbatches;
    Cost        cpu_per_tuple;
    QualCost    hash_qual_cost;
    QualCost    qp_qual_cost;
    double      hashjointuples;
    double      virtualbuckets;
    Selectivity innerbucketsize;
    Selectivity innermcvfreq;
    ListCell   *hcl;
 
    /* Mark the path with the correct row estimate */
    if (path->jpath.path.param_info)
        path->jpath.path.rows = path->jpath.path.param_info->ppi_rows;
    else
        path->jpath.path.rows = path->jpath.path.parent->rows;
 
    /* For partial paths, scale row estimate. */
    if (path->jpath.path.parallel_workers > 0)
    {
        double      parallel_divisor = get_parallel_divisor(&path->jpath.path);
 
        path->jpath.path.rows =
            clamp_row_est(path->jpath.path.rows / parallel_divisor);
    }
 
    /*
     * We could include disable_cost in the preliminary estimate, but that
     * would amount to optimizing for the case where the join method is
     * disabled, which doesn't seem like the way to bet.
     */
    if (!enable_hashjoin)
        startup_cost += disable_cost;
 
    /* mark the path with estimated # of batches */
    path->num_batches = numbatches;
 
    /* store the total number of tuples (sum of partial row estimates) */
    path->inner_rows_total = inner_path_rows_total;
 
    /* and compute the number of "virtual" buckets in the whole join */
    virtualbuckets = (double) numbuckets * (double) numbatches;
 
    /*
     * Determine bucketsize fraction and MCV frequency for the inner relation.
     * We use the smallest bucketsize or MCV frequency estimated for any
     * individual hashclause; this is undoubtedly conservative.
     *
     * BUT: if inner relation has been unique-ified, we can assume it's good
     * for hashing.  This is important both because it's the right answer, and
     * because we avoid contaminating the cache with a value that's wrong for
     * non-unique-ified paths.
     */
    if (IsA(inner_path, UniquePath))
    {
        innerbucketsize = 1.0 / virtualbuckets;
        innermcvfreq = 0.0;
    }
    else
    {
        innerbucketsize = 1.0;
        innermcvfreq = 1.0;
        foreach(hcl, hashclauses)
        {
            RestrictInfo *restrictinfo = lfirst_node(RestrictInfo, hcl);
            Selectivity thisbucketsize;
            Selectivity thismcvfreq;
 
            /*
             * First we have to figure out which side of the hashjoin clause
             * is the inner side.
             *
             * Since we tend to visit the same clauses over and over when
             * planning a large query, we cache the bucket stats estimates in
             * the RestrictInfo node to avoid repeated lookups of statistics.
             */
            if (bms_is_subset(restrictinfo->right_relids,
                              inner_path->parent->relids))
            {
                /* righthand side is inner */
                thisbucketsize = restrictinfo->right_bucketsize;
                if (thisbucketsize < 0)
                {
                    /* not cached yet */
                    estimate_hash_bucket_stats(root,
                                               get_rightop(restrictinfo->clause),
                                               virtualbuckets,
                                               &restrictinfo->right_mcvfreq,
                                               &restrictinfo->right_bucketsize);
                    thisbucketsize = restrictinfo->right_bucketsize;
                }
                thismcvfreq = restrictinfo->right_mcvfreq;
            }
            else
            {
                Assert(bms_is_subset(restrictinfo->left_relids,
                                     inner_path->parent->relids));
                /* lefthand side is inner */
                thisbucketsize = restrictinfo->left_bucketsize;
                if (thisbucketsize < 0)
                {
                    /* not cached yet */
                    estimate_hash_bucket_stats(root,
                                               get_leftop(restrictinfo->clause),
                                               virtualbuckets,
                                               &restrictinfo->left_mcvfreq,
                                               &restrictinfo->left_bucketsize);
                    thisbucketsize = restrictinfo->left_bucketsize;
                }
                thismcvfreq = restrictinfo->left_mcvfreq;
            }
 
            if (innerbucketsize > thisbucketsize)
                innerbucketsize = thisbucketsize;
            if (innermcvfreq > thismcvfreq)
                innermcvfreq = thismcvfreq;
        }
    }
 
    /*
     * If the bucket holding the inner MCV would exceed hash_mem, we don't
     * want to hash unless there is really no other alternative, so apply
     * disable_cost.  (The executor normally copes with excessive memory usage
     * by splitting batches, but obviously it cannot separate equal values
     * that way, so it will be unable to drive the batch size below hash_mem
     * when this is true.)
     */
    if (relation_byte_size(clamp_row_est(inner_path_rows * innermcvfreq),
                           inner_path->pathtarget->width) > get_hash_memory_limit())
        startup_cost += disable_cost;
 
    /*
     * Compute cost of the hashquals and qpquals (other restriction clauses)
     * separately.
     */
    cost_qual_eval(&hash_qual_cost, hashclauses, root);
    cost_qual_eval(&qp_qual_cost, path->jpath.joinrestrictinfo, root);
    qp_qual_cost.startup -= hash_qual_cost.startup;
    qp_qual_cost.per_tuple -= hash_qual_cost.per_tuple;
 
    /* CPU costs */
 
    if (path->jpath.jointype == JOIN_SEMI ||
        path->jpath.jointype == JOIN_ANTI ||
        extra->inner_unique)
    {
        double      outer_matched_rows;
        Selectivity inner_scan_frac;
 
        /*
         * With a SEMI or ANTI join, or if the innerrel is known unique, the
         * executor will stop after the first match.
         *
         * For an outer-rel row that has at least one match, we can expect the
         * bucket scan to stop after a fraction 1/(match_count+1) of the
         * bucket's rows, if the matches are evenly distributed.  Since they
         * probably aren't quite evenly distributed, we apply a fuzz factor of
         * 2.0 to that fraction.  (If we used a larger fuzz factor, we'd have
         * to clamp inner_scan_frac to at most 1.0; but since match_count is
         * at least 1, no such clamp is needed now.)
         */
        outer_matched_rows = rint(outer_path_rows * extra->semifactors.outer_match_frac);
        inner_scan_frac = 2.0 / (extra->semifactors.match_count + 1.0);
 
        startup_cost += hash_qual_cost.startup;
        run_cost += hash_qual_cost.per_tuple * outer_matched_rows *
            clamp_row_est(inner_path_rows * innerbucketsize * inner_scan_frac) * 0.5;
 
        /*
         * For unmatched outer-rel rows, the picture is quite a lot different.
         * In the first place, there is no reason to assume that these rows
         * preferentially hit heavily-populated buckets; instead assume they
         * are uncorrelated with the inner distribution and so they see an
         * average bucket size of inner_path_rows / virtualbuckets.  In the
         * second place, it seems likely that they will have few if any exact
         * hash-code matches and so very few of the tuples in the bucket will
         * actually require eval of the hash quals.  We don't have any good
         * way to estimate how many will, but for the moment assume that the
         * effective cost per bucket entry is one-tenth what it is for
         * matchable tuples.
         */
        run_cost += hash_qual_cost.per_tuple *
            (outer_path_rows - outer_matched_rows) *
            clamp_row_est(inner_path_rows / virtualbuckets) * 0.05;
 
        /* Get # of tuples that will pass the basic join */
        if (path->jpath.jointype == JOIN_ANTI)
            hashjointuples = outer_path_rows - outer_matched_rows;
        else
            hashjointuples = outer_matched_rows;
    }
    else
    {
        /*
         * The number of tuple comparisons needed is the number of outer
         * tuples times the typical number of tuples in a hash bucket, which
         * is the inner relation size times its bucketsize fraction.  At each
         * one, we need to evaluate the hashjoin quals.  But actually,
         * charging the full qual eval cost at each tuple is pessimistic,
         * since we don't evaluate the quals unless the hash values match
         * exactly.  For lack of a better idea, halve the cost estimate to
         * allow for that.
         */
        startup_cost += hash_qual_cost.startup;
        run_cost += hash_qual_cost.per_tuple * outer_path_rows *
            clamp_row_est(inner_path_rows * innerbucketsize) * 0.5;
 
        /*
         * Get approx # tuples passing the hashquals.  We use
         * approx_tuple_count here because we need an estimate done with
         * JOIN_INNER semantics.
         */
        hashjointuples = approx_tuple_count(root, &path->jpath, hashclauses);
    }
 
    /*
     * For each tuple that gets through the hashjoin proper, we charge
     * cpu_tuple_cost plus the cost of evaluating additional restriction
     * clauses that are to be applied at the join.  (This is pessimistic since
     * not all of the quals may get evaluated at each tuple.)
     */
    startup_cost += qp_qual_cost.startup;
    cpu_per_tuple = cpu_tuple_cost + qp_qual_cost.per_tuple;
    run_cost += cpu_per_tuple * hashjointuples;
 
    /* tlist eval costs are paid per output row, not per tuple scanned */
    startup_cost += path->jpath.path.pathtarget->cost.startup;
    run_cost += path->jpath.path.pathtarget->cost.per_tuple * path->jpath.path.rows;
 
    path->jpath.path.startup_cost = startup_cost;
    path->jpath.path.total_cost = startup_cost + run_cost;
}
 
 
/*
 * cost_subplan
 *      Figure the costs for a SubPlan (or initplan).
 *
 * Note: we could dig the subplan's Plan out of the root list, but in practice
 * all callers have it handy already, so we make them pass it.
 */
void
cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
{
    QualCost    sp_cost;
 
    /* Figure any cost for evaluating the testexpr */
    cost_qual_eval(&sp_cost,
                   make_ands_implicit((Expr *) subplan->testexpr),
                   root);
 
    if (subplan->useHashTable)
    {
        /*
         * If we are using a hash table for the subquery outputs, then the
         * cost of evaluating the query is a one-time cost.  We charge one
         * cpu_operator_cost per tuple for the work of loading the hashtable,
         * too.
         */
        sp_cost.startup += plan->total_cost +
            cpu_operator_cost * plan->plan_rows;
 
        /*
         * The per-tuple costs include the cost of evaluating the lefthand
         * expressions, plus the cost of probing the hashtable.  We already
         * accounted for the lefthand expressions as part of the testexpr, and
         * will also have counted one cpu_operator_cost for each comparison
         * operator.  That is probably too low for the probing cost, but it's
         * hard to make a better estimate, so live with it for now.
         */
    }
    else
    {
        /*
         * Otherwise we will be rescanning the subplan output on each
         * evaluation.  We need to estimate how much of the output we will
         * actually need to scan.  NOTE: this logic should agree with the
         * tuple_fraction estimates used by make_subplan() in
         * plan/subselect.c.
         */
        Cost        plan_run_cost = plan->total_cost - plan->startup_cost;
 
        if (subplan->subLinkType == EXISTS_SUBLINK)
        {
            /* we only need to fetch 1 tuple; clamp to avoid zero divide */
            sp_cost.per_tuple += plan_run_cost / clamp_row_est(plan->plan_rows);
        }
        else if (subplan->subLinkType == ALL_SUBLINK ||
                 subplan->subLinkType == ANY_SUBLINK)
        {
            /* assume we need 50% of the tuples */
            sp_cost.per_tuple += 0.50 * plan_run_cost;
            /* also charge a cpu_operator_cost per row examined */
            sp_cost.per_tuple += 0.50 * plan->plan_rows * cpu_operator_cost;
        }
        else
        {
            /* assume we need all tuples */
            sp_cost.per_tuple += plan_run_cost;
        }
 
        /*
         * Also account for subplan's startup cost. If the subplan is
         * uncorrelated or undirect correlated, AND its topmost node is one
         * that materializes its output, assume that we'll only need to pay
         * its startup cost once; otherwise assume we pay the startup cost
         * every time.
         */
        if (subplan->parParam == NIL &&
            ExecMaterializesOutput(nodeTag(plan)))
            sp_cost.startup += plan->startup_cost;
        else
            sp_cost.per_tuple += plan->startup_cost;
    }
 
    subplan->startup_cost = sp_cost.startup;
    subplan->per_call_cost = sp_cost.per_tuple;
}
 
 
/*
 * cost_rescan
 *      Given a finished Path, estimate the costs of rescanning it after
 *      having done so the first time.  For some Path types a rescan is
 *      cheaper than an original scan (if no parameters change), and this
 *      function embodies knowledge about that.  The default is to return
 *      the same costs stored in the Path.  (Note that the cost estimates
 *      actually stored in Paths are always for first scans.)
 *
 * This function is not currently intended to model effects such as rescans
 * being cheaper due to disk block caching; what we are concerned with is
 * plan types wherein the executor caches results explicitly, or doesn't
 * redo startup calculations, etc.
 */
static void
cost_rescan(PlannerInfo *root, Path *path,
            Cost *rescan_startup_cost,  /* output parameters */
            Cost *rescan_total_cost)
{
    switch (path->pathtype)
    {
        case T_FunctionScan:
 
            /*
             * Currently, nodeFunctionscan.c always executes the function to
             * completion before returning any rows, and caches the results in
             * a tuplestore.  So the function eval cost is all startup cost
             * and isn't paid over again on rescans. However, all run costs
             * will be paid over again.
             */
            *rescan_startup_cost = 0;
            *rescan_total_cost = path->total_cost - path->startup_cost;
            break;
        case T_HashJoin:
 
            /*
             * If it's a single-batch join, we don't need to rebuild the hash
             * table during a rescan.
             */
            if (((HashPath *) path)->num_batches == 1)
            {
                /* Startup cost is exactly the cost of hash table building */
                *rescan_startup_cost = 0;
                *rescan_total_cost = path->total_cost - path->startup_cost;
            }
            else
            {
                /* Otherwise, no special treatment */
                *rescan_startup_cost = path->startup_cost;
                *rescan_total_cost = path->total_cost;
            }
            break;
        case T_CteScan:
        case T_WorkTableScan:
            {
                /*
                 * These plan types materialize their final result in a
                 * tuplestore or tuplesort object.  So the rescan cost is only
                 * cpu_tuple_cost per tuple, unless the result is large enough
                 * to spill to disk.
                 */
                Cost        run_cost = cpu_tuple_cost * path->rows;
                double      nbytes = relation_byte_size(path->rows,
                                                        path->pathtarget->width);
                long        work_mem_bytes = work_mem * 1024L;
 
                if (nbytes > work_mem_bytes)
                {
                    /* It will spill, so account for re-read cost */
                    double      npages = ceil(nbytes / BLCKSZ);
 
                    run_cost += seq_page_cost * npages;
                }
                *rescan_startup_cost = 0;
                *rescan_total_cost = run_cost;
            }
            break;
        case T_Material:
        case T_Sort:
            {
                /*
                 * These plan types not only materialize their results, but do
                 * not implement qual filtering or projection.  So they are
                 * even cheaper to rescan than the ones above.  We charge only
                 * cpu_operator_cost per tuple.  (Note: keep that in sync with
                 * the run_cost charge in cost_sort, and also see comments in
                 * cost_material before you change it.)
                 */
                Cost        run_cost = cpu_operator_cost * path->rows;
                double      nbytes = relation_byte_size(path->rows,
                                                        path->pathtarget->width);
                long        work_mem_bytes = work_mem * 1024L;
 
                if (nbytes > work_mem_bytes)
                {
                    /* It will spill, so account for re-read cost */
                    double      npages = ceil(nbytes / BLCKSZ);
 
                    run_cost += seq_page_cost * npages;
                }
                *rescan_startup_cost = 0;
                *rescan_total_cost = run_cost;
            }
            break;
        case T_Memoize:
            /* All the hard work is done by cost_memoize_rescan */
            cost_memoize_rescan(root, (MemoizePath *) path,
                                rescan_startup_cost, rescan_total_cost);
            break;
        default:
            *rescan_startup_cost = path->startup_cost;
            *rescan_total_cost = path->total_cost;
            break;
    }
}
 
 
/*
 * cost_qual_eval
 *      Estimate the CPU costs of evaluating a WHERE clause.
 *      The input can be either an implicitly-ANDed list of boolean
 *      expressions, or a list of RestrictInfo nodes.  (The latter is
 *      preferred since it allows caching of the results.)
 *      The result includes both a one-time (startup) component,
 *      and a per-evaluation component.
 */
void
cost_qual_eval(QualCost *cost, List *quals, PlannerInfo *root)
{
    cost_qual_eval_context context;
    ListCell   *l;
 
    context.root = root;
    context.total.startup = 0;
    context.total.per_tuple = 0;
 
    /* We don't charge any cost for the implicit ANDing at top level ... */
 
    foreach(l, quals)
    {
        Node       *qual = (Node *) lfirst(l);
 
        cost_qual_eval_walker(qual, &context);
    }
 
    *cost = context.total;
}
 
/*
 * cost_qual_eval_node
 *      As above, for a single RestrictInfo or expression.
 */
void
cost_qual_eval_node(QualCost *cost, Node *qual, PlannerInfo *root)
{
    cost_qual_eval_context context;
 
    context.root = root;
    context.total.startup = 0;
    context.total.per_tuple = 0;
 
    cost_qual_eval_walker(qual, &context);
 
    *cost = context.total;
}
 
static bool
cost_qual_eval_walker(Node *node, cost_qual_eval_context *context)
{
    if (node == NULL)
        return false;
 
    /*
     * RestrictInfo nodes contain an eval_cost field reserved for this
     * routine's use, so that it's not necessary to evaluate the qual clause's
     * cost more than once.  If the clause's cost hasn't been computed yet,
     * the field's startup value will contain -1.
     */
    if (IsA(node, RestrictInfo))
    {
        RestrictInfo *rinfo = (RestrictInfo *) node;
 
        if (rinfo->eval_cost.startup < 0)
        {
            cost_qual_eval_context locContext;
 
            locContext.root = context->root;
            locContext.total.startup = 0;
            locContext.total.per_tuple = 0;
 
            /*
             * For an OR clause, recurse into the marked-up tree so that we
             * set the eval_cost for contained RestrictInfos too.
             */
            if (rinfo->orclause)
                cost_qual_eval_walker((Node *) rinfo->orclause, &locContext);
            else
                cost_qual_eval_walker((Node *) rinfo->clause, &locContext);
 
            /*
             * If the RestrictInfo is marked pseudoconstant, it will be tested
             * only once, so treat its cost as all startup cost.
             */
            if (rinfo->pseudoconstant)
            {
                /* count one execution during startup */
                locContext.total.startup += locContext.total.per_tuple;
                locContext.total.per_tuple = 0;
            }
            rinfo->eval_cost = locContext.total;
        }
        context->total.startup += rinfo->eval_cost.startup;
        context->total.per_tuple += rinfo->eval_cost.per_tuple;
        /* do NOT recurse into children */
        return false;
    }
 
    /*
     * For each operator or function node in the given tree, we charge the
     * estimated execution cost given by pg_proc.procost (remember to multiply
     * this by cpu_operator_cost).
     *
     * Vars and Consts are charged zero, and so are boolean operators (AND,
     * OR, NOT). Simplistic, but a lot better than no model at all.
     *
     * Should we try to account for the possibility of short-circuit
     * evaluation of AND/OR?  Probably *not*, because that would make the
     * results depend on the clause ordering, and we are not in any position
     * to expect that the current ordering of the clauses is the one that's
     * going to end up being used.  The above per-RestrictInfo caching would
     * not mix well with trying to re-order clauses anyway.
     *
     * Another issue that is entirely ignored here is that if a set-returning
     * function is below top level in the tree, the functions/operators above
     * it will need to be evaluated multiple times.  In practical use, such
     * cases arise so seldom as to not be worth the added complexity needed;
     * moreover, since our rowcount estimates for functions tend to be pretty
     * phony, the results would also be pretty phony.
     */
    if (IsA(node, FuncExpr))
    {
        add_function_cost(context->root, ((FuncExpr *) node)->funcid, node,
                          &context->total);
    }
    else if (IsA(node, OpExpr) ||
             IsA(node, DistinctExpr) ||
             IsA(node, NullIfExpr))
    {
        /* rely on struct equivalence to treat these all alike */
        set_opfuncid((OpExpr *) node);
        add_function_cost(context->root, ((OpExpr *) node)->opfuncid, node,
                          &context->total);
    }
    else if (IsA(node, ScalarArrayOpExpr))
    {
        ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) node;
        Node       *arraynode = (Node *) lsecond(saop->args);
        QualCost    sacosts;
        QualCost    hcosts;
        double      estarraylen = estimate_array_length(context->root, arraynode);
 
        set_sa_opfuncid(saop);
        sacosts.startup = sacosts.per_tuple = 0;
        add_function_cost(context->root, saop->opfuncid, NULL,
                          &sacosts);
 
        if (OidIsValid(saop->hashfuncid))
        {
            /* Handle costs for hashed ScalarArrayOpExpr */
            hcosts.startup = hcosts.per_tuple = 0;
 
            add_function_cost(context->root, saop->hashfuncid, NULL, &hcosts);
            context->total.startup += sacosts.startup + hcosts.startup;
 
            /* Estimate the cost of building the hashtable. */
            context->total.startup += estarraylen * hcosts.per_tuple;
 
            /*
             * XXX should we charge a little bit for sacosts.per_tuple when
             * building the table, or is it ok to assume there will be zero
             * hash collision?
             */
 
            /*
             * Charge for hashtable lookups.  Charge a single hash and a
             * single comparison.
             */
            context->total.per_tuple += hcosts.per_tuple + sacosts.per_tuple;
        }
        else
        {
            /*
             * Estimate that the operator will be applied to about half of the
             * array elements before the answer is determined.
             */
            context->total.startup += sacosts.startup;
            context->total.per_tuple += sacosts.per_tuple *
                estimate_array_length(context->root, arraynode) * 0.5;
        }
    }
    else if (IsA(node, Aggref) ||
             IsA(node, WindowFunc))
    {
        /*
         * Aggref and WindowFunc nodes are (and should be) treated like Vars,
         * ie, zero execution cost in the current model, because they behave
         * essentially like Vars at execution.  We disregard the costs of
         * their input expressions for the same reason.  The actual execution
         * costs of the aggregate/window functions and their arguments have to
         * be factored into plan-node-specific costing of the Agg or WindowAgg
         * plan node.
         */
        return false;           /* don't recurse into children */
    }
    else if (IsA(node, GroupingFunc))
    {
        /* Treat this as having cost 1 */
        context->total.per_tuple += cpu_operator_cost;
        return false;           /* don't recurse into children */
    }
    else if (IsA(node, CoerceViaIO))
    {
        CoerceViaIO *iocoerce = (CoerceViaIO *) node;
        Oid         iofunc;
        Oid         typioparam;
        bool        typisvarlena;
 
        /* check the result type's input function */
        getTypeInputInfo(iocoerce->resulttype,
                         &iofunc, &typioparam);
        add_function_cost(context->root, iofunc, NULL,
                          &context->total);
        /* check the input type's output function */
        getTypeOutputInfo(exprType((Node *) iocoerce->arg),
                          &iofunc, &typisvarlena);
        add_function_cost(context->root, iofunc, NULL,
                          &context->total);
    }
    else if (IsA(node, ArrayCoerceExpr))
    {
        ArrayCoerceExpr *acoerce = (ArrayCoerceExpr *) node;
        QualCost    perelemcost;
 
        cost_qual_eval_node(&perelemcost, (Node *) acoerce->elemexpr,
                            context->root);
        context->total.startup += perelemcost.startup;
        if (perelemcost.per_tuple > 0)
            context->total.per_tuple += perelemcost.per_tuple *
                estimate_array_length(context->root, (Node *) acoerce->arg);
    }
    else if (IsA(node, RowCompareExpr))
    {
        /* Conservatively assume we will check all the columns */
        RowCompareExpr *rcexpr = (RowCompareExpr *) node;
        ListCell   *lc;
 
        foreach(lc, rcexpr->opnos)
        {
            Oid         opid = lfirst_oid(lc);
 
            add_function_cost(context->root, get_opcode(opid), NULL,
                              &context->total);
        }
    }
    else if (IsA(node, MinMaxExpr) ||
             IsA(node, SQLValueFunction) ||
             IsA(node, XmlExpr) ||
             IsA(node, CoerceToDomain) ||
             IsA(node, NextValueExpr) ||
             IsA(node, JsonExpr))
    {
        /* Treat all these as having cost 1 */
        context->total.per_tuple += cpu_operator_cost;
    }
    else if (IsA(node, SubLink))
    {
        /* This routine should not be applied to un-planned expressions */
        elog(ERROR, "cannot handle unplanned sub-select");
    }
    else if (IsA(node, SubPlan))
    {
        /*
         * A subplan node in an expression typically indicates that the
         * subplan will be executed on each evaluation, so charge accordingly.
         * (Sub-selects that can be executed as InitPlans have already been
         * removed from the expression.)
         */
        SubPlan    *subplan = (SubPlan *) node;
 
        context->total.startup += subplan->startup_cost;
        context->total.per_tuple += subplan->per_call_cost;
 
        /*
         * We don't want to recurse into the testexpr, because it was already
         * counted in the SubPlan node's costs.  So we're done.
         */
        return false;
    }
    else if (IsA(node, AlternativeSubPlan))
    {
        /*
         * Arbitrarily use the first alternative plan for costing.  (We should
         * certainly only include one alternative, and we don't yet have
         * enough information to know which one the executor is most likely to
         * use.)
         */
        AlternativeSubPlan *asplan = (AlternativeSubPlan *) node;
 
        return cost_qual_eval_walker((Node *) linitial(asplan->subplans),
                                     context);
    }
    else if (IsA(node, PlaceHolderVar))
    {
        /*
         * A PlaceHolderVar should be given cost zero when considering general
         * expression evaluation costs.  The expense of doing the contained
         * expression is charged as part of the tlist eval costs of the scan
         * or join where the PHV is first computed (see set_rel_width and
         * add_placeholders_to_joinrel).  If we charged it again here, we'd be
         * double-counting the cost for each level of plan that the PHV
         * bubbles up through.  Hence, return without recursing into the
         * phexpr.
         */
        return false;
    }
 
    /* recurse into children */
    return expression_tree_walker(node, cost_qual_eval_walker,
                                  (void *) context);
}
 
/*
 * get_restriction_qual_cost
 *    Compute evaluation costs of a baserel's restriction quals, plus any
 *    movable join quals that have been pushed down to the scan.
 *    Results are returned into *qpqual_cost.
 *
 * This is a convenience subroutine that works for seqscans and other cases
 * where all the given quals will be evaluated the hard way.  It's not useful
 * for cost_index(), for example, where the index machinery takes care of
 * some of the quals.  We assume baserestrictcost was previously set by
 * set_baserel_size_estimates().
 */
static void
get_restriction_qual_cost(PlannerInfo *root, RelOptInfo *baserel,
                          ParamPathInfo *param_info,
                          QualCost *qpqual_cost)
{
    if (param_info)
    {
        /* Include costs of pushed-down clauses */
        cost_qual_eval(qpqual_cost, param_info->ppi_clauses, root);
 
        qpqual_cost->startup += baserel->baserestrictcost.startup;
        qpqual_cost->per_tuple += baserel->baserestrictcost.per_tuple;
    }
    else
        *qpqual_cost = baserel->baserestrictcost;
}
 
 
/*
 * compute_semi_anti_join_factors
 *    Estimate how much of the inner input a SEMI, ANTI, or inner_unique join
 *    can be expected to scan.
 *
 * In a hash or nestloop SEMI/ANTI join, the executor will stop scanning
 * inner rows as soon as it finds a match to the current outer row.
 * The same happens if we have detected the inner rel is unique.
 * We should therefore adjust some of the cost components for this effect.
 * This function computes some estimates needed for these adjustments.
 * These estimates will be the same regardless of the particular paths used
 * for the outer and inner relation, so we compute these once and then pass
 * them to all the join cost estimation functions.
 *
 * Input parameters:
 *  joinrel: join relation under consideration
 *  outerrel: outer relation under consideration
 *  innerrel: inner relation under consideration
 *  jointype: if not JOIN_SEMI or JOIN_ANTI, we assume it's inner_unique
 *  sjinfo: SpecialJoinInfo relevant to this join
 *  restrictlist: join quals
 * Output parameters:
 *  *semifactors is filled in (see pathnodes.h for field definitions)
 */
void
compute_semi_anti_join_factors(PlannerInfo *root,
                               RelOptInfo *joinrel,
                               RelOptInfo *outerrel,
                               RelOptInfo *innerrel,
                               JoinType jointype,
                               SpecialJoinInfo *sjinfo,
                               List *restrictlist,
                               SemiAntiJoinFactors *semifactors)
{
    Selectivity jselec;
    Selectivity nselec;
    Selectivity avgmatch;
    SpecialJoinInfo norm_sjinfo;
    List       *joinquals;
    ListCell   *l;
 
    /*
     * In an ANTI join, we must ignore clauses that are "pushed down", since
     * those won't affect the match logic.  In a SEMI join, we do not
     * distinguish joinquals from "pushed down" quals, so just use the whole
     * restrictinfo list.  For other outer join types, we should consider only
     * non-pushed-down quals, so that this devolves to an IS_OUTER_JOIN check.
     */
    if (IS_OUTER_JOIN(jointype))
    {
        joinquals = NIL;
        foreach(l, restrictlist)
        {
            RestrictInfo *rinfo = lfirst_node(RestrictInfo, l);
 
            if (!RINFO_IS_PUSHED_DOWN(rinfo, joinrel->relids))
                joinquals = lappend(joinquals, rinfo);
        }
    }
    else
        joinquals = restrictlist;
 
    /*
     * Get the JOIN_SEMI or JOIN_ANTI selectivity of the join clauses.
     */
    jselec = clauselist_selectivity(root,
                                    joinquals,
                                    0,
                                    (jointype == JOIN_ANTI) ? JOIN_ANTI : JOIN_SEMI,
                                    sjinfo);
 
    /*
     * Also get the normal inner-join selectivity of the join clauses.
     */
    init_dummy_sjinfo(&norm_sjinfo, outerrel->relids, innerrel->relids);
 
    nselec = clauselist_selectivity(root,
                                    joinquals,
                                    0,
                                    JOIN_INNER,
                                    &norm_sjinfo);
 
    /* Avoid leaking a lot of ListCells */
    if (IS_OUTER_JOIN(jointype))
        list_free(joinquals);
 
    /*
     * jselec can be interpreted as the fraction of outer-rel rows that have
     * any matches (this is true for both SEMI and ANTI cases).  And nselec is
     * the fraction of the Cartesian product that matches.  So, the average
     * number of matches for each outer-rel row that has at least one match is
     * nselec * inner_rows / jselec.
     *
     * Note: it is correct to use the inner rel's "rows" count here, even
     * though we might later be considering a parameterized inner path with
     * fewer rows.  This is because we have included all the join clauses in
     * the selectivity estimate.
     */
    if (jselec > 0)             /* protect against zero divide */
    {
        avgmatch = nselec * innerrel->rows / jselec;
        /* Clamp to sane range */
        avgmatch = Max(1.0, avgmatch);
    }
    else
        avgmatch = 1.0;
 
    semifactors->outer_match_frac = jselec;
    semifactors->match_count = avgmatch;
}
 
/*
 * has_indexed_join_quals
 *    Check whether all the joinquals of a nestloop join are used as
 *    inner index quals.
 *
 * If the inner path of a SEMI/ANTI join is an indexscan (including bitmap
 * indexscan) that uses all the joinquals as indexquals, we can assume that an
 * unmatched outer tuple is cheap to process, whereas otherwise it's probably
 * expensive.
 */
static bool
has_indexed_join_quals(NestPath *path)
{
    JoinPath   *joinpath = &path->jpath;
    Relids      joinrelids = joinpath->path.parent->relids;
    Path       *innerpath = joinpath->innerjoinpath;
    List       *indexclauses;
    bool        found_one;
    ListCell   *lc;
 
    /* If join still has quals to evaluate, it's not fast */
    if (joinpath->joinrestrictinfo != NIL)
        return false;
    /* Nor if the inner path isn't parameterized at all */
    if (innerpath->param_info == NULL)
        return false;
 
    /* Find the indexclauses list for the inner scan */
    switch (innerpath->pathtype)
    {
        case T_IndexScan:
        case T_IndexOnlyScan:
            indexclauses = ((IndexPath *) innerpath)->indexclauses;
            break;
        case T_BitmapHeapScan:
            {
                /* Accept only a simple bitmap scan, not AND/OR cases */
                Path       *bmqual = ((BitmapHeapPath *) innerpath)->bitmapqual;
 
                if (IsA(bmqual, IndexPath))
                    indexclauses = ((IndexPath *) bmqual)->indexclauses;
                else
                    return false;
                break;
            }
        default:
 
            /*
             * If it's not a simple indexscan, it probably doesn't run quickly
             * for zero rows out, even if it's a parameterized path using all
             * the joinquals.
             */
            return false;
    }
 
    /*
     * Examine the inner path's param clauses.  Any that are from the outer
     * path must be found in the indexclauses list, either exactly or in an
     * equivalent form generated by equivclass.c.  Also, we must find at least
     * one such clause, else it's a clauseless join which isn't fast.
     */
    found_one = false;
    foreach(lc, innerpath->param_info->ppi_clauses)
    {
        RestrictInfo *rinfo = (RestrictInfo *) lfirst(lc);
 
        if (join_clause_is_movable_into(rinfo,
                                        innerpath->parent->relids,
                                        joinrelids))
        {
            if (!is_redundant_with_indexclauses(rinfo, indexclauses))
                return false;
            found_one = true;
        }
    }
    return found_one;
}
 
 
/*
 * approx_tuple_count
 *      Quick-and-dirty estimation of the number of join rows passing
 *      a set of qual conditions.
 *
 * The quals can be either an implicitly-ANDed list of boolean expressions,
 * or a list of RestrictInfo nodes (typically the latter).
 *
 * We intentionally compute the selectivity under JOIN_INNER rules, even
 * if it's some type of outer join.  This is appropriate because we are
 * trying to figure out how many tuples pass the initial merge or hash
 * join step.
 *
 * This is quick-and-dirty because we bypass clauselist_selectivity, and
 * simply multiply the independent clause selectivities together.  Now
 * clauselist_selectivity often can't do any better than that anyhow, but
 * for some situations (such as range constraints) it is smarter.  However,
 * we can't effectively cache the results of clauselist_selectivity, whereas
 * the individual clause selectivities can be and are cached.
 *
 * Since we are only using the results to estimate how many potential
 * output tuples are generated and passed through qpqual checking, it
 * seems OK to live with the approximation.
 */
static double
approx_tuple_count(PlannerInfo *root, JoinPath *path, List *quals)
{
    double      tuples;
    double      outer_tuples = path->outerjoinpath->rows;
    double      inner_tuples = path->innerjoinpath->rows;
    SpecialJoinInfo sjinfo;
    Selectivity selec = 1.0;
    ListCell   *l;
 
    /*
     * Make up a SpecialJoinInfo for JOIN_INNER semantics.
     */
    init_dummy_sjinfo(&sjinfo, path->outerjoinpath->parent->relids,
                      path->innerjoinpath->parent->relids);
 
    /* Get the approximate selectivity */
    foreach(l, quals)
    {
        Node       *qual = (Node *) lfirst(l);
 
        /* Note that clause_selectivity will be able to cache its result */
        selec *= clause_selectivity(root, qual, 0, JOIN_INNER, &sjinfo);
    }
 
    /* Apply it to the input relation sizes */
    tuples = selec * outer_tuples * inner_tuples;
 
    return clamp_row_est(tuples);
}
 
 
/*
 * set_baserel_size_estimates
 *      Set the size estimates for the given base relation.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already, and rel->tuples must be set.
 *
 * We set the following fields of the rel node:
 *  rows: the estimated number of output tuples (after applying
 *        restriction clauses).
 *  width: the estimated average output tuple width in bytes.
 *  baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
 */
void
set_baserel_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    double      nrows;
 
    /* Should only be applied to base relations */
    Assert(rel->relid > 0);
 
    nrows = rel->tuples *
        clauselist_selectivity(root,
                               rel->baserestrictinfo,
                               0,
                               JOIN_INNER,
                               NULL);
 
    rel->rows = clamp_row_est(nrows);
 
    cost_qual_eval(&rel->baserestrictcost, rel->baserestrictinfo, root);
 
    set_rel_width(root, rel);
}
 
/*
 * get_parameterized_baserel_size
 *      Make a size estimate for a parameterized scan of a base relation.
 *
 * 'param_clauses' lists the additional join clauses to be used.
 *
 * set_baserel_size_estimates must have been applied already.
 */
double
get_parameterized_baserel_size(PlannerInfo *root, RelOptInfo *rel,
                               List *param_clauses)
{
    List       *allclauses;
    double      nrows;
 
    /*
     * Estimate the number of rows returned by the parameterized scan, knowing
     * that it will apply all the extra join clauses as well as the rel's own
     * restriction clauses.  Note that we force the clauses to be treated as
     * non-join clauses during selectivity estimation.
     */
    allclauses = list_concat_copy(param_clauses, rel->baserestrictinfo);
    nrows = rel->tuples *
        clauselist_selectivity(root,
                               allclauses,
                               rel->relid,  /* do not use 0! */
                               JOIN_INNER,
                               NULL);
    nrows = clamp_row_est(nrows);
    /* For safety, make sure result is not more than the base estimate */
    if (nrows > rel->rows)
        nrows = rel->rows;
    return nrows;
}
 
/*
 * set_joinrel_size_estimates
 *      Set the size estimates for the given join relation.
 *
 * The rel's targetlist must have been constructed already, and a
 * restriction clause list that matches the given component rels must
 * be provided.
 *
 * Since there is more than one way to make a joinrel for more than two
 * base relations, the results we get here could depend on which component
 * rel pair is provided.  In theory we should get the same answers no matter
 * which pair is provided; in practice, since the selectivity estimation
 * routines don't handle all cases equally well, we might not.  But there's
 * not much to be done about it.  (Would it make sense to repeat the
 * calculations for each pair of input rels that's encountered, and somehow
 * average the results?  Probably way more trouble than it's worth, and
 * anyway we must keep the rowcount estimate the same for all paths for the
 * joinrel.)
 *
 * We set only the rows field here.  The reltarget field was already set by
 * build_joinrel_tlist, and baserestrictcost is not used for join rels.
 */
void
set_joinrel_size_estimates(PlannerInfo *root, RelOptInfo *rel,
                           RelOptInfo *outer_rel,
                           RelOptInfo *inner_rel,
                           SpecialJoinInfo *sjinfo,
                           List *restrictlist)
{
    rel->rows = calc_joinrel_size_estimate(root,
                                           rel,
                                           outer_rel,
                                           inner_rel,
                                           outer_rel->rows,
                                           inner_rel->rows,
                                           sjinfo,
                                           restrictlist);
}
 
/*
 * get_parameterized_joinrel_size
 *      Make a size estimate for a parameterized scan of a join relation.
 *
 * 'rel' is the joinrel under consideration.
 * 'outer_path', 'inner_path' are (probably also parameterized) Paths that
 *      produce the relations being joined.
 * 'sjinfo' is any SpecialJoinInfo relevant to this join.
 * 'restrict_clauses' lists the join clauses that need to be applied at the
 * join node (including any movable clauses that were moved down to this join,
 * and not including any movable clauses that were pushed down into the
 * child paths).
 *
 * set_joinrel_size_estimates must have been applied already.
 */
double
get_parameterized_joinrel_size(PlannerInfo *root, RelOptInfo *rel,
                               Path *outer_path,
                               Path *inner_path,
                               SpecialJoinInfo *sjinfo,
                               List *restrict_clauses)
{
    double      nrows;
 
    /*
     * Estimate the number of rows returned by the parameterized join as the
     * sizes of the input paths times the selectivity of the clauses that have
     * ended up at this join node.
     *
     * As with set_joinrel_size_estimates, the rowcount estimate could depend
     * on the pair of input paths provided, though ideally we'd get the same
     * estimate for any pair with the same parameterization.
     */
    nrows = calc_joinrel_size_estimate(root,
                                       rel,
                                       outer_path->parent,
                                       inner_path->parent,
                                       outer_path->rows,
                                       inner_path->rows,
                                       sjinfo,
                                       restrict_clauses);
    /* For safety, make sure result is not more than the base estimate */
    if (nrows > rel->rows)
        nrows = rel->rows;
    return nrows;
}
 
/*
 * calc_joinrel_size_estimate
 *      Workhorse for set_joinrel_size_estimates and
 *      get_parameterized_joinrel_size.
 *
 * outer_rel/inner_rel are the relations being joined, but they should be
 * assumed to have sizes outer_rows/inner_rows; those numbers might be less
 * than what rel->rows says, when we are considering parameterized paths.
 */
static double
calc_joinrel_size_estimate(PlannerInfo *root,
                           RelOptInfo *joinrel,
                           RelOptInfo *outer_rel,
                           RelOptInfo *inner_rel,
                           double outer_rows,
                           double inner_rows,
                           SpecialJoinInfo *sjinfo,
                           List *restrictlist)
{
    JoinType    jointype = sjinfo->jointype;
    Selectivity fkselec;
    Selectivity jselec;
    Selectivity pselec;
    double      nrows;
 
    /*
     * Compute joinclause selectivity.  Note that we are only considering
     * clauses that become restriction clauses at this join level; we are not
     * double-counting them because they were not considered in estimating the
     * sizes of the component rels.
     *
     * First, see whether any of the joinclauses can be matched to known FK
     * constraints.  If so, drop those clauses from the restrictlist, and
     * instead estimate their selectivity using FK semantics.  (We do this
     * without regard to whether said clauses are local or "pushed down".
     * Probably, an FK-matching clause could never be seen as pushed down at
     * an outer join, since it would be strict and hence would be grounds for
     * join strength reduction.)  fkselec gets the net selectivity for
     * FK-matching clauses, or 1.0 if there are none.
     */
    fkselec = get_foreign_key_join_selectivity(root,
                                               outer_rel->relids,
                                               inner_rel->relids,
                                               sjinfo,
                                               &restrictlist);
 
    /*
     * For an outer join, we have to distinguish the selectivity of the join's
     * own clauses (JOIN/ON conditions) from any clauses that were "pushed
     * down".  For inner joins we just count them all as joinclauses.
     */
    if (IS_OUTER_JOIN(jointype))
    {
        List       *joinquals = NIL;
        List       *pushedquals = NIL;
        ListCell   *l;
 
        /* Grovel through the clauses to separate into two lists */
        foreach(l, restrictlist)
        {
            RestrictInfo *rinfo = lfirst_node(RestrictInfo, l);
 
            if (RINFO_IS_PUSHED_DOWN(rinfo, joinrel->relids))
                pushedquals = lappend(pushedquals, rinfo);
            else
                joinquals = lappend(joinquals, rinfo);
        }
 
        /* Get the separate selectivities */
        jselec = clauselist_selectivity(root,
                                        joinquals,
                                        0,
                                        jointype,
                                        sjinfo);
        pselec = clauselist_selectivity(root,
                                        pushedquals,
                                        0,
                                        jointype,
                                        sjinfo);
 
        /* Avoid leaking a lot of ListCells */
        list_free(joinquals);
        list_free(pushedquals);
    }
    else
    {
        jselec = clauselist_selectivity(root,
                                        restrictlist,
                                        0,
                                        jointype,
                                        sjinfo);
        pselec = 0.0;           /* not used, keep compiler quiet */
    }
 
    /*
     * Basically, we multiply size of Cartesian product by selectivity.
     *
     * If we are doing an outer join, take that into account: the joinqual
     * selectivity has to be clamped using the knowledge that the output must
     * be at least as large as the non-nullable input.  However, any
     * pushed-down quals are applied after the outer join, so their
     * selectivity applies fully.
     *
     * For JOIN_SEMI and JOIN_ANTI, the selectivity is defined as the fraction
     * of LHS rows that have matches, and we apply that straightforwardly.
     */
    switch (jointype)
    {
        case JOIN_INNER:
            nrows = outer_rows * inner_rows * fkselec * jselec;
            /* pselec not used */
            break;
        case JOIN_LEFT:
            nrows = outer_rows * inner_rows * fkselec * jselec;
            if (nrows < outer_rows)
                nrows = outer_rows;
            nrows *= pselec;
            break;
        case JOIN_FULL:
            nrows = outer_rows * inner_rows * fkselec * jselec;
            if (nrows < outer_rows)
                nrows = outer_rows;
            if (nrows < inner_rows)
                nrows = inner_rows;
            nrows *= pselec;
            break;
        case JOIN_SEMI:
            nrows = outer_rows * fkselec * jselec;
            /* pselec not used */
            break;
        case JOIN_ANTI:
            nrows = outer_rows * (1.0 - fkselec * jselec);
            nrows *= pselec;
            break;
        default:
            /* other values not expected here */
            elog(ERROR, "unrecognized join type: %d", (int) jointype);
            nrows = 0;          /* keep compiler quiet */
            break;
    }
 
    return clamp_row_est(nrows);
}
 
/*
 * get_foreign_key_join_selectivity
 *      Estimate join selectivity for foreign-key-related clauses.
 *
 * Remove any clauses that can be matched to FK constraints from *restrictlist,
 * and return a substitute estimate of their selectivity.  1.0 is returned
 * when there are no such clauses.
 *
 * The reason for treating such clauses specially is that we can get better
 * estimates this way than by relying on clauselist_selectivity(), especially
 * for multi-column FKs where that function's assumption that the clauses are
 * independent falls down badly.  But even with single-column FKs, we may be
 * able to get a better answer when the pg_statistic stats are missing or out
 * of date.
 */
static Selectivity
get_foreign_key_join_selectivity(PlannerInfo *root,
                                 Relids outer_relids,
                                 Relids inner_relids,
                                 SpecialJoinInfo *sjinfo,
                                 List **restrictlist)
{
    Selectivity fkselec = 1.0;
    JoinType    jointype = sjinfo->jointype;
    List       *worklist = *restrictlist;
    ListCell   *lc;
 
    /* Consider each FK constraint that is known to match the query */
    foreach(lc, root->fkey_list)
    {
        ForeignKeyOptInfo *fkinfo = (ForeignKeyOptInfo *) lfirst(lc);
        bool        ref_is_outer;
        List       *removedlist;
        ListCell   *cell;
 
        /*
         * This FK is not relevant unless it connects a baserel on one side of
         * this join to a baserel on the other side.
         */
        if (bms_is_member(fkinfo->con_relid, outer_relids) &&
            bms_is_member(fkinfo->ref_relid, inner_relids))
            ref_is_outer = false;
        else if (bms_is_member(fkinfo->ref_relid, outer_relids) &&
                 bms_is_member(fkinfo->con_relid, inner_relids))
            ref_is_outer = true;
        else
            continue;
 
        /*
         * If we're dealing with a semi/anti join, and the FK's referenced
         * relation is on the outside, then knowledge of the FK doesn't help
         * us figure out what we need to know (which is the fraction of outer
         * rows that have matches).  On the other hand, if the referenced rel
         * is on the inside, then all outer rows must have matches in the
         * referenced table (ignoring nulls).  But any restriction or join
         * clauses that filter that table will reduce the fraction of matches.
         * We can account for restriction clauses, but it's too hard to guess
         * how many table rows would get through a join that's inside the RHS.
         * Hence, if either case applies, punt and ignore the FK.
         */
        if ((jointype == JOIN_SEMI || jointype == JOIN_ANTI) &&
            (ref_is_outer || bms_membership(inner_relids) != BMS_SINGLETON))
            continue;
 
        /*
         * Modify the restrictlist by removing clauses that match the FK (and
         * putting them into removedlist instead).  It seems unsafe to modify
         * the originally-passed List structure, so we make a shallow copy the
         * first time through.
         */
        if (worklist == *restrictlist)
            worklist = list_copy(worklist);
 
        removedlist = NIL;
        foreach(cell, worklist)
        {
            RestrictInfo *rinfo = (RestrictInfo *) lfirst(cell);
            bool        remove_it = false;
            int         i;
 
            /* Drop this clause if it matches any column of the FK */
            for (i = 0; i < fkinfo->nkeys; i++)
            {
                if (rinfo->parent_ec)
                {
                    /*
                     * EC-derived clauses can only match by EC.  It is okay to
                     * consider any clause derived from the same EC as
                     * matching the FK: even if equivclass.c chose to generate
                     * a clause equating some other pair of Vars, it could
                     * have generated one equating the FK's Vars.  So for
                     * purposes of estimation, we can act as though it did so.
                     *
                     * Note: checking parent_ec is a bit of a cheat because
                     * there are EC-derived clauses that don't have parent_ec
                     * set; but such clauses must compare expressions that
                     * aren't just Vars, so they cannot match the FK anyway.
                     */
                    if (fkinfo->eclass[i] == rinfo->parent_ec)
                    {
                        remove_it = true;
                        break;
                    }
                }
                else
                {
                    /*
                     * Otherwise, see if rinfo was previously matched to FK as
                     * a "loose" clause.
                     */
                    if (list_member_ptr(fkinfo->rinfos[i], rinfo))
                    {
                        remove_it = true;
                        break;
                    }
                }
            }
            if (remove_it)
            {
                worklist = foreach_delete_current(worklist, cell);
                removedlist = lappend(removedlist, rinfo);
            }
        }
 
        /*
         * If we failed to remove all the matching clauses we expected to
         * find, chicken out and ignore this FK; applying its selectivity
         * might result in double-counting.  Put any clauses we did manage to
         * remove back into the worklist.
         *
         * Since the matching clauses are known not outerjoin-delayed, they
         * would normally have appeared in the initial joinclause list.  If we
         * didn't find them, there are two possibilities:
         *
         * 1. If the FK match is based on an EC that is ec_has_const, it won't
         * have generated any join clauses at all.  We discount such ECs while
         * checking to see if we have "all" the clauses.  (Below, we'll adjust
         * the selectivity estimate for this case.)
         *
         * 2. The clauses were matched to some other FK in a previous
         * iteration of this loop, and thus removed from worklist.  (A likely
         * case is that two FKs are matched to the same EC; there will be only
         * one EC-derived clause in the initial list, so the first FK will
         * consume it.)  Applying both FKs' selectivity independently risks
         * underestimating the join size; in particular, this would undo one
         * of the main things that ECs were invented for, namely to avoid
         * double-counting the selectivity of redundant equality conditions.
         * Later we might think of a reasonable way to combine the estimates,
         * but for now, just punt, since this is a fairly uncommon situation.
         */
        if (removedlist == NIL ||
            list_length(removedlist) !=
            (fkinfo->nmatched_ec - fkinfo->nconst_ec + fkinfo->nmatched_ri))
        {
            worklist = list_concat(worklist, removedlist);
            continue;
        }
 
        /*
         * Finally we get to the payoff: estimate selectivity using the
         * knowledge that each referencing row will match exactly one row in
         * the referenced table.
         *
         * XXX that's not true in the presence of nulls in the referencing
         * column(s), so in principle we should derate the estimate for those.
         * However (1) if there are any strict restriction clauses for the
         * referencing column(s) elsewhere in the query, derating here would
         * be double-counting the null fraction, and (2) it's not very clear
         * how to combine null fractions for multiple referencing columns. So
         * we do nothing for now about correcting for nulls.
         *
         * XXX another point here is that if either side of an FK constraint
         * is an inheritance parent, we estimate as though the constraint
         * covers all its children as well.  This is not an unreasonable
         * assumption for a referencing table, ie the user probably applied
         * identical constraints to all child tables (though perhaps we ought
         * to check that).  But it's not possible to have done that for a
         * referenced table.  Fortunately, precisely because that doesn't
         * work, it is uncommon in practice to have an FK referencing a parent
         * table.  So, at least for now, disregard inheritance here.
         */
        if (jointype == JOIN_SEMI || jointype == JOIN_ANTI)
        {
            /*
             * For JOIN_SEMI and JOIN_ANTI, we only get here when the FK's
             * referenced table is exactly the inside of the join.  The join
             * selectivity is defined as the fraction of LHS rows that have
             * matches.  The FK implies that every LHS row has a match *in the
             * referenced table*; but any restriction clauses on it will
             * reduce the number of matches.  Hence we take the join
             * selectivity as equal to the selectivity of the table's
             * restriction clauses, which is rows / tuples; but we must guard
             * against tuples == 0.
             */
            RelOptInfo *ref_rel = find_base_rel(root, fkinfo->ref_relid);
            double      ref_tuples = Max(ref_rel->tuples, 1.0);
 
            fkselec *= ref_rel->rows / ref_tuples;
        }
        else
        {
            /*
             * Otherwise, selectivity is exactly 1/referenced-table-size; but
             * guard against tuples == 0.  Note we should use the raw table
             * tuple count, not any estimate of its filtered or joined size.
             */
            RelOptInfo *ref_rel = find_base_rel(root, fkinfo->ref_relid);
            double      ref_tuples = Max(ref_rel->tuples, 1.0);
 
            fkselec *= 1.0 / ref_tuples;
        }
 
        /*
         * If any of the FK columns participated in ec_has_const ECs, then
         * equivclass.c will have generated "var = const" restrictions for
         * each side of the join, thus reducing the sizes of both input
         * relations.  Taking the fkselec at face value would amount to
         * double-counting the selectivity of the constant restriction for the
         * referencing Var.  Hence, look for the restriction clause(s) that
         * were applied to the referencing Var(s), and divide out their
         * selectivity to correct for this.
         */
        if (fkinfo->nconst_ec > 0)
        {
            for (int i = 0; i < fkinfo->nkeys; i++)
            {
                EquivalenceClass *ec = fkinfo->eclass[i];
 
                if (ec && ec->ec_has_const)
                {
                    EquivalenceMember *em = fkinfo->fk_eclass_member[i];
                    RestrictInfo *rinfo = find_derived_clause_for_ec_member(ec,
                                                                            em);
 
                    if (rinfo)
                    {
                        Selectivity s0;
 
                        s0 = clause_selectivity(root,
                                                (Node *) rinfo,
                                                0,
                                                jointype,
                                                sjinfo);
                        if (s0 > 0)
                            fkselec /= s0;
                    }
                }
            }
        }
    }
 
    *restrictlist = worklist;
    CLAMP_PROBABILITY(fkselec);
    return fkselec;
}
 
/*
 * set_subquery_size_estimates
 *      Set the size estimates for a base relation that is a subquery.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already, and the Paths for the subquery must have been completed.
 * We look at the subquery's PlannerInfo to extract data.
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_subquery_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    PlannerInfo *subroot = rel->subroot;
    RelOptInfo *sub_final_rel;
    ListCell   *lc;
 
    /* Should only be applied to base relations that are subqueries */
    Assert(rel->relid > 0);
    Assert(planner_rt_fetch(rel->relid, root)->rtekind == RTE_SUBQUERY);
 
    /*
     * Copy raw number of output rows from subquery.  All of its paths should
     * have the same output rowcount, so just look at cheapest-total.
     */
    sub_final_rel = fetch_upper_rel(subroot, UPPERREL_FINAL, NULL);
    rel->tuples = sub_final_rel->cheapest_total_path->rows;
 
    /*
     * Compute per-output-column width estimates by examining the subquery's
     * targetlist.  For any output that is a plain Var, get the width estimate
     * that was made while planning the subquery.  Otherwise, we leave it to
     * set_rel_width to fill in a datatype-based default estimate.
     */
    foreach(lc, subroot->parse->targetList)
    {
        TargetEntry *te = lfirst_node(TargetEntry, lc);
        Node       *texpr = (Node *) te->expr;
        int32       item_width = 0;
 
        /* junk columns aren't visible to upper query */
        if (te->resjunk)
            continue;
 
        /*
         * The subquery could be an expansion of a view that's had columns
         * added to it since the current query was parsed, so that there are
         * non-junk tlist columns in it that don't correspond to any column
         * visible at our query level.  Ignore such columns.
         */
        if (te->resno < rel->min_attr || te->resno > rel->max_attr)
            continue;
 
        /*
         * XXX This currently doesn't work for subqueries containing set
         * operations, because the Vars in their tlists are bogus references
         * to the first leaf subquery, which wouldn't give the right answer
         * even if we could still get to its PlannerInfo.
         *
         * Also, the subquery could be an appendrel for which all branches are
         * known empty due to constraint exclusion, in which case
         * set_append_rel_pathlist will have left the attr_widths set to zero.
         *
         * In either case, we just leave the width estimate zero until
         * set_rel_width fixes it.
         */
        if (IsA(texpr, Var) &&
            subroot->parse->setOperations == NULL)
        {
            Var        *var = (Var *) texpr;
            RelOptInfo *subrel = find_base_rel(subroot, var->varno);
 
            item_width = subrel->attr_widths[var->varattno - subrel->min_attr];
        }
        rel->attr_widths[te->resno - rel->min_attr] = item_width;
    }
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_function_size_estimates
 *      Set the size estimates for a base relation that is a function call.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_function_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    RangeTblEntry *rte;
    ListCell   *lc;
 
    /* Should only be applied to base relations that are functions */
    Assert(rel->relid > 0);
    rte = planner_rt_fetch(rel->relid, root);
    Assert(rte->rtekind == RTE_FUNCTION);
 
    /*
     * Estimate number of rows the functions will return. The rowcount of the
     * node is that of the largest function result.
     */
    rel->tuples = 0;
    foreach(lc, rte->functions)
    {
        RangeTblFunction *rtfunc = (RangeTblFunction *) lfirst(lc);
        double      ntup = expression_returns_set_rows(root, rtfunc->funcexpr);
 
        if (ntup > rel->tuples)
            rel->tuples = ntup;
    }
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_function_size_estimates
 *      Set the size estimates for a base relation that is a function call.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 *
 * We set the same fields as set_tablefunc_size_estimates.
 */
void
set_tablefunc_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    /* Should only be applied to base relations that are functions */
    Assert(rel->relid > 0);
    Assert(planner_rt_fetch(rel->relid, root)->rtekind == RTE_TABLEFUNC);
 
    rel->tuples = 100;
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_values_size_estimates
 *      Set the size estimates for a base relation that is a values list.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_values_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    RangeTblEntry *rte;
 
    /* Should only be applied to base relations that are values lists */
    Assert(rel->relid > 0);
    rte = planner_rt_fetch(rel->relid, root);
    Assert(rte->rtekind == RTE_VALUES);
 
    /*
     * Estimate number of rows the values list will return. We know this
     * precisely based on the list length (well, barring set-returning
     * functions in list items, but that's a refinement not catered for
     * anywhere else either).
     */
    rel->tuples = list_length(rte->values_lists);
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_cte_size_estimates
 *      Set the size estimates for a base relation that is a CTE reference.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already, and we need an estimate of the number of rows returned by the CTE
 * (if a regular CTE) or the non-recursive term (if a self-reference).
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_cte_size_estimates(PlannerInfo *root, RelOptInfo *rel, double cte_rows)
{
    RangeTblEntry *rte;
 
    /* Should only be applied to base relations that are CTE references */
    Assert(rel->relid > 0);
    rte = planner_rt_fetch(rel->relid, root);
    Assert(rte->rtekind == RTE_CTE);
 
    if (rte->self_reference)
    {
        /*
         * In a self-reference, we assume the average worktable size is a
         * multiple of the nonrecursive term's size.  The best multiplier will
         * vary depending on query "fan-out", so make its value adjustable.
         */
        rel->tuples = clamp_row_est(recursive_worktable_factor * cte_rows);
    }
    else
    {
        /* Otherwise just believe the CTE's rowcount estimate */
        rel->tuples = cte_rows;
    }
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_namedtuplestore_size_estimates
 *      Set the size estimates for a base relation that is a tuplestore reference.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_namedtuplestore_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    RangeTblEntry *rte;
 
    /* Should only be applied to base relations that are tuplestore references */
    Assert(rel->relid > 0);
    rte = planner_rt_fetch(rel->relid, root);
    Assert(rte->rtekind == RTE_NAMEDTUPLESTORE);
 
    /*
     * Use the estimate provided by the code which is generating the named
     * tuplestore.  In some cases, the actual number might be available; in
     * others the same plan will be re-used, so a "typical" value might be
     * estimated and used.
     */
    rel->tuples = rte->enrtuples;
    if (rel->tuples < 0)
        rel->tuples = 1000;
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_result_size_estimates
 *      Set the size estimates for an RTE_RESULT base relation
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 *
 * We set the same fields as set_baserel_size_estimates.
 */
void
set_result_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    /* Should only be applied to RTE_RESULT base relations */
    Assert(rel->relid > 0);
    Assert(planner_rt_fetch(rel->relid, root)->rtekind == RTE_RESULT);
 
    /* RTE_RESULT always generates a single row, natively */
    rel->tuples = 1;
 
    /* Now estimate number of output rows, etc */
    set_baserel_size_estimates(root, rel);
}
 
/*
 * set_foreign_size_estimates
 *      Set the size estimates for a base relation that is a foreign table.
 *
 * There is not a whole lot that we can do here; the foreign-data wrapper
 * is responsible for producing useful estimates.  We can do a decent job
 * of estimating baserestrictcost, so we set that, and we also set up width
 * using what will be purely datatype-driven estimates from the targetlist.
 * There is no way to do anything sane with the rows value, so we just put
 * a default estimate and hope that the wrapper can improve on it.  The
 * wrapper's GetForeignRelSize function will be called momentarily.
 *
 * The rel's targetlist and restrictinfo list must have been constructed
 * already.
 */
void
set_foreign_size_estimates(PlannerInfo *root, RelOptInfo *rel)
{
    /* Should only be applied to base relations */
    Assert(rel->relid > 0);
 
    rel->rows = 1000;           /* entirely bogus default estimate */
 
    cost_qual_eval(&rel->baserestrictcost, rel->baserestrictinfo, root);
 
    set_rel_width(root, rel);
}
 
 
/*
 * set_rel_width
 *      Set the estimated output width of a base relation.
 *
 * The estimated output width is the sum of the per-attribute width estimates
 * for the actually-referenced columns, plus any PHVs or other expressions
 * that have to be calculated at this relation.  This is the amount of data
 * we'd need to pass upwards in case of a sort, hash, etc.
 *
 * This function also sets reltarget->cost, so it's a bit misnamed now.
 *
 * NB: this works best on plain relations because it prefers to look at
 * real Vars.  For subqueries, set_subquery_size_estimates will already have
 * copied up whatever per-column estimates were made within the subquery,
 * and for other types of rels there isn't much we can do anyway.  We fall
 * back on (fairly stupid) datatype-based width estimates if we can't get
 * any better number.
 *
 * The per-attribute width estimates are cached for possible re-use while
 * building join relations or post-scan/join pathtargets.
 */
static void
set_rel_width(PlannerInfo *root, RelOptInfo *rel)
{
    Oid         reloid = planner_rt_fetch(rel->relid, root)->relid;
    int64       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);
            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)
    {
        int64       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] = clamp_width_est(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;
    }
 
    rel->reltarget->width = clamp_width_est(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)
{
    int64       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);
 
        tuple_width += get_expr_width(root, node);
 
        /* For non-Vars, account for evaluation cost */
        if (!IsA(node, Var))
        {
            QualCost    cost;
 
            cost_qual_eval_node(&cost, node, root);
            target->cost.startup += cost.startup;
            target->cost.per_tuple += cost.per_tuple;
        }
    }
 
    target->width = clamp_width_est(tuple_width);
 
    return target;
}
 
/*
 * get_expr_width
 *      Estimate the width of the given expr attempting to use the width
 *      cached in a Var's owning RelOptInfo, else fallback on the type's
 *      average width when unable to or when the given Node is not a Var.
 */
static int32
get_expr_width(PlannerInfo *root, const Node *expr)
{
    int32       width;
 
    if (IsA(expr, Var))
    {
        const Var  *var = (const Var *) expr;
 
        /* We should not see any upper-level Vars here */
        Assert(var->varlevelsup == 0);
 
        /* Try to get data from RelOptInfo cache */
        if (!IS_SPECIAL_VARNO(var->varno) &&
            var->varno < root->simple_rel_array_size)
        {
            RelOptInfo *rel = root->simple_rel_array[var->varno];
 
            if (rel != NULL &&
                var->varattno >= rel->min_attr &&
                var->varattno <= rel->max_attr)
            {
                int         ndx = var->varattno - rel->min_attr;
 
                if (rel->attr_widths[ndx] > 0)
                    return rel->attr_widths[ndx];
            }
        }
 
        /*
         * No cached data available, so estimate using just the type info.
         */
        width = get_typavgwidth(var->vartype, var->vartypmod);
        Assert(width > 0);
 
        return width;
    }
 
    width = get_typavgwidth(exprType(expr), exprTypmod(expr));
    Assert(width > 0);
    return width;
}
 
/*
 * relation_byte_size
 *    Estimate the storage space in bytes for a given number of tuples
 *    of a given width (size in bytes).
 */
static double
relation_byte_size(double tuples, int width)
{
    return tuples * (MAXALIGN(width) + MAXALIGN(SizeofHeapTupleHeader));
}
 
/*
 * page_size
 *    Returns an estimate of the number of pages covered by a given
 *    number of tuples of a given width (size in bytes).
 */
static double
page_size(double tuples, int width)
{
    return ceil(relation_byte_size(tuples, width) / BLCKSZ);
}
 
/*
 * Estimate the fraction of the work that each worker will do given the
 * number of workers budgeted for the path.
 */
static double
get_parallel_divisor(Path *path)
{
    double      parallel_divisor = path->parallel_workers;
 
    /*
     * Early experience with parallel query suggests that when there is only
     * one worker, the leader often makes a very substantial contribution to
     * executing the parallel portion of the plan, but as more workers are
     * added, it does less and less, because it's busy reading tuples from the
     * workers and doing whatever non-parallel post-processing is needed.  By
     * the time we reach 4 workers, the leader no longer makes a meaningful
     * contribution.  Thus, for now, estimate that the leader spends 30% of
     * its time servicing each worker, and the remainder executing the
     * parallel plan.
     */
    if (parallel_leader_participation)
    {
        double      leader_contribution;
 
        leader_contribution = 1.0 - (0.3 * path->parallel_workers);
        if (leader_contribution > 0)
            parallel_divisor += leader_contribution;
    }
 
    return parallel_divisor;
}
 
/*
 * compute_bitmap_pages
 *    Estimate number of pages fetched from heap in a bitmap heap scan.
 *
 * 'baserel' is the relation to be scanned
 * '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
 *
 * If cost_p isn't NULL, the indexTotalCost estimate is returned in *cost_p.
 * If tuples_p isn't NULL, the tuples_fetched estimate is returned in *tuples_p.
 */
double
compute_bitmap_pages(PlannerInfo *root, RelOptInfo *baserel,
                     Path *bitmapqual, double loop_count,
                     Cost *cost_p, double *tuples_p)
{
    Cost        indexTotalCost;
    Selectivity indexSelectivity;
    double      T;
    double      pages_fetched;
    double      tuples_fetched;
    double      heap_pages;
    long        maxentries;
 
    /*
     * Fetch total cost of obtaining the bitmap, as well as its total
     * selectivity.
     */
    cost_bitmap_tree_node(bitmapqual, &indexTotalCost, &indexSelectivity);
 
    /*
     * Estimate number of main-table pages fetched.
     */
    tuples_fetched = clamp_row_est(indexSelectivity * baserel->tuples);
 
    T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
 
    /*
     * For a single scan, the number of heap pages that need to be fetched is
     * the same as the Mackert and Lohman formula for the case T <= b (ie, no
     * re-reads needed).
     */
    pages_fetched = (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
 
    /*
     * Calculate the number of pages fetched from the heap.  Then based on
     * current work_mem estimate get the estimated maxentries in the bitmap.
     * (Note that we always do this calculation based on the number of pages
     * that would be fetched in a single iteration, even if loop_count > 1.
     * That's correct, because only that number of entries will be stored in
     * the bitmap at one time.)
     */
    heap_pages = Min(pages_fetched, baserel->pages);
    maxentries = tbm_calculate_entries(work_mem * 1024L);
 
    if (loop_count > 1)
    {
        /*
         * For repeated bitmap scans, scale up the number of tuples fetched in
         * the Mackert and Lohman formula by the number of scans, so that we
         * estimate the number of pages fetched by all the scans. Then
         * pro-rate for one scan.
         */
        pages_fetched = index_pages_fetched(tuples_fetched * loop_count,
                                            baserel->pages,
                                            get_indexpath_pages(bitmapqual),
                                            root);
        pages_fetched /= loop_count;
    }
 
    if (pages_fetched >= T)
        pages_fetched = T;
    else
        pages_fetched = ceil(pages_fetched);
 
    if (maxentries < heap_pages)
    {
        double      exact_pages;
        double      lossy_pages;
 
        /*
         * Crude approximation of the number of lossy pages.  Because of the
         * way tbm_lossify() is coded, the number of lossy pages increases
         * very sharply as soon as we run short of memory; this formula has
         * that property and seems to perform adequately in testing, but it's
         * possible we could do better somehow.
         */
        lossy_pages = Max(0, heap_pages - maxentries / 2);
        exact_pages = heap_pages - lossy_pages;
 
        /*
         * If there are lossy pages then recompute the number of tuples
         * processed by the bitmap heap node.  We assume here that the chance
         * of a given tuple coming from an exact page is the same as the
         * chance that a given page is exact.  This might not be true, but
         * it's not clear how we can do any better.
         */
        if (lossy_pages > 0)
            tuples_fetched =
                clamp_row_est(indexSelectivity *
                              (exact_pages / heap_pages) * baserel->tuples +
                              (lossy_pages / heap_pages) * baserel->tuples);
    }
 
    if (cost_p)
        *cost_p = indexTotalCost;
    if (tuples_p)
        *tuples_p = tuples_fetched;
 
    return pages_fetched;
}
 
/*
 * compute_gather_rows
 *    Estimate number of rows for gather (merge) nodes.
 *
 * In a parallel plan, each worker's row estimate is determined by dividing the
 * total number of rows by parallel_divisor, which accounts for the leader's
 * contribution in addition to the number of workers.  Accordingly, when
 * estimating the number of rows for gather (merge) nodes, we multiply the rows
 * per worker by the same parallel_divisor to undo the division.
 */
double
compute_gather_rows(Path *path)
{
    Assert(path->parallel_workers > 0);
 
    return clamp_row_est(path->rows * get_parallel_divisor(path));
}