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-/*-------------------------------------------------------------------------
- *
- * costsize.c
- * Routines to compute (and set) relation sizes and path costs
- *
- * Path costs are measured in units of disk accesses: one sequential page
- * fetch has cost 1. All else is scaled relative to a page fetch, using
- * the scaling parameters
- *
- * random_page_cost Cost of a non-sequential page fetch
- * cpu_tuple_cost Cost of typical CPU time to process a tuple
- * cpu_index_tuple_cost Cost of typical CPU time to process an index tuple
- * cpu_operator_cost Cost of CPU time to process a typical WHERE operator
- *
- * We also use a rough estimate "effective_cache_size" of the number of
- * disk pages in Postgres + OS-level disk cache. (We can't simply use
- * NBuffers for this purpose because that would ignore the effects of
- * the kernel's disk cache.)
- *
- * Obviously, taking constants for these values is an oversimplification,
- * but it's tough enough to get any useful estimates even at this level of
- * detail. Note that all of these parameters are user-settable, in case
- * the default values are drastically off for a particular platform.
- *
- * We compute two separate costs for each path:
- * total_cost: total estimated cost to fetch all tuples
- * startup_cost: cost that is expended before first tuple is fetched
- * In some scenarios, such as when there is a LIMIT or we are implementing
- * an EXISTS(...) sub-select, it is not necessary to fetch all tuples of the
- * path's result. A caller can estimate the cost of fetching a partial
- * result by interpolating between startup_cost and total_cost. In detail:
- * actual_cost = startup_cost +
- * (total_cost - startup_cost) * tuples_to_fetch / path->parent->rows;
- * Note that a base relation's rows count (and, by extension, plan_rows for
- * plan nodes below the LIMIT node) are set without regard to any LIMIT, so
- * that this equation works properly. (Also, these routines guarantee not to
- * set the rows count to zero, so there will be no zero divide.) The LIMIT is
- * applied as a top-level plan node.
- *
- *
- * Portions Copyright (c) 1996-2002, PostgreSQL Global Development Group
- * Portions Copyright (c) 1994, Regents of the University of California
- *
- * IDENTIFICATION
- * $Header: /cvsroot/pgsql/src/backend/optimizer/path/costsize.c,v 1.85 2002/06/20 20:29:29 momjian Exp $
- *
- *-------------------------------------------------------------------------
- */
-
-#include "postgres.h"
-
-#include <math.h>
-
-#include "catalog/pg_statistic.h"
-#include "executor/nodeHash.h"
-#include "miscadmin.h"
-#include "optimizer/clauses.h"
-#include "optimizer/cost.h"
-#include "optimizer/pathnode.h"
-#include "parser/parsetree.h"
-#include "utils/selfuncs.h"
-#include "utils/lsyscache.h"
-#include "utils/syscache.h"
-
-
-#define LOG2(x) (log(x) / 0.693147180559945)
-#define LOG6(x) (log(x) / 1.79175946922805)
-
-
-double effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;
-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;
-
-Cost disable_cost = 100000000.0;
-
-bool enable_seqscan = true;
-bool enable_indexscan = true;
-bool enable_tidscan = true;
-bool enable_sort = true;
-bool enable_nestloop = true;
-bool enable_mergejoin = true;
-bool enable_hashjoin = true;
-
-
-static Selectivity estimate_hash_bucketsize(Query *root, Var *var);
-static bool cost_qual_eval_walker(Node *node, Cost *total);
-static Selectivity approx_selectivity(Query *root, List *quals);
-static void set_rel_width(Query *root, RelOptInfo *rel);
-static double relation_byte_size(double tuples, int width);
-static double page_size(double tuples, int width);
-
-
-/*
- * cost_seqscan
- * Determines and returns the cost of scanning a relation sequentially.
- *
- * Note: for historical reasons, this routine and the others in this module
- * use the passed result Path only to store their startup_cost and total_cost
- * results into. All the input data they need is passed as separate
- * parameters, even though much of it could be extracted from the Path.
- */
-void
-cost_seqscan(Path *path, Query *root,
- RelOptInfo *baserel)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost cpu_per_tuple;
-
- /* Should only be applied to base relations */
- Assert(length(baserel->relids) == 1);
- Assert(baserel->rtekind == RTE_RELATION);
-
- if (!enable_seqscan)
- startup_cost += disable_cost;
-
- /*
- * disk costs
- *
- * The cost of reading a page sequentially is 1.0, by definition. Note
- * that the Unix kernel will typically do some amount of read-ahead
- * optimization, so that this cost is less than the true cost of
- * reading a page from disk. We ignore that issue here, but must take
- * it into account when estimating the cost of non-sequential
- * accesses!
- */
- run_cost += baserel->pages; /* sequential fetches with cost 1.0 */
-
- /* CPU costs */
- cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
- run_cost += cpu_per_tuple * baserel->tuples;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * cost_nonsequential_access
- * Estimate the cost of accessing one page at random from a relation
- * (or sort temp file) of the given size in pages.
- *
- * The simplistic model that the cost is random_page_cost is what we want
- * to use for large relations; but for small ones that is a serious
- * overestimate because of the effects of caching. This routine tries to
- * account for that.
- *
- * Unfortunately we don't have any good way of estimating the effective cache
- * size we are working with --- we know that Postgres itself has NBuffers
- * internal buffers, but the size of the kernel's disk cache is uncertain,
- * and how much of it we get to use is even less certain. We punt the problem
- * for now by assuming we are given an effective_cache_size parameter.
- *
- * Given a guesstimated cache size, we estimate the actual I/O cost per page
- * with the entirely ad-hoc equations:
- * for rel_size <= effective_cache_size:
- * 1 + (random_page_cost/2-1) * (rel_size/effective_cache_size) ** 2
- * for rel_size >= effective_cache_size:
- * random_page_cost * (1 - (effective_cache_size/rel_size)/2)
- * These give the right asymptotic behavior (=> 1.0 as rel_size becomes
- * small, => random_page_cost as it becomes large) and meet in the middle
- * with the estimate that the cache is about 50% effective for a relation
- * of the same size as effective_cache_size. (XXX this is probably all
- * wrong, but I haven't been able to find any theory about how effective
- * a disk cache should be presumed to be.)
- */
-static Cost
-cost_nonsequential_access(double relpages)
-{
- double relsize;
-
- /* don't crash on bad input data */
- if (relpages <= 0.0 || effective_cache_size <= 0.0)
- return random_page_cost;
-
- relsize = relpages / effective_cache_size;
-
- if (relsize >= 1.0)
- return random_page_cost * (1.0 - 0.5 / relsize);
- else
- return 1.0 + (random_page_cost * 0.5 - 1.0) * relsize * relsize;
-}
-
-/*
- * cost_index
- * Determines and returns the cost of scanning a relation using an index.
- *
- * NOTE: an indexscan plan node can actually represent several passes,
- * but here we consider the cost of just one pass.
- *
- * 'root' is the query root
- * 'baserel' is the base relation the index is for
- * 'index' is the index to be used
- * 'indexQuals' is the list of applicable qual clauses (implicit AND semantics)
- * 'is_injoin' is T if we are considering using the index scan as the inside
- * of a nestloop join (hence, some of the indexQuals are join clauses)
- *
- * NOTE: 'indexQuals' must contain only clauses usable as index restrictions.
- * Any additional quals evaluated as qpquals may reduce the number of returned
- * tuples, but they won't reduce the number of tuples we have to fetch from
- * the table, so they don't reduce the scan cost.
- */
-void
-cost_index(Path *path, Query *root,
- RelOptInfo *baserel,
- IndexOptInfo *index,
- List *indexQuals,
- bool is_injoin)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost indexStartupCost;
- Cost indexTotalCost;
- Selectivity indexSelectivity;
- double indexCorrelation,
- csquared;
- Cost min_IO_cost,
- max_IO_cost;
- Cost cpu_per_tuple;
- double tuples_fetched;
- double pages_fetched;
- double T,
- b;
-
- /* Should only be applied to base relations */
- Assert(IsA(baserel, RelOptInfo) &&
- IsA(index, IndexOptInfo));
- Assert(length(baserel->relids) == 1);
- Assert(baserel->rtekind == RTE_RELATION);
-
- if (!enable_indexscan && !is_injoin)
- startup_cost += disable_cost;
-
- /*
- * Call index-access-method-specific code to estimate the processing
- * cost for scanning the index, as well as the selectivity of the
- * index (ie, the fraction of main-table tuples we will have to
- * retrieve) and its correlation to the main-table tuple order.
- */
- OidFunctionCall8(index->amcostestimate,
- PointerGetDatum(root),
- PointerGetDatum(baserel),
- PointerGetDatum(index),
- PointerGetDatum(indexQuals),
- PointerGetDatum(&indexStartupCost),
- PointerGetDatum(&indexTotalCost),
- PointerGetDatum(&indexSelectivity),
- PointerGetDatum(&indexCorrelation));
-
- /* all costs for touching index itself included here */
- startup_cost += indexStartupCost;
- run_cost += indexTotalCost - indexStartupCost;
-
- /*----------
- * Estimate number of main-table tuples and pages fetched.
- *
- * When the index ordering is uncorrelated with the table ordering,
- * 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)
- *
- * When the index ordering is exactly correlated with the table ordering
- * (just after a CLUSTER, for example), the number of pages fetched should
- * be just sT. What's more, these will be sequential fetches, not the
- * random fetches that occur in the uncorrelated case. So, depending on
- * the extent of correlation, we should estimate the actual I/O cost
- * somewhere between s * T * 1.0 and PF * random_cost. We currently
- * interpolate linearly between these two endpoints based on the
- * correlation squared (XXX is that appropriate?).
- *
- * In any case the number of tuples fetched is Ns.
- *----------
- */
-
- tuples_fetched = indexSelectivity * baserel->tuples;
- /* Don't believe estimates less than 1... */
- if (tuples_fetched < 1.0)
- tuples_fetched = 1.0;
-
- /* This part is the Mackert and Lohman formula */
-
- T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
- b = (effective_cache_size > 1) ? effective_cache_size : 1.0;
-
- if (T <= b)
- {
- pages_fetched =
- (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
- if (pages_fetched > T)
- pages_fetched = T;
- }
- 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;
- }
- }
-
- /*
- * min_IO_cost corresponds to the perfectly correlated case
- * (csquared=1), max_IO_cost to the perfectly uncorrelated case
- * (csquared=0). Note that we just charge random_page_cost per page
- * in the uncorrelated case, rather than using
- * cost_nonsequential_access, since we've already accounted for
- * caching effects by using the Mackert model.
- */
- min_IO_cost = ceil(indexSelectivity * T);
- max_IO_cost = pages_fetched * random_page_cost;
-
- /*
- * 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.
- *
- * Normally the indexquals will be removed from the list of restriction
- * clauses that we have to evaluate as qpquals, so we should subtract
- * their costs from baserestrictcost. XXX For a lossy index, not all
- * the quals will be removed and so we really shouldn't subtract their
- * costs; but detecting that seems more expensive than it's worth.
- * Also, if we are doing a join then some of the indexquals are join
- * clauses and shouldn't be subtracted. Rather than work out exactly
- * how much to subtract, we don't subtract anything.
- */
- cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
-
- if (!is_injoin)
- cpu_per_tuple -= cost_qual_eval(indexQuals);
-
- run_cost += cpu_per_tuple * tuples_fetched;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * cost_tidscan
- * Determines and returns the cost of scanning a relation using TIDs.
- */
-void
-cost_tidscan(Path *path, Query *root,
- RelOptInfo *baserel, List *tideval)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost cpu_per_tuple;
- int ntuples = length(tideval);
-
- /* Should only be applied to base relations */
- Assert(length(baserel->relids) == 1);
- Assert(baserel->rtekind == RTE_RELATION);
-
- if (!enable_tidscan)
- startup_cost += disable_cost;
-
- /* disk costs --- assume each tuple on a different page */
- run_cost += random_page_cost * ntuples;
-
- /* CPU costs */
- cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
- run_cost += cpu_per_tuple * ntuples;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * cost_functionscan
- * Determines and returns the cost of scanning a function RTE.
- */
-void
-cost_functionscan(Path *path, Query *root, RelOptInfo *baserel)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost cpu_per_tuple;
-
- /* Should only be applied to base relations that are functions */
- Assert(length(baserel->relids) == 1);
- Assert(baserel->rtekind == RTE_FUNCTION);
-
- /*
- * For now, estimate function's cost at one operator eval per function
- * call. Someday we should revive the function cost estimate columns in
- * pg_proc...
- */
- cpu_per_tuple = cpu_operator_cost;
-
- /* Add scanning CPU costs */
- cpu_per_tuple += cpu_tuple_cost + baserel->baserestrictcost;
- run_cost += cpu_per_tuple * baserel->tuples;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * cost_sort
- * Determines and returns the cost of sorting a relation.
- *
- * The cost of supplying the input data is NOT included; the caller should
- * add that cost to both startup and total costs returned from this routine!
- *
- * If the total volume of data to sort is less than SortMem, we will do
- * an in-memory sort, which requires no I/O and about t*log2(t) tuple
- * comparisons for t tuples.
- *
- * If the total volume exceeds SortMem, we switch to a tape-style merge
- * algorithm. There will still be about t*log2(t) tuple comparisons in
- * total, but we will also need to write and read each tuple once per
- * merge pass. We expect about ceil(log6(r)) merge passes where r is the
- * number of initial runs formed (log6 because tuplesort.c uses six-tape
- * merging). Since the average initial run should be about twice SortMem,
- * we have
- * disk traffic = 2 * relsize * ceil(log6(p / (2*SortMem)))
- * cpu = comparison_cost * t * log2(t)
- *
- * The disk traffic is assumed to be half sequential and half random
- * accesses (XXX can't we refine that guess?)
- *
- * We charge two operator evals per tuple comparison, which should be in
- * the right ballpark in most cases.
- *
- * 'pathkeys' is a list of sort keys
- * 'tuples' is the number of tuples in the relation
- * 'width' is the average tuple width in bytes
- *
- * NOTE: some callers currently pass NIL for pathkeys because they
- * can't conveniently supply the sort keys. Since this routine doesn't
- * currently do anything with pathkeys anyway, that doesn't matter...
- * but if it ever does, it should react gracefully to lack of key data.
- */
-void
-cost_sort(Path *path, Query *root,
- List *pathkeys, double tuples, int width)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- double nbytes = relation_byte_size(tuples, width);
- long sortmembytes = SortMem * 1024L;
-
- if (!enable_sort)
- startup_cost += disable_cost;
-
- /*
- * We want to be sure the cost of a sort is never estimated as zero,
- * even if passed-in tuple count is zero. Besides, mustn't do
- * log(0)...
- */
- if (tuples < 2.0)
- tuples = 2.0;
-
- /*
- * CPU costs
- *
- * Assume about two operator evals per tuple comparison and N log2 N
- * comparisons
- */
- startup_cost += 2.0 * cpu_operator_cost * tuples * LOG2(tuples);
-
- /* disk costs */
- if (nbytes > sortmembytes)
- {
- double npages = ceil(nbytes / BLCKSZ);
- double nruns = nbytes / (sortmembytes * 2);
- double log_runs = ceil(LOG6(nruns));
- double npageaccesses;
-
- if (log_runs < 1.0)
- log_runs = 1.0;
- npageaccesses = 2.0 * npages * log_runs;
- /* Assume half are sequential (cost 1), half are not */
- startup_cost += npageaccesses *
- (1.0 + cost_nonsequential_access(npages)) * 0.5;
- }
-
- /*
- * Also charge a small amount (arbitrarily set equal to operator cost)
- * per extracted tuple.
- */
- run_cost += cpu_operator_cost * tuples;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-
-/*
- * cost_nestloop
- * Determines and returns the cost of joining two relations using the
- * nested loop algorithm.
- *
- * 'outer_path' is the path for the outer relation
- * 'inner_path' is the path for the inner relation
- * 'restrictlist' are the RestrictInfo nodes to be applied at the join
- */
-void
-cost_nestloop(Path *path, Query *root,
- Path *outer_path,
- Path *inner_path,
- List *restrictlist)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost cpu_per_tuple;
- double ntuples;
-
- if (!enable_nestloop)
- startup_cost += disable_cost;
-
- /* cost of source data */
-
- /*
- * NOTE: 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. What's not so clear is whether the inner path's
- * startup_cost must be paid again on each rescan of the inner path.
- * This is not true if the inner path is materialized, but probably is
- * true otherwise. Since we don't yet have clean handling of the
- * decision whether to materialize a path, we can't tell here which
- * will happen. As a compromise, charge 50% of the inner startup cost
- * for each restart.
- */
- startup_cost += outer_path->startup_cost + inner_path->startup_cost;
- run_cost += outer_path->total_cost - outer_path->startup_cost;
- run_cost += outer_path->parent->rows *
- (inner_path->total_cost - inner_path->startup_cost);
- if (outer_path->parent->rows > 1)
- run_cost += (outer_path->parent->rows - 1) *
- inner_path->startup_cost * 0.5;
-
- /*
- * Number of tuples processed (not number emitted!). If inner path is
- * an indexscan, be sure to use its estimated output row count, which
- * may be lower than the restriction-clause-only row count of its
- * parent.
- */
- if (IsA(inner_path, IndexPath))
- ntuples = ((IndexPath *) inner_path)->rows;
- else
- ntuples = inner_path->parent->rows;
- ntuples *= outer_path->parent->rows;
-
- /* CPU costs */
- cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
- run_cost += cpu_per_tuple * ntuples;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * cost_mergejoin
- * Determines and returns the cost of joining two relations using the
- * merge join algorithm.
- *
- * 'outer_path' is the path for the outer relation
- * 'inner_path' is the path for the inner relation
- * 'restrictlist' are the RestrictInfo nodes to be applied at the join
- * 'mergeclauses' are the RestrictInfo nodes to use as merge clauses
- * (this should be a subset of the restrictlist)
- * 'outersortkeys' and 'innersortkeys' are lists of the keys to be used
- * to sort the outer and inner relations, or NIL if no explicit
- * sort is needed because the source path is already ordered
- */
-void
-cost_mergejoin(Path *path, Query *root,
- Path *outer_path,
- Path *inner_path,
- List *restrictlist,
- List *mergeclauses,
- List *outersortkeys,
- List *innersortkeys)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost cpu_per_tuple;
- RestrictInfo *firstclause;
- Var *leftvar;
- double outer_rows,
- inner_rows;
- double ntuples;
- Selectivity outerscansel,
- innerscansel;
- Path sort_path; /* dummy for result of cost_sort */
-
- if (!enable_mergejoin)
- startup_cost += disable_cost;
-
- /*
- * A merge join will stop as soon as it exhausts either input stream.
- * Estimate fraction of the left and right inputs that will actually
- * need to be scanned. We use only the first (most significant)
- * merge clause for this purpose.
- *
- * Since this calculation is somewhat expensive, and will be the same
- * for all mergejoin paths associated with the merge clause, we cache
- * the results in the RestrictInfo node.
- */
- firstclause = (RestrictInfo *) lfirst(mergeclauses);
- if (firstclause->left_mergescansel < 0) /* not computed yet? */
- mergejoinscansel(root, (Node *) firstclause->clause,
- &firstclause->left_mergescansel,
- &firstclause->right_mergescansel);
-
- leftvar = get_leftop(firstclause->clause);
- Assert(IsA(leftvar, Var));
- if (VARISRELMEMBER(leftvar->varno, outer_path->parent))
- {
- /* left side of clause is outer */
- outerscansel = firstclause->left_mergescansel;
- innerscansel = firstclause->right_mergescansel;
- }
- else
- {
- /* left side of clause is inner */
- outerscansel = firstclause->right_mergescansel;
- innerscansel = firstclause->left_mergescansel;
- }
-
- outer_rows = outer_path->parent->rows * outerscansel;
- inner_rows = inner_path->parent->rows * innerscansel;
-
- /* cost of source data */
-
- /*
- * Note we are assuming that each source tuple is fetched just once,
- * which is not right in the presence of equal keys. If we had a way
- * of estimating the proportion of equal keys, we could apply a
- * correction factor...
- */
- if (outersortkeys) /* do we need to sort outer? */
- {
- startup_cost += outer_path->total_cost;
- cost_sort(&sort_path,
- root,
- outersortkeys,
- outer_path->parent->rows,
- outer_path->parent->width);
- startup_cost += sort_path.startup_cost;
- run_cost += (sort_path.total_cost - sort_path.startup_cost)
- * outerscansel;
- }
- else
- {
- startup_cost += outer_path->startup_cost;
- run_cost += (outer_path->total_cost - outer_path->startup_cost)
- * outerscansel;
- }
-
- if (innersortkeys) /* do we need to sort inner? */
- {
- startup_cost += inner_path->total_cost;
- cost_sort(&sort_path,
- root,
- innersortkeys,
- inner_path->parent->rows,
- inner_path->parent->width);
- startup_cost += sort_path.startup_cost;
- run_cost += (sort_path.total_cost - sort_path.startup_cost)
- * innerscansel;
- }
- else
- {
- startup_cost += inner_path->startup_cost;
- run_cost += (inner_path->total_cost - inner_path->startup_cost)
- * innerscansel;
- }
-
- /*
- * The number of tuple comparisons needed depends drastically on the
- * number of equal keys in the two source relations, which we have no
- * good way of estimating. (XXX could the MCV statistics help?)
- * Somewhat arbitrarily, we charge one tuple
- * comparison (one cpu_operator_cost) for each tuple in the two source
- * relations. This is probably a lower bound.
- */
- run_cost += cpu_operator_cost * (outer_rows + inner_rows);
-
- /*
- * 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. It's OK to use an
- * approximate selectivity here, since in most cases this is a minor
- * component of the cost. NOTE: it's correct to use the unscaled rows
- * counts here, not the scaled-down counts we obtained above.
- */
- ntuples = approx_selectivity(root, mergeclauses) *
- outer_path->parent->rows * inner_path->parent->rows;
-
- /* CPU costs */
- cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
- run_cost += cpu_per_tuple * ntuples;
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * cost_hashjoin
- * Determines and returns the cost of joining two relations using the
- * hash join algorithm.
- *
- * 'outer_path' is the path for the outer relation
- * 'inner_path' is the path for the inner relation
- * 'restrictlist' are the RestrictInfo nodes to be applied at the join
- * 'hashclauses' is a list of the hash join clause (always a 1-element list)
- * (this should be a subset of the restrictlist)
- */
-void
-cost_hashjoin(Path *path, Query *root,
- Path *outer_path,
- Path *inner_path,
- List *restrictlist,
- List *hashclauses)
-{
- Cost startup_cost = 0;
- Cost run_cost = 0;
- Cost cpu_per_tuple;
- double ntuples;
- double outerbytes = relation_byte_size(outer_path->parent->rows,
- outer_path->parent->width);
- double innerbytes = relation_byte_size(inner_path->parent->rows,
- inner_path->parent->width);
- long hashtablebytes = SortMem * 1024L;
- RestrictInfo *restrictinfo;
- Var *left,
- *right;
- Selectivity innerbucketsize;
-
- if (!enable_hashjoin)
- startup_cost += disable_cost;
-
- /* cost of source data */
- startup_cost += outer_path->startup_cost;
- run_cost += outer_path->total_cost - outer_path->startup_cost;
- startup_cost += inner_path->total_cost;
-
- /* cost of computing hash function: must do it once per input tuple */
- startup_cost += cpu_operator_cost * inner_path->parent->rows;
- run_cost += cpu_operator_cost * outer_path->parent->rows;
-
- /*
- * Determine bucketsize fraction for inner relation. First we have to
- * figure out which side of the hashjoin clause is the inner side.
- */
- Assert(length(hashclauses) == 1);
- Assert(IsA(lfirst(hashclauses), RestrictInfo));
- restrictinfo = (RestrictInfo *) lfirst(hashclauses);
- /* these must be OK, since check_hashjoinable accepted the clause */
- left = get_leftop(restrictinfo->clause);
- right = get_rightop(restrictinfo->clause);
-
- /*
- * Since we tend to visit the same clauses over and over when planning
- * a large query, we cache the bucketsize estimate in the RestrictInfo
- * node to avoid repeated lookups of statistics.
- */
- if (VARISRELMEMBER(right->varno, inner_path->parent))
- {
- /* righthand side is inner */
- innerbucketsize = restrictinfo->right_bucketsize;
- if (innerbucketsize < 0)
- {
- /* not cached yet */
- innerbucketsize = estimate_hash_bucketsize(root, right);
- restrictinfo->right_bucketsize = innerbucketsize;
- }
- }
- else
- {
- Assert(VARISRELMEMBER(left->varno, inner_path->parent));
- /* lefthand side is inner */
- innerbucketsize = restrictinfo->left_bucketsize;
- if (innerbucketsize < 0)
- {
- /* not cached yet */
- innerbucketsize = estimate_hash_bucketsize(root, left);
- restrictinfo->left_bucketsize = innerbucketsize;
- }
- }
-
- /*
- * 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. We charge
- * one cpu_operator_cost per tuple comparison.
- */
- run_cost += cpu_operator_cost * outer_path->parent->rows *
- ceil(inner_path->parent->rows * innerbucketsize);
-
- /*
- * 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. It's OK to use an
- * approximate selectivity here, since in most cases this is a minor
- * component of the cost.
- */
- ntuples = approx_selectivity(root, hashclauses) *
- outer_path->parent->rows * inner_path->parent->rows;
-
- /* CPU costs */
- cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
- run_cost += cpu_per_tuple * ntuples;
-
- /*
- * if inner relation is too big then we will need to "batch" the join,
- * which implies writing and reading most of the tuples to disk an
- * extra time. Charge one cost unit per page of I/O (correct since it
- * should be nice and sequential...). Writing the inner rel counts as
- * startup cost, all the rest as run cost.
- */
- if (innerbytes > hashtablebytes)
- {
- double outerpages = page_size(outer_path->parent->rows,
- outer_path->parent->width);
- double innerpages = page_size(inner_path->parent->rows,
- inner_path->parent->width);
-
- startup_cost += innerpages;
- run_cost += innerpages + 2 * outerpages;
- }
-
- /*
- * Bias against putting larger relation on inside. We don't want an
- * absolute prohibition, though, since larger relation might have
- * better bucketsize --- and we can't trust the size estimates
- * unreservedly, anyway. Instead, inflate the startup cost by the
- * square root of the size ratio. (Why square root? No real good
- * reason, but it seems reasonable...)
- */
- if (innerbytes > outerbytes && outerbytes > 0)
- startup_cost *= sqrt(innerbytes / outerbytes);
-
- path->startup_cost = startup_cost;
- path->total_cost = startup_cost + run_cost;
-}
-
-/*
- * Estimate hash bucketsize fraction (ie, number of entries in a bucket
- * divided by total tuples in relation) if the specified Var is used
- * as a hash key.
- *
- * XXX This is really pretty bogus since we're effectively assuming that the
- * distribution of hash keys will be the same after applying restriction
- * clauses as it was in the underlying relation. However, we are not nearly
- * smart enough to figure out how the restrict clauses might change the
- * distribution, so this will have to do for now.
- *
- * We can get the number of buckets the executor will use for the given
- * input relation. If the data were perfectly distributed, with the same
- * number of tuples going into each available bucket, then the bucketsize
- * fraction would be 1/nbuckets. But this happy state of affairs will occur
- * only if (a) there are at least nbuckets distinct data values, and (b)
- * we have a not-too-skewed data distribution. Otherwise the buckets will
- * be nonuniformly occupied. If the other relation in the join has a key
- * distribution similar to this one's, then the most-loaded buckets are
- * exactly those that will be probed most often. Therefore, the "average"
- * bucket size for costing purposes should really be taken as something close
- * to the "worst case" bucket size. We try to estimate this by adjusting the
- * fraction if there are too few distinct data values, and then scaling up
- * by the ratio of the most common value's frequency to the average frequency.
- *
- * If no statistics are available, use a default estimate of 0.1. This will
- * discourage use of a hash rather strongly if the inner relation is large,
- * which is what we want. We do not want to hash unless we know that the
- * inner rel is well-dispersed (or the alternatives seem much worse).
- */
-static Selectivity
-estimate_hash_bucketsize(Query *root, Var *var)
-{
- Oid relid;
- RelOptInfo *rel;
- int virtualbuckets;
- int physicalbuckets;
- int numbatches;
- HeapTuple tuple;
- Form_pg_statistic stats;
- double estfract,
- ndistinct,
- mcvfreq,
- avgfreq;
- float4 *numbers;
- int nnumbers;
-
- /*
- * Lookup info about var's relation and attribute; if none available,
- * return default estimate.
- */
- if (!IsA(var, Var))
- return 0.1;
-
- relid = getrelid(var->varno, root->rtable);
- if (relid == InvalidOid)
- return 0.1;
-
- rel = find_base_rel(root, var->varno);
-
- if (rel->tuples <= 0.0 || rel->rows <= 0.0)
- return 0.1; /* ensure we can divide below */
-
- /* Get hash table size that executor would use for this relation */
- ExecChooseHashTableSize(rel->rows, rel->width,
- &virtualbuckets,
- &physicalbuckets,
- &numbatches);
-
- tuple = SearchSysCache(STATRELATT,
- ObjectIdGetDatum(relid),
- Int16GetDatum(var->varattno),
- 0, 0);
- if (!HeapTupleIsValid(tuple))
- {
- /*
- * Perhaps the Var is a system attribute; if so, it will have no
- * entry in pg_statistic, but we may be able to guess something
- * about its distribution anyway.
- */
- switch (var->varattno)
- {
- case ObjectIdAttributeNumber:
- case SelfItemPointerAttributeNumber:
- /* these are unique, so buckets should be well-distributed */
- return 1.0 / (double) virtualbuckets;
- case TableOidAttributeNumber:
- /* hashing this is a terrible idea... */
- return 1.0;
- }
- return 0.1;
- }
- stats = (Form_pg_statistic) GETSTRUCT(tuple);
-
- /*
- * Obtain number of distinct data values in raw relation.
- */
- ndistinct = stats->stadistinct;
- if (ndistinct < 0.0)
- ndistinct = -ndistinct * rel->tuples;
-
- if (ndistinct <= 0.0) /* ensure we can divide */
- {
- ReleaseSysCache(tuple);
- return 0.1;
- }
-
- /* Also compute avg freq of all distinct data values in raw relation */
- avgfreq = (1.0 - stats->stanullfrac) / ndistinct;
-
- /*
- * Adjust ndistinct to account for restriction clauses. Observe we
- * are assuming that the data distribution is affected uniformly by
- * the restriction clauses!
- *
- * XXX Possibly better way, but much more expensive: multiply by
- * selectivity of rel's restriction clauses that mention the target
- * Var.
- */
- ndistinct *= rel->rows / rel->tuples;
-
- /*
- * Initial estimate of bucketsize fraction is 1/nbuckets as long as
- * the number of buckets is less than the expected number of distinct
- * values; otherwise it is 1/ndistinct.
- */
- if (ndistinct > (double) virtualbuckets)
- estfract = 1.0 / (double) virtualbuckets;
- else
- estfract = 1.0 / ndistinct;
-
- /*
- * Look up the frequency of the most common value, if available.
- */
- mcvfreq = 0.0;
-
- if (get_attstatsslot(tuple, var->vartype, var->vartypmod,
- STATISTIC_KIND_MCV, InvalidOid,
- NULL, NULL, &numbers, &nnumbers))
- {
- /*
- * The first MCV stat is for the most common value.
- */
- if (nnumbers > 0)
- mcvfreq = numbers[0];
- free_attstatsslot(var->vartype, NULL, 0,
- numbers, nnumbers);
- }
-
- /*
- * Adjust estimated bucketsize upward to account for skewed
- * distribution.
- */
- if (avgfreq > 0.0 && mcvfreq > avgfreq)
- estfract *= mcvfreq / avgfreq;
-
- ReleaseSysCache(tuple);
-
- return (Selectivity) estfract;
-}
-
-
-/*
- * cost_qual_eval
- * Estimate the CPU cost of evaluating a WHERE clause (once).
- * The input can be either an implicitly-ANDed list of boolean
- * expressions, or a list of RestrictInfo nodes.
- */
-Cost
-cost_qual_eval(List *quals)
-{
- Cost total = 0;
- List *l;
-
- /* We don't charge any cost for the implicit ANDing at top level ... */
-
- foreach(l, quals)
- {
- Node *qual = (Node *) lfirst(l);
-
- /*
- * 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 will contain -1.
- */
- if (qual && IsA(qual, RestrictInfo))
- {
- RestrictInfo *restrictinfo = (RestrictInfo *) qual;
-
- if (restrictinfo->eval_cost < 0)
- {
- restrictinfo->eval_cost = 0;
- cost_qual_eval_walker((Node *) restrictinfo->clause,
- &restrictinfo->eval_cost);
- }
- total += restrictinfo->eval_cost;
- }
- else
- {
- /* If it's a bare expression, must always do it the hard way */
- cost_qual_eval_walker(qual, &total);
- }
- }
- return total;
-}
-
-static bool
-cost_qual_eval_walker(Node *node, Cost *total)
-{
- if (node == NULL)
- return false;
-
- /*
- * Our basic strategy is to charge one cpu_operator_cost for each
- * operator or function node in the given tree. Vars and Consts are
- * charged zero, and so are boolean operators (AND, OR, NOT).
- * Simplistic, but a lot better than no model at all.
- *
- * Should we try to account for the possibility of short-circuit
- * evaluation of AND/OR?
- */
- if (IsA(node, Expr))
- {
- Expr *expr = (Expr *) node;
-
- switch (expr->opType)
- {
- case OP_EXPR:
- case FUNC_EXPR:
- *total += cpu_operator_cost;
- break;
- case OR_EXPR:
- case AND_EXPR:
- case NOT_EXPR:
- break;
- case SUBPLAN_EXPR:
-
- /*
- * A subplan node in an expression indicates that the
- * subplan will be executed on each evaluation, so charge
- * accordingly. (We assume that sub-selects that can be
- * executed as InitPlans have already been removed from
- * the expression.)
- *
- * NOTE: this logic should agree with the estimates used by
- * make_subplan() in plan/subselect.c.
- */
- {
- SubPlan *subplan = (SubPlan *) expr->oper;
- Plan *plan = subplan->plan;
- Cost subcost;
-
- if (subplan->sublink->subLinkType == EXISTS_SUBLINK)
- {
- /* we only need to fetch 1 tuple */
- subcost = plan->startup_cost +
- (plan->total_cost - plan->startup_cost) / plan->plan_rows;
- }
- else if (subplan->sublink->subLinkType == ALL_SUBLINK ||
- subplan->sublink->subLinkType == ANY_SUBLINK)
- {
- /* assume we need 50% of the tuples */
- subcost = plan->startup_cost +
- 0.50 * (plan->total_cost - plan->startup_cost);
- /* XXX what if subplan has been materialized? */
- }
- else
- {
- /* assume we need all tuples */
- subcost = plan->total_cost;
- }
- *total += subcost;
- }
- break;
- }
- /* fall through to examine args of Expr node */
- }
- return expression_tree_walker(node, cost_qual_eval_walker,
- (void *) total);
-}
-
-
-/*
- * approx_selectivity
- * Quick-and-dirty estimation of clause selectivities.
- * The input can be either an implicitly-ANDed list of boolean
- * expressions, or a list of RestrictInfo nodes (typically the latter).
- *
- * The "quick" part comes from caching the selectivity estimates so we can
- * avoid recomputing them later. (Since the same clauses are typically
- * examined over and over in different possible join trees, this makes a
- * big difference.)
- *
- * The "dirty" part comes from the fact that the selectivities of multiple
- * clauses are estimated independently and multiplied together. Now
- * clauselist_selectivity often can't do any better than that anyhow, but
- * for some situations (such as range constraints) it is smarter.
- *
- * 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 Selectivity
-approx_selectivity(Query *root, List *quals)
-{
- Selectivity total = 1.0;
- List *l;
-
- foreach(l, quals)
- {
- Node *qual = (Node *) lfirst(l);
- Selectivity selec;
-
- /*
- * RestrictInfo nodes contain a this_selec field reserved for this
- * routine's use, so that it's not necessary to evaluate the qual
- * clause's selectivity more than once. If the clause's
- * selectivity hasn't been computed yet, the field will contain
- * -1.
- */
- if (qual && IsA(qual, RestrictInfo))
- {
- RestrictInfo *restrictinfo = (RestrictInfo *) qual;
-
- if (restrictinfo->this_selec < 0)
- restrictinfo->this_selec =
- clause_selectivity(root,
- (Node *) restrictinfo->clause,
- 0);
- selec = restrictinfo->this_selec;
- }
- else
- {
- /* If it's a bare expression, must always do it the hard way */
- selec = clause_selectivity(root, qual, 0);
- }
- total *= selec;
- }
- return total;
-}
-
-
-/*
- * set_baserel_size_estimates
- * Set the size estimates for the given base relation.
- *
- * The rel's targetlist and restrictinfo list must have been constructed
- * already.
- *
- * We set the following fields of the rel node:
- * rows: the estimated number of output tuples (after applying
- * restriction clauses).
- * width: the estimated average output tuple width in bytes.
- * baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
- */
-void
-set_baserel_size_estimates(Query *root, RelOptInfo *rel)
-{
- /* Should only be applied to base relations */
- Assert(length(rel->relids) == 1);
-
- rel->rows = rel->tuples *
- restrictlist_selectivity(root,
- rel->baserestrictinfo,
- lfirsti(rel->relids));
-
- /*
- * Force estimate to be at least one row, to make explain output look
- * better and to avoid possible divide-by-zero when interpolating
- * cost.
- */
- if (rel->rows < 1.0)
- rel->rows = 1.0;
-
- rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
-
- set_rel_width(root, rel);
-}
-
-/*
- * set_joinrel_size_estimates
- * Set the size estimates for the given join relation.
- *
- * The rel's targetlist must have been constructed already, and a
- * restriction clause list that matches the given component rels must
- * be provided.
- *
- * Since there is more than one way to make a joinrel for more than two
- * base relations, the results we get here could depend on which component
- * rel pair is provided. In theory we should get the same answers no matter
- * which pair is provided; in practice, since the selectivity estimation
- * routines don't handle all cases equally well, we might not. But there's
- * not much to be done about it. (Would it make sense to repeat the
- * calculations for each pair of input rels that's encountered, and somehow
- * average the results? Probably way more trouble than it's worth.)
- *
- * We set the same relnode fields as set_baserel_size_estimates() does.
- */
-void
-set_joinrel_size_estimates(Query *root, RelOptInfo *rel,
- RelOptInfo *outer_rel,
- RelOptInfo *inner_rel,
- JoinType jointype,
- List *restrictlist)
-{
- double temp;
-
- /* Start with the Cartesian product */
- temp = outer_rel->rows * inner_rel->rows;
-
- /*
- * Apply join restrictivity. Note that we are only considering
- * clauses that become restriction clauses at this join level; we are
- * not double-counting them because they were not considered in
- * estimating the sizes of the component rels.
- */
- temp *= restrictlist_selectivity(root,
- restrictlist,
- 0);
-
- /*
- * If we are doing an outer join, take that into account: the output
- * must be at least as large as the non-nullable input. (Is there any
- * chance of being even smarter?)
- */
- switch (jointype)
- {
- case JOIN_INNER:
- break;
- case JOIN_LEFT:
- if (temp < outer_rel->rows)
- temp = outer_rel->rows;
- break;
- case JOIN_RIGHT:
- if (temp < inner_rel->rows)
- temp = inner_rel->rows;
- break;
- case JOIN_FULL:
- if (temp < outer_rel->rows)
- temp = outer_rel->rows;
- if (temp < inner_rel->rows)
- temp = inner_rel->rows;
- break;
- default:
- elog(ERROR, "set_joinrel_size_estimates: unsupported join type %d",
- (int) jointype);
- break;
- }
-
- /*
- * Force estimate to be at least one row, to make explain output look
- * better and to avoid possible divide-by-zero when interpolating
- * cost.
- */
- if (temp < 1.0)
- temp = 1.0;
-
- rel->rows = temp;
-
- /*
- * We could apply set_rel_width() to compute the output tuple width
- * from scratch, but at present it's always just the sum of the input
- * widths, so why work harder than necessary? If relnode.c is ever
- * taught to remove unneeded columns from join targetlists, go back to
- * using set_rel_width here.
- */
- rel->width = outer_rel->width + inner_rel->width;
-}
-
-/*
- * set_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 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_function_size_estimates(Query *root, RelOptInfo *rel)
-{
- /* Should only be applied to base relations that are functions */
- Assert(length(rel->relids) == 1);
- Assert(rel->rtekind == RTE_FUNCTION);
-
- /*
- * Estimate number of rows the function itself will return.
- *
- * XXX no idea how to do this yet; but should at least check whether
- * function returns set or not...
- */
- rel->tuples = 1000;
-
- /* Now estimate number of output rows */
- rel->rows = rel->tuples *
- restrictlist_selectivity(root,
- rel->baserestrictinfo,
- lfirsti(rel->relids));
-
- /*
- * Force estimate to be at least one row, to make explain output look
- * better and to avoid possible divide-by-zero when interpolating
- * cost.
- */
- if (rel->rows < 1.0)
- rel->rows = 1.0;
-
- rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
-
- set_rel_width(root, rel);
-}
-
-
-/*
- * set_rel_width
- * Set the estimated output width of the relation.
- *
- * NB: this works best on base relations because it prefers to look at
- * real Vars. It will fail to make use of pg_statistic info when applied
- * to a subquery relation, even if the subquery outputs are simple vars
- * that we could have gotten info for. Is it worth trying to be smarter
- * about subqueries?
- */
-static void
-set_rel_width(Query *root, RelOptInfo *rel)
-{
- int32 tuple_width = 0;
- List *tllist;
-
- foreach(tllist, rel->targetlist)
- {
- TargetEntry *tle = (TargetEntry *) lfirst(tllist);
- int32 item_width;
-
- /*
- * If it's a Var, try to get statistical info from pg_statistic.
- */
- if (tle->expr && IsA(tle->expr, Var))
- {
- Var *var = (Var *) tle->expr;
- Oid relid;
-
- relid = getrelid(var->varno, root->rtable);
- if (relid != InvalidOid)
- {
- item_width = get_attavgwidth(relid, var->varattno);
- if (item_width > 0)
- {
- tuple_width += item_width;
- continue;
- }
- }
- }
-
- /*
- * Not a Var, or can't find statistics for it. Estimate using
- * just the type info.
- */
- item_width = get_typavgwidth(tle->resdom->restype,
- tle->resdom->restypmod);
- Assert(item_width > 0);
- tuple_width += item_width;
- }
- Assert(tuple_width >= 0);
- rel->width = tuple_width;
-}
-
-/*
- * relation_byte_size
- * Estimate the storage space in bytes for a given number of tuples
- * of a given width (size in bytes).
- */
-static double
-relation_byte_size(double tuples, int width)
-{
- return tuples * ((double) MAXALIGN(width + sizeof(HeapTupleData)));
-}
-
-/*
- * page_size
- * Returns an estimate of the number of pages covered by a given
- * number of tuples of a given width (size in bytes).
- */
-static double
-page_size(double tuples, int width)
-{
- return ceil(relation_byte_size(tuples, width) / BLCKSZ);
-}