/*-------------------------------------------------------------------------
*
* 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) 1996-2001, 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 1.76 2001/06/10 02:59:35 tgl 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/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->issubquery);
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->issubquery);
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. For a lossy
* index, however, we will have to recheck all the quals and so
* mustn't subtract anything. Also, if we are doing a join then some
* of the indexquals are join clauses and shouldn't be subtracted.
* Rather than work out exactly how much to subtract, we don't
* subtract anything in that case either.
*/
cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
if (!index->lossy && !is_injoin)
cpu_per_tuple -= cost_qual_eval(indexQuals);
run_cost += cpu_per_tuple * tuples_fetched;
path->startup_cost = startup_cost;
path->total_cost = startup_cost + run_cost;
}
/*
* cost_tidscan
* Determines and returns the cost of scanning a relation using 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);
if (!enable_tidscan)
startup_cost += disable_cost;
/* disk costs --- assume each tuple on a different page */
run_cost += random_page_cost * ntuples;
/* CPU costs */
cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
run_cost += cpu_per_tuple * ntuples;
path->startup_cost = startup_cost;
path->total_cost = startup_cost + run_cost;
}
/*
* cost_sort
* Determines and returns the cost of sorting a relation.
*
* The cost of supplying the input data is NOT included; the caller should
* add that cost to both startup and total costs returned from this routine!
*
* If the total volume of data to sort is less than SortMem, we will do
* an in-memory sort, which requires no I/O and about t*log2(t) tuple
* comparisons for t tuples.
*
* If the total volume exceeds SortMem, we switch to a tape-style merge
* algorithm. There will still be about t*log2(t) tuple comparisons in
* total, but we will also need to write and read each tuple once per
* merge pass. We expect about ceil(log6(r)) merge passes where r is the
* number of initial runs formed (log6 because tuplesort.c uses six-tape
* merging). Since the average initial run should be about twice SortMem,
* we have
* disk traffic = 2 * relsize * ceil(log6(p / (2*SortMem)))
* cpu = comparison_cost * t * log2(t)
*
* The disk traffic is assumed to be half sequential and half random
* accesses (XXX can't we refine that guess?)
*
* We charge two operator evals per tuple comparison, which should be in
* the right ballpark in most cases.
*
* 'pathkeys' is a list of sort keys
* 'tuples' is the number of tuples in the relation
* 'width' is the average tuple width in bytes
*
* NOTE: some callers currently pass NIL for pathkeys because they
* can't conveniently supply the sort keys. Since this routine doesn't
* currently do anything with pathkeys anyway, that doesn't matter...
* but if it ever does, it should react gracefully to lack of key data.
*/
void
cost_sort(Path *path, 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;
}
/*
* Note: should we bother to assign a nonzero run_cost to reflect the
* overhead of extracting tuples from the sort result? Probably not
* worth worrying about.
*/
path->startup_cost = startup_cost;
path->total_cost = startup_cost + run_cost;
}
/*
* cost_nestloop
* Determines and returns the cost of joining two relations using the
* nested loop algorithm.
*
* 'outer_path' is the path for the outer relation
* 'inner_path' is the path for the inner relation
* 'restrictlist' are the RestrictInfo nodes to be applied at the join
*/
void
cost_nestloop(Path *path, 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;
double ntuples;
Path sort_path; /* dummy for result of cost_sort */
if (!enable_mergejoin)
startup_cost += disable_cost;
/* cost of source data */
/*
* Note we are assuming that each source tuple is fetched just once,
* which is not right in the presence of equal keys. If we had a way
* of estimating the proportion of equal keys, we could apply a
* correction factor...
*/
if (outersortkeys) /* do we need to sort outer? */
{
startup_cost += outer_path->total_cost;
cost_sort(&sort_path,
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;
}
else
{
startup_cost += outer_path->startup_cost;
run_cost += outer_path->total_cost - outer_path->startup_cost;
}
if (innersortkeys) /* do we need to sort inner? */
{
startup_cost += inner_path->total_cost;
cost_sort(&sort_path,
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;
}
else
{
startup_cost += inner_path->startup_cost;
run_cost += inner_path->total_cost - inner_path->startup_cost;
}
/*
* 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. 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_path->parent->rows + inner_path->parent->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.
*/
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 (intMember(right->varno, inner_path->parent->relids))
{
/* 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(intMember(left->varno, inner_path->parent->relids));
/* 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.
*
* The executor tries for average bucket loading of NTUP_PER_BUCKET by setting
* number of buckets equal to ntuples / NTUP_PER_BUCKET, which would yield
* a bucketsize fraction of NTUP_PER_BUCKET / ntuples. But that goal will
* be reached only if the data values are uniformly distributed among the
* buckets, which requires (a) at least ntuples / NTUP_PER_BUCKET distinct
* data values, and (b) a not-too-skewed data distribution. Otherwise the
* buckets will be nonuniformly occupied. If the other relation in the join
* has a similar distribution, 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 first scaling up if there
* are too few distinct data values, and then scaling up again 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;
HeapTuple tuple;
Form_pg_statistic stats;
double estfract,
ndistinct,
needdistinct,
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 */
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 (double) NTUP_PER_BUCKET / rel->rows;
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;
/* 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;
/*
* Form initial estimate of bucketsize fraction. Here we use rel->rows,
* ie the number of rows after applying restriction clauses, because
* that's what the fraction will eventually be multiplied by in
* cost_heapjoin.
*/
estfract = (double) NTUP_PER_BUCKET / rel->rows;
/*
* Adjust estimated bucketsize if too few distinct values (after
* restriction clauses) to fill all the buckets.
*/
needdistinct = rel->rows / (double) NTUP_PER_BUCKET;
if (ndistinct < needdistinct)
estfract *= needdistinct / 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. Currently,
* clauselist_selectivity can seldom do any better than that anyhow, but
* someday it might be 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_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);
}