1 /*-------------------------------------------------------------------------
4 * Routines to compute (and set) relation sizes and path costs
6 * Path costs are measured in units of disk accesses: one sequential page
7 * fetch has cost 1. All else is scaled relative to a page fetch, using
8 * the scaling parameters
10 * random_page_cost Cost of a non-sequential page fetch
11 * cpu_tuple_cost Cost of typical CPU time to process a tuple
12 * cpu_index_tuple_cost Cost of typical CPU time to process an index tuple
13 * cpu_operator_cost Cost of CPU time to process a typical WHERE operator
15 * We also use a rough estimate "effective_cache_size" of the number of
16 * disk pages in Postgres + OS-level disk cache. (We can't simply use
17 * NBuffers for this purpose because that would ignore the effects of
18 * the kernel's disk cache.)
20 * Obviously, taking constants for these values is an oversimplification,
21 * but it's tough enough to get any useful estimates even at this level of
22 * detail. Note that all of these parameters are user-settable, in case
23 * the default values are drastically off for a particular platform.
25 * We compute two separate costs for each path:
26 * total_cost: total estimated cost to fetch all tuples
27 * startup_cost: cost that is expended before first tuple is fetched
28 * In some scenarios, such as when there is a LIMIT or we are implementing
29 * an EXISTS(...) sub-select, it is not necessary to fetch all tuples of the
30 * path's result. A caller can estimate the cost of fetching a partial
31 * result by interpolating between startup_cost and total_cost. In detail:
32 * actual_cost = startup_cost +
33 * (total_cost - startup_cost) * tuples_to_fetch / path->parent->rows;
34 * Note that a base relation's rows count (and, by extension, plan_rows for
35 * plan nodes below the LIMIT node) are set without regard to any LIMIT, so
36 * that this equation works properly. (Also, these routines guarantee not to
37 * set the rows count to zero, so there will be no zero divide.) The LIMIT is
38 * applied as a top-level plan node.
41 * Portions Copyright (c) 1996-2002, PostgreSQL Global Development Group
42 * Portions Copyright (c) 1994, Regents of the University of California
45 * $Header: /cvsroot/pgsql/src/backend/optimizer/path/costsize.c,v 1.93 2002/11/30 05:21:02 tgl Exp $
47 *-------------------------------------------------------------------------
54 #include "catalog/pg_statistic.h"
55 #include "executor/nodeHash.h"
56 #include "miscadmin.h"
57 #include "optimizer/clauses.h"
58 #include "optimizer/cost.h"
59 #include "optimizer/pathnode.h"
60 #include "parser/parsetree.h"
61 #include "utils/selfuncs.h"
62 #include "utils/lsyscache.h"
63 #include "utils/syscache.h"
66 #define LOG2(x) (log(x) / 0.693147180559945)
67 #define LOG6(x) (log(x) / 1.79175946922805)
70 double effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;
71 double random_page_cost = DEFAULT_RANDOM_PAGE_COST;
72 double cpu_tuple_cost = DEFAULT_CPU_TUPLE_COST;
73 double cpu_index_tuple_cost = DEFAULT_CPU_INDEX_TUPLE_COST;
74 double cpu_operator_cost = DEFAULT_CPU_OPERATOR_COST;
76 Cost disable_cost = 100000000.0;
78 bool enable_seqscan = true;
79 bool enable_indexscan = true;
80 bool enable_tidscan = true;
81 bool enable_sort = true;
82 bool enable_hashagg = true;
83 bool enable_nestloop = true;
84 bool enable_mergejoin = true;
85 bool enable_hashjoin = true;
88 static Selectivity estimate_hash_bucketsize(Query *root, Var *var);
89 static bool cost_qual_eval_walker(Node *node, Cost *total);
90 static Selectivity approx_selectivity(Query *root, List *quals);
91 static void set_rel_width(Query *root, RelOptInfo *rel);
92 static double relation_byte_size(double tuples, int width);
93 static double page_size(double tuples, int width);
98 * Determines and returns the cost of scanning a relation sequentially.
100 * Note: for historical reasons, this routine and the others in this module
101 * use the passed result Path only to store their startup_cost and total_cost
102 * results into. All the input data they need is passed as separate
103 * parameters, even though much of it could be extracted from the Path.
106 cost_seqscan(Path *path, Query *root,
109 Cost startup_cost = 0;
113 /* Should only be applied to base relations */
114 Assert(length(baserel->relids) == 1);
115 Assert(baserel->rtekind == RTE_RELATION);
118 startup_cost += disable_cost;
123 * The cost of reading a page sequentially is 1.0, by definition. Note
124 * that the Unix kernel will typically do some amount of read-ahead
125 * optimization, so that this cost is less than the true cost of
126 * reading a page from disk. We ignore that issue here, but must take
127 * it into account when estimating the cost of non-sequential
130 run_cost += baserel->pages; /* sequential fetches with cost 1.0 */
133 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
134 run_cost += cpu_per_tuple * baserel->tuples;
136 path->startup_cost = startup_cost;
137 path->total_cost = startup_cost + run_cost;
141 * cost_nonsequential_access
142 * Estimate the cost of accessing one page at random from a relation
143 * (or sort temp file) of the given size in pages.
145 * The simplistic model that the cost is random_page_cost is what we want
146 * to use for large relations; but for small ones that is a serious
147 * overestimate because of the effects of caching. This routine tries to
150 * Unfortunately we don't have any good way of estimating the effective cache
151 * size we are working with --- we know that Postgres itself has NBuffers
152 * internal buffers, but the size of the kernel's disk cache is uncertain,
153 * and how much of it we get to use is even less certain. We punt the problem
154 * for now by assuming we are given an effective_cache_size parameter.
156 * Given a guesstimated cache size, we estimate the actual I/O cost per page
157 * with the entirely ad-hoc equations:
158 * if relpages >= effective_cache_size:
159 * random_page_cost * (1 - (effective_cache_size/relpages)/2)
160 * if relpages < effective_cache_size:
161 * 1 + (random_page_cost/2-1) * (relpages/effective_cache_size) ** 2
162 * These give the right asymptotic behavior (=> 1.0 as relpages becomes
163 * small, => random_page_cost as it becomes large) and meet in the middle
164 * with the estimate that the cache is about 50% effective for a relation
165 * of the same size as effective_cache_size. (XXX this is probably all
166 * wrong, but I haven't been able to find any theory about how effective
167 * a disk cache should be presumed to be.)
170 cost_nonsequential_access(double relpages)
174 /* don't crash on bad input data */
175 if (relpages <= 0.0 || effective_cache_size <= 0.0)
176 return random_page_cost;
178 relsize = relpages / effective_cache_size;
181 return random_page_cost * (1.0 - 0.5 / relsize);
183 return 1.0 + (random_page_cost * 0.5 - 1.0) * relsize * relsize;
188 * Determines and returns the cost of scanning a relation using an index.
190 * NOTE: an indexscan plan node can actually represent several passes,
191 * but here we consider the cost of just one pass.
193 * 'root' is the query root
194 * 'baserel' is the base relation the index is for
195 * 'index' is the index to be used
196 * 'indexQuals' is the list of applicable qual clauses (implicit AND semantics)
197 * 'is_injoin' is T if we are considering using the index scan as the inside
198 * of a nestloop join (hence, some of the indexQuals are join clauses)
200 * NOTE: 'indexQuals' must contain only clauses usable as index restrictions.
201 * Any additional quals evaluated as qpquals may reduce the number of returned
202 * tuples, but they won't reduce the number of tuples we have to fetch from
203 * the table, so they don't reduce the scan cost.
206 cost_index(Path *path, Query *root,
212 Cost startup_cost = 0;
214 Cost indexStartupCost;
216 Selectivity indexSelectivity;
217 double indexCorrelation,
222 double tuples_fetched;
223 double pages_fetched;
227 /* Should only be applied to base relations */
228 Assert(IsA(baserel, RelOptInfo) &&
229 IsA(index, IndexOptInfo));
230 Assert(length(baserel->relids) == 1);
231 Assert(baserel->rtekind == RTE_RELATION);
233 if (!enable_indexscan)
234 startup_cost += disable_cost;
237 * Call index-access-method-specific code to estimate the processing
238 * cost for scanning the index, as well as the selectivity of the
239 * index (ie, the fraction of main-table tuples we will have to
240 * retrieve) and its correlation to the main-table tuple order.
242 OidFunctionCall8(index->amcostestimate,
243 PointerGetDatum(root),
244 PointerGetDatum(baserel),
245 PointerGetDatum(index),
246 PointerGetDatum(indexQuals),
247 PointerGetDatum(&indexStartupCost),
248 PointerGetDatum(&indexTotalCost),
249 PointerGetDatum(&indexSelectivity),
250 PointerGetDatum(&indexCorrelation));
252 /* all costs for touching index itself included here */
253 startup_cost += indexStartupCost;
254 run_cost += indexTotalCost - indexStartupCost;
257 * Estimate number of main-table tuples and pages fetched.
259 * When the index ordering is uncorrelated with the table ordering,
260 * we use an approximation proposed by Mackert and Lohman, "Index Scans
261 * Using a Finite LRU Buffer: A Validated I/O Model", ACM Transactions
262 * on Database Systems, Vol. 14, No. 3, September 1989, Pages 401-424.
263 * The Mackert and Lohman approximation is that the number of pages
266 * min(2TNs/(2T+Ns), T) when T <= b
267 * 2TNs/(2T+Ns) when T > b and Ns <= 2Tb/(2T-b)
268 * b + (Ns - 2Tb/(2T-b))*(T-b)/T when T > b and Ns > 2Tb/(2T-b)
270 * T = # pages in table
271 * N = # tuples in table
272 * s = selectivity = fraction of table to be scanned
273 * b = # buffer pages available (we include kernel space here)
275 * When the index ordering is exactly correlated with the table ordering
276 * (just after a CLUSTER, for example), the number of pages fetched should
277 * be just sT. What's more, these will be sequential fetches, not the
278 * random fetches that occur in the uncorrelated case. So, depending on
279 * the extent of correlation, we should estimate the actual I/O cost
280 * somewhere between s * T * 1.0 and PF * random_cost. We currently
281 * interpolate linearly between these two endpoints based on the
282 * correlation squared (XXX is that appropriate?).
284 * In any case the number of tuples fetched is Ns.
288 tuples_fetched = indexSelectivity * baserel->tuples;
289 /* Don't believe estimates less than 1... */
290 if (tuples_fetched < 1.0)
291 tuples_fetched = 1.0;
293 /* This part is the Mackert and Lohman formula */
295 T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
296 b = (effective_cache_size > 1) ? effective_cache_size : 1.0;
301 (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
302 if (pages_fetched > T)
309 lim = (2.0 * T * b) / (2.0 * T - b);
310 if (tuples_fetched <= lim)
313 (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
318 b + (tuples_fetched - lim) * (T - b) / T;
323 * min_IO_cost corresponds to the perfectly correlated case
324 * (csquared=1), max_IO_cost to the perfectly uncorrelated case
325 * (csquared=0). Note that we just charge random_page_cost per page
326 * in the uncorrelated case, rather than using
327 * cost_nonsequential_access, since we've already accounted for
328 * caching effects by using the Mackert model.
330 min_IO_cost = ceil(indexSelectivity * T);
331 max_IO_cost = pages_fetched * random_page_cost;
334 * Now interpolate based on estimated index order correlation to get
335 * total disk I/O cost for main table accesses.
337 csquared = indexCorrelation * indexCorrelation;
339 run_cost += max_IO_cost + csquared * (min_IO_cost - max_IO_cost);
342 * Estimate CPU costs per tuple.
344 * Normally the indexquals will be removed from the list of restriction
345 * clauses that we have to evaluate as qpquals, so we should subtract
346 * their costs from baserestrictcost. XXX For a lossy index, not all
347 * the quals will be removed and so we really shouldn't subtract their
348 * costs; but detecting that seems more expensive than it's worth.
349 * Also, if we are doing a join then some of the indexquals are join
350 * clauses and shouldn't be subtracted. Rather than work out exactly
351 * how much to subtract, we don't subtract anything.
353 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
356 cpu_per_tuple -= cost_qual_eval(indexQuals);
358 run_cost += cpu_per_tuple * tuples_fetched;
360 path->startup_cost = startup_cost;
361 path->total_cost = startup_cost + run_cost;
366 * Determines and returns the cost of scanning a relation using TIDs.
369 cost_tidscan(Path *path, Query *root,
370 RelOptInfo *baserel, List *tideval)
372 Cost startup_cost = 0;
375 int ntuples = length(tideval);
377 /* Should only be applied to base relations */
378 Assert(length(baserel->relids) == 1);
379 Assert(baserel->rtekind == RTE_RELATION);
382 startup_cost += disable_cost;
384 /* disk costs --- assume each tuple on a different page */
385 run_cost += random_page_cost * ntuples;
388 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
389 run_cost += cpu_per_tuple * ntuples;
391 path->startup_cost = startup_cost;
392 path->total_cost = startup_cost + run_cost;
397 * Determines and returns the cost of scanning a function RTE.
400 cost_functionscan(Path *path, Query *root, RelOptInfo *baserel)
402 Cost startup_cost = 0;
406 /* Should only be applied to base relations that are functions */
407 Assert(length(baserel->relids) == 1);
408 Assert(baserel->rtekind == RTE_FUNCTION);
411 * For now, estimate function's cost at one operator eval per function
412 * call. Someday we should revive the function cost estimate columns
415 cpu_per_tuple = cpu_operator_cost;
417 /* Add scanning CPU costs */
418 cpu_per_tuple += cpu_tuple_cost + baserel->baserestrictcost;
419 run_cost += cpu_per_tuple * baserel->tuples;
421 path->startup_cost = startup_cost;
422 path->total_cost = startup_cost + run_cost;
427 * Determines and returns the cost of sorting a relation, including
428 * the cost of reading the input data.
430 * If the total volume of data to sort is less than SortMem, we will do
431 * an in-memory sort, which requires no I/O and about t*log2(t) tuple
432 * comparisons for t tuples.
434 * If the total volume exceeds SortMem, we switch to a tape-style merge
435 * algorithm. There will still be about t*log2(t) tuple comparisons in
436 * total, but we will also need to write and read each tuple once per
437 * merge pass. We expect about ceil(log6(r)) merge passes where r is the
438 * number of initial runs formed (log6 because tuplesort.c uses six-tape
439 * merging). Since the average initial run should be about twice SortMem,
441 * disk traffic = 2 * relsize * ceil(log6(p / (2*SortMem)))
442 * cpu = comparison_cost * t * log2(t)
444 * The disk traffic is assumed to be half sequential and half random
445 * accesses (XXX can't we refine that guess?)
447 * We charge two operator evals per tuple comparison, which should be in
448 * the right ballpark in most cases.
450 * 'pathkeys' is a list of sort keys
451 * 'input_cost' is the total cost for reading the input data
452 * 'tuples' is the number of tuples in the relation
453 * 'width' is the average tuple width in bytes
455 * NOTE: some callers currently pass NIL for pathkeys because they
456 * can't conveniently supply the sort keys. Since this routine doesn't
457 * currently do anything with pathkeys anyway, that doesn't matter...
458 * but if it ever does, it should react gracefully to lack of key data.
459 * (Actually, the thing we'd most likely be interested in is just the number
460 * of sort keys, which all callers *could* supply.)
463 cost_sort(Path *path, Query *root,
464 List *pathkeys, Cost input_cost, double tuples, int width)
466 Cost startup_cost = input_cost;
468 double nbytes = relation_byte_size(tuples, width);
469 long sortmembytes = SortMem * 1024L;
472 startup_cost += disable_cost;
475 * We want to be sure the cost of a sort is never estimated as zero,
476 * even if passed-in tuple count is zero. Besides, mustn't do
485 * Assume about two operator evals per tuple comparison and N log2 N
488 startup_cost += 2.0 * cpu_operator_cost * tuples * LOG2(tuples);
491 if (nbytes > sortmembytes)
493 double npages = ceil(nbytes / BLCKSZ);
494 double nruns = nbytes / (sortmembytes * 2);
495 double log_runs = ceil(LOG6(nruns));
496 double npageaccesses;
500 npageaccesses = 2.0 * npages * log_runs;
501 /* Assume half are sequential (cost 1), half are not */
502 startup_cost += npageaccesses *
503 (1.0 + cost_nonsequential_access(npages)) * 0.5;
507 * Also charge a small amount (arbitrarily set equal to operator cost)
508 * per extracted tuple.
510 run_cost += cpu_operator_cost * tuples;
512 path->startup_cost = startup_cost;
513 path->total_cost = startup_cost + run_cost;
518 * Determines and returns the cost of materializing a relation, including
519 * the cost of reading the input data.
521 * If the total volume of data to materialize exceeds SortMem, we will need
522 * to write it to disk, so the cost is much higher in that case.
525 cost_material(Path *path,
526 Cost input_cost, double tuples, int width)
528 Cost startup_cost = input_cost;
530 double nbytes = relation_byte_size(tuples, width);
531 long sortmembytes = SortMem * 1024L;
534 if (nbytes > sortmembytes)
536 double npages = ceil(nbytes / BLCKSZ);
538 /* We'll write during startup and read during retrieval */
539 startup_cost += npages;
544 * Also charge a small amount per extracted tuple. We use cpu_tuple_cost
545 * so that it doesn't appear worthwhile to materialize a bare seqscan.
547 run_cost += cpu_tuple_cost * tuples;
549 path->startup_cost = startup_cost;
550 path->total_cost = startup_cost + run_cost;
555 * Determines and returns the cost of performing an Agg plan node,
556 * including the cost of its input.
558 * Note: when aggstrategy == AGG_SORTED, caller must ensure that input costs
559 * are for appropriately-sorted input.
562 cost_agg(Path *path, Query *root,
563 AggStrategy aggstrategy, int numAggs,
564 int numGroupCols, double numGroups,
565 Cost input_startup_cost, Cost input_total_cost,
572 * We charge one cpu_operator_cost per aggregate function per input
573 * tuple, and another one per output tuple (corresponding to transfn
574 * and finalfn calls respectively). If we are grouping, we charge an
575 * additional cpu_operator_cost per grouping column per input tuple
576 * for grouping comparisons.
578 * We will produce a single output tuple if not grouping,
579 * and a tuple per group otherwise.
581 if (aggstrategy == AGG_PLAIN)
583 startup_cost = input_total_cost;
584 startup_cost += cpu_operator_cost * (input_tuples + 1) * numAggs;
585 /* we aren't grouping */
586 total_cost = startup_cost;
588 else if (aggstrategy == AGG_SORTED)
590 /* Here we are able to deliver output on-the-fly */
591 startup_cost = input_startup_cost;
592 total_cost = input_total_cost;
593 total_cost += cpu_operator_cost * (input_tuples + numGroups) * numAggs;
594 total_cost += cpu_operator_cost * input_tuples * numGroupCols;
598 /* must be AGG_HASHED */
599 startup_cost = input_total_cost;
600 startup_cost += cpu_operator_cost * input_tuples * numAggs;
601 startup_cost += cpu_operator_cost * input_tuples * numGroupCols;
602 total_cost = startup_cost;
603 total_cost += cpu_operator_cost * numGroups * numAggs;
606 path->startup_cost = startup_cost;
607 path->total_cost = total_cost;
612 * Determines and returns the cost of performing a Group plan node,
613 * including the cost of its input.
615 * Note: caller must ensure that input costs are for appropriately-sorted
619 cost_group(Path *path, Query *root,
620 int numGroupCols, double numGroups,
621 Cost input_startup_cost, Cost input_total_cost,
627 startup_cost = input_startup_cost;
628 total_cost = input_total_cost;
631 * Charge one cpu_operator_cost per comparison per input tuple. We
632 * assume all columns get compared at most of the tuples.
634 total_cost += cpu_operator_cost * input_tuples * numGroupCols;
636 path->startup_cost = startup_cost;
637 path->total_cost = total_cost;
642 * Determines and returns the cost of joining two relations using the
643 * nested loop algorithm.
645 * 'outer_path' is the path for the outer relation
646 * 'inner_path' is the path for the inner relation
647 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
650 cost_nestloop(Path *path, Query *root,
655 Cost startup_cost = 0;
660 if (!enable_nestloop)
661 startup_cost += disable_cost;
663 /* cost of source data */
666 * NOTE: clearly, we must pay both outer and inner paths' startup_cost
667 * before we can start returning tuples, so the join's startup cost is
668 * their sum. What's not so clear is whether the inner path's
669 * startup_cost must be paid again on each rescan of the inner path.
670 * This is not true if the inner path is materialized or is a hashjoin,
671 * but probably is true otherwise.
673 startup_cost += outer_path->startup_cost + inner_path->startup_cost;
674 run_cost += outer_path->total_cost - outer_path->startup_cost;
675 run_cost += outer_path->parent->rows *
676 (inner_path->total_cost - inner_path->startup_cost);
677 if (!(IsA(inner_path, MaterialPath) ||
678 IsA(inner_path, HashPath)) &&
679 outer_path->parent->rows > 1)
680 run_cost += (outer_path->parent->rows - 1) * inner_path->startup_cost;
683 * Number of tuples processed (not number emitted!). If inner path is
684 * an indexscan, be sure to use its estimated output row count, which
685 * may be lower than the restriction-clause-only row count of its
688 if (IsA(inner_path, IndexPath))
689 ntuples = ((IndexPath *) inner_path)->rows;
691 ntuples = inner_path->parent->rows;
692 ntuples *= outer_path->parent->rows;
695 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
696 run_cost += cpu_per_tuple * ntuples;
698 path->startup_cost = startup_cost;
699 path->total_cost = startup_cost + run_cost;
704 * Determines and returns the cost of joining two relations using the
705 * merge join algorithm.
707 * 'outer_path' is the path for the outer relation
708 * 'inner_path' is the path for the inner relation
709 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
710 * 'mergeclauses' are the RestrictInfo nodes to use as merge clauses
711 * (this should be a subset of the restrictlist)
712 * 'outersortkeys' and 'innersortkeys' are lists of the keys to be used
713 * to sort the outer and inner relations, or NIL if no explicit
714 * sort is needed because the source path is already ordered
717 cost_mergejoin(Path *path, Query *root,
725 Cost startup_cost = 0;
728 RestrictInfo *firstclause;
733 Selectivity outerscansel,
735 Path sort_path; /* dummy for result of cost_sort */
737 if (!enable_mergejoin)
738 startup_cost += disable_cost;
741 * A merge join will stop as soon as it exhausts either input stream.
742 * Estimate fraction of the left and right inputs that will actually
743 * need to be scanned. We use only the first (most significant) merge
744 * clause for this purpose.
746 * Since this calculation is somewhat expensive, and will be the same for
747 * all mergejoin paths associated with the merge clause, we cache the
748 * results in the RestrictInfo node.
750 firstclause = (RestrictInfo *) lfirst(mergeclauses);
751 if (firstclause->left_mergescansel < 0) /* not computed yet? */
752 mergejoinscansel(root, (Node *) firstclause->clause,
753 &firstclause->left_mergescansel,
754 &firstclause->right_mergescansel);
756 leftvar = get_leftop(firstclause->clause);
757 Assert(IsA(leftvar, Var));
758 if (VARISRELMEMBER(leftvar->varno, outer_path->parent))
760 /* left side of clause is outer */
761 outerscansel = firstclause->left_mergescansel;
762 innerscansel = firstclause->right_mergescansel;
766 /* left side of clause is inner */
767 outerscansel = firstclause->right_mergescansel;
768 innerscansel = firstclause->left_mergescansel;
771 outer_rows = outer_path->parent->rows * outerscansel;
772 inner_rows = inner_path->parent->rows * innerscansel;
774 /* cost of source data */
777 * Note we are assuming that each source tuple is fetched just once,
778 * which is not right in the presence of equal keys. If we had a way
779 * of estimating the proportion of equal keys, we could apply a
780 * correction factor...
782 if (outersortkeys) /* do we need to sort outer? */
784 cost_sort(&sort_path,
787 outer_path->total_cost,
788 outer_path->parent->rows,
789 outer_path->parent->width);
790 startup_cost += sort_path.startup_cost;
791 run_cost += (sort_path.total_cost - sort_path.startup_cost)
796 startup_cost += outer_path->startup_cost;
797 run_cost += (outer_path->total_cost - outer_path->startup_cost)
801 if (innersortkeys) /* do we need to sort inner? */
803 cost_sort(&sort_path,
806 inner_path->total_cost,
807 inner_path->parent->rows,
808 inner_path->parent->width);
809 startup_cost += sort_path.startup_cost;
810 run_cost += (sort_path.total_cost - sort_path.startup_cost)
815 startup_cost += inner_path->startup_cost;
816 run_cost += (inner_path->total_cost - inner_path->startup_cost)
821 * The number of tuple comparisons needed depends drastically on the
822 * number of equal keys in the two source relations, which we have no
823 * good way of estimating. (XXX could the MCV statistics help?)
824 * Somewhat arbitrarily, we charge one tuple comparison (one
825 * cpu_operator_cost) for each tuple in the two source relations.
826 * This is probably a lower bound.
828 run_cost += cpu_operator_cost * (outer_rows + inner_rows);
831 * For each tuple that gets through the mergejoin proper, we charge
832 * cpu_tuple_cost plus the cost of evaluating additional restriction
833 * clauses that are to be applied at the join. It's OK to use an
834 * approximate selectivity here, since in most cases this is a minor
835 * component of the cost. NOTE: it's correct to use the unscaled rows
836 * counts here, not the scaled-down counts we obtained above.
838 ntuples = approx_selectivity(root, mergeclauses) *
839 outer_path->parent->rows * inner_path->parent->rows;
842 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
843 run_cost += cpu_per_tuple * ntuples;
845 path->startup_cost = startup_cost;
846 path->total_cost = startup_cost + run_cost;
851 * Determines and returns the cost of joining two relations using the
852 * hash join algorithm.
854 * 'outer_path' is the path for the outer relation
855 * 'inner_path' is the path for the inner relation
856 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
857 * 'hashclauses' are the RestrictInfo nodes to use as hash clauses
858 * (this should be a subset of the restrictlist)
861 cost_hashjoin(Path *path, Query *root,
867 Cost startup_cost = 0;
871 double outerbytes = relation_byte_size(outer_path->parent->rows,
872 outer_path->parent->width);
873 double innerbytes = relation_byte_size(inner_path->parent->rows,
874 inner_path->parent->width);
875 long hashtablebytes = SortMem * 1024L;
876 Selectivity innerbucketsize;
879 if (!enable_hashjoin)
880 startup_cost += disable_cost;
882 /* cost of source data */
883 startup_cost += outer_path->startup_cost;
884 run_cost += outer_path->total_cost - outer_path->startup_cost;
885 startup_cost += inner_path->total_cost;
887 /* cost of computing hash function: must do it once per input tuple */
888 startup_cost += cpu_operator_cost * inner_path->parent->rows;
889 run_cost += cpu_operator_cost * outer_path->parent->rows;
892 * Determine bucketsize fraction for inner relation. We use the
893 * smallest bucketsize estimated for any individual hashclause;
894 * this is undoubtedly conservative.
896 innerbucketsize = 1.0;
897 foreach(hcl, hashclauses)
899 RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(hcl);
902 Selectivity thisbucketsize;
904 Assert(IsA(restrictinfo, RestrictInfo));
905 /* these must be OK, since check_hashjoinable accepted the clause */
906 left = get_leftop(restrictinfo->clause);
907 right = get_rightop(restrictinfo->clause);
910 * First we have to figure out which side of the hashjoin clause is the
913 * Since we tend to visit the same clauses over and over when planning
914 * a large query, we cache the bucketsize estimate in the RestrictInfo
915 * node to avoid repeated lookups of statistics.
917 if (VARISRELMEMBER(right->varno, inner_path->parent))
919 /* righthand side is inner */
920 thisbucketsize = restrictinfo->right_bucketsize;
921 if (thisbucketsize < 0)
924 thisbucketsize = estimate_hash_bucketsize(root, right);
925 restrictinfo->right_bucketsize = thisbucketsize;
930 Assert(VARISRELMEMBER(left->varno, inner_path->parent));
931 /* lefthand side is inner */
932 thisbucketsize = restrictinfo->left_bucketsize;
933 if (thisbucketsize < 0)
936 thisbucketsize = estimate_hash_bucketsize(root, left);
937 restrictinfo->left_bucketsize = thisbucketsize;
941 if (innerbucketsize > thisbucketsize)
942 innerbucketsize = thisbucketsize;
946 * The number of tuple comparisons needed is the number of outer
947 * tuples times the typical number of tuples in a hash bucket, which
948 * is the inner relation size times its bucketsize fraction. We charge
949 * one cpu_operator_cost per tuple comparison.
951 run_cost += cpu_operator_cost * outer_path->parent->rows *
952 ceil(inner_path->parent->rows * innerbucketsize);
955 * For each tuple that gets through the hashjoin proper, we charge
956 * cpu_tuple_cost plus the cost of evaluating additional restriction
957 * clauses that are to be applied at the join. It's OK to use an
958 * approximate selectivity here, since in most cases this is a minor
959 * component of the cost.
961 ntuples = approx_selectivity(root, hashclauses) *
962 outer_path->parent->rows * inner_path->parent->rows;
965 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
966 run_cost += cpu_per_tuple * ntuples;
969 * if inner relation is too big then we will need to "batch" the join,
970 * which implies writing and reading most of the tuples to disk an
971 * extra time. Charge one cost unit per page of I/O (correct since it
972 * should be nice and sequential...). Writing the inner rel counts as
973 * startup cost, all the rest as run cost.
975 if (innerbytes > hashtablebytes)
977 double outerpages = page_size(outer_path->parent->rows,
978 outer_path->parent->width);
979 double innerpages = page_size(inner_path->parent->rows,
980 inner_path->parent->width);
982 startup_cost += innerpages;
983 run_cost += innerpages + 2 * outerpages;
987 * Bias against putting larger relation on inside. We don't want an
988 * absolute prohibition, though, since larger relation might have
989 * better bucketsize --- and we can't trust the size estimates
990 * unreservedly, anyway. Instead, inflate the startup cost by the
991 * square root of the size ratio. (Why square root? No real good
992 * reason, but it seems reasonable...)
994 if (innerbytes > outerbytes && outerbytes > 0)
995 startup_cost *= sqrt(innerbytes / outerbytes);
997 path->startup_cost = startup_cost;
998 path->total_cost = startup_cost + run_cost;
1002 * Estimate hash bucketsize fraction (ie, number of entries in a bucket
1003 * divided by total tuples in relation) if the specified Var is used
1006 * XXX This is really pretty bogus since we're effectively assuming that the
1007 * distribution of hash keys will be the same after applying restriction
1008 * clauses as it was in the underlying relation. However, we are not nearly
1009 * smart enough to figure out how the restrict clauses might change the
1010 * distribution, so this will have to do for now.
1012 * We can get the number of buckets the executor will use for the given
1013 * input relation. If the data were perfectly distributed, with the same
1014 * number of tuples going into each available bucket, then the bucketsize
1015 * fraction would be 1/nbuckets. But this happy state of affairs will occur
1016 * only if (a) there are at least nbuckets distinct data values, and (b)
1017 * we have a not-too-skewed data distribution. Otherwise the buckets will
1018 * be nonuniformly occupied. If the other relation in the join has a key
1019 * distribution similar to this one's, then the most-loaded buckets are
1020 * exactly those that will be probed most often. Therefore, the "average"
1021 * bucket size for costing purposes should really be taken as something close
1022 * to the "worst case" bucket size. We try to estimate this by adjusting the
1023 * fraction if there are too few distinct data values, and then scaling up
1024 * by the ratio of the most common value's frequency to the average frequency.
1026 * If no statistics are available, use a default estimate of 0.1. This will
1027 * discourage use of a hash rather strongly if the inner relation is large,
1028 * which is what we want. We do not want to hash unless we know that the
1029 * inner rel is well-dispersed (or the alternatives seem much worse).
1032 estimate_hash_bucketsize(Query *root, Var *var)
1037 int physicalbuckets;
1040 Form_pg_statistic stats;
1049 * Lookup info about var's relation and attribute; if none available,
1050 * return default estimate.
1055 relid = getrelid(var->varno, root->rtable);
1056 if (relid == InvalidOid)
1059 rel = find_base_rel(root, var->varno);
1061 if (rel->tuples <= 0.0 || rel->rows <= 0.0)
1062 return 0.1; /* ensure we can divide below */
1064 /* Get hash table size that executor would use for this relation */
1065 ExecChooseHashTableSize(rel->rows, rel->width,
1070 tuple = SearchSysCache(STATRELATT,
1071 ObjectIdGetDatum(relid),
1072 Int16GetDatum(var->varattno),
1074 if (!HeapTupleIsValid(tuple))
1077 * Perhaps the Var is a system attribute; if so, it will have no
1078 * entry in pg_statistic, but we may be able to guess something
1079 * about its distribution anyway.
1081 switch (var->varattno)
1083 case ObjectIdAttributeNumber:
1084 case SelfItemPointerAttributeNumber:
1085 /* these are unique, so buckets should be well-distributed */
1086 return 1.0 / (double) virtualbuckets;
1087 case TableOidAttributeNumber:
1088 /* hashing this is a terrible idea... */
1093 stats = (Form_pg_statistic) GETSTRUCT(tuple);
1096 * Obtain number of distinct data values in raw relation.
1098 ndistinct = stats->stadistinct;
1099 if (ndistinct < 0.0)
1100 ndistinct = -ndistinct * rel->tuples;
1102 if (ndistinct <= 0.0) /* ensure we can divide */
1104 ReleaseSysCache(tuple);
1108 /* Also compute avg freq of all distinct data values in raw relation */
1109 avgfreq = (1.0 - stats->stanullfrac) / ndistinct;
1112 * Adjust ndistinct to account for restriction clauses. Observe we
1113 * are assuming that the data distribution is affected uniformly by
1114 * the restriction clauses!
1116 * XXX Possibly better way, but much more expensive: multiply by
1117 * selectivity of rel's restriction clauses that mention the target
1120 ndistinct *= rel->rows / rel->tuples;
1123 * Initial estimate of bucketsize fraction is 1/nbuckets as long as
1124 * the number of buckets is less than the expected number of distinct
1125 * values; otherwise it is 1/ndistinct.
1127 if (ndistinct > (double) virtualbuckets)
1128 estfract = 1.0 / (double) virtualbuckets;
1130 estfract = 1.0 / ndistinct;
1133 * Look up the frequency of the most common value, if available.
1137 if (get_attstatsslot(tuple, var->vartype, var->vartypmod,
1138 STATISTIC_KIND_MCV, InvalidOid,
1139 NULL, NULL, &numbers, &nnumbers))
1142 * The first MCV stat is for the most common value.
1145 mcvfreq = numbers[0];
1146 free_attstatsslot(var->vartype, NULL, 0,
1151 * Adjust estimated bucketsize upward to account for skewed
1154 if (avgfreq > 0.0 && mcvfreq > avgfreq)
1155 estfract *= mcvfreq / avgfreq;
1157 ReleaseSysCache(tuple);
1159 return (Selectivity) estfract;
1165 * Estimate the CPU cost of evaluating a WHERE clause (once).
1166 * The input can be either an implicitly-ANDed list of boolean
1167 * expressions, or a list of RestrictInfo nodes.
1170 cost_qual_eval(List *quals)
1175 /* We don't charge any cost for the implicit ANDing at top level ... */
1179 Node *qual = (Node *) lfirst(l);
1182 * RestrictInfo nodes contain an eval_cost field reserved for this
1183 * routine's use, so that it's not necessary to evaluate the qual
1184 * clause's cost more than once. If the clause's cost hasn't been
1185 * computed yet, the field will contain -1.
1187 if (qual && IsA(qual, RestrictInfo))
1189 RestrictInfo *restrictinfo = (RestrictInfo *) qual;
1191 if (restrictinfo->eval_cost < 0)
1193 restrictinfo->eval_cost = 0;
1194 cost_qual_eval_walker((Node *) restrictinfo->clause,
1195 &restrictinfo->eval_cost);
1197 total += restrictinfo->eval_cost;
1201 /* If it's a bare expression, must always do it the hard way */
1202 cost_qual_eval_walker(qual, &total);
1209 cost_qual_eval_walker(Node *node, Cost *total)
1215 * Our basic strategy is to charge one cpu_operator_cost for each
1216 * operator or function node in the given tree. Vars and Consts are
1217 * charged zero, and so are boolean operators (AND, OR, NOT).
1218 * Simplistic, but a lot better than no model at all.
1220 * Should we try to account for the possibility of short-circuit
1221 * evaluation of AND/OR?
1223 if (IsA(node, Expr))
1225 Expr *expr = (Expr *) node;
1227 switch (expr->opType)
1232 *total += cpu_operator_cost;
1241 * A subplan node in an expression indicates that the
1242 * subplan will be executed on each evaluation, so charge
1243 * accordingly. (We assume that sub-selects that can be
1244 * executed as InitPlans have already been removed from
1247 * NOTE: this logic should agree with the estimates used by
1248 * make_subplan() in plan/subselect.c.
1251 SubPlan *subplan = (SubPlan *) expr->oper;
1252 Plan *plan = subplan->plan;
1255 if (subplan->sublink->subLinkType == EXISTS_SUBLINK)
1257 /* we only need to fetch 1 tuple */
1258 subcost = plan->startup_cost +
1259 (plan->total_cost - plan->startup_cost) / plan->plan_rows;
1261 else if (subplan->sublink->subLinkType == ALL_SUBLINK ||
1262 subplan->sublink->subLinkType == ANY_SUBLINK)
1264 /* assume we need 50% of the tuples */
1265 subcost = plan->startup_cost +
1266 0.50 * (plan->total_cost - plan->startup_cost);
1267 /* XXX what if subplan has been materialized? */
1271 /* assume we need all tuples */
1272 subcost = plan->total_cost;
1278 /* fall through to examine args of Expr node */
1280 return expression_tree_walker(node, cost_qual_eval_walker,
1286 * approx_selectivity
1287 * Quick-and-dirty estimation of clause selectivities.
1288 * The input can be either an implicitly-ANDed list of boolean
1289 * expressions, or a list of RestrictInfo nodes (typically the latter).
1291 * The "quick" part comes from caching the selectivity estimates so we can
1292 * avoid recomputing them later. (Since the same clauses are typically
1293 * examined over and over in different possible join trees, this makes a
1296 * The "dirty" part comes from the fact that the selectivities of multiple
1297 * clauses are estimated independently and multiplied together. Now
1298 * clauselist_selectivity often can't do any better than that anyhow, but
1299 * for some situations (such as range constraints) it is smarter.
1301 * Since we are only using the results to estimate how many potential
1302 * output tuples are generated and passed through qpqual checking, it
1303 * seems OK to live with the approximation.
1306 approx_selectivity(Query *root, List *quals)
1308 Selectivity total = 1.0;
1313 Node *qual = (Node *) lfirst(l);
1317 * RestrictInfo nodes contain a this_selec field reserved for this
1318 * routine's use, so that it's not necessary to evaluate the qual
1319 * clause's selectivity more than once. If the clause's
1320 * selectivity hasn't been computed yet, the field will contain
1323 if (qual && IsA(qual, RestrictInfo))
1325 RestrictInfo *restrictinfo = (RestrictInfo *) qual;
1327 if (restrictinfo->this_selec < 0)
1328 restrictinfo->this_selec =
1329 clause_selectivity(root,
1330 (Node *) restrictinfo->clause,
1332 selec = restrictinfo->this_selec;
1336 /* If it's a bare expression, must always do it the hard way */
1337 selec = clause_selectivity(root, qual, 0);
1346 * set_baserel_size_estimates
1347 * Set the size estimates for the given base relation.
1349 * The rel's targetlist and restrictinfo list must have been constructed
1352 * We set the following fields of the rel node:
1353 * rows: the estimated number of output tuples (after applying
1354 * restriction clauses).
1355 * width: the estimated average output tuple width in bytes.
1356 * baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
1359 set_baserel_size_estimates(Query *root, RelOptInfo *rel)
1361 /* Should only be applied to base relations */
1362 Assert(length(rel->relids) == 1);
1364 rel->rows = rel->tuples *
1365 restrictlist_selectivity(root,
1366 rel->baserestrictinfo,
1367 lfirsti(rel->relids));
1370 * Force estimate to be at least one row, to make explain output look
1371 * better and to avoid possible divide-by-zero when interpolating
1374 if (rel->rows < 1.0)
1377 rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
1379 set_rel_width(root, rel);
1383 * set_joinrel_size_estimates
1384 * Set the size estimates for the given join relation.
1386 * The rel's targetlist must have been constructed already, and a
1387 * restriction clause list that matches the given component rels must
1390 * Since there is more than one way to make a joinrel for more than two
1391 * base relations, the results we get here could depend on which component
1392 * rel pair is provided. In theory we should get the same answers no matter
1393 * which pair is provided; in practice, since the selectivity estimation
1394 * routines don't handle all cases equally well, we might not. But there's
1395 * not much to be done about it. (Would it make sense to repeat the
1396 * calculations for each pair of input rels that's encountered, and somehow
1397 * average the results? Probably way more trouble than it's worth.)
1399 * We set the same relnode fields as set_baserel_size_estimates() does.
1402 set_joinrel_size_estimates(Query *root, RelOptInfo *rel,
1403 RelOptInfo *outer_rel,
1404 RelOptInfo *inner_rel,
1410 /* Start with the Cartesian product */
1411 temp = outer_rel->rows * inner_rel->rows;
1414 * Apply join restrictivity. Note that we are only considering
1415 * clauses that become restriction clauses at this join level; we are
1416 * not double-counting them because they were not considered in
1417 * estimating the sizes of the component rels.
1419 temp *= restrictlist_selectivity(root,
1424 * If we are doing an outer join, take that into account: the output
1425 * must be at least as large as the non-nullable input. (Is there any
1426 * chance of being even smarter?)
1433 if (temp < outer_rel->rows)
1434 temp = outer_rel->rows;
1437 if (temp < inner_rel->rows)
1438 temp = inner_rel->rows;
1441 if (temp < outer_rel->rows)
1442 temp = outer_rel->rows;
1443 if (temp < inner_rel->rows)
1444 temp = inner_rel->rows;
1447 elog(ERROR, "set_joinrel_size_estimates: unsupported join type %d",
1453 * Force estimate to be at least one row, to make explain output look
1454 * better and to avoid possible divide-by-zero when interpolating
1463 * We could apply set_rel_width() to compute the output tuple width
1464 * from scratch, but at present it's always just the sum of the input
1465 * widths, so why work harder than necessary? If relnode.c is ever
1466 * taught to remove unneeded columns from join targetlists, go back to
1467 * using set_rel_width here.
1469 rel->width = outer_rel->width + inner_rel->width;
1473 * set_function_size_estimates
1474 * Set the size estimates for a base relation that is a function call.
1476 * The rel's targetlist and restrictinfo list must have been constructed
1479 * We set the following fields of the rel node:
1480 * rows: the estimated number of output tuples (after applying
1481 * restriction clauses).
1482 * width: the estimated average output tuple width in bytes.
1483 * baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
1486 set_function_size_estimates(Query *root, RelOptInfo *rel)
1488 /* Should only be applied to base relations that are functions */
1489 Assert(length(rel->relids) == 1);
1490 Assert(rel->rtekind == RTE_FUNCTION);
1493 * Estimate number of rows the function itself will return.
1495 * XXX no idea how to do this yet; but should at least check whether
1496 * function returns set or not...
1500 /* Now estimate number of output rows */
1501 rel->rows = rel->tuples *
1502 restrictlist_selectivity(root,
1503 rel->baserestrictinfo,
1504 lfirsti(rel->relids));
1507 * Force estimate to be at least one row, to make explain output look
1508 * better and to avoid possible divide-by-zero when interpolating
1511 if (rel->rows < 1.0)
1514 rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
1516 set_rel_width(root, rel);
1522 * Set the estimated output width of the relation.
1524 * NB: this works best on base relations because it prefers to look at
1525 * real Vars. It will fail to make use of pg_statistic info when applied
1526 * to a subquery relation, even if the subquery outputs are simple vars
1527 * that we could have gotten info for. Is it worth trying to be smarter
1531 set_rel_width(Query *root, RelOptInfo *rel)
1533 int32 tuple_width = 0;
1536 foreach(tllist, rel->targetlist)
1538 TargetEntry *tle = (TargetEntry *) lfirst(tllist);
1542 * If it's a Var, try to get statistical info from pg_statistic.
1544 if (tle->expr && IsA(tle->expr, Var))
1546 Var *var = (Var *) tle->expr;
1549 relid = getrelid(var->varno, root->rtable);
1550 if (relid != InvalidOid)
1552 item_width = get_attavgwidth(relid, var->varattno);
1555 tuple_width += item_width;
1562 * Not a Var, or can't find statistics for it. Estimate using
1563 * just the type info.
1565 item_width = get_typavgwidth(tle->resdom->restype,
1566 tle->resdom->restypmod);
1567 Assert(item_width > 0);
1568 tuple_width += item_width;
1570 Assert(tuple_width >= 0);
1571 rel->width = tuple_width;
1575 * relation_byte_size
1576 * Estimate the storage space in bytes for a given number of tuples
1577 * of a given width (size in bytes).
1580 relation_byte_size(double tuples, int width)
1582 return tuples * (MAXALIGN(width) + MAXALIGN(sizeof(HeapTupleData)));
1587 * Returns an estimate of the number of pages covered by a given
1588 * number of tuples of a given width (size in bytes).
1591 page_size(double tuples, int width)
1593 return ceil(relation_byte_size(tuples, width) / BLCKSZ);