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) 1996-2001, 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 1.75 2001/06/05 05:26:04 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/lsyscache.h"
62 #include "utils/syscache.h"
65 #define LOG2(x) (log(x) / 0.693147180559945)
66 #define LOG6(x) (log(x) / 1.79175946922805)
69 double effective_cache_size = DEFAULT_EFFECTIVE_CACHE_SIZE;
70 double random_page_cost = DEFAULT_RANDOM_PAGE_COST;
71 double cpu_tuple_cost = DEFAULT_CPU_TUPLE_COST;
72 double cpu_index_tuple_cost = DEFAULT_CPU_INDEX_TUPLE_COST;
73 double cpu_operator_cost = DEFAULT_CPU_OPERATOR_COST;
75 Cost disable_cost = 100000000.0;
77 bool enable_seqscan = true;
78 bool enable_indexscan = true;
79 bool enable_tidscan = true;
80 bool enable_sort = true;
81 bool enable_nestloop = true;
82 bool enable_mergejoin = true;
83 bool enable_hashjoin = true;
86 static Selectivity estimate_hash_bucketsize(Query *root, Var *var);
87 static bool cost_qual_eval_walker(Node *node, Cost *total);
88 static Selectivity approx_selectivity(Query *root, List *quals);
89 static void set_rel_width(Query *root, RelOptInfo *rel);
90 static double relation_byte_size(double tuples, int width);
91 static double page_size(double tuples, int width);
96 * Determines and returns the cost of scanning a relation sequentially.
98 * Note: for historical reasons, this routine and the others in this module
99 * use the passed result Path only to store their startup_cost and total_cost
100 * results into. All the input data they need is passed as separate
101 * parameters, even though much of it could be extracted from the Path.
104 cost_seqscan(Path *path, Query *root,
107 Cost startup_cost = 0;
111 /* Should only be applied to base relations */
112 Assert(length(baserel->relids) == 1);
113 Assert(!baserel->issubquery);
116 startup_cost += disable_cost;
121 * The cost of reading a page sequentially is 1.0, by definition. Note
122 * that the Unix kernel will typically do some amount of read-ahead
123 * optimization, so that this cost is less than the true cost of
124 * reading a page from disk. We ignore that issue here, but must take
125 * it into account when estimating the cost of non-sequential
128 run_cost += baserel->pages; /* sequential fetches with cost 1.0 */
131 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
132 run_cost += cpu_per_tuple * baserel->tuples;
134 path->startup_cost = startup_cost;
135 path->total_cost = startup_cost + run_cost;
139 * cost_nonsequential_access
140 * Estimate the cost of accessing one page at random from a relation
141 * (or sort temp file) of the given size in pages.
143 * The simplistic model that the cost is random_page_cost is what we want
144 * to use for large relations; but for small ones that is a serious
145 * overestimate because of the effects of caching. This routine tries to
148 * Unfortunately we don't have any good way of estimating the effective cache
149 * size we are working with --- we know that Postgres itself has NBuffers
150 * internal buffers, but the size of the kernel's disk cache is uncertain,
151 * and how much of it we get to use is even less certain. We punt the problem
152 * for now by assuming we are given an effective_cache_size parameter.
154 * Given a guesstimated cache size, we estimate the actual I/O cost per page
155 * with the entirely ad-hoc equations:
156 * for rel_size <= effective_cache_size:
157 * 1 + (random_page_cost/2-1) * (rel_size/effective_cache_size) ** 2
158 * for rel_size >= effective_cache_size:
159 * random_page_cost * (1 - (effective_cache_size/rel_size)/2)
160 * These give the right asymptotic behavior (=> 1.0 as rel_size becomes
161 * small, => random_page_cost as it becomes large) and meet in the middle
162 * with the estimate that the cache is about 50% effective for a relation
163 * of the same size as effective_cache_size. (XXX this is probably all
164 * wrong, but I haven't been able to find any theory about how effective
165 * a disk cache should be presumed to be.)
168 cost_nonsequential_access(double relpages)
172 /* don't crash on bad input data */
173 if (relpages <= 0.0 || effective_cache_size <= 0.0)
174 return random_page_cost;
176 relsize = relpages / effective_cache_size;
179 return random_page_cost * (1.0 - 0.5 / relsize);
181 return 1.0 + (random_page_cost * 0.5 - 1.0) * relsize * relsize;
186 * Determines and returns the cost of scanning a relation using an index.
188 * NOTE: an indexscan plan node can actually represent several passes,
189 * but here we consider the cost of just one pass.
191 * 'root' is the query root
192 * 'baserel' is the base relation the index is for
193 * 'index' is the index to be used
194 * 'indexQuals' is the list of applicable qual clauses (implicit AND semantics)
195 * 'is_injoin' is T if we are considering using the index scan as the inside
196 * of a nestloop join (hence, some of the indexQuals are join clauses)
198 * NOTE: 'indexQuals' must contain only clauses usable as index restrictions.
199 * Any additional quals evaluated as qpquals may reduce the number of returned
200 * tuples, but they won't reduce the number of tuples we have to fetch from
201 * the table, so they don't reduce the scan cost.
204 cost_index(Path *path, Query *root,
210 Cost startup_cost = 0;
212 Cost indexStartupCost;
214 Selectivity indexSelectivity;
215 double indexCorrelation,
220 double tuples_fetched;
221 double pages_fetched;
225 /* Should only be applied to base relations */
226 Assert(IsA(baserel, RelOptInfo) &&IsA(index, IndexOptInfo));
227 Assert(length(baserel->relids) == 1);
228 Assert(!baserel->issubquery);
230 if (!enable_indexscan && !is_injoin)
231 startup_cost += disable_cost;
234 * Call index-access-method-specific code to estimate the processing
235 * cost for scanning the index, as well as the selectivity of the
236 * index (ie, the fraction of main-table tuples we will have to
237 * retrieve) and its correlation to the main-table tuple order.
239 OidFunctionCall8(index->amcostestimate,
240 PointerGetDatum(root),
241 PointerGetDatum(baserel),
242 PointerGetDatum(index),
243 PointerGetDatum(indexQuals),
244 PointerGetDatum(&indexStartupCost),
245 PointerGetDatum(&indexTotalCost),
246 PointerGetDatum(&indexSelectivity),
247 PointerGetDatum(&indexCorrelation));
249 /* all costs for touching index itself included here */
250 startup_cost += indexStartupCost;
251 run_cost += indexTotalCost - indexStartupCost;
254 * Estimate number of main-table tuples and pages fetched.
256 * When the index ordering is uncorrelated with the table ordering,
257 * we use an approximation proposed by Mackert and Lohman, "Index Scans
258 * Using a Finite LRU Buffer: A Validated I/O Model", ACM Transactions
259 * on Database Systems, Vol. 14, No. 3, September 1989, Pages 401-424.
260 * The Mackert and Lohman approximation is that the number of pages
263 * min(2TNs/(2T+Ns), T) when T <= b
264 * 2TNs/(2T+Ns) when T > b and Ns <= 2Tb/(2T-b)
265 * b + (Ns - 2Tb/(2T-b))*(T-b)/T when T > b and Ns > 2Tb/(2T-b)
267 * T = # pages in table
268 * N = # tuples in table
269 * s = selectivity = fraction of table to be scanned
270 * b = # buffer pages available (we include kernel space here)
272 * When the index ordering is exactly correlated with the table ordering
273 * (just after a CLUSTER, for example), the number of pages fetched should
274 * be just sT. What's more, these will be sequential fetches, not the
275 * random fetches that occur in the uncorrelated case. So, depending on
276 * the extent of correlation, we should estimate the actual I/O cost
277 * somewhere between s * T * 1.0 and PF * random_cost. We currently
278 * interpolate linearly between these two endpoints based on the
279 * correlation squared (XXX is that appropriate?).
281 * In any case the number of tuples fetched is Ns.
285 tuples_fetched = indexSelectivity * baserel->tuples;
286 /* Don't believe estimates less than 1... */
287 if (tuples_fetched < 1.0)
288 tuples_fetched = 1.0;
290 /* This part is the Mackert and Lohman formula */
292 T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
293 b = (effective_cache_size > 1) ? effective_cache_size : 1.0;
298 (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
299 if (pages_fetched > T)
306 lim = (2.0 * T * b) / (2.0 * T - b);
307 if (tuples_fetched <= lim)
310 (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
315 b + (tuples_fetched - lim) * (T - b) / T;
320 * min_IO_cost corresponds to the perfectly correlated case (csquared=1),
321 * max_IO_cost to the perfectly uncorrelated case (csquared=0). Note
322 * that we just charge random_page_cost per page in the uncorrelated
323 * case, rather than using cost_nonsequential_access, since we've already
324 * accounted for caching effects by using the Mackert model.
326 min_IO_cost = ceil(indexSelectivity * T);
327 max_IO_cost = pages_fetched * random_page_cost;
330 * Now interpolate based on estimated index order correlation
331 * to get total disk I/O cost for main table accesses.
333 csquared = indexCorrelation * indexCorrelation;
335 run_cost += max_IO_cost + csquared * (min_IO_cost - max_IO_cost);
338 * Estimate CPU costs per tuple.
340 * Normally the indexquals will be removed from the list of
341 * restriction clauses that we have to evaluate as qpquals, so we
342 * should subtract their costs from baserestrictcost. For a lossy
343 * index, however, we will have to recheck all the quals and so
344 * mustn't subtract anything. Also, if we are doing a join then some
345 * of the indexquals are join clauses and shouldn't be subtracted.
346 * Rather than work out exactly how much to subtract, we don't
347 * subtract anything in that case either.
349 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
351 if (!index->lossy && !is_injoin)
352 cpu_per_tuple -= cost_qual_eval(indexQuals);
354 run_cost += cpu_per_tuple * tuples_fetched;
356 path->startup_cost = startup_cost;
357 path->total_cost = startup_cost + run_cost;
362 * Determines and returns the cost of scanning a relation using TIDs.
365 cost_tidscan(Path *path, Query *root,
366 RelOptInfo *baserel, List *tideval)
368 Cost startup_cost = 0;
371 int ntuples = length(tideval);
374 startup_cost += disable_cost;
376 /* disk costs --- assume each tuple on a different page */
377 run_cost += random_page_cost * ntuples;
380 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
381 run_cost += cpu_per_tuple * ntuples;
383 path->startup_cost = startup_cost;
384 path->total_cost = startup_cost + run_cost;
389 * Determines and returns the cost of sorting a relation.
391 * The cost of supplying the input data is NOT included; the caller should
392 * add that cost to both startup and total costs returned from this routine!
394 * If the total volume of data to sort is less than SortMem, we will do
395 * an in-memory sort, which requires no I/O and about t*log2(t) tuple
396 * comparisons for t tuples.
398 * If the total volume exceeds SortMem, we switch to a tape-style merge
399 * algorithm. There will still be about t*log2(t) tuple comparisons in
400 * total, but we will also need to write and read each tuple once per
401 * merge pass. We expect about ceil(log6(r)) merge passes where r is the
402 * number of initial runs formed (log6 because tuplesort.c uses six-tape
403 * merging). Since the average initial run should be about twice SortMem,
405 * disk traffic = 2 * relsize * ceil(log6(p / (2*SortMem)))
406 * cpu = comparison_cost * t * log2(t)
408 * The disk traffic is assumed to be half sequential and half random
409 * accesses (XXX can't we refine that guess?)
411 * We charge two operator evals per tuple comparison, which should be in
412 * the right ballpark in most cases.
414 * 'pathkeys' is a list of sort keys
415 * 'tuples' is the number of tuples in the relation
416 * 'width' is the average tuple width in bytes
418 * NOTE: some callers currently pass NIL for pathkeys because they
419 * can't conveniently supply the sort keys. Since this routine doesn't
420 * currently do anything with pathkeys anyway, that doesn't matter...
421 * but if it ever does, it should react gracefully to lack of key data.
424 cost_sort(Path *path, Query *root,
425 List *pathkeys, double tuples, int width)
427 Cost startup_cost = 0;
429 double nbytes = relation_byte_size(tuples, width);
430 long sortmembytes = SortMem * 1024L;
433 startup_cost += disable_cost;
436 * We want to be sure the cost of a sort is never estimated as zero,
437 * even if passed-in tuple count is zero. Besides, mustn't do
446 * Assume about two operator evals per tuple comparison and N log2 N
449 startup_cost += 2.0 * cpu_operator_cost * tuples * LOG2(tuples);
452 if (nbytes > sortmembytes)
454 double npages = ceil(nbytes / BLCKSZ);
455 double nruns = nbytes / (sortmembytes * 2);
456 double log_runs = ceil(LOG6(nruns));
457 double npageaccesses;
461 npageaccesses = 2.0 * npages * log_runs;
462 /* Assume half are sequential (cost 1), half are not */
463 startup_cost += npageaccesses *
464 (1.0 + cost_nonsequential_access(npages)) * 0.5;
468 * Note: should we bother to assign a nonzero run_cost to reflect the
469 * overhead of extracting tuples from the sort result? Probably not
470 * worth worrying about.
472 path->startup_cost = startup_cost;
473 path->total_cost = startup_cost + run_cost;
479 * Determines and returns the cost of joining two relations using the
480 * nested loop algorithm.
482 * 'outer_path' is the path for the outer relation
483 * 'inner_path' is the path for the inner relation
484 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
487 cost_nestloop(Path *path, Query *root,
492 Cost startup_cost = 0;
497 if (!enable_nestloop)
498 startup_cost += disable_cost;
500 /* cost of source data */
503 * NOTE: clearly, we must pay both outer and inner paths' startup_cost
504 * before we can start returning tuples, so the join's startup cost
505 * is their sum. What's not so clear is whether the inner path's
506 * startup_cost must be paid again on each rescan of the inner path.
507 * This is not true if the inner path is materialized, but probably
508 * is true otherwise. Since we don't yet have clean handling of the
509 * decision whether to materialize a path, we can't tell here which
510 * will happen. As a compromise, charge 50% of the inner startup cost
513 startup_cost += outer_path->startup_cost + inner_path->startup_cost;
514 run_cost += outer_path->total_cost - outer_path->startup_cost;
515 run_cost += outer_path->parent->rows *
516 (inner_path->total_cost - inner_path->startup_cost);
517 if (outer_path->parent->rows > 1)
518 run_cost += (outer_path->parent->rows - 1) *
519 inner_path->startup_cost * 0.5;
522 * Number of tuples processed (not number emitted!). If inner path is
523 * an indexscan, be sure to use its estimated output row count, which
524 * may be lower than the restriction-clause-only row count of its
527 if (IsA(inner_path, IndexPath))
528 ntuples = ((IndexPath *) inner_path)->rows;
530 ntuples = inner_path->parent->rows;
531 ntuples *= outer_path->parent->rows;
534 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
535 run_cost += cpu_per_tuple * ntuples;
537 path->startup_cost = startup_cost;
538 path->total_cost = startup_cost + run_cost;
543 * Determines and returns the cost of joining two relations using the
544 * merge join algorithm.
546 * 'outer_path' is the path for the outer relation
547 * 'inner_path' is the path for the inner relation
548 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
549 * 'mergeclauses' are the RestrictInfo nodes to use as merge clauses
550 * (this should be a subset of the restrictlist)
551 * 'outersortkeys' and 'innersortkeys' are lists of the keys to be used
552 * to sort the outer and inner relations, or NIL if no explicit
553 * sort is needed because the source path is already ordered
556 cost_mergejoin(Path *path, Query *root,
564 Cost startup_cost = 0;
568 Path sort_path; /* dummy for result of cost_sort */
570 if (!enable_mergejoin)
571 startup_cost += disable_cost;
573 /* cost of source data */
576 * Note we are assuming that each source tuple is fetched just once,
577 * which is not right in the presence of equal keys. If we had a way
578 * of estimating the proportion of equal keys, we could apply a
579 * correction factor...
581 if (outersortkeys) /* do we need to sort outer? */
583 startup_cost += outer_path->total_cost;
584 cost_sort(&sort_path,
587 outer_path->parent->rows,
588 outer_path->parent->width);
589 startup_cost += sort_path.startup_cost;
590 run_cost += sort_path.total_cost - sort_path.startup_cost;
594 startup_cost += outer_path->startup_cost;
595 run_cost += outer_path->total_cost - outer_path->startup_cost;
598 if (innersortkeys) /* do we need to sort inner? */
600 startup_cost += inner_path->total_cost;
601 cost_sort(&sort_path,
604 inner_path->parent->rows,
605 inner_path->parent->width);
606 startup_cost += sort_path.startup_cost;
607 run_cost += sort_path.total_cost - sort_path.startup_cost;
611 startup_cost += inner_path->startup_cost;
612 run_cost += inner_path->total_cost - inner_path->startup_cost;
616 * The number of tuple comparisons needed depends drastically on the
617 * number of equal keys in the two source relations, which we have no
618 * good way of estimating. Somewhat arbitrarily, we charge one
619 * tuple comparison (one cpu_operator_cost) for each tuple in the
620 * two source relations. This is probably a lower bound.
622 run_cost += cpu_operator_cost *
623 (outer_path->parent->rows + inner_path->parent->rows);
626 * For each tuple that gets through the mergejoin proper, we charge
627 * cpu_tuple_cost plus the cost of evaluating additional restriction
628 * clauses that are to be applied at the join. It's OK to use an
629 * approximate selectivity here, since in most cases this is a minor
630 * component of the cost.
632 ntuples = approx_selectivity(root, mergeclauses) *
633 outer_path->parent->rows * inner_path->parent->rows;
636 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
637 run_cost += cpu_per_tuple * ntuples;
639 path->startup_cost = startup_cost;
640 path->total_cost = startup_cost + run_cost;
645 * Determines and returns the cost of joining two relations using the
646 * hash join algorithm.
648 * 'outer_path' is the path for the outer relation
649 * 'inner_path' is the path for the inner relation
650 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
651 * 'hashclauses' is a list of the hash join clause (always a 1-element list)
652 * (this should be a subset of the restrictlist)
655 cost_hashjoin(Path *path, Query *root,
661 Cost startup_cost = 0;
665 double outerbytes = relation_byte_size(outer_path->parent->rows,
666 outer_path->parent->width);
667 double innerbytes = relation_byte_size(inner_path->parent->rows,
668 inner_path->parent->width);
669 long hashtablebytes = SortMem * 1024L;
670 RestrictInfo *restrictinfo;
673 Selectivity innerbucketsize;
675 if (!enable_hashjoin)
676 startup_cost += disable_cost;
678 /* cost of source data */
679 startup_cost += outer_path->startup_cost;
680 run_cost += outer_path->total_cost - outer_path->startup_cost;
681 startup_cost += inner_path->total_cost;
683 /* cost of computing hash function: must do it once per input tuple */
684 startup_cost += cpu_operator_cost * inner_path->parent->rows;
685 run_cost += cpu_operator_cost * outer_path->parent->rows;
688 * Determine bucketsize fraction for inner relation. First we have
689 * to figure out which side of the hashjoin clause is the inner side.
691 Assert(length(hashclauses) == 1);
692 Assert(IsA(lfirst(hashclauses), RestrictInfo));
693 restrictinfo = (RestrictInfo *) lfirst(hashclauses);
694 /* these must be OK, since check_hashjoinable accepted the clause */
695 left = get_leftop(restrictinfo->clause);
696 right = get_rightop(restrictinfo->clause);
699 * Since we tend to visit the same clauses over and over when
700 * planning a large query, we cache the bucketsize estimate in
701 * the RestrictInfo node to avoid repeated lookups of statistics.
703 if (intMember(right->varno, inner_path->parent->relids))
705 /* righthand side is inner */
706 innerbucketsize = restrictinfo->right_bucketsize;
707 if (innerbucketsize < 0)
710 innerbucketsize = estimate_hash_bucketsize(root, right);
711 restrictinfo->right_bucketsize = innerbucketsize;
716 Assert(intMember(left->varno, inner_path->parent->relids));
717 /* lefthand side is inner */
718 innerbucketsize = restrictinfo->left_bucketsize;
719 if (innerbucketsize < 0)
722 innerbucketsize = estimate_hash_bucketsize(root, left);
723 restrictinfo->left_bucketsize = innerbucketsize;
728 * The number of tuple comparisons needed is the number of outer
729 * tuples times the typical number of tuples in a hash bucket,
730 * which is the inner relation size times its bucketsize fraction.
731 * We charge one cpu_operator_cost per tuple comparison.
733 run_cost += cpu_operator_cost * outer_path->parent->rows *
734 ceil(inner_path->parent->rows * innerbucketsize);
737 * For each tuple that gets through the hashjoin proper, we charge
738 * cpu_tuple_cost plus the cost of evaluating additional restriction
739 * clauses that are to be applied at the join. It's OK to use an
740 * approximate selectivity here, since in most cases this is a minor
741 * component of the cost.
743 ntuples = approx_selectivity(root, hashclauses) *
744 outer_path->parent->rows * inner_path->parent->rows;
747 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
748 run_cost += cpu_per_tuple * ntuples;
751 * if inner relation is too big then we will need to "batch" the join,
752 * which implies writing and reading most of the tuples to disk an
753 * extra time. Charge one cost unit per page of I/O (correct since it
754 * should be nice and sequential...). Writing the inner rel counts as
755 * startup cost, all the rest as run cost.
757 if (innerbytes > hashtablebytes)
759 double outerpages = page_size(outer_path->parent->rows,
760 outer_path->parent->width);
761 double innerpages = page_size(inner_path->parent->rows,
762 inner_path->parent->width);
764 startup_cost += innerpages;
765 run_cost += innerpages + 2 * outerpages;
769 * Bias against putting larger relation on inside. We don't want an
770 * absolute prohibition, though, since larger relation might have
771 * better bucketsize --- and we can't trust the size estimates
772 * unreservedly, anyway. Instead, inflate the startup cost by the
773 * square root of the size ratio. (Why square root? No real good
774 * reason, but it seems reasonable...)
776 if (innerbytes > outerbytes && outerbytes > 0)
777 startup_cost *= sqrt(innerbytes / outerbytes);
779 path->startup_cost = startup_cost;
780 path->total_cost = startup_cost + run_cost;
784 * Estimate hash bucketsize fraction (ie, number of entries in a bucket
785 * divided by total tuples in relation) if the specified Var is used
788 * XXX This is really pretty bogus since we're effectively assuming that the
789 * distribution of hash keys will be the same after applying restriction
790 * clauses as it was in the underlying relation. However, we are not nearly
791 * smart enough to figure out how the restrict clauses might change the
792 * distribution, so this will have to do for now.
794 * The executor tries for average bucket loading of NTUP_PER_BUCKET by setting
795 * number of buckets equal to ntuples / NTUP_PER_BUCKET, which would yield
796 * a bucketsize fraction of NTUP_PER_BUCKET / ntuples. But that goal will
797 * be reached only if the data values are uniformly distributed among the
798 * buckets, which requires (a) at least ntuples / NTUP_PER_BUCKET distinct
799 * data values, and (b) a not-too-skewed data distribution. Otherwise the
800 * buckets will be nonuniformly occupied. If the other relation in the join
801 * has a similar distribution, the most-loaded buckets are exactly those
802 * that will be probed most often. Therefore, the "average" bucket size for
803 * costing purposes should really be taken as something close to the "worst
804 * case" bucket size. We try to estimate this by first scaling up if there
805 * are too few distinct data values, and then scaling up again by the
806 * ratio of the most common value's frequency to the average frequency.
808 * If no statistics are available, use a default estimate of 0.1. This will
809 * discourage use of a hash rather strongly if the inner relation is large,
810 * which is what we want. We do not want to hash unless we know that the
811 * inner rel is well-dispersed (or the alternatives seem much worse).
814 estimate_hash_bucketsize(Query *root, Var *var)
819 Form_pg_statistic stats;
829 * Lookup info about var's relation and attribute;
830 * if none available, return default estimate.
835 relid = getrelid(var->varno, root->rtable);
836 if (relid == InvalidOid)
839 rel = find_base_rel(root, var->varno);
841 if (rel->tuples <= 0.0 || rel->rows <= 0.0)
842 return 0.1; /* ensure we can divide below */
844 tuple = SearchSysCache(STATRELATT,
845 ObjectIdGetDatum(relid),
846 Int16GetDatum(var->varattno),
848 if (!HeapTupleIsValid(tuple))
851 * Perhaps the Var is a system attribute; if so, it will have no
852 * entry in pg_statistic, but we may be able to guess something
853 * about its distribution anyway.
855 switch (var->varattno)
857 case ObjectIdAttributeNumber:
858 case SelfItemPointerAttributeNumber:
859 /* these are unique, so buckets should be well-distributed */
860 return (double) NTUP_PER_BUCKET / rel->rows;
861 case TableOidAttributeNumber:
862 /* hashing this is a terrible idea... */
867 stats = (Form_pg_statistic) GETSTRUCT(tuple);
870 * Obtain number of distinct data values in raw relation.
872 ndistinct = stats->stadistinct;
874 ndistinct = -ndistinct * rel->tuples;
877 * Adjust ndistinct to account for restriction clauses. Observe we are
878 * assuming that the data distribution is affected uniformly by the
879 * restriction clauses!
881 * XXX Possibly better way, but much more expensive: multiply by
882 * selectivity of rel's restriction clauses that mention the target Var.
884 ndistinct *= rel->rows / rel->tuples;
887 * Discourage use of hash join if there seem not to be very many distinct
888 * data values. The threshold here is somewhat arbitrary, as is the
889 * fraction used to "discourage" the choice.
891 if (ndistinct < 50.0)
893 ReleaseSysCache(tuple);
898 * Form initial estimate of bucketsize fraction. Here we use rel->rows,
899 * ie the number of rows after applying restriction clauses, because
900 * that's what the fraction will eventually be multiplied by in
903 estfract = (double) NTUP_PER_BUCKET / rel->rows;
906 * Adjust estimated bucketsize if too few distinct values to fill
909 needdistinct = rel->rows / (double) NTUP_PER_BUCKET;
910 if (ndistinct < needdistinct)
911 estfract *= needdistinct / ndistinct;
914 * Look up the frequency of the most common value, if available.
918 if (get_attstatsslot(tuple, var->vartype, var->vartypmod,
919 STATISTIC_KIND_MCV, InvalidOid,
920 NULL, NULL, &numbers, &nnumbers))
923 * The first MCV stat is for the most common value.
926 mcvfreq = numbers[0];
927 free_attstatsslot(var->vartype, NULL, 0,
932 * Adjust estimated bucketsize upward to account for skewed distribution.
934 avgfreq = (1.0 - stats->stanullfrac) / ndistinct;
936 if (avgfreq > 0.0 && mcvfreq > avgfreq)
937 estfract *= mcvfreq / avgfreq;
939 ReleaseSysCache(tuple);
941 return (Selectivity) estfract;
947 * Estimate the CPU cost of evaluating a WHERE clause (once).
948 * The input can be either an implicitly-ANDed list of boolean
949 * expressions, or a list of RestrictInfo nodes.
952 cost_qual_eval(List *quals)
957 /* We don't charge any cost for the implicit ANDing at top level ... */
961 Node *qual = (Node *) lfirst(l);
964 * RestrictInfo nodes contain an eval_cost field reserved for this
965 * routine's use, so that it's not necessary to evaluate the qual
966 * clause's cost more than once. If the clause's cost hasn't been
967 * computed yet, the field will contain -1.
969 if (qual && IsA(qual, RestrictInfo))
971 RestrictInfo *restrictinfo = (RestrictInfo *) qual;
973 if (restrictinfo->eval_cost < 0)
975 restrictinfo->eval_cost = 0;
976 cost_qual_eval_walker((Node *) restrictinfo->clause,
977 &restrictinfo->eval_cost);
979 total += restrictinfo->eval_cost;
983 /* If it's a bare expression, must always do it the hard way */
984 cost_qual_eval_walker(qual, &total);
991 cost_qual_eval_walker(Node *node, Cost *total)
997 * Our basic strategy is to charge one cpu_operator_cost for each
998 * operator or function node in the given tree. Vars and Consts are
999 * charged zero, and so are boolean operators (AND, OR, NOT).
1000 * Simplistic, but a lot better than no model at all.
1002 * Should we try to account for the possibility of short-circuit
1003 * evaluation of AND/OR?
1005 if (IsA(node, Expr))
1007 Expr *expr = (Expr *) node;
1009 switch (expr->opType)
1013 *total += cpu_operator_cost;
1022 * A subplan node in an expression indicates that the
1023 * subplan will be executed on each evaluation, so charge
1024 * accordingly. (We assume that sub-selects that can be
1025 * executed as InitPlans have already been removed from
1028 * NOTE: this logic should agree with the estimates used by
1029 * make_subplan() in plan/subselect.c.
1032 SubPlan *subplan = (SubPlan *) expr->oper;
1033 Plan *plan = subplan->plan;
1036 if (subplan->sublink->subLinkType == EXISTS_SUBLINK)
1038 /* we only need to fetch 1 tuple */
1039 subcost = plan->startup_cost +
1040 (plan->total_cost - plan->startup_cost) / plan->plan_rows;
1042 else if (subplan->sublink->subLinkType == ALL_SUBLINK ||
1043 subplan->sublink->subLinkType == ANY_SUBLINK)
1045 /* assume we need 50% of the tuples */
1046 subcost = plan->startup_cost +
1047 0.50 * (plan->total_cost - plan->startup_cost);
1048 /* XXX what if subplan has been materialized? */
1052 /* assume we need all tuples */
1053 subcost = plan->total_cost;
1059 /* fall through to examine args of Expr node */
1061 return expression_tree_walker(node, cost_qual_eval_walker,
1067 * approx_selectivity
1068 * Quick-and-dirty estimation of clause selectivities.
1069 * The input can be either an implicitly-ANDed list of boolean
1070 * expressions, or a list of RestrictInfo nodes (typically the latter).
1072 * The "quick" part comes from caching the selectivity estimates so we can
1073 * avoid recomputing them later. (Since the same clauses are typically
1074 * examined over and over in different possible join trees, this makes a
1077 * The "dirty" part comes from the fact that the selectivities of multiple
1078 * clauses are estimated independently and multiplied together. Currently,
1079 * clauselist_selectivity can seldom do any better than that anyhow, but
1080 * someday it might be smarter.
1082 * Since we are only using the results to estimate how many potential
1083 * output tuples are generated and passed through qpqual checking, it
1084 * seems OK to live with the approximation.
1087 approx_selectivity(Query *root, List *quals)
1089 Selectivity total = 1.0;
1094 Node *qual = (Node *) lfirst(l);
1098 * RestrictInfo nodes contain a this_selec field reserved for this
1099 * routine's use, so that it's not necessary to evaluate the qual
1100 * clause's selectivity more than once. If the clause's selectivity
1101 * hasn't been computed yet, the field will contain -1.
1103 if (qual && IsA(qual, RestrictInfo))
1105 RestrictInfo *restrictinfo = (RestrictInfo *) qual;
1107 if (restrictinfo->this_selec < 0)
1108 restrictinfo->this_selec =
1109 clause_selectivity(root,
1110 (Node *) restrictinfo->clause,
1112 selec = restrictinfo->this_selec;
1116 /* If it's a bare expression, must always do it the hard way */
1117 selec = clause_selectivity(root, qual, 0);
1126 * set_baserel_size_estimates
1127 * Set the size estimates for the given base relation.
1129 * The rel's targetlist and restrictinfo list must have been constructed
1132 * We set the following fields of the rel node:
1133 * rows: the estimated number of output tuples (after applying
1134 * restriction clauses).
1135 * width: the estimated average output tuple width in bytes.
1136 * baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
1139 set_baserel_size_estimates(Query *root, RelOptInfo *rel)
1141 /* Should only be applied to base relations */
1142 Assert(length(rel->relids) == 1);
1144 rel->rows = rel->tuples *
1145 restrictlist_selectivity(root,
1146 rel->baserestrictinfo,
1147 lfirsti(rel->relids));
1150 * Force estimate to be at least one row, to make explain output look
1151 * better and to avoid possible divide-by-zero when interpolating
1154 if (rel->rows < 1.0)
1157 rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
1159 set_rel_width(root, rel);
1163 * set_joinrel_size_estimates
1164 * Set the size estimates for the given join relation.
1166 * The rel's targetlist must have been constructed already, and a
1167 * restriction clause list that matches the given component rels must
1170 * Since there is more than one way to make a joinrel for more than two
1171 * base relations, the results we get here could depend on which component
1172 * rel pair is provided. In theory we should get the same answers no matter
1173 * which pair is provided; in practice, since the selectivity estimation
1174 * routines don't handle all cases equally well, we might not. But there's
1175 * not much to be done about it. (Would it make sense to repeat the
1176 * calculations for each pair of input rels that's encountered, and somehow
1177 * average the results? Probably way more trouble than it's worth.)
1179 * We set the same relnode fields as set_baserel_size_estimates() does.
1182 set_joinrel_size_estimates(Query *root, RelOptInfo *rel,
1183 RelOptInfo *outer_rel,
1184 RelOptInfo *inner_rel,
1190 /* Start with the Cartesian product */
1191 temp = outer_rel->rows * inner_rel->rows;
1194 * Apply join restrictivity. Note that we are only considering
1195 * clauses that become restriction clauses at this join level; we are
1196 * not double-counting them because they were not considered in
1197 * estimating the sizes of the component rels.
1199 temp *= restrictlist_selectivity(root,
1204 * If we are doing an outer join, take that into account: the output
1205 * must be at least as large as the non-nullable input. (Is there any
1206 * chance of being even smarter?)
1213 if (temp < outer_rel->rows)
1214 temp = outer_rel->rows;
1217 if (temp < inner_rel->rows)
1218 temp = inner_rel->rows;
1221 if (temp < outer_rel->rows)
1222 temp = outer_rel->rows;
1223 if (temp < inner_rel->rows)
1224 temp = inner_rel->rows;
1227 elog(ERROR, "set_joinrel_size_estimates: unsupported join type %d",
1233 * Force estimate to be at least one row, to make explain output look
1234 * better and to avoid possible divide-by-zero when interpolating
1243 * We could apply set_rel_width() to compute the output tuple width
1244 * from scratch, but at present it's always just the sum of the input
1245 * widths, so why work harder than necessary? If relnode.c is ever
1246 * taught to remove unneeded columns from join targetlists, go back to
1247 * using set_rel_width here.
1249 rel->width = outer_rel->width + inner_rel->width;
1254 * Set the estimated output width of the relation.
1256 * NB: this works best on base relations because it prefers to look at
1257 * real Vars. It will fail to make use of pg_statistic info when applied
1258 * to a subquery relation, even if the subquery outputs are simple vars
1259 * that we could have gotten info for. Is it worth trying to be smarter
1263 set_rel_width(Query *root, RelOptInfo *rel)
1265 int32 tuple_width = 0;
1268 foreach(tllist, rel->targetlist)
1270 TargetEntry *tle = (TargetEntry *) lfirst(tllist);
1274 * If it's a Var, try to get statistical info from pg_statistic.
1276 if (tle->expr && IsA(tle->expr, Var))
1278 Var *var = (Var *) tle->expr;
1281 relid = getrelid(var->varno, root->rtable);
1282 if (relid != InvalidOid)
1284 item_width = get_attavgwidth(relid, var->varattno);
1287 tuple_width += item_width;
1293 * Not a Var, or can't find statistics for it. Estimate using
1294 * just the type info.
1296 item_width = get_typavgwidth(tle->resdom->restype,
1297 tle->resdom->restypmod);
1298 Assert(item_width > 0);
1299 tuple_width += item_width;
1301 Assert(tuple_width >= 0);
1302 rel->width = tuple_width;
1306 * relation_byte_size
1307 * Estimate the storage space in bytes for a given number of tuples
1308 * of a given width (size in bytes).
1311 relation_byte_size(double tuples, int width)
1313 return tuples * ((double) MAXALIGN(width + sizeof(HeapTupleData)));
1318 * Returns an estimate of the number of pages covered by a given
1319 * number of tuples of a given width (size in bytes).
1322 page_size(double tuples, int width)
1324 return ceil(relation_byte_size(tuples, width) / BLCKSZ);