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 1.90 2002/09/04 20:31:20 momjian 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_nestloop = true;
83 bool enable_mergejoin = true;
84 bool enable_hashjoin = true;
87 static Selectivity estimate_hash_bucketsize(Query *root, Var *var);
88 static bool cost_qual_eval_walker(Node *node, Cost *total);
89 static Selectivity approx_selectivity(Query *root, List *quals);
90 static void set_rel_width(Query *root, RelOptInfo *rel);
91 static double relation_byte_size(double tuples, int width);
92 static double page_size(double tuples, int width);
97 * Determines and returns the cost of scanning a relation sequentially.
99 * Note: for historical reasons, this routine and the others in this module
100 * use the passed result Path only to store their startup_cost and total_cost
101 * results into. All the input data they need is passed as separate
102 * parameters, even though much of it could be extracted from the Path.
105 cost_seqscan(Path *path, Query *root,
108 Cost startup_cost = 0;
112 /* Should only be applied to base relations */
113 Assert(length(baserel->relids) == 1);
114 Assert(baserel->rtekind == RTE_RELATION);
117 startup_cost += disable_cost;
122 * The cost of reading a page sequentially is 1.0, by definition. Note
123 * that the Unix kernel will typically do some amount of read-ahead
124 * optimization, so that this cost is less than the true cost of
125 * reading a page from disk. We ignore that issue here, but must take
126 * it into account when estimating the cost of non-sequential
129 run_cost += baserel->pages; /* sequential fetches with cost 1.0 */
132 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
133 run_cost += cpu_per_tuple * baserel->tuples;
135 path->startup_cost = startup_cost;
136 path->total_cost = startup_cost + run_cost;
140 * cost_nonsequential_access
141 * Estimate the cost of accessing one page at random from a relation
142 * (or sort temp file) of the given size in pages.
144 * The simplistic model that the cost is random_page_cost is what we want
145 * to use for large relations; but for small ones that is a serious
146 * overestimate because of the effects of caching. This routine tries to
149 * Unfortunately we don't have any good way of estimating the effective cache
150 * size we are working with --- we know that Postgres itself has NBuffers
151 * internal buffers, but the size of the kernel's disk cache is uncertain,
152 * and how much of it we get to use is even less certain. We punt the problem
153 * for now by assuming we are given an effective_cache_size parameter.
155 * Given a guesstimated cache size, we estimate the actual I/O cost per page
156 * with the entirely ad-hoc equations:
157 * if relpages >= effective_cache_size:
158 * random_page_cost * (1 - (effective_cache_size/relpages)/2)
159 * if relpages < effective_cache_size:
160 * 1 + (random_page_cost/2-1) * (relpages/effective_cache_size) ** 2
161 * These give the right asymptotic behavior (=> 1.0 as relpages becomes
162 * small, => random_page_cost as it becomes large) and meet in the middle
163 * with the estimate that the cache is about 50% effective for a relation
164 * of the same size as effective_cache_size. (XXX this is probably all
165 * wrong, but I haven't been able to find any theory about how effective
166 * a disk cache should be presumed to be.)
169 cost_nonsequential_access(double relpages)
173 /* don't crash on bad input data */
174 if (relpages <= 0.0 || effective_cache_size <= 0.0)
175 return random_page_cost;
177 relsize = relpages / effective_cache_size;
180 return random_page_cost * (1.0 - 0.5 / relsize);
182 return 1.0 + (random_page_cost * 0.5 - 1.0) * relsize * relsize;
187 * Determines and returns the cost of scanning a relation using an index.
189 * NOTE: an indexscan plan node can actually represent several passes,
190 * but here we consider the cost of just one pass.
192 * 'root' is the query root
193 * 'baserel' is the base relation the index is for
194 * 'index' is the index to be used
195 * 'indexQuals' is the list of applicable qual clauses (implicit AND semantics)
196 * 'is_injoin' is T if we are considering using the index scan as the inside
197 * of a nestloop join (hence, some of the indexQuals are join clauses)
199 * NOTE: 'indexQuals' must contain only clauses usable as index restrictions.
200 * Any additional quals evaluated as qpquals may reduce the number of returned
201 * tuples, but they won't reduce the number of tuples we have to fetch from
202 * the table, so they don't reduce the scan cost.
205 cost_index(Path *path, Query *root,
211 Cost startup_cost = 0;
213 Cost indexStartupCost;
215 Selectivity indexSelectivity;
216 double indexCorrelation,
221 double tuples_fetched;
222 double pages_fetched;
226 /* Should only be applied to base relations */
227 Assert(IsA(baserel, RelOptInfo) &&
228 IsA(index, IndexOptInfo));
229 Assert(length(baserel->relids) == 1);
230 Assert(baserel->rtekind == RTE_RELATION);
232 if (!enable_indexscan && !is_injoin)
233 startup_cost += disable_cost;
236 * Call index-access-method-specific code to estimate the processing
237 * cost for scanning the index, as well as the selectivity of the
238 * index (ie, the fraction of main-table tuples we will have to
239 * retrieve) and its correlation to the main-table tuple order.
241 OidFunctionCall8(index->amcostestimate,
242 PointerGetDatum(root),
243 PointerGetDatum(baserel),
244 PointerGetDatum(index),
245 PointerGetDatum(indexQuals),
246 PointerGetDatum(&indexStartupCost),
247 PointerGetDatum(&indexTotalCost),
248 PointerGetDatum(&indexSelectivity),
249 PointerGetDatum(&indexCorrelation));
251 /* all costs for touching index itself included here */
252 startup_cost += indexStartupCost;
253 run_cost += indexTotalCost - indexStartupCost;
256 * Estimate number of main-table tuples and pages fetched.
258 * When the index ordering is uncorrelated with the table ordering,
259 * we use an approximation proposed by Mackert and Lohman, "Index Scans
260 * Using a Finite LRU Buffer: A Validated I/O Model", ACM Transactions
261 * on Database Systems, Vol. 14, No. 3, September 1989, Pages 401-424.
262 * The Mackert and Lohman approximation is that the number of pages
265 * min(2TNs/(2T+Ns), T) when T <= b
266 * 2TNs/(2T+Ns) when T > b and Ns <= 2Tb/(2T-b)
267 * b + (Ns - 2Tb/(2T-b))*(T-b)/T when T > b and Ns > 2Tb/(2T-b)
269 * T = # pages in table
270 * N = # tuples in table
271 * s = selectivity = fraction of table to be scanned
272 * b = # buffer pages available (we include kernel space here)
274 * When the index ordering is exactly correlated with the table ordering
275 * (just after a CLUSTER, for example), the number of pages fetched should
276 * be just sT. What's more, these will be sequential fetches, not the
277 * random fetches that occur in the uncorrelated case. So, depending on
278 * the extent of correlation, we should estimate the actual I/O cost
279 * somewhere between s * T * 1.0 and PF * random_cost. We currently
280 * interpolate linearly between these two endpoints based on the
281 * correlation squared (XXX is that appropriate?).
283 * In any case the number of tuples fetched is Ns.
287 tuples_fetched = indexSelectivity * baserel->tuples;
288 /* Don't believe estimates less than 1... */
289 if (tuples_fetched < 1.0)
290 tuples_fetched = 1.0;
292 /* This part is the Mackert and Lohman formula */
294 T = (baserel->pages > 1) ? (double) baserel->pages : 1.0;
295 b = (effective_cache_size > 1) ? effective_cache_size : 1.0;
300 (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
301 if (pages_fetched > T)
308 lim = (2.0 * T * b) / (2.0 * T - b);
309 if (tuples_fetched <= lim)
312 (2.0 * T * tuples_fetched) / (2.0 * T + tuples_fetched);
317 b + (tuples_fetched - lim) * (T - b) / T;
322 * min_IO_cost corresponds to the perfectly correlated case
323 * (csquared=1), max_IO_cost to the perfectly uncorrelated case
324 * (csquared=0). Note that we just charge random_page_cost per page
325 * in the uncorrelated case, rather than using
326 * cost_nonsequential_access, since we've already accounted for
327 * caching effects by using the Mackert model.
329 min_IO_cost = ceil(indexSelectivity * T);
330 max_IO_cost = pages_fetched * random_page_cost;
333 * Now interpolate based on estimated index order correlation to get
334 * total disk I/O cost for main table accesses.
336 csquared = indexCorrelation * indexCorrelation;
338 run_cost += max_IO_cost + csquared * (min_IO_cost - max_IO_cost);
341 * Estimate CPU costs per tuple.
343 * Normally the indexquals will be removed from the list of restriction
344 * clauses that we have to evaluate as qpquals, so we should subtract
345 * their costs from baserestrictcost. XXX For a lossy index, not all
346 * the quals will be removed and so we really shouldn't subtract their
347 * costs; but detecting that seems more expensive than it's worth.
348 * Also, if we are doing a join then some of the indexquals are join
349 * clauses and shouldn't be subtracted. Rather than work out exactly
350 * how much to subtract, we don't subtract anything.
352 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
355 cpu_per_tuple -= cost_qual_eval(indexQuals);
357 run_cost += cpu_per_tuple * tuples_fetched;
359 path->startup_cost = startup_cost;
360 path->total_cost = startup_cost + run_cost;
365 * Determines and returns the cost of scanning a relation using TIDs.
368 cost_tidscan(Path *path, Query *root,
369 RelOptInfo *baserel, List *tideval)
371 Cost startup_cost = 0;
374 int ntuples = length(tideval);
376 /* Should only be applied to base relations */
377 Assert(length(baserel->relids) == 1);
378 Assert(baserel->rtekind == RTE_RELATION);
381 startup_cost += disable_cost;
383 /* disk costs --- assume each tuple on a different page */
384 run_cost += random_page_cost * ntuples;
387 cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost;
388 run_cost += cpu_per_tuple * ntuples;
390 path->startup_cost = startup_cost;
391 path->total_cost = startup_cost + run_cost;
396 * Determines and returns the cost of scanning a function RTE.
399 cost_functionscan(Path *path, Query *root, RelOptInfo *baserel)
401 Cost startup_cost = 0;
405 /* Should only be applied to base relations that are functions */
406 Assert(length(baserel->relids) == 1);
407 Assert(baserel->rtekind == RTE_FUNCTION);
410 * For now, estimate function's cost at one operator eval per function
411 * call. Someday we should revive the function cost estimate columns
414 cpu_per_tuple = cpu_operator_cost;
416 /* Add scanning CPU costs */
417 cpu_per_tuple += cpu_tuple_cost + baserel->baserestrictcost;
418 run_cost += cpu_per_tuple * baserel->tuples;
420 path->startup_cost = startup_cost;
421 path->total_cost = startup_cost + run_cost;
426 * Determines and returns the cost of sorting a relation.
428 * The cost of supplying the input data is NOT included; the caller should
429 * add that cost to both startup and total costs returned from this routine!
431 * If the total volume of data to sort is less than SortMem, we will do
432 * an in-memory sort, which requires no I/O and about t*log2(t) tuple
433 * comparisons for t tuples.
435 * If the total volume exceeds SortMem, we switch to a tape-style merge
436 * algorithm. There will still be about t*log2(t) tuple comparisons in
437 * total, but we will also need to write and read each tuple once per
438 * merge pass. We expect about ceil(log6(r)) merge passes where r is the
439 * number of initial runs formed (log6 because tuplesort.c uses six-tape
440 * merging). Since the average initial run should be about twice SortMem,
442 * disk traffic = 2 * relsize * ceil(log6(p / (2*SortMem)))
443 * cpu = comparison_cost * t * log2(t)
445 * The disk traffic is assumed to be half sequential and half random
446 * accesses (XXX can't we refine that guess?)
448 * We charge two operator evals per tuple comparison, which should be in
449 * the right ballpark in most cases.
451 * 'pathkeys' is a list of sort keys
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.
461 cost_sort(Path *path, Query *root,
462 List *pathkeys, double tuples, int width)
464 Cost startup_cost = 0;
466 double nbytes = relation_byte_size(tuples, width);
467 long sortmembytes = SortMem * 1024L;
470 startup_cost += disable_cost;
473 * We want to be sure the cost of a sort is never estimated as zero,
474 * even if passed-in tuple count is zero. Besides, mustn't do
483 * Assume about two operator evals per tuple comparison and N log2 N
486 startup_cost += 2.0 * cpu_operator_cost * tuples * LOG2(tuples);
489 if (nbytes > sortmembytes)
491 double npages = ceil(nbytes / BLCKSZ);
492 double nruns = nbytes / (sortmembytes * 2);
493 double log_runs = ceil(LOG6(nruns));
494 double npageaccesses;
498 npageaccesses = 2.0 * npages * log_runs;
499 /* Assume half are sequential (cost 1), half are not */
500 startup_cost += npageaccesses *
501 (1.0 + cost_nonsequential_access(npages)) * 0.5;
505 * Also charge a small amount (arbitrarily set equal to operator cost)
506 * per extracted tuple.
508 run_cost += cpu_operator_cost * tuples;
510 path->startup_cost = startup_cost;
511 path->total_cost = startup_cost + run_cost;
517 * Determines and returns the cost of joining two relations using the
518 * nested loop algorithm.
520 * 'outer_path' is the path for the outer relation
521 * 'inner_path' is the path for the inner relation
522 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
525 cost_nestloop(Path *path, Query *root,
530 Cost startup_cost = 0;
535 if (!enable_nestloop)
536 startup_cost += disable_cost;
538 /* cost of source data */
541 * NOTE: clearly, we must pay both outer and inner paths' startup_cost
542 * before we can start returning tuples, so the join's startup cost is
543 * their sum. What's not so clear is whether the inner path's
544 * startup_cost must be paid again on each rescan of the inner path.
545 * This is not true if the inner path is materialized, but probably is
546 * true otherwise. Since we don't yet have clean handling of the
547 * decision whether to materialize a path, we can't tell here which
548 * will happen. As a compromise, charge 50% of the inner startup cost
551 startup_cost += outer_path->startup_cost + inner_path->startup_cost;
552 run_cost += outer_path->total_cost - outer_path->startup_cost;
553 run_cost += outer_path->parent->rows *
554 (inner_path->total_cost - inner_path->startup_cost);
555 if (outer_path->parent->rows > 1)
556 run_cost += (outer_path->parent->rows - 1) *
557 inner_path->startup_cost * 0.5;
560 * Number of tuples processed (not number emitted!). If inner path is
561 * an indexscan, be sure to use its estimated output row count, which
562 * may be lower than the restriction-clause-only row count of its
565 if (IsA(inner_path, IndexPath))
566 ntuples = ((IndexPath *) inner_path)->rows;
568 ntuples = inner_path->parent->rows;
569 ntuples *= outer_path->parent->rows;
572 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
573 run_cost += cpu_per_tuple * ntuples;
575 path->startup_cost = startup_cost;
576 path->total_cost = startup_cost + run_cost;
581 * Determines and returns the cost of joining two relations using the
582 * merge join algorithm.
584 * 'outer_path' is the path for the outer relation
585 * 'inner_path' is the path for the inner relation
586 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
587 * 'mergeclauses' are the RestrictInfo nodes to use as merge clauses
588 * (this should be a subset of the restrictlist)
589 * 'outersortkeys' and 'innersortkeys' are lists of the keys to be used
590 * to sort the outer and inner relations, or NIL if no explicit
591 * sort is needed because the source path is already ordered
594 cost_mergejoin(Path *path, Query *root,
602 Cost startup_cost = 0;
605 RestrictInfo *firstclause;
610 Selectivity outerscansel,
612 Path sort_path; /* dummy for result of cost_sort */
614 if (!enable_mergejoin)
615 startup_cost += disable_cost;
618 * A merge join will stop as soon as it exhausts either input stream.
619 * Estimate fraction of the left and right inputs that will actually
620 * need to be scanned. We use only the first (most significant) merge
621 * clause for this purpose.
623 * Since this calculation is somewhat expensive, and will be the same for
624 * all mergejoin paths associated with the merge clause, we cache the
625 * results in the RestrictInfo node.
627 firstclause = (RestrictInfo *) lfirst(mergeclauses);
628 if (firstclause->left_mergescansel < 0) /* not computed yet? */
629 mergejoinscansel(root, (Node *) firstclause->clause,
630 &firstclause->left_mergescansel,
631 &firstclause->right_mergescansel);
633 leftvar = get_leftop(firstclause->clause);
634 Assert(IsA(leftvar, Var));
635 if (VARISRELMEMBER(leftvar->varno, outer_path->parent))
637 /* left side of clause is outer */
638 outerscansel = firstclause->left_mergescansel;
639 innerscansel = firstclause->right_mergescansel;
643 /* left side of clause is inner */
644 outerscansel = firstclause->right_mergescansel;
645 innerscansel = firstclause->left_mergescansel;
648 outer_rows = outer_path->parent->rows * outerscansel;
649 inner_rows = inner_path->parent->rows * innerscansel;
651 /* cost of source data */
654 * Note we are assuming that each source tuple is fetched just once,
655 * which is not right in the presence of equal keys. If we had a way
656 * of estimating the proportion of equal keys, we could apply a
657 * correction factor...
659 if (outersortkeys) /* do we need to sort outer? */
661 startup_cost += outer_path->total_cost;
662 cost_sort(&sort_path,
665 outer_path->parent->rows,
666 outer_path->parent->width);
667 startup_cost += sort_path.startup_cost;
668 run_cost += (sort_path.total_cost - sort_path.startup_cost)
673 startup_cost += outer_path->startup_cost;
674 run_cost += (outer_path->total_cost - outer_path->startup_cost)
678 if (innersortkeys) /* do we need to sort inner? */
680 startup_cost += inner_path->total_cost;
681 cost_sort(&sort_path,
684 inner_path->parent->rows,
685 inner_path->parent->width);
686 startup_cost += sort_path.startup_cost;
687 run_cost += (sort_path.total_cost - sort_path.startup_cost)
692 startup_cost += inner_path->startup_cost;
693 run_cost += (inner_path->total_cost - inner_path->startup_cost)
698 * The number of tuple comparisons needed depends drastically on the
699 * number of equal keys in the two source relations, which we have no
700 * good way of estimating. (XXX could the MCV statistics help?)
701 * Somewhat arbitrarily, we charge one tuple comparison (one
702 * cpu_operator_cost) for each tuple in the two source relations.
703 * This is probably a lower bound.
705 run_cost += cpu_operator_cost * (outer_rows + inner_rows);
708 * For each tuple that gets through the mergejoin proper, we charge
709 * cpu_tuple_cost plus the cost of evaluating additional restriction
710 * clauses that are to be applied at the join. It's OK to use an
711 * approximate selectivity here, since in most cases this is a minor
712 * component of the cost. NOTE: it's correct to use the unscaled rows
713 * counts here, not the scaled-down counts we obtained above.
715 ntuples = approx_selectivity(root, mergeclauses) *
716 outer_path->parent->rows * inner_path->parent->rows;
719 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
720 run_cost += cpu_per_tuple * ntuples;
722 path->startup_cost = startup_cost;
723 path->total_cost = startup_cost + run_cost;
728 * Determines and returns the cost of joining two relations using the
729 * hash join algorithm.
731 * 'outer_path' is the path for the outer relation
732 * 'inner_path' is the path for the inner relation
733 * 'restrictlist' are the RestrictInfo nodes to be applied at the join
734 * 'hashclauses' is a list of the hash join clause (always a 1-element list)
735 * (this should be a subset of the restrictlist)
738 cost_hashjoin(Path *path, Query *root,
744 Cost startup_cost = 0;
748 double outerbytes = relation_byte_size(outer_path->parent->rows,
749 outer_path->parent->width);
750 double innerbytes = relation_byte_size(inner_path->parent->rows,
751 inner_path->parent->width);
752 long hashtablebytes = SortMem * 1024L;
753 RestrictInfo *restrictinfo;
756 Selectivity innerbucketsize;
758 if (!enable_hashjoin)
759 startup_cost += disable_cost;
761 /* cost of source data */
762 startup_cost += outer_path->startup_cost;
763 run_cost += outer_path->total_cost - outer_path->startup_cost;
764 startup_cost += inner_path->total_cost;
766 /* cost of computing hash function: must do it once per input tuple */
767 startup_cost += cpu_operator_cost * inner_path->parent->rows;
768 run_cost += cpu_operator_cost * outer_path->parent->rows;
771 * Determine bucketsize fraction for inner relation. First we have to
772 * figure out which side of the hashjoin clause is the inner side.
774 Assert(length(hashclauses) == 1);
775 Assert(IsA(lfirst(hashclauses), RestrictInfo));
776 restrictinfo = (RestrictInfo *) lfirst(hashclauses);
777 /* these must be OK, since check_hashjoinable accepted the clause */
778 left = get_leftop(restrictinfo->clause);
779 right = get_rightop(restrictinfo->clause);
782 * Since we tend to visit the same clauses over and over when planning
783 * a large query, we cache the bucketsize estimate in the RestrictInfo
784 * node to avoid repeated lookups of statistics.
786 if (VARISRELMEMBER(right->varno, inner_path->parent))
788 /* righthand side is inner */
789 innerbucketsize = restrictinfo->right_bucketsize;
790 if (innerbucketsize < 0)
793 innerbucketsize = estimate_hash_bucketsize(root, right);
794 restrictinfo->right_bucketsize = innerbucketsize;
799 Assert(VARISRELMEMBER(left->varno, inner_path->parent));
800 /* lefthand side is inner */
801 innerbucketsize = restrictinfo->left_bucketsize;
802 if (innerbucketsize < 0)
805 innerbucketsize = estimate_hash_bucketsize(root, left);
806 restrictinfo->left_bucketsize = innerbucketsize;
811 * The number of tuple comparisons needed is the number of outer
812 * tuples times the typical number of tuples in a hash bucket, which
813 * is the inner relation size times its bucketsize fraction. We charge
814 * one cpu_operator_cost per tuple comparison.
816 run_cost += cpu_operator_cost * outer_path->parent->rows *
817 ceil(inner_path->parent->rows * innerbucketsize);
820 * For each tuple that gets through the hashjoin proper, we charge
821 * cpu_tuple_cost plus the cost of evaluating additional restriction
822 * clauses that are to be applied at the join. It's OK to use an
823 * approximate selectivity here, since in most cases this is a minor
824 * component of the cost.
826 ntuples = approx_selectivity(root, hashclauses) *
827 outer_path->parent->rows * inner_path->parent->rows;
830 cpu_per_tuple = cpu_tuple_cost + cost_qual_eval(restrictlist);
831 run_cost += cpu_per_tuple * ntuples;
834 * if inner relation is too big then we will need to "batch" the join,
835 * which implies writing and reading most of the tuples to disk an
836 * extra time. Charge one cost unit per page of I/O (correct since it
837 * should be nice and sequential...). Writing the inner rel counts as
838 * startup cost, all the rest as run cost.
840 if (innerbytes > hashtablebytes)
842 double outerpages = page_size(outer_path->parent->rows,
843 outer_path->parent->width);
844 double innerpages = page_size(inner_path->parent->rows,
845 inner_path->parent->width);
847 startup_cost += innerpages;
848 run_cost += innerpages + 2 * outerpages;
852 * Bias against putting larger relation on inside. We don't want an
853 * absolute prohibition, though, since larger relation might have
854 * better bucketsize --- and we can't trust the size estimates
855 * unreservedly, anyway. Instead, inflate the startup cost by the
856 * square root of the size ratio. (Why square root? No real good
857 * reason, but it seems reasonable...)
859 if (innerbytes > outerbytes && outerbytes > 0)
860 startup_cost *= sqrt(innerbytes / outerbytes);
862 path->startup_cost = startup_cost;
863 path->total_cost = startup_cost + run_cost;
867 * Estimate hash bucketsize fraction (ie, number of entries in a bucket
868 * divided by total tuples in relation) if the specified Var is used
871 * XXX This is really pretty bogus since we're effectively assuming that the
872 * distribution of hash keys will be the same after applying restriction
873 * clauses as it was in the underlying relation. However, we are not nearly
874 * smart enough to figure out how the restrict clauses might change the
875 * distribution, so this will have to do for now.
877 * We can get the number of buckets the executor will use for the given
878 * input relation. If the data were perfectly distributed, with the same
879 * number of tuples going into each available bucket, then the bucketsize
880 * fraction would be 1/nbuckets. But this happy state of affairs will occur
881 * only if (a) there are at least nbuckets distinct data values, and (b)
882 * we have a not-too-skewed data distribution. Otherwise the buckets will
883 * be nonuniformly occupied. If the other relation in the join has a key
884 * distribution similar to this one's, then the most-loaded buckets are
885 * exactly those that will be probed most often. Therefore, the "average"
886 * bucket size for costing purposes should really be taken as something close
887 * to the "worst case" bucket size. We try to estimate this by adjusting the
888 * fraction if there are too few distinct data values, and then scaling up
889 * by the ratio of the most common value's frequency to the average frequency.
891 * If no statistics are available, use a default estimate of 0.1. This will
892 * discourage use of a hash rather strongly if the inner relation is large,
893 * which is what we want. We do not want to hash unless we know that the
894 * inner rel is well-dispersed (or the alternatives seem much worse).
897 estimate_hash_bucketsize(Query *root, Var *var)
905 Form_pg_statistic stats;
914 * Lookup info about var's relation and attribute; if none available,
915 * return default estimate.
920 relid = getrelid(var->varno, root->rtable);
921 if (relid == InvalidOid)
924 rel = find_base_rel(root, var->varno);
926 if (rel->tuples <= 0.0 || rel->rows <= 0.0)
927 return 0.1; /* ensure we can divide below */
929 /* Get hash table size that executor would use for this relation */
930 ExecChooseHashTableSize(rel->rows, rel->width,
935 tuple = SearchSysCache(STATRELATT,
936 ObjectIdGetDatum(relid),
937 Int16GetDatum(var->varattno),
939 if (!HeapTupleIsValid(tuple))
942 * Perhaps the Var is a system attribute; if so, it will have no
943 * entry in pg_statistic, but we may be able to guess something
944 * about its distribution anyway.
946 switch (var->varattno)
948 case ObjectIdAttributeNumber:
949 case SelfItemPointerAttributeNumber:
950 /* these are unique, so buckets should be well-distributed */
951 return 1.0 / (double) virtualbuckets;
952 case TableOidAttributeNumber:
953 /* hashing this is a terrible idea... */
958 stats = (Form_pg_statistic) GETSTRUCT(tuple);
961 * Obtain number of distinct data values in raw relation.
963 ndistinct = stats->stadistinct;
965 ndistinct = -ndistinct * rel->tuples;
967 if (ndistinct <= 0.0) /* ensure we can divide */
969 ReleaseSysCache(tuple);
973 /* Also compute avg freq of all distinct data values in raw relation */
974 avgfreq = (1.0 - stats->stanullfrac) / ndistinct;
977 * Adjust ndistinct to account for restriction clauses. Observe we
978 * are assuming that the data distribution is affected uniformly by
979 * the restriction clauses!
981 * XXX Possibly better way, but much more expensive: multiply by
982 * selectivity of rel's restriction clauses that mention the target
985 ndistinct *= rel->rows / rel->tuples;
988 * Initial estimate of bucketsize fraction is 1/nbuckets as long as
989 * the number of buckets is less than the expected number of distinct
990 * values; otherwise it is 1/ndistinct.
992 if (ndistinct > (double) virtualbuckets)
993 estfract = 1.0 / (double) virtualbuckets;
995 estfract = 1.0 / ndistinct;
998 * Look up the frequency of the most common value, if available.
1002 if (get_attstatsslot(tuple, var->vartype, var->vartypmod,
1003 STATISTIC_KIND_MCV, InvalidOid,
1004 NULL, NULL, &numbers, &nnumbers))
1007 * The first MCV stat is for the most common value.
1010 mcvfreq = numbers[0];
1011 free_attstatsslot(var->vartype, NULL, 0,
1016 * Adjust estimated bucketsize upward to account for skewed
1019 if (avgfreq > 0.0 && mcvfreq > avgfreq)
1020 estfract *= mcvfreq / avgfreq;
1022 ReleaseSysCache(tuple);
1024 return (Selectivity) estfract;
1030 * Estimate the CPU cost of evaluating a WHERE clause (once).
1031 * The input can be either an implicitly-ANDed list of boolean
1032 * expressions, or a list of RestrictInfo nodes.
1035 cost_qual_eval(List *quals)
1040 /* We don't charge any cost for the implicit ANDing at top level ... */
1044 Node *qual = (Node *) lfirst(l);
1047 * RestrictInfo nodes contain an eval_cost field reserved for this
1048 * routine's use, so that it's not necessary to evaluate the qual
1049 * clause's cost more than once. If the clause's cost hasn't been
1050 * computed yet, the field will contain -1.
1052 if (qual && IsA(qual, RestrictInfo))
1054 RestrictInfo *restrictinfo = (RestrictInfo *) qual;
1056 if (restrictinfo->eval_cost < 0)
1058 restrictinfo->eval_cost = 0;
1059 cost_qual_eval_walker((Node *) restrictinfo->clause,
1060 &restrictinfo->eval_cost);
1062 total += restrictinfo->eval_cost;
1066 /* If it's a bare expression, must always do it the hard way */
1067 cost_qual_eval_walker(qual, &total);
1074 cost_qual_eval_walker(Node *node, Cost *total)
1080 * Our basic strategy is to charge one cpu_operator_cost for each
1081 * operator or function node in the given tree. Vars and Consts are
1082 * charged zero, and so are boolean operators (AND, OR, NOT).
1083 * Simplistic, but a lot better than no model at all.
1085 * Should we try to account for the possibility of short-circuit
1086 * evaluation of AND/OR?
1088 if (IsA(node, Expr))
1090 Expr *expr = (Expr *) node;
1092 switch (expr->opType)
1097 *total += cpu_operator_cost;
1106 * A subplan node in an expression indicates that the
1107 * subplan will be executed on each evaluation, so charge
1108 * accordingly. (We assume that sub-selects that can be
1109 * executed as InitPlans have already been removed from
1112 * NOTE: this logic should agree with the estimates used by
1113 * make_subplan() in plan/subselect.c.
1116 SubPlan *subplan = (SubPlan *) expr->oper;
1117 Plan *plan = subplan->plan;
1120 if (subplan->sublink->subLinkType == EXISTS_SUBLINK)
1122 /* we only need to fetch 1 tuple */
1123 subcost = plan->startup_cost +
1124 (plan->total_cost - plan->startup_cost) / plan->plan_rows;
1126 else if (subplan->sublink->subLinkType == ALL_SUBLINK ||
1127 subplan->sublink->subLinkType == ANY_SUBLINK)
1129 /* assume we need 50% of the tuples */
1130 subcost = plan->startup_cost +
1131 0.50 * (plan->total_cost - plan->startup_cost);
1132 /* XXX what if subplan has been materialized? */
1136 /* assume we need all tuples */
1137 subcost = plan->total_cost;
1143 /* fall through to examine args of Expr node */
1145 return expression_tree_walker(node, cost_qual_eval_walker,
1151 * approx_selectivity
1152 * Quick-and-dirty estimation of clause selectivities.
1153 * The input can be either an implicitly-ANDed list of boolean
1154 * expressions, or a list of RestrictInfo nodes (typically the latter).
1156 * The "quick" part comes from caching the selectivity estimates so we can
1157 * avoid recomputing them later. (Since the same clauses are typically
1158 * examined over and over in different possible join trees, this makes a
1161 * The "dirty" part comes from the fact that the selectivities of multiple
1162 * clauses are estimated independently and multiplied together. Now
1163 * clauselist_selectivity often can't do any better than that anyhow, but
1164 * for some situations (such as range constraints) it is smarter.
1166 * Since we are only using the results to estimate how many potential
1167 * output tuples are generated and passed through qpqual checking, it
1168 * seems OK to live with the approximation.
1171 approx_selectivity(Query *root, List *quals)
1173 Selectivity total = 1.0;
1178 Node *qual = (Node *) lfirst(l);
1182 * RestrictInfo nodes contain a this_selec field reserved for this
1183 * routine's use, so that it's not necessary to evaluate the qual
1184 * clause's selectivity more than once. If the clause's
1185 * selectivity hasn't been computed yet, the field will contain
1188 if (qual && IsA(qual, RestrictInfo))
1190 RestrictInfo *restrictinfo = (RestrictInfo *) qual;
1192 if (restrictinfo->this_selec < 0)
1193 restrictinfo->this_selec =
1194 clause_selectivity(root,
1195 (Node *) restrictinfo->clause,
1197 selec = restrictinfo->this_selec;
1201 /* If it's a bare expression, must always do it the hard way */
1202 selec = clause_selectivity(root, qual, 0);
1211 * set_baserel_size_estimates
1212 * Set the size estimates for the given base relation.
1214 * The rel's targetlist and restrictinfo list must have been constructed
1217 * We set the following fields of the rel node:
1218 * rows: the estimated number of output tuples (after applying
1219 * restriction clauses).
1220 * width: the estimated average output tuple width in bytes.
1221 * baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
1224 set_baserel_size_estimates(Query *root, RelOptInfo *rel)
1226 /* Should only be applied to base relations */
1227 Assert(length(rel->relids) == 1);
1229 rel->rows = rel->tuples *
1230 restrictlist_selectivity(root,
1231 rel->baserestrictinfo,
1232 lfirsti(rel->relids));
1235 * Force estimate to be at least one row, to make explain output look
1236 * better and to avoid possible divide-by-zero when interpolating
1239 if (rel->rows < 1.0)
1242 rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
1244 set_rel_width(root, rel);
1248 * set_joinrel_size_estimates
1249 * Set the size estimates for the given join relation.
1251 * The rel's targetlist must have been constructed already, and a
1252 * restriction clause list that matches the given component rels must
1255 * Since there is more than one way to make a joinrel for more than two
1256 * base relations, the results we get here could depend on which component
1257 * rel pair is provided. In theory we should get the same answers no matter
1258 * which pair is provided; in practice, since the selectivity estimation
1259 * routines don't handle all cases equally well, we might not. But there's
1260 * not much to be done about it. (Would it make sense to repeat the
1261 * calculations for each pair of input rels that's encountered, and somehow
1262 * average the results? Probably way more trouble than it's worth.)
1264 * We set the same relnode fields as set_baserel_size_estimates() does.
1267 set_joinrel_size_estimates(Query *root, RelOptInfo *rel,
1268 RelOptInfo *outer_rel,
1269 RelOptInfo *inner_rel,
1275 /* Start with the Cartesian product */
1276 temp = outer_rel->rows * inner_rel->rows;
1279 * Apply join restrictivity. Note that we are only considering
1280 * clauses that become restriction clauses at this join level; we are
1281 * not double-counting them because they were not considered in
1282 * estimating the sizes of the component rels.
1284 temp *= restrictlist_selectivity(root,
1289 * If we are doing an outer join, take that into account: the output
1290 * must be at least as large as the non-nullable input. (Is there any
1291 * chance of being even smarter?)
1298 if (temp < outer_rel->rows)
1299 temp = outer_rel->rows;
1302 if (temp < inner_rel->rows)
1303 temp = inner_rel->rows;
1306 if (temp < outer_rel->rows)
1307 temp = outer_rel->rows;
1308 if (temp < inner_rel->rows)
1309 temp = inner_rel->rows;
1312 elog(ERROR, "set_joinrel_size_estimates: unsupported join type %d",
1318 * Force estimate to be at least one row, to make explain output look
1319 * better and to avoid possible divide-by-zero when interpolating
1328 * We could apply set_rel_width() to compute the output tuple width
1329 * from scratch, but at present it's always just the sum of the input
1330 * widths, so why work harder than necessary? If relnode.c is ever
1331 * taught to remove unneeded columns from join targetlists, go back to
1332 * using set_rel_width here.
1334 rel->width = outer_rel->width + inner_rel->width;
1338 * set_function_size_estimates
1339 * Set the size estimates for a base relation that is a function call.
1341 * The rel's targetlist and restrictinfo list must have been constructed
1344 * We set the following fields of the rel node:
1345 * rows: the estimated number of output tuples (after applying
1346 * restriction clauses).
1347 * width: the estimated average output tuple width in bytes.
1348 * baserestrictcost: estimated cost of evaluating baserestrictinfo clauses.
1351 set_function_size_estimates(Query *root, RelOptInfo *rel)
1353 /* Should only be applied to base relations that are functions */
1354 Assert(length(rel->relids) == 1);
1355 Assert(rel->rtekind == RTE_FUNCTION);
1358 * Estimate number of rows the function itself will return.
1360 * XXX no idea how to do this yet; but should at least check whether
1361 * function returns set or not...
1365 /* Now estimate number of output rows */
1366 rel->rows = rel->tuples *
1367 restrictlist_selectivity(root,
1368 rel->baserestrictinfo,
1369 lfirsti(rel->relids));
1372 * Force estimate to be at least one row, to make explain output look
1373 * better and to avoid possible divide-by-zero when interpolating
1376 if (rel->rows < 1.0)
1379 rel->baserestrictcost = cost_qual_eval(rel->baserestrictinfo);
1381 set_rel_width(root, rel);
1387 * Set the estimated output width of the relation.
1389 * NB: this works best on base relations because it prefers to look at
1390 * real Vars. It will fail to make use of pg_statistic info when applied
1391 * to a subquery relation, even if the subquery outputs are simple vars
1392 * that we could have gotten info for. Is it worth trying to be smarter
1396 set_rel_width(Query *root, RelOptInfo *rel)
1398 int32 tuple_width = 0;
1401 foreach(tllist, rel->targetlist)
1403 TargetEntry *tle = (TargetEntry *) lfirst(tllist);
1407 * If it's a Var, try to get statistical info from pg_statistic.
1409 if (tle->expr && IsA(tle->expr, Var))
1411 Var *var = (Var *) tle->expr;
1414 relid = getrelid(var->varno, root->rtable);
1415 if (relid != InvalidOid)
1417 item_width = get_attavgwidth(relid, var->varattno);
1420 tuple_width += item_width;
1427 * Not a Var, or can't find statistics for it. Estimate using
1428 * just the type info.
1430 item_width = get_typavgwidth(tle->resdom->restype,
1431 tle->resdom->restypmod);
1432 Assert(item_width > 0);
1433 tuple_width += item_width;
1435 Assert(tuple_width >= 0);
1436 rel->width = tuple_width;
1440 * relation_byte_size
1441 * Estimate the storage space in bytes for a given number of tuples
1442 * of a given width (size in bytes).
1445 relation_byte_size(double tuples, int width)
1447 return tuples * ((double) MAXALIGN(width + sizeof(HeapTupleData)));
1452 * Returns an estimate of the number of pages covered by a given
1453 * number of tuples of a given width (size in bytes).
1456 page_size(double tuples, int width)
1458 return ceil(relation_byte_size(tuples, width) / BLCKSZ);