MySQL 8.0.32
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27 @file
29 Tracks which tuple streams follow which orders, and in particular whether
30 they follow interesting orders.
32 An interesting order (and/or grouping) is one that we might need to sort by
33 at some point during query execution (e.g. to satisfy an ORDER BY predicate);
34 if the rows already are produced in that order, for instance because we
35 scanned along the right index, we can skip the sort and get a lower cost.
37 We generally follow these papers:
39 [Neu04] Neumann and Moerkotte: “An efficient framework for order
40 optimization”
41 [Neu04b] Neumann and Moerkotte: “A Combined Framework for
42 Grouping and Order Optimization”
44 [Neu04b] is an updated version of [Neu04] that also deals with interesting
45 groupings but omits some details to make more space, so both are needed.
46 A combined and updated version of the same material is available in
47 Moerkotte's “Query compilers” PDF.
49 Some further details, like order homogenization, come from
51 [Sim96] Simmen et al: “Fundamental Techniques for Order Optimization”
53 All three papers deal with the issue of _logical_ orderings, where any
54 row stream may follow more than one order simultaneously, as inferred
55 through functional dependencies (FDs). For instance, if we have an ordering
56 (ab) but also an active FD {a} → c (c is uniquely determined by a,
57 for instance because a is a primary key in the same table as c), this means
58 we also implicitly follow the orders (acb) and (abc). In addition,
59 we trivially follow the orders (a), (ac) and (ab). However, note that we
60 do _not_ necessarily follow the order (cab).
62 Similarly, equivalences, such as WHERE conditions and joins, give rise
63 to a stronger form of FDs. If we have an ordering (ab) and the FD b = c,
64 we can be said to follow (ac), (acb) or (abc). The former would not be
65 inferable from {b} → c and {c} → b alone. Equivalences with constants
66 are perhaps even stronger, e.g. WHERE x=3 would give rise to {} → x,
67 which could extend (a) to (xa), (ax) or (x).
69 Neumann et al solve this by modelling which ordering we're following as a
70 state in a non-deterministic finite state machine (NFSM). By repeatedly
71 applying FDs (which become edges in the NFSM), we can build up all possible
72 orderings from a base (which can be either the empty ordering, ordering from
73 scanning along an index, or one produced by an explicit sort) and then
74 checking whether we are in a state matching the ordering we are interested
75 in. (There can be quite a bit of states, so we need a fair amount of pruning
76 to keep the count manageable, or else performance will suffer.) Of course,
77 since NFSMs are nondeterministic, a base ordering and a set of FDs can
78 necessarily put us in a number of states, so we need to convert the NFSM
79 to a DFSM (using the standard powerset construction for NFAs; see
80 ConvertNFSMToDFSM()). This means that the ordering state for an access path
81 is only a single integer, the DFSM state number. When we activate more FDs,
82 for instance because we apply joins, we will move throughout the DFSM into
83 more attractive states. By checking simple precomputed lookup tables,
84 we can quickly find whether a given DFSM state follows a given ordering.
86 The other kind of edges we follow are from the artificial starting state;
87 they represent setting a specific ordering (e.g. because we sort by that
88 ordering). This is set up in the NFSM and preserved in the DFSM.
90 The actual collection of FDs and interesting orders happen outside this
91 class, in the caller.
93 A weakness in the approach is that transitive FDs are not always followed
94 correctly. E.g., if we have an ordering (a), and FDs {a} → b and {b} → c,
95 we will create (ab) and (abc), but _not_ (ac). This is not a problem for
96 equivalences, though, and most of the FDs we collect are equivalences.
97 We do have some heuristics to produce a new FD {a} → c where it is relevant,
98 but they are not always effective.
100 Neumann and Moerkotte distinguish between “tested-for” (O_T) and
101 “producing” (O_P) orderings, where all orders are interesting but only
102 some can be produced by explicit operators, such as sorts. Our implementation
103 is exactly opposite; we allow every ordering to be produced (by means of
104 sort-ahead), but there are orders that can be produced (e.g. when scanning
105 an index) that are not interesting in themselves. Such orders can be
106 pruned away early if we can show they do not produce anything interesting.
109 The operations related to interesting orders, in particular the concept
110 of functional dependencies, are related to the ones we are doing when
111 checking ONLY_FULL_GROUP_BY legality in sql/aggregate_check.h. However,
112 there are some key differences as well:
114 - Orderings are lexical, while groupings are just a bag of attributes.
115 This increases the state space for orderings significantly; groupings
116 can add elements at will and just grow the set freely, while orderings
117 need more care. In particular, this means that groupings only need
118 FDs on the form S → x (where S is a set), while orderings also benefit
119 from those of the type x = y, which replace an element instead of
120 adding a new one.
122 - ONLY_FULL_GROUP_BY is for correctness of rejecting or accepting the
123 query, while interesting orders is just an optimization, so not
124 recognizing rare cases is more acceptable.
126 - ONLY_FULL_GROUP_BY testing only cares about the set of FDs that hold
127 at one specific point (GROUP BY testing, naturally), while interesting
128 orders must be tracked throughout the entire operator tree. In particular,
129 if using interesting orders for merge join, the status at nearly every
130 join is relevant. Also, performance matters much more.
132 Together, these mean that the code ends up being fairly different,
133 and some cases are recognized by ONLY_FULL_GROUP_BY but not by interesting
134 orders. (The actual FD collection happens in BuildInterestingOrders in
135; see the comment there for FD differences.)
137 A note about nomenclature: Like Neumann et al, we use the term “ordering”
138 (and “grouping”) instead of “order”, with the special exception of the
139 already-established term “interesting order”.
140 */
142#include "my_table_map.h"
144#include "sql/mem_root_array.h"
145#include "sql/sql_array.h"
147#include <bitset>
148#include <string>
150// Represents a (potentially interesting) ordering or grouping;
151// OrderElement::direction will signify which one. Immutable,
152// and usually lives on the MEM_ROOT.
155class Window;
158 enum {
159 // A special “empty” kind of edge in the FSM that signifies
160 // adding no functional dependency, ie., a state we can reach
161 // with no further effort. This can happen in two ways:
162 //
163 // 1. An ordering can drop its last element, ie.,
164 // if a tuple stream is ordered on (a,b,c), it is also
165 // ordered on (a,b).
166 // 2. An ordering can be converted to a grouping, i.e,
167 // if a tuple stream is ordered on (a,b,c), it is also
168 // grouped on {a,b,c}.
169 //
170 // head must be empty, tail must be 0. Often called ϵ.
171 // Must be the first in the edge list.
174 // A standard functional dependency {a} → b; if a row tuple
175 // is ordered on all elements of a and this FD is applied,
176 // it is also ordered on b. A typical example is if {a}
177 // is an unique key in a table, and b is a column of the
178 // same table. head can be empty.
181 // An equivalence a = b; implies a → b and b → a, but is
182 // stronger (e.g. if ordered on (a,c), there is also an
183 // ordering on (b,c), which wouldn't be true just from
184 // applying FDs individually). head must be a single element.
191 // Whether this functional dependency can always be applied, ie.,
192 // there is never a point during query processing where it does not hold.
193 //
194 // Examples of not-always-active FDs include join conditions;
195 // e.g. for t1.x = t2.x, it is not true before the join has actually
196 // happened (and t1.x won't be the same order as t2.x before that,
197 // and thus cannot be used in e.g. a merge join).
198 //
199 // However, FDs that stem from unique indexes are always true; e.g. if
200 // t1.x is a primary key, {t1.x} → t1.y will always be true, and we can
201 // always reduce t1.y from an order if t1.x is present earlier.
202 // Similarly, WHERE conditions that are applied on the base table
203 // (ie., it is not delayed due to outer joins) will always be true,
204 // if t1.x = 3, we can safely assume {} → t1.x holds even before
205 // joining in t1, so a sort on (t1.x, t2.y) can be satisfied just by
206 // sorting t2 on y.
207 //
208 // Always-active FDs are baked into the DFSM, so that we need to follow
209 // fewer arcs during query processing. They can also be used for reducing
210 // the final order (to get more efficient sorting), but we don't do it yet.
211 bool always_active = false;
215 public:
216 explicit LogicalOrderings(THD *thd);
218 // Maps the Item to an opaque integer handle. Deduplicates items as we go,
219 // inserting new ones if needed.
222 Item *item(ItemHandle item) const { return m_items[item].item; }
224 // These are only available before Build() has been called.
226 // Mark an interesting ordering (or grouping) as interesting,
227 // returning an index that can be given to SetOrder() later.
228 // Will deduplicate against previous entries; if not deduplicated
229 // away, a copy will be taken.
230 //
231 // Uninteresting orderings are those that can be produced by some
232 // operator (for instance, index scan) but are not interesting to
233 // test for. Orderings may be merged, pruned (if uninteresting)
234 // and moved around after Build(); see RemapOrderingIndex().
235 //
236 // If used_at_end is true, the ordering is assumed to be used only
237 // after all joins have happened, so all FDs are assumed to be
238 // active. This enables reducing the ordering more (which can in
239 // some cases help with better sortahead or the likes), but is not
240 // correct if the ordering wants to be used earlier on, e.g.
241 // in merge join or for semijoin duplicate removal. If it is false,
242 // then it is also only attempted homogenized onto the given set
243 // of tables (otherwise, it is ignored, and homogenization is over
244 // all tables).
245 //
246 // The empty ordering/grouping is always index 0.
247 int AddOrdering(THD *thd, Ordering order, bool interesting, bool used_at_end,
248 table_map homogenize_tables) {
249 return AddOrderingInternal(thd, order,
252 used_at_end, homogenize_tables);
253 }
255 // NOTE: Will include the empty ordering.
256 int num_orderings() const { return m_orderings.size(); }
258 Ordering ordering(int ordering_idx) const {
259 return m_orderings[ordering_idx].ordering;
260 }
262 bool ordering_is_relevant_for_sortahead(int ordering_idx) const {
263 return !m_orderings[ordering_idx].ordering.empty() &&
264 m_orderings[ordering_idx].type != OrderingWithInfo::UNINTERESTING;
265 }
267 // Add a functional dependency that may be applied at some point
268 // during the query planning. Same guarantees as AddOrdering().
269 // The special “decay” FD is always index 0.
272 // NOTE: Will include the decay (epsilon) FD.
273 int num_fds() const { return m_fds.size(); }
275 // Set the list of GROUP BY expressions, if any. This is used as the
276 // head of the functional dependencies for all aggregate functions
277 // (which by definition are functionally dependent on the GROUP BY
278 // expressions, unless ROLLUP is active -- see below), and must be
279 // valid (ie., not freed or modified) until Build() has run.
280 //
281 // If none is set, and there are aggregates present in orderings,
282 // implicit aggregation is assumed (ie., all aggregate functions
283 // are constant).
285 m_aggregate_head = head;
286 }
288 // Set whether ROLLUP is active; if so, we can no longer assume that
289 // aggregate functions are functionally dependent on (nullable)
290 // GROUP BY expressions, as two NULLs may be for different reasons.
291 void SetRollup(bool rollup) { m_rollup = rollup; }
293 // Builds the actual FSMs; all information about orderings and FDs is locked,
294 // optimized and then the state machine is built. After this, you can no
295 // longer add new orderings or FDs, ie., you are moving into the actual
296 // planning phase.
297 //
298 // Build() may prune away orderings and FDs, and it may also add homogenized
299 // orderings, ie., orderings derived from given interesting orders but
300 // modified so that they only require a single table (but will become an
301 // actual interesting order later, after the FDs have been applied). These are
302 // usually at the end, but may also be deduplicated against uninteresting
303 // orders, which will then be marked as interesting.
304 //
305 // trace can be nullptr; if not, it get human-readable optimizer trace
306 // appended to it.
307 void Build(THD *thd, std::string *trace);
309 // These are only available after Build() has been called.
310 // They are stateless and used in the actual planning phase.
312 // Converts an index returned by AddOrdering() to one that can be given
313 // to SetOrder() or DoesFollowOrder(). They don't convert themselves
314 // since it's completely legitimate to iterate over all orderings using
315 // num_orderings() and orderings(), and those indexes should _not_ be
316 // remapped.
317 //
318 // If an ordering has been pruned away, will return zero (the empty ordering),
319 // which is a valid input to SetOrder().
320 int RemapOrderingIndex(int ordering_idx) const {
321 assert(m_built);
322 return m_optimized_ordering_mapping[ordering_idx];
323 }
325 using StateIndex = int;
327 StateIndex SetOrder(int ordering_idx) const {
328 assert(m_built);
329 return m_orderings[ordering_idx].state_idx;
330 }
332 // Get a bitmap representing the given functional dependency. The bitmap
333 // can be all-zero if the given FD is optimized away, or outside the range
334 // of the representable bits. The bitmaps may be ORed together, but are
335 // otherwise to be treated as opaque to the client.
338 int new_fd_idx = m_optimized_fd_mapping[fd_idx];
339 if (new_fd_idx >= 1 && new_fd_idx <= kMaxSupportedFDs) {
340 fd_set.set(new_fd_idx - 1);
341 }
342 return fd_set;
343 }
345 // For a given state, see what other (better) state we can move to given a
346 // set of active functional dependencies, e.g. if we are in state ((),a) and
347 // the FD a=b becomes active, we can set its bit (see GetFDSet()) in the FD
348 // mask and use that to move to the state ((),a,b,ab,ba). Note that “fds”
349 // should contain the entire set of active FDs, not just newly-applied ones.
350 // This is because “old” FDs can suddenly become relevant when new logical
351 // orderings are possible, and the DFSM is not always able to bake this in.
354 bool DoesFollowOrder(StateIndex state_idx, int ordering_idx) const {
355 assert(m_built);
356 if (ordering_idx == 0) {
357 return true;
358 }
359 if (ordering_idx >= kMaxSupportedOrderings) {
360 return false;
361 }
362 return m_dfsm_states[state_idx].follows_interesting_order.test(
363 ordering_idx);
364 }
366 // Whether "a" follows any interesting orders than "b" does not, or could
367 // do so in the future. If !MoreOrderedThan(a, b) && !MoreOrderedThan(b, a)
368 // the states are equal (they follow the same interesting orders, and could
369 // lead to the same interesting orders given the same FDs -- see below).
370 // It is possible to have MoreOrderedThan(a, b) && MoreOrderedThan(b, a), e.g.
371 // if they simply follow disjunct orders.
372 //
373 // This is used in the planner, when pruning access paths -- an AP A can be
374 // kept even if it has higher cost than AP B, if it follows orders that B does
375 // not. Why is it enough to check interesting orders -- must we also not check
376 // uninteresting orders, since they could lead to new interesting orders
377 // later? This is because in the planner, two states will only ever be
378 // compared if the same functional dependencies have been applied to both
379 // sides:
380 //
381 // The set of logical orders, and thus the state, is uniquely determined
382 // by the initial ordering and applied FDs. Thus, if A has _uninteresting_
383 // orders that B does not, the initial ordering must have differed -- but the
384 // initial states only contain (and thus differ in) interesting orders.
385 // Thus, the additional uninteresting orders must have been caused by
386 // additional interesting orders (that do not go away), so testing the
387 // interesting ones really suffices in planner context.
388 //
389 // Note that this also means that in planner context, !MoreOrderedThan(a, b)
390 // && !MoreOrderedThan(b, a) implies that a == b.
392 StateIndex a_idx, StateIndex b_idx,
393 std::bitset<kMaxSupportedOrderings> ignored_orderings) const {
394 assert(m_built);
395 std::bitset<kMaxSupportedOrderings> a =
396 m_dfsm_states[a_idx].follows_interesting_order & ~ignored_orderings;
397 std::bitset<kMaxSupportedOrderings> b =
398 m_dfsm_states[b_idx].follows_interesting_order & ~ignored_orderings;
399 std::bitset<kMaxSupportedOrderings> future_a =
400 m_dfsm_states[a_idx].can_reach_interesting_order & ~ignored_orderings;
401 std::bitset<kMaxSupportedOrderings> future_b =
402 m_dfsm_states[b_idx].can_reach_interesting_order & ~ignored_orderings;
403 return (a & b) != a || (future_a & future_b) != future_a;
404 }
406 // See comment in .cc file.
408 OrderElement *tmpbuf) const;
410 private:
411 bool m_built = false;
413 struct ItemInfo {
414 // Used to translate Item * to ItemHandle and back.
417 // Points to the head of this item's equivalence class. (If the item
418 // is not equivalent to anything, points to itself.) The equivalence class
419 // is defined by EQUIVALENCE FDs, transitively, and the head is the one with
420 // the lowest index. So if we have FDs a = b and b = c, all three {a,b,c}
421 // will point to a here. This is useful for pruning and homogenization;
422 // if two elements have the same equivalence class (ie., the same canonical
423 // item), they could become equivalent after applying FDs. See also
424 // m_can_be_added_by_fd, which deals with non-EQUIVALENCE FDs.
425 //
426 // Set by BuildEquivalenceClasses().
429 // Whether the given item (after canonicalization by means of
430 // m_canonical_item[]) shows up as the tail of any functional dependency.
431 //
432 // Set by FindElementsThatCanBeAddedByFDs();
433 bool can_be_added_by_fd = false;
435 // Whether the given item ever shows up in orderings as ASC or DESC,
436 // respectively. Used to see whether adding the item in that direction
437 // is worthwhile or not. Note that this is propagated through equivalences,
438 // so if a = b and any ordering contains b DESC and a is the head of that
439 // equivalence class, then a is also marked as used_desc = true.
440 bool used_asc = false;
441 bool used_desc = false;
442 bool used_in_grouping = false;
443 };
444 // All items we have seen in use (in orderings or FDs), deduplicated
445 // and indexed by ItemHandle.
448 // Head for all FDs generated for aggregate functions.
449 // See SetHeadForAggregates().
452 // Whether rollup is active; if so, we need to take care not to create
453 // FDs for aggregates in some cases. See SetHeadForAggregates() and
454 // SetRollup().
455 bool m_rollup = false;
457 struct NFSMState {
461 int satisfied_ordering_idx; // Only for type == INTERESTING.
463 // Indexed by ordering.
464 std::bitset<kMaxSupportedOrderings> can_reach_interesting_order{0};
466 // Used during traversal, to keep track of which states we have
467 // already seen (for fast deduplication). We use the standard trick
468 // of using a generational counter instead of a bool, so that we don't
469 // have to clear it every time; we can just increase the generation
470 // and treat everything with lower/different “seen” as unseen.
471 int seen = 0;
472 };
473 struct DFSMState {
474 Mem_root_array<int> outgoing_edges; // Index into dfsm_edges.
475 Mem_root_array<int> nfsm_states; // Index into states.
477 // Structures derived from the above, but in forms for faster access.
479 // Indexed by FD.
482 // Indexed by ordering.
483 std::bitset<kMaxSupportedOrderings> follows_interesting_order{0};
485 // Interesting orders that this state can eventually reach,
486 // given that all FDs are applied (a superset of follows_interesting_order).
487 // We track this instead of the producing orders (e.g. which homogenized
488 // order are we following), because it allows for more access paths to
489 // compare equal. See also OrderingWithInfo::Type::HOMOGENIZED.
490 std::bitset<kMaxSupportedOrderings> can_reach_interesting_order{0};
492 // Whether applying the given functional dependency will take us to a
493 // different state from this one. Used to quickly intersect with the
494 // available FDs to find out what we can apply.
496 };
498 struct NFSMEdge {
499 // Which FD is required to follow this edge. Index into m_fd, with one
500 // exception; from the initial state (0), we have constructor edges for
501 // setting a specific order without following an FD. Such edges have
502 // required_fd_idx = INT_MIN + order_idx, ie., they are negative.
505 // Destination state (index into m_states).
509 const LogicalOrderings *orderings) const {
510 return &orderings->m_fds[required_fd_idx];
511 }
512 const NFSMState *state(const LogicalOrderings *orderings) const {
513 return &orderings->m_states[state_idx];
514 }
515 };
516 struct DFSMEdge {
521 const LogicalOrderings *orderings) const {
522 return &orderings->m_fds[required_fd_idx];
523 }
524 const DFSMState *state(const LogicalOrderings *orderings) const {
525 return &orderings->m_dfsm_states[state_idx];
526 }
527 };
532 // Status of the ordering. Note that types with higher indexes dominate
533 // lower, ie., two orderings can be collapsed into the one with the higher
534 // type index if they are otherwise equal.
535 enum Type {
536 // An ordering that is interesting in its own right,
537 // e.g. because it is given to ORDER BY.
540 // An ordering that is derived from an interesting order, but refers to
541 // one table only (or conceptually, a subset of tables -- but we don't
542 // support that in this implementation). Guaranteed to reach some
543 // interesting order at some point, but we don't track it as interesting
544 // in the FSM states. This means that these orderings don't get state bits
545 // in follows_interesting_order for themselves, but they will always have
546 // one or more interesting orders in can_reach_interesting_order.
547 // This helps us collapse access paths more efficiently; if we have
548 // an interesting order t3.x and create homogenized orderings t1.x
549 // and t2.x (due to some equality with t3.x), an access path following one
550 // isn't better than an access path following the other. They will lead
551 // to the same given the same FDs anyway (see MoreOrderedThan()), and
552 // thus are equally good.
555 // An ordering that is just added because it is easy to produce;
556 // e.g. because it is produced by scanning along an index. Such orderings
557 // can be shortened or pruned away entirely (in
558 // PruneUninterestingOrders())
559 // unless we find that they may lead to an interesting order.
565 // Only used if used_at_end = false (see AddOrdering()).
568 // Which initial state to use for this ordering (in SetOrder()).
570 };
574 // The longest ordering in m_orderings.
579 // NFSM. 0 is the initial state, all others are found by following edges.
583 // DFSM. 0 is the initial state, all others are found by following edges.
587 // After PruneUninterestingOrders has run, maps from the old indexes to the
588 // new indexes.
591 // After PruneFDs() has run, maps from the old indexes to the new indexes.
594 // The canonical order for two items in a grouping
595 // (after BuildEquivalenceClasses() has run; enforced by
596 // RecanonicalizeGroupings()). The reason why we sort by
597 // canonical_item first is so that switching out one element
598 // with an equivalent one (ie., applying an EQUIVALENCE
599 // functional dependency) does not change the order of the
600 // elements in the grouing, which could give false negatives
601 // in CouldBecomeInterestingOrdering().
603 if (m_items[a].canonical_item != m_items[b].canonical_item)
604 return m_items[a].canonical_item < m_items[b].canonical_item;
605 return a < b;
606 }
608 inline bool ItemBeforeInGroup(const OrderElement &a, const OrderElement &b) {
609 return ItemHandleBeforeInGroup(a.item, b.item);
610 }
612 // Helper for AddOrdering().
614 bool used_at_end, table_map homogenize_tables);
616 // See comment in .cc file.
617 void PruneUninterestingOrders(THD *thd);
619 // See comment in .cc file.
620 void PruneFDs(THD *thd);
622 // See comment in .cc file.
624 bool all_fds) const;
626 // Populates ItemInfo::canonical_item.
629 // See comment in .cc file.
632 // See comment in .cc file.
633 void AddFDsFromComputedItems(THD *thd);
635 // See comment in .cc file.
636 void AddFDsFromAggregateItems(THD *thd);
638 // See comment in .cc file.
640 THD *thd, ItemHandle argument_item, Window *window);
642 // See comment in .cc file.
643 void AddFDsFromConstItems(THD *thd);
645 // Populates ItemInfo::can_be_added_by_fd.
648 void PreReduceOrderings(THD *thd);
652 THD *thd, Ordering reduced_ordering, bool used_at_end, int table_idx,
653 Bounds_checked_array<std::pair<ItemHandle, ItemHandle>> reverse_canonical,
654 OrderElement *tmpbuf);
656 // See comment in .cc file.
659 void BuildNFSM(THD *thd);
660 void AddGroupingFromOrdering(THD *thd, int state_idx, Ordering ordering,
661 OrderElement *tmpbuf);
662 void TryAddingOrderWithElementInserted(THD *thd, int state_idx, int fd_idx,
663 Ordering old_ordering,
664 size_t start_point,
665 ItemHandle item_to_add,
666 enum_order direction,
667 OrderElement *tmpbuf);
668 void PruneNFSM(THD *thd);
669 bool AlwaysActiveFD(int fd_idx);
670 void FinalizeDFSMState(THD *thd, int state_idx);
672 int *generation, int extra_allowed_fd_idx);
673 void ConvertNFSMToDFSM(THD *thd);
675 // Populates state_idx for every ordering in m_ordering.
678 // If a state with the given ordering already exists (artificial or not),
679 // returns its index. Otherwise, adds an artificial state with the given
680 // order and returns its index.
683 // Add an edge from state_idx to an state with the given ordering; if there is
684 // no such state, adds an artificial state with it (taking a copy, so does not
685 // need to take ownership).
686 void AddEdge(THD *thd, int state_idx, int required_fd_idx, Ordering ordering);
688 // Returns true if the given (non-DECAY) functional dependency applies to the
689 // given ordering, and the index of the element from which the FD is active
690 // (ie., the last element that was part of the head). One can start inserting
691 // the tail element at any point _after_ this index; if it is an EQUIVALENCE
692 // FD, one can instead choose to replace the element at start_point entirely.
694 const Ordering ordering,
695 int *start_point) const;
697 // Used for optimizer trace.
699 std::string PrintOrdering(Ordering ordering) const;
701 bool html) const;
702 void PrintFunctionalDependencies(std::string *trace);
703 void PrintInterestingOrders(std::string *trace);
704 void PrintNFSMDottyGraph(std::string *trace) const;
705 void PrintDFSMDottyGraph(std::string *trace) const;
Base class that is used to represent any kind of expression in a relational query.
Definition: item.h:850
Definition: interesting_orders.h:214
void SetHeadForAggregates(Bounds_checked_array< ItemHandle > head)
Definition: interesting_orders.h:284
void CreateOrderingsFromGroupings(THD *thd)
We don't currently have any operators that only group and do not sort (e.g.
Ordering ReduceOrdering(Ordering ordering, bool all_fds, OrderElement *tmpbuf) const
Remove redundant elements using the functional dependencies that we have, to give a more canonical fo...
bool ItemHandleBeforeInGroup(ItemHandle a, ItemHandle b)
Definition: interesting_orders.h:602
void AddFDsFromComputedItems(THD *thd)
Try to add new FDs from items that are not base items; e.g., if we have an item (a + 1),...
Mem_root_array< OrderingWithInfo > m_orderings
Definition: interesting_orders.h:572
Bounds_checked_array< int > m_optimized_fd_mapping
Definition: interesting_orders.h:592
StateIndex SetOrder(int ordering_idx) const
Definition: interesting_orders.h:327
int num_orderings() const
Definition: interesting_orders.h:256
bool DoesFollowOrder(StateIndex state_idx, int ordering_idx) const
Definition: interesting_orders.h:354
bool m_rollup
Definition: interesting_orders.h:455
int m_longest_ordering
Definition: interesting_orders.h:575
int AddArtificialState(THD *thd, Ordering ordering)
bool CouldBecomeInterestingOrdering(Ordering ordering) const
For a given ordering, check whether it ever has the hope of becoming an interesting ordering.
Mem_root_array< DFSMState > m_dfsm_states
Definition: interesting_orders.h:584
bool m_built
Definition: interesting_orders.h:411
int RemapOrderingIndex(int ordering_idx) const
Definition: interesting_orders.h:320
void FinalizeDFSMState(THD *thd, int state_idx)
bool ImpliedByEarlierElements(ItemHandle item, Ordering prefix, bool all_fds) const
Checks whether the given item is redundant given previous elements in the ordering; ie....
void PrintDFSMDottyGraph(std::string *trace) const
bool ordering_is_relevant_for_sortahead(int ordering_idx) const
Definition: interesting_orders.h:262
void PreReduceOrderings(THD *thd)
Do safe reduction on all orderings (some of them may get merged by PruneUninterestingOrders() later),...
void SetRollup(bool rollup)
Definition: interesting_orders.h:291
void PrintFunctionalDependencies(std::string *trace)
void CreateHomogenizedOrderings(THD *thd)
For each interesting ordering, see if we can homogenize it onto each table.
Mem_root_array< NFSMState > m_states
Definition: interesting_orders.h:580
int AddOrderingInternal(THD *thd, Ordering order, OrderingWithInfo::Type type, bool used_at_end, table_map homogenize_tables)
void AddFDsFromConstItems(THD *thd)
Try to add FDs from items that are constant by themselves, e.g.
int AddFunctionalDependency(THD *thd, FunctionalDependency fd)
void PrintNFSMDottyGraph(std::string *trace) const
Mem_root_array< DFSMEdge > m_dfsm_edges
Definition: interesting_orders.h:585
bool MoreOrderedThan(StateIndex a_idx, StateIndex b_idx, std::bitset< kMaxSupportedOrderings > ignored_orderings) const
Definition: interesting_orders.h:391
bool AlwaysActiveFD(int fd_idx)
void BuildNFSM(THD *thd)
Mem_root_array< NFSMEdge > m_edges
Definition: interesting_orders.h:581
void BuildEquivalenceClasses()
int StateIndex
Definition: interesting_orders.h:325
void AddHomogenizedOrderingIfPossible(THD *thd, Ordering reduced_ordering, bool used_at_end, int table_idx, Bounds_checked_array< std::pair< ItemHandle, ItemHandle > > reverse_canonical, OrderElement *tmpbuf)
Helper function for CreateHomogenizedOrderings().
Ordering ordering(int ordering_idx) const
Definition: interesting_orders.h:258
bool FunctionalDependencyApplies(const FunctionalDependency &fd, const Ordering ordering, int *start_point) const
void PruneNFSM(THD *thd)
Try to prune away irrelevant nodes from the NFSM; it is worth spending some time on this,...
Item * item(ItemHandle item) const
Definition: interesting_orders.h:222
void FindElementsThatCanBeAddedByFDs()
void PrintInterestingOrders(std::string *trace)
StateIndex ApplyFDs(StateIndex state_idx, FunctionalDependencySet fds) const
Bounds_checked_array< int > m_optimized_ordering_mapping
Definition: interesting_orders.h:589
void AddGroupingFromOrdering(THD *thd, int state_idx, Ordering ordering, OrderElement *tmpbuf)
int AddOrdering(THD *thd, Ordering order, bool interesting, bool used_at_end, table_map homogenize_tables)
Definition: interesting_orders.h:247
void ExpandThroughAlwaysActiveFDs(Mem_root_array< int > *nfsm_states, int *generation, int extra_allowed_fd_idx)
void TryAddingOrderWithElementInserted(THD *thd, int state_idx, int fd_idx, Ordering old_ordering, size_t start_point, ItemHandle item_to_add, enum_order direction, OrderElement *tmpbuf)
void PruneFDs(THD *thd)
void PruneUninterestingOrders(THD *thd)
Try to get rid of uninteresting orders, possibly by discarding irrelevant suffixes and merging them w...
void AddFDsFromAggregateItems(THD *thd)
std::string PrintOrdering(Ordering ordering) const
bool ItemBeforeInGroup(const OrderElement &a, const OrderElement &b)
Definition: interesting_orders.h:608
Bounds_checked_array< ItemHandle > CollectHeadForStaticWindowFunction(THD *thd, ItemHandle argument_item, Window *window)
Mem_root_array< ItemInfo > m_items
Definition: interesting_orders.h:446
ItemHandle GetHandle(Item *item)
void FindInitialStatesForOrdering()
LogicalOrderings(THD *thd)
Mem_root_array< FunctionalDependency > m_fds
Definition: interesting_orders.h:577
void ConvertNFSMToDFSM(THD *thd)
From the NFSM, convert an equivalent DFSM.
Bounds_checked_array< ItemHandle > m_aggregate_head
Definition: interesting_orders.h:450
FunctionalDependencySet GetFDSet(int fd_idx) const
Definition: interesting_orders.h:336
void RecanonicalizeGroupings()
std::string PrintFunctionalDependency(const FunctionalDependency &fd, bool html) const
void AddEdge(THD *thd, int state_idx, int required_fd_idx, Ordering ordering)
int num_fds() const
Definition: interesting_orders.h:273
void Build(THD *thd, std::string *trace)
A typesafe replacement for DYNAMIC_ARRAY.
Definition: mem_root_array.h:425
For each client connection we create a separate thread with THD serving as a thread/connection descri...
Definition: sql_lexer_thd.h:33
Represents the (explicit) window of a SQL 2003 section 7.11 <window clause>, or the implicit (inlined...
Definition: window.h:104
std::bitset< kMaxSupportedFDs > FunctionalDependencySet
Definition: interesting_orders_defs.h:62
static constexpr int kMaxSupportedFDs
Definition: interesting_orders_defs.h:61
static constexpr int kMaxSupportedOrderings
Definition: interesting_orders_defs.h:64
int ItemHandle
Definition: interesting_orders_defs.h:38
Definition: key_spec.h:64
uint64_t table_map
Definition: my_table_map.h:29
required string type
Definition: replication_group_member_actions.proto:33
Definition: interesting_orders.h:157
ItemHandle tail
Definition: interesting_orders.h:189
bool always_active
Definition: interesting_orders.h:211
Bounds_checked_array< ItemHandle > head
Definition: interesting_orders.h:188
enum FunctionalDependency::@100 type
@ FD
Definition: interesting_orders.h:179
Definition: interesting_orders.h:172
Definition: interesting_orders.h:185
Definition: interesting_orders.h:516
int state_idx
Definition: interesting_orders.h:518
int required_fd_idx
Definition: interesting_orders.h:517
const DFSMState * state(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:524
const FunctionalDependency * required_fd(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:520
Definition: interesting_orders.h:473
FunctionalDependencySet can_use_fd
Definition: interesting_orders.h:495
Mem_root_array< int > nfsm_states
Definition: interesting_orders.h:475
std::bitset< kMaxSupportedOrderings > follows_interesting_order
Definition: interesting_orders.h:483
Mem_root_array< int > outgoing_edges
Definition: interesting_orders.h:474
std::bitset< kMaxSupportedOrderings > can_reach_interesting_order
Definition: interesting_orders.h:490
Bounds_checked_array< int > next_state
Definition: interesting_orders.h:480
Definition: interesting_orders.h:413
bool used_desc
Definition: interesting_orders.h:441
bool used_in_grouping
Definition: interesting_orders.h:442
ItemHandle canonical_item
Definition: interesting_orders.h:427
bool can_be_added_by_fd
Definition: interesting_orders.h:433
bool used_asc
Definition: interesting_orders.h:440
Item * item
Definition: interesting_orders.h:415
Definition: interesting_orders.h:498
const NFSMState * state(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:512
int required_fd_idx
Definition: interesting_orders.h:503
const FunctionalDependency * required_fd(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:508
int state_idx
Definition: interesting_orders.h:506
Definition: interesting_orders.h:457
Mem_root_array< int > outgoing_edges
Definition: interesting_orders.h:459
std::bitset< kMaxSupportedOrderings > can_reach_interesting_order
Definition: interesting_orders.h:464
int satisfied_ordering_idx
Definition: interesting_orders.h:461
Definition: interesting_orders.h:458
Definition: interesting_orders.h:458
Definition: interesting_orders.h:458
int seen
Definition: interesting_orders.h:471
enum LogicalOrderings::NFSMState::@101 type
Ordering satisfied_ordering
Definition: interesting_orders.h:460
Definition: interesting_orders.h:529
StateIndex state_idx
Definition: interesting_orders.h:569
Ordering ordering
Definition: interesting_orders.h:530
bool used_at_end
Definition: interesting_orders.h:563
Definition: interesting_orders.h:535
Definition: interesting_orders.h:560
Definition: interesting_orders.h:538
Definition: interesting_orders.h:553
enum LogicalOrderings::OrderingWithInfo::Type type
table_map homogenize_tables
Definition: interesting_orders.h:566
Definition: interesting_orders_defs.h:43
ItemHandle item
Definition: interesting_orders_defs.h:44