MySQL 9.0.0
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28 @file
30 Tracks which tuple streams follow which orders, and in particular whether
31 they follow interesting orders.
33 An interesting order (and/or grouping) is one that we might need to sort by
34 at some point during query execution (e.g. to satisfy an ORDER BY predicate);
35 if the rows already are produced in that order, for instance because we
36 scanned along the right index, we can skip the sort and get a lower cost.
38 We generally follow these papers:
40 [Neu04] Neumann and Moerkotte: “An efficient framework for order
41 optimization”
42 [Neu04b] Neumann and Moerkotte: “A Combined Framework for
43 Grouping and Order Optimization”
45 [Neu04b] is an updated version of [Neu04] that also deals with interesting
46 groupings but omits some details to make more space, so both are needed.
47 A combined and updated version of the same material is available in
48 Moerkotte's “Query compilers” PDF.
50 Some further details, like order homogenization, come from
52 [Sim96] Simmen et al: “Fundamental Techniques for Order Optimization”
54 All three papers deal with the issue of _logical_ orderings, where any
55 tuple stream may follow more than one order simultaneously, as inferred
56 through functional dependencies (FDs). For instance, if we have an ordering
57 (ab) but also an active FD {a} → c (c is uniquely determined by a,
58 for instance because a is a primary key in the same table as c), this means
59 we also implicitly follow the orders (acb) and (abc). In addition,
60 we trivially follow the orders (a), (ac) and (ab). However, note that we
61 do _not_ necessarily follow the order (cab).
63 Similarly, equivalences, such as WHERE conditions and joins, give rise
64 to a stronger form of FDs. If we have an ordering (ab) and the FD b = c,
65 we can be said to follow (ac), (acb) or (abc). The former would not be
66 inferable from {b} → c and {c} → b alone. Equivalences with constants
67 are perhaps even stronger, e.g. WHERE x=3 would give rise to {} → x,
68 which could extend (a) to (xa), (ax) or (x).
70 Neumann et al solve this by modelling which ordering we're following as a
71 state in a non-deterministic finite state machine (NFSM). By repeatedly
72 applying FDs (which become edges in the NFSM), we can build up all possible
73 orderings from a base (which can be either the empty ordering, ordering from
74 scanning along an index, or one produced by an explicit sort) and then
75 checking whether we are in a state matching the ordering we are interested
76 in. (There can be quite a bit of states, so we need a fair amount of pruning
77 to keep the count manageable, or else performance will suffer.) Of course,
78 since NFSMs are nondeterministic, a base ordering and a set of FDs can
79 necessarily put us in a number of states, so we need to convert the NFSM
80 to a DFSM (using the standard powerset construction for NFAs; see
81 ConvertNFSMToDFSM()). This means that the ordering state for an access path
82 is only a single integer, the DFSM state number. When we activate more FDs,
83 for instance because we apply joins, we will move throughout the DFSM into
84 more attractive states. By checking simple precomputed lookup tables,
85 we can quickly find whether a given DFSM state follows a given ordering.
87 The other kind of edges we follow are from the artificial starting state;
88 they represent setting a specific ordering (e.g. because we sort by that
89 ordering). This is set up in the NFSM and preserved in the DFSM.
91 The actual collection of FDs and interesting orders happen outside this
92 class, in the caller.
94 A weakness in the approach is that transitive FDs are not always followed
95 correctly. E.g., if we have an ordering (a), and FDs {a} → b and {b} → c,
96 we will create (ab) and (abc), but _not_ (ac). This is not a problem for
97 equivalences, though, and most of the FDs we collect are equivalences.
98 We do have some heuristics to produce a new FD {a} → c where it is relevant,
99 but they are not always effective.
101 Neumann and Moerkotte distinguish between “tested-for” (O_T) and
102 “producing” (O_P) orderings, where all orders are interesting but only
103 some can be produced by explicit operators, such as sorts. Our implementation
104 is exactly opposite; we allow every ordering to be produced (by means of
105 sort-ahead), but there are orders that can be produced (e.g. when scanning
106 an index) that are not interesting in themselves. Such orders can be
107 pruned away early if we can show they do not produce anything interesting.
110 The operations related to interesting orders, in particular the concept
111 of functional dependencies, are related to the ones we are doing when
112 checking ONLY_FULL_GROUP_BY legality in sql/aggregate_check.h. However,
113 there are some key differences as well:
115 - Orderings are lexical, while groupings are just a bag of attributes.
116 This increases the state space for orderings significantly; groupings
117 can add elements at will and just grow the set freely, while orderings
118 need more care. In particular, this means that groupings only need
119 FDs on the form S → x (where S is a set), while orderings also benefit
120 from those of the type x = y, which replace an element instead of
121 adding a new one.
123 - ONLY_FULL_GROUP_BY is for correctness of rejecting or accepting the
124 query, while interesting orders is just an optimization, so not
125 recognizing rare cases is more acceptable.
127 - ONLY_FULL_GROUP_BY testing only cares about the set of FDs that hold
128 at one specific point (GROUP BY testing, naturally), while interesting
129 orders must be tracked throughout the entire operator tree. In particular,
130 if using interesting orders for merge join, the status at nearly every
131 join is relevant. Also, performance matters much more.
133 Together, these mean that the code ends up being fairly different,
134 and some cases are recognized by ONLY_FULL_GROUP_BY but not by interesting
135 orders. (The actual FD collection happens in BuildInterestingOrders in
136; see the comment there for FD differences.)
138 A note about nomenclature: Like Neumann et al, we use the term “ordering”
139 (and “grouping”) instead of “order”, with the special exception of the
140 already-established term “interesting order”.
141 */
143#include "my_table_map.h"
145#include "sql/key_spec.h"
146#include "sql/mem_root_array.h"
147#include "sql/sql_array.h"
149#include <bitset>
150#include <sstream>
151#include <string>
153class LogicalOrderings;
154class Window;
157 Represents a (potentially interesting) ordering, rollup or (non-rollup)
158 grouping.
160class Ordering final {
161 friend bool operator==(const Ordering &a, const Ordering &b);
163 public:
164 /// This type hold the individual elements of the ordering.
167 /// The kind of ordering that an Ordering instance may represent.
168 enum class Kind : char {
169 /// An ordering with no elements. Such an ordering is not useful in itself,
170 /// but may appear as an intermediate result.
171 kEmpty,
173 /// Specific sequence of m_elements, and specific direction of each element.
174 /// Needed for e.g. ORDER BY.
175 kOrder,
177 /// Specific sequence of m_elements, but each element may be ordered in any
178 /// direction. Needed for ROLLUP:
179 kRollup,
181 /// Elements may appear in any sequence and may be ordered in any direction.
182 /// Needed for GROUP BY (with out ROLLUP), DISCTINCT, semi-join etc.
183 kGroup
184 };
186 Ordering() : m_kind{Kind::kEmpty} {}
188 Ordering(Elements elements, Kind kind) : m_elements{elements}, m_kind{kind} {
189 assert(Valid());
190 }
192 /// Copy constructor. Only defined explicitly to check Valid().
193 Ordering(const Ordering &other)
194 : m_elements{other.m_elements}, m_kind{other.m_kind} {
195 assert(Valid());
196 }
198 /// Assignment operator. Only defined explicitly to check Valid().
199 Ordering &operator=(const Ordering &other) {
200 assert(Valid());
201 m_kind = other.m_kind;
202 m_elements = other.m_elements;
203 return *this;
204 }
206 /// Make a copy of *this. Allocate new memory for m_elements from mem_root.
208 assert(Valid());
210 }
212 Kind GetKind() const {
213 assert(Valid());
214 return m_kind;
215 }
217 const Elements &GetElements() const {
218 assert(Valid());
219 return m_elements;
220 }
223 assert(Valid());
224 return m_elements;
225 }
227 size_t size() const { return m_elements.size(); }
229 /**
230 Remove duplicate entries, in-place.
231 */
232 void Deduplicate();
234 private:
235 /// The ordering terms.
238 /// The kind of this ordering.
241 /// @returns true iff *this passes a consistency check.
242 bool Valid() const;
245/// Check if 'a' and 'b' has the same kind and contains the same elements.
246inline bool operator==(const Ordering &a, const Ordering &b) {
247 assert(a.Valid());
248 assert(b.Valid());
249 return a.m_kind == b.m_kind &&
254inline bool operator!=(const Ordering &a, const Ordering &b) {
255 return !(a == b);
259 enum {
260 // A special “empty” kind of edge in the FSM that signifies
261 // adding no functional dependency, ie., a state we can reach
262 // with no further effort. This can happen in two ways:
263 //
264 // 1. An ordering can drop its last element, ie.,
265 // if a tuple stream is ordered on (a,b,c), it is also
266 // ordered on (a,b).
267 // 2. An ordering can be converted to a grouping, i.e,
268 // if a tuple stream is ordered on (a,b,c), it is also
269 // grouped on {a,b,c}.
270 //
271 // head must be empty, tail must be 0. Often called ϵ.
272 // Must be the first in the edge list.
275 // A standard functional dependency {a} → b; if a tuple stream
276 // is ordered on all elements of a and this FD is applied,
277 // it is also ordered on (a,b). A typical example is if {a}
278 // is an unique key in a table, and b is a column of the
279 // same table. head can be empty.
282 // An equivalence a = b; implies a → b and b → a, but is
283 // stronger (e.g. if ordered on (a,c), there is also an
284 // ordering on (b,c), which wouldn't be true just from
285 // applying FDs individually). head must be a single element.
292 // Whether this functional dependency can always be applied, ie.,
293 // there is never a point during query processing where it does not hold.
294 //
295 // Examples of not-always-active FDs include join conditions;
296 // e.g. for t1.x = t2.x, it is not true before the join has actually
297 // happened (and t1.x won't be the same order as t2.x before that,
298 // and thus cannot be used in e.g. a merge join).
299 //
300 // However, FDs that stem from unique indexes are always true; e.g. if
301 // t1.x is a primary key, {t1.x} → t1.y will always be true, and we can
302 // always reduce t1.y from an order if t1.x is present earlier.
303 // Similarly, WHERE conditions that are applied on the base table
304 // (ie., it is not delayed due to outer joins) will always be true,
305 // if t1.x = 3, we can safely assume {} → t1.x holds even before
306 // joining in t1, so a sort on (t1.x, t2.y) can be satisfied just by
307 // sorting t2 on y.
308 //
309 // Always-active FDs are baked into the DFSM, so that we need to follow
310 // fewer arcs during query processing. They can also be used for reducing
311 // the final order (to get more efficient sorting), but we don't do it yet.
312 bool always_active = false;
318 public:
319 explicit LogicalOrderings(THD *thd);
321 // Maps the Item to an opaque integer handle. Deduplicates items as we go,
322 // inserting new ones if needed.
325 Item *item(ItemHandle item) const { return m_items[item].item; }
326 int num_items() const { return m_items.size(); }
328 // These are only available before Build() has been called.
330 // Mark an interesting ordering (or grouping) as interesting,
331 // returning an index that can be given to SetOrder() later.
332 // Will deduplicate against previous entries; if not deduplicated
333 // away, a copy will be taken.
334 //
335 // Uninteresting orderings are those that can be produced by some
336 // operator (for instance, index scan) but are not interesting to
337 // test for. Orderings may be merged, pruned (if uninteresting)
338 // and moved around after Build(); see RemapOrderingIndex().
339 //
340 // If used_at_end is true, the ordering is assumed to be used only
341 // after all joins have happened, so all FDs are assumed to be
342 // active. This enables reducing the ordering more (which can in
343 // some cases help with better sortahead or the likes), but is not
344 // correct if the ordering wants to be used earlier on, e.g.
345 // in merge join or for semijoin duplicate removal. If it is false,
346 // then it is also only attempted homogenized onto the given set
347 // of tables (otherwise, it is ignored, and homogenization is over
348 // all tables).
349 //
350 // The empty ordering/grouping is always index 0.
351 int AddOrdering(THD *thd, Ordering order, bool interesting, bool used_at_end,
352 table_map homogenize_tables) {
353 return AddOrderingInternal(thd, order,
356 used_at_end, homogenize_tables);
357 }
359 // NOTE: Will include the empty ordering.
360 int num_orderings() const { return m_orderings.size(); }
362 const Ordering &ordering(int ordering_idx) const {
363 return m_orderings[ordering_idx].ordering;
364 }
366 bool ordering_is_relevant_for_sortahead(int ordering_idx) const {
367 return !m_orderings[ordering_idx].ordering.GetElements().empty() &&
368 m_orderings[ordering_idx].type != OrderingWithInfo::UNINTERESTING;
369 }
371 // Add a functional dependency that may be applied at some point
372 // during the query planning. Same guarantees as AddOrdering().
373 // The special “decay” FD is always index 0.
376 // NOTE: Will include the decay (epsilon) FD.
377 int num_fds() const { return m_fds.size(); }
379 // Set the list of GROUP BY expressions, if any. This is used as the
380 // head of the functional dependencies for all aggregate functions
381 // (which by definition are functionally dependent on the GROUP BY
382 // expressions, unless ROLLUP is active -- see below), and must be
383 // valid (ie., not freed or modified) until Build() has run.
384 //
385 // If none is set, and there are aggregates present in orderings,
386 // implicit aggregation is assumed (ie., all aggregate functions
387 // are constant).
389 m_aggregate_head = head;
390 }
392 // Set whether ROLLUP is active; if so, we can no longer assume that
393 // aggregate functions are functionally dependent on (nullable)
394 // GROUP BY expressions, as two NULLs may be for different reasons.
395 void SetRollup(bool rollup) { m_rollup = rollup; }
397 // Builds the actual FSMs; all information about orderings and FDs is locked,
398 // optimized and then the state machine is built. After this, you can no
399 // longer add new orderings or FDs, ie., you are moving into the actual
400 // planning phase.
401 //
402 // Build() may prune away orderings and FDs, and it may also add homogenized
403 // orderings, ie., orderings derived from given interesting orders but
404 // modified so that they only require a single table (but will become an
405 // actual interesting order later, after the FDs have been applied). These are
406 // usually at the end, but may also be deduplicated against uninteresting
407 // orders, which will then be marked as interesting.
408 void Build(THD *thd);
410 // These are only available after Build() has been called.
411 // They are stateless and used in the actual planning phase.
413 // Converts an index returned by AddOrdering() to one that can be given
414 // to SetOrder() or DoesFollowOrder(). They don't convert themselves
415 // since it's completely legitimate to iterate over all orderings using
416 // num_orderings() and orderings(), and those indexes should _not_ be
417 // remapped.
418 //
419 // If an ordering has been pruned away, will return zero (the empty ordering),
420 // which is a valid input to SetOrder().
421 int RemapOrderingIndex(int ordering_idx) const {
422 assert(m_built);
423 return m_optimized_ordering_mapping[ordering_idx];
424 }
426 using StateIndex = int;
428 StateIndex SetOrder(int ordering_idx) const {
429 assert(m_built);
430 return m_orderings[ordering_idx].state_idx;
431 }
433 // Get a bitmap representing the given functional dependency. The bitmap
434 // can be all-zero if the given FD is optimized away, or outside the range
435 // of the representable bits. The bitmaps may be ORed together, but are
436 // otherwise to be treated as opaque to the client.
439 int new_fd_idx = m_optimized_fd_mapping[fd_idx];
440 if (new_fd_idx >= 1 && new_fd_idx <= kMaxSupportedFDs) {
441 fd_set.set(new_fd_idx - 1);
442 }
443 return fd_set;
444 }
446 // For a given state, see what other (better) state we can move to given a
447 // set of active functional dependencies, e.g. if we are in state ((),a) and
448 // the FD a=b becomes active, we can set its bit (see GetFDSet()) in the FD
449 // mask and use that to move to the state ((),a,b,ab,ba). Note that “fds”
450 // should contain the entire set of active FDs, not just newly-applied ones.
451 // This is because “old” FDs can suddenly become relevant when new logical
452 // orderings are possible, and the DFSM is not always able to bake this in.
455 bool DoesFollowOrder(StateIndex state_idx, int ordering_idx) const {
456 assert(m_built);
457 if (ordering_idx == 0) {
458 return true;
459 }
460 if (ordering_idx >= kMaxSupportedOrderings) {
461 return false;
462 }
463 return m_dfsm_states[state_idx].follows_interesting_order.test(
464 ordering_idx);
465 }
467 // Whether "a" follows any interesting orders than "b" does not, or could
468 // do so in the future. If !MoreOrderedThan(a, b) && !MoreOrderedThan(b, a)
469 // the states are equal (they follow the same interesting orders, and could
470 // lead to the same interesting orders given the same FDs -- see below).
471 // It is possible to have MoreOrderedThan(a, b) && MoreOrderedThan(b, a), e.g.
472 // if they simply follow disjunct orders.
473 //
474 // This is used in the planner, when pruning access paths -- an AP A can be
475 // kept even if it has higher cost than AP B, if it follows orders that B does
476 // not. Why is it enough to check interesting orders -- must we also not check
477 // uninteresting orders, since they could lead to new interesting orders
478 // later? This is because in the planner, two states will only ever be
479 // compared if the same functional dependencies have been applied to both
480 // sides:
481 //
482 // The set of logical orders, and thus the state, is uniquely determined
483 // by the initial ordering and applied FDs. Thus, if A has _uninteresting_
484 // orders that B does not, the initial ordering must have differed -- but the
485 // initial states only contain (and thus differ in) interesting orders.
486 // Thus, the additional uninteresting orders must have been caused by
487 // additional interesting orders (that do not go away), so testing the
488 // interesting ones really suffices in planner context.
489 //
490 // Note that this also means that in planner context, !MoreOrderedThan(a, b)
491 // && !MoreOrderedThan(b, a) implies that a == b.
493 StateIndex a_idx, StateIndex b_idx,
494 std::bitset<kMaxSupportedOrderings> ignored_orderings) const {
495 assert(m_built);
496 std::bitset<kMaxSupportedOrderings> a =
497 m_dfsm_states[a_idx].follows_interesting_order & ~ignored_orderings;
498 std::bitset<kMaxSupportedOrderings> b =
499 m_dfsm_states[b_idx].follows_interesting_order & ~ignored_orderings;
500 std::bitset<kMaxSupportedOrderings> future_a =
501 m_dfsm_states[a_idx].can_reach_interesting_order & ~ignored_orderings;
502 std::bitset<kMaxSupportedOrderings> future_b =
503 m_dfsm_states[b_idx].can_reach_interesting_order & ~ignored_orderings;
504 return (a & b) != a || (future_a & future_b) != future_a;
505 }
507 // See comment in .cc file.
509 Ordering::Elements tmp) const;
511 private:
512 struct NFSMState;
513 class OrderWithElementInserted;
515 bool m_built = false;
517 struct ItemInfo {
518 // Used to translate Item * to ItemHandle and back.
521 // Points to the head of this item's equivalence class. (If the item
522 // is not equivalent to anything, points to itself.) The equivalence class
523 // is defined by EQUIVALENCE FDs, transitively, and the head is the one with
524 // the lowest index. So if we have FDs a = b and b = c, all three {a,b,c}
525 // will point to a here. This is useful for pruning and homogenization;
526 // if two elements have the same equivalence class (ie., the same canonical
527 // item), they could become equivalent after applying FDs. See also
528 // m_can_be_added_by_fd, which deals with non-EQUIVALENCE FDs.
529 //
530 // Set by BuildEquivalenceClasses().
533 // Whether the given item (after canonicalization by means of
534 // m_canonical_item[]) shows up as the tail of any functional dependency.
535 //
536 // Set by FindElementsThatCanBeAddedByFDs();
537 bool can_be_added_by_fd = false;
539 // Whether the given item ever shows up in orderings as ASC or DESC,
540 // respectively. Used to see whether adding the item in that direction
541 // is worthwhile or not. Note that this is propagated through equivalences,
542 // so if a = b and any ordering contains b DESC and a is the head of that
543 // equivalence class, then a is also marked as used_desc = true.
544 bool used_asc = false;
545 bool used_desc = false;
546 bool used_in_grouping = false;
547 };
548 // All items we have seen in use (in orderings or FDs), deduplicated
549 // and indexed by ItemHandle.
552 // Head for all FDs generated for aggregate functions.
553 // See SetHeadForAggregates().
556 // Whether rollup is active; if so, we need to take care not to create
557 // FDs for aggregates in some cases. See SetHeadForAggregates() and
558 // SetRollup().
559 bool m_rollup = false;
561 struct NFSMEdge {
562 // Which FD is required to follow this edge. Index into m_fd, with one
563 // exception; from the initial state (0), we have constructor edges for
564 // setting a specific order without following an FD. Such edges have
565 // required_fd_idx = INT_MIN + order_idx, ie., they are negative.
568 // Destination state (index into m_states).
572 const LogicalOrderings *orderings) const {
573 return &orderings->m_fds[required_fd_idx];
574 }
575 const NFSMState *state(const LogicalOrderings *orderings) const {
576 return &orderings->m_states[state_idx];
577 }
578 };
580 friend bool operator==(const NFSMEdge &a, const NFSMEdge &b);
581 friend bool operator!=(const NFSMEdge &a, const NFSMEdge &b);
583 struct NFSMState {
587 int satisfied_ordering_idx; // Only for type == INTERESTING.
589 // Indexed by ordering.
590 std::bitset<kMaxSupportedOrderings> can_reach_interesting_order{0};
592 // Used during traversal, to keep track of which states we have
593 // already seen (for fast deduplication). We use the standard trick
594 // of using a generational counter instead of a bool, so that we don't
595 // have to clear it every time; we can just increase the generation
596 // and treat everything with lower/different “seen” as unseen.
597 int seen = 0;
598 };
599 struct DFSMState {
600 Mem_root_array<int> outgoing_edges; // Index into dfsm_edges.
601 Mem_root_array<int> nfsm_states; // Index into states.
603 // Structures derived from the above, but in forms for faster access.
605 // Indexed by FD.
608 // Indexed by ordering.
609 std::bitset<kMaxSupportedOrderings> follows_interesting_order{0};
611 // Interesting orders that this state can eventually reach,
612 // given that all FDs are applied (a superset of follows_interesting_order).
613 // We track this instead of the producing orders (e.g. which homogenized
614 // order are we following), because it allows for more access paths to
615 // compare equal. See also OrderingWithInfo::Type::HOMOGENIZED.
616 std::bitset<kMaxSupportedOrderings> can_reach_interesting_order{0};
618 // Whether applying the given functional dependency will take us to a
619 // different state from this one. Used to quickly intersect with the
620 // available FDs to find out what we can apply.
622 };
624 struct DFSMEdge {
629 const LogicalOrderings *orderings) const {
630 return &orderings->m_fds[required_fd_idx];
631 }
632 const DFSMState *state(const LogicalOrderings *orderings) const {
633 return &orderings->m_dfsm_states[state_idx];
634 }
635 };
640 // Status of the ordering. Note that types with higher indexes dominate
641 // lower, ie., two orderings can be collapsed into the one with the higher
642 // type index if they are otherwise equal.
643 enum Type {
644 // An ordering that is interesting in its own right,
645 // e.g. because it is given to ORDER BY.
648 // An ordering that is derived from an interesting order, but refers to
649 // one table only (or conceptually, a subset of tables -- but we don't
650 // support that in this implementation). Guaranteed to reach some
651 // interesting order at some point, but we don't track it as interesting
652 // in the FSM states. This means that these orderings don't get state bits
653 // in follows_interesting_order for themselves, but they will always have
654 // one or more interesting orders in can_reach_interesting_order.
655 // This helps us collapse access paths more efficiently; if we have
656 // an interesting order t3.x and create homogenized orderings t1.x
657 // and t2.x (due to some equality with t3.x), an access path following one
658 // isn't better than an access path following the other. They will lead
659 // to the same given the same FDs anyway (see MoreOrderedThan()), and
660 // thus are equally good.
663 // An ordering that is just added because it is easy to produce;
664 // e.g. because it is produced by scanning along an index. Such orderings
665 // can be shortened or pruned away entirely (in
666 // PruneUninterestingOrders())
667 // unless we find that they may lead to an interesting order.
673 // Only used if used_at_end = false (see AddOrdering()).
676 // Which initial state to use for this ordering (in SetOrder()).
678 };
682 // The longest ordering in m_orderings.
687 // NFSM. 0 is the initial state, all others are found by following edges.
690 // DFSM. 0 is the initial state, all others are found by following edges.
694 // After PruneUninterestingOrders has run, maps from the old indexes to the
695 // new indexes.
698 // After PruneFDs() has run, maps from the old indexes to the new indexes.
701 /// We may potentially use a lot of Ordering::Elements objects, with short and
702 /// non-overlapping life times. Therefore we have a pool
703 /// to allow reuse and avoid allocating from MEM_ROOT each time.
706 // The canonical order for two items in a grouping
707 // (after BuildEquivalenceClasses() has run; enforced by
708 // RecanonicalizeGroupings()). The reason why we sort by
709 // canonical_item first is so that switching out one element
710 // with an equivalent one (ie., applying an EQUIVALENCE
711 // functional dependency) does not change the order of the
712 // elements in the grouing, which could give false negatives
713 // in CouldBecomeInterestingOrdering().
715 if (m_items[a].canonical_item != m_items[b].canonical_item)
716 return m_items[a].canonical_item < m_items[b].canonical_item;
717 return a < b;
718 }
720 inline bool ItemBeforeInGroup(const OrderElement &a,
721 const OrderElement &b) const {
722 return ItemHandleBeforeInGroup(a.item, b.item);
723 }
725 // Helper for AddOrdering().
727 bool used_at_end, table_map homogenize_tables);
729 // See comment in .cc file.
730 void PruneUninterestingOrders(THD *thd);
732 // See comment in .cc file.
733 void PruneFDs(THD *thd);
735 // See comment in .cc file.
737 bool all_fds) const;
739 // Populates ItemInfo::canonical_item.
742 // See comment in .cc file.
745 // See comment in .cc file.
746 void AddFDsFromComputedItems(THD *thd);
748 // See comment in .cc file.
749 void AddFDsFromAggregateItems(THD *thd);
751 // See comment in .cc file.
753 THD *thd, ItemHandle argument_item, Window *window);
755 // See comment in .cc file.
756 void AddFDsFromConstItems(THD *thd);
758 // Populates ItemInfo::can_be_added_by_fd.
761 void PreReduceOrderings(THD *thd);
766 THD *thd, const Ordering &reduced_ordering, bool used_at_end,
767 int table_idx,
768 Bounds_checked_array<std::pair<ItemHandle, ItemHandle>>
769 reverse_canonical);
771 /// Sort the elements so that a will appear before b if
772 /// ItemBeforeInGroup(a,b)==true.
773 void SortElements(Ordering::Elements elements) const;
775 // See comment in .cc file.
778 void BuildNFSM(THD *thd);
779 void AddRollupFromOrder(THD *thd, int state_idx, const Ordering &ordering);
780 void AddGroupingFromOrder(THD *thd, int state_idx, const Ordering &ordering);
781 void AddGroupingFromRollup(THD *thd, int state_idx, const Ordering &ordering);
782 void TryAddingOrderWithElementInserted(THD *thd, int state_idx, int fd_idx,
783 Ordering old_ordering,
784 size_t start_point,
785 ItemHandle item_to_add,
786 enum_order direction);
787 void PruneNFSM(THD *thd);
788 bool AlwaysActiveFD(int fd_idx);
789 void FinalizeDFSMState(THD *thd, int state_idx);
791 int *generation, int extra_allowed_fd_idx);
792 void ConvertNFSMToDFSM(THD *thd);
794 // Populates state_idx for every ordering in m_ordering.
797 // If a state with the given ordering already exists (artificial or not),
798 // returns its index. Otherwise, adds an artificial state with the given
799 // order and returns its index.
800 int AddArtificialState(THD *thd, const Ordering &ordering);
802 // Add an edge from state_idx to an state with the given ordering; if there is
803 // no such state, adds an artificial state with it (taking a copy, so does not
804 // need to take ownership).
805 void AddEdge(THD *thd, int state_idx, int required_fd_idx,
806 const Ordering &ordering);
808 // Returns true if the given (non-DECAY) functional dependency applies to the
809 // given ordering, and the index of the element from which the FD is active
810 // (ie., the last element that was part of the head). One can start inserting
811 // the tail element at any point _after_ this index; if it is an EQUIVALENCE
812 // FD, one can instead choose to replace the element at start_point entirely.
814 const Ordering &ordering,
815 int *start_point) const;
817 /**
818 Fetch an Ordering::Elements object with size()==m_longest_ordering.
819 Get it from m_elements_pool if that is non-empty, otherwise allocate
820 from mem_root.
821 */
823 if (m_elements_pool.empty()) {
825 } else {
827 m_elements_pool.pop_back();
829 }
830 }
832 /**
833 Return an Ordering::Elements object with size()==m_longest_ordering
834 to m_elements_pool.
835 */
837 // Overwrite the array with garbage, so that we have a better chance
838 // of detecting it if we by mistake access it afterwards.
839 TRASH(, m_longest_ordering * sizeof([0]));
840 m_elements_pool.push_back(;
841 }
842 // Used for optimizer trace.
844 std::string PrintOrdering(const Ordering &ordering) const;
846 bool html) const;
847 void PrintFunctionalDependencies(std::ostream *trace);
848 void PrintInterestingOrders(std::ostream *trace);
849 void PrintNFSMDottyGraph(std::ostream *trace) const;
850 void PrintDFSMDottyGraph(std::ostream *trace) const;
855 return a.required_fd_idx == b.required_fd_idx && a.state_idx == b.state_idx;
860 return !(a == b);
Element_type * data()
Definition: sql_array.h:116
static Bounds_checked_array Alloc(MEM_ROOT *mem_root, size_t size)
Definition: sql_array.h:70
const_iterator cbegin() const
Returns a pointer to the first element in the array.
Definition: sql_array.h:144
size_t size() const
Definition: sql_array.h:154
Bounds_checked_array Clone(MEM_ROOT *mem_root) const
Make a copy of '*this'. Allocate memory for m_array on 'mem_root'.
Definition: sql_array.h:75
const_iterator cend() const
Returns a pointer to the past-the-end element in the array.
Definition: sql_array.h:146
Base class that is used to represent any kind of expression in a relational query.
Definition: item.h:930
Definition: interesting_orders.h:315
void SetHeadForAggregates(Bounds_checked_array< ItemHandle > head)
Definition: interesting_orders.h:388
void AddRollupFromOrder(THD *thd, int state_idx, const Ordering &ordering)
void AddEdge(THD *thd, int state_idx, int required_fd_idx, const Ordering &ordering)
bool ItemHandleBeforeInGroup(ItemHandle a, ItemHandle b) const
Definition: interesting_orders.h:714
void CreateOrderingsFromGroupings(THD *thd)
We don't currently have any operators that only group and do not sort (e.g.
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:680
bool ImpliedByEarlierElements(ItemHandle item, Ordering::Elements prefix, bool all_fds) const
Checks whether the given item is redundant given previous elements in the ordering; ie....
Bounds_checked_array< int > m_optimized_fd_mapping
Definition: interesting_orders.h:699
StateIndex SetOrder(int ordering_idx) const
Definition: interesting_orders.h:428
int num_orderings() const
Definition: interesting_orders.h:360
bool DoesFollowOrder(StateIndex state_idx, int ordering_idx) const
Definition: interesting_orders.h:455
bool m_rollup
Definition: interesting_orders.h:559
int m_longest_ordering
Definition: interesting_orders.h:683
Mem_root_array< DFSMState > m_dfsm_states
Definition: interesting_orders.h:691
bool m_built
Definition: interesting_orders.h:515
void AddHomogenizedOrderingIfPossible(THD *thd, const Ordering &reduced_ordering, bool used_at_end, int table_idx, Bounds_checked_array< std::pair< ItemHandle, ItemHandle > > reverse_canonical)
Helper function for CreateHomogenizedOrderings().
friend bool operator==(const NFSMEdge &a, const NFSMEdge &b)
Definition: interesting_orders.h:853
std::string PrintOrdering(const Ordering &ordering) const
Ordering ReduceOrdering(Ordering ordering, bool all_fds, Ordering::Elements tmp) const
Remove redundant elements using the functional dependencies that we have, to give a more canonical fo...
void PrintFunctionalDependencies(std::ostream *trace)
int RemapOrderingIndex(int ordering_idx) const
Definition: interesting_orders.h:421
void FinalizeDFSMState(THD *thd, int state_idx)
void AddGroupingFromRollup(THD *thd, int state_idx, const Ordering &ordering)
void PrintDFSMDottyGraph(std::ostream *trace) const
friend bool operator!=(const NFSMEdge &a, const NFSMEdge &b)
Definition: interesting_orders.h:858
Mem_root_array< OrderElement * > m_elements_pool
We may potentially use a lot of Ordering::Elements objects, with short and non-overlapping life times...
Definition: interesting_orders.h:704
int num_items() const
Definition: interesting_orders.h:326
bool ordering_is_relevant_for_sortahead(int ordering_idx) const
Definition: interesting_orders.h:366
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:395
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:688
void SortElements(Ordering::Elements elements) const
Sort the elements so that a will appear before b if ItemBeforeInGroup(a,b)==true.
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)
bool FunctionalDependencyApplies(const FunctionalDependency &fd, const Ordering &ordering, int *start_point) const
Mem_root_array< DFSMEdge > m_dfsm_edges
Definition: interesting_orders.h:692
void ReturnElements(Ordering::Elements elements)
Return an Ordering::Elements object with size()==m_longest_ordering to m_elements_pool.
Definition: interesting_orders.h:836
bool MoreOrderedThan(StateIndex a_idx, StateIndex b_idx, std::bitset< kMaxSupportedOrderings > ignored_orderings) const
Definition: interesting_orders.h:492
bool AlwaysActiveFD(int fd_idx)
void BuildNFSM(THD *thd)
void PrintInterestingOrders(std::ostream *trace)
void BuildEquivalenceClasses()
int AddArtificialState(THD *thd, const Ordering &ordering)
int StateIndex
Definition: interesting_orders.h:426
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:325
void PrintNFSMDottyGraph(std::ostream *trace) const
const Ordering & ordering(int ordering_idx) const
Definition: interesting_orders.h:362
void FindElementsThatCanBeAddedByFDs()
StateIndex ApplyFDs(StateIndex state_idx, FunctionalDependencySet fds) const
Bounds_checked_array< int > m_optimized_ordering_mapping
Definition: interesting_orders.h:696
int AddOrdering(THD *thd, Ordering order, bool interesting, bool used_at_end, table_map homogenize_tables)
Definition: interesting_orders.h:351
Ordering::Elements RetrieveElements(MEM_ROOT *mem_root)
Fetch an Ordering::Elements object with size()==m_longest_ordering.
Definition: interesting_orders.h:822
void ExpandThroughAlwaysActiveFDs(Mem_root_array< int > *nfsm_states, int *generation, int extra_allowed_fd_idx)
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)
Bounds_checked_array< ItemHandle > CollectHeadForStaticWindowFunction(THD *thd, ItemHandle argument_item, Window *window)
Mem_root_array< ItemInfo > m_items
Definition: interesting_orders.h:550
ItemHandle GetHandle(Item *item)
void FindInitialStatesForOrdering()
void AddGroupingFromOrder(THD *thd, int state_idx, const Ordering &ordering)
LogicalOrderings(THD *thd)
Mem_root_array< FunctionalDependency > m_fds
Definition: interesting_orders.h:685
void ConvertNFSMToDFSM(THD *thd)
From the NFSM, convert an equivalent DFSM.
Bounds_checked_array< ItemHandle > m_aggregate_head
Definition: interesting_orders.h:554
void TryAddingOrderWithElementInserted(THD *thd, int state_idx, int fd_idx, Ordering old_ordering, size_t start_point, ItemHandle item_to_add, enum_order direction)
FunctionalDependencySet GetFDSet(int fd_idx) const
Definition: interesting_orders.h:437
void RecanonicalizeGroupings()
void Build(THD *thd)
std::string PrintFunctionalDependency(const FunctionalDependency &fd, bool html) const
void CreateOrderingsFromRollups(THD *thd)
bool ItemBeforeInGroup(const OrderElement &a, const OrderElement &b) const
Definition: interesting_orders.h:720
bool CouldBecomeInterestingOrdering(const Ordering &ordering) const
For a given ordering, check whether it ever has the hope of becoming an interesting ordering.
int num_fds() const
Definition: interesting_orders.h:377
A typesafe replacement for DYNAMIC_ARRAY.
Definition: mem_root_array.h:426
A scope-guard class for allocating an Ordering::Elements instance which is automatically returned to ...
Represents a (potentially interesting) ordering, rollup or (non-rollup) grouping.
Definition: interesting_orders.h:160
Elements & GetElements()
Definition: interesting_orders.h:222
size_t size() const
Definition: interesting_orders.h:227
The kind of ordering that an Ordering instance may represent.
Definition: interesting_orders.h:168
@ kOrder
Specific sequence of m_elements, and specific direction of each element.
@ kGroup
Elements may appear in any sequence and may be ordered in any direction.
@ kRollup
Specific sequence of m_elements, but each element may be ordered in any direction.
@ kEmpty
An ordering with no elements.
Ordering & operator=(const Ordering &other)
Assignment operator. Only defined explicitly to check Valid().
Definition: interesting_orders.h:199
Kind GetKind() const
Definition: interesting_orders.h:212
Definition: interesting_orders.h:186
Ordering(Elements elements, Kind kind)
Definition: interesting_orders.h:188
void Deduplicate()
Remove duplicate entries, in-place.
Bounds_checked_array< OrderElement > Elements
This type hold the individual elements of the ordering.
Definition: interesting_orders.h:165
Kind m_kind
The kind of this ordering.
Definition: interesting_orders.h:239
Ordering Clone(MEM_ROOT *mem_root) const
Make a copy of *this. Allocate new memory for m_elements from mem_root.
Definition: interesting_orders.h:207
Elements m_elements
The ordering terms.
Definition: interesting_orders.h:236
friend bool operator==(const Ordering &a, const Ordering &b)
Check if 'a' and 'b' has the same kind and contains the same elements.
Definition: interesting_orders.h:246
Ordering(const Ordering &other)
Copy constructor. Only defined explicitly to check Valid().
Definition: interesting_orders.h:193
bool Valid() const
const Elements & GetElements() const
Definition: interesting_orders.h:217
For each client connection we create a separate thread with THD serving as a thread/connection descri...
Definition: sql_lexer_thd.h:36
Represents the (explicit) window of a SQL 2003 section 7.11 <window clause>, or the implicit (inlined...
Definition: window.h:110
static MEM_ROOT mem_root
static bool equal(const Item *i1, const Item *i2, const Field *f2)
bool operator!=(const Ordering &a, const Ordering &b)
Definition: interesting_orders.h:254
bool operator==(const Ordering &a, const Ordering &b)
Check if 'a' and 'b' has the same kind and contains the same elements.
Definition: interesting_orders.h:246
std::bitset< kMaxSupportedFDs > FunctionalDependencySet
Definition: interesting_orders_defs.h:63
static constexpr int kMaxSupportedFDs
Definition: interesting_orders_defs.h:62
static constexpr int kMaxSupportedOrderings
Definition: interesting_orders_defs.h:65
int ItemHandle
Definition: interesting_orders_defs.h:39
Definition: key_spec.h:65
void TRASH(void *ptr, size_t length)
Put bad content in memory to be sure it will segfault if dereferenced.
Definition: memory_debugging.h:71
uint64_t table_map
Definition: my_table_map.h:30
mutable_buffer buffer(void *p, size_t n) noexcept
Definition: buffer.h:418
required string type
Definition: replication_group_member_actions.proto:34
Definition: interesting_orders.h:258
ItemHandle tail
Definition: interesting_orders.h:290
enum FunctionalDependency::@109 type
bool always_active
Definition: interesting_orders.h:312
Bounds_checked_array< ItemHandle > head
Definition: interesting_orders.h:289
@ FD
Definition: interesting_orders.h:280
Definition: interesting_orders.h:273
Definition: interesting_orders.h:286
Definition: interesting_orders.h:624
int state_idx
Definition: interesting_orders.h:626
int required_fd_idx
Definition: interesting_orders.h:625
const DFSMState * state(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:632
const FunctionalDependency * required_fd(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:628
Definition: interesting_orders.h:599
FunctionalDependencySet can_use_fd
Definition: interesting_orders.h:621
Mem_root_array< int > nfsm_states
Definition: interesting_orders.h:601
std::bitset< kMaxSupportedOrderings > follows_interesting_order
Definition: interesting_orders.h:609
Mem_root_array< int > outgoing_edges
Definition: interesting_orders.h:600
std::bitset< kMaxSupportedOrderings > can_reach_interesting_order
Definition: interesting_orders.h:616
Bounds_checked_array< int > next_state
Definition: interesting_orders.h:606
Definition: interesting_orders.h:517
bool used_desc
Definition: interesting_orders.h:545
bool used_in_grouping
Definition: interesting_orders.h:546
ItemHandle canonical_item
Definition: interesting_orders.h:531
bool can_be_added_by_fd
Definition: interesting_orders.h:537
bool used_asc
Definition: interesting_orders.h:544
Item * item
Definition: interesting_orders.h:519
Definition: interesting_orders.h:561
const NFSMState * state(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:575
int required_fd_idx
Definition: interesting_orders.h:566
const FunctionalDependency * required_fd(const LogicalOrderings *orderings) const
Definition: interesting_orders.h:571
int state_idx
Definition: interesting_orders.h:569
Definition: interesting_orders.h:583
enum LogicalOrderings::NFSMState::@110 type
Mem_root_array< NFSMEdge > outgoing_edges
Definition: interesting_orders.h:585
std::bitset< kMaxSupportedOrderings > can_reach_interesting_order
Definition: interesting_orders.h:590
int satisfied_ordering_idx
Definition: interesting_orders.h:587
int seen
Definition: interesting_orders.h:597
Ordering satisfied_ordering
Definition: interesting_orders.h:586
Definition: interesting_orders.h:584
Definition: interesting_orders.h:584
Definition: interesting_orders.h:584
Definition: interesting_orders.h:637
StateIndex state_idx
Definition: interesting_orders.h:677
Ordering ordering
Definition: interesting_orders.h:638
bool used_at_end
Definition: interesting_orders.h:671
Definition: interesting_orders.h:643
Definition: interesting_orders.h:668
Definition: interesting_orders.h:646
Definition: interesting_orders.h:661
enum LogicalOrderings::OrderingWithInfo::Type type
table_map homogenize_tables
Definition: interesting_orders.h:674
The MEM_ROOT is a simple arena, where allocations are carved out of larger blocks.
Definition: my_alloc.h:83
Definition: interesting_orders_defs.h:44
ItemHandle item
Definition: interesting_orders_defs.h:45