MySQL 9.1.0
Source Code Documentation
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#include <interesting_orders.h>
Classes | |
struct | DFSMEdge |
struct | DFSMState |
struct | ItemInfo |
struct | NFSMEdge |
struct | NFSMState |
struct | OrderingWithInfo |
class | OrderWithElementInserted |
Given an order O and a functional dependency FD: S → x where S is a subset of O, create new orderings by inserting x into O at different positions, and add those to the set of orderings if they could become interesting (. More... | |
Public Types | |
using | StateIndex = int |
Public Member Functions | |
LogicalOrderings (THD *thd) | |
ItemHandle | GetHandle (Item *item) |
Item * | item (ItemHandle item) const |
int | num_items () const |
int | AddOrdering (THD *thd, Ordering order, bool interesting, bool used_at_end, table_map homogenize_tables) |
int | num_orderings () const |
const Ordering & | ordering (int ordering_idx) const |
bool | ordering_is_relevant_for_sortahead (int ordering_idx) const |
int | AddFunctionalDependency (THD *thd, FunctionalDependency fd) |
int | num_fds () const |
void | SetHeadForAggregates (Bounds_checked_array< ItemHandle > head) |
void | SetRollup (bool rollup) |
void | Build (THD *thd) |
int | RemapOrderingIndex (int ordering_idx) const |
StateIndex | SetOrder (int ordering_idx) const |
FunctionalDependencySet | GetFDSet (int fd_idx) const |
StateIndex | ApplyFDs (StateIndex state_idx, FunctionalDependencySet fds) const |
bool | DoesFollowOrder (StateIndex state_idx, int ordering_idx) const |
bool | MoreOrderedThan (StateIndex a_idx, StateIndex b_idx, std::bitset< kMaxSupportedOrderings > ignored_orderings) 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 form before homogenization. More... | |
Private Member Functions | |
bool | ItemHandleBeforeInGroup (ItemHandle a, ItemHandle b) const |
bool | ItemBeforeInGroup (const OrderElement &a, const OrderElement &b) const |
int | AddOrderingInternal (THD *thd, Ordering order, OrderingWithInfo::Type type, bool used_at_end, table_map homogenize_tables) |
void | PruneUninterestingOrders (THD *thd) |
Try to get rid of uninteresting orders, possibly by discarding irrelevant suffixes and merging them with others. More... | |
void | PruneFDs (THD *thd) |
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., whether adding it will never change the ordering. More... | |
void | BuildEquivalenceClasses () |
void | RecanonicalizeGroupings () |
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), we add {a} → (a + 1) (since addition is deterministic). More... | |
void | AddFDsFromAggregateItems (THD *thd) |
Bounds_checked_array< ItemHandle > | CollectHeadForStaticWindowFunction (THD *thd, ItemHandle argument_item, Window *window) |
void | AddFDsFromConstItems (THD *thd) |
Try to add FDs from items that are constant by themselves, e.g. More... | |
void | FindElementsThatCanBeAddedByFDs () |
void | PreReduceOrderings (THD *thd) |
Do safe reduction on all orderings (some of them may get merged by PruneUninterestingOrders() later), ie., remove all items that may be removed using only FDs that always are active. More... | |
void | CreateOrderingsFromGroupings (THD *thd) |
We don't currently have any operators that only group and do not sort (e.g. More... | |
void | CreateOrderingsFromRollups (THD *thd) |
void | CreateHomogenizedOrderings (THD *thd) |
For each interesting ordering, see if we can homogenize it onto each table. More... | |
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(). More... | |
void | SortElements (Ordering::Elements elements) const |
Sort the elements so that a will appear before b if ItemBeforeInGroup(a,b)==true. More... | |
bool | CouldBecomeInterestingOrdering (const Ordering &ordering) const |
For a given ordering, check whether it ever has the hope of becoming an interesting ordering. More... | |
void | BuildNFSM (THD *thd) |
void | AddRollupFromOrder (THD *thd, int state_idx, const Ordering &ordering) |
void | AddGroupingFromOrder (THD *thd, int state_idx, const Ordering &ordering) |
void | AddGroupingFromRollup (THD *thd, int state_idx, const Ordering &ordering) |
void | TryAddingOrderWithElementInserted (THD *thd, int state_idx, int fd_idx, Ordering old_ordering, size_t start_point, ItemHandle item_to_add, enum_order direction) |
void | PruneNFSM (THD *thd) |
Try to prune away irrelevant nodes from the NFSM; it is worth spending some time on this, since the number of NFSM states can explode the size of the DFSM. More... | |
bool | AlwaysActiveFD (int fd_idx) |
void | FinalizeDFSMState (THD *thd, int state_idx) |
void | ExpandThroughAlwaysActiveFDs (Mem_root_array< int > *nfsm_states, int *generation, int extra_allowed_fd_idx) |
void | ConvertNFSMToDFSM (THD *thd) |
From the NFSM, convert an equivalent DFSM. More... | |
void | FindInitialStatesForOrdering () |
int | AddArtificialState (THD *thd, const Ordering &ordering) |
void | AddEdge (THD *thd, int state_idx, int required_fd_idx, const Ordering &ordering) |
bool | FunctionalDependencyApplies (const FunctionalDependency &fd, const Ordering &ordering, int *start_point) const |
Ordering::Elements | RetrieveElements (MEM_ROOT *mem_root) |
Fetch an Ordering::Elements object with size()==m_longest_ordering. More... | |
void | ReturnElements (Ordering::Elements elements) |
Return an Ordering::Elements object with size()==m_longest_ordering to m_elements_pool. More... | |
std::string | PrintOrdering (const Ordering &ordering) const |
std::string | PrintFunctionalDependency (const FunctionalDependency &fd, bool html) const |
void | PrintFunctionalDependencies (std::ostream *trace) |
void | PrintInterestingOrders (std::ostream *trace) |
void | PrintNFSMDottyGraph (std::ostream *trace) const |
void | PrintDFSMDottyGraph (std::ostream *trace) const |
Private Attributes | |
bool | m_built = false |
Mem_root_array< ItemInfo > | m_items |
Bounds_checked_array< ItemHandle > | m_aggregate_head |
bool | m_rollup = false |
Mem_root_array< OrderingWithInfo > | m_orderings |
int | m_longest_ordering = 0 |
Mem_root_array< FunctionalDependency > | m_fds |
Mem_root_array< NFSMState > | m_states |
Mem_root_array< DFSMState > | m_dfsm_states |
Mem_root_array< DFSMEdge > | m_dfsm_edges |
Bounds_checked_array< int > | m_optimized_ordering_mapping |
Bounds_checked_array< int > | m_optimized_fd_mapping |
Mem_root_array< OrderElement * > | m_elements_pool |
We may potentially use a lot of Ordering::Elements objects, with short and non-overlapping life times. More... | |
Friends | |
class | OrderingElementsGuard |
bool | operator== (const NFSMEdge &a, const NFSMEdge &b) |
bool | operator!= (const NFSMEdge &a, const NFSMEdge &b) |
using LogicalOrderings::StateIndex = int |
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Try to add new FDs from items that are not base items; e.g., if we have an item (a + 1), we add {a} → (a + 1) (since addition is deterministic).
This can help reducing orderings that are on such derived items. For simplicity, we only bother doing this for items that derive from a single base field; i.e., from (a + b), we don't add {a,b} → (a + b) even though we could. Also note that these are functional dependencies, not equivalences; even though ORDER BY (a + 1) could be satisfied by an ordering on (a) (barring overflow issues), this does not hold in general, e.g. ORDER BY (-a) is not satisfied by an ordering on (a), not to mention ORDER BY (a*a). We do not have the framework in Item to understand which functions are monotonous, so we do not attempt to create equivalences.
This is really the only the case where we can get transitive FDs that are not equivalences. Since our approach does not apply FDs transitively without adding the intermediate item (e.g., for {a} → b and {b} → c, we won't extend (a) to (ac), only to (abc)), we extend any existing FDs here when needed.
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Try to add FDs from items that are constant by themselves, e.g.
if someone does ORDER BY 'x', add a new FD {} → 'x' so that the ORDER BY can be elided.
TODO(sgunders): This can potentially remove subqueries or other functions that would throw errors if actually executed, potentially modifying semantics. See if that is illegal, and thus, if we need to test-execute them at least once somehow (ideally not during optimization).
int LogicalOrderings::AddFunctionalDependency | ( | THD * | thd, |
FunctionalDependency | fd | ||
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Helper function for CreateHomogenizedOrderings().
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LogicalOrderings::StateIndex LogicalOrderings::ApplyFDs | ( | LogicalOrderings::StateIndex | state_idx, |
FunctionalDependencySet | fds | ||
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void LogicalOrderings::Build | ( | THD * | thd | ) |
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From the NFSM, convert an equivalent DFSM.
This is by means of the so-called powerset conversion, which is more commonly used to convert NFAs to DFAs. (The only real difference is that FAs have accepting states, while our FSM instead needs to store information about constituent interesting order states.)
The powerset algorithm works by creating DFSM states that represent sets of NFSM states we could be in. E.g., if we have a state (a) and an FD {} → x can lead to new states () (ϵ-edge), (a) (implicit self-edge), (x), (ax), (xa), then we create a single new DFSM state that represent all those five states, and an {} → x edge from {(a)} to that new state. When creating edges from such superstates, we need to follow that FD from all of them, so the list of constituent states can be fairly large.
In theory, we could get 2^n DFSM states from n NFSM states, but in practice, we get fewer since our orderings generally only increase, not decrease. We only generate DFSM states by following FDs from the initial NFSM state; we don't create states eagerly for all 2^n possibilities.
When creating DFSM states, we always include states that can be reached by means of always-active FDs. The ϵ edge (drop the last element from the ordering) is always active, and the client can also mark others as such. This means we get fewer DFSM states and fewer FDs to follow. See FunctionalDependency::always_active.
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For a given ordering, check whether it ever has the hope of becoming an interesting ordering.
In its base form, this is a prefix check; if we have an ordering (a,b) and an interesting order (a,b,c), it passes. However, we add some slightly more lax heuristics in order to make the graph a bit wider at build time (and thus require fewer FD applications at runtime); namely, if there's a prefix mismatch but the item could be added by some FD later (without the ordering becoming too long), we let it slide and just skip that item.
E.g.: If we have an ordering (a,b) and an interesting order (a,x,b), we first match a. x does not match b, but we check whether x is ever on the right side of any FD (for instance because there might be an FD a → x). If it is, we skip it and match b with b. There's an example of this in the DoesNotStrictlyPruneOnPrefixes unit test.
Obviously, this leads to false positives, but that is fine; this is just to prune down the amount of states in the NFSM. [Neu04] points out that such pruning is pretty much essential for performance, and our experience is the same.
There is one extra quirk; the prefix check needs to take equivalences into account, or we would prune away orderings that could become interesting after equivalences. We solve this by always mapping to an equivalence class when doing the prefix comparison. There's an example of this in the TwoEquivalences unit test.
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For each interesting ordering, see if we can homogenize it onto each table.
A homogenized ordering is one that refers to fewer tables than the original one – in our case, a single table. (If we wanted to, we could homogenize down to sets of tables instead of single tables only. However, that would open up for O(2^n) orderings, so we restrict to single-table.)
The idea is to enable sort-ahead; find an ordering we can sort a single table in that, after later applying functional dependencies, eventually gives the desired ordering. This is just a heuristic (in particular, we only consider equivalences, not other functional dependencies), but in most cases will give us an ordering if any exist.
Neumann et al do not talk much about this, so this comes from the Simmen paper, where it is called “Homogenize Order”.
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We don't currently have any operators that only group and do not sort (e.g.
hash grouping), so we always implement grouping by sorting. This function makes that representation explicit – for each grouping, it will make sure there is at least one ordering representing that grouping. This means we never need to “sort by a grouping”, which would destroy ordering information that could be useful later.
As an example, take SELECT ... GROUP BY a, b ORDER BY a. This needs to group first by {a,b} (assume we're using filesort, not an index), then sort by (a). If we just represent the sort we're doing as going directly to {a,b}, we can't elide the sort on (a). Instead, we create a sort (a,b) (implicitly convertible to {a,b}), which makes the FSM understand that we're both sorted on (a,b) and grouped on {a,b}, and then also sorted on (a).
Any given grouping would be satisfied by lots of different orderings: {a,b} could be (a,b), (b,a), (a DESC, b) etc.. We look through all interesting orders that are a subset of our grouping, and if they are, we extend them arbitrarily to complete the grouping. E.g., if our grouping is {a,b,c,d} and the ordering (c DESC, b) is interesting, we make a homogenized ordering (c DESC, b, a, d). This is roughly equivalent to Simmen's “Cover Order” procedure. If we cannot make such a cover, we simply make a new last-resort ordering (a,b,c,d).
We don't consider equivalences here; perhaps we should, at least for at-end groupings.
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ItemHandle LogicalOrderings::GetHandle | ( | Item * | item | ) |
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Checks whether the given item is redundant given previous elements in the ordering; ie., whether adding it will never change the ordering.
This could either be because it's a duplicate, or because it is implied by functional dependencies. When this is applied to all elements in turn, it is called “reducing” the ordering. [Neu04] claims that this operation is not confluent, which is erroneous (their example is faulty, ignoring that Simmen reduces from the back). [Neu04b] has modified the claim to be that it is not confluent for groupings, which is correct. We make no attempt at optimality.
If all_fds is true, we consider all functional dependencies, including those that may not always be active; e.g. a FD a=b may come from a join, and thus does not hold before the join is actually done, but we assume it holds anyway. This is OK from order homogenization, which is concerned with making orderings that will turn into the desired interesting ordering (e.g. for ORDER BY) only after all joins have been done. It would not be OK if we were to use it for merge joins somehow.
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Do safe reduction on all orderings (some of them may get merged by PruneUninterestingOrders() later), ie., remove all items that may be removed using only FDs that always are active.
There's a problem in [Neu04] that is never adequately addressed; orderings are only ever expanded, and then eventually compared against interesting orders. But the interesting order itself is not necessarily extended, due to pruning. For instance, if an index could yield (x,y) and we have {} → x, there's no way we could get it to match the interesting order (y) even though they are logically equivalent. For an even trickier case, imagine an index (x,y) and an interesting order (y,z), with {} → x and y → z. For this to match, we'd need to have a “super-order” (x,y,z) and infer that from both orderings.
Instead, we do a pre-step related to Simmen's “Test Ordering” procedure; we reduce the orderings. In the example above, both will be reduced to (y), and then match. This is mostly a band-aid around the problem; for instance, it cannot deal with FDs that are not always active, and it does not deal adequately with groupings (since reduction does not).
Note that this could make the empty ordering interesting after merging.
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Try to prune away irrelevant nodes from the NFSM; it is worth spending some time on this, since the number of NFSM states can explode the size of the DFSM.
Like with PruneFDs(), we don't do any of the pruning described in [Neu04]; it is unclear exactly what is meant, but it would seem the state removal/merging there is either underdefined or simply does not do anything except remove trivially bad nodes (those that cannot reach anything).
This also sets the can_reach_interesting_order bitmap on each NFSM node.
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Try to get rid of uninteresting orders, possibly by discarding irrelevant suffixes and merging them with others.
In a typical query, this removes a large amount of index-created orderings that will never get to something interesting, reducing the end FSM size (and thus, reducing the number of different access paths we have to keep around).
This step is the only one that can move orderings around, and thus also populates m_optimized_ordering_mapping.
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Ordering LogicalOrderings::ReduceOrdering | ( | Ordering | ordering, |
bool | all_fds, | ||
Ordering::Elements | tmp | ||
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Remove redundant elements using the functional dependencies that we have, to give a more canonical form before homogenization.
Note that we assume here that every functional dependency holds, so this is not applicable generally throughout the tree, only at the end (e.g. final ORDER BY). This is called “Reduce Order” in the Simmen paper.
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Fetch an Ordering::Elements object with size()==m_longest_ordering.
Get it from m_elements_pool if that is non-empty, otherwise allocate from mem_root.
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Return an Ordering::Elements object with size()==m_longest_ordering to m_elements_pool.
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Sort the elements so that a will appear before b if ItemBeforeInGroup(a,b)==true.
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We may potentially use a lot of Ordering::Elements objects, with short and non-overlapping life times.
Therefore we have a pool to allow reuse and avoid allocating from MEM_ROOT each time.
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