mz_transform/analysis.rs
1// Copyright Materialize, Inc. and contributors. All rights reserved.
2//
3// Use of this software is governed by the Business Source License
4// included in the LICENSE file.
5//
6// As of the Change Date specified in that file, in accordance with
7// the Business Source License, use of this software will be governed
8// by the Apache License, Version 2.0.
9
10//! Traits and types for reusable expression analysis
11
12pub mod equivalences;
13pub mod monotonic;
14
15use mz_expr::MirRelationExpr;
16
17pub use arity::Arity;
18pub use cardinality::Cardinality;
19pub use column_names::{ColumnName, ColumnNames};
20pub use common::{Derived, DerivedBuilder, DerivedView};
21pub use explain::annotate_plan;
22pub use non_negative::NonNegative;
23pub use subtree::SubtreeSize;
24pub use types::RelationType;
25pub use unique_keys::UniqueKeys;
26
27/// An analysis that can be applied bottom-up to a `MirRelationExpr`.
28pub trait Analysis: 'static {
29 /// The type of value this analysis associates with an expression.
30 type Value: std::fmt::Debug;
31 /// Announce any dependencies this analysis has on other analyses.
32 ///
33 /// The method should invoke `builder.require::<Foo>()` for each other
34 /// analysis `Foo` this analysis depends upon.
35 fn announce_dependencies(_builder: &mut DerivedBuilder) {}
36 /// The analysis value derived for an expression, given other analysis results.
37 ///
38 /// The other analysis results include the results of this analysis for all children,
39 /// in `results`, and the results of other analyses this analysis has expressed a
40 /// dependence upon, in `depends`, for children and the expression itself.
41 /// The analysis results for `Self` can only be found in `results`, and are not
42 /// available in `depends`.
43 ///
44 /// Implementors of this method must defensively check references into `results`, as
45 /// it may be invoked on `LetRec` bindings that have not yet been populated. It is up
46 /// to the analysis what to do in that case, but conservative behavior is recommended.
47 ///
48 /// The `index` indicates the post-order index for the expression, for use in finding
49 /// the corresponding information in `results` and `depends`.
50 ///
51 /// The returned result will be associated with this expression for this analysis,
52 /// and the analyses will continue.
53 fn derive(
54 &self,
55 expr: &MirRelationExpr,
56 index: usize,
57 results: &[Self::Value],
58 depends: &Derived,
59 ) -> Self::Value;
60
61 /// When available, provide a lattice interface to allow optimistic recursion.
62 ///
63 /// Providing a non-`None` output indicates that the analysis intends re-iteration.
64 fn lattice() -> Option<Box<dyn Lattice<Self::Value>>> {
65 None
66 }
67}
68
69/// Lattice methods for repeated analysis
70pub trait Lattice<T> {
71 /// An element greater than all other elements.
72 fn top(&self) -> T;
73 /// Set `a` to the greatest lower bound of `a` and `b`, and indicate if `a` changed as a result.
74 fn meet_assign(&self, a: &mut T, b: T) -> bool;
75}
76
77/// Types common across multiple analyses
78pub mod common {
79
80 use std::any::{Any, TypeId};
81 use std::collections::BTreeMap;
82
83 use itertools::Itertools;
84 use mz_expr::LocalId;
85 use mz_expr::MirRelationExpr;
86 use mz_ore::assert_none;
87 use mz_repr::optimize::OptimizerFeatures;
88
89 use super::Analysis;
90 use super::subtree::SubtreeSize;
91
92 /// Container for analysis state and binding context.
93 #[derive(Default)]
94 #[allow(missing_debug_implementations)]
95 pub struct Derived {
96 /// A record of active analyses and their results, indexed by their type id.
97 analyses: BTreeMap<TypeId, Box<dyn AnalysisBundle>>,
98 /// Analyses ordered where each depends only on strictly prior analyses.
99 order: Vec<TypeId>,
100 /// Map from local identifier to result offset for analysis values.
101 bindings: BTreeMap<LocalId, usize>,
102 }
103
104 impl Derived {
105 /// Return the analysis results derived so far.
106 ///
107 /// # Panics
108 ///
109 /// This method panics if `A` was not installed as a required analysis.
110 pub fn results<A: Analysis>(&self) -> &[A::Value] {
111 let type_id = TypeId::of::<Bundle<A>>();
112 if let Some(bundle) = self.analyses.get(&type_id) {
113 if let Some(bundle) = bundle.as_any().downcast_ref::<Bundle<A>>() {
114 return &bundle.results[..];
115 }
116 }
117 panic!("Analysis {:?} missing", std::any::type_name::<A>());
118 }
119 /// Bindings from local identifiers to result offsets for analysis values.
120 pub fn bindings(&self) -> &BTreeMap<LocalId, usize> {
121 &self.bindings
122 }
123 /// Result offsets for the state of a various number of children of the current expression.
124 ///
125 /// The integers are the zero-offset locations in the `SubtreeSize` analysis. The order of
126 /// the children is descending, from last child to first, because of how the information is
127 /// laid out, and the non-reversibility of the look-ups.
128 ///
129 /// It is an error to call this method with more children than expression has.
130 pub fn children_of_rev<'a>(
131 &'a self,
132 start: usize,
133 count: usize,
134 ) -> impl Iterator<Item = usize> + 'a {
135 let sizes = self.results::<SubtreeSize>();
136 let offset = 1;
137 (0..count).scan(offset, move |offset, _| {
138 let result = start - *offset;
139 *offset += sizes[result];
140 Some(result)
141 })
142 }
143
144 /// Recast the derived data as a view that can be subdivided into views over child state.
145 pub fn as_view<'a>(&'a self) -> DerivedView<'a> {
146 DerivedView {
147 derived: self,
148 lower: 0,
149 upper: self.results::<SubtreeSize>().len(),
150 }
151 }
152 }
153
154 /// The subset of a `Derived` corresponding to an expression and its children.
155 ///
156 /// Specifically, bounds an interval `[lower, upper)` that ends with the state
157 /// of an expression, at `upper-1`, and is preceded by the state of descendents.
158 ///
159 /// This is best thought of as a node in a tree rather
160 #[allow(missing_debug_implementations)]
161 #[derive(Copy, Clone)]
162 pub struct DerivedView<'a> {
163 derived: &'a Derived,
164 lower: usize,
165 upper: usize,
166 }
167
168 impl<'a> DerivedView<'a> {
169 /// The value associated with the expression.
170 pub fn value<A: Analysis>(&self) -> Option<&'a A::Value> {
171 self.results::<A>().last()
172 }
173
174 /// The post-order traversal index for the expression.
175 ///
176 /// This can be used to index into the full set of results, as provided by an
177 /// instance of `Derived`.
178 pub fn index(&self) -> usize {
179 self.upper - 1
180 }
181
182 /// The value bound to an identifier, if it has been derived.
183 ///
184 /// There are several reasons the value could not be derived, and this method
185 /// does not distinguish between them.
186 pub fn bound<A: Analysis>(&self, id: LocalId) -> Option<&'a A::Value> {
187 self.derived
188 .bindings
189 .get(&id)
190 .and_then(|index| self.derived.results::<A>().get(*index))
191 }
192
193 /// The results for expression and its children.
194 ///
195 /// The results for the expression itself will be the last element.
196 ///
197 /// # Panics
198 ///
199 /// This method panics if `A` was not installed as a required analysis.
200 pub fn results<A: Analysis>(&self) -> &'a [A::Value] {
201 &self.derived.results::<A>()[self.lower..self.upper]
202 }
203
204 /// Bindings from local identifiers to result offsets for analysis values.
205 ///
206 /// This method returns all bindings, which may include bindings not in scope for
207 /// the expression and its children; they should be ignored.
208 pub fn bindings(&self) -> &'a BTreeMap<LocalId, usize> {
209 self.derived.bindings()
210 }
211
212 /// Subviews over `self` corresponding to the children of the expression, in reverse order.
213 ///
214 /// These views should disjointly cover the same interval as `self`, except for the last element
215 /// which corresponds to the expression itself.
216 ///
217 /// The number of produced items should exactly match the number of children, which need not
218 /// be provided as an argument. This relies on the well-formedness of the view, which should
219 /// exhaust itself just as it enumerates its last (the first) child view.
220 pub fn children_rev(&self) -> impl Iterator<Item = DerivedView<'a>> + 'a {
221 // This logic is copy/paste from `Derived::children_of_rev` but it was annoying to layer
222 // it over the output of that function, and perhaps clearer to rewrite in any case.
223
224 // Discard the last element (the size of the expression's subtree).
225 // Repeatedly read out the last element, then peel off that many elements.
226 // Each extracted slice corresponds to a child of the current expression.
227 // We should end cleanly with an empty slice, otherwise there is an issue.
228 let sizes = self.results::<SubtreeSize>();
229 let sizes = &sizes[..sizes.len() - 1];
230
231 let offset = self.lower;
232 let derived = self.derived;
233 (0..).scan(sizes, move |sizes, _| {
234 if let Some(size) = sizes.last() {
235 *sizes = &sizes[..sizes.len() - size];
236 Some(Self {
237 derived,
238 lower: offset + sizes.len(),
239 upper: offset + sizes.len() + size,
240 })
241 } else {
242 None
243 }
244 })
245 }
246
247 /// A convenience method for the view over the expressions last child.
248 ///
249 /// This method is appropriate to call on expressions with multiple children,
250 /// and in particular for `Let` and `LetRecv` variants where the body is the
251 /// last child.
252 ///
253 /// It is an error to call this on a view for an expression with no children.
254 pub fn last_child(&self) -> DerivedView<'a> {
255 self.children_rev().next().unwrap()
256 }
257 }
258
259 /// A builder wrapper to accumulate announced dependencies and construct default state.
260 #[allow(missing_debug_implementations)]
261 pub struct DerivedBuilder<'a> {
262 result: Derived,
263 features: &'a OptimizerFeatures,
264 }
265
266 impl<'a> DerivedBuilder<'a> {
267 /// Create a new [`DerivedBuilder`] parameterized by [`OptimizerFeatures`].
268 pub fn new(features: &'a OptimizerFeatures) -> Self {
269 // The default builder should include `SubtreeSize` to facilitate navigation.
270 let mut builder = DerivedBuilder {
271 result: Derived::default(),
272 features,
273 };
274 builder.require(SubtreeSize);
275 builder
276 }
277 }
278
279 impl<'a> DerivedBuilder<'a> {
280 /// Announces a dependence on an analysis `A`.
281 ///
282 /// This ensures that `A` will be performed, and before any analysis that
283 /// invokes this method.
284 pub fn require<A: Analysis>(&mut self, analysis: A) {
285 // The method recursively descends through required analyses, first
286 // installing each in `result.analyses` and second in `result.order`.
287 // The first is an obligation, and serves as an indication that we have
288 // found a cycle in dependencies.
289 let type_id = TypeId::of::<Bundle<A>>();
290 if !self.result.order.contains(&type_id) {
291 // If we have not sequenced `type_id` but have a bundle, it means
292 // we are in the process of fulfilling its requirements: a cycle.
293 if self.result.analyses.contains_key(&type_id) {
294 panic!("Cyclic dependency detected: {}", std::any::type_name::<A>());
295 }
296 // Insert the analysis bundle first, so that we can detect cycles.
297 self.result.analyses.insert(
298 type_id,
299 Box::new(Bundle::<A> {
300 analysis,
301 results: Vec::new(),
302 fuel: 100,
303 allow_optimistic: self.features.enable_letrec_fixpoint_analysis,
304 }),
305 );
306 A::announce_dependencies(self);
307 // All dependencies are successfully sequenced; sequence `type_id`.
308 self.result.order.push(type_id);
309 }
310 }
311 /// Complete the building: perform analyses and return the resulting `Derivation`.
312 pub fn visit(mut self, expr: &MirRelationExpr) -> Derived {
313 // A stack of expressions to process (`Ok`) and let bindings to fill (`Err`).
314 let mut todo = vec![Ok(expr)];
315 // Expressions in reverse post-order: each expression, followed by its children in reverse order.
316 // We will reverse this to get the post order, but must form it in reverse.
317 let mut rev_post_order = Vec::new();
318 while let Some(command) = todo.pop() {
319 match command {
320 // An expression to visit.
321 Ok(expr) => {
322 match expr {
323 MirRelationExpr::Let { id, value, body } => {
324 todo.push(Ok(value));
325 todo.push(Err(*id));
326 todo.push(Ok(body));
327 }
328 MirRelationExpr::LetRec {
329 ids, values, body, ..
330 } => {
331 for (id, value) in ids.iter().zip_eq(values) {
332 todo.push(Ok(value));
333 todo.push(Err(*id));
334 }
335 todo.push(Ok(body));
336 }
337 _ => {
338 todo.extend(expr.children().map(Ok));
339 }
340 }
341 rev_post_order.push(expr);
342 }
343 // A local id to install
344 Err(local_id) => {
345 // Capture the *remaining* work, which we'll need to flip around.
346 let prior = self.result.bindings.insert(local_id, rev_post_order.len());
347 assert_none!(prior, "Shadowing not allowed");
348 }
349 }
350 }
351 // Flip the offsets now that we know a length.
352 for value in self.result.bindings.values_mut() {
353 *value = rev_post_order.len() - *value - 1;
354 }
355 // Visit the pre-order in reverse order: post-order.
356 rev_post_order.reverse();
357
358 // Apply each analysis to `expr` in order.
359 for id in self.result.order.iter() {
360 if let Some(mut bundle) = self.result.analyses.remove(id) {
361 bundle.analyse(&rev_post_order[..], &self.result);
362 self.result.analyses.insert(*id, bundle);
363 }
364 }
365
366 self.result
367 }
368 }
369
370 /// An abstraction for an analysis and associated state.
371 trait AnalysisBundle: Any {
372 /// Populates internal state for all of `exprs`.
373 ///
374 /// Result indicates whether new information was produced for `exprs.last()`.
375 fn analyse(&mut self, exprs: &[&MirRelationExpr], depends: &Derived) -> bool;
376 /// Upcasts `self` to a `&dyn Any`.
377 ///
378 /// NOTE: This is required until <https://github.com/rust-lang/rfcs/issues/2765> is fixed
379 fn as_any(&self) -> &dyn std::any::Any;
380 }
381
382 /// A wrapper for analysis state.
383 struct Bundle<A: Analysis> {
384 /// The algorithm instance used to derive the results.
385 analysis: A,
386 /// A vector of results.
387 results: Vec<A::Value>,
388 /// Counts down with each `LetRec` re-iteration, to avoid unbounded effort.
389 /// Should it reach zero, the analysis should discard its results and restart as if pessimistic.
390 fuel: usize,
391 /// Allow optimistic analysis for `A` (otherwise we always do pesimistic
392 /// analysis, even if a [`crate::analysis::Lattice`] is available for `A`).
393 allow_optimistic: bool,
394 }
395
396 impl<A: Analysis> AnalysisBundle for Bundle<A> {
397 fn analyse(&mut self, exprs: &[&MirRelationExpr], depends: &Derived) -> bool {
398 self.results.clear();
399 // Attempt optimistic analysis, and if that fails go pessimistic.
400 let update = A::lattice()
401 .filter(|_| self.allow_optimistic)
402 .and_then(|lattice| {
403 for _ in exprs.iter() {
404 self.results.push(lattice.top());
405 }
406 self.analyse_optimistic(exprs, 0, exprs.len(), depends, &*lattice)
407 .ok()
408 })
409 .unwrap_or_else(|| {
410 self.results.clear();
411 self.analyse_pessimistic(exprs, depends)
412 });
413 assert_eq!(self.results.len(), exprs.len());
414 update
415 }
416 fn as_any(&self) -> &dyn std::any::Any {
417 self
418 }
419 }
420
421 impl<A: Analysis> Bundle<A> {
422 /// Analysis that starts optimistically but is only correct at a fixed point.
423 ///
424 /// Will fail out to `analyse_pessimistic` if the lattice is missing, or `self.fuel` is exhausted.
425 /// When successful, the result indicates whether new information was produced for `exprs.last()`.
426 fn analyse_optimistic(
427 &mut self,
428 exprs: &[&MirRelationExpr],
429 lower: usize,
430 upper: usize,
431 depends: &Derived,
432 lattice: &dyn crate::analysis::Lattice<A::Value>,
433 ) -> Result<bool, ()> {
434 // Repeatedly re-evaluate the whole tree bottom up, until no changes of fuel spent.
435 let mut changed = true;
436 while changed {
437 changed = false;
438
439 // Bail out if we have done too many `LetRec` passes in this analysis.
440 self.fuel -= 1;
441 if self.fuel == 0 {
442 return Err(());
443 }
444
445 // Track if repetitions may be required, to avoid iteration if they are not.
446 let mut is_recursive = false;
447 // Update each derived value and track if any have changed.
448 for index in lower..upper {
449 let value = self.derive(exprs[index], index, depends);
450 changed = lattice.meet_assign(&mut self.results[index], value) || changed;
451 if let MirRelationExpr::LetRec { .. } = &exprs[index] {
452 is_recursive = true;
453 }
454 }
455
456 // Un-set the potential loop if there was no recursion.
457 if !is_recursive {
458 changed = false;
459 }
460 }
461 Ok(true)
462 }
463
464 /// Analysis that starts conservatively and can be stopped at any point.
465 ///
466 /// Result indicates whether new information was produced for `exprs.last()`.
467 fn analyse_pessimistic(&mut self, exprs: &[&MirRelationExpr], depends: &Derived) -> bool {
468 // TODO: consider making iterative, from some `bottom()` up using `join_assign()`.
469 self.results.clear();
470 for (index, expr) in exprs.iter().enumerate() {
471 self.results.push(self.derive(expr, index, depends));
472 }
473 true
474 }
475
476 #[inline]
477 fn derive(&self, expr: &MirRelationExpr, index: usize, depends: &Derived) -> A::Value {
478 self.analysis
479 .derive(expr, index, &self.results[..], depends)
480 }
481 }
482}
483
484/// Expression subtree sizes
485///
486/// This analysis counts the number of expressions in each subtree, and is most useful
487/// for navigating the results of other analyses that are offset by subtree sizes.
488pub mod subtree {
489
490 use super::{Analysis, Derived};
491 use mz_expr::MirRelationExpr;
492
493 /// Analysis that determines the size in child expressions of relation expressions.
494 #[derive(Debug)]
495 pub struct SubtreeSize;
496
497 impl Analysis for SubtreeSize {
498 type Value = usize;
499
500 fn derive(
501 &self,
502 expr: &MirRelationExpr,
503 index: usize,
504 results: &[Self::Value],
505 _depends: &Derived,
506 ) -> Self::Value {
507 match expr {
508 MirRelationExpr::Constant { .. } | MirRelationExpr::Get { .. } => 1,
509 _ => {
510 let mut offset = 1;
511 for _ in expr.children() {
512 offset += results[index - offset];
513 }
514 offset
515 }
516 }
517 }
518 }
519}
520
521/// Expression arities
522mod arity {
523
524 use super::{Analysis, Derived};
525 use mz_expr::MirRelationExpr;
526
527 /// Analysis that determines the number of columns of relation expressions.
528 #[derive(Debug)]
529 pub struct Arity;
530
531 impl Analysis for Arity {
532 type Value = usize;
533
534 fn derive(
535 &self,
536 expr: &MirRelationExpr,
537 index: usize,
538 results: &[Self::Value],
539 depends: &Derived,
540 ) -> Self::Value {
541 let mut offsets = depends
542 .children_of_rev(index, expr.children().count())
543 .map(|child| results[child])
544 .collect::<Vec<_>>();
545 offsets.reverse();
546 expr.arity_with_input_arities(offsets.into_iter())
547 }
548 }
549}
550
551/// Expression types
552mod types {
553
554 use super::{Analysis, Derived, Lattice};
555 use itertools::Itertools;
556 use mz_expr::MirRelationExpr;
557 use mz_repr::ColumnType;
558
559 /// Analysis that determines the type of relation expressions.
560 ///
561 /// The value is `Some` when it discovers column types, and `None` in the case that
562 /// it has discovered no constraining information on the column types. The `None`
563 /// variant should only occur in the course of iteration, and should not be revealed
564 /// as an output of the analysis. One can `unwrap()` the result, and if it errors then
565 /// either the expression is malformed or the analysis has a bug.
566 ///
567 /// The analysis will panic if an expression is not well typed (i.e. if `try_col_with_input_cols`
568 /// returns an error).
569 #[derive(Debug)]
570 pub struct RelationType;
571
572 impl Analysis for RelationType {
573 type Value = Option<Vec<ColumnType>>;
574
575 fn derive(
576 &self,
577 expr: &MirRelationExpr,
578 index: usize,
579 results: &[Self::Value],
580 depends: &Derived,
581 ) -> Self::Value {
582 let offsets = depends
583 .children_of_rev(index, expr.children().count())
584 .map(|child| &results[child])
585 .collect::<Vec<_>>();
586
587 // For most expressions we'll apply `try_col_with_input_cols`, but for `Get` expressions
588 // we'll want to combine what we know (iteratively) with the stated `Get::typ`.
589 match expr {
590 MirRelationExpr::Get {
591 id: mz_expr::Id::Local(i),
592 typ,
593 ..
594 } => {
595 let mut result = typ.column_types.clone();
596 if let Some(o) = depends.bindings().get(i) {
597 if let Some(t) = results.get(*o) {
598 if let Some(rec_typ) = t {
599 // Reconcile nullability statements.
600 // Unclear if we should trust `typ`.
601 assert_eq!(result.len(), rec_typ.len());
602 result.clone_from(rec_typ);
603 for (res, col) in result.iter_mut().zip_eq(typ.column_types.iter())
604 {
605 if !col.nullable {
606 res.nullable = false;
607 }
608 }
609 } else {
610 // Our `None` information indicates that we are optimistically
611 // assuming the best, including that all columns are non-null.
612 // This should only happen in the first visit to a `Get` expr.
613 // Use `typ`, but flatten nullability.
614 for col in result.iter_mut() {
615 col.nullable = false;
616 }
617 }
618 }
619 }
620 Some(result)
621 }
622 _ => {
623 // Every expression with inputs should have non-`None` inputs at this point.
624 let input_cols = offsets.into_iter().rev().map(|o| {
625 o.as_ref()
626 .expect("RelationType analysis discovered type-less expression")
627 });
628 Some(expr.try_col_with_input_cols(input_cols).unwrap())
629 }
630 }
631 }
632
633 fn lattice() -> Option<Box<dyn Lattice<Self::Value>>> {
634 Some(Box::new(RTLattice))
635 }
636 }
637
638 struct RTLattice;
639
640 impl Lattice<Option<Vec<ColumnType>>> for RTLattice {
641 fn top(&self) -> Option<Vec<ColumnType>> {
642 None
643 }
644 fn meet_assign(&self, a: &mut Option<Vec<ColumnType>>, b: Option<Vec<ColumnType>>) -> bool {
645 match (a, b) {
646 (_, None) => false,
647 (Some(a), Some(b)) => {
648 let mut changed = false;
649 assert_eq!(a.len(), b.len());
650 for (at, bt) in a.iter_mut().zip_eq(b.iter()) {
651 assert_eq!(at.scalar_type, bt.scalar_type);
652 if !at.nullable && bt.nullable {
653 at.nullable = true;
654 changed = true;
655 }
656 }
657 changed
658 }
659 (a, b) => {
660 *a = b;
661 true
662 }
663 }
664 }
665 }
666}
667
668/// Expression unique keys
669mod unique_keys {
670
671 use super::arity::Arity;
672 use super::{Analysis, Derived, DerivedBuilder, Lattice};
673 use mz_expr::MirRelationExpr;
674
675 /// Analysis that determines the unique keys of relation expressions.
676 ///
677 /// The analysis value is a `Vec<Vec<usize>>`, which should be interpreted as a list
678 /// of sets of column identifiers, each set of which has the property that there is at
679 /// most one instance of each assignment of values to those columns.
680 ///
681 /// The sets are minimal, in that any superset of another set is removed from the list.
682 /// Any superset of unique key columns are also unique key columns.
683 #[derive(Debug)]
684 pub struct UniqueKeys;
685
686 impl Analysis for UniqueKeys {
687 type Value = Vec<Vec<usize>>;
688
689 fn announce_dependencies(builder: &mut DerivedBuilder) {
690 builder.require(Arity);
691 }
692
693 fn derive(
694 &self,
695 expr: &MirRelationExpr,
696 index: usize,
697 results: &[Self::Value],
698 depends: &Derived,
699 ) -> Self::Value {
700 let mut offsets = depends
701 .children_of_rev(index, expr.children().count())
702 .collect::<Vec<_>>();
703 offsets.reverse();
704
705 match expr {
706 MirRelationExpr::Get {
707 id: mz_expr::Id::Local(i),
708 typ,
709 ..
710 } => {
711 // We have information from `typ` and from the analysis.
712 // We should "join" them, unioning and reducing the keys.
713 let mut keys = typ.keys.clone();
714 if let Some(o) = depends.bindings().get(i) {
715 if let Some(ks) = results.get(*o) {
716 for k in ks.iter() {
717 antichain_insert(&mut keys, k.clone());
718 }
719 keys.extend(ks.iter().cloned());
720 keys.sort();
721 keys.dedup();
722 }
723 }
724 keys
725 }
726 _ => {
727 let arity = depends.results::<Arity>();
728 expr.keys_with_input_keys(
729 offsets.iter().map(|o| arity[*o]),
730 offsets.iter().map(|o| &results[*o]),
731 )
732 }
733 }
734 }
735
736 fn lattice() -> Option<Box<dyn Lattice<Self::Value>>> {
737 Some(Box::new(UKLattice))
738 }
739 }
740
741 fn antichain_insert(into: &mut Vec<Vec<usize>>, item: Vec<usize>) {
742 // Insert only if there is not a dominating element of `into`.
743 if into.iter().all(|key| !key.iter().all(|k| item.contains(k))) {
744 into.retain(|key| !key.iter().all(|k| item.contains(k)));
745 into.push(item);
746 }
747 }
748
749 /// Lattice for sets of columns that define a unique key.
750 ///
751 /// An element `Vec<Vec<usize>>` describes all sets of columns `Vec<usize>` that are a
752 /// superset of some set of columns in the lattice element.
753 struct UKLattice;
754
755 impl Lattice<Vec<Vec<usize>>> for UKLattice {
756 fn top(&self) -> Vec<Vec<usize>> {
757 vec![vec![]]
758 }
759 fn meet_assign(&self, a: &mut Vec<Vec<usize>>, b: Vec<Vec<usize>>) -> bool {
760 a.sort();
761 a.dedup();
762 let mut c = Vec::new();
763 for cols_a in a.iter_mut() {
764 cols_a.sort();
765 cols_a.dedup();
766 for cols_b in b.iter() {
767 let mut cols_c = cols_a.iter().chain(cols_b).cloned().collect::<Vec<_>>();
768 cols_c.sort();
769 cols_c.dedup();
770 antichain_insert(&mut c, cols_c);
771 }
772 }
773 c.sort();
774 c.dedup();
775 std::mem::swap(a, &mut c);
776 a != &mut c
777 }
778 }
779}
780
781/// Determines if accumulated frequences can be negative.
782///
783/// This analysis assumes that globally identified collection have the property, and it is
784/// incorrect to apply it to expressions that reference external collections that may have
785/// negative accumulations.
786mod non_negative {
787
788 use super::{Analysis, Derived, Lattice};
789 use crate::analysis::common_lattice::BoolLattice;
790 use mz_expr::{Id, MirRelationExpr};
791
792 /// Analysis that determines if all accumulations at all times are non-negative.
793 ///
794 /// The analysis assumes that `Id::Global` references only refer to non-negative collections.
795 #[derive(Debug)]
796 pub struct NonNegative;
797
798 impl Analysis for NonNegative {
799 type Value = bool;
800
801 fn derive(
802 &self,
803 expr: &MirRelationExpr,
804 index: usize,
805 results: &[Self::Value],
806 depends: &Derived,
807 ) -> Self::Value {
808 match expr {
809 MirRelationExpr::Constant { rows, .. } => rows
810 .as_ref()
811 .map(|r| r.iter().all(|(_, diff)| *diff >= mz_repr::Diff::ZERO))
812 .unwrap_or(true),
813 MirRelationExpr::Get { id, .. } => match id {
814 Id::Local(id) => {
815 let index = *depends
816 .bindings()
817 .get(id)
818 .expect("Dependency info not found");
819 *results.get(index).unwrap_or(&false)
820 }
821 Id::Global(_) => true,
822 },
823 // Negate must be false unless input is "non-positive".
824 MirRelationExpr::Negate { .. } => false,
825 // Threshold ensures non-negativity.
826 MirRelationExpr::Threshold { .. } => true,
827 // Reduce errors on negative input.
828 MirRelationExpr::Reduce { .. } => true,
829 MirRelationExpr::Join { .. } => {
830 // If all inputs are non-negative, the join is non-negative.
831 depends
832 .children_of_rev(index, expr.children().count())
833 .all(|off| results[off])
834 }
835 MirRelationExpr::Union { base, inputs } => {
836 // If all inputs are non-negative, the union is non-negative.
837 let all_non_negative = depends
838 .children_of_rev(index, expr.children().count())
839 .all(|off| results[off]);
840
841 if all_non_negative {
842 return true;
843 }
844
845 // We look for the pattern `Union { base, Negate(Subset(base)) }`.
846 // TODO: take some care to ensure that union fusion does not introduce a regression.
847 if inputs.len() == 1 {
848 if let MirRelationExpr::Negate { input } = &inputs[0] {
849 // If `base` is non-negative, and `is_superset_of(base, input)`, return true.
850 // TODO: this is not correct until we have `is_superset_of` validate non-negativity
851 // as it goes, but it matches the current implementation.
852 let mut children = depends.children_of_rev(index, 2);
853 let _negate = children.next().unwrap();
854 let base_id = children.next().unwrap();
855 debug_assert_eq!(children.next(), None);
856 if results[base_id] && is_superset_of(&*base, &*input) {
857 return true;
858 }
859 }
860 }
861
862 false
863 }
864 _ => results[index - 1],
865 }
866 }
867
868 fn lattice() -> Option<Box<dyn Lattice<Self::Value>>> {
869 Some(Box::new(BoolLattice))
870 }
871 }
872
873 /// Returns true only if `rhs.negate().union(lhs)` contains only non-negative multiplicities
874 /// once consolidated.
875 ///
876 /// Informally, this happens when `rhs` is a multiset subset of `lhs`, meaning the multiplicity
877 /// of any record in `rhs` is at most the multiplicity of the same record in `lhs`.
878 ///
879 /// This method recursively descends each of `lhs` and `rhs` and performs a great many equality
880 /// tests, which has the potential to be quadratic. We should consider restricting its attention
881 /// to `Get` identifiers, under the premise that equal AST nodes would necessarily be identified
882 /// by common subexpression elimination. This requires care around recursively bound identifiers.
883 ///
884 /// These rules are .. somewhat arbitrary, and likely reflect observed opportunities. For example,
885 /// while we do relate `distinct(filter(A)) <= distinct(A)`, we do not relate `distinct(A) <= A`.
886 /// Further thoughts about the class of optimizations, and whether there should be more or fewer,
887 /// can be found here: <https://github.com/MaterializeInc/database-issues/issues/4044>.
888 fn is_superset_of(mut lhs: &MirRelationExpr, mut rhs: &MirRelationExpr) -> bool {
889 // This implementation is iterative.
890 // Before converting this implementation to recursive (e.g. to improve its accuracy)
891 // make sure to use the `CheckedRecursion` struct to avoid blowing the stack.
892 while lhs != rhs {
893 match rhs {
894 MirRelationExpr::Filter { input, .. } => rhs = &**input,
895 MirRelationExpr::TopK { input, .. } => rhs = &**input,
896 // Descend in both sides if the current roots are
897 // projections with the same `outputs` vector.
898 MirRelationExpr::Project {
899 input: rhs_input,
900 outputs: rhs_outputs,
901 } => match lhs {
902 MirRelationExpr::Project {
903 input: lhs_input,
904 outputs: lhs_outputs,
905 } if lhs_outputs == rhs_outputs => {
906 rhs = &**rhs_input;
907 lhs = &**lhs_input;
908 }
909 _ => return false,
910 },
911 // Descend in both sides if the current roots are reduces with empty aggregates
912 // on the same set of keys (that is, a distinct operation on those keys).
913 MirRelationExpr::Reduce {
914 input: rhs_input,
915 group_key: rhs_group_key,
916 aggregates: rhs_aggregates,
917 monotonic: _,
918 expected_group_size: _,
919 } if rhs_aggregates.is_empty() => match lhs {
920 MirRelationExpr::Reduce {
921 input: lhs_input,
922 group_key: lhs_group_key,
923 aggregates: lhs_aggregates,
924 monotonic: _,
925 expected_group_size: _,
926 } if lhs_aggregates.is_empty() && lhs_group_key == rhs_group_key => {
927 rhs = &**rhs_input;
928 lhs = &**lhs_input;
929 }
930 _ => return false,
931 },
932 _ => {
933 // TODO: Imagine more complex reasoning here!
934 return false;
935 }
936 }
937 }
938 true
939 }
940}
941
942mod column_names {
943 use std::ops::Range;
944 use std::sync::Arc;
945
946 use super::Analysis;
947 use mz_expr::{AggregateFunc, Id, MirRelationExpr, MirScalarExpr, TableFunc};
948 use mz_repr::GlobalId;
949 use mz_repr::explain::ExprHumanizer;
950 use mz_sql::ORDINALITY_COL_NAME;
951
952 /// An abstract type denoting an inferred column name.
953 #[derive(Debug, Clone)]
954 pub enum ColumnName {
955 /// A column with name inferred to be equal to a GlobalId schema column.
956 Global(GlobalId, usize),
957 /// An anonymous expression named after the top-level function name.
958 Aggregate(AggregateFunc, Box<ColumnName>),
959 /// A column with a name that has been saved from the original SQL query.
960 Annotated(Arc<str>),
961 /// An column with an unknown name.
962 Unknown,
963 }
964
965 impl ColumnName {
966 /// Return `true` iff the variant has an inferred name.
967 pub fn is_known(&self) -> bool {
968 match self {
969 Self::Global(..) | Self::Aggregate(..) => true,
970 // We treat annotated columns as unknown because we would rather
971 // override them with inferred names, if we can.
972 Self::Annotated(..) | Self::Unknown => false,
973 }
974 }
975
976 /// Humanize the column to a [`String`], returns an empty [`String`] for
977 /// unknown columns (or columns named `"?column?"`).
978 pub fn humanize(&self, humanizer: &dyn ExprHumanizer) -> String {
979 match self {
980 Self::Global(id, c) => humanizer.humanize_column(*id, *c).unwrap_or_default(),
981 Self::Aggregate(func, expr) => {
982 let func = func.name();
983 let expr = expr.humanize(humanizer);
984 if expr.is_empty() {
985 String::from(func)
986 } else {
987 format!("{func}_{expr}")
988 }
989 }
990 Self::Annotated(name) => name.to_string(),
991 Self::Unknown => String::new(),
992 }
993 }
994
995 /// Clone this column name if it is known, otherwise try to use the provided
996 /// name if it is available.
997 pub fn cloned_or_annotated(&self, name: &Option<Arc<str>>) -> Self {
998 match self {
999 Self::Global(..) | Self::Aggregate(..) | Self::Annotated(..) => self.clone(),
1000 Self::Unknown => name
1001 .as_ref()
1002 .filter(|name| name.as_ref() != "\"?column?\"")
1003 .map_or_else(|| Self::Unknown, |name| Self::Annotated(Arc::clone(name))),
1004 }
1005 }
1006 }
1007
1008 /// Compute the column types of each subtree of a [MirRelationExpr] from the
1009 /// bottom-up.
1010 #[derive(Debug)]
1011 pub struct ColumnNames;
1012
1013 impl ColumnNames {
1014 /// fallback schema consisting of ordinal column names: #0, #1, ...
1015 fn anonymous(range: Range<usize>) -> impl Iterator<Item = ColumnName> {
1016 range.map(|_| ColumnName::Unknown)
1017 }
1018
1019 /// fallback schema consisting of ordinal column names: #0, #1, ...
1020 fn extend_with_scalars(column_names: &mut Vec<ColumnName>, scalars: &Vec<MirScalarExpr>) {
1021 for scalar in scalars {
1022 column_names.push(match scalar {
1023 MirScalarExpr::Column(c, name) => column_names[*c].cloned_or_annotated(&name.0),
1024 _ => ColumnName::Unknown,
1025 });
1026 }
1027 }
1028 }
1029
1030 impl Analysis for ColumnNames {
1031 type Value = Vec<ColumnName>;
1032
1033 fn derive(
1034 &self,
1035 expr: &MirRelationExpr,
1036 index: usize,
1037 results: &[Self::Value],
1038 depends: &crate::analysis::Derived,
1039 ) -> Self::Value {
1040 use MirRelationExpr::*;
1041
1042 match expr {
1043 Constant { rows: _, typ } => {
1044 // Fallback to an anonymous schema for constants.
1045 ColumnNames::anonymous(0..typ.arity()).collect()
1046 }
1047 Get {
1048 id: Id::Global(id),
1049 typ,
1050 access_strategy: _,
1051 } => {
1052 // Emit ColumnName::Global instances for each column in the
1053 // `Get` type. Those can be resolved to real names later when an
1054 // ExpressionHumanizer is available.
1055 (0..typ.columns().len())
1056 .map(|c| ColumnName::Global(*id, c))
1057 .collect()
1058 }
1059 Get {
1060 id: Id::Local(id),
1061 typ,
1062 access_strategy: _,
1063 } => {
1064 let index_child = *depends.bindings().get(id).expect("id in scope");
1065 if index_child < results.len() {
1066 results[index_child].clone()
1067 } else {
1068 // Possible because we infer LetRec bindings in order. This
1069 // can be improved by introducing a fixpoint loop in the
1070 // Env<A>::schedule_tasks LetRec handling block.
1071 ColumnNames::anonymous(0..typ.arity()).collect()
1072 }
1073 }
1074 Let {
1075 id: _,
1076 value: _,
1077 body: _,
1078 } => {
1079 // Return the column names of the `body`.
1080 results[index - 1].clone()
1081 }
1082 LetRec {
1083 ids: _,
1084 values: _,
1085 limits: _,
1086 body: _,
1087 } => {
1088 // Return the column names of the `body`.
1089 results[index - 1].clone()
1090 }
1091 Project { input: _, outputs } => {
1092 // Permute the column names of the input.
1093 let input_column_names = &results[index - 1];
1094 let mut column_names = vec![];
1095 for col in outputs {
1096 column_names.push(input_column_names[*col].clone());
1097 }
1098 column_names
1099 }
1100 Map { input: _, scalars } => {
1101 // Extend the column names of the input with anonymous columns.
1102 let mut column_names = results[index - 1].clone();
1103 Self::extend_with_scalars(&mut column_names, scalars);
1104 column_names
1105 }
1106 FlatMap {
1107 input: _,
1108 func,
1109 exprs: _,
1110 } => {
1111 // Extend the column names of the input with anonymous columns.
1112 let mut column_names = results[index - 1].clone();
1113 let func_output_start = column_names.len();
1114 let func_output_end = column_names.len() + func.output_arity();
1115 column_names.extend(Self::anonymous(func_output_start..func_output_end));
1116 if let TableFunc::WithOrdinality { .. } = func {
1117 // We know the name of the last column
1118 // TODO(ggevay): generalize this to meaningful col names for all table functions
1119 **column_names.last_mut().as_mut().expect(
1120 "there is at least one output column, from the WITH ORDINALITY",
1121 ) = ColumnName::Annotated(ORDINALITY_COL_NAME.into());
1122 }
1123 column_names
1124 }
1125 Filter {
1126 input: _,
1127 predicates: _,
1128 } => {
1129 // Return the column names of the `input`.
1130 results[index - 1].clone()
1131 }
1132 Join {
1133 inputs: _,
1134 equivalences: _,
1135 implementation: _,
1136 } => {
1137 let mut input_results = depends
1138 .children_of_rev(index, expr.children().count())
1139 .map(|child| &results[child])
1140 .collect::<Vec<_>>();
1141 input_results.reverse();
1142
1143 let mut column_names = vec![];
1144 for input_column_names in input_results {
1145 column_names.extend(input_column_names.iter().cloned());
1146 }
1147 column_names
1148 }
1149 Reduce {
1150 input: _,
1151 group_key,
1152 aggregates,
1153 monotonic: _,
1154 expected_group_size: _,
1155 } => {
1156 // We clone and extend the input vector and then remove the part
1157 // associated with the input at the end.
1158 let mut column_names = results[index - 1].clone();
1159 let input_arity = column_names.len();
1160
1161 // Infer the group key part.
1162 Self::extend_with_scalars(&mut column_names, group_key);
1163 // Infer the aggregates part.
1164 for aggregate in aggregates.iter() {
1165 // The inferred name will consist of (1) the aggregate
1166 // function name and (2) the aggregate expression (iff
1167 // it is a simple column reference).
1168 let func = aggregate.func.clone();
1169 let expr = match aggregate.expr.as_column() {
1170 Some(c) => column_names.get(c).unwrap_or(&ColumnName::Unknown).clone(),
1171 None => ColumnName::Unknown,
1172 };
1173 column_names.push(ColumnName::Aggregate(func, Box::new(expr)));
1174 }
1175 // Remove the prefix associated with the input
1176 column_names.drain(0..input_arity);
1177
1178 column_names
1179 }
1180 TopK {
1181 input: _,
1182 group_key: _,
1183 order_key: _,
1184 limit: _,
1185 offset: _,
1186 monotonic: _,
1187 expected_group_size: _,
1188 } => {
1189 // Return the column names of the `input`.
1190 results[index - 1].clone()
1191 }
1192 Negate { input: _ } => {
1193 // Return the column names of the `input`.
1194 results[index - 1].clone()
1195 }
1196 Threshold { input: _ } => {
1197 // Return the column names of the `input`.
1198 results[index - 1].clone()
1199 }
1200 Union { base: _, inputs: _ } => {
1201 // Use the first non-empty column across all inputs.
1202 let mut column_names = vec![];
1203
1204 let mut inputs_results = depends
1205 .children_of_rev(index, expr.children().count())
1206 .map(|child| &results[child])
1207 .collect::<Vec<_>>();
1208
1209 let base_results = inputs_results.pop().unwrap();
1210 inputs_results.reverse();
1211
1212 for (i, mut column_name) in base_results.iter().cloned().enumerate() {
1213 for input_results in inputs_results.iter() {
1214 if !column_name.is_known() && input_results[i].is_known() {
1215 column_name = input_results[i].clone();
1216 break;
1217 }
1218 }
1219 column_names.push(column_name);
1220 }
1221
1222 column_names
1223 }
1224 ArrangeBy { input: _, keys: _ } => {
1225 // Return the column names of the `input`.
1226 results[index - 1].clone()
1227 }
1228 }
1229 }
1230 }
1231}
1232
1233mod explain {
1234 //! Derived Analysis framework and definitions.
1235
1236 use std::collections::BTreeMap;
1237
1238 use mz_expr::MirRelationExpr;
1239 use mz_expr::explain::{ExplainContext, HumanizedExplain, HumanizerMode};
1240 use mz_ore::stack::RecursionLimitError;
1241 use mz_repr::explain::{Analyses, AnnotatedPlan};
1242
1243 use crate::analysis::equivalences::{Equivalences, HumanizedEquivalenceClasses};
1244
1245 // Analyses should have shortened paths when exported.
1246 use super::DerivedBuilder;
1247
1248 impl<'c> From<&ExplainContext<'c>> for DerivedBuilder<'c> {
1249 fn from(context: &ExplainContext<'c>) -> DerivedBuilder<'c> {
1250 let mut builder = DerivedBuilder::new(context.features);
1251 if context.config.subtree_size {
1252 builder.require(super::SubtreeSize);
1253 }
1254 if context.config.non_negative {
1255 builder.require(super::NonNegative);
1256 }
1257 if context.config.types {
1258 builder.require(super::RelationType);
1259 }
1260 if context.config.arity {
1261 builder.require(super::Arity);
1262 }
1263 if context.config.keys {
1264 builder.require(super::UniqueKeys);
1265 }
1266 if context.config.cardinality {
1267 builder.require(super::Cardinality::with_stats(
1268 context.cardinality_stats.clone(),
1269 ));
1270 }
1271 if context.config.column_names || context.config.humanized_exprs {
1272 builder.require(super::ColumnNames);
1273 }
1274 if context.config.equivalences {
1275 builder.require(Equivalences);
1276 }
1277 builder
1278 }
1279 }
1280
1281 /// Produce an [`AnnotatedPlan`] wrapping the given [`MirRelationExpr`] along
1282 /// with [`Analyses`] derived from the given context configuration.
1283 pub fn annotate_plan<'a>(
1284 plan: &'a MirRelationExpr,
1285 context: &'a ExplainContext,
1286 ) -> Result<AnnotatedPlan<'a, MirRelationExpr>, RecursionLimitError> {
1287 let mut annotations = BTreeMap::<&MirRelationExpr, Analyses>::default();
1288 let config = context.config;
1289
1290 // We want to annotate the plan with analyses in the following cases:
1291 // 1. An Analysis was explicitly requested in the ExplainConfig.
1292 // 2. Humanized expressions were requested in the ExplainConfig (in which
1293 // case we need to derive the ColumnNames Analysis).
1294 if config.requires_analyses() || config.humanized_exprs {
1295 // get the annotation keys
1296 let subtree_refs = plan.post_order_vec();
1297 // get the annotation values
1298 let builder = DerivedBuilder::from(context);
1299 let derived = builder.visit(plan);
1300
1301 if config.subtree_size {
1302 for (expr, subtree_size) in std::iter::zip(
1303 subtree_refs.iter(),
1304 derived.results::<super::SubtreeSize>().into_iter(),
1305 ) {
1306 let analyses = annotations.entry(expr).or_default();
1307 analyses.subtree_size = Some(*subtree_size);
1308 }
1309 }
1310 if config.non_negative {
1311 for (expr, non_negative) in std::iter::zip(
1312 subtree_refs.iter(),
1313 derived.results::<super::NonNegative>().into_iter(),
1314 ) {
1315 let analyses = annotations.entry(expr).or_default();
1316 analyses.non_negative = Some(*non_negative);
1317 }
1318 }
1319
1320 if config.arity {
1321 for (expr, arity) in std::iter::zip(
1322 subtree_refs.iter(),
1323 derived.results::<super::Arity>().into_iter(),
1324 ) {
1325 let analyses = annotations.entry(expr).or_default();
1326 analyses.arity = Some(*arity);
1327 }
1328 }
1329
1330 if config.types {
1331 for (expr, types) in std::iter::zip(
1332 subtree_refs.iter(),
1333 derived.results::<super::RelationType>().into_iter(),
1334 ) {
1335 let analyses = annotations.entry(expr).or_default();
1336 analyses.types = Some(types.clone());
1337 }
1338 }
1339
1340 if config.keys {
1341 for (expr, keys) in std::iter::zip(
1342 subtree_refs.iter(),
1343 derived.results::<super::UniqueKeys>().into_iter(),
1344 ) {
1345 let analyses = annotations.entry(expr).or_default();
1346 analyses.keys = Some(keys.clone());
1347 }
1348 }
1349
1350 if config.cardinality {
1351 for (expr, card) in std::iter::zip(
1352 subtree_refs.iter(),
1353 derived.results::<super::Cardinality>().into_iter(),
1354 ) {
1355 let analyses = annotations.entry(expr).or_default();
1356 analyses.cardinality = Some(card.to_string());
1357 }
1358 }
1359
1360 if config.column_names || config.humanized_exprs {
1361 for (expr, column_names) in std::iter::zip(
1362 subtree_refs.iter(),
1363 derived.results::<super::ColumnNames>().into_iter(),
1364 ) {
1365 let analyses = annotations.entry(expr).or_default();
1366 let value = column_names
1367 .iter()
1368 .map(|column_name| column_name.humanize(context.humanizer))
1369 .collect();
1370 analyses.column_names = Some(value);
1371 }
1372 }
1373
1374 if config.equivalences {
1375 for (expr, equivs) in std::iter::zip(
1376 subtree_refs.iter(),
1377 derived.results::<Equivalences>().into_iter(),
1378 ) {
1379 let analyses = annotations.entry(expr).or_default();
1380 analyses.equivalences = Some(match equivs.as_ref() {
1381 Some(equivs) => HumanizedEquivalenceClasses {
1382 equivalence_classes: equivs,
1383 cols: analyses.column_names.as_ref(),
1384 mode: HumanizedExplain::new(config.redacted),
1385 }
1386 .to_string(),
1387 None => "<empty collection>".to_string(),
1388 });
1389 }
1390 }
1391 }
1392
1393 Ok(AnnotatedPlan { plan, annotations })
1394 }
1395}
1396
1397/// Definition and helper structs for the [`Cardinality`] Analysis.
1398mod cardinality {
1399 use std::collections::{BTreeMap, BTreeSet};
1400
1401 use mz_expr::{
1402 BinaryFunc, Id, JoinImplementation, MirRelationExpr, MirScalarExpr, TableFunc, UnaryFunc,
1403 VariadicFunc,
1404 };
1405 use mz_ore::cast::{CastFrom, CastLossy, TryCastFrom};
1406 use mz_repr::GlobalId;
1407
1408 use ordered_float::OrderedFloat;
1409
1410 use super::{Analysis, Arity, SubtreeSize, UniqueKeys};
1411
1412 /// Compute the estimated cardinality of each subtree of a [MirRelationExpr] from the bottom up.
1413 #[allow(missing_debug_implementations)]
1414 pub struct Cardinality {
1415 /// Cardinalities for globally named entities
1416 pub stats: BTreeMap<GlobalId, usize>,
1417 }
1418
1419 impl Cardinality {
1420 /// A cardinality estimator with provided statistics for the given global identifiers
1421 pub fn with_stats(stats: BTreeMap<GlobalId, usize>) -> Self {
1422 Cardinality { stats }
1423 }
1424 }
1425
1426 impl Default for Cardinality {
1427 fn default() -> Self {
1428 Cardinality {
1429 stats: BTreeMap::new(),
1430 }
1431 }
1432 }
1433
1434 /// Cardinality estimates
1435 #[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord)]
1436 pub enum CardinalityEstimate {
1437 Unknown,
1438 Estimate(OrderedFloat<f64>),
1439 }
1440
1441 impl CardinalityEstimate {
1442 pub fn max(lhs: CardinalityEstimate, rhs: CardinalityEstimate) -> CardinalityEstimate {
1443 use CardinalityEstimate::*;
1444 match (lhs, rhs) {
1445 (Estimate(lhs), Estimate(rhs)) => Estimate(std::cmp::max(lhs, rhs)),
1446 _ => Unknown,
1447 }
1448 }
1449
1450 pub fn rounded(&self) -> Option<usize> {
1451 match self {
1452 CardinalityEstimate::Estimate(OrderedFloat(f)) => {
1453 let rounded = f.ceil();
1454 let flattened = usize::cast_from(
1455 u64::try_cast_from(rounded)
1456 .expect("positive and representable cardinality estimate"),
1457 );
1458
1459 Some(flattened)
1460 }
1461 CardinalityEstimate::Unknown => None,
1462 }
1463 }
1464 }
1465
1466 impl std::ops::Add for CardinalityEstimate {
1467 type Output = CardinalityEstimate;
1468
1469 fn add(self, rhs: Self) -> Self::Output {
1470 use CardinalityEstimate::*;
1471 match (self, rhs) {
1472 (Estimate(lhs), Estimate(rhs)) => Estimate(lhs + rhs),
1473 _ => Unknown,
1474 }
1475 }
1476 }
1477
1478 impl std::ops::Sub for CardinalityEstimate {
1479 type Output = CardinalityEstimate;
1480
1481 fn sub(self, rhs: Self) -> Self::Output {
1482 use CardinalityEstimate::*;
1483 match (self, rhs) {
1484 (Estimate(lhs), Estimate(rhs)) => Estimate(lhs - rhs),
1485 _ => Unknown,
1486 }
1487 }
1488 }
1489
1490 impl std::ops::Sub<CardinalityEstimate> for f64 {
1491 type Output = CardinalityEstimate;
1492
1493 fn sub(self, rhs: CardinalityEstimate) -> Self::Output {
1494 use CardinalityEstimate::*;
1495 if let Estimate(OrderedFloat(rhs)) = rhs {
1496 Estimate(OrderedFloat(self - rhs))
1497 } else {
1498 Unknown
1499 }
1500 }
1501 }
1502
1503 impl std::ops::Mul for CardinalityEstimate {
1504 type Output = CardinalityEstimate;
1505
1506 fn mul(self, rhs: Self) -> Self::Output {
1507 use CardinalityEstimate::*;
1508 match (self, rhs) {
1509 (Estimate(lhs), Estimate(rhs)) => Estimate(lhs * rhs),
1510 _ => Unknown,
1511 }
1512 }
1513 }
1514
1515 impl std::ops::Mul<f64> for CardinalityEstimate {
1516 type Output = CardinalityEstimate;
1517
1518 fn mul(self, rhs: f64) -> Self::Output {
1519 if let CardinalityEstimate::Estimate(OrderedFloat(lhs)) = self {
1520 CardinalityEstimate::Estimate(OrderedFloat(lhs * rhs))
1521 } else {
1522 CardinalityEstimate::Unknown
1523 }
1524 }
1525 }
1526
1527 impl std::ops::Div for CardinalityEstimate {
1528 type Output = CardinalityEstimate;
1529
1530 fn div(self, rhs: Self) -> Self::Output {
1531 use CardinalityEstimate::*;
1532 match (self, rhs) {
1533 (Estimate(lhs), Estimate(rhs)) => Estimate(lhs / rhs),
1534 _ => Unknown,
1535 }
1536 }
1537 }
1538
1539 impl std::ops::Div<f64> for CardinalityEstimate {
1540 type Output = CardinalityEstimate;
1541
1542 fn div(self, rhs: f64) -> Self::Output {
1543 use CardinalityEstimate::*;
1544 if let Estimate(lhs) = self {
1545 Estimate(lhs / OrderedFloat(rhs))
1546 } else {
1547 Unknown
1548 }
1549 }
1550 }
1551
1552 impl std::iter::Sum for CardinalityEstimate {
1553 fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
1554 iter.fold(CardinalityEstimate::from(0.0), |acc, elt| acc + elt)
1555 }
1556 }
1557
1558 impl std::iter::Product for CardinalityEstimate {
1559 fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
1560 iter.fold(CardinalityEstimate::from(1.0), |acc, elt| acc * elt)
1561 }
1562 }
1563
1564 impl From<usize> for CardinalityEstimate {
1565 fn from(value: usize) -> Self {
1566 Self::Estimate(OrderedFloat(f64::cast_lossy(value)))
1567 }
1568 }
1569
1570 impl From<f64> for CardinalityEstimate {
1571 fn from(value: f64) -> Self {
1572 Self::Estimate(OrderedFloat(value))
1573 }
1574 }
1575
1576 /// The default selectivity for predicates we know nothing about.
1577 ///
1578 /// But see also expr/src/scalar.rs for `FilterCharacteristics::worst_case_scaling_factor()` for a more nuanced take.
1579 pub const WORST_CASE_SELECTIVITY: OrderedFloat<f64> = OrderedFloat(0.1);
1580
1581 // This section defines how we estimate cardinality for each syntactic construct.
1582 //
1583 // We split it up into functions to make it all a bit more tractable to work with.
1584 impl Cardinality {
1585 fn flat_map(&self, tf: &TableFunc, input: CardinalityEstimate) -> CardinalityEstimate {
1586 match tf {
1587 TableFunc::Wrap { types, width } => {
1588 input * (f64::cast_lossy(types.len()) / f64::cast_lossy(*width))
1589 }
1590 _ => {
1591 // TODO(mgree) what explosion factor should we make up?
1592 input * CardinalityEstimate::from(4.0)
1593 }
1594 }
1595 }
1596
1597 fn predicate(
1598 &self,
1599 predicate_expr: &MirScalarExpr,
1600 unique_columns: &BTreeSet<usize>,
1601 ) -> OrderedFloat<f64> {
1602 let index_selectivity = |expr: &MirScalarExpr| -> Option<OrderedFloat<f64>> {
1603 match expr {
1604 MirScalarExpr::Column(col, _) => {
1605 if unique_columns.contains(col) {
1606 // TODO(mgree): when we have index cardinality statistics, they should go here when `expr` is a `MirScalarExpr::Column` that's in `unique_columns`
1607 None
1608 } else {
1609 None
1610 }
1611 }
1612 _ => None,
1613 }
1614 };
1615
1616 match predicate_expr {
1617 MirScalarExpr::Column(_, _)
1618 | MirScalarExpr::Literal(_, _)
1619 | MirScalarExpr::CallUnmaterializable(_) => OrderedFloat(1.0),
1620 MirScalarExpr::CallUnary { func, expr } => match func {
1621 UnaryFunc::Not(_) => OrderedFloat(1.0) - self.predicate(expr, unique_columns),
1622 UnaryFunc::IsTrue(_) | UnaryFunc::IsFalse(_) => OrderedFloat(0.5),
1623 UnaryFunc::IsNull(_) => {
1624 if let Some(icard) = index_selectivity(expr) {
1625 icard
1626 } else {
1627 WORST_CASE_SELECTIVITY
1628 }
1629 }
1630 _ => WORST_CASE_SELECTIVITY,
1631 },
1632 MirScalarExpr::CallBinary { func, expr1, expr2 } => {
1633 match func {
1634 BinaryFunc::Eq => {
1635 match (index_selectivity(expr1), index_selectivity(expr2)) {
1636 (Some(isel1), Some(isel2)) => std::cmp::max(isel1, isel2),
1637 (Some(isel), None) | (None, Some(isel)) => isel,
1638 (None, None) => WORST_CASE_SELECTIVITY,
1639 }
1640 }
1641 // 1.0 - the Eq case
1642 BinaryFunc::NotEq => {
1643 match (index_selectivity(expr1), index_selectivity(expr2)) {
1644 (Some(isel1), Some(isel2)) => {
1645 OrderedFloat(1.0) - std::cmp::max(isel1, isel2)
1646 }
1647 (Some(isel), None) | (None, Some(isel)) => OrderedFloat(1.0) - isel,
1648 (None, None) => OrderedFloat(1.0) - WORST_CASE_SELECTIVITY,
1649 }
1650 }
1651 BinaryFunc::Lt | BinaryFunc::Lte | BinaryFunc::Gt | BinaryFunc::Gte => {
1652 // TODO(mgree) if we have high/low key values and one of the columns is an index, we can do better
1653 OrderedFloat(0.33)
1654 }
1655 _ => OrderedFloat(1.0), // TOOD(mgree): are there other interesting cases?
1656 }
1657 }
1658 MirScalarExpr::CallVariadic { func, exprs } => match func {
1659 VariadicFunc::And => exprs
1660 .iter()
1661 .map(|expr| self.predicate(expr, unique_columns))
1662 .product(),
1663 VariadicFunc::Or => {
1664 // TODO(mgree): BETWEEN will get compiled down to an AND of appropriate bounds---we could try to detect it and be clever
1665
1666 // F(expr1 OR expr2) = F(expr1) + F(expr2) - F(expr1) * F(expr2), but generalized
1667 let mut exprs = exprs.into_iter();
1668
1669 let mut expr1;
1670
1671 if let Some(first) = exprs.next() {
1672 expr1 = self.predicate(first, unique_columns);
1673 } else {
1674 return OrderedFloat(1.0);
1675 }
1676
1677 for expr2 in exprs {
1678 let expr2 = self.predicate(expr2, unique_columns);
1679 expr1 = expr1 + expr2 - expr1 * expr2;
1680 }
1681 expr1
1682 }
1683 _ => OrderedFloat(1.0),
1684 },
1685 MirScalarExpr::If { cond: _, then, els } => std::cmp::max(
1686 self.predicate(then, unique_columns),
1687 self.predicate(els, unique_columns),
1688 ),
1689 }
1690 }
1691
1692 fn filter(
1693 &self,
1694 predicates: &Vec<MirScalarExpr>,
1695 keys: &Vec<Vec<usize>>,
1696 input: CardinalityEstimate,
1697 ) -> CardinalityEstimate {
1698 // TODO(mgree): should we try to do something for indices built on multiple columns?
1699 let mut unique_columns = BTreeSet::new();
1700 for key in keys {
1701 if key.len() == 1 {
1702 unique_columns.insert(key[0]);
1703 }
1704 }
1705
1706 let mut estimate = input;
1707 for expr in predicates {
1708 let selectivity = self.predicate(expr, &unique_columns);
1709 debug_assert!(
1710 OrderedFloat(0.0) <= selectivity && selectivity <= OrderedFloat(1.0),
1711 "predicate selectivity {selectivity} should be in the range [0,1]"
1712 );
1713 estimate = estimate * selectivity.0;
1714 }
1715
1716 estimate
1717 }
1718
1719 fn join(
1720 &self,
1721 equivalences: &Vec<Vec<MirScalarExpr>>,
1722 _implementation: &JoinImplementation,
1723 unique_columns: BTreeMap<usize, usize>,
1724 mut inputs: Vec<CardinalityEstimate>,
1725 ) -> CardinalityEstimate {
1726 if inputs.is_empty() {
1727 return CardinalityEstimate::from(0.0);
1728 }
1729
1730 for equiv in equivalences {
1731 // those sources which have a unique key
1732 let mut unique_sources = BTreeSet::new();
1733 let mut all_unique = true;
1734
1735 for expr in equiv {
1736 if let MirScalarExpr::Column(col, _) = expr {
1737 if let Some(idx) = unique_columns.get(col) {
1738 unique_sources.insert(*idx);
1739 } else {
1740 all_unique = false;
1741 }
1742 } else {
1743 all_unique = false;
1744 }
1745 }
1746
1747 // no unique columns in this equivalence
1748 if unique_sources.is_empty() {
1749 continue;
1750 }
1751
1752 // ALL unique columns in this equivalence
1753 if all_unique {
1754 // these inputs have unique keys for _all_ of the equivalence, so they're a bound on how many rows we'll get from those sources
1755 // we'll find the leftmost such input and use it to hold the minimum; the other sources we set to 1.0 (so they have no effect)
1756 let mut sources = unique_sources.iter();
1757
1758 let lhs_idx = *sources.next().unwrap();
1759 let mut lhs =
1760 std::mem::replace(&mut inputs[lhs_idx], CardinalityEstimate::from(1.0));
1761 for &rhs_idx in sources {
1762 let rhs =
1763 std::mem::replace(&mut inputs[rhs_idx], CardinalityEstimate::from(1.0));
1764 lhs = CardinalityEstimate::min(lhs, rhs);
1765 }
1766
1767 inputs[lhs_idx] = lhs;
1768
1769 // best option! go look at the next equivalence
1770 continue;
1771 }
1772
1773 // some unique columns in this equivalence
1774 for idx in unique_sources {
1775 // when joining R and S on R.x = S.x, if R.x is unique and S.x is not, we're bounded above by the cardinality of S
1776 inputs[idx] = CardinalityEstimate::from(1.0);
1777 }
1778 }
1779
1780 let mut product = CardinalityEstimate::from(1.0);
1781 for input in inputs {
1782 product = product * input;
1783 }
1784 product
1785 }
1786
1787 fn reduce(
1788 &self,
1789 group_key: &Vec<MirScalarExpr>,
1790 expected_group_size: &Option<u64>,
1791 input: CardinalityEstimate,
1792 ) -> CardinalityEstimate {
1793 // TODO(mgree): if no `group_key` is present, we can do way better
1794
1795 if let Some(group_size) = expected_group_size {
1796 input / f64::cast_lossy(*group_size)
1797 } else if group_key.is_empty() {
1798 CardinalityEstimate::from(1.0)
1799 } else {
1800 // in the worst case, every row is its own group
1801 input
1802 }
1803 }
1804
1805 fn topk(
1806 &self,
1807 group_key: &Vec<usize>,
1808 limit: &Option<MirScalarExpr>,
1809 expected_group_size: &Option<u64>,
1810 input: CardinalityEstimate,
1811 ) -> CardinalityEstimate {
1812 // TODO: support simple arithmetic expressions
1813 let k = limit
1814 .as_ref()
1815 .and_then(|l| l.as_literal_int64())
1816 .map_or(1, |l| std::cmp::max(0, l));
1817
1818 if let Some(group_size) = expected_group_size {
1819 input * (f64::cast_lossy(k) / f64::cast_lossy(*group_size))
1820 } else if group_key.is_empty() {
1821 CardinalityEstimate::from(f64::cast_lossy(k))
1822 } else {
1823 // in the worst case, every row is its own group
1824 input.clone()
1825 }
1826 }
1827
1828 fn threshold(&self, input: CardinalityEstimate) -> CardinalityEstimate {
1829 // worst case scaling factor is 1
1830 input.clone()
1831 }
1832 }
1833
1834 impl Analysis for Cardinality {
1835 type Value = CardinalityEstimate;
1836
1837 fn announce_dependencies(builder: &mut crate::analysis::DerivedBuilder) {
1838 builder.require(crate::analysis::Arity);
1839 builder.require(crate::analysis::UniqueKeys);
1840 }
1841
1842 fn derive(
1843 &self,
1844 expr: &MirRelationExpr,
1845 index: usize,
1846 results: &[Self::Value],
1847 depends: &crate::analysis::Derived,
1848 ) -> Self::Value {
1849 use MirRelationExpr::*;
1850
1851 let sizes = depends.as_view().results::<SubtreeSize>();
1852 let arity = depends.as_view().results::<Arity>();
1853 let keys = depends.as_view().results::<UniqueKeys>();
1854
1855 match expr {
1856 Constant { rows, .. } => {
1857 CardinalityEstimate::from(rows.as_ref().map_or_else(|_| 0, |v| v.len()))
1858 }
1859 Get { id, .. } => match id {
1860 Id::Local(id) => depends
1861 .bindings()
1862 .get(id)
1863 .and_then(|id| results.get(*id))
1864 .copied()
1865 .unwrap_or(CardinalityEstimate::Unknown),
1866 Id::Global(id) => self
1867 .stats
1868 .get(id)
1869 .copied()
1870 .map(CardinalityEstimate::from)
1871 .unwrap_or(CardinalityEstimate::Unknown),
1872 },
1873 Let { .. } | Project { .. } | Map { .. } | ArrangeBy { .. } | Negate { .. } => {
1874 results[index - 1].clone()
1875 }
1876 LetRec { .. } =>
1877 // TODO(mgree): implement a recurrence-based approach (or at least identify common idioms, e.g. transitive closure)
1878 {
1879 CardinalityEstimate::Unknown
1880 }
1881 Union { base: _, inputs: _ } => depends
1882 .children_of_rev(index, expr.children().count())
1883 .map(|off| results[off].clone())
1884 .sum(),
1885 FlatMap { func, .. } => {
1886 let input = results[index - 1];
1887 self.flat_map(func, input)
1888 }
1889 Filter { predicates, .. } => {
1890 let input = results[index - 1];
1891 let keys = depends.results::<UniqueKeys>();
1892 let keys = &keys[index - 1];
1893 self.filter(predicates, keys, input)
1894 }
1895 Join {
1896 equivalences,
1897 implementation,
1898 inputs,
1899 ..
1900 } => {
1901 let mut input_results = Vec::with_capacity(inputs.len());
1902
1903 // maps a column to the index in `inputs` that it belongs to
1904 let mut unique_columns = BTreeMap::new();
1905 let mut key_offset = 0;
1906
1907 let mut offset = 1;
1908 for idx in 0..inputs.len() {
1909 let input = results[index - offset];
1910 input_results.push(input);
1911
1912 let arity = arity[index - offset];
1913 let keys = &keys[index - offset];
1914 for key in keys {
1915 if key.len() == 1 {
1916 unique_columns.insert(key_offset + key[0], idx);
1917 }
1918 }
1919 key_offset += arity;
1920
1921 offset += &sizes[index - offset];
1922 }
1923
1924 self.join(equivalences, implementation, unique_columns, input_results)
1925 }
1926 Reduce {
1927 group_key,
1928 expected_group_size,
1929 ..
1930 } => {
1931 let input = results[index - 1];
1932 self.reduce(group_key, expected_group_size, input)
1933 }
1934 TopK {
1935 group_key,
1936 limit,
1937 expected_group_size,
1938 ..
1939 } => {
1940 let input = results[index - 1];
1941 self.topk(group_key, limit, expected_group_size, input)
1942 }
1943 Threshold { .. } => {
1944 let input = results[index - 1];
1945 self.threshold(input)
1946 }
1947 }
1948 }
1949 }
1950
1951 impl std::fmt::Display for CardinalityEstimate {
1952 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
1953 match self {
1954 CardinalityEstimate::Estimate(OrderedFloat(estimate)) => write!(f, "{estimate}"),
1955 CardinalityEstimate::Unknown => write!(f, "<UNKNOWN>"),
1956 }
1957 }
1958 }
1959}
1960
1961mod common_lattice {
1962 use crate::analysis::Lattice;
1963
1964 pub struct BoolLattice;
1965
1966 impl Lattice<bool> for BoolLattice {
1967 // `true` > `false`.
1968 fn top(&self) -> bool {
1969 true
1970 }
1971 // `false` is the greatest lower bound. `into` changes if it's true and `item` is false.
1972 fn meet_assign(&self, into: &mut bool, item: bool) -> bool {
1973 let changed = *into && !item;
1974 *into = *into && item;
1975 changed
1976 }
1977 }
1978}