1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503
// Copyright Materialize, Inc. and contributors. All rights reserved.
//
// Use of this software is governed by the Business Source License
// included in the LICENSE file.
//
// As of the Change Date specified in that file, in accordance with
// the Business Source License, use of this software will be governed
// by the Apache License, Version 2.0.
//! Utility functions to transform parts of a single `MirRelationExpr`
//! into canonical form.
use std::cmp::Ordering;
use std::collections::{BTreeMap, BTreeSet};
use mz_ore::soft_assert_or_log;
use mz_repr::{ColumnType, Datum, ScalarType};
use crate::visit::Visit;
use crate::{func, MirScalarExpr, UnaryFunc, VariadicFunc};
/// Canonicalize equivalence classes of a join and expressions contained in them.
///
/// `input_types` can be the [ColumnType]s of the join or the [ColumnType]s of
/// the individual inputs of the join in order.
///
/// This function:
/// * simplifies expressions to involve the least number of non-literal nodes.
/// This ensures that we only replace expressions by "even simpler"
/// expressions and that repeated substitutions reduce the complexity of
/// expressions and a fixed point is certain to be reached. Without this
/// rule, we might repeatedly replace a simple expression with an equivalent
/// complex expression containing that (or another replaceable) simple
/// expression, and repeat indefinitely.
/// * reduces all expressions contained in `equivalences`.
/// * Does everything that [canonicalize_equivalence_classes] does.
pub fn canonicalize_equivalences<'a, I>(
equivalences: &mut Vec<Vec<MirScalarExpr>>,
input_column_types: I,
) where
I: Iterator<Item = &'a Vec<ColumnType>>,
{
let column_types = input_column_types
.flat_map(|f| f.clone())
.collect::<Vec<_>>();
// Calculate the number of non-leaves for each expression.
let mut to_reduce = equivalences
.drain(..)
.filter_map(|mut cls| {
let mut result = cls
.drain(..)
.map(|expr| (rank_complexity(&expr), expr))
.collect::<Vec<_>>();
result.sort();
result.dedup();
if result.len() > 1 {
Some(result)
} else {
None
}
})
.collect::<Vec<_>>();
let mut expressions_rewritten = true;
while expressions_rewritten {
expressions_rewritten = false;
for i in 0..to_reduce.len() {
// `to_reduce` will be borrowed as immutable, so in order to modify
// elements of `to_reduce[i]`, we are going to pop them out of
// `to_reduce[i]` and put the modified version in `new_equivalence`,
// which will then replace `to_reduce[i]`.
let mut new_equivalence = Vec::with_capacity(to_reduce[i].len());
while let Some((_, mut popped_expr)) = to_reduce[i].pop() {
#[allow(deprecated)]
popped_expr.visit_mut_post_nolimit(&mut |e: &mut MirScalarExpr| {
// If a simpler expression can be found that is equivalent
// to e,
if let Some(simpler_e) = to_reduce.iter().find_map(|cls| {
if cls.iter().skip(1).position(|(_, expr)| e == expr).is_some() {
Some(cls[0].1.clone())
} else {
None
}
}) {
// Replace e with the simpler expression.
*e = simpler_e;
expressions_rewritten = true;
}
});
popped_expr.reduce(&column_types);
new_equivalence.push((rank_complexity(&popped_expr), popped_expr));
}
new_equivalence.sort();
new_equivalence.dedup();
to_reduce[i] = new_equivalence;
}
}
// Map away the complexity rating.
*equivalences = to_reduce
.drain(..)
.map(|mut cls| cls.drain(..).map(|(_, expr)| expr).collect::<Vec<_>>())
.collect::<Vec<_>>();
canonicalize_equivalence_classes(equivalences);
}
/// Canonicalize only the equivalence classes of a join.
///
/// This function:
/// * ensures the same expression appears in only one equivalence class.
/// * ensures the equivalence classes are sorted and dedupped.
/// ```rust
/// use mz_expr::MirScalarExpr;
/// use mz_expr::canonicalize::canonicalize_equivalence_classes;
///
/// let mut equivalences = vec![
/// vec![MirScalarExpr::Column(1), MirScalarExpr::Column(4)],
/// vec![MirScalarExpr::Column(3), MirScalarExpr::Column(5)],
/// vec![MirScalarExpr::Column(0), MirScalarExpr::Column(3)],
/// vec![MirScalarExpr::Column(2), MirScalarExpr::Column(2)],
/// ];
/// let expected = vec![
/// vec![MirScalarExpr::Column(0),
/// MirScalarExpr::Column(3),
/// MirScalarExpr::Column(5)],
/// vec![MirScalarExpr::Column(1), MirScalarExpr::Column(4)],
/// ];
/// canonicalize_equivalence_classes(&mut equivalences);
/// assert_eq!(expected, equivalences)
/// ````
pub fn canonicalize_equivalence_classes(equivalences: &mut Vec<Vec<MirScalarExpr>>) {
// Fuse equivalence classes containing the same expression.
for index in 1..equivalences.len() {
for inner in 0..index {
if equivalences[index]
.iter()
.any(|pair| equivalences[inner].contains(pair))
{
let to_extend = std::mem::replace(&mut equivalences[index], Vec::new());
equivalences[inner].extend(to_extend);
}
}
}
for equivalence in equivalences.iter_mut() {
equivalence.sort();
equivalence.dedup();
}
equivalences.retain(|es| es.len() > 1);
equivalences.sort();
}
/// Gives a relative complexity ranking for an expression. Higher numbers mean
/// greater complexity.
///
/// Currently, this method weighs literals as the least complex and weighs all
/// other expressions by the number of non-literals. In the future, we can
/// change how complexity is ranked so that repeated substitutions would result
/// in arriving at "better" fixed points. For example, we could try to improve
/// performance by ranking expressions by their estimated computation time.
///
/// To ensure we arrive at a fixed point after repeated substitutions, valid
/// complexity rankings must fulfill the following property:
/// For any expression `e`, there does not exist a SQL function `f` such
/// that `complexity(e) >= complexity(f(e))`.
///
/// For ease of intuiting the fixed point that we will arrive at after
/// repeated substitutions, it is nice but not required that complexity
/// rankings additionally fulfill the following property:
/// If expressions `e1` and `e2` are such that
/// `complexity(e1) < complexity(e2)` then for all SQL functions `f`,
/// `complexity(f(e1)) < complexity(f(e2))`.
fn rank_complexity(expr: &MirScalarExpr) -> usize {
if expr.is_literal() {
// literals are the least complex
return 0;
}
let mut non_literal_count = 1;
expr.visit_pre(|e| {
if !e.is_literal() {
non_literal_count += 1
}
});
non_literal_count
}
/// Applies a flat_map on a Vec, and overwrites the vec with the result.
fn flat_map_modify<T, I, F>(v: &mut Vec<T>, f: F)
where
F: FnMut(T) -> I,
I: IntoIterator<Item = T>,
{
let mut xx = v.drain(..).flat_map(f).collect();
v.append(&mut xx);
}
/// Canonicalize predicates of a filter.
///
/// This function reduces and canonicalizes the structure of each individual
/// predicate. Then, it transforms predicates of the form "A and B" into two: "A"
/// and "B". Afterwards, it reduces predicates based on information from other
/// predicates in the set. Finally, it sorts and deduplicates the predicates.
///
/// Additionally, it also removes IS NOT NULL predicates if there is another
/// null rejecting predicate for the same sub-expression.
pub fn canonicalize_predicates(predicates: &mut Vec<MirScalarExpr>, column_types: &[ColumnType]) {
soft_assert_or_log!(
predicates
.iter()
.all(|p| p.typ(column_types).scalar_type == ScalarType::Bool),
"cannot canonicalize predicates that are not of type bool"
);
// 1) Reduce each individual predicate.
predicates.iter_mut().for_each(|p| p.reduce(column_types));
// 2) Split "A and B" into two predicates: "A" and "B"
// Relies on the `reduce` above having flattened nested ANDs.
flat_map_modify(predicates, |p| {
if let MirScalarExpr::CallVariadic {
func: VariadicFunc::And,
exprs,
} = p
{
exprs
} else {
vec![p]
}
});
// 3) Make non-null requirements explicit as predicates in order for
// step 4) to be able to simplify AND/OR expressions with IS NULL
// sub-predicates. This redundancy is removed later by step 5).
let mut non_null_columns = BTreeSet::new();
for p in predicates.iter() {
p.non_null_requirements(&mut non_null_columns);
}
predicates.extend(non_null_columns.iter().map(|c| {
MirScalarExpr::column(*c)
.call_unary(UnaryFunc::IsNull(func::IsNull))
.call_unary(UnaryFunc::Not(func::Not))
}));
// 4) Reduce across `predicates`.
// If a predicate `p` cannot be null, and `f(p)` is a nullable bool
// then the predicate `p & f(p)` is equal to `p & f(true)`, and
// `!p & f(p)` is equal to `!p & f(false)`. For any index i, the `Vec` of
// predicates `[p1, ... pi, ... pn]` is equivalent to the single predicate
// `pi & (p1 & ... & p(i-1) & p(i+1) ... & pn)`. Thus, if `pi`
// (resp. `!pi`) cannot be null, it is valid to replace with `true` (resp.
// `false`) every subexpression in `(p1 & ... & p(i-1) & p(i+1) ... & pn)`
// that is equal to `pi`.
// If `p` is null and `q` is a nullable bool, then `p & q` can be either
// `null` or `false` depending on what `q`. Our rendering pipeline treats
// both as "remove this row." Thus, in the specific context of filter
// predicates, it is acceptable to make the aforementioned substitution
// even if `pi` can be null.
// Note that this does some dedupping of predicates since if `p1 = p2`
// then this reduction process will replace `p1` with true.
// Maintain respectively:
// 1) A list of predicates for which we have checked for matching
// subexpressions
// 2) A list of predicates for which we have yet to do so.
let mut completed = Vec::new();
let mut todo = Vec::new();
// Seed `todo` with all predicates.
std::mem::swap(&mut todo, predicates);
while let Some(predicate_to_apply) = todo.pop() {
// Helper method: for each predicate `p`, see if all other predicates
// (a.k.a. the union of todo & completed) contains `p` as a
// subexpression, and replace the subexpression accordingly.
// This method lives inside the loop because in order to comply with
// Rust rules that only one mutable reference to `todo` can be held at a
// time.
let mut replace_subexpr_other_predicates =
|expr: &MirScalarExpr, constant_bool: &MirScalarExpr| {
// Do not replace subexpressions equal to `expr` if `expr` is a
// literal to avoid infinite looping.
if !expr.is_literal() {
for other_predicate in todo.iter_mut() {
replace_subexpr_and_reduce(
other_predicate,
expr,
constant_bool,
column_types,
);
}
for other_idx in (0..completed.len()).rev() {
if replace_subexpr_and_reduce(
&mut completed[other_idx],
expr,
constant_bool,
column_types,
) {
// If a predicate in the `completed` list has
// been simplified, stick it back into the `todo` list.
todo.push(completed.remove(other_idx));
}
}
}
};
// Meat of loop starts here. If a predicate p is of the form `!q`, replace
// every instance of `q` in every other predicate with `false.`
// Otherwise, replace every instance of `p` in every other predicate
// with `true`.
if let MirScalarExpr::CallUnary {
func: UnaryFunc::Not(func::Not),
expr,
} = &predicate_to_apply
{
replace_subexpr_other_predicates(
expr,
&MirScalarExpr::literal_ok(Datum::False, ScalarType::Bool),
)
} else {
replace_subexpr_other_predicates(
&predicate_to_apply,
&MirScalarExpr::literal_ok(Datum::True, ScalarType::Bool),
);
}
completed.push(predicate_to_apply);
}
// 5) Remove redundant !isnull/isnull predicates after performing the replacements
// in the loop above.
std::mem::swap(&mut todo, &mut completed);
while let Some(predicate_to_apply) = todo.pop() {
// Remove redundant !isnull(x) predicates if there is another predicate
// that evaluates to NULL when `x` is NULL.
if let Some(operand) = is_not_null(&predicate_to_apply) {
if todo
.iter_mut()
.chain(completed.iter_mut())
.any(|p| is_null_rejecting_predicate(p, &operand))
{
// skip this predicate
continue;
}
} else if let MirScalarExpr::CallUnary {
func: UnaryFunc::IsNull(func::IsNull),
expr,
} = &predicate_to_apply
{
if todo
.iter_mut()
.chain(completed.iter_mut())
.any(|p| is_null_rejecting_predicate(p, expr))
{
completed.push(MirScalarExpr::literal_ok(Datum::False, ScalarType::Bool));
break;
}
}
completed.push(predicate_to_apply);
}
if completed.iter().any(|p| {
(p.is_literal_false() || p.is_literal_null()) &&
// This extra check is only needed if we determine that the soft-assert
// at the top of this function would ever fail for a good reason.
p.typ(column_types).scalar_type == ScalarType::Bool
}) {
// all rows get filtered away if any predicate is null or false.
*predicates = vec![MirScalarExpr::literal_ok(Datum::False, ScalarType::Bool)]
} else {
// Remove any predicates that have been reduced to "true"
completed.retain(|p| !p.is_literal_true());
*predicates = completed;
}
// 6) Sort and dedup predicates.
predicates.sort_by(compare_predicates);
predicates.dedup();
}
/// Replace any matching subexpressions in `predicate`, and if `predicate` has
/// changed, reduce it. Return whether `predicate` has changed.
fn replace_subexpr_and_reduce(
predicate: &mut MirScalarExpr,
replace_if_equal_to: &MirScalarExpr,
replace_with: &MirScalarExpr,
column_types: &[ColumnType],
) -> bool {
let mut changed = false;
#[allow(deprecated)]
predicate.visit_mut_pre_post_nolimit(
&mut |e| {
// The `cond` of an if statement is not visited to prevent `then`
// or `els` from being evaluated before `cond`, resulting in a
// correctness error.
if let MirScalarExpr::If { then, els, .. } = e {
return Some(vec![then, els]);
}
None
},
&mut |e| {
if e == replace_if_equal_to {
*e = replace_with.clone();
changed = true;
} else if let MirScalarExpr::CallBinary {
func: r_func,
expr1: r_expr1,
expr2: r_expr2,
} = replace_if_equal_to
{
if let Some(negation) = r_func.negate() {
if let MirScalarExpr::CallBinary {
func: l_func,
expr1: l_expr1,
expr2: l_expr2,
} = e
{
if negation == *l_func && l_expr1 == r_expr1 && l_expr2 == r_expr2 {
*e = MirScalarExpr::CallUnary {
func: UnaryFunc::Not(func::Not),
expr: Box::new(replace_with.clone()),
};
changed = true;
}
}
}
}
},
);
if changed {
predicate.reduce(column_types);
}
changed
}
/// Returns the inner operand if the given predicate is an IS NOT NULL expression.
fn is_not_null(predicate: &MirScalarExpr) -> Option<MirScalarExpr> {
if let MirScalarExpr::CallUnary {
func: UnaryFunc::Not(func::Not),
expr,
} = &predicate
{
if let MirScalarExpr::CallUnary {
func: UnaryFunc::IsNull(func::IsNull),
expr,
} = &**expr
{
return Some((**expr).clone());
}
}
None
}
/// Whether the given predicate evaluates to NULL when the given operand expression is NULL.
#[inline(always)]
fn is_null_rejecting_predicate(predicate: &MirScalarExpr, operand: &MirScalarExpr) -> bool {
propagates_null_from_subexpression(predicate, operand)
}
fn propagates_null_from_subexpression(expr: &MirScalarExpr, operand: &MirScalarExpr) -> bool {
if operand == expr {
true
} else if let MirScalarExpr::CallVariadic { func, exprs } = &expr {
func.propagates_nulls()
&& (exprs
.iter()
.any(|e| propagates_null_from_subexpression(e, operand)))
} else if let MirScalarExpr::CallBinary { func, expr1, expr2 } = &expr {
func.propagates_nulls()
&& (propagates_null_from_subexpression(expr1, operand)
|| propagates_null_from_subexpression(expr2, operand))
} else if let MirScalarExpr::CallUnary { func, expr } = &expr {
func.propagates_nulls() && propagates_null_from_subexpression(expr, operand)
} else {
false
}
}
/// Comparison method for sorting predicates by their complexity, measured by the total
/// number of non-literal expression nodes within the expression.
fn compare_predicates(x: &MirScalarExpr, y: &MirScalarExpr) -> Ordering {
(rank_complexity(x), x).cmp(&(rank_complexity(y), y))
}
/// For each equivalence class, it finds the simplest expression, which will be the canonical one.
/// Returns a Map that maps from each expression in each equivalence class to the canonical
/// expression in the same equivalence class.
pub fn get_canonicalizer_map(
equivalences: &Vec<Vec<MirScalarExpr>>,
) -> BTreeMap<MirScalarExpr, MirScalarExpr> {
let mut canonicalizer_map = BTreeMap::new();
for equivalence in equivalences {
// The unwrap is ok, because a join equivalence class can't be empty.
let canonical_expr = equivalence
.iter()
.min_by(|a, b| compare_predicates(*a, *b))
.unwrap();
for e in equivalence {
if e != canonical_expr {
canonicalizer_map.insert(e.clone(), canonical_expr.clone());
}
}
}
canonicalizer_map
}