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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998
// Copyright Materialize, Inc. and contributors. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License in the LICENSE file at the
// root of this repository, or online at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//! ## Notation
//!
//! Collections are represented with capital letters (T, S, R), collection traces as bold letters
//! (π, π, π), and difference traces as Ξ΄π.
//!
//! Indexing a collection trace π to obtain its version at `t` is written as π(t). Indexing a
//! collection to obtain the multiplicity of a record `x` is written as T\[x\]. These can be combined
//! to obtain the multiplicity of a record `x` at some version `t` as π(t)\[x\].
//!
//! ## Overview
//!
//! Reclocking transforms a source collection `S` that evolves with some timestamp `FromTime` into
//! a collection `T` that evolves with some other timestamp `IntoTime`. The reclocked collection T
//! contains all updates `u β S` that are not beyond some `FromTime` frontier R(t). The collection
//! `R` is called the remap collection.
//!
//! More formally, for some arbitrary time `t` of `IntoTime` and some arbitrary record `x`, the
//! reclocked collection `T(t)[x]` is defined to be the `sum{Ξ΄π(s)[x]: !(π(t) βͺ― s)}`. Since this
//! holds for any record we can write the definition of Reclock(π, π) as:
//!
//! > Reclock(π, π) β π: β t β IntoTime : π(t) = sum{Ξ΄π(s): !(π(t) βͺ― s)}
//!
//! In order for the reclocked collection `T` to have a sensible definition of progress we require
//! that `t1 β€ t2 β π(t1) βͺ― π(t2)` where the first `β€` is the partial order of `IntoTime` and the
//! second one the partial order of `FromTime` antichains.
//!
//! ## Total order simplification
//!
//! In order to simplify the implementation we will require that `IntoTime` is a total order. This
//! limitation can be lifted in the future but further elaboration on the mechanics of reclocking
//! is required to ensure a correct implementation.
//!
//! ## The difference trace
//!
//! By the definition of difference traces we have:
//!
//! ```text
//! Ξ΄π(t) = T(t) - sum{Ξ΄π(s): s < t}
//! ```
//!
//! Due to the total order assumption we only need to consider two cases.
//!
//! **Case 1:** `t` is the minimum timestamp
//!
//! In this case `sum{Ξ΄π(s): s < t}` is the empty set and so we obtain:
//!
//! ```text
//! Ξ΄π(min) = T(min) = sum{Ξ΄π(s): !(π(min) β€ s}
//! ```
//!
//! **Case 2:** `t` is a timestamp with a predecessor `prev`
//!
//! In this case `sum{Ξ΄π(s): s < t}` is equal to `T(prev)` because:
//!
//! ```text
//! sum{Ξ΄π(s): s < t} = sum{Ξ΄π(s): s β€ prev} + sum{Ξ΄π(s): prev < s < t}
//! = T(prev) + β
//! = T(prev)
//! ```
//!
//! And therefore the difference trace of T is:
//!
//! ```text
//! Ξ΄π(t) = π(t) - π(prev)
//! = sum{Ξ΄π(s): !(π(t) βͺ― s)} - sum{Ξ΄π(s): !(π(prev) βͺ― s)}
//! = sum{Ξ΄π(s): (π(prev) βͺ― s) β§ !(π(t) βͺ― s)}
//! ```
//!
//! ## Unique mapping property
//!
//! Given the definition above we can derive the fact that for any source difference Ξ΄π(s) there is
//! at most one target timestamp t that it must be reclocked to. This property can be exploited by
//! the implementation of the operator as it can safely discard source updates once a matching
//! Ξ΄T(t) has been found, making it "stateless" with respect to the source trace. A formal proof of
//! this property is [provided below](#unique-mapping-property-proof).
//!
//! ## Operational description
//!
//! The operator follows a run-to-completion model where on each scheduling it completes all
//! outstanding work that can be completed.
//!
//! ### Unique mapping property proof
//!
//! This section contains the formal proof the unique mapping property. The proof follows the
//! structure proof notation created by Leslie Lamport. Readers unfamiliar with structured proofs
//! can read about them here <https://lamport.azurewebsites.net/pubs/proof.pdf>.
//!
//! #### Statement
//!
//! AtMostOne(X, Ο(x)) β β x1, x2 β X : Ο(x1) β§ Ο(x2) β x1 = x2
//!
//! * **THEOREM** UniqueMapping β
//! * **ASSUME**
//! * **NEW** (FromTime, βͺ―) β PartiallyOrderedTimestamps
//! * **NEW** (IntoTime, β€) β TotallyOrderedTimestamps
//! * **NEW** π β SetOfCollectionTraces(FromTime)
//! * **NEW** π β SetOfCollectionTraces(IntoTime)
//! * β t β IntoTime: π(t) β SetOfAntichains(FromTime)
//! * β t1, t1 β IntoTime: t1 β€ t2 β π(t1) βͺ― π(t2)
//! * **NEW** π = Reclock(π, π)
//! * **PROVE** β s β FromTime : AtMostOne(IntoTime, Ξ΄π(s) β Ξ΄π(x))
//!
//! #### Proof
//!
//! 1. **SUFFICES ASSUME** β s β FromTime: Β¬AtMostOne(IntoTime, Ξ΄π(s) β Ξ΄π(x))
//! * **PROVE FALSE**
//! * _By proof by contradiction._
//! 2. **PICK** s β FromTime : Β¬AtMostOne(IntoTime, Ξ΄π(s) β Ξ΄π(x))
//! * _Proof: Such time exists by <1>1._
//! 3. β t1, t2 β IntoTime : t1 β t2 β§ Ξ΄π(s) β Ξ΄π(t1) β§ Ξ΄π(s) β Ξ΄π(t2)
//! 1. Β¬(β x1, x2 β X : (Ξ΄π(s) β Ξ΄π(x1)) β§ (Ξ΄π(s) β Ξ΄π(x2)) β x1 = x2)
//! * _Proof: By <1>2 and definition of AtMostOne._
//! 2. Q.E.D
//! * _Proof: By <2>1, quantifier negation rules, and theorem of propositional logic Β¬(P β Q) β‘ P β§ Β¬Q._
//! 4. **PICK** t1, t2 β IntoTime : t1 < t2 β§ Ξ΄π(s) β Ξ΄π(t1) β§ Ξ΄π(s) β Ξ΄π(t2)
//! * _Proof: By <1>3. Assume t1 < t2 without loss of generality._
//! 5. Β¬(π(t1) βͺ― s)
//! 1. **CASE** t1 = min(IntoTime)
//! 1. Ξ΄π(t1) = sum{Ξ΄π(s): !(π(t1)) βͺ― s}
//! * _Proof: By definition of Ξ΄π(min)._
//! 2. Ξ΄π(s) β Ξ΄π(t1)
//! * _Proof: By <1>4._
//! 3. Q.E.D
//! * _Proof: By <3>1 and <3>2._
//! 2. **CASE** t1 > min(IntoTime)
//! 1. **PICK** t1_prev = Predecessor(t1)
//! * _Proof: Predecessor exists because the set {t: t < t1} is non-empty since it must contain at least min(IntoTime)._
//! 2. Ξ΄π(t1) = sum{Ξ΄π(s): (π(t1_prev) βͺ― s) β§ !(π(t1) βͺ― s)}
//! * _Proof: By definition of Ξ΄π(t)._
//! 3. Ξ΄π(s) β Ξ΄π(t1)
//! * _Proof: By <1>4._
//! 3. Q.E.D
//! * _Proof: By <3>2 and <3>3._
//! 3. Q.E.D
//! * _Proof: From cases <2>1 and <2>2 which are exhaustive_
//! 6. **PICK** t2_prev β IntoTime : t2_prev = Predecessor(t2)
//! * _Proof: Predecessor exists because by <1>4 the set {t: t < t2} is non empty since it must contain at least t1._
//! 7. t1 β€ t2_prev
//! * _Proof: t1 β {t: t < t2} and t2_prev is the maximum element of the set._
//! 8. π(t2) βͺ― s
//! 1. t2 > min(IntoTime)
//! * _Proof: By <1>5._
//! 2. **PICK** t2_prev = Predecessor(t2)
//! * _Proof: Predecessor exists because the set {t: t < t2} is non-empty since it must contain at least min(IntoTime)._
//! 3. Ξ΄π(t) = sum{Ξ΄π(s): (π(t2_prev) βͺ― s) β§ !(π(t) βͺ― s)}
//! * _Proof: By definition of Ξ΄π(t)_
//! 4. Ξ΄π(s) β Ξ΄π(t1)
//! * _Proof: By <1>4._
//! 5. Q.E.D
//! * _Proof: By <2>3 and <2>4._
//! 9. π(t1) βͺ― π(t2_prev)
//! * _Proof: By <1>.7 and hypothesis on R_
//! 10. π(t1) βͺ― s
//! * _Proof: By <1>8 and <1>9._
//! 11. Q.E.D
//! * _Proof: By <1>5 and <1>10_
use std::cmp::{Ordering, Reverse};
use std::collections::binary_heap::{BinaryHeap, PeekMut};
use std::collections::VecDeque;
use std::iter::FromIterator;
use differential_dataflow::difference::Semigroup;
use differential_dataflow::lattice::Lattice;
use differential_dataflow::{consolidation, AsCollection, Collection, ExchangeData};
use mz_ore::collections::CollectionExt;
use timely::communication::{Message, Pull, Push};
use timely::dataflow::channels::pact::Pipeline;
use timely::dataflow::operators::capture::Event;
use timely::dataflow::operators::generic::builder_rc::OperatorBuilder;
use timely::dataflow::operators::CapabilitySet;
use timely::dataflow::Scope;
use timely::order::{PartialOrder, TotalOrder};
use timely::progress::frontier::{AntichainRef, MutableAntichain};
use timely::progress::{Antichain, Timestamp};
/// Constructs an operator that reclocks a `source` collection varying with some time `FromTime`
/// into the corresponding `reclocked` collection varying over some time `IntoTime` using the
/// provided `remap` collection.
///
/// In order for the operator to read the `source` collection a `Pusher` is returned which can be
/// used with timely's capture facilities to connect a collection from a foreign scope to this
/// operator.
pub fn reclock<G, D, FromTime, IntoTime, R>(
remap_collection: &Collection<G, FromTime, i64>,
as_of: Antichain<G::Timestamp>,
) -> (
Box<dyn Push<Message<Event<FromTime, Vec<(D, FromTime, R)>>>>>,
Collection<G, D, R>,
)
where
G: Scope<Timestamp = IntoTime>,
D: ExchangeData,
FromTime: Timestamp,
IntoTime: Timestamp + Lattice + TotalOrder,
R: Semigroup + 'static,
{
let mut scope = remap_collection.scope();
let mut builder = OperatorBuilder::new("Reclock".into(), scope.clone());
// Here we create a channel that can be used to send data from a foreign scope into this
// operator. The channel is associated with this operator's address so that it is activated
// every time events are available for consumption. This mechanism is similar to Timely's input
// handles where data can be introduced into a timely scope from an exogenous source.
let info = builder.operator_info();
let channel_id = scope.new_identifier();
let (pusher, mut events) =
scope.pipeline::<Event<FromTime, Vec<(D, FromTime, R)>>>(channel_id, info.address);
let mut remap_input = builder.new_input(&remap_collection.inner, Pipeline);
let (mut output, reclocked) = builder.new_output();
builder.build(move |caps| {
let mut capset = CapabilitySet::from_elem(caps.into_element());
capset.downgrade(&as_of.borrow());
// Received remap updates at times `into_time` greater or equal to `remap_input`'s input
// frontier. As the input frontier advances, we drop elements out of this priority queue
// and mint new associations.
let mut pending_remap: BinaryHeap<Reverse<(IntoTime, FromTime, i64)>> = BinaryHeap::new();
// A trace of `remap_input` that accumulates correctly for all times that are beyond
// `remap_since` and not beyond `remap_upper`. The updates in `remap_trace` are maintained
// in time order. An actual DD trace could be used here at the expense of a more
// complicated API to traverse it. This is left for future work if the naive trace
// maintenance implemented in this operator becomes problematic.
let mut remap_upper = Antichain::from_elem(IntoTime::minimum());
let mut remap_since = as_of;
let mut remap_trace = Vec::new();
// A stash of source updates for which we don't know the corresponding binding yet.
let mut deferred_source_updates: Vec<ChainBatch<_, _, _>> = Vec::new();
// The frontier of the `events` input
let mut source_frontier = MutableAntichain::new_bottom(FromTime::minimum());
let mut binding_buffer = Vec::new();
let mut remap_buffer = Vec::new();
let mut interesting_times = Vec::new();
// The operator drains `remap_input` and organizes new bindings that are not beyond
// `remap_input`'s frontier into the time ordered `remap_trace`.
//
// All received data events can either be reclocked to a time included in the
// `remap_trace`, or deferred until new associations are minted. Each data event that
// happens at some `FromTime` is mapped to the first `IntoTime` whose associated antichain
// is not less or equal to the input `FromTime`.
//
// As progress events are received from the `events` input, we can advance our
// held capability to track the least `IntoTime` a newly received `FromTime` could possibly
// map to and also compact the maintained `remap_trace` to that time.
move |frontiers| {
let Some(cap) = capset.get(0) else {
return;
};
let mut output = output.activate();
let mut session = output.session(cap);
// STEP 1. Accept new bindings into `pending_remap`.
while let Some((_, data)) = remap_input.next() {
data.swap(&mut remap_buffer);
for (from, into, diff) in remap_buffer.drain(..) {
pending_remap.push(Reverse((into, from, diff)));
}
}
// STEP 2. Extract bindings not beyond `remap_frontier` and commit them into `remap_trace`.
let prev_remap_upper =
std::mem::replace(&mut remap_upper, frontiers[0].frontier().to_owned());
while let Some(update) = pending_remap.peek_mut() {
if !remap_upper.less_equal(&update.0 .0) {
let Reverse((into, from, diff)) = PeekMut::pop(update);
remap_trace.push((from, into, diff));
} else {
break;
}
}
// STEP 3. Receive new data updates
// The `events` input describes arbitrary progress and data over `FromTime`,
// which must be translated to `IntoTime`. Each `FromTime` can be found as the
// first `IntoTime` associated with a `[FromTime]` that is not less or equal to
// the input `FromTime`. Received events that are not yet associated to an
// `IntoTime` are collected, and formed into a "chain batch": a sequence of
// chains that results from sorting the updates by `FromTime`, and then
// segmenting the sequence at elements where the partial order on `FromTime` is
// violated.
let mut stash = Vec::new();
while let Some(event) = events.pull() {
match event.as_mut() {
Event::Progress(changes) => {
source_frontier.update_iter(changes.drain(..));
}
Event::Messages(_, data) => stash.append(data),
}
}
stash.sort_unstable_by(|(_, t1, _): &(D, FromTime, R), (_, t2, _)| t1.cmp(t2));
let mut new_source_updates = ChainBatch::from_iter(stash);
// STEP 4: Reclock new and deferred updates
// We are now ready to step through the remap bindings in time order and
// perform the following actions:
// 4.1. Match `new_source_updates` against the entirety of bindings contained
// in the trace.
// 4.2. Match `deferred_source_updates` against the bindings that were just
// added in the trace.
// 4.3. Reclock `source_frontier` to calculate the new since frontier of the
// remap trace.
//
// The steps above only make sense to perform if there are any times for which
// we can correctly accumulate the remap trace, which is what we check here.
if remap_since.iter().all(|t| !remap_upper.less_equal(t)) {
let mut cur_binding = MutableAntichain::new();
let mut remap = remap_trace.iter().peekable();
let mut reclocked_source_frontier = remap_upper.clone();
// We go over all the times for which we might need to output data at. These times
// are restrticted to the times at which there exists an update in `remap_trace`
// and the minimum timestamp for the case where `remap_trace` is completely empty,
// in which case the minimum timestamp maps to the empty `FromTime` frontier and
// therefore all data events map to that minimum timestamp.
//
// The approach taken here will take time proportional to the number of elements in
// `remap_trace`. During development an alternative approach was considered where
// the updates in `remap_trace` are instead fully materialized into an ordered list
// of antichains in which every data update can be binary searched into. The are
// two concerns with this alternative approach that led to preferring this one:
// 1. Materializing very wide antichains with small differences between them
// needs memory proportial to the number of bindings times the width of the
// antichain.
// 2. It locks in the requirement of a totally ordered target timestamp since only
// in that case can one binary search a binding.
// The linear scan is expected to be fine due to the run-to-completion nature of
// the operator since its cost is amortized among the number of outstanding
// updates.
let mut min_time = IntoTime::minimum();
min_time.advance_by(remap_since.borrow());
interesting_times.push(min_time);
interesting_times.extend(remap_trace.iter().map(|(_, t, _)| t.clone()));
interesting_times.dedup();
for cur_time in interesting_times.drain(..) {
// 4.0. Load updates of `cur_time` from the trace into `cur_binding` to
// construct the `[FromTime]` frontier that `cur_time` maps to.
while let Some((t_from, _, diff)) = remap.next_if(|(_, t, _)| t == &cur_time) {
binding_buffer.push((t_from.clone(), *diff));
}
cur_binding.update_iter(binding_buffer.drain(..));
let cur_binding = cur_binding.frontier();
// 4.1. Extract updates from `new_source_updates`
for (data, _, diff) in new_source_updates.extract(cur_binding) {
session.give((data, cur_time.clone(), diff));
}
// 4.2. Extract updates from `deferred_source_updates`.
// The deferred updates contain all updates that were not able to be
// reclocked with the bindings until `prev_remap_upper`. For this reason
// we only need to reconsider these updates when we start looking at new
// bindings, i.e bindings that are beyond `prev_remap_upper`.
if prev_remap_upper.less_equal(&cur_time) {
deferred_source_updates.retain_mut(|batch| {
for (data, _, diff) in batch.extract(cur_binding) {
session.give((data, cur_time.clone(), diff));
}
// Retain non-empty batches
!batch.is_empty()
})
}
// 4.3. Reclock `source_frontier`
// If any FromTime in source frontier could possibly be reclocked to this
// binding then we must maintain our capability to emit data at that time
// and not compact past it.
if source_frontier
.frontier()
.iter()
.any(|t| !cur_binding.less_equal(t))
{
reclocked_source_frontier.insert(cur_time);
}
}
// STEP 5. Downgrade capability and compact remap trace
capset.downgrade(&reclocked_source_frontier.borrow());
remap_since = reclocked_source_frontier;
for (_, t, _) in remap_trace.iter_mut() {
t.advance_by(remap_since.borrow());
}
consolidation::consolidate_updates(&mut remap_trace);
remap_trace
.sort_unstable_by(|(_, t1, _): &(_, IntoTime, _), (_, t2, _)| t1.cmp(t2));
}
// STEP 6. Tidy up deferred updates
// Deferred updates are represented as a list of chain batches where each batch
// contains two times the updates of the batch proceeding it. This organization
// leads to a logarithmic number of batches with respect to the outstanding
// number of updates.
deferred_source_updates.sort_unstable_by_key(|b| Reverse(b.len()));
if !new_source_updates.is_empty() {
deferred_source_updates.push(new_source_updates);
}
let dsu = &mut deferred_source_updates;
while dsu.len() > 1 && (dsu[dsu.len() - 1].len() >= dsu[dsu.len() - 2].len() / 2) {
let a = dsu.pop().unwrap();
let b = dsu.pop().unwrap();
dsu.push(a.merge_with(b));
}
}
});
(Box::new(pusher), reclocked.as_collection())
}
/// A batch of differential updates that vary over some partial order. This type maintains the data
/// as a set of chains that allows for efficient extraction of batches given a frontier.
#[derive(Debug, PartialEq)]
struct ChainBatch<D, T, R> {
/// A list of chains (sets of mutually comparable times) sorted by the partial order.
chains: Vec<VecDeque<(D, T, R)>>,
}
impl<D, T: Timestamp, R> ChainBatch<D, T, R> {
/// Extracts all updates with time not greater or equal to any time in `upper`.
fn extract<'a>(
&'a mut self,
upper: AntichainRef<'a, T>,
) -> impl Iterator<Item = (D, T, R)> + 'a {
self.chains.retain(|chain| !chain.is_empty());
self.chains.iter_mut().flat_map(move |chain| {
// A chain is a sorted list of mutually comparable elements so we keep extracting
// elements that are not beyond upper.
std::iter::from_fn(move || {
let (_, into, _) = chain.front()?;
if !upper.less_equal(into) {
chain.pop_front()
} else {
None
}
})
})
}
fn merge_with(
mut self: ChainBatch<D, T, R>,
mut other: ChainBatch<D, T, R>,
) -> ChainBatch<D, T, R>
where
D: ExchangeData,
T: Timestamp,
R: Semigroup,
{
let mut updates1 = self.chains.drain(..).flatten().peekable();
let mut updates2 = other.chains.drain(..).flatten().peekable();
let merged = std::iter::from_fn(|| {
match (updates1.peek(), updates2.peek()) {
(Some((d1, t1, _)), Some((d2, t2, _))) => {
match (t1, d1).cmp(&(t2, d2)) {
Ordering::Less => updates1.next(),
Ordering::Greater => updates2.next(),
// If the same (d, t) pair is found, consolidate their diffs
Ordering::Equal => {
let (d1, t1, mut r1) = updates1.next().unwrap();
while let Some((_, _, r)) =
updates1.next_if(|(d, t, _)| (d, t) == (&d1, &t1))
{
r1.plus_equals(&r);
}
while let Some((_, _, r)) =
updates2.next_if(|(d, t, _)| (d, t) == (&d1, &t1))
{
r1.plus_equals(&r);
}
Some((d1, t1, r1))
}
}
}
(Some(_), None) => updates1.next(),
(None, Some(_)) => updates2.next(),
(None, None) => None,
}
});
ChainBatch::from_iter(merged.filter(|(_, _, r)| !r.is_zero()))
}
/// Returns the number of updates in the batch.
fn len(&self) -> usize {
self.chains.iter().map(|chain| chain.len()).sum()
}
/// Returns true if the batch contains no updates.
fn is_empty(&self) -> bool {
self.len() == 0
}
}
impl<D, T: Timestamp, R> FromIterator<(D, T, R)> for ChainBatch<D, T, R> {
/// Computes the chain decomposition of updates according to the partial order `T`.
fn from_iter<I: IntoIterator<Item = (D, T, R)>>(updates: I) -> Self {
let mut chains = vec![];
let mut updates = updates.into_iter();
if let Some((d, t, r)) = updates.next() {
let mut chain = VecDeque::new();
chain.push_back((d, t, r));
for (d, t, r) in updates {
let prev_t = &chain[chain.len() - 1].1;
if !PartialOrder::less_equal(prev_t, &t) {
chains.push(chain);
chain = VecDeque::new();
}
chain.push_back((d, t, r));
}
chains.push(chain);
}
Self { chains }
}
}
#[cfg(test)]
mod test {
use std::sync::mpsc::{Receiver, TryRecvError};
use differential_dataflow::consolidation;
use differential_dataflow::input::{Input, InputSession};
use timely::communication::allocator::Thread;
use timely::dataflow::operators::capture::{Event, Extract};
use timely::dataflow::operators::unordered_input::UnorderedHandle;
use timely::dataflow::operators::{ActivateCapability, Capture, UnorderedInput};
use timely::worker::Worker;
use crate::capture::PusherCapture;
use crate::order::Partitioned;
use super::*;
type FromTime = Partitioned<u64, u64>;
type IntoTime = u64;
type BindingHandle = InputSession<IntoTime, FromTime, i64>;
type DataHandle<D> = (
UnorderedHandle<FromTime, (D, FromTime, i64)>,
ActivateCapability<FromTime>,
);
type ReclockedStream<D> = Receiver<Event<IntoTime, Vec<(D, IntoTime, i64)>>>;
/// A helper function that sets up a dataflow program to test the reclocking operator. Each
/// test provides a test logic closure which accepts four arguments:
///
/// * A reference to the worker that allows the test to step the computation
/// * A `BindingHandle` that allows the test to manipulate the remap bindings
/// * A `DataHandle` that allows the test to submit the data to be reclocked
/// * A `ReclockedStream` that allows observing the result of the reclocking process
fn harness<D, F, R>(as_of: Antichain<IntoTime>, test_logic: F) -> R
where
D: ExchangeData,
F: FnOnce(&mut Worker<Thread>, BindingHandle, DataHandle<D>, ReclockedStream<D>) -> R
+ Send
+ Sync
+ 'static,
R: Send + 'static,
{
timely::execute_directly(move |worker| {
let (bindings, data, data_cap, reclocked) = worker.dataflow::<(), _, _>(|scope| {
let (bindings, data_pusher, reclocked) =
scope.scoped::<IntoTime, _, _>("IntoScope", move |scope| {
let (binding_handle, binding_collection) = scope.new_collection();
let (data_pusher, reclocked_collection) =
reclock(&binding_collection, as_of);
let reclocked_capture = reclocked_collection.inner.capture();
(binding_handle, data_pusher, reclocked_capture)
});
let (data, data_cap) = scope.scoped::<FromTime, _, _>("FromScope", move |scope| {
let ((handle, cap), data) = scope.new_unordered_input();
data.capture_into(PusherCapture(data_pusher));
(handle, cap)
});
(bindings, data, data_cap, reclocked)
});
test_logic(worker, bindings, (data, data_cap), reclocked)
})
}
/// Steps the worker four times which is the required number of times for both data and
/// frontier updates to propagate across the two scopes and into the probing channels.
fn step(worker: &mut Worker<Thread>) {
for _ in 0..4 {
worker.step();
}
}
#[mz_ore::test]
fn basic_reclocking() {
let as_of = Antichain::from_elem(IntoTime::minimum());
harness(
as_of,
|worker, bindings, (mut data, data_cap), reclocked| {
// Reclock everything at the minimum IntoTime
bindings.close();
data.session(data_cap)
.give(('a', Partitioned::minimum(), 1));
step(worker);
let extracted = reclocked.extract();
let expected = vec![(0, vec![('a', 0, 1)])];
assert_eq!(extracted, expected);
},
)
}
/// Generates a `Partitioned<u64, u64>` Antichain where all the provided
/// partitions are at the specified offset and the gaps in between are filled with range
/// timestamps at offset zero.
fn partitioned_frontier<I>(items: I) -> Antichain<Partitioned<u64, u64>>
where
I: IntoIterator<Item = (u64, u64)>,
{
let mut frontier = Antichain::new();
let mut prev = 0;
for (pid, offset) in items {
if prev < pid {
frontier.insert(Partitioned::new_range(prev, pid - 1, 0));
}
frontier.insert(Partitioned::new_singleton(pid, offset));
prev = pid + 1
}
frontier.insert(Partitioned::new_range(prev, u64::MAX, 0));
frontier
}
#[mz_ore::test]
fn test_basic_usage() {
let as_of = Antichain::from_elem(IntoTime::minimum());
harness(
as_of,
|worker, mut bindings, (mut data, data_cap), reclocked| {
// Reclock offsets 1 and 3 to timestamp 1000
bindings.update_at(Partitioned::minimum(), 0, 1);
bindings.update_at(Partitioned::minimum(), 1000, -1);
for time in partitioned_frontier([(0, 4)]) {
bindings.update_at(time, 1000, 1);
}
bindings.advance_to(1001);
bindings.flush();
data.session(data_cap.clone()).give_iterator(
vec![
(1, Partitioned::new_singleton(0, 1), 1),
(1, Partitioned::new_singleton(0, 1), 1),
(3, Partitioned::new_singleton(0, 3), 1),
]
.into_iter(),
);
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Messages(
0u64,
vec![(1, 1000, 1), (1, 1000, 1), (3, 1000, 1)]
))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(0, -1), (1000, 1)]))
);
// Reclock more messages for offsets 3 to the same timestamp
data.session(data_cap.clone()).give_iterator(
vec![
(3, Partitioned::new_singleton(0, 3), 1),
(3, Partitioned::new_singleton(0, 3), 1),
]
.into_iter(),
);
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Messages(1000u64, vec![(3, 1000, 1), (3, 1000, 1)]))
);
// Drop the capability which should advance the reclocked frontier to 1001.
drop(data_cap);
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(1000, -1), (1001, 1)]))
);
},
);
}
#[mz_ore::test]
fn test_reclock_frontier() {
let as_of = Antichain::from_elem(IntoTime::minimum());
harness::<(), _, _>(
as_of,
|worker, mut bindings, (_data, data_cap), reclocked| {
// Initialize the bindings such that the minimum IntoTime contains the minimum FromTime
// frontier.
bindings.update_at(Partitioned::minimum(), 0, 1);
bindings.advance_to(1);
bindings.flush();
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(0, -1), (1, 1)]))
);
// Mint a couple of bindings for multiple partitions
bindings.update_at(Partitioned::minimum(), 1000, -1);
for time in partitioned_frontier([(1, 10)]) {
bindings.update_at(time.clone(), 1000, 1);
bindings.update_at(time, 2000, -1);
}
for time in partitioned_frontier([(1, 10), (2, 10)]) {
bindings.update_at(time, 2000, 1);
}
bindings.advance_to(2001);
bindings.flush();
// The initial frontier should now map to the minimum between the two partitions
step(worker);
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(1, -1), (1000, 1)]))
);
// Downgrade data frontier such that only one of the partitions is advanced
let mut part1_cap = data_cap.delayed(&Partitioned::new_singleton(1, 9));
let mut part2_cap = data_cap.delayed(&Partitioned::new_singleton(2, 0));
let _rest_cap = data_cap.delayed(&Partitioned::new_range(3, u64::MAX, 0));
drop(data_cap);
step(worker);
assert_eq!(reclocked.try_recv(), Err(TryRecvError::Empty));
// Downgrade the data frontier past the first binding
part1_cap.downgrade(&Partitioned::new_singleton(1, 10));
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(1000, -1), (2000, 1)]))
);
// Downgrade the data frontier past the second binding
part2_cap.downgrade(&Partitioned::new_singleton(2, 10));
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(2000, -1), (2001, 1)]))
);
// Advance the binding frontier and confirm that we get to the next timestamp
bindings.advance_to(3001);
bindings.flush();
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(2001, -1), (3001, 1)]))
);
},
);
}
#[mz_ore::test]
fn test_reclock() {
let as_of = Antichain::from_elem(IntoTime::minimum());
harness(
as_of,
|worker, mut bindings, (mut data, data_cap), reclocked| {
// Initialize the bindings such that the minimum IntoTime contains the minimum FromTime
// frontier.
bindings.update_at(Partitioned::minimum(), 0, 1);
// Setup more precise capabilities for the rest of the test
let mut part0_cap = data_cap.delayed(&Partitioned::new_singleton(0, 0));
let rest_cap = data_cap.delayed(&Partitioned::new_range(1, u64::MAX, 0));
drop(data_cap);
// Reclock offsets 1 and 2 to timestamp 1000
data.session(part0_cap.clone()).give_iterator(
vec![
(1, Partitioned::new_singleton(0, 1), 1),
(2, Partitioned::new_singleton(0, 2), 1),
]
.into_iter(),
);
part0_cap.downgrade(&Partitioned::new_singleton(0, 3));
bindings.update_at(Partitioned::minimum(), 1000, -1);
bindings.update_at(part0_cap.time().clone(), 1000, 1);
bindings.update_at(rest_cap.time().clone(), 1000, 1);
bindings.advance_to(1001);
bindings.flush();
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Messages(0, vec![(1, 1000, 1), (2, 1000, 1)]))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(0, -1), (1000, 1)]))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(1000, -1), (1001, 1)]))
);
// Reclock offsets 3 and 4 to timestamp 2000
data.session(part0_cap.clone()).give_iterator(
vec![
(3, Partitioned::new_singleton(0, 3), 1),
(3, Partitioned::new_singleton(0, 3), 1),
(4, Partitioned::new_singleton(0, 4), 1),
]
.into_iter(),
);
bindings.update_at(part0_cap.time().clone(), 2000, -1);
part0_cap.downgrade(&Partitioned::new_singleton(0, 5));
bindings.update_at(part0_cap.time().clone(), 2000, 1);
bindings.advance_to(2001);
bindings.flush();
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Messages(
1001,
vec![(3, 2000, 1), (3, 2000, 1), (4, 2000, 1)]
))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(1001, -1), (2000, 1)]))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(2000, -1), (2001, 1)]))
);
},
);
}
#[mz_ore::test]
fn test_reclock_gh16318() {
let as_of = Antichain::from_elem(IntoTime::minimum());
harness(
as_of,
|worker, mut bindings, (mut data, data_cap), reclocked| {
// Initialize the bindings such that the minimum IntoTime contains the minimum FromTime
// frontier.
bindings.update_at(Partitioned::minimum(), 0, 1);
// First mint bindings for 0 at timestamp 1000
bindings.update_at(Partitioned::minimum(), 1000, -1);
for time in partitioned_frontier([(0, 50)]) {
bindings.update_at(time, 1000, 1);
}
// Then only for 1 at timestamp 2000
for time in partitioned_frontier([(0, 50)]) {
bindings.update_at(time, 2000, -1);
}
for time in partitioned_frontier([(0, 50), (1, 50)]) {
bindings.update_at(time, 2000, 1);
}
// Then again only for 0 at timestamp 3000
for time in partitioned_frontier([(0, 50), (1, 50)]) {
bindings.update_at(time, 3000, -1);
}
for time in partitioned_frontier([(0, 100), (1, 50)]) {
bindings.update_at(time, 3000, 1);
}
bindings.advance_to(3001);
bindings.flush();
// Reclockng (0, 50) must ignore the updates on the FromTime frontier that happened at
// timestamp 2000 since those are completely unrelated
data.session(data_cap)
.give((50, Partitioned::new_singleton(0, 50), 1));
step(worker);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Messages(0, vec![(50, 3000, 1),]))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(0, -1), (1000, 1)]))
);
assert_eq!(
reclocked.try_recv(),
Ok(Event::Progress(vec![(1000, -1), (3001, 1)]))
);
},
);
}
/// Test that compact(reclock(remap, source)) == reclock(compact(remap), source)
#[mz_ore::test]
fn test_compaction() {
let mut remap = vec![];
remap.push((Partitioned::minimum(), 0, 1));
// Reclock offsets 1 and 2 to timestamp 1000
remap.push((Partitioned::minimum(), 1000, -1));
for time in partitioned_frontier([(0, 3)]) {
remap.push((time, 1000, 1));
}
// Reclock offsets 3 and 4 to timestamp 2000
for time in partitioned_frontier([(0, 3)]) {
remap.push((time, 2000, -1));
}
for time in partitioned_frontier([(0, 5)]) {
remap.push((time, 2000, 1));
}
let source_updates = vec![
(1, Partitioned::new_singleton(0, 1), 1),
(2, Partitioned::new_singleton(0, 2), 1),
(3, Partitioned::new_singleton(0, 3), 1),
(4, Partitioned::new_singleton(0, 4), 1),
];
let since = Antichain::from_elem(1500);
// Compute reclock(remap, source)
let as_of = Antichain::from_elem(IntoTime::minimum());
let remap1 = remap.clone();
let source_updates1 = source_updates.clone();
let reclock_remap = harness(
as_of,
move |worker, mut bindings, (mut data, data_cap), reclocked| {
for (from_ts, into_ts, diff) in remap1 {
bindings.update_at(from_ts, into_ts, diff);
}
bindings.close();
data.session(data_cap)
.give_iterator(source_updates1.iter().cloned());
step(worker);
reclocked.extract()
},
);
// Compute compact(reclock(remap, source))
let mut compact_reclock_remap = reclock_remap;
for (t, updates) in compact_reclock_remap.iter_mut() {
t.advance_by(since.borrow());
for (_, t, _) in updates.iter_mut() {
t.advance_by(since.borrow());
}
}
// Compute compact(remap)
let mut compact_remap = remap;
for (_, t, _) in compact_remap.iter_mut() {
t.advance_by(since.borrow());
}
consolidation::consolidate_updates(&mut compact_remap);
// Compute reclock(compact(remap), source)
let reclock_compact_remap = harness(
since,
move |worker, mut bindings, (mut data, data_cap), reclocked| {
for (from_ts, into_ts, diff) in compact_remap {
bindings.update_at(from_ts, into_ts, diff);
}
bindings.close();
data.session(data_cap)
.give_iterator(source_updates.iter().cloned());
step(worker);
reclocked.extract()
},
);
let expected = vec![(
1500,
vec![(1, 1500, 1), (2, 1500, 1), (3, 2000, 1), (4, 2000, 1)],
)];
assert_eq!(expected, reclock_compact_remap);
assert_eq!(expected, compact_reclock_remap);
}
#[mz_ore::test]
fn test_chainbatch_merge() {
let a = ChainBatch::from_iter([('a', 0, 1)]);
let b = ChainBatch::from_iter([('a', 0, -1), ('a', 1, 1)]);
assert_eq!(a.merge_with(b), ChainBatch::from_iter([('a', 1, 1)]));
}
}