1 use crate::vec::{Idx, IndexVec};
2 use arrayvec::ArrayVec;
5 use std::marker::PhantomData;
7 use std::ops::{BitAnd, BitAndAssign, BitOrAssign, Bound, Not, Range, RangeBounds, Shl};
11 use rustc_macros::{Decodable, Encodable};
19 const WORD_BYTES: usize = mem::size_of::<Word>();
20 const WORD_BITS: usize = WORD_BYTES * 8;
22 // The choice of chunk size has some trade-offs.
24 // A big chunk size tends to favour cases where many large `ChunkedBitSet`s are
25 // present, because they require fewer `Chunk`s, reducing the number of
26 // allocations and reducing peak memory usage. Also, fewer chunk operations are
27 // required, though more of them might be `Mixed`.
29 // A small chunk size tends to favour cases where many small `ChunkedBitSet`s
30 // are present, because less space is wasted at the end of the final chunk (if
32 const CHUNK_WORDS: usize = 32;
33 const CHUNK_BITS: usize = CHUNK_WORDS * WORD_BITS; // 2048 bits
35 /// ChunkSize is small to keep `Chunk` small. The static assertion ensures it's
38 const _: () = assert!(CHUNK_BITS <= ChunkSize::MAX as usize);
40 pub trait BitRelations<Rhs> {
41 fn union(&mut self, other: &Rhs) -> bool;
42 fn subtract(&mut self, other: &Rhs) -> bool;
43 fn intersect(&mut self, other: &Rhs) -> bool;
47 fn inclusive_start_end<T: Idx>(
48 range: impl RangeBounds<T>,
50 ) -> Option<(usize, usize)> {
51 // Both start and end are inclusive.
52 let start = match range.start_bound().cloned() {
53 Bound::Included(start) => start.index(),
54 Bound::Excluded(start) => start.index() + 1,
55 Bound::Unbounded => 0,
57 let end = match range.end_bound().cloned() {
58 Bound::Included(end) => end.index(),
59 Bound::Excluded(end) => end.index().checked_sub(1)?,
60 Bound::Unbounded => domain - 1,
62 assert!(end < domain);
69 macro_rules! bit_relations_inherent_impls {
71 /// Sets `self = self | other` and returns `true` if `self` changed
72 /// (i.e., if new bits were added).
73 pub fn union<Rhs>(&mut self, other: &Rhs) -> bool
75 Self: BitRelations<Rhs>,
77 <Self as BitRelations<Rhs>>::union(self, other)
80 /// Sets `self = self - other` and returns `true` if `self` changed.
81 /// (i.e., if any bits were removed).
82 pub fn subtract<Rhs>(&mut self, other: &Rhs) -> bool
84 Self: BitRelations<Rhs>,
86 <Self as BitRelations<Rhs>>::subtract(self, other)
89 /// Sets `self = self & other` and return `true` if `self` changed.
90 /// (i.e., if any bits were removed).
91 pub fn intersect<Rhs>(&mut self, other: &Rhs) -> bool
93 Self: BitRelations<Rhs>,
95 <Self as BitRelations<Rhs>>::intersect(self, other)
100 /// A fixed-size bitset type with a dense representation.
102 /// NOTE: Use [`GrowableBitSet`] if you need support for resizing after creation.
104 /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also
107 /// All operations that involve an element will panic if the element is equal
108 /// to or greater than the domain size. All operations that involve two bitsets
109 /// will panic if the bitsets have differing domain sizes.
111 #[derive(Eq, PartialEq, Hash, Decodable, Encodable)]
112 pub struct BitSet<T> {
115 marker: PhantomData<T>,
119 /// Gets the domain size.
120 pub fn domain_size(&self) -> usize {
125 impl<T: Idx> BitSet<T> {
126 /// Creates a new, empty bitset with a given `domain_size`.
128 pub fn new_empty(domain_size: usize) -> BitSet<T> {
129 let num_words = num_words(domain_size);
130 BitSet { domain_size, words: vec![0; num_words], marker: PhantomData }
133 /// Creates a new, filled bitset with a given `domain_size`.
135 pub fn new_filled(domain_size: usize) -> BitSet<T> {
136 let num_words = num_words(domain_size);
137 let mut result = BitSet { domain_size, words: vec![!0; num_words], marker: PhantomData };
138 result.clear_excess_bits();
142 /// Clear all elements.
144 pub fn clear(&mut self) {
148 /// Clear excess bits in the final word.
149 fn clear_excess_bits(&mut self) {
150 clear_excess_bits_in_final_word(self.domain_size, &mut self.words);
153 /// Count the number of set bits in the set.
154 pub fn count(&self) -> usize {
155 self.words.iter().map(|e| e.count_ones() as usize).sum()
158 /// Returns `true` if `self` contains `elem`.
160 pub fn contains(&self, elem: T) -> bool {
161 assert!(elem.index() < self.domain_size);
162 let (word_index, mask) = word_index_and_mask(elem);
163 (self.words[word_index] & mask) != 0
166 /// Is `self` is a (non-strict) superset of `other`?
168 pub fn superset(&self, other: &BitSet<T>) -> bool {
169 assert_eq!(self.domain_size, other.domain_size);
170 self.words.iter().zip(&other.words).all(|(a, b)| (a & b) == *b)
173 /// Is the set empty?
175 pub fn is_empty(&self) -> bool {
176 self.words.iter().all(|a| *a == 0)
179 /// Insert `elem`. Returns whether the set has changed.
181 pub fn insert(&mut self, elem: T) -> bool {
182 assert!(elem.index() < self.domain_size);
183 let (word_index, mask) = word_index_and_mask(elem);
184 let word_ref = &mut self.words[word_index];
185 let word = *word_ref;
186 let new_word = word | mask;
187 *word_ref = new_word;
192 pub fn insert_range(&mut self, elems: impl RangeBounds<T>) {
193 let Some((start, end)) = inclusive_start_end(elems, self.domain_size) else {
197 let (start_word_index, start_mask) = word_index_and_mask(start);
198 let (end_word_index, end_mask) = word_index_and_mask(end);
200 // Set all words in between start and end (exclusively of both).
201 for word_index in (start_word_index + 1)..end_word_index {
202 self.words[word_index] = !0;
205 if start_word_index != end_word_index {
206 // Start and end are in different words, so we handle each in turn.
208 // We set all leading bits. This includes the start_mask bit.
209 self.words[start_word_index] |= !(start_mask - 1);
210 // And all trailing bits (i.e. from 0..=end) in the end word,
211 // including the end.
212 self.words[end_word_index] |= end_mask | end_mask - 1;
214 self.words[start_word_index] |= end_mask | (end_mask - start_mask);
218 /// Sets all bits to true.
219 pub fn insert_all(&mut self) {
221 self.clear_excess_bits();
224 /// Returns `true` if the set has changed.
226 pub fn remove(&mut self, elem: T) -> bool {
227 assert!(elem.index() < self.domain_size);
228 let (word_index, mask) = word_index_and_mask(elem);
229 let word_ref = &mut self.words[word_index];
230 let word = *word_ref;
231 let new_word = word & !mask;
232 *word_ref = new_word;
236 /// Gets a slice of the underlying words.
237 pub fn words(&self) -> &[Word] {
241 /// Iterates over the indices of set bits in a sorted order.
243 pub fn iter(&self) -> BitIter<'_, T> {
244 BitIter::new(&self.words)
247 /// Duplicates the set as a hybrid set.
248 pub fn to_hybrid(&self) -> HybridBitSet<T> {
249 // Note: we currently don't bother trying to make a Sparse set.
250 HybridBitSet::Dense(self.to_owned())
253 /// Set `self = self | other`. In contrast to `union` returns `true` if the set contains at
254 /// least one bit that is not in `other` (i.e. `other` is not a superset of `self`).
256 /// This is an optimization for union of a hybrid bitset.
257 fn reverse_union_sparse(&mut self, sparse: &SparseBitSet<T>) -> bool {
258 assert!(sparse.domain_size == self.domain_size);
259 self.clear_excess_bits();
261 let mut not_already = false;
262 // Index of the current word not yet merged.
263 let mut current_index = 0;
264 // Mask of bits that came from the sparse set in the current word.
265 let mut new_bit_mask = 0;
266 for (word_index, mask) in sparse.iter().map(|x| word_index_and_mask(*x)) {
267 // Next bit is in a word not inspected yet.
268 if word_index > current_index {
269 self.words[current_index] |= new_bit_mask;
270 // Were there any bits in the old word that did not occur in the sparse set?
271 not_already |= (self.words[current_index] ^ new_bit_mask) != 0;
272 // Check all words we skipped for any set bit.
273 not_already |= self.words[current_index + 1..word_index].iter().any(|&x| x != 0);
275 current_index = word_index;
276 // Reset bit mask, no bits have been merged yet.
279 // Add bit and mark it as coming from the sparse set.
280 // self.words[word_index] |= mask;
281 new_bit_mask |= mask;
283 self.words[current_index] |= new_bit_mask;
284 // Any bits in the last inspected word that were not in the sparse set?
285 not_already |= (self.words[current_index] ^ new_bit_mask) != 0;
286 // Any bits in the tail? Note `clear_excess_bits` before.
287 not_already |= self.words[current_index + 1..].iter().any(|&x| x != 0);
292 fn last_set_in(&self, range: impl RangeBounds<T>) -> Option<T> {
293 let (start, end) = inclusive_start_end(range, self.domain_size)?;
294 let (start_word_index, _) = word_index_and_mask(start);
295 let (end_word_index, end_mask) = word_index_and_mask(end);
297 let end_word = self.words[end_word_index] & (end_mask | (end_mask - 1));
299 let pos = max_bit(end_word) + WORD_BITS * end_word_index;
301 return Some(T::new(pos));
305 // We exclude end_word_index from the range here, because we don't want
306 // to limit ourselves to *just* the last word: the bits set it in may be
307 // after `end`, so it may not work out.
308 if let Some(offset) =
309 self.words[start_word_index..end_word_index].iter().rposition(|&w| w != 0)
311 let word_idx = start_word_index + offset;
312 let start_word = self.words[word_idx];
313 let pos = max_bit(start_word) + WORD_BITS * word_idx;
315 return Some(T::new(pos));
322 bit_relations_inherent_impls! {}
326 impl<T: Idx> BitRelations<BitSet<T>> for BitSet<T> {
327 fn union(&mut self, other: &BitSet<T>) -> bool {
328 assert_eq!(self.domain_size, other.domain_size);
329 bitwise(&mut self.words, &other.words, |a, b| a | b)
332 fn subtract(&mut self, other: &BitSet<T>) -> bool {
333 assert_eq!(self.domain_size, other.domain_size);
334 bitwise(&mut self.words, &other.words, |a, b| a & !b)
337 fn intersect(&mut self, other: &BitSet<T>) -> bool {
338 assert_eq!(self.domain_size, other.domain_size);
339 bitwise(&mut self.words, &other.words, |a, b| a & b)
343 /// A fixed-size bitset type with a partially dense, partially sparse
344 /// representation. The bitset is broken into chunks, and chunks that are all
345 /// zeros or all ones are represented and handled very efficiently.
347 /// This type is especially efficient for sets that typically have a large
348 /// `domain_size` with significant stretches of all zeros or all ones, and also
349 /// some stretches with lots of 0s and 1s mixed in a way that causes trouble
350 /// for `IntervalSet`.
352 /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also
355 /// All operations that involve an element will panic if the element is equal
356 /// to or greater than the domain size. All operations that involve two bitsets
357 /// will panic if the bitsets have differing domain sizes.
358 #[derive(Debug, PartialEq, Eq)]
359 pub struct ChunkedBitSet<T> {
362 /// The chunks. Each one contains exactly CHUNK_BITS values, except the
363 /// last one which contains 1..=CHUNK_BITS values.
364 chunks: Box<[Chunk]>,
366 marker: PhantomData<T>,
369 // Note: the chunk domain size is duplicated in each variant. This is a bit
370 // inconvenient, but it allows the type size to be smaller than if we had an
371 // outer struct containing a chunk domain size plus the `Chunk`, because the
372 // compiler can place the chunk domain size after the tag.
373 #[derive(Clone, Debug, PartialEq, Eq)]
375 /// A chunk that is all zeros; we don't represent the zeros explicitly.
378 /// A chunk that is all ones; we don't represent the ones explicitly.
381 /// A chunk that has a mix of zeros and ones, which are represented
382 /// explicitly and densely. It never has all zeros or all ones.
384 /// If this is the final chunk there may be excess, unused words. This
385 /// turns out to be both simpler and have better performance than
386 /// allocating the minimum number of words, largely because we avoid having
387 /// to store the length, which would make this type larger. These excess
388 /// words are always be zero, as are any excess bits in the final in-use
391 /// The second field is the count of 1s set in the chunk, and must satisfy
392 /// `0 < count < chunk_domain_size`.
394 /// The words are within an `Rc` because it's surprisingly common to
395 /// duplicate an entire chunk, e.g. in `ChunkedBitSet::clone_from()`, or
396 /// when a `Mixed` chunk is union'd into a `Zeros` chunk. When we do need
397 /// to modify a chunk we use `Rc::make_mut`.
398 Mixed(ChunkSize, ChunkSize, Rc<[Word; CHUNK_WORDS]>),
401 // This type is used a lot. Make sure it doesn't unintentionally get bigger.
402 #[cfg(all(target_arch = "x86_64", target_pointer_width = "64"))]
403 crate::static_assert_size!(Chunk, 16);
405 impl<T> ChunkedBitSet<T> {
406 pub fn domain_size(&self) -> usize {
411 fn assert_valid(&self) {
412 if self.domain_size == 0 {
413 assert!(self.chunks.is_empty());
417 assert!((self.chunks.len() - 1) * CHUNK_BITS <= self.domain_size);
418 assert!(self.chunks.len() * CHUNK_BITS >= self.domain_size);
419 for chunk in self.chunks.iter() {
420 chunk.assert_valid();
425 impl<T: Idx> ChunkedBitSet<T> {
426 /// Creates a new bitset with a given `domain_size` and chunk kind.
427 fn new(domain_size: usize, is_empty: bool) -> Self {
428 let chunks = if domain_size == 0 {
431 // All the chunks have a chunk_domain_size of `CHUNK_BITS` except
433 let final_chunk_domain_size = {
434 let n = domain_size % CHUNK_BITS;
435 if n == 0 { CHUNK_BITS } else { n }
438 vec![Chunk::new(CHUNK_BITS, is_empty); num_chunks(domain_size)].into_boxed_slice();
439 *chunks.last_mut().unwrap() = Chunk::new(final_chunk_domain_size, is_empty);
442 ChunkedBitSet { domain_size, chunks, marker: PhantomData }
445 /// Creates a new, empty bitset with a given `domain_size`.
447 pub fn new_empty(domain_size: usize) -> Self {
448 ChunkedBitSet::new(domain_size, /* is_empty */ true)
451 /// Creates a new, filled bitset with a given `domain_size`.
453 pub fn new_filled(domain_size: usize) -> Self {
454 ChunkedBitSet::new(domain_size, /* is_empty */ false)
458 fn chunks(&self) -> &[Chunk] {
462 /// Count the number of bits in the set.
463 pub fn count(&self) -> usize {
464 self.chunks.iter().map(|chunk| chunk.count()).sum()
467 /// Returns `true` if `self` contains `elem`.
469 pub fn contains(&self, elem: T) -> bool {
470 assert!(elem.index() < self.domain_size);
471 let chunk = &self.chunks[chunk_index(elem)];
475 Mixed(_, _, words) => {
476 let (word_index, mask) = chunk_word_index_and_mask(elem);
477 (words[word_index] & mask) != 0
482 /// Insert `elem`. Returns whether the set has changed.
483 pub fn insert(&mut self, elem: T) -> bool {
484 assert!(elem.index() < self.domain_size);
485 let chunk_index = chunk_index(elem);
486 let chunk = &mut self.chunks[chunk_index];
488 Zeros(chunk_domain_size) => {
489 if chunk_domain_size > 1 {
490 // We take some effort to avoid copying the words.
491 let words = Rc::<[Word; CHUNK_WORDS]>::new_zeroed();
492 // SAFETY: `words` can safely be all zeroes.
493 let mut words = unsafe { words.assume_init() };
494 let words_ref = Rc::get_mut(&mut words).unwrap();
496 let (word_index, mask) = chunk_word_index_and_mask(elem);
497 words_ref[word_index] |= mask;
498 *chunk = Mixed(chunk_domain_size, 1, words);
500 *chunk = Ones(chunk_domain_size);
505 Mixed(chunk_domain_size, ref mut count, ref mut words) => {
506 // We skip all the work if the bit is already set.
507 let (word_index, mask) = chunk_word_index_and_mask(elem);
508 if (words[word_index] & mask) == 0 {
510 if *count < chunk_domain_size {
511 let words = Rc::make_mut(words);
512 words[word_index] |= mask;
514 *chunk = Ones(chunk_domain_size);
524 /// Sets all bits to true.
525 pub fn insert_all(&mut self) {
526 for chunk in self.chunks.iter_mut() {
527 *chunk = match *chunk {
528 Zeros(chunk_domain_size)
529 | Ones(chunk_domain_size)
530 | Mixed(chunk_domain_size, ..) => Ones(chunk_domain_size),
535 /// Returns `true` if the set has changed.
536 pub fn remove(&mut self, elem: T) -> bool {
537 assert!(elem.index() < self.domain_size);
538 let chunk_index = chunk_index(elem);
539 let chunk = &mut self.chunks[chunk_index];
542 Ones(chunk_domain_size) => {
543 if chunk_domain_size > 1 {
544 // We take some effort to avoid copying the words.
545 let words = Rc::<[Word; CHUNK_WORDS]>::new_zeroed();
546 // SAFETY: `words` can safely be all zeroes.
547 let mut words = unsafe { words.assume_init() };
548 let words_ref = Rc::get_mut(&mut words).unwrap();
550 // Set only the bits in use.
551 let num_words = num_words(chunk_domain_size as usize);
552 words_ref[..num_words].fill(!0);
553 clear_excess_bits_in_final_word(
554 chunk_domain_size as usize,
555 &mut words_ref[..num_words],
557 let (word_index, mask) = chunk_word_index_and_mask(elem);
558 words_ref[word_index] &= !mask;
559 *chunk = Mixed(chunk_domain_size, chunk_domain_size - 1, words);
561 *chunk = Zeros(chunk_domain_size);
565 Mixed(chunk_domain_size, ref mut count, ref mut words) => {
566 // We skip all the work if the bit is already clear.
567 let (word_index, mask) = chunk_word_index_and_mask(elem);
568 if (words[word_index] & mask) != 0 {
571 let words = Rc::make_mut(words);
572 words[word_index] &= !mask;
574 *chunk = Zeros(chunk_domain_size);
584 bit_relations_inherent_impls! {}
587 impl<T: Idx> BitRelations<ChunkedBitSet<T>> for ChunkedBitSet<T> {
588 fn union(&mut self, other: &ChunkedBitSet<T>) -> bool {
589 assert_eq!(self.domain_size, other.domain_size);
590 debug_assert_eq!(self.chunks.len(), other.chunks.len());
592 let mut changed = false;
593 for (mut self_chunk, other_chunk) in self.chunks.iter_mut().zip(other.chunks.iter()) {
594 match (&mut self_chunk, &other_chunk) {
595 (_, Zeros(_)) | (Ones(_), _) => {}
596 (Zeros(self_chunk_domain_size), Ones(other_chunk_domain_size))
597 | (Mixed(self_chunk_domain_size, ..), Ones(other_chunk_domain_size))
598 | (Zeros(self_chunk_domain_size), Mixed(other_chunk_domain_size, ..)) => {
599 // `other_chunk` fully overwrites `self_chunk`
600 debug_assert_eq!(self_chunk_domain_size, other_chunk_domain_size);
601 *self_chunk = other_chunk.clone();
606 self_chunk_domain_size,
607 ref mut self_chunk_count,
608 ref mut self_chunk_words,
610 Mixed(_other_chunk_domain_size, _other_chunk_count, other_chunk_words),
612 // First check if the operation would change
613 // `self_chunk.words`. If not, we can avoid allocating some
614 // words, and this happens often enough that it's a
615 // performance win. Also, we only need to operate on the
616 // in-use words, hence the slicing.
617 let op = |a, b| a | b;
618 let num_words = num_words(*self_chunk_domain_size as usize);
620 &self_chunk_words[0..num_words],
621 &other_chunk_words[0..num_words],
624 let self_chunk_words = Rc::make_mut(self_chunk_words);
625 let has_changed = bitwise(
626 &mut self_chunk_words[0..num_words],
627 &other_chunk_words[0..num_words],
630 debug_assert!(has_changed);
631 *self_chunk_count = self_chunk_words[0..num_words]
633 .map(|w| w.count_ones() as ChunkSize)
635 if *self_chunk_count == *self_chunk_domain_size {
636 *self_chunk = Ones(*self_chunk_domain_size);
646 fn subtract(&mut self, _other: &ChunkedBitSet<T>) -> bool {
647 unimplemented!("implement if/when necessary");
650 fn intersect(&mut self, _other: &ChunkedBitSet<T>) -> bool {
651 unimplemented!("implement if/when necessary");
655 impl<T: Idx> BitRelations<HybridBitSet<T>> for ChunkedBitSet<T> {
656 fn union(&mut self, other: &HybridBitSet<T>) -> bool {
657 // FIXME: This is slow if `other` is dense, but it hasn't been a problem
658 // in practice so far.
659 // If a a faster implementation of this operation is required, consider
660 // reopening https://github.com/rust-lang/rust/pull/94625
661 assert_eq!(self.domain_size, other.domain_size());
662 sequential_update(|elem| self.insert(elem), other.iter())
665 fn subtract(&mut self, other: &HybridBitSet<T>) -> bool {
666 // FIXME: This is slow if `other` is dense, but it hasn't been a problem
667 // in practice so far.
668 // If a a faster implementation of this operation is required, consider
669 // reopening https://github.com/rust-lang/rust/pull/94625
670 assert_eq!(self.domain_size, other.domain_size());
671 sequential_update(|elem| self.remove(elem), other.iter())
674 fn intersect(&mut self, _other: &HybridBitSet<T>) -> bool {
675 unimplemented!("implement if/when necessary");
679 impl<T> Clone for ChunkedBitSet<T> {
680 fn clone(&self) -> Self {
682 domain_size: self.domain_size,
683 chunks: self.chunks.clone(),
688 /// WARNING: this implementation of clone_from will panic if the two
689 /// bitsets have different domain sizes. This constraint is not inherent to
690 /// `clone_from`, but it works with the existing call sites and allows a
691 /// faster implementation, which is important because this function is hot.
692 fn clone_from(&mut self, from: &Self) {
693 assert_eq!(self.domain_size, from.domain_size);
694 debug_assert_eq!(self.chunks.len(), from.chunks.len());
696 self.chunks.clone_from(&from.chunks)
702 fn assert_valid(&self) {
704 Zeros(chunk_domain_size) | Ones(chunk_domain_size) => {
705 assert!(chunk_domain_size as usize <= CHUNK_BITS);
707 Mixed(chunk_domain_size, count, ref words) => {
708 assert!(chunk_domain_size as usize <= CHUNK_BITS);
709 assert!(0 < count && count < chunk_domain_size);
711 // Check the number of set bits matches `count`.
713 words.iter().map(|w| w.count_ones() as ChunkSize).sum::<ChunkSize>(),
717 // Check the not-in-use words are all zeroed.
718 let num_words = num_words(chunk_domain_size as usize);
719 if num_words < CHUNK_WORDS {
723 .map(|w| w.count_ones() as ChunkSize)
732 fn new(chunk_domain_size: usize, is_empty: bool) -> Self {
733 debug_assert!(chunk_domain_size <= CHUNK_BITS);
734 let chunk_domain_size = chunk_domain_size as ChunkSize;
735 if is_empty { Zeros(chunk_domain_size) } else { Ones(chunk_domain_size) }
738 /// Count the number of 1s in the chunk.
739 fn count(&self) -> usize {
742 Ones(chunk_domain_size) => chunk_domain_size as usize,
743 Mixed(_, count, _) => count as usize,
748 // Applies a function to mutate a bitset, and returns true if any
749 // of the applications return true
750 fn sequential_update<T: Idx>(
751 mut self_update: impl FnMut(T) -> bool,
752 it: impl Iterator<Item = T>,
754 let mut changed = false;
756 changed |= self_update(elem);
761 // Optimization of intersection for SparseBitSet that's generic
763 fn sparse_intersect<T: Idx>(
764 set: &mut SparseBitSet<T>,
765 other_contains: impl Fn(&T) -> bool,
767 let size = set.elems.len();
768 set.elems.retain(|elem| other_contains(elem));
769 set.elems.len() != size
772 // Optimization of dense/sparse intersection. The resulting set is
773 // guaranteed to be at most the size of the sparse set, and hence can be
774 // represented as a sparse set. Therefore the sparse set is copied and filtered,
775 // then returned as the new set.
776 fn dense_sparse_intersect<T: Idx>(
778 sparse: &SparseBitSet<T>,
779 ) -> (SparseBitSet<T>, bool) {
780 let mut sparse_copy = sparse.clone();
781 sparse_intersect(&mut sparse_copy, |el| dense.contains(*el));
782 let n = sparse_copy.len();
783 (sparse_copy, n != dense.count())
787 impl<T: Idx> BitRelations<BitSet<T>> for HybridBitSet<T> {
788 fn union(&mut self, other: &BitSet<T>) -> bool {
789 assert_eq!(self.domain_size(), other.domain_size);
791 HybridBitSet::Sparse(sparse) => {
792 // `self` is sparse and `other` is dense. To
793 // merge them, we have two available strategies:
794 // * Densify `self` then merge other
795 // * Clone other then integrate bits from `self`
796 // The second strategy requires dedicated method
797 // since the usual `union` returns the wrong
798 // result. In the dedicated case the computation
799 // is slightly faster if the bits of the sparse
800 // bitset map to only few words of the dense
801 // representation, i.e. indices are near each
804 // Benchmarking seems to suggest that the second
805 // option is worth it.
806 let mut new_dense = other.clone();
807 let changed = new_dense.reverse_union_sparse(sparse);
808 *self = HybridBitSet::Dense(new_dense);
812 HybridBitSet::Dense(dense) => dense.union(other),
816 fn subtract(&mut self, other: &BitSet<T>) -> bool {
817 assert_eq!(self.domain_size(), other.domain_size);
819 HybridBitSet::Sparse(sparse) => {
820 sequential_update(|elem| sparse.remove(elem), other.iter())
822 HybridBitSet::Dense(dense) => dense.subtract(other),
826 fn intersect(&mut self, other: &BitSet<T>) -> bool {
827 assert_eq!(self.domain_size(), other.domain_size);
829 HybridBitSet::Sparse(sparse) => sparse_intersect(sparse, |elem| other.contains(*elem)),
830 HybridBitSet::Dense(dense) => dense.intersect(other),
836 impl<T: Idx> BitRelations<HybridBitSet<T>> for BitSet<T> {
837 fn union(&mut self, other: &HybridBitSet<T>) -> bool {
838 assert_eq!(self.domain_size, other.domain_size());
840 HybridBitSet::Sparse(sparse) => {
841 sequential_update(|elem| self.insert(elem), sparse.iter().cloned())
843 HybridBitSet::Dense(dense) => self.union(dense),
847 fn subtract(&mut self, other: &HybridBitSet<T>) -> bool {
848 assert_eq!(self.domain_size, other.domain_size());
850 HybridBitSet::Sparse(sparse) => {
851 sequential_update(|elem| self.remove(elem), sparse.iter().cloned())
853 HybridBitSet::Dense(dense) => self.subtract(dense),
857 fn intersect(&mut self, other: &HybridBitSet<T>) -> bool {
858 assert_eq!(self.domain_size, other.domain_size());
860 HybridBitSet::Sparse(sparse) => {
861 let (updated, changed) = dense_sparse_intersect(self, sparse);
863 // We can't directly assign the SparseBitSet to the BitSet, and
864 // doing `*self = updated.to_dense()` would cause a drop / reallocation. Instead,
865 // the BitSet is cleared and `updated` is copied into `self`.
867 for elem in updated.iter() {
872 HybridBitSet::Dense(dense) => self.intersect(dense),
878 impl<T: Idx> BitRelations<HybridBitSet<T>> for HybridBitSet<T> {
879 fn union(&mut self, other: &HybridBitSet<T>) -> bool {
880 assert_eq!(self.domain_size(), other.domain_size());
882 HybridBitSet::Sparse(_) => {
884 HybridBitSet::Sparse(other_sparse) => {
885 // Both sets are sparse. Add the elements in
886 // `other_sparse` to `self` one at a time. This
887 // may or may not cause `self` to be densified.
888 let mut changed = false;
889 for elem in other_sparse.iter() {
890 changed |= self.insert(*elem);
895 HybridBitSet::Dense(other_dense) => self.union(other_dense),
899 HybridBitSet::Dense(self_dense) => self_dense.union(other),
903 fn subtract(&mut self, other: &HybridBitSet<T>) -> bool {
904 assert_eq!(self.domain_size(), other.domain_size());
906 HybridBitSet::Sparse(self_sparse) => {
907 sequential_update(|elem| self_sparse.remove(elem), other.iter())
909 HybridBitSet::Dense(self_dense) => self_dense.subtract(other),
913 fn intersect(&mut self, other: &HybridBitSet<T>) -> bool {
914 assert_eq!(self.domain_size(), other.domain_size());
916 HybridBitSet::Sparse(self_sparse) => {
917 sparse_intersect(self_sparse, |elem| other.contains(*elem))
919 HybridBitSet::Dense(self_dense) => match other {
920 HybridBitSet::Sparse(other_sparse) => {
921 let (updated, changed) = dense_sparse_intersect(self_dense, other_sparse);
922 *self = HybridBitSet::Sparse(updated);
925 HybridBitSet::Dense(other_dense) => self_dense.intersect(other_dense),
931 impl<T> Clone for BitSet<T> {
932 fn clone(&self) -> Self {
933 BitSet { domain_size: self.domain_size, words: self.words.clone(), marker: PhantomData }
936 fn clone_from(&mut self, from: &Self) {
937 if self.domain_size != from.domain_size {
938 self.words.resize(from.domain_size, 0);
939 self.domain_size = from.domain_size;
942 self.words.copy_from_slice(&from.words);
946 impl<T: Idx> fmt::Debug for BitSet<T> {
947 fn fmt(&self, w: &mut fmt::Formatter<'_>) -> fmt::Result {
948 w.debug_list().entries(self.iter()).finish()
952 impl<T: Idx> ToString for BitSet<T> {
953 fn to_string(&self) -> String {
954 let mut result = String::new();
957 // Note: this is a little endian printout of bytes.
959 // i tracks how many bits we have printed so far.
961 for word in &self.words {
962 let mut word = *word;
963 for _ in 0..WORD_BYTES {
964 // for each byte in `word`:
965 let remain = self.domain_size - i;
966 // If less than a byte remains, then mask just that many bits.
967 let mask = if remain <= 8 { (1 << remain) - 1 } else { 0xFF };
968 assert!(mask <= 0xFF);
969 let byte = word & mask;
971 result.push_str(&format!("{}{:02x}", sep, byte));
988 pub struct BitIter<'a, T: Idx> {
989 /// A copy of the current word, but with any already-visited bits cleared.
990 /// (This lets us use `trailing_zeros()` to find the next set bit.) When it
991 /// is reduced to 0, we move onto the next word.
994 /// The offset (measured in bits) of the current word.
997 /// Underlying iterator over the words.
998 iter: slice::Iter<'a, Word>,
1000 marker: PhantomData<T>,
1003 impl<'a, T: Idx> BitIter<'a, T> {
1005 fn new(words: &'a [Word]) -> BitIter<'a, T> {
1006 // We initialize `word` and `offset` to degenerate values. On the first
1007 // call to `next()` we will fall through to getting the first word from
1008 // `iter`, which sets `word` to the first word (if there is one) and
1009 // `offset` to 0. Doing it this way saves us from having to maintain
1010 // additional state about whether we have started.
1013 offset: usize::MAX - (WORD_BITS - 1),
1015 marker: PhantomData,
1020 impl<'a, T: Idx> Iterator for BitIter<'a, T> {
1022 fn next(&mut self) -> Option<T> {
1025 // Get the position of the next set bit in the current word,
1026 // then clear the bit.
1027 let bit_pos = self.word.trailing_zeros() as usize;
1028 let bit = 1 << bit_pos;
1030 return Some(T::new(bit_pos + self.offset));
1033 // Move onto the next word. `wrapping_add()` is needed to handle
1034 // the degenerate initial value given to `offset` in `new()`.
1035 let word = self.iter.next()?;
1037 self.offset = self.offset.wrapping_add(WORD_BITS);
1043 fn bitwise<Op>(out_vec: &mut [Word], in_vec: &[Word], op: Op) -> bool
1045 Op: Fn(Word, Word) -> Word,
1047 assert_eq!(out_vec.len(), in_vec.len());
1048 let mut changed = 0;
1049 for (out_elem, in_elem) in iter::zip(out_vec, in_vec) {
1050 let old_val = *out_elem;
1051 let new_val = op(old_val, *in_elem);
1052 *out_elem = new_val;
1053 // This is essentially equivalent to a != with changed being a bool, but
1054 // in practice this code gets auto-vectorized by the compiler for most
1055 // operators. Using != here causes us to generate quite poor code as the
1056 // compiler tries to go back to a boolean on each loop iteration.
1057 changed |= old_val ^ new_val;
1062 /// Does this bitwise operation change `out_vec`?
1064 fn bitwise_changes<Op>(out_vec: &[Word], in_vec: &[Word], op: Op) -> bool
1066 Op: Fn(Word, Word) -> Word,
1068 assert_eq!(out_vec.len(), in_vec.len());
1069 for (out_elem, in_elem) in iter::zip(out_vec, in_vec) {
1070 let old_val = *out_elem;
1071 let new_val = op(old_val, *in_elem);
1072 if old_val != new_val {
1079 const SPARSE_MAX: usize = 8;
1081 /// A fixed-size bitset type with a sparse representation and a maximum of
1082 /// `SPARSE_MAX` elements. The elements are stored as a sorted `ArrayVec` with
1085 /// This type is used by `HybridBitSet`; do not use directly.
1086 #[derive(Clone, Debug)]
1087 pub struct SparseBitSet<T> {
1089 elems: ArrayVec<T, SPARSE_MAX>,
1092 impl<T: Idx> SparseBitSet<T> {
1093 fn new_empty(domain_size: usize) -> Self {
1094 SparseBitSet { domain_size, elems: ArrayVec::new() }
1097 fn len(&self) -> usize {
1101 fn is_empty(&self) -> bool {
1102 self.elems.len() == 0
1105 fn contains(&self, elem: T) -> bool {
1106 assert!(elem.index() < self.domain_size);
1107 self.elems.contains(&elem)
1110 fn insert(&mut self, elem: T) -> bool {
1111 assert!(elem.index() < self.domain_size);
1112 let changed = if let Some(i) = self.elems.iter().position(|&e| e.index() >= elem.index()) {
1113 if self.elems[i] == elem {
1114 // `elem` is already in the set.
1117 // `elem` is smaller than one or more existing elements.
1118 self.elems.insert(i, elem);
1122 // `elem` is larger than all existing elements.
1123 self.elems.push(elem);
1126 assert!(self.len() <= SPARSE_MAX);
1130 fn remove(&mut self, elem: T) -> bool {
1131 assert!(elem.index() < self.domain_size);
1132 if let Some(i) = self.elems.iter().position(|&e| e == elem) {
1133 self.elems.remove(i);
1140 fn to_dense(&self) -> BitSet<T> {
1141 let mut dense = BitSet::new_empty(self.domain_size);
1142 for elem in self.elems.iter() {
1143 dense.insert(*elem);
1148 fn iter(&self) -> slice::Iter<'_, T> {
1152 bit_relations_inherent_impls! {}
1155 impl<T: Idx + Ord> SparseBitSet<T> {
1156 fn last_set_in(&self, range: impl RangeBounds<T>) -> Option<T> {
1157 let mut last_leq = None;
1158 for e in self.iter() {
1159 if range.contains(e) {
1160 last_leq = Some(*e);
1167 /// A fixed-size bitset type with a hybrid representation: sparse when there
1168 /// are up to a `SPARSE_MAX` elements in the set, but dense when there are more
1169 /// than `SPARSE_MAX`.
1171 /// This type is especially efficient for sets that typically have a small
1172 /// number of elements, but a large `domain_size`, and are cleared frequently.
1174 /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also
1175 /// just be `usize`.
1177 /// All operations that involve an element will panic if the element is equal
1178 /// to or greater than the domain size. All operations that involve two bitsets
1179 /// will panic if the bitsets have differing domain sizes.
1181 pub enum HybridBitSet<T> {
1182 Sparse(SparseBitSet<T>),
1186 impl<T: Idx> fmt::Debug for HybridBitSet<T> {
1187 fn fmt(&self, w: &mut fmt::Formatter<'_>) -> fmt::Result {
1189 Self::Sparse(b) => b.fmt(w),
1190 Self::Dense(b) => b.fmt(w),
1195 impl<T: Idx> HybridBitSet<T> {
1196 pub fn new_empty(domain_size: usize) -> Self {
1197 HybridBitSet::Sparse(SparseBitSet::new_empty(domain_size))
1200 pub fn domain_size(&self) -> usize {
1202 HybridBitSet::Sparse(sparse) => sparse.domain_size,
1203 HybridBitSet::Dense(dense) => dense.domain_size,
1207 pub fn clear(&mut self) {
1208 let domain_size = self.domain_size();
1209 *self = HybridBitSet::new_empty(domain_size);
1212 pub fn contains(&self, elem: T) -> bool {
1214 HybridBitSet::Sparse(sparse) => sparse.contains(elem),
1215 HybridBitSet::Dense(dense) => dense.contains(elem),
1219 pub fn superset(&self, other: &HybridBitSet<T>) -> bool {
1220 match (self, other) {
1221 (HybridBitSet::Dense(self_dense), HybridBitSet::Dense(other_dense)) => {
1222 self_dense.superset(other_dense)
1225 assert!(self.domain_size() == other.domain_size());
1226 other.iter().all(|elem| self.contains(elem))
1231 pub fn is_empty(&self) -> bool {
1233 HybridBitSet::Sparse(sparse) => sparse.is_empty(),
1234 HybridBitSet::Dense(dense) => dense.is_empty(),
1238 /// Returns the previous element present in the bitset from `elem`,
1239 /// inclusively of elem. That is, will return `Some(elem)` if elem is in the
1241 pub fn last_set_in(&self, range: impl RangeBounds<T>) -> Option<T>
1246 HybridBitSet::Sparse(sparse) => sparse.last_set_in(range),
1247 HybridBitSet::Dense(dense) => dense.last_set_in(range),
1251 pub fn insert(&mut self, elem: T) -> bool {
1252 // No need to check `elem` against `self.domain_size` here because all
1253 // the match cases check it, one way or another.
1255 HybridBitSet::Sparse(sparse) if sparse.len() < SPARSE_MAX => {
1256 // The set is sparse and has space for `elem`.
1259 HybridBitSet::Sparse(sparse) if sparse.contains(elem) => {
1260 // The set is sparse and does not have space for `elem`, but
1261 // that doesn't matter because `elem` is already present.
1264 HybridBitSet::Sparse(sparse) => {
1265 // The set is sparse and full. Convert to a dense set.
1266 let mut dense = sparse.to_dense();
1267 let changed = dense.insert(elem);
1269 *self = HybridBitSet::Dense(dense);
1272 HybridBitSet::Dense(dense) => dense.insert(elem),
1276 pub fn insert_range(&mut self, elems: impl RangeBounds<T>) {
1277 // No need to check `elem` against `self.domain_size` here because all
1278 // the match cases check it, one way or another.
1279 let start = match elems.start_bound().cloned() {
1280 Bound::Included(start) => start.index(),
1281 Bound::Excluded(start) => start.index() + 1,
1282 Bound::Unbounded => 0,
1284 let end = match elems.end_bound().cloned() {
1285 Bound::Included(end) => end.index() + 1,
1286 Bound::Excluded(end) => end.index(),
1287 Bound::Unbounded => self.domain_size() - 1,
1289 let Some(len) = end.checked_sub(start) else { return };
1291 HybridBitSet::Sparse(sparse) if sparse.len() + len < SPARSE_MAX => {
1292 // The set is sparse and has space for `elems`.
1293 for elem in start..end {
1294 sparse.insert(T::new(elem));
1297 HybridBitSet::Sparse(sparse) => {
1298 // The set is sparse and full. Convert to a dense set.
1299 let mut dense = sparse.to_dense();
1300 dense.insert_range(elems);
1301 *self = HybridBitSet::Dense(dense);
1303 HybridBitSet::Dense(dense) => dense.insert_range(elems),
1307 pub fn insert_all(&mut self) {
1308 let domain_size = self.domain_size();
1310 HybridBitSet::Sparse(_) => {
1311 *self = HybridBitSet::Dense(BitSet::new_filled(domain_size));
1313 HybridBitSet::Dense(dense) => dense.insert_all(),
1317 pub fn remove(&mut self, elem: T) -> bool {
1318 // Note: we currently don't bother going from Dense back to Sparse.
1320 HybridBitSet::Sparse(sparse) => sparse.remove(elem),
1321 HybridBitSet::Dense(dense) => dense.remove(elem),
1325 /// Converts to a dense set, consuming itself in the process.
1326 pub fn to_dense(self) -> BitSet<T> {
1328 HybridBitSet::Sparse(sparse) => sparse.to_dense(),
1329 HybridBitSet::Dense(dense) => dense,
1333 pub fn iter(&self) -> HybridIter<'_, T> {
1335 HybridBitSet::Sparse(sparse) => HybridIter::Sparse(sparse.iter()),
1336 HybridBitSet::Dense(dense) => HybridIter::Dense(dense.iter()),
1340 bit_relations_inherent_impls! {}
1343 pub enum HybridIter<'a, T: Idx> {
1344 Sparse(slice::Iter<'a, T>),
1345 Dense(BitIter<'a, T>),
1348 impl<'a, T: Idx> Iterator for HybridIter<'a, T> {
1351 fn next(&mut self) -> Option<T> {
1353 HybridIter::Sparse(sparse) => sparse.next().copied(),
1354 HybridIter::Dense(dense) => dense.next(),
1359 /// A resizable bitset type with a dense representation.
1361 /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also
1362 /// just be `usize`.
1364 /// All operations that involve an element will panic if the element is equal
1365 /// to or greater than the domain size.
1366 #[derive(Clone, Debug, PartialEq)]
1367 pub struct GrowableBitSet<T: Idx> {
1371 impl<T: Idx> Default for GrowableBitSet<T> {
1372 fn default() -> Self {
1373 GrowableBitSet::new_empty()
1377 impl<T: Idx> GrowableBitSet<T> {
1378 /// Ensure that the set can hold at least `min_domain_size` elements.
1379 pub fn ensure(&mut self, min_domain_size: usize) {
1380 if self.bit_set.domain_size < min_domain_size {
1381 self.bit_set.domain_size = min_domain_size;
1384 let min_num_words = num_words(min_domain_size);
1385 if self.bit_set.words.len() < min_num_words {
1386 self.bit_set.words.resize(min_num_words, 0)
1390 pub fn new_empty() -> GrowableBitSet<T> {
1391 GrowableBitSet { bit_set: BitSet::new_empty(0) }
1394 pub fn with_capacity(capacity: usize) -> GrowableBitSet<T> {
1395 GrowableBitSet { bit_set: BitSet::new_empty(capacity) }
1398 /// Returns `true` if the set has changed.
1400 pub fn insert(&mut self, elem: T) -> bool {
1401 self.ensure(elem.index() + 1);
1402 self.bit_set.insert(elem)
1405 /// Returns `true` if the set has changed.
1407 pub fn remove(&mut self, elem: T) -> bool {
1408 self.ensure(elem.index() + 1);
1409 self.bit_set.remove(elem)
1413 pub fn is_empty(&self) -> bool {
1414 self.bit_set.is_empty()
1418 pub fn contains(&self, elem: T) -> bool {
1419 let (word_index, mask) = word_index_and_mask(elem);
1420 self.bit_set.words.get(word_index).map_or(false, |word| (word & mask) != 0)
1424 /// A fixed-size 2D bit matrix type with a dense representation.
1426 /// `R` and `C` are index types used to identify rows and columns respectively;
1427 /// typically newtyped `usize` wrappers, but they can also just be `usize`.
1429 /// All operations that involve a row and/or column index will panic if the
1430 /// index exceeds the relevant bound.
1431 #[derive(Clone, Eq, PartialEq, Hash, Decodable, Encodable)]
1432 pub struct BitMatrix<R: Idx, C: Idx> {
1436 marker: PhantomData<(R, C)>,
1439 impl<R: Idx, C: Idx> BitMatrix<R, C> {
1440 /// Creates a new `rows x columns` matrix, initially empty.
1441 pub fn new(num_rows: usize, num_columns: usize) -> BitMatrix<R, C> {
1442 // For every element, we need one bit for every other
1443 // element. Round up to an even number of words.
1444 let words_per_row = num_words(num_columns);
1448 words: vec![0; num_rows * words_per_row],
1449 marker: PhantomData,
1453 /// Creates a new matrix, with `row` used as the value for every row.
1454 pub fn from_row_n(row: &BitSet<C>, num_rows: usize) -> BitMatrix<R, C> {
1455 let num_columns = row.domain_size();
1456 let words_per_row = num_words(num_columns);
1457 assert_eq!(words_per_row, row.words().len());
1461 words: iter::repeat(row.words()).take(num_rows).flatten().cloned().collect(),
1462 marker: PhantomData,
1466 pub fn rows(&self) -> impl Iterator<Item = R> {
1467 (0..self.num_rows).map(R::new)
1470 /// The range of bits for a given row.
1471 fn range(&self, row: R) -> (usize, usize) {
1472 let words_per_row = num_words(self.num_columns);
1473 let start = row.index() * words_per_row;
1474 (start, start + words_per_row)
1477 /// Sets the cell at `(row, column)` to true. Put another way, insert
1478 /// `column` to the bitset for `row`.
1480 /// Returns `true` if this changed the matrix.
1481 pub fn insert(&mut self, row: R, column: C) -> bool {
1482 assert!(row.index() < self.num_rows && column.index() < self.num_columns);
1483 let (start, _) = self.range(row);
1484 let (word_index, mask) = word_index_and_mask(column);
1485 let words = &mut self.words[..];
1486 let word = words[start + word_index];
1487 let new_word = word | mask;
1488 words[start + word_index] = new_word;
1492 /// Do the bits from `row` contain `column`? Put another way, is
1493 /// the matrix cell at `(row, column)` true? Put yet another way,
1494 /// if the matrix represents (transitive) reachability, can
1495 /// `row` reach `column`?
1496 pub fn contains(&self, row: R, column: C) -> bool {
1497 assert!(row.index() < self.num_rows && column.index() < self.num_columns);
1498 let (start, _) = self.range(row);
1499 let (word_index, mask) = word_index_and_mask(column);
1500 (self.words[start + word_index] & mask) != 0
1503 /// Returns those indices that are true in rows `a` and `b`. This
1504 /// is an *O*(*n*) operation where *n* is the number of elements
1505 /// (somewhat independent from the actual size of the
1506 /// intersection, in particular).
1507 pub fn intersect_rows(&self, row1: R, row2: R) -> Vec<C> {
1508 assert!(row1.index() < self.num_rows && row2.index() < self.num_rows);
1509 let (row1_start, row1_end) = self.range(row1);
1510 let (row2_start, row2_end) = self.range(row2);
1511 let mut result = Vec::with_capacity(self.num_columns);
1512 for (base, (i, j)) in (row1_start..row1_end).zip(row2_start..row2_end).enumerate() {
1513 let mut v = self.words[i] & self.words[j];
1514 for bit in 0..WORD_BITS {
1519 result.push(C::new(base * WORD_BITS + bit));
1527 /// Adds the bits from row `read` to the bits from row `write`, and
1528 /// returns `true` if anything changed.
1530 /// This is used when computing transitive reachability because if
1531 /// you have an edge `write -> read`, because in that case
1532 /// `write` can reach everything that `read` can (and
1533 /// potentially more).
1534 pub fn union_rows(&mut self, read: R, write: R) -> bool {
1535 assert!(read.index() < self.num_rows && write.index() < self.num_rows);
1536 let (read_start, read_end) = self.range(read);
1537 let (write_start, write_end) = self.range(write);
1538 let words = &mut self.words[..];
1539 let mut changed = false;
1540 for (read_index, write_index) in iter::zip(read_start..read_end, write_start..write_end) {
1541 let word = words[write_index];
1542 let new_word = word | words[read_index];
1543 words[write_index] = new_word;
1544 changed |= word != new_word;
1549 /// Adds the bits from `with` to the bits from row `write`, and
1550 /// returns `true` if anything changed.
1551 pub fn union_row_with(&mut self, with: &BitSet<C>, write: R) -> bool {
1552 assert!(write.index() < self.num_rows);
1553 assert_eq!(with.domain_size(), self.num_columns);
1554 let (write_start, write_end) = self.range(write);
1555 let mut changed = false;
1556 for (read_index, write_index) in iter::zip(0..with.words().len(), write_start..write_end) {
1557 let word = self.words[write_index];
1558 let new_word = word | with.words()[read_index];
1559 self.words[write_index] = new_word;
1560 changed |= word != new_word;
1565 /// Sets every cell in `row` to true.
1566 pub fn insert_all_into_row(&mut self, row: R) {
1567 assert!(row.index() < self.num_rows);
1568 let (start, end) = self.range(row);
1569 let words = &mut self.words[..];
1570 for index in start..end {
1573 clear_excess_bits_in_final_word(self.num_columns, &mut self.words[..end]);
1576 /// Gets a slice of the underlying words.
1577 pub fn words(&self) -> &[Word] {
1581 /// Iterates through all the columns set to true in a given row of
1583 pub fn iter(&self, row: R) -> BitIter<'_, C> {
1584 assert!(row.index() < self.num_rows);
1585 let (start, end) = self.range(row);
1586 BitIter::new(&self.words[start..end])
1589 /// Returns the number of elements in `row`.
1590 pub fn count(&self, row: R) -> usize {
1591 let (start, end) = self.range(row);
1592 self.words[start..end].iter().map(|e| e.count_ones() as usize).sum()
1596 impl<R: Idx, C: Idx> fmt::Debug for BitMatrix<R, C> {
1597 fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
1598 /// Forces its contents to print in regular mode instead of alternate mode.
1599 struct OneLinePrinter<T>(T);
1600 impl<T: fmt::Debug> fmt::Debug for OneLinePrinter<T> {
1601 fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
1602 write!(fmt, "{:?}", self.0)
1606 write!(fmt, "BitMatrix({}x{}) ", self.num_rows, self.num_columns)?;
1607 let items = self.rows().flat_map(|r| self.iter(r).map(move |c| (r, c)));
1608 fmt.debug_set().entries(items.map(OneLinePrinter)).finish()
1612 /// A fixed-column-size, variable-row-size 2D bit matrix with a moderately
1613 /// sparse representation.
1615 /// Initially, every row has no explicit representation. If any bit within a
1616 /// row is set, the entire row is instantiated as `Some(<HybridBitSet>)`.
1617 /// Furthermore, any previously uninstantiated rows prior to it will be
1618 /// instantiated as `None`. Those prior rows may themselves become fully
1619 /// instantiated later on if any of their bits are set.
1621 /// `R` and `C` are index types used to identify rows and columns respectively;
1622 /// typically newtyped `usize` wrappers, but they can also just be `usize`.
1623 #[derive(Clone, Debug)]
1624 pub struct SparseBitMatrix<R, C>
1630 rows: IndexVec<R, Option<HybridBitSet<C>>>,
1633 impl<R: Idx, C: Idx> SparseBitMatrix<R, C> {
1634 /// Creates a new empty sparse bit matrix with no rows or columns.
1635 pub fn new(num_columns: usize) -> Self {
1636 Self { num_columns, rows: IndexVec::new() }
1639 fn ensure_row(&mut self, row: R) -> &mut HybridBitSet<C> {
1640 // Instantiate any missing rows up to and including row `row` with an empty HybridBitSet.
1641 // Then replace row `row` with a full HybridBitSet if necessary.
1642 self.rows.get_or_insert_with(row, || HybridBitSet::new_empty(self.num_columns))
1645 /// Sets the cell at `(row, column)` to true. Put another way, insert
1646 /// `column` to the bitset for `row`.
1648 /// Returns `true` if this changed the matrix.
1649 pub fn insert(&mut self, row: R, column: C) -> bool {
1650 self.ensure_row(row).insert(column)
1653 /// Sets the cell at `(row, column)` to false. Put another way, delete
1654 /// `column` from the bitset for `row`. Has no effect if `row` does not
1657 /// Returns `true` if this changed the matrix.
1658 pub fn remove(&mut self, row: R, column: C) -> bool {
1659 match self.rows.get_mut(row) {
1660 Some(Some(row)) => row.remove(column),
1665 /// Sets all columns at `row` to false. Has no effect if `row` does
1667 pub fn clear(&mut self, row: R) {
1668 if let Some(Some(row)) = self.rows.get_mut(row) {
1673 /// Do the bits from `row` contain `column`? Put another way, is
1674 /// the matrix cell at `(row, column)` true? Put yet another way,
1675 /// if the matrix represents (transitive) reachability, can
1676 /// `row` reach `column`?
1677 pub fn contains(&self, row: R, column: C) -> bool {
1678 self.row(row).map_or(false, |r| r.contains(column))
1681 /// Adds the bits from row `read` to the bits from row `write`, and
1682 /// returns `true` if anything changed.
1684 /// This is used when computing transitive reachability because if
1685 /// you have an edge `write -> read`, because in that case
1686 /// `write` can reach everything that `read` can (and
1687 /// potentially more).
1688 pub fn union_rows(&mut self, read: R, write: R) -> bool {
1689 if read == write || self.row(read).is_none() {
1693 self.ensure_row(write);
1694 if let (Some(read_row), Some(write_row)) = self.rows.pick2_mut(read, write) {
1695 write_row.union(read_row)
1701 /// Insert all bits in the given row.
1702 pub fn insert_all_into_row(&mut self, row: R) {
1703 self.ensure_row(row).insert_all();
1706 pub fn rows(&self) -> impl Iterator<Item = R> {
1710 /// Iterates through all the columns set to true in a given row of
1712 pub fn iter<'a>(&'a self, row: R) -> impl Iterator<Item = C> + 'a {
1713 self.row(row).into_iter().flat_map(|r| r.iter())
1716 pub fn row(&self, row: R) -> Option<&HybridBitSet<C>> {
1717 if let Some(Some(row)) = self.rows.get(row) { Some(row) } else { None }
1720 /// Interescts `row` with `set`. `set` can be either `BitSet` or
1721 /// `HybridBitSet`. Has no effect if `row` does not exist.
1723 /// Returns true if the row was changed.
1724 pub fn intersect_row<Set>(&mut self, row: R, set: &Set) -> bool
1726 HybridBitSet<C>: BitRelations<Set>,
1728 match self.rows.get_mut(row) {
1729 Some(Some(row)) => row.intersect(set),
1734 /// Subtracts `set from `row`. `set` can be either `BitSet` or
1735 /// `HybridBitSet`. Has no effect if `row` does not exist.
1737 /// Returns true if the row was changed.
1738 pub fn subtract_row<Set>(&mut self, row: R, set: &Set) -> bool
1740 HybridBitSet<C>: BitRelations<Set>,
1742 match self.rows.get_mut(row) {
1743 Some(Some(row)) => row.subtract(set),
1748 /// Unions `row` with `set`. `set` can be either `BitSet` or
1751 /// Returns true if the row was changed.
1752 pub fn union_row<Set>(&mut self, row: R, set: &Set) -> bool
1754 HybridBitSet<C>: BitRelations<Set>,
1756 self.ensure_row(row).union(set)
1761 fn num_words<T: Idx>(domain_size: T) -> usize {
1762 (domain_size.index() + WORD_BITS - 1) / WORD_BITS
1766 fn num_chunks<T: Idx>(domain_size: T) -> usize {
1767 assert!(domain_size.index() > 0);
1768 (domain_size.index() + CHUNK_BITS - 1) / CHUNK_BITS
1772 fn word_index_and_mask<T: Idx>(elem: T) -> (usize, Word) {
1773 let elem = elem.index();
1774 let word_index = elem / WORD_BITS;
1775 let mask = 1 << (elem % WORD_BITS);
1780 fn chunk_index<T: Idx>(elem: T) -> usize {
1781 elem.index() / CHUNK_BITS
1785 fn chunk_word_index_and_mask<T: Idx>(elem: T) -> (usize, Word) {
1786 let chunk_elem = elem.index() % CHUNK_BITS;
1787 word_index_and_mask(chunk_elem)
1790 fn clear_excess_bits_in_final_word(domain_size: usize, words: &mut [Word]) {
1791 let num_bits_in_final_word = domain_size % WORD_BITS;
1792 if num_bits_in_final_word > 0 {
1793 let mask = (1 << num_bits_in_final_word) - 1;
1794 words[words.len() - 1] &= mask;
1799 fn max_bit(word: Word) -> usize {
1800 WORD_BITS - 1 - word.leading_zeros() as usize
1803 /// Integral type used to represent the bit set.
1804 pub trait FiniteBitSetTy:
1805 BitAnd<Output = Self>
1811 + Not<Output = Self>
1815 /// Size of the domain representable by this type, e.g. 64 for `u64`.
1816 const DOMAIN_SIZE: u32;
1818 /// Value which represents the `FiniteBitSet` having every bit set.
1820 /// Value which represents the `FiniteBitSet` having no bits set.
1823 /// Value for one as the integral type.
1825 /// Value for zero as the integral type.
1828 /// Perform a checked left shift on the integral type.
1829 fn checked_shl(self, rhs: u32) -> Option<Self>;
1830 /// Perform a checked right shift on the integral type.
1831 fn checked_shr(self, rhs: u32) -> Option<Self>;
1834 impl FiniteBitSetTy for u32 {
1835 const DOMAIN_SIZE: u32 = 32;
1837 const FILLED: Self = Self::MAX;
1838 const EMPTY: Self = Self::MIN;
1840 const ONE: Self = 1u32;
1841 const ZERO: Self = 0u32;
1843 fn checked_shl(self, rhs: u32) -> Option<Self> {
1844 self.checked_shl(rhs)
1847 fn checked_shr(self, rhs: u32) -> Option<Self> {
1848 self.checked_shr(rhs)
1852 impl std::fmt::Debug for FiniteBitSet<u32> {
1853 fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
1854 write!(f, "{:032b}", self.0)
1858 impl FiniteBitSetTy for u64 {
1859 const DOMAIN_SIZE: u32 = 64;
1861 const FILLED: Self = Self::MAX;
1862 const EMPTY: Self = Self::MIN;
1864 const ONE: Self = 1u64;
1865 const ZERO: Self = 0u64;
1867 fn checked_shl(self, rhs: u32) -> Option<Self> {
1868 self.checked_shl(rhs)
1871 fn checked_shr(self, rhs: u32) -> Option<Self> {
1872 self.checked_shr(rhs)
1876 impl std::fmt::Debug for FiniteBitSet<u64> {
1877 fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
1878 write!(f, "{:064b}", self.0)
1882 impl FiniteBitSetTy for u128 {
1883 const DOMAIN_SIZE: u32 = 128;
1885 const FILLED: Self = Self::MAX;
1886 const EMPTY: Self = Self::MIN;
1888 const ONE: Self = 1u128;
1889 const ZERO: Self = 0u128;
1891 fn checked_shl(self, rhs: u32) -> Option<Self> {
1892 self.checked_shl(rhs)
1895 fn checked_shr(self, rhs: u32) -> Option<Self> {
1896 self.checked_shr(rhs)
1900 impl std::fmt::Debug for FiniteBitSet<u128> {
1901 fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
1902 write!(f, "{:0128b}", self.0)
1906 /// A fixed-sized bitset type represented by an integer type. Indices outwith than the range
1907 /// representable by `T` are considered set.
1908 #[derive(Copy, Clone, Eq, PartialEq, Decodable, Encodable)]
1909 pub struct FiniteBitSet<T: FiniteBitSetTy>(pub T);
1911 impl<T: FiniteBitSetTy> FiniteBitSet<T> {
1912 /// Creates a new, empty bitset.
1913 pub fn new_empty() -> Self {
1917 /// Sets the `index`th bit.
1918 pub fn set(&mut self, index: u32) {
1919 self.0 |= T::ONE.checked_shl(index).unwrap_or(T::ZERO);
1922 /// Unsets the `index`th bit.
1923 pub fn clear(&mut self, index: u32) {
1924 self.0 &= !T::ONE.checked_shl(index).unwrap_or(T::ZERO);
1927 /// Sets the `i`th to `j`th bits.
1928 pub fn set_range(&mut self, range: Range<u32>) {
1929 let bits = T::FILLED
1930 .checked_shl(range.end - range.start)
1933 .checked_shl(range.start)
1934 .unwrap_or(T::ZERO);
1938 /// Is the set empty?
1939 pub fn is_empty(&self) -> bool {
1943 /// Returns the domain size of the bitset.
1944 pub fn within_domain(&self, index: u32) -> bool {
1945 index < T::DOMAIN_SIZE
1948 /// Returns if the `index`th bit is set.
1949 pub fn contains(&self, index: u32) -> Option<bool> {
1950 self.within_domain(index)
1951 .then(|| ((self.0.checked_shr(index).unwrap_or(T::ONE)) & T::ONE) == T::ONE)
1955 impl<T: FiniteBitSetTy> Default for FiniteBitSet<T> {
1956 fn default() -> Self {