use crate::vec::{Idx, IndexVec}; use arrayvec::ArrayVec; use std::fmt; use std::iter; use std::marker::PhantomData; use std::mem; use std::ops::{BitAnd, BitAndAssign, BitOrAssign, Bound, Not, Range, RangeBounds, Shl}; use std::rc::Rc; use std::slice; use rustc_macros::{Decodable, Encodable}; use Chunk::*; #[cfg(test)] mod tests; type Word = u64; const WORD_BYTES: usize = mem::size_of::(); const WORD_BITS: usize = WORD_BYTES * 8; // The choice of chunk size has some trade-offs. // // A big chunk size tends to favour cases where many large `ChunkedBitSet`s are // present, because they require fewer `Chunk`s, reducing the number of // allocations and reducing peak memory usage. Also, fewer chunk operations are // required, though more of them might be `Mixed`. // // A small chunk size tends to favour cases where many small `ChunkedBitSet`s // are present, because less space is wasted at the end of the final chunk (if // it's not full). const CHUNK_WORDS: usize = 32; const CHUNK_BITS: usize = CHUNK_WORDS * WORD_BITS; // 2048 bits /// ChunkSize is small to keep `Chunk` small. The static assertion ensures it's /// not too small. type ChunkSize = u16; const _: () = assert!(CHUNK_BITS <= ChunkSize::MAX as usize); pub trait BitRelations { fn union(&mut self, other: &Rhs) -> bool; fn subtract(&mut self, other: &Rhs) -> bool; fn intersect(&mut self, other: &Rhs) -> bool; } #[inline] fn inclusive_start_end( range: impl RangeBounds, domain: usize, ) -> Option<(usize, usize)> { // Both start and end are inclusive. let start = match range.start_bound().cloned() { Bound::Included(start) => start.index(), Bound::Excluded(start) => start.index() + 1, Bound::Unbounded => 0, }; let end = match range.end_bound().cloned() { Bound::Included(end) => end.index(), Bound::Excluded(end) => end.index().checked_sub(1)?, Bound::Unbounded => domain - 1, }; assert!(end < domain); if start > end { return None; } Some((start, end)) } macro_rules! bit_relations_inherent_impls { () => { /// Sets `self = self | other` and returns `true` if `self` changed /// (i.e., if new bits were added). pub fn union(&mut self, other: &Rhs) -> bool where Self: BitRelations, { >::union(self, other) } /// Sets `self = self - other` and returns `true` if `self` changed. /// (i.e., if any bits were removed). pub fn subtract(&mut self, other: &Rhs) -> bool where Self: BitRelations, { >::subtract(self, other) } /// Sets `self = self & other` and return `true` if `self` changed. /// (i.e., if any bits were removed). pub fn intersect(&mut self, other: &Rhs) -> bool where Self: BitRelations, { >::intersect(self, other) } }; } /// A fixed-size bitset type with a dense representation. /// /// NOTE: Use [`GrowableBitSet`] if you need support for resizing after creation. /// /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also /// just be `usize`. /// /// All operations that involve an element will panic if the element is equal /// to or greater than the domain size. All operations that involve two bitsets /// will panic if the bitsets have differing domain sizes. /// #[derive(Eq, PartialEq, Hash, Decodable, Encodable)] pub struct BitSet { domain_size: usize, words: Vec, marker: PhantomData, } impl BitSet { /// Gets the domain size. pub fn domain_size(&self) -> usize { self.domain_size } } impl BitSet { /// Creates a new, empty bitset with a given `domain_size`. #[inline] pub fn new_empty(domain_size: usize) -> BitSet { let num_words = num_words(domain_size); BitSet { domain_size, words: vec![0; num_words], marker: PhantomData } } /// Creates a new, filled bitset with a given `domain_size`. #[inline] pub fn new_filled(domain_size: usize) -> BitSet { let num_words = num_words(domain_size); let mut result = BitSet { domain_size, words: vec![!0; num_words], marker: PhantomData }; result.clear_excess_bits(); result } /// Clear all elements. #[inline] pub fn clear(&mut self) { self.words.fill(0); } /// Clear excess bits in the final word. fn clear_excess_bits(&mut self) { clear_excess_bits_in_final_word(self.domain_size, &mut self.words); } /// Count the number of set bits in the set. pub fn count(&self) -> usize { self.words.iter().map(|e| e.count_ones() as usize).sum() } /// Returns `true` if `self` contains `elem`. #[inline] pub fn contains(&self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let (word_index, mask) = word_index_and_mask(elem); (self.words[word_index] & mask) != 0 } /// Is `self` is a (non-strict) superset of `other`? #[inline] pub fn superset(&self, other: &BitSet) -> bool { assert_eq!(self.domain_size, other.domain_size); self.words.iter().zip(&other.words).all(|(a, b)| (a & b) == *b) } /// Is the set empty? #[inline] pub fn is_empty(&self) -> bool { self.words.iter().all(|a| *a == 0) } /// Insert `elem`. Returns whether the set has changed. #[inline] pub fn insert(&mut self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let (word_index, mask) = word_index_and_mask(elem); let word_ref = &mut self.words[word_index]; let word = *word_ref; let new_word = word | mask; *word_ref = new_word; new_word != word } #[inline] pub fn insert_range(&mut self, elems: impl RangeBounds) { let Some((start, end)) = inclusive_start_end(elems, self.domain_size) else { return; }; let (start_word_index, start_mask) = word_index_and_mask(start); let (end_word_index, end_mask) = word_index_and_mask(end); // Set all words in between start and end (exclusively of both). for word_index in (start_word_index + 1)..end_word_index { self.words[word_index] = !0; } if start_word_index != end_word_index { // Start and end are in different words, so we handle each in turn. // // We set all leading bits. This includes the start_mask bit. self.words[start_word_index] |= !(start_mask - 1); // And all trailing bits (i.e. from 0..=end) in the end word, // including the end. self.words[end_word_index] |= end_mask | (end_mask - 1); } else { self.words[start_word_index] |= end_mask | (end_mask - start_mask); } } /// Sets all bits to true. pub fn insert_all(&mut self) { self.words.fill(!0); self.clear_excess_bits(); } /// Returns `true` if the set has changed. #[inline] pub fn remove(&mut self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let (word_index, mask) = word_index_and_mask(elem); let word_ref = &mut self.words[word_index]; let word = *word_ref; let new_word = word & !mask; *word_ref = new_word; new_word != word } /// Gets a slice of the underlying words. pub fn words(&self) -> &[Word] { &self.words } /// Iterates over the indices of set bits in a sorted order. #[inline] pub fn iter(&self) -> BitIter<'_, T> { BitIter::new(&self.words) } /// Duplicates the set as a hybrid set. pub fn to_hybrid(&self) -> HybridBitSet { // Note: we currently don't bother trying to make a Sparse set. HybridBitSet::Dense(self.to_owned()) } /// Set `self = self | other`. In contrast to `union` returns `true` if the set contains at /// least one bit that is not in `other` (i.e. `other` is not a superset of `self`). /// /// This is an optimization for union of a hybrid bitset. fn reverse_union_sparse(&mut self, sparse: &SparseBitSet) -> bool { assert!(sparse.domain_size == self.domain_size); self.clear_excess_bits(); let mut not_already = false; // Index of the current word not yet merged. let mut current_index = 0; // Mask of bits that came from the sparse set in the current word. let mut new_bit_mask = 0; for (word_index, mask) in sparse.iter().map(|x| word_index_and_mask(*x)) { // Next bit is in a word not inspected yet. if word_index > current_index { self.words[current_index] |= new_bit_mask; // Were there any bits in the old word that did not occur in the sparse set? not_already |= (self.words[current_index] ^ new_bit_mask) != 0; // Check all words we skipped for any set bit. not_already |= self.words[current_index + 1..word_index].iter().any(|&x| x != 0); // Update next word. current_index = word_index; // Reset bit mask, no bits have been merged yet. new_bit_mask = 0; } // Add bit and mark it as coming from the sparse set. // self.words[word_index] |= mask; new_bit_mask |= mask; } self.words[current_index] |= new_bit_mask; // Any bits in the last inspected word that were not in the sparse set? not_already |= (self.words[current_index] ^ new_bit_mask) != 0; // Any bits in the tail? Note `clear_excess_bits` before. not_already |= self.words[current_index + 1..].iter().any(|&x| x != 0); not_already } fn last_set_in(&self, range: impl RangeBounds) -> Option { let (start, end) = inclusive_start_end(range, self.domain_size)?; let (start_word_index, _) = word_index_and_mask(start); let (end_word_index, end_mask) = word_index_and_mask(end); let end_word = self.words[end_word_index] & (end_mask | (end_mask - 1)); if end_word != 0 { let pos = max_bit(end_word) + WORD_BITS * end_word_index; if start <= pos { return Some(T::new(pos)); } } // We exclude end_word_index from the range here, because we don't want // to limit ourselves to *just* the last word: the bits set it in may be // after `end`, so it may not work out. if let Some(offset) = self.words[start_word_index..end_word_index].iter().rposition(|&w| w != 0) { let word_idx = start_word_index + offset; let start_word = self.words[word_idx]; let pos = max_bit(start_word) + WORD_BITS * word_idx; if start <= pos { return Some(T::new(pos)); } } None } bit_relations_inherent_impls! {} } // dense REL dense impl BitRelations> for BitSet { fn union(&mut self, other: &BitSet) -> bool { assert_eq!(self.domain_size, other.domain_size); bitwise(&mut self.words, &other.words, |a, b| a | b) } fn subtract(&mut self, other: &BitSet) -> bool { assert_eq!(self.domain_size, other.domain_size); bitwise(&mut self.words, &other.words, |a, b| a & !b) } fn intersect(&mut self, other: &BitSet) -> bool { assert_eq!(self.domain_size, other.domain_size); bitwise(&mut self.words, &other.words, |a, b| a & b) } } impl From> for BitSet { fn from(bit_set: GrowableBitSet) -> Self { bit_set.bit_set } } /// A fixed-size bitset type with a partially dense, partially sparse /// representation. The bitset is broken into chunks, and chunks that are all /// zeros or all ones are represented and handled very efficiently. /// /// This type is especially efficient for sets that typically have a large /// `domain_size` with significant stretches of all zeros or all ones, and also /// some stretches with lots of 0s and 1s mixed in a way that causes trouble /// for `IntervalSet`. /// /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also /// just be `usize`. /// /// All operations that involve an element will panic if the element is equal /// to or greater than the domain size. All operations that involve two bitsets /// will panic if the bitsets have differing domain sizes. #[derive(Debug, PartialEq, Eq)] pub struct ChunkedBitSet { domain_size: usize, /// The chunks. Each one contains exactly CHUNK_BITS values, except the /// last one which contains 1..=CHUNK_BITS values. chunks: Box<[Chunk]>, marker: PhantomData, } // Note: the chunk domain size is duplicated in each variant. This is a bit // inconvenient, but it allows the type size to be smaller than if we had an // outer struct containing a chunk domain size plus the `Chunk`, because the // compiler can place the chunk domain size after the tag. #[derive(Clone, Debug, PartialEq, Eq)] enum Chunk { /// A chunk that is all zeros; we don't represent the zeros explicitly. Zeros(ChunkSize), /// A chunk that is all ones; we don't represent the ones explicitly. Ones(ChunkSize), /// A chunk that has a mix of zeros and ones, which are represented /// explicitly and densely. It never has all zeros or all ones. /// /// If this is the final chunk there may be excess, unused words. This /// turns out to be both simpler and have better performance than /// allocating the minimum number of words, largely because we avoid having /// to store the length, which would make this type larger. These excess /// words are always be zero, as are any excess bits in the final in-use /// word. /// /// The second field is the count of 1s set in the chunk, and must satisfy /// `0 < count < chunk_domain_size`. /// /// The words are within an `Rc` because it's surprisingly common to /// duplicate an entire chunk, e.g. in `ChunkedBitSet::clone_from()`, or /// when a `Mixed` chunk is union'd into a `Zeros` chunk. When we do need /// to modify a chunk we use `Rc::make_mut`. Mixed(ChunkSize, ChunkSize, Rc<[Word; CHUNK_WORDS]>), } // This type is used a lot. Make sure it doesn't unintentionally get bigger. #[cfg(all(target_arch = "x86_64", target_pointer_width = "64"))] crate::static_assert_size!(Chunk, 16); impl ChunkedBitSet { pub fn domain_size(&self) -> usize { self.domain_size } #[cfg(test)] fn assert_valid(&self) { if self.domain_size == 0 { assert!(self.chunks.is_empty()); return; } assert!((self.chunks.len() - 1) * CHUNK_BITS <= self.domain_size); assert!(self.chunks.len() * CHUNK_BITS >= self.domain_size); for chunk in self.chunks.iter() { chunk.assert_valid(); } } } impl ChunkedBitSet { /// Creates a new bitset with a given `domain_size` and chunk kind. fn new(domain_size: usize, is_empty: bool) -> Self { let chunks = if domain_size == 0 { Box::new([]) } else { // All the chunks have a chunk_domain_size of `CHUNK_BITS` except // the final one. let final_chunk_domain_size = { let n = domain_size % CHUNK_BITS; if n == 0 { CHUNK_BITS } else { n } }; let mut chunks = vec![Chunk::new(CHUNK_BITS, is_empty); num_chunks(domain_size)].into_boxed_slice(); *chunks.last_mut().unwrap() = Chunk::new(final_chunk_domain_size, is_empty); chunks }; ChunkedBitSet { domain_size, chunks, marker: PhantomData } } /// Creates a new, empty bitset with a given `domain_size`. #[inline] pub fn new_empty(domain_size: usize) -> Self { ChunkedBitSet::new(domain_size, /* is_empty */ true) } /// Creates a new, filled bitset with a given `domain_size`. #[inline] pub fn new_filled(domain_size: usize) -> Self { ChunkedBitSet::new(domain_size, /* is_empty */ false) } #[cfg(test)] fn chunks(&self) -> &[Chunk] { &self.chunks } /// Count the number of bits in the set. pub fn count(&self) -> usize { self.chunks.iter().map(|chunk| chunk.count()).sum() } /// Returns `true` if `self` contains `elem`. #[inline] pub fn contains(&self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let chunk = &self.chunks[chunk_index(elem)]; match &chunk { Zeros(_) => false, Ones(_) => true, Mixed(_, _, words) => { let (word_index, mask) = chunk_word_index_and_mask(elem); (words[word_index] & mask) != 0 } } } #[inline] pub fn iter(&self) -> ChunkedBitIter<'_, T> { ChunkedBitIter::new(self) } /// Insert `elem`. Returns whether the set has changed. pub fn insert(&mut self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let chunk_index = chunk_index(elem); let chunk = &mut self.chunks[chunk_index]; match *chunk { Zeros(chunk_domain_size) => { if chunk_domain_size > 1 { // We take some effort to avoid copying the words. let words = Rc::<[Word; CHUNK_WORDS]>::new_zeroed(); // SAFETY: `words` can safely be all zeroes. let mut words = unsafe { words.assume_init() }; let words_ref = Rc::get_mut(&mut words).unwrap(); let (word_index, mask) = chunk_word_index_and_mask(elem); words_ref[word_index] |= mask; *chunk = Mixed(chunk_domain_size, 1, words); } else { *chunk = Ones(chunk_domain_size); } true } Ones(_) => false, Mixed(chunk_domain_size, ref mut count, ref mut words) => { // We skip all the work if the bit is already set. let (word_index, mask) = chunk_word_index_and_mask(elem); if (words[word_index] & mask) == 0 { *count += 1; if *count < chunk_domain_size { let words = Rc::make_mut(words); words[word_index] |= mask; } else { *chunk = Ones(chunk_domain_size); } true } else { false } } } } /// Sets all bits to true. pub fn insert_all(&mut self) { for chunk in self.chunks.iter_mut() { *chunk = match *chunk { Zeros(chunk_domain_size) | Ones(chunk_domain_size) | Mixed(chunk_domain_size, ..) => Ones(chunk_domain_size), } } } /// Returns `true` if the set has changed. pub fn remove(&mut self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let chunk_index = chunk_index(elem); let chunk = &mut self.chunks[chunk_index]; match *chunk { Zeros(_) => false, Ones(chunk_domain_size) => { if chunk_domain_size > 1 { // We take some effort to avoid copying the words. let words = Rc::<[Word; CHUNK_WORDS]>::new_zeroed(); // SAFETY: `words` can safely be all zeroes. let mut words = unsafe { words.assume_init() }; let words_ref = Rc::get_mut(&mut words).unwrap(); // Set only the bits in use. let num_words = num_words(chunk_domain_size as usize); words_ref[..num_words].fill(!0); clear_excess_bits_in_final_word( chunk_domain_size as usize, &mut words_ref[..num_words], ); let (word_index, mask) = chunk_word_index_and_mask(elem); words_ref[word_index] &= !mask; *chunk = Mixed(chunk_domain_size, chunk_domain_size - 1, words); } else { *chunk = Zeros(chunk_domain_size); } true } Mixed(chunk_domain_size, ref mut count, ref mut words) => { // We skip all the work if the bit is already clear. let (word_index, mask) = chunk_word_index_and_mask(elem); if (words[word_index] & mask) != 0 { *count -= 1; if *count > 0 { let words = Rc::make_mut(words); words[word_index] &= !mask; } else { *chunk = Zeros(chunk_domain_size); } true } else { false } } } } bit_relations_inherent_impls! {} } impl BitRelations> for ChunkedBitSet { fn union(&mut self, other: &ChunkedBitSet) -> bool { assert_eq!(self.domain_size, other.domain_size); debug_assert_eq!(self.chunks.len(), other.chunks.len()); let mut changed = false; for (mut self_chunk, other_chunk) in self.chunks.iter_mut().zip(other.chunks.iter()) { match (&mut self_chunk, &other_chunk) { (_, Zeros(_)) | (Ones(_), _) => {} (Zeros(self_chunk_domain_size), Ones(other_chunk_domain_size)) | (Mixed(self_chunk_domain_size, ..), Ones(other_chunk_domain_size)) | (Zeros(self_chunk_domain_size), Mixed(other_chunk_domain_size, ..)) => { // `other_chunk` fully overwrites `self_chunk` debug_assert_eq!(self_chunk_domain_size, other_chunk_domain_size); *self_chunk = other_chunk.clone(); changed = true; } ( Mixed( self_chunk_domain_size, ref mut self_chunk_count, ref mut self_chunk_words, ), Mixed(_other_chunk_domain_size, _other_chunk_count, other_chunk_words), ) => { // First check if the operation would change // `self_chunk.words`. If not, we can avoid allocating some // words, and this happens often enough that it's a // performance win. Also, we only need to operate on the // in-use words, hence the slicing. let op = |a, b| a | b; let num_words = num_words(*self_chunk_domain_size as usize); if bitwise_changes( &self_chunk_words[0..num_words], &other_chunk_words[0..num_words], op, ) { let self_chunk_words = Rc::make_mut(self_chunk_words); let has_changed = bitwise( &mut self_chunk_words[0..num_words], &other_chunk_words[0..num_words], op, ); debug_assert!(has_changed); *self_chunk_count = self_chunk_words[0..num_words] .iter() .map(|w| w.count_ones() as ChunkSize) .sum(); if *self_chunk_count == *self_chunk_domain_size { *self_chunk = Ones(*self_chunk_domain_size); } changed = true; } } } } changed } fn subtract(&mut self, _other: &ChunkedBitSet) -> bool { unimplemented!("implement if/when necessary"); } fn intersect(&mut self, _other: &ChunkedBitSet) -> bool { unimplemented!("implement if/when necessary"); } } impl BitRelations> for ChunkedBitSet { fn union(&mut self, other: &HybridBitSet) -> bool { // FIXME: This is slow if `other` is dense, but it hasn't been a problem // in practice so far. // If a faster implementation of this operation is required, consider // reopening https://github.com/rust-lang/rust/pull/94625 assert_eq!(self.domain_size, other.domain_size()); sequential_update(|elem| self.insert(elem), other.iter()) } fn subtract(&mut self, other: &HybridBitSet) -> bool { // FIXME: This is slow if `other` is dense, but it hasn't been a problem // in practice so far. // If a faster implementation of this operation is required, consider // reopening https://github.com/rust-lang/rust/pull/94625 assert_eq!(self.domain_size, other.domain_size()); sequential_update(|elem| self.remove(elem), other.iter()) } fn intersect(&mut self, _other: &HybridBitSet) -> bool { unimplemented!("implement if/when necessary"); } } impl BitRelations> for BitSet { fn union(&mut self, other: &ChunkedBitSet) -> bool { sequential_update(|elem| self.insert(elem), other.iter()) } fn subtract(&mut self, _other: &ChunkedBitSet) -> bool { unimplemented!("implement if/when necessary"); } fn intersect(&mut self, other: &ChunkedBitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size); let mut changed = false; for (i, chunk) in other.chunks.iter().enumerate() { let mut words = &mut self.words[i * CHUNK_WORDS..]; if words.len() > CHUNK_WORDS { words = &mut words[..CHUNK_WORDS]; } match chunk { Chunk::Zeros(..) => { for word in words { if *word != 0 { changed = true; *word = 0; } } } Chunk::Ones(..) => (), Chunk::Mixed(_, _, data) => { for (i, word) in words.iter_mut().enumerate() { let new_val = *word & data[i]; if new_val != *word { changed = true; *word = new_val; } } } } } changed } } impl Clone for ChunkedBitSet { fn clone(&self) -> Self { ChunkedBitSet { domain_size: self.domain_size, chunks: self.chunks.clone(), marker: PhantomData, } } /// WARNING: this implementation of clone_from will panic if the two /// bitsets have different domain sizes. This constraint is not inherent to /// `clone_from`, but it works with the existing call sites and allows a /// faster implementation, which is important because this function is hot. fn clone_from(&mut self, from: &Self) { assert_eq!(self.domain_size, from.domain_size); debug_assert_eq!(self.chunks.len(), from.chunks.len()); self.chunks.clone_from(&from.chunks) } } pub struct ChunkedBitIter<'a, T: Idx> { index: usize, bitset: &'a ChunkedBitSet, } impl<'a, T: Idx> ChunkedBitIter<'a, T> { #[inline] fn new(bitset: &'a ChunkedBitSet) -> ChunkedBitIter<'a, T> { ChunkedBitIter { index: 0, bitset } } } impl<'a, T: Idx> Iterator for ChunkedBitIter<'a, T> { type Item = T; fn next(&mut self) -> Option { while self.index < self.bitset.domain_size() { let elem = T::new(self.index); let chunk = &self.bitset.chunks[chunk_index(elem)]; match &chunk { Zeros(chunk_domain_size) => { self.index += *chunk_domain_size as usize; } Ones(_chunk_domain_size) => { self.index += 1; return Some(elem); } Mixed(_chunk_domain_size, _, words) => loop { let elem = T::new(self.index); self.index += 1; let (word_index, mask) = chunk_word_index_and_mask(elem); if (words[word_index] & mask) != 0 { return Some(elem); } if self.index % CHUNK_BITS == 0 { break; } }, } } None } fn fold(mut self, mut init: B, mut f: F) -> B where F: FnMut(B, Self::Item) -> B, { // If `next` has already been called, we may not be at the start of a chunk, so we first // advance the iterator to the start of the next chunk, before proceeding in chunk sized // steps. while self.index % CHUNK_BITS != 0 { let Some(item) = self.next() else { return init }; init = f(init, item); } let start_chunk = self.index / CHUNK_BITS; let chunks = &self.bitset.chunks[start_chunk..]; for (i, chunk) in chunks.iter().enumerate() { let base = (start_chunk + i) * CHUNK_BITS; match chunk { Chunk::Zeros(_) => (), Chunk::Ones(limit) => { for j in 0..(*limit as usize) { init = f(init, T::new(base + j)); } } Chunk::Mixed(_, _, words) => { init = BitIter::new(&**words).fold(init, |val, mut item: T| { item.increment_by(base); f(val, item) }); } } } init } } impl Chunk { #[cfg(test)] fn assert_valid(&self) { match *self { Zeros(chunk_domain_size) | Ones(chunk_domain_size) => { assert!(chunk_domain_size as usize <= CHUNK_BITS); } Mixed(chunk_domain_size, count, ref words) => { assert!(chunk_domain_size as usize <= CHUNK_BITS); assert!(0 < count && count < chunk_domain_size); // Check the number of set bits matches `count`. assert_eq!( words.iter().map(|w| w.count_ones() as ChunkSize).sum::(), count ); // Check the not-in-use words are all zeroed. let num_words = num_words(chunk_domain_size as usize); if num_words < CHUNK_WORDS { assert_eq!( words[num_words..] .iter() .map(|w| w.count_ones() as ChunkSize) .sum::(), 0 ); } } } } fn new(chunk_domain_size: usize, is_empty: bool) -> Self { debug_assert!(chunk_domain_size <= CHUNK_BITS); let chunk_domain_size = chunk_domain_size as ChunkSize; if is_empty { Zeros(chunk_domain_size) } else { Ones(chunk_domain_size) } } /// Count the number of 1s in the chunk. fn count(&self) -> usize { match *self { Zeros(_) => 0, Ones(chunk_domain_size) => chunk_domain_size as usize, Mixed(_, count, _) => count as usize, } } } // Applies a function to mutate a bitset, and returns true if any // of the applications return true fn sequential_update( mut self_update: impl FnMut(T) -> bool, it: impl Iterator, ) -> bool { it.fold(false, |changed, elem| self_update(elem) | changed) } // Optimization of intersection for SparseBitSet that's generic // over the RHS fn sparse_intersect( set: &mut SparseBitSet, other_contains: impl Fn(&T) -> bool, ) -> bool { let size = set.elems.len(); set.elems.retain(|elem| other_contains(elem)); set.elems.len() != size } // Optimization of dense/sparse intersection. The resulting set is // guaranteed to be at most the size of the sparse set, and hence can be // represented as a sparse set. Therefore the sparse set is copied and filtered, // then returned as the new set. fn dense_sparse_intersect( dense: &BitSet, sparse: &SparseBitSet, ) -> (SparseBitSet, bool) { let mut sparse_copy = sparse.clone(); sparse_intersect(&mut sparse_copy, |el| dense.contains(*el)); let n = sparse_copy.len(); (sparse_copy, n != dense.count()) } // hybrid REL dense impl BitRelations> for HybridBitSet { fn union(&mut self, other: &BitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size); match self { HybridBitSet::Sparse(sparse) => { // `self` is sparse and `other` is dense. To // merge them, we have two available strategies: // * Densify `self` then merge other // * Clone other then integrate bits from `self` // The second strategy requires dedicated method // since the usual `union` returns the wrong // result. In the dedicated case the computation // is slightly faster if the bits of the sparse // bitset map to only few words of the dense // representation, i.e. indices are near each // other. // // Benchmarking seems to suggest that the second // option is worth it. let mut new_dense = other.clone(); let changed = new_dense.reverse_union_sparse(sparse); *self = HybridBitSet::Dense(new_dense); changed } HybridBitSet::Dense(dense) => dense.union(other), } } fn subtract(&mut self, other: &BitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size); match self { HybridBitSet::Sparse(sparse) => { sequential_update(|elem| sparse.remove(elem), other.iter()) } HybridBitSet::Dense(dense) => dense.subtract(other), } } fn intersect(&mut self, other: &BitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size); match self { HybridBitSet::Sparse(sparse) => sparse_intersect(sparse, |elem| other.contains(*elem)), HybridBitSet::Dense(dense) => dense.intersect(other), } } } // dense REL hybrid impl BitRelations> for BitSet { fn union(&mut self, other: &HybridBitSet) -> bool { assert_eq!(self.domain_size, other.domain_size()); match other { HybridBitSet::Sparse(sparse) => { sequential_update(|elem| self.insert(elem), sparse.iter().cloned()) } HybridBitSet::Dense(dense) => self.union(dense), } } fn subtract(&mut self, other: &HybridBitSet) -> bool { assert_eq!(self.domain_size, other.domain_size()); match other { HybridBitSet::Sparse(sparse) => { sequential_update(|elem| self.remove(elem), sparse.iter().cloned()) } HybridBitSet::Dense(dense) => self.subtract(dense), } } fn intersect(&mut self, other: &HybridBitSet) -> bool { assert_eq!(self.domain_size, other.domain_size()); match other { HybridBitSet::Sparse(sparse) => { let (updated, changed) = dense_sparse_intersect(self, sparse); // We can't directly assign the SparseBitSet to the BitSet, and // doing `*self = updated.to_dense()` would cause a drop / reallocation. Instead, // the BitSet is cleared and `updated` is copied into `self`. self.clear(); for elem in updated.iter() { self.insert(*elem); } changed } HybridBitSet::Dense(dense) => self.intersect(dense), } } } // hybrid REL hybrid impl BitRelations> for HybridBitSet { fn union(&mut self, other: &HybridBitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size()); match self { HybridBitSet::Sparse(_) => { match other { HybridBitSet::Sparse(other_sparse) => { // Both sets are sparse. Add the elements in // `other_sparse` to `self` one at a time. This // may or may not cause `self` to be densified. let mut changed = false; for elem in other_sparse.iter() { changed |= self.insert(*elem); } changed } HybridBitSet::Dense(other_dense) => self.union(other_dense), } } HybridBitSet::Dense(self_dense) => self_dense.union(other), } } fn subtract(&mut self, other: &HybridBitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size()); match self { HybridBitSet::Sparse(self_sparse) => { sequential_update(|elem| self_sparse.remove(elem), other.iter()) } HybridBitSet::Dense(self_dense) => self_dense.subtract(other), } } fn intersect(&mut self, other: &HybridBitSet) -> bool { assert_eq!(self.domain_size(), other.domain_size()); match self { HybridBitSet::Sparse(self_sparse) => { sparse_intersect(self_sparse, |elem| other.contains(*elem)) } HybridBitSet::Dense(self_dense) => match other { HybridBitSet::Sparse(other_sparse) => { let (updated, changed) = dense_sparse_intersect(self_dense, other_sparse); *self = HybridBitSet::Sparse(updated); changed } HybridBitSet::Dense(other_dense) => self_dense.intersect(other_dense), }, } } } impl Clone for BitSet { fn clone(&self) -> Self { BitSet { domain_size: self.domain_size, words: self.words.clone(), marker: PhantomData } } fn clone_from(&mut self, from: &Self) { self.domain_size = from.domain_size; self.words.clone_from(&from.words); } } impl fmt::Debug for BitSet { fn fmt(&self, w: &mut fmt::Formatter<'_>) -> fmt::Result { w.debug_list().entries(self.iter()).finish() } } impl ToString for BitSet { fn to_string(&self) -> String { let mut result = String::new(); let mut sep = '['; // Note: this is a little endian printout of bytes. // i tracks how many bits we have printed so far. let mut i = 0; for word in &self.words { let mut word = *word; for _ in 0..WORD_BYTES { // for each byte in `word`: let remain = self.domain_size - i; // If less than a byte remains, then mask just that many bits. let mask = if remain <= 8 { (1 << remain) - 1 } else { 0xFF }; assert!(mask <= 0xFF); let byte = word & mask; result.push_str(&format!("{sep}{byte:02x}")); if remain <= 8 { break; } word >>= 8; i += 8; sep = '-'; } sep = '|'; } result.push(']'); result } } pub struct BitIter<'a, T: Idx> { /// A copy of the current word, but with any already-visited bits cleared. /// (This lets us use `trailing_zeros()` to find the next set bit.) When it /// is reduced to 0, we move onto the next word. word: Word, /// The offset (measured in bits) of the current word. offset: usize, /// Underlying iterator over the words. iter: slice::Iter<'a, Word>, marker: PhantomData, } impl<'a, T: Idx> BitIter<'a, T> { #[inline] fn new(words: &'a [Word]) -> BitIter<'a, T> { // We initialize `word` and `offset` to degenerate values. On the first // call to `next()` we will fall through to getting the first word from // `iter`, which sets `word` to the first word (if there is one) and // `offset` to 0. Doing it this way saves us from having to maintain // additional state about whether we have started. BitIter { word: 0, offset: usize::MAX - (WORD_BITS - 1), iter: words.iter(), marker: PhantomData, } } } impl<'a, T: Idx> Iterator for BitIter<'a, T> { type Item = T; fn next(&mut self) -> Option { loop { if self.word != 0 { // Get the position of the next set bit in the current word, // then clear the bit. let bit_pos = self.word.trailing_zeros() as usize; let bit = 1 << bit_pos; self.word ^= bit; return Some(T::new(bit_pos + self.offset)); } // Move onto the next word. `wrapping_add()` is needed to handle // the degenerate initial value given to `offset` in `new()`. let word = self.iter.next()?; self.word = *word; self.offset = self.offset.wrapping_add(WORD_BITS); } } } #[inline] fn bitwise(out_vec: &mut [Word], in_vec: &[Word], op: Op) -> bool where Op: Fn(Word, Word) -> Word, { assert_eq!(out_vec.len(), in_vec.len()); let mut changed = 0; for (out_elem, in_elem) in iter::zip(out_vec, in_vec) { let old_val = *out_elem; let new_val = op(old_val, *in_elem); *out_elem = new_val; // This is essentially equivalent to a != with changed being a bool, but // in practice this code gets auto-vectorized by the compiler for most // operators. Using != here causes us to generate quite poor code as the // compiler tries to go back to a boolean on each loop iteration. changed |= old_val ^ new_val; } changed != 0 } /// Does this bitwise operation change `out_vec`? #[inline] fn bitwise_changes(out_vec: &[Word], in_vec: &[Word], op: Op) -> bool where Op: Fn(Word, Word) -> Word, { assert_eq!(out_vec.len(), in_vec.len()); for (out_elem, in_elem) in iter::zip(out_vec, in_vec) { let old_val = *out_elem; let new_val = op(old_val, *in_elem); if old_val != new_val { return true; } } false } const SPARSE_MAX: usize = 8; /// A fixed-size bitset type with a sparse representation and a maximum of /// `SPARSE_MAX` elements. The elements are stored as a sorted `ArrayVec` with /// no duplicates. /// /// This type is used by `HybridBitSet`; do not use directly. #[derive(Clone, Debug)] pub struct SparseBitSet { domain_size: usize, elems: ArrayVec, } impl SparseBitSet { fn new_empty(domain_size: usize) -> Self { SparseBitSet { domain_size, elems: ArrayVec::new() } } fn len(&self) -> usize { self.elems.len() } fn is_empty(&self) -> bool { self.elems.len() == 0 } fn contains(&self, elem: T) -> bool { assert!(elem.index() < self.domain_size); self.elems.contains(&elem) } fn insert(&mut self, elem: T) -> bool { assert!(elem.index() < self.domain_size); let changed = if let Some(i) = self.elems.iter().position(|&e| e.index() >= elem.index()) { if self.elems[i] == elem { // `elem` is already in the set. false } else { // `elem` is smaller than one or more existing elements. self.elems.insert(i, elem); true } } else { // `elem` is larger than all existing elements. self.elems.push(elem); true }; assert!(self.len() <= SPARSE_MAX); changed } fn remove(&mut self, elem: T) -> bool { assert!(elem.index() < self.domain_size); if let Some(i) = self.elems.iter().position(|&e| e == elem) { self.elems.remove(i); true } else { false } } fn to_dense(&self) -> BitSet { let mut dense = BitSet::new_empty(self.domain_size); for elem in self.elems.iter() { dense.insert(*elem); } dense } fn iter(&self) -> slice::Iter<'_, T> { self.elems.iter() } bit_relations_inherent_impls! {} } impl SparseBitSet { fn last_set_in(&self, range: impl RangeBounds) -> Option { let mut last_leq = None; for e in self.iter() { if range.contains(e) { last_leq = Some(*e); } } last_leq } } /// A fixed-size bitset type with a hybrid representation: sparse when there /// are up to a `SPARSE_MAX` elements in the set, but dense when there are more /// than `SPARSE_MAX`. /// /// This type is especially efficient for sets that typically have a small /// number of elements, but a large `domain_size`, and are cleared frequently. /// /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also /// just be `usize`. /// /// All operations that involve an element will panic if the element is equal /// to or greater than the domain size. All operations that involve two bitsets /// will panic if the bitsets have differing domain sizes. #[derive(Clone)] pub enum HybridBitSet { Sparse(SparseBitSet), Dense(BitSet), } impl fmt::Debug for HybridBitSet { fn fmt(&self, w: &mut fmt::Formatter<'_>) -> fmt::Result { match self { Self::Sparse(b) => b.fmt(w), Self::Dense(b) => b.fmt(w), } } } impl HybridBitSet { pub fn new_empty(domain_size: usize) -> Self { HybridBitSet::Sparse(SparseBitSet::new_empty(domain_size)) } pub fn domain_size(&self) -> usize { match self { HybridBitSet::Sparse(sparse) => sparse.domain_size, HybridBitSet::Dense(dense) => dense.domain_size, } } pub fn clear(&mut self) { let domain_size = self.domain_size(); *self = HybridBitSet::new_empty(domain_size); } pub fn contains(&self, elem: T) -> bool { match self { HybridBitSet::Sparse(sparse) => sparse.contains(elem), HybridBitSet::Dense(dense) => dense.contains(elem), } } pub fn superset(&self, other: &HybridBitSet) -> bool { match (self, other) { (HybridBitSet::Dense(self_dense), HybridBitSet::Dense(other_dense)) => { self_dense.superset(other_dense) } _ => { assert!(self.domain_size() == other.domain_size()); other.iter().all(|elem| self.contains(elem)) } } } pub fn is_empty(&self) -> bool { match self { HybridBitSet::Sparse(sparse) => sparse.is_empty(), HybridBitSet::Dense(dense) => dense.is_empty(), } } /// Returns the previous element present in the bitset from `elem`, /// inclusively of elem. That is, will return `Some(elem)` if elem is in the /// bitset. pub fn last_set_in(&self, range: impl RangeBounds) -> Option where T: Ord, { match self { HybridBitSet::Sparse(sparse) => sparse.last_set_in(range), HybridBitSet::Dense(dense) => dense.last_set_in(range), } } pub fn insert(&mut self, elem: T) -> bool { // No need to check `elem` against `self.domain_size` here because all // the match cases check it, one way or another. match self { HybridBitSet::Sparse(sparse) if sparse.len() < SPARSE_MAX => { // The set is sparse and has space for `elem`. sparse.insert(elem) } HybridBitSet::Sparse(sparse) if sparse.contains(elem) => { // The set is sparse and does not have space for `elem`, but // that doesn't matter because `elem` is already present. false } HybridBitSet::Sparse(sparse) => { // The set is sparse and full. Convert to a dense set. let mut dense = sparse.to_dense(); let changed = dense.insert(elem); assert!(changed); *self = HybridBitSet::Dense(dense); changed } HybridBitSet::Dense(dense) => dense.insert(elem), } } pub fn insert_range(&mut self, elems: impl RangeBounds) { // No need to check `elem` against `self.domain_size` here because all // the match cases check it, one way or another. let start = match elems.start_bound().cloned() { Bound::Included(start) => start.index(), Bound::Excluded(start) => start.index() + 1, Bound::Unbounded => 0, }; let end = match elems.end_bound().cloned() { Bound::Included(end) => end.index() + 1, Bound::Excluded(end) => end.index(), Bound::Unbounded => self.domain_size() - 1, }; let Some(len) = end.checked_sub(start) else { return }; match self { HybridBitSet::Sparse(sparse) if sparse.len() + len < SPARSE_MAX => { // The set is sparse and has space for `elems`. for elem in start..end { sparse.insert(T::new(elem)); } } HybridBitSet::Sparse(sparse) => { // The set is sparse and full. Convert to a dense set. let mut dense = sparse.to_dense(); dense.insert_range(elems); *self = HybridBitSet::Dense(dense); } HybridBitSet::Dense(dense) => dense.insert_range(elems), } } pub fn insert_all(&mut self) { let domain_size = self.domain_size(); match self { HybridBitSet::Sparse(_) => { *self = HybridBitSet::Dense(BitSet::new_filled(domain_size)); } HybridBitSet::Dense(dense) => dense.insert_all(), } } pub fn remove(&mut self, elem: T) -> bool { // Note: we currently don't bother going from Dense back to Sparse. match self { HybridBitSet::Sparse(sparse) => sparse.remove(elem), HybridBitSet::Dense(dense) => dense.remove(elem), } } /// Converts to a dense set, consuming itself in the process. pub fn to_dense(self) -> BitSet { match self { HybridBitSet::Sparse(sparse) => sparse.to_dense(), HybridBitSet::Dense(dense) => dense, } } pub fn iter(&self) -> HybridIter<'_, T> { match self { HybridBitSet::Sparse(sparse) => HybridIter::Sparse(sparse.iter()), HybridBitSet::Dense(dense) => HybridIter::Dense(dense.iter()), } } bit_relations_inherent_impls! {} } pub enum HybridIter<'a, T: Idx> { Sparse(slice::Iter<'a, T>), Dense(BitIter<'a, T>), } impl<'a, T: Idx> Iterator for HybridIter<'a, T> { type Item = T; fn next(&mut self) -> Option { match self { HybridIter::Sparse(sparse) => sparse.next().copied(), HybridIter::Dense(dense) => dense.next(), } } } /// A resizable bitset type with a dense representation. /// /// `T` is an index type, typically a newtyped `usize` wrapper, but it can also /// just be `usize`. /// /// All operations that involve an element will panic if the element is equal /// to or greater than the domain size. #[derive(Clone, Debug, PartialEq)] pub struct GrowableBitSet { bit_set: BitSet, } impl Default for GrowableBitSet { fn default() -> Self { GrowableBitSet::new_empty() } } impl GrowableBitSet { /// Ensure that the set can hold at least `min_domain_size` elements. pub fn ensure(&mut self, min_domain_size: usize) { if self.bit_set.domain_size < min_domain_size { self.bit_set.domain_size = min_domain_size; } let min_num_words = num_words(min_domain_size); if self.bit_set.words.len() < min_num_words { self.bit_set.words.resize(min_num_words, 0) } } pub fn new_empty() -> GrowableBitSet { GrowableBitSet { bit_set: BitSet::new_empty(0) } } pub fn with_capacity(capacity: usize) -> GrowableBitSet { GrowableBitSet { bit_set: BitSet::new_empty(capacity) } } /// Returns `true` if the set has changed. #[inline] pub fn insert(&mut self, elem: T) -> bool { self.ensure(elem.index() + 1); self.bit_set.insert(elem) } /// Returns `true` if the set has changed. #[inline] pub fn remove(&mut self, elem: T) -> bool { self.ensure(elem.index() + 1); self.bit_set.remove(elem) } #[inline] pub fn is_empty(&self) -> bool { self.bit_set.is_empty() } #[inline] pub fn contains(&self, elem: T) -> bool { let (word_index, mask) = word_index_and_mask(elem); self.bit_set.words.get(word_index).map_or(false, |word| (word & mask) != 0) } #[inline] pub fn iter(&self) -> BitIter<'_, T> { self.bit_set.iter() } #[inline] pub fn len(&self) -> usize { self.bit_set.count() } } impl From> for GrowableBitSet { fn from(bit_set: BitSet) -> Self { Self { bit_set } } } /// A fixed-size 2D bit matrix type with a dense representation. /// /// `R` and `C` are index types used to identify rows and columns respectively; /// typically newtyped `usize` wrappers, but they can also just be `usize`. /// /// All operations that involve a row and/or column index will panic if the /// index exceeds the relevant bound. #[derive(Clone, Eq, PartialEq, Hash, Decodable, Encodable)] pub struct BitMatrix { num_rows: usize, num_columns: usize, words: Vec, marker: PhantomData<(R, C)>, } impl BitMatrix { /// Creates a new `rows x columns` matrix, initially empty. pub fn new(num_rows: usize, num_columns: usize) -> BitMatrix { // For every element, we need one bit for every other // element. Round up to an even number of words. let words_per_row = num_words(num_columns); BitMatrix { num_rows, num_columns, words: vec![0; num_rows * words_per_row], marker: PhantomData, } } /// Creates a new matrix, with `row` used as the value for every row. pub fn from_row_n(row: &BitSet, num_rows: usize) -> BitMatrix { let num_columns = row.domain_size(); let words_per_row = num_words(num_columns); assert_eq!(words_per_row, row.words().len()); BitMatrix { num_rows, num_columns, words: iter::repeat(row.words()).take(num_rows).flatten().cloned().collect(), marker: PhantomData, } } pub fn rows(&self) -> impl Iterator { (0..self.num_rows).map(R::new) } /// The range of bits for a given row. fn range(&self, row: R) -> (usize, usize) { let words_per_row = num_words(self.num_columns); let start = row.index() * words_per_row; (start, start + words_per_row) } /// Sets the cell at `(row, column)` to true. Put another way, insert /// `column` to the bitset for `row`. /// /// Returns `true` if this changed the matrix. pub fn insert(&mut self, row: R, column: C) -> bool { assert!(row.index() < self.num_rows && column.index() < self.num_columns); let (start, _) = self.range(row); let (word_index, mask) = word_index_and_mask(column); let words = &mut self.words[..]; let word = words[start + word_index]; let new_word = word | mask; words[start + word_index] = new_word; word != new_word } /// Do the bits from `row` contain `column`? Put another way, is /// the matrix cell at `(row, column)` true? Put yet another way, /// if the matrix represents (transitive) reachability, can /// `row` reach `column`? pub fn contains(&self, row: R, column: C) -> bool { assert!(row.index() < self.num_rows && column.index() < self.num_columns); let (start, _) = self.range(row); let (word_index, mask) = word_index_and_mask(column); (self.words[start + word_index] & mask) != 0 } /// Returns those indices that are true in rows `a` and `b`. This /// is an *O*(*n*) operation where *n* is the number of elements /// (somewhat independent from the actual size of the /// intersection, in particular). pub fn intersect_rows(&self, row1: R, row2: R) -> Vec { assert!(row1.index() < self.num_rows && row2.index() < self.num_rows); let (row1_start, row1_end) = self.range(row1); let (row2_start, row2_end) = self.range(row2); let mut result = Vec::with_capacity(self.num_columns); for (base, (i, j)) in (row1_start..row1_end).zip(row2_start..row2_end).enumerate() { let mut v = self.words[i] & self.words[j]; for bit in 0..WORD_BITS { if v == 0 { break; } if v & 0x1 != 0 { result.push(C::new(base * WORD_BITS + bit)); } v >>= 1; } } result } /// Adds the bits from row `read` to the bits from row `write`, and /// returns `true` if anything changed. /// /// This is used when computing transitive reachability because if /// you have an edge `write -> read`, because in that case /// `write` can reach everything that `read` can (and /// potentially more). pub fn union_rows(&mut self, read: R, write: R) -> bool { assert!(read.index() < self.num_rows && write.index() < self.num_rows); let (read_start, read_end) = self.range(read); let (write_start, write_end) = self.range(write); let words = &mut self.words[..]; let mut changed = false; for (read_index, write_index) in iter::zip(read_start..read_end, write_start..write_end) { let word = words[write_index]; let new_word = word | words[read_index]; words[write_index] = new_word; changed |= word != new_word; } changed } /// Adds the bits from `with` to the bits from row `write`, and /// returns `true` if anything changed. pub fn union_row_with(&mut self, with: &BitSet, write: R) -> bool { assert!(write.index() < self.num_rows); assert_eq!(with.domain_size(), self.num_columns); let (write_start, write_end) = self.range(write); let mut changed = false; for (read_index, write_index) in iter::zip(0..with.words().len(), write_start..write_end) { let word = self.words[write_index]; let new_word = word | with.words()[read_index]; self.words[write_index] = new_word; changed |= word != new_word; } changed } /// Sets every cell in `row` to true. pub fn insert_all_into_row(&mut self, row: R) { assert!(row.index() < self.num_rows); let (start, end) = self.range(row); let words = &mut self.words[..]; for index in start..end { words[index] = !0; } clear_excess_bits_in_final_word(self.num_columns, &mut self.words[..end]); } /// Gets a slice of the underlying words. pub fn words(&self) -> &[Word] { &self.words } /// Iterates through all the columns set to true in a given row of /// the matrix. pub fn iter(&self, row: R) -> BitIter<'_, C> { assert!(row.index() < self.num_rows); let (start, end) = self.range(row); BitIter::new(&self.words[start..end]) } /// Returns the number of elements in `row`. pub fn count(&self, row: R) -> usize { let (start, end) = self.range(row); self.words[start..end].iter().map(|e| e.count_ones() as usize).sum() } } impl fmt::Debug for BitMatrix { fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result { /// Forces its contents to print in regular mode instead of alternate mode. struct OneLinePrinter(T); impl fmt::Debug for OneLinePrinter { fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result { write!(fmt, "{:?}", self.0) } } write!(fmt, "BitMatrix({}x{}) ", self.num_rows, self.num_columns)?; let items = self.rows().flat_map(|r| self.iter(r).map(move |c| (r, c))); fmt.debug_set().entries(items.map(OneLinePrinter)).finish() } } /// A fixed-column-size, variable-row-size 2D bit matrix with a moderately /// sparse representation. /// /// Initially, every row has no explicit representation. If any bit within a /// row is set, the entire row is instantiated as `Some()`. /// Furthermore, any previously uninstantiated rows prior to it will be /// instantiated as `None`. Those prior rows may themselves become fully /// instantiated later on if any of their bits are set. /// /// `R` and `C` are index types used to identify rows and columns respectively; /// typically newtyped `usize` wrappers, but they can also just be `usize`. #[derive(Clone, Debug)] pub struct SparseBitMatrix where R: Idx, C: Idx, { num_columns: usize, rows: IndexVec>>, } impl SparseBitMatrix { /// Creates a new empty sparse bit matrix with no rows or columns. pub fn new(num_columns: usize) -> Self { Self { num_columns, rows: IndexVec::new() } } fn ensure_row(&mut self, row: R) -> &mut HybridBitSet { // Instantiate any missing rows up to and including row `row` with an empty HybridBitSet. // Then replace row `row` with a full HybridBitSet if necessary. self.rows.get_or_insert_with(row, || HybridBitSet::new_empty(self.num_columns)) } /// Sets the cell at `(row, column)` to true. Put another way, insert /// `column` to the bitset for `row`. /// /// Returns `true` if this changed the matrix. pub fn insert(&mut self, row: R, column: C) -> bool { self.ensure_row(row).insert(column) } /// Sets the cell at `(row, column)` to false. Put another way, delete /// `column` from the bitset for `row`. Has no effect if `row` does not /// exist. /// /// Returns `true` if this changed the matrix. pub fn remove(&mut self, row: R, column: C) -> bool { match self.rows.get_mut(row) { Some(Some(row)) => row.remove(column), _ => false, } } /// Sets all columns at `row` to false. Has no effect if `row` does /// not exist. pub fn clear(&mut self, row: R) { if let Some(Some(row)) = self.rows.get_mut(row) { row.clear(); } } /// Do the bits from `row` contain `column`? Put another way, is /// the matrix cell at `(row, column)` true? Put yet another way, /// if the matrix represents (transitive) reachability, can /// `row` reach `column`? pub fn contains(&self, row: R, column: C) -> bool { self.row(row).map_or(false, |r| r.contains(column)) } /// Adds the bits from row `read` to the bits from row `write`, and /// returns `true` if anything changed. /// /// This is used when computing transitive reachability because if /// you have an edge `write -> read`, because in that case /// `write` can reach everything that `read` can (and /// potentially more). pub fn union_rows(&mut self, read: R, write: R) -> bool { if read == write || self.row(read).is_none() { return false; } self.ensure_row(write); if let (Some(read_row), Some(write_row)) = self.rows.pick2_mut(read, write) { write_row.union(read_row) } else { unreachable!() } } /// Insert all bits in the given row. pub fn insert_all_into_row(&mut self, row: R) { self.ensure_row(row).insert_all(); } pub fn rows(&self) -> impl Iterator { self.rows.indices() } /// Iterates through all the columns set to true in a given row of /// the matrix. pub fn iter<'a>(&'a self, row: R) -> impl Iterator + 'a { self.row(row).into_iter().flat_map(|r| r.iter()) } pub fn row(&self, row: R) -> Option<&HybridBitSet> { self.rows.get(row)?.as_ref() } /// Intersects `row` with `set`. `set` can be either `BitSet` or /// `HybridBitSet`. Has no effect if `row` does not exist. /// /// Returns true if the row was changed. pub fn intersect_row(&mut self, row: R, set: &Set) -> bool where HybridBitSet: BitRelations, { match self.rows.get_mut(row) { Some(Some(row)) => row.intersect(set), _ => false, } } /// Subtracts `set from `row`. `set` can be either `BitSet` or /// `HybridBitSet`. Has no effect if `row` does not exist. /// /// Returns true if the row was changed. pub fn subtract_row(&mut self, row: R, set: &Set) -> bool where HybridBitSet: BitRelations, { match self.rows.get_mut(row) { Some(Some(row)) => row.subtract(set), _ => false, } } /// Unions `row` with `set`. `set` can be either `BitSet` or /// `HybridBitSet`. /// /// Returns true if the row was changed. pub fn union_row(&mut self, row: R, set: &Set) -> bool where HybridBitSet: BitRelations, { self.ensure_row(row).union(set) } } #[inline] fn num_words(domain_size: T) -> usize { (domain_size.index() + WORD_BITS - 1) / WORD_BITS } #[inline] fn num_chunks(domain_size: T) -> usize { assert!(domain_size.index() > 0); (domain_size.index() + CHUNK_BITS - 1) / CHUNK_BITS } #[inline] fn word_index_and_mask(elem: T) -> (usize, Word) { let elem = elem.index(); let word_index = elem / WORD_BITS; let mask = 1 << (elem % WORD_BITS); (word_index, mask) } #[inline] fn chunk_index(elem: T) -> usize { elem.index() / CHUNK_BITS } #[inline] fn chunk_word_index_and_mask(elem: T) -> (usize, Word) { let chunk_elem = elem.index() % CHUNK_BITS; word_index_and_mask(chunk_elem) } fn clear_excess_bits_in_final_word(domain_size: usize, words: &mut [Word]) { let num_bits_in_final_word = domain_size % WORD_BITS; if num_bits_in_final_word > 0 { let mask = (1 << num_bits_in_final_word) - 1; words[words.len() - 1] &= mask; } } #[inline] fn max_bit(word: Word) -> usize { WORD_BITS - 1 - word.leading_zeros() as usize } /// Integral type used to represent the bit set. pub trait FiniteBitSetTy: BitAnd + BitAndAssign + BitOrAssign + Clone + Copy + Shl + Not + PartialEq + Sized { /// Size of the domain representable by this type, e.g. 64 for `u64`. const DOMAIN_SIZE: u32; /// Value which represents the `FiniteBitSet` having every bit set. const FILLED: Self; /// Value which represents the `FiniteBitSet` having no bits set. const EMPTY: Self; /// Value for one as the integral type. const ONE: Self; /// Value for zero as the integral type. const ZERO: Self; /// Perform a checked left shift on the integral type. fn checked_shl(self, rhs: u32) -> Option; /// Perform a checked right shift on the integral type. fn checked_shr(self, rhs: u32) -> Option; } impl FiniteBitSetTy for u32 { const DOMAIN_SIZE: u32 = 32; const FILLED: Self = Self::MAX; const EMPTY: Self = Self::MIN; const ONE: Self = 1u32; const ZERO: Self = 0u32; fn checked_shl(self, rhs: u32) -> Option { self.checked_shl(rhs) } fn checked_shr(self, rhs: u32) -> Option { self.checked_shr(rhs) } } impl std::fmt::Debug for FiniteBitSet { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{:032b}", self.0) } } impl FiniteBitSetTy for u64 { const DOMAIN_SIZE: u32 = 64; const FILLED: Self = Self::MAX; const EMPTY: Self = Self::MIN; const ONE: Self = 1u64; const ZERO: Self = 0u64; fn checked_shl(self, rhs: u32) -> Option { self.checked_shl(rhs) } fn checked_shr(self, rhs: u32) -> Option { self.checked_shr(rhs) } } impl std::fmt::Debug for FiniteBitSet { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{:064b}", self.0) } } impl FiniteBitSetTy for u128 { const DOMAIN_SIZE: u32 = 128; const FILLED: Self = Self::MAX; const EMPTY: Self = Self::MIN; const ONE: Self = 1u128; const ZERO: Self = 0u128; fn checked_shl(self, rhs: u32) -> Option { self.checked_shl(rhs) } fn checked_shr(self, rhs: u32) -> Option { self.checked_shr(rhs) } } impl std::fmt::Debug for FiniteBitSet { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{:0128b}", self.0) } } /// A fixed-sized bitset type represented by an integer type. Indices outwith than the range /// representable by `T` are considered set. #[derive(Copy, Clone, Eq, PartialEq, Decodable, Encodable)] pub struct FiniteBitSet(pub T); impl FiniteBitSet { /// Creates a new, empty bitset. pub fn new_empty() -> Self { Self(T::EMPTY) } /// Sets the `index`th bit. pub fn set(&mut self, index: u32) { self.0 |= T::ONE.checked_shl(index).unwrap_or(T::ZERO); } /// Unsets the `index`th bit. pub fn clear(&mut self, index: u32) { self.0 &= !T::ONE.checked_shl(index).unwrap_or(T::ZERO); } /// Sets the `i`th to `j`th bits. pub fn set_range(&mut self, range: Range) { let bits = T::FILLED .checked_shl(range.end - range.start) .unwrap_or(T::ZERO) .not() .checked_shl(range.start) .unwrap_or(T::ZERO); self.0 |= bits; } /// Is the set empty? pub fn is_empty(&self) -> bool { self.0 == T::EMPTY } /// Returns the domain size of the bitset. pub fn within_domain(&self, index: u32) -> bool { index < T::DOMAIN_SIZE } /// Returns if the `index`th bit is set. pub fn contains(&self, index: u32) -> Option { self.within_domain(index) .then(|| ((self.0.checked_shr(index).unwrap_or(T::ONE)) & T::ONE) == T::ONE) } } impl Default for FiniteBitSet { fn default() -> Self { Self::new_empty() } }