| use crate::indexed_vec::{Idx, IndexVec}; |
| use smallvec::SmallVec; |
| use std::fmt; |
| use std::iter; |
| use std::marker::PhantomData; |
| use std::mem; |
| use std::slice; |
| #[cfg(test)] |
| extern crate test; |
| #[cfg(test)] |
| use test::Bencher; |
| |
| pub type Word = u64; |
| pub const WORD_BYTES: usize = mem::size_of::<Word>(); |
| pub const WORD_BITS: usize = WORD_BYTES * 8; |
| |
| /// A fixed-size bitset type with a dense representation. It does not support |
| /// resizing after creation; use `GrowableBitSet` for that. |
| /// |
| /// `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, Eq, PartialEq, RustcDecodable, RustcEncodable)] |
| pub struct BitSet<T: Idx> { |
| domain_size: usize, |
| words: Vec<Word>, |
| marker: PhantomData<T>, |
| } |
| |
| impl<T: Idx> BitSet<T> { |
| /// Creates a new, empty bitset with a given `domain_size`. |
| #[inline] |
| pub fn new_empty(domain_size: usize) -> BitSet<T> { |
| 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<T> { |
| 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 |
| } |
| |
| /// Gets the domain size. |
| pub fn domain_size(&self) -> usize { |
| self.domain_size |
| } |
| |
| /// Clear all elements. |
| #[inline] |
| pub fn clear(&mut self) { |
| for word in &mut self.words { |
| *word = 0; |
| } |
| } |
| |
| /// Clear excess bits in the final word. |
| fn clear_excess_bits(&mut self) { |
| let num_bits_in_final_word = self.domain_size % WORD_BITS; |
| if num_bits_in_final_word > 0 { |
| let mask = (1 << num_bits_in_final_word) - 1; |
| let final_word_idx = self.words.len() - 1; |
| self.words[final_word_idx] &= mask; |
| } |
| } |
| |
| /// Efficiently overwrite `self` with `other`. |
| pub fn overwrite(&mut self, other: &BitSet<T>) { |
| assert!(self.domain_size == other.domain_size); |
| self.words.clone_from_slice(&other.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<T>) -> 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 |
| } |
| |
| /// Sets all bits to true. |
| pub fn insert_all(&mut self) { |
| for word in &mut self.words { |
| *word = !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 |
| } |
| |
| /// Sets `self = self | other` and returns `true` if `self` changed |
| /// (i.e., if new bits were added). |
| pub fn union(&mut self, other: &impl UnionIntoBitSet<T>) -> bool { |
| other.union_into(self) |
| } |
| |
| /// Sets `self = self - other` and returns `true` if `self` changed. |
| /// (i.e., if any bits were removed). |
| pub fn subtract(&mut self, other: &impl SubtractFromBitSet<T>) -> bool { |
| other.subtract_from(self) |
| } |
| |
| /// Sets `self = self & other` and return `true` if `self` changed. |
| /// (i.e., if any bits were removed). |
| pub fn intersect(&mut self, other: &BitSet<T>) -> bool { |
| assert_eq!(self.domain_size, other.domain_size); |
| bitwise(&mut self.words, &other.words, |a, b| { a & b }) |
| } |
| |
| /// 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<'a>(&'a self) -> BitIter<'a, T> { |
| BitIter { |
| cur: None, |
| iter: self.words.iter().enumerate(), |
| marker: PhantomData, |
| } |
| } |
| |
| /// Duplicates the set as a hybrid set. |
| pub fn to_hybrid(&self) -> HybridBitSet<T> { |
| // 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<T>) -> 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 |
| } |
| } |
| |
| /// This is implemented by all the bitsets so that BitSet::union() can be |
| /// passed any type of bitset. |
| pub trait UnionIntoBitSet<T: Idx> { |
| // Performs `other = other | self`. |
| fn union_into(&self, other: &mut BitSet<T>) -> bool; |
| } |
| |
| /// This is implemented by all the bitsets so that BitSet::subtract() can be |
| /// passed any type of bitset. |
| pub trait SubtractFromBitSet<T: Idx> { |
| // Performs `other = other - self`. |
| fn subtract_from(&self, other: &mut BitSet<T>) -> bool; |
| } |
| |
| impl<T: Idx> UnionIntoBitSet<T> for BitSet<T> { |
| fn union_into(&self, other: &mut BitSet<T>) -> bool { |
| assert_eq!(self.domain_size, other.domain_size); |
| bitwise(&mut other.words, &self.words, |a, b| { a | b }) |
| } |
| } |
| |
| impl<T: Idx> SubtractFromBitSet<T> for BitSet<T> { |
| fn subtract_from(&self, other: &mut BitSet<T>) -> bool { |
| assert_eq!(self.domain_size, other.domain_size); |
| bitwise(&mut other.words, &self.words, |a, b| { a & !b }) |
| } |
| } |
| |
| impl<T: Idx> fmt::Debug for BitSet<T> { |
| fn fmt(&self, w: &mut fmt::Formatter<'_>) -> fmt::Result { |
| w.debug_list() |
| .entries(self.iter()) |
| .finish() |
| } |
| } |
| |
| impl<T: Idx> ToString for BitSet<T> { |
| 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!("{}{:02x}", sep, byte)); |
| |
| if remain <= 8 { break; } |
| word >>= 8; |
| i += 8; |
| sep = '-'; |
| } |
| sep = '|'; |
| } |
| result.push(']'); |
| |
| result |
| } |
| } |
| |
| pub struct BitIter<'a, T: Idx> { |
| cur: Option<(Word, usize)>, |
| iter: iter::Enumerate<slice::Iter<'a, Word>>, |
| marker: PhantomData<T> |
| } |
| |
| impl<'a, T: Idx> Iterator for BitIter<'a, T> { |
| type Item = T; |
| fn next(&mut self) -> Option<T> { |
| loop { |
| if let Some((ref mut word, offset)) = self.cur { |
| let bit_pos = word.trailing_zeros() as usize; |
| if bit_pos != WORD_BITS { |
| let bit = 1 << bit_pos; |
| *word ^= bit; |
| return Some(T::new(bit_pos + offset)) |
| } |
| } |
| |
| let (i, word) = self.iter.next()?; |
| self.cur = Some((*word, WORD_BITS * i)); |
| } |
| } |
| } |
| |
| #[inline] |
| fn bitwise<Op>(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 = false; |
| for (out_elem, in_elem) in out_vec.iter_mut().zip(in_vec.iter()) { |
| let old_val = *out_elem; |
| let new_val = op(old_val, *in_elem); |
| *out_elem = new_val; |
| changed |= old_val != new_val; |
| } |
| changed |
| } |
| |
| 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 `SmallVec` with |
| /// no duplicates; although `SmallVec` can spill its elements to the heap, that |
| /// never happens within this type because of the `SPARSE_MAX` limit. |
| /// |
| /// This type is used by `HybridBitSet`; do not use directly. |
| #[derive(Clone, Debug)] |
| pub struct SparseBitSet<T: Idx> { |
| domain_size: usize, |
| elems: SmallVec<[T; SPARSE_MAX]>, |
| } |
| |
| impl<T: Idx> SparseBitSet<T> { |
| fn new_empty(domain_size: usize) -> Self { |
| SparseBitSet { |
| domain_size, |
| elems: SmallVec::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 >= elem) { |
| 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<T> { |
| 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() |
| } |
| } |
| |
| impl<T: Idx> UnionIntoBitSet<T> for SparseBitSet<T> { |
| fn union_into(&self, other: &mut BitSet<T>) -> bool { |
| assert_eq!(self.domain_size, other.domain_size); |
| let mut changed = false; |
| for elem in self.iter() { |
| changed |= other.insert(*elem); |
| } |
| changed |
| } |
| } |
| |
| impl<T: Idx> SubtractFromBitSet<T> for SparseBitSet<T> { |
| fn subtract_from(&self, other: &mut BitSet<T>) -> bool { |
| assert_eq!(self.domain_size, other.domain_size); |
| let mut changed = false; |
| for elem in self.iter() { |
| changed |= other.remove(*elem); |
| } |
| changed |
| } |
| } |
| |
| /// 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, Debug)] |
| pub enum HybridBitSet<T: Idx> { |
| Sparse(SparseBitSet<T>), |
| Dense(BitSet<T>), |
| } |
| |
| impl<T: Idx> HybridBitSet<T> { |
| pub fn new_empty(domain_size: usize) -> Self { |
| HybridBitSet::Sparse(SparseBitSet::new_empty(domain_size)) |
| } |
| |
| 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<T>) -> 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(), |
| } |
| } |
| |
| 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_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), |
| } |
| } |
| |
| pub fn union(&mut self, other: &HybridBitSet<T>) -> bool { |
| match self { |
| HybridBitSet::Sparse(self_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. |
| assert_eq!(self.domain_size(), other.domain_size()); |
| let mut changed = false; |
| for elem in other_sparse.iter() { |
| changed |= self.insert(*elem); |
| } |
| changed |
| } |
| HybridBitSet::Dense(other_dense) => { |
| // `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_dense.clone(); |
| let changed = new_dense.reverse_union_sparse(self_sparse); |
| *self = HybridBitSet::Dense(new_dense); |
| changed |
| } |
| } |
| } |
| |
| HybridBitSet::Dense(self_dense) => self_dense.union(other), |
| } |
| } |
| |
| /// Converts to a dense set, consuming itself in the process. |
| pub fn to_dense(self) -> BitSet<T> { |
| 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()), |
| } |
| } |
| } |
| |
| impl<T: Idx> UnionIntoBitSet<T> for HybridBitSet<T> { |
| fn union_into(&self, other: &mut BitSet<T>) -> bool { |
| match self { |
| HybridBitSet::Sparse(sparse) => sparse.union_into(other), |
| HybridBitSet::Dense(dense) => dense.union_into(other), |
| } |
| } |
| } |
| |
| impl<T: Idx> SubtractFromBitSet<T> for HybridBitSet<T> { |
| fn subtract_from(&self, other: &mut BitSet<T>) -> bool { |
| match self { |
| HybridBitSet::Sparse(sparse) => sparse.subtract_from(other), |
| HybridBitSet::Dense(dense) => dense.subtract_from(other), |
| } |
| } |
| } |
| |
| 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<T> { |
| match self { |
| HybridIter::Sparse(sparse) => sparse.next().map(|e| *e), |
| 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<T: Idx> { |
| bit_set: BitSet<T>, |
| } |
| |
| impl<T: Idx> GrowableBitSet<T> { |
| /// 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<T> { |
| GrowableBitSet { bit_set: BitSet::new_empty(0) } |
| } |
| |
| pub fn with_capacity(capacity: usize) -> GrowableBitSet<T> { |
| 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) |
| } |
| |
| #[inline] |
| pub fn contains(&self, elem: T) -> bool { |
| let (word_index, mask) = word_index_and_mask(elem); |
| if let Some(word) = self.bit_set.words.get(word_index) { |
| (word & mask) != 0 |
| } else { |
| false |
| } |
| } |
| } |
| |
| /// 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, Debug, Eq, PartialEq, RustcDecodable, RustcEncodable)] |
| pub struct BitMatrix<R: Idx, C: Idx> { |
| num_rows: usize, |
| num_columns: usize, |
| words: Vec<Word>, |
| marker: PhantomData<(R, C)>, |
| } |
| |
| impl<R: Idx, C: Idx> BitMatrix<R, C> { |
| /// Creates a new `rows x columns` matrix, initially empty. |
| pub fn new(num_rows: usize, num_columns: usize) -> BitMatrix<R, C> { |
| // 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<C>, num_rows: usize) -> BitMatrix<R, C> { |
| 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<Item = R> { |
| (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<C> { |
| 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 (read_start..read_end).zip(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<C>, 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 (0..with.words().len()).zip(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; |
| } |
| self.clear_excess_bits(row); |
| } |
| |
| /// Clear excess bits in the final word of the row. |
| fn clear_excess_bits(&mut self, row: R) { |
| let num_bits_in_final_word = self.num_columns % WORD_BITS; |
| if num_bits_in_final_word > 0 { |
| let mask = (1 << num_bits_in_final_word) - 1; |
| let (_, end) = self.range(row); |
| let final_word_idx = end - 1; |
| self.words[final_word_idx] &= mask; |
| } |
| } |
| |
| /// 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<'a>(&'a self, row: R) -> BitIter<'a, C> { |
| assert!(row.index() < self.num_rows); |
| let (start, end) = self.range(row); |
| BitIter { |
| cur: None, |
| iter: self.words[start..end].iter().enumerate(), |
| marker: PhantomData, |
| } |
| } |
| |
| /// 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() |
| } |
| } |
| |
| /// 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(<HybridBitSet>)`. |
| /// 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<R, C> |
| where |
| R: Idx, |
| C: Idx, |
| { |
| num_columns: usize, |
| rows: IndexVec<R, Option<HybridBitSet<C>>>, |
| } |
| |
| impl<R: Idx, C: Idx> SparseBitMatrix<R, C> { |
| /// 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<C> { |
| // Instantiate any missing rows up to and including row `row` with an |
| // empty HybridBitSet. |
| self.rows.ensure_contains_elem(row, || None); |
| |
| // Then replace row `row` with a full HybridBitSet if necessary. |
| let num_columns = self.num_columns; |
| self.rows[row].get_or_insert_with(|| HybridBitSet::new_empty(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) |
| } |
| |
| /// 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!() |
| } |
| } |
| |
| /// Union a row, `from`, into the `into` row. |
| pub fn union_into_row(&mut self, into: R, from: &HybridBitSet<C>) -> bool { |
| self.ensure_row(into).union(from) |
| } |
| |
| /// 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<Item = R> { |
| 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<Item = C> + 'a { |
| self.row(row).into_iter().flat_map(|r| r.iter()) |
| } |
| |
| pub fn row(&self, row: R) -> Option<&HybridBitSet<C>> { |
| if let Some(Some(row)) = self.rows.get(row) { |
| Some(row) |
| } else { |
| None |
| } |
| } |
| } |
| |
| #[inline] |
| fn num_words<T: Idx>(domain_size: T) -> usize { |
| (domain_size.index() + WORD_BITS - 1) / WORD_BITS |
| } |
| |
| #[inline] |
| fn word_index_and_mask<T: Idx>(elem: T) -> (usize, Word) { |
| let elem = elem.index(); |
| let word_index = elem / WORD_BITS; |
| let mask = 1 << (elem % WORD_BITS); |
| (word_index, mask) |
| } |
| |
| #[test] |
| fn test_new_filled() { |
| for i in 0..128 { |
| let idx_buf = BitSet::new_filled(i); |
| let elems: Vec<usize> = idx_buf.iter().collect(); |
| let expected: Vec<usize> = (0..i).collect(); |
| assert_eq!(elems, expected); |
| } |
| } |
| |
| #[test] |
| fn bitset_iter_works() { |
| let mut bitset: BitSet<usize> = BitSet::new_empty(100); |
| bitset.insert(1); |
| bitset.insert(10); |
| bitset.insert(19); |
| bitset.insert(62); |
| bitset.insert(63); |
| bitset.insert(64); |
| bitset.insert(65); |
| bitset.insert(66); |
| bitset.insert(99); |
| assert_eq!( |
| bitset.iter().collect::<Vec<_>>(), |
| [1, 10, 19, 62, 63, 64, 65, 66, 99] |
| ); |
| } |
| |
| #[test] |
| fn bitset_iter_works_2() { |
| let mut bitset: BitSet<usize> = BitSet::new_empty(320); |
| bitset.insert(0); |
| bitset.insert(127); |
| bitset.insert(191); |
| bitset.insert(255); |
| bitset.insert(319); |
| assert_eq!(bitset.iter().collect::<Vec<_>>(), [0, 127, 191, 255, 319]); |
| } |
| |
| #[test] |
| fn union_two_sets() { |
| let mut set1: BitSet<usize> = BitSet::new_empty(65); |
| let mut set2: BitSet<usize> = BitSet::new_empty(65); |
| assert!(set1.insert(3)); |
| assert!(!set1.insert(3)); |
| assert!(set2.insert(5)); |
| assert!(set2.insert(64)); |
| assert!(set1.union(&set2)); |
| assert!(!set1.union(&set2)); |
| assert!(set1.contains(3)); |
| assert!(!set1.contains(4)); |
| assert!(set1.contains(5)); |
| assert!(!set1.contains(63)); |
| assert!(set1.contains(64)); |
| } |
| |
| #[test] |
| fn hybrid_bitset() { |
| let mut sparse038: HybridBitSet<usize> = HybridBitSet::new_empty(256); |
| assert!(sparse038.is_empty()); |
| assert!(sparse038.insert(0)); |
| assert!(sparse038.insert(1)); |
| assert!(sparse038.insert(8)); |
| assert!(sparse038.insert(3)); |
| assert!(!sparse038.insert(3)); |
| assert!(sparse038.remove(1)); |
| assert!(!sparse038.is_empty()); |
| assert_eq!(sparse038.iter().collect::<Vec<_>>(), [0, 3, 8]); |
| |
| for i in 0..256 { |
| if i == 0 || i == 3 || i == 8 { |
| assert!(sparse038.contains(i)); |
| } else { |
| assert!(!sparse038.contains(i)); |
| } |
| } |
| |
| let mut sparse01358 = sparse038.clone(); |
| assert!(sparse01358.insert(1)); |
| assert!(sparse01358.insert(5)); |
| assert_eq!(sparse01358.iter().collect::<Vec<_>>(), [0, 1, 3, 5, 8]); |
| |
| let mut dense10 = HybridBitSet::new_empty(256); |
| for i in 0..10 { |
| assert!(dense10.insert(i)); |
| } |
| assert!(!dense10.is_empty()); |
| assert_eq!(dense10.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]); |
| |
| let mut dense256 = HybridBitSet::new_empty(256); |
| assert!(dense256.is_empty()); |
| dense256.insert_all(); |
| assert!(!dense256.is_empty()); |
| for i in 0..256 { |
| assert!(dense256.contains(i)); |
| } |
| |
| assert!(sparse038.superset(&sparse038)); // sparse + sparse (self) |
| assert!(sparse01358.superset(&sparse038)); // sparse + sparse |
| assert!(dense10.superset(&sparse038)); // dense + sparse |
| assert!(dense10.superset(&dense10)); // dense + dense (self) |
| assert!(dense256.superset(&dense10)); // dense + dense |
| |
| let mut hybrid = sparse038; |
| assert!(!sparse01358.union(&hybrid)); // no change |
| assert!(hybrid.union(&sparse01358)); |
| assert!(hybrid.superset(&sparse01358) && sparse01358.superset(&hybrid)); |
| assert!(!dense10.union(&sparse01358)); |
| assert!(!dense256.union(&dense10)); |
| let mut dense = dense10; |
| assert!(dense.union(&dense256)); |
| assert!(dense.superset(&dense256) && dense256.superset(&dense)); |
| assert!(hybrid.union(&dense256)); |
| assert!(hybrid.superset(&dense256) && dense256.superset(&hybrid)); |
| |
| assert_eq!(dense256.iter().count(), 256); |
| let mut dense0 = dense256; |
| for i in 0..256 { |
| assert!(dense0.remove(i)); |
| } |
| assert!(!dense0.remove(0)); |
| assert!(dense0.is_empty()); |
| } |
| |
| #[test] |
| fn grow() { |
| let mut set: GrowableBitSet<usize> = GrowableBitSet::with_capacity(65); |
| for index in 0..65 { |
| assert!(set.insert(index)); |
| assert!(!set.insert(index)); |
| } |
| set.ensure(128); |
| |
| // Check if the bits set before growing are still set |
| for index in 0..65 { |
| assert!(set.contains(index)); |
| } |
| |
| // Check if the new bits are all un-set |
| for index in 65..128 { |
| assert!(!set.contains(index)); |
| } |
| |
| // Check that we can set all new bits without running out of bounds |
| for index in 65..128 { |
| assert!(set.insert(index)); |
| assert!(!set.insert(index)); |
| } |
| } |
| |
| #[test] |
| fn matrix_intersection() { |
| let mut matrix: BitMatrix<usize, usize> = BitMatrix::new(200, 200); |
| |
| // (*) Elements reachable from both 2 and 65. |
| |
| matrix.insert(2, 3); |
| matrix.insert(2, 6); |
| matrix.insert(2, 10); // (*) |
| matrix.insert(2, 64); // (*) |
| matrix.insert(2, 65); |
| matrix.insert(2, 130); |
| matrix.insert(2, 160); // (*) |
| |
| matrix.insert(64, 133); |
| |
| matrix.insert(65, 2); |
| matrix.insert(65, 8); |
| matrix.insert(65, 10); // (*) |
| matrix.insert(65, 64); // (*) |
| matrix.insert(65, 68); |
| matrix.insert(65, 133); |
| matrix.insert(65, 160); // (*) |
| |
| let intersection = matrix.intersect_rows(2, 64); |
| assert!(intersection.is_empty()); |
| |
| let intersection = matrix.intersect_rows(2, 65); |
| assert_eq!(intersection, &[10, 64, 160]); |
| } |
| |
| #[test] |
| fn matrix_iter() { |
| let mut matrix: BitMatrix<usize, usize> = BitMatrix::new(64, 100); |
| matrix.insert(3, 22); |
| matrix.insert(3, 75); |
| matrix.insert(2, 99); |
| matrix.insert(4, 0); |
| matrix.union_rows(3, 5); |
| matrix.insert_all_into_row(6); |
| |
| let expected = [99]; |
| let mut iter = expected.iter(); |
| for i in matrix.iter(2) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| let expected = [22, 75]; |
| let mut iter = expected.iter(); |
| assert_eq!(matrix.count(3), expected.len()); |
| for i in matrix.iter(3) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| let expected = [0]; |
| let mut iter = expected.iter(); |
| assert_eq!(matrix.count(4), expected.len()); |
| for i in matrix.iter(4) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| let expected = [22, 75]; |
| let mut iter = expected.iter(); |
| assert_eq!(matrix.count(5), expected.len()); |
| for i in matrix.iter(5) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| assert_eq!(matrix.count(6), 100); |
| let mut count = 0; |
| for (idx, i) in matrix.iter(6).enumerate() { |
| assert_eq!(idx, i); |
| count += 1; |
| } |
| assert_eq!(count, 100); |
| |
| if let Some(i) = matrix.iter(7).next() { |
| panic!("expected no elements in row, but contains element {:?}", i); |
| } |
| } |
| |
| #[test] |
| fn sparse_matrix_iter() { |
| let mut matrix: SparseBitMatrix<usize, usize> = SparseBitMatrix::new(100); |
| matrix.insert(3, 22); |
| matrix.insert(3, 75); |
| matrix.insert(2, 99); |
| matrix.insert(4, 0); |
| matrix.union_rows(3, 5); |
| |
| let expected = [99]; |
| let mut iter = expected.iter(); |
| for i in matrix.iter(2) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| let expected = [22, 75]; |
| let mut iter = expected.iter(); |
| for i in matrix.iter(3) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| let expected = [0]; |
| let mut iter = expected.iter(); |
| for i in matrix.iter(4) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| |
| let expected = [22, 75]; |
| let mut iter = expected.iter(); |
| for i in matrix.iter(5) { |
| let j = *iter.next().unwrap(); |
| assert_eq!(i, j); |
| } |
| assert!(iter.next().is_none()); |
| } |
| |
| /// Merge dense hybrid set into empty sparse hybrid set. |
| #[bench] |
| fn union_hybrid_sparse_empty_to_dense(b: &mut Bencher) { |
| let mut pre_dense: HybridBitSet<usize> = HybridBitSet::new_empty(256); |
| for i in 0..10 { |
| assert!(pre_dense.insert(i)); |
| } |
| let pre_sparse: HybridBitSet<usize> = HybridBitSet::new_empty(256); |
| b.iter(|| { |
| let dense = pre_dense.clone(); |
| let mut sparse = pre_sparse.clone(); |
| sparse.union(&dense); |
| }) |
| } |
| |
| /// Merge dense hybrid set into full hybrid set with same indices. |
| #[bench] |
| fn union_hybrid_sparse_full_to_dense(b: &mut Bencher) { |
| let mut pre_dense: HybridBitSet<usize> = HybridBitSet::new_empty(256); |
| for i in 0..10 { |
| assert!(pre_dense.insert(i)); |
| } |
| let mut pre_sparse: HybridBitSet<usize> = HybridBitSet::new_empty(256); |
| for i in 0..SPARSE_MAX { |
| assert!(pre_sparse.insert(i)); |
| } |
| b.iter(|| { |
| let dense = pre_dense.clone(); |
| let mut sparse = pre_sparse.clone(); |
| sparse.union(&dense); |
| }) |
| } |
| |
| /// Merge dense hybrid set into full hybrid set with indices over the whole domain. |
| #[bench] |
| fn union_hybrid_sparse_domain_to_dense(b: &mut Bencher) { |
| let mut pre_dense: HybridBitSet<usize> = HybridBitSet::new_empty(SPARSE_MAX*64); |
| for i in 0..10 { |
| assert!(pre_dense.insert(i)); |
| } |
| let mut pre_sparse: HybridBitSet<usize> = HybridBitSet::new_empty(SPARSE_MAX*64); |
| for i in 0..SPARSE_MAX { |
| assert!(pre_sparse.insert(i*64)); |
| } |
| b.iter(|| { |
| let dense = pre_dense.clone(); |
| let mut sparse = pre_sparse.clone(); |
| sparse.union(&dense); |
| }) |
| } |
| |
| /// Merge dense hybrid set into empty hybrid set where the domain is very small. |
| #[bench] |
| fn union_hybrid_sparse_empty_small_domain(b: &mut Bencher) { |
| let mut pre_dense: HybridBitSet<usize> = HybridBitSet::new_empty(SPARSE_MAX); |
| for i in 0..SPARSE_MAX { |
| assert!(pre_dense.insert(i)); |
| } |
| let pre_sparse: HybridBitSet<usize> = HybridBitSet::new_empty(SPARSE_MAX); |
| b.iter(|| { |
| let dense = pre_dense.clone(); |
| let mut sparse = pre_sparse.clone(); |
| sparse.union(&dense); |
| }) |
| } |
| |
| /// Merge dense hybrid set into full hybrid set where the domain is very small. |
| #[bench] |
| fn union_hybrid_sparse_full_small_domain(b: &mut Bencher) { |
| let mut pre_dense: HybridBitSet<usize> = HybridBitSet::new_empty(SPARSE_MAX); |
| for i in 0..SPARSE_MAX { |
| assert!(pre_dense.insert(i)); |
| } |
| let mut pre_sparse: HybridBitSet<usize> = HybridBitSet::new_empty(SPARSE_MAX); |
| for i in 0..SPARSE_MAX { |
| assert!(pre_sparse.insert(i)); |
| } |
| b.iter(|| { |
| let dense = pre_dense.clone(); |
| let mut sparse = pre_sparse.clone(); |
| sparse.union(&dense); |
| }) |
| } |
