DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

Git (4fb54ed484)

VCS Links

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988
use crate::vec::{Idx, IndexVec};
use smallvec::SmallVec;
use std::fmt;
use std::iter;
use std::marker::PhantomData;
use std::mem;
use std::slice;

#[cfg(test)]
mod tests;

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.
///
/// 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.
///
/// [`GrowableBitSet`]: struct.GrowableBitSet.html
#[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(&self) -> BitIter<'_, T> {
        BitIter::new(&self.words)
    }

    /// 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> {
    /// 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<T>,
}

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<T> {
        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<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().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<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(&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()
    }
}

/// 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)
}