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< h1 id = "persistentbitvec-and-persistentbitmatrix" > PersistentBitVec and PersistentBitMatrix</ h1 >
< h2 id = "purpose" > Purpose</ h2 >
< p >< code > PersistentBitVec</ code > stores a dense bit vector (presence/absence per slot) backed by a single mmap'd file. It is the binary counterpart of < code > PersistentCompactIntVec</ code > and shares the same lifecycle pattern (builder → close → reader). All bulk operations work on u64 words rather than bytes, giving 8× </ p >
< p > Typical use: converting k-mer count vectors to presence/absence vectors (with optional threshold), then computing set-theoretic distances (Jaccard) or edit distances (Hamming) between samples.</ p >
< p >< code > PersistentBitMatrix</ code > wraps multiple < code > PersistentBitVec</ code > columns in a directory, exposing a column-major binary matrix with row-access API. A single-column bit matrix is a vector at the API level.</ p >
< hr />
< h2 id = "persistentbitvec-single-column-file" > PersistentBitVec — single-column file</ h2 >
< h3 id = "file-format" > File format</ h3 >
< p > Single < code > .pbiv</ code > file.</ p >
< div class = "highlight" >< pre >< span ></ span >< code > offset 0:
magic: [u8; 4] = b" PBIV"
_pad: [u8; 4] = 0 alignment padding
n: u64 number of bits
offset 16:
data: [u64; ⌈n/64⌉] bit words, LSB-first, zero-padded
</ code ></ pre ></ div >
< p >< strong > Header is 16 bytes</ strong > , so data starts at an offset divisible by 8. Since < code > mmap</ code > returns page-aligned memory (≥ 4096-byte aligned), the data slice is u64-aligned, enabling a zero-copy < code > & [u8] → & [u64]</ code > reinterpretation.</ p >
< p >< strong > Bit layout</ strong > : bit < code > i</ code > is in < code > data[i >> 6]</ code > at bit position < code > i & 63</ code > (LSB-first). Bits < code > [n, ⌈n/64⌉×64)</ code > are < strong > always zero</ strong > (padding). This invariant is maintained by all write operations and must be restored by < code > not()</ code > after flipping.</ p >
< p >< strong > Total file size</ strong > : < code > 16 + ⌈n/64⌉ × </ code > bytes.</ p >
< h3 id = "lifecycle" > Lifecycle</ h3 >
< h4 id = "builder-persistentbitvecbuilder" > Builder (< code > PersistentBitVecBuilder</ code > )</ h4 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > struct</ span >< span class = "w" > </ span >< span class = "nc" > PersistentBitVecBuilder</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "n" > mmap</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "nc" > MmapMut</ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > ,</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p > The file and mmap are created immediately at construction. The header is written once at < code > new()</ code > or copied from the source at < code > build_from*()</ code > . < code > close()</ code > is a single flush — there is no tail to append, unlike < code > PersistentCompactIntVec</ code > .</ p >
< p >< strong >< code > new(n: usize, path: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > Creates the file, writes the header, zero-extends to < code > 16 + ⌈n/64⌉×8</ code > bytes, mmaps immediately. All bits default to 0.</ p >
< p >< strong >< code > build_from(source: & PersistentBitVec, path: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > OS-level file copy (no per-bit iteration), then mmap. Initialisation cost: O(file_size).</ p >
< p >< strong >< code > build_from_counts(source: & PersistentCompactIntVec, threshold: u32, path: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > Creates a new file, iterates < code > source</ code > with its merge-scan iterator (O(n)), and writes bits directly into u64 words:</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "c1" > // bit i = 1 iff source[i] > = threshold</ span >
< span class = "n" > words</ span >< span class = "p" > [</ span >< span class = "n" > slot</ span >< span class = "w" > </ span >< span class = "o" > >> </ span >< span class = "w" > </ span >< span class = "mi" > 6</ span >< span class = "p" > ]</ span >< span class = "w" > </ span >< span class = "o" > |=</ span >< span class = "w" > </ span >< span class = "mi" > 1</ span >< span class = "k" > u64</ span >< span class = "w" > </ span >< span class = "o" > << </ span >< span class = "w" > </ span >< span class = "p" > (</ span >< span class = "n" > slot</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mi" > 63</ span >< span class = "p" > );</ span >
</ code ></ pre ></ div >
< p > Handles overflow values (≥ 255) transparently — the count iterator returns the true u32 value regardless.</ p >
< p >< strong >< code > build_from_presence(source: & PersistentCompactIntVec, path: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > Shorthand for < code > build_from_counts(source, 1, path)</ code > .</ p >
< p >< strong > Bit-level access</ strong ></ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > get</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > ,</ span >< span class = "w" > </ span >< span class = "n" > slot</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "kt" > bool</ span >
< span class = "nc" > fn</ span >< span class = "w" > </ span >< span class = "n" > set</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "k" > mut</ span >< span class = "w" > </ span >< span class = "bp" > self</ span >< span class = "p" > ,</ span >< span class = "w" > </ span >< span class = "n" > slot</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > ,</ span >< span class = "w" > </ span >< span class = "n" > value</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > bool</ span >< span class = "p" > )</ span >
</ code ></ pre ></ div >
< p > Byte-level mmap access: < code > mmap[16 + slot/8]</ code > , bit < code > slot % 8</ code > . O(1).</ p >
< p >< strong > Word-level bulk operations</ strong ></ p >
< p > All operate on < code > ⌈n/64⌉</ code > u64 words. O(n/64) per call.</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "n" > builder</ span >< span class = "p" > .</ span >< span class = "n" > and</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "n" > other</ span >< span class = "p" > );</ span >< span class = "w" > </ span >< span class = "c1" > // self[i] & = other[i] for all i</ span >
< span class = "n" > builder</ span >< span class = "p" > .</ span >< span class = "n" > or</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "n" > other</ span >< span class = "p" > );</ span >< span class = "w" > </ span >< span class = "c1" > // self[i] |= other[i]</ span >
< span class = "n" > builder</ span >< span class = "p" > .</ span >< span class = "n" > xor</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "n" > other</ span >< span class = "p" > );</ span >< span class = "w" > </ span >< span class = "c1" > // self[i] ^= other[i]</ span >
< span class = "n" > builder</ span >< span class = "p" > .</ span >< span class = "n" > not</ span >< span class = "p" > ();</ span >< span class = "w" > </ span >< span class = "c1" > // self[i] = !self[i], then re-zero padding bits</ span >
</ code ></ pre ></ div >
< p >< code > and</ code > /< code > or</ code > /< code > xor</ code > read < code > other</ code > 's word slice directly (no allocation). < code > not()</ code > flips all words then masks the last word's padding bits to restore the invariant.</ p >
< p >< strong >< code > close(self) -> io::Result< ()> </ code ></ strong ></ p >
< p > Flushes the mmap. The header was written at construction and is never rewritten. O(1) in Rust code.</ p >
< h4 id = "reader-persistentbitvec" > Reader (< code > PersistentBitVec</ code > )</ h4 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > struct</ span >< span class = "w" > </ span >< span class = "nc" > PersistentBitVec</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "n" > mmap</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "nc" > Mmap</ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "n" > path</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "nc" > PathBuf</ span >< span class = "p" > ,</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< strong >< code > open(path: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > Mmaps the file, validates magic, reads < code > n</ code > from bytes < code > [8..16]</ code > . O(1).</ p >
< p >< strong >< code > get(slot: usize) -> bool</ code ></ strong ></ p >
< p > Byte-level read from < code > mmap[16 + slot/8]</ code > . O(1).</ p >
< p >< strong >< code > iter() -> BitIter< '_> </ code ></ strong ></ p >
< p > Sequential scan, byte by byte, yielding < code > bool</ code > values in slot order. Implements < code > ExactSizeIterator</ code > . O(n).</ p >
< p >< strong > Aggregates</ strong ></ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > count_ones</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "kt" > u64</ span >< span class = "w" > </ span >< span class = "c1" > // popcount over all words; padding bits are 0</ span >
< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > count_zeros</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "kt" > u64</ span >< span class = "w" > </ span >< span class = "c1" > // n - count_ones()</ span >
</ code ></ pre ></ div >
< p >< code > count_ones</ code > iterates < code > ⌈n/64⌉</ code > words and calls < code > u64::count_ones()</ code > (maps to < code > POPCNT</ code > ). O(n/64).</ p >
< p >< strong > Distance methods</ strong ></ p >
< p > Both operate word by word. O(n/64).</ p >
< table >
< thead >
< tr >
< th > Method</ th >
< th > Formula</ th >
< th > Notes</ th >
</ tr >
</ thead >
< tbody >
< tr >
< td >< code > jaccard_dist(& other) -> f64</ code ></ td >
< td >< code > 1 − ∪ </ code ></ td >
< td >< code > (a& b).count_ones()</ code > , < code > (a\|b).count_ones()</ code > per word</ td >
</ tr >
< tr >
< td >< code > hamming_dist(& other) -> u64</ code ></ td >
< td > number of differing bits</ td >
< td >< code > (a^b).count_ones()</ code > per word</ td >
</ tr >
</ tbody >
</ table >
< p > Edge case (both all-zero → union = 0): < code > jaccard_dist</ code > returns 0.0.</ p >
< h3 id = "implementation-notes" > Implementation notes</ h3 >
< h4 id = "u64-word-view" > u64 word view</ h4 >
< p > The unsafe cast from < code > & [u8]</ code > to < code > & [u64]</ code > is sound because:</ p >
< ol >
< li >< code > mmap</ code > base is page-aligned (≥ 4096-byte boundary).</ li >
< li > Data offset = 16, and < code > 16 % 8 == 0</ code > → the data pointer is 8-byte aligned.</ li >
< li > Data length = < code > ⌈n/64⌉ × </ code > bytes — always a multiple of 8.</ li >
</ ol >
< p > This gives zero-copy word-level access with no intermediate allocation.</ p >
< h4 id = "padding-invariant" > Padding invariant</ h4 >
< p > Writing < code > not()</ code > without masking the last word would corrupt < code > count_ones()</ code > , < code > hamming_dist()</ code > , and < code > jaccard_dist()</ code > . The mask applied after flipping is < code > (1u64 << (n % 64)) - 1</ code > (no-op if < code > n % 64 == 0</ code > ). All other operations (< code > and</ code > , < code > or</ code > , < code > xor</ code > ) preserve existing zero padding since they can only clear or preserve bits already set by < code > not()</ code > .</ p >
< h3 id = "complexity" > Complexity</ h3 >
< table >
< thead >
< tr >
< th > Operation</ th >
< th > Time</ th >
< th > Notes</ th >
</ tr >
</ thead >
< tbody >
< tr >
< td >< code > new</ code > / < code > open</ code ></ td >
< td > O(1)</ td >
< td > mmap setup + header parse</ td >
</ tr >
< tr >
< td >< code > get</ code > / < code > set</ code > (builder or reader)</ td >
< td > O(1)</ td >
< td > byte-level mmap</ td >
</ tr >
< tr >
< td >< code > iter()</ code ></ td >
< td > O(n)</ td >
< td > byte-by-byte scan</ td >
</ tr >
< tr >
< td >< code > count_ones</ code > / < code > count_zeros</ code ></ td >
< td > O(n/64)</ td >
< td > POPCNT per u64 word</ td >
</ tr >
< tr >
< td >< code > and</ code > / < code > or</ code > / < code > xor</ code > / < code > not</ code ></ td >
< td > O(n/64)</ td >
< td > word-level bitwise ops</ td >
</ tr >
< tr >
< td >< code > jaccard_dist</ code > / < code > hamming_dist</ code ></ td >
< td > O(n/64)</ td >
< td > word AND/OR/XOR + POPCNT</ td >
</ tr >
< tr >
< td >< code > build_from</ code ></ td >
< td > O(file_size)</ td >
< td > OS copy</ td >
</ tr >
< tr >
< td >< code > build_from_counts</ code > / < code > build_from_presence</ code ></ td >
< td > O(n)</ td >
< td > count iter + word fill</ td >
</ tr >
< tr >
< td >< code > close</ code ></ td >
< td > O(1)</ td >
< td > flush only</ td >
</ tr >
</ tbody >
</ table >
< hr />
< h2 id = "persistentbitmatrix-column-major-directory" > PersistentBitMatrix — column-major directory</ h2 >
< h3 id = "design" > Design</ h3 >
< p > A directory containing < code > meta.json</ code > and N column files < code > col_000000.pbiv</ code > , < code > col_000001.pbiv</ code > , …, each a < code > PersistentBitVec</ code > . Used for presence/absence matrices: one column per genome, one bit per MPHF slot.</ p >
< div class = "highlight" >< pre >< span ></ span >< code > presence/
meta.json {" n" : < n_slots> , " n_cols" : < G> }
col_000000.pbiv genome 0
col_000001.pbiv genome 1
...
</ code ></ pre ></ div >
< p > Column-major layout makes per-genome set operations (Jaccard, Hamming, AND/OR) cache-friendly — each genome is a contiguous file. Row access (which genomes contain a given kmer) requires one O(1) read per column.</ p >
< h3 id = "builder-persistentbitmatrixbuilder" > Builder (< code > PersistentBitMatrixBuilder</ code > )</ h3 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > struct</ span >< span class = "w" > </ span >< span class = "nc" > PersistentBitMatrixBuilder</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "n" > dir</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "nc" > PathBuf</ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "n" > n_cols</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > ,</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< strong >< code > new(n: usize, dir: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > Creates the directory (including parents).</ p >
< p >< strong >< code > add_col(& mut self) -> io::Result< PersistentBitVecBuilder> </ code ></ strong ></ p >
< p > Creates < code > col_NNNNNN.pbiv</ code > for the next column and returns its builder. The caller fills the column and calls < code > builder.close()</ code > before calling < code > add_col</ code > again.</ p >
< p >< strong >< code > close(self) -> io::Result< ()> </ code ></ strong ></ p >
< p > Writes < code > meta.json</ code > with the final < code > n</ code > and < code > n_cols</ code > .</ p >
< h3 id = "reader-persistentbitmatrix" > Reader (< code > PersistentBitMatrix</ code > )</ h3 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > struct</ span >< span class = "w" > </ span >< span class = "nc" > PersistentBitMatrix</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "n" > cols</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "nb" > Vec</ span >< span class = "o" > < </ span >< span class = "n" > PersistentBitVec</ span >< span class = "o" > > </ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > ,</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< strong >< code > open(dir: & Path) -> io::Result< Self> </ code ></ strong ></ p >
< p > Reads < code > meta.json</ code > , opens all < code > col_NNNNNN.pbiv</ code > files.</ p >
< p >< strong >< code > row(slot: usize) -> Box< [bool]> </ code ></ strong ></ p >
< p > Returns the presence vector: < code > [col_0[slot], col_1[slot], …, col_{G-1}[slot]]</ code > . One byte read per column. O(G).</ p >
< p >< strong >< code > col(c: usize) -> & PersistentBitVec</ code ></ strong ></ p >
< p > Direct access to a single column for column-oriented operations.</ p >
< h3 id = "layerdata-implementation" > LayerData implementation</ h3 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > impl</ span >< span class = "w" > </ span >< span class = "n" > LayerData</ span >< span class = "w" > </ span >< span class = "k" > for</ span >< span class = "w" > </ span >< span class = "n" > PersistentBitMatrix</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "k" > type</ span >< span class = "w" > </ span >< span class = "nc" > Item</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "nb" > Box</ span >< span class = "o" > < </ span >< span class = "p" > [</ span >< span class = "kt" > bool</ span >< span class = "p" > ]</ span >< span class = "o" > > </ span >< span class = "p" > ;</ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > open</ span >< span class = "p" > (</ span >< span class = "n" > layer_dir</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kp" > & </ span >< span class = "nc" > Path</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "nc" > OLMResult</ span >< span class = "o" > < </ span >< span class = "bp" > Self</ span >< span class = "o" > > </ span >< span class = "w" > </ span >< span class = "p" > {</ span >< span class = "w" > </ span >< span class = "cm" > /* opens layer_dir/presence/ */</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > read</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > ,</ span >< span class = "w" > </ span >< span class = "n" > slot</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > usize</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "nb" > Box</ span >< span class = "o" > < </ span >< span class = "p" > [</ span >< span class = "kt" > bool</ span >< span class = "p" > ]</ span >< span class = "o" > > </ span >< span class = "w" > </ span >< span class = "p" > {</ span >< span class = "w" > </ span >< span class = "bp" > self</ span >< span class = "p" > .</ span >< span class = "n" > row</ span >< span class = "p" > (</ span >< span class = "n" > slot</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
2026-05-17 10:20:22 +08:00
< hr />
< h2 id = "aggregation-traits-obicompactvectraits" > Aggregation traits — < code > obicompactvec::traits</ code ></ h2 >
< p >< code > PersistentBitMatrix</ code > implements two aggregation traits used by < code > LayeredStore< S> </ code > for cross-layer and cross-partition distance computations.</ p >
< h3 id = "columnweights" > ColumnWeights</ h3 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > impl</ span >< span class = "w" > </ span >< span class = "n" > ColumnWeights</ span >< span class = "w" > </ span >< span class = "k" > for</ span >< span class = "w" > </ span >< span class = "n" > PersistentBitMatrix</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > col_weights</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "nc" > Array1</ span >< span class = "o" > < </ span >< span class = "kt" > u64</ span >< span class = "o" > > </ span >< span class = "w" > </ span >< span class = "c1" > // = self.count_ones()</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< code > col_weights()[c]</ code > = number of set bits in column < code > c</ code > across all slots.</ p >
< h3 id = "bitpartials" > BitPartials</ h3 >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > impl</ span >< span class = "w" > </ span >< span class = "n" > BitPartials</ span >< span class = "w" > </ span >< span class = "k" > for</ span >< span class = "w" > </ span >< span class = "n" > PersistentBitMatrix</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "c1" > // Self-contained partials (additive across layers)</ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > partial_jaccard</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "p" > (</ span >< span class = "n" > Array2</ span >< span class = "o" > < </ span >< span class = "kt" > u64</ span >< span class = "o" > > </ span >< span class = "p" > ,</ span >< span class = "w" > </ span >< span class = "n" > Array2</ span >< span class = "o" > < </ span >< span class = "kt" > u64</ span >< span class = "o" > > </ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "c1" > // (inter, union)</ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > partial_hamming</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "nc" > Array2</ span >< span class = "o" > < </ span >< span class = "kt" > u64</ span >< span class = "o" > > </ span >< span class = "w" > </ span >< span class = "c1" > // differing bits</ span >
< span class = "w" > </ span >< span class = "c1" > // Provided finalisations</ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > jaccard_dist_matrix</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "nc" > Array2</ span >< span class = "o" > < </ span >< span class = "kt" > f64</ span >< span class = "o" > > </ span >
< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > hamming_dist_matrix</ span >< span class = "p" > (</ span >< span class = "o" > & </ span >< span class = "bp" > self</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "nc" > Array2</ span >< span class = "o" > < </ span >< span class = "kt" > u64</ span >< span class = "o" > > </ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< code > partial_jaccard</ code > returns < code > (inter, union)</ code > as a pair because < code > union</ code > is not reconstructible from per-column < code > count_ones()</ code > — it depends on both columns simultaneously. Both components are additively decomposable across < code > (partition, layer)</ code > pairs; the final < code > jaccard_dist_matrix()</ code > is computed from their element-wise sums.</ p >
2026-05-15 21:07:23 +08:00
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