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< h1 id = "superkmer-implementation" > SuperKmer — implementation</ h1 >
< h2 id = "memory-layout" > Memory layout</ h2 >
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< p >< code > SuperKmer</ code > holds two separate fields:</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > pub</ span >< span class = "w" > </ span >< span class = "k" > struct</ span >< span class = "w" > </ span >< span class = "nc" > SuperKmer</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "k" > pub</ span >< span class = "p" > (</ span >< span class = "k" > crate</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "n" > count</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > u32</ span >< span class = "p" > ,</ span >
< span class = "w" > </ span >< span class = "k" > pub</ span >< span class = "p" > (</ span >< span class = "k" > crate</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "n" > inner</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "nc" > PackedSeq</ span >< span class = "p" > ,</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< code > PackedSeq</ code > stores a 2-bit packed DNA sequence as a heap-allocated < code > Box< [u8]> </ code > plus a < code > tail: u8</ code > field:</ p >
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< table >
< thead >
< tr >
< th > Field</ th >
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< th > Type</ th >
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< th > Role</ th >
</ tr >
</ thead >
< tbody >
< tr >
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< td >< code > tail</ code ></ td >
< td >< code > u8</ code ></ td >
< td > Number of valid nucleotides in the last byte: 0 encodes 4, 1– </ td >
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</ tr >
< tr >
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< td >< code > seq</ code ></ td >
< td >< code > Box< [u8]> </ code ></ td >
< td > 2-bit packed bytes, nucleotide 0 at bits 7– < code > seq[0]</ code ></ td >
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</ tr >
</ tbody >
</ table >
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< p > Nucleotide length is recovered without storing it explicitly:</ p >
< div class = "highlight" >< pre >< span ></ span >< code > seql = (seq.len() - 1) * 4 + tail_count(tail)
</ code ></ pre ></ div >
< p > There is no packed header word — < code > count</ code > and the sequence live in separate fields.</ p >
< p > The on-disk binary format (produced by < code > write_to_binary</ code > ) is:</ p >
< div class = "highlight" >< pre >< span ></ span >< code > [varint(count)] [u8: seql −
</ code ></ pre ></ div >
< p >< code > seql − </ code > fits in a < code > u8</ code > when < code > n_kmers = seql − </ code > . If a super-kmer exceeds 256 kmers, < code > write_to_binary</ code > splits it into overlapping chunks (k− < code > read_from_binary</ code > .</ p >
< p > The public accessors operate on the struct fields directly:</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > seql</ 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" > usize</ 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" > inner</ span >< span class = "p" > .</ span >< span class = "n" > seql</ span >< span class = "p" > ()</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > count</ 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" > u32</ 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" > count</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > increment</ 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 = "p" > {</ span >< span class = "w" > </ span >< span class = "bp" > self</ span >< span class = "p" > .</ span >< span class = "n" > count</ span >< span class = "w" > </ span >< span class = "o" > +=</ span >< span class = "w" > </ span >< span class = "mi" > 1</ span >< span class = "p" > ;</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > add</ 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" > n</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > u32</ span >< span class = "p" > )</ 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" > count</ span >< span class = "w" > </ span >< span class = "o" > +=</ span >< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "p" > ;</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > set_count</ 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" > n</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > u32</ span >< span class = "p" > )</ 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" > count</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "p" > ;</ span >< span class = "w" > </ span >< span class = "p" > }</ span >
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</ code ></ pre ></ div >
< h2 id = "ascii-encoding-and-decoding" > ASCII encoding and decoding</ h2 >
< p > Two lookup tables handle ASCII ↔ 2-bit conversion:</ p >
< ul >
< li >< strong >< code > ENC: [u8; 32]</ code ></ strong > — indexed by < code > b & 0x1F</ code > (lower 5 bits of the ASCII byte). Maps A/a→0, C/c→1, G/g→2, T/t and U/u→3; ambiguous bases and unknowns silently map to 0 (A). 32 entries, fits entirely in L1 cache. Upper- and lowercase are handled identically.</ li >
< li >< strong >< code > DEC4: [u32; 256]</ code ></ strong > — maps a packed byte (4 nucleotides) to 4 ASCII characters packed as a big-endian < code > u32</ code > . 1 KB total, fits in L1 cache. One lookup per output byte yields 4 decoded characters.</ li >
</ ul >
< p > Encoding 4 nucleotides into one byte:</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "n" > byte</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "n" > ENC</ span >< span class = "p" > [</ span >< span class = "n" > c0</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mh" > 0x1F</ span >< span class = "p" > ]</ span >< span class = "w" > </ span >< span class = "o" > << </ span >< span class = "w" > </ span >< span class = "mi" > 6</ span >< span class = "w" > </ span >< span class = "o" > |</ span >< span class = "w" > </ span >< span class = "n" > ENC</ span >< span class = "p" > [</ span >< span class = "n" > c1</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mh" > 0x1F</ span >< span class = "p" > ]</ span >< span class = "w" > </ span >< span class = "o" > << </ span >< span class = "w" > </ span >< span class = "mi" > 4</ span >< span class = "w" > </ span >< span class = "o" > |</ span >< span class = "w" > </ span >< span class = "n" > ENC</ span >< span class = "p" > [</ span >< span class = "n" > c2</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mh" > 0x1F</ span >< span class = "p" > ]</ span >< span class = "w" > </ span >< span class = "o" > << </ span >< span class = "w" > </ span >< span class = "mi" > 2</ span >< span class = "w" > </ span >< span class = "o" > |</ span >< span class = "w" > </ span >< span class = "n" > ENC</ span >< span class = "p" > [</ span >< span class = "n" > c3</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mh" > 0x1F</ span >< span class = "p" > ]</ span >
</ code ></ pre ></ div >
< p > Decoding one byte into 4 ASCII characters:</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "n" > DEC4</ span >< span class = "p" > [</ span >< span class = "n" > byte</ span >< span class = "p" > ].</ span >< span class = "n" > to_be_bytes</ span >< span class = "p" > ()</ span >< span class = "w" > </ span >< span class = "c1" > // [nuc0, nuc1, nuc2, nuc3] in ASCII</ span >
</ code ></ pre ></ div >
< h2 id = "reverse-complement" > Reverse complement</ h2 >
< p > The reverse complement is computed < strong > in place</ strong > with zero allocation in two steps.</ p >
< p >< strong > Step 1 — byte swap with < code > REVCOMP4</ code > .</ strong > A 256-byte lookup table < code > REVCOMP4</ code > maps each byte (4 nucleotides) to its reverse complement. Bytes are swapped from the outside in, applying < code > REVCOMP4</ code > to each:</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > const</ span >< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > revcomp4</ span >< span class = "p" > (</ span >< span class = "n" > x</ span >< span class = "p" > :</ span >< span class = "w" > </ span >< span class = "kt" > u8</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "p" > -> </ span >< span class = "w" > </ span >< span class = "kt" > u8</ span >< span class = "w" > </ span >< span class = "p" > {</ span >
< span class = "w" > </ span >< span class = "kd" > let</ span >< span class = "w" > </ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "o" > !</ span >< span class = "n" > x</ span >< span class = "p" > ;</ span >< span class = "w" > </ span >< span class = "c1" > // complement all bases</ span >
< span class = "w" > </ span >< span class = "kd" > let</ span >< span class = "w" > </ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "p" > (</ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > >> </ span >< span class = "w" > </ span >< span class = "mi" > 4</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "o" > |</ span >< span class = "w" > </ span >< span class = "p" > (</ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > << </ span >< span class = "w" > </ span >< span class = "mi" > 4</ span >< span class = "p" > );</ span >< span class = "w" > </ span >< span class = "c1" > // swap nibbles</ span >
< span class = "w" > </ span >< span class = "kd" > let</ span >< span class = "w" > </ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "p" > ((</ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > >> </ span >< span class = "w" > </ span >< span class = "mi" > 2</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mh" > 0x33</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "o" > |</ span >< span class = "w" > </ span >< span class = "p" > ((</ span >< span class = "n" > x</ span >< span class = "w" > </ span >< span class = "o" > & </ span >< span class = "w" > </ span >< span class = "mh" > 0x33</ span >< span class = "p" > )</ span >< span class = "w" > </ span >< span class = "o" > << </ span >< span class = "w" > </ span >< span class = "mi" > 2</ span >< span class = "p" > );</ span >< span class = "w" > </ span >< span class = "c1" > // swap 2-bit groups</ span >
< span class = "w" > </ span >< span class = "n" > x</ span >
< span class = "p" > }</ span >
</ code ></ pre ></ div >
< p >< code > REVCOMP4</ code > is 256 bytes (fits in L1 cache), computed at compile time. No endianness dependency — all operations are pure arithmetic on byte values.</ p >
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< p >< strong > Step 2 — realignment.</ strong > After step 1, < code > padding = n × − × </ code > spurious bits (complements of the original padding A's) appear at the start of the array. They are flushed left using < code > BitSlice< u8, Msb0> ::rotate_left(padding)</ code > from the < code > bitvec</ code > crate, which is SIMD-accelerated. The trailing < code > padding</ code > bits are then zeroed:</ p >
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< div class = "highlight" >< pre >< span ></ span >< code >< span class = "kd" > let</ span >< span class = "w" > </ span >< span class = "n" > seql</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "bp" > self</ span >< span class = "p" > .</ span >< span class = "n" > seql</ span >< span class = "p" > ();</ span >
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< span class = "n" > shift</ span >< span class = "w" > </ span >< span class = "o" > =</ span >< span class = "w" > </ span >< span class = "n" > n</ span >< span class = "w" > </ span >< span class = "o" > *</ span >< span class = "w" > </ span >< span class = "mi" > 8</ span >< span class = "w" > </ span >< span class = "o" > -</ span >< span class = "w" > </ span >< span class = "n" > seql</ span >< span class = "w" > </ span >< span class = "o" > *</ span >< span class = "w" > </ span >< span class = "mi" > 2</ span >< span class = "w" > </ span >< span class = "c1" > // number of padding bits</ span >
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< span class = "n" > bits</ span >< span class = "p" > .</ span >< span class = "n" > rotate_left</ span >< span class = "p" > (</ span >< span class = "n" > shift</ span >< span class = "p" > )</ span >
< span class = "n" > bits</ span >< span class = "p" > [</ span >< span class = "n" > len</ span >< span class = "w" > </ span >< span class = "o" > -</ span >< span class = "w" > </ span >< span class = "n" > shift</ span >< span class = "o" > ..</ span >< span class = "p" > ].</ span >< span class = "n" > fill</ span >< span class = "p" > (</ span >< span class = "kc" > false</ span >< span class = "p" > )</ span >
</ code ></ pre ></ div >
< p >< code > Msb0</ code > ordering makes the bit layout hardware-independent.</ p >
< div class = "admonition abstract" >
< p class = "admonition-title" > Algorithm — Super-kmer canonisation</ p >
< div class = "highlight" >< pre >< span ></ span >< code > procedure SuperKmerCanonical(seq, SEQL):
for i ← 0 to SEQL −
fwd ← nucleotide(seq, i)
rev ← complement(nucleotide(seq, SEQL − −
if fwd < rev: return seq -- forward is canonical
if fwd > rev: return SuperKmerRevcomp(seq, SEQL) -- revcomp is canonical
return seq -- palindrome: either orientation valid
</ code ></ pre ></ div >
</ div >
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< h2 id = "minimizer-sliding-window" > Minimizer sliding window</ h2 >
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< p > Super-kmers are built by < code > SuperKmerIter</ code > (crate < code > obiskbuilder</ code > ), which tracks the current minimizer with a < strong > monotonic deque</ strong > (< code > Ring< MmerItem, 32> </ code > ) inside < code > RollingStat</ code > , a rolling-window entropy and minimizer tracker.</ p >
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< p > Each deque entry stores:</ p >
< table >
< thead >
< tr >
< th > Field</ th >
< th > Type</ th >
< th > Purpose</ th >
</ tr >
</ thead >
< tbody >
< tr >
< td >< code > position</ code ></ td >
< td > usize</ td >
< td > 0-based start of this m-mer in the segment</ td >
</ tr >
< tr >
< td >< code > canonical</ code ></ td >
< td > u64</ td >
< td > right-aligned canonical m-mer value (lex-min of fwd and rc); used as partition key</ td >
</ tr >
< tr >
< td >< code > hash</ code ></ td >
< td > u64</ td >
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< td >< code > hash_kmer(canonical << (64 − </ code > — ordering key for random minimizer selection</ td >
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</ tr >
</ tbody >
</ table >
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< p > The hash uses the seeded splitmix64 finalizer (< code > mix64(raw ^ 0x9e3779b97f4a7c15)</ code > ), the same function as < code > kmer::hash_kmer</ code > .</ p >
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< p > On each new nucleotide, once the window is full, the deque is updated:</ p >
< div class = "admonition abstract" >
< p class = "admonition-title" > Algorithm — minimizer deque update</ p >
< div class = "highlight" >< pre >< span ></ span >< code > procedure UpdateMinimizer(deque, position, canonical, hash, k, received):
-- pop dominated entries from the back
while deque.back.hash ≥ hash:
deque.pop_back()
deque.push_back({position, canonical, hash})
-- evict expired entries from the front
while deque.front.position + k < received:
deque.pop_front()
</ code ></ pre ></ div >
</ div >
< p > The front of the deque is always the current minimizer. Because the deque is maintained in strictly increasing hash order, each entry is popped at most once — O(1) amortized per nucleotide.</ p >
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< p > A super-kmer boundary is emitted when the minimizer changes: < code > current_minimizer != prev_minimizer</ code > . < code > SuperKmerIter</ code > also emits a boundary when:</ p >
< ul >
< li > entropy of the current k-mer falls at or below the threshold θ (cursor retreated by k− </ li >
< li > super-kmer length reaches 256 nucleotides (cursor retreated by k)</ li >
</ ul >
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< h2 id = "kmer-extraction" > Kmer extraction</ h2 >
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< p > A k-mer is extracted from a super-kmer with < code > SuperKmer::kmer(i)</ code > , which delegates to < code > PackedSeq::extract::< KLen> (i)</ code > and returns a < code > Kmer</ code > — a left-aligned < code > u64</ code > newtype (see < a href = "../kmer/" > Kmer implementation</ a > ):</ p >
< div class = "highlight" >< pre >< span ></ span >< code >< span class = "k" > pub</ span >< span class = "w" > </ span >< span class = "k" > fn</ span >< span class = "w" > </ span >< span class = "nf" > kmer</ 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" > i</ 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" > Result</ span >< span class = "o" > < </ span >< span class = "n" > Kmer</ span >< span class = "p" > ,</ span >< span class = "w" > </ span >< span class = "n" > KmerError</ span >< span class = "o" > > </ span >
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</ code ></ pre ></ div >
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< p > The bit slice < code > seq[i*2 .. (i+k)*2]</ code > (Msb0 order) is loaded as a < code > u64</ code > via < code > bitvec::load_be</ code > , then left-shifted to produce the canonical left-aligned layout. One call — no loop, no allocation.</ p >
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< hr />
< div class = "admonition abstract" >
< p class = "admonition-title" > Algorithm — Super-kmer reverse complement</ p >
< div class = "highlight" >< pre >< span ></ span >< code > procedure SuperKmerRevcomp(seq, SEQL):
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seql ← nucleotide length
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n ← ⌈seql / 4⌉ -- number of bytes
shift ← n × − ×
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-- step 1: swap bytes outside-in, applying REVCOMP4 to each (256-byte L1 table)
lo ← 0 ; hi ← n −
while lo < hi:
seq[lo], seq[hi] ← REVCOMP4[seq[hi]], REVCOMP4[seq[lo]]
lo ← lo + 1 ; hi ← hi −
if lo == hi: seq[lo] ← REVCOMP4[seq[lo]]
-- step 2: left-rotate entire bit array by shift, zero trailing bits (SIMD via bitvec)
if shift > 0:
bits.rotate_left(shift)
bits[n× − ×
</ code ></ pre ></ div >
</ div >
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