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< h1 id = "dna-encoding" > DNA encoding</ h1 >
< h2 id = "2-bit-nucleotide-encoding" > 2-bit nucleotide encoding</ h2 >
< p > All nucleotides are encoded on 2 bits, MSB-first within each word. Nucleotides are numbered 0-based from the 5′ </ p >
< table >
< thead >
< tr >
< th > Base</ th >
< th > Encoding</ th >
</ tr >
</ thead >
< tbody >
< tr >
< td > A</ td >
< td >< code > 00</ code ></ td >
</ tr >
< tr >
< td > C</ td >
< td >< code > 01</ code ></ td >
</ tr >
< tr >
< td > G</ td >
< td >< code > 10</ code ></ td >
</ tr >
< tr >
< td > T</ td >
< td >< code > 11</ code ></ td >
</ tr >
</ tbody >
</ table >
< p > The Watson-Crick complement of any base is its bitwise NOT on 2 bits: < code > complement(base) = ~base & 0b11</ code > .</ p >
< h2 id = "kmer-encoding" > Kmer encoding</ h2 >
< p > A kmer fits in a single < code > u64</ code > . Nucleotide 0 occupies bits 63– − − − < k): < code > (kmer >> (62 - 2*i)) & 0b11</ code > .</ p >
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< p > Reverse complement is computed by < strong > bit manipulation in four steps</ strong > , with no lookup table:</ p >
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< div class = "admonition abstract" >
< p class = "admonition-title" > Algorithm — Kmer reverse complement</ p >
< div class = "highlight" >< pre >< span ></ span >< code > procedure KmerRevcomp(kmer, k):
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x ← ~kmer -- complement all bases
x ← swap_bytes(x) -- reverse byte order
x ← ((x >> 4) & 0x0F0F0F0F0F0F0F0F)
| ((x & 0x0F0F0F0F0F0F0F0F) << 4) -- swap nibbles within each byte
x ← ((x >> 2) & 0x3333333333333333)
| ((x & 0x3333333333333333) << 2) -- swap 2-bit pairs within each nibble
return x << (64 - 2*k) -- re-align to MSB
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</ code ></ pre ></ div >
</ div >
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< p > The three reorder passes together reverse the order of all 2-bit base codes across the 64-bit word. The bitwise NOT in the first step complements each base (A↔T, C↔G). The final left shift clears the low 64− </ p >
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< p > The < strong > canonical form</ strong > is the lexicographic minimum of the kmer and its reverse complement:</ p >
< div class = "highlight" >< pre >< span ></ span >< code > canonical(kmer) = min(kmer, revcomp(kmer))
</ code ></ pre ></ div >
< p > This halves the kmer space and ensures strand-independent counting.</ p >
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