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# DNA encoding

## 2-bit nucleotide encoding

All nucleotides are encoded on 2 bits, MSB-first within each word. Nucleotides are numbered 0-based from the 5′ end across all sequence types:

Base | Encoding
--- | ---
A | `00`
C | `01`
G | `10`
T | `11`

The Watson-Crick complement of any base is its bitwise NOT on 2 bits: `complement(base) = ~base & 0b11`.

## Kmer encoding

A kmer fits in a single `u64`. Nucleotide 0 occupies bits 63–62, nucleotide i occupies bits 63−2i and 62−2i, and the low 64−2k bits are zero. Extraction of nucleotide i (0 ≤ i < k): `(kmer >> (62 - 2*i)) & 0b11`.

Reverse complement is computed via a 16-bit lookup table (65 536 entries × 2 bytes = 128 KB, fits in L2 cache) storing the reverse-complement of every 8-base chunk.

Algorithm — Kmer reverse complement

    procedure KmerRevcomp(kmer, k):
        raw ←   TABLE16[kmer & 0xFFFF]         << 48
              | TABLE16[(kmer >> 16) & 0xFFFF] << 32
              | TABLE16[(kmer >> 32) & 0xFFFF] << 16
              | TABLE16[(kmer >> 48) & 0xFFFF]
        return raw << (64 - 2*k)

The canonical form is the lexicographic minimum of the kmer and its reverse complement:

    canonical(kmer) = min(kmer, revcomp(kmer))

This halves the kmer space and ensures strand-independent counting.