# 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.

!!! abstract "Algorithm — Kmer reverse complement"
    ```text
    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.