# DNA encoding

## 2-bit nucleotide encoding

Every nucleotide is encoded on 2 bits, most-significant-bit first within each word:

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

The Watson-Crick complement of a base is its bitwise NOT on 2 bits: $\text{complement}(base) = \lnot base \mathbin{\&} \texttt{0b11}$.

## Kmer encoding

A kmer of length $k$ ($k \le 31$) fits in a single 64-bit word. The first nucleotide occupies the two most significant bits, each following nucleotide occupies the next two bits, and unused low-order bits are zero. Extracting nucleotide i (0-indexed from the 5′ end) is a shift-and-mask operation.

Reverse complement is computed by bit manipulation directly on the packed word, without any lookup table: complement every base, reverse the byte order, then reverse the order of 2-bit groups within each byte in two more passes, and finally realign the result to the most-significant bits.

## Canonical form

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

$$\text{canonical}(kmer) = \min\big(kmer,\ \text{revcomp}(kmer)\big)$$

Using the canonical form halves the kmer space and makes counting strand-independent: a kmer and its reverse complement are always treated as the same entity, regardless of which DNA strand was sequenced.
