# SuperKmer — implementation

## Memory layout

A super-kmer is stored as a **32-bit header** followed by a **byte-aligned nucleotide sequence** (2 bits/base, nucleotide 0 at the MSB of the first byte, max 256 nt):

| Field | Bits | Role |
|-------|------|------|
| COUNT | 24   | Occurrence count (≤ 16 M) |
| SEQL  | 8    | Sequence length in nucleotides (1–256) |

Bit layout (MSB to LSB): `[31:8] COUNT  [7:0] SEQL`

SEQL is stored as a raw `u8`: values 1–255 represent lengths 1–255; **0 represents 256** (wrapping convention). The public accessor returns a `usize` and performs the conversion:

```rust
fn seql(&self)               -> usize { if s == 0 { 256 } else { s as usize } }
fn count(&self)              -> u32   { self.0 >> 8 }
fn increment(&mut self)               { self.0 += 1 << 8; }
fn add(&mut self, n: u32)             { self.0 += n << 8; }
fn set_count(&mut self, n: u32)       { self.0 = (self.0 & 0xFF) | (n << 8); }
```

The SEQL field is 8 bits, capping the stored sequence at 256 nt. Given the expected length of ~40 nt, this cap is almost never reached; when it is, the super-kmer is split at 256 nt with a k−1 overlap, preserving all kmers without duplication.

The sequence is always stored in canonical form (lexicographic minimum of forward and reverse complement), with nucleotide 0 at the MSB of the first byte. The byte array can be hashed directly without any adjustment.

## ASCII encoding and decoding

Two lookup tables handle ASCII ↔ 2-bit conversion:

- **`ENC: [u8; 32]`** — indexed by `b & 0x1F` (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.
- **`DEC4: [u32; 256]`** — maps a packed byte (4 nucleotides) to 4 ASCII characters packed as a big-endian `u32`. 1 KB total, fits in L1 cache. One lookup per output byte yields 4 decoded characters.

Encoding 4 nucleotides into one byte:

```rust
byte = ENC[c0 & 0x1F] << 6 | ENC[c1 & 0x1F] << 4 | ENC[c2 & 0x1F] << 2 | ENC[c3 & 0x1F]
```

Decoding one byte into 4 ASCII characters:

```rust
DEC4[byte].to_be_bytes()   // [nuc0, nuc1, nuc2, nuc3] in ASCII
```

## Reverse complement

The reverse complement is computed **in place** with zero allocation in two steps.

**Step 1 — byte swap with `REVCOMP4`.**  A 256-byte lookup table `REVCOMP4` maps each byte (4 nucleotides) to its reverse complement. Bytes are swapped from the outside in, applying `REVCOMP4` to each:

```rust
const fn revcomp4(x: u8) -> u8 {
    let x = !x;                                       // complement all bases
    let x = (x >> 4) | (x << 4);                     // swap nibbles
    let x = ((x >> 2) & 0x33) | ((x & 0x33) << 2);  // swap 2-bit groups
    x
}
```

`REVCOMP4` is 256 bytes (fits in L1 cache), computed at compile time. No endianness dependency — all operations are pure arithmetic on byte values.

**Step 2 — realignment.**  After step 1, `padding = n × 8 − SEQL × 2` spurious bits (complements of the original padding A's) appear at the start of the array. They are flushed left using `BitSlice<u8, Msb0>::rotate_left(padding)` from the `bitvec` crate, which is SIMD-accelerated. The trailing `padding` bits are then zeroed:

```rust
shift = n * 8 - SEQL * 2          // number of padding bits
bits.rotate_left(shift)
bits[len - shift..].fill(false)
```

`Msb0` ordering makes the bit layout hardware-independent.

!!! abstract "Algorithm — Super-kmer canonisation"
    ```text
    procedure SuperKmerCanonical(seq, SEQL):
        for i ← 0 to SEQL − 1:
            fwd ← nucleotide(seq, i)
            rev ← complement(nucleotide(seq, SEQL − 1 − i))
            if fwd < rev: return seq                          -- forward is canonical
            if fwd > rev: return SuperKmerRevcomp(seq, SEQL) -- revcomp is canonical
        return seq                                            -- palindrome: either orientation valid
    ```

## Kmer extraction

A k-mer is extracted from a super-kmer with `SuperKmer::kmer(i, k)`, which returns a `Kmer` — a left-aligned `u64` newtype (see [Kmer implementation](kmer.md)):

```rust
pub fn kmer(&self, i: usize, k: usize) -> Result<Kmer, KmerError>
```

The bit slice `seq[i*2 .. (i+k)*2]` (Msb0 order) is loaded as a big-endian `u64` via `bitvec::load_be`, then left-shifted to produce the canonical left-aligned layout. One call — no loop, no allocation.

---

!!! abstract "Algorithm — Super-kmer reverse complement"
    ```text
    procedure SuperKmerRevcomp(seq, SEQL):
        n     ← ⌈SEQL / 4⌉                  -- number of bytes
        shift ← n × 8 − SEQL × 2            -- padding bits to flush

        -- step 1: swap bytes outside-in, applying REVCOMP4 to each (256-byte L1 table)
        lo ← 0 ; hi ← n − 1
        while lo < hi:
            seq[lo], seq[hi] ← REVCOMP4[seq[hi]], REVCOMP4[seq[lo]]
            lo ← lo + 1 ; hi ← hi − 1
        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×8 − shift .. n×8].fill(0)
    ```