obikmer/docmd/implementation/superkmer.md

# SuperKmer — implementation

## Memory layout

`SuperKmer` holds two separate fields:

```rust
pub struct SuperKmer {
    pub(crate) count: u32,
    pub(crate) inner: PackedSeq,
}
```

`PackedSeq` stores a 2-bit packed DNA sequence as a heap-allocated `Box<[u8]>` plus a `tail: u8` field:

| Field | Type | Role |
|-------|------|------|
| `tail` | `u8` | Number of valid nucleotides in the last byte: 0 encodes 4, 1–3 are identity |
| `seq`  | `Box<[u8]>` | 2-bit packed bytes, nucleotide 0 at bits 7–6 of `seq[0]` |

Nucleotide length is recovered without storing it explicitly:

```text
seql = (seq.len() - 1) * 4 + tail_count(tail)
```

There is no packed header word — `count` and the sequence live in separate fields.

The on-disk binary format (produced by `write_to_binary`) is:

```text
[varint(count)] [u8: seql − k] [packed bytes…]
```

`seql − k` fits in a `u8` when `n_kmers = seql − k + 1 ≤ MAX_KMERS_PER_CHUNK (= 256)`. If a super-kmer exceeds 256 kmers, `write_to_binary` splits it into overlapping chunks (k−1 nucleotide overlap, same count per chunk), each a self-contained record readable by `read_from_binary`.

The public accessors operate on the struct fields directly:

```rust
fn seql(&self)            -> usize { self.inner.seql() }
fn count(&self)           -> u32   { self.count }
fn increment(&mut self)            { self.count += 1; }
fn add(&mut self, n: u32)          { self.count += n; }
fn set_count(&mut self, n: u32)    { self.count = n; }
```

## 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
let seql = self.seql();
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
    ```

## Minimizer sliding window

Super-kmers are built by `SuperKmerIter` (crate `obiskbuilder`), which tracks the current minimizer with a **monotonic deque** (`Ring<MmerItem, 32>`) inside `RollingStat`, a rolling-window entropy and minimizer tracker.

Each deque entry stores:

| Field      | Type  | Purpose                                      |
|------------|-------|----------------------------------------------|
| `position` | usize | 0-based start of this m-mer in the segment   |
| `canonical`| u64   | right-aligned canonical m-mer value (lex-min of fwd and rc); used as partition key |
| `hash`     | u64   | `hash_kmer(canonical << (64 − 2m))` — ordering key for random minimizer selection |

The hash uses the seeded splitmix64 finalizer (`mix64(raw ^ 0x9e3779b97f4a7c15)`), the same function as `kmer::hash_kmer`.

On each new nucleotide, once the window is full, the deque is updated:

!!! abstract "Algorithm — minimizer deque update"
    ```text
    procedure UpdateMinimizer(deque, position, canonical, hash, k, received):
        -- pop dominated entries from the back
        while deque.back.hash ≥ hash:
            deque.pop_back()
        deque.push_back({position, canonical, hash})

        -- evict expired entries from the front
        while deque.front.position + k < received:
            deque.pop_front()
    ```

The front of the deque is always the current minimizer. Because the deque is maintained in strictly increasing hash order, each entry is popped at most once — O(1) amortized per nucleotide.

A super-kmer boundary is emitted when the minimizer changes: `current_minimizer != prev_minimizer`. `SuperKmerIter` also emits a boundary when:

- entropy of the current k-mer falls at or below the threshold θ (cursor retreated by k−1)
- super-kmer length reaches 256 nucleotides (cursor retreated by k)

## Kmer extraction

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

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

The bit slice `seq[i*2 .. (i+k)*2]` (Msb0 order) is loaded as a `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):
        seql  ← nucleotide length
        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)
    ```