Eric Coissac
58391886a3
- Add `hash` field to MmerItem for stable, randomized minimizer ordering - Introduce hash_mMER() using mix64 with XOR seed to avoid fixed points (e.g., poly-A/T) - Remove is_degenerate() and minimizer_worse(), simplifying comparison to hash-only - Update push logic: compare hashes instead of canonical values with degeneracy checks
159 lines
7.4 KiB
Markdown
159 lines
7.4 KiB
Markdown
# SuperKmer — implementation
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## Memory layout
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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):
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| Field | Bits | Role |
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|-------|------|------|
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| COUNT | 24 | Occurrence count (≤ 16 M) |
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| SEQL | 8 | Sequence length in nucleotides (1–256) |
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Bit layout (MSB to LSB): `[31:8] COUNT [7:0] SEQL`
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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:
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```rust
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fn seql(&self) -> usize { if s == 0 { 256 } else { s as usize } }
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fn count(&self) -> u32 { self.0 >> 8 }
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fn increment(&mut self) { self.0 += 1 << 8; }
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fn add(&mut self, n: u32) { self.0 += n << 8; }
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fn set_count(&mut self, n: u32) { self.0 = (self.0 & 0xFF) | (n << 8); }
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```
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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.
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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.
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## ASCII encoding and decoding
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Two lookup tables handle ASCII ↔ 2-bit conversion:
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- **`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.
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- **`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.
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Encoding 4 nucleotides into one byte:
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```rust
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byte = ENC[c0 & 0x1F] << 6 | ENC[c1 & 0x1F] << 4 | ENC[c2 & 0x1F] << 2 | ENC[c3 & 0x1F]
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```
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Decoding one byte into 4 ASCII characters:
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```rust
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DEC4[byte].to_be_bytes() // [nuc0, nuc1, nuc2, nuc3] in ASCII
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```
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## Reverse complement
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The reverse complement is computed **in place** with zero allocation in two steps.
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**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:
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```rust
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const fn revcomp4(x: u8) -> u8 {
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let x = !x; // complement all bases
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let x = (x >> 4) | (x << 4); // swap nibbles
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let x = ((x >> 2) & 0x33) | ((x & 0x33) << 2); // swap 2-bit groups
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x
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}
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```
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`REVCOMP4` is 256 bytes (fits in L1 cache), computed at compile time. No endianness dependency — all operations are pure arithmetic on byte values.
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**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:
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```rust
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shift = n * 8 - SEQL * 2 // number of padding bits
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bits.rotate_left(shift)
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bits[len - shift..].fill(false)
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```
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`Msb0` ordering makes the bit layout hardware-independent.
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!!! abstract "Algorithm — Super-kmer canonisation"
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```text
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procedure SuperKmerCanonical(seq, SEQL):
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for i ← 0 to SEQL − 1:
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fwd ← nucleotide(seq, i)
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rev ← complement(nucleotide(seq, SEQL − 1 − i))
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if fwd < rev: return seq -- forward is canonical
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if fwd > rev: return SuperKmerRevcomp(seq, SEQL) -- revcomp is canonical
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return seq -- palindrome: either orientation valid
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```
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## Minimizer sliding window
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Super-kmers are built by `SuperKmerIter` (crate `obiskbuilder`), which maintains the current minimizer with a **monotonic deque** over a sliding window of W = k − m + 1 m-mer positions.
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Each deque entry stores:
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| Field | Type | Purpose |
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|------------|-------|----------------------------------------------|
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| `position` | usize | 0-based start of this m-mer in the segment |
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| `canonical`| u64 | right-aligned canonical m-mer value (lex-min of fwd and rc); used as partition key |
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| `hash` | u64 | $H(\text{canonical})$ — ordering key for random minimizer selection |
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The hash $H$ is the seeded splitmix64 finalizer (see [Minimizer selection](../theory/minimizer.md)):
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```rust
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fn hash_mmer(canonical: u64) -> u64 {
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let x = canonical ^ 0x9e3779b97f4a7c15; // seed: eliminates fixed point at 0
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let x = x ^ (x >> 30);
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let x = x.wrapping_mul(0xbf58476d1ce4e5b9);
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let x = x ^ (x >> 27);
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let x = x.wrapping_mul(0x94d049bb133111eb);
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x ^ (x >> 31)
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}
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```
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On each new nucleotide, once the window is full, the deque is updated:
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!!! abstract "Algorithm — minimizer deque update"
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```text
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procedure UpdateMinimizer(deque, position, canonical, hash, k, received):
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-- pop dominated entries from the back
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while deque.back.hash ≥ hash:
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deque.pop_back()
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deque.push_back({position, canonical, hash})
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-- evict expired entries from the front
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while deque.front.position + k < received:
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deque.pop_front()
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```
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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.
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A super-kmer boundary is emitted when the minimizer changes: `deque.front.hash ≠ prev_hash`. The `canonical` field of the front entry is **not** used for boundary detection — that uses the hash alone. The canonical value is stored so that the partition key $H(\text{canonical})$ can be recomputed independently at routing time from the stored `minimizer_pos`, without inheriting the minimum-order-statistic bias (see [Minimizer selection — partition key independence](../theory/minimizer.md#partition-key-independence)).
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## Kmer extraction
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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)):
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```rust
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pub fn kmer(&self, i: usize, k: usize) -> Result<Kmer, KmerError>
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```
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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.
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---
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!!! abstract "Algorithm — Super-kmer reverse complement"
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```text
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procedure SuperKmerRevcomp(seq, SEQL):
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n ← ⌈SEQL / 4⌉ -- number of bytes
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shift ← n × 8 − SEQL × 2 -- padding bits to flush
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-- step 1: swap bytes outside-in, applying REVCOMP4 to each (256-byte L1 table)
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lo ← 0 ; hi ← n − 1
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while lo < hi:
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seq[lo], seq[hi] ← REVCOMP4[seq[hi]], REVCOMP4[seq[lo]]
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lo ← lo + 1 ; hi ← hi − 1
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if lo == hi: seq[lo] ← REVCOMP4[seq[lo]]
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-- step 2: left-rotate entire bit array by shift, zero trailing bits (SIMD via bitvec)
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if shift > 0:
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bits.rotate_left(shift)
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bits[n×8 − shift .. n×8].fill(0)
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```
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