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<h1 id="superkmer-implementation">SuperKmer — implementation</h1>
<h2 id="memory-layout">Memory layout</h2>
<p>A super-kmer is stored as a <strong>32-bit header</strong> followed by a <strong>byte-aligned nucleotide sequence</strong> (2 bits/base, nucleotide 0 at the MSB of the first byte, max 256 nt):</p>
<table>
<thead>
<tr>
<th>Field</th>
<th>Bits</th>
<th>Role</th>
</tr>
</thead>
<tbody>
<tr>
<td>COUNT</td>
<td>24</td>
<td>Occurrence count (≤ 16 M)</td>
</tr>
<tr>
<td>SEQL</td>
<td>8</td>
<td>Sequence length in nucleotides (1–256)</td>
</tr>
</tbody>
</table>
<p>Bit layout (MSB to LSB): <code>[31:8] COUNT [7:0] SEQL</code></p>
<p>SEQL is stored as a raw <code>u8</code>: values 1–255 represent lengths 1–255; <strong>0 represents 256</strong> (wrapping convention). The public accessor returns a <code>usize</code> and performs the conversion:</p>
<div class="highlight"><pre><span></span><code><span class="k">fn</span><span class="w"> </span><span class="nf">seql</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">256</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="p">}</span>
<span class="k">fn</span><span class="w"> </span><span class="nf">count</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">u32</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="mi">0</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">8</span><span class="w"> </span><span class="p">}</span>
<span class="k">fn</span><span class="w"> </span><span class="nf">increment</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="mi">0</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">8</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
<span class="k">fn</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">u32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="mi">0</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">8</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
<span class="k">fn</span><span class="w"> </span><span class="nf">set_count</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">u32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="mi">0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0xFF</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">8</span><span class="p">);</span><span class="w"> </span><span class="p">}</span>
</code></pre></div>
<p>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.</p>
<p>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.</p>
<h2 id="ascii-encoding-and-decoding">ASCII encoding and decoding</h2>
<p>Two lookup tables handle ASCII ↔ 2-bit conversion:</p>
<ul>
<li><strong><code>ENC: [u8; 32]</code></strong> — indexed by <code>b &amp; 0x1F</code> (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.</li>
<li><strong><code>DEC4: [u32; 256]</code></strong> — maps a packed byte (4 nucleotides) to 4 ASCII characters packed as a big-endian <code>u32</code>. 1 KB total, fits in L1 cache. One lookup per output byte yields 4 decoded characters.</li>
</ul>
<p>Encoding 4 nucleotides into one byte:</p>
<div class="highlight"><pre><span></span><code><span class="n">byte</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ENC</span><span class="p">[</span><span class="n">c0</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0x1F</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">6</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="n">ENC</span><span class="p">[</span><span class="n">c1</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0x1F</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="n">ENC</span><span class="p">[</span><span class="n">c2</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0x1F</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="n">ENC</span><span class="p">[</span><span class="n">c3</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0x1F</span><span class="p">]</span>
</code></pre></div>
<p>Decoding one byte into 4 ASCII characters:</p>
<div class="highlight"><pre><span></span><code><span class="n">DEC4</span><span class="p">[</span><span class="n">byte</span><span class="p">].</span><span class="n">to_be_bytes</span><span class="p">()</span><span class="w"> </span><span class="c1">// [nuc0, nuc1, nuc2, nuc3] in ASCII</span>
</code></pre></div>
<h2 id="reverse-complement">Reverse complement</h2>
<p>The reverse complement is computed <strong>in place</strong> with zero allocation in two steps.</p>
<p><strong>Step 1 — byte swap with <code>REVCOMP4</code>.</strong> A 256-byte lookup table <code>REVCOMP4</code> maps each byte (4 nucleotides) to its reverse complement. Bytes are swapped from the outside in, applying <code>REVCOMP4</code> to each:</p>
<div class="highlight"><pre><span></span><code><span class="k">const</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">revcomp4</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="kt">u8</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">u8</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">!</span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="c1">// complement all bases</span>
<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">);</span><span class="w"> </span><span class="c1">// swap nibbles</span>
<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">x</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0x33</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="p">((</span><span class="n">x</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="mh">0x33</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// swap 2-bit groups</span>
<span class="w"> </span><span class="n">x</span>
<span class="p">}</span>
</code></pre></div>
<p><code>REVCOMP4</code> is 256 bytes (fits in L1 cache), computed at compile time. No endianness dependency — all operations are pure arithmetic on byte values.</p>
<p><strong>Step 2 — realignment.</strong> After step 1, <code>padding = n × 8 − SEQL × 2</code> spurious bits (complements of the original padding A's) appear at the start of the array. They are flushed left using <code>BitSlice&lt;u8, Msb0&gt;::rotate_left(padding)</code> from the <code>bitvec</code> crate, which is SIMD-accelerated. The trailing <code>padding</code> bits are then zeroed:</p>
<div class="highlight"><pre><span></span><code><span class="n">shift</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">8</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">SEQL</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// number of padding bits</span>
<span class="n">bits</span><span class="p">.</span><span class="n">rotate_left</span><span class="p">(</span><span class="n">shift</span><span class="p">)</span>
<span class="n">bits</span><span class="p">[</span><span class="n">len</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">shift</span><span class="o">..</span><span class="p">].</span><span class="n">fill</span><span class="p">(</span><span class="kc">false</span><span class="p">)</span>
</code></pre></div>
<p><code>Msb0</code> ordering makes the bit layout hardware-independent.</p>
<div class="admonition abstract">
<p class="admonition-title">Algorithm — Super-kmer canonisation</p>
<div class="highlight"><pre><span></span><code>procedure SuperKmerCanonical(seq, SEQL):
for i ← 0 to SEQL − 1:
fwd ← nucleotide(seq, i)
rev ← complement(nucleotide(seq, SEQL − 1 − i))
if fwd &lt; rev: return seq -- forward is canonical
if fwd &gt; rev: return SuperKmerRevcomp(seq, SEQL) -- revcomp is canonical
return seq -- palindrome: either orientation valid
</code></pre></div>
</div>
<h2 id="kmer-extraction">Kmer extraction</h2>
<p>A k-mer is extracted from a super-kmer with <code>SuperKmer::kmer(i, k)</code>, which returns a <code>Kmer</code> — a left-aligned <code>u64</code> newtype (see <a href="../kmer/">Kmer implementation</a>):</p>
<div class="highlight"><pre><span></span><code><span class="k">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="nf">kmer</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="p">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Result</span><span class="o">&lt;</span><span class="n">Kmer</span><span class="p">,</span><span class="w"> </span><span class="n">KmerError</span><span class="o">&gt;</span>
</code></pre></div>
<p>The bit slice <code>seq[i*2 .. (i+k)*2]</code> (Msb0 order) is loaded as a big-endian <code>u64</code> via <code>bitvec::load_be</code>, then left-shifted to produce the canonical left-aligned layout. One call — no loop, no allocation.</p>
<hr />
<div class="admonition abstract">
<p class="admonition-title">Algorithm — Super-kmer reverse complement</p>
<div class="highlight"><pre><span></span><code>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 &lt; 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 &gt; 0:
bits.rotate_left(shift)
bits[n×8 − shift .. n×8].fill(0)
</code></pre></div>
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