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<h1>Module sequin</h1>

<h2 id="sequin" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code>            <span class="doc doc-object-name doc-module-name">sequin</span>

<p>A Python reimplementation of James Coglan&rsquo;s &ldquo;sequin&rdquo; Node.js module.</p>
<p>James Coglan&rsquo;s &ldquo;sequin&rdquo; Node.js module provides a pseudorandom number
generator (using rejection sampling on a stream of input numbers) that
attempts to minimize the amount of information it throws away:
(non-degenerate) rejected samples are fed into a stream of higher-order
numbers from which the next random number generation request will be
served.  The sequin module is used in Coglan&rsquo;s &ldquo;vault&rdquo; module (a
deterministic, stateless password manager that recomputes passwords
instead of storing them), and this reimplementation is used for
a similar purpose.</p>
<p>The main API is the <a class="autorefs autorefs-internal" href="#sequin.Sequin"><code>Sequin</code></a> class, which is
thoroughly documented.</p>

<h3 id="sequin.Sequin" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-class"></code>            <span class="doc doc-object-name doc-class-name">Sequin</span>

<a href="#sequin.Sequin" class="headerlink" title="Permanent link">&para;</a></h3>
<div class="doc-signature highlight"><pre><span></span><code><span class="nf">Sequin</span><span class="p">(</span>
    <span class="n">sequence</span><span class="p">:</span> <span class="nb">str</span> <span class="o">|</span> <span class="nb">bytes</span> <span class="o">|</span> <span class="nb">bytearray</span> <span class="o">|</span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
    <span class="o">/</span><span class="p">,</span>
    <span class="o">*</span><span class="p">,</span>
    <span class="n">is_bitstring</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
<span class="p">)</span>
</code></pre></div>

<p>Generate pseudorandom non-negative numbers in different ranges.</p>
<p>Given a (presumed high-quality) uniformly random sequence of input
bits, generate pseudorandom non-negative integers in a certain range
on each call of the <code>generate</code> method.  (It is permissible to
specify a different range per call to <code>generate</code>; this is the main
use case.)  We use a modified version of rejection sampling, where
rejected values are stored in &ldquo;rejection queues&rdquo; if possible, and
these rejection queues re-seed the next round of rejection sampling.</p>
<p>This is a Python reimplementation of James Coglan&rsquo;s <a href="https://www.npmjs.com/package/sequin">Node.js sequin
module</a>, as introduced in <a href="https://blog.jcoglan.com/2012/07/16/designing-vaults-generator-algorithm/">his blog post</a>.  It
uses a <a href="https://checkmyworking.com/2012/06/converting-a-stream-of-binary-digits-to-a-stream-of-base-n-digits/">technique by Christian Lawson-Perfect</a>.
I do not know why the original module is called &ldquo;sequin&rdquo;; I presume
it to be a pun on &ldquo;sequence&rdquo;.</p>

<p><span class="doc-section-title">Parameters:</span></p>
    <table>
      <thead>
        <tr>
          <th>Name</th>
          <th>Type</th>
          <th>Description</th>
          <th>Default</th>
        </tr>
      </thead>
      <tbody>
          <tr class="doc-section-item">
            <td><code>sequence</code></td>
            <td>
                  <code><a class="autorefs autorefs-external" href="https://docs.python.org/3/library/stdtypes.html#str">str</a> | <a class="autorefs autorefs-external" href="https://docs.python.org/3/library/stdtypes.html#bytes">bytes</a> | <a class="autorefs autorefs-external" href="https://docs.python.org/3/library/stdtypes.html#bytearray">bytearray</a> | <a class="autorefs autorefs-external" title="collections.abc.Sequence" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence">Sequence</a>[<a class="autorefs autorefs-external" href="https://docs.python.org/3/library/functions.html#int">int</a>]</code>
            </td>
            <td>
              <div class="doc-md-description">
                <p>A sequence of bits, or things convertible to bits, to
seed the pseudorandom number generator.  Byte and text
strings are converted to 8-bit integer sequences.
(Conversion will fail if the text string contains
non-ISO-8859-1 characters.)  The numbers are then
converted to bits.</p>
              </div>
            </td>
            <td>
                <em>required</em>
            </td>
          </tr>
          <tr class="doc-section-item">
            <td><code>is_bitstring</code></td>
            <td>
                  <code><a class="autorefs autorefs-external" href="https://docs.python.org/3/library/functions.html#bool">bool</a></code>
            </td>
            <td>
              <div class="doc-md-description">
                <p>If true, treat the input as a bitstring.  By default,
the input is treated as a string of 8-bit integers, from
which the individual bits must still be extracted.</p>
              </div>
            </td>
            <td>
                  <code>False</code>
            </td>
          </tr>
      </tbody>
    </table>

<h4 id="sequin.Sequin.generate" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-method"></code>            <span class="doc doc-object-name doc-function-name">generate</span>

<a href="#sequin.Sequin.generate" class="headerlink" title="Permanent link">&para;</a></h4>
<div class="doc-signature highlight"><pre><span></span><code><span class="nf">generate</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span>
</code></pre></div>

<p>Generate a base <code>n</code> non-negative integer.</p>
<p>We attempt to generate a value using rejection sampling.  If the
generated sample is outside the desired range (i.e., is
rejected), then attempt to reuse the sample by seeding
a &ldquo;higher-order&rdquo; input sequence of uniformly random numbers (for
a different base).</p>

<p><span class="doc-section-title">Returns:</span></p>
    <table>
      <thead>
        <tr>
          <th>Type</th>
          <th>Description</th>
        </tr>
      </thead>
      <tbody>
          <tr class="doc-section-item">
            <td>
                  <code><a class="autorefs autorefs-external" href="https://docs.python.org/3/library/functions.html#int">int</a></code>
            </td>
            <td>
              <div class="doc-md-description">
                <p>A pseudorandom number in the range 0, &hellip;, <code>n</code> - 1.</p>
              </div>
            </td>
          </tr>
      </tbody>
    </table>

<p><span class="doc-section-title">Raises:</span></p>
    <table>
      <thead>
        <tr>
          <th>Type</th>
          <th>Description</th>
        </tr>
      </thead>
      <tbody>
          <tr class="doc-section-item">
            <td>
                  <code><a class="autorefs autorefs-external" href="https://docs.python.org/3/library/exceptions.html#ValueError">ValueError</a></code>
            </td>
            <td>
              <div class="doc-md-description">
                <p>The range is empty.</p>
              </div>
            </td>
          </tr>
          <tr class="doc-section-item">
            <td>
                  <code><a class="autorefs autorefs-internal" title="sequin.SequinExhaustedError" href="#sequin.SequinExhaustedError">SequinExhaustedError</a></code>
            </td>
            <td>
              <div class="doc-md-description">
                <p>The sequin is exhausted.</p>
              </div>
            </td>
          </tr>
      </tbody>
    </table>

<p><span class="doc-section-title">Examples:</span></p>
    <div class="highlight"><pre><span></span><code><span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span> <span class="o">=</span> <span class="n">Sequin</span><span class="p">(</span>
<span class="gp">... </span>    <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="gp">... </span>    <span class="n">is_bitstring</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seq2</span> <span class="o">=</span> <span class="n">Sequin</span><span class="p">(</span>
<span class="gp">... </span>    <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="gp">... </span>    <span class="n">is_bitstring</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="go">3</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="go">3</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="go">1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="w">    </span><span class="o">...</span>
<span class="gr">SequinExhaustedError</span>: <span class="n">Sequin is exhausted</span>
</code></pre></div>
    <p>Using <code>n = 1</code> does not actually consume input bits:</p>
    <div class="highlight"><pre><span></span><code><span class="gp">&gt;&gt;&gt; </span><span class="n">seq2</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="go">0</span>
</code></pre></div>
    <p>But it still won&rsquo;t work on exhausted sequins:</p>
    <div class="highlight"><pre><span></span><code><span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="w">    </span><span class="o">...</span>
<span class="gr">SequinExhaustedError</span>: <span class="n">Sequin is exhausted</span>
</code></pre></div>

</div>

<h3 id="sequin.SequinExhaustedError" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-class"></code>            <span class="doc doc-object-name doc-class-name">SequinExhaustedError</span>

<a href="#sequin.SequinExhaustedError" class="headerlink" title="Permanent link">&para;</a></h3>
<div class="doc-signature highlight"><pre><span></span><code><span class="nf">SequinExhaustedError</span><span class="p">()</span>
</code></pre></div>

<div class="doc doc-contents ">
            <p class="doc doc-class-bases">
              Bases: <code><a class="autorefs autorefs-external" href="https://docs.python.org/3/library/exceptions.html#Exception">Exception</a></code></p>

<p>The sequin is exhausted.</p>
<p>No more values can be generated from this sequin.</p>

</div>

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