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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code> — Numeric abstract base classes</a><ul>
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<li><a class="reference internal" href="#the-numeric-tower">The numeric tower</a></li>
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<li><a class="reference internal" href="#notes-for-type-implementers">Notes for type implementers</a><ul>
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<section id="module-numbers">
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<span id="numbers-numeric-abstract-base-classes"></span><h1><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code> — Numeric abstract base classes<a class="headerlink" href="#module-numbers" title="Link to this heading">¶</a></h1>
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<p><strong>Source code:</strong> <a class="extlink-source reference external" href="https://github.com/python/cpython/tree/3.13/Lib/numbers.py">Lib/numbers.py</a></p>
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<hr class="docutils" />
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<p>The <code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code> module (<span class="target" id="index-0"></span><a class="pep reference external" href="https://peps.python.org/pep-3141/"><strong>PEP 3141</strong></a>) defines a hierarchy of numeric
|
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<a class="reference internal" href="../glossary.html#term-abstract-base-class"><span class="xref std std-term">abstract base classes</span></a> which progressively define
|
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more operations. None of the types defined in this module are intended to be instantiated.</p>
|
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<dl class="py class">
|
||
<dt class="sig sig-object py" id="numbers.Number">
|
||
<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">numbers.</span></span><span class="sig-name descname"><span class="pre">Number</span></span><a class="headerlink" href="#numbers.Number" title="Link to this definition">¶</a></dt>
|
||
<dd><p>The root of the numeric hierarchy. If you just want to check if an argument
|
||
<em>x</em> is a number, without caring what kind, use <code class="docutils literal notranslate"><span class="pre">isinstance(x,</span> <span class="pre">Number)</span></code>.</p>
|
||
</dd></dl>
|
||
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<section id="the-numeric-tower">
|
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<h2>The numeric tower<a class="headerlink" href="#the-numeric-tower" title="Link to this heading">¶</a></h2>
|
||
<dl class="py class">
|
||
<dt class="sig sig-object py" id="numbers.Complex">
|
||
<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">numbers.</span></span><span class="sig-name descname"><span class="pre">Complex</span></span><a class="headerlink" href="#numbers.Complex" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Subclasses of this type describe complex numbers and include the operations
|
||
that work on the built-in <a class="reference internal" href="functions.html#complex" title="complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a> type. These are: conversions to
|
||
<a class="reference internal" href="functions.html#complex" title="complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a> and <a class="reference internal" href="functions.html#bool" title="bool"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>, <a class="reference internal" href="#numbers.Complex.real" title="numbers.Complex.real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">real</span></code></a>, <a class="reference internal" href="#numbers.Complex.imag" title="numbers.Complex.imag"><code class="xref py py-attr docutils literal notranslate"><span class="pre">imag</span></code></a>, <code class="docutils literal notranslate"><span class="pre">+</span></code>,
|
||
<code class="docutils literal notranslate"><span class="pre">-</span></code>, <code class="docutils literal notranslate"><span class="pre">*</span></code>, <code class="docutils literal notranslate"><span class="pre">/</span></code>, <code class="docutils literal notranslate"><span class="pre">**</span></code>, <a class="reference internal" href="functions.html#abs" title="abs"><code class="xref py py-func docutils literal notranslate"><span class="pre">abs()</span></code></a>, <a class="reference internal" href="#numbers.Complex.conjugate" title="numbers.Complex.conjugate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">conjugate()</span></code></a>, <code class="docutils literal notranslate"><span class="pre">==</span></code>, and
|
||
<code class="docutils literal notranslate"><span class="pre">!=</span></code>. All except <code class="docutils literal notranslate"><span class="pre">-</span></code> and <code class="docutils literal notranslate"><span class="pre">!=</span></code> are abstract.</p>
|
||
<dl class="py attribute">
|
||
<dt class="sig sig-object py" id="numbers.Complex.real">
|
||
<span class="sig-name descname"><span class="pre">real</span></span><a class="headerlink" href="#numbers.Complex.real" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Abstract. Retrieves the real component of this number.</p>
|
||
</dd></dl>
|
||
|
||
<dl class="py attribute">
|
||
<dt class="sig sig-object py" id="numbers.Complex.imag">
|
||
<span class="sig-name descname"><span class="pre">imag</span></span><a class="headerlink" href="#numbers.Complex.imag" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Abstract. Retrieves the imaginary component of this number.</p>
|
||
</dd></dl>
|
||
|
||
<dl class="py method">
|
||
<dt class="sig sig-object py" id="numbers.Complex.conjugate">
|
||
<em class="property"><span class="k"><span class="pre">abstractmethod</span></span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">conjugate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#numbers.Complex.conjugate" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Abstract. Returns the complex conjugate. For example, <code class="docutils literal notranslate"><span class="pre">(1+3j).conjugate()</span>
|
||
<span class="pre">==</span> <span class="pre">(1-3j)</span></code>.</p>
|
||
</dd></dl>
|
||
|
||
</dd></dl>
|
||
|
||
<dl class="py class">
|
||
<dt class="sig sig-object py" id="numbers.Real">
|
||
<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">numbers.</span></span><span class="sig-name descname"><span class="pre">Real</span></span><a class="headerlink" href="#numbers.Real" title="Link to this definition">¶</a></dt>
|
||
<dd><p>To <a class="reference internal" href="#numbers.Complex" title="numbers.Complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code> adds the operations that work on real
|
||
numbers.</p>
|
||
<p>In short, those are: a conversion to <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference internal" href="math.html#math.trunc" title="math.trunc"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.trunc()</span></code></a>,
|
||
<a class="reference internal" href="functions.html#round" title="round"><code class="xref py py-func docutils literal notranslate"><span class="pre">round()</span></code></a>, <a class="reference internal" href="math.html#math.floor" title="math.floor"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.floor()</span></code></a>, <a class="reference internal" href="math.html#math.ceil" title="math.ceil"><code class="xref py py-func docutils literal notranslate"><span class="pre">math.ceil()</span></code></a>, <a class="reference internal" href="functions.html#divmod" title="divmod"><code class="xref py py-func docutils literal notranslate"><span class="pre">divmod()</span></code></a>, <code class="docutils literal notranslate"><span class="pre">//</span></code>,
|
||
<code class="docutils literal notranslate"><span class="pre">%</span></code>, <code class="docutils literal notranslate"><span class="pre"><</span></code>, <code class="docutils literal notranslate"><span class="pre"><=</span></code>, <code class="docutils literal notranslate"><span class="pre">></span></code>, and <code class="docutils literal notranslate"><span class="pre">>=</span></code>.</p>
|
||
<p>Real also provides defaults for <a class="reference internal" href="functions.html#complex" title="complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">complex()</span></code></a>, <a class="reference internal" href="#numbers.Complex.real" title="numbers.Complex.real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">real</span></code></a>,
|
||
<a class="reference internal" href="#numbers.Complex.imag" title="numbers.Complex.imag"><code class="xref py py-attr docutils literal notranslate"><span class="pre">imag</span></code></a>, and <a class="reference internal" href="#numbers.Complex.conjugate" title="numbers.Complex.conjugate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">conjugate()</span></code></a>.</p>
|
||
</dd></dl>
|
||
|
||
<dl class="py class">
|
||
<dt class="sig sig-object py" id="numbers.Rational">
|
||
<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">numbers.</span></span><span class="sig-name descname"><span class="pre">Rational</span></span><a class="headerlink" href="#numbers.Rational" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Subtypes <a class="reference internal" href="#numbers.Real" title="numbers.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a> and adds <a class="reference internal" href="#numbers.Rational.numerator" title="numbers.Rational.numerator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">numerator</span></code></a> and
|
||
<a class="reference internal" href="#numbers.Rational.denominator" title="numbers.Rational.denominator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">denominator</span></code></a> properties. It also provides a default for
|
||
<a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-func docutils literal notranslate"><span class="pre">float()</span></code></a>.</p>
|
||
<p>The <a class="reference internal" href="#numbers.Rational.numerator" title="numbers.Rational.numerator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">numerator</span></code></a> and <a class="reference internal" href="#numbers.Rational.denominator" title="numbers.Rational.denominator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">denominator</span></code></a> values
|
||
should be instances of <a class="reference internal" href="#numbers.Integral" title="numbers.Integral"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a> and should be in lowest terms with
|
||
<a class="reference internal" href="#numbers.Rational.denominator" title="numbers.Rational.denominator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">denominator</span></code></a> positive.</p>
|
||
<dl class="py attribute">
|
||
<dt class="sig sig-object py" id="numbers.Rational.numerator">
|
||
<span class="sig-name descname"><span class="pre">numerator</span></span><a class="headerlink" href="#numbers.Rational.numerator" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Abstract.</p>
|
||
</dd></dl>
|
||
|
||
<dl class="py attribute">
|
||
<dt class="sig sig-object py" id="numbers.Rational.denominator">
|
||
<span class="sig-name descname"><span class="pre">denominator</span></span><a class="headerlink" href="#numbers.Rational.denominator" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Abstract.</p>
|
||
</dd></dl>
|
||
|
||
</dd></dl>
|
||
|
||
<dl class="py class">
|
||
<dt class="sig sig-object py" id="numbers.Integral">
|
||
<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">numbers.</span></span><span class="sig-name descname"><span class="pre">Integral</span></span><a class="headerlink" href="#numbers.Integral" title="Link to this definition">¶</a></dt>
|
||
<dd><p>Subtypes <a class="reference internal" href="#numbers.Rational" title="numbers.Rational"><code class="xref py py-class docutils literal notranslate"><span class="pre">Rational</span></code></a> and adds a conversion to <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>. Provides
|
||
defaults for <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-func docutils literal notranslate"><span class="pre">float()</span></code></a>, <a class="reference internal" href="#numbers.Rational.numerator" title="numbers.Rational.numerator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">numerator</span></code></a>, and
|
||
<a class="reference internal" href="#numbers.Rational.denominator" title="numbers.Rational.denominator"><code class="xref py py-attr docutils literal notranslate"><span class="pre">denominator</span></code></a>. Adds abstract methods for <a class="reference internal" href="functions.html#pow" title="pow"><code class="xref py py-func docutils literal notranslate"><span class="pre">pow()</span></code></a> with
|
||
modulus and bit-string operations: <code class="docutils literal notranslate"><span class="pre"><<</span></code>, <code class="docutils literal notranslate"><span class="pre">>></span></code>, <code class="docutils literal notranslate"><span class="pre">&</span></code>, <code class="docutils literal notranslate"><span class="pre">^</span></code>, <code class="docutils literal notranslate"><span class="pre">|</span></code>,
|
||
<code class="docutils literal notranslate"><span class="pre">~</span></code>.</p>
|
||
</dd></dl>
|
||
|
||
</section>
|
||
<section id="notes-for-type-implementers">
|
||
<h2>Notes for type implementers<a class="headerlink" href="#notes-for-type-implementers" title="Link to this heading">¶</a></h2>
|
||
<p>Implementers should be careful to make equal numbers equal and hash
|
||
them to the same values. This may be subtle if there are two different
|
||
extensions of the real numbers. For example, <a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">fractions.Fraction</span></code></a>
|
||
implements <a class="reference internal" href="functions.html#hash" title="hash"><code class="xref py py-func docutils literal notranslate"><span class="pre">hash()</span></code></a> as follows:</p>
|
||
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">denominator</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<span class="c1"># Get integers right.</span>
|
||
<span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">numerator</span><span class="p">)</span>
|
||
<span class="c1"># Expensive check, but definitely correct.</span>
|
||
<span class="k">if</span> <span class="bp">self</span> <span class="o">==</span> <span class="nb">float</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="bp">self</span><span class="p">))</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="c1"># Use tuple's hash to avoid a high collision rate on</span>
|
||
<span class="c1"># simple fractions.</span>
|
||
<span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">numerator</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">denominator</span><span class="p">))</span>
|
||
</pre></div>
|
||
</div>
|
||
<section id="adding-more-numeric-abcs">
|
||
<h3>Adding More Numeric ABCs<a class="headerlink" href="#adding-more-numeric-abcs" title="Link to this heading">¶</a></h3>
|
||
<p>There are, of course, more possible ABCs for numbers, and this would
|
||
be a poor hierarchy if it precluded the possibility of adding
|
||
those. You can add <code class="docutils literal notranslate"><span class="pre">MyFoo</span></code> between <a class="reference internal" href="#numbers.Complex" title="numbers.Complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a> and
|
||
<a class="reference internal" href="#numbers.Real" title="numbers.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a> with:</p>
|
||
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">MyFoo</span><span class="p">(</span><span class="n">Complex</span><span class="p">):</span> <span class="o">...</span>
|
||
<span class="n">MyFoo</span><span class="o">.</span><span class="n">register</span><span class="p">(</span><span class="n">Real</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="implementing-the-arithmetic-operations">
|
||
<span id="id1"></span><h3>Implementing the arithmetic operations<a class="headerlink" href="#implementing-the-arithmetic-operations" title="Link to this heading">¶</a></h3>
|
||
<p>We want to implement the arithmetic operations so that mixed-mode
|
||
operations either call an implementation whose author knew about the
|
||
types of both arguments, or convert both to the nearest built in type
|
||
and do the operation there. For subtypes of <a class="reference internal" href="#numbers.Integral" title="numbers.Integral"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, this
|
||
means that <a class="reference internal" href="../reference/datamodel.html#object.__add__" title="object.__add__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__add__()</span></code></a> and <a class="reference internal" href="../reference/datamodel.html#object.__radd__" title="object.__radd__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__radd__()</span></code></a> should be
|
||
defined as:</p>
|
||
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">MyIntegral</span><span class="p">(</span><span class="n">Integral</span><span class="p">):</span>
|
||
|
||
<span class="k">def</span><span class="w"> </span><span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">MyIntegral</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">do_my_adding_stuff</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">OtherTypeIKnowAbout</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">do_my_other_adding_stuff</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="k">return</span> <span class="bp">NotImplemented</span>
|
||
|
||
<span class="k">def</span><span class="w"> </span><span class="fm">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">MyIntegral</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">do_my_adding_stuff</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">OtherTypeIKnowAbout</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">do_my_other_adding_stuff</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Integral</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">other</span><span class="p">)</span> <span class="o">+</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Real</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">other</span><span class="p">)</span> <span class="o">+</span> <span class="nb">float</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Complex</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="nb">complex</span><span class="p">(</span><span class="n">other</span><span class="p">)</span> <span class="o">+</span> <span class="nb">complex</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="k">return</span> <span class="bp">NotImplemented</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>There are 5 different cases for a mixed-type operation on subclasses
|
||
of <a class="reference internal" href="#numbers.Complex" title="numbers.Complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a>. I’ll refer to all of the above code that doesn’t
|
||
refer to <code class="docutils literal notranslate"><span class="pre">MyIntegral</span></code> and <code class="docutils literal notranslate"><span class="pre">OtherTypeIKnowAbout</span></code> as
|
||
“boilerplate”. <code class="docutils literal notranslate"><span class="pre">a</span></code> will be an instance of <code class="docutils literal notranslate"><span class="pre">A</span></code>, which is a subtype
|
||
of <a class="reference internal" href="#numbers.Complex" title="numbers.Complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a> (<code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">:</span> <span class="pre">A</span> <span class="pre"><:</span> <span class="pre">Complex</span></code>), and <code class="docutils literal notranslate"><span class="pre">b</span> <span class="pre">:</span> <span class="pre">B</span> <span class="pre"><:</span>
|
||
<span class="pre">Complex</span></code>. I’ll consider <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">b</span></code>:</p>
|
||
<ol class="arabic simple">
|
||
<li><p>If <code class="docutils literal notranslate"><span class="pre">A</span></code> defines an <a class="reference internal" href="../reference/datamodel.html#object.__add__" title="object.__add__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__add__()</span></code></a> which accepts <code class="docutils literal notranslate"><span class="pre">b</span></code>, all is
|
||
well.</p></li>
|
||
<li><p>If <code class="docutils literal notranslate"><span class="pre">A</span></code> falls back to the boilerplate code, and it were to
|
||
return a value from <a class="reference internal" href="../reference/datamodel.html#object.__add__" title="object.__add__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__add__()</span></code></a>, we’d miss the possibility
|
||
that <code class="docutils literal notranslate"><span class="pre">B</span></code> defines a more intelligent <a class="reference internal" href="../reference/datamodel.html#object.__radd__" title="object.__radd__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__radd__()</span></code></a>, so the
|
||
boilerplate should return <a class="reference internal" href="constants.html#NotImplemented" title="NotImplemented"><code class="xref py py-data docutils literal notranslate"><span class="pre">NotImplemented</span></code></a> from
|
||
<code class="xref py py-meth docutils literal notranslate"><span class="pre">__add__()</span></code>. (Or <code class="docutils literal notranslate"><span class="pre">A</span></code> may not implement <code class="xref py py-meth docutils literal notranslate"><span class="pre">__add__()</span></code> at
|
||
all.)</p></li>
|
||
<li><p>Then <code class="docutils literal notranslate"><span class="pre">B</span></code>’s <a class="reference internal" href="../reference/datamodel.html#object.__radd__" title="object.__radd__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__radd__()</span></code></a> gets a chance. If it accepts
|
||
<code class="docutils literal notranslate"><span class="pre">a</span></code>, all is well.</p></li>
|
||
<li><p>If it falls back to the boilerplate, there are no more possible
|
||
methods to try, so this is where the default implementation
|
||
should live.</p></li>
|
||
<li><p>If <code class="docutils literal notranslate"><span class="pre">B</span> <span class="pre"><:</span> <span class="pre">A</span></code>, Python tries <code class="docutils literal notranslate"><span class="pre">B.__radd__</span></code> before
|
||
<code class="docutils literal notranslate"><span class="pre">A.__add__</span></code>. This is ok, because it was implemented with
|
||
knowledge of <code class="docutils literal notranslate"><span class="pre">A</span></code>, so it can handle those instances before
|
||
delegating to <a class="reference internal" href="#numbers.Complex" title="numbers.Complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a>.</p></li>
|
||
</ol>
|
||
<p>If <code class="docutils literal notranslate"><span class="pre">A</span> <span class="pre"><:</span> <span class="pre">Complex</span></code> and <code class="docutils literal notranslate"><span class="pre">B</span> <span class="pre"><:</span> <span class="pre">Real</span></code> without sharing any other knowledge,
|
||
then the appropriate shared operation is the one involving the built
|
||
in <a class="reference internal" href="functions.html#complex" title="complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a>, and both <a class="reference internal" href="../reference/datamodel.html#object.__radd__" title="object.__radd__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__radd__()</span></code></a> s land there, so <code class="docutils literal notranslate"><span class="pre">a+b</span>
|
||
<span class="pre">==</span> <span class="pre">b+a</span></code>.</p>
|
||
<p>Because most of the operations on any given type will be very similar,
|
||
it can be useful to define a helper function which generates the
|
||
forward and reverse instances of any given operator. For example,
|
||
<a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">fractions.Fraction</span></code></a> uses:</p>
|
||
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">_operator_fallbacks</span><span class="p">(</span><span class="n">monomorphic_operator</span><span class="p">,</span> <span class="n">fallback_operator</span><span class="p">):</span>
|
||
<span class="k">def</span><span class="w"> </span><span class="nf">forward</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">Fraction</span><span class="p">)):</span>
|
||
<span class="k">return</span> <span class="n">monomorphic_operator</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">fallback_operator</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="n">b</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="nb">complex</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">fallback_operator</span><span class="p">(</span><span class="nb">complex</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="n">b</span><span class="p">)</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="k">return</span> <span class="bp">NotImplemented</span>
|
||
<span class="n">forward</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="s1">'__'</span> <span class="o">+</span> <span class="n">fallback_operator</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">+</span> <span class="s1">'__'</span>
|
||
<span class="n">forward</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="n">monomorphic_operator</span><span class="o">.</span><span class="vm">__doc__</span>
|
||
|
||
<span class="k">def</span><span class="w"> </span><span class="nf">reverse</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
|
||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">Rational</span><span class="p">):</span>
|
||
<span class="c1"># Includes ints.</span>
|
||
<span class="k">return</span> <span class="n">monomorphic_operator</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">Real</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">fallback_operator</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="nb">float</span><span class="p">(</span><span class="n">b</span><span class="p">))</span>
|
||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">Complex</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">fallback_operator</span><span class="p">(</span><span class="nb">complex</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="nb">complex</span><span class="p">(</span><span class="n">b</span><span class="p">))</span>
|
||
<span class="k">else</span><span class="p">:</span>
|
||
<span class="k">return</span> <span class="bp">NotImplemented</span>
|
||
<span class="n">reverse</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="s1">'__r'</span> <span class="o">+</span> <span class="n">fallback_operator</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">+</span> <span class="s1">'__'</span>
|
||
<span class="n">reverse</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="n">monomorphic_operator</span><span class="o">.</span><span class="vm">__doc__</span>
|
||
|
||
<span class="k">return</span> <span class="n">forward</span><span class="p">,</span> <span class="n">reverse</span>
|
||
|
||
<span class="k">def</span><span class="w"> </span><span class="nf">_add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||
<span class="w"> </span><span class="sd">"""a + b"""</span>
|
||
<span class="k">return</span> <span class="n">Fraction</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">numerator</span> <span class="o">*</span> <span class="n">b</span><span class="o">.</span><span class="n">denominator</span> <span class="o">+</span>
|
||
<span class="n">b</span><span class="o">.</span><span class="n">numerator</span> <span class="o">*</span> <span class="n">a</span><span class="o">.</span><span class="n">denominator</span><span class="p">,</span>
|
||
<span class="n">a</span><span class="o">.</span><span class="n">denominator</span> <span class="o">*</span> <span class="n">b</span><span class="o">.</span><span class="n">denominator</span><span class="p">)</span>
|
||
|
||
<span class="fm">__add__</span><span class="p">,</span> <span class="fm">__radd__</span> <span class="o">=</span> <span class="n">_operator_fallbacks</span><span class="p">(</span><span class="n">_add</span><span class="p">,</span> <span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">)</span>
|
||
|
||
<span class="c1"># ...</span>
|
||
</pre></div>
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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numbers</span></code> — Numeric abstract base classes</a><ul>
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