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<li class="toctree-l2"><a class="reference internal" href="nep-0056-array-api-main-namespace.html">NEP 56 — Array API standard support in NumPy's main namespace</a></li>
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<li class="toctree-l2"><a class="reference internal" href="nep-0047-array-api-standard.html">NEP 47 — Adopting the array API standard</a></li>
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<section id="nep-42-new-and-extensible-dtypes">
<span id="nep42"></span><h1>NEP 42 — New and extensible DTypes<a class="headerlink" href="#nep-42-new-and-extensible-dtypes" title="Link to this heading">#</a></h1>
<dl class="field-list simple">
<dt class="field-odd">title<span class="colon">:</span></dt>
<dd class="field-odd"><p>New and extensible DTypes</p>
</dd>
<dt class="field-even">Author<span class="colon">:</span></dt>
<dd class="field-even"><p>Sebastian Berg</p>
</dd>
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Ben Nathanson</p>
</dd>
<dt class="field-even">Author<span class="colon">:</span></dt>
<dd class="field-even"><p>Marten van Kerkwijk</p>
</dd>
<dt class="field-odd">Status<span class="colon">:</span></dt>
<dd class="field-odd"><p>Accepted</p>
</dd>
<dt class="field-even">Type<span class="colon">:</span></dt>
<dd class="field-even"><p>Standard</p>
</dd>
<dt class="field-odd">Created<span class="colon">:</span></dt>
<dd class="field-odd"><p>2019-07-17</p>
</dd>
<dt class="field-even">Resolution<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference external" href="https://mail.python.org/pipermail/numpy-discussion/2020-October/081038.html">https://mail.python.org/pipermail/numpy-discussion/2020-October/081038.html</a></p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This NEP is third in a series:</p>
<ul class="simple">
<li><p><a class="reference internal" href="nep-0040-legacy-datatype-impl.html#nep40"><span class="std std-ref">NEP 40</span></a> explains the shortcomings of NumPy’s dtype implementation.</p></li>
<li><p><a class="reference internal" href="nep-0041-improved-dtype-support.html#nep41"><span class="std std-ref">NEP 41</span></a> gives an overview of our proposed replacement.</p></li>
<li><p>NEP 42 (this document) describes the new design’s datatype-related APIs.</p></li>
<li><p><a class="reference internal" href="nep-0043-extensible-ufuncs.html#nep43"><span class="std std-ref">NEP 43</span></a> describes the new design’s API for universal functions.</p></li>
</ul>
</div>
<section id="abstract">
<h2>Abstract<a class="headerlink" href="#abstract" title="Link to this heading">#</a></h2>
<p>NumPy’s dtype architecture is monolithic – each dtype is an instance of a
single class. There’s no principled way to expand it for new dtypes, and the
code is difficult to read and maintain.</p>
<p>As <a class="reference internal" href="nep-0041-improved-dtype-support.html#nep41"><span class="std std-ref">NEP 41</span></a> explains, we are proposing a new architecture that is
modular and open to user additions. dtypes will derive from a new <code class="docutils literal notranslate"><span class="pre">DType</span></code>
class serving as the extension point for new types. <code class="docutils literal notranslate"><span class="pre">np.dtype("float64")</span></code>
will return an instance of a <code class="docutils literal notranslate"><span class="pre">Float64</span></code> class, a subclass of root class
<code class="docutils literal notranslate"><span class="pre">np.dtype</span></code>.</p>
<p>This NEP is one of two that lay out the design and API of this new
architecture. This NEP addresses dtype implementation; <a class="reference internal" href="nep-0043-extensible-ufuncs.html#nep43"><span class="std std-ref">NEP 43</span></a> addresses
universal functions.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Details of the private and external APIs may change to reflect user
comments and implementation constraints. The underlying principles and
choices should not change significantly.</p>
</div>
</section>
<section id="motivation-and-scope">
<h2>Motivation and scope<a class="headerlink" href="#motivation-and-scope" title="Link to this heading">#</a></h2>
<p>Our goal is to allow user code to create fully featured dtypes for a broad
variety of uses, from physical units (such as meters) to domain-specific
representations of geometric objects. <a class="reference internal" href="nep-0041-improved-dtype-support.html#nep41"><span class="std std-ref">NEP 41</span></a> describes a number
of these new dtypes and their benefits.</p>
<p>Any design supporting dtypes must consider:</p>
<ul class="simple">
<li><p>How shape and dtype are determined when an array is created</p></li>
<li><p>How array elements are stored and accessed</p></li>
<li><p>The rules for casting dtypes to other dtypes</p></li>
</ul>
<p>In addition:</p>
<ul class="simple">
<li><p>We want dtypes to comprise a class hierarchy open to new types and to
subhierarchies, as motivated in <a class="reference internal" href="nep-0041-improved-dtype-support.html#nep41"><span class="std std-ref">NEP 41</span></a>.</p></li>
</ul>
<p>And to provide this,</p>
<ul class="simple">
<li><p>We need to define a user API.</p></li>
</ul>
<p>All these are the subjects of this NEP.</p>
<ul class="simple">
<li><p>The class hierarchy, its relation to the Python scalar types, and its
important attributes are described in <a class="reference internal" href="#nep42-dtype-class">nep42_DType class</a>.</p></li>
<li><p>The functionality that will support dtype casting is described in <a class="reference internal" href="#casting">Casting</a>.</p></li>
<li><p>The implementation of item access and storage, and the way shape and dtype
are determined when creating an array, are described in <a class="reference internal" href="#nep42-array-coercion"><span class="std std-ref">Coercion to and from Python objects</span></a>.</p></li>
<li><p>The functionality for users to define their own DTypes is described in
<a class="reference internal" href="#public-c-api">Public C-API</a>.</p></li>
</ul>
<p>The API here and in <a class="reference internal" href="nep-0043-extensible-ufuncs.html#nep43"><span class="std std-ref">NEP 43</span></a> is entirely on the C side. A Python-side version
will be proposed in a future NEP. A future Python API is expected to be
similar, but provide a more convenient API to reuse the functionality of
existing DTypes. It could also provide shorthands to create structured DTypes
similar to Python’s
<a class="reference external" href="https://docs.python.org/3.8/library/dataclasses.html">dataclasses</a>.</p>
</section>
<section id="backward-compatibility">
<h2>Backward compatibility<a class="headerlink" href="#backward-compatibility" title="Link to this heading">#</a></h2>
<p>The disruption is expected to be no greater than that of a typical NumPy
release.</p>
<ul class="simple">
<li><p>The main issues are noted in <a class="reference internal" href="nep-0041-improved-dtype-support.html#nep41"><span class="std std-ref">NEP 41</span></a> and will mostly affect
heavy users of the NumPy C-API.</p></li>
<li><p>Eventually we will want to deprecate the API currently used for creating
user-defined dtypes.</p></li>
<li><p>Small, rarely noticed inconsistencies are likely to change. Examples:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">np.array(np.nan,</span> <span class="pre">dtype=np.int64)</span></code> behaves differently from
<code class="docutils literal notranslate"><span class="pre">np.array([np.nan],</span> <span class="pre">dtype=np.int64)</span></code> with the latter raising an error.
This may require identical results (either both error or both succeed).</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">np.array([array_like])</span></code> sometimes behaves differently from
<code class="docutils literal notranslate"><span class="pre">np.array([np.array(array_like)])</span></code></p></li>
<li><p>array operations may or may not preserve dtype metadata</p></li>
</ul>
</li>
<li><p>Documentation that describes the internal structure of dtypes will need
to be updated.</p></li>
</ul>
<p>The new code must pass NumPy’s regular test suite, giving some assurance that
the changes are compatible with existing code.</p>
</section>
<section id="usage-and-impact">
<h2>Usage and impact<a class="headerlink" href="#usage-and-impact" title="Link to this heading">#</a></h2>
<p>We believe the few structures in this section are sufficient to consolidate
NumPy’s present functionality and also to support complex user-defined DTypes.</p>
<p>The rest of the NEP fills in details and provides support for the claim.</p>
<p>Again, though Python is used for illustration, the implementation is a C API only; a
future NEP will tackle the Python API.</p>
<p>After implementing this NEP, creating a DType will be possible by implementing
the following outlined DType base class,
that is further described in <a class="reference internal" href="#nep42-dtype-class">nep42_DType class</a>:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">DType</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">):</span>
<span class="nb">type</span> <span class="p">:</span> <span class="nb">type</span> <span class="c1"># Python scalar type</span>
<span class="n">parametric</span> <span class="p">:</span> <span class="nb">bool</span> <span class="c1"># (may be indicated by superclass)</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">canonical</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span> <span class="nf">ensure_canonical</span><span class="p">(</span><span class="bp">self</span> <span class="p">:</span> <span class="n">DType</span><span class="p">)</span> <span class="o">-></span> <span class="n">DType</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
</pre></div>
</div>
<p>For casting, a large part of the functionality is provided by the “methods” stored
in <code class="docutils literal notranslate"><span class="pre">_castingimpl</span></code></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">common_dtype</span><span class="p">(</span><span class="bp">cls</span> <span class="p">:</span> <span class="n">DTypeMeta</span><span class="p">,</span> <span class="n">other</span> <span class="p">:</span> <span class="n">DTypeMeta</span><span class="p">)</span> <span class="o">-></span> <span class="n">DTypeMeta</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span> <span class="nf">common_instance</span><span class="p">(</span><span class="bp">self</span> <span class="p">:</span> <span class="n">DType</span><span class="p">,</span> <span class="n">other</span> <span class="p">:</span> <span class="n">DType</span><span class="p">)</span> <span class="o">-></span> <span class="n">DType</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="c1"># A mapping of "methods" each detailing how to cast to another DType</span>
<span class="c1"># (further specified at the end of the section)</span>
<span class="n">_castingimpl</span> <span class="o">=</span> <span class="p">{}</span>
</pre></div>
</div>
<p>For array-coercion, also part of casting:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span> <span class="k">def</span> <span class="nf">__dtype_setitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_pointer</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span> <span class="nf">__dtype_getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_pointer</span><span class="p">,</span> <span class="n">base_obj</span><span class="p">)</span> <span class="o">-></span> <span class="nb">object</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">__discover_descr_from_pyobject__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">obj</span> <span class="p">:</span> <span class="nb">object</span><span class="p">)</span> <span class="o">-></span> <span class="n">DType</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="c1"># initially private:</span>
<span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">_known_scalar_type</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">obj</span> <span class="p">:</span> <span class="nb">object</span><span class="p">)</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
</pre></div>
</div>
<p>Other elements of the casting implementation is the <code class="docutils literal notranslate"><span class="pre">CastingImpl</span></code>:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">casting</span> <span class="o">=</span> <span class="n">Union</span><span class="p">[</span><span class="s2">"safe"</span><span class="p">,</span> <span class="s2">"same_kind"</span><span class="p">,</span> <span class="s2">"unsafe"</span><span class="p">]</span>
<span class="k">class</span> <span class="nc">CastingImpl</span><span class="p">:</span>
<span class="c1"># Object describing and performing the cast</span>
<span class="n">casting</span> <span class="p">:</span> <span class="n">casting</span>
<span class="k">def</span> <span class="nf">resolve_descriptors</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">DTypeMeta</span><span class="p">],</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">DType</span><span class="o">|</span><span class="kc">None</span><span class="p">]</span> <span class="p">:</span> <span class="nb">input</span><span class="p">)</span> <span class="o">-></span> <span class="p">(</span><span class="n">casting</span><span class="p">,</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">DType</span><span class="p">]):</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="c1"># initially private:</span>
<span class="k">def</span> <span class="nf">_get_loop</span><span class="p">(</span><span class="o">...</span><span class="p">)</span> <span class="o">-></span> <span class="n">lowlevel_C_loop</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
</pre></div>
</div>
<p>which describes the casting from one DType to another. In
<a class="reference internal" href="nep-0043-extensible-ufuncs.html#nep43"><span class="std std-ref">NEP 43</span></a> this <code class="docutils literal notranslate"><span class="pre">CastingImpl</span></code> object is used unchanged to
support universal functions.
Note that the name <code class="docutils literal notranslate"><span class="pre">CastingImpl</span></code> here will be generically called
<code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> to accommodate both casting and universal functions.</p>
</section>
<section id="definitions">
<h2>Definitions<a class="headerlink" href="#definitions" title="Link to this heading">#</a></h2>
<dl class="simple glossary">
<dt id="term-dtype">dtype<a class="headerlink" href="#term-dtype" title="Link to this term">#</a></dt><dd><p>The dtype <em>instance</em>; this is the object attached to a numpy array.</p>
</dd>
<dt id="term-DType">DType<a class="headerlink" href="#term-DType" title="Link to this term">#</a></dt><dd><p>Any subclass of the base type <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code>.</p>
</dd>
<dt id="term-coercion">coercion<a class="headerlink" href="#term-coercion" title="Link to this term">#</a></dt><dd><p>Conversion of Python types to NumPy arrays and values stored in a NumPy
array.</p>
</dd>
<dt id="term-cast">cast<a class="headerlink" href="#term-cast" title="Link to this term">#</a></dt><dd><p>Conversion of an array to a different dtype.</p>
</dd>
<dt id="term-parametric-type">parametric type<a class="headerlink" href="#term-parametric-type" title="Link to this term">#</a></dt><dd><p>A dtype whose representation can change based on a parameter value,
like a string dtype with a length parameter. All members of the current
<code class="docutils literal notranslate"><span class="pre">flexible</span></code> dtype class are parametric. See
<a class="reference internal" href="nep-0040-legacy-datatype-impl.html#parametric-datatype-discussion"><span class="std std-ref">NEP 40</span></a>.</p>
</dd>
<dt id="term-promotion">promotion<a class="headerlink" href="#term-promotion" title="Link to this term">#</a></dt><dd><p>Finding a dtype that can perform an operation on a mix of dtypes without
loss of information.</p>
</dd>
<dt id="term-safe-cast">safe cast<a class="headerlink" href="#term-safe-cast" title="Link to this term">#</a></dt><dd><p>A cast is safe if no information is lost when changing type.</p>
</dd>
</dl>
<p>On the C level we use <code class="docutils literal notranslate"><span class="pre">descriptor</span></code> or <code class="docutils literal notranslate"><span class="pre">descr</span></code> to mean
<em>dtype instance</em>. In the proposed C-API, these terms will distinguish
dtype instances from DType classes.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>NumPy has an existing class hierarchy for scalar types, as
seen <a class="reference internal" href="nep-0040-legacy-datatype-impl.html#nep-0040-dtype-hierarchy"><span class="std std-ref">in the figure</span></a> of
<a class="reference internal" href="nep-0040-legacy-datatype-impl.html#nep40"><span class="std std-ref">NEP 40</span></a>, and the new DType hierarchy will resemble it. The
types are used as an attribute of the single dtype class in the current
NumPy; they’re not dtype classes. They neither harm nor help this work.</p>
</div>
</section>
<section id="the-dtype-class">
<span id="nep42-dtype-class"></span><h2>The DType class<a class="headerlink" href="#the-dtype-class" title="Link to this heading">#</a></h2>
<p>This section reviews the structure underlying the proposed DType class,
including the type hierarchy and the use of abstract DTypes.</p>
<section id="class-getter">
<h3>Class getter<a class="headerlink" href="#class-getter" title="Link to this heading">#</a></h3>
<p>To create a DType instance from a scalar type users now call
<code class="docutils literal notranslate"><span class="pre">np.dtype</span></code> (for instance, <code class="docutils literal notranslate"><span class="pre">np.dtype(np.int64)</span></code>). Sometimes it is
also necessary to access the underlying DType class; this comes up in
particular with type hinting because the “type” of a DType instance is
the DType class. Taking inspiration from type hinting, we propose the
following getter syntax:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">]</span>
</pre></div>
</div>
<p>to get the DType class corresponding to a scalar type. The notation
works equally well with built-in and user-defined DTypes.</p>
<p>This getter eliminates the need to create an explicit name for every
DType, crowding the <code class="docutils literal notranslate"><span class="pre">np</span></code> namespace; the getter itself signifies the
type. It also opens the possibility of making <code class="docutils literal notranslate"><span class="pre">np.ndarray</span></code> generic
over DType class using annotations like:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">]]</span>
</pre></div>
</div>
<p>The above is fairly verbose, so it is possible that we will include
aliases like:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Float64</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">]</span>
</pre></div>
</div>
<p>in <code class="docutils literal notranslate"><span class="pre">numpy.typing</span></code>, thus keeping annotations concise but still
avoiding crowding the <code class="docutils literal notranslate"><span class="pre">np</span></code> namespace as discussed above. For a
user-defined DType:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">UserDtype</span><span class="p">(</span><span class="n">dtype</span><span class="p">):</span> <span class="o">...</span>
</pre></div>
</div>
<p>one can do <code class="docutils literal notranslate"><span class="pre">np.ndarray[UserDtype]</span></code>, keeping annotations concise in
that case without introducing boilerplate in NumPy itself. For a
user-defined scalar type:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">UserScalar</span><span class="p">(</span><span class="n">generic</span><span class="p">):</span> <span class="o">...</span>
</pre></div>
</div>
<p>we would need to add a typing overload to <code class="docutils literal notranslate"><span class="pre">dtype</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nd">@overload</span>
<span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">dtype</span><span class="p">:</span> <span class="n">Type</span><span class="p">[</span><span class="n">UserScalar</span><span class="p">],</span> <span class="o">...</span><span class="p">)</span> <span class="o">-></span> <span class="n">UserDtype</span>
</pre></div>
</div>
<p>to allow <code class="docutils literal notranslate"><span class="pre">np.dtype[UserScalar]</span></code>.</p>
<p>The initial implementation probably will return only concrete (not abstract)
DTypes.</p>
<p><em>This item is still under review.</em></p>
</section>
<section id="hierarchy-and-abstract-classes">
<h3>Hierarchy and abstract classes<a class="headerlink" href="#hierarchy-and-abstract-classes" title="Link to this heading">#</a></h3>
<p>We will use abstract classes as building blocks of our extensible DType class
hierarchy.</p>
<ol class="arabic simple">
<li><p>Abstract classes are inherited cleanly, in principle allowing checks like
<code class="docutils literal notranslate"><span class="pre">isinstance(np.dtype("float64"),</span> <span class="pre">np.inexact)</span></code>.</p></li>
<li><p>Abstract classes allow a single piece of code to handle a multiplicity of
input types. Code written to accept Complex objects can work with numbers
of any precision; the precision of the results is determined by the
precision of the arguments.</p></li>
<li><p>There’s room for user-created families of DTypes. We can envision an
abstract <code class="docutils literal notranslate"><span class="pre">Unit</span></code> class for physical units, with a concrete subclass like
<code class="docutils literal notranslate"><span class="pre">Float64Unit</span></code>. Calling <code class="docutils literal notranslate"><span class="pre">Unit(np.float64,</span> <span class="pre">"m")</span></code> (<code class="docutils literal notranslate"><span class="pre">m</span></code> for meters) would
be equivalent to <code class="docutils literal notranslate"><span class="pre">Float64Unit("m")</span></code>.</p></li>
<li><p>The implementation of universal functions in <a class="reference internal" href="nep-0043-extensible-ufuncs.html#nep43"><span class="std std-ref">NEP 43</span></a> may require
a class hierarchy.</p></li>
</ol>
<p><strong>Example:</strong> A NumPy <code class="docutils literal notranslate"><span class="pre">Categorical</span></code> class would be a match for pandas
<code class="docutils literal notranslate"><span class="pre">Categorical</span></code> objects, which can contain integers or general Python objects.
NumPy needs a DType that it can assign a Categorical to, but it also needs
DTypes like <code class="docutils literal notranslate"><span class="pre">CategoricalInt64</span></code> and <code class="docutils literal notranslate"><span class="pre">CategoricalObject</span></code> such that
<code class="docutils literal notranslate"><span class="pre">common_dtype(CategoricalInt64,</span> <span class="pre">String)</span></code> raises an error, but
<code class="docutils literal notranslate"><span class="pre">common_dtype(CategoricalObject,</span> <span class="pre">String)</span></code> returns an <code class="docutils literal notranslate"><span class="pre">object</span></code> DType. In
our scheme, <code class="docutils literal notranslate"><span class="pre">Categorical</span></code> is an abstract type with <code class="docutils literal notranslate"><span class="pre">CategoricalInt64</span></code> and
<code class="docutils literal notranslate"><span class="pre">CategoricalObject</span></code> subclasses.</p>
<p>Rules for the class structure, illustrated <a class="reference internal" href="#nep42-hierarchy-figure"><span class="std std-ref">below</span></a>:</p>
<ol class="arabic simple">
<li><p>Abstract DTypes cannot be instantiated. Instantiating an abstract DType
raises an error, or perhaps returns an instance of a concrete subclass.
Raising an error will be the default behavior and may be required initially.</p></li>
<li><p>While abstract DTypes may be superclasses, they may also act like Python’s
abstract base classes (ABC) allowing registration instead of subclassing.
It may be possible to simply use or inherit from Python ABCs.</p></li>
<li><p>Concrete DTypes may not be subclassed. In the future this might be relaxed
to allow specialized implementations such as a GPU float64 subclassing a
NumPy float64.</p></li>
</ol>
<p>The
<a class="reference external" href="https://docs.julialang.org/en/v1/manual/types/#man-abstract-types-1">Julia language</a>
has a similar prohibition against subclassing concrete types.
For example methods such as the later <code class="docutils literal notranslate"><span class="pre">__common_instance__</span></code> or
<code class="docutils literal notranslate"><span class="pre">__common_dtype__</span></code> cannot work for a subclass unless they were designed
very carefully.
It helps avoid unintended vulnerabilities to implementation changes that
result from subclassing types that were not written to be subclassed.
We believe that the DType API should rather be extended to simplify wrapping
of existing functionality.</p>
<p>The DType class requires C-side storage of methods and additional information,
to be implemented by a <code class="docutils literal notranslate"><span class="pre">DTypeMeta</span></code> class. Each <code class="docutils literal notranslate"><span class="pre">DType</span></code> class is an
instance of <code class="docutils literal notranslate"><span class="pre">DTypeMeta</span></code> with a well-defined and extensible interface;
end users ignore it.</p>
<figure class="align-center align-default" id="nep42-hierarchy-figure">
<img alt="_images/dtype_hierarchy.svg" src="_images/dtype_hierarchy.svg" /></figure>
</section>
<section id="miscellaneous-methods-and-attributes">
<h3>Miscellaneous methods and attributes<a class="headerlink" href="#miscellaneous-methods-and-attributes" title="Link to this heading">#</a></h3>
<p>This section collects definitions in the DType class that are not used in
casting and array coercion, which are described in detail below.</p>
<ul class="simple">
<li><p>Existing dtype methods (<a class="reference external" href="https://numpy.org/devdocs/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v2.2.dev0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.dtype</span></code></a>) and C-side fields are preserved.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">DType.type</span></code> replaces <code class="docutils literal notranslate"><span class="pre">dtype.type</span></code>. Unless a use case arises,
<code class="docutils literal notranslate"><span class="pre">dtype.type</span></code> will be deprecated.
This indicates a Python scalar type which represents the same values as
the DType. This is the same type as used in the proposed <a class="reference internal" href="#class-getter">Class getter</a>
and for <a class="reference internal" href="#dtype-discovery-during-array-coercion">DType discovery during array coercion</a>.
(This can may also be set for abstract DTypes, this is necessary
for array coercion.)</p></li>
<li><p>A new <code class="docutils literal notranslate"><span class="pre">self.canonical</span></code> property generalizes the notion of byte order to
indicate whether data has been stored in a default/canonical way. For
existing code, “canonical” will just signify native byte order, but it can
take on new meanings in new DTypes – for instance, to distinguish a
complex-conjugated instance of Complex which stores <code class="docutils literal notranslate"><span class="pre">real</span> <span class="pre">-</span> <span class="pre">imag</span></code> instead
of <code class="docutils literal notranslate"><span class="pre">real</span> <span class="pre">+</span> <span class="pre">imag</span></code>. The ISNBO (“is
native byte order”) flag might be repurposed as the canonical flag.</p></li>
<li><p>Support is included for parametric DTypes. A DType will be deemed parametric
if it inherits from ParametricDType.</p></li>
<li><p>DType methods may resemble or even reuse existing Python slots. Thus Python
special slots are off-limits for user-defined DTypes (for instance, defining
<code class="docutils literal notranslate"><span class="pre">Unit("m")</span> <span class="pre">></span> <span class="pre">Unit("cm")</span></code>), since we may want to develop a meaning for these
operators that is common to all DTypes.</p></li>
<li><p>Sorting functions are moved to the DType class. They may be implemented by
defining a method <code class="docutils literal notranslate"><span class="pre">dtype_get_sort_function(self,</span> <span class="pre">sortkind="stable")</span> <span class="pre">-></span>
<span class="pre">sortfunction</span></code> that must return <code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code> if the given <code class="docutils literal notranslate"><span class="pre">sortkind</span></code>
is not known.</p></li>
<li><p>Functions that cannot be removed are implemented as special methods.
Many of these were previously defined part of the <a class="reference external" href="https://numpy.org/devdocs/reference/c-api/types-and-structures.html#c.PyArray_ArrFuncs" title="(in NumPy v2.2.dev0)"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyArray_ArrFuncs</span></code></a>
slot of the dtype instance (<code class="docutils literal notranslate"><span class="pre">PyArray_Descr</span> <span class="pre">*</span></code>) and include functions
such as <code class="docutils literal notranslate"><span class="pre">nonzero</span></code>, <code class="docutils literal notranslate"><span class="pre">fill</span></code> (used for <code class="docutils literal notranslate"><span class="pre">np.arange</span></code>), and
<code class="docutils literal notranslate"><span class="pre">fromstr</span></code> (used to parse text files).
These old methods will be deprecated and replacements
following the new design principles added.
The API is not defined here. Since these methods can be deprecated and renamed
replacements added, it is acceptable if these new methods have to be modified.</p></li>
<li><p>Use of <code class="docutils literal notranslate"><span class="pre">kind</span></code> for non-built-in types is discouraged in favor of
<code class="docutils literal notranslate"><span class="pre">isinstance</span></code> checks. <code class="docutils literal notranslate"><span class="pre">kind</span></code> will return the <code class="docutils literal notranslate"><span class="pre">__qualname__</span></code> of the
object to ensure uniqueness for all DTypes. On the C side, <code class="docutils literal notranslate"><span class="pre">kind</span></code> and
<code class="docutils literal notranslate"><span class="pre">char</span></code> are set to <code class="docutils literal notranslate"><span class="pre">\0</span></code> (NULL character).
While <code class="docutils literal notranslate"><span class="pre">kind</span></code> will be discouraged, the current <code class="docutils literal notranslate"><span class="pre">np.issubdtype</span></code>
may remain the preferred method for this type of check.</p></li>
<li><p>A method <code class="docutils literal notranslate"><span class="pre">ensure_canonical(self)</span> <span class="pre">-></span> <span class="pre">dtype</span></code> returns a new dtype (or
<code class="docutils literal notranslate"><span class="pre">self</span></code>) with the <code class="docutils literal notranslate"><span class="pre">canonical</span></code> flag set.</p></li>
<li><p>Since NumPy’s approach is to provide functionality through unfuncs,
functions like sorting that will be implemented in DTypes might eventually be
reimplemented as generalized ufuncs.</p></li>
</ul>
</section>
</section>
<section id="casting">
<span id="nep-42-casting"></span><h2>Casting<a class="headerlink" href="#casting" title="Link to this heading">#</a></h2>
<p>We review here the operations related to casting arrays:</p>
<ul class="simple">
<li><p>Finding the “common dtype,” returned by <a class="reference external" href="https://numpy.org/devdocs/reference/generated/numpy.promote_types.html#numpy.promote_types" title="(in NumPy v2.2.dev0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.promote_types()</span></code></a> and
<a class="reference external" href="https://numpy.org/devdocs/reference/generated/numpy.result_type.html#numpy.result_type" title="(in NumPy v2.2.dev0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.result_type()</span></code></a></p></li>
<li><p>The result of calling <a class="reference external" href="https://numpy.org/devdocs/reference/generated/numpy.can_cast.html#numpy.can_cast" title="(in NumPy v2.2.dev0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.can_cast()</span></code></a></p></li>
</ul>
<p>We show how casting arrays with <code class="docutils literal notranslate"><span class="pre">astype(new_dtype)</span></code> will be implemented.</p>
<section id="common-dtype-operations">
<h3><cite>Common DType</cite> operations<a class="headerlink" href="#common-dtype-operations" title="Link to this heading">#</a></h3>
<p>When input types are mixed, a first step is to find a DType that can hold
the result without loss of information – a “common DType.”</p>
<p>Array coercion and concatenation both return a common dtype instance. Most
universal functions use the common DType for dispatching, though they might
not use it for a result (for instance, the result of a comparison is always
bool).</p>
<p>We propose the following implementation:</p>
<ul>
<li><p>For two DType classes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">__common_dtype__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">other</span> <span class="p">:</span> <span class="n">DTypeMeta</span><span class="p">)</span> <span class="o">-></span> <span class="n">DTypeMeta</span>
</pre></div>
</div>
<p>Returns a new DType, often one of the inputs, which can represent values
of both input DTypes. This should usually be minimal:
the common DType of <code class="docutils literal notranslate"><span class="pre">Int16</span></code> and <code class="docutils literal notranslate"><span class="pre">Uint16</span></code> is <code class="docutils literal notranslate"><span class="pre">Int32</span></code> and not <code class="docutils literal notranslate"><span class="pre">Int64</span></code>.
<code class="docutils literal notranslate"><span class="pre">__common_dtype__</span></code> may return NotImplemented to defer to other and,
like Python operators, subclasses take precedence (their
<code class="docutils literal notranslate"><span class="pre">__common_dtype__</span></code> method is tried first).</p>
</li>
<li><p>For two instances of the same DType:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">__common_instance__</span><span class="p">(</span><span class="bp">self</span><span class="p">:</span> <span class="n">SelfT</span><span class="p">,</span> <span class="n">other</span> <span class="p">:</span> <span class="n">SelfT</span><span class="p">)</span> <span class="o">-></span> <span class="n">SelfT</span>
</pre></div>
</div>
<p>For nonparametric built-in dtypes, this returns a canonicalized copy of
<code class="docutils literal notranslate"><span class="pre">self</span></code>, preserving metadata. For nonparametric user types, this provides
a default implementation.</p>
</li>
<li><p>For instances of different DTypes, for example <code class="docutils literal notranslate"><span class="pre">>float64</span></code> and <code class="docutils literal notranslate"><span class="pre">S8</span></code>,
the operation is done in three steps:</p>
<ol class="arabic simple">
<li><p><code class="docutils literal notranslate"><span class="pre">Float64.__common_dtype__(type(>float64),</span> <span class="pre">type(S8))</span></code>
returns <code class="docutils literal notranslate"><span class="pre">String</span></code> (or defers to <code class="docutils literal notranslate"><span class="pre">String.__common_dtype__</span></code>).</p></li>
<li><p>The casting machinery (explained in detail below) provides the
information that <code class="docutils literal notranslate"><span class="pre">">float64"</span></code> casts to <code class="docutils literal notranslate"><span class="pre">"S32"</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">String.__common_instance__("S8",</span> <span class="pre">"S32")</span></code> returns the final <code class="docutils literal notranslate"><span class="pre">"S32"</span></code>.</p></li>
</ol>
</li>
</ul>
<p>The benefit of this handoff is to reduce duplicated code and keep concerns
separate. DType implementations don’t need to know how to cast, and the
results of casting can be extended to new types, such as a new string encoding.</p>
<p>This means the implementation will work like this:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">common_dtype</span><span class="p">(</span><span class="n">DType1</span><span class="p">,</span> <span class="n">DType2</span><span class="p">):</span>
<span class="n">common_dtype</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="n">dtype1</span><span class="p">)</span><span class="o">.</span><span class="n">__common_dtype__</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">dtype2</span><span class="p">))</span>
<span class="k">if</span> <span class="n">common_dtype</span> <span class="ow">is</span> <span class="bp">NotImplemented</span><span class="p">:</span>
<span class="n">common_dtype</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="n">dtype2</span><span class="p">)</span><span class="o">.</span><span class="n">__common_dtype__</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">dtype1</span><span class="p">))</span>
<span class="k">if</span> <span class="n">common_dtype</span> <span class="ow">is</span> <span class="bp">NotImplemented</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">"no common dtype"</span><span class="p">)</span>
<span class="k">return</span> <span class="n">common_dtype</span>
<span class="k">def</span> <span class="nf">promote_types</span><span class="p">(</span><span class="n">dtype1</span><span class="p">,</span> <span class="n">dtype2</span><span class="p">):</span>
<span class="n">common</span> <span class="o">=</span> <span class="n">common_dtype</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">dtype1</span><span class="p">),</span> <span class="nb">type</span><span class="p">(</span><span class="n">dtype2</span><span class="p">))</span>
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">dtype1</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">common</span><span class="p">:</span>
<span class="c1"># Find what dtype1 is cast to when cast to the common DType</span>
<span class="c1"># by using the CastingImpl as described below:</span>
<span class="n">castingimpl</span> <span class="o">=</span> <span class="n">get_castingimpl</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">dtype1</span><span class="p">),</span> <span class="n">common</span><span class="p">)</span>
<span class="n">safety</span><span class="p">,</span> <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">dtype1</span><span class="p">)</span> <span class="o">=</span> <span class="n">castingimpl</span><span class="o">.</span><span class="n">resolve_descriptors</span><span class="p">(</span>
<span class="p">(</span><span class="n">common</span><span class="p">,</span> <span class="n">common</span><span class="p">),</span> <span class="p">(</span><span class="n">dtype1</span><span class="p">,</span> <span class="kc">None</span><span class="p">))</span>
<span class="k">assert</span> <span class="n">safety</span> <span class="o">==</span> <span class="s2">"safe"</span> <span class="c1"># promotion should normally be a safe cast</span>
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">dtype2</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">common</span><span class="p">:</span>
<span class="c1"># Same as above branch for dtype1.</span>
<span class="k">if</span> <span class="n">dtype1</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">dtype2</span><span class="p">:</span>
<span class="k">return</span> <span class="n">common</span><span class="o">.</span><span class="n">__common_instance__</span><span class="p">(</span><span class="n">dtype1</span><span class="p">,</span> <span class="n">dtype2</span><span class="p">)</span>
</pre></div>
</div>
<p>Some of these steps may be optimized for nonparametric DTypes.</p>
<p>Since the type returned by <code class="docutils literal notranslate"><span class="pre">__common_dtype__</span></code> is not necessarily one of the
two arguments, it’s not equivalent to NumPy’s “safe” casting.
Safe casting works for <code class="docutils literal notranslate"><span class="pre">np.promote_types(int16,</span> <span class="pre">int64)</span></code>, which returns
<code class="docutils literal notranslate"><span class="pre">int64</span></code>, but fails for:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">promote_types</span><span class="p">(</span><span class="s2">"int64"</span><span class="p">,</span> <span class="s2">"float32"</span><span class="p">)</span> <span class="o">-></span> <span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">(</span><span class="s2">"float64"</span><span class="p">)</span>
</pre></div>
</div>
<p>It is the responsibility of the DType author to ensure that the inputs
can be safely cast to the <code class="docutils literal notranslate"><span class="pre">__common_dtype__</span></code>.</p>
<p>Exceptions may apply. For example, casting <code class="docutils literal notranslate"><span class="pre">int32</span></code> to
a (long enough) string is at least at this time considered “safe”.
However <code class="docutils literal notranslate"><span class="pre">np.promote_types(int32,</span> <span class="pre">String)</span></code> will <em>not</em> be defined.</p>
<p><strong>Example:</strong></p>
<p><code class="docutils literal notranslate"><span class="pre">object</span></code> always chooses <code class="docutils literal notranslate"><span class="pre">object</span></code> as the common DType. For
<code class="docutils literal notranslate"><span class="pre">datetime64</span></code> type promotion is defined with no other datatype, but if
someone were to implement a new higher precision datetime, then:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">HighPrecisionDatetime</span><span class="o">.</span><span class="n">__common_dtype__</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">datetime64</span><span class="p">])</span>
</pre></div>
</div>
<p>would return <code class="docutils literal notranslate"><span class="pre">HighPrecisionDatetime</span></code>, and the casting implementation,
as described below, may need to decide how to handle the datetime unit.</p>
<p><strong>Alternatives:</strong></p>
<ul>
<li><p>We’re pushing the decision on common DTypes to the DType classes. Suppose
instead we could turn to a universal algorithm based on safe casting,
imposing a total order on DTypes and returning the first type that both
arguments could cast to safely.</p>
<p>It would be difficult to devise a reasonable total order, and it would have
to accept new entries. Beyond that, the approach is flawed because
importing a type can change the behavior of a program. For example, a
program requiring the common DType of <code class="docutils literal notranslate"><span class="pre">int16</span></code> and <code class="docutils literal notranslate"><span class="pre">uint16</span></code> would
ordinarily get the built-in type <code class="docutils literal notranslate"><span class="pre">int32</span></code> as the first match; if the
program adds <code class="docutils literal notranslate"><span class="pre">import</span> <span class="pre">int24</span></code>, the first match becomes <code class="docutils literal notranslate"><span class="pre">int24</span></code> and the
smaller type might make the program overflow for the first time. <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a></p>
</li>
<li><p>A more flexible common DType could be implemented in the future where
<code class="docutils literal notranslate"><span class="pre">__common_dtype__</span></code> relies on information from the casting logic.
Since <code class="docutils literal notranslate"><span class="pre">__commond_dtype__</span></code> is a method a such a default implementation
could be added at a later time.</p></li>
<li><p>The three-step handling of differing dtypes could, of course, be coalesced.
It would lose the value of splitting in return for a possibly faster
execution. But few cases would benefit. Most cases, such as array coercion,
involve a single Python type (and thus dtype).</p></li>
</ul>
</section>
<section id="the-cast-operation">
<h3>The cast operation<a class="headerlink" href="#the-cast-operation" title="Link to this heading">#</a></h3>
<p>Casting is perhaps the most complex and interesting DType operation. It
is much like a typical universal function on arrays, converting one input to a
new output, with two distinctions:</p>
<ul class="simple">
<li><p>Casting always requires an explicit output datatype.</p></li>
<li><p>The NumPy iterator API requires access to functions that are lower-level
than what universal functions currently need.</p></li>
</ul>
<p>Casting can be complex and may not implement all details of each input