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<section id="nep-41-first-step-towards-a-new-datatype-system">
<span id="nep41"></span><h1>NEP 41 — First step towards a new datatype system<a class="headerlink" href="#nep-41-first-step-towards-a-new-datatype-system" 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>First step towards a new Datatype System</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>Stéfan van der Walt</p>
</dd>
<dt class="field-even">Author<span class="colon">:</span></dt>
<dd class="field-even"><p>Matti Picus</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 Track</p>
</dd>
<dt class="field-odd">Created<span class="colon">:</span></dt>
<dd class="field-odd"><p>2020-02-03</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-April/080573.html">https://mail.python.org/pipermail/numpy-discussion/2020-April/080573.html</a> and <a class="reference external" href="https://mail.python.org/pipermail/numpy-discussion/2020-March/080495.html">https://mail.python.org/pipermail/numpy-discussion/2020-March/080495.html</a></p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This NEP is second 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>NEP 41 (this document) gives an overview of our proposed replacement.</p></li>
<li><p><a class="reference internal" href="nep-0042-new-dtypes.html#nep42"><span class="std std-ref">NEP 42</span></a> 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><a class="reference external" href="https://numpy.org/devdocs/reference/arrays.dtypes.html#arrays-dtypes" title="(in NumPy v2.5.dev0)"><span class="xref std std-ref">Datatypes</span></a> in NumPy describe how to interpret each
element in arrays. NumPy provides <code class="docutils literal notranslate"><span class="pre">int</span></code>, <code class="docutils literal notranslate"><span class="pre">float</span></code>, and <code class="docutils literal notranslate"><span class="pre">complex</span></code> numerical
types, as well as string, datetime, and structured datatype capabilities.
The growing Python community, however, has need for more diverse datatypes.
Examples are datatypes with unit information attached (such as meters) or
categorical datatypes (fixed set of possible values).
However, the current NumPy datatype API is too limited to allow the creation
of these.</p>
<p>This NEP is the first step to enable such growth; it will lead to
a simpler development path for new datatypes.
In the long run the new datatype system will also support the creation
of datatypes directly from Python rather than C.
Refactoring the datatype API will improve maintainability and facilitate
development of both user-defined external datatypes,
as well as new features for existing datatypes internal to NumPy.</p>
</section>
<section id="motivation-and-scope">
<h2>Motivation and scope<a class="headerlink" href="#motivation-and-scope" title="Link to this heading">#</a></h2>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p>The user impact section includes examples of what kind of new datatypes
will be enabled by the proposed changes in the long run.
It may thus help to read these section out of order.</p>
</div>
<section id="motivation">
<h3>Motivation<a class="headerlink" href="#motivation" title="Link to this heading">#</a></h3>
<p>One of the main issues with the current API is the definition of typical
functions such as addition and multiplication for parametric datatypes
(see also <a class="reference internal" href="nep-0040-legacy-datatype-impl.html#nep40"><span class="std std-ref">NEP 40</span></a>)
which require additional steps to determine the output type.
For example when adding two strings of length 4, the result is a string
of length 8, which is different from the input.
Similarly, a datatype which embeds a physical unit must calculate the new unit
information: dividing a distance by a time results in a speed.
A related difficulty is that the <a class="reference external" href="https://numpy.org/devdocs/user/basics.ufuncs.html#ufuncs-casting" title="(in NumPy v2.5.dev0)"><span class="xref std std-ref">current casting rules</span></a>
– the conversion between different datatypes –
cannot describe casting for such parametric datatypes implemented outside of NumPy.</p>
<p>This additional functionality for supporting parametric datatypes introduces
increased complexity within NumPy itself,
and furthermore is not available to external user-defined datatypes.
In general the concerns of different datatypes are not well-encapsulated.
This burden is exacerbated by the exposure of internal C structures,
limiting the addition of new fields
(for example to support new sorting methods <a class="reference internal" href="#new-sort" id="id1"><span>[new_sort]</span></a>).</p>
<p>Currently there are many factors which limit the creation of new user-defined
datatypes:</p>
<ul class="simple">
<li><p>Creating casting rules for parametric user-defined dtypes is either impossible
or so complex that it has never been attempted.</p></li>
<li><p>Type promotion, e.g. the operation deciding that adding float and integer
values should return a float value, is very valuable for numeric datatypes
but is limited in scope for user-defined and especially parametric datatypes.</p></li>
<li><p>Much of the logic (e.g. promotion) is written in single functions
instead of being split as methods on the datatype itself.</p></li>
<li><p>In the current design datatypes cannot have methods that do not generalize
to other datatypes. For example a unit datatype cannot have a <code class="docutils literal notranslate"><span class="pre">.to_si()</span></code> method to
easily find the datatype which would represent the same values in SI units.</p></li>
</ul>
<p>The large need to solve these issues has driven the scientific community
to create work-arounds in multiple projects implementing physical units as an
array-like class instead of a datatype, which would generalize better across
multiple array-likes (Dask, pandas, etc.).
Already, Pandas has made a push into the same direction with its
extension arrays <a class="reference internal" href="#pandas-extension-arrays" id="id2"><span>[pandas_extension_arrays]</span></a> and undoubtedly
the community would be best served if such new features could be common
between NumPy, Pandas, and other projects.</p>
</section>
<section id="scope">
<h3>Scope<a class="headerlink" href="#scope" title="Link to this heading">#</a></h3>
<p>The proposed refactoring of the datatype system is a large undertaking and
thus is proposed to be split into various phases, roughly:</p>
<ul class="simple">
<li><p>Phase I: Restructure and extend the datatype infrastructure (This NEP 41)</p></li>
<li><p>Phase II: Incrementally define or rework API (Detailed largely in NEPs 42/43)</p></li>
<li><p>Phase III: Growth of NumPy and Scientific Python Ecosystem capabilities.</p></li>
</ul>
<p>For a more detailed accounting of the various phases, see
“Plan to Approach the Full Refactor” in the Implementation section below.
This NEP proposes to move ahead with the necessary creation of new dtype
subclasses (Phase I),
and start working on implementing current functionality.
Within the context of this NEP all development will be fully private API or
use preliminary underscored names which must be changed in the future.
Most of the internal and public API choices are part of a second Phase
and will be discussed in more detail in the following NEPs 42 and 43.
The initial implementation of this NEP will have little or no effect on users,
but provides the necessary ground work for incrementally addressing the
full rework.</p>
<p>The implementation of this NEP and the following, implied large rework of how
datatypes are defined in NumPy is expected to create small incompatibilities
(see backward compatibility section).
However, a transition requiring large code adaption is not anticipated and not
within scope.</p>
<p>Specifically, this NEP makes the following design choices which are discussed
in more details in the detailed description section:</p>
<ol class="arabic simple">
<li><p>Each datatype will be an instance of a subclass of <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code>, with most of the
datatype-specific logic being implemented
as special methods on the class. In the C-API, these correspond to specific
slots. In short, for <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">=</span> <span class="pre">np.dtype("f8")</span></code>, <code class="docutils literal notranslate"><span class="pre">isinstance(f,</span> <span class="pre">np.dtype)</span></code> will remain true,
but <code class="docutils literal notranslate"><span class="pre">type(f)</span></code> will be a subclass of <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code> rather than just <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code> itself.
The <code class="docutils literal notranslate"><span class="pre">PyArray_ArrFuncs</span></code> which are currently stored as a pointer on the instance (as <code class="docutils literal notranslate"><span class="pre">PyArray_Descr->f</span></code>),
should instead be stored on the class as typically done in Python.
In the future these may correspond to python side dunder methods.
Storage information such as itemsize and byteorder can differ between
different dtype instances (e.g. “S3” vs. “S8”) and will remain part of the instance.
This means that in the long run the current lowlevel access to dtype methods
will be removed (see <code class="docutils literal notranslate"><span class="pre">PyArray_ArrFuncs</span></code> in
<a class="reference internal" href="nep-0040-legacy-datatype-impl.html#nep40"><span class="std std-ref">NEP 40</span></a>).</p></li>
<li><p>The current NumPy scalars will <em>not</em> change, they will not be instances of
datatypes. This will also be true for new datatypes, scalars will not be
instances of a dtype (although <code class="docutils literal notranslate"><span class="pre">isinstance(scalar,</span> <span class="pre">dtype)</span></code> may be made
to return <code class="docutils literal notranslate"><span class="pre">True</span></code> when appropriate).</p></li>
</ol>
<p>Detailed technical decisions to follow in NEP 42.</p>
<p>Further, the public API will be designed in a way that is extensible in the future:</p>
<ol class="arabic simple" start="3">
<li><p>All new C-API functions provided to the user will hide implementation details
as much as possible. The public API should be an identical, but limited,
version of the C-API used for the internal NumPy datatypes.</p></li>
</ol>
<p>The datatype system may be targeted to work with NumPy arrays,
for example by providing strided-loops, but should avoid direct
interactions with the array-object (typically <cite>np.ndarray</cite> instances).
Instead, the design principle will be that the array-object is a consumer
of the datatype.
While only a guiding principle, this may allow splitting the datatype system
or even the NumPy datatypes into their own project which NumPy depends on.</p>
<p>The changes to the datatype system in Phase II must include a large refactor of the
UFunc machinery, which will be further defined in NEP 43:</p>
<ol class="arabic simple" start="4">
<li><p>To enable all of the desired functionality for new user-defined datatypes,
the UFunc machinery will be changed to replace the current dispatching
and type resolution system.
The old system should be <em>mostly</em> supported as a legacy version for some time.</p></li>
</ol>
<p>Additionally, as a general design principle, the addition of new user-defined
datatypes will <em>not</em> change the behaviour of programs.
For example <code class="docutils literal notranslate"><span class="pre">common_dtype(a,</span> <span class="pre">b)</span></code> must not be <code class="docutils literal notranslate"><span class="pre">c</span></code> unless <code class="docutils literal notranslate"><span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">b</span></code> know
that <code class="docutils literal notranslate"><span class="pre">c</span></code> exists.</p>
</section>
</section>
<section id="user-impact">
<h2>User impact<a class="headerlink" href="#user-impact" title="Link to this heading">#</a></h2>
<p>The current ecosystem has very few user-defined datatypes using NumPy, the
two most prominent being: <code class="docutils literal notranslate"><span class="pre">rational</span></code> and <code class="docutils literal notranslate"><span class="pre">quaternion</span></code>.
These represent fairly simple datatypes which are not strongly impacted
by the current limitations.
However, we have identified a need for datatypes such as:</p>
<ul class="simple">
<li><p>bfloat16, used in deep learning</p></li>
<li><p>categorical types</p></li>
<li><p>physical units (such as meters)</p></li>
<li><p>datatypes for tracing/automatic differentiation</p></li>
<li><p>high, fixed precision math</p></li>
<li><p>specialized integer types such as int2, int24</p></li>
<li><p>new, better datetime representations</p></li>
<li><p>extending e.g. integer dtypes to have a sentinel NA value</p></li>
<li><p>geometrical objects <a class="reference internal" href="#pygeos" id="id3"><span>[pygeos]</span></a></p></li>
</ul>
<p>Some of these are partially solved; for example unit capability is provided
in <code class="docutils literal notranslate"><span class="pre">astropy.units</span></code>, <code class="docutils literal notranslate"><span class="pre">unyt</span></code>, or <code class="docutils literal notranslate"><span class="pre">pint</span></code>, as <cite>numpy.ndarray</cite> subclasses.
Most of these datatypes, however, simply cannot be reasonably defined
right now.
An advantage of having such datatypes in NumPy is that they should integrate
seamlessly with other array or array-like packages such as Pandas,
<code class="docutils literal notranslate"><span class="pre">xarray</span></code> <a class="reference internal" href="#xarray-dtype-issue" id="id4"><span>[xarray_dtype_issue]</span></a>, or <code class="docutils literal notranslate"><span class="pre">Dask</span></code>.</p>
<p>The long term user impact of implementing this NEP will be to allow both
the growth of the whole ecosystem by having such new datatypes, as well as
consolidating implementation of such datatypes within NumPy to achieve
better interoperability.</p>
<section id="examples">
<h3>Examples<a class="headerlink" href="#examples" title="Link to this heading">#</a></h3>
<p>The following examples represent future user-defined datatypes we wish to enable.
These datatypes are not part the NEP and choices (e.g. choice of casting rules)
are possibilities we wish to enable and do not represent recommendations.</p>
<section id="simple-numerical-types">
<h4>Simple numerical types<a class="headerlink" href="#simple-numerical-types" title="Link to this heading">#</a></h4>
<p>Mainly used where memory is a consideration, lower-precision numeric types
such as <a class="reference external" href="https://en.wikipedia.org/wiki/Bfloat16_floating-point_format">bfloat16</a>
are common in other computational frameworks.
For these types the definitions of things such as <code class="docutils literal notranslate"><span class="pre">np.common_type</span></code> and
<code class="docutils literal notranslate"><span class="pre">np.can_cast</span></code> are some of the most important interfaces. Once they
support <code class="docutils literal notranslate"><span class="pre">np.common_type</span></code>, it is (for the most part) possible to find
the correct ufunc loop to call, since most ufuncs – such as add – effectively
only require <code class="docutils literal notranslate"><span class="pre">np.result_type</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">arr1</span><span class="p">,</span> <span class="n">arr2</span><span class="p">)</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">arr1</span><span class="p">,</span> <span class="n">arr2</span><span class="p">)</span>
</pre></div>
</div>
<p>and <cite>~numpy.result_type</cite> is largely identical to <cite>~numpy.common_type</cite>.</p>
</section>
<section id="fixed-high-precision-math">
<h4>Fixed, high precision math<a class="headerlink" href="#fixed-high-precision-math" title="Link to this heading">#</a></h4>
<p>Allowing arbitrary precision or higher precision math is important in
simulations. For instance <code class="docutils literal notranslate"><span class="pre">mpmath</span></code> defines a precision:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">mpmath</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">mp</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">mp</span><span class="o">.</span><span class="n">dps</span><span class="p">)</span> <span class="c1"># the current (default) precision</span>
<span class="go">15</span>
</pre></div>
</div>
<p>NumPy should be able to construct a native, memory-efficient array from
a list of <code class="docutils literal notranslate"><span class="pre">mpmath.mpf</span></code> floating point objects:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">arr_15_dps</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span> <span class="c1"># (mp.arange returns a list)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">arr_15_dps</span><span class="p">)</span> <span class="c1"># Must find the correct precision from the objects:</span>
<span class="go">array(['0.0', '1.0', '2.0'], dtype=mpf[dps=15])</span>
</pre></div>
</div>
<p>We should also be able to specify the desired precision when
creating the datatype for an array. Here, we use <code class="docutils literal notranslate"><span class="pre">np.dtype[mp.mpf]</span></code>
to find the DType class (the notation is not part of this NEP),
which is then instantiated with the desired parameter.
This could also be written as <code class="docutils literal notranslate"><span class="pre">MpfDType</span></code> class:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">arr_100_dps</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">dtype</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">mp</span><span class="o">.</span><span class="n">mpf</span><span class="p">](</span><span class="n">dps</span><span class="o">=</span><span class="mi">100</span><span class="p">))</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">arr_15_dps</span> <span class="o">+</span> <span class="n">arr_100_dps</span><span class="p">)</span>
<span class="go">array(['0.0', '2.0', '4.0'], dtype=mpf[dps=100])</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">mpf</span></code> datatype can decide that the result of the operation should be the
higher precision one of the two, so uses a precision of 100.
Furthermore, we should be able to define casting, for example as in:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">can_cast</span><span class="p">(</span><span class="n">arr_15_dps</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">arr_100_dps</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">casting</span><span class="o">=</span><span class="s2">"safe"</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">can_cast</span><span class="p">(</span><span class="n">arr_100_dps</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">arr_15_dps</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">casting</span><span class="o">=</span><span class="s2">"safe"</span><span class="p">)</span>
<span class="go">False # loses precision</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">can_cast</span><span class="p">(</span><span class="n">arr_100_dps</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">arr_100_dps</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">casting</span><span class="o">=</span><span class="s2">"same_kind"</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<p>Casting from float is a probably always at least a <code class="docutils literal notranslate"><span class="pre">same_kind</span></code> cast, but
in general, it is not safe:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">can_cast</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</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">mp</span><span class="o">.</span><span class="n">mpf</span><span class="p">](</span><span class="n">dps</span><span class="o">=</span><span class="mi">4</span><span class="p">),</span> <span class="n">casting</span><span class="o">=</span><span class="s2">"safe"</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<p>since a float64 has a higher precision than the <code class="docutils literal notranslate"><span class="pre">mpf</span></code> datatype with
<code class="docutils literal notranslate"><span class="pre">dps=4</span></code>.</p>
<p>Alternatively, we can say that:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">common_type</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">mp</span><span class="o">.</span><span class="n">mpf</span><span class="p">](</span><span class="n">dps</span><span class="o">=</span><span class="mi">5</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">mp</span><span class="o">.</span><span class="n">mpf</span><span class="p">](</span><span class="n">dps</span><span class="o">=</span><span class="mi">10</span><span class="p">))</span>
<span class="go">np.dtype[mp.mpf](dps=10)</span>
</pre></div>
</div>
<p>And possibly even:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">common_type</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">mp</span><span class="o">.</span><span class="n">mpf</span><span class="p">](</span><span class="n">dps</span><span class="o">=</span><span class="mi">5</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
<span class="go">np.dtype[mp.mpf](dps=16) # equivalent precision to float64 (I believe)</span>
</pre></div>
</div>
<p>since <code class="docutils literal notranslate"><span class="pre">np.float64</span></code> can be cast to a <code class="docutils literal notranslate"><span class="pre">np.dtype[mp.mpf](dps=16)</span></code> safely.</p>
</section>
<section id="categoricals">
<h4>Categoricals<a class="headerlink" href="#categoricals" title="Link to this heading">#</a></h4>
<p>Categoricals are interesting in that they can have fixed, predefined values,
or can be dynamic with the ability to modify categories when necessary.
The fixed categories (defined ahead of time) is the most straight forward
categorical definition.
Categoricals are <em>hard</em>, since there are many strategies to implement them,
suggesting NumPy should only provide the scaffolding for user-defined
categorical types. For instance:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">cat</span> <span class="o">=</span> <span class="n">Categorical</span><span class="p">([</span><span class="s2">"eggs"</span><span class="p">,</span> <span class="s2">"spam"</span><span class="p">,</span> <span class="s2">"toast"</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">breakfast</span> <span class="o">=</span> <span class="n">array</span><span class="p">([</span><span class="s2">"eggs"</span><span class="p">,</span> <span class="s2">"spam"</span><span class="p">,</span> <span class="s2">"eggs"</span><span class="p">,</span> <span class="s2">"toast"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">cat</span><span class="p">)</span>
</pre></div>
</div>
<p>could store the array very efficiently, since it knows that there are only 3
categories.
Since a categorical in this sense knows almost nothing about the data stored
in it, few operations makes, sense, although equality does:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">breakfast2</span> <span class="o">=</span> <span class="n">array</span><span class="p">([</span><span class="s2">"eggs"</span><span class="p">,</span> <span class="s2">"eggs"</span><span class="p">,</span> <span class="s2">"eggs"</span><span class="p">,</span> <span class="s2">"eggs"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">cat</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">breakfast</span> <span class="o">==</span> <span class="n">breakfast2</span>
<span class="go">array[True, False, True, False])</span>
</pre></div>
</div>
<p>The categorical datatype could work like a dictionary: no two
items names can be equal (checked on dtype creation), so that the equality
operation above can be performed very efficiently.
If the values define an order, the category labels (internally integers) could
be ordered the same way to allow efficient sorting and comparison.</p>
<p>Whether or not casting is defined from one categorical with less to one with
strictly more values defined, is something that the Categorical datatype would
need to decide. Both options should be available.</p>
</section>
<section id="unit-on-the-datatype">
<h4>Unit on the datatype<a class="headerlink" href="#unit-on-the-datatype" title="Link to this heading">#</a></h4>
<p>There are different ways to define Units, depending on how the internal
machinery would be organized, one way is to have a single Unit datatype
for every existing numerical type.
This will be written as <code class="docutils literal notranslate"><span class="pre">Unit[float64]</span></code>, the unit itself is part of the
DType instance <code class="docutils literal notranslate"><span class="pre">Unit[float64]("m")</span></code> is a <code class="docutils literal notranslate"><span class="pre">float64</span></code> with meters attached:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">astropy</span><span class="w"> </span><span class="kn">import</span> <span class="n">units</span>
<span class="gp">>>> </span><span class="n">meters</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span> <span class="o">*</span> <span class="n">units</span><span class="o">.</span><span class="n">m</span> <span class="c1"># meters</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">meters</span><span class="p">)</span>
<span class="go">array([1.0, 2.0, 3.0], dtype=Unit[float64]("m"))</span>
</pre></div>
</div>
<p>Note that units are a bit tricky. It is debatable, whether:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">Unit</span><span class="p">[</span><span class="n">float64</span><span class="p">](</span><span class="s2">"m"</span><span class="p">))</span>
</pre></div>
</div>
<p>should be valid syntax (coercing the float scalars without a unit to meters).
Once the array is created, math will work without any issue:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">meters</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">unit</span><span class="o">.</span><span class="n">seconds</span><span class="p">)</span>
<span class="go">array([0.5, 1.0, 1.5], dtype=Unit[float64]("m/s"))</span>
</pre></div>
</div>
<p>Casting is not valid from one unit to the other, but can be valid between
different scales of the same dimensionality (although this may be “unsafe”):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">meters</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">Unit</span><span class="p">[</span><span class="n">float64</span><span class="p">](</span><span class="s2">"s"</span><span class="p">))</span>
<span class="go">TypeError: Cannot cast meters to seconds.</span>
<span class="gp">>>> </span><span class="n">meters</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">Unit</span><span class="p">[</span><span class="n">float64</span><span class="p">](</span><span class="s2">"km"</span><span class="p">))</span>
<span class="gp">>>> </span><span class="c1"># Convert to centimeter-gram-second (cgs) units:</span>
<span class="gp">>>> </span><span class="n">meters</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">meters</span><span class="o">.</span><span class="n">dtype</span><span class="o">.</span><span class="n">to_cgs</span><span class="p">())</span>
</pre></div>
</div>
<p>The above notation is somewhat clumsy. Functions
could be used instead to convert between units.
There may be ways to make these more convenient, but those must be left
for future discussions:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">units</span><span class="o">.</span><span class="n">convert</span><span class="p">(</span><span class="n">meters</span><span class="p">,</span> <span class="s2">"km"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">units</span><span class="o">.</span><span class="n">to_cgs</span><span class="p">(</span><span class="n">meters</span><span class="p">)</span>
</pre></div>
</div>
<p>There are some open questions. For example, whether additional methods
on the array object could exist to simplify some of the notions, and how these
would percolate from the datatype to the <code class="docutils literal notranslate"><span class="pre">ndarray</span></code>.</p>
<p>The interaction with other scalars would likely be defined through:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">common_type</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">,</span> <span class="n">Unit</span><span class="p">)</span>
<span class="go">Unit[np.float64](dimensionless)</span>
</pre></div>
</div>
<p>Ufunc output datatype determination can be more involved than for simple
numerical dtypes since there is no “universal” output type:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">meters</span><span class="p">,</span> <span class="n">seconds</span><span class="p">)</span><span class="o">.</span><span class="n">dtype</span> <span class="o">!=</span> <span class="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">meters</span><span class="p">,</span> <span class="n">seconds</span><span class="p">)</span>
</pre></div>
</div>
<p>In fact <code class="docutils literal notranslate"><span class="pre">np.result_type(meters,</span> <span class="pre">seconds)</span></code> must error without context
of the operation being done.
This example highlights how the specific ufunc loop
(loop with known, specific DTypes as inputs), has to be able to make
certain decisions before the actual calculation can start.</p>
</section>
</section>
</section>
<section id="implementation">
<h2>Implementation<a class="headerlink" href="#implementation" title="Link to this heading">#</a></h2>
<section id="plan-to-approach-the-full-refactor">
<h3>Plan to approach the full refactor<a class="headerlink" href="#plan-to-approach-the-full-refactor" title="Link to this heading">#</a></h3>
<p>To address these issues in NumPy and enable new datatypes,
multiple development stages are required:</p>
<ul class="simple">
<li><p>Phase I: Restructure and extend the datatype infrastructure (This NEP)</p>
<ul>
<li><p>Organize Datatypes like normal Python classes [<cite>PR 15508</cite>]_</p></li>
</ul>
</li>
<li><p>Phase II: Incrementally define or rework API</p>
<ul>
<li><p>Incrementally define all necessary functionality through methods and
properties on the DType (NEP 42):</p>
<ul>
<li><p>The properties of the class hierarchy and DType class itself,
including methods not covered by the following, most central, points.</p></li>
<li><p>The functionality that will support dtype casting using <code class="docutils literal notranslate"><span class="pre">arr.astype()</span></code>
and casting related operations such as <code class="docutils literal notranslate"><span class="pre">np.common_type</span></code>.</p></li>
<li><p>The implementation of item access and storage, and the way shape and
dtype are determined when creating an array with <code class="docutils literal notranslate"><span class="pre">np.array()</span></code></p></li>
<li><p>Create a public C-API to define new DTypes.</p></li>
</ul>
</li>
<li><p>Restructure how universal functions work (NEP 43), to allow extending
a <cite>~numpy.ufunc</cite> such as <code class="docutils literal notranslate"><span class="pre">np.add</span></code> for user-defined datatypes
such as Units:</p>
<ul>
<li><p>Refactor how the low-level C functions are organized to make it
extensible and flexible enough for complicated DTypes such as Units.</p></li>
<li><p>Implement registration and efficient lookup for these low-level C
functions as defined by the user.</p></li>
<li><p>Define how promotion will be used to implement behaviour when casting
is required. For example <code class="docutils literal notranslate"><span class="pre">np.float64(3)</span> <span class="pre">+</span> <span class="pre">np.int32(3)</span></code> promotes the
<code class="docutils literal notranslate"><span class="pre">int32</span></code> to a <code class="docutils literal notranslate"><span class="pre">float64</span></code>.</p></li>
</ul>
</li>
</ul>
</li>
<li><p>Phase III: Growth of NumPy and Scientific Python Ecosystem capabilities:</p>
<ul>
<li><p>Cleanup of legacy behaviour where it is considered buggy or undesirable.</p></li>
<li><p>Provide a path to define new datatypes from Python.</p></li>
<li><p>Assist the community in creating types such as Units or Categoricals</p></li>
<li><p>Allow strings to be used in functions such as <code class="docutils literal notranslate"><span class="pre">np.equal</span></code> or <code class="docutils literal notranslate"><span class="pre">np.add</span></code>.</p></li>
<li><p>Remove legacy code paths within NumPy to improve long term maintainability</p></li>
</ul>
</li>
</ul>
<p>This document serves as a basis for phase I and provides the vision and
motivation for the full project.
Phase I does not introduce any new user-facing features,
but is concerned with the necessary conceptual cleanup of the current datatype system.
It provides a more “pythonic” datatype Python type object, with a clear class hierarchy.</p>
<p>The second phase is the incremental creation of all APIs necessary to define
fully featured datatypes and reorganization of the NumPy datatype system.
This phase will thus be primarily concerned with defining an,
initially preliminary, stable public API.</p>
<p>Some of the benefits of a large refactor may only become evident after the full
deprecation of the current legacy implementation (i.e. larger code removals).
However, these steps are necessary for improvements to many parts of the
core NumPy API, and are expected to make the implementation generally
easier to understand.</p>
<p>The following figure illustrates the proposed design at a high level,
and roughly delineates the components of the overall design.
Note that this NEP only regards Phase I (shaded area),
the rest encompasses Phase II and the design choices are up for discussion,
however, it highlights that the DType datatype class is the central, necessary
concept:</p>
<img alt="_images/nep-0041-mindmap.svg" src="_images/nep-0041-mindmap.svg" /></section>
<section id="first-steps-directly-related-to-this-nep">
<h3>First steps directly related to this NEP<a class="headerlink" href="#first-steps-directly-related-to-this-nep" title="Link to this heading">#</a></h3>
<p>The required changes necessary to NumPy are large and touch many areas
of the code base
but many of these changes can be addressed incrementally.</p>
<p>To enable an incremental approach we will start by creating a C defined
<code class="docutils literal notranslate"><span class="pre">PyArray_DTypeMeta</span></code> class with its instances being the <code class="docutils literal notranslate"><span class="pre">DType</span></code> classes,
subclasses of <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code>.
This is necessary to add the ability of storing custom slots on the DType in C.
This <code class="docutils literal notranslate"><span class="pre">DTypeMeta</span></code> will be implemented first to then enable incremental
restructuring of current code.</p>
<p>The addition of <code class="docutils literal notranslate"><span class="pre">DType</span></code> will then enable addressing other changes
incrementally, some of which may begin before the settling the full internal
API:</p>
<ol class="arabic simple">
<li><p>New machinery for array coercion, with the goal of enabling user DTypes
with appropriate class methods.</p></li>
<li><p>The replacement or wrapping of the current casting machinery.</p></li>
<li><p>Incremental redefinition of the current <code class="docutils literal notranslate"><span class="pre">PyArray_ArrFuncs</span></code> slots into
DType method slots.</p></li>
</ol>
<p>At this point, no or only very limited new public API will be added and
the internal API is considered to be in flux.
Any new public API may be set up give warnings and will have leading underscores
to indicate that it is not finalized and can be changed without warning.</p>
</section>
</section>
<section id="backward-compatibility">
<h2>Backward compatibility<a class="headerlink" href="#backward-compatibility" title="Link to this heading">#</a></h2>
<p>While the actual backward compatibility impact of implementing Phase I and II
are not yet fully clear, we anticipate, and accept the following changes:</p>
<ul class="simple">
<li><p><strong>Python API</strong>:</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">type(np.dtype("f8"))</span></code> will be a subclass of <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code>, while right
now <code class="docutils literal notranslate"><span class="pre">type(np.dtype("f8"))</span> <span class="pre">is</span> <span class="pre">np.dtype</span></code>.
Code should use <code class="docutils literal notranslate"><span class="pre">isinstance</span></code> checks, and in very rare cases may have to
be adapted to use it.</p></li>
</ul>
</li>
<li><p><strong>C-API</strong>:</p>
<ul>
<li><p>In old versions of NumPy <code class="docutils literal notranslate"><span class="pre">PyArray_DescrCheck</span></code> is a macro which uses
<code class="docutils literal notranslate"><span class="pre">type(dtype)</span> <span class="pre">is</span> <span class="pre">np.dtype</span></code>. When compiling against an old NumPy version,
the macro may have to be replaced with the corresponding
<code class="docutils literal notranslate"><span class="pre">PyObject_IsInstance</span></code> call. (If this is a problem, we could backport
fixing the macro)</p></li>
<li><p>The UFunc machinery changes will break <em>limited</em> parts of the current
implementation. Replacing e.g. the default <code class="docutils literal notranslate"><span class="pre">TypeResolver</span></code> is expected
to remain supported for a time, although optimized masked inner loop iteration
(which is not even used <em>within</em> NumPy) will no longer be supported.</p></li>
<li><p>All functions currently defined on the dtypes, such as
<code class="docutils literal notranslate"><span class="pre">PyArray_Descr->f->nonzero</span></code>, will be defined and accessed differently.
This means that in the long run lowlevel access code will
have to be changed to use the new API. Such changes are expected to be
necessary in very few project.</p></li>
</ul>
</li>
<li><p><strong>dtype implementers (C-API)</strong>:</p>
<ul>
<li><p>The array which is currently provided to some functions (such as cast functions),
will no longer be provided.
For example <code class="docutils literal notranslate"><span class="pre">PyArray_Descr->f->nonzero</span></code> or <code class="docutils literal notranslate"><span class="pre">PyArray_Descr->f->copyswapn</span></code>,
may instead receive a dummy array object with only some fields (mainly the
dtype), being valid.
At least in some code paths, a similar mechanism is already used.</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">scalarkind</span></code> slot and registration of scalar casting will be
removed/ignored without replacement.
It currently allows partial value-based casting.
The <code class="docutils literal notranslate"><span class="pre">PyArray_ScalarKind</span></code> function will continue to work for builtin types,
but will not be used internally and be deprecated.</p></li>
<li><p>Currently user dtypes are defined as instances of <code class="docutils literal notranslate"><span class="pre">np.dtype</span></code>.
The creation works by the user providing a prototype instance.
NumPy will need to modify at least the type during registration.
This has no effect for either <code class="docutils literal notranslate"><span class="pre">rational</span></code> or <code class="docutils literal notranslate"><span class="pre">quaternion</span></code> and mutation
of the structure seems unlikely after registration.</p></li>
</ul>
</li>
</ul>
<p>Since there is a fairly large API surface concerning datatypes, further changes
or the limitation certain function to currently existing datatypes is
likely to occur.