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<section id="nep-43-enhancing-the-extensibility-of-ufuncs">
<span id="nep43"></span><h1>NEP 43 — Enhancing the extensibility of UFuncs<a class="headerlink" href="#nep-43-enhancing-the-extensibility-of-ufuncs" 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>Enhancing the Extensibility of UFuncs</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">Status<span class="colon">:</span></dt>
<dd class="field-odd"><p>Draft</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>2020-06-20</p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This NEP is fourth 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><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>NEP 43 (this document) 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>The previous NEP 42 proposes the creation of new DTypes which can
be defined by users outside of NumPy itself.
The implementation of NEP 42 will enable users to create arrays with a custom dtype
and stored values.
This NEP outlines how NumPy will operate on arrays with custom dtypes in the future.
The most important functions operating on NumPy arrays are the so called
“universal functions” (ufunc) which include all math functions, such as
<code class="docutils literal notranslate"><span class="pre">np.add</span></code>, <code class="docutils literal notranslate"><span class="pre">np.multiply</span></code>, and even <code class="docutils literal notranslate"><span class="pre">np.matmul</span></code>.
These ufuncs must operate efficiently on multiple arrays with
different datatypes.</p>
<p>This NEP proposes to expand the design of ufuncs.
It makes a new distinction between the ufunc which can operate
on many different dtypes such as floats or integers,
and a new <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> which defines the efficient operation for
specific dtypes.</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>The goal of this NEP is to extend universal
functions support the new DType system detailed in NEPs 41 and 42.
While the main motivation is enabling new user-defined DTypes, this will
also significantly simplify defining universal functions for NumPy strings or
structured DTypes.
Until now, these DTypes are not supported by any of NumPy’s functions
(such as <code class="docutils literal notranslate"><span class="pre">np.add</span></code> or <code class="docutils literal notranslate"><span class="pre">np.equal</span></code>), due to difficulties arising from
their parametric nature (compare NEP 41 and 42), e.g. the string length.</p>
<p>Functions on arrays must handle a number of distinct steps which are
described in more detail in section “<a class="reference internal" href="#steps-involved-in-a-ufunc-call">Steps involved in a UFunc call</a>”.
The most important ones are:</p>
<ul class="simple">
<li><p>Organizing all functionality required to define a ufunc call for specific
DTypes. This is often called the “inner-loop”.</p></li>
<li><p>Deal with input for which no exact matching implementation is found.
For example when <code class="docutils literal notranslate"><span class="pre">int32</span></code> and <code class="docutils literal notranslate"><span class="pre">float64</span></code> are added, the <code class="docutils literal notranslate"><span class="pre">int32</span></code>
is cast to <code class="docutils literal notranslate"><span class="pre">float64</span></code>. This requires a distinct “promotion” step.</p></li>
</ul>
<p>After organizing and defining these, we need to:</p>
<ul class="simple">
<li><p>Define the user API for customizing both of the above points.</p></li>
<li><p>Allow convenient reuse of existing functionality.
For example a DType representing physical units, such as meters,
should be able to fall back to NumPy’s existing math implementations.</p></li>
</ul>
<p>This NEP details how these requirements will be achieved in NumPy:</p>
<ul class="simple">
<li><p>All DTyper-specific functionality currently part of the ufunc
definition will be defined as part of a new <a class="reference internal" href="#arraymethod">ArrayMethod</a> object.
This <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> object will be the new, preferred, way to describe any
function operating on arrays.</p></li>
<li><p>Ufuncs will dispatch to the <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> and potentially use promotion
to find the correct <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> to use.
This will be described in the <a class="reference internal" href="#id1">Promotion and dispatching</a> section.</p></li>
</ul>
<p>A new C-API will be outlined in each section. A future Python API is
expected to be very similar and the C-API is presented in terms of Python
code for readability.</p>
<p>The NEP proposes a large, but necessary, refactor of the NumPy ufunc internals.
This modernization will not affect end users directly and is not only a necessary
step for new DTypes, but in itself a maintenance effort which is expected to
help with future improvements to the ufunc machinery.</p>
<p>While the most important restructure proposed is the new <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code>
object, the largest long-term consideration is the API choice for
promotion and dispatching.</p>
</section>
<section id="backwards-compatibility">
<h2>Backwards compatibility<a class="headerlink" href="#backwards-compatibility" title="Link to this heading">#</a></h2>
<p>The general backwards compatibility issues have also been listed
previously in NEP 41.</p>
<p>The vast majority of users should not see any changes beyond those typical
for NumPy releases.
There are three main users or use-cases impacted by the proposed changes:</p>
<ol class="arabic simple">
<li><p>The Numba package uses direct access to the NumPy C-loops and modifies
the NumPy ufunc struct directly for its own purposes.</p></li>
<li><p>Astropy uses its own “type resolver”, meaning that a default switch over
from the existing type resolution to a new default Promoter requires care.</p></li>
<li><p>It is currently possible to register loops for dtype <em>instances</em>.
This is theoretically useful for structured dtypes and is a resolution
step happening <em>after</em> the DType resolution step proposed here.</p></li>
</ol>
<p>This NEP will try hard to maintain backward compatibility as much as
possible. However, both of these projects have signaled willingness to adapt
to breaking changes.</p>
<p>The main reason why NumPy will be able to provide backward compatibility
is that:</p>
<ul class="simple">
<li><p>Existing inner-loops can be wrapped, adding an indirection to the call but
maintaining full backwards compatibility.
The <code class="docutils literal notranslate"><span class="pre">get_loop</span></code> function can, in this case, search the existing
inner-loop functions (which are stored on the ufunc directly) in order
to maintain full compatibility even with potential direct structure access.</p></li>
<li><p>Legacy type resolvers can be called as a fallback (potentially caching
the result). The resolver may need to be called twice (once for the DType
resolution and once for the <code class="docutils literal notranslate"><span class="pre">resolve_descriptor</span></code> implementation).</p></li>
<li><p>The fallback to the legacy type resolver should in most cases handle loops
defined for such structured dtype instances. This is because if there is no
other <code class="docutils literal notranslate"><span class="pre">np.Void</span></code> implementation, the legacy fallback will retain the old
behaviour at least initially.</p></li>
</ul>
<p>The masked type resolvers specifically will <em>not</em> remain supported, but
has no known users (including NumPy itself, which only uses the default
version).</p>
<p>Further, no compatibility attempt will be made for <em>calling</em> as opposed
to providing either the normal or the masked type resolver. As NumPy
will use it only as a fallback. There are no known users of this
(undocumented) possibility.</p>
<p>While the above changes potentially break some workflows,
we believe that the long-term improvements vastly outweigh this.
Further, packages such as astropy and Numba are capable of adapting so that
end-users may need to update their libraries but not their 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>This NEP restructures how operations on NumPy arrays are defined both
within NumPy and for external implementers.
The NEP mainly concerns those who either extend ufuncs for custom DTypes
or create custom ufuncs. It does not aim to finalize all
potential use-cases, but rather restructure NumPy to be extensible and allow
addressing new issues or feature requests as they arise.</p>
<section id="overview-and-end-user-api">
<h3>Overview and end user API<a class="headerlink" href="#overview-and-end-user-api" title="Link to this heading">#</a></h3>
<p>To give an overview of how this NEP proposes to structure ufuncs,
the following describes the potential exposure of the proposed restructure
to the end user.</p>
<p>Universal functions are much like a Python method defined on the DType of
the array when considering a ufunc with only a single input:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">res</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">positive</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
</pre></div>
</div>
<p>could be implemented (conceptually) as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">positive_impl</span> <span class="o">=</span> <span class="n">arr</span><span class="o">.</span><span class="n">dtype</span><span class="o">.</span><span class="n">positive</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">positive_impl</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
</pre></div>
</div>
<p>However, unlike methods, <code class="docutils literal notranslate"><span class="pre">positive_impl</span></code> is not stored on the dtype itself.
It is rather the implementation of <code class="docutils literal notranslate"><span class="pre">np.positive</span></code> for a specific DType.
Current NumPy partially exposes this “choice of implementation” using
the <code class="docutils literal notranslate"><span class="pre">dtype</span></code> (or more exact <code class="docutils literal notranslate"><span class="pre">signature</span></code>) attribute in universal functions,
although these are rarely used:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">positive</span><span class="p">(</span><span class="n">arr</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>
</pre></div>
</div>
<p>forces NumPy to use the <code class="docutils literal notranslate"><span class="pre">positive_impl</span></code> written specifically for the Float64
DType.</p>
<p>This NEP makes the distinction more explicit, by creating a new object to
represent <code class="docutils literal notranslate"><span class="pre">positive_impl</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">positive_impl</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">positive</span><span class="o">.</span><span class="n">resolve_impl</span><span class="p">((</span><span class="nb">type</span><span class="p">(</span><span class="n">arr</span><span class="o">.</span><span class="n">dtype</span><span class="p">),</span> <span class="kc">None</span><span class="p">))</span>
<span class="c1"># The `None` represents the output DType which is automatically chosen.</span>
</pre></div>
</div>
<p>While the creation of a <code class="docutils literal notranslate"><span class="pre">positive_impl</span></code> object and the <code class="docutils literal notranslate"><span class="pre">resolve_impl</span></code>
method is part of this NEP, the following code:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">res</span> <span class="o">=</span> <span class="n">positive_impl</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
</pre></div>
</div>
<p>may not be implemented initially and is not central to the redesign.</p>
<p>In general NumPy universal functions can take many inputs.
This requires looking up the implementation by considering all of them
and makes ufuncs “multi-methods” with respect to the input DTypes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">add_impl</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">add</span><span class="o">.</span><span class="n">resolve_impl</span><span class="p">((</span><span class="nb">type</span><span class="p">(</span><span class="n">arr1</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="n">arr2</span><span class="o">.</span><span class="n">dtype</span><span class="p">),</span> <span class="kc">None</span><span class="p">))</span>
</pre></div>
</div>
<p>This NEP defines how <code class="docutils literal notranslate"><span class="pre">positive_impl</span></code> and <code class="docutils literal notranslate"><span class="pre">add_impl</span></code> will be represented
as a new <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> which can be implemented outside of NumPy.
Further, it defines how <code class="docutils literal notranslate"><span class="pre">resolve_impl</span></code> will implement and solve dispatching
and promotion.</p>
<p>The reasons for this split may be more clear after reviewing the
<a class="reference internal" href="#steps-involved-in-a-ufunc-call">Steps involved in a UFunc call</a> section.</p>
</section>
<section id="defining-a-new-ufunc-implementation">
<h3>Defining a new ufunc implementation<a class="headerlink" href="#defining-a-new-ufunc-implementation" title="Link to this heading">#</a></h3>
<p>The following is a mock-up of how a new implementation, in this case
to define string equality, will be added to a ufunc.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">StringEquality</span><span class="p">(</span><span class="n">BoundArrayMethod</span><span class="p">):</span>
<span class="n">nin</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">nout</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1"># DTypes are stored on the BoundArrayMethod and not on the internal</span>
<span class="c1"># ArrayMethod, to reference cyles.</span>
<span class="n">DTypes</span> <span class="o">=</span> <span class="p">(</span><span class="n">String</span><span class="p">,</span> <span class="n">String</span><span class="p">,</span> <span class="n">Bool</span><span class="p">)</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">ArrayMethod</span><span class="p">,</span> <span class="n">DTypes</span><span class="p">,</span> <span class="n">given_descrs</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""The strided loop supports all input string dtype instances</span>
<span class="sd"> and always returns a boolean. (String is always native byte order.)</span>
<span class="sd"> Defining this function is not necessary, since NumPy can provide</span>
<span class="sd"> it by default.</span>
<span class="sd"> The `self` argument here refers to the unbound array method, so</span>
<span class="sd"> that DTypes are passed in explicitly.</span>
<span class="sd"> """</span>
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">given_descrs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">DTypes</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">given_descrs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">DTypes</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="k">assert</span> <span class="n">given_descrs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">given_descrs</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">DTypes</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
<span class="n">out_descr</span> <span class="o">=</span> <span class="n">given_descrs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="c1"># preserve input (e.g. metadata)</span>
<span class="k">if</span> <span class="n">given_descrs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">out_descr</span> <span class="o">=</span> <span class="n">DTypes</span><span class="p">[</span><span class="mi">2</span><span class="p">]()</span>
<span class="c1"># The operation is always "no" casting (most ufuncs are)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">given_descrs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">given_descrs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">out_descr</span><span class="p">),</span> <span class="s2">"no"</span>
<span class="k">def</span> <span class="nf">strided_loop</span><span class="p">(</span><span class="n">context</span><span class="p">,</span> <span class="n">dimensions</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">strides</span><span class="p">,</span> <span class="n">innerloop_data</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""The 1-D strided loop, similar to those used in current ufuncs"""</span>
<span class="c1"># dimensions: Number of loop items and core dimensions</span>
<span class="c1"># data: Pointers to the array data.</span>
<span class="c1"># strides: strides to iterate all elements</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">dimensions</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># number of items to loop over</span>
<span class="n">num_chars1</span> <span class="o">=</span> <span class="n">context</span><span class="o">.</span><span class="n">descriptors</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">itemsize</span>
<span class="n">num_chars2</span> <span class="o">=</span> <span class="n">context</span><span class="o">.</span><span class="n">descriptors</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">itemsize</span>
<span class="c1"># C code using the above information to compare the strings in</span>
<span class="c1"># both arrays. In particular, this loop requires the `num_chars1`</span>
<span class="c1"># and `num_chars2`. Information which is currently not easily</span>
<span class="c1"># available.</span>
<span class="n">np</span><span class="o">.</span><span class="n">equal</span><span class="o">.</span><span class="n">register_impl</span><span class="p">(</span><span class="n">StringEquality</span><span class="p">)</span>
<span class="k">del</span> <span class="n">StringEquality</span> <span class="c1"># may be deleted.</span>
</pre></div>
</div>
<p>This definition will be sufficient to create a new loop, and the
structure allows for expansion in the future; something that is already
required to implement casting within NumPy itself.
We use <code class="docutils literal notranslate"><span class="pre">BoundArrayMethod</span></code> and a <code class="docutils literal notranslate"><span class="pre">context</span></code> structure here. These
are described and motivated in details later. Briefly:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">context</span></code> is a generalization of the <code class="docutils literal notranslate"><span class="pre">self</span></code> that Python passes to its
methods.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">BoundArrayMethod</span></code> is equivalent to the Python distinction that
<code class="docutils literal notranslate"><span class="pre">class.method</span></code> is a method, while <code class="docutils literal notranslate"><span class="pre">class().method</span></code> returns a “bound” method.</p></li>
</ul>
</section>
<section id="customizing-dispatching-and-promotion">
<h3>Customizing dispatching and Promotion<a class="headerlink" href="#customizing-dispatching-and-promotion" title="Link to this heading">#</a></h3>
<p>Finding the correct implementation when <code class="docutils literal notranslate"><span class="pre">np.positive.resolve_impl()</span></code> is
called is largely an implementation detail.
But, in some cases it may be necessary to influence this process when no
implementation matches the requested DTypes exactly:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">multiple</span><span class="o">.</span><span class="n">resolve_impl</span><span class="p">((</span><span class="n">Timedelta64</span><span class="p">,</span> <span class="n">Int8</span><span class="p">,</span> <span class="kc">None</span><span class="p">))</span>
</pre></div>
</div>
<p>will not have an exact match, because NumPy only has an implementation for
multiplying <code class="docutils literal notranslate"><span class="pre">Timedelta64</span></code> with <code class="docutils literal notranslate"><span class="pre">Int64</span></code>.
In simple cases, NumPy will use a default promotion step to attempt to find
the correct implementation, but to implement the above step, we will allow
the following:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">promote_timedelta_integer</span><span class="p">(</span><span class="n">ufunc</span><span class="p">,</span> <span class="n">dtypes</span><span class="p">):</span>
<span class="n">new_dtypes</span> <span class="o">=</span> <span class="p">(</span><span class="n">Timdelta64</span><span class="p">,</span> <span class="n">Int64</span><span class="p">,</span> <span class="n">dtypes</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="c1"># Resolve again, using Int64:</span>
<span class="k">return</span> <span class="n">ufunc</span><span class="o">.</span><span class="n">resolve_impl</span><span class="p">(</span><span class="n">new_dtypes</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">multiple</span><span class="o">.</span><span class="n">register_promoter</span><span class="p">(</span>
<span class="p">(</span><span class="n">Timedelta64</span><span class="p">,</span> <span class="n">Integer</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span> <span class="n">promote_timedelta_integer</span><span class="p">)</span>
</pre></div>
</div>
<p>Where <code class="docutils literal notranslate"><span class="pre">Integer</span></code> is an abstract DType (compare NEP 42).</p>
</section>
</section>
<section id="steps-involved-in-a-ufunc-call">
<span id="steps-of-a-ufunc-call"></span><h2>Steps involved in a UFunc call<a class="headerlink" href="#steps-involved-in-a-ufunc-call" title="Link to this heading">#</a></h2>
<p>Before going into more detailed API choices, it is helpful to review the
steps involved in a call to a universal function in NumPy.</p>
<p>A UFunc call is split into the following steps:</p>
<ol class="arabic simple">
<li><p>Handle <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> protocol:</p>
<ul class="simple">
<li><p>For array-likes such as a Dask arrays, NumPy can defer the operation.
This step is performed first, and unaffected by this NEP (compare <a class="reference internal" href="nep-0018-array-function-protocol.html#nep18"><span class="std std-ref">NEP 18 — A dispatch mechanism for NumPy’s high level array functions</span></a>).</p></li>
</ul>
</li>
<li><p>Promotion and dispatching</p>
<ul class="simple">
<li><p>Given the DTypes of all inputs, find the correct implementation.
E.g. an implementation for <code class="docutils literal notranslate"><span class="pre">float64</span></code>, <code class="docutils literal notranslate"><span class="pre">int64</span></code> or a user-defined DType.</p></li>
<li><p>When no exact implementation exists, <em>promotion</em> has to be performed.
For example, adding a <code class="docutils literal notranslate"><span class="pre">float32</span></code> and a <code class="docutils literal notranslate"><span class="pre">float64</span></code> is implemented by
first casting the <code class="docutils literal notranslate"><span class="pre">float32</span></code> to <code class="docutils literal notranslate"><span class="pre">float64</span></code>.</p></li>
</ul>
</li>
<li><p>Parametric <code class="docutils literal notranslate"><span class="pre">dtype</span></code> resolution:</p>
<ul class="simple">
<li><p>In general, whenever an output DType is parametric the parameters have
to be found (resolved).</p></li>
<li><p>For example, if a loop adds two strings, it is necessary to define the
correct output (and possibly input) dtypes. <code class="docutils literal notranslate"><span class="pre">S5</span> <span class="pre">+</span> <span class="pre">S4</span> <span class="pre">-></span> <span class="pre">S9</span></code>, while
an <code class="docutils literal notranslate"><span class="pre">upper</span></code> function has the signature <code class="docutils literal notranslate"><span class="pre">S5</span> <span class="pre">-></span> <span class="pre">S5</span></code>.</p></li>
<li><p>When they are not parametric, a default implementation is provided
which fills in the default dtype instances (ensuring for example native
byte order).</p></li>
</ul>
</li>
<li><p>Preparing the iteration:</p>
<ul class="simple">
<li><p>This step is largely handled by <code class="docutils literal notranslate"><span class="pre">NpyIter</span></code> internally (the iterator).</p></li>
<li><p>Allocate all outputs and temporary buffers necessary to perform casts.
This <em>requires</em> the dtypes as resolved in step 3.</p></li>
<li><p>Find the best iteration order, which includes information to efficiently
implement broadcasting. For example, adding a single value to an array
repeats the same value.</p></li>
</ul>
</li>
<li><p>Setup and fetch the C-level function:</p>
<ul class="simple">
<li><p>If necessary, allocate temporary working space.</p></li>
<li><p>Find the C-implemented, light weight, inner-loop function.
Finding the inner-loop function can allow specialized implementations
in the future.
For example casting currently optimizes contiguous casts and
reductions have optimizations that are currently handled
inside the inner-loop function itself.</p></li>
<li><p>Signal whether the inner-loop requires the Python API or whether
the GIL may be released (to allow threading).</p></li>
<li><p>Clear floating point exception flags.</p></li>
</ul>
</li>
<li><p>Perform the actual calculation:</p>
<ul class="simple">
<li><p>Run the DType specific inner-loop function.</p></li>
<li><p>The inner-loop may require access to additional data, such as dtypes or
additional data set in the previous step.</p></li>
<li><p>The inner-loop function may be called an undefined number of times.</p></li>
</ul>
</li>
<li><p>Finalize:</p>
<ul class="simple">
<li><p>Free any temporary working space allocated in step 5.</p></li>
<li><p>Check for floating point exception flags.</p></li>
<li><p>Return the result.</p></li>
</ul>
</li>
</ol>
<p>The <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> provides a concept to group steps 3 to 6 and partially 7.
However, implementers of a new ufunc or <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> usually do not need to
customize the behaviour in steps 4 or 6 which NumPy can and does provide.
For the <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> implementer, the central steps to customize
are step 3 and step 5. These provide the custom inner-loop function and
potentially inner-loop specific setup.
Further customization is possible and anticipated as future extensions.</p>
<p>Step 2. is promotion and dispatching and will be restructured
with new API to allow customization of the process where necessary.</p>
<p>Step 1 is listed for completeness and is unaffected by this NEP.</p>
<p>The following sketch provides an overview of step 2 to 6 with an emphasize
of how dtypes are handled and which parts are customizable (“Registered”)
and which are handled by NumPy:</p>
<figure class="align-center align-default">
<img alt="_images/nep43-sketch.svg" src="_images/nep43-sketch.svg" /></figure>
</section>
<section id="arraymethod">
<h2>ArrayMethod<a class="headerlink" href="#arraymethod" title="Link to this heading">#</a></h2>
<p>A central proposal of this NEP is the creation of the <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> as an object
describing each implementation specific to a given set of DTypes.
We use the <code class="docutils literal notranslate"><span class="pre">class</span></code> syntax to describe the information required to create
a new <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> object:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">ArrayMethod</span><span class="p">:</span>
<span class="n">name</span><span class="p">:</span> <span class="nb">str</span> <span class="c1"># Name, mainly useful for debugging</span>
<span class="c1"># Casting safety information (almost always "safe", necessary to</span>
<span class="c1"># unify casting and universal functions)</span>
<span class="n">casting</span><span class="p">:</span> <span class="n">Casting</span> <span class="o">=</span> <span class="s2">"no"</span>
<span class="c1"># More general flags:</span>
<span class="n">flags</span><span class="p">:</span> <span class="nb">int</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="n">given_descrs</span><span class="p">)</span> <span class="o">-></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="w"> </span><span class="sd">"""Returns the safety of the operation (casting safety) and the</span>
<span class="sd"> """</span>
<span class="c1"># A default implementation can be provided for non-parametric</span>
<span class="c1"># output dtypes.</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">get_loop</span><span class="p">(</span><span class="n">Context</span> <span class="p">:</span> <span class="n">context</span><span class="p">,</span> <span class="n">strides</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span> <span class="o">-></span> <span class="n">strided_loop_function</span><span class="p">,</span> <span class="n">flags</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""Returns the low-level C (strided inner-loop) function which</span>
<span class="sd"> performs the actual operation.</span>
<span class="sd"> This method may initially private, users will be able to provide</span>
<span class="sd"> a set of optimized inner-loop functions instead:</span>
<span class="sd"> * `strided_inner_loop`</span>
<span class="sd"> * `contiguous_inner_loop`</span>
<span class="sd"> * `unaligned_strided_loop`</span>
<span class="sd"> * ...</span>
<span class="sd"> """</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">strided_inner_loop</span><span class="p">(</span>
<span class="n">Context</span> <span class="p">:</span> <span class="n">context</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">dimensions</span><span class="p">,</span> <span class="n">strides</span><span class="p">,</span> <span class="n">innerloop_data</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""The inner-loop (equivalent to the current ufunc loop)</span>
<span class="sd"> which is returned by the default `get_loop()` implementation."""</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
</pre></div>
</div>
<p>With <code class="docutils literal notranslate"><span class="pre">Context</span></code> providing mostly static information about the function call:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Context</span><span class="p">:</span>
<span class="c1"># The ArrayMethod object itself:</span>
<span class="n">ArrayMethod</span> <span class="p">:</span> <span class="n">method</span>
<span class="c1"># Information about the caller, e.g. the ufunc, such as `np.add`:</span>
<span class="nb">callable</span> <span class="p">:</span> <span class="n">caller</span> <span class="o">=</span> <span class="kc">None</span>
<span class="c1"># The number of input arguments:</span>
<span class="nb">int</span> <span class="p">:</span> <span class="n">nin</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1"># The number of output arguments:</span>
<span class="nb">int</span> <span class="p">:</span> <span class="n">nout</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1"># The actual dtypes instances the inner-loop operates on:</span>
<span class="n">Tuple</span><span class="p">[</span><span class="n">DType</span><span class="p">]</span> <span class="p">:</span> <span class="n">descriptors</span>
<span class="c1"># Any additional information required. In the future, this will</span>
<span class="c1"># generalize or duplicate things currently stored on the ufunc:</span>
<span class="c1"># - The ufunc signature of generalized ufuncs</span>
<span class="c1"># - The identity used for reductions</span>
</pre></div>
</div>
<p>And <code class="docutils literal notranslate"><span class="pre">flags</span></code> stored properties, for whether:</p>
<ul class="simple">
<li><p>the <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> supports unaligned input and output arrays</p></li>
<li><p>the inner-loop function requires the Python API (GIL)</p></li>
<li><p>NumPy has to check the floating point error CPU flags.</p></li>
</ul>
<p><em>Note: More information is expected to be added as necessary.</em></p>
<section id="the-call-context">
<h3>The call <code class="docutils literal notranslate"><span class="pre">Context</span></code><a class="headerlink" href="#the-call-context" title="Link to this heading">#</a></h3>
<p>The “context” object is analogous to Python’s <code class="docutils literal notranslate"><span class="pre">self</span></code> that is
passed to all methods.
To understand why the “context” object is necessary and its
internal structure, it is helpful to remember
that a Python method can be written in the following way
(see also the <a class="reference external" href="https://docs.python.org/3.8/reference/datamodel.html#object.__get__">documentation of __get__</a>):</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">BoundMethod</span><span class="p">:</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">instance</span><span class="p">,</span> <span class="n">method</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">instance</span> <span class="o">=</span> <span class="n">instance</span>
<span class="bp">self</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="n">method</span>
<span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">function</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">instance</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">class</span> <span class="nc">Method</span><span class="p">:</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">function</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">function</span> <span class="o">=</span> <span class="n">function</span>
<span class="k">def</span> <span class="fm">__get__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">instance</span><span class="p">,</span> <span class="n">owner</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">assert</span> <span class="n">instance</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="c1"># unsupported here</span>
<span class="k">return</span> <span class="n">BoundMethod</span><span class="p">(</span><span class="n">instance</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span>
</pre></div>
</div>
<p>With which the following <code class="docutils literal notranslate"><span class="pre">method1</span></code> and <code class="docutils literal notranslate"><span class="pre">method2</span></code> below, behave identically:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">function</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
<span class="k">class</span> <span class="nc">MyClass</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">method1</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
<span class="n">method2</span> <span class="o">=</span> <span class="n">Method</span><span class="p">(</span><span class="n">function</span><span class="p">)</span>
</pre></div>
</div>
<p>And both will print the same result:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">myinstance</span> <span class="o">=</span> <span class="n">MyClass</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">myinstance</span><span class="o">.</span><span class="n">method1</span><span class="p">()</span>
<span class="go"><__main__.MyClass object at 0x7eff65436d00></span>
<span class="gp">>>> </span><span class="n">myinstance</span><span class="o">.</span><span class="n">method2</span><span class="p">()</span>
<span class="go"><__main__.MyClass object at 0x7eff65436d00></span>
</pre></div>
</div>
<p>Here <code class="docutils literal notranslate"><span class="pre">self.instance</span></code> would be all information passed on by <code class="docutils literal notranslate"><span class="pre">Context</span></code>.
The <code class="docutils literal notranslate"><span class="pre">Context</span></code> is a generalization and has to pass additional information:</p>
<ul class="simple">
<li><p>Unlike a method which operates on a single class instance, the <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code>
operates on many input arrays and thus multiple dtypes.</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">__call__</span></code> of the <code class="docutils literal notranslate"><span class="pre">BoundMethod</span></code> above contains only a single call
to a function. But an <code class="docutils literal notranslate"><span class="pre">ArrayMethod</span></code> has to call <code class="docutils literal notranslate"><span class="pre">resolve_descriptors</span></code>
and later pass on that information to the inner-loop function.</p></li>
<li><p>A Python function has no state except that defined by its outer scope.
Within C, <code class="docutils literal notranslate"><span class="pre">Context</span></code> is able to provide additional state if necessary.</p></li>
</ul>
<p>Just as Python requires the distinction of a method and a bound method,
NumPy will have a <code class="docutils literal notranslate"><span class="pre">BoundArrayMethod</span></code>.
This stores all of the constant information that is part of the <code class="docutils literal notranslate"><span class="pre">Context</span></code>,
such as:</p>
<ul class="simple">
<li><p>the <code class="docutils literal notranslate"><span class="pre">DTypes</span></code></p></li>
<li><p>the number of input and output arguments</p></li>
<li><p>the ufunc signature (specific to generalized ufuncs, compare <a class="reference internal" href="nep-0020-gufunc-signature-enhancement.html#nep20"><span class="std std-ref">NEP 20 — Expansion of generalized universal function signatures</span></a>).</p></li>
</ul>
<p>Fortunately, most users and even ufunc implementers will not have to worry
about these internal details; just like few Python users need to know
about the <code class="docutils literal notranslate"><span class="pre">__get__</span></code> dunder method.