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<section id="nep-50-promotion-rules-for-python-scalars">
<span id="nep50"></span><h1>NEP 50 — Promotion rules for Python scalars<a class="headerlink" href="#nep-50-promotion-rules-for-python-scalars" title="Link to this heading">#</a></h1>
<dl class="field-list simple">
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Sebastian Berg</p>
</dd>
<dt class="field-even">Status<span class="colon">:</span></dt>
<dd class="field-even"><p>Final</p>
</dd>
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Standards Track</p>
</dd>
<dt class="field-even">Created<span class="colon">:</span></dt>
<dd class="field-even"><p>2021-05-25</p>
</dd>
</dl>
<section id="abstract">
<h2>Abstract<a class="headerlink" href="#abstract" title="Link to this heading">#</a></h2>
<p>Since NumPy 1.7, promotion rules use so-called “safe casting”
which relies on inspection of the values involved.
This helped identify a number of edge cases for users, but was
complex to implement and also made behavior hard to predict.</p>
<p>There are two kinds of confusing results:</p>
<ol class="arabic">
<li><p>Value-based promotion means that the value, for example of a Python integer,
can determine output type as found by <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="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int8</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int8</span>
<span class="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int8</span><span class="p">,</span> <span class="mi">255</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int16</span>
</pre></div>
</div>
<p>This logic arises because <code class="docutils literal notranslate"><span class="pre">1</span></code> can be represented by a <code class="docutils literal notranslate"><span class="pre">uint8</span></code> or
<code class="docutils literal notranslate"><span class="pre">int8</span></code> while <code class="docutils literal notranslate"><span class="pre">255</span></code> cannot be represented by an <code class="docutils literal notranslate"><span class="pre">int8</span></code> but only by
by a <code class="docutils literal notranslate"><span class="pre">uint8</span></code> or <code class="docutils literal notranslate"><span class="pre">int16</span></code>.</p>
<p>This also holds when working with 0-D arrays (so-called “scalar arrays”):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">int64_0d_array</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="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int8</span><span class="p">,</span> <span class="n">int64_0d_array</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int8</span>
</pre></div>
</div>
<p>Where the fact that <code class="docutils literal notranslate"><span class="pre">int64_0d_array</span></code> has an <code class="docutils literal notranslate"><span class="pre">int64</span></code> dtype has no
influence on the resulting dtype. The <code class="docutils literal notranslate"><span class="pre">dtype=np.int64</span></code> is effectively
ignored in this example since only its value matters.</p>
</li>
<li><p>For a Python <code class="docutils literal notranslate"><span class="pre">int</span></code>, <code class="docutils literal notranslate"><span class="pre">float</span></code>, or <code class="docutils literal notranslate"><span class="pre">complex</span></code> the value is inspected as
previously shown. But surprisingly <em>not</em> when the NumPy object is a 0-D array
or NumPy scalar:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</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="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int64</span>
<span class="n">np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int8</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int64</span>
</pre></div>
</div>
<p>The reason is that value-based promotion is disabled when all
objects are scalars or 0-D arrays.
NumPy thus returns the same type as <code class="docutils literal notranslate"><span class="pre">np.array(1)</span></code>, which is usually
an <code class="docutils literal notranslate"><span class="pre">int64</span></code> (this depends on the system).</p>
</li>
</ol>
<p>Note that the examples apply also to operations like multiplication,
addition, comparisons, and their corresponding functions like <code class="docutils literal notranslate"><span class="pre">np.multiply</span></code>.</p>
<p>This NEP proposes to refactor the behaviour around two guiding principles:</p>
<ol class="arabic simple">
<li><p>Values must never influence result type.</p></li>
<li><p>NumPy scalars and 0-D arrays should behave consistently with their
N-D counterparts.</p></li>
</ol>
<p>We propose to remove all value-based logic and add special handling for
Python scalars to preserve some convenient behaviors.
Python scalars will be considered “weakly” typed.
When a NumPy array/scalar is combined with a Python scalar, it will
be converted to the NumPy dtype, such that:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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">uint8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1"># returns a uint8 array</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">float32</span><span class="p">)</span> <span class="o">+</span> <span class="mf">2.</span> <span class="c1"># returns a float32 array</span>
</pre></div>
</div>
<p>There will be no dependence on the Python value itself.</p>
<p>The proposed changes also apply to <code class="docutils literal notranslate"><span class="pre">np.can_cast(100,</span> <span class="pre">np.int8)</span></code>, however,
we expect that the behaviour in functions (promotion) will, in practice, be far
more important than the casting change itself.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>As of the NumPy 1.24.x series, NumPy has preliminary and limited support to
test this proposal.</p>
<p>It is further necessary to set the following environment variable:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">export</span> <span class="n">NPY_PROMOTION_STATE</span><span class="o">=</span><span class="n">weak</span>
</pre></div>
</div>
<p>Valid values are <code class="docutils literal notranslate"><span class="pre">weak</span></code>, <code class="docutils literal notranslate"><span class="pre">weak_and_warn</span></code>, and <code class="docutils literal notranslate"><span class="pre">legacy</span></code>. Note that
<code class="docutils literal notranslate"><span class="pre">weak_and_warn</span></code> implements the optional warnings proposed in this NEP
and is expected to be <em>very</em> noisy.
We recommend starting using the <code class="docutils literal notranslate"><span class="pre">weak</span></code> option and use <code class="docutils literal notranslate"><span class="pre">weak_and_warn</span></code>
mainly to understand a specific observed change in behaviour.</p>
<p>The following additional API exists:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">np._set_promotion_state()</span></code> and <code class="docutils literal notranslate"><span class="pre">np._get_promotion_state()</span></code> which is
equivalent to the environment variable. (Not thread/context safe.)</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">with</span> <span class="pre">np._no_nep50_warning():</span></code> allows to suppress warnings when
<code class="docutils literal notranslate"><span class="pre">weak_and_warn</span></code> promotion is used. (Thread and context safe.)</p></li>
</ul>
<p>At this time overflow warnings on integer power are missing.
Further, <code class="docutils literal notranslate"><span class="pre">np.can_cast</span></code> fails to give warnings in the
<code class="docutils literal notranslate"><span class="pre">weak_and_warn</span></code> mode. Its behavior with respect to Python scalar input
may still be in flux (this should affect very few users).</p>
</div>
<section id="schema-of-the-new-proposed-promotion-rules">
<h3>Schema of the new proposed promotion rules<a class="headerlink" href="#schema-of-the-new-proposed-promotion-rules" title="Link to this heading">#</a></h3>
<p>After the change, the promotions in NumPy will follow the schema below.
Promotion always occurs along the green lines:
from left to right within their kind and to a higher kind only when
necessary.
The result kind is always the largest kind of the inputs.
Note that <code class="docutils literal notranslate"><span class="pre">float32</span></code> has a lower precision than <code class="docutils literal notranslate"><span class="pre">int32</span></code> or <code class="docutils literal notranslate"><span class="pre">uint32</span></code> and
is thus sorted slightly to the left in the schematic. This is because
<code class="docutils literal notranslate"><span class="pre">float32</span></code> cannot represent all <code class="docutils literal notranslate"><span class="pre">int32</span></code> values exactly.
However, for practical reasons, NumPy allows promoting <code class="docutils literal notranslate"><span class="pre">int64</span></code> to <code class="docutils literal notranslate"><span class="pre">float64</span></code>
effectively considering them to have the same precision.</p>
<p>The Python scalars are inserted at the very left of each “kind” and the
Python integer does not distinguish signed and unsigned. NumPy promotion
thus uses the following, ordered, kind categories:</p>
<ul class="simple">
<li><p><cite>boolean</cite></p></li>
<li><p><cite>integral</cite>: signed or unsigned integers</p></li>
<li><p><cite>inexact</cite>: floating point numbers and complex floating point numbers</p></li>
</ul>
<p>When promoting a Python scalar with a dtype of lower kind
category (<cite>boolean < integral < inexact</cite>) with a higher one, we use the
minimum/default precision: that is <code class="docutils literal notranslate"><span class="pre">float64</span></code>, <code class="docutils literal notranslate"><span class="pre">complex128</span></code> or <code class="docutils literal notranslate"><span class="pre">int64</span></code>
(<code class="docutils literal notranslate"><span class="pre">int32</span></code> is used on some systems, e.g. windows).</p>
<figure class="align-center align-default">
<img alt="_images/nep-0050-promotion-no-fonts.svg" src="_images/nep-0050-promotion-no-fonts.svg" /></figure>
<p>See the next section for examples which clarify the proposed behavior.
Further examples with a comparison to the current behavior can be found
in the table below.</p>
</section>
<section id="examples-of-new-behaviour">
<h3>Examples of new behaviour<a class="headerlink" href="#examples-of-new-behaviour" title="Link to this heading">#</a></h3>
<p>To make interpretation of above text and figure easier, we provide a few examples of the new behaviour. Below, the Python integer has no influence on the result type:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
<p>In the following the Python <code class="docutils literal notranslate"><span class="pre">float</span></code> and <code class="docutils literal notranslate"><span class="pre">complex</span></code> are “inexact”, but the
NumPy value is integral, so we use at least <code class="docutils literal notranslate"><span class="pre">float64</span></code>/<code class="docutils literal notranslate"><span class="pre">complex128</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">uint16</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="mf">3.0</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="mf">6.0</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">int16</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span> <span class="o">+</span> <span class="mi">4</span><span class="n">j</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">complex128</span><span class="p">(</span><span class="mi">4</span><span class="o">+</span><span class="mi">4</span><span class="n">j</span><span class="p">)</span>
</pre></div>
</div>
<p>But this does not happen for <code class="docutils literal notranslate"><span class="pre">float</span></code> to <code class="docutils literal notranslate"><span class="pre">complex</span></code> promotions, where
<code class="docutils literal notranslate"><span class="pre">float32</span></code> and <code class="docutils literal notranslate"><span class="pre">complex64</span></code> have the same precision:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="o">+</span> <span class="mi">5</span><span class="n">j</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">complex64</span><span class="p">(</span><span class="mi">5</span><span class="o">+</span><span class="mi">5</span><span class="n">j</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that the schematic omits <code class="docutils literal notranslate"><span class="pre">bool</span></code>. It is set below “integral”, so that the
following hold:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">bool_</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="kc">True</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that while this NEP uses simple operators as example, the rules described
generally apply to all of NumPy operations.</p>
</section>
<section id="table-comparing-new-and-old-behaviour">
<h3>Table comparing new and old behaviour<a class="headerlink" href="#table-comparing-new-and-old-behaviour" title="Link to this heading">#</a></h3>
<p>The following table lists relevant changes and unchanged behaviours.
Please see the <a class="reference internal" href="#old-implementation">Old implementation</a> for a detailed explanation of the rules
that lead to the “Old result”, and the following sections for the rules
detailing the new.
The backwards compatibility section discusses how these changes are likely
to impact users.</p>
<p>Note the important distinction between a 0-D array like <code class="docutils literal notranslate"><span class="pre">array(2)</span></code> and
arrays that are not 0-D, such as <code class="docutils literal notranslate"><span class="pre">array([2])</span></code>.</p>
<div class="pst-scrollable-table-container"><table class="table" id="id18">
<caption><span class="caption-text">Table of changed behaviours</span><a class="headerlink" href="#id18" title="Link to this table">#</a></caption>
<colgroup>
<col style="width: 45.5%" />
<col style="width: 27.3%" />
<col style="width: 27.3%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Expression</p></th>
<th class="head"><p>Old result</p></th>
<th class="head"><p>New result</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">uint8(1)</span> <span class="pre">+</span> <span class="pre">2</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">int64(3)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">uint8(3)</span></code> <a class="reference internal" href="#t1" id="id1"><span>[T1]</span></a></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">array([1],</span> <span class="pre">uint8)</span> <span class="pre">+</span> <span class="pre">int64(1)</span></code> or</p>
<p><code class="docutils literal notranslate"><span class="pre">array([1],</span> <span class="pre">uint8)</span> <span class="pre">+</span> <span class="pre">array(1,</span> <span class="pre">int64)</span></code></p>
</td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([2],</span> <span class="pre">uint8)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([2],</span> <span class="pre">int64)</span></code> <a class="reference internal" href="#t2" id="id2"><span>[T2]</span></a></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">array([1.],</span> <span class="pre">float32)</span> <span class="pre">+</span> <span class="pre">float64(1.)</span></code> or</p>
<p><code class="docutils literal notranslate"><span class="pre">array([1.],</span> <span class="pre">float32)</span> <span class="pre">+</span> <span class="pre">array(1.,</span> <span class="pre">float64)</span></code></p>
</td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([2.],</span> <span class="pre">float32)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([2.],</span> <span class="pre">float64)</span></code></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">array([1],</span> <span class="pre">uint8)</span> <span class="pre">+</span> <span class="pre">1</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([2],</span> <span class="pre">uint8)</span></code></p></td>
<td><p><em>unchanged</em></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">array([1],</span> <span class="pre">uint8)</span> <span class="pre">+</span> <span class="pre">200</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([201],</span> <span class="pre">np.uint8)</span></code></p></td>
<td><p><em>unchanged</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">array([100],</span> <span class="pre">uint8)</span> <span class="pre">+</span> <span class="pre">200</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([</span> <span class="pre">44],</span> <span class="pre">uint8)</span></code></p></td>
<td><p><em>unchanged</em> <a class="reference internal" href="#t3" id="id3"><span>[T3]</span></a></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">array([1],</span> <span class="pre">uint8)</span> <span class="pre">+</span> <span class="pre">300</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([301],</span> <span class="pre">uint16)</span></code></p></td>
<td><p><em>Exception</em> <a class="reference internal" href="#t4" id="id4"><span>[T4]</span></a></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">uint8(1)</span> <span class="pre">+</span> <span class="pre">300</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">int64(301)</span></code></p></td>
<td><p><em>Exception</em> <a class="reference internal" href="#t5" id="id5"><span>[T5]</span></a></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">uint8(100)</span> <span class="pre">+</span> <span class="pre">200</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">int64(301)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">uint8(44)</span></code> <em>and</em> <code class="docutils literal notranslate"><span class="pre">RuntimeWarning</span></code> <a class="reference internal" href="#t6" id="id6"><span>[T6]</span></a></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">float32(1)</span> <span class="pre">+</span> <span class="pre">3e100</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">float64(3e100)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">float32(Inf)</span></code> <em>and</em> <code class="docutils literal notranslate"><span class="pre">RuntimeWarning</span></code> <a class="reference internal" href="#t7" id="id7"><span>[T7]</span></a></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">array([1.0],</span> <span class="pre">float32)</span> <span class="pre">+</span> <span class="pre">1e-14</span> <span class="pre">==</span> <span class="pre">1.0</span></code> <a class="reference internal" href="#t8" id="id8"><span>[T8]</span></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([True])</span></code></p></td>
<td><p><em>unchanged</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">array(1.0,</span> <span class="pre">float32)</span> <span class="pre">+</span> <span class="pre">1e-14</span> <span class="pre">==</span> <span class="pre">1.0</span></code> <a class="reference internal" href="#t8" id="id9"><span>[T8]</span></a></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">False</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">True</span></code></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">array([1.],</span> <span class="pre">float32)</span> <span class="pre">+</span> <span class="pre">3</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([4.],</span> <span class="pre">float32)</span></code></p></td>
<td><p><em>unchanged</em></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">array([1.],</span> <span class="pre">float32)</span> <span class="pre">+</span> <span class="pre">int64(3)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([4.],</span> <span class="pre">float32)</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">array([4.],</span> <span class="pre">float64)</span></code> <a class="reference internal" href="#t9" id="id10"><span>[T9]</span></a></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">(3j</span> <span class="pre">+</span> <span class="pre">array(3,</span> <span class="pre">complex64)).dtype</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">complex128</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">complex64</span></code> <a class="reference internal" href="#t10" id="id11"><span>[T10]</span></a></p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">(float32(1)</span> <span class="pre">+</span> <span class="pre">1j)).dtype</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">complex128</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">complex64</span></code> <a class="reference internal" href="#t11" id="id12"><span>[T11]</span></a></p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">(int32(1)</span> <span class="pre">+</span> <span class="pre">5j).dtype</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">complex128</span></code></p></td>
<td><p><em>unchanged</em> <a class="reference internal" href="#t12" id="id13"><span>[T12]</span></a></p></td>
</tr>
</tbody>
</table>
</div>
<div role="list" class="citation-list">
<div class="citation" id="t1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">T1</a><span class="fn-bracket">]</span></span>
<p>New behaviour honours the dtype of the <code class="docutils literal notranslate"><span class="pre">uint8</span></code> scalar.</p>
</div>
<div class="citation" id="t2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">T2</a><span class="fn-bracket">]</span></span>
<p>Current NumPy ignores the precision of 0-D arrays or NumPy scalars
when combined with arrays.</p>
</div>
<div class="citation" id="t3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">T3</a><span class="fn-bracket">]</span></span>
<p>Current NumPy ignores the precision of 0-D arrays or NumPy scalars
when combined with arrays.</p>
</div>
<div class="citation" id="t4" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">T4</a><span class="fn-bracket">]</span></span>
<p>Old behaviour uses <code class="docutils literal notranslate"><span class="pre">uint16</span></code> because <code class="docutils literal notranslate"><span class="pre">300</span></code> does not fit <code class="docutils literal notranslate"><span class="pre">uint8</span></code>,
new behaviour raises an error for the same reason.</p>
</div>
<div class="citation" id="t5" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">T5</a><span class="fn-bracket">]</span></span>
<p><code class="docutils literal notranslate"><span class="pre">300</span></code> cannot be converted to <code class="docutils literal notranslate"><span class="pre">uint8</span></code>.</p>
</div>
<div class="citation" id="t6" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id6">T6</a><span class="fn-bracket">]</span></span>
<p>One of the most dangerous changes maybe. Retaining the type leads to
overflow. A <code class="docutils literal notranslate"><span class="pre">RuntimeWarning</span></code> indicating overflow is given for the
NumPy scalars.</p>
</div>
<div class="citation" id="t7" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id7">T7</a><span class="fn-bracket">]</span></span>
<p><code class="docutils literal notranslate"><span class="pre">np.float32(3e100)</span></code> overflows to infinity with a warning.</p>
</div>
<div class="citation" id="t8" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>T8<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#id8">1</a>,<a role="doc-backlink" href="#id9">2</a>)</span>
<p><code class="docutils literal notranslate"><span class="pre">1</span> <span class="pre">+</span> <span class="pre">1e-14</span></code> loses precision when done in float32 but not in float64.
The old behavior was casting the scalar argument to float32 or float64
differently depending on the dimensionality of the array; with the new
behavior the computation is always done in the array
precision (float32 in this case).</p>
</div>
<div class="citation" id="t9" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id10">T9</a><span class="fn-bracket">]</span></span>
<p>NumPy promotes <code class="docutils literal notranslate"><span class="pre">float32</span></code> and <code class="docutils literal notranslate"><span class="pre">int64</span></code> to <code class="docutils literal notranslate"><span class="pre">float64</span></code>. The old
behaviour ignored the <code class="docutils literal notranslate"><span class="pre">int64</span></code> here.</p>
</div>
<div class="citation" id="t10" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id11">T10</a><span class="fn-bracket">]</span></span>
<p>The new behavior is consistent between <code class="docutils literal notranslate"><span class="pre">array(3,</span> <span class="pre">complex64)</span></code> and
<code class="docutils literal notranslate"><span class="pre">array([3],</span> <span class="pre">complex64)</span></code>: the dtype of the result is that of the
array argument.</p>
</div>
<div class="citation" id="t11" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id12">T11</a><span class="fn-bracket">]</span></span>
<p>The new behavior uses the complex dtype of the precision compatible
with the array argument, <code class="docutils literal notranslate"><span class="pre">float32</span></code>.</p>
</div>
<div class="citation" id="t12" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id13">T12</a><span class="fn-bracket">]</span></span>
<p>Since the array kind is integer, the result uses the default complex
precision, which is <code class="docutils literal notranslate"><span class="pre">complex128</span></code>.</p>
</div>
</div>
</section>
</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 motivation for changing the behaviour with respect to inspecting the value
of Python scalars and NumPy scalars/0-D arrays is three-fold:</p>
<ol class="arabic simple">
<li><p>The special handling of NumPy scalars/0-D arrays as well as the value
inspection can be very surprising to users,</p></li>
<li><p>The value-inspection logic is much harder to explain and implement.
It is further harder to make it available to user-defined DTypes through
<a class="reference internal" href="nep-0042-new-dtypes.html#nep42"><span class="std std-ref">NEP 42</span></a>.
Currently, this leads to a dual implementation of a new and an old (value
sensitive) system. Fixing this will greatly simplify the internal logic
and make results more consistent.</p></li>
<li><p>It largely aligns with the choice of other projects like <cite>JAX</cite> and
<cite>data-apis.org</cite> (see also <cite>Related Work</cite>).</p></li>
</ol>
<p>We believe that the proposal of “weak” Python scalars will help users by
providing a clear mental model for which datatype an operation will
result in.
This model fits well with the preservation of array precisions that NumPy
currently often follows, and also uses for in-place operations:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">arr</span> <span class="o">+=</span> <span class="n">value</span>
</pre></div>
</div>
<p>Preserves precision as long as “kind” boundaries are not crossed (otherwise
an error is raised).</p>
<p>While some users will potentially miss the value inspecting behavior, even for
those cases where it seems useful it quickly leads to surprises. This may be
expected:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">100</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">uint8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1000</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">1100</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">uint16</span><span class="p">)</span>
</pre></div>
</div>
<p>But the following will then be a surprise:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">100</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">uint8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">200</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">44</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">uint8</span><span class="p">)</span>
</pre></div>
</div>
<p>Considering that the proposal aligns with the behavior of in-place operands
and avoids the surprising switch in behavior that only sometimes avoids
overflow in the result,
we believe that the proposal follows the “principle of least surprise”.</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 is expected to be implemented with <strong>no</strong> transition period that warns
for all changes. Such a transition period would create many (often harmless)
warnings which would be difficult to silence.
We expect that most users will benefit long term from the clearer promotion
rules and that few are directly (negatively) impacted by the change.
However, certain usage patterns may lead to problematic changes, these are
detailed in the backwards compatibility section.</p>
<p>The solution to this will be an <em>optional</em> warning mode capable of notifying
users of potential changes in behavior.
This mode is expected to generate many harmless warnings, but provide a way
to systematically vet code and track down changes if problems are observed.</p>
<section id="impact-on-can-cast">
<h3>Impact on <code class="docutils literal notranslate"><span class="pre">can_cast</span></code><a class="headerlink" href="#impact-on-can-cast" title="Link to this heading">#</a></h3>
<p><cite>can_cast</cite> will never inspect the value anymore. So that the following results
are expected to change from <code class="docutils literal notranslate"><span class="pre">True</span></code> to <code class="docutils literal notranslate"><span class="pre">False</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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">int64</span><span class="p">(</span><span class="mi">100</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</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">array</span><span class="p">(</span><span class="mi">100</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">int64</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">can_cast</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span>
</pre></div>
</div>
<p>We expect that the impact of this change will be small compared to that of
the following changes.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The last example where the input is a Python scalar _may_ be preserved
since <code class="docutils literal notranslate"><span class="pre">100</span></code> can be represented by a <code class="docutils literal notranslate"><span class="pre">uint8</span></code>.</p>
</div>
</section>
<section id="impact-on-operators-and-functions-involving-numpy-arrays-or-scalars">
<h3>Impact on operators and functions involving NumPy arrays or scalars<a class="headerlink" href="#impact-on-operators-and-functions-involving-numpy-arrays-or-scalars" title="Link to this heading">#</a></h3>
<p>The main impact on operations not involving Python scalars (<code class="docutils literal notranslate"><span class="pre">float</span></code>, <code class="docutils literal notranslate"><span class="pre">int</span></code>,
<code class="docutils literal notranslate"><span class="pre">complex</span></code>) will be that operations on 0-D arrays and NumPy scalars will never
depend on their values.
This removes currently surprising cases. For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</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">uint8</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># and:</span>
<span class="n">np</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</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">uint8</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
</pre></div>
</div>
<p>Will return an <code class="docutils literal notranslate"><span class="pre">int64</span></code> array in the future because the type of
<code class="docutils literal notranslate"><span class="pre">np.int64(1)</span></code> is strictly honoured.
Currently a <code class="docutils literal notranslate"><span class="pre">uint8</span></code> array is returned.</p>
</section>
<section id="impact-on-operators-involving-python-int-float-and-complex">
<h3>Impact on operators involving Python <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><a class="headerlink" href="#impact-on-operators-involving-python-int-float-and-complex" title="Link to this heading">#</a></h3>
<p>This NEP attempts to preserve the convenience of the old behaviour
when working with literal values.
The current value-based logic had some nice properties when “untyped”,
literal Python scalars are involved:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</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">int8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1"># returns an int8 array</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</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">float32</span><span class="p">)</span> <span class="o">*</span> <span class="mf">3.5</span> <span class="c1"># returns a float32 array</span>
</pre></div>
</div>
<p>But led to surprises when it came to “unrepresentable” values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</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">int8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">256</span> <span class="c1"># returns int16</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</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">float32</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e200</span> <span class="c1"># returns float64</span>
</pre></div>
</div>
<p>The proposal is to preserve this behaviour for the most part. This is achieved
by considering Python <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> to be “weakly” typed
in operations.
However, to avoid surprises, we plan to make conversion to the new type
more strict: The results will be unchanged in the first two examples,
but in the second one, it will change the following way:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</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">int8</span><span class="p">)</span> <span class="o">+</span> <span class="mi">256</span> <span class="c1"># raises a TypeError</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</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">float32</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e200</span> <span class="c1"># warning and returns infinity</span>
</pre></div>
</div>
<p>The second one warns because <code class="docutils literal notranslate"><span class="pre">np.float32(1e200)</span></code> overflows to infinity.
It will then continue to do the calculation with <code class="docutils literal notranslate"><span class="pre">inf</span></code> as usual.</p>
<div class="admonition-behaviour-in-other-libraries admonition">
<p class="admonition-title">Behaviour in other libraries</p>
<p>Overflowing in the conversion rather than raising an error is a choice;
it is one that is the default in most C setups (similar to NumPy C can be
set up to raise an error due to the overflow, however).
It is also for example the behaviour of <code class="docutils literal notranslate"><span class="pre">pytorch</span></code> 1.10.</p>
</div>
<section id="particular-behavior-of-python-integers">
<h4>Particular behavior of Python integers<a class="headerlink" href="#particular-behavior-of-python-integers" title="Link to this heading">#</a></h4>
<p>The NEPs promotion rules stated in terms of the resulting dtype which is
typically also the operation dtype (in terms of result precision).
This leads to what may seem like exceptions for Python integers:
While <code class="docutils literal notranslate"><span class="pre">uint8(3)</span> <span class="pre">+</span> <span class="pre">1000</span></code> must be rejected because operating
in <code class="docutils literal notranslate"><span class="pre">uint8</span></code> is not possible, <code class="docutils literal notranslate"><span class="pre">uint8(3)</span> <span class="pre">/</span> <span class="pre">1000</span></code> returns a <code class="docutils literal notranslate"><span class="pre">float64</span></code> and
can convert both inputs to <code class="docutils literal notranslate"><span class="pre">float64</span></code> to find the result.</p>
<p>In practice this means that arbitrary Python integer values are accepted in
the following cases:</p>
<ul class="simple">
<li><p>All comparisons (<code class="docutils literal notranslate"><span class="pre">==</span></code>, <code class="docutils literal notranslate"><span class="pre"><</span></code>, etc.) between NumPy and Python integers are
always well defined.</p></li>
<li><p>Unary functions like <code class="docutils literal notranslate"><span class="pre">np.sqrt</span></code> that give a floating point result can and
will convert the Python integer to a float.</p></li>
<li><p>Division of integers returns floating point by casting input to <code class="docutils literal notranslate"><span class="pre">float64</span></code>.</p></li>
</ul>
<p>Note that there may be additional functions where these exceptions could be
applied but are not. In these cases it should be considered an improvement
to allow them, but when the user impact is low we may not do so for simplicity.</p>
</section>
</section>
</section>
<section id="backward-compatibility">
<h2>Backward compatibility<a class="headerlink" href="#backward-compatibility" title="Link to this heading">#</a></h2>
<p>In general, code which only uses the default dtypes float64, or int32/int64
or more precise ones should not be affected.</p>
<p>However, the proposed changes will modify results in quite a few cases where
0-D or scalar values (with non-default dtypes) are mixed.
In many cases, these will be bug-fixes, however, there are certain changes
which may be problematic to the end-user.</p>
<p>The most important possible failure is probably the following example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">arr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">100</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">uint8</span><span class="p">)</span> <span class="c1"># storage array with low precision</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">arr</span><span class="p">[</span><span class="mi">10</span><span class="p">]</span>
<span class="c1"># calculation continues with "value" without considering where it came from</span>
<span class="n">value</span> <span class="o">*</span> <span class="mi">100</span>
</pre></div>
</div>
<p>Where previously the <code class="docutils literal notranslate"><span class="pre">value</span> <span class="pre">*</span> <span class="pre">100</span></code> would cause an up-cast to
<code class="docutils literal notranslate"><span class="pre">int32</span></code>/<code class="docutils literal notranslate"><span class="pre">int64</span></code> (because value is a scalar).
The new behaviour will preserve the lower precision unless explicitly
dealt with (just as if <code class="docutils literal notranslate"><span class="pre">value</span></code> was an array).
This can lead to integer overflows and thus incorrect results beyond precision.
In many cases this may be silent, although NumPy usually gives warnings for the
scalar operators.</p>
<p>Similarly, if the storage array is <code class="docutils literal notranslate"><span class="pre">float32</span></code> a calculation may retain the
lower <code class="docutils literal notranslate"><span class="pre">float32</span></code> precision rather than use the default <code class="docutils literal notranslate"><span class="pre">float64</span></code>.</p>
<p>Further issues can occur. For example:</p>
<ul>
<li><p>Floating point comparisons, especially equality, may change when mixing
precisions:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="mi">3</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="o">/</span><span class="mi">3</span> <span class="c1"># was False, will be True.</span>
</pre></div>
</div>
</li>
<li><p>Certain operations are expected to start failing:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span> <span class="o">*</span> <span class="mi">1000</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="n">np</span><span class="o">.</span><span class="n">uint8</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1000</span> <span class="c1"># possibly also</span>
</pre></div>
</div>
<p>to protect users in cases where previous value-based casting led to an
upcast. (Failures occur when converting <code class="docutils literal notranslate"><span class="pre">1000</span></code> to a <code class="docutils literal notranslate"><span class="pre">uint8</span></code>.)</p>
</li>
<li><p>Floating point overflow may occur in odder cases:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">(</span><span class="mf">1e-30</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e50</span> <span class="c1"># will return ``inf`` and a warning</span>
</pre></div>
</div>
<p>Because <code class="docutils literal notranslate"><span class="pre">np.float32(1e50)</span></code> returns <code class="docutils literal notranslate"><span class="pre">inf</span></code>. Previously, this would return
a double precision result even if the <code class="docutils literal notranslate"><span class="pre">1e50</span></code> was not a 0-D array</p>
</li>
</ul>
<p>In other cases, increased precision may occur. For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">multiple</span><span class="p">(</span><span class="n">float32_arr</span><span class="p">,</span> <span class="mf">2.</span><span class="p">)</span>
<span class="n">float32_arr</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="mf">2.</span><span class="p">)</span>
</pre></div>
</div>
<p>Will both return a float64 rather than <code class="docutils literal notranslate"><span class="pre">float32</span></code>. This improves precision but
slightly changes results and uses double the memory.</p>
<section id="changes-due-to-the-integer-ladder-of-precision">
<h3>Changes due to the integer “ladder of precision”<a class="headerlink" href="#changes-due-to-the-integer-ladder-of-precision" title="Link to this heading">#</a></h3>