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<section id="nep-10-optimizing-iterator-ufunc-performance">
<span id="nep10"></span><h1><a class="toc-backref" href="#id1" role="doc-backlink">NEP 10 — Optimizing iterator/UFunc performance</a><a class="headerlink" href="#nep-10-optimizing-iterator-ufunc-performance" 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>Mark Wiebe <<a class="reference external" href="mailto:mwwiebe%40gmail.com">mwwiebe<span>@</span>gmail<span>.</span>com</a>></p>
</dd>
<dt class="field-even">Content-Type<span class="colon">:</span></dt>
<dd class="field-even"><p>text/x-rst</p>
</dd>
<dt class="field-odd">Created<span class="colon">:</span></dt>
<dd class="field-odd"><p>25-Nov-2010</p>
</dd>
<dt class="field-even">Status<span class="colon">:</span></dt>
<dd class="field-even"><p>Final</p>
</dd>
</dl>
<section id="table-of-contents">
<h2><a class="toc-backref" href="#id2" role="doc-backlink">Table of contents</a><a class="headerlink" href="#table-of-contents" title="Link to this heading">#</a></h2>
<nav class="contents" id="contents">
<p class="topic-title">Contents</p>
<ul class="simple">
<li><p><a class="reference internal" href="#nep-10-optimizing-iterator-ufunc-performance" id="id1">NEP 10 — Optimizing iterator/UFunc performance</a></p>
<ul>
<li><p><a class="reference internal" href="#table-of-contents" id="id2">Table of contents</a></p></li>
<li><p><a class="reference internal" href="#abstract" id="id3">Abstract</a></p></li>
<li><p><a class="reference internal" href="#motivation" id="id4">Motivation</a></p>
<ul>
<li><p><a class="reference internal" href="#image-compositing-example" id="id5">Image compositing example</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#improving-cache-coherency" id="id6">Improving cache-coherency</a></p>
<ul>
<li><p><a class="reference internal" href="#output-layout-selection-algorithm" id="id7">Output layout selection algorithm</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#coalescing-dimensions" id="id8">Coalescing dimensions</a></p></li>
<li><p><a class="reference internal" href="#inner-loop-specialization" id="id9">Inner loop specialization</a></p></li>
<li><p><a class="reference internal" href="#implementation-details" id="id10">Implementation details</a></p>
<ul>
<li><p><a class="reference internal" href="#iterator-rewrite" id="id11">Iterator rewrite</a></p></li>
<li><p><a class="reference internal" href="#proposed-iterator-memory-layout" id="id12">Proposed iterator memory layout</a></p></li>
<li><p><a class="reference internal" href="#proposed-iterator-api" id="id13">Proposed iterator API</a></p>
<ul>
<li><p><a class="reference internal" href="#old-new-iterator-api-conversion" id="id14">Old -> new iterator API conversion</a></p></li>
<li><p><a class="reference internal" href="#iterator-pointer-type" id="id15">Iterator pointer type</a></p></li>
<li><p><a class="reference internal" href="#construction-and-destruction" id="id16">Construction and destruction</a></p></li>
<li><p><a class="reference internal" href="#functions-for-iteration" id="id17">Functions for iteration</a></p></li>
<li><p><a class="reference internal" href="#examples" id="id18">Examples</a></p></li>
<li><p><a class="reference internal" href="#python-lambda-ufunc-example" id="id19">Python lambda UFunc example</a></p></li>
<li><p><a class="reference internal" href="#python-addition-example" id="id20">Python addition example</a></p></li>
<li><p><a class="reference internal" href="#image-compositing-example-revisited" id="id21">Image compositing example revisited</a></p></li>
<li><p><a class="reference internal" href="#image-compositing-with-numexpr" id="id22">Image compositing with NumExpr</a></p></li>
</ul>
</li>
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</section>
<section id="abstract">
<h2><a class="toc-backref" href="#id3" role="doc-backlink">Abstract</a><a class="headerlink" href="#abstract" title="Link to this heading">#</a></h2>
<p>This NEP proposes to replace the NumPy iterator and multi-iterator
with a single new iterator, designed to be more flexible and allow for
more cache-friendly data access. The new iterator also subsumes much
of the core ufunc functionality, making it easy to get the current
ufunc benefits in contexts which don’t precisely fit the ufunc mold.
Key benefits include:</p>
<ul class="simple">
<li><p>automatic reordering to find a cache-friendly access pattern</p></li>
<li><p>standard and customizable broadcasting</p></li>
<li><p>automatic type/byte-order/alignment conversions</p></li>
<li><p>optional buffering to minimize conversion memory usage</p></li>
<li><p>optional output arrays, with automatic allocation when unsupplied</p></li>
<li><p>automatic output or common type selection</p></li>
</ul>
<p>A large fraction of this iterator design has already been implemented with
promising results. Construction overhead is slightly greater (a.flat:
0.5 us, nditer(a): 1.4 us and broadcast(a,b): 1.4 us, nditer([a,b]):
2.2 us), but, as shown in an example, it is already possible to improve
on the performance of the built-in NumPy mechanisms in pure Python code
together with the iterator. One example rewrites np.add, getting a
four times improvement with some Fortran-contiguous arrays, and
another improves image compositing code from 1.4s to 180ms.</p>
<p>The implementation attempts to take into account
the design decisions made in the NumPy 2.0 refactor, to make its future
integration into libndarray relatively simple.</p>
</section>
<section id="motivation">
<h2><a class="toc-backref" href="#id4" role="doc-backlink">Motivation</a><a class="headerlink" href="#motivation" title="Link to this heading">#</a></h2>
<p>NumPy defaults to returning C-contiguous arrays from UFuncs. This can
result in extremely poor memory access patterns when dealing with data
that is structured differently. A simple timing example illustrates
this with a more than eight times performance hit from adding
Fortran-contiguous arrays together. All timings are done using NumPy
2.0dev (Nov 22, 2010) on an Athlon 64 X2 4200+, with a 64-bit OS.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">In</span> <span class="p">[</span><span class="mi">1</span><span class="p">]:</span> <span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">2</span><span class="p">]:</span> <span class="n">a</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">1000000</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="n">reshape</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">3</span><span class="p">]:</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">copy</span><span class="p">(),</span> <span class="n">a</span><span class="o">.</span><span class="n">copy</span><span class="p">(),</span> <span class="n">a</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">4</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="o">+</span><span class="n">c</span><span class="o">+</span><span class="n">d</span>
<span class="mi">10</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mf">28.5</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">5</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">a</span><span class="o">.</span><span class="n">T</span><span class="o">+</span><span class="n">b</span><span class="o">.</span><span class="n">T</span><span class="o">+</span><span class="n">c</span><span class="o">.</span><span class="n">T</span><span class="o">+</span><span class="n">d</span><span class="o">.</span><span class="n">T</span>
<span class="mi">1</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mi">237</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">6</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">a</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="s1">'A'</span><span class="p">)</span><span class="o">+</span><span class="n">b</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="s1">'A'</span><span class="p">)</span><span class="o">+</span><span class="n">c</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="s1">'A'</span><span class="p">)</span><span class="o">+</span><span class="n">d</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="s1">'A'</span><span class="p">)</span>
<span class="mi">10</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mf">29.6</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
</pre></div>
</div>
<p>In this case, it is simple to recover the performance by switching to
a view of the memory, adding, then reshaping back. To further examine
the problem and see how it isn’t always as trivial to work around,
let’s consider simple code for working with image buffers in NumPy.</p>
<section id="image-compositing-example">
<h3><a class="toc-backref" href="#id5" role="doc-backlink">Image compositing example</a><a class="headerlink" href="#image-compositing-example" title="Link to this heading">#</a></h3>
<p>For a more realistic example, consider an image buffer. Images are
generally stored in a Fortran-contiguous order, and the colour
channel can be treated as either a structured ‘RGB’ type or an extra
dimension of length three. The resulting memory layout is neither C-
nor Fortran-contiguous, but is easy to work with directly in NumPy,
because of the flexibility of the ndarray. This appears ideal, because
it makes the memory layout compatible with typical C or C++ image code,
while simultaneously giving natural access in Python. Getting the color
of pixel (x,y) is just ‘image[x,y]’.</p>
<p>The performance of this layout in NumPy turns out to be very poor.
Here is code which creates two black images, and does an ‘over’
compositing operation on them.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">In</span> <span class="p">[</span><span class="mi">9</span><span class="p">]:</span> <span class="n">image1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">swapaxes</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">10</span><span class="p">]:</span> <span class="n">alpha1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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">float32</span><span class="p">)</span><span class="o">.</span><span class="n">swapaxes</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">11</span><span class="p">]:</span> <span class="n">image2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">swapaxes</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">12</span><span class="p">]:</span> <span class="n">alpha2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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">float32</span><span class="p">)</span><span class="o">.</span><span class="n">swapaxes</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">13</span><span class="p">]:</span> <span class="k">def</span><span class="w"> </span><span class="nf">composite_over</span><span class="p">(</span><span class="n">im1</span><span class="p">,</span> <span class="n">al1</span><span class="p">,</span> <span class="n">im2</span><span class="p">,</span> <span class="n">al2</span><span class="p">):</span>
<span class="o">....</span><span class="p">:</span> <span class="k">return</span> <span class="p">(</span><span class="n">im1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">al1</span><span class="p">)</span><span class="o">*</span><span class="n">im2</span><span class="p">,</span> <span class="n">al1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">al1</span><span class="p">)</span><span class="o">*</span><span class="n">al2</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">14</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">composite_over</span><span class="p">(</span><span class="n">image1</span><span class="p">,</span><span class="n">alpha1</span><span class="p">,</span><span class="n">image2</span><span class="p">,</span><span class="n">alpha2</span><span class="p">)</span>
<span class="mi">1</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mf">3.51</span> <span class="n">s</span> <span class="n">per</span> <span class="n">loop</span>
</pre></div>
</div>
<p>If we give up the convenient layout, and use the C-contiguous default,
the performance is about seven times better.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">In</span> <span class="p">[</span><span class="mi">16</span><span class="p">]:</span> <span class="n">image1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">In</span> <span class="p">[</span><span class="mi">17</span><span class="p">]:</span> <span class="n">alpha1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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">float32</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">18</span><span class="p">]:</span> <span class="n">image2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">In</span> <span class="p">[</span><span class="mi">19</span><span class="p">]:</span> <span class="n">alpha2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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">float32</span><span class="p">)</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">20</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">composite_over</span><span class="p">(</span><span class="n">image1</span><span class="p">,</span><span class="n">alpha1</span><span class="p">,</span><span class="n">image2</span><span class="p">,</span><span class="n">alpha2</span><span class="p">)</span>
<span class="mi">1</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mi">581</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
</pre></div>
</div>
<p>But this is not all, since it turns out that broadcasting the alpha
channel is exacting a performance price as well. If we use an alpha
channel with 3 values instead of one, we get:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">In</span> <span class="p">[</span><span class="mi">21</span><span class="p">]:</span> <span class="n">image1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">In</span> <span class="p">[</span><span class="mi">22</span><span class="p">]:</span> <span class="n">alpha1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">In</span> <span class="p">[</span><span class="mi">23</span><span class="p">]:</span> <span class="n">image2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">In</span> <span class="p">[</span><span class="mi">24</span><span class="p">]:</span> <span class="n">alpha2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</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="n">In</span> <span class="p">[</span><span class="mi">25</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">composite_over</span><span class="p">(</span><span class="n">image1</span><span class="p">,</span><span class="n">alpha1</span><span class="p">,</span><span class="n">image2</span><span class="p">,</span><span class="n">alpha2</span><span class="p">)</span>
<span class="mi">1</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mi">313</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
</pre></div>
</div>
<p>For a final comparison, let’s see how it performs when we use
one-dimensional arrays to ensure just a single loop does the
calculation.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">In</span> <span class="p">[</span><span class="mi">26</span><span class="p">]:</span> <span class="n">image1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="o">*</span><span class="mi">1920</span><span class="o">*</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="n">In</span> <span class="p">[</span><span class="mi">27</span><span class="p">]:</span> <span class="n">alpha1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="o">*</span><span class="mi">1920</span><span class="o">*</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="n">In</span> <span class="p">[</span><span class="mi">28</span><span class="p">]:</span> <span class="n">image2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="o">*</span><span class="mi">1920</span><span class="o">*</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="n">In</span> <span class="p">[</span><span class="mi">29</span><span class="p">]:</span> <span class="n">alpha2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="o">*</span><span class="mi">1920</span><span class="o">*</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="n">In</span> <span class="p">[</span><span class="mi">30</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">composite_over</span><span class="p">(</span><span class="n">image1</span><span class="p">,</span><span class="n">alpha1</span><span class="p">,</span><span class="n">image2</span><span class="p">,</span><span class="n">alpha2</span><span class="p">)</span>
<span class="mi">1</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mi">312</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
</pre></div>
</div>
<p>To get a reference performance number, I implemented this simple operation
straightforwardly in C (careful to use the same compile options as NumPy).
If I emulated the memory allocation and layout of the Python code, the
performance was roughly 0.3 seconds, very much in line with NumPy’s
performance. Combining the operations into one pass reduced the time
to roughly 0.15 seconds.</p>
<p>A slight variation of this example is to use a single memory block
with four channels (1920,1080,4) instead of separate image and alpha.
This is more typical in image processing applications, and here’s how
that looks with a C-contiguous layout.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">In</span> <span class="p">[</span><span class="mi">31</span><span class="p">]:</span> <span class="n">image1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</span><span class="p">,</span><span class="mi">4</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="n">In</span> <span class="p">[</span><span class="mi">32</span><span class="p">]:</span> <span class="n">image2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1080</span><span class="p">,</span><span class="mi">1920</span><span class="p">,</span><span class="mi">4</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="n">In</span> <span class="p">[</span><span class="mi">33</span><span class="p">]:</span> <span class="k">def</span><span class="w"> </span><span class="nf">composite_over</span><span class="p">(</span><span class="n">im1</span><span class="p">,</span> <span class="n">im2</span><span class="p">):</span>
<span class="o">....</span><span class="p">:</span> <span class="n">ret</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">im1</span><span class="p">[:,:,</span><span class="o">-</span><span class="mi">1</span><span class="p">])[:,:,</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span><span class="o">*</span><span class="n">im2</span>
<span class="o">....</span><span class="p">:</span> <span class="n">ret</span> <span class="o">+=</span> <span class="n">im1</span>
<span class="o">....</span><span class="p">:</span> <span class="k">return</span> <span class="n">ret</span>
<span class="n">In</span> <span class="p">[</span><span class="mi">34</span><span class="p">]:</span> <span class="n">timeit</span> <span class="n">composite_over</span><span class="p">(</span><span class="n">image1</span><span class="p">,</span><span class="n">image2</span><span class="p">)</span>
<span class="mi">1</span> <span class="n">loops</span><span class="p">,</span> <span class="n">best</span> <span class="n">of</span> <span class="mi">3</span><span class="p">:</span> <span class="mi">481</span> <span class="n">ms</span> <span class="n">per</span> <span class="n">loop</span>
</pre></div>
</div>
<p>To see the improvements that implementation of the new iterator as
proposed can produce, go to the example continued after the
proposed API, near the bottom of the document.</p>
</section>
</section>
<section id="improving-cache-coherency">
<h2><a class="toc-backref" href="#id6" role="doc-backlink">Improving cache-coherency</a><a class="headerlink" href="#improving-cache-coherency" title="Link to this heading">#</a></h2>
<p>In order to get the best performance from UFunc calls, the pattern of
memory reads should be as regular as possible. Modern CPUs attempt to
predict the memory read/write pattern and fill the cache ahead of time.
The most predictable pattern is for all the inputs and outputs to be
sequentially processed in the same order.</p>
<p>I propose that by default, the memory layout of the UFunc outputs be as
close to that of the inputs as possible. Whenever there is an ambiguity
or a mismatch, it defaults to a C-contiguous layout.</p>
<p>To understand how to accomplish this, we first consider the strides of
all the inputs after the shapes have been normalized for broadcasting.
By determining whether a set of strides are compatible and/or ambiguous,
we can determine an output memory layout which maximizes coherency.</p>
<p>In broadcasting, the input shapes are first transformed to broadcast
shapes by prepending singular dimensions, then the broadcast strides
are created, where any singular dimension’s stride is set to zero.</p>
<p>Strides may be negative as well, and in certain cases this can be
normalized to fit the following discussion. If all the strides for a
particular axis are negative or zero, the strides for that dimension
can be negated after adjusting the base data pointers appropriately.</p>
<p>Here’s an example of how three inputs with C-contiguous layouts result in
broadcast strides. To simplify things, the examples use an itemsize of 1.</p>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p>Input shapes:</p></td>
<td><p>(5,3,7)</p></td>
<td><p>(5,3,1)</p></td>
<td><p>(1,7)</p></td>
</tr>
<tr class="row-even"><td><p>Broadcast shapes:</p></td>
<td><p>(5,3,7)</p></td>
<td><p>(5,3,1)</p></td>
<td><p>(1,1,7)</p></td>
</tr>
<tr class="row-odd"><td><p>Broadcast strides:</p></td>
<td><p>(21,7,1)</p></td>
<td><p>(3,1,0)</p></td>
<td><p>(0,0,1)</p></td>
</tr>
</tbody>
</table>
</div>
<p><em>Compatible Strides</em> - A set of strides are compatible if there exists
a permutation of the axes such that the strides are decreasing for every
stride in the set, excluding entries that are zero.</p>
<p>The example above satisfies the definition with the identity permutation.
In the motivation image example, the strides are slightly different if
we separate the colour and alpha information or not. The permutation
which demonstrates compatibility here is the transposition (0,1).</p>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p>Input/Broadcast shapes:</p></td>
<td><p>Image (1920, 1080, 3)</p></td>
<td><p>Alpha (1920, 1080, 1)</p></td>
</tr>
<tr class="row-even"><td><p>Broadcast strides (separate):</p></td>
<td><p>(3,5760,1)</p></td>
<td><p>(1,1920,0)</p></td>
</tr>
<tr class="row-odd"><td><p>Broadcast strides (together):</p></td>
<td><p>(4,7680,1)</p></td>
<td><p>(4,7680,0)</p></td>
</tr>
</tbody>
</table>
</div>
<p><em>Ambiguous Strides</em> - A set of compatible strides are ambiguous if
more than one permutation of the axes exists such that the strides are
decreasing for every stride in the set, excluding entries that are zero.</p>
<p>This typically occurs when every axis has a 0-stride somewhere in the
set of strides. The simplest example is in two dimensions, as follows.</p>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p>Broadcast shapes:</p></td>
<td><p>(1,3)</p></td>
<td><p>(5,1)</p></td>
</tr>
<tr class="row-even"><td><p>Broadcast strides:</p></td>
<td><p>(0,1)</p></td>
<td><p>(1,0)</p></td>
</tr>
</tbody>
</table>
</div>
<p>There may, however, be unambiguous compatible strides without a single
input forcing the entire layout, as in this example:</p>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p>Broadcast shapes:</p></td>
<td><p>(1,3,4)</p></td>
<td><p>(5,3,1)</p></td>
</tr>
<tr class="row-even"><td><p>Broadcast strides:</p></td>
<td><p>(0,4,1)</p></td>
<td><p>(3,1,0)</p></td>
</tr>
</tbody>
</table>
</div>
<p>In the face of ambiguity, we have a choice to either completely throw away
the fact that the strides are compatible, or try to resolve the ambiguity
by adding an additional constraint. I think the appropriate choice
is to resolve it by picking the memory layout closest to C-contiguous,
but still compatible with the input strides.</p>
<section id="output-layout-selection-algorithm">
<h3><a class="toc-backref" href="#id7" role="doc-backlink">Output layout selection algorithm</a><a class="headerlink" href="#output-layout-selection-algorithm" title="Link to this heading">#</a></h3>
<p>The output ndarray memory layout we would like to produce is as follows:</p>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p>Consistent/Unambiguous strides:</p></td>
<td><p>The single consistent layout</p></td>
</tr>
<tr class="row-even"><td><p>Consistent/Ambiguous strides:</p></td>
<td><p>The consistent layout closest to C-contiguous</p></td>
</tr>
<tr class="row-odd"><td><p>Inconsistent strides:</p></td>
<td><p>C-contiguous</p></td>
</tr>
</tbody>
</table>
</div>
<p>Here is pseudo-code for an algorithm to compute the permutation for the
output layout.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">perm</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">ndim</span><span class="p">)</span> <span class="c1"># Identity, i.e. C-contiguous</span>
<span class="c1"># Insertion sort, ignoring 0-strides</span>
<span class="c1"># Note that the sort must be stable, and 0-strides may</span>
<span class="c1"># be reordered if necessary, but should be moved as little</span>
<span class="c1"># as possible.</span>
<span class="k">for</span> <span class="n">i0</span> <span class="o">=</span> <span class="mi">1</span> <span class="n">to</span> <span class="n">ndim</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="c1"># ipos is where perm[i0] will get inserted</span>
<span class="n">ipos</span> <span class="o">=</span> <span class="n">i0</span>
<span class="n">j0</span> <span class="o">=</span> <span class="n">perm</span><span class="p">[</span><span class="n">i0</span><span class="p">]</span>
<span class="k">for</span> <span class="n">i1</span> <span class="o">=</span> <span class="n">i0</span><span class="o">-</span><span class="mi">1</span> <span class="n">to</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">j1</span> <span class="o">=</span> <span class="n">perm</span><span class="p">[</span><span class="n">i1</span><span class="p">]</span>
<span class="n">ambig</span><span class="p">,</span> <span class="n">shouldswap</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span>
<span class="c1"># Check whether any strides are ordered wrong</span>
<span class="k">for</span> <span class="n">strides</span> <span class="ow">in</span> <span class="n">broadcast_strides</span><span class="p">:</span>
<span class="k">if</span> <span class="n">strides</span><span class="p">[</span><span class="n">j0</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">strides</span><span class="p">[</span><span class="n">j1</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">if</span> <span class="n">strides</span><span class="p">[</span><span class="n">j0</span><span class="p">]</span> <span class="o">></span> <span class="n">strides</span><span class="p">[</span><span class="n">j1</span><span class="p">]:</span>
<span class="c1"># Only set swap if it's still ambiguous.</span>
<span class="k">if</span> <span class="n">ambig</span><span class="p">:</span>
<span class="n">shouldswap</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># Set swap even if it's not ambiguous,</span>
<span class="c1"># because not swapping is the choice</span>
<span class="c1"># for conflicts as well.</span>
<span class="n">shouldswap</span> <span class="o">=</span> <span class="kc">False</span>
<span class="n">ambig</span> <span class="o">=</span> <span class="kc">False</span>
<span class="c1"># If there was an unambiguous comparison, either shift ipos</span>
<span class="c1"># to i1 or stop looking for the comparison</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">ambig</span><span class="p">:</span>
<span class="k">if</span> <span class="n">shouldswap</span><span class="p">:</span>
<span class="n">ipos</span> <span class="o">=</span> <span class="n">i1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># Insert perm[i0] into the right place</span>
<span class="k">if</span> <span class="n">ipos</span> <span class="o">!=</span> <span class="n">i0</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i1</span> <span class="o">=</span> <span class="n">i0</span><span class="o">-</span><span class="mi">1</span> <span class="n">to</span> <span class="n">ipos</span><span class="p">:</span>
<span class="n">perm</span><span class="p">[</span><span class="n">i1</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">perm</span><span class="p">[</span><span class="n">i1</span><span class="p">]</span>
<span class="n">perm</span><span class="p">[</span><span class="n">ipos</span><span class="p">]</span> <span class="o">=</span> <span class="n">j0</span>
<span class="c1"># perm is now the closest consistent ordering to C-contiguous</span>
<span class="k">return</span> <span class="n">perm</span>
</pre></div>
</div>
</section>
</section>
<section id="coalescing-dimensions">
<h2><a class="toc-backref" href="#id8" role="doc-backlink">Coalescing dimensions</a><a class="headerlink" href="#coalescing-dimensions" title="Link to this heading">#</a></h2>
<p>In many cases, the memory layout allows for the use of a one-dimensional
loop instead of tracking multiple coordinates within the iterator.
The existing code already exploits this when the data is C-contiguous,
but since we’re reordering the axes, we can apply this optimization
more generally.</p>
<p>Once the iteration strides have been sorted to be monotonically
decreasing, any dimensions which could be coalesced are side by side.
If for all the operands, incrementing by strides[i+1] shape[i+1] times
is the same as incrementing by strides[i], or strides[i+1]*shape[i+1] ==
strides[i], dimensions i and i+1 can be coalesced into a single dimension.</p>
<p>Here is pseudo-code for coalescing.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Figure out which pairs of dimensions can be coalesced</span>
<span class="n">can_coalesce</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span><span class="o">*</span><span class="n">ndim</span>
<span class="k">for</span> <span class="n">strides</span><span class="p">,</span> <span class="n">shape</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">broadcast_strides</span><span class="p">,</span> <span class="n">broadcast_shape</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span> <span class="n">to</span> <span class="n">ndim</span><span class="o">-</span><span class="mi">2</span><span class="p">:</span>
<span class="k">if</span> <span class="n">strides</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">strides</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
<span class="n">can_coalesce</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
<span class="c1"># Coalesce the types</span>
<span class="n">new_ndim</span> <span class="o">=</span> <span class="n">ndim</span> <span class="o">-</span> <span class="n">count_nonzero</span><span class="p">(</span><span class="n">can_coalesce</span><span class="p">)</span>
<span class="k">for</span> <span class="n">strides</span><span class="p">,</span> <span class="n">shape</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">broadcast_strides</span><span class="p">,</span> <span class="n">broadcast_shape</span><span class="p">):</span>
<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span> <span class="n">to</span> <span class="n">ndim</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="c1"># Note that can_coalesce[ndim-1] is always False, so</span>
<span class="c1"># there is no out-of-bounds access here.</span>
<span class="k">if</span> <span class="n">can_coalesce</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
<span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">strides</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">strides</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">shape</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
</pre></div>
</div>
</section>
<section id="inner-loop-specialization">
<h2><a class="toc-backref" href="#id9" role="doc-backlink">Inner loop specialization</a><a class="headerlink" href="#inner-loop-specialization" title="Link to this heading">#</a></h2>
<p>Specialization is handled purely by the inner loop function, so this
optimization is independent of the others. Some specialization is
already done, like for the reduce operation. The idea is mentioned in
<a class="reference external" href="http://projects.scipy.org/numpy/wiki/ProjectIdeas">http://projects.scipy.org/numpy/wiki/ProjectIdeas</a>, “use intrinsics
(SSE-instructions) to speed up low-level loops in NumPy.”</p>
<p>Here are some possibilities for two-argument functions,
covering the important cases of add/subtract/multiply/divide.</p>
<ul class="simple">
<li><p>The first or second argument is a single value (i.e. a 0 stride
value) and does not alias the output. arr = arr + 1; arr = 1 + arr</p>
<ul>
<li><p>Can load the constant once instead of reloading it from memory every time</p></li>
</ul>
</li>
<li><p>The strides match the size of the data type. C- or
Fortran-contiguous data, for example</p>
<ul>
<li><p>Can do a simple loop without using strides</p></li>
</ul>
</li>
<li><p>The strides match the size of the data type, and they are
both 16-byte aligned (or differ from 16-byte aligned by the same offset)</p>
<ul>
<li><p>Can use SSE to process multiple values at once</p></li>
</ul>
</li>
<li><p>The first input and the output are the same single value
(i.e. a reduction operation).</p>
<ul>
<li><p>This is already specialized for many UFuncs in the existing code</p></li>
</ul>
</li>
</ul>
<p>The above cases are not generally mutually exclusive, for example a
constant argument may be combined with SSE when the strides match the
data type size, and reductions can be optimized with SSE as well.</p>
</section>
<section id="implementation-details">
<h2><a class="toc-backref" href="#id10" role="doc-backlink">Implementation details</a><a class="headerlink" href="#implementation-details" title="Link to this heading">#</a></h2>
<p>Except for inner loop specialization, the discussed
optimizations significantly affect ufunc_object.c and the
PyArrayIterObject/PyArrayMultiIterObject used to do the broadcasting.
In general, it should be possible to emulate the current behavior where it
is desired, but I believe the default should be to produce and manipulate
memory layouts which will give the best performance.</p>
<p>To support the new cache-friendly behavior, we introduce a new
option ‘K’ (for “keep”) for any <code class="docutils literal notranslate"><span class="pre">order=</span></code> parameter.</p>
<p>The proposed ‘order=’ flags become as follows:</p>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p>‘C’</p></td>
<td><p>C-contiguous layout</p></td>
</tr>
<tr class="row-even"><td><p>‘F’</p></td>
<td><p>Fortran-contiguous layout</p></td>
</tr>
<tr class="row-odd"><td><p>‘A’</p></td>
<td><p>‘F’ if the input(s) have a Fortran-contiguous layout, ‘C’ otherwise (“Any Contiguous”)</p></td>
</tr>
<tr class="row-even"><td><p>‘K’</p></td>
<td><p>a layout equivalent to ‘C’ followed by some permutation of the axes, as close to the layout of the input(s) as possible (“Keep Layout”)</p></td>
</tr>
</tbody>
</table>
</div>
<p>Or as an enum:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="cm">/* For specifying array memory layout or iteration order */</span>
<span class="k">typedef</span><span class="w"> </span><span class="k">enum</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="cm">/* Fortran order if inputs are all Fortran, C otherwise */</span>
<span class="w"> </span><span class="n">NPY_ANYORDER</span><span class="o">=</span><span class="mi">-1</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* C order */</span>
<span class="w"> </span><span class="n">NPY_CORDER</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* Fortran order */</span>
<span class="w"> </span><span class="n">NPY_FORTRANORDER</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* An order as close to the inputs as possible */</span>
<span class="w"> </span><span class="n">NPY_KEEPORDER</span><span class="o">=</span><span class="mi">2</span>
<span class="p">}</span><span class="w"> </span><span class="n">NPY_ORDER</span><span class="p">;</span>
</pre></div>
</div>
<p>Perhaps a good strategy is to first implement the capabilities discussed
here without changing the defaults. Once they are implemented and
well-tested, the defaults can change from <code class="docutils literal notranslate"><span class="pre">order='C'</span></code> to <code class="docutils literal notranslate"><span class="pre">order='K'</span></code>
everywhere appropriate. UFuncs additionally should gain an <code class="docutils literal notranslate"><span class="pre">order=</span></code>
parameter to control the layout of their output(s).</p>
<p>The iterator can do automatic casting, and I have created a sequence
of progressively more permissive casting rules. Perhaps for 2.0, NumPy
could adopt this enum as its preferred way of dealing with casting.</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="cm">/* For specifying allowed casting in operations which support it */</span>
<span class="k">typedef</span><span class="w"> </span><span class="k">enum</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="cm">/* Only allow identical types */</span>
<span class="w"> </span><span class="n">NPY_NO_CASTING</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* Allow identical and byte swapped types */</span>
<span class="w"> </span><span class="n">NPY_EQUIV_CASTING</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* Only allow safe casts */</span>
<span class="w"> </span><span class="n">NPY_SAFE_CASTING</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* Allow safe casts and casts within the same kind */</span>
<span class="w"> </span><span class="n">NPY_SAME_KIND_CASTING</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="w"> </span><span class="cm">/* Allow any casts */</span>
<span class="w"> </span><span class="n">NPY_UNSAFE_CASTING</span><span class="o">=</span><span class="mi">4</span>
<span class="p">}</span><span class="w"> </span><span class="n">NPY_CASTING</span><span class="p">;</span>
</pre></div>
</div>
<section id="iterator-rewrite">
<h3><a class="toc-backref" href="#id11" role="doc-backlink">Iterator rewrite</a><a class="headerlink" href="#iterator-rewrite" title="Link to this heading">#</a></h3>
<p>Based on an analysis of the code, it appears that refactoring the existing
iteration objects to implement these optimizations is prohibitively
difficult. Additionally, some usage of the iterator requires modifying
internal values or flags, so code using the iterator would have to
change anyway. Thus we propose creating a new iterator object which
subsumes the existing iterator functionality and expands it to account
for the optimizations.</p>
<p>High level goals for the replacement iterator include:</p>
<ul class="simple">
<li><p>Small memory usage and a low number of memory allocations.</p></li>
<li><p>Simple cases (like flat arrays) should have very little overhead.</p></li>
<li><p>Combine single and multiple iteration into one object.</p></li>
</ul>
<p>Capabilities that should be provided to user code:</p>
<ul class="simple">
<li><p>Iterate in C, Fortran, or “Fastest” (default) order.</p></li>
<li><p>Track a C-style or Fortran-style flat index if requested
(existing iterator always tracks a C-style index). This can be done
independently of the iteration order.</p></li>
<li><p>Track the coordinates if requested (the existing iterator requires
manually changing an internal iterator flag to guarantee this).</p></li>
<li><p>Skip iteration of the last internal dimension so that it can be
processed with an inner loop.</p></li>
<li><p>Jump to a specific coordinate in the array.</p></li>
<li><p>Iterate an arbitrary subset of axes (to support, for example, reduce
with multiple axes at once).</p></li>