add RSS/RDF feed: https://nedbatchelder.com/blog/rss.xml - sfeed_tests - sfeed tests and RSS and Atom files
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(DIR) commit 867de918bd38122d0410482621516f1ce442cd1e
(DIR) parent 43ebbd6f886a5fa96887e88f119341aeb9248727
(HTM) Author: Hiltjo Posthuma <hiltjo@codemadness.org>
Date: Wed, 8 Oct 2025 19:01:52 +0200
add RSS/RDF feed: https://nedbatchelder.com/blog/rss.xml
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+<?xml version="1.0" encoding="UTF-8"?>
+<?xml-stylesheet type="text/xsl" href="https://nedbatchelder.com/rssfull2html.xslt" media="screen" ?>
+
+<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns="http://purl.org/rss/1.0/">
+ <channel rdf:about="https://nedbatchelder.com/blog">
+ <title>Ned Batchelder's blog</title>
+ <link>https://nedbatchelder.com/blog</link>
+ <description>Ned Batchelder's personal blog.</description>
+ <dc:language>en-US</dc:language>
+ <image rdf:resource="https://nedbatchelder.com/pix/rss-banner.gif"/>
+ <items>
+ <rdf:Seq>
+ <rdf:li resource="https://nedbatchelder.com/blog/202509/hobby_hilbert_simplex.html"/><rdf:li resource="https://nedbatchelder.com/blog/202509/testing_is_better_than_dsa.html"/><rdf:li resource="https://nedbatchelder.com/blog/202508/finding_unneeded_pragmas.html"/><rdf:li resource="https://nedbatchelder.com/blog/202508/starting_with_pytests_parametrize.html"/><rdf:li resource="https://nedbatchelder.com/blog/202507/coveragepy_regex_pragmas.html"/><rdf:li resource="https://nedbatchelder.com/blog/202507/coverage_7100_patch.html"/><rdf:li resource="https://nedbatchelder.com/blog/202507/2048_iterators_and_iterables.html"/><rdf:li resource="https://nedbatchelder.com/blog/202506/math_factoid_of_the_day_63.html"/><rdf:li resource="https://nedbatchelder.com/blog/202506/digital_equipment_corporation_no_more.html"/><rdf:li resource="https://nedbatchelder.com/blog/202505/pycon_summer_camp.html"/>
+ </rdf:Seq>
+ </items>
+ </channel>
+ <image rdf:about="https://nedbatchelder.com/pix/rss-banner.gif">
+ <title>Ned Batchelder's blog</title>
+ <link>https://nedbatchelder.com/blog</link>
+ <url>https://nedbatchelder.com/pix/rss-banner.gif</url>
+ </image>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202509/hobby_hilbert_simplex.html">
+ <title>Hobby Hilbert Simplex</title>
+ <link>https://nedbatchelder.com/blog/202509/hobby_hilbert_simplex.html</link>
+
+ <dc:date>2025-09-26T08:14:04-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>I saw a generative art piece I liked and wanted to learn how it was made.
+Starting with the artist’s Kotlin code, I dug into three new algorithms, hacked
+together some Python code, experimented with alternatives, and learned a lot.
+Now I can explain it to you.</p><p>It all started with this post by
+<a href="https://genart.social/@hamoid/115125620138280715" rel="external noopener">aBe on Mastodon</a>:</p><blockquote class="mastodon-post" lang="en" cite="https://genart.social/@hamoid/115125620138280715" data-source="fediverse">
+ <p>I love how these lines separate and reunite. And the fact that I can express this idea in 3 or 4 lines of code.</p><p>For me they’re lives represented by closed paths that end where they started, spending part of the journey together, separating while we go in different directions and maybe reconnecting again in the future.</p><p><a href="https://genart.social/tags/CreativeCoding" rel="nofollow noopener" class="mention hashtag" target="_blank">#<span>CreativeCoding</span></a> <a href="https://genart.social/tags/algorithmicart" rel="nofollow noopener" class="mention hashtag" target="_blank">#<span>algorithmicart</span></a> <a href="https://genart.social/tags/proceduralArt" rel="nofollow noopener" class="mention hashtag" target="_blank">#<span>proceduralArt</span></a> <a href="https://genart.social/tags/OPENRNDR" rel="nofollow noopener" class="mention hashtag" target="_blank">#<span>OPENRNDR</span></a> <a href="https://genart.social/tags/Kotlin" rel="nofollow noopener" class="mention hashtag" target="_blank">#<span>Kotlin</span></a></p>
+ <figure><figure><img src="https://media.hachyderm.io/cache/media_attachments/files/115/125/620/285/265/947/small/5a73d40e6a4a81c1.png" alt="80 wobbly black hobby curves with low opacity. In some places the curves travel together, but sometimes they split in 2 or 3 groups and later reunite. Due to the low opacity, depending on how many curves overlap the result is brighter or darker." width="480" height="480"></figure></figure>
+ <footer>
+ — aBe (@hamoid@genart.social) <a href="https://genart.social/@hamoid/115125620138280715" rel="external noopener"><time datetime="2025-08-31T21:59:13.000Z">8/31/2025, 5:59:13 PM</time></a>
+ </footer>
+</blockquote><p>The drawing is made by choosing 10 random points, drawing a curve through
+those points, then slightly scooching the points and drawing another curve.
+There are 40 curves, each slightly different than the last. Occasionally
+the next curve makes a jump, which is why they separate and reunite.</p><p>Eventually I made something similar:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/repro_139.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/repro_139.png" alt="" width="600" height="600" class="hairline"></picture></figure></div><p>Along the way I had to learn about three techniques I got from the Kotlin
+code: Hobby curves, Hilbert sorting, and simplex noise.</p><p>Each of these algorithms tries to do something “natural” automatically, so
+that we can generate art that looks nice without any manual steps.</p><h1 id="h_hobby_curves">Hobby curves<a class="headerlink" aria-label="Link to this header" href="#h_hobby_curves"></a></h1><p>To draw swoopy curves through our random points, we use an algorithm
+developed by John Hobby as part of Donald Knuth’s Metafont type design system.
+Jake Low has a <a rel="external noopener" href="https://www.jakelow.com/blog/hobby-curves">great interactive page for playing with Hobby
+curves</a>, you should try it.</p><p>Here are three examples of Hobby curves through ten random points:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/hobby_unsorted.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/hobby_unsorted.png" alt="" width="600" height="200" class="hairline"></picture></figure></div><p>The curves are nice, but kind of a scribble, because we’re joining points
+together in the order we generated them (shown by the green lines). If you
+asked a person to connect random points, they wouldn’t jump back and forth
+across the canvas like this. They would find a nearby point to use next,
+producing a more natural tour of the set.</p><p>We’re generating everything automatically, so we can’t manually intervene
+to choose a natural order for the points. Instead we use Hilbert sorting.</p><h1 id="h_hilbert_sorting">Hilbert sorting<a class="headerlink" aria-label="Link to this header" href="#h_hilbert_sorting"></a></h1><p>The Hilbert space-filling fractal visits every square in a 2D grid.
+<a rel="external noopener" href="https://doc.cgal.org/latest/Spatial_sorting/index.html">Hilbert sorting</a> uses a Hilbert fractal traversing
+the canvas, and sorts the points by when their square is visited by the fractal.
+This gives a tour of the points that corresponds more closely to what people
+expect. Points that are close together in space are likely (but not guaranteed)
+to be close in the ordering.</p><p>If we sort the points using Hilbert sorting, we get much nicer curves. Here
+are the same points as last time:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/hobby_sorted.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/hobby_sorted.png" alt="" width="600" height="200" class="hairline"></picture></figure></div><p>Here are pairs of the same points, unsorted and sorted side-by-side:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/hilbert_compared.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/hilbert_compared.png" alt="" width="400" height="800" class="hairline"></picture></figure></div><p>If you compare closely, the points in each pair are the same, but the sorted
+points are connected in a better order, producing nicer curves.</p><h1 id="h_simplex_noise">Simplex noise<a class="headerlink" aria-label="Link to this header" href="#h_simplex_noise"></a></h1><p>Choosing random points would be easy to do with a random number generator,
+but we want the points to move in interesting graceful ways. To do that, we use
+simplex noise. This is a 2D function (let’s call the inputs u and v) that
+produces a value from -1 to 1. The important thing is the function is
+continuous: if you sample it at two (u,v) coordinates that are close together,
+the results will be close together. But it’s also random: the continuous curves
+you get are wavy in unpredictable ways. Think of the simplex noise function as
+a smooth hilly landscape.</p><p>To get an (x,y) point for our drawing, we choose a (u,v) coordinate to
+produce an x value and a completely different (u,v) coordinate for the y. To
+get the next (x,y) point, we keep the u values the same and change the v values by
+just a tiny bit. That makes the (x,y) points move smoothly but interestingly.</p><p>Here are the trails of four points taking 50 steps using this scheme:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/point_motion.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/point_motion.png" alt="" width="400" height="400" class="hairline"></picture></figure></div><p>If we use seven points taking five steps, and draw curves through the seven
+points at each step, we get examples like this:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/small_runs.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/small_runs.png" alt="" width="600" height="300" class="hairline"></picture></figure></div><p>I’ve left the points visible, and given them large steps so the lines are
+very widely spaced to show the motion. Taking out the points and drawing more
+lines with smaller steps gives us this:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/large_runs.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/large_runs.png" alt="" width="600" height="300" class="hairline"></picture></figure></div><p>With 40 lines drawn wider with some transparency, we start to see the smoky
+fluidity:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/larger_runs.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/larger_runs.png" alt="" width="600" height="300" class="hairline"></picture></figure></div><h1 id="h_jumps">Jumps<a class="headerlink" aria-label="Link to this header" href="#h_jumps"></a></h1><p>In his Mastodon post, aBe commented on the separating of the lines as one of
+the things he liked about this. But why do they do that? If we are moving the
+points in small increments, why do the curves sometimes make large jumps?</p><p>The first reason is because of Hobby curves. They do a great job drawing a
+curve through a set of points as a person might. But a downside of the
+algorithm is sometimes changing a point a small amount makes the entire curve
+take a different route. If you play around with the interactive examples on
+<a rel="external noopener" href="https://www.jakelow.com/blog/hobby-curves">Jake Low’s page</a> you will see the curve can unexpectedly
+take a different shape.</p><p>As we inch our points along, sometimes the Hobby curve jumps.</p><p>The second reason is due to Hilbert sorting. Each of our lines is sorted
+independently of how the previous line was sorted. If a point’s small motion
+moves it into a different grid square, it can change the sorting order, which
+changes the Hobby curve even more.</p><p>If we sort the first line, and then keep that order of points for all the
+lines, the result has fewer jumps, but the Hobby curves still act
+unpredictably:</p><div class="figurep"><figure><picture><source type="image/webp" srcset="https://nedbatchelder.com/iv/webp/pix/fluidity/first_line_runs.png.webp"><img src="https://nedbatchelder.com/pix/fluidity/first_line_runs.png" alt="" width="600" height="300" class="hairline"></picture></figure></div><h1 id="h_colophon">Colophon<a class="headerlink" aria-label="Link to this header" href="#h_colophon"></a></h1><p>This was all done with Python, using other people’s implementations of the
+hard parts:
+<a href="https://github.com/ltrujello/Hobby_Curve_Algorithm/blob/main/python/hobby.py" rel="external noopener">hobby.py</a>,
+<a href="https://pypi.org/project/hilbertcurve/" rel="external noopener">hilbertcurve</a>, and
+<a href="https://pypi.org/project/super-simplex/" rel="external noopener">super-simplex</a>. My code
+is on GitHub
+(<a href="https://github.com/nedbat/fluidity" rel="external noopener">nedbat/fluidity</a>), but it’s a
+mess. Think of it as a woodworking studio with half-finished pieces and wood
+chips strewn everywhere.</p><p>A lot of the learning and experimentation was in
+<a href="https://github.com/nedbat/fluidity/blob/main/play.ipynb" rel="external noopener">my Jupyter
+notebook</a>. Part of the process for work like this is playing around with
+different values of tweakable parameters and seeds for the random numbers to get
+the effect you want, either artistic or pedagogical. The notebook shows some of
+the thumbnail galleries I used to pick the examples to show.</p><p>I went on to play with animations, which led to other learnings, but those
+will have to wait for another blog post.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202509/testing_is_better_than_dsa.html">
+ <title>Testing is better than DSA</title>
+ <link>https://nedbatchelder.com/blog/202509/testing_is_better_than_dsa.html</link>
+
+ <dc:date>2025-09-22T12:04:08-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>I see new learners asking about “DSA” a lot. Data Structures and Algorithms
+are of course important: considered broadly, they are the two ingredients that
+make up all programs. But in my opinion, “DSA” as an abstract field of study
+is over-emphasized.</p><p>I understand why people focus on DSA: it’s a concrete thing to learn about,
+there are web sites devoted to testing you on it, and most importantly, because
+job interviews often involve DSA coding questions.</p><p>Before I get to other opinions, let me make clear that anything you can do to
+help you get a job is a good thing to do. If grinding
+<a rel="external noopener" href="https://leetcode.com/">leetcode</a> will land you a position, then do it.</p><p>But I hope companies hiring entry-level engineers aren’t asking them to
+reverse linked lists or balance trees. Asking about techniques that can be
+memorized ahead of time won’t tell them anything about how well you can work.
+The stated purpose of those interviews is to see how well you can figure out
+solutions, in which case memorization will defeat the point.</p><p>The thing new learners don’t understand about DSA is that actual software
+engineering almost never involves implementing the kinds of algorithms that
+“DSA” teaches you. Sure, it can be helpful to work through some of these
+puzzles and see how they are solved, but writing real code just doesn’t involve
+writing that kind of code.</p><p>Here is what I think in-the-trenches software engineers should know about
+data structures and algorithms:</p><ul>
+
+<li>Data structures are ways to organize data. Learn some of the basics: linked
+list, array, hash table, tree. By “learn” I mean understand what it does
+and why you might want to use one.</li>
+
+<li>Different data structures can be used to organize the same data in different
+ways. Learn some of the trade-offs between structures that are similar.</li>
+
+<li>Algorithms are ways of manipulating data. I don’t mean named algorithms
+like Quicksort, but algorithms as any chunk of code that works on data and
+does something with it.</li>
+
+<li>How you organize data affects what algorithms you can use to work with the
+data. Some data structures will be slow for some operations where another
+structure will be fast.</li>
+
+<li>Algorithms have a “time complexity” (Big O): <a rel="external noopener" href="/text/bigo.html">how the code
+slows as the data grows</a>. Get a sense of what this means.</li>
+
+<li>Python has a number of built-in data structures. Learn how they work, and
+the time complexity of their operations.</li>
+
+<li>Learn how to think about your code to understand its time complexity.</li>
+
+<li>Read a little about more esoteric things like <a rel="external noopener" href="https://systemdesign.one/bloom-filters-explained/">Bloom
+filters</a>, so you can find them later in the unlikely case you need them.</li>
+
+</ul><p>Here are some things you don’t need to learn:</p><ul>
+
+<li>The details of a dozen different sorting algorithms. Look at two to see
+different ways of approaching the same problem, then move on.</li>
+
+<li>The names of “important” algorithms. Those have all been implemented for
+you.</li>
+
+<li>The answers to all N problems on some quiz web site. You won’t be asked
+these exact questions, and they won’t come up in your real work. Again: try a
+few to get a feel for how some algorithms work. The exact answers are not what
+you need.</li>
+
+</ul><p>Of course some engineers need to implement hash tables, or sorting algorithms
+or whatever. We love those engineers: they write libraries we can use off the
+shelf so we don’t have to implement them ourselves.</p><p>There have been times when I implemented something that felt like An
+Algorithm (for example, <a href="https://nedbatchelder.com/blog/201707/finding_fuzzy_floats.html">Finding fuzzy floats</a>), but it was
+more about considering another perspective on my data, looking at the time
+complexity, and moving operations around to avoid quadratic behavior. It wasn’t
+opening a textbook to find the famous algorithm that would solve my problem.</p><p>Again: if it will help you get a job, deep-study DSA. But don’t be
+disappointed when you don’t use it on the job.</p><p>If you want to prepare yourself for a career, and also stand out in job
+interviews, learn how to write tests:</p><ul>
+
+<li>This will be a skill you use constantly. Real-world software means writing
+tests much more than school teaches you to.</li>
+
+<li>In a job search, testing experience will stand out more than DSA depth. It
+shows you’ve thought about what it takes to write high-quality software instead
+of just academic exercises.</li>
+
+<li>It’s not obvious how to test code well. It’s a puzzle and a problem to
+solve. If you like figuring out solutions to tricky questions, focus on how to
+write code so that it can be tested, and how to test it.</li>
+
+<li>Testing not only gives you more confidence in your code, it helps you write
+better code in the first place.</li>
+
+<li>Testing applies everywhere, from tiny bits of code to entire architectures,
+assisting you in design and implementation at all scales.</li>
+
+<li>If pursued diligently, testing is an engineering discipline in its own
+right, with a fascinating array of tools and techniques.</li>
+
+</ul><p>Less DSA, more testing.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202508/finding_unneeded_pragmas.html">
+ <title>Finding unneeded pragmas</title>
+ <link>https://nedbatchelder.com/blog/202508/finding_unneeded_pragmas.html</link>
+
+ <dc:date>2025-08-24T17:28:12-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>To answer a <a rel="external noopener" href="https://github.com/nedbat/coveragepy/issues/251">long-standing coverage.py feature request</a>, I
+threw together an experiment: a tool to identify lines that have been excluded
+from coverage, but which were actually executed.</p><p>The program is a standalone file in the coverage.py repo. It is unsupported.
+I’d like people to try it to see what they think of the idea. Later we can
+decide what to do with it.</p><p>To try it: copy <a rel="external noopener" href="https://github.com/nedbat/coveragepy/blob/master/lab/warn_executed.py">warn_executed.py</a> from
+GitHub. Create a .toml file that looks something like this:</p><blockquote class="code"><pre class="toml"><div class="source"><span class="c1"># Regexes that identify excluded lines:</span>
+<br><span class="n">warn-executed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span>
+<br><span class="w">    </span><span class="s2">"pragma: no cover"</span><span class="p">,</span>
+<br><span class="w">    </span><span class="s2">"raise AssertionError"</span><span class="p">,</span>
+<br><span class="w">    </span><span class="s2">"pragma: cant happen"</span><span class="p">,</span>
+<br><span class="w">    </span><span class="s2">"pragma: never called"</span><span class="p">,</span>
+<br><span class="w">    </span><span class="p">]</span>
+<br>
+<br><span class="c1"># Regexes that identify partial branch lines:</span>
+<br><span class="n">warn-not-partial</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span>
+<br><span class="w">    </span><span class="s2">"pragma: no branch"</span><span class="p">,</span>
+<br><span class="w">    </span><span class="p">]</span>
+<br></div>
+</pre></blockquote><p>These are exclusion regexes that you’ve used in your coverage runs. The
+program will print out any line identified by a pattern and that ran during your
+tests. It might be that you don’t need to exclude the line, because it ran.</p><p>In this file, none of your coverage settings or the default regexes are
+assumed: you need to explicitly specify all the patterns you want flagged.</p><p>Run the program with Python 3.11 or higher, giving the name of the coverage
+data file and the name of your new TOML configuration file. It will print the
+lines that might not need excluding:</p><blockquote class="code"><pre class="shell"><div class="source">$<span class="w"> </span>python3.12<span class="w"> </span>warn_executed.py<span class="w"> </span>.coverage<span class="w"> </span><span>warn.toml</span>
+<br></div>
+</pre></blockquote><p>The reason for a new list of patterns instead of just reading the existing
+coverage settings is that some exclusions are “don’t care” rather than “this
+will never happen.” For example, I exclude “def __repr__” because some
+__repr__’s are just to make my debugging easier. I don’t care if the test suite
+runs them or not. It might run them, so I don’t want it to be a warning that
+they actually ran.</p><p>This tool is not perfect. For example, I exclude “if TYPE_CHECKING:” because
+I want that entire clause excluded. But the if-line itself is actually run. If
+I include that pattern in the warn-executed list, it will flag all of those
+lines. Maybe I’m forgetting a way to do this: it would be good to have a way to
+exclude the body of the if clause while understanding that the if-line itself is
+executed.</p><p>Give <a rel="external noopener" href="https://github.com/nedbat/coveragepy/blob/master/lab/warn_executed.py">warn_executed.py</a> a try and comment on
+<a rel="external noopener" href="https://github.com/nedbat/coveragepy/issues/251">the issue</a> about what you think of it.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202508/starting_with_pytests_parametrize.html">
+ <title>Starting with pytest’s parametrize</title>
+ <link>https://nedbatchelder.com/blog/202508/starting_with_pytests_parametrize.html</link>
+
+ <dc:date>2025-08-13T06:14:46-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>Writing tests can be difficult and repetitive. Pytest has a feature called
+parametrize that can make it reduce duplication, but it can be hard to
+understand if you are new to the testing world. It’s not as complicated as it
+seems.</p><p>Let’s say you have a function called <code>add_nums()</code> that adds up a list of
+numbers, and you want to write tests for it. Your tests might look like
+this:</p><blockquote class="code"><pre class="python"><div class="source"><span class="k">def</span><span class="w"> </span><span class="nf">test_123</span><span class="p">():</span>
+<br>    <span class="k">assert</span> <span class="n">add_nums</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="o">==</span> <span class="mi">6</span>
+<br>
+<br><span class="k">def</span><span class="w"> </span><span class="nf">test_negatives</span><span class="p">():</span>
+<br>    <span class="k">assert</span> <span class="n">add_nums</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="o">-</span><span class="mi">3</span><span class="p">])</span> <span class="o">==</span> <span class="mi">0</span>
+<br>
+<br><span class="k">def</span><span class="w"> </span><span class="nf">test_empty</span><span class="p">():</span>
+<br>    <span class="k">assert</span> <span class="n">add_nums</span><span class="p">([])</span> <span class="o">==</span> <span class="mi">0</span>
+<br></div>
+</pre></blockquote><p>This is great: you’ve tested some behaviors of your <code>add_nums()</code>
+function. But it’s getting tedious to write out more test cases. The names of the
+function have to be different from each other, and they don’t mean anything, so
+it’s extra work for no benefit. The test functions all have the same structure,
+so you’re repeating uninteresting details. You want to add more cases but it
+feels like there’s friction that you want to avoid.</p><p>If we look at these functions, they are very similar. In any software, when
+we have functions that are similar in structure, but differ in some details, we
+can refactor them to be one function with parameters for the differences. We can
+do the same for our test functions.</p><p>Here the functions all have the same structure: call <code>add_nums()</code> and
+assert what the return value should be. The differences are the list we pass to
+<code>add_nums()</code> and the value we expect it to return. So we can turn those
+into two parameters in our refactored function:</p><blockquote class="code"><pre class="python"><div class="source"><span class="k">def</span><span class="w"> </span><span class="nf">test_add_nums</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">expected_total</span><span class="p">):</span>
+<br>    <span class="k">assert</span> <span class="n">add_nums</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">==</span> <span class="n">expected_total</span>
+<br></div>
+</pre></blockquote><p>Unfortunately, tests aren’t run like regular functions. We write the test
+functions, but we don’t call them ourselves. That’s the reason the names of the
+test functions don’t matter. The test runner (pytest) finds functions named
+<code>test_*</code> and calls them for us. When they have no parameters, pytest can
+call them directly. But now that our test function has two parameters, we have
+to give pytest instructions about how to call it.</p><p>To do that, we use the <code>@pytest.mark.parametrize</code> decorator. Using it
+looks like this:</p><blockquote class="code"><pre class="python"><div class="source"><span class="kn">import</span><span class="w"> </span><span class="nn">pytest</span>
+<br>
+<br><span class="nd">@pytest</span><span class="o">.</span><span class="n">mark</span><span class="o">.</span><span class="n">parametrize</span><span class="p">(</span>
+<br>    <span class="s2">"nums, expected_total"</span><span class="p">,</span>
+<br>    <span class="p">[</span>
+<br>        <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="mi">6</span><span class="p">),</span>
+<br>        <span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</span><span class="p">],</span> <span class="mi">0</span><span class="p">),</span>
+<br>        <span class="p">([],</span> <span class="mi">0</span><span class="p">),</span>
+<br>    <span class="p">]</span>
+<br><span class="p">)</span>
+<br><span class="k">def</span><span class="w"> </span><span class="nf">test_add_nums</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">expected_total</span><span class="p">):</span>
+<br>    <span class="k">assert</span> <span class="n">add_nums</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">==</span> <span class="n">expected_total</span>
+<br></div>
+</pre></blockquote><p>There’s a lot going on here, so let’s take it step by step.</p><p>If you haven’t seen a decorator before, it starts with <code>@</code> and is like a
+prologue to a function definition. It can affect how the function is defined or
+provide information about the function.</p><p>The parametrize decorator is itself a function call that takes two arguments.
+The first is a string (“nums, expected_total”) that names the two arguments to
+the test function. Here the decorator is instructing pytest, “when you call
+<code>test_add_nums</code>, you will need to provide values for its <code>nums and</code>
+<code>expected_total parameters</code>.”</p><p>The second argument to <code>parametrize</code> is a list of the values to supply
+as the arguments. Each element of the list will become one call to our test
+function. In this example, the list has three tuples, so pytest will call our
+test function three times. Since we have two parameters to provide, each
+element of the list is a tuple of two values.</p><p>The first tuple is <code>([1, 2, 3], 6)</code>, so the first time pytest calls
+test_add_nums, it will call it as test_add_nums([1, 2, 3], 6). All together,
+pytest will call us three times, like this:</p><blockquote class="code"><pre class="python"><div class="source"><span class="n">test_add_nums</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="mi">6</span><span class="p">)</span>
+<br><span class="n">test_add_nums</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="o">-</span><span class="mi">3</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
+<br><span class="n">test_add_nums</span><span class="p">([],</span> <span class="mi">0</span><span class="p">)</span>
+<br></div>
+</pre></blockquote><p>This will all happen automatically. With our original test functions, when
+we ran pytest, it showed the results as three passing tests because we had three
+separate test functions. Now even though we only have one function, it still
+shows as three passing tests! Each set of values is considered a separate test
+that can pass or fail independently. This is the main advantage of using
+parametrize instead of writing three separate assert lines in the body of a
+simple test function.</p><p>What have we gained?</p><ul>
+
+<li>We don’t have to write three separate functions with different names.</li>
+
+<li>We don’t have to repeat the same details in each function (<code>assert</code>,
+<code>add_nums()</code>, <code>==</code>).</li>
+
+<li>The differences between the tests (the actual data) are written succinctly
+all in one place.</li>
+
+<li>Adding another test case is as simple as adding another line of data to the
+decorator.</li>
+
+</ul>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202507/coveragepy_regex_pragmas.html">
+ <title>Coverage.py regex pragmas</title>
+ <link>https://nedbatchelder.com/blog/202507/coveragepy_regex_pragmas.html</link>
+
+ <dc:date>2025-07-28T12:04:12-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p><a rel="external noopener" href="https://coverage.readthedocs.io/">Coverage.py</a> lets you indicate code to exclude from
+measurement by adding comments to your Python files. But coverage implements
+them differently than other similar tools. Rather than having fixed syntax for
+these comments, they are defined using regexes that you can change or add to.
+This has been surprisingly powerful.</p><p>The basic behavior: coverage finds lines in your source files that match the
+regexes. These lines are excluded from measurement, that is, it’s OK if they
+aren’t executed. If a matched line is part of a multi-line statement the
+whole multi-line statement is excluded. If a matched line introduces a block of
+code the entire block is excluded.</p><p>At first, these regexes were just to make it easier to implement the basic
+“here’s the comment you use” behavior for pragma comments. But it also enabled
+pragma-less exclusions. You could decide (for example) that you didn’t care to
+test any <code>__repr__</code> methods. By adding <code>def __repr__</code> as an exclusion
+regex, all of those methods were automatically excluded from coverage
+measurement without having to add a comment to each one. Very nice.</p><p>Not only did this let people add custom exclusions in their projects, but
+it enabled third-party plugins that could configure regexes in other interesting
+ways:</p><ul>
+
+<li><a href="https://pypi.org/project/covdefaults/" rel="external noopener">covdefaults</a> adds a
+bunch of default exclusions, and also platform- and version-specific comment
+syntaxes.</li>
+
+<li><a href="https://pypi.org/project/coverage-conditional-plugin/" rel="external noopener">coverage-conditional-plugin</a>
+gives you a way to create comment syntaxes for entire files, for whether other
+packages are installed, and so on.</li>
+
+</ul><p>Then about a year ago, <a rel="external noopener" href="https://github.com/nedbat/coveragepy/pull/1807">Daniel Diniz contributed a
+change</a> that amped up the power: regexes could match multi-line patterns.
+This sounds like not that large a change, but it enabled much more powerful
+exclusions. As a sign, it made it possible to support <a rel="external noopener" href="https://coverage.readthedocs.io/en/latest/changes.html#version-7-6-0-2024-07-11">four
+different feature requests</a>.</p><p>To make it work, Daniel changed the matching code. Originally, it was a loop
+over the lines in the source file, checking each line for a match against the
+regexes. The new code uses the entire source file as the target string, and
+loops over the matches against that text. Each match is converted into a set of
+line numbers and added to the results.</p><p>The power comes from being able to use one pattern to match many lines. For
+example, one of the four feature requests was <a rel="external noopener" href="https://github.com/nedbat/coveragepy/issues/118">how to exclude an
+entire file</a>. With configurable multi-line regex patterns, you can do this
+yourself:</p><blockquote class="code"><pre>\A(?s:.*# pragma: exclude file.*)\Z<br></pre></blockquote><p>With this regex, if you put the comment “# pragma: exclude file” in your
+source file, the entire file will be excluded. The <code>\A</code> and <code>\Z</code>
+match the start and end of the target text, which remember is the entire file.
+The <code>(?s:...)</code> means the <a rel="external noopener" href="https://docs.python.org/3/library/re.html#re.S">s/DOTALL</a> flag is in
+effect, so <code>.</code> can match newlines. This pattern matches the entire source
+file if the desired pragma is somewhere in the file.</p><p>Another requested feature was <a rel="external noopener" href="https://github.com/nedbat/coveragepy/issues/1803">excluding code between two
+lines</a>. We can use “# no cover: start” and “# no cover: end” as delimiters
+with this regex:</p><blockquote class="code"><pre># no cover: start(?s:.*?)# no cover: stop<br></pre></blockquote><p>Here <code>(?s:.*?)</code> means any number of any character at all, but as few as
+possible. A star in regexes means as many as possible, but star-question-mark
+means as few as possible. We need the minimal match so that we don’t match from
+the start of one pair of comments all the way through to the end of a different
+pair of comments.</p><p>This regex approach is powerful, but is still fairly shallow. For example,
+either of these two examples would get the wrong lines if you had a string
+literal with the pragma text in it. There isn’t a regex that skips easily over
+string literals.</p><p>This kind of difficulty hit home when I added a new default pattern to
+exclude empty placeholder methods like this:</p><blockquote class="code"><pre class="python"><div class="source"><span class="k">def</span><span class="w"> </span><span class="nf">not_yet</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> <span class="o">...</span>
+<br>
+<br><span class="k">def</span><span class="w"> </span><span class="nf">also_not_this</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<br>    <span class="o">...</span>
+<br>
+<br><span class="k">async</span> <span class="k">def</span><span class="w"> </span><span class="nf">definitely_not_this</span><span class="p">(</span>
+<br>    <span class="bp">self</span><span class="p">,</span>
+<br>    <span class="n">arg1</span><span class="p">,</span>
+<br><span class="p">):</span>
+<br>    <span class="o">...</span>
+<br></div>
+</pre></blockquote><p>We can’t just match three dots, because ellipses can be used in other places
+than empty function bodies. We need to be more delicate. I ended up with:</p><blockquote class="code"><pre>^\s*(((async )?def .*?)?\)(\s*->.*?)?:\s*)?\.\.\.\s*(#|$)<br></pre></blockquote><p>This craziness ensures the ellipsis is part of an (async) def, that the
+ellipsis appears first in the body (but no docstring allowed, doh!), allows for
+a comment on the line, and so on. And even with a pattern this complex, it
+would incorrectly match this contrived line:</p><blockquote class="code"><pre class="python"><div class="source"><span class="k">def</span><span class="w"> </span><span class="nf">f</span><span class="p">():</span> <span class="nb">print</span><span class="p">(</span><span class="s2">"(well): ... #2 false positive!"</span><span class="p">)</span>
+<br></div>
+</pre></blockquote><p>So regexes aren’t perfect, but they’re a pretty good balance: flexible and
+powerful, and will work great on real code even if we can invent weird edge
+cases where they fail.</p><p>What started as a simple implementation expediency has turned into a powerful
+configuration option that has done more than I would have thought.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202507/coverage_7100_patch.html">
+ <title>Coverage 7.10.0: patch</title>
+ <link>https://nedbatchelder.com/blog/202507/coverage_7100_patch.html</link>
+
+ <dc:date>2025-07-24T19:03:27-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>Years ago I greeted a friend returning from vacation and asked how it had
+been. She answered, “It was good, I got a lot done!” I understand that feeling.
+I just had a long vacation myself, and used the time to clean up some old issues
+and add some new features in <a rel="external noopener" href="https://pypi.org/project/coverage/">coverage.py v7.10</a>.</p><p>The major new feature is a configuration option,
+<a rel="external noopener" href="https://coverage.readthedocs.io/en/latest/config.html#run-patch"><code>[run] patch</code></a>. With it, you specify named
+patches that coverage can use to monkey-patch some behavior that gets in the way
+of coverage measurement.</p><p>The first is <code>subprocess</code>. Coverage works great when you start your
+program with coverage measurement, but has long had the problem of how to also
+measure the coverage of sub-processes that your program created. The existing
+solution had been a complicated two-step process of creating obscure .pth files
+and setting environment variables. Whole projects appeared on PyPI to handle
+this for you.</p><p>Now, <code>patch = subprocess</code> will do this for you automatically, and clean
+itself up when the program ends. It handles sub-processes created by the
+<a rel="external noopener" href="https://docs.python.org/3/library/subprocess.html#module-subprocess">subprocess</a> module, the
+<a rel="external noopener" href="https://docs.python.org/3/library/os.html#os.system">os.system()</a> function, and any of the
+<a rel="external noopener" href="https://docs.python.org/3/library/os.html#os.execl">execv</a> or <a rel="external noopener" href="https://docs.python.org/3/library/os.html#os.spawnl">spawnv</a> families of
+functions.</p><p>This alone has spurred <a rel="external noopener" href="https://bsky.app/profile/did:plc:yj4vzsbzzkpswr7x5yagzhhx/post/3luqfffiiqk27">one user to exclaim</a>,</p><blockquote><div><p>The latest release of Coverage feels like a Christmas present!
+The native support for Python subprocesses is so good!</p></div></blockquote><p>Another patch is <code>_exit</code>. This patches
+<a rel="external noopener" href="https://docs.python.org/3/library/os.html#os._exit">os._exit()</a> so that coverage saves its data before
+exiting. The os._exit() function is an immediate and abrupt termination of the
+program, skipping all kinds of registered clean up code. This patch makes it
+possible to collect coverage data from programs that end this way.</p><p>The third patch is <code>execv</code>. The <a rel="external noopener" href="https://docs.python.org/3/library/os.html#os.execl">execv</a> functions
+end the current program and replace it with a new program in the same process.
+The <code>execv</code> patch arranges for coverage to save its data before the
+current program is ended.</p><p>Now that these patches are available, it seems silly that it’s taken so long.
+They (mostly) weren’t difficult. I guess it took looking at the old issues,
+realizing the friction they caused, and thinking up a new way to let users
+control the patching. Monkey-patching is a bit invasive, so I’ve never wanted
+to do it implicitly. The patch option gives the user an explicit way to request
+what they need without having to get into the dirty details themselves.</p><p>Another process-oriented feature was contributed by Arkady Gilinsky: with
+<code>--save-signal=USR1</code> you can specify a user signal that coverage will
+attend to. When you send the signal to your running coverage process, it will
+save the collected data to disk. This gives a way to measure coverage in a
+long-running process without having to end the process.</p><p>There were some other fixes and features along the way, like better HTML
+coloring of multi-line statements, and more default exclusions
+(<code>if TYPE_CHECKING:</code> and <code>...</code>).</p><p>It feels good to finally address some of these pain points. I also closed
+some stale issues and pull requests. There is more to do, always more to do,
+but this feels like a real step forward. Give <a rel="external noopener" href="https://coverage.readthedocs.io/en/7.10.0/changes.html#version-7-10-0-2025-07-24">coverage
+7.10.0</a> a try and let me know how it works for you.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202507/2048_iterators_and_iterables.html">
+ <title>2048: iterators and iterables</title>
+ <link>https://nedbatchelder.com/blog/202507/2048_iterators_and_iterables.html</link>
+
+ <dc:date>2025-07-15T06:52:29-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>I wrote a <a rel="external noopener" href="https://github.com/nedbat/odds/blob/master/2048/2048.py">low-tech terminal-based version</a> of the
+classic <a rel="external noopener" href="https://play2048.co/">2048 game</a> and had some interesting difficulties
+with iterators along the way.</p><p>2048 has a 4<span class="times">×</span>4 grid with sliding tiles. Because the tiles can slide
+left or right and up or down, sometimes we want to loop over the rows and
+columns from 0 to 3, and sometimes from 3 to 0. My first attempt looked like
+this:</p><blockquote class="code"><pre class="python"><div class="source"><span class="n">N</span> <span class="o">=</span> <span class="mi">4</span>
+<br><span class="k">if</span> <span class="n">sliding_right</span><span class="p">:</span>
+<br>    <span class="n">cols</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>   <span class="c1"># 3 2 1 0</span>
+<br><span class="k">else</span><span class="p">:</span>
+<br>    <span class="n">cols</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>             <span class="c1"># 0 1 2 3</span>
+<br>
+<br><span class="k">if</span> <span class="n">sliding_down</span><span class="p">:</span>
+<br>    <span class="n">rows</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>   <span class="c1"># 3 2 1 0</span>
+<br><span class="k">else</span><span class="p">:</span>
+<br>    <span class="n">rows</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>             <span class="c1"># 0 1 2 3</span>
+<br>
+<br><span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">rows</span><span class="p">:</span>
+<br>    <span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">cols</span><span class="p">:</span>
+<br>        <span class="o">...</span>
+<br></div>
+</pre></blockquote><p>This worked, but those counting-down ranges are ugly. Let’s make it
+nicer:</p><blockquote class="code"><pre class="python"><div class="source"><span class="n">cols</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>                 <span class="c1"># 0 1 2 3</span>
+<br><span class="k">if</span> <span class="n">sliding_right</span><span class="p">:</span>
+<br>    <span class="n">cols</span> <span class="o">=</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">cols</span><span class="p">)</span>       <span class="c1"># 3 2 1 0</span>
+<br>
+<br><span class="n">rows</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>                 <span class="c1"># 0 1 2 3</span>
+<br><span class="k">if</span> <span class="n">sliding_down</span><span class="p">:</span>
+<br>    <span class="n">rows</span> <span class="o">=</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>       <span class="c1"># 3 2 1 0</span>
+<br>
+<br><span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">rows</span><span class="p">:</span>
+<br>    <span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">cols</span><span class="p">:</span>
+<br>        <span class="o">...</span>
+<br></div>
+</pre></blockquote><p>Looks cleaner, but it doesn’t work! Can you see why? It took me a bit of
+debugging to see the light.</p><p><code>range()</code> produces an iterable: something that can be iterated over.
+Similar but different is that <code>reversed()</code> produces an iterator: something
+that is already iterating. Some iterables (like ranges) can be used more than
+once, creating a new iterator each time. But once an iterator like
+<code>reversed()</code> has been consumed, it is done. Iterating it again will
+produce no values.</p><p>If “iterable” vs “iterator” is already confusing here’s a quick definition:
+an iterable is something that can be iterated, that can produce values in a
+particular order. An iterator tracks the state of an iteration in progress. An
+analogy: the pages of a book are iterable; a bookmark is an iterator. The
+English hints at it: an iter-able is able to be iterated at some point, an
+iterator is actively iterating.</p><p>The outer loop of my double loop was iterating only once over the rows, so
+the row iteration was fine whether it was going forward or backward. But the
+columns were being iterated again for each row. If the columns were going
+forward, they were a range, a reusable iterable, and everything worked fine.</p><p>But if the columns were meant to go backward, they were a one-use-only
+iterator made by <code>reversed()</code>. The first row would get all the columns,
+but the other rows would try to iterate using a fully consumed iterator and get
+nothing.</p><p>The simple fix was to use <code>list()</code> to turn my iterator into a reusable
+iterable:</p><blockquote class="code"><pre class="python"><div class="source"><span class="n">cols</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">reversed</span><span class="p">(</span><span class="n">cols</span><span class="p">))</span>
+<br></div>
+</pre></blockquote><p>The code was slightly less nice, but it worked. An even better fix
+was to change my doubly nested loop into a single loop:</p><blockquote class="code"><pre class="python"><div class="source"><span class="k">for</span> <span class="n">row</span><span class="p">,</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="n">cols</span><span class="p">):</span>
+<br></div>
+</pre></blockquote><p>That also takes care of the original iterator/iterable problem, so I can get
+rid of that first fix:</p><blockquote class="code"><pre class="python"><div class="source"><span class="n">cols</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
+<br><span class="k">if</span> <span class="n">sliding_right</span><span class="p">:</span>
+<br>    <span class="n">cols</span> <span class="o">=</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">cols</span><span class="p">)</span>
+<br>
+<br><span class="n">rows</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
+<br><span class="k">if</span> <span class="n">sliding_down</span><span class="p">:</span>
+<br>    <span class="n">rows</span> <span class="o">=</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span>
+<br>
+<br><span class="k">for</span> <span class="n">row</span><span class="p">,</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="n">cols</span><span class="p">):</span>
+<br>    <span class="o">...</span>
+<br></div>
+</pre></blockquote><p>Once I had this working, I wondered why <code>product()</code> solved the
+iterator/iterable problem. The <a rel="external noopener" href="https://docs.python.org/3/library/itertools.html#itertools.product">docs have a sample Python
+implementation</a> that shows why: internally, <code>product()</code> is doing just
+what my <code>list()</code> call did: it makes an explicit iterable from each of the
+iterables it was passed, then picks values from them to make the pairs. This
+lets <code>product()</code> accept iterators (like my reversed range) rather than
+forcing the caller to always pass iterables.</p><p>If your head is spinning from all this iterable / iterator / iteration talk,
+I don’t blame you. Just now I said, “it makes an explicit iterable from each of
+the iterables it was passed.” How does that make sense? Well, an iterator is an
+iterable. So <code>product()</code> can take either a reusable iterable (like a range
+or a list) or it can take a use-once iterator (like a reversed range). Either
+way, it populates its own reusable iterables internally.</p><p>Python’s iteration features are powerful but sometimes require careful
+thinking to get right. Don’t overlook the tools in itertools, and mind your
+iterators and iterables!</p><p class="bulletsep">• • •</p><p>Some more notes:</p><p>1: Another way to reverse a range: you can slice them!</p><blockquote class="code"><pre class="python"><div class="source"><span class="o">>>></span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<br><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
+<br><span class="o">>>></span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<br><span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<br><span class="o">>>></span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span>
+<br><span class="o"><</span><span class="n">range_iterator</span> <span class="nb">object</span> <span class="n">at</span> <span class="mh">0x10307cba0</span><span class="o">></span>
+<br></div>
+</pre></blockquote><p>It didn’t occur to me to reverse-slice the range, since <code>reversed</code> is
+right there, but the slice gives you a new reusable range object while reversing
+the range gives you a use-once iterator.</p><p>2: Why did <code>product()</code> explicitly store the values it would need but
+<code>reversed</code> did not? Two reasons: first, <code>reversed()</code> depends on the
+<code>__reversed__</code> dunder method, so it’s up to the original object to decide
+how to implement it. Ranges know how to produce their values in backward order,
+so they don’t need to store them all. Second, <code>product()</code> is going to need
+to use the values from each iterable many times and can’t depend on the
+iterables being reusable.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202506/math_factoid_of_the_day_63.html">
+ <title>Math factoid of the day: 63</title>
+ <link>https://nedbatchelder.com/blog/202506/math_factoid_of_the_day_63.html</link>
+
+ <dc:date>2025-06-16T00:00:00-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>63 is a <a rel="external noopener" href="https://en.wikipedia.org/wiki/Centered_octahedral_number">centered octahedral number</a>. That means if you
+build an approximation of an octahedron with cubes, one size of octahedron will
+have 63 cubes.</p><p>In the late 1700’s <a rel="external noopener" href="https://en.wikipedia.org/wiki/Ren%C3%A9_Just_Ha%C3%BCy">René Just Haüy</a> developed a theory
+about how crystals formed: successive layers of fundamental primitives in
+orderly arrangements. One of those arrangements was stacking cubes together to
+make an octahedron.</p><p>Start with one cube:</p><div class="figurep"><img src="https://nedbatchelder.com/code/diagrams/hauy/0.svg" alt="Just one lonely cube"></div><p>Add six more cubes around it, one on each face. Now we have seven:</p><div class="figurep"><img src="https://nedbatchelder.com/code/diagrams/hauy/1.svg" alt="Seven cubes as a crude octahedron"></div><p>Add another layer, adding a cube to touch each visible cube, making 25:</p><div class="figurep"><img src="https://nedbatchelder.com/code/diagrams/hauy/2.svg" alt="25 cubes arranged like an octahedron five cubes wide"></div><p>One more layer and we have a total of 63:</p><div class="figurep"><img src="https://nedbatchelder.com/code/diagrams/hauy/3.svg" alt="63 cubes arranged like an octahedron seven cubes wide"></div><p>The remaining numbers in <a href="https://oeis.org/A001845" rel="external noopener">the sequence</a>
+less than 10,000 are 129, 231, 377, 575, 833, 1159, 1561, 2047, 2625, 3303,
+4089, 4991, 6017, 7175, 8473, 9919.</p><p>63 also shows up in the <a rel="external noopener" href="https://en.wikipedia.org/wiki/Delannoy_number">Delannoy numbers</a>: the
+number of ways to traverse a grid from the lower left corner to upper right
+using only steps north, east, or northeast. Here are the 63 ways of moving on a
+3<span class="times">×</span>3 grid:</p><div class="figurep"><img src="https://nedbatchelder.com/code/diagrams/delannoy3.svg" alt="63 different ways to traverse a 3x3 grid"></div><p>(Diagram from <a href="https://en.wikipedia.org/wiki/File:Delannoy3x3.svg" rel="external noopener">Wikipedia</a>)</p><p>In fact, the number of cubes in a Haüy octahedron with N layers is the same
+as the number of Delannoy steps on a 3<span class="times">×</span>N grid!</p><p>Since the two ideas are both geometric and fairly simple, I would love to
+find a geometric explanation for the correspondence. The octahedron is
+three-dimensional, and the Delannoy grids have that tantalizing 3 in them. It
+seems like there should be a way to convert Haüy coordinates to Delannoy
+coordinates to show how they relate. But I haven’t found one...</p><p class="bulletsep">• • •</p><p>Colophon: I made the octahedron diagrams by asking Claude to write a
+<a href="https://nedbatchelder.com/code/diagrams/hauy/hauy_oct.py">Python program</a> to do it.
+It wasn’t a fast process because it took pushing and prodding to get the
+diagrams to come out the way I liked. But Claude was very competent, and I
+could think about the results rather than about projections or color spaces. I
+could dip into it for 10 minutes at a time over a number of days without having
+to somehow reconstruct a mental context.</p><p>This kind of casual hobby programming is perfect for AI assistance. I don’t
+need the code to be perfect or even good, I just want the diagrams to be nice.
+I don’t have the focus time to learn how to write the program, so I can leave it
+to an imperfect assistant.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202506/digital_equipment_corporation_no_more.html">
+ <title>Digital Equipment Corporation no more</title>
+ <link>https://nedbatchelder.com/blog/202506/digital_equipment_corporation_no_more.html</link>
+
+ <dc:date>2025-06-09T09:43:53-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>Today is the 39-year anniversary of my first day working for
+<a rel="external noopener" href="https://en.wikipedia.org/wiki/Digital_Equipment_Corporation">Digital Equipment Corporation</a>. It was my first real job in
+the tech world, two years out of college. <a href="https://nedbatchelder.com/blog/200606/digital_equipment_corporation.html">I wrote
+about it 19 years ago</a>, but it’s on my mind again.</p><p>More and more, I find that people have never heard of Digital (as we called
+it) or DEC (as they preferred we didn’t call it but everyone did). It’s
+something I’ve had to get used to. I try to relate a story from that time, and
+I find that even experienced engineers with deep knowledge of technologies don’t
+know of the company.</p><p>I mention this not in a crabby “kids these days” kind of way. It does
+surprise me, but I’m taking it as a learning opportunity. If there’s a lesson
+to learn, it is this:</p><blockquote><div><p>This too shall pass.</p></div></blockquote><p>I am now working for Netflix, and one of the great things about it is that
+everyone has heard of Netflix. I can mention my job to anyone and they are
+impressed in some way. Techies know it as one of the FAANG companies, and
+“civilians” know it for the entertainment it produces and delivers.</p><p>When I joined Digital in 1986, at least among tech people, it was similar.
+Everyone knew about Digital and what they had done: the creation of the
+minicomputer, the genesis of Unix and C, the ubiquitous VT100. Many foundations
+of the software world flowed directly and famously from Digital.</p><p>These days Digital isn’t quite yet a footnote to history, but it is more and
+more unknown even among the most tech-involved. And the tech world carries
+on!</p><p>My small team at Netflix has a number of young engineers, less than two years
+out of college, and even an intern still in college. I’m sure they felt
+incredibly excited to join a company as well-known and influential as Netflix.
+In 39 years when they tell a story from the early days of their career will they
+start with, “Have you heard of Netflix?” and have to adjust to the blank stares
+they get in return?</p><p>This too shall pass.</p>
+]]></description>
+ </item>
+
+ <item rdf:about="https://nedbatchelder.com/blog/202505/pycon_summer_camp.html">
+ <title>PyCon summer camp</title>
+ <link>https://nedbatchelder.com/blog/202505/pycon_summer_camp.html</link>
+
+ <dc:date>2025-05-15T07:05:20-04:00</dc:date>
+ <dc:creator>Ned Batchelder</dc:creator>
+ <description><![CDATA[<p>I’m headed to PyCon today, and I’m reminded about how it feels like summer
+camp, in mostly good ways, but also in a tricky way.</p><p>You take some time off from your “real” life, you go somewhere else, you hang
+out with old friends and meet some new friends. You do different things than in
+your real life, some are playful, some take real work. These are all good ways
+it’s like summer camp.</p><p>Here’s the tricky thing to watch out for: like summer camp, you can make
+connections to people or projects that are intense and feel like they could last
+forever. You make friends at summer camp, or even have semi-romantic crushes on
+people. You promise to stay in touch, you think it’s the “real thing.” When you
+get home, you write an email or two, maybe a phone call, but it fades away. The
+excitement of the summer is overtaken by your autumnal real life again.</p><p>PyCon can be the same way, either with people or projects. Not a romance,
+but the exciting feeling that you want to keep doing the project you started at
+PyCon, or be a member of some community you hung out with for those days. You
+want to keep talking about that exciting thing with that person. These are
+great feelings, but it’s easy to emotionally over-commit to those efforts and
+then have it fade away once PyCon is over.</p><p>How do you know what projects are just crushes, and which are permanent
+relationships? Maybe it doesn’t matter, and we should just get excited about
+things.</p><p>I know I started at least one effort last year that I thought would be done
+in a few months, but has since stalled. Now I am headed back to PyCon. Will I
+become attached to yet more things this time? Is that bad? Should I temper my
+enthusiasm, or is it fine to light a few fires and accept that some will peter
+out?</p>
+]]></description>
+ </item>
+
+</rdf:RDF>