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Here are a few tangentially-related ideas vaguely near the theme of comparison operators. comparison style clamp style clamp is median clamp in range range style style clash? comparison style Some languages such as BCPL, Icon, Python have chained comparison operators, like if min <= x <= max: ... In languages without chained comparison, I like to write comparisons as if they were chained, like, if min <= x && x <= max { // ... } A rule of thumb is to prefer less than (or equal) operators and avoid greater than. In a sequence of comparisons, order values from (expected) least to greatest. clamp style The clamp() function ensures a value is between some min and max, def clamp(min, x, max): if x < min: return min if max < x: return max return x I like to order its arguments matching the expected order of the values, following my rule of thumb for comparisons. (I used that flavour of clamp() in my article about GCRA.) But I seem to be unusual in this preference, based on a few examples I have seen recently. clamp is median Last month, Fabian Giesen pointed out a way to resolve this difference of opinion: A function that returns the median of three values is equivalent to a clamp() function that doesn’t care about the order of its arguments. This version is written so that it returns NaN if any of its arguments is NaN. (When an argument is NaN, both of its comparisons will be false.) fn med3(a: f64, b: f64, c: f64) -> f64 { match (a <= b, b <= c, c <= a) { (false, false, false) => f64::NAN, (false, false, true) => b, // a > b > c (false, true, false) => a, // c > a > b (false, true, true) => c, // b <= c <= a (true, false, false) => c, // b > c > a (true, false, true) => a, // c <= a <= b (true, true, false) => b, // a <= b <= c (true, true, true) => b, // a == b == c } } When two of its arguments are constant, med3() should compile to the same code as a simple clamp(); but med3()’s misuse-resistance comes at a small cost when the arguments are not known at compile time. clamp in range If your language has proper range types, there is a nicer way to make clamp() resistant to misuse: fn clamp(x: f64, r: RangeInclusive<f64>) -> f64 { let (&min,&max) = (r.start(), r.end()); if x < min { return min } if max < x { return max } return x; } let x = clamp(x, MIN..=MAX); range style For a long time I have been fond of the idea of a simple counting for loop that matches the syntax of chained comparisons, like for min <= x <= max: ... By itself this is silly: too cute and too ad-hoc. I’m also dissatisfied with the range or slice syntax in basically every programming language I’ve seen. I thought it might be nice if the cute comparison and iteration syntaxes were aspects of a more generally useful range syntax, but I couldn’t make it work. Until recently when I realised I could make use of prefix or mixfix syntax, instead of confining myself to infix. So now my fantasy pet range syntax looks like >= min < max // half-open >= min <= max // inclusive And you might use it in a pattern match if x is >= min < max { // ... } Or as an iterator for x in >= min < max { // ... } Or to take a slice xs[>= min < max] style clash? It’s kind of ironic that these range examples don’t follow the left-to-right, lesser-to-greater rule of thumb that this post started off with. (x is not lexically between min and max!) But that rule of thumb is really intended for languages such as C that don’t have ranges. Careful stylistic conventions can help to avoid mistakes in nontrivial conditional expressions. It’s much better if language and library features reduce the need for nontrivial conditions and catch mistakes automatically.
Here’s a story from nearly 10 years ago. the bug I think it was my friend Richard Kettlewell who told me about a bug he encountered with Let’s Encrypt in its early days in autumn 2015: it was failing to validate mail domains correctly. the context At the time I had previously been responsible for Cambridge University’s email anti-spam system for about 10 years, and in 2014 I had been given responsibility for Cambridge University’s DNS. So I knew how Let’s Encrypt should validate mail domains. Let’s Encrypt was about one year old. Unusually, the code that runs their operations, Boulder, is free software and open to external contributors. Boulder is written in Golang, and I had not previously written any code in Golang. But its reputation is to be easy to get to grips with. So, in principle, the bug was straightforward for me to fix. How difficult would it be as a Golang newbie? And what would Let’s Encrypt’s contribution process be like? the hack I cloned the Boulder repository and had a look around the code. As is pretty typical, there are a couple of stages to fixing a bug in an unfamiliar codebase: work out where the problem is try to understand if the obvious fix could be better In this case, I remember discovering a relatively substantial TODO item that intersected with the bug. I can’t remember the details, but I think there were wider issues with DNS lookups in Boulder. I decided it made sense to fix the immediate problem without getting involved in things that would require discussion with Let’s Encrypt staff. I faffed around with the code and pushed something that looked like it might work. A fun thing about this hack is that I never got a working Boulder test setup on my workstation (or even Golang, I think!) – I just relied on the Let’s Encrypt cloud test setup. The feedback time was very slow, but it was tolerable for a simple one-off change. the fix My pull request was small, +48-14. After a couple of rounds of review and within a few days, it was merged and put into production! A pleasing result. the upshot I thought Golang (at least as it was used in the Boulder codebase) was as easy to get to grips with as promised. I did not touch it again until several years later, because there was no need to, but it seemed fine. I was very impressed by the Let’s Encrypt continuous integration and automated testing setup, and by their low-friction workflow for external contributors. One of my fastest drive-by patches to get into worldwide production. My fix was always going to be temporary, and all trace of it was overwritten years ago. It’s good when “temporary” turns out to be true! the point I was reminded of this story in the pub this evening, and I thought it was worth writing down. It demonstrated to me that Let’s Encrypt really were doing all the good stuff they said they were doing. So thank you to Let’s Encrypt for providing an exemplary service and for giving me a happy little anecdote.
A couple of years ago I wrote about random floating point numbers. In that article I was mainly concerned about how neat the code is, and I didn’t pay attention to its performance. Recently, a comment from Oliver Hunt and a blog post from Alisa Sireneva prompted me to wonder if I made an unwarranted assumption. So I wrote a little benchmark, which you can find in pcg-dxsm.git. As a brief recap, there are two basic ways to convert a random integer to a floating point number between 0.0 and 1.0: Use bit fiddling to construct an integer whose format matches a float between 1.0 and 2.0; this is the same span as the result but with a simpler exponent. Bitcast the integer to a float and subtract 1.0 to get the result. Shift the integer down to the same range as the mantissa, convert to float, then multiply by a scaling factor that reduces it to the desired range. This produces one more bit of randomness than the bithacking conversion. (There are other less basic ways.) My benchmark has 2 x 2 x 2 tests: bithacking vs multiplying 32 bit vs 64 bit sequential integers vs random integers Each operation is isolated from the benchmark loop by putting it in a separate translation unit (to prevent the compiler from inlining) and there is a fence instruction (ISB SY on ARM, MFENCE on AMD) in the loop to stop the CPU from overlapping successive iterations. I ran the benchmark on my Apple M1 Pro and my AMD Ryzen 7950X. In the table below, the leftmost column is the number of random bits. The top half measures sequential numbers, the bottom half is random numbers. The times are nanoseconds per operation, which includes the overheads of the benchmark loop and function call. arm amd 23 12.15 11.22 24 13.37 11.21 52 12.11 11.02 53 13.38 11.20 23 14.75 12.62 24 15.85 12.81 52 16.78 14.23 53 18.02 14.41 The times vary a little from run to run but the difference in speed of the various loops is reasonably consistent. I think my conclusion is that the bithacking conversion is about 1ns faster than the multiply conversion on my ARM box. There’s a subnanosecond difference on my AMD box which might indicate that the conversion takes different amounts of time depending on the value? Dunno.
In hot weather I like to drink my coffee in an iced latte. To make it, I have a very large Bialetti Moka Express. Recently when I got it going again after a winter of disuse, it took me a couple of attempts to get the technique right, so here are some notes as a reminder to my future self next year. It’s worth noting that I’m not fussy about my coffee: I usually drink pre-ground beans from the supermarket, with cream (in winter hot coffee) or milk and ice. basic principle When I was getting the hang of my moka pot, I learned from YouTube coffee geeks such as James Hoffmann that the main aim is for the water to be pushed through the coffee smoothly and gently. Better to err on the side of too little flow than too much. I have not had much success trying to make fine temperature adjustments while the coffee is brewing, because the big moka pot has a lot of thermal inertia: it takes a long time for any change in gas level to have any effect on on the coffee flow. routine fill the kettle and turn it on put the moka pot’s basket in a mug to keep it stable fill it with coffee (mine needs about 4 Aeropress scoops) tamp it down firmly [1] when the kettle has boiled, fill the base of the pot to just below the pressure valve (which is also just below the filter screen in the basket) insert the coffee basket, making sure there are no stray grounds around the edge where the seal will mate screw on the upper chamber firmly put it on a small gas ring turned up to the max [2] leave the lid open and wait for the coffee to emerge immediately turn the gas down to the minimum [3] the coffee should now come out in a steady thin stream without spluttering or stalling when the upper chamber is filled near the mouths of the central spout, it’ll start fizzing or spluttering [4] turn off the gas and pour the coffee into a carafe notes If I don’t tamp the grounds, the pot tends to splutter. I guess tamping gives the puck better integrity to resist channelling, and to keep the water under even pressure. Might be an effect of the relatively coarse supermarket grind? It takes a long time to get the pot back up to boiling point and I’m not sure that heating it up slower helps. The main risk, I think, is overshooting the ideal steady brewing state too much, but: With my moka pot on my hob the lowest gas flow on the smallest rings is just enough to keep the coffee flowing without stalling. The flow when the coffee first emerges is relatively fast, and it slows to the steady state several seconds after I turn the heat down, so I think the overshoot isn’t too bad. This routine turns almost all of the water into coffee, which Hoffmann suggests is a good result, and a sign that the pressure and temperature aren’t getting too high.
TIL (or this week-ish I learned) why big-sigma and big-pi turn up in the notation of dependent type theory. I’ve long been aware of the zoo of more obscure Greek letters that turn up in papers about type system features of functional programming languages, μ, Λ, Π, Σ. Their meaning is usually clear from context but the reason for the choice of notation is usually not explained. I recently stumbled on an explanation for Π (dependent functions) and Σ (dependent pairs) which turn out to be nicer than I expected, and closely related to every-day algebraic data types. sizes of types The easiest way to understand algebraic data types is by counting the inhabitants of a type. For example: the unit type () has one inhabitant, (), and the number 1 is why it’s called the unit type; the bool type hass two inhabitants, false and true. I have even seen these types called 1 and 2 (cruelly, without explanation) in occasional papers. product types Or pairs or (more generally) tuples or records. Usually written, (A, B) The pair contains an A and a B, so the number of possible values is the number of possible A values multiplied by the number of possible B values. So it is spelled in type theory (and in Standard ML) like, A * B sum types Or disjoint union, or variant record. Declared in Haskell like, data Either a b = Left a | Right b Or in Rust like, enum Either<A, B> { Left(A), Right(B), } A value of the type is either an A or a B, so the number of possible values is the number of A values plus the number of B values. So it is spelled in type theory like, A + B dependent pairs In a dependent pair, the type of the second element depends on the value of the first. The classic example is a slice, roughly, struct IntSlice { len: usize, elem: &[i64; len], } (This might look a bit circular, but the idea is that an array [i64; N] must be told how big it is – its size is an explicit part of its type – but an IntSlice knows its own size. The traditional dependent “vector” type is a sized linked list, more like my array type than my slice type.) The classic way to write a dependent pair in type theory is like, Σ len: usize . Array(Int, len) The big sigma binds a variable that has a type annotation, with a scope covering the expression after the dot – similar syntax to a typed lambda expression. We can expand a simple example like this into a many-armed sum type: either an array of length zero, or an array of length 1, or an array of length 2, … but in a sigma type the discriminant is user-defined instead of hidden. The number of possible values of the type comes from adding up all the alternatives, a summation just like the big sigma summation we were taught in school. ∑ a ∈ A B a When the second element doesn’t depend on the first element, we can count the inhabitants like, ∑ A B = A*B And the sigma type simplifies to a product type. telescopes An aside from the main topic of these notes, I also recently encountered the name “telescope” for a multi-part dependent tuple or record. The name “telescope” comes from de Bruijn’s AUTOMATH, one of the first computerized proof assistants. (I first encountered de Bruijn as the inventor of numbered lambda bindings.) dependent functions The return type of a dependent function can vary according to the argument it is passed. For example, to construct an array we might write something like, fn repeat_zero(len: usize) -> [i64; len] { [0; len] } The classic way to write the type of repeat_zero() is very similar to the IntSlice dependent pair, but with a big pi instead of a big sigma: Π len: usize . Array(Int, len) Mmm, pie. To count the number of possible (pure, total) functions A ➞ B, we can think of each function as a big lookup table with A entries each containing a B. That is, a big tuple (B, B, … B), that is, B * B * … * B, that is, BA. Functions are exponential types. We can count a dependent function, where the number of possible Bs depends on which A we are passed, ∏ a ∈ A B a danger I have avoided the terms “dependent sum” and “dependent product”, because they seem perfectly designed to cause confusion over whether I am talking about variants, records, or functions. It kind of makes me want to avoid algebraic data type jargon, except that there isn’t a good alternative for “sum type”. Hmf.
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I've never seen so many developers curious about leaving the Mac and giving Linux a go. Something has really changed in the last few years. Maybe Linux just got better? Maybe powerful mini PCs made it easier? Maybe Apple just fumbled their relationship with developers one too many times? Maybe it's all of it. But whatever the reason, the vibe shift is noticeable. This is why the future is so hard to predict! People have been joking about "The Year of Linux on the Desktop" since the late 90s. Just like self-driving cars were supposed to be a thing back in 2017. And now, in the year of our Lord 2025, it seems like we're getting both! I also wouldn't underestimate the cultural influence of a few key people. PewDiePie sharing his journey into Arch and Hyprland with his 110 million followers is important. ThePrimeagen moving to Arch and Hyprland is important. Typecraft teaching beginners how to build an Arch and Hyprland setup from scratch is important (and who I just spoke to about Omarchy). Gabe Newell's Steam Deck being built on Arch and pushing Proton to over 20,000 compatible Linux games is important. You'll notice a trend here, which is that Arch Linux, a notoriously "difficult" distribution, is at the center of much of this new engagement. Despite the fact that it's been around since 2003! There's nothing new about Arch, but there's something new about the circles of people it's engaging. I've put Arch at the center of Omarchy too. Originally just because that was what Hyprland recommended. Then, after living with the wonders of 90,000+ packages on the community-driven AUR package repository, for its own sake. It's really good! But while Arch (and Hyprland) are having a moment amongst a new crowd, it's also "just" Linux at its core. And Linux really is the star of the show. The perfect, free, and open alternative that was just sitting around waiting for developers to finally have had enough of the commercial offerings from Apple and Microsoft. Now obviously there's a taste of "new vegan sees vegans everywhere" here. You start talking about Linux, and you'll hear from folks already in the community or those considering the move too. It's easy to confuse what you'd like to be true with what is actually true. And it's definitely true that Linux is still a niche operating system on the desktop. Even among developers. Apple and Microsoft sit on the lion's share of the market share. But the mind share? They've been losing that fast. The window is open for a major shift to happen. First gradually, then suddenly. It feels like morning in Linux land!
Snippets are a useful addition to Svelte 5. I use them in my Svelte 5 projects like Edna. Snippet basics A snippet is a function that renders html based on its arguments. Here’s how to define and use a snippet: {#snippet hello(name)} <div>Hello {name}!</div> {/snippet} {@render hello("Andrew")} {@render hello("Amy")} You can re-use snippets by exporting them: <script module> export { hello }; </script> {@snippet hello(name)}<div>Hello {name}!</div>{/snippet} Snippets use cases Snippets for less nesting Deeply nested html is hard to read. You can use snippets to extract some parts to make the structure clearer. For example, you can transform: <div> <div class="flex justify-end mt-2"> <button onclick={onclose} class="mr-4 px-4 py-1 border border-black hover:bg-gray-100" >Cancel</button > <button onclick={() => emitRename()} disabled={!canRename} class="px-4 py-1 border border-black hover:bg-gray-50 disabled:text-gray-400 disabled:border-gray-400 disabled:bg-white default:bg-slate-700" >Rename</button > </div> into: {#snippet buttonCancel()} <button onclick={onclose} class="mr-4 px-4 py-1 border border-black hover:bg-gray-100" >Cancel</button > {/snippet} {#snippet buttonRename()}...{/snippet} To make this easier to read: <div> <div class="flex justify-end mt-2"> {@render buttonCancel()} {@render buttonRename()} </div> </div> snippets replace default <slot/> In Svelte 4, if you wanted place some HTML inside the component, you used <slot />. Let’s say you have Overlay.svelte component used like this: <Overlay> <MyDialog></MyDialog> </Overlay> In Svelte 4, you would use <slot /> to render children: <div class="overlay-wrapper"> <slot /> </div> <slot /> would be replaced with <MyDialog></MyDialog>. In Svelte 5 <MyDialog></MyDialog> is passed to Overlay.svelte as children property so you would change Overlay.svelte to: <script> let { children } = $props(); </script> <div class="overlay-wrapper"> {@render children()} </div> children property is created by Svelte compiler so you should avoid naming your own props children. snippets replace named slots A component can have a default slot for rendering children and additional named slots. In Svelte 5 instead of named slots you pass snippets as props. An example of Dialog.svelte: <script> let { title, children } = $props(); </script> <div class="dialog"> <div class="title"> {@render title()} </div> {@render children()} </div> And use: {#snippet title()} <div class="fancy-title">My fancy title</div> {/snippet} <Dialog title={title}> <div>Body of the dialog</div> </Dialog> passing snippets as implicit props You can pass title snippet prop implicitly: <Dialog> {#snippet title()} <div class="fancy-title">My fancy title</div> {/snippet} <div>Body of the dialog</div> </Dialog> Because {snippet title()} is a child or <Dialog>, we don’t have to pass it as explicit title={title} prop. The compiler does it for us. snippets to reduce repetition Here’s part of how I render https://tools.arslexis.io/ {#snippet row(name, url, desc)} <tr> <td class="text-left align-top" ><a class="font-semibold whitespace-nowrap" href={url}>{name}</a> </td> <td class="pl-4 align-top">{@html desc}</td> </tr> {/snippet} {@render row("unzip", "/unzip/", "unzip a file in the browser")} {@render row("wc", "/wc/", "like <tt>wc</tt>, but in the browser")} It saves me copy & paste of the same HTML and makes the structure more readable. snippets for recursive rendering Sometimes you need to render a recursive structure, like nested menus or file tree. In Svelte 4 you could use <svelte:self> but the downside of that is that you create multiple instances of the component. That means that the state is also split among multiple instances. That makes it harder to implement functionality that requires a global view of the structure, like keyboard navigation. With snippets you can render things recursively in a single instance of the component. I used it to implement nested context menus. snippets to customize rendering Let’s say you’re building a Menu component. Each menu item is a <div> with some non-trivial children. To allow the client of Menu customize how items are rendered, you could provide props for things like colors, padding etc. or you could allow ultimate flexibility by accepting an optional menuitem prop that is a snippet that renders the item. You can think of it as a headless UI i.e. you provide the necessary structure and difficult logic like keyboard navigation etc. and allow the client lots of control over how things are rendered. snippets for library of icons Before snippets every SVG Icon I used was a Svelte component. Many icons means many files. Now I have a single Icons.svelte file, like: <script module> export { IconMenu, IconSettings }; </script> {#snippet IconMenu(arg1, arg2, ...)} <svg>... icon svg</svg> {/snippet}} {#snippet IconSettings()} <svg>... icon svg</svg> {/snippet}}
I realize that for all I've talked about Logic for Programmers in this newsletter, I never once explained basic logical quantifiers. They're both simple and incredibly useful, so let's do that this week! Sets and quantifiers A set is a collection of unordered, unique elements. {1, 2, 3, …} is a set, as are "every programming language", "every programming language's Wikipedia page", and "every function ever defined in any programming language's standard library". You can put whatever you want in a set, with some very specific limitations to avoid certain paradoxes.2 Once we have a set, we can ask "is something true for all elements of the set" and "is something true for at least one element of the set?" IE, is it true that every programming language has a set collection type in the core language? We would write it like this: # all of them all l in ProgrammingLanguages: HasSetType(l) # at least one some l in ProgrammingLanguages: HasSetType(l) This is the notation I use in the book because it's easy to read, type, and search for. Mathematicians historically had a few different formats; the one I grew up with was ∀x ∈ set: P(x) to mean all x in set, and ∃ to mean some. I use these when writing for just myself, but find them confusing to programmers when communicating. "All" and "some" are respectively referred to as "universal" and "existential" quantifiers. Some cool properties We can simplify expressions with quantifiers, in the same way that we can simplify !(x && y) to !x || !y. First of all, quantifiers are commutative with themselves. some x: some y: P(x,y) is the same as some y: some x: P(x, y). For this reason we can write some x, y: P(x,y) as shorthand. We can even do this when quantifying over different sets, writing some x, x' in X, y in Y instead of some x, x' in X: some y in Y. We can not do this with "alternating quantifiers": all p in Person: some m in Person: Mother(m, p) says that every person has a mother. some m in Person: all p in Person: Mother(m, p) says that someone is every person's mother. Second, existentials distribute over || while universals distribute over &&. "There is some url which returns a 403 or 404" is the same as "there is some url which returns a 403 or some url that returns a 404", and "all PRs pass the linter and the test suites" is the same as "all PRs pass the linter and all PRs pass the test suites". Finally, some and all are duals: some x: P(x) == !(all x: !P(x)), and vice-versa. Intuitively: if some file is malicious, it's not true that all files are benign. All these rules together mean we can manipulate quantifiers almost as easily as we can manipulate regular booleans, putting them in whatever form is easiest to use in programming. Speaking of which, how do we use this in in programming? How we use this in programming First of all, people clearly have a need for directly using quantifiers in code. If we have something of the form: for x in list: if P(x): return true return false That's just some x in list: P(x). And this is a prevalent pattern, as you can see by using GitHub code search. It finds over 500k examples of this pattern in Python alone! That can be simplified via using the language's built-in quantifiers: the Python would be any(P(x) for x in list). (Note this is not quantifying over sets but iterables. But the idea translates cleanly enough.) More generally, quantifiers are a key way we express higher-level properties of software. What does it mean for a list to be sorted in ascending order? That all i, j in 0..<len(l): if i < j then l[i] <= l[j]. When should a ratchet test fail? When some f in functions - exceptions: Uses(f, bad_function). Should the image classifier work upside down? all i in images: classify(i) == classify(rotate(i, 180)). These are the properties we verify with tests and types and MISU and whatnot;1 it helps to be able to make them explicit! One cool use case that'll be in the book's next version: database invariants are universal statements over the set of all records, like all a in accounts: a.balance > 0. That's enforceable with a CHECK constraint. But what about something like all i, i' in intervals: NoOverlap(i, i')? That isn't covered by CHECK, since it spans two rows. Quantifier duality to the rescue! The invariant is equivalent to !(some i, i' in intervals: Overlap(i, i')), so is preserved if the query SELECT COUNT(*) FROM intervals CROSS JOIN intervals … returns 0 rows. This means we can test it via a database trigger.3 There are a lot more use cases for quantifiers, but this is enough to introduce the ideas! Next week's the one year anniversary of the book entering early access, so I'll be writing a bit about that experience and how the book changed. It's crazy how crude v0.1 was compared to the current version. MISU ("make illegal states unrepresentable") means using data representations that rule out invalid values. For example, if you have a location -> Optional(item) lookup and want to make sure that each item is in exactly one location, consider instead changing the map to item -> location. This is a means of implementing the property all i in item, l, l' in location: if ItemIn(i, l) && l != l' then !ItemIn(i, l'). ↩ Specifically, a set can't be an element of itself, which rules out constructing things like "the set of all sets" or "the set of sets that don't contain themselves". ↩ Though note that when you're inserting or updating an interval, you already have that row's fields in the trigger's NEW keyword. So you can just query !(some i in intervals: Overlap(new, i')), which is more efficient. ↩
In the previous article, we peeked at the reset circuit of ESP-Prog with an oscilloscope, and reproduced it with basic components. We observed that it did not behave quite as expected. In this article, we’ll look into the missing pieces. An incomplete circuit For a hint, we’ll first look a bit more closely at the … Continue reading The missing part of Espressif’s reset circuit → The post The missing part of Espressif’s reset circuit appeared first on Quentin Santos.