Last year I wrote about inlining just the fast path of Lemire’s algorithm for nearly-divisionless unbiased bounded random numbers. The idea was to reduce code bloat by eliminating lots of copies of the random number generator in the rarely-executed slow paths. However a simple split prevented the compiler from being able to optimize cases like pcg32_rand(1 << n), so a lot of the blog post was toying around with ways to mitigate this problem. On Monday while procrastinating a different blog post, I realised that it’s possible to do better: there’s a more general optimization which gives us the 1 << n special case for free. nearly divisionless Lemire’s algorithm has about 4 neat tricks: use multiplication instead of division to reduce the output of a random number generator modulo some limit eliminate the bias in (1) by (counterintuitively) looking at the lower digits fun modular arithmetic to calculate the reject threshold for (2) arrange the reject tests to avoid the slow division in (3) in most cases The nearly-divisionless logic in (4) leads to two copies of the random number generator, in the fast path and the slow path. Generally speaking, compilers don’t try do deduplicate code that was written by the programmer, so they can’t simplify the nearly-divisionless algorithm very much when the limit is constant. constantly divisionless Two points occurred to me: when the limit is constant, the reject threshold (3) can be calculated at compile time when the division is free, there’s no need to avoid it using (4) These observations suggested that when the limit is constant, the function for random numbers less than a limit should be written: static inline uint32_t pcg32_rand_const(pcg32_t *rng, uint32_t limit) { uint32_t reject = -limit % limit; uint64_t sample; do sample = (uint64_t)pcg32_random(rng) * (uint64_t)limit); while ((uint32_t)(sample) < reject); return ((uint32_t)(sample >> 32)); } This has only one call to pcg32_random(), saving space as I wanted, and the compiler is able to eliminate the loop automatically when the limit is a power of two. The loop is smaller than a call to an out-of-line slow path function, so it’s better all round than the code I wrote last year. algorithm selection As before it’s possible to automatically choose the constantly-divisionless or nearly-divisionless algorithms depending on whether the limit is a compile-time constant or run-time variable, using arcane C tricks or GNU C __builtin_constant_p(). I have been idly wondering how to do something similar in other languages. Rust isn’t very keen on automatic specialization, but it has a reasonable alternative. The thing to avoid is passing a runtime variable to the constantly-divisionless algorithm, because then it becomes never-divisionless. Rust has a much richer notion of compile-time constants than C, so it’s possible to write a method like the follwing, which can’t be misused: pub fn upto<const LIMIT: u32>(&mut self) -> u32 { let reject = LIMIT.wrapping_neg().wrapping_rem(LIMIT); loop { let (lo, hi) = self.get_u32().embiggening_mul(LIMIT); if lo < reject { continue; } else { return hi; } } } assert!(rng.upto::<42>() < 42); (embiggening_mul is my stable replacement for the unstable widening_mul API.) This is a nugatory optimization, but there are more interesting cases where it makes sense to choose a different implementation for constant or variable arguments – that it, the constant case isn’t simply a constant-folded or partially-evaluated version of the variable case. Regular expressions might be lex-style or pcre-style, for example. It’s a curious question of language design whether it should be possible to write a library that provides a uniform API that automatically chooses constant or variable implementations, or whether the user of the library must make the choice explicit. Maybe I should learn some Zig to see how its comptime works.

I developed seasonal allergies relatively late in life. From my late twenties onward, I spent many miserable days in the throes of sneezing, headache, and runny eyes. I tried everything the doctors recommended for relief. About a million different types of medicine, several bouts of allergy vaccinations, and endless testing. But never once did an allergy doctor ask the basic question: What kind of air are you breathing? Turns out that's everything when you're allergic to pollen, grass, and dust mites! The air. That's what's carrying all this particulate matter, so if your idea of proper ventilation is merely to open a window, you're inviting in your nasal assailants. No wonder my symptoms kept escalating. For me, the answer was simply to stop breathing air full of everything I'm allergic to while working, sleeping, and generally just being inside. And the way to do that was to clean the air of all those allergens with air purifiers running HEPA-grade filters. That's it. That was the answer! After learning this, I outfitted everywhere we live with these machines of purifying wonder: One in the home office, one in the living area, one in the bedroom. All monitored for efficiency using Awair air sensors. Aiming to have the PM2.5 measure read a fat zero whenever possible. In America, I've used the Alen BreatheSmart series. They're great. And in Europe, I've used the Philips ones. Also good. It's been over a decade like this now. It's exceptionally rare that I have one of those bad allergy days now. It can still happen, of course — if I spend an entire day outside, breathing in allergens in vast quantities. But as with almost everything, the dose makes the poison. The difference between breathing in some allergens, some of the time, is entirely different from breathing all of it, all of the time. I think about this often when I see a doctor for something. Here was this entire profession of allergy specialists, and I saw at least a handful of them while I was trying to find a medical solution. None of them even thought about dealing with the environment. The cause of the allergy. Their entire field of view was restricted to dealing with mitigation rather than prevention. Not every problem, medical or otherwise, has a simple solution. But many problems do, and you have to be careful not to be so smart that you can't see it.

A few months ago I wrote about what it means to stay gold — to hold on to the best parts of ourselves, our communities, and the American Dream itself. But staying gold isn’t passive. It takes work. It takes action. It takes hard conversations that ask