A number of years ago I implemented xoshiro256** for the GFortran compiler. Previously it used Marsaglia&#x27;s KISS generator, which wasn&#x27;t bad but perhaps no longer state of the art on the TESTU1 etc. tests. Additionally, xoshiro256** can be used in parallel by multiple threads; that took a bit of clever hacking to work around the limitations of the Fortran intrinsics API.

Xorshift-36 for the PDP-10, with help from Sebastiano Vigna.<a href="https:&#x2F;&#x2F;github.com&#x2F;larsbrinkhoff&#x2F;xoroshiro-36" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;larsbrinkhoff&#x2F;xoroshiro-36</a>

Good to know. I use LuaJIT. But in any case I reverted that, befitting the overhead from my solution to Lua’s native was big.

Lua 5.4 and 5.5 use xoshiro256**: <a href="https:&#x2F;&#x2F;www.lua.org&#x2F;manual&#x2F;5.4&#x2F;manual.html#pdf-math.random" rel="nofollow">https:&#x2F;&#x2F;www.lua.org&#x2F;manual&#x2F;5.4&#x2F;manual.html#pdf-math.random</a>

I’ve replaced Lua’s random by this. I’ve posted about it here <a href="https:&#x2F;&#x2F;nullonerror.org&#x2F;2025&#x2F;08&#x2F;02&#x2F;replacing-lua-s-math-random-module-with-the-xorshift-algorithm&#x2F;" rel="nofollow">https:&#x2F;&#x2F;nullonerror.org&#x2F;2025&#x2F;08&#x2F;02&#x2F;replacing-lua-s-math-rand...</a>

<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Linear-feedback_shift_register" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Linear-feedback_shift_register</a>

&gt; I’m not sure what point you’re trying to make,Have you skimmed the linked thread?&gt; especially simulation&#x2F;sampling approaches that are bound by the number and quality of uniform variates per secondSorry, nobody does stochastic simulations where the number of uniform random numbers obtained per second is any sort of bottleneck. If you&#x27;ve spent considerable time on stochastic simulation, you already know this.But even if you insist that you alone are doing some very weird stochastic simulation which is somehow bottlenecked on sourcing random numbers fast enough, the falling in planes phenomenon linked above would make xorshift-type generators a poor choice for most sorts of simulations. It introduces spatial correlations into any sort of lattice dynamics simulation (Ising model, percolation) and every high dimensional Monte Carlo integration. Beyond falling in the planes, since xorshift is linear over GF(2), it is also a particularly bad choice for nondeterministic cellular automata and Boolean dynamical systems which use parity, bit masks, or xors.AES-CTR throughput on a modern CPU is higher than that of xoshiro256++, and much higher quality. No advances in non-CS PRNGs can beat that while maintaining the same quality. If your stochastic simulation is bottlenecked on random bits, CSPRNGs are still the way to go, and they don&#x27;t interact in nasty ways with any dynamical system you can actually sinulate quickly.

I’m not sure what point you’re trying to make, exactly, but a use case for better non-CS generators has always been stochastic simulation, especially simulation&#x2F;sampling approaches that are bound by the number and quality of uniform variates per second.As someone who has spent considerable time working in these areas, I still appreciate advances.

&gt; Not every system has the need or the resources to maintain a secure random sequence.I&#x27;m sure there&#x27;s something, but that category has to be shrinking every year. What does such a system look like this decade, that needs random numbers but can&#x27;t easily implement something like AES?&gt; You may also want a reproducible pseudo-random sequence in generative code that logs the seeds. Because of the misguided attitude that nobody needs these features, everyone who does need them has to roll their own now.I don&#x27;t know what difficulty you&#x27;re referring to. Basically every CSPRNG can be seeded easily and you can log the seed.

&gt; no real use caseYes there is. Not every system has the need or the resources to maintain a secure random sequence. You may also want a reproducible pseudo-random sequence in generative code that logs the seeds. Because of the misguided attitude that nobody needs these features, everyone who does need them has to roll their own now.

I agree! For many games (especially the ones running on old devices), xorshifts are pretty good! Not all applications need cryptographically safe generators! And sometimes it&#x27;s ok to trade complexity for speed!But I agree that if you&#x27;re building something new aimed for modern devices, Marsaglia&#x27;s xorshift128 wouldn&#x27;t be my first choice! But I&#x27;d definitely want it in my RNG library for backward compatibility!

I don&#x27;t know about all that, but I use Marsaglias for generating noise samples in MCUs like Pico. It&#x27;s the fastest option there is for such devices.

Ah yes, Xorshift, the RANDU [1] of the 21st century [2].There is no real use case for better non-CS generators, as explained by adrian_b back in 2021 [3].[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;RANDU" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;RANDU</a>
[2] <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1908.10020" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1908.10020</a>
[3] <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=28886698">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=28886698</a>

I should be faster next time then: my entry got tagged as [dupe] ahah!
Also: I somehow got 10x the usual amount of traffic today, and my website is sort of on fire!

I have your feed in my RSS reader! This seemed like something HN would be interested in.

I&#x27;m really curious... How did you manage to post this link before I did?

Then I am very sorry about that, I feel bad and should read more carefully next. I only glanced at first few paragraphs and encountered this line which is a very common LLM trope. I could see that article is long and has lots of images and other stuff but I could see em dashes too. As no one else had said that yet, I did.But I do want to say that this &#x27;witch hunt&#x27; is OK. We should keep calling out AI content which is mostly effortless to keep actual effort by humans separate from this flood of content.

I enjoyed the article, and thank you for sharing it. Don&#x27;t be demotivated by the current AI witch hunt, which I see as a form of tribal signaling that will pass.

This is unbelievably good work, thank you for writing it!

I understand that a big portion of online content is now 100% AI-generated, and that can be somewhat problematic. But for creators like me, who have been publishing articles and books for over 10 years, this AI witch hunt can be quite demotivating.I worked on this project for over one year. I wrote an entire distributed framework to calculate maximal triplets, and I have 130+ machines running 24&#x2F;7 for 12 weeks on N=8192. This article is an extended version of the script for the video documentary that will be released before the end of the year.If you look back at my website, I used to publish two small articles a week. I&#x27;ve since reduced to 1 or 2 large pieces a year. And one of the reasons was exactly to rise above the many blogs that post small, fragmented articles, which could be generated in 2 minutes by ChatGPT. If I wanted to continue in that direction, I could be publishing 100 short articles a week with ChatGPT.I started writing practical shader tutorials back in 2014 because there were not enough good, accessible resources online. I&#x27;m now focusing on large, in-depth pieces with original research, because that&#x27;s what&#x27;s valuable right now that ChatGPT has replaced StackOverflow.If you appreciated this article, I hope you&#x27;ll appreciate it even more knowing that YES, it was written by a human (it&#x27;s me, hi!). &lt;3

&gt; No multiplications. No divisions. No lookup tables. Just a few bitwise instructions.Would have appreciated this article more if it was written by a human.

Xorshift Generators