📝 Xorshift Generators ● Tutorial
Hi everyone! 👋
After a year of work, I can finally share with you my latest article about xorshift generators! If you have ever used Unity or JavaScript, you have likely used them without knowing. Many engines and framework rely on xorshift generators to produce random numbers. In this long article, I cover all major variations of this family of algorithms, including Unity's implementation of the Marsaglia's xorshift128.
The simplest xorshift algorithm that generates random 32 bits numbers consists of just three lines of code:
x ^= x << 13;
x ^= x >> 17;
x ^= x << 5;
I started this journey to understand what made 13, 17, and 5 special. And no, it's not because they are prime numbers... 🤔
Behind this article there was (and still is!) a lot of work and research. I've built a distributed programme to run the heavy calculations needed to find out all other possible triplets which can be used for xorshift generators. At this very moment, there are 200 machines calculating them for 8192-bit numbers, which has never been done before! 😎
And to my surprise, they form a rich structure which has never been characterised in the scientific literature:
You can find the preliminary results on the dedicated Appendix page, which I'm still updating as I discover new results.
This project was a lot of work, and in the coming months I'll be turning it into a video documentary.
Lastly, I'm really happy to report that the article ranked 4th in the Summer of Maths Exposition 2026 competition presented by 3blue1brown! 🏆🥹
I hope you'll enjoy this article as much as I enjoyed making! And if you have any question or suggestions, please don't hesitate to get in touch with me! ☺️
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