Hello, you are correct that part of it is done to death for standard integer division.

The `new` thing is the range-splitting which achieves the floor division for negative inputs (eg. sign-selected for 60% of divisors, and the negative/positive bump for the remaining 20%/20% of cases each).

I found this by accident because I wanted to speed up a part on my Pebble watch face, I didn't even know the history of past attempts. The floor variant was born out of a particular rounding optimisation attempt that felt like it could be easier if I just use floor/ceil and moved it into a large int-multiplication space. (this is very tempting because certain constants for rendering and angle calculations are based around large integer constants on that platform, kinda doing half the work towards this idea by creating this particular constraint)

Thanks for sharing that.

I have a mobile-friendly web-app where you can practice this technique, just click the link in the page's nav: "Weekle - Weekday Guessing Game"

Thanks! I'm pretty sure with this one I spent more time working on the blog post than I did developing the algorithms.

I would not normally spend such effort, but in this case I felt that the functions were too hard to understand without the visual aid, and too difficult to customise without the Function Explorer.

Then I think I just got a bit carried away with the detail.

Thanks for putting in the effort.

You might also https://www.redblobgames.com/ and learn a lot from how they do their presentations.

The theory is trivial for anyone with a Number Theory background. That's not the point. Picking a good and interesting problem and going all the way to an elegant optimal solution, AND presenting it well, is all that counts. Without the good presentation and proof, it could look like a hack / weird trick to a random reviewer. I have personally seen a few good algorithms of this sort being dismissed in codebases because they were hard for people to understand (or more precisely, the author hadn't been skilled / diligent enough to leave a good demonstration linked in the code).

I wish there was a place for good algorithms like this, where, unlike plain wikipedia, the good visualized proof could stay and serve. Or perhaps there are such places and I don't know about them.

Bret Victor did a bunch of work around visualizations ~12 years ago (IIRC) for teaching and showing math, but I am not sure if there was any following on that path.

You should consider publishing some of your work at https://pudding.cool/ - I think it would fit in well there.