I found a bug in Algorithm D, the long division algorithm in Knuth's "The Art of Computer Programming". It was discussed on HN a couple of times https://news.ycombinator.com/item?id=26562819 as well as on other websites.
I sent a letter to Knuth and received a check and an annotated reply. The updated Theorem B, which was unchanged since 1969 is now dated 2026.
While searching for vulnerable implementations I also found a "bug" in llvm, so I expanded a bit on that too.
> "I'm especially glad to have this correction, because I think the readers of TAOCP Vol 2 look at Algorithm 4.3.1 D more than any other algorithm!"
If you look at the fore edge of my copy of vol 2 will see a noticeably grubby line. Open the book at that page and you do indeed arrive at Algorithm D!
I've implemented multiple-precision arithmetic at least a couple of times. I'm tempted to dig up an old project I haven't touched for over a decade and make the correction...
Thank you for letting me now, but I cannot replicate the issue on Firefox.
There are some issues with math and the animations not breaking on mobile, which I am working on repairing.
EDIT: I have added a different fallback font so it should work on your Firefox now.
It renders fine for me, but I've also had the "extreme gaps between lines" thing happen before on Firefox, and in my case it was caused by a bad font fallback - I forget the precise details but I think it had something to do with having Arabic fonts installed, which were erroneously taking preference for certain non-arabic glyphs. (Check the Fonts tab in dev tools)
I found a bug in Algorithm D, the long division algorithm in Knuth's "The Art of Computer Programming". It was discussed on HN a couple of times https://news.ycombinator.com/item?id=26562819 as well as on other websites. I sent a letter to Knuth and received a check and an annotated reply. The updated Theorem B, which was unchanged since 1969 is now dated 2026.
While searching for vulnerable implementations I also found a "bug" in llvm, so I expanded a bit on that too.
Congratulations! Wow, you got a legendary $2.56 check....
Unfortunately, one no longer gets physical checks, instead, one gets an account in The Bank of the Island of San Seriffe:
https://www-cs-faculty.stanford.edu/~knuth/boss.html
(unfortunately, I have yet to find another typo since getting my $2.88 for _Digital Typography_)
You still get a physical piece of paper that looks like a check; it's just not a valid check.
It can still be cashed in, though not in any bank, you need to contact Knuth beforehand.
For me it will stay framed on the wall.
I wonder if one can do the reverse? Turn in a physical check and get an account?
Hopefully framed it and put it on the wall.
> "I'm especially glad to have this correction, because I think the readers of TAOCP Vol 2 look at Algorithm 4.3.1 D more than any other algorithm!"
If you look at the fore edge of my copy of vol 2 will see a noticeably grubby line. Open the book at that page and you do indeed arrive at Algorithm D!
I've implemented multiple-precision arithmetic at least a couple of times. I'm tempted to dig up an old project I haven't touched for over a decade and make the correction...
The typesetting of this looks very broken on firefox with extreme gaps between lines of text. Seems to render fine on chromium.
Thank you for letting me now, but I cannot replicate the issue on Firefox. There are some issues with math and the animations not breaking on mobile, which I am working on repairing.
EDIT: I have added a different fallback font so it should work on your Firefox now.
It renders fine for me, but I've also had the "extreme gaps between lines" thing happen before on Firefox, and in my case it was caused by a bad font fallback - I forget the precise details but I think it had something to do with having Arabic fonts installed, which were erroneously taking preference for certain non-arabic glyphs. (Check the Fonts tab in dev tools)
I use firefox and it renders approximately the same as Chrome for me.
Assuming OP didn't patch something, you may have a misbehaving extension.