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A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

kolja.rs

1–10 of 55 posts

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#2
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.

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#3
post #2

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 fo…

Congratulations! Wow, you got a legendary $2.56 check....

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#4
post #3
post #2

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 fo…

Congratulations! Wow, you got a legendary $2.56 check....

Hopefully framed it and put it on the wall.

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#5
post #3
post #2

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 fo…

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_)

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#7
post #6

The typesetting of this looks very broken on firefox with extreme gaps between lines of text. Seems to render fine on chromium.

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.

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#8
post #3

Earlier quoted context omitted.

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.

Re: A decades-old bug in Knuth's long division (TAOCP Vol II, Algorithm 4.3.1D)

#10
post #6

The typesetting of this looks very broken on firefox with extreme gaps between lines of text. Seems to render fine on chromium.

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)
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