The Art of Computer Programming, Volume 2

What Hacker News says

1. drallisonSep 2022
   I second this choice. Be sure to get the second edition and to read the various fascicles for Knuth's Volume 4 of Art of Computer Programming. Volume 2 has some useful content as well.
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2. nyrikkiMar 2026
   > Can't they run an example prompt and verify they get the exact same output token probabilities for all prompts?

   You don’t even get that with GPUs in general, or really floating point in general.

   The Art of Computer Programming. Volume 2: Seminumerical Algorithms section 4.2.2 with explain where it loses floating addition associativity property.

   Apartness relations are another possible lens.

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3. svatMay 2025
   Knuth also says that "Algorithm R is due to Alan G. Waterman", on TAOCP vol 2 page 144, just below "Algorithm R (Reservoir sampling)". This blog post seems to be a good history of the algorithm: https://markkm.com/blog/reservoir-sampling/ (it was given by Waterman in a letter to Knuth, as an improvement of Knuth's earlier "reservoir sampling" from the first edition).

   > All in all, Algorithm R was known to Knuth and Waterman by 1975, and to a wider audience by 1981, when the second edition of The Art of Computer Programming volume 2 was published.

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4. svatMar 2024
   BTW that one isn't a joke made up for this site: it's a verbatim quote from The Art of Computer Programming (Volume 2, page 2). TAOCP is full of silly-but-serious jokes like that.
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5. guessmynameOct 2019
   Read these articles to know what is wrong with Math.random()

   • https://medium.com/@betable/tifu-by-using-math-random-f1c308...

   • https://hackernoon.com/how-does-javascripts-math-random-gene...

   • https://news.ycombinator.com/item?id=10751396

   • https://v8.dev/blog/math-random

   > Many random number generators in use today are not very good. There is a tendency for people to avoid learning anything about such subroutines; quite often we find that some old method that is comparatively unsatisfactory has blindly been passed down from one programmer to another, and today’s users have no understanding of its limitations. — The Art of Computer Programming, Volume 2, by Donald Knuth

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