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Computer Science (@CompSciFact) profile picture

Computer Science

@CompSciFact

Daily tweets about computer science and related stuff @JohnDCook.

JohnDCook.com
Joined November 2010
  • Tweets13.4K
  • Following17
  • Followers25K
Numerical computing tip: If something goes wrong in theory *at* 0, expect difficulty in practice *near* 0.
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Computer Science retweeted
Jirka Knesl (@jiriknesl) profile picture
Jirka Knesl
@jirikneslNov 11
If you remove different representations, you find out that many algorithms are either the same, or almost the same. Shortest path is semiring based computation. More here: sciencedirect.com/science/ar… I realized this when I was writing my book on OR algorighms. There are hundreds of algos I went through. Sometimes, you could find 40-50 algorithms, that are different only in one parameter, or one function in the function composition. --- I am 100% sure, there are abstract algorithms in space search + reduction, that could simplify what already exist and provide dozens of real world useful algos for thousands of various usecases.
Image from Jirka Knesl (@jiriknesl)
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'Life as we know it would be very different without the FFT.' -- Charles Van Loan
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The hardest logarithm to compute johndcook.com/blog/2019/11/1…

The hardest logarithm to compute

The floating point number that requires the most extra precision to compute correctly to the last bit.

johndcook.com
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ً (@lightclients) profile picture
ً@lightclientsNov 11
🤖 Made with AI
Image from ً (@lightclients)
Nadim Kobeissi (@kaepora) profile pictureNadim Kobeissi
@kaeporaNov 10
Turns out we could have just written 6 million lines of Lean to verify Signal instead of messing with these papers and symbolic models this whole time deepmind.google/blog/introdu…
Formal Verification of Signal’s Protocol with Gemini

Formal Verification of Signal’s Protocol with Gemini

AlphaProof Code agents wrote over three million lines of machine-checked proof in Lean to verify the core cryptographic protections in Signal down to machine instructions.

deepmind.google
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The early development of programming languages. Knuth and Pardo, 1976 bitsavers.org/pdf/stanford/c… [pdf]
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'One of my most productive days was throwing away 1000 lines of code.' -- Ken Thompson
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The quality of an RNG depends on what you want to use it for johndcook.com/blog/2022/06/2…

The quality of an RNG depends on the application

Example of an RNG that does really well in one application and fails terribly in another.

johndcook.com
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The Fast Fourier Transform takes O(n log n) operations to transform a vector of length n.
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Parsing expressions by recursive descent engr.mun.ca/~theo/Misc/exp_p…
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'The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise' - Edsger Dijkstra
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Conceptually you define sinh in terms of exp, but numerically it's better to compute exp in terms of sinh. johndcook.com/blog/2020/08/0…

Conceptual vs Numerical

Numerical analysis often turns things on their head, using more advanced math to compute things that are conceptually less advanced.

johndcook.com
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'Premature abstraction is as bad as premature optimization.' -- Luciano Ramalho
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The Euclidean algorithm is not optimal among uniform processes github.com/jasondavies/eucli…
GitHub - jasondavies/euclid-uniform-processes: The Euclidean algorithm is not optimal among uniform...

GitHub - jasondavies/euclid-uniform-processes: The Euclidean algorithm is not optimal among uniform...

The Euclidean algorithm is not optimal among uniform processes: O(log a / log log a) remainder calls suffice. Paper and Lean formalisation. - jasondavies/euclid-uniform-processes

github.com
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The Church numeral for a non-negative integer n is λxy. x^n y
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How much can Boolean expressions be simplified? johndcook.com/blog/2020/11/1…

How much does Boolean expression minimization shorten?

If you have a Boolean function with n variables, how long can a minimized version of the expression be? How much does minimization save?

johndcook.com
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“Having functional programming as an ideal doesn’t imply that programs should never have side-effects. It just means that they should have no more than necessary.” — @paulg, On Lisp
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'One person's data is another person's program.' -- Guy L. Steele, Jr.
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How a programmer might reinvent the projective plane johndcook.com/blog/2026/11/0…

From a graphics hack to a rigorous model of the projective plane

How a graphic programmer's hack could lead to a rigorous definition of the projective plane.

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'One of the main causes of the fall of the Roman Empire was that-lacking zero-they had no way to indicate successful termination of their C programs.' — Robert Firth
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