1921
The Asynchronous Computability Theorem
In this post I describe the Asynchronous Computability Theorem, which uses tools from Algebraic Topology to show whether a task is solvable…
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The latest blog posts to take off on Hacker News. 2,851 posts.
1922
A Branchless UTF-8 Decoder
This week I took a crack at writing a branchless UTF-8 decoder: a function that decodes a single UTF-8 code point from a byte stream without any if statements, loops, short-circuit operators, or other sorts of conditional jumps. You can find the source code here along with a test suite and benchmark:
1923
1924
How to defeat Ed25519 and EdDSA using faults
The Latest News from Research at Kudelski Security
1925
Sieve of Eratosthenes in Python (2015)
Sieve of Eratosthenes animation Source: Wikipedia[0] One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of "small") this can be…
1926
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1928
Calculating the Distance Between Points in Wrap Around (Toroidal) Space
Let’s say you are trying to find the distance between two points in 2D, but that these points are in a universe that “wraps around” like old video games – leaving the screen…
1929
Vladimir Voevodsky has died
The Institute for Advanced Study is deeply saddened by the passing of Vladimir Voevodsky, Professor in the School of Mathematics.Voevodsky, a truly extraordinary and original mathematician, made many contributions to the field of mathematics, earning him numerous honors and awards, including the Fields Medal.
1930
Nonlinear Computation in Deep Linear Networks
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
1931
Floating Point Visually Explained
While I was writing the Wolfenstein 3D book [1] , I wanted to demonstrate how much of a handicap it was to work without floating points. My attempts at understanding floating points using canonical [2] articles [3] were met with resistance from my brain. I tried to find a different way. Something far from $(-1)^S *…
1932
LU Factorization and Linear Systems for Programers
Solving systems of linear equations is a staple food of linear algebra. It can be applied as a part of many machine learning tasks, although it is not always...
1933
1934
The Mathematics of 2048: Counting States with Combinatorics
How many board configurations are there in the game of 2048? Let's estimate using combinatorics.
1935
1936
How Useful Is Tufte for Making Maps? (2007)
Edward Tufte’s The Visual Display of Quantitative Information (1998, 2nd edition 2001) is a classic book, arguably his best, and certainly a key text in the field of information graphics (whi…
1937
The Minsky circle algorithm
Consider the following pseudocode: x <- 32; y <- 0; while(true){ x <- x – floor((1/8) * y); y <- y + floor((1/8) * x); plotPointAt(x, y); } x and y are always integers. This draws…
1938
Why category theory matters in programming
Divide and conquer has been a core strategy in software engineering. We decompose our systems into smaller modules with focused, simple…
1939
What Monoids teach us about software
Monoids are a pretty interesting concept in software development. Monoids are everywhere. Monoids are simple yet powerful. And Monoids have a lot to teach us about software, in particular about com…
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1943
Designing a Tree Diff Algorithm Using Dynamic Programming and A*
During my internship at Jane Street 1 , one of my projects was a config editing tool that at first sounded straightforward but culminated in me designing a custom tree diffing algorithm using dynamic programming, relentlessly optimizing it and then transforming it into an A* accelerated path finding algorithm. This…
1944
How are PCA and SVD related?
Exploring the relationship between singular value decomposition and principal component analysis.
1945
Recognizing when two arithmetic expressions are essentially the same
From the highly eclectic blog of Mark Dominus
1946
1947
Cracking random number generators (xoroshiro128+)
In software, we generate random numbers by calling a function called a "random number generator". Such functions have hidden states, so that repeated calls to the function generate new numbers that appear random. If you know this state, you can predict all future outcomes of the random number generators. O'Neill, a…
1948
What is Hindley-Milner and why is it cool? (2008)
Anyone who has taken even a cursory glance at the vast menagerie of programming languages should have at least heard the phrase "Hindley-Milner". F#, one of the most promising languages ever to emerge from the forbidding depths of Microsoft Research, makes use of this mysterious algorithm, as do Haskell, OCaml and ML…
1949
On Norbert Blum’s claimed proof that P does not equal NP
Edited 8/16 to correct attributions to Alon and Boppana and to Tardos, thanks to an anonymous commenter for the correction Yesterday, Norbert Blum posted a preprint with a claimed proof that $latex…
1950
Understanding the math behind 0x5f3759df and the fast inverse square root (2012)
This post is about the magic constant 0x5f3759df and an extremely neat hack, fast inverse square root, which is where the constant comes from.