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Insert D-Wave Post Here
In the two months since I last blogged, the US has continued its descent into madness. Yet even while so many certainties have proven ephemeral as the morning dew—the US’…
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Singular Value Decomposition for Programmers
Today's article is a short one. Not because Singular Value Decomposition (SVD) is not important, but because it is so ubiquitous that we'll touch it in other...
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Evolution Strategies as a Scalable Alternative to Reinforcement Learning
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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16-bit math look-up tables – the unexpected power of scaled-integer math
Floating-point math puts a big overhead on a computer that doesn't have a floating-point coprocessor; but we really do need floating-point for all but the simplest operations— or do we?? Can we really do things like trig, log, and square-root functions without floating point?
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The Axiom of Choice Is Wrong (2007)
When discussing the validity of the Axiom of Choice, the most common argument for not taking it as gospel is the Banach-Tarski paradox. Yet, this never particularly bothered me. The argument …
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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…
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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…
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From math to machine: translating a function to machine code
In this post I'm going to explore how a mathematical concept can be redefined in progressively more computer-oriented terms, all the way from high level languages down to machine code, ready for direct execution by a computer. To that end, I'm going to define the same logic in several different but related formats:
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Is SHA-3 slow?
In a recent post , Adam Langley complains that “SHA-3 is slow”. Similar comments appear from time to time on the web (see also David Wong's post ). But what does it mean precisely? Let us dig into it.
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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…
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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…
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Understanding LSTM Networks (2015)
Humans don’t start their thinking from scratch every second. As you read this essay, you understand each word based on your understanding of previous words. You don’t throw everything away and start thinking from scratch again. Your thoughts have persistence.
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Z-order curve usage to decrease dimensionality to 1
Personal blog about system engineering and devops
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Beyond public key encryption
One of the saddest and most fascinating things about applied cryptography is how little cryptography we actually use. This is not to say that cryptography isn’t widely used in industry —…
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On Melissa O’Neill’s PCG random number generator
Computers often need random numbers. Most times, random numbers are not actually random... in the sense that they are the output of a mathematical function that is purely deterministic. And it is not even entirely clear what "really random" would mean. It is not clear that we live in a randomized universe... it seems…
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Empirical Bayes for multiple sample sizes
The James-Stein Estimator with unequal variances
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The beauty of mixed-radix bases
On the relationship between mixed-radix bases and array indexing
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Markov's and Chebyshev's Inequalities Explained
A look at why Chebyshev's Inequality holds true and some potential applications.
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Multiplying and dividing with Hindu-Arabic numerals and with Roman ones
Last Sunday the eminent British historian of the twentieth century, Richard Evans, tweeted the following: Let’s remember we use Arabic numerals – 1, 2, 3 etc. Try dividing MCMLXVI by XX…
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Recognizing when two arithmetic expressions are essentially the same
From the highly eclectic blog of Mark Dominus
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Two-part Rubik's algorithms
When Rubik’s Cube first appeared decades ago, I jumped on it. I bought one, and spent an entire summer fiddling with it. Over that summer, I developed a solving technique that has stuck with me. My technique is not the fastest; that was never the goal. My algorithms make sense to me because they are constructed, and…
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Papers I like (part 2)
Continued from part 1. Once I was about a thousand words into describing background for GEMM, it became pretty clear that it made more sense to group the numerical math papers into one post, so her…