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Why can’t I go faster than the speed of light?
I should state from the very beginning that the title of this post is a bit of a tease. I don’t know why nothing can go faster than the speed of light. No one does. It is a fundamental pos…
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The Fourier transform is a neural network
The site of Sid
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The Fastest FizzBuzz Implementation
Benchmarks & Tips for Big Data, Hadoop, AWS, Google Cloud, PostgreSQL, Spark, Python & More...
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Introduction to Locality-Sensitive Hashing
Locality-sensitive hashing (LSH) is a set of techniques that dramatically speed up search-for-neighbors or near-duplication detection on data. These techniques can be used, for example, to filter out duplicates of scraped web pages at an impressive speed, or to perform near-constant-time lookups of nearby points from…
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Penrose: From mathematical notation to beautiful diagrams
Materials from our SIGGRAPH '20 paper.
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Speeding up atan2f
`atan2f` is an important but slow trigonometric function. In this article we'll explain how to approximate it, and implement a version 50x faster than `glibc` on batches of inputs.
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Apple’s M1 processor and the full 128-bit integer product
If I multiply two 64-bit integers (having values in [0, 264)), the product requires 128 bits. Intel and AMD processors (x64) can compute the full (128-bit) product of two 64-bit integers using a single instruction (mul). ARM processors, such as those found in your mobile phone, require two instructions to achieve the…
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Practical Reed-Solomon for Programmers
Recently I was doing some work decoding the new Galileo High Accuracy Service data. In short, this new service will allow Galileo (“European GPS”) users to achieve decimeter-level accuracy, which is nice. This “HAS” data is transmitted highly redundantly by making good use of Reed-Solomon encoding. To work with this…
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Claude Shannon: The Mathematical Theory of Cryptography
The foundation of modern cryptography.
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The Boyer-Moore Fast String Searching Algorithm
Our algorithm has the peculiar property that, roughly speaking, the longer the pattern is, the faster the algorithm goes. Furthermore, the algorithm is ``sublinear'' in the sense that it generally looks at fewer characters than it passes. The algorithm is described in
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The Hypnotic World of Degenerate Spirals
Doga Tekin's website.
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When did computer science theory get so hard?
I posted on When did Math get so hard? a commenter pointed out that one can also ask When did Computer Science Theory Get so Hard? For t...
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Deriving the piano keyboard from biological principles using clustering
Once upon a time we were creatures in the wilderness and we evolved the ability to hear sounds. Now here's an interesting thing, if you hear a sound of frequency f and others of frequency 2f, 3f, etc then there's a good chance these sounds come from the same object, due to the physical principle of resonance . And so…
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(Very) Basic Intro to Elliptic Curve Cryptography
Learn cryptography in Go by building ciphers, hashes, password security, and encryption tools. Understand security beneath the library call.
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How Tail Call Optimization Works
Most undergraduate computer sciences courses teach students about tail call optimization (TCO) , and even if you don't have a formal computer science background the concept is talked about enough that you might be familiar with it anyway, especially if you've ever done any functional programming. However, I think the…
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NP Complete 3rd Grade Math Problems (2018)
Leo’s third grade class got to try a Noyce Foundation math worksheet [1] the other day. They didn’t fare so well, but I gotta tell you, some of the problems are REALLY hard! In fact, on…
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Ribbon filter: Practically smaller than Bloom and Xor
What the research is: The Ribbon filter is a new data structure that is more space-efficient than the popular Bloom filters that are widely used for optimizing data retrieval. One of the ways that …
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The stack monoid revisited
This is a followup to my previous post on the stack monoid, but is intended to be self-contained.
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Dynamic Programming vs. Divide-and-Conquer (2018)
In this article I’m trying to explain the difference/similarities between dynamic programing and divide and conquer approaches based on two examples - binary search and minimum edit distance (Levenshtein distance)
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Euler's Fizzbuzz (2020)
FizzBuzz is a common coding problem asked in technical screenings or interviews. It goes something like this:
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Ordering movie credits with graph theory
How Graphs & Games Untangled "The Golden Hairball": A technical deep dive from the end credits experts at Endcrawl.
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Are deep neural networks dramatically overfitted? (2019)
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The Mathematics of 2048: Optimal Play with Markov Decision Processes (2018)
Finding provably optimal strategies for 2048 using Markov Decision Processes
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Foldable Words
Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message:
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Formalising Mathematics: An Introduction
An introduction to the TCC course “Formalising Mathematics”
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Ideas in statistics that have powered AI
Andrew Gelman, a statistics professor at Columbia, and Aki Vehtari, a computer science professor at Finland’s Aalto University, recently published a list of the most important statistical ideas in the last 50 years. Here, they break it down in easy-to-understand terms.