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The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
I have a simple fast Fourier transform implementation on the page Free small FFT in multiple languages , whose asymptotic time complexity is the optimal Θ( n log n ). I wanted to know how much additional speed-up could be obtained by reorganizing memory access patterns and using SIMD vector arithmetic instructions…
I know that floating-point arithmetic is a bit crazy on modern computers. For example, floating-point numbers are not associative: 0.1+(0.2+0.3) == 0.599999999999999978 (0.1+0.2)+0.3 == 0.600000000000000089 But, at least, this is fairly consistent in my experience. You should simply not assume fancy properties like…
Fast Fibonacci Computations With a Linear Algebra Twist
Hugo Hadfield - Cross stack robotics engineer and computer vision researcher specializing in deep learning, sensor fusion, geometric algebra and applications in self-driving cars and robotic manipulation.
I built an interactive Shiny application that uses simulated annealing to solve the famous traveling salesman problem. You can play around with it to create and solve your own tours at the bottom of …
This week we (me & Anton Kovsharov) published Paperproof, a Gentzen-tree-like proof interface for Lean 4. In this post I'll review proof visualisations from o...
EDIT: I never expected this post to garner so much interest. Just to be clear, using the constant is a very bad idea in almost every situation I can think of. Even instructions like RCPSS should only be used by people who are convinced that the tradeoffs are worth it (or don’t have any other choice). Subtracting from…
When developing software to run in a Unix environment, you will often be able to use the same system features and benefit from good developer tools, regardless of the particular platform you're working on, as most processors will provide a rich instruction set and virtual memory, among other things.
SAT is often described as the "mother of all NP-complete problems." This post goes over what SAT is and why it is considered to be so important. A simple SAT solver is implemented using Python in the process.
This web page is a revised and extended version of Appendix A from the book Conceptual Structures by John F. Sowa. It presents a brief summary of the following topics for students and general readers of that book and related books such as Knowledge Representation and books on logic, linguistics, and computer science.
Beneath the utilitarian purpose of computation, computing is also a source of delight and wonder . Software is not just databases and mail merges or SaaS and spreadsheets; it's creative coding and simulated cities , code poetry and bulletin board systems . It's websites that dazzle and iPhone apps that make the heart…
The missing chapter of Hacker's Delight
As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an...
Riffling from factory order to complete randomness.
While reading Real-World Cryptography , I came across the "million message attack" . This is an attack that Daniel Bleichenbacher demonstrated in 1998, which effectively broke RSA with a particular encoding function called PKCS #1 . It was only mentioned briefly, so I dug in and decided to try to understand the…
Welcome. This is the index page for a series of blog posts I’m currently writing about the D3D/OpenGL graphics pipelines as actually implemented by GPUs. A lot of this is well known among gra…
From the highly eclectic blog of Mark Dominus
Dual_EC was almost certainly an NSA backdoor. Extended Random is the TLS extension that would have made it practical to exploit. Did NSA plant that one too? A look at the evidence.
The myth A few years ago I saw a StackOverflow question (but I cannot find it now): allegedly Andrew Gelman blogged that Bayesian models would not overfit and would only underfit (I also cannot find Andrew’s blog post now but I think what he meant by “Bayesian models only underfits” is that you can never fully model…
Bézier curves are a core building block of text and 2D shapes rendering. There are several approaches to rendering them, but one especially challenging problem, both mathematically and technically, is computing the distance to a Bézier curve. For quadratic curves (one control point), this is fairly accessible, but for…
An explainer for people who don't know computer science and are mildly curious
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
There’s an old theory that memory is actually encoded in part in RNA. The argument is pretty simple: there’s no obvious way for all that sensory data to be captured in synapses as long …
In the last few months I taught three graduate mini-courses about string diagrams and graphical linear algebra – at Phd Open in Warsaw, a winter school in Estonia, and a graduate school in Le…
Deep dives into Cryptography and Privacy.
I recently had a problem where part of the solution was to do a series of pointer accesses that would walk around a chunk of memory in pseudo-random order. Sattolo's algorithm provides a solution to this because it produces a permutation of a list with exactly one cycle, which guarantees that we will reach every…
