Evaluation of Powers janmr.com/posts/evaluation-of-powe… #programming #algorithm #cpp #exponentiation #optimality

• $x^0 = 1$
• $x^{2k} = (x^k)^2$
• $x^{2k+1} = x \cdot x^{2k}$

The M/o/Vfuscator compiles programs into "mov" instructions, and only "mov" instructions. Arithmetic, comparisons, jumps, function calls, and everything else a program needs are all performed through mov operations; there is no self-modifying code, no transport-triggered calculation, and no other form of non-mov cheating. 🤯 github.com/xoreaxeaxeax/movfuscato… #programming #compiler #assembler

Prime Factors of Factorial Numbers janmr.com/posts/prime-factors-of-f… #math #prime #factors #factorials

$$d_p(n!) = \sum_{k=1}^\infty \left\lfloor \frac{n}{p^k} \right\rfloor = \sum_{k=1}^{\lfloor \log_p(n) \rfloor} \left\lfloor \frac{n}{p^k} \right\rfloor$$

Every position of Rubik's Cube can be solved in twenty moves or less www.cube20.org #math #combinatorics #rubikscube

Computing the Integer Binary Logarithm janmr.com/posts/computing-the-inte… #programming #algorithm #integer #binary #logarithm #numbers #cpp

$$k = \lfloor \log_2 n \rfloor \quad \Leftrightarrow \quad 2^k \leq n < 2^{k+1}$$

Stanford Lecture: Dr. Don Knuth - Adventures with Knight's Tours (2025-12-04) www.youtube.com/watch?v=MKiRte-tnM… (playlist with many of Knuth's lectures: www.youtube.com/playlist?list=PL94…) #math #computerscience #programming #online #lecture

Bit Twiddling Hacks, a collection of fast and tested code snippets graphics.stanford.edu/~seander/bit… #programming #binary #numbers #optimization

Bitwise Operators and Negative Numbers janmr.com/posts/bitwise-operators-… #programming #binary #numbers

$$\overline{x} = -1 - x$$

Test and benchmark suite for sort implementations, github.com/Voultapher/sort-researc….

The current slice::sort_unstable implementation of the Rust standard library is based on ipnsort github.com/Voultapher/sort-researc… doc.rust-lang.org/1.92.0/std/primi…

#sorting #algorithm #rust

Visualizing the Pythagorean Theorem janmr.com/posts/visualizing-the-py… #math #visualization #proof

How to Draw a Straight Line (Peaucellier–Lipkin linkage) www.futilitycloset.com/2014/12/05/… #math #geometry

Fractions and Circles janmr.com/posts/fractions-and-circ… #math #fractions

Two Notes on Notation by Donald E. Knuth (Iverson’s convention and Stirling numbers) arxiv.org/abs/math/9205211 #math #notation

$$[P] \quad \left[ { n \atop k } \right] \quad \left\{ { n \atop k } \right\}$$

The Stern-Brocot Tree of Fractions janmr.com/posts/the-stern-brocot-t… #math #fractions

Langford pairs: Arrange the 2n numbers {1, 1, 2, 2, ..., n, n} such that exactly k numbers occur between the two appearances of each digit k dialectrix.com/langford.html #math #combinatorics

Continued Fractions and Continuants janmr.com/posts/continued-fraction… #math #computerscience #algoritms #continuedfractions

$$a_0 + \displaystyle\frac{1}{a_1 + \displaystyle\frac{1}{\ddots + \displaystyle\frac{1}{a_{n-1} + \displaystyle\frac{1}{a_n}}}}$$

Online book: Mining of Massive Datasets www.mmds.org #online #book #computerscience #bigdata

Computing the Greatest Common Divisor janmr.com/posts/computing-the-grea… #math #programming #number-theory #algorithm

$$\text{gcd}(u,v) = \prod_{p \; \rm prime} p^{\min(u_p,v_p)}.$$

Guido on introducing the shortcut conditional expression to Python. Some usages are "intentionally ugly" and finishes by adding "It's still my language! :-)". mail.python.org/pipermail/python-d…

A if C else B

Useful Properties of the Floor and Ceil Functions janmr.com/posts/useful-properties-… #floor #ceil #functions #math #programming

$$\begin{aligned} n=\lfloor x \rfloor \quad &\Longleftrightarrow \quad n \leq x < n+1, \\ n=\lfloor x \rfloor \quad &\Longleftrightarrow \quad x-1 < n \leq x, \\ n=\lceil x \rceil \quad &\Longleftrightarrow \quad n-1 < x \leq n, \\ n=\lceil x \rceil \quad &\Longleftrightarrow \quad x \leq n < x+1 \end{aligned}$$

Google humor: Did you mean recursion? www.google.com/search?q=recursion

Twelve Ways of Counting janmr.com/posts/twelve-ways-of-cou… #math #combinatorics

Modern Computer Arithmetic, a book about algorithms for performing arithmetic, and their implementation on modern computers maths-people.anu.edu.au/~brent/pub… members.loria.fr/PZimmermann/mca/p… #multiple-precision #arithmetic #algorithms #online #book

Nice Proof of a Geometric Progression Sum janmr.com/posts/nice-geometric-pro… #math #visualization #visual-proof

The first website info.cern.ch

Math.sumPrecise developer.mozilla.org/en-US/docs/W…

A leap year check in three instructions hueffner.de/falk/blog/a-leap-year-…

Full unicode emoji list unicode.org/emoji/charts/full-emoj…

An ongoing multi-author open source project to formalise a proof of Fermat's Last Theorem in the Lean theorem prover imperialcollegelondon.github.io/FL… #lean

Fast and maintainable patterns for fetching from a database by @sophiebits.com sophiebits.com/2020/01/01/fast-mai…

Celebrate 50 years of Microsoft with the company’s original source code by Bill Gates www.gatesnotes.com/home/home-page-…

Free math texts by Jim Hefferon (Linear Algebra, Theory of Computation, Introduction to Proofs) hefferon.net

@acm.org ACM has named Andrew G. Barto and Richard S. Sutton as the recipients of the 2024 ACM A.M. Turing Award for developing the conceptual and algorithmic foundations of reinforcement learning awards.acm.org/about/2024-turing

Stanford's "The Fourier Transform and Its Applications"

Videos, problem sets & more: see.stanford.edu/course/ee261

An unexpected, and extremely inefficient, way to compute pi @3blue1brown.com www.youtube.com/watch?v=HEfHFsfGXj…

Introduction to Computer Graphics, a free, on-line textbook covering the fundamentals of computer graphics and computer graphics programming math.hws.edu/graphicsbook

Videos from Math Professor Jeffrey Chasnov. Some of the playlists are videos from his Coursera courses on Mathematics for Engineers. #math #lectures #mooc www.youtube.com/@Jeff-math/playlis… www.math.hkust.edu.hk/~machas/?men…

Computer Science lectures by @timroughgarden.bsky.social www.youtube.com/channel/UCcH4Ga14Y…

Online conversion from TeX/MathML to HTML/SVG (powered by MathJax) #math #tex #mathml #svg mathjax.github.io/MathJax-demos-we…

Temml is a LaTeX-to-MathML JavaScript conversion utility. Useful online converter on homepage. temml.org #math #tex #mathml

KaTeX: A math typesetting library for the web katex.org

👻 Ghostty is a fast, feature-rich, and cross-platform terminal emulator that uses platform-native UI and GPU acceleration. ghostty.org

#AdventOfCode 2024 complete!

MarkItDown: Python tool for converting various files to Markdown. It presently supports: PDF, PowerPoint, Word, Excel, Images, Audio, HTML, csv, json, xml, etc. github.com/microsoft/markitdown #python #microsoft

Vanilla JS vanilla-js.com #javascript

Donald Knuth's 28th annual Christmas Lecture: Strong Components and Weak Components www.youtube.com/watch?v=au26uZfuxV… (past recordings www.youtube.com/playlist?list=PLoR…) #computerscience #lecture

In Python, comparisons can be chained arbitrarily, e.g., x < y <= z is equivalent to x < y and y <= z docs.python.org/3/reference/expres… #python

Lean: First Steps leanfirststeps.blogspot.com/p/cont… #lean #math

Are all natural numbers interesting? If not, there must be a smallest uninteresting number - and that makes it interesting. 🤔 en.wikipedia.org/wiki/Interesting_…

Kaleidoscope: Implementing a Language with LLVM llvm.org/docs/tutorial #llvm #tutorial

Beating OpenBLAS and MKL in FP32 Matrix Multiplication From Scratch salykova.github.io/matmul-cpu

Note that the function $s(x)=(\ln x) / x$ from the post has the following property:

$$-s(e^{-x}) = -\frac{\ln(e^{-x})}{e^{-x}} = x e^x$$

and the inverse function (branches) of $x \mapsto x e^x$ is commonly called the Lambert W function, which has undergone a lot of study.

en.wikipedia.org/wiki/Lambert_W_fu… mathworld.wolfram.com/LambertW-Fun…

Journal of Open Source Software @joss joss.theoj.org

A curated list of awesome mathematics resources #math github.com/rossant/awesome-math

AlphaGeometry: An Olympiad-level AI system for geometry deepmind.google/discover/blog/alph… #math #geometry #ai

Math OCR model that outputs LaTeX and Markdown github.com/VikParuchuri/texify #math

Easily train AlphaZero-like agents on any environment you want github.com/s-casci/tinyzero

A chiral aperiodic monotile - one that tiles the plane aperiodically without reflections #math cs.uwaterloo.ca/~csk/spectre

Donald Knuth Annual Christmas Lectures #math #computerscience youtube.com/playlist?list=PLoROMvo…

Benchmarking LLMs in the Wild, an Elo-based LLM leaderboard huggingface.co/spaces/lmsys/chatbo…

The AWS SDK for Rust is now generally available and supported for production use aws.amazon.com/blogs/developer/ann… #aws #rustlang

The Miracle Sudoku. A puzzle with sudoku rules plus some extra restrictions. The host's reaction on seeing the puzzle for the first time (around 3:45) is hilarious. www.youtube.com/watch?v=yKf9aUIxdb…

MacTutor History of Mathematics Archive mathshistory.st-andrews.ac.uk