A technical guide implementing Wagon's algorithm in Python to solve x² + y² = p for large primes, using quadratic residues and a modified Euclidean algorithm.
Explains how to compute a square root of -1 modulo a prime p, using number theory and Python code examples.
Explores Fermat's theorem on expressing primes as sums of two squares, comparing Gauss's formula with a more efficient computational algorithm.
Explains enhancing a poetry app's share links with Myers Diff algorithm to show granular differences between poem snapshots and live edits.
Compares iterative vs. Binet's formula for computing large Fibonacci numbers in Python, analyzing performance and precision.
A tutorial on extracting clean shape perimeters from binary grids using greedy geometry algorithms, with a JavaScript implementation example.
Explains the greedy rectangle merging algorithm for simplifying binary grids into non-overlapping rectangles, with a JavaScript implementation.
Explores the mathematical and implementation challenges of adding high-precision transcendental functions (sine, cosine) to the Ivy programming language.
A technical proof and algorithm for fast unrounded scaling in floating-point formatting, part of a series on floating-point printing and parsing.
A technical deep dive into simple, fast algorithms for converting floating-point numbers to and from decimal text, with a Go implementation.
A speculative blog post predicting that a universal 'Last Algorithm' for AI problem-solving could emerge in 2026 through advanced iterative loops.
Explores a method for testing Cunningham prime chains efficiently, with applications in cryptocurrency proof-of-work systems.
A detailed analysis and new proof for Donald Knuth's fixed-point to decimal conversion program, exploring program correctness and algorithm design.
Explores bi-twin prime chains, a mathematical pattern where sequences of twin primes follow a doubling rule, with examples and Python verification code.
An analysis of scaling HNSW vector indexing in Redis, covering new contributions for efficient deletions and parallel queries across distributed nodes.
A developer details building a solver for the NYT Pips puzzle using TypeScript, DFS, and optimizations, including a debug UI and tree visualization.
Explains the non-random algorithm Kubernetes uses to select pods for deletion during scale-in operations, including the pod-deletion-cost annotation.
A step-by-step educational guide to building a Byte Pair Encoding (BPE) tokenizer from scratch, as used in models like GPT and Llama.
A step-by-step guide to implementing the Byte Pair Encoding (BPE) tokenizer from scratch, used in models like GPT and Llama.
A technical guide explaining the Sliding Window algorithm for solving the 'longest substring without repeating characters' LeetCode problem.
