This paper introduces a new class of "unbounded" spigot algorithms for calculating the decimal digits of $pi$, improving upon the classic Rabinowitz–Wagon method. While previous spigot algorithms required users to commit to a specific number of digits in advance and faced potential errors due to carry-over effects from truncated series, this proposed approach eliminates those limitations by allowing for infinite digit generation given sufficient memory. Although not intended to compete with high-performance state-of-the-art arithmetic-geometric mean algorithms, the author’s method offers a mathematically robust, simple, and incrementally efficient way to produce digits one by one without prior commitment or risk of truncation errors.
pi-autoresearch is an autonomous experiment loop for optimizing various targets like test speed, bundle size, LLM training, or build times. Inspired by karpathy/autoresearch, it utilizes a skill-extension architecture, allowing domain-agnostic infrastructure paired with domain-specific knowledge. The core workflow involves editing code, committing changes, running experiments, logging results, and either keeping or reverting the changes – a cycle that repeats indefinitely. Key components include a status widget, a detailed dashboard, and configuration options for customizing behavior. It persists experiment data in `autoresearch.jsonl` and session context in `autoresearch.md` for resilience and reproducibility.
AI agent toolkit: coding agent CLI, unified LLM API, TUI & web UI libraries
Mathematicians are using Srinivasa Ramanujan's century-old formulae to push the boundaries of high-performance computing and verify the accuracy of calculations.
