Webtagr - Technology News Summarizer

Making Miracles with Four 2s: An Elegant Solution to a Math Puzzle

2025-02-23

A seemingly simple math puzzle: using only four 2s and any mathematical operation, generate any natural number. From elementary school arithmetic to advanced university mathematics, everyone can participate. Initially a seemingly simple challenge, the difficulty increases with the introduction of exponents, factorials, etc. Ultimately, physicist Dirac, using nested square roots and logarithms, found a general solution, elegantly solving this century-old problem, even with just four 2s.

Python's JIT Decorators: Three Implementation Strategies

2025-02-03

This article delves into the popular JIT decorator pattern in Python, particularly its use in JAX and Triton libraries. The author implements three JIT decorators from scratch using a simplified example: AST-based, bytecode-based, and tracing-based. The AST-based approach directly manipulates the Abstract Syntax Tree; the bytecode-based approach leverages Python's bytecode interpreter; and the tracing-based approach builds an expression IR by tracing function execution at runtime. The article details the advantages and disadvantages of each approach and uses JAX and Numba as examples to illustrate their strategies in real-world applications.

Implementing Raft: A Deep Dive into Distributed Consensus

2024-12-21

This is the first post in a series detailing the Raft distributed consensus algorithm and its Go implementation. Raft solves the problem of replicating a deterministic state machine across multiple servers, ensuring service availability even with server failures. The post introduces core Raft components: the state machine, log, consensus module, leader/follower roles, and client interaction. It discusses Raft's fault tolerance, the CAP theorem, and the choice of Go as the implementation language. Subsequent posts will delve into the algorithm's implementation.