A note on extended Euclid's algorithm

TL;DR

This paper systematically transforms the recursive extended Euclid's algorithm into an iterative form using matrix notation, providing an elegant correctness proof and connecting the two versions.

Contribution

It introduces a systematic matrix-based approach to convert recursive algorithms into iterative ones, with a clear correctness proof.

Findings

Successful transformation of recursive to iterative algorithm

Elegant partial correctness proof derived from the transformation

Establishes a clear connection between recursive and iterative Euclid's algorithms

Abstract

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very elegant, and easy to follow. The paper provides a connection between recursive and iterative versions of extended Euclid's algorithm.