A Robust Complex Division in Scilab

TL;DR

This paper introduces two improved algorithms for floating point complex division that are more robust than Smith's method, with proven robustness and practical performance demonstrated through numerical simulations.

Contribution

It presents two new complex division algorithms with enhanced robustness, including a proven robust version and a combined method with scaling techniques.

Findings

The first improved algorithm is proven to be robust.

Numerical simulations confirm the algorithm's practical robustness.

The second algorithm, combining scaling, rarely fails.

Abstract

The most widely used algorithm for floating point complex division, known as Smith's method, may fail more often than expected. This document presents two improved complex division algorithms. We present a proof of the robustness of the first improved algorithm. Numerical simulations show that this algorithm performs well in practice and is significantly more robust than other known implementations. By combining additionnal scaling methods with this first algorithm, we were able to create a second algorithm, which rarely fails.