A Robust Complex Division in Scilab

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.