A Robust Complex Division in Scilab
This work addresses the reliability of floating-point complex division for numerical computing practitioners, though the improvements are incremental over existing methods.
The authors identified that Smith's method for complex division can fail more often than expected and proposed two improved algorithms. The first algorithm is proven robust and shown via simulations to be significantly more robust than other implementations; the second, combining additional scaling, rarely fails.
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.