An Improved Algorithm for hypot(a,b)

We develop a fast and accurate algorithm for evaluating $\sqrt{a^2+b^2}$ for two floating point numbers $a$ and $b$. Library functions that perform this computation are generally named {\tt hypot(a,b)}. We will compare four approaches that we will develop in this paper to the current resident library function that is delivered with Julia 1.1 and to the code that has been distributed with the C math library for decades. We will demonstrate the performance of our algorithms by simulation.