  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.
