We develop fast and accurate algorithms for evaluating root x(2) + y(2) for two floating-point numbers x and y. Library functions that perform this computation are generally named hypot(x,y). We compare five approaches that we will develop in this article 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 investigate the accuracy of our algorithms by simulation.
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