# An Improved Algorithm for hypot(a,b)

## TL;DR

This paper introduces a new, faster, and more accurate algorithm for computing the hypotenuse of two floating point numbers, improving upon existing library functions in Julia and C.

## Contribution

The paper presents four novel algorithms for hypot computation and compares their performance to standard library implementations.

## Key findings

- New algorithms outperform existing functions in speed and accuracy
- Simulation results demonstrate significant improvements
- Enhanced hypot computation benefits scientific and engineering applications

## Abstract

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.