Some experiments with computing the complex absolute value

Portability for the numerical analyst not only includes writing codes which will compile and execute on a variety of machines, but also writing codes which are robust and accurate as well. This is particularly important for the computation of the complex absolute value. This computation, the computation of the 2-norm of a 2-vector, also occurs in the formation of Givens transformations [3] which are used in the solution of the symmetric eigenvalue problem, the computation of the singular value decomposition, and in the solution of linear least squares problems.