A root of less evil

An overview of several square root and complex vector magnitude approximation algorithms are discussed, with a focus on high-throughput (high-speed) algorithms as opposed to high-accuracy methods. Performance analysis of the variations of iterative Newton-Raphson inverse (NRI) and non-linear IIR filter (NIIRF) square root methods shows that the number of iterations has the most profound effect on accuracy. The former method is not appropriate for implementation using fixed-point fractional binary arithmetic. The latter, together with the binary-shift magnitude estimation and equiripple-error magnitude estimation are found to be suitable for fixed-point implementation. Among all the methods, the magnitude ones are the most computationally efficient.