Optimal approximate computation of Euclidean distance in spiking neural P systems framework

A fast approximation for the Euclidean distance, i.e., the [Formula: see text]-norm of a complex number was investigated. The problem is obtaining an initial estimate with minimal effort and maximum numerical precision. We show how to eliminate the square root computation and improve the precision of an approximation with just a few shifts and additions from 41% to just 4%. This corresponds to an improvement of precision from 1 bit to almost 5 bits. As successive Newton iterations double the number of bits, this eliminates the need for two initial iterations. For example, a result with 16-bit precision can be obtained by just two iterations instead of four. We implement the computation by using two types of basic neurons, namely a high-pass (HP) neuron and a low-pass (LP) neuron, in the Spiking Neural P systems framework.