Searching of optimal weights for the Akushsky core function

Modern computational tasks involving the processing of large numbers require not only high accuracy but also significant speed. In this context, the use of the residue number system offers an approach to parallel big data processing used in cryptography, signal processing and artificial neural networks. Despite the advantages of the residue number system, its diffusion has been slow due to the computational complexity of the so-called non-modular operations of the residual class system. One of the universal tools for realising non-modular operations is the Akushsky core function. This paper studies the Akushsky core function as a tool for determining the positional characteristic of a number in the residue number system. The application of Monte Carlo method and genetic algorithm is proposed to find the optimal weights of the core function. Experimental results demonstrate that the genetic algorithm provides more stable results when the number of moduli increases, while the Monte Carlo method is effective on small dimensions. The genetic algorithm is on average 38% faster than the Monte Carlo method, making it the preferred choice. Additionally, the computation time of the core function with optimal weights and the Pirlo function were compared. The results showed that the core function with optimal weights is on average 14% faster than the Pirlo function.