Enhanced π Approximation Through MIMD Parallel Computing: An Efficiency Analysis Utilizing Raspberry Pi

Abstract

Multiple Instruction Multiple Data is one of the parallel computing architectures in Flynn's taxonomy, where cores can execute independent sets of instructions on independent sets of data. Parallel computing could be used in scientific subfields such as mathematics to approximate the number pi. One of the methods to approximate π is the Gregory-Leibniz method, which proposes the expansion of the arctan x series, which can then be used as an algorithm to approximate π. This method requires lots of term calculations to obtain the accurate digits of π, hence why parallel computing is needed. Building a cost-effective parallel computing architecture from standard desktop computers is difficult due to the high cost and space requirements. This study will build an MIMD parallel computing done by three Raspberry Pi 3Bs, small and affordable credit card sized single board computer, connected through a message-passing interface to get the performance analysis of MIMD parallel computing. The performance analysis shows that with three Raspberry Pis, there is a huge speedup of 6,2953020 and a faster time of 1.49 seconds compared to 9.38 seconds at 5 million terms. As a result of this discovery, the Raspberry Pi could be used in further projects to develop an affordable parallel computing architecture.