Parallel Numerical Computation: A Comparative Study on Cpu-Gpu Performance in Pi Digits Computation

Abstract

As the usage of GPU (Graphical Processing Unit) for non-graphical computation is rising, one important area is to study how the device helps improve numerical calculations. In this work, we present a time performance comparison between purely CPU (serial) and GPU-assisted (parallel) programs in numerical computation. Specifically, we design and implement the calculation of the hexadecimal -digit of the irrational number Pi in two ways: serial and parallel. Both programs are based upon the BBP formula for Pi in the form of infinite series identity. We then provide a detailed time performance analysis of both programs based on the magnitude. Our result shows that the GPU-assisted parallel algorithm ran a hundred times faster than the serial algorithm. To be more precise, we offer that as the value grows, the ratio between the execution time of the serial and parallel algorithms also increases. Moreover, when it is large enough, that is This GPU efficiency ratio converges to a constant, showing the GPU's maximally utilized capacity. On the other hand, for sufficiently small enough, the serial algorithm performed solely on the CPU works faster since the GPU's small usage of parallelism does not help much compared to the arithmetic complexity.