Analysis of scientific computing algorithms under different number representation systems

Scientific computing-based applications need a high load of computations. These computations are closely linked to the number representation system (NRS). A benchmark for decimal accuracy, storage space, computation time and energy consumption using multiple NRSs is needed for the base scientific computing algorithms. Eleven NRSs were evaluated under four types of benchmarks: matrix multiplication, solving a linear system of equations using the gradient conjugate method, integral calculation using Simpson's formula and N-body simulation. The results validate the posit "golden zone" and offer a perspective on different NRSs accuracy related to input ranges. IEEE754 performed well regarding decimal accuracy in all four benchmarks (top 3).