Empirical analysis of IEEE 754 and Posit in statistical methods

Abstract

Within statistical methods, mathematical operations play a crucial role in performing meaningful analyzes on processed data sets. However, mathematical operations can lead to unexpected results, which appear due to errors related to rounding and precision, and not due to errors in their implementation. The errors that can occur are related to the limitations of the computer that can only process a finite number of bits or to the limitations of the number representation system (NRS) used. So, for obtaining efficiency, it is necessary to choose a number representation system that can provide good accuracy, using the smallest possible number of bits. This paper aims to investigate the IEEE 754 standard via binary floating-point against the Unum type 3 standard via posit. Several tests were developed for various statistical methods to observe how the two number representation systems perform. The results show that a 16-bit posit number representation system is viable for energy and computing time efficiency.