An Investigation on Inherent Robustness of Posit Data Representation

TL;DR

This study compares the inherent robustness of posit and IEEE 754 floating-point formats, demonstrating posit's superior fault tolerance and accuracy in machine-learning applications through theoretical analysis and extensive fault injection experiments.

Contribution

It provides the first comprehensive robustness comparison between posit and IEEE 754 formats, including theoretical analysis and fault injection experiments in machine learning.

Findings

Posit format shows higher resilience to bit-flip faults than IEEE 754.

In over 95% of fault injections, posit maintains better integrity.

Posit-based systems achieve higher accuracy in all tested machine-learning applications.

Abstract

As the dimensions and operating voltages of computer electronics shrink to cope with consumers' demand for higher performance and lower power consumption, circuit sensitivity to soft errors increases dramatically. Recently, a new data-type is proposed in the literature called posit data type. Posit arithmetic has absolute advantages such as higher numerical accuracy, speed, and simpler hardware design than IEEE 754-2008 technical standard-compliant arithmetic. In this paper, we propose a comparative robustness study between 32-bit posit and 32-bit IEEE 754-2008 compliant representations. At first, we propose a theoretical analysis for IEEE 754 compliant numbers and posit numbers for single bit flip and double bit flips. Then, we conduct exhaustive fault injection experiments that show a considerable inherent resilience in posit format compared to classical IEEE 754 compliant representation. To show a relevant use-case of fault-tolerant applications, we perform experiments on a set of machine-learning applications. In more than 95% of the exhaustive fault injection exploration, posit representation is less impacted by faults than the IEEE 754 compliant floating-point representation. Moreover, in 100% of the tested machine-learning applications, the accuracy of posit-implemented systems is higher than the classical floating-point-based ones.