Arithmetic Coding for Floating-Points and Elementary Mathematical Functions

Abstract

Software-based fault tolerance enables the usage of standard hardware in safety-critical applications. Arithmetic coding is a promising approach for fault tolerance and is already used in the area of production systems. To enable the usage of complex safety functions, e.g. in human-robot collaboration, basic mathematical functions must be supported by the software-based fault-tolerance approach. Thereby, the basic mathematical functions require the full support of floating point values. Therefore, in this paper, we present a methodology to apply arithmetic coding on all types of floating-point functions including the basic mathematical functions. For each type, an example of implementation is shown. To validate our approach, we use the inverse kinematic of a cable robot as an example algorithm where the application of arithmetic coding is done automatically with a source-to-source transformation approach. Fault injection experiments validate the effectiveness of the presented approach.