An Increase in Trustworthiness of Result Checking in Arithmetic Components of Embedded Systems

Abstract

The extensive use of embedded systems to process approximate data from sensors in critical, cyber-physical, IoT and other applications orients online testing methods to check the validity of approximate results in arithmetic operations. Traditional methods of on-line testing are designed for exact data, i.e. integer by nature. The development of the data model from exact to approximate form changes the purpose of on-line testing for arithmetic components from fault detection to estimation of trustworthiness of the calculated results. The approximate result contains the most and least significant bits, in which the faults of the digital circuit produces essential and inessential errors with respect to the trustworthiness of the result. As a rule, the approximate calculations are characterized by a low probability of an essential error. Traditional on-line testing methods had high error detection probability and low trustworthiness, which approached the probability of an essential error. We propose a method of on-line testing with simplified operation in checking to increase trustworthiness in conditions of low probability of essential error. The method monitors the result of an operation on a limited set of inputs while maintaining the ability to detect typical array circuit faults in the same way as residue checking. The method uses conditions that restrict the input data and logical operations with them. An error detection circuit has been developed and an example of on-line testing of the iterative array multiplier has been considered. The advantages of the suggested method in trustworthiness compared to residue checking are shown.