ED4I: error detection by diverse data and duplicated instructions

Errors in computing systems can cause abnormal behavior and degrade data integrity and system availability. Errors should be avoided especially in embedded systems for critical applications. However, as the trend in VLSI technologies has been toward smaller feature sizes, lower supply voltages and higher frequencies, there is a growing concern about temporary errors as well as permanent errors in embedded systems; thus, it is very essential to detect those errors. Software-implemented hardware fault tolerance (SIHFT) is a low-cost alternative to hardware fault-tolerance techniques for embedded processors: It does not require any hardware modification of commercial off-the-shelf (COTS) processors. ED⁴I (error detection by data diversity and duplicated instructions) is a SIHFT technique that detects both permanent and temporary errors by executing two "different" programs (with the same functionality) and comparing their outputs. ED⁴I maps each number, x, in the original program into a new number x\´, and then transforms the program so that it operates on the new numbers so that the results can be mapped backwards for comparison with the results of the original program. The mapping in the transformation of ED⁴I is x\´ = k·x for integer numbers, where k_f determines the fault detection probability and data integrity of the system. For floating-point numbers, we find a value of k_f for the fraction and k_e for the exponent separately, and use k = k_f×2^k for the value of k. We have demonstrated how to choose an optimal value of k for the transformation. This paper shows that, for integer programs, the transformation with k = -2 was the most desirable choice in six out of seven benchmark programs we simulated. It maximizes the fault detection probability under the condition that the data integrity is highest