Algorithm-based fault tolerance for spaceborne computing: basis and implementations

We describe and test the mathematical background for using checksum methods to validate results returned by a numerical subroutine operating in a fault-prone environment that causes unpredictable errors in data. We can treat subroutines whose results satisfy a necessary condition of a linear form; the checksum tests compliance with this necessary condition. These checksum schemes are called algorithm-based fault tolerance (ABFT). We discuss the theory and practice of setting numerical tolerances to separate errors caused by a fault from those inherent in finite-precision numerical calculations. Two series of tests are described. The first tests the general effectiveness of the linear ABFT schemes we propose, and the second verifies the correct behavior of our parallel implementation of them. We find that under simulated fault conditions, it is possible to choose a fault detection scheme that for average case matrices can detect 99% of faults with no false alarms, and that for a "worst-case" matrix population can detect 80% of faults with no false alarms.