Tolerance determination for algorithm-based checks using simplified error analysis techniques

A scheme for dealing with roundoff errors in algorithm-based fault tolerance methods which complicate the check phases of the algorithm is presented. The method is based on error analysis incorporating some simplifications which result in easier derivation of error bounds and more useful error expressions in some cases where the theoretical error bound may be too wide to be of much use as a tolerance in the check phase. The methods are used to derive error bounds for three applications, and it is shown that the fault-tolerant encodings for these applications using the authors error expressions achieve high error coverage and no false alarms for a wide spectrum of data sets at low overheads. The authors contrast their tolerance bound calculation method with an earlier method and show that their method is much more robust. The authors believe that, to be of practical use, algorithm-based fault-tolerance techniques need to pay close attention to the thresholding issue, and they point out that their scheme is the first one which achieves good results across a wide range of data sets.