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Tests and tolerances for high-performance software-implemehted fault detection

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4 Author(s)
Turmon, M. ; Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA ; Granat, R. ; Katz, D.S. ; Lou, J.Z.

We describe and test a software approach to fault detection in common numerical algorithms. Such result checking or algorithm-based fault tolerance (ABFT) methods may be used, for example, to overcome single-event upsets in computational hardware or to detect errors in complex, high-efficiency implementations of the algorithms. Following earlier work, we use checksum methods to validate results returned by a numerical subroutine operating subject to unpredictable errors in data. We consider common matrix and Fourier algorithms which return results satisfying a necessary condition having a linear form; the checksum tests compliance with this condition. We discuss the theory and practice of setting numerical tolerances to separate errors caused by a fault from those inherent in finite-precision floating-point calculations. We concentrate on comprehensively defining and evaluating tests having various accuracy/computational burden tradeoffs, and we emphasize average-case algorithm behavior rather than using worst-case upper, bounds on error.

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Computers, IEEE Transactions on  (Volume:52 ,  Issue: 5 )