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

• Published in: IEEE transactions on computers Vol. 52; no. 5; pp. 579 - 591
• Main Authors: Turmon, M., Granat, R., Katz, D.S., Lou, J.Z.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computation; Computer fault tolerance; Error analysis; Errors; Fault detection; Fault tolerance; Floating point arithmetic; Mathematical models; Parallel algorithms; Roundoff errors; Software fault tolerance; Tolerances
• ISSN: 0018-9340; 1557-9956
• DOI: 10.1109/TC.2003.1197125

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.