Algorithm-based fault tolerance for floating-point operations in massively parallel systems

Considers the applicability of algorithm-based fault tolerance (ABFT) to massively parallel scientific computation. Existing ABFT schemes can provide effective fault tolerance at a low cost for computation on matrices of moderate size; however, the methods do not scale well to floating-point operations on large systems. The authors propose the use of a partitioned linear encoding scheme to provide scalability. Matrix algorithms employing this scheme are presented and compared to current ABFT schemes with respect to numerical stability and hardware/time overhead. The partitioned scheme is shown to provide scalable linear codes with improved numerical properties with only s small increase in hardware and time overhead. The partitioned approach prevents overflow in encoding and can preserve the reflectivity of codes, while guarding against roundoff error in encoding. The sharper bound on numerical encoding error allows the method to provide more complete fault coverage