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A new technique is proposed for fault-tolerant linear, sesquilinear andbijective (LSB) operations on $M$ integer data streams ($M\geq3$), such as:scaling, additions/subtractions, inner or outer vector products, permutationsand convolutions. In the proposed method, the $M$ input integer data streamsare linearly superimposed to form $M$ numerically-entangled integer datastreams that are stored in-place of the original inputs. A series of LSBoperations can then be performed directly using these entangled data streams.The results are extracted from the $M$ entangled output streams by additionsand arithmetic shifts. Any soft errors affecting any single disentangled outputstream are guaranteed to be detectable via a specific post-computationreliability check. In addition, when utilizing a separate processor core foreach of the $M$ streams, the proposed approach can recover all outputs afterany single fail-stop failure. Importantly, unlike algorithm-based faulttolerance (ABFT) methods, the number of operations required for theentanglement, extraction and validation of the results is linearly related tothe number of the inputs and does not depend on the complexity of the performedLSB operations. We have validated our proposal in an Intel processor (Haswellarchitecture with AVX2 support) via fast Fourier transforms, circularconvolutions, and matrix multiplication operations. Our analysis andexperiments reveal that the proposed approach incurs between $0.03\%$ to $7\%$reduction in processing throughput for a wide variety of LSB operations. Thisoverhead is 5 to 1000 times smaller than that of the equivalent ABFT methodthat uses a checksum stream. Thus, our proposal can be used in fault-generatingprocessor hardware or safety-critical applications, where high reliability isrequired without the cost of ABFT or modular redundancy.

Reliable Linear, Sesquilinear and Bijective Operations On Integer Data Streams Via Numerical Entanglement