Low-Cost Duplicate Multiplication

Rising levels of integration, decreasing component re liabilities, and the ubiquity of computer systems make error protection a rising concern. Meanwhile, the uncertainty of future fault and error modes motivates the design of strong error detection mechanisms that offer fault-agnostic error protection. Current concurrent hardware mechanisms, however, either offer strong error detection coverage at high cost or restrict their coverage to narrow synthetic error models. This paper investigates the potential for duplication using alternate number systems to lower the costs of duplicated multiplication without sacrificing error coverage. Two examples of such low-cost duplication schemes are described and evaluated; it is shown that specialized carry-save or residue number system checking can be used to increase the efficiency of duplicated multiplication.