Reliable floating-point arithmetic algorithms for error-coded operands

Reliable floating-point arithmetic is vital for dependable computing systems. It is also important for future high-density VLSI realizations that are vulnerable to soft-errors. However, the direct checking of floating-point arithmetic is still an open problem. The author presents a set of reliable floating-point arithmetic algorithms for low-cost residue encoded and Berger encoded operands, respectively. Closed form equations are derived for floating-point addition, subtraction, multiplication, and division. Given the standard IEEE floating-point numbers, the proposed reliable floating-point multiplication algorithms for low-cost residue encoded operands are extremely low-cost: it requires less than 8% of hardware redundancy in all cases. For reliable floating-point addition and subtraction, the author finds the hardware redundancy ratios of applying low-cost residue code is about the same as that of applying Berger code: less than 40% of hardware redundancy for single precision numbers and about 16% for double precision numbers. For reliable floating-point division, Berger encoded operands yields hardware cost-effectiveness: about 45% for single precision numbers and about 36% for double precision numbers.<
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