Hardware-Efficient Logarithmic Floating-Point Multipliers for Error-Tolerant Applications

Zijing Niu, Tingting Zhang, Honglan Jiang, Bruce F. Cockburn, Leibo Liu, Jie Han

Abstract: The increasing computational intensity of important new applications poses a challenge for their use in resource-restricted devices. Approximate computing using power-efficient arithmetic circuits is one of the emerging strategies to reach this objective. In this article, five hardware-efficient logarithmic floating-point (FP) multipliers are proposed, which all use simple operators, such as adders and multiplexers, to replace complex and more costly conventional FP multipliers. Radix-4 logarithms are used to further reduce the hardware complexity. These designs produce double-sided error distributions to mitigate error accumulation in complex computations. The proposed multipliers provide superior trade-offs between accuracy and hardware, with up to 30.8% higher accuracy than a recent logarithmic FP design or up to $68\times $ less energy than the conventional FP multiplier. Using the proposed FP logarithmic multipliers in JPEG image compression achieves higher image quality than a recent logarithmic multiplier design with up to 4.7 dB larger peak signal-to-noise ratio. For training in benchmark NN applications, the proposed FP multipliers can slightly improve the classification accuracy while achieving $4.2\times $ less energy and $2.2\times $ smaller area than the state-of-the-art design.