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

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$68\times $ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.2\times $ </tex-math></inline-formula> less energy and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.2\times $ </tex-math></inline-formula> smaller area than the state-of-the-art design.