DRUM: A Dynamic Range Unbiased Multiplier for approximate applications

Many applications for signal processing, computer vision and machine learning show an inherent tolerance to some computational error. This error resilience can be exploited to trade off accuracy for savings in power consumption and design area. Since multiplication is an essential arithmetic operation for these applications, in this paper we focus specifically on this operation and propose a novel approximate multiplier with a dynamic range selection scheme. We design the multiplier to have an unbiased error distribution, which leads to lower computational errors in real applications because errors cancel each other out, rather than accumulate, as the multiplier is used repeatedly for a computation. Our approximate multiplier design is also scalable, enabling designers to parameterize it depending on their accuracy and power targets. Furthermore, our multiplier benefits from a reduction in propagation delay, which enables its use on the critical path. We theoretically analyze the error of our design as a function of its parameters and evaluate its performance for a number of applications in image processing, and machine classification. We demonstrate that our design can achieve power savings of 54% - 80%, while introducing bounded errors with a Gaussian distribution with near-zero average and standard deviations of 0.45% - 3.61%. We also report power savings of up to 58% when using the proposed design in applications. We show that our design significantly outperforms other approximate multipliers recently proposed in the literature.

I. Introduction

In the recent years, power efficiency has emerged as one of the most critical goals of hardware design. Enormous efforts have already been devoted to improve the power consumption in various levels from algorithmic and software level down to circuit and transistor level. Emerging applications in digital signal processing, computer vision, and machine learning have created new power consumption challenges due to their high computational demands. At the same time, these applications also afford new opportunities for novel low-power implementations. In particular, the common feature of these application domains is an inherent tolerance for limited and insignificant inaccuracies. This error tolerance arises for multiple reasons, including imperfect perception in human sense, noisy input signal, redundancy in the input data or the absence of a universal best answer [1]. This inherent error tolerance can be exploited using approximate computing, which effectively allows designers to trade off computational accuracy for savings in power consumption and computational complexity.