AxRMs: Approximate Recursive Multipliers Using High-Performance Building Blocks

Recursive multipliers (RMs) have been classified as a class of low-power multipliers because they provide a wide-range of power-quality configuration options. 2×2 multipliers are the constitutional building blocks of this recursive topology; however, most of the state-of-the-art approximate recursive designs are based on a 4×4 building blocks. Therefore, the design space exploration of AxRMs using 2×2 multipliers is still an open-research problem. To add the configurability and flexibility in the design of AxRMs such 2-bit multipliers are required that exhibit high-performance and low-area. In this article, two approximate 2×2 multipliers are proposed that exhibit double-sided error distribution feature. Compared to the existing best-approximated 2×2 multiplier, the proposed design achieves a reduction of 52 percent in area and exhibits an improvement of 25 percent in terms of delay while having a bounded error behavior. Then, three 8×8 multipliers of variable accuracy are designed using different configurations of approximate 2×2 multiplier. AxRM1 is the most-accurate design; an improvement of 50 percent in terms of mean relative error distance (MRED) is achieved compared to the existing best MRED-optimized design. AxRM3 has similar MRED compared to the previous best 2×2-based AxRM (called MACISH); however, AxRM3 exhibits 13 percent better PDP than MACISH due to the use of low-power and high-performance 2×2 multipliers in building larger multipliers. The proposed approximate multipliers are applied to cutting-edge error-tolerant application, i.e., convolutional neural networks. AxRM2 provides the best quality-power trade-off, 32.64 percent power savings are achieved with 1.10 percent better classification accuracy.