MACISH: Designing Approximate MAC Accelerators with Internal-Self-Healing

Approximate computing studies the quality-efficiency trade-off to attain a best-efficiency (e.g., area, latency, and power) design for a given quality constraint and vice versa. Recently, self-healing methodologies for approximate computing have emerged that showed an effective quality-efficiency trade-off as compared to the conventional error-restricted approximate computing methodologies. However, the state-of-the-art self-healing methodologies are constrained to highly parallel implementations with similar modules (or parts of a datapath) in multiples of two and for square-accumulate functions through the pairing of mirror versions to achieve error cancellation. In this paper, we propose a novel methodology for an internal-self-healing (ISH) that allows exploiting self-healing within a computing element internally without requiring a paired, parallel module, which extends the applicability to irregular/asymmetric datapaths while relieving the restriction of multiples of two for modules in a given datapath, as well as going beyond square functions. We employ our ISH methodology to design an approximate multiply-accumulate (xMAC), wherein the multiplier is regarded as an approximation stage and the accumulator as a healing stage. We propose to approximate a recursive multiplier in such a way that a near-to-zero average error is achieved for a given input distribution to cancel out the error at an accurate accumulation stage. To increase the efficacy of such a multiplier, we propose a novel 2 x 2 approximate multiplier design that alleviates the overflow problem within an n x n approximate recursive multiplier. The proposed ISH methodology shows a more effective quality-efficiency trade-off for an xMAC as compared with the conventional error-restricted methodologies for random inputs and for radio-astronomy calibration processing (up to 55% better quality output for equivalent-efficiency designs).