A Time Efficient Comprehensive Model of Approximate Multipliers for Design Space Exploration

Multipliers play an essential role in various data processing applications and have garnered significant attention in approximate computing (AxC) for their energy-efficient features. However, formulating a precise error model for approximate data processing algorithms in conjunction with hardware metrics presents a challenge, leading to substantial time consumption in the design space exploration. This paper introduces an analytical model for approximate multipliers while considering input patterns. This model furnishes accurate error metrics, along with high-precision hardware metrics for various approximate multiplier configurations, impervious to variations in input data distribution. The proposed error model reduces the runtime by an average factor of 120.85 and, in some instances, by as much as 2,500 times, when contrasted with simulation-based methods. The design space exploration is performed on a 3×3 convolution circuit, revealing a comparable Pareto-optimal set and substantial reductions of up to 79.46% in the Power-Delay-Product (PDP) and 71.98% in area compared to the accurate counterpart. Additionally, the result of the Gaussian Blur application experiment demonstrates a 68.59% reduction in PDP and a 56.21% reduction in area, all while maintaining a PSNR of 30 dB.