AxMOD: VLSI Modular Reduction Design Exploring Approximate Arithmetic Units

This work investigates the design of approximate arithmetic operator units used in the VLSI modular reduction (AxMOD) architecture. The AxMOD architecture herein proposed explores the following arithmetic operators: i) two approximate iterative-based fixed-point and Goldschmidt (GLD) dividers, ii) five approximate adders (AxA): COPY adder, error-tolerant adder (ETA), lower-part OR adder (LOA), truncation (Trunc), and approximate parallel prefix adder (AxPPA), and iii) five approximate multipliers of approximate radix-4 multiplier units (AxRMU), dynamic range unbiased multiplier (DRUM), rounding-based approximate (RoBA), truncated multiplier (Trunc), and the leading one-bit based approximate (LoBA). Our demonstration of AxMOD’s efficiency using approximate arithmetic operators from the Pareto-optimal front illustrates the area and power-quality trade-off. Our results reveal that in fixed-point arithmetic, AxRMU with K = 16 and Trunc adder with K = 8 deliver energy savings of up to 4.14× compared to the state-of-the-art.