VLSI Architectures of Approximate Arithmetic Units Applied to Parallel Sensors Calibration

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 71; no. 3; pp. 1 - 0
• Main Authors: da Rosa, Morgana Macedo Azevedo, da Costa, Patricia Ucker Leleu, da Costa, Eduardo Antonio Cesar, Soares, Rafael I., Bampi, Sergio
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adders; Algorithms; Approximation algorithms; Arithmetic; Arithmetic and logic units; AxPPA; AxRMU; AxRSU; Calibration; Circuit design; Coders; Dividers; Goldschmidt; Iterative methods; Mathematical analysis; Newton-Raphson; Operators; Parameters; Radio astronomy; Sensors; Signal processing algorithms; SquASH; State of the art; StEFCal; Tradeoffs; Very large scale integration; VLSI
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2023.3331675

Approximate computing maximizes area and energy savings for a trade-off between quality and efficiency. Approximate arithmetic operators have emerged as an efficient alternative to design low-power VLSI circuits. This paper investigates the design of approximate arithmetic operator units used in the calibration procedure for radio astronomy light sensors - the so-called StEFCal (statistically efficient and fast calibration) method. The StEFCal algorithm comprises arithmetic operations like a divider, square-accumulate (SAC), and multiply-accumulate (MAC) units. The StEFCal circuit of this work explores the following arithmetic operators: i) two approximate squarer units from the literature, i.e., radix-4 (AxRSU) and SquASH, ii) two approximate iterative-based Newton-Raphson (NR) and Goldschmidt (GLD) dividers, iii) one approximate parallel prefix adder (AxPPA), and iv) a new approximate radix-4 multiplier (AxRMU), proposed in this work, explored in the StEFCal multiply-accumulate circuit design. The AxRSU utilizes the parameters <inline-formula> <tex-math notation="LaTeX">K1</tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">K2</tex-math> </inline-formula> to represent the number of exact encoders for squarer-and conventional-partial products, respectively, subsequently replaced with approximate encoders. The same principle applies to AxRMU, where the parameter <inline-formula> <tex-math notation="LaTeX">K</tex-math> </inline-formula> indicates the number of exact encoders for conventional-partial products, subsequently exchanged with approximate encoders. We demonstrate the efficiency of StEFCal using the approximate arithmetic operators from the Pareto-optimal front that expresses the area-and power-quality trade-off. The results show that using the AxRSU with <inline-formula> <tex-math notation="LaTeX">K1=4</tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">K2=6</tex-math> </inline-formula>, AxRMU, and AxPPA with <inline-formula> <tex-math notation="LaTeX">K=16</tex-math> </inline-formula> and NR with one iteration has an MSE equal to <inline-formula> <tex-math notation="LaTeX">89.98</tex-math> </inline-formula>dB and offers up to <inline-formula> <tex-math notation="LaTeX">158\times</tex-math> </inline-formula> energy-savings compared to the exact StEFCal, and up to <inline-formula> <tex-math notation="LaTeX">25\times</tex-math> </inline-formula> more energy-savings and <inline-formula> <tex-math notation="LaTeX">3.33\times</tex-math> </inline-formula> area-savings compared with our previous work, <inline-formula> <tex-math notation="LaTeX">440\times</tex-math> </inline-formula> energy-savings compared to the accurate state-of-the-art, and <inline-formula> <tex-math notation="LaTeX">258\times</tex-math> </inline-formula> compared with the approximate state-of-the-art.