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Erschienen in: Journal of Electronic Testing 5/2022

17.10.2022

Efficient Design of Rounding-Based Approximate Multiplier Using Modified Karatsuba Algorithm

verfasst von: E. Jagadeeswara Rao, K. Tarakeswara Rao, K. Sudha Ramya, D. Ajaykumar, R. Trinadh

Erschienen in: Journal of Electronic Testing | Ausgabe 5/2022

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Abstract

Arithmetic operations play a substantial role in many applications, such as image processing. In image processing applications, a multiplier is a predominantly used arithmetic operation. In recent designs of Approximate Multipliers (AMs), the design metrics of multipliers are made better at the cost of Error metrics and vice versa. So, in order to balance both the error and design metrics in a multiplier design with increasing the width of the input operands, a Rounding-based AM (RAM) using a modified Karatsuba algorithm is proposed, in which the usage of the number of multipliers is reduced. Small multipliers are used with shifting and rounding operations so as to reduce power consumption, delay, and area. Both the prior and proposed AMs are later synthesized in Verilog HDL using the Cadence RTL compiler. The simulation results divulge that the proposed RAM of sizes 8 and 16 bits are designed and their performance metrics in terms of delay, and area are decreased on an average of 61.8%, and 52.6% with an improvement in power by 53.8% for 8-bit AM and also the delay, area and power are reduced on an average of 53.2%, 59.7%, and 25% for a 16-bit AM’s, in comparison with the prior AMs. The proposed RAM is demonstrated using the smoothening image application, and we observe that an improved image quality is obtained with SSIM and PSNR of the ISFA incorporated proposed RAM within the range of 1.44%—84.47% and 0.28%- 24.4%, over the ISFA incorporated existing AMs.
Literatur
1.
Zurück zum Zitat Jain R, Pandey N (2021) Approximate Karatsuba multiplier for error-resilient applications. AEU-Int J Electron Commun 130:153–579 CrossRef Jain R, Pandey N (2021) Approximate Karatsuba multiplier for error-resilient applications. AEU-Int J Electron Commun 130:153–579 CrossRef
2.
Zurück zum Zitat Hashemi S, Bahar RI, Reda S (2015) DRUM: A dynamic range unbiased multiplier for approximate applications. In: Proc. of IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, pp. 418–25 Hashemi S, Bahar RI, Reda S (2015) DRUM: A dynamic range unbiased multiplier for approximate applications. In: Proc. of IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, pp. 418–25
3.
Zurück zum Zitat Zendegani R, Kamal M, Bahadori M, Afzali-Kusha A, Pedram M (2016) RoBA multiplier: A rounding-based approximate multiplier for high-speed yet energy-efficient digital signal processing. IEEE Transact Very Large Scale Integr (VLSI) Syst 25(2):393–401 CrossRef Zendegani R, Kamal M, Bahadori M, Afzali-Kusha A, Pedram M (2016) RoBA multiplier: A rounding-based approximate multiplier for high-speed yet energy-efficient digital signal processing. IEEE Transact Very Large Scale Integr (VLSI) Syst 25(2):393–401 CrossRef
4.
Zurück zum Zitat Akhlaghi V, Gao S, Gupta RK (2018) Lemax: learning-based energy consumption minimization in approximate computing with quality guarantee. In: Proc. of the 55th Annual Design Automation Conference. IEEE, pp. 1–6 Akhlaghi V, Gao S, Gupta RK (2018) Lemax: learning-based energy consumption minimization in approximate computing with quality guarantee. In: Proc. of the 55th Annual Design Automation Conference. IEEE, pp. 1–6
5.
Zurück zum Zitat Babič Z, Avramovič A, Bulič P (2008) An iterative Mitchell's algorithm based multiplier. In: Proc. of IEEE International Symposium on Signal Processing and Information Technology. IEEE, pp. 303–308 Babič Z, Avramovič A, Bulič P (2008) An iterative Mitchell's algorithm based multiplier. In: Proc. of IEEE International Symposium on Signal Processing and Information Technology. IEEE, pp. 303–308
6.
Zurück zum Zitat Bhardwaj K, Mane PS, Henkel J (2014) Power-and area-efficient approximate Wallace tree multiplier for error-resilient systems. In: Proc. of Fifteenth International Symposium on Quality Electronic Design. IEEE, pp. 263–269 Bhardwaj K, Mane PS, Henkel J (2014) Power-and area-efficient approximate Wallace tree multiplier for error-resilient systems. In: Proc. of Fifteenth International Symposium on Quality Electronic Design. IEEE, pp. 263–269
7.
Zurück zum Zitat Garg B, Sharma GK (2017) ACM: An energy-efficient accuracy configurable multiplier for error-resilient applications. J Electron Test 33(4):479–489 CrossRef Garg B, Sharma GK (2017) ACM: An energy-efficient accuracy configurable multiplier for error-resilient applications. J Electron Test 33(4):479–489 CrossRef
8.
Zurück zum Zitat Kundi DES, Bian S, Khalid A, Wang C, O'Neill M, Liu W (2020) AxMM: Area and power efficient approximate modular multiplier for R-LWE cryptosystem. In: Proc. of IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, pp. 1–5 Kundi DES, Bian S, Khalid A, Wang C, O'Neill M, Liu W (2020) AxMM: Area and power efficient approximate modular multiplier for R-LWE cryptosystem. In: Proc. of IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, pp. 1–5
9.
Zurück zum Zitat Leon V, Zervakis G, Soudris D, Pekmestzi K (2017) Approximate hybrid high radix encoding for energy-efficient inexact multipliers. IEEE Transact Very Large Scale Integr (VLSI) Syst 26(3):421–430 CrossRef Leon V, Zervakis G, Soudris D, Pekmestzi K (2017) Approximate hybrid high radix encoding for energy-efficient inexact multipliers. IEEE Transact Very Large Scale Integr (VLSI) Syst 26(3):421–430 CrossRef
10.
Zurück zum Zitat Pandey D, Singh S, Mishra V, Satapathy S, Banerjee DS (2021) SAM: A Segmentation based Approximate Multiplier for Error Tolerant Applications. In: Proc. of IEEE International Symposium on Circuits and Systems (ISCAS), IEEE, pp. 1–5 Pandey D, Singh S, Mishra V, Satapathy S, Banerjee DS (2021) SAM: A Segmentation based Approximate Multiplier for Error Tolerant Applications. In: Proc. of IEEE International Symposium on Circuits and Systems (ISCAS), IEEE, pp. 1–5
11.
Zurück zum Zitat Vahdat S, Kamal M, Afzali-Kusha A, Pedram M (2017) LETAM: A low energy truncation-based approximate multiplier. Comput Electr Eng 63:1–17 CrossRef Vahdat S, Kamal M, Afzali-Kusha A, Pedram M (2017) LETAM: A low energy truncation-based approximate multiplier. Comput Electr Eng 63:1–17 CrossRef
12.
Zurück zum Zitat Chandaka S, Narayanam B (2022) Hardware Efficient Approximate Multiplier Architecture for Image Processing Applications. J Electron Test 38:217–230 CrossRef Chandaka S, Narayanam B (2022) Hardware Efficient Approximate Multiplier Architecture for Image Processing Applications. J Electron Test 38:217–230 CrossRef
13.
Zurück zum Zitat Garg B, Patel S (2021) Reconfigurable Rounding Based Approximate Multiplier for Energy-Efficient Multimedia Applications. Wireless Personal Commun 118:919–931 CrossRef Garg B, Patel S (2021) Reconfigurable Rounding Based Approximate Multiplier for Energy-Efficient Multimedia Applications. Wireless Personal Commun 118:919–931 CrossRef
14.
Zurück zum Zitat Garg B, Patel SK, Dutt S (2020) Loba: A leading one bit based imprecise multiplier for efficient image processing. J Electron Test 36(3):429–437 CrossRef Garg B, Patel SK, Dutt S (2020) Loba: A leading one bit based imprecise multiplier for efficient image processing. J Electron Test 36(3):429–437 CrossRef
15.
Zurück zum Zitat Gorantla A, Deepa P (2019) Design of approximate adders and multipliers for error tolerant image processing. Microprocess Microsyst 72:1–7 Gorantla A, Deepa P (2019) Design of approximate adders and multipliers for error tolerant image processing. Microprocess Microsyst 72:1–7
16.
Zurück zum Zitat Jothin R, Vasanthanayaki C (2018) High-Performance Modified Static Segment Approximate Multiplier based on Significance Probability. J Electron Test 34:607–614 CrossRef Jothin R, Vasanthanayaki C (2018) High-Performance Modified Static Segment Approximate Multiplier based on Significance Probability. J Electron Test 34:607–614 CrossRef
17.
Zurück zum Zitat Liang J, Han J, Lombardi F (2013) New metrics for the reliability of approximate and probabilistic adders. IEEE Transact Computer 62(9):1760–1771 MathSciNetCrossRefMATH Liang J, Han J, Lombardi F (2013) New metrics for the reliability of approximate and probabilistic adders. IEEE Transact Computer 62(9):1760–1771 MathSciNetCrossRefMATH
18.
Zurück zum Zitat Moons B, Verhelst M (2015) Dvas: Dynamic voltage accuracy scaling for increased energy-efficiency in approximate computing. In: Proc. of IEEE/ACM International Symposium on Low Power Electronics and Design (ISLPED). IEEE, pp. 237–242 Moons B, Verhelst M (2015) Dvas: Dynamic voltage accuracy scaling for increased energy-efficiency in approximate computing. In: Proc. of IEEE/ACM International Symposium on Low Power Electronics and Design (ISLPED). IEEE, pp. 237–242
19.
Zurück zum Zitat Vahdat S, Kamal M, Afzali-Kusha A, Pedram M (2019) TOSAM: An energy-efficient truncation-and rounding-based scalable approximate multiplier. IEEE Transact Very Large Scale Integr (VLSI) Systems 27(5):1161–1173 CrossRef Vahdat S, Kamal M, Afzali-Kusha A, Pedram M (2019) TOSAM: An energy-efficient truncation-and rounding-based scalable approximate multiplier. IEEE Transact Very Large Scale Integr (VLSI) Systems 27(5):1161–1173 CrossRef
20.
Zurück zum Zitat Jiang H, Santiago FJH, Mo H, Liu L, Han J (2020) Approximate Arithmetic Circuits: A Survey, Characterization, and Recent Applications. In: Proc. of the IEEE, 108(12):2108–2135 Jiang H, Santiago FJH, Mo H, Liu L, Han J (2020) Approximate Arithmetic Circuits: A Survey, Characterization, and Recent Applications. In: Proc. of the IEEE, 108(12):2108–2135
21.
Zurück zum Zitat Myler HR, Weeks AR (2009) The Pocket Handbook of Image Processing Algorithms in C. Englewood Cliffs, NJ, and USA: Prentice-Hall Myler HR, Weeks AR (2009) The Pocket Handbook of Image Processing Algorithms in C. Englewood Cliffs, NJ, and USA: Prentice-Hall
22.
Zurück zum Zitat Garg B, Sharma G (2016) A quality-aware energy-scalable Gaussian smoothing filter for image processing applications. Microprocess Microsyst 45:1–9 CrossRef Garg B, Sharma G (2016) A quality-aware energy-scalable Gaussian smoothing filter for image processing applications. Microprocess Microsyst 45:1–9 CrossRef
23.
Zurück zum Zitat Wang Z, Bovik A, Sheikh H, Simoncelli E (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612 CrossRef Wang Z, Bovik A, Sheikh H, Simoncelli E (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612 CrossRef
Metadaten
Titel
Efficient Design of Rounding-Based Approximate Multiplier Using Modified Karatsuba Algorithm
verfasst von
E. Jagadeeswara Rao
K. Tarakeswara Rao
K. Sudha Ramya
D. Ajaykumar
R. Trinadh
Publikationsdatum
17.10.2022
Verlag
Springer US
Erschienen in
Journal of Electronic Testing / Ausgabe 5/2022
Print ISSN: 0923-8174
Elektronische ISSN: 1573-0727
DOI
https://doi.org/10.1007/s10836-022-06029-4

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