Skip to main content
SpringerLink
Log in

Error-Efficient Approximate Multiplier Design using Rounding Based Approach for Image Smoothing Application

  • Published:
Journal of Electronic Testing Aims and scope Submit manuscript

Abstract

We propose a novel, error-efficient approximate multiplier (EEAM), which is based on a rounding-based approach (RBA). Multiplication is performed using rounding, shift, and add operations. We round the input operands to the nearest power of two using RBA. The modified inputs are processed by an arithmetic block (AB), which consists of addition, subtraction, and shifter blocks. The proposed approximate multiplier has input operands whose widths range from 8-bit to 32-bits. We simulated the proposed multiplier by using Vivado and MATLAB. The proposed multiplier is also synthesized using the Cadence RTL compiler, and compared to prior approximate multiplier proposals, EEAM’s delay and energy consumption are about of 22% and 57% better than the best known approximate multipliers. We also show that the proposed approximate multiplier’s worst-case error, mean error distance, mean relative error distance, and normalized error distance are about 3%, 44%, 45%, and 13% improvement over existing approximate multipliers. Finally, we used the proposed approximate multiplier in an image smoothing filter., For this application, we observed that our multiplier provides higher PSNR and SSIM than any prior approximate multiplier.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the Proposed and Existing Approximate Multipliers.

References

  1. Akbari O, Kamal M, Afzali-Kusha A, Pedram M (2018) CLA: A reconfigurable approximate carry look-ahead adder. IEEE Transaction Circuits Systems II, Express 65(8):1089–1093

    Google Scholar 

  2. Barrois B, Sentieys O, Menard D (2017) The hidden cost of functional approximation against careful data sizing: a case study. In Proc. of Proceedings of Design, Automation & Test in Europe Conference & Exhibition (DATE), IEEE. pp. 181–186

  3. Garg B, Patel SK, Dutt S (2020) LoBA: a leading one bit based imprecise multiplier for efficient image processing. J Electron Test 36:429–437

    Article  Google Scholar 

  4. Garg B, Sharma G (2016) A quality-aware energy-scalable Gaussian smoothing filter for image processing applications. Microprocessors Microsystems 45:1–9

    Article  Google Scholar 

  5. Han J, Orshansky M (2013) Approximate computing: An emerging paradigm for energy-efficient design. In Proc. of 18th IEEE European Test Symposium (ETS), IEEE European, pp. 1–6

  6. Hashemi S, Bahar RI, Reda S (2015) DRUM: A dynamic range unbiased multiplier for approximate applications. In Proc. of IEEE/ACM International Conference Computing-Aided Design (ICCAD), IEEE Press. pp. 418–425

  7. Jagadeeswara RE, Samundiswary P (2021) A review of approximate multipliers and its applications. Advances in Automation, Signal Processing, Instrumentation, and Control Lecture Notes in Electrical Engineering. Springer, Singapore, pp 1381–1392

    Chapter  Google Scholar 

  8. Jiang H, Liu L, Lombardi F, Han J (2018) Approximate arithmetic circuits: Design and evaluation. Approximate Circuits, Springer, pp. 67–98

  9. Ko HJ, Hsiao SF (2011) Design and application of faithfully rounded and truncated multipliers with combined deletion, reduction, truncation, and rounding. IEEE Transaction Circuits Systems II, Express 58(5):304–308

    Google Scholar 

  10. Liang J, Han J, Lombardi F (2013) New metrics for the reliability of approximate and probabilistic adders. IEEE Transaction on Computer 62(9):1760–1771

    Article  MathSciNet  Google Scholar 

  11. Lingamneni A, Basu A, Enz C, Palem KV, Piguet C (2013) Improving energy gains of inexact DSP hardware through reciprocating error compensation. In Proc. of 50th ACM/EDAC/IEEE Design Automation Conference (DAC), IEEE. pp. 1–8

  12. Meng J, Chakradhar S, Raghunathan A (2009) Best-effort parallel execution framework for recognition and mining applications. In Proc. of International Symposium on Parallel & Distributed Processing, IEEE, pp. 1–12

  13. Mittal S (2016) A survey of techniques for approximate computing. ACM Comput Surv 48(4):1–4

    Google Scholar 

  14. Myler HR, Weeks AR (2009) The Pocket Handbook of Image Processing Algorithms in C. Englewood Cliffs, NJ, and USA: Prentice-Hall

  15. Narayanamoorthy S, Moghaddam HA, Liu Z, Park, T, Kim NS (2015) Energy-efficient approximate multiplication for digital signal processing and classification applications. IEEE Trans Very Large Scale Integr VLSI Syst 23(6):1180–1184

  16. Ramasubramanian SG, Venkataramani S, Parandhaman A, Raghunathan A (2013) Relax-and-retime: A methodology for energy-efficient recovery based design. In Proc. of 50th ACM/EDAC/IEEE Design Automation Conference (DAC), IEEE. pp. 111–117.

  17. Vahdat S, Kamal M, Afzali-Kusha A, Pedram M (2017) LETAM: A low energy truncation-based approximate multiplier. Comput Electr Eng 63:1–17

    Article  Google Scholar 

  18. Vahdat S, Kamal M, Afzali-Kusha A, Pedram M (2019) TOSAM: An Energy-Efficient Truncation and Rounding-Based Scalable Approximate Multiplier. IEEE Trans Very Large Scale Integr VLSI Syst 27(5):1161-1173

  19. Venkataramani S, Chakradhar ST, Roy K, Raghunathan A (2015) Approximate computing and the quest for computing efficiency. In Proc. of 52nd ACM/EDAC/IEEE of Design Automation Conference (DAC), IEEE Press, pp. 121–126

  20. Venkataramani S, Chippa VK, Chakradhar ST, Roy K, Raghunathan A (2013) Quality programmable vector processors for approximate computing. In Proc. of 46th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO), IEEE. pp. 1–12

  21. 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

    Article  Google Scholar 

  22. Zendegani R, Kamal M, Bahadori M, Afzali-Kusha A, Pedram M (2017) RoBa multiplier: A rounding-based approximate multiplier for high-speed yet energy-efficient digital signal processing. IEEE Trans Very Large Scale Integr VLSI Syst 25(2):393–401

Download references

Author information

Authors and Affiliations

  1. Department of Electronics Engineering, Pondicherry University, Kalapet, Puducherry, India

    E. Jagadeeswara Rao & P. Samundiswary

Authors
  1. E. Jagadeeswara Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Samundiswary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Jagadeeswara Rao.

Ethics declarations

Conflict of Interest

I certify that there is no actual or potential conflict of interest in relation to this article.

Additional information

Responsible editor: S. T. Chakradhar

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rao, E.J., Samundiswary, P. Error-Efficient Approximate Multiplier Design using Rounding Based Approach for Image Smoothing Application. J Electron Test 37, 623–631 (2021). https://doi.org/10.1007/s10836-021-05971-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10836-021-05971-z

Keywords

Search

Navigation