Design of Novel CMOS Based Inexact Subtractors and Dividers for Approximate Computing: An In-Depth Comparison with PTL Based Designs

Multimedia applications consume an immense amount of energy. These applications have division as one of the fundamental operations. Division is also one of the costliest operations in terms of energy consumption. Thus, various works have been done to address the issue of energy consumption in multimedia applications by using approximate dividers based on pass transistor logic (PTL). Since these applications have resilience towards erroneous computations huge energy benefits are obtained as a result of approximate computations with similar output quality. In this paper, we have shown that PTL based designs are not suitable for lower technology nodes. We performed an in-depth analysis using UMC 65nm and UMC 28nm to highlight the adverse effects of technology scaling on energy consumption and delay in PTL based design as compared to CMOS based designs. We also propose four different inexact CMOS subtractor (ICS) designs, as they are the basic repeated module in inexact restoring array dividers (IRADs). Our proposed ICS designs consume ~ 2× lesser dynamic energy, ~ 3× lesser static power and have ~ 2.5× lesser delay as compared to the existing PTL based designs in UMC 65nm. These benefits increase for UMC 28nm, which shows PTL based designs further worsens at lower technology nodes. IRADs also give about 50% reduction in energy consumption with only 3% degradation in Structural Similarity (SSIM) Index, an image quality metric in multimedia applications like change detection, background removal, and JPEG compression, as compared to exact restoring array divider (ERAD).

[1]  Kaushik Roy,et al.  MACACO: Modeling and analysis of circuits for approximate computing , 2011, 2011 IEEE/ACM International Conference on Computer-Aided Design (ICCAD).

[2]  Osman Hasan,et al.  Probabilistic Error Analysis of Approximate Adders and Multipliers , 2019, Approximate Circuits.

[3]  Zhou Wang,et al.  On the Mathematical Properties of the Structural Similarity Index , 2012, IEEE Transactions on Image Processing.

[4]  Detlev Marpe,et al.  Performance comparison of H.265/MPEG-HEVC, VP9, and H.264/MPEG-AVC encoders , 2013, 2013 Picture Coding Symposium (PCS).

[5]  Fabrizio Lombardi,et al.  Approximate XOR/XNOR-based adders for inexact computing , 2013, 2013 13th IEEE International Conference on Nanotechnology (IEEE-NANO 2013).

[6]  Fabrizio Lombardi,et al.  A Review, Classification, and Comparative Evaluation of Approximate Arithmetic Circuits , 2017, ACM J. Emerg. Technol. Comput. Syst..

[7]  Joycee Mekie,et al.  Energy and Error Analysis Framework for Approximate Computing in Mobile Applications , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Alexander Fish,et al.  An 800-MHz Mixed- $V_{\text{T}}$ 4T IFGC Embedded DRAM in 28-nm CMOS Bulk Process for Approximate Storage Applications , 2018, IEEE Journal of Solid-State Circuits.

[9]  Fabrizio Lombardi,et al.  Inexact designs for approximate low power addition by cell replacement , 2016, 2016 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[10]  Fabrizio Lombardi,et al.  Design, Evaluation and Application of Approximate High-Radix Dividers , 2018, IEEE Transactions on Multi-Scale Computing Systems.

[11]  Fabrizio Lombardi,et al.  Approximate Arithmetic Circuits: Design and Evaluation , 2019, Approximate Circuits.

[12]  Rahul Boyapati,et al.  APPROX-NoC: A data approximation framework for Network-on-Chip architectures , 2017, 2017 ACM/IEEE 44th Annual International Symposium on Computer Architecture (ISCA).

[13]  Chandan Kumar Jha,et al.  SEDA - Single Exact Dual Approximate Adders for Approximate Processors ∗ , 2019, 2019 56th ACM/IEEE Design Automation Conference (DAC).

[14]  Natalie D. Enright Jerger,et al.  Doppelgänger: A cache for approximate computing , 2015, 2015 48th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO).

[15]  Jing Li,et al.  Combining Restoring Array and Logarithmic Dividers into an Approximate Hybrid Design , 2018, 2018 IEEE 25th Symposium on Computer Arithmetic (ARITH).

[16]  Miodrag Potkonjak,et al.  Processors for mobile applications , 2000, Proceedings 2000 International Conference on Computer Design.

[17]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[18]  Sparsh Mittal,et al.  A Survey of Techniques for Approximate Computing , 2016, ACM Comput. Surv..

[19]  Fabrizio Lombardi,et al.  On the Design of Approximate Restoring Dividers for Error-Tolerant Applications , 2016, IEEE Transactions on Computers.

[20]  Kumar Y. B. Nithin,et al.  Design of Approximate Dividers for Error Tolerant Applications , 2018, 2018 IEEE 61st International Midwest Symposium on Circuits and Systems (MWSCAS).