Skip to main content
Top

2019 | OriginalPaper | Chapter

9. Automated Search-Based Functional Approximation for Digital Circuits

Authors : Lukas Sekanina, Zdenek Vasicek, Vojtech Mrazek

Published in: Approximate Circuits

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The problem of developing an approximate implementation of a given combinational circuit can be formulated as a multi-objective design problem and solved by means of a search algorithm. This approach usually provides many solutions showing high-quality tradeoffs between key design objectives; however, it is very computationally expensive. This chapter presents a general-purpose method based on genetic programming for an automated functional approximation of combinational circuits at the gate and register-transfer levels. It surveys relevant error metrics and circuit parameters that are typically optimized by genetic programming. A special attention is given to the techniques capable of providing formal guarantees in terms of error bounds and accelerating the search process. Case studies dealing with approximate implementations of arithmetic circuits and image operators are presented to highlight the quality of results obtained by the search-based functional approximation in completely different application domains.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Footnotes
1
Note that the SAT problem can be solved using a solver based on ROBDDs. By a SAT-based solver, we mean a variant of SAT algorithm typically based on DPLL backtracking operating at the level of CNF.
 
Literature
1.
go back to reference Ceska M, Matyas J, Mrazek V, Sekanina L, Vasicek Z, Vojnar T (2017) Approximating complex arithmetic circuits with formal error guarantees: 32-bit multipliers accomplished. In: Proceedings of 36th IEEE/ACM international conference on computer aided design. IEEE, Piscataway, pp 416–423 Ceska M, Matyas J, Mrazek V, Sekanina L, Vasicek Z, Vojnar T (2017) Approximating complex arithmetic circuits with formal error guarantees: 32-bit multipliers accomplished. In: Proceedings of 36th IEEE/ACM international conference on computer aided design. IEEE, Piscataway, pp 416–423
2.
go back to reference Chan WTJ, Kahng AB, Kang S, Kumar R, Sartori J (2013) Statistical analysis and modeling for error composition in approximate computation circuits. In: 31st IEEE international conference on computer design (ICCD), pp 47–53 Chan WTJ, Kahng AB, Kang S, Kumar R, Sartori J (2013) Statistical analysis and modeling for error composition in approximate computation circuits. In: 31st IEEE international conference on computer design (ICCD), pp 47–53
3.
go back to reference Chandrasekharan A, Soeken M, Große D, Drechsler R (2016) Precise error determination of approximated components in sequential circuits with model checking. In: Proceedings of DAC’16. ACM, New York, pp 129:1–129:6 Chandrasekharan A, Soeken M, Große D, Drechsler R (2016) Precise error determination of approximated components in sequential circuits with model checking. In: Proceedings of DAC’16. ACM, New York, pp 129:1–129:6
4.
go back to reference Chen TH, Alaghi A, Hayes JP (2014) Behavior of stochastic circuits under severe error conditions. Inf Technol 56:182–191 Chen TH, Alaghi A, Hayes JP (2014) Behavior of stochastic circuits under severe error conditions. Inf Technol 56:182–191
5.
go back to reference Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef
6.
go back to reference Hrbacek R, Mrazek V, Vasicek Z (2016) Automatic design of approximate circuits by means of multi-objective evolutionary algorithms. In: Proceedings of the 11th international conference on design and technology of integrated systems in nanoscale era. IEEE, Piscataway, pp 239–244 Hrbacek R, Mrazek V, Vasicek Z (2016) Automatic design of approximate circuits by means of multi-objective evolutionary algorithms. In: Proceedings of the 11th international conference on design and technology of integrated systems in nanoscale era. IEEE, Piscataway, pp 239–244
9.
go back to reference Jiang H, Liu C, Maheshwari N, Lombardi F, Han J (2016) A comparative evaluation of approximate multipliers. In: IEEE/ACM international symposium on nanoscale architectures. IEEE, Piscataway, pp 191–196 Jiang H, Liu C, Maheshwari N, Lombardi F, Han J (2016) A comparative evaluation of approximate multipliers. In: IEEE/ACM international symposium on nanoscale architectures. IEEE, Piscataway, pp 191–196
15.
go back to reference Miller JF, Thomson P, Fogarty T (1998) Designing electronic circuits using evolutionary algorithms. Arithmetic Circuits: A Case Study. Wiley, New York, pp 105–131 Miller JF, Thomson P, Fogarty T (1998) Designing electronic circuits using evolutionary algorithms. Arithmetic Circuits: A Case Study. Wiley, New York, pp 105–131
17.
go back to reference Mrazek V, Vasicek Z (2016) Automatic design of arbitrary-size approximate sorting networks with error guarantee. In: 2016 26th international workshop on power and timing modeling, optimization and simulation. IEEE Computer Society, Piscataway, pp 221–228 Mrazek V, Vasicek Z (2016) Automatic design of arbitrary-size approximate sorting networks with error guarantee. In: 2016 26th international workshop on power and timing modeling, optimization and simulation. IEEE Computer Society, Piscataway, pp 221–228
18.
go back to reference Mrazek V, Sarwar SS, Sekanina L, Vasicek Z, Roy K (2016) Design of power-efficient approximate multipliers for approximate artificial neural networks. In: Proceedings of the IEEE/ACM international conference on computer-aided design. ACM, New York, pp 811–817. https://doi.org/10.1145/2966986.2967021 Mrazek V, Sarwar SS, Sekanina L, Vasicek Z, Roy K (2016) Design of power-efficient approximate multipliers for approximate artificial neural networks. In: Proceedings of the IEEE/ACM international conference on computer-aided design. ACM, New York, pp 811–817. https://​doi.​org/​10.​1145/​2966986.​2967021
20.
go back to reference Nepal K, Li Y, Bahar RI, Reda S (2014) ABACUS: a technique for automated behavioral synthesis of approximate computing circuits. In: Proceedings of the conference on design, automation and test in Europe, EDA consortium, DATE’14, pp 1–6 Nepal K, Li Y, Bahar RI, Reda S (2014) ABACUS: a technique for automated behavioral synthesis of approximate computing circuits. In: Proceedings of the conference on design, automation and test in Europe, EDA consortium, DATE’14, pp 1–6
23.
go back to reference Sekanina L, Vasicek Z (2013) Approximate circuits by means of evolvable hardware. In: 2013 IEEE international conference on evolvable systems, IEEE CIS, Proceedings of the 2013 IEEE symposium series on computational intelligence (SSCI), pp 21–28 Sekanina L, Vasicek Z (2013) Approximate circuits by means of evolvable hardware. In: 2013 IEEE international conference on evolvable systems, IEEE CIS, Proceedings of the 2013 IEEE symposium series on computational intelligence (SSCI), pp 21–28
24.
go back to reference Sekanina L, Vasicek Z, Mrazek V (2017) Approximate circuits in low-power image and video processing: the approximate median filter. Radioengineering 26(3):623–632CrossRef Sekanina L, Vasicek Z, Mrazek V (2017) Approximate circuits in low-power image and video processing: the approximate median filter. Radioengineering 26(3):623–632CrossRef
27.
go back to reference Vasicek Z, Sekanina L (2007) An area-efficient alternative to adaptive median filtering in FPGAs. In: Proceedings of 2007 international conference on field programmable logic and applications. IEEE, Piscataway, pp 216–221CrossRef Vasicek Z, Sekanina L (2007) An area-efficient alternative to adaptive median filtering in FPGAs. In: Proceedings of 2007 international conference on field programmable logic and applications. IEEE, Piscataway, pp 216–221CrossRef
28.
go back to reference Vasicek Z, Sekanina L (2011) A global postsynthesis optimization method for combinational circuits. In: Proceedings of the design, automation and test in Europe DATE 2011, EDAA, pp 1525–1528 Vasicek Z, Sekanina L (2011) A global postsynthesis optimization method for combinational circuits. In: Proceedings of the design, automation and test in Europe DATE 2011, EDAA, pp 1525–1528
29.
go back to reference Vasicek Z, Sekanina L (2014) Evolutionary design of approximate multipliers under different error metrics. In: IEEE international symposium on design and diagnostics of electronic circuits and systems. IEEE, Piscataway, pp 135–140 Vasicek Z, Sekanina L (2014) Evolutionary design of approximate multipliers under different error metrics. In: IEEE international symposium on design and diagnostics of electronic circuits and systems. IEEE, Piscataway, pp 135–140
31.
go back to reference Vasicek Z, Sekanina L (2016) Evolutionary design of complex approximate combinational circuits. Genet Program Evolvable Mach 17(2):1–24CrossRef Vasicek Z, Sekanina L (2016) Evolutionary design of complex approximate combinational circuits. Genet Program Evolvable Mach 17(2):1–24CrossRef
32.
go back to reference Vasicek Z, Slany K (2012) Efficient phenotype evaluation in Cartesian genetic programming. In: Proceedings of the 15th European conference on genetic programming. LNCS, vol 7244. Springer, Berlin, pp 266–278 Vasicek Z, Slany K (2012) Efficient phenotype evaluation in Cartesian genetic programming. In: Proceedings of the 15th European conference on genetic programming. LNCS, vol 7244. Springer, Berlin, pp 266–278
35.
go back to reference Venkataramani S, Roy K, Raghunathan A (2013) Substitute-and-simplify: a unified design paradigm for approximate and quality configurable circuits. In: Design, automation and test in Europe, DATE’13, EDA consortium, pp 1367–1372 Venkataramani S, Roy K, Raghunathan A (2013) Substitute-and-simplify: a unified design paradigm for approximate and quality configurable circuits. In: Design, automation and test in Europe, DATE’13, EDA consortium, pp 1367–1372
36.
go back to reference Venkatesan R, Agarwal A, Roy K, Raghunathan A (2011) MACACO: modeling and analysis of circuits for approximate computing. In: 2011 IEEE/ACM international conference on computer-aided design (ICCAD). IEEE, Piscataway, pp 667–673CrossRef Venkatesan R, Agarwal A, Roy K, Raghunathan A (2011) MACACO: modeling and analysis of circuits for approximate computing. In: 2011 IEEE/ACM international conference on computer-aided design (ICCAD). IEEE, Piscataway, pp 667–673CrossRef
Metadata
Title
Automated Search-Based Functional Approximation for Digital Circuits
Authors
Lukas Sekanina
Zdenek Vasicek
Vojtech Mrazek
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-99322-5_9