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Probabilistic Error Analysis of Approximate Adders and Multipliers

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Approximate Circuits

Abstract

Approximate adders and multipliers are widely being advocated to be used in error resilient applications. A very important performance metric in this regard is the probability of occurrence of error in these arithmetic circuits as this allows us to choose the most efficient configuration of an adder or multiplier for a given application. In this chapter, we present an analytical error analysis approach for approximate adders, which comprise of subadder units, and recursive approximate multipliers with approximate partial products. We also derive probability mass function (PMF) of error for both of the considered adder and multiplier models. The results show that the proposed analysis serves as an effective tool for predicting, evaluating, and comparing the accuracy of various approximate adders and multipliers. For illustration purposes, we also show that the comparative performance of different approximate adders and multipliers can be correctly predicted in practical applications of image processing.

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Notes

  1. 1.

    Another class of inexact computing is probabilistic computing, in which probabilistic switches are used, so that, in addition to the random inputs, the circuit’s function is also random [22].

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Sana Mazahir

  2. School of Electrical Engineering and Computer Science, National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Muhammad Kamran Ayub & Osman Hasan

  3. Institute of Computer Engineering, Vienna University of Technology (TU Wien), Vienna, Austria

    Muhammad Shafique

Authors
  1. Sana Mazahir
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  2. Muhammad Kamran Ayub
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  3. Osman Hasan
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  4. Muhammad Shafique
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Corresponding author

Correspondence to Sana Mazahir .

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Editors and Affiliations

  1. Brown University, Rhode Island, Providence, USA

    Sherief Reda

  2. Vienna University of Technology, Wien, Wien, Austria

    Muhammad Shafique

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Mazahir, S., Ayub, M.K., Hasan, O., Shafique, M. (2019). Probabilistic Error Analysis of Approximate Adders and Multipliers. In: Reda, S., Shafique, M. (eds) Approximate Circuits. Springer, Cham. https://doi.org/10.1007/978-3-319-99322-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-99322-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99321-8

  • Online ISBN: 978-3-319-99322-5

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