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When Are Software Verification Results Valid for Approximate Hardware?

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Tests and Proofs (TAP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11823))

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Abstract

Approximate computing (AC) is an emerging paradigm for energy-efficient computation. The basic idea of AC is to sacrifice high precision for low energy by allowing hardware to carry out only “approximately correct” calculations. This provides a major challenge for software quality assurance: Programs successfully verified to be correct might be erroneous on approximate hardware.

In this paper, we present a novel approach for determining under what conditions a software verification result is valid for approximate hardware. To this end, we compute the allowed tolerances for AC hardware from successful verification runs. More precisely, we derive a set of constraints which – when met by the AC hardware – guarantee that the verification result carries over to AC. Our approach is based on the framework of abstract interpretation. Furthermore, we show (1) how to practically extract tolerances from verification runs employing predicate abstraction, and (2) how to check such constraints on hardware designs. We have implemented all techniques, and exemplify them on example C programs and a number of recently proposed approximate adders.

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901).

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Notes

  1. 1.

    For the practical evaluation we, however, allow arbitrary C programs.

  2. 2.

    The operation of interest is made configurable in CPAchecker.

  3. 3.

    A generalization to a family of constraints is straightforward.

  4. 4.

    Some additions first had to be brought into three-address code form and in some programs we replaced some constant assignments by proper addition.

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Authors and Affiliations

  1. Paderborn University, Paderborn, Germany

    Tobias Isenberg, Felix Pauck & Heike Wehrheim

  2. TU Darmstadt, Darmstadt, Germany

    Marie-Christine Jakobs

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  1. Tobias Isenberg
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  2. Marie-Christine Jakobs
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  3. Felix Pauck
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  4. Heike Wehrheim
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Correspondence to Heike Wehrheim .

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Editors and Affiliations

  1. Ludwig-Maximilians-Universität München, Munich, Germany

    Dirk Beyer

  2. University of Paris-Sud, Orsay, France

    Chantal Keller

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Isenberg, T., Jakobs, MC., Pauck, F., Wehrheim, H. (2019). When Are Software Verification Results Valid for Approximate Hardware?. In: Beyer, D., Keller, C. (eds) Tests and Proofs. TAP 2019. Lecture Notes in Computer Science(), vol 11823. Springer, Cham. https://doi.org/10.1007/978-3-030-31157-5_1

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  • DOI: https://doi.org/10.1007/978-3-030-31157-5_1

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