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Algorithm and Software Overhead: A Theoretical Approach to Performance Portability

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Parallel Processing and Applied Mathematics (PPAM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13827))

Abstract

In the last years, the portability term has enriched itself with new meanings: research communities are talking about how to measure the degree to which an application (or library, programming model, algorithm implementation, etc.) has become “performance portable”. The term “performance portability” has been informally used in computing communities to substantially refer to: (1) the ability to run one application across multiple hardware platforms; and (2) achieving some decent level of performance on these platforms [1, 2]. Among the efforts related to the “performance portability” issue, we note the annual performance portability workshops organized by the US Department of Energy [3]. This article intends to add a new point of view to the performance portability issue, starting from a more theoretical point of view, that shows the convenience of splitting the proper algorithm from the emphoverhead, and exploring the different factors that introduce different kind of overhead. The paper explores the theoretical framework to get a definition of the execution time of a software but that definition is not the point. The aim is to show and understand the link between that execution time and the beginning of the design, to exploit what part of any program is really environment-sensitive and exclude from performance portability formulas everything is not going to change, as theoretically shown.

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Notes

  1. 1.

    Decomposition matrix is the name we preferred in this work, but in [8] it is referred as dependency matrix.

  2. 2.

    These can be basic operations (arithmetic,\(\ldots \)), special functions evaluations (\(\sin ,\cos ,\ldots \)), solvers (integrals, equations system, non-linear equations\(\ldots \)).

  3. 3.

    For the general case, look at [12].

  4. 4.

    This assumption is necessary to compare two algorithms.

  5. 5.

    Scale Up is defined in [8] as the ratio \(SC(D_{k_i},D_{k_j}):=\frac{k_i}{k_j}\) and it measures the difference between the two algorithm respect to the number of operations they perform to solve the same problem.

  6. 6.

    This is an initial, not realistic, assumption.

  7. 7.

    There is no loss of generality because any operator can be rewritten as a number of elementary operators with execution time \(t_{calc}\).

  8. 8.

    This is a semplified and very general logical description of a memory hierarchy behavior useful to the aim of the framework. Of course it could be adapted to an actual architecture, but the following definitions hold the same.

  9. 9.

    Level 0 is the fastest one.

  10. 10.

    In general \(c_{AM}\le nd\), but we can assume \(c_{AM}=nd\) without loss of generality.

  11. 11.

    Meanly.

  12. 12.

    Meanly.

  13. 13.

    For example: in case of an algorithm like the one in [13], where the architecture is a heterogeneous GPU and Multicore based system, we can build different matrices for different parts of the algorithm.

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Authors and Affiliations

  1. University of Naples “Federico II”, Naples, Italy

    Valeria Mele & Giuliano Laccetti

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  1. Valeria Mele
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  2. Giuliano Laccetti
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Correspondence to Valeria Mele .

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Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  3. University of Southern California, Marina del Rey, CA, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Mele, V., Laccetti, G. (2023). Algorithm and Software Overhead: A Theoretical Approach to Performance Portability. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2022. Lecture Notes in Computer Science, vol 13827. Springer, Cham. https://doi.org/10.1007/978-3-031-30445-3_8

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