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Scaling Properties of Parallel Applications to Exascale

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Abstract

A detailed profile of exascale applications helps to understand the computation, communication and memory requirements for exascale systems and provides the insight necessary for fine-tuning the computing architecture. Obtaining such a profile is challenging as exascale systems will process unprecedented amounts of data. Profiling applications at the target scale would require the exascale machine itself. In this work we propose a methodology to extrapolate the exascale profile from experimental observations over datasets feasible for today’s machines. Extrapolation models are carefully selected by means of statistical techniques and a high-level complexity analysis is included in the selection process to speed up the learning phase and to improve the accuracy of the final model. We extrapolate run-time properties of the target applications including information about the instruction mix, memory access pattern, instruction-level parallelism, and communication requirements. Compared to state-of-the-art techniques, the proposed methodology reduces the prediction error by an order of magnitude on the instruction count and improves the accuracy by up to 1.3\(\times \) for the memory access pattern, and by more than 2\(\times \) for the communication requirements.

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Notes

  1. In theory, one may generate also predictions of worst and best case executions, but this exceeds the scope of this paper.

  2. During crossvalidation, the error for a given metric is measured relative to the difference between its maximum and minimum values in the training set. This approach avoids giving too much weight to runs with small values of \(\theta (\varvec{n})\).

  3. Decreasing trends are handled in a similar way, but are rarely found in practice.

  4. The relative error can be written as \(\hat{a}(\varvec{n})/a(\varvec{n})-1 \) and it measures 900 % when \(\hat{a}\) is 10 times larger than \(a\) and \(-90\) % when \(\hat{a}\) is 10 times smaller than \(a\).

  5. We adopt the default configuration available in the Mathematica environment [29].

  6. For these metrics the SOTA method refers to the same extrapolation technique used for the instruction count mix proposed by Calotoiu et al. [9].

  7. There are 512 sub-bands, each partitioned in 512 channels.

  8. Construction of the SKA is planned to begin in 2018. At that point in time, different Xeon-like architectures may be available providing different computational power.

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Acknowledgments

This work is conducted in the context of the joint ASTRON and IBM DOME project and is funded by the Netherlands Organisation for Scientific Research (NWO), the Dutch Ministry of EL&I, and the Province of Drenthe.

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Authors and Affiliations

  1. IBM Research, Dwingeloo, The Netherlands

    Giovanni Mariani & Rik Jongerius

  2. IBM Research – Zurich, Rüschlikon, Switzerland

    Andreea Anghel & Gero Dittmann

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  1. Giovanni Mariani
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  2. Andreea Anghel
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  3. Rik Jongerius
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Correspondence to Giovanni Mariani.

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Mariani, G., Anghel, A., Jongerius, R. et al. Scaling Properties of Parallel Applications to Exascale. Int J Parallel Prog 44, 975–1002 (2016). https://doi.org/10.1007/s10766-016-0412-y

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