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Parameter Estimation via Time Modeling for MLIR Implementation of GEMM

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Optimization and Applications (OPTIMA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14395))

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Abstract

We consider the problem of identifying optimal parameters for two implementations of the general matrix multiplication (GEMM). Optimal parameters are chosen based on time modeling for two GEMM implementations, which is done by analyzing the structure of each implementation and the characteristics of the hardware. Each implementation has specific packing strategies that influence data movement and time of data access. The data movement, as well as constraints for the registers and each level of the two-level cache, is considered to ensure proper data usage. Based on the proposed models, an exhaustive search procedure for microkernel and tiling parameters was used to obtain the best parameters for each of the considered implementations of GEMM for multi-level intermediate representation (MLIR). The results show that the performance of MLIR-based code generation for these GEMM implementations, when different matrix sizes are used, is comparable with the performance that can be obtained for Basic Linear Algebra Subprograms (BLAS).

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Notes

  1. 1.

    https://software.intel.com/content/www/us/en/develop/tools/oneapi/components/onemkl.html.

  2. 2.

    https://www.openblas.net/.

  3. 3.

    https://github.com/flame/blis.

  4. 4.

    See, for instance, https://en.wikichip.org/wiki/intel/microarchitectures/coffee_lake.

References

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  5. Low, T.M., Igual, F., Smith, T., Quintana-Ortí, E.S.: Analytical modeling is enough for high-performance BLIS. ACM Trans. Math. Softw. (TOMS) 43, 1–18 (2016)

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  7. Zee, F.G.V., van de Geijn, R.A.: BLIS: a framework for rapidly instantiating BLAS functionality. ACM Trans. Math. Softw. 41, 14:1–14:33 (2015)

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  8. Zhang, H., Cheng, X., Zang, H., Park, D.H.: Compiler-level matrix multiplication optimization for deep learning. arXiv, p. 1909.10616 (2019). https://doi.org/10.48550/arXiv.1909.10616

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Authors and Affiliations

  1. Huawei Technologies, Central Research Institute, 2012 Labs, Shenzhen, China

    Alexey Romanov, Andrei Turkin, Oleg Myakinin, Fiodar Tsupko & Jiexing Gao

Authors
  1. Alexey Romanov
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  2. Andrei Turkin
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  3. Oleg Myakinin
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  4. Fiodar Tsupko
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  5. Jiexing Gao
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Corresponding author

Correspondence to Jiexing Gao .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Romanov, A., Turkin, A., Myakinin, O., Tsupko, F., Gao, J. (2023). Parameter Estimation via Time Modeling for MLIR Implementation of GEMM. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2023. Lecture Notes in Computer Science, vol 14395. Springer, Cham. https://doi.org/10.1007/978-3-031-47859-8_12

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  • DOI: https://doi.org/10.1007/978-3-031-47859-8_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-47858-1

  • Online ISBN: 978-3-031-47859-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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