Advances in Mixed Precision Algorithms: 2021 Edition

Abdelfattah, A.; Anzt, H.; Ayala, A.; Boman, E.; Carson, E.; Cayrols, S.; Cojean, T.; Dongarra, J.; Falgout, R.; Gates, M.; Gruetzmacher, T.; Higham, N.; Kruger, S.; Li, X.; Lindquist, N.; Liu, Y.; Loe, J.; Luszczek, P.; Nayak, P.; Osei-Kuffuor, D.; Pranesh, S.; Rajamanickam, S.; Ribizel, T.; Smith, B.; Swirydowicz, K.; Thomas, S.; Tomov, S.; Tsai, Y.; Yamazaki, I.; Yang, U. M.

doi:10.2172/1814677

Title: Advances in Mixed Precision Algorithms: 2021 Edition

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Abstract

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are • Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; • Results and strategies for mixed precision IR using a sparse LU factorization; • A mixed precision eigenvalue solver; • Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; • Compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; • Preparing hypre for mixed precision execution; • Mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; • Detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase themore »« less

Authors:

Abdelfattah, A. ^[1]; Anzt, H. ^[2]; Ayala, A. ^[1]; Boman, E. ^[3]; Carson, E. ^[4]; Cayrols, S. ^[1]; Cojean, T. ^[2]; Dongarra, J. ^[1]; Falgout, R. ^[5]; Gates, M. ^[1]; Gruetzmacher, T. ^[2]; Higham, N. ^[6]; Kruger, S. ^[7]; Li, X. ^[8]; Lindquist, N. ^[1]; Liu, Y. ^[8]; Loe, J. ^[3]; Luszczek, P. ^[1]; Nayak, P. ^[2]; Osei-Kuffuor, D. ^[5] more »

Univ. of Tennessee, Knoxville, TN (United States)
Karlsruhe Inst. of Technology (KIT) (Germany)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Charles Univ., Prague (Czech Republic)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Manchester (United Kingdom)
Tech-X Corp., Boulder, CO (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Argonne National Lab. (ANL), Argonne, IL (United States)
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
National Renewable Energy Lab. (NREL), Golden, CO (United States)

Publication Date:: 2021-08-18

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1814677

Report Number(s):: LLNL-TR-825909
1040257

DOE Contract Number:: AC52-07NA27344

Resource Type:: Technical Report

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Abdelfattah, A., Anzt, H., Ayala, A., Boman, E., Carson, E., Cayrols, S., Cojean, T., Dongarra, J., Falgout, R., Gates, M., Gruetzmacher, T., Higham, N., Kruger, S., Li, X., Lindquist, N., Liu, Y., Loe, J., Luszczek, P., Nayak, P., Osei-Kuffuor, D., Pranesh, S., Rajamanickam, S., Ribizel, T., Smith, B., Swirydowicz, K., Thomas, S., Tomov, S., Tsai, Y., Yamazaki, I., and Yang, U. M.. Advances in Mixed Precision Algorithms: 2021 Edition.  United States: N. p., 2021. 
        Web.  doi:10.2172/1814677.

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                    Abdelfattah, A., Anzt, H., Ayala, A., Boman, E., Carson, E., Cayrols, S., Cojean, T., Dongarra, J., Falgout, R., Gates, M., Gruetzmacher, T., Higham, N., Kruger, S., Li, X., Lindquist, N., Liu, Y., Loe, J., Luszczek, P., Nayak, P., Osei-Kuffuor, D., Pranesh, S., Rajamanickam, S., Ribizel, T., Smith, B., Swirydowicz, K., Thomas, S., Tomov, S., Tsai, Y., Yamazaki, I., & Yang, U. M.. Advances in Mixed Precision Algorithms: 2021 Edition.  United States.  https://doi.org/10.2172/1814677

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                    Abdelfattah, A., Anzt, H., Ayala, A., Boman, E., Carson, E., Cayrols, S., Cojean, T., Dongarra, J., Falgout, R., Gates, M., Gruetzmacher, T., Higham, N., Kruger, S., Li, X., Lindquist, N., Liu, Y., Loe, J., Luszczek, P., Nayak, P., Osei-Kuffuor, D., Pranesh, S., Rajamanickam, S., Ribizel, T., Smith, B., Swirydowicz, K., Thomas, S., Tomov, S., Tsai, Y., Yamazaki, I., and Yang, U. M.. 2021.  
        "Advances in Mixed Precision Algorithms: 2021 Edition".  United States.  https://doi.org/10.2172/1814677.  https://www.osti.gov/servlets/purl/1814677.

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@article{osti_1814677,

  title        = {Advances in Mixed Precision Algorithms: 2021 Edition},

  author       = {Abdelfattah, A. and Anzt, H. and Ayala, A. and Boman, E. and Carson, E. and Cayrols, S. and Cojean, T. and Dongarra, J. and Falgout, R. and Gates, M. and Gruetzmacher, T. and Higham, N. and Kruger, S. and Li, X. and Lindquist, N. and Liu, Y. and Loe, J. and Luszczek, P. and Nayak, P. and Osei-Kuffuor, D. and Pranesh, S. and Rajamanickam, S. and Ribizel, T. and Smith, B. and Swirydowicz, K. and Thomas, S. and Tomov, S. and Tsai, Y. and Yamazaki, I. and Yang, U. M.},

  abstractNote = {Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are • Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; • Results and strategies for mixed precision IR using a sparse LU factorization; • A mixed precision eigenvalue solver; • Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; • Compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; • Preparing hypre for mixed precision execution; • Mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; • Detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.},

  doi          = {10.2172/1814677},

  url          = {https://www.osti.gov/biblio/1814677},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {2021},

  month        = {8}

}

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