Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

European Conference on Parallel Processing

Euro-Par 2011: Euro-Par 2011: Parallel Processing Workshops pp 355–366Cite as

  1. Home
  2. Euro-Par 2011: Parallel Processing Workshops
  3. Conference paper
Spherical Harmonic Transform with GPUs

Spherical Harmonic Transform with GPUs

  • Ioan Ovidiu Hupca30,32,
  • Joel Falcou30,32,
  • Laura Grigori30,32 &
  • …
  • Radek Stompor31 
  • Conference paper
  • 1402 Accesses

  • 6 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7155)

Abstract

We describe an algorithm for computing an inverse spherical harmonic transform suitable for graphic processing units (GPU). We use CUDA and base our implementation on a Fortran90 routine included in a publicly available parallel package, s 2 hat. We focus our attention on two major sequential steps involved in the transforms computation retaining the efficient parallel framework of the original code. We detail optimization techniques used to enhance the performance of the CUDA-based code and contrast them with those implemented in the Fortran90 version. We present performance comparisons of a single CPU plus GPU unit with the s 2 hat code running on either a single or 4 processors. In particular, we find that the latest generation of GPUs, such as NVIDIA GF100 (Fermi), can accelerate the spherical harmonic transforms by as much as 18 times with respect to s 2 hat executed on one core, and by as much as 5.5 with respect to s 2 hat on 4 cores, with the overall performance being limited by the Fast Fourier transforms. The work presented here has been performed in the context of the Cosmic Microwave Background simulations and analysis. However, we expect that the developed software will be of more general interest and applicability.

Keywords

  • Spherical Harmonic Transform
  • NVIDIA CUDA
  • GPU
  • Cosmic Microwave Background

Download conference paper PDF

References

  1. Szydlarski, M., Esterie, P., Falcou, J., Grigori, L., Stompor, R.: Spherical harmonic transform on heterogeneous architectures using hybrid programming, INRIA, Rapport de recherche RR-7635 (April 2011), http://hal.inria.fr/inria-00597576/en/

  2. Arfken, G.B., Weber, H.J.: Mathematical methods for physicists, 6th edn. Academic Press (2005)

    Google Scholar 

  3. Górski, K.M., et al.: HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere. Astrophysical Journal 622, 759–771 (2005)

    CrossRef  Google Scholar 

  4. Reinecke, M.: Libpsht - algorithms for efficient spherical harmonic transforms. Astronomy and Astrophysics 526, A108+ (2011)

    Google Scholar 

  5. Driscoll, J.R., Healy, D.M.: Computing fourier transforms and convolutions on the 2-sphere. Advances in Applied Mathematics 15(2), 202–250 (1994)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Muciaccia, P.F., Natoli, P., Vittorio, N.: Fast Spherical Harmonic Analysis: A Quick Algorithm for Generating and/or Inverting Full-Sky, High-Resolution Cosmic Microwave Background Maps. Astrophysical Journal Letters 488, L63(1997)

    Google Scholar 

  7. Doroshkevich, A.G., et al.: First Release of Gauss-Legendre Sky Pixelization (GLESP) software package for CMB analysis. ArXiv Astrophysics e-prints (January 2005)

    Google Scholar 

  8. Tygert, M.: Fast algorithms for spherical harmonic expansions, ii. Journal of Computational Physics 227(8), 4260–4279 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Nukada, A., Matsuoka, S.: Auto-tuning 3-D FFT library for CUDA GPUs. In: SC 2009: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, pp. 1–10 (2009)

    Google Scholar 

  10. Volkov, V., Demmel, J.W.: Benchmarking GPUs to tune dense linear algebra. In: ACM/IEEE Conference on Supercomputing, SC 2008 (2008)

    Google Scholar 

  11. Nvidia, NVIDIA CUDA Programming Guide (2010)

    Google Scholar 

  12. Nvidia, NVIDIA CUDA Best Practices Guide (2010)

    Google Scholar 

  13. Nvidia, Tuning CUDA Applications for Fermi (2010)

    Google Scholar 

  14. Frigo, M., Johnson, S.: The design and implementation of FFTW3. Proceedings of the IEEE 93(2), 216–231 (2005)

    CrossRef  Google Scholar 

  15. Nvidia, CUDA CUFFT Library (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LRI - INRIA Saclay-Ile de, France

    Ioan Ovidiu Hupca, Joel Falcou & Laura Grigori

  2. Astroparticule et Cosmologie, CNRS, Université Paris Diderot, Paris, France

    Radek Stompor

  3. Université Paris-Sud 11, Orsay, France

    Ioan Ovidiu Hupca, Joel Falcou & Laura Grigori

Authors
  1. Ioan Ovidiu Hupca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joel Falcou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laura Grigori
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Radek Stompor
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Scilytics, Koellnerhofgasse 3/15A, 1010, Vienna, Austria

    Michael Alexander

  2. ICAR-CNR, Via P. Castellino, 111, 80131, Napoli, Italy

    Pasqua D’Ambra

  3. University of Amsterdam, 1090, Amsterdam, Netherlands

    Adam Belloum

  4. Innovative Computing Laboratory, The University of Tennessee, USA

    George Bosilca

  5. Department of Experimental Medicine and Clinic, University Magna Græcia, 88100, Catanzaro, Italy

    Mario Cannataro

  6. Computer Science Department, University of Pisa, Italy

    Marco Danelutto

  7. Second University of Naples, Italy

    Beniamino Di Martino

  8. TU München, Boltzmannstr. 3, 85748, Garching, Germany

    Michael Gerndt

  9. Equipe Runtime, INRIA Bordeaux Sud-Ouest, 33405, Talence Cedex, France

    Emmanuel Jeannot & Raymond Namyst & 

  10. Equipe HIEPACS, INRIA Bordeaux Sud-Ouest, 33405, Talence Cedex, France

    Jean Roman

  11. Oak Ridge National Laboratory, Computer Science and Mathematics Division, 37831-6164, Oak Ridge, TN, USA

    Stephen L. Scott

  12. Department of Scientific Computing, University of Vienna, Nordbergstr. 15/3C, 1090, Vienna, Austrial

    Jesper Larsson Traff

  13. Computer Science and Mathematics Division, Oak Ridge National Laboratory, 37831, Oak Ridge, TN, USA

    Geoffroy Vallée

  14. Technische Universität München, Germany

    Josef Weidendorfer

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hupca, I.O., Falcou, J., Grigori, L., Stompor, R. (2012). Spherical Harmonic Transform with GPUs. In: Alexander, M., et al. Euro-Par 2011: Parallel Processing Workshops. Euro-Par 2011. Lecture Notes in Computer Science, vol 7155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29737-3_40

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-29737-3_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29736-6

  • Online ISBN: 978-3-642-29737-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature