---
_id: '56604'
abstract:
- lang: eng
  text: This manuscript makes the claim of having computed the 9th Dedekind number,
    D(9). This was done by accelerating the core operation of the process with an
    efficient FPGA design that outperforms an optimized 64-core CPU reference by 95x.
    The FPGA execution was parallelized on the Noctua 2 supercomputer at Paderborn
    University. The resulting value for D(9) is 286386577668298411128469151667598498812366.
    This value can be verified in two steps. We have made the data file containing
    the 490 M results available, each of which can be verified separately on CPU,
    and the whole file sums to our proposed value. The paper explains the mathematical
    approach in the first part, before putting the focus on a deep dive into the FPGA
    accelerator implementation followed by a performance analysis. The FPGA implementation
    was done in Register-Transfer Level using a dual-clock architecture and shows
    how we achieved an impressive FMax of 450 MHz on the targeted Stratix 10 GX 2,800
    FPGAs. The total compute time used was 47,000 FPGA hours.
author:
- first_name: Lennart
  full_name: Van Hirtum, Lennart
  id: '100210'
  last_name: Van Hirtum
- first_name: Patrick
  full_name: De Causmaecker, Patrick
  last_name: De Causmaecker
- first_name: Jens
  full_name: Goemaere, Jens
  last_name: Goemaere
- first_name: Tobias
  full_name: Kenter, Tobias
  id: '3145'
  last_name: Kenter
- first_name: Heinrich
  full_name: Riebler, Heinrich
  id: '8961'
  last_name: Riebler
- first_name: Michael
  full_name: Lass, Michael
  id: '24135'
  last_name: Lass
  orcid: 0000-0002-5708-7632
- first_name: Christian
  full_name: Plessl, Christian
  id: '16153'
  last_name: Plessl
  orcid: 0000-0001-5728-9982
citation:
  ama: Van Hirtum L, De Causmaecker P, Goemaere J, et al. A Computation of the Ninth
    Dedekind Number Using FPGA Supercomputing. <i>ACM Transactions on Reconfigurable
    Technology and Systems</i>. 2024;17(3):1-28. doi:<a href="https://doi.org/10.1145/3674147">10.1145/3674147</a>
  apa: Van Hirtum, L., De Causmaecker, P., Goemaere, J., Kenter, T., Riebler, H.,
    Lass, M., &#38; Plessl, C. (2024). A Computation of the Ninth Dedekind Number
    Using FPGA Supercomputing. <i>ACM Transactions on Reconfigurable Technology and
    Systems</i>, <i>17</i>(3), 1–28. <a href="https://doi.org/10.1145/3674147">https://doi.org/10.1145/3674147</a>
  bibtex: '@article{Van Hirtum_De Causmaecker_Goemaere_Kenter_Riebler_Lass_Plessl_2024,
    title={A Computation of the Ninth Dedekind Number Using FPGA Supercomputing},
    volume={17}, DOI={<a href="https://doi.org/10.1145/3674147">10.1145/3674147</a>},
    number={3}, journal={ACM Transactions on Reconfigurable Technology and Systems},
    publisher={Association for Computing Machinery (ACM)}, author={Van Hirtum, Lennart
    and De Causmaecker, Patrick and Goemaere, Jens and Kenter, Tobias and Riebler,
    Heinrich and Lass, Michael and Plessl, Christian}, year={2024}, pages={1–28} }'
  chicago: 'Van Hirtum, Lennart, Patrick De Causmaecker, Jens Goemaere, Tobias Kenter,
    Heinrich Riebler, Michael Lass, and Christian Plessl. “A Computation of the Ninth
    Dedekind Number Using FPGA Supercomputing.” <i>ACM Transactions on Reconfigurable
    Technology and Systems</i> 17, no. 3 (2024): 1–28. <a href="https://doi.org/10.1145/3674147">https://doi.org/10.1145/3674147</a>.'
  ieee: 'L. Van Hirtum <i>et al.</i>, “A Computation of the Ninth Dedekind Number
    Using FPGA Supercomputing,” <i>ACM Transactions on Reconfigurable Technology and
    Systems</i>, vol. 17, no. 3, pp. 1–28, 2024, doi: <a href="https://doi.org/10.1145/3674147">10.1145/3674147</a>.'
  mla: Van Hirtum, Lennart, et al. “A Computation of the Ninth Dedekind Number Using
    FPGA Supercomputing.” <i>ACM Transactions on Reconfigurable Technology and Systems</i>,
    vol. 17, no. 3, Association for Computing Machinery (ACM), 2024, pp. 1–28, doi:<a
    href="https://doi.org/10.1145/3674147">10.1145/3674147</a>.
  short: L. Van Hirtum, P. De Causmaecker, J. Goemaere, T. Kenter, H. Riebler, M.
    Lass, C. Plessl, ACM Transactions on Reconfigurable Technology and Systems 17
    (2024) 1–28.
date_created: 2024-10-14T07:38:29Z
date_updated: 2025-11-04T09:53:26Z
department:
- _id: '27'
- _id: '518'
doi: 10.1145/3674147
intvolume: '        17'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 1-28
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: ACM Transactions on Reconfigurable Technology and Systems
publication_identifier:
  issn:
  - 1936-7406
  - 1936-7414
publication_status: published
publisher: Association for Computing Machinery (ACM)
quality_controlled: '1'
status: public
title: A Computation of the Ninth Dedekind Number Using FPGA Supercomputing
type: journal_article
user_id: '3145'
volume: 17
year: '2024'
...