---
_id: '20'
abstract:
- lang: eng
  text: "Approximate computing has shown to provide new ways to improve performance\r\nand
    power consumption of error-resilient applications. While many of these\r\napplications
    can be found in image processing, data classification or machine\r\nlearning,
    we demonstrate its suitability to a problem from scientific\r\ncomputing. Utilizing
    the self-correcting behavior of iterative algorithms, we\r\nshow that approximate
    computing can be applied to the calculation of inverse\r\nmatrix p-th roots which
    are required in many applications in scientific\r\ncomputing. Results show great
    opportunities to reduce the computational effort\r\nand bandwidth required for
    the execution of the discussed algorithm, especially\r\nwhen targeting special
    accelerator hardware."
author:
- first_name: Michael
  full_name: Lass, Michael
  id: '24135'
  last_name: Lass
  orcid: 0000-0002-5708-7632
- first_name: Thomas
  full_name: Kühne, Thomas
  id: '49079'
  last_name: Kühne
- first_name: Christian
  full_name: Plessl, Christian
  id: '16153'
  last_name: Plessl
  orcid: 0000-0001-5728-9982
citation:
  ama: Lass M, Kühne T, Plessl C. Using Approximate Computing for the Calculation
    of Inverse Matrix p-th Roots. <i>Embedded Systems Letters</i>. 2018;10(2):33-36.
    doi:<a href="https://doi.org/10.1109/LES.2017.2760923">10.1109/LES.2017.2760923</a>
  apa: Lass, M., Kühne, T., &#38; Plessl, C. (2018). Using Approximate Computing for
    the Calculation of Inverse Matrix p-th Roots. <i>Embedded Systems Letters</i>,
    <i>10</i>(2), 33–36. <a href="https://doi.org/10.1109/LES.2017.2760923">https://doi.org/10.1109/LES.2017.2760923</a>
  bibtex: '@article{Lass_Kühne_Plessl_2018, title={Using Approximate Computing for
    the Calculation of Inverse Matrix p-th Roots}, volume={10}, DOI={<a href="https://doi.org/10.1109/LES.2017.2760923">10.1109/LES.2017.2760923</a>},
    number={2}, journal={Embedded Systems Letters}, publisher={IEEE}, author={Lass,
    Michael and Kühne, Thomas and Plessl, Christian}, year={2018}, pages={33–36} }'
  chicago: 'Lass, Michael, Thomas Kühne, and Christian Plessl. “Using Approximate
    Computing for the Calculation of Inverse Matrix P-Th Roots.” <i>Embedded Systems
    Letters</i> 10, no. 2 (2018): 33–36. <a href="https://doi.org/10.1109/LES.2017.2760923">https://doi.org/10.1109/LES.2017.2760923</a>.'
  ieee: M. Lass, T. Kühne, and C. Plessl, “Using Approximate Computing for the Calculation
    of Inverse Matrix p-th Roots,” <i>Embedded Systems Letters</i>, vol. 10, no. 2,
    pp. 33–36, 2018.
  mla: Lass, Michael, et al. “Using Approximate Computing for the Calculation of Inverse
    Matrix P-Th Roots.” <i>Embedded Systems Letters</i>, vol. 10, no. 2, IEEE, 2018,
    pp. 33–36, doi:<a href="https://doi.org/10.1109/LES.2017.2760923">10.1109/LES.2017.2760923</a>.
  short: M. Lass, T. Kühne, C. Plessl, Embedded Systems Letters 10 (2018) 33–36.
date_created: 2017-07-25T14:41:08Z
date_updated: 2022-01-06T06:54:18Z
department:
- _id: '27'
- _id: '518'
- _id: '304'
doi: 10.1109/LES.2017.2760923
external_id:
  arxiv:
  - '1703.02283'
intvolume: '        10'
issue: '2'
language:
- iso: eng
page: ' 33-36'
project:
- _id: '32'
  grant_number: PL 595/2-1
  name: Performance and Efficiency in HPC with Custom Computing
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Embedded Systems Letters
publication_identifier:
  eissn:
  - 1943-0671
  issn:
  - 1943-0663
publication_status: published
publisher: IEEE
status: public
title: Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots
type: journal_article
user_id: '16153'
volume: 10
year: '2018'
...
---
_id: '1043'
abstract:
- lang: eng
  text: 'Approximate computing (AC) is an emerging paradigm for energy-efficient computation.
    The basic idea of AC is to sacrifice high precision for low energy by allowing
    hardware to carry out “approximately correct” calculations. This provides a major
    challenge for software quality assurance: programs successfully verified to be
    correct might be erroneous on approximate hardware. In this letter, we present
    a novel approach for determining under what conditions a software verification
    result is valid for approximate hardware. To this end, we compute the allowed
    tolerances for AC hardware from successful verification runs. More precisely,
    we derive a set of constraints which—when met by the AC hardware—guarantees the
    verification result to carry over to AC. On the practical side, we furthermore:
    1) show how to extract tolerances from verification runs employing predicate abstraction
    as verification technology and 2) show how to check such constraints on hardware
    designs. We have implemented all techniques, and exemplify them on example C programs
    and a number of recently proposed approximate adders.'
author:
- first_name: Tobias
  full_name: Isenberg, Tobias
  last_name: Isenberg
- first_name: Marie-Christine
  full_name: Jakobs, Marie-Christine
  last_name: Jakobs
- first_name: Felix
  full_name: Pauck, Felix
  id: '22398'
  last_name: Pauck
- first_name: Heike
  full_name: Wehrheim, Heike
  id: '573'
  last_name: Wehrheim
citation:
  ama: Isenberg T, Jakobs M-C, Pauck F, Wehrheim H. Validity of Software Verification
    Results on Approximate Hardware. <i>IEEE Embedded Systems Letters</i>. 2018:22-25.
    doi:<a href="https://doi.org/10.1109/LES.2017.2758200">10.1109/LES.2017.2758200</a>
  apa: Isenberg, T., Jakobs, M.-C., Pauck, F., &#38; Wehrheim, H. (2018). Validity
    of Software Verification Results on Approximate Hardware. <i>IEEE Embedded Systems
    Letters</i>, 22–25. <a href="https://doi.org/10.1109/LES.2017.2758200">https://doi.org/10.1109/LES.2017.2758200</a>
  bibtex: '@article{Isenberg_Jakobs_Pauck_Wehrheim_2018, title={Validity of Software
    Verification Results on Approximate Hardware}, DOI={<a href="https://doi.org/10.1109/LES.2017.2758200">10.1109/LES.2017.2758200</a>},
    journal={IEEE Embedded Systems Letters}, publisher={Institute of Electrical and
    Electronics Engineers (IEEE)}, author={Isenberg, Tobias and Jakobs, Marie-Christine
    and Pauck, Felix and Wehrheim, Heike}, year={2018}, pages={22–25} }'
  chicago: Isenberg, Tobias, Marie-Christine Jakobs, Felix Pauck, and Heike Wehrheim.
    “Validity of Software Verification Results on Approximate Hardware.” <i>IEEE Embedded
    Systems Letters</i>, 2018, 22–25. <a href="https://doi.org/10.1109/LES.2017.2758200">https://doi.org/10.1109/LES.2017.2758200</a>.
  ieee: T. Isenberg, M.-C. Jakobs, F. Pauck, and H. Wehrheim, “Validity of Software
    Verification Results on Approximate Hardware,” <i>IEEE Embedded Systems Letters</i>,
    pp. 22–25, 2018.
  mla: Isenberg, Tobias, et al. “Validity of Software Verification Results on Approximate
    Hardware.” <i>IEEE Embedded Systems Letters</i>, Institute of Electrical and Electronics
    Engineers (IEEE), 2018, pp. 22–25, doi:<a href="https://doi.org/10.1109/LES.2017.2758200">10.1109/LES.2017.2758200</a>.
  short: T. Isenberg, M.-C. Jakobs, F. Pauck, H. Wehrheim, IEEE Embedded Systems Letters
    (2018) 22–25.
date_created: 2017-12-11T16:11:00Z
date_updated: 2022-01-06T06:50:39Z
ddc:
- '000'
department:
- _id: '77'
doi: 10.1109/LES.2017.2758200
file:
- access_level: closed
  content_type: application/pdf
  creator: ups
  date_created: 2018-11-02T15:27:04Z
  date_updated: 2018-11-02T15:27:04Z
  file_id: '5303'
  file_name: 08053741.pdf
  file_size: 523362
  relation: main_file
  success: 1
file_date_updated: 2018-11-02T15:27:04Z
has_accepted_license: '1'
language:
- iso: eng
page: 22-25
project:
- _id: '1'
  name: SFB 901
- _id: '3'
  name: SFB 901 - Project Area B
- _id: '12'
  name: SFB 901 - Subproject B4
publication: IEEE Embedded Systems Letters
publication_identifier:
  issn:
  - 1943-0663
  - 1943-0671
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: Validity of Software Verification Results on Approximate Hardware
type: journal_article
user_id: '477'
year: '2018'
...