| Revision as of 20:07, 11 July 2016 editMatthiaspaul (talk | contribs)Autopatrolled, Extended confirmed users, Page movers, New page reviewers, Pending changes reviewers, Rollbackers, Template editors137,492 edits improved ref← Previous edit | Revision as of 12:34, 12 July 2016 edit undoMatthiaspaul (talk | contribs)Autopatrolled, Extended confirmed users, Page movers, New page reviewers, Pending changes reviewers, Rollbackers, Template editors137,492 edits →Further readings: +refsNext edit → | ||
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| * {{cite web |author-first=John L. |author-last=Gustafson |author-link=John Gustafson (scientist) |title=A Radical Approach to Computation with Real Numbers |date=2016 |publisher=SuperFri.org |url=http://www.johngustafson.net/pubs/RadicalApproach.pdf |access-date=2016-07-10 |dead-url=no |archive-url=https://web.archive.org/web/20160710221518/http://www.johngustafson.net/pubs/RadicalApproach.pdf |archive-date=2016-07-10}} | * {{cite web |author-first=John L. |author-last=Gustafson |author-link=John Gustafson (scientist) |title=A Radical Approach to Computation with Real Numbers |date=2016 |publisher=SuperFri.org |url=http://www.johngustafson.net/pubs/RadicalApproach.pdf |access-date=2016-07-10 |dead-url=no |archive-url=https://web.archive.org/web/20160710221518/http://www.johngustafson.net/pubs/RadicalApproach.pdf |archive-date=2016-07-10}} | ||
| * {{cite paper |author-first=Ulrich W. |author-last=Kulisch |author-link=:de:Ulrich Kulisch |title=Up-to-date Interval Arithmetic from closed intervals to connected sets of real numbers |date=2015 |type=preprint |publisher=Institut für Angewandte und Numerische Mathematik - ] (KIT), Germany |id=ID 15/02 |url=http://www.math.kit.edu/iwrmm/seite/preprints/media/preprint%20nr.%2015-02.pdf |access-date=2016-07-12 |dead-url=no |archive-url=https://web.archive.org/web/20160712121728/http://www.math.kit.edu/iwrmm/seite/preprints/media/preprint%20nr.%2015-02.pdf |archive-date=2016-07-12}} | |||
| * {{cite paper |author-first=Thomas |author-last=Risse |title=Unum – an expedient extension of IEEE 754 |publisher=Institute of Informatics & Automation (IIA), Faculty EEE & CS, ], Germany |date=2016-03-10 |type=presentation |location=] (LSBU), UK |url=http://www.weblearn.hs-bremen.de/risse/papers/LSBU/LSBU_Unum.pdf |access-date=2016-07-12 |dead-url=no |archive-url=https://web.archive.org/web/20160712122236/http://www.weblearn.hs-bremen.de/risse/papers/LSBU/LSBU_Unum.pdf |archive-date=2016-07-12}} | |||
| ] | ] | ||
Revision as of 12:34, 12 July 2016
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The unum (universal number) format is a floating point format proposed by John Gustafson as an alternative to the now ubiquitous IEEE 754 format. The proposal and justification are explained in his somewhat ambitiously-titled book The End of Error.
The two defining features of the unum format are:
- a variable-width storage format for both the significand and exponent, and
- an u-bit, which determines whether the unum corresponds to an exact number (u=0), or an interval between consecutive exact unums (u=1). In this way, the unums cover the entire extended real number line .
For performing computation with the format, Gustafson proposes using interval arithmetic with a pair of unums, what he calls an ubound, providing the guarantee that the resulting interval contains the exact solution.
Unum implementations have been explored in Julia.
A "Great Debate" between William Kahan and John Gustafson is planned for the Arith23 conference on July 12, 2016.
See also
References
- Gustafson, John L. (February 2015). The End of Error: Unum Computing. Chapman & Hall/CRC Computational Science. Vol. 24 (1st ed.). CRC Press. ISBN 978-1-4822-3986-7. Retrieved 2016-05-30.
- Byrne, Simon (2016-03-29). "Implementing Unums in Julia". Retrieved 2016-05-30.
- "Unum arithmetic in Julia: Unums.jl". Retrieved 2016-05-30.
- "Julia Implementation of Unums: README". Retrieved 2016-05-30.
- "Unum (Universal Number) types and operations: Unums". Retrieved 2016-05-30.
- "Program: Special Session: The Great Debate: John Gustafson and William Kahan". Arith23: 23rd IEEE Symposium on Computer Arithmetic. Silicon Valley, USA. 2016-07-12. Archived from the original on 2016-05-30. Retrieved 2016-05-30.
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Further readings
- Gustafson, John L. (March 2013). "Right-Sizing Precision: Unleashed Computing: The need to right-size precision to save energy, bandwidth, storage, and electrical power" (PDF). Archived from the original (PDF) on 2016-06-06. Retrieved 2016-06-06.
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- Brueckner, Rich (2015-03-02). "Slidecast: John Gustafson Explains Energy Efficient Unum Computing". The Rich Report. Inside HPC. Archived from the original on 2016-07-10. Retrieved 2016-06-10.
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- Gustafson, John L. (2015). "The end of numerical error" (PDF). Archived from the original (PDF) on 2016-06-06. Retrieved 2016-06-06.
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- Tichy, Walter F. (April 2016). "The End of (Numeric) Error: An interview with John L. Gustafson". Ubiquity - Information everywhere. 2016 (April). Association for Computing Machinery (ACM): 1–14. doi:10.1145/2913029. Archived from the original on 2016-07-10. Retrieved 2016-07-10.
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- Gustafson, John L. (2016-06-03) . "A Radical Approach to Computation with Real Numbers - Unums version 2.0" (PPT). Archived from the original on 2016-07-10. Retrieved 2016-07-10.
{{cite web}}: Unknown parameter|dead-url=ignored (|url-status=suggested) (help) (NB. PDFs come without notes: )
- Gustafson, John L. (2016-06-06). "An Energy-Efficient and massively parallel approach to valid numerics" (PPT). OCRAR Seminar. Archived from the original on 2016-07-10. Retrieved 2016-07-10.
{{cite web}}: Unknown parameter|dead-url=ignored (|url-status=suggested) (help)
- Gustafson, John L. (2016). "A Radical Approach to Computation with Real Numbers" (PDF). SuperFri.org. Archived from the original (PDF) on 2016-07-10. Retrieved 2016-07-10.
{{cite web}}: Unknown parameter|dead-url=ignored (|url-status=suggested) (help)
- Kulisch, Ulrich W. (2015). "Up-to-date Interval Arithmetic from closed intervals to connected sets of real numbers" (PDF) (preprint). Institut für Angewandte und Numerische Mathematik - Karlsruhe Institute of Technology (KIT), Germany. ID 15/02. Archived from the original (PDF) on 2016-07-12. Retrieved 2016-07-12.
{{cite journal}}: Cite journal requires|journal=(help); Unknown parameter|dead-url=ignored (|url-status=suggested) (help)
- Risse, Thomas (2016-03-10). "Unum – an expedient extension of IEEE 754" (PDF) (presentation). London South Bank University (LSBU), UK: Institute of Informatics & Automation (IIA), Faculty EEE & CS, Bremen University of Applied Sciences, Germany. Archived from the original (PDF) on 2016-07-12. Retrieved 2016-07-12.
{{cite journal}}: Cite journal requires|journal=(help); Unknown parameter|dead-url=ignored (|url-status=suggested) (help)