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| * {{cite web |author-first=John L. |author-last=Gustafson |author-link=John Gustafson (scientist) |title=The end of numerical error |date=2015 |url=http://arith22.gforge.inria.fr/slides/06-gustafson.pdf |access-date=2016-06-06 |dead-url=no |archive-url=https://web.archive.org/web/20160606203155/http://arith22.gforge.inria.fr/slides/06-gustafson.pdf |archive-date=2016-06-06}} | * {{cite web |author-first=John L. |author-last=Gustafson |author-link=John Gustafson (scientist) |title=The end of numerical error |date=2015 |url=http://arith22.gforge.inria.fr/slides/06-gustafson.pdf |access-date=2016-06-06 |dead-url=no |archive-url=https://web.archive.org/web/20160606203155/http://arith22.gforge.inria.fr/slides/06-gustafson.pdf |archive-date=2016-06-06}} | ||
| * {{cite web |author-first=John L. |author-last=Gustafson |author-link=John Gustafson (scientist) |title=A Radical Approach to Computation with Real Numbers - Unums version 2.0 | |
* {{cite web |author-first=John L. |author-last=Gustafson |author-link=John Gustafson (scientist) |title=A Radical Approach to Computation with Real Numbers - Unums version 2.0 |orig-year=2016-02-22 |date=2016-04-14 |url=https://groups.google.com/group/unum-computing/attach/4249c4e9599a4/Unums2.0slides.pptx?part=0.1.1 |type=PPT |access-date=2016-07-10 |dead-url=no |archive-url=https://web.archive.org/web/20160507145408/http://www.johngustafson.net/presentations/Multicore2016-JLG.pptx |archive-date=2016-05-07}} (NB. Archived PPT version and PDF versions are of a previous revision. PDFs come without notes: ) | ||
| ] | ] | ||
Revision as of 19:31, 10 July 2016
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The unum 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. (2015). The End of Error: Unum Computing. 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.
{{cite web}}: Unknown parameter|dead-url=ignored (|url-status=suggested) (help)
- Gustafson, John L. (2015). "The end of numerical error" (PDF). Archived from the original (PDF) on 2016-06-06. Retrieved 2016-06-06.
{{cite web}}: Unknown parameter|dead-url=ignored (|url-status=suggested) (help)
- Gustafson, John L. (2016-04-14) . "A Radical Approach to Computation with Real Numbers - Unums version 2.0" (PPT). Archived from the original on 2016-05-07. Retrieved 2016-07-10.
{{cite web}}: Unknown parameter|dead-url=ignored (|url-status=suggested) (help) (NB. Archived PPT version and PDF versions are of a previous revision. PDFs come without notes: )