07-30-2016, 11:29 PM

Have you heard about ''unums'' (for "universal numbers") already?

This is a new number format and arithmetic environment proposed by John Gustafson since 2013. It is meant to be a superset of or long-term even a replacement for traditional floating point arithmetic as defined in IEEE 754 etc. It claims to address many of the shortcomings of floating point and interval arithmetic in general, while also being better suited for modern and future number crunching hardware (high integration, cheap transistors, parallel cores, but thermal and power limitations). One of the ideas is to use today's technology and progress to provide mathematically better solutions of limited precision with known accuracy, not necessarily more solutions per time or solutions with extreme precision but sometimes still only very limited accuracy.

Unums must be considered a work in progress. There are meanwhile two considerable different proposals, unum I and II. So far, there are a few software emulations (obviously very slow), but no hardware implementations.

The proposal has generated some heated discussions about the pros and cons of the format already (including one between Kahan and Gustafson). While I don't consider unums in their present form to be "the one-and-only solution", I find some of the underlying ideas very interesting and thought-provoking. While I love to push existing technologies to the limits, I also think it is important to reevaluate issues from new perspectives from time to time.

Well, since there are many people in this forum, who are interested in mathematics and computer sciences, some might be interested to learn about unums as well. I have therefore compiled a list of unum resources I am aware of.

What do you think about the unum proposal?

Greetings,

Matthias

Unum I presentations

Unum II presentations

The Great Debate

Book

This is a new number format and arithmetic environment proposed by John Gustafson since 2013. It is meant to be a superset of or long-term even a replacement for traditional floating point arithmetic as defined in IEEE 754 etc. It claims to address many of the shortcomings of floating point and interval arithmetic in general, while also being better suited for modern and future number crunching hardware (high integration, cheap transistors, parallel cores, but thermal and power limitations). One of the ideas is to use today's technology and progress to provide mathematically better solutions of limited precision with known accuracy, not necessarily more solutions per time or solutions with extreme precision but sometimes still only very limited accuracy.

Unums must be considered a work in progress. There are meanwhile two considerable different proposals, unum I and II. So far, there are a few software emulations (obviously very slow), but no hardware implementations.

The proposal has generated some heated discussions about the pros and cons of the format already (including one between Kahan and Gustafson). While I don't consider unums in their present form to be "the one-and-only solution", I find some of the underlying ideas very interesting and thought-provoking. While I love to push existing technologies to the limits, I also think it is important to reevaluate issues from new perspectives from time to time.

Well, since there are many people in this forum, who are interested in mathematics and computer sciences, some might be interested to learn about unums as well. I have therefore compiled a list of unum resources I am aware of.

What do you think about the unum proposal?

Greetings,

Matthias

Unum I presentations

- 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). http://www.johngustafson.net/presentatio...ision1.pdf
- Brueckner, Rich (2015-03-02). "Slidecast: John Gustafson Explains Energy Efficient Unum Computing". The Rich Report. Inside HPC. http://insidehpc.com/2015/03/slidecast-j...computing/
- Gustafson, John L. (2015). "The end of numerical error" (PDF). http://arith22.gforge.inria.fr/slides/06-gustafson.pdf
- Tichy, Walter F. (April 2016). "The End of (Numeric) Error: An interview with John L. Gustafson". Ubiquity - Information everywhere. Association for Computing Machinery. 2016 (April): 1–14. doi:10.1145/2913029. http://dx.doi.org/10.1145%2F2913029 http://ubiquity.acm.org/article.cfm?id=2913029
- Kahan, William M. (2016-07-15). "Prof. W. Kahan's Commentary on "THE END of ERROR — Unum Computing" by John L. Gustafson, (2015) CRC Press" (PDF). https://people.eecs.berkeley.edu/~wkahan/EndErErs.pdf
- Gustafson, John L. (2016-06-06). "An Energy-Efficient and massively parallel approach to valid numerics" (Powerpoint with comments). OCRAR Seminar. http://www.johngustafson.net/presentatio...minar.pptx (http://www.johngustafson.net/presentatio...eminar.pdf without comments)

Unum II presentations

- Gustafson, John L. (2016-06-03) [2016-02-22]. "A Radical Approach to Computation with Real Numbers - Unums version 2.0" (Powerpoint with comments). http://www.johngustafson.net/presentatio...ms2.0.pptx (http://www.johngustafson.net/presentations/Unums2.0.pdf without comments)
- Gustafson, John L. (2016). "A Radical Approach to Computation with Real Numbers" (PDF). SuperFri.org. http://www.johngustafson.net/pubs/RadicalApproach.pdf
- Kahan, William M. (2016-07-15). "Prof. W. Kahan's Comments on SORN Arithmetic" (PDF). https://people.eecs.berkeley.edu/~wkahan/SORNers.pdf

The Great Debate

- "Program: Special Session: The Great Debate: John Gustafson and William Kahan". Arith23: 23rd IEEE Symposium on Computer Arithmetic. Silicon Valley. 2016-07-12. http://arith23.gforge.inria.fr/program.html
- Gustafson, John L.; Kahan, William M. (2016-07-12). The Great Debate @ARITH23: John Gustafson and William Kahan (1:34:41 video). http://www.youtube.com/watch?v=LZAeZBVAz...e=youtu.be
- Kahan, William M. (2016-07-16) [2016-07-12]. "A Critique of John L. Gustafson's THE END of ERROR — Unum Computation and his A Radical Approach to Computation with Real Numbers". Santa Clara: IEEE Symposium on Computer Arithmetic, ARITH 23. http://people.eecs.berkeley.edu/~wkahan/UnumSORN.pdf http://arith23.gforge.inria.fr/slides/Kahan.pdf
- Gustafson, John L. (2016-07-12). ""The Great Debate": Unum arithmetic position paper". Santa Clara: IEEE Symposium on Computer Arithmetic, ARITH 23. https://groups.google.com/group/unum-com...f?part=0.1 http://arith23.gforge.inria.fr/slides/Gustafson.pdf

Book

- Gustafson, John L. (2016-02-04) [2015-02-05]. "The End of Error: Unum Computing". Chapman & Hall / CRC Computational Science. 24 (1st edition, 2nd corrected printing). CRC Press. ISBN 978-1-4822-3986-7. http://www.crcpress.com/The-End-of-Error...1482239867