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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

• Karlsruhe Accurate Arithmetic (KAA)
• Significant figures
• Q (number format)

References

1. Gustafson, John L. (February 2015). The End of Error: Unum Computing (1st ed.). CRC Press. ISBN 978-1-4822-3986-7. Retrieved 2016-05-30.
2. Byrne, Simon (2016-03-29). "Implementing Unums in Julia". Retrieved 2016-05-30.
3. "Unum arithmetic in Julia: Unums.jl". Retrieved 2016-05-30.
4. "Julia Implementation of Unums: README". Retrieved 2016-05-30.
5. "Unum (Universal Number) types and operations: Unums". Retrieved 2016-05-30.
6. "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. {{cite web}}: Unknown parameter |dead-url= ignored (|url-status= suggested) (help)

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)

• 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. {{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)

• 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. {{cite journal}}: Unknown parameter |dead-url= ignored (|url-status= suggested) (help)

• 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)

• Floating point types