| Revision as of 03:58, 2 January 2015 editVincent Lefèvre (talk | contribs)Extended confirmed users4,852 edits With a fixed format, avoiding overflows and providing exact arithmetic is simply not possible. The first paragraph is also ambiguous (number vs interval). Needs refs from the community.← Previous edit | Revision as of 08:27, 4 March 2015 edit undo89.115.21.136 (talk) Removed link to unrelated articleNext edit → | ||
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| The '''Universal Number Format''' (or Unum) is a number format which uses several novel techniques to ensure algebraically valid solutions to computations.<ref>J. L. Gustafson, The End of Error. To be published by CRC Press Taylor and Francis Goup, A Chapman and Hall Book, 2015.</ref> One of the primary techniques is storing meta-data along with each number, including its environment and precision (exponent and fraction/mantissa), which allows for rigorously bounded interval solutions without rounding error typical of ] arithmetic and with underflow or overflow.{{POV-statement|date=January 2015}} | The '''Universal Number Format''' (or Unum) is a number format which uses several novel techniques to ensure algebraically valid solutions to computations.<ref>J. L. Gustafson, The End of Error. To be published by CRC Press Taylor and Francis Goup, A Chapman and Hall Book, 2015.</ref> One of the primary techniques is storing meta-data along with each number, including its environment and precision (exponent and fraction/mantissa), which allows for rigorously bounded interval solutions without rounding error typical of ] arithmetic and with underflow or overflow.{{POV-statement|date=January 2015}} | ||
| First proposed by ] in ''The End of Error'', the |
First proposed by ] in ''The End of Error'', the Unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic.{{POV-statement|date=January 2015}} This number type can allow for more accurate answers than floating-point arithmetic in some situations. In many cases using fewer bits thereby saving memory, bandwidth, energy, and power. | ||
| ==References== | ==References== | ||
Revision as of 08:27, 4 March 2015
The Universal Number Format (or Unum) is a number format which uses several novel techniques to ensure algebraically valid solutions to computations. One of the primary techniques is storing meta-data along with each number, including its environment and precision (exponent and fraction/mantissa), which allows for rigorously bounded interval solutions without rounding error typical of floating-point arithmetic and with underflow or overflow.
First proposed by John Gustafson in The End of Error, the Unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic. This number type can allow for more accurate answers than floating-point arithmetic in some situations. In many cases using fewer bits thereby saving memory, bandwidth, energy, and power.
References
- J. L. Gustafson, The End of Error. To be published by CRC Press Taylor and Francis Goup, A Chapman and Hall Book, 2015.
External links
- Early IEEE presentation – IEEE Presentation on Unum and Ubox (PDF, 5.1 MB)
- IEEE Lecture - Recording Included
- John's Personal Website - John Gustafson's website with links to related works and "The End of Error" book.
See also
- IEEE Standard for Floating-Point Arithmetic (IEEE 754)
- Extended precision (80-bit)
- Significant digits
- Ubox