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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. 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. This is achieved with one of the novel techniques, an "uncertainty bit" (Ubit) which distinguishes exact values from open intervals that are between two exact values. In this manner the entire ] including minus and plus infinity is mapped to the Unum format. Underflow (but not zero) and overflow (excluding infinity) are represented by open intervals, too. | |||
| 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. 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. | |||
| Based on Unums, arbitrary intervals (both open and closed) are represented by two Unums (called Ubound) quite similar to ]. A further generalization, the Ubox represents n-dimensional shapes for describing sets of solutions. | |||
| ==References== | |||
| {{Reflist}} | |||
| ==External links== | |||
| * – IEEE Presentation on Unum and Ubox (PDF, 5.1 MB) | |||
| * - Recording Included | |||
| * - John Gustafson's website with links to related works and "The End of Error" book. | |||
| * - including explanation of how and why Unums work | |||
| * | |||
| * | |||
| ==See also== | |||
| *] | |||
| *] (80-bit) | |||
| *] | |||
| *] | |||
| ] | |||
| ] | |||
Revision as of 21:50, 23 June 2015
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