Unum (number format)
The Universal Number Format (or Unum) is a number format which uses several novel techniques to ensure algebraically valid solutions to computations.[1] 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. This is achieved with one of the novel techniques of including an "inexact bit" which helps define the answer on the real number line
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. 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.
- insideHPC Podcast - including explanation of how and why Unums work
- initial press release and scope of claims
See also
- IEEE Standard for Floating-Point Arithmetic (IEEE 754)
- Extended precision (80-bit)
- Significant digits
- Ubox