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| The unum is a floating point format proposed by ], proposed as an alternative to the now ubiquitous ]. The proposal and justification are explained in his somewhat ambitiously-titled book The end of error. | The '''unum''' is a floating point format proposed by ], proposed as an alternative to the now ubiquitous ]. 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: | The two defining features of the unum format are: | ||
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| 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. | 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 ].<ref>http://juliacomputing.com/blog/2016/03/29/unums.html</ref><ref>https://github.com/JuliaComputing/Unums.jl</ref><ref>https://github.com/REX-Computing/unumjl</ref><ref>https://github.com/tbreloff/Unums.jl</ref> |
Unum implementations have been explored in ].<ref>http://juliacomputing.com/blog/2016/03/29/unums.html</ref><ref>https://github.com/JuliaComputing/Unums.jl</ref><ref>https://github.com/REX-Computing/unumjl</ref><ref>https://github.com/tbreloff/Unums.jl</ref> | ||
| A "Great Debate" between ] and ] is planned for the Arith23 conference<ref>http://arith23.gforge.inria.fr/program.html</ref> on July 12, 2016. | A "Great Debate" between ] and ] is planned for the Arith23 conference<ref>http://arith23.gforge.inria.fr/program.html</ref> on July 12, 2016. | ||
| ==References== | ==References== | ||
| {{Reflist}} | |||
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The unum is a floating point format proposed by John Gustafson, proposed as an alternative to the now ubiquitous IEEE 754 formats. 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.