Unum (number format)

The unum (universal number) format is a format similar to floating point, proposed by John Gustafson as an alternative to the now ubiquitous IEEE 754 format. The proposal and justification are explained in his book The End of Error.

The two defining features of the unum 1.0 format (while unum 2.0 is different) are:

For performing computation with the format, Gustafson proposes using interval arithmetic with a pair of unums, what he calls a ubound, providing the guarantee that the resulting interval contains the exact solution.

Unum implementations have been explored in Julia. including unum 2.0 (or at least a modified version of his new proposal). Recently, unum has been explored in MATLAB.

William Kahan and John Gustafson discussed unums at the Arith23 conference on July 12, 2016.

William Kahan claims the following issues with unums:

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