Unum (number format)
family of numbering formats similar to floating point
Unums (universal numbers) are a family of number formats and arithmetic for implementing real numbers on a computer, proposed by John L. Gustafson in 2015. They are designed as an alternative to the ubiquitous IEEE 754 floating-point standard. The latest version is known as posits.
Type I Unum
The first version of unums, formally known as Type I unum, was introduced in Gustafson's book The End of Error as a superset of the IEEE-754 floating-point format. The defining features of the Type I unum format are:
a variable-width storage format for both the significand and exponent, and
a 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 computation with the format, Gustafson proposed using interval arithmetic with a pair of unums, what he called a ubound, providing the guarantee that the resulting interval contains the exact solution.
William M. Kahan and Gustafson debated unums at the Arith23 conference.
Type II Unum
Type II Unums were introduced in 2016 as a redesign of Unums that broke IEEE-754 compatibility. In addition to the sign bit and the interval bit mentioned earlier, the Type II Unum uses a bit to indicate inversion.
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