FYI, I found a reasonably clear set of slides introducing UNUM and some of its properties at the following URL:
To me, this seems like adding a metadata field in a known location within the variable itself. Unfortunately, I see only one actual, bit-level example of such a UNUM in the entire presentation, on slide# 31. IMHO, it would be far more understandable, in terms of weighing his assertions about economy of storage if the author had included more examples, especially some showing a size other than an IEEE-754 32-bit floating point value, with an (in this one example) eight bit “utag” on the end opposite the sign bit.
I’m somewhat skeptical about some of his arguments about economy. For individual variables, there might be some savings by using fewer bits. However, the number of needed bits (for a desired accuracy) becomes data-dependent.
IMHO, where this falls down is that compilers need to track the locations and sizes of variables. In most programs doing serious floating-point computation, one has lots of values, often in arrays, with all elements at known alignment. “Arrays” without uniform element size become a nightmare for indexing. So any savings in bits in such arrays would seem to come at the heavy price of having to go through the entire “array” of variably-sized elements, to find the one you wanted — every time you wanted to index into such an array. (To say nothing about how much work it would be to move things around, every time any element gains or loses a byte.)
Maybe somebody else can see a way around the apparent indexing issues, but to me it seems unlikely to change the computing world and is IMHO off topic for the Mill, for the reasons Ivan stated.