Food for thought: Unums

[Claudio L.]

Really interesting. The first part has a few concepts that are already implemented in newRPL:
* Numbers use minimum storage needed, and auto promote themselves to larger storage only when needed: newRPL uses small integers in the range +/-130000 that only have a prolog and no storage, then auto-promoted to 64-bit integers (prolog+64-bits), then auto-promoted to arbitrary precision reals which only store the needed digits in packs of 8, so the number 1.5 only stores 1 pack of 8 digits even though precision might be set to 32.
* A bit to indicate if the quantity is exact or inexact.
* A "tag" to indicate the number of digits in the number.

But that's about where the similarities end, as newRPL sticks with the traditional floating point concept from there on.

Those "unums" are interesting, though I'm not sure how they would work in real problems. I particularly like the idea to represent "exactly" the inverses of all the integers in the fractional part of the number, so any integer number can be inverted back and forth with no loss of precision, ever (3 INV INV --> 3 is like a dream come true!).
But for general arithmetic I'm not so sure it's practical, I imagine a number that's an inverse of an integer:
1/13 + 1/23 --> Storing the result would need a storage system capable of storing the inverse of 13*23, and things can quickly escalate from there, requiring the use of large precision numbers very quickly. And what happens when you reach the maximum system precision? Then the result would be approximated (rounded? more like "snapped" into the grid of the uneven spacing of the discrete fractions that can be represented) much like in the current floating point but perhaps with a harder to determine bias.
So in the end it's a cool idea, I think it saves storage up to a point, then it just becomes the same thing (assuming you can't scale this up to massive amounts of digits), unless you are willing to work with those SORN (Sets-Of-Real-Numbers) which is a different animal.

Or have I misinterpreted their concept?