I read the book (well, somewhere between a skim and a proper read). It's not formal but it is clear and the ideas are concise. I actually think it's a pretty good example of how to explain an idea without unnecessary jargon.
As for unums themselves, I am mostly convinced of his arguments on unums. I am less convinced on ubounds. My main takeaways are that a unum may represent a set of values, and it's most salient properties are: - Explicit (via ubit) handling of exact and inexact (i.e. set of) real number - Correct handling of open/closed bounds for sets of reals - Variable size with size of number stored in number - With hardware they could be as or more efficient in energy and speed as floating arithmetic but hardware would be more complex As a result of these properties, unums can be closed under arithmetic operations and won't hide your errors due to approximation. I don't buy the advantages he suggests over interval arithmetic; unums don't solve the dependency problem. I have been meaning to start a Unum.jl package myself. Zenna On Saturday, July 25, 2015 at 9:11:54 AM UTC-4, Job van der Zwan wrote: > > So I came across the concept of UNUMs on the Pony language mailing list > <http://lists.ponylang.org/pipermail/ponydev/2015-July/000071.html> this > morning. I hadn't heard of them before, and a quick search doesn't show up > anything on this mailing list, so I guess most people here haven't either. > They're a proposed alternate encoding for numbers by John L. Gustafson. > This presentation by him sums it up nicely: > > http://sites.ieee.org/scv-cs/files/2013/03/Right-SizingPrecision1.pdf > > “Unums”(universal numbers) are to floating point what floating point is to >> fixed point. >> Floating-point values self-describe their scale factor, but fix the >> exponent and fraction size. Unums self-describe the exponent size, fraction >> size, and inexact state, and include fixed point and IEEE floats as special >> cases. >> > > The presentation can be seen here, provided you have the Silverlight > plugin: > > > http://sites.ieee.org/scv-cs/archives/right-sizing-precision-to-save-energy-power-and-storage > > Now, I don't know enough about this topic to say if they're a good or bad > idea, but I figured the idea is interesting/relevant enough to share with > the Julia crowd. > > I'm also wondering if they could be implemented (relatively) easily within > Julia, given its flexible type system. If so, they might provide an > interesting advanced example, no? >
