On Wednesday, July 29, 2015 at 4:59:02 PM UTC-4, Zenna Tavares wrote: > > 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. >
Without hardware, the advantages of variable size (< Float64) are overwhelmed by the software overhead. Without solving the dependency problem, representing a set of reals (as opposed to an individual real as in standard FP) is useless for error estimation. And I don't see a clear practical use-case for an inexact bit per value, as opposed to a single inexact flag for a whole set of computations (as in IEEE).
