On Wednesday, 29 July 2015 16:50:21 UTC+3, Steven G. Johnson wrote: > > Regarding, unums, without hardware support, at first glance they don't > sound practical compared to the present alternatives (hardware or software > fixed-precision float types, or arbitrary precision if you need it). And > the "ubox" method for error analysis, even if it overcomes the problems of > interval arithmetic as claimed, sounds too expensive to use on anything > except for the smallest-scale problems because of the large number of boxes > that you seem to need for each value whose error is being tracked. >
Well, I don't know enough about traditional methods to say if they're really as limited as Gustafson claims in his book, or if he's just cherry-picking. Same about the cost of using uboxe However, ubound arithmetic tells you that 1 / (0, 1] = [1, inf), and that [1, inf) / inf = 0. The ubounds describing those interval results are effectively just a pair of floating point numbers, plus a ubit to signal whether an endpoint is open or not. That's a very simple thing to implement. Not sure if there's any arbitrary precision method that deal with this so elegantly - you probably know better than I do.
