On Wednesday, July 29, 2015 at 11:47:42 AM UTC-4, Tom Breloff wrote: > > The inexact exception flag isn't quite the same. That flag just signifies > that at some point in the calculation there was rounding. It doesn't give > any indication of how wrong the final number may be. The "ubit" coupled > with variable-sized unums allows for potentially very precise interval > arithmetic, but without requiring the full storage. >
Interval arithmetic is usually considered to be useless for error analysis in most cases unless it is coupled with sophisticated additional analysis (e.g. Taylor arithmetic) because of the dependency problem; that's why they are proposing "uboxes" but with vastly greater memory and computation requirements than interval arithmetic. (Interval arithmetic has other applications outside error analysis, though.) And the slight memory gain of using fewer than 64 bits will be completely swamped for any large computation (i.e., any computation where the memory matters) by the cost of software unums. If someone makes an efficient hardware implementation, matters would be different, but I'm not going to hold my breath for that.
