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. For example, if we want to represent the value "1e-1000000", the unum would effectively be the range (0, smallnum), where smallnum is the smallest positive number we can represent exactly. This actually requires very little actual storage for a packed unum, although it can be an extremely precise range.
On Wed, Jul 29, 2015 at 11:33 AM, Steven G. Johnson <[email protected]> wrote: > > > On Wednesday, July 29, 2015 at 11:23:34 AM UTC-4, Scott Jones wrote: >> >> For me, the nice thing (if I understand this correctly) is that UNUMs let >> me know that there *was* roundoff error, whereas with currently IEEE binary >> *and* decimal standards, you have no way of telling. >> > > IEEE floating-point has the inexact exception flag to signal that a > roundoff error occurred. The unum proposal would store an inexact bit in > each number, and I'm skeptical that this adds much value. (In practice, > almost all nontrivial computations with a fixed precision will incur a > rounding error, and if one output is inexact usually all of them are.) >
