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.
On Wednesday, July 29, 2015 at 11:14:43 AM UTC-4, Steven G. Johnson wrote: > > > > On Wednesday, July 29, 2015 at 10:30:41 AM UTC-4, Tom Breloff wrote: >> >> Correct me if I'm wrong, but (fixed-size) decimal floating-point has most >> of the same issues as floating point in terms of accumulation of errors, >> right? >> > > What "issues" are you referring to? There are a lot of crazy myths out > there about floating-point arithmetic. > > For any operation that you could perform exactly in fixed-point arithmetic > with a given number of bits, the same operation will also be performed > exactly in decimal floating-point with the same number of bits for the > signficand. However, for the same total width (e.g. 64 bits), decimal > floating point sacrifices a few bits of precision in exchange for dynamical > scaling (i.e. the exponent), which gives exact representations for a vastly > expanded dynamic range. > > Furthermore, for operations that *do* involve roundoff error in either > fixed- or decimal floating-point arithmetic with a fixed number of bits, > the error accumulation is usually vastly better in floating point than > fixed-point. (e.g. there is no equivalent of pairwise summation, with > logarithmic error growth, in fixed-point arithmetic.) > > If you want no roundoff errors, ever, then you have no choice but to use > some kind of (slow) arbitrary-precision type, and even then there are > plenty of operations you can't allow (e.g. division, unless you are willing > to use arbitrary-precision rationals with exponential complexity) or square > roots. > > >
