Re: IEEEP1788
Ulrich
On 19 Apr 2015, at 21:35, Ulrich Kulisch <ulrich.kulisch@xxxxxxx> wrote:
> In contrast to the simplicity of arithmetics in IR and IF, IEEE P1788 develops interval arithmetic on the base of IEEE 754 arithmetic with all its exceptions. This is a big mistake. It unnecessarily pulls all the IEEE 754 exceptions into interval arithmetic.
This is just not the case. At the start of the set-based flavor, with notation changed to match plain-text:
> 10.2. Intervals
>
> The set of mathematical intervals provided by this flavor is denoted IR. It comprises those subsets xx of the real line R that are closed and connected in the topological sense: that is, the empty set (denoted ∅ or Empty) together with all the nonempty intervals, denoted [xlo, xhi], defined by
>
> [xlo, xhi] = { x ∈ R | xlo ≤ x ≤ xhi }, (4) where xlo = inf xx and xhi = sup xx are extended-real numbers satisfying xlo ≤ xhi, xlo < +oo and xhi > −oo.
754 arithmetic is the dominant finite-precision approximation to R arithmetic at present which is why at Level 2 we have the idea of "754-conforming". But in 12.1.1:
> An implementation shall provide at least one supported bare interval type. If 754-conforming, it shall provide the inf-sup type, see 12.5.2, of at least one of the five basic formats in 3.3 of IEEE Std 754-2008.
Thus an implementation is free to ignore 754 arithmetic entirely! So, in what way does 1788 "develop interval arithmetic on the base of IEEE 754"?
John Pryce