Interchange formats (was: NaI's as decorated empty sets)
Michel and all
On 9 Sep 2009, at 11:23, Michel Hack wrote:
Arnold Neumaier wrote:
The standard should be silent about how things are actually
represented, and only specify the effect of operations on
the representations (whatever they are).
Except for interchange formats -- if we want to deal with that.
As far as I'm aware, this is the first time interchange formats for
intervals have been mentioned. Seems to me this is a good idea, as it
surely won't be too difficult, and will be found useful? ASSUMING, as
seems likely, that we define level 3 representation to be a version
of infsup form, I would suggest
1. Define interchange formats only for 754-conforming interval systems.
2. Have exactly one interval interchange format for each 754
interchange format.
3. Define it basically to consist of the concatenated bit-strings of
xlo and xhi where the level 3 representation of a nonempty interval
is floating-point datums xlo, xhi representing the bounds.
4. If the implementation uses an [xlo, xhi] representation at level
3, then use the same scheme for Empty, and for any NaI's that may be
defined.
5. But if the implementation uses a different representation, say [-
xlo, xhi], we need to define some conventions for how this maps to
the [xlo, xhi] form. Trivial for nonempty intervals, not quite so in
the case of Empty and NaI's.
Are there any other difficulties? Apart from endian-ness.
John