Re: formatOfMidpoint()
On 2012-02-11 16:20:06 -0500, Michel Hack wrote:
> It seems obvious to me that if a midpoint is not representable in the
> target format, the result should simply be NaN. I'm using the minimal
> definition of midpoint here: an interior point.
This is not very clear. I think that a Level-2 midpoint (i.e. as an
element of some number format F) must be an element of the interval,
else it is NaN. If possible, it should be an interior point.
If can be interesting to introduce a notion of a number format F
"compatible" with an interval type T. The conditions could be:
* For each x in F, [x,x] is an element of T.
* Each non-empty interval of T must contain an element of F
(or, equivalently, a point interval of T).
In particular, for such a number format, it is possible to define
a midpoint operation such that the Level-2 result (element of F)
is in the interval. Not sure whether it should be required that
such a number format necessarily exists, specially if you want to
allow:
> This might also be the case for some of the off-center implicit-format
> examples, where the issue is not range but precision: if the Level 1
> interval is entirely between two representable target-format values,
> then there is no representable midpoint, and the result should be NaN.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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