Re: Motion P1788/M0032.01:MidpointMeaning -- discussion period begins
Michel & P1788
On 15 Mar 2012, at 15:40, Michel Hack wrote:
> With regard to midpoint for implicit formats,
> Dan Zuras wrote, replying to Vincent Lefèvre:
>>> In particular, these requirements are valid for:
>>> X1 = hull_T([inf_F(X),mid_F(X)])
>>> X2 = hull_T([mid_F(X),sup_F(X)])
>>> if a hull_T function is defined.
>>
>> Also a fair point. Is hull any more unique
>> among the implicits than the "smallest"
>> superset in question?
>
> I seem to recall that part of the *definition* of an implicit format
> is an explicit hull function that is THE hull function by definition,
> precisely because there may not be a unique "natural" hull.
>
> For variable-precision formats there may indeed not be a "smallest",
or indeed a "minimal"
> at least in a practical sense. (An item that consumes the remainder
> of the address space may well be a tightest enclosure in any given
> situation, but would be useless since there would be no resources to
> continue with the computation.)
That's why I explicitly say in my draft Level 2 text that such an interpretation of "variable-precision" is incompatible with P1788. To conform with IEEE 1788, a VP interval system must interface in such a way that at any moment it is working with intervals of a given precision. I.e., it supports a potentially infinite family of interval types T_d, parameterized by some measure d of the number of digits of precision. Not a single type that is the union of these.
I suspect this will be unpopular with the authors of some VP systems, but it is a simple way to cut that Gordian knot; in fact the only way that I can see at present.
John