[std-interval] Mathematical relations and default initialization

[Guillaume Melquiond]

Le jeudi 14 septembre 2006 à 10:21 +0200, Frédéric Goualard a écrit :

> The nth_root_rel() operator does not appear in the standard. Is this
> omission on purpose? If indeed it is, why is it so?

The nth_root_rel is purposely out of the proposal because nth_root is
out too :-). I don't think the omission is on purpose though. If people
feel it is useful, it can be added.

> Side notes:
>   - on Page 12, the signatures for the mathematical relations are wrong
> (compare with page 27).
>   - div_rel() does not appear on page 27 while it is listed on page 12

Thanks, I will take a look.

> * Default initialization
> I see on page 15 that the default constructor creates an empty interval.
>  At some point in the discussion, Sylvain gave 6 possible ways of
> implementing this constructor:
> 
> 1- no default constructor at all
> 2- [0,0]
> 3- empty
> 4- whole
> 5- uninitialized tag
> 6- see below (something a la "singular iterator")
> 
> Possibility 4 was brushed away from the start, and the remaining
> possibilities heavily debated. In my opinion, it makes sense to have the
> default constructor return "whole" since interval arithmetic is often
> used in processes that try to gain some information on the possible
> value of a variable (that is, we start from a wide interval and narrow
> it down to some reasonably small one).

I don't remember 4 being brushed right away (proposition 1 was). As a
matter of fact, propositions 3 and 4 have reached a point in my opinion
where I consider them to be equally useful. So, at least on my side, it
is still 4 in the proposal, only because of inertia.

Best regards,

Guillaume