Re: Proposal for a new structure of the standard
> Date: Mon, 19 Jul 2010 00:49:44 +0200
> From: Vincent Lefevre <vincent@xxxxxxxxxx>
> To: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Proposal for a new structure of the standard
>
> On 2010-07-14 00:56:39 -0700, Dan Zuras Intervals wrote:
> > > According to the *specification*, the numbers are not bounded, thus
> > > the set is infinite.
> >
> > I'm not sure what specification you mean here.
>
> GMP's (for the mpz_t type). GMP doesn't document any limit on the
> size of the integers, so that the considered set is Z. In practice,
> there will be limits that depend on the available memory (thus are
> not fixed, so that making a specification with limits would be
> rather artificial).
>
> And since the set of endpoints is infinite, the set of the intervals
> based on mpz_t would be infinite too.
>
> For floating-point, note that there are feature requests for MPFR to
> have unbounded exponents, using the mpz_t type for the exponent.
Vincent,
I will pass on a detailed response to all of your points
& concentrate on this one. For it seems that the crux
of our misunderstanding lies here.
You are thinking of the whole of GMP as the basis for a
single interval datatype along the lines of MPFI.
I am thinking of these as a countably infinite set (in your
resource limited sense of the word 'infinite') of possible
interval datatypes indexed by base, precision, & range.
Each one of which is finite in both range & precision.
This is in analogy to the countably infinite class of
floating-point datatypes we defined in 754-2008 indexed
by b, p, & emax.
I think it makes more sense to have the set that lives
at level 2 be a single instantiation of a GMP object as
an interval type indexed by base, precision & range as
well as style (explicit/implicit).
That way when we want to project the solution to the Real
relation x^2 < 2 onto level 2 we have a definite object
to land on. Without that the mapping is ill defined.
There is more but that is the meat of it.
Does that make sense now?
Or is it that you understand but just disagree?
Dan