Re: About exact results and exact endpoints, also 11.11.7

[Vincent Lefevre <vincent@xxxxxxxxxx>]

On 2013-02-14 08:30:33 -0800, Richard Fateman wrote:
> On 2/14/2013 6:17 AM, Vincent Lefevre wrote:
> >Exact representations would not be provided by a different flavor
> >(an exact representation makes sense in every flavor), but would
> >be some specific parameterized implicit interval type (this is
> >already covered by "Multi-precision interval types", but P1788
> >gives little specification).

> There is a distinction between a multi-precision type and an exact type.

I don't think that there needs to be a distinction, as you can
regard an exact type as being a multi-precision type that includes
all the constructible values. For instance, this can be implemented
as a text string denoting an expression, and the precision would be
the size of the string.

Of course, you would have the same computability problems between
an "exact type" and such a multi-precision type.

> I was surprised to see in 11.11.7 that the standard seems to be
> anticipating implementations in which two numbers (scalars) x,y can be
> produced
> such that the implementation cannot tell whether x<=y.
> Or this computation "can be hard".

See the example I've given above.

> This seems so fundamentally a part of interval arithmetic
> implementation that it must be a solved problem if the
> implementation is to work.
[...]

It is well-accepted that problems are not decidable. You'll have
limitations, but you can still do some work and get useful results,
such as getting bounds. I suppose no-one proposes to reject powerful
programming languages just because the halting problem can't be
solved.

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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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