Re: Motion P1788/M0033.01 Number Format:NO
On 2012-06-06 11:34:06 +0100, John Pryce wrote:
> Alan
>
> On 6 Jun 2012, at 09:11, Alan Eliasen wrote:
> > My vote on Motion M0033.01 Number Format is NO.
> >
> > Currently, the text of the motion is ambiguous or impossible to meet
> > if the implementation of the numerical type uses arbitrary-precision
> > numbers. (And good numerical implementations will have arbitrary
> > precision numbers.)
Alan,
My main target is arbitrary precision. I wouldn't have written a
motion like that if it were impossible to meet. The idea is the
same as the one that is already present for intervals, in the
Level 2 text, as John says:
> It is made quite clear in the draft Level 2 text (have you read it?)
> that rounding, and interval hull, are with respect to a given finite
> set of numbers or intervals. There is nothing "ambiguous or
> impossible" given one accepts that concept, and you are one of
> *very* few people who have objected to it.
>
> If your system has an infinite set of possible numbers or intervals
> you have to express this set as a union of a (presumably increasing)
> sequence of finite sets, one of which is selected at any moment.
> Have you a good theoretical alternative? If not, live with it and
> adapt your system.
Basically, this means that for rounding, the target precision (or
some similar notion) needs to be provided (either explicitly or
implicitly). I think that most arbitrary-precision libraries behave
like that. I'm not sure what could be done for packages like iRRAM
(perhaps Level 1 is for such packages, after all).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)