Re: Discussion period started Re: Proposal of Motion 6, version 3
On 2009-08-07 05:11:34 +0100, John Pryce wrote:
> On 6 Aug 2009, at 00:00, Vincent Lefevre wrote:
> >Mixed-radix can still be implemented in "valid" accuracy mode, thanks
> >to implicit conversions.
>
> Yes. I had in mind that P1788 is a _language-independent_ standard.
> It seems to me that
> - implicit conversions are a language-dependent matter;
Not necessarily. P1788 could be implemented as a library. What I mean
is that if the library implements P1788 in binary for some formats and
in decimal for some formats and if P1788 requires conversions between
all supported formats (including between different radices), then the
library can implement mixed-radix for free in "valid" accuracy mode by
first converting every input into the destination format.
So, perhaps mixed-radix in "valid" accuracy mode could be recommended
(on course, the implementation is free to do better...), and perhaps
to be at least as tight as with such implicit conversions.
> - however, our expression-evaluation subgroup may well make
> recommendations (non-normative) on this issue in due course.
> My current wording is not ideal. Vincent, will you suggest an
> improvement?
I propose something like that:
Mixed-radix should be supported and an elementary function should
return an interval at least as tight as if the following operations
were done: each input is converted into the destination format, then
the single-format elementary function is applied on the converted
inputs.
> >Page 6, 3.6.1: "An *abstract floating point format* (*af-format*) F
> >is a finite subset of R* containing −∞ and +∞."
> >
> >I would have called it an "abstract discrete format". In particular,
> >it can correspond to a fixed-point format.
>
> Ah yes. It can indeed correspond to a fixed-point format, so the
> word "floating" in the name is misleading. But your "discrete" is
> not the right term to contrast with "interval". Whether point or
> interval, each set of level 2 datums is finite, so discrete. I think
>
> - "floating point" should just be changed to "point" here.
> - So af-format, cf-format should become ap-format, cp-format throughout.
>
> Arnold, you helped harden up this part of the text. Any comments?
I agree with Arnold's proposition: Abstract number format.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)