Re: The new motion
On 2013-06-10 22:05:27 +0200, Ulrich Kulisch wrote:
> In 2009 a motion requiring an EDP within P1788 passed by the given rules
> with shall. Shortly after that (April 2010) the EDP was listed in Draft 2.2
> of the standard on page 3, under
> 0.3. *Inclusions*. The standard specifies
> - Data type and operations for the calculation of exact sums and dot
> products.
> This was level 1, where it indeed should be installed to give it
> appropriate weight.
It seems that you make some confusion between levels and "weight".
Levels don't classify operations according to some "weight". They
are just there to make the structure of the standard clear. Level 1
operations don't have more importance than level 2 operations. It's
actually the opposite: Level 1 operations are just helper functions
to ease the specification at Level 2; they will never be a Level 1
implementation.
> Later it was argued it does not really fit to this location and will be
> listed later in the text. After a very long time it reappeared under
> 11.11.11. This was level 2. The text, however, did not quite reflect the
> intention of the motion. So Van Snyder and myself requested a few changes.
> But nothing happened. After some time we repeated our request for changes
> twice. But nothing happened until today.
I'm not satisfied either, because as currently specified by the
standard, EDP (and more generally CA) seems to be a dead end:
you get some exact result, but can't do anything with it except
losing information.
> Then it was argued there is some confusion around Motion 9 and clarification
> was requested. I answered with several detailed mails with attachments to
> the diverse requests. Please read these mails and the attachments (mail of
> May 18 with 4 attachmnents, 2 mails of May 20 with one attachment, mail of
> May 22, mail of May 31 with one attachment, mail of June 6 with one
> attachment). I got no serious response. I felt that I was talking to a
> wall.
>
> Then motion 45 was launched. It lowers the requirement for the EDP from
> shall to recommended and lifts its status from level 2 to level 3. This is
> momentarily the result of a long tactical journey. It has nothing to do with
> science. The next step in this chain could be lifting it to level 6? Under
> Rationale motion 45 shows the following text:
>
> (1) I do not think Prof Kulisch has made the case that there are
> many problems that can only (or even best) be solved by EDP, rather
> than a dot product correctly rounded, or faithfully rounded, to the
> working precision (CRDP and FRDP respectively). In current
> discussion, he cites the same two applications he did in late 2009:
> Rump operator & logistic map. And Lefevre, Neumaier & Rump all say
> these can be solved nearly as well using FRDP.
Actually this is rather ambiguous. One point is that with the current
specification, you don't have more than CRDP (except for intermediate
results). Then, what I'm saying is that most problems can be solved
using various forms of multiple precision; they don't require full
exactness. And what you said in your 28 May 2013 12:19:26 +0200 mail:
| It may well be possible to simulate the functionality of long
| interval arithmetic by multiple precision arithmetic and a correctly
| rounded dot product. But the simplest and fastest way of computing a
| correctly rounded dot product is via an exact dot product:
is clearly wrong. Whether EDP is simpler depends on how the API is
designed. And in the floating-point context, EDP is certainly not
faster, both in theory and in practice, because you can have very
small terms you don't need to take into account. EDP can also take
more memory, for the same reason.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)