Re: Information
On 2013-09-06 12:52:40 -0400, Michel Hack wrote:
> To get back to the Exact Dot Product: I continue to maintain that,
> without support for a reasonable set of operations on the format used
> to represent an EDP result, this would be pretty useless.
I agree.
> As I said before, the representation used may not have to be
> exposed, i.e. it could exploit Kulisch accumulators, lists of scaled
> FP numbers, or whatever else might be suitable.
IMHO, there are two cases:
1. One just wants to specify some operations (e.g. EDP), and actually
internals must not be exposed (more than: may not have to be exposed).
The additional format could be completely specified but this should
remain at Level 2 in such a case, and I don't think it would be a good
idea to specify a new format (taking an existing format, such as any
IEEE 754 extended one, could be OK, but such a format may not be
suitable); remaining abstract would be better for now, in particular
for exact operations, as the exact result won't depend on the format.
2. One wants to specify a completely new arithmetic (e.g. CA), so that
some operations may exploit it. But such an arithmetic shouldn't be in
P1788 for various reasons: we are too close to the deadline, P1788
would be too bug (since the new arithmetic isn't directly related to
interval arithmetic, there's nothing wrong in having 2 standards for
2 different things), there isn't a reference implementation yet, and
for related implementations (such as in *-XSC), the number of users
is too small for a standard. And more generally I don't think that
such an arithmetic is ready to be standardized.
> It would have to support at a minimum the ability perform
> correctly-rounded conversions to any other floating-point type, and
> exact sums.
If these are the only operations, I don't think that EDP would bring
more than a formatOf correctly-rounded dot product.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)