Re: IEEEP1788
On 2015-06-09 10:26:08 +0200, Ulrich Kulisch wrote:
> David,
>
> I feel that I still owe you an answer.
>
> Looking at the names of the colleagues you mention in your mail I
> wonder whether we are talking about the same matter. The subject
> of my mail is /interval arithmetic/ and in particular /long/ or
> /variable precision interval arithmetic. /It detects by itself
> whether it was successful or not.
I suppose that you meant: one particular form of variable precision
interval arithmetic, i.e. where an interval is represented as a
floating-point expansion (non-overlapping sum of floating-point
numbers) + a double-precision interval. Is that right?
But there are other ways of doing variable precision interval
arithmetic.
> An exact dot product for a modest data format (double precision) is
> the building block for the latter.
It may be one building block. There may be other solutions. There are
also other building blocks for various arithmetics and so on.
BTW, I would rather see *simpler* building blocks for *more common*
algorithms, starting with the error on a sum of two floating-point
numbers (which otherwise has to be computed with 5 or 6 operations
in the general case). But in any case, this is more something for
IEEE 754 than for IEEE 1788.
> By pipelining it can be computed in the time the processor needs to
> read the data, i.e., its arithmetic does not contribute to the
> computing time. The dot product also is a fundamental operation in
> all vector and matrix spaces as well as for residual refinement or
> defect correction techniques. It should already have been included
> in IEEE 754 35 years ago.
Well, correctly-rounded dot product should have been included in
IEEE 754 seven years ago. But this is not the exact dot product.
So, if I summarize, you wanted to standardize a particular
implementation (the one with a long accumulator) of a particular
complex building block of a particular arithmetic.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <https://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)