Re: IEEEP1788

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Am 19.05.2015 um 14:18 schrieb Vincent Lefevre:

Dear Ulrich,

On 2015-05-19 12:56:33 +0200, Ulrich Kulisch wrote:

Interval arithmetic carries the potential to replace floating-point
arithmetic by some general computing tool where results come with
highly accurate guarantees. Two things are definitely necessary to
reach this goal:

A. Fast double precision interval arithmetic and
B. An exact dot product (EDP).

This is just your opinion. P1788 covers arbitrary number and interval
formats. For many applications, double precision is not sufficient,
in particular when one takes into account that interval arithmetic is
pessimistic.

Dear Vincent and other friends of Interval arithmetic!

I am sorry to say this, but your mail shows that the matter is not yet really understood.
Why don' t you study the subject. I am sure and promise you, understanding it will make
you very happy. But everybody has to do this little work by himself.

I can only repeat myself: The exact dot product brings speed and accuracy to interval
arithmetic. It is the key operation for wide acceptance of interval arithmetic. It can be
computed in a fraction of the time that any other known method needs to compute a
correctly rounded dot product. It also is the key to many other valuable application like
variable precision interval arithmetic.

Please invest the little time to study it.

Best wishes
Ulrich

-- 
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
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Prof. Ulrich Kulisch

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