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Re: exact dot product

Vincent;
a number of applications are mentioned in my mails to IEEE P1788 of May 18 and May 22. Other applications are mentioned in the attachments to my mail of May 18 (The paper and poster entitled: "Very fast and exact accumulation of products"). Non of these applications can be solved with a correctly rounded dot product, i.e., the exact dot product is indeed needed for sloving these problems.
A fundamental tool of interval arithmetic is "long interval arithmetic" sometimes also called "dynamic precision interval arithmetic". It carries so many digits that the result always can be guaranteed. (The number of digits needed can be obtained by a test run in simple interval arithmetic of by trial and error.) I attach a copy of a few pages of my book "Computer Arithmetic and Validity". They show how "long interval arithmetic" is defined. The definition of the arithmetic operations (and applications also) are full of exact dot products. For other fascinating applications see the paper [5] on the poster.
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: 

Best wishes
Ulrich


Am 27.05.2013 15:46, schrieb Vincent Lefevre:

On 2013-05-24 22:04:32 +0200, Ulrich Kulisch wrote:

Vincent:

the exact dot product is the subject of the discussion, not a
correctly rounded dot product.

But do you have any application of the exact dot product? I mean
an application that directly uses and needs it, where a correctly
rounded dot product and/or multiple precision (without focusing
on exactness) could not be used.




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Prof. Ulrich Kulisch

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