Re: Please listen to Ulrich here...

[Richard Fateman <fateman@xxxxxxxxx>]

On 8/29/2013 2:43 PM, Langou, Julien wrote:

Hi all, 

Jumping in in the conversation and just want to give a pointer beside BLAST and XBLAS (see Jim's email for this). 

If EDP (exact dot product) is so important, why is it not in BLAS?  

I am not sure I am answering the question but, related to this and of historical note, the routine SDSDOT has been part of the since its inception. (That is year 1979 for Level 1.)

Cheers, 

Julien.

It's a dot product, but not exact.

Usually, making this code better seems to involving
unrolling the loop, or somehow doing the arithmetic on a GPU
(graphics processing unit).  There's another stream of papers on trying
to make it more accurate.

Here's some hacker's results on timing some random chips (I am
not endorsing this particularly, but I found it via Google)

http://blog.theincredibleholk.org/blog/2012/12/10/optimizing-dot-product/

There's much more discussion, including the role of a limited amount
of high precision (e.g. quad) arithmetic starting on page number 134  (in the PDF, it is page 144)  in

Basic Linear Algebra Subprograms Technical Forum Standard, International Journal of High Performance Applications and Supercomputing, Volume 16, Number 1, Spring 2002.
see first item here..

http://netlib.org/blas/blast-forum/

So it is not that BLAS people ignored extended precision.  I think they consider using
it with a more delicate touch, and recognizing the realities of current
computer architecture (multiple processors, caches and memory,
extended (80 bit) IEEE floats, etc.)

The document on Interval BLAS, which I had not seen, starts on page number 219.  (add 10 in the pdf)
or separately, in the reference from Chenyi Hu:  http://www.netlib.org/blas/blast-forum/chapter5.pdf

is 80 pages of fairly detailed descriptions, but a search reveals
that the BLAS forum participants who constructed the interval BLAS specification did not
require EDP, or even mention it.