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Re: Zhu&Hayes paper mentioned by Jim Demmel (was: Exact dot product)

Michel Hack wrote:

I found a slide presentation "Fast, guaranteed-accurate sums of many
floating-point numbers" on the RNC7 program -- but no full paper.
Is this the intended reference?


No. The published paper is

Yong-Kang Zhu and Wayne B. Hayes
Correct Rounding and a Hybrid Approach to Exact Floating-Point Summation
SIAM J. Sci. Comput. / Volume 31 / Issue 4
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SJOCE3000031000004002981000001&idtype=cvips&prog=normal


Its rounding is faithful, not necesarily correct.  I wonder whether
it remains faithful in directed rounding mode (in which case it would
automatically also be correct, according to the given definition of
faithful rounding: one of the two bounding machine numbers if in
between, otherwise the exact machine number).

So -- it works well for sums of numbers far from extreme exponents,
and is clever and fast in its intended domain of application -- but
it is a long shot from offering a tight dot product interval result
from a pair of vectors in the widest supported scalar format.
There are many variants of the same idea, and creation of an interval version requires only minor modifications, I think.
But even faithful rounding would give an accurate enclosure in the sense of the Vienna Proposal, which is enough for all applications I know of, 
including those mentioned by Kulisch.


Arnold Neumaier