Re: Motion P1788/M0009.01_ExactDotProduct
James Demmel wrote:
There are a number of papers on accurate summations and dot products in
software
(the most recent paper I know of is by Zhu and Hayes in SISC, 2009),
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
exhibiting
a big design space with lots of tradeoffs in space, time and accuracy
(correctly
rounded vs faithful vs at most a few ulps of error).
Hopefully any statement of standard will not discourage implementors from
continuing to explore this space.
In theory, the current proposal only concerns the exact dot product,
hence should not affect any inexact computation.
In practice, if a fast hardware exact dot product exists, it would make
the inexact variants obsolete. In software, the exact dot product seems
to be significant ly slower than the inexact variants.
Since apparently only an optimally enclosed dot product (or even only
an ``accurate'' dot product with a high relative accuracy) is needed
for most (or even all?) known applications, the question is whether
general hardware support will be available soon.
One also needs to take into account that if some hardware wants to claim
conformance to the standard, it would have to implement all of the
standard.
Thus; Would the requirement of an exact dot product be likely to delay
hardware support for all of interval arithmetic?
Arnold Neumaier