Zhu&Hayes paper mentioned by Jim Demmel (was: Exact dot product)
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?
That method uses the input array as scratch space -- but could obviously
have allocated a private array or list, either bounded by the same space
as a complete accumulator (assuming the input vector is in fact larger
than that, otherwise the input size is a coarse bound), or grown on
demand. It does not accomodate dot product as there is no provision
for exact products (but there are separate techniques for that, using
fma to a wider summation type perhaps, and handling summation overflow
with exponent-wrap, either via explicit scaling or via trap handling).
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.
Michel.
---Sent: 2009-10-30 21:58:40 UTC