Arnold Neumaier wrote:
I had therefore asked for providing evidence for applications that really
need the exact dot product, but this hasn't generated any response.
Jim Demmel replied:
Though I have not written this down formally, I think that an algorithm
that is correct for any underlying number of mantissa and exponent bits
must in effect do as much work as sorting (by the exponents).
Sorting in order to discover and eliminate cancellations (which is what the
real problem is) assumes that the entire input set is available at once.