In John Gustaffson's book The End of Error, he discusses Ulrich Kulisch's exact dot product, which (in double precision) requires a 2100 bit fixed point register which rounds only once after the computation of the dot product is complete.
I have found only one statement about how this instruction can be used in numerical analysis, namely Kulish claims "it is the EDP which makes residual correction effective . . " However, I could not find a reference demonstrating this claim.
What numerical methods would benefit from an exact dot product? And more interestingly, are there algorithms which become stable in the presence of a hardware dot product which are unstable otherwise?