5th operation?

[David Hough]

"If you don't care about the error then you don't care about the answer."

That this is the underlying problem in the bank example can be seen by 
considering the consequences of any uncertainty in the summands.
One correctly-rounded dot product won't help with that.   However, one
correctly-rounded INTERVAL dot product would demonstrate the error inherent
in the computed result.

But even considering only exact input data,
there are other ways of estimating the same error that may be more
economical, such as keeping track of the largest magnitude intermediate result.
For this purpose, a machine operation that implemented, or assisted in
fast implementation, of 

	z = |x| + |y|

would help, provided languages provided easy access.    Such an operation 
exists, for instance, in the Weitek 1164/5 chips used in the Sun-3
floating-point accelerator and the Sun-4/1x0 and 4/2x0 systems, but there's
no hardware access to it from the Sun-4's FP controller chip
and no language support in the FPA.

The crux of the argument about correctly-rounded dot products is whether
they provide or could provide
an economical solution to the problem of estimating the effects
of various kinds of errors, compared to other methods that have been or
might be implemented.   Arguments on both sides are somewhat impeded by
lack of best possible hardware implementations and inadequate access from
standard programming languages.   It's my belief that extending GCC and
when ready, GNU Fortran, is the best provide a widely-available solution
to the latter problem .