same results on every machine

[David Hough]

> As the computing world goes more an more parallel
> the idea that a sum reduction of an array of values will always yield
> the same result on every machine seems unattainable.

This statement might be about what happens when you try
to run a program on a system with a number of processors in
competition with other users, so that the number of processors
you get varies from run to run.  If you do the sum reduction
by dividing up the array by the number of available processors,
you'll get different results due to different rounding errors.  
So from this point of view, it seems pointless to
standardize base conversion, expression
evaluation, or elementary transcendental functions, in order to
get identical results.

If you don't cause any rounding errors in sum reduction or more
generally in scalar product accumulation of vectors, however, 
this problem goes away.  That's the point of the Kulisch reference.
Many of the standard problems that are readily vectorizable
or parallelizable are also amenable to the Kulisch approach.

Anyway nobody has even proposed requiring identical results on
all machines.  What I currently favor is a requirement to 
provide identical results on all IEEE 754 implementations by default, 
with the expectation that each implementation will also provide
an optional faster mode; the relative speedup will vary quite
a bit among systems and programs.  But in time hardware designers
will catch on and figure out ways to get the standard results
sufficiently fast that there won't be any need to have the
fast mode be any different.

This is already happening in a limited way, sooner than I
expected.  I just heard today that Solbourne has produced what
is apparently the first SPARC implementation that charges
no penalty for subnormal operands or results.  And I imagine
they did that without slowing down the normal case.  So on
that system, the SPARC nonstandard floating-point mode bit
will be a noop.