Re: a question about formatOf operations

[Nick Maclaren <nmm1@xxxxxxxxxxxxx>]

> > IMO 754R needs to restrict itself to things that are widely desired or
> > which at least don't have widespread opposition. 
>
> To put things into perspective, there is a lot unsaid in 754 about
> expression evaluation that has caused difficulties for almost 30 years.

Very true.

> Why do numerical results vary with compiler release and optimization
> level?   

Because nobody, in 50 years of trying, has ever thought of a way to
achieve both bitwise consistency and more than trivial optimisation?

And that ignores the fact that bitwise consistency is provably
incompatible with parallelism, which is beginning to bite on modern
systems.

> It's a big deal: differences in interpretation cause test vectors to
> pass or fail, and then even hardware vice presidents get excited if
> somebody concludes the hardware is defective (usually not true, but
> hard to prove at a casual glance).

That is true, but why shoot the messenger?  The difficulty is inherent
in the problem, at a deep mathematical level.  Surely the solution is
to educate the ignorami (e.g. technical vice presidents with no useful
technical background) and not try to 'solve' a mathematically insoluble
problem by defining it out of existence.

Because that won't work.

Look, I hit that problem in the early 1970s when working with NAG
on automatic test suites.  My trickiest problem was with multivariate
Gaussian random numbers, where the algorithm I invented used the L.L'
decomposition of a positive SEMI-definite matrix.  And that is
mathematically well-defined but with unspecified results.  Ouch.
The solution is to write the tests so that the comparison is done
on the recreated sample covariance matrix, which gives a considerable
level of immunity to that issue.

But even that doesn't extrapolate to all problems, such as global
optimisation and chaotic PDEs.  I sincerely hope that nobody here
thinks that defining a bitwise predictable solution to a chaotic
system actually makes any mathematical sense.


Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email:  nmm1@xxxxxxxxx
Tel.:  +44 1223 334761    Fax:  +44 1223 334679