Re: Meeting the Scope and Purpose of P754

[Nick Maclaren <nmm1@xxxxxxxxxxxxx>]

Guillaume Melquiond <guillaume.melquiond@xxxxxxxxxxx>wrote:
> In conclusion, bit-to-bit reproducibility makes it possible to write
> fast mathematical libraries. Without it, the algorithms are several
> times slower, because they have to take into account the discrepancies
> that may occur in the course of the computations.

Oh, really?  Then I must have been imagining the performance (and
accuracy) of my code and that of other people's.

I am sorry, but the only appropriate response to that is "nonsense".
Bitwise reproducibility makes it significantly easier, which may
help in these days of dumbing-down, and can make it SLIGHTLY faster,
but any competent programmer can do better than "several times
slower".

If you are comparing completely system-dependent code against
portable code, then the latter is often several times slower, but
most of that is because of the lack of the right primitives.  If
you compare two sets of portable code, one of which assumes ONLY
bitwise reproducibility, it is rare that there is much difference.

What you say may well be true if you are also demanding the
numerical nonsense of 'perfect' rounding.  But you did not say that,
I know of no evidence that it is (technically) particularly useful
(though it is politically), and many people regard it as not worth
the effort.  Except for a FEW functions (division, square root etc.),
0.505 ULPs is quite good enough for numerical purposes.


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