Re: [STDS-754] reproducibility of tininess detection for binary formats

[Guillaume Melquiond <guillaume.melquiond@xxxxxxxxxxx>]

Le lundi 15 octobre 2007 à 09:34 -0400, Michel Hack a écrit :
> > So can you please detail a practical use case where the second definition
> > would fail to give a proper answer, but the first one would?  This is what
> > my first mail was about: Is there a situation where the first definition
> > gives an answer more useful than the first definition.
>
> Here is a very important one:  in directed rounding away from zero,
> the "after rounding" rule would never signal underflow, even though
> the result may have no significant digits left at all.  (This is for
> default exception handling.)

I'm really surprised by your statement, so perhaps there is something I
don't understand. As the after-rounding behavior considers a theoretical
format without exponent limitations, if you have a result with no
significant digits left that does not signal underflow, it means that,
in another format with a bigger exponent range, you would have a result
inside the normalized range yet with no significant digits left. I
cannot think of any floating-point operation that would be allowed to
return such a wrong result, even when rounding away from zero. Which one
is it?

Best regards,

Guillaume