Re: reproducibility of tininess detection for binary formats

[Guillaume Melquiond <guillaume.melquiond@xxxxxxxxxxx>]

Le dimanche 14 octobre 2007 Ã  15:51 -0700, David Hough 754R work a
écrit :

> One extreme definition of exponent spill is:
> the magnitude of a non-zero finite unrounded result is larger than
> the largest normalized number in the destination format
> or smaller than the smallest normalized number in the destination format.
>
> The opposite extreme definition is:
> the numerical result rounded to the destination format differs from the
> numerical result rounded to a hypothetical format with the same precision
> as the destination format but unbounded exponent range.

> But the first one depends only on the magnitude of the unrounded exact
> result.     The second one also depends on the current rounding mode.
> Neither one will satisfy everybody all the time, but I prefer the first
> because it's easier to undo an unwanted exception when it is signaled than to 
> test for a unsignaled exception on every operation where it might have been
> signaled.

Could you detail a situation where the second definition will not
satisfy everybody? It seems like this is the definition that any user
actually expects. For example, if a developer checks the sticky flags
(or trap exceptions) in order to ensure that a sequence of operations
did not go astray (bounded relative error as predicted by the model),
then both definitions work. But only the second one has the advantage of
never raising a false positive.

Best regards,

Guillaume