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Re: [STDS-754] reproducibility of tininess detection for binary formats
Guillaume Melquiond <guillaume.melquiond@xxxxxxxxxxx> wrote on 15/10/2007
09:43:36:
Le lundi 15 octobre 2007 à 08:57 +0100, Mike Cowlishaw a écrit :
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.
I can. Consider an implementation that provides a Subnormal
flag (which
means: the magnitude of the result of the operation was less
than that of
the smallest normal number (Nmin, = b**emin)). In such an
implementation,
the first definition trivially defines Underflow as Subnormal
& Inexact.
This is easy to document and to explain to users: "Underflow
is when the
magnitude of a result is less than Nmin and cannot be represented
exactly". To me, 'this is the definition that any user
actually expects'.
Sorry, I am missing part of your point. I understand the part about the
first definition being easier to define. But I don't see where it
translates to being more useful for the user than the second definition.
If it's simpler to define it's simpler to learn and to remember, and so is
more likely to be learned and remembered. That makes it more useful.
Something that is hard to learn and is not remembered is an unknown, and
therefore useless.
In my experience, the primary (only?) use of these flags/traps is to
detect when the ideal model of floating-point arithmetic (unbounded
exponent range, as usually assumed by backward error analysis for
example) no longer applies to a given computation.
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.