Re: What is acceptable for -ffast-math? A numerical viewpoint

[dewar at gnat dot com]

<<Your Newton-Raphson example is bogus because it relies on the assumption
that anybody who asks for loose FP must not know what they're doing. It
wouldn't be a problem for me because I know perfectly well not to write
code like that. I expect most of the other people who have asked for
loose FP are at least as intelligent as I am.
>>

It was just an example, if you really think that it is acceptable to
allow any transofmration that is valid for real arithmetic under all
circumstances, then we are too far to even have a discussion, since 
this criterion is completely unworkable for many reasons. Again, 
briefly, it would allow transformations that would cause all programs
to immediately generate overflows. You can't really mean that you
support this criterion without any exceptions.

Going back to the NR example, there is nothing wrong at all about programming
an NR iteration to exact equality if analysis shows this is reliable, since
it is often the fastest way of doing things. Remember that the estimate in
an NR iteration is an *exact* representation of the estimate (if you were
doing interval arithmetic, you would shrink the interval to zero for
the estimate).