Re: Discussion about accuracy modes
On 2010-10-13 10:58:04 +0100, N.M. Maclaren wrote:
> On Oct 13 2010, Vincent Lefevre wrote:
> >Note also that even with a fixed precision (or if the target
> >precision is specified by the user, such as in MPFR), then
> >"tightest" or "accurate" modes may not be practically possible:
> >if the range is huge (such as in MPFR or in DPE), trig functions
> >can't be evaluated on very large arguments in a reasonable time
> >and with a reasonable amount of memory.
>
> A bad example. Unless the arguments are totally ridiculous (i.e.
> cannot occur as low powers of physical values, including such things
> as the diameter of the universe measured in Planck units), they can
> be.
I gave this example because the problem really occurred a few times
with MPFR.
Note that in FP arithmetic, it is very easy to get huge values:
just consider the result of an overflow rounded to zero. But
perhaps things are different in interval arithmetic (however
intervals can also be built from FP numbers). This might not be
a problem in most applications in practice, but for standard
conformance and security (where users could provide ridiculous
data to an online application to yield a DoS), it will.
> But there are plenty of important and common functions where
> there is no known method of doing so, so your point stands.
>
> Try the error function, for a start.
Yes, I guess that's why the maximum exponent has been reduced to 63
for the tests in MPFR...
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)