Re: math function accuracy -- was Re: text2interval again /
On 2013-03-12 08:14:16 +0000, N.M. Maclaren wrote:
> On Mar 12 2013, Vincent Lefevre wrote:
> >
> >I'm not saying that P1788 should demand tightest. On the contrary.
> >What I'm saying is that even if P1788 just demands containment,
> >a program will benefit from implementations providing a good
> >accuracy. This is not true for floating-point: a C program has
> >no way to compute an error bound on some result, because C doesn't
> >have any requirement concerning the accuracy of math functions;
> >even if the result is accurate, the program cannot know this in
> >a portable way.
>
> No, that isn't true. Floating-point programs do benefit from more
> accurate special functions, whether or not they calculate the error
> bounds. Also, there are ways to compute error bounds, but I agree
> that they are painful and very dependent on the algorithm.
Say, you compute sin(10^22) on two different x86 machines:
_ 32 bits: 0.46261304076460175
_ 64 bits: -0.85220084976718879
What benefit do you get if you don't know which one is the
"correct" result (if there is any)? (And if you already know
it, you don't need a program to compute it.)
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)