high precision mathematics

[Karl M. Syring]

"Paul Rubin" <phr-n2002a at nightsong.com> schrieb
> "Karl M. Syring" <syring at email.com> writes:
> > > > > Not likely.
> > > >
> > > > You really should have a look at high precison libraries (e.g.
> > > > http://www.hipilib.de). They will use rational numbers internally.
> > >
> > > Yes, but who actually uses those libraries, and for what?
> >
> > The author of the Piologie library said somewhere that extended
precision
> > floating point arithmetic is completely useless, but it is fun.  Then
there
> > is the secret message coded into pi ... locate your name in pi
> > (http://pi.nersc.gov)
>
> High precision floating point and exact rational arithmetic have their
> uses, but almost all ordinary numerical computing uses ordinary
> floating point.  It's very unlikely that anyone would use exact
> rational arithmetic for robot motion control.

But you really should to it. I have floating point code that was running for
a long time without a hitch and then the horrible happened. The ugly thing
is, the code often will not crash but produce wrong results that seem to be
plausible. If you don't have any results to check the output, the worst
nightmares might come true.

Karl M. Syring