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Re: Motion 6

Vincent Lefevre wrote:

On 2009-09-21 10:41:07 +0200, Arnold Neumaier wrote:

The little difference may be decisive, though, for example when
checking algebraic numbers for their sign, using multiprecision
arithmetic. x in 1e-10000 + [0,Inf] encodes sign information,
which is lost when going to midrad.


Yes, but such kind of application (where intervals can be very
large), you should use infsup. Don't use midrad if your application
is not suited for midrad.


I had thought it was you who had been recommending midrad for
rigorous multipresicion calculations.

One of the major uses of these is, as far as I know, to make correct
decisions in borderline cases of geometric algorithms such as
line-sweeping or ray tracing.

One can easily get very large intervals when dividing by a narrow
interval very close to zero. I don't know how frequent this is,
but it is certainly possible.


Arnold Neumaier