mid-rad representation

[Paul Zimmermann <Paul.Zimmermann@xxxxxxxx>]

       Hi,

I have read with interest the latest discussions on inf-sup vs mid-rad
representation.

Although I strongly agree that P1788 would fail if it would standardize
too many different representations or encodings of intervals, I see one
argument in favor of mid-rad representation which has not been mentioned
before.

When working with variable precision and narrow intervals, inf-sup
requires two values of large precision, whereas with mid-rad the
radius might have a very small precision (typically a few bits).
This will give a speedup of a factor 2 to 4 depending on the operation.

For example, the iRRAM Real RAM library from Norbert Müller uses that
representation.

Thus if P1788 wants to cover variable/arbitrary precision, this point might
be taken into account.

Paul Zimmermann