A quick precision test

[Paul Dale]

(06-05-2014 01:18 AM)Claudio L. Wrote:  I'd love to test some corner cases to see how the algorithms behave (like that case that needs 1600 digits, do you have any links to good material on this subject?). I did some tests of my own but I don't know what the corner cases are. I'd like to have some literature where they list cases that I can use to stress the algorithms and see the results.

I doubt that the 1600 bits (not digits) is actually required in reality. I suspect rather, that a proof was devised that this was sufficient for all possible input values rather than finding the absolute worst case. There has been a fair bit of work done on actually locating the worst cases in the past few years.

A quick check on google leads to two links:

For binary: http://hal.inria.fr/inria-00072594/PS/RR-4044.ps
For decimal: http://perso.ens-lyon.fr/damien.stehle/d...malexp.pdf

There are plenty of others a search away.

The example at the bottom of the second page of the second paper is interesting. Forty seven correct decimal digits being required to correctly round towards zero -- 34 plus 9 guards won't get this right and this is only a 16 digit input, a 34 digit one would be worse.

As I've said many times, "numerical analysis is hard".

- Pauli