FORTRAN floating point accuracy problems

[Dieter]

(03-30-2016 08:32 PM)rprosperi Wrote:  Dieter - what is the meaning of "9,3 decimal digits" ? I get that due to internal representation inaccuracies you can only get somewhere between 9 and 10 reliable decimal digits, but what is the meaning or interpretation of the ",3" ?

In mathematics, results here and there may not exactly match real life. ;-)

The meaning is exactly as you suggested: "somewhere between 9 and 10 reliable decimal digits". Say, 9 digits with an error less than 1 ULP. I think it should be about 0,5 ULP in this case, as 2^–31 is approx. 4,6 E–10. Or 2^–32 = 2,3 E–10 for 32 bits. Which BTW should translate to 9,6 digits (sorry).

(03-30-2016 08:32 PM)rprosperi Wrote:  These threads are interesting to follow, I'm always learning something new, but I've not seen this usage before. Or maybe have simply forgotten it in the last 30+ years since doing this stuff on a daily basis.

Specifying a number of valid digits with fractional values is quite common. For instance in discussions on the accuracy of approximation methods. I remember such notations ("10,7 digits") in a thread on various methods for the Gamma function. In that case it was simply the base-10 log of the relative error. ;-)

Dieter