Questions about enhancement and Correction to Java OpenJDK Floating Point?

[Martin Desruisseaux]

Hello A.Z

As far as I know, the difference in output that you observed between 
Java and C/C++ is not caused by a difference in floating-point 
computation, but in a difference in the way numbers are rounded by the 
"printf" command. Java has a policy of showing all significant digits, 
while C "printf" has a policy of rounding before printing. In my 
opinion, this is more dangerous because it hides what really happen in 
floating-point computation.

The following statement is not entirely true when using finite floating 
point precision:

> (…snip…) It is a mathematical fact that, for
> consistent, necessary and even fast term, 10% of 10% must
> always precisely be 1%, and by no means anything else.

Above statement can be true only when using base 10 or some other bases. 
We could also said "It is a mathematical fact that 1/3 of 1/3 must 
always precisely be 1/9 and nothing else", but it can not be represented 
fully accurately with base 10. It can be represented fully accurately 
with base 3 however. There will always be examples that work in one base 
and not in another, and natural laws has no preference for base 10. I 
understand that base 10 is special for financial applications, but for 
many other applications (scientific, engineering, rendering…) base 2 is 
as good as any other base. I would even argue that base 10 can be 
dangerous because it gives a false sense of accuracy: it gives the 
illusion that rounding errors do not happen when testing with a few 
sample values in base 10 (like 10% of 10%), while in reality rounding 
errors continue to exist in the general case.

     Martin