Saluton!

* Mike Hall; 2003-08-01, 20:19 UTC:
> I agree with Josef that if we were to rewrite our own Bessels
> (etc.), we'd want someone who really knows what they are doing.  I
> re-read 'What Every Computer Scientist Should Know About Floating
> Point" last night -- very scarey stuff!  :-)

There is reason to scare. Even the most trivial computations are
nontrivial when one has a closer look at them:

1.upto(16) { |i|
  puts 1.0 + (0.1 ** i) - 1.0 - (0.1 ** i)
}

on my machine results in:

 8.32667268468867e-17
 6.93889390390723e-18
-1.10371781159024e-16
-1.10317571050400e-17
 6.55095281406476e-17
-8.22670162108899e-17
 5.83866825033984e-17
-6.07747148815308e-17
 8.27403705232185e-17
 8.27403704456703e-18
 8.27403704133586e-19
 8.89005823404259e-17
-7.99277837359775e-17
-7.99277837359901e-18
 1.10223024625156e-16
-1               e-16

The mathematical results of course all are 0. I did stop at 16
because we have reached what is called 'machine's epsilon'. This
value is defined as the largest number that can be added to 1 without
changing the value. This means that at this point

1.0 + (0.1 ** i) - 1.0 - (0.1 ** i)

becomes equivalent to

- (0.1 ** i)

Gis,

Josef 'Jupp' Schugt
-- 
N'attribuez jamais la malice ce que l'incompñÕence explique !
-- NapolñÐn