Free42 possible accuracy flaw

[Werner]

(03-25-2022 07:03 AM)Werner Wrote:  Congatulations, Thomas!
3^729 is now equal to (3^9)^81, a feat never seen before (when using floating-point numbers).
Kahan himself mentioned this particular example somewhere in an article of his, and why the results would not agree.
Cheers, Werner

Found the reference (In 'Mathemathics written in Sand', pg 27), and as usual, I misremembered ;-)
The actual calculations are

729^33.5 vs. 3^201

Where on 10-digit machines the latter has an error of more than one ulp, that could only be avoided using more than three extra digits in the intermediary calculations.

Equivalent numbers for Free42 would be

531441^1072.5 vs 9^6435

The former is off by 2 ulps. (I must confess I'm a bit puzzled by the fact that in this case it is the one with the larger base that is off - which goes against my original reasoning. I'm sure Albert will come to the rescue ;-))

Cheers, Werner