Free42 possible accuracy flaw

[J-F Garnier]

(03-25-2022 08:53 AM)Werner Wrote:  LN(3) and LN(3^9) are both between 1 and 10, so the rounding error is the same. Yet in 3^729, it is multiplied by 729, and in (3^9)^81, only by 81 before the exp().
So the larger the base, the more accurate ^ is.
The 42S gives different results for these.

On the HP Saturn machines, the 3 internal guard digits are just a bit too short for power operations on large numbers.
I gave an example above, but here is one of the worst cases:
1E44^10.5 --> 9.99999999991E461 (9 ULP error)
Note that LN(1E44) has a mantissa close to 1.

J-F