Small challenge

[John Keith]

(04-23-2023 02:13 PM)J-F Garnier Wrote:  The implementation of the exponentiation changed between the Capricorn platform (Series 80 / 75C) and the Saturn machines (starting with the 71B).

Does anyone know exactly how the code changed and, more importantly, is either implementation generally better than the other?

The exact value of 23^10 is 41426511213649, and we can see that a 1 ULP error in the least significant digit ( 4142651121365 instead of 41426511213649) can propagate to give the answer 4.14265112137 rather than the correct answer 4.14265112136. However, if 23^10 is computed with 15-digit precision internally, this error should not occur. Since it does occur, it would be nice to know why it occurs in the Saturns and not the others.