Mini-challenge - accurate factorials

[J-F Garnier]

(07-07-2023 08:40 PM)EdS2 Wrote:  given a calculator which has a scientific notation, such that the trailing zeros can be implicit, and needing only to display the significant digits, we can display even larger factorials. How large is the largest n, such that n! is accurately displayed with 8, 10, 12 or 14 significant digits?

If by accurate you mean exact, the largest exact factorials we can get are:
on a 10-digit machine (e.g. 15C):
    15! = 1307674368000 displayed as 1.307674368e12
on a 12-digit machine (e.g. 32S):
    17! = 355687428096000 displayed as 3.55687428096e14

Now, if we understand accurate as correctly rounded, then several machines ensure that all factorials are accurate (that is the error is less than 0.5 ULP).
For instance, the 71B, the 28S, the series 48.

But it's not true for some machines, for instance the 22S/32S/32SII:
    159! = 2.94670227249e282 (correct value is 2.94670227250e282)
Could you find the other three incorrectly rounded cases on these machines?
BTW, the 35S gives all correct values :-)

J-F