Free42 possible accuracy flaw

[Thomas Okken]

It looks like the base being so close to 1 is the problem. I'm seeing similarly bad results in Free42 Binary. Free42 Decimal does actually get it right if I disable the repeated-squaring algorithm it uses for integer exponents up to 2^31-1. And both versions get it right if you calculate 1E-8 LN1+X 1E8 * E^X.

So maybe it should check the base for proximity to 1, and use log1p() and expm1() in that case.

The repeated squaring is not the issue by itself, you're not losing 7 digits of precision from calculating 39 multiplications unless something else is wrong. Note that if you calculate this using LN instead of LN1+X, you end up way off as well.