Which method is currently "the best"?

[MorgothV8]

Hi there, I'm a reader of this forum.
I've also tried to make some tetration code but currently failed.

Can some of You please point me to currently "the best" algorithm for tetration available?

By "the best" I mean algorithm which can handle most bases (both base and rank should be complex numbers)

Also if possible point me to some underlying math explaination....?

I rally want to understand how current methods works - I've tried several time - but possibly my math skills are too weak.

I also want to rewrite it in some wide available language like C or C++ etc.
I will of course publish C/C++ code if I manage to translate it.