fake id(x) for better 2sinh method.

[tommy1729]

For improving the 2sinh method so that it works for all bases > eta and other improvements I consider :

2sinh(fake id(x))

fake id(x) behaves like e/2 x for small x, like x for large real and like 0 for large imaginary part.

SO what is the best fake id(x) ? Remember we only want a single fixpoint (2sinh(fake id(x))=x) for any base.

maybe id(x) = exp(fakelog(x)) ...

Thinking...

regards

tommy1729