Is bugs or features for fatou.gp super-logarithm?

[Ember Edison]

I have been a big pressure test for fatou.gp in one month.
In the post(https://math.eretrandre.org/tetrationfor...p?pid=8952) I say \( Arg(base)\in({\frac{14\pi}{30}},{\frac{21\pi}{30}})\wedge({\frac{42\pi}{30}},{\frac{47\pi}{30}}),\left| base \right|<1.76. \)is ill-region for fatou.gp. In fact, the ill-region for slog is little bigger the sexp.

But, There's look like other problem out of the ill-region.This gif is slog for base = Pi*(-1)^(x/30), 0<=x<=59.

You can see the program be pathological close to branch cut.
This plot is slog for Sheldon base. It look like well-behaved.
   
This plot is slog for base = eta. It look like well-behaved too.

base = -eta. It look like pathological.
   
base = sqrt(2). It look like well-behaved.

base = -sqrt(2). 
   
base = (-1)^(1/100). It's the closest base to 1. Is look like well-behaved? No, the program crash when Im(z)>\( \frac{21\pi}{8} \)
   
base = 0.8. 

base = -0.105. It's the closest base to 0.