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Hi, I've used C++ code from TORI to make this tool.
Maybe anybody find it useful.
Code allows to apply:
Base is E (natural)
Natural tetration tet() to any complex z (superfunction of exp)
Natural arctetration ate() to any complex z (Abel function of exp)
Any complex fractional iteration of exp() to any complex z (using sexp(c+slog(z)):

This is readme.txt file from ZIP:
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This program is based on:
http://www.ils.uec.ac.jp/~dima/PAPERS/2010vladie.pdf
http://mizugadro.mydns.jp/t/index.php/Fslog.cin
http://mizugadro.mydns.jp/t/index.php/Fsexp.cin

For compilation see Makefile, in my system: "c++ -O3 -o prog_name source.cc -lm"
For running:
1. Compile
2. Run from terminal: ./cpptet:

./cpptet [e|l|h] [Re=1 [Im=0 [iterRe=0.5 [iterIm=0]]]]
e: sexp
l: slog
h: hexp


1st argument is type of function to compute, it can be:
e - compute tetration/sexp - exp superfunction
l - compute arctetration/superlogarithm - exp Abel function
h - compute fractional exp iteration (default 1/2) using sexp(c+slog(z))

Next two parameters are for specify function complex argument: Re(z) and Im(z)
2nd arguments is Re(z), if not given 1 is assumed
3rd argument is Im(z), if not given 0 is assumed

Next two parameters are only used for 'h' funcion (fractional iterate) and specify fractional iteration value c, default is 1/2 = half iterate exp()
4th argument is Re©, if not given 0.5 is assumed
5th argument is Im©, if not given 0 is assumed

For example to compute:
tet(2): e 2
tet(i): e 0 1
tet(2-pi*i): e 2 -3.14
ate(1000) l 1000
ate(-e*i) l 0 -2.718
exp[1/2](10) h 10
exp[0.9](e+pi*i) h 2.718 3.14 0.9
exp[i](i) h 0 1 0 1


And so on

*** I've ONLY adopted code from links at the beginning of this file ***
... and added way to call sexp, slog and any partial iterate of exp() from C++
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Attached: