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thank you for the idea with math.type.

Just I prefer a method, which is accessible directly by "basic Lua
function", and yes, of course without forcing the user accessing debug
or registry.

... so I think I will keep my "tostring" way (I want to do it as
"compatible" to standard Lua as possible, and in "standard Lua" the
liolib.c is the only lib function using user data, I hope it is then
fine that I use the same method as also shown in liolib.c for the
f_tostring...).