I would like to know the time complexity of int strncmp(const char *__s1, const char *__s2, size_t __n) which is in the C library(string.h).
I have to study the complexity of my whole program which is calling strncmp thousands of time, I can't ignore this complexity.
Where can I find documentation about the complexity of c library function ?
The standard imposes no requirements on the complexity. That is entirely up to the implementation. But there's absolutely no reason to expect it to be anything else than O(__n)
It's trivial to write an implementation that satisfies O(__n), so there's no reason to suspect that a real implementation made by professionals is worse.
It's impossible to write an implementation that is better than O(__n), so that will not happen.
But if you want to be sure, you have to study the particular implementation you're using.