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I think it can be O(logR) complexity.
It can be better than log(R). If R and L are 4 byte integers, it can be done in 31 steps worst case.
No, it's not worse, it's the same.
What you are saying is log2(R).
in computer science, log(n) means log2(n)
lg(n) means log2(n), log(n) means log10(n). usually
no it is not
doesn't matter, logs of any base are big-O equivalent