I have question when I compile an inline function in C++.
Can a recursive function work with inline. If yes then please describe how.
I am sure about loop
This particular function definitely can be inlined. That is because the compiler can figure out that this particular form of recursion (tail-recursion) can be trivially turned into a normal loop. And with a normal loop it has no problem inlining it at all.
Not only can the compiler inline it, it can even calculate the result for a compile-time constant without generating any code for the function.
With GCC 4.4
int fac = f(10);
produced this instruction:
movl $3628800, 4(%esp)
You can easily verify when checking assembly output, that the function is indeed inlined for input that is not known at compile-time.