A mystery!

Exercise 1.18

Explain what the following algorithm does and give its cost as a function of n.

int mystery(int n) { 
    int f = 1;
    for (int i = 2; i <= n; ++i) 
        f *= i;
    return f; 
}   

Cum grano salis

Does the cost give a realistic running time? How many bits has the output as a function of n (asymptotically)? What is the cost actually measuring?