3428. EvenOdd

Consider the following function $f(X)$, which takes a single positive integer as argument, and returns an integer.

function f(X):
    iterations := 0
    while X is not 1:
        if X is even:
            divide X by 2
        else:
            add 1 to X
        add 1 to iterations
    return iterations

It can be shown that for any positive integer $X$, this function terminates.

Given an interval $[L,R]$, compute the sum

$$S=f(L)+f(L+1)+\cdots +f(R-1)+f(R)$$