Learning a high-frequency, irregular objective function

I have an objective function f(x) that looks like (x%m_1)/m_1 for one range, then (x%m_2)/m_2 for another range, etc. for several ranges, with x ranging from 0 to 1 billion, and the m's are roughly a thousand. The ranges are not regularly spaced, I don't know where they are, I don't know what the m's are, and the total number of oscillations will be roughly a million. How can I learn f(x) (given noisy data)?

For extra credit: I actually don't have the values for f(x). I'm trying to learn g(x_1, x_2), where g(x_1, x_2) = h(f(x_1), f(x_2)) for some function h. How do I learn g, or h and f?