def count_zeros(s):
    if len(s) == 1: return ~s
    upper_bits = 1 << ceil_log2(len(s)) - 1
    upper = count_zeros(s[-upper_bits:])
    lower = count_zeros(s[:-upper_bits])
    lower = Cat(lower, C(0, len(upper) - len(lower)))

    msbs = Cat(lower[-1], upper[-1])
    out = Mux(msbs.matches("11"), C(1 << len(upper)),
        Mux(msbs.matches("10"), Cat(lower[:-1], C(1, 2)), Cat(upper, C(0))))
    return out