# Step 3: Preemptively check for catastrophic magnitude differences
    if abs(a) > sys.float_info.max / 2:
        logging.warning("Value of a might cause overflow. Returning infinity just to be sure")
        return math.copysign (float('inf'), a)
    if abs(b) < sys.float_info.epsilon:
        logging.warning("Value of b dangerously close to zero. Returning NaN defensively.")
        return math.nan

Does the above code make any sense? I've not worked with this sort of stuff before, but it seems entirely unreasonable to me to check them individually. E.g. if 1 < b < a, then it seems insane to me to return float('inf') for a large but finite a.