that's a good point. if the first guess point (60.000000N, 10.000000W) is a mile away from the wanted point. Then doing binary search on range say [60.001000N, 10.000000W] and [59.999000N, 10.000000W] will most likely to hit a boundary case (leap from 1 to 2 or 1 to 0). If not we then can make the search range a bit larger.
