fun binsearch x seq lower upper =
    let
      val half = lower + (upper - lower)div 2
      val current_val = Seq.nth seq half
    in
      case (Int.compare(upper, lower),Int.compare(current_val, x)) of
          (LESS, _ ) => lower
        | ( _ , EQUAL) => half
        | ( _ , LESS) => binsearch x seq lower (half)
        | ( _ , GREATER) => binsearch x seq (half + 1) upper
    end