type t = Num.num

let get_julian_day year month day = begin
  let y, m =
    if month > 2 then
      year, month
    else
      year - 1, month + 12
  in
  let b =
    if (year > 1582) || (year = 1582 && month > 10) || (year = 1582 && month = 10 && day >= 15) then
      let s = y / 100 in
      2 - s + (s / 4)
    else
      0
    in
    365 * y + y / 4
  + (int_of_float (30.6001 *. (float_of_int (m + 1))))
  + day
  + b
  + 1720995
  - 2415019         (* Shift to 30/12/1899 *)
  |> Num.num_of_int

end

let date_from_julian_day day = begin

  let shift_day = Num.floor_num day
    |> Num.add_num (Num.num_of_int 2415019) in

  let z = Num.int_of_num shift_day in
  let f =
    if z >= 2299161 then
      (* We use the Num module here to prevent overflow *)
      let day' = Num.(((num_of_int 4) */ shift_day +/ (num_of_int 274277)) // (num_of_int 146097))
              |> Num.floor_num
              |> Num.int_of_num in
      z + 1401 + ((day' * 3) / 4) - 38
    else
      z + 1401
    in
  let e = (4 * f) + 3 in
  let h = 5 * ((e mod 1461) / 4) + 2 in (* 1461 is 365.25 * 4 *)
  let d = ((h mod 153) / 5) + 1
  and m = (((h / 153) + 2) mod 12) + 1 in
  let y = (e / 1461) - 4716 + (14 - m) / 12 in (* 4716 is day 2 *)
  (y, m, d)

end

let time_from_julian_day j = begin Num.(
  let day = floor_num j in
  let time = j -/ day in

  let h = floor_num @@ time */ (num_of_int 24) in
  let h_24 = (h // (num_of_int 24)) in
  let m = floor_num @@ (num_of_int 1440) */ (time -/ h_24 ) in
  let s = (num_of_int 86400) */ (time -/ h_24 -/ (m // (num_of_int 1440))) in
  (h, m, s)
) end

(** Compute the julian for a given date.

    Integer return number of days since November 24, 4714 BC.
    Fractionnal part return the time since midnight.
*)
let from_string str = begin
  let n = Num.num_of_int in
  let date_regex = Str.regexp "[0-9]+-[0-9]+-[0-9]+"
  and time_regex = Str.regexp "[0-9]+-[0-9]+-[0-9]+T[0-9]+:[0-9]+:[0-9]" in
  if Str.string_match time_regex str 0 then
    Scanf.sscanf str "%d-%d-%dT%d:%d:%d" (fun year month day hour min sec ->
    Num.(
      let nhour = n hour // (n 24)
      and nmin  = n min // (n 1440)
      and nsec  = n sec // (n 86400) in
      (get_julian_day year month day) +/ nhour +/ nmin +/ nsec
    )
  ) else if Str.string_match date_regex str 0 then
    Scanf.sscanf str "%d-%d-%d" get_julian_day
  else (
    Num.num_of_int 0
  )
end

let to_string date = begin
  let y, m, d = date_from_julian_day date
  and h, n, s = time_from_julian_day date in

  Printf.sprintf "%d-%02d-%02dT%02d:%02d:%02g"
    y
    m
    d
    (Num.int_of_num h)
    (Num.int_of_num n)
    (Num.float_of_num s)

end