module type COMPARABLE = sig
  type t
  val eq: t -> t -> bool
  val neq: t -> t -> bool
  val lt: t -> t -> bool
  val le: t -> t -> bool
  val gt: t -> t -> bool
  val ge: t -> t -> bool
end

module Comparable = struct

  let eq = (=)
  let neq = (<>)
  let lt = (<)
  let le = (<=)
  let gt = (>)
  let ge = (>=)

end

module Num = struct

  let rnd () =
    let value = Random.bits () in
    Q.make (Z.of_int value) (Z.of_int (1 lsl 30))

  include Q

  let eq = Q.equal

  let neq a b = not (Q.equal a b)

  let mult = Q.mul

  let floor t =
    let num = Q.num t
    and den = Q.den t in
    Q.of_bigint @@ Z.fdiv num den

  let ge = Q.geq

  let ge = Q.geq

  let le = Q.leq

  let is_integer t = (Q.den t) == Z.one

  let pow t q_factor = begin

    if is_integer q_factor then

      let factor = Q.to_int q_factor
      and num = Q.num t
      and den = Q.den t in

      Q.make (Z.pow num factor) (Z.pow den factor)

    else

      let factor = Q.to_float q_factor
      and num = Z.to_float @@ Q.num t
      and den = Z.to_float @@ Q.den t in

      Q.div
        (Q.of_float (num ** factor))
        (Q.of_float (den ** factor))

  end

  let gcd t1 t2 =
    Q.of_bigint @@ Z.gcd (Q.to_bigint t1) (Q.to_bigint t2)

  let lcm t1 t2 =
    Q.of_bigint @@ Z.lcm (Q.to_bigint t1) (Q.to_bigint t2)

end

module Bool = struct

  type t = bool
  include Comparable

  let true_ = true
  let false_ = false

  let or_ = (||)
  let and_ = (&&)
  let not = Pervasives.not

end

module String = struct

  type t = UTF8.t
  include Comparable

end

module Date = Date.Make(Num)