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(* Open Source License                                                       *)
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type fp_tag (* Tag for fixed point computations *)

type integral_tag (* Tag for integral computations *)

module type Safe = sig
  type 'a t [@@coq_phantom]

  type fp = fp_tag t

  type integral = integral_tag t

  val integral_exn : Z.t -> integral

  val integral_of_int_exn : int -> integral

  val integral_to_z : integral -> Z.t

  val zero : 'a t

  val add : 'a t -> 'a t -> 'a t

  val sub : 'a t -> 'a t -> 'a t

  val ceil : fp -> integral

  val floor : fp -> integral

  val fp : 'a t -> fp

  val ( = ) : 'a t -> 'b t -> bool

  val ( <> ) : 'a t -> 'b t -> bool

  val ( < ) : 'a t -> 'b t -> bool

  val ( <= ) : 'a t -> 'b t -> bool

  val ( >= ) : 'a t -> 'b t -> bool

  val ( > ) : 'a t -> 'b t -> bool

  val compare : 'a t -> 'b t -> int

  val equal : 'a t -> 'b t -> bool

  val max : 'a t -> 'a t -> 'a t

  val min : 'a t -> 'a t -> 'a t

  val pp : Format.formatter -> 'a t -> unit

  val pp_integral : Format.formatter -> integral -> unit

  val n_fp_encoding : fp Data_encoding.t

  val n_integral_encoding : integral Data_encoding.t

  val z_fp_encoding : fp Data_encoding.t

  val z_integral_encoding : integral Data_encoding.t
end

module type Full = sig
  type 'a t [@@coq_phantom]

  include Safe with type 'a t := 'a t

  val unsafe_fp : Z.t -> fp
end