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(** Options available for the Liquidity Baking per-block vote *)

type liquidity_baking_toggle_vote = LB_on | LB_off | LB_pass

let liquidity_baking_toggle_vote_encoding =
  let of_int8 = function
    | 0 -> Ok LB_on
    | 1 -> Ok LB_off
    | 2 -> Ok LB_pass
    | _ -> Error "liquidity_baking_toggle_vote_of_int8"
  in
  let to_int8 = function LB_on -> 0 | LB_off -> 1 | LB_pass -> 2 in
  let open Data_encoding in
  (* union *)
  def "liquidity_baking_toggle_vote"
  @@ splitted
       ~binary:(conv_with_guard to_int8 of_int8 int8)
       ~json:(string_enum [("on", LB_on); ("off", LB_off); ("pass", LB_pass)])

module Toggle_EMA : sig
  (* The exponential moving average is represented as an Int32 between 0l and 2_000_000_000l *)

  type t

  val zero : t

  val of_int32 : Int32.t -> t tzresult Lwt.t

  val to_int32 : t -> Int32.t

  val update_ema_off : t -> t

  val update_ema_on : t -> t

  val ( < ) : t -> Int32.t -> bool

  val encoding : t Data_encoding.t
end = struct
  type t = Int32.t (* Invariant 0 <= ema <= 2_000_000_000l *)

  (* This error is not registered because we don't expect it to be
     raised. *)
  type error += Liquidity_baking_toggle_ema_out_of_bound of Int32.t

  let check_bounds x = Compare.Int32.(0l <= x && x <= 2_000_000_000l)

  let of_int32 x =
    if check_bounds x then return x
    else fail @@ Liquidity_baking_toggle_ema_out_of_bound x

  let zero = Int32.zero

  (* The conv_with_guard combinator of Data_encoding expects a (_, string) result. *)
  let of_int32_for_encoding x =
    if check_bounds x then Ok x else Error "out of bounds"

  let to_int32 ema = ema

  (* We perform the computations in Z to avoid overflows. *)

  let z_1999 = Z.of_int 1999

  let z_2000 = Z.of_int 2000

  let attenuate z = Z.(div (mul z_1999 z) z_2000)

  let z_1_000_000_000 = Z.of_int 1_000_000_000

  (* Outside of this module, the EMA is always between 0 and 2,000,000,000.
     This [recenter] wrappers, puts it in between -1,000,000,000 and 1,000,000,000.
     The goal of this recentering around zero is to make [update_ema_off] and
     [update_ema_on] behave symmetrically with respect to rounding. *)
  let recenter f ema = Z.(add z_1_000_000_000 (f (sub ema z_1_000_000_000)))

  let z_500_000 = Z.of_int 500_000

  let update_ema_off ema =
    let ema = Z.of_int32 ema in
    recenter (fun ema -> Z.add (attenuate ema) z_500_000) ema |> Z.to_int32

  let update_ema_on ema =
    let ema = Z.of_int32 ema in
    recenter (fun ema -> Z.sub (attenuate ema) z_500_000) ema |> Z.to_int32

  let ( < ) = Compare.Int32.( < )

  let encoding =
    Data_encoding.(conv_with_guard to_int32 of_int32_for_encoding int32)
end

(* Invariant: 0 <= ema <= 2_000_000 *)
let compute_new_ema ~toggle_vote ema =
  match toggle_vote with
  | LB_pass -> ema
  | LB_off -> Toggle_EMA.update_ema_off ema
  | LB_on -> Toggle_EMA.update_ema_on ema