type t =
  {
    bitstring : Z.t ;
    phase     : Phase.t ;
  }

let of_list l = 
  let rec aux accu nperm = function
  | [] -> { bitstring = accu;
            phase = Phase.of_nperm nperm; }
  | i :: rest -> 
    let i = pred i in
    let x = Z.(shift_left one i) in
    let accu = Z.logor accu x in
    let nperm =
      let mask = Z.(x-one) in
      let r = Z.logand accu mask in
      if r = Z.zero then
        nperm
      else
        nperm + (Z.popcount r)
    in
    aux accu nperm rest
  in
  List.rev l
  |> aux Z.zero 0


(* TODO Phase *)
let rec to_list spindet =
  let rec aux accu z =
    if z <> Z.zero then
      let element = (Z.(trailing_zeros z)+1) in
      aux (element::accu) Z.(z land (pred z))
    else List.rev accu
  in aux [] spindet
  

let pp_bitstring ppf bs =
  String.init (Z.numbits bs) (fun i -> if (Z.testbit bs i) then '+' else '-')
  |> Format.fprintf ppf "@[<h>%s@]"

let pp_spindet ppf s =
  Format.fprintf ppf "@[<h>%a %a@]" Phase.pp_phase s.phase pp_bitstring s.bitstring



let test_case () =

  let test_creation () =
      let l_a = [ 1 ; 2 ; 3 ; 5 ] in
      let det = of_list l_a in
      Alcotest.(check (list int )) "bitstring" (to_list det.bitstring) l_a;
      Alcotest.(check bool) "phase" (det.phase = Phase.Pos)  true;
      let l_b = [ 1 ; 3 ; 2 ; 5 ] in
      let det = of_list l_b in
      Alcotest.(check (list int )) "bitstring" (to_list det.bitstring) l_a;
      Alcotest.(check bool) "phase" (det.phase = Phase.Neg)  true;
  in
  [
    "Creation", `Quick, test_creation;
  ]