module One = struct
  type t = int


  let of_int x =
    assert (x > 0); x

  let numbits _ = 63
  let zero = 0
  let is_zero x = x = 0
  let shift_left x i = x lsl i
  let shift_right x i = x lsr i
  let shift_left_one i = 1 lsl i
  let testbit x i = ( (x lsr i) land 1 ) = 1  
  let logor a b = a lor b
  let neg a = - a 
  let logxor a b = a lxor b
  let logand a b = a land b
  let lognot a = lnot a
  let minus_one a = a - 1
  let plus_one a = a + 1

  let popcount = function
    | 0 -> 0
    | r  -> Util.popcnt (Int64.of_int r) 


  let trailing_zeros r = 
    Util.trailz (Int64.of_int r) 


  let hamdist a b =
    a lxor b
    |> popcount 


  let pp ppf s = 
    Format.fprintf ppf "@[@[%a@]@]" (Util.pp_bitstring 64) 
      (Z.of_int s)

end




module Many = struct

  type t = Z.t

  let of_int = Z.of_int
  let of_z x = x
  let zero = Z.zero
  let is_zero x = x = Z.zero
  let shift_left = Z.shift_left 
  let shift_right = Z.shift_right
  let shift_left_one i = Z.shift_left Z.one i
  let testbit = Z.testbit
  let logor = Z.logor
  let logxor = Z.logxor
  let logand = Z.logand
  let lognot = Z.lognot
  let neg = Z.neg
  let minus_one = Z.pred
  let plus_one = Z.succ
  let trailing_zeros = Z.trailing_zeros
  let hamdist = Z.hamdist
  let numbits i = max (Z.numbits i) 64

  let popcount z = 
    if z = Z.zero then 0 else Z.popcount z

  let pp ppf s = 
    Format.fprintf ppf "@[@[%a@]@]" (Util.pp_bitstring (Z.numbits s))  s

end


type t = 
| One of int
| Many of Z.t

let of_int x =
  One (One.of_int x)

let of_z x =
  if Z.numbits x < 64 then One (Z.to_int x) else Many (Many.of_z x)

let zero = function
| n when n < 64 -> One (One.zero)
| _ -> Many (Many.zero)

let numbits = function
| One x -> One.numbits x
| Many x -> Many.numbits x

let is_zero = function
| One x -> One.is_zero x
| Many x -> Many.is_zero x

let neg = function
| One x -> One (One.neg x)
| Many x -> Many (Many.neg x)

let shift_left x i = match x with
| One x -> One (One.shift_left x i)
| Many x -> Many (Many.shift_left x i)

let shift_right x i = match x with
| One x -> One (One.shift_right x i)
| Many x -> Many (Many.shift_right x i)

let shift_left_one = function
| n when n < 64 -> fun i -> One (One.shift_left_one i)
| _ -> fun i -> Many (Many.shift_left_one i)

let testbit = function
| One x -> One.testbit x
| Many x -> Many.testbit x

let logor a b = 
  match a,b with
  | One a, One b -> One (One.logor a b)
  | Many a, Many b -> Many (Many.logor a b)
  | _ -> invalid_arg "Bitstring.logor"

let logxor a b = 
  match a,b with
  | One a, One b -> One (One.logxor a b)
  | Many a, Many b -> Many (Many.logxor a b)
  | _ -> invalid_arg "Bitstring.logxor"

let logand a b = 
  match a,b with
  | One a, One b -> One (One.logand a b)
  | Many a, Many b -> Many (Many.logand a b)
  | _ -> invalid_arg "Bitstring.logand"

let lognot = function
| One x -> One (One.lognot x)
| Many x -> Many (Many.lognot x)

let minus_one = function
| One x -> One (One.minus_one x)
| Many x -> Many (Many.minus_one x)

let plus_one = function
| One x -> One (One.plus_one x)
| Many x -> Many (Many.plus_one x)

let trailing_zeros = function
| One x -> One.trailing_zeros x
| Many x -> Many.trailing_zeros x

let hamdist a b = match a, b with
| One a, One b -> One.hamdist a b
| Many a, Many b -> Many.hamdist a b
| _ -> invalid_arg "Bitstring.hamdist"

let popcount = function
| One x -> One.popcount x
| Many x -> Many.popcount x

let pp ppf = function
| One x -> One.pp ppf x
| Many x -> Many.pp ppf x


let rec to_list ?(accu=[]) = function
  | t when (is_zero t) -> List.rev accu
  | t -> let newlist =
           (trailing_zeros t + 1)::accu
         in
         logand t @@ minus_one t
         |> (to_list [@tailcall]) ~accu:newlist


(** [permtutations m n] generates the list of all possible [n]-bit
    strings with [m] bits set to 1.
    Algorithm adapted from
    {{:https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation}
    Bit twiddling hacks}.
    Example:
{[
    bit_permtutations 2 4 = [ 0011 ; 0101 ; 0110 ; 1001 ; 1010 ; 1100 ]
]}
*)
let permtutations m n =                                                                   

  let rec aux k u rest =
    if k=1 then
      List.rev (u :: rest)
    else
      let t   = logor u @@ minus_one u in
      let t'  = plus_one t in
      let not_t = lognot t in
      let neg_not_t = neg not_t in
      let t'' = shift_right (minus_one @@ logand not_t neg_not_t) (trailing_zeros u + 1) in
      (*
      let t'' = shift_right (minus_one (logand (lognot t) t')) (trailing_zeros u + 1) in
      *)
      (aux [@tailcall]) (k-1) (logor t' t'') (u :: rest)
  in
  aux (Util.binom n m) (minus_one (shift_left_one n m)) []


(*-----------------------------------------------------------------------------------*)

let test_case () =

  let test_one_many () =
    let x = 8745687 in
    let z = Z.of_int 8745687 in
    let one_x  = One x in
    let many_x = Many z in
    Alcotest.(check bool) "of_x" true (one_x = (of_int x));
    Alcotest.(check bool) "of_z" true (one_x = (of_z z));
    Alcotest.(check bool) "shift_left1" true (One (x lsl 3) = shift_left one_x 3);
    Alcotest.(check bool) "shift_left2" true (Many (Z.shift_left z 3) = shift_left many_x 3);
    Alcotest.(check bool) "shift_left3" true (Many (Z.shift_left z 100) = shift_left many_x 100);
    Alcotest.(check bool) "shift_right1" true (One (x lsr 3) = shift_right one_x 3);
    Alcotest.(check bool) "shift_right2" true (Many (Z.shift_right z 3) = shift_right many_x 3);
    Alcotest.(check bool) "shift_left_one1" true (One (1 lsl 3) = shift_left_one 4 3);
    Alcotest.(check bool) "shift_left_one2" true (Many (Z.shift_left Z.one 200) = shift_left_one 300 200);
    Alcotest.(check bool) "testbit1" true  (testbit (One 8) 3);
    Alcotest.(check bool) "testbit2" false (testbit (One 8) 2);
    Alcotest.(check bool) "testbit3" false (testbit (One 8) 4);
    Alcotest.(check bool) "testbit4" true  (testbit (Many (Z.of_int 8)) 3);
    Alcotest.(check bool) "testbit5" false (testbit (Many (Z.of_int 8)) 2);
    Alcotest.(check bool) "testbit6" false (testbit (Many (Z.of_int 8)) 4);
    Alcotest.(check bool) "logor1" true (One (1 lor 2) = logor (One 1) (One 2));
    Alcotest.(check bool) "logor2" true (Many (Z.of_int (1 lor 2)) = logor (Many Z.one) (Many (Z.of_int 2)));
    Alcotest.(check bool) "logxor1" true (One (1 lxor 2) = logxor (One 1) (One 2));
    Alcotest.(check bool) "logxor2" true (Many (Z.of_int (1 lxor 2)) = logxor (Many Z.one) (Many (Z.of_int 2)));
    Alcotest.(check bool) "logand1" true (One (1 land 2) = logand (One 1) (One 2));
    Alcotest.(check bool) "logand2" true (Many (Z.of_int (1 land 2)) = logand (Many Z.one) (Many (Z.of_int 2)));
    Alcotest.(check bool) "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (One 45)));
  in

  [
    "One-many", `Quick, test_one_many;
  ]