QCaml/common/lib/bitstring.ml

(** Single-integer implementation *)

module One = struct

  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


(** Zarith implementation *)
module Many = struct

  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


(** General implementation *)
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




(* [[file:~/QCaml/common/bitstring.org::*General implementation][General implementation:10]] *)
let rec to_list ?(accu=[]) = function
  | t when (is_zero t) -> List.rev accu
  | t -> let newlist =
           (trailing_zeros t + 1)::accu
      in
      let b = logand t @@ minus_one t in
      (to_list [@tailcall]) ~accu:newlist b
(* General implementation:10 ends here *)



(*    Example:
 *    #+begin_example
 * Bitstring.(to_list (of_int 45));;
 * - : int list = [1; 3; 4; 6]
 *    #+end_example *)


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