Source file bitv.ml

(**************************************************************************)
(*                                                                        *)
(*  Copyright (C) Jean-Christophe Filliatre                               *)
(*                                                                        *)
(*  This software is free software; you can redistribute it and/or        *)
(*  modify it under the terms of the GNU Library General Public           *)
(*  License version 2, with the special exception on linking              *)
(*  described in file LICENSE.                                            *)
(*                                                                        *)
(*  This software is distributed in the hope that it will be useful,      *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  *)
(*                                                                        *)
(**************************************************************************)

(*i $Id: bitv.ml,v 1.26 2012/08/14 07:26:00 filliatr Exp $ i*)

(*s Bit vectors. The interface and part of the code are borrowed from the
    [Array] module of the ocaml standard library (but things are simplified
    here since we can always initialize a bit vector). This module also
    provides bitwise operations. *)

(*s We represent a bit vector by a vector of integers (field [bits]),
    and we keep the information of the size of the bit vector since it
    can not be found out with the size of the array (field [length]). *)

type t = {
  length : int;
  bits   : int array }

let length v = v.length

(*s Each element of the array is an integer containing [bpi] bits, where
    [bpi] is determined according to the machine word size. Since we do not
    use the sign bit, [bpi] is 30 on a 32-bits machine and 62 on a 64-bits
    machines. We maintain the following invariant:
    {\em The unused bits of the last integer are always
    zeros.} This is ensured by [create] and maintained in other functions
    using [normalize]. [bit_j], [bit_not_j], [low_mask] and [up_mask]
    are arrays used to extract and mask bits in a single integer. *)

let bpi = Sys.word_size - 2

let max_length = Sys.max_array_length * bpi

let bit_j = Array.init bpi (fun j -> 1 lsl j)
let bit_not_j = Array.init bpi (fun j -> max_int - bit_j.(j))

let low_mask = Array.make (succ bpi) 0
let _ =
  for i = 1 to bpi do low_mask.(i) <- low_mask.(i-1) lor bit_j.(pred i) done

let keep_lowest_bits a j = a land low_mask.(j)

let high_mask = Array.init (succ bpi) (fun j -> low_mask.(j) lsl (bpi-j))

let keep_highest_bits a j = a land high_mask.(j)

(*s Creating and normalizing a bit vector is easy: it is just a matter of
    taking care of the invariant. Copy is immediate. *)

let create n b =
  if n < 0 || n > max_length then invalid_arg "Bitv.create";
  let initv = if b then max_int else 0 in
  let r = n mod bpi in
  if r = 0 then
    { length = n; bits = Array.make (n / bpi) initv }
  else begin
    let s = n / bpi in
    let b = Array.make (succ s) initv in
    b.(s) <- b.(s) land low_mask.(r);
    { length = n; bits = b }
  end

let normalize v =
  let r = v.length mod bpi in
  if r > 0 then
    let b = v.bits in
    let s = Array.length b in
    b.(s-1) <- b.(s-1) land low_mask.(r)

let copy v = { length = v.length; bits = Array.copy v.bits }

(*s Access and assignment. The [n]th bit of a bit vector is the [j]th
    bit of the [i]th integer, where [i = n / bpi] and [j = n mod
    bpi]. Both [i] and [j] and computed by the function [pos].
    Accessing a bit is testing whether the result of the corresponding
    mask operation is non-zero, and assigning it is done with a
    bitwiwe operation: an {\em or} with [bit_j] to set it, and an {\em
    and} with [bit_not_j] to unset it. *)

let pos n = n / bpi, n mod bpi

let unsafe_get v n =
  let (i,j) = pos n in
  ((Array.unsafe_get v.bits i) land (Array.unsafe_get bit_j j)) > 0

let unsafe_set v n b =
  let (i,j) = pos n in
  if b then
    Array.unsafe_set v.bits i
      ((Array.unsafe_get v.bits i) lor (Array.unsafe_get bit_j j))
  else
    Array.unsafe_set v.bits i
      ((Array.unsafe_get v.bits i) land (Array.unsafe_get bit_not_j j))

(*s The corresponding safe operations test the validiy of the access. *)

let get v n =
  if n < 0 || n >= v.length then invalid_arg "Bitv.get";
  let (i,j) = pos n in
  ((Array.unsafe_get v.bits i) land (Array.unsafe_get bit_j j)) > 0

let set v n b =
  if n < 0 || n >= v.length then invalid_arg "Bitv.set";
  let (i,j) = pos n in
  if b then
    Array.unsafe_set v.bits i
      ((Array.unsafe_get v.bits i) lor (Array.unsafe_get bit_j j))
  else
    Array.unsafe_set v.bits i
      ((Array.unsafe_get v.bits i) land (Array.unsafe_get bit_not_j j))

(*s [init] is implemented naively using [unsafe_set]. *)

let init n f =
  let v = create n false in
  for i = 0 to pred n do
    unsafe_set v i (f i)
  done;
  v

(*s Handling bits by packets is the key for efficiency of functions
    [append], [concat], [sub] and [blit].
    We start by a very general function [blit_bits a i m v n] which blits
    the bits [i] to [i+m-1] of a native integer [a]
    onto the bit vector [v] at index [n]. It assumes that [i..i+m-1] and
    [n..n+m-1] are respectively valid subparts of [a] and [v].
    It is optimized when the bits fit the lowest boundary of an integer
    (case [j == 0]). *)

let blit_bits a i m v n =
  let (i',j) = pos n in
  if j == 0 then
    Array.unsafe_set v i'
      ((keep_lowest_bits (a lsr i) m) lor
       (keep_highest_bits (Array.unsafe_get v i') (bpi - m)))
  else
    let d = m + j - bpi in
    if d > 0 then begin
      Array.unsafe_set v i'
	(((keep_lowest_bits (a lsr i) (bpi - j)) lsl j) lor
	 (keep_lowest_bits (Array.unsafe_get v i') j));
      Array.unsafe_set v (succ i')
	((keep_lowest_bits (a lsr (i + bpi - j)) d) lor
	 (keep_highest_bits (Array.unsafe_get v (succ i')) (bpi - d)))
    end else
      Array.unsafe_set v i'
	(((keep_lowest_bits (a lsr i) m) lsl j) lor
	 ((Array.unsafe_get v i') land (low_mask.(j) lor high_mask.(-d))))

(*s [blit_int] implements [blit_bits] in the particular case when
    [i=0] and [m=bpi] i.e. when we blit all the bits of [a]. *)

let blit_int a v n =
  let (i,j) = pos n in
  if j == 0 then
    Array.unsafe_set v i a
  else begin
    Array.unsafe_set v i
      ( (keep_lowest_bits (Array.unsafe_get v i) j) lor
       ((keep_lowest_bits a (bpi - j)) lsl j));
    Array.unsafe_set v (succ i)
      ((keep_highest_bits (Array.unsafe_get v (succ i)) (bpi - j)) lor
       (a lsr (bpi - j)))
  end

(*s When blitting a subpart of a bit vector into another bit vector, there
    are two possible cases: (1) all the bits are contained in a single integer
    of the first bit vector, and a single call to [blit_bits] is the
    only thing to do, or (2) the source bits overlap on several integers of
    the source array, and then we do a loop of [blit_int], with two calls
    to [blit_bits] for the two bounds. *)

let unsafe_blit v1 ofs1 v2 ofs2 len =
  if len > 0 then
    let (bi,bj) = pos ofs1 in
    let (ei,ej) = pos (ofs1 + len - 1) in
    if bi == ei then
      blit_bits (Array.unsafe_get v1 bi) bj len v2 ofs2
    else begin
      blit_bits (Array.unsafe_get v1 bi) bj (bpi - bj) v2 ofs2;
      let n = ref (ofs2 + bpi - bj) in
      for i = succ bi to pred ei do
	blit_int (Array.unsafe_get v1 i) v2 !n;
	n := !n + bpi
      done;
      blit_bits (Array.unsafe_get v1 ei) 0 (succ ej) v2 !n
    end

let blit v1 ofs1 v2 ofs2 len =
  if len < 0 || ofs1 < 0 || ofs1 + len > v1.length
             || ofs2 < 0 || ofs2 + len > v2.length
  then invalid_arg "Bitv.blit";
  unsafe_blit v1.bits ofs1 v2.bits ofs2 len

(*s Extracting the subvector [ofs..ofs+len-1] of [v] is just creating a
    new vector of length [len] and blitting the subvector of [v] inside. *)

let sub v ofs len =
  if ofs < 0 || len < 0 || ofs + len > v.length then invalid_arg "Bitv.sub";
  let r = create len false in
  unsafe_blit v.bits ofs r.bits 0 len;
  r

(*s The concatenation of two bit vectors [v1] and [v2] is obtained by
    creating a vector for the result and blitting inside the two vectors.
    [v1] is copied directly. *)

let append v1 v2 =
  let l1 = v1.length
  and l2 = v2.length in
  let r = create (l1 + l2) false in
  let b1 = v1.bits in
  let b2 = v2.bits in
  let b = r.bits in
  for i = 0 to Array.length b1 - 1 do
    Array.unsafe_set b i (Array.unsafe_get b1 i)
  done;
  unsafe_blit b2 0 b l1 l2;
  r

(*s The concatenation of a list of bit vectors is obtained by iterating
    [unsafe_blit]. *)

let concat vl =
  let size = List.fold_left (fun sz v -> sz + v.length) 0 vl in
  let res = create size false in
  let b = res.bits in
  let pos = ref 0 in
  List.iter
    (fun v ->
       let n = v.length in
       unsafe_blit v.bits 0 b !pos n;
       pos := !pos + n)
    vl;
  res

(*s Filling is a particular case of blitting with a source made of all
    ones || all zeros. Thus we instanciate [unsafe_blit], with 0 and
    [max_int]. *)

let blit_zeros v ofs len =
  if len > 0 then
    let (bi,bj) = pos ofs in
    let (ei,ej) = pos (ofs + len - 1) in
    if bi == ei then
      blit_bits 0 bj len v ofs
    else begin
      blit_bits 0 bj (bpi - bj) v ofs;
      let n = ref (ofs + bpi - bj) in
      for _i = succ bi to pred ei do
	blit_int 0 v !n;
	n := !n + bpi
      done;
      blit_bits 0 0 (succ ej) v !n
    end

let blit_ones v ofs len =
  if len > 0 then
    let (bi,bj) = pos ofs in
    let (ei,ej) = pos (ofs + len - 1) in
    if bi == ei then
      blit_bits max_int bj len v ofs
    else begin
      blit_bits max_int bj (bpi - bj) v ofs;
      let n = ref (ofs + bpi - bj) in
      for _i = succ bi to pred ei do
	blit_int max_int v !n;
	n := !n + bpi
      done;
      blit_bits max_int 0 (succ ej) v !n
    end

let fill v ofs len b =
  if ofs < 0 || len < 0 || ofs + len > v.length then invalid_arg "Bitv.fill";
  if b then blit_ones v.bits ofs len else blit_zeros v.bits ofs len

(*s All the iterators are implemented as for traditional arrays, using
    [unsafe_get]. For [iter] and [map], we do not precompute [(f
    true)] and [(f false)] since [f] may have side-effects. *)

let iter f v =
  for i = 0 to v.length - 1 do f (unsafe_get v i) done

let map f v =
  let l = v.length in
  let r = create l false in
  for i = 0 to l - 1 do
    unsafe_set r i (f (unsafe_get v i))
  done;
  r

let iteri f v =
  for i = 0 to v.length - 1 do f i (unsafe_get v i) done

let mapi f v =
  let l = v.length in
  let r = create l false in
  for i = 0 to l - 1 do
    unsafe_set r i (f i (unsafe_get v i))
  done;
  r

let fold_left f x v =
  let r = ref x in
  for i = 0 to v.length - 1 do
    r := f !r (unsafe_get v i)
  done;
  !r

let fold_right f v x =
  let r = ref x in
  for i = v.length - 1 downto 0 do
    r := f (unsafe_get v i) !r
  done;
  !r

let foldi_left f x v =
  let r = ref x in
  for i = 0 to v.length - 1 do
    r := f !r i (unsafe_get v i)
  done;
  !r

let foldi_right f v x =
  let r = ref x in
  for i = v.length - 1 downto 0 do
    r := f i (unsafe_get v i) !r
  done;
  !r

(*s Population count *)

let rec naive_pop x =
  assert (x < 0x10000);
  if x = 0 then 0 else 1 + naive_pop (x - (x land -x))

let pop16 = Array.init 0x10000 naive_pop
let pop16 n = Array.unsafe_get pop16 n

let popi x = match Sys.word_size with
  | 32 -> pop16 (x land 0xffff) + pop16 ((x lsr 16) land 0xffff)
  | 64 -> pop16 (x land 0xffff) + pop16 ((x lsr 16) land 0xffff)
        + pop16 ((x lsr 32) land 0xffff) + pop16 ((x lsr 48) land 0xffff)
  | _ -> assert false

let pop v =
  Array.fold_left (fun acc n -> acc + popi n) 0 v.bits

(*s Number of trailing zeros (on a 32-bit machine) *)

let hash32 x = ((0x34ca8b09 * x) land 0x3fffffff) lsr 24
let ntz_arr32 = Array.make 64 0
let () = for i = 0 to 30 do ntz_arr32.(hash32 (1 lsl i)) <- i done
let ntz32 x = if x == 0 then 31 else ntz_arr32.(hash32 (x land (-x)))

let iteri_true_ntz32 f v =
  Array.iteri
    (fun i n ->
       let i_bpi = i * bpi in
       let rec visit x =
	 if x != 0 then begin
	   let b = x land (-x) in
	   f (i_bpi + ntz32 b);
	   visit (x - b)
	 end
       in
       visit n)
    v.bits

let martin_constant = (0x03f79d71b lsl 28) lor 0x4ca8b09 (*0x03f79d71b4ca8b09*)
let hash64 x = ((martin_constant * x) land max_int) lsr 56
let ntz_arr64 = Array.make 64 0
let () = for i = 0 to 62 do ntz_arr64.(hash64 (1 lsl i)) <- i done
let ntz64 x = if x == 0 then 63 else ntz_arr64.(hash64 (x land (-x)))

let iteri_true_ntz64 f v =
  Array.iteri
    (fun i n ->
       let i_bpi = i * bpi in
       let rec visit x =
	 if x != 0 then begin
	   let b = x land (-x) in
	   f (i_bpi + ntz64 b);
	   visit (x - b)
	 end
       in
       visit n)
    v.bits

let iteri_true = match Sys.word_size with
  | 32 -> iteri_true_ntz32
  | 64 -> iteri_true_ntz64
  | _ -> assert false

(*s Bitwise operations. It is straigthforward, since bitwise operations
    can be realized by the corresponding bitwise operations over integers.
    However, one has to take care of normalizing the result of [bwnot]
    which introduces ones in highest significant positions. *)

let bw_and v1 v2 =
  let l = v1.length in
  if l <> v2.length then invalid_arg "Bitv.bw_and";
  let b1 = v1.bits
  and b2 = v2.bits in
  let n = Array.length b1 in
  let a = Array.make n 0 in
  for i = 0 to n - 1 do
    a.(i) <- b1.(i) land b2.(i)
  done;
  { length = l; bits = a }

let bw_or v1 v2 =
  let l = v1.length in
  if l <> v2.length then invalid_arg "Bitv.bw_or";
  let b1 = v1.bits
  and b2 = v2.bits in
  let n = Array.length b1 in
  let a = Array.make n 0 in
  for i = 0 to n - 1 do
    a.(i) <- b1.(i) lor b2.(i)
  done;
  { length = l; bits = a }

let bw_xor v1 v2 =
  let l = v1.length in
  if l <> v2.length then invalid_arg "Bitv.bw_xor";
  let b1 = v1.bits
  and b2 = v2.bits in
  let n = Array.length b1 in
  let a = Array.make n 0 in
  for i = 0 to n - 1 do
    a.(i) <- b1.(i) lxor b2.(i)
  done;
  { length = l; bits = a }

let bw_not v =
  let b = v.bits in
  let n = Array.length b in
  let a = Array.make n 0 in
  for i = 0 to n - 1 do
    a.(i) <- max_int land (lnot b.(i))
  done;
  let r = { length = v.length; bits = a } in
  normalize r;
  r

(*s Shift operations. It is easy to reuse [unsafe_blit], although it is
    probably slightly less efficient than a ad-hoc piece of code. *)

let rec shiftl v d =
  if d == 0 then
    copy v
  else if d < 0 then
    shiftr v (-d)
  else begin
    let n = v.length in
    let r = create n false in
    if d < n then unsafe_blit v.bits 0 r.bits d (n - d);
    r
  end

and shiftr v d =
  if d == 0 then
    copy v
  else if d < 0 then
    shiftl v (-d)
  else begin
    let n = v.length in
    let r = create n false in
    if d < n then unsafe_blit v.bits d r.bits 0 (n - d);
    r
  end

(*s Rotate operations. It is easy to reuse [unsafe_blit], although it is
    probably slightly less efficient than an ad-hoc piece of code. *)

let rec rotatel v d =
  if d < 0 then
    rotater v (-d)
  else
  let n = v.length in
  let d = d mod n in
  if d == 0 then
    copy v
  else begin
    let r = create n false in
    unsafe_blit v.bits 0 r.bits d (n - d); (* shiftl *)
    unsafe_blit v.bits (n - d) r.bits 0 d; (* wraparound ms to ls *)
    r
  end

and rotater v d =
  if d < 0 then
    rotatel v (-d)
  else
  let n = v.length in
  let d = d mod n in
  if d == 0 then
    copy v
  else begin
    let r = create n false in
    unsafe_blit v.bits d r.bits 0 (n - d); (* shiftr *)
    unsafe_blit v.bits 0 r.bits (n - d) d; (* wraparound ls to ms *)
    r
  end

(*s Testing for all zeros and all ones. *)

let all_zeros v =
  let b = v.bits in
  let n = Array.length b in
  let rec test i =
    (i == n) || ((Array.unsafe_get b i == 0) && test (succ i))
  in
  test 0

let all_ones v =
  let b = v.bits in
  let n = Array.length b in
  let rec test i =
    if i == n - 1 then
      let m = v.length mod bpi in
      (Array.unsafe_get b i) == (if m == 0 then max_int else low_mask.(m))
    else
      ((Array.unsafe_get b i) == max_int) && test (succ i)
  in
  test 0

(*s Conversions to and from strings. *)

module S(I : sig val least_first : bool end) = struct

  let to_string v =
    let n = v.length in
    let s = Bytes.make n '0' in
    for i = 0 to n - 1 do
      if unsafe_get v i then Bytes.set s (if I.least_first then i else n-1-i) '1'
    done;
    Bytes.unsafe_to_string s

  let print fmt v = Format.pp_print_string fmt (to_string v)

  let of_string s =
    let n = String.length s in
    let v = create n false in
    for i = 0 to n - 1 do
      let c = String.unsafe_get s i in
      if c = '1' then
	unsafe_set v (if I.least_first then i else n-1-i) true
      else
	if c <> '0' then invalid_arg "Bitv.of_string"
    done;
    v

end
module L = S(struct let least_first = true end)
module M = S(struct let least_first = false end)

(*s Input/output in a machine-independent format. *)

let bytes_of_int x =
  Bytes.init 8 (fun i -> Char.chr ((x lsr (8 * i)) land 0xFF))

let int_of_bytes b =
  assert (Bytes.length b = 8);
  let rec build x i =
    if i < 0 then x
    else build ((x lsl 8) lor Char.code (Bytes.get b i)) (pred i)
  in
  build 0 7

let to_bin write v =
  let len = length v in
  let rec loop i pow byte =
    let byte = if unsafe_get v i then byte lor pow else byte in
    if i = len - 1 then
      write byte
    else if i mod 8 = 7 then begin
      write byte;
      loop (i + 1) 1 0
    end else
      loop (i + 1) (pow * 2) byte
  in
  bytes_of_int len
  |> Bytes.iter (fun b -> Char.code b |> write);
  if len > 0 then loop 0 1 0

let output_bin out_ch v =
  let write = output_byte out_ch in
  to_bin write v

let to_bytes t =
  let buf = Buffer.create 0 in
  let write i = Buffer.add_char buf (Char.chr i) in
  to_bin write t;
  Buffer.to_bytes buf

let of_bin read =
  let len = Bytes.init 8 (fun _ -> read () |> Char.chr) |> int_of_bytes in
  let bits = create len false in
  let rec loop i byte =
    if i < len then begin
      let byte = if i mod 8 = 0 then read () else byte in
      if byte land 1 = 1 then unsafe_set bits i true;
      loop (i+1) (byte / 2)
    end
  in
  if len > 0 then loop 0 0;
  bits

let input_bin in_ch =
  let read () = input_byte in_ch in
  of_bin read

let of_bytes b =
  let read =
    let p = ref 0 in
    fun () ->
      let ret = Bytes.get b !p |> Char.code in
      incr p;
      ret
  in
  of_bin read

(* Iteration on all bit vectors of length [n] using a Gray code. *)

let first_set v n =
  let rec lookup i =
    if i = n then raise Not_found ;
    if unsafe_get v i then i else lookup (i + 1)
  in
  lookup 0

let gray_iter f n =
  let bv = create n false in
  let rec iter () =
    f bv;
    unsafe_set bv 0 (not (unsafe_get bv 0));
    f bv;
    let pos = succ (first_set bv n) in
    if pos < n then begin
      unsafe_set bv pos (not (unsafe_get bv pos));
      iter ()
    end
  in
  if n > 0 then iter ()


(*s Coercions to/from lists of integers *)

let of_list l =
  let n = List.fold_left max 0 l in
  let b = create (succ n) false in
  let add_element i =
    (* negative numbers are invalid *)
    if i < 0 then invalid_arg "Bitv.of_list";
    unsafe_set b i true
  in
  List.iter add_element l;
  b

let of_list_with_length l len =
  let b = create len false in
  let add_element i =
    if i < 0 || i >= len then invalid_arg "Bitv.of_list_with_length";
    unsafe_set b i true
  in
  List.iter add_element l;
  b

let to_list b =
  let n = length b in
  let rec make i acc =
    if i < 0 then acc
    else make (pred i) (if unsafe_get b i then i :: acc else acc)
  in
  make (pred n) []


(*s To/from integers. *)

(* [int] *)
let of_int_us i =
  { length = bpi; bits = [| i land max_int |] }
let to_int_us v =
  if v.length < bpi then invalid_arg "Bitv.to_int_us";
  v.bits.(0)

let of_int_s i =
  { length = succ bpi; bits = [| i land max_int; (i lsr bpi) land 1 |] }
let to_int_s v =
  if v.length < succ bpi then invalid_arg "Bitv.to_int_s";
  v.bits.(0) lor (v.bits.(1) lsl bpi)

(* [Int32] *)
let of_int32_us i = match Sys.word_size with
  | 32 -> { length = 31;
	    bits = [| (Int32.to_int i) land max_int;
		      let hi = Int32.shift_right_logical i 30 in
		      (Int32.to_int hi) land 1 |] }
  | 64 -> { length = 31; bits = [| (Int32.to_int i) land 0x7fffffff |] }
  | _ -> assert false
let to_int32_us v =
  if v.length < 31 then invalid_arg "Bitv.to_int32_us";
  match Sys.word_size with
    | 32 ->
	Int32.logor (Int32.of_int v.bits.(0))
	            (Int32.shift_left (Int32.of_int (v.bits.(1) land 1)) 30)
    | 64 ->
	Int32.of_int (v.bits.(0) land 0x7fffffff)
    | _ -> assert false

(* this is 0xffffffff (ocaml >= 3.08 checks for literal overflow) *)
let ffffffff = (0xffff lsl 16) lor 0xffff

let of_int32_s i = match Sys.word_size with
  | 32 -> { length = 32;
	    bits = [| (Int32.to_int i) land max_int;
		      let hi = Int32.shift_right_logical i 30 in
		      (Int32.to_int hi) land 3 |] }
  | 64 -> { length = 32; bits = [| (Int32.to_int i) land ffffffff |] }
  | _ -> assert false
let to_int32_s v =
  if v.length < 32 then invalid_arg "Bitv.to_int32_s";
  match Sys.word_size with
    | 32 ->
	Int32.logor (Int32.of_int v.bits.(0))
	            (Int32.shift_left (Int32.of_int (v.bits.(1) land 3)) 30)
    | 64 ->
	Int32.of_int (v.bits.(0) land ffffffff)
    | _ -> assert false

(* [Int64] *)
let of_int64_us i = match Sys.word_size with
  | 32 -> { length = 63;
	    bits = [| (Int64.to_int i) land max_int;
		      (let mi = Int64.shift_right_logical i 30 in
		       (Int64.to_int mi) land max_int);
		      let hi = Int64.shift_right_logical i 60 in
		      (Int64.to_int hi) land 7 |] }
  | 64 -> { length = 63;
	    bits = [| (Int64.to_int i) land max_int;
		      let hi = Int64.shift_right_logical i 62 in
		      (Int64.to_int hi) land 1 |] }
  | _ -> assert false
let to_int64_us v =
  if v.length < 63 then invalid_arg "Bitv.to_int64_us";
  match Sys.word_size with
    | 32 ->
	Int64.logor (Int64.of_int v.bits.(0))
        (Int64.logor (Int64.shift_left (Int64.of_int v.bits.(1)) 30)
                     (Int64.shift_left (Int64.of_int (v.bits.(2) land 7)) 60))
    | 64 ->
	Int64.logor (Int64.of_int v.bits.(0))
                    (Int64.shift_left (Int64.of_int (v.bits.(1) land 1)) 62)
    | _ ->
        assert false

let of_int64_s i = match Sys.word_size with
  | 32 -> { length = 64;
	    bits = [| (Int64.to_int i) land max_int;
		      (let mi = Int64.shift_right_logical i 30 in
		       (Int64.to_int mi) land max_int);
		      let hi = Int64.shift_right_logical i 60 in
		      (Int64.to_int hi) land 15 |] }
  | 64 -> { length = 64;
            bits = [| (Int64.to_int i) land max_int;
                      let hi = Int64.shift_right_logical i 62 in
		      (Int64.to_int hi) land 3 |] }
  | _ -> assert false
let to_int64_s v =
  if v.length < 64 then invalid_arg "Bitv.to_int64_s";
  match Sys.word_size with
    | 32 ->
	Int64.logor (Int64.of_int v.bits.(0))
        (Int64.logor (Int64.shift_left (Int64.of_int v.bits.(1)) 30)
                     (Int64.shift_left (Int64.of_int (v.bits.(2) land 15)) 60))
    | 64 ->
	Int64.logor (Int64.of_int v.bits.(0))
                    (Int64.shift_left (Int64.of_int (v.bits.(1) land 3)) 62)
    | _ -> assert false

(* [Nativeint] *)
let select_of f32 f64 = match Sys.word_size with
  | 32 -> (fun i -> f32 (Nativeint.to_int32 i))
  | 64 -> (fun i -> f64 (Int64.of_nativeint i))
  | _ -> assert false
let of_nativeint_s = select_of of_int32_s of_int64_s
let of_nativeint_us = select_of of_int32_us of_int64_us
let select_to f32 f64 = match Sys.word_size with
  | 32 -> (fun i -> Nativeint.of_int32 (f32 i))
  | 64 -> (fun i -> Int64.to_nativeint (f64 i))
  | _ -> assert false
let to_nativeint_s = select_to to_int32_s to_int64_s
let to_nativeint_us = select_to to_int32_us to_int64_us