(**************************************************************************)
(*                                                                        *)
(*  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           *)
(*  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
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
{ 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

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 =
let i = n / bpi and j = n mod bpi in
if j < 0 then (i - 1, j + bpi) else (i,j)

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

(*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

let iteri_true_naive f v =
Array.iteri
(fun i n -> if n != 0 then begin
let i_bpi = i * bpi in
for j = 0 to bpi - 1 do
if n land (Array.unsafe_get bit_j j) > 0 then f (i_bpi + j)
done
end)
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 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 = String.make n '0' in
for i = 0 to n - 1 do
if unsafe_get v i then s.[if I.least_first then i else n-1-i] <- '1'
done;
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 output_bin out_ch 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
output_byte out_ch byte
else if i mod 8 = 7 then begin
output_byte out_ch byte;
loop (i + 1) 1 0
end else
loop (i + 1) (pow * 2) byte
in
output_binary_int out_ch len;
if len > 0 then loop 0 1 0

let input_bin in_ch =
let len = input_binary_int in_ch 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 input_byte in_ch 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

(*s 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
(* negative numbers are invalid *)
if i < 0 then invalid_arg "Bitv.of_list";
unsafe_set b i true
in
b

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



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