LZW compression
The Lempel-Ziv-Welch (LZW) algorithm provides lossless data compression. You can read a complete description of it in the Wikipedia article on the subject. It was patented, but it fell in the public domain in 2004.
OCaml
<ocaml>#directory "+site-lib/extlib/"
- load "extLib.cma"
open ExtString
(** compress a string to a list of output symbols *) let compress ~uncompressed =
(* build the dictionary *) let dict_size = 256 in let dictionary = Hashtbl.create 397 in for i=0 to 255 do let str = String.make 1 (char_of_int i) in Hashtbl.add dictionary str i done; let f = (fun (w, dict_size, result) c -> let c = String.make 1 c in let wc = w ^ c in if Hashtbl.mem dictionary wc then (wc, dict_size, result) else begin (* add wc to the dictionary *) Hashtbl.add dictionary wc dict_size; let this = Hashtbl.find dictionary w in (c, dict_size + 1, this::result) end ) in let w, _, result = String.fold_left f ("", dict_size, []) uncompressed in
(* output the code for w *) let result = if w = "" then result else (Hashtbl.find dictionary w) :: result in
(List.rev result)
exception ValueError of string
(** decompress a list of output symbols to a string *) let decompress ~compressed =
(* build the dictionary *) let dict_size = 256 in let dictionary = Hashtbl.create 397 in for i=0 to pred dict_size do let str = String.make 1 (char_of_int i) in Hashtbl.add dictionary i str done;
let w, compressed = match compressed with | hd::tl -> (String.make 1 (char_of_int hd)), tl | [] -> failwith "empty input" in let result = w::[] in
let result, _, _ = List.fold_left (fun (result, w, dict_size) k -> let entry = if Hashtbl.mem dictionary k then Hashtbl.find dictionary k else if k = Hashtbl.length dictionary then w ^ (String.make 1 w.[0]) else raise(ValueError(Printf.sprintf "Bad compressed k: %d" k)) in let result = entry :: result in (* add (w ^ entry.[0]) to the dictionary *) Hashtbl.add dictionary dict_size (w ^ (String.make 1 entry.[0])); (result, entry, dict_size + 1) ) (result, w, dict_size) compressed in (List.rev result)
- </ocaml>
here is the interface: <ocaml>val compress : uncompressed:string -> int list val decompress : compressed:int list -> string list</ocaml>
How to use:
The compressed datas are a list of symbols (of type int) that will require more than 8 bits to be saved.
So to know how many bits are required, you need to know how many bits are required for the greatest symbol in the list.
<ocaml>let greatest = List.fold_left (fun m x -> max m x) 0 ;;
(** number of bits needed to encode the integer m *) let n_bits m =
let m = float m in let rec aux n = let max = (2. ** n) -. 1. in if max >= m then int_of_float n else aux (n +. 1.0) in aux 1.0
let write_compressed ~filename ~compressed =
let nbits = n_bits(greatest compressed) in let oc = open_out filename in output_byte oc nbits; let ob = IO.output_bits(IO.output_channel oc) in List.iter (fun code -> IO.write_bits ob nbits code ) compressed; IO.flush_bits ob; close_out oc;
let read_compressed ~filename =
let ic = open_in filename in let nbits = input_byte ic in let ib = IO.input_bits(IO.input_channel ic) in let rec loop acc = try let code = IO.read_bits ib nbits in loop (code::acc) with _ -> List.rev acc in let compressed = loop [] in let result = decompress ~compressed in let buf = Buffer.create 2048 in List.iter (Buffer.add_string buf) result; (Buffer.contents buf)
- </ocaml>