Toy compression implementations

About

This code is provided in the hope that someone might find it interesting/entertaining, and to demonstrate what an excellent programming language Haskell truly is. (A working polymorphic LZW implementation in 10 lines? Try that in Java!)

This is 'toy' code. Please don't try to use it to compress multi-GB of data. It has not been thoroughly checked for correctness, and I shudder to think what the time and space complexity would be like! However, it is enlightening and entertaining to see how many algorithms you can implement with a handful of lines...

MathematicalOrchid 16:46, 15 February 2007 (UTC)

Main module

module Compression where

import Data.List
import Data.Word   -- In case you want it. (Not actually used anywhere!)

chars = [' '..'~']   -- Becuase ' ' = 0x20 and '~' = 0x7F.


-- Run-length encoding

encode_RLE :: (Eq t) => [t] -> [(Int,t)]
encode_RLE = map (\xs -> (length xs, head xs)) . groupBy (==)

decode_RLE :: [(Int,t)] -> [t]
decode_RLE = concatMap (uncurry replicate)


-- Limpel-Ziv-Welch encoding

encode_LZW :: (Eq t) => [t] -> [t] -> [Int]
encode_LZW _        []     = []
encode_LZW alphabet (x:xs) = work (make alphabet) [x] xs where
  make = map (\x -> [x])
  work table buffer []     = [maybe undefined id $ elemIndex buffer table]
  work table buffer (x:xs) =
    let new = buffer ++ [x]
    in  case elemIndex new table of
          Nothing -> maybe undefined id (elemIndex buffer table) : work (table ++ [new]) [x] xs
          Just _  -> work table new xs

decode_LZW :: [t] -> [Int] -> [t]
decode_LZW _        []     = []
decode_LZW alphabet xs = work (length alphabet) (make alphabet) [] xs where
  make = map (\x -> [x])
  work _ t     _    []     = []
  work n table prev (x:xs) = case x >= n of
    True  -> error "underflow"   -- THIS NEEDS FIXING!
    False -> let out = table !! x
             in  out ++
                 if null prev
                   then work n table out xs
                   else work (n+1) (table ++ [prev ++ [head out]]) out xs

Some examples are in order:

> encode_RLE "AAAABBBBDDCCCCEEEGGFFFF"

[(4,'A'),(4,'B'),(2,'D'),(4,'C'),(3,'E'),(2,'G'),(4,'F')]


> decode_RLE [(4,'A'),(4,'B'),(2,'D'),(4,'C'),(3,'E'),(2,'G'),(4,'F')]

"AAAABBBBDDCCCCEEEGGFFFF"


> encode_LZW chars "This is just a simple test."

[52,72,73,83,0,97,0,74,85,83,84,0,65,0,83,73,77,80,76,69,0,84,69,104,14]


> decode_LZW chars [52,72,73,83,0,97,0,74,85,83,84,0,65,0,83,73,77,80,76,69,0,84,69,104,14]

"This is just a simple test."

Huffman coding

module Huffman
    (count, markov1, Tree, encode_huffman, decode_huffman)
  where

import Data.List (nub)

-- Marvok1 probability model...

count :: (Eq t) => [t] -> [(t,Int)]
count xs = map (\x -> (x, length $ filter (x ==) xs)) $ nub xs

markov1 :: (Eq t) => [t] -> [(t,Double)]
markov1 xs =
  let n = fromIntegral $ length xs
  in  map (\(x,c) -> (x, fromIntegral c / n)) $ count xs


-- Build a Huffman tree...

data Tree t = Leaf Double t | Branch Double (Tree t) (Tree t) deriving Show

prob :: Tree t -> Double
prob (Leaf   p _)   = p
prob (Branch p _ _) = p

get_tree :: [Tree t] -> (Tree t, [Tree t])
get_tree (t:ts) = work t [] ts where
  work x xs [] = (x,xs)
  work x xs (y:ys)
    | prob y < prob x = work y (x:xs) ys
    | otherwise       = work x (y:xs) ys

huffman_build :: [(t,Double)] -> Tree t
huffman_build = build . map (\(t,p) -> Leaf p t) where
  build [t] = t
  build ts =
    let (t0,ts0) = get_tree ts
        (t1,ts1) = get_tree ts0
    in  build $ Branch (prob t0 + prob t1) t0 t1 : ts1


-- Make codebook...

data Bit  = Zero | One deriving (Eq, Show)
type Bits = [Bit]

huffman_codebook :: Tree t -> [(t,Bits)]
huffman_codebook = work [] where
  work bs (Leaf _ x) = [(x,bs)]
  work bs (Branch _ t0 t1) = work (bs ++ [Zero]) t0 ++ work (bs ++ [One]) t1


-- Do the coding!

encode :: (Eq t) => [(t,Bits)] -> [t] -> Bits
encode cb = concatMap (\x -> maybe undefined id $ lookup x cb)

decode :: (Eq t) => Tree t -> Bits -> [t]
decode t = work t t where
  work _ (Leaf   _ x)        []  = [x]
  work t (Leaf   _ x)        bs  = x : work t t bs
  work t (Branch _ t0 t1) (b:bs)
    | b == Zero = work t t0 bs
    | otherwise = work t t1 bs

encode_huffman :: (Eq t) => [t] -> (Tree t, Bits)
encode_huffman xs =
  let t  = huffman_build $ markov1 xs
      bs = encode (huffman_codebook t) xs
  in (t,bs)

decode_huffman :: (Eq t) => Tree t -> Bits -> [t]
decode_huffman = decode

If anybody can make this code shorter / more elegant, feel free!

A short demo:

> encode_huffman "this is just a simple test"
<loads of data>

> decode_huffman (fst it) (snd it)
"this is just a simple test"