# Toy compression implementations

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Revision as of 15:04, 8 March 2007 by MathematicalOrchid (talk | contribs) (Added Huffman compression.)

## 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"
```