# Toy compression implementations

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(Lots of lushous example code.) |
(use laziness and HOFs to dramatically shrink lzw funcs) |
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[[Category:Code]] | [[Category:Code]] | ||

+ | |||

+ | == 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 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 | + | 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... |

[[User:MathematicalOrchid|MathematicalOrchid]] 16:46, 15 February 2007 (UTC) | [[User:MathematicalOrchid|MathematicalOrchid]] 16:46, 15 February 2007 (UTC) | ||

+ | |||

+ | == Main module == | ||

<haskell> | <haskell> | ||

module Compression where | module Compression where | ||

− | import | + | import List |

+ | import Maybe | ||

+ | import IO (hFlush, stdout) | ||

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

-- Run-length encoding | -- Run-length encoding | ||

− | encode_RLE :: (Eq | + | encode_RLE :: (Eq t) => [t] -> [(Int,t)] |

encode_RLE = map (\xs -> (length xs, head xs)) . groupBy (==) | encode_RLE = map (\xs -> (length xs, head xs)) . groupBy (==) | ||

− | decode_RLE :: [(Int, | + | decode_RLE :: [(Int,t)] -> [t] |

decode_RLE = concatMap (uncurry replicate) | decode_RLE = concatMap (uncurry replicate) | ||

− | -- Limpel-Ziv- | + | -- Limpel-Ziv-Welch encoding |

− | encode_LZW :: (Eq | + | encode_LZW :: (Eq t) => [t] -> [t] -> [Int] |

− | encode_LZW | + | encode_LZW alphabet = work (map (:[]) alphabet) where |

− | + | chunk pred lst = last . takeWhile (pred . fst) . tail $ zip (inits lst) (tails lst) | |

− | + | work table [] = [] | |

− | work table | + | work table lst = fromJust (elemIndex tok table) : work (table ++ [tok ++ [head rst]]) rst |

− | work table | + | where (tok, rst) = chunk (`elem` table) lst |

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | -- | + | decode_LZW :: [t] -> [Int] -> [t] |

+ | decode_LZW alphabet xs = concat output where | ||

+ | output = map (table !!) xs | ||

+ | table = map (:[]) alphabet ++ zipWith (++) output (map (take 1) (tail output)) | ||

− | - | + | main = do x <- take 20000 `fmap` readFile "/usr/share/dict/words" |

+ | let l = length x `div` 80 | ||

+ | a = ['\0' .. '\255'] | ||

+ | eq a b | a == b = putChar '=' >> hFlush stdout | ||

+ | | otherwise = error "data error" | ||

+ | cmp = zipWith eq x . decode_LZW a . encode_LZW a $ x | ||

+ | vl = map head $ unfoldr (\cm -> case cm of [] -> Nothing ; _ -> Just (splitAt l cm)) cmp | ||

+ | sequence_ vl | ||

− | |||

</haskell> | </haskell> | ||

− | + | Some examples are in order: | |

<haskell> | <haskell> | ||

− | + | > 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." | ||

</haskell> | </haskell> | ||

− | + | == Huffman coding == | |

+ | |||

+ | <haskell> | ||

+ | 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 | ||

+ | </haskell> | ||

+ | |||

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

+ | |||

+ | A short demo: | ||

+ | <haskell> | ||

+ | > encode_huffman "this is just a simple test" | ||

+ | <loads of data> | ||

+ | |||

+ | > decode_huffman (fst it) (snd it) | ||

+ | "this is just a simple test" | ||

+ | </haskell> |

## Latest revision as of 01:59, 9 March 2007

## [edit] 1 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)

## [edit] 2 Main module

module Compression where import List import Maybe import IO (hFlush, stdout) 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 alphabet = work (map (:[]) alphabet) where chunk pred lst = last . takeWhile (pred . fst) . tail $ zip (inits lst) (tails lst) work table [] = [] work table lst = fromJust (elemIndex tok table) : work (table ++ [tok ++ [head rst]]) rst where (tok, rst) = chunk (`elem` table) lst decode_LZW :: [t] -> [Int] -> [t] decode_LZW alphabet xs = concat output where output = map (table !!) xs table = map (:[]) alphabet ++ zipWith (++) output (map (take 1) (tail output)) main = do x <- take 20000 `fmap` readFile "/usr/share/dict/words" let l = length x `div` 80 a = ['\0' .. '\255'] eq a b | a == b = putChar '=' >> hFlush stdout | otherwise = error "data error" cmp = zipWith eq x . decode_LZW a . encode_LZW a $ x vl = map head $ unfoldr (\cm -> case cm of [] -> Nothing ; _ -> Just (splitAt l cm)) cmp sequence_ vl

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."

## [edit] 3 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"