module FFT ( fft ) where
import Data.Complex 
import System.Random 
cmpExp n k j = mkPolar 1 (-2 * pi * fromIntegral k / fromIntegral n) * j 
splitEvenOdd [] = ([], []) 
splitEvenOdd [x] = ([x],[]) 
splitEvenOdd (x:y:xs) = (x:xe, y:yo) 
    where (xe, yo) = splitEvenOdd xs
combine [] [] = [] 
combine xs [] = xs 
combine [] ys = ys 
combine xs ys = add ++ sub 
    where add = zipWith (+) xs ys 
          sub = zipWith (-) xs ys
fft :: [Complex Double] -> [Complex Double] 
fft [] = [] 
fft [x] = [x] 
fft xs = combine even cmpOdd 
    where (e, o) = splitEvenOdd xs 
          even = fft e 
          odd = fft o 
          size = length xs 
          cmpOdd = zipWith (cmpExp size) [0..] odd  
createList :: Int -> [Complex Double] 
createList n = take (2^n) $ zipWith (:+) (randoms (mkStdGen 10)) (randoms (mkStdGen 10)) 

main :: IO() 
main = interact (show . fft . createList . read)