module Main where

import Data.Array
import Data.Complex

import Numeric.Transform.Fourier.FFT
import Numeric.Transform.Fourier.FFTHard
import Numeric.Transform.Fourier.R2DIF
import Numeric.Transform.Fourier.R2DIT
import Numeric.Transform.Fourier.R4DIF
import Numeric.Transform.Fourier.SRDIF
import Numeric.Transform.Fourier.CT
import Numeric.Transform.Fourier.PFA
import Numeric.Transform.Fourier.Rader
import Numeric.Transform.Fourier.DFT

import Numeric.Random.Generator.MT19937
import Numeric.Random.Distribution.Uniform

len = 2048 :: Int
iter = 100 :: Int

m1 x = x - 1

real = map m1 $ map (2*) $ uniform53cc $ genrand 42
imag = map m1 $ map (2*) $ uniform53cc $ genrand 43

x = zipWith (:+) real imag

gendata :: [Complex Double] -> Int -> [Array Int (Complex Double)]
gendata xs n = map (listArray (0,n-1)) $ gendata' xs n
    where gendata' xs n = take n xs : gendata' (drop n xs) n

calc f xs iter = magnitude $ sum $ map sum $ map elems $ map f $ take iter xs

f1 xs | n == 2    = fft'2 xs
      | n == 4    = fft'4 xs
      | otherwise = fft_r2dit xs n f1
    where n = (snd $ bounds xs) + 1

f2 xs | n == 2    = fft'2 xs
      | n == 4    = fft'4 xs
      | otherwise = fft_r2dif xs n f2
    where n = (snd $ bounds xs) + 1

f3 xs | n == 2    = fft'2 xs
      | n == 4    = fft'4 xs
      | otherwise = fft_r4dif xs n f3
    where n = (snd $ bounds xs) + 1

f4 xs | n == 2    = fft'2 xs
      | n == 4    = fft'4 xs
      | otherwise = fft_srdif xs n f4
    where n = (snd $ bounds xs) + 1

choose1 :: Int -> Int
choose1 n = loop1 1 1
    where loop1 i f | i * i > n = f
	            | (n `mod` i) == 0 && gcd i (n `div` i) == 1 = loop1 (i+1) i
	            | otherwise = loop1 (i+1) f

choose2 :: Int -> Int
choose2 n = loop2 1 1
    where loop2 i f | i * i > n = f
                    | n `mod` i == 0 = loop2 (i+1) i
	            | otherwise = loop2 (i+1) f

choose_factor :: Int -> Int
choose_factor n | i > 1 = i
	        | otherwise = choose2 n
    where i = choose1 n

f5 xs | n == 2    = fft'2 xs
      | n == 4    = fft'4 xs
      | otherwise = fft_ct1 xs l m f5
    where n = (snd $ bounds xs) + 1
	  l = choose_factor n
          m = n `div` l

f6 xs | n == 2    = fft'2 xs
      | n == 4    = fft'4 xs
      | otherwise = fft_ct2 xs l m f6
    where n = (snd $ bounds xs) + 1
	  l = choose_factor n
          m = n `div` l

f7 xs = fft_rader1 xs n
    where n = (snd $ bounds xs) + 1

f8 xs = fft_rader2 xs n fft
    where n = (snd $ bounds xs) + 1

main = do
       let xs = (gendata x len)
       print $ calc f1 xs iter
       print $ calc f2 xs iter
       print $ calc f3 xs iter
       print $ calc f4 xs iter
       print $ calc f5 xs iter
       print $ calc f6 xs iter