{-# LANGUAGE BangPatterns #-}

import Data.Foldable
import System.Random
import System.Environment (getArgs)

intervals :: [(Double,Double)]
intervals = map conv [0..9]
    where xs = [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
          conv s = let { [h,l] = take 2 $ drop s xs } in (h,l)

count :: [Double] -> [Int]
count rands = map (\iv -> foldl' (loop iv) 0 rands) intervals
   where loop :: (Double,Double) -> Int -> Double -> Int
         loop (lo,hi) n x | lo <= x && x < hi = n+1
                          | otherwise         = n
         -- ^ fuses length and filter within (lo,hi)

data Pair a b = Pair !a !b

-- accumulate sum and length in one fold
sumLen :: [Double] -> Pair Double Double
sumLen = fion2 . foldl' (\(Pair s l) x -> Pair (s+x) (l+1)) (Pair 0.0 0)
  where fion2 :: Pair Double Int -> Pair Double Double
        fion2 (Pair s l) = Pair s (fromIntegral l)

-- safe division on pairs
divl :: Pair Double Double -> Double
divl (Pair _ 0.0) = 0.0
divl (Pair s   l) = s / l

-- sumLen and divl are separate for stddev below
mean :: [Double] -> Double
mean = divl . sumLen

stddev :: [Double] -> Double
stddev xs = sqrt $ foldl' (\s x -> s+(x-m)^2) 0 xs / l
   where p@(Pair s l) = sumLen xs
         m = divl p

main = do nr    <- read.head <$> getArgs
          rands <- take nr . randomRs (0.0,1.0) <$> newStdGen
          putStrLn $ "The mean is " ++ show (mean rands) ++ " !"
          putStrLn $ "The standard deviation is " ++ show (stddev rands) ++ " !"
          zipWithM_ (\iv fq -> putStrLn $ ivstr iv ++ ": " ++ fqstr fq) intervals (count rands)
    where
        fqstr i = replicate (if i > 50 then div i (div i 50) else i) '*'
        ivstr (lo,hi) = show lo ++ " - " ++ show hi