import System.Random
import Control.Monad (forM)
import Text.Printf (printf)

gamma  = 0.98
tGamma = 2.326

a      = 7
k      = 6
c      = 6.85

fk x = log (1 + a * x)
f x  = if ((sum (fmap fk x)) <= c) then 1.0 else 0.0

mc :: [a] -> (a -> Double) -> Double
mc lst func = sum (fmap func lst) / fromIntegral (length lst)

splitEvery :: Int -> [a] -> [[a]]
splitEvery _ [] = []
splitEvery n ls = (fst sp):(splitEvery n (snd sp)) where
    sp = splitAt n ls

countVolume :: Int -> IO ()
countVolume n = do
    putStrLn $ printf "n = %d" n
    let p = mc (take n $ splitEvery k (randoms (mkStdGen 42) :: [Double])) f
    putStrLn $ printf "p_n = %.8f" p
    let d = tGamma * sqrt(p * (1 - p) / fromIntegral n)
    putStrLn $ printf "d_n = %.8f" d
    putStrLn $ printf "Interval = [%.8f, %.8f]" (p - d) (p + d)

main = mapM countVolume [10 ^ 4, 10 ^ 6]