SamplingError.hs

#!/usr/bin/env stack
-- stack runghc --package random


import Control.Monad (replicateM)
import System.Random (randomRIO)


main :: IO ()
main = do
  let n = 1000000
  samples <- genSamples n
  let a = fastMethod samples
  let b = preciseMethod samples
  putStrLn $ show a
  putStrLn $ show b
  putStrLn $ show $ abs $ a - b



genSamples :: Int -> IO [Float]
genSamples n = replicateM n $ randomRIO (0.0, 1.0)


-- Fast method is not necessarily faster to run. It's called fast
-- because we have access to average at all times. During sampling
-- we would need to decide if the new average is sufficiently
-- different thant the old average. This is omitted here.


fastMethod :: [Float] -> Float
fastMethod (x:xs) = f x 1 xs where
  f ave n [] = ave
  f ave n (x:xs) = f (((ave * n) + x) / (succ n)) (succ n) xs


preciseMethod :: [Float] -> Float
preciseMethod (x:xs) = f x 1 xs where
  f sum n [] = sum / n
  f sum n (x:xs) = f (sum + x) (succ n) xs


-- Typically difference is 1e-6 ~ 1e-7 for Float and 1e-14 ~ 1e-15 for Double.