Back calculate pi from randomly generated numbers.

pifromrandomnumbers.hs

#!/usr/bin/env stack
-- stack --resolver lts-8.5 --nix runghc --package random
-- Requires the Haskell build tool Stack to be installed: https://docs.haskellstack.org/en/stable/README/
-- Create this file and make it executable using "chmod u+x pifromrandomnumbers.hs"
-- and run it with "./pifromrandomnumbers.hs" from a terminal.
{-# LANGUAGE StrictData #-}
{-# LANGUAGE Strict #-}

import System.Random

range :: (Int, Int)
range = (1, 10000000000)

numberOfRolls :: Int
numberOfRolls = 100000

coprimeRoll :: IO Bool
coprimeRoll = do
  first <- randomRIO range
  second <- randomRIO range
  return $ gcd first second <= 1

rollDice :: Int -> Int -> Int -> IO (Int, Int)
rollDice 0 coprimesSoFar countSoFar = return (coprimesSoFar, countSoFar)
rollDice rollsLeft coprimesSoFar countSoFar = do
  if rollsLeft < 0 then fail "Uh oh" else return ()
  isCoprime <- coprimeRoll
  let newCoprimesSoFar = if isCoprime then coprimesSoFar + 1 else coprimesSoFar
  rollDice (rollsLeft - 1) newCoprimesSoFar (countSoFar + 1)

main = do
  (coprime, total) <- rollDice numberOfRolls 0 0
  let probability = (fromIntegral coprime) / (fromIntegral total) :: Double
  let pi = sqrt (6 / probability)
  let result = "Estimated pi: " ++ (show pi)
  putStrLn result