pi-digits/src/Logic.hs

-- Calculate and store values of Pi.
module Logic (hexDigits) where

import Control.Parallel (par)


-- Get the hex digit of Pi at place n.
hexPi :: Integer -> Integer
hexPi n =
  let
    summation = let
      sone = (4 * sumPi n 1)
      sfour = (2 * sumPi n 4)
      sfive = (sumPi n 5)
      ssix = (sumPi n 6)
      in
      sone `par` sfour `par` sfive `par` ssix `par` sone - sfour - sfive - ssix

    skimmedSum = summation - (fromIntegral (floor summation :: Integer)) -- Take only the decimal portion
  in
    floor (16 * skimmedSum) :: Integer


-- Calculate the summation.
-- 5000 is used in place of Infinity. This value drops off quickly, so no need to go too far.
sumPi :: Integer -> Integer -> Double
sumPi n x =
  let
    summation1 = sum [(fromIntegral ((16^(n-k) `mod` ((8*k)+x)))) / (fromIntegral ((8*k)+x)) | k <- [0..n]]
    summation2 = sum [16^^(n-k) / (fromIntegral ((8*k)+x)) | k <- [(n+1)..5000]]
  in
    summation1 + summation2


-- The list of answers.
hexDigits :: [Integer]
hexDigits = [hexPi x | x <- [0..]]