lebs_pi.hs

-- leibniz's pi formula
-- a very elementary take i guess :P

odd_ds :: Int -> [Double]
odd_ds n = [x | x <- take n [1.0,3.0..]]

y_eq :: Double -> Double -> Double
y_eq d s = s * (1.0 / d) 

leibs_series :: [Double] -> Double -> Double
leibs_series [] _ = 0
leibs_series (d:ds) s = ((y_eq d s) + leibs_series ds (s * (-1.0)))

leibs_pi :: Int -> Double
leibs_pi 0 = 0.0
leibs_pi n = 4.0 * (leibs_series (odd_ds n) (1.0))

-- *Main> lebs_pi 1000
-- 3.140592653839793