arithmetic.hs

-- Miscellaneous arithmetic functions

-- Square roots using Newton's method
sqrtNewton :: (Floating a, Ord a) => a -> a
sqrtNewton n = head $ dropWhile (\g -> abs(n - g^2) > tolerance) $ iterate (newGuess n) 1
    where 
        tolerance = 0.000001

newGuess :: Floating a => a -> a -> a
newGuess n oldGuess = (oldGuess + n / oldGuess) / 2

-- Integer square root using Newton's method
sqrtNewtonInt :: Integer -> Integer
sqrtNewtonInt n = head $ dropWhile (\g -> g*g > n || (g+1)^2 < n ) $ iterate (newGuessInt n) 1

newGuessInt :: Integer -> Integer -> Integer
newGuessInt n oldGuess = (oldGuess + n `div` oldGuess) `div` 2