Euclidian Algorithms

DIRECTORY.md

@@ -24,6 +24,7 @@
     * [Directedgraph](https://github.com/TheAlgorithms/Haskell/blob/master/src/Graph/DirectedGraph.hs)
   * [Haskellalgorithms](https://github.com/TheAlgorithms/Haskell/blob/master/src/HaskellAlgorithms.hs)
   * Maths
+    * [Euclidianalgorithm](https://github.com/TheAlgorithms/Haskell/blob/master/src/Maths/EuclidianAlgorithm.hs)
     * [Factorial](https://github.com/TheAlgorithms/Haskell/blob/master/src/Maths/Factorial.hs)
     * [Fibonacci](https://github.com/TheAlgorithms/Haskell/blob/master/src/Maths/Fibonacci.hs)
     * [Graphdist](https://github.com/TheAlgorithms/Haskell/blob/master/src/Maths/GraphDist.hs)

src/Maths/EuclidianAlgorithm.hs

@@ -0,0 +1,19 @@
+module Maths.EuclidianAlgorithm where
+
+-- Computes the Greatest Common Divisor (GCD) of two numbers using the Euclidian Algorithm
+ea :: (Integral a) => a -> a -> a
+ea x 0 = x
+ea x y = gcd y (x `mod` y)
+
+-- Computes the modular multiplicative inverse of a modulo m using the Extended Euclidian Algorithm
+-- https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Computing_multiplicative_inverses_in_modular_structures
+eea :: (Integral a) => a -> a -> Maybe a
+eea a m = let (r, t) = eea' 0 m 1 a
+              in if r > 1 then Nothing else if t < 0 then Just (t + m) else Just t
+
+-- The looping part of the algorithm, implemented recursively
+eea' :: (Integral a) => a -> a -> a -> a -> (a, a)
+eea' t0 r0 t1 r1
+    | r1 /= 0 = let q = r0 `div` r1
+                    in eea' t1 r1 (t0 - q * t1) (r0 - q * r1)
+    | otherwise = (r0, t0)