A-M baby

Task/Modular-exponentiation/Haskell/modular-exponentiation.hs

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+-- Private type. Do not use outside of the modPow function
+newtype ModN = ModN (Integer, Integer) deriving (Eq, Show)
+instance Num ModN where
+  -- actually only multiplication needs to be implemented
+  -- but we do some of the other ones too for good measure
+  ModN (x, m) + ModN (y, m') | m == m' = ModN ((x + y) `mod` m, m)
+                             | otherwise = undefined
+  ModN (x, m) * ModN (y, m') | m == m' = ModN ((x * y) `mod` m, m)
+                             | otherwise = undefined
+  negate (ModN (x, m)) = ModN ((- x) `mod` m, m)
+  abs _ = undefined
+  signum _ = undefined
+  fromInteger _ = undefined
+
+modPow :: Integer -> Integer -> Integer -> Integer
+modPow _ 0 m = 1 `mod` m
+modPow a b m = c
+  where a' = ModN (a, m)
+        ModN (c, _) = a' ^ b
+
+main :: IO ()
+main = print $ modPow a b m
+  where a = 2988348162058574136915891421498819466320163312926952423791023078876139
+        b = 2351399303373464486466122544523690094744975233415544072992656881240319
+        m = 10 ^ 40