September Morn Update

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

@@ -1,16 +1,25 @@
--- Extended Euclidean algorithm.  Given non-negative a and b, return x, y and g
--- such that ax + by = g, where g = gcd(a,b).  Note that x or y may be negative.
+-- Given a and m, return Just x such that ax = 1 mod m.
+-- If there is no such x return Nothing.
+modInv :: Int -> Int -> Maybe Int
+modInv a m
+  | 1 == g = Just (mkPos i)
+  | otherwise = Nothing
+  where
+    (i, _, g) = gcdExt a m
+    mkPos x
+      | x < 0 = x + m
+      | otherwise = x
+
+-- Extended Euclidean algorithm.
+-- Given non-negative a and b, return x, y and g
+-- such that ax + by = g, where g = gcd(a,b).
+-- Note that x or y may be negative.
+gcdExt :: Int -> Int -> (Int, Int, Int)
 gcdExt a 0 = (1, 0, a)
-gcdExt a b = let (q, r) = a `quotRem` b
-                 (s, t, g) = gcdExt b r
-             in (t, s - q * t, g)
+gcdExt a b =
+  let (q, r) = a `quotRem` b
+      (s, t, g) = gcdExt b r
+  in (t, s - q * t, g)
 
--- Given a and m, return Just x such that ax = 1 mod m.  If there is no such x
--- return Nothing.
-modInv a m = let (i, _, g) = gcdExt a m
-             in if g == 1 then Just (mkPos i) else Nothing
-  where mkPos x = if x < 0 then x + m else x
-
-main = do
-  print $ 2 `modInv` 4
-  print $ 42 `modInv` 2017
+main :: IO ()
+main = mapM_ print [2 `modInv` 4, 42 `modInv` 2017]