Data commit

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

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+-- 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)
+
+main :: IO ()
+main = mapM_ print [2 `modInv` 4, 42 `modInv` 2017]