A-M baby

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

@@ -0,0 +1,16 @@
+-- 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 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)
+
+-- 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