Start with Elliptic Curve point math. Slow, but it works.

test-generator/gcd.hs

@@ -0,0 +1,34 @@
+import Numeric
+
+data Set = Set { r :: Integer, s :: Integer, t :: Integer }
+
+step :: Set -> Set -> Set
+step old new = Set r' s' t'
+ where
+  quotient = r old `div` r new
+  r' = r old - (r new * quotient)
+  s' = s old - (s new * quotient)
+  t' = t old - (t new * quotient)
+
+run :: Integer -> Integer -> IO Set
+run self rhs = go (Set self 1 0) (Set rhs 0 1)
+ where
+  go old new | r new == 0 =
+    do putStrLn "------------------------------"
+       putStrLn ("res_r: " ++ showX (r old))
+       putStrLn ("res_s: " ++ showX (s old))
+       putStrLn ("res_t: " ++ showX (t old))
+       return old
+             | otherwise  =
+    do putStrLn "------------------------------"
+       putStrLn ("old_r: " ++ showX (r old))
+       putStrLn ("old_s: " ++ showX (s old))
+       putStrLn ("old_t: " ++ showX (t old))
+       putStrLn ("new_r: " ++ showX (r new))
+       putStrLn ("new_s: " ++ showX (s new))
+       putStrLn ("new_t: " ++ showX (t new))
+       go new (step old new)
+
+showX :: Integer -> String
+showX x | x < 0 = "-" ++ showX (abs x)
+        | otherwise = showHex x ""