Data update

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-17.hs

@@ -1,35 +1,17 @@
-import Control.Arrow ((&&&))
+import Data.Ratio (numerator)
 
-fibstep :: (Integer, Integer) -> (Integer, Integer)
-fibstep (a, b) = (b, a + b)
+infixl 7 *.
+(*.) :: Num a => a -> [a] -> [a]
+x *. (p:ps) = x*p : x*.ps
 
-fibnums :: [Integer]
-fibnums = map fst $ iterate fibstep (0, 1)
+instance Num a => Num [a] where
+    negate = map negate
+    (+) = zipWith (+)
+    (*) (p:ps) (q:qs) = p*q : ((p*.qs) + ps*(q:qs))
+    fromInteger n = fromInteger n:repeat 0
 
-fibN2 :: Integer -> (Integer, Integer)
-fibN2 m
-  | m < 10 = iterate fibstep (0, 1) !! fromIntegral m
-fibN2 m = fibN2_next (n, r) (fibN2 n)
-  where
-    (n, r) = quotRem m 3
+instance (Eq a, Fractional a) => Fractional [a] where
+    (/) (0:ps) (0:qs) = ps/qs
+    (/) (p:ps) (q:qs) = let r=p/q in r : (ps - r*.qs)/(q:qs)
 
-fibN2_next (n, r) (f, g)
-  | r == 0 = (a, b) -- 3n  ,3n+1
-  | r == 1 = (b, c) -- 3n+1,3n+2
-  | r == 2 = (c, d) -- 3n+2,3n+3   (*)
-  where
-    a =
-      5 * f ^ 3 +
-      if even n
-        then 3 * f
-        else (-3 * f) -- 3n
-    b = g ^ 3 + 3 * g * f ^ 2 - f ^ 3 -- 3n+1
-    c = g ^ 3 + 3 * g ^ 2 * f + f ^ 3 -- 3n+2
-    d =
-      5 * g ^ 3 +
-      if even n
-        then (-3 * g)
-        else 3 * g -- 3(n+1)   (*)
-
-main :: IO ()
-main = print $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)
+    fromRational q = fromRational q:repeat 0