A-M baby

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-1.hs

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+fib = 0 : 1 : zipWith (+) fib (tail fib)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-2.hs

@@ -0,0 +1 @@
+fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-3.hs

@@ -0,0 +1 @@
+fib = 0 : scanl (+) 1 fib

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-4.hs

@@ -0,0 +1,15 @@
+import Data.List
+
+xs <+> ys = zipWith (+) xs ys
+xs <*> ys = sum $ zipWith (*) xs ys
+
+newtype Mat a = Mat {unMat :: [[a]]} deriving Eq
+
+instance Show a => Show (Mat a) where
+  show xm = "Mat " ++ show (unMat xm)
+
+instance Num a => Num (Mat a) where
+  negate xm = Mat $ map (map negate) $ unMat xm
+  xm + ym   = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
+  xm * ym   = Mat [[xs <*> ys | ys <- transpose $ unMat ym] | xs <- unMat xm]
+  fromInteger n = Mat [[fromInteger n]]

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-5.hs

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+fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately
+          -- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1
+fib n = last $ head $ unMat $ (Mat [[1,1],[1,0]]) ^ n

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-6.hs

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+fibsteps (a,b) n
+    | n <= 0 = (a,b)
+    | True   = fibsteps (b, a+b) (n-1)
+
+fibnums :: [Integer]
+fibnums = map fst $ iterate (`fibsteps` 1) (0,1)
+
+fibN2 :: Integer -> (Integer, Integer)
+fibN2 m | m < 10 = fibsteps (0,1) m
+fibN2 m          = fibN2_next (n,r) (fibN2 n)
+                     where (n,r) = quotRem m 3
+
+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
+      d = ( 5*g^3 + if even n then (- 3*g) else 3*g ) -- 3(n+1)   (*)
+      b = (   g^3 + 3 * g * f^2 - f^3               ) -- 3n+1
+      c = (   g^3 + 3 * g^2 * f + f^3               ) -- 3n+2

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-7.hs

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+ *Main> take 10 $ show $ fst $ fibN2 (10^6)
+ "1953282128"