2016 Update

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

@@ -1 +1 @@
-fib = 0 : 1 : zipWith (+) fib (tail fib)
+[floor(0.01+(1/p**n+p**n)/sqrt 5)|let p=(1+sqrt 5)/2, n<-[0..42]]

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-10.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-11.hs

@@ -0,0 +1,3 @@
+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-12.hs

@@ -0,0 +1,20 @@
+fibsteps (a,b) n
+    | n <= 0    = (a,b)
+    | otherwise = 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
+      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)   (*)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-13.hs

@@ -0,0 +1,2 @@
+ *Main> take 10 $ show $ fst $ fibN2 (10^6)
+ "1953282128"

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

@@ -1 +1 @@
-fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t
+fib x = if x < 1 then 0 else if x < 2 then 1 else fib(x - 1) + fib(x - 2)

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

@@ -1 +1,5 @@
-fib = 0 : scanl (+) 1 fib
+fib x = if x < 1 then 0
+                 else if x==1 then 1
+                 else fibs!!(x - 1) + fibs!!(x - 2)
+  where
+  fibs = map fib [0..]

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

@@ -1,15 +1,2 @@
-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]]
+fib :: Integer -> Integer
+fib n = fst $ foldl (\(a, b) _ -> (b, a + b)) (0, 1) [1 .. n]

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

@@ -1,3 +1,4 @@
-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
+fib n = go n 0 1
+    where
+    go n a b | n==0 = a
+             | otherwise = go (n-1) b (a+b)

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

@@ -1,20 +1 @@
-fibsteps (a,b) n
-    | n <= 0    = (a,b)
-    | otherwise = 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
+fib = 0 : 1 : zipWith (+) fib (tail fib)

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

@@ -1,2 +1 @@
- *Main> take 10 $ show $ fst $ fibN2 (10^6)
- "1953282128"
+ fib = 0 : 1 : (zipWith (+) <*> tail) fib

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-8.hs

@@ -1 +1 @@
-let fib x =  if x < 1 then 0 else (if x < 3 then 1 else (fib(x - 1) + fib(x - 2)))
+fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-9.hs

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