September 2017 Update

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

@@ -1 +1,6 @@
-[floor(0.01+(1/p**n+p**n)/sqrt 5)|let p=(1+sqrt 5)/2, n<-[0..42]]
+main :: IO ()
+main =
+  print
+    [ 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

@@ -1,15 +1,44 @@
-import Data.List
+import Data.List (transpose)
 
-xs <+> ys = zipWith (+) xs ys
-xs <*> ys = sum $ zipWith (*) xs ys
+fib
+  :: (Integral b, Num a)
+  => b -> a
+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)
 
-newtype Mat a = Mat {unMat :: [[a]]} deriving Eq
+-- Code adapted from Matrix exponentiation operator task ---------------------
+(<+>)
+  :: Num c
+  => [c] -> [c] -> [c]
+(<+>) = zipWith (+)
 
-instance Show a => Show (Mat a) where
+(<*>)
+  :: Num a
+  => [a] -> [a] -> a
+(<*>) = (sum .) . zipWith (*)
+
+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
+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]
+  xm + ym = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
+  xm * ym =
+    Mat
+      [ [ xs Main.<*> ys -- to distinguish from standard applicative operator
+        | ys <- transpose $ unMat ym ]
+      | xs <- unMat xm ]
   fromInteger n = Mat [[fromInteger n]]
+  abs = undefined
+  signum = undefined
+
+-- TEST ----------------------------------------------------------------------
+main :: IO ()
+main = (print . take 10 . show . fib) (10 ^ 5)

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

@@ -1,3 +1,35 @@
-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
+import Control.Arrow ((&&&))
+
+fibstep :: (Integer, Integer) -> (Integer, Integer)
+fibstep (a, b) = (b, a + b)
+
+fibnums :: [Integer]
+fibnums = map fst $ iterate fibstep (0, 1)
+
+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
+
+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)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-12.hs

@@ -1,20 +1,2 @@
-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)   (*)
+ *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
+(208988,"19532821287077577316")

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

@@ -1,2 +1 @@
- *Main> take 10 $ show $ fst $ fibN2 (10^6)
- "1953282128"
+f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b))     -- iterate f (1,(0,1)) ; b is nth

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-14.hs

@@ -0,0 +1 @@
+g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth

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

@@ -1 +1,6 @@
-fib x = if x < 1 then 0 else if x < 2 then 1 else fib(x - 1) + fib(x - 2)
+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

@@ -1,5 +1,8 @@
-fib x = if x < 1 then 0
-                 else if x==1 then 1
-                 else fibs!!(x - 1) + fibs!!(x - 2)
+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..]
+    fibs = map fib [0 ..]

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

@@ -1,2 +1,5 @@
-fib :: Integer -> Integer
-fib n = fst $ foldl (\(a, b) _ -> (b, a + b)) (0, 1) [1 .. 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-5.hs

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

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

@@ -1 +1 @@
-fib = 0 : 1 : zipWith (+) fib (tail fib)
+fib = 0 : 1 : (zipWith (+) <*> tail) fib

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

@@ -1 +1 @@
- fib = 0 : 1 : (zipWith (+) <*> tail) fib
+fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t

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

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

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

@@ -1 +1,9 @@
-fib = 0 : scanl (+) 1 fib
+import Data.List (foldl') --'
+
+fib :: Integer -> Integer
+fib n =
+  fst $
+  foldl' --'
+    (\(a, b) _ -> (b, a + b))
+    (0, 1)
+    [1 .. n]