Data update

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-15.hs

@@ -1,44 +1,7 @@
-import Data.List (transpose)
+import Data.List (unfoldr)
 
-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)
+fibs :: [Integer]
+fibs = unfoldr (\(x, y) -> Just (x, (y, x + y))) (0, 1)
 
--- Code adapted from Matrix exponentiation operator task ---------------------
-(<+>)
-  :: Num c
-  => [c] -> [c] -> [c]
-(<+>) = zipWith (+)
-
-(<*>)
-  :: 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
-  negate xm = Mat $ map (map negate) $ 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)
+fib n :: Integer -> Integer
+fib n = fibs !! n

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-16.hs

@@ -1,35 +1,44 @@
-import Control.Arrow ((&&&))
+import Data.List (transpose)
 
-fibstep :: (Integer, Integer) -> (Integer, Integer)
-fibstep (a, b) = (b, a + b)
+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)
 
-fibnums :: [Integer]
-fibnums = map fst $ iterate fibstep (0, 1)
+-- Code adapted from Matrix exponentiation operator task ---------------------
+(<+>)
+  :: Num c
+  => [c] -> [c] -> [c]
+(<+>) = zipWith (+)
 
-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
+(<*>)
+  :: Num a
+  => [a] -> [a] -> a
+(<*>) = (sum .) . zipWith (*)
 
-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)   (*)
+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 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 $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)
+main = (print . take 10 . show . fib) (10 ^ 5)

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

@@ -1,2 +1,35 @@
- *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
-(208988,"19532821287077577316")
+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-18.hs

@@ -1 +1,2 @@
-f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b))     -- iterate f (1,(0,1)) ; b is nth
+ *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
+(208988,"19532821287077577316")

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-19.hs

@@ -1 +1 @@
-g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth
+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-20.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