Initial data commit

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

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+import Data.CReal
+
+phi = (1 + sqrt 5) / 2
+
+fib :: (Integral b) => b -> CReal 0
+fib n = (phi^^n - (-phi)^^(-n))/sqrt 5

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

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

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

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

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

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

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

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+fib = 0 : scanl (+) 1 fib

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

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

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

@@ -0,0 +1,44 @@
+import Data.List (transpose)
+
+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)
+
+-- 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)

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

@@ -0,0 +1,35 @@
+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-17.hs

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

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-18.hs

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+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-19.hs

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+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

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+λ> fib 10 :: CReal 0
+55
+(0.01 secs, 137,576 bytes)
+λ> fib 100 :: CReal 0
+354224848179261915075
+(0.01 secs, 253,152 bytes)
+λ> fib 10000 :: CReal 0
+33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875
+(0.02 secs, 4,847,128 bytes)
+λ> fib (-10) :: CReal 0
+-55
+(0.01 secs, 138,408 bytes)

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

@@ -0,0 +1,6 @@
+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-4.hs

@@ -0,0 +1,8 @@
+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-5.hs

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+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo f where
+   f 0 = 0
+   f 1 = 1
+   f n = fib (n-1) + fib (n-2)

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

@@ -0,0 +1,6 @@
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \x -> case x of
+   0 -> 0
+   1 -> 1
+   n -> fib (n-1) + fib (n-2)

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

@@ -0,0 +1,7 @@
+{-# Language LambdaCase #-}
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \case
+   0 -> 0
+   1 -> 1
+   n -> fib (n-1) + fib (n-2)

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

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+{-# Language LambdaCase #-}
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \case
+   0 -> 0
+   1 -> 1
+   n | n>0 -> fib (n-1) + fib (n-2)
+     | otherwise -> fib (n+2) - fib (n+1)

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

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+fib n = go n 0 1
+  where
+    go n a b
+      | n == 0 = a
+      | otherwise = go (n - 1) b (a + b)