Data update

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

@@ -1,35 +1,17 @@
-import Control.Arrow ((&&&))
+import Data.Ratio (numerator)
 
-fibstep :: (Integer, Integer) -> (Integer, Integer)
-fibstep (a, b) = (b, a + b)
+infixl 7 *.
+(*.) :: Num a => a -> [a] -> [a]
+x *. (p:ps) = x*p : x*.ps
 
-fibnums :: [Integer]
-fibnums = map fst $ iterate fibstep (0, 1)
+instance Num a => Num [a] where
+    negate = map negate
+    (+) = zipWith (+)
+    (*) (p:ps) (q:qs) = p*q : ((p*.qs) + ps*(q:qs))
+    fromInteger n = fromInteger n:repeat 0
 
-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
+instance (Eq a, Fractional a) => Fractional [a] where
+    (/) (0:ps) (0:qs) = ps/qs
+    (/) (p:ps) (q:qs) = let r=p/q in r : (ps - r*.qs)/(q:qs)
 
-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)
+    fromRational q = fromRational q:repeat 0

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

@@ -1,2 +1,3 @@
- *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
-(208988,"19532821287077577316")
+fibs :: [Integer]
+fibs = map numerator
+    (1/(1 : (-1) : (-1) : repeat 0))

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-19.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
+ghci> take 15 fibs
+[1,1,2,3,5,8,13,21,34,55,89,144,233,377,610]

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-20.hs

@@ -1 +1,8 @@
-g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth
+import Data.Functor.Identity (Identity (..))
+
+fibs :: [Integer]
+fibs = runIdentity (hsequence (repeat f))
+    where f []  = Identity 1
+          f [_] = Identity 1
+          f xs  = Identity ((xs !! (i-1)) + (xs !! i))
+              where i = length xs-1

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-21.hs

@@ -0,0 +1,6 @@
+hsequence :: Monad m => [[x] -> m x] -> m [x]
+hsequence []     = pure []
+hsequence (r:rs) = do
+    x <- r []
+    xs <- hsequence [ \ys -> g (x:ys) | g <- rs ]
+    pure (x:xs)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-22.hs

@@ -0,0 +1,2 @@
+ghci> take 17 fibs
+[1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597]

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-23.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-24.hs

@@ -0,0 +1,2 @@
+ *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
+(208988,"19532821287077577316")

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-25.hs

@@ -0,0 +1 @@
+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-26.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