The Fibonacci sequence
From HaskellWiki
(Difference between revisions)
(Another fast fib) 
DonStewart (Talk  contribs) (→See also) 

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== See also == 
== See also == 

−  Discussion at haskell cafe: 
+  * [http://comments.gmane.org/gmane.comp.lang.haskell.cafe/19623 Discussion at haskell cafe] 
−  +  * [http://www.cubbi.org/serious/fibonacci/haskell.html Some other nice solutions] 

−  http://comments.gmane.org/gmane.comp.lang.haskell.cafe/19623 

[[Category:Code]] 
[[Category:Code]] 
Revision as of 12:35, 7 May 2007
Implementing the fibonacci sequence is considered the "Hello, world!" of Haskell programming. This page collects Haskell implementations of the sequence.
Contents 
1 Naive solution
fib 0 = 0 fib 1 = 1 fib n = fib (n1) + fib (n2)
2 Canonical zipWith implementation
fib = 1 : 1 : zipWith (+) fib (tail fib)
3 With scanl
fib = fix ((1:) . scanl (+) 1)
4 With unfoldr
unfoldr (\(f1,f2) > Just (f1,(f2,f1+f2))) (0,1)
5 A fairly fast version, using some identities
fib 0 = 0 fib 1 = 1 fib n  even n = f1 * (f1 + 2 * f2)  n `mod` 4 == 1 = (2 * f1 + f2) * (2 * f1  f2) + 2  otherwise = (2 * f1 + f2) * (2 * f1  f2)  2 where k = n `div` 2 f1 = fib k f2 = fib (k1)
6 Another fast fib
fib = fst . fib2   Return (fib n, fib (n + 1)) fib2 0 = (1, 1) fib2 1 = (1, 2) fib2 n  even n = (a*a + b*b, c*c  a*a)  otherwise = (c*c  a*a, b*b + c*c) where (a,b) = fib2 (n `div` 2  1) c = a + b
7 Fastest Fib in the West
This was contributed by wli
import System.Environment import Data.List fib n = snd . foldl fib' (1, 0) . map (toEnum . fromIntegral) $ unfoldl divs n where unfoldl f x = case f x of Nothing > [] Just (u, v) > unfoldl f v ++ [u] divs 0 = Nothing divs k = Just (uncurry (flip (,)) (k `divMod` 2)) fib' (f, g) p  p = (f*(f+2*g), f^2 + g^2)  otherwise = (f^2+g^2, g*(2*fg)) main = getArgs >>= mapM_ (print . fib . read)