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

36 lines
848 B
Haskell

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)