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2016 Update

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Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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21
Task/Fibonacci-sequence/Haskell/fibonacci-sequence-6.hs
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@ -1,20 +1 @@
fibsteps (a,b) n
| n <= 0 = (a,b)
| otherwise = fibsteps (b, a+b) (n-1)
fibnums :: [Integer]
fibnums = map fst $ iterate (`fibsteps` 1) (0,1)
fibN2 :: Integer -> (Integer, Integer)
fibN2 m | m < 10 = fibsteps (0,1) 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
d = ( 5*g^3 + if even n then (- 3*g) else 3*g ) -- 3(n+1) (*)
b = ( g^3 + 3 * g * f^2 - f^3 ) -- 3n+1
c = ( g^3 + 3 * g^2 * f + f^3 ) -- 3n+2
fib = 0 : 1 : zipWith (+) fib (tail fib)