# [Haskell-cafe] Using parallels for fibonacci

Michael Litchard michael at schmong.org
Wed May 11 15:49:34 UTC 2016

```Thank you Mario, that was interesting in and of itself.

On Wed, May 11, 2016 at 8:34 AM, Mario Lang <mlang at delysid.org> wrote:

> Michael Litchard <michael at schmong.org> writes:
>
> > I am trying to efficiently use multicores for my fizzbuzz
> > <https://github.com/mlitchard/swiftfizz> project. My fizzbuzz uses a
> > Fibonacci generator as input, and this is where it can get
> computationally
> > heavy. I believe I have picked the best algorithm for my project (please
> > correct this if wrong),
>
> I'd like to point you to this rather interesting task and code example I
> happened to stumble across recently:
>
> https://github.com/sean-parent/scratch/blob/master/scratch/main.cpp
>
> Sean is basically saying that doing fibonacci via recursion is wrong.
> Fibonacci is actually a linear recurrance, and can be calculated with a
> power algorithm.
>
>
> The code below gives fib of 100000000 in a few seconds on my PC.
> No need to go paralell.
>
> And if you need the complete series, [fib n | n <- [1..1000000]] still
> just takes a second here.
>
> module PowerFib where
> import Data.List (transpose)
>
> newtype Matrix a = Matrix [[a]] deriving (Eq, Show)
> instance Num a => Num (Matrix a) where
>    Matrix as + Matrix bs = Matrix (zipWith (zipWith (+)) as bs)
>    Matrix as - Matrix bs = Matrix (zipWith (zipWith (-)) as bs)
>    Matrix as * Matrix bs = Matrix [[sum \$ zipWith (*) a b | b <- transpose
> bs] | a <- as]
>    negate (Matrix as) = Matrix (map (map negate) as)
>    fromInteger x = Matrix (iterate (0:) (fromInteger x : repeat 0))
>    abs m = m
>    signum _ = 1
>
> apply (Matrix as) b = [sum (zipWith (*) a b) | a <- as]
>
> fib n = head (apply (Matrix [[0,1], [1,1]] ^ n) [0,1])
> ```
>
> --
> CYa,
>   ⡍⠁⠗⠊⠕
> _______________________________________________