[Haskell-cafe] Using parallels for fibonacci

[Mario Lang]

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://www.youtube.com/watch?v=32f6JrQPV8c (18:30-21:40)
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 Haskell Wiki has a section about this approach:
https://wiki.haskell.org/The_Fibonacci_sequence#Using_2x2_matrices

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.

```Haskell
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,
  ⡍⠁⠗⠊⠕