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As you may have gathered from some of my previous posts, I've been spending some quality time at Project Euler.  Normally I do my solutions in C#, but since I have also started learning F#, it only made sense to switch over to F# to get my math coding fix.
This week's post is just a small snippet - spefically, a simple function to return a fibonacci number given it's place in the sequence.  One popular example uses recursion:
let rec fib n = if n < 2 then 1 else fib (n-2) + fib(n-1)
While this is certainly elegant, the recursion is absolutely brutal on performance.  So I decided to spend a little time, and find an option that achieved the same functionality, but used a recursive function.  And since this is F#, I wanted to make sure I did it without the use of any mutable variables.
Here's the solution I came up with:

let rec fib (n1 : bigint)  (n2 : bigint) c =

    if c = 1 then



        fib n2 (n1+n2) (c-1);;


let GetFib num =

    (fib 1I 1I num);;

printfn "%O" (GetFib 1000);;


Essentially, this function works through the sequence moving forward, passing the two most recent numbers and a counter to the recursive calls until it has achieved the desired number of iterations.  At that point, it returns the latest fibonacci number.

 (Edited to change from Int to BigInt - Thanks for the feedback!)




Posted on Saturday, April 3, 2010 7:27 PM | Back to top

Comments on this post: Fibonacci numbers in F#

# re: Fibonacci numbers in F#
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Your solution is causing an integer overflow at some point and delivering wrong results. See here for a hint at what point int stops being adequate:

Here's mine:

let fibGen (a : bigint, b : bigint) =
let next = a + b
Some(next, (b, next))

let res = Seq.unfold fibGen (0I, 1I)
|> Seq.nth 1000

Left by fbcocq on Apr 04, 2010 10:13 AM

# re: Fibonacci numbers in F#
Requesting Gravatar...
Thanks for the feedback! I went ahead and adjusted the original code to use the BigInt v. default of Int - and that's a very nice alternate solution.
Left by Bob Palmer on Apr 04, 2010 10:27 AM

# re: Fibonacci numbers in F#
Requesting Gravatar...
this is my version of FIBONACCI (happy coding)

let rec fibonacci num1 num2 x =
let x = (x - 1)
printf "%A " num1
match x with
| _ when x > 0 -> fibonacci (num2) (num1+num2) x
Left by Winston Gubantes on Jul 06, 2010 5:58 AM

# re: Fibonacci numbers in F#
Requesting Gravatar...
First of all thank you for the code - I had similar idea but could not wrap my head around accumulator and tail, it clicked when I read this article.

My slight modification (in my case n=1 fib1 = 0..) and var name change for my understanding.

let rec fib prev curr counter = if counter = 2 then
//printfn "%A" counter
fib curr (curr + prev) (counter - 1)

let getFib n = fib 0 1 n
Left by sremani on Sep 20, 2014 7:54 AM

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