Create faster Fibonacci function for n > 100 in MATLAB / octave

Question

I have a function that tells me the nth number in a Fibonacci sequence. The problem is it becomes very slow when trying to find larger numbers in the Fibonacci sequence doe

Answer 1

If you have access to the Symbolic Math Toolbox in MATLAB, you could always just call the Fibonacci function from MuPAD:

>> fib = @(n) evalin(symengine, ['numlib::fibonacci(' num2str(n) ')'])
>> fib(274)
ans =
818706854228831001753880637535093596811413714795418360007

It is pretty fast:

>> timeit(@() fib(274))
ans =
    0.0011

---

Plus you can you go for as large numbers as you want (limited only by how much RAM you have!), it is still blazing fast:

% see if you can beat that!
>> tic
>> x = fib(100000);
>> toc               % Elapsed time is 0.004621 seconds.

% result has more than 20 thousand digits!
>> length(char(x))   % 20899

Here is the full value of fib(100000): http://pastebin.com/f6KPGKBg