On 22/02/2018 19:55, Jack Fearnley wrote:

I realize that this thread is about benchmarking and not really about
generating fibonacci numbers, but I hope nobody is using this code to
generate them on a 'production' basis,

Fibonacci numbers, any linearly recursive sequence for that matter, can
be generated in log time.

GP/Pari on my Intel I7 computes fibonacci(100000) in less than 1 ms,
fibonacci(1000000) in 5ms,

The simple method involves 1 million additions of numbers with an average length of 100,000 digits. 5ms would be pretty good going.

Presumably it uses a faster algorithm. I found this in Python (from stackoverflow):

def fib(n):
    v1, v2, v3 = 1, 1, 0    # initialise a matrix [[1,1],[1,0]]
    print (bin(n)[3:])
    for rec in bin(n)[3:]:  # perform fast exponentiation of the ....
        calc = v2*v2
        v1, v2, v3 = v1*v1+calc, (v1+v3)*v2, calc+v3*v3
        if rec=='1':
             v1, v2, v3 = v1+v2, v1, v2
    return v2

fib(1000000) took 200ms seconds in Python 3. Printing the result about another 1.6 seconds. I think now it's down to the efficiency of the big integer library, as little bytecode is being executed.


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