How to make Python run as fast (or faster) than Julia

[bartc]

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.

-- 
bartc