Re: Faster Recursive Fibonacci Numbers

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Date	2011-05-17 14:59 -0700
Subject	Re: Faster Recursive Fibonacci Numbers
From	geremy condra <debatem1@gmail.com>
Newsgroups	comp.lang.python
Message-ID	<mailman.1722.1305669549.9059.python-list@python.org> (permalink)

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On Tue, May 17, 2011 at 2:04 PM, Wolfram Hinderer
<wolfram.hinderer@googlemail.com> wrote:
> On 17 Mai, 20:56, geremy condra <debat...@gmail.com> wrote:
>> On Tue, May 17, 2011 at 10:19 AM, Jussi Piitulainen
>>
>> <jpiit...@ling.helsinki.fi> wrote:
>> > geremy condra writes:
>>
>> >> or O(1):
>>
>> >> ö = (1 + sqrt(5)) / 2
>> >> def fib(n):
>> >>     numerator = (ö**n) - (1 - ö)**n
>> >>     denominator = sqrt(5)
>> >>     return round(numerator/denominator)
>>
>> >> Testing indicates that it's faster somewhere around 7 or so.
>>
>> > And increasingly inaccurate from 71 on.
>>
>> Yup. That's floating point for you. For larger values you could just
>> add a linear search at the bottom using the 5f**2 +/- 4 rule, which
>> would still be quite fast out to about 10 times that. The decimal
>> module gets you a tiny bit further, and after that it's time to just
>> use Dijkstra's, like rusi suggested. In any event, I still think this
>> formulation is the most fun ;).
>
> I think you can write it even more funny
>
> def fib(n):
>    return round(((.5 + .5 * 5 ** .5) ** n -  (.5 - .5 * 5 ** .5) **
> n) * 5 ** -.5)
>
> ;-)

Ok, that's amusing. It does hide the interaction with the golden ratio
though, which is what I find so fascinating about the earlier one.

Geremy Condra

Thread

Faster Recursive Fibonacci Numbers RJB <rbotting@csusb.edu> - 2011-05-17 08:50 -0700
  Re: Faster Recursive Fibonacci Numbers Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-17 10:23 -0600
  Re: Faster Recursive Fibonacci Numbers rusi <rustompmody@gmail.com> - 2011-05-17 09:25 -0700
  Re: Faster Recursive Fibonacci Numbers rusi <rustompmody@gmail.com> - 2011-05-17 09:36 -0700
    Re: Faster Recursive Fibonacci Numbers geremy condra <debatem1@gmail.com> - 2011-05-17 10:02 -0700
      Re: Faster Recursive Fibonacci Numbers Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2011-05-17 20:19 +0300
        Re: Faster Recursive Fibonacci Numbers geremy condra <debatem1@gmail.com> - 2011-05-17 11:56 -0700
          Re: Faster Recursive Fibonacci Numbers Wolfram Hinderer <wolfram.hinderer@googlemail.com> - 2011-05-17 14:04 -0700
            Re: Faster Recursive Fibonacci Numbers geremy condra <debatem1@gmail.com> - 2011-05-17 14:59 -0700
            Re: Faster Recursive Fibonacci Numbers rusi <rustompmody@gmail.com> - 2011-05-17 21:43 -0700
      Re: Faster Recursive Fibonacci Numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-19 22:47 +0000
        Re: Faster Recursive Fibonacci Numbers Chris Angelico <rosuav@gmail.com> - 2011-05-20 09:37 +1000
          Re: Faster Recursive Fibonacci Numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-20 05:58 +0000
            Re: Faster Recursive Fibonacci Numbers Chris Angelico <rosuav@gmail.com> - 2011-05-20 16:06 +1000
              Re: Faster Recursive Fibonacci Numbers harrismh777 <harrismh777@charter.net> - 2011-05-20 01:26 -0500
                Re: Faster Recursive Fibonacci Numbers Chris Angelico <rosuav@gmail.com> - 2011-05-20 16:54 +1000
                Re: Faster Recursive Fibonacci Numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-20 17:07 +0000
                Re: Faster Recursive Fibonacci Numbers geremy condra <debatem1@gmail.com> - 2011-05-20 11:43 -0700
                Re: Faster Recursive Fibonacci Numbers Chris Angelico <rosuav@gmail.com> - 2011-05-21 10:44 +1000
              Re: Faster Recursive Fibonacci Numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2011-05-21 20:49 +1200
            Re: Faster Recursive Fibonacci Numbers Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-20 01:26 -0600
            Re: Faster Recursive Fibonacci Numbers Ian Kelly <ian.g.kelly@gmail.com> - 2011-05-20 01:32 -0600
              Re: Faster Recursive Fibonacci Numbers SigmundV <sigmundv@gmail.com> - 2011-05-20 03:53 -0700
        Re: Faster Recursive Fibonacci Numbers geremy condra <debatem1@gmail.com> - 2011-05-19 17:03 -0700
  Re: Faster Recursive Fibonacci Numbers Raymond Hettinger <python@rcn.com> - 2011-05-24 16:44 -0700

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