Re: Faster Recursive Fibonacci Numbers

Path	csiph.com!x330-a1.tempe.blueboxinc.net!usenet.pasdenom.info!aioe.org!feeder.news-service.com!newsfeed.xs4all.nl!newsfeed5.news.xs4all.nl!xs4all!post.news.xs4all.nl!not-for-mail
Return-Path	<debatem1@gmail.com>
X-Original-To	python-list@python.org
Delivered-To	python-list@mail.python.org
X-Spam-Status	OK 0.002
X-Spam-Evidence	'H': 1.00; 'S': 0.00; 'numeric': 0.07; 'semantic': 0.07; 'python': 0.08; '>>>>': 0.09; 'float.': 0.09; "it'd": 0.09; 'precision': 0.09; 'am,': 0.14; 'wrote:': 0.14; 'angelico': 0.16; 'computation': 0.16; 'floats': 0.16; 'subject:Fibonacci': 0.16; 'truncated': 0.16; 'long,': 0.16; 'cc:addr:python-list': 0.17; 'continuing': 0.17; 'awesome': 0.19; 'header:In-Reply-To:1': 0.21; 'cc:20': 0.22; 'cc:no real name:20': 0.23; 'integer': 0.23; 'fri,': 0.23; 'message- id:@mail.gmail.com': 0.28; 'problem': 0.28; '(as': 0.29; 'import': 0.29; 'cc:addr:python.org': 0.30; 'steven': 0.32; 'someone': 0.33; "isn't": 0.33; 'chris': 0.34; 'shows': 0.34; 'there': 0.35; "d'aprano": 0.35; 'fraction': 0.35; 'numbers.': 0.35; 'else': 0.35; 'using': 0.35; 'uses': 0.36; 'difference': 0.37; 'too.': 0.37; 'received:google.com': 0.37; 'something': 0.37; '20,': 0.37; 'received:74.125': 0.38; 'could': 0.38; 'but': 0.38; 'subject:: ': 0.38; 'more': 0.60; 'cost': 0.65; 'square': 0.67; 'promote': 0.78
DKIM-Signature	v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:in-reply-to:references:date :message-id:subject:from:to:cc:content-type; bh=nLh29BtuIQJMLhaZu0eprXrseCw8d/EdbdJ0V/+F5Hc=; b=B1KAYgmDfMVlS1aXfWdJOf8l5msj1+Ty+lReBuqKafWdk2CYtLjBLznhpDfhmgg4St mib888uaX1F4Y9QSahZmunpB0UCbwi7/7mOqixYgq0QrjjuCU1R5P1/8L7LEKv9uz9+f y99F2Yfdg09B0ba1GWIJJCIUZL1HAXWCOojW0=
DomainKey-Signature	a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :cc:content-type; b=JpglcobJUq7eWApPEkiPuAHuzbmYhY9f9koVrRE8lDIsWLp73kkPMTC2XWyZ3qbiHV vTrRB20dZPVDWUZJ6FoyozFmgxZ852S4yPF1rX+4MwN0bvb4M2ZSlRxzuMgZqzdredcW y+2s6jvgCIy4rmI0L9v2Y/9a32sgUrx1dvRpM=
MIME-Version	1.0
In-Reply-To	<4dd69fcd$0$29996$c3e8da3$5496439d@news.astraweb.com>
References	<108ce447-10fa-4cf7-84ef-440ee18dbfd4@22g2000prx.googlegroups.com> <9d9c163b-14fd-4131-81bb-105c3b97c432@h36g2000pro.googlegroups.com> <mailman.1680.1305651743.9059.python-list@python.org> <4dd59e1e$0$29996$c3e8da3$5496439d@news.astraweb.com> <mailman.1806.1305848281.9059.python-list@python.org> <4dd602ec$0$29996$c3e8da3$5496439d@news.astraweb.com> <mailman.1823.1305871603.9059.python-list@python.org> <IQnBp.7164$4d6.1646@newsfe01.iad> <mailman.1826.1305874451.9059.python-list@python.org> <4dd69fcd$0$29996$c3e8da3$5496439d@news.astraweb.com>
Date	Fri, 20 May 2011 11:43:43 -0700
Subject	Re: Faster Recursive Fibonacci Numbers
From	geremy condra <debatem1@gmail.com>
To	"Steven D'Aprano" <steve+comp.lang.python@pearwood.info>
Content-Type	text/plain; charset=ISO-8859-1
Cc	python-list@python.org
X-BeenThere	python-list@python.org
X-Mailman-Version	2.1.12
Precedence	list
List-Id	General discussion list for the Python programming language <python-list.python.org>
List-Unsubscribe	<http://mail.python.org/mailman/options/python-list>, <mailto:python-list-request@python.org?subject=unsubscribe>
List-Archive	<http://mail.python.org/pipermail/python-list>
List-Post	<mailto:python-list@python.org>
List-Help	<mailto:python-list-request@python.org?subject=help>
List-Subscribe	<http://mail.python.org/mailman/listinfo/python-list>, <mailto:python-list-request@python.org?subject=subscribe>
Newsgroups	comp.lang.python
Message-ID	<mailman.1853.1305917026.9059.python-list@python.org> (permalink)
Lines	34
NNTP-Posting-Host	82.94.164.166
X-Trace	1305917026 news.xs4all.nl 49181 [::ffff:82.94.164.166]:36687
X-Complaints-To	abuse@xs4all.nl
Xref	x330-a1.tempe.blueboxinc.net comp.lang.python:5871

Show key headers only | View raw

On Fri, May 20, 2011 at 10:07 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> On Fri, 20 May 2011 16:54:06 +1000, Chris Angelico wrote:
>
>> If someone has time to kill (as if!), it'd be awesome to get a new
>> numeric type that uses bc's code; any other numeric type (int, long,
>> float) could autopromote to it, removing the dilemma of which to promote
>> out of long and float. Hmm... Python 4.0, 'bc' is the new default
>> integer and everything else is a performance optimization? Heh.
>
> The problem is, it isn't *just* a performance optimization, there is a
> semantic difference too. Consider:
>
>>>> x = 1e-300
>>>> x*x == 0
> True
>
> But using something with more precision:
>
>>>> from fractions import Fraction
>>>> x = Fraction(10)**-300
>>>> x*x == 0
> False
>
>
> So you get different behaviour between floats and arbitrary precision
> numbers.

And this shows up in the above implementation; reimplementing it using
Fractions and a truncated continuing fraction approximation of phi and
the square root of 5 gets us up to about 500, at the cost of a very
long computation time.

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

csiph-web