Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!feeder.erje.net!us.feeder.erje.net!news2.arglkargh.de!newsfeed.fsmpi.rwth-aachen.de!newsfeed.straub-nv.de!feed.xsnews.nl!fbe001.ams.xsnews.nl!ecngs!feeder.ecngs.de!border1.nntp.ams1.giganews.com!nntp.giganews.com!newsfeed.xs4all.nl!newsfeed1.news.xs4all.nl!xs4all!newsgate.cistron.nl!newsgate.news.xs4all.nl!post.news.xs4all.nl!not-for-mail
Return-Path: <python-python-list@m.gmane.org>
X-Original-To: python-list@python.org
Delivered-To: python-list@mail.python.org
X-Spam-Status: OK 0.007
X-Spam-Evidence: '*H*': 0.99; '*S*': 0.00; 'received:80.91': 0.09; 'received:80.91.229': 0.09; 'received:gmane.org': 0.09; 'received:list': 0.09; 'tends': 0.09; 'algorithm': 0.13; 'wed,': 0.15; 'digits.': 0.16; 'doubles.': 0.16; 'fpu': 0.16; 'message- id:@4ax.com': 0.16; 'precision,': 0.16; 'received:80.91.229.3': 0.16; 'received:plane.gmane.org': 0.16; 'subject:distance': 0.16; 'intermediate': 0.18; 'url:home': 0.18; '(or': 0.21; '64-bit': 0.22; 'precise': 0.22; '2015': 0.23; 'header:X-Complaints-To:1': 0.26; 'decimal': 0.29; 'values': 0.30; 'point': 0.33; 'to:addr :python-list': 0.35; 'next': 0.35; 'but': 0.36; 'brian': 0.36; 'subject:: ': 0.37; 'charset:us-ascii': 0.37; 'received:org': 0.38; 'to:addr:python.org': 0.39; 'subject:more': 0.61; 'more': 0.62; 'overall': 0.70; '14-15': 0.84; 'loses': 0.84; 'dennis': 0.91; 'received:108': 0.93
X-Injected-Via-Gmane: http://gmane.org/
To: python-list@python.org
From: Dennis Lee Bieber <wlfraed@ix.netcom.com>
Subject: Re: a more precise distance algorithm
Date: Wed, 27 May 2015 23:04:51 -0400
Organization: IISS Elusive Unicorn
References: <b2e66a94-7a89-4be9-bbf7-9434396cc178@googlegroups.com> <5563e453$0$12990$c3e8da3$5496439d@news.astraweb.com> <CADzuzGNggKfgBiq3RMtWk3GBF3ynbkjm2brdXj4cuUQwQ5yQkg@mail.gmail.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-Gmane-NNTP-Posting-Host: adsl-108-79-221-217.dsl.klmzmi.sbcglobal.net
X-Newsreader: Forte Agent 6.00/32.1186
X-No-Archive: YES
X-BeenThere: python-list@python.org
X-Mailman-Version: 2.1.20+
Precedence: list
List-Id: General discussion list for the Python programming language <python-list.python.org>
List-Unsubscribe: <https://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: <https://mail.python.org/mailman/listinfo/python-list>, <mailto:python-list-request@python.org?subject=subscribe>
Newsgroups: comp.lang.python
Message-ID: <mailman.114.1432782300.5151.python-list@python.org>
Lines: 20
NNTP-Posting-Host: 2001:888:2000:d::a6
X-Trace: 1432782300 news.xs4all.nl 2885 [2001:888:2000:d::a6]:41412
X-Complaints-To: abuse@xs4all.nl
Xref: csiph.com comp.lang.python:91345

On Wed, 27 May 2015 14:00:24 -0400, Brian Blais <bblais@gmail.com>
declaimed the following:

>
>where all of the methods deviate at the 13/14 decimal place.
>
	Historically, double precision floating point is considered to have
14-15 significant /digits/ TOTAL. 

	Internally, IEEE floating point hardware tends to work with 80bit
floats -- so as long as the intermediate computations stay in the FPU for
the majority of the calculation one may get a more precise result when
downconverting to 64-bit doubles. But if the algorithm (or runtime) tends
to pull values out of the FPU and reloads them for the next stage, one
loses all the excess precision, and the resultant truncations may multiple
to give an overall result of less than 14 significant digits.
-- 
	Wulfraed                 Dennis Lee Bieber         AF6VN
    wlfraed@ix.netcom.com    HTTP://wlfraed.home.netcom.com/