Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.lang.python > #111705

Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)]

Path csiph.com!fu-berlin.de!uni-berlin.de!not-for-mail
From Chris Angelico <rosuav@gmail.com>
Newsgroups comp.lang.python
Subject Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)]
Date Thu, 21 Jul 2016 18:46:44 +1000
Lines 56
Message-ID <mailman.21.1469090808.22221.python-list@python.org> (permalink)
References <nlmpl5$9l4$1@dont-email.me> <mailman.28.1468652041.2307.python-list@python.org> <578a027c$0$1616$c3e8da3$5496439d@news.astraweb.com> <69d8d886-c18a-4c05-8bca-9a05afacd9a9@googlegroups.com> <578ca188$0$1505$c3e8da3$5496439d@news.astraweb.com> <877fcjcllf.fsf@elektro.pacujo.net> <CAPTjJmqYuhfR68g4EWWfj=GQSQMBmo3r3DRCej39xLtjPfR2ow@mail.gmail.com> <mailman.71.1468836914.2307.python-list@python.org> <578da1b5$0$1591$c3e8da3$5496439d@news.astraweb.com> <d0d6f677-35d0-4c79-a281-44317bbc11dd@googlegroups.com> <578f0f5c$0$11115$c3e8da3@news.astraweb.com> <578F23A9.7070105@rece.vub.ac.be> <mailman.2.1468998615.22221.python-list@python.org> <578f72d4$0$1610$c3e8da3$5496439d@news.astraweb.com> <87r3aopg7k.fsf@elektro.pacujo.net> <CAPTjJmrKXMJ=0E+2J0qfs31fhyr1YyPv8qan8kKgK1Lcomj=xQ@mail.gmail.com> <mailman.6.1469024775.22221.python-list@python.org> <87mvlcpd8g.fsf@elektro.pacujo.net> <6a6a2749-c2e1-42ca-923d-766b69fc35ad@googlegroups.com> <87h9bjpgw0.fsf@elektro.pacujo.net> <CAPTjJmrmZwrSTPMhkUL3-rWv9BrWb92V6PJe2aNe14hXJy=4Nw@mail.gmail.com>
Mime-Version 1.0
Content-Type text/plain; charset=UTF-8
Content-Transfer-Encoding quoted-printable
X-Trace news.uni-berlin.de n17OmcU6PWv3wCRSFhyLPATMD/HJvLolWdRWnvbn/CwA==
Return-Path <rosuav@gmail.com>
X-Original-To python-list@python.org
Delivered-To python-list@mail.python.org
X-Spam-Status OK 0.074
X-Spam-Evidence '*H*': 0.85; '*S*': 0.00; 'sufficient': 0.05; '21,': 0.07; 'cc:addr:python-list': 0.09; '0.1': 0.09; 'rounding': 0.09; 'sake': 0.09; 'successive': 0.09; 'assume': 0.11; 'result.': 0.15; 'subject: \n ': 0.15; 'thu,': 0.15; '2016': 0.16; 'argument)': 0.16; 'attributes,': 0.16; 'averaging': 0.16; 'big,': 0.16; 'from:addr:rosuav': 0.16; 'from:name:chris angelico': 0.16; 'inconvenient': 0.16; 'measurement': 0.16; 'received:io': 0.16; 'received:psf.io': 0.16; 'subject:Singleton': 0.16; 'systematic': 0.16; 'tolerance.': 0.16; 'wrote:': 0.16; 'attribute': 0.18; 'integer': 0.18; 'cc:2**0': 0.20; 'cc:addr:python.org': 0.20; 'fairly': 0.22; 'so.': 0.22; 'month,': 0.22; 'shifting': 0.22; '(or': 0.23; 'second': 0.24; 'header:In-Reply-To:1': 0.24; "i've": 0.25; "doesn't": 0.26; 'error': 0.27; 'least': 0.27; 'message- id:@mail.gmail.com': 0.27; '[2]': 0.27; 'cancel': 0.27; 'errors.': 0.27; 'tend': 0.27; 'actual': 0.28; 'resolution': 0.28; '0.5': 0.29; 'omitted': 0.29; 'subject: [': 0.29; "they'll": 0.29; 'random': 0.29; 'code': 0.30; "i'd": 0.31; 'error.': 0.31; 'seconds': 0.31; 'related': 0.32; '[1]': 0.32; 'generally': 0.32; 'ideal': 0.32; 'curious': 0.33; 'traditional': 0.33; 'values.': 0.33; '(for': 0.34; 'worked': 0.34; 'that,': 0.34; 'received:google.com': 0.35; 'done': 0.35; 'involving': 0.35; 'something': 0.35; 'but': 0.36; 'pm,': 0.36; 'subject:: ': 0.37; 'requirement': 0.37; 'thought': 0.37; "won't": 0.38; 'anything': 0.38; 'why': 0.39; 'rather': 0.39; 'where': 0.40; 'some': 0.40; 'ever': 0.60; 'your': 0.60; 'maximum': 0.61; 'entire': 0.61; 'real': 0.62; 'video': 0.62; 'back': 0.62; 'per': 0.62; 'skip:n 10': 0.62; 'more': 0.63; 'minutes': 0.64; 'within': 0.64; 'our': 0.64; 'balance': 0.64; 'world': 0.64; 'capable': 0.65; 'believe': 0.66; 'beat': 0.66; 'decided': 0.66; 'day': 0.67; 'apart': 0.70; 'jul': 0.72; 'surprise': 0.72; '5.9': 0.84; '6.5': 0.84; 'actually,': 0.84; 'are...': 0.84; 'calculations': 0.84; 'chrisa': 0.84; 'high-end': 0.84; 'negatives,': 0.84; 'resolution,': 0.84; 'signs,': 0.84; 'twelve': 0.84; 'worried': 0.84; 'to:none': 0.91; '6.1,': 0.91; 'closer.': 0.91; 'ratio': 0.91; 'swing': 0.91; 'divided': 0.93
DKIM-Signature v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:cc :content-transfer-encoding; bh=Rf/UjI0FEO4K6IRaE2DAvWZ+uxVOgTh9F9zjDgESrQY=; b=JIOJJPTSoFo0RmmdBWdJRVki9/1TfGfx80tbqYCSwo+ojdZP4hCdT3+4Z6daH8LK9y gYnSNPGvWjPWuNcuLOCJYuq15wNGVP63P+sQttKn+gunx6AYqUv4QWtjL4VCGFwD/sWj mGDVNRWPIINbLdyRGxji0AmW0prgzgHA6/xI+Pw9sVOEeAyleRSascm7SKimJXxcjtQb KPOxm/bfvMwpDF9AC6zq4BpAoNcKRQ0z3Jza0Zhqwz8sf3KuDlFmMXhoqW21SDij1VxS jpzizrpDf1TI46ncSg6HvRx4XCLaMXlK5+liwLS581gingUDTzuYAzo6oIV4PD/EH4kg 8Q/A==
X-Google-DKIM-Signature v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:cc:content-transfer-encoding; bh=Rf/UjI0FEO4K6IRaE2DAvWZ+uxVOgTh9F9zjDgESrQY=; b=IiW9xgSt8venEk4pc4dIoq2/We0ySneCqxfvR8+OQg6TFKhdeI0uRblUleConE57Ns LcQtQfhsiyVoocSuNPyqakY4JKESt3h0h8gi4QNxOjvnZG7p5gpIxf3UyQwpRVFApEJC EFh5Jllb+gcYXgmJ8UzIjR2UA8PzyuvMcWsAN/Gw367ZU+RXwZo2Ktgl4uBrZxPNtPfr kYri7+X9yXiYTVSV3w7e+AYT/Xv7WWEYYPOHyrZBiuHnhriv5xDqD0Q701gTq5lLh5KV aJ/x3OloH+GyOMbKq/I2JsHSQVuaY4Om7B3E74nBc8gsMSqyUNvvaIvJcwieFsXAq4No uskA==
X-Gm-Message-State ALyK8tI9yJL1S/cyMdxBKMbyJB6/0cT6JJSZJ0dRlRHHwPEua4nIsyXSgfuBFYWjuRQY0rrhki40/FLGiGrGuQ==
X-Received by 10.28.172.133 with SMTP id v127mr444051wme.81.1469090805666; Thu, 21 Jul 2016 01:46:45 -0700 (PDT)
In-Reply-To <87h9bjpgw0.fsf@elektro.pacujo.net>
X-BeenThere python-list@python.org
X-Mailman-Version 2.1.22
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>
X-Mailman-Original-Message-ID <CAPTjJmrmZwrSTPMhkUL3-rWv9BrWb92V6PJe2aNe14hXJy=4Nw@mail.gmail.com>
X-Mailman-Original-References <nlmpl5$9l4$1@dont-email.me> <mailman.28.1468652041.2307.python-list@python.org> <578a027c$0$1616$c3e8da3$5496439d@news.astraweb.com> <69d8d886-c18a-4c05-8bca-9a05afacd9a9@googlegroups.com> <578ca188$0$1505$c3e8da3$5496439d@news.astraweb.com> <877fcjcllf.fsf@elektro.pacujo.net> <CAPTjJmqYuhfR68g4EWWfj=GQSQMBmo3r3DRCej39xLtjPfR2ow@mail.gmail.com> <mailman.71.1468836914.2307.python-list@python.org> <578da1b5$0$1591$c3e8da3$5496439d@news.astraweb.com> <d0d6f677-35d0-4c79-a281-44317bbc11dd@googlegroups.com> <578f0f5c$0$11115$c3e8da3@news.astraweb.com> <578F23A9.7070105@rece.vub.ac.be> <mailman.2.1468998615.22221.python-list@python.org> <578f72d4$0$1610$c3e8da3$5496439d@news.astraweb.com> <87r3aopg7k.fsf@elektro.pacujo.net> <CAPTjJmrKXMJ=0E+2J0qfs31fhyr1YyPv8qan8kKgK1Lcomj=xQ@mail.gmail.com> <mailman.6.1469024775.22221.python-list@python.org> <87mvlcpd8g.fsf@elektro.pacujo.net> <6a6a2749-c2e1-42ca-923d-766b69fc35ad@googlegroups.com> <87h9bjpgw0.fsf@elektro.pacujo.net>
Xref csiph.com comp.lang.python:111705

Show key headers only | View raw

On Thu, Jul 21, 2016 at 5:52 PM, Marko Rauhamaa <marko@pacujo.net> wrote:
> A couple of related anecdotes involving integer errors.
>
> 1. I worked on a (video) product that had to execute a piece of code
>    every 7 µs or so. A key requirement was that the beat must not drift
>    far apart from the ideal over time. At first I thought the
>    traditional nanosecond resolution would be sufficient for the purpose
>    but then made a calculation:
>
>         maximum rounding error = 0.5 ns/7 µs
>                                = 70 µs/s
>                                = 6 s/day
>
>    That's why I decided to calculate the interval down to a femtosecond,
>    whose error was well within our tolerance.

I'd be curious to know whether, had you used nanosecond resolution,
you ever would have seen anything like that +/- 6s/day error. One
convenient attribute of the real world [1] is that, unless there's a
good reason for it to do otherwise [2], random error will tend to
cancel out rather than accumulate. With error of +/- 0.5 ns, assume
(for the sake of argument) that the actual error at each measurement
is random.choice((-0.4, -0.3, -0.2, -0.1, 0.1, 0.2, 0.3, 0.4)) ns,
with zero and the extremes omitted to make the calculations simpler.
In roughly twelve billion randomizations (86400 seconds divided by
7µs), the chances of having more than one billion more positive than
negative are... uhh.... actually, I don't know how to calculate
probabilities off numbers that big, but pretty tiny. So you're going
to have at least 5.5 billion negatives to offset your positives (or
positives to offset your negatives, same diff); more likely they'll be
even closer. So if you have (say) 5.5 to 6.5 ratio of signs, what
you're actually working with is half a second per day of accumulated
error - and I think you'd have a pretty tiny probability of even
*that* extreme a result. If it's more like 5.9 to 6.1, you'd have 0.1
seconds per day of error, at most. Plus, the same probabilistic
calculation can be done for days across a month, so even though the
theory would let you drift by three minutes a month, the chances of
shifting by even an entire second over that time are fairly slim.

This is something where I'd be more worried about systematic bias in
the code than anything from measurement or rounding error.

(I don't believe I've ever actually used a computer that's capable of
nanosecond-accurate time calculations. Generally they return time in
nanoseconds for consistency, but they won't return successive integer
values. You must have been on some seriously high-end hardware -
although that doesn't surprise me much, given that you were working on
a video product.)

ChrisA

[1] Believe you me, it has no shortage of INconvenient attributes, so
it's nice to have one swing the balance back a bit!
[2] If there's systematic error - if your 7 µs is actually averaging
7.25 µs - you need to deal with that separately.

Back to comp.lang.python | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

Clean Singleton Docstrings Rob Gaddi <rgaddi@highlandtechnology.invalid> - 2016-07-07 23:46 +0000
  Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-08 12:53 +1000
  Re: Clean Singleton Docstrings Michael Selik <michael.selik@gmail.com> - 2016-07-07 23:43 -0400
    Re: Clean Singleton Docstrings Rob Gaddi <rgaddi@highlandtechnology.invalid> - 2016-07-08 16:57 +0000
      Re: Clean Singleton Docstrings Ethan Furman <ethan@stoneleaf.us> - 2016-07-08 13:00 -0700
  Re: Clean Singleton Docstrings Peter Otten <__peter__@web.de> - 2016-07-08 09:38 +0200
    Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-08 19:20 +1000
      Re: Clean Singleton Docstrings Rob Gaddi <rgaddi@highlandtechnology.invalid> - 2016-07-08 16:47 +0000
    Re: Clean Singleton Docstrings Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-13 15:42 -0700
      Re: Clean Singleton Docstrings Peter Otten <__peter__@web.de> - 2016-07-14 01:54 +0200
        Re: Clean Singleton Docstrings Rustom Mody <rustompmody@gmail.com> - 2016-07-15 21:04 -0700
          Re: Clean Singleton Docstrings Ethan Furman <ethan@stoneleaf.us> - 2016-07-15 21:20 -0700
            Re: Clean Singleton Docstrings Rustom Mody <rustompmody@gmail.com> - 2016-07-15 22:51 -0700
            Re: Clean Singleton Docstrings Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-15 23:19 -0700
              Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-16 16:29 +1000
              Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-16 02:53 -0400
                Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-16 18:54 +1000
                Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-16 19:46 +1000
                What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-17 21:16 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 14:35 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-17 22:37 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 15:48 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 09:21 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-18 09:32 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ben Finney <ben+python@benfinney.id.au> - 2016-07-18 14:46 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-17 22:22 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-18 19:29 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 13:00 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 20:15 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 03:24 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-18 20:37 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 14:38 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Peter Otten <__peter__@web.de> - 2016-07-18 14:58 +0200
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:42 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 21:58 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-19 15:30 +1000
                Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-20 15:42 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-20 16:11 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-20 09:09 +0200
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 10:25 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve@pearwood.info> - 2016-07-20 22:47 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 16:54 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-21 00:26 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 17:59 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-20 22:38 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-21 10:52 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-21 18:46 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Marko Rauhamaa <marko@pacujo.net> - 2016-07-21 12:09 +0300
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-07-22 00:54 +0100
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Kaynor <ckaynor@zindagigames.com> - 2016-07-21 17:43 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-07-22 17:14 +0100
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-20 22:28 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Chris Angelico <rosuav@gmail.com> - 2016-07-21 15:35 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-20 22:52 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-21 16:34 +1000
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Rustom Mody <rustompmody@gmail.com> - 2016-07-21 06:14 -0700
                Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)] Steven D'Aprano <steve@pearwood.info> - 2016-07-22 02:10 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Chris Angelico <rosuav@gmail.com> - 2016-07-19 15:27 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 03:14 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-18 09:25 -0600
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 18:40 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 18:55 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-18 11:13 -0600
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-18 21:58 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 17:36 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:16 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Rustom Mody <rustompmody@gmail.com> - 2016-07-18 20:26 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gene Heskett <gheskett@shentel.net> - 2016-07-19 01:22 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-19 10:46 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gene Heskett <gheskett@shentel.net> - 2016-07-19 16:35 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 01:17 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-19 23:15 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 10:16 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-20 10:00 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-07-21 10:46 +1200
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-19 16:27 -0600
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 02:09 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) alister <alister.ware@ntlworld.com> - 2016-07-20 13:24 +0000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-21 14:04 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-19 17:01 -0700
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-07-20 11:07 +1200
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Marko Rauhamaa <marko@pacujo.net> - 2016-07-20 02:20 +0300
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:03 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Random832 <random832@fastmail.com> - 2016-07-18 09:25 -0400
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Steven D'Aprano <steve@pearwood.info> - 2016-07-19 13:21 +1000
                Re: What exactly is "exact" (was Clean Singleton Docstrings) Ben Finney <ben+python@benfinney.id.au> - 2016-07-19 10:21 +1000
              Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-16 17:27 +1000
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-16 10:58 +0300
              Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-16 14:04 -0400
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-16 21:43 +0300
              Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 07:02 +1000
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-17 00:27 +0300
                Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 08:18 +1000
                Re: Clean Singleton Docstrings Marko Rauhamaa <marko@pacujo.net> - 2016-07-17 10:41 +0300
                Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 17:51 +1000
                Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-17 04:03 -0400
                Re: Clean Singleton Docstrings Steven D'Aprano <steve@pearwood.info> - 2016-07-17 20:35 +1000
                Re: Clean Singleton Docstrings Random832 <random832@fastmail.com> - 2016-07-17 04:08 -0400
                Re: Clean Singleton Docstrings Chris Angelico <rosuav@gmail.com> - 2016-07-17 18:44 +1000
      Re: Clean Singleton Docstrings Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-13 18:25 -0600
  Re: Clean Singleton Docstrings Peter Otten <__peter__@web.de> - 2016-07-08 09:44 +0200
    Re: Clean Singleton Docstrings Rustom Mody <rustompmody@gmail.com> - 2016-07-08 01:53 -0700
  Re: What exactly is "exact" (was Clean Singleton Docstrings) Gene Heskett <gheskett@shentel.net> - 2016-07-19 23:16 -0400

csiph-web