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

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 2016-07-21 00:26 +1000
Message-ID <mailman.6.1469024775.22221.python-list@python.org> (permalink)
References (16 earlier) <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>

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On Wed, Jul 20, 2016 at 11:54 PM, Marko Rauhamaa <marko@pacujo.net> wrote:
>  2. Floating-point numbers are *imperfect approximations* of real
>     numbers. Even when real numbers are derived exactly, floating-point
>     operations may introduce "lossy compression artifacts" that have to
>     be compensated for in application programs.

This is the kind of black FUD that has to be fought off. What
"compression artifacts" are introduced? The *only* lossiness in IEEE
binary floating-point arithmetic is rounding. (This is the bit where
someone like Steven is going to point out that there's something else
as well.) Unless you are working with numbers that require more
precision than you have available, the result should be perfectly
accurate. And there are other systems far less 'simple'. Can you
imagine this second assertion failing?

assert x <= y # if not, swap the values
assert x <= (x+y)/2 <= y

Because it can with decimal.Decimal, due to the way rounding happens in decimal.

ChrisA

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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

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