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

From	Chris Kaynor <ckaynor@zindagigames.com>
Newsgroups	comp.lang.python
Subject	Re: Floating point equality [was Re: What exactly is "exact" (was Clean Singleton Docstrings)]
Date	2016-07-21 17:43 -0700
Message-ID	<mailman.38.1469148218.22221.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> <8760rybl8k.fsf@bsb.me.uk> <CALvWhxs-gw=kqMtQu114KN4gTL2uGd7+QYoCc18N7dYTxMjz6Q@mail.gmail.com>

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On Thu, Jul 21, 2016 at 4:54 PM, Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:

> Steven D'Aprano <steve@pearwood.info> writes:
> <snip>
> > Or you might be using a language like Javascript, which intentionally has
> > only floats for numbers. That's okay, you can still perform exact integer
> > arithmetic, so long as you stay within the bounds of ±2**16.
>
> Small point: it's 2**52.
>

If you really want to be picky, it is 2**53, inclusive:

>>> 2**53-2.0

9007199254740990.0

>>> 2**53-1.0

9007199254740991.0

>>> 2**53+0.0 # Can no longer store odd numbers, but 2**53 is even so it
can still be stored.

9007199254740992.0

>>> 2**53+1.0

9007199254740992.0

>>> 2**53+2.0
9007199254740994.0

This works as there is an implied one bit in the field for floats, giving
53 bits of storage despite only having 52 bits of storage. As the sign is
stored in a separate bit, the same limit applies to both positive and
negative numbers.

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

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