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

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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 Wed, 20 Jul 2016 16:11:23 +1000
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On Wed, Jul 20, 2016 at 3:42 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> Arithmetic on integer-values (e.g. 1.0) is always exact, up to a limit of
> either 2**53 or approximately 1e53, I forget which. (That's why most Javascript
> programmers fail to notice that they don't have an integer type.)

It's 2**53, because 64-bit floats use a 53-bit mantissa (52-bits
stored and an implicit 1 at the beginning, although I can never
remember how denormals are represented). Works out to a bit under
1e16. AIUI asm.js offers a 32-bit integer type, which in fall-back
mode is represented with the native "Number" type; for values that
could be stored in a 32-bit integer, a 64-bit float is perfectly
accurate (just stupidly inefficient compared to a real integer type).

ChrisA

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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
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                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
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                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
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    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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