Re: python 3.44 float addition bug?

References	(2 earlier) <53ab8bc4$0$11121$c3e8da3@news.astraweb.com> <mailman.11251.1403753977.18130.python-list@python.org> <53abe4ad$0$11121$c3e8da3@news.astraweb.com> <mailman.11254.1403775938.18130.python-list@python.org> <53acdc2d$0$29985$c3e8da3$5496439d@news.astraweb.com>
Date	2014-06-27 13:24 +1000
Subject	Re: python 3.44 float addition bug?
From	Chris Angelico <rosuav@gmail.com>
Newsgroups	comp.lang.python
Message-ID	<mailman.11277.1403839456.18130.python-list@python.org> (permalink)

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On Fri, Jun 27, 2014 at 12:51 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> Although you seem to have missed the critical issue: this is a failure
> mode which *binary floats cannot exhibit*, but decimal floats can. The
> failure being that
>
> assert x <= (x+y)/2 <= y
>
> may fail if x and y are base 10 floats.

No, I didn't miss that; I said that what you were looking at was
*also* caused by intermediate rounding. It happens because .516 + .518
= 1.034, which rounds to 1.03; half of that is .515, which is outside
of your original range - but the intermediate rounding really reduced
the "effective precision" to two digits, by discarding some of the
information in the original. If you accept that your result is now
accurate to only two digits of precision, then that result is within
one ULP of correct (you'll record the average as either .51 or .52,
and your two original inputs are both .52, and the average of .52 and
.52 is clearly .52).

But you're right that this can be very surprising. And it's inherent
to the concept of digits having more range than just "high" or "low",
so there's no way you can get this with binary floats.

ChrisA

Thread

python 3.44 float addition bug? FraserL <fraser.long+usenet@NOSPAMgmail.com> - 2014-06-20 19:57 -0500
  Re: python 3.44 float addition bug? FraserL <fraser.long+usenet@gmail.com> - 2014-06-20 20:11 -0500
    Re: python 3.44 float addition bug? Gary Herron <gary.herron@islandtraining.com> - 2014-06-20 18:19 -0700
  Re: python 3.44 float addition bug? Gary Herron <gary.herron@islandtraining.com> - 2014-06-20 18:07 -0700
  Re: python 3.44 float addition bug? Chris Angelico <rosuav@gmail.com> - 2014-06-21 11:33 +1000
  Re: python 3.44 float addition bug? INADA Naoki <songofacandy@gmail.com> - 2014-06-21 10:06 +0900
  Re: python 3.44 float addition bug? Grant Edwards <invalid@invalid.invalid> - 2014-06-21 14:25 +0000
  Re: python 3.44 float addition bug? Ned Deily <nad@acm.org> - 2014-06-21 12:24 -0700
    Re: python 3.44 float addition bug? buck <workitharder@gmail.com> - 2014-06-23 17:55 -0700
      Re: python 3.44 float addition bug? Chris Angelico <rosuav@gmail.com> - 2014-06-24 13:26 +1000
      Re: python 3.44 float addition bug? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-06-24 17:30 +1200
      Re: python 3.44 float addition bug? Steven D'Aprano <steve@pearwood.info> - 2014-06-24 06:34 +0000
  Re: python 3.44 float addition bug? Maciej Dziardziel <fiedzia@gmail.com> - 2014-06-25 14:12 -0700
    Re: python 3.44 float addition bug? Steven D'Aprano <steve@pearwood.info> - 2014-06-26 02:56 +0000
      Re: python 3.44 float addition bug? Chris Angelico <rosuav@gmail.com> - 2014-06-26 13:13 +1000
        Re: python 3.44 float addition bug? Steven D'Aprano <steve@pearwood.info> - 2014-06-26 04:17 +0000
          Re: python 3.44 float addition bug? Chris Angelico <rosuav@gmail.com> - 2014-06-26 14:41 +1000
      Re: python 3.44 float addition bug? Ben Finney <ben@benfinney.id.au> - 2014-06-26 13:39 +1000
        Re: python 3.44 float addition bug? Steven D'Aprano <steve@pearwood.info> - 2014-06-26 09:15 +0000
          Re: python 3.44 float addition bug? Chris Angelico <rosuav@gmail.com> - 2014-06-26 19:38 +1000
            Re: python 3.44 float addition bug? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-06-27 02:51 +0000
              Re: python 3.44 float addition bug? Chris Angelico <rosuav@gmail.com> - 2014-06-27 13:24 +1000
              Re: python 3.44 float addition bug? Ian Kelly <ian.g.kelly@gmail.com> - 2014-06-27 10:18 -0600
      Re: python 3.44 float addition bug? Stefan Behnel <stefan_ml@behnel.de> - 2014-06-26 07:53 +0200

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