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Re: python 3.44 float addition bug?

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On Thu, Jun 26, 2014 at 7:15 PM, Steven D'Aprano <steve@pearwood.info> wrote:
> Here's an error that *cannot* occur with binary floats: the average of
> two numbers x and y is not guaranteed to lie between x and y!
>
>
> py> from decimal import *
> py> getcontext().prec = 3
> py> x = Decimal('0.516')
> py> y = Decimal('0.518')
> py> (x + y) / 2
> Decimal('0.515')
>
>
> Ouch!

But what you're looking at is also a problem with intermediate
rounding, as the sum of .516 and .518 can't be represented in 3
digits. One rule of thumb that I learned back in my earliest coding
days was that your intermediate steps should have significantly more
precision than your end result; so if you want an end result with a
certain precision (say, 3 decimal digits), you should calculate with a
bit more. Of course, "a bit" is nearly impossible to define [1], but
if you're mostly adding and subtracting, or multiplying by smallish
constants, 1-2 extra digits' worth of precision is generally enough.
Or just give yourself lots of room, like using double-precision for
something like the above example. Compare this:

>>> from decimal import *
>>> getcontext().prec = 4
>>> x = Decimal('0.516')
>>> y = Decimal('0.519')
>>> avg = (x + y) / 2
>>> getcontext().prec = 3
>>> avg + 0
Decimal('0.518')
>>> (x + y) / 2
Decimal('0.52')

Doing the intermediate calculation with precision 3 exhibits the same
oddity Steven mentioned (only the other way around - result is too
high), but having a little extra room in the middle means the result
is as close to the correct answer as can be represented (0.517 would
be equally correct). With floating point on an 80x87, you can do this
with 80-bit FPU registers; I don't know of a way to do so with Python
floats, but (obviously) it's pretty easy with Decimal.

ChrisA

[1] Thank you, smart-aleck up the back, I am fully aware that "a bit"
is exactly one binary digit. That's not enough for a decimal float.
You've made your point, now shut up. :)

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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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