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Re: a.index(float('nan')) fails

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On Sat, Oct 27, 2012 at 5:40 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> On Sat, 27 Oct 2012 03:45:46 +1100, Chris Angelico wrote:
>>
>> Actually, as I see it, there's only one principle to take note of: the
>> "HMS Pinafore Floating Point Rule"...
>>
>> ** Floating point expressions should never be tested for equality **
>> ** What, never? **
>> ** Well, hardly ever! **
>>
>> The problem isn't with the associativity, it's with the equality
>> comparison. Replace "x == y" with "abs(x-y)<epsilon" for some epsilon
>> and all your statements fulfill people's expectations.
>
> O RYLY?
>
> Would you care to tell us which epsilon they should use?
>
> Hint: *whatever* epsilon you pick, there will be cases where that is
> either stupidly too small, stupidly too large, or one that degenerates to
> float equality. And you may not be able to tell if you have one of those
> cases or not.
>
> Here's a concrete example for you:
>
> What *single* value of epsilon should you pick such that the following
> two expressions evaluate correctly?
>
> sum([1e20, 0.1, -1e20, 0.1]*1000) == 200
> sum([1e20, 99.9, -1e20, 0.1]*1000) != 200

Your epsilon value needs to take into account the precisions of the
values involved, and each operation needs to modify the
precision/error value. That's how I was taught to do it in
mathematical calculations. Well, I was taught "significant digits",
counting decimal digits, and a computer would normally want to count
"bits of precision", but close enough.

So here's my heresy: When you add 1e20 and 0.1, the value should be
equal to the original 1e20 unless it has at least 21 significant
digits. Otherwise, you get stupidly accurate errors, like in the old
anecdote about the age of a museum piece: It's 1001 years, 2 months,
and 3 days old, because I asked last year how old it was and it was a
thousand years old.

Flame away!

ChrisA

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a.index(float('nan')) fails mamboknave@gmail.com - 2012-10-25 18:46 -0700
  Re: a.index(float('nan')) fails Terry Reedy <tjreedy@udel.edu> - 2012-10-25 22:04 -0400
    Re: a.index(float('nan')) fails Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-10-26 02:44 +0000
      Re: a.index(float('nan')) fails Terry Reedy <tjreedy@udel.edu> - 2012-10-26 03:54 -0400
        Re: a.index(float('nan')) fails Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-10-26 15:26 +0000
          Re: a.index(float('nan')) fails Terry Reedy <tjreedy@udel.edu> - 2012-10-26 14:49 -0400
    Re: a.index(float('nan')) fails Nobody <nobody@nowhere.com> - 2012-10-27 17:40 +0100
  Re: a.index(float('nan')) fails Cameron Simpson <cs@zip.com.au> - 2012-10-26 13:15 +1100
    Re: a.index(float('nan')) fails mamboknave@gmail.com - 2012-10-25 19:22 -0700
    Re: a.index(float('nan')) fails mamboknave@gmail.com - 2012-10-25 19:22 -0700
  Re: a.index(float('nan')) fails MRAB <python@mrabarnett.plus.com> - 2012-10-26 03:19 +0100
  Re: a.index(float('nan')) fails Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-10-26 02:33 +0000
    Re: a.index(float('nan')) fails Ethan Furman <ethan@stoneleaf.us> - 2012-10-28 06:07 -0700
  Re: a.index(float('nan')) fails Terry Reedy <tjreedy@udel.edu> - 2012-10-26 04:00 -0400
    Re: a.index(float('nan')) fails Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-10-26 16:23 +0000
      Re: a.index(float('nan')) fails MRAB <python@mrabarnett.plus.com> - 2012-10-26 17:43 +0100
      Re: a.index(float('nan')) fails Chris Angelico <rosuav@gmail.com> - 2012-10-27 03:45 +1100
        Re: a.index(float('nan')) fails Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-10-26 18:40 +0000
          Re: a.index(float('nan')) fails Devin Jeanpierre <jeanpierreda@gmail.com> - 2012-10-26 15:17 -0400
          Re: a.index(float('nan')) fails Chris Angelico <rosuav@gmail.com> - 2012-10-27 12:29 +1100
      Re: a.index(float('nan')) fails Terry Reedy <tjreedy@udel.edu> - 2012-10-26 14:58 -0400
      Re: a.index(float('nan')) fails Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-10-27 00:48 -0400
        Re: a.index(float('nan')) fails Thomas Rachel <nutznetz-0c1b6768-bfa9-48d5-a470-7603bd3aa915@spamschutz.glglgl.de> - 2012-10-27 08:56 +0200
          Re: a.index(float('nan')) fails Nobody <nobody@nowhere.com> - 2012-10-27 17:45 +0100
          Re: a.index(float('nan')) fails Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-10-27 13:07 -0400
  Re: a.index(float('nan')) fails Mark Adam <dreamingforward@gmail.com> - 2012-10-27 13:33 -0500

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