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Re: Short-circuit Logic

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On Thu, May 30, 2013 at 12:28 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> * de facto exact equality testing, only slower and with the *illusion* of
> avoiding equality, e.g. "abs(x-y) < sys.float_info.epsilon" is just a
> long and slow way of saying "x == y" when both numbers are sufficiently
> large;
>

The problem here, I think, is that "epsilon" has two meanings:

* sys.float_info.epsilon, which is an extremely specific value (the
smallest x such that 1.0+x != x)

* the mathematical concept, which is where the other got its name from.

Let's suppose someone is told to compare floating point numbers by
seeing if the absolute value of the difference is less than some
epsilon. They look up "absolute value" and find abs(); they look up
"epsilon" and think they've found it. Trouble is, they've found the
wrong epsilon... and really, there's an engineering issue here too.
Here's one of my favourite examples of equality comparisons:

http://xkcd.com/1047/

# Let's say we measured this accurately to one part in 40
x = one_light_year_in_meters

y = pow(99,8)
x == y  # False
abs(x-y) < x/40  # True

Measurement accuracy is usually far FAR worse than floating-point
accuracy. It's pretty pointless to compare for some kind of "equality"
that ignores this. Say you measure the diameter and circumference of a
circle, accurate to one meter, and got values of 79 and 248; does this
mean that pi is less than 3.14? No - in fact:

pi = 248/79
# math.pi = 3.141592653589793
abs(pi-math.pi) < pi/79  # True

Worst error is 1 in 79, so all comparisons are done with epsilon
derived from that.

ChrisA

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Short-circuit Logic Ahmed Abdulshafy <abdulshafy@gmail.com> - 2013-05-26 04:11 -0700
  Re: Short-circuit Logic Roy Smith <roy@panix.com> - 2013-05-26 07:38 -0400
  Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-26 12:13 +0000
    Re: Short-circuit Logic Ahmed Abdulshafy <abdulshafy@gmail.com> - 2013-05-27 13:11 -0700
      Re: Short-circuit Logic Nobody <nobody@nowhere.com> - 2013-05-28 01:10 +0100
        Re: Short-circuit Logic Ahmed Abdulshafy <abdulshafy@gmail.com> - 2013-05-28 01:39 -0700
          RE: Short-circuit Logic Carlos Nepomuceno <carlosnepomuceno@outlook.com> - 2013-05-28 12:32 +0300
          Re: Short-circuit Logic Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-05-28 12:45 +0100
          Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-28 13:51 +0000
            Re: Short-circuit Logic Grant Edwards <invalid@invalid.invalid> - 2013-05-28 15:14 +0000
              Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-28 15:55 +0000
      Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-28 13:48 +0000
        Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-29 00:01 +1000
        Re: Short-circuit Logic Ahmed Abdulshafy <abdulshafy@gmail.com> - 2013-05-29 07:27 -0700
          Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-30 00:32 +1000
          Re: Short-circuit Logic rusi <rustompmody@gmail.com> - 2013-05-29 07:33 -0700
            Re: Short-circuit Logic Ian Kelly <ian.g.kelly@gmail.com> - 2013-05-29 10:50 -0600
              Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 02:28 +0000
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-30 13:45 +1000
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 05:42 +0000
                Re: Short-circuit Logic Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2013-05-30 10:22 +0300
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 08:29 +0000
                Re: Short-circuit Logic Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2013-05-30 12:07 +0300
                Re: Short-circuit Logic Nobody <nobody@nowhere.com> - 2013-05-30 23:55 +0100
                Re: Short-circuit Logic Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2013-05-30 19:31 -0400
                Re: Short-circuit Logic Stefan Drees <stefan@drees.name> - 2013-05-31 17:34 +0200
                Re: Short-circuit Logic Roy Smith <roy@panix.com> - 2013-05-30 08:48 -0400
                Re: Short-circuit Logic Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2013-05-30 19:38 -0400
                Re: Short-circuit Logic Nobody <nobody@nowhere.com> - 2013-05-31 02:10 +0100
                Re: Short-circuit Logic Roy Smith <roy@panix.com> - 2013-05-30 21:21 -0400
                Re: Short-circuit Logic Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2013-05-30 21:57 -0400
                Re: Short-circuit Logic Michael Torrie <torriem@gmail.com> - 2013-05-30 21:33 -0600
                RE: Short-circuit Logic Carlos Nepomuceno <carlosnepomuceno@outlook.com> - 2013-05-31 03:03 +0300
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-30 18:29 +1000
                RE: Short-circuit Logic Carlos Nepomuceno <carlosnepomuceno@outlook.com> - 2013-05-31 00:03 +0300
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-31 05:13 +0000
                RE: Short-circuit Logic Carlos Nepomuceno <carlosnepomuceno@outlook.com> - 2013-05-31 09:42 +0300
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-31 08:11 +0000
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-31 17:09 +1000
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-31 08:45 +0000
                Re: Short-circuit Logic Roy Smith <roy@panix.com> - 2013-05-31 09:20 -0400
                RE: Short-circuit Logic Carlos Nepomuceno <carlosnepomuceno@outlook.com> - 2013-06-01 10:23 +0300
                Re: Short-circuit Logic 88888 Dihedral <dihedral88888@gmail.com> - 2013-05-30 20:11 -0700
            Re: Short-circuit Logic Dave Angel <davea@davea.name> - 2013-05-29 20:23 -0400
              Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 05:20 +0000
          Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 05:10 +0000
            Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-30 15:22 +1000
              Re: Short-circuit Logic Roy Smith <roy@panix.com> - 2013-05-30 08:40 -0400
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-30 22:58 +1000
                Re: Short-circuit Logic rusi <rustompmody@gmail.com> - 2013-05-30 09:58 -0700
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-31 03:23 +1000
                Re: Short-circuit Logic Rick Johnson <rantingrickjohnson@gmail.com> - 2013-05-30 17:13 -0700
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-31 12:29 +1000
                Re: Short-circuit Logic Ethan Furman <ethan@stoneleaf.us> - 2013-05-30 08:02 -0700
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-31 01:56 +1000
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 16:40 +0000
                Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-30 19:22 +0000
                Re: Short-circuit Logic Chris Angelico <rosuav@gmail.com> - 2013-05-31 07:46 +1000
                Re: Short-circuit Logic Ethan Furman <ethan@stoneleaf.us> - 2013-05-30 09:30 -0700
              Re: Short-circuit Logic Neil Cerutti <neilc@norwich.edu> - 2013-05-30 19:30 +0000
                Re: Short-circuit Logic Ian Kelly <ian.g.kelly@gmail.com> - 2013-05-30 13:49 -0600
  Re: Short-circuit Logic Terry Jan Reedy <tjreedy@udel.edu> - 2013-05-26 16:19 -0400
    Re: Short-circuit Logic Roy Smith <roy@panix.com> - 2013-05-26 16:22 -0400
      Re: Short-circuit Logic Terry Jan Reedy <tjreedy@udel.edu> - 2013-05-26 17:28 -0400
      Re: Short-circuit Logic Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-05-27 00:40 +0000
        Re: Short-circuit Logic Cameron Simpson <cs@zip.com.au> - 2013-05-27 11:57 +1000
        Re: Short-circuit Logic rusi <rustompmody@gmail.com> - 2013-05-26 21:44 -0700
        Re: Short-circuit Logic Vito De Tullio <vito.detullio@gmail.com> - 2013-05-27 06:59 +0200
  Re: Short-circuit Logic Nobody <nobody@nowhere.com> - 2013-05-27 18:52 +0100
  Re: Short-circuit Logic Ahmed Abdulshafy <abdulshafy@gmail.com> - 2013-05-27 13:08 -0700
    Re: Short-circuit Logic Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2013-05-27 21:36 -0400

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