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RE: Short-circuit Logic

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----------------------------------------
> From: steve+comp.lang.python@pearwood.info
> Subject: Re: Short-circuit Logic
> Date: Thu, 30 May 2013 05:42:17 +0000
> To: python-list@python.org
[...]
> Here's another way, mathematically equivalent (although not necessarily
> equivalent using floating point computations!) which avoids the divide-by-
> zero problem:
>
> abs(a - b) < epsilon*a

That's wrong! If abs(a) < abs(a-b)/epsilon you will break the commutative law. For example:

import sys
eps = sys.float_info.epsilon
def almost_equalSD(a,b):
    return abs(a-b) < eps*a

#special case
a=1
b=1/(1-eps)
almost_equalSD(a,b) == almost_equalSD(b,a)

Returns False.

This discussion reminded me of TAOCP and I paid a visit and bring the following functions:


#Floating Point Comparison Operations
#Knuth, Donald (1981). The Art of Computer Programming. 2nd ed. Vol. 2. p. 218. Addison-Wesley. ISBN 0-201-03822-6.
import sys

#floating point comparison: u ≺ v(ε) "definitely less than" (definition 21)
def fpc_dlt(u,v,eps=sys.float_info.epsilon):
    au=abs(u)
    av=abs(v)
    return (v-u)> (eps*(au if au>av else av))  # v-u> ε*max(|u|,|v|)

#floating point comparison: u ~ v(ε) "approximately equal to" (definition 22)
def fpc_aeq(u,v,eps=sys.float_info.epsilon):
    au=abs(u)
    av=abs(v)
    return abs(v-u) <= (eps*(au if au>av else av))  # |v-u| <= ε*max(|u|,|v|)

#floating point comparison: u ≻ v(ε) "definitely greater than" (definition 23)
def fpc_dgt(u,v,eps=sys.float_info.epsilon):
    au=abs(u)
    av=abs(v)
    return (u-v)> (eps*(au if au>av else av))  # u-v> ε*max(|u|,|v|)

#floating point comparison: u ≈ v(ε) "essentially equal to" (definition 24)
def fpc_eeq(u,v,eps=sys.float_info.epsilon):
    au=abs(u)
    av=abs(v)
    return abs(v-u) <= (eps*(au if au<av else av))  # |v-u| <= ε*min(|u|,|v|)


I've tried to make it look a bit pythonic. Please let me know if it can be improved. ;)

So, if you try the following you get the correct answer:

#special case
a=1
b=1/(1-eps)
fpc_aeq(a,b) == fpc_aeq(b,a)


>
> Whichever method you choose, there are gotchas to watch out for.
>
>> http://xkcd.com/1047/
>
> Nice!
>
>
> --
> Steven
> --
> http://mail.python.org/mailman/listinfo/python-list 		 	   		  

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Thread

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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