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Re: Confusing math problem

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Date Fri, 22 Feb 2013 08:23:27 +1100
Subject Re: Confusing math problem
From Chris Angelico <rosuav@gmail.com>
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On Fri, Feb 22, 2013 at 7:49 AM, Dave Angel <davea@davea.name> wrote:
> However, if I do:
>
> print 3**60, "\n", int(math.pow(3,60)), "\n", pow(3,60)
>
>
> I get:
>
> 42391158275216203514294433201
> 42391158275216203520420085760
> 42391158275216203514294433201
>
>
> and the middle one is the one that's wrong.

In theory, a float should hold the nearest representable value to the
exact result. Considering that only one operation is being performed,
there should be no accumulation of error. The integer results show a
small number (618) of collisions, eg 2**16 and 4**8; why should some
of those NOT collide when done with floating point? My initial thought
was "Oh, this is comparing floats for equality", but after one single
operation, that should be not a problem.

> You can tell by casting out 9's.  The middle one gets 1
> instead of zero, showing that it's NOT divisible by 3.

Which I thought so cool and magical and awesome, until I started
exploring other bases and found that you could cast out F's in hex and
7's in octal... and you can cast out 1's in binary to find out if it's
a multiple of 1, too.

ChrisA

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Thread

Confusing math problem "Schizoid Man" <schiz_man@21stcentury.com> - 2013-02-21 19:33 +0000
  Re: Confusing math problem Dave Angel <davea@davea.name> - 2013-02-21 15:25 -0500
    Re: Confusing math problem "Schizoid Man" <schiz_man@21stcentury.com> - 2013-02-21 22:39 +0000
      Re: Confusing math problem Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2013-02-21 22:53 +0000
        Re: Confusing math problem "Schizoid Man" <schiz_man@21stcentury.com> - 2013-02-21 23:41 +0000
          Re: Confusing math problem Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2013-02-22 00:04 +0000
          Re: Confusing math problem Ian Kelly <ian.g.kelly@gmail.com> - 2013-02-21 17:19 -0700
    Re: Confusing math problem "Schizoid Man" <schiz_man@21stcentury.com> - 2013-02-21 23:39 +0000
  Re: Confusing math problem Ian Kelly <ian.g.kelly@gmail.com> - 2013-02-21 13:42 -0700
  Re: Confusing math problem Chris Angelico <rosuav@gmail.com> - 2013-02-22 07:46 +1100
    Re: Confusing math problem "Schizoid Man" <schiz_man@21stcentury.com> - 2013-02-21 22:44 +0000
      Re: Confusing math problem Chris Angelico <rosuav@gmail.com> - 2013-02-22 11:29 +1100
      Re: Confusing math problem Dave Angel <davea@davea.name> - 2013-02-21 21:19 -0500
  Re: Confusing math problem Dave Angel <davea@davea.name> - 2013-02-21 15:49 -0500
  Re: Confusing math problem Chris Angelico <rosuav@gmail.com> - 2013-02-22 08:23 +1100
    Re: Confusing math problem Peter Pearson <ppearson@nowhere.invalid> - 2013-02-21 21:59 +0000
      Re: Confusing math problem Chris Angelico <rosuav@gmail.com> - 2013-02-22 09:11 +1100
      Re: Confusing math problem Dave Angel <davea@davea.name> - 2013-02-21 17:33 -0500
      Re: Confusing math problem Chris Angelico <rosuav@gmail.com> - 2013-02-22 10:15 +1100
    Re: Confusing math problem Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-02-22 09:16 +0000
      Re: Confusing math problem Serhiy Storchaka <storchaka@gmail.com> - 2013-02-22 13:48 +0200
  Re: Confusing math problem Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-02-22 09:27 +0000

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