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Re: Exact integer-valued floats

References <505ca3e9$0$29981$c3e8da3$5496439d@news.astraweb.com>
From Ian Kelly <ian.g.kelly@gmail.com>
Date 2012-09-21 12:13 -0600
Subject Re: Exact integer-valued floats
Newsgroups comp.lang.python
Message-ID <mailman.1027.1348251221.27098.python-list@python.org> (permalink)

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On Fri, Sep 21, 2012 at 11:29 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> The question is, what is the largest integer number N such that every
> whole number between -N and N inclusive can be represented as a float?
>
> If my tests are correct, that value is 9007199254740992.0 = 2**53.
>
> Have I got this right? Is there a way to work out the gap between one
> float and the next?

That looks mathematically correct.  The "gap" between floats is the
equivalent of a difference of 1 bit in the significand.  For a
floating point number represented as (sign * c * 2 ** q), where c is
an integer, the gap between floats is equal to 2 ** q.  There are 53
bits of precision in a double-precision float (technically an implicit
1 followed by 52 bits), so q becomes greater than 0 at 2 ** 53.

Cheers,
Ian

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Thread

Exact integer-valued floats Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-21 17:29 +0000
  Re: Exact integer-valued floats Ian Kelly <ian.g.kelly@gmail.com> - 2012-09-21 12:13 -0600
  Re: Exact integer-valued floats Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2012-09-21 22:47 +0300
  Re: Exact integer-valued floats Nobody <nobody@nowhere.com> - 2012-09-21 20:59 +0100
  Re: Exact integer-valued floats Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-09-21 16:26 -0400
    Re: Exact integer-valued floats Hans Mulder <hansmu@xs4all.nl> - 2012-09-21 23:04 +0200
      Re: Exact integer-valued floats Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-09-21 20:54 -0400
  Re: Exact integer-valued floats Alister <alister.ware@ntlworld.com> - 2012-09-21 21:14 +0000
  Re: Exact integer-valued floats Paul Rubin <no.email@nospam.invalid> - 2012-09-21 15:23 -0700
    Re: Exact integer-valued floats Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-22 01:36 +0000
      Re: Exact integer-valued floats Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-09-22 01:01 -0400
        Re: Exact integer-valued floats Tim Roberts <timr@probo.com> - 2012-09-22 14:05 -0700
          Re: Exact integer-valued floats Dave Angel <d@davea.name> - 2012-09-22 19:06 -0400
            Re: Exact integer-valued floats Hans Mulder <hansmu@xs4all.nl> - 2012-09-23 09:45 +0200
          Re: Exact integer-valued floats wrw@mac.com - 2012-09-24 11:29 -0400
    Re: Exact integer-valued floats Nobody <nobody@nowhere.com> - 2012-09-22 11:19 +0100

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