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Re: 64 bit code

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"Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> wrote in message 
news:yq9rpdkhtkbq.1a1dn96tarsn6.dlg@40tude.net...
> On Mon, 29 Oct 2012 04:38:33 -0000, LudovicoVan wrote:
>> "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> wrote in message
>> news:1cyg6bpqcn1uu$.w8upkuzwty9o$.dlg@40tude.net...
>>> On Sun, 28 Oct 2012 04:12:51 -0500, Robert Miles wrote:
>
>>>> Is that adequate for a-b when a and are nearly  the same?
>>>
>>> Yes, + or - makes no difference. In general, for intervals:
>>> [a,b]-[c,d]=[a-d,b-c] where a-d is rounded towards negative infinity, 
>>> b-c
>>> is rounded towards positive infinity.
>>
>> Some care is needed because, despite different formulations can be
>> mathematically equivalent, depending on how exactly a formula is written
>> down errors may or may not amplify, i.e. intervals may or may not widen.
>> This is called the "dependence problem": each occurrence of a variable in 
>> an
>> interval computation is treated as a different variables.  Of course, 
>> there
>> are techniques to tackle this problem.
>
> Yes, e.g. x*x /= x**2.
>
> But the question, as far as I understood it, was about what happens in the
> situations close to underflow. The answer is: nothing wrong. Interval
> bounds will capture precision loss.

The typical example of the dependence problem is X-X where X is, for 
instance, [0;1].  By the rule above, we get [-1;1] and not the more obvious 
and quite sharper [0;0].

Again, there are techniques to tackle the problem: rewriting the expression 
as you hint at above, but also using "improper" intervals (I think that was 
the term, but I am going from memory), i.e. relaxing the rule that the left 
end-point must be <= to the right end-point, so that we can rewrite 
[0;1]-[0;1] as [0;1]-[1;0] and get, still by the same rule, the sought for 
result [0;0].

As said, just from the top of my head: details and rules are of course in 
the technical treatments.

-LV
 

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64 bit code bob <bob@coolfone.comze.com> - 2012-10-10 08:22 -0700
  Re: 64 bit code Jongware <jongware@no-spam.plz> - 2012-10-10 17:35 +0200
    Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-10 17:37 +0100
      Re: 64 bit code Robert Wessel <robertwessel2@yahoo.com> - 2012-10-10 12:54 -0500
      Re: 64 bit code Fritz Wuehler <fritz@spamexpire-201210.rodent.frell.theremailer.net> - 2012-10-10 21:37 +0200
        Re: 64 bit code BGB <cr88192@hotmail.com> - 2012-10-10 21:46 -0500
      Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-10 20:43 +0100
        Re: 64 bit code "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-10-12 08:40 +0100
          Re: 64 bit code BGB <cr88192@hotmail.com> - 2012-10-12 12:36 -0500
          Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-12 20:57 +0100
            Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-12 21:30 +0100
              Re: 64 bit code BGB <cr88192@hotmail.com> - 2012-10-12 16:33 -0500
                Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-13 00:44 +0100
                Re: 64 bit code Ben Pfaff <blp@cs.stanford.edu> - 2012-10-12 20:07 -0700
              Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-13 11:11 +0100
                Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-13 13:11 +0100
                Re: 64 bit code Willem <willem@turtle.stack.nl> - 2012-10-13 12:34 +0000
                Re: 64 bit code BGB <cr88192@hotmail.com> - 2012-10-13 09:50 -0500
                Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-13 17:25 +0100
                Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-13 17:53 +0100
                Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-13 17:05 +0100
          Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-13 10:37 +0200
            Re: 64 bit code "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-10-27 12:18 +0100
              Re: 64 bit code "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-10-27 12:54 +0100
              Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-27 15:13 +0200
                Re: 64 bit code Robert Miles <milesrf@Usenet-News.net> - 2012-10-28 04:12 -0500
                Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-28 13:10 +0100
                Re: 64 bit code "LudovicoVan" <julio@diegidio.name> - 2012-10-29 04:38 +0000
                Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-29 09:30 +0100
                Re: 64 bit code "LudovicoVan" <julio@diegidio.name> - 2012-10-30 22:09 +0000
                Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-31 09:47 +0100
                Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-31 09:55 +0100
                Re: 64 bit code "LudovicoVan" <julio@diegidio.name> - 2012-10-31 14:32 +0000
            Re: 64 bit code Patricia Shanahan <pats@acm.org> - 2012-10-27 08:51 -0700
              Re: 64 bit code "LudovicoVan" <julio@diegidio.name> - 2012-10-27 17:23 +0100
              Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-27 20:43 +0200
                Re: 64 bit code "LudovicoVan" <julio@diegidio.name> - 2012-10-30 22:16 +0000
                Re: 64 bit code "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-10-31 09:53 +0100
                Re: 64 bit code "LudovicoVan" <julio@diegidio.name> - 2012-10-31 14:33 +0000
                Re: 64 bit code Fritz Wuehler <fritz@spamexpire-201211.rodent.frell.theremailer.net> - 2012-11-01 00:25 +0100
      Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-10 21:04 +0100
        Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-10 21:52 +0100
          Re: 64 bit code Ian Collins <ian-news@hotmail.com> - 2012-10-11 10:50 +1300
            Re: 64 bit code BGB <cr88192@hotmail.com> - 2012-10-10 21:54 -0500
              Re: 64 bit code "BartC" <bc@freeuk.com> - 2012-10-11 13:11 +0100
                Re: 64 bit code BGB <cr88192@hotmail.com> - 2012-10-11 11:17 -0500
      Re: 64 bit code Ben Pfaff <blp@cs.stanford.edu> - 2012-10-10 13:17 -0700
        Re: 64 bit code Fritz Wuehler <fritz@spamexpire-201210.rodent.frell.theremailer.net> - 2012-10-11 19:36 +0200
          Re: 64 bit code Ben Pfaff <blp@cs.stanford.edu> - 2012-10-12 08:13 -0700
    Re: 64 bit code Rui Maciel <rui.maciel@gmail.com> - 2012-10-10 20:38 +0100
    Re: 64 bit code Robin Vowels <robin.vowels@gmail.com> - 2012-10-10 15:22 -0700
  Re: 64 bit code Robert Miles <milesrf@Usenet-News.net> - 2012-10-12 02:13 -0500

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