From: Carsten Dominik <dominik@uva.nl>
To: r.thiel@uni-jena.de
Cc: emacs-orgmode@gnu.org
Subject: Re: adding up decimal fractions in the spreadsheet
Date: Sat, 27 Sep 2008 14:19:29 +0200 [thread overview]
Message-ID: <2550EE81-2105-41DC-B0A3-40D3D62B788C@uva.nl> (raw)
In-Reply-To: <d6b6c7740809270019s5b2d6a83k7ee7cb2ad8e165ae@mail.gmail.com>
Hi Rainer,
it is a common mis-conception that a number that has a limited number
of digits in base 10 can be represented exactly on a computer. This
is correct for integers, but not for fractional numbers.
Example:
1. Open the emacs calc with M-x calc RET
2. Type 12130.68 (first number from your example)
3. Press `p 200 RET' to switch to 200 digit precision.
4. press `d r 2 RET' o display the number in Base 2.
You'll see
10111101100010.1010111000010100011110101110000101000111101011100001010001111010111000010100011110101110000101000111101011100001010001111010111000010100011110101110000
................
It works the other way round as well, for example
0.33333333............. has an exact representation in base 3 (0.1).
This means that even simple additions like this do produce small
errors on computers, and the displayed result will depend upon how he
conversion is done.
(format "%s" x) just spits out digits, as many as possible. That is
why the fix I have pushed to the git repo uses
(number-to-string res)
and not
(format "%s" res)
number-to-string is an internal function that tries very hard to do
the conversion in the way you intend it.
- Carsten
On Sep 27, 2008, at 9:19 AM, Rainer Thiel wrote:
> Following a hint by Bernt Hansen, I have now changed org-table-sum to
> (format "%s" res) until I'll be able to use the corrected version
> Carsten Dominik uploaded to the git repository (which I am not sure
> how to access).
>
> Even so, org-table-sum at times shows a strange behaviour.
>
> When I try to sum up the following table:
>
> | 12130.68 |
> | -1444.19 |
> | -12744.90 |
> | -186.00 |
> | 7000.00 |
> | -7056.00 |
> | -335.58 |
> | -277.00 |
>
> I get -2912.9899999999993 (-2912.99 being the exact result). This is
> something I'd expect when square roots or logarithms are implied, but
> with such a simple addition and subtraction of decimal numbers I'd be
> inclined to call it a bug. Is there a way to improve org-mode in this
> respect?
>
> Many thanks again for this great mode
> --
> Prof. Dr. Rainer Thiel
> Institut für Altertumswissenschaften
> 07737 Jena, Germany (EU)
> r.thiel@uni-jena.de
>
>
> _______________________________________________
> Emacs-orgmode mailing list
> Remember: use `Reply All' to send replies to the list.
> Emacs-orgmode@gnu.org
> http://lists.gnu.org/mailman/listinfo/emacs-orgmode
next prev parent reply other threads:[~2008-09-27 12:19 UTC|newest]
Thread overview: 7+ messages / expand[flat|nested] mbox.gz Atom feed top
2008-09-27 7:19 adding up decimal fractions in the spreadsheet Rainer Thiel
2008-09-27 12:19 ` Carsten Dominik [this message]
[not found] ` <d6b6c7740809270606p679feb82n6fbe5f4d582ebcfa@mail.gmail.com>
[not found] ` <B1260157-B3E5-4704-8739-F4718BDFCAEC@uva.nl>
2008-09-27 14:20 ` Rainer Thiel
2008-09-27 17:59 ` Carsten Dominik
2008-09-27 13:21 ` Manish
2008-09-27 13:29 ` Rainer Thiel
2008-09-29 2:46 ` Manish
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