calculation error with built-in command CTRL + J?!

calculation error with built-in command CTRL + J?!

[Borde, Andreas]

Hello,

I calculated
(* 12 2.6) with the built in command CTRL + J and got
31.200000000000003

It is the same for
(* 2.6 12)

I am wondering about the tailing numbers after 31.2!

If I calculate (* 2.5 12) then the result is the expected 30.0.

Can someone tell me the reason?  Is there something wrong with
my calcuation?

I am using the official release:

This is GNU Emacs 22.1.1 (i386-mingw-nt5.0.2195)
 of 2007-06-02 on RELEASE

under Win2k.

Thank you and kind regards

Borde, Andreas

Re: calculation error with built-in command CTRL + J?!

[David Hansen]

On Mon, 14 Apr 2008 12:59:10 +0900 Andreas Borde wrote:

> Can someone tell me the reason?  Is there something wrong with
> my calcuation?

Normal floating point rounding error.

David

Re: calculation error with built-in command CTRL + J?!

[Thierry Volpiatto]

"Borde, Andreas" <andreas.borde@jp.bosch.com> writes:

> Hello,
>
> I calculated
> (* 12 2.6) with the built in command CTRL + J and got
> 31.200000000000003
Hello, you have to use round like that:
,----
| ELISP> (/ (round (* 100
|             (* 2.6 12)))
|    100.0)
| 31.2
`----

    
> It is the same for
> (* 2.6 12)
>
> I am wondering about the tailing numbers after 31.2!
>
> If I calculate (* 2.5 12) then the result is the expected 30.0.
>
> Can someone tell me the reason?  Is there something wrong with
> my calcuation?
>
> I am using the official release:
>
> This is GNU Emacs 22.1.1 (i386-mingw-nt5.0.2195)
>  of 2007-06-02 on RELEASE
>
> under Win2k.
>
> Thank you and kind regards
>
> Borde, Andreas
>
>

-- 
A + Thierry
Pub key: http://pgp.mit.edu

Re: calculation error with built-in command CTRL + J?!

[Sven Joachim]

On 2008-04-14 05:59 +0200, Andreas Borde wrote:

> I calculated
> (* 12 2.6) with the built in command CTRL + J and got
> 31.200000000000003

A normal rounding error for floating point numbers.

> It is the same for
> (* 2.6 12)

Multiplication is commutative. ;-)

> I am wondering about the tailing numbers after 31.2!

The computer can only represent real numbers that are a linear
combination of (possibly negative) powers of 2, all other numbers can
only be approximated.  See http://en.wikipedia.org/wiki/Floating_point
for details.

> If I calculate (* 2.5 12) then the result is the expected 30.0.

Because 2.5 = 2^1 + 2^(-1), therefore the computer can calculate exactly.

> Can someone tell me the reason?  Is there something wrong with
> my calcuation?

No, there's nothing wrong.  The following little C program prints the
same results as Emacs:

--8<---------------cut here---------------start------------->8---
#include <stdio.h>

int main(void)
{
  printf("12 * 2.6 = %.15f\n", 12 * 2.6);
  return 0;
}
--8<---------------cut here---------------end--------------->8---
  

Regards,
        Sven