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