Edit report at http://bugs.php.net/bug.php?id=51518&edit=1
ID: 51518
Comment by: krenshala at koboldi dot net
Reported by: krenshala at koboldi dot net
Summary: should add to zero, but gets 1.1102230246252E-16
instead
Status: Bogus
Type: Bug
Package: Math related
Operating System: Multiple
PHP Version: 5.2.13
New Comment:
That, and the problem with storing 0.1 in binary. I think those two
issues are where my problem came from.
Thank you for your time and the information. Hopefully this report (I
won't call it a bug anymore ;) will help others as well since I did not
see anything that matched it when searching before I submitted.
Previous Comments:
------------------------------------------------------------------------
[2010-04-09 20:47:32] [email protected]
The important thing to take away from that doc is that computers can not
store
fractions accurately in an efficient manner. They are much better and
faster at
dealing with integers. In your particular example where you are using
0.3, that
is one of many fractions that a computer cannot represent. It is
actually
stored as 0.299999999999999988897769753748434595763683319091796875 which
is very
close to 0.3, but if you start doing math on it and any sort of exact
comparisons, it simply won't work. You can see this with this simple
code:
ini_set('precision',64);
echo 0.3;
------------------------------------------------------------------------
[2010-04-09 20:40:58] krenshala at koboldi dot net
tested it on my system at home and was able to reproduce it.
$ php --version
PHP 5.2.13-pl0-gentoo (cli) (built: Apr 9 2010 03:35:37)
Copyright (c) 1997-2010 The PHP Group
Zend Engine v2.2.0, Copyright (c) 1998-2010 Zend Technologies
$ cat test.php
echo "0.9 - 0.9 returns ".(0.9 - 0.9)."\n";
echo "0.9 + (-3 * .3) returns ".(0.9 + (-3 * .3))."\n";
echo "-0.9 + (3 * .3) returns ".(-0.9 + (3 * .3))."\n";
echo "0.8 + (-3 * .3) returns ".(0.8 + (-3 * .3))."\n";
$ php test.php
0.9 - 0.9 returns 0
0.9 + (-3 * .3) returns 1.11022302463E-16
-0.9 + (3 * .3) returns -1.11022302463E-16
0.8 + (-3 * .3) returns -0.1
Also, I can understand the multiplication increasing the precision used,
from 1 to 3 significant digits in the function above. Jumping from 1E-3
to 1E-16 seems a bit much to me, however. I'm reading the Floating
Point doc you linked Rasmus in case it does address the issue. From the
little of it I've read so far it does seem to address at least some of
what is happening here.
My concern is with the differences between the output of the different
lines in my new script (this comment). Assuming it is due to the
floating point operation rounding/approximations mentioned in the doc,
I'm assuming the difference shows up due to the multiplication.
... off to finish reading the Floating Point doc.
------------------------------------------------------------------------
[2010-04-09 05:12:28] [email protected]
The fix here is to decide on your precision and do:
$output = round(0.9 + ($input * 0.3), 2); // 2-decimal precision
------------------------------------------------------------------------
[2010-04-09 05:05:12] [email protected]
Floating point values have a limited precision. Hence a value might
not have the same string representation after any processing. That also
includes writing a floating point value in your script and directly
printing it without any mathematical operations.
If you would like to know more about "floats" and what IEEE
754 is, read this:
http://docs.sun.com/source/806-3568/ncg_goldberg.html
Thank you for your interest in PHP.
.
------------------------------------------------------------------------
[2010-04-09 05:03:27] krenshala at koboldi dot net
Description:
------------
Math error for code that should be returning zero, but instead returns
1.1102230246252E-16 on multiple systems using multiple versions of PHP.
The problem is that when the input value is -3 the output value should
be zero: 0.9 + (-3 * 0.3) = 0.9 - 0.9 = 0. If the calculated value is
non-zero the error does not occur.
I first saw the error on a WinXP (Home SP3, 32bit) system running PHP
5.2.9-1, but it also shows up on a MAC (10.6.2) with PHP 5.3.0
installed. I'm in the process of upgrading PHP (to 5.2.13) on my Gentoo
box to test it there but haven't had a chance to do so yet.
Test script:
---------------
my_function(-3);
function my_function($input){
$output = 1;
if($input <= 0)
$output = 0.9 + ($input * 0.3);
// the above should give 0.9 - 0.9 = 0
echo "Verifying values: 0.9 - ".($input * 0.3)." is supposed to be
zero?\n";
echo "Input: $input\tOutput: $output\n";
return $output;
}
Expected result:
----------------
should have received zero (0).
Actual result:
--------------
actually received: 1.1102230246252E-16
------------------------------------------------------------------------
--
Edit this bug report at http://bugs.php.net/bug.php?id=51518&edit=1
