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Javascript arithmetic error

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Jul 09.2007

Hi folks. I’m going a little crazy here. I’m running into a javascript multiplication issue. Here’s the sample code (entire page); it just calculates a floating point multiplication problem and prints it to the screen:

[code]
<!DOCTYPE html PUBLIC “-//W3C//DTD
XHTML 1.1//EN” “http://www.w3.org/TR/2001/REC-xhtml11-20010531/DTD/xhtml11-flat.
dtd”>
<html xmlns=”http://www.w3.org/1999/xhtml”>
<head>
<meta http-equiv=”Content-Language” content=”en-gb” />
<meta http-equiv=”Content-Type” content=”text/html; charset=utf-8″ />
<meta name=”robots” content=”index, follow” />
<title>JS Test</title>
<script type=”text/javascript”>
//<![CDATA[
function jstest(){
document.getElementById(“testresult”).appendChild(
document.createTextNode(“.4 * .4 = “+(.4 * .4))
);
}
//]]>
</script>
</head>
<body onload=”jstest()”>
<p id=”testresult”></p>
</body>
</html>
[/code]

Everywhere I’ve tested this (IE, FF, Safari), it gives a page with the same result:

[B].4 * .4 = 0.16000000000000003[/B].

Where the heck is that .00000000000000003 coming from? Anyone seen this before?

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JavaScript

3 Comments(s) ↴

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@FangJul 09.2007 — All JavaScript maths uses floating point arithmetic, it is prudent to round off values.
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@angrytunaauthorJul 09.2007 — I suppose so. I've replicated the result in mysql:

<i>
</i>select .400000000000000000000000 * .4000000000000000000000000;
+--------------------------------------------------------+
| .400000000000000000000000 * .4000000000000000000000000 |
+--------------------------------------------------------+
| 0.1600000000000000310862447 |
+--------------------------------------------------------+


So I suppose it's nothing more than a consequence of multiplying float values limited register size. In my solution, I've already rounded appropriately; I just don't like that it's there. Where are those extra numbers coming from? What calculation is being done when it proceeds beyond the end of the register?
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@Orc_ScorcherJul 09.2007 — 0.4 is not a number that can be exactly represented in floating point arithmetic, instead the computer's will use the best possible approximation:

0.40000000000000002220446049250313080847263336181640625
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