99999999999999.99 problem in JavaScript

M

Mahsha

I tried following html code
<HTML>
<HEAD>
<TITLE> New Document </TITLE>
</HEAD>
<BODY>
<SCRIPT LANGUAGE="JavaScript">
<!--
alert(99999999999999.99)
//-->
</SCRIPT>
</BODY>
</HTML>

output i expecting alert popup 99999999999999.99
But output is 99999999999999.98
WHY????
 
T

Thomas 'PointedEars' Lahn

Mahsha said:
I tried following html code
<HTML>
<HEAD>
<TITLE> New Document </TITLE>
Click to expand...

</HEAD>
<BODY>
<SCRIPT LANGUAGE="JavaScript">
Click to expand...

<!--
Click to expand...

Remove this.
alert(99999999999999.99)
window.alert(...);

//-->
Click to expand...

Remove this.
</SCRIPT>
</BODY>
</HTML>

output i expecting alert popup 99999999999999.99
But output is 99999999999999.98
WHY????
Click to expand...

Floating-point rounding and/or string representation of Number values.

Your keyboard appears to be borken. RTFM, RTFFAQ, STFW.
<http://jibbering.com/faq/#posting>


PointedEars
 
R

rf

Mahsha said:
I tried following html code
<HTML>
<HEAD>
<TITLE> New Document </TITLE>
</HEAD>
<BODY>
<SCRIPT LANGUAGE="JavaScript">
<!--
alert(99999999999999.99)
//-->
</SCRIPT>
</BODY>
</HTML>

output i expecting alert popup 99999999999999.99
But output is 99999999999999.98
WHY????
Click to expand...

Why do so many many people come into CLJ without a basic understanding on
how floating point arithmatic is implemented on computers? Then again not
just within javascript but with computers in general.

And it's not just here. I see the same over in the C and C++ and PHP groups
as well. People who simply do not understand how binary floating point
works. Nor for that matter how any [base] floating point works.

Header: Organization: http://groups.google.com

In this case I've got a fair idea why.
 
J

Jorge

I tried following html code
<HTML>
<HEAD>
<TITLE> New Document </TITLE>
</HEAD>
<BODY>
<SCRIPT LANGUAGE="JavaScript">
<!--
alert(99999999999999.99)
//-->
</SCRIPT>
</BODY>
</HTML>

output i expecting alert popup 99999999999999.99
But output is 99999999999999.98
WHY????
Click to expand...

1.- Because in JS decimal numbers are represented internally in binary
"IEEE754 fp double (binary64)" format: 53 bits long mantissa * 10 bits
exponent * 1 bit sign.

2.- Because 0.99 isn't a sum of powers of 2, it can't be represented
exactly in a binary format: the best approximation possible in 53 bits
is: "0.1111110101110000101000111101011100001010001111010111".

3.- As 99999999999999 occupies 47 bits of the 53 bits internally
available: "10110101111001100010000011110100011111111111111"...

4.- ... there are only 6 bits left for the fractional part, so .99
becomes "0.111111" that is : (2^-1) + (2^-2) + (2^-3) + (2^-4) +
(2^-5) + (2^-6) === 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 === 0,984375.

5.- You can check it yourself:
javascript:alert(99999999999999.99-99999999999999) //-> 0.984375

Reducing the integer part of the number would "leave more bits
available" for the fractional part:
(2 "nines" less:)
javascript:alert(999999999999.99-999999999999) //-> 0.989990234375
(closer to .99)
(4 "nines" less:)
javascript:alert(9999999999.99-9999999999) //-> 0.9899997711181641
(even closer)
(7 "nines" less:)
javascript:alert(9999999.99-9999999) //-> 0.9900000002235174 (even
closer)
etc.

You can "see" the numbers here:
http://jorgechamorro.com/cljs/016/
 
D

Dr J R Stockton

In comp.lang.javascript message <11811341-7933-458a-9add-f9075802dd9d@r3
g2000vbp.googlegroups.com>, Wed, 1 Apr 2009 08:18:52, Jorge
1.- Because in JS decimal numbers are represented internally in binary
"IEEE754 fp double (binary64)" format: 53 bits long mantissa * 10 bits
exponent * 1 bit sign.
Click to expand...

The exponent is 11 bits.

See <URL:http://www.merlyn.demon.co.uk/js-misc0.htm#DW4>,
<URL:http://www.merlyn.demon.co.uk/pas-real.htm>,
<URL:http://www.merlyn.demon.co.uk/pas-type.htm>.
 
J

Jorge

In comp.lang.javascript message <11811341-7933-458a-9add-f9075802dd9d@r3
g2000vbp.googlegroups.com>, Wed, 1 Apr 2009 08:18:52, Jorge


The exponent is 11 bits.
Click to expand...

Yes I know. And the mantissa is made up of 52 explicit bits plus an
implicit (always-set-to-1) leading bit. Bus as that made it into a
longer explanation I chose to ~ cut it short. To know more he should
go to : http://www.google.com/search?&q=ieee754
 
M

Mike Duffy

@cache100.multikabel.net:

Tested in Safari, Opera, Mozilla(s), iCab : OK.
IE: don't even get me started...

Like yourself I am not a big IE fan (yep, understatement).
Click to expand...

I made the switch last night to FF. Not due to any great preferences in
terms of function or speed, but I was starting to get vexed with that
message box:

"Sorry for the inconvenience .... Internet Explorer will be shut down."

I even tried re-installing IE7, but that did not help.

I wonder how many of the people who use FF do so simply because IE is
broken. If you look at global statistics from the "Statcounter" service,

http://gs.statcounter.com/

it is clear that there are a lot of people who use IE weekdays and FF
weekends.
 
J

Jorge

Jorge schreef:
...




Onyour page:

cljs thread
Tested in Safari, Opera, Mozilla(s), iCab : OK.
IE: don't even get me started...

Like yourself I am not a big IE fan (yep, understatement). But I tested
it in IE and it runs fine. Why your remark?
Click to expand...

It always goes like this: I write something, debug-test it in
webInspector/fireBug until it runs/renders fine in Safari/FireFox.
Then test it in Opera, Chrome, etc : it runs/renders fine there as
well. Then comes IE(x) and it fails, either the code or the rendering,
due to any of the (hundreds of) stupid bugs and/or non-compliant
behaviour in IE. Always the same story, ever. Grrr. It makes me
happier to ignore it all together. Unless it's strictly unavoidable.
 

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