floating point numbers question

[Benedikt Wismans]

dear group!

<script language="javas cript">
var a = 60381.11;
var b = 1437261.58;
var c = a + b;
alert (c); -> 1497642.6900000 002

var a = 60381.11;
var b = 1437261.50;
var c = a + b;
alert (c); -> 1497642.61

</script>

can anybody help me with this? Obviously some kind of precision
problem, but those numbers are not big at all. Any ideas where to find
documentation of internal data representation in js? Any hint is
welcome.


Benedikt

[Douglas Crockford]

Re: floating point numbers question

> var a = 60381.11;[color=blue]
> var b = 1437261.58;
> var c = a + b;
> alert (c); // 1497642.6900000 002[/color]
[color=blue]
> can anybody help me with this? Obviously some kind of precision
> problem, but those numbers are not big at all. Any ideas where to find
> documentation of internal data representation in js?[/color]

JavaScript Numbers are 64-bit floating point as specified in IEEE 754. It is the
same representation that Java calls Double.

The scheme is intended to preserve as much precision as possible, but it has
some significant weakness. For example, it is not able to exactly represent
common fractions such as 1/10 or 1/100. It can at best approximate them. As you
can see, with a single operation you begin accumulating noticeable error. Also,
be aware that the associative law and distributive law do not apply.

I think floating point is the wrong representation for numbers in most
applications. However, it is extremely popular, and popularity is much more
important these days than suitability or reliability. I recommend that in
applications that require exactness (for example, when working with money) scale
your values by a suitable factor (such as 100) so that all of your arithmetic
will be on whole numbers, which are exact.

See http://docs.sun.com/db/doc/800-7895/6hos0aoua?a=view

[Lee]

Re: floating point numbers question

Benedikt Wismans said:[color=blue]
>
>dear group!
>
><script language="javas cript">
>var a = 60381.11;
>var b = 1437261.58;
>var c = a + b;
>alert (c); -> 1497642.6900000 002
>
>var a = 60381.11;
>var b = 1437261.50;
>var c = a + b;
>alert (c); -> 1497642.61
>
></script>
>
>can anybody help me with this? Obviously some kind of precision
>problem, but those numbers are not big at all. Any ideas where to find
>documentatio n of internal data representation in js? Any hint is
>welcome.[/color]

http://www.jibbering.com/faq/#FAQ4_7

[Richard Cornford]

Re: floating point numbers question

"Benedikt Wismans" <benedikt.wisma ns@wiai.uni-bamberg.de> wrote in
message news:f997040e.0 309221355.214f7 ae6@posting.goo gle.com...
<snip>[color=blue]
>... . Any ideas where to find documentation of internal
>data representation in js? Any hint is welcome.[/color]

ANSI/IEEE Std 754-1985: IEEE Standard for Binary
Floating-Point Arithmetic. Institute of Electrical
and Electronic Engineers, New York (1985).

Richard.

[VK]

Re: floating point numbers question

Try this:
....
// case 1
var a = 60381.11;
var b = 1437261.58;
var c = a + b;
alert (c); //-> 1497642.6900000 002

// case 2
var a = 60381.11;
var b = 1437261.50;
var c = a + b;
alert (c); //-> 1497642.61 !

// case 3
a = 60381.11;
b = 1437261.58;
c = a + b;
alert (c); //-> 1497642.6900000 002 again!

// case 4
var d = 60381.11;
var e = 1437261.50;
var f = a + b;
alert (f); //-> 1497642.6900000 002 !
....

So it's not so much problem of floating point, but how JavaScript allocates
new variables (case 1 and 4), reinitializes existing variables (case 2, it
evidently makes some kind of auto-rounding or hell knows what), assign new
value to existing variables (case 3)

Never noticed that before... Very interesting...
Any way, if you have to work with floating numbers, make a paper sticker for
yourself:
"(0 == -0) = false"
and place it near of your screen as a reminder that all math on the computer
is approximate and it's never equal to the real value, only up to some
point. This is why for example 0 never equal -0, unless you are using
special tricks and/or libraries.


Benedikt Wismans <benedikt.wisma ns@wiai.uni-bamberg.de> wrote in message
news:f997040e.0 309221355.214f7 ae6@posting.goo gle.com...[color=blue]
> dear group!
>
> <script language="javas cript">
> var a = 60381.11;
> var b = 1437261.58;
> var c = a + b;
> alert (c); -> 1497642.6900000 002
>
> var a = 60381.11;
> var b = 1437261.50;
> var c = a + b;
> alert (c); -> 1497642.61
>
> </script>
>
> can anybody help me with this? Obviously some kind of precision
> problem, but those numbers are not big at all. Any ideas where to find
> documentation of internal data representation in js? Any hint is
> welcome.
>
>
> Benedikt[/color]

[Lasse Reichstein Nielsen]

Re: floating point numbers question

"VK" <schools_ring@y ahoo.com> writes:
[color=blue]
> // case 4
> var d = 60381.11;
> var e = 1437261.50;
> var f = a + b;[/color]

do you mean "d + e"?
[color=blue]
> So it's not so much problem of floating point,[/color]

Yes it is :).
[color=blue]
> Never noticed that before... Very interesting...
> Any way, if you have to work with floating numbers, make a paper sticker for
> yourself:
> "(0 == -0) = false"[/color]

That would be confuzing, since
alert(0 == -0)
alerts "true". But yes, they have different internal representations .
There are also several million different versions of NaN in IEEE
floating point numbers, but Javascript/ECMAScript makes them all
equal.

/L
--
Lasse Reichstein Nielsen - lrn@hotpop.com
Art D'HTML: <URL:http://www.infimum.dk/HTML/randomArtSplit. html>
'Faith without judgement merely degrades the spirit divine.'

[Dr John Stockton]

Re: floating point numbers question

JRS: In article <f997040e.03092 21355.214f7ae6@ posting.google. com>, seen
in news:comp.lang. javascript, Benedikt Wismans
<benedikt.wisma ns@wiai.uni-bamberg.de> posted at Mon, 22 Sep 2003
14:55:48 :-
[color=blue]
><script language="javas cript">
>var a = 60381.11;
>var b = 1437261.58;
>var c = a + b;
>alert (c); -> 1497642.6900000 002
>
>var a = 60381.11;
>var b = 1437261.50;
>var c = a + b;
>alert (c); -> 1497642.61
>
></script>
>
>can anybody help me with this? Obviously some kind of precision
>problem, but those numbers are not big at all. Any ideas where to find
>documentatio n of internal data representation in js? Any hint is
>welcome.[/color]

See the Mon/Fri newsgroup FAQ, and js-maths.htm on my site, among
numerous others.

--
© John Stockton, Surrey, UK. ?@merlyn.demon. co.uk Turnpike v4.00 IE 4 ©
<URL:http://jibbering.com/faq/> Jim Ley's FAQ for news:comp.lang. javascript
<URL:http://www.merlyn.demo n.co.uk/js-index.htm> JS maths, dates, sources.
<URL:http://www.merlyn.demo n.co.uk/> TP/BP/Delphi/JS/&c., FAQ topics, links.

[Dr John Stockton]

Re: floating point numbers question

JRS: In article <bko047$ojs$1@t itan.btinternet .com>, seen in
news:comp.lang. javascript, Richard Cornford
<richard@litote s.demon.co.uk> posted at Mon, 22 Sep 2003 23:20:39 :-[color=blue]
>"Benedikt Wismans" <benedikt.wisma ns@wiai.uni-bamberg.de> wrote in
>message news:f997040e.0 309221355.214f7 ae6@posting.goo gle.com...
><snip>[color=green]
>>... . Any ideas where to find documentation of internal
>>data representation in js? Any hint is welcome.[/color]
>
>ANSI/IEEE Std 754-1985: IEEE Standard for Binary
>Floating-Point Arithmetic. Institute of Electrical
>and Electronic Engineers, New York (1985).[/color]

<URL:http://www.merlyn.demo n.co.uk/js-maths.htm#Float >
<URL:http://www.merlyn.demo n.co.uk/pas-real.htm>
<URL:http://www.merlyn.demo n.co.uk/pas-type.htm>
are on-line, containing information and links.

Present javascript numbers are IEEE Doubles, and so have one sign bit,
51 magnitude bits with an additional implicit 1, and 11 exponent bits.

Any integer from 0 up to 2^53 = 9,007,199,254,7 40,992 in magnitude
should be stored exactly. The range slightly exceeds +-1.7×10^308.

--
© John Stockton, Surrey, UK. ?@merlyn.demon. co.uk Turnpike v4.00 IE 4 ©
<URL:http://jibbering.com/faq/> Jim Ley's FAQ for news:comp.lang. javascript
<URL:http://www.merlyn.demo n.co.uk/js-index.htm> JS maths, dates, sources.
<URL:http://www.merlyn.demo n.co.uk/> TP/BP/Delphi/JS/&c., FAQ topics, links.

[asdf asdf]

Re: floating point numbers question

For a simpler demonstration:

alert(2-1.1);

This is also a problem in Java and databases. Solutions include:
-doing your math using whole numbers and remembering where you want
the decimal point just for formatting
-BigInteger, BigDecimal
-Currency datatype