Test if page has a horizontal scrollbar (computer & mobile devices)

On a web page, I need to test if there is a horizontal scrollbar or not (so that I programmatically change the css of some other element). Is there some way to get that information using jquery (or pure javascript)?

I tested

function isHorizontalScrollbarEnabled() {
    return $(document).width()!=$(window).width();
}

but it does not seem to work with all browsers (does not work for example with a recent Samsung phone I tested). I need it to work with all browsers, including recent mobile devices.

Thank you!

EDIT 1

I tested the solutions provided by plalx and laconbass, tested IE8, Firefox, Chrome and iPad. Works with IE, Firefox & Chrome but not as I want on the iPad.

The problem seems related to the zooming feature on mobile devices: even though, when I zoom in on the iPad, a horizontal scrollbar appears, document, window and document.body widths do not change (was also the same problem with the Samsung phone I tested earlier today).

Here is the code I used to test:

<!DOCTYPE html>
<html lang="en">
    <head>
      <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8/jquery.min.js"></script>
      <title>test</title>
    </head>

    <body>
      <div style="width: 500px; background: red;" id="test">click here to test</div>
      <script type="text/javascript">
        var i = 1;
        $("#test").click(function(){
          $(this).html("Test #" + (i++) 
    + "<br>document width=" + $(document).width() + ", windows width=" + $(window).width()
    + "<br>document width=" + $(document).width() + ", body width=" + $(document.body).width()
          );  
        });     
      </script>
    </body>
</html>

Any idea how to detect the presence of a horizontal scrollbar that also works after zooming in/out on a mobile device like iPad?

//scrol 1px to the left
$(document).scrollLeft(1);

if($(document).scrollLeft() != 0){
   //there's a scroll bar
}else{
   //there's no scrollbar
}

//scroll back to original location
$(document).scrollLeft(0);

This works because JQuery won't be able to scroll the screen if no scrollbar is available

EDIT 2: I got a downvote because this doesn't work for nothing but the page so I built a generic solution based on @Pabs123's answer, only for fun:

function hasScrollX( selector ){
    var e = $(selector), fn = 'scrollLeft';
    return e[fn](1) && e[fn]() > 0 && e[fn](0) && true;
}

or even

jQuery.fn.hasScrollX = function( ){
    var fn = 'scrollLeft';
    return this[fn](1) && this[fn]() > 0 && this[fn](0) && true;
}

See it here, and how it can be easily adapted to detect vertical scrollbar presence.

EDIT: Tested & working on chrome and firefox. As jQuery team does the crossbrowsing work, i suggest the use of jQuery rather than native javascript.

I were curious about how to do this in an elegant way than the suggested previously (which actually work)

The following comparison work to me