(minor) prolbem with JavaScript animdation fadein script

JavaScript
1

I have here a working fade out script:

function fadeOut(elem, time) {

    var startOpacity, elemId;

    elemId = document.getElementById(elem);

    startOpacity = elemId.style.opacity || 1;
    elemId.style.opacity = startOpacity;

    (function go() {
        elemId.style.opacity -= startOpacity / (time / 100);

        elemId.style.filter = 'alpha(opacity=' + elemId.style.opacity * 100 + ')';

        if (elemId.style.opacity > 0) {
            setTimeout(go, 100);
        } else {
            elemId.style.display = 'none';
        }

    })();
}

Below is the above but altered for fade in. It’s not working but I’m sure I’m almost there:

function fadeIn(elem, time) {

    var startOpacity, elemId;

    elemId = document.getElementById(elem);

    startOpacity = elemId.style.opacity || 0;
    elemId.style.opacity = startOpacity;

    (function go() {

        elemId.style.opacity += startOpacity / (time / 100);

        //elemId.style.filter = 'alpha(opacity=' + elemId.style.opacity * 100 + ')';

        if (elemId.style.opacity < 1) {
            setTimeout(go, 100);
        } else {
            elemId.style.display = 'block';
        }

    })();
}
2 
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">

<head>
  <title></title>
<script type="text/javascript">
/*<![CDATA[*/
function fadeOut(elem,time,ud) {
    var elemId = document.getElementById(elem);
    if (!elemId.zxc){
     elemId.zxc=ud?100:0;
    }
    elemId.style.display = 'block';
    clearTimeout(elemId.to);
    (function go() {
       elemId.zxc+=(ud?-1:1);
       elemId.style.opacity = elemId.zxc/100;
          elemId.style.filter = 'alpha(opacity=' + elemId.zxc + ')';
        if ((ud&&elemId.zxc >1)||(!ud&&elemId.zxc<100)) {
            elemId.to=setTimeout(go, 100);
        } else if (ud){
            elemId.style.display = 'none';
        }

    })();
}
/*]]>*/
</script></head>

<body>
<div id="tst" style="width:200px;height:200px;background-Color:red;" ></div>
<input type="button" name="" value="FadeOut" onmouseup="fadeOut('tst',1000,true);"/>
<input type="button" name="" value="FadeIn" onmouseup="fadeOut('tst',1000,false);"/>

</body>

</html>
3

thanks!