scrollTop animation without jquery

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Cross browser JavaScript (not jQuery…) scroll to top animation 18 answers

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HTML:

<button onclick="scrollToTop(1000);"></button>

1# JavaScript (linear):

function scrollToTop(scrollDuration) {
    var scrollStep = -window.scrollY / (scrollDuration / 15),
        scrollInterval = setInterval(function(){
        if ( window.scrollY != 0 ) {
            window.scrollBy( 0, scrollStep );
        }
        else clearInterval(scrollInterval); 
    },15);
}

2# JavaScript (ease in and out):

function scrollToTop(scrollDuration) {
const   scrollHeight = window.scrollY,
        scrollStep = Math.PI / ( scrollDuration / 15 ),
        cosParameter = scrollHeight / 2;
var     scrollCount = 0,
        scrollMargin,
        scrollInterval = setInterval( function() {
            if ( window.scrollY != 0 ) {
                scrollCount = scrollCount + 1;  
                scrollMargin = cosParameter - cosParameter * Math.cos( scrollCount * scrollStep );
                window.scrollTo( 0, ( scrollHeight - scrollMargin ) );
            } 
            else clearInterval(scrollInterval); 
        }, 15 );
}

Note:

Duration in milliseconds (1000ms = 1s)

Second script uses the cos function. Example curve:

Due to the high amount of up-voters, I rechecked my code I wrote a couple of years ago and tried to optimize it. Further more I added a little mathematical explanation at the bottom of my code.

UPDATE (ease in and out):

For a smoother slide/animation, done with the requestAnimationFrame method. (a little bit of stuttering happens on large windows, because the browser has to redraw a wide area)

function scrollToTop(scrollDuration) {
    var cosParameter = window.scrollY / 2,
        scrollCount = 0,
        oldTimestamp = performance.now();
    function step (newTimestamp) {
        scrollCount += Math.PI / (scrollDuration / (newTimestamp - oldTimestamp));
        if (scrollCount >= Math.PI) window.scrollTo(0, 0);
        if (window.scrollY === 0) return;
        window.scrollTo(0, Math.round(cosParameter + cosParameter * Math.cos(scrollCount)));
        oldTimestamp = newTimestamp;
        window.requestAnimationFrame(step);
    }
    window.requestAnimationFrame(step);
}
/* 
    Explanations:
    - pi is the length/end point of the cosinus intervall (see above)
    - newTimestamp indicates the current time when callbacks queued by requestAnimationFrame begin to fire.
      (for more information see https://developer.mozilla.org/en-US/docs/Web/API/window/requestAnimationFrame)
    - newTimestamp - oldTimestamp equals the duration

      a * cos (bx + c) + d                      | c translates along the x axis = 0
    = a * cos (bx) + d                          | d translates along the y axis = 1 -> only positive y values
    = a * cos (bx) + 1                          | a stretches along the y axis = cosParameter = window.scrollY / 2
    = cosParameter + cosParameter * (cos bx)    | b stretches along the x axis = scrollCount = Math.PI / (scrollDuration / (newTimestamp - oldTimestamp))
    = cosParameter + cosParameter * (cos scrollCount * x)
*/

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