クロスブラウザーのJavaScript（jQueryではない…）が一番上のアニメーションにスクロールする

function runScroll() {
  scrollTo(document.body, 0, 600);
}
var scrollme;
scrollme = document.querySelector("#scrollme");
scrollme.addEventListener("click",runScroll,false)

function scrollTo(element, to, duration) {
  if (duration <= 0) return;
  var difference = to - element.scrollTop;
  var perTick = difference / duration * 10;

  setTimeout(function() {
    element.scrollTop = element.scrollTop + perTick;
    if (element.scrollTop == to) return;
    scrollTo(element, to, duration - 10);
  }, 10);
}

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</p>
<button id=scrollme type="button">To the top</button>

// PURE JAVASCRIPT (OOP)

function Scroller(options) {
  this.options = options;
  this.button = null;
  this.stop = false;
}

Scroller.prototype.constructor = Scroller;

Scroller.prototype.createButton = function() {

  this.button = document.createElement('button');
  this.button.classList.add('scroll-button');
  this.button.classList.add('scroll-button--hidden');
  this.button.textContent = "^";
  document.body.appendChild(this.button);
}

Scroller.prototype.init = function() {
  this.createButton();
  this.checkPosition();
  this.click();
  this.stopListener();
}

Scroller.prototype.scroll = function() {
  if (this.options.animate == false || this.options.animate == "false") {
    this.scrollNoAnimate();
    return;
  }
  if (this.options.animate == "normal") {
    this.scrollAnimate();
    return;
  }
  if (this.options.animate == "linear") {
    this.scrollAnimateLinear();
    return;
  }
}
Scroller.prototype.scrollNoAnimate = function() {
  document.body.scrollTop = 0;
  document.documentElement.scrollTop = 0;
}
Scroller.prototype.scrollAnimate = function() {
  if (this.scrollTop() > 0 && this.stop == false) {
    setTimeout(function() {
      this.scrollAnimate();
      window.scrollBy(0, (-Math.abs(this.scrollTop()) / this.options.normal['steps']));
    }.bind(this), (this.options.normal['ms']));
  }
}
Scroller.prototype.scrollAnimateLinear = function() {
  if (this.scrollTop() > 0 && this.stop == false) {
    setTimeout(function() {
      this.scrollAnimateLinear();
      window.scrollBy(0, -Math.abs(this.options.linear['px']));
    }.bind(this), this.options.linear['ms']);
  }
}

Scroller.prototype.click = function() {

  this.button.addEventListener("click", function(e) {
    e.stopPropagation();
    this.scroll();
  }.bind(this), false);

  this.button.addEventListener("dblclick", function(e) {
    e.stopPropagation();
    this.scrollNoAnimate();
  }.bind(this), false);

}

Scroller.prototype.hide = function() {
  this.button.classList.add("scroll-button--hidden");
}

Scroller.prototype.show = function() {
  this.button.classList.remove("scroll-button--hidden");
}

Scroller.prototype.checkPosition = function() {
  window.addEventListener("scroll", function(e) {
    if (this.scrollTop() > this.options.showButtonAfter) {
      this.show();
    } else {
      this.hide();
    }
  }.bind(this), false);
}

Scroller.prototype.stopListener = function() {

  // stop animation on slider drag
  var position = this.scrollTop();
  window.addEventListener("scroll", function(e) {
    if (this.scrollTop() > position) {
      this.stopTimeout(200);
    } else {
      //...
    }
    position = this.scrollTop();
  }.bind(this, position), false);

  // stop animation on wheel scroll down
  window.addEventListener("wheel", function(e) {
    if (e.deltaY > 0) this.stopTimeout(200);
  }.bind(this), false);
}

Scroller.prototype.stopTimeout = function(ms) {
  this.stop = true;
  // console.log(this.stop); //
  setTimeout(function() {
    this.stop = false;
    console.log(this.stop); //
  }.bind(this), ms);
}

Scroller.prototype.scrollTop = function() {
  var curentScrollTop = document.documentElement.scrollTop || document.body.scrollTop;
  return curentScrollTop;
}



// ------------------- USE EXAMPLE ---------------------
// *Set options
var options = {
  'showButtonAfter': 200, // show button after scroling down this amount of px
  'animate': "normal", // [false|normal|linear] - for false no aditional settings are needed

  'normal': { // applys only if [animate: normal] - set scroll loop distanceLeft/steps|ms
    'steps': 20, // the more steps per loop the slower animation gets
    'ms': 10 // the less ms the quicker your animation gets
  },
  'linear': { // applys only if [animate: linear] - set scroll px|ms
    'px': 30, // the more px the quicker your animation gets
    'ms': 10 // the less ms the quicker your animation gets
  },
};
// *Create new Scroller and run it.
var scroll = new Scroller(options);
scroll.init();

/* CSS */

@import url(https://fonts.googleapis.com/css?family=Open+Sans);
 body {
  font-family: 'Open Sans', sans-serif;
  font-size: 1.2rem;
  line-height: 2rem;
  height: 100%;
  position: relative;
  padding: 0 25%;
}
.scroll-button {
  font-size: 1.2rem;
  line-height: 2rem;
  padding: 10px;
  width: 50px;
  height: 50px;
  background: black;
  color: white;
  border-radius: 50%;
  position: fixed;
  right: 20px;
  bottom: 20px;
  visibility: visible;
  filter: alpha(opacity=50);
  filter: progid: DXImageTransform.Microsoft.Alpha(Opacity=50);
  opacity: 0.5;
  cursor: pointer;
  transition: all 1.2s;
  -webkit-transition: all 1.2s;
  -moz-transition: all 1.2s;
  -ms-transition: all 1.2s;
  -o-transition: all 1.2s;
}
.scroll-button:hover {
  filter: alpha(opacity=100);
  filter: progid: DXImageTransform.Microsoft.Alpha(Opacity=100);
  opacity: 1;
}
.scroll-button--hidden {
  filter: alpha(opacity=0);
  filter: progid: DXImageTransform.Microsoft.Alpha(Opacity=0);
  opacity: 0;
  visibility: hidden;
}

<!-- HTML -->

<h1>Scroll down by 200px for button to appear</h1>
<ul>
  <li>Cross-browser</li>
  <li>Copy/Paste solution</li>
  <li>3 animate modes: <b>["normal"|"linear"|false]</b></li>
  <li>Customize your aniamtion with aveilable settings - make it snapy or fluent</li>
  <li>Double click to skip animation</li>
  <li>Every next single click adds initial speed</li>
  <li>Stop scroll animation by draging down the scroll bar</li>
  <li>Stop scroll animation by mouse wheel down</li>
  <li>Animated button fade-in-out on scroll</li>
</ul>

<br />
<br />
<pre>
// ------------------- USE EXAMPLE ---------------------
// *Set options
var options = {
  'showButtonAfter': 200, // show button after scroling down this amount of px
  'animate': "normal", // [false|normal|linear] - for false no aditional settings are needed
  
  'normal': { // applys only if [animate: normal] - set scroll loop distanceLeft/steps|ms
    'steps': 20, // the more steps the slower animation gets
    'ms': 20 // the less ms the quicker your animation gets
  }, 
  'linear': { // applys only if [animate: linear] - set scroll px|ms
    'px': 55, // the more px the quicker your animation gets
    'ms': 10 // the less ms the quicker your animation gets
  }, 
};

// *Create new Scroller and run it.
var scroll = new Scroller(options);
scroll.init();
</pre>
<br />
<br />
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<p><span>Lorem ipsum dolor sit amet, consectetur adipisicing elit. Labore qui ad assumenda placeat optio illo molestias corporis dolorum cum. Doloribus eius autem obcaecati minima, asperiores iure dignissimos ducimus suscipit dolorem.</span><span>Blanditiis earum accusamus eaque temporibus necessitatibus voluptatum dolorem enim debitis inventore assumenda quae error perspiciatis aut, nulla delectus quam ipsa sapiente ea aliquam laboriosam repudiandae. Nesciunt praesentium, beatae eos quasi!</span></p>
<p><span>Lorem ipsum dolor sit amet, consectetur adipisicing elit. Cupiditate dicta voluptate impedit? Ad voluptatum dicta earum perferendis asperiores. Dolore distinctio modi expedita consequatur provident perspiciatis neque totam rerum placeat quas.</span><span>Eveniet optio est possimus iste accusantium ipsum illum. Maiores saepe repudiandae facere, delectus iure dolorem vitae nihil pariatur minima, reprehenderit eligendi dolore impedit, nisi doloribus quidem similique. Optio, delectus, minus.</span></p>
<p><span>Lorem ipsum dolor sit amet, consectetur adipisicing elit. Iste ex molestiae architecto enim nihil tempore, atque consequuntur doloribus recusandae sed consequatur veniam quos, in consectetur perspiciatis magni nostrum ab voluptates.</span><span>Nisi quos mollitia quis in maiores asperiores labore deserunt! Voluptate voluptas adipisci qui hic officia molestias, laborum necessitatibus sint nam vel minus incidunt perspiciatis recusandae sunt, rerum suscipit doloremque possimus!</span></p>
<p><span>Lorem ipsum dolor sit amet, consectetur adipisicing elit. At nihil perferendis quae quidem facilis aliquid pariatur possimus hic asperiores, recusandae exercitationem adipisci atque laborum, delectus, odit ab reprehenderit distinctio dolor.</span><span>Non excepturi quos aspernatur repudiandae laboriosam, unde molestias, totam, sapiente harum accusamus delectus laborum ipsam velit amet nisi! Consectetur aliquam provident voluptatibus saepe repudiandae eveniet laborum beatae, animi, voluptate dolores.</span></p>
<p><span>Lorem ipsum dolor sit amet, consectetur adipisicing elit. Cumque magni, eum ipsa, veritatis facere voluptatem dolorum nobis neque minus debitis asperiores iste. Pariatur sequi quam, tempora. Dignissimos, esse similique tempora.</span><span>Ex delectus excepturi autem sunt, nemo repudiandae, recusandae nostrum accusantium nobis temporibus magnam eligendi similique veritatis deleniti, eaque blanditiis possimus at! Repellat alias laboriosam ipsum commodi dolorem, corporis dolore suscipit!</span></p>

function scroll(pxPerFrame, duration) {
        if (!pxPerFrame || !duration) return;
        const end = new Date().getTime() + duration;
        step(); 

        function step() {
          window.scrollBy(0, pxPerFrame);
          if (new Date().getTime() < end) {
            window.setTimeout(step, 1000 / 60);
          } else {
            console.log('done scrolling'); 
          }
        }
      }

body {
  width: 200px;
}

<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.</p>
<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.</p>
<p>
<button onclick="scroll(-5, 3000)">
scroll(-5, 3000)
</button>
</p>