PROJECT MOVED TO NEW ADDRESS: https://github.com/galambalazs/smoothscroll-for-websites

SmoothScroll.js

IMPORTANT

Please duplicate this radar for a Safari fix! 
This will clean up a 50-line workaround.

  rdar://22376037 (https://openradar.appspot.com/radar?id=4965070979203072)

//////////////////////////////////////////////////////////////////////////////

(Now available as a standalone repo.)

//////////////////////////////////////////////////////////////////////////////

UPDATE: THIS PROJECT MOVED TO A NEW ADDRESS:

https://github.com/galambalazs/smoothscroll-for-websites

//////////////////////////////////////////////////////////////////////////////

UPDATE: THIS PROJECT MOVED TO A NEW ADDRESS:

https://github.com/galambalazs/smoothscroll-for-websites

//////////////////////////////////////////////////////////////////////////////

UPDATE: THIS PROJECT MOVED TO A NEW ADDRESS:

https://github.com/galambalazs/smoothscroll-for-websites

//////////////////////////////////////////////////////////////////////////////


//
// I'll leave the old code below for historical purposes. 
// But this gist will no longer be updated.
// For the up-to-date version, use the link above!
//


//
// SmoothScroll for websites v1.3.8 (Balazs Galambosi)
// http://www.smoothscroll.net/
//
// Licensed under the terms of the MIT license.
//
// You may use it in your theme if you credit me. 
// It is also free to use on any individual website.
//
// Exception:
// The only restriction would be not to publish any  
// extension for browsers or native application
// without getting a written permission first.
//

(function () {
  
// Scroll Variables (tweakable)
var defaultOptions = {

    // Scrolling Core
    frameRate        : 150, // [Hz]
    animationTime    : 400, // [ms]
    stepSize         : 120, // [px]

    // Pulse (less tweakable)
    // ratio of "tail" to "acceleration"
    pulseAlgorithm   : true,
    pulseScale       : 4,
    pulseNormalize   : 1,

    // Acceleration
    accelerationDelta : 20,  // 20
    accelerationMax   : 1,   // 1

    // Keyboard Settings
    keyboardSupport   : true,  // option
    arrowScroll       : 50,     // [px]

    // Other
    touchpadSupport   : true,
    fixedBackground   : true, 
    excluded          : ''    
};

var options = defaultOptions;


// Other Variables
var isExcluded = false;
var isFrame = false;
var direction = { x: 0, y: 0 };
var initDone  = false;
var root = document.documentElement;
var activeElement;
var observer;
var deltaBuffer = [];
var isMac = /^Mac/.test(navigator.platform);

var key = { left: 37, up: 38, right: 39, down: 40, spacebar: 32, 
            pageup: 33, pagedown: 34, end: 35, home: 36 };


/***********************************************
 * SETTINGS
 ***********************************************/

var options = defaultOptions;


/***********************************************
 * INITIALIZE
 ***********************************************/

/**
 * Tests if smooth scrolling is allowed. Shuts down everything if not.
 */
function initTest() {
    if (options.keyboardSupport) {
        addEvent('keydown', keydown);
    }
}

/**
 * Sets up scrolls array, determines if frames are involved.
 */
function init() {
  
    if (initDone || !document.body) return;

    initDone = true;

    var body = document.body;
    var html = document.documentElement;
    var windowHeight = window.innerHeight; 
    var scrollHeight = body.scrollHeight;
    
    // check compat mode for root element
    root = (document.compatMode.indexOf('CSS') >= 0) ? html : body;
    activeElement = body;
    
    initTest();

    // Checks if this script is running in a frame
    if (top != self) {
        isFrame = true;
    }

    /**
     * This fixes a bug where the areas left and right to 
     * the content does not trigger the onmousewheel event
     * on some pages. e.g.: html, body { height: 100% }
     */
    else if (scrollHeight > windowHeight &&
            (body.offsetHeight <= windowHeight || 
             html.offsetHeight <= windowHeight)) {

        var fullPageElem = document.createElement('div');
        fullPageElem.style.cssText = 'position:absolute; z-index:-10000; ' +
                                     'top:0; left:0; right:0; height:' + 
                                      root.scrollHeight + 'px';
        document.body.appendChild(fullPageElem);
        
        // DOM changed (throttled) to fix height
        var pendingRefresh;
        var refresh = function () {
            if (pendingRefresh) return; // could also be: clearTimeout(pendingRefresh);
            pendingRefresh = setTimeout(function () {
                if (isExcluded) return; // could be running after cleanup
                fullPageElem.style.height = '0';
                fullPageElem.style.height = root.scrollHeight + 'px';
                pendingRefresh = null;
            }, 500); // act rarely to stay fast
        };
  
        setTimeout(refresh, 10);

        // TODO: attributeFilter?
        var config = {
            attributes: true, 
            childList: true, 
            characterData: false 
            // subtree: true
        };

        observer = new MutationObserver(refresh);
        observer.observe(body, config);

        if (root.offsetHeight <= windowHeight) {
            var clearfix = document.createElement('div');   
            clearfix.style.clear = 'both';
            body.appendChild(clearfix);
        }
    }

    // disable fixed background
    if (!options.fixedBackground && !isExcluded) {
        body.style.backgroundAttachment = 'scroll';
        html.style.backgroundAttachment = 'scroll';
    }
}

/**
 * Removes event listeners and other traces left on the page.
 */
function cleanup() {
    observer && observer.disconnect();
    removeEvent(wheelEvent, wheel);
    removeEvent('mousedown', mousedown);
    removeEvent('keydown', keydown);
}


/************************************************
 * SCROLLING 
 ************************************************/
 
var que = [];
var pending = false;
var lastScroll = Date.now();

/**
 * Pushes scroll actions to the scrolling queue.
 */
function scrollArray(elem, left, top) {
    
    directionCheck(left, top);

    if (options.accelerationMax != 1) {
        var now = Date.now();
        var elapsed = now - lastScroll;
        if (elapsed < options.accelerationDelta) {
            var factor = (1 + (50 / elapsed)) / 2;
            if (factor > 1) {
                factor = Math.min(factor, options.accelerationMax);
                left *= factor;
                top  *= factor;
            }
        }
        lastScroll = Date.now();
    }          
    
    // push a scroll command
    que.push({
        x: left, 
        y: top, 
        lastX: (left < 0) ? 0.99 : -0.99,
        lastY: (top  < 0) ? 0.99 : -0.99, 
        start: Date.now()
    });
        
    // don't act if there's a pending queue
    if (pending) {
        return;
    }  

    var scrollWindow = (elem === document.body);
    
    var step = function (time) {
        
        var now = Date.now();
        var scrollX = 0;
        var scrollY = 0; 
    
        for (var i = 0; i < que.length; i++) {
            
            var item = que[i];
            var elapsed  = now - item.start;
            var finished = (elapsed >= options.animationTime);
            
            // scroll position: [0, 1]
            var position = (finished) ? 1 : elapsed / options.animationTime;
            
            // easing [optional]
            if (options.pulseAlgorithm) {
                position = pulse(position);
            }
            
            // only need the difference
            var x = (item.x * position - item.lastX) >> 0;
            var y = (item.y * position - item.lastY) >> 0;
            
            // add this to the total scrolling
            scrollX += x;
            scrollY += y;            
            
            // update last values
            item.lastX += x;
            item.lastY += y;
        
            // delete and step back if it's over
            if (finished) {
                que.splice(i, 1); i--;
            }           
        }

        // scroll left and top
        if (scrollWindow) {
            window.scrollBy(scrollX, scrollY);
        } 
        else {
            if (scrollX) elem.scrollLeft += scrollX;
            if (scrollY) elem.scrollTop  += scrollY;                    
        }
        
        // clean up if there's nothing left to do
        if (!left && !top) {
            que = [];
        }
        
        if (que.length) { 
            requestFrame(step, elem, (1000 / options.frameRate + 1)); 
        } else { 
            pending = false;
        }
    };
    
    // start a new queue of actions
    requestFrame(step, elem, 0);
    pending = true;
}


/***********************************************
 * EVENTS
 ***********************************************/

/**
 * Mouse wheel handler.
 * @param {Object} event
 */
function wheel(event) {

    if (!initDone) {
        init();
    }
    
    var target = event.target;
    var overflowing = overflowingAncestor(target);

    // use default if there's no overflowing
    // element or default action is prevented   
    // or it's a zooming event with CTRL 
    if (!overflowing || event.defaultPrevented || event.ctrlKey) {
        return true;
    }
    
    // leave embedded content alone (flash & pdf)
    if (isNodeName(activeElement, 'embed') || 
       (isNodeName(target, 'embed') && /\.pdf/i.test(target.src)) ||
       isNodeName(activeElement, 'object')) {
        return true;
    }

    var deltaX = -event.wheelDeltaX || event.deltaX || 0;
    var deltaY = -event.wheelDeltaY || event.deltaY || 0;
    
    if (isMac) {
        if (event.wheelDeltaX && isDivisible(event.wheelDeltaX, 120)) {
            deltaX = -120 * (event.wheelDeltaX / Math.abs(event.wheelDeltaX));
        }
        if (event.wheelDeltaY && isDivisible(event.wheelDeltaY, 120)) {
            deltaY = -120 * (event.wheelDeltaY / Math.abs(event.wheelDeltaY));
        }
    }
    
    // use wheelDelta if deltaX/Y is not available
    if (!deltaX && !deltaY) {
        deltaY = -event.wheelDelta || 0;
    }

    // line based scrolling (Firefox mostly)
    if (event.deltaMode === 1) {
        deltaX *= 40;
        deltaY *= 40;
    }
    
    // check if it's a touchpad scroll that should be ignored
    if (!options.touchpadSupport && isTouchpad(deltaY)) {
        return true;
    }

    // scale by step size
    // delta is 120 most of the time
    // synaptics seems to send 1 sometimes
    if (Math.abs(deltaX) > 1.2) {
        deltaX *= options.stepSize / 120;
    }
    if (Math.abs(deltaY) > 1.2) {
        deltaY *= options.stepSize / 120;
    }
    
    scrollArray(overflowing, deltaX, deltaY);
    event.preventDefault();
    scheduleClearCache();
}

/**
 * Keydown event handler.
 * @param {Object} event
 */
function keydown(event) {

    var target   = event.target;
    var modifier = event.ctrlKey || event.altKey || event.metaKey || 
                  (event.shiftKey && event.keyCode !== key.spacebar);
    
    // our own tracked active element could've been removed from the DOM
    if (!document.contains(activeElement)) {
        activeElement = document.activeElement;
    }

    // do nothing if user is editing text
    // or using a modifier key (except shift)
    // or in a dropdown
    // or inside interactive elements
    var inputNodeNames = /^(textarea|select|embed|object)$/i;
    var buttonTypes = /^(button|submit|radio|checkbox|file|color|image)$/i;
    if ( inputNodeNames.test(target.nodeName) ||
         isNodeName(target, 'input') && !buttonTypes.test(target.type) ||
         isNodeName(activeElement, 'video') ||
         isInsideYoutubeVideo(event) ||
         target.isContentEditable || 
         event.defaultPrevented   ||
         modifier ) {
      return true;
    }
    
    // spacebar should trigger button press
    if ((isNodeName(target, 'button') ||
         isNodeName(target, 'input') && buttonTypes.test(target.type)) &&
        event.keyCode === key.spacebar) {
      return true;
    }
    
    var shift, x = 0, y = 0;
    var elem = overflowingAncestor(activeElement);
    var clientHeight = elem.clientHeight;

    if (elem == document.body) {
        clientHeight = window.innerHeight;
    }

    switch (event.keyCode) {
        case key.up:
            y = -options.arrowScroll;
            break;
        case key.down:
            y = options.arrowScroll;
            break;         
        case key.spacebar: // (+ shift)
            shift = event.shiftKey ? 1 : -1;
            y = -shift * clientHeight * 0.9;
            break;
        case key.pageup:
            y = -clientHeight * 0.9;
            break;
        case key.pagedown:
            y = clientHeight * 0.9;
            break;
        case key.home:
            y = -elem.scrollTop;
            break;
        case key.end:
            var damt = elem.scrollHeight - elem.scrollTop - clientHeight;
            y = (damt > 0) ? damt+10 : 0;
            break;
        case key.left:
            x = -options.arrowScroll;
            break;
        case key.right:
            x = options.arrowScroll;
            break;            
        default:
            return true; // a key we don't care about
    }

    scrollArray(elem, x, y);
    event.preventDefault();
    scheduleClearCache();
}

/**
 * Mousedown event only for updating activeElement
 */
function mousedown(event) {
    activeElement = event.target;
}


/***********************************************
 * OVERFLOW
 ***********************************************/

var uniqueID = (function () {
    var i = 0;
    return function (el) {
        return el.uniqueID || (el.uniqueID = i++);
    };
})();

var cache = {}; // cleared out after a scrolling session
var clearCacheTimer;

//setInterval(function () { cache = {}; }, 10 * 1000);

function scheduleClearCache() {
    clearTimeout(clearCacheTimer);
    clearCacheTimer = setInterval(function () { cache = {}; }, 1*1000);
}

function setCache(elems, overflowing) {
    for (var i = elems.length; i--;)
        cache[uniqueID(elems[i])] = overflowing;
    return overflowing;
}

//  (body)                (root)
//         | hidden | visible | scroll |  auto  |
// hidden  |   no   |    no   |   YES  |   YES  |
// visible |   no   |   YES   |   YES  |   YES  |
// scroll  |   no   |   YES   |   YES  |   YES  |
// auto    |   no   |   YES   |   YES  |   YES  |

function overflowingAncestor(el) {
    var elems = [];
    var body = document.body;
    var rootScrollHeight = root.scrollHeight;
    do {
        var cached = cache[uniqueID(el)];
        if (cached) {
            return setCache(elems, cached);
        }
        elems.push(el);
        if (rootScrollHeight === el.scrollHeight) {
            var topOverflowsNotHidden = overflowNotHidden(root) && overflowNotHidden(body);
            var isOverflowCSS = topOverflowsNotHidden || overflowAutoOrScroll(root);
            if (isFrame && isContentOverflowing(root) || 
               !isFrame && isOverflowCSS) {
                return setCache(elems, getScrollRoot()); 
            }
        } else if (isContentOverflowing(el) && overflowAutoOrScroll(el)) {
            return setCache(elems, el);
        }
    } while (el = el.parentElement);
}

function isContentOverflowing(el) {
    return (el.clientHeight + 10 < el.scrollHeight);
}

// typically for <body> and <html>
function overflowNotHidden(el) {
    var overflow = getComputedStyle(el, '').getPropertyValue('overflow-y');
    return (overflow !== 'hidden');
}

// for all other elements
function overflowAutoOrScroll(el) {
    var overflow = getComputedStyle(el, '').getPropertyValue('overflow-y');
    return (overflow === 'scroll' || overflow === 'auto');
}


/***********************************************
 * HELPERS
 ***********************************************/

function addEvent(type, fn) {
    window.addEventListener(type, fn, false);
}

function removeEvent(type, fn) {
    window.removeEventListener(type, fn, false);  
}

function isNodeName(el, tag) {
    return (el.nodeName||'').toLowerCase() === tag.toLowerCase();
}

function directionCheck(x, y) {
    x = (x > 0) ? 1 : -1;
    y = (y > 0) ? 1 : -1;
    if (direction.x !== x || direction.y !== y) {
        direction.x = x;
        direction.y = y;
        que = [];
        lastScroll = 0;
    }
}

var deltaBufferTimer;

if (window.localStorage && localStorage.SS_deltaBuffer) {
    deltaBuffer = localStorage.SS_deltaBuffer.split(',');
}

function isTouchpad(deltaY) {
    if (!deltaY) return;
    if (!deltaBuffer.length) {
        deltaBuffer = [deltaY, deltaY, deltaY];
    }
    deltaY = Math.abs(deltaY)
    deltaBuffer.push(deltaY);
    deltaBuffer.shift();
    clearTimeout(deltaBufferTimer);
    deltaBufferTimer = setTimeout(function () {
        if (window.localStorage) {
            localStorage.SS_deltaBuffer = deltaBuffer.join(',');
        }
    }, 1000);
    return !allDeltasDivisableBy(120) && !allDeltasDivisableBy(100);
} 

function isDivisible(n, divisor) {
    return (Math.floor(n / divisor) == n / divisor);
}

function allDeltasDivisableBy(divisor) {
    return (isDivisible(deltaBuffer[0], divisor) &&
            isDivisible(deltaBuffer[1], divisor) &&
            isDivisible(deltaBuffer[2], divisor));
}

function isInsideYoutubeVideo(event) {
    var elem = event.target;
    var isControl = false;
    if (document.URL.indexOf ('www.youtube.com/watch') != -1) {
        do {
            isControl = (elem.classList && 
                         elem.classList.contains('html5-video-controls'));
            if (isControl) break;
        } while (elem = elem.parentNode);
    }
    return isControl;
}

var requestFrame = (function () {
      return (window.requestAnimationFrame       || 
              window.webkitRequestAnimationFrame || 
              window.mozRequestAnimationFrame    ||
              function (callback, element, delay) {
                 window.setTimeout(callback, delay || (1000/60));
             });
})();

var MutationObserver = (window.MutationObserver || 
                        window.WebKitMutationObserver ||
                        window.MozMutationObserver);  

var getScrollRoot = (function() {
  var SCROLL_ROOT;
  return function() {
    if (!SCROLL_ROOT) {
      var dummy = document.createElement('div');
      dummy.style.cssText = 'height:10000px;width:1px;';
      document.body.appendChild(dummy);
      var bodyScrollTop  = document.body.scrollTop;
      var docElScrollTop = document.documentElement.scrollTop;
      window.scrollBy(0, 1);
      if (document.body.scrollTop != bodyScrollTop)
        (SCROLL_ROOT = document.body);
      else 
        (SCROLL_ROOT = document.documentElement);
      window.scrollBy(0, -1);
      document.body.removeChild(dummy);
    }
    return SCROLL_ROOT;
  };
})();


/***********************************************
 * PULSE (by Michael Herf)
 ***********************************************/
 
/**
 * Viscous fluid with a pulse for part and decay for the rest.
 * - Applies a fixed force over an interval (a damped acceleration), and
 * - Lets the exponential bleed away the velocity over a longer interval
 * - Michael Herf, http://stereopsis.com/stopping/
 */
function pulse_(x) {
    var val, start, expx;
    // test
    x = x * options.pulseScale;
    if (x < 1) { // acceleartion
        val = x - (1 - Math.exp(-x));
    } else {     // tail
        // the previous animation ended here:
        start = Math.exp(-1);
        // simple viscous drag
        x -= 1;
        expx = 1 - Math.exp(-x);
        val = start + (expx * (1 - start));
    }
    return val * options.pulseNormalize;
}

function pulse(x) {
    if (x >= 1) return 1;
    if (x <= 0) return 0;

    if (options.pulseNormalize == 1) {
        options.pulseNormalize /= pulse_(1);
    }
    return pulse_(x);
}

var wheelEvent;
if ('onwheel' in document.createElement('div'))
    wheelEvent = 'wheel';
else if ('onmousewheel' in document.createElement('div'))
    wheelEvent = 'mousewheel';

if (wheelEvent) {
    addEvent(wheelEvent, wheel);
    addEvent('mousedown', mousedown);
    addEvent('load', init);
}

})();

PROJECT MOVED TO NEW ADDRESS: https://github.com/galambalazs/smoothscroll-for-websites

please post your issues here: https://github.com/galambalazs/smoothscroll-for-websites/issues

Thank you so for this,
It helped lot to me ,

will it works for smart phones or small screen devices ?

Regards!