/**
 * BezierEasing - use bezier curve for transition easing function
 * by Gaëtan Renaudeau 2014 - 2015 – MIT License
 *
 * Credits: is based on Firefox's nsSMILKeySpline.cpp
 * Usage:
 * var spline = BezierEasing([ 0.25, 0.1, 0.25, 1.0 ])
 * spline.get(x) => returns the easing value | x must be in [0, 1] range
 *
 */

// These values are established by empiricism with tests (tradeoff: performance VS precision)
var NEWTON_ITERATIONS = 4;
var NEWTON_MIN_SLOPE = 0.001;
var SUBDIVISION_PRECISION = 0.0000001;
var SUBDIVISION_MAX_ITERATIONS = 10;

var kSplineTableSize = 11;
var kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);

var float32ArraySupported = typeof Float32Array === "function";

function A (aA1, aA2) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
function B (aA1, aA2) { return 3.0 * aA2 - 6.0 * aA1; }
function C (aA1)      { return 3.0 * aA1; }

// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
function calcBezier (aT, aA1, aA2) {
  return ((A(aA1, aA2)*aT + B(aA1, aA2))*aT + C(aA1))*aT;
}

// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
function getSlope (aT, aA1, aA2) {
  return 3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
}

function binarySubdivide (aX, aA, aB, mX1, mX2) {
  var currentX, currentT, i = 0;
  do {
    currentT = aA + (aB - aA) / 2.0;
    currentX = calcBezier(currentT, mX1, mX2) - aX;
    if (currentX > 0.0) {
      aB = currentT;
    } else {
      aA = currentT;
    }
  } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);
  return currentT;
}

function newtonRaphsonIterate (aX, aGuessT, mX1, mX2) {
  for (var i = 0; i < NEWTON_ITERATIONS; ++i) {
    var currentSlope = getSlope(aGuessT, mX1, mX2);
    if (currentSlope === 0.0) return aGuessT;
    var currentX = calcBezier(aGuessT, mX1, mX2) - aX;
    aGuessT -= currentX / currentSlope;
  }
  return aGuessT;
}

/**
 * points is an array of [ mX1, mY1, mX2, mY2 ]
 */
function BezierEasing (points, b, c, d) {
  if (arguments.length === 4) {
    return new BezierEasing([ points, b, c, d ]);
  }
  if (!(this instanceof BezierEasing)) return new BezierEasing(points);

  if (!points || points.length !== 4) {
    throw new Error("BezierEasing: points must contains 4 values");
  }
  for (var i=0; i<4; ++i) {
    if (typeof points[i] !== "number" || isNaN(points[i]) || !isFinite(points[i])) {
      throw new Error("BezierEasing: points should be integers.");
    }
  }
  if (points[0] < 0 || points[0] > 1 || points[2] < 0 || points[2] > 1) {
    throw new Error("BezierEasing x values must be in [0, 1] range.");
  }

  this._str = "BezierEasing("+points+")";
  this._css = "cubic-bezier("+points+")";
  this._p = points;
  this._mSampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
  this._precomputed = false;

  this.get = this.get.bind(this);
}

BezierEasing.prototype = {

  get: function (x) {
    var mX1 = this._p[0],
      mY1 = this._p[1],
      mX2 = this._p[2],
      mY2 = this._p[3];
    if (!this._precomputed) this._precompute();
    if (mX1 === mY1 && mX2 === mY2) return x; // linear
    // Because JavaScript number are imprecise, we should guarantee the extremes are right.
    if (x === 0) return 0;
    if (x === 1) return 1;
    return calcBezier(this._getTForX(x), mY1, mY2);
  },

  getPoints: function() {
    return this._p;
  },

  toString: function () {
    return this._str;
  },

  toCSS: function () {
    return this._css;
  },

  // Private part

  _precompute: function () {
    var mX1 = this._p[0],
      mY1 = this._p[1],
      mX2 = this._p[2],
      mY2 = this._p[3];
    this._precomputed = true;
    if (mX1 !== mY1 || mX2 !== mY2)
      this._calcSampleValues();
  },

  _calcSampleValues: function () {
    var mX1 = this._p[0],
      mX2 = this._p[2];
    for (var i = 0; i < kSplineTableSize; ++i) {
      this._mSampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
    }
  },

  /**
   * getTForX chose the fastest heuristic to determine the percentage value precisely from a given X projection.
   */
  _getTForX: function (aX) {
    var mX1 = this._p[0],
      mX2 = this._p[2],
      mSampleValues = this._mSampleValues;

    var intervalStart = 0.0;
    var currentSample = 1;
    var lastSample = kSplineTableSize - 1;

    for (; currentSample !== lastSample && mSampleValues[currentSample] <= aX; ++currentSample) {
      intervalStart += kSampleStepSize;
    }
    --currentSample;

    // Interpolate to provide an initial guess for t
    var dist = (aX - mSampleValues[currentSample]) / (mSampleValues[currentSample+1] - mSampleValues[currentSample]);
    var guessForT = intervalStart + dist * kSampleStepSize;

    var initialSlope = getSlope(guessForT, mX1, mX2);
    if (initialSlope >= NEWTON_MIN_SLOPE) {
      return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
    } else if (initialSlope === 0.0) {
      return guessForT;
    } else {
      return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
    }
  }
};

// CSS mapping
BezierEasing.css = {
  "ease":        BezierEasing.ease      = BezierEasing(0.25, 0.1, 0.25, 1.0),
  "linear":      BezierEasing.linear    = BezierEasing(0.00, 0.0, 1.00, 1.0),
  "ease-in":     BezierEasing.easeIn    = BezierEasing(0.42, 0.0, 1.00, 1.0),
  "ease-out":    BezierEasing.easeOut   = BezierEasing(0.00, 0.0, 0.58, 1.0),
  "ease-in-out": BezierEasing.easeInOut = BezierEasing(0.42, 0.0, 0.58, 1.0)
};