    /*! decimal.js-light v2.3.0 https://github.com/MikeMcl/decimal.js-light/LICENCE */
    ;(function (globalScope) {
      'use strict';

      /*
       *  decimal.js-light v2.3.0
       *  An arbitrary-precision Decimal type for JavaScript.
       *  https://github.com/MikeMcl/decimal.js-light
       *  Copyright (c) 2017 Michael Mclaughlin <M8ch88l@gmail.com>
       *  MIT Expat Licence
       */

      // -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //

        // The limit on the value of `precision`, and on the value of the first argument to
        // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
      var MAX_DIGITS = 1e9,                        // 0 to 1e9

        // The initial configuration properties of the Decimal constructor.
        Decimal = {

          // These values must be integers within the stated ranges (inclusive).
          // Most of these values can be changed during run-time using `Decimal.config`.

          // The maximum number of significant digits of the result of a calculation or base conversion.
          // E.g. `Decimal.config({ precision: 20 });`
          precision: 20,                         // 1 to MAX_DIGITS

          // The rounding mode used by default by `toInteger`, `toDecimalPlaces`, `toExponential`,
          // `toFixed`, `toPrecision` and `toSignificantDigits`.
          //
          // ROUND_UP         0 Away from zero.
          // ROUND_DOWN       1 Towards zero.
          // ROUND_CEIL       2 Towards +Infinity.
          // ROUND_FLOOR      3 Towards -Infinity.
          // ROUND_HALF_UP    4 Towards nearest neighbour. If equidistant, up.
          // ROUND_HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
          // ROUND_HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
          // ROUND_HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
          // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
          //
          // E.g.
          // `Decimal.rounding = 4;`
          // `Decimal.rounding = Decimal.ROUND_HALF_UP;`
          rounding: 4,                           // 0 to 8

          // The exponent value at and beneath which `toString` returns exponential notation.
          // JavaScript numbers: -7
          toExpNeg: -7,                          // 0 to -MAX_E

          // The exponent value at and above which `toString` returns exponential notation.
          // JavaScript numbers: 21
          toExpPos:  21,                         // 0 to MAX_E

          // The natural logarithm of 10.
          // 115 digits
          LN10: '2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298341967784042286'
        },

      // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //

        external = true,

        decimalError = '[DecimalError] ',
        invalidArgument = decimalError + 'Invalid argument: ',
        exponentOutOfRange = decimalError + 'Exponent out of range: ',

        mathfloor = Math.floor,
        mathpow = Math.pow,

        isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,

        ONE,
        BASE = 1e7,
        LOG_BASE = 7,
        MAX_SAFE_INTEGER = 9007199254740991,
        MAX_E = mathfloor(MAX_SAFE_INTEGER / LOG_BASE),    // 1286742750677284

        // Decimal.prototype object
        P = {};

      // Decimal prototype methods

      /*
       *  absoluteValue                       abs
       *  comparedTo                          cmp
       *  decimalPlaces                       dp
       *  dividedBy                           div
       *  dividedToIntegerBy                  idiv
       *  equals                              eq
       *  exponent
       *  greaterThan                         gt
       *  greaterThanOrEqualTo                gte
       *  isInteger                           isint
       *  isNegative                          isneg
       *  isPositive                          ispos
       *  isZero
       *  lessThan                            lt
       *  lessThanOrEqualTo                   lte
       *  logarithm                           log
       *  minus                               sub
       *  modulo                              mod
       *  naturalExponential                  exp
       *  naturalLogarithm                    ln
       *  negated                             neg
       *  plus                                add
       *  precision                           sd
       *  squareRoot                          sqrt
       *  times                               mul
       *  toDecimalPlaces                     todp
       *  toExponential
       *  toFixed
       *  toInteger                           toint
       *  toNumber
       *  toPower                             pow
       *  toPrecision
       *  toSignificantDigits                 tosd
       *  toString
       *  valueOf                             val
       */

      /*
       * Return a new Decimal whose value is the absolute value of this Decimal.
       *
       */
      P.absoluteValue = P.abs = function () {
        var x = new this.constructor(this);
        if (x.s) x.s = 1;
        return x;
      };

      /*
       * Return
       *   1    if the value of this Decimal is greater than the value of `y`,
       *  -1    if the value of this Decimal is less than the value of `y`,
       *   0    if they have the same value
       *
       */
      P.comparedTo = P.cmp = function (y) {
        var i, j, xdL, ydL,
          x = this;

        y = new x.constructor(y);

        // Signs differ?
        if (x.s !== y.s) return x.s || -y.s;

        // Compare exponents.
        if (x.e !== y.e) return x.e > y.e ^ x.s < 0 ? 1 : -1;

        xdL = x.d.length;
        ydL = y.d.length;

        // Compare digit by digit.
        for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
          if (x.d[i] !== y.d[i]) return x.d[i] > y.d[i] ^ x.s < 0 ? 1 : -1;
        }

        // Compare lengths.
        return xdL === ydL ? 0 : xdL > ydL ^ x.s < 0 ? 1 : -1;
      };

      /*
       * Return the number of decimal places of the value of this Decimal.
       *
       */
      P.decimalPlaces = P.dp = function () {
        var x = this,
          w = x.d.length - 1,
          dp = (w - x.e) * LOG_BASE;

        // Subtract the number of trailing zeros of the last word.
        w = x.d[w];
        if (w) for (; w % 10 == 0; w /= 10) dp--;

        return dp < 0 ? 0 : dp;
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal divided by `y`, truncated to
       * `precision` significant digits.
       *
       */
      P.dividedBy = P.div = function (y) {
        return divide(this, new this.constructor(y));
      };

      /*
       * Return a new Decimal whose value is the integer part of dividing the value of this Decimal
       * by the value of `y`, truncated to `precision` significant digits.
       *
       */
      P.dividedToIntegerBy = P.idiv = function (y) {
        var x = this,
          Ctor = x.constructor;
        return round(divide(x, new Ctor(y), 0, 1), Ctor.precision);
      };

      /*
       * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
       *
       */
      P.equals = P.eq = function (y) {
        return !this.cmp(y);
      };

      /*
       * Return the (base 10) exponent value of this Decimal (this.e is the base 10000000 exponent).
       *
       */
      P.exponent = function () {
        return getBase10Exponent(this);
      };

      /*
       * Return true if the value of this Decimal is greater than the value of `y`, otherwise return
       * false.
       *
       */
      P.greaterThan = P.gt = function (y) {
        return this.cmp(y) > 0;
      };

      /*
       * Return true if the value of this Decimal is greater than or equal to the value of `y`,
       * otherwise return false.
       *
       */
      P.greaterThanOrEqualTo = P.gte = function (y) {
        return this.cmp(y) >= 0;
      };

      /*
       * Return true if the value of this Decimal is an integer, otherwise return false.
       *
       */
      P.isInteger = P.isint = function () {
        return this.e > this.d.length - 2;
      };

      /*
       * Return true if the value of this Decimal is negative, otherwise return false.
       *
       */
      P.isNegative = P.isneg = function () {
        return this.s < 0;
      };

      /*
       * Return true if the value of this Decimal is positive, otherwise return false.
       *
       */
      P.isPositive = P.ispos = function () {
        return this.s > 0;
      };

      /*
       * Return true if the value of this Decimal is 0, otherwise return false.
       *
       */
      P.isZero = function () {
        return this.s === 0;
      };

      /*
       * Return true if the value of this Decimal is less than `y`, otherwise return false.
       *
       */
      P.lessThan = P.lt = function (y) {
        return this.cmp(y) < 0;
      };

      /*
       * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
       *
       */
      P.lessThanOrEqualTo = P.lte = function (y) {
        return this.cmp(y) < 1;
      };

      /*
       * Return the logarithm of the value of this Decimal to the specified base, truncated to
       * `precision` significant digits.
       *
       * If no base is specified, return log[10](x).
       *
       * log[base](x) = ln(x) / ln(base)
       *
       * The maximum error of the result is 1 ulp (unit in the last place).
       *
       * [base] {number|string|Decimal} The base of the logarithm.
       *
       */
      P.logarithm = P.log = function (base) {
        var r,
          x = this,
          Ctor = x.constructor,
          pr = Ctor.precision,
          wpr = pr + 5;

        // Default base is 10.
        if (base === void 0) {
          base = new Ctor(10);
        } else {
          base = new Ctor(base);

          // log[-b](x) = NaN
          // log[0](x)  = NaN
          // log[1](x)  = NaN
          if (base.s < 1 || base.eq(ONE)) throw Error(decimalError + 'NaN');
        }

        // log[b](-x) = NaN
        // log[b](0) = -Infinity
        if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));

        // log[b](1) = 0
        if (x.eq(ONE)) return new Ctor(0);

        external = false;
        r = divide(ln(x, wpr), ln(base, wpr), wpr);
        external = true;

        return round(r, pr);
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal minus `y`, truncated to
       * `precision` significant digits.
       *
       */
      P.minus = P.sub = function (y) {
        var x = this;
        y = new x.constructor(y);
        return x.s == y.s ? subtract(x, y) : add(x, (y.s = -y.s, y));
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal modulo `y`, truncated to
       * `precision` significant digits.
       *
       */
      P.modulo = P.mod = function (y) {
        var q,
          x = this,
          Ctor = x.constructor,
          pr = Ctor.precision;

        y = new Ctor(y);

        // x % 0 = NaN
        if (!y.s) throw Error(decimalError + 'NaN');

        // Return x if x is 0.
        if (!x.s) return round(new Ctor(x), pr);

        // Prevent rounding of intermediate calculations.
        external = false;
        q = divide(x, y, 0, 1).times(y);
        external = true;

        return x.minus(q);
      };

      /*
       * Return a new Decimal whose value is the natural exponential of the value of this Decimal,
       * i.e. the base e raised to the power the value of this Decimal, truncated to `precision`
       * significant digits.
       *
       */
      P.naturalExponential = P.exp = function () {
        return exp(this);
      };

      /*
       * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
       * truncated to `precision` significant digits.
       *
       */
      P.naturalLogarithm = P.ln = function () {
        return ln(this);
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
       * -1.
       *
       */
      P.negated = P.neg = function () {
        var x = new this.constructor(this);
        x.s = -x.s || 0;
        return x;
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal plus `y`, truncated to
       * `precision` significant digits.
       *
       */
      P.plus = P.add = function (y) {
        var x = this;
        y = new x.constructor(y);
        return x.s == y.s ? add(x, y) : subtract(x, (y.s = -y.s, y));
      };

      /*
       * Return the number of significant digits of the value of this Decimal.
       *
       * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
       *
       */
      P.precision = P.sd = function (z) {
        var e, sd, w,
          x = this;

        if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);

        e = getBase10Exponent(x) + 1;
        w = x.d.length - 1;
        sd = w * LOG_BASE + 1;
        w = x.d[w];

        // If non-zero...
        if (w) {

          // Subtract the number of trailing zeros of the last word.
          for (; w % 10 == 0; w /= 10) sd--;

          // Add the number of digits of the first word.
          for (w = x.d[0]; w >= 10; w /= 10) sd++;
        }

        return z && e > sd ? e : sd;
      };

      /*
       * Return a new Decimal whose value is the square root of this Decimal, truncated to `precision`
       * significant digits.
       *
       */
      P.squareRoot = P.sqrt = function () {
        var e, n, pr, r, s, t, wpr,
          x = this,
          Ctor = x.constructor;

        // Negative or zero?
        if (x.s < 1) {
          if (!x.s) return new Ctor(0);

          // sqrt(-x) = NaN
          throw Error(decimalError + 'NaN');
        }

        e = getBase10Exponent(x);
        external = false;

        // Initial estimate.
        s = Math.sqrt(+x);

        // Math.sqrt underflow/overflow?
        // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
        if (s == 0 || s == 1 / 0) {
          n = digitsToString(x.d);
          if ((n.length + e) % 2 == 0) n += '0';
          s = Math.sqrt(n);
          e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);

          if (s == 1 / 0) {
            n = '1e' + e;
          } else {
            n = s.toExponential();
            n = n.slice(0, n.indexOf('e') + 1) + e;
          }

          r = new Ctor(n);
        } else {
          r = new Ctor(s.toString());
        }

        pr = Ctor.precision;
        s = wpr = pr + 3;

        // Newton-Raphson iteration.
        for (;;) {
          t = r;
          r = t.plus(divide(x, t, wpr + 2)).times(0.5);

          if (digitsToString(t.d).slice(0, wpr) === (n = digitsToString(r.d)).slice(0, wpr)) {
            n = n.slice(wpr - 3, wpr + 1);

            // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
            // 4999, i.e. approaching a rounding boundary, continue the iteration.
            if (s == wpr && n == '4999') {

              // On the first iteration only, check to see if rounding up gives the exact result as the
              // nines may infinitely repeat.
              round(t, pr + 1, 0);

              if (t.times(t).eq(x)) {
                r = t;
                break;
              }
            } else if (n != '9999') {
              break;
            }

            wpr += 4;
          }
        }

        external = true;

        return round(r, pr);
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal times `y`, truncated to
       * `precision` significant digits.
       *
       */
      P.times = P.mul = function (y) {
        var carry, e, i, k, r, rL, t, xdL, ydL,
          x = this,
          Ctor = x.constructor,
          xd = x.d,
          yd = (y = new Ctor(y)).d;

        // Return 0 if either is 0.
        if (!x.s || !y.s) return new Ctor(0);

        y.s *= x.s;
        e = x.e + y.e;
        xdL = xd.length;
        ydL = yd.length;

        // Ensure xd points to the longer array.
        if (xdL < ydL) {
          r = xd;
          xd = yd;
          yd = r;
          rL = xdL;
          xdL = ydL;
          ydL = rL;
        }

        // Initialise the result array with zeros.
        r = [];
        rL = xdL + ydL;
        for (i = rL; i--;) r.push(0);

        // Multiply!
        for (i = ydL; --i >= 0;) {
          carry = 0;
          for (k = xdL + i; k > i;) {
            t = r[k] + yd[i] * xd[k - i - 1] + carry;
            r[k--] = t % BASE | 0;
            carry = t / BASE | 0;
          }

          r[k] = (r[k] + carry) % BASE | 0;
        }

        // Remove trailing zeros.
        for (; !r[--rL];) r.pop();

        if (carry) ++e;
        else r.shift();

        y.d = r;
        y.e = e;

        return external ? round(y, Ctor.precision) : y;
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
       * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
       *
       * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       */
      P.toDecimalPlaces = P.todp = function (dp, rm) {
        var x = this,
          Ctor = x.constructor;

        x = new Ctor(x);
        if (dp === void 0) return x;

        checkInt32(dp, 0, MAX_DIGITS);

        if (rm === void 0) rm = Ctor.rounding;
        else checkInt32(rm, 0, 8);

        return round(x, dp + getBase10Exponent(x) + 1, rm);
      };

      /*
       * Return a string representing the value of this Decimal in exponential notation rounded to
       * `dp` fixed decimal places using rounding mode `rounding`.
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       */
      P.toExponential = function (dp, rm) {
        var str,
          x = this,
          Ctor = x.constructor;

        if (dp === void 0) {
          str = toString(x, true);
        } else {
          checkInt32(dp, 0, MAX_DIGITS);

          if (rm === void 0) rm = Ctor.rounding;
          else checkInt32(rm, 0, 8);

          x = round(new Ctor(x), dp + 1, rm);
          str = toString(x, true, dp + 1);
        }

        return str;
      };

      /*
       * Return a string representing the value of this Decimal in normal (fixed-point) notation to
       * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
       * omitted.
       *
       * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
       *
       * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
       * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
       * (-0).toFixed(3) is '0.000'.
       * (-0.5).toFixed(0) is '-0'.
       *
       */
      P.toFixed = function (dp, rm) {
        var str, y,
          x = this,
          Ctor = x.constructor;

        if (dp === void 0) return toString(x);

        checkInt32(dp, 0, MAX_DIGITS);

        if (rm === void 0) rm = Ctor.rounding;
        else checkInt32(rm, 0, 8);

        y = round(new Ctor(x), dp + getBase10Exponent(x) + 1, rm);
        str = toString(y.abs(), false, dp + getBase10Exponent(y) + 1);

        // To determine whether to add the minus sign look at the value before it was rounded,
        // i.e. look at `x` rather than `y`.
        return x.isneg() && !x.isZero() ? '-' + str : str;
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
       * rounding mode `rounding`.
       *
       */
      P.toInteger = P.toint = function () {
        var x = this,
          Ctor = x.constructor;
        return round(new Ctor(x), getBase10Exponent(x) + 1, Ctor.rounding);
      };

      /*
       * Return the value of this Decimal converted to a number primitive.
       *
       */
      P.toNumber = function () {
        return +this;
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal raised to the power `y`,
       * truncated to `precision` significant digits.
       *
       * For non-integer or very large exponents pow(x, y) is calculated using
       *
       *   x^y = exp(y*ln(x))
       *
       * The maximum error is 1 ulp (unit in last place).
       *
       * y {number|string|Decimal} The power to which to raise this Decimal.
       *
       */
      P.toPower = P.pow = function (y) {
        var e, k, pr, r, sign, yIsInt,
          x = this,
          Ctor = x.constructor,
          guard = 12,
          yn = +(y = new Ctor(y));

        // pow(x, 0) = 1
        if (!y.s) return new Ctor(ONE);

        x = new Ctor(x);

        // pow(0, y > 0) = 0
        // pow(0, y < 0) = Infinity
        if (!x.s) {
          if (y.s < 1) throw Error(decimalError + 'Infinity');
          return x;
        }

        // pow(1, y) = 1
        if (x.eq(ONE)) return x;

        pr = Ctor.precision;

        // pow(x, 1) = x
        if (y.eq(ONE)) return round(x, pr);

        e = y.e;
        k = y.d.length - 1;
        yIsInt = e >= k;
        sign = x.s;

        if (!yIsInt) {

          // pow(x < 0, y non-integer) = NaN
          if (sign < 0) throw Error(decimalError + 'NaN');

        // If y is a small integer use the 'exponentiation by squaring' algorithm.
        } else if ((k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
          r = new Ctor(ONE);

          // Max k of 9007199254740991 takes 53 loop iterations.
          // Maximum digits array length; leaves [28, 34] guard digits.
          e = Math.ceil(pr / LOG_BASE + 4);

          external = false;

          for (;;) {
            if (k % 2) {
              r = r.times(x);
              truncate(r.d, e);
            }

            k = mathfloor(k / 2);
            if (k === 0) break;

            x = x.times(x);
            truncate(x.d, e);
          }

          external = true;

          return y.s < 0 ? new Ctor(ONE).div(r) : round(r, pr);
        }

        // Result is negative if x is negative and the last digit of integer y is odd.
        sign = sign < 0 && y.d[Math.max(e, k)] & 1 ? -1 : 1;

        x.s = 1;
        external = false;
        r = y.times(ln(x, pr + guard));
        external = true;
        r = exp(r);
        r.s = sign;

        return r;
      };

      /*
       * Return a string representing the value of this Decimal rounded to `sd` significant digits
       * using rounding mode `rounding`.
       *
       * Return exponential notation if `sd` is less than the number of digits necessary to represent
       * the integer part of the value in normal notation.
       *
       * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       */
      P.toPrecision = function (sd, rm) {
        var e, str,
          x = this,
          Ctor = x.constructor;

        if (sd === void 0) {
          e = getBase10Exponent(x);
          str = toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
        } else {
          checkInt32(sd, 1, MAX_DIGITS);

          if (rm === void 0) rm = Ctor.rounding;
          else checkInt32(rm, 0, 8);

          x = round(new Ctor(x), sd, rm);
          e = getBase10Exponent(x);
          str = toString(x, sd <= e || e <= Ctor.toExpNeg, sd);
        }

        return str;
      };

      /*
       * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
       * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
       * omitted.
       *
       * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
       * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
       *
       */
      P.toSignificantDigits = P.tosd = function (sd, rm) {
        var x = this,
          Ctor = x.constructor;

        if (sd === void 0) {
          sd = Ctor.precision;
          rm = Ctor.rounding;
        } else {
          checkInt32(sd, 1, MAX_DIGITS);

          if (rm === void 0) rm = Ctor.rounding;
          else checkInt32(rm, 0, 8);
        }

        return round(new Ctor(x), sd, rm);
      };

      /*
       * Return a string representing the value of this Decimal.
       *
       * Return exponential notation if this Decimal has a positive exponent equal to or greater than
       * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
       *
       */
      P.toString = P.valueOf = P.val = P.toJSON = function () {
        var x = this,
          e = getBase10Exponent(x),
          Ctor = x.constructor;

        return toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
      };

      // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.

      /*
       *  add                 P.minus, P.plus
       *  checkInt32          P.todp, P.toExponential, P.toFixed, P.toPrecision, P.tosd
       *  digitsToString      P.log, P.sqrt, P.pow, toString, exp, ln
       *  divide              P.div, P.idiv, P.log, P.mod, P.sqrt, exp, ln
       *  exp                 P.exp, P.pow
       *  getBase10Exponent   P.exponent, P.sd, P.toint, P.sqrt, P.todp, P.toFixed, P.toPrecision,
       *                      P.toString, divide, round, toString, exp, ln
       *  getLn10             P.log, ln
       *  getZeroString       digitsToString, toString
       *  ln                  P.log, P.ln, P.pow, exp
       *  parseDecimal        Decimal
       *  round               P.abs, P.idiv, P.log, P.minus, P.mod, P.neg, P.plus, P.toint, P.sqrt,
       *                      P.times, P.todp, P.toExponential, P.toFixed, P.pow, P.toPrecision, P.tosd,
       *                      divide, getLn10, exp, ln
       *  subtract            P.minus, P.plus
       *  toString            P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf
       *  truncate            P.pow
       *
       *  Throws:             P.log, P.mod, P.sd, P.sqrt, P.pow,  checkInt32, divide, round,
       *                      getLn10, exp, ln, parseDecimal, Decimal, config
       */

      function add(x, y) {
        var carry, d, e, i, k, len, xd, yd,
          Ctor = x.constructor,
          pr = Ctor.precision;

        // If either is zero...
        if (!x.s || !y.s) {

          // Return x if y is zero.
          // Return y if y is non-zero.
          if (!y.s) y = new Ctor(x);
          return external ? round(y, pr) : y;
        }

        xd = x.d;
        yd = y.d;

        // x and y are finite, non-zero numbers with the same sign.

        k = x.e;
        e = y.e;
        xd = xd.slice();
        i = k - e;

        // If base 1e7 exponents differ...
        if (i) {
          if (i < 0) {
            d = xd;
            i = -i;
            len = yd.length;
          } else {
            d = yd;
            e = k;
            len = xd.length;
          }

          // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
          k = Math.ceil(pr / LOG_BASE);
          len = k > len ? k + 1 : len + 1;

          if (i > len) {
            i = len;
            d.length = 1;
          }

          // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
          d.reverse();
          for (; i--;) d.push(0);
          d.reverse();
        }

        len = xd.length;
        i = yd.length;

        // If yd is longer than xd, swap xd and yd so xd points to the longer array.
        if (len - i < 0) {
          i = len;
          d = yd;
          yd = xd;
          xd = d;
        }

        // Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
        for (carry = 0; i;) {
          carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
          xd[i] %= BASE;
        }

        if (carry) {
          xd.unshift(carry);
          ++e;
        }

        // Remove trailing zeros.
        // No need to check for zero, as +x + +y != 0 && -x + -y != 0
        for (len = xd.length; xd[--len] == 0;) xd.pop();

        y.d = xd;
        y.e = e;

        return external ? round(y, pr) : y;
      }

      function checkInt32(i, min, max) {
        if (i !== ~~i || i < min || i > max) {
          throw Error(invalidArgument + i);
        }
      }

      function digitsToString(d) {
        var i, k, ws,
          indexOfLastWord = d.length - 1,
          str = '',
          w = d[0];

        if (indexOfLastWord > 0) {
          str += w;
          for (i = 1; i < indexOfLastWord; i++) {
            ws = d[i] + '';
            k = LOG_BASE - ws.length;
            if (k) str += getZeroString(k);
            str += ws;
          }

          w = d[i];
          ws = w + '';
          k = LOG_BASE - ws.length;
          if (k) str += getZeroString(k);
        } else if (w === 0) {
          return '0';
        }

        // Remove trailing zeros of last w.
        for (; w % 10 === 0;) w /= 10;

        return str + w;
      }

      var divide = (function () {

        // Assumes non-zero x and k, and hence non-zero result.
        function multiplyInteger(x, k) {
          var temp,
            carry = 0,
            i = x.length;

          for (x = x.slice(); i--;) {
            temp = x[i] * k + carry;
            x[i] = temp % BASE | 0;
            carry = temp / BASE | 0;
          }

          if (carry) x.unshift(carry);

          return x;
        }

        function compare(a, b, aL, bL) {
          var i, r;

          if (aL != bL) {
            r = aL > bL ? 1 : -1;
          } else {
            for (i = r = 0; i < aL; i++) {
              if (a[i] != b[i]) {
                r = a[i] > b[i] ? 1 : -1;
                break;
              }
            }
          }

          return r;
        }

        function subtract(a, b, aL) {
          var i = 0;

          // Subtract b from a.
          for (; aL--;) {
            a[aL] -= i;
            i = a[aL] < b[aL] ? 1 : 0;
            a[aL] = i * BASE + a[aL] - b[aL];
          }

          // Remove leading zeros.
          for (; !a[0] && a.length > 1;) a.shift();
        }

        return function (x, y, pr, dp) {
          var cmp, e, i, k, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, yL, yz,
            Ctor = x.constructor,
            sign = x.s == y.s ? 1 : -1,
            xd = x.d,
            yd = y.d;

          // Either 0?
          if (!x.s) return new Ctor(x);
          if (!y.s) throw Error(decimalError + 'Division by zero');

          e = x.e - y.e;
          yL = yd.length;
          xL = xd.length;
          q = new Ctor(sign);
          qd = q.d = [];

          // Result exponent may be one less than e.
          for (i = 0; yd[i] == (xd[i] || 0); ) ++i;
          if (yd[i] > (xd[i] || 0)) --e;

          if (pr == null) {
            sd = pr = Ctor.precision;
          } else if (dp) {
            sd = pr + (getBase10Exponent(x) - getBase10Exponent(y)) + 1;
          } else {
            sd = pr;
          }

          if (sd < 0) return new Ctor(0);

          // Convert precision in number of base 10 digits to base 1e7 digits.
          sd = sd / LOG_BASE + 2 | 0;
          i = 0;

          // divisor < 1e7
          if (yL == 1) {
            k = 0;
            yd = yd[0];
            sd++;

            // k is the carry.
            for (; (i < xL || k) && sd--; i++) {
              t = k * BASE + (xd[i] || 0);
              qd[i] = t / yd | 0;
              k = t % yd | 0;
            }

          // divisor >= 1e7
          } else {

            // Normalise xd and yd so highest order digit of yd is >= BASE/2
            k = BASE / (yd[0] + 1) | 0;

            if (k > 1) {
              yd = multiplyInteger(yd, k);
              xd = multiplyInteger(xd, k);
              yL = yd.length;
              xL = xd.length;
            }

            xi = yL;
            rem = xd.slice(0, yL);
            remL = rem.length;

            // Add zeros to make remainder as long as divisor.
            for (; remL < yL;) rem[remL++] = 0;

            yz = yd.slice();
            yz.unshift(0);
            yd0 = yd[0];

            if (yd[1] >= BASE / 2) ++yd0;

            do {
              k = 0;

              // Compare divisor and remainder.
              cmp = compare(yd, rem, yL, remL);

              // If divisor < remainder.
              if (cmp < 0) {

                // Calculate trial digit, k.
                rem0 = rem[0];
                if (yL != remL) rem0 = rem0 * BASE + (rem[1] || 0);

                // k will be how many times the divisor goes into the current remainder.
                k = rem0 / yd0 | 0;

                //  Algorithm:
                //  1. product = divisor * trial digit (k)
                //  2. if product > remainder: product -= divisor, k--
                //  3. remainder -= product
                //  4. if product was < remainder at 2:
                //    5. compare new remainder and divisor
                //    6. If remainder > divisor: remainder -= divisor, k++

                if (k > 1) {
                  if (k >= BASE) k = BASE - 1;

                  // product = divisor * trial digit.
                  prod = multiplyInteger(yd, k);
                  prodL = prod.length;
                  remL = rem.length;

                  // Compare product and remainder.
                  cmp = compare(prod, rem, prodL, remL);

                  // product > remainder.
                  if (cmp == 1) {
                    k--;

                    // Subtract divisor from product.
                    subtract(prod, yL < prodL ? yz : yd, prodL);
                  }
                } else {

                  // cmp is -1.
                  // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
                  // to avoid it. If k is 1 there is a need to compare yd and rem again below.
                  if (k == 0) cmp = k = 1;
                  prod = yd.slice();
                }

                prodL = prod.length;
                if (prodL < remL) prod.unshift(0);

                // Subtract product from remainder.
                subtract(rem, prod, remL);

                // If product was < previous remainder.
                if (cmp == -1) {
                  remL = rem.length;

                  // Compare divisor and new remainder.
                  cmp = compare(yd, rem, yL, remL);

                  // If divisor < new remainder, subtract divisor from remainder.
                  if (cmp < 1) {
                    k++;

                    // Subtract divisor from remainder.
                    subtract(rem, yL < remL ? yz : yd, remL);
                  }
                }

                remL = rem.length;
              } else if (cmp === 0) {
                k++;
                rem = [0];
              }    // if cmp === 1, k will be 0

              // Add the next digit, k, to the result array.
              qd[i++] = k;

              // Update the remainder.
              if (cmp && rem[0]) {
                rem[remL++] = xd[xi] || 0;
              } else {
                rem = [xd[xi]];
                remL = 1;
              }

            } while ((xi++ < xL || rem[0] !== void 0) && sd--);
          }

          // Leading zero?
          if (!qd[0]) qd.shift();

          q.e = e;

          return round(q, dp ? pr + getBase10Exponent(q) + 1 : pr);
        };
      })();

      /*
       * Return a new Decimal whose value is the natural exponential of `x` truncated to `sd`
       * significant digits.
       *
       * Taylor/Maclaurin series.
       *
       * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
       *
       * Argument reduction:
       *   Repeat x = x / 32, k += 5, until |x| < 0.1
       *   exp(x) = exp(x / 2^k)^(2^k)
       *
       * Previously, the argument was initially reduced by
       * exp(x) = exp(r) * 10^k  where r = x - k * ln10, k = floor(x / ln10)
       * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
       * found to be slower than just dividing repeatedly by 32 as above.
       *
       * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
       *
       *  exp(x) is non-terminating for any finite, non-zero x.
       *
       */
      function exp(x, sd) {
        var denominator, guard, pow, sum, t, wpr,
          i = 0,
          k = 0,
          Ctor = x.constructor,
          pr = Ctor.precision;

        if (getBase10Exponent(x) > 16) throw Error(exponentOutOfRange + getBase10Exponent(x));

        // exp(0) = 1
        if (!x.s) return new Ctor(ONE);

        if (sd == null) {
          external = false;
          wpr = pr;
        } else {
          wpr = sd;
        }

        t = new Ctor(0.03125);

        while (x.abs().gte(0.1)) {
          x = x.times(t);    // x = x / 2^5
          k += 5;
        }

        // Estimate the precision increase necessary to ensure the first 4 rounding digits are correct.
        guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
        wpr += guard;
        denominator = pow = sum = new Ctor(ONE);
        Ctor.precision = wpr;

        for (;;) {
          pow = round(pow.times(x), wpr);
          denominator = denominator.times(++i);
          t = sum.plus(divide(pow, denominator, wpr));

          if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
            while (k--) sum = round(sum.times(sum), wpr);
            Ctor.precision = pr;
            return sd == null ? (external = true, round(sum, pr)) : sum;
          }

          sum = t;
        }
      }

      // Calculate the base 10 exponent from the base 1e7 exponent.
      function getBase10Exponent(x) {
        var e = x.e * LOG_BASE,
          w = x.d[0];

        // Add the number of digits of the first word of the digits array.
        for (; w >= 10; w /= 10) e++;
        return e;
      }

      function getLn10(Ctor, sd, pr) {

        if (sd > Ctor.LN10.sd()) {

          // Reset global state in case the exception is caught.
          external = true;
          if (pr) Ctor.precision = pr;
          throw Error(decimalError + 'LN10 precision limit exceeded');
        }

        return round(new Ctor(Ctor.LN10), sd);
      }

      function getZeroString(k) {
        var zs = '';
        for (; k--;) zs += '0';
        return zs;
      }

      /*
       * Return a new Decimal whose value is the natural logarithm of `x` truncated to `sd` significant
       * digits.
       *
       *  ln(n) is non-terminating (n != 1)
       *
       */
      function ln(y, sd) {
        var c, c0, denominator, e, numerator, sum, t, wpr, x2,
          n = 1,
          guard = 10,
          x = y,
          xd = x.d,
          Ctor = x.constructor,
          pr = Ctor.precision;

        // ln(-x) = NaN
        // ln(0) = -Infinity
        if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));

        // ln(1) = 0
        if (x.eq(ONE)) return new Ctor(0);

        if (sd == null) {
          external = false;
          wpr = pr;
        } else {
          wpr = sd;
        }

        if (x.eq(10)) {
          if (sd == null) external = true;
          return getLn10(Ctor, wpr);
        }

        wpr += guard;
        Ctor.precision = wpr;
        c = digitsToString(xd);
        c0 = c.charAt(0);
        e = getBase10Exponent(x);

        if (Math.abs(e) < 1.5e15) {

          // Argument reduction.
          // The series converges faster the closer the argument is to 1, so using
          // ln(a^b) = b * ln(a),   ln(a) = ln(a^b) / b
          // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
          // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
          // later be divided by this number, then separate out the power of 10 using
          // ln(a*10^b) = ln(a) + b*ln(10).

          // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
          //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
          // max n is 6 (gives 0.7 - 1.3)
          while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
            x = x.times(y);
            c = digitsToString(x.d);
            c0 = c.charAt(0);
            n++;
          }

          e = getBase10Exponent(x);

          if (c0 > 1) {
            x = new Ctor('0.' + c);
            e++;
          } else {
            x = new Ctor(c0 + '.' + c.slice(1));
          }
        } else {

          // The argument reduction method above may result in overflow if the argument y is a massive
          // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
          // function using ln(x*10^e) = ln(x) + e*ln(10).
          t = getLn10(Ctor, wpr + 2, pr).times(e + '');
          x = ln(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);

          Ctor.precision = pr;
          return sd == null ? (external = true, round(x, pr)) : x;
        }

        // x is reduced to a value near 1.

        // Taylor series.
        // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
        // where x = (y - 1)/(y + 1)    (|x| < 1)
        sum = numerator = x = divide(x.minus(ONE), x.plus(ONE), wpr);
        x2 = round(x.times(x), wpr);
        denominator = 3;

        for (;;) {
          numerator = round(numerator.times(x2), wpr);
          t = sum.plus(divide(numerator, new Ctor(denominator), wpr));

          if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
            sum = sum.times(2);

            // Reverse the argument reduction.
            if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
            sum = divide(sum, new Ctor(n), wpr);

            Ctor.precision = pr;
            return sd == null ? (external = true, round(sum, pr)) : sum;
          }

          sum = t;
          denominator += 2;
        }
      }

      /*
       * Parse the value of a new Decimal `x` from string `str`.
       */
      function parseDecimal(x, str) {
        var e, i, len;

        // Decimal point?
        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');

        // Exponential form?
        if ((i = str.search(/e/i)) > 0) {

          // Determine exponent.
          if (e < 0) e = i;
          e += +str.slice(i + 1);
          str = str.substring(0, i);
        } else if (e < 0) {

          // Integer.
          e = str.length;
        }

        // Determine leading zeros.
        for (i = 0; str.charCodeAt(i) === 48;) ++i;

        // Determine trailing zeros.
        for (len = str.length; str.charCodeAt(len - 1) === 48;) --len;
        str = str.slice(i, len);

        if (str) {
          len -= i;
          e = e - i - 1;
          x.e = mathfloor(e / LOG_BASE);
          x.d = [];

          // Transform base

          // e is the base 10 exponent.
          // i is where to slice str to get the first word of the digits array.
          i = (e + 1) % LOG_BASE;
          if (e < 0) i += LOG_BASE;

          if (i < len) {
            if (i) x.d.push(+str.slice(0, i));
            for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
            str = str.slice(i);
            i = LOG_BASE - str.length;
          } else {
            i -= len;
          }

          for (; i--;) str += '0';
          x.d.push(+str);

          if (external && (x.e > MAX_E || x.e < -MAX_E)) throw Error(exponentOutOfRange + e);
        } else {

          // Zero.
          x.s = 0;
          x.e = 0;
          x.d = [0];
        }

        return x;
      }

      /*
       * Round `x` to `sd` significant digits, using rounding mode `rm` if present (truncate otherwise).
       */
       function round(x, sd, rm) {
        var i, j, k, n, rd, doRound, w, xdi,
          xd = x.d;

        // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
        // w: the word of xd which contains the rounding digit, a base 1e7 number.
        // xdi: the index of w within xd.
        // n: the number of digits of w.
        // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
        // they had leading zeros)
        // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).

        // Get the length of the first word of the digits array xd.
        for (n = 1, k = xd[0]; k >= 10; k /= 10) n++;
        i = sd - n;

        // Is the rounding digit in the first word of xd?
        if (i < 0) {
          i += LOG_BASE;
          j = sd;
          w = xd[xdi = 0];
        } else {
          xdi = Math.ceil((i + 1) / LOG_BASE);
          k = xd.length;
          if (xdi >= k) return x;
          w = k = xd[xdi];

          // Get the number of digits of w.
          for (n = 1; k >= 10; k /= 10) n++;

          // Get the index of rd within w.
          i %= LOG_BASE;

          // Get the index of rd within w, adjusted for leading zeros.
          // The number of leading zeros of w is given by LOG_BASE - n.
          j = i - LOG_BASE + n;
        }

        if (rm !== void 0) {
          k = mathpow(10, n - j - 1);

          // Get the rounding digit at index j of w.
          rd = w / k % 10 | 0;

          // Are there any non-zero digits after the rounding digit?
          doRound = sd < 0 || xd[xdi + 1] !== void 0 || w % k;

          // The expression `w % mathpow(10, n - j - 1)` returns all the digits of w to the right of the
          // digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression will give
          // 714.

          doRound = rm < 4
            ? (rd || doRound) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
            : rd > 5 || rd == 5 && (rm == 4 || doRound || rm == 6 &&

              // Check whether the digit to the left of the rounding digit is odd.
              ((i > 0 ? j > 0 ? w / mathpow(10, n - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
                rm == (x.s < 0 ? 8 : 7));
        }

        if (sd < 1 || !xd[0]) {
          if (doRound) {
            k = getBase10Exponent(x);
            xd.length = 1;

            // Convert sd to decimal places.
            sd = sd - k - 1;

            // 1, 0.1, 0.01, 0.001, 0.0001 etc.
            xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
            x.e = mathfloor(-sd / LOG_BASE) || 0;
          } else {
            xd.length = 1;

            // Zero.
            xd[0] = x.e = x.s = 0;
          }

          return x;
        }

        // Remove excess digits.
        if (i == 0) {
          xd.length = xdi;
          k = 1;
          xdi--;
        } else {
          xd.length = xdi + 1;
          k = mathpow(10, LOG_BASE - i);

          // E.g. 56700 becomes 56000 if 7 is the rounding digit.
          // j > 0 means i > number of leading zeros of w.
          xd[xdi] = j > 0 ? (w / mathpow(10, n - j) % mathpow(10, j) | 0) * k : 0;
        }

        if (doRound) {
          for (;;) {

            // Is the digit to be rounded up in the first word of xd?
            if (xdi == 0) {
              if ((xd[0] += k) == BASE) {
                xd[0] = 1;
                ++x.e;
              }

              break;
            } else {
              xd[xdi] += k;
              if (xd[xdi] != BASE) break;
              xd[xdi--] = 0;
              k = 1;
            }
          }
        }

        // Remove trailing zeros.
        for (i = xd.length; xd[--i] === 0;) xd.pop();

        if (external && (x.e > MAX_E || x.e < -MAX_E)) {
          throw Error(exponentOutOfRange + getBase10Exponent(x));
        }

        return x;
      }

      function subtract(x, y) {
        var d, e, i, j, k, len, xd, xe, xLTy, yd,
          Ctor = x.constructor,
          pr = Ctor.precision;

        // Return y negated if x is zero.
        // Return x if y is zero and x is non-zero.
        if (!x.s || !y.s) {
          if (y.s) y.s = -y.s;
          else y = new Ctor(x);
          return external ? round(y, pr) : y;
        }

        xd = x.d;
        yd = y.d;

        // x and y are non-zero numbers with the same sign.

        e = y.e;
        xe = x.e;
        xd = xd.slice();
        k = xe - e;

        // If exponents differ...
        if (k) {
          xLTy = k < 0;

          if (xLTy) {
            d = xd;
            k = -k;
            len = yd.length;
          } else {
            d = yd;
            e = xe;
            len = xd.length;
          }

          // Numbers with massively different exponents would result in a very high number of zeros
          // needing to be prepended, but this can be avoided while still ensuring correct rounding by
          // limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
          i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;

          if (k > i) {
            k = i;
            d.length = 1;
          }

          // Prepend zeros to equalise exponents.
          d.reverse();
          for (i = k; i--;) d.push(0);
          d.reverse();

        // Base 1e7 exponents equal.
        } else {

          // Check digits to determine which is the bigger number.

          i = xd.length;
          len = yd.length;
          xLTy = i < len;
          if (xLTy) len = i;

          for (i = 0; i < len; i++) {
            if (xd[i] != yd[i]) {
              xLTy = xd[i] < yd[i];
              break;
            }
          }

          k = 0;
        }

        if (xLTy) {
          d = xd;
          xd = yd;
          yd = d;
          y.s = -y.s;
        }

        len = xd.length;

        // Append zeros to xd if shorter.
        // Don't add zeros to yd if shorter as subtraction only needs to start at yd length.
        for (i = yd.length - len; i > 0; --i) xd[len++] = 0;

        // Subtract yd from xd.
        for (i = yd.length; i > k;) {
          if (xd[--i] < yd[i]) {
            for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
            --xd[j];
            xd[i] += BASE;
          }

          xd[i] -= yd[i];
        }

        // Remove trailing zeros.
        for (; xd[--len] === 0;) xd.pop();

        // Remove leading zeros and adjust exponent accordingly.
        for (; xd[0] === 0; xd.shift()) --e;

        // Zero?
        if (!xd[0]) return new Ctor(0);

        y.d = xd;
        y.e = e;

        //return external && xd.length >= pr / LOG_BASE ? round(y, pr) : y;
        return external ? round(y, pr) : y;
      }

      function toString(x, isExp, sd) {
        var k,
          e = getBase10Exponent(x),
          str = digitsToString(x.d),
          len = str.length;

        if (isExp) {
          if (sd && (k = sd - len) > 0) {
            str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
          } else if (len > 1) {
            str = str.charAt(0) + '.' + str.slice(1);
          }

          str = str + (e < 0 ? 'e' : 'e+') + e;
        } else if (e < 0) {
          str = '0.' + getZeroString(-e - 1) + str;
          if (sd && (k = sd - len) > 0) str += getZeroString(k);
        } else if (e >= len) {
          str += getZeroString(e + 1 - len);
          if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
        } else {
          if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
          if (sd && (k = sd - len) > 0) {
            if (e + 1 === len) str += '.';
            str += getZeroString(k);
          }
        }

        return x.s < 0 ? '-' + str : str;
      }

      // Does not strip trailing zeros.
      function truncate(arr, len) {
        if (arr.length > len) {
          arr.length = len;
          return true;
        }
      }

      // Decimal methods

      /*
       *  clone
       *  config/set
       */

      /*
       * Create and return a Decimal constructor with the same configuration properties as this Decimal
       * constructor.
       *
       */
      function clone(obj) {
        var i, p, ps;

        /*
         * The Decimal constructor and exported function.
         * Return a new Decimal instance.
         *
         * value {number|string|Decimal} A numeric value.
         *
         */
        function Decimal(value) {
          var x = this;

          // Decimal called without new.
          if (!(x instanceof Decimal)) return new Decimal(value);

          // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
          // which points to Object.
          x.constructor = Decimal;

          // Duplicate.
          if (value instanceof Decimal) {
            x.s = value.s;
            x.e = value.e;
            x.d = (value = value.d) ? value.slice() : value;
            return;
          }

          if (typeof value === 'number') {

            // Reject Infinity/NaN.
            if (value * 0 !== 0) {
              throw Error(invalidArgument + value);
            }

            if (value > 0) {
              x.s = 1;
            } else if (value < 0) {
              value = -value;
              x.s = -1;
            } else {
              x.s = 0;
              x.e = 0;
              x.d = [0];
              return;
            }

            // Fast path for small integers.
            if (value === ~~value && value < 1e7) {
              x.e = 0;
              x.d = [value];
              return;
            }

            return parseDecimal(x, value.toString());
          } else if (typeof value !== 'string') {
            throw Error(invalidArgument + value);
          }

          // Minus sign?
          if (value.charCodeAt(0) === 45) {
            value = value.slice(1);
            x.s = -1;
          } else {
            x.s = 1;
          }

          if (isDecimal.test(value)) parseDecimal(x, value);
          else throw Error(invalidArgument + value);
        }

        Decimal.prototype = P;

        Decimal.ROUND_UP = 0;
        Decimal.ROUND_DOWN = 1;
        Decimal.ROUND_CEIL = 2;
        Decimal.ROUND_FLOOR = 3;
        Decimal.ROUND_HALF_UP = 4;
        Decimal.ROUND_HALF_DOWN = 5;
        Decimal.ROUND_HALF_EVEN = 6;
        Decimal.ROUND_HALF_CEIL = 7;
        Decimal.ROUND_HALF_FLOOR = 8;

        Decimal.clone = clone;
        Decimal.config = Decimal.set = config;

        if (obj === void 0) obj = {};
        if (obj) {
          ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'LN10'];
          for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
        }

        Decimal.config(obj);

        return Decimal;
      }

      /*
       * Configure global settings for a Decimal constructor.
       *
       * `obj` is an object with one or more of the following properties,
       *
       *   precision  {number}
       *   rounding   {number}
       *   toExpNeg   {number}
       *   toExpPos   {number}
       *
       * E.g. Decimal.config({ precision: 20, rounding: 4 })
       *
       */
      function config(obj) {
        if (!obj || typeof obj !== 'object') {
          throw Error(decimalError + 'Object expected');
        }
        var i, p, v,
          ps = [
            'precision', 1, MAX_DIGITS,
            'rounding', 0, 8,
            'toExpNeg', -1 / 0, 0,
            'toExpPos', 0, 1 / 0
          ];

        for (i = 0; i < ps.length; i += 3) {
          if ((v = obj[p = ps[i]]) !== void 0) {
            if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
            else throw Error(invalidArgument + p + ': ' + v);
          }
        }

        if ((v = obj[p = 'LN10']) !== void 0) {
            if (v == Math.LN10) this[p] = new this(v);
            else throw Error(invalidArgument + p + ': ' + v);
        }

        return this;
      }

      // Create and configure initial Decimal constructor.
      Decimal = clone(Decimal);

      Decimal['default'] = Decimal.Decimal = Decimal;

      // Internal constant.
      ONE = new Decimal(1);

      // Export.

      // AMD.
      if (typeof define == 'function' && define.amd) {
        define(function () {
          return Decimal;
        });

      // Node and other environments that support module.exports.
      } else if (typeof module != 'undefined' && module.exports) {
        module.exports = Decimal;

        // Browser.
      } else {
        if (!globalScope) {
          globalScope = typeof self != 'undefined' && self && self.self == self
            ? self : Function('return this')();
        }

        globalScope.Decimal = Decimal;
      }
    })(this);

    //# sourceURL=lib_decimal-light.js