System.register(["cce:/internal/ml/cjs-loader.mjs"], function (_export, _context) {
  "use strict";

  var _loader, _cjsExports, __cjsMetaURL;

  _export("default", void 0);

  return {
    setters: [function (_cceInternalMlCjsLoaderMjs) {
      _loader = _cceInternalMlCjsLoaderMjs.default;
    }],
    execute: function () {
      _loader.define(_context.meta.url, function (exports, _require, module, __filename, __dirname) {
        var require = _loader.createRequireWithReqMap({}, _require);

        (function () {
          ;

          (function (globalScope) {
            'use strict';
            /*
             *  decimal.js v10.2.1
             *  An arbitrary-precision Decimal type for JavaScript.
             *  https://github.com/MikeMcl/decimal.js
             *  Copyright (c) 2020 Michael Mclaughlin <M8ch88l@gmail.com>
             *  MIT Licence
             */
            // -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //
            // The maximum exponent magnitude.
            // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.

            var EXP_LIMIT = 9e15,
                // 0 to 9e15
            // The limit on the value of `precision`, and on the value of the first argument to
            // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
            MAX_DIGITS = 1e9,
                // 0 to 1e9
            // Base conversion alphabet.
            NUMERALS = '0123456789abcdef',
                // The natural logarithm of 10 (1025 digits).
            LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
                // Pi (1025 digits).
            PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
                // The initial configuration properties of the Decimal constructor.
            DEFAULTS = {
              // These values must be integers within the stated ranges (inclusive).
              // Most of these values can be changed at run-time using the `Decimal.config` method.
              // 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 when rounding to `precision`.
              //
              // 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 modulo mode used when calculating the modulus: a mod n.
              // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
              // The remainder (r) is calculated as: r = a - n * q.
              //
              // UP         0 The remainder is positive if the dividend is negative, else is negative.
              // DOWN       1 The remainder has the same sign as the dividend (JavaScript %).
              // FLOOR      3 The remainder has the same sign as the divisor (Python %).
              // HALF_EVEN  6 The IEEE 754 remainder function.
              // EUCLID     9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.
              //
              // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian
              // division (9) are commonly used for the modulus operation. The other rounding modes can also
              // be used, but they may not give useful results.
              modulo: 1,
              // 0 to 9
              // The exponent value at and beneath which `toString` returns exponential notation.
              // JavaScript numbers: -7
              toExpNeg: -7,
              // 0 to -EXP_LIMIT
              // The exponent value at and above which `toString` returns exponential notation.
              // JavaScript numbers: 21
              toExpPos: 21,
              // 0 to EXP_LIMIT
              // The minimum exponent value, beneath which underflow to zero occurs.
              // JavaScript numbers: -324  (5e-324)
              minE: -EXP_LIMIT,
              // -1 to -EXP_LIMIT
              // The maximum exponent value, above which overflow to Infinity occurs.
              // JavaScript numbers: 308  (1.7976931348623157e+308)
              maxE: EXP_LIMIT,
              // 1 to EXP_LIMIT
              // Whether to use cryptographically-secure random number generation, if available.
              crypto: false // true/false

            },
                // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
            Decimal,
                inexact,
                noConflict,
                quadrant,
                external = true,
                decimalError = '[DecimalError] ',
                invalidArgument = decimalError + 'Invalid argument: ',
                precisionLimitExceeded = decimalError + 'Precision limit exceeded',
                cryptoUnavailable = decimalError + 'crypto unavailable',
                mathfloor = Math.floor,
                mathpow = Math.pow,
                isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,
                isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,
                isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,
                isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
                BASE = 1e7,
                LOG_BASE = 7,
                MAX_SAFE_INTEGER = 9007199254740991,
                LN10_PRECISION = LN10.length - 1,
                PI_PRECISION = PI.length - 1,
                // Decimal.prototype object
            P = {
              name: '[object Decimal]'
            }; // Decimal prototype methods

            /*
             *  absoluteValue             abs
             *  ceil
             *  comparedTo                cmp
             *  cosine                    cos
             *  cubeRoot                  cbrt
             *  decimalPlaces             dp
             *  dividedBy                 div
             *  dividedToIntegerBy        divToInt
             *  equals                    eq
             *  floor
             *  greaterThan               gt
             *  greaterThanOrEqualTo      gte
             *  hyperbolicCosine          cosh
             *  hyperbolicSine            sinh
             *  hyperbolicTangent         tanh
             *  inverseCosine             acos
             *  inverseHyperbolicCosine   acosh
             *  inverseHyperbolicSine     asinh
             *  inverseHyperbolicTangent  atanh
             *  inverseSine               asin
             *  inverseTangent            atan
             *  isFinite
             *  isInteger                 isInt
             *  isNaN
             *  isNegative                isNeg
             *  isPositive                isPos
             *  isZero
             *  lessThan                  lt
             *  lessThanOrEqualTo         lte
             *  logarithm                 log
             *  [maximum]                 [max]
             *  [minimum]                 [min]
             *  minus                     sub
             *  modulo                    mod
             *  naturalExponential        exp
             *  naturalLogarithm          ln
             *  negated                   neg
             *  plus                      add
             *  precision                 sd
             *  round
             *  sine                      sin
             *  squareRoot                sqrt
             *  tangent                   tan
             *  times                     mul
             *  toBinary
             *  toDecimalPlaces           toDP
             *  toExponential
             *  toFixed
             *  toFraction
             *  toHexadecimal             toHex
             *  toNearest
             *  toNumber
             *  toOctal
             *  toPower                   pow
             *  toPrecision
             *  toSignificantDigits       toSD
             *  toString
             *  truncated                 trunc
             *  valueOf                   toJSON
             */

            /*
             * 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 < 0) x.s = 1;
              return finalise(x);
            };
            /*
             * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
             * direction of positive Infinity.
             *
             */


            P.ceil = function () {
              return finalise(new this.constructor(this), this.e + 1, 2);
            };
            /*
             * 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,
             *   NaN  if the value of either Decimal is NaN.
             *
             */


            P.comparedTo = P.cmp = function (y) {
              var i,
                  j,
                  xdL,
                  ydL,
                  x = this,
                  xd = x.d,
                  yd = (y = new x.constructor(y)).d,
                  xs = x.s,
                  ys = y.s; // Either NaN or ±Infinity?

              if (!xd || !yd) {
                return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
              } // Either zero?


              if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; // Signs differ?

              if (xs !== ys) return xs; // Compare exponents.

              if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
              xdL = xd.length;
              ydL = yd.length; // Compare digit by digit.

              for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
                if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;
              } // Compare lengths.


              return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
            };
            /*
             * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-1, 1]
             *
             * cos(0)         = 1
             * cos(-0)        = 1
             * cos(Infinity)  = NaN
             * cos(-Infinity) = NaN
             * cos(NaN)       = NaN
             *
             */


            P.cosine = P.cos = function () {
              var pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (!x.d) return new Ctor(NaN); // cos(0) = cos(-0) = 1

              if (!x.d[0]) return new Ctor(1);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
              Ctor.rounding = 1;
              x = cosine(Ctor, toLessThanHalfPi(Ctor, x));
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);
            };
            /*
             *
             * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to
             * `precision` significant digits using rounding mode `rounding`.
             *
             *  cbrt(0)  =  0
             *  cbrt(-0) = -0
             *  cbrt(1)  =  1
             *  cbrt(-1) = -1
             *  cbrt(N)  =  N
             *  cbrt(-I) = -I
             *  cbrt(I)  =  I
             *
             * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))
             *
             */


            P.cubeRoot = P.cbrt = function () {
              var e,
                  m,
                  n,
                  r,
                  rep,
                  s,
                  sd,
                  t,
                  t3,
                  t3plusx,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite() || x.isZero()) return new Ctor(x);
              external = false; // Initial estimate.

              s = x.s * mathpow(x.s * x, 1 / 3); // Math.cbrt underflow/overflow?
              // Pass x to Math.pow as integer, then adjust the exponent of the result.

              if (!s || Math.abs(s) == 1 / 0) {
                n = digitsToString(x.d);
                e = x.e; // Adjust n exponent so it is a multiple of 3 away from x exponent.

                if (s = (e - n.length + 1) % 3) n += s == 1 || s == -2 ? '0' : '00';
                s = mathpow(n, 1 / 3); // Rarely, e may be one less than the result exponent value.

                e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));

                if (s == 1 / 0) {
                  n = '5e' + e;
                } else {
                  n = s.toExponential();
                  n = n.slice(0, n.indexOf('e') + 1) + e;
                }

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

              sd = (e = Ctor.precision) + 3; // Halley's method.
              // TODO? Compare Newton's method.

              for (;;) {
                t = r;
                t3 = t.times(t).times(t);
                t3plusx = t3.plus(x);
                r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); // TODO? Replace with for-loop and checkRoundingDigits.

                if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
                  n = n.slice(sd - 3, sd + 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 (n == '9999' || !rep && n == '4999') {
                    // On the first iteration only, check to see if rounding up gives the exact result as the
                    // nines may infinitely repeat.
                    if (!rep) {
                      finalise(t, e + 1, 0);

                      if (t.times(t).times(t).eq(x)) {
                        r = t;
                        break;
                      }
                    }

                    sd += 4;
                    rep = 1;
                  } else {
                    // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
                    // If not, then there are further digits and m will be truthy.
                    if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
                      // Truncate to the first rounding digit.
                      finalise(r, e + 1, 1);
                      m = !r.times(r).times(r).eq(x);
                    }

                    break;
                  }
                }
              }

              external = true;
              return finalise(r, e, Ctor.rounding, m);
            };
            /*
             * Return the number of decimal places of the value of this Decimal.
             *
             */


            P.decimalPlaces = P.dp = function () {
              var w,
                  d = this.d,
                  n = NaN;

              if (d) {
                w = d.length - 1;
                n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; // Subtract the number of trailing zeros of the last word.

                w = d[w];
                if (w) for (; w % 10 == 0; w /= 10) {
                  n--;
                }
                if (n < 0) n = 0;
              }

              return n;
            };
            /*
             *  n / 0 = I
             *  n / N = N
             *  n / I = 0
             *  0 / n = 0
             *  0 / 0 = N
             *  0 / N = N
             *  0 / I = 0
             *  N / n = N
             *  N / 0 = N
             *  N / N = N
             *  N / I = N
             *  I / n = I
             *  I / 0 = I
             *  I / N = N
             *  I / I = N
             *
             * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to
             * `precision` significant digits using rounding mode `rounding`.
             *
             */


            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`, rounded to `precision` significant digits using rounding mode `rounding`.
             *
             */


            P.dividedToIntegerBy = P.divToInt = function (y) {
              var x = this,
                  Ctor = x.constructor;
              return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
            };
            /*
             * 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) === 0;
            };
            /*
             * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
             * direction of negative Infinity.
             *
             */


            P.floor = function () {
              return finalise(new this.constructor(this), this.e + 1, 3);
            };
            /*
             * 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) {
              var k = this.cmp(y);
              return k == 1 || k === 0;
            };
            /*
             * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this
             * Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [1, Infinity]
             *
             * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...
             *
             * cosh(0)         = 1
             * cosh(-0)        = 1
             * cosh(Infinity)  = Infinity
             * cosh(-Infinity) = Infinity
             * cosh(NaN)       = NaN
             *
             *  x        time taken (ms)   result
             * 1000      9                 9.8503555700852349694e+433
             * 10000     25                4.4034091128314607936e+4342
             * 100000    171               1.4033316802130615897e+43429
             * 1000000   3817              1.5166076984010437725e+434294
             * 10000000  abandoned after 2 minute wait
             *
             * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))
             *
             */


            P.hyperbolicCosine = P.cosh = function () {
              var k,
                  n,
                  pr,
                  rm,
                  len,
                  x = this,
                  Ctor = x.constructor,
                  one = new Ctor(1);
              if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);
              if (x.isZero()) return one;
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
              Ctor.rounding = 1;
              len = x.d.length; // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1
              // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))
              // Estimate the optimum number of times to use the argument reduction.
              // TODO? Estimation reused from cosine() and may not be optimal here.

              if (len < 32) {
                k = Math.ceil(len / 3);
                n = (1 / tinyPow(4, k)).toString();
              } else {
                k = 16;
                n = '2.3283064365386962890625e-10';
              }

              x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); // Reverse argument reduction

              var cosh2_x,
                  i = k,
                  d8 = new Ctor(8);

              for (; i--;) {
                cosh2_x = x.times(x);
                x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));
              }

              return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);
            };
            /*
             * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this
             * Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-Infinity, Infinity]
             *
             * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...
             *
             * sinh(0)         = 0
             * sinh(-0)        = -0
             * sinh(Infinity)  = Infinity
             * sinh(-Infinity) = -Infinity
             * sinh(NaN)       = NaN
             *
             * x        time taken (ms)
             * 10       2 ms
             * 100      5 ms
             * 1000     14 ms
             * 10000    82 ms
             * 100000   886 ms            1.4033316802130615897e+43429
             * 200000   2613 ms
             * 300000   5407 ms
             * 400000   8824 ms
             * 500000   13026 ms          8.7080643612718084129e+217146
             * 1000000  48543 ms
             *
             * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))
             *
             */


            P.hyperbolicSine = P.sinh = function () {
              var k,
                  pr,
                  rm,
                  len,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite() || x.isZero()) return new Ctor(x);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
              Ctor.rounding = 1;
              len = x.d.length;

              if (len < 3) {
                x = taylorSeries(Ctor, 2, x, x, true);
              } else {
                // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))
                // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))
                // 3 multiplications and 1 addition
                // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))
                // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))
                // 4 multiplications and 2 additions
                // Estimate the optimum number of times to use the argument reduction.
                k = 1.4 * Math.sqrt(len);
                k = k > 16 ? 16 : k | 0;
                x = x.times(1 / tinyPow(5, k));
                x = taylorSeries(Ctor, 2, x, x, true); // Reverse argument reduction

                var sinh2_x,
                    d5 = new Ctor(5),
                    d16 = new Ctor(16),
                    d20 = new Ctor(20);

                for (; k--;) {
                  sinh2_x = x.times(x);
                  x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));
                }
              }

              Ctor.precision = pr;
              Ctor.rounding = rm;
              return finalise(x, pr, rm, true);
            };
            /*
             * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this
             * Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-1, 1]
             *
             * tanh(x) = sinh(x) / cosh(x)
             *
             * tanh(0)         = 0
             * tanh(-0)        = -0
             * tanh(Infinity)  = 1
             * tanh(-Infinity) = -1
             * tanh(NaN)       = NaN
             *
             */


            P.hyperbolicTangent = P.tanh = function () {
              var pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite()) return new Ctor(x.s);
              if (x.isZero()) return new Ctor(x);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + 7;
              Ctor.rounding = 1;
              return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);
            };
            /*
             * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of
             * this Decimal.
             *
             * Domain: [-1, 1]
             * Range: [0, pi]
             *
             * acos(x) = pi/2 - asin(x)
             *
             * acos(0)       = pi/2
             * acos(-0)      = pi/2
             * acos(1)       = 0
             * acos(-1)      = pi
             * acos(1/2)     = pi/3
             * acos(-1/2)    = 2*pi/3
             * acos(|x| > 1) = NaN
             * acos(NaN)     = NaN
             *
             */


            P.inverseCosine = P.acos = function () {
              var halfPi,
                  x = this,
                  Ctor = x.constructor,
                  k = x.abs().cmp(1),
                  pr = Ctor.precision,
                  rm = Ctor.rounding;

              if (k !== -1) {
                return k === 0 // |x| is 1
                ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) // |x| > 1 or x is NaN
                : new Ctor(NaN);
              }

              if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3

              Ctor.precision = pr + 6;
              Ctor.rounding = 1;
              x = x.asin();
              halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return halfPi.minus(x);
            };
            /*
             * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the
             * value of this Decimal.
             *
             * Domain: [1, Infinity]
             * Range: [0, Infinity]
             *
             * acosh(x) = ln(x + sqrt(x^2 - 1))
             *
             * acosh(x < 1)     = NaN
             * acosh(NaN)       = NaN
             * acosh(Infinity)  = Infinity
             * acosh(-Infinity) = NaN
             * acosh(0)         = NaN
             * acosh(-0)        = NaN
             * acosh(1)         = 0
             * acosh(-1)        = NaN
             *
             */


            P.inverseHyperbolicCosine = P.acosh = function () {
              var pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);
              if (!x.isFinite()) return new Ctor(x);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;
              Ctor.rounding = 1;
              external = false;
              x = x.times(x).minus(1).sqrt().plus(x);
              external = true;
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return x.ln();
            };
            /*
             * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value
             * of this Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-Infinity, Infinity]
             *
             * asinh(x) = ln(x + sqrt(x^2 + 1))
             *
             * asinh(NaN)       = NaN
             * asinh(Infinity)  = Infinity
             * asinh(-Infinity) = -Infinity
             * asinh(0)         = 0
             * asinh(-0)        = -0
             *
             */


            P.inverseHyperbolicSine = P.asinh = function () {
              var pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite() || x.isZero()) return new Ctor(x);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;
              Ctor.rounding = 1;
              external = false;
              x = x.times(x).plus(1).sqrt().plus(x);
              external = true;
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return x.ln();
            };
            /*
             * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the
             * value of this Decimal.
             *
             * Domain: [-1, 1]
             * Range: [-Infinity, Infinity]
             *
             * atanh(x) = 0.5 * ln((1 + x) / (1 - x))
             *
             * atanh(|x| > 1)   = NaN
             * atanh(NaN)       = NaN
             * atanh(Infinity)  = NaN
             * atanh(-Infinity) = NaN
             * atanh(0)         = 0
             * atanh(-0)        = -0
             * atanh(1)         = Infinity
             * atanh(-1)        = -Infinity
             *
             */


            P.inverseHyperbolicTangent = P.atanh = function () {
              var pr,
                  rm,
                  wpr,
                  xsd,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite()) return new Ctor(NaN);
              if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              xsd = x.sd();
              if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);
              Ctor.precision = wpr = xsd - x.e;
              x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);
              Ctor.precision = pr + 4;
              Ctor.rounding = 1;
              x = x.ln();
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return x.times(0.5);
            };
            /*
             * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this
             * Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-pi/2, pi/2]
             *
             * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))
             *
             * asin(0)       = 0
             * asin(-0)      = -0
             * asin(1/2)     = pi/6
             * asin(-1/2)    = -pi/6
             * asin(1)       = pi/2
             * asin(-1)      = -pi/2
             * asin(|x| > 1) = NaN
             * asin(NaN)     = NaN
             *
             * TODO? Compare performance of Taylor series.
             *
             */


            P.inverseSine = P.asin = function () {
              var halfPi,
                  k,
                  pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (x.isZero()) return new Ctor(x);
              k = x.abs().cmp(1);
              pr = Ctor.precision;
              rm = Ctor.rounding;

              if (k !== -1) {
                // |x| is 1
                if (k === 0) {
                  halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
                  halfPi.s = x.s;
                  return halfPi;
                } // |x| > 1 or x is NaN


                return new Ctor(NaN);
              } // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6


              Ctor.precision = pr + 6;
              Ctor.rounding = 1;
              x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return x.times(2);
            };
            /*
             * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value
             * of this Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-pi/2, pi/2]
             *
             * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
             *
             * atan(0)         = 0
             * atan(-0)        = -0
             * atan(1)         = pi/4
             * atan(-1)        = -pi/4
             * atan(Infinity)  = pi/2
             * atan(-Infinity) = -pi/2
             * atan(NaN)       = NaN
             *
             */


            P.inverseTangent = P.atan = function () {
              var i,
                  j,
                  k,
                  n,
                  px,
                  t,
                  r,
                  wpr,
                  x2,
                  x = this,
                  Ctor = x.constructor,
                  pr = Ctor.precision,
                  rm = Ctor.rounding;

              if (!x.isFinite()) {
                if (!x.s) return new Ctor(NaN);

                if (pr + 4 <= PI_PRECISION) {
                  r = getPi(Ctor, pr + 4, rm).times(0.5);
                  r.s = x.s;
                  return r;
                }
              } else if (x.isZero()) {
                return new Ctor(x);
              } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {
                r = getPi(Ctor, pr + 4, rm).times(0.25);
                r.s = x.s;
                return r;
              }

              Ctor.precision = wpr = pr + 10;
              Ctor.rounding = 1; // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);
              // Argument reduction
              // Ensure |x| < 0.42
              // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))

              k = Math.min(28, wpr / LOG_BASE + 2 | 0);

              for (i = k; i; --i) {
                x = x.div(x.times(x).plus(1).sqrt().plus(1));
              }

              external = false;
              j = Math.ceil(wpr / LOG_BASE);
              n = 1;
              x2 = x.times(x);
              r = new Ctor(x);
              px = x; // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...

              for (; i !== -1;) {
                px = px.times(x2);
                t = r.minus(px.div(n += 2));
                px = px.times(x2);
                r = t.plus(px.div(n += 2));
                if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;) {
                  ;
                }
              }

              if (k) r = r.times(2 << k - 1);
              external = true;
              return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);
            };
            /*
             * Return true if the value of this Decimal is a finite number, otherwise return false.
             *
             */


            P.isFinite = function () {
              return !!this.d;
            };
            /*
             * Return true if the value of this Decimal is an integer, otherwise return false.
             *
             */


            P.isInteger = P.isInt = function () {
              return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
            };
            /*
             * Return true if the value of this Decimal is NaN, otherwise return false.
             *
             */


            P.isNaN = function () {
              return !this.s;
            };
            /*
             * 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 or -0, otherwise return false.
             *
             */


            P.isZero = function () {
              return !!this.d && this.d[0] === 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, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * If no base is specified, return log[10](arg).
             *
             * log[base](arg) = ln(arg) / ln(base)
             *
             * The result will always be correctly rounded if the base of the log is 10, and 'almost always'
             * otherwise:
             *
             * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen
             * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error
             * between the result and the correctly rounded result will be one ulp (unit in the last place).
             *
             * log[-b](a)       = NaN
             * log[0](a)        = NaN
             * log[1](a)        = NaN
             * log[NaN](a)      = NaN
             * log[Infinity](a) = NaN
             * log[b](0)        = -Infinity
             * log[b](-0)       = -Infinity
             * log[b](-a)       = NaN
             * log[b](1)        = 0
             * log[b](Infinity) = Infinity
             * log[b](NaN)      = NaN
             *
             * [base] {number|string|Decimal} The base of the logarithm.
             *
             */


            P.logarithm = P.log = function (base) {
              var isBase10,
                  d,
                  denominator,
                  k,
                  inf,
                  num,
                  sd,
                  r,
                  arg = this,
                  Ctor = arg.constructor,
                  pr = Ctor.precision,
                  rm = Ctor.rounding,
                  guard = 5; // Default base is 10.

              if (base == null) {
                base = new Ctor(10);
                isBase10 = true;
              } else {
                base = new Ctor(base);
                d = base.d; // Return NaN if base is negative, or non-finite, or is 0 or 1.

                if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);
                isBase10 = base.eq(10);
              }

              d = arg.d; // Is arg negative, non-finite, 0 or 1?

              if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {
                return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);
              } // The result will have a non-terminating decimal expansion if base is 10 and arg is not an
              // integer power of 10.


              if (isBase10) {
                if (d.length > 1) {
                  inf = true;
                } else {
                  for (k = d[0]; k % 10 === 0;) {
                    k /= 10;
                  }

                  inf = k !== 1;
                }
              }

              external = false;
              sd = pr + guard;
              num = naturalLogarithm(arg, sd);
              denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); // The result will have 5 rounding digits.

              r = divide(num, denominator, sd, 1); // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,
              // calculate 10 further digits.
              //
              // If the result is known to have an infinite decimal expansion, repeat this until it is clear
              // that the result is above or below the boundary. Otherwise, if after calculating the 10
              // further digits, the last 14 are nines, round up and assume the result is exact.
              // Also assume the result is exact if the last 14 are zero.
              //
              // Example of a result that will be incorrectly rounded:
              // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...
              // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it
              // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so
              // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal
              // place is still 2.6.

              if (checkRoundingDigits(r.d, k = pr, rm)) {
                do {
                  sd += 10;
                  num = naturalLogarithm(arg, sd);
                  denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
                  r = divide(num, denominator, sd, 1);

                  if (!inf) {
                    // Check for 14 nines from the 2nd rounding digit, as the first may be 4.
                    if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {
                      r = finalise(r, pr + 1, 0);
                    }

                    break;
                  }
                } while (checkRoundingDigits(r.d, k += 10, rm));
              }

              external = true;
              return finalise(r, pr, rm);
            };
            /*
             * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.
             *
             * arguments {number|string|Decimal}
             *
            P.max = function () {
              Array.prototype.push.call(arguments, this);
              return maxOrMin(this.constructor, arguments, 'lt');
            };
             */

            /*
             * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
             *
             * arguments {number|string|Decimal}
             *
            P.min = function () {
              Array.prototype.push.call(arguments, this);
              return maxOrMin(this.constructor, arguments, 'gt');
            };
             */

            /*
             *  n - 0 = n
             *  n - N = N
             *  n - I = -I
             *  0 - n = -n
             *  0 - 0 = 0
             *  0 - N = N
             *  0 - I = -I
             *  N - n = N
             *  N - 0 = N
             *  N - N = N
             *  N - I = N
             *  I - n = I
             *  I - 0 = I
             *  I - N = N
             *  I - I = N
             *
             * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             */


            P.minus = P.sub = function (y) {
              var d,
                  e,
                  i,
                  j,
                  k,
                  len,
                  pr,
                  rm,
                  xd,
                  xe,
                  xLTy,
                  yd,
                  x = this,
                  Ctor = x.constructor;
              y = new Ctor(y); // If either is not finite...

              if (!x.d || !y.d) {
                // Return NaN if either is NaN.
                if (!x.s || !y.s) y = new Ctor(NaN); // Return y negated if x is finite and y is ±Infinity.
                else if (x.d) y.s = -y.s; // Return x if y is finite and x is ±Infinity.
                  // Return x if both are ±Infinity with different signs.
                  // Return NaN if both are ±Infinity with the same sign.
                  else y = new Ctor(y.d || x.s !== y.s ? x : NaN);
                return y;
              } // If signs differ...


              if (x.s != y.s) {
                y.s = -y.s;
                return x.plus(y);
              }

              xd = x.d;
              yd = y.d;
              pr = Ctor.precision;
              rm = Ctor.rounding; // If either is zero...

              if (!xd[0] || !yd[0]) {
                // Return y negated if x is zero and y is non-zero.
                if (yd[0]) y.s = -y.s; // Return x if y is zero and x is non-zero.
                else if (xd[0]) y = new Ctor(x); // Return zero if both are zero.
                  // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.
                  else return new Ctor(rm === 3 ? -0 : 0);
                return external ? finalise(y, pr, rm) : y;
              } // x and y are finite, non-zero numbers with the same sign.
              // Calculate base 1e7 exponents.


              e = mathfloor(y.e / LOG_BASE);
              xe = mathfloor(x.e / LOG_BASE);
              xd = xd.slice();
              k = xe - e; // If base 1e7 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(rm === 3 ? -0 : 0);
              y.d = xd;
              y.e = getBase10Exponent(xd, e);
              return external ? finalise(y, pr, rm) : y;
            };
            /*
             *   n % 0 =  N
             *   n % N =  N
             *   n % I =  n
             *   0 % n =  0
             *  -0 % n = -0
             *   0 % 0 =  N
             *   0 % N =  N
             *   0 % I =  0
             *   N % n =  N
             *   N % 0 =  N
             *   N % N =  N
             *   N % I =  N
             *   I % n =  N
             *   I % 0 =  N
             *   I % N =  N
             *   I % I =  N
             *
             * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to
             * `precision` significant digits using rounding mode `rounding`.
             *
             * The result depends on the modulo mode.
             *
             */


            P.modulo = P.mod = function (y) {
              var q,
                  x = this,
                  Ctor = x.constructor;
              y = new Ctor(y); // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.

              if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); // Return x if y is ±Infinity or x is ±0.

              if (!y.d || x.d && !x.d[0]) {
                return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);
              } // Prevent rounding of intermediate calculations.


              external = false;

              if (Ctor.modulo == 9) {
                // Euclidian division: q = sign(y) * floor(x / abs(y))
                // result = x - q * y    where  0 <= result < abs(y)
                q = divide(x, y.abs(), 0, 3, 1);
                q.s *= y.s;
              } else {
                q = divide(x, y, 0, Ctor.modulo, 1);
              }

              q = q.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, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             */


            P.naturalExponential = P.exp = function () {
              return naturalExponential(this);
            };
            /*
             * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
             * rounded to `precision` significant digits using rounding mode `rounding`.
             *
             */


            P.naturalLogarithm = P.ln = function () {
              return naturalLogarithm(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;
              return finalise(x);
            };
            /*
             *  n + 0 = n
             *  n + N = N
             *  n + I = I
             *  0 + n = n
             *  0 + 0 = 0
             *  0 + N = N
             *  0 + I = I
             *  N + n = N
             *  N + 0 = N
             *  N + N = N
             *  N + I = N
             *  I + n = I
             *  I + 0 = I
             *  I + N = N
             *  I + I = I
             *
             * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             */


            P.plus = P.add = function (y) {
              var carry,
                  d,
                  e,
                  i,
                  k,
                  len,
                  pr,
                  rm,
                  xd,
                  yd,
                  x = this,
                  Ctor = x.constructor;
              y = new Ctor(y); // If either is not finite...

              if (!x.d || !y.d) {
                // Return NaN if either is NaN.
                if (!x.s || !y.s) y = new Ctor(NaN); // Return x if y is finite and x is ±Infinity.
                // Return x if both are ±Infinity with the same sign.
                // Return NaN if both are ±Infinity with different signs.
                // Return y if x is finite and y is ±Infinity.
                else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);
                return y;
              } // If signs differ...


              if (x.s != y.s) {
                y.s = -y.s;
                return x.minus(y);
              }

              xd = x.d;
              yd = y.d;
              pr = Ctor.precision;
              rm = Ctor.rounding; // If either is zero...

              if (!xd[0] || !yd[0]) {
                // Return x if y is zero.
                // Return y if y is non-zero.
                if (!yd[0]) y = new Ctor(x);
                return external ? finalise(y, pr, rm) : y;
              } // x and y are finite, non-zero numbers with the same sign.
              // Calculate base 1e7 exponents.


              k = mathfloor(x.e / LOG_BASE);
              e = mathfloor(y.e / LOG_BASE);
              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 = getBase10Exponent(xd, e);
              return external ? finalise(y, pr, rm) : 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 k,
                  x = this;
              if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);

              if (x.d) {
                k = getPrecision(x.d);
                if (z && x.e + 1 > k) k = x.e + 1;
              } else {
                k = NaN;
              }

              return k;
            };
            /*
             * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
             * rounding mode `rounding`.
             *
             */


            P.round = function () {
              var x = this,
                  Ctor = x.constructor;
              return finalise(new Ctor(x), x.e + 1, Ctor.rounding);
            };
            /*
             * Return a new Decimal whose value is the sine of the value in radians of this Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-1, 1]
             *
             * sin(x) = x - x^3/3! + x^5/5! - ...
             *
             * sin(0)         = 0
             * sin(-0)        = -0
             * sin(Infinity)  = NaN
             * sin(-Infinity) = NaN
             * sin(NaN)       = NaN
             *
             */


            P.sine = P.sin = function () {
              var pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite()) return new Ctor(NaN);
              if (x.isZero()) return new Ctor(x);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
              Ctor.rounding = 1;
              x = sine(Ctor, toLessThanHalfPi(Ctor, x));
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);
            };
            /*
             * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             *  sqrt(-n) =  N
             *  sqrt(N)  =  N
             *  sqrt(-I) =  N
             *  sqrt(I)  =  I
             *  sqrt(0)  =  0
             *  sqrt(-0) = -0
             *
             */


            P.squareRoot = P.sqrt = function () {
              var m,
                  n,
                  sd,
                  r,
                  rep,
                  t,
                  x = this,
                  d = x.d,
                  e = x.e,
                  s = x.s,
                  Ctor = x.constructor; // Negative/NaN/Infinity/zero?

              if (s !== 1 || !d || !d[0]) {
                return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);
              }

              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(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 = '5e' + e;
                } else {
                  n = s.toExponential();
                  n = n.slice(0, n.indexOf('e') + 1) + e;
                }

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

              sd = (e = Ctor.precision) + 3; // Newton-Raphson iteration.

              for (;;) {
                t = r;
                r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); // TODO? Replace with for-loop and checkRoundingDigits.

                if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
                  n = n.slice(sd - 3, sd + 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 (n == '9999' || !rep && n == '4999') {
                    // On the first iteration only, check to see if rounding up gives the exact result as the
                    // nines may infinitely repeat.
                    if (!rep) {
                      finalise(t, e + 1, 0);

                      if (t.times(t).eq(x)) {
                        r = t;
                        break;
                      }
                    }

                    sd += 4;
                    rep = 1;
                  } else {
                    // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
                    // If not, then there are further digits and m will be truthy.
                    if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
                      // Truncate to the first rounding digit.
                      finalise(r, e + 1, 1);
                      m = !r.times(r).eq(x);
                    }

                    break;
                  }
                }
              }

              external = true;
              return finalise(r, e, Ctor.rounding, m);
            };
            /*
             * Return a new Decimal whose value is the tangent of the value in radians of this Decimal.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-Infinity, Infinity]
             *
             * tan(0)         = 0
             * tan(-0)        = -0
             * tan(Infinity)  = NaN
             * tan(-Infinity) = NaN
             * tan(NaN)       = NaN
             *
             */


            P.tangent = P.tan = function () {
              var pr,
                  rm,
                  x = this,
                  Ctor = x.constructor;
              if (!x.isFinite()) return new Ctor(NaN);
              if (x.isZero()) return new Ctor(x);
              pr = Ctor.precision;
              rm = Ctor.rounding;
              Ctor.precision = pr + 10;
              Ctor.rounding = 1;
              x = x.sin();
              x.s = 1;
              x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);
              Ctor.precision = pr;
              Ctor.rounding = rm;
              return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);
            };
            /*
             *  n * 0 = 0
             *  n * N = N
             *  n * I = I
             *  0 * n = 0
             *  0 * 0 = 0
             *  0 * N = N
             *  0 * I = N
             *  N * n = N
             *  N * 0 = N
             *  N * N = N
             *  N * I = N
             *  I * n = I
             *  I * 0 = N
             *  I * N = N
             *  I * I = I
             *
             * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             */


            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;
              y.s *= x.s; // If either is NaN, ±Infinity or ±0...

              if (!xd || !xd[0] || !yd || !yd[0]) {
                return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd // Return NaN if either is NaN.
                // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.
                ? NaN // Return ±Infinity if either is ±Infinity.
                // Return ±0 if either is ±0.
                : !xd || !yd ? y.s / 0 : y.s * 0);
              }

              e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);
              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 = getBase10Exponent(r, e);
              return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;
            };
            /*
             * Return a string representing the value of this Decimal in base 2, round to `sd` significant
             * digits using rounding mode `rm`.
             *
             * If the optional `sd` argument is present then return binary exponential notation.
             *
             * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
             * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
             *
             */


            P.toBinary = function (sd, rm) {
              return toStringBinary(this, 2, sd, rm);
            };
            /*
             * 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 finalise(x, dp + x.e + 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 = finiteToString(x, true);
              } else {
                checkInt32(dp, 0, MAX_DIGITS);
                if (rm === void 0) rm = Ctor.rounding;else checkInt32(rm, 0, 8);
                x = finalise(new Ctor(x), dp + 1, rm);
                str = finiteToString(x, true, dp + 1);
              }

              return x.isNeg() && !x.isZero() ? '-' + str : 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) {
                str = finiteToString(x);
              } else {
                checkInt32(dp, 0, MAX_DIGITS);
                if (rm === void 0) rm = Ctor.rounding;else checkInt32(rm, 0, 8);
                y = finalise(new Ctor(x), dp + x.e + 1, rm);
                str = finiteToString(y, false, dp + y.e + 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 an array representing the value of this Decimal as a simple fraction with an integer
             * numerator and an integer denominator.
             *
             * The denominator will be a positive non-zero value less than or equal to the specified maximum
             * denominator. If a maximum denominator is not specified, the denominator will be the lowest
             * value necessary to represent the number exactly.
             *
             * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity.
             *
             */


            P.toFraction = function (maxD) {
              var d,
                  d0,
                  d1,
                  d2,
                  e,
                  k,
                  n,
                  n0,
                  n1,
                  pr,
                  q,
                  r,
                  x = this,
                  xd = x.d,
                  Ctor = x.constructor;
              if (!xd) return new Ctor(x);
              n1 = d0 = new Ctor(1);
              d1 = n0 = new Ctor(0);
              d = new Ctor(d1);
              e = d.e = getPrecision(xd) - x.e - 1;
              k = e % LOG_BASE;
              d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);

              if (maxD == null) {
                // d is 10**e, the minimum max-denominator needed.
                maxD = e > 0 ? d : n1;
              } else {
                n = new Ctor(maxD);
                if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);
                maxD = n.gt(d) ? e > 0 ? d : n1 : n;
              }

              external = false;
              n = new Ctor(digitsToString(xd));
              pr = Ctor.precision;
              Ctor.precision = e = xd.length * LOG_BASE * 2;

              for (;;) {
                q = divide(n, d, 0, 1, 1);
                d2 = d0.plus(q.times(d1));
                if (d2.cmp(maxD) == 1) break;
                d0 = d1;
                d1 = d2;
                d2 = n1;
                n1 = n0.plus(q.times(d2));
                n0 = d2;
                d2 = d;
                d = n.minus(q.times(d2));
                n = d2;
              }

              d2 = divide(maxD.minus(d0), d1, 0, 1, 1);
              n0 = n0.plus(d2.times(n1));
              d0 = d0.plus(d2.times(d1));
              n0.s = n1.s = x.s; // Determine which fraction is closer to x, n0/d0 or n1/d1?

              r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
              Ctor.precision = pr;
              external = true;
              return r;
            };
            /*
             * Return a string representing the value of this Decimal in base 16, round to `sd` significant
             * digits using rounding mode `rm`.
             *
             * If the optional `sd` argument is present then return binary exponential notation.
             *
             * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
             * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
             *
             */


            P.toHexadecimal = P.toHex = function (sd, rm) {
              return toStringBinary(this, 16, sd, rm);
            };
            /*
             * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding
             * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.
             *
             * The return value will always have the same sign as this Decimal, unless either this Decimal
             * or `y` is NaN, in which case the return value will be also be NaN.
             *
             * The return value is not affected by the value of `precision`.
             *
             * y {number|string|Decimal} The magnitude to round to a multiple of.
             * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
             *
             * 'toNearest() rounding mode not an integer: {rm}'
             * 'toNearest() rounding mode out of range: {rm}'
             *
             */


            P.toNearest = function (y, rm) {
              var x = this,
                  Ctor = x.constructor;
              x = new Ctor(x);

              if (y == null) {
                // If x is not finite, return x.
                if (!x.d) return x;
                y = new Ctor(1);
                rm = Ctor.rounding;
              } else {
                y = new Ctor(y);

                if (rm === void 0) {
                  rm = Ctor.rounding;
                } else {
                  checkInt32(rm, 0, 8);
                } // If x is not finite, return x if y is not NaN, else NaN.


                if (!x.d) return y.s ? x : y; // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.

                if (!y.d) {
                  if (y.s) y.s = x.s;
                  return y;
                }
              } // If y is not zero, calculate the nearest multiple of y to x.


              if (y.d[0]) {
                external = false;
                x = divide(x, y, 0, rm, 1).times(y);
                external = true;
                finalise(x); // If y is zero, return zero with the sign of x.
              } else {
                y.s = x.s;
                x = y;
              }

              return x;
            };
            /*
             * Return the value of this Decimal converted to a number primitive.
             * Zero keeps its sign.
             *
             */


            P.toNumber = function () {
              return +this;
            };
            /*
             * Return a string representing the value of this Decimal in base 8, round to `sd` significant
             * digits using rounding mode `rm`.
             *
             * If the optional `sd` argument is present then return binary exponential notation.
             *
             * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
             * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
             *
             */


            P.toOctal = function (sd, rm) {
              return toStringBinary(this, 8, sd, rm);
            };
            /*
             * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded
             * to `precision` significant digits using rounding mode `rounding`.
             *
             * ECMAScript compliant.
             *
             *   pow(x, NaN)                           = NaN
             *   pow(x, ±0)                            = 1
               *   pow(NaN, non-zero)                    = NaN
             *   pow(abs(x) > 1, +Infinity)            = +Infinity
             *   pow(abs(x) > 1, -Infinity)            = +0
             *   pow(abs(x) == 1, ±Infinity)           = NaN
             *   pow(abs(x) < 1, +Infinity)            = +0
             *   pow(abs(x) < 1, -Infinity)            = +Infinity
             *   pow(+Infinity, y > 0)                 = +Infinity
             *   pow(+Infinity, y < 0)                 = +0
             *   pow(-Infinity, odd integer > 0)       = -Infinity
             *   pow(-Infinity, even integer > 0)      = +Infinity
             *   pow(-Infinity, odd integer < 0)       = -0
             *   pow(-Infinity, even integer < 0)      = +0
             *   pow(+0, y > 0)                        = +0
             *   pow(+0, y < 0)                        = +Infinity
             *   pow(-0, odd integer > 0)              = -0
             *   pow(-0, even integer > 0)             = +0
             *   pow(-0, odd integer < 0)              = -Infinity
             *   pow(-0, even integer < 0)             = +Infinity
             *   pow(finite x < 0, finite non-integer) = NaN
             *
             * For non-integer or very large exponents pow(x, y) is calculated using
             *
             *   x^y = exp(y*ln(x))
             *
             * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the
             * probability of an incorrectly rounded result
             * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14
             * i.e. 1 in 250,000,000,000,000
             *
             * If a result is incorrectly rounded the maximum error will be 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,
                  rm,
                  s,
                  x = this,
                  Ctor = x.constructor,
                  yn = +(y = new Ctor(y)); // Either ±Infinity, NaN or ±0?

              if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));
              x = new Ctor(x);
              if (x.eq(1)) return x;
              pr = Ctor.precision;
              rm = Ctor.rounding;
              if (y.eq(1)) return finalise(x, pr, rm); // y exponent

              e = mathfloor(y.e / LOG_BASE); // If y is a small integer use the 'exponentiation by squaring' algorithm.

              if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
                r = intPow(Ctor, x, k, pr);
                return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);
              }

              s = x.s; // if x is negative

              if (s < 0) {
                // if y is not an integer
                if (e < y.d.length - 1) return new Ctor(NaN); // Result is positive if x is negative and the last digit of integer y is even.

                if ((y.d[e] & 1) == 0) s = 1; // if x.eq(-1)

                if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {
                  x.s = s;
                  return x;
                }
              } // Estimate result exponent.
              // x^y = 10^e,  where e = y * log10(x)
              // log10(x) = log10(x_significand) + x_exponent
              // log10(x_significand) = ln(x_significand) / ln(10)


              k = mathpow(+x, yn);
              e = k == 0 || !isFinite(k) ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) : new Ctor(k + '').e; // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.
              // Overflow/underflow?

              if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);
              external = false;
              Ctor.rounding = x.s = 1; // Estimate the extra guard digits needed to ensure five correct rounding digits from
              // naturalLogarithm(x). Example of failure without these extra digits (precision: 10):
              // new Decimal(2.32456).pow('2087987436534566.46411')
              // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815

              k = Math.min(12, (e + '').length); // r = x^y = exp(y*ln(x))

              r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)

              if (r.d) {
                // Truncate to the required precision plus five rounding digits.
                r = finalise(r, pr + 5, 1); // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate
                // the result.

                if (checkRoundingDigits(r.d, pr, rm)) {
                  e = pr + 10; // Truncate to the increased precision plus five rounding digits.

                  r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).

                  if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {
                    r = finalise(r, pr + 1, 0);
                  }
                }
              }

              r.s = s;
              external = true;
              Ctor.rounding = rm;
              return finalise(r, pr, rm);
            };
            /*
             * 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 str,
                  x = this,
                  Ctor = x.constructor;

              if (sd === void 0) {
                str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
              } else {
                checkInt32(sd, 1, MAX_DIGITS);
                if (rm === void 0) rm = Ctor.rounding;else checkInt32(rm, 0, 8);
                x = finalise(new Ctor(x), sd, rm);
                str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);
              }

              return x.isNeg() && !x.isZero() ? '-' + str : 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.
             *
             * 'toSD() digits out of range: {sd}'
             * 'toSD() digits not an integer: {sd}'
             * 'toSD() rounding mode not an integer: {rm}'
             * 'toSD() rounding mode out of range: {rm}'
             *
             */


            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 finalise(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 = function () {
              var x = this,
                  Ctor = x.constructor,
                  str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
              return x.isNeg() && !x.isZero() ? '-' + str : str;
            };
            /*
             * Return a new Decimal whose value is the value of this Decimal truncated to a whole number.
             *
             */


            P.truncated = P.trunc = function () {
              return finalise(new this.constructor(this), this.e + 1, 1);
            };
            /*
             * Return a string representing the value of this Decimal.
             * Unlike `toString`, negative zero will include the minus sign.
             *
             */


            P.valueOf = P.toJSON = function () {
              var x = this,
                  Ctor = x.constructor,
                  str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
              return x.isNeg() ? '-' + str : str;
            };
            /*
            // Add aliases to match BigDecimal method names.
            // P.add = P.plus;
            P.subtract = P.minus;
            P.multiply = P.times;
            P.divide = P.div;
            P.remainder = P.mod;
            P.compareTo = P.cmp;
            P.negate = P.neg;
             */
            // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.

            /*
             *  digitsToString           P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,
             *                           finiteToString, naturalExponential, naturalLogarithm
             *  checkInt32               P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,
             *                           P.toPrecision, P.toSignificantDigits, toStringBinary, random
             *  checkRoundingDigits      P.logarithm, P.toPower, naturalExponential, naturalLogarithm
             *  convertBase              toStringBinary, parseOther
             *  cos                      P.cos
             *  divide                   P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,
             *                           P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,
             *                           P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,
             *                           taylorSeries, atan2, parseOther
             *  finalise                 P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,
             *                           P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,
             *                           P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,
             *                           P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,
             *                           P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,
             *                           P.truncated, divide, getLn10, getPi, naturalExponential,
             *                           naturalLogarithm, ceil, floor, round, trunc
             *  finiteToString           P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,
             *                           toStringBinary
             *  getBase10Exponent        P.minus, P.plus, P.times, parseOther
             *  getLn10                  P.logarithm, naturalLogarithm
             *  getPi                    P.acos, P.asin, P.atan, toLessThanHalfPi, atan2
             *  getPrecision             P.precision, P.toFraction
             *  getZeroString            digitsToString, finiteToString
             *  intPow                   P.toPower, parseOther
             *  isOdd                    toLessThanHalfPi
             *  maxOrMin                 max, min
             *  naturalExponential       P.naturalExponential, P.toPower
             *  naturalLogarithm         P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,
             *                           P.toPower, naturalExponential
             *  nonFiniteToString        finiteToString, toStringBinary
             *  parseDecimal             Decimal
             *  parseOther               Decimal
             *  sin                      P.sin
             *  taylorSeries             P.cosh, P.sinh, cos, sin
             *  toLessThanHalfPi         P.cos, P.sin
             *  toStringBinary           P.toBinary, P.toHexadecimal, P.toOctal
             *  truncate                 intPow
             *
             *  Throws:                  P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,
             *                           naturalLogarithm, config, parseOther, random, Decimal
             */


            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;
            }

            function checkInt32(i, min, max) {
              if (i !== ~~i || i < min || i > max) {
                throw Error(invalidArgument + i);
              }
            }
            /*
             * Check 5 rounding digits if `repeating` is null, 4 otherwise.
             * `repeating == null` if caller is `log` or `pow`,
             * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.
             */


            function checkRoundingDigits(d, i, rm, repeating) {
              var di, k, r, rd; // Get the length of the first word of the array d.

              for (k = d[0]; k >= 10; k /= 10) {
                --i;
              } // Is the rounding digit in the first word of d?


              if (--i < 0) {
                i += LOG_BASE;
                di = 0;
              } else {
                di = Math.ceil((i + 1) / LOG_BASE);
                i %= LOG_BASE;
              } // i is the index (0 - 6) of the rounding digit.
              // E.g. if within the word 3487563 the first rounding digit is 5,
              // then i = 4, k = 1000, rd = 3487563 % 1000 = 563


              k = mathpow(10, LOG_BASE - i);
              rd = d[di] % k | 0;

              if (repeating == null) {
                if (i < 3) {
                  if (i == 0) rd = rd / 100 | 0;else if (i == 1) rd = rd / 10 | 0;
                  r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;
                } else {
                  r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;
                }
              } else {
                if (i < 4) {
                  if (i == 0) rd = rd / 1000 | 0;else if (i == 1) rd = rd / 100 | 0;else if (i == 2) rd = rd / 10 | 0;
                  r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;
                } else {
                  r = ((repeating || rm < 4) && rd + 1 == k || !repeating && rm > 3 && rd + 1 == k / 2) && (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;
                }
              }

              return r;
            } // Convert string of `baseIn` to an array of numbers of `baseOut`.
            // Eg. convertBase('255', 10, 16) returns [15, 15].
            // Eg. convertBase('ff', 16, 10) returns [2, 5, 5].


            function convertBase(str, baseIn, baseOut) {
              var j,
                  arr = [0],
                  arrL,
                  i = 0,
                  strL = str.length;

              for (; i < strL;) {
                for (arrL = arr.length; arrL--;) {
                  arr[arrL] *= baseIn;
                }

                arr[0] += NUMERALS.indexOf(str.charAt(i++));

                for (j = 0; j < arr.length; j++) {
                  if (arr[j] > baseOut - 1) {
                    if (arr[j + 1] === void 0) arr[j + 1] = 0;
                    arr[j + 1] += arr[j] / baseOut | 0;
                    arr[j] %= baseOut;
                  }
                }
              }

              return arr.reverse();
            }
            /*
             * cos(x) = 1 - x^2/2! + x^4/4! - ...
             * |x| < pi/2
             *
             */


            function cosine(Ctor, x) {
              var k,
                  y,
                  len = x.d.length; // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1
              // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1
              // Estimate the optimum number of times to use the argument reduction.

              if (len < 32) {
                k = Math.ceil(len / 3);
                y = (1 / tinyPow(4, k)).toString();
              } else {
                k = 16;
                y = '2.3283064365386962890625e-10';
              }

              Ctor.precision += k;
              x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); // Reverse argument reduction

              for (var i = k; i--;) {
                var cos2x = x.times(x);
                x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);
              }

              Ctor.precision -= k;
              return x;
            }
            /*
             * Perform division in the specified base.
             */


            var divide = function () {
              // Assumes non-zero x and k, and hence non-zero result.
              function multiplyInteger(x, k, base) {
                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, base) {
                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, rm, dp, base) {
                var cmp,
                    e,
                    i,
                    k,
                    logBase,
                    more,
                    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 NaN, Infinity or 0?

                if (!xd || !xd[0] || !yd || !yd[0]) {
                  return new Ctor( // Return NaN if either NaN, or both Infinity or 0.
                  !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.
                  xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);
                }

                if (base) {
                  logBase = 1;
                  e = x.e - y.e;
                } else {
                  base = BASE;
                  logBase = LOG_BASE;
                  e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);
                }

                yL = yd.length;
                xL = xd.length;
                q = new Ctor(sign);
                qd = q.d = []; // Result exponent may be one less than e.
                // The digit array of a Decimal from toStringBinary may have trailing zeros.

                for (i = 0; yd[i] == (xd[i] || 0); i++) {
                  ;
                }

                if (yd[i] > (xd[i] || 0)) e--;

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

                if (sd < 0) {
                  qd.push(1);
                  more = true;
                } else {
                  // Convert precision in number of base 10 digits to base 1e7 digits.
                  sd = sd / logBase + 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;
                    }

                    more = k || i < xL; // 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, base);
                      xd = multiplyInteger(xd, k, base);
                      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, base);
                          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, base);
                          }
                        } 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, base); // 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, base);
                          }
                        }

                        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--);

                    more = rem[0] !== void 0;
                  } // Leading zero?


                  if (!qd[0]) qd.shift();
                } // logBase is 1 when divide is being used for base conversion.


                if (logBase == 1) {
                  q.e = e;
                  inexact = more;
                } else {
                  // To calculate q.e, first get the number of digits of qd[0].
                  for (i = 1, k = qd[0]; k >= 10; k /= 10) {
                    i++;
                  }

                  q.e = i + e * logBase - 1;
                  finalise(q, dp ? pr + q.e + 1 : pr, rm, more);
                }

                return q;
              };
            }();
            /*
             * Round `x` to `sd` significant digits using rounding mode `rm`.
             * Check for over/under-flow.
             */


            function finalise(x, sd, rm, isTruncated) {
              var digits,
                  i,
                  j,
                  k,
                  rd,
                  roundUp,
                  w,
                  xd,
                  xdi,
                  Ctor = x.constructor; // Don't round if sd is null or undefined.

              out: if (sd != null) {
                xd = x.d; // Infinity/NaN.

                if (!xd) return x; // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
                // w: the word of xd containing rd, a base 1e7 number.
                // xdi: the index of w within xd.
                // digits: 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 (digits = 1, k = xd[0]; k >= 10; k /= 10) {
                  digits++;
                }

                i = sd - digits; // Is the rounding digit in the first word of xd?

                if (i < 0) {
                  i += LOG_BASE;
                  j = sd;
                  w = xd[xdi = 0]; // Get the rounding digit at index j of w.

                  rd = w / mathpow(10, digits - j - 1) % 10 | 0;
                } else {
                  xdi = Math.ceil((i + 1) / LOG_BASE);
                  k = xd.length;

                  if (xdi >= k) {
                    if (isTruncated) {
                      // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.
                      for (; k++ <= xdi;) {
                        xd.push(0);
                      }

                      w = rd = 0;
                      digits = 1;
                      i %= LOG_BASE;
                      j = i - LOG_BASE + 1;
                    } else {
                      break out;
                    }
                  } else {
                    w = k = xd[xdi]; // Get the number of digits of w.

                    for (digits = 1; k >= 10; k /= 10) {
                      digits++;
                    } // 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 - digits.

                    j = i - LOG_BASE + digits; // Get the rounding digit at index j of w.

                    rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;
                  }
                } // Are there any non-zero digits after the rounding digit?


                isTruncated = isTruncated || sd < 0 || xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); // The expression `w % mathpow(10, digits - 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.

                roundUp = rm < 4 ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && // Check whether the digit to the left of the rounding digit is odd.
                (i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10 & 1 || rm == (x.s < 0 ? 8 : 7));

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

                  if (roundUp) {
                    // Convert sd to decimal places.
                    sd -= x.e + 1; // 1, 0.1, 0.01, 0.001, 0.0001 etc.

                    xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
                    x.e = -sd || 0;
                  } else {
                    // Zero.
                    xd[0] = x.e = 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, digits - j) % mathpow(10, j) | 0) * k : 0;
                }

                if (roundUp) {
                  for (;;) {
                    // Is the digit to be rounded up in the first word of xd?
                    if (xdi == 0) {
                      // i will be the length of xd[0] before k is added.
                      for (i = 1, j = xd[0]; j >= 10; j /= 10) {
                        i++;
                      }

                      j = xd[0] += k;

                      for (k = 1; j >= 10; j /= 10) {
                        k++;
                      } // if i != k the length has increased.


                      if (i != k) {
                        x.e++;
                        if (xd[0] == BASE) xd[0] = 1;
                      }

                      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) {
                // Overflow?
                if (x.e > Ctor.maxE) {
                  // Infinity.
                  x.d = null;
                  x.e = NaN; // Underflow?
                } else if (x.e < Ctor.minE) {
                  // Zero.
                  x.e = 0;
                  x.d = [0]; // Ctor.underflow = true;
                } // else Ctor.underflow = false;

              }

              return x;
            }

            function finiteToString(x, isExp, sd) {
              if (!x.isFinite()) return nonFiniteToString(x);
              var k,
                  e = x.e,
                  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 + (x.e < 0 ? 'e' : 'e+') + x.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 str;
            } // Calculate the base 10 exponent from the base 1e7 exponent.


            function getBase10Exponent(digits, e) {
              var w = digits[0]; // Add the number of digits of the first word of the digits array.

              for (e *= LOG_BASE; w >= 10; w /= 10) {
                e++;
              }

              return e;
            }

            function getLn10(Ctor, sd, pr) {
              if (sd > LN10_PRECISION) {
                // Reset global state in case the exception is caught.
                external = true;
                if (pr) Ctor.precision = pr;
                throw Error(precisionLimitExceeded);
              }

              return finalise(new Ctor(LN10), sd, 1, true);
            }

            function getPi(Ctor, sd, rm) {
              if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);
              return finalise(new Ctor(PI), sd, rm, true);
            }

            function getPrecision(digits) {
              var w = digits.length - 1,
                  len = w * LOG_BASE + 1;
              w = digits[w]; // If non-zero...

              if (w) {
                // Subtract the number of trailing zeros of the last word.
                for (; w % 10 == 0; w /= 10) {
                  len--;
                } // Add the number of digits of the first word.


                for (w = digits[0]; w >= 10; w /= 10) {
                  len++;
                }
              }

              return len;
            }

            function getZeroString(k) {
              var zs = '';

              for (; k--;) {
                zs += '0';
              }

              return zs;
            }
            /*
             * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an
             * integer of type number.
             *
             * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.
             *
             */


            function intPow(Ctor, x, n, pr) {
              var isTruncated,
                  r = new Ctor(1),
                  // Max n of 9007199254740991 takes 53 loop iterations.
              // Maximum digits array length; leaves [28, 34] guard digits.
              k = Math.ceil(pr / LOG_BASE + 4);
              external = false;

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

                n = mathfloor(n / 2);

                if (n === 0) {
                  // To ensure correct rounding when r.d is truncated, increment the last word if it is zero.
                  n = r.d.length - 1;
                  if (isTruncated && r.d[n] === 0) ++r.d[n];
                  break;
                }

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

              external = true;
              return r;
            }

            function isOdd(n) {
              return n.d[n.d.length - 1] & 1;
            }
            /*
             * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'.
             */


            function maxOrMin(Ctor, args, ltgt) {
              var y,
                  x = new Ctor(args[0]),
                  i = 0;

              for (; ++i < args.length;) {
                y = new Ctor(args[i]);

                if (!y.s) {
                  x = y;
                  break;
                } else if (x[ltgt](y)) {
                  x = y;
                }
              }

              return x;
            }
            /*
             * Return a new Decimal whose value is the natural exponential of `x` rounded 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.
             *
             * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000
             * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000
             * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
             *
             *  exp(Infinity)  = Infinity
             *  exp(-Infinity) = 0
             *  exp(NaN)       = NaN
             *  exp(±0)        = 1
             *
             *  exp(x) is non-terminating for any finite, non-zero x.
             *
             *  The result will always be correctly rounded.
             *
             */


            function naturalExponential(x, sd) {
              var denominator,
                  guard,
                  j,
                  pow,
                  sum,
                  t,
                  wpr,
                  rep = 0,
                  i = 0,
                  k = 0,
                  Ctor = x.constructor,
                  rm = Ctor.rounding,
                  pr = Ctor.precision; // 0/NaN/Infinity?

              if (!x.d || !x.d[0] || x.e > 17) {
                return new Ctor(x.d ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 : x.s ? x.s < 0 ? 0 : x : 0 / 0);
              }

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

              t = new Ctor(0.03125); // while abs(x) >= 0.1

              while (x.e > -2) {
                // x = x / 2^5
                x = x.times(t);
                k += 5;
              } // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision
              // 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(1);
              Ctor.precision = wpr;

              for (;;) {
                pow = finalise(pow.times(x), wpr, 1);
                denominator = denominator.times(++i);
                t = sum.plus(divide(pow, denominator, wpr, 1));

                if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
                  j = k;

                  while (j--) {
                    sum = finalise(sum.times(sum), wpr, 1);
                  } // Check to see if the first 4 rounding digits are [49]999.
                  // If so, repeat the summation with a higher precision, otherwise
                  // e.g. with precision: 18, rounding: 1
                  // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)
                  // `wpr - guard` is the index of first rounding digit.


                  if (sd == null) {
                    if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
                      Ctor.precision = wpr += 10;
                      denominator = pow = t = new Ctor(1);
                      i = 0;
                      rep++;
                    } else {
                      return finalise(sum, Ctor.precision = pr, rm, external = true);
                    }
                  } else {
                    Ctor.precision = pr;
                    return sum;
                  }
                }

                sum = t;
              }
            }
            /*
             * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant
             * digits.
             *
             *  ln(-n)        = NaN
             *  ln(0)         = -Infinity
             *  ln(-0)        = -Infinity
             *  ln(1)         = 0
             *  ln(Infinity)  = Infinity
             *  ln(-Infinity) = NaN
             *  ln(NaN)       = NaN
             *
             *  ln(n) (n != 1) is non-terminating.
             *
             */


            function naturalLogarithm(y, sd) {
              var c,
                  c0,
                  denominator,
                  e,
                  numerator,
                  rep,
                  sum,
                  t,
                  wpr,
                  x1,
                  x2,
                  n = 1,
                  guard = 10,
                  x = y,
                  xd = x.d,
                  Ctor = x.constructor,
                  rm = Ctor.rounding,
                  pr = Ctor.precision; // Is x negative or Infinity, NaN, 0 or 1?

              if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {
                return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);
              }

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

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

              if (Math.abs(e = x.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 = x.e;

                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 = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
                Ctor.precision = pr;
                return sd == null ? finalise(x, pr, rm, external = true) : x;
              } // x1 is x reduced to a value near 1.


              x1 = x; // 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(1), x.plus(1), wpr, 1);
              x2 = finalise(x.times(x), wpr, 1);
              denominator = 3;

              for (;;) {
                numerator = finalise(numerator.times(x2), wpr, 1);
                t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));

                if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
                  sum = sum.times(2); // Reverse the argument reduction. Check that e is not 0 because, besides preventing an
                  // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.

                  if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
                  sum = divide(sum, new Ctor(n), wpr, 1); // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has
                  // been repeated previously) and the first 4 rounding digits 9999?
                  // If so, restart the summation with a higher precision, otherwise
                  // e.g. with precision: 12, rounding: 1
                  // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.
                  // `wpr - guard` is the index of first rounding digit.

                  if (sd == null) {
                    if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
                      Ctor.precision = wpr += guard;
                      t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);
                      x2 = finalise(x.times(x), wpr, 1);
                      denominator = rep = 1;
                    } else {
                      return finalise(sum, Ctor.precision = pr, rm, external = true);
                    }
                  } else {
                    Ctor.precision = pr;
                    return sum;
                  }
                }

                sum = t;
                denominator += 2;
              }
            } // ±Infinity, NaN.


            function nonFiniteToString(x) {
              // Unsigned.
              return String(x.s * x.s / 0);
            }
            /*
             * 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;
                x.e = e = e - i - 1;
                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) {
                  // Overflow?
                  if (x.e > x.constructor.maxE) {
                    // Infinity.
                    x.d = null;
                    x.e = NaN; // Underflow?
                  } else if (x.e < x.constructor.minE) {
                    // Zero.
                    x.e = 0;
                    x.d = [0]; // x.constructor.underflow = true;
                  } // else x.constructor.underflow = false;

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

              return x;
            }
            /*
             * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.
             */


            function parseOther(x, str) {
              var base, Ctor, divisor, i, isFloat, len, p, xd, xe;

              if (str === 'Infinity' || str === 'NaN') {
                if (!+str) x.s = NaN;
                x.e = NaN;
                x.d = null;
                return x;
              }

              if (isHex.test(str)) {
                base = 16;
                str = str.toLowerCase();
              } else if (isBinary.test(str)) {
                base = 2;
              } else if (isOctal.test(str)) {
                base = 8;
              } else {
                throw Error(invalidArgument + str);
              } // Is there a binary exponent part?


              i = str.search(/p/i);

              if (i > 0) {
                p = +str.slice(i + 1);
                str = str.substring(2, i);
              } else {
                str = str.slice(2);
              } // Convert `str` as an integer then divide the result by `base` raised to a power such that the
              // fraction part will be restored.


              i = str.indexOf('.');
              isFloat = i >= 0;
              Ctor = x.constructor;

              if (isFloat) {
                str = str.replace('.', '');
                len = str.length;
                i = len - i; // log[10](16) = 1.2041... , log[10](88) = 1.9444....

                divisor = intPow(Ctor, new Ctor(base), i, i * 2);
              }

              xd = convertBase(str, base, BASE);
              xe = xd.length - 1; // Remove trailing zeros.

              for (i = xe; xd[i] === 0; --i) {
                xd.pop();
              }

              if (i < 0) return new Ctor(x.s * 0);
              x.e = getBase10Exponent(xd, xe);
              x.d = xd;
              external = false; // At what precision to perform the division to ensure exact conversion?
              // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)
              // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412
              // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.
              // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount
              // Therefore using 4 * the number of digits of str will always be enough.

              if (isFloat) x = divide(x, divisor, len * 4); // Multiply by the binary exponent part if present.

              if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));
              external = true;
              return x;
            }
            /*
             * sin(x) = x - x^3/3! + x^5/5! - ...
             * |x| < pi/2
             *
             */


            function sine(Ctor, x) {
              var k,
                  len = x.d.length;
              if (len < 3) return taylorSeries(Ctor, 2, x, x); // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)
              // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)
              // and  sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))
              // Estimate the optimum number of times to use the argument reduction.

              k = 1.4 * Math.sqrt(len);
              k = k > 16 ? 16 : k | 0;
              x = x.times(1 / tinyPow(5, k));
              x = taylorSeries(Ctor, 2, x, x); // Reverse argument reduction

              var sin2_x,
                  d5 = new Ctor(5),
                  d16 = new Ctor(16),
                  d20 = new Ctor(20);

              for (; k--;) {
                sin2_x = x.times(x);
                x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));
              }

              return x;
            } // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.


            function taylorSeries(Ctor, n, x, y, isHyperbolic) {
              var j,
                  t,
                  u,
                  x2,
                  i = 1,
                  pr = Ctor.precision,
                  k = Math.ceil(pr / LOG_BASE);
              external = false;
              x2 = x.times(x);
              u = new Ctor(y);

              for (;;) {
                t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);
                u = isHyperbolic ? y.plus(t) : y.minus(t);
                y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);
                t = u.plus(y);

                if (t.d[k] !== void 0) {
                  for (j = k; t.d[j] === u.d[j] && j--;) {
                    ;
                  }

                  if (j == -1) break;
                }

                j = u;
                u = y;
                y = t;
                t = j;
                i++;
              }

              external = true;
              t.d.length = k + 1;
              return t;
            } // Exponent e must be positive and non-zero.


            function tinyPow(b, e) {
              var n = b;

              while (--e) {
                n *= b;
              }

              return n;
            } // Return the absolute value of `x` reduced to less than or equal to half pi.


            function toLessThanHalfPi(Ctor, x) {
              var t,
                  isNeg = x.s < 0,
                  pi = getPi(Ctor, Ctor.precision, 1),
                  halfPi = pi.times(0.5);
              x = x.abs();

              if (x.lte(halfPi)) {
                quadrant = isNeg ? 4 : 1;
                return x;
              }

              t = x.divToInt(pi);

              if (t.isZero()) {
                quadrant = isNeg ? 3 : 2;
              } else {
                x = x.minus(t.times(pi)); // 0 <= x < pi

                if (x.lte(halfPi)) {
                  quadrant = isOdd(t) ? isNeg ? 2 : 3 : isNeg ? 4 : 1;
                  return x;
                }

                quadrant = isOdd(t) ? isNeg ? 1 : 4 : isNeg ? 3 : 2;
              }

              return x.minus(pi).abs();
            }
            /*
             * Return the value of Decimal `x` as a string in base `baseOut`.
             *
             * If the optional `sd` argument is present include a binary exponent suffix.
             */


            function toStringBinary(x, baseOut, sd, rm) {
              var base,
                  e,
                  i,
                  k,
                  len,
                  roundUp,
                  str,
                  xd,
                  y,
                  Ctor = x.constructor,
                  isExp = sd !== void 0;

              if (isExp) {
                checkInt32(sd, 1, MAX_DIGITS);
                if (rm === void 0) rm = Ctor.rounding;else checkInt32(rm, 0, 8);
              } else {
                sd = Ctor.precision;
                rm = Ctor.rounding;
              }

              if (!x.isFinite()) {
                str = nonFiniteToString(x);
              } else {
                str = finiteToString(x);
                i = str.indexOf('.'); // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:
                // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))
                // minBinaryExponent = floor(decimalExponent * log[2](10))
                // log[2](10) = 3.321928094887362347870319429489390175864

                if (isExp) {
                  base = 2;

                  if (baseOut == 16) {
                    sd = sd * 4 - 3;
                  } else if (baseOut == 8) {
                    sd = sd * 3 - 2;
                  }
                } else {
                  base = baseOut;
                } // Convert the number as an integer then divide the result by its base raised to a power such
                // that the fraction part will be restored.
                // Non-integer.


                if (i >= 0) {
                  str = str.replace('.', '');
                  y = new Ctor(1);
                  y.e = str.length - i;
                  y.d = convertBase(finiteToString(y), 10, base);
                  y.e = y.d.length;
                }

                xd = convertBase(str, 10, base);
                e = len = xd.length; // Remove trailing zeros.

                for (; xd[--len] == 0;) {
                  xd.pop();
                }

                if (!xd[0]) {
                  str = isExp ? '0p+0' : '0';
                } else {
                  if (i < 0) {
                    e--;
                  } else {
                    x = new Ctor(x);
                    x.d = xd;
                    x.e = e;
                    x = divide(x, y, sd, rm, 0, base);
                    xd = x.d;
                    e = x.e;
                    roundUp = inexact;
                  } // The rounding digit, i.e. the digit after the digit that may be rounded up.


                  i = xd[sd];
                  k = base / 2;
                  roundUp = roundUp || xd[sd + 1] !== void 0;
                  roundUp = rm < 4 ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || rm === (x.s < 0 ? 8 : 7));
                  xd.length = sd;

                  if (roundUp) {
                    // Rounding up may mean the previous digit has to be rounded up and so on.
                    for (; ++xd[--sd] > base - 1;) {
                      xd[sd] = 0;

                      if (!sd) {
                        ++e;
                        xd.unshift(1);
                      }
                    }
                  } // Determine trailing zeros.


                  for (len = xd.length; !xd[len - 1]; --len) {
                    ;
                  } // E.g. [4, 11, 15] becomes 4bf.


                  for (i = 0, str = ''; i < len; i++) {
                    str += NUMERALS.charAt(xd[i]);
                  } // Add binary exponent suffix?


                  if (isExp) {
                    if (len > 1) {
                      if (baseOut == 16 || baseOut == 8) {
                        i = baseOut == 16 ? 4 : 3;

                        for (--len; len % i; len++) {
                          str += '0';
                        }

                        xd = convertBase(str, base, baseOut);

                        for (len = xd.length; !xd[len - 1]; --len) {
                          ;
                        } // xd[0] will always be be 1


                        for (i = 1, str = '1.'; i < len; i++) {
                          str += NUMERALS.charAt(xd[i]);
                        }
                      } else {
                        str = str.charAt(0) + '.' + str.slice(1);
                      }
                    }

                    str = str + (e < 0 ? 'p' : 'p+') + e;
                  } else if (e < 0) {
                    for (; ++e;) {
                      str = '0' + str;
                    }

                    str = '0.' + str;
                  } else {
                    if (++e > len) for (e -= len; e--;) {
                      str += '0';
                    } else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);
                  }
                }

                str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;
              }

              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

            /*
             *  abs
             *  acos
             *  acosh
             *  add
             *  asin
             *  asinh
             *  atan
             *  atanh
             *  atan2
             *  cbrt
             *  ceil
             *  clone
             *  config
             *  cos
             *  cosh
             *  div
             *  exp
             *  floor
             *  hypot
             *  ln
             *  log
             *  log2
             *  log10
             *  max
             *  min
             *  mod
             *  mul
             *  pow
             *  random
             *  round
             *  set
             *  sign
             *  sin
             *  sinh
             *  sqrt
             *  sub
             *  tan
             *  tanh
             *  trunc
             */

            /*
             * Return a new Decimal whose value is the absolute value of `x`.
             *
             * x {number|string|Decimal}
             *
             */


            function abs(x) {
              return new this(x).abs();
            }
            /*
             * Return a new Decimal whose value is the arccosine in radians of `x`.
             *
             * x {number|string|Decimal}
             *
             */


            function acos(x) {
              return new this(x).acos();
            }
            /*
             * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to
             * `precision` significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function acosh(x) {
              return new this(x).acosh();
            }
            /*
             * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             * y {number|string|Decimal}
             *
             */


            function add(x, y) {
              return new this(x).plus(y);
            }
            /*
             * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function asin(x) {
              return new this(x).asin();
            }
            /*
             * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to
             * `precision` significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function asinh(x) {
              return new this(x).asinh();
            }
            /*
             * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function atan(x) {
              return new this(x).atan();
            }
            /*
             * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to
             * `precision` significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function atanh(x) {
              return new this(x).atanh();
            }
            /*
             * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi
             * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.
             *
             * Domain: [-Infinity, Infinity]
             * Range: [-pi, pi]
             *
             * y {number|string|Decimal} The y-coordinate.
             * x {number|string|Decimal} The x-coordinate.
             *
             * atan2(±0, -0)               = ±pi
             * atan2(±0, +0)               = ±0
             * atan2(±0, -x)               = ±pi for x > 0
             * atan2(±0, x)                = ±0 for x > 0
             * atan2(-y, ±0)               = -pi/2 for y > 0
             * atan2(y, ±0)                = pi/2 for y > 0
             * atan2(±y, -Infinity)        = ±pi for finite y > 0
             * atan2(±y, +Infinity)        = ±0 for finite y > 0
             * atan2(±Infinity, x)         = ±pi/2 for finite x
             * atan2(±Infinity, -Infinity) = ±3*pi/4
             * atan2(±Infinity, +Infinity) = ±pi/4
             * atan2(NaN, x) = NaN
             * atan2(y, NaN) = NaN
             *
             */


            function atan2(y, x) {
              y = new this(y);
              x = new this(x);
              var r,
                  pr = this.precision,
                  rm = this.rounding,
                  wpr = pr + 4; // Either NaN

              if (!y.s || !x.s) {
                r = new this(NaN); // Both ±Infinity
              } else if (!y.d && !x.d) {
                r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);
                r.s = y.s; // x is ±Infinity or y is ±0
              } else if (!x.d || y.isZero()) {
                r = x.s < 0 ? getPi(this, pr, rm) : new this(0);
                r.s = y.s; // y is ±Infinity or x is ±0
              } else if (!y.d || x.isZero()) {
                r = getPi(this, wpr, 1).times(0.5);
                r.s = y.s; // Both non-zero and finite
              } else if (x.s < 0) {
                this.precision = wpr;
                this.rounding = 1;
                r = this.atan(divide(y, x, wpr, 1));
                x = getPi(this, wpr, 1);
                this.precision = pr;
                this.rounding = rm;
                r = y.s < 0 ? r.minus(x) : r.plus(x);
              } else {
                r = this.atan(divide(y, x, wpr, 1));
              }

              return r;
            }
            /*
             * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function cbrt(x) {
              return new this(x).cbrt();
            }
            /*
             * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.
             *
             * x {number|string|Decimal}
             *
             */


            function ceil(x) {
              return finalise(x = new this(x), x.e + 1, 2);
            }
            /*
             * 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}
             *   maxE       {number}
             *   minE       {number}
             *   modulo     {number}
             *   crypto     {boolean|number}
             *   defaults   {true}
             *
             * 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,
                  useDefaults = obj.defaults === true,
                  ps = ['precision', 1, MAX_DIGITS, 'rounding', 0, 8, 'toExpNeg', -EXP_LIMIT, 0, 'toExpPos', 0, EXP_LIMIT, 'maxE', 0, EXP_LIMIT, 'minE', -EXP_LIMIT, 0, 'modulo', 0, 9];

              for (i = 0; i < ps.length; i += 3) {
                if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];

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

              if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];

              if ((v = obj[p]) !== void 0) {
                if (v === true || v === false || v === 0 || v === 1) {
                  if (v) {
                    if (typeof crypto != 'undefined' && crypto && (crypto.getRandomValues || crypto.randomBytes)) {
                      this[p] = true;
                    } else {
                      throw Error(cryptoUnavailable);
                    }
                  } else {
                    this[p] = false;
                  }
                } else {
                  throw Error(invalidArgument + p + ': ' + v);
                }
              }

              return this;
            }
            /*
             * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function cos(x) {
              return new this(x).cos();
            }
            /*
             * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function cosh(x) {
              return new this(x).cosh();
            }
            /*
             * 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.
               *
               * v {number|string|Decimal} A numeric value.
               *
               */

              function Decimal(v) {
                var e,
                    i,
                    t,
                    x = this; // Decimal called without new.

                if (!(x instanceof Decimal)) return new Decimal(v); // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
                // which points to Object.

                x.constructor = Decimal; // Duplicate.

                if (v instanceof Decimal) {
                  x.s = v.s;

                  if (external) {
                    if (!v.d || v.e > Decimal.maxE) {
                      // Infinity.
                      x.e = NaN;
                      x.d = null;
                    } else if (v.e < Decimal.minE) {
                      // Zero.
                      x.e = 0;
                      x.d = [0];
                    } else {
                      x.e = v.e;
                      x.d = v.d.slice();
                    }
                  } else {
                    x.e = v.e;
                    x.d = v.d ? v.d.slice() : v.d;
                  }

                  return;
                }

                t = typeof v;

                if (t === 'number') {
                  if (v === 0) {
                    x.s = 1 / v < 0 ? -1 : 1;
                    x.e = 0;
                    x.d = [0];
                    return;
                  }

                  if (v < 0) {
                    v = -v;
                    x.s = -1;
                  } else {
                    x.s = 1;
                  } // Fast path for small integers.


                  if (v === ~~v && v < 1e7) {
                    for (e = 0, i = v; i >= 10; i /= 10) {
                      e++;
                    }

                    if (external) {
                      if (e > Decimal.maxE) {
                        x.e = NaN;
                        x.d = null;
                      } else if (e < Decimal.minE) {
                        x.e = 0;
                        x.d = [0];
                      } else {
                        x.e = e;
                        x.d = [v];
                      }
                    } else {
                      x.e = e;
                      x.d = [v];
                    }

                    return; // Infinity, NaN.
                  } else if (v * 0 !== 0) {
                    if (!v) x.s = NaN;
                    x.e = NaN;
                    x.d = null;
                    return;
                  }

                  return parseDecimal(x, v.toString());
                } else if (t !== 'string') {
                  throw Error(invalidArgument + v);
                } // Minus sign?


                if ((i = v.charCodeAt(0)) === 45) {
                  v = v.slice(1);
                  x.s = -1;
                } else {
                  // Plus sign?
                  if (i === 43) v = v.slice(1);
                  x.s = 1;
                }

                return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);
              }

              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.EUCLID = 9;
              Decimal.config = Decimal.set = config;
              Decimal.clone = clone;
              Decimal.isDecimal = isDecimalInstance;
              Decimal.abs = abs;
              Decimal.acos = acos;
              Decimal.acosh = acosh; // ES6

              Decimal.add = add;
              Decimal.asin = asin;
              Decimal.asinh = asinh; // ES6

              Decimal.atan = atan;
              Decimal.atanh = atanh; // ES6

              Decimal.atan2 = atan2;
              Decimal.cbrt = cbrt; // ES6

              Decimal.ceil = ceil;
              Decimal.cos = cos;
              Decimal.cosh = cosh; // ES6

              Decimal.div = div;
              Decimal.exp = exp;
              Decimal.floor = floor;
              Decimal.hypot = hypot; // ES6

              Decimal.ln = ln;
              Decimal.log = log;
              Decimal.log10 = log10; // ES6

              Decimal.log2 = log2; // ES6

              Decimal.max = max;
              Decimal.min = min;
              Decimal.mod = mod;
              Decimal.mul = mul;
              Decimal.pow = pow;
              Decimal.random = random;
              Decimal.round = round;
              Decimal.sign = sign; // ES6

              Decimal.sin = sin;
              Decimal.sinh = sinh; // ES6

              Decimal.sqrt = sqrt;
              Decimal.sub = sub;
              Decimal.tan = tan;
              Decimal.tanh = tanh; // ES6

              Decimal.trunc = trunc; // ES6

              if (obj === void 0) obj = {};

              if (obj) {
                if (obj.defaults !== true) {
                  ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];

                  for (i = 0; i < ps.length;) {
                    if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
                  }
                }
              }

              Decimal.config(obj);
              return Decimal;
            }
            /*
             * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             * y {number|string|Decimal}
             *
             */


            function div(x, y) {
              return new this(x).div(y);
            }
            /*
             * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} The power to which to raise the base of the natural log.
             *
             */


            function exp(x) {
              return new this(x).exp();
            }
            /*
             * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.
             *
             * x {number|string|Decimal}
             *
             */


            function floor(x) {
              return finalise(x = new this(x), x.e + 1, 3);
            }
            /*
             * Return a new Decimal whose value is the square root of the sum of the squares of the arguments,
             * rounded to `precision` significant digits using rounding mode `rounding`.
             *
             * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)
             *
             * arguments {number|string|Decimal}
             *
             */


            function hypot() {
              var i,
                  n,
                  t = new this(0);
              external = false;

              for (i = 0; i < arguments.length;) {
                n = new this(arguments[i++]);

                if (!n.d) {
                  if (n.s) {
                    external = true;
                    return new this(1 / 0);
                  }

                  t = n;
                } else if (t.d) {
                  t = t.plus(n.times(n));
                }
              }

              external = true;
              return t.sqrt();
            }
            /*
             * Return true if object is a Decimal instance (where Decimal is any Decimal constructor),
             * otherwise return false.
             *
             */


            function isDecimalInstance(obj) {
              return obj instanceof Decimal || obj && obj.name === '[object Decimal]' || false;
            }
            /*
             * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function ln(x) {
              return new this(x).ln();
            }
            /*
             * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base
             * is specified, rounded to `precision` significant digits using rounding mode `rounding`.
             *
             * log[y](x)
             *
             * x {number|string|Decimal} The argument of the logarithm.
             * y {number|string|Decimal} The base of the logarithm.
             *
             */


            function log(x, y) {
              return new this(x).log(y);
            }
            /*
             * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function log2(x) {
              return new this(x).log(2);
            }
            /*
             * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function log10(x) {
              return new this(x).log(10);
            }
            /*
             * Return a new Decimal whose value is the maximum of the arguments.
             *
             * arguments {number|string|Decimal}
             *
             */


            function max() {
              return maxOrMin(this, arguments, 'lt');
            }
            /*
             * Return a new Decimal whose value is the minimum of the arguments.
             *
             * arguments {number|string|Decimal}
             *
             */


            function min() {
              return maxOrMin(this, arguments, 'gt');
            }
            /*
             * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
             * using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             * y {number|string|Decimal}
             *
             */


            function mod(x, y) {
              return new this(x).mod(y);
            }
            /*
             * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             * y {number|string|Decimal}
             *
             */


            function mul(x, y) {
              return new this(x).mul(y);
            }
            /*
             * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} The base.
             * y {number|string|Decimal} The exponent.
             *
             */


            function pow(x, y) {
              return new this(x).pow(y);
            }
            /*
             * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with
             * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros
             * are produced).
             *
             * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.
             *
             */


            function random(sd) {
              var d,
                  e,
                  k,
                  n,
                  i = 0,
                  r = new this(1),
                  rd = [];
              if (sd === void 0) sd = this.precision;else checkInt32(sd, 1, MAX_DIGITS);
              k = Math.ceil(sd / LOG_BASE);

              if (!this.crypto) {
                for (; i < k;) {
                  rd[i++] = Math.random() * 1e7 | 0;
                } // Browsers supporting crypto.getRandomValues.

              } else if (crypto.getRandomValues) {
                d = crypto.getRandomValues(new Uint32Array(k));

                for (; i < k;) {
                  n = d[i]; // 0 <= n < 4294967296
                  // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).

                  if (n >= 4.29e9) {
                    d[i] = crypto.getRandomValues(new Uint32Array(1))[0];
                  } else {
                    // 0 <= n <= 4289999999
                    // 0 <= (n % 1e7) <= 9999999
                    rd[i++] = n % 1e7;
                  }
                } // Node.js supporting crypto.randomBytes.

              } else if (crypto.randomBytes) {
                // buffer
                d = crypto.randomBytes(k *= 4);

                for (; i < k;) {
                  // 0 <= n < 2147483648
                  n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).

                  if (n >= 2.14e9) {
                    crypto.randomBytes(4).copy(d, i);
                  } else {
                    // 0 <= n <= 2139999999
                    // 0 <= (n % 1e7) <= 9999999
                    rd.push(n % 1e7);
                    i += 4;
                  }
                }

                i = k / 4;
              } else {
                throw Error(cryptoUnavailable);
              }

              k = rd[--i];
              sd %= LOG_BASE; // Convert trailing digits to zeros according to sd.

              if (k && sd) {
                n = mathpow(10, LOG_BASE - sd);
                rd[i] = (k / n | 0) * n;
              } // Remove trailing words which are zero.


              for (; rd[i] === 0; i--) {
                rd.pop();
              } // Zero?


              if (i < 0) {
                e = 0;
                rd = [0];
              } else {
                e = -1; // Remove leading words which are zero and adjust exponent accordingly.

                for (; rd[0] === 0; e -= LOG_BASE) {
                  rd.shift();
                } // Count the digits of the first word of rd to determine leading zeros.


                for (k = 1, n = rd[0]; n >= 10; n /= 10) {
                  k++;
                } // Adjust the exponent for leading zeros of the first word of rd.


                if (k < LOG_BASE) e -= LOG_BASE - k;
              }

              r.e = e;
              r.d = rd;
              return r;
            }
            /*
             * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.
             *
             * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).
             *
             * x {number|string|Decimal}
             *
             */


            function round(x) {
              return finalise(x = new this(x), x.e + 1, this.rounding);
            }
            /*
             * Return
             *   1    if x > 0,
             *  -1    if x < 0,
             *   0    if x is 0,
             *  -0    if x is -0,
             *   NaN  otherwise
             *
             * x {number|string|Decimal}
             *
             */


            function sign(x) {
              x = new this(x);
              return x.d ? x.d[0] ? x.s : 0 * x.s : x.s || NaN;
            }
            /*
             * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits
             * using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function sin(x) {
              return new this(x).sin();
            }
            /*
             * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function sinh(x) {
              return new this(x).sinh();
            }
            /*
             * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             *
             */


            function sqrt(x) {
              return new this(x).sqrt();
            }
            /*
             * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits
             * using rounding mode `rounding`.
             *
             * x {number|string|Decimal}
             * y {number|string|Decimal}
             *
             */


            function sub(x, y) {
              return new this(x).sub(y);
            }
            /*
             * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant
             * digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function tan(x) {
              return new this(x).tan();
            }
            /*
             * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`
             * significant digits using rounding mode `rounding`.
             *
             * x {number|string|Decimal} A value in radians.
             *
             */


            function tanh(x) {
              return new this(x).tanh();
            }
            /*
             * Return a new Decimal whose value is `x` truncated to an integer.
             *
             * x {number|string|Decimal}
             *
             */


            function trunc(x) {
              return finalise(x = new this(x), x.e + 1, 1);
            } // Create and configure initial Decimal constructor.


            Decimal = clone(DEFAULTS);
            Decimal['default'] = Decimal.Decimal = Decimal; // Create the internal constants from their string values.

            LN10 = new Decimal(LN10);
            PI = new Decimal(PI); // 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) {
              if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
                P[Symbol["for"]('nodejs.util.inspect.custom')] = P.toString;
                P[Symbol.toStringTag] = 'Decimal';
              }

              module.exports = Decimal; // Browser.
            } else {
              if (!globalScope) {
                globalScope = typeof self != 'undefined' && self && self.self == self ? self : window;
              }

              noConflict = globalScope.Decimal;

              Decimal.noConflict = function () {
                globalScope.Decimal = noConflict;
                return Decimal;
              };

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

        _export("default", _cjsExports = module.exports);
      });

      _export("__cjsMetaURL", __cjsMetaURL = _context.meta.url);
    }
  };
});
//# sourceMappingURL=decimal.js.map