text: (function (global, factory) {
    typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
    typeof define === 'function' && define.amd ? define(factory) :
    (global = global || self, global.Decimal = factory());
  }(this, function () { 'use strict';
  
    var padEnd = function (string, maxLength, fillString) {
  
      if (string === null || maxLength === null) {
        return string;
      }
  
      var result    = String(string);
      var targetLen = typeof maxLength === 'number'
        ? maxLength
        : parseInt(maxLength, 10);
  
      if (isNaN(targetLen) || !isFinite(targetLen)) {
        return result;
      }
  
  
      var length = result.length;
      if (length >= targetLen) {
        return result;
      }
  
  
      var filled = fillString === null ? '' : String(fillString);
      if (filled === '') {
        filled = ' ';
      }
  
  
      var fillLen = targetLen - length;
  
      while (filled.length < fillLen) {
        filled += filled;
      }
  
      var truncated = filled.length > fillLen ? filled.substr(0, fillLen) : filled;
  
      return result + truncated;
    };
  
    var MAX_SIGNIFICANT_DIGITS = 17; //Maximum number of digits of precision to assume in Number
  
    var EXP_LIMIT = 9e15; //If we're ABOVE this value, increase a layer. (9e15 is close to the largest integer that can fit in a Number.)
    
    var LAYER_DOWN = Math.log10(9e15); //If we're BELOW this value, drop down a layer. About 15.954.
    
    var FIRST_NEG_LAYER = 1/9e15; //At layer 0, smaller non-zero numbers than this become layer 1 numbers with negative mag. After that the pattern continues as normal.
  
    var NUMBER_EXP_MAX = 308; //The largest exponent that can appear in a Number, though not all mantissas are valid here.
  
    var NUMBER_EXP_MIN = -324; //The smallest exponent that can appear in a Number, though not all mantissas are valid here.
    
    var MAX_ES_IN_A_ROW = 5; //For default toString behaviour, when to swap from eee... to (e^n) syntax.
  
    var powerOf10 = function () {
      // We need this lookup table because Math.pow(10, exponent)
      // when exponent's absolute value is large is slightly inaccurate.
      // You can fix it with the power of math... or just make a lookup table.
      // Faster AND simpler
      var powersOf10 = [];
  
      for (var i = NUMBER_EXP_MIN + 1; i <= NUMBER_EXP_MAX; i++) {
        powersOf10.push(Number("1e" + i));
      }
  
      var indexOf0InPowersOf10 = 323;
      return function (power) {
        return powersOf10[power + indexOf0InPowersOf10];
      };
    }();
  
    var D = function D(value) {
      return Decimal.fromValue_noAlloc(value);
    };
  
    var FC = function FC(sign, layer, mag) {
      return Decimal.fromComponents(sign, layer, mag);
    };
  
    var FC_NN = function FC_NN(sign, layer, mag) {
      return Decimal.fromComponents_noNormalize(sign, layer, mag);
    };
    
    var ME = function ME(mantissa, exponent) {
      return Decimal.fromMantissaExponent(mantissa, exponent);
    };
  
    var ME_NN = function ME_NN(mantissa, exponent) {
      return Decimal.fromMantissaExponent_noNormalize(mantissa, exponent);
    };
    
    var decimalPlaces = function decimalPlaces(value, places) {
      var len = places + 1;
      var numDigits = Math.ceil(Math.log10(Math.abs(value)));
      var rounded = Math.round(value * Math.pow(10, len - numDigits)) * Math.pow(10, numDigits - len);
      return parseFloat(rounded.toFixed(Math.max(len - numDigits, 0)));
    };
    
    var f_maglog10 = function(n) {
      return Math.sign(n)*Math.log10(Math.abs(n));
    }
    
    //from HyperCalc source code
    var f_gamma = function(n) {
      if (!isFinite(n)) { return n; }
      if (n < -50)
      {
        if (n === Math.trunc(n)) { return Number.NEGATIVE_INFINITY; }
        return 0;
      }
      
      var scal1 = 1;
      while (n < 10)
      {
        scal1 = scal1*n;
        ++n;
      }
      
      n -= 1;
      var l = 0.9189385332046727; //0.5*Math.log(2*Math.PI)
      l = l + (n+0.5)*Math.log(n);
      l = l - n;
      var n2 = n*n;
      var np = n;
      l = l+1/(12*np);
      np = np*n2;
      l = l+1/(360*np);
      np = np*n2;
      l = l+1/(1260*np);
      np = np*n2;
      l = l+1/(1680*np);
      np = np*n2;
      l = l+1/(1188*np);
      np = np*n2;
      l = l+691/(360360*np);
      np = np*n2;
      l = l+7/(1092*np);
      np = np*n2;
      l = l+3617/(122400*np);
  
      return Math.exp(l)/scal1;
    };
    
    var twopi = 6.2831853071795864769252842;  // 2*pi
    var EXPN1 = 0.36787944117144232159553;  // exp(-1)
    var OMEGA = 0.56714329040978387299997;  // W(1, 0)
    //from https://math.stackexchange.com/a/465183
    // The evaluation can become inaccurate very close to the branch point
    var f_lambertw = function(z, tol = 1e-10) {
      var w;
      var wn;
  
      if (!Number.isFinite(z)) { return z; }
      if (z === 0)
      {
        return z;
      }
      if (z === 1)
      {
        return OMEGA;
      }
  
      if (z < 10)
      {
        w = 0;
      }
      else
      {
        w = Math.log(z)-Math.log(Math.log(z));
      }
  
      for (var i = 0; i < 100; ++i)
      {
        wn = (z * Math.exp(-w) + w * w)/(w + 1);
        if (Math.abs(wn - w) < tol*Math.abs(wn))
        {
          return wn;
        }
        else
        {
          w = wn;
        }
      }
  
      throw Error("Iteration failed to converge: " + z);
      //return Number.NaN;
    }
    
    var Decimal =
    /** @class */
    function () {
    
      function Decimal(value) {
        
        this.sign = Number.NaN;
        this.layer = Number.NaN;
        this.mag = Number.NaN;
  
        if (value instanceof Decimal) {
          this.fromDecimal(value);
        } else if (typeof value === "number") {
          this.fromNumber(value);
        } else if (typeof value === "string") {
          this.fromString(value);
        } else {
          this.sign = 0;
          this.layer = 0;
          this.mag = 0;
        }
      }
  
      Object.defineProperty(Decimal.prototype, "m", {
        get: function get() {
          if (this.sign === 0)
          {
            return 0;
          }
          else if (this.layer === 0)
          {
            var exp = Math.floor(Math.log10(this.mag));
            //handle special case 5e-324
            var man;
            if (this.mag === 5e-324)
            {
              man = 5;
            }
            else
            {
              man = this.mag / powerOf10(exp);
            }
            return this.sign*man;
          }
          else if (this.layer === 1)
          {
            var residue = this.mag-Math.floor(this.mag);
            return this.sign*Math.pow(10, residue);
          }
          else
          {
            //mantissa stops being relevant past 1e9e15 / ee15.954
            return this.sign;
          }
        },
        set: function set(value) {
          if (this.layer <= 2)
          {
            this.fromMantissaExponent(value, this.e);
          }
          else
          {
            //don't even pretend mantissa is meaningful
            this.sign = Math.sign(value);
            if (this.sign === 0) { this.layer === 0; this.exponent === 0; }
          }
        },
        enumerable: true,
        configurable: true
      });
      Object.defineProperty(Decimal.prototype, "e", {
        get: function get() {
          if (this.sign === 0)
          {
            return 0;
          }
          else if (this.layer === 0)
          {
            return Math.floor(Math.log10(this.mag));
          }
          else if (this.layer === 1)
          {
            return Math.floor(this.mag);
          }
          else if (this.layer === 2)
          {
            return Math.floor(Math.sign(this.mag)*Math.pow(10, Math.abs(this.mag)));
          }
          else
          {
            return this.mag*Number.POSITIVE_INFINITY;
          }
        },
        set: function set(value) {
          this.fromMantissaExponent(this.m, value);
        },
        enumerable: true,
        configurable: true
      });
      Object.defineProperty(Decimal.prototype, "s", {
        get: function get() {
          return this.sign;
        },
        set: function set(value) {
          if (value === 0) {
            this.sign = 0;
            this.layer = 0;
            this.mag = 0;
          }
          else
          {
            this.sign = value;
          }
        },
        enumerable: true,
        configurable: true
      });
      
      Object.defineProperty(Decimal.prototype, "mantissa", {
        get: function get() {
          return this.m;
        },
        set: function set(value) {
          this.m = value;
        },
        enumerable: true,
        configurable: true
      });
  
      Object.defineProperty(Decimal.prototype, "exponent", {
        get: function get() {
          return this.e;
        },
        set: function set(value) {
          this.e = value;
        },
        enumerable: true,
        configurable: true
      });
  
      Decimal.fromComponents = function (sign, layer, mag) {
        return new Decimal().fromComponents(sign, layer, mag);
      };
  
      Decimal.fromComponents_noNormalize = function (sign, layer, mag) {
        return new Decimal().fromComponents_noNormalize(sign, layer, mag);
      };
      
      Decimal.fromMantissaExponent = function (mantissa, exponent) {
        return new Decimal().fromMantissaExponent(mantissa, exponent);
      };
  
      Decimal.fromMantissaExponent_noNormalize = function (mantissa, exponent) {
        return new Decimal().fromMantissaExponent_noNormalize(mantissa, exponent);
      };
      
      Decimal.fromDecimal = function (value) {
        return new Decimal().fromDecimal(value);
      };
  
      Decimal.fromNumber = function (value) {
        return new Decimal().fromNumber(value);
      };
  
      Decimal.fromString = function (value) {
        return new Decimal().fromString(value);
      };
  
      Decimal.fromValue = function (value) {
        return new Decimal().fromValue(value);
      };
  
      Decimal.fromValue_noAlloc = function (value) {
        return value instanceof Decimal ? value : new Decimal(value);
      };
      
      Decimal.abs = function (value) {
        return D(value).abs();
      };
  
      Decimal.neg = function (value) {
        return D(value).neg();
      };
  
      Decimal.negate = function (value) {
        return D(value).neg();
      };
  
      Decimal.negated = function (value) {
        return D(value).neg();
      };
  
      Decimal.sign = function (value) {
        return D(value).sign();
      };
  
      Decimal.sgn = function (value) {
        return D(value).sign();
      };
  
      Decimal.round = function (value) {
        return D(value).round();
      };
  
      Decimal.floor = function (value) {
        return D(value).floor();
      };
  
      Decimal.ceil = function (value) {
        return D(value).ceil();
      };
  
      Decimal.trunc = function (value) {
        return D(value).trunc();
      };
  
      Decimal.add = function (value, other) {
        return D(value).add(other);
      };
  
      Decimal.plus = function (value, other) {
        return D(value).add(other);
      };
  
      Decimal.sub = function (value, other) {
        return D(value).sub(other);
      };
  
      Decimal.subtract = function (value, other) {
        return D(value).sub(other);
      };
  
      Decimal.minus = function (value, other) {
        return D(value).sub(other);
      };
  
      Decimal.mul = function (value, other) {
        return D(value).mul(other);
      };
  
      Decimal.multiply = function (value, other) {
        return D(value).mul(other);
      };
  
      Decimal.times = function (value, other) {
        return D(value).mul(other);
      };
  
      Decimal.div = function (value, other) {
        return D(value).div(other);
      };
  
      Decimal.divide = function (value, other) {
        return D(value).div(other);
      };
  
      Decimal.recip = function (value) {
        return D(value).recip();
      };
  
      Decimal.reciprocal = function (value) {
        return D(value).recip();
      };
  
      Decimal.reciprocate = function (value) {
        return D(value).reciprocate();
      };
  
      Decimal.cmp = function (value, other) {
        return D(value).cmp(other);
      };
  
  	Decimal.cmpabs = function (value, other) {
        return D(value).cmpabs(other);
      };
  	
      Decimal.compare = function (value, other) {
        return D(value).cmp(other);
      };
  
      Decimal.eq = function (value, other) {
        return D(value).eq(other);
      };
  
      Decimal.equals = function (value, other) {
        return D(value).eq(other);
      };
  
      Decimal.neq = function (value, other) {
        return D(value).neq(other);
      };
  
      Decimal.notEquals = function (value, other) {
        return D(value).notEquals(other);
      };
  
      Decimal.lt = function (value, other) {
        return D(value).lt(other);
      };
  
      Decimal.lte = function (value, other) {
        return D(value).lte(other);
      };
  
      Decimal.gt = function (value, other) {
        return D(value).gt(other);
      };
  
      Decimal.gte = function (value, other) {
        return D(value).gte(other);
      };
  
      Decimal.max = function (value, other) {
        return D(value).max(other);
      };
      
      Decimal.min = function (value, other) {
        return D(value).min(other);
      };
  
      Decimal.minabs = function (value, other) {
        return D(value).minabs(other);
      };
  	
      Decimal.maxabs = function (value, other) {
        return D(value).maxabs(other);
      };
      
      Decimal.clamp = function(value, min, max) {
        return D(value).clamp(min, max);
      }
      
      Decimal.clampMin = function(value, min) {
        return D(value).clampMin(min);
      }
      
      Decimal.clampMax = function(value, max) {
        return D(value).clampMax(max);
      }
  
      Decimal.cmp_tolerance = function (value, other, tolerance) {
        return D(value).cmp_tolerance(other, tolerance);
      };
  
      Decimal.compare_tolerance = function (value, other, tolerance) {
        return D(value).cmp_tolerance(other, tolerance);
      };
  
      Decimal.eq_tolerance = function (value, other, tolerance) {
        return D(value).eq_tolerance(other, tolerance);
      };
  
      Decimal.equals_tolerance = function (value, other, tolerance) {
        return D(value).eq_tolerance(other, tolerance);
      };
  
      Decimal.neq_tolerance = function (value, other, tolerance) {
        return D(value).neq_tolerance(other, tolerance);
      };
  
      Decimal.notEquals_tolerance = function (value, other, tolerance) {
        return D(value).notEquals_tolerance(other, tolerance);
      };
  
      Decimal.lt_tolerance = function (value, other, tolerance) {
        return D(value).lt_tolerance(other, tolerance);
      };
  
      Decimal.lte_tolerance = function (value, other, tolerance) {
        return D(value).lte_tolerance(other, tolerance);
      };
  
      Decimal.gt_tolerance = function (value, other, tolerance) {
        return D(value).gt_tolerance(other, tolerance);
      };
  
      Decimal.gte_tolerance = function (value, other, tolerance) {
        return D(value).gte_tolerance(other, tolerance);
      };
  
      Decimal.pLog10 = function (value) {
        return D(value).pLog10();
      };
      
      Decimal.absLog10 = function (value) {
        return D(value).absLog10();
      };
      
      Decimal.log10 = function (value) {
        return D(value).log10();
      };
  
      Decimal.log = function (value, base) {
        return D(value).log(base);
      };
  
      Decimal.log2 = function (value) {
        return D(value).log2();
      };
  
      Decimal.ln = function (value) {
        return D(value).ln();
      };
  
      Decimal.logarithm = function (value, base) {
        return D(value).logarithm(base);
      };
  
      Decimal.pow = function (value, other) {
        return D(value).pow(other);
      };
      
      Decimal.pow10 = function (value) {
        return D(value).pow10();
      };
      
      Decimal.root = function (value, other) {
        return D(value).root(other);
      };
      
      Decimal.factorial = function (value, other) {
        return D(value).factorial();
      };
      
      Decimal.gamma = function (value, other) {
        return D(value).gamma();
      };
      
      Decimal.lngamma = function (value, other) {
        return D(value).lngamma();
      };
  
      Decimal.exp = function (value) {
        return D(value).exp();
      };
  
      Decimal.sqr = function (value) {
        return D(value).sqr();
      };
  
      Decimal.sqrt = function (value) {
        return D(value).sqrt();
      };
  
      Decimal.cube = function (value) {
        return D(value).cube();
      };
  
      Decimal.cbrt = function (value) {
        return D(value).cbrt();
      };
      
      Decimal.tetrate = function (value, height = 2, payload = FC_NN(1, 0, 1)) {
        return D(value).tetrate(height, payload);
      }
      
      Decimal.iteratedexp = function (value, height = 2, payload = FC_NN(1, 0, 1)) {
        return D(value).iteratedexp(height, payload);
      }
      
      Decimal.iteratedlog = function (value, base = 10, times = 1) {
        return D(value).iteratedlog(base, times);
      }
      
      Decimal.layeradd10 = function (value, diff) {
        return D(value).layeradd10(diff);
      }
      
       Decimal.layeradd = function (value, diff, base = 10) {
        return D(value).layeradd(diff, base);
      }
      
      Decimal.slog = function (value, base = 10) {
        return D(value).slog(base);
      }
      
      Decimal.lambertw = function(value) {
        return D(value).lambertw();
      }
      
      Decimal.ssqrt = function(value) {
        return D(value).ssqrt();
      }
      
      Decimal.pentate = function (value, height = 2, payload = FC_NN(1, 0, 1)) {
        return D(value).pentate(height, payload);
      }
      
      /**
       * If you're willing to spend 'resourcesAvailable' and want to buy something
       * with exponentially increasing cost each purchase (start at priceStart,
       * multiply by priceRatio, already own currentOwned), how much of it can you buy?
       * Adapted from Trimps source code.
       */
  
  
      Decimal.affordGeometricSeries = function (resourcesAvailable, priceStart, priceRatio, currentOwned) {
        return this.affordGeometricSeries_core(D(resourcesAvailable), D(priceStart), D(priceRatio), currentOwned);
      };
      /**
       * How much resource would it cost to buy (numItems) items if you already have currentOwned,
       * the initial price is priceStart and it multiplies by priceRatio each purchase?
       */
  
  
      Decimal.sumGeometricSeries = function (numItems, priceStart, priceRatio, currentOwned) {
        return this.sumGeometricSeries_core(numItems, D(priceStart), D(priceRatio), currentOwned);
      };
      /**
       * If you're willing to spend 'resourcesAvailable' and want to buy something with additively
       * increasing cost each purchase (start at priceStart, add by priceAdd, already own currentOwned),
       * how much of it can you buy?
       */
  
  
      Decimal.affordArithmeticSeries = function (resourcesAvailable, priceStart, priceAdd, currentOwned) {
        return this.affordArithmeticSeries_core(D(resourcesAvailable), D(priceStart), D(priceAdd), D(currentOwned));
      };
      /**
       * How much resource would it cost to buy (numItems) items if you already have currentOwned,
       * the initial price is priceStart and it adds priceAdd each purchase?
       * Adapted from http://www.mathwords.com/a/arithmetic_series.htm
       */
  
  
      Decimal.sumArithmeticSeries = function (numItems, priceStart, priceAdd, currentOwned) {
        return this.sumArithmeticSeries_core(D(numItems), D(priceStart), D(priceAdd), D(currentOwned));
      };
      /**
       * When comparing two purchases that cost (resource) and increase your resource/sec by (deltaRpS),
       * the lowest efficiency score is the better one to purchase.
       * From Frozen Cookies:
       * http://cookieclicker.wikia.com/wiki/Frozen_Cookies_(JavaScript_Add-on)#Efficiency.3F_What.27s_that.3F
       */
  
  
      Decimal.efficiencyOfPurchase = function (cost, currentRpS, deltaRpS) {
        return this.efficiencyOfPurchase_core(D(cost), D(currentRpS), D(deltaRpS));
      };
  
      Decimal.randomDecimalForTesting = function (maxLayers) {
        // NOTE: This doesn't follow any kind of sane random distribution, so use this for testing purposes only.
        //5% of the time, return 0
        if (Math.random() * 20 < 1) {
          return FC_NN(0, 0, 0);
        }
        
        var randomsign = Math.random() > 0.5 ? 1 : -1;
        
        //5% of the time, return 1 or -1
        if (Math.random() * 20 < 1) {
          return FC_NN(randomsign, 0, 1);
        }
        
        //pick a random layer
        var layer = Math.floor(Math.random()*(maxLayers+1));
  
        var randomexp = layer === 0 ? Math.random()*616-308 : Math.random()*16;
        //10% of the time, make it a simple power of 10
        if (Math.random() > 0.9) { randomexp = Math.trunc(randomexp); }
        var randommag = Math.pow(10, randomexp);
        //10% of the time, trunc mag
        if (Math.random() > 0.9) { randommag = Math.trunc(randommag); }
        return FC(randomsign, layer, randommag);
      };
  
      Decimal.affordGeometricSeries_core = function (resourcesAvailable, priceStart, priceRatio, currentOwned) {
        var actualStart = priceStart.mul(priceRatio.pow(currentOwned));
        return Decimal.floor(resourcesAvailable.div(actualStart).mul(priceRatio.sub(1)).add(1).log10().div(priceRatio.log10()));
      };
  
      Decimal.sumGeometricSeries_core = function (numItems, priceStart, priceRatio, currentOwned) {
        return priceStart.mul(priceRatio.pow(currentOwned)).mul(Decimal.sub(1, priceRatio.pow(numItems))).div(Decimal.sub(1, priceRatio));
      };
  
      Decimal.affordArithmeticSeries_core = function (resourcesAvailable, priceStart, priceAdd, currentOwned) {
        // n = (-(a-d/2) + sqrt((a-d/2)^2+2dS))/d
        // where a is actualStart, d is priceAdd and S is resourcesAvailable
        // then floor it and you're done!
        var actualStart = priceStart.add(currentOwned.mul(priceAdd));
        var b = actualStart.sub(priceAdd.div(2));
        var b2 = b.pow(2);
        return b.neg().add(b2.add(priceAdd.mul(resourcesAvailable).mul(2)).sqrt()).div(priceAdd).floor();
      };
  
      Decimal.sumArithmeticSeries_core = function (numItems, priceStart, priceAdd, currentOwned) {
        var actualStart = priceStart.add(currentOwned.mul(priceAdd)); // (n/2)*(2*a+(n-1)*d)
  
        return numItems.div(2).mul(actualStart.mul(2).plus(numItems.sub(1).mul(priceAdd)));
      };
  
      Decimal.efficiencyOfPurchase_core = function (cost, currentRpS, deltaRpS) {
        return cost.div(currentRpS).add(cost.div(deltaRpS));
      };
      
      Decimal.prototype.normalize = function () {
        /*
        PSEUDOCODE:
        Whenever we are partially 0 (sign is 0 or mag and layer is 0), make it fully 0.
        Whenever we are at or hit layer 0, extract sign from negative mag.
        If layer === 0 and mag < FIRST_NEG_LAYER (1/9e15), shift to 'first negative layer' (add layer, log10 mag).
        While abs(mag) > EXP_LIMIT (9e15), layer += 1, mag = maglog10(mag).
        While abs(mag) < LAYER_DOWN (15.954) and layer > 0, layer -= 1, mag = pow(10, mag).
        
        When we're done, all of the following should be true OR one of the numbers is not IsFinite OR layer is not IsInteger (error state):
        Any 0 is totally zero (0, 0, 0).
        Anything layer 0 has mag 0 OR mag > 1/9e15 and < 9e15.
        Anything layer 1 or higher has abs(mag) >= 15.954 and < 9e15.
        We will assume in calculations that all Decimals are either erroneous or satisfy these criteria. (Otherwise: Garbage in, garbage out.)
        */
        if (this.sign === 0 || (this.mag === 0 && this.layer === 0))
        {
          this.sign = 0;
          this.mag = 0;
          this.layer = 0;
          return this;
        }
        
        if (this.layer === 0 && this.mag < 0)
        {
          //extract sign from negative mag at layer 0
          this.mag = -this.mag;
          this.sign = -this.sign;
        }
        
        //Handle shifting from layer 0 to negative layers.
        if (this.layer === 0 && this.mag < FIRST_NEG_LAYER)
        {
          this.layer += 1;
          this.mag = Math.log10(this.mag);
          return this;
        }
        
        var absmag = Math.abs(this.mag);
        var signmag = Math.sign(this.mag);
        
        if (absmag >= EXP_LIMIT)
        {
          this.layer += 1;
          this.mag = signmag*Math.log10(absmag);
          return this;
        }
        else
        {
          while (absmag < LAYER_DOWN && this.layer > 0)
          {
            this.layer -= 1;
            if (this.layer === 0)
            {
              this.mag = Math.pow(10, this.mag);
            }
            else
            {
              this.mag = signmag*Math.pow(10, absmag);
              absmag = Math.abs(this.mag);
              signmag = Math.sign(this.mag);
            }
          }
          if (this.layer === 0)
          {
            if (this.mag < 0)
            {
              //extract sign from negative mag at layer 0
              this.mag = -this.mag;
              this.sign = -this.sign;
            }
            else if (this.mag === 0)
            {
              //excessive rounding can give us all zeroes
              this.sign = 0;
            }
          }
        }
  
        return this;
      };
  
      Decimal.prototype.fromComponents = function (sign, layer, mag) {
        this.sign = sign;
        this.layer = layer;
        this.mag = mag;
  
        this.normalize();
        return this;
      };
  
      Decimal.prototype.fromComponents_noNormalize = function (sign, layer, mag) {
        this.sign = sign;
        this.layer = layer;
        this.mag = mag;
        return this;
      };
      
      Decimal.prototype.fromMantissaExponent = function (mantissa, exponent) {
        this.layer = 1;
        this.sign = Math.sign(mantissa);
        mantissa = Math.abs(mantissa);
        this.mag = exponent + Math.log10(mantissa);
  
        this.normalize();
        return this;
      };
  
  
      Decimal.prototype.fromMantissaExponent_noNormalize = function (mantissa, exponent) {
        //The idea of 'normalizing' a break_infinity.js style Decimal doesn't really apply. So just do the same thing.
        this.fromMantissaExponent(mantissa, exponent);
        return this;
      };
  
      Decimal.prototype.fromDecimal = function (value) {
        this.sign = value.sign;
        this.layer = value.layer;
        this.mag = value.mag;
        return this;
      };
  
      Decimal.prototype.fromNumber = function (value) {
        this.mag = Math.abs(value);
        this.sign = Math.sign(value);
        this.layer = 0;
        this.normalize();
        return this;
      };
  
      var IGNORE_COMMAS = true;
      var COMMAS_ARE_DECIMAL_POINTS = false;
      
      Decimal.prototype.fromString = function (value) {
        if (IGNORE_COMMAS) { value = value.replace(",", ""); }
        else if (COMMAS_ARE_DECIMAL_POINTS) { value = value.replace(",", "."); }
      
        //Handle x^^^y format.
        var pentationparts = value.split("^^^");
        if (pentationparts.length === 2)
        {
          var base = parseFloat(pentationparts[0]);
          var height = parseFloat(pentationparts[1]);
          var payload = 1;
          var heightparts = pentationparts[1].split(";");
          if (heightparts.length === 2)
          {
            var payload = parseFloat(heightparts[1]);
            if (!isFinite(payload)) { payload = 1; }
          }
          if (isFinite(base) && isFinite(height))
          {
            var result = Decimal.pentate(base, height, payload);
            this.sign = result.sign;
            this.layer = result.layer;
            this.mag = result.mag;
            return this;
          }
        }
      
        //Handle x^^y format.
        var tetrationparts = value.split("^^");
        if (tetrationparts.length === 2)
        {
          var base = parseFloat(tetrationparts[0]);
          var height = parseFloat(tetrationparts[1]);
          var heightparts = tetrationparts[1].split(";");
          if (heightparts.length === 2)
          {
            var payload = parseFloat(heightparts[1]);
            if (!isFinite(payload)) { payload = 1; }
          }
          if (isFinite(base) && isFinite(height))
          {
            var result = Decimal.tetrate(base, height, payload);
            this.sign = result.sign;
            this.layer = result.layer;
            this.mag = result.mag;
            return this;
          }
        }
        
        //Handle x^y format.
        var powparts = value.split("^");
        if (powparts.length === 2)
        {
          var base = parseFloat(powparts[0]);
          var exponent = parseFloat(powparts[1]);
          if (isFinite(base) && isFinite(exponent))
          {
            var result = Decimal.pow(base, exponent);
            this.sign = result.sign;
            this.layer = result.layer;
            this.mag = result.mag;
            return this;
          }
        }
        
        //Handle various cases involving it being a Big Number.
        value = value.trim().toLowerCase();
        
        //handle X PT Y format.
        var ptparts = value.split("pt");
        if (ptparts.length === 2)
        {
          base = 10;
          height = parseFloat(ptparts[0]);
          ptparts[1] = ptparts[1].replace("(", "");
          ptparts[1] = ptparts[1].replace(")", "");
          var payload = parseFloat(ptparts[1]);
          if (!isFinite(payload)) { payload = 1; }
          if (isFinite(base) && isFinite(height))
          {
            var result = Decimal.tetrate(base, height, payload);
            this.sign = result.sign;
            this.layer = result.layer;
            this.mag = result.mag;
            return this;
          }
        }
        
        //handle XpY format (it's the same thing just with p).
        var ptparts = value.split("p");
        if (ptparts.length === 2)
        {
          base = 10;
          height = parseFloat(ptparts[0]);
          ptparts[1] = ptparts[1].replace("(", "");
          ptparts[1] = ptparts[1].replace(")", "");
          var payload = parseFloat(ptparts[1]);
          if (!isFinite(payload)) { payload = 1; }
          if (isFinite(base) && isFinite(height))
          {
            var result = Decimal.tetrate(base, height, payload);
            this.sign = result.sign;
            this.layer = result.layer;
            this.mag = result.mag;
            return this;
          }
        }
  
        var parts = value.split("e");
        var ecount = parts.length-1;
      
        //Handle numbers that are exactly floats (0 or 1 es).
        if (ecount === 0)
        {
          var numberAttempt = parseFloat(value);
          if (isFinite(numberAttempt))
          {
            return this.fromNumber(numberAttempt);
          }
        }
        else if (ecount === 1)
        {
          //Very small numbers ("2e-3000" and so on) may look like valid floats but round to 0.
          var numberAttempt = parseFloat(value);
          if (isFinite(numberAttempt) && numberAttempt !== 0)
          {
            return this.fromNumber(numberAttempt);
          }
        }
        
        //Handle new (e^N)X format.
        var newparts = value.split("e^");
        if (newparts.length === 2)
        {
          this.sign = 1;
          if (newparts[0].charAt(0) == "-")
          {
            this.sign = -1;
          }
          var layerstring = "";
          for (var i = 0; i < newparts[1].length; ++i)
          {
            var chrcode = newparts[1].charCodeAt(i);
            if ((chrcode >= 43 && chrcode <= 57) || chrcode === 101) //is "0" to "9" or "+" or "-" or "." or "e" (or "," or "/")
            {
              layerstring += newparts[1].charAt(i);
            }
            else //we found the end of the layer count
            {
              this.layer = parseFloat(layerstring);
              this.mag = parseFloat(newparts[1].substr(i+1));
              this.normalize();
              return this;
            }
          }
        }
        
        if (ecount < 1) { this.sign = 0; this.layer = 0; this.mag = 0; return this; }
        var mantissa = parseFloat(parts[0]);
        if (mantissa === 0) { this.sign = 0; this.layer = 0; this.mag = 0; return this; }
        var exponent = parseFloat(parts[parts.length-1]);
        //handle numbers like AeBeC and AeeeeBeC
        if (ecount >= 2)
        {
          var me = parseFloat(parts[parts.length-2]);
          if (isFinite(me))
          {
            exponent *= Math.sign(me);
            exponent += f_maglog10(me);
          }
        }
        
        //Handle numbers written like eee... (N es) X
        if (!isFinite(mantissa))
        {
          this.sign = (parts[0] === "-") ? -1 : 1;
          this.layer = ecount;
          this.mag = exponent;
        }
        //Handle numbers written like XeY
        else if (ecount === 1)
        {
          this.sign = Math.sign(mantissa);
          this.layer = 1;
          //Example: 2e10 is equal to 10^log10(2e10) which is equal to 10^(10+log10(2))
          this.mag = exponent + Math.log10(Math.abs(mantissa));
        }
        //Handle numbers written like Xeee... (N es) Y
        else
        {
          this.sign = Math.sign(mantissa);
          this.layer = ecount;
          if (ecount === 2)
          {
            var result = Decimal.mul(FC(1, 2, exponent), D(mantissa));
            this.sign = result.sign;
            this.layer = result.layer;
            this.mag = result.mag;
            return this;
          }
          else
          {
            //at eee and above, mantissa is too small to be recognizable!
            this.mag = exponent;
          }
        }
        
        this.normalize();
        return this;
      };
  
      Decimal.prototype.fromValue = function (value) {
        if (value instanceof Decimal) {
          return this.fromDecimal(value);
        }
  
        if (typeof value === "number") {
          return this.fromNumber(value);
        }
  
        if (typeof value === "string") {
          return this.fromString(value);
        }
  
        this.sign = 0;
        this.layer = 0;
        this.mag = 0;
        return this;
      };
  
      Decimal.prototype.toNumber = function () {
        if (!Number.isFinite(this.layer)) { return Number.NaN; }
        if (this.layer === 0)
        {
          return this.sign*this.mag;
        }
        else if (this.layer === 1)
        {
          return this.sign*Math.pow(10, this.mag);
        }
        else //overflow for any normalized Decimal
        {
          return this.mag > 0 ? (this.sign > 0 ? Number.POSITIVE_INFINITY : Number.NEGATIVE_INFINITY) : 0;
        }
      };
      
      Decimal.prototype.mantissaWithDecimalPlaces = function (places) {
        // https://stackoverflow.com/a/37425022
        if (isNaN(this.m)) {
          return Number.NaN;
        }
  
        if (this.m === 0) {
          return 0;
        }
  
        return decimalPlaces(this.m, places);
      };
      
      Decimal.prototype.magnitudeWithDecimalPlaces = function (places) {
        // https://stackoverflow.com/a/37425022
        if (isNaN(this.mag)) {
          return Number.NaN;
        }
  
        if (this.mag === 0) {
          return 0;
        }
  
        return decimalPlaces(this.mag, places);
      };
      
      Decimal.prototype.toString = function () {
        if (this.layer === 0)
        {
          if ((this.mag < 1e21 && this.mag > 1e-7) || this.mag === 0)
          {
            return (this.sign*this.mag).toString();
          }
          return this.m + "e" + this.e;
        }
        else if (this.layer === 1)
        {
          return this.m + "e" + this.e;
        }
        else
        {
          //layer 2+
          if (this.layer <= MAX_ES_IN_A_ROW)
          {
            return (this.sign === -1 ? "-" : "") + "e".repeat(this.layer) + this.mag;
          }
          else
          {
            return (this.sign === -1 ? "-" : "") + "(e^" + this.layer + ")" + this.mag;
          }
        }
      };
      
      Decimal.prototype.toExponential = function (places) {
        if (this.layer === 0)
        {
          return (this.sign*this.mag).toExponential(places);
        }
        return this.toStringWithDecimalPlaces(places);
      };
      
      Decimal.prototype.toFixed = function (places) {
        if (this.layer === 0)
        {
          return (this.sign*this.mag).toFixed(places);
        }
        return this.toStringWithDecimalPlaces(places);
      };
      
      Decimal.prototype.toPrecision = function (places) {
        if (this.e <= -7) {
          return this.toExponential(places - 1);
        }
  
        if (places > this.e) {
          return this.toFixed(places - this.exponent - 1);
        }
  
        return this.toExponential(places - 1);
      };
      
      Decimal.prototype.valueOf = function () {
        return this.toString();
      };
  
      Decimal.prototype.toJSON = function () {
        return this.toString();
      };
      
      Decimal.prototype.toStringWithDecimalPlaces = function (places) {
        if (this.layer === 0)
        {
          if ((this.mag < 1e21 && this.mag > 1e-7) || this.mag === 0)
          {
            return (this.sign*this.mag).toFixed(places);
          }
          return decimalPlaces(this.m, places) + "e" + decimalPlaces(this.e, places);
        }
        else if (this.layer === 1)
        {
          return decimalPlaces(this.m, places) + "e" + decimalPlaces(this.e, places);
        }
        else
        {
          //layer 2+
          if (this.layer <= MAX_ES_IN_A_ROW)
          {
            return (this.sign === -1 ? "-" : "") + "e".repeat(this.layer) + decimalPlaces(this.mag, places);
          }
          else
          {
            return (this.sign === -1 ? "-" : "") + "(e^" + this.layer + ")" + decimalPlaces(this.mag, places);
          }
        }
      };
      
      Decimal.prototype.abs = function () {
        return FC_NN(this.sign === 0 ? 0 : 1, this.layer, this.mag);
      };
  
      Decimal.prototype.neg = function () {
        return FC_NN(-this.sign, this.layer, this.mag);
      };
  
      Decimal.prototype.negate = function () {
        return this.neg();
      };
  
      Decimal.prototype.negated = function () {
        return this.neg();
      };
  
      Decimal.prototype.sign = function () {
        return this.sign;
      };
  
      Decimal.prototype.sgn = function () {
        return this.sign;
      };
      
      Decimal.prototype.round = function () {
        if (this.mag < 0)
        {
          return Decimal.dZero;
        }
        if (this.layer === 0)
        {
          return FC(this.sign, 0, Math.round(this.mag));
        }
        return this;
      };
  
      Decimal.prototype.floor = function () {
        if (this.mag < 0)
        {
          return Decimal.dZero;
        }
        if (this.layer === 0)
        {
          return FC(this.sign, 0, Math.floor(this.mag));
        }
        return this;
      };
  
      Decimal.prototype.ceil = function () {
        if (this.mag < 0)
        {
          return Decimal.dZero;
        }
        if (this.layer === 0)
        {
          return FC(this.sign, 0, Math.ceil(this.mag));
        }
        return this;
      };
  
      Decimal.prototype.trunc = function () {
        if (this.mag < 0)
        {
          return Decimal.dZero;
        }
        if (this.layer === 0)
        {
          return FC(this.sign, 0, Math.trunc(this.mag));
        }
        return this;
      };
  
      Decimal.prototype.add = function (value) {
        var decimal = D(value);
        
        //inf/nan check
        if (!Number.isFinite(this.layer)) { return this; }
        if (!Number.isFinite(decimal.layer)) { return decimal; }
        
        //Special case - if one of the numbers is 0, return the other number.
        if (this.sign === 0) { return decimal; }
        if (decimal.sign === 0) { return this; }
        
        //Special case - Adding a number to its negation produces 0, no matter how large.
        if (this.sign === -(decimal.sign) && this.layer === decimal.layer && this.mag === decimal.mag) { return FC_NN(0, 0, 0); }
        
        var a;
        var b;
        
        //Special case: If one of the numbers is layer 2 or higher, just take the bigger number.
        if ((this.layer >= 2 || decimal.layer >= 2)) { return this.maxabs(decimal); }
        
        if (Decimal.cmpabs(this, decimal) > 0)
        {
          a = this;
          b = decimal;
        }
        else
        {
          a = decimal;
          b = this;
        }
        
        if (a.layer === 0 && b.layer === 0) { return D(a.sign*a.mag + b.sign*b.mag); }
        
        var layera = a.layer*Math.sign(a.mag);
        var layerb = b.layer*Math.sign(b.mag);
        
        //If one of the numbers is 2+ layers higher than the other, just take the bigger number.
        if (layera - layerb >= 2) { return a; }
        
        if (layera === 0 && layerb === -1)
        {
          if (Math.abs(b.mag-Math.log10(a.mag)) > MAX_SIGNIFICANT_DIGITS)
          {
            return a;
          }
          else
          {
            var magdiff = Math.pow(10, Math.log10(a.mag)-b.mag);
            var mantissa = (b.sign)+(a.sign*magdiff);
            return FC(Math.sign(mantissa), 1, b.mag+Math.log10(Math.abs(mantissa)));
          }
        }
        
        if (layera === 1 && layerb === 0)
        {
          if (Math.abs(a.mag-Math.log10(b.mag)) > MAX_SIGNIFICANT_DIGITS)
          {
            return a;
          }
          else
          {
            var magdiff = Math.pow(10, a.mag-Math.log10(b.mag));
            var mantissa = (b.sign)+(a.sign*magdiff);
            return FC(Math.sign(mantissa), 1, Math.log10(b.mag)+Math.log10(Math.abs(mantissa)));
          }
        }
        
        if (Math.abs(a.mag-b.mag) > MAX_SIGNIFICANT_DIGITS)
        {
          return a;
        }
        else
        {
          var magdiff = Math.pow(10, a.mag-b.mag);
          var mantissa = (b.sign)+(a.sign*magdiff);
          return FC(Math.sign(mantissa), 1, b.mag+Math.log10(Math.abs(mantissa)));
        }
        
        throw Error("Bad arguments to add: " + this + ", " + value);
      };
  
      Decimal.prototype.plus = function (value) {
        return this.add(value);
      };
  
      Decimal.prototype.sub = function (value) {
        return this.add(D(value).neg());
      };
  
      Decimal.prototype.subtract = function (value) {
        return this.sub(value);
      };
  
      Decimal.prototype.minus = function (value) {
        return this.sub(value);
      };
  
      Decimal.prototype.mul = function (value) {
        var decimal = D(value);
        
        //inf/nan check
        if (!Number.isFinite(this.layer)) { return this; }
        if (!Number.isFinite(decimal.layer)) { return decimal; }
        
        //Special case - if one of the numbers is 0, return 0.
        if (this.sign === 0 || decimal.sign === 0) { return FC_NN(0, 0, 0); }
        
        //Special case - Multiplying a number by its own reciprocal yields +/- 1, no matter how large.
        if (this.layer === decimal.layer && this.mag === -decimal.mag) { return FC_NN(this.sign*decimal.sign, 0, 1); }
              
        var a;
        var b;
        
        //Which number is bigger in terms of its multiplicative distance from 1?
        if ((this.layer > decimal.layer) || (this.layer == decimal.layer && Math.abs(this.mag) > Math.abs(decimal.mag)))
        {
          a = this;
          b = decimal;
        }
        else
        {
          a = decimal;
          b = this;
        }
        
        if (a.layer === 0 && b.layer === 0) { return D(a.sign*b.sign*a.mag*b.mag); }
        
        //Special case: If one of the numbers is layer 3 or higher or one of the numbers is 2+ layers bigger than the other, just take the bigger number.
        if (a.layer >= 3 || (a.layer - b.layer >= 2)) { return FC(a.sign*b.sign, a.layer, a.mag); }
  
        if (a.layer === 1 && b.layer === 0)
        { 
          return FC(a.sign*b.sign, 1, a.mag+Math.log10(b.mag));
        }
        
        if (a.layer === 1 && b.layer === 1)
        {
          return FC(a.sign*b.sign, 1, a.mag+b.mag);
        }
        
        if (a.layer === 2 && b.layer === 1)
        {
          var newmag = FC(Math.sign(a.mag), a.layer-1, Math.abs(a.mag)).add(FC(Math.sign(b.mag), b.layer-1, Math.abs(b.mag)));
          return FC(a.sign*b.sign, newmag.layer+1, newmag.sign*newmag.mag);
        }
        
        if (a.layer === 2 && b.layer === 2)
        {
          var newmag = FC(Math.sign(a.mag), a.layer-1, Math.abs(a.mag)).add(FC(Math.sign(b.mag), b.layer-1, Math.abs(b.mag)));
          return FC(a.sign*b.sign, newmag.layer+1, newmag.sign*newmag.mag);
        }
        
        throw Error("Bad arguments to mul: " + this + ", " + value);
      };
  
      Decimal.prototype.multiply = function (value) {
        return this.mul(value);
      };
  
      Decimal.prototype.times = function (value) {
        return this.mul(value);
      };
  
      Decimal.prototype.div = function (value) {
        var decimal = D(value);
        return this.mul(decimal.recip());
      };
  
      Decimal.prototype.divide = function (value) {
        return this.div(value);
      };
  
      Decimal.prototype.divideBy = function (value) {
        return this.div(value);
      };
  
      Decimal.prototype.dividedBy = function (value) {
        return this.div(value);
      };
  
      Decimal.prototype.recip = function () {
        if (this.mag === 0)
        {
  		if(!window.decimalError){alert((new Error("recip failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        else if (this.layer === 0)
        {
          return FC(this.sign, 0, 1/this.mag);
        }
        else
        {
          return FC(this.sign, this.layer, -this.mag);
        }
      };
  
      Decimal.prototype.reciprocal = function () {
        return this.recip();
      };
  
      Decimal.prototype.reciprocate = function () {
        return this.recip();
      };
      
      /**
       * -1 for less than value, 0 for equals value, 1 for greater than value
       */
      Decimal.prototype.cmp = function (value) {
        var decimal = D(value);
        if (this.sign > decimal.sign) { return 1; }
        if (this.sign < decimal.sign) { return -1; }
        return this.sign*this.cmpabs(value);
      };
  	
  	Decimal.prototype.cmpabs = function (value) {
        var decimal = D(value);
        var layera = this.mag > 0 ? this.layer : -this.layer;
        var layerb = decimal.mag > 0 ? decimal.layer : -decimal.layer;
        if (layera > layerb) { return 1; }
        if (layera < layerb) { return -1; }
        if (this.mag > decimal.mag) { return 1; }
        if (this.mag < decimal.mag) { return -1; }
        return 0;
      };
  
      Decimal.prototype.compare = function (value) {
        return this.cmp(value);
      };
  
      Decimal.prototype.eq = function (value) {
        var decimal = D(value);
        return this.sign === decimal.sign && this.layer === decimal.layer && this.mag === decimal.mag;
      };
  
      Decimal.prototype.equals = function (value) {
        return this.eq(value);
      };
  
      Decimal.prototype.neq = function (value) {
        return !this.eq(value);
      };
  
      Decimal.prototype.notEquals = function (value) {
        return this.neq(value);
      };
  
      Decimal.prototype.lt = function (value) {
        var decimal = D(value);
        return this.cmp(value) === -1;
      };
  
      Decimal.prototype.lte = function (value) {
        return !this.gt(value);
      };
  
      Decimal.prototype.gt = function (value) {
        var decimal = D(value);
        return this.cmp(value) === 1;
      };
  
      Decimal.prototype.gte = function (value) {
        return !this.lt(value);
      };
  
      Decimal.prototype.max = function (value) {
        var decimal = D(value);
        return this.lt(decimal) ? decimal : this;
      };
  
      Decimal.prototype.min = function (value) {
        var decimal = D(value);
        return this.gt(decimal) ? decimal : this;
      };
  	
  	Decimal.prototype.maxabs = function (value) {
        var decimal = D(value);
        return this.cmpabs(decimal) < 0 ? decimal : this;
      };
  
      Decimal.prototype.minabs = function (value) {
        var decimal = D(value);
        return this.cmpabs(decimal) > 0 ? decimal : this;
      };
      
      Decimal.prototype.clamp = function(min, max) {
        return this.max(min).min(max);
      }
      
      Decimal.prototype.clampMin = function(min) {
        return this.max(min);
      }
      
      Decimal.prototype.clampMax = function(max) {
        return this.min(max);
      }
  
      Decimal.prototype.cmp_tolerance = function (value, tolerance) {
        var decimal = D(value);
        return this.eq_tolerance(decimal, tolerance) ? 0 : this.cmp(decimal);
      };
  
      Decimal.prototype.compare_tolerance = function (value, tolerance) {
        return this.cmp_tolerance(value, tolerance);
      };
      
      /**
       * Tolerance is a relative tolerance, multiplied by the greater of the magnitudes of the two arguments.
       * For example, if you put in 1e-9, then any number closer to the
       * larger number than (larger number)*1e-9 will be considered equal.
       */
      Decimal.prototype.eq_tolerance = function (value, tolerance) {
        var decimal = D(value); // https://stackoverflow.com/a/33024979
        if (tolerance == null) { tolerance = 1e-7; }
        //Numbers that are too far away are never close.
        if (this.sign !== decimal.sign) { return false; }
        if (Math.abs(this.layer - decimal.layer) > 1) { return false; }
        // return abs(a-b) <= tolerance * max(abs(a), abs(b))
        var magA = this.mag;
        var magB = decimal.mag;
        if (this.layer > decimal.layer) { magB = f_maglog10(magB); }
        if (this.layer < decimal.layer) { magA = f_maglog10(magA); }
        return Math.abs(magA-magB) <= tolerance*Math.max(Math.abs(magA), Math.abs(magB));
      };
  
      Decimal.prototype.equals_tolerance = function (value, tolerance) {
        return this.eq_tolerance(value, tolerance);
      };
  
      Decimal.prototype.neq_tolerance = function (value, tolerance) {
        return !this.eq_tolerance(value, tolerance);
      };
  
      Decimal.prototype.notEquals_tolerance = function (value, tolerance) {
        return this.neq_tolerance(value, tolerance);
      };
  
      Decimal.prototype.lt_tolerance = function (value, tolerance) {
        var decimal = D(value);
        return !this.eq_tolerance(decimal, tolerance) && this.lt(decimal);
      };
  
      Decimal.prototype.lte_tolerance = function (value, tolerance) {
        var decimal = D(value);
        return this.eq_tolerance(decimal, tolerance) || this.lt(decimal);
      };
  
      Decimal.prototype.gt_tolerance = function (value, tolerance) {
        var decimal = D(value);
        return !this.eq_tolerance(decimal, tolerance) && this.gt(decimal);
      };
  
      Decimal.prototype.gte_tolerance = function (value, tolerance) {
        var decimal = D(value);
        return this.eq_tolerance(decimal, tolerance) || this.gt(decimal);
      };
      
      Decimal.prototype.pLog10 = function() {
        if (this.lt(Decimal.dZero)) { return Decimal.dZero; }
        return this.log10();
      }
  
      Decimal.prototype.absLog10 = function () {
        if (this.sign === 0)
        {
  		if(!window.decimalError){alert((new Error("absLog10 failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        else if (this.layer > 0)
        {
          return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag));
        }
        else
        {
          return FC(1, 0, Math.log10(this.mag));
        }
      };
      
      Decimal.prototype.log10 = function () {
        if (this.sign <= 0)
        {
  		if(!window.decimalError){alert((new Error("log10 failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        else if (this.layer > 0)
        {
          return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag));
        }
        else
        {
          return FC(this.sign, 0, Math.log10(this.mag));
        }
      };
  
      Decimal.prototype.log = function (base) {
        base = D(base);
        if (this.sign <= 0)
        {
  		if(!window.decimalError){alert((new Error("log failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        if (base.sign <= 0)
        {
  		if(!window.decimalError){alert((new Error("log failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        if (base.sign === 1 && base.layer === 0 && base.mag === 1)
        {
  		if(!window.decimalError){alert((new Error("log failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        else if (this.layer === 0 && base.layer === 0)
        {
          return FC(this.sign, 0, Math.log(this.mag)/Math.log(base.mag));
        }
        
        return Decimal.div(this.log10(), base.log10());
      };
  
      Decimal.prototype.log2 = function () {
        if (this.sign <= 0)
        {
  		if(!window.decimalError){alert((new Error("log2 failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        else if (this.layer === 0)
        {
          return FC(this.sign, 0, Math.log2(this.mag));
        }
        else if (this.layer === 1)
        {
          return FC(Math.sign(this.mag), 0, Math.abs(this.mag)*3.321928094887362); //log2(10)
        }
        else if (this.layer === 2)
        {
          return FC(Math.sign(this.mag), 1, Math.abs(this.mag)+0.5213902276543247); //-log10(log10(2))
        }
        else
        {
          return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag));
        }
      };
  
      Decimal.prototype.ln = function () {
        if (this.sign <= 0)
        {
  		if(!window.decimalError){alert((new Error("ln failed")).stack);window.decimalError=true;}
          return Decimal.dNaN;
        }
        else if (this.layer === 0)
        {
          return FC(this.sign, 0, Math.log(this.mag));
        }
        else if (this.layer === 1)
        {
          return FC(Math.sign(this.mag), 0, Math.abs(this.mag)*2.302585092994046); //ln(10)
        }
        else if (this.layer === 2)
        {
          return FC(Math.sign(this.mag), 1, Math.abs(this.mag)+0.36221568869946325); //log10(log10(e))
        }
        else
        {
          return FC(Math.sign(this.mag), this.layer-1, Math.abs(this.mag));
        }
      };
  
      Decimal.prototype.logarithm = function (base) {
        return this.log(base);
      };
  
      Decimal.prototype.pow = function (value) {
        var decimal = D(value);
        var a = this;
        var b = decimal;
  
        //special case: if a is 0, then return 0
        if (a.sign === 0) { return a; }
        //special case: if a is 1, then return 1
        if (a.sign === 1 && a.layer === 0 && a.mag === 1) { return a; }
        //special case: if b is 0, then return 1
        if (b.sign === 0) { return FC_NN(1, 0, 1); }
        //special case: if b is 1, then return a
        if (b.sign === 1 && b.layer === 0 && b.mag === 1) { return a; }
        
        var result = (a.absLog10().mul(b)).pow10();
  
        if (this.sign === -1 && b.toNumber() % 2 === 1) {
          return result.neg();
        }
  
        return result;
      };
      
      Decimal.prototype.pow10 = function() {
        /*
        There are four cases we need to consider:
        1) positive sign, positive mag (e15, ee15): +1 layer (e.g. 10^15 becomes e15, 10^e15 becomes ee15)
        2) negative sign, positive mag (-e15, -ee15): +1 layer but sign and mag sign are flipped (e.g. 10^-15 becomes e-15, 10^-e15 becomes ee-15)
        3) positive sign, negative mag (e-15, ee-15): layer 0 case would have been handled in the Math.pow check, so just return 1
        4) negative sign, negative mag (-e-15, -ee-15): layer 0 case would have been handled in the Math.pow check, so just return 1
        */
        
        if (!Number.isFinite(this.layer) || !Number.isFinite(this.mag)) { return Decimal.dNaN; }
        
        var a = this;
        
        //handle layer 0 case - if no precision is lost just use Math.pow, else promote one layer
        if (a.layer === 0)
        {
          var newmag = Math.pow(10, a.sign*a.mag);
          if (Number.isFinite(newmag) && Math.abs(newmag) > 0.1) { return FC(1, 0, newmag); }
          else
          {
            if (a.sign === 0) { return Decimal.dOne; }
            else { a = FC_NN(a.sign, a.layer+1, Math.log10(a.mag)); }
          }
        }
        
        //handle all 4 layer 1+ cases individually
        if (a.sign > 0 && a.mag > 0)
        {
          return FC(a.sign, a.layer+1, a.mag);
        }
        if (a.sign < 0 && a.mag > 0)
        {
          return FC(-a.sign, a.layer+1, -a.mag);
        }
        //both the negative mag cases are identical: one +/- rounding error
        return Decimal.dOne;
      }
  
      Decimal.prototype.pow_base = function (value) {
        return D(value).pow(this);
      };
      
      Decimal.prototype.root = function (value) {
        var decimal = D(value);
        return this.pow(decimal.recip());
      }
  
      Decimal.prototype.factorial = function () {
        if (this.mag < 0)
        {
          return this.toNumber().add(1).gamma();
        }
        else if (this.layer === 0)
        {
          return this.add(1).gamma();
        }
        else if (this.layer === 1)
        {
          return Decimal.exp(Decimal.mul(this, Decimal.ln(this).sub(1)));
        }
        else
        {
          return Decimal.exp(this);
        }
      };
      
      //from HyperCalc source code
      Decimal.prototype.gamma = function () {
        if (this.mag < 0)
        {
          return this.recip();
        }
        else if (this.layer === 0)
        {
          if (this.lt(FC_NN(1, 0, 24)))
          {
            return D(f_gamma(this.sign*this.mag));
          }
          
          var t = this.mag - 1;
          var l = 0.9189385332046727; //0.5*Math.log(2*Math.PI)
          l = (l+((t+0.5)*Math.log(t)));
          l = l-t;
          var n2 = t*t;
          var np = t;
          var lm = 12*np;
          var adj = 1/lm;
          var l2 = l+adj;
          if (l2 === l)
          {
            return Decimal.exp(l);
          }
          
          l = l2;
          np = np*n2;
          lm = 360*np;
          adj = 1/lm;
          l2 = l-adj;
          if (l2 === l)
          {
            return Decimal.exp(l);
          }
          
          l = l2;
          np = np*n2;
          lm = 1260*np;
          var lt = 1/lm;
          l = l+lt;
          np = np*n2;
          lm = 1680*np;
          lt = 1/lm;
          l = l-lt;
          return Decimal.exp(l);
        }
        else if (this.layer === 1)
        {
          return Decimal.exp(Decimal.mul(this, Decimal.ln(this).sub(1)));
        }
        else
        {
          return Decimal.exp(this);
        }
      };
      
      Decimal.prototype.lngamma = function () {
        return this.gamma().ln();
      }
  
      Decimal.prototype.exp = function () {
        if (this.mag < 0) { return Decimal.dOne; }
        if (this.layer === 0 && this.mag <= 709.7) { return D(Math.exp(this.sign*this.mag)); }
        else if (this.layer === 0) { return FC(1, 1, this.sign*Math.log10(Math.E)*this.mag); }
        else if (this.layer === 1) { return FC(1, 2, this.sign*(Math.log10(0.4342944819032518)+this.mag)); }
        else { return FC(1, this.layer+1, this.sign*this.mag); }
      };
  
      Decimal.prototype.sqr = function () {
        return this.pow(2);
      };
  
      Decimal.prototype.sqrt = function () {
        if (this.layer === 0) { return D(Math.sqrt(this.sign*this.mag)); }
        else if (this.layer === 1) { return FC(1, 2, Math.log10(this.mag)-0.3010299956639812); }
        else
        {
          var result = Decimal.div(FC_NN(this.sign, this.layer-1, this.mag), FC_NN(1, 0, 2));
          result.layer += 1;
          result.normalize();
          return result;
        }
      };
  
      Decimal.prototype.cube = function () {
        return this.pow(3);
      };
  
      Decimal.prototype.cbrt = function () {
        return this.pow(1/3);
      };
      
      //Tetration/tetrate: The result of exponentiating 'this' to 'this' 'height' times in a row.  https://en.wikipedia.org/wiki/Tetration
      //If payload != 1, then this is 'iterated exponentiation', the result of exping (payload) to base (this) (height) times. https://andydude.github.io/tetration/archives/tetration2/ident.html
      //Works with negative and positive real heights.
      Decimal.prototype.tetrate = function(height = 2, payload = FC_NN(1, 0, 1)) {
        if (height === Number.POSITIVE_INFINITY)
        {
          //Formula for infinite height power tower.
          var negln = Decimal.ln(this).neg();
          return negln.lambertw().div(negln);
        }
        
        if (height < 0)
        {
          return Decimal.iteratedlog(payload, this, -height);
        }
        
        payload = D(payload);
        var oldheight = height;
        height = Math.trunc(height);
        var fracheight = oldheight-height;
       
        if (fracheight !== 0)
        {
          if (payload.eq(Decimal.dOne))
          {
            ++height;
            payload = new Decimal(fracheight);
          }
          else
          {
            if (this.eq(10))
            {
              payload = payload.layeradd10(fracheight);
            }
            else
            {
              payload = payload.layeradd(fracheight, this);
            }
          }
        }
        
        for (var i = 0; i < height; ++i)
        {
          payload = this.pow(payload);
          //bail if we're NaN
          if (!isFinite(payload.layer) || !isFinite(payload.mag)) { return payload; }
          //shortcut 
          if (payload.layer - this.layer > 3) { return FC_NN(payload.sign, payload.layer + (height - i - 1), payload.mag); }
          //give up after 100 iterations if nothing is happening
          if (i > 100) { return payload; }
        }
        return payload;
      }
      
      //iteratedexp/iterated exponentiation: - all cases handled in tetrate, so just call it
      Decimal.prototype.iteratedexp = function(height = 2, payload = FC_NN(1, 0, 1)) {
        return this.tetrate(height, payload);
      }
      
      //iterated log/repeated log: The result of applying log(base) 'times' times in a row. Approximately equal to subtracting (times) from the number's slog representation. Equivalent to tetrating to a negative height.
      //Works with negative and positive real heights.
      Decimal.prototype.iteratedlog = function(base = 10, times = 1) {      
        if (times < 0)
        {
          return Decimal.tetrate(base, -times, this);
        }
        
        base = D(base);
        var result = D(this);
        var fulltimes = times;
        times = Math.trunc(times);
        var fraction = fulltimes - times;
        if (result.layer - base.layer > 3)
        {
          var layerloss = Math.min(times, (result.layer - base.layer - 3));
          times -= layerloss;
          result.layer -= layerloss;
        }
        
        for (var i = 0; i < times; ++i)
        {
          result = result.log(base);
          //bail if we're NaN
          if (!isFinite(result.layer) || !isFinite(result.mag)) { return result; }
          //give up after 100 iterations if nothing is happening
          if (i > 100) { return result; }
        }
        
        //handle fractional part
        if (fraction > 0 && fraction < 1)
        {
          if (base.eq(10))
          {
            result = result.layeradd10(-fraction);
          }
          else
          {
            result = result.layeradd(-fraction, base);
          }
        }
        
        return result;
      }
      
      //Super-logarithm, one of tetration's inverses, tells you what size power tower you'd have to tetrate base to to get number. By definition, will never be higher than 1.8e308 in break_eternity.js, since a power tower 1.8e308 numbers tall is the largest representable number.
      // https://en.wikipedia.org/wiki/Super-logarithm
      Decimal.prototype.slog = function(base = 10) {
        if (this.mag < 0) { return Decimal.dNegOne; }
        
        base = D(base);
        
        var result = 0;
        var copy = D(this);
        if (copy.layer - base.layer > 3)
        {
          var layerloss = (copy.layer - base.layer - 3);
          result += layerloss;
          copy.layer -= layerloss;
        }
        
        for (var i = 0; i < 100; ++i)
        {
          if (copy.lt(Decimal.dZero))
          {
            copy = Decimal.pow(base, copy);
            result -= 1;
          }
          else if (copy.lte(Decimal.dOne))
          {
            return D(result + copy.toNumber() - 1); //<-- THIS IS THE CRITICAL FUNCTION
            //^ Also have to change tetrate payload handling and layeradd10 if this is changed!
          }
          else
          {
            result += 1;
            copy = Decimal.log(copy, base);
          }
        }
        return D(result);
      }
      
      //Approximations taken from the excellent paper https://web.archive.org/web/20090201164836/http://tetration.itgo.com/paper.html !
      //Not using for now unless I can figure out how to use it in all the related functions.
      /*var slog_criticalfunction_1 = function(x, z) {
        z = z.toNumber();
        return -1 + z;
      }
      
      var slog_criticalfunction_2 = function(x, z) {
        z = z.toNumber();
        var lnx = x.ln();
        if (lnx.layer === 0)
        {
          lnx = lnx.toNumber();
          return -1 + z*2*lnx/(1+lnx) - z*z*(1-lnx)/(1+lnx);
        }
        else
        {
          var term1 = lnx.mul(z*2).div(lnx.add(1));
          var term2 = Decimal.sub(1, lnx).mul(z*z).div(lnx.add(1));
          Decimal.dNegOne.add(Decimal.sub(term1, term2));
        }
      }
      
      var slog_criticalfunction_3 = function(x, z) {
        z = z.toNumber();
        var lnx = x.ln();
        var lnx2 = lnx.sqr();
        var lnx3 = lnx.cube();
        if (lnx.layer === 0 && lnx2.layer === 0 && lnx3.layer === 0)
        {
          lnx = lnx.toNumber();
          lnx2 = lnx2.toNumber();
          lnx3 = lnx3.toNumber();
          
          var term1 = 6*z*(lnx+lnx3);
          var term2 = 3*z*z*(3*lnx2-2*lnx3);
          var term3 = 2*z*z*z*(1-lnx-2*lnx2+lnx3);
          var top = term1+term2+term3;
          var bottom = 2+4*lnx+5*lnx2+2*lnx3;
          
          return -1 + top/bottom;
        }
        else
        {
          var term1 = (lnx.add(lnx3)).mul(6*z);
          var term2 = (lnx2.mul(3).sub(lnx3.mul(2))).mul(3*z*z);
          var term3 = (Decimal.dOne.sub(lnx).sub(lnx2.mul(2)).add(lnx3)).mul(2*z*z*z);
          var top = term1.add(term2).add(term3);
          var bottom = new Decimal(2).add(lnx.mul(4)).add(lnx2.mul(5)).add(lnx3.mul(2));
          
          return Decimal.dNegOne.add(top.div(bottom));
        }
      }*/
      
      //Function for adding/removing layers from a Decimal, even fractional layers (e.g. its slog10 representation).
      //Everything continues to use the linear approximation ATM.
      Decimal.prototype.layeradd10 = function(diff) {
        diff = Decimal.fromValue_noAlloc(diff).toNumber();
        var result = D(this);
        if (diff >= 1)
        {
          var layeradd = Math.trunc(diff);
          diff -= layeradd;
          result.layer += layeradd;
        }
        if (diff <= -1)
        {
          var layeradd = Math.trunc(diff);
          diff -= layeradd;
          result.layer += layeradd;
          if (result.layer < 0)
          {
            for (var i = 0; i < 100; ++i)
            {
              result.layer++;
              result.mag = Math.log10(result.mag);
              if (!isFinite(result.mag)) { return result; }
              if (result.layer >= 0) { break; }
            }
          }
        }
        
        //layeradd10: like adding 'diff' to the number's slog(base) representation. Very similar to tetrate base 10 and iterated log base 10. Also equivalent to adding a fractional amount to the number's layer in its break_eternity.js representation.
        if (diff > 0)
        {
          var subtractlayerslater = 0;
          //Ironically, this edge case would be unnecessary if we had 'negative layers'.
          while (Number.isFinite(result.mag) && result.mag < 10)
          {
            result.mag = Math.pow(10, result.mag);
            ++subtractlayerslater;
          }
          
          //A^(10^B) === C, solve for B
          //B === log10(logA(C))
          
          if (result.mag > 1e10)
          {
            result.mag = Math.log10(result.mag);
            result.layer++;
          }
          
          //Note that every integer slog10 value, the formula changes, so if we're near such a number, we have to spend exactly enough layerdiff to hit it, and then use the new formula.
          var diffToNextSlog = Math.log10(Math.log(1e10)/Math.log(result.mag), 10);
          if (diffToNextSlog < diff)
          {
            result.mag = Math.log10(1e10);
            result.layer++;
            diff -= diffToNextSlog;
          }
          
          result.mag = Math.pow(result.mag, Math.pow(10, diff));
          
          while (subtractlayerslater > 0)
          {
            result.mag = Math.log10(result.mag);
            --subtractlayerslater;
          }
        }
        else if (diff < 0)
        {
          var subtractlayerslater = 0;
          
          while (Number.isFinite(result.mag) && result.mag < 10)
          {
            result.mag = Math.pow(10, result.mag);
            ++subtractlayerslater;
          }
          
          if (result.mag > 1e10)
          {
            result.mag = Math.log10(result.mag);
            result.layer++;
          }
          
          var diffToNextSlog = Math.log10(1/Math.log10(result.mag));
          if (diffToNextSlog > diff)
          {
            result.mag = 1e10;
            result.layer--;
            diff -= diffToNextSlog;
          }
          
          result.mag = Math.pow(result.mag, Math.pow(10, diff));
          
          while (subtractlayerslater > 0)
          {
            result.mag = Math.log10(result.mag);
            --subtractlayerslater;
          }
        }
        
        while (result.layer < 0)
        {
          result.layer++;
          result.mag = Math.log10(result.mag);
        }
        result.normalize();
        return result;
      }
      
      //layeradd: like adding 'diff' to the number's slog(base) representation. Very similar to tetrate base 'base' and iterated log base 'base'.
      Decimal.prototype.layeradd = function(diff, base) {
        var slogthis = this.slog(base).toNumber();
        var slogdest = slogthis+diff;
        if (slogdest >= 0)
        {
          return Decimal.tetrate(base, slogdest);
        }
        else if (!Number.isFinite(slogdest))
        {
          return Decimal.dNaN;
        }
        else if (slogdest >= -1)
        {
          return Decimal.log(Decimal.tetrate(base, slogdest+1), base);
        }
        else
        {
          Decimal.log(Decimal.log(Decimal.tetrate(base, slogdest+2), base), base);
        }
      }
      
      //The Lambert W function, also called the omega function or product logarithm, is the solution W(x) === x*e^x.
      // https://en.wikipedia.org/wiki/Lambert_W_function
      //Some special values, for testing: https://en.wikipedia.org/wiki/Lambert_W_function#Special_values
      Decimal.prototype.lambertw = function() {
        if (this.lt(-0.3678794411710499))
        {
          throw Error("lambertw is unimplemented for results less than -1, sorry!");
        }
        else if (this.mag < 0)
        {
          return D(f_lambertw(this.toNumber()));
        }
        else if (this.layer === 0)
        {
          return D(f_lambertw(this.sign*this.mag));
        }
        else if (this.layer === 1)
        {
          return d_lambertw(this);
        }
        else if (this.layer === 2)
        {
          return d_lambertw(this);
        }
        if (this.layer >= 3)
        {
          return FC_NN(this.sign, this.layer-1, this.mag);
        }
      }
    
      //from https://github.com/scipy/scipy/blob/8dba340293fe20e62e173bdf2c10ae208286692f/scipy/special/lambertw.pxd
      // The evaluation can become inaccurate very close to the branch point
      // at ``-1/e``. In some corner cases, `lambertw` might currently
      // fail to converge, or can end up on the wrong branch.
      var d_lambertw = function(z, tol = 1e-10) {
      var w;
      var ew, wew, wewz, wn;
      
      if (!Number.isFinite(z.mag)) { return z; }
      if (z === 0)
      {
        return z;
      }
      if (z === 1)
      {
        //Split out this case because the asymptotic series blows up
        return OMEGA;
      }
      
      var absz = Decimal.abs(z);
      //Get an initial guess for Halley's method
      w = Decimal.ln(z);
      
      //Halley's method; see 5.9 in [1]
      
      for (var i = 0; i < 100; ++i)
      {
        ew = Decimal.exp(-w);
        wewz = w.sub(z.mul(ew));
        wn = w.sub(wewz.div(w.add(1).sub((w.add(2)).mul(wewz).div((Decimal.mul(2, w).add(2))))));
        if (Decimal.abs(wn.sub(w)).lt(Decimal.abs(wn).mul(tol)))
        {
          return wn;
        }
        else
        {
          w = wn;
        }
      }
      
      throw Error("Iteration failed to converge: " + z);
      //return Decimal.dNaN;
      }
      
      //The super square-root function - what number, tetrated to height 2, equals this?
      //Other sroots are possible to calculate probably through guess and check methods, this one is easy though.
      // https://en.wikipedia.org/wiki/Tetration#Super-root
      Decimal.prototype.ssqrt = function() {
        if (this.sign == 1 && this.layer >= 3)
        {
            return FC_NN(this.sign, this.layer-1, this.mag)
        }
        var lnx = this.ln();
        return lnx.div(lnx.lambertw());
      }
  /*
  
  Unit tests for tetrate/iteratedexp/iteratedlog/layeradd10/layeradd/slog:
  
  for (var i = 0; i < 1000; ++i)
  {
      var first = Math.random()*100;
      var both = Math.random()*100;
      var expected = first+both+1;
      var result = new Decimal(10).layeradd10(first).layeradd10(both).slog();
      if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result))
      {
          console.log(first + ", " + both);
      }
  }
  
  for (var i = 0; i < 1000; ++i)
  {
      var first = Math.random()*100;
      var both = Math.random()*100;
      first += both;
      var expected = first-both+1;
      var result = new Decimal(10).layeradd10(first).layeradd10(-both).slog();
      if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result))
      {
          console.log(first + ", " + both);
      }
  }
  
  for (var i = 0; i < 1000; ++i)
  {
      var first = Math.random()*100;
      var both = Math.random()*100;
      var base = Math.random()*8+2;
      var expected = first+both+1;
      var result = new Decimal(base).layeradd(first, base).layeradd(both, base).slog(base);
      if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result))
      {
          console.log(first + ", " + both);
      }
  }
  
  for (var i = 0; i < 1000; ++i)
  {
      var first = Math.random()*100;
      var both = Math.random()*100;
      var base = Math.random()*8+2;
      first += both;
      var expected = first-both+1;
      var result = new Decimal(base).layeradd(first, base).layeradd(-both, base).slog(base);
      if (Number.isFinite(result.mag) && !Decimal.eq_tolerance(expected, result))
      {
          console.log(first + ", " + both);
      }
  }
  
  for (var i = 0; i < 1000; ++i)
  {
  	var first = Math.round((Math.random()*30))/10;
  	var both = Math.round((Math.random()*30))/10;
  	var tetrateonly = Decimal.tetrate(10, first);
  	var tetrateandlog = Decimal.tetrate(10, first+both).iteratedlog(10, both);
  	if (!Decimal.eq_tolerance(tetrateonly, tetrateandlog))
  	{
  		console.log(first + ", " + both);
  	}
  }
  
  for (var i = 0; i < 1000; ++i)
  {
  	var first = Math.round((Math.random()*30))/10;
  	var both = Math.round((Math.random()*30))/10;
    var base = Math.random()*8+2;
  	var tetrateonly = Decimal.tetrate(base, first);
  	var tetrateandlog = Decimal.tetrate(base, first+both).iteratedlog(base, both);
  	if (!Decimal.eq_tolerance(tetrateonly, tetrateandlog))
  	{
  		console.log(first + ", " + both);
  	}
  }
  
  for (var i = 0; i < 1000; ++i)
  {
  	var first = Math.round((Math.random()*30))/10;
  	var both = Math.round((Math.random()*30))/10;
    var base = Math.random()*8+2;
  	var tetrateonly = Decimal.tetrate(base, first, base);
  	var tetrateandlog = Decimal.tetrate(base, first+both, base).iteratedlog(base, both);
  	if (!Decimal.eq_tolerance(tetrateonly, tetrateandlog))
  	{
  		console.log(first + ", " + both);
  	}
  }
  
  for (var i = 0; i < 1000; ++i)
  {
      var xex = new Decimal(-0.3678794411710499+Math.random()*100);
      var x = Decimal.lambertw(xex);
      if (!Decimal.eq_tolerance(xex, x.mul(Decimal.exp(x))))
      {
          console.log(xex);
      }
  }
  
  for (var i = 0; i < 1000; ++i)
  {
      var xex = new Decimal(-0.3678794411710499+Math.exp(Math.random()*100));
      var x = Decimal.lambertw(xex);
      if (!Decimal.eq_tolerance(xex, x.mul(Decimal.exp(x))))
      {
          console.log(xex);
      }
  }
  
  for (var i = 0; i < 1000; ++i)
  {
      var a = Decimal.randomDecimalForTesting(Math.random() > 0.5 ? 0 : 1);
      var b = Decimal.randomDecimalForTesting(Math.random() > 0.5 ? 0 : 1);
      if (Math.random() > 0.5) { a = a.recip(); }
      if (Math.random() > 0.5) { b = b.recip(); }
      var c = a.add(b).toNumber();
      if (Number.isFinite(c) && !Decimal.eq_tolerance(c, a.toNumber()+b.toNumber()))
      {
          console.log(a + ", " + b);
      }
  }
  
  for (var i = 0; i < 100; ++i)
  {
      var a = Decimal.randomDecimalForTesting(Math.round(Math.random()*4));
      var b = Decimal.randomDecimalForTesting(Math.round(Math.random()*4));
      if (Math.random() > 0.5) { a = a.recip(); }
      if (Math.random() > 0.5) { b = b.recip(); }
      var c = a.mul(b).toNumber();
      if (Number.isFinite(c) && Number.isFinite(a.toNumber()) && Number.isFinite(b.toNumber()) && a.toNumber() != 0 && b.toNumber() != 0 && c != 0 && !Decimal.eq_tolerance(c, a.toNumber()*b.toNumber()))
      {
          console.log("Test 1: " + a + ", " + b);
      }
      else if (!Decimal.mul(a.recip(), b.recip()).eq_tolerance(Decimal.mul(a, b).recip()))
      {
          console.log("Test 3: " + a + ", " + b);
      }
  }
  
  for (var i = 0; i < 10; ++i)
  {
      var a = Decimal.randomDecimalForTesting(Math.round(Math.random()*4));
      var b = Decimal.randomDecimalForTesting(Math.round(Math.random()*4));
      if (Math.random() > 0.5 && a.sign !== 0) { a = a.recip(); }
      if (Math.random() > 0.5 && b.sign !== 0) { b = b.recip(); }
      var c = a.pow(b);
      var d = a.root(b.recip());
      var e = a.pow(b.recip());
      var f = a.root(b);
      
      if (!c.eq_tolerance(d) && a.sign !== 0 && b.sign !== 0)
      {
        console.log("Test 1: " + a + ", " + b);
      }
      if (!e.eq_tolerance(f) && a.sign !== 0 && b.sign !== 0)
      {
        console.log("Test 2: " + a + ", " + b);
      }
  }
  
  for (var i = 0; i < 10; ++i)
  {
      var a = Math.round(Math.random()*18-9);
      var b = Math.round(Math.random()*100-50);
      var c = Math.round(Math.random()*18-9);
      var d = Math.round(Math.random()*100-50);
      console.log("Decimal.pow(Decimal.fromMantissaExponent(" + a + ", " + b + "), Decimal.fromMantissaExponent(" + c + ", " + d + ")).toString()");
  }
  
  */
      
      //Pentation/pentate: The result of tetrating 'height' times in a row. An absurdly strong operator - Decimal.pentate(2, 4.28) and Decimal.pentate(10, 2.37) are already too huge for break_eternity.js!
      // https://en.wikipedia.org/wiki/Pentation
      Decimal.prototype.pentate = function(height = 2, payload = FC_NN(1, 0, 1)) {
        payload = D(payload);
        var oldheight = height;
        height = Math.trunc(height);
        var fracheight = oldheight-height;
        
        //I have no idea if this is a meaningful approximation for pentation to continuous heights, but it is monotonic and continuous.
        if (fracheight !== 0)
        {
          if (payload.eq(Decimal.dOne))
          {
            ++height;
            payload = new Decimal(fracheight);
          }
          else
          {
            if (this.eq(10))
            {
              payload = payload.layeradd10(fracheight);
            }
            else
            {
              payload = payload.layeradd(fracheight, this);
            }
          }
        }
        
        for (var i = 0; i < height; ++i)
        {
          payload = this.tetrate(payload);
          //bail if we're NaN
          if (!isFinite(payload.layer) || !isFinite(payload.mag)) { return payload; }
          //give up after 10 iterations if nothing is happening
          if (i > 10) { return payload; }
        }
        
        return payload;
      }
      
      // trig functions!
      Decimal.prototype.sin = function () {
        if (this.mag < 0) { return this; }
        if (this.layer === 0) { return D(Math.sin(this.sign*this.mag)); }
        return FC_NN(0, 0, 0);
      };
  
      Decimal.prototype.cos = function () {
        if (this.mag < 0) { return Decimal.dOne; }
        if (this.layer === 0) { return D(Math.cos(this.sign*this.mag)); }
        return FC_NN(0, 0, 0);
      };
  
      Decimal.prototype.tan = function () {
        if (this.mag < 0) { return this; }
        if (this.layer === 0) { return D(Math.tan(this.sign*this.mag)); }
        return FC_NN(0, 0, 0);
      };
  
      Decimal.prototype.asin = function () {
        if (this.mag < 0) { return this; }
        if (this.layer === 0) { return D(Math.asin(this.sign*this.mag)); }
        return FC_NN(Number.NaN, Number.NaN, Number.NaN);
      };
  
      Decimal.prototype.acos = function () {
        if (this.mag < 0) { return D(Math.acos(this.toNumber())); }
        if (this.layer === 0) { return D(Math.acos(this.sign*this.mag)); }
        return FC_NN(Number.NaN, Number.NaN, Number.NaN);
      };
  
      Decimal.prototype.atan = function () {
        if (this.mag < 0) { return this; }
        if (this.layer === 0) { return D(Math.atan(this.sign*this.mag)); }
        return D(Math.atan(this.sign*1.8e308));
      };
  
      Decimal.prototype.sinh = function () {
        return this.exp().sub(this.negate().exp()).div(2);
      };
  
      Decimal.prototype.cosh = function () {
        return this.exp().add(this.negate().exp()).div(2);
      };
  
      Decimal.prototype.tanh = function () {
        return this.sinh().div(this.cosh());
      };
  
      Decimal.prototype.asinh = function () {
        return Decimal.ln(this.add(this.sqr().add(1).sqrt()));
      };
  
      Decimal.prototype.acosh = function () {
        return Decimal.ln(this.add(this.sqr().sub(1).sqrt()));
      };
  
      Decimal.prototype.atanh = function () {
        if (this.abs().gte(1)) {
          return FC_NN(Number.NaN, Number.NaN, Number.NaN);
        }
  
        return Decimal.ln(this.add(1).div(D(1).sub(this))).div(2);
      };
      
      /**
       * Joke function from Realm Grinder
       */
      Decimal.prototype.ascensionPenalty = function (ascensions) {
        if (ascensions === 0) {
          return this;
        }
  
        return this.root(Decimal.pow(10, ascensions));
      };
      
      /**
       * Joke function from Cookie Clicker. It's 'egg'
       */
      Decimal.prototype.egg = function () {
        return this.add(9);
      };
      
      Decimal.prototype.lessThanOrEqualTo = function (other) {
        return this.cmp(other) < 1;
      };
  
      Decimal.prototype.lessThan = function (other) {
        return this.cmp(other) < 0;
      };
  
      Decimal.prototype.greaterThanOrEqualTo = function (other) {
        return this.cmp(other) > -1;
      };
  
      Decimal.prototype.greaterThan = function (other) {
        return this.cmp(other) > 0;
      };
  
      return Decimal;
    }();
  
  	Decimal.dZero = FC_NN(0, 0, 0);
  	Decimal.dOne = FC_NN(1, 0, 1);
  	Decimal.dNegOne = FC_NN(-1, 0, 1);
  	Decimal.dTwo = FC_NN(1, 0, 2);
  	Decimal.dTen = FC_NN(1, 0, 10);
  	Decimal.dNaN = FC_NN(Number.NaN, Number.NaN, Number.NaN);
  	Decimal.dInf = FC_NN(1, Number.POSITIVE_INFINITY, Number.POSITIVE_INFINITY);
  	Decimal.dNegInf = FC_NN(-1, Number.NEGATIVE_INFINITY, Number.NEGATIVE_INFINITY);
    Decimal.dNumberMax = FC(1, 0, Number.MAX_VALUE);
    Decimal.dNumberMin = FC(1, 0, Number.MIN_VALUE);
    
    return Decimal;
  
  }));