@radixdlt/radix-engine-toolkit/dist/radix-engine-toolkit.mjs

A TypeScript wrapper for the Radix Engine Toolkit that provides many of the necessary tools to interact with the Radix ledger

var __defProp = Object.defineProperty;
var __defNormalProp = (obj, key2, value) => key2 in obj ? __defProp(obj, key2, { enumerable: true, configurable: true, writable: true, value }) : obj[key2] = value;
var __publicField = (obj, key2, value) => __defNormalProp(obj, typeof key2 !== "symbol" ? key2 + "" : key2, value);
/*!
 *  decimal.js v10.6.0
 *  An arbitrary-precision Decimal type for JavaScript.
 *  https://github.com/MikeMcl/decimal.js
 *  Copyright (c) 2025 Michael Mclaughlin <M8ch88l@gmail.com>
 *  MIT Licence
 */
var _a2, _b, _c, _d2, _e, _f;
var EXP_LIMIT = 9e15, MAX_DIGITS = 1e9, NUMERALS = "0123456789abcdef", LN10 = "2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058", PI = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789", 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
}, inexact, quadrant, external = true, decimalError = "[DecimalError] ", invalidArgument = decimalError + "Invalid argument: ", precisionLimitExceeded = decimalError + "Precision limit exceeded", cryptoUnavailable = decimalError + "crypto unavailable", tag = "[object Decimal]", 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, P$1 = { toStringTag: tag };
P$1.absoluteValue = P$1.abs = function() {
  var x = new this.constructor(this);
  if (x.s < 0) x.s = 1;
  return finalise(x);
};
P$1.ceil = function() {
  return finalise(new this.constructor(this), this.e + 1, 2);
};
P$1.clampedTo = P$1.clamp = function(min2, max2) {
  var k, x = this, Ctor = x.constructor;
  min2 = new Ctor(min2);
  max2 = new Ctor(max2);
  if (!min2.s || !max2.s) return new Ctor(NaN);
  if (min2.gt(max2)) throw Error(invalidArgument + max2);
  k = x.cmp(min2);
  return k < 0 ? min2 : x.cmp(max2) > 0 ? max2 : new Ctor(x);
};
P$1.comparedTo = P$1.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;
  if (!xd || !yd) {
    return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
  }
  if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;
  if (xs !== ys) return xs;
  if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
  xdL = xd.length;
  ydL = yd.length;
  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;
  }
  return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
};
P$1.cosine = P$1.cos = function() {
  var pr, rm, x = this, Ctor = x.constructor;
  if (!x.d) return new Ctor(NaN);
  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);
};
P$1.cubeRoot = P$1.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;
  s = x.s * mathpow(x.s * x, 1 / 3);
  if (!s || Math.abs(s) == 1 / 0) {
    n = digitsToString(x.d);
    e = x.e;
    if (s = (e - n.length + 1) % 3) n += s == 1 || s == -2 ? "0" : "00";
    s = mathpow(n, 1 / 3);
    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;
  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);
    if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
      n = n.slice(sd - 3, sd + 1);
      if (n == "9999" || !rep && n == "4999") {
        if (!rep) {
          finalise(t, e + 1, 0);
          if (t.times(t).times(t).eq(x)) {
            r = t;
            break;
          }
        }
        sd += 4;
        rep = 1;
      } else {
        if (!+n || !+n.slice(1) && n.charAt(0) == "5") {
          finalise(r, e + 1, 1);
          m = !r.times(r).times(r).eq(x);
        }
        break;
      }
    }
  }
  external = true;
  return finalise(r, e, Ctor.rounding, m);
};
P$1.decimalPlaces = P$1.dp = function() {
  var w, d = this.d, n = NaN;
  if (d) {
    w = d.length - 1;
    n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;
    w = d[w];
    if (w) for (; w % 10 == 0; w /= 10) n--;
    if (n < 0) n = 0;
  }
  return n;
};
P$1.dividedBy = P$1.div = function(y) {
  return divide(this, new this.constructor(y));
};
P$1.dividedToIntegerBy = P$1.divToInt = function(y) {
  var x = this, Ctor = x.constructor;
  return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
};
P$1.equals = P$1.eq = function(y) {
  return this.cmp(y) === 0;
};
P$1.floor = function() {
  return finalise(new this.constructor(this), this.e + 1, 3);
};
P$1.greaterThan = P$1.gt = function(y) {
  return this.cmp(y) > 0;
};
P$1.greaterThanOrEqualTo = P$1.gte = function(y) {
  var k = this.cmp(y);
  return k == 1 || k === 0;
};
P$1.hyperbolicCosine = P$1.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;
  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);
  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);
};
P$1.hyperbolicSine = P$1.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 {
    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);
    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);
};
P$1.hyperbolicTangent = P$1.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);
};
P$1.inverseCosine = P$1.acos = function() {
  var x = this, Ctor = x.constructor, k = x.abs().cmp(1), pr = Ctor.precision, rm = Ctor.rounding;
  if (k !== -1) {
    return k === 0 ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) : new Ctor(NaN);
  }
  if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);
  Ctor.precision = pr + 6;
  Ctor.rounding = 1;
  x = new Ctor(1).minus(x).div(x.plus(1)).sqrt().atan();
  Ctor.precision = pr;
  Ctor.rounding = rm;
  return x.times(2);
};
P$1.inverseHyperbolicCosine = P$1.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();
};
P$1.inverseHyperbolicSine = P$1.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();
};
P$1.inverseHyperbolicTangent = P$1.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);
};
P$1.inverseSine = P$1.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) {
    if (k === 0) {
      halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
      halfPi.s = x.s;
      return halfPi;
    }
    return new Ctor(NaN);
  }
  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);
};
P$1.inverseTangent = P$1.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;
  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;
  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);
};
P$1.isFinite = function() {
  return !!this.d;
};
P$1.isInteger = P$1.isInt = function() {
  return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
};
P$1.isNaN = function() {
  return !this.s;
};
P$1.isNegative = P$1.isNeg = function() {
  return this.s < 0;
};
P$1.isPositive = P$1.isPos = function() {
  return this.s > 0;
};
P$1.isZero = function() {
  return !!this.d && this.d[0] === 0;
};
P$1.lessThan = P$1.lt = function(y) {
  return this.cmp(y) < 0;
};
P$1.lessThanOrEqualTo = P$1.lte = function(y) {
  return this.cmp(y) < 1;
};
P$1.logarithm = P$1.log = function(base2) {
  var isBase10, d, denominator, k, inf, num, sd, r, arg = this, Ctor = arg.constructor, pr = Ctor.precision, rm = Ctor.rounding, guard = 5;
  if (base2 == null) {
    base2 = new Ctor(10);
    isBase10 = true;
  } else {
    base2 = new Ctor(base2);
    d = base2.d;
    if (base2.s < 0 || !d || !d[0] || base2.eq(1)) return new Ctor(NaN);
    isBase10 = base2.eq(10);
  }
  d = arg.d;
  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);
  }
  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(base2, sd);
  r = divide(num, denominator, sd, 1);
  if (checkRoundingDigits(r.d, k = pr, rm)) {
    do {
      sd += 10;
      num = naturalLogarithm(arg, sd);
      denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base2, sd);
      r = divide(num, denominator, sd, 1);
      if (!inf) {
        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);
};
P$1.minus = P$1.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 (!x.d || !y.d) {
    if (!x.s || !y.s) y = new Ctor(NaN);
    else if (x.d) y.s = -y.s;
    else y = new Ctor(y.d || x.s !== y.s ? x : NaN);
    return y;
  }
  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 (!xd[0] || !yd[0]) {
    if (yd[0]) y.s = -y.s;
    else if (xd[0]) y = new Ctor(x);
    else return new Ctor(rm === 3 ? -0 : 0);
    return external ? finalise(y, pr, rm) : y;
  }
  e = mathfloor(y.e / LOG_BASE);
  xe = mathfloor(x.e / LOG_BASE);
  xd = xd.slice();
  k = xe - e;
  if (k) {
    xLTy = k < 0;
    if (xLTy) {
      d = xd;
      k = -k;
      len = yd.length;
    } else {
      d = yd;
      e = xe;
      len = xd.length;
    }
    i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
    if (k > i) {
      k = i;
      d.length = 1;
    }
    d.reverse();
    for (i = k; i--; ) d.push(0);
    d.reverse();
  } else {
    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;
  for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
  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];
  }
  for (; xd[--len] === 0; ) xd.pop();
  for (; xd[0] === 0; xd.shift()) --e;
  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;
};
P$1.modulo = P$1.mod = function(y) {
  var q, x = this, Ctor = x.constructor;
  y = new Ctor(y);
  if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);
  if (!y.d || x.d && !x.d[0]) {
    return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);
  }
  external = false;
  if (Ctor.modulo == 9) {
    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);
};
P$1.naturalExponential = P$1.exp = function() {
  return naturalExponential(this);
};
P$1.naturalLogarithm = P$1.ln = function() {
  return naturalLogarithm(this);
};
P$1.negated = P$1.neg = function() {
  var x = new this.constructor(this);
  x.s = -x.s;
  return finalise(x);
};
P$1.plus = P$1.add = function(y) {
  var carry, d, e, i, k, len, pr, rm, xd, yd, x = this, Ctor = x.constructor;
  y = new Ctor(y);
  if (!x.d || !y.d) {
    if (!x.s || !y.s) y = new Ctor(NaN);
    else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);
    return y;
  }
  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 (!xd[0] || !yd[0]) {
    if (!yd[0]) y = new Ctor(x);
    return external ? finalise(y, pr, rm) : y;
  }
  k = mathfloor(x.e / LOG_BASE);
  e = mathfloor(y.e / LOG_BASE);
  xd = xd.slice();
  i = k - e;
  if (i) {
    if (i < 0) {
      d = xd;
      i = -i;
      len = yd.length;
    } else {
      d = yd;
      e = k;
      len = xd.length;
    }
    k = Math.ceil(pr / LOG_BASE);
    len = k > len ? k + 1 : len + 1;
    if (i > len) {
      i = len;
      d.length = 1;
    }
    d.reverse();
    for (; i--; ) d.push(0);
    d.reverse();
  }
  len = xd.length;
  i = yd.length;
  if (len - i < 0) {
    i = len;
    d = yd;
    yd = xd;
    xd = d;
  }
  for (carry = 0; i; ) {
    carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
    xd[i] %= BASE;
  }
  if (carry) {
    xd.unshift(carry);
    ++e;
  }
  for (len = xd.length; xd[--len] == 0; ) xd.pop();
  y.d = xd;
  y.e = getBase10Exponent(xd, e);
  return external ? finalise(y, pr, rm) : y;
};
P$1.precision = P$1.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;
};
P$1.round = function() {
  var x = this, Ctor = x.constructor;
  return finalise(new Ctor(x), x.e + 1, Ctor.rounding);
};
P$1.sine = P$1.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);
};
P$1.squareRoot = P$1.sqrt = function() {
  var m, n, sd, r, rep, t, x = this, d = x.d, e = x.e, s = x.s, Ctor = x.constructor;
  if (s !== 1 || !d || !d[0]) {
    return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);
  }
  external = false;
  s = Math.sqrt(+x);
  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;
  for (; ; ) {
    t = r;
    r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);
    if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
      n = n.slice(sd - 3, sd + 1);
      if (n == "9999" || !rep && n == "4999") {
        if (!rep) {
          finalise(t, e + 1, 0);
          if (t.times(t).eq(x)) {
            r = t;
            break;
          }
        }
        sd += 4;
        rep = 1;
      } else {
        if (!+n || !+n.slice(1) && n.charAt(0) == "5") {
          finalise(r, e + 1, 1);
          m = !r.times(r).eq(x);
        }
        break;
      }
    }
  }
  external = true;
  return finalise(r, e, Ctor.rounding, m);
};
P$1.tangent = P$1.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);
};
P$1.times = P$1.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 (!xd || !xd[0] || !yd || !yd[0]) {
    return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd ? NaN : !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;
  if (xdL < ydL) {
    r = xd;
    xd = yd;
    yd = r;
    rL = xdL;
    xdL = ydL;
    ydL = rL;
  }
  r = [];
  rL = xdL + ydL;
  for (i = rL; i--; ) r.push(0);
  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;
  }
  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;
};
P$1.toBinary = function(sd, rm) {
  return toStringBinary(this, 2, sd, rm);
};
P$1.toDecimalPlaces = P$1.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);
};
P$1.toExponential = function(dp, rm) {
  var str2, x = this, Ctor = x.constructor;
  if (dp === void 0) {
    str2 = 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);
    str2 = finiteToString(x, true, dp + 1);
  }
  return x.isNeg() && !x.isZero() ? "-" + str2 : str2;
};
P$1.toFixed = function(dp, rm) {
  var str2, y, x = this, Ctor = x.constructor;
  if (dp === void 0) {
    str2 = 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);
    str2 = finiteToString(y, false, dp + y.e + 1);
  }
  return x.isNeg() && !x.isZero() ? "-" + str2 : str2;
};
P$1.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) {
    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;
  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;
};
P$1.toHexadecimal = P$1.toHex = function(sd, rm) {
  return toStringBinary(this, 16, sd, rm);
};
P$1.toNearest = function(y, rm) {
  var x = this, Ctor = x.constructor;
  x = new Ctor(x);
  if (y == null) {
    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.d) return y.s ? x : y;
    if (!y.d) {
      if (y.s) y.s = x.s;
      return y;
    }
  }
  if (y.d[0]) {
    external = false;
    x = divide(x, y, 0, rm, 1).times(y);
    external = true;
    finalise(x);
  } else {
    y.s = x.s;
    x = y;
  }
  return x;
};
P$1.toNumber = function() {
  return +this;
};
P$1.toOctal = function(sd, rm) {
  return toStringBinary(this, 8, sd, rm);
};
P$1.toPower = P$1.pow = function(y) {
  var e, k, pr, r, rm, s, x = this, Ctor = x.constructor, yn = +(y = new Ctor(y));
  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);
  e = mathfloor(y.e / LOG_BASE);
  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 (s < 0) {
    if (e < y.d.length - 1) return new Ctor(NaN);
    if ((y.d[e] & 1) == 0) s = 1;
    if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {
      x.s = s;
      return x;
    }
  }
  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;
  if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);
  external = false;
  Ctor.rounding = x.s = 1;
  k = Math.min(12, (e + "").length);
  r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);
  if (r.d) {
    r = finalise(r, pr + 5, 1);
    if (checkRoundingDigits(r.d, pr, rm)) {
      e = pr + 10;
      r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);
      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);
};
P$1.toPrecision = function(sd, rm) {
  var str2, x = this, Ctor = x.constructor;
  if (sd === void 0) {
    str2 = 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);
    str2 = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);
  }
  return x.isNeg() && !x.isZero() ? "-" + str2 : str2;
};
P$1.toSignificantDigits = P$1.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);
};
P$1.toString = function() {
  var x = this, Ctor = x.constructor, str2 = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
  return x.isNeg() && !x.isZero() ? "-" + str2 : str2;
};
P$1.truncated = P$1.trunc = function() {
  return finalise(new this.constructor(this), this.e + 1, 1);
};
P$1.valueOf = P$1.toJSON = function() {
  var x = this, Ctor = x.constructor, str2 = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
  return x.isNeg() ? "-" + str2 : str2;
};
function digitsToString(d) {
  var i, k, ws, indexOfLastWord = d.length - 1, str2 = "", w = d[0];
  if (indexOfLastWord > 0) {
    str2 += w;
    for (i = 1; i < indexOfLastWord; i++) {
      ws = d[i] + "";
      k = LOG_BASE - ws.length;
      if (k) str2 += getZeroString(k);
      str2 += ws;
    }
    w = d[i];
    ws = w + "";
    k = LOG_BASE - ws.length;
    if (k) str2 += getZeroString(k);
  } else if (w === 0) {
    return "0";
  }
  for (; w % 10 === 0; ) w /= 10;
  return str2 + w;
}
function checkInt32(i, min2, max2) {
  if (i !== ~~i || i < min2 || i > max2) {
    throw Error(invalidArgument + i);
  }
}
function checkRoundingDigits(d, i, rm, repeating) {
  var di, k, r, rd;
  for (k = d[0]; k >= 10; k /= 10) --i;
  if (--i < 0) {
    i += LOG_BASE;
    di = 0;
  } else {
    di = Math.ceil((i + 1) / LOG_BASE);
    i %= LOG_BASE;
  }
  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 == 5e4 || 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 / 1e3 | 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 / 1e3 | 0) == mathpow(10, i - 3) - 1;
    }
  }
  return r;
}
function convertBase(str2, baseIn, baseOut) {
  var j, arr = [0], arrL, i = 0, strL = str2.length;
  for (; i < strL; ) {
    for (arrL = arr.length; arrL--; ) arr[arrL] *= baseIn;
    arr[0] += NUMERALS.indexOf(str2.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();
}
function cosine(Ctor, x) {
  var k, len, y;
  if (x.isZero()) return x;
  len = x.d.length;
  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));
  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;
}
var divide = /* @__PURE__ */ (function() {
  function multiplyInteger(x, k, base2) {
    var temp, carry = 0, i = x.length;
    for (x = x.slice(); i--; ) {
      temp = x[i] * k + carry;
      x[i] = temp % base2 | 0;
      carry = temp / base2 | 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, base2) {
    var i = 0;
    for (; aL--; ) {
      a[aL] -= i;
      i = a[aL] < b[aL] ? 1 : 0;
      a[aL] = i * base2 + a[aL] - b[aL];
    }
    for (; !a[0] && a.length > 1; ) a.shift();
  }
  return function(x, y, pr, rm, dp, base2) {
    var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, yL, yz, Ctor = x.constructor, sign2 = x.s == y.s ? 1 : -1, xd = x.d, yd = y.d;
    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 ? sign2 * 0 : sign2 / 0
        )
      );
    }
    if (base2) {
      logBase = 1;
      e = x.e - y.e;
    } else {
      base2 = BASE;
      logBase = LOG_BASE;
      e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);
    }
    yL = yd.length;
    xL = xd.length;
    q = new Ctor(sign2);
    qd = q.d = [];
    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 {
      sd = sd / logBase + 2 | 0;
      i = 0;
      if (yL == 1) {
        k = 0;
        yd = yd[0];
        sd++;
        for (; (i < xL || k) && sd--; i++) {
          t = k * base2 + (xd[i] || 0);
          qd[i] = t / yd | 0;
          k = t % yd | 0;
        }
        more = k || i < xL;
      } else {
        k = base2 / (yd[0] + 1) | 0;
        if (k > 1) {
          yd = multiplyInteger(yd, k, base2);
          xd = multiplyInteger(xd, k, base2);
          yL = yd.length;
          xL = xd.length;
        }
        xi = yL;
        rem = xd.slice(0, yL);
        remL = rem.length;
        for (; remL < yL; ) rem[remL++] = 0;
        yz = yd.slice();
        yz.unshift(0);
        yd0 = yd[0];
        if (yd[1] >= base2 / 2) ++yd0;
        do {
          k = 0;
          cmp = compare(yd, rem, yL, remL);
          if (cmp < 0) {
            rem0 = rem[0];
            if (yL != remL) rem0 = rem0 * base2 + (rem[1] || 0);
            k = rem0 / yd0 | 0;
            if (k > 1) {
              if (k >= base2) k = base2 - 1;
              prod = multiplyInteger(yd, k, base2);
              prodL = prod.length;
              remL = rem.length;
              cmp = compare(prod, rem, prodL, remL);
              if (cmp == 1) {
                k--;
                subtract(prod, yL < prodL ? yz : yd, prodL, base2);
              }
            } else {
              if (k == 0) cmp = k = 1;
              prod = yd.slice();
            }
            prodL = prod.length;
            if (prodL < remL) prod.unshift(0);
            subtract(rem, prod, remL, base2);
            if (cmp == -1) {
              remL = rem.length;
              cmp = compare(yd, rem, yL, remL);
              if (cmp < 1) {
                k++;
                subtract(rem, yL < remL ? yz : yd, remL, base2);
              }
            }
            remL = rem.length;
          } else if (cmp === 0) {
            k++;
            rem = [0];
          }
          qd[i++] = k;
          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;
      }
      if (!qd[0]) qd.shift();
    }
    if (logBase == 1) {
      q.e = e;
      inexact = more;
    } else {
      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;
  };
})();
function finalise(x, sd, rm, isTruncated) {
  var digits, i, j, k, rd, roundUp, w, xd, xdi, Ctor = x.constructor;
  out: if (sd != null) {
    xd = x.d;
    if (!xd) return x;
    for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;
    i = sd - digits;
    if (i < 0) {
      i += LOG_BASE;
      j = sd;
      w = xd[xdi = 0];
      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) {
          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];
        for (digits = 1; k >= 10; k /= 10) digits++;
        i %= LOG_BASE;
        j = i - LOG_BASE + digits;
        rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;
      }
    }
    isTruncated = isTruncated || sd < 0 || xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));
    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) {
        sd -= x.e + 1;
        xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
        x.e = -sd || 0;
      } else {
        xd[0] = x.e = 0;
      }
      return x;
    }
    if (i == 0) {
      xd.length = xdi;
      k = 1;
      xdi--;
    } else {
      xd.length = xdi + 1;
      k = mathpow(10, LOG_BASE - i);
      xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;
    }
    if (roundUp) {
      for (; ; ) {
        if (xdi == 0) {
          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) {
            x.e++;
            if (xd[0] == BASE) xd[0] = 1;
          }
          break;
        } else {
          xd[xdi] += k;
          if (xd[xdi] != BASE) break;
          xd[xdi--] = 0;
          k = 1;
        }
      }
    }
    for (i = xd.length; xd[--i] === 0; ) xd.pop();
  }
  if (external) {
    if (x.e > Ctor.maxE) {
      x.d = null;
      x.e = NaN;
    } else if (x.e < Ctor.minE) {
      x.e = 0;
      x.d = [0];
    }
  }
  return x;
}
function finiteToString(x, isExp, sd) {
  if (!x.isFinite()) return nonFiniteToString(x);
  var k, e = x.e, str2 = digitsToString(x.d), len = str2.length;
  if (isExp) {
    if (sd && (k = sd - len) > 0) {
      str2 = str2.charAt(0) + "." + str2.slice(1) + getZeroString(k);
    } else if (len > 1) {
      str2 = str2.charAt(0) + "." + str2.slice(1);
    }
    str2 = str2 + (x.e < 0 ? "e" : "e+") + x.e;
  } else if (e < 0) {
    str2 = "0." + getZeroString(-e - 1) + str2;
    if (sd && (k = sd - len) > 0) str2 += getZeroString(k);
  } else if (e >= len) {
    str2 += getZeroString(e + 1 - len);
    if (sd && (k = sd - e - 1) > 0) str2 = str2 + "." + getZeroString(k);
  } else {
    if ((k = e + 1) < len) str2 = str2.slice(0, k) + "." + str2.slice(k);
    if (sd && (k = sd - len) > 0) {
      if (e + 1 === len) str2 += ".";
      str2 += getZeroString(k);
    }
  }
  return str2;
}
function getBase10Exponent(digits, e) {
  var w = digits[0];
  for (e *= LOG_BASE; w >= 10; w /= 10) e++;
  return e;
}
function getLn10(Ctor, sd, pr) {
  if (sd > LN10_PRECISION) {
    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 (w) {
    for (; w % 10 == 0; w /= 10) len--;
    for (w = digits[0]; w >= 10; w /= 10) len++;
  }
  return len;
}
function getZeroString(k) {
  var zs = "";
  for (; k--; ) zs += "0";
  return zs;
}
function intPow(Ctor, x, n, pr) {
  var isTruncated, r = new Ctor(1), 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) {
      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;
}
function maxOrMin(Ctor, args, n) {
  var k, y, x = new Ctor(args[0]), i = 0;
  for (; ++i < args.length; ) {
    y = new Ctor(args[i]);
    if (!y.s) {
      x = y;
      break;
    }
    k = x.cmp(y);
    if (k === n || k === 0 && x.s === n) {
      x = y;
    }
  }
  return x;
}
function naturalExponential(x, sd) {
  var denominator, guard, j, pow3, sum2, t, wpr, rep = 0, i = 0, k = 0, Ctor = x.constructor, rm = Ctor.rounding, pr = Ctor.precision;
  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 (x.e > -2) {
    x = x.times(t);
    k += 5;
  }
  guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
  wpr += guard;
  denominator = pow3 = sum2 = new Ctor(1);
  Ctor.precision = wpr;
  for (; ; ) {
    pow3 = finalise(pow3.times(x), wpr, 1);
    denominator = denominator.times(++i);
    t = sum2.plus(divide(pow3, denominator, wpr, 1));
    if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum2.d).slice(0, wpr)) {
      j = k;
      while (j--) sum2 = finalise(sum2.times(sum2), wpr, 1);
      if (sd == null) {
        if (rep < 3 && checkRoundingDigits(sum2.d, wpr - guard, rm, rep)) {
          Ctor.precision = wpr += 10;
          denominator = pow3 = t = new Ctor(1);
          i = 0;
          rep++;
        } else {
          return finalise(sum2, Ctor.precision = pr, rm, external = true);
        }
      } else {
        Ctor.precision = pr;
        return sum2;
      }
    }
    sum2 = t;
  }
}
function naturalLogarithm(y, sd) {
  var c, c0, denominator, e, numerator, rep, sum2, t, wpr, x1, x2, n = 1, guard = 10, x = y, xd = x.d, Ctor = x.constructor, rm = Ctor.rounding, pr = Ctor.precision;
  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) < 15e14) {
    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 {
    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 = x;
  sum2 = 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 = sum2.plus(divide(numerator, new Ctor(denominator), wpr, 1));
    if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum2.d).slice(0, wpr)) {
      sum2 = sum2.times(2);
      if (e !== 0) sum2 = sum2.plus(getLn10(Ctor, wpr + 2, pr).times(e + ""));
      sum2 = divide(sum2, new Ctor(n), wpr, 1);
      if (sd == null) {
        if (checkRoundingDigits(sum2.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(sum2, Ctor.precision = pr, rm, external = true);
        }
      } else {
        Ctor.precision = pr;
        return sum2;
      }
    }
    sum2 = t;
    denominator += 2;
  }
}
function nonFiniteToString(x) {
  return String(x.s * x.s / 0);
}
function parseDecimal(x, str2) {
  var e, i, len;
  if ((e = str2.indexOf(".")) > -1) str2 = str2.replace(".", "");
  if ((i = str2.search(/e/i)) > 0) {
    if (e < 0) e = i;
    e += +str2.slice(i + 1);
    str2 = str2.substring(0, i);
  } else if (e < 0) {
    e = str2.length;
  }
  for (i = 0; str2.charCodeAt(i) === 48; i++) ;
  for (len = str2.length; str2.charCodeAt(len - 1) === 48; --len) ;
  str2 = str2.slice(i, len);
  if (str2) {
    len -= i;
    x.e = e = e - i - 1;
    x.d = [];
    i = (e + 1) % LOG_BASE;
    if (e < 0) i += LOG_BASE;
    if (i < len) {
      if (i) x.d.push(+str2.slice(0, i));
      for (len -= LOG_BASE; i < len; ) x.d.push(+str2.slice(i, i += LOG_BASE));
      str2 = str2.slice(i);
      i = LOG_BASE - str2.length;
    } else {
      i -= len;
    }
    for (; i--; ) str2 += "0";
    x.d.push(+str2);
    if (external) {
      if (x.e > x.constructor.maxE) {
        x.d = null;
        x.e = NaN;
      } else if (x.e < x.constructor.minE) {
        x.e = 0;
        x.d = [0];
      }
    }
  } else {
    x.e = 0;
    x.d = [0];
  }
  return x;
}
function parseOther(x, str2) {
  var base2, Ctor, divisor, i, isFloat, len, p, xd, xe;
  if (str2.indexOf("_") > -1) {
    str2 = str2.replace(/(\d)_(?=\d)/g, "$1");
    if (isDecimal.test(str2)) return parseDecimal(x, str2);
  } else if (str2 === "Infinity" || str2 === "NaN") {
    if (!+str2) x.s = NaN;
    x.e = NaN;
    x.d = null;
    return x;
  }
  if (isHex.test(str2)) {
    base2 = 16;
    str2 = str2.toLowerCase();
  } else if (isBinary.test(str2)) {
    base2 = 2;
  } else if (isOctal.test(str2)) {
    base2 = 8;
  } else {
    throw Error(invalidArgument + str2);
  }
  i = str2.search(/p/i);
  if (i > 0) {
    p = +str2.slice(i + 1);
    str2 = str2.substring(2, i);
  } else {
    str2 = str2.slice(2);
  }
  i = str2.indexOf(".");
  isFloat = i >= 0;
  Ctor = x.constructor;
  if (isFloat) {
    str2 = str2.replace(".", "");
    len = str2.length;
    i = len - i;
    divisor = intPow(Ctor, new Ctor(base2), i, i * 2);
  }
  xd = convertBase(str2, base2, BASE);
  xe = xd.length - 1;
  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;
  if (isFloat) x = divide(x, divisor, len * 4);
  if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));
  external = true;
  return x;
}
function sine(Ctor, x) {
  var k, len = x.d.length;
  if (len < 3) {
    return x.isZero() ? x : taylorSeries(Ctor, 2, x, x);
  }
  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);
  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;
}
function taylorSeries(Ctor, n, x, y, isHyperbolic) {
  var j, t, u, x2, pr = Ctor.precision, k = Math.ceil(pr / LOG_BASE);
  external = false;
  x2 = x.times(