From 86cc799e81935a5750215a4d7d72d0f93a83c55e Mon Sep 17 00:00:00 2001
From: Dominik Z <dominykas.zubavicius@iovlabs.org>
Date: Fri, 31 May 2024 12:15:47 +0300
Subject: [PATCH 1/4] fix: GBI-1764 comments

---
 .../entrypoints/rest/assets/management.html   |   51 +-
 .../entrypoints/rest/assets/static/decimal.js | 2014 +++++++++++++++++
 .../rest/assets/static/questionIcon.svg       |    4 +
 .../entrypoints/rest/handlers/management.go   |    2 +-
 4 files changed, 2057 insertions(+), 14 deletions(-)
 create mode 100644 internal/adapters/entrypoints/rest/assets/static/decimal.js
 create mode 100644 internal/adapters/entrypoints/rest/assets/static/questionIcon.svg
diff --git a/internal/adapters/entrypoints/rest/assets/management.html b/internal/adapters/entrypoints/rest/assets/management.html
index 148d6152..d02a6a02 100644
--- a/internal/adapters/entrypoints/rest/assets/management.html
+++ b/internal/adapters/entrypoints/rest/assets/management.html
@@ -42,6 +42,17 @@
             border-width: 5px; border-style: solid; border-color: #333 transparent transparent transparent;
         }
         .nav{ margin-bottom: 1rem; }
+        .loading-bar {
+            display: none;
+            height: 2px;
+            background-color: #007bff;
+            animation: loading 1s infinite;
+        }
+        @keyframes loading {
+            0% { width: 0%; }
+            50% { width: 50%; }
+            100% { width: 100%; }
+        }
     </style>
 </head>
 <body>
@@ -85,6 +96,7 @@ <h5 class="card-title">Pegin Collateral</h5>
                                 </div>
                                 <div class="collateral-buttons">
                                     <button type="button" class="btn btn-primary" id="addPeginCollateralButton">Add Pegin Collateral</button>
+                                    <div class="loading-bar" id="peginLoadingBar"></div>
                                 </div>
                             </div>
                             <div class="tab-pane fade" id="pegout" role="tabpanel" aria-labelledby="pegout-tab">
@@ -98,6 +110,7 @@ <h5 class="card-title">Pegout Collateral</h5>
                                 </div>
                                 <div class="collateral-buttons">
                                     <button type="button" class="btn btn-primary" id="addPegoutCollateralButton">Add Pegout Collateral</button>
+                                    <div class="loading-bar" id="pegoutLoadingBar"></div>
                                 </div>
                             </div>
                         </div>
@@ -151,16 +164,20 @@ <h5 class="card-title">Current Configuration</h5>
     </div>
 
     <script src="../static/Bootstrap.js" crossorigin="anonymous"></script>
+    <script src="../static/decimal.js" crossorigin="anonymous"></script>
     <script nonce="{{ .ScriptNonce }}">
         document.addEventListener('DOMContentLoaded', () => {
             const data = {{.}};
-            const weiToEther = wei => (wei / 1e18).toString();
+            const weiToEther = wei => new Decimal(wei).dividedBy(new Decimal(1e18)).toString();
             const etherToWei = ether => {
-                const num = parseFloat(ether);
-                if (isNaN(num) || !/^\d+(\.\d+)?$/.test(ether)) {
+                try {
+                    const num = new Decimal(ether);
+                    const weiValue = num.times(new Decimal(1e18)).toFixed(0);
+                    return weiValue;
+                } catch (error) {
+                    console.error(`Error converting ether to wei: ${error.message}`);
                     throw new RangeError(`The input "${ether}" is not a valid number`);
                 }
-                return BigInt(num * 1e18);
             };
 
             let generalChanged = false, peginChanged = false, pegoutChanged = false;
@@ -255,12 +272,13 @@ <h5 class="card-title">Current Configuration</h5>
             const createQuestionIcon = (tooltipText) => {
                 const questionIcon = document.createElement('span');
                 questionIcon.classList.add('question-mark');
-                questionIcon.innerHTML = `
-                    <svg xmlns="http://www.w3.org/2000/svg" width="13" height="13" fill="currentColor" class="bi bi-question-circle" viewBox="0 0 16 16">
-                        <path d="M8 15A7 7 0 1 1 8 1a7 7 0 0 1 0 14m0 1A8 8 0 1 0 8 0a8 8 0 0 0 0 16"/>
-                        <path d="M5.255 5.786a.237.237 0 0 0 .241.247h.825c.138 0 .248-.113.266-.25.09-.656.54-1.134 1.342-1.134.686 0 1.314.343 1.314 1.168 0 .635-.374.927-.965 1.371-.673.489-1.206 1.06-1.168 1.987l.003.217a.25.25 0 0 0 .25.246h.811a.25.25 0 0 0 .25-.25v-.105c0-.718.273-.927 1.01-1.486.609-.463 1.244-.977 1.244-2.056 0-1.511-1.276-2.241-2.673-2.241-1.267 0-2.655.59-2.75 2.286m1.557 5.763c0 .533.425.927 1.01.927.609 0 1.028-.394 1.028-.927 0-.552-.42-.94-1.029-.94-.584 0-1.009.388-1.009.94"/>
-                    </svg>
-                `;
+                const img = document.createElement('img');
+                img.src = '../static/questionIcon.svg';
+                img.width = 13;
+                img.height = 13;
+                img.alt = 'Question Mark';
+                img.classList.add('bi', 'bi-question-circle');
+                questionIcon.appendChild(img);
                 const tooltip = document.createElement('div');
                 tooltip.classList.add('custom-tooltip');
                 tooltip.textContent = tooltipText;
@@ -459,8 +477,12 @@ <h5 class="card-title">Current Configuration</h5>
                 showSuccessToast();
             };
 
-            const addCollateral = async (amountId, endpoint, elementId) => {
+            const addCollateral = async (amountId, endpoint, elementId, loadingBarId, buttonId) => {
                 const amountInEther = document.getElementById(amountId).value;
+                const loadingBar = document.getElementById(loadingBarId);
+                const button = document.getElementById(buttonId);
+                loadingBar.style.display = 'block';
+                button.disabled = true; 
                 try {
                     const amountInWei = Number(etherToWei(amountInEther));
                     const response = await fetch(endpoint, {
@@ -475,11 +497,14 @@ <h5 class="card-title">Current Configuration</h5>
                     }
                 } catch (error) {
                     showErrorToast(`Invalid input "${amountInEther}" for collateral amount. Please enter a valid number.`);
+                } finally {
+                    loadingBar.style.display = 'none';
+                    button.disabled = false;
                 }
             };
 
-            document.getElementById('addPeginCollateralButton').addEventListener('click', () => addCollateral('addPeginCollateralAmount', '/pegin/addCollateral', 'peginCollateral'));
-            document.getElementById('addPegoutCollateralButton').addEventListener('click', () => addCollateral('addPegoutCollateralAmount', '/pegout/addCollateral', 'pegoutCollateral'));
+            document.getElementById('addPeginCollateralButton').addEventListener('click', () => addCollateral('addPeginCollateralAmount', '/pegin/addCollateral', 'peginCollateral', 'peginLoadingBar', 'addPeginCollateralButton'));
+            document.getElementById('addPegoutCollateralButton').addEventListener('click', () => addCollateral('addPegoutCollateralAmount', '/pegout/addCollateral', 'pegoutCollateral', 'pegoutLoadingBar', 'addPegoutCollateralButton'));
             document.getElementById('saveConfig').addEventListener('click', saveConfig);
 
             populateConfigSection('generalConfig', data.Configuration.general);
diff --git a/internal/adapters/entrypoints/rest/assets/static/decimal.js b/internal/adapters/entrypoints/rest/assets/static/decimal.js
new file mode 100644
index 00000000..b2cbe207
--- /dev/null
+++ b/internal/adapters/entrypoints/rest/assets/static/decimal.js
@@ -0,0 +1,2014 @@
+/*! decimal.js-light v2.5.1 https://github.com/MikeMcl/decimal.js-light/LICENCE */
+;(function (globalScope) {
+  'use strict';
+
+
+  /*
+   *  decimal.js-light v2.5.1
+   *  An arbitrary-precision Decimal type for JavaScript.
+   *  https://github.com/MikeMcl/decimal.js-light
+   *  Copyright (c) 2020 Michael Mclaughlin <M8ch88l@gmail.com>
+   *  MIT Expat Licence
+   */
+
+
+  // -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //
+
+
+    // The limit on the value of `precision`, and on the value of the first argument to
+    // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
+  var MAX_DIGITS = 1e9,                        // 0 to 1e9
+
+
+    // The initial configuration properties of the Decimal constructor.
+    Decimal = {
+
+      // These values must be integers within the stated ranges (inclusive).
+      // Most of these values can be changed during run-time using `Decimal.config`.
+
+      // The maximum number of significant digits of the result of a calculation or base conversion.
+      // E.g. `Decimal.config({ precision: 20 });`
+      precision: 20,                         // 1 to MAX_DIGITS
+
+      // The rounding mode used by default by `toInteger`, `toDecimalPlaces`, `toExponential`,
+      // `toFixed`, `toPrecision` and `toSignificantDigits`.
+      //
+      // ROUND_UP         0 Away from zero.
+      // ROUND_DOWN       1 Towards zero.
+      // ROUND_CEIL       2 Towards +Infinity.
+      // ROUND_FLOOR      3 Towards -Infinity.
+      // ROUND_HALF_UP    4 Towards nearest neighbour. If equidistant, up.
+      // ROUND_HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
+      // ROUND_HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
+      // ROUND_HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
+      // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
+      //
+      // E.g.
+      // `Decimal.rounding = 4;`
+      // `Decimal.rounding = Decimal.ROUND_HALF_UP;`
+      rounding: 4,                           // 0 to 8
+
+      // The exponent value at and beneath which `toString` returns exponential notation.
+      // JavaScript numbers: -7
+      toExpNeg: -7,                          // 0 to -MAX_E
+
+      // The exponent value at and above which `toString` returns exponential notation.
+      // JavaScript numbers: 21
+      toExpPos:  21,                         // 0 to MAX_E
+
+      // The natural logarithm of 10.
+      // 115 digits
+      LN10: '2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298341967784042286'
+    },
+
+
+  // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
+
+
+    external = true,
+
+    decimalError = '[DecimalError] ',
+    invalidArgument = decimalError + 'Invalid argument: ',
+    exponentOutOfRange = decimalError + 'Exponent out of range: ',
+
+    mathfloor = Math.floor,
+    mathpow = Math.pow,
+
+    isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
+
+    ONE,
+    BASE = 1e7,
+    LOG_BASE = 7,
+    MAX_SAFE_INTEGER = 9007199254740991,
+    MAX_E = mathfloor(MAX_SAFE_INTEGER / LOG_BASE),    // 1286742750677284
+
+    // Decimal.prototype object
+    P = {};
+
+
+  // Decimal prototype methods
+
+
+  /*
+   *  absoluteValue                       abs
+   *  comparedTo                          cmp
+   *  decimalPlaces                       dp
+   *  dividedBy                           div
+   *  dividedToIntegerBy                  idiv
+   *  equals                              eq
+   *  exponent
+   *  greaterThan                         gt
+   *  greaterThanOrEqualTo                gte
+   *  isInteger                           isint
+   *  isNegative                          isneg
+   *  isPositive                          ispos
+   *  isZero
+   *  lessThan                            lt
+   *  lessThanOrEqualTo                   lte
+   *  logarithm                           log
+   *  minus                               sub
+   *  modulo                              mod
+   *  naturalExponential                  exp
+   *  naturalLogarithm                    ln
+   *  negated                             neg
+   *  plus                                add
+   *  precision                           sd
+   *  squareRoot                          sqrt
+   *  times                               mul
+   *  toDecimalPlaces                     todp
+   *  toExponential
+   *  toFixed
+   *  toInteger                           toint
+   *  toNumber
+   *  toPower                             pow
+   *  toPrecision
+   *  toSignificantDigits                 tosd
+   *  toString
+   *  valueOf                             val
+   */
+
+
+  /*
+   * Return a new Decimal whose value is the absolute value of this Decimal.
+   *
+   */
+  P.absoluteValue = P.abs = function () {
+    var x = new this.constructor(this);
+    if (x.s) x.s = 1;
+    return x;
+  };
+
+
+  /*
+   * Return
+   *   1    if the value of this Decimal is greater than the value of `y`,
+   *  -1    if the value of this Decimal is less than the value of `y`,
+   *   0    if they have the same value
+   *
+   */
+  P.comparedTo = P.cmp = function (y) {
+    var i, j, xdL, ydL,
+      x = this;
+
+    y = new x.constructor(y);
+
+    // Signs differ?
+    if (x.s !== y.s) return x.s || -y.s;
+
+    // Compare exponents.
+    if (x.e !== y.e) return x.e > y.e ^ x.s < 0 ? 1 : -1;
+
+    xdL = x.d.length;
+    ydL = y.d.length;
+
+    // Compare digit by digit.
+    for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
+      if (x.d[i] !== y.d[i]) return x.d[i] > y.d[i] ^ x.s < 0 ? 1 : -1;
+    }
+
+    // Compare lengths.
+    return xdL === ydL ? 0 : xdL > ydL ^ x.s < 0 ? 1 : -1;
+  };
+
+
+  /*
+   * Return the number of decimal places of the value of this Decimal.
+   *
+   */
+  P.decimalPlaces = P.dp = function () {
+    var x = this,
+      w = x.d.length - 1,
+      dp = (w - x.e) * LOG_BASE;
+
+    // Subtract the number of trailing zeros of the last word.
+    w = x.d[w];
+    if (w) for (; w % 10 == 0; w /= 10) dp--;
+
+    return dp < 0 ? 0 : dp;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal divided by `y`, truncated to
+   * `precision` significant digits.
+   *
+   */
+  P.dividedBy = P.div = function (y) {
+    return divide(this, new this.constructor(y));
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the integer part of dividing the value of this Decimal
+   * by the value of `y`, truncated to `precision` significant digits.
+   *
+   */
+  P.dividedToIntegerBy = P.idiv = function (y) {
+    var x = this,
+      Ctor = x.constructor;
+    return round(divide(x, new Ctor(y), 0, 1), Ctor.precision);
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
+   *
+   */
+  P.equals = P.eq = function (y) {
+    return !this.cmp(y);
+  };
+
+
+  /*
+   * Return the (base 10) exponent value of this Decimal (this.e is the base 10000000 exponent).
+   *
+   */
+  P.exponent = function () {
+    return getBase10Exponent(this);
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is greater than the value of `y`, otherwise return
+   * false.
+   *
+   */
+  P.greaterThan = P.gt = function (y) {
+    return this.cmp(y) > 0;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is greater than or equal to the value of `y`,
+   * otherwise return false.
+   *
+   */
+  P.greaterThanOrEqualTo = P.gte = function (y) {
+    return this.cmp(y) >= 0;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is an integer, otherwise return false.
+   *
+   */
+  P.isInteger = P.isint = function () {
+    return this.e > this.d.length - 2;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is negative, otherwise return false.
+   *
+   */
+  P.isNegative = P.isneg = function () {
+    return this.s < 0;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is positive, otherwise return false.
+   *
+   */
+  P.isPositive = P.ispos = function () {
+    return this.s > 0;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is 0, otherwise return false.
+   *
+   */
+  P.isZero = function () {
+    return this.s === 0;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is less than `y`, otherwise return false.
+   *
+   */
+  P.lessThan = P.lt = function (y) {
+    return this.cmp(y) < 0;
+  };
+
+
+  /*
+   * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
+   *
+   */
+  P.lessThanOrEqualTo = P.lte = function (y) {
+    return this.cmp(y) < 1;
+  };
+
+
+  /*
+   * Return the logarithm of the value of this Decimal to the specified base, truncated to
+   * `precision` significant digits.
+   *
+   * If no base is specified, return log[10](x).
+   *
+   * log[base](x) = ln(x) / ln(base)
+   *
+   * The maximum error of the result is 1 ulp (unit in the last place).
+   *
+   * [base] {number|string|Decimal} The base of the logarithm.
+   *
+   */
+  P.logarithm = P.log = function (base) {
+    var r,
+      x = this,
+      Ctor = x.constructor,
+      pr = Ctor.precision,
+      wpr = pr + 5;
+
+    // Default base is 10.
+    if (base === void 0) {
+      base = new Ctor(10);
+    } else {
+      base = new Ctor(base);
+
+      // log[-b](x) = NaN
+      // log[0](x)  = NaN
+      // log[1](x)  = NaN
+      if (base.s < 1 || base.eq(ONE)) throw Error(decimalError + 'NaN');
+    }
+
+    // log[b](-x) = NaN
+    // log[b](0) = -Infinity
+    if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));
+
+    // log[b](1) = 0
+    if (x.eq(ONE)) return new Ctor(0);
+
+    external = false;
+    r = divide(ln(x, wpr), ln(base, wpr), wpr);
+    external = true;
+
+    return round(r, pr);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal minus `y`, truncated to
+   * `precision` significant digits.
+   *
+   */
+  P.minus = P.sub = function (y) {
+    var x = this;
+    y = new x.constructor(y);
+    return x.s == y.s ? subtract(x, y) : add(x, (y.s = -y.s, y));
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal modulo `y`, truncated to
+   * `precision` significant digits.
+   *
+   */
+  P.modulo = P.mod = function (y) {
+    var q,
+      x = this,
+      Ctor = x.constructor,
+      pr = Ctor.precision;
+
+    y = new Ctor(y);
+
+    // x % 0 = NaN
+    if (!y.s) throw Error(decimalError + 'NaN');
+
+    // Return x if x is 0.
+    if (!x.s) return round(new Ctor(x), pr);
+
+    // Prevent rounding of intermediate calculations.
+    external = false;
+    q = divide(x, y, 0, 1).times(y);
+    external = true;
+
+    return x.minus(q);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the natural exponential of the value of this Decimal,
+   * i.e. the base e raised to the power the value of this Decimal, truncated to `precision`
+   * significant digits.
+   *
+   */
+  P.naturalExponential = P.exp = function () {
+    return exp(this);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
+   * truncated to `precision` significant digits.
+   *
+   */
+  P.naturalLogarithm = P.ln = function () {
+    return ln(this);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
+   * -1.
+   *
+   */
+  P.negated = P.neg = function () {
+    var x = new this.constructor(this);
+    x.s = -x.s || 0;
+    return x;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal plus `y`, truncated to
+   * `precision` significant digits.
+   *
+   */
+  P.plus = P.add = function (y) {
+    var x = this;
+    y = new x.constructor(y);
+    return x.s == y.s ? add(x, y) : subtract(x, (y.s = -y.s, y));
+  };
+
+
+  /*
+   * Return the number of significant digits of the value of this Decimal.
+   *
+   * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
+   *
+   */
+  P.precision = P.sd = function (z) {
+    var e, sd, w,
+      x = this;
+
+    if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
+
+    e = getBase10Exponent(x) + 1;
+    w = x.d.length - 1;
+    sd = w * LOG_BASE + 1;
+    w = x.d[w];
+
+    // If non-zero...
+    if (w) {
+
+      // Subtract the number of trailing zeros of the last word.
+      for (; w % 10 == 0; w /= 10) sd--;
+
+      // Add the number of digits of the first word.
+      for (w = x.d[0]; w >= 10; w /= 10) sd++;
+    }
+
+    return z && e > sd ? e : sd;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the square root of this Decimal, truncated to `precision`
+   * significant digits.
+   *
+   */
+  P.squareRoot = P.sqrt = function () {
+    var e, n, pr, r, s, t, wpr,
+      x = this,
+      Ctor = x.constructor;
+
+    // Negative or zero?
+    if (x.s < 1) {
+      if (!x.s) return new Ctor(0);
+
+      // sqrt(-x) = NaN
+      throw Error(decimalError + 'NaN');
+    }
+
+    e = getBase10Exponent(x);
+    external = false;
+
+    // Initial estimate.
+    s = Math.sqrt(+x);
+
+    // Math.sqrt underflow/overflow?
+    // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+    if (s == 0 || s == 1 / 0) {
+      n = digitsToString(x.d);
+      if ((n.length + e) % 2 == 0) n += '0';
+      s = Math.sqrt(n);
+      e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
+
+      if (s == 1 / 0) {
+        n = '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());
+    }
+
+    pr = Ctor.precision;
+    s = wpr = pr + 3;
+
+    // Newton-Raphson iteration.
+    for (;;) {
+      t = r;
+      r = t.plus(divide(x, t, wpr + 2)).times(0.5);
+
+      if (digitsToString(t.d).slice(0, wpr) === (n = digitsToString(r.d)).slice(0, wpr)) {
+        n = n.slice(wpr - 3, wpr + 1);
+
+        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
+        // 4999, i.e. approaching a rounding boundary, continue the iteration.
+        if (s == wpr && n == '4999') {
+
+          // On the first iteration only, check to see if rounding up gives the exact result as the
+          // nines may infinitely repeat.
+          round(t, pr + 1, 0);
+
+          if (t.times(t).eq(x)) {
+            r = t;
+            break;
+          }
+        } else if (n != '9999') {
+          break;
+        }
+
+        wpr += 4;
+      }
+    }
+
+    external = true;
+
+    return round(r, pr);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal times `y`, truncated to
+   * `precision` significant digits.
+   *
+   */
+  P.times = P.mul = function (y) {
+    var carry, e, i, k, r, rL, t, xdL, ydL,
+      x = this,
+      Ctor = x.constructor,
+      xd = x.d,
+      yd = (y = new Ctor(y)).d;
+
+    // Return 0 if either is 0.
+    if (!x.s || !y.s) return new Ctor(0);
+
+    y.s *= x.s;
+    e = x.e + y.e;
+    xdL = xd.length;
+    ydL = yd.length;
+
+    // Ensure xd points to the longer array.
+    if (xdL < ydL) {
+      r = xd;
+      xd = yd;
+      yd = r;
+      rL = xdL;
+      xdL = ydL;
+      ydL = rL;
+    }
+
+    // Initialise the result array with zeros.
+    r = [];
+    rL = xdL + ydL;
+    for (i = rL; i--;) r.push(0);
+
+    // Multiply!
+    for (i = ydL; --i >= 0;) {
+      carry = 0;
+      for (k = xdL + i; k > i;) {
+        t = r[k] + yd[i] * xd[k - i - 1] + carry;
+        r[k--] = t % BASE | 0;
+        carry = t / BASE | 0;
+      }
+
+      r[k] = (r[k] + carry) % BASE | 0;
+    }
+
+    // Remove trailing zeros.
+    for (; !r[--rL];) r.pop();
+
+    if (carry) ++e;
+    else r.shift();
+
+    y.d = r;
+    y.e = e;
+
+    return external ? round(y, Ctor.precision) : y;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
+   * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
+   *
+   * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
+   *
+   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toDecimalPlaces = P.todp = function (dp, rm) {
+    var x = this,
+      Ctor = x.constructor;
+
+    x = new Ctor(x);
+    if (dp === void 0) return x;
+
+    checkInt32(dp, 0, MAX_DIGITS);
+
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+
+    return round(x, dp + getBase10Exponent(x) + 1, rm);
+  };
+
+
+  /*
+   * Return a string representing the value of this Decimal in exponential notation rounded to
+   * `dp` fixed decimal places using rounding mode `rounding`.
+   *
+   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toExponential = function (dp, rm) {
+    var str,
+      x = this,
+      Ctor = x.constructor;
+
+    if (dp === void 0) {
+      str = toString(x, true);
+    } else {
+      checkInt32(dp, 0, MAX_DIGITS);
+
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
+
+      x = round(new Ctor(x), dp + 1, rm);
+      str = toString(x, true, dp + 1);
+    }
+
+    return str;
+  };
+
+
+  /*
+   * Return a string representing the value of this Decimal in normal (fixed-point) notation to
+   * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
+   * omitted.
+   *
+   * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
+   *
+   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
+   * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
+   * (-0).toFixed(3) is '0.000'.
+   * (-0.5).toFixed(0) is '-0'.
+   *
+   */
+  P.toFixed = function (dp, rm) {
+    var str, y,
+      x = this,
+      Ctor = x.constructor;
+
+    if (dp === void 0) return toString(x);
+
+    checkInt32(dp, 0, MAX_DIGITS);
+
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
+
+    y = round(new Ctor(x), dp + getBase10Exponent(x) + 1, rm);
+    str = toString(y.abs(), false, dp + getBase10Exponent(y) + 1);
+
+    // To determine whether to add the minus sign look at the value before it was rounded,
+    // i.e. look at `x` rather than `y`.
+    return x.isneg() && !x.isZero() ? '-' + str : str;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
+   * rounding mode `rounding`.
+   *
+   */
+  P.toInteger = P.toint = function () {
+    var x = this,
+      Ctor = x.constructor;
+    return round(new Ctor(x), getBase10Exponent(x) + 1, Ctor.rounding);
+  };
+
+
+  /*
+   * Return the value of this Decimal converted to a number primitive.
+   *
+   */
+  P.toNumber = function () {
+    return +this;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal raised to the power `y`,
+   * truncated to `precision` significant digits.
+   *
+   * For non-integer or very large exponents pow(x, y) is calculated using
+   *
+   *   x^y = exp(y*ln(x))
+   *
+   * The maximum error is 1 ulp (unit in last place).
+   *
+   * y {number|string|Decimal} The power to which to raise this Decimal.
+   *
+   */
+  P.toPower = P.pow = function (y) {
+    var e, k, pr, r, sign, yIsInt,
+      x = this,
+      Ctor = x.constructor,
+      guard = 12,
+      yn = +(y = new Ctor(y));
+
+    // pow(x, 0) = 1
+    if (!y.s) return new Ctor(ONE);
+
+    x = new Ctor(x);
+
+    // pow(0, y > 0) = 0
+    // pow(0, y < 0) = Infinity
+    if (!x.s) {
+      if (y.s < 1) throw Error(decimalError + 'Infinity');
+      return x;
+    }
+
+    // pow(1, y) = 1
+    if (x.eq(ONE)) return x;
+
+    pr = Ctor.precision;
+
+    // pow(x, 1) = x
+    if (y.eq(ONE)) return round(x, pr);
+
+    e = y.e;
+    k = y.d.length - 1;
+    yIsInt = e >= k;
+    sign = x.s;
+
+    if (!yIsInt) {
+
+      // pow(x < 0, y non-integer) = NaN
+      if (sign < 0) throw Error(decimalError + 'NaN');
+
+    // If y is a small integer use the 'exponentiation by squaring' algorithm.
+    } else if ((k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
+      r = new Ctor(ONE);
+
+      // Max k of 9007199254740991 takes 53 loop iterations.
+      // Maximum digits array length; leaves [28, 34] guard digits.
+      e = Math.ceil(pr / LOG_BASE + 4);
+
+      external = false;
+
+      for (;;) {
+        if (k % 2) {
+          r = r.times(x);
+          truncate(r.d, e);
+        }
+
+        k = mathfloor(k / 2);
+        if (k === 0) break;
+
+        x = x.times(x);
+        truncate(x.d, e);
+      }
+
+      external = true;
+
+      return y.s < 0 ? new Ctor(ONE).div(r) : round(r, pr);
+    }
+
+    // Result is negative if x is negative and the last digit of integer y is odd.
+    sign = sign < 0 && y.d[Math.max(e, k)] & 1 ? -1 : 1;
+
+    x.s = 1;
+    external = false;
+    r = y.times(ln(x, pr + guard));
+    external = true;
+    r = exp(r);
+    r.s = sign;
+
+    return r;
+  };
+
+
+  /*
+   * Return a string representing the value of this Decimal rounded to `sd` significant digits
+   * using rounding mode `rounding`.
+   *
+   * Return exponential notation if `sd` is less than the number of digits necessary to represent
+   * the integer part of the value in normal notation.
+   *
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toPrecision = function (sd, rm) {
+    var e, str,
+      x = this,
+      Ctor = x.constructor;
+
+    if (sd === void 0) {
+      e = getBase10Exponent(x);
+      str = toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
+    } else {
+      checkInt32(sd, 1, MAX_DIGITS);
+
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
+
+      x = round(new Ctor(x), sd, rm);
+      e = getBase10Exponent(x);
+      str = toString(x, sd <= e || e <= Ctor.toExpNeg, sd);
+    }
+
+    return str;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
+   * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
+   * omitted.
+   *
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toSignificantDigits = P.tosd = function (sd, rm) {
+    var x = this,
+      Ctor = x.constructor;
+
+    if (sd === void 0) {
+      sd = Ctor.precision;
+      rm = Ctor.rounding;
+    } else {
+      checkInt32(sd, 1, MAX_DIGITS);
+
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
+    }
+
+    return round(new Ctor(x), sd, rm);
+  };
+
+
+  /*
+   * Return a string representing the value of this Decimal.
+   *
+   * Return exponential notation if this Decimal has a positive exponent equal to or greater than
+   * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
+   *
+   */
+  P.toString = P.valueOf = P.val = P.toJSON = function () {
+    var x = this,
+      e = getBase10Exponent(x),
+      Ctor = x.constructor;
+
+    return toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
+  };
+
+
+  // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
+
+
+  /*
+   *  add                 P.minus, P.plus
+   *  checkInt32          P.todp, P.toExponential, P.toFixed, P.toPrecision, P.tosd
+   *  digitsToString      P.log, P.sqrt, P.pow, toString, exp, ln
+   *  divide              P.div, P.idiv, P.log, P.mod, P.sqrt, exp, ln
+   *  exp                 P.exp, P.pow
+   *  getBase10Exponent   P.exponent, P.sd, P.toint, P.sqrt, P.todp, P.toFixed, P.toPrecision,
+   *                      P.toString, divide, round, toString, exp, ln
+   *  getLn10             P.log, ln
+   *  getZeroString       digitsToString, toString
+   *  ln                  P.log, P.ln, P.pow, exp
+   *  parseDecimal        Decimal
+   *  round               P.abs, P.idiv, P.log, P.minus, P.mod, P.neg, P.plus, P.toint, P.sqrt,
+   *                      P.times, P.todp, P.toExponential, P.toFixed, P.pow, P.toPrecision, P.tosd,
+   *                      divide, getLn10, exp, ln
+   *  subtract            P.minus, P.plus
+   *  toString            P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf
+   *  truncate            P.pow
+   *
+   *  Throws:             P.log, P.mod, P.sd, P.sqrt, P.pow,  checkInt32, divide, round,
+   *                      getLn10, exp, ln, parseDecimal, Decimal, config
+   */
+
+
+  function add(x, y) {
+    var carry, d, e, i, k, len, xd, yd,
+      Ctor = x.constructor,
+      pr = Ctor.precision;
+
+    // If either is zero...
+    if (!x.s || !y.s) {
+
+      // Return x if y is zero.
+      // Return y if y is non-zero.
+      if (!y.s) y = new Ctor(x);
+      return external ? round(y, pr) : y;
+    }
+
+    xd = x.d;
+    yd = y.d;
+
+    // x and y are finite, non-zero numbers with the same sign.
+
+    k = x.e;
+    e = y.e;
+    xd = xd.slice();
+    i = k - e;
+
+    // If base 1e7 exponents differ...
+    if (i) {
+      if (i < 0) {
+        d = xd;
+        i = -i;
+        len = yd.length;
+      } else {
+        d = yd;
+        e = k;
+        len = xd.length;
+      }
+
+      // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
+      k = Math.ceil(pr / LOG_BASE);
+      len = k > len ? k + 1 : len + 1;
+
+      if (i > len) {
+        i = len;
+        d.length = 1;
+      }
+
+      // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
+      d.reverse();
+      for (; i--;) d.push(0);
+      d.reverse();
+    }
+
+    len = xd.length;
+    i = yd.length;
+
+    // If yd is longer than xd, swap xd and yd so xd points to the longer array.
+    if (len - i < 0) {
+      i = len;
+      d = yd;
+      yd = xd;
+      xd = d;
+    }
+
+    // Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
+    for (carry = 0; i;) {
+      carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
+      xd[i] %= BASE;
+    }
+
+    if (carry) {
+      xd.unshift(carry);
+      ++e;
+    }
+
+    // Remove trailing zeros.
+    // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+    for (len = xd.length; xd[--len] == 0;) xd.pop();
+
+    y.d = xd;
+    y.e = e;
+
+    return external ? round(y, pr) : y;
+  }
+
+
+  function checkInt32(i, min, max) {
+    if (i !== ~~i || i < min || i > max) {
+      throw Error(invalidArgument + i);
+    }
+  }
+
+
+  function digitsToString(d) {
+    var i, k, ws,
+      indexOfLastWord = d.length - 1,
+      str = '',
+      w = d[0];
+
+    if (indexOfLastWord > 0) {
+      str += w;
+      for (i = 1; i < indexOfLastWord; i++) {
+        ws = d[i] + '';
+        k = LOG_BASE - ws.length;
+        if (k) str += getZeroString(k);
+        str += ws;
+      }
+
+      w = d[i];
+      ws = w + '';
+      k = LOG_BASE - ws.length;
+      if (k) str += getZeroString(k);
+    } else if (w === 0) {
+      return '0';
+    }
+
+    // Remove trailing zeros of last w.
+    for (; w % 10 === 0;) w /= 10;
+
+    return str + w;
+  }
+
+
+  var divide = (function () {
+
+    // Assumes non-zero x and k, and hence non-zero result.
+    function multiplyInteger(x, k) {
+      var temp,
+        carry = 0,
+        i = x.length;
+
+      for (x = x.slice(); i--;) {
+        temp = x[i] * k + carry;
+        x[i] = temp % BASE | 0;
+        carry = temp / BASE | 0;
+      }
+
+      if (carry) x.unshift(carry);
+
+      return x;
+    }
+
+    function compare(a, b, aL, bL) {
+      var i, r;
+
+      if (aL != bL) {
+        r = aL > bL ? 1 : -1;
+      } else {
+        for (i = r = 0; i < aL; i++) {
+          if (a[i] != b[i]) {
+            r = a[i] > b[i] ? 1 : -1;
+            break;
+          }
+        }
+      }
+
+      return r;
+    }
+
+    function subtract(a, b, aL) {
+      var i = 0;
+
+      // Subtract b from a.
+      for (; aL--;) {
+        a[aL] -= i;
+        i = a[aL] < b[aL] ? 1 : 0;
+        a[aL] = i * BASE + a[aL] - b[aL];
+      }
+
+      // Remove leading zeros.
+      for (; !a[0] && a.length > 1;) a.shift();
+    }
+
+    return function (x, y, pr, dp) {
+      var cmp, e, i, k, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, yL, yz,
+        Ctor = x.constructor,
+        sign = x.s == y.s ? 1 : -1,
+        xd = x.d,
+        yd = y.d;
+
+      // Either 0?
+      if (!x.s) return new Ctor(x);
+      if (!y.s) throw Error(decimalError + 'Division by zero');
+
+      e = x.e - y.e;
+      yL = yd.length;
+      xL = xd.length;
+      q = new Ctor(sign);
+      qd = q.d = [];
+
+      // Result exponent may be one less than e.
+      for (i = 0; yd[i] == (xd[i] || 0); ) ++i;
+      if (yd[i] > (xd[i] || 0)) --e;
+
+      if (pr == null) {
+        sd = pr = Ctor.precision;
+      } else if (dp) {
+        sd = pr + (getBase10Exponent(x) - getBase10Exponent(y)) + 1;
+      } else {
+        sd = pr;
+      }
+
+      if (sd < 0) return new Ctor(0);
+
+      // Convert precision in number of base 10 digits to base 1e7 digits.
+      sd = sd / LOG_BASE + 2 | 0;
+      i = 0;
+
+      // divisor < 1e7
+      if (yL == 1) {
+        k = 0;
+        yd = yd[0];
+        sd++;
+
+        // k is the carry.
+        for (; (i < xL || k) && sd--; i++) {
+          t = k * BASE + (xd[i] || 0);
+          qd[i] = t / yd | 0;
+          k = t % yd | 0;
+        }
+
+      // divisor >= 1e7
+      } else {
+
+        // Normalise xd and yd so highest order digit of yd is >= BASE/2
+        k = BASE / (yd[0] + 1) | 0;
+
+        if (k > 1) {
+          yd = multiplyInteger(yd, k);
+          xd = multiplyInteger(xd, k);
+          yL = yd.length;
+          xL = xd.length;
+        }
+
+        xi = yL;
+        rem = xd.slice(0, yL);
+        remL = rem.length;
+
+        // Add zeros to make remainder as long as divisor.
+        for (; remL < yL;) rem[remL++] = 0;
+
+        yz = yd.slice();
+        yz.unshift(0);
+        yd0 = yd[0];
+
+        if (yd[1] >= BASE / 2) ++yd0;
+
+        do {
+          k = 0;
+
+          // Compare divisor and remainder.
+          cmp = compare(yd, rem, yL, remL);
+
+          // If divisor < remainder.
+          if (cmp < 0) {
+
+            // Calculate trial digit, k.
+            rem0 = rem[0];
+            if (yL != remL) rem0 = rem0 * BASE + (rem[1] || 0);
+
+            // k will be how many times the divisor goes into the current remainder.
+            k = rem0 / yd0 | 0;
+
+            //  Algorithm:
+            //  1. product = divisor * trial digit (k)
+            //  2. if product > remainder: product -= divisor, k--
+            //  3. remainder -= product
+            //  4. if product was < remainder at 2:
+            //    5. compare new remainder and divisor
+            //    6. If remainder > divisor: remainder -= divisor, k++
+
+            if (k > 1) {
+              if (k >= BASE) k = BASE - 1;
+
+              // product = divisor * trial digit.
+              prod = multiplyInteger(yd, k);
+              prodL = prod.length;
+              remL = rem.length;
+
+              // Compare product and remainder.
+              cmp = compare(prod, rem, prodL, remL);
+
+              // product > remainder.
+              if (cmp == 1) {
+                k--;
+
+                // Subtract divisor from product.
+                subtract(prod, yL < prodL ? yz : yd, prodL);
+              }
+            } else {
+
+              // cmp is -1.
+              // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
+              // to avoid it. If k is 1 there is a need to compare yd and rem again below.
+              if (k == 0) cmp = k = 1;
+              prod = yd.slice();
+            }
+
+            prodL = prod.length;
+            if (prodL < remL) prod.unshift(0);
+
+            // Subtract product from remainder.
+            subtract(rem, prod, remL);
+
+            // If product was < previous remainder.
+            if (cmp == -1) {
+              remL = rem.length;
+
+              // Compare divisor and new remainder.
+              cmp = compare(yd, rem, yL, remL);
+
+              // If divisor < new remainder, subtract divisor from remainder.
+              if (cmp < 1) {
+                k++;
+
+                // Subtract divisor from remainder.
+                subtract(rem, yL < remL ? yz : yd, remL);
+              }
+            }
+
+            remL = rem.length;
+          } else if (cmp === 0) {
+            k++;
+            rem = [0];
+          }    // if cmp === 1, k will be 0
+
+          // Add the next digit, k, to the result array.
+          qd[i++] = k;
+
+          // Update the remainder.
+          if (cmp && rem[0]) {
+            rem[remL++] = xd[xi] || 0;
+          } else {
+            rem = [xd[xi]];
+            remL = 1;
+          }
+
+        } while ((xi++ < xL || rem[0] !== void 0) && sd--);
+      }
+
+      // Leading zero?
+      if (!qd[0]) qd.shift();
+
+      q.e = e;
+
+      return round(q, dp ? pr + getBase10Exponent(q) + 1 : pr);
+    };
+  })();
+
+
+  /*
+   * Return a new Decimal whose value is the natural exponential of `x` truncated to `sd`
+   * significant digits.
+   *
+   * Taylor/Maclaurin series.
+   *
+   * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
+   *
+   * Argument reduction:
+   *   Repeat x = x / 32, k += 5, until |x| < 0.1
+   *   exp(x) = exp(x / 2^k)^(2^k)
+   *
+   * Previously, the argument was initially reduced by
+   * exp(x) = exp(r) * 10^k  where r = x - k * ln10, k = floor(x / ln10)
+   * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
+   * found to be slower than just dividing repeatedly by 32 as above.
+   *
+   * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
+   *
+   *  exp(x) is non-terminating for any finite, non-zero x.
+   *
+   */
+  function exp(x, sd) {
+    var denominator, guard, pow, sum, t, wpr,
+      i = 0,
+      k = 0,
+      Ctor = x.constructor,
+      pr = Ctor.precision;
+
+    if (getBase10Exponent(x) > 16) throw Error(exponentOutOfRange + getBase10Exponent(x));
+
+    // exp(0) = 1
+    if (!x.s) return new Ctor(ONE);
+
+    if (sd == null) {
+      external = false;
+      wpr = pr;
+    } else {
+      wpr = sd;
+    }
+
+    t = new Ctor(0.03125);
+
+    while (x.abs().gte(0.1)) {
+      x = x.times(t);    // x = x / 2^5
+      k += 5;
+    }
+
+    // Estimate the precision increase necessary to ensure the first 4 rounding digits are correct.
+    guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
+    wpr += guard;
+    denominator = pow = sum = new Ctor(ONE);
+    Ctor.precision = wpr;
+
+    for (;;) {
+      pow = round(pow.times(x), wpr);
+      denominator = denominator.times(++i);
+      t = sum.plus(divide(pow, denominator, wpr));
+
+      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
+        while (k--) sum = round(sum.times(sum), wpr);
+        Ctor.precision = pr;
+        return sd == null ? (external = true, round(sum, pr)) : sum;
+      }
+
+      sum = t;
+    }
+  }
+
+
+  // Calculate the base 10 exponent from the base 1e7 exponent.
+  function getBase10Exponent(x) {
+    var e = x.e * LOG_BASE,
+      w = x.d[0];
+
+    // Add the number of digits of the first word of the digits array.
+    for (; w >= 10; w /= 10) e++;
+    return e;
+  }
+
+
+  function getLn10(Ctor, sd, pr) {
+
+    if (sd > Ctor.LN10.sd()) {
+
+
+      // Reset global state in case the exception is caught.
+      external = true;
+      if (pr) Ctor.precision = pr;
+      throw Error(decimalError + 'LN10 precision limit exceeded');
+    }
+
+    return round(new Ctor(Ctor.LN10), sd);
+  }
+
+
+  function getZeroString(k) {
+    var zs = '';
+    for (; k--;) zs += '0';
+    return zs;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the natural logarithm of `x` truncated to `sd` significant
+   * digits.
+   *
+   *  ln(n) is non-terminating (n != 1)
+   *
+   */
+  function ln(y, sd) {
+    var c, c0, denominator, e, numerator, sum, t, wpr, x2,
+      n = 1,
+      guard = 10,
+      x = y,
+      xd = x.d,
+      Ctor = x.constructor,
+      pr = Ctor.precision;
+
+    // ln(-x) = NaN
+    // ln(0) = -Infinity
+    if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));
+
+    // ln(1) = 0
+    if (x.eq(ONE)) return new Ctor(0);
+
+    if (sd == null) {
+      external = false;
+      wpr = pr;
+    } else {
+      wpr = sd;
+    }
+
+    if (x.eq(10)) {
+      if (sd == null) external = true;
+      return getLn10(Ctor, wpr);
+    }
+
+    wpr += guard;
+    Ctor.precision = wpr;
+    c = digitsToString(xd);
+    c0 = c.charAt(0);
+    e = getBase10Exponent(x);
+
+    if (Math.abs(e) < 1.5e15) {
+
+      // Argument reduction.
+      // The series converges faster the closer the argument is to 1, so using
+      // ln(a^b) = b * ln(a),   ln(a) = ln(a^b) / b
+      // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
+      // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
+      // later be divided by this number, then separate out the power of 10 using
+      // ln(a*10^b) = ln(a) + b*ln(10).
+
+      // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
+      //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
+      // max n is 6 (gives 0.7 - 1.3)
+      while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
+        x = x.times(y);
+        c = digitsToString(x.d);
+        c0 = c.charAt(0);
+        n++;
+      }
+
+      e = getBase10Exponent(x);
+
+      if (c0 > 1) {
+        x = new Ctor('0.' + c);
+        e++;
+      } else {
+        x = new Ctor(c0 + '.' + c.slice(1));
+      }
+    } else {
+
+      // The argument reduction method above may result in overflow if the argument y is a massive
+      // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
+      // function using ln(x*10^e) = ln(x) + e*ln(10).
+      t = getLn10(Ctor, wpr + 2, pr).times(e + '');
+      x = ln(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
+
+      Ctor.precision = pr;
+      return sd == null ? (external = true, round(x, pr)) : x;
+    }
+
+    // x is reduced to a value near 1.
+
+    // Taylor series.
+    // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
+    // where x = (y - 1)/(y + 1)    (|x| < 1)
+    sum = numerator = x = divide(x.minus(ONE), x.plus(ONE), wpr);
+    x2 = round(x.times(x), wpr);
+    denominator = 3;
+
+    for (;;) {
+      numerator = round(numerator.times(x2), wpr);
+      t = sum.plus(divide(numerator, new Ctor(denominator), wpr));
+
+      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
+        sum = sum.times(2);
+
+        // Reverse the argument reduction.
+        if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
+        sum = divide(sum, new Ctor(n), wpr);
+
+        Ctor.precision = pr;
+        return sd == null ? (external = true, round(sum, pr)) : sum;
+      }
+
+      sum = t;
+      denominator += 2;
+    }
+  }
+
+
+  /*
+   * Parse the value of a new Decimal `x` from string `str`.
+   */
+  function parseDecimal(x, str) {
+    var e, i, len;
+
+    // Decimal point?
+    if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+
+    // Exponential form?
+    if ((i = str.search(/e/i)) > 0) {
+
+      // Determine exponent.
+      if (e < 0) e = i;
+      e += +str.slice(i + 1);
+      str = str.substring(0, i);
+    } else if (e < 0) {
+
+      // Integer.
+      e = str.length;
+    }
+
+    // Determine leading zeros.
+    for (i = 0; str.charCodeAt(i) === 48;) ++i;
+
+    // Determine trailing zeros.
+    for (len = str.length; str.charCodeAt(len - 1) === 48;) --len;
+    str = str.slice(i, len);
+
+    if (str) {
+      len -= i;
+      e = e - i - 1;
+      x.e = mathfloor(e / LOG_BASE);
+      x.d = [];
+
+      // Transform base
+
+      // e is the base 10 exponent.
+      // i is where to slice str to get the first word of the digits array.
+      i = (e + 1) % LOG_BASE;
+      if (e < 0) i += LOG_BASE;
+
+      if (i < len) {
+        if (i) x.d.push(+str.slice(0, i));
+        for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
+        str = str.slice(i);
+        i = LOG_BASE - str.length;
+      } else {
+        i -= len;
+      }
+
+      for (; i--;) str += '0';
+      x.d.push(+str);
+
+      if (external && (x.e > MAX_E || x.e < -MAX_E)) throw Error(exponentOutOfRange + e);
+    } else {
+
+      // Zero.
+      x.s = 0;
+      x.e = 0;
+      x.d = [0];
+    }
+
+    return x;
+  }
+
+
+  /*
+   * Round `x` to `sd` significant digits, using rounding mode `rm` if present (truncate otherwise).
+   */
+   function round(x, sd, rm) {
+    var i, j, k, n, rd, doRound, w, xdi,
+      xd = x.d;
+
+    // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
+    // w: the word of xd which contains the rounding digit, a base 1e7 number.
+    // xdi: the index of w within xd.
+    // n: the number of digits of w.
+    // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
+    // they had leading zeros)
+    // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
+
+    // Get the length of the first word of the digits array xd.
+    for (n = 1, k = xd[0]; k >= 10; k /= 10) n++;
+    i = sd - n;
+
+    // Is the rounding digit in the first word of xd?
+    if (i < 0) {
+      i += LOG_BASE;
+      j = sd;
+      w = xd[xdi = 0];
+    } else {
+      xdi = Math.ceil((i + 1) / LOG_BASE);
+      k = xd.length;
+      if (xdi >= k) return x;
+      w = k = xd[xdi];
+
+      // Get the number of digits of w.
+      for (n = 1; k >= 10; k /= 10) n++;
+
+      // Get the index of rd within w.
+      i %= LOG_BASE;
+
+      // Get the index of rd within w, adjusted for leading zeros.
+      // The number of leading zeros of w is given by LOG_BASE - n.
+      j = i - LOG_BASE + n;
+    }
+
+    if (rm !== void 0) {
+      k = mathpow(10, n - j - 1);
+
+      // Get the rounding digit at index j of w.
+      rd = w / k % 10 | 0;
+
+      // Are there any non-zero digits after the rounding digit?
+      doRound = sd < 0 || xd[xdi + 1] !== void 0 || w % k;
+
+      // The expression `w % mathpow(10, n - j - 1)` returns all the digits of w to the right of the
+      // digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression will give
+      // 714.
+
+      doRound = rm < 4
+        ? (rd || doRound) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+        : rd > 5 || rd == 5 && (rm == 4 || doRound || rm == 6 &&
+
+          // Check whether the digit to the left of the rounding digit is odd.
+          ((i > 0 ? j > 0 ? w / mathpow(10, n - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
+            rm == (x.s < 0 ? 8 : 7));
+    }
+
+    if (sd < 1 || !xd[0]) {
+      if (doRound) {
+        k = getBase10Exponent(x);
+        xd.length = 1;
+
+        // Convert sd to decimal places.
+        sd = sd - k - 1;
+
+        // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+        xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
+        x.e = mathfloor(-sd / LOG_BASE) || 0;
+      } else {
+        xd.length = 1;
+
+        // Zero.
+        xd[0] = x.e = x.s = 0;
+      }
+
+      return x;
+    }
+
+    // Remove excess digits.
+    if (i == 0) {
+      xd.length = xdi;
+      k = 1;
+      xdi--;
+    } else {
+      xd.length = xdi + 1;
+      k = mathpow(10, LOG_BASE - i);
+
+      // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+      // j > 0 means i > number of leading zeros of w.
+      xd[xdi] = j > 0 ? (w / mathpow(10, n - j) % mathpow(10, j) | 0) * k : 0;
+    }
+
+    if (doRound) {
+      for (;;) {
+
+        // Is the digit to be rounded up in the first word of xd?
+        if (xdi == 0) {
+          if ((xd[0] += k) == BASE) {
+            xd[0] = 1;
+            ++x.e;
+          }
+
+          break;
+        } else {
+          xd[xdi] += k;
+          if (xd[xdi] != BASE) break;
+          xd[xdi--] = 0;
+          k = 1;
+        }
+      }
+    }
+
+    // Remove trailing zeros.
+    for (i = xd.length; xd[--i] === 0;) xd.pop();
+
+    if (external && (x.e > MAX_E || x.e < -MAX_E)) {
+      throw Error(exponentOutOfRange + getBase10Exponent(x));
+    }
+
+    return x;
+  }
+
+
+  function subtract(x, y) {
+    var d, e, i, j, k, len, xd, xe, xLTy, yd,
+      Ctor = x.constructor,
+      pr = Ctor.precision;
+
+    // Return y negated if x is zero.
+    // Return x if y is zero and x is non-zero.
+    if (!x.s || !y.s) {
+      if (y.s) y.s = -y.s;
+      else y = new Ctor(x);
+      return external ? round(y, pr) : y;
+    }
+
+    xd = x.d;
+    yd = y.d;
+
+    // x and y are non-zero numbers with the same sign.
+
+    e = y.e;
+    xe = x.e;
+    xd = xd.slice();
+    k = xe - e;
+
+    // If exponents differ...
+    if (k) {
+      xLTy = k < 0;
+
+      if (xLTy) {
+        d = xd;
+        k = -k;
+        len = yd.length;
+      } else {
+        d = yd;
+        e = xe;
+        len = xd.length;
+      }
+
+      // Numbers with massively different exponents would result in a very high number of zeros
+      // needing to be prepended, but this can be avoided while still ensuring correct rounding by
+      // limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
+      i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
+
+      if (k > i) {
+        k = i;
+        d.length = 1;
+      }
+
+      // Prepend zeros to equalise exponents.
+      d.reverse();
+      for (i = k; i--;) d.push(0);
+      d.reverse();
+
+    // Base 1e7 exponents equal.
+    } else {
+
+      // Check digits to determine which is the bigger number.
+
+      i = xd.length;
+      len = yd.length;
+      xLTy = i < len;
+      if (xLTy) len = i;
+
+      for (i = 0; i < len; i++) {
+        if (xd[i] != yd[i]) {
+          xLTy = xd[i] < yd[i];
+          break;
+        }
+      }
+
+      k = 0;
+    }
+
+    if (xLTy) {
+      d = xd;
+      xd = yd;
+      yd = d;
+      y.s = -y.s;
+    }
+
+    len = xd.length;
+
+    // Append zeros to xd if shorter.
+    // Don't add zeros to yd if shorter as subtraction only needs to start at yd length.
+    for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
+
+    // Subtract yd from xd.
+    for (i = yd.length; i > k;) {
+      if (xd[--i] < yd[i]) {
+        for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
+        --xd[j];
+        xd[i] += BASE;
+      }
+
+      xd[i] -= yd[i];
+    }
+
+    // Remove trailing zeros.
+    for (; xd[--len] === 0;) xd.pop();
+
+    // Remove leading zeros and adjust exponent accordingly.
+    for (; xd[0] === 0; xd.shift()) --e;
+
+    // Zero?
+    if (!xd[0]) return new Ctor(0);
+
+    y.d = xd;
+    y.e = e;
+
+    //return external && xd.length >= pr / LOG_BASE ? round(y, pr) : y;
+    return external ? round(y, pr) : y;
+  }
+
+
+  function toString(x, isExp, sd) {
+    var k,
+      e = getBase10Exponent(x),
+      str = digitsToString(x.d),
+      len = str.length;
+
+    if (isExp) {
+      if (sd && (k = sd - len) > 0) {
+        str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
+      } else if (len > 1) {
+        str = str.charAt(0) + '.' + str.slice(1);
+      }
+
+      str = str + (e < 0 ? 'e' : 'e+') + e;
+    } else if (e < 0) {
+      str = '0.' + getZeroString(-e - 1) + str;
+      if (sd && (k = sd - len) > 0) str += getZeroString(k);
+    } else if (e >= len) {
+      str += getZeroString(e + 1 - len);
+      if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
+    } else {
+      if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
+      if (sd && (k = sd - len) > 0) {
+        if (e + 1 === len) str += '.';
+        str += getZeroString(k);
+      }
+    }
+
+    return x.s < 0 ? '-' + str : str;
+  }
+
+
+  // Does not strip trailing zeros.
+  function truncate(arr, len) {
+    if (arr.length > len) {
+      arr.length = len;
+      return true;
+    }
+  }
+
+
+  // Decimal methods
+
+
+  /*
+   *  clone
+   *  config/set
+   */
+
+
+  /*
+   * Create and return a Decimal constructor with the same configuration properties as this Decimal
+   * constructor.
+   *
+   */
+  function clone(obj) {
+    var i, p, ps;
+
+    /*
+     * The Decimal constructor and exported function.
+     * Return a new Decimal instance.
+     *
+     * value {number|string|Decimal} A numeric value.
+     *
+     */
+    function Decimal(value) {
+      var x = this;
+
+      // Decimal called without new.
+      if (!(x instanceof Decimal)) return new Decimal(value);
+
+      // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
+      // which points to Object.
+      x.constructor = Decimal;
+
+      // Duplicate.
+      if (value instanceof Decimal) {
+        x.s = value.s;
+        x.e = value.e;
+        x.d = (value = value.d) ? value.slice() : value;
+        return;
+      }
+
+      if (typeof value === 'number') {
+
+        // Reject Infinity/NaN.
+        if (value * 0 !== 0) {
+          throw Error(invalidArgument + value);
+        }
+
+        if (value > 0) {
+          x.s = 1;
+        } else if (value < 0) {
+          value = -value;
+          x.s = -1;
+        } else {
+          x.s = 0;
+          x.e = 0;
+          x.d = [0];
+          return;
+        }
+
+        // Fast path for small integers.
+        if (value === ~~value && value < 1e7) {
+          x.e = 0;
+          x.d = [value];
+          return;
+        }
+
+        return parseDecimal(x, value.toString());
+      } else if (typeof value !== 'string') {
+        throw Error(invalidArgument + value);
+      }
+
+      // Minus sign?
+      if (value.charCodeAt(0) === 45) {
+        value = value.slice(1);
+        x.s = -1;
+      } else {
+        x.s = 1;
+      }
+
+      if (isDecimal.test(value)) parseDecimal(x, value);
+      else throw Error(invalidArgument + value);
+    }
+
+    Decimal.prototype = P;
+
+    Decimal.ROUND_UP = 0;
+    Decimal.ROUND_DOWN = 1;
+    Decimal.ROUND_CEIL = 2;
+    Decimal.ROUND_FLOOR = 3;
+    Decimal.ROUND_HALF_UP = 4;
+    Decimal.ROUND_HALF_DOWN = 5;
+    Decimal.ROUND_HALF_EVEN = 6;
+    Decimal.ROUND_HALF_CEIL = 7;
+    Decimal.ROUND_HALF_FLOOR = 8;
+
+    Decimal.clone = clone;
+    Decimal.config = Decimal.set = config;
+
+    if (obj === void 0) obj = {};
+    if (obj) {
+      ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'LN10'];
+      for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
+    }
+
+    Decimal.config(obj);
+
+    return Decimal;
+  }
+
+
+  /*
+   * Configure global settings for a Decimal constructor.
+   *
+   * `obj` is an object with one or more of the following properties,
+   *
+   *   precision  {number}
+   *   rounding   {number}
+   *   toExpNeg   {number}
+   *   toExpPos   {number}
+   *
+   * E.g. Decimal.config({ precision: 20, rounding: 4 })
+   *
+   */
+  function config(obj) {
+    if (!obj || typeof obj !== 'object') {
+      throw Error(decimalError + 'Object expected');
+    }
+    var i, p, v,
+      ps = [
+        'precision', 1, MAX_DIGITS,
+        'rounding', 0, 8,
+        'toExpNeg', -1 / 0, 0,
+        'toExpPos', 0, 1 / 0
+      ];
+
+    for (i = 0; i < ps.length; i += 3) {
+      if ((v = obj[p = ps[i]]) !== void 0) {
+        if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
+        else throw Error(invalidArgument + p + ': ' + v);
+      }
+    }
+
+    if ((v = obj[p = 'LN10']) !== void 0) {
+        if (v == Math.LN10) this[p] = new this(v);
+        else throw Error(invalidArgument + p + ': ' + v);
+    }
+
+    return this;
+  }
+
+
+  // Create and configure initial Decimal constructor.
+  Decimal = clone(Decimal);
+
+  Decimal['default'] = Decimal.Decimal = Decimal;
+
+  // Internal constant.
+  ONE = new Decimal(1);
+
+
+  // Export.
+
+
+  // AMD.
+  if (typeof define == 'function' && define.amd) {
+    define(function () {
+      return Decimal;
+    });
+
+  // Node and other environments that support module.exports.
+  } else if (typeof module != 'undefined' && module.exports) {
+    module.exports = Decimal;
+
+    // Browser.
+  } else {
+    if (!globalScope) {
+      globalScope = typeof self != 'undefined' && self && self.self == self
+        ? self : Function('return this')();
+    }
+
+    globalScope.Decimal = Decimal;
+  }
+})(this);
diff --git a/internal/adapters/entrypoints/rest/assets/static/questionIcon.svg b/internal/adapters/entrypoints/rest/assets/static/questionIcon.svg
new file mode 100644
index 00000000..28497e4b
--- /dev/null
+++ b/internal/adapters/entrypoints/rest/assets/static/questionIcon.svg
@@ -0,0 +1,4 @@
+<svg xmlns="http://www.w3.org/2000/svg" width="13" height="13" fill="currentColor" class="bi bi-question-circle" viewBox="0 0 16 16">
+    <path d="M8 15A7 7 0 1 1 8 1a7 7 0 0 1 0 14m0 1A8 8 0 1 0 8 0a8 8 0 0 0 0 16"/>
+    <path d="M5.255 5.786a.237.237 0 0 0 .241.247h.825c.138 0 .248-.113.266-.25.09-.656.54-1.134 1.342-1.134.686 0 1.314.343 1.314 1.168 0 .635-.374.927-.965 1.371-.673.489-1.206 1.06-1.168 1.987l.003.217a.25.25 0 0 0 .25.246h.811a.25.25 0 0 0 .25-.25v-.105c0-.718.273-.927 1.01-1.486.609-.463 1.244-.977 1.244-2.056 0-1.511-1.276-2.241-2.673-2.241-1.267 0-2.655.59-2.75 2.286m1.557 5.763c0 .533.425.927 1.01.927.609 0 1.028-.394 1.028-.927 0-.552-.42-.94-1.029-.94-.584 0-1.009.388-1.009.94"/>
+</svg>
\ No newline at end of file
diff --git a/internal/adapters/entrypoints/rest/handlers/management.go b/internal/adapters/entrypoints/rest/handlers/management.go
index ea150a6c..453766bb 100644
--- a/internal/adapters/entrypoints/rest/handlers/management.go
+++ b/internal/adapters/entrypoints/rest/handlers/management.go
@@ -60,7 +60,7 @@ func NewManagementInterfaceHandler(store sessions.Store, useCase *liquidity_prov
 }
 
 func htmlTemplateSecurityHeaders(w http.ResponseWriter, nonce string) {
-	cspHeader := fmt.Sprintf("default-src 'self'; font-src 'self' data:; style-src 'self' 'sha256-KoyuUqdEu+hxBz6L8yaiUAiFiD/fPDTxWrW817e498s='; object-src 'none'; frame-src 'self'; script-src 'self' 'nonce-%s'; img-src 'self' data:; connect-src 'self';", nonce)
+	cspHeader := fmt.Sprintf("default-src 'self'; font-src 'self' data:; style-src 'self' 'sha256-yr5DcAJJmu0m4Rv1KfUyA8AJj1t0kAJ1D2JuSBIT1DU='; object-src 'none'; frame-src 'self'; script-src 'self' 'nonce-%s'; img-src 'self' data:; connect-src 'self';", nonce)
 	w.Header().Set("Content-Type", "text/html")
 	w.Header().Set("Content-Security-Policy", cspHeader)
 	w.Header().Set("Strict-Transport-Security", "max-age=63072000; includeSubDomains; preload")

From 67e2399cce2010a83f098ab6915794c018f8d71f Mon Sep 17 00:00:00 2001
From: Dominik Z <dominykas.zubavicius@iovlabs.org>
Date: Fri, 31 May 2024 12:27:43 +0300
Subject: [PATCH 2/4] additional checks

---
 .../entrypoints/rest/assets/management.html   | 22 ++++++++++++++-----
 1 file changed, 17 insertions(+), 5 deletions(-)

diff --git a/internal/adapters/entrypoints/rest/assets/management.html b/internal/adapters/entrypoints/rest/assets/management.html
index d02a6a02..f05884f8 100644
--- a/internal/adapters/entrypoints/rest/assets/management.html
+++ b/internal/adapters/entrypoints/rest/assets/management.html
@@ -168,15 +168,27 @@ <h5 class="card-title">Current Configuration</h5>
     <script nonce="{{ .ScriptNonce }}">
         document.addEventListener('DOMContentLoaded', () => {
             const data = {{.}};
-            const weiToEther = wei => new Decimal(wei).dividedBy(new Decimal(1e18)).toString();
+            const weiToEther = wei => {
+                try {
+                    const decimalValue = new Decimal(wei);
+                    return decimalValue.dividedBy(new Decimal(1e18)).toString();
+                } catch (error) {
+                    throw new Error(`Failed to convert wei to ether. Input: "${wei}". Error: ${error.message}`);
+                }
+            };
+
             const etherToWei = ether => {
+                if (typeof ether !== 'string' && typeof ether !== 'number') {
+                    throw new TypeError(`Invalid input type for ether: ${typeof ether}. Expected a number or string.`);
+                }
                 try {
                     const num = new Decimal(ether);
-                    const weiValue = num.times(new Decimal(1e18)).toFixed(0);
-                    return weiValue;
+                    if (num.isNegative()) {
+                        throw new RangeError(`The input "${ether}" is not a valid number.`);
+                    }
+                    return num.times(new Decimal(1e18)).toString();
                 } catch (error) {
-                    console.error(`Error converting ether to wei: ${error.message}`);
-                    throw new RangeError(`The input "${ether}" is not a valid number`);
+                    throw new Error(`Failed to convert ether to wei. Input: "${ether}". Error: ${error.message}`);
                 }
             };
 

From 6d352b60604a849c41ab99c1b590fab288033d5b Mon Sep 17 00:00:00 2001
From: Dominik Z <dominykas.zubavicius@iovlabs.org>
Date: Fri, 31 May 2024 12:34:56 +0300
Subject: [PATCH 3/4] update decimal.js

---
 .../entrypoints/rest/assets/static/decimal.js | 5506 +++++++++++++----
 1 file changed, 4213 insertions(+), 1293 deletions(-)

diff --git a/internal/adapters/entrypoints/rest/assets/static/decimal.js b/internal/adapters/entrypoints/rest/assets/static/decimal.js
index b2cbe207..4a27c580 100644
--- a/internal/adapters/entrypoints/rest/assets/static/decimal.js
+++ b/internal/adapters/entrypoints/rest/assets/static/decimal.js
@@ -1,37 +1,48 @@
-/*! decimal.js-light v2.5.1 https://github.com/MikeMcl/decimal.js-light/LICENCE */
 ;(function (globalScope) {
   'use strict';
 
 
-  /*
-   *  decimal.js-light v2.5.1
+  /*!
+   *  decimal.js v10.4.3
    *  An arbitrary-precision Decimal type for JavaScript.
-   *  https://github.com/MikeMcl/decimal.js-light
-   *  Copyright (c) 2020 Michael Mclaughlin <M8ch88l@gmail.com>
-   *  MIT Expat Licence
+   *  https://github.com/MikeMcl/decimal.js
+   *  Copyright (c) 2022 Michael Mclaughlin <M8ch88l@gmail.com>
+   *  MIT Licence
    */
 
 
   // -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //
 
 
+    // The maximum exponent magnitude.
+    // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.
+  var EXP_LIMIT = 9e15,                      // 0 to 9e15
+
     // The limit on the value of `precision`, and on the value of the first argument to
     // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
-  var MAX_DIGITS = 1e9,                        // 0 to 1e9
+    MAX_DIGITS = 1e9,                        // 0 to 1e9
+
+    // Base conversion alphabet.
+    NUMERALS = '0123456789abcdef',
+
+    // The natural logarithm of 10 (1025 digits).
+    LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
+
+    // Pi (1025 digits).
+    PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
 
 
     // The initial configuration properties of the Decimal constructor.
-    Decimal = {
+    DEFAULTS = {
 
       // These values must be integers within the stated ranges (inclusive).
-      // Most of these values can be changed during run-time using `Decimal.config`.
+      // 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 by default by `toInteger`, `toDecimalPlaces`, `toExponential`,
-      // `toFixed`, `toPrecision` and `toSignificantDigits`.
+      // The rounding mode used when rounding to `precision`.
       //
       // ROUND_UP         0 Away from zero.
       // ROUND_DOWN       1 Towards zero.
@@ -48,83 +59,137 @@
       // `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 -MAX_E
+      toExpNeg: -7,                          // 0 to -EXP_LIMIT
 
       // The exponent value at and above which `toString` returns exponential notation.
       // JavaScript numbers: 21
-      toExpPos:  21,                         // 0 to MAX_E
+      toExpPos:  21,                         // 0 to EXP_LIMIT
 
-      // The natural logarithm of 10.
-      // 115 digits
-      LN10: '2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298341967784042286'
+      // The minimum exponent value, beneath which underflow to zero occurs.
+      // JavaScript numbers: -324  (5e-324)
+      minE: -EXP_LIMIT,                      // -1 to -EXP_LIMIT
+
+      // The maximum exponent value, above which overflow to Infinity occurs.
+      // JavaScript numbers: 308  (1.7976931348623157e+308)
+      maxE: EXP_LIMIT,                       // 1 to EXP_LIMIT
+
+      // Whether to use cryptographically-secure random number generation, if available.
+      crypto: false                          // true/false
     },
 
 
   // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
 
 
+    Decimal, inexact, noConflict, quadrant,
     external = true,
 
     decimalError = '[DecimalError] ',
     invalidArgument = decimalError + 'Invalid argument: ',
-    exponentOutOfRange = decimalError + 'Exponent out of range: ',
+    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,
 
-    ONE,
     BASE = 1e7,
     LOG_BASE = 7,
     MAX_SAFE_INTEGER = 9007199254740991,
-    MAX_E = mathfloor(MAX_SAFE_INTEGER / LOG_BASE),    // 1286742750677284
+
+    LN10_PRECISION = LN10.length - 1,
+    PI_PRECISION = PI.length - 1,
 
     // Decimal.prototype object
-    P = {};
+    P = { toStringTag: tag };
 
 
   // Decimal prototype methods
 
 
   /*
-   *  absoluteValue                       abs
-   *  comparedTo                          cmp
-   *  decimalPlaces                       dp
-   *  dividedBy                           div
-   *  dividedToIntegerBy                  idiv
-   *  equals                              eq
-   *  exponent
-   *  greaterThan                         gt
-   *  greaterThanOrEqualTo                gte
-   *  isInteger                           isint
-   *  isNegative                          isneg
-   *  isPositive                          ispos
+   *  absoluteValue             abs
+   *  ceil
+   *  clampedTo                 clamp
+   *  comparedTo                cmp
+   *  cosine                    cos
+   *  cubeRoot                  cbrt
+   *  decimalPlaces             dp
+   *  dividedBy                 div
+   *  dividedToIntegerBy        divToInt
+   *  equals                    eq
+   *  floor
+   *  greaterThan               gt
+   *  greaterThanOrEqualTo      gte
+   *  hyperbolicCosine          cosh
+   *  hyperbolicSine            sinh
+   *  hyperbolicTangent         tanh
+   *  inverseCosine             acos
+   *  inverseHyperbolicCosine   acosh
+   *  inverseHyperbolicSine     asinh
+   *  inverseHyperbolicTangent  atanh
+   *  inverseSine               asin
+   *  inverseTangent            atan
+   *  isFinite
+   *  isInteger                 isInt
+   *  isNaN
+   *  isNegative                isNeg
+   *  isPositive                isPos
    *  isZero
-   *  lessThan                            lt
-   *  lessThanOrEqualTo                   lte
-   *  logarithm                           log
-   *  minus                               sub
-   *  modulo                              mod
-   *  naturalExponential                  exp
-   *  naturalLogarithm                    ln
-   *  negated                             neg
-   *  plus                                add
-   *  precision                           sd
-   *  squareRoot                          sqrt
-   *  times                               mul
-   *  toDecimalPlaces                     todp
+   *  lessThan                  lt
+   *  lessThanOrEqualTo         lte
+   *  logarithm                 log
+   *  [maximum]                 [max]
+   *  [minimum]                 [min]
+   *  minus                     sub
+   *  modulo                    mod
+   *  naturalExponential        exp
+   *  naturalLogarithm          ln
+   *  negated                   neg
+   *  plus                      add
+   *  precision                 sd
+   *  round
+   *  sine                      sin
+   *  squareRoot                sqrt
+   *  tangent                   tan
+   *  times                     mul
+   *  toBinary
+   *  toDecimalPlaces           toDP
    *  toExponential
    *  toFixed
-   *  toInteger                           toint
+   *  toFraction
+   *  toHexadecimal             toHex
+   *  toNearest
    *  toNumber
-   *  toPower                             pow
+   *  toOctal
+   *  toPower                   pow
    *  toPrecision
-   *  toSignificantDigits                 tosd
+   *  toSignificantDigits       toSD
    *  toString
-   *  valueOf                             val
+   *  truncated                 trunc
+   *  valueOf                   toJSON
    */
 
 
@@ -134,8 +199,39 @@
    */
   P.absoluteValue = P.abs = function () {
     var x = new this.constructor(this);
-    if (x.s) x.s = 1;
-    return x;
+    if (x.s < 0) x.s = 1;
+    return finalise(x);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
+   * direction of positive Infinity.
+   *
+   */
+  P.ceil = function () {
+    return finalise(new this.constructor(this), this.e + 1, 2);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal clamped to the range
+   * delineated by `min` and `max`.
+   *
+   * min {number|string|Decimal}
+   * max {number|string|Decimal}
+   *
+   */
+  P.clampedTo = P.clamp = function (min, max) {
+    var k,
+      x = this,
+      Ctor = x.constructor;
+    min = new Ctor(min);
+    max = new Ctor(max);
+    if (!min.s || !max.s) return new Ctor(NaN);
+    if (min.gt(max)) throw Error(invalidArgument + max);
+    k = x.cmp(min);
+    return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x);
   };
 
 
@@ -143,31 +239,185 @@
    * Return
    *   1    if the value of this Decimal is greater than the value of `y`,
    *  -1    if the value of this Decimal is less than the value of `y`,
-   *   0    if they have the same value
+   *   0    if they have the same value,
+   *   NaN  if the value of either Decimal is NaN.
    *
    */
   P.comparedTo = P.cmp = function (y) {
     var i, j, xdL, ydL,
-      x = this;
+      x = this,
+      xd = x.d,
+      yd = (y = new x.constructor(y)).d,
+      xs = x.s,
+      ys = y.s;
+
+    // Either NaN or ±Infinity?
+    if (!xd || !yd) {
+      return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
+    }
 
-    y = new x.constructor(y);
+    // Either zero?
+    if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;
 
     // Signs differ?
-    if (x.s !== y.s) return x.s || -y.s;
+    if (xs !== ys) return xs;
 
     // Compare exponents.
-    if (x.e !== y.e) return x.e > y.e ^ x.s < 0 ? 1 : -1;
+    if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
 
-    xdL = x.d.length;
-    ydL = y.d.length;
+    xdL = xd.length;
+    ydL = yd.length;
 
     // Compare digit by digit.
     for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
-      if (x.d[i] !== y.d[i]) return x.d[i] > y.d[i] ^ x.s < 0 ? 1 : -1;
+      if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;
     }
 
     // Compare lengths.
-    return xdL === ydL ? 0 : xdL > ydL ^ x.s < 0 ? 1 : -1;
+    return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-1, 1]
+   *
+   * cos(0)         = 1
+   * cos(-0)        = 1
+   * cos(Infinity)  = NaN
+   * cos(-Infinity) = NaN
+   * cos(NaN)       = NaN
+   *
+   */
+  P.cosine = P.cos = function () {
+    var pr, rm,
+      x = this,
+      Ctor = x.constructor;
+
+    if (!x.d) return new Ctor(NaN);
+
+    // cos(0) = cos(-0) = 1
+    if (!x.d[0]) return new Ctor(1);
+
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
+    Ctor.rounding = 1;
+
+    x = cosine(Ctor, toLessThanHalfPi(Ctor, x));
+
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
+
+    return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);
+  };
+
+
+  /*
+   *
+   * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to
+   * `precision` significant digits using rounding mode `rounding`.
+   *
+   *  cbrt(0)  =  0
+   *  cbrt(-0) = -0
+   *  cbrt(1)  =  1
+   *  cbrt(-1) = -1
+   *  cbrt(N)  =  N
+   *  cbrt(-I) = -I
+   *  cbrt(I)  =  I
+   *
+   * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))
+   *
+   */
+  P.cubeRoot = P.cbrt = function () {
+    var e, m, n, r, rep, s, sd, t, t3, t3plusx,
+      x = this,
+      Ctor = x.constructor;
+
+    if (!x.isFinite() || x.isZero()) return new Ctor(x);
+    external = false;
+
+    // Initial estimate.
+    s = x.s * mathpow(x.s * x, 1 / 3);
+
+     // Math.cbrt underflow/overflow?
+     // Pass x to Math.pow as integer, then adjust the exponent of the result.
+    if (!s || Math.abs(s) == 1 / 0) {
+      n = digitsToString(x.d);
+      e = x.e;
+
+      // Adjust n exponent so it is a multiple of 3 away from x exponent.
+      if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');
+      s = mathpow(n, 1 / 3);
+
+      // Rarely, e may be one less than the result exponent value.
+      e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));
+
+      if (s == 1 / 0) {
+        n = '5e' + e;
+      } else {
+        n = s.toExponential();
+        n = n.slice(0, n.indexOf('e') + 1) + e;
+      }
+
+      r = new Ctor(n);
+      r.s = x.s;
+    } else {
+      r = new Ctor(s.toString());
+    }
+
+    sd = (e = Ctor.precision) + 3;
+
+    // Halley's method.
+    // TODO? Compare Newton's method.
+    for (;;) {
+      t = r;
+      t3 = t.times(t).times(t);
+      t3plusx = t3.plus(x);
+      r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);
+
+      // TODO? Replace with for-loop and checkRoundingDigits.
+      if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
+        n = n.slice(sd - 3, sd + 1);
+
+        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999
+        // , i.e. approaching a rounding boundary, continue the iteration.
+        if (n == '9999' || !rep && n == '4999') {
+
+          // On the first iteration only, check to see if rounding up gives the exact result as the
+          // nines may infinitely repeat.
+          if (!rep) {
+            finalise(t, e + 1, 0);
+
+            if (t.times(t).times(t).eq(x)) {
+              r = t;
+              break;
+            }
+          }
+
+          sd += 4;
+          rep = 1;
+        } else {
+
+          // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
+          // If not, then there are further digits and m will be truthy.
+          if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
+
+            // Truncate to the first rounding digit.
+            finalise(r, e + 1, 1);
+            m = !r.times(r).times(r).eq(x);
+          }
+
+          break;
+        }
+      }
+    }
+
+    external = true;
+
+    return finalise(r, e, Ctor.rounding, m);
   };
 
 
@@ -176,21 +426,43 @@
    *
    */
   P.decimalPlaces = P.dp = function () {
-    var x = this,
-      w = x.d.length - 1,
-      dp = (w - x.e) * LOG_BASE;
+    var w,
+      d = this.d,
+      n = NaN;
+
+    if (d) {
+      w = d.length - 1;
+      n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;
 
-    // Subtract the number of trailing zeros of the last word.
-    w = x.d[w];
-    if (w) for (; w % 10 == 0; w /= 10) dp--;
+      // Subtract the number of trailing zeros of the last word.
+      w = d[w];
+      if (w) for (; w % 10 == 0; w /= 10) n--;
+      if (n < 0) n = 0;
+    }
 
-    return dp < 0 ? 0 : dp;
+    return n;
   };
 
 
   /*
-   * Return a new Decimal whose value is the value of this Decimal divided by `y`, truncated to
-   * `precision` significant digits.
+   *  n / 0 = I
+   *  n / N = N
+   *  n / I = 0
+   *  0 / n = 0
+   *  0 / 0 = N
+   *  0 / N = N
+   *  0 / I = 0
+   *  N / n = N
+   *  N / 0 = N
+   *  N / N = N
+   *  N / I = N
+   *  I / n = I
+   *  I / 0 = I
+   *  I / N = N
+   *  I / I = N
+   *
+   * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to
+   * `precision` significant digits using rounding mode `rounding`.
    *
    */
   P.dividedBy = P.div = function (y) {
@@ -200,13 +472,13 @@
 
   /*
    * Return a new Decimal whose value is the integer part of dividing the value of this Decimal
-   * by the value of `y`, truncated to `precision` significant digits.
+   * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.
    *
    */
-  P.dividedToIntegerBy = P.idiv = function (y) {
+  P.dividedToIntegerBy = P.divToInt = function (y) {
     var x = this,
       Ctor = x.constructor;
-    return round(divide(x, new Ctor(y), 0, 1), Ctor.precision);
+    return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
   };
 
 
@@ -215,16 +487,17 @@
    *
    */
   P.equals = P.eq = function (y) {
-    return !this.cmp(y);
+    return this.cmp(y) === 0;
   };
 
 
   /*
-   * Return the (base 10) exponent value of this Decimal (this.e is the base 10000000 exponent).
+   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
+   * direction of negative Infinity.
    *
    */
-  P.exponent = function () {
-    return getBase10Exponent(this);
+  P.floor = function () {
+    return finalise(new this.constructor(this), this.e + 1, 3);
   };
 
 
@@ -244,703 +517,1069 @@
    *
    */
   P.greaterThanOrEqualTo = P.gte = function (y) {
-    return this.cmp(y) >= 0;
+    var k = this.cmp(y);
+    return k == 1 || k === 0;
   };
 
 
   /*
-   * Return true if the value of this Decimal is an integer, otherwise return false.
+   * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this
+   * Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [1, Infinity]
+   *
+   * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...
+   *
+   * cosh(0)         = 1
+   * cosh(-0)        = 1
+   * cosh(Infinity)  = Infinity
+   * cosh(-Infinity) = Infinity
+   * cosh(NaN)       = NaN
+   *
+   *  x        time taken (ms)   result
+   * 1000      9                 9.8503555700852349694e+433
+   * 10000     25                4.4034091128314607936e+4342
+   * 100000    171               1.4033316802130615897e+43429
+   * 1000000   3817              1.5166076984010437725e+434294
+   * 10000000  abandoned after 2 minute wait
+   *
+   * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))
    *
    */
-  P.isInteger = P.isint = function () {
-    return this.e > this.d.length - 2;
-  };
+  P.hyperbolicCosine = P.cosh = function () {
+    var k, n, pr, rm, len,
+      x = this,
+      Ctor = x.constructor,
+      one = new Ctor(1);
 
+    if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);
+    if (x.isZero()) return one;
 
-  /*
-   * Return true if the value of this Decimal is negative, otherwise return false.
-   *
-   */
-  P.isNegative = P.isneg = function () {
-    return this.s < 0;
-  };
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
+    Ctor.rounding = 1;
+    len = x.d.length;
+
+    // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1
+    // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))
+
+    // Estimate the optimum number of times to use the argument reduction.
+    // TODO? Estimation reused from cosine() and may not be optimal here.
+    if (len < 32) {
+      k = Math.ceil(len / 3);
+      n = (1 / tinyPow(4, k)).toString();
+    } else {
+      k = 16;
+      n = '2.3283064365386962890625e-10';
+    }
 
+    x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);
 
-  /*
-   * Return true if the value of this Decimal is positive, otherwise return false.
-   *
-   */
-  P.isPositive = P.ispos = function () {
-    return this.s > 0;
+    // Reverse argument reduction
+    var cosh2_x,
+      i = k,
+      d8 = new Ctor(8);
+    for (; i--;) {
+      cosh2_x = x.times(x);
+      x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));
+    }
+
+    return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);
   };
 
 
   /*
-   * Return true if the value of this Decimal is 0, otherwise return false.
+   * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this
+   * Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-Infinity, Infinity]
+   *
+   * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...
+   *
+   * sinh(0)         = 0
+   * sinh(-0)        = -0
+   * sinh(Infinity)  = Infinity
+   * sinh(-Infinity) = -Infinity
+   * sinh(NaN)       = NaN
+   *
+   * x        time taken (ms)
+   * 10       2 ms
+   * 100      5 ms
+   * 1000     14 ms
+   * 10000    82 ms
+   * 100000   886 ms            1.4033316802130615897e+43429
+   * 200000   2613 ms
+   * 300000   5407 ms
+   * 400000   8824 ms
+   * 500000   13026 ms          8.7080643612718084129e+217146
+   * 1000000  48543 ms
+   *
+   * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))
    *
    */
-  P.isZero = function () {
-    return this.s === 0;
-  };
+  P.hyperbolicSine = P.sinh = function () {
+    var k, pr, rm, len,
+      x = this,
+      Ctor = x.constructor;
 
+    if (!x.isFinite() || x.isZero()) return new Ctor(x);
 
-  /*
-   * Return true if the value of this Decimal is less than `y`, otherwise return false.
-   *
-   */
-  P.lessThan = P.lt = function (y) {
-    return this.cmp(y) < 0;
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
+    Ctor.rounding = 1;
+    len = x.d.length;
+
+    if (len < 3) {
+      x = taylorSeries(Ctor, 2, x, x, true);
+    } else {
+
+      // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))
+      // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))
+      // 3 multiplications and 1 addition
+
+      // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))
+      // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))
+      // 4 multiplications and 2 additions
+
+      // Estimate the optimum number of times to use the argument reduction.
+      k = 1.4 * Math.sqrt(len);
+      k = k > 16 ? 16 : k | 0;
+
+      x = x.times(1 / tinyPow(5, k));
+      x = taylorSeries(Ctor, 2, x, x, true);
+
+      // Reverse argument reduction
+      var sinh2_x,
+        d5 = new Ctor(5),
+        d16 = new Ctor(16),
+        d20 = new Ctor(20);
+      for (; k--;) {
+        sinh2_x = x.times(x);
+        x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));
+      }
+    }
+
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
+
+    return finalise(x, pr, rm, true);
   };
 
 
   /*
-   * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
+   * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this
+   * Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-1, 1]
+   *
+   * tanh(x) = sinh(x) / cosh(x)
+   *
+   * tanh(0)         = 0
+   * tanh(-0)        = -0
+   * tanh(Infinity)  = 1
+   * tanh(-Infinity) = -1
+   * tanh(NaN)       = NaN
    *
    */
-  P.lessThanOrEqualTo = P.lte = function (y) {
-    return this.cmp(y) < 1;
+  P.hyperbolicTangent = P.tanh = function () {
+    var pr, rm,
+      x = this,
+      Ctor = x.constructor;
+
+    if (!x.isFinite()) return new Ctor(x.s);
+    if (x.isZero()) return new Ctor(x);
+
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + 7;
+    Ctor.rounding = 1;
+
+    return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);
   };
 
 
   /*
-   * Return the logarithm of the value of this Decimal to the specified base, truncated to
-   * `precision` significant digits.
-   *
-   * If no base is specified, return log[10](x).
+   * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of
+   * this Decimal.
    *
-   * log[base](x) = ln(x) / ln(base)
+   * Domain: [-1, 1]
+   * Range: [0, pi]
    *
-   * The maximum error of the result is 1 ulp (unit in the last place).
+   * acos(x) = pi/2 - asin(x)
    *
-   * [base] {number|string|Decimal} The base of the logarithm.
+   * acos(0)       = pi/2
+   * acos(-0)      = pi/2
+   * acos(1)       = 0
+   * acos(-1)      = pi
+   * acos(1/2)     = pi/3
+   * acos(-1/2)    = 2*pi/3
+   * acos(|x| > 1) = NaN
+   * acos(NaN)     = NaN
    *
    */
-  P.logarithm = P.log = function (base) {
-    var r,
+  P.inverseCosine = P.acos = function () {
+    var halfPi,
       x = this,
       Ctor = x.constructor,
+      k = x.abs().cmp(1),
       pr = Ctor.precision,
-      wpr = pr + 5;
-
-    // Default base is 10.
-    if (base === void 0) {
-      base = new Ctor(10);
-    } else {
-      base = new Ctor(base);
+      rm = Ctor.rounding;
 
-      // log[-b](x) = NaN
-      // log[0](x)  = NaN
-      // log[1](x)  = NaN
-      if (base.s < 1 || base.eq(ONE)) throw Error(decimalError + 'NaN');
+    if (k !== -1) {
+      return k === 0
+        // |x| is 1
+        ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)
+        // |x| > 1 or x is NaN
+        : new Ctor(NaN);
     }
 
-    // log[b](-x) = NaN
-    // log[b](0) = -Infinity
-    if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));
+    if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);
 
-    // log[b](1) = 0
-    if (x.eq(ONE)) return new Ctor(0);
+    // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3
 
-    external = false;
-    r = divide(ln(x, wpr), ln(base, wpr), wpr);
-    external = true;
+    Ctor.precision = pr + 6;
+    Ctor.rounding = 1;
 
-    return round(r, pr);
-  };
+    x = x.asin();
+    halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
 
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
 
-  /*
-   * Return a new Decimal whose value is the value of this Decimal minus `y`, truncated to
-   * `precision` significant digits.
-   *
-   */
-  P.minus = P.sub = function (y) {
-    var x = this;
-    y = new x.constructor(y);
-    return x.s == y.s ? subtract(x, y) : add(x, (y.s = -y.s, y));
+    return halfPi.minus(x);
   };
 
 
   /*
-   * Return a new Decimal whose value is the value of this Decimal modulo `y`, truncated to
-   * `precision` significant digits.
+   * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the
+   * value of this Decimal.
+   *
+   * Domain: [1, Infinity]
+   * Range: [0, Infinity]
+   *
+   * acosh(x) = ln(x + sqrt(x^2 - 1))
+   *
+   * acosh(x < 1)     = NaN
+   * acosh(NaN)       = NaN
+   * acosh(Infinity)  = Infinity
+   * acosh(-Infinity) = NaN
+   * acosh(0)         = NaN
+   * acosh(-0)        = NaN
+   * acosh(1)         = 0
+   * acosh(-1)        = NaN
    *
    */
-  P.modulo = P.mod = function (y) {
-    var q,
+  P.inverseHyperbolicCosine = P.acosh = function () {
+    var pr, rm,
       x = this,
-      Ctor = x.constructor,
-      pr = Ctor.precision;
+      Ctor = x.constructor;
 
-    y = new Ctor(y);
+    if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);
+    if (!x.isFinite()) return new Ctor(x);
 
-    // x % 0 = NaN
-    if (!y.s) throw Error(decimalError + 'NaN');
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;
+    Ctor.rounding = 1;
+    external = false;
 
-    // Return x if x is 0.
-    if (!x.s) return round(new Ctor(x), pr);
+    x = x.times(x).minus(1).sqrt().plus(x);
 
-    // Prevent rounding of intermediate calculations.
-    external = false;
-    q = divide(x, y, 0, 1).times(y);
     external = true;
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
 
-    return x.minus(q);
+    return x.ln();
   };
 
 
   /*
-   * Return a new Decimal whose value is the natural exponential of the value of this Decimal,
-   * i.e. the base e raised to the power the value of this Decimal, truncated to `precision`
-   * significant digits.
+   * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value
+   * of this Decimal.
    *
-   */
-  P.naturalExponential = P.exp = function () {
-    return exp(this);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
-   * truncated to `precision` significant digits.
+   * Domain: [-Infinity, Infinity]
+   * Range: [-Infinity, Infinity]
+   *
+   * asinh(x) = ln(x + sqrt(x^2 + 1))
+   *
+   * asinh(NaN)       = NaN
+   * asinh(Infinity)  = Infinity
+   * asinh(-Infinity) = -Infinity
+   * asinh(0)         = 0
+   * asinh(-0)        = -0
    *
    */
-  P.naturalLogarithm = P.ln = function () {
-    return ln(this);
-  };
+  P.inverseHyperbolicSine = P.asinh = function () {
+    var pr, rm,
+      x = this,
+      Ctor = x.constructor;
 
+    if (!x.isFinite() || x.isZero()) return new Ctor(x);
 
-  /*
-   * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
-   * -1.
-   *
-   */
-  P.negated = P.neg = function () {
-    var x = new this.constructor(this);
-    x.s = -x.s || 0;
-    return x;
-  };
+    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);
 
-  /*
-   * Return a new Decimal whose value is the value of this Decimal plus `y`, truncated to
-   * `precision` significant digits.
-   *
-   */
-  P.plus = P.add = function (y) {
-    var x = this;
-    y = new x.constructor(y);
-    return x.s == y.s ? add(x, y) : subtract(x, (y.s = -y.s, y));
+    external = true;
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
+
+    return x.ln();
   };
 
 
   /*
-   * Return the number of significant digits of the value of this Decimal.
+   * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the
+   * value of this Decimal.
    *
-   * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
+   * Domain: [-1, 1]
+   * Range: [-Infinity, Infinity]
+   *
+   * atanh(x) = 0.5 * ln((1 + x) / (1 - x))
+   *
+   * atanh(|x| > 1)   = NaN
+   * atanh(NaN)       = NaN
+   * atanh(Infinity)  = NaN
+   * atanh(-Infinity) = NaN
+   * atanh(0)         = 0
+   * atanh(-0)        = -0
+   * atanh(1)         = Infinity
+   * atanh(-1)        = -Infinity
    *
    */
-  P.precision = P.sd = function (z) {
-    var e, sd, w,
-      x = this;
+  P.inverseHyperbolicTangent = P.atanh = function () {
+    var pr, rm, wpr, xsd,
+      x = this,
+      Ctor = x.constructor;
 
-    if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
+    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);
 
-    e = getBase10Exponent(x) + 1;
-    w = x.d.length - 1;
-    sd = w * LOG_BASE + 1;
-    w = x.d[w];
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    xsd = x.sd();
 
-    // If non-zero...
-    if (w) {
+    if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);
 
-      // Subtract the number of trailing zeros of the last word.
-      for (; w % 10 == 0; w /= 10) sd--;
+    Ctor.precision = wpr = xsd - x.e;
 
-      // Add the number of digits of the first word.
-      for (w = x.d[0]; w >= 10; w /= 10) sd++;
-    }
+    x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);
+
+    Ctor.precision = pr + 4;
+    Ctor.rounding = 1;
+
+    x = x.ln();
 
-    return z && e > sd ? e : sd;
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
+
+    return x.times(0.5);
   };
 
 
   /*
-   * Return a new Decimal whose value is the square root of this Decimal, truncated to `precision`
-   * significant digits.
+   * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this
+   * Decimal.
    *
-   */
-  P.squareRoot = P.sqrt = function () {
-    var e, n, pr, r, s, t, wpr,
-      x = this,
+   * Domain: [-Infinity, Infinity]
+   * Range: [-pi/2, pi/2]
+   *
+   * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))
+   *
+   * asin(0)       = 0
+   * asin(-0)      = -0
+   * asin(1/2)     = pi/6
+   * asin(-1/2)    = -pi/6
+   * asin(1)       = pi/2
+   * asin(-1)      = -pi/2
+   * asin(|x| > 1) = NaN
+   * asin(NaN)     = NaN
+   *
+   * TODO? Compare performance of Taylor series.
+   *
+   */
+  P.inverseSine = P.asin = function () {
+    var halfPi, k,
+      pr, rm,
+      x = this,
       Ctor = x.constructor;
 
-    // Negative or zero?
-    if (x.s < 1) {
-      if (!x.s) return new Ctor(0);
-
-      // sqrt(-x) = NaN
-      throw Error(decimalError + 'NaN');
-    }
-
-    e = getBase10Exponent(x);
-    external = false;
+    if (x.isZero()) return new Ctor(x);
 
-    // Initial estimate.
-    s = Math.sqrt(+x);
+    k = x.abs().cmp(1);
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
 
-    // Math.sqrt underflow/overflow?
-    // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
-    if (s == 0 || s == 1 / 0) {
-      n = digitsToString(x.d);
-      if ((n.length + e) % 2 == 0) n += '0';
-      s = Math.sqrt(n);
-      e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
+    if (k !== -1) {
 
-      if (s == 1 / 0) {
-        n = '5e' + e;
-      } else {
-        n = s.toExponential();
-        n = n.slice(0, n.indexOf('e') + 1) + e;
+      // |x| is 1
+      if (k === 0) {
+        halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
+        halfPi.s = x.s;
+        return halfPi;
       }
 
-      r = new Ctor(n);
-    } else {
-      r = new Ctor(s.toString());
+      // |x| > 1 or x is NaN
+      return new Ctor(NaN);
     }
 
-    pr = Ctor.precision;
-    s = wpr = pr + 3;
-
-    // Newton-Raphson iteration.
-    for (;;) {
-      t = r;
-      r = t.plus(divide(x, t, wpr + 2)).times(0.5);
-
-      if (digitsToString(t.d).slice(0, wpr) === (n = digitsToString(r.d)).slice(0, wpr)) {
-        n = n.slice(wpr - 3, wpr + 1);
-
-        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
-        // 4999, i.e. approaching a rounding boundary, continue the iteration.
-        if (s == wpr && n == '4999') {
-
-          // On the first iteration only, check to see if rounding up gives the exact result as the
-          // nines may infinitely repeat.
-          round(t, pr + 1, 0);
+    // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6
 
-          if (t.times(t).eq(x)) {
-            r = t;
-            break;
-          }
-        } else if (n != '9999') {
-          break;
-        }
+    Ctor.precision = pr + 6;
+    Ctor.rounding = 1;
 
-        wpr += 4;
-      }
-    }
+    x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();
 
-    external = true;
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
 
-    return round(r, pr);
+    return x.times(2);
   };
 
 
   /*
-   * Return a new Decimal whose value is the value of this Decimal times `y`, truncated to
-   * `precision` significant digits.
+   * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value
+   * of this Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-pi/2, pi/2]
+   *
+   * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
+   *
+   * atan(0)         = 0
+   * atan(-0)        = -0
+   * atan(1)         = pi/4
+   * atan(-1)        = -pi/4
+   * atan(Infinity)  = pi/2
+   * atan(-Infinity) = -pi/2
+   * atan(NaN)       = NaN
    *
    */
-  P.times = P.mul = function (y) {
-    var carry, e, i, k, r, rL, t, xdL, ydL,
+  P.inverseTangent = P.atan = function () {
+    var i, j, k, n, px, t, r, wpr, x2,
       x = this,
       Ctor = x.constructor,
-      xd = x.d,
-      yd = (y = new Ctor(y)).d;
-
-    // Return 0 if either is 0.
-    if (!x.s || !y.s) return new Ctor(0);
-
-    y.s *= x.s;
-    e = x.e + y.e;
-    xdL = xd.length;
-    ydL = yd.length;
+      pr = Ctor.precision,
+      rm = Ctor.rounding;
 
-    // Ensure xd points to the longer array.
-    if (xdL < ydL) {
-      r = xd;
-      xd = yd;
-      yd = r;
-      rL = xdL;
-      xdL = ydL;
-      ydL = rL;
+    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;
     }
 
-    // Initialise the result array with zeros.
-    r = [];
-    rL = xdL + ydL;
-    for (i = rL; i--;) r.push(0);
+    Ctor.precision = wpr = pr + 10;
+    Ctor.rounding = 1;
 
-    // Multiply!
-    for (i = ydL; --i >= 0;) {
-      carry = 0;
-      for (k = xdL + i; k > i;) {
-        t = r[k] + yd[i] * xd[k - i - 1] + carry;
-        r[k--] = t % BASE | 0;
-        carry = t / BASE | 0;
-      }
+    // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);
 
-      r[k] = (r[k] + carry) % BASE | 0;
-    }
+    // Argument reduction
+    // Ensure |x| < 0.42
+    // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
 
-    // Remove trailing zeros.
-    for (; !r[--rL];) r.pop();
+    k = Math.min(28, wpr / LOG_BASE + 2 | 0);
 
-    if (carry) ++e;
-    else r.shift();
+    for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));
 
-    y.d = r;
-    y.e = e;
+    external = false;
 
-    return external ? round(y, Ctor.precision) : y;
-  };
+    j = Math.ceil(wpr / LOG_BASE);
+    n = 1;
+    x2 = x.times(x);
+    r = new Ctor(x);
+    px = x;
 
+    // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
+    for (; i !== -1;) {
+      px = px.times(x2);
+      t = r.minus(px.div(n += 2));
 
-  /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
-   * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
-   *
-   * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
-   *
-   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toDecimalPlaces = P.todp = function (dp, rm) {
-    var x = this,
-      Ctor = x.constructor;
+      px = px.times(x2);
+      r = t.plus(px.div(n += 2));
 
-    x = new Ctor(x);
-    if (dp === void 0) return x;
+      if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);
+    }
 
-    checkInt32(dp, 0, MAX_DIGITS);
+    if (k) r = r.times(2 << (k - 1));
 
-    if (rm === void 0) rm = Ctor.rounding;
-    else checkInt32(rm, 0, 8);
+    external = true;
 
-    return round(x, dp + getBase10Exponent(x) + 1, rm);
+    return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);
   };
 
 
   /*
-   * Return a string representing the value of this Decimal in exponential notation rounded to
-   * `dp` fixed decimal places using rounding mode `rounding`.
-   *
-   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   * Return true if the value of this Decimal is a finite number, otherwise return false.
    *
    */
-  P.toExponential = function (dp, rm) {
-    var str,
-      x = this,
-      Ctor = x.constructor;
+  P.isFinite = function () {
+    return !!this.d;
+  };
 
-    if (dp === void 0) {
-      str = toString(x, true);
-    } else {
-      checkInt32(dp, 0, MAX_DIGITS);
 
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
+  /*
+   * Return true if the value of this Decimal is an integer, otherwise return false.
+   *
+   */
+  P.isInteger = P.isInt = function () {
+    return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
+  };
 
-      x = round(new Ctor(x), dp + 1, rm);
-      str = toString(x, true, dp + 1);
-    }
 
-    return str;
+  /*
+   * Return true if the value of this Decimal is NaN, otherwise return false.
+   *
+   */
+  P.isNaN = function () {
+    return !this.s;
   };
 
 
   /*
-   * Return a string representing the value of this Decimal in normal (fixed-point) notation to
-   * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
-   * omitted.
-   *
-   * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
-   *
-   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
-   * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
-   * (-0).toFixed(3) is '0.000'.
-   * (-0.5).toFixed(0) is '-0'.
+   * Return true if the value of this Decimal is negative, otherwise return false.
    *
    */
-  P.toFixed = function (dp, rm) {
-    var str, y,
-      x = this,
-      Ctor = x.constructor;
-
-    if (dp === void 0) return toString(x);
+  P.isNegative = P.isNeg = function () {
+    return this.s < 0;
+  };
 
-    checkInt32(dp, 0, MAX_DIGITS);
 
-    if (rm === void 0) rm = Ctor.rounding;
-    else checkInt32(rm, 0, 8);
+  /*
+   * Return true if the value of this Decimal is positive, otherwise return false.
+   *
+   */
+  P.isPositive = P.isPos = function () {
+    return this.s > 0;
+  };
 
-    y = round(new Ctor(x), dp + getBase10Exponent(x) + 1, rm);
-    str = toString(y.abs(), false, dp + getBase10Exponent(y) + 1);
 
-    // To determine whether to add the minus sign look at the value before it was rounded,
-    // i.e. look at `x` rather than `y`.
-    return x.isneg() && !x.isZero() ? '-' + str : str;
+  /*
+   * Return true if the value of this Decimal is 0 or -0, otherwise return false.
+   *
+   */
+  P.isZero = function () {
+    return !!this.d && this.d[0] === 0;
   };
 
 
   /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
-   * rounding mode `rounding`.
+   * Return true if the value of this Decimal is less than `y`, otherwise return false.
    *
    */
-  P.toInteger = P.toint = function () {
-    var x = this,
-      Ctor = x.constructor;
-    return round(new Ctor(x), getBase10Exponent(x) + 1, Ctor.rounding);
+  P.lessThan = P.lt = function (y) {
+    return this.cmp(y) < 0;
   };
 
 
   /*
-   * Return the value of this Decimal converted to a number primitive.
+   * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
    *
    */
-  P.toNumber = function () {
-    return +this;
+  P.lessThanOrEqualTo = P.lte = function (y) {
+    return this.cmp(y) < 1;
   };
 
 
   /*
-   * Return a new Decimal whose value is the value of this Decimal raised to the power `y`,
-   * truncated to `precision` significant digits.
+   * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
    *
-   * For non-integer or very large exponents pow(x, y) is calculated using
+   * If no base is specified, return log[10](arg).
    *
-   *   x^y = exp(y*ln(x))
+   * log[base](arg) = ln(arg) / ln(base)
    *
-   * The maximum error is 1 ulp (unit in last place).
+   * The result will always be correctly rounded if the base of the log is 10, and 'almost always'
+   * otherwise:
    *
-   * y {number|string|Decimal} The power to which to raise this Decimal.
+   * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen
+   * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error
+   * between the result and the correctly rounded result will be one ulp (unit in the last place).
+   *
+   * log[-b](a)       = NaN
+   * log[0](a)        = NaN
+   * log[1](a)        = NaN
+   * log[NaN](a)      = NaN
+   * log[Infinity](a) = NaN
+   * log[b](0)        = -Infinity
+   * log[b](-0)       = -Infinity
+   * log[b](-a)       = NaN
+   * log[b](1)        = 0
+   * log[b](Infinity) = Infinity
+   * log[b](NaN)      = NaN
+   *
+   * [base] {number|string|Decimal} The base of the logarithm.
    *
    */
-  P.toPower = P.pow = function (y) {
-    var e, k, pr, r, sign, yIsInt,
-      x = this,
-      Ctor = x.constructor,
-      guard = 12,
-      yn = +(y = new Ctor(y));
+  P.logarithm = P.log = function (base) {
+    var isBase10, d, denominator, k, inf, num, sd, r,
+      arg = this,
+      Ctor = arg.constructor,
+      pr = Ctor.precision,
+      rm = Ctor.rounding,
+      guard = 5;
 
-    // pow(x, 0) = 1
-    if (!y.s) return new Ctor(ONE);
+    // Default base is 10.
+    if (base == null) {
+      base = new Ctor(10);
+      isBase10 = true;
+    } else {
+      base = new Ctor(base);
+      d = base.d;
 
-    x = new Ctor(x);
+      // Return NaN if base is negative, or non-finite, or is 0 or 1.
+      if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);
 
-    // pow(0, y > 0) = 0
-    // pow(0, y < 0) = Infinity
-    if (!x.s) {
-      if (y.s < 1) throw Error(decimalError + 'Infinity');
-      return x;
+      isBase10 = base.eq(10);
     }
 
-    // pow(1, y) = 1
-    if (x.eq(ONE)) return x;
-
-    pr = Ctor.precision;
-
-    // pow(x, 1) = x
-    if (y.eq(ONE)) return round(x, pr);
-
-    e = y.e;
-    k = y.d.length - 1;
-    yIsInt = e >= k;
-    sign = x.s;
-
-    if (!yIsInt) {
+    d = arg.d;
 
-      // pow(x < 0, y non-integer) = NaN
-      if (sign < 0) throw Error(decimalError + 'NaN');
-
-    // If y is a small integer use the 'exponentiation by squaring' algorithm.
-    } else if ((k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
-      r = new Ctor(ONE);
+    // Is arg negative, non-finite, 0 or 1?
+    if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {
+      return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);
+    }
 
-      // Max k of 9007199254740991 takes 53 loop iterations.
-      // Maximum digits array length; leaves [28, 34] guard digits.
-      e = Math.ceil(pr / LOG_BASE + 4);
+    // The result will have a non-terminating decimal expansion if base is 10 and arg is not an
+    // integer power of 10.
+    if (isBase10) {
+      if (d.length > 1) {
+        inf = true;
+      } else {
+        for (k = d[0]; k % 10 === 0;) k /= 10;
+        inf = k !== 1;
+      }
+    }
 
-      external = false;
+    external = false;
+    sd = pr + guard;
+    num = naturalLogarithm(arg, sd);
+    denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
+
+    // The result will have 5 rounding digits.
+    r = divide(num, denominator, sd, 1);
+
+    // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,
+    // calculate 10 further digits.
+    //
+    // If the result is known to have an infinite decimal expansion, repeat this until it is clear
+    // that the result is above or below the boundary. Otherwise, if after calculating the 10
+    // further digits, the last 14 are nines, round up and assume the result is exact.
+    // Also assume the result is exact if the last 14 are zero.
+    //
+    // Example of a result that will be incorrectly rounded:
+    // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...
+    // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it
+    // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so
+    // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal
+    // place is still 2.6.
+    if (checkRoundingDigits(r.d, k = pr, rm)) {
+
+      do {
+        sd += 10;
+        num = naturalLogarithm(arg, sd);
+        denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
+        r = divide(num, denominator, sd, 1);
+
+        if (!inf) {
+
+          // Check for 14 nines from the 2nd rounding digit, as the first may be 4.
+          if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {
+            r = finalise(r, pr + 1, 0);
+          }
 
-      for (;;) {
-        if (k % 2) {
-          r = r.times(x);
-          truncate(r.d, e);
+          break;
         }
+      } while (checkRoundingDigits(r.d, k += 10, rm));
+    }
 
-        k = mathfloor(k / 2);
-        if (k === 0) break;
-
-        x = x.times(x);
-        truncate(x.d, e);
-      }
+    external = true;
 
-      external = true;
+    return finalise(r, pr, rm);
+  };
 
-      return y.s < 0 ? new Ctor(ONE).div(r) : round(r, pr);
-    }
 
-    // Result is negative if x is negative and the last digit of integer y is odd.
-    sign = sign < 0 && y.d[Math.max(e, k)] & 1 ? -1 : 1;
+  /*
+   * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.
+   *
+   * arguments {number|string|Decimal}
+   *
+  P.max = function () {
+    Array.prototype.push.call(arguments, this);
+    return maxOrMin(this.constructor, arguments, 'lt');
+  };
+   */
 
-    x.s = 1;
-    external = false;
-    r = y.times(ln(x, pr + guard));
-    external = true;
-    r = exp(r);
-    r.s = sign;
 
-    return r;
+  /*
+   * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
+   *
+   * arguments {number|string|Decimal}
+   *
+  P.min = function () {
+    Array.prototype.push.call(arguments, this);
+    return maxOrMin(this.constructor, arguments, 'gt');
   };
+   */
 
 
   /*
-   * Return a string representing the value of this Decimal rounded to `sd` significant digits
-   * using rounding mode `rounding`.
-   *
-   * Return exponential notation if `sd` is less than the number of digits necessary to represent
-   * the integer part of the value in normal notation.
+   *  n - 0 = n
+   *  n - N = N
+   *  n - I = -I
+   *  0 - n = -n
+   *  0 - 0 = 0
+   *  0 - N = N
+   *  0 - I = -I
+   *  N - n = N
+   *  N - 0 = N
+   *  N - N = N
+   *  N - I = N
+   *  I - n = I
+   *  I - 0 = I
+   *  I - N = N
+   *  I - I = N
    *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
    *
    */
-  P.toPrecision = function (sd, rm) {
-    var e, str,
+  P.minus = P.sub = function (y) {
+    var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,
       x = this,
       Ctor = x.constructor;
 
-    if (sd === void 0) {
-      e = getBase10Exponent(x);
-      str = toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
-    } else {
-      checkInt32(sd, 1, MAX_DIGITS);
+    y = new Ctor(y);
 
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
+    // If either is not finite...
+    if (!x.d || !y.d) {
 
-      x = round(new Ctor(x), sd, rm);
-      e = getBase10Exponent(x);
-      str = toString(x, sd <= e || e <= Ctor.toExpNeg, sd);
-    }
+      // Return NaN if either is NaN.
+      if (!x.s || !y.s) y = new Ctor(NaN);
 
-    return str;
+      // Return y negated if x is finite and y is ±Infinity.
+      else if (x.d) y.s = -y.s;
+
+      // Return x if y is finite and x is ±Infinity.
+      // Return x if both are ±Infinity with different signs.
+      // Return NaN if both are ±Infinity with the same sign.
+      else y = new Ctor(y.d || x.s !== y.s ? x : NaN);
+
+      return y;
+    }
+
+    // If signs differ...
+    if (x.s != y.s) {
+      y.s = -y.s;
+      return x.plus(y);
+    }
+
+    xd = x.d;
+    yd = y.d;
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+
+    // If either is zero...
+    if (!xd[0] || !yd[0]) {
+
+      // Return y negated if x is zero and y is non-zero.
+      if (yd[0]) y.s = -y.s;
+
+      // Return x if y is zero and x is non-zero.
+      else if (xd[0]) y = new Ctor(x);
+
+      // Return zero if both are zero.
+      // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.
+      else return new Ctor(rm === 3 ? -0 : 0);
+
+      return external ? finalise(y, pr, rm) : y;
+    }
+
+    // x and y are finite, non-zero numbers with the same sign.
+
+    // Calculate base 1e7 exponents.
+    e = mathfloor(y.e / LOG_BASE);
+    xe = mathfloor(x.e / LOG_BASE);
+
+    xd = xd.slice();
+    k = xe - e;
+
+    // If base 1e7 exponents differ...
+    if (k) {
+      xLTy = k < 0;
+
+      if (xLTy) {
+        d = xd;
+        k = -k;
+        len = yd.length;
+      } else {
+        d = yd;
+        e = xe;
+        len = xd.length;
+      }
+
+      // Numbers with massively different exponents would result in a very high number of
+      // zeros needing to be prepended, but this can be avoided while still ensuring correct
+      // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
+      i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
+
+      if (k > i) {
+        k = i;
+        d.length = 1;
+      }
+
+      // Prepend zeros to equalise exponents.
+      d.reverse();
+      for (i = k; i--;) d.push(0);
+      d.reverse();
+
+    // Base 1e7 exponents equal.
+    } else {
+
+      // Check digits to determine which is the bigger number.
+
+      i = xd.length;
+      len = yd.length;
+      xLTy = i < len;
+      if (xLTy) len = i;
+
+      for (i = 0; i < len; i++) {
+        if (xd[i] != yd[i]) {
+          xLTy = xd[i] < yd[i];
+          break;
+        }
+      }
+
+      k = 0;
+    }
+
+    if (xLTy) {
+      d = xd;
+      xd = yd;
+      yd = d;
+      y.s = -y.s;
+    }
+
+    len = xd.length;
+
+    // Append zeros to `xd` if shorter.
+    // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.
+    for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
+
+    // Subtract yd from xd.
+    for (i = yd.length; i > k;) {
+
+      if (xd[--i] < yd[i]) {
+        for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
+        --xd[j];
+        xd[i] += BASE;
+      }
+
+      xd[i] -= yd[i];
+    }
+
+    // Remove trailing zeros.
+    for (; xd[--len] === 0;) xd.pop();
+
+    // Remove leading zeros and adjust exponent accordingly.
+    for (; xd[0] === 0; xd.shift()) --e;
+
+    // Zero?
+    if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0);
+
+    y.d = xd;
+    y.e = getBase10Exponent(xd, e);
+
+    return external ? finalise(y, pr, rm) : y;
   };
 
 
   /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
-   * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
-   * omitted.
+   *   n % 0 =  N
+   *   n % N =  N
+   *   n % I =  n
+   *   0 % n =  0
+   *  -0 % n = -0
+   *   0 % 0 =  N
+   *   0 % N =  N
+   *   0 % I =  0
+   *   N % n =  N
+   *   N % 0 =  N
+   *   N % N =  N
+   *   N % I =  N
+   *   I % n =  N
+   *   I % 0 =  N
+   *   I % N =  N
+   *   I % I =  N
    *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to
+   * `precision` significant digits using rounding mode `rounding`.
+   *
+   * The result depends on the modulo mode.
    *
    */
-  P.toSignificantDigits = P.tosd = function (sd, rm) {
-    var x = this,
+  P.modulo = P.mod = function (y) {
+    var q,
+      x = this,
       Ctor = x.constructor;
 
-    if (sd === void 0) {
-      sd = Ctor.precision;
-      rm = Ctor.rounding;
-    } else {
-      checkInt32(sd, 1, MAX_DIGITS);
+    y = new Ctor(y);
 
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
+    // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.
+    if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);
+
+    // Return x if y is ±Infinity or x is ±0.
+    if (!y.d || x.d && !x.d[0]) {
+      return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);
+    }
+
+    // Prevent rounding of intermediate calculations.
+    external = false;
+
+    if (Ctor.modulo == 9) {
+
+      // Euclidian division: q = sign(y) * floor(x / abs(y))
+      // result = x - q * y    where  0 <= result < abs(y)
+      q = divide(x, y.abs(), 0, 3, 1);
+      q.s *= y.s;
+    } else {
+      q = divide(x, y, 0, Ctor.modulo, 1);
     }
 
-    return round(new Ctor(x), sd, rm);
+    q = q.times(y);
+
+    external = true;
+
+    return x.minus(q);
   };
 
 
   /*
-   * Return a string representing the value of this Decimal.
-   *
-   * Return exponential notation if this Decimal has a positive exponent equal to or greater than
-   * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
+   * Return a new Decimal whose value is the natural exponential of the value of this Decimal,
+   * i.e. the base e raised to the power the value of this Decimal, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
    *
    */
-  P.toString = P.valueOf = P.val = P.toJSON = function () {
-    var x = this,
-      e = getBase10Exponent(x),
-      Ctor = x.constructor;
+  P.naturalExponential = P.exp = function () {
+    return naturalExponential(this);
+  };
 
-    return toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
+
+  /*
+   * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
+   * rounded to `precision` significant digits using rounding mode `rounding`.
+   *
+   */
+  P.naturalLogarithm = P.ln = function () {
+    return naturalLogarithm(this);
   };
 
 
-  // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
+  /*
+   * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
+   * -1.
+   *
+   */
+  P.negated = P.neg = function () {
+    var x = new this.constructor(this);
+    x.s = -x.s;
+    return finalise(x);
+  };
 
 
   /*
-   *  add                 P.minus, P.plus
-   *  checkInt32          P.todp, P.toExponential, P.toFixed, P.toPrecision, P.tosd
-   *  digitsToString      P.log, P.sqrt, P.pow, toString, exp, ln
-   *  divide              P.div, P.idiv, P.log, P.mod, P.sqrt, exp, ln
-   *  exp                 P.exp, P.pow
-   *  getBase10Exponent   P.exponent, P.sd, P.toint, P.sqrt, P.todp, P.toFixed, P.toPrecision,
-   *                      P.toString, divide, round, toString, exp, ln
-   *  getLn10             P.log, ln
-   *  getZeroString       digitsToString, toString
-   *  ln                  P.log, P.ln, P.pow, exp
-   *  parseDecimal        Decimal
-   *  round               P.abs, P.idiv, P.log, P.minus, P.mod, P.neg, P.plus, P.toint, P.sqrt,
-   *                      P.times, P.todp, P.toExponential, P.toFixed, P.pow, P.toPrecision, P.tosd,
-   *                      divide, getLn10, exp, ln
-   *  subtract            P.minus, P.plus
-   *  toString            P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf
-   *  truncate            P.pow
+   *  n + 0 = n
+   *  n + N = N
+   *  n + I = I
+   *  0 + n = n
+   *  0 + 0 = 0
+   *  0 + N = N
+   *  0 + I = I
+   *  N + n = N
+   *  N + 0 = N
+   *  N + N = N
+   *  N + I = N
+   *  I + n = I
+   *  I + 0 = I
+   *  I + N = N
+   *  I + I = I
+   *
+   * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
    *
-   *  Throws:             P.log, P.mod, P.sd, P.sqrt, P.pow,  checkInt32, divide, round,
-   *                      getLn10, exp, ln, parseDecimal, Decimal, config
    */
+  P.plus = P.add = function (y) {
+    var carry, d, e, i, k, len, pr, rm, xd, yd,
+      x = this,
+      Ctor = x.constructor;
 
+    y = new Ctor(y);
 
-  function add(x, y) {
-    var carry, d, e, i, k, len, xd, yd,
-      Ctor = x.constructor,
-      pr = Ctor.precision;
+    // If either is not finite...
+    if (!x.d || !y.d) {
 
-    // If either is zero...
-    if (!x.s || !y.s) {
+      // Return NaN if either is NaN.
+      if (!x.s || !y.s) y = new Ctor(NaN);
 
-      // Return x if y is zero.
-      // Return y if y is non-zero.
-      if (!y.s) y = new Ctor(x);
-      return external ? round(y, pr) : y;
+      // Return x if y is finite and x is ±Infinity.
+      // Return x if both are ±Infinity with the same sign.
+      // Return NaN if both are ±Infinity with different signs.
+      // Return y if x is finite and y is ±Infinity.
+      else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);
+
+      return y;
+    }
+
+     // If signs differ...
+    if (x.s != y.s) {
+      y.s = -y.s;
+      return x.minus(y);
     }
 
     xd = x.d;
     yd = y.d;
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+
+    // If either is zero...
+    if (!xd[0] || !yd[0]) {
+
+      // Return x if y is zero.
+      // Return y if y is non-zero.
+      if (!yd[0]) y = new Ctor(x);
+
+      return external ? finalise(y, pr, rm) : y;
+    }
 
     // x and y are finite, non-zero numbers with the same sign.
 
-    k = x.e;
-    e = y.e;
+    // Calculate base 1e7 exponents.
+    k = mathfloor(x.e / LOG_BASE);
+    e = mathfloor(y.e / LOG_BASE);
+
     xd = xd.slice();
     i = k - e;
 
     // If base 1e7 exponents differ...
     if (i) {
+
       if (i < 0) {
         d = xd;
         i = -i;
@@ -993,1000 +1632,3271 @@
     for (len = xd.length; xd[--len] == 0;) xd.pop();
 
     y.d = xd;
-    y.e = e;
+    y.e = getBase10Exponent(xd, e);
 
-    return external ? round(y, pr) : y;
-  }
+    return external ? finalise(y, pr, rm) : y;
+  };
 
 
-  function checkInt32(i, min, max) {
-    if (i !== ~~i || i < min || i > max) {
-      throw Error(invalidArgument + i);
+  /*
+   * Return the number of significant digits of the value of this Decimal.
+   *
+   * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
+   *
+   */
+  P.precision = P.sd = function (z) {
+    var k,
+      x = this;
+
+    if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
+
+    if (x.d) {
+      k = getPrecision(x.d);
+      if (z && x.e + 1 > k) k = x.e + 1;
+    } else {
+      k = NaN;
     }
-  }
 
+    return k;
+  };
 
-  function digitsToString(d) {
-    var i, k, ws,
-      indexOfLastWord = d.length - 1,
-      str = '',
-      w = d[0];
 
-    if (indexOfLastWord > 0) {
-      str += w;
-      for (i = 1; i < indexOfLastWord; i++) {
-        ws = d[i] + '';
-        k = LOG_BASE - ws.length;
-        if (k) str += getZeroString(k);
-        str += ws;
-      }
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
+   * rounding mode `rounding`.
+   *
+   */
+  P.round = function () {
+    var x = this,
+      Ctor = x.constructor;
 
-      w = d[i];
-      ws = w + '';
-      k = LOG_BASE - ws.length;
-      if (k) str += getZeroString(k);
-    } else if (w === 0) {
-      return '0';
-    }
+    return finalise(new Ctor(x), x.e + 1, Ctor.rounding);
+  };
 
-    // Remove trailing zeros of last w.
-    for (; w % 10 === 0;) w /= 10;
 
-    return str + w;
-  }
+  /*
+   * Return a new Decimal whose value is the sine of the value in radians of this Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-1, 1]
+   *
+   * sin(x) = x - x^3/3! + x^5/5! - ...
+   *
+   * sin(0)         = 0
+   * sin(-0)        = -0
+   * sin(Infinity)  = NaN
+   * sin(-Infinity) = NaN
+   * sin(NaN)       = NaN
+   *
+   */
+  P.sine = P.sin = function () {
+    var pr, rm,
+      x = this,
+      Ctor = x.constructor;
 
+    if (!x.isFinite()) return new Ctor(NaN);
+    if (x.isZero()) return new Ctor(x);
 
-  var divide = (function () {
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
+    Ctor.rounding = 1;
 
-    // Assumes non-zero x and k, and hence non-zero result.
-    function multiplyInteger(x, k) {
-      var temp,
-        carry = 0,
-        i = x.length;
+    x = sine(Ctor, toLessThanHalfPi(Ctor, x));
 
-      for (x = x.slice(); i--;) {
-        temp = x[i] * k + carry;
-        x[i] = temp % BASE | 0;
-        carry = temp / BASE | 0;
-      }
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
 
-      if (carry) x.unshift(carry);
+    return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);
+  };
 
-      return x;
-    }
 
-    function compare(a, b, aL, bL) {
-      var i, r;
-
-      if (aL != bL) {
-        r = aL > bL ? 1 : -1;
-      } else {
-        for (i = r = 0; i < aL; i++) {
-          if (a[i] != b[i]) {
-            r = a[i] > b[i] ? 1 : -1;
-            break;
-          }
-        }
-      }
-
-      return r;
-    }
-
-    function subtract(a, b, aL) {
-      var i = 0;
-
-      // Subtract b from a.
-      for (; aL--;) {
-        a[aL] -= i;
-        i = a[aL] < b[aL] ? 1 : 0;
-        a[aL] = i * BASE + a[aL] - b[aL];
-      }
+  /*
+   * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   *  sqrt(-n) =  N
+   *  sqrt(N)  =  N
+   *  sqrt(-I) =  N
+   *  sqrt(I)  =  I
+   *  sqrt(0)  =  0
+   *  sqrt(-0) = -0
+   *
+   */
+  P.squareRoot = P.sqrt = function () {
+    var m, n, sd, r, rep, t,
+      x = this,
+      d = x.d,
+      e = x.e,
+      s = x.s,
+      Ctor = x.constructor;
 
-      // Remove leading zeros.
-      for (; !a[0] && a.length > 1;) a.shift();
+    // Negative/NaN/Infinity/zero?
+    if (s !== 1 || !d || !d[0]) {
+      return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);
     }
 
-    return function (x, y, pr, dp) {
-      var cmp, e, i, k, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, yL, yz,
-        Ctor = x.constructor,
-        sign = x.s == y.s ? 1 : -1,
-        xd = x.d,
-        yd = y.d;
+    external = false;
 
-      // Either 0?
-      if (!x.s) return new Ctor(x);
-      if (!y.s) throw Error(decimalError + 'Division by zero');
+    // Initial estimate.
+    s = Math.sqrt(+x);
 
-      e = x.e - y.e;
-      yL = yd.length;
-      xL = xd.length;
-      q = new Ctor(sign);
-      qd = q.d = [];
+    // Math.sqrt underflow/overflow?
+    // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+    if (s == 0 || s == 1 / 0) {
+      n = digitsToString(d);
 
-      // Result exponent may be one less than e.
-      for (i = 0; yd[i] == (xd[i] || 0); ) ++i;
-      if (yd[i] > (xd[i] || 0)) --e;
+      if ((n.length + e) % 2 == 0) n += '0';
+      s = Math.sqrt(n);
+      e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
 
-      if (pr == null) {
-        sd = pr = Ctor.precision;
-      } else if (dp) {
-        sd = pr + (getBase10Exponent(x) - getBase10Exponent(y)) + 1;
+      if (s == 1 / 0) {
+        n = '5e' + e;
       } else {
-        sd = pr;
+        n = s.toExponential();
+        n = n.slice(0, n.indexOf('e') + 1) + e;
       }
 
-      if (sd < 0) return new Ctor(0);
-
-      // Convert precision in number of base 10 digits to base 1e7 digits.
-      sd = sd / LOG_BASE + 2 | 0;
-      i = 0;
+      r = new Ctor(n);
+    } else {
+      r = new Ctor(s.toString());
+    }
 
-      // divisor < 1e7
-      if (yL == 1) {
-        k = 0;
-        yd = yd[0];
-        sd++;
-
-        // k is the carry.
-        for (; (i < xL || k) && sd--; i++) {
-          t = k * BASE + (xd[i] || 0);
-          qd[i] = t / yd | 0;
-          k = t % yd | 0;
-        }
+    sd = (e = Ctor.precision) + 3;
 
-      // divisor >= 1e7
-      } else {
+    // Newton-Raphson iteration.
+    for (;;) {
+      t = r;
+      r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);
 
-        // Normalise xd and yd so highest order digit of yd is >= BASE/2
-        k = BASE / (yd[0] + 1) | 0;
+      // TODO? Replace with for-loop and checkRoundingDigits.
+      if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
+        n = n.slice(sd - 3, sd + 1);
 
-        if (k > 1) {
-          yd = multiplyInteger(yd, k);
-          xd = multiplyInteger(xd, k);
-          yL = yd.length;
-          xL = xd.length;
-        }
+        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
+        // 4999, i.e. approaching a rounding boundary, continue the iteration.
+        if (n == '9999' || !rep && n == '4999') {
 
-        xi = yL;
-        rem = xd.slice(0, yL);
-        remL = rem.length;
+          // On the first iteration only, check to see if rounding up gives the exact result as the
+          // nines may infinitely repeat.
+          if (!rep) {
+            finalise(t, e + 1, 0);
 
-        // Add zeros to make remainder as long as divisor.
-        for (; remL < yL;) rem[remL++] = 0;
+            if (t.times(t).eq(x)) {
+              r = t;
+              break;
+            }
+          }
 
-        yz = yd.slice();
-        yz.unshift(0);
-        yd0 = yd[0];
+          sd += 4;
+          rep = 1;
+        } else {
 
-        if (yd[1] >= BASE / 2) ++yd0;
+          // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
+          // If not, then there are further digits and m will be truthy.
+          if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
 
-        do {
-          k = 0;
+            // Truncate to the first rounding digit.
+            finalise(r, e + 1, 1);
+            m = !r.times(r).eq(x);
+          }
 
-          // Compare divisor and remainder.
-          cmp = compare(yd, rem, yL, remL);
+          break;
+        }
+      }
+    }
 
-          // If divisor < remainder.
-          if (cmp < 0) {
+    external = true;
 
-            // Calculate trial digit, k.
-            rem0 = rem[0];
-            if (yL != remL) rem0 = rem0 * BASE + (rem[1] || 0);
+    return finalise(r, e, Ctor.rounding, m);
+  };
 
-            // k will be how many times the divisor goes into the current remainder.
-            k = rem0 / yd0 | 0;
 
-            //  Algorithm:
-            //  1. product = divisor * trial digit (k)
-            //  2. if product > remainder: product -= divisor, k--
-            //  3. remainder -= product
-            //  4. if product was < remainder at 2:
-            //    5. compare new remainder and divisor
-            //    6. If remainder > divisor: remainder -= divisor, k++
+  /*
+   * Return a new Decimal whose value is the tangent of the value in radians of this Decimal.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-Infinity, Infinity]
+   *
+   * tan(0)         = 0
+   * tan(-0)        = -0
+   * tan(Infinity)  = NaN
+   * tan(-Infinity) = NaN
+   * tan(NaN)       = NaN
+   *
+   */
+  P.tangent = P.tan = function () {
+    var pr, rm,
+      x = this,
+      Ctor = x.constructor;
 
-            if (k > 1) {
-              if (k >= BASE) k = BASE - 1;
+    if (!x.isFinite()) return new Ctor(NaN);
+    if (x.isZero()) return new Ctor(x);
 
-              // product = divisor * trial digit.
-              prod = multiplyInteger(yd, k);
-              prodL = prod.length;
-              remL = rem.length;
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
+    Ctor.precision = pr + 10;
+    Ctor.rounding = 1;
 
-              // Compare product and remainder.
-              cmp = compare(prod, rem, prodL, remL);
+    x = x.sin();
+    x.s = 1;
+    x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);
 
-              // product > remainder.
-              if (cmp == 1) {
-                k--;
+    Ctor.precision = pr;
+    Ctor.rounding = rm;
 
-                // Subtract divisor from product.
-                subtract(prod, yL < prodL ? yz : yd, prodL);
-              }
-            } else {
+    return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);
+  };
 
-              // cmp is -1.
-              // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
-              // to avoid it. If k is 1 there is a need to compare yd and rem again below.
-              if (k == 0) cmp = k = 1;
-              prod = yd.slice();
-            }
 
-            prodL = prod.length;
-            if (prodL < remL) prod.unshift(0);
+  /*
+   *  n * 0 = 0
+   *  n * N = N
+   *  n * I = I
+   *  0 * n = 0
+   *  0 * 0 = 0
+   *  0 * N = N
+   *  0 * I = N
+   *  N * n = N
+   *  N * 0 = N
+   *  N * N = N
+   *  N * I = N
+   *  I * n = I
+   *  I * 0 = N
+   *  I * N = N
+   *  I * I = I
+   *
+   * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   */
+  P.times = P.mul = function (y) {
+    var carry, e, i, k, r, rL, t, xdL, ydL,
+      x = this,
+      Ctor = x.constructor,
+      xd = x.d,
+      yd = (y = new Ctor(y)).d;
 
-            // Subtract product from remainder.
-            subtract(rem, prod, remL);
+    y.s *= x.s;
 
-            // If product was < previous remainder.
-            if (cmp == -1) {
-              remL = rem.length;
+     // If either is NaN, ±Infinity or ±0...
+    if (!xd || !xd[0] || !yd || !yd[0]) {
 
-              // Compare divisor and new remainder.
-              cmp = compare(yd, rem, yL, remL);
+      return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd
 
-              // If divisor < new remainder, subtract divisor from remainder.
-              if (cmp < 1) {
-                k++;
+        // Return NaN if either is NaN.
+        // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.
+        ? NaN
 
-                // Subtract divisor from remainder.
-                subtract(rem, yL < remL ? yz : yd, remL);
-              }
-            }
+        // Return ±Infinity if either is ±Infinity.
+        // Return ±0 if either is ±0.
+        : !xd || !yd ? y.s / 0 : y.s * 0);
+    }
 
-            remL = rem.length;
-          } else if (cmp === 0) {
-            k++;
-            rem = [0];
-          }    // if cmp === 1, k will be 0
+    e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);
+    xdL = xd.length;
+    ydL = yd.length;
 
-          // Add the next digit, k, to the result array.
-          qd[i++] = k;
+    // Ensure xd points to the longer array.
+    if (xdL < ydL) {
+      r = xd;
+      xd = yd;
+      yd = r;
+      rL = xdL;
+      xdL = ydL;
+      ydL = rL;
+    }
 
-          // Update the remainder.
-          if (cmp && rem[0]) {
-            rem[remL++] = xd[xi] || 0;
-          } else {
-            rem = [xd[xi]];
-            remL = 1;
-          }
+    // Initialise the result array with zeros.
+    r = [];
+    rL = xdL + ydL;
+    for (i = rL; i--;) r.push(0);
 
-        } while ((xi++ < xL || rem[0] !== void 0) && sd--);
+    // Multiply!
+    for (i = ydL; --i >= 0;) {
+      carry = 0;
+      for (k = xdL + i; k > i;) {
+        t = r[k] + yd[i] * xd[k - i - 1] + carry;
+        r[k--] = t % BASE | 0;
+        carry = t / BASE | 0;
       }
 
-      // Leading zero?
-      if (!qd[0]) qd.shift();
+      r[k] = (r[k] + carry) % BASE | 0;
+    }
 
-      q.e = e;
+    // Remove trailing zeros.
+    for (; !r[--rL];) r.pop();
 
-      return round(q, dp ? pr + getBase10Exponent(q) + 1 : pr);
-    };
-  })();
+    if (carry) ++e;
+    else r.shift();
+
+    y.d = r;
+    y.e = getBase10Exponent(r, e);
+
+    return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;
+  };
 
 
   /*
-   * Return a new Decimal whose value is the natural exponential of `x` truncated to `sd`
-   * significant digits.
-   *
-   * Taylor/Maclaurin series.
+   * Return a string representing the value of this Decimal in base 2, round to `sd` significant
+   * digits using rounding mode `rm`.
    *
-   * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
+   * If the optional `sd` argument is present then return binary exponential notation.
    *
-   * Argument reduction:
-   *   Repeat x = x / 32, k += 5, until |x| < 0.1
-   *   exp(x) = exp(x / 2^k)^(2^k)
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
    *
-   * Previously, the argument was initially reduced by
-   * exp(x) = exp(r) * 10^k  where r = x - k * ln10, k = floor(x / ln10)
-   * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
-   * found to be slower than just dividing repeatedly by 32 as above.
+   */
+  P.toBinary = function (sd, rm) {
+    return toStringBinary(this, 2, sd, rm);
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
+   * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
    *
-   * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
+   * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
    *
-   *  exp(x) is non-terminating for any finite, non-zero x.
+   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
    *
    */
-  function exp(x, sd) {
-    var denominator, guard, pow, sum, t, wpr,
-      i = 0,
-      k = 0,
-      Ctor = x.constructor,
-      pr = Ctor.precision;
+  P.toDecimalPlaces = P.toDP = function (dp, rm) {
+    var x = this,
+      Ctor = x.constructor;
 
-    if (getBase10Exponent(x) > 16) throw Error(exponentOutOfRange + getBase10Exponent(x));
+    x = new Ctor(x);
+    if (dp === void 0) return x;
 
-    // exp(0) = 1
-    if (!x.s) return new Ctor(ONE);
+    checkInt32(dp, 0, MAX_DIGITS);
 
-    if (sd == null) {
-      external = false;
-      wpr = pr;
-    } else {
-      wpr = sd;
-    }
+    if (rm === void 0) rm = Ctor.rounding;
+    else checkInt32(rm, 0, 8);
 
-    t = new Ctor(0.03125);
+    return finalise(x, dp + x.e + 1, rm);
+  };
 
-    while (x.abs().gte(0.1)) {
-      x = x.times(t);    // x = x / 2^5
-      k += 5;
-    }
 
-    // Estimate the precision increase necessary to ensure the first 4 rounding digits are correct.
-    guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
-    wpr += guard;
-    denominator = pow = sum = new Ctor(ONE);
-    Ctor.precision = wpr;
+  /*
+   * Return a string representing the value of this Decimal in exponential notation rounded to
+   * `dp` fixed decimal places using rounding mode `rounding`.
+   *
+   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toExponential = function (dp, rm) {
+    var str,
+      x = this,
+      Ctor = x.constructor;
 
-    for (;;) {
-      pow = round(pow.times(x), wpr);
-      denominator = denominator.times(++i);
-      t = sum.plus(divide(pow, denominator, wpr));
+    if (dp === void 0) {
+      str = finiteToString(x, true);
+    } else {
+      checkInt32(dp, 0, MAX_DIGITS);
 
-      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
-        while (k--) sum = round(sum.times(sum), wpr);
-        Ctor.precision = pr;
-        return sd == null ? (external = true, round(sum, pr)) : sum;
-      }
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
 
-      sum = t;
+      x = finalise(new Ctor(x), dp + 1, rm);
+      str = finiteToString(x, true, dp + 1);
     }
-  }
 
+    return x.isNeg() && !x.isZero() ? '-' + str : str;
+  };
 
-  // Calculate the base 10 exponent from the base 1e7 exponent.
-  function getBase10Exponent(x) {
-    var e = x.e * LOG_BASE,
-      w = x.d[0];
-
-    // Add the number of digits of the first word of the digits array.
-    for (; w >= 10; w /= 10) e++;
-    return e;
-  }
 
+  /*
+   * Return a string representing the value of this Decimal in normal (fixed-point) notation to
+   * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
+   * omitted.
+   *
+   * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
+   *
+   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
+   * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
+   * (-0).toFixed(3) is '0.000'.
+   * (-0.5).toFixed(0) is '-0'.
+   *
+   */
+  P.toFixed = function (dp, rm) {
+    var str, y,
+      x = this,
+      Ctor = x.constructor;
 
-  function getLn10(Ctor, sd, pr) {
+    if (dp === void 0) {
+      str = finiteToString(x);
+    } else {
+      checkInt32(dp, 0, MAX_DIGITS);
 
-    if (sd > Ctor.LN10.sd()) {
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
 
+      y = finalise(new Ctor(x), dp + x.e + 1, rm);
+      str = finiteToString(y, false, dp + y.e + 1);
+    }
 
-      // Reset global state in case the exception is caught.
-      external = true;
-      if (pr) Ctor.precision = pr;
-      throw Error(decimalError + 'LN10 precision limit exceeded');
-    }
-
-    return round(new Ctor(Ctor.LN10), sd);
-  }
-
-
-  function getZeroString(k) {
-    var zs = '';
-    for (; k--;) zs += '0';
-    return zs;
-  }
+    // To determine whether to add the minus sign look at the value before it was rounded,
+    // i.e. look at `x` rather than `y`.
+    return x.isNeg() && !x.isZero() ? '-' + str : str;
+  };
 
 
   /*
-   * Return a new Decimal whose value is the natural logarithm of `x` truncated to `sd` significant
-   * digits.
+   * Return an array representing the value of this Decimal as a simple fraction with an integer
+   * numerator and an integer denominator.
    *
-   *  ln(n) is non-terminating (n != 1)
+   * The denominator will be a positive non-zero value less than or equal to the specified maximum
+   * denominator. If a maximum denominator is not specified, the denominator will be the lowest
+   * value necessary to represent the number exactly.
+   *
+   * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity.
    *
    */
-  function ln(y, sd) {
-    var c, c0, denominator, e, numerator, sum, t, wpr, x2,
-      n = 1,
-      guard = 10,
-      x = y,
+  P.toFraction = function (maxD) {
+    var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r,
+      x = this,
       xd = x.d,
-      Ctor = x.constructor,
-      pr = Ctor.precision;
+      Ctor = x.constructor;
 
-    // ln(-x) = NaN
-    // ln(0) = -Infinity
-    if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));
+    if (!xd) return new Ctor(x);
 
-    // ln(1) = 0
-    if (x.eq(ONE)) return new Ctor(0);
+    n1 = d0 = new Ctor(1);
+    d1 = n0 = new Ctor(0);
 
-    if (sd == null) {
-      external = false;
-      wpr = pr;
+    d = new Ctor(d1);
+    e = d.e = getPrecision(xd) - x.e - 1;
+    k = e % LOG_BASE;
+    d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);
+
+    if (maxD == null) {
+
+      // d is 10**e, the minimum max-denominator needed.
+      maxD = e > 0 ? d : n1;
     } else {
-      wpr = sd;
+      n = new Ctor(maxD);
+      if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);
+      maxD = n.gt(d) ? (e > 0 ? d : n1) : n;
     }
 
-    if (x.eq(10)) {
-      if (sd == null) external = true;
-      return getLn10(Ctor, wpr);
+    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;
     }
 
-    wpr += guard;
-    Ctor.precision = wpr;
-    c = digitsToString(xd);
-    c0 = c.charAt(0);
-    e = getBase10Exponent(x);
+    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;
 
-    if (Math.abs(e) < 1.5e15) {
+    // Determine which fraction is closer to x, n0/d0 or n1/d1?
+    r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1
+        ? [n1, d1] : [n0, d0];
 
-      // Argument reduction.
-      // The series converges faster the closer the argument is to 1, so using
-      // ln(a^b) = b * ln(a),   ln(a) = ln(a^b) / b
-      // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
-      // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
-      // later be divided by this number, then separate out the power of 10 using
-      // ln(a*10^b) = ln(a) + b*ln(10).
+    Ctor.precision = pr;
+    external = true;
 
-      // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
-      //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
-      // max n is 6 (gives 0.7 - 1.3)
-      while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
-        x = x.times(y);
-        c = digitsToString(x.d);
-        c0 = c.charAt(0);
-        n++;
-      }
+    return r;
+  };
 
-      e = getBase10Exponent(x);
 
-      if (c0 > 1) {
-        x = new Ctor('0.' + c);
-        e++;
-      } else {
-        x = new Ctor(c0 + '.' + c.slice(1));
-      }
-    } else {
+  /*
+   * Return a string representing the value of this Decimal in base 16, round to `sd` significant
+   * digits using rounding mode `rm`.
+   *
+   * If the optional `sd` argument is present then return binary exponential notation.
+   *
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toHexadecimal = P.toHex = function (sd, rm) {
+    return toStringBinary(this, 16, sd, rm);
+  };
 
-      // The argument reduction method above may result in overflow if the argument y is a massive
-      // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
-      // function using ln(x*10^e) = ln(x) + e*ln(10).
-      t = getLn10(Ctor, wpr + 2, pr).times(e + '');
-      x = ln(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
 
-      Ctor.precision = pr;
-      return sd == null ? (external = true, round(x, pr)) : x;
-    }
+  /*
+   * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding
+   * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.
+   *
+   * The return value will always have the same sign as this Decimal, unless either this Decimal
+   * or `y` is NaN, in which case the return value will be also be NaN.
+   *
+   * The return value is not affected by the value of `precision`.
+   *
+   * y {number|string|Decimal} The magnitude to round to a multiple of.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   * 'toNearest() rounding mode not an integer: {rm}'
+   * 'toNearest() rounding mode out of range: {rm}'
+   *
+   */
+  P.toNearest = function (y, rm) {
+    var x = this,
+      Ctor = x.constructor;
 
-    // x is reduced to a value near 1.
+    x = new Ctor(x);
 
-    // Taylor series.
-    // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
-    // where x = (y - 1)/(y + 1)    (|x| < 1)
-    sum = numerator = x = divide(x.minus(ONE), x.plus(ONE), wpr);
-    x2 = round(x.times(x), wpr);
-    denominator = 3;
+    if (y == null) {
 
-    for (;;) {
-      numerator = round(numerator.times(x2), wpr);
-      t = sum.plus(divide(numerator, new Ctor(denominator), wpr));
+      // If x is not finite, return x.
+      if (!x.d) return x;
 
-      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
-        sum = sum.times(2);
+      y = new Ctor(1);
+      rm = Ctor.rounding;
+    } else {
+      y = new Ctor(y);
+      if (rm === void 0) {
+        rm = Ctor.rounding;
+      } else {
+        checkInt32(rm, 0, 8);
+      }
 
-        // Reverse the argument reduction.
-        if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
-        sum = divide(sum, new Ctor(n), wpr);
+      // If x is not finite, return x if y is not NaN, else NaN.
+      if (!x.d) return y.s ? x : y;
 
-        Ctor.precision = pr;
-        return sd == null ? (external = true, round(sum, pr)) : sum;
+      // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.
+      if (!y.d) {
+        if (y.s) y.s = x.s;
+        return y;
       }
+    }
 
-      sum = t;
-      denominator += 2;
+    // If y is not zero, calculate the nearest multiple of y to x.
+    if (y.d[0]) {
+      external = false;
+      x = divide(x, y, 0, rm, 1).times(y);
+      external = true;
+      finalise(x);
+
+    // If y is zero, return zero with the sign of x.
+    } else {
+      y.s = x.s;
+      x = y;
     }
-  }
+
+    return x;
+  };
 
 
   /*
-   * Parse the value of a new Decimal `x` from string `str`.
+   * Return the value of this Decimal converted to a number primitive.
+   * Zero keeps its sign.
+   *
    */
-  function parseDecimal(x, str) {
-    var e, i, len;
-
-    // Decimal point?
-    if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
-
-    // Exponential form?
-    if ((i = str.search(/e/i)) > 0) {
+  P.toNumber = function () {
+    return +this;
+  };
 
-      // Determine exponent.
-      if (e < 0) e = i;
-      e += +str.slice(i + 1);
-      str = str.substring(0, i);
-    } else if (e < 0) {
 
-      // Integer.
-      e = str.length;
-    }
+  /*
+   * Return a string representing the value of this Decimal in base 8, round to `sd` significant
+   * digits using rounding mode `rm`.
+   *
+   * If the optional `sd` argument is present then return binary exponential notation.
+   *
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toOctal = function (sd, rm) {
+    return toStringBinary(this, 8, sd, rm);
+  };
 
-    // Determine leading zeros.
-    for (i = 0; str.charCodeAt(i) === 48;) ++i;
 
-    // Determine trailing zeros.
-    for (len = str.length; str.charCodeAt(len - 1) === 48;) --len;
-    str = str.slice(i, len);
+  /*
+   * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded
+   * to `precision` significant digits using rounding mode `rounding`.
+   *
+   * ECMAScript compliant.
+   *
+   *   pow(x, NaN)                           = NaN
+   *   pow(x, ±0)                            = 1
+
+   *   pow(NaN, non-zero)                    = NaN
+   *   pow(abs(x) > 1, +Infinity)            = +Infinity
+   *   pow(abs(x) > 1, -Infinity)            = +0
+   *   pow(abs(x) == 1, ±Infinity)           = NaN
+   *   pow(abs(x) < 1, +Infinity)            = +0
+   *   pow(abs(x) < 1, -Infinity)            = +Infinity
+   *   pow(+Infinity, y > 0)                 = +Infinity
+   *   pow(+Infinity, y < 0)                 = +0
+   *   pow(-Infinity, odd integer > 0)       = -Infinity
+   *   pow(-Infinity, even integer > 0)      = +Infinity
+   *   pow(-Infinity, odd integer < 0)       = -0
+   *   pow(-Infinity, even integer < 0)      = +0
+   *   pow(+0, y > 0)                        = +0
+   *   pow(+0, y < 0)                        = +Infinity
+   *   pow(-0, odd integer > 0)              = -0
+   *   pow(-0, even integer > 0)             = +0
+   *   pow(-0, odd integer < 0)              = -Infinity
+   *   pow(-0, even integer < 0)             = +Infinity
+   *   pow(finite x < 0, finite non-integer) = NaN
+   *
+   * For non-integer or very large exponents pow(x, y) is calculated using
+   *
+   *   x^y = exp(y*ln(x))
+   *
+   * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the
+   * probability of an incorrectly rounded result
+   * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14
+   * i.e. 1 in 250,000,000,000,000
+   *
+   * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place).
+   *
+   * y {number|string|Decimal} The power to which to raise this Decimal.
+   *
+   */
+  P.toPower = P.pow = function (y) {
+    var e, k, pr, r, rm, s,
+      x = this,
+      Ctor = x.constructor,
+      yn = +(y = new Ctor(y));
 
-    if (str) {
-      len -= i;
-      e = e - i - 1;
-      x.e = mathfloor(e / LOG_BASE);
-      x.d = [];
+    // Either ±Infinity, NaN or ±0?
+    if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));
 
-      // Transform base
+    x = new Ctor(x);
 
-      // e is the base 10 exponent.
-      // i is where to slice str to get the first word of the digits array.
-      i = (e + 1) % LOG_BASE;
-      if (e < 0) i += LOG_BASE;
+    if (x.eq(1)) return x;
 
-      if (i < len) {
-        if (i) x.d.push(+str.slice(0, i));
-        for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
-        str = str.slice(i);
-        i = LOG_BASE - str.length;
-      } else {
-        i -= len;
-      }
+    pr = Ctor.precision;
+    rm = Ctor.rounding;
 
-      for (; i--;) str += '0';
-      x.d.push(+str);
+    if (y.eq(1)) return finalise(x, pr, rm);
 
-      if (external && (x.e > MAX_E || x.e < -MAX_E)) throw Error(exponentOutOfRange + e);
-    } else {
+    // y exponent
+    e = mathfloor(y.e / LOG_BASE);
 
-      // Zero.
-      x.s = 0;
-      x.e = 0;
-      x.d = [0];
+    // If y is a small integer use the 'exponentiation by squaring' algorithm.
+    if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
+      r = intPow(Ctor, x, k, pr);
+      return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);
     }
 
-    return x;
-  }
+    s = x.s;
 
+    // if x is negative
+    if (s < 0) {
 
-  /*
-   * Round `x` to `sd` significant digits, using rounding mode `rm` if present (truncate otherwise).
-   */
-   function round(x, sd, rm) {
-    var i, j, k, n, rd, doRound, w, xdi,
-      xd = x.d;
+      // if y is not an integer
+      if (e < y.d.length - 1) return new Ctor(NaN);
 
-    // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
-    // w: the word of xd which contains the rounding digit, a base 1e7 number.
-    // xdi: the index of w within xd.
-    // n: the number of digits of w.
-    // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
-    // they had leading zeros)
-    // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
+      // Result is positive if x is negative and the last digit of integer y is even.
+      if ((y.d[e] & 1) == 0) s = 1;
+
+      // if x.eq(-1)
+      if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {
+        x.s = s;
+        return x;
+      }
+    }
 
-    // Get the length of the first word of the digits array xd.
-    for (n = 1, k = xd[0]; k >= 10; k /= 10) n++;
-    i = sd - n;
+    // Estimate result exponent.
+    // x^y = 10^e,  where e = y * log10(x)
+    // log10(x) = log10(x_significand) + x_exponent
+    // log10(x_significand) = ln(x_significand) / ln(10)
+    k = mathpow(+x, yn);
+    e = k == 0 || !isFinite(k)
+      ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1))
+      : new Ctor(k + '').e;
 
-    // Is the rounding digit in the first word of xd?
-    if (i < 0) {
-      i += LOG_BASE;
-      j = sd;
-      w = xd[xdi = 0];
-    } else {
-      xdi = Math.ceil((i + 1) / LOG_BASE);
-      k = xd.length;
-      if (xdi >= k) return x;
-      w = k = xd[xdi];
+    // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.
 
-      // Get the number of digits of w.
-      for (n = 1; k >= 10; k /= 10) n++;
+    // Overflow/underflow?
+    if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);
 
-      // Get the index of rd within w.
-      i %= LOG_BASE;
+    external = false;
+    Ctor.rounding = x.s = 1;
 
-      // Get the index of rd within w, adjusted for leading zeros.
-      // The number of leading zeros of w is given by LOG_BASE - n.
-      j = i - LOG_BASE + n;
-    }
+    // Estimate the extra guard digits needed to ensure five correct rounding digits from
+    // naturalLogarithm(x). Example of failure without these extra digits (precision: 10):
+    // new Decimal(2.32456).pow('2087987436534566.46411')
+    // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815
+    k = Math.min(12, (e + '').length);
 
-    if (rm !== void 0) {
-      k = mathpow(10, n - j - 1);
+    // r = x^y = exp(y*ln(x))
+    r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);
 
-      // Get the rounding digit at index j of w.
-      rd = w / k % 10 | 0;
+    // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)
+    if (r.d) {
 
-      // Are there any non-zero digits after the rounding digit?
-      doRound = sd < 0 || xd[xdi + 1] !== void 0 || w % k;
+      // Truncate to the required precision plus five rounding digits.
+      r = finalise(r, pr + 5, 1);
 
-      // The expression `w % mathpow(10, n - j - 1)` returns all the digits of w to the right of the
-      // digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression will give
-      // 714.
+      // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate
+      // the result.
+      if (checkRoundingDigits(r.d, pr, rm)) {
+        e = pr + 10;
 
-      doRound = rm < 4
-        ? (rd || doRound) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
-        : rd > 5 || rd == 5 && (rm == 4 || doRound || rm == 6 &&
+        // Truncate to the increased precision plus five rounding digits.
+        r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);
 
-          // Check whether the digit to the left of the rounding digit is odd.
-          ((i > 0 ? j > 0 ? w / mathpow(10, n - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
-            rm == (x.s < 0 ? 8 : 7));
+        // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).
+        if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {
+          r = finalise(r, pr + 1, 0);
+        }
+      }
     }
 
-    if (sd < 1 || !xd[0]) {
-      if (doRound) {
-        k = getBase10Exponent(x);
-        xd.length = 1;
+    r.s = s;
+    external = true;
+    Ctor.rounding = rm;
 
-        // Convert sd to decimal places.
-        sd = sd - k - 1;
+    return finalise(r, pr, rm);
+  };
 
-        // 1, 0.1, 0.01, 0.001, 0.0001 etc.
-        xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
-        x.e = mathfloor(-sd / LOG_BASE) || 0;
-      } else {
-        xd.length = 1;
 
-        // Zero.
-        xd[0] = x.e = x.s = 0;
-      }
+  /*
+   * Return a string representing the value of this Decimal rounded to `sd` significant digits
+   * using rounding mode `rounding`.
+   *
+   * Return exponential notation if `sd` is less than the number of digits necessary to represent
+   * the integer part of the value in normal notation.
+   *
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   */
+  P.toPrecision = function (sd, rm) {
+    var str,
+      x = this,
+      Ctor = x.constructor;
 
-      return x;
+    if (sd === void 0) {
+      str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
+    } else {
+      checkInt32(sd, 1, MAX_DIGITS);
+
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
+
+      x = finalise(new Ctor(x), sd, rm);
+      str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);
     }
 
-    // Remove excess digits.
-    if (i == 0) {
-      xd.length = xdi;
-      k = 1;
-      xdi--;
+    return x.isNeg() && !x.isZero() ? '-' + str : str;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
+   * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
+   * omitted.
+   *
+   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
+   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+   *
+   * 'toSD() digits out of range: {sd}'
+   * 'toSD() digits not an integer: {sd}'
+   * 'toSD() rounding mode not an integer: {rm}'
+   * 'toSD() rounding mode out of range: {rm}'
+   *
+   */
+  P.toSignificantDigits = P.toSD = function (sd, rm) {
+    var x = this,
+      Ctor = x.constructor;
+
+    if (sd === void 0) {
+      sd = Ctor.precision;
+      rm = Ctor.rounding;
     } else {
-      xd.length = xdi + 1;
-      k = mathpow(10, LOG_BASE - i);
+      checkInt32(sd, 1, MAX_DIGITS);
 
-      // E.g. 56700 becomes 56000 if 7 is the rounding digit.
-      // j > 0 means i > number of leading zeros of w.
-      xd[xdi] = j > 0 ? (w / mathpow(10, n - j) % mathpow(10, j) | 0) * k : 0;
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
     }
 
-    if (doRound) {
-      for (;;) {
+    return finalise(new Ctor(x), sd, rm);
+  };
 
-        // Is the digit to be rounded up in the first word of xd?
-        if (xdi == 0) {
-          if ((xd[0] += k) == BASE) {
-            xd[0] = 1;
-            ++x.e;
-          }
 
-          break;
+  /*
+   * Return a string representing the value of this Decimal.
+   *
+   * Return exponential notation if this Decimal has a positive exponent equal to or greater than
+   * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
+   *
+   */
+  P.toString = function () {
+    var x = this,
+      Ctor = x.constructor,
+      str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
+
+    return x.isNeg() && !x.isZero() ? '-' + str : str;
+  };
+
+
+  /*
+   * Return a new Decimal whose value is the value of this Decimal truncated to a whole number.
+   *
+   */
+  P.truncated = P.trunc = function () {
+    return finalise(new this.constructor(this), this.e + 1, 1);
+  };
+
+
+  /*
+   * Return a string representing the value of this Decimal.
+   * Unlike `toString`, negative zero will include the minus sign.
+   *
+   */
+  P.valueOf = P.toJSON = function () {
+    var x = this,
+      Ctor = x.constructor,
+      str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
+
+    return x.isNeg() ? '-' + str : str;
+  };
+
+
+  // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
+
+
+  /*
+   *  digitsToString           P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,
+   *                           finiteToString, naturalExponential, naturalLogarithm
+   *  checkInt32               P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,
+   *                           P.toPrecision, P.toSignificantDigits, toStringBinary, random
+   *  checkRoundingDigits      P.logarithm, P.toPower, naturalExponential, naturalLogarithm
+   *  convertBase              toStringBinary, parseOther
+   *  cos                      P.cos
+   *  divide                   P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,
+   *                           P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,
+   *                           P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,
+   *                           taylorSeries, atan2, parseOther
+   *  finalise                 P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,
+   *                           P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,
+   *                           P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,
+   *                           P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,
+   *                           P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,
+   *                           P.truncated, divide, getLn10, getPi, naturalExponential,
+   *                           naturalLogarithm, ceil, floor, round, trunc
+   *  finiteToString           P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,
+   *                           toStringBinary
+   *  getBase10Exponent        P.minus, P.plus, P.times, parseOther
+   *  getLn10                  P.logarithm, naturalLogarithm
+   *  getPi                    P.acos, P.asin, P.atan, toLessThanHalfPi, atan2
+   *  getPrecision             P.precision, P.toFraction
+   *  getZeroString            digitsToString, finiteToString
+   *  intPow                   P.toPower, parseOther
+   *  isOdd                    toLessThanHalfPi
+   *  maxOrMin                 max, min
+   *  naturalExponential       P.naturalExponential, P.toPower
+   *  naturalLogarithm         P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,
+   *                           P.toPower, naturalExponential
+   *  nonFiniteToString        finiteToString, toStringBinary
+   *  parseDecimal             Decimal
+   *  parseOther               Decimal
+   *  sin                      P.sin
+   *  taylorSeries             P.cosh, P.sinh, cos, sin
+   *  toLessThanHalfPi         P.cos, P.sin
+   *  toStringBinary           P.toBinary, P.toHexadecimal, P.toOctal
+   *  truncate                 intPow
+   *
+   *  Throws:                  P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,
+   *                           naturalLogarithm, config, parseOther, random, Decimal
+   */
+
+
+  function digitsToString(d) {
+    var i, k, ws,
+      indexOfLastWord = d.length - 1,
+      str = '',
+      w = d[0];
+
+    if (indexOfLastWord > 0) {
+      str += w;
+      for (i = 1; i < indexOfLastWord; i++) {
+        ws = d[i] + '';
+        k = LOG_BASE - ws.length;
+        if (k) str += getZeroString(k);
+        str += ws;
+      }
+
+      w = d[i];
+      ws = w + '';
+      k = LOG_BASE - ws.length;
+      if (k) str += getZeroString(k);
+    } else if (w === 0) {
+      return '0';
+    }
+
+    // Remove trailing zeros of last w.
+    for (; w % 10 === 0;) w /= 10;
+
+    return str + w;
+  }
+
+
+  function checkInt32(i, min, max) {
+    if (i !== ~~i || i < min || i > max) {
+      throw Error(invalidArgument + i);
+    }
+  }
+
+
+  /*
+   * Check 5 rounding digits if `repeating` is null, 4 otherwise.
+   * `repeating == null` if caller is `log` or `pow`,
+   * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.
+   */
+  function checkRoundingDigits(d, i, rm, repeating) {
+    var di, k, r, rd;
+
+    // Get the length of the first word of the array d.
+    for (k = d[0]; k >= 10; k /= 10) --i;
+
+    // Is the rounding digit in the first word of d?
+    if (--i < 0) {
+      i += LOG_BASE;
+      di = 0;
+    } else {
+      di = Math.ceil((i + 1) / LOG_BASE);
+      i %= LOG_BASE;
+    }
+
+    // i is the index (0 - 6) of the rounding digit.
+    // E.g. if within the word 3487563 the first rounding digit is 5,
+    // then i = 4, k = 1000, rd = 3487563 % 1000 = 563
+    k = mathpow(10, LOG_BASE - i);
+    rd = d[di] % k | 0;
+
+    if (repeating == null) {
+      if (i < 3) {
+        if (i == 0) rd = rd / 100 | 0;
+        else if (i == 1) rd = rd / 10 | 0;
+        r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;
+      } else {
+        r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) &&
+          (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 ||
+            (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;
+      }
+    } else {
+      if (i < 4) {
+        if (i == 0) rd = rd / 1000 | 0;
+        else if (i == 1) rd = rd / 100 | 0;
+        else if (i == 2) rd = rd / 10 | 0;
+        r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;
+      } else {
+        r = ((repeating || rm < 4) && rd + 1 == k ||
+        (!repeating && rm > 3) && rd + 1 == k / 2) &&
+          (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;
+      }
+    }
+
+    return r;
+  }
+
+
+  // Convert string of `baseIn` to an array of numbers of `baseOut`.
+  // Eg. convertBase('255', 10, 16) returns [15, 15].
+  // Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
+  function convertBase(str, baseIn, baseOut) {
+    var j,
+      arr = [0],
+      arrL,
+      i = 0,
+      strL = str.length;
+
+    for (; i < strL;) {
+      for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn;
+      arr[0] += NUMERALS.indexOf(str.charAt(i++));
+      for (j = 0; j < arr.length; j++) {
+        if (arr[j] > baseOut - 1) {
+          if (arr[j + 1] === void 0) arr[j + 1] = 0;
+          arr[j + 1] += arr[j] / baseOut | 0;
+          arr[j] %= baseOut;
+        }
+      }
+    }
+
+    return arr.reverse();
+  }
+
+
+  /*
+   * cos(x) = 1 - x^2/2! + x^4/4! - ...
+   * |x| < pi/2
+   *
+   */
+  function cosine(Ctor, x) {
+    var k, len, y;
+
+    if (x.isZero()) return x;
+
+    // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1
+    // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1
+
+    // Estimate the optimum number of times to use the argument reduction.
+    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));
+
+    // Reverse argument reduction
+    for (var i = k; i--;) {
+      var cos2x = x.times(x);
+      x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);
+    }
+
+    Ctor.precision -= k;
+
+    return x;
+  }
+
+
+  /*
+   * Perform division in the specified base.
+   */
+  var divide = (function () {
+
+    // Assumes non-zero x and k, and hence non-zero result.
+    function multiplyInteger(x, k, base) {
+      var temp,
+        carry = 0,
+        i = x.length;
+
+      for (x = x.slice(); i--;) {
+        temp = x[i] * k + carry;
+        x[i] = temp % base | 0;
+        carry = temp / base | 0;
+      }
+
+      if (carry) x.unshift(carry);
+
+      return x;
+    }
+
+    function compare(a, b, aL, bL) {
+      var i, r;
+
+      if (aL != bL) {
+        r = aL > bL ? 1 : -1;
+      } else {
+        for (i = r = 0; i < aL; i++) {
+          if (a[i] != b[i]) {
+            r = a[i] > b[i] ? 1 : -1;
+            break;
+          }
+        }
+      }
+
+      return r;
+    }
+
+    function subtract(a, b, aL, base) {
+      var i = 0;
+
+      // Subtract b from a.
+      for (; aL--;) {
+        a[aL] -= i;
+        i = a[aL] < b[aL] ? 1 : 0;
+        a[aL] = i * base + a[aL] - b[aL];
+      }
+
+      // Remove leading zeros.
+      for (; !a[0] && a.length > 1;) a.shift();
+    }
+
+    return function (x, y, pr, rm, dp, base) {
+      var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0,
+        yL, yz,
+        Ctor = x.constructor,
+        sign = x.s == y.s ? 1 : -1,
+        xd = x.d,
+        yd = y.d;
+
+      // Either NaN, Infinity or 0?
+      if (!xd || !xd[0] || !yd || !yd[0]) {
+
+        return new Ctor(// Return NaN if either NaN, or both Infinity or 0.
+          !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN :
+
+          // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.
+          xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);
+      }
+
+      if (base) {
+        logBase = 1;
+        e = x.e - y.e;
+      } else {
+        base = BASE;
+        logBase = LOG_BASE;
+        e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);
+      }
+
+      yL = yd.length;
+      xL = xd.length;
+      q = new Ctor(sign);
+      qd = q.d = [];
+
+      // Result exponent may be one less than e.
+      // The digit array of a Decimal from toStringBinary may have trailing zeros.
+      for (i = 0; yd[i] == (xd[i] || 0); i++);
+
+      if (yd[i] > (xd[i] || 0)) e--;
+
+      if (pr == null) {
+        sd = pr = Ctor.precision;
+        rm = Ctor.rounding;
+      } else if (dp) {
+        sd = pr + (x.e - y.e) + 1;
+      } else {
+        sd = pr;
+      }
+
+      if (sd < 0) {
+        qd.push(1);
+        more = true;
+      } else {
+
+        // Convert precision in number of base 10 digits to base 1e7 digits.
+        sd = sd / logBase + 2 | 0;
+        i = 0;
+
+        // divisor < 1e7
+        if (yL == 1) {
+          k = 0;
+          yd = yd[0];
+          sd++;
+
+          // k is the carry.
+          for (; (i < xL || k) && sd--; i++) {
+            t = k * base + (xd[i] || 0);
+            qd[i] = t / yd | 0;
+            k = t % yd | 0;
+          }
+
+          more = k || i < xL;
+
+        // divisor >= 1e7
+        } else {
+
+          // Normalise xd and yd so highest order digit of yd is >= base/2
+          k = base / (yd[0] + 1) | 0;
+
+          if (k > 1) {
+            yd = multiplyInteger(yd, k, base);
+            xd = multiplyInteger(xd, k, base);
+            yL = yd.length;
+            xL = xd.length;
+          }
+
+          xi = yL;
+          rem = xd.slice(0, yL);
+          remL = rem.length;
+
+          // Add zeros to make remainder as long as divisor.
+          for (; remL < yL;) rem[remL++] = 0;
+
+          yz = yd.slice();
+          yz.unshift(0);
+          yd0 = yd[0];
+
+          if (yd[1] >= base / 2) ++yd0;
+
+          do {
+            k = 0;
+
+            // Compare divisor and remainder.
+            cmp = compare(yd, rem, yL, remL);
+
+            // If divisor < remainder.
+            if (cmp < 0) {
+
+              // Calculate trial digit, k.
+              rem0 = rem[0];
+              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
+
+              // k will be how many times the divisor goes into the current remainder.
+              k = rem0 / yd0 | 0;
+
+              //  Algorithm:
+              //  1. product = divisor * trial digit (k)
+              //  2. if product > remainder: product -= divisor, k--
+              //  3. remainder -= product
+              //  4. if product was < remainder at 2:
+              //    5. compare new remainder and divisor
+              //    6. If remainder > divisor: remainder -= divisor, k++
+
+              if (k > 1) {
+                if (k >= base) k = base - 1;
+
+                // product = divisor * trial digit.
+                prod = multiplyInteger(yd, k, base);
+                prodL = prod.length;
+                remL = rem.length;
+
+                // Compare product and remainder.
+                cmp = compare(prod, rem, prodL, remL);
+
+                // product > remainder.
+                if (cmp == 1) {
+                  k--;
+
+                  // Subtract divisor from product.
+                  subtract(prod, yL < prodL ? yz : yd, prodL, base);
+                }
+              } else {
+
+                // cmp is -1.
+                // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
+                // to avoid it. If k is 1 there is a need to compare yd and rem again below.
+                if (k == 0) cmp = k = 1;
+                prod = yd.slice();
+              }
+
+              prodL = prod.length;
+              if (prodL < remL) prod.unshift(0);
+
+              // Subtract product from remainder.
+              subtract(rem, prod, remL, base);
+
+              // If product was < previous remainder.
+              if (cmp == -1) {
+                remL = rem.length;
+
+                // Compare divisor and new remainder.
+                cmp = compare(yd, rem, yL, remL);
+
+                // If divisor < new remainder, subtract divisor from remainder.
+                if (cmp < 1) {
+                  k++;
+
+                  // Subtract divisor from remainder.
+                  subtract(rem, yL < remL ? yz : yd, remL, base);
+                }
+              }
+
+              remL = rem.length;
+            } else if (cmp === 0) {
+              k++;
+              rem = [0];
+            }    // if cmp === 1, k will be 0
+
+            // Add the next digit, k, to the result array.
+            qd[i++] = k;
+
+            // Update the remainder.
+            if (cmp && rem[0]) {
+              rem[remL++] = xd[xi] || 0;
+            } else {
+              rem = [xd[xi]];
+              remL = 1;
+            }
+
+          } while ((xi++ < xL || rem[0] !== void 0) && sd--);
+
+          more = rem[0] !== void 0;
+        }
+
+        // Leading zero?
+        if (!qd[0]) qd.shift();
+      }
+
+      // logBase is 1 when divide is being used for base conversion.
+      if (logBase == 1) {
+        q.e = e;
+        inexact = more;
+      } else {
+
+        // To calculate q.e, first get the number of digits of qd[0].
+        for (i = 1, k = qd[0]; k >= 10; k /= 10) i++;
+        q.e = i + e * logBase - 1;
+
+        finalise(q, dp ? pr + q.e + 1 : pr, rm, more);
+      }
+
+      return q;
+    };
+  })();
+
+
+  /*
+   * Round `x` to `sd` significant digits using rounding mode `rm`.
+   * Check for over/under-flow.
+   */
+   function finalise(x, sd, rm, isTruncated) {
+    var digits, i, j, k, rd, roundUp, w, xd, xdi,
+      Ctor = x.constructor;
+
+    // Don't round if sd is null or undefined.
+    out: if (sd != null) {
+      xd = x.d;
+
+      // Infinity/NaN.
+      if (!xd) return x;
+
+      // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
+      // w: the word of xd containing rd, a base 1e7 number.
+      // xdi: the index of w within xd.
+      // digits: the number of digits of w.
+      // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
+      // they had leading zeros)
+      // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
+
+      // Get the length of the first word of the digits array xd.
+      for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;
+      i = sd - digits;
+
+      // Is the rounding digit in the first word of xd?
+      if (i < 0) {
+        i += LOG_BASE;
+        j = sd;
+        w = xd[xdi = 0];
+
+        // Get the rounding digit at index j of w.
+        rd = w / mathpow(10, digits - j - 1) % 10 | 0;
+      } else {
+        xdi = Math.ceil((i + 1) / LOG_BASE);
+        k = xd.length;
+        if (xdi >= k) {
+          if (isTruncated) {
+
+            // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.
+            for (; k++ <= xdi;) xd.push(0);
+            w = rd = 0;
+            digits = 1;
+            i %= LOG_BASE;
+            j = i - LOG_BASE + 1;
+          } else {
+            break out;
+          }
+        } else {
+          w = k = xd[xdi];
+
+          // Get the number of digits of w.
+          for (digits = 1; k >= 10; k /= 10) digits++;
+
+          // Get the index of rd within w.
+          i %= LOG_BASE;
+
+          // Get the index of rd within w, adjusted for leading zeros.
+          // The number of leading zeros of w is given by LOG_BASE - digits.
+          j = i - LOG_BASE + digits;
+
+          // Get the rounding digit at index j of w.
+          rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;
+        }
+      }
+
+      // Are there any non-zero digits after the rounding digit?
+      isTruncated = isTruncated || sd < 0 ||
+        xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));
+
+      // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right
+      // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression
+      // will give 714.
+
+      roundUp = rm < 4
+        ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+        : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 &&
+
+          // Check whether the digit to the left of the rounding digit is odd.
+          ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
+            rm == (x.s < 0 ? 8 : 7));
+
+      if (sd < 1 || !xd[0]) {
+        xd.length = 0;
+        if (roundUp) {
+
+          // Convert sd to decimal places.
+          sd -= x.e + 1;
+
+          // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+          xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
+          x.e = -sd || 0;
+        } else {
+
+          // Zero.
+          xd[0] = x.e = 0;
+        }
+
+        return x;
+      }
+
+      // Remove excess digits.
+      if (i == 0) {
+        xd.length = xdi;
+        k = 1;
+        xdi--;
+      } else {
+        xd.length = xdi + 1;
+        k = mathpow(10, LOG_BASE - i);
+
+        // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+        // j > 0 means i > number of leading zeros of w.
+        xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;
+      }
+
+      if (roundUp) {
+        for (;;) {
+
+          // Is the digit to be rounded up in the first word of xd?
+          if (xdi == 0) {
+
+            // i will be the length of xd[0] before k is added.
+            for (i = 1, j = xd[0]; j >= 10; j /= 10) i++;
+            j = xd[0] += k;
+            for (k = 1; j >= 10; j /= 10) k++;
+
+            // if i != k the length has increased.
+            if (i != k) {
+              x.e++;
+              if (xd[0] == BASE) xd[0] = 1;
+            }
+
+            break;
+          } else {
+            xd[xdi] += k;
+            if (xd[xdi] != BASE) break;
+            xd[xdi--] = 0;
+            k = 1;
+          }
+        }
+      }
+
+      // Remove trailing zeros.
+      for (i = xd.length; xd[--i] === 0;) xd.pop();
+    }
+
+    if (external) {
+
+      // Overflow?
+      if (x.e > Ctor.maxE) {
+
+        // Infinity.
+        x.d = null;
+        x.e = NaN;
+
+      // Underflow?
+      } else if (x.e < Ctor.minE) {
+
+        // Zero.
+        x.e = 0;
+        x.d = [0];
+        // Ctor.underflow = true;
+      } // else Ctor.underflow = false;
+    }
+
+    return x;
+  }
+
+
+  function finiteToString(x, isExp, sd) {
+    if (!x.isFinite()) return nonFiniteToString(x);
+    var k,
+      e = x.e,
+      str = digitsToString(x.d),
+      len = str.length;
+
+    if (isExp) {
+      if (sd && (k = sd - len) > 0) {
+        str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
+      } else if (len > 1) {
+        str = str.charAt(0) + '.' + str.slice(1);
+      }
+
+      str = str + (x.e < 0 ? 'e' : 'e+') + x.e;
+    } else if (e < 0) {
+      str = '0.' + getZeroString(-e - 1) + str;
+      if (sd && (k = sd - len) > 0) str += getZeroString(k);
+    } else if (e >= len) {
+      str += getZeroString(e + 1 - len);
+      if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
+    } else {
+      if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
+      if (sd && (k = sd - len) > 0) {
+        if (e + 1 === len) str += '.';
+        str += getZeroString(k);
+      }
+    }
+
+    return str;
+  }
+
+
+  // Calculate the base 10 exponent from the base 1e7 exponent.
+  function getBase10Exponent(digits, e) {
+    var w = digits[0];
+
+    // Add the number of digits of the first word of the digits array.
+    for ( e *= LOG_BASE; w >= 10; w /= 10) e++;
+    return e;
+  }
+
+
+  function getLn10(Ctor, sd, pr) {
+    if (sd > LN10_PRECISION) {
+
+      // Reset global state in case the exception is caught.
+      external = true;
+      if (pr) Ctor.precision = pr;
+      throw Error(precisionLimitExceeded);
+    }
+    return finalise(new Ctor(LN10), sd, 1, true);
+  }
+
+
+  function getPi(Ctor, sd, rm) {
+    if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);
+    return finalise(new Ctor(PI), sd, rm, true);
+  }
+
+
+  function getPrecision(digits) {
+    var w = digits.length - 1,
+      len = w * LOG_BASE + 1;
+
+    w = digits[w];
+
+    // If non-zero...
+    if (w) {
+
+      // Subtract the number of trailing zeros of the last word.
+      for (; w % 10 == 0; w /= 10) len--;
+
+      // Add the number of digits of the first word.
+      for (w = digits[0]; w >= 10; w /= 10) len++;
+    }
+
+    return len;
+  }
+
+
+  function getZeroString(k) {
+    var zs = '';
+    for (; k--;) zs += '0';
+    return zs;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an
+   * integer of type number.
+   *
+   * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.
+   *
+   */
+  function intPow(Ctor, x, n, pr) {
+    var isTruncated,
+      r = new Ctor(1),
+
+      // Max n of 9007199254740991 takes 53 loop iterations.
+      // Maximum digits array length; leaves [28, 34] guard digits.
+      k = Math.ceil(pr / LOG_BASE + 4);
+
+    external = false;
+
+    for (;;) {
+      if (n % 2) {
+        r = r.times(x);
+        if (truncate(r.d, k)) isTruncated = true;
+      }
+
+      n = mathfloor(n / 2);
+      if (n === 0) {
+
+        // To ensure correct rounding when r.d is truncated, increment the last word if it is zero.
+        n = r.d.length - 1;
+        if (isTruncated && r.d[n] === 0) ++r.d[n];
+        break;
+      }
+
+      x = x.times(x);
+      truncate(x.d, k);
+    }
+
+    external = true;
+
+    return r;
+  }
+
+
+  function isOdd(n) {
+    return n.d[n.d.length - 1] & 1;
+  }
+
+
+  /*
+   * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'.
+   */
+  function maxOrMin(Ctor, args, ltgt) {
+    var y,
+      x = new Ctor(args[0]),
+      i = 0;
+
+    for (; ++i < args.length;) {
+      y = new Ctor(args[i]);
+      if (!y.s) {
+        x = y;
+        break;
+      } else if (x[ltgt](y)) {
+        x = y;
+      }
+    }
+
+    return x;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant
+   * digits.
+   *
+   * Taylor/Maclaurin series.
+   *
+   * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
+   *
+   * Argument reduction:
+   *   Repeat x = x / 32, k += 5, until |x| < 0.1
+   *   exp(x) = exp(x / 2^k)^(2^k)
+   *
+   * Previously, the argument was initially reduced by
+   * exp(x) = exp(r) * 10^k  where r = x - k * ln10, k = floor(x / ln10)
+   * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
+   * found to be slower than just dividing repeatedly by 32 as above.
+   *
+   * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000
+   * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000
+   * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
+   *
+   *  exp(Infinity)  = Infinity
+   *  exp(-Infinity) = 0
+   *  exp(NaN)       = NaN
+   *  exp(±0)        = 1
+   *
+   *  exp(x) is non-terminating for any finite, non-zero x.
+   *
+   *  The result will always be correctly rounded.
+   *
+   */
+  function naturalExponential(x, sd) {
+    var denominator, guard, j, pow, sum, t, wpr,
+      rep = 0,
+      i = 0,
+      k = 0,
+      Ctor = x.constructor,
+      rm = Ctor.rounding,
+      pr = Ctor.precision;
+
+    // 0/NaN/Infinity?
+    if (!x.d || !x.d[0] || x.e > 17) {
+
+      return new Ctor(x.d
+        ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0
+        : x.s ? x.s < 0 ? 0 : x : 0 / 0);
+    }
+
+    if (sd == null) {
+      external = false;
+      wpr = pr;
+    } else {
+      wpr = sd;
+    }
+
+    t = new Ctor(0.03125);
+
+    // while abs(x) >= 0.1
+    while (x.e > -2) {
+
+      // x = x / 2^5
+      x = x.times(t);
+      k += 5;
+    }
+
+    // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision
+    // necessary to ensure the first 4 rounding digits are correct.
+    guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
+    wpr += guard;
+    denominator = pow = sum = new Ctor(1);
+    Ctor.precision = wpr;
+
+    for (;;) {
+      pow = finalise(pow.times(x), wpr, 1);
+      denominator = denominator.times(++i);
+      t = sum.plus(divide(pow, denominator, wpr, 1));
+
+      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
+        j = k;
+        while (j--) sum = finalise(sum.times(sum), wpr, 1);
+
+        // Check to see if the first 4 rounding digits are [49]999.
+        // If so, repeat the summation with a higher precision, otherwise
+        // e.g. with precision: 18, rounding: 1
+        // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)
+        // `wpr - guard` is the index of first rounding digit.
+        if (sd == null) {
+
+          if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
+            Ctor.precision = wpr += 10;
+            denominator = pow = t = new Ctor(1);
+            i = 0;
+            rep++;
+          } else {
+            return finalise(sum, Ctor.precision = pr, rm, external = true);
+          }
+        } else {
+          Ctor.precision = pr;
+          return sum;
+        }
+      }
+
+      sum = t;
+    }
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant
+   * digits.
+   *
+   *  ln(-n)        = NaN
+   *  ln(0)         = -Infinity
+   *  ln(-0)        = -Infinity
+   *  ln(1)         = 0
+   *  ln(Infinity)  = Infinity
+   *  ln(-Infinity) = NaN
+   *  ln(NaN)       = NaN
+   *
+   *  ln(n) (n != 1) is non-terminating.
+   *
+   */
+  function naturalLogarithm(y, sd) {
+    var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2,
+      n = 1,
+      guard = 10,
+      x = y,
+      xd = x.d,
+      Ctor = x.constructor,
+      rm = Ctor.rounding,
+      pr = Ctor.precision;
+
+    // Is x negative or Infinity, NaN, 0 or 1?
+    if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {
+      return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);
+    }
+
+    if (sd == null) {
+      external = false;
+      wpr = pr;
+    } else {
+      wpr = sd;
+    }
+
+    Ctor.precision = wpr += guard;
+    c = digitsToString(xd);
+    c0 = c.charAt(0);
+
+    if (Math.abs(e = x.e) < 1.5e15) {
+
+      // Argument reduction.
+      // The series converges faster the closer the argument is to 1, so using
+      // ln(a^b) = b * ln(a),   ln(a) = ln(a^b) / b
+      // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
+      // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
+      // later be divided by this number, then separate out the power of 10 using
+      // ln(a*10^b) = ln(a) + b*ln(10).
+
+      // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
+      //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
+      // max n is 6 (gives 0.7 - 1.3)
+      while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
+        x = x.times(y);
+        c = digitsToString(x.d);
+        c0 = c.charAt(0);
+        n++;
+      }
+
+      e = x.e;
+
+      if (c0 > 1) {
+        x = new Ctor('0.' + c);
+        e++;
+      } else {
+        x = new Ctor(c0 + '.' + c.slice(1));
+      }
+    } else {
+
+      // The argument reduction method above may result in overflow if the argument y is a massive
+      // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
+      // function using ln(x*10^e) = ln(x) + e*ln(10).
+      t = getLn10(Ctor, wpr + 2, pr).times(e + '');
+      x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
+      Ctor.precision = pr;
+
+      return sd == null ? finalise(x, pr, rm, external = true) : x;
+    }
+
+    // x1 is x reduced to a value near 1.
+    x1 = x;
+
+    // Taylor series.
+    // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
+    // where x = (y - 1)/(y + 1)    (|x| < 1)
+    sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1);
+    x2 = finalise(x.times(x), wpr, 1);
+    denominator = 3;
+
+    for (;;) {
+      numerator = finalise(numerator.times(x2), wpr, 1);
+      t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));
+
+      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
+        sum = sum.times(2);
+
+        // Reverse the argument reduction. Check that e is not 0 because, besides preventing an
+        // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.
+        if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
+        sum = divide(sum, new Ctor(n), wpr, 1);
+
+        // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has
+        // been repeated previously) and the first 4 rounding digits 9999?
+        // If so, restart the summation with a higher precision, otherwise
+        // e.g. with precision: 12, rounding: 1
+        // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.
+        // `wpr - guard` is the index of first rounding digit.
+        if (sd == null) {
+          if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
+            Ctor.precision = wpr += guard;
+            t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);
+            x2 = finalise(x.times(x), wpr, 1);
+            denominator = rep = 1;
+          } else {
+            return finalise(sum, Ctor.precision = pr, rm, external = true);
+          }
+        } else {
+          Ctor.precision = pr;
+          return sum;
+        }
+      }
+
+      sum = t;
+      denominator += 2;
+    }
+  }
+
+
+  // ±Infinity, NaN.
+  function nonFiniteToString(x) {
+    // Unsigned.
+    return String(x.s * x.s / 0);
+  }
+
+
+  /*
+   * Parse the value of a new Decimal `x` from string `str`.
+   */
+  function parseDecimal(x, str) {
+    var e, i, len;
+
+    // Decimal point?
+    if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+
+    // Exponential form?
+    if ((i = str.search(/e/i)) > 0) {
+
+      // Determine exponent.
+      if (e < 0) e = i;
+      e += +str.slice(i + 1);
+      str = str.substring(0, i);
+    } else if (e < 0) {
+
+      // Integer.
+      e = str.length;
+    }
+
+    // Determine leading zeros.
+    for (i = 0; str.charCodeAt(i) === 48; i++);
+
+    // Determine trailing zeros.
+    for (len = str.length; str.charCodeAt(len - 1) === 48; --len);
+    str = str.slice(i, len);
+
+    if (str) {
+      len -= i;
+      x.e = e = e - i - 1;
+      x.d = [];
+
+      // Transform base
+
+      // e is the base 10 exponent.
+      // i is where to slice str to get the first word of the digits array.
+      i = (e + 1) % LOG_BASE;
+      if (e < 0) i += LOG_BASE;
+
+      if (i < len) {
+        if (i) x.d.push(+str.slice(0, i));
+        for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
+        str = str.slice(i);
+        i = LOG_BASE - str.length;
+      } else {
+        i -= len;
+      }
+
+      for (; i--;) str += '0';
+      x.d.push(+str);
+
+      if (external) {
+
+        // Overflow?
+        if (x.e > x.constructor.maxE) {
+
+          // Infinity.
+          x.d = null;
+          x.e = NaN;
+
+        // Underflow?
+        } else if (x.e < x.constructor.minE) {
+
+          // Zero.
+          x.e = 0;
+          x.d = [0];
+          // x.constructor.underflow = true;
+        } // else x.constructor.underflow = false;
+      }
+    } else {
+
+      // Zero.
+      x.e = 0;
+      x.d = [0];
+    }
+
+    return x;
+  }
+
+
+  /*
+   * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.
+   */
+  function parseOther(x, str) {
+    var base, Ctor, divisor, i, isFloat, len, p, xd, xe;
+
+    if (str.indexOf('_') > -1) {
+      str = str.replace(/(\d)_(?=\d)/g, '$1');
+      if (isDecimal.test(str)) return parseDecimal(x, str);
+    } else if (str === 'Infinity' || str === 'NaN') {
+      if (!+str) x.s = NaN;
+      x.e = NaN;
+      x.d = null;
+      return x;
+    }
+
+    if (isHex.test(str))  {
+      base = 16;
+      str = str.toLowerCase();
+    } else if (isBinary.test(str))  {
+      base = 2;
+    } else if (isOctal.test(str))  {
+      base = 8;
+    } else {
+      throw Error(invalidArgument + str);
+    }
+
+    // Is there a binary exponent part?
+    i = str.search(/p/i);
+
+    if (i > 0) {
+      p = +str.slice(i + 1);
+      str = str.substring(2, i);
+    } else {
+      str = str.slice(2);
+    }
+
+    // Convert `str` as an integer then divide the result by `base` raised to a power such that the
+    // fraction part will be restored.
+    i = str.indexOf('.');
+    isFloat = i >= 0;
+    Ctor = x.constructor;
+
+    if (isFloat) {
+      str = str.replace('.', '');
+      len = str.length;
+      i = len - i;
+
+      // log[10](16) = 1.2041... , log[10](88) = 1.9444....
+      divisor = intPow(Ctor, new Ctor(base), i, i * 2);
+    }
+
+    xd = convertBase(str, base, BASE);
+    xe = xd.length - 1;
+
+    // Remove trailing zeros.
+    for (i = xe; xd[i] === 0; --i) xd.pop();
+    if (i < 0) return new Ctor(x.s * 0);
+    x.e = getBase10Exponent(xd, xe);
+    x.d = xd;
+    external = false;
+
+    // At what precision to perform the division to ensure exact conversion?
+    // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)
+    // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412
+    // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.
+    // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount
+    // Therefore using 4 * the number of digits of str will always be enough.
+    if (isFloat) x = divide(x, divisor, len * 4);
+
+    // Multiply by the binary exponent part if present.
+    if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));
+    external = true;
+
+    return x;
+  }
+
+
+  /*
+   * sin(x) = x - x^3/3! + x^5/5! - ...
+   * |x| < pi/2
+   *
+   */
+  function sine(Ctor, x) {
+    var k,
+      len = x.d.length;
+
+    if (len < 3) {
+      return x.isZero() ? x : taylorSeries(Ctor, 2, x, x);
+    }
+
+    // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)
+    // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)
+    // and  sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))
+
+    // Estimate the optimum number of times to use the argument reduction.
+    k = 1.4 * Math.sqrt(len);
+    k = k > 16 ? 16 : k | 0;
+
+    x = x.times(1 / tinyPow(5, k));
+    x = taylorSeries(Ctor, 2, x, x);
+
+    // Reverse argument reduction
+    var sin2_x,
+      d5 = new Ctor(5),
+      d16 = new Ctor(16),
+      d20 = new Ctor(20);
+    for (; k--;) {
+      sin2_x = x.times(x);
+      x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));
+    }
+
+    return x;
+  }
+
+
+  // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.
+  function taylorSeries(Ctor, n, x, y, isHyperbolic) {
+    var j, t, u, x2,
+      i = 1,
+      pr = Ctor.precision,
+      k = Math.ceil(pr / LOG_BASE);
+
+    external = false;
+    x2 = x.times(x);
+    u = new Ctor(y);
+
+    for (;;) {
+      t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);
+      u = isHyperbolic ? y.plus(t) : y.minus(t);
+      y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);
+      t = u.plus(y);
+
+      if (t.d[k] !== void 0) {
+        for (j = k; t.d[j] === u.d[j] && j--;);
+        if (j == -1) break;
+      }
+
+      j = u;
+      u = y;
+      y = t;
+      t = j;
+      i++;
+    }
+
+    external = true;
+    t.d.length = k + 1;
+
+    return t;
+  }
+
+
+  // Exponent e must be positive and non-zero.
+  function tinyPow(b, e) {
+    var n = b;
+    while (--e) n *= b;
+    return n;
+  }
+
+
+  // Return the absolute value of `x` reduced to less than or equal to half pi.
+  function toLessThanHalfPi(Ctor, x) {
+    var t,
+      isNeg = x.s < 0,
+      pi = getPi(Ctor, Ctor.precision, 1),
+      halfPi = pi.times(0.5);
+
+    x = x.abs();
+
+    if (x.lte(halfPi)) {
+      quadrant = isNeg ? 4 : 1;
+      return x;
+    }
+
+    t = x.divToInt(pi);
+
+    if (t.isZero()) {
+      quadrant = isNeg ? 3 : 2;
+    } else {
+      x = x.minus(t.times(pi));
+
+      // 0 <= x < pi
+      if (x.lte(halfPi)) {
+        quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1);
+        return x;
+      }
+
+      quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2);
+    }
+
+    return x.minus(pi).abs();
+  }
+
+
+  /*
+   * Return the value of Decimal `x` as a string in base `baseOut`.
+   *
+   * If the optional `sd` argument is present include a binary exponent suffix.
+   */
+  function toStringBinary(x, baseOut, sd, rm) {
+    var base, e, i, k, len, roundUp, str, xd, y,
+      Ctor = x.constructor,
+      isExp = sd !== void 0;
+
+    if (isExp) {
+      checkInt32(sd, 1, MAX_DIGITS);
+      if (rm === void 0) rm = Ctor.rounding;
+      else checkInt32(rm, 0, 8);
+    } else {
+      sd = Ctor.precision;
+      rm = Ctor.rounding;
+    }
+
+    if (!x.isFinite()) {
+      str = nonFiniteToString(x);
+    } else {
+      str = finiteToString(x);
+      i = str.indexOf('.');
+
+      // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:
+      // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))
+      // minBinaryExponent = floor(decimalExponent * log[2](10))
+      // log[2](10) = 3.321928094887362347870319429489390175864
+
+      if (isExp) {
+        base = 2;
+        if (baseOut == 16) {
+          sd = sd * 4 - 3;
+        } else if (baseOut == 8) {
+          sd = sd * 3 - 2;
+        }
+      } else {
+        base = baseOut;
+      }
+
+      // Convert the number as an integer then divide the result by its base raised to a power such
+      // that the fraction part will be restored.
+
+      // Non-integer.
+      if (i >= 0) {
+        str = str.replace('.', '');
+        y = new Ctor(1);
+        y.e = str.length - i;
+        y.d = convertBase(finiteToString(y), 10, base);
+        y.e = y.d.length;
+      }
+
+      xd = convertBase(str, 10, base);
+      e = len = xd.length;
+
+      // Remove trailing zeros.
+      for (; xd[--len] == 0;) xd.pop();
+
+      if (!xd[0]) {
+        str = isExp ? '0p+0' : '0';
+      } else {
+        if (i < 0) {
+          e--;
+        } else {
+          x = new Ctor(x);
+          x.d = xd;
+          x.e = e;
+          x = divide(x, y, sd, rm, 0, base);
+          xd = x.d;
+          e = x.e;
+          roundUp = inexact;
+        }
+
+        // The rounding digit, i.e. the digit after the digit that may be rounded up.
+        i = xd[sd];
+        k = base / 2;
+        roundUp = roundUp || xd[sd + 1] !== void 0;
+
+        roundUp = rm < 4
+          ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))
+          : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||
+            rm === (x.s < 0 ? 8 : 7));
+
+        xd.length = sd;
+
+        if (roundUp) {
+
+          // Rounding up may mean the previous digit has to be rounded up and so on.
+          for (; ++xd[--sd] > base - 1;) {
+            xd[sd] = 0;
+            if (!sd) {
+              ++e;
+              xd.unshift(1);
+            }
+          }
+        }
+
+        // Determine trailing zeros.
+        for (len = xd.length; !xd[len - 1]; --len);
+
+        // E.g. [4, 11, 15] becomes 4bf.
+        for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]);
+
+        // Add binary exponent suffix?
+        if (isExp) {
+          if (len > 1) {
+            if (baseOut == 16 || baseOut == 8) {
+              i = baseOut == 16 ? 4 : 3;
+              for (--len; len % i; len++) str += '0';
+              xd = convertBase(str, base, baseOut);
+              for (len = xd.length; !xd[len - 1]; --len);
+
+              // xd[0] will always be be 1
+              for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]);
+            } else {
+              str = str.charAt(0) + '.' + str.slice(1);
+            }
+          }
+
+          str =  str + (e < 0 ? 'p' : 'p+') + e;
+        } else if (e < 0) {
+          for (; ++e;) str = '0' + str;
+          str = '0.' + str;
+        } else {
+          if (++e > len) for (e -= len; e-- ;) str += '0';
+          else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);
+        }
+      }
+
+      str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;
+    }
+
+    return x.s < 0 ? '-' + str : str;
+  }
+
+
+  // Does not strip trailing zeros.
+  function truncate(arr, len) {
+    if (arr.length > len) {
+      arr.length = len;
+      return true;
+    }
+  }
+
+
+  // Decimal methods
+
+
+  /*
+   *  abs
+   *  acos
+   *  acosh
+   *  add
+   *  asin
+   *  asinh
+   *  atan
+   *  atanh
+   *  atan2
+   *  cbrt
+   *  ceil
+   *  clamp
+   *  clone
+   *  config
+   *  cos
+   *  cosh
+   *  div
+   *  exp
+   *  floor
+   *  hypot
+   *  ln
+   *  log
+   *  log2
+   *  log10
+   *  max
+   *  min
+   *  mod
+   *  mul
+   *  pow
+   *  random
+   *  round
+   *  set
+   *  sign
+   *  sin
+   *  sinh
+   *  sqrt
+   *  sub
+   *  sum
+   *  tan
+   *  tanh
+   *  trunc
+   */
+
+
+  /*
+   * Return a new Decimal whose value is the absolute value of `x`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function abs(x) {
+    return new this(x).abs();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the arccosine in radians of `x`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function acos(x) {
+    return new this(x).acos();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to
+   * `precision` significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function acosh(x) {
+    return new this(x).acosh();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   * y {number|string|Decimal}
+   *
+   */
+  function add(x, y) {
+    return new this(x).plus(y);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function asin(x) {
+    return new this(x).asin();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to
+   * `precision` significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function asinh(x) {
+    return new this(x).asinh();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function atan(x) {
+    return new this(x).atan();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to
+   * `precision` significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function atanh(x) {
+    return new this(x).atanh();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi
+   * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.
+   *
+   * Domain: [-Infinity, Infinity]
+   * Range: [-pi, pi]
+   *
+   * y {number|string|Decimal} The y-coordinate.
+   * x {number|string|Decimal} The x-coordinate.
+   *
+   * atan2(±0, -0)               = ±pi
+   * atan2(±0, +0)               = ±0
+   * atan2(±0, -x)               = ±pi for x > 0
+   * atan2(±0, x)                = ±0 for x > 0
+   * atan2(-y, ±0)               = -pi/2 for y > 0
+   * atan2(y, ±0)                = pi/2 for y > 0
+   * atan2(±y, -Infinity)        = ±pi for finite y > 0
+   * atan2(±y, +Infinity)        = ±0 for finite y > 0
+   * atan2(±Infinity, x)         = ±pi/2 for finite x
+   * atan2(±Infinity, -Infinity) = ±3*pi/4
+   * atan2(±Infinity, +Infinity) = ±pi/4
+   * atan2(NaN, x) = NaN
+   * atan2(y, NaN) = NaN
+   *
+   */
+  function atan2(y, x) {
+    y = new this(y);
+    x = new this(x);
+    var r,
+      pr = this.precision,
+      rm = this.rounding,
+      wpr = pr + 4;
+
+    // Either NaN
+    if (!y.s || !x.s) {
+      r = new this(NaN);
+
+    // Both ±Infinity
+    } else if (!y.d && !x.d) {
+      r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);
+      r.s = y.s;
+
+    // x is ±Infinity or y is ±0
+    } else if (!x.d || y.isZero()) {
+      r = x.s < 0 ? getPi(this, pr, rm) : new this(0);
+      r.s = y.s;
+
+    // y is ±Infinity or x is ±0
+    } else if (!y.d || x.isZero()) {
+      r = getPi(this, wpr, 1).times(0.5);
+      r.s = y.s;
+
+    // Both non-zero and finite
+    } else if (x.s < 0) {
+      this.precision = wpr;
+      this.rounding = 1;
+      r = this.atan(divide(y, x, wpr, 1));
+      x = getPi(this, wpr, 1);
+      this.precision = pr;
+      this.rounding = rm;
+      r = y.s < 0 ? r.minus(x) : r.plus(x);
+    } else {
+      r = this.atan(divide(y, x, wpr, 1));
+    }
+
+    return r;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function cbrt(x) {
+    return new this(x).cbrt();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function ceil(x) {
+    return finalise(x = new this(x), x.e + 1, 2);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is `x` clamped to the range delineated by `min` and `max`.
+   *
+   * x {number|string|Decimal}
+   * min {number|string|Decimal}
+   * max {number|string|Decimal}
+   *
+   */
+  function clamp(x, min, max) {
+    return new this(x).clamp(min, max);
+  }
+
+
+  /*
+   * Configure global settings for a Decimal constructor.
+   *
+   * `obj` is an object with one or more of the following properties,
+   *
+   *   precision  {number}
+   *   rounding   {number}
+   *   toExpNeg   {number}
+   *   toExpPos   {number}
+   *   maxE       {number}
+   *   minE       {number}
+   *   modulo     {number}
+   *   crypto     {boolean|number}
+   *   defaults   {true}
+   *
+   * E.g. Decimal.config({ precision: 20, rounding: 4 })
+   *
+   */
+  function config(obj) {
+    if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected');
+    var i, p, v,
+      useDefaults = obj.defaults === true,
+      ps = [
+        'precision', 1, MAX_DIGITS,
+        'rounding', 0, 8,
+        'toExpNeg', -EXP_LIMIT, 0,
+        'toExpPos', 0, EXP_LIMIT,
+        'maxE', 0, EXP_LIMIT,
+        'minE', -EXP_LIMIT, 0,
+        'modulo', 0, 9
+      ];
+
+    for (i = 0; i < ps.length; i += 3) {
+      if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];
+      if ((v = obj[p]) !== void 0) {
+        if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
+        else throw Error(invalidArgument + p + ': ' + v);
+      }
+    }
+
+    if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];
+    if ((v = obj[p]) !== void 0) {
+      if (v === true || v === false || v === 0 || v === 1) {
+        if (v) {
+          if (typeof crypto != 'undefined' && crypto &&
+            (crypto.getRandomValues || crypto.randomBytes)) {
+            this[p] = true;
+          } else {
+            throw Error(cryptoUnavailable);
+          }
         } else {
-          xd[xdi] += k;
-          if (xd[xdi] != BASE) break;
-          xd[xdi--] = 0;
-          k = 1;
+          this[p] = false;
         }
+      } else {
+        throw Error(invalidArgument + p + ': ' + v);
       }
     }
 
-    // Remove trailing zeros.
-    for (i = xd.length; xd[--i] === 0;) xd.pop();
+    return this;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function cos(x) {
+    return new this(x).cos();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function cosh(x) {
+    return new this(x).cosh();
+  }
+
+
+  /*
+   * Create and return a Decimal constructor with the same configuration properties as this Decimal
+   * constructor.
+   *
+   */
+  function clone(obj) {
+    var i, p, ps;
+
+    /*
+     * The Decimal constructor and exported function.
+     * Return a new Decimal instance.
+     *
+     * v {number|string|Decimal} A numeric value.
+     *
+     */
+    function Decimal(v) {
+      var e, i, t,
+        x = this;
+
+      // Decimal called without new.
+      if (!(x instanceof Decimal)) return new Decimal(v);
+
+      // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
+      // which points to Object.
+      x.constructor = Decimal;
+
+      // Duplicate.
+      if (isDecimalInstance(v)) {
+        x.s = v.s;
+
+        if (external) {
+          if (!v.d || v.e > Decimal.maxE) {
+
+            // Infinity.
+            x.e = NaN;
+            x.d = null;
+          } else if (v.e < Decimal.minE) {
+
+            // Zero.
+            x.e = 0;
+            x.d = [0];
+          } else {
+            x.e = v.e;
+            x.d = v.d.slice();
+          }
+        } else {
+          x.e = v.e;
+          x.d = v.d ? v.d.slice() : v.d;
+        }
+
+        return;
+      }
+
+      t = typeof v;
+
+      if (t === 'number') {
+        if (v === 0) {
+          x.s = 1 / v < 0 ? -1 : 1;
+          x.e = 0;
+          x.d = [0];
+          return;
+        }
+
+        if (v < 0) {
+          v = -v;
+          x.s = -1;
+        } else {
+          x.s = 1;
+        }
+
+        // Fast path for small integers.
+        if (v === ~~v && v < 1e7) {
+          for (e = 0, i = v; i >= 10; i /= 10) e++;
+
+          if (external) {
+            if (e > Decimal.maxE) {
+              x.e = NaN;
+              x.d = null;
+            } else if (e < Decimal.minE) {
+              x.e = 0;
+              x.d = [0];
+            } else {
+              x.e = e;
+              x.d = [v];
+            }
+          } else {
+            x.e = e;
+            x.d = [v];
+          }
+
+          return;
+
+        // Infinity, NaN.
+        } else if (v * 0 !== 0) {
+          if (!v) x.s = NaN;
+          x.e = NaN;
+          x.d = null;
+          return;
+        }
+
+        return parseDecimal(x, v.toString());
+
+      } else if (t !== 'string') {
+        throw Error(invalidArgument + v);
+      }
+
+      // Minus sign?
+      if ((i = v.charCodeAt(0)) === 45) {
+        v = v.slice(1);
+        x.s = -1;
+      } else {
+        // Plus sign?
+        if (i === 43) v = v.slice(1);
+        x.s = 1;
+      }
+
+      return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);
+    }
+
+    Decimal.prototype = P;
+
+    Decimal.ROUND_UP = 0;
+    Decimal.ROUND_DOWN = 1;
+    Decimal.ROUND_CEIL = 2;
+    Decimal.ROUND_FLOOR = 3;
+    Decimal.ROUND_HALF_UP = 4;
+    Decimal.ROUND_HALF_DOWN = 5;
+    Decimal.ROUND_HALF_EVEN = 6;
+    Decimal.ROUND_HALF_CEIL = 7;
+    Decimal.ROUND_HALF_FLOOR = 8;
+    Decimal.EUCLID = 9;
+
+    Decimal.config = Decimal.set = config;
+    Decimal.clone = clone;
+    Decimal.isDecimal = isDecimalInstance;
+
+    Decimal.abs = abs;
+    Decimal.acos = acos;
+    Decimal.acosh = acosh;        // ES6
+    Decimal.add = add;
+    Decimal.asin = asin;
+    Decimal.asinh = asinh;        // ES6
+    Decimal.atan = atan;
+    Decimal.atanh = atanh;        // ES6
+    Decimal.atan2 = atan2;
+    Decimal.cbrt = cbrt;          // ES6
+    Decimal.ceil = ceil;
+    Decimal.clamp = clamp;
+    Decimal.cos = cos;
+    Decimal.cosh = cosh;          // ES6
+    Decimal.div = div;
+    Decimal.exp = exp;
+    Decimal.floor = floor;
+    Decimal.hypot = hypot;        // ES6
+    Decimal.ln = ln;
+    Decimal.log = log;
+    Decimal.log10 = log10;        // ES6
+    Decimal.log2 = log2;          // ES6
+    Decimal.max = max;
+    Decimal.min = min;
+    Decimal.mod = mod;
+    Decimal.mul = mul;
+    Decimal.pow = pow;
+    Decimal.random = random;
+    Decimal.round = round;
+    Decimal.sign = sign;          // ES6
+    Decimal.sin = sin;
+    Decimal.sinh = sinh;          // ES6
+    Decimal.sqrt = sqrt;
+    Decimal.sub = sub;
+    Decimal.sum = sum;
+    Decimal.tan = tan;
+    Decimal.tanh = tanh;          // ES6
+    Decimal.trunc = trunc;        // ES6
+
+    if (obj === void 0) obj = {};
+    if (obj) {
+      if (obj.defaults !== true) {
+        ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];
+        for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
+      }
+    }
+
+    Decimal.config(obj);
+
+    return Decimal;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   * y {number|string|Decimal}
+   *
+   */
+  function div(x, y) {
+    return new this(x).div(y);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} The power to which to raise the base of the natural log.
+   *
+   */
+  function exp(x) {
+    return new this(x).exp();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function floor(x) {
+    return finalise(x = new this(x), x.e + 1, 3);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the square root of the sum of the squares of the arguments,
+   * rounded to `precision` significant digits using rounding mode `rounding`.
+   *
+   * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)
+   *
+   * arguments {number|string|Decimal}
+   *
+   */
+  function hypot() {
+    var i, n,
+      t = new this(0);
+
+    external = false;
+
+    for (i = 0; i < arguments.length;) {
+      n = new this(arguments[i++]);
+      if (!n.d) {
+        if (n.s) {
+          external = true;
+          return new this(1 / 0);
+        }
+        t = n;
+      } else if (t.d) {
+        t = t.plus(n.times(n));
+      }
+    }
+
+    external = true;
+
+    return t.sqrt();
+  }
+
+
+  /*
+   * Return true if object is a Decimal instance (where Decimal is any Decimal constructor),
+   * otherwise return false.
+   *
+   */
+  function isDecimalInstance(obj) {
+    return obj instanceof Decimal || obj && obj.toStringTag === tag || false;
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function ln(x) {
+    return new this(x).ln();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base
+   * is specified, rounded to `precision` significant digits using rounding mode `rounding`.
+   *
+   * log[y](x)
+   *
+   * x {number|string|Decimal} The argument of the logarithm.
+   * y {number|string|Decimal} The base of the logarithm.
+   *
+   */
+  function log(x, y) {
+    return new this(x).log(y);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function log2(x) {
+    return new this(x).log(2);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function log10(x) {
+    return new this(x).log(10);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the maximum of the arguments.
+   *
+   * arguments {number|string|Decimal}
+   *
+   */
+  function max() {
+    return maxOrMin(this, arguments, 'lt');
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the minimum of the arguments.
+   *
+   * arguments {number|string|Decimal}
+   *
+   */
+  function min() {
+    return maxOrMin(this, arguments, 'gt');
+  }
+
+
+  /*
+   * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
+   * using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   * y {number|string|Decimal}
+   *
+   */
+  function mod(x, y) {
+    return new this(x).mod(y);
+  }
+
+
+  /*
+   * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   * y {number|string|Decimal}
+   *
+   */
+  function mul(x, y) {
+    return new this(x).mul(y);
+  }
 
-    if (external && (x.e > MAX_E || x.e < -MAX_E)) {
-      throw Error(exponentOutOfRange + getBase10Exponent(x));
-    }
 
-    return x;
+  /*
+   * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} The base.
+   * y {number|string|Decimal} The exponent.
+   *
+   */
+  function pow(x, y) {
+    return new this(x).pow(y);
   }
 
 
-  function subtract(x, y) {
-    var d, e, i, j, k, len, xd, xe, xLTy, yd,
-      Ctor = x.constructor,
-      pr = Ctor.precision;
-
-    // Return y negated if x is zero.
-    // Return x if y is zero and x is non-zero.
-    if (!x.s || !y.s) {
-      if (y.s) y.s = -y.s;
-      else y = new Ctor(x);
-      return external ? round(y, pr) : y;
-    }
+  /*
+   * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with
+   * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros
+   * are produced).
+   *
+   * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.
+   *
+   */
+  function random(sd) {
+    var d, e, k, n,
+      i = 0,
+      r = new this(1),
+      rd = [];
 
-    xd = x.d;
-    yd = y.d;
+    if (sd === void 0) sd = this.precision;
+    else checkInt32(sd, 1, MAX_DIGITS);
 
-    // x and y are non-zero numbers with the same sign.
+    k = Math.ceil(sd / LOG_BASE);
 
-    e = y.e;
-    xe = x.e;
-    xd = xd.slice();
-    k = xe - e;
+    if (!this.crypto) {
+      for (; i < k;) rd[i++] = Math.random() * 1e7 | 0;
 
-    // If exponents differ...
-    if (k) {
-      xLTy = k < 0;
+    // Browsers supporting crypto.getRandomValues.
+    } else if (crypto.getRandomValues) {
+      d = crypto.getRandomValues(new Uint32Array(k));
 
-      if (xLTy) {
-        d = xd;
-        k = -k;
-        len = yd.length;
-      } else {
-        d = yd;
-        e = xe;
-        len = xd.length;
-      }
+      for (; i < k;) {
+        n = d[i];
 
-      // Numbers with massively different exponents would result in a very high number of zeros
-      // needing to be prepended, but this can be avoided while still ensuring correct rounding by
-      // limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
-      i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
+        // 0 <= n < 4294967296
+        // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).
+        if (n >= 4.29e9) {
+          d[i] = crypto.getRandomValues(new Uint32Array(1))[0];
+        } else {
 
-      if (k > i) {
-        k = i;
-        d.length = 1;
+          // 0 <= n <= 4289999999
+          // 0 <= (n % 1e7) <= 9999999
+          rd[i++] = n % 1e7;
+        }
       }
 
-      // Prepend zeros to equalise exponents.
-      d.reverse();
-      for (i = k; i--;) d.push(0);
-      d.reverse();
+    // Node.js supporting crypto.randomBytes.
+    } else if (crypto.randomBytes) {
 
-    // Base 1e7 exponents equal.
-    } else {
+      // buffer
+      d = crypto.randomBytes(k *= 4);
 
-      // Check digits to determine which is the bigger number.
+      for (; i < k;) {
 
-      i = xd.length;
-      len = yd.length;
-      xLTy = i < len;
-      if (xLTy) len = i;
+        // 0 <= n < 2147483648
+        n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24);
 
-      for (i = 0; i < len; i++) {
-        if (xd[i] != yd[i]) {
-          xLTy = xd[i] < yd[i];
-          break;
+        // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).
+        if (n >= 2.14e9) {
+          crypto.randomBytes(4).copy(d, i);
+        } else {
+
+          // 0 <= n <= 2139999999
+          // 0 <= (n % 1e7) <= 9999999
+          rd.push(n % 1e7);
+          i += 4;
         }
       }
 
-      k = 0;
-    }
-
-    if (xLTy) {
-      d = xd;
-      xd = yd;
-      yd = d;
-      y.s = -y.s;
+      i = k / 4;
+    } else {
+      throw Error(cryptoUnavailable);
     }
 
-    len = xd.length;
-
-    // Append zeros to xd if shorter.
-    // Don't add zeros to yd if shorter as subtraction only needs to start at yd length.
-    for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
-
-    // Subtract yd from xd.
-    for (i = yd.length; i > k;) {
-      if (xd[--i] < yd[i]) {
-        for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
-        --xd[j];
-        xd[i] += BASE;
-      }
+    k = rd[--i];
+    sd %= LOG_BASE;
 
-      xd[i] -= yd[i];
+    // Convert trailing digits to zeros according to sd.
+    if (k && sd) {
+      n = mathpow(10, LOG_BASE - sd);
+      rd[i] = (k / n | 0) * n;
     }
 
-    // Remove trailing zeros.
-    for (; xd[--len] === 0;) xd.pop();
-
-    // Remove leading zeros and adjust exponent accordingly.
-    for (; xd[0] === 0; xd.shift()) --e;
+    // Remove trailing words which are zero.
+    for (; rd[i] === 0; i--) rd.pop();
 
     // Zero?
-    if (!xd[0]) return new Ctor(0);
-
-    y.d = xd;
-    y.e = e;
-
-    //return external && xd.length >= pr / LOG_BASE ? round(y, pr) : y;
-    return external ? round(y, pr) : y;
-  }
-
-
-  function toString(x, isExp, sd) {
-    var k,
-      e = getBase10Exponent(x),
-      str = digitsToString(x.d),
-      len = str.length;
-
-    if (isExp) {
-      if (sd && (k = sd - len) > 0) {
-        str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
-      } else if (len > 1) {
-        str = str.charAt(0) + '.' + str.slice(1);
-      }
-
-      str = str + (e < 0 ? 'e' : 'e+') + e;
-    } else if (e < 0) {
-      str = '0.' + getZeroString(-e - 1) + str;
-      if (sd && (k = sd - len) > 0) str += getZeroString(k);
-    } else if (e >= len) {
-      str += getZeroString(e + 1 - len);
-      if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
+    if (i < 0) {
+      e = 0;
+      rd = [0];
     } else {
-      if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
-      if (sd && (k = sd - len) > 0) {
-        if (e + 1 === len) str += '.';
-        str += getZeroString(k);
-      }
-    }
+      e = -1;
 
-    return x.s < 0 ? '-' + str : str;
-  }
+      // Remove leading words which are zero and adjust exponent accordingly.
+      for (; rd[0] === 0; e -= LOG_BASE) rd.shift();
 
+      // Count the digits of the first word of rd to determine leading zeros.
+      for (k = 1, n = rd[0]; n >= 10; n /= 10) k++;
 
-  // Does not strip trailing zeros.
-  function truncate(arr, len) {
-    if (arr.length > len) {
-      arr.length = len;
-      return true;
+      // Adjust the exponent for leading zeros of the first word of rd.
+      if (k < LOG_BASE) e -= LOG_BASE - k;
     }
-  }
 
+    r.e = e;
+    r.d = rd;
 
-  // Decimal methods
+    return r;
+  }
 
 
   /*
-   *  clone
-   *  config/set
+   * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.
+   *
+   * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).
+   *
+   * x {number|string|Decimal}
+   *
    */
+  function round(x) {
+    return finalise(x = new this(x), x.e + 1, this.rounding);
+  }
 
 
   /*
-   * Create and return a Decimal constructor with the same configuration properties as this Decimal
-   * constructor.
+   * Return
+   *   1    if x > 0,
+   *  -1    if x < 0,
+   *   0    if x is 0,
+   *  -0    if x is -0,
+   *   NaN  otherwise
+   *
+   * x {number|string|Decimal}
    *
    */
-  function clone(obj) {
-    var i, p, ps;
-
-    /*
-     * The Decimal constructor and exported function.
-     * Return a new Decimal instance.
-     *
-     * value {number|string|Decimal} A numeric value.
-     *
-     */
-    function Decimal(value) {
-      var x = this;
-
-      // Decimal called without new.
-      if (!(x instanceof Decimal)) return new Decimal(value);
-
-      // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
-      // which points to Object.
-      x.constructor = Decimal;
-
-      // Duplicate.
-      if (value instanceof Decimal) {
-        x.s = value.s;
-        x.e = value.e;
-        x.d = (value = value.d) ? value.slice() : value;
-        return;
-      }
-
-      if (typeof value === 'number') {
+  function sign(x) {
+    x = new this(x);
+    return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN;
+  }
 
-        // Reject Infinity/NaN.
-        if (value * 0 !== 0) {
-          throw Error(invalidArgument + value);
-        }
 
-        if (value > 0) {
-          x.s = 1;
-        } else if (value < 0) {
-          value = -value;
-          x.s = -1;
-        } else {
-          x.s = 0;
-          x.e = 0;
-          x.d = [0];
-          return;
-        }
+  /*
+   * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits
+   * using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function sin(x) {
+    return new this(x).sin();
+  }
 
-        // Fast path for small integers.
-        if (value === ~~value && value < 1e7) {
-          x.e = 0;
-          x.d = [value];
-          return;
-        }
 
-        return parseDecimal(x, value.toString());
-      } else if (typeof value !== 'string') {
-        throw Error(invalidArgument + value);
-      }
+  /*
+   * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal} A value in radians.
+   *
+   */
+  function sinh(x) {
+    return new this(x).sinh();
+  }
 
-      // Minus sign?
-      if (value.charCodeAt(0) === 45) {
-        value = value.slice(1);
-        x.s = -1;
-      } else {
-        x.s = 1;
-      }
 
-      if (isDecimal.test(value)) parseDecimal(x, value);
-      else throw Error(invalidArgument + value);
-    }
+  /*
+   * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function sqrt(x) {
+    return new this(x).sqrt();
+  }
 
-    Decimal.prototype = P;
 
-    Decimal.ROUND_UP = 0;
-    Decimal.ROUND_DOWN = 1;
-    Decimal.ROUND_CEIL = 2;
-    Decimal.ROUND_FLOOR = 3;
-    Decimal.ROUND_HALF_UP = 4;
-    Decimal.ROUND_HALF_DOWN = 5;
-    Decimal.ROUND_HALF_EVEN = 6;
-    Decimal.ROUND_HALF_CEIL = 7;
-    Decimal.ROUND_HALF_FLOOR = 8;
+  /*
+   * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits
+   * using rounding mode `rounding`.
+   *
+   * x {number|string|Decimal}
+   * y {number|string|Decimal}
+   *
+   */
+  function sub(x, y) {
+    return new this(x).sub(y);
+  }
 
-    Decimal.clone = clone;
-    Decimal.config = Decimal.set = config;
 
-    if (obj === void 0) obj = {};
-    if (obj) {
-      ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'LN10'];
-      for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
-    }
+  /*
+   * Return a new Decimal whose value is the sum of the arguments, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
+   *
+   * Only the result is rounded, not the intermediate calculations.
+   *
+   * arguments {number|string|Decimal}
+   *
+   */
+  function sum() {
+    var i = 0,
+      args = arguments,
+      x = new this(args[i]);
 
-    Decimal.config(obj);
+    external = false;
+    for (; x.s && ++i < args.length;) x = x.plus(args[i]);
+    external = true;
 
-    return Decimal;
+    return finalise(x, this.precision, this.rounding);
   }
 
 
   /*
-   * Configure global settings for a Decimal constructor.
+   * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant
+   * digits using rounding mode `rounding`.
    *
-   * `obj` is an object with one or more of the following properties,
+   * x {number|string|Decimal} A value in radians.
    *
-   *   precision  {number}
-   *   rounding   {number}
-   *   toExpNeg   {number}
-   *   toExpPos   {number}
+   */
+  function tan(x) {
+    return new this(x).tan();
+  }
+
+
+  /*
+   * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`
+   * significant digits using rounding mode `rounding`.
    *
-   * E.g. Decimal.config({ precision: 20, rounding: 4 })
+   * x {number|string|Decimal} A value in radians.
    *
    */
-  function config(obj) {
-    if (!obj || typeof obj !== 'object') {
-      throw Error(decimalError + 'Object expected');
-    }
-    var i, p, v,
-      ps = [
-        'precision', 1, MAX_DIGITS,
-        'rounding', 0, 8,
-        'toExpNeg', -1 / 0, 0,
-        'toExpPos', 0, 1 / 0
-      ];
-
-    for (i = 0; i < ps.length; i += 3) {
-      if ((v = obj[p = ps[i]]) !== void 0) {
-        if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
-        else throw Error(invalidArgument + p + ': ' + v);
-      }
-    }
+  function tanh(x) {
+    return new this(x).tanh();
+  }
 
-    if ((v = obj[p = 'LN10']) !== void 0) {
-        if (v == Math.LN10) this[p] = new this(v);
-        else throw Error(invalidArgument + p + ': ' + v);
-    }
 
-    return this;
+  /*
+   * Return a new Decimal whose value is `x` truncated to an integer.
+   *
+   * x {number|string|Decimal}
+   *
+   */
+  function trunc(x) {
+    return finalise(x = new this(x), x.e + 1, 1);
   }
 
 
   // Create and configure initial Decimal constructor.
-  Decimal = clone(Decimal);
-
+  Decimal = clone(DEFAULTS);
+  Decimal.prototype.constructor = Decimal;
   Decimal['default'] = Decimal.Decimal = Decimal;
 
-  // Internal constant.
-  ONE = new Decimal(1);
+  // Create the internal constants from their string values.
+  LN10 = new Decimal(LN10);
+  PI = new Decimal(PI);
 
 
   // Export.
@@ -2000,15 +4910,25 @@
 
   // Node and other environments that support module.exports.
   } else if (typeof module != 'undefined' && module.exports) {
+    if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
+      P[Symbol['for']('nodejs.util.inspect.custom')] = P.toString;
+      P[Symbol.toStringTag] = 'Decimal';
+    }
+
     module.exports = Decimal;
 
-    // Browser.
+  // Browser.
   } else {
     if (!globalScope) {
-      globalScope = typeof self != 'undefined' && self && self.self == self
-        ? self : Function('return this')();
+      globalScope = typeof self != 'undefined' && self && self.self == self ? self : window;
     }
 
+    noConflict = globalScope.Decimal;
+    Decimal.noConflict = function () {
+      globalScope.Decimal = noConflict;
+      return Decimal;
+    };
+
     globalScope.Decimal = Decimal;
   }
-})(this);
+})(this);
\ No newline at end of file

From 8cb162fd9c2a7222ec9cf1d17d8100f3fa4143cd Mon Sep 17 00:00:00 2001
From: Dominik Z <dominykas.zubavicius@iovlabs.org>
Date: Fri, 31 May 2024 16:30:25 +0300
Subject: [PATCH 4/4] Update decimal.js to minified version

---
 .../entrypoints/rest/assets/static/decimal.js | 4937 +----------------
 1 file changed, 3 insertions(+), 4934 deletions(-)

diff --git a/internal/adapters/entrypoints/rest/assets/static/decimal.js b/internal/adapters/entrypoints/rest/assets/static/decimal.js
index 4a27c580..77615c1e 100644
--- a/internal/adapters/entrypoints/rest/assets/static/decimal.js
+++ b/internal/adapters/entrypoints/rest/assets/static/decimal.js
@@ -1,4934 +1,3 @@
-;(function (globalScope) {
-  'use strict';
-
-
-  /*!
-   *  decimal.js v10.4.3
-   *  An arbitrary-precision Decimal type for JavaScript.
-   *  https://github.com/MikeMcl/decimal.js
-   *  Copyright (c) 2022 Michael Mclaughlin <M8ch88l@gmail.com>
-   *  MIT Licence
-   */
-
-
-  // -----------------------------------  EDITABLE DEFAULTS  ------------------------------------ //
-
-
-    // The maximum exponent magnitude.
-    // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.
-  var EXP_LIMIT = 9e15,                      // 0 to 9e15
-
-    // The limit on the value of `precision`, and on the value of the first argument to
-    // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
-    MAX_DIGITS = 1e9,                        // 0 to 1e9
-
-    // Base conversion alphabet.
-    NUMERALS = '0123456789abcdef',
-
-    // The natural logarithm of 10 (1025 digits).
-    LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
-
-    // Pi (1025 digits).
-    PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
-
-
-    // The initial configuration properties of the Decimal constructor.
-    DEFAULTS = {
-
-      // These values must be integers within the stated ranges (inclusive).
-      // Most of these values can be changed at run-time using the `Decimal.config` method.
-
-      // The maximum number of significant digits of the result of a calculation or base conversion.
-      // E.g. `Decimal.config({ precision: 20 });`
-      precision: 20,                         // 1 to MAX_DIGITS
-
-      // The rounding mode used when rounding to `precision`.
-      //
-      // ROUND_UP         0 Away from zero.
-      // ROUND_DOWN       1 Towards zero.
-      // ROUND_CEIL       2 Towards +Infinity.
-      // ROUND_FLOOR      3 Towards -Infinity.
-      // ROUND_HALF_UP    4 Towards nearest neighbour. If equidistant, up.
-      // ROUND_HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
-      // ROUND_HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
-      // ROUND_HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
-      // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
-      //
-      // E.g.
-      // `Decimal.rounding = 4;`
-      // `Decimal.rounding = Decimal.ROUND_HALF_UP;`
-      rounding: 4,                           // 0 to 8
-
-      // The modulo mode used when calculating the modulus: a mod n.
-      // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
-      // The remainder (r) is calculated as: r = a - n * q.
-      //
-      // UP         0 The remainder is positive if the dividend is negative, else is negative.
-      // DOWN       1 The remainder has the same sign as the dividend (JavaScript %).
-      // FLOOR      3 The remainder has the same sign as the divisor (Python %).
-      // HALF_EVEN  6 The IEEE 754 remainder function.
-      // EUCLID     9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.
-      //
-      // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian
-      // division (9) are commonly used for the modulus operation. The other rounding modes can also
-      // be used, but they may not give useful results.
-      modulo: 1,                             // 0 to 9
-
-      // The exponent value at and beneath which `toString` returns exponential notation.
-      // JavaScript numbers: -7
-      toExpNeg: -7,                          // 0 to -EXP_LIMIT
-
-      // The exponent value at and above which `toString` returns exponential notation.
-      // JavaScript numbers: 21
-      toExpPos:  21,                         // 0 to EXP_LIMIT
-
-      // The minimum exponent value, beneath which underflow to zero occurs.
-      // JavaScript numbers: -324  (5e-324)
-      minE: -EXP_LIMIT,                      // -1 to -EXP_LIMIT
-
-      // The maximum exponent value, above which overflow to Infinity occurs.
-      // JavaScript numbers: 308  (1.7976931348623157e+308)
-      maxE: EXP_LIMIT,                       // 1 to EXP_LIMIT
-
-      // Whether to use cryptographically-secure random number generation, if available.
-      crypto: false                          // true/false
-    },
-
-
-  // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
-
-
-    Decimal, inexact, noConflict, quadrant,
-    external = true,
-
-    decimalError = '[DecimalError] ',
-    invalidArgument = decimalError + 'Invalid argument: ',
-    precisionLimitExceeded = decimalError + 'Precision limit exceeded',
-    cryptoUnavailable = decimalError + 'crypto unavailable',
-    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,
-
-    // Decimal.prototype object
-    P = { toStringTag: tag };
-
-
-  // Decimal prototype methods
-
-
-  /*
-   *  absoluteValue             abs
-   *  ceil
-   *  clampedTo                 clamp
-   *  comparedTo                cmp
-   *  cosine                    cos
-   *  cubeRoot                  cbrt
-   *  decimalPlaces             dp
-   *  dividedBy                 div
-   *  dividedToIntegerBy        divToInt
-   *  equals                    eq
-   *  floor
-   *  greaterThan               gt
-   *  greaterThanOrEqualTo      gte
-   *  hyperbolicCosine          cosh
-   *  hyperbolicSine            sinh
-   *  hyperbolicTangent         tanh
-   *  inverseCosine             acos
-   *  inverseHyperbolicCosine   acosh
-   *  inverseHyperbolicSine     asinh
-   *  inverseHyperbolicTangent  atanh
-   *  inverseSine               asin
-   *  inverseTangent            atan
-   *  isFinite
-   *  isInteger                 isInt
-   *  isNaN
-   *  isNegative                isNeg
-   *  isPositive                isPos
-   *  isZero
-   *  lessThan                  lt
-   *  lessThanOrEqualTo         lte
-   *  logarithm                 log
-   *  [maximum]                 [max]
-   *  [minimum]                 [min]
-   *  minus                     sub
-   *  modulo                    mod
-   *  naturalExponential        exp
-   *  naturalLogarithm          ln
-   *  negated                   neg
-   *  plus                      add
-   *  precision                 sd
-   *  round
-   *  sine                      sin
-   *  squareRoot                sqrt
-   *  tangent                   tan
-   *  times                     mul
-   *  toBinary
-   *  toDecimalPlaces           toDP
-   *  toExponential
-   *  toFixed
-   *  toFraction
-   *  toHexadecimal             toHex
-   *  toNearest
-   *  toNumber
-   *  toOctal
-   *  toPower                   pow
-   *  toPrecision
-   *  toSignificantDigits       toSD
-   *  toString
-   *  truncated                 trunc
-   *  valueOf                   toJSON
-   */
-
-
-  /*
-   * Return a new Decimal whose value is the absolute value of this Decimal.
-   *
-   */
-  P.absoluteValue = P.abs = function () {
-    var x = new this.constructor(this);
-    if (x.s < 0) x.s = 1;
-    return finalise(x);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
-   * direction of positive Infinity.
-   *
-   */
-  P.ceil = function () {
-    return finalise(new this.constructor(this), this.e + 1, 2);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal clamped to the range
-   * delineated by `min` and `max`.
-   *
-   * min {number|string|Decimal}
-   * max {number|string|Decimal}
-   *
-   */
-  P.clampedTo = P.clamp = function (min, max) {
-    var k,
-      x = this,
-      Ctor = x.constructor;
-    min = new Ctor(min);
-    max = new Ctor(max);
-    if (!min.s || !max.s) return new Ctor(NaN);
-    if (min.gt(max)) throw Error(invalidArgument + max);
-    k = x.cmp(min);
-    return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x);
-  };
-
-
-  /*
-   * Return
-   *   1    if the value of this Decimal is greater than the value of `y`,
-   *  -1    if the value of this Decimal is less than the value of `y`,
-   *   0    if they have the same value,
-   *   NaN  if the value of either Decimal is NaN.
-   *
-   */
-  P.comparedTo = P.cmp = function (y) {
-    var i, j, xdL, ydL,
-      x = this,
-      xd = x.d,
-      yd = (y = new x.constructor(y)).d,
-      xs = x.s,
-      ys = y.s;
-
-    // Either NaN or ±Infinity?
-    if (!xd || !yd) {
-      return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
-    }
-
-    // Either zero?
-    if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;
-
-    // Signs differ?
-    if (xs !== ys) return xs;
-
-    // Compare exponents.
-    if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
-
-    xdL = xd.length;
-    ydL = yd.length;
-
-    // Compare digit by digit.
-    for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
-      if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;
-    }
-
-    // Compare lengths.
-    return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the cosine of the value in radians of this Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-1, 1]
-   *
-   * cos(0)         = 1
-   * cos(-0)        = 1
-   * cos(Infinity)  = NaN
-   * cos(-Infinity) = NaN
-   * cos(NaN)       = NaN
-   *
-   */
-  P.cosine = P.cos = function () {
-    var pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.d) return new Ctor(NaN);
-
-    // cos(0) = cos(-0) = 1
-    if (!x.d[0]) return new Ctor(1);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
-    Ctor.rounding = 1;
-
-    x = cosine(Ctor, toLessThanHalfPi(Ctor, x));
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);
-  };
-
-
-  /*
-   *
-   * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to
-   * `precision` significant digits using rounding mode `rounding`.
-   *
-   *  cbrt(0)  =  0
-   *  cbrt(-0) = -0
-   *  cbrt(1)  =  1
-   *  cbrt(-1) = -1
-   *  cbrt(N)  =  N
-   *  cbrt(-I) = -I
-   *  cbrt(I)  =  I
-   *
-   * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))
-   *
-   */
-  P.cubeRoot = P.cbrt = function () {
-    var e, m, n, r, rep, s, sd, t, t3, t3plusx,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite() || x.isZero()) return new Ctor(x);
-    external = false;
-
-    // Initial estimate.
-    s = x.s * mathpow(x.s * x, 1 / 3);
-
-     // Math.cbrt underflow/overflow?
-     // Pass x to Math.pow as integer, then adjust the exponent of the result.
-    if (!s || Math.abs(s) == 1 / 0) {
-      n = digitsToString(x.d);
-      e = x.e;
-
-      // Adjust n exponent so it is a multiple of 3 away from x exponent.
-      if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');
-      s = mathpow(n, 1 / 3);
-
-      // Rarely, e may be one less than the result exponent value.
-      e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));
-
-      if (s == 1 / 0) {
-        n = '5e' + e;
-      } else {
-        n = s.toExponential();
-        n = n.slice(0, n.indexOf('e') + 1) + e;
-      }
-
-      r = new Ctor(n);
-      r.s = x.s;
-    } else {
-      r = new Ctor(s.toString());
-    }
-
-    sd = (e = Ctor.precision) + 3;
-
-    // Halley's method.
-    // TODO? Compare Newton's method.
-    for (;;) {
-      t = r;
-      t3 = t.times(t).times(t);
-      t3plusx = t3.plus(x);
-      r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);
-
-      // TODO? Replace with for-loop and checkRoundingDigits.
-      if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
-        n = n.slice(sd - 3, sd + 1);
-
-        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999
-        // , i.e. approaching a rounding boundary, continue the iteration.
-        if (n == '9999' || !rep && n == '4999') {
-
-          // On the first iteration only, check to see if rounding up gives the exact result as the
-          // nines may infinitely repeat.
-          if (!rep) {
-            finalise(t, e + 1, 0);
-
-            if (t.times(t).times(t).eq(x)) {
-              r = t;
-              break;
-            }
-          }
-
-          sd += 4;
-          rep = 1;
-        } else {
-
-          // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
-          // If not, then there are further digits and m will be truthy.
-          if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
-
-            // Truncate to the first rounding digit.
-            finalise(r, e + 1, 1);
-            m = !r.times(r).times(r).eq(x);
-          }
-
-          break;
-        }
-      }
-    }
-
-    external = true;
-
-    return finalise(r, e, Ctor.rounding, m);
-  };
-
-
-  /*
-   * Return the number of decimal places of the value of this Decimal.
-   *
-   */
-  P.decimalPlaces = P.dp = function () {
-    var w,
-      d = this.d,
-      n = NaN;
-
-    if (d) {
-      w = d.length - 1;
-      n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;
-
-      // Subtract the number of trailing zeros of the last word.
-      w = d[w];
-      if (w) for (; w % 10 == 0; w /= 10) n--;
-      if (n < 0) n = 0;
-    }
-
-    return n;
-  };
-
-
-  /*
-   *  n / 0 = I
-   *  n / N = N
-   *  n / I = 0
-   *  0 / n = 0
-   *  0 / 0 = N
-   *  0 / N = N
-   *  0 / I = 0
-   *  N / n = N
-   *  N / 0 = N
-   *  N / N = N
-   *  N / I = N
-   *  I / n = I
-   *  I / 0 = I
-   *  I / N = N
-   *  I / I = N
-   *
-   * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to
-   * `precision` significant digits using rounding mode `rounding`.
-   *
-   */
-  P.dividedBy = P.div = function (y) {
-    return divide(this, new this.constructor(y));
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the integer part of dividing the value of this Decimal
-   * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.
-   *
-   */
-  P.dividedToIntegerBy = P.divToInt = function (y) {
-    var x = this,
-      Ctor = x.constructor;
-    return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
-   *
-   */
-  P.equals = P.eq = function (y) {
-    return this.cmp(y) === 0;
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
-   * direction of negative Infinity.
-   *
-   */
-  P.floor = function () {
-    return finalise(new this.constructor(this), this.e + 1, 3);
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is greater than the value of `y`, otherwise return
-   * false.
-   *
-   */
-  P.greaterThan = P.gt = function (y) {
-    return this.cmp(y) > 0;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is greater than or equal to the value of `y`,
-   * otherwise return false.
-   *
-   */
-  P.greaterThanOrEqualTo = P.gte = function (y) {
-    var k = this.cmp(y);
-    return k == 1 || k === 0;
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this
-   * Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [1, Infinity]
-   *
-   * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...
-   *
-   * cosh(0)         = 1
-   * cosh(-0)        = 1
-   * cosh(Infinity)  = Infinity
-   * cosh(-Infinity) = Infinity
-   * cosh(NaN)       = NaN
-   *
-   *  x        time taken (ms)   result
-   * 1000      9                 9.8503555700852349694e+433
-   * 10000     25                4.4034091128314607936e+4342
-   * 100000    171               1.4033316802130615897e+43429
-   * 1000000   3817              1.5166076984010437725e+434294
-   * 10000000  abandoned after 2 minute wait
-   *
-   * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))
-   *
-   */
-  P.hyperbolicCosine = P.cosh = function () {
-    var k, n, pr, rm, len,
-      x = this,
-      Ctor = x.constructor,
-      one = new Ctor(1);
-
-    if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);
-    if (x.isZero()) return one;
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
-    Ctor.rounding = 1;
-    len = x.d.length;
-
-    // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1
-    // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))
-
-    // Estimate the optimum number of times to use the argument reduction.
-    // TODO? Estimation reused from cosine() and may not be optimal here.
-    if (len < 32) {
-      k = Math.ceil(len / 3);
-      n = (1 / tinyPow(4, k)).toString();
-    } else {
-      k = 16;
-      n = '2.3283064365386962890625e-10';
-    }
-
-    x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);
-
-    // Reverse argument reduction
-    var cosh2_x,
-      i = k,
-      d8 = new Ctor(8);
-    for (; i--;) {
-      cosh2_x = x.times(x);
-      x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));
-    }
-
-    return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this
-   * Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-Infinity, Infinity]
-   *
-   * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...
-   *
-   * sinh(0)         = 0
-   * sinh(-0)        = -0
-   * sinh(Infinity)  = Infinity
-   * sinh(-Infinity) = -Infinity
-   * sinh(NaN)       = NaN
-   *
-   * x        time taken (ms)
-   * 10       2 ms
-   * 100      5 ms
-   * 1000     14 ms
-   * 10000    82 ms
-   * 100000   886 ms            1.4033316802130615897e+43429
-   * 200000   2613 ms
-   * 300000   5407 ms
-   * 400000   8824 ms
-   * 500000   13026 ms          8.7080643612718084129e+217146
-   * 1000000  48543 ms
-   *
-   * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))
-   *
-   */
-  P.hyperbolicSine = P.sinh = function () {
-    var k, pr, rm, len,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite() || x.isZero()) return new Ctor(x);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
-    Ctor.rounding = 1;
-    len = x.d.length;
-
-    if (len < 3) {
-      x = taylorSeries(Ctor, 2, x, x, true);
-    } else {
-
-      // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))
-      // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))
-      // 3 multiplications and 1 addition
-
-      // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))
-      // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))
-      // 4 multiplications and 2 additions
-
-      // Estimate the optimum number of times to use the argument reduction.
-      k = 1.4 * Math.sqrt(len);
-      k = k > 16 ? 16 : k | 0;
-
-      x = x.times(1 / tinyPow(5, k));
-      x = taylorSeries(Ctor, 2, x, x, true);
-
-      // Reverse argument reduction
-      var sinh2_x,
-        d5 = new Ctor(5),
-        d16 = new Ctor(16),
-        d20 = new Ctor(20);
-      for (; k--;) {
-        sinh2_x = x.times(x);
-        x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));
-      }
-    }
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return finalise(x, pr, rm, true);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this
-   * Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-1, 1]
-   *
-   * tanh(x) = sinh(x) / cosh(x)
-   *
-   * tanh(0)         = 0
-   * tanh(-0)        = -0
-   * tanh(Infinity)  = 1
-   * tanh(-Infinity) = -1
-   * tanh(NaN)       = NaN
-   *
-   */
-  P.hyperbolicTangent = P.tanh = function () {
-    var pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite()) return new Ctor(x.s);
-    if (x.isZero()) return new Ctor(x);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + 7;
-    Ctor.rounding = 1;
-
-    return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of
-   * this Decimal.
-   *
-   * Domain: [-1, 1]
-   * Range: [0, pi]
-   *
-   * acos(x) = pi/2 - asin(x)
-   *
-   * acos(0)       = pi/2
-   * acos(-0)      = pi/2
-   * acos(1)       = 0
-   * acos(-1)      = pi
-   * acos(1/2)     = pi/3
-   * acos(-1/2)    = 2*pi/3
-   * acos(|x| > 1) = NaN
-   * acos(NaN)     = NaN
-   *
-   */
-  P.inverseCosine = P.acos = function () {
-    var halfPi,
-      x = this,
-      Ctor = x.constructor,
-      k = x.abs().cmp(1),
-      pr = Ctor.precision,
-      rm = Ctor.rounding;
-
-    if (k !== -1) {
-      return k === 0
-        // |x| is 1
-        ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)
-        // |x| > 1 or x is NaN
-        : new Ctor(NaN);
-    }
-
-    if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);
-
-    // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3
-
-    Ctor.precision = pr + 6;
-    Ctor.rounding = 1;
-
-    x = x.asin();
-    halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return halfPi.minus(x);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the
-   * value of this Decimal.
-   *
-   * Domain: [1, Infinity]
-   * Range: [0, Infinity]
-   *
-   * acosh(x) = ln(x + sqrt(x^2 - 1))
-   *
-   * acosh(x < 1)     = NaN
-   * acosh(NaN)       = NaN
-   * acosh(Infinity)  = Infinity
-   * acosh(-Infinity) = NaN
-   * acosh(0)         = NaN
-   * acosh(-0)        = NaN
-   * acosh(1)         = 0
-   * acosh(-1)        = NaN
-   *
-   */
-  P.inverseHyperbolicCosine = P.acosh = function () {
-    var pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);
-    if (!x.isFinite()) return new Ctor(x);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;
-    Ctor.rounding = 1;
-    external = false;
-
-    x = x.times(x).minus(1).sqrt().plus(x);
-
-    external = true;
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return x.ln();
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value
-   * of this Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-Infinity, Infinity]
-   *
-   * asinh(x) = ln(x + sqrt(x^2 + 1))
-   *
-   * asinh(NaN)       = NaN
-   * asinh(Infinity)  = Infinity
-   * asinh(-Infinity) = -Infinity
-   * asinh(0)         = 0
-   * asinh(-0)        = -0
-   *
-   */
-  P.inverseHyperbolicSine = P.asinh = function () {
-    var pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite() || x.isZero()) return new Ctor(x);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;
-    Ctor.rounding = 1;
-    external = false;
-
-    x = x.times(x).plus(1).sqrt().plus(x);
-
-    external = true;
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return x.ln();
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the
-   * value of this Decimal.
-   *
-   * Domain: [-1, 1]
-   * Range: [-Infinity, Infinity]
-   *
-   * atanh(x) = 0.5 * ln((1 + x) / (1 - x))
-   *
-   * atanh(|x| > 1)   = NaN
-   * atanh(NaN)       = NaN
-   * atanh(Infinity)  = NaN
-   * atanh(-Infinity) = NaN
-   * atanh(0)         = 0
-   * atanh(-0)        = -0
-   * atanh(1)         = Infinity
-   * atanh(-1)        = -Infinity
-   *
-   */
-  P.inverseHyperbolicTangent = P.atanh = function () {
-    var pr, rm, wpr, xsd,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite()) return new Ctor(NaN);
-    if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    xsd = x.sd();
-
-    if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);
-
-    Ctor.precision = wpr = xsd - x.e;
-
-    x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);
-
-    Ctor.precision = pr + 4;
-    Ctor.rounding = 1;
-
-    x = x.ln();
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return x.times(0.5);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this
-   * Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-pi/2, pi/2]
-   *
-   * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))
-   *
-   * asin(0)       = 0
-   * asin(-0)      = -0
-   * asin(1/2)     = pi/6
-   * asin(-1/2)    = -pi/6
-   * asin(1)       = pi/2
-   * asin(-1)      = -pi/2
-   * asin(|x| > 1) = NaN
-   * asin(NaN)     = NaN
-   *
-   * TODO? Compare performance of Taylor series.
-   *
-   */
-  P.inverseSine = P.asin = function () {
-    var halfPi, k,
-      pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (x.isZero()) return new Ctor(x);
-
-    k = x.abs().cmp(1);
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-
-    if (k !== -1) {
-
-      // |x| is 1
-      if (k === 0) {
-        halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
-        halfPi.s = x.s;
-        return halfPi;
-      }
-
-      // |x| > 1 or x is NaN
-      return new Ctor(NaN);
-    }
-
-    // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6
-
-    Ctor.precision = pr + 6;
-    Ctor.rounding = 1;
-
-    x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return x.times(2);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value
-   * of this Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-pi/2, pi/2]
-   *
-   * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
-   *
-   * atan(0)         = 0
-   * atan(-0)        = -0
-   * atan(1)         = pi/4
-   * atan(-1)        = -pi/4
-   * atan(Infinity)  = pi/2
-   * atan(-Infinity) = -pi/2
-   * atan(NaN)       = NaN
-   *
-   */
-  P.inverseTangent = P.atan = function () {
-    var i, j, k, n, px, t, r, wpr, x2,
-      x = this,
-      Ctor = x.constructor,
-      pr = Ctor.precision,
-      rm = Ctor.rounding;
-
-    if (!x.isFinite()) {
-      if (!x.s) return new Ctor(NaN);
-      if (pr + 4 <= PI_PRECISION) {
-        r = getPi(Ctor, pr + 4, rm).times(0.5);
-        r.s = x.s;
-        return r;
-      }
-    } else if (x.isZero()) {
-      return new Ctor(x);
-    } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {
-      r = getPi(Ctor, pr + 4, rm).times(0.25);
-      r.s = x.s;
-      return r;
-    }
-
-    Ctor.precision = wpr = pr + 10;
-    Ctor.rounding = 1;
-
-    // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);
-
-    // Argument reduction
-    // Ensure |x| < 0.42
-    // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
-
-    k = Math.min(28, wpr / LOG_BASE + 2 | 0);
-
-    for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));
-
-    external = false;
-
-    j = Math.ceil(wpr / LOG_BASE);
-    n = 1;
-    x2 = x.times(x);
-    r = new Ctor(x);
-    px = x;
-
-    // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
-    for (; i !== -1;) {
-      px = px.times(x2);
-      t = r.minus(px.div(n += 2));
-
-      px = px.times(x2);
-      r = t.plus(px.div(n += 2));
-
-      if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);
-    }
-
-    if (k) r = r.times(2 << (k - 1));
-
-    external = true;
-
-    return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is a finite number, otherwise return false.
-   *
-   */
-  P.isFinite = function () {
-    return !!this.d;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is an integer, otherwise return false.
-   *
-   */
-  P.isInteger = P.isInt = function () {
-    return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is NaN, otherwise return false.
-   *
-   */
-  P.isNaN = function () {
-    return !this.s;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is negative, otherwise return false.
-   *
-   */
-  P.isNegative = P.isNeg = function () {
-    return this.s < 0;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is positive, otherwise return false.
-   *
-   */
-  P.isPositive = P.isPos = function () {
-    return this.s > 0;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is 0 or -0, otherwise return false.
-   *
-   */
-  P.isZero = function () {
-    return !!this.d && this.d[0] === 0;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is less than `y`, otherwise return false.
-   *
-   */
-  P.lessThan = P.lt = function (y) {
-    return this.cmp(y) < 0;
-  };
-
-
-  /*
-   * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
-   *
-   */
-  P.lessThanOrEqualTo = P.lte = function (y) {
-    return this.cmp(y) < 1;
-  };
-
-
-  /*
-   * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * If no base is specified, return log[10](arg).
-   *
-   * log[base](arg) = ln(arg) / ln(base)
-   *
-   * The result will always be correctly rounded if the base of the log is 10, and 'almost always'
-   * otherwise:
-   *
-   * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen
-   * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error
-   * between the result and the correctly rounded result will be one ulp (unit in the last place).
-   *
-   * log[-b](a)       = NaN
-   * log[0](a)        = NaN
-   * log[1](a)        = NaN
-   * log[NaN](a)      = NaN
-   * log[Infinity](a) = NaN
-   * log[b](0)        = -Infinity
-   * log[b](-0)       = -Infinity
-   * log[b](-a)       = NaN
-   * log[b](1)        = 0
-   * log[b](Infinity) = Infinity
-   * log[b](NaN)      = NaN
-   *
-   * [base] {number|string|Decimal} The base of the logarithm.
-   *
-   */
-  P.logarithm = P.log = function (base) {
-    var isBase10, d, denominator, k, inf, num, sd, r,
-      arg = this,
-      Ctor = arg.constructor,
-      pr = Ctor.precision,
-      rm = Ctor.rounding,
-      guard = 5;
-
-    // Default base is 10.
-    if (base == null) {
-      base = new Ctor(10);
-      isBase10 = true;
-    } else {
-      base = new Ctor(base);
-      d = base.d;
-
-      // Return NaN if base is negative, or non-finite, or is 0 or 1.
-      if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);
-
-      isBase10 = base.eq(10);
-    }
-
-    d = arg.d;
-
-    // Is arg negative, non-finite, 0 or 1?
-    if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {
-      return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);
-    }
-
-    // The result will have a non-terminating decimal expansion if base is 10 and arg is not an
-    // integer power of 10.
-    if (isBase10) {
-      if (d.length > 1) {
-        inf = true;
-      } else {
-        for (k = d[0]; k % 10 === 0;) k /= 10;
-        inf = k !== 1;
-      }
-    }
-
-    external = false;
-    sd = pr + guard;
-    num = naturalLogarithm(arg, sd);
-    denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
-
-    // The result will have 5 rounding digits.
-    r = divide(num, denominator, sd, 1);
-
-    // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,
-    // calculate 10 further digits.
-    //
-    // If the result is known to have an infinite decimal expansion, repeat this until it is clear
-    // that the result is above or below the boundary. Otherwise, if after calculating the 10
-    // further digits, the last 14 are nines, round up and assume the result is exact.
-    // Also assume the result is exact if the last 14 are zero.
-    //
-    // Example of a result that will be incorrectly rounded:
-    // log[1048576](4503599627370502) = 2.60000000000000009610279511444746...
-    // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it
-    // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so
-    // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal
-    // place is still 2.6.
-    if (checkRoundingDigits(r.d, k = pr, rm)) {
-
-      do {
-        sd += 10;
-        num = naturalLogarithm(arg, sd);
-        denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
-        r = divide(num, denominator, sd, 1);
-
-        if (!inf) {
-
-          // Check for 14 nines from the 2nd rounding digit, as the first may be 4.
-          if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {
-            r = finalise(r, pr + 1, 0);
-          }
-
-          break;
-        }
-      } while (checkRoundingDigits(r.d, k += 10, rm));
-    }
-
-    external = true;
-
-    return finalise(r, pr, rm);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.
-   *
-   * arguments {number|string|Decimal}
-   *
-  P.max = function () {
-    Array.prototype.push.call(arguments, this);
-    return maxOrMin(this.constructor, arguments, 'lt');
-  };
-   */
-
-
-  /*
-   * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
-   *
-   * arguments {number|string|Decimal}
-   *
-  P.min = function () {
-    Array.prototype.push.call(arguments, this);
-    return maxOrMin(this.constructor, arguments, 'gt');
-  };
-   */
-
-
-  /*
-   *  n - 0 = n
-   *  n - N = N
-   *  n - I = -I
-   *  0 - n = -n
-   *  0 - 0 = 0
-   *  0 - N = N
-   *  0 - I = -I
-   *  N - n = N
-   *  N - 0 = N
-   *  N - N = N
-   *  N - I = N
-   *  I - n = I
-   *  I - 0 = I
-   *  I - N = N
-   *  I - I = N
-   *
-   * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   */
-  P.minus = P.sub = function (y) {
-    var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,
-      x = this,
-      Ctor = x.constructor;
-
-    y = new Ctor(y);
-
-    // If either is not finite...
-    if (!x.d || !y.d) {
-
-      // Return NaN if either is NaN.
-      if (!x.s || !y.s) y = new Ctor(NaN);
-
-      // Return y negated if x is finite and y is ±Infinity.
-      else if (x.d) y.s = -y.s;
-
-      // Return x if y is finite and x is ±Infinity.
-      // Return x if both are ±Infinity with different signs.
-      // Return NaN if both are ±Infinity with the same sign.
-      else y = new Ctor(y.d || x.s !== y.s ? x : NaN);
-
-      return y;
-    }
-
-    // If signs differ...
-    if (x.s != y.s) {
-      y.s = -y.s;
-      return x.plus(y);
-    }
-
-    xd = x.d;
-    yd = y.d;
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-
-    // If either is zero...
-    if (!xd[0] || !yd[0]) {
-
-      // Return y negated if x is zero and y is non-zero.
-      if (yd[0]) y.s = -y.s;
-
-      // Return x if y is zero and x is non-zero.
-      else if (xd[0]) y = new Ctor(x);
-
-      // Return zero if both are zero.
-      // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.
-      else return new Ctor(rm === 3 ? -0 : 0);
-
-      return external ? finalise(y, pr, rm) : y;
-    }
-
-    // x and y are finite, non-zero numbers with the same sign.
-
-    // Calculate base 1e7 exponents.
-    e = mathfloor(y.e / LOG_BASE);
-    xe = mathfloor(x.e / LOG_BASE);
-
-    xd = xd.slice();
-    k = xe - e;
-
-    // If base 1e7 exponents differ...
-    if (k) {
-      xLTy = k < 0;
-
-      if (xLTy) {
-        d = xd;
-        k = -k;
-        len = yd.length;
-      } else {
-        d = yd;
-        e = xe;
-        len = xd.length;
-      }
-
-      // Numbers with massively different exponents would result in a very high number of
-      // zeros needing to be prepended, but this can be avoided while still ensuring correct
-      // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
-      i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
-
-      if (k > i) {
-        k = i;
-        d.length = 1;
-      }
-
-      // Prepend zeros to equalise exponents.
-      d.reverse();
-      for (i = k; i--;) d.push(0);
-      d.reverse();
-
-    // Base 1e7 exponents equal.
-    } else {
-
-      // Check digits to determine which is the bigger number.
-
-      i = xd.length;
-      len = yd.length;
-      xLTy = i < len;
-      if (xLTy) len = i;
-
-      for (i = 0; i < len; i++) {
-        if (xd[i] != yd[i]) {
-          xLTy = xd[i] < yd[i];
-          break;
-        }
-      }
-
-      k = 0;
-    }
-
-    if (xLTy) {
-      d = xd;
-      xd = yd;
-      yd = d;
-      y.s = -y.s;
-    }
-
-    len = xd.length;
-
-    // Append zeros to `xd` if shorter.
-    // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.
-    for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
-
-    // Subtract yd from xd.
-    for (i = yd.length; i > k;) {
-
-      if (xd[--i] < yd[i]) {
-        for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
-        --xd[j];
-        xd[i] += BASE;
-      }
-
-      xd[i] -= yd[i];
-    }
-
-    // Remove trailing zeros.
-    for (; xd[--len] === 0;) xd.pop();
-
-    // Remove leading zeros and adjust exponent accordingly.
-    for (; xd[0] === 0; xd.shift()) --e;
-
-    // Zero?
-    if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0);
-
-    y.d = xd;
-    y.e = getBase10Exponent(xd, e);
-
-    return external ? finalise(y, pr, rm) : y;
-  };
-
-
-  /*
-   *   n % 0 =  N
-   *   n % N =  N
-   *   n % I =  n
-   *   0 % n =  0
-   *  -0 % n = -0
-   *   0 % 0 =  N
-   *   0 % N =  N
-   *   0 % I =  0
-   *   N % n =  N
-   *   N % 0 =  N
-   *   N % N =  N
-   *   N % I =  N
-   *   I % n =  N
-   *   I % 0 =  N
-   *   I % N =  N
-   *   I % I =  N
-   *
-   * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to
-   * `precision` significant digits using rounding mode `rounding`.
-   *
-   * The result depends on the modulo mode.
-   *
-   */
-  P.modulo = P.mod = function (y) {
-    var q,
-      x = this,
-      Ctor = x.constructor;
-
-    y = new Ctor(y);
-
-    // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.
-    if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);
-
-    // Return x if y is ±Infinity or x is ±0.
-    if (!y.d || x.d && !x.d[0]) {
-      return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);
-    }
-
-    // Prevent rounding of intermediate calculations.
-    external = false;
-
-    if (Ctor.modulo == 9) {
-
-      // Euclidian division: q = sign(y) * floor(x / abs(y))
-      // result = x - q * y    where  0 <= result < abs(y)
-      q = divide(x, y.abs(), 0, 3, 1);
-      q.s *= y.s;
-    } else {
-      q = divide(x, y, 0, Ctor.modulo, 1);
-    }
-
-    q = q.times(y);
-
-    external = true;
-
-    return x.minus(q);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the natural exponential of the value of this Decimal,
-   * i.e. the base e raised to the power the value of this Decimal, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   */
-  P.naturalExponential = P.exp = function () {
-    return naturalExponential(this);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
-   * rounded to `precision` significant digits using rounding mode `rounding`.
-   *
-   */
-  P.naturalLogarithm = P.ln = function () {
-    return naturalLogarithm(this);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
-   * -1.
-   *
-   */
-  P.negated = P.neg = function () {
-    var x = new this.constructor(this);
-    x.s = -x.s;
-    return finalise(x);
-  };
-
-
-  /*
-   *  n + 0 = n
-   *  n + N = N
-   *  n + I = I
-   *  0 + n = n
-   *  0 + 0 = 0
-   *  0 + N = N
-   *  0 + I = I
-   *  N + n = N
-   *  N + 0 = N
-   *  N + N = N
-   *  N + I = N
-   *  I + n = I
-   *  I + 0 = I
-   *  I + N = N
-   *  I + I = I
-   *
-   * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   */
-  P.plus = P.add = function (y) {
-    var carry, d, e, i, k, len, pr, rm, xd, yd,
-      x = this,
-      Ctor = x.constructor;
-
-    y = new Ctor(y);
-
-    // If either is not finite...
-    if (!x.d || !y.d) {
-
-      // Return NaN if either is NaN.
-      if (!x.s || !y.s) y = new Ctor(NaN);
-
-      // Return x if y is finite and x is ±Infinity.
-      // Return x if both are ±Infinity with the same sign.
-      // Return NaN if both are ±Infinity with different signs.
-      // Return y if x is finite and y is ±Infinity.
-      else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);
-
-      return y;
-    }
-
-     // If signs differ...
-    if (x.s != y.s) {
-      y.s = -y.s;
-      return x.minus(y);
-    }
-
-    xd = x.d;
-    yd = y.d;
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-
-    // If either is zero...
-    if (!xd[0] || !yd[0]) {
-
-      // Return x if y is zero.
-      // Return y if y is non-zero.
-      if (!yd[0]) y = new Ctor(x);
-
-      return external ? finalise(y, pr, rm) : y;
-    }
-
-    // x and y are finite, non-zero numbers with the same sign.
-
-    // Calculate base 1e7 exponents.
-    k = mathfloor(x.e / LOG_BASE);
-    e = mathfloor(y.e / LOG_BASE);
-
-    xd = xd.slice();
-    i = k - e;
-
-    // If base 1e7 exponents differ...
-    if (i) {
-
-      if (i < 0) {
-        d = xd;
-        i = -i;
-        len = yd.length;
-      } else {
-        d = yd;
-        e = k;
-        len = xd.length;
-      }
-
-      // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
-      k = Math.ceil(pr / LOG_BASE);
-      len = k > len ? k + 1 : len + 1;
-
-      if (i > len) {
-        i = len;
-        d.length = 1;
-      }
-
-      // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
-      d.reverse();
-      for (; i--;) d.push(0);
-      d.reverse();
-    }
-
-    len = xd.length;
-    i = yd.length;
-
-    // If yd is longer than xd, swap xd and yd so xd points to the longer array.
-    if (len - i < 0) {
-      i = len;
-      d = yd;
-      yd = xd;
-      xd = d;
-    }
-
-    // Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
-    for (carry = 0; i;) {
-      carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
-      xd[i] %= BASE;
-    }
-
-    if (carry) {
-      xd.unshift(carry);
-      ++e;
-    }
-
-    // Remove trailing zeros.
-    // No need to check for zero, as +x + +y != 0 && -x + -y != 0
-    for (len = xd.length; xd[--len] == 0;) xd.pop();
-
-    y.d = xd;
-    y.e = getBase10Exponent(xd, e);
-
-    return external ? finalise(y, pr, rm) : y;
-  };
-
-
-  /*
-   * Return the number of significant digits of the value of this Decimal.
-   *
-   * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
-   *
-   */
-  P.precision = P.sd = function (z) {
-    var k,
-      x = this;
-
-    if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
-
-    if (x.d) {
-      k = getPrecision(x.d);
-      if (z && x.e + 1 > k) k = x.e + 1;
-    } else {
-      k = NaN;
-    }
-
-    return k;
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
-   * rounding mode `rounding`.
-   *
-   */
-  P.round = function () {
-    var x = this,
-      Ctor = x.constructor;
-
-    return finalise(new Ctor(x), x.e + 1, Ctor.rounding);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the sine of the value in radians of this Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-1, 1]
-   *
-   * sin(x) = x - x^3/3! + x^5/5! - ...
-   *
-   * sin(0)         = 0
-   * sin(-0)        = -0
-   * sin(Infinity)  = NaN
-   * sin(-Infinity) = NaN
-   * sin(NaN)       = NaN
-   *
-   */
-  P.sine = P.sin = function () {
-    var pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite()) return new Ctor(NaN);
-    if (x.isZero()) return new Ctor(x);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
-    Ctor.rounding = 1;
-
-    x = sine(Ctor, toLessThanHalfPi(Ctor, x));
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   *  sqrt(-n) =  N
-   *  sqrt(N)  =  N
-   *  sqrt(-I) =  N
-   *  sqrt(I)  =  I
-   *  sqrt(0)  =  0
-   *  sqrt(-0) = -0
-   *
-   */
-  P.squareRoot = P.sqrt = function () {
-    var m, n, sd, r, rep, t,
-      x = this,
-      d = x.d,
-      e = x.e,
-      s = x.s,
-      Ctor = x.constructor;
-
-    // Negative/NaN/Infinity/zero?
-    if (s !== 1 || !d || !d[0]) {
-      return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);
-    }
-
-    external = false;
-
-    // Initial estimate.
-    s = Math.sqrt(+x);
-
-    // Math.sqrt underflow/overflow?
-    // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
-    if (s == 0 || s == 1 / 0) {
-      n = digitsToString(d);
-
-      if ((n.length + e) % 2 == 0) n += '0';
-      s = Math.sqrt(n);
-      e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
-
-      if (s == 1 / 0) {
-        n = '5e' + e;
-      } else {
-        n = s.toExponential();
-        n = n.slice(0, n.indexOf('e') + 1) + e;
-      }
-
-      r = new Ctor(n);
-    } else {
-      r = new Ctor(s.toString());
-    }
-
-    sd = (e = Ctor.precision) + 3;
-
-    // Newton-Raphson iteration.
-    for (;;) {
-      t = r;
-      r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);
-
-      // TODO? Replace with for-loop and checkRoundingDigits.
-      if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
-        n = n.slice(sd - 3, sd + 1);
-
-        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
-        // 4999, i.e. approaching a rounding boundary, continue the iteration.
-        if (n == '9999' || !rep && n == '4999') {
-
-          // On the first iteration only, check to see if rounding up gives the exact result as the
-          // nines may infinitely repeat.
-          if (!rep) {
-            finalise(t, e + 1, 0);
-
-            if (t.times(t).eq(x)) {
-              r = t;
-              break;
-            }
-          }
-
-          sd += 4;
-          rep = 1;
-        } else {
-
-          // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
-          // If not, then there are further digits and m will be truthy.
-          if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
-
-            // Truncate to the first rounding digit.
-            finalise(r, e + 1, 1);
-            m = !r.times(r).eq(x);
-          }
-
-          break;
-        }
-      }
-    }
-
-    external = true;
-
-    return finalise(r, e, Ctor.rounding, m);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the tangent of the value in radians of this Decimal.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-Infinity, Infinity]
-   *
-   * tan(0)         = 0
-   * tan(-0)        = -0
-   * tan(Infinity)  = NaN
-   * tan(-Infinity) = NaN
-   * tan(NaN)       = NaN
-   *
-   */
-  P.tangent = P.tan = function () {
-    var pr, rm,
-      x = this,
-      Ctor = x.constructor;
-
-    if (!x.isFinite()) return new Ctor(NaN);
-    if (x.isZero()) return new Ctor(x);
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-    Ctor.precision = pr + 10;
-    Ctor.rounding = 1;
-
-    x = x.sin();
-    x.s = 1;
-    x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);
-
-    Ctor.precision = pr;
-    Ctor.rounding = rm;
-
-    return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);
-  };
-
-
-  /*
-   *  n * 0 = 0
-   *  n * N = N
-   *  n * I = I
-   *  0 * n = 0
-   *  0 * 0 = 0
-   *  0 * N = N
-   *  0 * I = N
-   *  N * n = N
-   *  N * 0 = N
-   *  N * N = N
-   *  N * I = N
-   *  I * n = I
-   *  I * 0 = N
-   *  I * N = N
-   *  I * I = I
-   *
-   * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   */
-  P.times = P.mul = function (y) {
-    var carry, e, i, k, r, rL, t, xdL, ydL,
-      x = this,
-      Ctor = x.constructor,
-      xd = x.d,
-      yd = (y = new Ctor(y)).d;
-
-    y.s *= x.s;
-
-     // If either is NaN, ±Infinity or ±0...
-    if (!xd || !xd[0] || !yd || !yd[0]) {
-
-      return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd
-
-        // Return NaN if either is NaN.
-        // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.
-        ? NaN
-
-        // Return ±Infinity if either is ±Infinity.
-        // Return ±0 if either is ±0.
-        : !xd || !yd ? y.s / 0 : y.s * 0);
-    }
-
-    e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);
-    xdL = xd.length;
-    ydL = yd.length;
-
-    // Ensure xd points to the longer array.
-    if (xdL < ydL) {
-      r = xd;
-      xd = yd;
-      yd = r;
-      rL = xdL;
-      xdL = ydL;
-      ydL = rL;
-    }
-
-    // Initialise the result array with zeros.
-    r = [];
-    rL = xdL + ydL;
-    for (i = rL; i--;) r.push(0);
-
-    // Multiply!
-    for (i = ydL; --i >= 0;) {
-      carry = 0;
-      for (k = xdL + i; k > i;) {
-        t = r[k] + yd[i] * xd[k - i - 1] + carry;
-        r[k--] = t % BASE | 0;
-        carry = t / BASE | 0;
-      }
-
-      r[k] = (r[k] + carry) % BASE | 0;
-    }
-
-    // Remove trailing zeros.
-    for (; !r[--rL];) r.pop();
-
-    if (carry) ++e;
-    else r.shift();
-
-    y.d = r;
-    y.e = getBase10Exponent(r, e);
-
-    return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal in base 2, round to `sd` significant
-   * digits using rounding mode `rm`.
-   *
-   * If the optional `sd` argument is present then return binary exponential notation.
-   *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toBinary = function (sd, rm) {
-    return toStringBinary(this, 2, sd, rm);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
-   * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
-   *
-   * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
-   *
-   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toDecimalPlaces = P.toDP = function (dp, rm) {
-    var x = this,
-      Ctor = x.constructor;
-
-    x = new Ctor(x);
-    if (dp === void 0) return x;
-
-    checkInt32(dp, 0, MAX_DIGITS);
-
-    if (rm === void 0) rm = Ctor.rounding;
-    else checkInt32(rm, 0, 8);
-
-    return finalise(x, dp + x.e + 1, rm);
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal in exponential notation rounded to
-   * `dp` fixed decimal places using rounding mode `rounding`.
-   *
-   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toExponential = function (dp, rm) {
-    var str,
-      x = this,
-      Ctor = x.constructor;
-
-    if (dp === void 0) {
-      str = finiteToString(x, true);
-    } else {
-      checkInt32(dp, 0, MAX_DIGITS);
-
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
-
-      x = finalise(new Ctor(x), dp + 1, rm);
-      str = finiteToString(x, true, dp + 1);
-    }
-
-    return x.isNeg() && !x.isZero() ? '-' + str : str;
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal in normal (fixed-point) notation to
-   * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
-   * omitted.
-   *
-   * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
-   *
-   * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
-   * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
-   * (-0).toFixed(3) is '0.000'.
-   * (-0.5).toFixed(0) is '-0'.
-   *
-   */
-  P.toFixed = function (dp, rm) {
-    var str, y,
-      x = this,
-      Ctor = x.constructor;
-
-    if (dp === void 0) {
-      str = finiteToString(x);
-    } else {
-      checkInt32(dp, 0, MAX_DIGITS);
-
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
-
-      y = finalise(new Ctor(x), dp + x.e + 1, rm);
-      str = finiteToString(y, false, dp + y.e + 1);
-    }
-
-    // To determine whether to add the minus sign look at the value before it was rounded,
-    // i.e. look at `x` rather than `y`.
-    return x.isNeg() && !x.isZero() ? '-' + str : str;
-  };
-
-
-  /*
-   * Return an array representing the value of this Decimal as a simple fraction with an integer
-   * numerator and an integer denominator.
-   *
-   * The denominator will be a positive non-zero value less than or equal to the specified maximum
-   * denominator. If a maximum denominator is not specified, the denominator will be the lowest
-   * value necessary to represent the number exactly.
-   *
-   * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity.
-   *
-   */
-  P.toFraction = function (maxD) {
-    var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r,
-      x = this,
-      xd = x.d,
-      Ctor = x.constructor;
-
-    if (!xd) return new Ctor(x);
-
-    n1 = d0 = new Ctor(1);
-    d1 = n0 = new Ctor(0);
-
-    d = new Ctor(d1);
-    e = d.e = getPrecision(xd) - x.e - 1;
-    k = e % LOG_BASE;
-    d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);
-
-    if (maxD == null) {
-
-      // d is 10**e, the minimum max-denominator needed.
-      maxD = e > 0 ? d : n1;
-    } else {
-      n = new Ctor(maxD);
-      if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);
-      maxD = n.gt(d) ? (e > 0 ? d : n1) : n;
-    }
-
-    external = false;
-    n = new Ctor(digitsToString(xd));
-    pr = Ctor.precision;
-    Ctor.precision = e = xd.length * LOG_BASE * 2;
-
-    for (;;)  {
-      q = divide(n, d, 0, 1, 1);
-      d2 = d0.plus(q.times(d1));
-      if (d2.cmp(maxD) == 1) break;
-      d0 = d1;
-      d1 = d2;
-      d2 = n1;
-      n1 = n0.plus(q.times(d2));
-      n0 = d2;
-      d2 = d;
-      d = n.minus(q.times(d2));
-      n = d2;
-    }
-
-    d2 = divide(maxD.minus(d0), d1, 0, 1, 1);
-    n0 = n0.plus(d2.times(n1));
-    d0 = d0.plus(d2.times(d1));
-    n0.s = n1.s = x.s;
-
-    // Determine which fraction is closer to x, n0/d0 or n1/d1?
-    r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1
-        ? [n1, d1] : [n0, d0];
-
-    Ctor.precision = pr;
-    external = true;
-
-    return r;
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal in base 16, round to `sd` significant
-   * digits using rounding mode `rm`.
-   *
-   * If the optional `sd` argument is present then return binary exponential notation.
-   *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toHexadecimal = P.toHex = function (sd, rm) {
-    return toStringBinary(this, 16, sd, rm);
-  };
-
-
-  /*
-   * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding
-   * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.
-   *
-   * The return value will always have the same sign as this Decimal, unless either this Decimal
-   * or `y` is NaN, in which case the return value will be also be NaN.
-   *
-   * The return value is not affected by the value of `precision`.
-   *
-   * y {number|string|Decimal} The magnitude to round to a multiple of.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   * 'toNearest() rounding mode not an integer: {rm}'
-   * 'toNearest() rounding mode out of range: {rm}'
-   *
-   */
-  P.toNearest = function (y, rm) {
-    var x = this,
-      Ctor = x.constructor;
-
-    x = new Ctor(x);
-
-    if (y == null) {
-
-      // If x is not finite, return x.
-      if (!x.d) return x;
-
-      y = new Ctor(1);
-      rm = Ctor.rounding;
-    } else {
-      y = new Ctor(y);
-      if (rm === void 0) {
-        rm = Ctor.rounding;
-      } else {
-        checkInt32(rm, 0, 8);
-      }
-
-      // If x is not finite, return x if y is not NaN, else NaN.
-      if (!x.d) return y.s ? x : y;
-
-      // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.
-      if (!y.d) {
-        if (y.s) y.s = x.s;
-        return y;
-      }
-    }
-
-    // If y is not zero, calculate the nearest multiple of y to x.
-    if (y.d[0]) {
-      external = false;
-      x = divide(x, y, 0, rm, 1).times(y);
-      external = true;
-      finalise(x);
-
-    // If y is zero, return zero with the sign of x.
-    } else {
-      y.s = x.s;
-      x = y;
-    }
-
-    return x;
-  };
-
-
-  /*
-   * Return the value of this Decimal converted to a number primitive.
-   * Zero keeps its sign.
-   *
-   */
-  P.toNumber = function () {
-    return +this;
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal in base 8, round to `sd` significant
-   * digits using rounding mode `rm`.
-   *
-   * If the optional `sd` argument is present then return binary exponential notation.
-   *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toOctal = function (sd, rm) {
-    return toStringBinary(this, 8, sd, rm);
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded
-   * to `precision` significant digits using rounding mode `rounding`.
-   *
-   * ECMAScript compliant.
-   *
-   *   pow(x, NaN)                           = NaN
-   *   pow(x, ±0)                            = 1
-
-   *   pow(NaN, non-zero)                    = NaN
-   *   pow(abs(x) > 1, +Infinity)            = +Infinity
-   *   pow(abs(x) > 1, -Infinity)            = +0
-   *   pow(abs(x) == 1, ±Infinity)           = NaN
-   *   pow(abs(x) < 1, +Infinity)            = +0
-   *   pow(abs(x) < 1, -Infinity)            = +Infinity
-   *   pow(+Infinity, y > 0)                 = +Infinity
-   *   pow(+Infinity, y < 0)                 = +0
-   *   pow(-Infinity, odd integer > 0)       = -Infinity
-   *   pow(-Infinity, even integer > 0)      = +Infinity
-   *   pow(-Infinity, odd integer < 0)       = -0
-   *   pow(-Infinity, even integer < 0)      = +0
-   *   pow(+0, y > 0)                        = +0
-   *   pow(+0, y < 0)                        = +Infinity
-   *   pow(-0, odd integer > 0)              = -0
-   *   pow(-0, even integer > 0)             = +0
-   *   pow(-0, odd integer < 0)              = -Infinity
-   *   pow(-0, even integer < 0)             = +Infinity
-   *   pow(finite x < 0, finite non-integer) = NaN
-   *
-   * For non-integer or very large exponents pow(x, y) is calculated using
-   *
-   *   x^y = exp(y*ln(x))
-   *
-   * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the
-   * probability of an incorrectly rounded result
-   * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14
-   * i.e. 1 in 250,000,000,000,000
-   *
-   * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place).
-   *
-   * y {number|string|Decimal} The power to which to raise this Decimal.
-   *
-   */
-  P.toPower = P.pow = function (y) {
-    var e, k, pr, r, rm, s,
-      x = this,
-      Ctor = x.constructor,
-      yn = +(y = new Ctor(y));
-
-    // Either ±Infinity, NaN or ±0?
-    if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));
-
-    x = new Ctor(x);
-
-    if (x.eq(1)) return x;
-
-    pr = Ctor.precision;
-    rm = Ctor.rounding;
-
-    if (y.eq(1)) return finalise(x, pr, rm);
-
-    // y exponent
-    e = mathfloor(y.e / LOG_BASE);
-
-    // If y is a small integer use the 'exponentiation by squaring' algorithm.
-    if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
-      r = intPow(Ctor, x, k, pr);
-      return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);
-    }
-
-    s = x.s;
-
-    // if x is negative
-    if (s < 0) {
-
-      // if y is not an integer
-      if (e < y.d.length - 1) return new Ctor(NaN);
-
-      // Result is positive if x is negative and the last digit of integer y is even.
-      if ((y.d[e] & 1) == 0) s = 1;
-
-      // if x.eq(-1)
-      if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {
-        x.s = s;
-        return x;
-      }
-    }
-
-    // Estimate result exponent.
-    // x^y = 10^e,  where e = y * log10(x)
-    // log10(x) = log10(x_significand) + x_exponent
-    // log10(x_significand) = ln(x_significand) / ln(10)
-    k = mathpow(+x, yn);
-    e = k == 0 || !isFinite(k)
-      ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1))
-      : new Ctor(k + '').e;
-
-    // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.
-
-    // Overflow/underflow?
-    if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);
-
-    external = false;
-    Ctor.rounding = x.s = 1;
-
-    // Estimate the extra guard digits needed to ensure five correct rounding digits from
-    // naturalLogarithm(x). Example of failure without these extra digits (precision: 10):
-    // new Decimal(2.32456).pow('2087987436534566.46411')
-    // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815
-    k = Math.min(12, (e + '').length);
-
-    // r = x^y = exp(y*ln(x))
-    r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);
-
-    // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)
-    if (r.d) {
-
-      // Truncate to the required precision plus five rounding digits.
-      r = finalise(r, pr + 5, 1);
-
-      // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate
-      // the result.
-      if (checkRoundingDigits(r.d, pr, rm)) {
-        e = pr + 10;
-
-        // Truncate to the increased precision plus five rounding digits.
-        r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);
-
-        // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).
-        if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {
-          r = finalise(r, pr + 1, 0);
-        }
-      }
-    }
-
-    r.s = s;
-    external = true;
-    Ctor.rounding = rm;
-
-    return finalise(r, pr, rm);
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal rounded to `sd` significant digits
-   * using rounding mode `rounding`.
-   *
-   * Return exponential notation if `sd` is less than the number of digits necessary to represent
-   * the integer part of the value in normal notation.
-   *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   */
-  P.toPrecision = function (sd, rm) {
-    var str,
-      x = this,
-      Ctor = x.constructor;
-
-    if (sd === void 0) {
-      str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
-    } else {
-      checkInt32(sd, 1, MAX_DIGITS);
-
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
-
-      x = finalise(new Ctor(x), sd, rm);
-      str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);
-    }
-
-    return x.isNeg() && !x.isZero() ? '-' + str : str;
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
-   * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
-   * omitted.
-   *
-   * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
-   * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-   *
-   * 'toSD() digits out of range: {sd}'
-   * 'toSD() digits not an integer: {sd}'
-   * 'toSD() rounding mode not an integer: {rm}'
-   * 'toSD() rounding mode out of range: {rm}'
-   *
-   */
-  P.toSignificantDigits = P.toSD = function (sd, rm) {
-    var x = this,
-      Ctor = x.constructor;
-
-    if (sd === void 0) {
-      sd = Ctor.precision;
-      rm = Ctor.rounding;
-    } else {
-      checkInt32(sd, 1, MAX_DIGITS);
-
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
-    }
-
-    return finalise(new Ctor(x), sd, rm);
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal.
-   *
-   * Return exponential notation if this Decimal has a positive exponent equal to or greater than
-   * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
-   *
-   */
-  P.toString = function () {
-    var x = this,
-      Ctor = x.constructor,
-      str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
-
-    return x.isNeg() && !x.isZero() ? '-' + str : str;
-  };
-
-
-  /*
-   * Return a new Decimal whose value is the value of this Decimal truncated to a whole number.
-   *
-   */
-  P.truncated = P.trunc = function () {
-    return finalise(new this.constructor(this), this.e + 1, 1);
-  };
-
-
-  /*
-   * Return a string representing the value of this Decimal.
-   * Unlike `toString`, negative zero will include the minus sign.
-   *
-   */
-  P.valueOf = P.toJSON = function () {
-    var x = this,
-      Ctor = x.constructor,
-      str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
-
-    return x.isNeg() ? '-' + str : str;
-  };
-
-
-  // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
-
-
-  /*
-   *  digitsToString           P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,
-   *                           finiteToString, naturalExponential, naturalLogarithm
-   *  checkInt32               P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,
-   *                           P.toPrecision, P.toSignificantDigits, toStringBinary, random
-   *  checkRoundingDigits      P.logarithm, P.toPower, naturalExponential, naturalLogarithm
-   *  convertBase              toStringBinary, parseOther
-   *  cos                      P.cos
-   *  divide                   P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,
-   *                           P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,
-   *                           P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,
-   *                           taylorSeries, atan2, parseOther
-   *  finalise                 P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,
-   *                           P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,
-   *                           P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,
-   *                           P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,
-   *                           P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,
-   *                           P.truncated, divide, getLn10, getPi, naturalExponential,
-   *                           naturalLogarithm, ceil, floor, round, trunc
-   *  finiteToString           P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,
-   *                           toStringBinary
-   *  getBase10Exponent        P.minus, P.plus, P.times, parseOther
-   *  getLn10                  P.logarithm, naturalLogarithm
-   *  getPi                    P.acos, P.asin, P.atan, toLessThanHalfPi, atan2
-   *  getPrecision             P.precision, P.toFraction
-   *  getZeroString            digitsToString, finiteToString
-   *  intPow                   P.toPower, parseOther
-   *  isOdd                    toLessThanHalfPi
-   *  maxOrMin                 max, min
-   *  naturalExponential       P.naturalExponential, P.toPower
-   *  naturalLogarithm         P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,
-   *                           P.toPower, naturalExponential
-   *  nonFiniteToString        finiteToString, toStringBinary
-   *  parseDecimal             Decimal
-   *  parseOther               Decimal
-   *  sin                      P.sin
-   *  taylorSeries             P.cosh, P.sinh, cos, sin
-   *  toLessThanHalfPi         P.cos, P.sin
-   *  toStringBinary           P.toBinary, P.toHexadecimal, P.toOctal
-   *  truncate                 intPow
-   *
-   *  Throws:                  P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,
-   *                           naturalLogarithm, config, parseOther, random, Decimal
-   */
-
-
-  function digitsToString(d) {
-    var i, k, ws,
-      indexOfLastWord = d.length - 1,
-      str = '',
-      w = d[0];
-
-    if (indexOfLastWord > 0) {
-      str += w;
-      for (i = 1; i < indexOfLastWord; i++) {
-        ws = d[i] + '';
-        k = LOG_BASE - ws.length;
-        if (k) str += getZeroString(k);
-        str += ws;
-      }
-
-      w = d[i];
-      ws = w + '';
-      k = LOG_BASE - ws.length;
-      if (k) str += getZeroString(k);
-    } else if (w === 0) {
-      return '0';
-    }
-
-    // Remove trailing zeros of last w.
-    for (; w % 10 === 0;) w /= 10;
-
-    return str + w;
-  }
-
-
-  function checkInt32(i, min, max) {
-    if (i !== ~~i || i < min || i > max) {
-      throw Error(invalidArgument + i);
-    }
-  }
-
-
-  /*
-   * Check 5 rounding digits if `repeating` is null, 4 otherwise.
-   * `repeating == null` if caller is `log` or `pow`,
-   * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.
-   */
-  function checkRoundingDigits(d, i, rm, repeating) {
-    var di, k, r, rd;
-
-    // Get the length of the first word of the array d.
-    for (k = d[0]; k >= 10; k /= 10) --i;
-
-    // Is the rounding digit in the first word of d?
-    if (--i < 0) {
-      i += LOG_BASE;
-      di = 0;
-    } else {
-      di = Math.ceil((i + 1) / LOG_BASE);
-      i %= LOG_BASE;
-    }
-
-    // i is the index (0 - 6) of the rounding digit.
-    // E.g. if within the word 3487563 the first rounding digit is 5,
-    // then i = 4, k = 1000, rd = 3487563 % 1000 = 563
-    k = mathpow(10, LOG_BASE - i);
-    rd = d[di] % k | 0;
-
-    if (repeating == null) {
-      if (i < 3) {
-        if (i == 0) rd = rd / 100 | 0;
-        else if (i == 1) rd = rd / 10 | 0;
-        r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;
-      } else {
-        r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) &&
-          (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 ||
-            (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;
-      }
-    } else {
-      if (i < 4) {
-        if (i == 0) rd = rd / 1000 | 0;
-        else if (i == 1) rd = rd / 100 | 0;
-        else if (i == 2) rd = rd / 10 | 0;
-        r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;
-      } else {
-        r = ((repeating || rm < 4) && rd + 1 == k ||
-        (!repeating && rm > 3) && rd + 1 == k / 2) &&
-          (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;
-      }
-    }
-
-    return r;
-  }
-
-
-  // Convert string of `baseIn` to an array of numbers of `baseOut`.
-  // Eg. convertBase('255', 10, 16) returns [15, 15].
-  // Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
-  function convertBase(str, baseIn, baseOut) {
-    var j,
-      arr = [0],
-      arrL,
-      i = 0,
-      strL = str.length;
-
-    for (; i < strL;) {
-      for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn;
-      arr[0] += NUMERALS.indexOf(str.charAt(i++));
-      for (j = 0; j < arr.length; j++) {
-        if (arr[j] > baseOut - 1) {
-          if (arr[j + 1] === void 0) arr[j + 1] = 0;
-          arr[j + 1] += arr[j] / baseOut | 0;
-          arr[j] %= baseOut;
-        }
-      }
-    }
-
-    return arr.reverse();
-  }
-
-
-  /*
-   * cos(x) = 1 - x^2/2! + x^4/4! - ...
-   * |x| < pi/2
-   *
-   */
-  function cosine(Ctor, x) {
-    var k, len, y;
-
-    if (x.isZero()) return x;
-
-    // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1
-    // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1
-
-    // Estimate the optimum number of times to use the argument reduction.
-    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));
-
-    // Reverse argument reduction
-    for (var i = k; i--;) {
-      var cos2x = x.times(x);
-      x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);
-    }
-
-    Ctor.precision -= k;
-
-    return x;
-  }
-
-
-  /*
-   * Perform division in the specified base.
-   */
-  var divide = (function () {
-
-    // Assumes non-zero x and k, and hence non-zero result.
-    function multiplyInteger(x, k, base) {
-      var temp,
-        carry = 0,
-        i = x.length;
-
-      for (x = x.slice(); i--;) {
-        temp = x[i] * k + carry;
-        x[i] = temp % base | 0;
-        carry = temp / base | 0;
-      }
-
-      if (carry) x.unshift(carry);
-
-      return x;
-    }
-
-    function compare(a, b, aL, bL) {
-      var i, r;
-
-      if (aL != bL) {
-        r = aL > bL ? 1 : -1;
-      } else {
-        for (i = r = 0; i < aL; i++) {
-          if (a[i] != b[i]) {
-            r = a[i] > b[i] ? 1 : -1;
-            break;
-          }
-        }
-      }
-
-      return r;
-    }
-
-    function subtract(a, b, aL, base) {
-      var i = 0;
-
-      // Subtract b from a.
-      for (; aL--;) {
-        a[aL] -= i;
-        i = a[aL] < b[aL] ? 1 : 0;
-        a[aL] = i * base + a[aL] - b[aL];
-      }
-
-      // Remove leading zeros.
-      for (; !a[0] && a.length > 1;) a.shift();
-    }
-
-    return function (x, y, pr, rm, dp, base) {
-      var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0,
-        yL, yz,
-        Ctor = x.constructor,
-        sign = x.s == y.s ? 1 : -1,
-        xd = x.d,
-        yd = y.d;
-
-      // Either NaN, Infinity or 0?
-      if (!xd || !xd[0] || !yd || !yd[0]) {
-
-        return new Ctor(// Return NaN if either NaN, or both Infinity or 0.
-          !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN :
-
-          // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.
-          xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);
-      }
-
-      if (base) {
-        logBase = 1;
-        e = x.e - y.e;
-      } else {
-        base = BASE;
-        logBase = LOG_BASE;
-        e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);
-      }
-
-      yL = yd.length;
-      xL = xd.length;
-      q = new Ctor(sign);
-      qd = q.d = [];
-
-      // Result exponent may be one less than e.
-      // The digit array of a Decimal from toStringBinary may have trailing zeros.
-      for (i = 0; yd[i] == (xd[i] || 0); i++);
-
-      if (yd[i] > (xd[i] || 0)) e--;
-
-      if (pr == null) {
-        sd = pr = Ctor.precision;
-        rm = Ctor.rounding;
-      } else if (dp) {
-        sd = pr + (x.e - y.e) + 1;
-      } else {
-        sd = pr;
-      }
-
-      if (sd < 0) {
-        qd.push(1);
-        more = true;
-      } else {
-
-        // Convert precision in number of base 10 digits to base 1e7 digits.
-        sd = sd / logBase + 2 | 0;
-        i = 0;
-
-        // divisor < 1e7
-        if (yL == 1) {
-          k = 0;
-          yd = yd[0];
-          sd++;
-
-          // k is the carry.
-          for (; (i < xL || k) && sd--; i++) {
-            t = k * base + (xd[i] || 0);
-            qd[i] = t / yd | 0;
-            k = t % yd | 0;
-          }
-
-          more = k || i < xL;
-
-        // divisor >= 1e7
-        } else {
-
-          // Normalise xd and yd so highest order digit of yd is >= base/2
-          k = base / (yd[0] + 1) | 0;
-
-          if (k > 1) {
-            yd = multiplyInteger(yd, k, base);
-            xd = multiplyInteger(xd, k, base);
-            yL = yd.length;
-            xL = xd.length;
-          }
-
-          xi = yL;
-          rem = xd.slice(0, yL);
-          remL = rem.length;
-
-          // Add zeros to make remainder as long as divisor.
-          for (; remL < yL;) rem[remL++] = 0;
-
-          yz = yd.slice();
-          yz.unshift(0);
-          yd0 = yd[0];
-
-          if (yd[1] >= base / 2) ++yd0;
-
-          do {
-            k = 0;
-
-            // Compare divisor and remainder.
-            cmp = compare(yd, rem, yL, remL);
-
-            // If divisor < remainder.
-            if (cmp < 0) {
-
-              // Calculate trial digit, k.
-              rem0 = rem[0];
-              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
-
-              // k will be how many times the divisor goes into the current remainder.
-              k = rem0 / yd0 | 0;
-
-              //  Algorithm:
-              //  1. product = divisor * trial digit (k)
-              //  2. if product > remainder: product -= divisor, k--
-              //  3. remainder -= product
-              //  4. if product was < remainder at 2:
-              //    5. compare new remainder and divisor
-              //    6. If remainder > divisor: remainder -= divisor, k++
-
-              if (k > 1) {
-                if (k >= base) k = base - 1;
-
-                // product = divisor * trial digit.
-                prod = multiplyInteger(yd, k, base);
-                prodL = prod.length;
-                remL = rem.length;
-
-                // Compare product and remainder.
-                cmp = compare(prod, rem, prodL, remL);
-
-                // product > remainder.
-                if (cmp == 1) {
-                  k--;
-
-                  // Subtract divisor from product.
-                  subtract(prod, yL < prodL ? yz : yd, prodL, base);
-                }
-              } else {
-
-                // cmp is -1.
-                // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
-                // to avoid it. If k is 1 there is a need to compare yd and rem again below.
-                if (k == 0) cmp = k = 1;
-                prod = yd.slice();
-              }
-
-              prodL = prod.length;
-              if (prodL < remL) prod.unshift(0);
-
-              // Subtract product from remainder.
-              subtract(rem, prod, remL, base);
-
-              // If product was < previous remainder.
-              if (cmp == -1) {
-                remL = rem.length;
-
-                // Compare divisor and new remainder.
-                cmp = compare(yd, rem, yL, remL);
-
-                // If divisor < new remainder, subtract divisor from remainder.
-                if (cmp < 1) {
-                  k++;
-
-                  // Subtract divisor from remainder.
-                  subtract(rem, yL < remL ? yz : yd, remL, base);
-                }
-              }
-
-              remL = rem.length;
-            } else if (cmp === 0) {
-              k++;
-              rem = [0];
-            }    // if cmp === 1, k will be 0
-
-            // Add the next digit, k, to the result array.
-            qd[i++] = k;
-
-            // Update the remainder.
-            if (cmp && rem[0]) {
-              rem[remL++] = xd[xi] || 0;
-            } else {
-              rem = [xd[xi]];
-              remL = 1;
-            }
-
-          } while ((xi++ < xL || rem[0] !== void 0) && sd--);
-
-          more = rem[0] !== void 0;
-        }
-
-        // Leading zero?
-        if (!qd[0]) qd.shift();
-      }
-
-      // logBase is 1 when divide is being used for base conversion.
-      if (logBase == 1) {
-        q.e = e;
-        inexact = more;
-      } else {
-
-        // To calculate q.e, first get the number of digits of qd[0].
-        for (i = 1, k = qd[0]; k >= 10; k /= 10) i++;
-        q.e = i + e * logBase - 1;
-
-        finalise(q, dp ? pr + q.e + 1 : pr, rm, more);
-      }
-
-      return q;
-    };
-  })();
-
-
-  /*
-   * Round `x` to `sd` significant digits using rounding mode `rm`.
-   * Check for over/under-flow.
-   */
-   function finalise(x, sd, rm, isTruncated) {
-    var digits, i, j, k, rd, roundUp, w, xd, xdi,
-      Ctor = x.constructor;
-
-    // Don't round if sd is null or undefined.
-    out: if (sd != null) {
-      xd = x.d;
-
-      // Infinity/NaN.
-      if (!xd) return x;
-
-      // rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
-      // w: the word of xd containing rd, a base 1e7 number.
-      // xdi: the index of w within xd.
-      // digits: the number of digits of w.
-      // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
-      // they had leading zeros)
-      // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
-
-      // Get the length of the first word of the digits array xd.
-      for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;
-      i = sd - digits;
-
-      // Is the rounding digit in the first word of xd?
-      if (i < 0) {
-        i += LOG_BASE;
-        j = sd;
-        w = xd[xdi = 0];
-
-        // Get the rounding digit at index j of w.
-        rd = w / mathpow(10, digits - j - 1) % 10 | 0;
-      } else {
-        xdi = Math.ceil((i + 1) / LOG_BASE);
-        k = xd.length;
-        if (xdi >= k) {
-          if (isTruncated) {
-
-            // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.
-            for (; k++ <= xdi;) xd.push(0);
-            w = rd = 0;
-            digits = 1;
-            i %= LOG_BASE;
-            j = i - LOG_BASE + 1;
-          } else {
-            break out;
-          }
-        } else {
-          w = k = xd[xdi];
-
-          // Get the number of digits of w.
-          for (digits = 1; k >= 10; k /= 10) digits++;
-
-          // Get the index of rd within w.
-          i %= LOG_BASE;
-
-          // Get the index of rd within w, adjusted for leading zeros.
-          // The number of leading zeros of w is given by LOG_BASE - digits.
-          j = i - LOG_BASE + digits;
-
-          // Get the rounding digit at index j of w.
-          rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;
-        }
-      }
-
-      // Are there any non-zero digits after the rounding digit?
-      isTruncated = isTruncated || sd < 0 ||
-        xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));
-
-      // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right
-      // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression
-      // will give 714.
-
-      roundUp = rm < 4
-        ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
-        : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 &&
-
-          // Check whether the digit to the left of the rounding digit is odd.
-          ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
-            rm == (x.s < 0 ? 8 : 7));
-
-      if (sd < 1 || !xd[0]) {
-        xd.length = 0;
-        if (roundUp) {
-
-          // Convert sd to decimal places.
-          sd -= x.e + 1;
-
-          // 1, 0.1, 0.01, 0.001, 0.0001 etc.
-          xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
-          x.e = -sd || 0;
-        } else {
-
-          // Zero.
-          xd[0] = x.e = 0;
-        }
-
-        return x;
-      }
-
-      // Remove excess digits.
-      if (i == 0) {
-        xd.length = xdi;
-        k = 1;
-        xdi--;
-      } else {
-        xd.length = xdi + 1;
-        k = mathpow(10, LOG_BASE - i);
-
-        // E.g. 56700 becomes 56000 if 7 is the rounding digit.
-        // j > 0 means i > number of leading zeros of w.
-        xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;
-      }
-
-      if (roundUp) {
-        for (;;) {
-
-          // Is the digit to be rounded up in the first word of xd?
-          if (xdi == 0) {
-
-            // i will be the length of xd[0] before k is added.
-            for (i = 1, j = xd[0]; j >= 10; j /= 10) i++;
-            j = xd[0] += k;
-            for (k = 1; j >= 10; j /= 10) k++;
-
-            // if i != k the length has increased.
-            if (i != k) {
-              x.e++;
-              if (xd[0] == BASE) xd[0] = 1;
-            }
-
-            break;
-          } else {
-            xd[xdi] += k;
-            if (xd[xdi] != BASE) break;
-            xd[xdi--] = 0;
-            k = 1;
-          }
-        }
-      }
-
-      // Remove trailing zeros.
-      for (i = xd.length; xd[--i] === 0;) xd.pop();
-    }
-
-    if (external) {
-
-      // Overflow?
-      if (x.e > Ctor.maxE) {
-
-        // Infinity.
-        x.d = null;
-        x.e = NaN;
-
-      // Underflow?
-      } else if (x.e < Ctor.minE) {
-
-        // Zero.
-        x.e = 0;
-        x.d = [0];
-        // Ctor.underflow = true;
-      } // else Ctor.underflow = false;
-    }
-
-    return x;
-  }
-
-
-  function finiteToString(x, isExp, sd) {
-    if (!x.isFinite()) return nonFiniteToString(x);
-    var k,
-      e = x.e,
-      str = digitsToString(x.d),
-      len = str.length;
-
-    if (isExp) {
-      if (sd && (k = sd - len) > 0) {
-        str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
-      } else if (len > 1) {
-        str = str.charAt(0) + '.' + str.slice(1);
-      }
-
-      str = str + (x.e < 0 ? 'e' : 'e+') + x.e;
-    } else if (e < 0) {
-      str = '0.' + getZeroString(-e - 1) + str;
-      if (sd && (k = sd - len) > 0) str += getZeroString(k);
-    } else if (e >= len) {
-      str += getZeroString(e + 1 - len);
-      if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
-    } else {
-      if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
-      if (sd && (k = sd - len) > 0) {
-        if (e + 1 === len) str += '.';
-        str += getZeroString(k);
-      }
-    }
-
-    return str;
-  }
-
-
-  // Calculate the base 10 exponent from the base 1e7 exponent.
-  function getBase10Exponent(digits, e) {
-    var w = digits[0];
-
-    // Add the number of digits of the first word of the digits array.
-    for ( e *= LOG_BASE; w >= 10; w /= 10) e++;
-    return e;
-  }
-
-
-  function getLn10(Ctor, sd, pr) {
-    if (sd > LN10_PRECISION) {
-
-      // Reset global state in case the exception is caught.
-      external = true;
-      if (pr) Ctor.precision = pr;
-      throw Error(precisionLimitExceeded);
-    }
-    return finalise(new Ctor(LN10), sd, 1, true);
-  }
-
-
-  function getPi(Ctor, sd, rm) {
-    if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);
-    return finalise(new Ctor(PI), sd, rm, true);
-  }
-
-
-  function getPrecision(digits) {
-    var w = digits.length - 1,
-      len = w * LOG_BASE + 1;
-
-    w = digits[w];
-
-    // If non-zero...
-    if (w) {
-
-      // Subtract the number of trailing zeros of the last word.
-      for (; w % 10 == 0; w /= 10) len--;
-
-      // Add the number of digits of the first word.
-      for (w = digits[0]; w >= 10; w /= 10) len++;
-    }
-
-    return len;
-  }
-
-
-  function getZeroString(k) {
-    var zs = '';
-    for (; k--;) zs += '0';
-    return zs;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an
-   * integer of type number.
-   *
-   * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.
-   *
-   */
-  function intPow(Ctor, x, n, pr) {
-    var isTruncated,
-      r = new Ctor(1),
-
-      // Max n of 9007199254740991 takes 53 loop iterations.
-      // Maximum digits array length; leaves [28, 34] guard digits.
-      k = Math.ceil(pr / LOG_BASE + 4);
-
-    external = false;
-
-    for (;;) {
-      if (n % 2) {
-        r = r.times(x);
-        if (truncate(r.d, k)) isTruncated = true;
-      }
-
-      n = mathfloor(n / 2);
-      if (n === 0) {
-
-        // To ensure correct rounding when r.d is truncated, increment the last word if it is zero.
-        n = r.d.length - 1;
-        if (isTruncated && r.d[n] === 0) ++r.d[n];
-        break;
-      }
-
-      x = x.times(x);
-      truncate(x.d, k);
-    }
-
-    external = true;
-
-    return r;
-  }
-
-
-  function isOdd(n) {
-    return n.d[n.d.length - 1] & 1;
-  }
-
-
-  /*
-   * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'.
-   */
-  function maxOrMin(Ctor, args, ltgt) {
-    var y,
-      x = new Ctor(args[0]),
-      i = 0;
-
-    for (; ++i < args.length;) {
-      y = new Ctor(args[i]);
-      if (!y.s) {
-        x = y;
-        break;
-      } else if (x[ltgt](y)) {
-        x = y;
-      }
-    }
-
-    return x;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant
-   * digits.
-   *
-   * Taylor/Maclaurin series.
-   *
-   * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
-   *
-   * Argument reduction:
-   *   Repeat x = x / 32, k += 5, until |x| < 0.1
-   *   exp(x) = exp(x / 2^k)^(2^k)
-   *
-   * Previously, the argument was initially reduced by
-   * exp(x) = exp(r) * 10^k  where r = x - k * ln10, k = floor(x / ln10)
-   * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
-   * found to be slower than just dividing repeatedly by 32 as above.
-   *
-   * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000
-   * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000
-   * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
-   *
-   *  exp(Infinity)  = Infinity
-   *  exp(-Infinity) = 0
-   *  exp(NaN)       = NaN
-   *  exp(±0)        = 1
-   *
-   *  exp(x) is non-terminating for any finite, non-zero x.
-   *
-   *  The result will always be correctly rounded.
-   *
-   */
-  function naturalExponential(x, sd) {
-    var denominator, guard, j, pow, sum, t, wpr,
-      rep = 0,
-      i = 0,
-      k = 0,
-      Ctor = x.constructor,
-      rm = Ctor.rounding,
-      pr = Ctor.precision;
-
-    // 0/NaN/Infinity?
-    if (!x.d || !x.d[0] || x.e > 17) {
-
-      return new Ctor(x.d
-        ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0
-        : x.s ? x.s < 0 ? 0 : x : 0 / 0);
-    }
-
-    if (sd == null) {
-      external = false;
-      wpr = pr;
-    } else {
-      wpr = sd;
-    }
-
-    t = new Ctor(0.03125);
-
-    // while abs(x) >= 0.1
-    while (x.e > -2) {
-
-      // x = x / 2^5
-      x = x.times(t);
-      k += 5;
-    }
-
-    // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision
-    // necessary to ensure the first 4 rounding digits are correct.
-    guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
-    wpr += guard;
-    denominator = pow = sum = new Ctor(1);
-    Ctor.precision = wpr;
-
-    for (;;) {
-      pow = finalise(pow.times(x), wpr, 1);
-      denominator = denominator.times(++i);
-      t = sum.plus(divide(pow, denominator, wpr, 1));
-
-      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
-        j = k;
-        while (j--) sum = finalise(sum.times(sum), wpr, 1);
-
-        // Check to see if the first 4 rounding digits are [49]999.
-        // If so, repeat the summation with a higher precision, otherwise
-        // e.g. with precision: 18, rounding: 1
-        // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)
-        // `wpr - guard` is the index of first rounding digit.
-        if (sd == null) {
-
-          if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
-            Ctor.precision = wpr += 10;
-            denominator = pow = t = new Ctor(1);
-            i = 0;
-            rep++;
-          } else {
-            return finalise(sum, Ctor.precision = pr, rm, external = true);
-          }
-        } else {
-          Ctor.precision = pr;
-          return sum;
-        }
-      }
-
-      sum = t;
-    }
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant
-   * digits.
-   *
-   *  ln(-n)        = NaN
-   *  ln(0)         = -Infinity
-   *  ln(-0)        = -Infinity
-   *  ln(1)         = 0
-   *  ln(Infinity)  = Infinity
-   *  ln(-Infinity) = NaN
-   *  ln(NaN)       = NaN
-   *
-   *  ln(n) (n != 1) is non-terminating.
-   *
-   */
-  function naturalLogarithm(y, sd) {
-    var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2,
-      n = 1,
-      guard = 10,
-      x = y,
-      xd = x.d,
-      Ctor = x.constructor,
-      rm = Ctor.rounding,
-      pr = Ctor.precision;
-
-    // Is x negative or Infinity, NaN, 0 or 1?
-    if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {
-      return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);
-    }
-
-    if (sd == null) {
-      external = false;
-      wpr = pr;
-    } else {
-      wpr = sd;
-    }
-
-    Ctor.precision = wpr += guard;
-    c = digitsToString(xd);
-    c0 = c.charAt(0);
-
-    if (Math.abs(e = x.e) < 1.5e15) {
-
-      // Argument reduction.
-      // The series converges faster the closer the argument is to 1, so using
-      // ln(a^b) = b * ln(a),   ln(a) = ln(a^b) / b
-      // multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
-      // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
-      // later be divided by this number, then separate out the power of 10 using
-      // ln(a*10^b) = ln(a) + b*ln(10).
-
-      // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
-      //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
-      // max n is 6 (gives 0.7 - 1.3)
-      while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
-        x = x.times(y);
-        c = digitsToString(x.d);
-        c0 = c.charAt(0);
-        n++;
-      }
-
-      e = x.e;
-
-      if (c0 > 1) {
-        x = new Ctor('0.' + c);
-        e++;
-      } else {
-        x = new Ctor(c0 + '.' + c.slice(1));
-      }
-    } else {
-
-      // The argument reduction method above may result in overflow if the argument y is a massive
-      // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
-      // function using ln(x*10^e) = ln(x) + e*ln(10).
-      t = getLn10(Ctor, wpr + 2, pr).times(e + '');
-      x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
-      Ctor.precision = pr;
-
-      return sd == null ? finalise(x, pr, rm, external = true) : x;
-    }
-
-    // x1 is x reduced to a value near 1.
-    x1 = x;
-
-    // Taylor series.
-    // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
-    // where x = (y - 1)/(y + 1)    (|x| < 1)
-    sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1);
-    x2 = finalise(x.times(x), wpr, 1);
-    denominator = 3;
-
-    for (;;) {
-      numerator = finalise(numerator.times(x2), wpr, 1);
-      t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));
-
-      if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
-        sum = sum.times(2);
-
-        // Reverse the argument reduction. Check that e is not 0 because, besides preventing an
-        // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.
-        if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
-        sum = divide(sum, new Ctor(n), wpr, 1);
-
-        // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has
-        // been repeated previously) and the first 4 rounding digits 9999?
-        // If so, restart the summation with a higher precision, otherwise
-        // e.g. with precision: 12, rounding: 1
-        // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.
-        // `wpr - guard` is the index of first rounding digit.
-        if (sd == null) {
-          if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
-            Ctor.precision = wpr += guard;
-            t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);
-            x2 = finalise(x.times(x), wpr, 1);
-            denominator = rep = 1;
-          } else {
-            return finalise(sum, Ctor.precision = pr, rm, external = true);
-          }
-        } else {
-          Ctor.precision = pr;
-          return sum;
-        }
-      }
-
-      sum = t;
-      denominator += 2;
-    }
-  }
-
-
-  // ±Infinity, NaN.
-  function nonFiniteToString(x) {
-    // Unsigned.
-    return String(x.s * x.s / 0);
-  }
-
-
-  /*
-   * Parse the value of a new Decimal `x` from string `str`.
-   */
-  function parseDecimal(x, str) {
-    var e, i, len;
-
-    // Decimal point?
-    if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
-
-    // Exponential form?
-    if ((i = str.search(/e/i)) > 0) {
-
-      // Determine exponent.
-      if (e < 0) e = i;
-      e += +str.slice(i + 1);
-      str = str.substring(0, i);
-    } else if (e < 0) {
-
-      // Integer.
-      e = str.length;
-    }
-
-    // Determine leading zeros.
-    for (i = 0; str.charCodeAt(i) === 48; i++);
-
-    // Determine trailing zeros.
-    for (len = str.length; str.charCodeAt(len - 1) === 48; --len);
-    str = str.slice(i, len);
-
-    if (str) {
-      len -= i;
-      x.e = e = e - i - 1;
-      x.d = [];
-
-      // Transform base
-
-      // e is the base 10 exponent.
-      // i is where to slice str to get the first word of the digits array.
-      i = (e + 1) % LOG_BASE;
-      if (e < 0) i += LOG_BASE;
-
-      if (i < len) {
-        if (i) x.d.push(+str.slice(0, i));
-        for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
-        str = str.slice(i);
-        i = LOG_BASE - str.length;
-      } else {
-        i -= len;
-      }
-
-      for (; i--;) str += '0';
-      x.d.push(+str);
-
-      if (external) {
-
-        // Overflow?
-        if (x.e > x.constructor.maxE) {
-
-          // Infinity.
-          x.d = null;
-          x.e = NaN;
-
-        // Underflow?
-        } else if (x.e < x.constructor.minE) {
-
-          // Zero.
-          x.e = 0;
-          x.d = [0];
-          // x.constructor.underflow = true;
-        } // else x.constructor.underflow = false;
-      }
-    } else {
-
-      // Zero.
-      x.e = 0;
-      x.d = [0];
-    }
-
-    return x;
-  }
-
-
-  /*
-   * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.
-   */
-  function parseOther(x, str) {
-    var base, Ctor, divisor, i, isFloat, len, p, xd, xe;
-
-    if (str.indexOf('_') > -1) {
-      str = str.replace(/(\d)_(?=\d)/g, '$1');
-      if (isDecimal.test(str)) return parseDecimal(x, str);
-    } else if (str === 'Infinity' || str === 'NaN') {
-      if (!+str) x.s = NaN;
-      x.e = NaN;
-      x.d = null;
-      return x;
-    }
-
-    if (isHex.test(str))  {
-      base = 16;
-      str = str.toLowerCase();
-    } else if (isBinary.test(str))  {
-      base = 2;
-    } else if (isOctal.test(str))  {
-      base = 8;
-    } else {
-      throw Error(invalidArgument + str);
-    }
-
-    // Is there a binary exponent part?
-    i = str.search(/p/i);
-
-    if (i > 0) {
-      p = +str.slice(i + 1);
-      str = str.substring(2, i);
-    } else {
-      str = str.slice(2);
-    }
-
-    // Convert `str` as an integer then divide the result by `base` raised to a power such that the
-    // fraction part will be restored.
-    i = str.indexOf('.');
-    isFloat = i >= 0;
-    Ctor = x.constructor;
-
-    if (isFloat) {
-      str = str.replace('.', '');
-      len = str.length;
-      i = len - i;
-
-      // log[10](16) = 1.2041... , log[10](88) = 1.9444....
-      divisor = intPow(Ctor, new Ctor(base), i, i * 2);
-    }
-
-    xd = convertBase(str, base, BASE);
-    xe = xd.length - 1;
-
-    // Remove trailing zeros.
-    for (i = xe; xd[i] === 0; --i) xd.pop();
-    if (i < 0) return new Ctor(x.s * 0);
-    x.e = getBase10Exponent(xd, xe);
-    x.d = xd;
-    external = false;
-
-    // At what precision to perform the division to ensure exact conversion?
-    // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)
-    // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412
-    // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.
-    // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount
-    // Therefore using 4 * the number of digits of str will always be enough.
-    if (isFloat) x = divide(x, divisor, len * 4);
-
-    // Multiply by the binary exponent part if present.
-    if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));
-    external = true;
-
-    return x;
-  }
-
-
-  /*
-   * sin(x) = x - x^3/3! + x^5/5! - ...
-   * |x| < pi/2
-   *
-   */
-  function sine(Ctor, x) {
-    var k,
-      len = x.d.length;
-
-    if (len < 3) {
-      return x.isZero() ? x : taylorSeries(Ctor, 2, x, x);
-    }
-
-    // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)
-    // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)
-    // and  sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))
-
-    // Estimate the optimum number of times to use the argument reduction.
-    k = 1.4 * Math.sqrt(len);
-    k = k > 16 ? 16 : k | 0;
-
-    x = x.times(1 / tinyPow(5, k));
-    x = taylorSeries(Ctor, 2, x, x);
-
-    // Reverse argument reduction
-    var sin2_x,
-      d5 = new Ctor(5),
-      d16 = new Ctor(16),
-      d20 = new Ctor(20);
-    for (; k--;) {
-      sin2_x = x.times(x);
-      x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));
-    }
-
-    return x;
-  }
-
-
-  // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.
-  function taylorSeries(Ctor, n, x, y, isHyperbolic) {
-    var j, t, u, x2,
-      i = 1,
-      pr = Ctor.precision,
-      k = Math.ceil(pr / LOG_BASE);
-
-    external = false;
-    x2 = x.times(x);
-    u = new Ctor(y);
-
-    for (;;) {
-      t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);
-      u = isHyperbolic ? y.plus(t) : y.minus(t);
-      y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);
-      t = u.plus(y);
-
-      if (t.d[k] !== void 0) {
-        for (j = k; t.d[j] === u.d[j] && j--;);
-        if (j == -1) break;
-      }
-
-      j = u;
-      u = y;
-      y = t;
-      t = j;
-      i++;
-    }
-
-    external = true;
-    t.d.length = k + 1;
-
-    return t;
-  }
-
-
-  // Exponent e must be positive and non-zero.
-  function tinyPow(b, e) {
-    var n = b;
-    while (--e) n *= b;
-    return n;
-  }
-
-
-  // Return the absolute value of `x` reduced to less than or equal to half pi.
-  function toLessThanHalfPi(Ctor, x) {
-    var t,
-      isNeg = x.s < 0,
-      pi = getPi(Ctor, Ctor.precision, 1),
-      halfPi = pi.times(0.5);
-
-    x = x.abs();
-
-    if (x.lte(halfPi)) {
-      quadrant = isNeg ? 4 : 1;
-      return x;
-    }
-
-    t = x.divToInt(pi);
-
-    if (t.isZero()) {
-      quadrant = isNeg ? 3 : 2;
-    } else {
-      x = x.minus(t.times(pi));
-
-      // 0 <= x < pi
-      if (x.lte(halfPi)) {
-        quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1);
-        return x;
-      }
-
-      quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2);
-    }
-
-    return x.minus(pi).abs();
-  }
-
-
-  /*
-   * Return the value of Decimal `x` as a string in base `baseOut`.
-   *
-   * If the optional `sd` argument is present include a binary exponent suffix.
-   */
-  function toStringBinary(x, baseOut, sd, rm) {
-    var base, e, i, k, len, roundUp, str, xd, y,
-      Ctor = x.constructor,
-      isExp = sd !== void 0;
-
-    if (isExp) {
-      checkInt32(sd, 1, MAX_DIGITS);
-      if (rm === void 0) rm = Ctor.rounding;
-      else checkInt32(rm, 0, 8);
-    } else {
-      sd = Ctor.precision;
-      rm = Ctor.rounding;
-    }
-
-    if (!x.isFinite()) {
-      str = nonFiniteToString(x);
-    } else {
-      str = finiteToString(x);
-      i = str.indexOf('.');
-
-      // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:
-      // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))
-      // minBinaryExponent = floor(decimalExponent * log[2](10))
-      // log[2](10) = 3.321928094887362347870319429489390175864
-
-      if (isExp) {
-        base = 2;
-        if (baseOut == 16) {
-          sd = sd * 4 - 3;
-        } else if (baseOut == 8) {
-          sd = sd * 3 - 2;
-        }
-      } else {
-        base = baseOut;
-      }
-
-      // Convert the number as an integer then divide the result by its base raised to a power such
-      // that the fraction part will be restored.
-
-      // Non-integer.
-      if (i >= 0) {
-        str = str.replace('.', '');
-        y = new Ctor(1);
-        y.e = str.length - i;
-        y.d = convertBase(finiteToString(y), 10, base);
-        y.e = y.d.length;
-      }
-
-      xd = convertBase(str, 10, base);
-      e = len = xd.length;
-
-      // Remove trailing zeros.
-      for (; xd[--len] == 0;) xd.pop();
-
-      if (!xd[0]) {
-        str = isExp ? '0p+0' : '0';
-      } else {
-        if (i < 0) {
-          e--;
-        } else {
-          x = new Ctor(x);
-          x.d = xd;
-          x.e = e;
-          x = divide(x, y, sd, rm, 0, base);
-          xd = x.d;
-          e = x.e;
-          roundUp = inexact;
-        }
-
-        // The rounding digit, i.e. the digit after the digit that may be rounded up.
-        i = xd[sd];
-        k = base / 2;
-        roundUp = roundUp || xd[sd + 1] !== void 0;
-
-        roundUp = rm < 4
-          ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))
-          : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||
-            rm === (x.s < 0 ? 8 : 7));
-
-        xd.length = sd;
-
-        if (roundUp) {
-
-          // Rounding up may mean the previous digit has to be rounded up and so on.
-          for (; ++xd[--sd] > base - 1;) {
-            xd[sd] = 0;
-            if (!sd) {
-              ++e;
-              xd.unshift(1);
-            }
-          }
-        }
-
-        // Determine trailing zeros.
-        for (len = xd.length; !xd[len - 1]; --len);
-
-        // E.g. [4, 11, 15] becomes 4bf.
-        for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]);
-
-        // Add binary exponent suffix?
-        if (isExp) {
-          if (len > 1) {
-            if (baseOut == 16 || baseOut == 8) {
-              i = baseOut == 16 ? 4 : 3;
-              for (--len; len % i; len++) str += '0';
-              xd = convertBase(str, base, baseOut);
-              for (len = xd.length; !xd[len - 1]; --len);
-
-              // xd[0] will always be be 1
-              for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]);
-            } else {
-              str = str.charAt(0) + '.' + str.slice(1);
-            }
-          }
-
-          str =  str + (e < 0 ? 'p' : 'p+') + e;
-        } else if (e < 0) {
-          for (; ++e;) str = '0' + str;
-          str = '0.' + str;
-        } else {
-          if (++e > len) for (e -= len; e-- ;) str += '0';
-          else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);
-        }
-      }
-
-      str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;
-    }
-
-    return x.s < 0 ? '-' + str : str;
-  }
-
-
-  // Does not strip trailing zeros.
-  function truncate(arr, len) {
-    if (arr.length > len) {
-      arr.length = len;
-      return true;
-    }
-  }
-
-
-  // Decimal methods
-
-
-  /*
-   *  abs
-   *  acos
-   *  acosh
-   *  add
-   *  asin
-   *  asinh
-   *  atan
-   *  atanh
-   *  atan2
-   *  cbrt
-   *  ceil
-   *  clamp
-   *  clone
-   *  config
-   *  cos
-   *  cosh
-   *  div
-   *  exp
-   *  floor
-   *  hypot
-   *  ln
-   *  log
-   *  log2
-   *  log10
-   *  max
-   *  min
-   *  mod
-   *  mul
-   *  pow
-   *  random
-   *  round
-   *  set
-   *  sign
-   *  sin
-   *  sinh
-   *  sqrt
-   *  sub
-   *  sum
-   *  tan
-   *  tanh
-   *  trunc
-   */
-
-
-  /*
-   * Return a new Decimal whose value is the absolute value of `x`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function abs(x) {
-    return new this(x).abs();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the arccosine in radians of `x`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function acos(x) {
-    return new this(x).acos();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to
-   * `precision` significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function acosh(x) {
-    return new this(x).acosh();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   * y {number|string|Decimal}
-   *
-   */
-  function add(x, y) {
-    return new this(x).plus(y);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function asin(x) {
-    return new this(x).asin();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to
-   * `precision` significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function asinh(x) {
-    return new this(x).asinh();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function atan(x) {
-    return new this(x).atan();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to
-   * `precision` significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function atanh(x) {
-    return new this(x).atanh();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi
-   * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.
-   *
-   * Domain: [-Infinity, Infinity]
-   * Range: [-pi, pi]
-   *
-   * y {number|string|Decimal} The y-coordinate.
-   * x {number|string|Decimal} The x-coordinate.
-   *
-   * atan2(±0, -0)               = ±pi
-   * atan2(±0, +0)               = ±0
-   * atan2(±0, -x)               = ±pi for x > 0
-   * atan2(±0, x)                = ±0 for x > 0
-   * atan2(-y, ±0)               = -pi/2 for y > 0
-   * atan2(y, ±0)                = pi/2 for y > 0
-   * atan2(±y, -Infinity)        = ±pi for finite y > 0
-   * atan2(±y, +Infinity)        = ±0 for finite y > 0
-   * atan2(±Infinity, x)         = ±pi/2 for finite x
-   * atan2(±Infinity, -Infinity) = ±3*pi/4
-   * atan2(±Infinity, +Infinity) = ±pi/4
-   * atan2(NaN, x) = NaN
-   * atan2(y, NaN) = NaN
-   *
-   */
-  function atan2(y, x) {
-    y = new this(y);
-    x = new this(x);
-    var r,
-      pr = this.precision,
-      rm = this.rounding,
-      wpr = pr + 4;
-
-    // Either NaN
-    if (!y.s || !x.s) {
-      r = new this(NaN);
-
-    // Both ±Infinity
-    } else if (!y.d && !x.d) {
-      r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);
-      r.s = y.s;
-
-    // x is ±Infinity or y is ±0
-    } else if (!x.d || y.isZero()) {
-      r = x.s < 0 ? getPi(this, pr, rm) : new this(0);
-      r.s = y.s;
-
-    // y is ±Infinity or x is ±0
-    } else if (!y.d || x.isZero()) {
-      r = getPi(this, wpr, 1).times(0.5);
-      r.s = y.s;
-
-    // Both non-zero and finite
-    } else if (x.s < 0) {
-      this.precision = wpr;
-      this.rounding = 1;
-      r = this.atan(divide(y, x, wpr, 1));
-      x = getPi(this, wpr, 1);
-      this.precision = pr;
-      this.rounding = rm;
-      r = y.s < 0 ? r.minus(x) : r.plus(x);
-    } else {
-      r = this.atan(divide(y, x, wpr, 1));
-    }
-
-    return r;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function cbrt(x) {
-    return new this(x).cbrt();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function ceil(x) {
-    return finalise(x = new this(x), x.e + 1, 2);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` clamped to the range delineated by `min` and `max`.
-   *
-   * x {number|string|Decimal}
-   * min {number|string|Decimal}
-   * max {number|string|Decimal}
-   *
-   */
-  function clamp(x, min, max) {
-    return new this(x).clamp(min, max);
-  }
-
-
-  /*
-   * Configure global settings for a Decimal constructor.
-   *
-   * `obj` is an object with one or more of the following properties,
-   *
-   *   precision  {number}
-   *   rounding   {number}
-   *   toExpNeg   {number}
-   *   toExpPos   {number}
-   *   maxE       {number}
-   *   minE       {number}
-   *   modulo     {number}
-   *   crypto     {boolean|number}
-   *   defaults   {true}
-   *
-   * E.g. Decimal.config({ precision: 20, rounding: 4 })
-   *
-   */
-  function config(obj) {
-    if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected');
-    var i, p, v,
-      useDefaults = obj.defaults === true,
-      ps = [
-        'precision', 1, MAX_DIGITS,
-        'rounding', 0, 8,
-        'toExpNeg', -EXP_LIMIT, 0,
-        'toExpPos', 0, EXP_LIMIT,
-        'maxE', 0, EXP_LIMIT,
-        'minE', -EXP_LIMIT, 0,
-        'modulo', 0, 9
-      ];
-
-    for (i = 0; i < ps.length; i += 3) {
-      if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];
-      if ((v = obj[p]) !== void 0) {
-        if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
-        else throw Error(invalidArgument + p + ': ' + v);
-      }
-    }
-
-    if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];
-    if ((v = obj[p]) !== void 0) {
-      if (v === true || v === false || v === 0 || v === 1) {
-        if (v) {
-          if (typeof crypto != 'undefined' && crypto &&
-            (crypto.getRandomValues || crypto.randomBytes)) {
-            this[p] = true;
-          } else {
-            throw Error(cryptoUnavailable);
-          }
-        } else {
-          this[p] = false;
-        }
-      } else {
-        throw Error(invalidArgument + p + ': ' + v);
-      }
-    }
-
-    return this;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function cos(x) {
-    return new this(x).cos();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function cosh(x) {
-    return new this(x).cosh();
-  }
-
-
-  /*
-   * Create and return a Decimal constructor with the same configuration properties as this Decimal
-   * constructor.
-   *
-   */
-  function clone(obj) {
-    var i, p, ps;
-
-    /*
-     * The Decimal constructor and exported function.
-     * Return a new Decimal instance.
-     *
-     * v {number|string|Decimal} A numeric value.
-     *
-     */
-    function Decimal(v) {
-      var e, i, t,
-        x = this;
-
-      // Decimal called without new.
-      if (!(x instanceof Decimal)) return new Decimal(v);
-
-      // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
-      // which points to Object.
-      x.constructor = Decimal;
-
-      // Duplicate.
-      if (isDecimalInstance(v)) {
-        x.s = v.s;
-
-        if (external) {
-          if (!v.d || v.e > Decimal.maxE) {
-
-            // Infinity.
-            x.e = NaN;
-            x.d = null;
-          } else if (v.e < Decimal.minE) {
-
-            // Zero.
-            x.e = 0;
-            x.d = [0];
-          } else {
-            x.e = v.e;
-            x.d = v.d.slice();
-          }
-        } else {
-          x.e = v.e;
-          x.d = v.d ? v.d.slice() : v.d;
-        }
-
-        return;
-      }
-
-      t = typeof v;
-
-      if (t === 'number') {
-        if (v === 0) {
-          x.s = 1 / v < 0 ? -1 : 1;
-          x.e = 0;
-          x.d = [0];
-          return;
-        }
-
-        if (v < 0) {
-          v = -v;
-          x.s = -1;
-        } else {
-          x.s = 1;
-        }
-
-        // Fast path for small integers.
-        if (v === ~~v && v < 1e7) {
-          for (e = 0, i = v; i >= 10; i /= 10) e++;
-
-          if (external) {
-            if (e > Decimal.maxE) {
-              x.e = NaN;
-              x.d = null;
-            } else if (e < Decimal.minE) {
-              x.e = 0;
-              x.d = [0];
-            } else {
-              x.e = e;
-              x.d = [v];
-            }
-          } else {
-            x.e = e;
-            x.d = [v];
-          }
-
-          return;
-
-        // Infinity, NaN.
-        } else if (v * 0 !== 0) {
-          if (!v) x.s = NaN;
-          x.e = NaN;
-          x.d = null;
-          return;
-        }
-
-        return parseDecimal(x, v.toString());
-
-      } else if (t !== 'string') {
-        throw Error(invalidArgument + v);
-      }
-
-      // Minus sign?
-      if ((i = v.charCodeAt(0)) === 45) {
-        v = v.slice(1);
-        x.s = -1;
-      } else {
-        // Plus sign?
-        if (i === 43) v = v.slice(1);
-        x.s = 1;
-      }
-
-      return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);
-    }
-
-    Decimal.prototype = P;
-
-    Decimal.ROUND_UP = 0;
-    Decimal.ROUND_DOWN = 1;
-    Decimal.ROUND_CEIL = 2;
-    Decimal.ROUND_FLOOR = 3;
-    Decimal.ROUND_HALF_UP = 4;
-    Decimal.ROUND_HALF_DOWN = 5;
-    Decimal.ROUND_HALF_EVEN = 6;
-    Decimal.ROUND_HALF_CEIL = 7;
-    Decimal.ROUND_HALF_FLOOR = 8;
-    Decimal.EUCLID = 9;
-
-    Decimal.config = Decimal.set = config;
-    Decimal.clone = clone;
-    Decimal.isDecimal = isDecimalInstance;
-
-    Decimal.abs = abs;
-    Decimal.acos = acos;
-    Decimal.acosh = acosh;        // ES6
-    Decimal.add = add;
-    Decimal.asin = asin;
-    Decimal.asinh = asinh;        // ES6
-    Decimal.atan = atan;
-    Decimal.atanh = atanh;        // ES6
-    Decimal.atan2 = atan2;
-    Decimal.cbrt = cbrt;          // ES6
-    Decimal.ceil = ceil;
-    Decimal.clamp = clamp;
-    Decimal.cos = cos;
-    Decimal.cosh = cosh;          // ES6
-    Decimal.div = div;
-    Decimal.exp = exp;
-    Decimal.floor = floor;
-    Decimal.hypot = hypot;        // ES6
-    Decimal.ln = ln;
-    Decimal.log = log;
-    Decimal.log10 = log10;        // ES6
-    Decimal.log2 = log2;          // ES6
-    Decimal.max = max;
-    Decimal.min = min;
-    Decimal.mod = mod;
-    Decimal.mul = mul;
-    Decimal.pow = pow;
-    Decimal.random = random;
-    Decimal.round = round;
-    Decimal.sign = sign;          // ES6
-    Decimal.sin = sin;
-    Decimal.sinh = sinh;          // ES6
-    Decimal.sqrt = sqrt;
-    Decimal.sub = sub;
-    Decimal.sum = sum;
-    Decimal.tan = tan;
-    Decimal.tanh = tanh;          // ES6
-    Decimal.trunc = trunc;        // ES6
-
-    if (obj === void 0) obj = {};
-    if (obj) {
-      if (obj.defaults !== true) {
-        ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];
-        for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
-      }
-    }
-
-    Decimal.config(obj);
-
-    return Decimal;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   * y {number|string|Decimal}
-   *
-   */
-  function div(x, y) {
-    return new this(x).div(y);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} The power to which to raise the base of the natural log.
-   *
-   */
-  function exp(x) {
-    return new this(x).exp();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function floor(x) {
-    return finalise(x = new this(x), x.e + 1, 3);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the square root of the sum of the squares of the arguments,
-   * rounded to `precision` significant digits using rounding mode `rounding`.
-   *
-   * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)
-   *
-   * arguments {number|string|Decimal}
-   *
-   */
-  function hypot() {
-    var i, n,
-      t = new this(0);
-
-    external = false;
-
-    for (i = 0; i < arguments.length;) {
-      n = new this(arguments[i++]);
-      if (!n.d) {
-        if (n.s) {
-          external = true;
-          return new this(1 / 0);
-        }
-        t = n;
-      } else if (t.d) {
-        t = t.plus(n.times(n));
-      }
-    }
-
-    external = true;
-
-    return t.sqrt();
-  }
-
-
-  /*
-   * Return true if object is a Decimal instance (where Decimal is any Decimal constructor),
-   * otherwise return false.
-   *
-   */
-  function isDecimalInstance(obj) {
-    return obj instanceof Decimal || obj && obj.toStringTag === tag || false;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function ln(x) {
-    return new this(x).ln();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base
-   * is specified, rounded to `precision` significant digits using rounding mode `rounding`.
-   *
-   * log[y](x)
-   *
-   * x {number|string|Decimal} The argument of the logarithm.
-   * y {number|string|Decimal} The base of the logarithm.
-   *
-   */
-  function log(x, y) {
-    return new this(x).log(y);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function log2(x) {
-    return new this(x).log(2);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function log10(x) {
-    return new this(x).log(10);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the maximum of the arguments.
-   *
-   * arguments {number|string|Decimal}
-   *
-   */
-  function max() {
-    return maxOrMin(this, arguments, 'lt');
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the minimum of the arguments.
-   *
-   * arguments {number|string|Decimal}
-   *
-   */
-  function min() {
-    return maxOrMin(this, arguments, 'gt');
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
-   * using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   * y {number|string|Decimal}
-   *
-   */
-  function mod(x, y) {
-    return new this(x).mod(y);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   * y {number|string|Decimal}
-   *
-   */
-  function mul(x, y) {
-    return new this(x).mul(y);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} The base.
-   * y {number|string|Decimal} The exponent.
-   *
-   */
-  function pow(x, y) {
-    return new this(x).pow(y);
-  }
-
-
-  /*
-   * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with
-   * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros
-   * are produced).
-   *
-   * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.
-   *
-   */
-  function random(sd) {
-    var d, e, k, n,
-      i = 0,
-      r = new this(1),
-      rd = [];
-
-    if (sd === void 0) sd = this.precision;
-    else checkInt32(sd, 1, MAX_DIGITS);
-
-    k = Math.ceil(sd / LOG_BASE);
-
-    if (!this.crypto) {
-      for (; i < k;) rd[i++] = Math.random() * 1e7 | 0;
-
-    // Browsers supporting crypto.getRandomValues.
-    } else if (crypto.getRandomValues) {
-      d = crypto.getRandomValues(new Uint32Array(k));
-
-      for (; i < k;) {
-        n = d[i];
-
-        // 0 <= n < 4294967296
-        // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).
-        if (n >= 4.29e9) {
-          d[i] = crypto.getRandomValues(new Uint32Array(1))[0];
-        } else {
-
-          // 0 <= n <= 4289999999
-          // 0 <= (n % 1e7) <= 9999999
-          rd[i++] = n % 1e7;
-        }
-      }
-
-    // Node.js supporting crypto.randomBytes.
-    } else if (crypto.randomBytes) {
-
-      // buffer
-      d = crypto.randomBytes(k *= 4);
-
-      for (; i < k;) {
-
-        // 0 <= n < 2147483648
-        n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24);
-
-        // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).
-        if (n >= 2.14e9) {
-          crypto.randomBytes(4).copy(d, i);
-        } else {
-
-          // 0 <= n <= 2139999999
-          // 0 <= (n % 1e7) <= 9999999
-          rd.push(n % 1e7);
-          i += 4;
-        }
-      }
-
-      i = k / 4;
-    } else {
-      throw Error(cryptoUnavailable);
-    }
-
-    k = rd[--i];
-    sd %= LOG_BASE;
-
-    // Convert trailing digits to zeros according to sd.
-    if (k && sd) {
-      n = mathpow(10, LOG_BASE - sd);
-      rd[i] = (k / n | 0) * n;
-    }
-
-    // Remove trailing words which are zero.
-    for (; rd[i] === 0; i--) rd.pop();
-
-    // Zero?
-    if (i < 0) {
-      e = 0;
-      rd = [0];
-    } else {
-      e = -1;
-
-      // Remove leading words which are zero and adjust exponent accordingly.
-      for (; rd[0] === 0; e -= LOG_BASE) rd.shift();
-
-      // Count the digits of the first word of rd to determine leading zeros.
-      for (k = 1, n = rd[0]; n >= 10; n /= 10) k++;
-
-      // Adjust the exponent for leading zeros of the first word of rd.
-      if (k < LOG_BASE) e -= LOG_BASE - k;
-    }
-
-    r.e = e;
-    r.d = rd;
-
-    return r;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.
-   *
-   * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function round(x) {
-    return finalise(x = new this(x), x.e + 1, this.rounding);
-  }
-
-
-  /*
-   * Return
-   *   1    if x > 0,
-   *  -1    if x < 0,
-   *   0    if x is 0,
-   *  -0    if x is -0,
-   *   NaN  otherwise
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function sign(x) {
-    x = new this(x);
-    return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN;
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits
-   * using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function sin(x) {
-    return new this(x).sin();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function sinh(x) {
-    return new this(x).sinh();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function sqrt(x) {
-    return new this(x).sqrt();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits
-   * using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal}
-   * y {number|string|Decimal}
-   *
-   */
-  function sub(x, y) {
-    return new this(x).sub(y);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the sum of the arguments, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * Only the result is rounded, not the intermediate calculations.
-   *
-   * arguments {number|string|Decimal}
-   *
-   */
-  function sum() {
-    var i = 0,
-      args = arguments,
-      x = new this(args[i]);
-
-    external = false;
-    for (; x.s && ++i < args.length;) x = x.plus(args[i]);
-    external = true;
-
-    return finalise(x, this.precision, this.rounding);
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant
-   * digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function tan(x) {
-    return new this(x).tan();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`
-   * significant digits using rounding mode `rounding`.
-   *
-   * x {number|string|Decimal} A value in radians.
-   *
-   */
-  function tanh(x) {
-    return new this(x).tanh();
-  }
-
-
-  /*
-   * Return a new Decimal whose value is `x` truncated to an integer.
-   *
-   * x {number|string|Decimal}
-   *
-   */
-  function trunc(x) {
-    return finalise(x = new this(x), x.e + 1, 1);
-  }
-
-
-  // Create and configure initial Decimal constructor.
-  Decimal = clone(DEFAULTS);
-  Decimal.prototype.constructor = Decimal;
-  Decimal['default'] = Decimal.Decimal = Decimal;
-
-  // Create the internal constants from their string values.
-  LN10 = new Decimal(LN10);
-  PI = new Decimal(PI);
-
-
-  // Export.
-
-
-  // AMD.
-  if (typeof define == 'function' && define.amd) {
-    define(function () {
-      return Decimal;
-    });
-
-  // Node and other environments that support module.exports.
-  } else if (typeof module != 'undefined' && module.exports) {
-    if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
-      P[Symbol['for']('nodejs.util.inspect.custom')] = P.toString;
-      P[Symbol.toStringTag] = 'Decimal';
-    }
-
-    module.exports = Decimal;
-
-  // Browser.
-  } else {
-    if (!globalScope) {
-      globalScope = typeof self != 'undefined' && self && self.self == self ? self : window;
-    }
-
-    noConflict = globalScope.Decimal;
-    Decimal.noConflict = function () {
-      globalScope.Decimal = noConflict;
-      return Decimal;
-    };
-
-    globalScope.Decimal = Decimal;
-  }
-})(this);
\ No newline at end of file
+/* decimal.js-light v2.5.1 https://github.com/MikeMcl/decimal.js-light/LICENCE */
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