From 9e22961379dd504472833ea49d06c74d9575bc33 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 13 May 2019 15:54:31 -0400
Subject: [PATCH 1/2] Adding PR from @johhonn made on other repo

adding this PR https://github.com/hatgit/BIP39-Mnemonic-Tools/pull/13 by #johhonn to this repo on a new dev branch so that I can run tests prior to committing to master.
---
 index.html | 3052 ++--------------------------------------------------
 1 file changed, 83 insertions(+), 2969 deletions(-)

diff --git a/index.html b/index.html
index 3d5be54..142839a 100644
--- a/index.html
+++ b/index.html
@@ -64,2928 +64,12 @@
 b){var c={},d;for(d=0;d<b.length;d++)void 0!==a[b[d]]&&(c[b[d]]=a[b[d]]);return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.pa={};sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.pa,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=void 0===b.salt?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};
 "undefined"!==typeof module&&module.exports&&(module.exports=sjcl);"function"===typeof define&&define([],function(){return sjcl});
     </script>
-    //<script src='./bignumber.js'></script>
-	  
-	  <script name='bignumber.js'>
-  ;(function (globalObject) {
-  'use strict';
-
-/*
- *      bignumber.js v8.1.1
- *      A JavaScript library for arbitrary-precision arithmetic.
- *      https://github.com/MikeMcl/bignumber.js
- *      Copyright (c) 2019 Michael Mclaughlin <M8ch88l@gmail.com>
- *      MIT Licensed.
- *
- *      BigNumber.prototype methods     |  BigNumber methods
- *                                      |
- *      absoluteValue            abs    |  clone
- *      comparedTo                      |  config               set
- *      decimalPlaces            dp     |      DECIMAL_PLACES
- *      dividedBy                div    |      ROUNDING_MODE
- *      dividedToIntegerBy       idiv   |      EXPONENTIAL_AT
- *      exponentiatedBy          pow    |      RANGE
- *      integerValue                    |      CRYPTO
- *      isEqualTo                eq     |      MODULO_MODE
- *      isFinite                        |      POW_PRECISION
- *      isGreaterThan            gt     |      FORMAT
- *      isGreaterThanOrEqualTo   gte    |      ALPHABET
- *      isInteger                       |  isBigNumber
- *      isLessThan               lt     |  maximum              max
- *      isLessThanOrEqualTo      lte    |  minimum              min
- *      isNaN                           |  random
- *      isNegative                      |  sum
- *      isPositive                      |
- *      isZero                          |
- *      minus                           |
- *      modulo                   mod    |
- *      multipliedBy             times  |
- *      negated                         |
- *      plus                            |
- *      precision                sd     |
- *      shiftedBy                       |
- *      squareRoot               sqrt   |
- *      toExponential                   |
- *      toFixed                         |
- *      toFormat                        |
- *      toFraction                      |
- *      toJSON                          |
- *      toNumber                        |
- *      toPrecision                     |
- *      toString                        |
- *      valueOf                         |
- *
- */
-
-
-  var BigNumber,
-    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
-    hasSymbol = typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol',
-
-    mathceil = Math.ceil,
-    mathfloor = Math.floor,
-
-    bignumberError = '[BigNumber Error] ',
-    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
-
-    BASE = 1e14,
-    LOG_BASE = 14,
-    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
-    // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
-    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
-    SQRT_BASE = 1e7,
-
-    // EDITABLE
-    // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
-    // the arguments to toExponential, toFixed, toFormat, and toPrecision.
-    MAX = 1E9;                                   // 0 to MAX_INT32
-
-
-  /*
-   * Create and return a BigNumber constructor.
-   */
-  function clone(configObject) {
-    var div, convertBase, parseNumeric,
-      P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
-      ONE = new BigNumber(1),
-
-
-      //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
-
-
-      // The default values below must be integers within the inclusive ranges stated.
-      // The values can also be changed at run-time using BigNumber.set.
-
-      // The maximum number of decimal places for operations involving division.
-      DECIMAL_PLACES = 20,                     // 0 to MAX
-
-      // The rounding mode used when rounding to the above decimal places, and when using
-      // toExponential, toFixed, toFormat and toPrecision, and round (default value).
-      // UP         0 Away from zero.
-      // DOWN       1 Towards zero.
-      // CEIL       2 Towards +Infinity.
-      // FLOOR      3 Towards -Infinity.
-      // HALF_UP    4 Towards nearest neighbour. If equidistant, up.
-      // HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
-      // HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
-      // HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
-      // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
-      ROUNDING_MODE = 4,                       // 0 to 8
-
-      // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
-
-      // The exponent value at and beneath which toString returns exponential notation.
-      // Number type: -7
-      TO_EXP_NEG = -7,                         // 0 to -MAX
-
-      // The exponent value at and above which toString returns exponential notation.
-      // Number type: 21
-      TO_EXP_POS = 21,                         // 0 to MAX
-
-      // RANGE : [MIN_EXP, MAX_EXP]
-
-      // The minimum exponent value, beneath which underflow to zero occurs.
-      // Number type: -324  (5e-324)
-      MIN_EXP = -1e7,                          // -1 to -MAX
-
-      // The maximum exponent value, above which overflow to Infinity occurs.
-      // Number type:  308  (1.7976931348623157e+308)
-      // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
-      MAX_EXP = 1e7,                           // 1 to MAX
-
-      // Whether to use cryptographically-secure random number generation, if available.
-      CRYPTO = false,                          // true or false
-
-      // 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.
-      //             This modulo mode is commonly known as 'truncated division' and is
-      //             equivalent to (a % n) in JavaScript.
-      // FLOOR     3 The remainder has the same sign as the divisor (Python %).
-      // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
-      // EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
-      //             The remainder is always positive.
-      //
-      // The truncated division, floored division, Euclidian division and IEEE 754 remainder
-      // modes are commonly used for the modulus operation.
-      // Although the other rounding modes can also be used, they may not give useful results.
-      MODULO_MODE = 1,                         // 0 to 9
-
-      // The maximum number of significant digits of the result of the exponentiatedBy operation.
-      // If POW_PRECISION is 0, there will be unlimited significant digits.
-      POW_PRECISION = 0,                    // 0 to MAX
-
-      // The format specification used by the BigNumber.prototype.toFormat method.
-      FORMAT = {
-        prefix: '',
-        groupSize: 3,
-        secondaryGroupSize: 0,
-        groupSeparator: ',',
-        decimalSeparator: '.',
-        fractionGroupSize: 0,
-        fractionGroupSeparator: '\xA0',      // non-breaking space
-        suffix: ''
-      },
-
-      // The alphabet used for base conversion. It must be at least 2 characters long, with no '+',
-      // '-', '.', whitespace, or repeated character.
-      // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
-      ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
-
-
-    //------------------------------------------------------------------------------------------
-
-
-    // CONSTRUCTOR
-
-
-    /*
-     * The BigNumber constructor and exported function.
-     * Create and return a new instance of a BigNumber object.
-     *
-     * v {number|string|BigNumber} A numeric value.
-     * [b] {number} The base of v. Integer, 2 to ALPHABET.length inclusive.
-     */
-    function BigNumber(v, b) {
-      var alphabet, c, caseChanged, e, i, isNum, len, str,
-        x = this;
-
-      // Enable constructor call without `new`.
-      if (!(x instanceof BigNumber)) return new BigNumber(v, b);
-
-      if (b == null) {
-
-        if (v && v._isBigNumber === true) {
-          x.s = v.s;
-
-          if (!v.c || v.e > MAX_EXP) {
-            x.c = x.e = null;
-          } else if (v.e < MIN_EXP) {
-            x.c = [x.e = 0];
-          } else {
-            x.e = v.e;
-            x.c = v.c.slice();
-          }
-
-          return;
-        }
-
-        if ((isNum = typeof v == 'number') && v * 0 == 0) {
-
-          // Use `1 / n` to handle minus zero also.
-          x.s = 1 / v < 0 ? (v = -v, -1) : 1;
-
-          // Fast path for integers, where n < 2147483648 (2**31).
-          if (v === ~~v) {
-            for (e = 0, i = v; i >= 10; i /= 10, e++);
-
-            if (e > MAX_EXP) {
-              x.c = x.e = null;
-            } else {
-              x.e = e;
-              x.c = [v];
-            }
-
-            return;
-          }
-
-          str = String(v);
-        } else {
-
-          if (!isNumeric.test(str = String(v))) return parseNumeric(x, str, isNum);
-
-          x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
-        }
-
-        // 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;
-        }
-
-      } else {
-
-        // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
-        intCheck(b, 2, ALPHABET.length, 'Base');
-
-        // Allow exponential notation to be used with base 10 argument, while
-        // also rounding to DECIMAL_PLACES as with other bases.
-        if (b == 10) {
-          x = new BigNumber(v);
-          return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
-        }
-
-        str = String(v);
-
-        if (isNum = typeof v == 'number') {
-
-          // Avoid potential interpretation of Infinity and NaN as base 44+ values.
-          if (v * 0 != 0) return parseNumeric(x, str, isNum, b);
-
-          x.s = 1 / v < 0 ? (str = str.slice(1), -1) : 1;
-
-          // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
-          if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
-            throw Error
-             (tooManyDigits + v);
-          }
-        } else {
-          x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
-        }
-
-        alphabet = ALPHABET.slice(0, b);
-        e = i = 0;
-
-        // Check that str is a valid base b number.
-        // Don't use RegExp, so alphabet can contain special characters.
-        for (len = str.length; i < len; i++) {
-          if (alphabet.indexOf(c = str.charAt(i)) < 0) {
-            if (c == '.') {
-
-              // If '.' is not the first character and it has not be found before.
-              if (i > e) {
-                e = len;
-                continue;
-              }
-            } else if (!caseChanged) {
-
-              // Allow e.g. hexadecimal 'FF' as well as 'ff'.
-              if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
-                  str == str.toLowerCase() && (str = str.toUpperCase())) {
-                caseChanged = true;
-                i = -1;
-                e = 0;
-                continue;
-              }
-            }
-
-            return parseNumeric(x, String(v), isNum, b);
-          }
-        }
-
-        // Prevent later check for length on converted number.
-        isNum = false;
-        str = convertBase(str, b, 10, x.s);
-
-        // Decimal point?
-        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
-        else e = str.length;
-      }
-
-      // Determine leading zeros.
-      for (i = 0; str.charCodeAt(i) === 48; i++);
-
-      // Determine trailing zeros.
-      for (len = str.length; str.charCodeAt(--len) === 48;);
-
-      if (str = str.slice(i, ++len)) {
-        len -= i;
-
-        // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
-        if (isNum && BigNumber.DEBUG &&
-          len > 15 && (v > MAX_SAFE_INTEGER || v !== mathfloor(v))) {
-            throw Error
-             (tooManyDigits + (x.s * v));
-        }
-
-         // Overflow?
-        if ((e = e - i - 1) > MAX_EXP) {
-
-          // Infinity.
-          x.c = x.e = null;
-
-        // Underflow?
-        } else if (e < MIN_EXP) {
-
-          // Zero.
-          x.c = [x.e = 0];
-        } else {
-          x.e = e;
-          x.c = [];
-
-          // Transform base
-
-          // e is the base 10 exponent.
-          // i is where to slice str to get the first element of the coefficient array.
-          i = (e + 1) % LOG_BASE;
-          if (e < 0) i += LOG_BASE;  // i < 1
-
-          if (i < len) {
-            if (i) x.c.push(+str.slice(0, i));
-
-            for (len -= LOG_BASE; i < len;) {
-              x.c.push(+str.slice(i, i += LOG_BASE));
-            }
-
-            i = LOG_BASE - (str = str.slice(i)).length;
-          } else {
-            i -= len;
-          }
-
-          for (; i--; str += '0');
-          x.c.push(+str);
-        }
-      } else {
-
-        // Zero.
-        x.c = [x.e = 0];
-      }
-    }
-
-
-    // CONSTRUCTOR PROPERTIES
-
-
-    BigNumber.clone = clone;
-
-    BigNumber.ROUND_UP = 0;
-    BigNumber.ROUND_DOWN = 1;
-    BigNumber.ROUND_CEIL = 2;
-    BigNumber.ROUND_FLOOR = 3;
-    BigNumber.ROUND_HALF_UP = 4;
-    BigNumber.ROUND_HALF_DOWN = 5;
-    BigNumber.ROUND_HALF_EVEN = 6;
-    BigNumber.ROUND_HALF_CEIL = 7;
-    BigNumber.ROUND_HALF_FLOOR = 8;
-    BigNumber.EUCLID = 9;
-
-
-    /*
-     * Configure infrequently-changing library-wide settings.
-     *
-     * Accept an object with the following optional properties (if the value of a property is
-     * a number, it must be an integer within the inclusive range stated):
-     *
-     *   DECIMAL_PLACES   {number}           0 to MAX
-     *   ROUNDING_MODE    {number}           0 to 8
-     *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
-     *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
-     *   CRYPTO           {boolean}          true or false
-     *   MODULO_MODE      {number}           0 to 9
-     *   POW_PRECISION       {number}           0 to MAX
-     *   ALPHABET         {string}           A string of two or more unique characters which does
-     *                                       not contain '.'.
-     *   FORMAT           {object}           An object with some of the following properties:
-     *     prefix                 {string}
-     *     groupSize              {number}
-     *     secondaryGroupSize     {number}
-     *     groupSeparator         {string}
-     *     decimalSeparator       {string}
-     *     fractionGroupSize      {number}
-     *     fractionGroupSeparator {string}
-     *     suffix                 {string}
-     *
-     * (The values assigned to the above FORMAT object properties are not checked for validity.)
-     *
-     * E.g.
-     * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
-     *
-     * Ignore properties/parameters set to null or undefined, except for ALPHABET.
-     *
-     * Return an object with the properties current values.
-     */
-    BigNumber.config = BigNumber.set = function (obj) {
-      var p, v;
-
-      if (obj != null) {
-
-        if (typeof obj == 'object') {
-
-          // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
-          // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
-          if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
-            v = obj[p];
-            intCheck(v, 0, MAX, p);
-            DECIMAL_PLACES = v;
-          }
-
-          // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
-          // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
-          if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
-            v = obj[p];
-            intCheck(v, 0, 8, p);
-            ROUNDING_MODE = v;
-          }
-
-          // EXPONENTIAL_AT {number|number[]}
-          // Integer, -MAX to MAX inclusive or
-          // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
-          // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
-          if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
-            v = obj[p];
-            if (v && v.pop) {
-              intCheck(v[0], -MAX, 0, p);
-              intCheck(v[1], 0, MAX, p);
-              TO_EXP_NEG = v[0];
-              TO_EXP_POS = v[1];
-            } else {
-              intCheck(v, -MAX, MAX, p);
-              TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
-            }
-          }
-
-          // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
-          // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
-          // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
-          if (obj.hasOwnProperty(p = 'RANGE')) {
-            v = obj[p];
-            if (v && v.pop) {
-              intCheck(v[0], -MAX, -1, p);
-              intCheck(v[1], 1, MAX, p);
-              MIN_EXP = v[0];
-              MAX_EXP = v[1];
-            } else {
-              intCheck(v, -MAX, MAX, p);
-              if (v) {
-                MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
-              } else {
-                throw Error
-                 (bignumberError + p + ' cannot be zero: ' + v);
-              }
-            }
-          }
-
-          // CRYPTO {boolean} true or false.
-          // '[BigNumber Error] CRYPTO not true or false: {v}'
-          // '[BigNumber Error] crypto unavailable'
-          if (obj.hasOwnProperty(p = 'CRYPTO')) {
-            v = obj[p];
-            if (v === !!v) {
-              if (v) {
-                if (typeof crypto != 'undefined' && crypto &&
-                 (crypto.getRandomValues || crypto.randomBytes)) {
-                  CRYPTO = v;
-                } else {
-                  CRYPTO = !v;
-                  throw Error
-                   (bignumberError + 'crypto unavailable');
-                }
-              } else {
-                CRYPTO = v;
-              }
-            } else {
-              throw Error
-               (bignumberError + p + ' not true or false: ' + v);
-            }
-          }
-
-          // MODULO_MODE {number} Integer, 0 to 9 inclusive.
-          // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
-          if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
-            v = obj[p];
-            intCheck(v, 0, 9, p);
-            MODULO_MODE = v;
-          }
-
-          // POW_PRECISION {number} Integer, 0 to MAX inclusive.
-          // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
-          if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
-            v = obj[p];
-            intCheck(v, 0, MAX, p);
-            POW_PRECISION = v;
-          }
-
-          // FORMAT {object}
-          // '[BigNumber Error] FORMAT not an object: {v}'
-          if (obj.hasOwnProperty(p = 'FORMAT')) {
-            v = obj[p];
-            if (typeof v == 'object') FORMAT = v;
-            else throw Error
-             (bignumberError + p + ' not an object: ' + v);
-          }
-
-          // ALPHABET {string}
-          // '[BigNumber Error] ALPHABET invalid: {v}'
-          if (obj.hasOwnProperty(p = 'ALPHABET')) {
-            v = obj[p];
-
-            // Disallow if only one character,
-            // or if it contains '+', '-', '.', whitespace, or a repeated character.
-            if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
-              ALPHABET = v;
-            } else {
-              throw Error
-               (bignumberError + p + ' invalid: ' + v);
-            }
-          }
-
-        } else {
-
-          // '[BigNumber Error] Object expected: {v}'
-          throw Error
-           (bignumberError + 'Object expected: ' + obj);
-        }
-      }
-
-      return {
-        DECIMAL_PLACES: DECIMAL_PLACES,
-        ROUNDING_MODE: ROUNDING_MODE,
-        EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
-        RANGE: [MIN_EXP, MAX_EXP],
-        CRYPTO: CRYPTO,
-        MODULO_MODE: MODULO_MODE,
-        POW_PRECISION: POW_PRECISION,
-        FORMAT: FORMAT,
-        ALPHABET: ALPHABET
-      };
-    };
-
-
-    /*
-     * Return true if v is a BigNumber instance, otherwise return false.
-     *
-     * If BigNumber.DEBUG is true, throw if a BigNumber instance is not well-formed.
-     *
-     * v {any}
-     *
-     * '[BigNumber Error] Invalid BigNumber: {v}'
-     */
-    BigNumber.isBigNumber = function (v) {
-      if (!v || v._isBigNumber !== true) return false;
-      if (!BigNumber.DEBUG) return true;
-
-      var i, n,
-        c = v.c,
-        e = v.e,
-        s = v.s;
-
-      out: if ({}.toString.call(c) == '[object Array]') {
-
-        if ((s === 1 || s === -1) && e >= -MAX && e <= MAX && e === mathfloor(e)) {
-
-          // If the first element is zero, the BigNumber value must be zero.
-          if (c[0] === 0) {
-            if (e === 0 && c.length === 1) return true;
-            break out;
-          }
-
-          // Calculate number of digits that c[0] should have, based on the exponent.
-          i = (e + 1) % LOG_BASE;
-          if (i < 1) i += LOG_BASE;
-
-          // Calculate number of digits of c[0].
-          //if (Math.ceil(Math.log(c[0] + 1) / Math.LN10) == i) {
-          if (String(c[0]).length == i) {
-
-            for (i = 0; i < c.length; i++) {
-              n = c[i];
-              if (n < 0 || n >= BASE || n !== mathfloor(n)) break out;
-            }
-
-            // Last element cannot be zero, unless it is the only element.
-            if (n !== 0) return true;
-          }
-        }
-
-      // Infinity/NaN
-      } else if (c === null && e === null && (s === null || s === 1 || s === -1)) {
-        return true;
-      }
-
-      throw Error
-        (bignumberError + 'Invalid BigNumber: ' + v);
-    };
-
-
-    /*
-     * Return a new BigNumber whose value is the maximum of the arguments.
-     *
-     * arguments {number|string|BigNumber}
-     */
-    BigNumber.maximum = BigNumber.max = function () {
-      return maxOrMin(arguments, P.lt);
-    };
-
-
-    /*
-     * Return a new BigNumber whose value is the minimum of the arguments.
-     *
-     * arguments {number|string|BigNumber}
-     */
-    BigNumber.minimum = BigNumber.min = function () {
-      return maxOrMin(arguments, P.gt);
-    };
-
-
-    /*
-     * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
-     * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
-     * zeros are produced).
-     *
-     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
-     * '[BigNumber Error] crypto unavailable'
-     */
-    BigNumber.random = (function () {
-      var pow2_53 = 0x20000000000000;
-
-      // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
-      // Check if Math.random() produces more than 32 bits of randomness.
-      // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
-      // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
-      var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
-       ? function () { return mathfloor(Math.random() * pow2_53); }
-       : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
-         (Math.random() * 0x800000 | 0); };
-
-      return function (dp) {
-        var a, b, e, k, v,
-          i = 0,
-          c = [],
-          rand = new BigNumber(ONE);
-
-        if (dp == null) dp = DECIMAL_PLACES;
-        else intCheck(dp, 0, MAX);
-
-        k = mathceil(dp / LOG_BASE);
-
-        if (CRYPTO) {
-
-          // Browsers supporting crypto.getRandomValues.
-          if (crypto.getRandomValues) {
-
-            a = crypto.getRandomValues(new Uint32Array(k *= 2));
-
-            for (; i < k;) {
-
-              // 53 bits:
-              // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
-              // 11111 11111111 11111111 11111111 11100000 00000000 00000000
-              // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
-              //                                     11111 11111111 11111111
-              // 0x20000 is 2^21.
-              v = a[i] * 0x20000 + (a[i + 1] >>> 11);
-
-              // Rejection sampling:
-              // 0 <= v < 9007199254740992
-              // Probability that v >= 9e15, is
-              // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
-              if (v >= 9e15) {
-                b = crypto.getRandomValues(new Uint32Array(2));
-                a[i] = b[0];
-                a[i + 1] = b[1];
-              } else {
-
-                // 0 <= v <= 8999999999999999
-                // 0 <= (v % 1e14) <= 99999999999999
-                c.push(v % 1e14);
-                i += 2;
-              }
-            }
-            i = k / 2;
-
-          // Node.js supporting crypto.randomBytes.
-          } else if (crypto.randomBytes) {
-
-            // buffer
-            a = crypto.randomBytes(k *= 7);
-
-            for (; i < k;) {
-
-              // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
-              // 0x100000000 is 2^32, 0x1000000 is 2^24
-              // 11111 11111111 11111111 11111111 11111111 11111111 11111111
-              // 0 <= v < 9007199254740992
-              v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
-                 (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
-                 (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
-
-              if (v >= 9e15) {
-                crypto.randomBytes(7).copy(a, i);
-              } else {
-
-                // 0 <= (v % 1e14) <= 99999999999999
-                c.push(v % 1e14);
-                i += 7;
-              }
-            }
-            i = k / 7;
-          } else {
-            CRYPTO = false;
-            throw Error
-             (bignumberError + 'crypto unavailable');
-          }
-        }
-
-        // Use Math.random.
-        if (!CRYPTO) {
-
-          for (; i < k;) {
-            v = random53bitInt();
-            if (v < 9e15) c[i++] = v % 1e14;
-          }
-        }
-
-        k = c[--i];
-        dp %= LOG_BASE;
-
-        // Convert trailing digits to zeros according to dp.
-        if (k && dp) {
-          v = POWS_TEN[LOG_BASE - dp];
-          c[i] = mathfloor(k / v) * v;
-        }
-
-        // Remove trailing elements which are zero.
-        for (; c[i] === 0; c.pop(), i--);
-
-        // Zero?
-        if (i < 0) {
-          c = [e = 0];
-        } else {
-
-          // Remove leading elements which are zero and adjust exponent accordingly.
-          for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
-
-          // Count the digits of the first element of c to determine leading zeros, and...
-          for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
-
-          // adjust the exponent accordingly.
-          if (i < LOG_BASE) e -= LOG_BASE - i;
-        }
-
-        rand.e = e;
-        rand.c = c;
-        return rand;
-      };
-    })();
-
-
-    /*
-     * Return a BigNumber whose value is the sum of the arguments.
-     *
-     * arguments {number|string|BigNumber}
-     */
-    BigNumber.sum = function () {
-      var i = 1,
-        args = arguments,
-        sum = new BigNumber(args[0]);
-      for (; i < args.length;) sum = sum.plus(args[i++]);
-      return sum;
-    };
-
-
-    // PRIVATE FUNCTIONS
-
-
-    // Called by BigNumber and BigNumber.prototype.toString.
-    convertBase = (function () {
-      var decimal = '0123456789';
-
-      /*
-       * Convert string of baseIn to an array of numbers of baseOut.
-       * Eg. toBaseOut('255', 10, 16) returns [15, 15].
-       * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
-       */
-      function toBaseOut(str, baseIn, baseOut, alphabet) {
-        var j,
-          arr = [0],
-          arrL,
-          i = 0,
-          len = str.length;
-
-        for (; i < len;) {
-          for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
-
-          arr[0] += alphabet.indexOf(str.charAt(i++));
-
-          for (j = 0; j < arr.length; j++) {
-
-            if (arr[j] > baseOut - 1) {
-              if (arr[j + 1] == null) arr[j + 1] = 0;
-              arr[j + 1] += arr[j] / baseOut | 0;
-              arr[j] %= baseOut;
-            }
-          }
-        }
-
-        return arr.reverse();
-      }
-
-      // Convert a numeric string of baseIn to a numeric string of baseOut.
-      // If the caller is toString, we are converting from base 10 to baseOut.
-      // If the caller is BigNumber, we are converting from baseIn to base 10.
-      return function (str, baseIn, baseOut, sign, callerIsToString) {
-        var alphabet, d, e, k, r, x, xc, y,
-          i = str.indexOf('.'),
-          dp = DECIMAL_PLACES,
-          rm = ROUNDING_MODE;
-
-        // Non-integer.
-        if (i >= 0) {
-          k = POW_PRECISION;
-
-          // Unlimited precision.
-          POW_PRECISION = 0;
-          str = str.replace('.', '');
-          y = new BigNumber(baseIn);
-          x = y.pow(str.length - i);
-          POW_PRECISION = k;
-
-          // Convert str as if an integer, then restore the fraction part by dividing the
-          // result by its base raised to a power.
-
-          y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
-           10, baseOut, decimal);
-          y.e = y.c.length;
-        }
-
-        // Convert the number as integer.
-
-        xc = toBaseOut(str, baseIn, baseOut, callerIsToString
-         ? (alphabet = ALPHABET, decimal)
-         : (alphabet = decimal, ALPHABET));
-
-        // xc now represents str as an integer and converted to baseOut. e is the exponent.
-        e = k = xc.length;
-
-        // Remove trailing zeros.
-        for (; xc[--k] == 0; xc.pop());
-
-        // Zero?
-        if (!xc[0]) return alphabet.charAt(0);
-
-        // Does str represent an integer? If so, no need for the division.
-        if (i < 0) {
-          --e;
-        } else {
-          x.c = xc;
-          x.e = e;
-
-          // The sign is needed for correct rounding.
-          x.s = sign;
-          x = div(x, y, dp, rm, baseOut);
-          xc = x.c;
-          r = x.r;
-          e = x.e;
-        }
-
-        // xc now represents str converted to baseOut.
-
-        // THe index of the rounding digit.
-        d = e + dp + 1;
-
-        // The rounding digit: the digit to the right of the digit that may be rounded up.
-        i = xc[d];
-
-        // Look at the rounding digits and mode to determine whether to round up.
-
-        k = baseOut / 2;
-        r = r || d < 0 || xc[d + 1] != null;
-
-        r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
-              : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
-               rm == (x.s < 0 ? 8 : 7));
-
-        // If the index of the rounding digit is not greater than zero, or xc represents
-        // zero, then the result of the base conversion is zero or, if rounding up, a value
-        // such as 0.00001.
-        if (d < 1 || !xc[0]) {
-
-          // 1^-dp or 0
-          str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
-        } else {
-
-          // Truncate xc to the required number of decimal places.
-          xc.length = d;
-
-          // Round up?
-          if (r) {
-
-            // Rounding up may mean the previous digit has to be rounded up and so on.
-            for (--baseOut; ++xc[--d] > baseOut;) {
-              xc[d] = 0;
-
-              if (!d) {
-                ++e;
-                xc = [1].concat(xc);
-              }
-            }
-          }
-
-          // Determine trailing zeros.
-          for (k = xc.length; !xc[--k];);
-
-          // E.g. [4, 11, 15] becomes 4bf.
-          for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
-
-          // Add leading zeros, decimal point and trailing zeros as required.
-          str = toFixedPoint(str, e, alphabet.charAt(0));
-        }
-
-        // The caller will add the sign.
-        return str;
-      };
-    })();
-
-
-    // Perform division in the specified base. Called by div and convertBase.
-    div = (function () {
-
-      // Assume non-zero x and k.
-      function multiply(x, k, base) {
-        var m, temp, xlo, xhi,
-          carry = 0,
-          i = x.length,
-          klo = k % SQRT_BASE,
-          khi = k / SQRT_BASE | 0;
-
-        for (x = x.slice(); i--;) {
-          xlo = x[i] % SQRT_BASE;
-          xhi = x[i] / SQRT_BASE | 0;
-          m = khi * xlo + xhi * klo;
-          temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
-          carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
-          x[i] = temp % base;
-        }
-
-        if (carry) x = [carry].concat(x);
-
-        return x;
-      }
-
-      function compare(a, b, aL, bL) {
-        var i, cmp;
-
-        if (aL != bL) {
-          cmp = aL > bL ? 1 : -1;
-        } else {
-
-          for (i = cmp = 0; i < aL; i++) {
-
-            if (a[i] != b[i]) {
-              cmp = a[i] > b[i] ? 1 : -1;
-              break;
-            }
-          }
-        }
-
-        return cmp;
-      }
-
-      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.splice(0, 1));
-      }
-
-      // x: dividend, y: divisor.
-      return function (x, y, dp, rm, base) {
-        var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
-          yL, yz,
-          s = x.s == y.s ? 1 : -1,
-          xc = x.c,
-          yc = y.c;
-
-        // Either NaN, Infinity or 0?
-        if (!xc || !xc[0] || !yc || !yc[0]) {
-
-          return new BigNumber(
-
-           // Return NaN if either NaN, or both Infinity or 0.
-           !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
-
-            // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
-            xc && xc[0] == 0 || !yc ? s * 0 : s / 0
-         );
-        }
-
-        q = new BigNumber(s);
-        qc = q.c = [];
-        e = x.e - y.e;
-        s = dp + e + 1;
-
-        if (!base) {
-          base = BASE;
-          e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
-          s = s / LOG_BASE | 0;
-        }
-
-        // Result exponent may be one less then the current value of e.
-        // The coefficients of the BigNumbers from convertBase may have trailing zeros.
-        for (i = 0; yc[i] == (xc[i] || 0); i++);
-
-        if (yc[i] > (xc[i] || 0)) e--;
-
-        if (s < 0) {
-          qc.push(1);
-          more = true;
-        } else {
-          xL = xc.length;
-          yL = yc.length;
-          i = 0;
-          s += 2;
-
-          // Normalise xc and yc so highest order digit of yc is >= base / 2.
-
-          n = mathfloor(base / (yc[0] + 1));
-
-          // Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
-          // if (n > 1 || n++ == 1 && yc[0] < base / 2) {
-          if (n > 1) {
-            yc = multiply(yc, n, base);
-            xc = multiply(xc, n, base);
-            yL = yc.length;
-            xL = xc.length;
-          }
-
-          xi = yL;
-          rem = xc.slice(0, yL);
-          remL = rem.length;
-
-          // Add zeros to make remainder as long as divisor.
-          for (; remL < yL; rem[remL++] = 0);
-          yz = yc.slice();
-          yz = [0].concat(yz);
-          yc0 = yc[0];
-          if (yc[1] >= base / 2) yc0++;
-          // Not necessary, but to prevent trial digit n > base, when using base 3.
-          // else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
-
-          do {
-            n = 0;
-
-            // Compare divisor and remainder.
-            cmp = compare(yc, rem, yL, remL);
-
-            // If divisor < remainder.
-            if (cmp < 0) {
-
-              // Calculate trial digit, n.
-
-              rem0 = rem[0];
-              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
-
-              // n is how many times the divisor goes into the current remainder.
-              n = mathfloor(rem0 / yc0);
-
-              //  Algorithm:
-              //  product = divisor multiplied by trial digit (n).
-              //  Compare product and remainder.
-              //  If product is greater than remainder:
-              //    Subtract divisor from product, decrement trial digit.
-              //  Subtract product from remainder.
-              //  If product was less than remainder at the last compare:
-              //    Compare new remainder and divisor.
-              //    If remainder is greater than divisor:
-              //      Subtract divisor from remainder, increment trial digit.
-
-              if (n > 1) {
-
-                // n may be > base only when base is 3.
-                if (n >= base) n = base - 1;
-
-                // product = divisor * trial digit.
-                prod = multiply(yc, n, base);
-                prodL = prod.length;
-                remL = rem.length;
-
-                // Compare product and remainder.
-                // If product > remainder then trial digit n too high.
-                // n is 1 too high about 5% of the time, and is not known to have
-                // ever been more than 1 too high.
-                while (compare(prod, rem, prodL, remL) == 1) {
-                  n--;
-
-                  // Subtract divisor from product.
-                  subtract(prod, yL < prodL ? yz : yc, prodL, base);
-                  prodL = prod.length;
-                  cmp = 1;
-                }
-              } else {
-
-                // n is 0 or 1, cmp is -1.
-                // If n is 0, there is no need to compare yc and rem again below,
-                // so change cmp to 1 to avoid it.
-                // If n is 1, leave cmp as -1, so yc and rem are compared again.
-                if (n == 0) {
-
-                  // divisor < remainder, so n must be at least 1.
-                  cmp = n = 1;
-                }
-
-                // product = divisor
-                prod = yc.slice();
-                prodL = prod.length;
-              }
-
-              if (prodL < remL) prod = [0].concat(prod);
-
-              // Subtract product from remainder.
-              subtract(rem, prod, remL, base);
-              remL = rem.length;
-
-               // If product was < remainder.
-              if (cmp == -1) {
-
-                // Compare divisor and new remainder.
-                // If divisor < new remainder, subtract divisor from remainder.
-                // Trial digit n too low.
-                // n is 1 too low about 5% of the time, and very rarely 2 too low.
-                while (compare(yc, rem, yL, remL) < 1) {
-                  n++;
-
-                  // Subtract divisor from remainder.
-                  subtract(rem, yL < remL ? yz : yc, remL, base);
-                  remL = rem.length;
-                }
-              }
-            } else if (cmp === 0) {
-              n++;
-              rem = [0];
-            } // else cmp === 1 and n will be 0
-
-            // Add the next digit, n, to the result array.
-            qc[i++] = n;
-
-            // Update the remainder.
-            if (rem[0]) {
-              rem[remL++] = xc[xi] || 0;
-            } else {
-              rem = [xc[xi]];
-              remL = 1;
-            }
-          } while ((xi++ < xL || rem[0] != null) && s--);
-
-          more = rem[0] != null;
-
-          // Leading zero?
-          if (!qc[0]) qc.splice(0, 1);
-        }
-
-        if (base == BASE) {
-
-          // To calculate q.e, first get the number of digits of qc[0].
-          for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
-
-          round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
-
-        // Caller is convertBase.
-        } else {
-          q.e = e;
-          q.r = +more;
-        }
-
-        return q;
-      };
-    })();
-
-
-    /*
-     * Return a string representing the value of BigNumber n in fixed-point or exponential
-     * notation rounded to the specified decimal places or significant digits.
-     *
-     * n: a BigNumber.
-     * i: the index of the last digit required (i.e. the digit that may be rounded up).
-     * rm: the rounding mode.
-     * id: 1 (toExponential) or 2 (toPrecision).
-     */
-    function format(n, i, rm, id) {
-      var c0, e, ne, len, str;
-
-      if (rm == null) rm = ROUNDING_MODE;
-      else intCheck(rm, 0, 8);
-
-      if (!n.c) return n.toString();
-
-      c0 = n.c[0];
-      ne = n.e;
-
-      if (i == null) {
-        str = coeffToString(n.c);
-        str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
-         ? toExponential(str, ne)
-         : toFixedPoint(str, ne, '0');
-      } else {
-        n = round(new BigNumber(n), i, rm);
-
-        // n.e may have changed if the value was rounded up.
-        e = n.e;
-
-        str = coeffToString(n.c);
-        len = str.length;
-
-        // toPrecision returns exponential notation if the number of significant digits
-        // specified is less than the number of digits necessary to represent the integer
-        // part of the value in fixed-point notation.
-
-        // Exponential notation.
-        if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
-
-          // Append zeros?
-          for (; len < i; str += '0', len++);
-          str = toExponential(str, e);
-
-        // Fixed-point notation.
-        } else {
-          i -= ne;
-          str = toFixedPoint(str, e, '0');
-
-          // Append zeros?
-          if (e + 1 > len) {
-            if (--i > 0) for (str += '.'; i--; str += '0');
-          } else {
-            i += e - len;
-            if (i > 0) {
-              if (e + 1 == len) str += '.';
-              for (; i--; str += '0');
-            }
-          }
-        }
-      }
-
-      return n.s < 0 && c0 ? '-' + str : str;
-    }
-
-
-    // Handle BigNumber.max and BigNumber.min.
-    function maxOrMin(args, method) {
-      var n,
-        i = 1,
-        m = new BigNumber(args[0]);
-
-      for (; i < args.length; i++) {
-        n = new BigNumber(args[i]);
-
-        // If any number is NaN, return NaN.
-        if (!n.s) {
-          m = n;
-          break;
-        } else if (method.call(m, n)) {
-          m = n;
-        }
-      }
-
-      return m;
-    }
-
-
-    /*
-     * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
-     * Called by minus, plus and times.
-     */
-    function normalise(n, c, e) {
-      var i = 1,
-        j = c.length;
-
-       // Remove trailing zeros.
-      for (; !c[--j]; c.pop());
-
-      // Calculate the base 10 exponent. First get the number of digits of c[0].
-      for (j = c[0]; j >= 10; j /= 10, i++);
-
-      // Overflow?
-      if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
-
-        // Infinity.
-        n.c = n.e = null;
-
-      // Underflow?
-      } else if (e < MIN_EXP) {
-
-        // Zero.
-        n.c = [n.e = 0];
-      } else {
-        n.e = e;
-        n.c = c;
-      }
-
-      return n;
-    }
-
-
-    // Handle values that fail the validity test in BigNumber.
-    parseNumeric = (function () {
-      var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
-        dotAfter = /^([^.]+)\.$/,
-        dotBefore = /^\.([^.]+)$/,
-        isInfinityOrNaN = /^-?(Infinity|NaN)$/,
-        whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
-
-      return function (x, str, isNum, b) {
-        var base,
-          s = isNum ? str : str.replace(whitespaceOrPlus, '');
-
-        // No exception on ±Infinity or NaN.
-        if (isInfinityOrNaN.test(s)) {
-          x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
-        } else {
-          if (!isNum) {
-
-            // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
-            s = s.replace(basePrefix, function (m, p1, p2) {
-              base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
-              return !b || b == base ? p1 : m;
-            });
-
-            if (b) {
-              base = b;
-
-              // E.g. '1.' to '1', '.1' to '0.1'
-              s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
-            }
-
-            if (str != s) return new BigNumber(s, base);
-          }
-
-          // '[BigNumber Error] Not a number: {n}'
-          // '[BigNumber Error] Not a base {b} number: {n}'
-          if (BigNumber.DEBUG) {
-            throw Error
-              (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
-          }
-
-          // NaN
-          x.s = null;
-        }
-
-        x.c = x.e = null;
-      }
-    })();
-
-
-    /*
-     * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
-     * If r is truthy, it is known that there are more digits after the rounding digit.
-     */
-    function round(x, sd, rm, r) {
-      var d, i, j, k, n, ni, rd,
-        xc = x.c,
-        pows10 = POWS_TEN;
-
-      // if x is not Infinity or NaN...
-      if (xc) {
-
-        // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
-        // n is a base 1e14 number, the value of the element of array x.c containing rd.
-        // ni is the index of n within x.c.
-        // d is the number of digits of n.
-        // i is the index of rd within n including leading zeros.
-        // j is the actual index of rd within n (if < 0, rd is a leading zero).
-        out: {
-
-          // Get the number of digits of the first element of xc.
-          for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
-          i = sd - d;
-
-          // If the rounding digit is in the first element of xc...
-          if (i < 0) {
-            i += LOG_BASE;
-            j = sd;
-            n = xc[ni = 0];
-
-            // Get the rounding digit at index j of n.
-            rd = n / pows10[d - j - 1] % 10 | 0;
-          } else {
-            ni = mathceil((i + 1) / LOG_BASE);
-
-            if (ni >= xc.length) {
-
-              if (r) {
-
-                // Needed by sqrt.
-                for (; xc.length <= ni; xc.push(0));
-                n = rd = 0;
-                d = 1;
-                i %= LOG_BASE;
-                j = i - LOG_BASE + 1;
-              } else {
-                break out;
-              }
-            } else {
-              n = k = xc[ni];
-
-              // Get the number of digits of n.
-              for (d = 1; k >= 10; k /= 10, d++);
-
-              // Get the index of rd within n.
-              i %= LOG_BASE;
-
-              // Get the index of rd within n, adjusted for leading zeros.
-              // The number of leading zeros of n is given by LOG_BASE - d.
-              j = i - LOG_BASE + d;
-
-              // Get the rounding digit at index j of n.
-              rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
-            }
-          }
-
-          r = r || sd < 0 ||
-
-          // Are there any non-zero digits after the rounding digit?
-          // The expression  n % pows10[d - j - 1]  returns all digits of n to the right
-          // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
-           xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
-
-          r = rm < 4
-           ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
-           : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
-
-            // Check whether the digit to the left of the rounding digit is odd.
-            ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
-             rm == (x.s < 0 ? 8 : 7));
-
-          if (sd < 1 || !xc[0]) {
-            xc.length = 0;
-
-            if (r) {
-
-              // Convert sd to decimal places.
-              sd -= x.e + 1;
-
-              // 1, 0.1, 0.01, 0.001, 0.0001 etc.
-              xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
-              x.e = -sd || 0;
-            } else {
-
-              // Zero.
-              xc[0] = x.e = 0;
-            }
-
-            return x;
-          }
-
-          // Remove excess digits.
-          if (i == 0) {
-            xc.length = ni;
-            k = 1;
-            ni--;
-          } else {
-            xc.length = ni + 1;
-            k = pows10[LOG_BASE - i];
-
-            // E.g. 56700 becomes 56000 if 7 is the rounding digit.
-            // j > 0 means i > number of leading zeros of n.
-            xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
-          }
-
-          // Round up?
-          if (r) {
-
-            for (; ;) {
-
-              // If the digit to be rounded up is in the first element of xc...
-              if (ni == 0) {
-
-                // i will be the length of xc[0] before k is added.
-                for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
-                j = xc[0] += k;
-                for (k = 1; j >= 10; j /= 10, k++);
-
-                // if i != k the length has increased.
-                if (i != k) {
-                  x.e++;
-                  if (xc[0] == BASE) xc[0] = 1;
-                }
-
-                break;
-              } else {
-                xc[ni] += k;
-                if (xc[ni] != BASE) break;
-                xc[ni--] = 0;
-                k = 1;
-              }
-            }
-          }
-
-          // Remove trailing zeros.
-          for (i = xc.length; xc[--i] === 0; xc.pop());
-        }
-
-        // Overflow? Infinity.
-        if (x.e > MAX_EXP) {
-          x.c = x.e = null;
-
-        // Underflow? Zero.
-        } else if (x.e < MIN_EXP) {
-          x.c = [x.e = 0];
-        }
-      }
-
-      return x;
-    }
-
-
-    function valueOf(n) {
-      var str,
-        e = n.e;
-
-      if (e === null) return n.toString();
-
-      str = coeffToString(n.c);
-
-      str = e <= TO_EXP_NEG || e >= TO_EXP_POS
-        ? toExponential(str, e)
-        : toFixedPoint(str, e, '0');
-
-      return n.s < 0 ? '-' + str : str;
-    }
-
-
-    // PROTOTYPE/INSTANCE METHODS
-
-
-    /*
-     * Return a new BigNumber whose value is the absolute value of this BigNumber.
-     */
-    P.absoluteValue = P.abs = function () {
-      var x = new BigNumber(this);
-      if (x.s < 0) x.s = 1;
-      return x;
-    };
-
-
-    /*
-     * Return
-     *   1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
-     *   -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
-     *   0 if they have the same value,
-     *   or null if the value of either is NaN.
-     */
-    P.comparedTo = function (y, b) {
-      return compare(this, new BigNumber(y, b));
-    };
-
-
-    /*
-     * If dp is undefined or null or true or false, return the number of decimal places of the
-     * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
-     *
-     * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
-     * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
-     * ROUNDING_MODE if rm is omitted.
-     *
-     * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
-     */
-    P.decimalPlaces = P.dp = function (dp, rm) {
-      var c, n, v,
-        x = this;
-
-      if (dp != null) {
-        intCheck(dp, 0, MAX);
-        if (rm == null) rm = ROUNDING_MODE;
-        else intCheck(rm, 0, 8);
-
-        return round(new BigNumber(x), dp + x.e + 1, rm);
-      }
-
-      if (!(c = x.c)) return null;
-      n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
-
-      // Subtract the number of trailing zeros of the last number.
-      if (v = c[v]) for (; v % 10 == 0; v /= 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 BigNumber whose value is the value of this BigNumber divided by the value of
-     * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
-     */
-    P.dividedBy = P.div = function (y, b) {
-      return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
-    };
-
-
-    /*
-     * Return a new BigNumber whose value is the integer part of dividing the value of this
-     * BigNumber by the value of BigNumber(y, b).
-     */
-    P.dividedToIntegerBy = P.idiv = function (y, b) {
-      return div(this, new BigNumber(y, b), 0, 1);
-    };
-
-
-    /*
-     * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
-     *
-     * If m is present, return the result modulo m.
-     * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
-     * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
-     *
-     * The modular power operation works efficiently when x, n, and m are integers, otherwise it
-     * is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
-     *
-     * n {number|string|BigNumber} The exponent. An integer.
-     * [m] {number|string|BigNumber} The modulus.
-     *
-     * '[BigNumber Error] Exponent not an integer: {n}'
-     */
-    P.exponentiatedBy = P.pow = function (n, m) {
-      var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
-        x = this;
-
-      n = new BigNumber(n);
-
-      // Allow NaN and ±Infinity, but not other non-integers.
-      if (n.c && !n.isInteger()) {
-        throw Error
-          (bignumberError + 'Exponent not an integer: ' + valueOf(n));
-      }
-
-      if (m != null) m = new BigNumber(m);
-
-      // Exponent of MAX_SAFE_INTEGER is 15.
-      nIsBig = n.e > 14;
-
-      // If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
-      if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
-
-        // The sign of the result of pow when x is negative depends on the evenness of n.
-        // If +n overflows to ±Infinity, the evenness of n would be not be known.
-        y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
-        return m ? y.mod(m) : y;
-      }
-
-      nIsNeg = n.s < 0;
-
-      if (m) {
-
-        // x % m returns NaN if abs(m) is zero, or m is NaN.
-        if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
-
-        isModExp = !nIsNeg && x.isInteger() && m.isInteger();
-
-        if (isModExp) x = x.mod(m);
-
-      // Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
-      // Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
-      } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
-        // [1, 240000000]
-        ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
-        // [80000000000000]  [99999750000000]
-        : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
-
-        // If x is negative and n is odd, k = -0, else k = 0.
-        k = x.s < 0 && isOdd(n) ? -0 : 0;
-
-        // If x >= 1, k = ±Infinity.
-        if (x.e > -1) k = 1 / k;
-
-        // If n is negative return ±0, else return ±Infinity.
-        return new BigNumber(nIsNeg ? 1 / k : k);
-
-      } else if (POW_PRECISION) {
-
-        // Truncating each coefficient array to a length of k after each multiplication
-        // equates to truncating significant digits to POW_PRECISION + [28, 41],
-        // i.e. there will be a minimum of 28 guard digits retained.
-        k = mathceil(POW_PRECISION / LOG_BASE + 2);
-      }
-
-      if (nIsBig) {
-        half = new BigNumber(0.5);
-        if (nIsNeg) n.s = 1;
-        nIsOdd = isOdd(n);
-      } else {
-        i = Math.abs(+valueOf(n));
-        nIsOdd = i % 2;
-      }
-
-      y = new BigNumber(ONE);
-
-      // Performs 54 loop iterations for n of 9007199254740991.
-      for (; ;) {
-
-        if (nIsOdd) {
-          y = y.times(x);
-          if (!y.c) break;
-
-          if (k) {
-            if (y.c.length > k) y.c.length = k;
-          } else if (isModExp) {
-            y = y.mod(m);    //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
-          }
-        }
-
-        if (i) {
-          i = mathfloor(i / 2);
-          if (i === 0) break;
-          nIsOdd = i % 2;
-        } else {
-          n = n.times(half);
-          round(n, n.e + 1, 1);
-
-          if (n.e > 14) {
-            nIsOdd = isOdd(n);
-          } else {
-            i = +valueOf(n);
-            if (i === 0) break;
-            nIsOdd = i % 2;
-          }
-        }
-
-        x = x.times(x);
-
-        if (k) {
-          if (x.c && x.c.length > k) x.c.length = k;
-        } else if (isModExp) {
-          x = x.mod(m);    //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
-        }
-      }
-
-      if (isModExp) return y;
-      if (nIsNeg) y = ONE.div(y);
-
-      return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
-    };
-
-
-    /*
-     * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
-     * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
-     *
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
-     */
-    P.integerValue = function (rm) {
-      var n = new BigNumber(this);
-      if (rm == null) rm = ROUNDING_MODE;
-      else intCheck(rm, 0, 8);
-      return round(n, n.e + 1, rm);
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
-     * otherwise return false.
-     */
-    P.isEqualTo = P.eq = function (y, b) {
-      return compare(this, new BigNumber(y, b)) === 0;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is a finite number, otherwise return false.
-     */
-    P.isFinite = function () {
-      return !!this.c;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
-     * otherwise return false.
-     */
-    P.isGreaterThan = P.gt = function (y, b) {
-      return compare(this, new BigNumber(y, b)) > 0;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is greater than or equal to the value of
-     * BigNumber(y, b), otherwise return false.
-     */
-    P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
-      return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
-
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is an integer, otherwise return false.
-     */
-    P.isInteger = function () {
-      return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
-     * otherwise return false.
-     */
-    P.isLessThan = P.lt = function (y, b) {
-      return compare(this, new BigNumber(y, b)) < 0;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is less than or equal to the value of
-     * BigNumber(y, b), otherwise return false.
-     */
-    P.isLessThanOrEqualTo = P.lte = function (y, b) {
-      return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is NaN, otherwise return false.
-     */
-    P.isNaN = function () {
-      return !this.s;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is negative, otherwise return false.
-     */
-    P.isNegative = function () {
-      return this.s < 0;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is positive, otherwise return false.
-     */
-    P.isPositive = function () {
-      return this.s > 0;
-    };
-
-
-    /*
-     * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
-     */
-    P.isZero = function () {
-      return !!this.c && this.c[0] == 0;
-    };
-
-
-    /*
-     *  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 BigNumber whose value is the value of this BigNumber minus the value of
-     * BigNumber(y, b).
-     */
-    P.minus = function (y, b) {
-      var i, j, t, xLTy,
-        x = this,
-        a = x.s;
-
-      y = new BigNumber(y, b);
-      b = y.s;
-
-      // Either NaN?
-      if (!a || !b) return new BigNumber(NaN);
-
-      // Signs differ?
-      if (a != b) {
-        y.s = -b;
-        return x.plus(y);
-      }
-
-      var xe = x.e / LOG_BASE,
-        ye = y.e / LOG_BASE,
-        xc = x.c,
-        yc = y.c;
-
-      if (!xe || !ye) {
-
-        // Either Infinity?
-        if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
-
-        // Either zero?
-        if (!xc[0] || !yc[0]) {
-
-          // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
-          return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
-
-           // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
-           ROUNDING_MODE == 3 ? -0 : 0);
-        }
-      }
-
-      xe = bitFloor(xe);
-      ye = bitFloor(ye);
-      xc = xc.slice();
-
-      // Determine which is the bigger number.
-      if (a = xe - ye) {
-
-        if (xLTy = a < 0) {
-          a = -a;
-          t = xc;
-        } else {
-          ye = xe;
-          t = yc;
-        }
-
-        t.reverse();
-
-        // Prepend zeros to equalise exponents.
-        for (b = a; b--; t.push(0));
-        t.reverse();
-      } else {
-
-        // Exponents equal. Check digit by digit.
-        j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
-
-        for (a = b = 0; b < j; b++) {
-
-          if (xc[b] != yc[b]) {
-            xLTy = xc[b] < yc[b];
-            break;
-          }
-        }
-      }
-
-      // x < y? Point xc to the array of the bigger number.
-      if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
-
-      b = (j = yc.length) - (i = xc.length);
-
-      // Append zeros to xc if shorter.
-      // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
-      if (b > 0) for (; b--; xc[i++] = 0);
-      b = BASE - 1;
-
-      // Subtract yc from xc.
-      for (; j > a;) {
-
-        if (xc[--j] < yc[j]) {
-          for (i = j; i && !xc[--i]; xc[i] = b);
-          --xc[i];
-          xc[j] += BASE;
-        }
-
-        xc[j] -= yc[j];
-      }
-
-      // Remove leading zeros and adjust exponent accordingly.
-      for (; xc[0] == 0; xc.splice(0, 1), --ye);
-
-      // Zero?
-      if (!xc[0]) {
-
-        // Following IEEE 754 (2008) 6.3,
-        // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
-        y.s = ROUNDING_MODE == 3 ? -1 : 1;
-        y.c = [y.e = 0];
-        return y;
-      }
-
-      // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
-      // for finite x and y.
-      return normalise(y, xc, ye);
-    };
-
-
-    /*
-     *   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 BigNumber whose value is the value of this BigNumber modulo the value of
-     * BigNumber(y, b). The result depends on the value of MODULO_MODE.
-     */
-    P.modulo = P.mod = function (y, b) {
-      var q, s,
-        x = this;
-
-      y = new BigNumber(y, b);
-
-      // Return NaN if x is Infinity or NaN, or y is NaN or zero.
-      if (!x.c || !y.s || y.c && !y.c[0]) {
-        return new BigNumber(NaN);
-
-      // Return x if y is Infinity or x is zero.
-      } else if (!y.c || x.c && !x.c[0]) {
-        return new BigNumber(x);
-      }
-
-      if (MODULO_MODE == 9) {
-
-        // Euclidian division: q = sign(y) * floor(x / abs(y))
-        // r = x - qy    where  0 <= r < abs(y)
-        s = y.s;
-        y.s = 1;
-        q = div(x, y, 0, 3);
-        y.s = s;
-        q.s *= s;
-      } else {
-        q = div(x, y, 0, MODULO_MODE);
-      }
-
-      y = x.minus(q.times(y));
-
-      // To match JavaScript %, ensure sign of zero is sign of dividend.
-      if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
-
-      return y;
-    };
-
-
-    /*
-     *  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 BigNumber whose value is the value of this BigNumber multiplied by the value
-     * of BigNumber(y, b).
-     */
-    P.multipliedBy = P.times = function (y, b) {
-      var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
-        base, sqrtBase,
-        x = this,
-        xc = x.c,
-        yc = (y = new BigNumber(y, b)).c;
-
-      // Either NaN, ±Infinity or ±0?
-      if (!xc || !yc || !xc[0] || !yc[0]) {
-
-        // Return NaN if either is NaN, or one is 0 and the other is Infinity.
-        if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
-          y.c = y.e = y.s = null;
-        } else {
-          y.s *= x.s;
-
-          // Return ±Infinity if either is ±Infinity.
-          if (!xc || !yc) {
-            y.c = y.e = null;
-
-          // Return ±0 if either is ±0.
-          } else {
-            y.c = [0];
-            y.e = 0;
-          }
-        }
-
-        return y;
-      }
-
-      e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
-      y.s *= x.s;
-      xcL = xc.length;
-      ycL = yc.length;
-
-      // Ensure xc points to longer array and xcL to its length.
-      if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
-
-      // Initialise the result array with zeros.
-      for (i = xcL + ycL, zc = []; i--; zc.push(0));
-
-      base = BASE;
-      sqrtBase = SQRT_BASE;
-
-      for (i = ycL; --i >= 0;) {
-        c = 0;
-        ylo = yc[i] % sqrtBase;
-        yhi = yc[i] / sqrtBase | 0;
-
-        for (k = xcL, j = i + k; j > i;) {
-          xlo = xc[--k] % sqrtBase;
-          xhi = xc[k] / sqrtBase | 0;
-          m = yhi * xlo + xhi * ylo;
-          xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
-          c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
-          zc[j--] = xlo % base;
-        }
-
-        zc[j] = c;
-      }
-
-      if (c) {
-        ++e;
-      } else {
-        zc.splice(0, 1);
-      }
-
-      return normalise(y, zc, e);
-    };
-
-
-    /*
-     * Return a new BigNumber whose value is the value of this BigNumber negated,
-     * i.e. multiplied by -1.
-     */
-    P.negated = function () {
-      var x = new BigNumber(this);
-      x.s = -x.s || null;
-      return 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 BigNumber whose value is the value of this BigNumber plus the value of
-     * BigNumber(y, b).
-     */
-    P.plus = function (y, b) {
-      var t,
-        x = this,
-        a = x.s;
-
-      y = new BigNumber(y, b);
-      b = y.s;
-
-      // Either NaN?
-      if (!a || !b) return new BigNumber(NaN);
-
-      // Signs differ?
-       if (a != b) {
-        y.s = -b;
-        return x.minus(y);
-      }
-
-      var xe = x.e / LOG_BASE,
-        ye = y.e / LOG_BASE,
-        xc = x.c,
-        yc = y.c;
-
-      if (!xe || !ye) {
-
-        // Return ±Infinity if either ±Infinity.
-        if (!xc || !yc) return new BigNumber(a / 0);
-
-        // Either zero?
-        // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
-        if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
-      }
-
-      xe = bitFloor(xe);
-      ye = bitFloor(ye);
-      xc = xc.slice();
-
-      // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
-      if (a = xe - ye) {
-        if (a > 0) {
-          ye = xe;
-          t = yc;
-        } else {
-          a = -a;
-          t = xc;
-        }
-
-        t.reverse();
-        for (; a--; t.push(0));
-        t.reverse();
-      }
-
-      a = xc.length;
-      b = yc.length;
-
-      // Point xc to the longer array, and b to the shorter length.
-      if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
-
-      // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
-      for (a = 0; b;) {
-        a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
-        xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
-      }
-
-      if (a) {
-        xc = [a].concat(xc);
-        ++ye;
-      }
-
-      // No need to check for zero, as +x + +y != 0 && -x + -y != 0
-      // ye = MAX_EXP + 1 possible
-      return normalise(y, xc, ye);
-    };
-
-
-    /*
-     * If sd is undefined or null or true or false, return the number of significant digits of
-     * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
-     * If sd is true include integer-part trailing zeros in the count.
-     *
-     * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
-     * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
-     * ROUNDING_MODE if rm is omitted.
-     *
-     * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
-     *                     boolean: whether to count integer-part trailing zeros: true or false.
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
-     */
-    P.precision = P.sd = function (sd, rm) {
-      var c, n, v,
-        x = this;
-
-      if (sd != null && sd !== !!sd) {
-        intCheck(sd, 1, MAX);
-        if (rm == null) rm = ROUNDING_MODE;
-        else intCheck(rm, 0, 8);
-
-        return round(new BigNumber(x), sd, rm);
-      }
-
-      if (!(c = x.c)) return null;
-      v = c.length - 1;
-      n = v * LOG_BASE + 1;
-
-      if (v = c[v]) {
-
-        // Subtract the number of trailing zeros of the last element.
-        for (; v % 10 == 0; v /= 10, n--);
-
-        // Add the number of digits of the first element.
-        for (v = c[0]; v >= 10; v /= 10, n++);
-      }
-
-      if (sd && x.e + 1 > n) n = x.e + 1;
-
-      return n;
-    };
-
-
-    /*
-     * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
-     * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
-     *
-     * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
-     */
-    P.shiftedBy = function (k) {
-      intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
-      return this.times('1e' + k);
-    };
-
-
-    /*
-     *  sqrt(-n) =  N
-     *  sqrt(N) =  N
-     *  sqrt(-I) =  N
-     *  sqrt(I) =  I
-     *  sqrt(0) =  0
-     *  sqrt(-0) = -0
-     *
-     * Return a new BigNumber whose value is the square root of the value of this BigNumber,
-     * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
-     */
-    P.squareRoot = P.sqrt = function () {
-      var m, n, r, rep, t,
-        x = this,
-        c = x.c,
-        s = x.s,
-        e = x.e,
-        dp = DECIMAL_PLACES + 4,
-        half = new BigNumber('0.5');
-
-      // Negative/NaN/Infinity/zero?
-      if (s !== 1 || !c || !c[0]) {
-        return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
-      }
-
-      // Initial estimate.
-      s = Math.sqrt(+valueOf(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 = coeffToString(c);
-        if ((n.length + e) % 2 == 0) n += '0';
-        s = Math.sqrt(+n);
-        e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);
-
-        if (s == 1 / 0) {
-          n = '1e' + e;
-        } else {
-          n = s.toExponential();
-          n = n.slice(0, n.indexOf('e') + 1) + e;
-        }
-
-        r = new BigNumber(n);
-      } else {
-        r = new BigNumber(s + '');
-      }
-
-      // Check for zero.
-      // r could be zero if MIN_EXP is changed after the this value was created.
-      // This would cause a division by zero (x/t) and hence Infinity below, which would cause
-      // coeffToString to throw.
-      if (r.c[0]) {
-        e = r.e;
-        s = e + dp;
-        if (s < 3) s = 0;
-
-        // Newton-Raphson iteration.
-        for (; ;) {
-          t = r;
-          r = half.times(t.plus(div(x, t, dp, 1)));
-
-          if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
-
-            // The exponent of r may here be one less than the final result exponent,
-            // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
-            // are indexed correctly.
-            if (r.e < e) --s;
-            n = n.slice(s - 3, s + 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) {
-                round(t, t.e + DECIMAL_PLACES + 2, 0);
-
-                if (t.times(t).eq(x)) {
-                  r = t;
-                  break;
-                }
-              }
-
-              dp += 4;
-              s += 4;
-              rep = 1;
-            } else {
-
-              // If rounding digits are null, 0{0,4} or 50{0,3}, check for 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.
-                round(r, r.e + DECIMAL_PLACES + 2, 1);
-                m = !r.times(r).eq(x);
-              }
-
-              break;
-            }
-          }
-        }
-      }
-
-      return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
-    };
-
-
-    /*
-     * Return a string representing the value of this BigNumber in exponential notation and
-     * rounded using ROUNDING_MODE to dp fixed decimal places.
-     *
-     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
-     */
-    P.toExponential = function (dp, rm) {
-      if (dp != null) {
-        intCheck(dp, 0, MAX);
-        dp++;
-      }
-      return format(this, dp, rm, 1);
-    };
-
-
-    /*
-     * Return a string representing the value of this BigNumber in fixed-point notation rounding
-     * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
-     *
-     * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
-     * but e.g. (-0.00001).toFixed(0) is '-0'.
-     *
-     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
-     */
-    P.toFixed = function (dp, rm) {
-      if (dp != null) {
-        intCheck(dp, 0, MAX);
-        dp = dp + this.e + 1;
-      }
-      return format(this, dp, rm);
-    };
-
-
-    /*
-     * Return a string representing the value of this BigNumber in fixed-point notation rounded
-     * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
-     * of the format or FORMAT object (see BigNumber.set).
-     *
-     * The formatting object may contain some or all of the properties shown below.
-     *
-     * FORMAT = {
-     *   prefix: '',
-     *   groupSize: 3,
-     *   secondaryGroupSize: 0,
-     *   groupSeparator: ',',
-     *   decimalSeparator: '.',
-     *   fractionGroupSize: 0,
-     *   fractionGroupSeparator: '\xA0',      // non-breaking space
-     *   suffix: ''
-     * };
-     *
-     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     * [format] {object} Formatting options. See FORMAT pbject above.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
-     * '[BigNumber Error] Argument not an object: {format}'
-     */
-    P.toFormat = function (dp, rm, format) {
-      var str,
-        x = this;
-
-      if (format == null) {
-        if (dp != null && rm && typeof rm == 'object') {
-          format = rm;
-          rm = null;
-        } else if (dp && typeof dp == 'object') {
-          format = dp;
-          dp = rm = null;
-        } else {
-          format = FORMAT;
-        }
-      } else if (typeof format != 'object') {
-        throw Error
-          (bignumberError + 'Argument not an object: ' + format);
-      }
-
-      str = x.toFixed(dp, rm);
-
-      if (x.c) {
-        var i,
-          arr = str.split('.'),
-          g1 = +format.groupSize,
-          g2 = +format.secondaryGroupSize,
-          groupSeparator = format.groupSeparator || '',
-          intPart = arr[0],
-          fractionPart = arr[1],
-          isNeg = x.s < 0,
-          intDigits = isNeg ? intPart.slice(1) : intPart,
-          len = intDigits.length;
-
-        if (g2) i = g1, g1 = g2, g2 = i, len -= i;
-
-        if (g1 > 0 && len > 0) {
-          i = len % g1 || g1;
-          intPart = intDigits.substr(0, i);
-          for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
-          if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
-          if (isNeg) intPart = '-' + intPart;
-        }
-
-        str = fractionPart
-         ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
-          ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
-           '$&' + (format.fractionGroupSeparator || ''))
-          : fractionPart)
-         : intPart;
-      }
-
-      return (format.prefix || '') + str + (format.suffix || '');
-    };
-
-
-    /*
-     * Return an array of two BigNumbers representing the value of this BigNumber 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.
-     *
-     * [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
-     *
-     * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
-     */
-    P.toFraction = function (md) {
-      var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
-        x = this,
-        xc = x.c;
-
-      if (md != null) {
-        n = new BigNumber(md);
-
-        // Throw if md is less than one or is not an integer, unless it is Infinity.
-        if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
-          throw Error
-            (bignumberError + 'Argument ' +
-              (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
-        }
-      }
-
-      if (!xc) return new BigNumber(x);
-
-      d = new BigNumber(ONE);
-      n1 = d0 = new BigNumber(ONE);
-      d1 = n0 = new BigNumber(ONE);
-      s = coeffToString(xc);
-
-      // Determine initial denominator.
-      // d is a power of 10 and the minimum max denominator that specifies the value exactly.
-      e = d.e = s.length - x.e - 1;
-      d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
-      md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
-
-      exp = MAX_EXP;
-      MAX_EXP = 1 / 0;
-      n = new BigNumber(s);
-
-      // n0 = d1 = 0
-      n0.c[0] = 0;
-
-      for (; ;)  {
-        q = div(n, d, 0, 1);
-        d2 = d0.plus(q.times(d1));
-        if (d2.comparedTo(md) == 1) break;
-        d0 = d1;
-        d1 = d2;
-        n1 = n0.plus(q.times(d2 = n1));
-        n0 = d2;
-        d = n.minus(q.times(d2 = d));
-        n = d2;
-      }
-
-      d2 = div(md.minus(d0), d1, 0, 1);
-      n0 = n0.plus(d2.times(n1));
-      d0 = d0.plus(d2.times(d1));
-      n0.s = n1.s = x.s;
-      e = e * 2;
-
-      // Determine which fraction is closer to x, n0/d0 or n1/d1
-      r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
-          div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
-
-      MAX_EXP = exp;
-
-      return r;
-    };
-
-
-    /*
-     * Return the value of this BigNumber converted to a number primitive.
-     */
-    P.toNumber = function () {
-      return +valueOf(this);
-    };
-
-
-    /*
-     * Return a string representing the value of this BigNumber rounded to sd significant digits
-     * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
-     * necessary to represent the integer part of the value in fixed-point notation, then use
-     * exponential notation.
-     *
-     * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
-     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-     *
-     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
-     */
-    P.toPrecision = function (sd, rm) {
-      if (sd != null) intCheck(sd, 1, MAX);
-      return format(this, sd, rm, 2);
-    };
-
-
-    /*
-     * Return a string representing the value of this BigNumber in base b, or base 10 if b is
-     * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
-     * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
-     * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
-     * TO_EXP_NEG, return exponential notation.
-     *
-     * [b] {number} Integer, 2 to ALPHABET.length inclusive.
-     *
-     * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
-     */
-    P.toString = function (b) {
-      var str,
-        n = this,
-        s = n.s,
-        e = n.e;
-
-      // Infinity or NaN?
-      if (e === null) {
-        if (s) {
-          str = 'Infinity';
-          if (s < 0) str = '-' + str;
-        } else {
-          str = 'NaN';
-        }
-      } else {
-        if (b == null) {
-          str = e <= TO_EXP_NEG || e >= TO_EXP_POS
-           ? toExponential(coeffToString(n.c), e)
-           : toFixedPoint(coeffToString(n.c), e, '0');
-        } else if (b === 10) {
-          n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
-          str = toFixedPoint(coeffToString(n.c), n.e, '0');
-        } else {
-          intCheck(b, 2, ALPHABET.length, 'Base');
-          str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
-        }
-
-        if (s < 0 && n.c[0]) str = '-' + str;
-      }
-
-      return str;
-    };
-
-
-    /*
-     * Return as toString, but do not accept a base argument, and include the minus sign for
-     * negative zero.
-     */
-    P.valueOf = P.toJSON = function () {
-      return valueOf(this);
-    };
-
-
-    P._isBigNumber = true;
-
-    if (hasSymbol) {
-      P[Symbol.toStringTag] = 'BigNumber';
-
-      // Node.js v10.12.0+
-      P[Symbol.for('nodejs.util.inspect.custom')] = P.valueOf;
-    }
-
-    if (configObject != null) BigNumber.set(configObject);
-
-    return BigNumber;
-  }
-
-
-  // PRIVATE HELPER FUNCTIONS
-
-  // These functions don't need access to variables,
-  // e.g. DECIMAL_PLACES, in the scope of the `clone` function above.
-
-
-  function bitFloor(n) {
-    var i = n | 0;
-    return n > 0 || n === i ? i : i - 1;
-  }
-
-
-  // Return a coefficient array as a string of base 10 digits.
-  function coeffToString(a) {
-    var s, z,
-      i = 1,
-      j = a.length,
-      r = a[0] + '';
-
-    for (; i < j;) {
-      s = a[i++] + '';
-      z = LOG_BASE - s.length;
-      for (; z--; s = '0' + s);
-      r += s;
-    }
-
-    // Determine trailing zeros.
-    for (j = r.length; r.charCodeAt(--j) === 48;);
-
-    return r.slice(0, j + 1 || 1);
-  }
-
-
-  // Compare the value of BigNumbers x and y.
-  function compare(x, y) {
-    var a, b,
-      xc = x.c,
-      yc = y.c,
-      i = x.s,
-      j = y.s,
-      k = x.e,
-      l = y.e;
-
-    // Either NaN?
-    if (!i || !j) return null;
-
-    a = xc && !xc[0];
-    b = yc && !yc[0];
-
-    // Either zero?
-    if (a || b) return a ? b ? 0 : -j : i;
-
-    // Signs differ?
-    if (i != j) return i;
-
-    a = i < 0;
-    b = k == l;
-
-    // Either Infinity?
-    if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
-
-    // Compare exponents.
-    if (!b) return k > l ^ a ? 1 : -1;
-
-    j = (k = xc.length) < (l = yc.length) ? k : l;
-
-    // Compare digit by digit.
-    for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
-
-    // Compare lengths.
-    return k == l ? 0 : k > l ^ a ? 1 : -1;
-  }
-
-
-  /*
-   * Check that n is a primitive number, an integer, and in range, otherwise throw.
-   */
-  function intCheck(n, min, max, name) {
-    if (n < min || n > max || n !== mathfloor(n)) {
-      throw Error
-       (bignumberError + (name || 'Argument') + (typeof n == 'number'
-         ? n < min || n > max ? ' out of range: ' : ' not an integer: '
-         : ' not a primitive number: ') + String(n));
-    }
-  }
-
-
-  // Assumes finite n.
-  function isOdd(n) {
-    var k = n.c.length - 1;
-    return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
-  }
-
-
-  function toExponential(str, e) {
-    return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
-     (e < 0 ? 'e' : 'e+') + e;
-  }
-
-
-  function toFixedPoint(str, e, z) {
-    var len, zs;
-
-    // Negative exponent?
-    if (e < 0) {
-
-      // Prepend zeros.
-      for (zs = z + '.'; ++e; zs += z);
-      str = zs + str;
-
-    // Positive exponent
-    } else {
-      len = str.length;
-
-      // Append zeros.
-      if (++e > len) {
-        for (zs = z, e -= len; --e; zs += z);
-        str += zs;
-      } else if (e < len) {
-        str = str.slice(0, e) + '.' + str.slice(e);
-      }
-    }
-
-    return str;
-  }
-
-
-  // EXPORT
-
-
-  BigNumber = clone();
-  BigNumber['default'] = BigNumber.BigNumber = BigNumber;
-
-  // AMD.
-  if (typeof define == 'function' && define.amd) {
-    define(function () { return BigNumber; });
-
-  // Node.js and other environments that support module.exports.
-  } else if (typeof module != 'undefined' && module.exports) {
-    module.exports = BigNumber;
-
-  // Browser.
-  } else {
-    if (!globalObject) {
-      globalObject = typeof self != 'undefined' && self ? self : window;
-    }
-
-    globalObject.BigNumber = BigNumber;
-  }
-})(this);
-</script>
+    <script src='./bignumber.js'></script>
     <script type="text/javascript">
     // bip39 Valid Mnemonic Generator Javascript App
     /*
     Author: Steven Hatzakis @ 2018
-
     Version 2.1 beta
-
     Description: A simplified javascript program for generating
     valid bip39 mnemonics, using an initial random entropy via the
     secrets module in Javascript for cryptographically secure entropy,
@@ -2993,14 +77,11 @@
     and as a bytearray before hashing to obtain the leading required
     number of bits from the hash digest in order to compute the
     checksum and complete the final word group.
-
     Formula: Initial entropy in bits /32 = checksum length in bits
     initial entropy mod 11 = remaining bits + checksum = last word
     Initial entropy + checksum = total bits /11 = total words.
-
     Example usage: 128 bits entropy, will require a 4 bit checksum,
     for a total of 132 bits.
-
     Notes: while this code could be re-written to further condense/clean it,
     my goal was initially just to get it to work. For example, starting with the
     secret.randbits() function, I noticed often the value returned was less
@@ -3008,17 +89,14 @@
     in length to help assure that I got at least 129 bits (or 130) and then from
     there slice at least 128 bits to obtain the desired starting amount of entorpy
     neeeded.
-
-
     */
-
     "use strict"
-
     function generateBIP39() {
         output = ''
         const wordCount = document.getElementById('wordLength').value;
         addElementToOutput('Number of mnemonic words:',wordCount)
         var entropy = document.getElementById('entropy').value;
+        console.log(entropy+ 'init entropy')
         const checksumBitCount = Math.floor(wordCount/3)
 	   
         const totalBitCount = wordCount * 11
@@ -3029,13 +107,22 @@
           alert('check the correctness of entropy inserted and generate again.')
           return
         }
+        console.log(TestHash(entropy, generatedCharCount, checksumBitCount))
+        while(TestHash(entropy, generatedCharCount, checksumBitCount)===false){
+            console.log(TestHash(entropy, generatedCharCount, checksumBitCount))
+            entropy = generateEntropy(generatedBitCount)
+            if(entropy == null) {
+                alert('check the correctness of entropy inserted and generate again.')
+                return
+             }
+        }
         const entropyWithChecksum = getHash(entropy, generatedCharCount, checksumBitCount)
         const words = pickWords(entropyWithChecksum)
         output += 'mnemonic is valid.<br />'
         output = addWordsToOutput(words) + output
         document.getElementById('output').innerHTML = output;
     }
-
+   
     function generateBIP39Palindromic() {
         var palindromic = false
         var firstTimeEntropy = true
@@ -3085,9 +172,7 @@
                 document.getElementById("outputPal").innerHTML = outputPal;
             }
         }
-
     }
-
     function checkEntropy(entropy, generatedBitCount, generatedCharCount) {
         if(entropy.length == 0) {
             entropy = generateEntropy(generatedBitCount)
@@ -3103,16 +188,13 @@
         }
         return entropy
     }
-
     function addWordsToOutput(words) {
       var mnemonicOutput = ''
       mnemonicOutput += "Generated mnemonic words:<br />"
       mnemonicOutput += "<textarea rows='3' cols='100'>"+words.join(' ')+"<"+"/textarea>"
       mnemonicOutput += "<br /><br />"
       return mnemonicOutput
-
     }
-
     function addElementToOutput(details,value,mode='classic') {
         if(mode=='classic') {
             output += details + "<br />"
@@ -3124,7 +206,6 @@
             outputPal += "<br /><br />"
         }
     }
-
     function reverseOrder(entropyHash) {
         var reverseOrder = [];
         const blen = entropyHash.length / 11;
@@ -3134,7 +215,6 @@
         }
         return reverseOrder.join('')
     }
-
     // It generates entropy as bytearray
     function generateEntropy(generatedBitCount) {
         const buffer = new Uint8Array(generatedBitCount/8)
@@ -3144,7 +224,6 @@
         }
         return entropy
     }
-
     function byteArrayToWordArray(data) {
         var a = [];
         for(var i=0; i<data.length/4; i++) {
@@ -3157,7 +236,6 @@
         }
         return a;
     }
-
     function byteArrayToBinaryString(data) {
         var bin = "";
         for(var i=0; i<data.length; i++) {
@@ -3165,7 +243,6 @@
         }
         return bin;
     }
-
     function binaryStringToByteArray(data) {
         var byteArray = []
         for(var i=0; i<data.length; i=i+8) {
@@ -3177,12 +254,11 @@
         var byteArray = []
         
         for(var i=0; i<data.length; i=i+2) {
-            console.log(data.slice(i,i+2))  
+           // console.log(data.slice(i,i+2))  
           byteArray.push(parseInt(data.slice(i,i+2),16))
         }
         return byteArray
     }
-
     // Pad a numeric string on the left with zero digits until the given width
     // is reached.
     // Note this differs to the python implementation because it does not
@@ -3194,7 +270,6 @@
         }
         return source;
     }
-
     function hexStringToBinaryString(hexString) {
         var binaryString = "";
         for(var i=0; i<hexString.length; i++) {
@@ -3202,29 +277,28 @@
         }
         return binaryString;
     }
-
     function getHash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic') {
-        console.log(generatedCharCount)
-        console.log(entropyBytearray)
-        console.log(checksumBitCount)
+       
         const entropyBinary = byteArrayToBinaryString(entropyBytearray)
         const data = byteArrayToWordArray(entropyBytearray)
+        
         const hexData = '0x' + sjcl.codec.hex.fromBits(data)
         const hexDataNoPadding = hexData.slice(2)
-        // sha256
         const hash = sjcl.hash.sha256.hash(data)
         const hashHex = sjcl.codec.hex.fromBits(hash)
         //console.log(hexData)
         //console.log(hashHex)
        // console.log(entropyBinary)
-        console.log(hexStringToBinaryString(hashHex))
+    
         const c = zfill(hexStringToBinaryString(hashHex), 256)
         const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+        
         const checksumCharCount = Math.floor(checksumBitCount/4)
         const bit = hashHex.slice(0,checksumCharCount)
         // final entropy + checksum bits
         const b = entropyBinary + checksum;
-        const hatNotation= base64en(hexData)
+        const hatNotation= base64en(b)
+       
         addElementToOutput('Initial entropy:', entropyBinary, mode)
         addElementToOutput('Length of initial entropy:', entropyBinary.length, mode)
         addElementToOutput('Initial entropy as hex:', hexData, mode)
@@ -3246,6 +320,33 @@
         addElementToOutput('Hash digest of initial entropy bytes:', hashHex, mode)
         return b
     }
+    function TestHash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic') {
+        
+        const entropyBinary = byteArrayToBinaryString(entropyBytearray)
+        const data = byteArrayToWordArray(entropyBytearray)
+       
+        const hexData = '0x' + sjcl.codec.hex.fromBits(data)
+        const hexDataNoPadding = hexData.slice(2)
+        const hash = sjcl.hash.sha256.hash(data)
+        const hashHex = sjcl.codec.hex.fromBits(hash)
+        //console.log(hexData)
+        //console.log(hashHex)
+       // console.log(entropyBinary)
+       
+        const c = zfill(hexStringToBinaryString(hashHex), 256)
+        const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
+       
+        const checksumCharCount = Math.floor(checksumBitCount/4)
+        const bit = hashHex.slice(0,checksumCharCount)
+        // final entropy + checksum bits
+        const b = entropyBinary + checksum;
+        const hatNotation= base64en(b)
+        console.log(hatNotation)
+        const bool=(hatNotation.length===22)
+        console.log(bool)
+        return bool
+        
+    }
     function getDecodedhash(entropyBytearray, generatedCharCount, checksumBitCount, mode='classic'){
         console.log(generatedCharCount)
         console.log(entropyBytearray)
@@ -3260,7 +361,7 @@
         //console.log(hexData)
         //console.log(hashHex)
        // console.log(entropyBinary)
-        console.log(hexStringToBinaryString(hashHex))
+       
         const c = zfill(hexStringToBinaryString(hashHex), 256)
         const checksum = c.substring(0, entropyBytearray.length * 8 / 32)
         const checksumCharCount = Math.floor(checksumBitCount/4)
@@ -3273,10 +374,17 @@
     }
     function Decrypt(){
         var entropy64 = document.getElementById('base64entropy').value;
-        console.log(entropy64)
+        
         var hex=decodeAsHex(entropy64)
-        hex=hex.slice(1)
-        var hex2=decodeAsBin(entropy64)
+        var bin=decodeAsBin(entropy64)
+        console.log(hex.length+'hex length')
+        if(hex.length>32){
+            
+            var words=pickWords(bin) 
+            console.log(words)
+        document.getElementById('result').innerHTML=words
+        } 
+        else{
         var bytes=HexstringToByteArray(hex)
         var wordCount=12
         const checksumBitCount = Math.floor(wordCount/3)
@@ -3285,13 +393,12 @@
         const generatedBitCount = totalBitCount - checksumBitCount
         const generatedCharCount = Math.floor(generatedBitCount/4)
         const entropyWithChecksum = getDecodedhash(bytes, generatedCharCount, checksumBitCount)
-        
-        console.log(bytes)
-        console.log(hex)
-       //console.log(hex2)
         var words=pickWords(entropyWithChecksum) 
-        console.log(words)
+            
         document.getElementById('result').innerHTML=words
+        }
+        
+       
     }
     function pickWords(entropyHash) {
         var result = [];
@@ -3302,17 +409,14 @@
         }
         return result
     }
-
     function clearClassic() {
         output = ''
         document.getElementById("output").innerHTML = ''
     }
-
     function clearPalindromic() {
         outputPal = ''
         document.getElementById("outputPal").innerHTML = ''
     }
-
     var output = ''
     var outputPal = ''
     var __cfRLUnblockHandlers = 1 ;
@@ -3349,8 +453,8 @@
         "adjust",
         "admit",
         "adult",
-        "advance",
-        "advice",
+        "advance",   
+        "advice",   
         "aerobic",
         "affair",
         "afford",
@@ -5435,45 +2539,46 @@
     for(var i=0;i<base64library.length;i++) {
         b64dict[base64library[i]] = i;
     }
-
     
-
     function decodeAsBin(string) {
         var output = [];
         var s='';
         for(var j=0;j<string.length;j++) {
             if(string[j] != ' ') {
+                console.log(string[j] +'symbol '+j)
+                console.log(zfill(b64dict[string[j].toUpperCase()].toString(2)))
+                console.log(zfill(b64dict[string[j].toUpperCase()].toString(2), 6))
                 output.push(zfill(b64dict[string[j].toUpperCase()].toString(2), 6));
             }
         }
         return output.join('');
     }
-
     function decodeAsHex(string) {
     var bin = decodeAsBin(string);
+    console.log(bin+ 'bin')
     var output = [];
     var s='';
     // Pad with 0 for binaries not divisible by 4, for hex conversion
     var binModule = bin.length % 4;
+    console.log(binModule+'aofijeow***********************************************************************************************************************')
     if(binModule != 0) {
         bin = zfill(bin, bin.length + 4 - binModule);
     }
     for(var i=0;i<bin.length;i=i+4) {
+        console.log(parseInt(bin.slice(i,i+4), 2).toString(16)+ 'first character')
         output.push(parseInt(bin.slice(i,i+4), 2).toString(16));
     }
     return output.join('');
     }
-
     function base64en(address_hex) {  // important never to rename base64en to "base64" which can corrupt the Python installation.
     // (renamed alphabet to base64library below) alphabet = string.digits+string.ascii_uppercase+string.punctuation
     
     var b64_string = '';
     // Convert hex to decimal
-    var x= new BigNumber(address_hex);
+    var x= new BigNumber(address_hex,2);
     
     // Append digits to the start of string
     
-
     while(x > 0) {
        var digit = x.mod(64)
 	     //console.log(digit,'digit')
@@ -5484,8 +2589,6 @@
     }
     return b64_string;
 }
-
-
     </script>
   </head>
   <body>
@@ -5504,10 +2607,21 @@ <h2>REGULAR: BIP39 Mnemonic Tool</h2>
      <br>
      <br>
      <div id="output"></div>
-  
+     <h2>REVERSIBLE: BIP39 Palindromic Mnemonic Tool</h2>
+     <p>STEP 1: Select word count:<p>
+     <select id="wordLengthPal">
+       <option value=12>SELECT 12 Words (128 bits of security)</option>
+       <option value=24>SELECT 24 Words (256 bits of security)</option>
+     </select>
+     <p>OPTIONAL: Insert entropy in the form of a 0x-padded hex string of length 32 (for 12 words) or 64 (for 24 words):</p>
+     <input id="entropyPal">
      <br>
      <br>
-    
+     <button onclick="generateBIP39Palindromic()">STEP 2: Click Here to GENERATE Palindromic Mnemonic Words (Reversible Mnemonic will appear below)</button>
+     <button onclick="clearPalindromic()"> Click Here to CLEAR (Will Delete Data)</button>
+     <br>
+     <br>
+     <div id='outputPal'></div>
      <h2>Decode Base64 Entropy </h2>
      <input id="base64entropy">
      <button onclick="Decrypt()"> Get Seed Words</button>

From fb0ea3440a99a0c432136a407d61ee7403472e75 Mon Sep 17 00:00:00 2001
From: Steven Hatzakis <hatgit@users.noreply.github.com>
Date: Mon, 13 May 2019 16:07:12 -0400
Subject: [PATCH 2/2] added bignumber.js inline again for dev

---
 index.html | 2326 +++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 2325 insertions(+), 1 deletion(-)

diff --git a/index.html b/index.html
index 142839a..ef82126 100644
--- a/index.html
+++ b/index.html
@@ -64,7 +64,2331 @@
 b){var c={},d;for(d=0;d<b.length;d++)void 0!==a[b[d]]&&(c[b[d]]=a[b[d]]);return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.pa={};sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.pa,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=void 0===b.salt?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};
 "undefined"!==typeof module&&module.exports&&(module.exports=sjcl);"function"===typeof define&&define([],function(){return sjcl});
     </script>
-    <script src='./bignumber.js'></script>
+    // <script src='./bignumber.js'></script>
+	  <script name='bignumber.js'>
+  ;(function (globalObject) {
+  'use strict';
+/*
+ *      bignumber.js v8.1.1
+ *      A JavaScript library for arbitrary-precision arithmetic.
+ *      https://github.com/MikeMcl/bignumber.js
+ *      Copyright (c) 2019 Michael Mclaughlin <M8ch88l@gmail.com>
+ *      MIT Licensed.
+ *
+ *      BigNumber.prototype methods     |  BigNumber methods
+ *                                      |
+ *      absoluteValue            abs    |  clone
+ *      comparedTo                      |  config               set
+ *      decimalPlaces            dp     |      DECIMAL_PLACES
+ *      dividedBy                div    |      ROUNDING_MODE
+ *      dividedToIntegerBy       idiv   |      EXPONENTIAL_AT
+ *      exponentiatedBy          pow    |      RANGE
+ *      integerValue                    |      CRYPTO
+ *      isEqualTo                eq     |      MODULO_MODE
+ *      isFinite                        |      POW_PRECISION
+ *      isGreaterThan            gt     |      FORMAT
+ *      isGreaterThanOrEqualTo   gte    |      ALPHABET
+ *      isInteger                       |  isBigNumber
+ *      isLessThan               lt     |  maximum              max
+ *      isLessThanOrEqualTo      lte    |  minimum              min
+ *      isNaN                           |  random
+ *      isNegative                      |  sum
+ *      isPositive                      |
+ *      isZero                          |
+ *      minus                           |
+ *      modulo                   mod    |
+ *      multipliedBy             times  |
+ *      negated                         |
+ *      plus                            |
+ *      precision                sd     |
+ *      shiftedBy                       |
+ *      squareRoot               sqrt   |
+ *      toExponential                   |
+ *      toFixed                         |
+ *      toFormat                        |
+ *      toFraction                      |
+ *      toJSON                          |
+ *      toNumber                        |
+ *      toPrecision                     |
+ *      toString                        |
+ *      valueOf                         |
+ *
+ */
+  var BigNumber,
+    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
+    hasSymbol = typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol',
+    mathceil = Math.ceil,
+    mathfloor = Math.floor,
+    bignumberError = '[BigNumber Error] ',
+    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
+    BASE = 1e14,
+    LOG_BASE = 14,
+    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
+    // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
+    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
+    SQRT_BASE = 1e7,
+    // EDITABLE
+    // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
+    // the arguments to toExponential, toFixed, toFormat, and toPrecision.
+    MAX = 1E9;                                   // 0 to MAX_INT32
+  /*
+   * Create and return a BigNumber constructor.
+   */
+  function clone(configObject) {
+    var div, convertBase, parseNumeric,
+      P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
+      ONE = new BigNumber(1),
+      //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
+      // The default values below must be integers within the inclusive ranges stated.
+      // The values can also be changed at run-time using BigNumber.set.
+      // The maximum number of decimal places for operations involving division.
+      DECIMAL_PLACES = 20,                     // 0 to MAX
+      // The rounding mode used when rounding to the above decimal places, and when using
+      // toExponential, toFixed, toFormat and toPrecision, and round (default value).
+      // UP         0 Away from zero.
+      // DOWN       1 Towards zero.
+      // CEIL       2 Towards +Infinity.
+      // FLOOR      3 Towards -Infinity.
+      // HALF_UP    4 Towards nearest neighbour. If equidistant, up.
+      // HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
+      // HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
+      // HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
+      // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
+      ROUNDING_MODE = 4,                       // 0 to 8
+      // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
+      // The exponent value at and beneath which toString returns exponential notation.
+      // Number type: -7
+      TO_EXP_NEG = -7,                         // 0 to -MAX
+      // The exponent value at and above which toString returns exponential notation.
+      // Number type: 21
+      TO_EXP_POS = 21,                         // 0 to MAX
+      // RANGE : [MIN_EXP, MAX_EXP]
+      // The minimum exponent value, beneath which underflow to zero occurs.
+      // Number type: -324  (5e-324)
+      MIN_EXP = -1e7,                          // -1 to -MAX
+      // The maximum exponent value, above which overflow to Infinity occurs.
+      // Number type:  308  (1.7976931348623157e+308)
+      // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
+      MAX_EXP = 1e7,                           // 1 to MAX
+      // Whether to use cryptographically-secure random number generation, if available.
+      CRYPTO = false,                          // true or false
+      // 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.
+      //             This modulo mode is commonly known as 'truncated division' and is
+      //             equivalent to (a % n) in JavaScript.
+      // FLOOR     3 The remainder has the same sign as the divisor (Python %).
+      // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
+      // EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
+      //             The remainder is always positive.
+      //
+      // The truncated division, floored division, Euclidian division and IEEE 754 remainder
+      // modes are commonly used for the modulus operation.
+      // Although the other rounding modes can also be used, they may not give useful results.
+      MODULO_MODE = 1,                         // 0 to 9
+      // The maximum number of significant digits of the result of the exponentiatedBy operation.
+      // If POW_PRECISION is 0, there will be unlimited significant digits.
+      POW_PRECISION = 0,                    // 0 to MAX
+      // The format specification used by the BigNumber.prototype.toFormat method.
+      FORMAT = {
+        prefix: '',
+        groupSize: 3,
+        secondaryGroupSize: 0,
+        groupSeparator: ',',
+        decimalSeparator: '.',
+        fractionGroupSize: 0,
+        fractionGroupSeparator: '\xA0',      // non-breaking space
+        suffix: ''
+      },
+      // The alphabet used for base conversion. It must be at least 2 characters long, with no '+',
+      // '-', '.', whitespace, or repeated character.
+      // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+      ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
+    //------------------------------------------------------------------------------------------
+    // CONSTRUCTOR
+    /*
+     * The BigNumber constructor and exported function.
+     * Create and return a new instance of a BigNumber object.
+     *
+     * v {number|string|BigNumber} A numeric value.
+     * [b] {number} The base of v. Integer, 2 to ALPHABET.length inclusive.
+     */
+    function BigNumber(v, b) {
+      var alphabet, c, caseChanged, e, i, isNum, len, str,
+        x = this;
+      // Enable constructor call without `new`.
+      if (!(x instanceof BigNumber)) return new BigNumber(v, b);
+      if (b == null) {
+        if (v && v._isBigNumber === true) {
+          x.s = v.s;
+          if (!v.c || v.e > MAX_EXP) {
+            x.c = x.e = null;
+          } else if (v.e < MIN_EXP) {
+            x.c = [x.e = 0];
+          } else {
+            x.e = v.e;
+            x.c = v.c.slice();
+          }
+          return;
+        }
+        if ((isNum = typeof v == 'number') && v * 0 == 0) {
+          // Use `1 / n` to handle minus zero also.
+          x.s = 1 / v < 0 ? (v = -v, -1) : 1;
+          // Fast path for integers, where n < 2147483648 (2**31).
+          if (v === ~~v) {
+            for (e = 0, i = v; i >= 10; i /= 10, e++);
+            if (e > MAX_EXP) {
+              x.c = x.e = null;
+            } else {
+              x.e = e;
+              x.c = [v];
+            }
+            return;
+          }
+          str = String(v);
+        } else {
+          if (!isNumeric.test(str = String(v))) return parseNumeric(x, str, isNum);
+          x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
+        }
+        // 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;
+        }
+      } else {
+        // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+        intCheck(b, 2, ALPHABET.length, 'Base');
+        // Allow exponential notation to be used with base 10 argument, while
+        // also rounding to DECIMAL_PLACES as with other bases.
+        if (b == 10) {
+          x = new BigNumber(v);
+          return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
+        }
+        str = String(v);
+        if (isNum = typeof v == 'number') {
+          // Avoid potential interpretation of Infinity and NaN as base 44+ values.
+          if (v * 0 != 0) return parseNumeric(x, str, isNum, b);
+          x.s = 1 / v < 0 ? (str = str.slice(1), -1) : 1;
+          // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+          if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
+            throw Error
+             (tooManyDigits + v);
+          }
+        } else {
+          x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
+        }
+        alphabet = ALPHABET.slice(0, b);
+        e = i = 0;
+        // Check that str is a valid base b number.
+        // Don't use RegExp, so alphabet can contain special characters.
+        for (len = str.length; i < len; i++) {
+          if (alphabet.indexOf(c = str.charAt(i)) < 0) {
+            if (c == '.') {
+              // If '.' is not the first character and it has not be found before.
+              if (i > e) {
+                e = len;
+                continue;
+              }
+            } else if (!caseChanged) {
+              // Allow e.g. hexadecimal 'FF' as well as 'ff'.
+              if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
+                  str == str.toLowerCase() && (str = str.toUpperCase())) {
+                caseChanged = true;
+                i = -1;
+                e = 0;
+                continue;
+              }
+            }
+            return parseNumeric(x, String(v), isNum, b);
+          }
+        }
+        // Prevent later check for length on converted number.
+        isNum = false;
+        str = convertBase(str, b, 10, x.s);
+        // Decimal point?
+        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+        else e = str.length;
+      }
+      // Determine leading zeros.
+      for (i = 0; str.charCodeAt(i) === 48; i++);
+      // Determine trailing zeros.
+      for (len = str.length; str.charCodeAt(--len) === 48;);
+      if (str = str.slice(i, ++len)) {
+        len -= i;
+        // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+        if (isNum && BigNumber.DEBUG &&
+          len > 15 && (v > MAX_SAFE_INTEGER || v !== mathfloor(v))) {
+            throw Error
+             (tooManyDigits + (x.s * v));
+        }
+         // Overflow?
+        if ((e = e - i - 1) > MAX_EXP) {
+          // Infinity.
+          x.c = x.e = null;
+        // Underflow?
+        } else if (e < MIN_EXP) {
+          // Zero.
+          x.c = [x.e = 0];
+        } else {
+          x.e = e;
+          x.c = [];
+          // Transform base
+          // e is the base 10 exponent.
+          // i is where to slice str to get the first element of the coefficient array.
+          i = (e + 1) % LOG_BASE;
+          if (e < 0) i += LOG_BASE;  // i < 1
+          if (i < len) {
+            if (i) x.c.push(+str.slice(0, i));
+            for (len -= LOG_BASE; i < len;) {
+              x.c.push(+str.slice(i, i += LOG_BASE));
+            }
+            i = LOG_BASE - (str = str.slice(i)).length;
+          } else {
+            i -= len;
+          }
+          for (; i--; str += '0');
+          x.c.push(+str);
+        }
+      } else {
+        // Zero.
+        x.c = [x.e = 0];
+      }
+    }
+    // CONSTRUCTOR PROPERTIES
+    BigNumber.clone = clone;
+    BigNumber.ROUND_UP = 0;
+    BigNumber.ROUND_DOWN = 1;
+    BigNumber.ROUND_CEIL = 2;
+    BigNumber.ROUND_FLOOR = 3;
+    BigNumber.ROUND_HALF_UP = 4;
+    BigNumber.ROUND_HALF_DOWN = 5;
+    BigNumber.ROUND_HALF_EVEN = 6;
+    BigNumber.ROUND_HALF_CEIL = 7;
+    BigNumber.ROUND_HALF_FLOOR = 8;
+    BigNumber.EUCLID = 9;
+    /*
+     * Configure infrequently-changing library-wide settings.
+     *
+     * Accept an object with the following optional properties (if the value of a property is
+     * a number, it must be an integer within the inclusive range stated):
+     *
+     *   DECIMAL_PLACES   {number}           0 to MAX
+     *   ROUNDING_MODE    {number}           0 to 8
+     *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
+     *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
+     *   CRYPTO           {boolean}          true or false
+     *   MODULO_MODE      {number}           0 to 9
+     *   POW_PRECISION       {number}           0 to MAX
+     *   ALPHABET         {string}           A string of two or more unique characters which does
+     *                                       not contain '.'.
+     *   FORMAT           {object}           An object with some of the following properties:
+     *     prefix                 {string}
+     *     groupSize              {number}
+     *     secondaryGroupSize     {number}
+     *     groupSeparator         {string}
+     *     decimalSeparator       {string}
+     *     fractionGroupSize      {number}
+     *     fractionGroupSeparator {string}
+     *     suffix                 {string}
+     *
+     * (The values assigned to the above FORMAT object properties are not checked for validity.)
+     *
+     * E.g.
+     * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
+     *
+     * Ignore properties/parameters set to null or undefined, except for ALPHABET.
+     *
+     * Return an object with the properties current values.
+     */
+    BigNumber.config = BigNumber.set = function (obj) {
+      var p, v;
+      if (obj != null) {
+        if (typeof obj == 'object') {
+          // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
+          // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
+            v = obj[p];
+            intCheck(v, 0, MAX, p);
+            DECIMAL_PLACES = v;
+          }
+          // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
+          // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
+            v = obj[p];
+            intCheck(v, 0, 8, p);
+            ROUNDING_MODE = v;
+          }
+          // EXPONENTIAL_AT {number|number[]}
+          // Integer, -MAX to MAX inclusive or
+          // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
+          // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
+            v = obj[p];
+            if (v && v.pop) {
+              intCheck(v[0], -MAX, 0, p);
+              intCheck(v[1], 0, MAX, p);
+              TO_EXP_NEG = v[0];
+              TO_EXP_POS = v[1];
+            } else {
+              intCheck(v, -MAX, MAX, p);
+              TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
+            }
+          }
+          // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
+          // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
+          // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
+          if (obj.hasOwnProperty(p = 'RANGE')) {
+            v = obj[p];
+            if (v && v.pop) {
+              intCheck(v[0], -MAX, -1, p);
+              intCheck(v[1], 1, MAX, p);
+              MIN_EXP = v[0];
+              MAX_EXP = v[1];
+            } else {
+              intCheck(v, -MAX, MAX, p);
+              if (v) {
+                MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
+              } else {
+                throw Error
+                 (bignumberError + p + ' cannot be zero: ' + v);
+              }
+            }
+          }
+          // CRYPTO {boolean} true or false.
+          // '[BigNumber Error] CRYPTO not true or false: {v}'
+          // '[BigNumber Error] crypto unavailable'
+          if (obj.hasOwnProperty(p = 'CRYPTO')) {
+            v = obj[p];
+            if (v === !!v) {
+              if (v) {
+                if (typeof crypto != 'undefined' && crypto &&
+                 (crypto.getRandomValues || crypto.randomBytes)) {
+                  CRYPTO = v;
+                } else {
+                  CRYPTO = !v;
+                  throw Error
+                   (bignumberError + 'crypto unavailable');
+                }
+              } else {
+                CRYPTO = v;
+              }
+            } else {
+              throw Error
+               (bignumberError + p + ' not true or false: ' + v);
+            }
+          }
+          // MODULO_MODE {number} Integer, 0 to 9 inclusive.
+          // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
+            v = obj[p];
+            intCheck(v, 0, 9, p);
+            MODULO_MODE = v;
+          }
+          // POW_PRECISION {number} Integer, 0 to MAX inclusive.
+          // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
+          if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
+            v = obj[p];
+            intCheck(v, 0, MAX, p);
+            POW_PRECISION = v;
+          }
+          // FORMAT {object}
+          // '[BigNumber Error] FORMAT not an object: {v}'
+          if (obj.hasOwnProperty(p = 'FORMAT')) {
+            v = obj[p];
+            if (typeof v == 'object') FORMAT = v;
+            else throw Error
+             (bignumberError + p + ' not an object: ' + v);
+          }
+          // ALPHABET {string}
+          // '[BigNumber Error] ALPHABET invalid: {v}'
+          if (obj.hasOwnProperty(p = 'ALPHABET')) {
+            v = obj[p];
+            // Disallow if only one character,
+            // or if it contains '+', '-', '.', whitespace, or a repeated character.
+            if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
+              ALPHABET = v;
+            } else {
+              throw Error
+               (bignumberError + p + ' invalid: ' + v);
+            }
+          }
+        } else {
+          // '[BigNumber Error] Object expected: {v}'
+          throw Error
+           (bignumberError + 'Object expected: ' + obj);
+        }
+      }
+      return {
+        DECIMAL_PLACES: DECIMAL_PLACES,
+        ROUNDING_MODE: ROUNDING_MODE,
+        EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
+        RANGE: [MIN_EXP, MAX_EXP],
+        CRYPTO: CRYPTO,
+        MODULO_MODE: MODULO_MODE,
+        POW_PRECISION: POW_PRECISION,
+        FORMAT: FORMAT,
+        ALPHABET: ALPHABET
+      };
+    };
+    /*
+     * Return true if v is a BigNumber instance, otherwise return false.
+     *
+     * If BigNumber.DEBUG is true, throw if a BigNumber instance is not well-formed.
+     *
+     * v {any}
+     *
+     * '[BigNumber Error] Invalid BigNumber: {v}'
+     */
+    BigNumber.isBigNumber = function (v) {
+      if (!v || v._isBigNumber !== true) return false;
+      if (!BigNumber.DEBUG) return true;
+      var i, n,
+        c = v.c,
+        e = v.e,
+        s = v.s;
+      out: if ({}.toString.call(c) == '[object Array]') {
+        if ((s === 1 || s === -1) && e >= -MAX && e <= MAX && e === mathfloor(e)) {
+          // If the first element is zero, the BigNumber value must be zero.
+          if (c[0] === 0) {
+            if (e === 0 && c.length === 1) return true;
+            break out;
+          }
+          // Calculate number of digits that c[0] should have, based on the exponent.
+          i = (e + 1) % LOG_BASE;
+          if (i < 1) i += LOG_BASE;
+          // Calculate number of digits of c[0].
+          //if (Math.ceil(Math.log(c[0] + 1) / Math.LN10) == i) {
+          if (String(c[0]).length == i) {
+            for (i = 0; i < c.length; i++) {
+              n = c[i];
+              if (n < 0 || n >= BASE || n !== mathfloor(n)) break out;
+            }
+            // Last element cannot be zero, unless it is the only element.
+            if (n !== 0) return true;
+          }
+        }
+      // Infinity/NaN
+      } else if (c === null && e === null && (s === null || s === 1 || s === -1)) {
+        return true;
+      }
+      throw Error
+        (bignumberError + 'Invalid BigNumber: ' + v);
+    };
+    /*
+     * Return a new BigNumber whose value is the maximum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.maximum = BigNumber.max = function () {
+      return maxOrMin(arguments, P.lt);
+    };
+    /*
+     * Return a new BigNumber whose value is the minimum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.minimum = BigNumber.min = function () {
+      return maxOrMin(arguments, P.gt);
+    };
+    /*
+     * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
+     * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
+     * zeros are produced).
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
+     * '[BigNumber Error] crypto unavailable'
+     */
+    BigNumber.random = (function () {
+      var pow2_53 = 0x20000000000000;
+      // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
+      // Check if Math.random() produces more than 32 bits of randomness.
+      // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
+      // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
+      var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
+       ? function () { return mathfloor(Math.random() * pow2_53); }
+       : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
+         (Math.random() * 0x800000 | 0); };
+      return function (dp) {
+        var a, b, e, k, v,
+          i = 0,
+          c = [],
+          rand = new BigNumber(ONE);
+        if (dp == null) dp = DECIMAL_PLACES;
+        else intCheck(dp, 0, MAX);
+        k = mathceil(dp / LOG_BASE);
+        if (CRYPTO) {
+          // Browsers supporting crypto.getRandomValues.
+          if (crypto.getRandomValues) {
+            a = crypto.getRandomValues(new Uint32Array(k *= 2));
+            for (; i < k;) {
+              // 53 bits:
+              // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
+              // 11111 11111111 11111111 11111111 11100000 00000000 00000000
+              // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
+              //                                     11111 11111111 11111111
+              // 0x20000 is 2^21.
+              v = a[i] * 0x20000 + (a[i + 1] >>> 11);
+              // Rejection sampling:
+              // 0 <= v < 9007199254740992
+              // Probability that v >= 9e15, is
+              // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
+              if (v >= 9e15) {
+                b = crypto.getRandomValues(new Uint32Array(2));
+                a[i] = b[0];
+                a[i + 1] = b[1];
+              } else {
+                // 0 <= v <= 8999999999999999
+                // 0 <= (v % 1e14) <= 99999999999999
+                c.push(v % 1e14);
+                i += 2;
+              }
+            }
+            i = k / 2;
+          // Node.js supporting crypto.randomBytes.
+          } else if (crypto.randomBytes) {
+            // buffer
+            a = crypto.randomBytes(k *= 7);
+            for (; i < k;) {
+              // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
+              // 0x100000000 is 2^32, 0x1000000 is 2^24
+              // 11111 11111111 11111111 11111111 11111111 11111111 11111111
+              // 0 <= v < 9007199254740992
+              v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
+                 (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
+                 (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
+              if (v >= 9e15) {
+                crypto.randomBytes(7).copy(a, i);
+              } else {
+                // 0 <= (v % 1e14) <= 99999999999999
+                c.push(v % 1e14);
+                i += 7;
+              }
+            }
+            i = k / 7;
+          } else {
+            CRYPTO = false;
+            throw Error
+             (bignumberError + 'crypto unavailable');
+          }
+        }
+        // Use Math.random.
+        if (!CRYPTO) {
+          for (; i < k;) {
+            v = random53bitInt();
+            if (v < 9e15) c[i++] = v % 1e14;
+          }
+        }
+        k = c[--i];
+        dp %= LOG_BASE;
+        // Convert trailing digits to zeros according to dp.
+        if (k && dp) {
+          v = POWS_TEN[LOG_BASE - dp];
+          c[i] = mathfloor(k / v) * v;
+        }
+        // Remove trailing elements which are zero.
+        for (; c[i] === 0; c.pop(), i--);
+        // Zero?
+        if (i < 0) {
+          c = [e = 0];
+        } else {
+          // Remove leading elements which are zero and adjust exponent accordingly.
+          for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
+          // Count the digits of the first element of c to determine leading zeros, and...
+          for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
+          // adjust the exponent accordingly.
+          if (i < LOG_BASE) e -= LOG_BASE - i;
+        }
+        rand.e = e;
+        rand.c = c;
+        return rand;
+      };
+    })();
+    /*
+     * Return a BigNumber whose value is the sum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.sum = function () {
+      var i = 1,
+        args = arguments,
+        sum = new BigNumber(args[0]);
+      for (; i < args.length;) sum = sum.plus(args[i++]);
+      return sum;
+    };
+    // PRIVATE FUNCTIONS
+    // Called by BigNumber and BigNumber.prototype.toString.
+    convertBase = (function () {
+      var decimal = '0123456789';
+      /*
+       * Convert string of baseIn to an array of numbers of baseOut.
+       * Eg. toBaseOut('255', 10, 16) returns [15, 15].
+       * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
+       */
+      function toBaseOut(str, baseIn, baseOut, alphabet) {
+        var j,
+          arr = [0],
+          arrL,
+          i = 0,
+          len = str.length;
+        for (; i < len;) {
+          for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
+          arr[0] += alphabet.indexOf(str.charAt(i++));
+          for (j = 0; j < arr.length; j++) {
+            if (arr[j] > baseOut - 1) {
+              if (arr[j + 1] == null) arr[j + 1] = 0;
+              arr[j + 1] += arr[j] / baseOut | 0;
+              arr[j] %= baseOut;
+            }
+          }
+        }
+        return arr.reverse();
+      }
+      // Convert a numeric string of baseIn to a numeric string of baseOut.
+      // If the caller is toString, we are converting from base 10 to baseOut.
+      // If the caller is BigNumber, we are converting from baseIn to base 10.
+      return function (str, baseIn, baseOut, sign, callerIsToString) {
+        var alphabet, d, e, k, r, x, xc, y,
+          i = str.indexOf('.'),
+          dp = DECIMAL_PLACES,
+          rm = ROUNDING_MODE;
+        // Non-integer.
+        if (i >= 0) {
+          k = POW_PRECISION;
+          // Unlimited precision.
+          POW_PRECISION = 0;
+          str = str.replace('.', '');
+          y = new BigNumber(baseIn);
+          x = y.pow(str.length - i);
+          POW_PRECISION = k;
+          // Convert str as if an integer, then restore the fraction part by dividing the
+          // result by its base raised to a power.
+          y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
+           10, baseOut, decimal);
+          y.e = y.c.length;
+        }
+        // Convert the number as integer.
+        xc = toBaseOut(str, baseIn, baseOut, callerIsToString
+         ? (alphabet = ALPHABET, decimal)
+         : (alphabet = decimal, ALPHABET));
+        // xc now represents str as an integer and converted to baseOut. e is the exponent.
+        e = k = xc.length;
+        // Remove trailing zeros.
+        for (; xc[--k] == 0; xc.pop());
+        // Zero?
+        if (!xc[0]) return alphabet.charAt(0);
+        // Does str represent an integer? If so, no need for the division.
+        if (i < 0) {
+          --e;
+        } else {
+          x.c = xc;
+          x.e = e;
+          // The sign is needed for correct rounding.
+          x.s = sign;
+          x = div(x, y, dp, rm, baseOut);
+          xc = x.c;
+          r = x.r;
+          e = x.e;
+        }
+        // xc now represents str converted to baseOut.
+        // THe index of the rounding digit.
+        d = e + dp + 1;
+        // The rounding digit: the digit to the right of the digit that may be rounded up.
+        i = xc[d];
+        // Look at the rounding digits and mode to determine whether to round up.
+        k = baseOut / 2;
+        r = r || d < 0 || xc[d + 1] != null;
+        r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+              : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
+               rm == (x.s < 0 ? 8 : 7));
+        // If the index of the rounding digit is not greater than zero, or xc represents
+        // zero, then the result of the base conversion is zero or, if rounding up, a value
+        // such as 0.00001.
+        if (d < 1 || !xc[0]) {
+          // 1^-dp or 0
+          str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
+        } else {
+          // Truncate xc to the required number of decimal places.
+          xc.length = d;
+          // Round up?
+          if (r) {
+            // Rounding up may mean the previous digit has to be rounded up and so on.
+            for (--baseOut; ++xc[--d] > baseOut;) {
+              xc[d] = 0;
+              if (!d) {
+                ++e;
+                xc = [1].concat(xc);
+              }
+            }
+          }
+          // Determine trailing zeros.
+          for (k = xc.length; !xc[--k];);
+          // E.g. [4, 11, 15] becomes 4bf.
+          for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
+          // Add leading zeros, decimal point and trailing zeros as required.
+          str = toFixedPoint(str, e, alphabet.charAt(0));
+        }
+        // The caller will add the sign.
+        return str;
+      };
+    })();
+    // Perform division in the specified base. Called by div and convertBase.
+    div = (function () {
+      // Assume non-zero x and k.
+      function multiply(x, k, base) {
+        var m, temp, xlo, xhi,
+          carry = 0,
+          i = x.length,
+          klo = k % SQRT_BASE,
+          khi = k / SQRT_BASE | 0;
+        for (x = x.slice(); i--;) {
+          xlo = x[i] % SQRT_BASE;
+          xhi = x[i] / SQRT_BASE | 0;
+          m = khi * xlo + xhi * klo;
+          temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
+          carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
+          x[i] = temp % base;
+        }
+        if (carry) x = [carry].concat(x);
+        return x;
+      }
+      function compare(a, b, aL, bL) {
+        var i, cmp;
+        if (aL != bL) {
+          cmp = aL > bL ? 1 : -1;
+        } else {
+          for (i = cmp = 0; i < aL; i++) {
+            if (a[i] != b[i]) {
+              cmp = a[i] > b[i] ? 1 : -1;
+              break;
+            }
+          }
+        }
+        return cmp;
+      }
+      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.splice(0, 1));
+      }
+      // x: dividend, y: divisor.
+      return function (x, y, dp, rm, base) {
+        var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
+          yL, yz,
+          s = x.s == y.s ? 1 : -1,
+          xc = x.c,
+          yc = y.c;
+        // Either NaN, Infinity or 0?
+        if (!xc || !xc[0] || !yc || !yc[0]) {
+          return new BigNumber(
+           // Return NaN if either NaN, or both Infinity or 0.
+           !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
+            // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
+            xc && xc[0] == 0 || !yc ? s * 0 : s / 0
+         );
+        }
+        q = new BigNumber(s);
+        qc = q.c = [];
+        e = x.e - y.e;
+        s = dp + e + 1;
+        if (!base) {
+          base = BASE;
+          e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
+          s = s / LOG_BASE | 0;
+        }
+        // Result exponent may be one less then the current value of e.
+        // The coefficients of the BigNumbers from convertBase may have trailing zeros.
+        for (i = 0; yc[i] == (xc[i] || 0); i++);
+        if (yc[i] > (xc[i] || 0)) e--;
+        if (s < 0) {
+          qc.push(1);
+          more = true;
+        } else {
+          xL = xc.length;
+          yL = yc.length;
+          i = 0;
+          s += 2;
+          // Normalise xc and yc so highest order digit of yc is >= base / 2.
+          n = mathfloor(base / (yc[0] + 1));
+          // Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
+          // if (n > 1 || n++ == 1 && yc[0] < base / 2) {
+          if (n > 1) {
+            yc = multiply(yc, n, base);
+            xc = multiply(xc, n, base);
+            yL = yc.length;
+            xL = xc.length;
+          }
+          xi = yL;
+          rem = xc.slice(0, yL);
+          remL = rem.length;
+          // Add zeros to make remainder as long as divisor.
+          for (; remL < yL; rem[remL++] = 0);
+          yz = yc.slice();
+          yz = [0].concat(yz);
+          yc0 = yc[0];
+          if (yc[1] >= base / 2) yc0++;
+          // Not necessary, but to prevent trial digit n > base, when using base 3.
+          // else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
+          do {
+            n = 0;
+            // Compare divisor and remainder.
+            cmp = compare(yc, rem, yL, remL);
+            // If divisor < remainder.
+            if (cmp < 0) {
+              // Calculate trial digit, n.
+              rem0 = rem[0];
+              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
+              // n is how many times the divisor goes into the current remainder.
+              n = mathfloor(rem0 / yc0);
+              //  Algorithm:
+              //  product = divisor multiplied by trial digit (n).
+              //  Compare product and remainder.
+              //  If product is greater than remainder:
+              //    Subtract divisor from product, decrement trial digit.
+              //  Subtract product from remainder.
+              //  If product was less than remainder at the last compare:
+              //    Compare new remainder and divisor.
+              //    If remainder is greater than divisor:
+              //      Subtract divisor from remainder, increment trial digit.
+              if (n > 1) {
+                // n may be > base only when base is 3.
+                if (n >= base) n = base - 1;
+                // product = divisor * trial digit.
+                prod = multiply(yc, n, base);
+                prodL = prod.length;
+                remL = rem.length;
+                // Compare product and remainder.
+                // If product > remainder then trial digit n too high.
+                // n is 1 too high about 5% of the time, and is not known to have
+                // ever been more than 1 too high.
+                while (compare(prod, rem, prodL, remL) == 1) {
+                  n--;
+                  // Subtract divisor from product.
+                  subtract(prod, yL < prodL ? yz : yc, prodL, base);
+                  prodL = prod.length;
+                  cmp = 1;
+                }
+              } else {
+                // n is 0 or 1, cmp is -1.
+                // If n is 0, there is no need to compare yc and rem again below,
+                // so change cmp to 1 to avoid it.
+                // If n is 1, leave cmp as -1, so yc and rem are compared again.
+                if (n == 0) {
+                  // divisor < remainder, so n must be at least 1.
+                  cmp = n = 1;
+                }
+                // product = divisor
+                prod = yc.slice();
+                prodL = prod.length;
+              }
+              if (prodL < remL) prod = [0].concat(prod);
+              // Subtract product from remainder.
+              subtract(rem, prod, remL, base);
+              remL = rem.length;
+               // If product was < remainder.
+              if (cmp == -1) {
+                // Compare divisor and new remainder.
+                // If divisor < new remainder, subtract divisor from remainder.
+                // Trial digit n too low.
+                // n is 1 too low about 5% of the time, and very rarely 2 too low.
+                while (compare(yc, rem, yL, remL) < 1) {
+                  n++;
+                  // Subtract divisor from remainder.
+                  subtract(rem, yL < remL ? yz : yc, remL, base);
+                  remL = rem.length;
+                }
+              }
+            } else if (cmp === 0) {
+              n++;
+              rem = [0];
+            } // else cmp === 1 and n will be 0
+            // Add the next digit, n, to the result array.
+            qc[i++] = n;
+            // Update the remainder.
+            if (rem[0]) {
+              rem[remL++] = xc[xi] || 0;
+            } else {
+              rem = [xc[xi]];
+              remL = 1;
+            }
+          } while ((xi++ < xL || rem[0] != null) && s--);
+          more = rem[0] != null;
+          // Leading zero?
+          if (!qc[0]) qc.splice(0, 1);
+        }
+        if (base == BASE) {
+          // To calculate q.e, first get the number of digits of qc[0].
+          for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
+          round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
+        // Caller is convertBase.
+        } else {
+          q.e = e;
+          q.r = +more;
+        }
+        return q;
+      };
+    })();
+    /*
+     * Return a string representing the value of BigNumber n in fixed-point or exponential
+     * notation rounded to the specified decimal places or significant digits.
+     *
+     * n: a BigNumber.
+     * i: the index of the last digit required (i.e. the digit that may be rounded up).
+     * rm: the rounding mode.
+     * id: 1 (toExponential) or 2 (toPrecision).
+     */
+    function format(n, i, rm, id) {
+      var c0, e, ne, len, str;
+      if (rm == null) rm = ROUNDING_MODE;
+      else intCheck(rm, 0, 8);
+      if (!n.c) return n.toString();
+      c0 = n.c[0];
+      ne = n.e;
+      if (i == null) {
+        str = coeffToString(n.c);
+        str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
+         ? toExponential(str, ne)
+         : toFixedPoint(str, ne, '0');
+      } else {
+        n = round(new BigNumber(n), i, rm);
+        // n.e may have changed if the value was rounded up.
+        e = n.e;
+        str = coeffToString(n.c);
+        len = str.length;
+        // toPrecision returns exponential notation if the number of significant digits
+        // specified is less than the number of digits necessary to represent the integer
+        // part of the value in fixed-point notation.
+        // Exponential notation.
+        if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
+          // Append zeros?
+          for (; len < i; str += '0', len++);
+          str = toExponential(str, e);
+        // Fixed-point notation.
+        } else {
+          i -= ne;
+          str = toFixedPoint(str, e, '0');
+          // Append zeros?
+          if (e + 1 > len) {
+            if (--i > 0) for (str += '.'; i--; str += '0');
+          } else {
+            i += e - len;
+            if (i > 0) {
+              if (e + 1 == len) str += '.';
+              for (; i--; str += '0');
+            }
+          }
+        }
+      }
+      return n.s < 0 && c0 ? '-' + str : str;
+    }
+    // Handle BigNumber.max and BigNumber.min.
+    function maxOrMin(args, method) {
+      var n,
+        i = 1,
+        m = new BigNumber(args[0]);
+      for (; i < args.length; i++) {
+        n = new BigNumber(args[i]);
+        // If any number is NaN, return NaN.
+        if (!n.s) {
+          m = n;
+          break;
+        } else if (method.call(m, n)) {
+          m = n;
+        }
+      }
+      return m;
+    }
+    /*
+     * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
+     * Called by minus, plus and times.
+     */
+    function normalise(n, c, e) {
+      var i = 1,
+        j = c.length;
+       // Remove trailing zeros.
+      for (; !c[--j]; c.pop());
+      // Calculate the base 10 exponent. First get the number of digits of c[0].
+      for (j = c[0]; j >= 10; j /= 10, i++);
+      // Overflow?
+      if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
+        // Infinity.
+        n.c = n.e = null;
+      // Underflow?
+      } else if (e < MIN_EXP) {
+        // Zero.
+        n.c = [n.e = 0];
+      } else {
+        n.e = e;
+        n.c = c;
+      }
+      return n;
+    }
+    // Handle values that fail the validity test in BigNumber.
+    parseNumeric = (function () {
+      var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
+        dotAfter = /^([^.]+)\.$/,
+        dotBefore = /^\.([^.]+)$/,
+        isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+        whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+      return function (x, str, isNum, b) {
+        var base,
+          s = isNum ? str : str.replace(whitespaceOrPlus, '');
+        // No exception on ±Infinity or NaN.
+        if (isInfinityOrNaN.test(s)) {
+          x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
+        } else {
+          if (!isNum) {
+            // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
+            s = s.replace(basePrefix, function (m, p1, p2) {
+              base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
+              return !b || b == base ? p1 : m;
+            });
+            if (b) {
+              base = b;
+              // E.g. '1.' to '1', '.1' to '0.1'
+              s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
+            }
+            if (str != s) return new BigNumber(s, base);
+          }
+          // '[BigNumber Error] Not a number: {n}'
+          // '[BigNumber Error] Not a base {b} number: {n}'
+          if (BigNumber.DEBUG) {
+            throw Error
+              (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
+          }
+          // NaN
+          x.s = null;
+        }
+        x.c = x.e = null;
+      }
+    })();
+    /*
+     * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
+     * If r is truthy, it is known that there are more digits after the rounding digit.
+     */
+    function round(x, sd, rm, r) {
+      var d, i, j, k, n, ni, rd,
+        xc = x.c,
+        pows10 = POWS_TEN;
+      // if x is not Infinity or NaN...
+      if (xc) {
+        // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
+        // n is a base 1e14 number, the value of the element of array x.c containing rd.
+        // ni is the index of n within x.c.
+        // d is the number of digits of n.
+        // i is the index of rd within n including leading zeros.
+        // j is the actual index of rd within n (if < 0, rd is a leading zero).
+        out: {
+          // Get the number of digits of the first element of xc.
+          for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
+          i = sd - d;
+          // If the rounding digit is in the first element of xc...
+          if (i < 0) {
+            i += LOG_BASE;
+            j = sd;
+            n = xc[ni = 0];
+            // Get the rounding digit at index j of n.
+            rd = n / pows10[d - j - 1] % 10 | 0;
+          } else {
+            ni = mathceil((i + 1) / LOG_BASE);
+            if (ni >= xc.length) {
+              if (r) {
+                // Needed by sqrt.
+                for (; xc.length <= ni; xc.push(0));
+                n = rd = 0;
+                d = 1;
+                i %= LOG_BASE;
+                j = i - LOG_BASE + 1;
+              } else {
+                break out;
+              }
+            } else {
+              n = k = xc[ni];
+              // Get the number of digits of n.
+              for (d = 1; k >= 10; k /= 10, d++);
+              // Get the index of rd within n.
+              i %= LOG_BASE;
+              // Get the index of rd within n, adjusted for leading zeros.
+              // The number of leading zeros of n is given by LOG_BASE - d.
+              j = i - LOG_BASE + d;
+              // Get the rounding digit at index j of n.
+              rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
+            }
+          }
+          r = r || sd < 0 ||
+          // Are there any non-zero digits after the rounding digit?
+          // The expression  n % pows10[d - j - 1]  returns all digits of n to the right
+          // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
+           xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
+          r = rm < 4
+           ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+           : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
+            // Check whether the digit to the left of the rounding digit is odd.
+            ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
+             rm == (x.s < 0 ? 8 : 7));
+          if (sd < 1 || !xc[0]) {
+            xc.length = 0;
+            if (r) {
+              // Convert sd to decimal places.
+              sd -= x.e + 1;
+              // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+              xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
+              x.e = -sd || 0;
+            } else {
+              // Zero.
+              xc[0] = x.e = 0;
+            }
+            return x;
+          }
+          // Remove excess digits.
+          if (i == 0) {
+            xc.length = ni;
+            k = 1;
+            ni--;
+          } else {
+            xc.length = ni + 1;
+            k = pows10[LOG_BASE - i];
+            // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+            // j > 0 means i > number of leading zeros of n.
+            xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
+          }
+          // Round up?
+          if (r) {
+            for (; ;) {
+              // If the digit to be rounded up is in the first element of xc...
+              if (ni == 0) {
+                // i will be the length of xc[0] before k is added.
+                for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
+                j = xc[0] += k;
+                for (k = 1; j >= 10; j /= 10, k++);
+                // if i != k the length has increased.
+                if (i != k) {
+                  x.e++;
+                  if (xc[0] == BASE) xc[0] = 1;
+                }
+                break;
+              } else {
+                xc[ni] += k;
+                if (xc[ni] != BASE) break;
+                xc[ni--] = 0;
+                k = 1;
+              }
+            }
+          }
+          // Remove trailing zeros.
+          for (i = xc.length; xc[--i] === 0; xc.pop());
+        }
+        // Overflow? Infinity.
+        if (x.e > MAX_EXP) {
+          x.c = x.e = null;
+        // Underflow? Zero.
+        } else if (x.e < MIN_EXP) {
+          x.c = [x.e = 0];
+        }
+      }
+      return x;
+    }
+    function valueOf(n) {
+      var str,
+        e = n.e;
+      if (e === null) return n.toString();
+      str = coeffToString(n.c);
+      str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+        ? toExponential(str, e)
+        : toFixedPoint(str, e, '0');
+      return n.s < 0 ? '-' + str : str;
+    }
+    // PROTOTYPE/INSTANCE METHODS
+    /*
+     * Return a new BigNumber whose value is the absolute value of this BigNumber.
+     */
+    P.absoluteValue = P.abs = function () {
+      var x = new BigNumber(this);
+      if (x.s < 0) x.s = 1;
+      return x;
+    };
+    /*
+     * Return
+     *   1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
+     *   -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
+     *   0 if they have the same value,
+     *   or null if the value of either is NaN.
+     */
+    P.comparedTo = function (y, b) {
+      return compare(this, new BigNumber(y, b));
+    };
+    /*
+     * If dp is undefined or null or true or false, return the number of decimal places of the
+     * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+     *
+     * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
+     * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
+     * ROUNDING_MODE if rm is omitted.
+     *
+     * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.decimalPlaces = P.dp = function (dp, rm) {
+      var c, n, v,
+        x = this;
+      if (dp != null) {
+        intCheck(dp, 0, MAX);
+        if (rm == null) rm = ROUNDING_MODE;
+        else intCheck(rm, 0, 8);
+        return round(new BigNumber(x), dp + x.e + 1, rm);
+      }
+      if (!(c = x.c)) return null;
+      n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
+      // Subtract the number of trailing zeros of the last number.
+      if (v = c[v]) for (; v % 10 == 0; v /= 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 BigNumber whose value is the value of this BigNumber divided by the value of
+     * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+     */
+    P.dividedBy = P.div = function (y, b) {
+      return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
+    };
+    /*
+     * Return a new BigNumber whose value is the integer part of dividing the value of this
+     * BigNumber by the value of BigNumber(y, b).
+     */
+    P.dividedToIntegerBy = P.idiv = function (y, b) {
+      return div(this, new BigNumber(y, b), 0, 1);
+    };
+    /*
+     * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
+     *
+     * If m is present, return the result modulo m.
+     * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
+     * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
+     *
+     * The modular power operation works efficiently when x, n, and m are integers, otherwise it
+     * is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
+     *
+     * n {number|string|BigNumber} The exponent. An integer.
+     * [m] {number|string|BigNumber} The modulus.
+     *
+     * '[BigNumber Error] Exponent not an integer: {n}'
+     */
+    P.exponentiatedBy = P.pow = function (n, m) {
+      var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
+        x = this;
+      n = new BigNumber(n);
+      // Allow NaN and ±Infinity, but not other non-integers.
+      if (n.c && !n.isInteger()) {
+        throw Error
+          (bignumberError + 'Exponent not an integer: ' + valueOf(n));
+      }
+      if (m != null) m = new BigNumber(m);
+      // Exponent of MAX_SAFE_INTEGER is 15.
+      nIsBig = n.e > 14;
+      // If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
+      if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
+        // The sign of the result of pow when x is negative depends on the evenness of n.
+        // If +n overflows to ±Infinity, the evenness of n would be not be known.
+        y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
+        return m ? y.mod(m) : y;
+      }
+      nIsNeg = n.s < 0;
+      if (m) {
+        // x % m returns NaN if abs(m) is zero, or m is NaN.
+        if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
+        isModExp = !nIsNeg && x.isInteger() && m.isInteger();
+        if (isModExp) x = x.mod(m);
+      // Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
+      // Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
+      } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
+        // [1, 240000000]
+        ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
+        // [80000000000000]  [99999750000000]
+        : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
+        // If x is negative and n is odd, k = -0, else k = 0.
+        k = x.s < 0 && isOdd(n) ? -0 : 0;
+        // If x >= 1, k = ±Infinity.
+        if (x.e > -1) k = 1 / k;
+        // If n is negative return ±0, else return ±Infinity.
+        return new BigNumber(nIsNeg ? 1 / k : k);
+      } else if (POW_PRECISION) {
+        // Truncating each coefficient array to a length of k after each multiplication
+        // equates to truncating significant digits to POW_PRECISION + [28, 41],
+        // i.e. there will be a minimum of 28 guard digits retained.
+        k = mathceil(POW_PRECISION / LOG_BASE + 2);
+      }
+      if (nIsBig) {
+        half = new BigNumber(0.5);
+        if (nIsNeg) n.s = 1;
+        nIsOdd = isOdd(n);
+      } else {
+        i = Math.abs(+valueOf(n));
+        nIsOdd = i % 2;
+      }
+      y = new BigNumber(ONE);
+      // Performs 54 loop iterations for n of 9007199254740991.
+      for (; ;) {
+        if (nIsOdd) {
+          y = y.times(x);
+          if (!y.c) break;
+          if (k) {
+            if (y.c.length > k) y.c.length = k;
+          } else if (isModExp) {
+            y = y.mod(m);    //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
+          }
+        }
+        if (i) {
+          i = mathfloor(i / 2);
+          if (i === 0) break;
+          nIsOdd = i % 2;
+        } else {
+          n = n.times(half);
+          round(n, n.e + 1, 1);
+          if (n.e > 14) {
+            nIsOdd = isOdd(n);
+          } else {
+            i = +valueOf(n);
+            if (i === 0) break;
+            nIsOdd = i % 2;
+          }
+        }
+        x = x.times(x);
+        if (k) {
+          if (x.c && x.c.length > k) x.c.length = k;
+        } else if (isModExp) {
+          x = x.mod(m);    //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
+        }
+      }
+      if (isModExp) return y;
+      if (nIsNeg) y = ONE.div(y);
+      return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
+    };
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
+     * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+     *
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
+     */
+    P.integerValue = function (rm) {
+      var n = new BigNumber(this);
+      if (rm == null) rm = ROUNDING_MODE;
+      else intCheck(rm, 0, 8);
+      return round(n, n.e + 1, rm);
+    };
+    /*
+     * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isEqualTo = P.eq = function (y, b) {
+      return compare(this, new BigNumber(y, b)) === 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is a finite number, otherwise return false.
+     */
+    P.isFinite = function () {
+      return !!this.c;
+    };
+    /*
+     * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isGreaterThan = P.gt = function (y, b) {
+      return compare(this, new BigNumber(y, b)) > 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is greater than or equal to the value of
+     * BigNumber(y, b), otherwise return false.
+     */
+    P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
+      return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is an integer, otherwise return false.
+     */
+    P.isInteger = function () {
+      return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
+    };
+    /*
+     * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isLessThan = P.lt = function (y, b) {
+      return compare(this, new BigNumber(y, b)) < 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is less than or equal to the value of
+     * BigNumber(y, b), otherwise return false.
+     */
+    P.isLessThanOrEqualTo = P.lte = function (y, b) {
+      return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is NaN, otherwise return false.
+     */
+    P.isNaN = function () {
+      return !this.s;
+    };
+    /*
+     * Return true if the value of this BigNumber is negative, otherwise return false.
+     */
+    P.isNegative = function () {
+      return this.s < 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is positive, otherwise return false.
+     */
+    P.isPositive = function () {
+      return this.s > 0;
+    };
+    /*
+     * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
+     */
+    P.isZero = function () {
+      return !!this.c && this.c[0] == 0;
+    };
+    /*
+     *  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 BigNumber whose value is the value of this BigNumber minus the value of
+     * BigNumber(y, b).
+     */
+    P.minus = function (y, b) {
+      var i, j, t, xLTy,
+        x = this,
+        a = x.s;
+      y = new BigNumber(y, b);
+      b = y.s;
+      // Either NaN?
+      if (!a || !b) return new BigNumber(NaN);
+      // Signs differ?
+      if (a != b) {
+        y.s = -b;
+        return x.plus(y);
+      }
+      var xe = x.e / LOG_BASE,
+        ye = y.e / LOG_BASE,
+        xc = x.c,
+        yc = y.c;
+      if (!xe || !ye) {
+        // Either Infinity?
+        if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
+        // Either zero?
+        if (!xc[0] || !yc[0]) {
+          // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+          return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
+           // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
+           ROUNDING_MODE == 3 ? -0 : 0);
+        }
+      }
+      xe = bitFloor(xe);
+      ye = bitFloor(ye);
+      xc = xc.slice();
+      // Determine which is the bigger number.
+      if (a = xe - ye) {
+        if (xLTy = a < 0) {
+          a = -a;
+          t = xc;
+        } else {
+          ye = xe;
+          t = yc;
+        }
+        t.reverse();
+        // Prepend zeros to equalise exponents.
+        for (b = a; b--; t.push(0));
+        t.reverse();
+      } else {
+        // Exponents equal. Check digit by digit.
+        j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
+        for (a = b = 0; b < j; b++) {
+          if (xc[b] != yc[b]) {
+            xLTy = xc[b] < yc[b];
+            break;
+          }
+        }
+      }
+      // x < y? Point xc to the array of the bigger number.
+      if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
+      b = (j = yc.length) - (i = xc.length);
+      // Append zeros to xc if shorter.
+      // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
+      if (b > 0) for (; b--; xc[i++] = 0);
+      b = BASE - 1;
+      // Subtract yc from xc.
+      for (; j > a;) {
+        if (xc[--j] < yc[j]) {
+          for (i = j; i && !xc[--i]; xc[i] = b);
+          --xc[i];
+          xc[j] += BASE;
+        }
+        xc[j] -= yc[j];
+      }
+      // Remove leading zeros and adjust exponent accordingly.
+      for (; xc[0] == 0; xc.splice(0, 1), --ye);
+      // Zero?
+      if (!xc[0]) {
+        // Following IEEE 754 (2008) 6.3,
+        // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
+        y.s = ROUNDING_MODE == 3 ? -1 : 1;
+        y.c = [y.e = 0];
+        return y;
+      }
+      // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
+      // for finite x and y.
+      return normalise(y, xc, ye);
+    };
+    /*
+     *   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 BigNumber whose value is the value of this BigNumber modulo the value of
+     * BigNumber(y, b). The result depends on the value of MODULO_MODE.
+     */
+    P.modulo = P.mod = function (y, b) {
+      var q, s,
+        x = this;
+      y = new BigNumber(y, b);
+      // Return NaN if x is Infinity or NaN, or y is NaN or zero.
+      if (!x.c || !y.s || y.c && !y.c[0]) {
+        return new BigNumber(NaN);
+      // Return x if y is Infinity or x is zero.
+      } else if (!y.c || x.c && !x.c[0]) {
+        return new BigNumber(x);
+      }
+      if (MODULO_MODE == 9) {
+        // Euclidian division: q = sign(y) * floor(x / abs(y))
+        // r = x - qy    where  0 <= r < abs(y)
+        s = y.s;
+        y.s = 1;
+        q = div(x, y, 0, 3);
+        y.s = s;
+        q.s *= s;
+      } else {
+        q = div(x, y, 0, MODULO_MODE);
+      }
+      y = x.minus(q.times(y));
+      // To match JavaScript %, ensure sign of zero is sign of dividend.
+      if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
+      return y;
+    };
+    /*
+     *  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 BigNumber whose value is the value of this BigNumber multiplied by the value
+     * of BigNumber(y, b).
+     */
+    P.multipliedBy = P.times = function (y, b) {
+      var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
+        base, sqrtBase,
+        x = this,
+        xc = x.c,
+        yc = (y = new BigNumber(y, b)).c;
+      // Either NaN, ±Infinity or ±0?
+      if (!xc || !yc || !xc[0] || !yc[0]) {
+        // Return NaN if either is NaN, or one is 0 and the other is Infinity.
+        if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
+          y.c = y.e = y.s = null;
+        } else {
+          y.s *= x.s;
+          // Return ±Infinity if either is ±Infinity.
+          if (!xc || !yc) {
+            y.c = y.e = null;
+          // Return ±0 if either is ±0.
+          } else {
+            y.c = [0];
+            y.e = 0;
+          }
+        }
+        return y;
+      }
+      e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
+      y.s *= x.s;
+      xcL = xc.length;
+      ycL = yc.length;
+      // Ensure xc points to longer array and xcL to its length.
+      if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
+      // Initialise the result array with zeros.
+      for (i = xcL + ycL, zc = []; i--; zc.push(0));
+      base = BASE;
+      sqrtBase = SQRT_BASE;
+      for (i = ycL; --i >= 0;) {
+        c = 0;
+        ylo = yc[i] % sqrtBase;
+        yhi = yc[i] / sqrtBase | 0;
+        for (k = xcL, j = i + k; j > i;) {
+          xlo = xc[--k] % sqrtBase;
+          xhi = xc[k] / sqrtBase | 0;
+          m = yhi * xlo + xhi * ylo;
+          xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
+          c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
+          zc[j--] = xlo % base;
+        }
+        zc[j] = c;
+      }
+      if (c) {
+        ++e;
+      } else {
+        zc.splice(0, 1);
+      }
+      return normalise(y, zc, e);
+    };
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber negated,
+     * i.e. multiplied by -1.
+     */
+    P.negated = function () {
+      var x = new BigNumber(this);
+      x.s = -x.s || null;
+      return 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 BigNumber whose value is the value of this BigNumber plus the value of
+     * BigNumber(y, b).
+     */
+    P.plus = function (y, b) {
+      var t,
+        x = this,
+        a = x.s;
+      y = new BigNumber(y, b);
+      b = y.s;
+      // Either NaN?
+      if (!a || !b) return new BigNumber(NaN);
+      // Signs differ?
+       if (a != b) {
+        y.s = -b;
+        return x.minus(y);
+      }
+      var xe = x.e / LOG_BASE,
+        ye = y.e / LOG_BASE,
+        xc = x.c,
+        yc = y.c;
+      if (!xe || !ye) {
+        // Return ±Infinity if either ±Infinity.
+        if (!xc || !yc) return new BigNumber(a / 0);
+        // Either zero?
+        // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+        if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
+      }
+      xe = bitFloor(xe);
+      ye = bitFloor(ye);
+      xc = xc.slice();
+      // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
+      if (a = xe - ye) {
+        if (a > 0) {
+          ye = xe;
+          t = yc;
+        } else {
+          a = -a;
+          t = xc;
+        }
+        t.reverse();
+        for (; a--; t.push(0));
+        t.reverse();
+      }
+      a = xc.length;
+      b = yc.length;
+      // Point xc to the longer array, and b to the shorter length.
+      if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
+      // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
+      for (a = 0; b;) {
+        a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
+        xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
+      }
+      if (a) {
+        xc = [a].concat(xc);
+        ++ye;
+      }
+      // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+      // ye = MAX_EXP + 1 possible
+      return normalise(y, xc, ye);
+    };
+    /*
+     * If sd is undefined or null or true or false, return the number of significant digits of
+     * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+     * If sd is true include integer-part trailing zeros in the count.
+     *
+     * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
+     * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
+     * ROUNDING_MODE if rm is omitted.
+     *
+     * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
+     *                     boolean: whether to count integer-part trailing zeros: true or false.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+     */
+    P.precision = P.sd = function (sd, rm) {
+      var c, n, v,
+        x = this;
+      if (sd != null && sd !== !!sd) {
+        intCheck(sd, 1, MAX);
+        if (rm == null) rm = ROUNDING_MODE;
+        else intCheck(rm, 0, 8);
+        return round(new BigNumber(x), sd, rm);
+      }
+      if (!(c = x.c)) return null;
+      v = c.length - 1;
+      n = v * LOG_BASE + 1;
+      if (v = c[v]) {
+        // Subtract the number of trailing zeros of the last element.
+        for (; v % 10 == 0; v /= 10, n--);
+        // Add the number of digits of the first element.
+        for (v = c[0]; v >= 10; v /= 10, n++);
+      }
+      if (sd && x.e + 1 > n) n = x.e + 1;
+      return n;
+    };
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
+     * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
+     *
+     * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
+     */
+    P.shiftedBy = function (k) {
+      intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
+      return this.times('1e' + k);
+    };
+    /*
+     *  sqrt(-n) =  N
+     *  sqrt(N) =  N
+     *  sqrt(-I) =  N
+     *  sqrt(I) =  I
+     *  sqrt(0) =  0
+     *  sqrt(-0) = -0
+     *
+     * Return a new BigNumber whose value is the square root of the value of this BigNumber,
+     * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+     */
+    P.squareRoot = P.sqrt = function () {
+      var m, n, r, rep, t,
+        x = this,
+        c = x.c,
+        s = x.s,
+        e = x.e,
+        dp = DECIMAL_PLACES + 4,
+        half = new BigNumber('0.5');
+      // Negative/NaN/Infinity/zero?
+      if (s !== 1 || !c || !c[0]) {
+        return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
+      }
+      // Initial estimate.
+      s = Math.sqrt(+valueOf(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 = coeffToString(c);
+        if ((n.length + e) % 2 == 0) n += '0';
+        s = Math.sqrt(+n);
+        e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);
+        if (s == 1 / 0) {
+          n = '1e' + e;
+        } else {
+          n = s.toExponential();
+          n = n.slice(0, n.indexOf('e') + 1) + e;
+        }
+        r = new BigNumber(n);
+      } else {
+        r = new BigNumber(s + '');
+      }
+      // Check for zero.
+      // r could be zero if MIN_EXP is changed after the this value was created.
+      // This would cause a division by zero (x/t) and hence Infinity below, which would cause
+      // coeffToString to throw.
+      if (r.c[0]) {
+        e = r.e;
+        s = e + dp;
+        if (s < 3) s = 0;
+        // Newton-Raphson iteration.
+        for (; ;) {
+          t = r;
+          r = half.times(t.plus(div(x, t, dp, 1)));
+          if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
+            // The exponent of r may here be one less than the final result exponent,
+            // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
+            // are indexed correctly.
+            if (r.e < e) --s;
+            n = n.slice(s - 3, s + 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) {
+                round(t, t.e + DECIMAL_PLACES + 2, 0);
+                if (t.times(t).eq(x)) {
+                  r = t;
+                  break;
+                }
+              }
+              dp += 4;
+              s += 4;
+              rep = 1;
+            } else {
+              // If rounding digits are null, 0{0,4} or 50{0,3}, check for 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.
+                round(r, r.e + DECIMAL_PLACES + 2, 1);
+                m = !r.times(r).eq(x);
+              }
+              break;
+            }
+          }
+        }
+      }
+      return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
+    };
+    /*
+     * Return a string representing the value of this BigNumber in exponential notation and
+     * rounded using ROUNDING_MODE to dp fixed decimal places.
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toExponential = function (dp, rm) {
+      if (dp != null) {
+        intCheck(dp, 0, MAX);
+        dp++;
+      }
+      return format(this, dp, rm, 1);
+    };
+    /*
+     * Return a string representing the value of this BigNumber in fixed-point notation rounding
+     * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+     *
+     * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
+     * but e.g. (-0.00001).toFixed(0) is '-0'.
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toFixed = function (dp, rm) {
+      if (dp != null) {
+        intCheck(dp, 0, MAX);
+        dp = dp + this.e + 1;
+      }
+      return format(this, dp, rm);
+    };
+    /*
+     * Return a string representing the value of this BigNumber in fixed-point notation rounded
+     * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
+     * of the format or FORMAT object (see BigNumber.set).
+     *
+     * The formatting object may contain some or all of the properties shown below.
+     *
+     * FORMAT = {
+     *   prefix: '',
+     *   groupSize: 3,
+     *   secondaryGroupSize: 0,
+     *   groupSeparator: ',',
+     *   decimalSeparator: '.',
+     *   fractionGroupSize: 0,
+     *   fractionGroupSeparator: '\xA0',      // non-breaking space
+     *   suffix: ''
+     * };
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     * [format] {object} Formatting options. See FORMAT pbject above.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     * '[BigNumber Error] Argument not an object: {format}'
+     */
+    P.toFormat = function (dp, rm, format) {
+      var str,
+        x = this;
+      if (format == null) {
+        if (dp != null && rm && typeof rm == 'object') {
+          format = rm;
+          rm = null;
+        } else if (dp && typeof dp == 'object') {
+          format = dp;
+          dp = rm = null;
+        } else {
+          format = FORMAT;
+        }
+      } else if (typeof format != 'object') {
+        throw Error
+          (bignumberError + 'Argument not an object: ' + format);
+      }
+      str = x.toFixed(dp, rm);
+      if (x.c) {
+        var i,
+          arr = str.split('.'),
+          g1 = +format.groupSize,
+          g2 = +format.secondaryGroupSize,
+          groupSeparator = format.groupSeparator || '',
+          intPart = arr[0],
+          fractionPart = arr[1],
+          isNeg = x.s < 0,
+          intDigits = isNeg ? intPart.slice(1) : intPart,
+          len = intDigits.length;
+        if (g2) i = g1, g1 = g2, g2 = i, len -= i;
+        if (g1 > 0 && len > 0) {
+          i = len % g1 || g1;
+          intPart = intDigits.substr(0, i);
+          for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
+          if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
+          if (isNeg) intPart = '-' + intPart;
+        }
+        str = fractionPart
+         ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
+          ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
+           '$&' + (format.fractionGroupSeparator || ''))
+          : fractionPart)
+         : intPart;
+      }
+      return (format.prefix || '') + str + (format.suffix || '');
+    };
+    /*
+     * Return an array of two BigNumbers representing the value of this BigNumber 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.
+     *
+     * [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
+     *
+     * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
+     */
+    P.toFraction = function (md) {
+      var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
+        x = this,
+        xc = x.c;
+      if (md != null) {
+        n = new BigNumber(md);
+        // Throw if md is less than one or is not an integer, unless it is Infinity.
+        if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
+          throw Error
+            (bignumberError + 'Argument ' +
+              (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
+        }
+      }
+      if (!xc) return new BigNumber(x);
+      d = new BigNumber(ONE);
+      n1 = d0 = new BigNumber(ONE);
+      d1 = n0 = new BigNumber(ONE);
+      s = coeffToString(xc);
+      // Determine initial denominator.
+      // d is a power of 10 and the minimum max denominator that specifies the value exactly.
+      e = d.e = s.length - x.e - 1;
+      d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
+      md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
+      exp = MAX_EXP;
+      MAX_EXP = 1 / 0;
+      n = new BigNumber(s);
+      // n0 = d1 = 0
+      n0.c[0] = 0;
+      for (; ;)  {
+        q = div(n, d, 0, 1);
+        d2 = d0.plus(q.times(d1));
+        if (d2.comparedTo(md) == 1) break;
+        d0 = d1;
+        d1 = d2;
+        n1 = n0.plus(q.times(d2 = n1));
+        n0 = d2;
+        d = n.minus(q.times(d2 = d));
+        n = d2;
+      }
+      d2 = div(md.minus(d0), d1, 0, 1);
+      n0 = n0.plus(d2.times(n1));
+      d0 = d0.plus(d2.times(d1));
+      n0.s = n1.s = x.s;
+      e = e * 2;
+      // Determine which fraction is closer to x, n0/d0 or n1/d1
+      r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
+          div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
+      MAX_EXP = exp;
+      return r;
+    };
+    /*
+     * Return the value of this BigNumber converted to a number primitive.
+     */
+    P.toNumber = function () {
+      return +valueOf(this);
+    };
+    /*
+     * Return a string representing the value of this BigNumber rounded to sd significant digits
+     * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
+     * necessary to represent the integer part of the value in fixed-point notation, then use
+     * exponential notation.
+     *
+     * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+     */
+    P.toPrecision = function (sd, rm) {
+      if (sd != null) intCheck(sd, 1, MAX);
+      return format(this, sd, rm, 2);
+    };
+    /*
+     * Return a string representing the value of this BigNumber in base b, or base 10 if b is
+     * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
+     * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
+     * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
+     * TO_EXP_NEG, return exponential notation.
+     *
+     * [b] {number} Integer, 2 to ALPHABET.length inclusive.
+     *
+     * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+     */
+    P.toString = function (b) {
+      var str,
+        n = this,
+        s = n.s,
+        e = n.e;
+      // Infinity or NaN?
+      if (e === null) {
+        if (s) {
+          str = 'Infinity';
+          if (s < 0) str = '-' + str;
+        } else {
+          str = 'NaN';
+        }
+      } else {
+        if (b == null) {
+          str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+           ? toExponential(coeffToString(n.c), e)
+           : toFixedPoint(coeffToString(n.c), e, '0');
+        } else if (b === 10) {
+          n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
+          str = toFixedPoint(coeffToString(n.c), n.e, '0');
+        } else {
+          intCheck(b, 2, ALPHABET.length, 'Base');
+          str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
+        }
+        if (s < 0 && n.c[0]) str = '-' + str;
+      }
+      return str;
+    };
+    /*
+     * Return as toString, but do not accept a base argument, and include the minus sign for
+     * negative zero.
+     */
+    P.valueOf = P.toJSON = function () {
+      return valueOf(this);
+    };
+    P._isBigNumber = true;
+    if (hasSymbol) {
+      P[Symbol.toStringTag] = 'BigNumber';
+      // Node.js v10.12.0+
+      P[Symbol.for('nodejs.util.inspect.custom')] = P.valueOf;
+    }
+    if (configObject != null) BigNumber.set(configObject);
+    return BigNumber;
+  }
+  // PRIVATE HELPER FUNCTIONS
+  // These functions don't need access to variables,
+  // e.g. DECIMAL_PLACES, in the scope of the `clone` function above.
+  function bitFloor(n) {
+    var i = n | 0;
+    return n > 0 || n === i ? i : i - 1;
+  }
+  // Return a coefficient array as a string of base 10 digits.
+  function coeffToString(a) {
+    var s, z,
+      i = 1,
+      j = a.length,
+      r = a[0] + '';
+    for (; i < j;) {
+      s = a[i++] + '';
+      z = LOG_BASE - s.length;
+      for (; z--; s = '0' + s);
+      r += s;
+    }
+    // Determine trailing zeros.
+    for (j = r.length; r.charCodeAt(--j) === 48;);
+    return r.slice(0, j + 1 || 1);
+  }
+  // Compare the value of BigNumbers x and y.
+  function compare(x, y) {
+    var a, b,
+      xc = x.c,
+      yc = y.c,
+      i = x.s,
+      j = y.s,
+      k = x.e,
+      l = y.e;
+    // Either NaN?
+    if (!i || !j) return null;
+    a = xc && !xc[0];
+    b = yc && !yc[0];
+    // Either zero?
+    if (a || b) return a ? b ? 0 : -j : i;
+    // Signs differ?
+    if (i != j) return i;
+    a = i < 0;
+    b = k == l;
+    // Either Infinity?
+    if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
+    // Compare exponents.
+    if (!b) return k > l ^ a ? 1 : -1;
+    j = (k = xc.length) < (l = yc.length) ? k : l;
+    // Compare digit by digit.
+    for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
+    // Compare lengths.
+    return k == l ? 0 : k > l ^ a ? 1 : -1;
+  }
+  /*
+   * Check that n is a primitive number, an integer, and in range, otherwise throw.
+   */
+  function intCheck(n, min, max, name) {
+    if (n < min || n > max || n !== mathfloor(n)) {
+      throw Error
+       (bignumberError + (name || 'Argument') + (typeof n == 'number'
+         ? n < min || n > max ? ' out of range: ' : ' not an integer: '
+         : ' not a primitive number: ') + String(n));
+    }
+  }
+  // Assumes finite n.
+  function isOdd(n) {
+    var k = n.c.length - 1;
+    return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
+  }
+  function toExponential(str, e) {
+    return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
+     (e < 0 ? 'e' : 'e+') + e;
+  }
+  function toFixedPoint(str, e, z) {
+    var len, zs;
+    // Negative exponent?
+    if (e < 0) {
+      // Prepend zeros.
+      for (zs = z + '.'; ++e; zs += z);
+      str = zs + str;
+    // Positive exponent
+    } else {
+      len = str.length;
+      // Append zeros.
+      if (++e > len) {
+        for (zs = z, e -= len; --e; zs += z);
+        str += zs;
+      } else if (e < len) {
+        str = str.slice(0, e) + '.' + str.slice(e);
+      }
+    }
+    return str;
+  }
+  // EXPORT
+  BigNumber = clone();
+  BigNumber['default'] = BigNumber.BigNumber = BigNumber;
+  // AMD.
+  if (typeof define == 'function' && define.amd) {
+    define(function () { return BigNumber; });
+  // Node.js and other environments that support module.exports.
+  } else if (typeof module != 'undefined' && module.exports) {
+    module.exports = BigNumber;
+  // Browser.
+  } else {
+    if (!globalObject) {
+      globalObject = typeof self != 'undefined' && self ? self : window;
+    }
+    globalObject.BigNumber = BigNumber;
+  }
+})(this);
+</script>
     <script type="text/javascript">
     // bip39 Valid Mnemonic Generator Javascript App
     /*