bignumber.js

; (function (globalObject) {
    'use strict';

    /*
     *      bignumber.js v8.0.2
     *      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,

        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.
         *
         * n {number|string|BigNumber} A numeric value.
         * [b] {number} The base of n. Integer, 2 to ALPHABET.length inclusive.
         */
        function BigNumber(n, b) {
            var alphabet, c, caseChanged, e, i, isNum, len, str,
                x = this;

            // Enable constructor usage without new.
            if (!(x instanceof BigNumber)) {

                // Don't throw on constructor call without new (#81).
                // '[BigNumber Error] Constructor call without new: {n}'
                //throw Error(bignumberError + ' Constructor call without new: ' + n);
                return new BigNumber(n, b);
            }

            if (b == null) {

                // Duplicate.
                if (n instanceof BigNumber) {
                    x.s = n.s;
                    x.e = n.e;
                    x.c = (n = n.c) ? n.slice() : n;
                    return;
                }

                isNum = typeof n == 'number';

                if (isNum && n * 0 == 0) {

                    // Use `1 / n` to handle minus zero also.
                    x.s = 1 / n < 0 ? (n = -n, -1) : 1;

                    // Faster path for integers.
                    if (n === ~~n) {
                        for (e = 0, i = n; i >= 10; i /= 10, e++);
                        x.e = e;
                        x.c = [n];
                        return;
                    }

                    str = String(n);
                } else {
                    str = String(n);
                    if (!isNumeric.test(str)) 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');
                str = String(n);

                // 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(n instanceof BigNumber ? n : str);
                    return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
                }

                isNum = typeof n == 'number';

                if (isNum) {

                    // Avoid potential interpretation of Infinity and NaN as base 44+ values.
                    if (n * 0 != 0) return parseNumeric(x, str, isNum, b);

                    x.s = 1 / n < 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 + n);
                    }

                    // Prevent later check for length on converted number.
                    isNum = false;
                } 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(n), isNum, b);
                    }
                }

                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;);

            str = str.slice(i, ++len);

            if (str) {
                len -= i;

                // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
                if (isNum && BigNumber.DEBUG &&
                    len > 15 && (n > MAX_SAFE_INTEGER || n !== mathfloor(n))) {
                    throw Error
                        (tooManyDigits + (x.s * n));
                }

                e = e - i - 1;

                // Overflow?
                if (e > 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;

                    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));
                        }

                        str = str.slice(i);
                        i = LOG_BASE - str.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.
         *
         * v {any}
         */
        BigNumber.isBigNumber = function (v) {
            return v instanceof BigNumber || v && v._isBigNumber === true || false;
        };


        /*
         * 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;
                    x.c = x.e = null;
                } 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.c = x.e = x.s = 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 (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
            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


    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 !== (n < 0 ? mathceil(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);