'use strict';

Object.defineProperty(exports, "__esModule", {
    value: true
});
/*
 *      bignumber.js v9.0.0
 *      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 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',
        suffix: ''
    },

    // The alphabet used for base conversion. It must be at least 2 characters long, with no '+',
    // '-', '.', whitespace, or repeated character.
    // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
    ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
    //------------------------------------------------------------------------------------------
    // CONSTRUCTOR
    /*
     * The BigNumber constructor and exported function.
     * Create and return a new instance of a BigNumber object.
     *
     * v {number|string|BigNumber} A numeric value.
     * [b] {number} The base of v. Integer, 2 to ALPHABET.length inclusive.
     */
    //@ts-ignore
    function BigNumber(v, b) {
        var alphabet,
            c,
            caseChanged,
            e,
            i,
            isNum,
            len,
            str,
            x = this;
        // Enable constructor call without `new`.
        if (!(x instanceof BigNumber)) return new BigNumber(v, b);
        if (b == null) {
            if (v && v._isBigNumber === true) {
                x.s = v.s;
                if (!v.c || v.e > MAX_EXP) {
                    x.c = x.e = null;
                } else if (v.e < MIN_EXP) {
                    x.c = [x.e = 0];
                } else {
                    x.e = v.e;
                    x.c = v.c.slice();
                }
                return;
            }
            if ((isNum = typeof v == 'number') && v * 0 == 0) {
                // Use `1 / n` to handle minus zero also.
                x.s = 1 / v < 0 ? (v = -v, -1) : 1;
                // Fast path for integers, where n < 2147483648 (2**31).
                if (v === ~~v) {
                    for (e = 0, i = v; i >= 10; i /= 10, e++) {}
                    if (e > MAX_EXP) {
                        x.c = x.e = null;
                    } else {
                        x.e = e;
                        x.c = [v];
                    }
                    return;
                }
                str = String(v);
            } else {
                if (!isNumeric.test(str = String(v))) return parseNumeric(x, str, isNum);
                x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
            }
            // Decimal point?
            if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
            // Exponential form?
            if ((i = str.search(/e/i)) > 0) {
                // Determine exponent.
                if (e < 0) e = i;
                e += +str.slice(i + 1);
                str = str.substring(0, i);
            } else if (e < 0) {
                // Integer.
                e = str.length;
            }
        } else {
            // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
            intCheck(b, 2, ALPHABET.length, 'Base');
            // Allow exponential notation to be used with base 10 argument, while
            // also rounding to DECIMAL_PLACES as with other bases.
            if (b == 10) {
                x = new BigNumber(v);
                return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
            }
            str = String(v);
            if (isNum = typeof v == 'number') {
                // Avoid potential interpretation of Infinity and NaN as base 44+ values.
                if (v * 0 != 0) return parseNumeric(x, str, isNum, b);
                x.s = 1 / v < 0 ? (str = str.slice(1), -1) : 1;
                // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
                if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
                    throw Error(tooManyDigits + v);
                }
            } else {
                x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
            }
            alphabet = ALPHABET.slice(0, b);
            e = i = 0;
            // Check that str is a valid base b number.
            // Don't use RegExp, so alphabet can contain special characters.
            for (len = str.length; i < len; i++) {
                if (alphabet.indexOf(c = str.charAt(i)) < 0) {
                    if (c == '.') {
                        // If '.' is not the first character and it has not be found before.
                        if (i > e) {
                            e = len;
                            continue;
                        }
                    } else if (!caseChanged) {
                        // Allow e.g. hexadecimal 'FF' as well as 'ff'.
                        if (str == str.toUpperCase() && (str = str.toLowerCase()) || str == str.toLowerCase() && (str = str.toUpperCase())) {
                            caseChanged = true;
                            i = -1;
                            e = 0;
                            continue;
                        }
                    }
                    return parseNumeric(x, String(v), isNum, b);
                }
            }
            // Prevent later check for length on converted number.
            isNum = false;
            str = convertBase(str, b, 10, x.s);
            // Decimal point?
            if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');else e = str.length;
        }
        // Determine leading zeros.
        for (i = 0; str.charCodeAt(i) === 48; i++) {}
        // Determine trailing zeros.
        for (len = str.length; str.charCodeAt(--len) === 48;) {}
        if (str = str.slice(i, ++len)) {
            len -= i;
            // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
            if (isNum && BigNumber.DEBUG && len > 15 && (v > MAX_SAFE_INTEGER || v !== mathfloor(v))) {
                throw Error(tooManyDigits + x.s * v);
            }
            // Overflow?
            if ((e = e - i - 1) > MAX_EXP) {
                // Infinity.
                x.c = x.e = null;
                // Underflow?
            } else if (e < MIN_EXP) {
                // Zero.
                x.c = [x.e = 0];
            } else {
                x.e = e;
                x.c = [];
                // Transform base
                // e is the base 10 exponent.
                // i is where to slice str to get the first element of the coefficient array.
                i = (e + 1) % LOG_BASE;
                if (e < 0) i += LOG_BASE; // i < 1
                if (i < len) {
                    if (i) x.c.push(+str.slice(0, i));
                    for (len -= LOG_BASE; i < len;) {
                        x.c.push(+str.slice(i, i += LOG_BASE));
                    }
                    i = LOG_BASE - (str = str.slice(i)).length;
                } else {
                    i -= len;
                }
                for (; i--; str += '0') {}
                x.c.push(+str);
            }
        } else {
            // Zero.
            x.c = [x.e = 0];
        }
    }
    // CONSTRUCTOR PROPERTIES
    BigNumber.clone = clone;
    BigNumber.ROUND_UP = 0;
    BigNumber.ROUND_DOWN = 1;
    BigNumber.ROUND_CEIL = 2;
    BigNumber.ROUND_FLOOR = 3;
    BigNumber.ROUND_HALF_UP = 4;
    BigNumber.ROUND_HALF_DOWN = 5;
    BigNumber.ROUND_HALF_EVEN = 6;
    BigNumber.ROUND_HALF_CEIL = 7;
    BigNumber.ROUND_HALF_FLOOR = 8;
    BigNumber.EUCLID = 9;
    /*
     * Configure infrequently-changing library-wide settings.
     *
     * Accept an object with the following optional properties (if the value of a property is
     * a number, it must be an integer within the inclusive range stated):
     *
     *   DECIMAL_PLACES   {number}           0 to MAX
     *   ROUNDING_MODE    {number}           0 to 8
     *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
     *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
     *   CRYPTO           {boolean}          true or false
     *   MODULO_MODE      {number}           0 to 9
     *   POW_PRECISION       {number}           0 to MAX
     *   ALPHABET         {string}           A string of two or more unique characters which does
     *                                     not contain '.'.
     *   FORMAT           {object}           An object with some of the following properties:
     *     prefix                 {string}
     *     groupSize              {number}
     *     secondaryGroupSize     {number}
     *     groupSeparator         {string}
     *     decimalSeparator       {string}
     *     fractionGroupSize      {number}
     *     fractionGroupSeparator {string}
     *     suffix                 {string}
     *
     * (The values assigned to the above FORMAT object properties are not checked for validity.)
     *
     * E.g.
     * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
     *
     * Ignore properties/parameters set to null or undefined, except for ALPHABET.
     *
     * Return an object with the properties current values.
     */
    BigNumber.config = BigNumber.set = function (obj) {
        var p, v;
        if (obj != null) {
            if (typeof obj == 'object') {
                // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
                // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
                if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
                    v = obj[p];
                    intCheck(v, 0, MAX, p);
                    DECIMAL_PLACES = v;
                }
                // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
                // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
                if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
                    v = obj[p];
                    intCheck(v, 0, 8, p);
                    ROUNDING_MODE = v;
                }
                // EXPONENTIAL_AT {number|number[]}
                // Integer, -MAX to MAX inclusive or
                // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
                // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
                if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
                    v = obj[p];
                    if (v && v.pop) {
                        intCheck(v[0], -MAX, 0, p);
                        intCheck(v[1], 0, MAX, p);
                        TO_EXP_NEG = v[0];
                        TO_EXP_POS = v[1];
                    } else {
                        intCheck(v, -MAX, MAX, p);
                        TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
                    }
                }
                // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
                // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
                // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
                if (obj.hasOwnProperty(p = 'RANGE')) {
                    v = obj[p];
                    if (v && v.pop) {
                        intCheck(v[0], -MAX, -1, p);
                        intCheck(v[1], 1, MAX, p);
                        MIN_EXP = v[0];
                        MAX_EXP = v[1];
                    } else {
                        intCheck(v, -MAX, MAX, p);
                        if (v) {
                            MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
                        } else {
                            throw Error(bignumberError + p + ' cannot be zero: ' + v);
                        }
                    }
                }
                // CRYPTO {boolean} true or false.
                // '[BigNumber Error] CRYPTO not true or false: {v}'
                // '[BigNumber Error] crypto unavailable'
                if (obj.hasOwnProperty(p = 'CRYPTO')) {
                    v = obj[p];
                    if (v === !!v) {
                        if (v) {
                            if (typeof crypto != 'undefined' && crypto && (crypto.getRandomValues || crypto.randomBytes)) {
                                CRYPTO = v;
                            } else {
                                CRYPTO = !v;
                                throw Error(bignumberError + 'crypto unavailable');
                            }
                        } else {
                            CRYPTO = v;
                        }
                    } else {
                        throw Error(bignumberError + p + ' not true or false: ' + v);
                    }
                }
                // MODULO_MODE {number} Integer, 0 to 9 inclusive.
                // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
                if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
                    v = obj[p];
                    intCheck(v, 0, 9, p);
                    MODULO_MODE = v;
                }
                // POW_PRECISION {number} Integer, 0 to MAX inclusive.
                // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
                if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
                    v = obj[p];
                    intCheck(v, 0, MAX, p);
                    POW_PRECISION = v;
                }
                // FORMAT {object}
                // '[BigNumber Error] FORMAT not an object: {v}'
                if (obj.hasOwnProperty(p = 'FORMAT')) {
                    v = obj[p];
                    if (typeof v == 'object') FORMAT = v;else throw Error(bignumberError + p + ' not an object: ' + v);
                }
                // ALPHABET {string}
                // '[BigNumber Error] ALPHABET invalid: {v}'
                if (obj.hasOwnProperty(p = 'ALPHABET')) {
                    v = obj[p];
                    // Disallow if only one character,
                    // or if it contains '+', '-', '.', whitespace, or a repeated character.
                    if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
                        ALPHABET = v;
                    } else {
                        throw Error(bignumberError + p + ' invalid: ' + v);
                    }
                }
            } else {
                // '[BigNumber Error] Object expected: {v}'
                throw Error(bignumberError + 'Object expected: ' + obj);
            }
        }
        return {
            DECIMAL_PLACES: DECIMAL_PLACES,
            ROUNDING_MODE: ROUNDING_MODE,
            EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
            RANGE: [MIN_EXP, MAX_EXP],
            CRYPTO: CRYPTO,
            MODULO_MODE: MODULO_MODE,
            POW_PRECISION: POW_PRECISION,
            FORMAT: FORMAT,
            ALPHABET: ALPHABET
        };
    };
    /*
     * Return true if v is a BigNumber instance, otherwise return false.
     *
     * If BigNumber.DEBUG is true, throw if a BigNumber instance is not well-formed.
     *
     * v {any}
     *
     * '[BigNumber Error] Invalid BigNumber: {v}'
     */
    BigNumber.isBigNumber = function (v) {
        if (!v || v._isBigNumber !== true) return false;
        if (!BigNumber.DEBUG) return true;
        var i,
            n,
            c = v.c,
            e = v.e,
            s = v.s;
        out: if ({}.toString.call(c) == '[object Array]') {
            if ((s === 1 || s === -1) && e >= -MAX && e <= MAX && e === mathfloor(e)) {
                // If the first element is zero, the BigNumber value must be zero.
                if (c[0] === 0) {
                    if (e === 0 && c.length === 1) return true;
                    break out;
                }
                // Calculate number of digits that c[0] should have, based on the exponent.
                i = (e + 1) % LOG_BASE;
                if (i < 1) i += LOG_BASE;
                // Calculate number of digits of c[0].
                //if (Math.ceil(Math.log(c[0] + 1) / Math.LN10) == i) {
                if (String(c[0]).length == i) {
                    for (i = 0; i < c.length; i++) {
                        n = c[i];
                        if (n < 0 || n >= BASE || n !== mathfloor(n)) break out;
                    }
                    // Last element cannot be zero, unless it is the only element.
                    if (n !== 0) return true;
                }
            }
            // Infinity/NaN
        } else if (c === null && e === null && (s === null || s === 1 || s === -1)) {
            return true;
        }
        throw Error(bignumberError + 'Invalid BigNumber: ' + v);
    };
    /*
     * Return a new BigNumber whose value is the maximum of the arguments.
     *
     * arguments {number|string|BigNumber}
     */
    BigNumber.maximum = BigNumber.max = function () {
        return maxOrMin(arguments, P.lt);
    };
    /*
     * Return a new BigNumber whose value is the minimum of the arguments.
     *
     * arguments {number|string|BigNumber}
     */
    BigNumber.minimum = BigNumber.min = function () {
        return maxOrMin(arguments, P.gt);
    };
    /*
     * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
     * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
     * zeros are produced).
     *
     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
     * '[BigNumber Error] crypto unavailable'
     */
    BigNumber.random = function () {
        var pow2_53 = 0x20000000000000;
        // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
        // Check if Math.random() produces more than 32 bits of randomness.
        // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
        // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
        var random53bitInt = Math.random() * pow2_53 & 0x1fffff ? function () {
            return mathfloor(Math.random() * pow2_53);
        } : function () {
            return (Math.random() * 0x40000000 | 0) * 0x800000 + (Math.random() * 0x800000 | 0);
        };
        return function (dp) {
            var a,
                b,
                e,
                k,
                v,
                i = 0,
                c = [],
                rand = new BigNumber(ONE);
            if (dp == null) dp = DECIMAL_PLACES;else intCheck(dp, 0, MAX);
            k = mathceil(dp / LOG_BASE);
            if (CRYPTO) {
                // Browsers supporting crypto.getRandomValues.
                if (crypto.getRandomValues) {
                    a = crypto.getRandomValues(new Uint32Array(k *= 2));
                    for (; i < k;) {
                        // 53 bits:
                        // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
                        // 11111 11111111 11111111 11111111 11100000 00000000 00000000
                        // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
                        //                                     11111 11111111 11111111
                        // 0x20000 is 2^21.
                        v = a[i] * 0x20000 + (a[i + 1] >>> 11);
                        // Rejection sampling:
                        // 0 <= v < 9007199254740992
                        // Probability that v >= 9e15, is
                        // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
                        if (v >= 9e15) {
                            b = crypto.getRandomValues(new Uint32Array(2));
                            a[i] = b[0];
                            a[i + 1] = b[1];
                        } else {
                            // 0 <= v <= 8999999999999999
                            // 0 <= (v % 1e14) <= 99999999999999
                            c.push(v % 1e14);
                            i += 2;
                        }
                    }
                    i = k / 2;
                    // Node.js supporting crypto.randomBytes.
                } else if (crypto.randomBytes) {
                    // buffer
                    a = crypto.randomBytes(k *= 7);
                    for (; i < k;) {
                        // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
                        // 0x100000000 is 2^32, 0x1000000 is 2^24
                        // 11111 11111111 11111111 11111111 11111111 11111111 11111111
                        // 0 <= v < 9007199254740992
                        v = (a[i] & 31) * 0x1000000000000 + a[i + 1] * 0x10000000000 + a[i + 2] * 0x100000000 + a[i + 3] * 0x1000000 + (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
                        if (v >= 9e15) {
                            crypto.randomBytes(7).copy(a, i);
                        } else {
                            // 0 <= (v % 1e14) <= 99999999999999
                            c.push(v % 1e14);
                            i += 7;
                        }
                    }
                    i = k / 7;
                } else {
                    CRYPTO = false;
                    throw Error(bignumberError + 'crypto unavailable');
                }
            }
            // Use Math.random.
            if (!CRYPTO) {
                for (; i < k;) {
                    v = random53bitInt();
                    if (v < 9e15) c[i++] = v % 1e14;
                }
            }
            k = c[--i];
            dp %= LOG_BASE;
            // Convert trailing digits to zeros according to dp.
            if (k && dp) {
                v = POWS_TEN[LOG_BASE - dp];
                c[i] = mathfloor(k / v) * v;
            }
            // Remove trailing elements which are zero.
            for (; c[i] === 0; c.pop(), i--) {}
            // Zero?
            if (i < 0) {
                c = [e = 0];
            } else {
                // Remove leading elements which are zero and adjust exponent accordingly.
                for (e = -1; c[0] === 0; c.splice(0, 1), e -= LOG_BASE) {}
                // Count the digits of the first element of c to determine leading zeros, and...
                for (i = 1, v = c[0]; v >= 10; v /= 10, i++) {}
                // adjust the exponent accordingly.
                if (i < LOG_BASE) e -= LOG_BASE - i;
            }
            rand.e = e;
            rand.c = c;
            return rand;
        };
    }();
    /*
    * Return a BigNumber whose value is the sum of the arguments.
    *
    * arguments {number|string|BigNumber}
    */
    BigNumber.sum = function () {
        var i = 1,
            args = arguments,
            sum = new BigNumber(args[0]);
        for (; i < args.length;) {
            sum = sum.plus(args[i++]);
        }return sum;
    };
    // PRIVATE FUNCTIONS
    // Called by BigNumber and BigNumber.prototype.toString.
    convertBase = function () {
        var decimal = '0123456789';
        /*
         * Convert string of baseIn to an array of numbers of baseOut.
         * Eg. toBaseOut('255', 10, 16) returns [15, 15].
         * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
         */
        function toBaseOut(str, baseIn, baseOut, alphabet) {
            var j,
                arr = [0],
                arrL,
                i = 0,
                len = str.length;
            for (; i < len;) {
                for (arrL = arr.length; arrL--; arr[arrL] *= baseIn) {}
                arr[0] += alphabet.indexOf(str.charAt(i++));
                for (j = 0; j < arr.length; j++) {
                    if (arr[j] > baseOut - 1) {
                        if (arr[j + 1] == null) arr[j + 1] = 0;
                        arr[j + 1] += arr[j] / baseOut | 0;
                        arr[j] %= baseOut;
                    }
                }
            }
            return arr.reverse();
        }
        // Convert a numeric string of baseIn to a numeric string of baseOut.
        // If the caller is toString, we are converting from base 10 to baseOut.
        // If the caller is BigNumber, we are converting from baseIn to base 10.
        return function (str, baseIn, baseOut, sign, callerIsToString) {
            var alphabet,
                d,
                e,
                k,
                r,
                x,
                xc,
                y,
                i = str.indexOf('.'),
                dp = DECIMAL_PLACES,
                rm = ROUNDING_MODE;
            // Non-integer.
            if (i >= 0) {
                k = POW_PRECISION;
                // Unlimited precision.
                POW_PRECISION = 0;
                str = str.replace('.', '');
                y = new BigNumber(baseIn);
                x = y.pow(str.length - i);
                POW_PRECISION = k;
                // Convert str as if an integer, then restore the fraction part by dividing the
                // result by its base raised to a power.
                y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'), 10, baseOut, decimal);
                y.e = y.c.length;
            }
            // Convert the number as integer.
            xc = toBaseOut(str, baseIn, baseOut, callerIsToString ? (alphabet = ALPHABET, decimal) : (alphabet = decimal, ALPHABET));
            // xc now represents str as an integer and converted to baseOut. e is the exponent.
            e = k = xc.length;
            // Remove trailing zeros.
            for (; xc[--k] == 0; xc.pop()) {}
            // Zero?
            if (!xc[0]) return alphabet.charAt(0);
            // Does str represent an integer? If so, no need for the division.
            if (i < 0) {
                --e;
            } else {
                x.c = xc;
                x.e = e;
                // The sign is needed for correct rounding.
                x.s = sign;
                x = div(x, y, dp, rm, baseOut);
                xc = x.c;
                r = x.r;
                e = x.e;
            }
            // xc now represents str converted to baseOut.
            // THe index of the rounding digit.
            d = e + dp + 1;
            // The rounding digit: the digit to the right of the digit that may be rounded up.
            i = xc[d];
            // Look at the rounding digits and mode to determine whether to round up.
            k = baseOut / 2;
            r = r || d < 0 || xc[d + 1] != null;
            r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) : i > k || i == k && (rm == 4 || r || rm == 6 && xc[d - 1] & 1 || rm == (x.s < 0 ? 8 : 7));
            // If the index of the rounding digit is not greater than zero, or xc represents
            // zero, then the result of the base conversion is zero or, if rounding up, a value
            // such as 0.00001.
            if (d < 1 || !xc[0]) {
                // 1^-dp or 0
                str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
            } else {
                // Truncate xc to the required number of decimal places.
                xc.length = d;
                // Round up?
                if (r) {
                    // Rounding up may mean the previous digit has to be rounded up and so on.
                    for (--baseOut; ++xc[--d] > baseOut;) {
                        xc[d] = 0;
                        if (!d) {
                            ++e;
                            xc = [1].concat(xc);
                        }
                    }
                }
                // Determine trailing zeros.
                for (k = xc.length; !xc[--k];) {}
                // E.g. [4, 11, 15] becomes 4bf.
                for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++])) {}
                // Add leading zeros, decimal point and trailing zeros as required.
                str = toFixedPoint(str, e, alphabet.charAt(0));
            }
            // The caller will add the sign.
            return str;
        };
    }();
    // Perform division in the specified base. Called by div and convertBase.
    div = function () {
        // Assume non-zero x and k.
        function multiply(x, k, base) {
            var m,
                temp,
                xlo,
                xhi,
                carry = 0,
                i = x.length,
                klo = k % SQRT_BASE,
                khi = k / SQRT_BASE | 0;
            for (x = x.slice(); i--;) {
                xlo = x[i] % SQRT_BASE;
                xhi = x[i] / SQRT_BASE | 0;
                m = khi * xlo + xhi * klo;
                temp = klo * xlo + m % SQRT_BASE * SQRT_BASE + carry;
                carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
                x[i] = temp % base;
            }
            if (carry) x = [carry].concat(x);
            return x;
        }
        function compare(a, b, aL, bL) {
            var i, cmp;
            if (aL != bL) {
                cmp = aL > bL ? 1 : -1;
            } else {
                for (i = cmp = 0; i < aL; i++) {
                    if (a[i] != b[i]) {
                        cmp = a[i] > b[i] ? 1 : -1;
                        break;
                    }
                }
            }
            return cmp;
        }
        function subtract(a, b, aL, base) {
            var i = 0;
            // Subtract b from a.
            for (; aL--;) {
                a[aL] -= i;
                i = a[aL] < b[aL] ? 1 : 0;
                a[aL] = i * base + a[aL] - b[aL];
            }
            // Remove leading zeros.
            for (; !a[0] && a.length > 1; a.splice(0, 1)) {}
        }
        // x: dividend, y: divisor.
        return function (x, y, dp, rm, base) {
            var cmp,
                e,
                i,
                more,
                n,
                prod,
                prodL,
                q,
                qc,
                rem,
                remL,
                rem0,
                xi,
                xL,
                yc0,
                yL,
                yz,
                s = x.s == y.s ? 1 : -1,
                xc = x.c,
                yc = y.c;
            // Either NaN, Infinity or 0?
            if (!xc || !xc[0] || !yc || !yc[0]) {
                return new BigNumber(
                // Return NaN if either NaN, or both Infinity or 0.
                !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
                // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
                xc && xc[0] == 0 || !yc ? s * 0 : s / 0);
            }
            q = new BigNumber(s);
            qc = q.c = [];
            e = x.e - y.e;
            s = dp + e + 1;
            if (!base) {
                base = BASE;
                e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
                s = s / LOG_BASE | 0;
            }
            // Result exponent may be one less then the current value of e.
            // The coefficients of the BigNumbers from convertBase may have trailing zeros.
            for (i = 0; yc[i] == (xc[i] || 0); i++) {}
            if (yc[i] > (xc[i] || 0)) e--;
            if (s < 0) {
                qc.push(1);
                more = true;
            } else {
                xL = xc.length;
                yL = yc.length;
                i = 0;
                s += 2;
                // Normalise xc and yc so highest order digit of yc is >= base / 2.
                n = mathfloor(base / (yc[0] + 1));
                // Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
                // if (n > 1 || n++ == 1 && yc[0] < base / 2) {
                if (n > 1) {
                    yc = multiply(yc, n, base);
                    xc = multiply(xc, n, base);
                    yL = yc.length;
                    xL = xc.length;
                }
                xi = yL;
                rem = xc.slice(0, yL);
                remL = rem.length;
                // Add zeros to make remainder as long as divisor.
                for (; remL < yL; rem[remL++] = 0) {}
                yz = yc.slice();
                yz = [0].concat(yz);
                yc0 = yc[0];
                if (yc[1] >= base / 2) yc0++;
                // Not necessary, but to prevent trial digit n > base, when using base 3.
                // else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
                do {
                    n = 0;
                    // Compare divisor and remainder.
                    cmp = compare(yc, rem, yL, remL);
                    // If divisor < remainder.
                    if (cmp < 0) {
                        // Calculate trial digit, n.
                        rem0 = rem[0];
                        if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
                        // n is how many times the divisor goes into the current remainder.
                        n = mathfloor(rem0 / yc0);
                        //  Algorithm:
                        //  product = divisor multiplied by trial digit (n).
                        //  Compare product and remainder.
                        //  If product is greater than remainder:
                        //    Subtract divisor from product, decrement trial digit.
                        //  Subtract product from remainder.
                        //  If product was less than remainder at the last compare:
                        //    Compare new remainder and divisor.
                        //    If remainder is greater than divisor:
                        //      Subtract divisor from remainder, increment trial digit.
                        if (n > 1) {
                            // n may be > base only when base is 3.
                            if (n >= base) n = base - 1;
                            // product = divisor * trial digit.
                            prod = multiply(yc, n, base);
                            prodL = prod.length;
                            remL = rem.length;
                            // Compare product and remainder.
                            // If product > remainder then trial digit n too high.
                            // n is 1 too high about 5% of the time, and is not known to have
                            // ever been more than 1 too high.
                            while (compare(prod, rem, prodL, remL) == 1) {
                                n--;
                                // Subtract divisor from product.
                                subtract(prod, yL < prodL ? yz : yc, prodL, base);
                                prodL = prod.length;
                                cmp = 1;
                            }
                        } else {
                            // n is 0 or 1, cmp is -1.
                            // If n is 0, there is no need to compare yc and rem again below,
                            // so change cmp to 1 to avoid it.
                            // If n is 1, leave cmp as -1, so yc and rem are compared again.
                            if (n == 0) {
                                // divisor < remainder, so n must be at least 1.
                                cmp = n = 1;
                            }
                            // product = divisor
                            prod = yc.slice();
                            prodL = prod.length;
                        }
                        if (prodL < remL) prod = [0].concat(prod);
                        // Subtract product from remainder.
                        subtract(rem, prod, remL, base);
                        remL = rem.length;
                        // If product was < remainder.
                        if (cmp == -1) {
                            // Compare divisor and new remainder.
                            // If divisor < new remainder, subtract divisor from remainder.
                            // Trial digit n too low.
                            // n is 1 too low about 5% of the time, and very rarely 2 too low.
                            while (compare(yc, rem, yL, remL) < 1) {
                                n++;
                                // Subtract divisor from remainder.
                                subtract(rem, yL < remL ? yz : yc, remL, base);
                                remL = rem.length;
                            }
                        }
                    } else if (cmp === 0) {
                        n++;
                        rem = [0];
                    } // else cmp === 1 and n will be 0
                    // Add the next digit, n, to the result array.
                    qc[i++] = n;
                    // Update the remainder.
                    if (rem[0]) {
                        rem[remL++] = xc[xi] || 0;
                    } else {
                        rem = [xc[xi]];
                        remL = 1;
                    }
                } while ((xi++ < xL || rem[0] != null) && s--);
                more = rem[0] != null;
                // Leading zero?
                if (!qc[0]) qc.splice(0, 1);
            }
            if (base == BASE) {
                // To calculate q.e, first get the number of digits of qc[0].
                for (i = 1, s = qc[0]; s >= 10; s /= 10, i++) {}
                round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
                // Caller is convertBase.
            } else {
                q.e = e;
                q.r = +more;
            }
            return q;
        };
    }();
    /*
     * Return a string representing the value of BigNumber n in fixed-point or exponential
     * notation rounded to the specified decimal places or significant digits.
     *
     * n: a BigNumber.
     * i: the index of the last digit required (i.e. the digit that may be rounded up).
     * rm: the rounding mode.
     * id: 1 (toExponential) or 2 (toPrecision).
     */
    function format(n, i, rm, id) {
        var c0, e, ne, len, str;
        if (rm == null) rm = ROUNDING_MODE;else intCheck(rm, 0, 8);
        if (!n.c) return n.toString();
        c0 = n.c[0];
        ne = n.e;
        if (i == null) {
            str = coeffToString(n.c);
            str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS) ? toExponential(str, ne) : toFixedPoint(str, ne, '0');
        } else {
            n = round(new BigNumber(n), i, rm);
            // n.e may have changed if the value was rounded up.
            e = n.e;
            str = coeffToString(n.c);
            len = str.length;
            // toPrecision returns exponential notation if the number of significant digits
            // specified is less than the number of digits necessary to represent the integer
            // part of the value in fixed-point notation.
            // Exponential notation.
            if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
                // Append zeros?
                for (; len < i; str += '0', len++) {}
                str = toExponential(str, e);
                // Fixed-point notation.
            } else {
                i -= ne;
                str = toFixedPoint(str, e, '0');
                // Append zeros?
                if (e + 1 > len) {
                    if (--i > 0) for (str += '.'; i--; str += '0') {}
                } else {
                    i += e - len;
                    if (i > 0) {
                        if (e + 1 == len) str += '.';
                        for (; i--; str += '0') {}
                    }
                }
            }
        }
        return n.s < 0 && c0 ? '-' + str : str;
    }
    // Handle BigNumber.max and BigNumber.min.
    function maxOrMin(args, method) {
        var n,
            i = 1,
            m = new BigNumber(args[0]);
        for (; i < args.length; i++) {
            n = new BigNumber(args[i]);
            // If any number is NaN, return NaN.
            if (!n.s) {
                m = n;
                break;
            } else if (method.call(m, n)) {
                m = n;
            }
        }
        return m;
    }
    /*
     * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
     * Called by minus, plus and times.
     */
    function normalise(n, c, e) {
        var i = 1,
            j = c.length;
        // Remove trailing zeros.
        for (; !c[--j]; c.pop()) {}
        // Calculate the base 10 exponent. First get the number of digits of c[0].
        for (j = c[0]; j >= 10; j /= 10, i++) {}
        // Overflow?
        if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
            // Infinity.
            n.c = n.e = null;
            // Underflow?
        } else if (e < MIN_EXP) {
            // Zero.
            n.c = [n.e = 0];
        } else {
            n.e = e;
            n.c = c;
        }
        return n;
    }
    // Handle values that fail the validity test in BigNumber.
    parseNumeric = function () {
        var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
            dotAfter = /^([^.]+)\.$/,
            dotBefore = /^\.([^.]+)$/,
            isInfinityOrNaN = /^-?(Infinity|NaN)$/,
            whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
        return function (x, str, isNum, b) {
            var base,
                s = isNum ? str : str.replace(whitespaceOrPlus, '');
            // No exception on ±Infinity or NaN.
            if (isInfinityOrNaN.test(s)) {
                x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
            } else {
                if (!isNum) {
                    // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
                    s = s.replace(basePrefix, function (m, p1, p2) {
                        base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
                        return !b || b == base ? p1 : m;
                    });
                    if (b) {
                        base = b;
                        // E.g. '1.' to '1', '.1' to '0.1'
                        s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
                    }
                    if (str != s) return new BigNumber(s, base);
                }
                // '[BigNumber Error] Not a number: {n}'
                // '[BigNumber Error] Not a base {b} number: {n}'
                if (BigNumber.DEBUG) {
                    throw Error(bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
                }
                // NaN
                x.s = null;
            }
            x.c = x.e = null;
        };
    }();
    /*
     * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
     * If r is truthy, it is known that there are more digits after the rounding digit.
     */
    function round(x, sd, rm, r) {
        var d,
            i,
            j,
            k,
            n,
            ni,
            rd,
            xc = x.c,
            pows10 = POWS_TEN;
        // if x is not Infinity or NaN...
        if (xc) {
            // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
            // n is a base 1e14 number, the value of the element of array x.c containing rd.
            // ni is the index of n within x.c.
            // d is the number of digits of n.
            // i is the index of rd within n including leading zeros.
            // j is the actual index of rd within n (if < 0, rd is a leading zero).
            out: {
                // Get the number of digits of the first element of xc.
                for (d = 1, k = xc[0]; k >= 10; k /= 10, d++) {}
                i = sd - d;
                // If the rounding digit is in the first element of xc...
                if (i < 0) {
                    i += LOG_BASE;
                    j = sd;
                    n = xc[ni = 0];
                    // Get the rounding digit at index j of n.
                    rd = n / pows10[d - j - 1] % 10 | 0;
                } else {
                    ni = mathceil((i + 1) / LOG_BASE);
                    if (ni >= xc.length) {
                        if (r) {
                            // Needed by sqrt.
                            for (; xc.length <= ni; xc.push(0)) {}
                            n = rd = 0;
                            d = 1;
                            i %= LOG_BASE;
                            j = i - LOG_BASE + 1;
                        } else {
                            break out;
                        }
                    } else {
                        n = k = xc[ni];
                        // Get the number of digits of n.
                        for (d = 1; k >= 10; k /= 10, d++) {}
                        // Get the index of rd within n.
                        i %= LOG_BASE;
                        // Get the index of rd within n, adjusted for leading zeros.
                        // The number of leading zeros of n is given by LOG_BASE - d.
                        j = i - LOG_BASE + d;
                        // Get the rounding digit at index j of n.
                        rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
                    }
                }
                r = r || sd < 0 ||
                // Are there any non-zero digits after the rounding digit?
                // The expression  n % pows10[d - j - 1]  returns all digits of n to the right
                // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
                xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
                r = rm < 4 ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
                // Check whether the digit to the left of the rounding digit is odd.
                (i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10 & 1 || rm == (x.s < 0 ? 8 : 7));
                if (sd < 1 || !xc[0]) {
                    xc.length = 0;
                    if (r) {
                        // Convert sd to decimal places.
                        sd -= x.e + 1;
                        // 1, 0.1, 0.01, 0.001, 0.0001 etc.
                        xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
                        x.e = -sd || 0;
                    } else {
                        // Zero.
                        xc[0] = x.e = 0;
                    }
                    return x;
                }
                // Remove excess digits.
                if (i == 0) {
                    xc.length = ni;
                    k = 1;
                    ni--;
                } else {
                    xc.length = ni + 1;
                    k = pows10[LOG_BASE - i];
                    // E.g. 56700 becomes 56000 if 7 is the rounding digit.
                    // j > 0 means i > number of leading zeros of n.
                    xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
                }
                // Round up?
                if (r) {
                    for (;;) {
                        // If the digit to be rounded up is in the first element of xc...
                        if (ni == 0) {
                            // i will be the length of xc[0] before k is added.
                            for (i = 1, j = xc[0]; j >= 10; j /= 10, i++) {}
                            j = xc[0] += k;
                            for (k = 1; j >= 10; j /= 10, k++) {}
                            // if i != k the length has increased.
                            if (i != k) {
                                x.e++;
                                if (xc[0] == BASE) xc[0] = 1;
                            }
                            break;
                        } else {
                            xc[ni] += k;
                            if (xc[ni] != BASE) break;
                            xc[ni--] = 0;
                            k = 1;
                        }
                    }
                }
                // Remove trailing zeros.
                for (i = xc.length; xc[--i] === 0; xc.pop()) {}
            }
            // Overflow? Infinity.
            if (x.e > MAX_EXP) {
                x.c = x.e = null;
                // Underflow? Zero.
            } else if (x.e < MIN_EXP) {
                x.c = [x.e = 0];
            }
        }
        return x;
    }
    function valueOf(n) {
        var str,
            e = n.e;
        if (e === null) return n.toString();
        str = coeffToString(n.c);
        str = e <= TO_EXP_NEG || e >= TO_EXP_POS ? toExponential(str, e) : toFixedPoint(str, e, '0');
        return n.s < 0 ? '-' + str : str;
    }
    // PROTOTYPE/INSTANCE METHODS
    /*
     * Return a new BigNumber whose value is the absolute value of this BigNumber.
     */
    P.absoluteValue = P.abs = function () {
        var x = new BigNumber(this);
        if (x.s < 0) x.s = 1;
        return x;
    };
    /*
     * Return
     *   1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
     *   -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
     *   0 if they have the same value,
     *   or null if the value of either is NaN.
     */
    P.comparedTo = function (y, b) {
        return compare(this, new BigNumber(y, b));
    };
    /*
     * If dp is undefined or null or true or false, return the number of decimal places of the
     * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
     *
     * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
     * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
     * ROUNDING_MODE if rm is omitted.
     *
     * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
     */
    P.decimalPlaces = P.dp = function (dp, rm) {
        var c,
            n,
            v,
            x = this;
        if (dp != null) {
            intCheck(dp, 0, MAX);
            if (rm == null) rm = ROUNDING_MODE;else intCheck(rm, 0, 8);
            return round(new BigNumber(x), dp + x.e + 1, rm);
        }
        if (!(c = x.c)) return null;
        n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
        // Subtract the number of trailing zeros of the last number.
        if (v = c[v]) for (; v % 10 == 0; v /= 10, n--) {}
        if (n < 0) n = 0;
        return n;
    };
    /*
     *  n / 0 = I
     *  n / N = N
     *  n / I = 0
     *  0 / n = 0
     *  0 / 0 = N
     *  0 / N = N
     *  0 / I = 0
     *  N / n = N
     *  N / 0 = N
     *  N / N = N
     *  N / I = N
     *  I / n = I
     *  I / 0 = I
     *  I / N = N
     *  I / I = N
     *
     * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
     * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
     */
    P.dividedBy = P.div = function (y, b) {
        return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
    };
    /*
     * Return a new BigNumber whose value is the integer part of dividing the value of this
     * BigNumber by the value of BigNumber(y, b).
     */
    P.dividedToIntegerBy = P.idiv = function (y, b) {
        return div(this, new BigNumber(y, b), 0, 1);
    };
    /*
     * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
     *
     * If m is present, return the result modulo m.
     * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
     * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
     *
     * The modular power operation works efficiently when x, n, and m are integers, otherwise it
     * is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
     *
     * n {number|string|BigNumber} The exponent. An integer.
     * [m] {number|string|BigNumber} The modulus.
     *
     * '[BigNumber Error] Exponent not an integer: {n}'
     */
    P.exponentiatedBy = P.pow = function (n, m) {
        var half,
            isModExp,
            i,
            k,
            more,
            nIsBig,
            nIsNeg,
            nIsOdd,
            y,
            x = this;
        n = new BigNumber(n);
        // Allow NaN and ±Infinity, but not other non-integers.
        if (n.c && !n.isInteger()) {
            throw Error(bignumberError + 'Exponent not an integer: ' + valueOf(n));
        }
        if (m != null) m = new BigNumber(m);
        // Exponent of MAX_SAFE_INTEGER is 15.
        nIsBig = n.e > 14;
        // If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
        if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
            // The sign of the result of pow when x is negative depends on the evenness of n.
            // If +n overflows to ±Infinity, the evenness of n would be not be known.
            y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
            return m ? y.mod(m) : y;
        }
        nIsNeg = n.s < 0;
        if (m) {
            // x % m returns NaN if abs(m) is zero, or m is NaN.
            if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
            isModExp = !nIsNeg && x.isInteger() && m.isInteger();
            if (isModExp) x = x.mod(m);
            // Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
            // Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
        } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
        // [1, 240000000]
        ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
        // [80000000000000]  [99999750000000]
        : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
            // If x is negative and n is odd, k = -0, else k = 0.
            k = x.s < 0 && isOdd(n) ? -0 : 0;
            // If x >= 1, k = ±Infinity.
            if (x.e > -1) k = 1 / k;
            // If n is negative return ±0, else return ±Infinity.
            return new BigNumber(nIsNeg ? 1 / k : k);
        } else if (POW_PRECISION) {
            // Truncating each coefficient array to a length of k after each multiplication
            // equates to truncating significant digits to POW_PRECISION + [28, 41],
            // i.e. there will be a minimum of 28 guard digits retained.
            k = mathceil(POW_PRECISION / LOG_BASE + 2);
        }
        if (nIsBig) {
            half = new BigNumber(0.5);
            if (nIsNeg) n.s = 1;
            nIsOdd = isOdd(n);
        } else {
            i = Math.abs(+valueOf(n));
            nIsOdd = i % 2;
        }
        y = new BigNumber(ONE);
        // Performs 54 loop iterations for n of 9007199254740991.
        for (;;) {
            if (nIsOdd) {
                y = y.times(x);
                if (!y.c) break;
                if (k) {
                    if (y.c.length > k) y.c.length = k;
                } else if (isModExp) {
                    y = y.mod(m); //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
                }
            }
            if (i) {
                i = mathfloor(i / 2);
                if (i === 0) break;
                nIsOdd = i % 2;
            } else {
                n = n.times(half);
                round(n, n.e + 1, 1);
                if (n.e > 14) {
                    nIsOdd = isOdd(n);
                } else {
                    i = +valueOf(n);
                    if (i === 0) break;
                    nIsOdd = i % 2;
                }
            }
            x = x.times(x);
            if (k) {
                if (x.c && x.c.length > k) x.c.length = k;
            } else if (isModExp) {
                x = x.mod(m); //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
            }
        }
        if (isModExp) return y;
        if (nIsNeg) y = ONE.div(y);
        return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
    };
    /*
     * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
     * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
     *
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
     */
    P.integerValue = function (rm) {
        var n = new BigNumber(this);
        if (rm == null) rm = ROUNDING_MODE;else intCheck(rm, 0, 8);
        return round(n, n.e + 1, rm);
    };
    /*
     * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
     * otherwise return false.
     */
    P.isEqualTo = P.eq = function (y, b) {
        return compare(this, new BigNumber(y, b)) === 0;
    };
    /*
     * Return true if the value of this BigNumber is a finite number, otherwise return false.
     */
    P.isFinite = function () {
        return !!this.c;
    };
    /*
     * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
     * otherwise return false.
     */
    P.isGreaterThan = P.gt = function (y, b) {
        return compare(this, new BigNumber(y, b)) > 0;
    };
    /*
     * Return true if the value of this BigNumber is greater than or equal to the value of
     * BigNumber(y, b), otherwise return false.
     */
    P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
        return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
    };
    /*
     * Return true if the value of this BigNumber is an integer, otherwise return false.
     */
    P.isInteger = function () {
        return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
    };
    /*
     * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
     * otherwise return false.
     */
    P.isLessThan = P.lt = function (y, b) {
        return compare(this, new BigNumber(y, b)) < 0;
    };
    /*
     * Return true if the value of this BigNumber is less than or equal to the value of
     * BigNumber(y, b), otherwise return false.
     */
    P.isLessThanOrEqualTo = P.lte = function (y, b) {
        return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
    };
    /*
     * Return true if the value of this BigNumber is NaN, otherwise return false.
     */
    P.isNaN = function () {
        return !this.s;
    };
    /*
     * Return true if the value of this BigNumber is negative, otherwise return false.
     */
    P.isNegative = function () {
        return this.s < 0;
    };
    /*
     * Return true if the value of this BigNumber is positive, otherwise return false.
     */
    P.isPositive = function () {
        return this.s > 0;
    };
    /*
     * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
     */
    P.isZero = function () {
        return !!this.c && this.c[0] == 0;
    };
    /*
     *  n - 0 = n
     *  n - N = N
     *  n - I = -I
     *  0 - n = -n
     *  0 - 0 = 0
     *  0 - N = N
     *  0 - I = -I
     *  N - n = N
     *  N - 0 = N
     *  N - N = N
     *  N - I = N
     *  I - n = I
     *  I - 0 = I
     *  I - N = N
     *  I - I = N
     *
     * Return a new BigNumber whose value is the value of this BigNumber minus the value of
     * BigNumber(y, b).
     */
    P.minus = function (y, b) {
        var i,
            j,
            t,
            xLTy,
            x = this,
            a = x.s;
        y = new BigNumber(y, b);
        b = y.s;
        // Either NaN?
        if (!a || !b) return new BigNumber(NaN);
        // Signs differ?
        if (a != b) {
            y.s = -b;
            return x.plus(y);
        }
        var xe = x.e / LOG_BASE,
            ye = y.e / LOG_BASE,
            xc = x.c,
            yc = y.c;
        if (!xe || !ye) {
            // Either Infinity?
            if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
            // Either zero?
            if (!xc[0] || !yc[0]) {
                // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
                return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
                // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
                ROUNDING_MODE == 3 ? -0 : 0);
            }
        }
        xe = bitFloor(xe);
        ye = bitFloor(ye);
        xc = xc.slice();
        // Determine which is the bigger number.
        if (a = xe - ye) {
            if (xLTy = a < 0) {
                a = -a;
                t = xc;
            } else {
                ye = xe;
                t = yc;
            }
            t.reverse();
            // Prepend zeros to equalise exponents.
            for (b = a; b--; t.push(0)) {}
            t.reverse();
        } else {
            // Exponents equal. Check digit by digit.
            j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
            for (a = b = 0; b < j; b++) {
                if (xc[b] != yc[b]) {
                    xLTy = xc[b] < yc[b];
                    break;
                }
            }
        }
        // x < y? Point xc to the array of the bigger number.
        if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s; //eslint-disable-line
        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; //eslint-disable-line
        // 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; //eslint-disable-line
        // 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; //eslint-disable-line
            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;
    // @ts-ignore
    P[Symbol.toStringTag] = 'BigNumber';
    // Node.js v10.12.0+
    // @ts-ignore
    P[Symbol['for']('nodejs.util.inspect.custom')] = P.valueOf;
    if (configObject != null) BigNumber.set(configObject);
    return BigNumber;
}
// PRIVATE HELPER FUNCTIONS
// These functions don't need access to variables,
// e.g. DECIMAL_PLACES, in the scope of the `clone` function above.
function bitFloor(n) {
    var i = n | 0;
    return n > 0 || n === i ? i : i - 1;
}
// Return a coefficient array as a string of base 10 digits.
function coeffToString(a) {
    var s,
        z,
        i = 1,
        j = a.length,
        r = a[0] + '';
    for (; i < j;) {
        s = a[i++] + '';
        z = LOG_BASE - s.length;
        for (; z--; s = '0' + s) {}
        r += s;
    }
    // Determine trailing zeros.
    for (j = r.length; r.charCodeAt(--j) === 48;) {}
    return r.slice(0, j + 1 || 1);
}
// Compare the value of BigNumbers x and y.
function compare(x, y) {
    var a,
        b,
        xc = x.c,
        yc = y.c,
        i = x.s,
        j = y.s,
        k = x.e,
        l = y.e;
    // Either NaN?
    if (!i || !j) return null;
    a = xc && !xc[0];
    b = yc && !yc[0];
    // Either zero?
    if (a || b) return a ? b ? 0 : -j : i;
    // Signs differ?
    if (i != j) return i;
    a = i < 0;
    b = k == l;
    // Either Infinity?
    // @ts-ignore
    if (!xc || !yc) return b ? 0 : !(xc ^ a) ? 1 : -1;
    // Compare exponents.
    // @ts-ignore
    if (!b) return k > (l ^ a) ? 1 : -1;
    j = (k = xc.length) < (l = yc.length) ? k : l;
    // Compare digit by digit.
    // @ts-ignore
    for (i = 0; i < j; i++) {
        if (xc[i] != yc[i]) return xc[i] > (yc[i] ^ a) ? 1 : -1;
    } // Compare lengths.
    // @ts-ignore
    return k == l ? 0 : k > (l ^ a) ? 1 : -1;
}
/*
 * Check that n is a primitive number, an integer, and in range, otherwise throw.
 */
function intCheck(n, min, max, name) {
    if (n < min || n > max || n !== mathfloor(n)) {
        throw Error(bignumberError + (name || 'Argument') + (typeof n == 'number' ? n < min || n > max ? ' out of range: ' : ' not an integer: ' : ' not a primitive number: ') + String(n));
    }
}
// Assumes finite n.
function isOdd(n) {
    var k = n.c.length - 1;
    return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
}
function toExponential(str, e) {
    return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) + (e < 0 ? 'e' : 'e+') + e;
}
function toFixedPoint(str, e, z) {
    var len, zs;
    // Negative exponent?
    if (e < 0) {
        // Prepend zeros.
        for (zs = z + '.'; ++e; zs += z) {}
        str = zs + str;
        // Positive exponent
    } else {
        len = str.length;
        // Append zeros.
        if (++e > len) {
            for (zs = z, e -= len; --e; zs += z) {}
            str += zs;
        } else if (e < len) {
            str = str.slice(0, e) + '.' + str.slice(e);
        }
    }
    return str;
}
// EXPORT
var BigNumber = exports.BigNumber = clone();
exports['default'] = BigNumber;