+ * 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', // non-breaking space
+ suffix: ''
+ },
+
+ // The alphabet used for base conversion. It must be at least 2 characters long, with no '+',
+ // '-', '.', whitespace, or repeated character.
+ // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+ ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
+
+
+ //------------------------------------------------------------------------------------------
+
+
+ // CONSTRUCTOR
+
+
+ /*
+ * The BigNumber constructor and exported function.
+ * Create and return a new instance of a BigNumber object.
+ *
+ * v {number|string|BigNumber} A numeric value.
+ * [b] {number} The base of v. Integer, 2 to ALPHABET.length inclusive.
+ */
+ function BigNumber(v, b) {
+ var alphabet, c, caseChanged, e, i, isNum, len, str,
+ x = this;
+
+ // Enable constructor call without `new`.
+ if (!(x instanceof BigNumber)) return new BigNumber(v, b);
+
+ if (b == null) {
+
+ if (v && v._isBigNumber === true) {
+ x.s = v.s;
+
+ if (!v.c || v.e > MAX_EXP) {
+ x.c = x.e = null;
+ } else if (v.e < MIN_EXP) {
+ x.c = [x.e = 0];
+ } else {
+ x.e = v.e;
+ x.c = v.c.slice();
+ }
+
+ return;
+ }
+
+ if ((isNum = typeof v == 'number') && v * 0 == 0) {
+
+ // Use `1 / n` to handle minus zero also.
+ x.s = 1 / v < 0 ? (v = -v, -1) : 1;
+
+ // Fast path for integers, where n < 2147483648 (2**31).
+ if (v === ~~v) {
+ for (e = 0, i = v; i >= 10; i /= 10, e++);
+
+ if (e > MAX_EXP) {
+ x.c = x.e = null;
+ } else {
+ x.e = e;
+ x.c = [v];
+ }
+
+ return;
+ }
+
+ str = String(v);
+ } else {
+
+ if (!isNumeric.test(str = String(v))) return parseNumeric(x, str, isNum);
+
+ x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
+ }
+
+ // Decimal point?
+ if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+
+ // Exponential form?
+ if ((i = str.search(/e/i)) > 0) {
+
+ // Determine exponent.
+ if (e < 0) e = i;
+ e += +str.slice(i + 1);
+ str = str.substring(0, i);
+ } else if (e < 0) {
+
+ // Integer.
+ e = str.length;
+ }
+
+ } else {
+
+ // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+ intCheck(b, 2, ALPHABET.length, 'Base');
+
+ // Allow exponential notation to be used with base 10 argument, while
+ // also rounding to DECIMAL_PLACES as with other bases.
+ if (b == 10) {
+ x = new BigNumber(v);
+ return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
+ }
+
+ str = String(v);
+
+ if (isNum = typeof v == 'number') {
+
+ // Avoid potential interpretation of Infinity and NaN as base 44+ values.
+ if (v * 0 != 0) return parseNumeric(x, str, isNum, b);
+
+ x.s = 1 / v < 0 ? (str = str.slice(1), -1) : 1;
+
+ // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+ if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
+ throw Error
+ (tooManyDigits + v);
+ }
+ } else {
+ x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
+ }
+
+ alphabet = ALPHABET.slice(0, b);
+ e = i = 0;
+
+ // Check that str is a valid base b number.
+ // Don't use RegExp, so alphabet can contain special characters.
+ for (len = str.length; i < len; i++) {
+ if (alphabet.indexOf(c = str.charAt(i)) < 0) {
+ if (c == '.') {
+
+ // If '.' is not the first character and it has not be found before.
+ if (i > e) {
+ e = len;
+ continue;
+ }
+ } else if (!caseChanged) {
+
+ // Allow e.g. hexadecimal 'FF' as well as 'ff'.
+ if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
+ str == str.toLowerCase() && (str = str.toUpperCase())) {
+ caseChanged = true;
+ i = -1;
+ e = 0;
+ continue;
+ }
+ }
+
+ return parseNumeric(x, String(v), isNum, b);
+ }
+ }
+
+ // Prevent later check for length on converted number.
+ isNum = false;
+ str = convertBase(str, b, 10, x.s);
+
+ // Decimal point?
+ if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
+ else e = str.length;
+ }
+
+ // Determine leading zeros.
+ for (i = 0; str.charCodeAt(i) === 48; i++);
+
+ // Determine trailing zeros.
+ for (len = str.length; str.charCodeAt(--len) === 48;);
+
+ if (str = str.slice(i, ++len)) {
+ len -= i;
+
+ // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+ if (isNum && BigNumber.DEBUG &&
+ len > 15 && (v > MAX_SAFE_INTEGER || v !== mathfloor(v))) {
+ throw Error
+ (tooManyDigits + (x.s * v));
+ }
+
+ // Overflow?
+ if ((e = e - i - 1) > MAX_EXP) {
+
+ // Infinity.
+ x.c = x.e = null;
+
+ // Underflow?
+ } else if (e < MIN_EXP) {
+
+ // Zero.
+ x.c = [x.e = 0];
+ } else {
+ x.e = e;
+ x.c = [];
+
+ // Transform base
+
+ // e is the base 10 exponent.
+ // i is where to slice str to get the first element of the coefficient array.
+ i = (e + 1) % LOG_BASE;
+ if (e < 0) i += LOG_BASE; // i < 1
+
+ if (i < len) {
+ if (i) x.c.push(+str.slice(0, i));
+
+ for (len -= LOG_BASE; i < len;) {
+ x.c.push(+str.slice(i, i += LOG_BASE));
+ }
+
+ i = LOG_BASE - (str = str.slice(i)).length;
+ } else {
+ i -= len;
+ }
+
+ for (; i--; str += '0');
+ x.c.push(+str);
+ }
+ } else {
+
+ // Zero.
+ x.c = [x.e = 0];
+ }
+ }
+
+
+ // CONSTRUCTOR PROPERTIES
+
+
+ BigNumber.clone = clone;
+
+ BigNumber.ROUND_UP = 0;
+ BigNumber.ROUND_DOWN = 1;
+ BigNumber.ROUND_CEIL = 2;
+ BigNumber.ROUND_FLOOR = 3;
+ BigNumber.ROUND_HALF_UP = 4;
+ BigNumber.ROUND_HALF_DOWN = 5;
+ BigNumber.ROUND_HALF_EVEN = 6;
+ BigNumber.ROUND_HALF_CEIL = 7;
+ BigNumber.ROUND_HALF_FLOOR = 8;
+ BigNumber.EUCLID = 9;
+
+
+ /*
+ * Configure infrequently-changing library-wide settings.
+ *
+ * Accept an object with the following optional properties (if the value of a property is
+ * a number, it must be an integer within the inclusive range stated):
+ *
+ * DECIMAL_PLACES {number} 0 to MAX
+ * ROUNDING_MODE {number} 0 to 8
+ * EXPONENTIAL_AT {number|number[]} -MAX to MAX or [-MAX to 0, 0 to MAX]
+ * RANGE {number|number[]} -MAX to MAX (not zero) or [-MAX to -1, 1 to MAX]
+ * CRYPTO {boolean} true or false
+ * MODULO_MODE {number} 0 to 9
+ * POW_PRECISION {number} 0 to MAX
+ * ALPHABET {string} A string of two or more unique characters which does
+ * not contain '.'.
+ * FORMAT {object} An object with some of the following properties:
+ * prefix {string}
+ * groupSize {number}
+ * secondaryGroupSize {number}
+ * groupSeparator {string}
+ * decimalSeparator {string}
+ * fractionGroupSize {number}
+ * fractionGroupSeparator {string}
+ * suffix {string}
+ *
+ * (The values assigned to the above FORMAT object properties are not checked for validity.)
+ *
+ * E.g.
+ * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
+ *
+ * Ignore properties/parameters set to null or undefined, except for ALPHABET.
+ *
+ * Return an object with the properties current values.
+ */
+ BigNumber.config = BigNumber.set = function (obj) {
+ var p, v;
+
+ if (obj != null) {
+
+ if (typeof obj == 'object') {
+
+ // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
+ // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
+ if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
+ v = obj[p];
+ intCheck(v, 0, MAX, p);
+ DECIMAL_PLACES = v;
+ }
+
+ // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
+ // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
+ if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
+ v = obj[p];
+ intCheck(v, 0, 8, p);
+ ROUNDING_MODE = v;
+ }
+
+ // EXPONENTIAL_AT {number|number[]}
+ // Integer, -MAX to MAX inclusive or
+ // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
+ // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
+ if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
+ v = obj[p];
+ if (v && v.pop) {
+ intCheck(v[0], -MAX, 0, p);
+ intCheck(v[1], 0, MAX, p);
+ TO_EXP_NEG = v[0];
+ TO_EXP_POS = v[1];
+ } else {
+ intCheck(v, -MAX, MAX, p);
+ TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
+ }
+ }
+
+ // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
+ // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
+ // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
+ if (obj.hasOwnProperty(p = 'RANGE')) {
+ v = obj[p];
+ if (v && v.pop) {
+ intCheck(v[0], -MAX, -1, p);
+ intCheck(v[1], 1, MAX, p);
+ MIN_EXP = v[0];
+ MAX_EXP = v[1];
+ } else {
+ intCheck(v, -MAX, MAX, p);
+ if (v) {
+ MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
+ } else {
+ throw Error
+ (bignumberError + p + ' cannot be zero: ' + v);
+ }
+ }
+ }
+
+ // CRYPTO {boolean} true or false.
+ // '[BigNumber Error] CRYPTO not true or false: {v}'
+ // '[BigNumber Error] crypto unavailable'
+ if (obj.hasOwnProperty(p = 'CRYPTO')) {
+ v = obj[p];
+ if (v === !!v) {
+ if (v) {
+ if (typeof crypto != 'undefined' && crypto &&
+ (crypto.getRandomValues || crypto.randomBytes)) {
+ CRYPTO = v;
+ } else {
+ CRYPTO = !v;
+ throw Error
+ (bignumberError + 'crypto unavailable');
+ }
+ } else {
+ CRYPTO = v;
+ }
+ } else {
+ throw Error
+ (bignumberError + p + ' not true or false: ' + v);
+ }
+ }
+
+ // MODULO_MODE {number} Integer, 0 to 9 inclusive.
+ // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
+ if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
+ v = obj[p];
+ intCheck(v, 0, 9, p);
+ MODULO_MODE = v;
+ }
+
+ // POW_PRECISION {number} Integer, 0 to MAX inclusive.
+ // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
+ if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
+ v = obj[p];
+ intCheck(v, 0, MAX, p);
+ POW_PRECISION = v;
+ }
+
+ // FORMAT {object}
+ // '[BigNumber Error] FORMAT not an object: {v}'
+ if (obj.hasOwnProperty(p = 'FORMAT')) {
+ v = obj[p];
+ if (typeof v == 'object') FORMAT = v;
+ else throw Error
+ (bignumberError + p + ' not an object: ' + v);
+ }
+
+ // ALPHABET {string}
+ // '[BigNumber Error] ALPHABET invalid: {v}'
+ if (obj.hasOwnProperty(p = 'ALPHABET')) {
+ v = obj[p];
+
+ // Disallow if only one character,
+ // or if it contains '+', '-', '.', whitespace, or a repeated character.
+ if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
+ ALPHABET = v;
+ } else {
+ throw Error
+ (bignumberError + p + ' invalid: ' + v);
+ }
+ }
+
+ } else {
+
+ // '[BigNumber Error] Object expected: {v}'
+ throw Error
+ (bignumberError + 'Object expected: ' + obj);
+ }
+ }
+
+ return {
+ DECIMAL_PLACES: DECIMAL_PLACES,
+ ROUNDING_MODE: ROUNDING_MODE,
+ EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
+ RANGE: [MIN_EXP, MAX_EXP],
+ CRYPTO: CRYPTO,
+ MODULO_MODE: MODULO_MODE,
+ POW_PRECISION: POW_PRECISION,
+ FORMAT: FORMAT,
+ ALPHABET: ALPHABET
+ };
+ };
+
+
+ /*
+ * Return true if v is a BigNumber instance, otherwise return false.
+ *
+ * If BigNumber.DEBUG is true, throw if a BigNumber instance is not well-formed.
+ *
+ * v {any}
+ *
+ * '[BigNumber Error] Invalid BigNumber: {v}'
+ */
+ BigNumber.isBigNumber = function (v) {
+ if (!v || v._isBigNumber !== true) return false;
+ if (!BigNumber.DEBUG) return true;
+
+ var i, n,
+ c = v.c,
+ e = v.e,
+ s = v.s;
+
+ out: if ({}.toString.call(c) == '[object Array]') {
+
+ if ((s === 1 || s === -1) && e >= -MAX && e <= MAX && e === mathfloor(e)) {
+
+ // If the first element is zero, the BigNumber value must be zero.
+ if (c[0] === 0) {
+ if (e === 0 && c.length === 1) return true;
+ break out;
+ }
+
+ // Calculate number of digits that c[0] should have, based on the exponent.
+ i = (e + 1) % LOG_BASE;
+ if (i < 1) i += LOG_BASE;
+
+ // Calculate number of digits of c[0].
+ //if (Math.ceil(Math.log(c[0] + 1) / Math.LN10) == i) {
+ if (String(c[0]).length == i) {
+
+ for (i = 0; i < c.length; i++) {
+ n = c[i];
+ if (n < 0 || n >= BASE || n !== mathfloor(n)) break out;
+ }
+
+ // Last element cannot be zero, unless it is the only element.
+ if (n !== 0) return true;
+ }
+ }
+
+ // Infinity/NaN
+ } else if (c === null && e === null && (s === null || s === 1 || s === -1)) {
+ return true;
+ }
+
+ throw Error
+ (bignumberError + 'Invalid BigNumber: ' + v);
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the maximum of the arguments.
+ *
+ * arguments {number|string|BigNumber}
+ */
+ BigNumber.maximum = BigNumber.max = function () {
+ return maxOrMin(arguments, P.lt);
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the minimum of the arguments.
+ *
+ * arguments {number|string|BigNumber}
+ */
+ BigNumber.minimum = BigNumber.min = function () {
+ return maxOrMin(arguments, P.gt);
+ };
+
+
+ /*
+ * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
+ * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
+ * zeros are produced).
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
+ * '[BigNumber Error] crypto unavailable'
+ */
+ BigNumber.random = (function () {
+ var pow2_53 = 0x20000000000000;
+
+ // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
+ // Check if Math.random() produces more than 32 bits of randomness.
+ // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
+ // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
+ var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
+ ? function () { return mathfloor(Math.random() * pow2_53); }
+ : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
+ (Math.random() * 0x800000 | 0); };
+
+ return function (dp) {
+ var a, b, e, k, v,
+ i = 0,
+ c = [],
+ rand = new BigNumber(ONE);
+
+ if (dp == null) dp = DECIMAL_PLACES;
+ else intCheck(dp, 0, MAX);
+
+ k = mathceil(dp / LOG_BASE);
+
+ if (CRYPTO) {
+
+ // Browsers supporting crypto.getRandomValues.
+ if (crypto.getRandomValues) {
+
+ a = crypto.getRandomValues(new Uint32Array(k *= 2));
+
+ for (; i < k;) {
+
+ // 53 bits:
+ // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
+ // 11111 11111111 11111111 11111111 11100000 00000000 00000000
+ // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
+ // 11111 11111111 11111111
+ // 0x20000 is 2^21.
+ v = a[i] * 0x20000 + (a[i + 1] >>> 11);
+
+ // Rejection sampling:
+ // 0 <= v < 9007199254740992
+ // Probability that v >= 9e15, is
+ // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
+ if (v >= 9e15) {
+ b = crypto.getRandomValues(new Uint32Array(2));
+ a[i] = b[0];
+ a[i + 1] = b[1];
+ } else {
+
+ // 0 <= v <= 8999999999999999
+ // 0 <= (v % 1e14) <= 99999999999999
+ c.push(v % 1e14);
+ i += 2;
+ }
+ }
+ i = k / 2;
+
+ // Node.js supporting crypto.randomBytes.
+ } else if (crypto.randomBytes) {
+
+ // buffer
+ a = crypto.randomBytes(k *= 7);
+
+ for (; i < k;) {
+
+ // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
+ // 0x100000000 is 2^32, 0x1000000 is 2^24
+ // 11111 11111111 11111111 11111111 11111111 11111111 11111111
+ // 0 <= v < 9007199254740992
+ v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
+ (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
+ (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
+
+ if (v >= 9e15) {
+ crypto.randomBytes(7).copy(a, i);
+ } else {
+
+ // 0 <= (v % 1e14) <= 99999999999999
+ c.push(v % 1e14);
+ i += 7;
+ }
+ }
+ i = k / 7;
+ } else {
+ CRYPTO = false;
+ throw Error
+ (bignumberError + 'crypto unavailable');
+ }
+ }
+
+ // Use Math.random.
+ if (!CRYPTO) {
+
+ for (; i < k;) {
+ v = random53bitInt();
+ if (v < 9e15) c[i++] = v % 1e14;
+ }
+ }
+
+ k = c[--i];
+ dp %= LOG_BASE;
+
+ // Convert trailing digits to zeros according to dp.
+ if (k && dp) {
+ v = POWS_TEN[LOG_BASE - dp];
+ c[i] = mathfloor(k / v) * v;
+ }
+
+ // Remove trailing elements which are zero.
+ for (; c[i] === 0; c.pop(), i--);
+
+ // Zero?
+ if (i < 0) {
+ c = [e = 0];
+ } else {
+
+ // Remove leading elements which are zero and adjust exponent accordingly.
+ for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
+
+ // Count the digits of the first element of c to determine leading zeros, and...
+ for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
+
+ // adjust the exponent accordingly.
+ if (i < LOG_BASE) e -= LOG_BASE - i;
+ }
+
+ rand.e = e;
+ rand.c = c;
+ return rand;
+ };
+ })();
+
+
+ /*
+ * Return a BigNumber whose value is the sum of the arguments.
+ *
+ * arguments {number|string|BigNumber}
+ */
+ BigNumber.sum = function () {
+ var i = 1,
+ args = arguments,
+ sum = new BigNumber(args[0]);
+ for (; i < args.length;) sum = sum.plus(args[i++]);
+ return sum;
+ };
+
+
+ // PRIVATE FUNCTIONS
+
+
+ // Called by BigNumber and BigNumber.prototype.toString.
+ convertBase = (function () {
+ var decimal = '0123456789';
+
+ /*
+ * Convert string of baseIn to an array of numbers of baseOut.
+ * Eg. toBaseOut('255', 10, 16) returns [15, 15].
+ * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
+ */
+ function toBaseOut(str, baseIn, baseOut, alphabet) {
+ var j,
+ arr = [0],
+ arrL,
+ i = 0,
+ len = str.length;
+
+ for (; i < len;) {
+ for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
+
+ arr[0] += alphabet.indexOf(str.charAt(i++));
+
+ for (j = 0; j < arr.length; j++) {
+
+ if (arr[j] > baseOut - 1) {
+ if (arr[j + 1] == null) arr[j + 1] = 0;
+ arr[j + 1] += arr[j] / baseOut | 0;
+ arr[j] %= baseOut;
+ }
+ }
+ }
+
+ return arr.reverse();
+ }
+
+ // Convert a numeric string of baseIn to a numeric string of baseOut.
+ // If the caller is toString, we are converting from base 10 to baseOut.
+ // If the caller is BigNumber, we are converting from baseIn to base 10.
+ return function (str, baseIn, baseOut, sign, callerIsToString) {
+ var alphabet, d, e, k, r, x, xc, y,
+ i = str.indexOf('.'),
+ dp = DECIMAL_PLACES,
+ rm = ROUNDING_MODE;
+
+ // Non-integer.
+ if (i >= 0) {
+ k = POW_PRECISION;
+
+ // Unlimited precision.
+ POW_PRECISION = 0;
+ str = str.replace('.', '');
+ y = new BigNumber(baseIn);
+ x = y.pow(str.length - i);
+ POW_PRECISION = k;
+
+ // Convert str as if an integer, then restore the fraction part by dividing the
+ // result by its base raised to a power.
+
+ y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
+ 10, baseOut, decimal);
+ y.e = y.c.length;
+ }
+
+ // Convert the number as integer.
+
+ xc = toBaseOut(str, baseIn, baseOut, callerIsToString
+ ? (alphabet = ALPHABET, decimal)
+ : (alphabet = decimal, ALPHABET));
+
+ // xc now represents str as an integer and converted to baseOut. e is the exponent.
+ e = k = xc.length;
+
+ // Remove trailing zeros.
+ for (; xc[--k] == 0; xc.pop());
+
+ // Zero?
+ if (!xc[0]) return alphabet.charAt(0);
+
+ // Does str represent an integer? If so, no need for the division.
+ if (i < 0) {
+ --e;
+ } else {
+ x.c = xc;
+ x.e = e;
+
+ // The sign is needed for correct rounding.
+ x.s = sign;
+ x = div(x, y, dp, rm, baseOut);
+ xc = x.c;
+ r = x.r;
+ e = x.e;
+ }
+
+ // xc now represents str converted to baseOut.
+
+ // THe index of the rounding digit.
+ d = e + dp + 1;
+
+ // The rounding digit: the digit to the right of the digit that may be rounded up.
+ i = xc[d];
+
+ // Look at the rounding digits and mode to determine whether to round up.
+
+ k = baseOut / 2;
+ r = r || d < 0 || xc[d + 1] != null;
+
+ r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+ : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
+ rm == (x.s < 0 ? 8 : 7));
+
+ // If the index of the rounding digit is not greater than zero, or xc represents
+ // zero, then the result of the base conversion is zero or, if rounding up, a value
+ // such as 0.00001.
+ if (d < 1 || !xc[0]) {
+
+ // 1^-dp or 0
+ str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
+ } else {
+
+ // Truncate xc to the required number of decimal places.
+ xc.length = d;
+
+ // Round up?
+ if (r) {
+
+ // Rounding up may mean the previous digit has to be rounded up and so on.
+ for (--baseOut; ++xc[--d] > baseOut;) {
+ xc[d] = 0;
+
+ if (!d) {
+ ++e;
+ xc = [1].concat(xc);
+ }
+ }
+ }
+
+ // Determine trailing zeros.
+ for (k = xc.length; !xc[--k];);
+
+ // E.g. [4, 11, 15] becomes 4bf.
+ for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
+
+ // Add leading zeros, decimal point and trailing zeros as required.
+ str = toFixedPoint(str, e, alphabet.charAt(0));
+ }
+
+ // The caller will add the sign.
+ return str;
+ };
+ })();
+
+
+ // Perform division in the specified base. Called by div and convertBase.
+ div = (function () {
+
+ // Assume non-zero x and k.
+ function multiply(x, k, base) {
+ var m, temp, xlo, xhi,
+ carry = 0,
+ i = x.length,
+ klo = k % SQRT_BASE,
+ khi = k / SQRT_BASE | 0;
+
+ for (x = x.slice(); i--;) {
+ xlo = x[i] % SQRT_BASE;
+ xhi = x[i] / SQRT_BASE | 0;
+ m = khi * xlo + xhi * klo;
+ temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
+ carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
+ x[i] = temp % base;
+ }
+
+ if (carry) x = [carry].concat(x);
+
+ return x;
+ }
+
+ function compare(a, b, aL, bL) {
+ var i, cmp;
+
+ if (aL != bL) {
+ cmp = aL > bL ? 1 : -1;
+ } else {
+
+ for (i = cmp = 0; i < aL; i++) {
+
+ if (a[i] != b[i]) {
+ cmp = a[i] > b[i] ? 1 : -1;
+ break;
+ }
+ }
+ }
+
+ return cmp;
+ }
+
+ function subtract(a, b, aL, base) {
+ var i = 0;
+
+ // Subtract b from a.
+ for (; aL--;) {
+ a[aL] -= i;
+ i = a[aL] < b[aL] ? 1 : 0;
+ a[aL] = i * base + a[aL] - b[aL];
+ }
+
+ // Remove leading zeros.
+ for (; !a[0] && a.length > 1; a.splice(0, 1));
+ }
+
+ // x: dividend, y: divisor.
+ return function (x, y, dp, rm, base) {
+ var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
+ yL, yz,
+ s = x.s == y.s ? 1 : -1,
+ xc = x.c,
+ yc = y.c;
+
+ // Either NaN, Infinity or 0?
+ if (!xc || !xc[0] || !yc || !yc[0]) {
+
+ return new BigNumber(
+
+ // Return NaN if either NaN, or both Infinity or 0.
+ !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
+
+ // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
+ xc && xc[0] == 0 || !yc ? s * 0 : s / 0
+ );
+ }
+
+ q = new BigNumber(s);
+ qc = q.c = [];
+ e = x.e - y.e;
+ s = dp + e + 1;
+
+ if (!base) {
+ base = BASE;
+ e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
+ s = s / LOG_BASE | 0;
+ }
+
+ // Result exponent may be one less then the current value of e.
+ // The coefficients of the BigNumbers from convertBase may have trailing zeros.
+ for (i = 0; yc[i] == (xc[i] || 0); i++);
+
+ if (yc[i] > (xc[i] || 0)) e--;
+
+ if (s < 0) {
+ qc.push(1);
+ more = true;
+ } else {
+ xL = xc.length;
+ yL = yc.length;
+ i = 0;
+ s += 2;
+
+ // Normalise xc and yc so highest order digit of yc is >= base / 2.
+
+ n = mathfloor(base / (yc[0] + 1));
+
+ // Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
+ // if (n > 1 || n++ == 1 && yc[0] < base / 2) {
+ if (n > 1) {
+ yc = multiply(yc, n, base);
+ xc = multiply(xc, n, base);
+ yL = yc.length;
+ xL = xc.length;
+ }
+
+ xi = yL;
+ rem = xc.slice(0, yL);
+ remL = rem.length;
+
+ // Add zeros to make remainder as long as divisor.
+ for (; remL < yL; rem[remL++] = 0);
+ yz = yc.slice();
+ yz = [0].concat(yz);
+ yc0 = yc[0];
+ if (yc[1] >= base / 2) yc0++;
+ // Not necessary, but to prevent trial digit n > base, when using base 3.
+ // else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
+
+ do {
+ n = 0;
+
+ // Compare divisor and remainder.
+ cmp = compare(yc, rem, yL, remL);
+
+ // If divisor < remainder.
+ if (cmp < 0) {
+
+ // Calculate trial digit, n.
+
+ rem0 = rem[0];
+ if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
+
+ // n is how many times the divisor goes into the current remainder.
+ n = mathfloor(rem0 / yc0);
+
+ // Algorithm:
+ // product = divisor multiplied by trial digit (n).
+ // Compare product and remainder.
+ // If product is greater than remainder:
+ // Subtract divisor from product, decrement trial digit.
+ // Subtract product from remainder.
+ // If product was less than remainder at the last compare:
+ // Compare new remainder and divisor.
+ // If remainder is greater than divisor:
+ // Subtract divisor from remainder, increment trial digit.
+
+ if (n > 1) {
+
+ // n may be > base only when base is 3.
+ if (n >= base) n = base - 1;
+
+ // product = divisor * trial digit.
+ prod = multiply(yc, n, base);
+ prodL = prod.length;
+ remL = rem.length;
+
+ // Compare product and remainder.
+ // If product > remainder then trial digit n too high.
+ // n is 1 too high about 5% of the time, and is not known to have
+ // ever been more than 1 too high.
+ while (compare(prod, rem, prodL, remL) == 1) {
+ n--;
+
+ // Subtract divisor from product.
+ subtract(prod, yL < prodL ? yz : yc, prodL, base);
+ prodL = prod.length;
+ cmp = 1;
+ }
+ } else {
+
+ // n is 0 or 1, cmp is -1.
+ // If n is 0, there is no need to compare yc and rem again below,
+ // so change cmp to 1 to avoid it.
+ // If n is 1, leave cmp as -1, so yc and rem are compared again.
+ if (n == 0) {
+
+ // divisor < remainder, so n must be at least 1.
+ cmp = n = 1;
+ }
+
+ // product = divisor
+ prod = yc.slice();
+ prodL = prod.length;
+ }
+
+ if (prodL < remL) prod = [0].concat(prod);
+
+ // Subtract product from remainder.
+ subtract(rem, prod, remL, base);
+ remL = rem.length;
+
+ // If product was < remainder.
+ if (cmp == -1) {
+
+ // Compare divisor and new remainder.
+ // If divisor < new remainder, subtract divisor from remainder.
+ // Trial digit n too low.
+ // n is 1 too low about 5% of the time, and very rarely 2 too low.
+ while (compare(yc, rem, yL, remL) < 1) {
+ n++;
+
+ // Subtract divisor from remainder.
+ subtract(rem, yL < remL ? yz : yc, remL, base);
+ remL = rem.length;
+ }
+ }
+ } else if (cmp === 0) {
+ n++;
+ rem = [0];
+ } // else cmp === 1 and n will be 0
+
+ // Add the next digit, n, to the result array.
+ qc[i++] = n;
+
+ // Update the remainder.
+ if (rem[0]) {
+ rem[remL++] = xc[xi] || 0;
+ } else {
+ rem = [xc[xi]];
+ remL = 1;
+ }
+ } while ((xi++ < xL || rem[0] != null) && s--);
+
+ more = rem[0] != null;
+
+ // Leading zero?
+ if (!qc[0]) qc.splice(0, 1);
+ }
+
+ if (base == BASE) {
+
+ // To calculate q.e, first get the number of digits of qc[0].
+ for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
+
+ round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
+
+ // Caller is convertBase.
+ } else {
+ q.e = e;
+ q.r = +more;
+ }
+
+ return q;
+ };
+ })();
+
+
+ /*
+ * Return a string representing the value of BigNumber n in fixed-point or exponential
+ * notation rounded to the specified decimal places or significant digits.
+ *
+ * n: a BigNumber.
+ * i: the index of the last digit required (i.e. the digit that may be rounded up).
+ * rm: the rounding mode.
+ * id: 1 (toExponential) or 2 (toPrecision).
+ */
+ function format(n, i, rm, id) {
+ var c0, e, ne, len, str;
+
+ if (rm == null) rm = ROUNDING_MODE;
+ else intCheck(rm, 0, 8);
+
+ if (!n.c) return n.toString();
+
+ c0 = n.c[0];
+ ne = n.e;
+
+ if (i == null) {
+ str = coeffToString(n.c);
+ str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
+ ? toExponential(str, ne)
+ : toFixedPoint(str, ne, '0');
+ } else {
+ n = round(new BigNumber(n), i, rm);
+
+ // n.e may have changed if the value was rounded up.
+ e = n.e;
+
+ str = coeffToString(n.c);
+ len = str.length;
+
+ // toPrecision returns exponential notation if the number of significant digits
+ // specified is less than the number of digits necessary to represent the integer
+ // part of the value in fixed-point notation.
+
+ // Exponential notation.
+ if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
+
+ // Append zeros?
+ for (; len < i; str += '0', len++);
+ str = toExponential(str, e);
+
+ // Fixed-point notation.
+ } else {
+ i -= ne;
+ str = toFixedPoint(str, e, '0');
+
+ // Append zeros?
+ if (e + 1 > len) {
+ if (--i > 0) for (str += '.'; i--; str += '0');
+ } else {
+ i += e - len;
+ if (i > 0) {
+ if (e + 1 == len) str += '.';
+ for (; i--; str += '0');
+ }
+ }
+ }
+ }
+
+ return n.s < 0 && c0 ? '-' + str : str;
+ }
+
+
+ // Handle BigNumber.max and BigNumber.min.
+ function maxOrMin(args, method) {
+ var n,
+ i = 1,
+ m = new BigNumber(args[0]);
+
+ for (; i < args.length; i++) {
+ n = new BigNumber(args[i]);
+
+ // If any number is NaN, return NaN.
+ if (!n.s) {
+ m = n;
+ break;
+ } else if (method.call(m, n)) {
+ m = n;
+ }
+ }
+
+ return m;
+ }
+
+
+ /*
+ * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
+ * Called by minus, plus and times.
+ */
+ function normalise(n, c, e) {
+ var i = 1,
+ j = c.length;
+
+ // Remove trailing zeros.
+ for (; !c[--j]; c.pop());
+
+ // Calculate the base 10 exponent. First get the number of digits of c[0].
+ for (j = c[0]; j >= 10; j /= 10, i++);
+
+ // Overflow?
+ if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
+
+ // Infinity.
+ n.c = n.e = null;
+
+ // Underflow?
+ } else if (e < MIN_EXP) {
+
+ // Zero.
+ n.c = [n.e = 0];
+ } else {
+ n.e = e;
+ n.c = c;
+ }
+
+ return n;
+ }
+
+
+ // Handle values that fail the validity test in BigNumber.
+ parseNumeric = (function () {
+ var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
+ dotAfter = /^([^.]+)\.$/,
+ dotBefore = /^\.([^.]+)$/,
+ isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+ whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+
+ return function (x, str, isNum, b) {
+ var base,
+ s = isNum ? str : str.replace(whitespaceOrPlus, '');
+
+ // No exception on ±Infinity or NaN.
+ if (isInfinityOrNaN.test(s)) {
+ x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
+ } else {
+ if (!isNum) {
+
+ // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
+ s = s.replace(basePrefix, function (m, p1, p2) {
+ base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
+ return !b || b == base ? p1 : m;
+ });
+
+ if (b) {
+ base = b;
+
+ // E.g. '1.' to '1', '.1' to '0.1'
+ s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
+ }
+
+ if (str != s) return new BigNumber(s, base);
+ }
+
+ // '[BigNumber Error] Not a number: {n}'
+ // '[BigNumber Error] Not a base {b} number: {n}'
+ if (BigNumber.DEBUG) {
+ throw Error
+ (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
+ }
+
+ // NaN
+ x.s = null;
+ }
+
+ x.c = x.e = null;
+ }
+ })();
+
+
+ /*
+ * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
+ * If r is truthy, it is known that there are more digits after the rounding digit.
+ */
+ function round(x, sd, rm, r) {
+ var d, i, j, k, n, ni, rd,
+ xc = x.c,
+ pows10 = POWS_TEN;
+
+ // if x is not Infinity or NaN...
+ if (xc) {
+
+ // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
+ // n is a base 1e14 number, the value of the element of array x.c containing rd.
+ // ni is the index of n within x.c.
+ // d is the number of digits of n.
+ // i is the index of rd within n including leading zeros.
+ // j is the actual index of rd within n (if < 0, rd is a leading zero).
+ out: {
+
+ // Get the number of digits of the first element of xc.
+ for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
+ i = sd - d;
+
+ // If the rounding digit is in the first element of xc...
+ if (i < 0) {
+ i += LOG_BASE;
+ j = sd;
+ n = xc[ni = 0];
+
+ // Get the rounding digit at index j of n.
+ rd = n / pows10[d - j - 1] % 10 | 0;
+ } else {
+ ni = mathceil((i + 1) / LOG_BASE);
+
+ if (ni >= xc.length) {
+
+ if (r) {
+
+ // Needed by sqrt.
+ for (; xc.length <= ni; xc.push(0));
+ n = rd = 0;
+ d = 1;
+ i %= LOG_BASE;
+ j = i - LOG_BASE + 1;
+ } else {
+ break out;
+ }
+ } else {
+ n = k = xc[ni];
+
+ // Get the number of digits of n.
+ for (d = 1; k >= 10; k /= 10, d++);
+
+ // Get the index of rd within n.
+ i %= LOG_BASE;
+
+ // Get the index of rd within n, adjusted for leading zeros.
+ // The number of leading zeros of n is given by LOG_BASE - d.
+ j = i - LOG_BASE + d;
+
+ // Get the rounding digit at index j of n.
+ rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
+ }
+ }
+
+ r = r || sd < 0 ||
+
+ // Are there any non-zero digits after the rounding digit?
+ // The expression n % pows10[d - j - 1] returns all digits of n to the right
+ // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
+ xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
+
+ r = rm < 4
+ ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
+ : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
+
+ // Check whether the digit to the left of the rounding digit is odd.
+ ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
+ rm == (x.s < 0 ? 8 : 7));
+
+ if (sd < 1 || !xc[0]) {
+ xc.length = 0;
+
+ if (r) {
+
+ // Convert sd to decimal places.
+ sd -= x.e + 1;
+
+ // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+ xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
+ x.e = -sd || 0;
+ } else {
+
+ // Zero.
+ xc[0] = x.e = 0;
+ }
+
+ return x;
+ }
+
+ // Remove excess digits.
+ if (i == 0) {
+ xc.length = ni;
+ k = 1;
+ ni--;
+ } else {
+ xc.length = ni + 1;
+ k = pows10[LOG_BASE - i];
+
+ // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+ // j > 0 means i > number of leading zeros of n.
+ xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
+ }
+
+ // Round up?
+ if (r) {
+
+ for (; ;) {
+
+ // If the digit to be rounded up is in the first element of xc...
+ if (ni == 0) {
+
+ // i will be the length of xc[0] before k is added.
+ for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
+ j = xc[0] += k;
+ for (k = 1; j >= 10; j /= 10, k++);
+
+ // if i != k the length has increased.
+ if (i != k) {
+ x.e++;
+ if (xc[0] == BASE) xc[0] = 1;
+ }
+
+ break;
+ } else {
+ xc[ni] += k;
+ if (xc[ni] != BASE) break;
+ xc[ni--] = 0;
+ k = 1;
+ }
+ }
+ }
+
+ // Remove trailing zeros.
+ for (i = xc.length; xc[--i] === 0; xc.pop());
+ }
+
+ // Overflow? Infinity.
+ if (x.e > MAX_EXP) {
+ x.c = x.e = null;
+
+ // Underflow? Zero.
+ } else if (x.e < MIN_EXP) {
+ x.c = [x.e = 0];
+ }
+ }
+
+ return x;
+ }
+
+
+ function valueOf(n) {
+ var str,
+ e = n.e;
+
+ if (e === null) return n.toString();
+
+ str = coeffToString(n.c);
+
+ str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+ ? toExponential(str, e)
+ : toFixedPoint(str, e, '0');
+
+ return n.s < 0 ? '-' + str : str;
+ }
+
+
+ // PROTOTYPE/INSTANCE METHODS
+
+
+ /*
+ * Return a new BigNumber whose value is the absolute value of this BigNumber.
+ */
+ P.absoluteValue = P.abs = function () {
+ var x = new BigNumber(this);
+ if (x.s < 0) x.s = 1;
+ return x;
+ };
+
+
+ /*
+ * Return
+ * 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
+ * -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
+ * 0 if they have the same value,
+ * or null if the value of either is NaN.
+ */
+ P.comparedTo = function (y, b) {
+ return compare(this, new BigNumber(y, b));
+ };
+
+
+ /*
+ * If dp is undefined or null or true or false, return the number of decimal places of the
+ * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+ *
+ * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
+ * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
+ * ROUNDING_MODE if rm is omitted.
+ *
+ * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.decimalPlaces = P.dp = function (dp, rm) {
+ var c, n, v,
+ x = this;
+
+ if (dp != null) {
+ intCheck(dp, 0, MAX);
+ if (rm == null) rm = ROUNDING_MODE;
+ else intCheck(rm, 0, 8);
+
+ return round(new BigNumber(x), dp + x.e + 1, rm);
+ }
+
+ if (!(c = x.c)) return null;
+ n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
+
+ // Subtract the number of trailing zeros of the last number.
+ if (v = c[v]) for (; v % 10 == 0; v /= 10, n--);
+ if (n < 0) n = 0;
+
+ return n;
+ };
+
+
+ /*
+ * n / 0 = I
+ * n / N = N
+ * n / I = 0
+ * 0 / n = 0
+ * 0 / 0 = N
+ * 0 / N = N
+ * 0 / I = 0
+ * N / n = N
+ * N / 0 = N
+ * N / N = N
+ * N / I = N
+ * I / n = I
+ * I / 0 = I
+ * I / N = N
+ * I / I = N
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
+ * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+ */
+ P.dividedBy = P.div = function (y, b) {
+ return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the integer part of dividing the value of this
+ * BigNumber by the value of BigNumber(y, b).
+ */
+ P.dividedToIntegerBy = P.idiv = function (y, b) {
+ return div(this, new BigNumber(y, b), 0, 1);
+ };
+
+
+ /*
+ * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
+ *
+ * If m is present, return the result modulo m.
+ * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
+ * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
+ *
+ * The modular power operation works efficiently when x, n, and m are integers, otherwise it
+ * is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
+ *
+ * n {number|string|BigNumber} The exponent. An integer.
+ * [m] {number|string|BigNumber} The modulus.
+ *
+ * '[BigNumber Error] Exponent not an integer: {n}'
+ */
+ P.exponentiatedBy = P.pow = function (n, m) {
+ var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
+ x = this;
+
+ n = new BigNumber(n);
+
+ // Allow NaN and ±Infinity, but not other non-integers.
+ if (n.c && !n.isInteger()) {
+ throw Error
+ (bignumberError + 'Exponent not an integer: ' + valueOf(n));
+ }
+
+ if (m != null) m = new BigNumber(m);
+
+ // Exponent of MAX_SAFE_INTEGER is 15.
+ nIsBig = n.e > 14;
+
+ // If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
+ if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
+
+ // The sign of the result of pow when x is negative depends on the evenness of n.
+ // If +n overflows to ±Infinity, the evenness of n would be not be known.
+ y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
+ return m ? y.mod(m) : y;
+ }
+
+ nIsNeg = n.s < 0;
+
+ if (m) {
+
+ // x % m returns NaN if abs(m) is zero, or m is NaN.
+ if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
+
+ isModExp = !nIsNeg && x.isInteger() && m.isInteger();
+
+ if (isModExp) x = x.mod(m);
+
+ // Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
+ // Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
+ } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
+ // [1, 240000000]
+ ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
+ // [80000000000000] [99999750000000]
+ : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
+
+ // If x is negative and n is odd, k = -0, else k = 0.
+ k = x.s < 0 && isOdd(n) ? -0 : 0;
+
+ // If x >= 1, k = ±Infinity.
+ if (x.e > -1) k = 1 / k;
+
+ // If n is negative return ±0, else return ±Infinity.
+ return new BigNumber(nIsNeg ? 1 / k : k);
+
+ } else if (POW_PRECISION) {
+
+ // Truncating each coefficient array to a length of k after each multiplication
+ // equates to truncating significant digits to POW_PRECISION + [28, 41],
+ // i.e. there will be a minimum of 28 guard digits retained.
+ k = mathceil(POW_PRECISION / LOG_BASE + 2);
+ }
+
+ if (nIsBig) {
+ half = new BigNumber(0.5);
+ if (nIsNeg) n.s = 1;
+ nIsOdd = isOdd(n);
+ } else {
+ i = Math.abs(+valueOf(n));
+ nIsOdd = i % 2;
+ }
+
+ y = new BigNumber(ONE);
+
+ // Performs 54 loop iterations for n of 9007199254740991.
+ for (; ;) {
+
+ if (nIsOdd) {
+ y = y.times(x);
+ if (!y.c) break;
+
+ if (k) {
+ if (y.c.length > k) y.c.length = k;
+ } else if (isModExp) {
+ y = y.mod(m); //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
+ }
+ }
+
+ if (i) {
+ i = mathfloor(i / 2);
+ if (i === 0) break;
+ nIsOdd = i % 2;
+ } else {
+ n = n.times(half);
+ round(n, n.e + 1, 1);
+
+ if (n.e > 14) {
+ nIsOdd = isOdd(n);
+ } else {
+ i = +valueOf(n);
+ if (i === 0) break;
+ nIsOdd = i % 2;
+ }
+ }
+
+ x = x.times(x);
+
+ if (k) {
+ if (x.c && x.c.length > k) x.c.length = k;
+ } else if (isModExp) {
+ x = x.mod(m); //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
+ }
+ }
+
+ if (isModExp) return y;
+ if (nIsNeg) y = ONE.div(y);
+
+ return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
+ * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+ *
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
+ */
+ P.integerValue = function (rm) {
+ var n = new BigNumber(this);
+ if (rm == null) rm = ROUNDING_MODE;
+ else intCheck(rm, 0, 8);
+ return round(n, n.e + 1, rm);
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
+ * otherwise return false.
+ */
+ P.isEqualTo = P.eq = function (y, b) {
+ return compare(this, new BigNumber(y, b)) === 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is a finite number, otherwise return false.
+ */
+ P.isFinite = function () {
+ return !!this.c;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
+ * otherwise return false.
+ */
+ P.isGreaterThan = P.gt = function (y, b) {
+ return compare(this, new BigNumber(y, b)) > 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is greater than or equal to the value of
+ * BigNumber(y, b), otherwise return false.
+ */
+ P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
+ return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
+
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is an integer, otherwise return false.
+ */
+ P.isInteger = function () {
+ return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
+ * otherwise return false.
+ */
+ P.isLessThan = P.lt = function (y, b) {
+ return compare(this, new BigNumber(y, b)) < 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is less than or equal to the value of
+ * BigNumber(y, b), otherwise return false.
+ */
+ P.isLessThanOrEqualTo = P.lte = function (y, b) {
+ return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is NaN, otherwise return false.
+ */
+ P.isNaN = function () {
+ return !this.s;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is negative, otherwise return false.
+ */
+ P.isNegative = function () {
+ return this.s < 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is positive, otherwise return false.
+ */
+ P.isPositive = function () {
+ return this.s > 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
+ */
+ P.isZero = function () {
+ return !!this.c && this.c[0] == 0;
+ };
+
+
+ /*
+ * n - 0 = n
+ * n - N = N
+ * n - I = -I
+ * 0 - n = -n
+ * 0 - 0 = 0
+ * 0 - N = N
+ * 0 - I = -I
+ * N - n = N
+ * N - 0 = N
+ * N - N = N
+ * N - I = N
+ * I - n = I
+ * I - 0 = I
+ * I - N = N
+ * I - I = N
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber minus the value of
+ * BigNumber(y, b).
+ */
+ P.minus = function (y, b) {
+ var i, j, t, xLTy,
+ x = this,
+ a = x.s;
+
+ y = new BigNumber(y, b);
+ b = y.s;
+
+ // Either NaN?
+ if (!a || !b) return new BigNumber(NaN);
+
+ // Signs differ?
+ if (a != b) {
+ y.s = -b;
+ return x.plus(y);
+ }
+
+ var xe = x.e / LOG_BASE,
+ ye = y.e / LOG_BASE,
+ xc = x.c,
+ yc = y.c;
+
+ if (!xe || !ye) {
+
+ // Either Infinity?
+ if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
+
+ // Either zero?
+ if (!xc[0] || !yc[0]) {
+
+ // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+ return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
+
+ // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
+ ROUNDING_MODE == 3 ? -0 : 0);
+ }
+ }
+
+ xe = bitFloor(xe);
+ ye = bitFloor(ye);
+ xc = xc.slice();
+
+ // Determine which is the bigger number.
+ if (a = xe - ye) {
+
+ if (xLTy = a < 0) {
+ a = -a;
+ t = xc;
+ } else {
+ ye = xe;
+ t = yc;
+ }
+
+ t.reverse();
+
+ // Prepend zeros to equalise exponents.
+ for (b = a; b--; t.push(0));
+ t.reverse();
+ } else {
+
+ // Exponents equal. Check digit by digit.
+ j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
+
+ for (a = b = 0; b < j; b++) {
+
+ if (xc[b] != yc[b]) {
+ xLTy = xc[b] < yc[b];
+ break;
+ }
+ }
+ }
+
+ // x < y? Point xc to the array of the bigger number.
+ if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
+
+ b = (j = yc.length) - (i = xc.length);
+
+ // Append zeros to xc if shorter.
+ // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
+ if (b > 0) for (; b--; xc[i++] = 0);
+ b = BASE - 1;
+
+ // Subtract yc from xc.
+ for (; j > a;) {
+
+ if (xc[--j] < yc[j]) {
+ for (i = j; i && !xc[--i]; xc[i] = b);
+ --xc[i];
+ xc[j] += BASE;
+ }
+
+ xc[j] -= yc[j];
+ }
+
+ // Remove leading zeros and adjust exponent accordingly.
+ for (; xc[0] == 0; xc.splice(0, 1), --ye);
+
+ // Zero?
+ if (!xc[0]) {
+
+ // Following IEEE 754 (2008) 6.3,
+ // n - n = +0 but n - n = -0 when rounding towards -Infinity.
+ y.s = ROUNDING_MODE == 3 ? -1 : 1;
+ y.c = [y.e = 0];
+ return y;
+ }
+
+ // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
+ // for finite x and y.
+ return normalise(y, xc, ye);
+ };
+
+
+ /*
+ * n % 0 = N
+ * n % N = N
+ * n % I = n
+ * 0 % n = 0
+ * -0 % n = -0
+ * 0 % 0 = N
+ * 0 % N = N
+ * 0 % I = 0
+ * N % n = N
+ * N % 0 = N
+ * N % N = N
+ * N % I = N
+ * I % n = N
+ * I % 0 = N
+ * I % N = N
+ * I % I = N
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
+ * BigNumber(y, b). The result depends on the value of MODULO_MODE.
+ */
+ P.modulo = P.mod = function (y, b) {
+ var q, s,
+ x = this;
+
+ y = new BigNumber(y, b);
+
+ // Return NaN if x is Infinity or NaN, or y is NaN or zero.
+ if (!x.c || !y.s || y.c && !y.c[0]) {
+ return new BigNumber(NaN);
+
+ // Return x if y is Infinity or x is zero.
+ } else if (!y.c || x.c && !x.c[0]) {
+ return new BigNumber(x);
+ }
+
+ if (MODULO_MODE == 9) {
+
+ // Euclidian division: q = sign(y) * floor(x / abs(y))
+ // r = x - qy where 0 <= r < abs(y)
+ s = y.s;
+ y.s = 1;
+ q = div(x, y, 0, 3);
+ y.s = s;
+ q.s *= s;
+ } else {
+ q = div(x, y, 0, MODULO_MODE);
+ }
+
+ y = x.minus(q.times(y));
+
+ // To match JavaScript %, ensure sign of zero is sign of dividend.
+ if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
+
+ return y;
+ };
+
+
+ /*
+ * n * 0 = 0
+ * n * N = N
+ * n * I = I
+ * 0 * n = 0
+ * 0 * 0 = 0
+ * 0 * N = N
+ * 0 * I = N
+ * N * n = N
+ * N * 0 = N
+ * N * N = N
+ * N * I = N
+ * I * n = I
+ * I * 0 = N
+ * I * N = N
+ * I * I = I
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber multiplied by the value
+ * of BigNumber(y, b).
+ */
+ P.multipliedBy = P.times = function (y, b) {
+ var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
+ base, sqrtBase,
+ x = this,
+ xc = x.c,
+ yc = (y = new BigNumber(y, b)).c;
+
+ // Either NaN, ±Infinity or ±0?
+ if (!xc || !yc || !xc[0] || !yc[0]) {
+
+ // Return NaN if either is NaN, or one is 0 and the other is Infinity.
+ if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
+ y.c = y.e = y.s = null;
+ } else {
+ y.s *= x.s;
+
+ // Return ±Infinity if either is ±Infinity.
+ if (!xc || !yc) {
+ y.c = y.e = null;
+
+ // Return ±0 if either is ±0.
+ } else {
+ y.c = [0];
+ y.e = 0;
+ }
+ }
+
+ return y;
+ }
+
+ e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
+ y.s *= x.s;
+ xcL = xc.length;
+ ycL = yc.length;
+
+ // Ensure xc points to longer array and xcL to its length.
+ if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
+
+ // Initialise the result array with zeros.
+ for (i = xcL + ycL, zc = []; i--; zc.push(0));
+
+ base = BASE;
+ sqrtBase = SQRT_BASE;
+
+ for (i = ycL; --i >= 0;) {
+ c = 0;
+ ylo = yc[i] % sqrtBase;
+ yhi = yc[i] / sqrtBase | 0;
+
+ for (k = xcL, j = i + k; j > i;) {
+ xlo = xc[--k] % sqrtBase;
+ xhi = xc[k] / sqrtBase | 0;
+ m = yhi * xlo + xhi * ylo;
+ xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
+ c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
+ zc[j--] = xlo % base;
+ }
+
+ zc[j] = c;
+ }
+
+ if (c) {
+ ++e;
+ } else {
+ zc.splice(0, 1);
+ }
+
+ return normalise(y, zc, e);
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the value of this BigNumber negated,
+ * i.e. multiplied by -1.
+ */
+ P.negated = function () {
+ var x = new BigNumber(this);
+ x.s = -x.s || null;
+ return x;
+ };
+
+
+ /*
+ * n + 0 = n
+ * n + N = N
+ * n + I = I
+ * 0 + n = n
+ * 0 + 0 = 0
+ * 0 + N = N
+ * 0 + I = I
+ * N + n = N
+ * N + 0 = N
+ * N + N = N
+ * N + I = N
+ * I + n = I
+ * I + 0 = I
+ * I + N = N
+ * I + I = I
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber plus the value of
+ * BigNumber(y, b).
+ */
+ P.plus = function (y, b) {
+ var t,
+ x = this,
+ a = x.s;
+
+ y = new BigNumber(y, b);
+ b = y.s;
+
+ // Either NaN?
+ if (!a || !b) return new BigNumber(NaN);
+
+ // Signs differ?
+ if (a != b) {
+ y.s = -b;
+ return x.minus(y);
+ }
+
+ var xe = x.e / LOG_BASE,
+ ye = y.e / LOG_BASE,
+ xc = x.c,
+ yc = y.c;
+
+ if (!xe || !ye) {
+
+ // Return ±Infinity if either ±Infinity.
+ if (!xc || !yc) return new BigNumber(a / 0);
+
+ // Either zero?
+ // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+ if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
+ }
+
+ xe = bitFloor(xe);
+ ye = bitFloor(ye);
+ xc = xc.slice();
+
+ // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
+ if (a = xe - ye) {
+ if (a > 0) {
+ ye = xe;
+ t = yc;
+ } else {
+ a = -a;
+ t = xc;
+ }
+
+ t.reverse();
+ for (; a--; t.push(0));
+ t.reverse();
+ }
+
+ a = xc.length;
+ b = yc.length;
+
+ // Point xc to the longer array, and b to the shorter length.
+ if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
+
+ // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
+ for (a = 0; b;) {
+ a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
+ xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
+ }
+
+ if (a) {
+ xc = [a].concat(xc);
+ ++ye;
+ }
+
+ // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+ // ye = MAX_EXP + 1 possible
+ return normalise(y, xc, ye);
+ };
+
+
+ /*
+ * If sd is undefined or null or true or false, return the number of significant digits of
+ * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+ * If sd is true include integer-part trailing zeros in the count.
+ *
+ * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
+ * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
+ * ROUNDING_MODE if rm is omitted.
+ *
+ * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
+ * boolean: whether to count integer-part trailing zeros: true or false.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+ */
+ P.precision = P.sd = function (sd, rm) {
+ var c, n, v,
+ x = this;
+
+ if (sd != null && sd !== !!sd) {
+ intCheck(sd, 1, MAX);
+ if (rm == null) rm = ROUNDING_MODE;
+ else intCheck(rm, 0, 8);
+
+ return round(new BigNumber(x), sd, rm);
+ }
+
+ if (!(c = x.c)) return null;
+ v = c.length - 1;
+ n = v * LOG_BASE + 1;
+
+ if (v = c[v]) {
+
+ // Subtract the number of trailing zeros of the last element.
+ for (; v % 10 == 0; v /= 10, n--);
+
+ // Add the number of digits of the first element.
+ for (v = c[0]; v >= 10; v /= 10, n++);
+ }
+
+ if (sd && x.e + 1 > n) n = x.e + 1;
+
+ return n;
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
+ * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
+ *
+ * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
+ */
+ P.shiftedBy = function (k) {
+ intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
+ return this.times('1e' + k);
+ };
+
+
+ /*
+ * sqrt(-n) = N
+ * sqrt(N) = N
+ * sqrt(-I) = N
+ * sqrt(I) = I
+ * sqrt(0) = 0
+ * sqrt(-0) = -0
+ *
+ * Return a new BigNumber whose value is the square root of the value of this BigNumber,
+ * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+ */
+ P.squareRoot = P.sqrt = function () {
+ var m, n, r, rep, t,
+ x = this,
+ c = x.c,
+ s = x.s,
+ e = x.e,
+ dp = DECIMAL_PLACES + 4,
+ half = new BigNumber('0.5');
+
+ // Negative/NaN/Infinity/zero?
+ if (s !== 1 || !c || !c[0]) {
+ return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
+ }
+
+ // Initial estimate.
+ s = Math.sqrt(+valueOf(x));
+
+ // Math.sqrt underflow/overflow?
+ // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+ if (s == 0 || s == 1 / 0) {
+ n = coeffToString(c);
+ if ((n.length + e) % 2 == 0) n += '0';
+ s = Math.sqrt(+n);
+ e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);
+
+ if (s == 1 / 0) {
+ n = '1e' + e;
+ } else {
+ n = s.toExponential();
+ n = n.slice(0, n.indexOf('e') + 1) + e;
+ }
+
+ r = new BigNumber(n);
+ } else {
+ r = new BigNumber(s + '');
+ }
+
+ // Check for zero.
+ // r could be zero if MIN_EXP is changed after the this value was created.
+ // This would cause a division by zero (x/t) and hence Infinity below, which would cause
+ // coeffToString to throw.
+ if (r.c[0]) {
+ e = r.e;
+ s = e + dp;
+ if (s < 3) s = 0;
+
+ // Newton-Raphson iteration.
+ for (; ;) {
+ t = r;
+ r = half.times(t.plus(div(x, t, dp, 1)));
+
+ if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
+
+ // The exponent of r may here be one less than the final result exponent,
+ // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
+ // are indexed correctly.
+ if (r.e < e) --s;
+ n = n.slice(s - 3, s + 1);
+
+ // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
+ // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
+ // iteration.
+ if (n == '9999' || !rep && n == '4999') {
+
+ // On the first iteration only, check to see if rounding up gives the
+ // exact result as the nines may infinitely repeat.
+ if (!rep) {
+ round(t, t.e + DECIMAL_PLACES + 2, 0);
+
+ if (t.times(t).eq(x)) {
+ r = t;
+ break;
+ }
+ }
+
+ dp += 4;
+ s += 4;
+ rep = 1;
+ } else {
+
+ // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
+ // result. If not, then there are further digits and m will be truthy.
+ if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
+
+ // Truncate to the first rounding digit.
+ round(r, r.e + DECIMAL_PLACES + 2, 1);
+ m = !r.times(r).eq(x);
+ }
+
+ break;
+ }
+ }
+ }
+ }
+
+ return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in exponential notation and
+ * rounded using ROUNDING_MODE to dp fixed decimal places.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.toExponential = function (dp, rm) {
+ if (dp != null) {
+ intCheck(dp, 0, MAX);
+ dp++;
+ }
+ return format(this, dp, rm, 1);
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in fixed-point notation rounding
+ * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+ *
+ * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
+ * but e.g. (-0.00001).toFixed(0) is '-0'.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.toFixed = function (dp, rm) {
+ if (dp != null) {
+ intCheck(dp, 0, MAX);
+ dp = dp + this.e + 1;
+ }
+ return format(this, dp, rm);
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in fixed-point notation rounded
+ * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
+ * of the format or FORMAT object (see BigNumber.set).
+ *
+ * The formatting object may contain some or all of the properties shown below.
+ *
+ * FORMAT = {
+ * prefix: '',
+ * groupSize: 3,
+ * secondaryGroupSize: 0,
+ * groupSeparator: ',',
+ * decimalSeparator: '.',
+ * fractionGroupSize: 0,
+ * fractionGroupSeparator: '\xA0', // non-breaking space
+ * suffix: ''
+ * };
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ * [format] {object} Formatting options. See FORMAT pbject above.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ * '[BigNumber Error] Argument not an object: {format}'
+ */
+ P.toFormat = function (dp, rm, format) {
+ var str,
+ x = this;
+
+ if (format == null) {
+ if (dp != null && rm && typeof rm == 'object') {
+ format = rm;
+ rm = null;
+ } else if (dp && typeof dp == 'object') {
+ format = dp;
+ dp = rm = null;
+ } else {
+ format = FORMAT;
+ }
+ } else if (typeof format != 'object') {
+ throw Error
+ (bignumberError + 'Argument not an object: ' + format);
+ }
+
+ str = x.toFixed(dp, rm);
+
+ if (x.c) {
+ var i,
+ arr = str.split('.'),
+ g1 = +format.groupSize,
+ g2 = +format.secondaryGroupSize,
+ groupSeparator = format.groupSeparator || '',
+ intPart = arr[0],
+ fractionPart = arr[1],
+ isNeg = x.s < 0,
+ intDigits = isNeg ? intPart.slice(1) : intPart,
+ len = intDigits.length;
+
+ if (g2) i = g1, g1 = g2, g2 = i, len -= i;
+
+ if (g1 > 0 && len > 0) {
+ i = len % g1 || g1;
+ intPart = intDigits.substr(0, i);
+ for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
+ if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
+ if (isNeg) intPart = '-' + intPart;
+ }
+
+ str = fractionPart
+ ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
+ ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
+ '$&' + (format.fractionGroupSeparator || ''))
+ : fractionPart)
+ : intPart;
+ }
+
+ return (format.prefix || '') + str + (format.suffix || '');
+ };
+
+
+ /*
+ * Return an array of two BigNumbers representing the value of this BigNumber as a simple
+ * fraction with an integer numerator and an integer denominator.
+ * The denominator will be a positive non-zero value less than or equal to the specified
+ * maximum denominator. If a maximum denominator is not specified, the denominator will be
+ * the lowest value necessary to represent the number exactly.
+ *
+ * [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
+ *
+ * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
+ */
+ P.toFraction = function (md) {
+ var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
+ x = this,
+ xc = x.c;
+
+ if (md != null) {
+ n = new BigNumber(md);
+
+ // Throw if md is less than one or is not an integer, unless it is Infinity.
+ if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
+ throw Error
+ (bignumberError + 'Argument ' +
+ (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
+ }
+ }
+
+ if (!xc) return new BigNumber(x);
+
+ d = new BigNumber(ONE);
+ n1 = d0 = new BigNumber(ONE);
+ d1 = n0 = new BigNumber(ONE);
+ s = coeffToString(xc);
+
+ // Determine initial denominator.
+ // d is a power of 10 and the minimum max denominator that specifies the value exactly.
+ e = d.e = s.length - x.e - 1;
+ d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
+ md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
+
+ exp = MAX_EXP;
+ MAX_EXP = 1 / 0;
+ n = new BigNumber(s);
+
+ // n0 = d1 = 0
+ n0.c[0] = 0;
+
+ for (; ;) {
+ q = div(n, d, 0, 1);
+ d2 = d0.plus(q.times(d1));
+ if (d2.comparedTo(md) == 1) break;
+ d0 = d1;
+ d1 = d2;
+ n1 = n0.plus(q.times(d2 = n1));
+ n0 = d2;
+ d = n.minus(q.times(d2 = d));
+ n = d2;
+ }
+
+ d2 = div(md.minus(d0), d1, 0, 1);
+ n0 = n0.plus(d2.times(n1));
+ d0 = d0.plus(d2.times(d1));
+ n0.s = n1.s = x.s;
+ e = e * 2;
+
+ // Determine which fraction is closer to x, n0/d0 or n1/d1
+ r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
+ div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
+
+ MAX_EXP = exp;
+
+ return r;
+ };
+
+
+ /*
+ * Return the value of this BigNumber converted to a number primitive.
+ */
+ P.toNumber = function () {
+ return +valueOf(this);
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber rounded to sd significant digits
+ * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
+ * necessary to represent the integer part of the value in fixed-point notation, then use
+ * exponential notation.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+ */
+ P.toPrecision = function (sd, rm) {
+ if (sd != null) intCheck(sd, 1, MAX);
+ return format(this, sd, rm, 2);
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in base b, or base 10 if b is
+ * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
+ * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
+ * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
+ * TO_EXP_NEG, return exponential notation.
+ *
+ * [b] {number} Integer, 2 to ALPHABET.length inclusive.
+ *
+ * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+ */
+ P.toString = function (b) {
+ var str,
+ n = this,
+ s = n.s,
+ e = n.e;
+
+ // Infinity or NaN?
+ if (e === null) {
+ if (s) {
+ str = 'Infinity';
+ if (s < 0) str = '-' + str;
+ } else {
+ str = 'NaN';
+ }
+ } else {
+ if (b == null) {
+ str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+ ? toExponential(coeffToString(n.c), e)
+ : toFixedPoint(coeffToString(n.c), e, '0');
+ } else if (b === 10) {
+ n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
+ str = toFixedPoint(coeffToString(n.c), n.e, '0');
+ } else {
+ intCheck(b, 2, ALPHABET.length, 'Base');
+ str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
+ }
+
+ if (s < 0 && n.c[0]) str = '-' + str;
+ }
+
+ return str;
+ };
+
+
+ /*
+ * Return as toString, but do not accept a base argument, and include the minus sign for
+ * negative zero.
+ */
+ P.valueOf = P.toJSON = function () {
+ return valueOf(this);
+ };
+
+
+ P._isBigNumber = true;
+
+ P[Symbol.toStringTag] = 'BigNumber';
+
+ // Node.js v10.12.0+
+ P[Symbol.for('nodejs.util.inspect.custom')] = P.valueOf;
+
+ if (configObject != null) BigNumber.set(configObject);
+
+ return BigNumber;
+}
+
+
+// PRIVATE HELPER FUNCTIONS
+
+// These functions don't need access to variables,
+// e.g. DECIMAL_PLACES, in the scope of the `clone` function above.
+
+
+function bitFloor(n) {
+ var i = n | 0;
+ return n > 0 || n === i ? i : i - 1;
+}
+
+
+// Return a coefficient array as a string of base 10 digits.
+function coeffToString(a) {
+ var s, z,
+ i = 1,
+ j = a.length,
+ r = a[0] + '';
+
+ for (; i < j;) {
+ s = a[i++] + '';
+ z = LOG_BASE - s.length;
+ for (; z--; s = '0' + s);
+ r += s;
+ }
+
+ // Determine trailing zeros.
+ for (j = r.length; r.charCodeAt(--j) === 48;);
+
+ return r.slice(0, j + 1 || 1);
+}
+
+
+// Compare the value of BigNumbers x and y.
+function compare(x, y) {
+ var a, b,
+ xc = x.c,
+ yc = y.c,
+ i = x.s,
+ j = y.s,
+ k = x.e,
+ l = y.e;
+
+ // Either NaN?
+ if (!i || !j) return null;
+
+ a = xc && !xc[0];
+ b = yc && !yc[0];
+
+ // Either zero?
+ if (a || b) return a ? b ? 0 : -j : i;
+
+ // Signs differ?
+ if (i != j) return i;
+
+ a = i < 0;
+ b = k == l;
+
+ // Either Infinity?
+ if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
+
+ // Compare exponents.
+ if (!b) return k > l ^ a ? 1 : -1;
+
+ j = (k = xc.length) < (l = yc.length) ? k : l;
+
+ // Compare digit by digit.
+ for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
+
+ // Compare lengths.
+ return k == l ? 0 : k > l ^ a ? 1 : -1;
+}
+
+
+/*
+ * Check that n is a primitive number, an integer, and in range, otherwise throw.
+ */
+function intCheck(n, min, max, name) {
+ if (n < min || n > max || n !== mathfloor(n)) {
+ throw Error
+ (bignumberError + (name || 'Argument') + (typeof n == 'number'
+ ? n < min || n > max ? ' out of range: ' : ' not an integer: '
+ : ' not a primitive number: ') + String(n));
+ }
+}
+
+
+// Assumes finite n.
+function isOdd(n) {
+ var k = n.c.length - 1;
+ return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
+}
+
+
+function toExponential(str, e) {
+ return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
+ (e < 0 ? 'e' : 'e+') + e;
+}
+
+
+function toFixedPoint(str, e, z) {
+ var len, zs;
+
+ // Negative exponent?
+ if (e < 0) {
+
+ // Prepend zeros.
+ for (zs = z + '.'; ++e; zs += z);
+ str = zs + str;
+
+ // Positive exponent
+ } else {
+ len = str.length;
+
+ // Append zeros.
+ if (++e > len) {
+ for (zs = z, e -= len; --e; zs += z);
+ str += zs;
+ } else if (e < len) {
+ str = str.slice(0, e) + '.' + str.slice(e);
+ }
+ }
+
+ return str;
+}
+
+
+// EXPORT
+
+
+export var BigNumber = clone();
+
+export default BigNumber;
diff --git a/node_modules/bignumber.js/doc/API.html b/node_modules/bignumber.js/doc/API.html
index 424a914..1ed4a87 100644
--- a/node_modules/bignumber.js/doc/API.html
+++ b/node_modules/bignumber.js/doc/API.html
@@ -1,2237 +1,2237 @@
-
-
-
-
-
-
-bignumber.js API
-
-
-
-
-
-
-
-
-
bignumber.js
-
-
A JavaScript library for arbitrary-precision arithmetic.
-
Hosted on GitHub.
-
-
API
-
-
- See the README on GitHub for a
- quick-start introduction.
-
-
- In all examples below, var and semicolons are not shown, and if a commented-out
- value is in quotes it means toString has been called on the preceding expression.
-
-
-
-
CONSTRUCTOR
-
-
-
- BigNumberBigNumber(n [, base]) ⇒ BigNumber
-
-
- n: number|string|BigNumber
- base: number: integer, 2 to 36 inclusive. (See
- ALPHABET to extend this range).
-
-
- Returns a new instance of a BigNumber object with value n, where n
- is a numeric value in the specified base, or base 10 if
- base is omitted or is null or undefined.
-
-
-x = new BigNumber(123.4567) // '123.4567'
-// 'new' is optional
-y = BigNumber(x) // '123.4567'
-
- If n is a base 10 value it can be in normal (fixed-point) or
- exponential notation. Values in other bases must be in normal notation. Values in any base can
- have fraction digits, i.e. digits after the decimal point.
-
-
-new BigNumber(43210) // '43210'
-new BigNumber('4.321e+4') // '43210'
-new BigNumber('-735.0918e-430') // '-7.350918e-428'
-new BigNumber('123412421.234324', 5) // '607236.557696'
-
- Signed 0, signed Infinity and NaN are supported.
-
-
-new BigNumber('-Infinity') // '-Infinity'
-new BigNumber(NaN) // 'NaN'
-new BigNumber(-0) // '0'
-new BigNumber('.5') // '0.5'
-new BigNumber('+2') // '2'
-
- String values in hexadecimal literal form, e.g. '0xff', are valid, as are
- string values with the octal and binary prefixs '0o' and '0b'.
- String values in octal literal form without the prefix will be interpreted as
- decimals, e.g. '011' is interpreted as 11, not 9.
-
-
-new BigNumber(-10110100.1, 2) // '-180.5'
-new BigNumber('-0b10110100.1') // '-180.5'
-new BigNumber('ff.8', 16) // '255.5'
-new BigNumber('0xff.8') // '255.5'
-
- If a base is specified, n is rounded according to the current
- DECIMAL_PLACES and
- ROUNDING_MODE settings. This includes base
- 10 so don't include a base parameter for decimal values unless
- this behaviour is wanted.
-
-
BigNumber.config({ DECIMAL_PLACES: 5 })
-new BigNumber(1.23456789) // '1.23456789'
-new BigNumber(1.23456789, 10) // '1.23457'
-
An error is thrown if base is invalid. See Errors.
-
- There is no limit to the number of digits of a value of type string (other than
- that of JavaScript's maximum array size). See RANGE to set
- the maximum and minimum possible exponent value of a BigNumber.
-
-
-new BigNumber('5032485723458348569331745.33434346346912144534543')
-new BigNumber('4.321e10000000')
-
BigNumber NaN is returned if n is invalid
- (unless BigNumber.DEBUG is true, see below).
-
-new BigNumber('.1*') // 'NaN'
-new BigNumber('blurgh') // 'NaN'
-new BigNumber(9, 2) // 'NaN'
-
- To aid in debugging, if BigNumber.DEBUG is true then an error will
- be thrown on an invalid n. An error will also be thrown if n is of
- type number with more than 15 significant digits, as calling
- toString or valueOf on
- these numbers may not result in the intended value.
-
-
-console.log(823456789123456.3) // 823456789123456.2
-new BigNumber(823456789123456.3) // '823456789123456.2'
-BigNumber.DEBUG = true
-// '[BigNumber Error] Number primitive has more than 15 significant digits'
-new BigNumber(823456789123456.3)
-// '[BigNumber Error] Not a base 2 number'
-new BigNumber(9, 2)
-
- A BigNumber can also be created from an object literal.
- Use isBigNumber to check that it is well-formed.
-
-
new BigNumber({ s: 1, e: 2, c: [ 777, 12300000000000 ], _isBigNumber: true }) // '777.123'
-
-
-
-
-
Methods
-
The static methods of a BigNumber constructor.
-
-
-
-
-
clone
- .clone([object]) ⇒ BigNumber constructor
-
-
object: object
-
- Returns a new independent BigNumber constructor with configuration as described by
- object (see config), or with the default
- configuration if object is null or undefined.
-
-
- Throws if object is not an object. See Errors.
-
-
BigNumber.config({ DECIMAL_PLACES: 5 })
-BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
-
-x = new BigNumber(1)
-y = new BN(1)
-
-x.div(3) // 0.33333
-y.div(3) // 0.333333333
-
-// BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
-BN = BigNumber.clone()
-BN.config({ DECIMAL_PLACES: 9 })
-
-
-
-
configset([object]) ⇒ object
-
- object: object: an object that contains some or all of the following
- properties.
-
-
Configures the settings for this particular BigNumber constructor.
-
-
- DECIMAL_PLACES-
- number: integer,
0 to 1e+9 inclusive
- Default value: 20
-
- -
- The maximum number of decimal places of the results of operations involving
- division, i.e. division, square root and base conversion operations, and power
- operations with negative exponents.
-
- -
-
BigNumber.config({ DECIMAL_PLACES: 5 })
-BigNumber.set({ DECIMAL_PLACES: 5 }) // equivalent
-
-
-
-
- ROUNDING_MODE-
- number: integer,
0 to 8 inclusive
- Default value: 4 (ROUND_HALF_UP)
-
- -
- The rounding mode used in the above operations and the default rounding mode of
-
decimalPlaces,
- precision,
- toExponential,
- toFixed,
- toFormat and
- toPrecision.
-
- - The modes are available as enumerated properties of the BigNumber constructor.
- -
-
BigNumber.config({ ROUNDING_MODE: 0 })
-BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP }) // equivalent
-
-
-
-
- EXPONENTIAL_AT-
- number: integer, magnitude
0 to 1e+9 inclusive, or
-
- number[]: [ integer -1e+9 to 0 inclusive, integer
- 0 to 1e+9 inclusive ]
- Default value: [-7, 20]
-
- -
- The exponent value(s) at which
toString returns exponential notation.
-
- -
- If a single number is assigned, the value is the exponent magnitude.
- If an array of two numbers is assigned then the first number is the negative exponent
- value at and beneath which exponential notation is used, and the second number is the
- positive exponent value at and above which the same.
-
- -
- For example, to emulate JavaScript numbers in terms of the exponent values at which they
- begin to use exponential notation, use
[-7, 20].
-
- -
-
BigNumber.config({ EXPONENTIAL_AT: 2 })
-new BigNumber(12.3) // '12.3' e is only 1
-new BigNumber(123) // '1.23e+2'
-new BigNumber(0.123) // '0.123' e is only -1
-new BigNumber(0.0123) // '1.23e-2'
-
-BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
-new BigNumber(123456789) // '123456789' e is only 8
-new BigNumber(0.000000123) // '1.23e-7'
-
-// Almost never return exponential notation:
-BigNumber.config({ EXPONENTIAL_AT: 1e+9 })
-
-// Always return exponential notation:
-BigNumber.config({ EXPONENTIAL_AT: 0 })
-
- -
- Regardless of the value of
EXPONENTIAL_AT, the toFixed method
- will always return a value in normal notation and the toExponential method
- will always return a value in exponential form.
-
- -
- Calling
toString with a base argument, e.g. toString(10), will
- also always return normal notation.
-
-
-
-
- RANGE-
- number: integer, magnitude
1 to 1e+9 inclusive, or
-
- number[]: [ integer -1e+9 to -1 inclusive, integer
- 1 to 1e+9 inclusive ]
- Default value: [-1e+9, 1e+9]
-
- -
- The exponent value(s) beyond which overflow to
Infinity and underflow to
- zero occurs.
-
- -
- If a single number is assigned, it is the maximum exponent magnitude: values wth a
- positive exponent of greater magnitude become
Infinity and those with a
- negative exponent of greater magnitude become zero.
- -
- If an array of two numbers is assigned then the first number is the negative exponent
- limit and the second number is the positive exponent limit.
-
- -
- For example, to emulate JavaScript numbers in terms of the exponent values at which they
- become zero and
Infinity, use [-324, 308].
-
- -
-
BigNumber.config({ RANGE: 500 })
-BigNumber.config().RANGE // [ -500, 500 ]
-new BigNumber('9.999e499') // '9.999e+499'
-new BigNumber('1e500') // 'Infinity'
-new BigNumber('1e-499') // '1e-499'
-new BigNumber('1e-500') // '0'
-
-BigNumber.config({ RANGE: [-3, 4] })
-new BigNumber(99999) // '99999' e is only 4
-new BigNumber(100000) // 'Infinity' e is 5
-new BigNumber(0.001) // '0.01' e is only -3
-new BigNumber(0.0001) // '0' e is -4
-
- -
- The largest possible magnitude of a finite BigNumber is
-
9.999...e+1000000000.
- The smallest possible magnitude of a non-zero BigNumber is 1e-1000000000.
-
-
-
-
- CRYPTO-
- boolean:
true or false.
- Default value: false
-
- -
- The value that determines whether cryptographically-secure pseudo-random number
- generation is used.
-
- -
- If
CRYPTO is set to true then the
- random method will generate random digits using
- crypto.getRandomValues in browsers that support it, or
- crypto.randomBytes if using Node.js.
-
- -
- If neither function is supported by the host environment then attempting to set
-
CRYPTO to true will fail and an exception will be thrown.
-
- -
- If
CRYPTO is false then the source of randomness used will be
- Math.random (which is assumed to generate at least 30 bits of
- randomness).
-
- - See
random.
- -
-
-// Node.js
-global.crypto = require('crypto')
-
-BigNumber.config({ CRYPTO: true })
-BigNumber.config().CRYPTO // true
-BigNumber.random() // 0.54340758610486147524
-
-
-
-
- MODULO_MODE-
- number: integer,
0 to 9 inclusive
- Default value: 1 (ROUND_DOWN)
-
- - The modulo mode used when calculating the modulus:
a mod n.
- -
- The quotient,
q = a / n, is calculated according to the
- ROUNDING_MODE that corresponds to the chosen
- MODULO_MODE.
-
- - The remainder,
r, is calculated as: r = a - n * q.
- -
- The modes that are most commonly used for the modulus/remainder operation are shown in
- the following table. Although the other rounding modes can be used, they may not give
- useful results.
-
- -
-
- | Property | Value | Description |
|---|
-
- | ROUND_UP | 0 |
-
- The remainder is positive if the dividend is negative, otherwise it is negative.
- |
-
-
- | ROUND_DOWN | 1 |
-
- The remainder has the same sign as the dividend.
- This uses 'truncating division' and matches the behaviour of JavaScript's
- remainder operator %.
- |
-
-
- | ROUND_FLOOR | 3 |
-
- The remainder has the same sign as the divisor.
- This matches Python's % operator.
- |
-
-
- | ROUND_HALF_EVEN | 6 |
- The IEEE 754 remainder function. |
-
-
- | EUCLID | 9 |
-
- The remainder is always positive. Euclidian division:
- q = sign(n) * floor(a / abs(n))
- |
-
-
-
- -
- The rounding/modulo modes are available as enumerated properties of the BigNumber
- constructor.
-
- - See
modulo.
- -
-
BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
-BigNumber.config({ MODULO_MODE: 9 }) // equivalent
-
-
-
-
- POW_PRECISION-
- number: integer,
0 to 1e+9 inclusive.
- Default value: 0
-
- -
- The maximum precision, i.e. number of significant digits, of the result of the power
- operation (unless a modulus is specified).
-
- - If set to
0, the number of significant digits will not be limited.
- - See
exponentiatedBy.
- BigNumber.config({ POW_PRECISION: 100 })FORMAT- object
- -
- The
FORMAT object configures the format of the string returned by the
- toFormat method.
-
- -
- The example below shows the properties of the
FORMAT object that are
- recognised, and their default values.
-
- -
- Unlike the other configuration properties, the values of the properties of the
-
FORMAT object will not be checked for validity. The existing
- FORMAT object will simply be replaced by the object that is passed in.
- The object can include any number of the properties shown below.
-
- - See
toFormat for examples of usage.
- -
-
-BigNumber.config({
- FORMAT: {
- // string to prepend
- prefix: '',
- // decimal separator
- decimalSeparator: '.',
- // grouping separator of the integer part
- groupSeparator: ',',
- // primary grouping size of the integer part
- groupSize: 3,
- // secondary grouping size of the integer part
- secondaryGroupSize: 0,
- // grouping separator of the fraction part
- fractionGroupSeparator: ' ',
- // grouping size of the fraction part
- fractionGroupSize: 0,
- // string to append
- suffix: ''
- }
-});
-
-
-
-
- ALPHABET-
- string
- Default value: '0123456789abcdefghijklmnopqrstuvwxyz'
-
- -
- The alphabet used for base conversion. The length of the alphabet corresponds to the
- maximum value of the base argument that can be passed to the
-
BigNumber constructor or
- toString.
-
- -
- There is no maximum length for the alphabet, but it must be at least 2 characters long, and
- it must not contain whitespace or a repeated character, or the sign indicators
-
'+' and '-', or the decimal separator '.'.
-
- -
-
// duodecimal (base 12)
-BigNumber.config({ ALPHABET: '0123456789TE' })
-x = new BigNumber('T', 12)
-x.toString() // '10'
-x.toString(12) // 'T'
-
-
-
-
-
-
-
Returns an object with the above properties and their current values.
-
- Throws if object is not an object, or if an invalid value is assigned to
- one or more of the above properties. See Errors.
-
-
-BigNumber.config({
- DECIMAL_PLACES: 40,
- ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
- EXPONENTIAL_AT: [-10, 20],
- RANGE: [-500, 500],
- CRYPTO: true,
- MODULO_MODE: BigNumber.ROUND_FLOOR,
- POW_PRECISION: 80,
- FORMAT: {
- groupSize: 3,
- groupSeparator: ' ',
- decimalSeparator: ','
- },
- ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
-});
-
-obj = BigNumber.config();
-obj.DECIMAL_PLACES // 40
-obj.RANGE // [-500, 500]
-
-
-
-
- isBigNumber.isBigNumber(value) ⇒ boolean
-
-
value: any
-
- Returns true if value is a BigNumber instance, otherwise returns
- false.
-
-
x = 42
-y = new BigNumber(x)
-
-BigNumber.isBigNumber(x) // false
-y instanceof BigNumber // true
-BigNumber.isBigNumber(y) // true
-
-BN = BigNumber.clone();
-z = new BN(x)
-z instanceof BigNumber // false
-BigNumber.isBigNumber(z) // true
-
- If value is a BigNumber instance and BigNumber.DEBUG is true,
- then this method will also check if value is well-formed, and throw if it is not.
- See Errors.
-
-
- The check can be useful if creating a BigNumber from an object literal.
- See BigNumber.
-
-
-x = new BigNumber(10)
-
-// Change x.c to an illegitimate value.
-x.c = NaN
-
-BigNumber.DEBUG = false
-
-// No error.
-BigNumber.isBigNumber(x) // true
-
-BigNumber.DEBUG = true
-
-// Error.
-BigNumber.isBigNumber(x) // '[BigNumber Error] Invalid BigNumber'
-
-
-
-
maximum.max(n...) ⇒ BigNumber
-
- n: number|string|BigNumber
- See BigNumber for further parameter details.
-
-
- Returns a BigNumber whose value is the maximum of the arguments.
-
-
The return value is always exact and unrounded.
-
x = new BigNumber('3257869345.0378653')
-BigNumber.maximum(4e9, x, '123456789.9') // '4000000000'
-
-arr = [12, '13', new BigNumber(14)]
-BigNumber.max.apply(null, arr) // '14'
-
-
-
-
minimum.min(n...) ⇒ BigNumber
-
- n: number|string|BigNumber
- See BigNumber for further parameter details.
-
-
- Returns a BigNumber whose value is the minimum of the arguments.
-
-
The return value is always exact and unrounded.
-
x = new BigNumber('3257869345.0378653')
-BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9'
-
-arr = [2, new BigNumber(-14), '-15.9999', -12]
-BigNumber.min.apply(null, arr) // '-15.9999'
-
-
-
-
- random.random([dp]) ⇒ BigNumber
-
-
dp: number: integer, 0 to 1e+9 inclusive
-
- Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and
- less than 1.
-
-
- The return value will have dp decimal places (or less if trailing zeros are
- produced).
- If dp is omitted then the number of decimal places will default to the current
- DECIMAL_PLACES setting.
-
-
- Depending on the value of this BigNumber constructor's
- CRYPTO setting and the support for the
- crypto object in the host environment, the random digits of the return value are
- generated by either Math.random (fastest), crypto.getRandomValues
- (Web Cryptography API in recent browsers) or crypto.randomBytes (Node.js).
-
-
- To be able to set CRYPTO to true when using
- Node.js, the crypto object must be available globally:
-
-
global.crypto = require('crypto')
-
- If CRYPTO is true, i.e. one of the
- crypto methods is to be used, the value of a returned BigNumber should be
- cryptographically-secure and statistically indistinguishable from a random value.
-
-
- Throws if dp is invalid. See Errors.
-
-
BigNumber.config({ DECIMAL_PLACES: 10 })
-BigNumber.random() // '0.4117936847'
-BigNumber.random(20) // '0.78193327636914089009'
-
-
-
-
sum.sum(n...) ⇒ BigNumber
-
- n: number|string|BigNumber
- See BigNumber for further parameter details.
-
-
Returns a BigNumber whose value is the sum of the arguments.
-
The return value is always exact and unrounded.
-
x = new BigNumber('3257869345.0378653')
-BigNumber.sum(4e9, x, '123456789.9') // '7381326134.9378653'
-
-arr = [2, new BigNumber(14), '15.9999', 12]
-BigNumber.sum.apply(null, arr) // '43.9999'
-
-
-
-
Properties
-
- The library's enumerated rounding modes are stored as properties of the constructor.
- (They are not referenced internally by the library itself.)
-
-
- Rounding modes 0 to 6 (inclusive) are the same as those of Java's
- BigDecimal class.
-
-
-
- | Property |
- Value |
- Description |
-
-
- | ROUND_UP |
- 0 |
- Rounds away from zero |
-
-
- | ROUND_DOWN |
- 1 |
- Rounds towards zero |
-
-
- | ROUND_CEIL |
- 2 |
- Rounds towards Infinity |
-
-
- | ROUND_FLOOR |
- 3 |
- Rounds towards -Infinity |
-
-
- | ROUND_HALF_UP |
- 4 |
-
- Rounds towards nearest neighbour.
- If equidistant, rounds away from zero
- |
-
-
- | ROUND_HALF_DOWN |
- 5 |
-
- Rounds towards nearest neighbour.
- If equidistant, rounds towards zero
- |
-
-
- | ROUND_HALF_EVEN |
- 6 |
-
- Rounds towards nearest neighbour.
- If equidistant, rounds towards even neighbour
- |
-
-
- | ROUND_HALF_CEIL |
- 7 |
-
- Rounds towards nearest neighbour.
- If equidistant, rounds towards Infinity
- |
-
-
- | ROUND_HALF_FLOOR |
- 8 |
-
- Rounds towards nearest neighbour.
- If equidistant, rounds towards -Infinity
- |
-
-
-
-BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL })
-BigNumber.config({ ROUNDING_MODE: 2 }) // equivalent
-
-
DEBUG
-
undefined|false|true
-
- If BigNumber.DEBUG is set true then an error will be thrown
- if this BigNumber constructor receives an invalid value, such as
- a value of type number with more than 15 significant digits.
- See BigNumber.
-
-
- An error will also be thrown if the isBigNumber
- method receives a BigNumber that is not well-formed.
- See isBigNumber.
-
-
BigNumber.DEBUG = true
-
-
-
INSTANCE
-
-
-
Methods
-
The methods inherited by a BigNumber instance from its constructor's prototype object.
-
A BigNumber is immutable in the sense that it is not changed by its methods.
-
- The treatment of ±0, ±Infinity and NaN is
- consistent with how JavaScript treats these values.
-
-
Many method names have a shorter alias.
-
-
-
-
absoluteValue.abs() ⇒ BigNumber
-
- Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of
- this BigNumber.
-
-
The return value is always exact and unrounded.
-
-x = new BigNumber(-0.8)
-y = x.absoluteValue() // '0.8'
-z = y.abs() // '0.8'
-
-
-
-
- comparedTo.comparedTo(n [, base]) ⇒ number
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- | Returns | |
|---|
-
- 1 |
- If the value of this BigNumber is greater than the value of n |
-
-
- -1 |
- If the value of this BigNumber is less than the value of n |
-
-
- 0 |
- If this BigNumber and n have the same value |
-
-
- null |
- If the value of either this BigNumber or n is NaN |
-
-
-
-x = new BigNumber(Infinity)
-y = new BigNumber(5)
-x.comparedTo(y) // 1
-x.comparedTo(x.minus(1)) // 0
-y.comparedTo(NaN) // null
-y.comparedTo('110', 2) // -1
-
-
-
-
- decimalPlaces.dp([dp [, rm]]) ⇒ BigNumber|number
-
-
- dp: number: integer, 0 to 1e+9 inclusive
- rm: number: integer, 0 to 8 inclusive
-
-
- If dp is a number, returns a BigNumber whose value is the value of this BigNumber
- rounded by rounding mode rm to a maximum of dp decimal places.
-
-
- If dp is omitted, or is null or undefined, the return
- value is the number of decimal places of the value of this BigNumber, or null if
- the value of this BigNumber is ±Infinity or NaN.
-
-
- If rm is omitted, or is null or undefined,
- ROUNDING_MODE is used.
-
-
- Throws if dp or rm is invalid. See Errors.
-
-
-x = new BigNumber(1234.56)
-x.decimalPlaces(1) // '1234.6'
-x.dp() // 2
-x.decimalPlaces(2) // '1234.56'
-x.dp(10) // '1234.56'
-x.decimalPlaces(0, 1) // '1234'
-x.dp(0, 6) // '1235'
-x.decimalPlaces(1, 1) // '1234.5'
-x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
-x // '1234.56'
-y = new BigNumber('9.9e-101')
-y.dp() // 102
-
-
-
-
dividedBy.div(n [, base]) ⇒ BigNumber
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns a BigNumber whose value is the value of this BigNumber divided by
- n, rounded according to the current
- DECIMAL_PLACES and
- ROUNDING_MODE settings.
-
-
-x = new BigNumber(355)
-y = new BigNumber(113)
-x.dividedBy(y) // '3.14159292035398230088'
-x.div(5) // '71'
-x.div(47, 16) // '5'
-
-
-
-
- dividedToIntegerBy.idiv(n [, base]) ⇒
- BigNumber
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
- n.
-
-
-x = new BigNumber(5)
-y = new BigNumber(3)
-x.dividedToIntegerBy(y) // '1'
-x.idiv(0.7) // '7'
-x.idiv('0.f', 16) // '5'
-
-
-
-
- exponentiatedBy.pow(n [, m]) ⇒ BigNumber
-
-
- n: number|string|BigNumber: integer
- m: number|string|BigNumber
-
-
- Returns a BigNumber whose value is the value of this BigNumber exponentiated by
- n, i.e. raised to the power n, and optionally modulo a modulus
- m.
-
-
- Throws if n is not an integer. See Errors.
-
-
- If n is negative the result is rounded according to the current
- DECIMAL_PLACES and
- ROUNDING_MODE settings.
-
-
- As the number of digits of the result of the power operation can grow so large so quickly,
- e.g. 123.45610000 has over 50000 digits, the number of significant
- digits calculated is limited to the value of the
- POW_PRECISION setting (unless a modulus
- m is specified).
-
-
- By default POW_PRECISION is set to 0.
- This means that an unlimited number of significant digits will be calculated, and that the
- method's performance will decrease dramatically for larger exponents.
-
-
- If m is specified and the value of m, n and this
- BigNumber are integers, and n is positive, then a fast modular exponentiation
- algorithm is used, otherwise the operation will be performed as
- x.exponentiatedBy(n).modulo(m) with a
- POW_PRECISION of 0.
-
-
-Math.pow(0.7, 2) // 0.48999999999999994
-x = new BigNumber(0.7)
-x.exponentiatedBy(2) // '0.49'
-BigNumber(3).pow(-2) // '0.11111111111111111111'
-
-
-
-
- integerValue.integerValue([rm]) ⇒ BigNumber
-
-
- rm: number: integer, 0 to 8 inclusive
-
-
- Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
- rounding mode rm.
-
-
- If rm is omitted, or is null or undefined,
- ROUNDING_MODE is used.
-
-
- Throws if rm is invalid. See Errors.
-
-
-x = new BigNumber(123.456)
-x.integerValue() // '123'
-x.integerValue(BigNumber.ROUND_CEIL) // '124'
-y = new BigNumber(-12.7)
-y.integerValue() // '-13'
-y.integerValue(BigNumber.ROUND_DOWN) // '-12'
-
- The following is an example of how to add a prototype method that emulates JavaScript's
- Math.round function. Math.ceil, Math.floor and
- Math.trunc can be emulated in the same way with
- BigNumber.ROUND_CEIL, BigNumber.ROUND_FLOOR and
- BigNumber.ROUND_DOWN respectively.
-
-
-BigNumber.prototype.round = function (n) {
- return n.integerValue(BigNumber.ROUND_HALF_CEIL);
-};
-x.round() // '123'
-
-
-
-
isEqualTo.eq(n [, base]) ⇒ boolean
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns true if the value of this BigNumber is equal to the value of
- n, otherwise returns false.
- As with JavaScript, NaN does not equal NaN.
-
-
Note: This method uses the comparedTo method internally.
-
-0 === 1e-324 // true
-x = new BigNumber(0)
-x.isEqualTo('1e-324') // false
-BigNumber(-0).eq(x) // true ( -0 === 0 )
-BigNumber(255).eq('ff', 16) // true
-
-y = new BigNumber(NaN)
-y.isEqualTo(NaN) // false
-
-
-
-
isFinite.isFinite() ⇒ boolean
-
- Returns true if the value of this BigNumber is a finite number, otherwise
- returns false.
-
-
- The only possible non-finite values of a BigNumber are NaN, Infinity
- and -Infinity.
-
-
-x = new BigNumber(1)
-x.isFinite() // true
-y = new BigNumber(Infinity)
-y.isFinite() // false
-
- Note: The native method isFinite() can be used if
- n <= Number.MAX_VALUE.
-
-
-
-
-
isGreaterThan.gt(n [, base]) ⇒ boolean
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns true if the value of this BigNumber is greater than the value of
- n, otherwise returns false.
-
-
Note: This method uses the comparedTo method internally.
-
-0.1 > (0.3 - 0.2) // true
-x = new BigNumber(0.1)
-x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false
-BigNumber(0).gt(x) // false
-BigNumber(11, 3).gt(11.1, 2) // true
-
-
-
-
- isGreaterThanOrEqualTo.gte(n [, base]) ⇒ boolean
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns true if the value of this BigNumber is greater than or equal to the value
- of n, otherwise returns false.
-
-
Note: This method uses the comparedTo method internally.
-
-(0.3 - 0.2) >= 0.1 // false
-x = new BigNumber(0.3).minus(0.2)
-x.isGreaterThanOrEqualTo(0.1) // true
-BigNumber(1).gte(x) // true
-BigNumber(10, 18).gte('i', 36) // true
-
-
-
-
isInteger.isInteger() ⇒ boolean
-
- Returns true if the value of this BigNumber is an integer, otherwise returns
- false.
-
-
-x = new BigNumber(1)
-x.isInteger() // true
-y = new BigNumber(123.456)
-y.isInteger() // false
-
-
-
-
isLessThan.lt(n [, base]) ⇒ boolean
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns true if the value of this BigNumber is less than the value of
- n, otherwise returns false.
-
-
Note: This method uses the comparedTo method internally.
-
-(0.3 - 0.2) < 0.1 // true
-x = new BigNumber(0.3).minus(0.2)
-x.isLessThan(0.1) // false
-BigNumber(0).lt(x) // true
-BigNumber(11.1, 2).lt(11, 3) // true
-
-
-
-
- isLessThanOrEqualTo.lte(n [, base]) ⇒ boolean
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns true if the value of this BigNumber is less than or equal to the value of
- n, otherwise returns false.
-
-
Note: This method uses the comparedTo method internally.
-
-0.1 <= (0.3 - 0.2) // false
-x = new BigNumber(0.1)
-x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true
-BigNumber(-1).lte(x) // true
-BigNumber(10, 18).lte('i', 36) // true
-
-
-
-
isNaN.isNaN() ⇒ boolean
-
- Returns true if the value of this BigNumber is NaN, otherwise
- returns false.
-
-
-x = new BigNumber(NaN)
-x.isNaN() // true
-y = new BigNumber('Infinity')
-y.isNaN() // false
-
Note: The native method isNaN() can also be used.
-
-
-
-
isNegative.isNegative() ⇒ boolean
-
- Returns true if the sign of this BigNumber is negative, otherwise returns
- false.
-
-
-x = new BigNumber(-0)
-x.isNegative() // true
-y = new BigNumber(2)
-y.isNegative() // false
-
Note: n < 0 can be used if n <= -Number.MIN_VALUE.
-
-
-
-
isPositive.isPositive() ⇒ boolean
-
- Returns true if the sign of this BigNumber is positive, otherwise returns
- false.
-
-
-x = new BigNumber(-0)
-x.isPositive() // false
-y = new BigNumber(2)
-y.isPositive() // true
-
-
-
-
isZero.isZero() ⇒ boolean
-
- Returns true if the value of this BigNumber is zero or minus zero, otherwise
- returns false.
-
-
-x = new BigNumber(-0)
-x.isZero() && x.isNegative() // true
-y = new BigNumber(Infinity)
-y.isZero() // false
-
Note: n == 0 can be used if n >= Number.MIN_VALUE.
-
-
-
-
- minus.minus(n [, base]) ⇒ BigNumber
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
Returns a BigNumber whose value is the value of this BigNumber minus n.
-
The return value is always exact and unrounded.
-
-0.3 - 0.1 // 0.19999999999999998
-x = new BigNumber(0.3)
-x.minus(0.1) // '0.2'
-x.minus(0.6, 20) // '0'
-
-
-
-
modulo.mod(n [, base]) ⇒ BigNumber
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns a BigNumber whose value is the value of this BigNumber modulo n, i.e.
- the integer remainder of dividing this BigNumber by n.
-
-
- The value returned, and in particular its sign, is dependent on the value of the
- MODULO_MODE setting of this BigNumber constructor.
- If it is 1 (default value), the result will have the same sign as this BigNumber,
- and it will match that of Javascript's % operator (within the limits of double
- precision) and BigDecimal's remainder method.
-
-
The return value is always exact and unrounded.
-
- See MODULO_MODE for a description of the other
- modulo modes.
-
-
-1 % 0.9 // 0.09999999999999998
-x = new BigNumber(1)
-x.modulo(0.9) // '0.1'
-y = new BigNumber(33)
-y.mod('a', 33) // '3'
-
-
-
-
- multipliedBy.times(n [, base]) ⇒ BigNumber
-
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
- Returns a BigNumber whose value is the value of this BigNumber multiplied by n.
-
-
The return value is always exact and unrounded.
-
-0.6 * 3 // 1.7999999999999998
-x = new BigNumber(0.6)
-y = x.multipliedBy(3) // '1.8'
-BigNumber('7e+500').times(y) // '1.26e+501'
-x.multipliedBy('-a', 16) // '-6'
-
-
-
-
negated.negated() ⇒ BigNumber
-
- Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by
- -1.
-
-
-x = new BigNumber(1.8)
-x.negated() // '-1.8'
-y = new BigNumber(-1.3)
-y.negated() // '1.3'
-
-
-
-
plus.plus(n [, base]) ⇒ BigNumber
-
- n: number|string|BigNumber
- base: number
- See BigNumber for further parameter details.
-
-
Returns a BigNumber whose value is the value of this BigNumber plus n.
-
The return value is always exact and unrounded.
-
-0.1 + 0.2 // 0.30000000000000004
-x = new BigNumber(0.1)
-y = x.plus(0.2) // '0.3'
-BigNumber(0.7).plus(x).plus(y) // '1'
-x.plus('0.1', 8) // '0.225'
-
-
-
-
- precision.sd([d [, rm]]) ⇒ BigNumber|number
-
-
- d: number|boolean: integer, 1 to 1e+9
- inclusive, or true or false
- rm: number: integer, 0 to 8 inclusive.
-
-
- If d is a number, returns a BigNumber whose value is the value of this BigNumber
- rounded to a precision of d significant digits using rounding mode
- rm.
-
-
- If d is omitted or is null or undefined, the return
- value is the number of significant digits of the value of this BigNumber, or null
- if the value of this BigNumber is ±Infinity or NaN.
-
-
- If d is true then any trailing zeros of the integer
- part of a number are counted as significant digits, otherwise they are not.
-
-
- If rm is omitted or is null or undefined,
- ROUNDING_MODE will be used.
-
-
- Throws if d or rm is invalid. See Errors.
-
-
-x = new BigNumber(9876.54321)
-x.precision(6) // '9876.54'
-x.sd() // 9
-x.precision(6, BigNumber.ROUND_UP) // '9876.55'
-x.sd(2) // '9900'
-x.precision(2, 1) // '9800'
-x // '9876.54321'
-y = new BigNumber(987000)
-y.precision() // 3
-y.sd(true) // 6
-
-
-
-
shiftedBy.shiftedBy(n) ⇒ BigNumber
-
- n: number: integer,
- -9007199254740991 to 9007199254740991 inclusive
-
-
- Returns a BigNumber whose value is the value of this BigNumber shifted by n
- places.
-
- The shift is of the decimal point, i.e. of powers of ten, and is to the left if n
- is negative or to the right if n is positive.
-
-
The return value is always exact and unrounded.
-
- Throws if n is invalid. See Errors.
-
-
-x = new BigNumber(1.23)
-x.shiftedBy(3) // '1230'
-x.shiftedBy(-3) // '0.00123'
-
-
-
-
squareRoot.sqrt() ⇒ BigNumber
-
- Returns a BigNumber whose value is the square root of the value of this BigNumber,
- rounded according to the current
- DECIMAL_PLACES and
- ROUNDING_MODE settings.
-
-
- The return value will be correctly rounded, i.e. rounded as if the result was first calculated
- to an infinite number of correct digits before rounding.
-
-
-x = new BigNumber(16)
-x.squareRoot() // '4'
-y = new BigNumber(3)
-y.sqrt() // '1.73205080756887729353'
-
-
-
-
- toExponential.toExponential([dp [, rm]]) ⇒ string
-
-
- dp: number: integer, 0 to 1e+9 inclusive
- rm: number: integer, 0 to 8 inclusive
-
-
- Returns a string representing the value of this BigNumber in exponential notation rounded
- using rounding mode rm to dp decimal places, i.e with one digit
- before the decimal point and dp digits after it.
-
-
- If the value of this BigNumber in exponential notation has fewer than dp fraction
- digits, the return value will be appended with zeros accordingly.
-
-
- If dp is omitted, or is null or undefined, the number
- of digits after the decimal point defaults to the minimum number of digits necessary to
- represent the value exactly.
- If rm is omitted or is null or undefined,
- ROUNDING_MODE is used.
-
-
- Throws if dp or rm is invalid. See Errors.
-
-
-x = 45.6
-y = new BigNumber(x)
-x.toExponential() // '4.56e+1'
-y.toExponential() // '4.56e+1'
-x.toExponential(0) // '5e+1'
-y.toExponential(0) // '5e+1'
-x.toExponential(1) // '4.6e+1'
-y.toExponential(1) // '4.6e+1'
-y.toExponential(1, 1) // '4.5e+1' (ROUND_DOWN)
-x.toExponential(3) // '4.560e+1'
-y.toExponential(3) // '4.560e+1'
-
-
-
-
- toFixed.toFixed([dp [, rm]]) ⇒ string
-
-
- dp: number: integer, 0 to 1e+9 inclusive
- rm: number: integer, 0 to 8 inclusive
-
-
- Returns a string representing the value of this BigNumber in normal (fixed-point) notation
- rounded to dp decimal places using rounding mode rm.
-
-
- If the value of this BigNumber in normal notation has fewer than dp fraction
- digits, the return value will be appended with zeros accordingly.
-
-
- Unlike Number.prototype.toFixed, which returns exponential notation if a number
- is greater or equal to 1021, this method will always return normal
- notation.
-
-
- If dp is omitted or is null or undefined, the return
- value will be unrounded and in normal notation. This is also unlike
- Number.prototype.toFixed, which returns the value to zero decimal places.
- It is useful when fixed-point notation is required and the current
- EXPONENTIAL_AT setting causes
- toString to return exponential notation.
- If rm is omitted or is null or undefined,
- ROUNDING_MODE is used.
-
-
- Throws if dp or rm is invalid. See Errors.
-
-
-x = 3.456
-y = new BigNumber(x)
-x.toFixed() // '3'
-y.toFixed() // '3.456'
-y.toFixed(0) // '3'
-x.toFixed(2) // '3.46'
-y.toFixed(2) // '3.46'
-y.toFixed(2, 1) // '3.45' (ROUND_DOWN)
-x.toFixed(5) // '3.45600'
-y.toFixed(5) // '3.45600'
-
-
-
-
- toFormat.toFormat([dp [, rm[, format]]]) ⇒ string
-
-
- dp: number: integer, 0 to 1e+9 inclusive
- rm: number: integer, 0 to 8 inclusive
- format: object: see FORMAT
-
-
-
- Returns a string representing the value of this BigNumber in normal (fixed-point) notation
- rounded to dp decimal places using rounding mode rm, and formatted
- according to the properties of the format object.
-
-
- See FORMAT and the examples below for the properties of the
- format object, their types, and their usage. A formatting object may contain
- some or all of the recognised properties.
-
-
- If dp is omitted or is null or undefined, then the
- return value is not rounded to a fixed number of decimal places.
- If rm is omitted or is null or undefined,
- ROUNDING_MODE is used.
- If format is omitted or is null or undefined, the
- FORMAT object is used.
-
-
- Throws if dp, rm or format is invalid. See
- Errors.
-
-
-fmt = {
- prefix = '',
- decimalSeparator: '.',
- groupSeparator: ',',
- groupSize: 3,
- secondaryGroupSize: 0,
- fractionGroupSeparator: ' ',
- fractionGroupSize: 0,
- suffix = ''
-}
-
-x = new BigNumber('123456789.123456789')
-
-// Set the global formatting options
-BigNumber.config({ FORMAT: fmt })
-
-x.toFormat() // '123,456,789.123456789'
-x.toFormat(3) // '123,456,789.123'
-
-// If a reference to the object assigned to FORMAT has been retained,
-// the format properties can be changed directly
-fmt.groupSeparator = ' '
-fmt.fractionGroupSize = 5
-x.toFormat() // '123 456 789.12345 6789'
-
-// Alternatively, pass the formatting options as an argument
-fmt = {
- prefix: '=> ',
- decimalSeparator: ',',
- groupSeparator: '.',
- groupSize: 3,
- secondaryGroupSize: 2
-}
-
-x.toFormat() // '123 456 789.12345 6789'
-x.toFormat(fmt) // '=> 12.34.56.789,123456789'
-x.toFormat(2, fmt) // '=> 12.34.56.789,12'
-x.toFormat(3, BigNumber.ROUND_UP, fmt) // '=> 12.34.56.789,124'
-
-
-
-
- toFraction.toFraction([maximum_denominator])
- ⇒ [BigNumber, BigNumber]
-
-
- maximum_denominator:
- number|string|BigNumber: integer >= 1 and <=
- Infinity
-
-
- Returns 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 maximum_denominator.
-
-
- If a maximum_denominator is not specified, or is null or
- undefined, the denominator will be the lowest value necessary to represent the
- number exactly.
-
-
- Throws if maximum_denominator is invalid. See Errors.
-
-
-x = new BigNumber(1.75)
-x.toFraction() // '7, 4'
-
-pi = new BigNumber('3.14159265358')
-pi.toFraction() // '157079632679,50000000000'
-pi.toFraction(100000) // '312689, 99532'
-pi.toFraction(10000) // '355, 113'
-pi.toFraction(100) // '311, 99'
-pi.toFraction(10) // '22, 7'
-pi.toFraction(1) // '3, 1'
-
-
-
-
toJSON.toJSON() ⇒ string
-
As valueOf.
-
-x = new BigNumber('177.7e+457')
-y = new BigNumber(235.4325)
-z = new BigNumber('0.0098074')
-
-// Serialize an array of three BigNumbers
-str = JSON.stringify( [x, y, z] )
-// "["1.777e+459","235.4325","0.0098074"]"
-
-// Return an array of three BigNumbers
-JSON.parse(str, function (key, val) {
- return key === '' ? val : new BigNumber(val)
-})
-
-
-
-
toNumber.toNumber() ⇒ number
-
Returns the value of this BigNumber as a JavaScript number primitive.
-
- This method is identical to using type coercion with the unary plus operator.
-
-
-x = new BigNumber(456.789)
-x.toNumber() // 456.789
-+x // 456.789
-
-y = new BigNumber('45987349857634085409857349856430985')
-y.toNumber() // 4.598734985763409e+34
-
-z = new BigNumber(-0)
-1 / z.toNumber() // -Infinity
-1 / +z // -Infinity
-
-
-
-
- toPrecision.toPrecision([sd [, rm]]) ⇒ string
-
-
- sd: number: integer, 1 to 1e+9 inclusive
- rm: number: integer, 0 to 8 inclusive
-
-
- Returns a string representing the value of this BigNumber rounded to sd
- significant digits using rounding mode rm.
-
-
- If sd is less than the number of digits necessary to represent the integer part
- of the value in normal (fixed-point) notation, then exponential notation is used.
-
-
- If sd is omitted, or is null or undefined, then the
- return value is the same as n.toString().
- If rm is omitted or is null or undefined,
- ROUNDING_MODE is used.
-
-
- Throws if sd or rm is invalid. See Errors.
-
-
-x = 45.6
-y = new BigNumber(x)
-x.toPrecision() // '45.6'
-y.toPrecision() // '45.6'
-x.toPrecision(1) // '5e+1'
-y.toPrecision(1) // '5e+1'
-y.toPrecision(2, 0) // '4.6e+1' (ROUND_UP)
-y.toPrecision(2, 1) // '4.5e+1' (ROUND_DOWN)
-x.toPrecision(5) // '45.600'
-y.toPrecision(5) // '45.600'
-
-
-
-
toString.toString([base]) ⇒ string
-
- base: number: integer, 2 to ALPHABET.length
- inclusive (see ALPHABET).
-
-
- Returns a string representing the value of this BigNumber in the specified base, or base
- 10 if base is omitted or is null or
- undefined.
-
-
- For bases above 10, and using the default base conversion alphabet
- (see ALPHABET), values from 10 to
- 35 are represented by a-z
- (as with Number.prototype.toString).
-
-
- If a base is specified the value is rounded according to the current
- DECIMAL_PLACES
- and ROUNDING_MODE settings.
-
-
- If a base is not specified, and this BigNumber has a positive
- exponent that is equal to or greater than the positive component of the
- current EXPONENTIAL_AT setting,
- or a negative exponent equal to or less than the negative component of the
- setting, then exponential notation is returned.
-
-
If base is null or undefined it is ignored.
-
- Throws if base is invalid. See Errors.
-
-
-x = new BigNumber(750000)
-x.toString() // '750000'
-BigNumber.config({ EXPONENTIAL_AT: 5 })
-x.toString() // '7.5e+5'
-
-y = new BigNumber(362.875)
-y.toString(2) // '101101010.111'
-y.toString(9) // '442.77777777777777777778'
-y.toString(32) // 'ba.s'
-
-BigNumber.config({ DECIMAL_PLACES: 4 });
-z = new BigNumber('1.23456789')
-z.toString() // '1.23456789'
-z.toString(10) // '1.2346'
-
-
-
-
valueOf.valueOf() ⇒ string
-
- As toString, but does not accept a base argument and includes
- the minus sign for negative zero.
-
-
-x = new BigNumber('-0')
-x.toString() // '0'
-x.valueOf() // '-0'
-y = new BigNumber('1.777e+457')
-y.valueOf() // '1.777e+457'
-
-
-
-
Properties
-
The properties of a BigNumber instance:
-
-
- | Property |
- Description |
- Type |
- Value |
-
-
- | c |
- coefficient* |
- number[] |
- Array of base 1e14 numbers |
-
-
- | e |
- exponent |
- number |
- Integer, -1000000000 to 1000000000 inclusive |
-
-
- | s |
- sign |
- number |
- -1 or 1 |
-
-
-
*significand
-
- The value of any of the c, e and s properties may also
- be null.
-
-
- The above properties are best considered to be read-only. In early versions of this library it
- was okay to change the exponent of a BigNumber by writing to its exponent property directly,
- but this is no longer reliable as the value of the first element of the coefficient array is
- now dependent on the exponent.
-
-
- Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are
- not necessarily preserved.
-
-
x = new BigNumber(0.123) // '0.123'
-x.toExponential() // '1.23e-1'
-x.c // '1,2,3'
-x.e // -1
-x.s // 1
-
-y = new Number(-123.4567000e+2) // '-12345.67'
-y.toExponential() // '-1.234567e+4'
-z = new BigNumber('-123.4567000e+2') // '-12345.67'
-z.toExponential() // '-1.234567e+4'
-z.c // '1,2,3,4,5,6,7'
-z.e // 4
-z.s // -1
-
-
-
-
Zero, NaN and Infinity
-
- The table below shows how ±0, NaN and
- ±Infinity are stored.
-
-
-
- | |
- c |
- e |
- s |
-
-
- | ±0 |
- [0] |
- 0 |
- ±1 |
-
-
- | NaN |
- null |
- null |
- null |
-
-
- | ±Infinity |
- null |
- null |
- ±1 |
-
-
-
-x = new Number(-0) // 0
-1 / x == -Infinity // true
-
-y = new BigNumber(-0) // '0'
-y.c // '0' ( [0].toString() )
-y.e // 0
-y.s // -1
-
-
-
-
Errors
-
The table below shows the errors that are thrown.
-
- The errors are generic Error objects whose message begins
- '[BigNumber Error]'.
-
-
-
- | Method |
- Throws |
-
-
-
- BigNumber
- comparedTo
- dividedBy
- dividedToIntegerBy
- isEqualTo
- isGreaterThan
- isGreaterThanOrEqualTo
- isLessThan
- isLessThanOrEqualTo
- minus
- modulo
- plus
- multipliedBy
- |
- Base not a primitive number |
-
-
- | Base not an integer |
-
-
- | Base out of range |
-
-
- | Number primitive has more than 15 significant digits* |
-
-
- | Not a base... number* |
-
-
- | Not a number* |
-
-
- clone |
- Object expected |
-
-
- config |
- Object expected |
-
-
- DECIMAL_PLACES not a primitive number |
-
-
- DECIMAL_PLACES not an integer |
-
-
- DECIMAL_PLACES out of range |
-
-
- ROUNDING_MODE not a primitive number |
-
-
- ROUNDING_MODE not an integer |
-
-
- ROUNDING_MODE out of range |
-
-
- EXPONENTIAL_AT not a primitive number |
-
-
- EXPONENTIAL_AT not an integer |
-
-
- EXPONENTIAL_AT out of range |
-
-
- RANGE not a primitive number |
-
-
- RANGE not an integer |
-
-
- RANGE cannot be zero |
-
-
- RANGE cannot be zero |
-
-
- CRYPTO not true or false |
-
-
- crypto unavailable |
-
-
- MODULO_MODE not a primitive number |
-
-
- MODULO_MODE not an integer |
-
-
- MODULO_MODE out of range |
-
-
- POW_PRECISION not a primitive number |
-
-
- POW_PRECISION not an integer |
-
-
- POW_PRECISION out of range |
-
-
- FORMAT not an object |
-
-
- ALPHABET invalid |
-
-
-
- decimalPlaces
- precision
- random
- shiftedBy
- toExponential
- toFixed
- toFormat
- toPrecision
- |
- Argument not a primitive number |
-
-
- | Argument not an integer |
-
-
- | Argument out of range |
-
-
-
- decimalPlaces
- precision
- |
- Argument not true or false |
-
-
- exponentiatedBy |
- Argument not an integer |
-
-
- isBigNumber |
- Invalid BigNumber* |
-
-
-
- minimum
- maximum
- |
- Not a number* |
-
-
-
- random
- |
- crypto unavailable |
-
-
-
- toFormat
- |
- Argument not an object |
-
-
- toFraction |
- Argument not an integer |
-
-
- | Argument out of range |
-
-
- toString |
- Base not a primitive number |
-
-
- | Base not an integer |
-
-
- | Base out of range |
-
-
-
*Only thrown if BigNumber.DEBUG is true.
-
To determine if an exception is a BigNumber Error:
-
-try {
- // ...
-} catch (e) {
- if (e instanceof Error && e.message.indexOf('[BigNumber Error]') === 0) {
- // ...
- }
-}
-
-
-
-
Type coercion
-
- To prevent the accidental use of a BigNumber in primitive number operations, or the
- accidental addition of a BigNumber to a string, the valueOf method can be safely
- overwritten as shown below.
-
-
- The valueOf method is the same as the
- toJSON method, and both are the same as the
- toString method except they do not take a base
- argument and they include the minus sign for negative zero.
-
-
-BigNumber.prototype.valueOf = function () {
- throw Error('valueOf called!')
-}
-
-x = new BigNumber(1)
-x / 2 // '[BigNumber Error] valueOf called!'
-x + 'abc' // '[BigNumber Error] valueOf called!'
-
-
-
-
-
FAQ
-
-
Why are trailing fractional zeros removed from BigNumbers?
-
- Some arbitrary-precision libraries retain trailing fractional zeros as they can indicate the
- precision of a value. This can be useful but the results of arithmetic operations can be
- misleading.
-
-
-x = new BigDecimal("1.0")
-y = new BigDecimal("1.1000")
-z = x.add(y) // 2.1000
-
-x = new BigDecimal("1.20")
-y = new BigDecimal("3.45000")
-z = x.multiply(y) // 4.1400000
-
- To specify the precision of a value is to specify that the value lies
- within a certain range.
-
-
- In the first example, x has a value of 1.0. The trailing zero shows
- the precision of the value, implying that it is in the range 0.95 to
- 1.05. Similarly, the precision indicated by the trailing zeros of y
- indicates that the value is in the range 1.09995 to 1.10005.
-
-
- If we add the two lowest values in the ranges we have, 0.95 + 1.09995 = 2.04995,
- and if we add the two highest values we have, 1.05 + 1.10005 = 2.15005, so the
- range of the result of the addition implied by the precision of its operands is
- 2.04995 to 2.15005.
-
-
- The result given by BigDecimal of 2.1000 however, indicates that the value is in
- the range 2.09995 to 2.10005 and therefore the precision implied by
- its trailing zeros may be misleading.
-
-
- In the second example, the true range is 4.122744 to 4.157256 yet
- the BigDecimal answer of 4.1400000 indicates a range of 4.13999995
- to 4.14000005. Again, the precision implied by the trailing zeros may be
- misleading.
-
-
- This library, like binary floating point and most calculators, does not retain trailing
- fractional zeros. Instead, the toExponential, toFixed and
- toPrecision methods enable trailing zeros to be added if and when required.
-
-
+
+
bignumber.js
+
+
A JavaScript library for arbitrary-precision arithmetic.
+
Hosted on GitHub.
+
+
API
+
+
+ See the README on GitHub for a
+ quick-start introduction.
+
+
+ In all examples below, var and semicolons are not shown, and if a commented-out
+ value is in quotes it means toString has been called on the preceding expression.
+
+
+
+
CONSTRUCTOR
+
+
+
+ BigNumberBigNumber(n [, base]) ⇒ BigNumber
+
+
+ n: number|string|BigNumber
+ base: number: integer, 2 to 36 inclusive. (See
+ ALPHABET to extend this range).
+
+
+ Returns a new instance of a BigNumber object with value n, where n
+ is a numeric value in the specified base, or base 10 if
+ base is omitted or is null or undefined.
+
+
+x = new BigNumber(123.4567) // '123.4567'
+// 'new' is optional
+y = BigNumber(x) // '123.4567'
+
+ If n is a base 10 value it can be in normal (fixed-point) or
+ exponential notation. Values in other bases must be in normal notation. Values in any base can
+ have fraction digits, i.e. digits after the decimal point.
+
+
+new BigNumber(43210) // '43210'
+new BigNumber('4.321e+4') // '43210'
+new BigNumber('-735.0918e-430') // '-7.350918e-428'
+new BigNumber('123412421.234324', 5) // '607236.557696'
+
+ Signed 0, signed Infinity and NaN are supported.
+
+
+new BigNumber('-Infinity') // '-Infinity'
+new BigNumber(NaN) // 'NaN'
+new BigNumber(-0) // '0'
+new BigNumber('.5') // '0.5'
+new BigNumber('+2') // '2'
+
+ String values in hexadecimal literal form, e.g. '0xff', are valid, as are
+ string values with the octal and binary prefixs '0o' and '0b'.
+ String values in octal literal form without the prefix will be interpreted as
+ decimals, e.g. '011' is interpreted as 11, not 9.
+
+
+new BigNumber(-10110100.1, 2) // '-180.5'
+new BigNumber('-0b10110100.1') // '-180.5'
+new BigNumber('ff.8', 16) // '255.5'
+new BigNumber('0xff.8') // '255.5'
+
+ If a base is specified, n is rounded according to the current
+ DECIMAL_PLACES and
+ ROUNDING_MODE settings. This includes base
+ 10 so don't include a base parameter for decimal values unless
+ this behaviour is wanted.
+
+
BigNumber.config({ DECIMAL_PLACES: 5 })
+new BigNumber(1.23456789) // '1.23456789'
+new BigNumber(1.23456789, 10) // '1.23457'
+
An error is thrown if base is invalid. See Errors.
+
+ There is no limit to the number of digits of a value of type string (other than
+ that of JavaScript's maximum array size). See RANGE to set
+ the maximum and minimum possible exponent value of a BigNumber.
+
+
+new BigNumber('5032485723458348569331745.33434346346912144534543')
+new BigNumber('4.321e10000000')
+
BigNumber NaN is returned if n is invalid
+ (unless BigNumber.DEBUG is true, see below).
+
+new BigNumber('.1*') // 'NaN'
+new BigNumber('blurgh') // 'NaN'
+new BigNumber(9, 2) // 'NaN'
+
+ To aid in debugging, if BigNumber.DEBUG is true then an error will
+ be thrown on an invalid n. An error will also be thrown if n is of
+ type number with more than 15 significant digits, as calling
+ toString or valueOf on
+ these numbers may not result in the intended value.
+
+
+console.log(823456789123456.3) // 823456789123456.2
+new BigNumber(823456789123456.3) // '823456789123456.2'
+BigNumber.DEBUG = true
+// '[BigNumber Error] Number primitive has more than 15 significant digits'
+new BigNumber(823456789123456.3)
+// '[BigNumber Error] Not a base 2 number'
+new BigNumber(9, 2)
+
+ A BigNumber can also be created from an object literal.
+ Use isBigNumber to check that it is well-formed.
+
+
new BigNumber({ s: 1, e: 2, c: [ 777, 12300000000000 ], _isBigNumber: true }) // '777.123'
+
+
+
+
+
Methods
+
The static methods of a BigNumber constructor.
+
+
+
+
+
clone
+ .clone([object]) ⇒ BigNumber constructor
+
+
object: object
+
+ Returns a new independent BigNumber constructor with configuration as described by
+ object (see config), or with the default
+ configuration if object is null or undefined.
+
+
+ Throws if object is not an object. See Errors.
+
+
BigNumber.config({ DECIMAL_PLACES: 5 })
+BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
+
+x = new BigNumber(1)
+y = new BN(1)
+
+x.div(3) // 0.33333
+y.div(3) // 0.333333333
+
+// BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
+BN = BigNumber.clone()
+BN.config({ DECIMAL_PLACES: 9 })
+
+
+
+
configset([object]) ⇒ object
+
+ object: object: an object that contains some or all of the following
+ properties.
+
+
Configures the settings for this particular BigNumber constructor.
+
+
+ DECIMAL_PLACES-
+ number: integer,
0 to 1e+9 inclusive
+ Default value: 20
+
+ -
+ The maximum number of decimal places of the results of operations involving
+ division, i.e. division, square root and base conversion operations, and power
+ operations with negative exponents.
+
+ -
+
BigNumber.config({ DECIMAL_PLACES: 5 })
+BigNumber.set({ DECIMAL_PLACES: 5 }) // equivalent
+
+
+
+
+ ROUNDING_MODE-
+ number: integer,
0 to 8 inclusive
+ Default value: 4 (ROUND_HALF_UP)
+
+ -
+ The rounding mode used in the above operations and the default rounding mode of
+
decimalPlaces,
+ precision,
+ toExponential,
+ toFixed,
+ toFormat and
+ toPrecision.
+
+ - The modes are available as enumerated properties of the BigNumber constructor.
+ -
+
BigNumber.config({ ROUNDING_MODE: 0 })
+BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP }) // equivalent
+
+
+
+
+ EXPONENTIAL_AT-
+ number: integer, magnitude
0 to 1e+9 inclusive, or
+
+ number[]: [ integer -1e+9 to 0 inclusive, integer
+ 0 to 1e+9 inclusive ]
+ Default value: [-7, 20]
+
+ -
+ The exponent value(s) at which
toString returns exponential notation.
+
+ -
+ If a single number is assigned, the value is the exponent magnitude.
+ If an array of two numbers is assigned then the first number is the negative exponent
+ value at and beneath which exponential notation is used, and the second number is the
+ positive exponent value at and above which the same.
+
+ -
+ For example, to emulate JavaScript numbers in terms of the exponent values at which they
+ begin to use exponential notation, use
[-7, 20].
+
+ -
+
BigNumber.config({ EXPONENTIAL_AT: 2 })
+new BigNumber(12.3) // '12.3' e is only 1
+new BigNumber(123) // '1.23e+2'
+new BigNumber(0.123) // '0.123' e is only -1
+new BigNumber(0.0123) // '1.23e-2'
+
+BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
+new BigNumber(123456789) // '123456789' e is only 8
+new BigNumber(0.000000123) // '1.23e-7'
+
+// Almost never return exponential notation:
+BigNumber.config({ EXPONENTIAL_AT: 1e+9 })
+
+// Always return exponential notation:
+BigNumber.config({ EXPONENTIAL_AT: 0 })
+
+ -
+ Regardless of the value of
EXPONENTIAL_AT, the toFixed method
+ will always return a value in normal notation and the toExponential method
+ will always return a value in exponential form.
+
+ -
+ Calling
toString with a base argument, e.g. toString(10), will
+ also always return normal notation.
+
+
+
+
+ RANGE-
+ number: integer, magnitude
1 to 1e+9 inclusive, or
+
+ number[]: [ integer -1e+9 to -1 inclusive, integer
+ 1 to 1e+9 inclusive ]
+ Default value: [-1e+9, 1e+9]
+
+ -
+ The exponent value(s) beyond which overflow to
Infinity and underflow to
+ zero occurs.
+
+ -
+ If a single number is assigned, it is the maximum exponent magnitude: values wth a
+ positive exponent of greater magnitude become
Infinity and those with a
+ negative exponent of greater magnitude become zero.
+ -
+ If an array of two numbers is assigned then the first number is the negative exponent
+ limit and the second number is the positive exponent limit.
+
+ -
+ For example, to emulate JavaScript numbers in terms of the exponent values at which they
+ become zero and
Infinity, use [-324, 308].
+
+ -
+
BigNumber.config({ RANGE: 500 })
+BigNumber.config().RANGE // [ -500, 500 ]
+new BigNumber('9.999e499') // '9.999e+499'
+new BigNumber('1e500') // 'Infinity'
+new BigNumber('1e-499') // '1e-499'
+new BigNumber('1e-500') // '0'
+
+BigNumber.config({ RANGE: [-3, 4] })
+new BigNumber(99999) // '99999' e is only 4
+new BigNumber(100000) // 'Infinity' e is 5
+new BigNumber(0.001) // '0.01' e is only -3
+new BigNumber(0.0001) // '0' e is -4
+
+ -
+ The largest possible magnitude of a finite BigNumber is
+
9.999...e+1000000000.
+ The smallest possible magnitude of a non-zero BigNumber is 1e-1000000000.
+
+
+
+
+ CRYPTO-
+ boolean:
true or false.
+ Default value: false
+
+ -
+ The value that determines whether cryptographically-secure pseudo-random number
+ generation is used.
+
+ -
+ If
CRYPTO is set to true then the
+ random method will generate random digits using
+ crypto.getRandomValues in browsers that support it, or
+ crypto.randomBytes if using Node.js.
+
+ -
+ If neither function is supported by the host environment then attempting to set
+
CRYPTO to true will fail and an exception will be thrown.
+
+ -
+ If
CRYPTO is false then the source of randomness used will be
+ Math.random (which is assumed to generate at least 30 bits of
+ randomness).
+
+ - See
random.
+ -
+
+// Node.js
+global.crypto = require('crypto')
+
+BigNumber.config({ CRYPTO: true })
+BigNumber.config().CRYPTO // true
+BigNumber.random() // 0.54340758610486147524
+
+
+
+
+ MODULO_MODE-
+ number: integer,
0 to 9 inclusive
+ Default value: 1 (ROUND_DOWN)
+
+ - The modulo mode used when calculating the modulus:
a mod n.
+ -
+ The quotient,
q = a / n, is calculated according to the
+ ROUNDING_MODE that corresponds to the chosen
+ MODULO_MODE.
+
+ - The remainder,
r, is calculated as: r = a - n * q.
+ -
+ The modes that are most commonly used for the modulus/remainder operation are shown in
+ the following table. Although the other rounding modes can be used, they may not give
+ useful results.
+
+ -
+
+ | Property | Value | Description |
|---|
+
+ | ROUND_UP | 0 |
+
+ The remainder is positive if the dividend is negative, otherwise it is negative.
+ |
+
+
+ | ROUND_DOWN | 1 |
+
+ The remainder has the same sign as the dividend.
+ This uses 'truncating division' and matches the behaviour of JavaScript's
+ remainder operator %.
+ |
+
+
+ | ROUND_FLOOR | 3 |
+
+ The remainder has the same sign as the divisor.
+ This matches Python's % operator.
+ |
+
+
+ | ROUND_HALF_EVEN | 6 |
+ The IEEE 754 remainder function. |
+
+
+ | EUCLID | 9 |
+
+ The remainder is always positive. Euclidian division:
+ q = sign(n) * floor(a / abs(n))
+ |
+
+
+
+ -
+ The rounding/modulo modes are available as enumerated properties of the BigNumber
+ constructor.
+
+ - See
modulo.
+ -
+
BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
+BigNumber.config({ MODULO_MODE: 9 }) // equivalent
+
+
+
+
+ POW_PRECISION-
+ number: integer,
0 to 1e+9 inclusive.
+ Default value: 0
+
+ -
+ The maximum precision, i.e. number of significant digits, of the result of the power
+ operation (unless a modulus is specified).
+
+ - If set to
0, the number of significant digits will not be limited.
+ - See
exponentiatedBy.
+ BigNumber.config({ POW_PRECISION: 100 })FORMAT- object
+ -
+ The
FORMAT object configures the format of the string returned by the
+ toFormat method.
+
+ -
+ The example below shows the properties of the
FORMAT object that are
+ recognised, and their default values.
+
+ -
+ Unlike the other configuration properties, the values of the properties of the
+
FORMAT object will not be checked for validity. The existing
+ FORMAT object will simply be replaced by the object that is passed in.
+ The object can include any number of the properties shown below.
+
+ - See
toFormat for examples of usage.
+ -
+
+BigNumber.config({
+ FORMAT: {
+ // string to prepend
+ prefix: '',
+ // decimal separator
+ decimalSeparator: '.',
+ // grouping separator of the integer part
+ groupSeparator: ',',
+ // primary grouping size of the integer part
+ groupSize: 3,
+ // secondary grouping size of the integer part
+ secondaryGroupSize: 0,
+ // grouping separator of the fraction part
+ fractionGroupSeparator: ' ',
+ // grouping size of the fraction part
+ fractionGroupSize: 0,
+ // string to append
+ suffix: ''
+ }
+});
+
+
+
+
+ ALPHABET-
+ string
+ Default value: '0123456789abcdefghijklmnopqrstuvwxyz'
+
+ -
+ The alphabet used for base conversion. The length of the alphabet corresponds to the
+ maximum value of the base argument that can be passed to the
+
BigNumber constructor or
+ toString.
+
+ -
+ There is no maximum length for the alphabet, but it must be at least 2 characters long, and
+ it must not contain whitespace or a repeated character, or the sign indicators
+
'+' and '-', or the decimal separator '.'.
+
+ -
+
// duodecimal (base 12)
+BigNumber.config({ ALPHABET: '0123456789TE' })
+x = new BigNumber('T', 12)
+x.toString() // '10'
+x.toString(12) // 'T'
+
+
+
+
+
+
+
Returns an object with the above properties and their current values.
+
+ Throws if object is not an object, or if an invalid value is assigned to
+ one or more of the above properties. See Errors.
+
+
+BigNumber.config({
+ DECIMAL_PLACES: 40,
+ ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
+ EXPONENTIAL_AT: [-10, 20],
+ RANGE: [-500, 500],
+ CRYPTO: true,
+ MODULO_MODE: BigNumber.ROUND_FLOOR,
+ POW_PRECISION: 80,
+ FORMAT: {
+ groupSize: 3,
+ groupSeparator: ' ',
+ decimalSeparator: ','
+ },
+ ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+});
+
+obj = BigNumber.config();
+obj.DECIMAL_PLACES // 40
+obj.RANGE // [-500, 500]
+
+
+
+
+ isBigNumber.isBigNumber(value) ⇒ boolean
+
+
value: any
+
+ Returns true if value is a BigNumber instance, otherwise returns
+ false.
+
+
x = 42
+y = new BigNumber(x)
+
+BigNumber.isBigNumber(x) // false
+y instanceof BigNumber // true
+BigNumber.isBigNumber(y) // true
+
+BN = BigNumber.clone();
+z = new BN(x)
+z instanceof BigNumber // false
+BigNumber.isBigNumber(z) // true
+
+ If value is a BigNumber instance and BigNumber.DEBUG is true,
+ then this method will also check if value is well-formed, and throw if it is not.
+ See Errors.
+
+
+ The check can be useful if creating a BigNumber from an object literal.
+ See BigNumber.
+
+
+x = new BigNumber(10)
+
+// Change x.c to an illegitimate value.
+x.c = NaN
+
+BigNumber.DEBUG = false
+
+// No error.
+BigNumber.isBigNumber(x) // true
+
+BigNumber.DEBUG = true
+
+// Error.
+BigNumber.isBigNumber(x) // '[BigNumber Error] Invalid BigNumber'
+
+
+
+
maximum.max(n...) ⇒ BigNumber
+
+ n: number|string|BigNumber
+ See BigNumber for further parameter details.
+
+
+ Returns a BigNumber whose value is the maximum of the arguments.
+
+
The return value is always exact and unrounded.
+
x = new BigNumber('3257869345.0378653')
+BigNumber.maximum(4e9, x, '123456789.9') // '4000000000'
+
+arr = [12, '13', new BigNumber(14)]
+BigNumber.max.apply(null, arr) // '14'
+
+
+
+
minimum.min(n...) ⇒ BigNumber
+
+ n: number|string|BigNumber
+ See BigNumber for further parameter details.
+
+
+ Returns a BigNumber whose value is the minimum of the arguments.
+
+
The return value is always exact and unrounded.
+
x = new BigNumber('3257869345.0378653')
+BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9'
+
+arr = [2, new BigNumber(-14), '-15.9999', -12]
+BigNumber.min.apply(null, arr) // '-15.9999'
+
+
+
+
+ random.random([dp]) ⇒ BigNumber
+
+
dp: number: integer, 0 to 1e+9 inclusive
+
+ Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and
+ less than 1.
+
+
+ The return value will have dp decimal places (or less if trailing zeros are
+ produced).
+ If dp is omitted then the number of decimal places will default to the current
+ DECIMAL_PLACES setting.
+
+
+ Depending on the value of this BigNumber constructor's
+ CRYPTO setting and the support for the
+ crypto object in the host environment, the random digits of the return value are
+ generated by either Math.random (fastest), crypto.getRandomValues
+ (Web Cryptography API in recent browsers) or crypto.randomBytes (Node.js).
+
+
+ To be able to set CRYPTO to true when using
+ Node.js, the crypto object must be available globally:
+
+
global.crypto = require('crypto')
+
+ If CRYPTO is true, i.e. one of the
+ crypto methods is to be used, the value of a returned BigNumber should be
+ cryptographically-secure and statistically indistinguishable from a random value.
+
+
+ Throws if dp is invalid. See Errors.
+
+
BigNumber.config({ DECIMAL_PLACES: 10 })
+BigNumber.random() // '0.4117936847'
+BigNumber.random(20) // '0.78193327636914089009'
+
+
+
+
sum.sum(n...) ⇒ BigNumber
+
+ n: number|string|BigNumber
+ See BigNumber for further parameter details.
+
+
Returns a BigNumber whose value is the sum of the arguments.
+
The return value is always exact and unrounded.
+
x = new BigNumber('3257869345.0378653')
+BigNumber.sum(4e9, x, '123456789.9') // '7381326134.9378653'
+
+arr = [2, new BigNumber(14), '15.9999', 12]
+BigNumber.sum.apply(null, arr) // '43.9999'
+
+
+
+
Properties
+
+ The library's enumerated rounding modes are stored as properties of the constructor.
+ (They are not referenced internally by the library itself.)
+
+
+ Rounding modes 0 to 6 (inclusive) are the same as those of Java's
+ BigDecimal class.
+
+
+
+ | Property |
+ Value |
+ Description |
+
+
+ | ROUND_UP |
+ 0 |
+ Rounds away from zero |
+
+
+ | ROUND_DOWN |
+ 1 |
+ Rounds towards zero |
+
+
+ | ROUND_CEIL |
+ 2 |
+ Rounds towards Infinity |
+
+
+ | ROUND_FLOOR |
+ 3 |
+ Rounds towards -Infinity |
+
+
+ | ROUND_HALF_UP |
+ 4 |
+
+ Rounds towards nearest neighbour.
+ If equidistant, rounds away from zero
+ |
+
+
+ | ROUND_HALF_DOWN |
+ 5 |
+
+ Rounds towards nearest neighbour.
+ If equidistant, rounds towards zero
+ |
+
+
+ | ROUND_HALF_EVEN |
+ 6 |
+
+ Rounds towards nearest neighbour.
+ If equidistant, rounds towards even neighbour
+ |
+
+
+ | ROUND_HALF_CEIL |
+ 7 |
+
+ Rounds towards nearest neighbour.
+ If equidistant, rounds towards Infinity
+ |
+
+
+ | ROUND_HALF_FLOOR |
+ 8 |
+
+ Rounds towards nearest neighbour.
+ If equidistant, rounds towards -Infinity
+ |
+
+
+
+BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL })
+BigNumber.config({ ROUNDING_MODE: 2 }) // equivalent
+
+
DEBUG
+
undefined|false|true
+
+ If BigNumber.DEBUG is set true then an error will be thrown
+ if this BigNumber constructor receives an invalid value, such as
+ a value of type number with more than 15 significant digits.
+ See BigNumber.
+
+
+ An error will also be thrown if the isBigNumber
+ method receives a BigNumber that is not well-formed.
+ See isBigNumber.
+
+
BigNumber.DEBUG = true
+
+
+
INSTANCE
+
+
+
Methods
+
The methods inherited by a BigNumber instance from its constructor's prototype object.
+
A BigNumber is immutable in the sense that it is not changed by its methods.
+
+ The treatment of ±0, ±Infinity and NaN is
+ consistent with how JavaScript treats these values.
+
+
Many method names have a shorter alias.
+
+
+
+
absoluteValue.abs() ⇒ BigNumber
+
+ Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of
+ this BigNumber.
+
+
The return value is always exact and unrounded.
+
+x = new BigNumber(-0.8)
+y = x.absoluteValue() // '0.8'
+z = y.abs() // '0.8'
+
+
+
+
+ comparedTo.comparedTo(n [, base]) ⇒ number
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ | Returns | |
|---|
+
+ 1 |
+ If the value of this BigNumber is greater than the value of n |
+
+
+ -1 |
+ If the value of this BigNumber is less than the value of n |
+
+
+ 0 |
+ If this BigNumber and n have the same value |
+
+
+ null |
+ If the value of either this BigNumber or n is NaN |
+
+
+
+x = new BigNumber(Infinity)
+y = new BigNumber(5)
+x.comparedTo(y) // 1
+x.comparedTo(x.minus(1)) // 0
+y.comparedTo(NaN) // null
+y.comparedTo('110', 2) // -1
+
+
+
+
+ decimalPlaces.dp([dp [, rm]]) ⇒ BigNumber|number
+
+
+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive
+
+
+ If dp is a number, returns a BigNumber whose value is the value of this BigNumber
+ rounded by rounding mode rm to a maximum of dp decimal places.
+
+
+ If dp is omitted, or is null or undefined, the return
+ value is the number of decimal places of the value of this BigNumber, or null if
+ the value of this BigNumber is ±Infinity or NaN.
+
+
+ If rm is omitted, or is null or undefined,
+ ROUNDING_MODE is used.
+
+
+ Throws if dp or rm is invalid. See Errors.
+
+
+x = new BigNumber(1234.56)
+x.decimalPlaces(1) // '1234.6'
+x.dp() // 2
+x.decimalPlaces(2) // '1234.56'
+x.dp(10) // '1234.56'
+x.decimalPlaces(0, 1) // '1234'
+x.dp(0, 6) // '1235'
+x.decimalPlaces(1, 1) // '1234.5'
+x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
+x // '1234.56'
+y = new BigNumber('9.9e-101')
+y.dp() // 102
+
+
+
+
dividedBy.div(n [, base]) ⇒ BigNumber
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns a BigNumber whose value is the value of this BigNumber divided by
+ n, rounded according to the current
+ DECIMAL_PLACES and
+ ROUNDING_MODE settings.
+
+
+x = new BigNumber(355)
+y = new BigNumber(113)
+x.dividedBy(y) // '3.14159292035398230088'
+x.div(5) // '71'
+x.div(47, 16) // '5'
+
+
+
+
+ dividedToIntegerBy.idiv(n [, base]) ⇒
+ BigNumber
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
+ n.
+
+
+x = new BigNumber(5)
+y = new BigNumber(3)
+x.dividedToIntegerBy(y) // '1'
+x.idiv(0.7) // '7'
+x.idiv('0.f', 16) // '5'
+
+
+
+
+ exponentiatedBy.pow(n [, m]) ⇒ BigNumber
+
+
+ n: number|string|BigNumber: integer
+ m: number|string|BigNumber
+
+
+ Returns a BigNumber whose value is the value of this BigNumber exponentiated by
+ n, i.e. raised to the power n, and optionally modulo a modulus
+ m.
+
+
+ Throws if n is not an integer. See Errors.
+
+
+ If n is negative the result is rounded according to the current
+ DECIMAL_PLACES and
+ ROUNDING_MODE settings.
+
+
+ As the number of digits of the result of the power operation can grow so large so quickly,
+ e.g. 123.45610000 has over 50000 digits, the number of significant
+ digits calculated is limited to the value of the
+ POW_PRECISION setting (unless a modulus
+ m is specified).
+
+
+ By default POW_PRECISION is set to 0.
+ This means that an unlimited number of significant digits will be calculated, and that the
+ method's performance will decrease dramatically for larger exponents.
+
+
+ If m is specified and the value of m, n and this
+ BigNumber are integers, and n is positive, then a fast modular exponentiation
+ algorithm is used, otherwise the operation will be performed as
+ x.exponentiatedBy(n).modulo(m) with a
+ POW_PRECISION of 0.
+
+
+Math.pow(0.7, 2) // 0.48999999999999994
+x = new BigNumber(0.7)
+x.exponentiatedBy(2) // '0.49'
+BigNumber(3).pow(-2) // '0.11111111111111111111'
+
+
+
+
+ integerValue.integerValue([rm]) ⇒ BigNumber
+
+
+ rm: number: integer, 0 to 8 inclusive
+
+
+ Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
+ rounding mode rm.
+
+
+ If rm is omitted, or is null or undefined,
+ ROUNDING_MODE is used.
+
+
+ Throws if rm is invalid. See Errors.
+
+
+x = new BigNumber(123.456)
+x.integerValue() // '123'
+x.integerValue(BigNumber.ROUND_CEIL) // '124'
+y = new BigNumber(-12.7)
+y.integerValue() // '-13'
+y.integerValue(BigNumber.ROUND_DOWN) // '-12'
+
+ The following is an example of how to add a prototype method that emulates JavaScript's
+ Math.round function. Math.ceil, Math.floor and
+ Math.trunc can be emulated in the same way with
+ BigNumber.ROUND_CEIL, BigNumber.ROUND_FLOOR and
+ BigNumber.ROUND_DOWN respectively.
+
+
+BigNumber.prototype.round = function (n) {
+ return n.integerValue(BigNumber.ROUND_HALF_CEIL);
+};
+x.round() // '123'
+
+
+
+
isEqualTo.eq(n [, base]) ⇒ boolean
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns true if the value of this BigNumber is equal to the value of
+ n, otherwise returns false.
+ As with JavaScript, NaN does not equal NaN.
+
+
Note: This method uses the comparedTo method internally.
+
+0 === 1e-324 // true
+x = new BigNumber(0)
+x.isEqualTo('1e-324') // false
+BigNumber(-0).eq(x) // true ( -0 === 0 )
+BigNumber(255).eq('ff', 16) // true
+
+y = new BigNumber(NaN)
+y.isEqualTo(NaN) // false
+
+
+
+
isFinite.isFinite() ⇒ boolean
+
+ Returns true if the value of this BigNumber is a finite number, otherwise
+ returns false.
+
+
+ The only possible non-finite values of a BigNumber are NaN, Infinity
+ and -Infinity.
+
+
+x = new BigNumber(1)
+x.isFinite() // true
+y = new BigNumber(Infinity)
+y.isFinite() // false
+
+ Note: The native method isFinite() can be used if
+ n <= Number.MAX_VALUE.
+
+
+
+
+
isGreaterThan.gt(n [, base]) ⇒ boolean
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns true if the value of this BigNumber is greater than the value of
+ n, otherwise returns false.
+
+
Note: This method uses the comparedTo method internally.
+
+0.1 > (0.3 - 0.2) // true
+x = new BigNumber(0.1)
+x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false
+BigNumber(0).gt(x) // false
+BigNumber(11, 3).gt(11.1, 2) // true
+
+
+
+
+ isGreaterThanOrEqualTo.gte(n [, base]) ⇒ boolean
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns true if the value of this BigNumber is greater than or equal to the value
+ of n, otherwise returns false.
+
+
Note: This method uses the comparedTo method internally.
+
+(0.3 - 0.2) >= 0.1 // false
+x = new BigNumber(0.3).minus(0.2)
+x.isGreaterThanOrEqualTo(0.1) // true
+BigNumber(1).gte(x) // true
+BigNumber(10, 18).gte('i', 36) // true
+
+
+
+
isInteger.isInteger() ⇒ boolean
+
+ Returns true if the value of this BigNumber is an integer, otherwise returns
+ false.
+
+
+x = new BigNumber(1)
+x.isInteger() // true
+y = new BigNumber(123.456)
+y.isInteger() // false
+
+
+
+
isLessThan.lt(n [, base]) ⇒ boolean
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns true if the value of this BigNumber is less than the value of
+ n, otherwise returns false.
+
+
Note: This method uses the comparedTo method internally.
+
+(0.3 - 0.2) < 0.1 // true
+x = new BigNumber(0.3).minus(0.2)
+x.isLessThan(0.1) // false
+BigNumber(0).lt(x) // true
+BigNumber(11.1, 2).lt(11, 3) // true
+
+
+
+
+ isLessThanOrEqualTo.lte(n [, base]) ⇒ boolean
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns true if the value of this BigNumber is less than or equal to the value of
+ n, otherwise returns false.
+
+
Note: This method uses the comparedTo method internally.
+
+0.1 <= (0.3 - 0.2) // false
+x = new BigNumber(0.1)
+x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true
+BigNumber(-1).lte(x) // true
+BigNumber(10, 18).lte('i', 36) // true
+
+
+
+
isNaN.isNaN() ⇒ boolean
+
+ Returns true if the value of this BigNumber is NaN, otherwise
+ returns false.
+
+
+x = new BigNumber(NaN)
+x.isNaN() // true
+y = new BigNumber('Infinity')
+y.isNaN() // false
+
Note: The native method isNaN() can also be used.
+
+
+
+
isNegative.isNegative() ⇒ boolean
+
+ Returns true if the sign of this BigNumber is negative, otherwise returns
+ false.
+
+
+x = new BigNumber(-0)
+x.isNegative() // true
+y = new BigNumber(2)
+y.isNegative() // false
+
Note: n < 0 can be used if n <= -Number.MIN_VALUE.
+
+
+
+
isPositive.isPositive() ⇒ boolean
+
+ Returns true if the sign of this BigNumber is positive, otherwise returns
+ false.
+
+
+x = new BigNumber(-0)
+x.isPositive() // false
+y = new BigNumber(2)
+y.isPositive() // true
+
+
+
+
isZero.isZero() ⇒ boolean
+
+ Returns true if the value of this BigNumber is zero or minus zero, otherwise
+ returns false.
+
+
+x = new BigNumber(-0)
+x.isZero() && x.isNegative() // true
+y = new BigNumber(Infinity)
+y.isZero() // false
+
Note: n == 0 can be used if n >= Number.MIN_VALUE.
+
+
+
+
+ minus.minus(n [, base]) ⇒ BigNumber
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
Returns a BigNumber whose value is the value of this BigNumber minus n.
+
The return value is always exact and unrounded.
+
+0.3 - 0.1 // 0.19999999999999998
+x = new BigNumber(0.3)
+x.minus(0.1) // '0.2'
+x.minus(0.6, 20) // '0'
+
+
+
+
modulo.mod(n [, base]) ⇒ BigNumber
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns a BigNumber whose value is the value of this BigNumber modulo n, i.e.
+ the integer remainder of dividing this BigNumber by n.
+
+
+ The value returned, and in particular its sign, is dependent on the value of the
+ MODULO_MODE setting of this BigNumber constructor.
+ If it is 1 (default value), the result will have the same sign as this BigNumber,
+ and it will match that of Javascript's % operator (within the limits of double
+ precision) and BigDecimal's remainder method.
+
+
The return value is always exact and unrounded.
+
+ See MODULO_MODE for a description of the other
+ modulo modes.
+
+
+1 % 0.9 // 0.09999999999999998
+x = new BigNumber(1)
+x.modulo(0.9) // '0.1'
+y = new BigNumber(33)
+y.mod('a', 33) // '3'
+
+
+
+
+ multipliedBy.times(n [, base]) ⇒ BigNumber
+
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
+ Returns a BigNumber whose value is the value of this BigNumber multiplied by n.
+
+
The return value is always exact and unrounded.
+
+0.6 * 3 // 1.7999999999999998
+x = new BigNumber(0.6)
+y = x.multipliedBy(3) // '1.8'
+BigNumber('7e+500').times(y) // '1.26e+501'
+x.multipliedBy('-a', 16) // '-6'
+
+
+
+
negated.negated() ⇒ BigNumber
+
+ Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by
+ -1.
+
+
+x = new BigNumber(1.8)
+x.negated() // '-1.8'
+y = new BigNumber(-1.3)
+y.negated() // '1.3'
+
+
+
+
plus.plus(n [, base]) ⇒ BigNumber
+
+ n: number|string|BigNumber
+ base: number
+ See BigNumber for further parameter details.
+
+
Returns a BigNumber whose value is the value of this BigNumber plus n.
+
The return value is always exact and unrounded.
+
+0.1 + 0.2 // 0.30000000000000004
+x = new BigNumber(0.1)
+y = x.plus(0.2) // '0.3'
+BigNumber(0.7).plus(x).plus(y) // '1'
+x.plus('0.1', 8) // '0.225'
+
+
+
+
+ precision.sd([d [, rm]]) ⇒ BigNumber|number
+
+
+ d: number|boolean: integer, 1 to 1e+9
+ inclusive, or true or false
+ rm: number: integer, 0 to 8 inclusive.
+
+
+ If d is a number, returns a BigNumber whose value is the value of this BigNumber
+ rounded to a precision of d significant digits using rounding mode
+ rm.
+
+
+ If d is omitted or is null or undefined, the return
+ value is the number of significant digits of the value of this BigNumber, or null
+ if the value of this BigNumber is ±Infinity or NaN.
+
+
+ If d is true then any trailing zeros of the integer
+ part of a number are counted as significant digits, otherwise they are not.
+
+
+ If rm is omitted or is null or undefined,
+ ROUNDING_MODE will be used.
+
+
+ Throws if d or rm is invalid. See Errors.
+
+
+x = new BigNumber(9876.54321)
+x.precision(6) // '9876.54'
+x.sd() // 9
+x.precision(6, BigNumber.ROUND_UP) // '9876.55'
+x.sd(2) // '9900'
+x.precision(2, 1) // '9800'
+x // '9876.54321'
+y = new BigNumber(987000)
+y.precision() // 3
+y.sd(true) // 6
+
+
+
+
shiftedBy.shiftedBy(n) ⇒ BigNumber
+
+ n: number: integer,
+ -9007199254740991 to 9007199254740991 inclusive
+
+
+ Returns a BigNumber whose value is the value of this BigNumber shifted by n
+ places.
+
+ The shift is of the decimal point, i.e. of powers of ten, and is to the left if n
+ is negative or to the right if n is positive.
+
+
The return value is always exact and unrounded.
+
+ Throws if n is invalid. See Errors.
+
+
+x = new BigNumber(1.23)
+x.shiftedBy(3) // '1230'
+x.shiftedBy(-3) // '0.00123'
+
+
+
+
squareRoot.sqrt() ⇒ BigNumber
+
+ Returns a BigNumber whose value is the square root of the value of this BigNumber,
+ rounded according to the current
+ DECIMAL_PLACES and
+ ROUNDING_MODE settings.
+
+
+ The return value will be correctly rounded, i.e. rounded as if the result was first calculated
+ to an infinite number of correct digits before rounding.
+
+
+x = new BigNumber(16)
+x.squareRoot() // '4'
+y = new BigNumber(3)
+y.sqrt() // '1.73205080756887729353'
+
+
+
+
+ toExponential.toExponential([dp [, rm]]) ⇒ string
+
+
+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive
+
+
+ Returns a string representing the value of this BigNumber in exponential notation rounded
+ using rounding mode rm to dp decimal places, i.e with one digit
+ before the decimal point and dp digits after it.
+
+
+ If the value of this BigNumber in exponential notation has fewer than dp fraction
+ digits, the return value will be appended with zeros accordingly.
+
+
+ If dp is omitted, or is null or undefined, the number
+ of digits after the decimal point defaults to the minimum number of digits necessary to
+ represent the value exactly.
+ If rm is omitted or is null or undefined,
+ ROUNDING_MODE is used.
+
+
+ Throws if dp or rm is invalid. See Errors.
+
+
+x = 45.6
+y = new BigNumber(x)
+x.toExponential() // '4.56e+1'
+y.toExponential() // '4.56e+1'
+x.toExponential(0) // '5e+1'
+y.toExponential(0) // '5e+1'
+x.toExponential(1) // '4.6e+1'
+y.toExponential(1) // '4.6e+1'
+y.toExponential(1, 1) // '4.5e+1' (ROUND_DOWN)
+x.toExponential(3) // '4.560e+1'
+y.toExponential(3) // '4.560e+1'
+
+
+
+
+ toFixed.toFixed([dp [, rm]]) ⇒ string
+
+
+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive
+
+
+ Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+ rounded to dp decimal places using rounding mode rm.
+
+
+ If the value of this BigNumber in normal notation has fewer than dp fraction
+ digits, the return value will be appended with zeros accordingly.
+
+
+ Unlike Number.prototype.toFixed, which returns exponential notation if a number
+ is greater or equal to 1021, this method will always return normal
+ notation.
+
+
+ If dp is omitted or is null or undefined, the return
+ value will be unrounded and in normal notation. This is also unlike
+ Number.prototype.toFixed, which returns the value to zero decimal places.
+ It is useful when fixed-point notation is required and the current
+ EXPONENTIAL_AT setting causes
+ toString to return exponential notation.
+ If rm is omitted or is null or undefined,
+ ROUNDING_MODE is used.
+
+
+ Throws if dp or rm is invalid. See Errors.
+
+
+x = 3.456
+y = new BigNumber(x)
+x.toFixed() // '3'
+y.toFixed() // '3.456'
+y.toFixed(0) // '3'
+x.toFixed(2) // '3.46'
+y.toFixed(2) // '3.46'
+y.toFixed(2, 1) // '3.45' (ROUND_DOWN)
+x.toFixed(5) // '3.45600'
+y.toFixed(5) // '3.45600'
+
+
+
+
+ toFormat.toFormat([dp [, rm[, format]]]) ⇒ string
+
+
+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive
+ format: object: see FORMAT
+
+
+
+ Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+ rounded to dp decimal places using rounding mode rm, and formatted
+ according to the properties of the format object.
+
+
+ See FORMAT and the examples below for the properties of the
+ format object, their types, and their usage. A formatting object may contain
+ some or all of the recognised properties.
+
+
+ If dp is omitted or is null or undefined, then the
+ return value is not rounded to a fixed number of decimal places.
+ If rm is omitted or is null or undefined,
+ ROUNDING_MODE is used.
+ If format is omitted or is null or undefined, the
+ FORMAT object is used.
+
+
+ Throws if dp, rm or format is invalid. See
+ Errors.
+
+
+fmt = {
+ prefix = '',
+ decimalSeparator: '.',
+ groupSeparator: ',',
+ groupSize: 3,
+ secondaryGroupSize: 0,
+ fractionGroupSeparator: ' ',
+ fractionGroupSize: 0,
+ suffix = ''
+}
+
+x = new BigNumber('123456789.123456789')
+
+// Set the global formatting options
+BigNumber.config({ FORMAT: fmt })
+
+x.toFormat() // '123,456,789.123456789'
+x.toFormat(3) // '123,456,789.123'
+
+// If a reference to the object assigned to FORMAT has been retained,
+// the format properties can be changed directly
+fmt.groupSeparator = ' '
+fmt.fractionGroupSize = 5
+x.toFormat() // '123 456 789.12345 6789'
+
+// Alternatively, pass the formatting options as an argument
+fmt = {
+ prefix: '=> ',
+ decimalSeparator: ',',
+ groupSeparator: '.',
+ groupSize: 3,
+ secondaryGroupSize: 2
+}
+
+x.toFormat() // '123 456 789.12345 6789'
+x.toFormat(fmt) // '=> 12.34.56.789,123456789'
+x.toFormat(2, fmt) // '=> 12.34.56.789,12'
+x.toFormat(3, BigNumber.ROUND_UP, fmt) // '=> 12.34.56.789,124'
+
+
+
+
+ toFraction.toFraction([maximum_denominator])
+ ⇒ [BigNumber, BigNumber]
+
+
+ maximum_denominator:
+ number|string|BigNumber: integer >= 1 and <=
+ Infinity
+
+
+ Returns 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 maximum_denominator.
+
+
+ If a maximum_denominator is not specified, or is null or
+ undefined, the denominator will be the lowest value necessary to represent the
+ number exactly.
+
+
+ Throws if maximum_denominator is invalid. See Errors.
+
+
+x = new BigNumber(1.75)
+x.toFraction() // '7, 4'
+
+pi = new BigNumber('3.14159265358')
+pi.toFraction() // '157079632679,50000000000'
+pi.toFraction(100000) // '312689, 99532'
+pi.toFraction(10000) // '355, 113'
+pi.toFraction(100) // '311, 99'
+pi.toFraction(10) // '22, 7'
+pi.toFraction(1) // '3, 1'
+
+
+
+
toJSON.toJSON() ⇒ string
+
As valueOf.
+
+x = new BigNumber('177.7e+457')
+y = new BigNumber(235.4325)
+z = new BigNumber('0.0098074')
+
+// Serialize an array of three BigNumbers
+str = JSON.stringify( [x, y, z] )
+// "["1.777e+459","235.4325","0.0098074"]"
+
+// Return an array of three BigNumbers
+JSON.parse(str, function (key, val) {
+ return key === '' ? val : new BigNumber(val)
+})
+
+
+
+
toNumber.toNumber() ⇒ number
+
Returns the value of this BigNumber as a JavaScript number primitive.
+
+ This method is identical to using type coercion with the unary plus operator.
+
+
+x = new BigNumber(456.789)
+x.toNumber() // 456.789
++x // 456.789
+
+y = new BigNumber('45987349857634085409857349856430985')
+y.toNumber() // 4.598734985763409e+34
+
+z = new BigNumber(-0)
+1 / z.toNumber() // -Infinity
+1 / +z // -Infinity
+
+
+
+
+ toPrecision.toPrecision([sd [, rm]]) ⇒ string
+
+
+ sd: number: integer, 1 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive
+
+
+ Returns a string representing the value of this BigNumber rounded to sd
+ significant digits using rounding mode rm.
+
+
+ If sd is less than the number of digits necessary to represent the integer part
+ of the value in normal (fixed-point) notation, then exponential notation is used.
+
+
+ If sd is omitted, or is null or undefined, then the
+ return value is the same as n.toString().
+ If rm is omitted or is null or undefined,
+ ROUNDING_MODE is used.
+
+
+ Throws if sd or rm is invalid. See Errors.
+
+
+x = 45.6
+y = new BigNumber(x)
+x.toPrecision() // '45.6'
+y.toPrecision() // '45.6'
+x.toPrecision(1) // '5e+1'
+y.toPrecision(1) // '5e+1'
+y.toPrecision(2, 0) // '4.6e+1' (ROUND_UP)
+y.toPrecision(2, 1) // '4.5e+1' (ROUND_DOWN)
+x.toPrecision(5) // '45.600'
+y.toPrecision(5) // '45.600'
+
+
+
+
toString.toString([base]) ⇒ string
+
+ base: number: integer, 2 to ALPHABET.length
+ inclusive (see ALPHABET).
+
+
+ Returns a string representing the value of this BigNumber in the specified base, or base
+ 10 if base is omitted or is null or
+ undefined.
+
+
+ For bases above 10, and using the default base conversion alphabet
+ (see ALPHABET), values from 10 to
+ 35 are represented by a-z
+ (as with Number.prototype.toString).
+
+
+ If a base is specified the value is rounded according to the current
+ DECIMAL_PLACES
+ and ROUNDING_MODE settings.
+
+
+ If a base is not specified, and this BigNumber has a positive
+ exponent that is equal to or greater than the positive component of the
+ current EXPONENTIAL_AT setting,
+ or a negative exponent equal to or less than the negative component of the
+ setting, then exponential notation is returned.
+
+
If base is null or undefined it is ignored.
+
+ Throws if base is invalid. See Errors.
+
+
+x = new BigNumber(750000)
+x.toString() // '750000'
+BigNumber.config({ EXPONENTIAL_AT: 5 })
+x.toString() // '7.5e+5'
+
+y = new BigNumber(362.875)
+y.toString(2) // '101101010.111'
+y.toString(9) // '442.77777777777777777778'
+y.toString(32) // 'ba.s'
+
+BigNumber.config({ DECIMAL_PLACES: 4 });
+z = new BigNumber('1.23456789')
+z.toString() // '1.23456789'
+z.toString(10) // '1.2346'
+
+
+
+
valueOf.valueOf() ⇒ string
+
+ As toString, but does not accept a base argument and includes
+ the minus sign for negative zero.
+
+
+x = new BigNumber('-0')
+x.toString() // '0'
+x.valueOf() // '-0'
+y = new BigNumber('1.777e+457')
+y.valueOf() // '1.777e+457'
+
+
+
+
Properties
+
The properties of a BigNumber instance:
+
+
+ | Property |
+ Description |
+ Type |
+ Value |
+
+
+ | c |
+ coefficient* |
+ number[] |
+ Array of base 1e14 numbers |
+
+
+ | e |
+ exponent |
+ number |
+ Integer, -1000000000 to 1000000000 inclusive |
+
+
+ | s |
+ sign |
+ number |
+ -1 or 1 |
+
+
+
*significand
+
+ The value of any of the c, e and s properties may also
+ be null.
+
+
+ The above properties are best considered to be read-only. In early versions of this library it
+ was okay to change the exponent of a BigNumber by writing to its exponent property directly,
+ but this is no longer reliable as the value of the first element of the coefficient array is
+ now dependent on the exponent.
+
+
+ Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are
+ not necessarily preserved.
+
+
x = new BigNumber(0.123) // '0.123'
+x.toExponential() // '1.23e-1'
+x.c // '1,2,3'
+x.e // -1
+x.s // 1
+
+y = new Number(-123.4567000e+2) // '-12345.67'
+y.toExponential() // '-1.234567e+4'
+z = new BigNumber('-123.4567000e+2') // '-12345.67'
+z.toExponential() // '-1.234567e+4'
+z.c // '1,2,3,4,5,6,7'
+z.e // 4
+z.s // -1
+
+
+
+
Zero, NaN and Infinity
+
+ The table below shows how ±0, NaN and
+ ±Infinity are stored.
+
+
+
+ | |
+ c |
+ e |
+ s |
+
+
+ | ±0 |
+ [0] |
+ 0 |
+ ±1 |
+
+
+ | NaN |
+ null |
+ null |
+ null |
+
+
+ | ±Infinity |
+ null |
+ null |
+ ±1 |
+
+
+
+x = new Number(-0) // 0
+1 / x == -Infinity // true
+
+y = new BigNumber(-0) // '0'
+y.c // '0' ( [0].toString() )
+y.e // 0
+y.s // -1
+
+
+
+
Errors
+
The table below shows the errors that are thrown.
+
+ The errors are generic Error objects whose message begins
+ '[BigNumber Error]'.
+
+
+
+ | Method |
+ Throws |
+
+
+
+ BigNumber
+ comparedTo
+ dividedBy
+ dividedToIntegerBy
+ isEqualTo
+ isGreaterThan
+ isGreaterThanOrEqualTo
+ isLessThan
+ isLessThanOrEqualTo
+ minus
+ modulo
+ plus
+ multipliedBy
+ |
+ Base not a primitive number |
+
+
+ | Base not an integer |
+
+
+ | Base out of range |
+
+
+ | Number primitive has more than 15 significant digits* |
+
+
+ | Not a base... number* |
+
+
+ | Not a number* |
+
+
+ clone |
+ Object expected |
+
+
+ config |
+ Object expected |
+
+
+ DECIMAL_PLACES not a primitive number |
+
+
+ DECIMAL_PLACES not an integer |
+
+
+ DECIMAL_PLACES out of range |
+
+
+ ROUNDING_MODE not a primitive number |
+
+
+ ROUNDING_MODE not an integer |
+
+
+ ROUNDING_MODE out of range |
+
+
+ EXPONENTIAL_AT not a primitive number |
+
+
+ EXPONENTIAL_AT not an integer |
+
+
+ EXPONENTIAL_AT out of range |
+
+
+ RANGE not a primitive number |
+
+
+ RANGE not an integer |
+
+
+ RANGE cannot be zero |
+
+
+ RANGE cannot be zero |
+
+
+ CRYPTO not true or false |
+
+
+ crypto unavailable |
+
+
+ MODULO_MODE not a primitive number |
+
+
+ MODULO_MODE not an integer |
+
+
+ MODULO_MODE out of range |
+
+
+ POW_PRECISION not a primitive number |
+
+
+ POW_PRECISION not an integer |
+
+
+ POW_PRECISION out of range |
+
+
+ FORMAT not an object |
+
+
+ ALPHABET invalid |
+
+
+
+ decimalPlaces
+ precision
+ random
+ shiftedBy
+ toExponential
+ toFixed
+ toFormat
+ toPrecision
+ |
+ Argument not a primitive number |
+
+
+ | Argument not an integer |
+
+
+ | Argument out of range |
+
+
+
+ decimalPlaces
+ precision
+ |
+ Argument not true or false |
+
+
+ exponentiatedBy |
+ Argument not an integer |
+
+
+ isBigNumber |
+ Invalid BigNumber* |
+
+
+
+ minimum
+ maximum
+ |
+ Not a number* |
+
+
+
+ random
+ |
+ crypto unavailable |
+
+
+
+ toFormat
+ |
+ Argument not an object |
+
+
+ toFraction |
+ Argument not an integer |
+
+
+ | Argument out of range |
+
+
+ toString |
+ Base not a primitive number |
+
+
+ | Base not an integer |
+
+
+ | Base out of range |
+
+
+
*Only thrown if BigNumber.DEBUG is true.
+
To determine if an exception is a BigNumber Error:
+
+try {
+ // ...
+} catch (e) {
+ if (e instanceof Error && e.message.indexOf('[BigNumber Error]') === 0) {
+ // ...
+ }
+}
+
+
+
+
Type coercion
+
+ To prevent the accidental use of a BigNumber in primitive number operations, or the
+ accidental addition of a BigNumber to a string, the valueOf method can be safely
+ overwritten as shown below.
+
+
+ The valueOf method is the same as the
+ toJSON method, and both are the same as the
+ toString method except they do not take a base
+ argument and they include the minus sign for negative zero.
+
+
+BigNumber.prototype.valueOf = function () {
+ throw Error('valueOf called!')
+}
+
+x = new BigNumber(1)
+x / 2 // '[BigNumber Error] valueOf called!'
+x + 'abc' // '[BigNumber Error] valueOf called!'
+
+
+
+
+
FAQ
+
+
Why are trailing fractional zeros removed from BigNumbers?
+
+ Some arbitrary-precision libraries retain trailing fractional zeros as they can indicate the
+ precision of a value. This can be useful but the results of arithmetic operations can be
+ misleading.
+
+
+x = new BigDecimal("1.0")
+y = new BigDecimal("1.1000")
+z = x.add(y) // 2.1000
+
+x = new BigDecimal("1.20")
+y = new BigDecimal("3.45000")
+z = x.multiply(y) // 4.1400000
+
+ To specify the precision of a value is to specify that the value lies
+ within a certain range.
+
+
+ In the first example, x has a value of 1.0. The trailing zero shows
+ the precision of the value, implying that it is in the range 0.95 to
+ 1.05. Similarly, the precision indicated by the trailing zeros of y
+ indicates that the value is in the range 1.09995 to 1.10005.
+
+
+ If we add the two lowest values in the ranges we have, 0.95 + 1.09995 = 2.04995,
+ and if we add the two highest values we have, 1.05 + 1.10005 = 2.15005, so the
+ range of the result of the addition implied by the precision of its operands is
+ 2.04995 to 2.15005.
+
+
+ The result given by BigDecimal of 2.1000 however, indicates that the value is in
+ the range 2.09995 to 2.10005 and therefore the precision implied by
+ its trailing zeros may be misleading.
+
+
+ In the second example, the true range is 4.122744 to 4.157256 yet
+ the BigDecimal answer of 4.1400000 indicates a range of 4.13999995
+ to 4.14000005. Again, the precision implied by the trailing zeros may be
+ misleading.
+
+
+ This library, like binary floating point and most calculators, does not retain trailing
+ fractional zeros. Instead, the toExponential, toFixed and
+ toPrecision methods enable trailing zeros to be added if and when required.
+
+
+
+
+
+
+
+ 
+ |
+
+
+
+ Welcome, ${firstName}!
+
+ Thank you for signing up with GuardianCall.ai. Your account registration request has been received and is currently under review.
+
+
+ Once your account is approved, you'll receive a confirmation email with next steps and login instructions.
+
+
+ In the meantime, feel free to explore more about what GuardianCall.ai can do for you.
+
+ Warm regards,
The GuardianCall.ai Team
+ |
+
+
+ |
+ © 2025 GuardianCall.ai. All rights reserved.
+ |
+
+
+ |
+
+
+
+`
+ };
+
+ return transporter.sendMail(mailOptions);
+}
+
+// Send signup request to admin + acknowledgment to user
+async function sendSignupEmail(email, firstName, lastName, password) {
+ if (!canSendEmail(email)) {
+ const error = new Error(`Rate limit exceeded for ${email}. Please try again later.`);
+ error.status = 429; // Too Many Requests
+ throw error;
+ }
+
+ const mailOptions = {
+ from: `"GuardianCall.ai" <${process.env.GMAIL_USER}>`,
+ to: process.env.gmail_admin,
+ subject: 'Signup request',
+ html: `
+
+
+
+ New Signup Request - GuardianCall
+
+
+
+
+
+
+
+ |
+
+ |
+
+
+
+ New Signup Request Received
+ Hi Admin,
+ A new user has requested signup on GuardianCall.ai.
+ User Details:
+
+ - First Name: ${firstName}
+ - Last Name: ${lastName}
+ - Email: ${email}
+ - Suggested Password: ${password}
+
+ Please verify the information and take appropriate action.
+ Cheers,
The GuardianCall.ai Team
+ |
+
+
+ |
+ © 2025 GuardianCall.ai. All rights reserved.
+ |
+
+
+ |
+
+
+
+`
+ };
+
+ // Send both emails
+ await sendAcknowledgementEmail(firstName, email);
+ return transporter.sendMail(mailOptions);
+}
+
+
+
+module.exports = { sendSignupEmail };
[Dmitriy Mozgovoy](https://github.com/DigitalBrainJS "+14/-9 (#6410 )")
-# [1.7.0](https://github.com/axios/axios/compare/v1.7.0-beta.2...v1.7.0) (2024-05-19)
-
-
-### Features
-
-* **adapter:** add fetch adapter; ([#6371](https://github.com/axios/axios/issues/6371)) ([a3ff99b](https://github.com/axios/axios/commit/a3ff99b59d8ec2ab5dd049e68c043617a4072e42))
-
-### Bug Fixes
-
-* **core/axios:** handle un-writable error stack ([#6362](https://github.com/axios/axios/issues/6362)) ([81e0455](https://github.com/axios/axios/commit/81e0455b7b57fbaf2be16a73ebe0e6591cc6d8f9))
-
-### Contributors to this release
-
-- 
[Jay](https://github.com/jasonsaayman "+30/-14 ()")
-- 
[Alexandre ABRIOUX](https://github.com/alexandre-abrioux "+56/-6 (#6362 )")
-
-# [1.7.0-beta.2](https://github.com/axios/axios/compare/v1.7.0-beta.1...v1.7.0-beta.2) (2024-05-19)
-
-
-### Bug Fixes
-
-* **fetch:** capitalize HTTP method names; ([#6395](https://github.com/axios/axios/issues/6395)) ([ad3174a](https://github.com/axios/axios/commit/ad3174a3515c3c2573f4bcb94818d582826f3914))
-* **fetch:** fix & optimize progress capturing for cases when the request data has a nullish value or zero data length ([#6400](https://github.com/axios/axios/issues/6400)) ([95a3e8e](https://github.com/axios/axios/commit/95a3e8e346cfd6a5548e171f2341df3235d0e26b))
-* **fetch:** fix headers getting from a stream response; ([#6401](https://github.com/axios/axios/issues/6401)) ([870e0a7](https://github.com/axios/axios/commit/870e0a76f60d0094774a6a63fa606eec52a381af))
-
-### Contributors to this release
-
-- 
[Mitchell](https://github.com/Creaous "+9/-9 (#6300 )")
-- 
[Emmanuel](https://github.com/mannoeu "+2/-2 (#6196 )")
-- 
[Lucas Keller](https://github.com/ljkeller "+3/-0 (#6194 )")
-- 
[Aditya Mogili](https://github.com/ADITYA-176 "+1/-1 ()")
-- 
[Miroslav Petrov](https://github.com/petrovmiroslav "+1/-1 (#6243 )")
-
-## [1.6.7](https://github.com/axios/axios/compare/v1.6.6...v1.6.7) (2024-01-25)
-
-
-### Bug Fixes
-
-* capture async stack only for rejections with native error objects; ([#6203](https://github.com/axios/axios/issues/6203)) ([1a08f90](https://github.com/axios/axios/commit/1a08f90f402336e4d00e9ee82f211c6adb1640b0))
-
-### Contributors to this release
-
-- 
[zhoulixiang](https://github.com/zh-lx "+0/-3 (#6186 )")
-
-## [1.6.6](https://github.com/axios/axios/compare/v1.6.5...v1.6.6) (2024-01-24)
-
-
-### Bug Fixes
-
-* fixed missed dispatchBeforeRedirect argument ([#5778](https://github.com/axios/axios/issues/5778)) ([a1938ff](https://github.com/axios/axios/commit/a1938ff073fcb0f89011f001dfbc1fa1dc995e39))
-* wrap errors to improve async stack trace ([#5987](https://github.com/axios/axios/issues/5987)) ([123f354](https://github.com/axios/axios/commit/123f354b920f154a209ea99f76b7b2ef3d9ebbab))
-
-### Contributors to this release
-
-- 
[Ilya Priven](https://github.com/ikonst "+91/-8 (#5987 )")
-- 
[Zao Soula](https://github.com/zaosoula "+6/-6 (#5778 )")
-
-## [1.6.5](https://github.com/axios/axios/compare/v1.6.4...v1.6.5) (2024-01-05)
-
-
-### Bug Fixes
-
-* **ci:** refactor notify action as a job of publish action; ([#6176](https://github.com/axios/axios/issues/6176)) ([0736f95](https://github.com/axios/axios/commit/0736f95ce8776366dc9ca569f49ba505feb6373c))
-* **dns:** fixed lookup error handling; ([#6175](https://github.com/axios/axios/issues/6175)) ([f4f2b03](https://github.com/axios/axios/commit/f4f2b039dd38eb4829e8583caede4ed6d2dd59be))
-
-### Contributors to this release
-
-- 
[Guy Nesher](https://github.com/gnesher "+10/-10 (#6163 )")
-
-## [1.6.3](https://github.com/axios/axios/compare/v1.6.2...v1.6.3) (2023-12-26)
-
-
-### Bug Fixes
-
-* Regular Expression Denial of Service (ReDoS) ([#6132](https://github.com/axios/axios/issues/6132)) ([5e7ad38](https://github.com/axios/axios/commit/5e7ad38fb0f819fceb19fb2ee5d5d38f56aa837d))
-
-### Contributors to this release
-
-- 
[Willian Agostini](https://github.com/WillianAgostini "+17/-2 (#6132 )")
-- 
[Ng Choon Khon (CK)](https://github.com/ckng0221 "+4/-4 (#6073 )")
-- 
[Muhammad Noman](https://github.com/mnomanmemon "+2/-2 (#6048 )")
-
-## [1.6.1](https://github.com/axios/axios/compare/v1.6.0...v1.6.1) (2023-11-08)
-
-
-### Bug Fixes
-
-* **formdata:** fixed content-type header normalization for non-standard browser environments; ([#6056](https://github.com/axios/axios/issues/6056)) ([dd465ab](https://github.com/axios/axios/commit/dd465ab22bbfa262c6567be6574bf46a057d5288))
-* **platform:** fixed emulated browser detection in node.js environment; ([#6055](https://github.com/axios/axios/issues/6055)) ([3dc8369](https://github.com/axios/axios/commit/3dc8369e505e32a4e12c22f154c55fd63ac67fbb))
-
-### Contributors to this release
-
-- 
[Fabian Meyer](https://github.com/meyfa "+5/-2 (#5835 )")
-
-### PRs
-- feat(withXSRFToken): added withXSRFToken option as a workaround to achieve the old `withCredentials` behavior; ( [#6046](https://api.github.com/repos/axios/axios/pulls/6046) )
-```
-
-📢 This PR added 'withXSRFToken' option as a replacement for old withCredentials behaviour.
-You should now use withXSRFToken along with withCredential to get the old behavior.
-This functionality is considered as a fix.
-```
-
-# [1.6.0](https://github.com/axios/axios/compare/v1.5.1...v1.6.0) (2023-10-26)
-
-
-### Bug Fixes
-
-* **CSRF:** fixed CSRF vulnerability CVE-2023-45857 ([#6028](https://github.com/axios/axios/issues/6028)) ([96ee232](https://github.com/axios/axios/commit/96ee232bd3ee4de2e657333d4d2191cd389e14d0))
-* **dns:** fixed lookup function decorator to work properly in node v20; ([#6011](https://github.com/axios/axios/issues/6011)) ([5aaff53](https://github.com/axios/axios/commit/5aaff532a6b820bb9ab6a8cd0f77131b47e2adb8))
-* **types:** fix AxiosHeaders types; ([#5931](https://github.com/axios/axios/issues/5931)) ([a1c8ad0](https://github.com/axios/axios/commit/a1c8ad008b3c13d53e135bbd0862587fb9d3fc09))
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-### Contributors to this release
-
-- 
[Valentin Panov](https://github.com/valentin-panov "+4/-4 (#6028 )")
-- 
[Rinku Chaudhari](https://github.com/therealrinku "+1/-1 (#5889 )")
-
-## [1.5.1](https://github.com/axios/axios/compare/v1.5.0...v1.5.1) (2023-09-26)
-
-
-### Bug Fixes
-
-* **adapters:** improved adapters loading logic to have clear error messages; ([#5919](https://github.com/axios/axios/issues/5919)) ([e410779](https://github.com/axios/axios/commit/e4107797a7a1376f6209fbecfbbce73d3faa7859))
-* **formdata:** fixed automatic addition of the `Content-Type` header for FormData in non-browser environments; ([#5917](https://github.com/axios/axios/issues/5917)) ([bc9af51](https://github.com/axios/axios/commit/bc9af51b1886d1b3529617702f2a21a6c0ed5d92))
-* **headers:** allow `content-encoding` header to handle case-insensitive values ([#5890](https://github.com/axios/axios/issues/5890)) ([#5892](https://github.com/axios/axios/issues/5892)) ([4c89f25](https://github.com/axios/axios/commit/4c89f25196525e90a6e75eda9cb31ae0a2e18acd))
-* **types:** removed duplicated code ([9e62056](https://github.com/axios/axios/commit/9e6205630e1c9cf863adf141c0edb9e6d8d4b149))
-
-### Contributors to this release
-
-- 
[David Dallas](https://github.com/DavidJDallas "+11/-5 ()")
-- 
[Sean Sattler](https://github.com/fb-sean "+2/-8 ()")
-- 
[Mustafa Ateş Uzun](https://github.com/0o001 "+4/-4 ()")
-- 
[Przemyslaw Motacki](https://github.com/sfc-gh-pmotacki "+2/-1 (#5892 )")
-- 
[Michael Di Prisco](https://github.com/Cadienvan "+1/-1 ()")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-# [1.5.0](https://github.com/axios/axios/compare/v1.4.0...v1.5.0) (2023-08-26)
-
-
-### Bug Fixes
-
-* **adapter:** make adapter loading error more clear by using platform-specific adapters explicitly ([#5837](https://github.com/axios/axios/issues/5837)) ([9a414bb](https://github.com/axios/axios/commit/9a414bb6c81796a95c6c7fe668637825458e8b6d))
-* **dns:** fixed `cacheable-lookup` integration; ([#5836](https://github.com/axios/axios/issues/5836)) ([b3e327d](https://github.com/axios/axios/commit/b3e327dcc9277bdce34c7ef57beedf644b00d628))
-* **headers:** added support for setting header names that overlap with class methods; ([#5831](https://github.com/axios/axios/issues/5831)) ([d8b4ca0](https://github.com/axios/axios/commit/d8b4ca0ea5f2f05efa4edfe1e7684593f9f68273))
-* **headers:** fixed common Content-Type header merging; ([#5832](https://github.com/axios/axios/issues/5832)) ([8fda276](https://github.com/axios/axios/commit/8fda2766b1e6bcb72c3fabc146223083ef13ce17))
-
-
-### Features
-
-* export getAdapter function ([#5324](https://github.com/axios/axios/issues/5324)) ([ca73eb8](https://github.com/axios/axios/commit/ca73eb878df0ae2dace81fe3a7f1fb5986231bf1))
-* **export:** export adapters without `unsafe` prefix ([#5839](https://github.com/axios/axios/issues/5839)) ([1601f4a](https://github.com/axios/axios/commit/1601f4a27a81ab47fea228f1e244b2c4e3ce28bf))
-
-### Contributors to this release
-
-- 
[夜葬](https://github.com/geekact "+42/-0 (#5324 )")
-- 
[Jonathan Budiman](https://github.com/JBudiman00 "+30/-0 (#5788 )")
-- 
[Arthur Fiorette](https://github.com/arthurfiorette "+19/-19 (#5525 )")
-- 
[PIYUSH NEGI](https://github.com/npiyush97 "+2/-18 (#5670 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.3.6](https://github.com/axios/axios/compare/v1.3.5...v1.3.6) (2023-04-19)
-
-
-### Bug Fixes
-
-* **types:** added transport to RawAxiosRequestConfig ([#5445](https://github.com/axios/axios/issues/5445)) ([6f360a2](https://github.com/axios/axios/commit/6f360a2531d8d70363fd9becef6a45a323f170e2))
-* **utils:** make isFormData detection logic stricter to avoid unnecessary calling of the `toString` method on the target; ([#5661](https://github.com/axios/axios/issues/5661)) ([aa372f7](https://github.com/axios/axios/commit/aa372f7306295dfd1100c1c2c77ce95c95808e76))
-
-### Contributors to this release
-
-- 
[lcysgsg](https://github.com/lcysgsg "+4/-0 (#5548 )")
-- 
[陈若枫](https://github.com/ruofee "+2/-2 (#5467 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.3.2](https://github.com/axios/axios/compare/v1.3.1...v1.3.2) (2023-02-03)
-
-
-### Bug Fixes
-
-* **http:** treat http://localhost as base URL for relative paths to avoid `ERR_INVALID_URL` error; ([#5528](https://github.com/axios/axios/issues/5528)) ([128d56f](https://github.com/axios/axios/commit/128d56f4a0fb8f5f2ed6e0dd80bc9225fee9538c))
-* **http:** use explicit import instead of TextEncoder global; ([#5530](https://github.com/axios/axios/issues/5530)) ([6b3c305](https://github.com/axios/axios/commit/6b3c305fc40c56428e0afabedc6f4d29c2830f6f))
-
-### Contributors to this release
-
-- 
[ItsNotGoodName](https://github.com/ItsNotGoodName "+43/-2 (#5497 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.2.6](https://github.com/axios/axios/compare/v1.2.5...v1.2.6) (2023-01-28)
-
-
-### Bug Fixes
-
-* **headers:** added missed Authorization accessor; ([#5502](https://github.com/axios/axios/issues/5502)) ([342c0ba](https://github.com/axios/axios/commit/342c0ba9a16ea50f5ed7d2366c5c1a2c877e3f26))
-* **types:** fixed `CommonRequestHeadersList` & `CommonResponseHeadersList` types to be private in commonJS; ([#5503](https://github.com/axios/axios/issues/5503)) ([5a3d0a3](https://github.com/axios/axios/commit/5a3d0a3234d77361a1bc7cedee2da1e11df08e2c))
-
-### Contributors to this release
-
--  [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS "+24/-9 (#5503 #5502 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.2.5](https://github.com/axios/axios/compare/v1.2.4...v1.2.5) (2023-01-26)
-
-
-### Bug Fixes
-
-* **types:** fixed AxiosHeaders to handle spread syntax by making all methods non-enumerable; ([#5499](https://github.com/axios/axios/issues/5499)) ([580f1e8](https://github.com/axios/axios/commit/580f1e8033a61baa38149d59fd16019de3932c22))
-
-### Contributors to this release
-
--  [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS "+82/-54 (#5499 )")
--  [Elliot Ford](https://github.com/EFord36 "+1/-1 (#5462 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.2.4](https://github.com/axios/axios/compare/v1.2.3...v1.2.4) (2023-01-22)
-
-
-### Bug Fixes
-
-* **types:** renamed `RawAxiosRequestConfig` back to `AxiosRequestConfig`; ([#5486](https://github.com/axios/axios/issues/5486)) ([2a71f49](https://github.com/axios/axios/commit/2a71f49bc6c68495fa419003a3107ed8bd703ad0))
-* **types:** fix `AxiosRequestConfig` generic; ([#5478](https://github.com/axios/axios/issues/5478)) ([9bce81b](https://github.com/axios/axios/commit/186ea062da8b7d578ae78b1a5c220986b9bce81b))
-
-### Contributors to this release
-
--  [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS "+242/-108 (#5486 #5482 )")
--  [Daniel Hillmann](https://github.com/hilleer "+1/-1 (#5478 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.2.3](https://github.com/axios/axios/compare/1.2.2...1.2.3) (2023-01-10)
-
-
-### Bug Fixes
-
-* **types:** fixed AxiosRequestConfig header interface by refactoring it to RawAxiosRequestConfig; ([#5420](https://github.com/axios/axios/issues/5420)) ([0811963](https://github.com/axios/axios/commit/08119634a22f1d5b19f5c9ea0adccb6d3eebc3bc))
-
-### Contributors to this release
-
--  [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS "+938/-442 (#5456 #5455 #5453 #5451 #5449 #5447 #5446 #5443 #5442 #5439 #5420 )")
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.2.2] - 2022-12-29
-
-### Fixed
-- fix(ci): fix release script inputs [#5392](https://github.com/axios/axios/pull/5392)
-- fix(ci): prerelease scipts [#5377](https://github.com/axios/axios/pull/5377)
-- fix(ci): release scripts [#5376](https://github.com/axios/axios/pull/5376)
-- fix(ci): typescript tests [#5375](https://github.com/axios/axios/pull/5375)
-- fix: Brotli decompression [#5353](https://github.com/axios/axios/pull/5353)
-- fix: add missing HttpStatusCode [#5345](https://github.com/axios/axios/pull/5345)
-
-### Chores
-- chore(ci): set conventional-changelog header config [#5406](https://github.com/axios/axios/pull/5406)
-- chore(ci): fix automatic contributors resolving [#5403](https://github.com/axios/axios/pull/5403)
-- chore(ci): improved logging for the contributors list generator [#5398](https://github.com/axios/axios/pull/5398)
-- chore(ci): fix release action [#5397](https://github.com/axios/axios/pull/5397)
-- chore(ci): fix version bump script by adding bump argument for target version [#5393](https://github.com/axios/axios/pull/5393)
-- chore(deps): bump decode-uri-component from 0.2.0 to 0.2.2 [#5342](https://github.com/axios/axios/pull/5342)
-- chore(ci): GitHub Actions Release script [#5384](https://github.com/axios/axios/pull/5384)
-- chore(ci): release scripts [#5364](https://github.com/axios/axios/pull/5364)
-
-### Contributors to this release
--  [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS)
--  [Winnie](https://github.com/winniehell)
-
-## [1.2.1] - 2022-12-05
-
-### Changed
-- feat(exports): export mergeConfig [#5151](https://github.com/axios/axios/pull/5151)
-
-### Fixed
-- fix(CancelledError): include config [#4922](https://github.com/axios/axios/pull/4922)
-- fix(general): removing multiple/trailing/leading whitespace [#5022](https://github.com/axios/axios/pull/5022)
-- fix(headers): decompression for responses without Content-Length header [#5306](https://github.com/axios/axios/pull/5306)
-- fix(webWorker): exception to sending form data in web worker [#5139](https://github.com/axios/axios/pull/5139)
-
-### Refactors
-- refactor(types): AxiosProgressEvent.event type to any [#5308](https://github.com/axios/axios/pull/5308)
-- refactor(types): add missing types for static AxiosError.from method [#4956](https://github.com/axios/axios/pull/4956)
-
-### Chores
-- chore(docs): remove README link to non-existent upgrade guide [#5307](https://github.com/axios/axios/pull/5307)
-- chore(docs): typo in issue template name [#5159](https://github.com/axios/axios/pull/5159)
-
-### Contributors to this release
-
-- [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS)
-- [Zachary Lysobey](https://github.com/zachlysobey)
-- [Kevin Ennis](https://github.com/kevincennis)
-- [Philipp Loose](https://github.com/phloose)
-- [secondl1ght](https://github.com/secondl1ght)
-- [wenzheng](https://github.com/0x30)
-- [Ivan Barsukov](https://github.com/ovarn)
-- [Arthur Fiorette](https://github.com/arthurfiorette)
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.2.0] - 2022-11-10
-
-### Changed
-
-- changed: refactored module exports [#5162](https://github.com/axios/axios/pull/5162)
-- change: re-added support for loading Axios with require('axios').default [#5225](https://github.com/axios/axios/pull/5225)
-
-### Fixed
-
-- fix: improve AxiosHeaders class [#5224](https://github.com/axios/axios/pull/5224)
-- fix: TypeScript type definitions for commonjs [#5196](https://github.com/axios/axios/pull/5196)
-- fix: type definition of use method on AxiosInterceptorManager to match the the README [#5071](https://github.com/axios/axios/pull/5071)
-- fix: __dirname is not defined in the sandbox [#5269](https://github.com/axios/axios/pull/5269)
-- fix: AxiosError.toJSON method to avoid circular references [#5247](https://github.com/axios/axios/pull/5247)
-- fix: Z_BUF_ERROR when content-encoding is set but the response body is empty [#5250](https://github.com/axios/axios/pull/5250)
-
-### Refactors
-- refactor: allowing adapters to be loaded by name [#5277](https://github.com/axios/axios/pull/5277)
-
-### Chores
-
-- chore: force CI restart [#5243](https://github.com/axios/axios/pull/5243)
-- chore: update ECOSYSTEM.md [#5077](https://github.com/axios/axios/pull/5077)
-- chore: update get/index.html [#5116](https://github.com/axios/axios/pull/5116)
-- chore: update Sandbox UI/UX [#5205](https://github.com/axios/axios/pull/5205)
-- chore:(actions): remove git credentials after checkout [#5235](https://github.com/axios/axios/pull/5235)
-- chore(actions): bump actions/dependency-review-action from 2 to 3 [#5266](https://github.com/axios/axios/pull/5266)
-- chore(packages): bump loader-utils from 1.4.1 to 1.4.2 [#5295](https://github.com/axios/axios/pull/5295)
-- chore(packages): bump engine.io from 6.2.0 to 6.2.1 [#5294](https://github.com/axios/axios/pull/5294)
-- chore(packages): bump socket.io-parser from 4.0.4 to 4.0.5 [#5241](https://github.com/axios/axios/pull/5241)
-- chore(packages): bump loader-utils from 1.4.0 to 1.4.1 [#5245](https://github.com/axios/axios/pull/5245)
-- chore(docs): update Resources links in README [#5119](https://github.com/axios/axios/pull/5119)
-- chore(docs): update the link for JSON url [#5265](https://github.com/axios/axios/pull/5265)
-- chore(docs): fix broken links [#5218](https://github.com/axios/axios/pull/5218)
-- chore(docs): update and rename UPGRADE_GUIDE.md to MIGRATION_GUIDE.md [#5170](https://github.com/axios/axios/pull/5170)
-- chore(docs): typo fix line #856 and #920 [#5194](https://github.com/axios/axios/pull/5194)
-- chore(docs): typo fix #800 [#5193](https://github.com/axios/axios/pull/5193)
-- chore(docs): fix typos [#5184](https://github.com/axios/axios/pull/5184)
-- chore(docs): fix punctuation in README.md [#5197](https://github.com/axios/axios/pull/5197)
-- chore(docs): update readme in the Handling Errors section - issue reference #5260 [#5261](https://github.com/axios/axios/pull/5261)
-- chore: remove \b from filename [#5207](https://github.com/axios/axios/pull/5207)
-- chore(docs): update CHANGELOG.md [#5137](https://github.com/axios/axios/pull/5137)
-- chore: add sideEffects false to package.json [#5025](https://github.com/axios/axios/pull/5025)
-
-### Contributors to this release
-
-- [Maddy Miller](https://github.com/me4502)
-- [Amit Saini](https://github.com/amitsainii)
-- [ecyrbe](https://github.com/ecyrbe)
-- [Ikko Ashimine](https://github.com/eltociear)
-- [Geeth Gunnampalli](https://github.com/thetechie7)
-- [Shreem Asati](https://github.com/shreem-123)
-- [Frieder Bluemle](https://github.com/friederbluemle)
-- [윤세영](https://github.com/yunseyeong)
-- [Claudio Busatto](https://github.com/cjcbusatto)
-- [Remco Haszing](https://github.com/remcohaszing)
-- [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS)
-- [Csaba Maulis](https://github.com/om4csaba)
-- [MoPaMo](https://github.com/MoPaMo)
-- [Daniel Fjeldstad](https://github.com/w3bdesign)
-- [Adrien Brunet](https://github.com/adrien-may)
-- [Frazer Smith](https://github.com/Fdawgs)
-- [HaiTao](https://github.com/836334258)
-- [AZM](https://github.com/aziyatali)
-- [relbns](https://github.com/relbns)
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.1.3] - 2022-10-15
-
-### Added
-
-- Added custom params serializer support [#5113](https://github.com/axios/axios/pull/5113)
-
-### Fixed
-
-- Fixed top-level export to keep them in-line with static properties [#5109](https://github.com/axios/axios/pull/5109)
-- Stopped including null values to query string. [#5108](https://github.com/axios/axios/pull/5108)
-- Restored proxy config backwards compatibility with 0.x [#5097](https://github.com/axios/axios/pull/5097)
-- Added back AxiosHeaders in AxiosHeaderValue [#5103](https://github.com/axios/axios/pull/5103)
-- Pin CDN install instructions to a specific version [#5060](https://github.com/axios/axios/pull/5060)
-- Handling of array values fixed for AxiosHeaders [#5085](https://github.com/axios/axios/pull/5085)
-
-### Chores
-
-- docs: match badge style, add link to them [#5046](https://github.com/axios/axios/pull/5046)
-- chore: fixing comments typo [#5054](https://github.com/axios/axios/pull/5054)
-- chore: update issue template [#5061](https://github.com/axios/axios/pull/5061)
-- chore: added progress capturing section to the docs; [#5084](https://github.com/axios/axios/pull/5084)
-
-### Contributors to this release
-
-- [Jason Saayman](https://github.com/jasonsaayman)
-- [scarf](https://github.com/scarf005)
-- [Lenz Weber-Tronic](https://github.com/phryneas)
-- [Arvindh](https://github.com/itsarvindh)
-- [Félix Legrelle](https://github.com/FelixLgr)
-- [Patrick Petrovic](https://github.com/ppati000)
-- [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS)
-- [littledian](https://github.com/littledian)
-- [ChronosMasterOfAllTime](https://github.com/ChronosMasterOfAllTime)
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.1.2] - 2022-10-07
-
-### Fixed
-
-- Fixed broken exports for UMD builds.
-
-### Contributors to this release
-
-- [Jason Saayman](https://github.com/jasonsaayman)
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.1.1] - 2022-10-07
-
-### Fixed
-
-- Fixed broken exports for common js. This fix breaks a prior fix, I will fix both issues ASAP but the commonJS use is more impactful.
-
-### Contributors to this release
-
-- [Jason Saayman](https://github.com/jasonsaayman)
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.1.0] - 2022-10-06
-
-### Fixed
-
-- Fixed missing exports in type definition index.d.ts [#5003](https://github.com/axios/axios/pull/5003)
-- Fixed query params composing [#5018](https://github.com/axios/axios/pull/5018)
-- Fixed GenericAbortSignal interface by making it more generic [#5021](https://github.com/axios/axios/pull/5021)
-- Fixed adding "clear" to AxiosInterceptorManager [#5010](https://github.com/axios/axios/pull/5010)
-- Fixed commonjs & umd exports [#5030](https://github.com/axios/axios/pull/5030)
-- Fixed inability to access response headers when using axios 1.x with Jest [#5036](https://github.com/axios/axios/pull/5036)
-
-### Contributors to this release
-
-- [Trim21](https://github.com/trim21)
-- [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS)
-- [shingo.sasaki](https://github.com/s-sasaki-0529)
-- [Ivan Pepelko](https://github.com/ivanpepelko)
-- [Richard Kořínek](https://github.com/risa)
-
-### PRs
-- CVE 2023 45857 ( [#6028](https://api.github.com/repos/axios/axios/pulls/6028) )
-```
-
-⚠️ Critical vulnerability fix. See https://security.snyk.io/vuln/SNYK-JS-AXIOS-6032459
-```
-
-## [1.0.0] - 2022-10-04
-
-### Added
-
-- Added stack trace to AxiosError [#4624](https://github.com/axios/axios/pull/4624)
-- Add AxiosError to AxiosStatic [#4654](https://github.com/axios/axios/pull/4654)
-- Replaced Rollup as our build runner [#4596](https://github.com/axios/axios/pull/4596)
-- Added generic TS types for the exposed toFormData helper [#4668](https://github.com/axios/axios/pull/4668)
-- Added listen callback function [#4096](https://github.com/axios/axios/pull/4096)
-- Added instructions for installing using PNPM [#4207](https://github.com/axios/axios/pull/4207)
-- Added generic AxiosAbortSignal TS interface to avoid importing AbortController polyfill [#4229](https://github.com/axios/axios/pull/4229)
-- Added axios-url-template in ECOSYSTEM.md [#4238](https://github.com/axios/axios/pull/4238)
-- Added a clear() function to the request and response interceptors object so a user can ensure that all interceptors have been removed from an axios instance [#4248](https://github.com/axios/axios/pull/4248)
-- Added react hook plugin [#4319](https://github.com/axios/axios/pull/4319)
-- Adding HTTP status code for transformResponse [#4580](https://github.com/axios/axios/pull/4580)
-- Added blob to the list of protocols supported by the browser [#4678](https://github.com/axios/axios/pull/4678)
-- Resolving proxy from env on redirect [#4436](https://github.com/axios/axios/pull/4436)
-- Added enhanced toFormData implementation with additional options [4704](https://github.com/axios/axios/pull/4704)
-- Adding Canceler parameters config and request [#4711](https://github.com/axios/axios/pull/4711)
-- Added automatic payload serialization to application/x-www-form-urlencoded [#4714](https://github.com/axios/axios/pull/4714)
-- Added the ability for webpack users to overwrite built-ins [#4715](https://github.com/axios/axios/pull/4715)
-- Added string[] to AxiosRequestHeaders type [#4322](https://github.com/axios/axios/pull/4322)
-- Added the ability for the url-encoded-form serializer to respect the formSerializer config [#4721](https://github.com/axios/axios/pull/4721)
-- Added isCancel type assert [#4293](https://github.com/axios/axios/pull/4293)
-- Added data URL support for node.js [#4725](https://github.com/axios/axios/pull/4725)
-- Adding types for progress event callbacks [#4675](https://github.com/axios/axios/pull/4675)
-- URL params serializer [#4734](https://github.com/axios/axios/pull/4734)
-- Added axios.formToJSON method [#4735](https://github.com/axios/axios/pull/4735)
-- Bower platform add data protocol [#4804](https://github.com/axios/axios/pull/4804)
-- Use WHATWG URL API instead of url.parse() [#4852](https://github.com/axios/axios/pull/4852)
-- Add ENUM containing Http Status Codes to typings [#4903](https://github.com/axios/axios/pull/4903)
-- Improve typing of timeout in index.d.ts [#4934](https://github.com/axios/axios/pull/4934)
-
-### Changed
-
-- Updated AxiosError.config to be optional in the type definition [#4665](https://github.com/axios/axios/pull/4665)
-- Updated README emphasizing the URLSearchParam built-in interface over other solutions [#4590](https://github.com/axios/axios/pull/4590)
-- Include request and config when creating a CanceledError instance [#4659](https://github.com/axios/axios/pull/4659)
-- Changed func-names eslint rule to as-needed [#4492](https://github.com/axios/axios/pull/4492)
-- Replacing deprecated substr() with slice() as substr() is deprecated [#4468](https://github.com/axios/axios/pull/4468)
-- Updating HTTP links in README.md to use HTTPS [#4387](https://github.com/axios/axios/pull/4387)
-- Updated to a better trim() polyfill [#4072](https://github.com/axios/axios/pull/4072)
-- Updated types to allow specifying partial default headers on instance create [#4185](https://github.com/axios/axios/pull/4185)
-- Expanded isAxiosError types [#4344](https://github.com/axios/axios/pull/4344)
-- Updated type definition for axios instance methods [#4224](https://github.com/axios/axios/pull/4224)
-- Updated eslint config [#4722](https://github.com/axios/axios/pull/4722)
-- Updated Docs [#4742](https://github.com/axios/axios/pull/4742)
-- Refactored Axios to use ES2017 [#4787](https://github.com/axios/axios/pull/4787)
-
-
-### Deprecated
-- There are multiple deprecations, refactors and fixes provided in this release. Please read through the full release notes to see how this may impact your project and use case.
-
-### Removed
-
-- Removed incorrect argument for NetworkError constructor [#4656](https://github.com/axios/axios/pull/4656)
-- Removed Webpack [#4596](https://github.com/axios/axios/pull/4596)
-- Removed function that transform arguments to array [#4544](https://github.com/axios/axios/pull/4544)
-
-### Fixed
-
-- Fixed grammar in README [#4649](https://github.com/axios/axios/pull/4649)
-- Fixed code error in README [#4599](https://github.com/axios/axios/pull/4599)
-- Optimized the code that checks cancellation [#4587](https://github.com/axios/axios/pull/4587)
-- Fix url pointing to defaults.js in README [#4532](https://github.com/axios/axios/pull/4532)
-- Use type alias instead of interface for AxiosPromise [#4505](https://github.com/axios/axios/pull/4505)
-- Fix some word spelling and lint style in code comments [#4500](https://github.com/axios/axios/pull/4500)
-- Edited readme with 3 updated browser icons of Chrome, FireFox and Safari [#4414](https://github.com/axios/axios/pull/4414)
-- Bump follow-redirects from 1.14.9 to 1.15.0 [#4673](https://github.com/axios/axios/pull/4673)
-- Fixing http tests to avoid hanging when assertions fail [#4435](https://github.com/axios/axios/pull/4435)
-- Fix TS definition for AxiosRequestTransformer [#4201](https://github.com/axios/axios/pull/4201)
-- Fix grammatical issues in README [#4232](https://github.com/axios/axios/pull/4232)
-- Fixing instance.defaults.headers type [#4557](https://github.com/axios/axios/pull/4557)
-- Fixed race condition on immediate requests cancellation [#4261](https://github.com/axios/axios/pull/4261)
-- Fixing Z_BUF_ERROR when no content [#4701](https://github.com/axios/axios/pull/4701)
-- Fixing proxy beforeRedirect regression [#4708](https://github.com/axios/axios/pull/4708)
-- Fixed AxiosError status code type [#4717](https://github.com/axios/axios/pull/4717)
-- Fixed AxiosError stack capturing [#4718](https://github.com/axios/axios/pull/4718)
-- Fixing AxiosRequestHeaders typings [#4334](https://github.com/axios/axios/pull/4334)
-- Fixed max body length defaults [#4731](https://github.com/axios/axios/pull/4731)
-- Fixed toFormData Blob issue on node>v17 [#4728](https://github.com/axios/axios/pull/4728)
-- Bump grunt from 1.5.2 to 1.5.3 [#4743](https://github.com/axios/axios/pull/4743)
-- Fixing content-type header repeated [#4745](https://github.com/axios/axios/pull/4745)
-- Fixed timeout error message for http [4738](https://github.com/axios/axios/pull/4738)
-- Request ignores false, 0 and empty string as body values [#4785](https://github.com/axios/axios/pull/4785)
-- Added back missing minified builds [#4805](https://github.com/axios/axios/pull/4805)
-- Fixed a type error [#4815](https://github.com/axios/axios/pull/4815)
-- Fixed a regression bug with unsubscribing from cancel token; [#4819](https://github.com/axios/axios/pull/4819)
-- Remove repeated compression algorithm [#4820](https://github.com/axios/axios/pull/4820)
-- The error of calling extend to pass parameters [#4857](https://github.com/axios/axios/pull/4857)
-- SerializerOptions.indexes allows boolean | null | undefined [#4862](https://github.com/axios/axios/pull/4862)
-- Require interceptors to return values [#4874](https://github.com/axios/axios/pull/4874)
-- Removed unused imports [#4949](https://github.com/axios/axios/pull/4949)
-- Allow null indexes on formSerializer and paramsSerializer [#4960](https://github.com/axios/axios/pull/4960)
-
-### Chores
-- Set permissions for GitHub actions [#4765](https://github.com/axios/axios/pull/4765)
-- Included githubactions in the dependabot config [#4770](https://github.com/axios/axios/pull/4770)
-- Included dependency review [#4771](https://github.com/axios/axios/pull/4771)
-- Update security.md [#4784](https://github.com/axios/axios/pull/4784)
-- Remove unnecessary spaces [#4854](https://github.com/axios/axios/pull/4854)
-- Simplify the import path of AxiosError [#4875](https://github.com/axios/axios/pull/4875)
-- Fix Gitpod dead link [#4941](https://github.com/axios/axios/pull/4941)
-- Enable syntax highlighting for a code block [#4970](https://github.com/axios/axios/pull/4970)
-- Using Logo Axios in Readme.md [#4993](https://github.com/axios/axios/pull/4993)
-- Fix markup for note in README [#4825](https://github.com/axios/axios/pull/4825)
-- Fix typo and formatting, add colons [#4853](https://github.com/axios/axios/pull/4853)
-- Fix typo in readme [#4942](https://github.com/axios/axios/pull/4942)
-
-### Security
-
-- Update SECURITY.md [#4687](https://github.com/axios/axios/pull/4687)
-
-### Contributors to this release
-
-- [Bertrand Marron](https://github.com/tusbar)
-- [Dmitriy Mozgovoy](https://github.com/DigitalBrainJS)
-- [Dan Mooney](https://github.com/danmooney)
-- [Michael Li](https://github.com/xiaoyu-tamu)
-- [aong](https://github.com/yxwzaxns)
-- [Des Preston](https://github.com/despreston)
-- [Ted Robertson](https://github.com/tredondo)
-- [zhoulixiang](https://github.com/zh-lx)
-- [Arthur Fiorette](https://github.com/arthurfiorette)
-- [Kumar Shanu](https://github.com/Kr-Shanu)
-- [JALAL](https://github.com/JLL32)
-- [Jingyi Lin](https://github.com/MageeLin)
-- [Philipp Loose](https://github.com/phloose)
-- [Alexander Shchukin](https://github.com/sashsvamir)
-- [Dave Cardwell](https://github.com/davecardwell)
-- [Cat Scarlet](https://github.com/catscarlet)
-- [Luca Pizzini](https://github.com/lpizzinidev)
-- [Kai](https://github.com/Schweinepriester)
-- [Maxime Bargiel](https://github.com/mbargiel)
-- [Brian Helba](https://github.com/brianhelba)
-- [reslear](https://github.com/reslear)
-- [Jamie Slome](https://github.com/JamieSlome)
-- [Landro3](https://github.com/Landro3)
-- [rafw87](https://github.com/rafw87)
-- [Afzal Sayed](https://github.com/afzalsayed96)
-- [Koki Oyatsu](https://github.com/kaishuu0123)
-- [Dave](https://github.com/wangcch)
-- [暴走老七](https://github.com/baozouai)
-- [Spencer](https://github.com/spalger)
-- [Adrian Wieprzkowicz](https://github.com/Argeento)
-- [Jamie Telin](https://github.com/lejahmie)
-- [毛呆](https://github.com/aweikalee)
-- [Kirill Shakirov](https://github.com/turisap)
-- [Rraji Abdelbari](https://github.com/estarossa0)
-- [Jelle Schutter](https://github.com/jelleschutter)
-- [Tom Ceuppens](https://github.com/KyorCode)
-- [Johann Cooper](https://github.com/JohannCooper)
-- [Dimitris Halatsis](https://github.com/mitsos1os)
-- [chenjigeng](https://github.com/chenjigeng)
-- [João Gabriel Quaresma](https://github.com/joaoGabriel55)
-- [Victor Augusto](https://github.com/VictorAugDB)
-- [neilnaveen](https://github.com/neilnaveen)
-- [Pavlos](https://github.com/psmoros)
-- [Kiryl Valkovich](https://github.com/visortelle)
-- [Naveen](https://github.com/naveensrinivasan)
-- [wenzheng](https://github.com/0x30)
-- [hcwhan](https://github.com/hcwhan)
-- [Bassel Rachid](https://github.com/basselworkforce)
-- [Grégoire Pineau](https://github.com/lyrixx)
-- [felipedamin](https://github.com/felipedamin)
-- [Karl Horky](https://github.com/karlhorky)
-- [Yue JIN](https://github.com/kingyue737)
-- [Usman Ali Siddiqui](https://github.com/usman250994)
-- [WD](https://github.com/techbirds)
-- [Günther Foidl](https://github.com/gfoidl)
-- [Stephen Jennings](https://github.com/jennings)
-- [C.T.Lin](https://github.com/chentsulin)
-- [mia-z](https://github.com/mia-z)
-- [Parth Banathia](https://github.com/Parth0105)
-- [parth0105pluang](https://github.com/parth0105pluang)
-- [Marco Weber](https://github.com/mrcwbr)
-- [Luca Pizzini](https://github.com/lpizzinidev)
-- [Willian Agostini](https://github.com/WillianAgostini)
+# [1.7.0](https://github.com/axios/axios/compare/v1.7.0-beta.2...v1.7.0) (2024-05-19)
+
+
+### Features
+
+* **adapter:** add fetch adapter; ([#6371](https://github.com/axios/axios/issues/6371)) ([a3ff99b](https://github.com/axios/axios/commit/a3ff99b59d8ec2ab5dd049e68c043617a4072e42))
+
+### Bug Fixes
+
+* **core/axios:** handle un-writable error stack ([#6362](https://github.com/axios/axios/issues/6362)) ([81e0455](https://github.com/axios/axios/commit/81e0455b7b57fbaf2be16a73ebe0e6591cc6d8f9))
+
+### Contributors to this release
+
+-