/*
* bignumber.js v9.0.0
* A JavaScript library for arbitrary-precision arithmetic.
* https://github.com/MikeMcl/bignumber.js
* Copyright (c) 2019 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licensed.
*
* BigNumber.prototype methods | BigNumber methods
* |
* absoluteValue abs | clone
* comparedTo | config set
* decimalPlaces dp | DECIMAL_PLACES
* dividedBy div | ROUNDING_MODE
* dividedToIntegerBy idiv | EXPONENTIAL_AT
* exponentiatedBy pow | RANGE
* integerValue | CRYPTO
* isEqualTo eq | MODULO_MODE
* isFinite | POW_PRECISION
* isGreaterThan gt | FORMAT
* isGreaterThanOrEqualTo gte | ALPHABET
* isInteger | isBigNumber
* isLessThan lt | maximum max
* isLessThanOrEqualTo lte | minimum min
* isNaN | random
* isNegative | sum
* isPositive |
* isZero |
* minus |
* modulo mod |
* multipliedBy times |
* negated |
* plus |
* precision sd |
* shiftedBy |
* squareRoot sqrt |
* toExponential |
* toFixed |
* toFormat |
* toFraction |
* toJSON |
* toNumber |
* toPrecision |
* toString |
* valueOf |
*
*/
var
isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
mathceil = Math.ceil,
mathfloor = Math.floor,
bignumberError = '[BigNumber Error] ',
tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
BASE = 1e14,
LOG_BASE = 14,
MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1
// MAX_INT32 = 0x7fffffff, // 2^31 - 1
POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
SQRT_BASE = 1e7,
// EDITABLE
// The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
// the arguments to toExponential, toFixed, toFormat, and toPrecision.
MAX = 1E9; // 0 to MAX_INT32
/*
* Create and return a BigNumber constructor.
*/
function clone(configObject) {
var div, convertBase, parseNumeric,
P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
ONE = new BigNumber(1),
//----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
// The default values below must be integers within the inclusive ranges stated.
// The values can also be changed at run-time using BigNumber.set.
// The maximum number of decimal places for operations involving division.
DECIMAL_PLACES = 20, // 0 to MAX
// The rounding mode used when rounding to the above decimal places, and when using
// toExponential, toFixed, toFormat and toPrecision, and round (default value).
// UP 0 Away from zero.
// DOWN 1 Towards zero.
// CEIL 2 Towards +Infinity.
// FLOOR 3 Towards -Infinity.
// HALF_UP 4 Towards nearest neighbour. If equidistant, up.
// HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
// HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
// HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
// HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
ROUNDING_MODE = 4, // 0 to 8
// EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
// The exponent value at and beneath which toString returns exponential notation.
// Number type: -7
TO_EXP_NEG = -7, // 0 to -MAX
// The exponent value at and above which toString returns exponential notation.
// Number type: 21
TO_EXP_POS = 21, // 0 to MAX
// RANGE : [MIN_EXP, MAX_EXP]
// The minimum exponent value, beneath which underflow to zero occurs.
// Number type: -324 (5e-324)
MIN_EXP = -1e7, // -1 to -MAX
// The maximum exponent value, above which overflow to Infinity occurs.
// Number type: 308 (1.7976931348623157e+308)
// For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
MAX_EXP = 1e7, // 1 to MAX
// Whether to use cryptographically-secure random number generation, if available.
CRYPTO = false, // true or false
// The modulo mode used when calculating the modulus: a mod n.
// The quotient (q = a / n) is calculated according to the corresponding rounding mode.
// The remainder (r) is calculated as: r = a - n * q.
//
// UP 0 The remainder is positive if the dividend is negative, else is negative.
// DOWN 1 The remainder has the same sign as the dividend.
// This modulo mode is commonly known as 'truncated division' and is
// equivalent to (a % n) in JavaScript.
// FLOOR 3 The remainder has the same sign as the divisor (Python %).
// HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
// EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)).
// The remainder is always positive.
//
// The truncated division, floored division, Euclidian division and IEEE 754 remainder
// modes are commonly used for the modulus operation.
// Although the other rounding modes can also be used, they may not give useful results.
MODULO_MODE = 1, // 0 to 9
// The maximum number of significant digits of the result of the exponentiatedBy operation.
// If POW_PRECISION is 0, there will be unlimited significant digits.
POW_PRECISION = 0, // 0 to MAX
// The format specification used by the BigNumber.prototype.toFormat method.
FORMAT = {
prefix: '',
groupSize: 3,
secondaryGroupSize: 0,
groupSeparator: ',',
decimalSeparator: '.',
fractionGroupSize: 0,
fractionGroupSeparator: '\xA0', // 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;