2908 lines
80 KiB
JavaScript
2908 lines
80 KiB
JavaScript
/*
|
|
* bignumber.js v9.3.0
|
|
* A JavaScript library for arbitrary-precision arithmetic.
|
|
* https://github.com/MikeMcl/bignumber.js
|
|
* Copyright (c) 2025 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',
|
|
alphabetHasNormalDecimalDigits = true;
|
|
|
|
|
|
//------------------------------------------------------------------------------------------
|
|
|
|
|
|
// 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 && alphabetHasNormalDecimalDigits) {
|
|
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 less than two characters,
|
|
// or if it contains '+', '-', '.', whitespace, or a repeated character.
|
|
if (typeof v == 'string' && !/^.?$|[+\-.\s]|(.).*\1/.test(v)) {
|
|
alphabetHasNormalDecimalDigits = v.slice(0, 10) == '0123456789';
|
|
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, -1);
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a new BigNumber whose value is the minimum of the arguments.
|
|
*
|
|
* arguments {number|string|BigNumber}
|
|
*/
|
|
BigNumber.minimum = BigNumber.min = function () {
|
|
return maxOrMin(arguments, 1);
|
|
};
|
|
|
|
|
|
/*
|
|
* 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.
|
|
// If any number is NaN, return NaN.
|
|
function maxOrMin(args, n) {
|
|
var k, y,
|
|
i = 1,
|
|
x = new BigNumber(args[0]);
|
|
|
|
for (; i < args.length; i++) {
|
|
y = new BigNumber(args[i]);
|
|
if (!y.s || (k = compare(x, y)) === n || k === 0 && x.s === n) {
|
|
x = y;
|
|
}
|
|
}
|
|
|
|
return x;
|
|
}
|
|
|
|
|
|
/*
|
|
* 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 = mathfloor(n / pows10[d - j - 1] % 10);
|
|
} 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 : mathfloor(n / pows10[d - j - 1] % 10);
|
|
}
|
|
}
|
|
|
|
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 ? n.s * (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 = '5e' + 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 && alphabetHasNormalDecimalDigits) {
|
|
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;
|