From a5e1a5eba3aac9f8cdeca602bfb9e22b72ec40c2 Mon Sep 17 00:00:00 2001 From: "DESKTOP-5IPRP36\\joe-m" Date: Wed, 28 Jul 2021 11:54:26 -0600 Subject: [PATCH] Fix eol issues? --- .gitattributes | 2 + docs/example/bignumber.js | 5804 ++++++++++++++++++------------------- 2 files changed, 2904 insertions(+), 2902 deletions(-) create mode 100644 .gitattributes diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 00000000..9cc28019 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,2 @@ +* text=auto eol=lf +*.{png,jpg,jpeg,gif,gz,ttf,webp,woff,woff2} binary diff --git a/docs/example/bignumber.js b/docs/example/bignumber.js index 846772d0..691d527a 100644 --- a/docs/example/bignumber.js +++ b/docs/example/bignumber.js @@ -1,2902 +1,2902 @@ -;(function (globalObject) { - 'use strict'; - -/* - * bignumber.js v9.0.1 - * A JavaScript library for arbitrary-precision arithmetic. - * https://github.com/MikeMcl/bignumber.js - * Copyright (c) 2020 Michael Mclaughlin - * MIT Licensed. - * - * BigNumber.prototype methods | BigNumber methods - * | - * absoluteValue abs | clone - * comparedTo | config set - * decimalPlaces dp | DECIMAL_PLACES - * dividedBy div | ROUNDING_MODE - * dividedToIntegerBy idiv | EXPONENTIAL_AT - * exponentiatedBy pow | RANGE - * integerValue | CRYPTO - * isEqualTo eq | MODULO_MODE - * isFinite | POW_PRECISION - * isGreaterThan gt | FORMAT - * isGreaterThanOrEqualTo gte | ALPHABET - * isInteger | isBigNumber - * isLessThan lt | maximum max - * isLessThanOrEqualTo lte | minimum min - * isNaN | random - * isNegative | sum - * isPositive | - * isZero | - * minus | - * modulo mod | - * multipliedBy times | - * negated | - * plus | - * precision sd | - * shiftedBy | - * squareRoot sqrt | - * toExponential | - * toFixed | - * toFormat | - * toFraction | - * toJSON | - * toNumber | - * toPrecision | - * toString | - * valueOf | - * - */ - - - var BigNumber, - isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i, - mathceil = Math.ceil, - mathfloor = Math.floor, - - bignumberError = '[BigNumber Error] ', - tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ', - - BASE = 1e14, - LOG_BASE = 14, - MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1 - // MAX_INT32 = 0x7fffffff, // 2^31 - 1 - POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13], - SQRT_BASE = 1e7, - - // EDITABLE - // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and - // the arguments to toExponential, toFixed, toFormat, and toPrecision. - MAX = 1E9; // 0 to MAX_INT32 - - - /* - * Create and return a BigNumber constructor. - */ - function clone(configObject) { - var div, convertBase, parseNumeric, - P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null }, - ONE = new BigNumber(1), - - - //----------------------------- EDITABLE CONFIG DEFAULTS ------------------------------- - - - // The default values below must be integers within the inclusive ranges stated. - // The values can also be changed at run-time using BigNumber.set. - - // The maximum number of decimal places for operations involving division. - DECIMAL_PLACES = 20, // 0 to MAX - - // The rounding mode used when rounding to the above decimal places, and when using - // toExponential, toFixed, toFormat and toPrecision, and round (default value). - // UP 0 Away from zero. - // DOWN 1 Towards zero. - // CEIL 2 Towards +Infinity. - // FLOOR 3 Towards -Infinity. - // HALF_UP 4 Towards nearest neighbour. If equidistant, up. - // HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. - // HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. - // HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. - // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. - ROUNDING_MODE = 4, // 0 to 8 - - // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS] - - // The exponent value at and beneath which toString returns exponential notation. - // Number type: -7 - TO_EXP_NEG = -7, // 0 to -MAX - - // The exponent value at and above which toString returns exponential notation. - // Number type: 21 - TO_EXP_POS = 21, // 0 to MAX - - // RANGE : [MIN_EXP, MAX_EXP] - - // The minimum exponent value, beneath which underflow to zero occurs. - // Number type: -324 (5e-324) - MIN_EXP = -1e7, // -1 to -MAX - - // The maximum exponent value, above which overflow to Infinity occurs. - // Number type: 308 (1.7976931348623157e+308) - // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow. - MAX_EXP = 1e7, // 1 to MAX - - // Whether to use cryptographically-secure random number generation, if available. - CRYPTO = false, // true or false - - // The modulo mode used when calculating the modulus: a mod n. - // The quotient (q = a / n) is calculated according to the corresponding rounding mode. - // The remainder (r) is calculated as: r = a - n * q. - // - // UP 0 The remainder is positive if the dividend is negative, else is negative. - // DOWN 1 The remainder has the same sign as the dividend. - // This modulo mode is commonly known as 'truncated division' and is - // equivalent to (a % n) in JavaScript. - // FLOOR 3 The remainder has the same sign as the divisor (Python %). - // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function. - // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). - // The remainder is always positive. - // - // The truncated division, floored division, Euclidian division and IEEE 754 remainder - // modes are commonly used for the modulus operation. - // Although the other rounding modes can also be used, they may not give useful results. - MODULO_MODE = 1, // 0 to 9 - - // The maximum number of significant digits of the result of the exponentiatedBy operation. - // If POW_PRECISION is 0, there will be unlimited significant digits. - POW_PRECISION = 0, // 0 to MAX - - // The format specification used by the BigNumber.prototype.toFormat method. - FORMAT = { - prefix: '', - groupSize: 3, - secondaryGroupSize: 0, - groupSeparator: ',', - decimalSeparator: '.', - fractionGroupSize: 0, - fractionGroupSeparator: '\xA0', // non-breaking space - suffix: '' - }, - - // The alphabet used for base conversion. It must be at least 2 characters long, with no '+', - // '-', '.', whitespace, or repeated character. - // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_' - ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz'; - - - //------------------------------------------------------------------------------------------ - - - // CONSTRUCTOR - - - /* - * The BigNumber constructor and exported function. - * Create and return a new instance of a BigNumber object. - * - * 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 less than two characters, - // 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 = '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) { - n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE); - str = toFixedPoint(coeffToString(n.c), n.e, '0'); - } else { - intCheck(b, 2, ALPHABET.length, 'Base'); - str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true); - } - - if (s < 0 && n.c[0]) str = '-' + str; - } - - return str; - }; - - - /* - * Return as toString, but do not accept a base argument, and include the minus sign for - * negative zero. - */ - P.valueOf = P.toJSON = function () { - return valueOf(this); - }; - - - P._isBigNumber = true; - - if (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 - - - BigNumber = clone(); - BigNumber['default'] = BigNumber.BigNumber = BigNumber; - - // AMD. - if (typeof define == 'function' && define.amd) { - define(function () { return BigNumber; }); - - // Node.js and other environments that support module.exports. - } else if (typeof module != 'undefined' && module.exports) { - module.exports = BigNumber; - - // Browser. - } else { - if (!globalObject) { - globalObject = typeof self != 'undefined' && self ? self : window; - } - - globalObject.BigNumber = BigNumber; - } -})(this); +;(function (globalObject) { + 'use strict'; + +/* + * bignumber.js v9.0.1 + * A JavaScript library for arbitrary-precision arithmetic. + * https://github.com/MikeMcl/bignumber.js + * Copyright (c) 2020 Michael Mclaughlin + * MIT Licensed. + * + * BigNumber.prototype methods | BigNumber methods + * | + * absoluteValue abs | clone + * comparedTo | config set + * decimalPlaces dp | DECIMAL_PLACES + * dividedBy div | ROUNDING_MODE + * dividedToIntegerBy idiv | EXPONENTIAL_AT + * exponentiatedBy pow | RANGE + * integerValue | CRYPTO + * isEqualTo eq | MODULO_MODE + * isFinite | POW_PRECISION + * isGreaterThan gt | FORMAT + * isGreaterThanOrEqualTo gte | ALPHABET + * isInteger | isBigNumber + * isLessThan lt | maximum max + * isLessThanOrEqualTo lte | minimum min + * isNaN | random + * isNegative | sum + * isPositive | + * isZero | + * minus | + * modulo mod | + * multipliedBy times | + * negated | + * plus | + * precision sd | + * shiftedBy | + * squareRoot sqrt | + * toExponential | + * toFixed | + * toFormat | + * toFraction | + * toJSON | + * toNumber | + * toPrecision | + * toString | + * valueOf | + * + */ + + + var BigNumber, + isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i, + mathceil = Math.ceil, + mathfloor = Math.floor, + + bignumberError = '[BigNumber Error] ', + tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ', + + BASE = 1e14, + LOG_BASE = 14, + MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1 + // MAX_INT32 = 0x7fffffff, // 2^31 - 1 + POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13], + SQRT_BASE = 1e7, + + // EDITABLE + // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and + // the arguments to toExponential, toFixed, toFormat, and toPrecision. + MAX = 1E9; // 0 to MAX_INT32 + + + /* + * Create and return a BigNumber constructor. + */ + function clone(configObject) { + var div, convertBase, parseNumeric, + P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null }, + ONE = new BigNumber(1), + + + //----------------------------- EDITABLE CONFIG DEFAULTS ------------------------------- + + + // The default values below must be integers within the inclusive ranges stated. + // The values can also be changed at run-time using BigNumber.set. + + // The maximum number of decimal places for operations involving division. + DECIMAL_PLACES = 20, // 0 to MAX + + // The rounding mode used when rounding to the above decimal places, and when using + // toExponential, toFixed, toFormat and toPrecision, and round (default value). + // UP 0 Away from zero. + // DOWN 1 Towards zero. + // CEIL 2 Towards +Infinity. + // FLOOR 3 Towards -Infinity. + // HALF_UP 4 Towards nearest neighbour. If equidistant, up. + // HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. + // HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. + // HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. + // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. + ROUNDING_MODE = 4, // 0 to 8 + + // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS] + + // The exponent value at and beneath which toString returns exponential notation. + // Number type: -7 + TO_EXP_NEG = -7, // 0 to -MAX + + // The exponent value at and above which toString returns exponential notation. + // Number type: 21 + TO_EXP_POS = 21, // 0 to MAX + + // RANGE : [MIN_EXP, MAX_EXP] + + // The minimum exponent value, beneath which underflow to zero occurs. + // Number type: -324 (5e-324) + MIN_EXP = -1e7, // -1 to -MAX + + // The maximum exponent value, above which overflow to Infinity occurs. + // Number type: 308 (1.7976931348623157e+308) + // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow. + MAX_EXP = 1e7, // 1 to MAX + + // Whether to use cryptographically-secure random number generation, if available. + CRYPTO = false, // true or false + + // The modulo mode used when calculating the modulus: a mod n. + // The quotient (q = a / n) is calculated according to the corresponding rounding mode. + // The remainder (r) is calculated as: r = a - n * q. + // + // UP 0 The remainder is positive if the dividend is negative, else is negative. + // DOWN 1 The remainder has the same sign as the dividend. + // This modulo mode is commonly known as 'truncated division' and is + // equivalent to (a % n) in JavaScript. + // FLOOR 3 The remainder has the same sign as the divisor (Python %). + // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function. + // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). + // The remainder is always positive. + // + // The truncated division, floored division, Euclidian division and IEEE 754 remainder + // modes are commonly used for the modulus operation. + // Although the other rounding modes can also be used, they may not give useful results. + MODULO_MODE = 1, // 0 to 9 + + // The maximum number of significant digits of the result of the exponentiatedBy operation. + // If POW_PRECISION is 0, there will be unlimited significant digits. + POW_PRECISION = 0, // 0 to MAX + + // The format specification used by the BigNumber.prototype.toFormat method. + FORMAT = { + prefix: '', + groupSize: 3, + secondaryGroupSize: 0, + groupSeparator: ',', + decimalSeparator: '.', + fractionGroupSize: 0, + fractionGroupSeparator: '\xA0', // non-breaking space + suffix: '' + }, + + // The alphabet used for base conversion. It must be at least 2 characters long, with no '+', + // '-', '.', whitespace, or repeated character. + // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_' + ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz'; + + + //------------------------------------------------------------------------------------------ + + + // CONSTRUCTOR + + + /* + * The BigNumber constructor and exported function. + * Create and return a new instance of a BigNumber object. + * + * 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 less than two characters, + // 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 = '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) { + n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE); + str = toFixedPoint(coeffToString(n.c), n.e, '0'); + } else { + intCheck(b, 2, ALPHABET.length, 'Base'); + str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true); + } + + if (s < 0 && n.c[0]) str = '-' + str; + } + + return str; + }; + + + /* + * Return as toString, but do not accept a base argument, and include the minus sign for + * negative zero. + */ + P.valueOf = P.toJSON = function () { + return valueOf(this); + }; + + + P._isBigNumber = true; + + if (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 + + + BigNumber = clone(); + BigNumber['default'] = BigNumber.BigNumber = BigNumber; + + // AMD. + if (typeof define == 'function' && define.amd) { + define(function () { return BigNumber; }); + + // Node.js and other environments that support module.exports. + } else if (typeof module != 'undefined' && module.exports) { + module.exports = BigNumber; + + // Browser. + } else { + if (!globalObject) { + globalObject = typeof self != 'undefined' && self ? self : window; + } + + globalObject.BigNumber = BigNumber; + } +})(this);