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bignumber.mjs
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/*
* bignumber.js v7.2.1
* A JavaScript library for arbitrary-precision arithmetic.
* https://github.com/MikeMcl/bignumber.js
* Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licensed.
*
* BigNumber.prototype methods | BigNumber methods
* |
* absoluteValue abs | clone
* comparedTo | config set
* decimalPlaces dp | DECIMAL_PLACES
* dividedBy div | ROUNDING_MODE
* dividedToIntegerBy idiv | EXPONENTIAL_AT
* exponentiatedBy pow | RANGE
* integerValue | CRYPTO
* isEqualTo eq | MODULO_MODE
* isFinite | POW_PRECISION
* isGreaterThan gt | FORMAT
* isGreaterThanOrEqualTo gte | ALPHABET
* isInteger | isBigNumber
* isLessThan lt | maximum max
* isLessThanOrEqualTo lte | minimum min
* isNaN | random
* isNegative |
* isPositive |
* isZero |
* minus |
* modulo mod |
* multipliedBy times |
* negated |
* plus |
* precision sd |
* shiftedBy |
* squareRoot sqrt |
* toExponential |
* toFixed |
* toFormat |
* toFraction |
* toJSON |
* toNumber |
* toPrecision |
* toString |
* valueOf |
*
*/
var isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
mathceil = Math.ceil,
mathfloor = Math.floor,
bignumberError = '[BigNumber Error] ',
tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
BASE = 1e14,
LOG_BASE = 14,
MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1
// MAX_INT32 = 0x7fffffff, // 2^31 - 1
POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
SQRT_BASE = 1e7,
// EDITABLE
// The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
// the arguments to toExponential, toFixed, toFormat, and toPrecision.
MAX = 1E9; // 0 to MAX_INT32
/*
* Create and return a BigNumber constructor.
*/
function clone(configObject) {
var div, convertBase, parseNumeric,
P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
ONE = new BigNumber(1),
//----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
// The default values below must be integers within the inclusive ranges stated.
// The values can also be changed at run-time using BigNumber.set.
// The maximum number of decimal places for operations involving division.
DECIMAL_PLACES = 20, // 0 to MAX
// The rounding mode used when rounding to the above decimal places, and when using
// toExponential, toFixed, toFormat and toPrecision, and round (default value).
// UP 0 Away from zero.
// DOWN 1 Towards zero.
// CEIL 2 Towards +Infinity.
// FLOOR 3 Towards -Infinity.
// HALF_UP 4 Towards nearest neighbour. If equidistant, up.
// HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
// HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
// HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
// HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
ROUNDING_MODE = 4, // 0 to 8
// EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
// The exponent value at and beneath which toString returns exponential notation.
// Number type: -7
TO_EXP_NEG = -7, // 0 to -MAX
// The exponent value at and above which toString returns exponential notation.
// Number type: 21
TO_EXP_POS = 21, // 0 to MAX
// RANGE : [MIN_EXP, MAX_EXP]
// The minimum exponent value, beneath which underflow to zero occurs.
// Number type: -324 (5e-324)
MIN_EXP = -1e7, // -1 to -MAX
// The maximum exponent value, above which overflow to Infinity occurs.
// Number type: 308 (1.7976931348623157e+308)
// For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
MAX_EXP = 1e7, // 1 to MAX
// Whether to use cryptographically-secure random number generation, if available.
CRYPTO = false, // true or false
// The modulo mode used when calculating the modulus: a mod n.
// The quotient (q = a / n) is calculated according to the corresponding rounding mode.
// The remainder (r) is calculated as: r = a - n * q.
//
// UP 0 The remainder is positive if the dividend is negative, else is negative.
// DOWN 1 The remainder has the same sign as the dividend.
// This modulo mode is commonly known as 'truncated division' and is
// equivalent to (a % n) in JavaScript.
// FLOOR 3 The remainder has the same sign as the divisor (Python %).
// HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
// EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)).
// The remainder is always positive.
//
// The truncated division, floored division, Euclidian division and IEEE 754 remainder
// modes are commonly used for the modulus operation.
// Although the other rounding modes can also be used, they may not give useful results.
MODULO_MODE = 1, // 0 to 9
// The maximum number of significant digits of the result of the exponentiatedBy operation.
// If POW_PRECISION is 0, there will be unlimited significant digits.
POW_PRECISION = 0, // 0 to MAX
// The format specification used by the BigNumber.prototype.toFormat method.
FORMAT = {
decimalSeparator: '.',
groupSeparator: ',',
groupSize: 3,
secondaryGroupSize: 0,
fractionGroupSeparator: '\xA0', // non-breaking space
fractionGroupSize: 0
},
// The alphabet used for base conversion.
// It must be at least 2 characters long, with no '.' or repeated character.
// '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
//------------------------------------------------------------------------------------------
// CONSTRUCTOR
/*
* The BigNumber constructor and exported function.
* Create and return a new instance of a BigNumber object.
*
* n {number|string|BigNumber} A numeric value.
* [b] {number} The base of n. Integer, 2 to ALPHABET.length inclusive.
*/
function BigNumber(n, b) {
var alphabet, c, caseChanged, e, i, isNum, len, str,
x = this;
// Enable constructor usage without new.
if (!(x instanceof BigNumber)) {
// Don't throw on constructor call without new (#81).
// '[BigNumber Error] Constructor call without new: {n}'
//throw Error(bignumberError + ' Constructor call without new: ' + n);
return new BigNumber(n, b);
}
if (b == null) {
// Duplicate.
if (n instanceof BigNumber) {
x.s = n.s;
x.e = n.e;
x.c = (n = n.c) ? n.slice() : n;
return;
}
isNum = typeof n == 'number';
if (isNum && n * 0 == 0) {
// Use `1 / n` to handle minus zero also.
x.s = 1 / n < 0 ? (n = -n, -1) : 1;
// Faster path for integers.
if (n === ~~n) {
for (e = 0, i = n; i >= 10; i /= 10, e++);
x.e = e;
x.c = [n];
return;
}
str = n + '';
} else {
if (!isNumeric.test(str = n + '')) 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');
str = n + '';
// 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(n instanceof BigNumber ? n : str);
return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
}
isNum = typeof n == 'number';
if (isNum) {
// Avoid potential interpretation of Infinity and NaN as base 44+ values.
if (n * 0 != 0) return parseNumeric(x, str, isNum, b);
x.s = 1 / n < 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 + n);
}
// Prevent later check for length on converted number.
isNum = false;
} 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, n + '', isNum, b);
}
}
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;);
str = str.slice(i, ++len);
if (str) {
len -= i;
// '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
if (isNum && BigNumber.DEBUG &&
len > 15 && (n > MAX_SAFE_INTEGER || n !== mathfloor(n))) {
throw Error
(tooManyDigits + (x.s * n));
}
e = e - i - 1;
// Overflow?
if (e > 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;
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));
}
str = str.slice(i);
i = LOG_BASE - str.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:
* decimalSeparator {string}
* groupSeparator {string}
* groupSize {number}
* secondaryGroupSize {number}
* fractionGroupSeparator {string}
* fractionGroupSize {number}
*
* (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 (isArray(v)) {
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 (isArray(v)) {
intCheck(v[0], -MAX, -1, p);
intCheck(v[1], 1, MAX, p);
MIN_EXP = v[0];
MAX_EXP = v[1];
} else {
intCheck(v, -MAX, MAX, p);
if (v) {
MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
} else {
throw Error
(bignumberError + p + ' cannot be zero: ' + v);
}
}
}
// CRYPTO {boolean} true or false.
// '[BigNumber Error] CRYPTO not true or false: {v}'
// '[BigNumber Error] crypto unavailable'
if (obj.hasOwnProperty(p = 'CRYPTO')) {
v = obj[p];
if (v === !!v) {
if (v) {
if (typeof crypto != 'undefined' && crypto &&
(crypto.getRandomValues || crypto.randomBytes)) {
CRYPTO = v;
} else {
CRYPTO = !v;
throw Error
(bignumberError + 'crypto unavailable');
}
} else {
CRYPTO = v;
}
} else {
throw Error
(bignumberError + p + ' not true or false: ' + v);
}
}
// MODULO_MODE {number} Integer, 0 to 9 inclusive.
// '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
v = obj[p];
intCheck(v, 0, 9, p);
MODULO_MODE = v;
}
// POW_PRECISION {number} Integer, 0 to MAX inclusive.
// '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
v = obj[p];
intCheck(v, 0, MAX, p);
POW_PRECISION = v;
}
// FORMAT {object}
// '[BigNumber Error] FORMAT not an object: {v}'
if (obj.hasOwnProperty(p = 'FORMAT')) {
v = obj[p];
if (typeof v == 'object') FORMAT = v;
else throw Error
(bignumberError + p + ' not an object: ' + v);
}
// ALPHABET {string}
// '[BigNumber Error] ALPHABET invalid: {v}'
if (obj.hasOwnProperty(p = 'ALPHABET')) {
v = obj[p];
// Disallow if only one character, or contains '.' or a repeated character.
if (typeof v == 'string' && !/^.$|\.|(.).*\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.
*
* v {any}
*/
BigNumber.isBigNumber = function (v) {
return v instanceof BigNumber || v && v._isBigNumber === true || false;
};
/*
* 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;
};
})();
// 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;