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/*! bignumber.js v4.0.0 https://github.com/MikeMcl/bignumber.js/LICENCE */
;(function (globalObj) {
'use strict';
/*
bignumber.js v4.0.0
A JavaScript library for arbitrary-precision arithmetic.
https://github.com/MikeMcl/bignumber.js
Copyright (c) 2017 Michael Mclaughlin <M8ch88l@gmail.com>
MIT Expat Licence
*/
var BigNumber,
isNumeric = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
mathceil = Math.ceil,
mathfloor = Math.floor,
notBool = ' not a boolean or binary digit',
roundingMode = 'rounding mode',
tooManyDigits = 'number type has more than 15 significant digits',
ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_',
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,
/*
* 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, beyond which an
* exception is thrown (if ERRORS is true).
*/
MAX = 1E9; // 0 to MAX_INT32
/*
* Create and return a BigNumber constructor.
*/
function constructorFactory(config) {
var div, parseNumeric,
// id tracks the caller function, so its name can be included in error messages.
id = 0,
P = BigNumber.prototype,
ONE = new BigNumber(1),
/********************************* EDITABLE DEFAULTS **********************************/
/*
* The default values below must be integers within the inclusive ranges stated.
* The values can also be changed at run-time using BigNumber.config.
*/
// 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 BigNumber Errors are ever thrown.
ERRORS = true, // true or false
// Change to intValidatorNoErrors if ERRORS is false.
isValidInt = intValidatorWithErrors, // intValidatorWithErrors/intValidatorNoErrors
// 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 toPower 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
};
/******************************************************************************************/
// 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 64 inclusive.
*/
function BigNumber( n, b ) {
var c, e, i, num, len, str,
x = this;
// Enable constructor usage without new.
if ( !( x instanceof BigNumber ) ) {
// 'BigNumber() constructor call without new: {n}'
if (ERRORS) raise( 26, 'constructor call without new', n );
return new BigNumber( n, b );
}
// 'new BigNumber() base not an integer: {b}'
// 'new BigNumber() base out of range: {b}'
if ( b == null || !isValidInt( b, 2, 64, id, 'base' ) ) {
// Duplicate.
if ( n instanceof BigNumber ) {
x.s = n.s;
x.e = n.e;
x.c = ( n = n.c ) ? n.slice() : n;
id = 0;
return;
}
if ( ( num = typeof n == 'number' ) && n * 0 == 0 ) {
x.s = 1 / n < 0 ? ( n = -n, -1 ) : 1;
// Fast path for integers.
if ( n === ~~n ) {
for ( e = 0, i = n; i >= 10; i /= 10, e++ );
x.e = e;
x.c = [n];
id = 0;
return;
}
str = n + '';
} else {
if ( !isNumeric.test( str = n + '' ) ) return parseNumeric( x, str, num );
x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
}
} else {
b = b | 0;
str = n + '';
// Ensure return value is rounded to DECIMAL_PLACES as with other bases.
// Allow exponential notation to be used with base 10 argument.
if ( b == 10 ) {
x = new BigNumber( n instanceof BigNumber ? n : str );
return round( x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE );
}
// Avoid potential interpretation of Infinity and NaN as base 44+ values.
// Any number in exponential form will fail due to the [Ee][+-].
if ( ( num = typeof n == 'number' ) && n * 0 != 0 ||
!( new RegExp( '^-?' + ( c = '[' + ALPHABET.slice( 0, b ) + ']+' ) +
'(?:\\.' + c + ')?$',b < 37 ? 'i' : '' ) ).test(str) ) {
return parseNumeric( x, str, num, b );
}
if (num) {
x.s = 1 / n < 0 ? ( str = str.slice(1), -1 ) : 1;
if ( ERRORS && str.replace( /^0\.0*|\./, '' ).length > 15 ) {
// 'new BigNumber() number type has more than 15 significant digits: {n}'
raise( id, tooManyDigits, n );
}
// Prevent later check for length on converted number.
num = false;
} else {
x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
}
str = convertBase( str, 10, b, x.s );
}
// 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;
}
// 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 + 1 );
if (str) {
len = str.length;
// Disallow numbers with over 15 significant digits if number type.
// 'new BigNumber() number type has more than 15 significant digits: {n}'
if ( num && ERRORS && len > 15 && ( n > MAX_SAFE_INTEGER || n !== mathfloor(n) ) ) {
raise( id, 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 ];
}
id = 0;
}
// CONSTRUCTOR PROPERTIES
BigNumber.another = constructorFactory;
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 or an argument list, with one or many of the following properties or
* parameters respectively:
*
* DECIMAL_PLACES {number} Integer, 0 to MAX inclusive
* ROUNDING_MODE {number} Integer, 0 to 8 inclusive
* EXPONENTIAL_AT {number|number[]} Integer, -MAX to MAX inclusive or
* [integer -MAX to 0 incl., 0 to MAX incl.]
* RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
* [integer -MAX to -1 incl., integer 1 to MAX incl.]
* ERRORS {boolean|number} true, false, 1 or 0
* CRYPTO {boolean|number} true, false, 1 or 0
* MODULO_MODE {number} 0 to 9 inclusive
* POW_PRECISION {number} 0 to MAX inclusive
* FORMAT {object} See BigNumber.prototype.toFormat
* 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(20, 4) is equivalent to
* BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
*
* Ignore properties/parameters set to null or undefined.
* Return an object with the properties current values.
*/
BigNumber.config = BigNumber.set = function () {
var v, p,
i = 0,
r = {},
a = arguments,
o = a[0],
has = o && typeof o == 'object'
? function () { if ( o.hasOwnProperty(p) ) return ( v = o[p] ) != null; }
: function () { if ( a.length > i ) return ( v = a[i++] ) != null; };
// DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
// 'config() DECIMAL_PLACES not an integer: {v}'
// 'config() DECIMAL_PLACES out of range: {v}'
if ( has( p = 'DECIMAL_PLACES' ) && isValidInt( v, 0, MAX, 2, p ) ) {
DECIMAL_PLACES = v | 0;
}
r[p] = DECIMAL_PLACES;
// ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
// 'config() ROUNDING_MODE not an integer: {v}'
// 'config() ROUNDING_MODE out of range: {v}'
if ( has( p = 'ROUNDING_MODE' ) && isValidInt( v, 0, 8, 2, p ) ) {
ROUNDING_MODE = v | 0;
}
r[p] = ROUNDING_MODE;
// EXPONENTIAL_AT {number|number[]}
// Integer, -MAX to MAX inclusive or [integer -MAX to 0 inclusive, 0 to MAX inclusive].
// 'config() EXPONENTIAL_AT not an integer: {v}'
// 'config() EXPONENTIAL_AT out of range: {v}'
if ( has( p = 'EXPONENTIAL_AT' ) ) {
if ( isArray(v) ) {
if ( isValidInt( v[0], -MAX, 0, 2, p ) && isValidInt( v[1], 0, MAX, 2, p ) ) {
TO_EXP_NEG = v[0] | 0;
TO_EXP_POS = v[1] | 0;
}
} else if ( isValidInt( v, -MAX, MAX, 2, p ) ) {
TO_EXP_NEG = -( TO_EXP_POS = ( v < 0 ? -v : v ) | 0 );
}
}
r[p] = [ TO_EXP_NEG, TO_EXP_POS ];
// RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
// [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
// 'config() RANGE not an integer: {v}'
// 'config() RANGE cannot be zero: {v}'
// 'config() RANGE out of range: {v}'
if ( has( p = 'RANGE' ) ) {
if ( isArray(v) ) {
if ( isValidInt( v[0], -MAX, -1, 2, p ) && isValidInt( v[1], 1, MAX, 2, p ) ) {
MIN_EXP = v[0] | 0;
MAX_EXP = v[1] | 0;
}
} else if ( isValidInt( v, -MAX, MAX, 2, p ) ) {
if ( v | 0 ) MIN_EXP = -( MAX_EXP = ( v < 0 ? -v : v ) | 0 );
else if (ERRORS) raise( 2, p + ' cannot be zero', v );
}
}
r[p] = [ MIN_EXP, MAX_EXP ];
// ERRORS {boolean|number} true, false, 1 or 0.
// 'config() ERRORS not a boolean or binary digit: {v}'
if ( has( p = 'ERRORS' ) ) {
if ( v === !!v || v === 1 || v === 0 ) {
id = 0;
isValidInt = ( ERRORS = !!v ) ? intValidatorWithErrors : intValidatorNoErrors;
} else if (ERRORS) {
raise( 2, p + notBool, v );
}
}
r[p] = ERRORS;
// CRYPTO {boolean|number} true, false, 1 or 0.
// 'config() CRYPTO not a boolean or binary digit: {v}'
// 'config() crypto unavailable: {crypto}'
if ( has( p = 'CRYPTO' ) ) {
if ( v === true || v === false || v === 1 || v === 0 ) {
if (v) {
v = typeof crypto == 'undefined';
if ( !v && crypto && (crypto.getRandomValues || crypto.randomBytes)) {
CRYPTO = true;
} else if (ERRORS) {
raise( 2, 'crypto unavailable', v ? void 0 : crypto );
} else {
CRYPTO = false;
}
} else {
CRYPTO = false;
}
} else if (ERRORS) {
raise( 2, p + notBool, v );
}
}
r[p] = CRYPTO;
// MODULO_MODE {number} Integer, 0 to 9 inclusive.
// 'config() MODULO_MODE not an integer: {v}'
// 'config() MODULO_MODE out of range: {v}'
if ( has( p = 'MODULO_MODE' ) && isValidInt( v, 0, 9, 2, p ) ) {
MODULO_MODE = v | 0;
}
r[p] = MODULO_MODE;
// POW_PRECISION {number} Integer, 0 to MAX inclusive.
// 'config() POW_PRECISION not an integer: {v}'
// 'config() POW_PRECISION out of range: {v}'
if ( has( p = 'POW_PRECISION' ) && isValidInt( v, 0, MAX, 2, p ) ) {
POW_PRECISION = v | 0;
}
r[p] = POW_PRECISION;
// FORMAT {object}
// 'config() FORMAT not an object: {v}'
if ( has( p = 'FORMAT' ) ) {
if ( typeof v == 'object' ) {
FORMAT = v;
} else if (ERRORS) {
raise( 2, p + ' not an object', v );
}
}
r[p] = FORMAT;
return r;
};
/*
* Return a new BigNumber whose value is the maximum of the arguments.
*
* arguments {number|string|BigNumber}
*/
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.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.
*
* 'random() decimal places not an integer: {dp}'
* 'random() decimal places out of range: {dp}'
* 'random() crypto unavailable: {crypto}'
*/
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);
dp = dp == null || !isValidInt( dp, 0, MAX, 14 ) ? DECIMAL_PLACES : dp | 0;
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;
if (ERRORS) raise( 14, 'crypto unavailable', crypto );
}
}
// 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.shift(), 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
// Convert a numeric string of baseIn to a numeric string of baseOut.
function convertBase( str, baseOut, baseIn, sign ) {
var d, e, k, r, x, xc, y,
i = str.indexOf( '.' ),
dp = DECIMAL_PLACES,
rm = ROUNDING_MODE;
if ( baseIn < 37 ) str = str.toLowerCase();
// 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 ), 10, baseOut );
y.e = y.c.length;
}
// Convert the number as integer.
xc = toBaseOut( str, baseIn, baseOut );
e = k = xc.length;
// Remove trailing zeros.
for ( ; xc[--k] == 0; xc.pop() );
if ( !xc[0] ) return '0';
if ( i < 0 ) {
--e;
} else {
x.c = xc;
x.e = e;
// 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;
}
d = e + dp + 1;
// The rounding digit, i.e. the digit to the right of the digit that may be rounded up.
i = xc[d];
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 ( d < 1 || !xc[0] ) {
// 1^-dp or 0.
str = r ? toFixedPoint( '1', -dp ) : '0';
} else {
xc.length = d;
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.unshift(1);
}
}
}
// 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++] ) );
str = toFixedPoint( str, e );
}
// 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.unshift(carry);
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.shift() );
}
// 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.unshift(0);
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:
// 1. product = divisor * trial digit (n)
// 2. if product > remainder: product -= divisor, n--
// 3. remainder -= product
// 4. if product was < remainder at 2:
// 5. compare new remainder and divisor
// 6. If remainder > divisor: remainder -= divisor, n++
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.
// 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.unshift(0);
// 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.shift();
}
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 is a BigNumber.
* i is the index of the last digit required (i.e. the digit that may be rounded up).
* rm is the rounding mode.
* caller is caller id: toExponential 19, toFixed 20, toFormat 21, toPrecision 24.
*/
function format( n, i, rm, caller ) {
var c0, e, ne, len, str;
rm = rm != null && isValidInt( rm, 0, 8, caller, roundingMode )
? rm | 0 : ROUNDING_MODE;
if ( !n.c ) return n.toString();
c0 = n.c[0];
ne = n.e;
if ( i == null ) {
str = coeffToString( n.c );
str = caller == 19 || caller == 24 && ne <= TO_EXP_NEG
? toExponential( str, ne )
: toFixedPoint( str, ne );
} 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 ( caller == 19 || caller == 24 && ( 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 );
// 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 m, n,
i = 0;
if ( isArray( args[0] ) ) args = args[0];
m = new BigNumber( args[0] );
for ( ; ++i < args.length; ) {
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;
}
/*
* Return true if n is an integer in range, otherwise throw.
* Use for argument validation when ERRORS is true.
*/
function intValidatorWithErrors( n, min, max, caller, name ) {
if ( n < min || n > max || n != truncate(n) ) {
raise( caller, ( name || 'decimal places' ) +
( n < min || n > max ? ' out of range' : ' not an integer' ), n );
}
return true;
}
/*
* 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, num, b ) {
var base,
s = num ? 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 ( !num ) {
// 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 );
}
// 'new BigNumber() not a number: {n}'
// 'new BigNumber() not a base {b} number: {n}'
if (ERRORS) raise( id, 'not a' + ( b ? ' base ' + b : '' ) + ' number', str );
x.s = null;
}
x.c = x.e = null;
id = 0;
}
})();
// Throw a BigNumber Error.
function raise( caller, msg, val ) {
var error = new Error( [
'new BigNumber', // 0
'cmp', // 1
'config', // 2
'div', // 3
'divToInt', // 4
'eq', // 5
'gt', // 6
'gte', // 7
'lt', // 8
'lte', // 9
'minus', // 10
'mod', // 11
'plus', // 12
'precision', // 13
'random', // 14
'round', // 15
'shift', // 16
'times', // 17
'toDigits', // 18
'toExponential', // 19
'toFixed', // 20
'toFormat', // 21
'toFraction', // 22
'pow', // 23
'toPrecision', // 24
'toString', // 25
'BigNumber' // 26
][caller] + '() ' + msg + ': ' + val );
error.name = 'BigNumber Error';
id = 0;
throw error;
}
/*
* 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;
}
// 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 a new BigNumber whose value is the value of this BigNumber rounded to a whole
* number in the direction of Infinity.
*/
P.ceil = function () {
return round( new BigNumber(this), this.e + 1, 2 );
};
/*
* 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 = P.cmp = function ( y, b ) {
id = 1;
return compare( this, new BigNumber( y, b ) );
};
/*
* Return the number of decimal places of the value of this BigNumber, or null if the value
* of this BigNumber is ±Infinity or NaN.
*/
P.decimalPlaces = P.dp = function () {
var n, v,
c = this.c;
if ( !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 ) {
id = 3;
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.divToInt = function ( y, b ) {
id = 4;
return div( this, new BigNumber( y, b ), 0, 1 );
};
/*
* Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
* otherwise returns false.
*/
P.equals = P.eq = function ( y, b ) {
id = 5;
return compare( this, new BigNumber( y, b ) ) === 0;
};
/*
* Return a new BigNumber whose value is the value of this BigNumber rounded to a whole
* number in the direction of -Infinity.
*/
P.floor = function () {
return round( new BigNumber(this), this.e + 1, 3 );
};
/*
* Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
* otherwise returns false.
*/
P.greaterThan = P.gt = function ( y, b ) {
id = 6;
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 returns false.
*/
P.greaterThanOrEqualTo = P.gte = function ( y, b ) {
id = 7;
return ( b = compare( this, new BigNumber( y, b ) ) ) === 1 || b === 0;
};
/*
* Return true if the value of this BigNumber is a finite number, otherwise returns false.
*/
P.isFinite = function () {
return !!this.c;
};
/*
* Return true if the value of this BigNumber is an integer, otherwise return false.
*/
P.isInteger = P.isInt = function () {
return !!this.c && bitFloor( this.e / LOG_BASE ) > this.c.length - 2;
};
/*
* Return true if the value of this BigNumber is NaN, otherwise returns false.
*/
P.isNaN = function () {
return !this.s;
};
/*
* Return true if the value of this BigNumber is negative, otherwise returns false.
*/
P.isNegative = P.isNeg = function () {
return this.s < 0;
};
/*
* Return true if the value of this BigNumber is 0 or -0, otherwise returns false.
*/
P.isZero = function () {
return !!this.c && this.c[0] == 0;
};
/*
* Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
* otherwise returns false.
*/
P.lessThan = P.lt = function ( y, b ) {
id = 8;
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 returns false.
*/
P.lessThanOrEqualTo = P.lte = function ( y, b ) {
id = 9;
return ( b = compare( this, new BigNumber( y, b ) ) ) === -1 || b === 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 = P.sub = function ( y, b ) {
var i, j, t, xLTy,
x = this,
a = x.s;
id = 10;
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.shift(), --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;
id = 11;
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 );
}
return x.minus( q.times(y) );
};
/*
* Return a new BigNumber whose value is the value of this BigNumber negated,
* i.e. multiplied by -1.
*/
P.negated = P.neg = 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 = P.add = function ( y, b ) {
var t,
x = this,
a = x.s;
id = 12;
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.unshift(a);
++ye;
}
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
// ye = MAX_EXP + 1 possible
return normalise( y, xc, ye );
};
/*
* Return the number of significant digits of the value of this BigNumber.
*
* [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
*/
P.precision = P.sd = function (z) {
var n, v,
x = this,
c = x.c;
// 'precision() argument not a boolean or binary digit: {z}'
if ( z != null && z !== !!z && z !== 1 && z !== 0 ) {
if (ERRORS) raise( 13, 'argument' + notBool, z );
if ( z != !!z ) z = null;
}
if ( !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 ( z && x.e + 1 > n ) n = x.e + 1;
return n;
};
/*
* 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 to 0 and ROUNDING_MODE respectively if
* omitted.
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* 'round() decimal places out of range: {dp}'
* 'round() decimal places not an integer: {dp}'
* 'round() rounding mode not an integer: {rm}'
* 'round() rounding mode out of range: {rm}'
*/
P.round = function ( dp, rm ) {
var n = new BigNumber(this);
if ( dp == null || isValidInt( dp, 0, MAX, 15 ) ) {
round( n, ~~dp + this.e + 1, rm == null ||
!isValidInt( rm, 0, 8, 15, roundingMode ) ? ROUNDING_MODE : rm | 0 );
}
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.
*
* If k is out of range and ERRORS is false, the result will be ±0 if k < 0, or ±Infinity
* otherwise.
*
* 'shift() argument not an integer: {k}'
* 'shift() argument out of range: {k}'
*/
P.shift = function (k) {
var n = this;
return isValidInt( k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER, 16, 'argument' )
// k < 1e+21, or truncate(k) will produce exponential notation.
? n.times( '1e' + truncate(k) )
: new BigNumber( n.c && n.c[0] && ( k < -MAX_SAFE_INTEGER || k > MAX_SAFE_INTEGER )
? n.s * ( k < 0 ? 0 : 1 / 0 )
: n );
};
/*
* 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( +x );
// Math.sqrt underflow/overflow?
// Pass x to Math.sqrt as integer, then adjust the exponent of the result.
if ( s == 0 || s == 1 / 0 ) {
n = coeffToString(c);
if ( ( n.length + e ) % 2 == 0 ) n += '0';
s = Math.sqrt(n);
e = bitFloor( ( e + 1 ) / 2 ) - ( e < 0 || e % 2 );
if ( s == 1 / 0 ) {
n = '1e' + e;
} else {
n = s.toExponential();
n = n.slice( 0, n.indexOf('e') + 1 ) + e;
}
r = new BigNumber(n);
} else {
r = new BigNumber( s + '' );
}
// Check for zero.
// r could be zero if MIN_EXP is changed after the this value was created.
// This would cause a division by zero (x/t) and hence Infinity below, which would cause
// coeffToString to throw.
if ( r.c[0] ) {
e = r.e;
s = e + dp;
if ( s < 3 ) s = 0;
// Newton-Raphson iteration.
for ( ; ; ) {
t = r;
r = half.times( t.plus( div( x, t, dp, 1 ) ) );
if ( coeffToString( t.c ).slice( 0, s ) === ( n =
coeffToString( r.c ) ).slice( 0, s ) ) {
// The exponent of r may here be one less than the final result exponent,
// e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
// are indexed correctly.
if ( r.e < e ) --s;
n = n.slice( s - 3, s + 1 );
// The 4th rounding digit may be in error by -1 so if the 4 rounding digits
// are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
// iteration.
if ( n == '9999' || !rep && n == '4999' ) {
// On the first iteration only, check to see if rounding up gives the
// exact result as the nines may infinitely repeat.
if ( !rep ) {
round( t, t.e + DECIMAL_PLACES + 2, 0 );
if ( t.times(t).eq(x) ) {
r = t;
break;
}
}
dp += 4;
s += 4;
rep = 1;
} else {
// If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
// result. If not, then there are further digits and m will be truthy.
if ( !+n || !+n.slice(1) && n.charAt(0) == '5' ) {
// Truncate to the first rounding digit.
round( r, r.e + DECIMAL_PLACES + 2, 1 );
m = !r.times(r).eq(x);
}
break;
}
}
}
}
return round( r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m );
};
/*
* 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 times the value of
* BigNumber(y, b).
*/
P.times = P.mul = 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 = ( id = 17, 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.shift();
}
return normalise( y, zc, e );
};
/*
* 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} Significant digits. Integer, 1 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* 'toDigits() precision out of range: {sd}'
* 'toDigits() precision not an integer: {sd}'
* 'toDigits() rounding mode not an integer: {rm}'
* 'toDigits() rounding mode out of range: {rm}'
*/
P.toDigits = function ( sd, rm ) {
var n = new BigNumber(this);
sd = sd == null || !isValidInt( sd, 1, MAX, 18, 'precision' ) ? null : sd | 0;
rm = rm == null || !isValidInt( rm, 0, 8, 18, roundingMode ) ? ROUNDING_MODE : rm | 0;
return sd ? round( n, sd, rm ) : n;
};
/*
* 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.
*
* 'toExponential() decimal places not an integer: {dp}'
* 'toExponential() decimal places out of range: {dp}'
* 'toExponential() rounding mode not an integer: {rm}'
* 'toExponential() rounding mode out of range: {rm}'
*/
P.toExponential = function ( dp, rm ) {
return format( this,
dp != null && isValidInt( dp, 0, MAX, 19 ) ? ~~dp + 1 : null, rm, 19 );
};
/*
* 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.
*
* 'toFixed() decimal places not an integer: {dp}'
* 'toFixed() decimal places out of range: {dp}'
* 'toFixed() rounding mode not an integer: {rm}'
* 'toFixed() rounding mode out of range: {rm}'
*/
P.toFixed = function ( dp, rm ) {
return format( this, dp != null && isValidInt( dp, 0, MAX, 20 )
? ~~dp + this.e + 1 : null, rm, 20 );
};
/*
* 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 object (see BigNumber.config).
*
* FORMAT = {
* decimalSeparator : '.',
* groupSeparator : ',',
* groupSize : 3,
* secondaryGroupSize : 0,
* fractionGroupSeparator : '\xA0', // non-breaking space
* fractionGroupSize : 0
* };
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* 'toFormat() decimal places not an integer: {dp}'
* 'toFormat() decimal places out of range: {dp}'
* 'toFormat() rounding mode not an integer: {rm}'
* 'toFormat() rounding mode out of range: {rm}'
*/
P.toFormat = function ( dp, rm ) {
var str = format( this, dp != null && isValidInt( dp, 0, MAX, 21 )
? ~~dp + this.e + 1 : null, rm, 21 );
if ( this.c ) {
var i,
arr = str.split('.'),
g1 = +FORMAT.groupSize,
g2 = +FORMAT.secondaryGroupSize,
groupSeparator = FORMAT.groupSeparator,
intPart = arr[0],
fractionPart = arr[1],
isNeg = this.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 str;
};
/*
* Return a string array 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 and < Infinity. The maximum denominator.
*
* 'toFraction() max denominator not an integer: {md}'
* 'toFraction() max denominator out of range: {md}'
*/
P.toFraction = function (md) {
var arr, d0, d2, e, exp, n, n0, q, s,
k = ERRORS,
x = this,
xc = x.c,
d = new BigNumber(ONE),
n1 = d0 = new BigNumber(ONE),
d1 = n0 = new BigNumber(ONE);
if ( md != null ) {
ERRORS = false;
n = new BigNumber(md);
ERRORS = k;
if ( !( k = n.isInt() ) || n.lt(ONE) ) {
if (ERRORS) {
raise( 22,
'max denominator ' + ( k ? 'out of range' : 'not an integer' ), md );
}
// ERRORS is false:
// If md is a finite non-integer >= 1, round it to an integer and use it.
md = !k && n.c && round( n, n.e + 1, 1 ).gte(ONE) ? n : null;
}
}
if ( !xc ) return x.toString();
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.cmp(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.cmp(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 *= 2;
// Determine which fraction is closer to x, n0/d0 or n1/d1
arr = div( n1, d1, e, ROUNDING_MODE ).minus(x).abs().cmp(
div( n0, d0, e, ROUNDING_MODE ).minus(x).abs() ) < 1
? [ n1.toString(), d1.toString() ]
: [ n0.toString(), d0.toString() ];
MAX_EXP = exp;
return arr;
};
/*
* Return the value of this BigNumber converted to a number primitive.
*/
P.toNumber = function () {
return +this;
};
/*
* Return a BigNumber whose value is the value of this BigNumber raised to the power 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 positive integers,
* otherwise it is equivalent to calculating x.toPower(n).modulo(m) (with POW_PRECISION 0).
*
* n {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
* [m] {number|string|BigNumber} The modulus.
*
* 'pow() exponent not an integer: {n}'
* 'pow() exponent out of range: {n}'
*
* Performs 54 loop iterations for n of 9007199254740991.
*/
P.toPower = P.pow = function ( n, m ) {
var k, y, z,
i = mathfloor( n < 0 ? -n : +n ),
x = this;
if ( m != null ) {
id = 23;
m = new BigNumber(m);
}
// Pass ±Infinity to Math.pow if exponent is out of range.
if ( !isValidInt( n, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER, 23, 'exponent' ) &&
( !isFinite(n) || i > MAX_SAFE_INTEGER && ( n /= 0 ) ||
parseFloat(n) != n && !( n = NaN ) ) || n == 0 ) {
k = Math.pow( +x, n );
return new BigNumber( m ? k % m : k );
}
if (m) {
if ( n > 1 && x.gt(ONE) && x.isInt() && m.gt(ONE) && m.isInt() ) {
x = x.mod(m);
} else {
z = m;
// Nullify m so only a single mod operation is performed at the end.
m = null;
}
} 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.
// (Using + 1.5 would give [9, 21] guard digits.)
k = mathceil( POW_PRECISION / LOG_BASE + 2 );
}
y = new BigNumber(ONE);
for ( ; ; ) {
if ( i % 2 ) {
y = y.times(x);
if ( !y.c ) break;
if (k) {
if ( y.c.length > k ) y.c.length = k;
} else if (m) {
y = y.mod(m);
}
}
i = mathfloor( i / 2 );
if ( !i ) break;
x = x.times(x);
if (k) {
if ( x.c && x.c.length > k ) x.c.length = k;
} else if (m) {
x = x.mod(m);
}
}
if (m) return y;
if ( n < 0 ) y = ONE.div(y);
return z ? y.mod(z) : k ? round( y, POW_PRECISION, ROUNDING_MODE ) : y;
};
/*
* 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.
*
* 'toPrecision() precision not an integer: {sd}'
* 'toPrecision() precision out of range: {sd}'
* 'toPrecision() rounding mode not an integer: {rm}'
* 'toPrecision() rounding mode out of range: {rm}'
*/
P.toPrecision = function ( sd, rm ) {
return format( this, sd != null && isValidInt( sd, 1, MAX, 24, 'precision' )
? sd | 0 : null, rm, 24 );
};
/*
* 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 64 inclusive.
*
* 'toString() base not an integer: {b}'
* 'toString() base 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 {
str = coeffToString( n.c );
if ( b == null || !isValidInt( b, 2, 64, 25, 'base' ) ) {
str = e <= TO_EXP_NEG || e >= TO_EXP_POS
? toExponential( str, e )
: toFixedPoint( str, e );
} else {
str = convertBase( toFixedPoint( str, e ), b | 0, 10, s );
}
if ( s < 0 && n.c[0] ) str = '-' + str;
}
return str;
};
/*
* Return a new BigNumber whose value is the value of this BigNumber truncated to a whole
* number.
*/
P.truncated = P.trunc = function () {
return round( new BigNumber(this), this.e + 1, 1 );
};
/*
* Return as toString, but do not accept a base argument, and include the minus sign for
* negative zero.
*/
P.valueOf = P.toJSON = function () {
var str,
n = this,
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 );
return n.s < 0 ? '-' + str : str;
};
P.isBigNumber = true;
if ( config != null ) BigNumber.config(config);
return BigNumber;
}
// PRIVATE HELPER FUNCTIONS
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;
}
/*
* Return true if n is a valid number in range, otherwise false.
* Use for argument validation when ERRORS is false.
* Note: parseInt('1e+1') == 1 but parseFloat('1e+1') == 10.
*/
function intValidatorNoErrors( n, min, max ) {
return ( n = truncate(n) ) >= min && n <= max;
}
function isArray(obj) {
return Object.prototype.toString.call(obj) == '[object Array]';
}
/*
* Convert string of baseIn to an array of numbers of baseOut.
* Eg. convertBase('255', 10, 16) returns [15, 15].
* Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
*/
function toBaseOut( str, baseIn, baseOut ) {
var j,
arr = [0],
arrL,
i = 0,
len = str.length;
for ( ; i < len; ) {
for ( arrL = arr.length; arrL--; arr[arrL] *= baseIn );
arr[ j = 0 ] += ALPHABET.indexOf( str.charAt( i++ ) );
for ( ; 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();
}
function toExponential( str, e ) {
return ( str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str ) +
( e < 0 ? 'e' : 'e+' ) + e;
}
function toFixedPoint( str, e ) {
var len, z;
// Negative exponent?
if ( e < 0 ) {
// Prepend zeros.
for ( z = '0.'; ++e; z += '0' );
str = z + str;
// Positive exponent
} else {
len = str.length;
// Append zeros.
if ( ++e > len ) {
for ( z = '0', e -= len; --e; z += '0' );
str += z;
} else if ( e < len ) {
str = str.slice( 0, e ) + '.' + str.slice(e);
}
}
return str;
}
function truncate(n) {
n = parseFloat(n);
return n < 0 ? mathceil(n) : mathfloor(n);
}
// EXPORT
BigNumber = constructorFactory();
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 ( !globalObj ) globalObj = typeof self != 'undefined' ? self : Function('return this')();
globalObj.BigNumber = BigNumber;
}
})(this);
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