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/* * * bignumber.js v4.1.0 * 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.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
// 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 = [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++] ) ); 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 = [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: // 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 = [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 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.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;
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 = [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 ); };
/* * 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.splice(0, 1); }
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;
export default BigNumber;
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