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bignumber.js
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bignumber.js
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/*! bignumber.js v2.0.7 https://github.com/MikeMcl/bignumber.js/LICENCE */
;(function (global) {
'use strict';
/*
bignumber.js v2.0.7
A JavaScript library for arbitrary-precision arithmetic.
https://github.com/MikeMcl/bignumber.js
Copyright (c) 2015 Michael Mclaughlin <[email protected]>
MIT Expat Licence
*/
var BigNumber, crypto, parseNumeric,
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 another(configObj) {
var div,
// 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 = 100, // 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 ) 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 = another;
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 = 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 === !!v || v === 1 || v === 0 ) {
CRYPTO = !!( v && crypto && typeof crypto == 'object' );
if ( v && !CRYPTO && ERRORS ) raise( 2, 'crypto unavailable', crypto );
} 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 && 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 && 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 if (ERRORS) {
raise( 14, 'crypto unavailable', crypto );
}
}
// Use Math.random: CRYPTO is false or crypto is unavailable and ERRORS is false.
if (!i) {
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 ) {