A JavaScript library for arbitrary-precision arithmetic.
+ + ++ See the README on GitHub for a + quick-start introduction. +
+
+ In all examples below, var
and semicolons are not shown, and if a commented-out
+ value is in quotes it means toString
has been called on the preceding expression.
+
BigNumber(n [, base]) ⇒ BigNumber
+
+ n
: number|string|BigNumber
+ base
: number: integer, 2
to 36
inclusive. (See
+ ALPHABET
to extend this range).
+
+ Returns a new instance of a BigNumber object with value n
, where n
+ is a numeric value in the specified base
, or base 10
if
+ base
is omitted or is null
or undefined
.
+
+ Note that the BigNnumber constructor accepts an n
of type number purely
+ as a convenience so that string quotes don't have to be typed when entering literal values,
+ and that it is the toString
value of n
that is used rather than its
+ underlying binary floating point value converted to decimal.
+
+x = new BigNumber(123.4567) // '123.4567' +// 'new' is optional +y = BigNumber(x) // '123.4567'+
+ If n
is a base 10
value it can be in normal or exponential notation.
+ Values in other bases must be in normal notation. Values in any base can have fraction digits,
+ i.e. digits after the decimal point.
+
+new BigNumber(43210) // '43210' +new BigNumber('4.321e+4') // '43210' +new BigNumber('-735.0918e-430') // '-7.350918e-428' +new BigNumber('123412421.234324', 5) // '607236.557696'+
+ Signed 0
, signed Infinity
and NaN
are supported.
+
+new BigNumber('-Infinity') // '-Infinity' +new BigNumber(NaN) // 'NaN' +new BigNumber(-0) // '0' +new BigNumber('.5') // '0.5' +new BigNumber('+2') // '2'+
+ String values in hexadecimal literal form, e.g. '0xff'
or '0xFF'
+ (but not '0xfF'
), are valid, as are string values with the octal and binary
+ prefixs '0o'
and '0b'
. String values in octal literal form without
+ the prefix will be interpreted as decimals, e.g. '011'
is interpreted as 11, not 9.
+
+new BigNumber(-10110100.1, 2) // '-180.5' +new BigNumber('-0b10110100.1') // '-180.5' +new BigNumber('ff.8', 16) // '255.5' +new BigNumber('0xff.8') // '255.5'+
+ If a base is specified, n
is rounded according to the current
+ DECIMAL_PLACES
and
+ ROUNDING_MODE
settings. This includes base
+ 10
so don't include a base
parameter for decimal values unless
+ this behaviour is wanted.
+
BigNumber.config({ DECIMAL_PLACES: 5 }) +new BigNumber(1.23456789) // '1.23456789' +new BigNumber(1.23456789, 10) // '1.23457'+
An error is thrown if base
is invalid. See Errors.
+ There is no limit to the number of digits of a value of type string (other than
+ that of JavaScript's maximum array size). See RANGE
to set
+ the maximum and minimum possible exponent value of a BigNumber.
+
+new BigNumber('5032485723458348569331745.33434346346912144534543') +new BigNumber('4.321e10000000')+
BigNumber NaN
is returned if n
is invalid
+ (unless BigNumber.DEBUG
is true
, see below).
+new BigNumber('.1*') // 'NaN' +new BigNumber('blurgh') // 'NaN' +new BigNumber(9, 2) // 'NaN'+
+ To aid in debugging, if BigNumber.DEBUG
is true
then an error will
+ be thrown on an invalid n
. An error will also be thrown if n
is of
+ type number and has more than 15
significant digits, as calling
+ toString
or valueOf
on
+ these numbers may not result in the intended value.
+
+console.log(823456789123456.3) // 823456789123456.2 +new BigNumber(823456789123456.3) // '823456789123456.2' +BigNumber.DEBUG = true +// '[BigNumber Error] Number primitive has more than 15 significant digits' +new BigNumber(823456789123456.3) +// '[BigNumber Error] Not a base 2 number' +new BigNumber(9, 2)+
+ A BigNumber can also be created from an object literal.
+ Use isBigNumber
to check that it is well-formed.
+
new BigNumber({ s: 1, e: 2, c: [ 777, 12300000000000 ], _isBigNumber: true }) // '777.123'+ + + + +
The static methods of a BigNumber constructor.
+ + + + +.clone([object]) ⇒ BigNumber constructor
+ object
: object
+ Returns a new independent BigNumber constructor with configuration as described by
+ object
(see config
), or with the default
+ configuration if object
is null
or undefined
.
+
+ Throws if object
is not an object. See Errors.
+
BigNumber.config({ DECIMAL_PLACES: 5 }) +BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) + +x = new BigNumber(1) +y = new BN(1) + +x.div(3) // 0.33333 +y.div(3) // 0.333333333 + +// BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to: +BN = BigNumber.clone() +BN.config({ DECIMAL_PLACES: 9 })+ + + +
set([object]) ⇒ object
+ object
: object: an object that contains some or all of the following
+ properties.
+
Configures the settings for this particular BigNumber constructor.
+ +DECIMAL_PLACES
0
to 1e+9
inclusive20
+ BigNumber.config({ DECIMAL_PLACES: 5 }) +BigNumber.set({ DECIMAL_PLACES: 5 }) // equivalent+
ROUNDING_MODE
0
to 8
inclusive4
(ROUND_HALF_UP
)
+ decimalPlaces
,
+ precision
,
+ toExponential
,
+ toFixed
,
+ toFormat
and
+ toPrecision
.
+ BigNumber.config({ ROUNDING_MODE: 0 }) +BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP }) // equivalent+
EXPONENTIAL_AT
0
to 1e+9
inclusive, or
+ -1e+9
to 0
inclusive, integer
+ 0
to 1e+9
inclusive ][-7, 20]
+ toString
returns exponential notation.
+ [-7, 20]
.
+ BigNumber.config({ EXPONENTIAL_AT: 2 }) +new BigNumber(12.3) // '12.3' e is only 1 +new BigNumber(123) // '1.23e+2' +new BigNumber(0.123) // '0.123' e is only -1 +new BigNumber(0.0123) // '1.23e-2' + +BigNumber.config({ EXPONENTIAL_AT: [-7, 20] }) +new BigNumber(123456789) // '123456789' e is only 8 +new BigNumber(0.000000123) // '1.23e-7' + +// Almost never return exponential notation: +BigNumber.config({ EXPONENTIAL_AT: 1e+9 }) + +// Always return exponential notation: +BigNumber.config({ EXPONENTIAL_AT: 0 })+
EXPONENTIAL_AT
, the toFixed
method
+ will always return a value in normal notation and the toExponential
method
+ will always return a value in exponential form.
+ toString
with a base argument, e.g. toString(10)
, will
+ also always return normal notation.
+ RANGE
1
to 1e+9
inclusive, or
+ -1e+9
to -1
inclusive, integer
+ 1
to 1e+9
inclusive ][-1e+9, 1e+9]
+ Infinity
and underflow to
+ zero occurs.
+ Infinity
and those with a
+ negative exponent of greater magnitude become zero.
+ Infinity
, use [-324, 308]
.
+ BigNumber.config({ RANGE: 500 }) +BigNumber.config().RANGE // [ -500, 500 ] +new BigNumber('9.999e499') // '9.999e+499' +new BigNumber('1e500') // 'Infinity' +new BigNumber('1e-499') // '1e-499' +new BigNumber('1e-500') // '0' + +BigNumber.config({ RANGE: [-3, 4] }) +new BigNumber(99999) // '99999' e is only 4 +new BigNumber(100000) // 'Infinity' e is 5 +new BigNumber(0.001) // '0.01' e is only -3 +new BigNumber(0.0001) // '0' e is -4+
9.999...e+1000000000
.1e-1000000000
.
+ CRYPTO
true
or false
.false
+ CRYPTO
is set to true
then the
+ random
method will generate random digits using
+ crypto.getRandomValues
in browsers that support it, or
+ crypto.randomBytes
if using Node.js.
+ CRYPTO
to true
will fail and an exception will be thrown.
+ CRYPTO
is false
then the source of randomness used will be
+ Math.random
(which is assumed to generate at least 30
bits of
+ randomness).
+ random
.+// Node.js +const crypto = require('crypto'); // CommonJS +import * as crypto from 'crypto'; // ES module + +global.crypto = crypto; + +BigNumber.config({ CRYPTO: true }) +BigNumber.config().CRYPTO // true +BigNumber.random() // 0.54340758610486147524+
MODULO_MODE
0
to 9
inclusive1
(ROUND_DOWN
)
+ a mod n
.q = a / n
, is calculated according to the
+ ROUNDING_MODE
that corresponds to the chosen
+ MODULO_MODE
.
+ r
, is calculated as: r = a - n * q
.Property | Value | Description |
---|---|---|
ROUND_UP | 0 | ++ The remainder is positive if the dividend is negative, otherwise it is negative. + | +
ROUND_DOWN | 1 | +
+ The remainder has the same sign as the dividend. + This uses 'truncating division' and matches the behaviour of JavaScript's + remainder operator % .
+ |
+
ROUND_FLOOR | 3 | +
+ The remainder has the same sign as the divisor. + This matches Python's % operator.
+ |
+
ROUND_HALF_EVEN | 6 | +The IEEE 754 remainder function. | +
EUCLID | 9 | +
+ The remainder is always positive. Euclidian division: + q = sign(n) * floor(a / abs(n))
+ |
+
modulo
.BigNumber.config({ MODULO_MODE: BigNumber.EUCLID }) +BigNumber.config({ MODULO_MODE: 9 }) // equivalent+
POW_PRECISION
0
to 1e+9
inclusive.0
+ 0
, the number of significant digits will not be limited.exponentiatedBy
.BigNumber.config({ POW_PRECISION: 100 })
FORMAT
FORMAT
object configures the format of the string returned by the
+ toFormat
method.
+ FORMAT
object that are
+ recognised, and their default values.
+ FORMAT
object will not be checked for validity. The existing
+ FORMAT
object will simply be replaced by the object that is passed in.
+ The object can include any number of the properties shown below.
+ toFormat
for examples of usage.+BigNumber.config({ + FORMAT: { + // string to prepend + prefix: '', + // decimal separator + decimalSeparator: '.', + // grouping separator of the integer part + groupSeparator: ',', + // primary grouping size of the integer part + groupSize: 3, + // secondary grouping size of the integer part + secondaryGroupSize: 0, + // grouping separator of the fraction part + fractionGroupSeparator: ' ', + // grouping size of the fraction part + fractionGroupSize: 0, + // string to append + suffix: '' + } +});+
ALPHABET
'0123456789abcdefghijklmnopqrstuvwxyz'
+ BigNumber
constructor or
+ toString
.
+ '+'
and '-'
, or the decimal separator '.'
.
+ // duodecimal (base 12) +BigNumber.config({ ALPHABET: '0123456789TE' }) +x = new BigNumber('T', 12) +x.toString() // '10' +x.toString(12) // 'T'+
Returns an object with the above properties and their current values.
+
+ Throws if object
is not an object, or if an invalid value is assigned to
+ one or more of the above properties. See Errors.
+
+BigNumber.config({ + DECIMAL_PLACES: 40, + ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL, + EXPONENTIAL_AT: [-10, 20], + RANGE: [-500, 500], + CRYPTO: true, + MODULO_MODE: BigNumber.ROUND_FLOOR, + POW_PRECISION: 80, + FORMAT: { + groupSize: 3, + groupSeparator: ' ', + decimalSeparator: ',' + }, + ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_' +}); + +obj = BigNumber.config(); +obj.DECIMAL_PLACES // 40 +obj.RANGE // [-500, 500]+ + + +
.isBigNumber(value) ⇒ boolean
+ value
: any
+ Returns true
if value
is a BigNumber instance, otherwise returns
+ false
.
+
x = 42 +y = new BigNumber(x) + +BigNumber.isBigNumber(x) // false +y instanceof BigNumber // true +BigNumber.isBigNumber(y) // true + +BN = BigNumber.clone(); +z = new BN(x) +z instanceof BigNumber // false +BigNumber.isBigNumber(z) // true+
+ If value
is a BigNumber instance and BigNumber.DEBUG
is true
,
+ then this method will also check if value
is well-formed, and throw if it is not.
+ See Errors.
+
+ The check can be useful if creating a BigNumber from an object literal. + See BigNumber. +
++x = new BigNumber(10) + +// Change x.c to an illegitimate value. +x.c = NaN + +BigNumber.DEBUG = false + +// No error. +BigNumber.isBigNumber(x) // true + +BigNumber.DEBUG = true + +// Error. +BigNumber.isBigNumber(x) // '[BigNumber Error] Invalid BigNumber'+ + + +
.max(n...) ⇒ BigNumber
+ n
: number|string|BigNumber
+ See BigNumber
for further parameter details.
+
+ Returns a BigNumber whose value is the maximum of the arguments. +
+The return value is always exact and unrounded.
+x = new BigNumber('3257869345.0378653') +BigNumber.maximum(4e9, x, '123456789.9') // '4000000000' + +arr = [12, '13', new BigNumber(14)] +BigNumber.max.apply(null, arr) // '14'+ + + +
.min(n...) ⇒ BigNumber
+ n
: number|string|BigNumber
+ See BigNumber
for further parameter details.
+
+ Returns a BigNumber whose value is the minimum of the arguments. +
+The return value is always exact and unrounded.
+x = new BigNumber('3257869345.0378653') +BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9' + +arr = [2, new BigNumber(-14), '-15.9999', -12] +BigNumber.min.apply(null, arr) // '-15.9999'+ + + +
.random([dp]) ⇒ BigNumber
+ dp
: number: integer, 0
to 1e+9
inclusive
+ Returns a new BigNumber with a pseudo-random value equal to or greater than 0
and
+ less than 1
.
+
+ The return value will have dp
decimal places (or less if trailing zeros are
+ produced).
+ If dp
is omitted then the number of decimal places will default to the current
+ DECIMAL_PLACES
setting.
+
+ Depending on the value of this BigNumber constructor's
+ CRYPTO
setting and the support for the
+ crypto
object in the host environment, the random digits of the return value are
+ generated by either Math.random
(fastest), crypto.getRandomValues
+ (Web Cryptography API in recent browsers) or crypto.randomBytes
(Node.js).
+
+ To be able to set CRYPTO
to true
when using
+ Node.js, the crypto
object must be available globally:
+
// Node.js +const crypto = require('crypto'); // CommonJS +import * as crypto from 'crypto'; // ES module +global.crypto = crypto;+
+ If CRYPTO
is true
, i.e. one of the
+ crypto
methods is to be used, the value of a returned BigNumber should be
+ cryptographically-secure and statistically indistinguishable from a random value.
+
+ Throws if dp
is invalid. See Errors.
+
BigNumber.config({ DECIMAL_PLACES: 10 }) +BigNumber.random() // '0.4117936847' +BigNumber.random(20) // '0.78193327636914089009'+ + + +
.sum(n...) ⇒ BigNumber
+ n
: number|string|BigNumber
+ See BigNumber
for further parameter details.
+
Returns a BigNumber whose value is the sum of the arguments.
+The return value is always exact and unrounded.
+x = new BigNumber('3257869345.0378653') +BigNumber.sum(4e9, x, '123456789.9') // '7381326134.9378653' + +arr = [2, new BigNumber(14), '15.9999', 12] +BigNumber.sum.apply(null, arr) // '43.9999'+ + + +
+ The library's enumerated rounding modes are stored as properties of the constructor.
+ (They are not referenced internally by the library itself.)
+
+ Rounding modes 0
to 6
(inclusive) are the same as those of Java's
+ BigDecimal class.
+
Property | +Value | +Description | +
---|---|---|
ROUND_UP | +0 | +Rounds away from zero | +
ROUND_DOWN | +1 | +Rounds towards zero | +
ROUND_CEIL | +2 | +Rounds towards Infinity |
+
ROUND_FLOOR | +3 | +Rounds towards -Infinity |
+
ROUND_HALF_UP | +4 | +
+ Rounds towards nearest neighbour. + If equidistant, rounds away from zero + |
+
ROUND_HALF_DOWN | +5 | +
+ Rounds towards nearest neighbour. + If equidistant, rounds towards zero + |
+
ROUND_HALF_EVEN | +6 | +
+ Rounds towards nearest neighbour. + If equidistant, rounds towards even neighbour + |
+
ROUND_HALF_CEIL | +7 | +
+ Rounds towards nearest neighbour. + If equidistant, rounds towards Infinity
+ |
+
ROUND_HALF_FLOOR | +8 | +
+ Rounds towards nearest neighbour. + If equidistant, rounds towards -Infinity
+ |
+
+BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL }) +BigNumber.config({ ROUNDING_MODE: 2 }) // equivalent+ +
undefined|false|true
+
+ If BigNumber.DEBUG
is set true
then an error will be thrown
+ if this BigNumber constructor receives an invalid value, such as
+ a value of type number with more than 15
significant digits.
+ See BigNumber.
+
+ An error will also be thrown if the isBigNumber
+ method receives a BigNumber that is not well-formed.
+ See isBigNumber
.
+
BigNumber.DEBUG = true+ + +
The methods inherited by a BigNumber instance from its constructor's prototype object.
+A BigNumber is immutable in the sense that it is not changed by its methods.
+
+ The treatment of ±0
, ±Infinity
and NaN
is
+ consistent with how JavaScript treats these values.
+
Many method names have a shorter alias.
+ + + +.abs() ⇒ BigNumber
+ Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of + this BigNumber. +
+The return value is always exact and unrounded.
++x = new BigNumber(-0.8) +y = x.absoluteValue() // '0.8' +z = y.abs() // '0.8'+ + + +
.comparedTo(n [, base]) ⇒ number
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
Returns | |
---|---|
1 |
+ If the value of this BigNumber is greater than the value of n |
+
-1 |
+ If the value of this BigNumber is less than the value of n |
+
0 |
+ If this BigNumber and n have the same value |
+
null |
+ If the value of either this BigNumber or n is NaN |
+
+x = new BigNumber(Infinity) +y = new BigNumber(5) +x.comparedTo(y) // 1 +x.comparedTo(x.minus(1)) // 0 +y.comparedTo(NaN) // null +y.comparedTo('110', 2) // -1+ + + +
.dp([dp [, rm]]) ⇒ BigNumber|number
+
+ dp
: number: integer, 0
to 1e+9
inclusive
+ rm
: number: integer, 0
to 8
inclusive
+
+ If dp
is a number, returns a BigNumber whose value is the value of this BigNumber
+ rounded by rounding mode rm
to a maximum of dp
decimal places.
+
+ If dp
is omitted, or is null
or undefined
, the return
+ value is the number of decimal places of the value of this BigNumber, or null
if
+ the value of this BigNumber is ±Infinity
or NaN
.
+
+ If rm
is omitted, or is null
or undefined
,
+ ROUNDING_MODE
is used.
+
+ Throws if dp
or rm
is invalid. See Errors.
+
+x = new BigNumber(1234.56) +x.decimalPlaces(1) // '1234.6' +x.dp() // 2 +x.decimalPlaces(2) // '1234.56' +x.dp(10) // '1234.56' +x.decimalPlaces(0, 1) // '1234' +x.dp(0, 6) // '1235' +x.decimalPlaces(1, 1) // '1234.5' +x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6' +x // '1234.56' +y = new BigNumber('9.9e-101') +y.dp() // 102+ + + +
.div(n [, base]) ⇒ BigNumber
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns a BigNumber whose value is the value of this BigNumber divided by
+ n
, rounded according to the current
+ DECIMAL_PLACES
and
+ ROUNDING_MODE
settings.
+
+x = new BigNumber(355) +y = new BigNumber(113) +x.dividedBy(y) // '3.14159292035398230088' +x.div(5) // '71' +x.div(47, 16) // '5'+ + + +
.idiv(n [, base]) ⇒
+ BigNumber
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
+ n
.
+
+x = new BigNumber(5) +y = new BigNumber(3) +x.dividedToIntegerBy(y) // '1' +x.idiv(0.7) // '7' +x.idiv('0.f', 16) // '5'+ + + +
.pow(n [, m]) ⇒ BigNumber
+
+ n
: number|string|BigNumber: integer
+ m
: number|string|BigNumber
+
+ Returns a BigNumber whose value is the value of this BigNumber exponentiated by
+ n
, i.e. raised to the power n
, and optionally modulo a modulus
+ m
.
+
+ Throws if n
is not an integer. See Errors.
+
+ If n
is negative the result is rounded according to the current
+ DECIMAL_PLACES
and
+ ROUNDING_MODE
settings.
+
+ As the number of digits of the result of the power operation can grow so large so quickly,
+ e.g. 123.45610000 has over 50000
digits, the number of significant
+ digits calculated is limited to the value of the
+ POW_PRECISION
setting (unless a modulus
+ m
is specified).
+
+ By default POW_PRECISION
is set to 0
.
+ This means that an unlimited number of significant digits will be calculated, and that the
+ method's performance will decrease dramatically for larger exponents.
+
+ If m
is specified and the value of m
, n
and this
+ BigNumber are integers, and n
is positive, then a fast modular exponentiation
+ algorithm is used, otherwise the operation will be performed as
+ x.exponentiatedBy(n).modulo(m)
with a
+ POW_PRECISION
of 0
.
+
+Math.pow(0.7, 2) // 0.48999999999999994 +x = new BigNumber(0.7) +x.exponentiatedBy(2) // '0.49' +BigNumber(3).pow(-2) // '0.11111111111111111111'+ + + +
.integerValue([rm]) ⇒ BigNumber
+
+ rm
: number: integer, 0
to 8
inclusive
+
+ Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
+ rounding mode rm
.
+
+ If rm
is omitted, or is null
or undefined
,
+ ROUNDING_MODE
is used.
+
+ Throws if rm
is invalid. See Errors.
+
+x = new BigNumber(123.456) +x.integerValue() // '123' +x.integerValue(BigNumber.ROUND_CEIL) // '124' +y = new BigNumber(-12.7) +y.integerValue() // '-13' +y.integerValue(BigNumber.ROUND_DOWN) // '-12'+
+ The following is an example of how to add a prototype method that emulates JavaScript's
+ Math.round
function. Math.ceil
, Math.floor
and
+ Math.trunc
can be emulated in the same way with
+ BigNumber.ROUND_CEIL
, BigNumber.ROUND_FLOOR
and
+ BigNumber.ROUND_DOWN
respectively.
+
+BigNumber.prototype.round = function () { + return this.integerValue(BigNumber.ROUND_HALF_CEIL); +}; +x.round() // '123'+ + + +
.eq(n [, base]) ⇒ boolean
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns true
if the value of this BigNumber is equal to the value of
+ n
, otherwise returns false
.
+ As with JavaScript, NaN
does not equal NaN
.
+
Note: This method uses the comparedTo
method internally.
+0 === 1e-324 // true +x = new BigNumber(0) +x.isEqualTo('1e-324') // false +BigNumber(-0).eq(x) // true ( -0 === 0 ) +BigNumber(255).eq('ff', 16) // true + +y = new BigNumber(NaN) +y.isEqualTo(NaN) // false+ + + +
.isFinite() ⇒ boolean
+ Returns true
if the value of this BigNumber is a finite number, otherwise
+ returns false
.
+
+ The only possible non-finite values of a BigNumber are NaN
, Infinity
+ and -Infinity
.
+
+x = new BigNumber(1) +x.isFinite() // true +y = new BigNumber(Infinity) +y.isFinite() // false+
+ Note: The native method isFinite()
can be used if
+ n <= Number.MAX_VALUE
.
+
.gt(n [, base]) ⇒ boolean
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns true
if the value of this BigNumber is greater than the value of
+ n
, otherwise returns false
.
+
Note: This method uses the comparedTo
method internally.
+0.1 > (0.3 - 0.2) // true +x = new BigNumber(0.1) +x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false +BigNumber(0).gt(x) // false +BigNumber(11, 3).gt(11.1, 2) // true+ + + +
.gte(n [, base]) ⇒ boolean
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns true
if the value of this BigNumber is greater than or equal to the value
+ of n
, otherwise returns false
.
+
Note: This method uses the comparedTo
method internally.
+(0.3 - 0.2) >= 0.1 // false +x = new BigNumber(0.3).minus(0.2) +x.isGreaterThanOrEqualTo(0.1) // true +BigNumber(1).gte(x) // true +BigNumber(10, 18).gte('i', 36) // true+ + + +
.isInteger() ⇒ boolean
+ Returns true
if the value of this BigNumber is an integer, otherwise returns
+ false
.
+
+x = new BigNumber(1) +x.isInteger() // true +y = new BigNumber(123.456) +y.isInteger() // false+ + + +
.lt(n [, base]) ⇒ boolean
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns true
if the value of this BigNumber is less than the value of
+ n
, otherwise returns false
.
+
Note: This method uses the comparedTo
method internally.
+(0.3 - 0.2) < 0.1 // true +x = new BigNumber(0.3).minus(0.2) +x.isLessThan(0.1) // false +BigNumber(0).lt(x) // true +BigNumber(11.1, 2).lt(11, 3) // true+ + + +
.lte(n [, base]) ⇒ boolean
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns true
if the value of this BigNumber is less than or equal to the value of
+ n
, otherwise returns false
.
+
Note: This method uses the comparedTo
method internally.
+0.1 <= (0.3 - 0.2) // false +x = new BigNumber(0.1) +x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true +BigNumber(-1).lte(x) // true +BigNumber(10, 18).lte('i', 36) // true+ + + +
.isNaN() ⇒ boolean
+ Returns true
if the value of this BigNumber is NaN
, otherwise
+ returns false
.
+
+x = new BigNumber(NaN) +x.isNaN() // true +y = new BigNumber('Infinity') +y.isNaN() // false+
Note: The native method isNaN()
can also be used.
.isNegative() ⇒ boolean
+ Returns true
if the sign of this BigNumber is negative, otherwise returns
+ false
.
+
+x = new BigNumber(-0) +x.isNegative() // true +y = new BigNumber(2) +y.isNegative() // false+
Note: n < 0
can be used if n <= -Number.MIN_VALUE
.
.isPositive() ⇒ boolean
+ Returns true
if the sign of this BigNumber is positive, otherwise returns
+ false
.
+
+x = new BigNumber(-0) +x.isPositive() // false +y = new BigNumber(2) +y.isPositive() // true+ + + +
.isZero() ⇒ boolean
+ Returns true
if the value of this BigNumber is zero or minus zero, otherwise
+ returns false
.
+
+x = new BigNumber(-0) +x.isZero() && x.isNegative() // true +y = new BigNumber(Infinity) +y.isZero() // false+
Note: n == 0
can be used if n >= Number.MIN_VALUE
.
.minus(n [, base]) ⇒ BigNumber
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
Returns a BigNumber whose value is the value of this BigNumber minus n
.
The return value is always exact and unrounded.
++0.3 - 0.1 // 0.19999999999999998 +x = new BigNumber(0.3) +x.minus(0.1) // '0.2' +x.minus(0.6, 20) // '0'+ + + +
.mod(n [, base]) ⇒ BigNumber
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns a BigNumber whose value is the value of this BigNumber modulo n
, i.e.
+ the integer remainder of dividing this BigNumber by n
.
+
+ The value returned, and in particular its sign, is dependent on the value of the
+ MODULO_MODE
setting of this BigNumber constructor.
+ If it is 1
(default value), the result will have the same sign as this BigNumber,
+ and it will match that of Javascript's %
operator (within the limits of double
+ precision) and BigDecimal's remainder
method.
+
The return value is always exact and unrounded.
+
+ See MODULO_MODE
for a description of the other
+ modulo modes.
+
+1 % 0.9 // 0.09999999999999998 +x = new BigNumber(1) +x.modulo(0.9) // '0.1' +y = new BigNumber(33) +y.mod('a', 33) // '3'+ + + +
.times(n [, base]) ⇒ BigNumber
+
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
+ Returns a BigNumber whose value is the value of this BigNumber multiplied by n
.
+
The return value is always exact and unrounded.
++0.6 * 3 // 1.7999999999999998 +x = new BigNumber(0.6) +y = x.multipliedBy(3) // '1.8' +BigNumber('7e+500').times(y) // '1.26e+501' +x.multipliedBy('-a', 16) // '-6'+ + + +
.negated() ⇒ BigNumber
+ Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by
+ -1
.
+
+x = new BigNumber(1.8) +x.negated() // '-1.8' +y = new BigNumber(-1.3) +y.negated() // '1.3'+ + + +
.plus(n [, base]) ⇒ BigNumber
+ n
: number|string|BigNumber
+ base
: number
+ See BigNumber for further parameter details.
+
Returns a BigNumber whose value is the value of this BigNumber plus n
.
The return value is always exact and unrounded.
++0.1 + 0.2 // 0.30000000000000004 +x = new BigNumber(0.1) +y = x.plus(0.2) // '0.3' +BigNumber(0.7).plus(x).plus(y) // '1.1' +x.plus('0.1', 8) // '0.225'+ + + +
.sd([d [, rm]]) ⇒ BigNumber|number
+
+ d
: number|boolean: integer, 1
to 1e+9
+ inclusive, or true
or false
+ rm
: number: integer, 0
to 8
inclusive.
+
+ If d
is a number, returns a BigNumber whose value is the value of this BigNumber
+ rounded to a precision of d
significant digits using rounding mode
+ rm
.
+
+ If d
is omitted or is null
or undefined
, the return
+ value is the number of significant digits of the value of this BigNumber, or null
+ if the value of this BigNumber is ±Infinity
or NaN
.
+
+ If d
is true
then any trailing zeros of the integer
+ part of a number are counted as significant digits, otherwise they are not.
+
+ If rm
is omitted or is null
or undefined
,
+ ROUNDING_MODE
will be used.
+
+ Throws if d
or rm
is invalid. See Errors.
+
+x = new BigNumber(9876.54321) +x.precision(6) // '9876.54' +x.sd() // 9 +x.precision(6, BigNumber.ROUND_UP) // '9876.55' +x.sd(2) // '9900' +x.precision(2, 1) // '9800' +x // '9876.54321' +y = new BigNumber(987000) +y.precision() // 3 +y.sd(true) // 6+ + + +
.shiftedBy(n) ⇒ BigNumber
+ n
: number: integer,
+ -9007199254740991
to 9007199254740991
inclusive
+
+ Returns a BigNumber whose value is the value of this BigNumber shifted by n
+ places.
+
+ The shift is of the decimal point, i.e. of powers of ten, and is to the left if n
+ is negative or to the right if n
is positive.
+
The return value is always exact and unrounded.
+
+ Throws if n
is invalid. See Errors.
+
+x = new BigNumber(1.23) +x.shiftedBy(3) // '1230' +x.shiftedBy(-3) // '0.00123'+ + + +
.sqrt() ⇒ BigNumber
+ Returns a BigNumber whose value is the square root of the value of this BigNumber,
+ rounded according to the current
+ DECIMAL_PLACES
and
+ ROUNDING_MODE
settings.
+
+ The return value will be correctly rounded, i.e. rounded as if the result was first calculated + to an infinite number of correct digits before rounding. +
++x = new BigNumber(16) +x.squareRoot() // '4' +y = new BigNumber(3) +y.sqrt() // '1.73205080756887729353'+ + + +
.toExponential([dp [, rm]]) ⇒ string
+
+ dp
: number: integer, 0
to 1e+9
inclusive
+ rm
: number: integer, 0
to 8
inclusive
+
+ Returns a string representing the value of this BigNumber in exponential notation rounded
+ using rounding mode rm
to dp
decimal places, i.e with one digit
+ before the decimal point and dp
digits after it.
+
+ If the value of this BigNumber in exponential notation has fewer than dp
fraction
+ digits, the return value will be appended with zeros accordingly.
+
+ If dp
is omitted, or is null
or undefined
, the number
+ of digits after the decimal point defaults to the minimum number of digits necessary to
+ represent the value exactly.
+ If rm
is omitted or is null
or undefined
,
+ ROUNDING_MODE
is used.
+
+ Throws if dp
or rm
is invalid. See Errors.
+
+x = 45.6 +y = new BigNumber(x) +x.toExponential() // '4.56e+1' +y.toExponential() // '4.56e+1' +x.toExponential(0) // '5e+1' +y.toExponential(0) // '5e+1' +x.toExponential(1) // '4.6e+1' +y.toExponential(1) // '4.6e+1' +y.toExponential(1, 1) // '4.5e+1' (ROUND_DOWN) +x.toExponential(3) // '4.560e+1' +y.toExponential(3) // '4.560e+1'+ + + +
.toFixed([dp [, rm]]) ⇒ string
+
+ dp
: number: integer, 0
to 1e+9
inclusive
+ rm
: number: integer, 0
to 8
inclusive
+
+ Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+ rounded to dp
decimal places using rounding mode rm
.
+
+ If the value of this BigNumber in normal notation has fewer than dp
fraction
+ digits, the return value will be appended with zeros accordingly.
+
+ Unlike Number.prototype.toFixed
, which returns exponential notation if a number
+ is greater or equal to 1021
, this method will always return normal
+ notation.
+
+ If dp
is omitted or is null
or undefined
, the return
+ value will be unrounded and in normal notation. This is also unlike
+ Number.prototype.toFixed
, which returns the value to zero decimal places.
+ It is useful when fixed-point notation is required and the current
+ EXPONENTIAL_AT
setting causes
+ toString
to return exponential notation.
+ If rm
is omitted or is null
or undefined
,
+ ROUNDING_MODE
is used.
+
+ Throws if dp
or rm
is invalid. See Errors.
+
+x = 3.456 +y = new BigNumber(x) +x.toFixed() // '3' +y.toFixed() // '3.456' +y.toFixed(0) // '3' +x.toFixed(2) // '3.46' +y.toFixed(2) // '3.46' +y.toFixed(2, 1) // '3.45' (ROUND_DOWN) +x.toFixed(5) // '3.45600' +y.toFixed(5) // '3.45600'+ + + +
.toFormat([dp [, rm[, format]]]) ⇒ string
+
+ dp
: number: integer, 0
to 1e+9
inclusive
+ rm
: number: integer, 0
to 8
inclusive
+ format
: object: see FORMAT
+
+
+ Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+ rounded to dp
decimal places using rounding mode rm
, and formatted
+ according to the properties of the format
object.
+
+ See FORMAT
and the examples below for the properties of the
+ format
object, their types, and their usage. A formatting object may contain
+ some or all of the recognised properties.
+
+ If dp
is omitted or is null
or undefined
, then the
+ return value is not rounded to a fixed number of decimal places.
+ If rm
is omitted or is null
or undefined
,
+ ROUNDING_MODE
is used.
+ If format
is omitted or is null
or undefined
, the
+ FORMAT
object is used.
+
+ Throws if dp
, rm
or format
is invalid. See
+ Errors.
+
+fmt = { + prefix: '', + decimalSeparator: '.', + groupSeparator: ',', + groupSize: 3, + secondaryGroupSize: 0, + fractionGroupSeparator: ' ', + fractionGroupSize: 0, + suffix: '' +} + +x = new BigNumber('123456789.123456789') + +// Set the global formatting options +BigNumber.config({ FORMAT: fmt }) + +x.toFormat() // '123,456,789.123456789' +x.toFormat(3) // '123,456,789.123' + +// If a reference to the object assigned to FORMAT has been retained, +// the format properties can be changed directly +fmt.groupSeparator = ' ' +fmt.fractionGroupSize = 5 +x.toFormat() // '123 456 789.12345 6789' + +// Alternatively, pass the formatting options as an argument +fmt = { + prefix: '=> ', + decimalSeparator: ',', + groupSeparator: '.', + groupSize: 3, + secondaryGroupSize: 2 +} + +x.toFormat() // '123 456 789.12345 6789' +x.toFormat(fmt) // '=> 12.34.56.789,123456789' +x.toFormat(2, fmt) // '=> 12.34.56.789,12' +x.toFormat(3, BigNumber.ROUND_UP, fmt) // '=> 12.34.56.789,124'+ + + +
.toFraction([maximum_denominator])
+ ⇒ [BigNumber, BigNumber]
+
+ maximum_denominator
:
+ number|string|BigNumber: integer >= 1
and <=
+ Infinity
+
+ Returns an array of two BigNumbers representing the value of this BigNumber as a simple
+ fraction with an integer numerator and an integer denominator. The denominator will be a
+ positive non-zero value less than or equal to maximum_denominator
.
+
+ If a maximum_denominator
is not specified, or is null
or
+ undefined
, the denominator will be the lowest value necessary to represent the
+ number exactly.
+
+ Throws if maximum_denominator
is invalid. See Errors.
+
+x = new BigNumber(1.75) +x.toFraction() // '7, 4' + +pi = new BigNumber('3.14159265358') +pi.toFraction() // '157079632679,50000000000' +pi.toFraction(100000) // '312689, 99532' +pi.toFraction(10000) // '355, 113' +pi.toFraction(100) // '311, 99' +pi.toFraction(10) // '22, 7' +pi.toFraction(1) // '3, 1'+ + + +
.toJSON() ⇒ string
As valueOf
.
+x = new BigNumber('177.7e+457') +y = new BigNumber(235.4325) +z = new BigNumber('0.0098074') + +// Serialize an array of three BigNumbers +str = JSON.stringify( [x, y, z] ) +// "["1.777e+459","235.4325","0.0098074"]" + +// Return an array of three BigNumbers +JSON.parse(str, function (key, val) { + return key === '' ? val : new BigNumber(val) +})+ + + +
.toNumber() ⇒ number
Returns the value of this BigNumber as a JavaScript number primitive.
++ This method is identical to using type coercion with the unary plus operator. +
++x = new BigNumber(456.789) +x.toNumber() // 456.789 ++x // 456.789 + +y = new BigNumber('45987349857634085409857349856430985') +y.toNumber() // 4.598734985763409e+34 + +z = new BigNumber(-0) +1 / z.toNumber() // -Infinity +1 / +z // -Infinity+ + + +
.toPrecision([sd [, rm]]) ⇒ string
+
+ sd
: number: integer, 1
to 1e+9
inclusive
+ rm
: number: integer, 0
to 8
inclusive
+
+ Returns a string representing the value of this BigNumber rounded to sd
+ significant digits using rounding mode rm
.
+
+ If sd
is less than the number of digits necessary to represent the integer part
+ of the value in normal (fixed-point) notation, then exponential notation is used.
+
+ If sd
is omitted, or is null
or undefined
, then the
+ return value is the same as n.toString()
.
+ If rm
is omitted or is null
or undefined
,
+ ROUNDING_MODE
is used.
+
+ Throws if sd
or rm
is invalid. See Errors.
+
+x = 45.6 +y = new BigNumber(x) +x.toPrecision() // '45.6' +y.toPrecision() // '45.6' +x.toPrecision(1) // '5e+1' +y.toPrecision(1) // '5e+1' +y.toPrecision(2, 0) // '4.6e+1' (ROUND_UP) +y.toPrecision(2, 1) // '4.5e+1' (ROUND_DOWN) +x.toPrecision(5) // '45.600' +y.toPrecision(5) // '45.600'+ + + +
.toString([base]) ⇒ string
+ base
: number: integer, 2
to ALPHABET.length
+ inclusive (see ALPHABET
).
+
+ Returns a string representing the value of this BigNumber in the specified base, or base
+ 10
if base
is omitted or is null
or
+ undefined
.
+
+ For bases above 10
, and using the default base conversion alphabet
+ (see ALPHABET
), values from 10
to
+ 35
are represented by a-z
+ (as with Number.prototype.toString
).
+
+ If a base is specified the value is rounded according to the current
+ DECIMAL_PLACES
+ and ROUNDING_MODE
settings.
+
+ If a base is not specified, and this BigNumber has a positive
+ exponent that is equal to or greater than the positive component of the
+ current EXPONENTIAL_AT
setting,
+ or a negative exponent equal to or less than the negative component of the
+ setting, then exponential notation is returned.
+
If base
is null
or undefined
it is ignored.
+ Throws if base
is invalid. See Errors.
+
+x = new BigNumber(750000) +x.toString() // '750000' +BigNumber.config({ EXPONENTIAL_AT: 5 }) +x.toString() // '7.5e+5' + +y = new BigNumber(362.875) +y.toString(2) // '101101010.111' +y.toString(9) // '442.77777777777777777778' +y.toString(32) // 'ba.s' + +BigNumber.config({ DECIMAL_PLACES: 4 }); +z = new BigNumber('1.23456789') +z.toString() // '1.23456789' +z.toString(10) // '1.2346'+ + + +
.valueOf() ⇒ string
+ As toString
, but does not accept a base argument and includes
+ the minus sign for negative zero.
+
+x = new BigNumber('-0') +x.toString() // '0' +x.valueOf() // '-0' +y = new BigNumber('1.777e+457') +y.valueOf() // '1.777e+457'+ + + +
The properties of a BigNumber instance:
+Property | +Description | +Type | +Value | +
---|---|---|---|
c | +coefficient* | +number[] |
+ Array of base 1e14 numbers |
+
e | +exponent | +number | +Integer, -1000000000 to 1000000000 inclusive |
+
s | +sign | +number | +-1 or 1 |
+
*significand
+
+ The value of any of the c
, e
and s
properties may also
+ be null
.
+
+ The above properties are best considered to be read-only. In early versions of this library it + was okay to change the exponent of a BigNumber by writing to its exponent property directly, + but this is no longer reliable as the value of the first element of the coefficient array is + now dependent on the exponent. +
++ Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are + not necessarily preserved. +
+x = new BigNumber(0.123) // '0.123' +x.toExponential() // '1.23e-1' +x.c // '1,2,3' +x.e // -1 +x.s // 1 + +y = new Number(-123.4567000e+2) // '-12345.67' +y.toExponential() // '-1.234567e+4' +z = new BigNumber('-123.4567000e+2') // '-12345.67' +z.toExponential() // '-1.234567e+4' +z.c // '1,2,3,4,5,6,7' +z.e // 4 +z.s // -1+ + + +
+ The table below shows how ±0
, NaN
and
+ ±Infinity
are stored.
+
+ | c | +e | +s | +
---|---|---|---|
±0 | +[0] |
+ 0 |
+ ±1 |
+
NaN | +null |
+ null |
+ null |
+
±Infinity | +null |
+ null |
+ ±1 |
+
+x = new Number(-0) // 0 +1 / x == -Infinity // true + +y = new BigNumber(-0) // '0' +y.c // '0' ( [0].toString() ) +y.e // 0 +y.s // -1+ + + +
The table below shows the errors that are thrown.
+
+ The errors are generic Error
objects whose message begins
+ '[BigNumber Error]'
.
+
Method | +Throws | +
---|---|
+ BigNumber + comparedTo + dividedBy + dividedToIntegerBy + isEqualTo + isGreaterThan + isGreaterThanOrEqualTo + isLessThan + isLessThanOrEqualTo + minus + modulo + plus + multipliedBy
+ |
+ Base not a primitive number | +
Base not an integer | +|
Base out of range | +|
Number primitive has more than 15 significant digits* | +|
Not a base... number* | +|
Not a number* | +|
clone |
+ Object expected | +
config |
+ Object expected | +
DECIMAL_PLACES not a primitive number |
+ |
DECIMAL_PLACES not an integer |
+ |
DECIMAL_PLACES out of range |
+ |
ROUNDING_MODE not a primitive number |
+ |
ROUNDING_MODE not an integer |
+ |
ROUNDING_MODE out of range |
+ |
EXPONENTIAL_AT not a primitive number |
+ |
EXPONENTIAL_AT not an integer |
+ |
EXPONENTIAL_AT out of range |
+ |
RANGE not a primitive number |
+ |
RANGE not an integer |
+ |
RANGE cannot be zero |
+ |
RANGE cannot be zero |
+ |
CRYPTO not true or false |
+ |
crypto unavailable |
+ |
MODULO_MODE not a primitive number |
+ |
MODULO_MODE not an integer |
+ |
MODULO_MODE out of range |
+ |
POW_PRECISION not a primitive number |
+ |
POW_PRECISION not an integer |
+ |
POW_PRECISION out of range |
+ |
FORMAT not an object |
+ |
ALPHABET invalid |
+ |
+ decimalPlaces + precision + random + shiftedBy + toExponential + toFixed + toFormat + toPrecision
+ |
+ Argument not a primitive number | +
Argument not an integer | +|
Argument out of range | +|
+ decimalPlaces + precision
+ |
+ Argument not true or false | +
exponentiatedBy |
+ Argument not an integer | +
isBigNumber |
+ Invalid BigNumber* | +
+ minimum + maximum
+ |
+ Not a number* | +
+ random
+ |
+ crypto unavailable | +
+ toFormat
+ |
+ Argument not an object | +
toFraction |
+ Argument not an integer | +
Argument out of range | +|
toString |
+ Base not a primitive number | +
Base not an integer | +|
Base out of range | +
*Only thrown if BigNumber.DEBUG
is true
.
To determine if an exception is a BigNumber Error:
++try { + // ... +} catch (e) { + if (e instanceof Error && e.message.indexOf('[BigNumber Error]') === 0) { + // ... + } +}+ + + +
+ To prevent the accidental use of a BigNumber in primitive number operations, or the
+ accidental addition of a BigNumber to a string, the valueOf
method can be safely
+ overwritten as shown below.
+
+ The valueOf
method is the same as the
+ toJSON
method, and both are the same as the
+ toString
method except they do not take a base
+ argument and they include the minus sign for negative zero.
+
+BigNumber.prototype.valueOf = function () { + throw Error('valueOf called!') +} + +x = new BigNumber(1) +x / 2 // '[BigNumber Error] valueOf called!' +x + 'abc' // '[BigNumber Error] valueOf called!' ++ + + +
+ Some arbitrary-precision libraries retain trailing fractional zeros as they can indicate the + precision of a value. This can be useful but the results of arithmetic operations can be + misleading. +
++x = new BigDecimal("1.0") +y = new BigDecimal("1.1000") +z = x.add(y) // 2.1000 + +x = new BigDecimal("1.20") +y = new BigDecimal("3.45000") +z = x.multiply(y) // 4.1400000+
+ To specify the precision of a value is to specify that the value lies + within a certain range. +
+
+ In the first example, x
has a value of 1.0
. The trailing zero shows
+ the precision of the value, implying that it is in the range 0.95
to
+ 1.05
. Similarly, the precision indicated by the trailing zeros of y
+ indicates that the value is in the range 1.09995
to 1.10005
.
+
+ If we add the two lowest values in the ranges we have, 0.95 + 1.09995 = 2.04995
,
+ and if we add the two highest values we have, 1.05 + 1.10005 = 2.15005
, so the
+ range of the result of the addition implied by the precision of its operands is
+ 2.04995
to 2.15005
.
+
+ The result given by BigDecimal of 2.1000
however, indicates that the value is in
+ the range 2.09995
to 2.10005
and therefore the precision implied by
+ its trailing zeros may be misleading.
+
+ In the second example, the true range is 4.122744
to 4.157256
yet
+ the BigDecimal answer of 4.1400000
indicates a range of 4.13999995
+ to 4.14000005
. Again, the precision implied by the trailing zeros may be
+ misleading.
+
+ This library, like binary floating point and most calculators, does not retain trailing
+ fractional zeros. Instead, the toExponential
, toFixed
and
+ toPrecision
methods enable trailing zeros to be added if and when required.
+
Promise<[Response](#class-response)>
+
+Perform an HTTP(S) fetch.
+
+`url` should be an absolute url, such as `https://example.com/`. A path-relative URL (`/file/under/root`) or protocol-relative URL (`//can-be-http-or-https.com/`) will result in a rejected `Promise`.
+
+
+### Options
+
+The default values are shown after each option key.
+
+```js
+{
+ // These properties are part of the Fetch Standard
+ method: 'GET',
+ headers: {}, // request headers. format is the identical to that accepted by the Headers constructor (see below)
+ body: null, // request body. can be null, a string, a Buffer, a Blob, or a Node.js Readable stream
+ redirect: 'follow', // set to `manual` to extract redirect headers, `error` to reject redirect
+ signal: null, // pass an instance of AbortSignal to optionally abort requests
+
+ // The following properties are node-fetch extensions
+ follow: 20, // maximum redirect count. 0 to not follow redirect
+ timeout: 0, // req/res timeout in ms, it resets on redirect. 0 to disable (OS limit applies). Signal is recommended instead.
+ compress: true, // support gzip/deflate content encoding. false to disable
+ size: 0, // maximum response body size in bytes. 0 to disable
+ agent: null // http(s).Agent instance or function that returns an instance (see below)
+}
+```
+
+##### Default Headers
+
+If no values are set, the following request headers will be sent automatically:
+
+Header | Value
+------------------- | --------------------------------------------------------
+`Accept-Encoding` | `gzip,deflate` _(when `options.compress === true`)_
+`Accept` | `*/*`
+`Content-Length` | _(automatically calculated, if possible)_
+`Transfer-Encoding` | `chunked` _(when `req.body` is a stream)_
+`User-Agent` | `node-fetch/1.0 (+https://github.com/bitinn/node-fetch)`
+
+Note: when `body` is a `Stream`, `Content-Length` is not set automatically.
+
+##### Custom Agent
+
+The `agent` option allows you to specify networking related options which are out of the scope of Fetch, including and not limited to the following:
+
+- Support self-signed certificate
+- Use only IPv4 or IPv6
+- Custom DNS Lookup
+
+See [`http.Agent`](https://nodejs.org/api/http.html#http_new_agent_options) for more information.
+
+If no agent is specified, the default agent provided by Node.js is used. Note that [this changed in Node.js 19](https://github.com/nodejs/node/blob/4267b92604ad78584244488e7f7508a690cb80d0/lib/_http_agent.js#L564) to have `keepalive` true by default. If you wish to enable `keepalive` in an earlier version of Node.js, you can override the agent as per the following code sample.
+
+In addition, the `agent` option accepts a function that returns `http`(s)`.Agent` instance given current [URL](https://nodejs.org/api/url.html), this is useful during a redirection chain across HTTP and HTTPS protocol.
+
+```js
+const httpAgent = new http.Agent({
+ keepAlive: true
+});
+const httpsAgent = new https.Agent({
+ keepAlive: true
+});
+
+const options = {
+ agent: function (_parsedURL) {
+ if (_parsedURL.protocol == 'http:') {
+ return httpAgent;
+ } else {
+ return httpsAgent;
+ }
+ }
+}
+```
+
+
+### Class: Request
+
+An HTTP(S) request containing information about URL, method, headers, and the body. This class implements the [Body](#iface-body) interface.
+
+Due to the nature of Node.js, the following properties are not implemented at this moment:
+
+- `type`
+- `destination`
+- `referrer`
+- `referrerPolicy`
+- `mode`
+- `credentials`
+- `cache`
+- `integrity`
+- `keepalive`
+
+The following node-fetch extension properties are provided:
+
+- `follow`
+- `compress`
+- `counter`
+- `agent`
+
+See [options](#fetch-options) for exact meaning of these extensions.
+
+#### new Request(input[, options])
+
+*(spec-compliant)*
+
+- `input` A string representing a URL, or another `Request` (which will be cloned)
+- `options` [Options][#fetch-options] for the HTTP(S) request
+
+Constructs a new `Request` object. The constructor is identical to that in the [browser](https://developer.mozilla.org/en-US/docs/Web/API/Request/Request).
+
+In most cases, directly `fetch(url, options)` is simpler than creating a `Request` object.
+
+
+### Class: Response
+
+An HTTP(S) response. This class implements the [Body](#iface-body) interface.
+
+The following properties are not implemented in node-fetch at this moment:
+
+- `Response.error()`
+- `Response.redirect()`
+- `type`
+- `trailer`
+
+#### new Response([body[, options]])
+
+*(spec-compliant)*
+
+- `body` A `String` or [`Readable` stream][node-readable]
+- `options` A [`ResponseInit`][response-init] options dictionary
+
+Constructs a new `Response` object. The constructor is identical to that in the [browser](https://developer.mozilla.org/en-US/docs/Web/API/Response/Response).
+
+Because Node.js does not implement service workers (for which this class was designed), one rarely has to construct a `Response` directly.
+
+#### response.ok
+
+*(spec-compliant)*
+
+Convenience property representing if the request ended normally. Will evaluate to true if the response status was greater than or equal to 200 but smaller than 300.
+
+#### response.redirected
+
+*(spec-compliant)*
+
+Convenience property representing if the request has been redirected at least once. Will evaluate to true if the internal redirect counter is greater than 0.
+
+
+### Class: Headers
+
+This class allows manipulating and iterating over a set of HTTP headers. All methods specified in the [Fetch Standard][whatwg-fetch] are implemented.
+
+#### new Headers([init])
+
+*(spec-compliant)*
+
+- `init` Optional argument to pre-fill the `Headers` object
+
+Construct a new `Headers` object. `init` can be either `null`, a `Headers` object, an key-value map object or any iterable object.
+
+```js
+// Example adapted from https://fetch.spec.whatwg.org/#example-headers-class
+
+const meta = {
+ 'Content-Type': 'text/xml',
+ 'Breaking-Bad': '<3'
+};
+const headers = new Headers(meta);
+
+// The above is equivalent to
+const meta = [
+ [ 'Content-Type', 'text/xml' ],
+ [ 'Breaking-Bad', '<3' ]
+];
+const headers = new Headers(meta);
+
+// You can in fact use any iterable objects, like a Map or even another Headers
+const meta = new Map();
+meta.set('Content-Type', 'text/xml');
+meta.set('Breaking-Bad', '<3');
+const headers = new Headers(meta);
+const copyOfHeaders = new Headers(headers);
+```
+
+
+### Interface: Body
+
+`Body` is an abstract interface with methods that are applicable to both `Request` and `Response` classes.
+
+The following methods are not yet implemented in node-fetch at this moment:
+
+- `formData()`
+
+#### body.body
+
+*(deviation from spec)*
+
+* Node.js [`Readable` stream][node-readable]
+
+Data are encapsulated in the `Body` object. Note that while the [Fetch Standard][whatwg-fetch] requires the property to always be a WHATWG `ReadableStream`, in node-fetch it is a Node.js [`Readable` stream][node-readable].
+
+#### body.bodyUsed
+
+*(spec-compliant)*
+
+* `Boolean`
+
+A boolean property for if this body has been consumed. Per the specs, a consumed body cannot be used again.
+
+#### body.arrayBuffer()
+#### body.blob()
+#### body.json()
+#### body.text()
+
+*(spec-compliant)*
+
+* Returns: Promise
+
+Consume the body and return a promise that will resolve to one of these formats.
+
+#### body.buffer()
+
+*(node-fetch extension)*
+
+* Returns: Promise<Buffer>
+
+Consume the body and return a promise that will resolve to a Buffer.
+
+#### body.textConverted()
+
+*(node-fetch extension)*
+
+* Returns: Promise<String>
+
+Identical to `body.text()`, except instead of always converting to UTF-8, encoding sniffing will be performed and text converted to UTF-8 if possible.
+
+(This API requires an optional dependency of the npm package [encoding](https://www.npmjs.com/package/encoding), which you need to install manually. `webpack` users may see [a warning message](https://github.com/bitinn/node-fetch/issues/412#issuecomment-379007792) due to this optional dependency.)
+
+
+### Class: FetchError
+
+*(node-fetch extension)*
+
+An operational error in the fetching process. See [ERROR-HANDLING.md][] for more info.
+
+
+### Class: AbortError
+
+*(node-fetch extension)*
+
+An Error thrown when the request is aborted in response to an `AbortSignal`'s `abort` event. It has a `name` property of `AbortError`. See [ERROR-HANDLING.MD][] for more info.
+
+## Acknowledgement
+
+Thanks to [github/fetch](https://github.com/github/fetch) for providing a solid implementation reference.
+
+`node-fetch` v1 was maintained by [@bitinn](https://github.com/bitinn); v2 was maintained by [@TimothyGu](https://github.com/timothygu), [@bitinn](https://github.com/bitinn) and [@jimmywarting](https://github.com/jimmywarting); v2 readme is written by [@jkantr](https://github.com/jkantr).
+
+## License
+
+MIT
+
+[npm-image]: https://flat.badgen.net/npm/v/node-fetch
+[npm-url]: https://www.npmjs.com/package/node-fetch
+[travis-image]: https://flat.badgen.net/travis/bitinn/node-fetch
+[travis-url]: https://travis-ci.org/bitinn/node-fetch
+[codecov-image]: https://flat.badgen.net/codecov/c/github/bitinn/node-fetch/master
+[codecov-url]: https://codecov.io/gh/bitinn/node-fetch
+[install-size-image]: https://flat.badgen.net/packagephobia/install/node-fetch
+[install-size-url]: https://packagephobia.now.sh/result?p=node-fetch
+[discord-image]: https://img.shields.io/discord/619915844268326952?color=%237289DA&label=Discord&style=flat-square
+[discord-url]: https://discord.gg/Zxbndcm
+[opencollective-image]: https://opencollective.com/node-fetch/backers.svg
+[opencollective-url]: https://opencollective.com/node-fetch
+[whatwg-fetch]: https://fetch.spec.whatwg.org/
+[response-init]: https://fetch.spec.whatwg.org/#responseinit
+[node-readable]: https://nodejs.org/api/stream.html#stream_readable_streams
+[mdn-headers]: https://developer.mozilla.org/en-US/docs/Web/API/Headers
+[LIMITS.md]: https://github.com/bitinn/node-fetch/blob/master/LIMITS.md
+[ERROR-HANDLING.md]: https://github.com/bitinn/node-fetch/blob/master/ERROR-HANDLING.md
+[UPGRADE-GUIDE.md]: https://github.com/bitinn/node-fetch/blob/master/UPGRADE-GUIDE.md
diff --git a/node/node_modules/node-fetch/browser.js b/node/node_modules/node-fetch/browser.js
new file mode 100644
index 0000000..ee86265
--- /dev/null
+++ b/node/node_modules/node-fetch/browser.js
@@ -0,0 +1,25 @@
+"use strict";
+
+// ref: https://github.com/tc39/proposal-global
+var getGlobal = function () {
+ // the only reliable means to get the global object is
+ // `Function('return this')()`
+ // However, this causes CSP violations in Chrome apps.
+ if (typeof self !== 'undefined') { return self; }
+ if (typeof window !== 'undefined') { return window; }
+ if (typeof global !== 'undefined') { return global; }
+ throw new Error('unable to locate global object');
+}
+
+var globalObject = getGlobal();
+
+module.exports = exports = globalObject.fetch;
+
+// Needed for TypeScript and Webpack.
+if (globalObject.fetch) {
+ exports.default = globalObject.fetch.bind(globalObject);
+}
+
+exports.Headers = globalObject.Headers;
+exports.Request = globalObject.Request;
+exports.Response = globalObject.Response;
diff --git a/node/node_modules/node-fetch/lib/index.es.js b/node/node_modules/node-fetch/lib/index.es.js
new file mode 100644
index 0000000..aae9799
--- /dev/null
+++ b/node/node_modules/node-fetch/lib/index.es.js
@@ -0,0 +1,1777 @@
+process.emitWarning("The .es.js file is deprecated. Use .mjs instead.");
+
+import Stream from 'stream';
+import http from 'http';
+import Url from 'url';
+import whatwgUrl from 'whatwg-url';
+import https from 'https';
+import zlib from 'zlib';
+
+// Based on https://github.com/tmpvar/jsdom/blob/aa85b2abf07766ff7bf5c1f6daafb3726f2f2db5/lib/jsdom/living/blob.js
+
+// fix for "Readable" isn't a named export issue
+const Readable = Stream.Readable;
+
+const BUFFER = Symbol('buffer');
+const TYPE = Symbol('type');
+
+class Blob {
+ constructor() {
+ this[TYPE] = '';
+
+ const blobParts = arguments[0];
+ const options = arguments[1];
+
+ const buffers = [];
+ let size = 0;
+
+ if (blobParts) {
+ const a = blobParts;
+ const length = Number(a.length);
+ for (let i = 0; i < length; i++) {
+ const element = a[i];
+ let buffer;
+ if (element instanceof Buffer) {
+ buffer = element;
+ } else if (ArrayBuffer.isView(element)) {
+ buffer = Buffer.from(element.buffer, element.byteOffset, element.byteLength);
+ } else if (element instanceof ArrayBuffer) {
+ buffer = Buffer.from(element);
+ } else if (element instanceof Blob) {
+ buffer = element[BUFFER];
+ } else {
+ buffer = Buffer.from(typeof element === 'string' ? element : String(element));
+ }
+ size += buffer.length;
+ buffers.push(buffer);
+ }
+ }
+
+ this[BUFFER] = Buffer.concat(buffers);
+
+ let type = options && options.type !== undefined && String(options.type).toLowerCase();
+ if (type && !/[^\u0020-\u007E]/.test(type)) {
+ this[TYPE] = type;
+ }
+ }
+ get size() {
+ return this[BUFFER].length;
+ }
+ get type() {
+ return this[TYPE];
+ }
+ text() {
+ return Promise.resolve(this[BUFFER].toString());
+ }
+ arrayBuffer() {
+ const buf = this[BUFFER];
+ const ab = buf.buffer.slice(buf.byteOffset, buf.byteOffset + buf.byteLength);
+ return Promise.resolve(ab);
+ }
+ stream() {
+ const readable = new Readable();
+ readable._read = function () {};
+ readable.push(this[BUFFER]);
+ readable.push(null);
+ return readable;
+ }
+ toString() {
+ return '[object Blob]';
+ }
+ slice() {
+ const size = this.size;
+
+ const start = arguments[0];
+ const end = arguments[1];
+ let relativeStart, relativeEnd;
+ if (start === undefined) {
+ relativeStart = 0;
+ } else if (start < 0) {
+ relativeStart = Math.max(size + start, 0);
+ } else {
+ relativeStart = Math.min(start, size);
+ }
+ if (end === undefined) {
+ relativeEnd = size;
+ } else if (end < 0) {
+ relativeEnd = Math.max(size + end, 0);
+ } else {
+ relativeEnd = Math.min(end, size);
+ }
+ const span = Math.max(relativeEnd - relativeStart, 0);
+
+ const buffer = this[BUFFER];
+ const slicedBuffer = buffer.slice(relativeStart, relativeStart + span);
+ const blob = new Blob([], { type: arguments[2] });
+ blob[BUFFER] = slicedBuffer;
+ return blob;
+ }
+}
+
+Object.defineProperties(Blob.prototype, {
+ size: { enumerable: true },
+ type: { enumerable: true },
+ slice: { enumerable: true }
+});
+
+Object.defineProperty(Blob.prototype, Symbol.toStringTag, {
+ value: 'Blob',
+ writable: false,
+ enumerable: false,
+ configurable: true
+});
+
+/**
+ * fetch-error.js
+ *
+ * FetchError interface for operational errors
+ */
+
+/**
+ * Create FetchError instance
+ *
+ * @param String message Error message for human
+ * @param String type Error type for machine
+ * @param String systemError For Node.js system error
+ * @return FetchError
+ */
+function FetchError(message, type, systemError) {
+ Error.call(this, message);
+
+ this.message = message;
+ this.type = type;
+
+ // when err.type is `system`, err.code contains system error code
+ if (systemError) {
+ this.code = this.errno = systemError.code;
+ }
+
+ // hide custom error implementation details from end-users
+ Error.captureStackTrace(this, this.constructor);
+}
+
+FetchError.prototype = Object.create(Error.prototype);
+FetchError.prototype.constructor = FetchError;
+FetchError.prototype.name = 'FetchError';
+
+let convert;
+try {
+ convert = require('encoding').convert;
+} catch (e) {}
+
+const INTERNALS = Symbol('Body internals');
+
+// fix an issue where "PassThrough" isn't a named export for node <10
+const PassThrough = Stream.PassThrough;
+
+/**
+ * Body mixin
+ *
+ * Ref: https://fetch.spec.whatwg.org/#body
+ *
+ * @param Stream body Readable stream
+ * @param Object opts Response options
+ * @return Void
+ */
+function Body(body) {
+ var _this = this;
+
+ var _ref = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {},
+ _ref$size = _ref.size;
+
+ let size = _ref$size === undefined ? 0 : _ref$size;
+ var _ref$timeout = _ref.timeout;
+ let timeout = _ref$timeout === undefined ? 0 : _ref$timeout;
+
+ if (body == null) {
+ // body is undefined or null
+ body = null;
+ } else if (isURLSearchParams(body)) {
+ // body is a URLSearchParams
+ body = Buffer.from(body.toString());
+ } else if (isBlob(body)) ; else if (Buffer.isBuffer(body)) ; else if (Object.prototype.toString.call(body) === '[object ArrayBuffer]') {
+ // body is ArrayBuffer
+ body = Buffer.from(body);
+ } else if (ArrayBuffer.isView(body)) {
+ // body is ArrayBufferView
+ body = Buffer.from(body.buffer, body.byteOffset, body.byteLength);
+ } else if (body instanceof Stream) ; else {
+ // none of the above
+ // coerce to string then buffer
+ body = Buffer.from(String(body));
+ }
+ this[INTERNALS] = {
+ body,
+ disturbed: false,
+ error: null
+ };
+ this.size = size;
+ this.timeout = timeout;
+
+ if (body instanceof Stream) {
+ body.on('error', function (err) {
+ const error = err.name === 'AbortError' ? err : new FetchError(`Invalid response body while trying to fetch ${_this.url}: ${err.message}`, 'system', err);
+ _this[INTERNALS].error = error;
+ });
+ }
+}
+
+Body.prototype = {
+ get body() {
+ return this[INTERNALS].body;
+ },
+
+ get bodyUsed() {
+ return this[INTERNALS].disturbed;
+ },
+
+ /**
+ * Decode response as ArrayBuffer
+ *
+ * @return Promise
+ */
+ arrayBuffer() {
+ return consumeBody.call(this).then(function (buf) {
+ return buf.buffer.slice(buf.byteOffset, buf.byteOffset + buf.byteLength);
+ });
+ },
+
+ /**
+ * Return raw response as Blob
+ *
+ * @return Promise
+ */
+ blob() {
+ let ct = this.headers && this.headers.get('content-type') || '';
+ return consumeBody.call(this).then(function (buf) {
+ return Object.assign(
+ // Prevent copying
+ new Blob([], {
+ type: ct.toLowerCase()
+ }), {
+ [BUFFER]: buf
+ });
+ });
+ },
+
+ /**
+ * Decode response as json
+ *
+ * @return Promise
+ */
+ json() {
+ var _this2 = this;
+
+ return consumeBody.call(this).then(function (buffer) {
+ try {
+ return JSON.parse(buffer.toString());
+ } catch (err) {
+ return Body.Promise.reject(new FetchError(`invalid json response body at ${_this2.url} reason: ${err.message}`, 'invalid-json'));
+ }
+ });
+ },
+
+ /**
+ * Decode response as text
+ *
+ * @return Promise
+ */
+ text() {
+ return consumeBody.call(this).then(function (buffer) {
+ return buffer.toString();
+ });
+ },
+
+ /**
+ * Decode response as buffer (non-spec api)
+ *
+ * @return Promise
+ */
+ buffer() {
+ return consumeBody.call(this);
+ },
+
+ /**
+ * Decode response as text, while automatically detecting the encoding and
+ * trying to decode to UTF-8 (non-spec api)
+ *
+ * @return Promise
+ */
+ textConverted() {
+ var _this3 = this;
+
+ return consumeBody.call(this).then(function (buffer) {
+ return convertBody(buffer, _this3.headers);
+ });
+ }
+};
+
+// In browsers, all properties are enumerable.
+Object.defineProperties(Body.prototype, {
+ body: { enumerable: true },
+ bodyUsed: { enumerable: true },
+ arrayBuffer: { enumerable: true },
+ blob: { enumerable: true },
+ json: { enumerable: true },
+ text: { enumerable: true }
+});
+
+Body.mixIn = function (proto) {
+ for (const name of Object.getOwnPropertyNames(Body.prototype)) {
+ // istanbul ignore else: future proof
+ if (!(name in proto)) {
+ const desc = Object.getOwnPropertyDescriptor(Body.prototype, name);
+ Object.defineProperty(proto, name, desc);
+ }
+ }
+};
+
+/**
+ * Consume and convert an entire Body to a Buffer.
+ *
+ * Ref: https://fetch.spec.whatwg.org/#concept-body-consume-body
+ *
+ * @return Promise
+ */
+function consumeBody() {
+ var _this4 = this;
+
+ if (this[INTERNALS].disturbed) {
+ return Body.Promise.reject(new TypeError(`body used already for: ${this.url}`));
+ }
+
+ this[INTERNALS].disturbed = true;
+
+ if (this[INTERNALS].error) {
+ return Body.Promise.reject(this[INTERNALS].error);
+ }
+
+ let body = this.body;
+
+ // body is null
+ if (body === null) {
+ return Body.Promise.resolve(Buffer.alloc(0));
+ }
+
+ // body is blob
+ if (isBlob(body)) {
+ body = body.stream();
+ }
+
+ // body is buffer
+ if (Buffer.isBuffer(body)) {
+ return Body.Promise.resolve(body);
+ }
+
+ // istanbul ignore if: should never happen
+ if (!(body instanceof Stream)) {
+ return Body.Promise.resolve(Buffer.alloc(0));
+ }
+
+ // body is stream
+ // get ready to actually consume the body
+ let accum = [];
+ let accumBytes = 0;
+ let abort = false;
+
+ return new Body.Promise(function (resolve, reject) {
+ let resTimeout;
+
+ // allow timeout on slow response body
+ if (_this4.timeout) {
+ resTimeout = setTimeout(function () {
+ abort = true;
+ reject(new FetchError(`Response timeout while trying to fetch ${_this4.url} (over ${_this4.timeout}ms)`, 'body-timeout'));
+ }, _this4.timeout);
+ }
+
+ // handle stream errors
+ body.on('error', function (err) {
+ if (err.name === 'AbortError') {
+ // if the request was aborted, reject with this Error
+ abort = true;
+ reject(err);
+ } else {
+ // other errors, such as incorrect content-encoding
+ reject(new FetchError(`Invalid response body while trying to fetch ${_this4.url}: ${err.message}`, 'system', err));
+ }
+ });
+
+ body.on('data', function (chunk) {
+ if (abort || chunk === null) {
+ return;
+ }
+
+ if (_this4.size && accumBytes + chunk.length > _this4.size) {
+ abort = true;
+ reject(new FetchError(`content size at ${_this4.url} over limit: ${_this4.size}`, 'max-size'));
+ return;
+ }
+
+ accumBytes += chunk.length;
+ accum.push(chunk);
+ });
+
+ body.on('end', function () {
+ if (abort) {
+ return;
+ }
+
+ clearTimeout(resTimeout);
+
+ try {
+ resolve(Buffer.concat(accum, accumBytes));
+ } catch (err) {
+ // handle streams that have accumulated too much data (issue #414)
+ reject(new FetchError(`Could not create Buffer from response body for ${_this4.url}: ${err.message}`, 'system', err));
+ }
+ });
+ });
+}
+
+/**
+ * Detect buffer encoding and convert to target encoding
+ * ref: http://www.w3.org/TR/2011/WD-html5-20110113/parsing.html#determining-the-character-encoding
+ *
+ * @param Buffer buffer Incoming buffer
+ * @param String encoding Target encoding
+ * @return String
+ */
+function convertBody(buffer, headers) {
+ if (typeof convert !== 'function') {
+ throw new Error('The package `encoding` must be installed to use the textConverted() function');
+ }
+
+ const ct = headers.get('content-type');
+ let charset = 'utf-8';
+ let res, str;
+
+ // header
+ if (ct) {
+ res = /charset=([^;]*)/i.exec(ct);
+ }
+
+ // no charset in content type, peek at response body for at most 1024 bytes
+ str = buffer.slice(0, 1024).toString();
+
+ // html5
+ if (!res && str) {
+ res = /