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.

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 (fixed-point) 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', 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 desired.

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.

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 with 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
// 'Error: Number has more than 15 significant digits'
new BigNumber(823456789123456.3)
// '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'

Used internally to identify a BigNumber instance.

The coefficient of the value of this BigNumber, an array of base 1e14 integer numbers, or null.

The exponent of the value of this BigNumber, an integer number, -1000000000 to 1000000000, or null.

The sign of the value of this BigNumber, -1, 1, or null.

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)
x.abs()                     // '0.8'

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)
x.absoluteValue()           // '0.8'

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

Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode roundingMode to a maximum of decimalPlaces decimal places.

If decimalPlaces 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 roundingMode is omitted, or is null or undefined, ROUNDING_MODE is used.

Throws if decimalPlaces or roundingMode is invalid.

x = new BigNumber(1234.56)
x.decimalPlaces()                      // 2
x.decimalPlaces(1)                     // '1234.6'
x.decimalPlaces(2)                     // '1234.56'
x.decimalPlaces(10)                    // '1234.56'
x.decimalPlaces(0, 1)                  // '1234'
x.decimalPlaces(0, 6)                  // '1235'
x.decimalPlaces(1, 1)                  // '1234.5'
x.decimalPlaces(1, BigNumber.ROUND_HALF_EVEN)     // '1234.6'
x                                      // '1234.56'
y = new BigNumber('9.9e-101')
y.decimalPlaces()                      // 102

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.div(y)                    // '3.14159292035398230088'
x.div(5)                    // '71'
x.div(47, 16)               // '5'

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.dividedBy(5)                  // '71'
x.dividedBy(47, 16)             // '5'

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.dividedToIntegerBy(0.7)            // '7'
x.dividedToIntegerBy('0.f', 16)      // '5'

Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode roundingMode to a maximum of decimalPlaces decimal places.

If decimalPlaces 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 roundingMode is omitted, or is null or undefined, ROUNDING_MODE is used.

Throws if decimalPlaces or roundingMode is invalid.

x = new BigNumber(1234.56)
x.dp()                                 // 2
x.dp(1)                                // '1234.6'
x.dp(2)                                // '1234.56'
x.dp(10)                               // '1234.56'
x.dp(0, 1)                             // '1234'
x.dp(0, 6)                             // '1235'
x.dp(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

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.

0 === 1e-324                    // true
x = new BigNumber(0)
x.eq('1e-324')                  // false
BigNumber(-0).eq(x)             // true  ( -0 === 0 )
BigNumber(255).eq('ff', 16)     // true

y = new BigNumber(NaN)
y.eq(NaN)                       // false

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.

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. 123.456**10000 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.

Throws if n is not an integer.

Math.pow(0.7, 2)                    // 0.48999999999999994
x = new BigNumber(0.7)
x.exponentiatedBy(2)                // '0.49'
BigNumber(3).exponentiatedBy(-2)    // '0.11111111111111111111'

Returns true if the value of this BigNumber is greater than the value of n, otherwise returns false.

0.1 > (0.3 - 0                     // true
x = new BigNumber(0.1)
x.gt(BigNumber(0.3).minus(0.2))    // false
BigNumber(0).gt(x)                 // false
BigNumber(11, 3).gt(11.1, 2)       // true

Returns true if the value of this BigNumber is greater than or equal to the value of n, otherwise returns false.

(0.3 - 0.2) >= 0.1                    // false
x = new BigNumber(0.3).minus(0.2)
x.gte(0.1)                            // true
BigNumber(1).gte(x)                   // true
BigNumber(10, 18).gte('i', 36)        // true

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.idiv(y)                       // '1'
x.idiv(0.7)                     // '7'
x.idiv('0.f', 16)               // '5'

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.

x = new BigNumber(123.456)
x.integerValue()                        // '123'
x.integerValue(BigNumber.ROUND_CEIL)    // '124'
y = new BigNumber(-12.7)
y.integerValue()                        // '-13'
x.integerValue(BigNumber.ROUND_DOWN)    // '-12'

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.

0 === 1e-324                           // true
x = new BigNumber(0)
x.isEqualTo('1e-324')                  // false
BigNumber(-0).isEqualTo(x)             // true  ( -0 === 0 )
BigNumber(255).isEqualTo('ff', 16)     // true

y = new BigNumber(NaN)
y.isEqualTo(NaN)                // false

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

Returns true if the value of this BigNumber is greater than the value of n, otherwise returns false.

0.1 > (0.3 - 0.2)                             // true
x = new BigNumber(0.1)
x.isGreaterThan(BigNumber(0.3).minus(0.2))    // false
BigNumber(0).isGreaterThan(x)                 // false
BigNumber(11, 3).isGreaterThan(11.1, 2)       // true

Returns true if the value of this BigNumber is greater than or equal to the value of n, otherwise returns false.

(0.3 - 0.2) >= 0.1                                  // false
x = new BigNumber(0.3).minus(0.2)
x.isGreaterThanOrEqualTo(0.1)                       // true
BigNumber(1).isGreaterThanOrEqualTo(x)              // true
BigNumber(10, 18).isGreaterThanOrEqualTo('i', 36)   // true

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

Returns true if the value of this BigNumber is less than the value of n, otherwise returns false.

(0.3 - 0.2) < 0.1                       // true
x = new BigNumber(0.3).minus(0.2)
x.isLessThan(0.1)                       // false
BigNumber(0).isLessThan(x)              // true
BigNumber(11.1, 2).isLessThan(11, 3)    // true

Returns true if the value of this BigNumber is less than or equal to the value of n, otherwise returns false.

0.1 <= (0.3 - 0.2)                                 // false
x = new BigNumber(0.1)
x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2))   // true
BigNumber(-1).isLessThanOrEqualTo(x)               // true
BigNumber(10, 18).isLessThanOrEqualTo('i', 36)     // true

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

Returns true if the value of this BigNumber is negative, otherwise returns false.

x = new BigNumber(-0)
x.isNegative()                  // true
y = new BigNumber(2)
y.isNegative()                  // false

Returns true if the value of this BigNumber is positive, otherwise returns false.

x = new BigNumber(-0)
x.isPositive()                  // false
y = new BigNumber(2)
y.isPositive()                  // true

Returns true if the value of this BigNumber is zero or minus zero, otherwise returns false.

x = new BigNumber(-0)
x.isZero()                 // true

Returns true if the value of this BigNumber is less than the value of n, otherwise returns false.

(0.3 - 0.2) < 0.1                       // true
x = new BigNumber(0.3).minus(0.2)
x.lt(0.1)                               // false
BigNumber(0).lt(x)                      // true
BigNumber(11.1, 2).lt(11, 3)            // true

Returns true if the value of this BigNumber is less than or equal to the value of n, otherwise returns false.

0.1 <= (0.3 - 0.2)                  // false
x = new BigNumber(0.1)
x.lte(BigNumber(0.3).minus(0.2))    // true
BigNumber(-1).lte(x)                // true
BigNumber(10, 18).lte('i', 36)      // true

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'

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.mod(0.9)                   // '0.1'
y = new BigNumber(33)
y.mod('a', 33)               // '3'

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.modulo('a', 33)               // '3'

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').multipliedBy(y)    // '1.26e+501'
x.multipliedBy('-a', 16)               // '-6'

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'

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'

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.

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. 123.456**10000 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.pow(n).modulo(m) with a POW_PRECISION of 0.

Throws if n is not an integer.

Math.pow(0.7, 2)                   // 0.48999999999999994
x = new BigNumber(0.7)
x.pow(2)                           // '0.49'
BigNumber(3).pow(-2)               // '0.11111111111111111111'

Returns the number of significant digits of the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.

If includeZeros is true then any trailing zeros of the integer part of the value of this BigNumber are counted as significant digits, otherwise they are not.

Throws if includeZeros is invalid.

x = new BigNumber(9876.54321)
x.precision()                         // 9
y = new BigNumber(987000)
y.precision(false)                    // 3
y.precision(true)                     // 6

Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of significantDigits significant digits using rounding mode roundingMode.

If roundingMode is omitted or is null or undefined, ROUNDING_MODE will be used.

Throws if significantDigits or roundingMode is invalid.

x = new BigNumber(9876.54321)
x.precision(6)                         // '9876.54'
x.precision(6, BigNumber.ROUND_UP)     // '9876.55'
x.precision(2)                         // '9900'
x.precision(2, 1)                      // '9800'
x                                      // '9876.54321'

Returns the number of significant digits of the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.

If includeZeros is true then any trailing zeros of the integer part of the value of this BigNumber are counted as significant digits, otherwise they are not.

Throws if includeZeros is invalid.

x = new BigNumber(9876.54321)
x.sd()                         // 9
y = new BigNumber(987000)
y.sd(false)                    // 3
y.sd(true)                     // 6

Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of significantDigits significant digits using rounding mode roundingMode.

If roundingMode is omitted or is null or undefined, ROUNDING_MODE will be used.

Throws if significantDigits or roundingMode is invalid.

x = new BigNumber(9876.54321)
x.sd(6)                           // '9876.54'
x.sd(6, BigNumber.ROUND_UP)       // '9876.55'
x.sd(2)                           // '9900'
x.sd(2, 1)                        // '9800'
x                                 // '9876.54321'

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.

x = new BigNumber(1.23)
x.shiftedBy(3)                      // '1230'
x.shiftedBy(-3)                     // '0.00123'

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.sqrt()                  // '4'
y = new BigNumber(3)
y.sqrt()                  // '1.73205080756887729353'

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.squareRoot()                  // '1.73205080756887729353'

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.times(3)                  // '1.8'
BigNumber('7e+500').times(y)    // '1.26e+501'
x.times('-a', 16)               // '-6'

Returns a string representing the value of this BigNumber in exponential notation rounded using rounding mode roundingMode to decimalPlaces decimal places, i.e with one digit before the decimal point and decimalPlaces digits after it.

If the value of this BigNumber in exponential notation has fewer than decimalPlaces fraction digits, the return value will be appended with zeros accordingly.

If decimalPlaces 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 roundingMode is omitted or is null or undefined, ROUNDING_MODE is used.

Throws if decimalPlaces or roundingMode is invalid.

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'

Returns a string representing the value of this BigNumber in normal (fixed-point) notation rounded to decimalPlaces decimal places using rounding mode roundingMode.

If the value of this BigNumber in normal notation has fewer than decimalPlaces 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 10**21, this method will always return normal notation.

If decimalPlaces 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 normal notation is required and the current EXPONENTIAL_AT setting causes toString to return exponential notation.

If roundingMode is omitted or is null or undefined, ROUNDING_MODE is used.

Throws if decimalPlaces or roundingMode is invalid.

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'

Returns a string representing the value of this BigNumber in normal (fixed-point) notation rounded to decimalPlaces decimal places using rounding mode roundingMode, and formatted according to the properties of the format or FORMAT object.

The formatting object may contain some or all of the properties shown in the examples below.

If decimalPlaces is omitted or is null or undefined, then the return value is not rounded to a fixed number of decimal places.

If roundingMode is omitted or is null or undefined, ROUNDING_MODE is used.

If format is omitted or is null or undefined, FORMAT is used.

Throws if decimalPlaces, roundingMode, or format is invalid.

fmt = {
  decimalSeparator: '.',
  groupSeparator: ',',
  groupSize: 3,
  secondaryGroupSize: 0,
  fractionGroupSeparator: ' ',
  fractionGroupSize: 0
}

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 = {
  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'

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 max_denominator. If a maximum denominator, max_denominator, is not specified, or is null or undefined, the denominator will be the lowest value necessary to represent the number exactly.

Throws if max_denominator is invalid.

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'

As valueOf.

Returns the value of this BigNumber as a JavaScript primitive number.

Using the unary plus operator gives the same result.

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

Returns a string representing the value of this BigNumber rounded to significantDigits significant digits using rounding mode roundingMode.

If significantDigits 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 significantDigits is omitted, or is null or undefined, then the return value is the same as n.toString().

If roundingMode is omitted or is null or undefined, ROUNDING_MODE is used.

Throws if significantDigits or roundingMode is invalid.

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'

Returns a string representing the value of this BigNumber in base 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 (the same as Number.prototype.toString).

If a base is specified the value is rounded according to the current DECIMAL_PLACES and ROUNDING_MODE settings, otherwise it is not.

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.

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'

As toString, but does not accept a base argument and includes the minus sign for negative zero.

``ts x = new BigNumber('-0') x.toString() // '0' x.valueOf() // '-0' y = new BigNumber('1.777e+457') y.valueOf() // '1.777e+457'

Helps ES6 import.

Helps ES6 import.

To aid in debugging, if a BigNumber.DEBUG property is true then an error will be thrown if the BigNumber constructor receives an invalid BigNumber.Value, or if BigNumber.isBigNumber receives a BigNumber instance that is malformed.

// No error, and BigNumber NaN is returned.
new BigNumber('blurgh')    // 'NaN'
new BigNumber(9, 2)        // 'NaN'
BigNumber.DEBUG = true
new BigNumber('blurgh')    // '[BigNumber Error] Not a number'
new BigNumber(9, 2)        // '[BigNumber Error] Not a base 2 number'

An error will also be thrown if a BigNumber.Value is of type number with more than 15 significant digits, as calling toString or valueOf on such numbers may not result in the intended value.

console.log(823456789123456.3)       //  823456789123456.2
// No error, and the returned BigNumber does not have the same value as the number literal.
new BigNumber(823456789123456.3)     // '823456789123456.2'
BigNumber.DEBUG = true
new BigNumber(823456789123456.3)
// '[BigNumber Error] Number primitive has more than 15 significant digits'

Check that a BigNumber instance is well-formed:

x = new BigNumber(10)

BigNumber.DEBUG = false
// Change x.c to an illegitimate value.
x.c = NaN
// No error, as BigNumber.DEBUG is false.
BigNumber.isBigNumber(x)    // true

BigNumber.DEBUG = true
BigNumber.isBigNumber(x)    // '[BigNumber Error] Invalid BigNumber'

See MODULO_MODE.

Rounds towards Infinity.

Rounds towards zero.

Rounds towards -Infinity.

Rounds towards nearest neighbour. If equidistant, rounds towards Infinity.

Rounds towards nearest neighbour. If equidistant, rounds towards zero.

Rounds towards nearest neighbour. If equidistant, rounds towards even neighbour.

Rounds towards nearest neighbour. If equidistant, rounds towards -Infinity.

Rounds towards nearest neighbour. If equidistant, rounds away from zero .

Rounds away from zero.

Returns a new independent BigNumber constructor with configuration as described by object, or with the default configuration if object is null or undefined.

Throws if object is not an object.

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 })

Configures the settings that apply to this BigNumber constructor.

The configuration object, object, contains any number of the properties shown in the example below.

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 properties.

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$_'
});

BigNumber.config().DECIMAL_PLACES        // 40

Returns true if value is a BigNumber instance, otherwise returns false.

If BigNumber.DEBUG is true, throws if a BigNumber instance is not well-formed.

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

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.max(4e9, x, '123456789.9')      // '4000000000'

arr = [12, '13', new BigNumber(14)]
BigNumber.max.apply(null, arr)            // '14'

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.maximum.apply(null, arr)            // '14'

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.min(4e9, x, '123456789.9')             // '123456789.9'

arr = [2, new BigNumber(-14), '-15.9999', -12]
BigNumber.min.apply(null, arr)                   // '-15.9999'

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.minimum.apply(null, arr)                // '-15.9999'

Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and less than 1.

The return value will have decimalPlaces decimal places, or less if trailing zeros are produced. If decimalPlaces is omitted, the current DECIMAL_PLACES setting will be used.

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:

global.crypto = require('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 decimalPlaces is invalid.

BigNumber.config({ DECIMAL_PLACES: 10 })
BigNumber.random()              // '0.4117936847'
BigNumber.random(20)            // '0.78193327636914089009'

Configures the settings that apply to this BigNumber constructor.

The configuration object, object, contains any number of the properties shown in the example below.

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 properties.

BigNumber.set({
    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$_'
});

BigNumber.set().DECIMAL_PLACES        // 40

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'