decimal.js

An arbitrary-precision Decimal type for JavaScript.

API

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.

When the library is loaded, it defines a single function object, Decimal, the constructor of Decimal instances.

If necessary, multiple Decimal constructors can be created, each with their own independent configuration, e.g. precision and range, which applies to all Decimal instances created from it.

A new Decimal constructor is created by calling the clone method of an already existing Decimal constructor.

CONSTRUCTOR

Decimal`Decimal(value) ⇒ Decimal`

value: number|string|Decimal: A legitimate value is an integer or float, including ±0, or is ±Infinity, or NaN.; The number of digits of value is not limited, except by JavaScript's maximum array size and, in practice, the processing time required.; The allowable range of value is defined in terms of a maximum exponent, see maxE, and a minimum exponent, see minE.; As well as in decimal, a string value may be expressed in binary, hexadecimal or octal, if the appropriate prefix is included: 0x or 0X for hexadecimal, 0b or 0B for binary, and 0o or 0O for octal.; Both decimal and non-decimal string values may use exponential (floating-point), as well as normal (fixed-point) notation.; In exponential notation, e or E defines a power-of-ten exponent for decimal values, and p or P defines a power-of-two exponent for non-decimal values, i.e. binary, hexadecimal or octal.

Returns a new Decimal object instance.

Throws on an invalid value.

x = new Decimal(9)                       // '9'
y = new Decimal(x)                       // '9'

new Decimal('5032485723458348569331745.33434346346912144534543')
new Decimal('4.321e+4')                  // '43210'
new Decimal('-735.0918e-430')            // '-7.350918e-428'
new Decimal('5.6700000')                 // '5.67'
new Decimal(Infinity)                    // 'Infinity'
new Decimal(NaN)                         // 'NaN'
new Decimal('.5')                        // '0.5'
new Decimal('-0b10110100.1')             // '-180.5'
new Decimal('0xff.8')                    // '255.5'

new Decimal(0.046875)                    // '0.046875'
new Decimal('0.046875000000')            // '0.046875'
new Decimal('0.046_875_000_000')         // '0.046875'

new Decimal(4.6875e-2)                   // '0.046875'
new Decimal('468.75e-4')                 // '0.046875'

new Decimal('0b0.000011')                // '0.046875'
new Decimal('0o0.03')                    // '0.046875'
new Decimal('0x0.0c')                    // '0.046875'

new Decimal('0b1.1p-5')                  // '0.046875'
new Decimal('0o1.4p-5')                  // '0.046875'
new Decimal('0x1.8p-5')                  // '0.046875'

Methods

The methods of a Decimal constructor.

abs`.abs(x) ⇒ Decimal`

x: number|string|Decimal

See absoluteValue.

a = Decimal.abs(x)
b = new Decimal(x).abs()
a.equals(b)                    // true

acos`.acos(x) ⇒ Decimal`

x: number|string|Decimal

See inverseCosine.

a = Decimal.acos(x)
b = new Decimal(x).acos()
a.equals(b)                    // true

acosh`.acosh(x) ⇒ Decimal`

x: number|string|Decimal

See inverseHyperbolicCosine.

a = Decimal.acosh(x)
b = new Decimal(x).acosh()
a.equals(b)                    // true

add`.add(x, y) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

See plus.

a = Decimal.add(x, y)
b = new Decimal(x).plus(y)
a.equals(b)                    // true

asin`.asin(x) ⇒ Decimal`

x: number|string|Decimal

See inverseSine.

a = Decimal.asin(x)
b = new Decimal(x).asin()
a.equals(b)                    // true

asinh`.asinh(x) ⇒ Decimal`

x: number|string|Decimal

See inverseHyperbolicSine.

a = Decimal.asinh(x)
b = new Decimal(x).asinh()
a.equals(b)                    // true

atan`.atan(x) ⇒ Decimal`

x: number|string|Decimal

See inverseTangent.

a = Decimal.atan(x)
b = new Decimal(x).atan()
a.equals(b)                    // true

atanh`.atanh(x) ⇒ Decimal`

x: number|string|Decimal

See inverseHyperbolicTangent.

a = Decimal.atanh(x)
b = new Decimal(x).atanh()
a.equals(b)                    // true

atan2`.atan2(y, x) ⇒ Decimal`

y: number|string|Decimal
x: number|string|Decimal

Returns a new Decimal whose value is the inverse tangent in radians of the quotient of y and x, rounded to precision significant digits using rounding mode rounding.

The signs of y and x are used to determine the quadrant of the result.

Domain: [-Infinity, Infinity]
Range: [-pi, pi]

See Pi and Math.atan2().

r = Decimal.atan2(y, x)

cbrt`.cbrt(x) ⇒ Decimal`

x: number|string|Decimal

See cubeRoot.

a = Decimal.cbrt(x)
b = new Decimal(x).cbrt()
a.equals(b)                    // true

ceil`.ceil(x) ⇒ Decimal`

x: number|string|Decimal

See ceil.

a = Decimal.ceil(x)
b = new Decimal(x).ceil()
a.equals(b)                    // true

clamp`.clamp(min, max) ⇒ Decimal`

min: number|string|Decimal
max: number|string|Decimal

See clampedTo.

Decimal.clamp(10.1, 0, 10)     // '10'

clone `.clone([object]) ⇒ Decimal constructor`

object: object

Returns a new independent Decimal constructor with configuration settings as described by object (see set), or with the same settings as this Decimal constructor if object is omitted.

Decimal.set({ precision: 5 })
Decimal9 = Decimal.clone({ precision: 9 })

a = new Decimal(1)
b = new Decimal9(1)

a.div(3)                           // 0.33333
b.div(3)                           // 0.333333333

// Decimal9 = Decimal.clone({ precision: 9 }) is equivalent to:
Decimal9 = Decimal.clone()
Decimal9.set({ precision: 9 })

If object has a 'defaults' property with value true then the new constructor will use the default configuration.

D1 = Decimal.clone({ defaults: true })

// Use the defaults except for precision
D2 = Decimal.clone({ defaults: true, precision: 50 })

It is not inefficient in terms of memory usage to use multiple Decimal constructors as functions are shared between them.

cos`.cos(x) ⇒ Decimal`

x: number|string|Decimal

See cosine.

a = Decimal.cos(x)
b = new Decimal(x).cos()
a.equals(b)                    // true

cosh`.cosh(x) ⇒ Decimal`

x: number|string|Decimal

See hyperbolicCosine.

a = Decimal.cosh(x)
b = new Decimal(x).cosh()
a.equals(b)                    // true

div`.div(x, y) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

See dividedBy.

a = Decimal.div(x, y)
b = new Decimal(x).div(y)
a.equals(b)                    // true

exp`.exp(x) ⇒ Decimal`

x: number|string|Decimal

See naturalExponential.

a = Decimal.exp(x)
b = new Decimal(x).exp()
a.equals(b)                    // true

floor`.floor(x) ⇒ Decimal`

x: number|string|Decimal

See floor.

a = Decimal.floor(x)
b = new Decimal(x).floor()
a.equals(b)                    // true

hypot`.hypot([x [, y, ...]]) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

Returns a new Decimal whose value is the square root of the sum of the squares of the arguments, rounded to precision significant digits using rounding mode rounding.

r = Decimal.hypot(x, y)

ln`.ln(x) ⇒ Decimal`

x: number|string|Decimal

See naturalLogarithm.

a = Decimal.ln(x)
b = new Decimal(x).ln()
a.equals(b)                    // true

isDecimal`.isDecimal(object) ⇒ boolean`

object: any

Returns true if object is a Decimal instance (where Decimal is any Decimal constructor), or false if it is not.

a = new Decimal(1)
b = {}
a instanceof Decimal           // true
Decimal.isDecimal(a)           // true
Decimal.isDecimal(b)           // false

log`.log(x [, base]) ⇒ Decimal`

x: number|string|Decimal
base: number|string|Decimal

See logarithm.

The default base is 10, which is not the same as JavaScript's Math.log(), which returns the natural logarithm (base e).

a = Decimal.log(x, y)
b = new Decimal(x).log(y)
a.equals(b)                    // true

log2`.log2(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the base 2 logarithm of x, rounded to precision significant digits using rounding mode rounding.

r = Decimal.log2(x)

log10`.log10(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the base 10 logarithm of x, rounded to precision significant digits using rounding mode rounding.

r = Decimal.log10(x)

max`.max(x [, y, ...]) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

Returns a new Decimal whose value is the maximum of the arguments.

r = Decimal.max(x, y, z)

min`.min(x [, y, ...]) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

Returns a new Decimal whose value is the minimum of the arguments.

r = Decimal.min(x, y, z)

mod`.mod(x, y) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

See modulo.

a = Decimal.mod(x, y)
b = new Decimal(x).mod(y)
a.equals(b)                    // true

mul`.mul(x, y) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

See times.

a = Decimal.mul(x, y)
b = new Decimal(x).mul(y)
a.equals(b)                    // true

noConflict`.noConflict() ⇒ Decimal constructor`

Browsers only.

Reverts the Decimal variable to the value it had before this library was loaded and returns a reference to the original Decimal constructor so it can be assigned to a variable with a different name.

<script> Decimal = 1 </script>
<script src='/path/to/decimal.js'></script>
<script>
  a = new Decimal(2)      // '2'
  D = Decimal.noConflict()
  Decimal                 // 1
  b = new D(3)            // '3'
</script>

pow`.pow(base, exponent) ⇒ Decimal`

base: number|string|Decimal
exponent: number|string|Decimal

See toPower.

a = Decimal.pow(x, y)
b = new Decimal(x).pow(y)
a.equals(b)                    // true

random`.random([dp]) ⇒ Decimal`

dp: number: integer, 0 to 1e+9 inclusive

Returns a new Decimal 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 precision setting.

If the value of this Decimal constructor's crypto property is true, and the crypto object is available globally in the host environment, the random digits of the return value are generated by either crypto.getRandomValues (Web Cryptography API in modern browsers) or crypto.randomBytes (Node.js), otherwise, if the the value of the property is false the return value is generated by Math.random (fastest).

To make the crypto object available globally in Node.js use

global.crypto = require('crypto')

If the value of this Decimal constructor's crypto property is set true and the crypto object and associated method are not available, an exception will be thrown.

If one of the crypto methods is used, the value of the returned Decimal should be cryptographically-secure and statistically indistinguishable from a random value.

Decimal.set({ precision: 10 })
Decimal.random()                    // '0.4117936847'
Decimal.random(20)                  // '0.78193327636914089009'

round`.round(x) ⇒ Decimal`

x: number|string|Decimal

See round.

a = Decimal.round(x)
b = new Decimal(x).round()
a.equals(b)                    // true

set`.set(object) ⇒ Decimal constructor`

object: object

Configures the 'global' settings for this particular Decimal constructor, i.e. the settings which apply to operations performed on the Decimal instances created by it.

Returns this Decimal constructor.

The configuration object, object, can contain some or all of the properties described in detail at Properties and shown in the example below.

The values of the configuration object properties are checked for validity and then stored as equivalently-named properties of this Decimal constructor.

If object has a 'defaults' property with value true then any unspecified properties will be reset to their default values.

Throws on an invalid object or configuration property value.

// Defaults
Decimal.set({
    precision: 20,
    rounding: 4,
    toExpNeg: -7,
    toExpPos: 21,
    maxE: 9e15,
    minE: -9e15,
    modulo: 1,
    crypto: false
})

// Reset all properties to their default values
Decimal.set({ defaults: true })

// Set precision to 50 and all other properties to their default values
Decimal.set({ precision: 50, defaults: true })

The properties of a Decimal constructor can also be set by direct assignment, but that will by-pass the validity checking that this method performs - this is not a problem if the user knows that the assignment is valid.

Decimal.precision = 40

sign`.sign(x) ⇒ number`

x: number|string|Decimal

Returns
`1`	if the value of `x` is non-zero and its sign is positive
`-1`	if the value of `x` is non-zero and its sign is negative
`0`	if the value of `x` is positive zero
`-0`	if the value of `x` is negative zero
`NaN`	if the value of `x` is `NaN`

r = Decimal.sign(x)

sin`.sin(x) ⇒ Decimal`

x: number|string|Decimal

See sine.

a = Decimal.sin(x)
b = new Decimal(x).sin()
a.equals(b)                    // true

sinh`.sinh(x) ⇒ Decimal`

x: number|string|Decimal

See hyperbolicSine.

a = Decimal.sinh(x)
b = new Decimal(x).sinh()
a.equals(b)                    // true

sqrt`.sqrt(x) ⇒ Decimal`

x: number|string|Decimal

See squareRoot.

a = Decimal.sqrt(x)
b = new Decimal(x).sqrt()
a.equals(b)                    // true

sub`.sub(x, y) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

See minus.

a = Decimal.sub(x, y)
b = new Decimal(x).sub(y)
a.equals(b)                    // true

sum`.sum(x [, y, ...]) ⇒ Decimal`

x: number|string|Decimal
y: number|string|Decimal

Returns a new Decimal whose value is the sum of the arguments, rounded to precision significant digits using rounding mode rounding.
Only the result is rounded, not the intermediate summations.

x = 5
y = '16'
z = new Decimal(-11)
Decimal.sum(x, y, z)           // '10'

tan`.tan(x) ⇒ Decimal`

x: number|string|Decimal

See tangent.

a = Decimal.tan(x)
b = new Decimal(x).tan()
a.equals(b)                    // true

tanh`.tanh(x) ⇒ Decimal`

x: number|string|Decimal

See hyperbolicTangent.

a = Decimal.tanh(x)
b = new Decimal(x).tanh()
a.equals(b)                    // true

trunc`.trunc(x) ⇒ Decimal`

x: number|string|Decimal

See truncated.

a = Decimal.trunc(x)
b = new Decimal(x).trunc()
a.equals(b)                    // true

Properties

The properties of a Decimal constructor.

Configuration properties

The values of the configuration properties precision, rounding, minE, maxE, toExpNeg, toExpPos, modulo, and crypto are set using the set method.

As simple object properties they can be set directly without using set, and it is fine to do so, but the values assigned will not then be checked for validity. For example:

Decimal.set({ precision: 0 })
// '[DecimalError] Invalid argument: precision: 0'

Decimal.precision = 0
// No error is thrown and the results of calculations are unreliable

precision

number: integer, 1 to 1e+9 inclusive
Default value: 20

The maximum number of significant digits of the result of an operation.

All functions which return a Decimal will round the return value to precision significant digits except Decimal, absoluteValue, ceil, floor, negated, round, toDecimalPlaces, toNearest and truncated.

See Pi for the precision limit of the trigonometric methods.

Decimal.set({ precision: 5 })
Decimal.precision                  // 5

rounding

number: integer, 0 to 8 inclusive
Default value: 4 (ROUND_HALF_UP)

The default rounding mode used when rounding the result of an operation to precision significant digits, and when rounding the return value of the round, toBinary, toDecimalPlaces, toExponential, toFixed, toHexadecimal, toNearest, toOctal, toPrecision and toSignificantDigits methods.

The rounding modes are available as enumerated properties of the constructor.

Decimal.set({ rounding: Decimal.ROUND_UP })
Decimal.set({ rounding: 0 })       // equivalent
Decimal.rounding                   // 0

minE

number: integer, -9e15 to 0 inclusive
Default value: -9e15

The negative exponent limit, i.e. the exponent value below which underflow to zero occurs.

If the Decimal to be returned by a calculation would have an exponent lower than minE then the value of that Decimal becomes zero.

JavaScript numbers underflow to zero for exponents below -324.

Decimal.set({ minE: -500 })
Decimal.minE                       // -500
new Decimal('1e-500')              // '1e-500'
new Decimal('9.9e-501')            // '0'

Decimal.set({ minE: -3 })
new Decimal(0.001)                 // '0.01'       e is -3
new Decimal(0.0001)                // '0'          e is -4

The smallest possible magnitude of a non-zero Decimal is 1e-9000000000000000

maxE

number: integer, 0 to 9e15 inclusive
Default value: 9e15

The positive exponent limit, i.e. the exponent value above which overflow to Infinity occurs.

If the Decimal to be returned by a calculation would have an exponent higher than maxE then the value of that Decimal becomes Infinity.

JavaScript numbers overflow to Infinity for exponents above 308.

Decimal.set({ maxE: 500 })
Decimal.maxE                       // 500
new Decimal('9.999e500')           // '9.999e+500'
new Decimal('1e501')               // 'Infinity'

Decimal.set({ maxE: 4 })
new Decimal(99999)                 // '99999'      e is 4
new Decimal(100000)                // 'Infinity'

The largest possible magnitude of a finite Decimal is 9.999...e+9000000000000000

toExpNeg

number: integer, -9e15 to 0 inclusive
Default value: -7

The negative exponent value at and below which toString returns exponential notation.

Decimal.set({ toExpNeg: -7 })
Decimal.toExpNeg                   // -7
new Decimal(0.00000123)            // '0.00000123'       e is -6
new Decimal(0.000000123)           // '1.23e-7'

// Always return exponential notation:
Decimal.set({ toExpNeg: 0 })

JavaScript numbers use exponential notation for negative exponents of -7 and below.

Regardless of the value of toExpNeg, the toFixed method will always return a value in normal notation and the toExponential method will always return a value in exponential form.

toExpPos

number: integer, 0 to 9e15 inclusive
Default value: 20

The positive exponent value at and above which toString returns exponential notation.

Decimal.set({ toExpPos: 2 })
Decimal.toExpPos                   // 2
new Decimal(12.3)                  // '12.3'        e is 1
new Decimal(123)                   // '1.23e+2'

// Always return exponential notation:
Decimal.set({ toExpPos: 0 })

JavaScript numbers use exponential notation for positive exponents of 20 and above.

Regardless of the value of toExpPos, the toFixed method will always return a value in normal notation and the toExponential method will always return a value in exponential form.

modulo

number: integer, 0 to 9 inclusive
Default value: 1 (ROUND_DOWN)

The modulo mode used when calculating the modulus: a mod n.

The quotient, q = a / n, is calculated according to the rounding mode that corresponds to the chosen modulo mode.

The remainder, r, is calculated as: r = a - n * q.

The modes that are most commonly used for the modulus/remainder operation are shown in the following table. Although the other rounding modes can be used, they may not give useful results.

Property	Value	Description
ROUND_UP	0	The remainder is positive if the dividend is negative, else 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(x) * floor(a / abs(x))`.

The rounding/modulo modes are available as enumerated properties of the Decimal constructor.

Decimal.set({ modulo: Decimal.EUCLID })
Decimal.set({ modulo: 9 })         // equivalent
Decimal.modulo                     // 9

crypto

boolean: true/false
Default value: false

The value that determines whether cryptographically-secure pseudo-random number generation is used.

See random.

// Node.js
global.crypto = require('crypto')

Decimal.crypto                     // false
Decimal.set({ crypto: true })
Decimal.crypto                     // true

Rounding modes

The library's enumerated rounding modes are stored as properties of the Decimal 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
EUCLID	9	Not a rounding mode, see modulo

Decimal.set({ rounding: Decimal.ROUND_CEIL })
Decimal.set({ rounding: 2 })       // equivalent
Decimal.rounding                   // 2

INSTANCE

Methods

The methods inherited by a Decimal instance from its constructor's prototype object.

A Decimal instance is immutable in the sense that it is not changed by its methods.

Methods that return a Decimal can be chained:

x = new Decimal(2).times('999.999999999999999').dividedBy(4).ceil()

Methods do not round their arguments before execution.

The treatment of ±0, ±Infinity and NaN is consistent with how JavaScript treats these values.

Many method names have a shorter alias. (Internally, the library always uses the shorter method names.)

absoluteValue`.abs() ⇒ Decimal`

Returns a new Decimal whose value is the absolute value, i.e. the magnitude, of the value of this Decimal.

The return value is not affected by the value of the precision setting.

x = new Decimal(-0.8)
y = x.absoluteValue()         // '0.8'
z = y.abs()                   // '0.8'

ceil`.ceil() ⇒ Decimal`

Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in the direction of positive Infinity.

The return value is not affected by the value of the precision setting.

x = new Decimal(1.3)
x.ceil()                      // '2'
y = new Decimal(-1.8)
y.ceil()                      // '-1'

clampedTo`.clamp(min, max) ⇒ Decimal`

min: number|string|Decimal
max: number|string|Decimal

Returns a new Decimal whose value is the value of this Decimal clamped to the range delineated by min and max.

The return value is not affected by the value of the precision setting.

x = new Decimal(5)
min = new Decimal(100)
max = new Decimal(Infinity)
x.clampedTo(min, max)         // '100'
x.clamp(-10, -0.1)            // '-0.1'

comparedTo`.cmp(x) ⇒ number`

x: number|string|Decimal

Returns
`1`	if the value of this Decimal is greater than the value of `x`
`-1`	if the value of this Decimal is less than the value of `x`
`0`	if this Decimal and `x` have the same value
`NaN`	if the value of either this Decimal or `x` is `NaN`

x = new Decimal(Infinity)
y = new Decimal(5)
x.comparedTo(y)                // 1
x.comparedTo(x.minus(1))       // 0
y.cmp(NaN)                     // NaN

cosine`.cos() ⇒ Decimal`

Returns a new Decimal whose value is the cosine of the value in radians of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-1, 1]

See Pi for the precision limit of this method.

x = new Decimal(0.25)
x.cosine()                      // '0.96891242171064478414'
y = new Decimal(-0.25)
y.cos()                         // '0.96891242171064478414'

cubeRoot`.cbrt() ⇒ Decimal`

Returns a new Decimal whose value is the cube root of this Decimal, rounded to precision significant digits using rounding mode rounding.

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 Decimal(125)
x.cubeRoot()                    // '5'
y = new Decimal(3)
y.cbrt()                        // '1.4422495703074083823'

decimalPlaces`.dp() ⇒ number`

Returns the number of decimal places, i.e. the number of digits after the decimal point, of the value of this Decimal.

x = new Decimal(1.234)
x.decimalPlaces()              // '3'
y = new Decimal(987.654321)
y.dp()                         // '6'

dividedBy`.div(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the value of this Decimal divided by x, rounded to precision significant digits using rounding mode rounding.

x = new Decimal(355)
y = new Decimal(113)
x.dividedBy(y)             // '3.14159292035398230088'
x.div(5)                   // '71'

dividedToIntegerBy`.divToInt(x) ⇒ Decimal`

x: number|string|Decimal

Return a new Decimal whose value is the integer part of dividing this Decimal by x, rounded to precision significant digits using rounding mode rounding.

x = new Decimal(5)
y = new Decimal(3)
x.dividedToIntegerBy(y)     // '1'
x.divToInt(0.7)             // '7'

equals`.eq(x) ⇒ boolean`

x: number|string|Decimal

Returns true if the value of this Decimal equals the value of x, otherwise returns false.
As with JavaScript, NaN does not equal NaN.

Note: This method uses the cmp method internally.

0 === 1e-324                     // true
x = new Decimal(0)
x.equals('1e-324')               // false
new Decimal(-0).eq(x)            // true  ( -0 === 0 )

y = new Decimal(NaN)
y.equals(NaN)                    // false

floor`.floor() ⇒ Decimal`

Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in the direction of negative Infinity.

The return value is not affected by the value of the precision setting.

x = new Decimal(1.8)
x.floor()                   // '1'
y = new Decimal(-1.3)
y.floor()                   // '-2'

greaterThan`.gt(x) ⇒ boolean`

x: number|string|Decimal

Returns true if the value of this Decimal is greater than the value of x, otherwise returns false.

Note: This method uses the cmp method internally.

0.1 > (0.3 - 0.2)                            // true
x = new Decimal(0.1)
x.greaterThan(Decimal(0.3).minus(0.2))       // false
new Decimal(0).gt(x)                         // false

greaterThanOrEqualTo`.gte(x) ⇒ boolean`

x: number|string|Decimal

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

Note: This method uses the cmp method internally.

(0.3 - 0.2) >= 0.1                       // false
x = new Decimal(0.3).minus(0.2)
x.greaterThanOrEqualTo(0.1)              // true
new Decimal(1).gte(x)                    // true

hyperbolicCosine`.cosh() ⇒ Decimal`

Returns a new Decimal whose value is the hyperbolic cosine of the value in radians of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [1, Infinity]

See Pi for the precision limit of this method.

x = new Decimal(1)
x.hyperbolicCosine()                     // '1.5430806348152437785'
y = new Decimal(0.5)
y.cosh()                                 // '1.1276259652063807852'

hyperbolicSine`.sinh() ⇒ Decimal`

Returns a new Decimal whose value is the hyperbolic sine of the value in radians of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-Infinity, Infinity]

See Pi for the precision limit of this method.

x = new Decimal(1)
x.hyperbolicSine()                       // '1.1752011936438014569'
y = new Decimal(0.5)
y.sinh()                                 // '0.52109530549374736162'

hyperbolicTangent`.tanh() ⇒ Decimal`

Returns a new Decimal whose value is the hyperbolic tangent of the value in radians of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-1, 1]

See Pi for the precision limit of this method.

x = new Decimal(1)
x.hyperbolicTangent()                    // '0.76159415595576488812'
y = new Decimal(0.5)
y.tanh()                                 // '0.4621171572600097585'

inverseCosine`.acos() ⇒ Decimal`

Returns a new Decimal whose value is the inverse cosine in radians of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-1, 1]
Range: [0, pi]

See Pi for the precision limit of this method.

x = new Decimal(0)
x.inverseCosine()                        // '1.5707963267948966192'
y = new Decimal(0.5)
y.acos()                                 // '1.0471975511965977462'

inverseHyperbolicCosine`.acosh() ⇒ Decimal`

Returns a new Decimal whose value is the inverse hyperbolic cosine in radians of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [1, Infinity]
Range: [0, Infinity]

See Pi for the precision limit of this method.

x = new Decimal(5)
x.inverseHyperbolicCosine()              // '2.2924316695611776878'
y = new Decimal(50)
y.acosh()                                // '4.6050701709847571595'

inverseHyperbolicSine`.asinh() ⇒ Decimal`

Returns a new Decimal whose value is the inverse hyperbolic sine in radians of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-Infinity, Infinity]

See Pi for the precision limit of this method.

x = new Decimal(5)
x.inverseHyperbolicSine()                // '2.3124383412727526203'
y = new Decimal(50)
y.asinh()                                // '4.6052701709914238266'

inverseHyperbolicTangent`.atanh() ⇒ Decimal`

Returns a new Decimal whose value is the inverse hyperbolic tangent in radians of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-1, 1]
Range: [-Infinity, Infinity]

See Pi for the precision limit of this method.

x = new Decimal(0.5)
x.inverseHyperbolicTangent()             // '0.5493061443340548457'
y = new Decimal(0.75)
y.atanh()                                // '0.97295507452765665255'

inverseSine`.asin() ⇒ Decimal`

Returns a new Decimal whose value is the inverse sine in radians of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-1, 1]
Range: [-pi/2, pi/2]

See Pi for the precision limit of this method.

x = new Decimal(0.5)
x.inverseSine()                          // '0.52359877559829887308'
y = new Decimal(0.75)
y.asin()                                 // '0.84806207898148100805'

inverseTangent`.atan() ⇒ Decimal`

Returns a new Decimal whose value is the inverse tangent in radians of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-pi/2, pi/2]

See Pi for the precision limit of this method.

x = new Decimal(0.5)
x.inverseTangent()                       // '0.46364760900080611621'
y = new Decimal(0.75)
y.atan()                                 // '0.6435011087932843868'

isFinite`.isFinite() ⇒ boolean`

Returns true if the value of this Decimal is a finite number, otherwise returns false.
The only possible non-finite values of a Decimal are NaN, Infinity and -Infinity.

x = new Decimal(1)
x.isFinite()                             // true
y = new Decimal(Infinity)
y.isFinite()                             // false

Note: The native method isFinite() can be used if n <= Number.MAX_VALUE.

isInteger`.isInt() ⇒ boolean`

Returns true if the value of this Decimal is a whole number, otherwise returns false.

x = new Decimal(1)
x.isInteger()                            // true
y = new Decimal(123.456)
y.isInt()                                // false

isNaN`.isNaN() ⇒ boolean`

Returns true if the value of this Decimal is NaN, otherwise returns false.

x = new Decimal(NaN)
x.isNaN()                                // true
y = new Decimal('Infinity')
y.isNaN()                                // false

Note: The native method isNaN() can also be used.

isNegative`.isNeg() ⇒ boolean`

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

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

Note: n < 0 can be used if n <= -Number.MIN_VALUE.

Also note that signed zeroes are implemented, following the IEEE Standard for Floating-Point Arithmetic (IEEE 754).

Decimal(0).valueOf()                 // '0'
Decimal(0).isNegative()              // false
Decimal(0).negated().valueOf()       // '-0'
Decimal(0).negated().isNegative()    // true

isPositive`.isPos() ⇒ boolean`

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

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

Note: n < 0 can be used if n <= -Number.MIN_VALUE.

isZero`.isZero() ⇒ boolean`

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

x = new Decimal(-0)
x.isZero() && x.isNeg()                  // true
y = new Decimal(Infinity)
y.isZero()                               // false

Note: n == 0 can be used if n >= Number.MIN_VALUE.

lessThan`.lt(x) ⇒ boolean`

x: number|string|Decimal

Returns true if the value of this Decimal is less than the value of x, otherwise returns false.

Note: This method uses the cmp method internally.

(0.3 - 0.2) < 0.1                        // true
x = new Decimal(0.3).minus(0.2)
x.lessThan(0.1)                          // false
new Decimal(0).lt(x)                     // true

lessThanOrEqualTo`.lte(x) ⇒ boolean`

x: number|string|Decimal

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

Note: This method uses the cmp method internally.

0.1 <= (0.3 - 0.2)                              // false
x = new Decimal(0.1)
x.lessThanOrEqualTo(Decimal(0.3).minus(0.2))    // true
new Decimal(-1).lte(x)                          // true

logarithm`.log(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the base x logarithm of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

If x is omitted, the base 10 logarithm of the value of this Decimal will be returned.

x = new Decimal(1000)
x.logarithm()                            // '3'
y = new Decimal(256)
y.log(2)                                 // '8'

The return value will almost always be correctly rounded, i.e. rounded as if the result was first calculated to an infinite number of correct digits before rounding. If a result is incorrectly rounded the maximum error will be 1 ulp (unit in the last place).

Logarithms to base 2 or 10 will always be correctly rounded.

See toPower for the circumstances in which this method may return an incorrectly rounded result, and see naturalLogarithm for the precision limit.

The performance of this method degrades exponentially with increasing digits.

minus`.minus(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the value of this Decimal minus x, rounded to precision significant digits using rounding mode rounding.

0.3 - 0.1                                // 0.19999999999999998
x = new Decimal(0.3)
x.minus(0.1)                             // '0.2'

modulo`.mod(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the value of this Decimal modulo x, rounded to precision significant digits using rounding mode rounding.

The value returned, and in particular its sign, is dependent on the value of the modulo property of this Decimal's constructor. If it is 1 (default value), the result will have the same sign as this Decimal, and it will match that of Javascript's % operator (within the limits of double precision) and BigDecimal's remainder method.

See modulo for a description of the other modulo modes.

1 % 0.9                                  // 0.09999999999999998
x = new Decimal(1)
x.modulo(0.9)                            // '0.1'

y = new Decimal(8)
z = new Decimal(-3)
Decimal.modulo = 1
y.mod(z)                                 // '2'
Decimal.modulo = 3
y.mod(z)                                 // '-1'

naturalExponential`.exp() ⇒ Decimal`

Returns a new Decimal whose value is the base e (Euler's number, the base of the natural logarithm) exponential of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

The naturalLogarithm function is the inverse of this function.

x = new Decimal(1)
x.naturalExponential()                   // '2.7182818284590452354'
y = new Decimal(2)
y.exp()                                  // '7.3890560989306502272'

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. (The mathematical result of the exponential function is non-terminating, unless its argument is 0).

The performance of this method degrades exponentially with increasing digits.

naturalLogarithm`.ln() ⇒ Decimal`

Returns a new Decimal whose value is the natural logarithm of the value of this Decimal, rounded to precision significant digits using rounding mode rounding.

The natural logarithm is the inverse of the naturalExponential function.

x = new Decimal(10)
x.naturalLogarithm()                     // '2.3026'
y = new Decimal('1.23e+30')
y.ln()                                   // '69.28'

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. (The mathematical result of the natural logarithm function is non-terminating, unless its argument is 1).

Internally, this method is dependent on a constant whose value is the natural logarithm of 10. This LN10 variable in the source code currently has a precision of 1025 digits, meaning that this method can accurately calculate up to 1000 digits.

If more than 1000 digits is required then the precision of LN10 will need to be increased to 25 digits more than is required - though, as the time-taken by this method increases exponentially with increasing digits, it is unlikely to be viable to calculate over 1000 digits anyway.

negated`.neg() ⇒ Decimal`

Returns a new Decimal whose value is the value of this Decimal negated, i.e. multiplied by -1.

The return value is not affected by the value of the precision setting.

x = new Decimal(1.8)
x.negated()                              // '-1.8'
y = new Decimal(-1.3)
y.neg()                                  // '1.3'

plus`.plus(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the value of this Decimal plus x, rounded to precision significant digits using rounding mode rounding.

0.1 + 0.2                                // 0.30000000000000004
x = new Decimal(0.1)
y = x.plus(0.2)                          // '0.3'
new Decimal(0.7).plus(x).plus(y)         // '1.1'

precision`.sd([include_zeros]) ⇒ number`

Returns the number of significant digits of the value of this Decimal.

If include_zeros is true or 1 then any trailing zeros of the integer part of a number are counted as significant digits, otherwise they are not.

x = new Decimal(1.234)
x.precision()                            // '4'
y = new Decimal(987000)
y.sd()                                   // '3'
y.sd(true)                               // '6'

round`.round() ⇒ Decimal`

Returns a new Decimal whose value is the value of this Decimal rounded to a whole number using rounding mode rounding.

To emulate Math.round, set rounding to 7, i.e. ROUND_HALF_CEIL.

Decimal.set({ rounding: 4 })
x = 1234.5
x.round()                                // '1235'

Decimal.rounding = Decimal.ROUND_DOWN
x.round()                                // '1234'
x                                        // '1234.5'

sine`.sin() ⇒ Decimal`

Returns a new Decimal whose value is the sine of the value in radians of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-1, 1]

See Pi for the precision limit of this method.

x = new Decimal(0.5)
x.sine()                                 // '0.47942553860420300027'
y = new Decimal(0.75)
y.sin()                                  // '0.68163876002333416673'

squareRoot`.sqrt() ⇒ Decimal`

Returns a new Decimal whose value is the square root of this Decimal, rounded to precision significant digits using rounding mode rounding.

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.

This method is much faster than using the toPower method with an exponent of 0.5.

x = new Decimal(16)
x.squareRoot()                           // '4'
y = new Decimal(3)
y.sqrt()                                 // '1.73205080756887729353'
y.sqrt().eq( y.pow(0.5) )                // true

tangent`.tan() ⇒ Decimal`

Returns a new Decimal whose value is the tangent of the value in radians of this Decimal, rounded to precision significant digits using rounding mode rounding.

Domain: [-Infinity, Infinity]
Range: [-Infinity, Infinity]

See Pi for the precision limit of this method.

x = new Decimal(0.5)
x.tangent()                              // '0.54630248984379051326'
y = new Decimal(0.75)
y.tan()                                  // '0.93159645994407246117'

times`.times(x) ⇒ Decimal`

x: number|string|Decimal

Returns a new Decimal whose value is the value of this Decimal times x, rounded to precision significant digits using rounding mode rounding.

0.6 * 3                                  // 1.7999999999999998
x = new Decimal(0.6)
y = x.times(3)                           // '1.8'
new Decimal('7e+500').times(y)           // '1.26e+501'

toBinary`.toBinary([sd [, rm]]) ⇒ string`

sd: number: integer, 0 to 1e+9 inclusive
rm: number: integer, 0 to 8 inclusive

Returns a string representing the value of this Decimal in binary, rounded to sd significant digits using rounding mode rm.

If sd is defined, the return value will use binary exponential notation.

If sd is omitted, the return value will be rounded to precision significant digits.

If rm is omitted, rounding mode rounding will be used.

Throws on an invalid sd or rm value.

x = new Decimal(256)
x.toBinary()                             // '0b100000000'
x.toBinary(1)                            // '0b1p+8'

toDecimalPlaces`.toDP([dp [, rm]]) ⇒ Decimal`

dp: number: integer, 0 to 1e+9 inclusive
rm: number: integer, 0 to 8 inclusive.

Returns a new Decimal whose value is the value of this Decimal rounded to dp decimal places using rounding mode rm.

If dp is omitted, the return value will have the same value as this Decimal.

If rm is omitted, rounding mode rounding is used.

Throws on an invalid dp or rm value.

x = new Decimal(12.34567)
x.toDecimalPlaces(0)                      // '12'
x.toDecimalPlaces(1, Decimal.ROUND_UP)    // '12.4'

y = new Decimal(9876.54321)
y.toDP(3)                           // '9876.543'
y.toDP(1, 0)                        // '9876.6'
y.toDP(1, Decimal.ROUND_DOWN)       // '9876.5'

toExponential`.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 Decimal 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 Decimal in exponential notation has fewer than dp fraction digits, the return value will be appended with zeros accordingly.

If dp is omitted, 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, rounding mode rounding is used.

Throws on an invalid dp or rm value.

x = 45.6
y = new Decimal(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, Decimal.ROUND_DOWN)   // '4.5e+1'
x.toExponential(3)                       // '4.560e+1'
y.toExponential(3)                       // '4.560e+1'

toFixed`.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 Decimal in normal (fixed-point) notation rounded to dp decimal places using rounding mode rm.

If the value of this Decimal 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, the return value will be unrounded and in normal notation. This is unlike Number.prototype.toFixed, which returns the value to zero decimal places, but is useful when because of the current toExpNeg or toExpNeg values, toString returns exponential notation.

If rm is omitted, rounding mode rounding is used.

Throws on an invalid dp or rm value.

x = 3.456
y = new Decimal(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, Decimal.ROUND_DOWN)  // '3.45'
x.toFixed(5)                      // '3.45600'
y.toFixed(5)                      // '3.45600'

toFraction `.toFraction([max_denominator]) ⇒ [Decimal, Decimal]`

max_denominator: number|string|Decimal: 1 >= integer < Infinity

Returns an array of two Decimals representing the value of this Decimal 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 is omitted, the denominator will be the lowest value necessary to represent the number exactly.

Throws on an invalid max_denominator value.

x = new Decimal(1.75)
x.toFraction()                       // '7, 4'

pi = new Decimal('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'

toHexadecimal`.toHex([sd [, rm]]) ⇒ string`

sd: number: integer, 0 to 1e+9 inclusive
rm: number: integer, 0 to 8 inclusive

Returns a string representing the value of this Decimal in hexadecimal, rounded to sd significant digits using rounding mode rm.

If sd is defined, the return value will use binary exponential notation.

If sd is omitted, the return value will be rounded to precision significant digits.

If rm is omitted, rounding mode rounding will be used.

Throws on an invalid sd or rm value.

x = new Decimal(256)
x.toHexadecimal()                        // '0x100'
x.toHex(1)                               // '0x1p+8'

toJSON`.toJSON() ⇒ string`

As valueOf.

toNearest`.toNearest(x [, rm]) ⇒ Decimal`

x: number|string|Decimal
rm: number: integer, 0 to 8 inclusive

Returns a new Decimal whose value is the nearest multiple of x in the direction of rounding mode rm, or rounding if rm is omitted, to the value of this Decimal.

The return value will always have the same sign as this Decimal, unless either this Decimal or x is NaN, in which case the return value will be also be NaN.

The return value is not affected by the value of the precision setting.

x = new Decimal(1.39)
x.toNearest(0.25)                        // '1.5'

y = new Decimal(9.499)
y.toNearest(0.5, Decimal.ROUND_UP)       // '9.5'
y.toNearest(0.5, Decimal.ROUND_DOWN)     // '9'

toNumber`.toNumber() ⇒ number`

Returns the value of this Decimal converted to a primitive number.

Type coercion with, for example, JavaScript's unary plus operator will also work, except that a Decimal with the value minus zero will convert to positive zero.

x = new Decimal(456.789)
x.toNumber()                   // 456.789
+x                             // 456.789

y = new Decimal('45987349857634085409857349856430985')
y.toNumber()                   // 4.598734985763409e+34

z = new Decimal(-0)
1 / +z                         // Infinity
1 / z.toNumber()               // -Infinity

toOctal`.toOctal([sd [, rm]]) ⇒ string`

sd: number: integer, 0 to 1e+9 inclusive
rm: number: integer, 0 to 8 inclusive

Returns a string representing the value of this Decimal in octal, rounded to sd significant digits using rounding mode rm.

If sd is defined, the return value will use binary exponential notation.

If sd is omitted, the return value will be rounded to precision significant digits.

If rm is omitted, rounding mode rounding will be used.

Throws on an invalid sd or rm value.

x = new Decimal(256)
x.toOctal()                              // '0o400'
x.toOctal(1)                             // '0o1p+8'

toPower`.pow(x) ⇒ Decimal`

x: number|string|Decimal: integer or non-integer

Returns a new Decimal whose value is the value of this Decimal raised to the power x, rounded to precision significant digits using rounding mode rounding.

The performance of this method degrades exponentially with increasing digits. For non-integer exponents in particular, the performance of this method may not be adequate.

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

new Decimal(1217652.23).pow('98765.489305603941')
// '4.8227010515242461181e+601039'

Is the pow function guaranteed to be correctly rounded?

For non-integer and larger exponents this method uses the formula

x^y = exp(y*ln(x))

As the mathematical return values of the exp and ln functions are both non-terminating (excluding arguments of 0 or 1), the values of the Decimals returned by the functions as implemented by this library will necessarily be rounded approximations, which means that there can be no guarantee of correct rounding when they are combined in the above formula.

The return value may, depending on the rounding mode, be incorrectly rounded only if the first 15 rounding digits are 15 zeros (and there are non-zero digits following at some point), or 15 nines, or a 5 or 4 followed by 14 nines.

Therefore, assuming the first 15 rounding digits are each equally likely to be any digit, 0-9, the probability of an incorrectly rounded result is less than 1 in 250,000,000,000,000.

An example of incorrect rounding:

Decimal.set({ precision: 20, rounding: 1 })
new Decimal(28).pow('6.166675020000903537297764507632802193308677149')
// 839756321.64088511

As the exact mathematical result begins

839756321.6408851099999999999999999999999999998969466049426031167...

and the rounding mode is set to ROUND_DOWN, the correct return value should be

839756321.64088510999

toPrecision`.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 Decimal 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, the return value is the same as toString.

If rm is omitted, rounding mode rounding is used.

Throws on an invalid sd or rm value.

x = 45.6
y = new Decimal(x)
x.toPrecision()                          // '45.6'
y.toPrecision()                          // '45.6'
x.toPrecision(1)                         // '5e+1'
y.toPrecision(1)                         // '5e+1'
y.toPrecision(2, Decimal.ROUND_UP)       // '46'
y.toPrecision(2, Decimal.ROUND_DOWN)     // '45'
x.toPrecision(5)                         // '45.600'
y.toPrecision(5)                         // '45.600'

toSignificantDigits`.toSD([sd [, rm]]) ⇒ Decimal`

sd: number: integer, 1 to 1e+9 inclusive.
rm: number: integer, 0 to 8 inclusive.

Returns a new Decimal whose value is the value of this Decimal rounded to sd significant digits using rounding mode rm.

If sd is omitted, the return value will be rounded to precision significant digits.

If rm is omitted, rounding mode rounding will be used.

Throws on an invalid sd or rm value.

Decimal.set({ precision: 5, rounding: 4 })
x = new Decimal(9876.54321)

x.toSignificantDigits()                          // '9876.5'
x.toSignificantDigits(6)                         // '9876.54'
x.toSignificantDigits(6, Decimal.ROUND_UP)       // '9876.55'
x.toSD(2)                                        // '9900'
x.toSD(2, 1)                                     // '9800'
x                                                // '9876.54321'

toString`.toString() ⇒ string`

Returns a string representing the value of this Decimal.

If this Decimal has a positive exponent that is equal to or greater than toExpPos, or a negative exponent equal to or less than toExpNeg, then exponential notation will be returned.

x = new Decimal(750000)
x.toString()                             // '750000'
Decimal.set({ toExpPos: 5 })
x.toString()                             // '7.5e+5'

Decimal.set({ precision: 4 })
y = new Decimal('1.23456789')
y.toString()                             // '1.23456789'

truncated`.trunc() ⇒ Decimal`

Returns a new Decimal whose value is the value of this Decimal truncated to a whole number.

The return value is not affected by the value of the precision setting.

x = new Decimal(123.456)
x.truncated()                            // '123'
y = new Decimal(-12.3)
y.trunc()                                // '-12'

valueOf`.valueOf() ⇒ string`

As toString, but zero is signed.

x = new Decimal(-0)
x.valueOf()                              // '-0'

Properties

The value of a Decimal is stored in a normalised base 10000000 floating point format.

A Decimal instance is an object with three properties:

Property	Description	Type	Value
d	digits	number`[]`	Array of integers, each `0` - `1e7`, or `null`
e	exponent	number	Integer, `-9e15` to `9e15` inclusive, or `NaN`
s	sign	number	`-1`, `1`, or `NaN`

All the properties are best considered to be read-only.

As with JavaScript numbers, the original exponent and fractional trailing zeros of a value are not preserved.

x = new Decimal(0.123)                   // '0.123'
x.toExponential()                        // '1.23e-1'
x.d                                      // [ 1230000 ]
x.e                                      // -1
x.s                                      // 1

y = new Number(-123.4567000e+2)          // '-12345.67'
y.toExponential()                        // '-1.234567e+4'
z = new Decimal('-123.4567000e+2')       // '-12345.67'
z.toExponential()                        // '-1.234567e+4'
z.d                                      // [ 12345, 6700000 ]
z.e                                      // 4
z.s                                      // -1

Zero, NaN and Infinity

The table below shows how ±0, NaN and ±Infinity are stored.

	±0	NaN	±Infinity
d	`[0]`	`null`	`null`
e	`0`	`NaN`	`NaN`
s	`±1`	`NaN`	`±1`

x = new Number(-0)                       // 0
1 / x == -Infinity                       // true

y = new Decimal(-0)
y.d                                      // '0' ( [0].toString() )
y.e                                      //  0
y.s                                      // -1
y.toString()                             // '0'
y.valueOf()                              // '-0'

Errors

The errors that are thrown are generic Error objects whose message property begins with "[DecimalError]".

To determine if an exception is a Decimal Error:

try {
    // ...
} catch (e) {
    if ( e instanceof Error && /DecimalError/.test(e.message) ) {
        // ...
    }
}

Pi

The maximum precision of the trigonometric methods is dependent on the internal value of the constant pi, which is defined as the string PI near the top of the source file.

It has a precision of 1025 digits, meaning that the trigonometric methods can calculate up to just over 1000 digits, but the actual figure depends on the precision of the argument passed to them. To calculate the actual figure use:

maximum_result_precision = 1000 - argument_precision

For example, the following both work fine:

Decimal.set({precision: 991}).tan(123456789)
Decimal.set({precision: 9}).tan(991_digit_number)

as, for each, the result precision plus the argument precision, i.e. 991 + 9 and 9 + 991, is less than or equal to 1000.

If greater precision is required then the value of PI will need to be extended to about 25 digits more than the precision required. The time taken by the methods will then be the limiting factor.

The value can also be shortened to reduce the size of the source file if such high precision is not required.

To get the value of pi:

pi = Decimal.acos(-1)

FAQ

Why are trailing fractional zeros removed from Decimals?

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.

decimal.js

API

CONSTRUCTOR

DecimalDecimal(value) ⇒ Decimal

Methods

abs.abs(x) ⇒ Decimal

acos.acos(x) ⇒ Decimal

acosh.acosh(x) ⇒ Decimal

add.add(x, y) ⇒ Decimal

asin.asin(x) ⇒ Decimal

asinh.asinh(x) ⇒ Decimal

atan.atan(x) ⇒ Decimal

atanh.atanh(x) ⇒ Decimal

atan2.atan2(y, x) ⇒ Decimal

cbrt.cbrt(x) ⇒ Decimal

ceil.ceil(x) ⇒ Decimal

clamp.clamp(min, max) ⇒ Decimal

clone .clone([object]) ⇒ Decimal constructor

cos.cos(x) ⇒ Decimal

cosh.cosh(x) ⇒ Decimal

div.div(x, y) ⇒ Decimal

exp.exp(x) ⇒ Decimal

floor.floor(x) ⇒ Decimal

hypot.hypot([x [, y, ...]]) ⇒ Decimal

ln.ln(x) ⇒ Decimal

isDecimal.isDecimal(object) ⇒ boolean

log.log(x [, base]) ⇒ Decimal

log2.log2(x) ⇒ Decimal

log10.log10(x) ⇒ Decimal

max.max(x [, y, ...]) ⇒ Decimal

min.min(x [, y, ...]) ⇒ Decimal

mod.mod(x, y) ⇒ Decimal

mul.mul(x, y) ⇒ Decimal

noConflict.noConflict() ⇒ Decimal constructor

pow.pow(base, exponent) ⇒ Decimal

random.random([dp]) ⇒ Decimal

round.round(x) ⇒ Decimal

set.set(object) ⇒ Decimal constructor

sign.sign(x) ⇒ number

sin.sin(x) ⇒ Decimal

sinh.sinh(x) ⇒ Decimal

sqrt.sqrt(x) ⇒ Decimal

sub.sub(x, y) ⇒ Decimal

sum.sum(x [, y, ...]) ⇒ Decimal

tan.tan(x) ⇒ Decimal

tanh.tanh(x) ⇒ Decimal

trunc.trunc(x) ⇒ Decimal

Properties

Configuration properties

precision

rounding

minE

maxE

toExpNeg

toExpPos

modulo

crypto

Rounding modes

INSTANCE

Methods

absoluteValue.abs() ⇒ Decimal

ceil.ceil() ⇒ Decimal

clampedTo.clamp(min, max) ⇒ Decimal

comparedTo.cmp(x) ⇒ number

cosine.cos() ⇒ Decimal

cubeRoot.cbrt() ⇒ Decimal

decimalPlaces.dp() ⇒ number

dividedBy.div(x) ⇒ Decimal

dividedToIntegerBy.divToInt(x) ⇒ Decimal

equals.eq(x) ⇒ boolean

floor.floor() ⇒ Decimal

greaterThan.gt(x) ⇒ boolean

greaterThanOrEqualTo.gte(x) ⇒ boolean

hyperbolicCosine.cosh() ⇒ Decimal

hyperbolicSine.sinh() ⇒ Decimal

hyperbolicTangent.tanh() ⇒ Decimal

inverseCosine.acos() ⇒ Decimal

inverseHyperbolicCosine.acosh() ⇒ Decimal

inverseHyperbolicSine.asinh() ⇒ Decimal

inverseHyperbolicTangent.atanh() ⇒ Decimal

Decimal`Decimal(value) ⇒ Decimal`

abs`.abs(x) ⇒ Decimal`

acos`.acos(x) ⇒ Decimal`

acosh`.acosh(x) ⇒ Decimal`

add`.add(x, y) ⇒ Decimal`

asin`.asin(x) ⇒ Decimal`

asinh`.asinh(x) ⇒ Decimal`

atan`.atan(x) ⇒ Decimal`

atanh`.atanh(x) ⇒ Decimal`

atan2`.atan2(y, x) ⇒ Decimal`

cbrt`.cbrt(x) ⇒ Decimal`

ceil`.ceil(x) ⇒ Decimal`

clamp`.clamp(min, max) ⇒ Decimal`

clone `.clone([object]) ⇒ Decimal constructor`

cos`.cos(x) ⇒ Decimal`

cosh`.cosh(x) ⇒ Decimal`

div`.div(x, y) ⇒ Decimal`

exp`.exp(x) ⇒ Decimal`

floor`.floor(x) ⇒ Decimal`

hypot`.hypot([x [, y, ...]]) ⇒ Decimal`

ln`.ln(x) ⇒ Decimal`

isDecimal`.isDecimal(object) ⇒ boolean`

log`.log(x [, base]) ⇒ Decimal`

log2`.log2(x) ⇒ Decimal`

log10`.log10(x) ⇒ Decimal`

max`.max(x [, y, ...]) ⇒ Decimal`

min`.min(x [, y, ...]) ⇒ Decimal`

mod`.mod(x, y) ⇒ Decimal`

mul`.mul(x, y) ⇒ Decimal`

noConflict`.noConflict() ⇒ Decimal constructor`

pow`.pow(base, exponent) ⇒ Decimal`

random`.random([dp]) ⇒ Decimal`

round`.round(x) ⇒ Decimal`

set`.set(object) ⇒ Decimal constructor`

sign`.sign(x) ⇒ number`

sin`.sin(x) ⇒ Decimal`

sinh`.sinh(x) ⇒ Decimal`

sqrt`.sqrt(x) ⇒ Decimal`

sub`.sub(x, y) ⇒ Decimal`

sum`.sum(x [, y, ...]) ⇒ Decimal`

tan`.tan(x) ⇒ Decimal`

tanh`.tanh(x) ⇒ Decimal`

trunc`.trunc(x) ⇒ Decimal`

absoluteValue`.abs() ⇒ Decimal`

ceil`.ceil() ⇒ Decimal`

clampedTo`.clamp(min, max) ⇒ Decimal`

comparedTo`.cmp(x) ⇒ number`

cosine`.cos() ⇒ Decimal`

cubeRoot`.cbrt() ⇒ Decimal`

decimalPlaces`.dp() ⇒ number`

dividedBy`.div(x) ⇒ Decimal`

dividedToIntegerBy`.divToInt(x) ⇒ Decimal`

equals`.eq(x) ⇒ boolean`

floor`.floor() ⇒ Decimal`

greaterThan`.gt(x) ⇒ boolean`

greaterThanOrEqualTo`.gte(x) ⇒ boolean`

hyperbolicCosine`.cosh() ⇒ Decimal`

hyperbolicSine`.sinh() ⇒ Decimal`

hyperbolicTangent`.tanh() ⇒ Decimal`

inverseCosine`.acos() ⇒ Decimal`

inverseHyperbolicCosine`.acosh() ⇒ Decimal`

inverseHyperbolicSine`.asinh() ⇒ Decimal`

inverseHyperbolicTangent`.atanh() ⇒ Decimal`

inverseSine`.asin() ⇒ Decimal`

inverseTangent`.atan() ⇒ Decimal`

isFinite`.isFinite() ⇒ boolean`

isInteger`.isInt() ⇒ boolean`

isNaN`.isNaN() ⇒ boolean`

isNegative`.isNeg() ⇒ boolean`

isPositive`.isPos() ⇒ boolean`

isZero`.isZero() ⇒ boolean`

lessThan`.lt(x) ⇒ boolean`

lessThanOrEqualTo`.lte(x) ⇒ boolean`

logarithm`.log(x) ⇒ Decimal`

minus`.minus(x) ⇒ Decimal`

modulo`.mod(x) ⇒ Decimal`

naturalExponential`.exp() ⇒ Decimal`

naturalLogarithm`.ln() ⇒ Decimal`

negated`.neg() ⇒ Decimal`

plus`.plus(x) ⇒ Decimal`