# decimal.js

An arbitrary-precision Decimal type for JavaScript.

Hosted on GitHub.

## 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 numbers.

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

A new Decimal constructor is created by calling the `constructor` method of an already existing Decimal constructor - when the library is loaded this will be `Decimal`.

### CONSTRUCTOR

##### Decimal`Decimal(value [, base]) ⇒ Decimal`

`value`
  number|string|Decimal
  A numeric value.
  Legitimate values include ±`0`, ±`Infinity` and `NaN`.
  Values of type number with more than 15 significant digits are considered invalid (if `errors` is true) as calling `toString` or `valueOf` on such numbers may not result in the intended value.

      console.log( 823456789123456.3 );    // 823456789123456.2

  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 minE and maxE for the allowable range of a Decimal in terms of exponent limits.
  Decimal string values may be in exponential, as well as normal (fixed-point) notation. Non-decimal values must be in normal notation.
  String values in hexadecimal literal form, e.g. `'0xff'`, are invalid, and string values in octal literal form will be interpreted as decimals, e.g. `'011'` is interpreted as 11, not 9.
  Values in any base may have fraction digits.
  For bases from 10 to 36, lower and/or upper case letters can be used to represent values from 10 to 35.
  For bases above 36, `a-z` represents values from 10 to 35, `A-Z` from 36 to 61, and `$` and `_` represent 62 and 63 respectively.

`base`
  number: integer, `2` to `64` inclusive
  The base of `value`.
  If `base` is omitted or is `null` or undefined, base 10 is assumed.

Returns a new instance of a Decimal object.

If a base is specified, `value` is rounded according to the current `precision` and `rounding` settings.

See Errors for the treatment of an invalid `value` or `base`.

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

     // 'new' is optional if errors is false
    Decimal(435.345)

    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('+2')                        // '2'
    new Decimal(-10110100.1, 2)              // '-180.5'
    new Decimal('123412421.234324', 5)       // '607236.557696'
    new Decimal('ff.8', 16)                  // '255.5'

The following throws `'not a base 2 number'` if `errors` is true, otherwise it returns a Decimal with value `NaN`.

    new Decimal(9, 2)

The following throws `'number type has more than 15 significant digits'` if `errors` is true, otherwise it returns a Decimal with value `96517860459076820`.

    new Decimal(96517860459076817.4395)

The following throws `'not a number'` if `errors` is true, otherwise it returns a Decimal with value `NaN`.

    new Decimal('blurgh')

A value is rounded only if a base is specified.

    Decimal.config({ precision: 5 })
    new Decimal(1.23456789)                  // '1.23456789'
    new Decimal(1.23456789, 10)              // '1.2346'

#### Methods

The static methods of a Decimal constructor.

##### config`.config(object) ⇒ Decimal constructor`

`object`: object

Configures the 'global' settings for this particular Decimal constructor.

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 the value to be assigned to any of the properties is `null` or undefined it is ignored.
See Errors for the treatment of invalid values.

    // Defaults
    Decimal.config({
        precision: 20,
        rounding: 4,
        toExpNeg: -7,
        toExpPos: 21,
        minE: -9e15,
        maxE: 9e15,
        errors: true,
        crypto: false,
        modulo: 1,
        format: {
            decimalSeparator : '.',
            groupSeparator : ',',
            groupSize : 3,
            secondaryGroupSize : 0,
            fractionGroupSeparator : '\xA0',    // non-breaking space
            fractionGroupSize : 0
        }
    })

The properties of a Decimal constructor can also be set by direct assignment, but that will obviously by-pass the validity checking that this method performs.

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

`object`: object

Returns a new independent Decimal constructor with configuration settings as described by `object` (see `config`).

    Decimal.config({ precision: 5 })
    D9 = Decimal.constructor({ precision: 9 })

    x = new Decimal(1)
    y = new D9(1)

    x.div(3)                           // 0.33333
    y.div(3)                           // 0.333333333

    // D9 = Decimal.constructor({ precision: 9 }) is equivalent to:
    D9 = Decimal.constructor()
    D9.config({ precision: 9 })

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

`constructor` is a factory method so it is not necessary or desirable to use `new` but it will do no harm.

    D = new Decimal.constructor()

##### exp`.exp() ⇒ Decimal`

See `exponential`.

    x = Decimal.exp(3)
    y = new Decimal(3).exp()
    x.equals(y)                    // true

##### ln`.ln() ⇒ Decimal`

See `naturalLogarithm`.

    x = Decimal.ln(4.321)
    y = new Decimal(4.321).ln()
    x.equals(y)                    // true

##### log`.log(arg [, base]) ⇒ Decimal`

`arg`: number|string|Decimal
`base`: number|string|Decimal
See `Decimal` for further parameter details.

See `logarithm`.

    x = Decimal.log(100, 2.5)
    y = new Decimal(100).log(2.5)
    x.equals(y)                    // true

##### max`.max([arg1 [, arg2, ...]]) ⇒ Decimal`

`arg1`, `arg2`, ... : number|string|Decimal
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the maximum of `arg1`, `arg2`,... .

Alternatively, the argument to this method can be an array of values.

    x = new Decimal('3257869345.0378653')
    Decimal.max(4e9, x, '123456789.9')          // '4000000000'

    arr = [12, '13', new Decimal(14)]
    Decimal.max(arr)                            // '14'

##### min`.min([arg1 [, arg2, ...]]) ⇒ Decimal`

`arg1`, `arg2`, ... : number|string|Decimal
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the minimum of `arg1`, `arg2`,... .

Alternatively, the argument to this method can be an array of values.

    x = new Decimal('3257869345.0378653')
    Decimal.min(4e9, x, '123456789.9')          // '123456789.9'

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

##### 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>
      x = new Decimal(2)      // '2'
      D = Decimal.noConflict()
      Decimal                 // 1
      y = new D(3)            // '3'
    </script>

##### pow`.pow(base, exponent) ⇒ Decimal`

`base`: number|string|Decimal
`exponent`: number|string|Decimal
See `Decimal` for further parameter details.

See `toPower`.

    x = Decimal.pow(3257.4, 17.01)
    y = new Decimal(3257.4).pow(17.01)
    x.equals(y)                    // 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.

Depending on the value of a Decimal constructor's `crypto` property 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).

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

    Decimal.config({ precision: 10 })
    Decimal.random()                    // '0.4117936847'

    Decimal.random(20)                  // '0.78193327636914089009'

##### sqrt`.sqrt() ⇒ Decimal`

See squareRoot.

    x = Decimal.sqrt('987654321.123456789')
    y = new Decimal('987654321.123456789').sqrt()
    x.equals(y)                         // true

#### Properties

The static properties of a Decimal constructor.

##### ONE

A Decimal instance with value one.

    new Decimal(3).times(Decimal.ONE)    // '3'

###### Configuration properties

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

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

    Decimal.config({ precision: 0 })
    // 'Decimal Error: config() precision out of range: 0'

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

##### precision

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

The maximum number of significant digits of the result of a calculation or base conversion.

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

A Decimal constructor will also not round to `precision` unless a base is specified.

    Decimal.config({ 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 a calculation or base conversion to `precision` significant digits, and when rounding the return value of the `round`, `toDecimalPlaces`, `toExponential`, `toFixed`, `toFormat`, `toNearest`, `toPrecision` and `toSignificantDigits` methods.

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

    Decimal.config({ rounding: Decimal.ROUND_UP })
    Decimal.config({ 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 its value becomes zero.

JavaScript numbers underflow to zero for exponents below `-324`.

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

    Decimal.config({ 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 its value becomes `Infinity`.

JavaScript numbers overflow to `Infinity` for exponents above `308`.

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

    Decimal.config({ 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.config({ 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.config({ 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.

Calling `toString` with a base argument, e.g. `toString(10)`, will also always return normal notation.

##### toExpPos

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

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

    Decimal.config({ 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.config({ 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.

Calling `toString` with a base argument, e.g. `toString(10)`, will also always return normal notation.

##### errors

boolean/number: `true, false, 1 or 0`
Default value: `true`

The value that determines whether Decimal Errors are thrown.
If `errors` is false, this library will not throw errors.

See Errors.

    Decimal.config({ errors: false })
    Decimal.errors                     // false

##### 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(n) * floor(a / abs(n))`.

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

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

##### crypto

boolean/number: `true, false, 1 or 0`
Default value: `false`

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

If `crypto` is truthy then the `random` method will generate random digits using `crypto.getRandomValues` in browsers that support it, or `crypto.randomBytes` if using a version of Node.js that supports it.

If neither function is supported by the host environment or if `crypto` is falsey then the source of randomness will be `Math.random`. If the `crypto` property is set directly (i.e. without using `config`) to `true`, then at the time the `random` method is called, if `errors` is `true`, an error will be thrown if the `crypto` methods are unavailable.

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

If `crypto.getRandomValues` and `crypto.randomBytes` are undefined, the crypto property will remain `false`.

    Decimal.crypto                     // false

##### format

object

The `format` object configures the format of the string returned by the `toFormat` method.

The example below shows the properties of the `format` object that are recognised, and their default values.

Unlike setting other properties using `config`, the values of the properties of the `format` object will not be checked for validity. The existing `format` object will simply be replaced by the object that is passed in. Only the `toFormat` method ever references a Decimal constructor's `format` object property.

See `toFormat` for examples of usage, and of setting `format` properties individually and directly without using `config`.

    Decimal.config({
        format : {
            // the decimal separator
            decimalSeparator : '.',
            // the grouping separator of the integer part of the number
            groupSeparator : ',',
            // the primary grouping size of the integer part of the number
            groupSize : 3,
            // the secondary grouping size of the integer part of the number
            secondaryGroupSize : 0,
            // the grouping separator of the fraction part of the number
            fractionGroupSeparator : ' ',
            // the grouping size of the fraction part of the number
            fractionGroupSize : 0
        }
    });

###### Rounding modes

The library's enumerated rounding modes are stored as properties of a 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.config({ rounding: Decimal.ROUND_CEIL })
    Decimal.config({ rounding: 2 })    // equivalent
    Decimal.rounding                   // 2

### INSTANCE

#### Methods

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

A Decimal 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.

Some 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 rounded.

    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 rounded to `precision`.

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

##### comparedTo`.cmp(n [, base]) ⇒ number`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns |
--- | ---
`1` | If the value of this Decimal is greater than the value of `n`
`-1` | If the value of this Decimal is less than the value of `n`
`0` | If this Decimal and `n` have the same value
`null` | If the value of either this Decimal or `n` is `NaN`

    x = new Decimal(Infinity)
    y = new Decimal(5)
    x.comparedTo(y)                // 1
    x.comparedTo(x.minus(1))       // 0
    y.cmp(NaN)                     // null
    y.cmp('110', 2)                // -1

##### 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(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the value of this Decimal divided by `n`, 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'
    x.div(47, 16)              // '5'

##### dividedToIntegerBy`.divToInt(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Return a new Decimal whose value is the integer part of dividing this Decimal by `n`, 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'
    x.divToInt('0.f', 16)       // '5'

##### equals`.eq(n [, base]) ⇒ boolean`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns `true` if the value of this Decimal equals the value of `n`, 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 )
    new Decimal(255).eq('ff', 16)    // true

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

##### exponential`.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.exponential()             // '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.

##### 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 rounded to `precision`.

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

##### greaterThan`.gt(n [, base]) ⇒ boolean`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns `true` if the value of this Decimal is greater than the value of `n`, 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
    new Decimal(11, 3).gt(11.1, 2)               // true

##### greaterThanOrEqualTo`.gte(n [, base]) ⇒ boolean`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns `true` if the value of this Decimal is greater than or equal to the value of `n`, 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
    new Decimal(10, 18).gte('i', 36)         // true

##### 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`.

##### 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(n [, base]) ⇒ boolean`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns `true` if the value of this Decimal is less than the value of `n`, 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
    new Decimal(11.1, 2).lt(11, 3)       // true

##### lessThanOrEqualTo`.lte(n [, base]) ⇒ boolean`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns `true` if the value of this Decimal is less than or equal to the value of `n`, 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
    new Decimal(10, 18).lte('i', 36)                // true

##### logarithm`.log([n [, base]]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number (This is not the base of the logarithm but the base of `n`)
See `Decimal` for further parameter details.

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

If `n` is `null` or undefined, then 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.

The performance of this method degrades exponentially with increasing digits.

##### minus`.minus(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the value of this Decimal minus `n`, 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'
    x.minus(0.6, 20)           // '0'

##### modulo`.mod(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the value of this Decimal modulo `n`, 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(33)
    y.mod('a', 33)             // '3'

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

##### 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 natual logarithm is the inverse of the `exponential` 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 rounded.

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

##### plus`.plus(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the value of this Decimal plus `n`, 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'
    x.plus('0.1', 8)                   // '0.225'

##### 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.config({ rounding: 4 })
    x = 1234.5
    x.round()                                  // '1235'

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

##### 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

##### times`.times(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal
`base`: number
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the value of this Decimal times `n`, 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'
    x.times('-a', 16)                   // '-6'

##### 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 or is `null` or undefined, the return value will have the same value as this Decimal.

if `rm` is omitted or is `null` or undefined, rounding mode `rounding` is used.

See Errors for the treatment of other non-integer or out of range `dp` values.

    x = new Decimal(12.24567)
    x.toDecimalPlaces(0)                // '12'
    x.toDecimalPlaces(1, 0)             // '12.3'

    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, or is `null` or undefined, the number of digits after the decimal point defaults to the minimum number of digits necessary to represent the value exactly.

If `rm` is omitted or is `null` or undefined, rounding mode `rounding` is used.

See Errors for the treatment of other non-integer or out of range `decimal_places` values.

    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, 1)          // '4.5e+1'  (ROUND_DOWN)
    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 or is `null` or undefined, then 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 or is `null` or undefined, rounding mode `rounding` is used.

See Errors for the treatment of other non-integer or out of range `dp` values.

    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, 1)          // '3.45'  (ROUND_DOWN)
    x.toFixed(5)             // '3.45600'
    y.toFixed(5)             // '3.45600'

##### toFormat`.toFormat([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 fixed-point notation rounded to `dp` decimal places using rounding mode `rm` (as `toFixed`), and formatted according to the properties of this Decimal's constructor's `format` object property.

See the examples below for the properties of the `format` object, their types and their usage.

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

if `rm` is omitted or is `null` or undefined, rounding mode `rounding` is used.

    // Using config to assign values to the format object
    Decimal.config({
        format : {
            decimalSeparator : '.',
            groupSeparator : ',',
            groupSize : 3,
            secondaryGroupSize : 0,
            fractionGroupSeparator : ' ',
            fractionGroupSize : 0
        }
    });

    x = new Decimal('123456789.123456789')
    x.toFormat()                     // '123,456,789.123456789'
    x.toFormat(1)                    // '123,456,789.1'

    // Assigning the format properties directly
    Decimal.format.groupSeparator = ' ';
    Decimal.format.fractionGroupSize = 5;
    x.toFormat()                     // '123 456 789.12345 6789'

    // Assigning the format object directly
    Decimal.format = {
        decimalSeparator = ',',
        groupSeparator = '.',
        groupSize = 3,
        secondaryGroupSize = 2
    }

    x.toFormat()                     // '12.34.56.789,123456789'

##### toFraction `.toFraction([max_denominator]) ⇒ [string, string]`

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

Returns a string array 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 not specified, or is `null` or undefined, the denominator will be the lowest value necessary to represent the number exactly.

See Errors for the treatment of other non-integer or out of range `max_denominator` values.

    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'

##### toJSON`.toJSON() ⇒ string`

As `valueOf`.

    x = new Decimal('177.7e+457')
    y = new Decimal(235.4325)
    z = new Decimal('0.0098074')

    // Serialize an array of three Decimals
    str = JSON.stringify( [x, y, z] )
    // "["1.777e+459","235.4325","0.0098074"]"

    // Return an array of three Decimals
    JSON.parse(str, function (key, val) {
        return key === '' ? val : new Decimal(val)
    })

If the `toJSON` method was not present, the objects (Decimal instances) themselves would be serialized, rather then the string returned by `valueOf`:

    JSON.stringify( [x, y, z] )
    /*
    "[{"s":1,"e":459,"c":[17770]},
      {"s":1,"e":2,"c":[235,4325000]},
      {"s":1,"e":-3,"c":[98074]}]"
     */

##### toNearest`.toNearest(n [, rm]) ⇒ Decimal`

`n`: number|string|Decimal
`rm`: number: integer, 0 to 8 inclusive
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the nearest multiple of `n` to the value of this Decimal.

If the value of this Decimal is equidistant from two multiples of `n`, the rounding mode `rm`, or `rounding` if `rm` is omitted or is `null` or undefined, determines the direction of the nearest.

In this context, rounding mode `ROUND_HALF_UP` is interpreted the same as rounding mode `ROUND_UP`, and so on. I.e. the rounding is either up, down, to ceil, to floor or to even.

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

The return value is not rounded to `precision`.

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

    y = new Decimal(0.75)          // equidistant from 0.5 and 1
    y.toNearest(0.5, 0)            // '1'    (ROUND_UP)
    y.toNearest(0.5, 1)            // '0.5'  (ROUND_DOWN)

##### toNumber`.toNumber() ⇒ number`

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

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

##### toPower`.pow(n [, base]) ⇒ Decimal`

`n`: number|string|Decimal: integer or non-integer
`base`: number
See `Decimal` for further parameter details.

Returns a new Decimal whose value is the value of this Decimal raised to the power `n`, 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?

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).

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

> `xy = 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 Decimal return values of the functions as implemented by this library will 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 (the first rounding digit may also be `5` or `4` respectively).

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.config({ 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 or is `null` or undefined, then the return value is the same as `toString`.

if `rm` is omitted or is `null` or undefined, rounding mode `rounding` is used.

See Errors for the treatment of other non-integer or out of range `sd` values.

    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, 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'

##### 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 or is `null` or undefined, the return value will be rounded to `precision` significant digits.

if `rm` is omitted or is `null` or undefined, rounding mode `rounding` will be used.

See Errors for the treatment of other non-integer or out of range `sd` or `rm` values.

    Decimal.config({ 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([base]) ⇒ string`

`base`: number: integer, 2 to 64 inclusive

Returns a string representing the value of this Decimal in the specified base, or base 10 if `base` is omitted or is `null` or undefined.

For bases above 10, values from 10 to 35 are represented by `a-z` (as with `Number.prototype.toString`), 36 to 61 by `A-Z`, and 62 and 63 by `$` and `_` respectively.

If a base is specified the value is rounded to `precision` significant digits using rounding mode `rounding`.

If a base is not specified and 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 is returned.

If `base` is `null` or undefined it is ignored.

See Errors for the treatment of other non-integer or out of range `base` values.

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

    y = new Decimal(362.875)
    y.toString(2)                   // '101101010.111'
    y.toString(9)                   // '442.77777777777777777778'
    y.toString(32)                  // 'ba.s'

    Decimal.config({ precision: 4 });
    z = new Decimal('1.23456789')
    z.toString()                    // '1.23456789'
    z.toString(10)                  // '1.2346'

##### 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 rounded to `precision`.

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

##### valueOf`.valueOf() ⇒ string`

As `toString`, but does not accept a base argument.

    x = new Decimal('1.777e+457')
    x.valueOf()                     // '1.777e+457'

#### Properties

A Decimal is an object with three properties:

Property | Description | Type | Value
--- | --- | --- | ---
c | coefficient* | number`[]` | Array of integers, each 0 - 1e7
e | exponent | number | Integer, -9e15 to 9e15 inclusive
s | sign | number | -1 or 1

*significand

The value of any of the three properties may also be `null`.

The properties are best considered to be read-only.

From version 3 of this library, the value of a Decimal is stored in a normalised base `10000` floating point format. While previously it was acceptable to change the exponent of a Decimal by writing to its exponent property directly, this is no longer recommended (as the number of digits in the first element of the coefficient array is dependent on the exponent, so the coefficient would also need to be altered).

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

    x = new Decimal(0.123)                // '0.123'
    x.toExponential()                     // '1.23e-1'
    x.c                                   // [ 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.c                                   // [ 12345, 6700000 ]
    z.e                                   // 4
    z.s                                   // -1

#### Zero, NaN and Infinity

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

| c | e | s
--- | --- | --- | ---
±0 | `[0]` | `0` | `±1`
NaN | `null` | `null` | `null`
±Infinity | `null` | `null` | `±1`

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

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

#### Errors

The errors that are thrown are generic `Error` objects with `name` Decimal Error.

The table below shows the errors that may be thrown if `errors` is `true`, and the action taken if `errors` is `false`.

Method(s) | errors: true Throw Decimal Error | errors: false Action on invalid argument
--- | --- | ---
`comparedTo Decimal dividedBy dividedToIntegerBy equals greaterThan greaterThanOrEqualTo lessThan lessThanOrEqualTo logarithm minus modulo naturalLogarithm plus times toPower` | number type has more than 15 significant digits | Accept.
not a base... number | Substitute `NaN`
base not an integer | Truncate to integer. Ignore if not a number
base out of range | Ignore
not a number* | Substitute `NaN`
`config` | `precision` not an integer | Truncate to integer. Ignore if not a number
`precision` out of range | Ignore
`rounding` not an integer | Truncate to integer. Ignore if not a number
`rounding` out of range | Ignore
`toExpNeg` not an integer | Truncate to integer. Ignore if not a number
`toExpNeg` out of range | Ignore
`toExpPos` not an integer | Truncate to integer. Ignore if not a number
`toExpPos` out of range | Ignore
`minE` not an integer | Truncate to integer. Ignore if not a number
`minE` out of range | Ignore
`maxE` not an integer | Truncate to integer. Ignore if not a number
`maxE` out of range | Ignore
`errors` not a boolean or binary digit | Ignore
`crypto` not a boolean or binary digit | Ignore
`modulo` not an integer | Truncate to integer. Ignore if not a number
`modulo` out of range | Ignore
`logarithm naturalLogarithm` | LN10 out of digits | Ignore
`precision` | argument not a boolean or binary digit | Ignore
`random` | `crypto` unavailable | Use `Math.random`
`toDecimalPlaces toExponential toFixed toPrecision toSignificantDigits` | argument not an integer | Truncate to integer. Ignore if not a number
argument out of range | Ignore
rounding mode not an integer | Truncate to integer. Ignore if not a number
rounding mode out of range | Ignore
`toFraction` | number type has more than 15 significant digits | Accept.
max denominator not an integer | Truncate to integer. Ignore if not a number
max denominator out of range | Ignore
`toNearest` | number type has more than 15 significant digits | Accept.
rounding mode out of range | Ignore
`toString` | base not an integer | Truncate to integer. Ignore if not a number
base out of range | Ignore

*No error is thrown if the value is `NaN` or 'NaN'.

The message of a Decimal Error will also contain the name of the method from which the error originated.

To determine if an exception is a Decimal Error:

    try {
        // ...
    } catch (e) {
        if ( e instanceof Error && e.name == 'Decimal Error' ) {
            // ...
        }
    }

## 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.