# BigNumbers #

For calculations with an arbitrary precision, math.js supports a `BigNumber` datatype. BigNumber support is powered by decimal.js.

## Usage #

A BigNumber can be created using the function `bignumber`:

``````math.bignumber('2.3e+500') // BigNumber, 2.3e+500
``````

Most functions can determine the type of output from the type of input: a number as input will return a number as output, a BigNumber as input returns a BigNumber as output. Functions which cannot determine the type of output from the input (for example `math.evaluate`) use the default number type `number`, which can be configured when instantiating math.js. To configure the use of BigNumbers instead of numbers by default, configure math.js like:

``````math.config({
number: 'BigNumber',      // Default type of number:
// 'number' (default), 'BigNumber', or 'Fraction'
precision: 64             // Number of significant digits for BigNumbers
})

// use math
math.evaluate('0.1 + 0.2')  // BigNumber, 0.3
``````

The default precision for BigNumber is 64 digits, and can be configured with the option `precision`.

## Support #

Most functions in math.js support BigNumbers, but not all of them. For example the function `random` doesn’t support BigNumbers.

## Round-off errors #

Calculations with BigNumber are much slower than calculations with Number, but they can be executed with an arbitrary precision. By using a higher precision, it is less likely that round-off errors occur:

``````// round-off errors with numbers
math.divide(0.3, 0.2)                                  // Number, 1.4999999999999998

// no round-off errors with BigNumbers :)
math.divide(math.bignumber(0.3), math.bignumber(0.2))  // BigNumber, 1.5
``````

## Limitations #

It’s important to realize that BigNumbers do not solve all problems related to precision and round-off errors. Numbers with an infinite number of digits cannot be represented with a regular number nor a BigNumber. Though a BigNumber can store a much larger number of digits, the amount of digits remains limited if only to keep calculations fast enough to remain practical.

``````const one = math.bignumber(1)
const three = math.bignumber(3)
const third = math.divide(one, three)
console.log(third.toString())
// outputs 0.3333333333333333333333333333333333333333333333333333333333333333

const ans = math.multiply(third, three)
console.log(ans.toString())
// outputs 0.9999999999999999999999999999999999999999999999999999999999999999
// this should be 1 again, but `third` is rounded to a limited number of digits 3
``````

## Conversion #

BigNumbers can be converted to numbers and vice versa using the functions `number` and `bignumber`. When converting a BigNumber to a number, the high precision of the BigNumber will be lost. When a BigNumber is too large to be represented as Number, it will be initialized as `Infinity`.

``````// converting numbers and BigNumbers
const a = math.number(0.3)                         // number, 0.3
const b = math.bignumber(a)                        // BigNumber, 0.3
const c = math.number(b)                           // number, 0.3

// exceeding the maximum of a number
const d = math.bignumber('1.2e500')                // BigNumber, 1.2e+500
const e = math.number(d)                           // number, Infinity

// loosing precision when converting to number
const f = math.bignumber('0.2222222222222222222')  // BigNumber, 0.2222222222222222222
const g = math.number(f)                           // number,    0.2222222222222222
``````