**BigRational.js** is an arbitrary-length rational number library for Javascript, allowing arithmetic operations on rational numbers of unlimited size, notwithstanding memory and time limitations.

A *rational number* is stored internally as a pair of two big integers. Because of this, BigRational.js depends on my big integer library, BigInteger.js.

If you are using a browser, you can download BigRational.js from GitHub or just hotlink to it.

```
<script src="http://peterolson.github.com/BigRational.js/BigInt_BigRat.min.js"></script>
```

This will include both the `bigInt`

library and the `bigRat`

library. If you want to reference them separately, you can use the non-combined BigRational.js script.

If you are using node, you can install BigRational.js with npm.

```
npm install big-rational
```

Then you can include it in your code

```
var bigRat = require("big-rational");
```

`bigRat(num?, denom?)`

You can create a bigRational by calling the `bigRat`

function. You can pass in up to two paramers.

`bigRat()`

If you pass in zero parameters, it will return zero.

`bigRat(n)`

If you pass in one parameter, it must be one of the following:

- a string, which may be
- an integer, such as
`"12345"`

, - a numerator over a denominator, such as
`"2/3"`

, - a mixed fraction, such as
`"1_1/2"`

- a decimal number, such as
`"54.05446"`

- an integer, such as
- a Javascript number
- a bigInteger
- a bigRational

`bigRat(num, denom)`

If you pass in two parameters, the first will be interpreted as the numerator, and the second as the denominator. Both parameters must be one of the following:

- a string in integer form, such as
`"12345"`

- a JavaScript number that is an integer, such as
`12345`

- a bigInteger

**Examples:**

```
var zero = bigRat();
var threeFourths = bigRat("3/4") ||
bigRat("3", "4") ||
bigRat(3, 4) ||
bigRat(3 / 4) ||
bigRat(0.75);
var fiveHalves = bigRat("5/2") ||
bigRat("2_1/2");
```

Note that bigRat operations return bigRats, which allows you to chain methods, for example:

```
var salary = bigRat(dollarsPerHour).times(hoursWorked).plus(randomBonuses)
```

There are three constants already stored that you do not have to construct with the `bigRat`

function yourself:

`bigRat.one`

, equivalent to`bigRat(1)`

`bigRat.zero`

, equivalent to`bigRat(0)`

`bigRat.minusOne`

, equivalent to`bigRat(-1)`

You can obtain the numerator and denominator of a bigRational with these properties:

`numerator`

Returns the numerator of a bigRational. This will be a bigInt.

`bigRat(34, 3).numerator`

=>`bigInt(34)`

`denominator`

Returns the denominator of a bigRational. This will be a bigInt.

`bigRat(34, 3).denominator`

=>`bigInt(3)`

`num`

Alias for the `numerator`

property

`denom`

Alias for the `denominator`

property

`abs`

Returns the absolute value of a number.

`bigRat(-424).abs().equals(424)`

`add`

Performs addition.

`bigRat("1/3").add(1, 3).equals(2, 3)`

`ceil(toBigInt?)`

Rounds up to the nearest integer. If the `toBigInt`

argument is `true`

, then it will return a bigInteger instead of a bigRational.

`bigRat(12345.4).ceil().equals(12346)`

`compareAbs`

Performs a comparison between the absolute values of two numbers. If the numbers are of equal magnitude, it returns `0`

. If the first number is of greater magnitude, it returns `1`

. Otherwise, it returns `-1`

.

`bigRat(-3).compareAbs(3) === 0`

`bigRat(3).compareAbs(-4) === -1`

`bigRat(-4).compareAbs(3) === 1`

`compare`

Performs a comparison between two numbers. If the numbers are equal, it returns `0`

. If the first number is greater, it returns `1`

. If the first number is lesser, it returns `-1`

.

`bigRat(3).compare(3) === 0`

`bigRat(3).compare(4) === -1`

`bigRat(4).compare(3) === 1`

`compareTo`

Alias for the `compare`

function.

`divide`

Performs division.

`bigRat("354.25").divide(1, 4).equals(1417)`

`eq`

Alias for the `equals`

function.

`equals`

Checks if two numbers are equal.

`bigRat(1).equals(1)`

`floor(toBigInt?)`

Rounds down to the nearest integer. If the `toBigInt`

argument is `true`

, then it will return a bigInteger instead of a bigRational.

`bigRat(987.99999).floor().equals(987)`

`geq`

Alias for the `greaterOrEquals`

function.

`greater`

Checks if the first number is greater than the second

`bigRat(5).greater(4)`

`greaterOrEquals`

Checks if the first number is greater than or equal to the second

`bigRat(5).greaterOrEquals(5)`

`bigRat(5).greaterOrEquals(4)`

`gt`

Alias for the `greater`

function.

`isNegative`

Returns `true`

if the number is negative, `false`

otherwise.

`bigRat(-7).isNegative()`

`isPositive`

Returns `true`

if the number is positive, `false`

otherwise.

`bigRat(7).isPositive()`

`isZero`

Returns `true`

if the number equals 0, `false`

otherwise.

`bigRat(0).isZero()`

`lesser`

Checks if the first number is lesser than the second

`bigRat(4).lesser(5)`

`lesserOrEquals`

Checks if the first number is lesser than or equal to the second

`bigRat(4).lesserOrEquals(4)`

`bigRat(4).lesserOrEquals(5)`

`leq`

Alias for the `lesserOrEquals`

function.

`lt`

Alias for the `lesser`

function.

`minus`

Alias for `subtract`

.

`mod`

Performs the modulo operation.

`bigRat(3).mod(2).equals(1)`

`multiply`

Performs multiplication.

`bigRat(70, 2).multiply(4).equals(140)`

`negate`

Returns the negation of a number.

`bigRat(234).negate().equals(-234)`

`neq`

Alias for the `notEquals`

function.

`notEquals`

Checks if two numbers are not equal.

`bigRat(1).notEquals(2)`

`over`

Alias for `divide`

.

`plus`

Alias for `add`

.

`pow`

Performs exponentiation. The argument will be parsed as a bigInt.

`bigRat("3/2").pow(3)`

=>`bigRat("27/8")`

`reciprocate`

Returns the reciprocal of a number.

`bigRat("3/2").reciprocate()`

=>`bigRat("2/3")`

`round(toBigInt?)`

Rounds a number to the nearest integer. If the number is exactly half-way between two integers, it will round up.
If the `toBigInt`

argument is `true`

, then it will return a bigInteger instead of a bigRational.

`bigRat(54345.12566).round().equals(54345)`

`bigRat(1234567.5).round().equals(1234568)`

`bigRat(69.8).round().equals(70)`

`subtract`

Performs subtraction.

`bigRat(3).subtract(2).equals(1)`

`times`

Alias for `multiply`

.

`toDecimal(digits?)`

Converts a bigRational to a string in decimal notation, cut off after the number of digits specified in the `digits`

argument. The default number of digits is 10.

`bigRat(1,3).toDecimal() === "0.33333333333"`

`bigRat(1,7).toDecimal(14) === "0.14285714285714"`

`toString()`

Converts a bigRat to a string in "numerator/denominator" notation.

`bigRat(145.545).toString() === "29109/200"`

`valueOf()`

Converts a bigRat to a native Javascript number. This override allows you to use native arithmetic operators without explicit conversion:

`bigRat(1, 4) + bigRat(3, 4) === 1`