BigRational.js

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.

Installation

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"
• 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");

Method Chaining

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

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

Constants

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)

Properties

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

Methods

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"

Override Methods

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