# BigInteger.js [![Build Status][travis-img]][travis-url] [![Coverage Status][coveralls-img]][coveralls-url] [![Monthly Downloads][downloads-img]][downloads-url]

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**BigInteger.js** is an arbitrary-length integer library for Javascript, allowing arithmetic operations on integers of unlimited size, notwithstanding memory and time limitations.

**Update (December 2, 2018):** [`BigInt` is being added as a native feature of JavaScript](https://tc39.github.io/proposal-bigint/). This library now works as a polyfill: if the environment supports the native `BigInt`, this library acts as a thin wrapper over the native implementation.

## Installation

If you are using a browser, you can download [BigInteger.js from GitHub](http://peterolson.github.com/BigInteger.js/BigInteger.min.js) or just hotlink to it:

	<script src="https://peterolson.github.io/BigInteger.js/BigInteger.min.js"></script>

If you are using node, you can install BigInteger with [npm](https://npmjs.org/).

    npm install big-integer

Then you can include it in your code:

	var bigInt = require("big-integer");


## Usage
### `bigInt(number, [base], [alphabet], [caseSensitive])`

You can create a bigInt by calling the `bigInt` function. You can pass in

 - a string, which it will parse as an bigInt and throw an `"Invalid integer"` error if the parsing fails.
 - a Javascript number, which it will parse as an bigInt and throw an `"Invalid integer"` error if the parsing fails.
 - another bigInt.
 - nothing, and it will return `bigInt.zero`.

 If you provide a second parameter, then it will parse `number` as a number in base `base`. Note that `base` can be any bigInt (even negative or zero). The letters "a-z" and "A-Z" will be interpreted as the numbers 10 to 35. Higher digits can be specified in angle brackets (`<` and `>`). The default `base` is `10`.

 You can specify a custom alphabet for base conversion with the third parameter. The default `alphabet` is `"0123456789abcdefghijklmnopqrstuvwxyz"`.

 The fourth parameter specifies whether or not the number string should be case-sensitive, i.e. whether `a` and `A` should be treated as different digits. By default `caseSensitive` is `false`.

Examples:

    var zero = bigInt();
    var ninetyThree = bigInt(93);
	var largeNumber = bigInt("75643564363473453456342378564387956906736546456235345");
	var googol = bigInt("1e100");
	var bigNumber = bigInt(largeNumber);

	var maximumByte = bigInt("FF", 16);
	var fiftyFiveGoogol = bigInt("<55>0", googol);

Note that Javascript numbers larger than `9007199254740992` and smaller than `-9007199254740992` are not precisely represented numbers and will not produce exact results. If you are dealing with numbers outside that range, it is better to pass in strings.

### Method Chaining

Note that bigInt operations return bigInts, which allows you to chain methods, for example:

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

### Constants

There are three named constants already stored that you do not have to construct with the `bigInt` function yourself:

 - `bigInt.one`, equivalent to `bigInt(1)`
 - `bigInt.zero`, equivalent to `bigInt(0)`
 - `bigInt.minusOne`, equivalent to `bigInt(-1)`

The numbers from -999 to 999 are also already prestored and can be accessed using `bigInt[index]`, for example:

 - `bigInt[-999]`, equivalent to `bigInt(-999)`
 - `bigInt[256]`, equivalent to `bigInt(256)`

### Methods

#### `abs()`

Returns the absolute value of a bigInt.

 - `bigInt(-45).abs()` => `45`
 - `bigInt(45).abs()` => `45`

#### `add(number)`

Performs addition.

 - `bigInt(5).add(7)` => `12`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Addition)

#### `and(number)`

Performs the bitwise AND operation. The operands are treated as if they were represented using [two's complement representation](http://en.wikipedia.org/wiki/Two%27s_complement).

 - `bigInt(6).and(3)` => `2`
 - `bigInt(6).and(-3)` => `4`

#### `bitLength()`

Returns the number of digits required to represent a bigInt in binary.

 - `bigInt(5)` => `3` (since 5 is `101` in binary, which is three digits long)

#### `compare(number)`

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`.

 - `bigInt(5).compare(5)` => `0`
 - `bigInt(5).compare(4)` => `1`
 - `bigInt(4).compare(5)` => `-1`

#### `compareAbs(number)`

Performs a comparison between the absolute value of two numbers.

 - `bigInt(5).compareAbs(-5)` => `0`
 - `bigInt(5).compareAbs(4)` => `1`
 - `bigInt(4).compareAbs(-5)` => `-1`

#### `compareTo(number)`

Alias for the `compare` method.

#### `divide(number)`

Performs integer division, disregarding the remainder.

 - `bigInt(59).divide(5)` => `11`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Division)

#### `divmod(number)`

Performs division and returns an object with two properties: `quotient` and `remainder`. The sign of the remainder will match the sign of the dividend.

 - `bigInt(59).divmod(5)` => `{quotient: bigInt(11), remainder: bigInt(4) }`
 - `bigInt(-5).divmod(2)` => `{quotient: bigInt(-2), remainder: bigInt(-1) }`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Division)

#### `eq(number)`

Alias for the `equals` method.

#### `equals(number)`

Checks if two numbers are equal.

 - `bigInt(5).equals(5)` => `true`
 - `bigInt(4).equals(7)` => `false`

#### `geq(number)`

Alias for the `greaterOrEquals` method.


#### `greater(number)`

Checks if the first number is greater than the second.

 - `bigInt(5).greater(6)` => `false`
 - `bigInt(5).greater(5)` => `false`
 - `bigInt(5).greater(4)` => `true`

#### `greaterOrEquals(number)`

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

 - `bigInt(5).greaterOrEquals(6)` => `false`
 - `bigInt(5).greaterOrEquals(5)` => `true`
 - `bigInt(5).greaterOrEquals(4)` => `true`

#### `gt(number)`

Alias for the `greater` method.

#### `isDivisibleBy(number)`

Returns `true` if the first number is divisible by the second number, `false` otherwise.

 - `bigInt(999).isDivisibleBy(333)` => `true`
 - `bigInt(99).isDivisibleBy(5)` => `false`

#### `isEven()`

Returns `true` if the number is even, `false` otherwise.

 - `bigInt(6).isEven()` => `true`
 - `bigInt(3).isEven()` => `false`

#### `isNegative()`

Returns `true` if the number is negative, `false` otherwise.
Returns `false` for `0` and `-0`.

 - `bigInt(-23).isNegative()` => `true`
 - `bigInt(50).isNegative()` => `false`

#### `isOdd()`

Returns `true` if the number is odd, `false` otherwise.

 - `bigInt(13).isOdd()` => `true`
 - `bigInt(40).isOdd()` => `false`

#### `isPositive()`

Return `true` if the number is positive, `false` otherwise.
Returns `false` for `0` and `-0`.

 - `bigInt(54).isPositive()` => `true`
 - `bigInt(-1).isPositive()` => `false`

#### `isPrime()`

Returns `true` if the number is prime, `false` otherwise.

 - `bigInt(5).isPrime()` => `true`
 - `bigInt(6).isPrime()` => `false`

#### `isProbablePrime([iterations], [rng])`

Returns `true` if the number is very likely to be prime, `false` otherwise.
Supplying `iterations` is optional - it determines the number of iterations of the test (default: `5`). The more iterations, the lower chance of getting a false positive.
This uses the [Miller Rabin test](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test).

 - `bigInt(5).isProbablePrime()` => `true`
 - `bigInt(49).isProbablePrime()` => `false`
 - `bigInt(1729).isProbablePrime()` => `false`

Note that this function is not deterministic, since it relies on random sampling of factors, so the result for some numbers is not always the same - unless you pass a predictable random number generator as `rng`. The behavior and requirements are the same as with `randBetween`.

 - `bigInt(1729).isProbablePrime(1, () => 0.1)` => `false`
 - `bigInt(1729).isProbablePrime(1, () => 0.2)` => `true`

If the number is composite then the Miller–Rabin primality test declares the number probably prime with a probability at most `4` to the power `−iterations`.
If the number is prime, this function always returns `true`.

#### `isUnit()`

Returns `true` if the number is `1` or `-1`, `false` otherwise.

 - `bigInt.one.isUnit()` => `true`
 - `bigInt.minusOne.isUnit()` => `true`
 - `bigInt(5).isUnit()` => `false`

#### `isZero()`

Return `true` if the number is `0` or `-0`, `false` otherwise.

 - `bigInt.zero.isZero()` => `true`
 - `bigInt("-0").isZero()` => `true`
 - `bigInt(50).isZero()` => `false`

#### `leq(number)`

Alias for the `lesserOrEquals` method.

#### `lesser(number)`

Checks if the first number is lesser than the second.

 - `bigInt(5).lesser(6)` => `true`
 - `bigInt(5).lesser(5)` => `false`
 - `bigInt(5).lesser(4)` => `false`

#### `lesserOrEquals(number)`

Checks if the first number is less than or equal to the second.

 - `bigInt(5).lesserOrEquals(6)` => `true`
 - `bigInt(5).lesserOrEquals(5)` => `true`
 - `bigInt(5).lesserOrEquals(4)` => `false`

#### `lt(number)`

Alias for the `lesser` method.

#### `minus(number)`

Alias for the `subtract` method.

 - `bigInt(3).minus(5)` => `-2`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Subtraction)

#### `mod(number)`

Performs division and returns the remainder, disregarding the quotient. The sign of the remainder will match the sign of the dividend.

 - `bigInt(59).mod(5)` =>  `4`
 - `bigInt(-5).mod(2)` => `-1`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Division)

#### `modInv(mod)`

Finds the [multiplicative inverse](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse) of the number modulo `mod`.

 - `bigInt(3).modInv(11)` => `4`
 - `bigInt(42).modInv(2017)` => `1969`

#### `modPow(exp, mod)`

Takes the number to the power `exp` modulo `mod`.

 - `bigInt(10).modPow(3, 30)` => `10`

#### `multiply(number)`

Performs multiplication.

 - `bigInt(111).multiply(111)` => `12321`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Multiplication)

#### `neq(number)`

Alias for the `notEquals` method.

#### `next()`

Adds one to the number.

 - `bigInt(6).next()` => `7`

#### `not()`

Performs the bitwise NOT operation. The operands are treated as if they were represented using [two's complement representation](http://en.wikipedia.org/wiki/Two%27s_complement).

 - `bigInt(10).not()` => `-11`
 - `bigInt(0).not()` => `-1`

#### `notEquals(number)`

Checks if two numbers are not equal.

 - `bigInt(5).notEquals(5)` => `false`
 - `bigInt(4).notEquals(7)` => `true`

#### `or(number)`

Performs the bitwise OR operation. The operands are treated as if they were represented using [two's complement representation](http://en.wikipedia.org/wiki/Two%27s_complement).

 - `bigInt(13).or(10)` => `15`
 - `bigInt(13).or(-8)` => `-3`

#### `over(number)`

Alias for the `divide` method.

 - `bigInt(59).over(5)` => `11`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Division)

#### `plus(number)`

Alias for the `add` method.

 - `bigInt(5).plus(7)` => `12`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Addition)

#### `pow(number)`

Performs exponentiation. If the exponent is less than `0`, `pow` returns `0`. `bigInt.zero.pow(0)` returns `1`.

 - `bigInt(16).pow(16)` => `18446744073709551616`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Exponentiation)

#### `prev(number)`

Subtracts one from the number.

 - `bigInt(6).prev()` => `5`

#### `remainder(number)`

Alias for the `mod` method.

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Division)

#### `shiftLeft(n)`

Shifts the number left by `n` places in its binary representation. If a negative number is provided, it will shift right. Throws an error if `n` is outside of the range `[-9007199254740992, 9007199254740992]`.

 - `bigInt(8).shiftLeft(2)` => `32`
 - `bigInt(8).shiftLeft(-2)` => `2`

#### `shiftRight(n)`

Shifts the number right by `n` places in its binary representation. If a negative number is provided, it will shift left. Throws an error if `n` is outside of the range `[-9007199254740992, 9007199254740992]`.

 - `bigInt(8).shiftRight(2)` => `2`
 - `bigInt(8).shiftRight(-2)` => `32`

#### `square()`

Squares the number

 - `bigInt(3).square()` => `9`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Squaring)

#### `subtract(number)`

Performs subtraction.

 - `bigInt(3).subtract(5)` => `-2`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Subtraction)

#### `times(number)`

Alias for the `multiply` method.

 - `bigInt(111).times(111)` => `12321`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#Multiplication)

#### `toArray(radix)`

Converts a bigInt into an object with the properties "value" and "isNegative." "Value" is an array of integers modulo the given radix. "isNegative" is a boolean that represents the sign of the result.

 - `bigInt("1e9").toArray(10)` => {
     value: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
     isNegative: false
   }
 - `bigInt("1e9").toArray(16)` => {
     value: [3, 11, 9, 10, 12, 10, 0, 0],
     isNegative: false
   }
 - `bigInt(567890).toArray(100)` => {
     value: [56, 78, 90],
     isNegative: false
   }

Negative bases are supported.

 - `bigInt(12345).toArray(-10)` => {
     value: [2, 8, 4, 6, 5],
     isNegative: false
   }

Base 1 and base -1 are also supported.

 - `bigInt(-15).toArray(1)` => {
     value: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
     isNegative: true
   }
 - `bigInt(-15).toArray(-1)` => {
     value: [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
             0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0],
     isNegative: false
   }

Base 0 is only allowed for the number zero.

 - `bigInt(0).toArray(0)` => {
     value: [0],
     isNegative: false
   }
 - `bigInt(1).toArray(0)` => `Error: Cannot convert nonzero numbers to base 0.`

#### `toJSNumber()`

Converts a bigInt into a native Javascript number. Loses precision for numbers outside the range `[-9007199254740992, 9007199254740992]`.

 - `bigInt("18446744073709551616").toJSNumber()` => `18446744073709552000`

#### `xor(number)`

Performs the bitwise XOR operation. The operands are treated as if they were represented using [two's complement representation](http://en.wikipedia.org/wiki/Two%27s_complement).

 - `bigInt(12).xor(5)` => `9`
 - `bigInt(12).xor(-5)` => `-9`

### Static Methods

#### `fromArray(digits, base = 10, isNegative?)`

Constructs a bigInt from an array of digits in base `base`. The optional `isNegative` flag will make the number negative.

 - `bigInt.fromArray([1, 2, 3, 4, 5], 10)` => `12345`
 - `bigInt.fromArray([1, 0, 0], 2, true)` => `-4`

#### `gcd(a, b)`

Finds the greatest common denominator of `a` and `b`.

 - `bigInt.gcd(42,56)` => `14`

#### `isInstance(x)`

Returns `true` if `x` is a BigInteger, `false` otherwise.

 - `bigInt.isInstance(bigInt(14))` => `true`
 - `bigInt.isInstance(14)` => `false`

#### `lcm(a,b)`

Finds the least common multiple of `a` and `b`.

 - `bigInt.lcm(21, 6)` => `42`

#### `max(a,b)`

Returns the largest of `a` and `b`.

 - `bigInt.max(77, 432)` => `432`

#### `min(a,b)`

Returns the smallest of `a` and `b`.

 - `bigInt.min(77, 432)` => `77`

#### `randBetween(min, max, [rng])`

Returns a random number between `min` and `max`, optionally using `rng` to generate randomness.

 - `bigInt.randBetween("-1e100", "1e100")` => (for example) `8494907165436643479673097939554427056789510374838494147955756275846226209006506706784609314471378745`

`rng` should take no arguments and return a `number` between 0 and 1. It defaults to `Math.random`.

  - `bigInt.randBetween("-1e100", "1e100", () => 0.5)` => (always) `50000005000000500000050000005000000500000050000005000000500000050000005000000500000050000005000000`


### Override Methods

#### `toString(radix = 10, [alphabet])`

Converts a bigInt to a string. There is an optional radix parameter (which defaults to 10) that converts the number to the given radix. Digits in the range `10-35` will use the letters `a-z`.

 - `bigInt("1e9").toString()` => `"1000000000"`
 - `bigInt("1e9").toString(16)` => `"3b9aca00"`

 You can use a custom base alphabet with the second parameter. The default `alphabet` is `"0123456789abcdefghijklmnopqrstuvwxyz"`.

  - `bigInt("5").toString(2, "aA")` => `"AaA"`

**Note that arithmetical operators will trigger the `valueOf` function rather than the `toString` function.** When converting a bigInteger to a string, you should use the `toString` method or the `String` function instead of adding the empty string.

 - `bigInt("999999999999999999").toString()` => `"999999999999999999"`
 - `String(bigInt("999999999999999999"))` => `"999999999999999999"`
 - `bigInt("999999999999999999") + ""` => `1000000000000000000`

Bases larger than 36 are supported. If a digit is greater than or equal to 36, it will be enclosed in angle brackets.

 - `bigInt(567890).toString(100)` => `"<56><78><90>"`

Negative bases are also supported.

 - `bigInt(12345).toString(-10)` => `"28465"`

Base 1 and base -1 are also supported.

 - `bigInt(-15).toString(1)` => `"-111111111111111"`
 - `bigInt(-15).toString(-1)` => `"101010101010101010101010101010"`

Base 0 is only allowed for the number zero.

 - `bigInt(0).toString(0)` => `0`
 - `bigInt(1).toString(0)` => `Error: Cannot convert nonzero numbers to base 0.`

[View benchmarks for this method](http://peterolson.github.io/BigInteger.js/benchmark/#toString)

#### `valueOf()`

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

 - `bigInt("100") + bigInt("200") === 300; //true`

## Contributors

To contribute, just fork the project, make some changes, and submit a pull request. Please verify that the unit tests pass before submitting.

The unit tests are contained in the `spec/spec.js` file. You can run them locally by opening the `spec/SpecRunner.html` or file or running `npm test`. You can also [run the tests online from GitHub](http://peterolson.github.io/BigInteger.js/spec/SpecRunner.html).

There are performance benchmarks that can be viewed from the `benchmarks/index.html` page. You can [run them online from GitHub](http://peterolson.github.io/BigInteger.js/benchmark/).

## License

This project is public domain. For more details, read about the [Unlicense](http://unlicense.org/).