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+# BigInteger.js [![Build Status][travis-img]][travis-url] [![Coverage Status][coveralls-img]][coveralls-url] [![Monthly Downloads][downloads-img]][downloads-url]
+
+[travis-url]: https://travis-ci.org/peterolson/BigInteger.js
+[travis-img]: https://travis-ci.org/peterolson/BigInteger.js.svg?branch=master
+[coveralls-url]: https://coveralls.io/github/peterolson/BigInteger.js?branch=master
+[coveralls-img]: https://coveralls.io/repos/peterolson/BigInteger.js/badge.svg?branch=master&service=github
+[downloads-url]: https://www.npmjs.com/package/big-integer
+[downloads-img]: https://img.shields.io/npm/dm/big-integer.svg
+
+**BigInteger.js** is an arbitrary-length integer library for Javascript, allowing arithmetic operations on integers of unlimited size, notwithstanding memory and time limitations.
+
+## 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="http://peterolson.github.com/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])`
+
+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 `>`).
+
+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])`
+
+Returns `true` if the number is very likely to be prime, `false` otherwise.
+Argument is optional and determines the amount of iterations of the test (default: `5`). The more iterations, the lower chance of getting a false positive.
+This uses the [Fermat primality test](https://en.wikipedia.org/wiki/Fermat_primality_test).
+
+ - `bigInt(5).isProbablePrime()` => `true`
+ - `bigInt(49).isProbablePrime()` => `false`
+ - `bigInt(1729).isProbablePrime(50)` => `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. [Carmichael numbers](https://en.wikipedia.org/wiki/Carmichael_number) are particularly prone to give unreliable results.
+
+For example, `bigInt(1729).isProbablePrime()` returns `false` about 76% of the time and `true` about 24% of the time. The correct result is `false`.
+
+#### `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)`
+
+Returns a random number between `min` and `max`.
+
+ - `bigInt.randBetween("-1e100", "1e100")` => (for example) `8494907165436643479673097939554427056789510374838494147955756275846226209006506706784609314471378745`
+
+
+### Override Methods
+
+#### `toString(radix = 10)`
+
+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"`
+
+**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/).