big-integer

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# big-integer

An arbitrary length integer library for Javascript

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Package description

## What is big-integer?

The big-integer npm package is designed for arithmetic and logical operations on large integers beyond the safe limit for JavaScript's native number type. It provides a way to work with integers of arbitrary size, allowing for precise calculations that would otherwise be impossible due to the limitations of standard number precision in JavaScript.

## What are big-integer's main functionalities?

Arithmetic Operations

Demonstrates basic arithmetic operations such as addition, subtraction, multiplication, division, and modulo on large integers.

"use strict";\nconst bigInt = require('big-integer');\nlet x = bigInt('123456789012345678901234567890');\nlet y = bigInt('98765432109876543210987654321');\nlet sum = x.add(y);\nlet difference = x.minus(y);\nlet product = x.multiply(y);\nlet quotient = x.divide(y);\nlet remainder = x.mod(y);\nconsole.log('Sum:', sum.toString());\nconsole.log('Difference:', difference.toString());\nconsole.log('Product:', product.toString());\nconsole.log('Quotient:', quotient.toString());\nconsole.log('Remainder:', remainder.toString());

Logical Operations

Shows how to perform bitwise logical operations such as AND, OR, and XOR on large integers.

"use strict";\nconst bigInt = require('big-integer');\nlet x = bigInt('12345678901234567890');\nlet y = bigInt('9876543210987654321');\nlet andResult = x.and(y);\nlet orResult = x.or(y);\nlet xorResult = x.xor(y);\nconsole.log('AND:', andResult.toString());\nconsole.log('OR:', orResult.toString());\nconsole.log('XOR:', xorResult.toString());

Comparison Operations

Illustrates how to compare two large integers, checking for greater than, less than, and equality.

"use strict";\nconst bigInt = require('big-integer');\nlet x = bigInt('12345678901234567890');\nlet y = bigInt('9876543210987654321');\nconsole.log('x > y:', x.greater(y));\nconsole.log('x < y:', x.lesser(y));\nconsole.log('x == y:', x.equals(y));

## Other packages similar to big-integer

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. 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 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.

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

View benchmarks for this method

##### and(number)

Performs the bitwise AND operation. The operands are treated as if they were represented using two's complement representation.

• 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

##### 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

##### 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.

• 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

##### 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

##### modInv(mod)

Finds the 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

##### neq(number)

Alias for the notEquals method.

##### next()

• bigInt(6).next() => 7
##### not()

Performs the bitwise NOT operation. The operands are treated as if they were represented using two's complement representation.

• 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.

• 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

##### plus(number)

• bigInt(5).plus(7) => 12

View benchmarks for this method

##### 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

##### prev(number)

Subtracts one from the number.

• bigInt(6).prev() => 5
##### remainder(number)

Alias for the mod method.

View benchmarks for this method

##### 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

##### subtract(number)

Performs subtraction.

• bigInt(3).subtract(5) => -2

View benchmarks for this method

##### times(number)

Alias for the multiply method.

• bigInt(111).times(111) => 12321

View benchmarks for this method

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.

• 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

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

##### 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.

There are performance benchmarks that can be viewed from the benchmarks/index.html page. You can run them online from GitHub.

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Last updated on 30 Sep 2019

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