源码：zk-SNARKs实战：使用circom和snarkjs实现简单版的Tornado

# 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. **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(strict?)` Returns `true` if the number is prime, `false` otherwise. Set "strict" boolean to true to force GRH-supported lower bound of 2*log(N)^2. - `bigInt(5).isPrime()` => `true` - `bigInt(6).isPrime()` => `false` #### `isProbablePrime([iterations], [rng])` Returns `true` if the number is very likely to be prime, `fa