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diff --git a/node_modules/bn.js/README.md b/node_modules/bn.js/README.md deleted file mode 100644 index 83030ba..0000000 --- a/node_modules/bn.js/README.md +++ /dev/null @@ -1,228 +0,0 @@ -# <img src="./logo.png" alt="bn.js" width="160" height="160" /> - -> BigNum in pure javascript - -[](http://travis-ci.org/indutny/bn.js) - -## Install -`npm install --save bn.js` - -## Usage - -```js -const BN = require('bn.js'); - -var a = new BN('dead', 16); -var b = new BN('101010', 2); - -var res = a.add(b); -console.log(res.toString(10)); // 57047 -``` - -**Note**: decimals are not supported in this library. - -## Notation - -### Prefixes - -There are several prefixes to instructions that affect the way the work. Here -is the list of them in the order of appearance in the function name: - -* `i` - perform operation in-place, storing the result in the host object (on - which the method was invoked). Might be used to avoid number allocation costs -* `u` - unsigned, ignore the sign of operands when performing operation, or - always return positive value. Second case applies to reduction operations - like `mod()`. In such cases if the result will be negative - modulo will be - added to the result to make it positive - -### Postfixes - -* `n` - the argument of the function must be a plain JavaScript - Number. Decimals are not supported. -* `rn` - both argument and return value of the function are plain JavaScript - Numbers. Decimals are not supported. - -### Examples - -* `a.iadd(b)` - perform addition on `a` and `b`, storing the result in `a` -* `a.umod(b)` - reduce `a` modulo `b`, returning positive value -* `a.iushln(13)` - shift bits of `a` left by 13 - -## Instructions - -Prefixes/postfixes are put in parens at the of the line. `endian` - could be -either `le` (little-endian) or `be` (big-endian). - -### Utilities - -* `a.clone()` - clone number -* `a.toString(base, length)` - convert to base-string and pad with zeroes -* `a.toNumber()` - convert to Javascript Number (limited to 53 bits) -* `a.toJSON()` - convert to JSON compatible hex string (alias of `toString(16)`) -* `a.toArray(endian, length)` - convert to byte `Array`, and optionally zero - pad to length, throwing if already exceeding -* `a.toArrayLike(type, endian, length)` - convert to an instance of `type`, - which must behave like an `Array` -* `a.toBuffer(endian, length)` - convert to Node.js Buffer (if available). For - compatibility with browserify and similar tools, use this instead: - `a.toArrayLike(Buffer, endian, length)` -* `a.bitLength()` - get number of bits occupied -* `a.zeroBits()` - return number of less-significant consequent zero bits - (example: `1010000` has 4 zero bits) -* `a.byteLength()` - return number of bytes occupied -* `a.isNeg()` - true if the number is negative -* `a.isEven()` - no comments -* `a.isOdd()` - no comments -* `a.isZero()` - no comments -* `a.cmp(b)` - compare numbers and return `-1` (a `<` b), `0` (a `==` b), or `1` (a `>` b) - depending on the comparison result (`ucmp`, `cmpn`) -* `a.lt(b)` - `a` less than `b` (`n`) -* `a.lte(b)` - `a` less than or equals `b` (`n`) -* `a.gt(b)` - `a` greater than `b` (`n`) -* `a.gte(b)` - `a` greater than or equals `b` (`n`) -* `a.eq(b)` - `a` equals `b` (`n`) -* `a.toTwos(width)` - convert to two's complement representation, where `width` is bit width -* `a.fromTwos(width)` - convert from two's complement representation, where `width` is the bit width -* `BN.isBN(object)` - returns true if the supplied `object` is a BN.js instance -* `BN.max(a, b)` - return `a` if `a` bigger than `b` -* `BN.min(a, b)` - return `a` if `a` less than `b` - -### Arithmetics - -* `a.neg()` - negate sign (`i`) -* `a.abs()` - absolute value (`i`) -* `a.add(b)` - addition (`i`, `n`, `in`) -* `a.sub(b)` - subtraction (`i`, `n`, `in`) -* `a.mul(b)` - multiply (`i`, `n`, `in`) -* `a.sqr()` - square (`i`) -* `a.pow(b)` - raise `a` to the power of `b` -* `a.div(b)` - divide (`divn`, `idivn`) -* `a.mod(b)` - reduct (`u`, `n`) (but no `umodn`) -* `a.divRound(b)` - rounded division - -### Bit operations - -* `a.or(b)` - or (`i`, `u`, `iu`) -* `a.and(b)` - and (`i`, `u`, `iu`, `andln`) (NOTE: `andln` is going to be replaced - with `andn` in future) -* `a.xor(b)` - xor (`i`, `u`, `iu`) -* `a.setn(b)` - set specified bit to `1` -* `a.shln(b)` - shift left (`i`, `u`, `iu`) -* `a.shrn(b)` - shift right (`i`, `u`, `iu`) -* `a.testn(b)` - test if specified bit is set -* `a.maskn(b)` - clear bits with indexes higher or equal to `b` (`i`) -* `a.bincn(b)` - add `1 << b` to the number -* `a.notn(w)` - not (for the width specified by `w`) (`i`) - -### Reduction - -* `a.gcd(b)` - GCD -* `a.egcd(b)` - Extended GCD results (`{ a: ..., b: ..., gcd: ... }`) -* `a.invm(b)` - inverse `a` modulo `b` - -## Fast reduction - -When doing lots of reductions using the same modulo, it might be beneficial to -use some tricks: like [Montgomery multiplication][0], or using special algorithm -for [Mersenne Prime][1]. - -### Reduction context - -To enable this tricks one should create a reduction context: - -```js -var red = BN.red(num); -``` -where `num` is just a BN instance. - -Or: - -```js -var red = BN.red(primeName); -``` - -Where `primeName` is either of these [Mersenne Primes][1]: - -* `'k256'` -* `'p224'` -* `'p192'` -* `'p25519'` - -Or: - -```js -var red = BN.mont(num); -``` - -To reduce numbers with [Montgomery trick][0]. `.mont()` is generally faster than -`.red(num)`, but slower than `BN.red(primeName)`. - -### Converting numbers - -Before performing anything in reduction context - numbers should be converted -to it. Usually, this means that one should: - -* Convert inputs to reducted ones -* Operate on them in reduction context -* Convert outputs back from the reduction context - -Here is how one may convert numbers to `red`: - -```js -var redA = a.toRed(red); -``` -Where `red` is a reduction context created using instructions above - -Here is how to convert them back: - -```js -var a = redA.fromRed(); -``` - -### Red instructions - -Most of the instructions from the very start of this readme have their -counterparts in red context: - -* `a.redAdd(b)`, `a.redIAdd(b)` -* `a.redSub(b)`, `a.redISub(b)` -* `a.redShl(num)` -* `a.redMul(b)`, `a.redIMul(b)` -* `a.redSqr()`, `a.redISqr()` -* `a.redSqrt()` - square root modulo reduction context's prime -* `a.redInvm()` - modular inverse of the number -* `a.redNeg()` -* `a.redPow(b)` - modular exponentiation - -### Number Size - -Optimized for elliptic curves that work with 256-bit numbers. -There is no limitation on the size of the numbers. - -## LICENSE - -This software is licensed under the MIT License. - -Copyright Fedor Indutny, 2015. - -Permission is hereby granted, free of charge, to any person obtaining a -copy of this software and associated documentation files (the -"Software"), to deal in the Software without restriction, including -without limitation the rights to use, copy, modify, merge, publish, -distribute, sublicense, and/or sell copies of the Software, and to permit -persons to whom the Software is furnished to do so, subject to the -following conditions: - -The above copyright notice and this permission notice shall be included -in all copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS -OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF -MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN -NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, -DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR -OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE -USE OR OTHER DEALINGS IN THE SOFTWARE. - -[0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication -[1]: https://en.wikipedia.org/wiki/Mersenne_prime |