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+# <img src="./logo.png" alt="bn.js" width="160" height="160" />
+
+> BigNum in pure javascript
+
+[![Build Status](https://secure.travis-ci.org/indutny/bn.js.png)](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