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\n\n> BigNum in pure javascript\n\n[](http://travis-ci.org/indutny/bn.js)\n\n## Install\n`npm install --save bn.js`\n\n## Usage\n\n```js\nconst BN = require('bn.js');\n\nvar a = new BN('dead', 16);\nvar b = new BN('101010', 2);\n\nvar res = a.add(b);\nconsole.log(res.toString(10)); // 57047\n```\n\n**Note**: decimals are not supported in this library.\n\n## Notation\n\n### Prefixes\n\nThere are several prefixes to instructions that affect the way the work. Here\nis the list of them in the order of appearance in the function name:\n\n* `i` - perform operation in-place, storing the result in the host object (on\n which the method was invoked). Might be used to avoid number allocation costs\n* `u` - unsigned, ignore the sign of operands when performing operation, or\n always return positive value. Second case applies to reduction operations\n like `mod()`. In such cases if the result will be negative - modulo will be\n added to the result to make it positive\n\n### Postfixes\n\nThe only available postfix at the moment is:\n\n* `n` - which means that the argument of the function must be a plain JavaScript\n Number. Decimals are not supported.\n\n### Examples\n\n* `a.iadd(b)` - perform addition on `a` and `b`, storing the result in `a`\n* `a.umod(b)` - reduce `a` modulo `b`, returning positive value\n* `a.iushln(13)` - shift bits of `a` left by 13\n\n## Instructions\n\nPrefixes/postfixes are put in parens at the of the line. `endian` - could be\neither `le` (little-endian) or `be` (big-endian).\n\n### Utilities\n\n* `a.clone()` - clone number\n* `a.toString(base, length)` - convert to base-string and pad with zeroes\n* `a.toNumber()` - convert to Javascript Number (limited to 53 bits)\n* `a.toJSON()` - convert to JSON compatible hex string (alias of `toString(16)`)\n* `a.toArray(endian, length)` - convert to byte `Array`, and optionally zero\n pad to length, throwing if already exceeding\n* `a.toArrayLike(type, endian, length)` - convert to an instance of `type`,\n which must behave like an `Array`\n* `a.toBuffer(endian, length)` - convert to Node.js Buffer (if available). For\n compatibility with browserify and similar tools, use this instead:\n `a.toArrayLike(Buffer, endian, length)`\n* `a.bitLength()` - get number of bits occupied\n* `a.zeroBits()` - return number of less-significant consequent zero bits\n (example: `1010000` has 4 zero bits)\n* `a.byteLength()` - return number of bytes occupied\n* `a.isNeg()` - true if the number is negative\n* `a.isEven()` - no comments\n* `a.isOdd()` - no comments\n* `a.isZero()` - no comments\n* `a.cmp(b)` - compare numbers and return `-1` (a `<` b), `0` (a `==` b), or `1` (a `>` b)\n depending on the comparison result (`ucmp`, `cmpn`)\n* `a.lt(b)` - `a` less than `b` (`n`)\n* `a.lte(b)` - `a` less than or equals `b` (`n`)\n* `a.gt(b)` - `a` greater than `b` (`n`)\n* `a.gte(b)` - `a` greater than or equals `b` (`n`)\n* `a.eq(b)` - `a` equals `b` (`n`)\n* `a.toTwos(width)` - convert to two's complement representation, where `width` is bit width\n* `a.fromTwos(width)` - convert from two's complement representation, where `width` is the bit width\n* `BN.isBN(object)` - returns true if the supplied `object` is a BN.js instance\n\n### Arithmetics\n\n* `a.neg()` - negate sign (`i`)\n* `a.abs()` - absolute value (`i`)\n* `a.add(b)` - addition (`i`, `n`, `in`)\n* `a.sub(b)` - subtraction (`i`, `n`, `in`)\n* `a.mul(b)` - multiply (`i`, `n`, `in`)\n* `a.sqr()` - square (`i`)\n* `a.pow(b)` - raise `a` to the power of `b`\n* `a.div(b)` - divide (`divn`, `idivn`)\n* `a.mod(b)` - reduct (`u`, `n`) (but no `umodn`)\n* `a.divRound(b)` - rounded division\n\n### Bit operations\n\n* `a.or(b)` - or (`i`, `u`, `iu`)\n* `a.and(b)` - and (`i`, `u`, `iu`, `andln`) (NOTE: `andln` is going to be replaced\n with `andn` in future)\n* `a.xor(b)` - xor (`i`, `u`, `iu`)\n* `a.setn(b)` - set specified bit to `1`\n* `a.shln(b)` - shift left (`i`, `u`, `iu`)\n* `a.shrn(b)` - shift right (`i`, `u`, `iu`)\n* `a.testn(b)` - test if specified bit is set\n* `a.maskn(b)` - clear bits with indexes higher or equal to `b` (`i`)\n* `a.bincn(b)` - add `1 << b` to the number\n* `a.notn(w)` - not (for the width specified by `w`) (`i`)\n\n### Reduction\n\n* `a.gcd(b)` - GCD\n* `a.egcd(b)` - Extended GCD results (`{ a: ..., b: ..., gcd: ... }`)\n* `a.invm(b)` - inverse `a` modulo `b`\n\n## Fast reduction\n\nWhen doing lots of reductions using the same modulo, it might be beneficial to\nuse some tricks: like [Montgomery multiplication][0], or using special algorithm\nfor [Mersenne Prime][1].\n\n### Reduction context\n\nTo enable this tricks one should create a reduction context:\n\n```js\nvar red = BN.red(num);\n```\nwhere `num` is just a BN instance.\n\nOr:\n\n```js\nvar red = BN.red(primeName);\n```\n\nWhere `primeName` is either of these [Mersenne Primes][1]:\n\n* `'k256'`\n* `'p224'`\n* `'p192'`\n* `'p25519'`\n\nOr:\n\n```js\nvar red = BN.mont(num);\n```\n\nTo reduce numbers with [Montgomery trick][0]. `.mont()` is generally faster than\n`.red(num)`, but slower than `BN.red(primeName)`.\n\n### Converting numbers\n\nBefore performing anything in reduction context - numbers should be converted\nto it. Usually, this means that one should:\n\n* Convert inputs to reducted ones\n* Operate on them in reduction context\n* Convert outputs back from the reduction context\n\nHere is how one may convert numbers to `red`:\n\n```js\nvar redA = a.toRed(red);\n```\nWhere `red` is a reduction context created using instructions above\n\nHere is how to convert them back:\n\n```js\nvar a = redA.fromRed();\n```\n\n### Red instructions\n\nMost of the instructions from the very start of this readme have their\ncounterparts in red context:\n\n* `a.redAdd(b)`, `a.redIAdd(b)`\n* `a.redSub(b)`, `a.redISub(b)`\n* `a.redShl(num)`\n* `a.redMul(b)`, `a.redIMul(b)`\n* `a.redSqr()`, `a.redISqr()`\n* `a.redSqrt()` - square root modulo reduction context's prime\n* `a.redInvm()` - modular inverse of the number\n* `a.redNeg()`\n* `a.redPow(b)` - modular exponentiation\n\n## LICENSE\n\nThis software is licensed under the MIT License.\n\n[0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication\n[1]: 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