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# <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 The only available postfix at the moment is: * `n` - which means that the argument of the function must be a plain JavaScript Number. 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 ### 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 ## LICENSE This software is licensed under the MIT License. [0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication [1]: https://en.wikipedia.org/wiki/Mersenne_prime