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README.md
BigNum in pure javascript
Install
npm install --save bn.js
Usage
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 costsu
- unsigned, ignore the sign of operands when performing operation, or always return positive value. Second case applies to reduction operations likemod()
. 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 ona
andb
, storing the result ina
a.umod(b)
- reducea
modulob
, returning positive valuea.iushln(13)
- shift bits ofa
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 numbera.toString(base, length)
- convert to base-string and pad with zeroesa.toNumber()
- convert to Javascript Number (limited to 53 bits)a.toJSON()
- convert to JSON compatible hex string (alias oftoString(16)
)a.toArray(endian, length)
- convert to byteArray
, and optionally zero pad to length, throwing if already exceedinga.toArrayLike(type, endian, length)
- convert to an instance oftype
, which must behave like anArray
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 occupieda.zeroBits()
- return number of less-significant consequent zero bits (example:1010000
has 4 zero bits)a.byteLength()
- return number of bytes occupieda.isNeg()
- true if the number is negativea.isEven()
- no commentsa.isOdd()
- no commentsa.isZero()
- no commentsa.cmp(b)
- compare numbers and return-1
(a<
b),0
(a==
b), or1
(a>
b) depending on the comparison result (ucmp
,cmpn
)a.lt(b)
-a
less thanb
(n
)a.lte(b)
-a
less than or equalsb
(n
)a.gt(b)
-a
greater thanb
(n
)a.gte(b)
-a
greater than or equalsb
(n
)a.eq(b)
-a
equalsb
(n
)a.toTwos(width)
- convert to two's complement representation, wherewidth
is bit widtha.fromTwos(width)
- convert from two's complement representation, wherewidth
is the bit widthBN.isBN(object)
- returns true if the suppliedobject
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)
- raisea
to the power ofb
a.div(b)
- divide (divn
,idivn
)a.mod(b)
- reduct (u
,n
) (but noumodn
)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 withandn
in future)a.xor(b)
- xor (i
,u
,iu
)a.setn(b)
- set specified bit to1
a.shln(b)
- shift left (i
,u
,iu
)a.shrn(b)
- shift right (i
,u
,iu
)a.testn(b)
- test if specified bit is seta.maskn(b)
- clear bits with indexes higher or equal tob
(i
)a.bincn(b)
- add1 << b
to the numbera.notn(w)
- not (for the width specified byw
) (i
)
Reduction
a.gcd(b)
- GCDa.egcd(b)
- Extended GCD results ({ a: ..., b: ..., gcd: ... }
)a.invm(b)
- inversea
modulob
Fast reduction
When doing lots of reductions using the same modulo, it might be beneficial to use some tricks: like Montgomery multiplication, or using special algorithm for Mersenne Prime.
Reduction context
To enable this tricks one should create a reduction context:
var red = BN.red(num);
where num
is just a BN instance.
Or:
var red = BN.red(primeName);
Where primeName
is either of these Mersenne Primes:
'k256'
'p224'
'p192'
'p25519'
Or:
var red = BN.mont(num);
To reduce numbers with Montgomery trick. .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
:
var redA = a.toRed(red);
Where red
is a reduction context created using instructions above
Here is how to convert them back:
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 primea.redInvm()
- modular inverse of the numbera.redNeg()
a.redPow(b)
- modular exponentiation
LICENSE
This software is licensed under the MIT License.