bignum

bignum
======


Arbitrary precision integral arithmetic for Node.js using
OpenSSL.

This library is based on
node-bigint by
substack, but instead of using libgmp,
it uses the builtin bignum functionality provided by OpenSSL. The
advantage is that OpenSSL is already part of Node.js, so this
library does not add any external dependency whatsoever.

BigInt
======

JavaScript now has a BigInt object. If you are using Node 10.4 or newer, you should use or migrate to BigInt.

differences
===========

When switching from node-bigint to node-bignum, please be aware of
these differences:

- Bignum rounds towards zero for integer divisions, e.g. 10 / -3 = -3, whereas bigint
rounds towards negative infinity, e.g. 10 / -3 = -4.
- nextPrime() is not supported.
- sqrt() and root() are not supported.

(Patches for the missing functionality are welcome.)

example
=======

simple.js
---------

``js
var bignum = require('bignum');

var b = bignum('782910138827292261791972728324982')
.sub('182373273283402171237474774728373')
.div(8)
;
console.log(b);
`

*
$ node simple.js


perfect.js
----------

Generate the perfect numbers:

`js
// If 2n-1 is prime, then (2n-1) 2*(n-1) is perfect.
var bignum = require('bignum');

for (var n = 0; n < 100; n++) {
var p = bignum.pow(2, n).sub(1);
if (p.probPrime(50)) {
var perfect = p.mul(bignum.pow(2, n - 1));
console.log(perfect.toString());
}
}
`

*

6
28
496
8128
33550336
8589869056
137438691328
2305843008139952128
2658455991569831744654692615953842176
191561942608236107294793378084303638130997321548169216

methods[0]
==========

bignum(n, base=10)
------------------

Create a new bignum from n and a base. n can be a string, integer, or
another bignum.

If you pass in a string you can set the base that string is encoded in.

.toString(base=10)
------------------

Print out the bignum instance in the requested base as a string.

bignum.fromBuffer(buf, opts)
----------------------------

Create a new bignum from a Buffer.

The default options are:

`js
{
endian : 'big',
size : 1, // number of bytes in each word
}
`

Note that endian doesn't matter when size = 1. If you wish to reverse the entire buffer byte by byte, pass size: 'auto'.

bignum.prime(bits, safe=true)
-----------------------------

Generate a probable prime of length bits. If safe is true, it will be a "safe" prime of the form p=2p'+1 where p' is also prime.

bignum.isBigNum(num)
-----------------------------

Return true if num is identified as a bignum instance. Otherwise, return false.

methods[1]
==========

For all of the instance methods below you can write either

`js
bignum.method(x, y, z)
`

or if x is a bignum instance

`js
x.method(y, z)
`

.toNumber()
-----------

Turn a bignum into a Number. If the bignum is too big you'll lose
precision or you'll get ±Infinity.

.toBuffer(opts)
-------------

Return a new Buffer with the data from the bignum.

The default options are:

`js
{
endian : 'big',
size : 1, // number of bytes in each word
}
`

Note that endian doesn't matter when size = 1. If you wish to reverse the entire buffer byte by byte, pass size: 'auto'.

.add(n)
-------

Return a new bignum containing the instance value plus n.

.sub(n)
-------

Return a new bignum containing the instance value minus n.

.mul(n)
-------

Return a new bignum containing the instance value multiplied by n.

.div(n)
-------

Return a new bignum containing the instance value integrally divided by n.

.abs()
------

Return a new bignum with the absolute value of the instance.

.neg()
------

Return a new bignum with the negative of the instance value.

.cmp(n)
-------

Compare the instance value to n. Return a positive integer if > n, a
negative integer if < n, and 0 if == n.

.gt(n)
------

Return a boolean: whether the instance value is greater than n (> n).

.ge(n)
------

Return a boolean: whether the instance value is greater than or equal to n
(>= n).

.eq(n)
------

Return a boolean: whether the instance value is equal to n (== n).

.lt(n)
------

Return a boolean: whether the instance value is less than n (< n).

.le(n)
------

Return a boolean: whether the instance value is less than or equal to n
(<= n).

.and(n)
-------

Return a new bignum with the instance value bitwise AND (&)-ed with n.

.or(n)
------

Return a new bignum with the instance value bitwise inclusive-OR (|)-ed with
n.

.xor(n)
-------

Return a new bignum with the instance value bitwise exclusive-OR (^)-ed with
n.

.mod(n)
-------

Return a new bignum with the instance value modulo n.

m.
.pow(n)
-------

Return a new bignum with the instance value raised to the nth power.

.powm(n, m)
-----------

Return a new bignum with the instance value raised to the nth power modulo
m.

.invertm(m)
-----------

Compute the multiplicative inverse modulo m.

.rand()
-------
.rand(upperBound)
-----------------

If upperBound is supplied, return a random bignum between the instance value
and upperBound - 1, inclusive.

Otherwise, return a random bignum between 0 and the instance value - 1,
inclusive.

.probPrime()
------------

Return whether the bignum is:

* certainly prime (true)
* probably prime ('maybe')
* certainly composite (false)

using BN_is_prime_ex.

.sqrt()
-------

Return a new bignum that is the square root. This truncates.

.root(n)
-------

Return a new bignum that is the nth root. This truncates.

.shiftLeft(n)
-------------

Return a new bignum that is the 2^n multiple. Equivalent of the <<
operator.

.shiftRight(n)
--------------

Return a new bignum of the value integer divided by
2^n. Equivalent of the >> operator.

.gcd(n)
-------

Return the greatest common divisor of the current bignum with n as a new
bignum.

.jacobi(n)
-------

Return the Jacobi symbol (or Legendre symbol if n is prime) of the current
bignum (= a) over n. Note that n must be odd and >= 3. 0 <= a < n.

Returns -1 or 1 as an int (NOT a bignum). Throws an error on failure.

.bitLength()
------------

Return the number of bits used to represent the current bignum`.

install
=======

To compile the package, your system needs to be set up for building Node.js
modules.

You can install node-bignum with npm:

npm install bignum

develop
=======

You can clone the git repo and compile with

git clone git://github.com/justmoon/node-bignum.git
cd node-bignum
npm install

Run the tests with

npm test