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 from OpenSSL. The advantage is that OpenSSL is already a soft dependency of Node.js and therefore often already installed on systems with Node.js.

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.
• Boolean operations (and, or, xor) are not supported.

example

simple.js

var bignum = require('bignum');

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

---

$ node simple.js
<Bignum 75067108192986261319312244199576>

perfect.js

Generate the perfect numbers:

// If 2**n-1 is prime, then (2**n-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: { order : 'forward', // low-to-high indexed word ordering endian : 'big', size : 1, // number of bytes in each word }

Note that endian doesn't matter when size = 1.

methods[1]

For all of the instance methods below you can write either

bignum.method(x, y, z)

or if x is a bignum instance``

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: { order : 'forward', // low-to-high indexed word ordering endian : 'big', size : 1, // number of bytes in each word }

Note that endian doesn't matter when size = 1.

.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 mpz_probab_prime.

.nextPrime()

Return the next prime greater than this using mpz_nextprime.

.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.

install

You'll need the libssl (OpenSSL) source to compile this package. If you compiled Node.js using the official instructions, you'll already have it. Otherwise install it using the instructions below.

Under Debian-based systems,

sudo aptitude install libssl3-dev

On a Mac with Homebrew,

brew install openssl

And then install with npm:

npm install bignum