mpzjs 0.7.1

Arbitrary precision integral arithmetic for node.js. Based on node-bigint

This library wraps around libgmp's integer functions to perform infinite-precision arithmetic. It can be used with worker threads.

mpzjs is several times faster than BigInt.

Install

You'll need the libgmp to work this package. Under Debian-based systems,

sudo apt-get install libgmp-dev

On a Mac with Homebrew,

brew install gmp

And then install with npm:

npm install mpzjs

Example

simple.js

const MPZ = require('mpzjs');

const n = MPZ('782910138827292261791972728324982');
MPZ.sub(n, n, '182373273283402171237474774728373');
MPZ.div(n, n, 8);

console.log(n);

const b = MPZ('782910138827292261791972728324982')
    .sub('182373273283402171237474774728373')
    .div(8);

console.log(b);

---

$ node simple.js
<MPZ 75067108192986261319312244199576>
<MPZ 75067108192986261319312244199576>

perfect.js

Generate the perfect numbers:

// If 2**n-1 is prime, then (2**n-1) * 2**(n-1) is perfect.
const MPZ = require('mpzjs');

for (let n = 0; n < 100; n++) {
    const p = MPZ(2).pow(n).sub(1);
    if (p.probPrime(50)) {
        const perfect = p.mul(MPZ(2).pow(n - 1));
        console.log(perfect.toString());
    }
}

---

6
28
496
8128
33550336
8589869056
137438691328
2305843008139952128
2658455991569831744654692615953842176
191561942608236107294793378084303638130997321548169216

Limitations

It doesn't work in Windows now.

API

There are two sets of methods

Instance methods that create new MPZ.

const num = value.method(operand);

for example

const value = MPZ(7);
const result = value.mul(6);

And static methods that save the result to the specified variable.

MPZ.method(result, value, operand);

for example

const result = MPZ();
MPZ.mul(result, 7, 6);

Static methods are noticeably faster.

MPZ(num, base=10)

Create a new MPZ from num and a base. num can be a string, number, BigInt, empty or another MPZ.

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

value.toString(base=10)

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

value.toNumber()

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

value.toBigInt(), value.toJSON()

Convert MPZ to the specified format

value.valueOf()

Convert MPZ to BigInt

MPZ.fromBuffer(buf, opts)

Create a new MPZ 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.

value.toBuffer(opts)

Return a new Buffer with the data from the MPZ.

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.

value.set(num), MPZ.set(value, num)

Assigns num to value.

result = value.add(num), MPZ.add(result, value, num)

Set result to value plus num.

result = value.sub(num), MPZ.sub(result, value, num)

Set result to value minus num.

result = value.mul(num), MPZ.mul(result, value, num)

Set result to value multiplied by num.

result = value.div(num), MPZ.div(result, value, num)

Set result to value integrally divided by num.

result = value.mod(num), MPZ.mod(result, value, num)

Set result to value modulo num.

MPZ.addMul(result, value1, value2)

Set result to result plus value1 times value2.

MPZ.subMul(result, value1, value2)

Set result to result minus value1 times value2.

result = value.and(num), MPZ.and(result, value, num)

Set result to value bitwise AND (&)-ed with num.

result = value.or(num), MPZ.or(result, value, num)

Set result to value bitwise inclusive-OR (|)-ed with num.

result = value.xor(num), MPZ.xor(result, value, num)

Set result to value bitwise exclusive-OR (^)-ed with num.

result = value.not(), MPZ.not(result, value)

Set result to value bitwise NOT (~)ed.

result = value.shiftLeft(num), MPZ.shiftLeft(result, value, num)

Set result to value multiplied by 2^num. Equivalent of the << operator.

result = value.shiftRight(num), MPZ.shiftRight(result, value, num)

Set result to value integrally divided by 2^num. Equivalent of the >> operator.

result = value.abs(), MPZ.abs(result, value)

Set result to the absolute value of value.

result = value.neg(), MPZ.neg(result, value)

Set result to the negative of value.

result = value.sqrt(), MPZ.sqrt(result, value)

Set result to square root of value. This truncates.

result = value.root(nth), MPZ.root(result, value, nth)

Set result to nth root of value. This truncates.

result = value.pow(exp), MPZ.pow(result, value, exp)

Set result to value raised to the exp power.

result = value.powm(exp, mod), MPZ.powm(result, value, exp, mod)

Set result to value raised to the exp power modulo mod.

value.cmp(num)

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

value.gt(num)

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

value.ge(num)

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

value.eq(num)

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

value.lt(num)

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

value.le(num)

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

result = value.rand(upperBound), MPZ.rand(result, lowerBound, upperBound), MPZ.rand(result, upperBound)

If upperBound is supplied, set resultto a random MPZ between the value (lowerBound) and upperBound - 1, inclusive.

Otherwise, set resultto a random MPZ between 0 and the value - 1, inclusive.

value.probPrime()

Return whether the value is:

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

using mpz_probab_prime.

result = value.nextPrime(), MPZ.nextPrime(result, value)

Set result to the next prime greater than value using mpz_nextprime.

result = value.invert(mod), MPZ.invert(result, value, mod)

Compute the multiplicative inverse modulo mod.

result = value.gcd(num), MPZ.gcd(result, value, num)

Set result to the greatest common divisor of the value with num.

value.bitLength()

Return the number of bits used to represent the current MPZ as a javascript Number.

License

MIT or LGPL-3 license.