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justmoon
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Description

Big integers for Node.js using OpenSSL

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bignum

Build Status

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

var bignum = require('bignum');

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


$ node simple.js

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:

{
    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

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:

{
    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
n
th power.

.powm(n, m)

Return a new

bignum
with the instance value raised to the
n
th 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 BNisprime_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

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