Mersenne Twister

A 32-bit Mersenne Twister pseudorandom number generator.

Usage

var mt19937 = require( '@stdlib/random/base/mt19937' );

mt19937()

Returns a pseudorandom integer on the interval [1, 4294967295].

var r = mt19937();
// returns <number>

mt19937.normalized()

Returns a pseudorandom number on the interval [0,1) with 53-bit precision.

var r = mt19937.normalized();
// returns <number>

mt19937.factory( [options] )

Returns a 32-bit Mersenne Twister pseudorandom number generator.

var rand = mt19937.factory();

The function accepts the following options:

  • seed: pseudorandom number generator seed.
  • state: a Uint32Array containing pseudorandom number generator state. If provided, the function ignores the seed option.
  • copy: boolean indicating whether to copy a provided pseudorandom number generator state. Setting this option to false allows sharing state between two or more pseudorandom number generators. Setting this option to true ensures that a returned generator has exclusive control over its internal state. Default: true.

By default, a random integer is used to seed the returned generator. To seed the generator, provide either an integer on the interval [1, 4294967295]

var rand = mt19937.factory({
    'seed': 1234
});

var r = rand();
// returns 822569775

or, for arbitrary length seeds, an array-like object containing unsigned 32-bit integers

var Uint32Array = require( '@stdlib/array/uint32' );

var rand = mt19937.factory({
    'seed': new Uint32Array( [ 291, 564, 837, 1110 ] )
});

var r = rand();
// returns 1067595299

To return a generator having a specific initial state, set the generator state option.

var rand;
var bool;
var r;
var i;

// Generate pseudorandom numbers, thus progressing the generator state:
for ( i = 0; i < 1000; i++ ) {
    r = mt19937();
}

// Create a new MT19937 PRNG initialized to the current state of `mt19937`:
rand = mt19937.factory({
    'state': mt19937.state
});

// Test that the generated pseudorandom numbers are the same:
bool = ( rand() === mt19937() );
// returns true

mt19937.NAME

The generator name.

var str = mt19937.NAME;
// returns 'mt19937'

mt19937.MIN

Minimum possible value.

var min = mt19937.MIN;
// returns 1

mt19937.MAX

Maximum possible value.

var max = mt19937.MAX;
// returns 4294967295

mt19937.seed

The value used to seed mt19937().

var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
    r = mt19937();
}

// Generate the same pseudorandom values...
rand = mt19937.factory({
    'seed': mt19937.seed
});
for ( i = 0; i < 100; i++ ) {
    r = rand();
}

mt19937.seedLength

Length of generator seed.

var len = mt19937.seedLength;
// returns <number>

mt19937.state

Writable property for getting and setting the generator state.

var r = mt19937();
// returns <number>

r = mt19937();
// returns <number>

// ...

// Get a copy of the current state:
var state = mt19937.state;
// returns <Uint32Array>

r = mt19937();
// returns <number>

r = mt19937();
// returns <number>

// Reset the state:
mt19937.state = state;

// Replay the last two pseudorandom numbers:
r = mt19937();
// returns <number>

r = mt19937();
// returns <number>

// ...

mt19937.stateLength

Length of generator state.

var len = mt19937.stateLength;
// returns <number>

mt19937.byteLength

Size (in bytes) of generator state.

var sz = mt19937.byteLength;
// returns <number>

mt19937.toJSON()

Serializes the pseudorandom number generator as a JSON object.

var o = mt19937.toJSON();
// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }

Notes

  • Mersenne Twister is not a cryptographically secure PRNG, as the PRNG is based on a linear recursion. Any pseudorandom number sequence generated by a linear recursion is insecure, due to the fact that one can predict future generated outputs by observing a sufficiently long subsequence of generated values.
  • Compared to other PRNGs, Mersenne Twister has a large state size (~2.5kB). Because of the large state size, beware of increased memory consumption when using the factory() method to create many Mersenne Twister PRNGs. When appropriate (e.g., when external state mutation is not a concern), consider sharing PRNG state.
  • A seed array of length 1 is considered equivalent to an integer seed equal to the lone seed array element and vice versa.
  • If PRNG state is "shared" (meaning a state array was provided during PRNG creation and not copied) and one sets the generator state to a state array having a different length, the PRNG does not update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for each relevant PRNG must be explicitly set.
  • If PRNG state is "shared" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).
  • The PRNG has a period of 2^19937 - 1.

Examples

var mt19937 = require( '@stdlib/random/base/mt19937' );

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
    console.log( mt19937() );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = mt19937.factory({
    'seed': seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = mt19937.factory({
    'seed': mt19937.seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

References

  • Matsumoto, Makoto, and Takuji Nishimura. 1998. "Mersenne Twister: A 623-dimensionally Equidistributed Uniform Pseudo-random Number Generator." ACM Transactions on Modeling and Computer Simulation 8 (1). New York, NY, USA: ACM: 3–30. doi:10.1145/272991.272995.
  • Harase, Shin. 2017. "Conversion of Mersenne Twister to double-precision floating-point numbers." ArXiv abs/1708.06018 (September). https://arxiv.org/abs/1708.06018.