time-to-botec/squiggle/node_modules/@stdlib/random/iter/mt19937/README.md

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# MT19937

> Create an iterator for a 32-bit [Mersenne Twister][mersenne-twister] pseudorandom number generator.

<section class="usage">

## Usage

```javascript
var iterator = require( '@stdlib/random/iter/mt19937' );
```

#### iterator( \[options] )

Returns an iterator for generating pseudorandom numbers via a 32-bit [Mersenne Twister][mersenne-twister] pseudorandom number generator.

```javascript
var it = iterator();
// returns <Object>

var r = it.next().value;
// returns <number>

r = it.next().value;
// returns <number>

r = it.next().value;
// returns <number>

// ...
```

The function accepts the following `options`:

-   **normalized**: `boolean` indicating whether to return pseudorandom numbers on the interval `[0,1)`.
-   **seed**: pseudorandom number generator seed.
-   **state**: a [`Uint32Array`][@stdlib/array/uint32] 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 iterator has exclusive control over its internal pseudorandom number generator state. Default: `true`.
-   **iter**: number of iterations.

To return pseudorandom numbers on the interval `[0,1)`, set the `normalized` option.

```javascript
var it = iterator({
    'normalized': true
});

var r = it.next().value;
// returns <number>
```

To return an iterator having a specific initial state, set the iterator `state` option.

```javascript
var bool;
var it1;
var it2;
var r;
var i;

it1 = iterator();

// Generate pseudorandom numbers, thus progressing the generator state:
for ( i = 0; i < 1000; i++ ) {
    r = it1.next().value;
}

// Create a new iterator initialized to the current state of `it1`:
it2 = iterator({
    'state': it1.state
});

// Test that the generated pseudorandom numbers are the same:
bool = ( it1.next().value === it2.next().value );
// returns true
```

To seed the iterator, set the `seed` option.

```javascript
var it = iterator({
    'seed': 12345
});

var r = it.next().value;
// returns 3992670690

it = iterator({
    'seed': 12345
});

r = it.next().value;
// returns 3992670690
```

To limit the number of iterations, set the `iter` option.

```javascript
var it = iterator({
    'iter': 2
});

var r = it.next().value;
// returns <number>

r = it.next().value;
// returns <number>

r = it.next().done;
// returns true
```

The returned iterator protocol-compliant object has the following properties:

-   **next**: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a `value` property and a `done` property having a `boolean` value indicating whether the iterator is finished.
-   **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.
-   **seed**: pseudorandom number generator seed.
-   **seedLength**: length of generator seed.
-   **state**: writable property for getting and setting the generator state.
-   **stateLength**: length of generator state.
-   **byteLength**: size (in bytes) of generator state.

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If an environment supports `Symbol.iterator`, the returned iterator is iterable.
-   [Mersenne Twister][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.
-   The PRNG has a period of `2^19937 - 1`.
-   If PRNG state is "shared" (meaning a state array was provided during iterator creation and **not** copied) and one sets the underlying generator state to a state array having a different length, the iterator does **not** update the existing shared state and, instead, points to the newly provided state array. In order to synchronize the output of the underlying generator according to the new shared state array, the state array for **each** relevant iterator and/or PRNG must be **explicitly** set.
-   If PRNG state is "shared" and one sets the underlying generator state to a state array of the same length, the PRNG state is updated (along with the state of all other iterator and/or PRNGs sharing the PRNG's state array).

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var iterator = require( '@stdlib/random/iter/mt19937' );

var it;
var r;

// Create a seeded iterator for generating pseudorandom numbers:
it = iterator({
    'seed': 1234,
    'iter': 10
});

// Perform manual iteration...
while ( true ) {
    r = it.next();
    if ( r.done ) {
        break;
    }
    console.log( r.value );
}
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## 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][@matsumoto:1998a].
-   Harase, Shin. 2017. "Conversion of Mersenne Twister to double-precision floating-point numbers." _ArXiv_ abs/1708.06018 (September). <https://arxiv.org/abs/1708.06018>.

</section>

<!-- /.references -->

<section class="links">

[mersenne-twister]: https://en.wikipedia.org/wiki/Mersenne_Twister

[@matsumoto:1998a]: https://doi.org/10.1145/272991.272995

[@stdlib/array/uint32]: https://www.npmjs.com/package/@stdlib/array-uint32

</section>

<!-- /.links -->