# MINSTD
> A linear congruential pseudorandom number generator ([LCG][lcg]) based on Park and Miller.
## Usage
```javascript
var minstd = require( '@stdlib/random/base/minstd' );
```
#### minstd()
Returns a pseudorandom integer on the interval `[1, 2147483646]`.
```javascript
var r = minstd();
// returns
```
#### minstd.normalized()
Returns a pseudorandom number on the interval `[0,1)`.
```javascript
var r = minstd.normalized();
// returns
```
#### minstd.factory( \[options] )
Returns a linear congruential pseudorandom number generator ([LCG][lcg]).
```javascript
var rand = minstd.factory();
```
The function accepts the following `options`:
- **seed**: pseudorandom number generator seed.
- **state**: an [`Int32Array`][@stdlib/array/int32] 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, 2147483646]`
```javascript
var rand = minstd.factory({
'seed': 1234
});
var r = rand();
// returns 20739838
```
or, for arbitrary length seeds, an array-like `object` containing signed 32-bit integers
```javascript
var Int32Array = require( '@stdlib/array/int32' );
var rand = minstd.factory({
'seed': new Int32Array( [ 1234 ] )
});
var r = rand();
// returns 20739838
```
To return a generator having a specific initial state, set the generator `state` option.
```javascript
var rand;
var bool;
var r;
var i;
// Generate pseudorandom numbers, thus progressing the generator state:
for ( i = 0; i < 1000; i++ ) {
r = minstd();
}
// Create a new PRNG initialized to the current state of `minstd`:
rand = minstd.factory({
'state': minstd.state
});
// Test that the generated pseudorandom numbers are the same:
bool = ( rand() === minstd() );
// returns true
```
#### minstd.NAME
The generator name.
```javascript
var str = minstd.NAME;
// returns 'minstd'
```
#### minstd.MIN
Minimum possible value.
```javascript
var min = minstd.MIN;
// returns 1
```
#### minstd.MAX
Maximum possible value.
```javascript
var max = minstd.MAX;
// returns 2147483646
```
#### minstd.seed
The value used to seed `minstd()`.
```javascript
var rand;
var r;
var i;
// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
r = minstd();
}
// Generate the same pseudorandom values...
rand = minstd.factory({
'seed': minstd.seed
});
for ( i = 0; i < 100; i++ ) {
r = rand();
}
```
#### minstd.seedLength
Length of generator seed.
```javascript
var len = minstd.seedLength;
// returns
```
#### minstd.state
Writable property for getting and setting the generator state.
```javascript
var r = minstd();
// returns
r = minstd();
// returns
// ...
// Get the current state:
var state = minstd.state;
// returns
r = minstd();
// returns
r = minstd();
// returns
// Reset the state:
minstd.state = state;
// Replay the last two pseudorandom numbers:
r = minstd();
// returns
r = minstd();
// returns
// ...
```
#### minstd.stateLength
Length of generator state.
```javascript
var len = minstd.stateLength;
// returns
```
#### minstd.byteLength
Size (in bytes) of generator state.
```javascript
var sz = minstd.byteLength;
// returns
```
#### minstd.toJSON()
Serializes the pseudorandom number generator as a JSON object.
```javascript
var o = minstd.toJSON();
// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }
```
## Notes
- The generator has a period of approximately `2.1e9` (see [Numerical Recipes in C, 2nd Edition](#references), p. 279).
- An [LCG][lcg] is fast and uses little memory. On the other hand, because the generator is a simple [linear congruential generator][lcg], the generator has recognized shortcomings. By today's PRNG standards, the generator's period is relatively short. More importantly, the "randomness quality" of the generator's output is lacking. These defects make the generator unsuitable, for example, in Monte Carlo simulations and in cryptographic applications. For more on the advantages and disadvantages of [LCGs][lcg], see [Wikipedia][pros-cons].
- 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).
## Examples
```javascript
var minstd = require( '@stdlib/random/base/minstd' );
var seed;
var rand;
var i;
// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
console.log( minstd() );
}
// Create a new pseudorandom number generator...
seed = 1234;
rand = minstd.factory({
'seed': seed
});
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}
// Create another pseudorandom number generator using a previous seed...
rand = minstd.factory({
'seed': minstd.seed
});
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}
```
* * *
## References
- Park, S. K., and K. W. Miller. 1988. "Random Number Generators: Good Ones Are Hard to Find." _Communications of the ACM_ 31 (10). New York, NY, USA: ACM: 1192–1201. doi:[10.1145/63039.63042][@park:1988].
- Press, William H., Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. 1992. _Numerical Recipes in C: The Art of Scientific Computing, Second Edition_. Cambridge University Press.
[lcg]: https://en.wikipedia.org/wiki/Linear_congruential_generator
[pros-cons]: http://en.wikipedia.org/wiki/Linear_congruential_generator#Advantages_and_disadvantages_of_LCGs
[@park:1988]: http://dx.doi.org/10.1145/63039.63042
[@stdlib/array/int32]: https://www.npmjs.com/package/@stdlib/array-int32