Usage

`javascript
var cauchy = require( '@stdlib/random-base-cauchy' );
`

#### cauchy( x0, gamma )

Returns a pseudorandom number drawn from a [Cauchy][cauchy] distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).

`javascript
var r = cauchy( 2.0, 5.0 );
// returns
`

If x0 or gamma is NaN or gamma <= 0, the function returns NaN.

`javascript
var r = cauchy( 2.0, -2.0 );
// returns NaN

r = cauchy( NaN, 5.0 );
// returns NaN

r = cauchy( 2.0, NaN );
// returns NaN
`

#### cauchy.factory( \[x0, gamma, ]\[options] )

Returns a pseudorandom number generator (PRNG) for generating pseudorandom numbers drawn from a [Cauchy][cauchy] distribution.

`javascript
var rand = cauchy.factory();

var r = rand( 0.0, 1.5 );
// returns
`

If provided x0 and gamma, the returned generator returns random variates from the specified distribution.

`javascript
// Draw from Cauchy( 0.0, 1.5 ) distribution:
var rand = cauchy.factory( 0.0, 1.5 );

var r = rand();
// returns

r = rand();
// returns
`

If not provided x0 and gamma, the returned generator requires that both parameters be provided at each invocation.

`javascript
var rand = cauchy.factory();

var r = rand( 0.0, 1.0 );
// returns

r = rand( -2.0, 2.0 );
// returns
`

The function accepts the following options:

- prng: pseudorandom number generator for generating uniformly distributed pseudorandom numbers on the interval [0,1). If provided, the function ignores both the state and seed options. In order to seed the returned pseudorandom number generator, one must seed the provided prng (assuming the provided prng is seedable).
- 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 generator has exclusive control over its internal state. Default: true.

To use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the prng option.

`javascript
var minstd = require( '@stdlib/random-base-minstd' );

var rand = cauchy.factory({
'prng': minstd.normalized
});

var r = rand( 2.0, 3.0 );
// returns
`

To seed a pseudorandom number generator, set the seed option.

`javascript
var rand1 = cauchy.factory({
'seed': 12345
});

var r1 = rand1( 2.0, 3.0 );
// returns

var rand2 = cauchy.factory( 2.0, 3.0, {
'seed': 12345
});

var r2 = rand2();
// returns

var bool = ( r1 === r2 );
// returns true
`

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 = cauchy( 2.0, 3.0 );
}

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

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 2.0, 3.0 ) === cauchy( 2.0, 3.0 ) );
// returns true
`

#### cauchy.NAME

The generator name.

`javascript
var str = cauchy.NAME;
// returns 'cauchy'
`

#### cauchy.PRNG

The underlying pseudorandom number generator.

`javascript
var prng = cauchy.PRNG;
// returns
`

#### cauchy.seed

The value used to seed cauchy().

`javascript
var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
r = cauchy( 0.0, 2.0 );
}

// Generate the same pseudorandom values...
rand = cauchy.factory( 0.0, 2.0, {
'seed': cauchy.seed
});
for ( i = 0; i < 100; i++ ) {
r = rand();
}
`

If provided a PRNG for uniformly distributed numbers, this value is null.

`javascript
var rand = cauchy.factory({
'prng': Math.random
});

var seed = rand.seed;
// returns null
`

#### cauchy.seedLength

Length of generator seed.

`javascript
var len = cauchy.seedLength;
// returns
`

If provided a PRNG for uniformly distributed numbers, this value is null.

`javascript
var rand = cauchy.factory({
'prng': Math.random
});

var len = rand.seedLength;
// returns null
`

#### cauchy.state

Writable property for getting and setting the generator state.

`javascript
var r = cauchy( 2.0, 5.0 );
// returns

r = cauchy( 2.0, 5.0 );
// returns

// ...

// Get a copy of the current state:
var state = cauchy.state;
// returns

r = cauchy( 2.0, 5.0 );
// returns

r = cauchy( 2.0, 5.0 );
// returns

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

// Replay the last two pseudorandom numbers:
r = cauchy( 2.0, 5.0 );
// returns

r = cauchy( 2.0, 5.0 );
// returns

// ...
`

If provided a PRNG for uniformly distributed numbers, this value is null.

`javascript
var rand = cauchy.factory({
'prng': Math.random
});

var state = rand.state;
// returns null
`

#### cauchy.stateLength

Length of generator state.

`javascript
var len = cauchy.stateLength;
// returns
`

If provided a PRNG for uniformly distributed numbers, this value is null.

`javascript
var rand = cauchy.factory({
'prng': Math.random
});

var len = rand.stateLength;
// returns null
`

#### cauchy.byteLength

Size (in bytes) of generator state.

`javascript
var sz = cauchy.byteLength;
// returns
`

If provided a PRNG for uniformly distributed numbers, this value is null.

`javascript
var rand = cauchy.factory({
'prng': Math.random
});

var sz = rand.byteLength;
// returns null
`

#### cauchy.toJSON()

Serializes the pseudorandom number generator as a JSON object.

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

If provided a PRNG for uniformly distributed numbers, this method returns null.

`javascript
var rand = cauchy.factory({
'prng': Math.random
});

var o = rand.toJSON();
// returns null
`