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# incrmprod

> Compute a moving product incrementally.

<section class="intro">

For a window of size `W`, the moving product is defined as

<!-- <equation class="equation" label="eq:moving_product" align="center" raw="\prod_{i=0}^{W-1} x_i" alt="Equation for the moving product."> -->

<div class="equation" align="center" data-raw-text="\prod_{i=0}^{W-1} x_i" data-equation="eq:moving_product">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/27e2a43c70db648bb5bbc3fd0cdee050c25adc0b/lib/node_modules/@stdlib/stats/incr/mprod/docs/img/equation_moving_product.svg" alt="Equation for the moving product.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmprod = require( '@stdlib/stats/incr/mprod' );
```

#### incrmprod( window )

Returns an accumulator `function` which incrementally computes a moving product. The `window` parameter defines the number of values over which to compute the moving product.

```javascript
var accumulator = incrmprod( 3 );
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated product. If not provided an input value `x`, the accumulator function returns the current product.

```javascript
var accumulator = incrmprod( 3 );

var p = accumulator();
// returns null

// Fill the window...
p = accumulator( 2.0 ); // [2.0]
// returns 2.0

p = accumulator( 1.0 ); // [2.0, 1.0]
// returns 2.0

p = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 6.0

// Window begins sliding...
p = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns -21.0

p = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns 105.0

p = accumulator();
// returns 105.0
```

Under certain conditions, overflow may be transient.

```javascript
// Large values:
var x = 5.0e+300;
var y = 1.0e+300;

// Tiny value:
var z = 2.0e-302;

// Initialize an accumulator:
var accumulator = incrmprod( 3 );

var p = accumulator( x );
// returns 5.0e+300

// Transient overflow:
p = accumulator( y );
// returns Infinity

// Recover a finite result:
p = accumulator( z );
// returns 1.0e+299
```

Similarly, under certain conditions, underflow may be transient.

```javascript
// Tiny values:
var x = 4.0e-302;
var y = 9.0e-303;

// Large value:
var z = 2.0e+300;

// Initialize an accumulator:
var accumulator = incrmprod( 3 );

var p = accumulator( x );
// returns 4.0e-302

// Transient underflow:
p = accumulator( y );
// returns 0.0

// Recover a non-zero result:
p = accumulator( z );
// returns 7.2e-304
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **at least** `W-1` future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
-   As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
-   For large accumulation windows or accumulations of either large or small numbers, care should be taken to prevent overflow and underflow. Note, however, that overflow/underflow may be transient, as the accumulator does not use a double-precision floating-point number to store an accumulated product. Instead, the accumulator splits an accumulated product into a normalized **fraction** and **exponent** and updates each component separately. Doing so guards against a loss in precision.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmprod = require( '@stdlib/stats/incr/mprod' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrmprod( 5 );

// For each simulated datum, update the moving product...
for ( i = 0; i < 100; i++ ) {
    v = ( randu()*10.0 ) - 5.0;
    accumulator( v );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="links">

</section>

<!-- /.links -->
