# incrmprod
> Compute a moving product incrementally.
For a window of size `W`, the moving product is defined as
## 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
```
## 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.
## Examples
```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() );
```
