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# gammasgn

> Sign of the [gamma function][@stdlib/math/base/special/gamma].

<section class="intro">

The sign of the [gamma-function][@stdlib/math/base/special/gamma] is defined as

<!-- <equation class="equation" label="eq:gamma_sign_function" align="center" raw="\operatorname{gammasgn} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}" alt="Sign of the gamma function"> -->

<div class="equation" align="center" data-raw-text="\operatorname{gammasgn} ( x ) = \begin{cases} 1 &amp; \textrm{if}\ \Gamma &gt; 1 \\ -1 &amp; \textrm{if}\ \Gamma &lt; 1 \\ 0 &amp; \textrm{otherwise}\ \end{cases}" data-equation="eq:gamma_sign_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@50b141156b147529227e2eb4247eda81c781dec9/lib/node_modules/@stdlib/math/base/special/gammasgn/docs/img/equation_gamma_sign_function.svg" alt="Sign of the gamma function">
    <br>
</div>

<!-- </equation> -->

The [gamma function][@stdlib/math/base/special/gamma] can be computed as the product of `gammasgn(x)` and `exp(gammaln(x))`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var gammasgn = require( '@stdlib/math/base/special/gammasgn' );
```

#### gammasgn( x )

Returns the sign of the [gamma function][@stdlib/math/base/special/gamma].

```javascript
var v = gammasgn( 1.0 );
// returns 1.0

v = gammasgn( -2.5 );
// returns -1.0

v = gammasgn( 0.0 );
// returns 0.0

v = gammasgn( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   The [gamma function][@stdlib/math/base/special/gamma] is not defined for negative integer values (i.e., `gamma(x) === NaN` when `x` is a negative integer). The [natural logarithm of the gamma function][@stdlib/math/base/special/gammaln] is defined for negative integer values (i.e., `gammaln(x) === Infinity` when `x` is a negative integer). Accordingly, in order for the equality `gamma(x) === gammasgn(x) * exp(gammaln(x))` to hold (i.e., return `NaN`), `gammasgn` needs to either return `NaN` or `0`. By convention, this function returns `0`.

</section>

<!-- /. notes -->

<section class="examples">

## Examples

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

```javascript
var linspace = require( '@stdlib/array/base/linspace' );
var gammasgn = require( '@stdlib/math/base/special/gammasgn' );

var x = linspace( -10.0, 10.0, 100 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( 'x: %d, f(x): %d', x[ i ], gammasgn( x[ i ] ) );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="links">

[@stdlib/math/base/special/gamma]: https://github.com/stdlib-js/math/tree/main/base/special/gamma

[@stdlib/math/base/special/gammaln]: https://github.com/stdlib-js/math/tree/main/base/special/gammaln

<!-- <related-links> -->

<!-- </related-links> -->

</section>

<!-- /.links -->
