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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 > 0 \\ -1 & \textrm{if}\ \Gamma < 0 \\ 0 & \textrm{otherwise}\ \end{cases}" alt="Sign of the gamma function"> -->

<!-- </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 uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var gammasgn = require( '@stdlib/math/base/special/gammasgn' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, -10.0, 10.0, opts );

logEachMap( 'x: %0.4f, f(x): %0.4f', x, gammasgn );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/gammasgn.h"
```

#### stdlib_base_gammasgn( x )

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

```c
double out = stdlib_base_gammasgn( 1.0 );
// returns 1.0

out = stdlib_base_gammasgn( -2.5 );
// returns -1.0
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_gammasgn( const double x );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/gammasgn.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double x;
    double v;
    int i;

    for ( i = 0; i < 100; i++ ) {
        x = ( (double)rand() / (double)RAND_MAX ) * 100.0;
        v = stdlib_base_gammasgn( x );
        printf( "gammasgn(%lf) = %lf\n", x, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/gamma`][@stdlib/math/base/special/gamma]</span><span class="delimiter">: </span><span class="description">gamma function.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<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 -->
