npm package: @stdlib/math-base-special-gammasgn
Description: Sign of the gamma function.
Author: The Stdlib Authors
Latest version: 0.3.1

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# gammasgn

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> 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="installation">

## Installation

```bash
npm install @stdlib/math-base-special-gammasgn
```

</section>

<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 -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma

[@stdlib/math/base/special/gammaln]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaln

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