README.md

gammasgn

Sign of the gamma function.

The sign of the gamma-function is defined as

$$\mathop{\mathrm{gammasgn}} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}$$

The gamma function can be computed as the product of gammasgn(x) and exp(gammaln(x)).

Usage

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

gammasgn( x )

Returns the sign of the gamma function.

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

Notes

• The gamma function 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 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.

Examples

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 );

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C APIs

Usage

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

stdlib_base_gammasgn( x )

Returns the sign of the gamma-function.

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.

double stdlib_base_gammasgn( const double x );

Examples

#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 );
    }
}

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See Also

• @stdlib/math/base/special/gamma: gamma function.