Arcversine

Compute the inverse versed sine.

The inverse versed sine is defined as

$$\mathrm{aversin}(\theta )=\arccos (1-\theta )$$

Usage

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

aversin( x )

Computes the inverse versed sine.

var v = aversin( 0.0 );
// returns 0.0

v = aversin( 3.141592653589793/2.0 );
// returns ~2.1783

v = aversin( 3.141592653589793/6.0 );
// returns ~1.0742

If x < 0, x > 2, or x is NaN, the function returns NaN.

var v = aversin( -1.0 );
// returns NaN

v = aversin( 3.14 );
// returns NaN

v = aversin( NaN );
// returns NaN

Examples

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

var x = uniform( 100, 0.0, 2.0, {
    'dtype': 'float64'
});

logEachMap( 'aversin(%0.4f) = %0.4f', x, aversin );

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C APIs

Usage

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

stdlib_base_aversin( x )

Computes the inverse versed sine of a double-precision floating-point number (in radians).

double out = stdlib_base_aversin( 3.141592653589793/2.0 );
// returns ~2.1783

If x < 0, x > 2, or x is NaN, the function returns NaN.

double out = stdlib_base_aversin( 3.141592653589793 );
// returns NaN

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_aversin( const double x );

Examples

#include "stdlib/math/base/special/aversin.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { -2.5, -2.0, -1.5, -1.0, -0.5, 0.5, 1.0, 1.5, 2.0, 2.5 };

    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_aversin( x[ i ] );
        printf( "aversin(%lf) = %lf\n", x[ i ], v );
    }
}

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See Also

• @stdlib/math/base/special/avercos: compute the inverse versed cosine.
• @stdlib/math/base/special/vercos: compute the versed cosine.