Archavercosine

Compute the inverse half-value versed cosine.

The inverse half-value versed cosine is defined as

$$\mathop{\mathrm{ahavercos}}(\theta) = 2 \cdot \arccos(\sqrt{\theta})$$

Usage

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

ahavercos( x )

Computes the inverse half-value versed cosine.

var v = ahavercos( 0.0 );
// returns ~3.1416

v = ahavercos( 1.0 );
// returns 0.0

v = ahavercos( 0.5 );
// returns ~1.5708

If x < 0, x > 1, or x is NaN, the function returns NaN.

var v = ahavercos( 1.5 );
// returns NaN

v = ahavercos( -3.14 );
// returns NaN

v = ahavercos( NaN );
// returns NaN

Examples

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

var x = uniform( 100, 0.0, 1.0, {
    'dtype': 'float64'
});

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

---

C APIs

Usage

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

stdlib_base_ahavercos( x )

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

double out = stdlib_base_ahavercos( 0.0 );
// returns ~3.1416

If x < 0, x > 1, or x is NaN, the function returns NaN.

double out = stdlib_base_ahavercos( -3.14 );
// returns NaN

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_ahavercos( const double x );

Examples

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

int main( void ) {
    const double x[] = { -2.0, -1.6, -1.2, -0.8, -0.4, 0.4, 0.8, 1.2, 1.6, 2.0 };

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

---

See Also

• @stdlib/math/base/special/ahaversin: compute the inverse half-value versed sine.
• @stdlib/math/base/special/havercos: compute the half-value versed cosine.
• @stdlib/math/base/special/vercos: compute the versed cosine.