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ahaversin

README.md

Archaversine

Compute the inverse half-value versed sine.

The inverse half-value versed sine is defined as

$$\mathop{\mathrm{ahaversin}}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})$$

Usage

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

ahaversin( x )

Computes the inverse half-value versed sine.

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

v = ahaversin( 1.0 );
// returns ~3.1416

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

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

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

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

v = ahaversin( NaN );
// returns NaN

Examples

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

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

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

C APIs

Usage

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

stdlib_base_ahaversin( x )

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

double out = stdlib_base_ahaversin( 0.0 );
// returns 0.0

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

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

The function accepts the following arguments:

  • x: [in] double input value.
double stdlib_base_ahaversin( const double x );

Examples

#include "stdlib/math/base/special/ahaversin.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_ahaversin( x[ i ] );
        printf( "ahaversin(%lf) = %lf\n", x[ i ], v );
    }
}

See Also