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Archavercosine

Compute the inverse half-value versed cosine.

The inverse half-value versed cosine is defined as

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

Installation

npm install @stdlib/math-base-special-ahavercos

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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

var x = linspace( 0.0, 1.0, 100 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( ahavercos( x[ i ] ) );
}

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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 );
    }
}

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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.

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.