npm package: @stdlib/math-base-special-ahaversin
Description: Compute the inverse half-value versed sine.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Archaversine

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the [inverse half-value versed sine][archaversine].

<section class="intro">

The [inverse half-value versed sine][archaversine] is defined as

<!-- <equation class="equation" label="eq:archaversine" align="center" raw="\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})" alt="Inverse half-value versed sine."> -->

<div class="equation" align="center" data-raw-text="\operatorname{ahaversin}(\theta) = 2 \cdot \arcsin(\sqrt{\theta})" data-equation="eq:archaversine">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/ahaversin/docs/img/equation_archaversine.svg" alt="Inverse half-value versed sine.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-ahaversin
```

</section>

<section class="usage">

## Usage

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

#### ahaversin( x )

Computes the [inverse half-value versed sine][archaversine].

```javascript
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`.

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

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

v = ahaversin( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
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 );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

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

#### stdlib_base_ahaversin( x )

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

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

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

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

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_ahaversin( const double x );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#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 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/ahavercos`][@stdlib/math/base/special/ahavercos]</span><span class="delimiter">: </span><span class="description">compute the inverse half-value versed cosine.</span>
-   <span class="package-name">[`@stdlib/math-base/special/haversin`][@stdlib/math/base/special/haversin]</span><span class="delimiter">: </span><span class="description">compute the half-value versed sine.</span>
-   <span class="package-name">[`@stdlib/math-base/special/versin`][@stdlib/math/base/special/versin]</span><span class="delimiter">: </span><span class="description">compute the versed sine.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

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

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-ahaversin/main/LICENSE

[archaversine]: https://en.wikipedia.org/wiki/Versine

<!-- <related-links> -->

[@stdlib/math/base/special/ahavercos]: https://www.npmjs.com/package/@stdlib/math-base-special-ahavercos

[@stdlib/math/base/special/haversin]: https://www.npmjs.com/package/@stdlib/math-base-special-haversin

[@stdlib/math/base/special/versin]: https://www.npmjs.com/package/@stdlib/math-base-special-versin

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</section>

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