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@anandkaranubc
anandkaranubc committedJun 20, 2025
commit 39814972fc0f2581b235145f36758647b8112263
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<!--

@license Apache-2.0

Copyright (c) 2018 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# Versine

> Compute the [versed sine][versed-sine].

<section class="intro">

The [versed sine][versed-sine] is defined as

<!-- <equation class="equation" label="eq:versine" align="center" raw="\operatorname{versin}(\theta) = 1 - \cos \theta" alt="Versed sine."> -->

```math
\mathop{\mathrm{versin}}(\theta) = 1 - \cos \theta
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{versin}(\theta) = 1 - \cos \theta" data-equation="eq:versine">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/versin/docs/img/equation_versine.svg" alt="Versed sine.">
<br>
</div> -->

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### versin( x )

Computes the [versed sine][versed-sine] of a `number` (in radians).

```javascript
var v = versin( 0.0 );
// returns 0.0

v = versin( 3.141592653589793/2.0 );
// returns ~1.0

v = versin( -3.141592653589793/6.0 );
// returns ~0.13397
```

</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 TWO_PI = require( '@stdlib/constants/float64/two-pi' );
var versin = require( '@stdlib/math/base/special/versin' );

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

logEachMap( 'versin(%0.4f) = %0.4f', x, versin );
```

</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/versin.h"
```

#### stdlib_base_versin( x )

Computes the [versed sine][versed-sine] of a `number` (in radians).

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

out = stdlib_base_versin( 3.141592653589793 / 2.0 );
// returns ~1.0
```

The function accepts the following arguments:

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

```c
double stdlib_base_versin( 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/versin.h"
#include <stdio.h>

int main( void ) {
const double x[] = { 0.0, 0.523, 0.785, 1.047, 3.14 };

double y;
int i;
for ( i = 0; i < 5; i++ ) {
y = stdlib_base_versin( x[ i ] );
printf( "versin(%lf) = %lf\n", x[ i ], y );
}
}
```

</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/cos`][@stdlib/math/base/special/cos]</span><span class="delimiter">: </span><span class="description">compute the cosine of a number.</span>
- <span class="package-name">[`@stdlib/math/base/special/sin`][@stdlib/math/base/special/sin]</span><span class="delimiter">: </span><span class="description">compute the sine of a number.</span>
- <span class="package-name">[`@stdlib/math/base/special/vercos`][@stdlib/math/base/special/vercos]</span><span class="delimiter">: </span><span class="description">compute the versed cosine.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[versed-sine]: https://en.wikipedia.org/wiki/Versine

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

[@stdlib/math/base/special/cos]: https://.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos

[@stdlib/math/base/special/sin]: https://.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sin

[@stdlib/math/base/special/vercos]: https://.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/vercos

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

</section>

<!-- /.links -->
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/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var bench = require( '@stdlib/bench' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pkg = require( './../package.json' ).name;
var versin = require( './../lib' );


// MAIN //

bench( pkg, function benchmark( b ) {
var x;
var y;
var i;

x = uniform( 100, -10.0, 10.0 );

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
y = versin( x[ i % x.length ] );
if ( isnan( y ) ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( isnan( y ) ) {
b.fail( 'should not return NaN' );
}
b.pass( 'benchmark finished' );
b.end();
});
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