npm package: @stdlib/math-base-special-fast-atanh
Description: Compute the hyperbolic arctangent of a number.
Author: The Stdlib Authors
Latest version: 0.3.1

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# atanh

[![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 [hyperbolic arctangent][inverse-hyperbolic] of a number.

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-fast-atanh
```

</section>

<section class="usage">

## Usage

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

#### atanh( x )

Computes the [hyperbolic arctangent][inverse-hyperbolic] of a `number` (in radians).

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

v = atanh( -0.0 );
// returns -0.0

v = atanh( 0.5 );
// returns ~0.549

v = atanh( 0.9 );
// returns ~1.472

v = atanh( 1.0 );
// returns Infinity

v = atanh( -1.0 );
// returns -Infinity
```

The domain of `x` is restricted to `[-1,1]`. If `|x| > 1`, the function returns `NaN`.

```javascript
var v = atanh( -3.14 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   For small `x`, the function will underflow.

    ```javascript
    var v = atanh( 1.0e-17 );
    // returns 0.0
    // (expected 1.0e-17)
    ```

</section>

<!-- /.notes -->

<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 atanh = require( '@stdlib/math-base-special-fast-atanh' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 103, -1.0, 1.0, opts );

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

</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/fast/atanh.h"
```

#### stdlib_base_fast_atanh( x )

Computes the [hyperbolic arctangent][inverse-hyperbolic] of a double-precision floating-point number (in radians).

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

out = stdlib_base_fast_atanh( -0.0 );
// returns -0.0
```

The function accepts the following arguments:

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

```c
double stdlib_base_fast_atanh( 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/fast/atanh.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { -1.0, -0.78, -0.56, -0.33, -0.11, 0.11, 0.33, 0.56, 0.78, 1.0 };

    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_fast_atanh( x[ i ] );
        printf( "atanh(%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/atanh`][@stdlib/math/base/special/atanh]</span><span class="delimiter">: </span><span class="description">compute the hyperbolic arctangent of a double-precision floating-point number.</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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[inverse-hyperbolic]: https://en.wikipedia.org/wiki/Inverse_hyperbolic_function

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</section>

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