# @stdlib/math-base-special-fast-atanh

0.3.0 • Public • Published

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# atanh

Compute the hyperbolic arctangent of a number.

## Installation

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

## Usage

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

#### atanh( x )

Computes the hyperbolic arctangent of a `number` (in radians).

```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`.

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

## Notes

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

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

## Examples

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

var x = linspace( -1.0, 1.0, 103 );

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

## C APIs

### Usage

`#include "stdlib/math/base/special/fast/atanh.h"`

#### stdlib_base_fast_atanh( x )

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

```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.
`double stdlib_base_fast_atanh( const double x );`

### Examples

```#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 );
}
}```

## 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.

## Package Sidebar

### Install

`npm i @stdlib/math-base-special-fast-atanh`

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