atanh

Compute the hyperbolic arctangent of a number.

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 );
    }
}