atanh

Compute the hyperbolic arctangent of a number.

Usage

var atanh = require( '@stdlib/fastmath/special/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/math/utils/linspace' );
var atanh = require( '@stdlib/fastmath/special/atanh' );

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

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