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<?php

/**
 *
 * Function code for the complex atanh() function
 *
 * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
 * @license    https://opensource.org/licenses/MIT    MIT
 */
namespace Complex;

/**
 * Returns the inverse hyperbolic tangent of a complex number.
 *
 * @param     Complex|mixed    $complex    Complex number or a numeric value.
 * @return    Complex          The inverse hyperbolic tangent of the complex argument.
 * @throws    Exception        If argument isn't a valid real or complex number.
 */
function atanh($complex): Complex
{
    $complex = Complex::validateComplexArgument($complex);

    if ($complex->isReal()) {
        $real = $complex->getReal();
        if ($real >= -1.0 && $real <= 1.0) {
            return new Complex(\atanh($real));
        } else {
            return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2));
        }
    }

    $iComplex = clone $complex;
    $iComplex = $iComplex->invertImaginary()
        ->reverse();
    return atan($iComplex)
        ->invertReal()
        ->reverse();
}

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