<?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    $complex    Complex number or a numeric value.
 * @return    Complex          The inverse hyperbolic tangent of the complex argument.
 * @throws    Exception        If argument isn't a valid real or complex number.
 */
if (!function_exists(__NAMESPACE__ . '\\atanh')) {
    function atanh($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();
    }
}