atanh.hpp

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// SPDX-License-Identifier: BSD-2-Clause
 
#ifndef pRC_CORE_COMPLEX_FUNCTIONS_ATANH_H
#define pRC_CORE_COMPLEX_FUNCTIONS_ATANH_H
 
#include <prc/core/complex/complex.hpp>
 
namespace pRC
{
    template<IsComplex T>
    static inline constexpr auto atanh(T const &a)
    {
        using R = typename T::Type;
 
        auto const is = a.imag() * a.imag();
        auto const t = unit<R>() - is - a.real() * a.real();
 
        auto num = unit<R>() + a.real();
        auto den = unit<R>() - a.real();
 
        num = is + num * num;
        den = is + den * den;
 
        auto const real = identity<R>(0.25) * (log(num) - log(den));
        auto const imag =
            identity<R>(0.5) * atan2(identity<R>(2) * a.imag(), t);
 
        return Complex(real, imag);
    }
}
#endif // pRC_CORE_COMPLEX_FUNCTIONS_ATANH_H