Sprout/sprout/complex/tanh.hpp
2014-07-19 20:03:13 +09:00

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/*=============================================================================
Copyright (c) 2011-2014 Bolero MURAKAMI
https://github.com/bolero-MURAKAMI/Sprout
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_COMPLEX_TANH_HPP
#define SPROUT_COMPLEX_TANH_HPP
#include <sprout/config.hpp>
#include <sprout/limits.hpp>
#include <sprout/math/isnan.hpp>
#include <sprout/math/isinf.hpp>
#include <sprout/math/sin.hpp>
#include <sprout/math/copysign.hpp>
#include <sprout/complex/complex.hpp>
#include <sprout/complex/operators.hpp>
#include <sprout/complex/cosh.hpp>
#include <sprout/complex/sinh.hpp>
namespace sprout {
//
// tanh
//
// G.6.2.6 The ctanh functions
// ctanh(conj(z)) = conj(ctanh(z))and ctanh is odd.
// ctanh(+0 + i0) returns +0 + i0.
// ctanh(x + i<>‡) returns NaN + iNaN and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
// ctanh(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
// ctanh(+<2B>‡+ iy) returns 1 + i0 sin(2y), for positive-signed finite y.
// ctanh(+<2B>‡+ i<>‡) returns 1 <20>} i0 (where the sign of the imaginary part of the result is unspecified).
// ctanh(+<2B>‡+ iNaN) returns 1 <20>} i0 (where the sign of the imaginary part of the result is unspecified).
// ctanh(NaN + i0) returns NaN + i0.
// ctanh(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for all nonzero numbers y.
// ctanh(NaN + iNaN) returns NaN + iNaN.
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::complex<T>
tanh(sprout::complex<T> const& x) {
typedef sprout::complex<T> type;
return sprout::math::isnan(x.real())
? sprout::math::isnan(x.imag()) ? x
: x.imag() == 0 ? x
: type(x.real(), x.real())
: sprout::math::isnan(x.imag())
? sprout::math::isinf(x.real()) ? type(T(1), T(0))
: type(x.imag(), x.imag())
: sprout::math::isinf(x.real())
? sprout::math::isinf(x.imag()) ? type(T(1), T(0))
: type(T(1), T(0) * sprout::math::sin(T(2) * x.imag()))
: sprout::math::isinf(x.imag())
? type(-sprout::numeric_limits<T>::quiet_NaN(), -sprout::numeric_limits<T>::quiet_NaN())
: x.real() == 0 && x.imag() == 0 ? x
: sprout::sinh(x) / sprout::cosh(x)
;
}
} // namespace sprout
#endif // #ifndef SPROUT_COMPLEX_TANH_HPP