mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-12-25 21:35:41 +00:00
61 lines
2.5 KiB
C++
61 lines
2.5 KiB
C++
|
/*=============================================================================
|
|||
|
|
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<><69>) 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<><69>) 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
|