mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-11-14 10:39:05 +00:00
64 lines
3.2 KiB
C++
64 lines
3.2 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_ACOSH_HPP
|
|||
|
|
#define SPROUT_COMPLEX_ACOSH_HPP
|
|||
|
|
|
|||
|
|
#include <sprout/config.hpp>
|
|||
|
|
#include <sprout/limits.hpp>
|
|||
|
|
#include <sprout/math/constants.hpp>
|
|||
|
|
#include <sprout/math/isnan.hpp>
|
|||
|
|
#include <sprout/math/isinf.hpp>
|
|||
|
|
#include <sprout/math/copysign.hpp>
|
|||
|
|
#include <sprout/complex/complex.hpp>
|
|||
|
|
#include <sprout/complex/log.hpp>
|
|||
|
|
#include <sprout/complex/sqrt.hpp>
|
|||
|
|
|
|||
|
|
namespace sprout {
|
|||
|
|
//
|
|||
|
|
// acosh
|
|||
|
|
//
|
|||
|
|
// G.6.2.1 The cacosh functions
|
|||
|
|
// cacosh(conj(z)) = conj(cacosh(z)).
|
|||
|
|
// cacosh(<28>}0 + i0) returns +0 + ip /2.
|
|||
|
|
// cacosh(x + i<><69>) returns +<2B><>+ ip /2, for finite x.
|
|||
|
|
// cacosh(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
|
|||
|
|
// cacosh(-<2D><>+ iy) returns +<2B><>+ ip , for positive-signed finite y.
|
|||
|
|
// cacosh(+<2B><>+ iy) returns +<2B><>+ i0, for positive-signed finite y.
|
|||
|
|
// cacosh(-<2D><>+ i<><69>) returns +<2B><>+ i3p /4.
|
|||
|
|
// cacosh(+<2B><>+ i<><69>) returns +<2B><>+ ip /4.
|
|||
|
|
// cacosh(<28>}<7D><>+ iNaN) returns +<2B><>+ iNaN.
|
|||
|
|
// cacosh(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite y.
|
|||
|
|
// cacosh(NaN + i<><69>) returns +<2B><>+ iNaN.
|
|||
|
|
// cacosh(NaN + iNaN) returns NaN + iNaN.
|
|||
|
|
//
|
|||
|
|
template<typename T>
|
|||
|
|
inline SPROUT_CONSTEXPR sprout::complex<T>
|
|||
|
|
acosh(sprout::complex<T> const& x) {
|
|||
|
|
typedef sprout::complex<T> type;
|
|||
|
|
return sprout::math::isnan(x.real())
|
|||
|
|
? sprout::math::isnan(x.imag()) ? x
|
|||
|
|
: sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), x.real())
|
|||
|
|
: type(x.real(), x.real())
|
|||
|
|
: sprout::math::isnan(x.imag())
|
|||
|
|
? sprout::math::isinf(x.real()) ? type(sprout::numeric_limits<T>::infinity(), x.imag())
|
|||
|
|
: type(sprout::numeric_limits<T>::quiet_NaN(), x.imag())
|
|||
|
|
: x.real() == sprout::numeric_limits<T>::infinity()
|
|||
|
|
? sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::quarter_pi<T>(), x.imag()))
|
|||
|
|
: type(sprout::numeric_limits<T>::infinity(), (x.imag() == 0 ? x.imag() : sprout::math::copysign(T(0), x.imag())))
|
|||
|
|
: x.real() == -sprout::numeric_limits<T>::infinity()
|
|||
|
|
? sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::three_quarters_pi<T>(), x.imag()))
|
|||
|
|
: type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::pi<T>(), x.imag()))
|
|||
|
|
: sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
|
|||
|
|
: x.real() == 0 && x.imag() == 0 ? type(T(0), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
|
|||
|
|
: T(2) * sprout::log(sprout::sqrt(sprout::math::half<T>() * (x + T(1))) + sprout::sqrt(sprout::math::half<T>() * (x - T(1))))
|
|||
|
|
;
|
|||
|
|
}
|
|||
|
|
} // namespace sprout
|
|||
|
|
|
|||
|
|
#endif // #ifndef SPROUT_COMPLEX_ACOSH_HPP
|