mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-11-29 01:03:45 +00:00
71 lines
3.7 KiB
C++
71 lines
3.7 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_LOG_HPP
|
|||
|
|
#define SPROUT_COMPLEX_LOG_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/math/signbit.hpp>
|
|||
|
|
#include <sprout/math/log.hpp>
|
|||
|
|
#include <sprout/complex/complex.hpp>
|
|||
|
|
#include <sprout/complex/abs.hpp>
|
|||
|
|
#include <sprout/complex/arg.hpp>
|
|||
|
|
|
|||
|
|
namespace sprout {
|
|||
|
|
//
|
|||
|
|
// log
|
|||
|
|
//
|
|||
|
|
// G.6.3.2 The clog functions
|
|||
|
|
// clog(conj(z)) = conj(clog(z)).
|
|||
|
|
// clog(-0 + i0) returns -<2D><>+ ip and raises the <20>e<EFBFBD>edivide-by-zero<72>f<EFBFBD>f floating-point exception.
|
|||
|
|
// clog(+0 + i0) returns -<2D><>+ i0 and raises the <20>e<EFBFBD>edivide-by-zero<72>f<EFBFBD>f floating-point exception.
|
|||
|
|
// clog(x + i<><69>) returns +<2B><>+ ip /2, for finite x.
|
|||
|
|
// clog(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
|
|||
|
|
// clog(-<2D><>+ iy) returns +<2B><>+ ip , for finite positive-signed y.
|
|||
|
|
// clog(+<2B><>+ iy) returns +<2B><>+ i0, for finite positive-signed y.
|
|||
|
|
// clog(-<2D><>+ i<><69>) returns +<2B><>+ i3p /4.
|
|||
|
|
// clog(+<2B><>+ i<><69>) returns +<2B><>+ ip /4.
|
|||
|
|
// clog(<28>}<7D><>+ iNaN) returns +<2B><>+ iNaN.
|
|||
|
|
// clog(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite y.
|
|||
|
|
// clog(NaN + i<><69>) returns +<2B><>+ iNaN.
|
|||
|
|
// clog(NaN + iNaN) returns NaN + iNaN.
|
|||
|
|
//
|
|||
|
|
template<typename T>
|
|||
|
|
inline SPROUT_CONSTEXPR sprout::complex<T>
|
|||
|
|
log(sprout::complex<T> const& x) {
|
|||
|
|
typedef sprout::complex<T> type;
|
|||
|
|
return sprout::math::isnan(x.real())
|
|||
|
|
? sprout::math::isnan(x.imag()) ? type(sprout::numeric_limits<T>::quiet_NaN(), x.real())
|
|||
|
|
: sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), x.real())
|
|||
|
|
: type(sprout::numeric_limits<T>::quiet_NaN(), 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()
|
|||
|
|
? x.imag() == sprout::numeric_limits<T>::infinity() ? type(sprout::numeric_limits<T>::infinity(), sprout::math::quarter_pi<T>())
|
|||
|
|
: x.imag() == -sprout::numeric_limits<T>::infinity() ? type(sprout::numeric_limits<T>::infinity(), -sprout::math::quarter_pi<T>())
|
|||
|
|
: 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()
|
|||
|
|
? x.imag() == sprout::numeric_limits<T>::infinity() ? type(sprout::numeric_limits<T>::infinity(), sprout::math::three_quarters_pi<T>())
|
|||
|
|
: x.imag() == -sprout::numeric_limits<T>::infinity() ? type(sprout::numeric_limits<T>::infinity(), -sprout::math::three_quarters_pi<T>())
|
|||
|
|
: 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
|
|||
|
|
? sprout::math::signbit(x.real()) ? type(-sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::pi<T>(), x.imag()))
|
|||
|
|
: type(-sprout::numeric_limits<T>::infinity(), x.imag())
|
|||
|
|
: type(sprout::math::log(sprout::abs(x)), sprout::arg(x))
|
|||
|
|
;
|
|||
|
|
}
|
|||
|
|
} // namespace sprout
|
|||
|
|
|
|||
|
|
#endif // #ifndef SPROUT_COMPLEX_LOG_HPP
|