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re-implementation complex transcendental functions

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bolero-MURAKAMI 2014-07-19 20:03:13 +09:00
parent c830cab086
commit 22c3f6e132
32 changed files with 1460 additions and 486 deletions
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sprout/complex/exp.hpp Normal file
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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_EXP_HPP
#define SPROUT_COMPLEX_EXP_HPP
#include <sprout/config.hpp>
#include <sprout/limits.hpp>
#include <sprout/math/isnan.hpp>
#include <sprout/math/isinf.hpp>
#include <sprout/math/isinf.hpp>
#include <sprout/math/copysign.hpp>
#include <sprout/complex/complex.hpp>
#include <sprout/complex/polar.hpp>
#include <sprout/complex/euler.hpp>
#include <sprout/complex/detail/copysign_mul.hpp>
namespace sprout {
//
// exp
//
// G.6.3.1 The cexp functions
// cexp(conj(z)) = conj(cexp(z)).
// cexp(<28>}0 + i0) returns 1 + i0.
// cexp(x + i<>‡) returns NaN + iNaN and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
// cexp(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
// cexp(+<2B>‡+ i0) returns +<2B>‡+ i0.
// cexp(-<2D>‡+ iy) returns +0 cis(y), for finite y.
// cexp(+<2B>‡+ iy) returns +<2B>‡ cis(y), for finite nonzero y.
// cexp(-<2D>‡+ i<>‡) returns <20>}0 <20>} i0 (where the signs of the real and imaginary parts of the result are unspecified).
// cexp(+<2B>‡+ i<>‡) returns <20>}<7D>‡+ iNaN and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception (where the sign of the real part of the result is unspecified).
// cexp(-<2D>‡+ iNaN) returns <20>}0 <20>} i0 (where the signs of the real and imaginary parts of the result are unspecified).
// cexp(+<2B>‡+ iNaN) returns <20>}<7D>‡+ iNaN (where the sign of the real part of the result is unspecified).
// cexp(NaN + i0) returns NaN + i0.
// cexp(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for all non-zero numbers y.
// cexp(NaN + iNaN) returns NaN + iNaN.
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::complex<T>
exp(sprout::complex<T> const& x) {
typedef sprout::complex<T> type;
return sprout::math::isnan(x.real())
? sprout::math::isnan(x.imag()) ? type(x.real(), x.real())
: x.imag() == 0 ? type(x.real(), x.imag())
: type(x.real(), x.real())
: sprout::math::isnan(x.imag())
? x.real() == sprout::numeric_limits<T>::infinity() ? type(x.real(), x.imag())
: x.real() == -sprout::numeric_limits<T>::infinity() ? type(T(0), T(0))
: sprout::math::isinf(x.real()) ? type(sprout::numeric_limits<T>::infinity(), sprout::numeric_limits<T>::quiet_NaN())
: type(x.imag(), x.imag())
: x.real() == sprout::numeric_limits<T>::infinity()
? sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::numeric_limits<T>::quiet_NaN())
: x.imag() == 0 ? type(sprout::numeric_limits<T>::infinity(), x.imag())
: sprout::detail::copysign_mul(sprout::numeric_limits<T>::infinity(), sprout::euler(x.imag()))
: x.real() == -sprout::numeric_limits<T>::infinity()
? sprout::math::isinf(x.imag()) ? type(T(0), T(0))
: T(0) * sprout::euler(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 ? type(T(1), x.imag())
: sprout::polar(sprout::math::exp(x.real()), x.imag())
;
}
} // namespace sprout
#endif // #ifndef SPROUT_COMPLEX_EXP_HPP