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Editing: cstdfloat_complex_std.hpp
/////////////////////////////////////////////////////////////////////////////// // Copyright Christopher Kormanyos 2014. // Copyright John Maddock 2014. // Copyright Paul Bristow 2014. // 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) // // Implement a specialization of std::complex<> for *anything* that // is defined as BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE. #ifndef BOOST_MATH_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ #define BOOST_MATH_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ #if defined(__GNUC__) #pragma GCC system_header #endif #include <complex> #include <boost/math/constants/constants.hpp> #include <boost/math/tools/cxx03_warn.hpp> namespace std { // Forward declarations. template<class float_type> class complex; template<> class complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>; inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE abs (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE arg (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE norm(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> conj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> proj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& = 0); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sqrt (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sin (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cos (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tan (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asin (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acos (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atan (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> exp (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&, int); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sinh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cosh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tanh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); template<class char_type, class traits_type> inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>&, const std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); template<class char_type, class traits_type> inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>&, std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); // Template specialization of the complex class. template<> class complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> { public: typedef BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE value_type; explicit complex(const complex<float>&); explicit complex(const complex<double>&); explicit complex(const complex<long double>&); #if defined(BOOST_NO_CXX11_CONSTEXPR) complex(const value_type& r = value_type(), const value_type& i = value_type()) : re(r), im(i) { } template<typename X> complex(const complex<X>& x) : re(x.real()), im(x.imag()) { } const value_type& real() const { return re; } const value_type& imag() const { return im; } value_type& real() { return re; } value_type& imag() { return im; } #else BOOST_CONSTEXPR complex(const value_type& r = value_type(), const value_type& i = value_type()) : re(r), im(i) { } template<typename X> BOOST_CONSTEXPR complex(const complex<X>& x) : re(x.real()), im(x.imag()) { } value_type real() const { return re; } value_type imag() const { return im; } #endif void real(value_type r) { re = r; } void imag(value_type i) { im = i; } complex<value_type>& operator=(const value_type& v) { re = v; im = value_type(0); return *this; } complex<value_type>& operator+=(const value_type& v) { re += v; return *this; } complex<value_type>& operator-=(const value_type& v) { re -= v; return *this; } complex<value_type>& operator*=(const value_type& v) { re *= v; im *= v; return *this; } complex<value_type>& operator/=(const value_type& v) { re /= v; im /= v; return *this; } template<typename X> complex<value_type>& operator=(const complex<X>& x) { re = x.real(); im = x.imag(); return *this; } template<typename X> complex<value_type>& operator+=(const complex<X>& x) { re += x.real(); im += x.imag(); return *this; } template<typename X> complex<value_type>& operator-=(const complex<X>& x) { re -= x.real(); im -= x.imag(); return *this; } template<typename X> complex<value_type>& operator*=(const complex<X>& x) { const value_type tmp_real = (re * x.real()) - (im * x.imag()); im = (re * x.imag()) + (im * x.real()); re = tmp_real; return *this; } template<typename X> complex<value_type>& operator/=(const complex<X>& x) { const value_type tmp_real = (re * x.real()) + (im * x.imag()); const value_type the_norm = std::norm(x); im = ((im * x.real()) - (re * x.imag())) / the_norm; re = tmp_real / the_norm; return *this; } private: value_type re; value_type im; }; // Constructors from built-in complex representation of floating-point types. inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::complex(const complex<float>& f) : re(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( f.real())), im(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( f.imag())) { } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::complex(const complex<double>& d) : re(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( d.real())), im(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( d.imag())) { } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::complex(const complex<long double>& ld) : re(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(ld.real())), im(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(ld.imag())) { } } // namespace std namespace boost { namespace math { namespace cstdfloat { namespace detail { template<class float_type> inline std::complex<float_type> multiply_by_i(const std::complex<float_type>& x) { // Multiply x (in C) by I (the imaginary component), and return the result. return std::complex<float_type>(-x.imag(), x.real()); } } } } } // boost::math::cstdfloat::detail namespace std { // ISO/IEC 14882:2011, Section 26.4.7, specific values. inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return x.real(); } inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return x.imag(); } inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE abs (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sqrt; return sqrt ((real(x) * real(x)) + (imag(x) * imag(x))); } inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE arg (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::atan2; return atan2(x.imag(), x.real()); } inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE norm(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return (real(x) * real(x)) + (imag(x) * imag(x)); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> conj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(x.real(), -x.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> proj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE m = (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)(); if ((x.real() > m) || (x.real() < -m) || (x.imag() > m) || (x.imag() < -m)) { // We have an infinity, return a normalized infinity, respecting the sign of the imaginary part: return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity(), x.imag() < 0 ? -0 : 0); } return x; } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& rho, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& theta) { using std::sin; using std::cos; return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(rho * cos(theta), rho * sin(theta)); } // Global add, sub, mul, div. inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() + v.real(), u.imag() + v.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() - v.real(), u.imag() - v.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator*(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>((u.real() * v.real()) - (u.imag() * v.imag()), (u.real() * v.imag()) + (u.imag() * v.real())); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator/(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE the_norm = std::norm(v); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(((u.real() * v.real()) + (u.imag() * v.imag())) / the_norm, ((u.imag() * v.real()) - (u.real() * v.imag())) / the_norm); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() + v, u.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() - v, u.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator*(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() * v, u.imag() * v); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator/(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() / v, u.imag() / v); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u + v.real(), v.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u - v.real(), -v.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator*(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u * v.real(), u * v.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator/(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE v_norm = norm(v); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>((u * v.real()) / v_norm, (-u * v.imag()) / v_norm); } // Unary plus / minus. inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u) { return u; } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(-u.real(), -u.imag()); } // Equality and inequality. inline bool operator==(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x.real() == y.real()) && (x.imag() == y.imag())); } inline bool operator==(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& y) { return ((x.real() == y) && (x.imag() == BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); } inline bool operator==(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x == y.real()) && (y.imag() == BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); } inline bool operator!=(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x.real() != y.real()) || (x.imag() != y.imag())); } inline bool operator!=(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& y) { return ((x.real() != y) || (x.imag() != BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); } inline bool operator!=(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x != y.real()) || (y.imag() != BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); } // ISO/IEC 14882:2011, Section 26.4.8, transcendentals. inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sqrt(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::fabs; using std::sqrt; // Compute sqrt(x) for x in C: // sqrt(x) = (s , xi / 2s) : for xr > 0, // (|xi| / 2s, +-s) : for xr < 0, // (sqrt(xi), sqrt(xi) : for xr = 0, // where s = sqrt{ [ |xr| + sqrt(xr^2 + xi^2) ] / 2 }, // and the +- sign is the same as the sign of xi. if(x.real() > 0) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE s = sqrt((fabs(x.real()) + std::abs(x)) / 2); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(s, x.imag() / (s * 2)); } else if(x.real() < 0) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE s = sqrt((fabs(x.real()) + std::abs(x)) / 2); const bool imag_is_neg = (x.imag() < 0); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(fabs(x.imag()) / (s * 2), (imag_is_neg ? -s : s)); } else { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sqrt_xi_half = sqrt(x.imag() / 2); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sqrt_xi_half, sqrt_xi_half); } } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sin; using std::cos; using std::exp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2; return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sin_x * cosh_y, cos_x * sinh_y); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sin; using std::cos; using std::exp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2; return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_x * cosh_y, -(sin_x * sinh_y)); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sin; using std::cos; using std::exp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2; return ( complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sin_x * cosh_y, cos_x * sinh_y) / complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_x * cosh_y, -sin_x * sinh_y)); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return -boost::math::cstdfloat::detail::multiply_by_i(std::log(boost::math::cstdfloat::detail::multiply_by_i(x) + std::sqrt(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - (x * x)))); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return boost::math::constants::half_pi<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>() - std::asin(x); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> izz = boost::math::cstdfloat::detail::multiply_by_i(x); return boost::math::cstdfloat::detail::multiply_by_i(std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - izz) - std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) + izz)) / 2; } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> exp(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::exp; return std::polar(exp(x.real()), x.imag()); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::atan2; using std::log; return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(log(std::norm(x)) / 2, atan2(x.imag(), x.real())); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return std::log(x) / boost::math::constants::ln_ten<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, int p) { const bool re_isneg = (x.real() < 0); const bool re_isnan = (x.real() != x.real()); const bool re_isinf = ((!re_isneg) ? bool(+x.real() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()) : bool(-x.real() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())); const bool im_isneg = (x.imag() < 0); const bool im_isnan = (x.imag() != x.imag()); const bool im_isinf = ((!im_isneg) ? bool(+x.imag() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()) : bool(-x.imag() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())); if(re_isnan || im_isnan) { return x; } if(re_isinf || im_isinf) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::quiet_NaN(), std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::quiet_NaN()); } if(p < 0) { if(std::abs(x) < (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::min)()) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity(), std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()); } else { return BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / std::pow(x, -p); } } if(p == 0) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1)); } else { if(p == 1) { return x; } if(std::abs(x) > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE re = (re_isneg ? -std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity() : +std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE im = (im_isneg ? -std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity() : +std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(re, im); } if (p == 2) { return (x * x); } else if(p == 3) { return ((x * x) * x); } else if(p == 4) { const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> x2 = (x * x); return (x2 * x2); } else { // The variable xn stores the binary powers of x. complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> result(((p % 2) != 0) ? x : complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1))); complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> xn (x); int p2 = p; while((p2 /= 2) != 0) { // Square xn for each binary power. xn *= xn; const bool has_binary_power = ((p2 % 2) != 0); if(has_binary_power) { // Multiply the result with each binary power contained in the exponent. result *= xn; } } return result; } } } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& a) { return std::exp(a * std::log(x)); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& a) { return std::exp(a * std::log(x)); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& a) { return std::exp(a * std::log(x)); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sin; using std::cos; using std::exp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_y = sin (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_y = cos (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xp = exp (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xm = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_xp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_x = (exp_xp - exp_xm) / 2; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_x = (exp_xp + exp_xm) / 2; return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_y * sinh_x, cosh_x * sin_y); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sin; using std::cos; using std::exp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_y = sin (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_y = cos (x.imag()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xp = exp (x.real()); const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xm = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_xp; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_x = (exp_xp - exp_xm) / 2; const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_x = (exp_xp + exp_xm) / 2; return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_y * cosh_x, sin_y * sinh_x); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> ex_plus = std::exp(x); const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> ex_minus = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / ex_plus; return (ex_plus - ex_minus) / (ex_plus + ex_minus); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return std::log(x + std::sqrt((x * x) + BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1))); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE my_one(1); const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> zp(x.real() + my_one, x.imag()); const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> zm(x.real() - my_one, x.imag()); return std::log(x + (zp * std::sqrt(zm / zp))); } inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return (std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) + x) - std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - x)) / 2.0; } template<class char_type, class traits_type> inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>& os, const std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { std::basic_ostringstream<char_type, traits_type> ostr; ostr.flags(os.flags()); ostr.imbue(os.getloc()); ostr.precision(os.precision()); ostr << char_type('(') << x.real() << char_type(',') << x.imag() << char_type(')'); return (os << ostr.str()); } template<class char_type, class traits_type> inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>& is, std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE rx; BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE ix; char_type the_char; static_cast<void>(is >> the_char); if(the_char == static_cast<char_type>('(')) { static_cast<void>(is >> rx >> the_char); if(the_char == static_cast<char_type>(',')) { static_cast<void>(is >> ix >> the_char); if(the_char == static_cast<char_type>(')')) { x = complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(rx, ix); } else { is.setstate(ios_base::failbit); } } else if(the_char == static_cast<char_type>(')')) { x = rx; } else { is.setstate(ios_base::failbit); } } else { static_cast<void>(is.putback(the_char)); static_cast<void>(is >> rx); x = rx; } return is; } } // namespace std #endif // BOOST_MATH_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_
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