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Diffstat (limited to 'boost/math/cstdfloat/cstdfloat_complex_std.hpp')
| -rw-r--r-- | boost/math/cstdfloat/cstdfloat_complex_std.hpp | 641 |
1 files changed, 641 insertions, 0 deletions
diff --git a/boost/math/cstdfloat/cstdfloat_complex_std.hpp b/boost/math/cstdfloat/cstdfloat_complex_std.hpp new file mode 100644 index 0000000000..f949a9aa46 --- /dev/null +++ b/boost/math/cstdfloat/cstdfloat_complex_std.hpp @@ -0,0 +1,641 @@ +/////////////////////////////////////////////////////////////////////////////// +// 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_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ + #define _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ + + #if defined(__GNUC__) + #pragma GCC system_header + #endif + + #include <complex> + #include <boost/math/constants/constants.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. + 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())) { } + 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())) { } + 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> 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_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ |