1 /////////////////////////////////////////////////////////////////////////////// 2 // Copyright Christopher Kormanyos 2014. 3 // Copyright John Maddock 2014. 4 // Copyright Paul Bristow 2014. 5 // Distributed under the Boost Software License, 6 // Version 1.0. (See accompanying file LICENSE_1_0.txt 7 // or copy at http://www.boost.org/LICENSE_1_0.txt) 8 // 9 10 // Implement a specialization of std::complex<> for *anything* that 11 // is defined as BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE. 12 13 #ifndef _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ 14 #define _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ 15 16 #if defined(__GNUC__) 17 #pragma GCC system_header 18 #endif 19 20 #include <complex> 21 #include <boost/math/constants/constants.hpp> 22 23 namespace std 24 { 25 // Forward declarations. 26 template<class float_type> 27 class complex; 28 29 template<> 30 class complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>; 31 32 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 33 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 34 35 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE abs (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 36 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE arg (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 37 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE norm(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 38 39 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> conj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 40 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> proj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 41 42 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&, 43 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& = 0); 44 45 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sqrt (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 46 47 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sin (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 48 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cos (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 49 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tan (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 50 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asin (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 51 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acos (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 52 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atan (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 53 54 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> exp (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 55 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 56 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 57 58 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&, 59 int); 60 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&, 61 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&); 62 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&, 63 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 64 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&, 65 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 66 67 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sinh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 68 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cosh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 69 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tanh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 70 71 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 72 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 73 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 74 75 template<class char_type, class traits_type> 76 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>&); 77 78 template<class char_type, class traits_type> 79 inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>&, std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&); 80 81 // Template specialization of the complex class. 82 template<> 83 class complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> 84 { 85 public: 86 typedef BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE value_type; 87 88 explicit complex(const complex<float>&); 89 explicit complex(const complex<double>&); 90 explicit complex(const complex<long double>&); 91 92 #if defined(BOOST_NO_CXX11_CONSTEXPR) complex(const value_type & r=value_type (),const value_type & i=value_type ())93 complex(const value_type& r = value_type(), 94 const value_type& i = value_type()) : re(r), 95 im(i) { } 96 97 template<typename X> complex(const complex<X> & x)98 complex(const complex<X>& x) : re(x.real()), 99 im(x.imag()) { } 100 real() const101 const value_type& real() const { return re; } imag() const102 const value_type& imag() const { return im; } 103 real()104 value_type& real() { return re; } imag()105 value_type& imag() { return im; } 106 #else complex(const value_type & r=value_type (),const value_type & i=value_type ())107 BOOST_CONSTEXPR complex(const value_type& r = value_type(), 108 const value_type& i = value_type()) : re(r), 109 im(i) { } 110 111 template<typename X> complex(const complex<X> & x)112 BOOST_CONSTEXPR complex(const complex<X>& x) : re(x.real()), 113 im(x.imag()) { } 114 real() const115 value_type real() const { return re; } imag() const116 value_type imag() const { return im; } 117 #endif 118 real(value_type r)119 void real(value_type r) { re = r; } imag(value_type i)120 void imag(value_type i) { im = i; } 121 operator =(const value_type & v)122 complex<value_type>& operator=(const value_type& v) 123 { 124 re = v; 125 im = value_type(0); 126 return *this; 127 } 128 operator +=(const value_type & v)129 complex<value_type>& operator+=(const value_type& v) 130 { 131 re += v; 132 return *this; 133 } 134 operator -=(const value_type & v)135 complex<value_type>& operator-=(const value_type& v) 136 { 137 re -= v; 138 return *this; 139 } 140 operator *=(const value_type & v)141 complex<value_type>& operator*=(const value_type& v) 142 { 143 re *= v; 144 im *= v; 145 return *this; 146 } 147 operator /=(const value_type & v)148 complex<value_type>& operator/=(const value_type& v) 149 { 150 re /= v; 151 im /= v; 152 return *this; 153 } 154 155 template<typename X> operator =(const complex<X> & x)156 complex<value_type>& operator=(const complex<X>& x) 157 { 158 re = x.real(); 159 im = x.imag(); 160 return *this; 161 } 162 163 template<typename X> operator +=(const complex<X> & x)164 complex<value_type>& operator+=(const complex<X>& x) 165 { 166 re += x.real(); 167 im += x.imag(); 168 return *this; 169 } 170 171 template<typename X> operator -=(const complex<X> & x)172 complex<value_type>& operator-=(const complex<X>& x) 173 { 174 re -= x.real(); 175 im -= x.imag(); 176 return *this; 177 } 178 179 template<typename X> operator *=(const complex<X> & x)180 complex<value_type>& operator*=(const complex<X>& x) 181 { 182 const value_type tmp_real = (re * x.real()) - (im * x.imag()); 183 im = (re * x.imag()) + (im * x.real()); 184 re = tmp_real; 185 return *this; 186 } 187 188 template<typename X> operator /=(const complex<X> & x)189 complex<value_type>& operator/=(const complex<X>& x) 190 { 191 const value_type tmp_real = (re * x.real()) + (im * x.imag()); 192 const value_type the_norm = std::norm(x); 193 im = ((im * x.real()) - (re * x.imag())) / the_norm; 194 re = tmp_real / the_norm; 195 return *this; 196 } 197 198 private: 199 value_type re; 200 value_type im; 201 }; 202 203 // Constructors from built-in complex representation of floating-point types. complex(const complex<float> & f)204 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(const complex<double> & d)205 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(const complex<long double> & ld)206 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())) { } 207 } // namespace std 208 209 namespace boost { namespace math { namespace cstdfloat { namespace detail { multiply_by_i(const std::complex<float_type> & x)210 template<class float_type> std::complex<float_type> multiply_by_i(const std::complex<float_type>& x) 211 { 212 // Multiply x (in C) by I (the imaginary component), and return the result. 213 return std::complex<float_type>(-x.imag(), x.real()); 214 } 215 } } } } // boost::math::cstdfloat::detail 216 217 namespace std 218 { 219 // ISO/IEC 14882:2011, Section 26.4.7, specific values. real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)220 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return x.real(); } imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)221 inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return x.imag(); } 222 abs(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)223 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))); } arg(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)224 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()); } norm(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)225 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)); } 226 conj(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)227 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()); } 228 proj(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)229 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> proj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 230 { 231 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE m = (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)(); 232 if ((x.real() > m) 233 || (x.real() < -m) 234 || (x.imag() > m) 235 || (x.imag() < -m)) 236 { 237 // We have an infinity, return a normalized infinity, respecting the sign of the imaginary part: 238 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity(), x.imag() < 0 ? -0 : 0); 239 } 240 return x; 241 } 242 polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & rho,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & theta)243 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& rho, 244 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& theta) 245 { 246 using std::sin; 247 using std::cos; 248 249 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(rho * cos(theta), rho * sin(theta)); 250 } 251 252 // Global add, sub, mul, div. operator +(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)253 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()); } operator -(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)254 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()); } 255 operator *(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)256 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) 257 { 258 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>((u.real() * v.real()) - (u.imag() * v.imag()), 259 (u.real() * v.imag()) + (u.imag() * v.real())); 260 } 261 operator /(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)262 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) 263 { 264 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE the_norm = std::norm(v); 265 266 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(((u.real() * v.real()) + (u.imag() * v.imag())) / the_norm, 267 ((u.imag() * v.real()) - (u.real() * v.imag())) / the_norm); 268 } 269 operator +(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & v)270 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()); } operator -(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & v)271 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()); } operator *(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & v)272 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); } operator /(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & v)273 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); } 274 operator +(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)275 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()); } operator -(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)276 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()); } operator *(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)277 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()); } operator /(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & u,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & v)278 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); } 279 280 // Unary plus / minus. operator +(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u)281 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u) { return u; } operator -(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & u)282 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()); } 283 284 // Equality and inequality. operator ==(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & y)285 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())); } operator ==(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & y)286 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))); } operator ==(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & x,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & y)287 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))); } operator !=(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & y)288 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())); } operator !=(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & y)289 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))); } operator !=(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & x,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & y)290 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))); } 291 292 // ISO/IEC 14882:2011, Section 26.4.8, transcendentals. sqrt(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)293 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sqrt(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 294 { 295 using std::fabs; 296 using std::sqrt; 297 298 // Compute sqrt(x) for x in C: 299 // sqrt(x) = (s , xi / 2s) : for xr > 0, 300 // (|xi| / 2s, +-s) : for xr < 0, 301 // (sqrt(xi), sqrt(xi) : for xr = 0, 302 // where s = sqrt{ [ |xr| + sqrt(xr^2 + xi^2) ] / 2 }, 303 // and the +- sign is the same as the sign of xi. 304 305 if(x.real() > 0) 306 { 307 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE s = sqrt((fabs(x.real()) + std::abs(x)) / 2); 308 309 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(s, x.imag() / (s * 2)); 310 } 311 else if(x.real() < 0) 312 { 313 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE s = sqrt((fabs(x.real()) + std::abs(x)) / 2); 314 315 const bool imag_is_neg = (x.imag() < 0); 316 317 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(fabs(x.imag()) / (s * 2), (imag_is_neg ? -s : s)); 318 } 319 else 320 { 321 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sqrt_xi_half = sqrt(x.imag() / 2); 322 323 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sqrt_xi_half, sqrt_xi_half); 324 } 325 } 326 sin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)327 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 328 { 329 using std::sin; 330 using std::cos; 331 using std::exp; 332 333 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real()); 334 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real()); 335 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag()); 336 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp; 337 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2; 338 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2; 339 340 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sin_x * cosh_y, cos_x * sinh_y); 341 } 342 cos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)343 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 344 { 345 using std::sin; 346 using std::cos; 347 using std::exp; 348 349 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real()); 350 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real()); 351 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag()); 352 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp; 353 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2; 354 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2; 355 356 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_x * cosh_y, -(sin_x * sinh_y)); 357 } 358 tan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)359 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 360 { 361 using std::sin; 362 using std::cos; 363 using std::exp; 364 365 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real()); 366 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real()); 367 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag()); 368 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp; 369 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2; 370 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2; 371 372 return ( complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sin_x * cosh_y, cos_x * sinh_y) 373 / complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_x * cosh_y, -sin_x * sinh_y)); 374 } 375 asin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)376 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 377 { 378 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)))); 379 } 380 acos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)381 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 382 { 383 return boost::math::constants::half_pi<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>() - std::asin(x); 384 } 385 atan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)386 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 387 { 388 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> izz = boost::math::cstdfloat::detail::multiply_by_i(x); 389 390 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; 391 } 392 exp(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)393 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> exp(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 394 { 395 using std::exp; 396 397 return std::polar(exp(x.real()), x.imag()); 398 } 399 log(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)400 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 401 { 402 using std::atan2; 403 using std::log; 404 405 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(log(std::norm(x)) / 2, atan2(x.imag(), x.real())); 406 } 407 log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)408 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 409 { 410 return std::log(x) / boost::math::constants::ln_ten<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(); 411 } 412 pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,int p)413 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, 414 int p) 415 { 416 const bool re_isneg = (x.real() < 0); 417 const bool re_isnan = (x.real() != x.real()); 418 const bool re_isinf = ((!re_isneg) ? bool(+x.real() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()) 419 : bool(-x.real() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())); 420 421 const bool im_isneg = (x.imag() < 0); 422 const bool im_isnan = (x.imag() != x.imag()); 423 const bool im_isinf = ((!im_isneg) ? bool(+x.imag() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()) 424 : bool(-x.imag() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())); 425 426 if(re_isnan || im_isnan) { return x; } 427 428 if(re_isinf || im_isinf) 429 { 430 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::quiet_NaN(), 431 std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::quiet_NaN()); 432 } 433 434 if(p < 0) 435 { 436 if(std::abs(x) < (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::min)()) 437 { 438 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity(), 439 std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()); 440 } 441 else 442 { 443 return BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / std::pow(x, -p); 444 } 445 } 446 447 if(p == 0) 448 { 449 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1)); 450 } 451 else 452 { 453 if(p == 1) { return x; } 454 455 if(std::abs(x) > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()) 456 { 457 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE re = (re_isneg ? -std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity() 458 : +std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()); 459 460 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE im = (im_isneg ? -std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity() 461 : +std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()); 462 463 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(re, im); 464 } 465 466 if (p == 2) { return (x * x); } 467 else if(p == 3) { return ((x * x) * x); } 468 else if(p == 4) { const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> x2 = (x * x); return (x2 * x2); } 469 else 470 { 471 // The variable xn stores the binary powers of x. 472 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))); 473 complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> xn (x); 474 475 int p2 = p; 476 477 while((p2 /= 2) != 0) 478 { 479 // Square xn for each binary power. 480 xn *= xn; 481 482 const bool has_binary_power = ((p2 % 2) != 0); 483 484 if(has_binary_power) 485 { 486 // Multiply the result with each binary power contained in the exponent. 487 result *= xn; 488 } 489 } 490 491 return result; 492 } 493 } 494 } 495 pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & a)496 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, 497 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& a) 498 { 499 return std::exp(a * std::log(x)); 500 } 501 pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & a)502 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, 503 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& a) 504 { 505 return std::exp(a * std::log(x)); 506 } 507 pow(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE & x,const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & a)508 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x, 509 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& a) 510 { 511 return std::exp(a * std::log(x)); 512 } 513 sinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)514 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 515 { 516 using std::sin; 517 using std::cos; 518 using std::exp; 519 520 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_y = sin (x.imag()); 521 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_y = cos (x.imag()); 522 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xp = exp (x.real()); 523 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xm = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_xp; 524 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_x = (exp_xp - exp_xm) / 2; 525 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_x = (exp_xp + exp_xm) / 2; 526 527 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_y * sinh_x, cosh_x * sin_y); 528 } 529 cosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)530 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 531 { 532 using std::sin; 533 using std::cos; 534 using std::exp; 535 536 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_y = sin (x.imag()); 537 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_y = cos (x.imag()); 538 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xp = exp (x.real()); 539 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xm = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_xp; 540 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_x = (exp_xp - exp_xm) / 2; 541 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_x = (exp_xp + exp_xm) / 2; 542 543 return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_y * cosh_x, sin_y * sinh_x); 544 } 545 tanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)546 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 547 { 548 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> ex_plus = std::exp(x); 549 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> ex_minus = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / ex_plus; 550 551 return (ex_plus - ex_minus) / (ex_plus + ex_minus); 552 } 553 asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)554 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 555 { 556 return std::log(x + std::sqrt((x * x) + BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1))); 557 } 558 acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)559 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 560 { 561 const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE my_one(1); 562 563 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> zp(x.real() + my_one, x.imag()); 564 const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> zm(x.real() - my_one, x.imag()); 565 566 return std::log(x + (zp * std::sqrt(zm / zp))); 567 } 568 atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)569 inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) 570 { 571 return (std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) + x) - std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - x)) / 2.0; 572 } 573 574 template<class char_type, class traits_type> operator <<(std::basic_ostream<char_type,traits_type> & os,const std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)575 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) 576 { 577 std::basic_ostringstream<char_type, traits_type> ostr; 578 579 ostr.flags(os.flags()); 580 ostr.imbue(os.getloc()); 581 ostr.precision(os.precision()); 582 583 ostr << char_type('(') 584 << x.real() 585 << char_type(',') 586 << x.imag() 587 << char_type(')'); 588 589 return (os << ostr.str()); 590 } 591 592 template<class char_type, class traits_type> operator >>(std::basic_istream<char_type,traits_type> & is,std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> & x)593 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) 594 { 595 BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE rx; 596 BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE ix; 597 598 char_type the_char; 599 600 static_cast<void>(is >> the_char); 601 602 if(the_char == static_cast<char_type>('(')) 603 { 604 static_cast<void>(is >> rx >> the_char); 605 606 if(the_char == static_cast<char_type>(',')) 607 { 608 static_cast<void>(is >> ix >> the_char); 609 610 if(the_char == static_cast<char_type>(')')) 611 { 612 x = complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(rx, ix); 613 } 614 else 615 { 616 is.setstate(ios_base::failbit); 617 } 618 } 619 else if(the_char == static_cast<char_type>(')')) 620 { 621 x = rx; 622 } 623 else 624 { 625 is.setstate(ios_base::failbit); 626 } 627 } 628 else 629 { 630 static_cast<void>(is.putback(the_char)); 631 632 static_cast<void>(is >> rx); 633 634 x = rx; 635 } 636 637 return is; 638 } 639 } // namespace std 640 641 #endif // _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_ 642