libstdc++-v3/include/tr1/complex

   1 // TR1 complex -*- C++ -*-
   2
   3 // Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011
   4 // Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16
  17 // Under Section 7 of GPL version 3, you are granted additional
  18 // permissions described in the GCC Runtime Library Exception, version
  19 // 3.1, as published by the Free Software Foundation.
  20
  21 // You should have received a copy of the GNU General Public License and
  22 // a copy of the GCC Runtime Library Exception along with this program;
  23 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  24 // <http://www.gnu.org/licenses/>.
  25
  26 /** @file tr1/complex
  27  *  This is a TR1 C++ Library header.
  28  */
  29
  30 #ifndef _GLIBCXX_TR1_COMPLEX
  31 #define _GLIBCXX_TR1_COMPLEX 1
  32
  33 #pragma GCC system_header
  34
  35 #include <complex>
  36
  37 namespace std _GLIBCXX_VISIBILITY(default)
  38 {
  39 namespace tr1
  40 {
  41 _GLIBCXX_BEGIN_NAMESPACE_VERSION
  42
  43   /**
  44    * @addtogroup complex_numbers
  45    * @{
  46    */
  47
  48 #if __cplusplus >= 201103L
  49   using std::acos;
  50   using std::asin;
  51   using std::atan;
  52 #else
  53   template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
  54   template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
  55   template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
  56 #endif
  57
  58   template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
  59   template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
  60   template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
  61
  62   // The std::fabs return type in C++0x mode is different (just _Tp).
  63   template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
  64
  65 #if __cplusplus < 201103L
  66   template<typename _Tp>
  67     inline std::complex<_Tp>
  68     __complex_acos(const std::complex<_Tp>& __z)
  69     {
  70       const std::complex<_Tp> __t = std::tr1::asin(__z);
  71       const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
  72       return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
  73     }
  74
  75 #if _GLIBCXX_USE_C99_COMPLEX_TR1
  76   inline __complex__ float
  77   __complex_acos(__complex__ float __z)
  78   { return __builtin_cacosf(__z); }
  79
  80   inline __complex__ double
  81   __complex_acos(__complex__ double __z)
  82   { return __builtin_cacos(__z); }
  83
  84   inline __complex__ long double
  85   __complex_acos(const __complex__ long double& __z)
  86   { return __builtin_cacosl(__z); }
  87
  88   template<typename _Tp>
  89     inline std::complex<_Tp>
  90     acos(const std::complex<_Tp>& __z)
  91     { return __complex_acos(__z.__rep()); }
  92 #else
  93   /// acos(__z) [8.1.2].
  94   //  Effects:  Behaves the same as C99 function cacos, defined
  95   //            in subclause 7.3.5.1.
  96   template<typename _Tp>
  97     inline std::complex<_Tp>
  98     acos(const std::complex<_Tp>& __z)
  99     { return __complex_acos(__z); }
 100 #endif
 101
 102   template<typename _Tp>
 103     inline std::complex<_Tp>
 104     __complex_asin(const std::complex<_Tp>& __z)
 105     {
 106       std::complex<_Tp> __t(-__z.imag(), __z.real());
 107       __t = std::tr1::asinh(__t);
 108       return std::complex<_Tp>(__t.imag(), -__t.real());
 109     }
 110
 111 #if _GLIBCXX_USE_C99_COMPLEX_TR1
 112   inline __complex__ float
 113   __complex_asin(__complex__ float __z)
 114   { return __builtin_casinf(__z); }
 115
 116   inline __complex__ double
 117   __complex_asin(__complex__ double __z)
 118   { return __builtin_casin(__z); }
 119
 120   inline __complex__ long double
 121   __complex_asin(const __complex__ long double& __z)
 122   { return __builtin_casinl(__z); }
 123
 124   template<typename _Tp>
 125     inline std::complex<_Tp>
 126     asin(const std::complex<_Tp>& __z)
 127     { return __complex_asin(__z.__rep()); }
 128 #else
 129   /// asin(__z) [8.1.3].
 130   //  Effects:  Behaves the same as C99 function casin, defined
 131   //            in subclause 7.3.5.2.
 132   template<typename _Tp>
 133     inline std::complex<_Tp>
 134     asin(const std::complex<_Tp>& __z)
 135     { return __complex_asin(__z); }
 136 #endif
 137
 138   template<typename _Tp>
 139     std::complex<_Tp>
 140     __complex_atan(const std::complex<_Tp>& __z)
 141     {
 142       const _Tp __r2 = __z.real() * __z.real();
 143       const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
 144
 145       _Tp __num = __z.imag() + _Tp(1.0);
 146       _Tp __den = __z.imag() - _Tp(1.0);
 147
 148       __num = __r2 + __num * __num;
 149       __den = __r2 + __den * __den;
 150
 151       return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
 152                                _Tp(0.25) * log(__num / __den));
 153     }
 154
 155 #if _GLIBCXX_USE_C99_COMPLEX_TR1
 156   inline __complex__ float
 157   __complex_atan(__complex__ float __z)
 158   { return __builtin_catanf(__z); }
 159
 160   inline __complex__ double
 161   __complex_atan(__complex__ double __z)
 162   { return __builtin_catan(__z); }
 163
 164   inline __complex__ long double
 165   __complex_atan(const __complex__ long double& __z)
 166   { return __builtin_catanl(__z); }
 167
 168   template<typename _Tp>
 169     inline std::complex<_Tp>
 170     atan(const std::complex<_Tp>& __z)
 171     { return __complex_atan(__z.__rep()); }
 172 #else
 173   /// atan(__z) [8.1.4].
 174   //  Effects:  Behaves the same as C99 function catan, defined
 175   //            in subclause 7.3.5.3.
 176   template<typename _Tp>
 177     inline std::complex<_Tp>
 178     atan(const std::complex<_Tp>& __z)
 179     { return __complex_atan(__z); }
 180 #endif
 181
 182 #endif // C++11
 183
 184   template<typename _Tp>
 185     std::complex<_Tp>
 186     __complex_acosh(const std::complex<_Tp>& __z)
 187     {
 188       // Kahan's formula.
 189       return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
 190                                  + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
 191     }
 192
 193 #if _GLIBCXX_USE_C99_COMPLEX_TR1
 194   inline __complex__ float
 195   __complex_acosh(__complex__ float __z)
 196   { return __builtin_cacoshf(__z); }
 197
 198   inline __complex__ double
 199   __complex_acosh(__complex__ double __z)
 200   { return __builtin_cacosh(__z); }
 201
 202   inline __complex__ long double
 203   __complex_acosh(const __complex__ long double& __z)
 204   { return __builtin_cacoshl(__z); }
 205
 206   template<typename _Tp>
 207     inline std::complex<_Tp>
 208     acosh(const std::complex<_Tp>& __z)
 209     { return __complex_acosh(__z.__rep()); }
 210 #else
 211   /// acosh(__z) [8.1.5].
 212   //  Effects:  Behaves the same as C99 function cacosh, defined
 213   //            in subclause 7.3.6.1.
 214   template<typename _Tp>
 215     inline std::complex<_Tp>
 216     acosh(const std::complex<_Tp>& __z)
 217     { return __complex_acosh(__z); }
 218 #endif
 219
 220   template<typename _Tp>
 221     std::complex<_Tp>
 222     __complex_asinh(const std::complex<_Tp>& __z)
 223     {
 224       std::complex<_Tp> __t((__z.real() - __z.imag())
 225                             * (__z.real() + __z.imag()) + _Tp(1.0),
 226                             _Tp(2.0) * __z.real() * __z.imag());
 227       __t = std::sqrt(__t);
 228
 229       return std::log(__t + __z);
 230     }
 231
 232 #if _GLIBCXX_USE_C99_COMPLEX_TR1
 233   inline __complex__ float
 234   __complex_asinh(__complex__ float __z)
 235   { return __builtin_casinhf(__z); }
 236
 237   inline __complex__ double
 238   __complex_asinh(__complex__ double __z)
 239   { return __builtin_casinh(__z); }
 240
 241   inline __complex__ long double
 242   __complex_asinh(const __complex__ long double& __z)
 243   { return __builtin_casinhl(__z); }
 244
 245   template<typename _Tp>
 246     inline std::complex<_Tp>
 247     asinh(const std::complex<_Tp>& __z)
 248     { return __complex_asinh(__z.__rep()); }
 249 #else
 250   /// asinh(__z) [8.1.6].
 251   //  Effects:  Behaves the same as C99 function casin, defined
 252   //            in subclause 7.3.6.2.
 253   template<typename _Tp>
 254     inline std::complex<_Tp>
 255     asinh(const std::complex<_Tp>& __z)
 256     { return __complex_asinh(__z); }
 257 #endif
 258
 259   template<typename _Tp>
 260     std::complex<_Tp>
 261     __complex_atanh(const std::complex<_Tp>& __z)
 262     {
 263       const _Tp __i2 = __z.imag() * __z.imag();
 264       const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
 265
 266       _Tp __num = _Tp(1.0) + __z.real();
 267       _Tp __den = _Tp(1.0) - __z.real();
 268
 269       __num = __i2 + __num * __num;
 270       __den = __i2 + __den * __den;
 271
 272       return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
 273                                _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
 274     }
 275
 276 #if _GLIBCXX_USE_C99_COMPLEX_TR1
 277   inline __complex__ float
 278   __complex_atanh(__complex__ float __z)
 279   { return __builtin_catanhf(__z); }
 280
 281   inline __complex__ double
 282   __complex_atanh(__complex__ double __z)
 283   { return __builtin_catanh(__z); }
 284
 285   inline __complex__ long double
 286   __complex_atanh(const __complex__ long double& __z)
 287   { return __builtin_catanhl(__z); }
 288
 289   template<typename _Tp>
 290     inline std::complex<_Tp>
 291     atanh(const std::complex<_Tp>& __z)
 292     { return __complex_atanh(__z.__rep()); }
 293 #else
 294   /// atanh(__z) [8.1.7].
 295   //  Effects:  Behaves the same as C99 function catanh, defined
 296   //            in subclause 7.3.6.3.
 297   template<typename _Tp>
 298     inline std::complex<_Tp>
 299     atanh(const std::complex<_Tp>& __z)
 300     { return __complex_atanh(__z); }
 301 #endif
 302
 303   template<typename _Tp>
 304     inline std::complex<_Tp>
 305     /// fabs(__z) [8.1.8].
 306     //  Effects:  Behaves the same as C99 function cabs, defined
 307     //            in subclause 7.3.8.1.
 308     fabs(const std::complex<_Tp>& __z)
 309     { return std::abs(__z); }
 310
 311   /// Additional overloads [8.1.9].
 312 #if __cplusplus < 201103L
 313
 314   template<typename _Tp>
 315     inline typename __gnu_cxx::__promote<_Tp>::__type
 316     arg(_Tp __x)
 317     {
 318       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
 319 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
 320       return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
 321                                : __type();
 322 #else
 323       return std::arg(std::complex<__type>(__x));
 324 #endif
 325     }
 326
 327   template<typename _Tp>
 328     inline typename __gnu_cxx::__promote<_Tp>::__type
 329     imag(_Tp)
 330     { return _Tp(); }
 331
 332   template<typename _Tp>
 333     inline typename __gnu_cxx::__promote<_Tp>::__type
 334     norm(_Tp __x)
 335     {
 336       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
 337       return __type(__x) * __type(__x);
 338     }
 339
 340   template<typename _Tp>
 341     inline typename __gnu_cxx::__promote<_Tp>::__type
 342     real(_Tp __x)
 343     { return __x; }
 344
 345 #endif
 346
 347   template<typename _Tp, typename _Up>
 348     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
 349     pow(const std::complex<_Tp>& __x, const _Up& __y)
 350     {
 351       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
 352       return std::pow(std::complex<__type>(__x), __type(__y));
 353     }
 354
 355   template<typename _Tp, typename _Up>
 356     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
 357     pow(const _Tp& __x, const std::complex<_Up>& __y)
 358     {
 359       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
 360       return std::pow(__type(__x), std::complex<__type>(__y));
 361     }
 362
 363   template<typename _Tp, typename _Up>
 364     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
 365     pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
 366     {
 367       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
 368       return std::pow(std::complex<__type>(__x),
 369                       std::complex<__type>(__y));
 370     }
 371
 372   using std::arg;
 373
 374   template<typename _Tp>
 375     inline std::complex<_Tp>
 376     conj(const std::complex<_Tp>& __z)
 377     { return std::conj(__z); }
 378
 379   template<typename _Tp>
 380     inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
 381     conj(_Tp __x)
 382     { return __x; }
 383
 384   using std::imag;
 385   using std::norm;
 386   using std::polar;
 387
 388   template<typename _Tp, typename _Up>
 389     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
 390     polar(const _Tp& __rho, const _Up& __theta)
 391     {
 392       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
 393       return std::polar(__type(__rho), __type(__theta));
 394     }
 395
 396   using std::real;
 397
 398   template<typename _Tp>
 399     inline std::complex<_Tp>
 400     pow(const std::complex<_Tp>& __x, const _Tp& __y)
 401     { return std::pow(__x, __y); }
 402
 403   template<typename _Tp>
 404     inline std::complex<_Tp>
 405     pow(const _Tp& __x, const std::complex<_Tp>& __y)
 406     { return std::pow(__x, __y); }
 407
 408   template<typename _Tp>
 409     inline std::complex<_Tp>
 410     pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y)
 411     { return std::pow(__x, __y); }
 412
 413 // @} group complex_numbers
 414
 415 _GLIBCXX_END_NAMESPACE_VERSION
 416 }
 417 }
 418
 419 #endif // _GLIBCXX_TR1_COMPLEX