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  1. // Math extensions -*- C++ -*-
  2.  
  3. // Copyright (C) 2013 Free Software Foundation, Inc.
  4. //
  5. // This file is part of the GNU ISO C++ Library.  This library is free
  6. // software; you can redistribute it and/or modify it under the
  7. // terms of the GNU General Public License as published by the
  8. // Free Software Foundation; either version 3, or (at your option)
  9. // any later version.
  10.  
  11. // This library is distributed in the hope that it will be useful,
  12. // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13. // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14. // GNU General Public License for more details.
  15.  
  16. // Under Section 7 of GPL version 3, you are granted additional
  17. // permissions described in the GCC Runtime Library Exception, version
  18. // 3.1, as published by the Free Software Foundation.
  19.  
  20. // You should have received a copy of the GNU General Public License and
  21. // a copy of the GCC Runtime Library Exception along with this program;
  22. // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  23. // <http://www.gnu.org/licenses/>.
  24.  
  25. /** @file ext/cmath
  26.  *  This file is a GNU extension to the Standard C++ Library.
  27.  */
  28.  
  29. #ifndef _EXT_CMATH
  30. #define _EXT_CMATH 1
  31.  
  32. #pragma GCC system_header
  33.  
  34. #if __cplusplus < 201103L
  35. # include <bits/c++0x_warning.h>
  36. #else
  37.  
  38. #include <cmath>
  39. #include <type_traits>
  40.  
  41. namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
  42. {
  43. _GLIBCXX_BEGIN_NAMESPACE_VERSION
  44.  
  45.   // A class for math constants.
  46.   template<typename _RealType>
  47.     struct __math_constants
  48.     {
  49.       static_assert(std::is_floating_point<_RealType>::value,
  50.                     "template argument not a floating point type");
  51.  
  52.       // Constant @f$ \pi @f$.
  53.       static constexpr _RealType __pi = 3.1415926535897932384626433832795029L;
  54.       // Constant @f$ \pi / 2 @f$.
  55.       static constexpr _RealType __pi_half = 1.5707963267948966192313216916397514L;
  56.       // Constant @f$ \pi / 3 @f$.
  57.       static constexpr _RealType __pi_third = 1.0471975511965977461542144610931676L;
  58.       // Constant @f$ \pi / 4 @f$.
  59.       static constexpr _RealType __pi_quarter = 0.7853981633974483096156608458198757L;
  60.       // Constant @f$ \sqrt(\pi / 2) @f$.
  61.       static constexpr _RealType __root_pi_div_2 = 1.2533141373155002512078826424055226L;
  62.       // Constant @f$ 1 / \pi @f$.
  63.       static constexpr _RealType __one_div_pi = 0.3183098861837906715377675267450287L;
  64.       // Constant @f$ 2 / \pi @f$.
  65.       static constexpr _RealType __two_div_pi = 0.6366197723675813430755350534900574L;
  66.       // Constant @f$ 2 / \sqrt(\pi) @f$.
  67.       static constexpr _RealType __two_div_root_pi = 1.1283791670955125738961589031215452L;
  68.  
  69.       // Constant Euler's number @f$ e @f$.
  70.       static constexpr _RealType __e = 2.7182818284590452353602874713526625L;
  71.       // Constant @f$ 1 / e @f$.
  72.       static constexpr _RealType __one_div_e = 0.36787944117144232159552377016146087L;
  73.       // Constant @f$ \log_2(e) @f$.
  74.       static constexpr _RealType __log2_e = 1.4426950408889634073599246810018921L;
  75.       // Constant @f$ \log_10(e) @f$.
  76.       static constexpr _RealType __log10_e = 0.4342944819032518276511289189166051L;
  77.       // Constant @f$ \ln(2) @f$.
  78.       static constexpr _RealType __ln_2 = 0.6931471805599453094172321214581766L;
  79.       // Constant @f$ \ln(3) @f$.
  80.       static constexpr _RealType __ln_3 = 1.0986122886681096913952452369225257L;
  81.       // Constant @f$ \ln(10) @f$.
  82.       static constexpr _RealType __ln_10 = 2.3025850929940456840179914546843642L;
  83.  
  84.       // Constant Euler-Mascheroni @f$ \gamma_E @f$.
  85.       static constexpr _RealType __gamma_e = 0.5772156649015328606065120900824024L;
  86.       // Constant Golden Ratio @f$ \phi @f$.
  87.       static constexpr _RealType __phi = 1.6180339887498948482045868343656381L;
  88.  
  89.       // Constant @f$ \sqrt(2) @f$.
  90.       static constexpr _RealType __root_2 = 1.4142135623730950488016887242096981L;
  91.       // Constant @f$ \sqrt(3) @f$.
  92.       static constexpr _RealType __root_3 = 1.7320508075688772935274463415058724L;
  93.       // Constant @f$ \sqrt(5) @f$.
  94.       static constexpr _RealType __root_5 = 2.2360679774997896964091736687312762L;
  95.       // Constant @f$ \sqrt(7) @f$.
  96.       static constexpr _RealType __root_7 = 2.6457513110645905905016157536392604L;
  97.       // Constant @f$ 1 / \sqrt(2) @f$.
  98.       static constexpr _RealType __one_div_root_2 = 0.7071067811865475244008443621048490L;
  99.     };
  100.  
  101.   // And the template definitions for the constants.
  102.   template<typename _RealType>
  103.     constexpr _RealType __math_constants<_RealType>::__pi;
  104.   template<typename _RealType>
  105.     constexpr _RealType __math_constants<_RealType>::__pi_half;
  106.   template<typename _RealType>
  107.     constexpr _RealType __math_constants<_RealType>::__pi_third;
  108.   template<typename _RealType>
  109.     constexpr _RealType __math_constants<_RealType>::__pi_quarter;
  110.   template<typename _RealType>
  111.     constexpr _RealType __math_constants<_RealType>::__root_pi_div_2;
  112.   template<typename _RealType>
  113.     constexpr _RealType __math_constants<_RealType>::__one_div_pi;
  114.   template<typename _RealType>
  115.     constexpr _RealType __math_constants<_RealType>::__two_div_pi;
  116.   template<typename _RealType>
  117.     constexpr _RealType __math_constants<_RealType>::__two_div_root_pi;
  118.   template<typename _RealType>
  119.     constexpr _RealType __math_constants<_RealType>::__e;
  120.   template<typename _RealType>
  121.     constexpr _RealType __math_constants<_RealType>::__one_div_e;
  122.   template<typename _RealType>
  123.     constexpr _RealType __math_constants<_RealType>::__log2_e;
  124.   template<typename _RealType>
  125.     constexpr _RealType __math_constants<_RealType>::__log10_e;
  126.   template<typename _RealType>
  127.     constexpr _RealType __math_constants<_RealType>::__ln_2;
  128.   template<typename _RealType>
  129.     constexpr _RealType __math_constants<_RealType>::__ln_3;
  130.   template<typename _RealType>
  131.     constexpr _RealType __math_constants<_RealType>::__ln_10;
  132.   template<typename _RealType>
  133.     constexpr _RealType __math_constants<_RealType>::__gamma_e;
  134.   template<typename _RealType>
  135.     constexpr _RealType __math_constants<_RealType>::__phi;
  136.   template<typename _RealType>
  137.     constexpr _RealType __math_constants<_RealType>::__root_2;
  138.   template<typename _RealType>
  139.     constexpr _RealType __math_constants<_RealType>::__root_3;
  140.   template<typename _RealType>
  141.     constexpr _RealType __math_constants<_RealType>::__root_5;
  142.   template<typename _RealType>
  143.     constexpr _RealType __math_constants<_RealType>::__root_7;
  144.   template<typename _RealType>
  145.     constexpr _RealType __math_constants<_RealType>::__one_div_root_2;
  146.  
  147. _GLIBCXX_END_NAMESPACE_VERSION
  148. } // namespace __gnu_cxx
  149.  
  150. #endif // C++11
  151.  
  152. #endif // _EXT_CMATH
  153.