// Math extensions -*- C++ -*- // Copyright (C) 2013-2020 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free // software; you can redistribute it and/or modify it under the // terms of the GNU General Public License as published by the // Free Software Foundation; either version 3, or (at your option) // any later version. // This library is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // Under Section 7 of GPL version 3, you are granted additional // permissions described in the GCC Runtime Library Exception, version // 3.1, as published by the Free Software Foundation. // You should have received a copy of the GNU General Public License and // a copy of the GCC Runtime Library Exception along with this program; // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see // <http://www.gnu.org/licenses/>. /** @file ext/cmath * This file is a GNU extension to the Standard C++ Library. */ #ifndef _EXT_CMATH #define _EXT_CMATH 1 #pragma GCC system_header #if __cplusplus < 201103L # include <bits/c++0x_warning.h> #else #include <cmath> #include <type_traits> namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) { _GLIBCXX_BEGIN_NAMESPACE_VERSION // A class for math constants. template<typename _RealType> struct __math_constants { static_assert(std::is_floating_point<_RealType>::value, "template argument not a floating point type"); // Constant @f$ \pi @f$. static constexpr _RealType __pi = 3.1415926535897932384626433832795029L; // Constant @f$ \pi / 2 @f$. static constexpr _RealType __pi_half = 1.5707963267948966192313216916397514L; // Constant @f$ \pi / 3 @f$. static constexpr _RealType __pi_third = 1.0471975511965977461542144610931676L; // Constant @f$ \pi / 4 @f$. static constexpr _RealType __pi_quarter = 0.7853981633974483096156608458198757L; // Constant @f$ \sqrt(\pi / 2) @f$. static constexpr _RealType __root_pi_div_2 = 1.2533141373155002512078826424055226L; // Constant @f$ 1 / \pi @f$. static constexpr _RealType __one_div_pi = 0.3183098861837906715377675267450287L; // Constant @f$ 2 / \pi @f$. static constexpr _RealType __two_div_pi = 0.6366197723675813430755350534900574L; // Constant @f$ 2 / \sqrt(\pi) @f$. static constexpr _RealType __two_div_root_pi = 1.1283791670955125738961589031215452L; // Constant Euler's number @f$ e @f$. static constexpr _RealType __e = 2.7182818284590452353602874713526625L; // Constant @f$ 1 / e @f$. static constexpr _RealType __one_div_e = 0.36787944117144232159552377016146087L; // Constant @f$ \log_2(e) @f$. static constexpr _RealType __log2_e = 1.4426950408889634073599246810018921L; // Constant @f$ \log_10(e) @f$. static constexpr _RealType __log10_e = 0.4342944819032518276511289189166051L; // Constant @f$ \ln(2) @f$. static constexpr _RealType __ln_2 = 0.6931471805599453094172321214581766L; // Constant @f$ \ln(3) @f$. static constexpr _RealType __ln_3 = 1.0986122886681096913952452369225257L; // Constant @f$ \ln(10) @f$. static constexpr _RealType __ln_10 = 2.3025850929940456840179914546843642L; // Constant Euler-Mascheroni @f$ \gamma_E @f$. static constexpr _RealType __gamma_e = 0.5772156649015328606065120900824024L; // Constant Golden Ratio @f$ \phi @f$. static constexpr _RealType __phi = 1.6180339887498948482045868343656381L; // Constant @f$ \sqrt(2) @f$. static constexpr _RealType __root_2 = 1.4142135623730950488016887242096981L; // Constant @f$ \sqrt(3) @f$. static constexpr _RealType __root_3 = 1.7320508075688772935274463415058724L; // Constant @f$ \sqrt(5) @f$. static constexpr _RealType __root_5 = 2.2360679774997896964091736687312762L; // Constant @f$ \sqrt(7) @f$. static constexpr _RealType __root_7 = 2.6457513110645905905016157536392604L; // Constant @f$ 1 / \sqrt(2) @f$. static constexpr _RealType __one_div_root_2 = 0.7071067811865475244008443621048490L; }; // And the template definitions for the constants. template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__pi; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__pi_half; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__pi_third; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__pi_quarter; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__root_pi_div_2; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__one_div_pi; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__two_div_pi; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__two_div_root_pi; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__e; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__one_div_e; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__log2_e; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__log10_e; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__ln_2; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__ln_3; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__ln_10; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__gamma_e; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__phi; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__root_2; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__root_3; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__root_5; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__root_7; template<typename _RealType> constexpr _RealType __math_constants<_RealType>::__one_div_root_2; _GLIBCXX_END_NAMESPACE_VERSION } // namespace __gnu_cxx #endif // C++11 #endif // _EXT_CMATH