numbers
Go to the documentation of this file.
// <numbers> -*- C++ -*-
// Copyright (C) 2019-2025 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 include/numbers
* This is a Standard C++ Library header.
*/
#ifndef _GLIBCXX_NUMBERS
#define _GLIBCXX_NUMBERS 1
#ifdef _GLIBCXX_SYSHDR
#pragma GCC system_header
#endif
#define __glibcxx_want_math_constants
#include <bits/version.h>
#ifdef __cpp_lib_math_constants // C++ >= 20
#include <type_traits>
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpedantic" // Q extension
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/** @defgroup math_constants Mathematical constants
* @ingroup numerics
* @{
*/
/// Namespace for mathematical constants
namespace numbers
{
/// @cond undocumented
template<typename _Tp>
using _Enable_if_floating = enable_if_t<is_floating_point_v<_Tp>, _Tp>;
/// @endcond
/// e
template<typename _Tp>
inline constexpr _Tp e_v
= _Enable_if_floating<_Tp>(2.718281828459045235360287471352662498L);
/// log_2 e
template<typename _Tp>
inline constexpr _Tp log2e_v
= _Enable_if_floating<_Tp>(1.442695040888963407359924681001892137L);
/// log_10 e
template<typename _Tp>
inline constexpr _Tp log10e_v
= _Enable_if_floating<_Tp>(0.434294481903251827651128918916605082L);
/// pi
template<typename _Tp>
inline constexpr _Tp pi_v
= _Enable_if_floating<_Tp>(3.141592653589793238462643383279502884L);
/// 1/pi
template<typename _Tp>
inline constexpr _Tp inv_pi_v
= _Enable_if_floating<_Tp>(0.318309886183790671537767526745028724L);
/// 1/sqrt(pi)
template<typename _Tp>
inline constexpr _Tp inv_sqrtpi_v
= _Enable_if_floating<_Tp>(0.564189583547756286948079451560772586L);
/// log_e 2
template<typename _Tp>
inline constexpr _Tp ln2_v
= _Enable_if_floating<_Tp>(0.693147180559945309417232121458176568L);
/// log_e 10
template<typename _Tp>
inline constexpr _Tp ln10_v
= _Enable_if_floating<_Tp>(2.302585092994045684017991454684364208L);
/// sqrt(2)
template<typename _Tp>
inline constexpr _Tp sqrt2_v
= _Enable_if_floating<_Tp>(1.414213562373095048801688724209698079L);
/// sqrt(3)
template<typename _Tp>
inline constexpr _Tp sqrt3_v
= _Enable_if_floating<_Tp>(1.732050807568877293527446341505872367L);
/// 1/sqrt(3)
template<typename _Tp>
inline constexpr _Tp inv_sqrt3_v
= _Enable_if_floating<_Tp>(0.577350269189625764509148780501957456L);
/// The Euler-Mascheroni constant
template<typename _Tp>
inline constexpr _Tp egamma_v
= _Enable_if_floating<_Tp>(0.577215664901532860606512090082402431L);
/// The golden ratio, (1+sqrt(5))/2
template<typename _Tp>
inline constexpr _Tp phi_v
= _Enable_if_floating<_Tp>(1.618033988749894848204586834365638118L);
inline constexpr double e = e_v<double>;
inline constexpr double log2e = log2e_v<double>;
inline constexpr double log10e = log10e_v<double>;
inline constexpr double pi = pi_v<double>;
inline constexpr double inv_pi = inv_pi_v<double>;
inline constexpr double inv_sqrtpi = inv_sqrtpi_v<double>;
inline constexpr double ln2 = ln2_v<double>;
inline constexpr double ln10 = ln10_v<double>;
inline constexpr double sqrt2 = sqrt2_v<double>;
inline constexpr double sqrt3 = sqrt3_v<double>;
inline constexpr double inv_sqrt3 = inv_sqrt3_v<double>;
inline constexpr double egamma = egamma_v<double>;
inline constexpr double phi = phi_v<double>;
#define __glibcxx_numbers(TYPE, SUFFIX) \
/* e */ \
template<> \
inline constexpr TYPE e_v<TYPE> \
= 2.718281828459045235360287471352662498##SUFFIX; \
\
/* log_2 e */ \
template<> \
inline constexpr TYPE log2e_v<TYPE> \
= 1.442695040888963407359924681001892137##SUFFIX; \
\
/* log_10 e */ \
template<> \
inline constexpr TYPE log10e_v<TYPE> \
= 0.434294481903251827651128918916605082##SUFFIX; \
\
/* pi */ \
template<> \
inline constexpr TYPE pi_v<TYPE> \
= 3.141592653589793238462643383279502884##SUFFIX; \
\
/* 1/pi */ \
template<> \
inline constexpr TYPE inv_pi_v<TYPE> \
= 0.318309886183790671537767526745028724##SUFFIX; \
\
/* 1/sqrt(pi) */ \
template<> \
inline constexpr TYPE inv_sqrtpi_v<TYPE> \
= 0.564189583547756286948079451560772586##SUFFIX; \
\
/* log_e 2 */ \
template<> \
inline constexpr TYPE ln2_v<TYPE> \
= 0.693147180559945309417232121458176568##SUFFIX; \
\
/* log_e 10 */ \
template<> \
inline constexpr TYPE ln10_v<TYPE> \
= 2.302585092994045684017991454684364208##SUFFIX; \
\
/* sqrt(2) */ \
template<> \
inline constexpr TYPE sqrt2_v<TYPE> \
= 1.414213562373095048801688724209698079##SUFFIX; \
\
/* sqrt(3) */ \
template<> \
inline constexpr TYPE sqrt3_v<TYPE> \
= 1.732050807568877293527446341505872367##SUFFIX; \
\
/* 1/sqrt(3) */ \
template<> \
inline constexpr TYPE inv_sqrt3_v<TYPE> \
= 0.577350269189625764509148780501957456##SUFFIX; \
\
/* The Euler-Mascheroni constant */ \
template<> \
inline constexpr TYPE egamma_v<TYPE> \
= 0.577215664901532860606512090082402431##SUFFIX; \
\
/* The golden ratio, (1+sqrt(5))/2 */ \
template<> \
inline constexpr TYPE phi_v<TYPE> \
= 1.618033988749894848204586834365638118##SUFFIX
#ifdef __STDCPP_FLOAT16_T__
__glibcxx_numbers (_Float16, F16);
#endif
#ifdef __STDCPP_FLOAT32_T__
__glibcxx_numbers (_Float32, F32);
#endif
#ifdef __STDCPP_FLOAT64_T__
__glibcxx_numbers (_Float64, F64);
#endif
#ifdef __STDCPP_FLOAT128_T__
__glibcxx_numbers (_Float128, F128);
#endif
#ifdef __STDCPP_BFLOAT128_T__
__glibcxx_numbers (__gnu_cxx::__bfloat16_t, BF16);
#endif
#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_FLOAT128) && !defined(__CUDACC__)
__glibcxx_numbers (__float128, Q);
#endif // USE_FLOAT128
#undef __glibcxx_numbers
} // namespace numbers
/// @}
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
#pragma GCC diagnostic pop
#endif // __cpp_lib_math_constants
#endif // _GLIBCXX_NUMBERS
type_traits
version.h
std
ISO C++ entities toplevel namespace is std.