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numeric_traits.h
// Definition of numeric_limits replacement traits P1841R1 -*- C++ -*- // Copyright (C) 2020-2021 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/>. #ifndef _GLIBCXX_EXPERIMENTAL_BITS_NUMERIC_TRAITS_H #define _GLIBCXX_EXPERIMENTAL_BITS_NUMERIC_TRAITS_H #include <type_traits> namespace std { template <template <typename> class _Trait, typename _Tp, typename = void> struct __value_exists_impl : false_type {}; template <template <typename> class _Trait, typename _Tp> struct __value_exists_impl<_Trait, _Tp, void_t<decltype(_Trait<_Tp>::value)>> : true_type {}; template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __digits_impl {}; template <typename _Tp> struct __digits_impl<_Tp, true> { static inline constexpr int value = sizeof(_Tp) * __CHAR_BIT__ - is_signed_v<_Tp>; }; template <> struct __digits_impl<float, true> { static inline constexpr int value = __FLT_MANT_DIG__; }; template <> struct __digits_impl<double, true> { static inline constexpr int value = __DBL_MANT_DIG__; }; template <> struct __digits_impl<long double, true> { static inline constexpr int value = __LDBL_MANT_DIG__; }; template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __digits10_impl {}; template <typename _Tp> struct __digits10_impl<_Tp, true> { // The fraction 643/2136 approximates log10(2) to 7 significant digits. static inline constexpr int value = __digits_impl<_Tp>::value * 643L / 2136; }; template <> struct __digits10_impl<float, true> { static inline constexpr int value = __FLT_DIG__; }; template <> struct __digits10_impl<double, true> { static inline constexpr int value = __DBL_DIG__; }; template <> struct __digits10_impl<long double, true> { static inline constexpr int value = __LDBL_DIG__; }; template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __max_digits10_impl {}; template <typename _Tp> struct __max_digits10_impl<_Tp, true> { static inline constexpr int value = is_floating_point_v<_Tp> ? 2 + __digits_impl<_Tp>::value * 643L / 2136 : __digits10_impl<_Tp>::value + 1; }; template <typename _Tp> struct __max_exponent_impl {}; template <> struct __max_exponent_impl<float> { static inline constexpr int value = __FLT_MAX_EXP__; }; template <> struct __max_exponent_impl<double> { static inline constexpr int value = __DBL_MAX_EXP__; }; template <> struct __max_exponent_impl<long double> { static inline constexpr int value = __LDBL_MAX_EXP__; }; template <typename _Tp> struct __max_exponent10_impl {}; template <> struct __max_exponent10_impl<float> { static inline constexpr int value = __FLT_MAX_10_EXP__; }; template <> struct __max_exponent10_impl<double> { static inline constexpr int value = __DBL_MAX_10_EXP__; }; template <> struct __max_exponent10_impl<long double> { static inline constexpr int value = __LDBL_MAX_10_EXP__; }; template <typename _Tp> struct __min_exponent_impl {}; template <> struct __min_exponent_impl<float> { static inline constexpr int value = __FLT_MIN_EXP__; }; template <> struct __min_exponent_impl<double> { static inline constexpr int value = __DBL_MIN_EXP__; }; template <> struct __min_exponent_impl<long double> { static inline constexpr int value = __LDBL_MIN_EXP__; }; template <typename _Tp> struct __min_exponent10_impl {}; template <> struct __min_exponent10_impl<float> { static inline constexpr int value = __FLT_MIN_10_EXP__; }; template <> struct __min_exponent10_impl<double> { static inline constexpr int value = __DBL_MIN_10_EXP__; }; template <> struct __min_exponent10_impl<long double> { static inline constexpr int value = __LDBL_MIN_10_EXP__; }; template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __radix_impl {}; template <typename _Tp> struct __radix_impl<_Tp, true> { static inline constexpr int value = is_floating_point_v<_Tp> ? __FLT_RADIX__ : 2; }; // [num.traits.util], numeric utility traits template <template <typename> class _Trait, typename _Tp> struct __value_exists : __value_exists_impl<_Trait, _Tp> {}; template <template <typename> class _Trait, typename _Tp> inline constexpr bool __value_exists_v = __value_exists<_Trait, _Tp>::value; template <template <typename> class _Trait, typename _Tp, typename _Up = _Tp> inline constexpr _Up __value_or(_Up __def = _Up()) noexcept { if constexpr (__value_exists_v<_Trait, _Tp>) return static_cast<_Up>(_Trait<_Tp>::value); else return __def; } template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __norm_min_impl {}; template <typename _Tp> struct __norm_min_impl<_Tp, true> { static inline constexpr _Tp value = 1; }; template <> struct __norm_min_impl<float, true> { static inline constexpr float value = __FLT_MIN__; }; template <> struct __norm_min_impl<double, true> { static inline constexpr double value = __DBL_MIN__; }; template <> struct __norm_min_impl<long double, true> { static inline constexpr long double value = __LDBL_MIN__; }; template <typename _Tp> struct __denorm_min_impl : __norm_min_impl<_Tp> {}; #if __FLT_HAS_DENORM__ template <> struct __denorm_min_impl<float> { static inline constexpr float value = __FLT_DENORM_MIN__; }; #endif #if __DBL_HAS_DENORM__ template <> struct __denorm_min_impl<double> { static inline constexpr double value = __DBL_DENORM_MIN__; }; #endif #if __LDBL_HAS_DENORM__ template <> struct __denorm_min_impl<long double> { static inline constexpr long double value = __LDBL_DENORM_MIN__; }; #endif template <typename _Tp> struct __epsilon_impl {}; template <> struct __epsilon_impl<float> { static inline constexpr float value = __FLT_EPSILON__; }; template <> struct __epsilon_impl<double> { static inline constexpr double value = __DBL_EPSILON__; }; template <> struct __epsilon_impl<long double> { static inline constexpr long double value = __LDBL_EPSILON__; }; template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __finite_min_impl {}; template <typename _Tp> struct __finite_min_impl<_Tp, true> { static inline constexpr _Tp value = is_unsigned_v<_Tp> ? _Tp() : -2 * (_Tp(1) << __digits_impl<_Tp>::value - 1); }; template <> struct __finite_min_impl<float, true> { static inline constexpr float value = -__FLT_MAX__; }; template <> struct __finite_min_impl<double, true> { static inline constexpr double value = -__DBL_MAX__; }; template <> struct __finite_min_impl<long double, true> { static inline constexpr long double value = -__LDBL_MAX__; }; template <typename _Tp, bool = is_arithmetic_v<_Tp>> struct __finite_max_impl {}; template <typename _Tp> struct __finite_max_impl<_Tp, true> { static inline constexpr _Tp value = ~__finite_min_impl<_Tp>::value; }; template <> struct __finite_max_impl<float, true> { static inline constexpr float value = __FLT_MAX__; }; template <> struct __finite_max_impl<double, true> { static inline constexpr double value = __DBL_MAX__; }; template <> struct __finite_max_impl<long double, true> { static inline constexpr long double value = __LDBL_MAX__; }; template <typename _Tp> struct __infinity_impl {}; #if __FLT_HAS_INFINITY__ template <> struct __infinity_impl<float> { static inline constexpr float value = __builtin_inff(); }; #endif #if __DBL_HAS_INFINITY__ template <> struct __infinity_impl<double> { static inline constexpr double value = __builtin_inf(); }; #endif #if __LDBL_HAS_INFINITY__ template <> struct __infinity_impl<long double> { static inline constexpr long double value = __builtin_infl(); }; #endif template <typename _Tp> struct __quiet_NaN_impl {}; #if __FLT_HAS_QUIET_NAN__ template <> struct __quiet_NaN_impl<float> { static inline constexpr float value = __builtin_nanf(""); }; #endif #if __DBL_HAS_QUIET_NAN__ template <> struct __quiet_NaN_impl<double> { static inline constexpr double value = __builtin_nan(""); }; #endif #if __LDBL_HAS_QUIET_NAN__ template <> struct __quiet_NaN_impl<long double> { static inline constexpr long double value = __builtin_nanl(""); }; #endif template <typename _Tp, bool = is_floating_point_v<_Tp>> struct __reciprocal_overflow_threshold_impl {}; template <typename _Tp> struct __reciprocal_overflow_threshold_impl<_Tp, true> { // This typically yields a subnormal value. Is this incorrect for // flush-to-zero configurations? static constexpr _Tp _S_search(_Tp __ok, _Tp __overflows) { const _Tp __mid = (__ok + __overflows) / 2; // 1/__mid without -ffast-math is not a constant expression if it // overflows. Therefore divide 1 by the radix before division. // Consequently finite_max (the threshold) must be scaled by the // same value. if (__mid == __ok || __mid == __overflows) return __ok; else if (_Tp(1) / (__radix_impl<_Tp>::value * __mid) <= __finite_max_impl<_Tp>::value / __radix_impl<_Tp>::value) return _S_search(__mid, __overflows); else return _S_search(__ok, __mid); } static inline constexpr _Tp value = _S_search(_Tp(1.01) / __finite_max_impl<_Tp>::value, _Tp(0.99) / __finite_max_impl<_Tp>::value); }; template <typename _Tp, bool = is_floating_point_v<_Tp>> struct __round_error_impl {}; template <typename _Tp> struct __round_error_impl<_Tp, true> { static inline constexpr _Tp value = 0.5; }; template <typename _Tp> struct __signaling_NaN_impl {}; #if __FLT_HAS_QUIET_NAN__ template <> struct __signaling_NaN_impl<float> { static inline constexpr float value = __builtin_nansf(""); }; #endif #if __DBL_HAS_QUIET_NAN__ template <> struct __signaling_NaN_impl<double> { static inline constexpr double value = __builtin_nans(""); }; #endif #if __LDBL_HAS_QUIET_NAN__ template <> struct __signaling_NaN_impl<long double> { static inline constexpr long double value = __builtin_nansl(""); }; #endif // [num.traits.val], numeric distinguished value traits template <typename _Tp> struct __denorm_min : __denorm_min_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __epsilon : __epsilon_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __finite_max : __finite_max_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __finite_min : __finite_min_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __infinity : __infinity_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __norm_min : __norm_min_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __quiet_NaN : __quiet_NaN_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __reciprocal_overflow_threshold : __reciprocal_overflow_threshold_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __round_error : __round_error_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __signaling_NaN : __signaling_NaN_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> inline constexpr auto __denorm_min_v = __denorm_min<_Tp>::value; template <typename _Tp> inline constexpr auto __epsilon_v = __epsilon<_Tp>::value; template <typename _Tp> inline constexpr auto __finite_max_v = __finite_max<_Tp>::value; template <typename _Tp> inline constexpr auto __finite_min_v = __finite_min<_Tp>::value; template <typename _Tp> inline constexpr auto __infinity_v = __infinity<_Tp>::value; template <typename _Tp> inline constexpr auto __norm_min_v = __norm_min<_Tp>::value; template <typename _Tp> inline constexpr auto __quiet_NaN_v = __quiet_NaN<_Tp>::value; template <typename _Tp> inline constexpr auto __reciprocal_overflow_threshold_v = __reciprocal_overflow_threshold<_Tp>::value; template <typename _Tp> inline constexpr auto __round_error_v = __round_error<_Tp>::value; template <typename _Tp> inline constexpr auto __signaling_NaN_v = __signaling_NaN<_Tp>::value; // [num.traits.char], numeric characteristics traits template <typename _Tp> struct __digits : __digits_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __digits10 : __digits10_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __max_digits10 : __max_digits10_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __max_exponent : __max_exponent_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __max_exponent10 : __max_exponent10_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __min_exponent : __min_exponent_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __min_exponent10 : __min_exponent10_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> struct __radix : __radix_impl<remove_cv_t<_Tp>> {}; template <typename _Tp> inline constexpr auto __digits_v = __digits<_Tp>::value; template <typename _Tp> inline constexpr auto __digits10_v = __digits10<_Tp>::value; template <typename _Tp> inline constexpr auto __max_digits10_v = __max_digits10<_Tp>::value; template <typename _Tp> inline constexpr auto __max_exponent_v = __max_exponent<_Tp>::value; template <typename _Tp> inline constexpr auto __max_exponent10_v = __max_exponent10<_Tp>::value; template <typename _Tp> inline constexpr auto __min_exponent_v = __min_exponent<_Tp>::value; template <typename _Tp> inline constexpr auto __min_exponent10_v = __min_exponent10<_Tp>::value; template <typename _Tp> inline constexpr auto __radix_v = __radix<_Tp>::value; // mkretz's extensions // TODO: does GCC tell me? __GCC_IEC_559 >= 2 is not the right answer template <typename _Tp> struct __has_iec559_storage_format : true_type {}; template <typename _Tp> inline constexpr bool __has_iec559_storage_format_v = __has_iec559_storage_format<_Tp>::value; /* To propose: If __has_iec559_behavior<__quiet_NaN, T> is true the following holds: - nan == nan is false - isnan(nan) is true - isnan(nan + x) is true - isnan(inf/inf) is true - isnan(0/0) is true - isunordered(nan, x) is true If __has_iec559_behavior<__infinity, T> is true the following holds (x is neither nan nor inf): - isinf(inf) is true - isinf(inf + x) is true - isinf(1/0) is true */ template <template <typename> class _Trait, typename _Tp> struct __has_iec559_behavior : false_type {}; template <template <typename> class _Trait, typename _Tp> inline constexpr bool __has_iec559_behavior_v = __has_iec559_behavior<_Trait, _Tp>::value; #if !__FINITE_MATH_ONLY__ #if __FLT_HAS_QUIET_NAN__ template <> struct __has_iec559_behavior<__quiet_NaN, float> : true_type {}; #endif #if __DBL_HAS_QUIET_NAN__ template <> struct __has_iec559_behavior<__quiet_NaN, double> : true_type {}; #endif #if __LDBL_HAS_QUIET_NAN__ template <> struct __has_iec559_behavior<__quiet_NaN, long double> : true_type {}; #endif #if __FLT_HAS_INFINITY__ template <> struct __has_iec559_behavior<__infinity, float> : true_type {}; #endif #if __DBL_HAS_INFINITY__ template <> struct __has_iec559_behavior<__infinity, double> : true_type {}; #endif #if __LDBL_HAS_INFINITY__ template <> struct __has_iec559_behavior<__infinity, long double> : true_type {}; #endif #ifdef __SUPPORT_SNAN__ #if __FLT_HAS_QUIET_NAN__ template <> struct __has_iec559_behavior<__signaling_NaN, float> : true_type {}; #endif #if __DBL_HAS_QUIET_NAN__ template <> struct __has_iec559_behavior<__signaling_NaN, double> : true_type {}; #endif #if __LDBL_HAS_QUIET_NAN__ template <> struct __has_iec559_behavior<__signaling_NaN, long double> : true_type {}; #endif #endif #endif // __FINITE_MATH_ONLY__ } // namespace std #endif // _GLIBCXX_EXPERIMENTAL_BITS_NUMERIC_TRAITS_H