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// 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/>.
#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
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