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      1 // -*- C++ -*-
      2 //===---------------------------- limits ----------------------------------===//
      3 //
      4 //                     The LLVM Compiler Infrastructure
      5 //
      6 // This file is dual licensed under the MIT and the University of Illinois Open
      7 // Source Licenses. See LICENSE.TXT for details.
      8 //
      9 //===----------------------------------------------------------------------===//
     10 
     11 #ifndef _LIBCPP_LIMITS
     12 #define _LIBCPP_LIMITS
     13 
     14 /*
     15     limits synopsis
     16 
     17 namespace std
     18 {
     19 
     20 template<class T>
     21 class numeric_limits
     22 {
     23 public:
     24     static constexpr bool is_specialized = false;
     25     static constexpr T min() noexcept;
     26     static constexpr T max() noexcept;
     27     static constexpr T lowest() noexcept;
     28 
     29     static constexpr int  digits = 0;
     30     static constexpr int  digits10 = 0;
     31     static constexpr int  max_digits10 = 0;
     32     static constexpr bool is_signed = false;
     33     static constexpr bool is_integer = false;
     34     static constexpr bool is_exact = false;
     35     static constexpr int  radix = 0;
     36     static constexpr T epsilon() noexcept;
     37     static constexpr T round_error() noexcept;
     38 
     39     static constexpr int  min_exponent = 0;
     40     static constexpr int  min_exponent10 = 0;
     41     static constexpr int  max_exponent = 0;
     42     static constexpr int  max_exponent10 = 0;
     43 
     44     static constexpr bool has_infinity = false;
     45     static constexpr bool has_quiet_NaN = false;
     46     static constexpr bool has_signaling_NaN = false;
     47     static constexpr float_denorm_style has_denorm = denorm_absent;
     48     static constexpr bool has_denorm_loss = false;
     49     static constexpr T infinity() noexcept;
     50     static constexpr T quiet_NaN() noexcept;
     51     static constexpr T signaling_NaN() noexcept;
     52     static constexpr T denorm_min() noexcept;
     53 
     54     static constexpr bool is_iec559 = false;
     55     static constexpr bool is_bounded = false;
     56     static constexpr bool is_modulo = false;
     57 
     58     static constexpr bool traps = false;
     59     static constexpr bool tinyness_before = false;
     60     static constexpr float_round_style round_style = round_toward_zero;
     61 };
     62 
     63 enum float_round_style
     64 {
     65     round_indeterminate       = -1,
     66     round_toward_zero         =  0,
     67     round_to_nearest          =  1,
     68     round_toward_infinity     =  2,
     69     round_toward_neg_infinity =  3
     70 };
     71 
     72 enum float_denorm_style
     73 {
     74     denorm_indeterminate = -1,
     75     denorm_absent = 0,
     76     denorm_present = 1
     77 };
     78 
     79 template<> class numeric_limits<cv bool>;
     80 
     81 template<> class numeric_limits<cv char>;
     82 template<> class numeric_limits<cv signed char>;
     83 template<> class numeric_limits<cv unsigned char>;
     84 template<> class numeric_limits<cv wchar_t>;
     85 template<> class numeric_limits<cv char16_t>;
     86 template<> class numeric_limits<cv char32_t>;
     87 
     88 template<> class numeric_limits<cv short>;
     89 template<> class numeric_limits<cv int>;
     90 template<> class numeric_limits<cv long>;
     91 template<> class numeric_limits<cv long long>;
     92 template<> class numeric_limits<cv unsigned short>;
     93 template<> class numeric_limits<cv unsigned int>;
     94 template<> class numeric_limits<cv unsigned long>;
     95 template<> class numeric_limits<cv unsigned long long>;
     96 
     97 template<> class numeric_limits<cv float>;
     98 template<> class numeric_limits<cv double>;
     99 template<> class numeric_limits<cv long double>;
    100 
    101 }  // std
    102 
    103 */
    104 #include <__config>
    105 #include <type_traits>
    106 
    107 #if defined(_LIBCPP_COMPILER_MSVC)
    108 #include "support/win32/limits_msvc_win32.h"
    109 #endif // _LIBCPP_MSVCRT
    110 
    111 #if defined(__IBMCPP__)
    112 #include "support/ibm/limits.h"
    113 #endif // __IBMCPP__
    114 
    115 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
    116 #pragma GCC system_header
    117 #endif
    118 
    119 _LIBCPP_PUSH_MACROS
    120 #include <__undef_macros>
    121 
    122 
    123 _LIBCPP_BEGIN_NAMESPACE_STD
    124 
    125 enum float_round_style
    126 {
    127     round_indeterminate       = -1,
    128     round_toward_zero         =  0,
    129     round_to_nearest          =  1,
    130     round_toward_infinity     =  2,
    131     round_toward_neg_infinity =  3
    132 };
    133 
    134 enum float_denorm_style
    135 {
    136     denorm_indeterminate = -1,
    137     denorm_absent = 0,
    138     denorm_present = 1
    139 };
    140 
    141 template <class _Tp, bool = is_arithmetic<_Tp>::value>
    142 class __libcpp_numeric_limits
    143 {
    144 protected:
    145     typedef _Tp type;
    146 
    147     static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
    148     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
    149     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
    150     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
    151 
    152     static _LIBCPP_CONSTEXPR const int  digits = 0;
    153     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    154     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    155     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    156     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    157     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    158     static _LIBCPP_CONSTEXPR const int  radix = 0;
    159     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
    160     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
    161 
    162     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    163     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    164     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    165     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    166 
    167     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    168     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    169     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    170     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    171     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    172     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
    173     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
    174     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
    175     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
    176 
    177     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    178     static _LIBCPP_CONSTEXPR const bool is_bounded = false;
    179     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    180 
    181     static _LIBCPP_CONSTEXPR const bool traps = false;
    182     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    183     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    184 };
    185 
    186 template <class _Tp, int __digits, bool _IsSigned>
    187 struct __libcpp_compute_min
    188 {
    189     static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << __digits);
    190 };
    191 
    192 template <class _Tp, int __digits>
    193 struct __libcpp_compute_min<_Tp, __digits, false>
    194 {
    195     static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
    196 };
    197 
    198 template <class _Tp>
    199 class __libcpp_numeric_limits<_Tp, true>
    200 {
    201 protected:
    202     typedef _Tp type;
    203 
    204     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    205 
    206     static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
    207     static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
    208     static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
    209     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    210     static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
    211     static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
    212     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    213     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    214     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    215 
    216     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    217     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    218     static _LIBCPP_CONSTEXPR const int  radix = 2;
    219     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    220     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    221 
    222     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    223     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    224     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    225     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    226 
    227     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    228     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    229     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    230     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    231     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    232     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    233     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    234     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    235     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    236 
    237     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    238     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    239     static _LIBCPP_CONSTEXPR const bool is_modulo = !_VSTD::is_signed<_Tp>::value;
    240 
    241 #if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__) || \
    242     defined(__wasm__)
    243     static _LIBCPP_CONSTEXPR const bool traps = true;
    244 #else
    245     static _LIBCPP_CONSTEXPR const bool traps = false;
    246 #endif
    247     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    248     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    249 };
    250 
    251 template <>
    252 class __libcpp_numeric_limits<bool, true>
    253 {
    254 protected:
    255     typedef bool type;
    256 
    257     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    258 
    259     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    260     static _LIBCPP_CONSTEXPR const int  digits = 1;
    261     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    262     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    263     static _LIBCPP_CONSTEXPR const type __min = false;
    264     static _LIBCPP_CONSTEXPR const type __max = true;
    265     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    266     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    267     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    268 
    269     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    270     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    271     static _LIBCPP_CONSTEXPR const int  radix = 2;
    272     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    273     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    274 
    275     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    276     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    277     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    278     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    279 
    280     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    281     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    282     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    283     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    284     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    285     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    286     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    287     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    288     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    289 
    290     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    291     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    292     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    293 
    294     static _LIBCPP_CONSTEXPR const bool traps = false;
    295     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    296     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    297 };
    298 
    299 template <>
    300 class __libcpp_numeric_limits<float, true>
    301 {
    302 protected:
    303     typedef float type;
    304 
    305     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    306 
    307     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    308     static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
    309     static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
    310     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    311     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
    312     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
    313     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    314 
    315     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    316     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    317     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    318     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
    319     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
    320 
    321     static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
    322     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
    323     static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
    324     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
    325 
    326     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    327     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    328     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    329     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    330     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    331     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
    332     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
    333     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
    334     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
    335 
    336     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    337     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    338     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    339 
    340     static _LIBCPP_CONSTEXPR const bool traps = false;
    341     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    342     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    343 };
    344 
    345 template <>
    346 class __libcpp_numeric_limits<double, true>
    347 {
    348 protected:
    349     typedef double type;
    350 
    351     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    352 
    353     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    354     static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
    355     static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
    356     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    357     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
    358     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
    359     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    360 
    361     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    362     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    363     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    364     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
    365     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    366 
    367     static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
    368     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
    369     static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
    370     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
    371 
    372     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    373     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    374     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    375     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    376     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    377     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
    378     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
    379     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
    380     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
    381 
    382     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    383     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    384     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    385 
    386     static _LIBCPP_CONSTEXPR const bool traps = false;
    387     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    388     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    389 };
    390 
    391 template <>
    392 class __libcpp_numeric_limits<long double, true>
    393 {
    394 protected:
    395     typedef long double type;
    396 
    397     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    398 
    399     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    400     static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
    401     static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
    402     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    403     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
    404     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
    405     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    406 
    407     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    408     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    409     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    410     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
    411     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    412 
    413     static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
    414     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
    415     static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
    416     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
    417 
    418     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    419     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    420     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    421     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    422     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    423     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
    424     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
    425     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
    426     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
    427 
    428 #if (defined(__ppc__) || defined(__ppc64__))
    429     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    430 #else
    431     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    432 #endif
    433     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    434     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    435 
    436     static _LIBCPP_CONSTEXPR const bool traps = false;
    437     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    438     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    439 };
    440 
    441 template <class _Tp>
    442 class _LIBCPP_TEMPLATE_VIS numeric_limits
    443     : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
    444 {
    445     typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
    446     typedef typename __base::type type;
    447 public:
    448     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    449     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    450     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    451     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    452 
    453     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    454     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    455     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    456     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    457     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    458     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    459     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    460     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    461     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    462 
    463     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    464     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    465     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    466     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    467 
    468     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    469     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    470     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    471     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    472     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    473     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    474     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    475     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    476     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    477 
    478     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    479     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    480     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    481 
    482     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    483     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    484     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    485 };
    486 
    487 template <class _Tp>
    488     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
    489 template <class _Tp>
    490     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
    491 template <class _Tp>
    492     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
    493 template <class _Tp>
    494     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
    495 template <class _Tp>
    496     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
    497 template <class _Tp>
    498     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
    499 template <class _Tp>
    500     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
    501 template <class _Tp>
    502     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
    503 template <class _Tp>
    504     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
    505 template <class _Tp>
    506     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
    507 template <class _Tp>
    508     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
    509 template <class _Tp>
    510     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
    511 template <class _Tp>
    512     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
    513 template <class _Tp>
    514     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
    515 template <class _Tp>
    516     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
    517 template <class _Tp>
    518     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
    519 template <class _Tp>
    520     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
    521 template <class _Tp>
    522     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
    523 template <class _Tp>
    524     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
    525 template <class _Tp>
    526     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
    527 template <class _Tp>
    528     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
    529 template <class _Tp>
    530     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
    531 template <class _Tp>
    532     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
    533 
    534 template <class _Tp>
    535 class _LIBCPP_TEMPLATE_VIS numeric_limits<const _Tp>
    536     : private numeric_limits<_Tp>
    537 {
    538     typedef numeric_limits<_Tp> __base;
    539     typedef _Tp type;
    540 public:
    541     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    542     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    543     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    544     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    545 
    546     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    547     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    548     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    549     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    550     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    551     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    552     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    553     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    554     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    555 
    556     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    557     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    558     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    559     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    560 
    561     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    562     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    563     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    564     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    565     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    566     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    567     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    568     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    569     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    570 
    571     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    572     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    573     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    574 
    575     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    576     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    577     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    578 };
    579 
    580 template <class _Tp>
    581     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
    582 template <class _Tp>
    583     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
    584 template <class _Tp>
    585     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
    586 template <class _Tp>
    587     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
    588 template <class _Tp>
    589     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
    590 template <class _Tp>
    591     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
    592 template <class _Tp>
    593     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
    594 template <class _Tp>
    595     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
    596 template <class _Tp>
    597     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
    598 template <class _Tp>
    599     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
    600 template <class _Tp>
    601     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
    602 template <class _Tp>
    603     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
    604 template <class _Tp>
    605     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
    606 template <class _Tp>
    607     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
    608 template <class _Tp>
    609     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
    610 template <class _Tp>
    611     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
    612 template <class _Tp>
    613     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
    614 template <class _Tp>
    615     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
    616 template <class _Tp>
    617     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
    618 template <class _Tp>
    619     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
    620 template <class _Tp>
    621     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
    622 template <class _Tp>
    623     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
    624 template <class _Tp>
    625     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
    626 
    627 template <class _Tp>
    628 class _LIBCPP_TEMPLATE_VIS numeric_limits<volatile _Tp>
    629     : private numeric_limits<_Tp>
    630 {
    631     typedef numeric_limits<_Tp> __base;
    632     typedef _Tp type;
    633 public:
    634     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    635     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    636     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    637     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    638 
    639     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    640     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    641     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    642     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    643     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    644     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    645     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    646     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    647     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    648 
    649     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    650     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    651     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    652     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    653 
    654     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    655     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    656     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    657     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    658     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    659     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    660     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    661     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    662     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    663 
    664     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    665     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    666     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    667 
    668     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    669     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    670     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    671 };
    672 
    673 template <class _Tp>
    674     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
    675 template <class _Tp>
    676     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
    677 template <class _Tp>
    678     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
    679 template <class _Tp>
    680     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
    681 template <class _Tp>
    682     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
    683 template <class _Tp>
    684     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
    685 template <class _Tp>
    686     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
    687 template <class _Tp>
    688     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
    689 template <class _Tp>
    690     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
    691 template <class _Tp>
    692     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
    693 template <class _Tp>
    694     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
    695 template <class _Tp>
    696     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
    697 template <class _Tp>
    698     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
    699 template <class _Tp>
    700     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
    701 template <class _Tp>
    702     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
    703 template <class _Tp>
    704     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
    705 template <class _Tp>
    706     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
    707 template <class _Tp>
    708     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
    709 template <class _Tp>
    710     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
    711 template <class _Tp>
    712     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
    713 template <class _Tp>
    714     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
    715 template <class _Tp>
    716     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
    717 template <class _Tp>
    718     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
    719 
    720 template <class _Tp>
    721 class _LIBCPP_TEMPLATE_VIS numeric_limits<const volatile _Tp>
    722     : private numeric_limits<_Tp>
    723 {
    724     typedef numeric_limits<_Tp> __base;
    725     typedef _Tp type;
    726 public:
    727     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    728     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    729     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    730     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    731 
    732     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    733     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    734     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    735     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    736     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    737     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    738     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    739     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    740     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    741 
    742     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    743     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    744     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    745     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    746 
    747     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    748     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    749     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    750     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    751     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    752     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    753     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    754     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    755     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    756 
    757     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    758     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    759     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    760 
    761     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    762     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    763     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    764 };
    765 
    766 template <class _Tp>
    767     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
    768 template <class _Tp>
    769     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
    770 template <class _Tp>
    771     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
    772 template <class _Tp>
    773     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
    774 template <class _Tp>
    775     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
    776 template <class _Tp>
    777     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
    778 template <class _Tp>
    779     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
    780 template <class _Tp>
    781     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
    782 template <class _Tp>
    783     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
    784 template <class _Tp>
    785     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
    786 template <class _Tp>
    787     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
    788 template <class _Tp>
    789     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
    790 template <class _Tp>
    791     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
    792 template <class _Tp>
    793     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
    794 template <class _Tp>
    795     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
    796 template <class _Tp>
    797     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
    798 template <class _Tp>
    799     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
    800 template <class _Tp>
    801     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
    802 template <class _Tp>
    803     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
    804 template <class _Tp>
    805     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
    806 template <class _Tp>
    807     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
    808 template <class _Tp>
    809     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
    810 template <class _Tp>
    811     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
    812 
    813 _LIBCPP_END_NAMESPACE_STD
    814 
    815 _LIBCPP_POP_MACROS
    816 
    817 #endif  // _LIBCPP_LIMITS
    818