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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 
    105 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
    106 #pragma GCC system_header
    107 #endif
    108 
    109 #include <__config>
    110 #include <type_traits>
    111 
    112 #include <__undef_min_max>
    113 
    114 #if defined(_LIBCPP_MSVCRT)
    115 #include "support/win32/limits_win32.h"
    116 #endif // _LIBCPP_MSVCRT
    117 
    118 #if defined(__IBMCPP__)
    119 #include "support/ibm/limits.h"
    120 #endif // __IBMCPP__
    121 
    122 _LIBCPP_BEGIN_NAMESPACE_STD
    123 
    124 enum float_round_style
    125 {
    126     round_indeterminate       = -1,
    127     round_toward_zero         =  0,
    128     round_to_nearest          =  1,
    129     round_toward_infinity     =  2,
    130     round_toward_neg_infinity =  3
    131 };
    132 
    133 enum float_denorm_style
    134 {
    135     denorm_indeterminate = -1,
    136     denorm_absent = 0,
    137     denorm_present = 1
    138 };
    139 
    140 template <class _Tp, bool = is_arithmetic<_Tp>::value>
    141 class __libcpp_numeric_limits
    142 {
    143 protected:
    144     typedef _Tp type;
    145 
    146     static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
    147     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
    148     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
    149     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
    150 
    151     static _LIBCPP_CONSTEXPR const int  digits = 0;
    152     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    153     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    154     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    155     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    156     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    157     static _LIBCPP_CONSTEXPR const int  radix = 0;
    158     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
    159     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
    160 
    161     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    162     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    163     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    164     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    165 
    166     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    167     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    168     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    169     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    170     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    171     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
    172     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
    173     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
    174     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
    175 
    176     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    177     static _LIBCPP_CONSTEXPR const bool is_bounded = false;
    178     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    179 
    180     static _LIBCPP_CONSTEXPR const bool traps = false;
    181     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    182     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    183 };
    184 
    185 template <class _Tp, int digits, bool is_signed>
    186 struct __libcpp_compute_min
    187 {
    188     static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << digits);
    189 };
    190 
    191 template <class _Tp, int digits>
    192 struct __libcpp_compute_min<_Tp, digits, false>
    193 {
    194     static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
    195 };
    196 
    197 template <class _Tp>
    198 class __libcpp_numeric_limits<_Tp, true>
    199 {
    200 protected:
    201     typedef _Tp type;
    202 
    203     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    204 
    205     static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
    206     static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
    207     static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
    208     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    209     static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
    210     static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
    211     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    212     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    213     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    214 
    215     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    216     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    217     static _LIBCPP_CONSTEXPR const int  radix = 2;
    218     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    219     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    220 
    221     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    222     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    223     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    224     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    225 
    226     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    227     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    228     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    229     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    230     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    231     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    232     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    233     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    234     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    235 
    236     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    237     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    238     static _LIBCPP_CONSTEXPR const bool is_modulo = true;
    239 
    240 #if __i386__ || __x86_64__
    241     static _LIBCPP_CONSTEXPR const bool traps = true;
    242 #else
    243     static _LIBCPP_CONSTEXPR const bool traps = false;
    244 #endif
    245     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    246     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    247 };
    248 
    249 template <>
    250 class __libcpp_numeric_limits<bool, true>
    251 {
    252 protected:
    253     typedef bool type;
    254 
    255     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    256 
    257     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    258     static _LIBCPP_CONSTEXPR const int  digits = 1;
    259     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    260     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    261     static _LIBCPP_CONSTEXPR const type __min = false;
    262     static _LIBCPP_CONSTEXPR const type __max = true;
    263     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    264     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    265     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    266 
    267     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    268     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    269     static _LIBCPP_CONSTEXPR const int  radix = 2;
    270     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    271     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    272 
    273     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    274     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    275     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    276     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    277 
    278     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    279     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    280     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    281     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    282     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    283     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    284     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    285     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    286     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    287 
    288     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    289     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    290     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    291 
    292     static _LIBCPP_CONSTEXPR const bool traps = false;
    293     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    294     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    295 };
    296 
    297 template <>
    298 class __libcpp_numeric_limits<float, true>
    299 {
    300 protected:
    301     typedef float type;
    302 
    303     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    304 
    305     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    306     static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
    307     static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
    308     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
    309     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
    310     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
    311     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    312 
    313     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    314     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    315     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    316     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
    317     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
    318 
    319     static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
    320     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
    321     static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
    322     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
    323 
    324     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    325     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    326     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    327     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    328     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    329     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
    330     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
    331     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
    332     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
    333 
    334     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    335     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    336     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    337 
    338     static _LIBCPP_CONSTEXPR const bool traps = false;
    339     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    340     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    341 };
    342 
    343 template <>
    344 class __libcpp_numeric_limits<double, true>
    345 {
    346 protected:
    347     typedef double type;
    348 
    349     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    350 
    351     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    352     static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
    353     static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
    354     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
    355     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
    356     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
    357     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    358 
    359     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    360     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    361     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    362     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
    363     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    364 
    365     static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
    366     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
    367     static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
    368     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
    369 
    370     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    371     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    372     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    373     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    374     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    375     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
    376     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
    377     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
    378     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
    379 
    380     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    381     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    382     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    383 
    384     static _LIBCPP_CONSTEXPR const bool traps = false;
    385     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    386     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    387 };
    388 
    389 template <>
    390 class __libcpp_numeric_limits<long double, true>
    391 {
    392 protected:
    393     typedef long double type;
    394 
    395     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    396 
    397     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    398     static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
    399     static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
    400     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
    401     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
    402     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
    403     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    404 
    405     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    406     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    407     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    408     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
    409     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    410 
    411     static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
    412     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
    413     static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
    414     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
    415 
    416     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    417     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    418     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    419     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    420     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    421     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
    422     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
    423     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
    424     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
    425 
    426 #if (defined(__ppc__) || defined(__ppc64__))
    427     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    428 #else
    429     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    430 #endif
    431     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    432     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    433 
    434     static _LIBCPP_CONSTEXPR const bool traps = false;
    435     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    436     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    437 };
    438 
    439 template <class _Tp>
    440 class _LIBCPP_TYPE_VIS_ONLY numeric_limits
    441     : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
    442 {
    443     typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
    444     typedef typename __base::type type;
    445 public:
    446     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    447     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    448     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    449     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    450 
    451     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    452     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    453     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    454     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    455     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    456     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    457     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    458     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    459     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    460 
    461     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    462     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    463     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    464     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    465 
    466     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    467     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    468     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    469     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    470     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    471     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    472     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    473     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    474     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    475 
    476     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    477     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    478     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    479 
    480     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    481     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    482     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    483 };
    484 
    485 template <class _Tp>
    486     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
    487 template <class _Tp>
    488     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
    489 template <class _Tp>
    490     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
    491 template <class _Tp>
    492     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
    493 template <class _Tp>
    494     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
    495 template <class _Tp>
    496     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
    497 template <class _Tp>
    498     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
    499 template <class _Tp>
    500     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
    501 template <class _Tp>
    502     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
    503 template <class _Tp>
    504     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
    505 template <class _Tp>
    506     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
    507 template <class _Tp>
    508     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
    509 template <class _Tp>
    510     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
    511 template <class _Tp>
    512     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
    513 template <class _Tp>
    514     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
    515 template <class _Tp>
    516     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
    517 template <class _Tp>
    518     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
    519 template <class _Tp>
    520     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
    521 template <class _Tp>
    522     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
    523 template <class _Tp>
    524     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
    525 template <class _Tp>
    526     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
    527 template <class _Tp>
    528     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
    529 template <class _Tp>
    530     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
    531 
    532 template <class _Tp>
    533 class _LIBCPP_TYPE_VIS_ONLY numeric_limits<const _Tp>
    534     : private numeric_limits<_Tp>
    535 {
    536     typedef numeric_limits<_Tp> __base;
    537     typedef _Tp type;
    538 public:
    539     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    540     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    541     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    542     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    543 
    544     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    545     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    546     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    547     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    548     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    549     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    550     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    551     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    552     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    553 
    554     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    555     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    556     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    557     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    558 
    559     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    560     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    561     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    562     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    563     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    564     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    565     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    566     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    567     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    568 
    569     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    570     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    571     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    572 
    573     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    574     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    575     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    576 };
    577 
    578 template <class _Tp>
    579     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
    580 template <class _Tp>
    581     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
    582 template <class _Tp>
    583     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
    584 template <class _Tp>
    585     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
    586 template <class _Tp>
    587     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
    588 template <class _Tp>
    589     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
    590 template <class _Tp>
    591     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
    592 template <class _Tp>
    593     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
    594 template <class _Tp>
    595     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
    596 template <class _Tp>
    597     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
    598 template <class _Tp>
    599     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
    600 template <class _Tp>
    601     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
    602 template <class _Tp>
    603     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
    604 template <class _Tp>
    605     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
    606 template <class _Tp>
    607     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
    608 template <class _Tp>
    609     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
    610 template <class _Tp>
    611     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
    612 template <class _Tp>
    613     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
    614 template <class _Tp>
    615     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
    616 template <class _Tp>
    617     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
    618 template <class _Tp>
    619     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
    620 template <class _Tp>
    621     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
    622 template <class _Tp>
    623     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
    624 
    625 template <class _Tp>
    626 class _LIBCPP_TYPE_VIS_ONLY numeric_limits<volatile _Tp>
    627     : private numeric_limits<_Tp>
    628 {
    629     typedef numeric_limits<_Tp> __base;
    630     typedef _Tp type;
    631 public:
    632     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    633     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    634     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    635     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    636 
    637     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    638     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    639     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    640     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    641     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    642     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    643     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    644     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    645     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    646 
    647     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    648     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    649     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    650     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    651 
    652     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    653     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    654     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    655     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    656     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    657     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    658     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    659     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    660     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    661 
    662     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    663     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    664     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    665 
    666     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    667     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    668     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    669 };
    670 
    671 template <class _Tp>
    672     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
    673 template <class _Tp>
    674     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
    675 template <class _Tp>
    676     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
    677 template <class _Tp>
    678     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
    679 template <class _Tp>
    680     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
    681 template <class _Tp>
    682     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
    683 template <class _Tp>
    684     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
    685 template <class _Tp>
    686     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
    687 template <class _Tp>
    688     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
    689 template <class _Tp>
    690     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
    691 template <class _Tp>
    692     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
    693 template <class _Tp>
    694     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
    695 template <class _Tp>
    696     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
    697 template <class _Tp>
    698     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
    699 template <class _Tp>
    700     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
    701 template <class _Tp>
    702     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
    703 template <class _Tp>
    704     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
    705 template <class _Tp>
    706     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
    707 template <class _Tp>
    708     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
    709 template <class _Tp>
    710     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
    711 template <class _Tp>
    712     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
    713 template <class _Tp>
    714     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
    715 template <class _Tp>
    716     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
    717 
    718 template <class _Tp>
    719 class _LIBCPP_TYPE_VIS_ONLY numeric_limits<const volatile _Tp>
    720     : private numeric_limits<_Tp>
    721 {
    722     typedef numeric_limits<_Tp> __base;
    723     typedef _Tp type;
    724 public:
    725     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    726     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    727     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    728     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    729 
    730     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    731     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    732     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    733     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    734     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    735     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    736     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    737     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    738     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    739 
    740     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    741     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    742     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    743     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    744 
    745     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    746     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    747     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    748     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    749     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    750     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    751     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    752     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    753     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    754 
    755     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    756     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    757     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    758 
    759     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    760     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    761     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    762 };
    763 
    764 template <class _Tp>
    765     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
    766 template <class _Tp>
    767     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
    768 template <class _Tp>
    769     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
    770 template <class _Tp>
    771     const int numeric_limits<const volatile _Tp>::max_digits10;
    772 template <class _Tp>
    773     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
    774 template <class _Tp>
    775     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
    776 template <class _Tp>
    777     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
    778 template <class _Tp>
    779     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
    780 template <class _Tp>
    781     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
    782 template <class _Tp>
    783     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
    784 template <class _Tp>
    785     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
    786 template <class _Tp>
    787     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
    788 template <class _Tp>
    789     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
    790 template <class _Tp>
    791     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
    792 template <class _Tp>
    793     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
    794 template <class _Tp>
    795     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
    796 template <class _Tp>
    797     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
    798 template <class _Tp>
    799     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
    800 template <class _Tp>
    801     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
    802 template <class _Tp>
    803     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
    804 template <class _Tp>
    805     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
    806 template <class _Tp>
    807     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
    808 template <class _Tp>
    809     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
    810 
    811 _LIBCPP_END_NAMESPACE_STD
    812 
    813 #endif  // _LIBCPP_LIMITS
    814