Home | History | Annotate | Download | only in include 
      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 char8_t>; // C++20
     86 template<> class numeric_limits<cv char16_t>;
     87 template<> class numeric_limits<cv char32_t>;
     88 
     89 template<> class numeric_limits<cv short>;
     90 template<> class numeric_limits<cv int>;
     91 template<> class numeric_limits<cv long>;
     92 template<> class numeric_limits<cv long long>;
     93 template<> class numeric_limits<cv unsigned short>;
     94 template<> class numeric_limits<cv unsigned int>;
     95 template<> class numeric_limits<cv unsigned long>;
     96 template<> class numeric_limits<cv unsigned long long>;
     97 
     98 template<> class numeric_limits<cv float>;
     99 template<> class numeric_limits<cv double>;
    100 template<> class numeric_limits<cv long double>;
    101 
    102 }  // std
    103 
    104 */
    105 #include <__config>
    106 #include <type_traits>
    107 
    108 #if defined(_LIBCPP_COMPILER_MSVC)
    109 #include "support/win32/limits_msvc_win32.h"
    110 #endif // _LIBCPP_MSVCRT
    111 
    112 #if defined(__IBMCPP__)
    113 #include "support/ibm/limits.h"
    114 #endif // __IBMCPP__
    115 
    116 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
    117 #pragma GCC system_header
    118 #endif
    119 
    120 _LIBCPP_PUSH_MACROS
    121 #include <__undef_macros>
    122 #include <version>
    123 
    124 
    125 _LIBCPP_BEGIN_NAMESPACE_STD
    126 
    127 enum float_round_style
    128 {
    129     round_indeterminate       = -1,
    130     round_toward_zero         =  0,
    131     round_to_nearest          =  1,
    132     round_toward_infinity     =  2,
    133     round_toward_neg_infinity =  3
    134 };
    135 
    136 enum float_denorm_style
    137 {
    138     denorm_indeterminate = -1,
    139     denorm_absent = 0,
    140     denorm_present = 1
    141 };
    142 
    143 template <class _Tp, bool = is_arithmetic<_Tp>::value>
    144 class __libcpp_numeric_limits
    145 {
    146 protected:
    147     typedef _Tp type;
    148 
    149     static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
    150     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
    151     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
    152     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
    153 
    154     static _LIBCPP_CONSTEXPR const int  digits = 0;
    155     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    156     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    157     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    158     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    159     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    160     static _LIBCPP_CONSTEXPR const int  radix = 0;
    161     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
    162     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
    163 
    164     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    165     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    166     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    167     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    168 
    169     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    170     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    171     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    172     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    173     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    174     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
    175     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
    176     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
    177     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
    178 
    179     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    180     static _LIBCPP_CONSTEXPR const bool is_bounded = false;
    181     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    182 
    183     static _LIBCPP_CONSTEXPR const bool traps = false;
    184     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    185     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    186 };
    187 
    188 template <class _Tp, int __digits, bool _IsSigned>
    189 struct __libcpp_compute_min
    190 {
    191     static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << __digits);
    192 };
    193 
    194 template <class _Tp, int __digits>
    195 struct __libcpp_compute_min<_Tp, __digits, false>
    196 {
    197     static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
    198 };
    199 
    200 template <class _Tp>
    201 class __libcpp_numeric_limits<_Tp, true>
    202 {
    203 protected:
    204     typedef _Tp type;
    205 
    206     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    207 
    208     static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
    209     static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
    210     static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
    211     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    212     static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
    213     static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
    214     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    215     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    216     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    217 
    218     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    219     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    220     static _LIBCPP_CONSTEXPR const int  radix = 2;
    221     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    222     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    223 
    224     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    225     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    226     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    227     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    228 
    229     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    230     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    231     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    232     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    233     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    234     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    235     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    236     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    237     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    238 
    239     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    240     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    241     static _LIBCPP_CONSTEXPR const bool is_modulo = !_VSTD::is_signed<_Tp>::value;
    242 
    243 #if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__) || \
    244     defined(__wasm__)
    245     static _LIBCPP_CONSTEXPR const bool traps = true;
    246 #else
    247     static _LIBCPP_CONSTEXPR const bool traps = false;
    248 #endif
    249     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    250     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    251 };
    252 
    253 template <>
    254 class __libcpp_numeric_limits<bool, true>
    255 {
    256 protected:
    257     typedef bool type;
    258 
    259     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    260 
    261     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    262     static _LIBCPP_CONSTEXPR const int  digits = 1;
    263     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    264     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    265     static _LIBCPP_CONSTEXPR const type __min = false;
    266     static _LIBCPP_CONSTEXPR const type __max = true;
    267     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    268     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    269     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    270 
    271     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    272     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    273     static _LIBCPP_CONSTEXPR const int  radix = 2;
    274     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    275     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    276 
    277     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    278     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    279     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    280     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    281 
    282     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    283     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    284     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    285     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    286     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    287     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    288     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    289     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    290     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    291 
    292     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    293     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    294     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    295 
    296     static _LIBCPP_CONSTEXPR const bool traps = false;
    297     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    298     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    299 };
    300 
    301 template <>
    302 class __libcpp_numeric_limits<float, true>
    303 {
    304 protected:
    305     typedef float type;
    306 
    307     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    308 
    309     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    310     static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
    311     static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
    312     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    313     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
    314     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
    315     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    316 
    317     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    318     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    319     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    320     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
    321     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
    322 
    323     static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
    324     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
    325     static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
    326     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
    327 
    328     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    329     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    330     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    331     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    332     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    333     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
    334     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
    335     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
    336     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
    337 
    338     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    339     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    340     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    341 
    342     static _LIBCPP_CONSTEXPR const bool traps = false;
    343     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    344     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    345 };
    346 
    347 template <>
    348 class __libcpp_numeric_limits<double, true>
    349 {
    350 protected:
    351     typedef double type;
    352 
    353     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    354 
    355     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    356     static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
    357     static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
    358     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    359     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
    360     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
    361     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    362 
    363     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    364     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    365     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    366     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
    367     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    368 
    369     static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
    370     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
    371     static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
    372     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
    373 
    374     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    375     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    376     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    377     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    378     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    379     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
    380     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
    381     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
    382     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
    383 
    384     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    385     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    386     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    387 
    388     static _LIBCPP_CONSTEXPR const bool traps = false;
    389     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    390     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    391 };
    392 
    393 template <>
    394 class __libcpp_numeric_limits<long double, true>
    395 {
    396 protected:
    397     typedef long double type;
    398 
    399     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    400 
    401     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    402     static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
    403     static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
    404     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    405     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
    406     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
    407     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    408 
    409     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    410     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    411     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    412     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
    413     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    414 
    415     static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
    416     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
    417     static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
    418     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
    419 
    420     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    421     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    422     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    423     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    424     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    425     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
    426     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
    427     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
    428     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
    429 
    430 #if (defined(__ppc__) || defined(__ppc64__))
    431     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    432 #else
    433     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    434 #endif
    435     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    436     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    437 
    438     static _LIBCPP_CONSTEXPR const bool traps = false;
    439     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    440     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    441 };
    442 
    443 template <class _Tp>
    444 class _LIBCPP_TEMPLATE_VIS numeric_limits
    445     : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
    446 {
    447     typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
    448     typedef typename __base::type type;
    449 public:
    450     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    451     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    452     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    453     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    454 
    455     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    456     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    457     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    458     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    459     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    460     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    461     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    462     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    463     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    464 
    465     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    466     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    467     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    468     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    469 
    470     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    471     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    472     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    473     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    474     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    475     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    476     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    477     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    478     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    479 
    480     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    481     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    482     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    483 
    484     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    485     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    486     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    487 };
    488 
    489 template <class _Tp>
    490     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
    491 template <class _Tp>
    492     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
    493 template <class _Tp>
    494     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
    495 template <class _Tp>
    496     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
    497 template <class _Tp>
    498     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
    499 template <class _Tp>
    500     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
    501 template <class _Tp>
    502     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
    503 template <class _Tp>
    504     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
    505 template <class _Tp>
    506     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
    507 template <class _Tp>
    508     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
    509 template <class _Tp>
    510     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
    511 template <class _Tp>
    512     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
    513 template <class _Tp>
    514     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
    515 template <class _Tp>
    516     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
    517 template <class _Tp>
    518     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
    519 template <class _Tp>
    520     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
    521 template <class _Tp>
    522     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
    523 template <class _Tp>
    524     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
    525 template <class _Tp>
    526     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
    527 template <class _Tp>
    528     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
    529 template <class _Tp>
    530     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
    531 template <class _Tp>
    532     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
    533 template <class _Tp>
    534     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
    535 
    536 template <class _Tp>
    537 class _LIBCPP_TEMPLATE_VIS numeric_limits<const _Tp>
    538     : private numeric_limits<_Tp>
    539 {
    540     typedef numeric_limits<_Tp> __base;
    541     typedef _Tp type;
    542 public:
    543     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    544     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    545     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    546     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    547 
    548     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    549     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    550     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    551     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    552     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    553     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    554     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    555     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    556     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    557 
    558     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    559     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    560     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    561     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    562 
    563     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    564     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    565     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    566     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    567     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    568     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    569     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    570     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    571     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    572 
    573     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    574     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    575     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    576 
    577     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    578     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    579     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    580 };
    581 
    582 template <class _Tp>
    583     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
    584 template <class _Tp>
    585     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
    586 template <class _Tp>
    587     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
    588 template <class _Tp>
    589     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
    590 template <class _Tp>
    591     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
    592 template <class _Tp>
    593     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
    594 template <class _Tp>
    595     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
    596 template <class _Tp>
    597     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
    598 template <class _Tp>
    599     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
    600 template <class _Tp>
    601     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
    602 template <class _Tp>
    603     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
    604 template <class _Tp>
    605     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
    606 template <class _Tp>
    607     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
    608 template <class _Tp>
    609     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
    610 template <class _Tp>
    611     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
    612 template <class _Tp>
    613     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
    614 template <class _Tp>
    615     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
    616 template <class _Tp>
    617     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
    618 template <class _Tp>
    619     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
    620 template <class _Tp>
    621     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
    622 template <class _Tp>
    623     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
    624 template <class _Tp>
    625     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
    626 template <class _Tp>
    627     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
    628 
    629 template <class _Tp>
    630 class _LIBCPP_TEMPLATE_VIS numeric_limits<volatile _Tp>
    631     : private numeric_limits<_Tp>
    632 {
    633     typedef numeric_limits<_Tp> __base;
    634     typedef _Tp type;
    635 public:
    636     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    637     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    638     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    639     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    640 
    641     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    642     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    643     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    644     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    645     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    646     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    647     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    648     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    649     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    650 
    651     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    652     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    653     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    654     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    655 
    656     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    657     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    658     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    659     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    660     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    661     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    662     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    663     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    664     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    665 
    666     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    667     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    668     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    669 
    670     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    671     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    672     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    673 };
    674 
    675 template <class _Tp>
    676     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
    677 template <class _Tp>
    678     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
    679 template <class _Tp>
    680     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
    681 template <class _Tp>
    682     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
    683 template <class _Tp>
    684     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
    685 template <class _Tp>
    686     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
    687 template <class _Tp>
    688     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
    689 template <class _Tp>
    690     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
    691 template <class _Tp>
    692     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
    693 template <class _Tp>
    694     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
    695 template <class _Tp>
    696     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
    697 template <class _Tp>
    698     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
    699 template <class _Tp>
    700     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
    701 template <class _Tp>
    702     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
    703 template <class _Tp>
    704     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
    705 template <class _Tp>
    706     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
    707 template <class _Tp>
    708     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
    709 template <class _Tp>
    710     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
    711 template <class _Tp>
    712     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
    713 template <class _Tp>
    714     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
    715 template <class _Tp>
    716     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
    717 template <class _Tp>
    718     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
    719 template <class _Tp>
    720     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
    721 
    722 template <class _Tp>
    723 class _LIBCPP_TEMPLATE_VIS numeric_limits<const volatile _Tp>
    724     : private numeric_limits<_Tp>
    725 {
    726     typedef numeric_limits<_Tp> __base;
    727     typedef _Tp type;
    728 public:
    729     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    730     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    731     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    732     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    733 
    734     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    735     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    736     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    737     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    738     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    739     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    740     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    741     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    742     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    743 
    744     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    745     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    746     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    747     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    748 
    749     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    750     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    751     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    752     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    753     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    754     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    755     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    756     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    757     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    758 
    759     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    760     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    761     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    762 
    763     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    764     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    765     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    766 };
    767 
    768 template <class _Tp>
    769     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
    770 template <class _Tp>
    771     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
    772 template <class _Tp>
    773     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
    774 template <class _Tp>
    775     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
    776 template <class _Tp>
    777     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
    778 template <class _Tp>
    779     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
    780 template <class _Tp>
    781     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
    782 template <class _Tp>
    783     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
    784 template <class _Tp>
    785     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
    786 template <class _Tp>
    787     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
    788 template <class _Tp>
    789     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
    790 template <class _Tp>
    791     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
    792 template <class _Tp>
    793     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
    794 template <class _Tp>
    795     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
    796 template <class _Tp>
    797     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
    798 template <class _Tp>
    799     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
    800 template <class _Tp>
    801     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
    802 template <class _Tp>
    803     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
    804 template <class _Tp>
    805     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
    806 template <class _Tp>
    807     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
    808 template <class _Tp>
    809     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
    810 template <class _Tp>
    811     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
    812 template <class _Tp>
    813     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
    814 
    815 _LIBCPP_END_NAMESPACE_STD
    816 
    817 _LIBCPP_POP_MACROS
    818 
    819 #endif  // _LIBCPP_LIMITS
    820