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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 _IsSigned>
    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 = !_VSTD::is_signed<_Tp>::value;
    239 
    240 #if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__) || \
    241     defined(__wasm__)
    242     static _LIBCPP_CONSTEXPR const bool traps = true;
    243 #else
    244     static _LIBCPP_CONSTEXPR const bool traps = false;
    245 #endif
    246     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    247     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    248 };
    249 
    250 template <>
    251 class __libcpp_numeric_limits<bool, true>
    252 {
    253 protected:
    254     typedef bool type;
    255 
    256     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    257 
    258     static _LIBCPP_CONSTEXPR const bool is_signed = false;
    259     static _LIBCPP_CONSTEXPR const int  digits = 1;
    260     static _LIBCPP_CONSTEXPR const int  digits10 = 0;
    261     static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
    262     static _LIBCPP_CONSTEXPR const type __min = false;
    263     static _LIBCPP_CONSTEXPR const type __max = true;
    264     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
    265     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
    266     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
    267 
    268     static _LIBCPP_CONSTEXPR const bool is_integer = true;
    269     static _LIBCPP_CONSTEXPR const bool is_exact = true;
    270     static _LIBCPP_CONSTEXPR const int  radix = 2;
    271     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
    272     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
    273 
    274     static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
    275     static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
    276     static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
    277     static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
    278 
    279     static _LIBCPP_CONSTEXPR const bool has_infinity = false;
    280     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
    281     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
    282     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
    283     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    284     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
    285     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
    286     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
    287     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
    288 
    289     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    290     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    291     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    292 
    293     static _LIBCPP_CONSTEXPR const bool traps = false;
    294     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    295     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
    296 };
    297 
    298 template <>
    299 class __libcpp_numeric_limits<float, true>
    300 {
    301 protected:
    302     typedef float type;
    303 
    304     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    305 
    306     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    307     static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
    308     static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
    309     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    310     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
    311     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
    312     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    313 
    314     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    315     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    316     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    317     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
    318     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
    319 
    320     static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
    321     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
    322     static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
    323     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
    324 
    325     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    326     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    327     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    328     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    329     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    330     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
    331     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
    332     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
    333     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
    334 
    335     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    336     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    337     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    338 
    339     static _LIBCPP_CONSTEXPR const bool traps = false;
    340     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    341     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    342 };
    343 
    344 template <>
    345 class __libcpp_numeric_limits<double, true>
    346 {
    347 protected:
    348     typedef double type;
    349 
    350     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    351 
    352     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    353     static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
    354     static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
    355     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    356     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
    357     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
    358     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    359 
    360     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    361     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    362     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    363     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
    364     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    365 
    366     static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
    367     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
    368     static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
    369     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
    370 
    371     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    372     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    373     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    374     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    375     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    376     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
    377     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
    378     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
    379     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
    380 
    381     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    382     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    383     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    384 
    385     static _LIBCPP_CONSTEXPR const bool traps = false;
    386     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    387     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    388 };
    389 
    390 template <>
    391 class __libcpp_numeric_limits<long double, true>
    392 {
    393 protected:
    394     typedef long double type;
    395 
    396     static _LIBCPP_CONSTEXPR const bool is_specialized = true;
    397 
    398     static _LIBCPP_CONSTEXPR const bool is_signed = true;
    399     static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
    400     static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
    401     static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
    402     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
    403     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
    404     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
    405 
    406     static _LIBCPP_CONSTEXPR const bool is_integer = false;
    407     static _LIBCPP_CONSTEXPR const bool is_exact = false;
    408     static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
    409     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
    410     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
    411 
    412     static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
    413     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
    414     static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
    415     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
    416 
    417     static _LIBCPP_CONSTEXPR const bool has_infinity = true;
    418     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
    419     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
    420     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
    421     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
    422     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
    423     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
    424     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
    425     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
    426 
    427 #if (defined(__ppc__) || defined(__ppc64__))
    428     static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
    429 #else
    430     static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
    431 #endif
    432     static _LIBCPP_CONSTEXPR const bool is_bounded = true;
    433     static _LIBCPP_CONSTEXPR const bool is_modulo = false;
    434 
    435     static _LIBCPP_CONSTEXPR const bool traps = false;
    436     static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
    437     static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
    438 };
    439 
    440 template <class _Tp>
    441 class _LIBCPP_TEMPLATE_VIS numeric_limits
    442     : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
    443 {
    444     typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
    445     typedef typename __base::type type;
    446 public:
    447     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    448     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    449     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    450     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    451 
    452     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    453     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    454     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    455     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    456     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    457     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    458     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    459     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    460     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    461 
    462     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    463     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    464     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    465     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    466 
    467     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    468     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    469     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    470     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    471     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    472     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    473     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    474     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    475     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    476 
    477     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    478     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    479     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    480 
    481     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    482     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    483     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    484 };
    485 
    486 template <class _Tp>
    487     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
    488 template <class _Tp>
    489     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
    490 template <class _Tp>
    491     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
    492 template <class _Tp>
    493     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
    494 template <class _Tp>
    495     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
    496 template <class _Tp>
    497     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
    498 template <class _Tp>
    499     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
    500 template <class _Tp>
    501     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
    502 template <class _Tp>
    503     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
    504 template <class _Tp>
    505     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
    506 template <class _Tp>
    507     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
    508 template <class _Tp>
    509     _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
    510 template <class _Tp>
    511     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
    512 template <class _Tp>
    513     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
    514 template <class _Tp>
    515     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
    516 template <class _Tp>
    517     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
    518 template <class _Tp>
    519     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
    520 template <class _Tp>
    521     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
    522 template <class _Tp>
    523     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
    524 template <class _Tp>
    525     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
    526 template <class _Tp>
    527     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
    528 template <class _Tp>
    529     _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
    530 template <class _Tp>
    531     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
    532 
    533 template <class _Tp>
    534 class _LIBCPP_TEMPLATE_VIS numeric_limits<const _Tp>
    535     : private numeric_limits<_Tp>
    536 {
    537     typedef numeric_limits<_Tp> __base;
    538     typedef _Tp type;
    539 public:
    540     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    541     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    542     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    543     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    544 
    545     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    546     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    547     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    548     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    549     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    550     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    551     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    552     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    553     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    554 
    555     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    556     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    557     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    558     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    559 
    560     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    561     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    562     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    563     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    564     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    565     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    566     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    567     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    568     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    569 
    570     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    571     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    572     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    573 
    574     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    575     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    576     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    577 };
    578 
    579 template <class _Tp>
    580     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
    581 template <class _Tp>
    582     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
    583 template <class _Tp>
    584     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
    585 template <class _Tp>
    586     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
    587 template <class _Tp>
    588     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
    589 template <class _Tp>
    590     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
    591 template <class _Tp>
    592     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
    593 template <class _Tp>
    594     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
    595 template <class _Tp>
    596     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
    597 template <class _Tp>
    598     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
    599 template <class _Tp>
    600     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
    601 template <class _Tp>
    602     _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
    603 template <class _Tp>
    604     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
    605 template <class _Tp>
    606     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
    607 template <class _Tp>
    608     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
    609 template <class _Tp>
    610     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
    611 template <class _Tp>
    612     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
    613 template <class _Tp>
    614     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
    615 template <class _Tp>
    616     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
    617 template <class _Tp>
    618     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
    619 template <class _Tp>
    620     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
    621 template <class _Tp>
    622     _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
    623 template <class _Tp>
    624     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
    625 
    626 template <class _Tp>
    627 class _LIBCPP_TEMPLATE_VIS numeric_limits<volatile _Tp>
    628     : private numeric_limits<_Tp>
    629 {
    630     typedef numeric_limits<_Tp> __base;
    631     typedef _Tp type;
    632 public:
    633     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    634     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    635     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    636     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    637 
    638     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    639     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    640     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    641     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    642     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    643     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    644     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    645     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    646     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    647 
    648     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    649     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    650     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    651     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    652 
    653     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    654     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    655     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    656     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    657     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    658     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    659     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    660     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    661     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    662 
    663     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    664     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    665     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    666 
    667     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    668     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    669     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    670 };
    671 
    672 template <class _Tp>
    673     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
    674 template <class _Tp>
    675     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
    676 template <class _Tp>
    677     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
    678 template <class _Tp>
    679     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
    680 template <class _Tp>
    681     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
    682 template <class _Tp>
    683     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
    684 template <class _Tp>
    685     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
    686 template <class _Tp>
    687     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
    688 template <class _Tp>
    689     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
    690 template <class _Tp>
    691     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
    692 template <class _Tp>
    693     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
    694 template <class _Tp>
    695     _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
    696 template <class _Tp>
    697     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
    698 template <class _Tp>
    699     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
    700 template <class _Tp>
    701     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
    702 template <class _Tp>
    703     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
    704 template <class _Tp>
    705     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
    706 template <class _Tp>
    707     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
    708 template <class _Tp>
    709     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
    710 template <class _Tp>
    711     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
    712 template <class _Tp>
    713     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
    714 template <class _Tp>
    715     _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
    716 template <class _Tp>
    717     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
    718 
    719 template <class _Tp>
    720 class _LIBCPP_TEMPLATE_VIS numeric_limits<const volatile _Tp>
    721     : private numeric_limits<_Tp>
    722 {
    723     typedef numeric_limits<_Tp> __base;
    724     typedef _Tp type;
    725 public:
    726     static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
    727     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
    728     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
    729     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
    730 
    731     static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
    732     static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
    733     static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
    734     static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
    735     static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
    736     static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
    737     static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
    738     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
    739     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
    740 
    741     static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
    742     static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
    743     static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
    744     static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
    745 
    746     static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
    747     static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
    748     static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
    749     static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
    750     static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
    751     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
    752     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
    753     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
    754     _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
    755 
    756     static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
    757     static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
    758     static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
    759 
    760     static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
    761     static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
    762     static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
    763 };
    764 
    765 template <class _Tp>
    766     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
    767 template <class _Tp>
    768     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
    769 template <class _Tp>
    770     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
    771 template <class _Tp>
    772     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
    773 template <class _Tp>
    774     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
    775 template <class _Tp>
    776     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
    777 template <class _Tp>
    778     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
    779 template <class _Tp>
    780     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
    781 template <class _Tp>
    782     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
    783 template <class _Tp>
    784     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
    785 template <class _Tp>
    786     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
    787 template <class _Tp>
    788     _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
    789 template <class _Tp>
    790     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
    791 template <class _Tp>
    792     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
    793 template <class _Tp>
    794     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
    795 template <class _Tp>
    796     _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
    797 template <class _Tp>
    798     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
    799 template <class _Tp>
    800     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
    801 template <class _Tp>
    802     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
    803 template <class _Tp>
    804     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
    805 template <class _Tp>
    806     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
    807 template <class _Tp>
    808     _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
    809 template <class _Tp>
    810     _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
    811 
    812 _LIBCPP_END_NAMESPACE_STD
    813 
    814 #endif  // _LIBCPP_LIMITS
    815