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