Restoring authorship annotation for Andrey Khalyavin <[email protected]>. Commit 1 of 2.

1 files changed, 813 insertions, 813 deletions

diff --git a/contrib/libs/cxxsupp/libcxx/include/limits b/contrib/libs/cxxsupp/libcxx/include/limits
index a6d51785249..5d3a6272dec 100644
--- a/contrib/libs/cxxsupp/libcxx/include/limits
+++ b/contrib/libs/cxxsupp/libcxx/include/limits
@@ -1,818 +1,818 @@
-// -*- C++ -*-
-//===---------------------------- limits ----------------------------------===//
-//
+// -*- C++ -*- 
+//===---------------------------- limits ----------------------------------===// 
+// 
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#ifndef _LIBCPP_LIMITS
-#define _LIBCPP_LIMITS
-
-/*
-    limits synopsis
-
-namespace std
-{
-
-template<class T>
-class numeric_limits
-{
-public:
-    static constexpr bool is_specialized = false;
-    static constexpr T min() noexcept;
-    static constexpr T max() noexcept;
-    static constexpr T lowest() noexcept;
-
-    static constexpr int  digits = 0;
-    static constexpr int  digits10 = 0;
-    static constexpr int  max_digits10 = 0;
-    static constexpr bool is_signed = false;
-    static constexpr bool is_integer = false;
-    static constexpr bool is_exact = false;
-    static constexpr int  radix = 0;
-    static constexpr T epsilon() noexcept;
-    static constexpr T round_error() noexcept;
-
-    static constexpr int  min_exponent = 0;
-    static constexpr int  min_exponent10 = 0;
-    static constexpr int  max_exponent = 0;
-    static constexpr int  max_exponent10 = 0;
-
-    static constexpr bool has_infinity = false;
-    static constexpr bool has_quiet_NaN = false;
-    static constexpr bool has_signaling_NaN = false;
-    static constexpr float_denorm_style has_denorm = denorm_absent;
-    static constexpr bool has_denorm_loss = false;
-    static constexpr T infinity() noexcept;
-    static constexpr T quiet_NaN() noexcept;
-    static constexpr T signaling_NaN() noexcept;
-    static constexpr T denorm_min() noexcept;
-
-    static constexpr bool is_iec559 = false;
-    static constexpr bool is_bounded = false;
-    static constexpr bool is_modulo = false;
-
-    static constexpr bool traps = false;
-    static constexpr bool tinyness_before = false;
-    static constexpr float_round_style round_style = round_toward_zero;
-};
-
-enum float_round_style
-{
-    round_indeterminate       = -1,
-    round_toward_zero         =  0,
-    round_to_nearest          =  1,
-    round_toward_infinity     =  2,
-    round_toward_neg_infinity =  3
-};
-
-enum float_denorm_style
-{
-    denorm_indeterminate = -1,
-    denorm_absent = 0,
-    denorm_present = 1
-};
-
-template<> class numeric_limits<cv bool>;
-
-template<> class numeric_limits<cv char>;
-template<> class numeric_limits<cv signed char>;
-template<> class numeric_limits<cv unsigned char>;
-template<> class numeric_limits<cv wchar_t>;
+// 
+//===----------------------------------------------------------------------===// 
+ 
+#ifndef _LIBCPP_LIMITS 
+#define _LIBCPP_LIMITS 
+ 
+/* 
+    limits synopsis 
+ 
+namespace std 
+{ 
+ 
+template<class T> 
+class numeric_limits 
+{ 
+public: 
+    static constexpr bool is_specialized = false; 
+    static constexpr T min() noexcept; 
+    static constexpr T max() noexcept; 
+    static constexpr T lowest() noexcept; 
+ 
+    static constexpr int  digits = 0; 
+    static constexpr int  digits10 = 0; 
+    static constexpr int  max_digits10 = 0; 
+    static constexpr bool is_signed = false; 
+    static constexpr bool is_integer = false; 
+    static constexpr bool is_exact = false; 
+    static constexpr int  radix = 0; 
+    static constexpr T epsilon() noexcept; 
+    static constexpr T round_error() noexcept; 
+ 
+    static constexpr int  min_exponent = 0; 
+    static constexpr int  min_exponent10 = 0; 
+    static constexpr int  max_exponent = 0; 
+    static constexpr int  max_exponent10 = 0; 
+ 
+    static constexpr bool has_infinity = false; 
+    static constexpr bool has_quiet_NaN = false; 
+    static constexpr bool has_signaling_NaN = false; 
+    static constexpr float_denorm_style has_denorm = denorm_absent; 
+    static constexpr bool has_denorm_loss = false; 
+    static constexpr T infinity() noexcept; 
+    static constexpr T quiet_NaN() noexcept; 
+    static constexpr T signaling_NaN() noexcept; 
+    static constexpr T denorm_min() noexcept; 
+ 
+    static constexpr bool is_iec559 = false; 
+    static constexpr bool is_bounded = false; 
+    static constexpr bool is_modulo = false; 
+ 
+    static constexpr bool traps = false; 
+    static constexpr bool tinyness_before = false; 
+    static constexpr float_round_style round_style = round_toward_zero; 
+}; 
+ 
+enum float_round_style 
+{ 
+    round_indeterminate       = -1, 
+    round_toward_zero         =  0, 
+    round_to_nearest          =  1, 
+    round_toward_infinity     =  2, 
+    round_toward_neg_infinity =  3 
+}; 
+ 
+enum float_denorm_style 
+{ 
+    denorm_indeterminate = -1, 
+    denorm_absent = 0, 
+    denorm_present = 1 
+}; 
+ 
+template<> class numeric_limits<cv bool>; 
+ 
+template<> class numeric_limits<cv char>; 
+template<> class numeric_limits<cv signed char>; 
+template<> class numeric_limits<cv unsigned char>; 
+template<> class numeric_limits<cv wchar_t>; 
 template<> class numeric_limits<cv char8_t>; // C++20
-template<> class numeric_limits<cv char16_t>;
-template<> class numeric_limits<cv char32_t>;
-
-template<> class numeric_limits<cv short>;
-template<> class numeric_limits<cv int>;
-template<> class numeric_limits<cv long>;
-template<> class numeric_limits<cv long long>;
-template<> class numeric_limits<cv unsigned short>;
-template<> class numeric_limits<cv unsigned int>;
-template<> class numeric_limits<cv unsigned long>;
-template<> class numeric_limits<cv unsigned long long>;
-
-template<> class numeric_limits<cv float>;
-template<> class numeric_limits<cv double>;
-template<> class numeric_limits<cv long double>;
-
-}  // std
-
-*/
-#include <__config>
-#include <type_traits>
-
-#if defined(_LIBCPP_COMPILER_MSVC)
-#include "__support/win32/limits_msvc_win32.h"
-#endif // _LIBCPP_MSVCRT
-
-#if defined(__IBMCPP__)
-#include "__support/ibm/limits.h"
-#endif // __IBMCPP__
-
-#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
-#pragma GCC system_header
-#endif
-
-_LIBCPP_PUSH_MACROS
-#include <__undef_macros>
+template<> class numeric_limits<cv char16_t>; 
+template<> class numeric_limits<cv char32_t>; 
+ 
+template<> class numeric_limits<cv short>; 
+template<> class numeric_limits<cv int>; 
+template<> class numeric_limits<cv long>; 
+template<> class numeric_limits<cv long long>; 
+template<> class numeric_limits<cv unsigned short>; 
+template<> class numeric_limits<cv unsigned int>; 
+template<> class numeric_limits<cv unsigned long>; 
+template<> class numeric_limits<cv unsigned long long>; 
+ 
+template<> class numeric_limits<cv float>; 
+template<> class numeric_limits<cv double>; 
+template<> class numeric_limits<cv long double>; 
+ 
+}  // std 
+ 
+*/ 
+#include <__config> 
+#include <type_traits> 
+ 
+#if defined(_LIBCPP_COMPILER_MSVC) 
+#include "__support/win32/limits_msvc_win32.h" 
+#endif // _LIBCPP_MSVCRT 
+ 
+#if defined(__IBMCPP__) 
+#include "__support/ibm/limits.h" 
+#endif // __IBMCPP__ 
+ 
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 
+#pragma GCC system_header 
+#endif 
+ 
+_LIBCPP_PUSH_MACROS 
+#include <__undef_macros> 
 #include <version>
-
-
-_LIBCPP_BEGIN_NAMESPACE_STD
-
-enum float_round_style
-{
-    round_indeterminate       = -1,
-    round_toward_zero         =  0,
-    round_to_nearest          =  1,
-    round_toward_infinity     =  2,
-    round_toward_neg_infinity =  3
-};
-
-enum float_denorm_style
-{
-    denorm_indeterminate = -1,
-    denorm_absent = 0,
-    denorm_present = 1
-};
-
-template <class _Tp, bool = is_arithmetic<_Tp>::value>
-class __libcpp_numeric_limits
-{
-protected:
-    typedef _Tp type;
-
-    static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
-
-    static _LIBCPP_CONSTEXPR const int  digits = 0;
-    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
-    static _LIBCPP_CONSTEXPR const bool is_signed = false;
-    static _LIBCPP_CONSTEXPR const bool is_integer = false;
-    static _LIBCPP_CONSTEXPR const bool is_exact = false;
-    static _LIBCPP_CONSTEXPR const int  radix = 0;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = false;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
-
-    static _LIBCPP_CONSTEXPR const bool traps = false;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
-};
-
-template <class _Tp, int __digits, bool _IsSigned>
-struct __libcpp_compute_min
-{
-    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << __digits);
-};
-
-template <class _Tp, int __digits>
-struct __libcpp_compute_min<_Tp, __digits, false>
-{
-    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
-};
-
-template <class _Tp>
-class __libcpp_numeric_limits<_Tp, true>
-{
-protected:
-    typedef _Tp type;
-
-    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
-
-    static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
-    static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
-    static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
-    static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
-    static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
-
-    static _LIBCPP_CONSTEXPR const bool is_integer = true;
-    static _LIBCPP_CONSTEXPR const bool is_exact = true;
-    static _LIBCPP_CONSTEXPR const int  radix = 2;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = !_VSTD::is_signed<_Tp>::value;
-
-#if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__) || \
-    defined(__wasm__)
-    static _LIBCPP_CONSTEXPR const bool traps = true;
-#else
-    static _LIBCPP_CONSTEXPR const bool traps = false;
-#endif
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
-};
-
-template <>
-class __libcpp_numeric_limits<bool, true>
-{
-protected:
-    typedef bool type;
-
-    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
-
-    static _LIBCPP_CONSTEXPR const bool is_signed = false;
-    static _LIBCPP_CONSTEXPR const int  digits = 1;
-    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
-    static _LIBCPP_CONSTEXPR const type __min = false;
-    static _LIBCPP_CONSTEXPR const type __max = true;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
-
-    static _LIBCPP_CONSTEXPR const bool is_integer = true;
-    static _LIBCPP_CONSTEXPR const bool is_exact = true;
-    static _LIBCPP_CONSTEXPR const int  radix = 2;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
-
-    static _LIBCPP_CONSTEXPR const bool traps = false;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
-};
-
-template <>
-class __libcpp_numeric_limits<float, true>
-{
-protected:
-    typedef float type;
-
-    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
-
-    static _LIBCPP_CONSTEXPR const bool is_signed = true;
-    static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
-
-    static _LIBCPP_CONSTEXPR const bool is_integer = false;
-    static _LIBCPP_CONSTEXPR const bool is_exact = false;
-    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
-
-    static _LIBCPP_CONSTEXPR const bool traps = false;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
-};
-
-template <>
-class __libcpp_numeric_limits<double, true>
-{
-protected:
-    typedef double type;
-
-    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
-
-    static _LIBCPP_CONSTEXPR const bool is_signed = true;
-    static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
-
-    static _LIBCPP_CONSTEXPR const bool is_integer = false;
-    static _LIBCPP_CONSTEXPR const bool is_exact = false;
-    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
-
-    static _LIBCPP_CONSTEXPR const bool traps = false;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
-};
-
-template <>
-class __libcpp_numeric_limits<long double, true>
-{
-protected:
-    typedef long double type;
-
-    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
-
-    static _LIBCPP_CONSTEXPR const bool is_signed = true;
-    static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
-
-    static _LIBCPP_CONSTEXPR const bool is_integer = false;
-    static _LIBCPP_CONSTEXPR const bool is_exact = false;
-    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5L;}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
-
-#if (defined(__ppc__) || defined(__ppc64__))
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
-#else
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
-#endif
-    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
-
-    static _LIBCPP_CONSTEXPR const bool traps = false;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
-};
-
-template <class _Tp>
-class _LIBCPP_TEMPLATE_VIS numeric_limits
-    : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
-{
-    typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
-    typedef typename __base::type type;
-public:
-    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
-
-    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
-    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
-    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
-    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
-    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
-
-    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
-};
-
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
-
-template <class _Tp>
-class _LIBCPP_TEMPLATE_VIS numeric_limits<const _Tp>
-    : private numeric_limits<_Tp>
-{
-    typedef numeric_limits<_Tp> __base;
-    typedef _Tp type;
-public:
-    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
-
-    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
-    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
-    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
-    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
-    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
-
-    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
-};
-
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
-
-template <class _Tp>
-class _LIBCPP_TEMPLATE_VIS numeric_limits<volatile _Tp>
-    : private numeric_limits<_Tp>
-{
-    typedef numeric_limits<_Tp> __base;
-    typedef _Tp type;
-public:
-    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
-
-    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
-    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
-    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
-    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
-    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
-
-    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
-};
-
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
-
-template <class _Tp>
-class _LIBCPP_TEMPLATE_VIS numeric_limits<const volatile _Tp>
-    : private numeric_limits<_Tp>
-{
-    typedef numeric_limits<_Tp> __base;
-    typedef _Tp type;
-public:
-    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
-
-    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
-    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
-    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
-    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
-    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
-    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
-    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
-
-    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
-    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
-    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
-    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
-
-    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
-    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
-    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
-    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
-    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
-    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
-
-    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
-    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
-    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
-
-    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
-    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
-    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
-};
-
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
-template <class _Tp>
-    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
-
-_LIBCPP_END_NAMESPACE_STD
-
-_LIBCPP_POP_MACROS
-
-#endif // _LIBCPP_LIMITS
+ 
+ 
+_LIBCPP_BEGIN_NAMESPACE_STD 
+ 
+enum float_round_style 
+{ 
+    round_indeterminate       = -1, 
+    round_toward_zero         =  0, 
+    round_to_nearest          =  1, 
+    round_toward_infinity     =  2, 
+    round_toward_neg_infinity =  3 
+}; 
+ 
+enum float_denorm_style 
+{ 
+    denorm_indeterminate = -1, 
+    denorm_absent = 0, 
+    denorm_present = 1 
+}; 
+ 
+template <class _Tp, bool = is_arithmetic<_Tp>::value> 
+class __libcpp_numeric_limits 
+{ 
+protected: 
+    typedef _Tp type; 
+ 
+    static _LIBCPP_CONSTEXPR const  bool is_specialized = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  digits = 0; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0; 
+    static _LIBCPP_CONSTEXPR const bool is_signed = false; 
+    static _LIBCPP_CONSTEXPR const bool is_integer = false; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = false; 
+    static _LIBCPP_CONSTEXPR const int  radix = 0; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = 0; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = false; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = false; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = false; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = false; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = false; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = false; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero; 
+}; 
+ 
+template <class _Tp, int __digits, bool _IsSigned> 
+struct __libcpp_compute_min 
+{ 
+    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << __digits); 
+}; 
+ 
+template <class _Tp, int __digits> 
+struct __libcpp_compute_min<_Tp, __digits, false> 
+{ 
+    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0); 
+}; 
+ 
+template <class _Tp> 
+class __libcpp_numeric_limits<_Tp, true> 
+{ 
+protected: 
+    typedef _Tp type; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = true; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0); 
+    static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed); 
+    static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0; 
+    static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value; 
+    static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0); 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_integer = true; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = true; 
+    static _LIBCPP_CONSTEXPR const int  radix = 2; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = 0; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = false; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = false; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = true; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = !_VSTD::is_signed<_Tp>::value; 
+ 
+#if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__) || \ 
+    defined(__wasm__) 
+    static _LIBCPP_CONSTEXPR const bool traps = true; 
+#else 
+    static _LIBCPP_CONSTEXPR const bool traps = false; 
+#endif 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = false; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero; 
+}; 
+ 
+template <> 
+class __libcpp_numeric_limits<bool, true> 
+{ 
+protected: 
+    typedef bool type; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = true; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_signed = false; 
+    static _LIBCPP_CONSTEXPR const int  digits = 1; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0; 
+    static _LIBCPP_CONSTEXPR const type __min = false; 
+    static _LIBCPP_CONSTEXPR const type __max = true; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_integer = true; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = true; 
+    static _LIBCPP_CONSTEXPR const int  radix = 2; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = 0; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = 0; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = false; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = false; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = true; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = false; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = false; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = false; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero; 
+}; 
+ 
+template <> 
+class __libcpp_numeric_limits<float, true> 
+{ 
+protected: 
+    typedef float type; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = true; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_signed = true; 
+    static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_integer = false; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = false; 
+    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = true; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = true; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = true; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = false; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = false; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = false; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest; 
+}; 
+ 
+template <> 
+class __libcpp_numeric_limits<double, true> 
+{ 
+protected: 
+    typedef double type; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = true; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_signed = true; 
+    static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_integer = false; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = false; 
+    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = true; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = true; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = true; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = false; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = false; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = false; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest; 
+}; 
+ 
+template <> 
+class __libcpp_numeric_limits<long double, true> 
+{ 
+protected: 
+    typedef long double type; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = true; 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_signed = true; 
+    static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_integer = false; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = false; 
+    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5L;} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = true; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;} 
+ 
+#if (defined(__ppc__) || defined(__ppc64__)) 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = false; 
+#else 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = true; 
+#endif 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = true; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = false; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = false; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = false; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest; 
+}; 
+ 
+template <class _Tp> 
+class _LIBCPP_TEMPLATE_VIS numeric_limits 
+    : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type> 
+{ 
+    typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base; 
+    typedef typename __base::type type; 
+public: 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  digits = __base::digits; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10; 
+    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed; 
+    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact; 
+    static _LIBCPP_CONSTEXPR const int  radix = __base::radix; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = __base::traps; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style; 
+}; 
+ 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style; 
+ 
+template <class _Tp> 
+class _LIBCPP_TEMPLATE_VIS numeric_limits<const _Tp> 
+    : private numeric_limits<_Tp> 
+{ 
+    typedef numeric_limits<_Tp> __base; 
+    typedef _Tp type; 
+public: 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  digits = __base::digits; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10; 
+    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed; 
+    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact; 
+    static _LIBCPP_CONSTEXPR const int  radix = __base::radix; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = __base::traps; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style; 
+}; 
+ 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style; 
+ 
+template <class _Tp> 
+class _LIBCPP_TEMPLATE_VIS numeric_limits<volatile _Tp> 
+    : private numeric_limits<_Tp> 
+{ 
+    typedef numeric_limits<_Tp> __base; 
+    typedef _Tp type; 
+public: 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  digits = __base::digits; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10; 
+    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed; 
+    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact; 
+    static _LIBCPP_CONSTEXPR const int  radix = __base::radix; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = __base::traps; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style; 
+}; 
+ 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style; 
+ 
+template <class _Tp> 
+class _LIBCPP_TEMPLATE_VIS numeric_limits<const volatile _Tp> 
+    : private numeric_limits<_Tp> 
+{ 
+    typedef numeric_limits<_Tp> __base; 
+    typedef _Tp type; 
+public: 
+    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  digits = __base::digits; 
+    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10; 
+    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10; 
+    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed; 
+    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer; 
+    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact; 
+    static _LIBCPP_CONSTEXPR const int  radix = __base::radix; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();} 
+ 
+    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent; 
+    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent; 
+    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10; 
+ 
+    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity; 
+    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN; 
+    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN; 
+    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm; 
+    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss; 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();} 
+    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();} 
+ 
+    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559; 
+    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded; 
+    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo; 
+ 
+    static _LIBCPP_CONSTEXPR const bool traps = __base::traps; 
+    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before; 
+    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style; 
+}; 
+ 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before; 
+template <class _Tp> 
+    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style; 
+ 
+_LIBCPP_END_NAMESPACE_STD 
+ 
+_LIBCPP_POP_MACROS 
+ 
+#endif // _LIBCPP_LIMITS