chrono.h

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// chrono::duration and chrono::time_point -*- C++ -*-

// Copyright (C) 2008-2022 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file include/bits/chrono.h
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{chrono}
 */

#ifndef _GLIBCXX_CHRONO_H
#define _GLIBCXX_CHRONO_H 1

#pragma GCC system_header

#if __cplusplus >= 201103L

#include <ratio>
#include <type_traits>
#include <limits>
#include <ctime>
#include <bits/parse_numbers.h> // for literals support.
#if __cplusplus >= 202002L
# include <concepts>
# include <compare>
#endif

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

#if __cplusplus >= 201703L
  namespace filesystem { struct __file_clock; };
#endif

  namespace chrono
  {
    /// @addtogroup chrono
    /// @{

    /// `chrono::duration` represents a distance between two points in time
    template<typename _Rep, typename _Period = ratio<1>>
      class duration;

    /// `chrono::time_point` represents a point in time as measured by a clock
    template<typename _Clock, typename _Dur = typename _Clock::duration>
      class time_point;
    /// @}
  }

  /// @addtogroup chrono
  /// @{

  // 20.11.4.3 specialization of common_type (for duration, sfinae-friendly)

  /// @cond undocumented

  template<typename _CT, typename _Period1, typename _Period2, typename = void>
    struct __duration_common_type
    { };

  template<typename _CT, typename _Period1, typename _Period2>
    struct __duration_common_type<_CT, _Period1, _Period2,
                                  __void_t<typename _CT::type>>
    {
    private:
      using __gcd_num = __static_gcd<_Period1::num, _Period2::num>;
      using __gcd_den = __static_gcd<_Period1::den, _Period2::den>;
      using __cr = typename _CT::type;
      using __r = ratio<__gcd_num::value,
                        (_Period1::den / __gcd_den::value) * _Period2::den>;

    public:
      using type = chrono::duration<__cr, typename __r::type>;
    };

  /// @endcond

  /// @{
  /// @relates chrono::duration

  /// Specialization of common_type for chrono::duration types.
  template<typename _Rep1, typename _Period1, typename _Rep2, typename _Period2>
    struct common_type<chrono::duration<_Rep1, _Period1>,
                       chrono::duration<_Rep2, _Period2>>
    : __duration_common_type<common_type<_Rep1, _Rep2>,
                             typename _Period1::type,
                             typename _Period2::type>
    { };

  /// Specialization of common_type for two identical chrono::duration types.
  template<typename _Rep, typename _Period>
    struct common_type<chrono::duration<_Rep, _Period>,
                       chrono::duration<_Rep, _Period>>
    {
      using type = chrono::duration<typename common_type<_Rep>::type,
                                    typename _Period::type>;
    };

  /// Specialization of common_type for one chrono::duration type.
  template<typename _Rep, typename _Period>
    struct common_type<chrono::duration<_Rep, _Period>>
    {
      using type = chrono::duration<typename common_type<_Rep>::type,
                                    typename _Period::type>;
    };
  /// @}

  // 20.11.4.3 specialization of common_type (for time_point, sfinae-friendly)

  /// @cond undocumented

  template<typename _CT, typename _Clock, typename = void>
    struct __timepoint_common_type
    { };

  template<typename _CT, typename _Clock>
    struct __timepoint_common_type<_CT, _Clock, __void_t<typename _CT::type>>
    {
      using type = chrono::time_point<_Clock, typename _CT::type>;
    };

  /// @endcond

  /// @{
  /// @relates chrono::time_point

  /// Specialization of common_type for chrono::time_point types.
  template<typename _Clock, typename _Duration1, typename _Duration2>
    struct common_type<chrono::time_point<_Clock, _Duration1>,
                       chrono::time_point<_Clock, _Duration2>>
    : __timepoint_common_type<common_type<_Duration1, _Duration2>, _Clock>
    { };

  /// Specialization of common_type for two identical chrono::time_point types.
  template<typename _Clock, typename _Duration>
    struct common_type<chrono::time_point<_Clock, _Duration>,
                       chrono::time_point<_Clock, _Duration>>
    { using type = chrono::time_point<_Clock, _Duration>; };

  /// Specialization of common_type for one chrono::time_point type.
  template<typename _Clock, typename _Duration>
    struct common_type<chrono::time_point<_Clock, _Duration>>
    { using type = chrono::time_point<_Clock, _Duration>; };
  /// @}

  /// @} group chrono

  namespace chrono
  {
    /// @addtogroup chrono
    /// @{

    /// @cond undocumented

    // Primary template for duration_cast impl.
    template<typename _ToDur, typename _CF, typename _CR,
             bool _NumIsOne = false, bool _DenIsOne = false>
      struct __duration_cast_impl
      {
        template<typename _Rep, typename _Period>
          static constexpr _ToDur
          __cast(const duration<_Rep, _Period>& __d)
          {
            typedef typename _ToDur::rep                        __to_rep;
            return _ToDur(static_cast<__to_rep>(static_cast<_CR>(__d.count())
              * static_cast<_CR>(_CF::num)
              / static_cast<_CR>(_CF::den)));
          }
      };

    template<typename _ToDur, typename _CF, typename _CR>
      struct __duration_cast_impl<_ToDur, _CF, _CR, true, true>
      {
        template<typename _Rep, typename _Period>
          static constexpr _ToDur
          __cast(const duration<_Rep, _Period>& __d)
          {
            typedef typename _ToDur::rep                        __to_rep;
            return _ToDur(static_cast<__to_rep>(__d.count()));
          }
      };

    template<typename _ToDur, typename _CF, typename _CR>
      struct __duration_cast_impl<_ToDur, _CF, _CR, true, false>
      {
        template<typename _Rep, typename _Period>
          static constexpr _ToDur
          __cast(const duration<_Rep, _Period>& __d)
          {
            typedef typename _ToDur::rep                        __to_rep;
            return _ToDur(static_cast<__to_rep>(
              static_cast<_CR>(__d.count()) / static_cast<_CR>(_CF::den)));
          }
      };

    template<typename _ToDur, typename _CF, typename _CR>
      struct __duration_cast_impl<_ToDur, _CF, _CR, false, true>
      {
        template<typename _Rep, typename _Period>
          static constexpr _ToDur
          __cast(const duration<_Rep, _Period>& __d)
          {
            typedef typename _ToDur::rep                        __to_rep;
            return _ToDur(static_cast<__to_rep>(
              static_cast<_CR>(__d.count()) * static_cast<_CR>(_CF::num)));
          }
      };

    template<typename _Tp>
      struct __is_duration
      : std::false_type
      { };

    template<typename _Rep, typename _Period>
      struct __is_duration<duration<_Rep, _Period>>
      : std::true_type
      { };

    template<typename _Tp>
      using __enable_if_is_duration
        = typename enable_if<__is_duration<_Tp>::value, _Tp>::type;

    template<typename _Tp>
      using __disable_if_is_duration
        = typename enable_if<!__is_duration<_Tp>::value, _Tp>::type;

    /// @endcond

    /** Convert a `duration` to type `ToDur`.
     *
     * If the duration cannot be represented accurately in the result type,
     * returns the result of integer truncation (i.e., rounded towards zero).
     *
     * @tparam _ToDur The result type must be a `duration`.
     * @param __d A duration.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++11
     */
    template<typename _ToDur, typename _Rep, typename _Period>
      _GLIBCXX_NODISCARD
      constexpr __enable_if_is_duration<_ToDur>
      duration_cast(const duration<_Rep, _Period>& __d)
      {
        typedef typename _ToDur::period                         __to_period;
        typedef typename _ToDur::rep                            __to_rep;
        typedef ratio_divide<_Period, __to_period>              __cf;
        typedef typename common_type<__to_rep, _Rep, intmax_t>::type __cr;
        typedef  __duration_cast_impl<_ToDur, __cf, __cr,
                                      __cf::num == 1, __cf::den == 1> __dc;
        return __dc::__cast(__d);
      }

    /** Trait indicating whether to treat a type as a floating-point type.
     *
     * The chrono library uses this trait to tell whether a `duration` can
     * represent fractional values of the given precision, or only integral
     * values.
     *
     * You should specialize this trait for your own numeric types that are
     * used with `duration` and can represent non-integral values.
     *
     * @since C++11
     */
    template<typename _Rep>
      struct treat_as_floating_point
      : is_floating_point<_Rep>
      { };

#if __cplusplus > 201402L
    template <typename _Rep>
      inline constexpr bool treat_as_floating_point_v =
        treat_as_floating_point<_Rep>::value;
#endif // C++17

#if __cplusplus > 201703L
    template<typename _Tp>
      struct is_clock;

    template<typename _Tp>
      inline constexpr bool is_clock_v = is_clock<_Tp>::value;

#if __cpp_lib_concepts
    template<typename _Tp>
      struct is_clock : false_type
      { };

    template<typename _Tp>
      requires requires {
        typename _Tp::rep;
        typename _Tp::period;
        typename _Tp::duration;
        typename _Tp::time_point::clock;
        typename _Tp::time_point::duration;
        { &_Tp::is_steady } -> same_as<const bool*>;
        { _Tp::now() } -> same_as<typename _Tp::time_point>;
        requires same_as<typename _Tp::duration,
                         duration<typename _Tp::rep, typename _Tp::period>>;
        requires same_as<typename _Tp::time_point::duration,
                         typename _Tp::duration>;
      }
      struct is_clock<_Tp> : true_type
      { };
#else
    template<typename _Tp, typename = void>
      struct __is_clock_impl : false_type
      { };

    template<typename _Tp>
      struct __is_clock_impl<_Tp,
                             void_t<typename _Tp::rep, typename _Tp::period,
                                    typename _Tp::duration,
                                    typename _Tp::time_point::duration,
                                    decltype(_Tp::is_steady),
                                    decltype(_Tp::now())>>
      : __and_<is_same<typename _Tp::duration,
                       duration<typename _Tp::rep, typename _Tp::period>>,
               is_same<typename _Tp::time_point::duration,
                       typename _Tp::duration>,
               is_same<decltype(&_Tp::is_steady), const bool*>,
               is_same<decltype(_Tp::now()), typename _Tp::time_point>>::type
      { };

    template<typename _Tp>
      struct is_clock : __is_clock_impl<_Tp>::type
      { };
#endif
#endif // C++20

#if __cplusplus >= 201703L
# define __cpp_lib_chrono 201611L

    /** Convert a `duration` to type `ToDur` and round down.
     *
     * If the duration cannot be represented exactly in the result type,
     * returns the closest value that is less than the argument.
     *
     * @tparam _ToDur The result type must be a `duration`.
     * @param __d A duration.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++17
     */
    template<typename _ToDur, typename _Rep, typename _Period>
      [[nodiscard]] constexpr __enable_if_is_duration<_ToDur>
      floor(const duration<_Rep, _Period>& __d)
      {
        auto __to = chrono::duration_cast<_ToDur>(__d);
        if (__to > __d)
          return __to - _ToDur{1};
        return __to;
      }

    /** Convert a `duration` to type `ToDur` and round up.
     *
     * If the duration cannot be represented exactly in the result type,
     * returns the closest value that is greater than the argument.
     *
     * @tparam _ToDur The result type must be a `duration`.
     * @param __d A duration.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++17
     */
    template<typename _ToDur, typename _Rep, typename _Period>
      [[nodiscard]] constexpr __enable_if_is_duration<_ToDur>
      ceil(const duration<_Rep, _Period>& __d)
      {
        auto __to = chrono::duration_cast<_ToDur>(__d);
        if (__to < __d)
          return __to + _ToDur{1};
        return __to;
      }

    /** Convert a `duration` to type `ToDur` and round to the closest value.
     *
     * If the duration cannot be represented exactly in the result type,
     * returns the closest value, rounding ties to even.
     *
     * @tparam _ToDur The result type must be a `duration` with a
     *                non-floating-point `rep` type.
     * @param __d A duration.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++17
     */
    template <typename _ToDur, typename _Rep, typename _Period>
      [[nodiscard]] constexpr
      enable_if_t<
        __and_<__is_duration<_ToDur>,
               __not_<treat_as_floating_point<typename _ToDur::rep>>>::value,
        _ToDur>
      round(const duration<_Rep, _Period>& __d)
      {
        _ToDur __t0 = chrono::floor<_ToDur>(__d);
        _ToDur __t1 = __t0 + _ToDur{1};
        auto __diff0 = __d - __t0;
        auto __diff1 = __t1 - __d;
        if (__diff0 == __diff1)
          {
            if (__t0.count() & 1)
              return __t1;
            return __t0;
          }
        else if (__diff0 < __diff1)
          return __t0;
        return __t1;
      }

    /** The absolute (non-negative) value of a duration.
     *
     * @param __d A duration with a signed `rep` type.
     * @return A duration of the same type as the argument, with value |d|.
     * @since C++17
     */
    template<typename _Rep, typename _Period>
      [[nodiscard]] constexpr
      enable_if_t<numeric_limits<_Rep>::is_signed, duration<_Rep, _Period>>
      abs(duration<_Rep, _Period> __d)
      {
        if (__d >= __d.zero())
          return __d;
        return -__d;
      }

    // Make chrono::ceil<D> also usable as chrono::__detail::ceil<D>.
    namespace __detail { using chrono::ceil; }

#else // ! C++17

    // We want to use ceil even when compiling for earlier standards versions.
    // C++11 only allows a single statement in a constexpr function, so we
    // need to move the comparison into a separate function, __ceil_impl.
    namespace __detail
    {
      template<typename _Tp, typename _Up>
        constexpr _Tp
        __ceil_impl(const _Tp& __t, const _Up& __u)
        {
          return (__t < __u) ? (__t + _Tp{1}) : __t;
        }

      // C++11-friendly version of std::chrono::ceil<D> for internal use.
      template<typename _ToDur, typename _Rep, typename _Period>
        constexpr _ToDur
        ceil(const duration<_Rep, _Period>& __d)
        {
          return __detail::__ceil_impl(chrono::duration_cast<_ToDur>(__d), __d);
        }
    }
#endif // C++17

    /// duration_values
    template<typename _Rep>
      struct duration_values
      {
        static constexpr _Rep
        zero() noexcept
        { return _Rep(0); }

        static constexpr _Rep
        max() noexcept
        { return numeric_limits<_Rep>::max(); }

        static constexpr _Rep
        min() noexcept
        { return numeric_limits<_Rep>::lowest(); }
      };

    template<typename _Rep, typename _Period>
      class duration
      {
        static_assert(!__is_duration<_Rep>::value,
                      "rep cannot be a std::chrono::duration");
        static_assert(__is_ratio<_Period>::value,
                      "period must be a specialization of std::ratio");
        static_assert(_Period::num > 0, "period must be positive");

        template<typename _Rep2>
          using __is_float = treat_as_floating_point<_Rep2>;

        static constexpr intmax_t
        _S_gcd(intmax_t __m, intmax_t __n) noexcept
        {
          // Duration only allows positive periods so we don't need to
          // handle negative values here (unlike __static_gcd and std::gcd).
#if __cplusplus >= 201402L
          do
            {
              intmax_t __rem = __m % __n;
              __m = __n;
              __n = __rem;
            }
          while (__n != 0);
          return __m;
#else
          // C++11 doesn't allow loops in constexpr functions, but this
          // recursive version can be more expensive to evaluate.
          return (__n == 0) ? __m : _S_gcd(__n, __m % __n);
#endif
        }

        // _GLIBCXX_RESOLVE_LIB_DEFECTS
        // 2094. overflow shouldn't participate in overload resolution
        // 3090. What is [2094] intended to mean?
        // This only produces a valid type if no overflow occurs.
        template<typename _R1, typename _R2,
                 intmax_t __gcd1 = _S_gcd(_R1::num, _R2::num),
                 intmax_t __gcd2 = _S_gcd(_R1::den, _R2::den)>
          using __divide = ratio<(_R1::num / __gcd1) * (_R2::den / __gcd2),
                                 (_R1::den / __gcd2) * (_R2::num / __gcd1)>;

        // _Period2 is an exact multiple of _Period
        template<typename _Period2>
          using __is_harmonic
            = __bool_constant<__divide<_Period2, _Period>::den == 1>;

      public:

        using rep = _Rep;
        using period = typename _Period::type;

        // 20.11.5.1 construction / copy / destroy
        constexpr duration() = default;

        duration(const duration&) = default;

        // _GLIBCXX_RESOLVE_LIB_DEFECTS
        // 3050. Conversion specification problem in chrono::duration
        template<typename _Rep2, typename = _Require<
                 is_convertible<const _Rep2&, rep>,
                 __or_<__is_float<rep>, __not_<__is_float<_Rep2>>>>>
          constexpr explicit duration(const _Rep2& __rep)
          : __r(static_cast<rep>(__rep)) { }

        template<typename _Rep2, typename _Period2, typename = _Require<
                 is_convertible<const _Rep2&, rep>,
                 __or_<__is_float<rep>,
                       __and_<__is_harmonic<_Period2>,
                              __not_<__is_float<_Rep2>>>>>>
          constexpr duration(const duration<_Rep2, _Period2>& __d)
          : __r(duration_cast<duration>(__d).count()) { }

        ~duration() = default;
        duration& operator=(const duration&) = default;

        // 20.11.5.2 observer
        constexpr rep
        count() const
        { return __r; }

        // 20.11.5.3 arithmetic

        constexpr duration<typename common_type<rep>::type, period>
        operator+() const
        { return duration<typename common_type<rep>::type, period>(__r); }

        constexpr duration<typename common_type<rep>::type, period>
        operator-() const
        { return duration<typename common_type<rep>::type, period>(-__r); }

        _GLIBCXX17_CONSTEXPR duration&
        operator++()
        {
          ++__r;
          return *this;
        }

        _GLIBCXX17_CONSTEXPR duration
        operator++(int)
        { return duration(__r++); }

        _GLIBCXX17_CONSTEXPR duration&
        operator--()
        {
          --__r;
          return *this;
        }

        _GLIBCXX17_CONSTEXPR duration
        operator--(int)
        { return duration(__r--); }

        _GLIBCXX17_CONSTEXPR duration&
        operator+=(const duration& __d)
        {
          __r += __d.count();
          return *this;
        }

        _GLIBCXX17_CONSTEXPR duration&
        operator-=(const duration& __d)
        {
          __r -= __d.count();
          return *this;
        }

        _GLIBCXX17_CONSTEXPR duration&
        operator*=(const rep& __rhs)
        {
          __r *= __rhs;
          return *this;
        }

        _GLIBCXX17_CONSTEXPR duration&
        operator/=(const rep& __rhs)
        {
          __r /= __rhs;
          return *this;
        }

        // DR 934.
        template<typename _Rep2 = rep>
          _GLIBCXX17_CONSTEXPR
          typename enable_if<!treat_as_floating_point<_Rep2>::value,
                             duration&>::type
          operator%=(const rep& __rhs)
          {
            __r %= __rhs;
            return *this;
          }

        template<typename _Rep2 = rep>
          _GLIBCXX17_CONSTEXPR
          typename enable_if<!treat_as_floating_point<_Rep2>::value,
                             duration&>::type
          operator%=(const duration& __d)
          {
            __r %= __d.count();
            return *this;
          }

        // 20.11.5.4 special values
        static constexpr duration
        zero() noexcept
        { return duration(duration_values<rep>::zero()); }

        static constexpr duration
        min() noexcept
        { return duration(duration_values<rep>::min()); }

        static constexpr duration
        max() noexcept
        { return duration(duration_values<rep>::max()); }

      private:
        rep __r;
      };

    /// @{
    /// @relates std::chrono::duration

    /// The sum of two durations.
    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr typename common_type<duration<_Rep1, _Period1>,
                                     duration<_Rep2, _Period2>>::type
      operator+(const duration<_Rep1, _Period1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<__dur1,__dur2>::type       __cd;
        return __cd(__cd(__lhs).count() + __cd(__rhs).count());
      }

    /// The difference between two durations.
    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr typename common_type<duration<_Rep1, _Period1>,
                                     duration<_Rep2, _Period2>>::type
      operator-(const duration<_Rep1, _Period1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<__dur1,__dur2>::type       __cd;
        return __cd(__cd(__lhs).count() - __cd(__rhs).count());
      }

    /// @}

    /// @cond undocumented

    // SFINAE helper to obtain common_type<_Rep1, _Rep2> only if _Rep2
    // is implicitly convertible to it.
    // _GLIBCXX_RESOLVE_LIB_DEFECTS
    // 3050. Conversion specification problem in chrono::duration constructor
    template<typename _Rep1, typename _Rep2,
             typename _CRep = typename common_type<_Rep1, _Rep2>::type>
      using __common_rep_t = typename
        enable_if<is_convertible<const _Rep2&, _CRep>::value, _CRep>::type;

    /// @endcond

    /** @{
     * Arithmetic operators for chrono::duration
     * @relates std::chrono::duration
     */

    template<typename _Rep1, typename _Period, typename _Rep2>
      constexpr duration<__common_rep_t<_Rep1, _Rep2>, _Period>
      operator*(const duration<_Rep1, _Period>& __d, const _Rep2& __s)
      {
        typedef duration<typename common_type<_Rep1, _Rep2>::type, _Period>
          __cd;
        return __cd(__cd(__d).count() * __s);
      }

    template<typename _Rep1, typename _Rep2, typename _Period>
      constexpr duration<__common_rep_t<_Rep2, _Rep1>, _Period>
      operator*(const _Rep1& __s, const duration<_Rep2, _Period>& __d)
      { return __d * __s; }

    template<typename _Rep1, typename _Period, typename _Rep2>
      constexpr
      duration<__common_rep_t<_Rep1, __disable_if_is_duration<_Rep2>>, _Period>
      operator/(const duration<_Rep1, _Period>& __d, const _Rep2& __s)
      {
        typedef duration<typename common_type<_Rep1, _Rep2>::type, _Period>
          __cd;
        return __cd(__cd(__d).count() / __s);
      }

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr typename common_type<_Rep1, _Rep2>::type
      operator/(const duration<_Rep1, _Period1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<__dur1,__dur2>::type       __cd;
        return __cd(__lhs).count() / __cd(__rhs).count();
      }

    // DR 934.
    template<typename _Rep1, typename _Period, typename _Rep2>
      constexpr
      duration<__common_rep_t<_Rep1, __disable_if_is_duration<_Rep2>>, _Period>
      operator%(const duration<_Rep1, _Period>& __d, const _Rep2& __s)
      {
        typedef duration<typename common_type<_Rep1, _Rep2>::type, _Period>
          __cd;
        return __cd(__cd(__d).count() % __s);
      }

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr typename common_type<duration<_Rep1, _Period1>,
                                     duration<_Rep2, _Period2>>::type
      operator%(const duration<_Rep1, _Period1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<__dur1,__dur2>::type       __cd;
        return __cd(__cd(__lhs).count() % __cd(__rhs).count());
      }
    /// @}

    // comparisons

    /** @{
     * Comparisons for chrono::duration
     * @relates std::chrono::duration
     */

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr bool
      operator==(const duration<_Rep1, _Period1>& __lhs,
                 const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<__dur1,__dur2>::type       __ct;
        return __ct(__lhs).count() == __ct(__rhs).count();
      }

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr bool
      operator<(const duration<_Rep1, _Period1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<__dur1,__dur2>::type       __ct;
        return __ct(__lhs).count() < __ct(__rhs).count();
      }

#if __cpp_lib_three_way_comparison
    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      requires three_way_comparable<common_type_t<_Rep1, _Rep2>>
      constexpr auto
      operator<=>(const duration<_Rep1, _Period1>& __lhs,
                  const duration<_Rep2, _Period2>& __rhs)
      {
        using __ct = common_type_t<duration<_Rep1, _Period1>,
                                   duration<_Rep2, _Period2>>;
        return __ct(__lhs).count() <=> __ct(__rhs).count();
      }
#else
    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr bool
      operator!=(const duration<_Rep1, _Period1>& __lhs,
                 const duration<_Rep2, _Period2>& __rhs)
      { return !(__lhs == __rhs); }
#endif

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr bool
      operator<=(const duration<_Rep1, _Period1>& __lhs,
                 const duration<_Rep2, _Period2>& __rhs)
      { return !(__rhs < __lhs); }

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr bool
      operator>(const duration<_Rep1, _Period1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      { return __rhs < __lhs; }

    template<typename _Rep1, typename _Period1,
             typename _Rep2, typename _Period2>
      constexpr bool
      operator>=(const duration<_Rep1, _Period1>& __lhs,
                 const duration<_Rep2, _Period2>& __rhs)
      { return !(__lhs < __rhs); }

    /// @}

    /// @cond undocumented
#ifdef _GLIBCXX_USE_C99_STDINT_TR1
# define _GLIBCXX_CHRONO_INT64_T int64_t
#elif defined __INT64_TYPE__
# define _GLIBCXX_CHRONO_INT64_T __INT64_TYPE__
#else
    static_assert(std::numeric_limits<unsigned long long>::digits >= 64,
        "Representation type for nanoseconds must have at least 64 bits");
# define _GLIBCXX_CHRONO_INT64_T long long
#endif
    /// @endcond

    /// nanoseconds
    using nanoseconds   = duration<_GLIBCXX_CHRONO_INT64_T, nano>;

    /// microseconds
    using microseconds  = duration<_GLIBCXX_CHRONO_INT64_T, micro>;

    /// milliseconds
    using milliseconds  = duration<_GLIBCXX_CHRONO_INT64_T, milli>;

    /// seconds
    using seconds       = duration<_GLIBCXX_CHRONO_INT64_T>;

    /// minutes
    using minutes       = duration<_GLIBCXX_CHRONO_INT64_T, ratio< 60>>;

    /// hours
    using hours         = duration<_GLIBCXX_CHRONO_INT64_T, ratio<3600>>;

#if __cplusplus > 201703L
    /// days
    using days          = duration<_GLIBCXX_CHRONO_INT64_T, ratio<86400>>;

    /// weeks
    using weeks         = duration<_GLIBCXX_CHRONO_INT64_T, ratio<604800>>;

    /// years
    using years         = duration<_GLIBCXX_CHRONO_INT64_T, ratio<31556952>>;

    /// months
    using months        = duration<_GLIBCXX_CHRONO_INT64_T, ratio<2629746>>;
#endif // C++20

#undef _GLIBCXX_CHRONO_INT64_T

    template<typename _Clock, typename _Dur>
      class time_point
      {
        static_assert(__is_duration<_Dur>::value,
            "duration must be a specialization of std::chrono::duration");

      public:
        typedef _Clock                                          clock;
        typedef _Dur                                            duration;
        typedef typename duration::rep                          rep;
        typedef typename duration::period                       period;

        constexpr time_point() : __d(duration::zero())
        { }

        constexpr explicit time_point(const duration& __dur)
        : __d(__dur)
        { }

        // conversions
        template<typename _Dur2,
                 typename = _Require<is_convertible<_Dur2, _Dur>>>
          constexpr time_point(const time_point<clock, _Dur2>& __t)
          : __d(__t.time_since_epoch())
          { }

        // observer
        constexpr duration
        time_since_epoch() const
        { return __d; }

#if __cplusplus > 201703L
        constexpr time_point&
        operator++()
        {
          ++__d;
          return *this;
        }

        constexpr time_point
        operator++(int)
        { return time_point{__d++}; }

        constexpr time_point&
        operator--()
        {
          --__d;
          return *this;
        }

        constexpr time_point
        operator--(int)
        { return time_point{__d--}; }
#endif

        // arithmetic
        _GLIBCXX17_CONSTEXPR time_point&
        operator+=(const duration& __dur)
        {
          __d += __dur;
          return *this;
        }

        _GLIBCXX17_CONSTEXPR time_point&
        operator-=(const duration& __dur)
        {
          __d -= __dur;
          return *this;
        }

        // special values
        static constexpr time_point
        min() noexcept
        { return time_point(duration::min()); }

        static constexpr time_point
        max() noexcept
        { return time_point(duration::max()); }

      private:
        duration __d;
      };

    /** Convert a `time_point` to use `duration` type `ToDur`.
     *
     * The result is the same time point as measured by the same clock, but
     * using the specified `duration` to represent the time.
     * If the time point cannot be represented accurately in the result type,
     * returns the result of integer truncation (i.e., rounded towards zero).
     *
     * @tparam _ToDur The `duration` type to use for the result.
     * @param __t A time point.
     * @return The value of `__t` converted to use type `_ToDur`.
     * @since C++11
     */
    template<typename _ToDur, typename _Clock, typename _Dur>
      _GLIBCXX_NODISCARD constexpr
      __enable_if_t<__is_duration<_ToDur>::value, time_point<_Clock, _ToDur>>
      time_point_cast(const time_point<_Clock, _Dur>& __t)
      {
        typedef time_point<_Clock, _ToDur>                      __time_point;
        return __time_point(duration_cast<_ToDur>(__t.time_since_epoch()));
      }

#if __cplusplus > 201402L
    /** Convert a `time_point` to type `ToDur` and round down.
     *
     * The result is the same time point as measured by the same clock, but
     * using the specified `duration` to represent the time.
     * If the time point cannot be represented exactly in the result type,
     * returns the closest value that is less than the argument.
     *
     * @tparam _ToDur The `duration` type to use for the result.
     * @param __t A time point.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++17
     */
    template<typename _ToDur, typename _Clock, typename _Dur>
      [[nodiscard]] constexpr
      enable_if_t<__is_duration<_ToDur>::value, time_point<_Clock, _ToDur>>
      floor(const time_point<_Clock, _Dur>& __tp)
      {
        return time_point<_Clock, _ToDur>{
            chrono::floor<_ToDur>(__tp.time_since_epoch())};
      }

    /** Convert a `time_point` to type `ToDur` and round up.
     *
     * The result is the same time point as measured by the same clock, but
     * using the specified `duration` to represent the time.
     * If the time point cannot be represented exactly in the result type,
     * returns the closest value that is greater than the argument.
     *
     * @tparam _ToDur The `duration` type to use for the result.
     * @param __t A time point.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++17
     */
    template<typename _ToDur, typename _Clock, typename _Dur>
      [[nodiscard]] constexpr
      enable_if_t<__is_duration<_ToDur>::value, time_point<_Clock, _ToDur>>
      ceil(const time_point<_Clock, _Dur>& __tp)
      {
        return time_point<_Clock, _ToDur>{
            chrono::ceil<_ToDur>(__tp.time_since_epoch())};
      }

    /** Convert a `time_point` to type `ToDur` and round to the closest value.
     *
     * The result is the same time point as measured by the same clock, but
     * using the specified `duration` to represent the time.
     * If the time point cannot be represented exactly in the result type,
     * returns the closest value, rounding ties to even.
     *
     * @tparam _ToDur The `duration` type to use for the result,
     *                which must have a non-floating-point `rep` type.
     * @param __t A time point.
     * @return The value of `__d` converted to type `_ToDur`.
     * @since C++17
     */
    template<typename _ToDur, typename _Clock, typename _Dur>
      [[nodiscard]] constexpr
      enable_if_t<
        __and_<__is_duration<_ToDur>,
               __not_<treat_as_floating_point<typename _ToDur::rep>>>::value,
        time_point<_Clock, _ToDur>>
      round(const time_point<_Clock, _Dur>& __tp)
      {
        return time_point<_Clock, _ToDur>{
            chrono::round<_ToDur>(__tp.time_since_epoch())};
      }
#endif // C++17

    /// @{
    /// @relates time_point

    /// Adjust a time point forwards by the given duration.
    template<typename _Clock, typename _Dur1,
             typename _Rep2, typename _Period2>
      constexpr time_point<_Clock,
        typename common_type<_Dur1, duration<_Rep2, _Period2>>::type>
      operator+(const time_point<_Clock, _Dur1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<_Dur1,__dur2>::type        __ct;
        typedef time_point<_Clock, __ct>                        __time_point;
        return __time_point(__lhs.time_since_epoch() + __rhs);
      }

    /// Adjust a time point forwards by the given duration.
    template<typename _Rep1, typename _Period1,
             typename _Clock, typename _Dur2>
      constexpr time_point<_Clock,
        typename common_type<duration<_Rep1, _Period1>, _Dur2>::type>
      operator+(const duration<_Rep1, _Period1>& __lhs,
                const time_point<_Clock, _Dur2>& __rhs)
      {
        typedef duration<_Rep1, _Period1>                       __dur1;
        typedef typename common_type<__dur1,_Dur2>::type        __ct;
        typedef time_point<_Clock, __ct>                        __time_point;
        return __time_point(__rhs.time_since_epoch() + __lhs);
      }

    /// Adjust a time point backwards by the given duration.
    template<typename _Clock, typename _Dur1,
             typename _Rep2, typename _Period2>
      constexpr time_point<_Clock,
        typename common_type<_Dur1, duration<_Rep2, _Period2>>::type>
      operator-(const time_point<_Clock, _Dur1>& __lhs,
                const duration<_Rep2, _Period2>& __rhs)
      {
        typedef duration<_Rep2, _Period2>                       __dur2;
        typedef typename common_type<_Dur1,__dur2>::type        __ct;
        typedef time_point<_Clock, __ct>                        __time_point;
        return __time_point(__lhs.time_since_epoch() -__rhs);
      }

    /// The difference between two time points (as a duration)
    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr typename common_type<_Dur1, _Dur2>::type
      operator-(const time_point<_Clock, _Dur1>& __lhs,
                const time_point<_Clock, _Dur2>& __rhs)
      { return __lhs.time_since_epoch() - __rhs.time_since_epoch(); }
    /// @}

    /** @{
     * Comparisons for time_point
     * @relates chrono::time_point
     */

    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr bool
      operator==(const time_point<_Clock, _Dur1>& __lhs,
                 const time_point<_Clock, _Dur2>& __rhs)
      { return __lhs.time_since_epoch() == __rhs.time_since_epoch(); }

#if __cpp_lib_three_way_comparison
    template<typename _Clock, typename _Dur1,
             three_way_comparable_with<_Dur1> _Dur2>
      constexpr auto
      operator<=>(const time_point<_Clock, _Dur1>& __lhs,
                  const time_point<_Clock, _Dur2>& __rhs)
      { return __lhs.time_since_epoch() <=> __rhs.time_since_epoch(); }
#else
    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr bool
      operator!=(const time_point<_Clock, _Dur1>& __lhs,
                 const time_point<_Clock, _Dur2>& __rhs)
      { return !(__lhs == __rhs); }
#endif

    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr bool
      operator<(const time_point<_Clock, _Dur1>& __lhs,
                const time_point<_Clock, _Dur2>& __rhs)
      { return  __lhs.time_since_epoch() < __rhs.time_since_epoch(); }

    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr bool
      operator<=(const time_point<_Clock, _Dur1>& __lhs,
                 const time_point<_Clock, _Dur2>& __rhs)
      { return !(__rhs < __lhs); }

    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr bool
      operator>(const time_point<_Clock, _Dur1>& __lhs,
                const time_point<_Clock, _Dur2>& __rhs)
      { return __rhs < __lhs; }

    template<typename _Clock, typename _Dur1, typename _Dur2>
      constexpr bool
      operator>=(const time_point<_Clock, _Dur1>& __lhs,
                 const time_point<_Clock, _Dur2>& __rhs)
      { return !(__lhs < __rhs); }

    /// @}
    /// @} group chrono

    // Clocks.

    // Why nanosecond resolution as the default?
    // Why have std::system_clock always count in the highest
    // resolution (ie nanoseconds), even if on some OSes the low 3
    // or 9 decimal digits will be always zero? This allows later
    // implementations to change the system_clock::now()
    // implementation any time to provide better resolution without
    // changing function signature or units.

    // To support the (forward) evolution of the library's defined
    // clocks, wrap inside inline namespace so that the current
    // defintions of system_clock, steady_clock, and
    // high_resolution_clock types are uniquely mangled. This way, new
    // code can use the latests clocks, while the library can contain
    // compatibility definitions for previous versions.  At some
    // point, when these clocks settle down, the inlined namespaces
    // can be removed.  XXX GLIBCXX_ABI Deprecated
_GLIBCXX_BEGIN_INLINE_ABI_NAMESPACE(_V2)

    /**
     *  @brief System clock.
     *
     *  Time returned represents wall time from the system-wide clock.
     *  @ingroup chrono
    */
    struct system_clock
    {
      typedef chrono::nanoseconds                               duration;
      typedef duration::rep                                     rep;
      typedef duration::period                                  period;
      typedef chrono::time_point<system_clock, duration>        time_point;

      static_assert(system_clock::duration::min()
                    < system_clock::duration::zero(),
                    "a clock's minimum duration cannot be less than its epoch");

      static constexpr bool is_steady = false;

      static time_point
      now() noexcept;

      // Map to C API
      [[__gnu__::__always_inline__]]
      static std::time_t
      to_time_t(const time_point& __t) noexcept
      {
        return std::time_t(duration_cast<chrono::seconds>
                           (__t.time_since_epoch()).count());
      }

      [[__gnu__::__always_inline__]]
      static time_point
      from_time_t(std::time_t __t) noexcept
      {
        typedef chrono::time_point<system_clock, seconds>       __from;
        return time_point_cast<system_clock::duration>
               (__from(chrono::seconds(__t)));
      }
    };


    /**
     *  @brief Monotonic clock
     *
     *  Time returned has the property of only increasing at a uniform rate.
     *  @ingroup chrono
    */
    struct steady_clock
    {
      typedef chrono::nanoseconds                               duration;
      typedef duration::rep                                     rep;
      typedef duration::period                                  period;
      typedef chrono::time_point<steady_clock, duration>        time_point;

      static constexpr bool is_steady = true;

      static time_point
      now() noexcept;
    };


    /**
     *  @brief Highest-resolution clock
     *
     *  This is the clock "with the shortest tick period." Alias to
     *  std::system_clock until higher-than-nanosecond definitions
     *  become feasible.
     *  @ingroup chrono
    */
    using high_resolution_clock = system_clock;

_GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)

#if __cplusplus >= 202002L
    /// @addtogroup chrono
    /// @{
    template<typename _Duration>
      using sys_time = time_point<system_clock, _Duration>;
    using sys_seconds = sys_time<seconds>;
    using sys_days = sys_time<days>;

    using file_clock = ::std::filesystem::__file_clock;

    template<typename _Duration>
      using file_time = time_point<file_clock, _Duration>;

    template<> struct is_clock<system_clock> : true_type { };
    template<> struct is_clock<steady_clock> : true_type { };
    template<> struct is_clock<file_clock> : true_type { };

    template<> inline constexpr bool is_clock_v<system_clock> = true;
    template<> inline constexpr bool is_clock_v<steady_clock> = true;
    template<> inline constexpr bool is_clock_v<file_clock> = true;
    /// @}
#endif // C++20
  } // namespace chrono

#if __cplusplus >= 201402L
#define __cpp_lib_chrono_udls 201304L

  inline namespace literals
  {
  /** ISO C++ 2014  namespace for suffixes for duration literals.
   *
   * These suffixes can be used to create `chrono::duration` values with
   * tick periods of hours, minutes, seconds, milliseconds, microseconds
   * or nanoseconds. For example, `std::chrono::seconds(5)` can be written
   * as `5s` after making the suffix visible in the current scope.
   * The suffixes can be made visible by a using-directive or
   * using-declaration such as:
   *  - `using namespace std::chrono_literals;`
   *  - `using namespace std::literals;`
   *  - `using namespace std::chrono;`
   *  - `using namespace std;`
   *  - `using std::chrono_literals::operator""s;`
   *
   * The result of these suffixes on an integer literal is one of the
   * standard typedefs such as `std::chrono::hours`.
   * The result on a floating-point literal is a duration type with the
   * specified tick period and an unspecified floating-point representation,
   * for example `1.5e2ms` might be equivalent to
   * `chrono::duration<long double, chrono::milli>(1.5e2)`.
   *
   * @since C+14
   * @ingroup chrono
   */
  inline namespace chrono_literals
  {
    /// @addtogroup chrono
    /// @{

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wliteral-suffix"
    /// @cond undocumented
    template<typename _Dur, char... _Digits>
      constexpr _Dur __check_overflow()
      {
        using _Val = __parse_int::_Parse_int<_Digits...>;
        constexpr typename _Dur::rep __repval = _Val::value;
        static_assert(__repval >= 0 && __repval == _Val::value,
                      "literal value cannot be represented by duration type");
        return _Dur(__repval);
      }
    /// @endcond

    /// Literal suffix for durations representing non-integer hours
    constexpr chrono::duration<long double, ratio<3600,1>>
    operator""h(long double __hours)
    { return chrono::duration<long double, ratio<3600,1>>{__hours}; }

    /// Literal suffix for durations of type `std::chrono::hours`
    template <char... _Digits>
      constexpr chrono::hours
      operator""h()
      { return __check_overflow<chrono::hours, _Digits...>(); }

    /// Literal suffix for durations representing non-integer minutes
    constexpr chrono::duration<long double, ratio<60,1>>
    operator""min(long double __mins)
    { return chrono::duration<long double, ratio<60,1>>{__mins}; }

    /// Literal suffix for durations of type `std::chrono::minutes`
    template <char... _Digits>
      constexpr chrono::minutes
      operator""min()
      { return __check_overflow<chrono::minutes, _Digits...>(); }

    /// Literal suffix for durations representing non-integer seconds
    constexpr chrono::duration<long double>
    operator""s(long double __secs)
    { return chrono::duration<long double>{__secs}; }

    /// Literal suffix for durations of type `std::chrono::seconds`
    template <char... _Digits>
      constexpr chrono::seconds
      operator""s()
      { return __check_overflow<chrono::seconds, _Digits...>(); }

    /// Literal suffix for durations representing non-integer milliseconds
    constexpr chrono::duration<long double, milli>
    operator""ms(long double __msecs)
    { return chrono::duration<long double, milli>{__msecs}; }

    /// Literal suffix for durations of type `std::chrono::milliseconds`
    template <char... _Digits>
      constexpr chrono::milliseconds
      operator""ms()
      { return __check_overflow<chrono::milliseconds, _Digits...>(); }

    /// Literal suffix for durations representing non-integer microseconds
    constexpr chrono::duration<long double, micro>
    operator""us(long double __usecs)
    { return chrono::duration<long double, micro>{__usecs}; }

    /// Literal suffix for durations of type `std::chrono::microseconds`
    template <char... _Digits>
      constexpr chrono::microseconds
      operator""us()
      { return __check_overflow<chrono::microseconds, _Digits...>(); }

    /// Literal suffix for durations representing non-integer nanoseconds
    constexpr chrono::duration<long double, nano>
    operator""ns(long double __nsecs)
    { return chrono::duration<long double, nano>{__nsecs}; }

    /// Literal suffix for durations of type `std::chrono::nanoseconds`
    template <char... _Digits>
      constexpr chrono::nanoseconds
      operator""ns()
      { return __check_overflow<chrono::nanoseconds, _Digits...>(); }

#pragma GCC diagnostic pop
    /// @}
  } // inline namespace chrono_literals
  } // inline namespace literals

  namespace chrono
  {
    using namespace literals::chrono_literals;
  } // namespace chrono
#endif // C++14

#if __cplusplus >= 201703L
  namespace filesystem
  {
    struct __file_clock
    {
      using duration                  = chrono::nanoseconds;
      using rep                       = duration::rep;
      using period                    = duration::period;
      using time_point                = chrono::time_point<__file_clock>;
      static constexpr bool is_steady = false;

      static time_point
      now() noexcept
      { return _S_from_sys(chrono::system_clock::now()); }

#if __cplusplus > 201703L
      template<typename _Dur>
        static
        chrono::file_time<_Dur>
        from_sys(const chrono::sys_time<_Dur>& __t) noexcept
        { return _S_from_sys(__t); }

      // For internal use only
      template<typename _Dur>
        static
        chrono::sys_time<_Dur>
        to_sys(const chrono::file_time<_Dur>& __t) noexcept
        { return _S_to_sys(__t); }
#endif // C++20

    private:
      using __sys_clock = chrono::system_clock;

      // This clock's (unspecified) epoch is 2174-01-01 00:00:00 UTC.
      // A signed 64-bit duration with nanosecond resolution gives roughly
      // +/- 292 years, which covers the 1901-2446 date range for ext4.
      static constexpr chrono::seconds _S_epoch_diff{6437664000};

    protected:
      // For internal use only
      template<typename _Dur>
        static
        chrono::time_point<__file_clock, _Dur>
        _S_from_sys(const chrono::time_point<__sys_clock, _Dur>& __t) noexcept
        {
          using __file_time = chrono::time_point<__file_clock, _Dur>;
          return __file_time{__t.time_since_epoch()} - _S_epoch_diff;
        }

      // For internal use only
      template<typename _Dur>
        static
        chrono::time_point<__sys_clock, _Dur>
        _S_to_sys(const chrono::time_point<__file_clock, _Dur>& __t) noexcept
        {
          using __sys_time = chrono::time_point<__sys_clock, _Dur>;
          return __sys_time{__t.time_since_epoch()} + _S_epoch_diff;
        }
    };
  } // namespace filesystem
#endif // C++17

_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std

#endif // C++11

#endif //_GLIBCXX_CHRONO_H