[thirdparty/gcc.git] / libstdc++-v3 / include / bits / random.tcc

// random number generation (out of line) -*- C++ -*-

// Copyright (C) 2009-2022 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 bits/random.tcc
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{random}
 */

#ifndef _RANDOM_TCC
#define _RANDOM_TCC 1

#include <numeric> // std::accumulate and std::partial_sum

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  /// @cond undocumented
  // (Further) implementation-space details.
  namespace __detail
  {
    // General case for x = (ax + c) mod m -- use Schrage's algorithm
    // to avoid integer overflow.
    //
    // Preconditions:  a > 0, m > 0.
    //
    // Note: only works correctly for __m % __a < __m / __a.
    template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
      _Tp
      _Mod<_Tp, __m, __a, __c, false, true>::
      __calc(_Tp __x)
      {
        if (__a == 1)
          __x %= __m;
        else
          {
            static const _Tp __q = __m / __a;
            static const _Tp __r = __m % __a;

            _Tp __t1 = __a * (__x % __q);
            _Tp __t2 = __r * (__x / __q);
            if (__t1 >= __t2)
              __x = __t1 - __t2;
            else
              __x = __m - __t2 + __t1;
          }

        if (__c != 0)
          {
            const _Tp __d = __m - __x;
            if (__d > __c)
              __x += __c;
            else
              __x = __c - __d;
          }
        return __x;
      }

    template<typename _InputIterator, typename _OutputIterator,
             typename _Tp>
      _OutputIterator
      __normalize(_InputIterator __first, _InputIterator __last,
                  _OutputIterator __result, const _Tp& __factor)
      {
        for (; __first != __last; ++__first, ++__result)
          *__result = *__first / __factor;
        return __result;
      }

  } // namespace __detail
  /// @endcond

#if ! __cpp_inline_variables
  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    constexpr _UIntType
    linear_congruential_engine<_UIntType, __a, __c, __m>::multiplier;

  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    constexpr _UIntType
    linear_congruential_engine<_UIntType, __a, __c, __m>::increment;

  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    constexpr _UIntType
    linear_congruential_engine<_UIntType, __a, __c, __m>::modulus;

  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    constexpr _UIntType
    linear_congruential_engine<_UIntType, __a, __c, __m>::default_seed;
#endif

  /**
   * Seeds the LCR with integral value @p __s, adjusted so that the
   * ring identity is never a member of the convergence set.
   */
  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    void
    linear_congruential_engine<_UIntType, __a, __c, __m>::
    seed(result_type __s)
    {
      if ((__detail::__mod<_UIntType, __m>(__c) == 0)
          && (__detail::__mod<_UIntType, __m>(__s) == 0))
        _M_x = 1;
      else
        _M_x = __detail::__mod<_UIntType, __m>(__s);
    }

  /**
   * Seeds the LCR engine with a value generated by @p __q.
   */
  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    template<typename _Sseq>
      auto
      linear_congruential_engine<_UIntType, __a, __c, __m>::
      seed(_Sseq& __q)
      -> _If_seed_seq<_Sseq>
      {
        const _UIntType __k0 = __m == 0 ? std::numeric_limits<_UIntType>::digits
                                        : std::__lg(__m);
        const _UIntType __k = (__k0 + 31) / 32;
        uint_least32_t __arr[__k + 3];
        __q.generate(__arr + 0, __arr + __k + 3);
        _UIntType __factor = 1u;
        _UIntType __sum = 0u;
        for (size_t __j = 0; __j < __k; ++__j)
          {
            __sum += __arr[__j + 3] * __factor;
            __factor *= __detail::_Shift<_UIntType, 32>::__value;
          }
        seed(__sum);
      }

  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const linear_congruential_engine<_UIntType,
                                                __a, __c, __m>& __lcr)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
      __os.fill(__os.widen(' '));

      __os << __lcr._M_x;

      __os.flags(__flags);
      __os.fill(__fill);
      return __os;
    }

  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec);

      __is >> __lcr._M_x;

      __is.flags(__flags);
      return __is;
    }

#if ! __cpp_inline_variables
  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::word_size;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::state_size;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::shift_size;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::mask_bits;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr _UIntType
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::xor_mask;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_u;
   
  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr _UIntType
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_d;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_s;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr _UIntType
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_b;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_t;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr _UIntType
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_c;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr size_t
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::tempering_l;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr _UIntType
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::
                                              initialization_multiplier;

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    constexpr _UIntType
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::default_seed;
#endif

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    void
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::
    seed(result_type __sd)
    {
      _M_x[0] = __detail::__mod<_UIntType,
        __detail::_Shift<_UIntType, __w>::__value>(__sd);

      for (size_t __i = 1; __i < state_size; ++__i)
        {
          _UIntType __x = _M_x[__i - 1];
          __x ^= __x >> (__w - 2);
          __x *= __f;
          __x += __detail::__mod<_UIntType, __n>(__i);
          _M_x[__i] = __detail::__mod<_UIntType,
            __detail::_Shift<_UIntType, __w>::__value>(__x);
        }
      _M_p = state_size;
    }

  template<typename _UIntType,
           size_t __w, size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    template<typename _Sseq>
      auto
      mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                              __s, __b, __t, __c, __l, __f>::
      seed(_Sseq& __q)
      -> _If_seed_seq<_Sseq>
      {
        const _UIntType __upper_mask = (~_UIntType()) << __r;
        const size_t __k = (__w + 31) / 32;
        uint_least32_t __arr[__n * __k];
        __q.generate(__arr + 0, __arr + __n * __k);

        bool __zero = true;
        for (size_t __i = 0; __i < state_size; ++__i)
          {
            _UIntType __factor = 1u;
            _UIntType __sum = 0u;
            for (size_t __j = 0; __j < __k; ++__j)
              {
                __sum += __arr[__k * __i + __j] * __factor;
                __factor *= __detail::_Shift<_UIntType, 32>::__value;
              }
            _M_x[__i] = __detail::__mod<_UIntType,
              __detail::_Shift<_UIntType, __w>::__value>(__sum);

            if (__zero)
              {
                if (__i == 0)
                  {
                    if ((_M_x[0] & __upper_mask) != 0u)
                      __zero = false;
                  }
                else if (_M_x[__i] != 0u)
                  __zero = false;
              }
          }
        if (__zero)
          _M_x[0] = __detail::_Shift<_UIntType, __w - 1>::__value;
        _M_p = state_size;
      }

  template<typename _UIntType, size_t __w,
           size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    void
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::
    _M_gen_rand(void)
    {
      const _UIntType __upper_mask = (~_UIntType()) << __r;
      const _UIntType __lower_mask = ~__upper_mask;

      for (size_t __k = 0; __k < (__n - __m); ++__k)
        {
          _UIntType __y = ((_M_x[__k] & __upper_mask)
                           | (_M_x[__k + 1] & __lower_mask));
          _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
                       ^ ((__y & 0x01) ? __a : 0));
        }

      for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
        {
          _UIntType __y = ((_M_x[__k] & __upper_mask)
                           | (_M_x[__k + 1] & __lower_mask));
          _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
                       ^ ((__y & 0x01) ? __a : 0));
        }

      _UIntType __y = ((_M_x[__n - 1] & __upper_mask)
                       | (_M_x[0] & __lower_mask));
      _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
                       ^ ((__y & 0x01) ? __a : 0));
      _M_p = 0;
    }

  template<typename _UIntType, size_t __w,
           size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    void
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::
    discard(unsigned long long __z)
    {
      while (__z > state_size - _M_p)
        {
          __z -= state_size - _M_p;
          _M_gen_rand();
        }
      _M_p += __z;
    }

  template<typename _UIntType, size_t __w,
           size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f>
    typename
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::result_type
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
                            __s, __b, __t, __c, __l, __f>::
    operator()()
    {
      // Reload the vector - cost is O(n) amortized over n calls.
      if (_M_p >= state_size)
        _M_gen_rand();

      // Calculate o(x(i)).
      result_type __z = _M_x[_M_p++];
      __z ^= (__z >> __u) & __d;
      __z ^= (__z << __s) & __b;
      __z ^= (__z << __t) & __c;
      __z ^= (__z >> __l);

      return __z;
    }

  template<typename _UIntType, size_t __w,
           size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const mersenne_twister_engine<_UIntType, __w, __n, __m,
               __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
      __os.fill(__space);

      for (size_t __i = 0; __i < __n; ++__i)
        __os << __x._M_x[__i] << __space;
      __os << __x._M_p;

      __os.flags(__flags);
      __os.fill(__fill);
      return __os;
    }

  template<typename _UIntType, size_t __w,
           size_t __n, size_t __m, size_t __r,
           _UIntType __a, size_t __u, _UIntType __d, size_t __s,
           _UIntType __b, size_t __t, _UIntType __c, size_t __l,
           _UIntType __f, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               mersenne_twister_engine<_UIntType, __w, __n, __m,
               __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      for (size_t __i = 0; __i < __n; ++__i)
        __is >> __x._M_x[__i];
      __is >> __x._M_p;

      __is.flags(__flags);
      return __is;
    }

#if ! __cpp_inline_variables
  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    constexpr size_t
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::word_size;

  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    constexpr size_t
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::short_lag;

  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    constexpr size_t
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::long_lag;

  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    constexpr _UIntType
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::default_seed;
#endif

  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    void
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::
    seed(result_type __value)
    {
      std::linear_congruential_engine<result_type, 40014u, 0u, 2147483563u>
        __lcg(__value == 0u ? default_seed : __value);

      const size_t __n = (__w + 31) / 32;

      for (size_t __i = 0; __i < long_lag; ++__i)
        {
          _UIntType __sum = 0u;
          _UIntType __factor = 1u;
          for (size_t __j = 0; __j < __n; ++__j)
            {
              __sum += __detail::__mod<uint_least32_t,
                       __detail::_Shift<uint_least32_t, 32>::__value>
                         (__lcg()) * __factor;
              __factor *= __detail::_Shift<_UIntType, 32>::__value;
            }
          _M_x[__i] = __detail::__mod<_UIntType,
            __detail::_Shift<_UIntType, __w>::__value>(__sum);
        }
      _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
      _M_p = 0;
    }

  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    template<typename _Sseq>
      auto
      subtract_with_carry_engine<_UIntType, __w, __s, __r>::
      seed(_Sseq& __q)
      -> _If_seed_seq<_Sseq>
      {
        const size_t __k = (__w + 31) / 32;
        uint_least32_t __arr[__r * __k];
        __q.generate(__arr + 0, __arr + __r * __k);

        for (size_t __i = 0; __i < long_lag; ++__i)
          {
            _UIntType __sum = 0u;
            _UIntType __factor = 1u;
            for (size_t __j = 0; __j < __k; ++__j)
              {
                __sum += __arr[__k * __i + __j] * __factor;
                __factor *= __detail::_Shift<_UIntType, 32>::__value;
              }
            _M_x[__i] = __detail::__mod<_UIntType,
              __detail::_Shift<_UIntType, __w>::__value>(__sum);
          }
        _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
        _M_p = 0;
      }

  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
    typename subtract_with_carry_engine<_UIntType, __w, __s, __r>::
             result_type
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::
    operator()()
    {
      // Derive short lag index from current index.
      long __ps = _M_p - short_lag;
      if (__ps < 0)
        __ps += long_lag;

      // Calculate new x(i) without overflow or division.
      // NB: Thanks to the requirements for _UIntType, _M_x[_M_p] + _M_carry
      // cannot overflow.
      _UIntType __xi;
      if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
        {
          __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
          _M_carry = 0;
        }
      else
        {
          __xi = (__detail::_Shift<_UIntType, __w>::__value
                  - _M_x[_M_p] - _M_carry + _M_x[__ps]);
          _M_carry = 1;
        }
      _M_x[_M_p] = __xi;

      // Adjust current index to loop around in ring buffer.
      if (++_M_p >= long_lag)
        _M_p = 0;

      return __xi;
    }

  template<typename _UIntType, size_t __w, size_t __s, size_t __r,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const subtract_with_carry_engine<_UIntType,
                                                __w, __s, __r>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
      __os.fill(__space);

      for (size_t __i = 0; __i < __r; ++__i)
        __os << __x._M_x[__i] << __space;
      __os << __x._M_carry << __space << __x._M_p;

      __os.flags(__flags);
      __os.fill(__fill);
      return __os;
    }

  template<typename _UIntType, size_t __w, size_t __s, size_t __r,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               subtract_with_carry_engine<_UIntType, __w, __s, __r>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      for (size_t __i = 0; __i < __r; ++__i)
        __is >> __x._M_x[__i];
      __is >> __x._M_carry;
      __is >> __x._M_p;

      __is.flags(__flags);
      return __is;
    }

#if ! __cpp_inline_variables
  template<typename _RandomNumberEngine, size_t __p, size_t __r>
    constexpr size_t
    discard_block_engine<_RandomNumberEngine, __p, __r>::block_size;

  template<typename _RandomNumberEngine, size_t __p, size_t __r>
    constexpr size_t
    discard_block_engine<_RandomNumberEngine, __p, __r>::used_block;
#endif

  template<typename _RandomNumberEngine, size_t __p, size_t __r>
    typename discard_block_engine<_RandomNumberEngine,
                           __p, __r>::result_type
    discard_block_engine<_RandomNumberEngine, __p, __r>::
    operator()()
    {
      if (_M_n >= used_block)
        {
          _M_b.discard(block_size - _M_n);
          _M_n = 0;
        }
      ++_M_n;
      return _M_b();
    }

  template<typename _RandomNumberEngine, size_t __p, size_t __r,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const discard_block_engine<_RandomNumberEngine,
               __p, __r>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
      __os.fill(__space);

      __os << __x.base() << __space << __x._M_n;

      __os.flags(__flags);
      __os.fill(__fill);
      return __os;
    }

  template<typename _RandomNumberEngine, size_t __p, size_t __r,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               discard_block_engine<_RandomNumberEngine, __p, __r>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      __is >> __x._M_b >> __x._M_n;

      __is.flags(__flags);
      return __is;
    }


  template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
    typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
      result_type
    independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
    operator()()
    {
      typedef typename _RandomNumberEngine::result_type _Eresult_type;
      const _Eresult_type __r
        = (_M_b.max() - _M_b.min() < std::numeric_limits<_Eresult_type>::max()
           ? _M_b.max() - _M_b.min() + 1 : 0);
      const unsigned __edig = std::numeric_limits<_Eresult_type>::digits;
      const unsigned __m = __r ? std::__lg(__r) : __edig;

      typedef typename std::common_type<_Eresult_type, result_type>::type
        __ctype;
      const unsigned __cdig = std::numeric_limits<__ctype>::digits;

      unsigned __n, __n0;
      __ctype __s0, __s1, __y0, __y1;

      for (size_t __i = 0; __i < 2; ++__i)
        {
          __n = (__w + __m - 1) / __m + __i;
          __n0 = __n - __w % __n;
          const unsigned __w0 = __w / __n;  // __w0 <= __m

          __s0 = 0;
          __s1 = 0;
          if (__w0 < __cdig)
            {
              __s0 = __ctype(1) << __w0;
              __s1 = __s0 << 1;
            }

          __y0 = 0;
          __y1 = 0;
          if (__r)
            {
              __y0 = __s0 * (__r / __s0);
              if (__s1)
                __y1 = __s1 * (__r / __s1);

              if (__r - __y0 <= __y0 / __n)
                break;
            }
          else
            break;
        }

      result_type __sum = 0;
      for (size_t __k = 0; __k < __n0; ++__k)
        {
          __ctype __u;
          do
            __u = _M_b() - _M_b.min();
          while (__y0 && __u >= __y0);
          __sum = __s0 * __sum + (__s0 ? __u % __s0 : __u);
        }
      for (size_t __k = __n0; __k < __n; ++__k)
        {
          __ctype __u;
          do
            __u = _M_b() - _M_b.min();
          while (__y1 && __u >= __y1);
          __sum = __s1 * __sum + (__s1 ? __u % __s1 : __u);
        }
      return __sum;
    }

#if ! __cpp_inline_variables
  template<typename _RandomNumberEngine, size_t __k>
    constexpr size_t
    shuffle_order_engine<_RandomNumberEngine, __k>::table_size;
#endif

  namespace __detail
  {
    // Determine whether an integer is representable as double.
    template<typename _Tp>
      constexpr bool
      __representable_as_double(_Tp __x) noexcept
      {
        static_assert(numeric_limits<_Tp>::is_integer, "");
        static_assert(!numeric_limits<_Tp>::is_signed, "");
        // All integers <= 2^53 are representable.
        return (__x <= (1ull << __DBL_MANT_DIG__))
          // Between 2^53 and 2^54 only even numbers are representable.
          || (!(__x & 1) && __detail::__representable_as_double(__x >> 1));
      }

    // Determine whether x+1 is representable as double.
    template<typename _Tp>
      constexpr bool
      __p1_representable_as_double(_Tp __x) noexcept
      {
        static_assert(numeric_limits<_Tp>::is_integer, "");
        static_assert(!numeric_limits<_Tp>::is_signed, "");
        return numeric_limits<_Tp>::digits < __DBL_MANT_DIG__
          || (bool(__x + 1u) // return false if x+1 wraps around to zero
              && __detail::__representable_as_double(__x + 1u));
      }
  }

  template<typename _RandomNumberEngine, size_t __k>
    typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
    shuffle_order_engine<_RandomNumberEngine, __k>::
    operator()()
    {
      constexpr result_type __range = max() - min();
      size_t __j = __k;
      const result_type __y = _M_y - min();
      // Avoid using slower long double arithmetic if possible.
      if _GLIBCXX17_CONSTEXPR (__detail::__p1_representable_as_double(__range))
        __j *= __y / (__range + 1.0);
      else
        __j *= __y / (__range + 1.0L);
      _M_y = _M_v[__j];
      _M_v[__j] = _M_b();

      return _M_y;
    }

  template<typename _RandomNumberEngine, size_t __k,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const shuffle_order_engine<_RandomNumberEngine, __k>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
      __os.fill(__space);

      __os << __x.base();
      for (size_t __i = 0; __i < __k; ++__i)
        __os << __space << __x._M_v[__i];
      __os << __space << __x._M_y;

      __os.flags(__flags);
      __os.fill(__fill);
      return __os;
    }

  template<typename _RandomNumberEngine, size_t __k,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               shuffle_order_engine<_RandomNumberEngine, __k>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      __is >> __x._M_b;
      for (size_t __i = 0; __i < __k; ++__i)
        __is >> __x._M_v[__i];
      __is >> __x._M_y;

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const uniform_int_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);

      __os << __x.a() << __space << __x.b();

      __os.flags(__flags);
      __os.fill(__fill);
      return __os;
    }

  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               uniform_int_distribution<_IntType>& __x)
    {
      using param_type
        = typename uniform_int_distribution<_IntType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _IntType __a, __b;
      if (__is >> __a >> __b)
        __x.param(param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      uniform_real_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        auto __range = __p.b() - __p.a();
        while (__f != __t)
          *__f++ = __aurng() * __range + __p.a();
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const uniform_real_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.a() << __space << __x.b();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               uniform_real_distribution<_RealType>& __x)
    {
      using param_type
        = typename uniform_real_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::skipws);

      _RealType __a, __b;
      if (__is >> __a >> __b)
        __x.param(param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _ForwardIterator,
           typename _UniformRandomNumberGenerator>
    void
    std::bernoulli_distribution::
    __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                    _UniformRandomNumberGenerator& __urng,
                    const param_type& __p)
    {
      __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
      __detail::_Adaptor<_UniformRandomNumberGenerator, double>
        __aurng(__urng);
      auto __limit = __p.p() * (__aurng.max() - __aurng.min());

      while (__f != __t)
        *__f++ = (__aurng() - __aurng.min()) < __limit;
    }

  template<typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const bernoulli_distribution& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__os.widen(' '));
      __os.precision(std::numeric_limits<double>::max_digits10);

      __os << __x.p();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }


  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename geometric_distribution<_IntType>::result_type
      geometric_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        // About the epsilon thing see this thread:
        // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
        const double __naf =
          (1 - std::numeric_limits<double>::epsilon()) / 2;
        // The largest _RealType convertible to _IntType.
        const double __thr =
          std::numeric_limits<_IntType>::max() + __naf;
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        double __cand;
        do
          __cand = std::floor(std::log(1.0 - __aurng()) / __param._M_log_1_p);
        while (__cand >= __thr);

        return result_type(__cand + __naf);
      }

  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      geometric_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        // About the epsilon thing see this thread:
        // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
        const double __naf =
          (1 - std::numeric_limits<double>::epsilon()) / 2;
        // The largest _RealType convertible to _IntType.
        const double __thr =
          std::numeric_limits<_IntType>::max() + __naf;
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        while (__f != __t)
          {
            double __cand;
            do
              __cand = std::floor(std::log(1.0 - __aurng())
                                  / __param._M_log_1_p);
            while (__cand >= __thr);

            *__f++ = __cand + __naf;
          }
      }

  template<typename _IntType,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const geometric_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__os.widen(' '));
      __os.precision(std::numeric_limits<double>::max_digits10);

      __os << __x.p();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _IntType,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               geometric_distribution<_IntType>& __x)
    {
      using param_type = typename geometric_distribution<_IntType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::skipws);

      double __p;
      if (__is >> __p)
        __x.param(param_type(__p));

      __is.flags(__flags);
      return __is;
    }

  // This is Leger's algorithm, also in Devroye, Ch. X, Example 1.5.
  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename negative_binomial_distribution<_IntType>::result_type
      negative_binomial_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng)
      {
        const double __y = _M_gd(__urng);

        // XXX Is the constructor too slow?
        std::poisson_distribution<result_type> __poisson(__y);
        return __poisson(__urng);
      }

  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename negative_binomial_distribution<_IntType>::result_type
      negative_binomial_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __p)
      {
        typedef typename std::gamma_distribution<double>::param_type
          param_type;
        
        const double __y =
          _M_gd(__urng, param_type(__p.k(), (1.0 - __p.p()) / __p.p()));

        std::poisson_distribution<result_type> __poisson(__y);
        return __poisson(__urng);
      }

  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      negative_binomial_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        while (__f != __t)
          {
            const double __y = _M_gd(__urng);

            // XXX Is the constructor too slow?
            std::poisson_distribution<result_type> __poisson(__y);
            *__f++ = __poisson(__urng);
          }
      }

  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      negative_binomial_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        typename std::gamma_distribution<result_type>::param_type
          __p2(__p.k(), (1.0 - __p.p()) / __p.p());

        while (__f != __t)
          {
            const double __y = _M_gd(__urng, __p2);

            std::poisson_distribution<result_type> __poisson(__y);
            *__f++ = __poisson(__urng);
          }
      }

  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const negative_binomial_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__os.widen(' '));
      __os.precision(std::numeric_limits<double>::max_digits10);

      __os << __x.k() << __space << __x.p()
           << __space << __x._M_gd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               negative_binomial_distribution<_IntType>& __x)
    {
      using param_type
        = typename negative_binomial_distribution<_IntType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::skipws);

      _IntType __k;
      double __p;
      if (__is >> __k >> __p >> __x._M_gd)
        __x.param(param_type(__k, __p));

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType>
    void
    poisson_distribution<_IntType>::param_type::
    _M_initialize()
    {
#if _GLIBCXX_USE_C99_MATH_TR1
      if (_M_mean >= 12)
        {
          const double __m = std::floor(_M_mean);
          _M_lm_thr = std::log(_M_mean);
          _M_lfm = std::lgamma(__m + 1);
          _M_sm = std::sqrt(__m);

          const double __pi_4 = 0.7853981633974483096156608458198757L;
          const double __dx = std::sqrt(2 * __m * std::log(32 * __m
                                                              / __pi_4));
          _M_d = std::round(std::max<double>(6.0, std::min(__m, __dx)));
          const double __cx = 2 * __m + _M_d;
          _M_scx = std::sqrt(__cx / 2);
          _M_1cx = 1 / __cx;

          _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
          _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2))
                / _M_d;
        }
      else
#endif
        _M_lm_thr = std::exp(-_M_mean);
      }

  /**
   * A rejection algorithm when mean >= 12 and a simple method based
   * upon the multiplication of uniform random variates otherwise.
   * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
   * is defined.
   *
   * Reference:
   * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
   * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
   */
  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename poisson_distribution<_IntType>::result_type
      poisson_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);
#if _GLIBCXX_USE_C99_MATH_TR1
        if (__param.mean() >= 12)
          {
            double __x;

            // See comments above...
            const double __naf =
              (1 - std::numeric_limits<double>::epsilon()) / 2;
            const double __thr =
              std::numeric_limits<_IntType>::max() + __naf;

            const double __m = std::floor(__param.mean());
            // sqrt(pi / 2)
            const double __spi_2 = 1.2533141373155002512078826424055226L;
            const double __c1 = __param._M_sm * __spi_2;
            const double __c2 = __param._M_c2b + __c1;
            const double __c3 = __c2 + 1;
            const double __c4 = __c3 + 1;
            // 1 / 78
            const double __178 = 0.0128205128205128205128205128205128L;
            // e^(1 / 78)
            const double __e178 = 1.0129030479320018583185514777512983L;
            const double __c5 = __c4 + __e178;
            const double __c = __param._M_cb + __c5;
            const double __2cx = 2 * (2 * __m + __param._M_d);

            bool __reject = true;
            do
              {
                const double __u = __c * __aurng();
                const double __e = -std::log(1.0 - __aurng());

                double __w = 0.0;

                if (__u <= __c1)
                  {
                    const double __n = _M_nd(__urng);
                    const double __y = -std::abs(__n) * __param._M_sm - 1;
                    __x = std::floor(__y);
                    __w = -__n * __n / 2;
                    if (__x < -__m)
                      continue;
                  }
                else if (__u <= __c2)
                  {
                    const double __n = _M_nd(__urng);
                    const double __y = 1 + std::abs(__n) * __param._M_scx;
                    __x = std::ceil(__y);
                    __w = __y * (2 - __y) * __param._M_1cx;
                    if (__x > __param._M_d)
                      continue;
                  }
                else if (__u <= __c3)
                  // NB: This case not in the book, nor in the Errata,
                  // but should be ok...
                  __x = -1;
                else if (__u <= __c4)
                  __x = 0;
                else if (__u <= __c5)
                  {
                    __x = 1;
                    // Only in the Errata, see libstdc++/83237.
                    __w = __178;
                  }
                else
                  {
                    const double __v = -std::log(1.0 - __aurng());
                    const double __y = __param._M_d
                                     + __v * __2cx / __param._M_d;
                    __x = std::ceil(__y);
                    __w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
                  }

                __reject = (__w - __e - __x * __param._M_lm_thr
                            > __param._M_lfm - std::lgamma(__x + __m + 1));

                __reject |= __x + __m >= __thr;

              } while (__reject);

            return result_type(__x + __m + __naf);
          }
        else
#endif
          {
            _IntType     __x = 0;
            double __prod = 1.0;

            do
              {
                __prod *= __aurng();
                __x += 1;
              }
            while (__prod > __param._M_lm_thr);

            return __x - 1;
          }
      }

  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      poisson_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        // We could duplicate everything from operator()...
        while (__f != __t)
          *__f++ = this->operator()(__urng, __param);
      }

  template<typename _IntType,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const poisson_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<double>::max_digits10);

      __os << __x.mean() << __space << __x._M_nd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _IntType,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               poisson_distribution<_IntType>& __x)
    {
      using param_type = typename poisson_distribution<_IntType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::skipws);

      double __mean;
      if (__is >> __mean >> __x._M_nd)
        __x.param(param_type(__mean));

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType>
    void
    binomial_distribution<_IntType>::param_type::
    _M_initialize()
    {
      const double __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;

      _M_easy = true;

#if _GLIBCXX_USE_C99_MATH_TR1
      if (_M_t * __p12 >= 8)
        {
          _M_easy = false;
          const double __np = std::floor(_M_t * __p12);
          const double __pa = __np / _M_t;
          const double __1p = 1 - __pa;

          const double __pi_4 = 0.7853981633974483096156608458198757L;
          const double __d1x =
            std::sqrt(__np * __1p * std::log(32 * __np
                                             / (81 * __pi_4 * __1p)));
          _M_d1 = std::round(std::max<double>(1.0, __d1x));
          const double __d2x =
            std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
                                             / (__pi_4 * __pa)));
          _M_d2 = std::round(std::max<double>(1.0, __d2x));

          // sqrt(pi / 2)
          const double __spi_2 = 1.2533141373155002512078826424055226L;
          _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
          _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p));
          _M_c = 2 * _M_d1 / __np;
          _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
          const double __a12 = _M_a1 + _M_s2 * __spi_2;
          const double __s1s = _M_s1 * _M_s1;
          _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
                             * 2 * __s1s / _M_d1
                             * std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
          const double __s2s = _M_s2 * _M_s2;
          _M_s = (_M_a123 + 2 * __s2s / _M_d2
                  * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
          _M_lf = (std::lgamma(__np + 1)
                   + std::lgamma(_M_t - __np + 1));
          _M_lp1p = std::log(__pa / __1p);

          _M_q = -std::log(1 - (__p12 - __pa) / __1p);
        }
      else
#endif
        _M_q = -std::log(1 - __p12);
    }

  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename binomial_distribution<_IntType>::result_type
      binomial_distribution<_IntType>::
      _M_waiting(_UniformRandomNumberGenerator& __urng,
                 _IntType __t, double __q)
      {
        _IntType __x = 0;
        double __sum = 0.0;
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        do
          {
            if (__t == __x)
              return __x;
            const double __e = -std::log(1.0 - __aurng());
            __sum += __e / (__t - __x);
            __x += 1;
          }
        while (__sum <= __q);

        return __x - 1;
      }

  /**
   * A rejection algorithm when t * p >= 8 and a simple waiting time
   * method - the second in the referenced book - otherwise.
   * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
   * is defined.
   *
   * Reference:
   * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
   * New York, 1986, Ch. X, Sect. 4 (+ Errata!).
   */
  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename binomial_distribution<_IntType>::result_type
      binomial_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        result_type __ret;
        const _IntType __t = __param.t();
        const double __p = __param.p();
        const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

#if _GLIBCXX_USE_C99_MATH_TR1
        if (!__param._M_easy)
          {
            double __x;

            // See comments above...
            const double __naf =
              (1 - std::numeric_limits<double>::epsilon()) / 2;
            const double __thr =
              std::numeric_limits<_IntType>::max() + __naf;

            const double __np = std::floor(__t * __p12);

            // sqrt(pi / 2)
            const double __spi_2 = 1.2533141373155002512078826424055226L;
            const double __a1 = __param._M_a1;
            const double __a12 = __a1 + __param._M_s2 * __spi_2;
            const double __a123 = __param._M_a123;
            const double __s1s = __param._M_s1 * __param._M_s1;
            const double __s2s = __param._M_s2 * __param._M_s2;

            bool __reject;
            do
              {
                const double __u = __param._M_s * __aurng();

                double __v;

                if (__u <= __a1)
                  {
                    const double __n = _M_nd(__urng);
                    const double __y = __param._M_s1 * std::abs(__n);
                    __reject = __y >= __param._M_d1;
                    if (!__reject)
                      {
                        const double __e = -std::log(1.0 - __aurng());
                        __x = std::floor(__y);
                        __v = -__e - __n * __n / 2 + __param._M_c;
                      }
                  }
                else if (__u <= __a12)
                  {
                    const double __n = _M_nd(__urng);
                    const double __y = __param._M_s2 * std::abs(__n);
                    __reject = __y >= __param._M_d2;
                    if (!__reject)
                      {
                        const double __e = -std::log(1.0 - __aurng());
                        __x = std::floor(-__y);
                        __v = -__e - __n * __n / 2;
                      }
                  }
                else if (__u <= __a123)
                  {
                    const double __e1 = -std::log(1.0 - __aurng());
                    const double __e2 = -std::log(1.0 - __aurng());

                    const double __y = __param._M_d1
                                     + 2 * __s1s * __e1 / __param._M_d1;
                    __x = std::floor(__y);
                    __v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
                                                    -__y / (2 * __s1s)));
                    __reject = false;
                  }
                else
                  {
                    const double __e1 = -std::log(1.0 - __aurng());
                    const double __e2 = -std::log(1.0 - __aurng());

                    const double __y = __param._M_d2
                                     + 2 * __s2s * __e1 / __param._M_d2;
                    __x = std::floor(-__y);
                    __v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
                    __reject = false;
                  }

                __reject = __reject || __x < -__np || __x > __t - __np;
                if (!__reject)
                  {
                    const double __lfx =
                      std::lgamma(__np + __x + 1)
                      + std::lgamma(__t - (__np + __x) + 1);
                    __reject = __v > __param._M_lf - __lfx
                             + __x * __param._M_lp1p;
                  }

                __reject |= __x + __np >= __thr;
              }
            while (__reject);

            __x += __np + __naf;

            const _IntType __z = _M_waiting(__urng, __t - _IntType(__x),
                                            __param._M_q);
            __ret = _IntType(__x) + __z;
          }
        else
#endif
          __ret = _M_waiting(__urng, __t, __param._M_q);

        if (__p12 != __p)
          __ret = __t - __ret;
        return __ret;
      }

  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      binomial_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        // We could duplicate everything from operator()...
        while (__f != __t)
          *__f++ = this->operator()(__urng, __param);
      }

  template<typename _IntType,
           typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const binomial_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<double>::max_digits10);

      __os << __x.t() << __space << __x.p()
           << __space << __x._M_nd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _IntType,
           typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               binomial_distribution<_IntType>& __x)
    {
      using param_type = typename binomial_distribution<_IntType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _IntType __t;
      double __p;
      if (__is >> __t >> __p >> __x._M_nd)
        __x.param(param_type(__t, __p));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::exponential_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        while (__f != __t)
          *__f++ = -std::log(result_type(1) - __aurng()) / __p.lambda();
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const exponential_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__os.widen(' '));
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.lambda();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               exponential_distribution<_RealType>& __x)
    {
      using param_type
        = typename exponential_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __lambda;
      if (__is >> __lambda)
        __x.param(param_type(__lambda));

      __is.flags(__flags);
      return __is;
    }


  /**
   * Polar method due to Marsaglia.
   *
   * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
   * New York, 1986, Ch. V, Sect. 4.4.
   */
  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename normal_distribution<_RealType>::result_type
      normal_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        result_type __ret;
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);

        if (_M_saved_available)
          {
            _M_saved_available = false;
            __ret = _M_saved;
          }
        else
          {
            result_type __x, __y, __r2;
            do
              {
                __x = result_type(2.0) * __aurng() - 1.0;
                __y = result_type(2.0) * __aurng() - 1.0;
                __r2 = __x * __x + __y * __y;
              }
            while (__r2 > 1.0 || __r2 == 0.0);

            const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
            _M_saved = __x * __mult;
            _M_saved_available = true;
            __ret = __y * __mult;
          }

        __ret = __ret * __param.stddev() + __param.mean();
        return __ret;
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      normal_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)

        if (__f == __t)
          return;

        if (_M_saved_available)
          {
            _M_saved_available = false;
            *__f++ = _M_saved * __param.stddev() + __param.mean();

            if (__f == __t)
              return;
          }

        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);

        while (__f + 1 < __t)
          {
            result_type __x, __y, __r2;
            do
              {
                __x = result_type(2.0) * __aurng() - 1.0;
                __y = result_type(2.0) * __aurng() - 1.0;
                __r2 = __x * __x + __y * __y;
              }
            while (__r2 > 1.0 || __r2 == 0.0);

            const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
            *__f++ = __y * __mult * __param.stddev() + __param.mean();
            *__f++ = __x * __mult * __param.stddev() + __param.mean();
          }

        if (__f != __t)
          {
            result_type __x, __y, __r2;
            do
              {
                __x = result_type(2.0) * __aurng() - 1.0;
                __y = result_type(2.0) * __aurng() - 1.0;
                __r2 = __x * __x + __y * __y;
              }
            while (__r2 > 1.0 || __r2 == 0.0);

            const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
            _M_saved = __x * __mult;
            _M_saved_available = true;
            *__f = __y * __mult * __param.stddev() + __param.mean();
          }
      }

  template<typename _RealType>
    bool
    operator==(const std::normal_distribution<_RealType>& __d1,
               const std::normal_distribution<_RealType>& __d2)
    {
      if (__d1._M_param == __d2._M_param
          && __d1._M_saved_available == __d2._M_saved_available)
        {
          if (__d1._M_saved_available
              && __d1._M_saved == __d2._M_saved)
            return true;
          else if(!__d1._M_saved_available)
            return true;
          else
            return false;
        }
      else
        return false;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const normal_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.mean() << __space << __x.stddev()
           << __space << __x._M_saved_available;
      if (__x._M_saved_available)
        __os << __space << __x._M_saved;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               normal_distribution<_RealType>& __x)
    {
      using param_type = typename normal_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      double __mean, __stddev;
      bool __saved_avail;
      if (__is >> __mean >> __stddev >> __saved_avail)
        {
          if (!__saved_avail || (__is >> __x._M_saved))
            {
              __x._M_saved_available = __saved_avail;
              __x.param(param_type(__mean, __stddev));
            }
        }

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      lognormal_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
          while (__f != __t)
            *__f++ = std::exp(__p.s() * _M_nd(__urng) + __p.m());
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const lognormal_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.m() << __space << __x.s()
           << __space << __x._M_nd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               lognormal_distribution<_RealType>& __x)
    {
      using param_type
        = typename lognormal_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __m, __s;
      if (__is >> __m >> __s >> __x._M_nd)
        __x.param(param_type(__m, __s));

      __is.flags(__flags);
      return __is;
    }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::chi_squared_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        while (__f != __t)
          *__f++ = 2 * _M_gd(__urng);
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::chi_squared_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const typename
                      std::gamma_distribution<result_type>::param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        while (__f != __t)
          *__f++ = 2 * _M_gd(__urng, __p);
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const chi_squared_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.n() << __space << __x._M_gd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               chi_squared_distribution<_RealType>& __x)
    {
      using param_type
        = typename chi_squared_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __n;
      if (__is >> __n >> __x._M_gd)
        __x.param(param_type(__n));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename cauchy_distribution<_RealType>::result_type
      cauchy_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __p)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        _RealType __u;
        do
          __u = __aurng();
        while (__u == 0.5);

        const _RealType __pi = 3.1415926535897932384626433832795029L;
        return __p.a() + __p.b() * std::tan(__pi * __u);
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      cauchy_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        const _RealType __pi = 3.1415926535897932384626433832795029L;
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        while (__f != __t)
          {
            _RealType __u;
            do
              __u = __aurng();
            while (__u == 0.5);

            *__f++ = __p.a() + __p.b() * std::tan(__pi * __u);
          }
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const cauchy_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.a() << __space << __x.b();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               cauchy_distribution<_RealType>& __x)
    {
      using param_type = typename cauchy_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __a, __b;
      if (__is >> __a >> __b)
        __x.param(param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::fisher_f_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        while (__f != __t)
          *__f++ = ((_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()));
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::fisher_f_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        typedef typename std::gamma_distribution<result_type>::param_type
          param_type;
        param_type __p1(__p.m() / 2);
        param_type __p2(__p.n() / 2);
        while (__f != __t)
          *__f++ = ((_M_gd_x(__urng, __p1) * n())
                    / (_M_gd_y(__urng, __p2) * m()));
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const fisher_f_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.m() << __space << __x.n()
           << __space << __x._M_gd_x << __space << __x._M_gd_y;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               fisher_f_distribution<_RealType>& __x)
    {
      using param_type
        = typename fisher_f_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __m, __n;
      if (__is >> __m >> __n >> __x._M_gd_x >> __x._M_gd_y)
        __x.param(param_type(__m, __n));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::student_t_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        while (__f != __t)
          *__f++ = _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng));
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      std::student_t_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        typename std::gamma_distribution<result_type>::param_type
          __p2(__p.n() / 2, 2);
        while (__f != __t)
          *__f++ =  _M_nd(__urng) * std::sqrt(__p.n() / _M_gd(__urng, __p2));
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const student_t_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.n() << __space << __x._M_nd << __space << __x._M_gd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               student_t_distribution<_RealType>& __x)
    {
      using param_type
        = typename student_t_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __n;
      if (__is >> __n >> __x._M_nd >> __x._M_gd)
        __x.param(param_type(__n));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    void
    gamma_distribution<_RealType>::param_type::
    _M_initialize()
    {
      _M_malpha = _M_alpha < 1.0 ? _M_alpha + _RealType(1.0) : _M_alpha;

      const _RealType __a1 = _M_malpha - _RealType(1.0) / _RealType(3.0);
      _M_a2 = _RealType(1.0) / std::sqrt(_RealType(9.0) * __a1);
    }

  /**
   * Marsaglia, G. and Tsang, W. W.
   * "A Simple Method for Generating Gamma Variables"
   * ACM Transactions on Mathematical Software, 26, 3, 363-372, 2000.
   */
  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename gamma_distribution<_RealType>::result_type
      gamma_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);

        result_type __u, __v, __n;
        const result_type __a1 = (__param._M_malpha
                                  - _RealType(1.0) / _RealType(3.0));

        do
          {
            do
              {
                __n = _M_nd(__urng);
                __v = result_type(1.0) + __param._M_a2 * __n; 
              }
            while (__v <= 0.0);

            __v = __v * __v * __v;
            __u = __aurng();
          }
        while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
               && (std::log(__u) > (0.5 * __n * __n + __a1
                                    * (1.0 - __v + std::log(__v)))));

        if (__param.alpha() == __param._M_malpha)
          return __a1 * __v * __param.beta();
        else
          {
            do
              __u = __aurng();
            while (__u == 0.0);
            
            return (std::pow(__u, result_type(1.0) / __param.alpha())
                    * __a1 * __v * __param.beta());
          }
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      gamma_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);

        result_type __u, __v, __n;
        const result_type __a1 = (__param._M_malpha
                                  - _RealType(1.0) / _RealType(3.0));

        if (__param.alpha() == __param._M_malpha)
          while (__f != __t)
            {
              do
                {
                  do
                    {
                      __n = _M_nd(__urng);
                      __v = result_type(1.0) + __param._M_a2 * __n;
                    }
                  while (__v <= 0.0);

                  __v = __v * __v * __v;
                  __u = __aurng();
                }
              while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
                     && (std::log(__u) > (0.5 * __n * __n + __a1
                                          * (1.0 - __v + std::log(__v)))));

              *__f++ = __a1 * __v * __param.beta();
            }
        else
          while (__f != __t)
            {
              do
                {
                  do
                    {
                      __n = _M_nd(__urng);
                      __v = result_type(1.0) + __param._M_a2 * __n;
                    }
                  while (__v <= 0.0);

                  __v = __v * __v * __v;
                  __u = __aurng();
                }
              while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
                     && (std::log(__u) > (0.5 * __n * __n + __a1
                                          * (1.0 - __v + std::log(__v)))));

              do
                __u = __aurng();
              while (__u == 0.0);

              *__f++ = (std::pow(__u, result_type(1.0) / __param.alpha())
                        * __a1 * __v * __param.beta());
            }
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const gamma_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.alpha() << __space << __x.beta()
           << __space << __x._M_nd;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               gamma_distribution<_RealType>& __x)
    {
      using param_type = typename gamma_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __alpha_val, __beta_val;
      if (__is >> __alpha_val >> __beta_val >> __x._M_nd)
        __x.param(param_type(__alpha_val, __beta_val));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename weibull_distribution<_RealType>::result_type
      weibull_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __p)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        return __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
                                  result_type(1) / __p.a());
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      weibull_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        auto __inv_a = result_type(1) / __p.a();

        while (__f != __t)
          *__f++ = __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
                                      __inv_a);
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const weibull_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.a() << __space << __x.b();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               weibull_distribution<_RealType>& __x)
    {
      using param_type = typename weibull_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __a, __b;
      if (__is >> __a >> __b)
        __x.param(param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename extreme_value_distribution<_RealType>::result_type
      extreme_value_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __p)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);
        return __p.a() - __p.b() * std::log(-std::log(result_type(1)
                                                      - __aurng()));
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      extreme_value_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __p)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
          __aurng(__urng);

        while (__f != __t)
          *__f++ = __p.a() - __p.b() * std::log(-std::log(result_type(1)
                                                          - __aurng()));
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const extreme_value_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      __os << __x.a() << __space << __x.b();

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               extreme_value_distribution<_RealType>& __x)
    {
      using param_type
        = typename extreme_value_distribution<_RealType>::param_type;
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      _RealType __a, __b;
      if (__is >> __a >> __b)
        __x.param(param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType>
    void
    discrete_distribution<_IntType>::param_type::
    _M_initialize()
    {
      if (_M_prob.size() < 2)
        {
          _M_prob.clear();
          return;
        }

      const double __sum = std::accumulate(_M_prob.begin(),
                                           _M_prob.end(), 0.0);
      __glibcxx_assert(__sum > 0);
      // Now normalize the probabilites.
      __detail::__normalize(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
                            __sum);
      // Accumulate partial sums.
      _M_cp.reserve(_M_prob.size());
      std::partial_sum(_M_prob.begin(), _M_prob.end(),
                       std::back_inserter(_M_cp));
      // Make sure the last cumulative probability is one.
      _M_cp[_M_cp.size() - 1] = 1.0;
    }

  template<typename _IntType>
    template<typename _Func>
      discrete_distribution<_IntType>::param_type::
      param_type(size_t __nw, double __xmin, double __xmax, _Func __fw)
      : _M_prob(), _M_cp()
      {
        const size_t __n = __nw == 0 ? 1 : __nw;
        const double __delta = (__xmax - __xmin) / __n;

        _M_prob.reserve(__n);
        for (size_t __k = 0; __k < __nw; ++__k)
          _M_prob.push_back(__fw(__xmin + __k * __delta + 0.5 * __delta));

        _M_initialize();
      }

  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename discrete_distribution<_IntType>::result_type
      discrete_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        if (__param._M_cp.empty())
          return result_type(0);

        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        const double __p = __aurng();
        auto __pos = std::lower_bound(__param._M_cp.begin(),
                                      __param._M_cp.end(), __p);

        return __pos - __param._M_cp.begin();
      }

  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      discrete_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)

        if (__param._M_cp.empty())
          {
            while (__f != __t)
              *__f++ = result_type(0);
            return;
          }

        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        while (__f != __t)
          {
            const double __p = __aurng();
            auto __pos = std::lower_bound(__param._M_cp.begin(),
                                          __param._M_cp.end(), __p);

            *__f++ = __pos - __param._M_cp.begin();
          }
      }

  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const discrete_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<double>::max_digits10);

      std::vector<double> __prob = __x.probabilities();
      __os << __prob.size();
      for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
        __os << __space << *__dit;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

namespace __detail
{
  template<typename _ValT, typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    __extract_params(basic_istream<_CharT, _Traits>& __is,
                     vector<_ValT>& __vals, size_t __n)
    {
      __vals.reserve(__n);
      while (__n--)
        {
          _ValT __val;
          if (__is >> __val)
            __vals.push_back(__val);
          else
            break;
        }
      return __is;
    }
} // namespace __detail

  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               discrete_distribution<_IntType>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      size_t __n;
      if (__is >> __n)
        {
          std::vector<double> __prob_vec;
          if (__detail::__extract_params(__is, __prob_vec, __n))
            __x.param({__prob_vec.begin(), __prob_vec.end()});
        }

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    void
    piecewise_constant_distribution<_RealType>::param_type::
    _M_initialize()
    {
      if (_M_int.size() < 2
          || (_M_int.size() == 2
              && _M_int[0] == _RealType(0)
              && _M_int[1] == _RealType(1)))
        {
          _M_int.clear();
          _M_den.clear();
          return;
        }

      const double __sum = std::accumulate(_M_den.begin(),
                                           _M_den.end(), 0.0);
      __glibcxx_assert(__sum > 0);

      __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
                            __sum);

      _M_cp.reserve(_M_den.size());
      std::partial_sum(_M_den.begin(), _M_den.end(),
                       std::back_inserter(_M_cp));

      // Make sure the last cumulative probability is one.
      _M_cp[_M_cp.size() - 1] = 1.0;

      for (size_t __k = 0; __k < _M_den.size(); ++__k)
        _M_den[__k] /= _M_int[__k + 1] - _M_int[__k];
    }

  template<typename _RealType>
    template<typename _InputIteratorB, typename _InputIteratorW>
      piecewise_constant_distribution<_RealType>::param_type::
      param_type(_InputIteratorB __bbegin,
                 _InputIteratorB __bend,
                 _InputIteratorW __wbegin)
      : _M_int(), _M_den(), _M_cp()
      {
        if (__bbegin != __bend)
          {
            for (;;)
              {
                _M_int.push_back(*__bbegin);
                ++__bbegin;
                if (__bbegin == __bend)
                  break;

                _M_den.push_back(*__wbegin);
                ++__wbegin;
              }
          }

        _M_initialize();
      }

  template<typename _RealType>
    template<typename _Func>
      piecewise_constant_distribution<_RealType>::param_type::
      param_type(initializer_list<_RealType> __bl, _Func __fw)
      : _M_int(), _M_den(), _M_cp()
      {
        _M_int.reserve(__bl.size());
        for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
          _M_int.push_back(*__biter);

        _M_den.reserve(_M_int.size() - 1);
        for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
          _M_den.push_back(__fw(0.5 * (_M_int[__k + 1] + _M_int[__k])));

        _M_initialize();
      }

  template<typename _RealType>
    template<typename _Func>
      piecewise_constant_distribution<_RealType>::param_type::
      param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
      : _M_int(), _M_den(), _M_cp()
      {
        const size_t __n = __nw == 0 ? 1 : __nw;
        const _RealType __delta = (__xmax - __xmin) / __n;

        _M_int.reserve(__n + 1);
        for (size_t __k = 0; __k <= __nw; ++__k)
          _M_int.push_back(__xmin + __k * __delta);

        _M_den.reserve(__n);
        for (size_t __k = 0; __k < __nw; ++__k)
          _M_den.push_back(__fw(_M_int[__k] + 0.5 * __delta));

        _M_initialize();
      }

  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename piecewise_constant_distribution<_RealType>::result_type
      piecewise_constant_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        const double __p = __aurng();
        if (__param._M_cp.empty())
          return __p;

        auto __pos = std::lower_bound(__param._M_cp.begin(),
                                      __param._M_cp.end(), __p);
        const size_t __i = __pos - __param._M_cp.begin();

        const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;

        return __param._M_int[__i] + (__p - __pref) / __param._M_den[__i];
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      piecewise_constant_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        if (__param._M_cp.empty())
          {
            while (__f != __t)
              *__f++ = __aurng();
            return;
          }

        while (__f != __t)
          {
            const double __p = __aurng();

            auto __pos = std::lower_bound(__param._M_cp.begin(),
                                          __param._M_cp.end(), __p);
            const size_t __i = __pos - __param._M_cp.begin();

            const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;

            *__f++ = (__param._M_int[__i]
                      + (__p - __pref) / __param._M_den[__i]);
          }
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const piecewise_constant_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      std::vector<_RealType> __int = __x.intervals();
      __os << __int.size() - 1;

      for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
        __os << __space << *__xit;

      std::vector<double> __den = __x.densities();
      for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
        __os << __space << *__dit;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               piecewise_constant_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      size_t __n;
      if (__is >> __n)
        {
          std::vector<_RealType> __int_vec;
          if (__detail::__extract_params(__is, __int_vec, __n + 1))
            {
              std::vector<double> __den_vec;
              if (__detail::__extract_params(__is, __den_vec, __n))
                {
                  __x.param({ __int_vec.begin(), __int_vec.end(),
                              __den_vec.begin() });
                }
            }
        }

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    void
    piecewise_linear_distribution<_RealType>::param_type::
    _M_initialize()
    {
      if (_M_int.size() < 2
          || (_M_int.size() == 2
              && _M_int[0] == _RealType(0)
              && _M_int[1] == _RealType(1)
              && _M_den[0] == _M_den[1]))
        {
          _M_int.clear();
          _M_den.clear();
          return;
        }

      double __sum = 0.0;
      _M_cp.reserve(_M_int.size() - 1);
      _M_m.reserve(_M_int.size() - 1);
      for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
        {
          const _RealType __delta = _M_int[__k + 1] - _M_int[__k];
          __sum += 0.5 * (_M_den[__k + 1] + _M_den[__k]) * __delta;
          _M_cp.push_back(__sum);
          _M_m.push_back((_M_den[__k + 1] - _M_den[__k]) / __delta);
        }
      __glibcxx_assert(__sum > 0);

      //  Now normalize the densities...
      __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
                            __sum);
      //  ... and partial sums... 
      __detail::__normalize(_M_cp.begin(), _M_cp.end(), _M_cp.begin(), __sum);
      //  ... and slopes.
      __detail::__normalize(_M_m.begin(), _M_m.end(), _M_m.begin(), __sum);

      //  Make sure the last cumulative probablility is one.
      _M_cp[_M_cp.size() - 1] = 1.0;
     }

  template<typename _RealType>
    template<typename _InputIteratorB, typename _InputIteratorW>
      piecewise_linear_distribution<_RealType>::param_type::
      param_type(_InputIteratorB __bbegin,
                 _InputIteratorB __bend,
                 _InputIteratorW __wbegin)
      : _M_int(), _M_den(), _M_cp(), _M_m()
      {
        for (; __bbegin != __bend; ++__bbegin, ++__wbegin)
          {
            _M_int.push_back(*__bbegin);
            _M_den.push_back(*__wbegin);
          }

        _M_initialize();
      }

  template<typename _RealType>
    template<typename _Func>
      piecewise_linear_distribution<_RealType>::param_type::
      param_type(initializer_list<_RealType> __bl, _Func __fw)
      : _M_int(), _M_den(), _M_cp(), _M_m()
      {
        _M_int.reserve(__bl.size());
        _M_den.reserve(__bl.size());
        for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
          {
            _M_int.push_back(*__biter);
            _M_den.push_back(__fw(*__biter));
          }

        _M_initialize();
      }

  template<typename _RealType>
    template<typename _Func>
      piecewise_linear_distribution<_RealType>::param_type::
      param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
      : _M_int(), _M_den(), _M_cp(), _M_m()
      {
        const size_t __n = __nw == 0 ? 1 : __nw;
        const _RealType __delta = (__xmax - __xmin) / __n;

        _M_int.reserve(__n + 1);
        _M_den.reserve(__n + 1);
        for (size_t __k = 0; __k <= __nw; ++__k)
          {
            _M_int.push_back(__xmin + __k * __delta);
            _M_den.push_back(__fw(_M_int[__k] + __delta));
          }

        _M_initialize();
      }

  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename piecewise_linear_distribution<_RealType>::result_type
      piecewise_linear_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
                 const param_type& __param)
      {
        __detail::_Adaptor<_UniformRandomNumberGenerator, double>
          __aurng(__urng);

        const double __p = __aurng();
        if (__param._M_cp.empty())
          return __p;

        auto __pos = std::lower_bound(__param._M_cp.begin(),
                                      __param._M_cp.end(), __p);
        const size_t __i = __pos - __param._M_cp.begin();

        const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;

        const double __a = 0.5 * __param._M_m[__i];
        const double __b = __param._M_den[__i];
        const double __cm = __p - __pref;

        _RealType __x = __param._M_int[__i];
        if (__a == 0)
          __x += __cm / __b;
        else
          {
            const double __d = __b * __b + 4.0 * __a * __cm;
            __x += 0.5 * (std::sqrt(__d) - __b) / __a;
          }

        return __x;
      }

  template<typename _RealType>
    template<typename _ForwardIterator,
             typename _UniformRandomNumberGenerator>
      void
      piecewise_linear_distribution<_RealType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomNumberGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        // We could duplicate everything from operator()...
        while (__f != __t)
          *__f++ = this->operator()(__urng, __param);
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
               const piecewise_linear_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __os.flags();
      const _CharT __fill = __os.fill();
      const std::streamsize __precision = __os.precision();
      const _CharT __space = __os.widen(' ');
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__space);
      __os.precision(std::numeric_limits<_RealType>::max_digits10);

      std::vector<_RealType> __int = __x.intervals();
      __os << __int.size() - 1;

      for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
        __os << __space << *__xit;

      std::vector<double> __den = __x.densities();
      for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
        __os << __space << *__dit;

      __os.flags(__flags);
      __os.fill(__fill);
      __os.precision(__precision);
      return __os;
    }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
               piecewise_linear_distribution<_RealType>& __x)
    {
      using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;

      const typename __ios_base::fmtflags __flags = __is.flags();
      __is.flags(__ios_base::dec | __ios_base::skipws);

      size_t __n;
      if (__is >> __n)
        {
          vector<_RealType> __int_vec;
          if (__detail::__extract_params(__is, __int_vec, __n + 1))
            {
              vector<double> __den_vec;
              if (__detail::__extract_params(__is, __den_vec, __n + 1))
                {
                  __x.param({ __int_vec.begin(), __int_vec.end(),
                              __den_vec.begin() });
                }
            }
        }
      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType, typename>
    seed_seq::seed_seq(std::initializer_list<_IntType> __il)
    {
      _M_v.reserve(__il.size());
      for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
        _M_v.push_back(__detail::__mod<result_type,
                       __detail::_Shift<result_type, 32>::__value>(*__iter));
    }

  template<typename _InputIterator>
    seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
    {
      if _GLIBCXX17_CONSTEXPR (__is_random_access_iter<_InputIterator>::value)
        _M_v.reserve(std::distance(__begin, __end));

      for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
        _M_v.push_back(__detail::__mod<result_type,
                       __detail::_Shift<result_type, 32>::__value>(*__iter));
    }

  template<typename _RandomAccessIterator>
    void
    seed_seq::generate(_RandomAccessIterator __begin,
                       _RandomAccessIterator __end)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
        _Type;

      if (__begin == __end)
        return;

      std::fill(__begin, __end, _Type(0x8b8b8b8bu));

      const size_t __n = __end - __begin;
      const size_t __s = _M_v.size();
      const size_t __t = (__n >= 623) ? 11
                       : (__n >=  68) ? 7
                       : (__n >=  39) ? 5
                       : (__n >=   7) ? 3
                       : (__n - 1) / 2;
      const size_t __p = (__n - __t) / 2;
      const size_t __q = __p + __t;
      const size_t __m = std::max(size_t(__s + 1), __n);

#ifndef __UINT32_TYPE__
      struct _Up
      {
        _Up(uint_least32_t v) : _M_v(v & 0xffffffffu) { }

        operator uint_least32_t() const { return _M_v; }

        uint_least32_t _M_v;
      };
      using uint32_t = _Up;
#endif

      // k == 0, every element in [begin,end) equals 0x8b8b8b8bu
        {
          uint32_t __r1 = 1371501266u;
          uint32_t __r2 = __r1 + __s;
          __begin[__p] += __r1;
          __begin[__q] = (uint32_t)__begin[__q] + __r2;
          __begin[0] = __r2;
        }

      for (size_t __k = 1; __k <= __s; ++__k)
        {
          const size_t __kn = __k % __n;
          const size_t __kpn = (__k + __p) % __n;
          const size_t __kqn = (__k + __q) % __n;
          uint32_t __arg = (__begin[__kn]
                            ^ __begin[__kpn]
                            ^ __begin[(__k - 1) % __n]);
          uint32_t __r1 = 1664525u * (__arg ^ (__arg >> 27));
          uint32_t __r2 = __r1 + (uint32_t)__kn + _M_v[__k - 1];
          __begin[__kpn] = (uint32_t)__begin[__kpn] + __r1;
          __begin[__kqn] = (uint32_t)__begin[__kqn] + __r2;
          __begin[__kn] = __r2;
        }

      for (size_t __k = __s + 1; __k < __m; ++__k)
        {
          const size_t __kn = __k % __n;
          const size_t __kpn = (__k + __p) % __n;
          const size_t __kqn = (__k + __q) % __n;
          uint32_t __arg = (__begin[__kn]
                                 ^ __begin[__kpn]
                                 ^ __begin[(__k - 1) % __n]);
          uint32_t __r1 = 1664525u * (__arg ^ (__arg >> 27));
          uint32_t __r2 = __r1 + (uint32_t)__kn;
          __begin[__kpn] = (uint32_t)__begin[__kpn] + __r1;
          __begin[__kqn] = (uint32_t)__begin[__kqn] + __r2;
          __begin[__kn] = __r2;
        }

      for (size_t __k = __m; __k < __m + __n; ++__k)
        {
          const size_t __kn = __k % __n;
          const size_t __kpn = (__k + __p) % __n;
          const size_t __kqn = (__k + __q) % __n;
          uint32_t __arg = (__begin[__kn]
                            + __begin[__kpn]
                            + __begin[(__k - 1) % __n]);
          uint32_t __r3 = 1566083941u * (__arg ^ (__arg >> 27));
          uint32_t __r4 = __r3 - __kn;
          __begin[__kpn] ^= __r3;
          __begin[__kqn] ^= __r4;
          __begin[__kn] = __r4;
        }
    }

  template<typename _RealType, size_t __bits,
           typename _UniformRandomNumberGenerator>
    _RealType
    generate_canonical(_UniformRandomNumberGenerator& __urng)
    {
      static_assert(std::is_floating_point<_RealType>::value,
                    "template argument must be a floating point type");

      const size_t __b
        = std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
                   __bits);
      const long double __r = static_cast<long double>(__urng.max())
                            - static_cast<long double>(__urng.min()) + 1.0L;
      const size_t __log2r = std::log(__r) / std::log(2.0L);
      const size_t __m = std::max<size_t>(1UL,
                                          (__b + __log2r - 1UL) / __log2r);
      _RealType __ret;
      _RealType __sum = _RealType(0);
      _RealType __tmp = _RealType(1);
      for (size_t __k = __m; __k != 0; --__k)
        {
          __sum += _RealType(__urng() - __urng.min()) * __tmp;
          __tmp *= __r;
        }
      __ret = __sum / __tmp;
      if (__builtin_expect(__ret >= _RealType(1), 0))
        {
#if _GLIBCXX_USE_C99_MATH_TR1
          __ret = std::nextafter(_RealType(1), _RealType(0));
#else
          __ret = _RealType(1)
            - std::numeric_limits<_RealType>::epsilon() / _RealType(2);
#endif
        }
      return __ret;
    }

_GLIBCXX_END_NAMESPACE_VERSION
} // namespace

#endif