gcc/libstdc++-v3/include/bits/random.tcc

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

// Copyright (C) 2009 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 2, 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.

// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

/** @file bits/random.tcc
 *  This is an internal header file, included by other library headers.
 *  You should not attempt to use it directly.
 */

#include <numeric>
#include <algorithm>

namespace std
{
  /*
   * (Further) implementation-space details.
   */
  namespace __detail
  {
    // General case for x = (ax + c) mod m -- use Schrage's algorithm to
    // avoid integer overflow.
    //
    // Because a and c are compile-time integral constants the compiler
    // kindly elides any unreachable paths.
    //
    // Preconditions:  a > 0, m > 0.
    //
    template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool>
      struct _Mod
      {
	static _Tp
	__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;
	}
      };

    // Special case for m == 0 -- use unsigned integer overflow as modulo
    // operator.
    template<typename _Tp, _Tp __a, _Tp __c, _Tp __m>
      struct _Mod<_Tp, __a, __c, __m, true>
      {
	static _Tp
	__calc(_Tp __x)
	{ return __a * __x + __c; }
      };
  } // namespace __detail

  /**
   * Seeds the LCR with integral value @p __x0, 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(_UIntType __x0)
    {
      if ((__detail::__mod<_UIntType, 1U, 0U, __m>(__c) == 0U)
	  && (__detail::__mod<_UIntType, 1U, 0U, __m>(__x0) == 0U))
	_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(1U);
      else
	_M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(__x0);
    }

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

      if ((__detail::__mod<_UIntType, 1U, 0U, __m>(__c) == 0U)
	  && (__detail::__mod<_UIntType, 1U, 0U, __m>(__sum) == 0U))
        _M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(1U);
      else
        _M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(__sum);
    }

  /**
   * Seeds the LCR engine with a value generated by @p __g.
   */
  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    template<typename _Gen>
      void
      linear_congruential_engine<_UIntType, __a, __c, __m>::
      seed(_Gen& __g, false_type)
      {
	_UIntType __x0 = __g();
	if ((__detail::__mod<_UIntType, 1U, 0U, __m>(__c) == 0U)
	    && (__detail::__mod<_UIntType, 1U, 0U, __m>(__x0) == 0U))
	  _M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(1U);
	else
	  _M_x = __detail::__mod<_UIntType, 1U, 0U, __m>(__x0);
      }

  /**
   * Gets the next generated value in sequence.
   */
  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    typename linear_congruential_engine<_UIntType, __a, __c, __m>::
	     result_type
    linear_congruential_engine<_UIntType, __a, __c, __m>::
    operator()()
    {
      _M_x = __detail::__mod<_UIntType, __a, __c, __m>(_M_x);
      return _M_x;
    }

  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      __is >> __lcr._M_x;

      __is.flags(__flags);
      return __is;
    }


  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, 1, 0,
	__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 += __i;
	  _M_x[__i] = __detail::__mod<_UIntType, 1, 0,
	    __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>
    void
    mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
			      __s, __b, __t, __c, __l, __f>::
    seed(seed_seq& __q)
    {
      const _UIntType __upper_mask = (~_UIntType()) << __r;
      const size_t __k = (__w + 31) / 32;
      _UIntType __arr[__k * __n];
      __q.generate(__arr + 0, __arr + __k * __n);

      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[__i * __k + __j] * __factor;
	      __factor *= __detail::_Shift<_UIntType, 32>::__value;
            }
          _M_x[__i] = __detail::__mod<_UIntType, 1U, 0U,
		      __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 - 1U>::__value;
    }

  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)
	{
	  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;
	}

      // 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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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 - 1; ++__i)
	__os << __x._M_x[__i] << __space;
      __os << __x._M_x[__n - 1];

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __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.flags(__flags);
      return __is;
    }


  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)
    {
      if (__value == 0)
	__value = default_seed;

      std::linear_congruential_engine<result_type, 40014U, 0U, 2147483563U>
	__lcg(__value);

      //  I hope this is right.  The "10000" tests work for the ranluxen.
      const size_t __n = (word_size + 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<__detail::_UInt32Type, 1, 0, 0>
			 (__lcg()) * __factor;
	      __factor *= __detail::_Shift<_UIntType, 32>::__value;
	    }
	  _M_x[__i] = __detail::__mod<_UIntType, 1, 0, _S_modulus>(__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>
    void
    subtract_with_carry_engine<_UIntType, __w, __s, __r>::
    seed(seed_seq& __q)
    {
      const size_t __n = (word_size + 31) / 32;
      unsigned int __arr[long_lag + __n];
      __q.generate(__arr + 0, __arr + long_lag + __n);

      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<__detail::_UInt32Type, 1, 0, 0>
		         (__arr[__i * __n + __j]) * __factor;
	      __factor *= __detail::_Shift<_UIntType, 32>::__value;
            }
          _M_x[__i] = __detail::__mod<_UIntType, 1, 0, _S_modulus>(__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 = _S_modulus - _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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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;

      __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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __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.flags(__flags);
      return __is;
    }


  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __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()()
    {
      const long double __r = static_cast<long double>(this->max())
			    - static_cast<long double>(this->min()) + 1.0L;
      const result_type __m = std::log10(__r) / std::log10(2.0L);
      result_type __n, __n0, __y0, __y1, __s0, __s1;
      for (size_t __i = 0; __i < 2; ++__i)
	{
	  __n = (__w + __m - 1) / __m + __i;
	  __n0 = __n - __w % __n;
	  const result_type __w0 = __w / __n;
	  const result_type __w1 = __w0 + 1;
	  __s0 = 1UL << __w0;
	  __s1 = 1UL << __w1;
	  __y0 = __s0 * (__r / __s0);
	  __y1 = __s1 * (__r / __s1);
	  if (__r - __y0 <= __y0 / __n)
	    break;
	}

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


  template<typename _RandomNumberEngine, size_t __k>
    typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
    shuffle_order_engine<_RandomNumberEngine, __k>::
    operator()()
    {
      size_t __j = (__k * (_M_y - _M_b.min()))
		 / (_M_b.max() - _M_b.min() + 1);
      _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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __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>
    template<typename _UniformRandomNumberGenerator>
      typename uniform_int_distribution<_IntType>::result_type
      uniform_int_distribution<_IntType>::
      _M_call(_UniformRandomNumberGenerator& __urng,
	      result_type __min, result_type __max, true_type)
      {
	// XXX Must be fixed to work well for *arbitrary* __urng.max(),
	// __urng.min(), __max, __min.  Currently works fine only in the
	// most common case __urng.max() - __urng.min() >= __max - __min,
	// with __urng.max() > __urng.min() >= 0.
	typedef typename __gnu_cxx::__add_unsigned<typename
	  _UniformRandomNumberGenerator::result_type>::__type __urntype;
	typedef typename __gnu_cxx::__add_unsigned<result_type>::__type
							      __utype;
	typedef typename __gnu_cxx::__conditional_type<(sizeof(__urntype)
							> sizeof(__utype)),
	  __urntype, __utype>::__type                         __uctype;

	result_type __ret;

	const __urntype __urnmin = __urng.min();
	const __urntype __urnmax = __urng.max();
	const __urntype __urnrange = __urnmax - __urnmin;
	const __uctype __urange = __max - __min;
	const __uctype __udenom = (__urnrange <= __urange
				   ? 1 : __urnrange / (__urange + 1));
	do
	  __ret = (__urntype(__urng()) -  __urnmin) / __udenom;
	while (__ret > __max - __min);

	return __ret + __min;
      }

  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _IntType __a, __b;
      __is >> __a >> __b;
      __x.param(typename uniform_int_distribution<_IntType>::
		param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __a, __b;
      __is >> __a >> __b;
      __x.param(typename uniform_real_distribution<_RealType>::
		param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const bernoulli_distribution& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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, result_type>
	  __aurng(__urng);

	double __cand;
	do
	  __cand = std::ceil(std::log(__aurng()) / __param._M_log_p);
	while (__cand >= __thr);

	return result_type(__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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      double __p;
      __is >> __p;
      __x.param(typename geometric_distribution<_IntType>::param_type(__p));

      __is.flags(__flags);
      return __is;
    }

  template<typename _IntType>
    template<typename _UniformRandomNumberGenerator>
      typename negative_binomial_distribution<_IntType>::result_type
      negative_binomial_distribution<_IntType>::
      operator()(_UniformRandomNumberGenerator& __urng,
		 const param_type& __p)
      {
	typename gamma_distribution<>::param_type
	  __gamma_param(__p.k(), 1.0);
	gamma_distribution<> __gamma(__gamma_param);
	double __x = __gamma(__urng);

	typename poisson_distribution<result_type>::param_type
	  __poisson_param(__x * __p.p() / (1.0 - __p.p()));
	poisson_distribution<result_type> __poisson(__poisson_param);
	result_type __m = __poisson(__urng);

	return __m;
      }

  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __os << __x.k() << __space << __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,
	       negative_binomial_distribution<_IntType>& __x)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _IntType __k;
      double __p;
      __is >> __k >> __p;
      __x.param(typename negative_binomial_distribution<_IntType>::
		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(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;
	    // 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(__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;
		else
		  {
		    const double __v = -std::log(__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,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const poisson_distribution<_IntType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      double __mean;
      __is >> __mean >> __x._M_nd;
      __x.param(typename poisson_distribution<_IntType>::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(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(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)
      {
	_IntType __x = 0;
	double __sum = 0.0;
	__detail::_Adaptor<_UniformRandomNumberGenerator, double>
	  __aurng(__urng);

	do
	  {
	    const double __e = -std::log(__aurng());
	    __sum += __e / (__t - __x);
	    __x += 1;
	  }
	while (__sum <= _M_param._M_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 _IntType __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(__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(__aurng());
			__x = std::floor(-__y);
			__v = -__e - __n * __n / 2;
		      }
		  }
		else if (__u <= __a123)
		  {
		    const double __e1 = -std::log(__aurng());
		    const double __e2 = -std::log(__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(__aurng());
		    const double __e2 = -std::log(__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));
	    __ret = _IntType(__x) + __z;
	  }
	else
#endif
	  __ret = _M_waiting(__urng, __t);

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

  template<typename _IntType,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const binomial_distribution<_IntType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _IntType __t;
      double __p;
      __is >> __t >> __p >> __x._M_nd;
      __x.param(typename binomial_distribution<_IntType>::
		param_type(__t, __p));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const exponential_distribution<_RealType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __lambda;
      __is >> __lambda;
      __x.param(typename exponential_distribution<_RealType>::
		param_type(__lambda));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    bool
    operator==(const normal_distribution<_RealType>& __d1,
	       const normal_distribution<_RealType>& __d2)
    {
      if (__d1._M_param == __d2._M_param)
	{
	  if (__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;
	}
      else
	return false;
    }

  /**
   * 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, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const normal_distribution<_RealType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      double __mean, __stddev;
      __is >> __mean >> __stddev
	   >> __x._M_saved_available;
      if (__x._M_saved_available)
	__is >> __x._M_saved;
      __x.param(typename normal_distribution<_RealType>::
		param_type(__mean, __stddev));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename lognormal_distribution<_RealType>::result_type
      lognormal_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
		 const param_type& __p)
      {
	_RealType __u, __v, __r2, __normal;
	__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
	  __aurng(__urng);

	do
	  {
	    // Choose x,y in uniform square (-1,-1) to (+1,+1).
	    __u = 2 * __aurng() - 1;
	    __v = 2 * __aurng() - 1;

	    // See if it is in the unit circle.
	    __r2 = __u * __u + __v * __v;
	  }
	while (__r2 > 1 || __r2 == 0);

	__normal = __u * std::sqrt(-2 * std::log(__r2) / __r2);

	return std::exp(__p.s() * __normal + __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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

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

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __m, __s;
      __is >> __m >> __s;
      __x.param(typename lognormal_distribution<_RealType>::
		param_type(__m, __s));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename chi_squared_distribution<_RealType>::result_type
      chi_squared_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
		 const param_type& __p)
      {
	typename gamma_distribution<_RealType>::param_type
	  __gamma_param(__p.n() / 2, 1.0);
	gamma_distribution<_RealType> __gamma(__gamma_param);
	return 2 * __gamma(__urng);
      }

  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __os << __x.n();

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __n;
      __is >> __n;
      __x.param(typename chi_squared_distribution<_RealType>::
		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);

	return __p.a() + __p.b() * std::tan(M_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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __a, __b;
      __is >> __a >> __b;
      __x.param(typename cauchy_distribution<_RealType>::
		param_type(__a, __b));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename fisher_f_distribution<_RealType>::result_type
      fisher_f_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
		 const param_type& __p)
      {
	gamma_distribution<_RealType> __gamma;
	_RealType __ym = __gamma(__urng,
	 typename gamma_distribution<_RealType>::param_type(__p.m() / 2, 2));

	_RealType __yn = __gamma(__urng,
	 typename gamma_distribution<_RealType>::param_type(__p.n() / 2, 2));

	return (__ym * __p.n()) / (__yn * __p.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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

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

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __m, __n;
      __is >> __m >> __n;
      __x.param(typename fisher_f_distribution<_RealType>::
		param_type(__m, __n));

      __is.flags(__flags);
      return __is;
    }


  //
  //  This could be operator() for a Gaussian distribution.
  //
  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename student_t_distribution<_RealType>::result_type
      student_t_distribution<_RealType>::
      _M_gaussian(_UniformRandomNumberGenerator& __urng,
		  const result_type __sigma)
      {
	_RealType __x, __y, __r2;
	__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
	  __aurng(__urng);

	do
	  {
	    // Choose x,y in uniform square (-1,-1) to (+1,+1).
	    __x = 2 * __aurng() - 1;
	    __y = 2 * __aurng() - 1;

	    // See if it is in the unit circle.
	    __r2 = __x * __x + __y * __y;
	  }
	while (__r2 > 1 || __r2 == 0);

	// Box-Muller transform.
	return __sigma * __y * std::sqrt(-2 * std::log(__r2) / __r2);
      }

  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename student_t_distribution<_RealType>::result_type
      student_t_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
		 const param_type& __param)
      {
	if (__param.n() <= 2.0)
	  {
	    _RealType __y1 = _M_gaussian(__urng, 1.0);
	    typename chi_squared_distribution<_RealType>::param_type
	      __chisq_param(__param.n());
	    chi_squared_distribution<_RealType> __chisq(__chisq_param);
	    _RealType __y2 = __chisq(__urng);

	    return __y1 / std::sqrt(__y2 / __param.n());
	  }
	else
	  {
	    _RealType __y1, __y2, __z;
	    do
	      {
		__y1 = _M_gaussian(__urng, 1.0);
		typename exponential_distribution<_RealType>::param_type
		  __exp_param(1.0 / (__param.n() / 2.0 - 1.0));
		exponential_distribution<_RealType>
		  __exponential(__exp_param);
		__y2 = __exponential(__urng);

		__z = __y1 * __y1 / (__param.n() - 2.0);
	      }
	    while (1.0 - __z < 0.0 || std::exp(-__y2 - __z) > (1.0 - __z));

	    // Note that there is a typo in Knuth's formula, the line below
	    // is taken from the original paper of Marsaglia, Mathematics of
	    // Computation, 34 (1980), p 234-256
	    return __y1 / std::sqrt((1.0 - 2.0 / __param.n()) * (1.0 - __z));
	  }
      }

  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __os << __x.n();

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __n;
      __is >> __n;
      __x.param(typename student_t_distribution<_RealType>::param_type(__n));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    void
    gamma_distribution<_RealType>::param_type::
    _M_initialize()
    {
      if (_M_alpha >= 1)
	_M_l_d = std::sqrt(2 * _M_alpha - 1);
      else
	_M_l_d = (std::pow(_M_alpha, _M_alpha / (1 - _M_alpha))
		  * (1 - _M_alpha));
    }

  /**
   * Cheng's rejection algorithm GB for alpha >= 1 and a modification
   * of Vaduva's rejection from Weibull algorithm due to Devroye for
   * alpha < 1.
   *
   * References:
   * Cheng, R. C. "The Generation of Gamma Random Variables with Non-integral
   * Shape Parameter." Applied Statistics, 26, 71-75, 1977.
   *
   * Vaduva, I. "Computer Generation of Gamma Gandom Variables by Rejection
   * and Composition Procedures." Math. Operationsforschung and Statistik,
   * Series in Statistics, 8, 545-576, 1977.
   *
   * Devroye, L. "Non-Uniform Random Variates Generation." Springer-Verlag,
   * New York, 1986, Ch. IX, Sect. 3.4 (+ Errata!).
   */
  template<typename _RealType>
    template<typename _UniformRandomNumberGenerator>
      typename gamma_distribution<_RealType>::result_type
      gamma_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng,
		 const param_type& __param)
      {
	result_type __x;
	__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
	  __aurng(__urng);

	bool __reject;
	const _RealType __alpha = __param.alpha();
	const _RealType __beta = __param.beta();
	if (__alpha >= 1)
	  {
	    // alpha - log(4)
	    const result_type __b = __alpha
	      - result_type(1.3862943611198906188344642429163531L);
	    const result_type __c = __alpha + __param._M_l_d;
	    const result_type __1l = 1 / __param._M_l_d;

	    // 1 + log(9 / 2)
	    const result_type __k = 2.5040773967762740733732583523868748L;

	    do
	      {
		const result_type __u = __aurng() / __beta;
		const result_type __v = __aurng() / __beta;

		const result_type __y = __1l * std::log(__v / (1 - __v));
		__x = __alpha * std::exp(__y);

		const result_type __z = __u * __v * __v;
		const result_type __r = __b + __c * __y - __x;

		__reject = __r < result_type(4.5) * __z - __k;
		if (__reject)
		  __reject = __r < std::log(__z);
	      }
	    while (__reject);
	  }
	else
	  {
	    const result_type __c = 1 / __alpha;

	    do
	      {
		const result_type __z = -std::log(__aurng() / __beta);
		const result_type __e = -std::log(__aurng() / __beta);

		__x = std::pow(__z, __c);

		__reject = __z + __e < __param._M_l_d + __x;
	      }
	    while (__reject);
	  }

	return __beta * __x;
      }

  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const gamma_distribution<_RealType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

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

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __alpha, __beta;
      __is >> __alpha >> __beta;
      __x.param(typename gamma_distribution<_RealType>::
		param_type(__alpha, __beta));

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const weibull_distribution<_RealType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __a, __b;
      __is >> __a >> __b;
      __x.param(typename weibull_distribution<_RealType>::
		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(__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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      __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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      _RealType __a, __b;
      __is >> __a >> __b;
      __x.param(typename extreme_value_distribution<_RealType>::
		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();
	  _M_prob.push_back(1.0);
	  return;
	}

      double __sum = std::accumulate(_M_prob.begin(), _M_prob.end(), 0.0);
      //  Now normalize the densities.
      std::transform(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
		     std::bind2nd(std::divides<double>(), __sum));
      //  Accumulate partial sums.
      std::partial_sum(_M_prob.begin(), _M_prob.end(),
		       std::back_inserter(_M_cp));
      //  Make sure the last cumulative probablility 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()
      {
	for (size_t __i = 0; __i < __nw; ++__i)
	  {
	    const double __x = ((__nw - __i - 0.5) * __xmin
				     + (__i + 0.5) * __xmax) / __nw;
	    _M_prob.push_back(__fw(__x));
	  }

	_M_initialize();
      }

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

	const double __p = __aurng();
	auto __pos = std::lower_bound(__param._M_cp.begin(),
				      __param._M_cp.end(), __p);
	if (__pos == __param._M_cp.end())
	  return 0;
	const size_t __i = __pos - __param._M_cp.begin();

	return __i;
      }

  template<typename _IntType, typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const discrete_distribution<_IntType>& __x)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      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;
    }

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

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

      size_t __n;
      __is >> __n;

      std::vector<double> __prob_vec;
      for (; __n != 0; --__n)
	{
	  double __prob;
	  __is >> __prob;
	  __prob_vec.push_back(__prob);
	}

      __x.param(typename discrete_distribution<_IntType>::
		param_type(__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.clear();
	  _M_int.push_back(_RealType(0));
	  _M_int.push_back(_RealType(1));

	  _M_den.clear();
	  _M_den.push_back(1.0);

	  return;
	}

      double __sum = 0.0;
      for (size_t __i = 0; __i < _M_den.size(); ++__i)
	{
	  __sum += _M_den[__i] * (_M_int[__i + 1] - _M_int[__i]);
	  _M_cp.push_back(__sum);
	}

      //  Now normalize the densities...
      std::transform(_M_den.begin(), _M_den.end(), _M_den.begin(),
		     std::bind2nd(std::divides<double>(), __sum));
      //  ... and partial sums.
      std::transform(_M_cp.begin(), _M_cp.end(), _M_cp.begin(),
		     std::bind2nd(std::divides<double>(), __sum));
      //  Make sure the last cumulative probablility is one.
      _M_cp[_M_cp.size() - 1] = 1.0;
    }

  template<typename _RealType>
    piecewise_constant_distribution<_RealType>::param_type::
    param_type()
    : _M_int(), _M_den(), _M_cp()
    { _M_initialize(); }

  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()
      {
	do
	  {
	    _M_int.push_back(*__bbegin);
	    ++__bbegin;
	    if (__bbegin != __bend)
	      {
		_M_den.push_back(*__wbegin);
		++__wbegin;
	      }
	  }
	while (__bbegin != __bend);

	_M_initialize();
      }

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

	for (size_t __i = 0; __i < _M_int.size() - 1; ++__i)
	  {
	    _RealType __x = 0.5 * (_M_int[__i] + _M_int[__i + 1]);
	    _M_den.push_back(__fw(__x));
	  }

	_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()
      {
	for (size_t __i = 0; __i <= __nw; ++__i)
	  {
	    const _RealType __x = ((__nw - __i) * __xmin
					  + __i * __xmax) / __nw;
	    _M_int.push_back(__x);
	  }
	for (size_t __i = 0; __i < __nw; ++__i)
	  {
	    const _RealType __x = ((__nw - __i - 0.5) * __xmin
					+ (__i + 0.5) * __xmax) / __nw;
	    _M_den.push_back(__fw(__x));
	  }

	_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, result_type>
	  __aurng(__urng);

	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();

	return __param._M_int[__i]
	     + (__p - __param._M_cp[__i]) / __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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      size_t __n;
      __is >> __n;

      std::vector<_RealType> __int_vec;
      for (size_t __i = 0; __i <= __n; ++__i)
	{
	  _RealType __int;
	  __is >> __int;
	  __int_vec.push_back(__int);
	}

      std::vector<double> __den_vec;
      for (size_t __i = 0; __i < __n; ++__i)
	{
	  double __den;
	  __is >> __den;
	  __den_vec.push_back(__den);
	}

      __x.param(typename piecewise_constant_distribution<_RealType>::
	  param_type(__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.clear();
	  _M_int.push_back(_RealType(0));
	  _M_int.push_back(_RealType(1));

	  _M_den.clear();
	  _M_den.push_back(1.0);
	  _M_den.push_back(1.0);

	  return;
	}

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

      //  Now normalize the densities...
      std::transform(_M_den.begin(), _M_den.end(), _M_den.begin(),
		     std::bind2nd(std::divides<double>(),__sum));
      //  ... and partial sums... 
      std::transform(_M_cp.begin(), _M_cp.end(), _M_cp.begin(),
		     std::bind2nd(std::divides<double>(), __sum));
      //  ... and slopes.
      std::transform(_M_m.begin(), _M_m.end(), _M_m.begin(),
		     std::bind2nd(std::divides<double>(), __sum));
      //  Make sure the last cumulative probablility is one.
      _M_cp[_M_cp.size() - 1] = 1.0;
    }

  template<typename _RealType>
    piecewise_linear_distribution<_RealType>::param_type::
    param_type()
    : _M_int(), _M_den(), _M_cp(), _M_m()
    { _M_initialize(); }

  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> __bil, _Func __fw)
      : _M_int(), _M_den(), _M_cp(), _M_m()
      {
	for (auto __biter = __bil.begin(); __biter != __bil.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()
      {
	for (size_t __i = 0; __i <= __nw; ++__i)
	  {
	    const _RealType __x = ((__nw - __i) * __xmin
					  + __i * __xmax) / __nw;
	    _M_int.push_back(__x);
	    _M_den.push_back(__fw(__x));
	  }

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

	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 __a = 0.5 * __param._M_m[__i];
	const double __b = __param._M_den[__i];
	const double __c = __param._M_cp[__i];
	const double __q = -0.5 * (__b
#if _GLIBCXX_USE_C99_MATH_TR1
			 + std::copysign(std::sqrt(__b * __b
						 - 4.0 * __a * __c), __b));
#else
			 + (__b < 0.0 ? -1.0 : 1.0)
			 * std::sqrt(__b * __b - 4.0 * __a * __c));
#endif
	const double __x0 = __param._M_int[__i];
	const double __x1 = __q / __a;
	const double __x2 = __c / __q;
	__x = std::max(__x0 + __x1, __x0 + __x2);

	return __x;
      }

  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)
    {
      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
      typedef typename __ostream_type::ios_base    __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>::digits10 + 1);

      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)
    {
      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
      typedef typename __istream_type::ios_base    __ios_base;

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

      size_t __n;
      __is >> __n;

      std::vector<_RealType> __int_vec;
      for (size_t __i = 0; __i <= __n; ++__i)
	{
	  _RealType __int;
	  __is >> __int;
	  __int_vec.push_back(__int);
	}

      std::vector<double> __den_vec;
      for (size_t __i = 0; __i <= __n; ++__i)
	{
	  double __den;
	  __is >> __den;
	  __den_vec.push_back(__den);
	}

      __x.param(typename piecewise_linear_distribution<_RealType>::
	  param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType>
    seed_seq::seed_seq(std::initializer_list<_IntType> __il)
    {
      for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
	_M_v.push_back(__detail::__mod<result_type, 1, 0,
		       __detail::_Shift<result_type, 32>::__value>(*__iter));
    }

  template<typename _InputIterator>
    seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
    {
      for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
	_M_v.push_back(__detail::__mod<result_type, 1, 0,
		       __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(__s + 1, __n);

      for (size_t __k = 0; __k < __m; ++__k)
	{
	  __Type __arg = __begin[__k % __n]
		       ^ __begin[(__k + __p) % __n]
		       ^ __begin[(__k - 1) % __n];
	  __Type __r1 = __arg ^ (__arg << 27);
	  __r1 = __detail::__mod<__Type, 1664525U, 0U,
		   __detail::_Shift<__Type, 32>::__value>(__r1);
	  __Type __r2 = __r1;
	  if (__k == 0)
	    __r2 += __s;
	  else if (__k <= __s)
	    __r2 += __k % __n + _M_v[__k - 1];
	  else
	    __r2 += __k % __n;
	  __r2 = __detail::__mod<__Type, 1U, 0U,
		   __detail::_Shift<__Type, 32>::__value>(__r2);
	  __begin[(__k + __p) % __n] += __r1;
	  __begin[(__k + __q) % __n] += __r2;
	  __begin[__k % __n] = __r2;
	}

      for (size_t __k = __m; __k < __m + __n; ++__k)
	{
	  __Type __arg = __begin[__k % __n]
		       + __begin[(__k + __p) % __n]
		       + __begin[(__k - 1) % __n];
	  __Type __r3 = __arg ^ (__arg << 27);
	  __r3 = __detail::__mod<__Type, 1566083941U, 0U,
		   __detail::_Shift<__Type, 32>::__value>(__r3);
	  __Type __r4 = __r3 - __k % __n;
	  __r4 = __detail::__mod<__Type, 1U, 0U,
		   __detail::_Shift<__Type, 32>::__value>(__r4);
	  __begin[(__k + __p) % __n] ^= __r4;
	  __begin[(__k + __q) % __n] ^= __r3;
	  __begin[__k % __n] = __r4;
	}
    }

  template<typename _RealType, size_t __bits,
	   typename _UniformRandomNumberGenerator>
    _RealType
    generate_canonical(_UniformRandomNumberGenerator& __urng)
    {
      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::log10(__r) / std::log10(2.0L);
      size_t __k = std::max<size_t>(1UL, (__b + __log2r - 1UL) / __log2r);
      _RealType __sum = _RealType(0);
      _RealType __tmp = _RealType(1);
      for (; __k != 0; --__k)
	{
	  __sum += _RealType(__urng() - __urng.min()) * __tmp;
	  __tmp *= __r;
	}
      return __sum / __tmp;
    }
}