xref: /freebsd-12.1/contrib/libstdc++/include/tr1/random.tcc (revision f8a1b7d9)

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

// Copyright (C) 2006, 2007 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 tr1/random.tcc
 *  This is a TR1 C++ Library header.
 */

namespace std
{
_GLIBCXX_BEGIN_NAMESPACE(tr1)

  /*
   * (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<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
    void
    linear_congruential<_UIntType, __a, __c, __m>::
    seed(unsigned long __x0)
    {
      if ((__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0)
	  && (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0))
	_M_x = __detail::__mod<_UIntType, 1, 0, __m>(1);
      else
	_M_x = __detail::__mod<_UIntType, 1, 0, __m>(__x0);
    }

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

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

  template<class _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<_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<class _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<_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<class _UIntType, int __w, int __n, int __m, int __r,
	   _UIntType __a, int __u, int __s,
	   _UIntType __b, int __t, _UIntType __c, int __l>
    void
    mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
		     __b, __t, __c, __l>::
    seed(unsigned long __value)
    {
      _M_x[0] = __detail::__mod<_UIntType, 1, 0,
	__detail::_Shift<_UIntType, __w>::__value>(__value);

      for (int __i = 1; __i < state_size; ++__i)
	{
	  _UIntType __x = _M_x[__i - 1];
	  __x ^= __x >> (__w - 2);
	  __x *= 1812433253ul;
	  __x += __i;
	  _M_x[__i] = __detail::__mod<_UIntType, 1, 0,
	    __detail::_Shift<_UIntType, __w>::__value>(__x);
	}
      _M_p = state_size;
    }

  template<class _UIntType, int __w, int __n, int __m, int __r,
	   _UIntType __a, int __u, int __s,
	   _UIntType __b, int __t, _UIntType __c, int __l>
    template<class _Gen>
      void
      mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
		       __b, __t, __c, __l>::
      seed(_Gen& __gen, false_type)
      {
	for (int __i = 0; __i < state_size; ++__i)
	  _M_x[__i] = __detail::__mod<_UIntType, 1, 0,
	    __detail::_Shift<_UIntType, __w>::__value>(__gen());
	_M_p = state_size;
      }

  template<class _UIntType, int __w, int __n, int __m, int __r,
	   _UIntType __a, int __u, int __s,
	   _UIntType __b, int __t, _UIntType __c, int __l>
    typename
    mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
		     __b, __t, __c, __l>::result_type
    mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
		     __b, __t, __c, __l>::
    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 (int __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 (int __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);
      __z ^= (__z << __s) & __b;
      __z ^= (__z << __t) & __c;
      __z ^= (__z >> __l);

      return __z;
    }

  template<class _UIntType, int __w, int __n, int __m, int __r,
	   _UIntType __a, int __u, int __s, _UIntType __b, int __t,
	   _UIntType __c, int __l,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const mersenne_twister<_UIntType, __w, __n, __m,
	       __r, __a, __u, __s, __b, __t, __c, __l>& __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 (int __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<class _UIntType, int __w, int __n, int __m, int __r,
	   _UIntType __a, int __u, int __s, _UIntType __b, int __t,
	   _UIntType __c, int __l,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       mersenne_twister<_UIntType, __w, __n, __m,
	       __r, __a, __u, __s, __b, __t, __c, __l>& __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 (int __i = 0; __i < __n; ++__i)
	__is >> __x._M_x[__i];

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType, _IntType __m, int __s, int __r>
    void
    subtract_with_carry<_IntType, __m, __s, __r>::
    seed(unsigned long __value)
    {
      if (__value == 0)
	__value = 19780503;

      std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563>
	__lcg(__value);

      for (int __i = 0; __i < long_lag; ++__i)
	_M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__lcg());

      _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
      _M_p = 0;
    }

  template<typename _IntType, _IntType __m, int __s, int __r>
    template<class _Gen>
      void
      subtract_with_carry<_IntType, __m, __s, __r>::
      seed(_Gen& __gen, false_type)
      {
	const int __n = (std::numeric_limits<_UIntType>::digits + 31) / 32;

	for (int __i = 0; __i < long_lag; ++__i)
	  {
	    _UIntType __tmp = 0;
	    _UIntType __factor = 1;
	    for (int __j = 0; __j < __n; ++__j)
	      {
		__tmp += __detail::__mod<__detail::_UInt32Type, 1, 0, 0>
		         (__gen()) * __factor;
		__factor *= __detail::_Shift<_UIntType, 32>::__value;
	      }
	    _M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__tmp);
	  }
	_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
	_M_p = 0;
      }

  template<typename _IntType, _IntType __m, int __s, int __r>
    typename subtract_with_carry<_IntType, __m, __s, __r>::result_type
    subtract_with_carry<_IntType, __m, __s, __r>::
    operator()()
    {
      // Derive short lag index from current index.
      int __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 _IntType, _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 = 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 _IntType, _IntType __m, int __s, int __r,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const subtract_with_carry<_IntType, __m, __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 (int __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 _IntType, _IntType __m, int __s, int __r,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       subtract_with_carry<_IntType, __m, __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 (int __i = 0; __i < __r; ++__i)
	__is >> __x._M_x[__i];
      __is >> __x._M_carry;

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType, int __w, int __s, int __r>
    void
    subtract_with_carry_01<_RealType, __w, __s, __r>::
    _M_initialize_npows()
    {
      for (int __j = 0; __j < __n; ++__j)
#if _GLIBCXX_USE_C99_MATH_TR1
	_M_npows[__j] = std::tr1::ldexp(_RealType(1), -__w + __j * 32);
#else
        _M_npows[__j] = std::pow(_RealType(2), -__w + __j * 32);
#endif
    }

  template<typename _RealType, int __w, int __s, int __r>
    void
    subtract_with_carry_01<_RealType, __w, __s, __r>::
    seed(unsigned long __value)
    {
      if (__value == 0)
	__value = 19780503;

      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 512. Seeding subtract_with_carry_01 from a single unsigned long.
      std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563>
	__lcg(__value);

      this->seed(__lcg);
    }

  template<typename _RealType, int __w, int __s, int __r>
    template<class _Gen>
      void
      subtract_with_carry_01<_RealType, __w, __s, __r>::
      seed(_Gen& __gen, false_type)
      {
	for (int __i = 0; __i < long_lag; ++__i)
	  {
	    for (int __j = 0; __j < __n - 1; ++__j)
	      _M_x[__i][__j] = __detail::__mod<_UInt32Type, 1, 0, 0>(__gen());
	    _M_x[__i][__n - 1] = __detail::__mod<_UInt32Type, 1, 0,
	      __detail::_Shift<_UInt32Type, __w % 32>::__value>(__gen());
	  }

	_M_carry = 1;
	for (int __j = 0; __j < __n; ++__j)
	  if (_M_x[long_lag - 1][__j] != 0)
	    {
	      _M_carry = 0;
	      break;
	    }

	_M_p = 0;
      }

  template<typename _RealType, int __w, int __s, int __r>
    typename subtract_with_carry_01<_RealType, __w, __s, __r>::result_type
    subtract_with_carry_01<_RealType, __w, __s, __r>::
    operator()()
    {
      // Derive short lag index from current index.
      int __ps = _M_p - short_lag;
      if (__ps < 0)
	__ps += long_lag;

      _UInt32Type __new_carry;
      for (int __j = 0; __j < __n - 1; ++__j)
	{
	  if (_M_x[__ps][__j] > _M_x[_M_p][__j]
	      || (_M_x[__ps][__j] == _M_x[_M_p][__j] && _M_carry == 0))
	    __new_carry = 0;
	  else
	    __new_carry = 1;

	  _M_x[_M_p][__j] = _M_x[__ps][__j] - _M_x[_M_p][__j] - _M_carry;
	  _M_carry = __new_carry;
	}

      if (_M_x[__ps][__n - 1] > _M_x[_M_p][__n - 1]
	  || (_M_x[__ps][__n - 1] == _M_x[_M_p][__n - 1] && _M_carry == 0))
	__new_carry = 0;
      else
	__new_carry = 1;

      _M_x[_M_p][__n - 1] = __detail::__mod<_UInt32Type, 1, 0,
	__detail::_Shift<_UInt32Type, __w % 32>::__value>
	(_M_x[__ps][__n - 1] - _M_x[_M_p][__n - 1] - _M_carry);
      _M_carry = __new_carry;

      result_type __ret = 0.0;
      for (int __j = 0; __j < __n; ++__j)
	__ret += _M_x[_M_p][__j] * _M_npows[__j];

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

      return __ret;
    }

  template<typename _RealType, int __w, int __s, int __r,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const subtract_with_carry_01<_RealType, __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 (int __i = 0; __i < __r; ++__i)
	for (int __j = 0; __j < __x.__n; ++__j)
	  __os << __x._M_x[__i][__j] << __space;
      __os << __x._M_carry;

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

  template<typename _RealType, int __w, int __s, int __r,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       subtract_with_carry_01<_RealType, __w, __s, __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);

      for (int __i = 0; __i < __r; ++__i)
	for (int __j = 0; __j < __x.__n; ++__j)
	  __is >> __x._M_x[__i][__j];
      __is >> __x._M_carry;

      __is.flags(__flags);
      return __is;
    }


  template<class _UniformRandomNumberGenerator, int __p, int __r>
    typename discard_block<_UniformRandomNumberGenerator,
			   __p, __r>::result_type
    discard_block<_UniformRandomNumberGenerator, __p, __r>::
    operator()()
    {
      if (_M_n >= used_block)
	{
	  while (_M_n < block_size)
	    {
	      _M_b();
	      ++_M_n;
	    }
	  _M_n = 0;
	}
      ++_M_n;
      return _M_b();
    }

  template<class _UniformRandomNumberGenerator, int __p, int __r,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const discard_block<_UniformRandomNumberGenerator,
	       __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._M_b << __space << __x._M_n;

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

  template<class _UniformRandomNumberGenerator, int __p, int __r,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       discard_block<_UniformRandomNumberGenerator, __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<class _UniformRandomNumberGenerator1, int __s1,
	   class _UniformRandomNumberGenerator2, int __s2>
    void
    xor_combine<_UniformRandomNumberGenerator1, __s1,
		_UniformRandomNumberGenerator2, __s2>::
    _M_initialize_max()
    {
      const int __w = std::numeric_limits<result_type>::digits;

      const result_type __m1 =
	std::min(result_type(_M_b1.max() - _M_b1.min()),
		 __detail::_Shift<result_type, __w - __s1>::__value - 1);

      const result_type __m2 =
	std::min(result_type(_M_b2.max() - _M_b2.min()),
		 __detail::_Shift<result_type, __w - __s2>::__value - 1);

      // NB: In TR1 s1 is not required to be >= s2.
      if (__s1 < __s2)
	_M_max = _M_initialize_max_aux(__m2, __m1, __s2 - __s1) << __s1;
      else
	_M_max = _M_initialize_max_aux(__m1, __m2, __s1 - __s2) << __s2;
    }

  template<class _UniformRandomNumberGenerator1, int __s1,
	   class _UniformRandomNumberGenerator2, int __s2>
    typename xor_combine<_UniformRandomNumberGenerator1, __s1,
			 _UniformRandomNumberGenerator2, __s2>::result_type
    xor_combine<_UniformRandomNumberGenerator1, __s1,
		_UniformRandomNumberGenerator2, __s2>::
    _M_initialize_max_aux(result_type __a, result_type __b, int __d)
    {
      const result_type __two2d = result_type(1) << __d;
      const result_type __c = __a * __two2d;

      if (__a == 0 || __b < __two2d)
	return __c + __b;

      const result_type __t = std::max(__c, __b);
      const result_type __u = std::min(__c, __b);

      result_type __ub = __u;
      result_type __p;
      for (__p = 0; __ub != 1; __ub >>= 1)
	++__p;

      const result_type __two2p = result_type(1) << __p;
      const result_type __k = __t / __two2p;

      if (__k & 1)
	return (__k + 1) * __two2p - 1;

      if (__c >= __b)
	return (__k + 1) * __two2p + _M_initialize_max_aux((__t % __two2p)
							   / __two2d,
							   __u % __two2p, __d);
      else
	return (__k + 1) * __two2p + _M_initialize_max_aux((__u % __two2p)
							   / __two2d,
							   __t % __two2p, __d);
    }

  template<class _UniformRandomNumberGenerator1, int __s1,
	   class _UniformRandomNumberGenerator2, int __s2,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const xor_combine<_UniformRandomNumberGenerator1, __s1,
	       _UniformRandomNumberGenerator2, __s2>& __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.base1() << __space << __x.base2();

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

  template<class _UniformRandomNumberGenerator1, int __s1,
	   class _UniformRandomNumberGenerator2, int __s2,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       xor_combine<_UniformRandomNumberGenerator1, __s1,
	       _UniformRandomNumberGenerator2, __s2>& __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);

      __is >> __x._M_b1 >> __x._M_b2;

      __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<_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.min() << __space << __x.max();

      __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<_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);

      __is >> __x._M_min >> __x._M_max;

      __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(__gnu_cxx::__numeric_traits<double>::__max_digits10);

      __os << __x.p();

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


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

	_RealType __cand;
	do
	  __cand = std::ceil(std::log(__urng()) / _M_log_p);
	while (__cand >= __thr);

	return result_type(__cand + __naf);
      }

  template<typename _IntType, typename _RealType,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const geometric_distribution<_IntType, _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(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);

      __os << __x.p();

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


  template<typename _IntType, typename _RealType>
    void
    poisson_distribution<_IntType, _RealType>::
    _M_initialize()
    {
#if _GLIBCXX_USE_C99_MATH_TR1
      if (_M_mean >= 12)
	{
	  const _RealType __m = std::floor(_M_mean);
	  _M_lm_thr = std::log(_M_mean);
	  _M_lfm = std::tr1::lgamma(__m + 1);
	  _M_sm = std::sqrt(__m);

	  const _RealType __pi_4 = 0.7853981633974483096156608458198757L;
	  const _RealType __dx = std::sqrt(2 * __m * std::log(32 * __m
							      / __pi_4));
	  _M_d = std::tr1::round(std::max(_RealType(6),
					  std::min(__m, __dx)));
	  const _RealType __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, typename _RealType>
    template<class _UniformRandomNumberGenerator>
      typename poisson_distribution<_IntType, _RealType>::result_type
      poisson_distribution<_IntType, _RealType>::
      operator()(_UniformRandomNumberGenerator& __urng)
      {
#if _GLIBCXX_USE_C99_MATH_TR1
	if (_M_mean >= 12)
	  {
	    _RealType __x;

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

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

	    bool __reject = true;
	    do
	      {
		const _RealType __u = __c * __urng();
		const _RealType __e = -std::log(__urng());

		_RealType __w = 0.0;

		if (__u <= __c1)
		  {
		    const _RealType __n = _M_nd(__urng);
		    const _RealType __y = -std::abs(__n) * _M_sm - 1;
		    __x = std::floor(__y);
		    __w = -__n * __n / 2;
		    if (__x < -__m)
		      continue;
		  }
		else if (__u <= __c2)
		  {
		    const _RealType __n = _M_nd(__urng);
		    const _RealType __y = 1 + std::abs(__n) * _M_scx;
		    __x = std::ceil(__y);
		    __w = __y * (2 - __y) * _M_1cx;
		    if (__x > _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 _RealType __v = -std::log(__urng());
		    const _RealType __y = _M_d + __v * __2cx / _M_d;
		    __x = std::ceil(__y);
		    __w = -_M_d * _M_1cx * (1 + __y / 2);
		  }

		__reject = (__w - __e - __x * _M_lm_thr
			    > _M_lfm - std::tr1::lgamma(__x + __m + 1));

		__reject |= __x + __m >= __thr;

	      } while (__reject);

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

	    do
	      {
		__prod *= __urng();
		__x += 1;
	      }
	    while (__prod > _M_lm_thr);

	    return __x - 1;
	  }
      }

  template<typename _IntType, typename _RealType,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const poisson_distribution<_IntType, _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(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);

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

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

  template<typename _IntType, typename _RealType,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       poisson_distribution<_IntType, _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);

      __is >> __x._M_mean >> __x._M_nd;
      __x._M_initialize();

      __is.flags(__flags);
      return __is;
    }


  template<typename _IntType, typename _RealType>
    void
    binomial_distribution<_IntType, _RealType>::
    _M_initialize()
    {
      const _RealType __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 _RealType __np = std::floor(_M_t * __p12);
	  const _RealType __pa = __np / _M_t;
	  const _RealType __1p = 1 - __pa;

	  const _RealType __pi_4 = 0.7853981633974483096156608458198757L;
	  const _RealType __d1x =
	    std::sqrt(__np * __1p * std::log(32 * __np
					     / (81 * __pi_4 * __1p)));
	  _M_d1 = std::tr1::round(std::max(_RealType(1), __d1x));
	  const _RealType __d2x =
	    std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
					     / (__pi_4 * __pa)));
	  _M_d2 = std::tr1::round(std::max(_RealType(1), __d2x));

	  // sqrt(pi / 2)
	  const _RealType __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 _RealType __a12 = _M_a1 + _M_s2 * __spi_2;
	  const _RealType __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 _RealType __s2s = _M_s2 * _M_s2;
	  _M_s = (_M_a123 + 2 * __s2s / _M_d2
		  * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
	  _M_lf = (std::tr1::lgamma(__np + 1)
		   + std::tr1::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, typename _RealType>
    template<class _UniformRandomNumberGenerator>
      typename binomial_distribution<_IntType, _RealType>::result_type
      binomial_distribution<_IntType, _RealType>::
      _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t)
      {
	_IntType    __x = 0;
	_RealType __sum = 0;

	do
	  {
	    const _RealType __e = -std::log(__urng());
	    __sum += __e / (__t - __x);
	    __x += 1;
	  }
	while (__sum <= _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, typename _RealType>
    template<class _UniformRandomNumberGenerator>
      typename binomial_distribution<_IntType, _RealType>::result_type
      binomial_distribution<_IntType, _RealType>::
      operator()(_UniformRandomNumberGenerator& __urng)
      {
	result_type __ret;
	const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;

#if _GLIBCXX_USE_C99_MATH_TR1
	if (!_M_easy)
	  {
	    _RealType __x;

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

	    const _RealType __np = std::floor(_M_t * __p12);
	    const _RealType __pa = __np / _M_t;

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

	    bool __reject;
	    do
	      {
		const _RealType __u = _M_s * __urng();

		_RealType __v;

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

		    const _RealType __y = _M_d1 + 2 * __s1s * __e1 / _M_d1;
		    __x = std::floor(__y);
		    __v = (-__e2 + _M_d1 * (1 / (_M_t - __np)
					    -__y / (2 * __s1s)));
		    __reject = false;
		  }
		else
		  {
		    const _RealType __e1 = -std::log(__urng());
		    const _RealType __e2 = -std::log(__urng());

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

		__reject = __reject || __x < -__np || __x > _M_t - __np;
		if (!__reject)
		  {
		    const _RealType __lfx =
		      std::tr1::lgamma(__np + __x + 1)
		      + std::tr1::lgamma(_M_t - (__np + __x) + 1);
		    __reject = __v > _M_lf - __lfx + __x * _M_lp1p;
		  }

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

	    __x += __np + __naf;

	    const _IntType __z = _M_waiting(__urng, _M_t - _IntType(__x));
	    __ret = _IntType(__x) + __z;
	  }
	else
#endif
	  __ret = _M_waiting(__urng, _M_t);

	if (__p12 != _M_p)
	  __ret = _M_t - __ret;
	return __ret;
      }

  template<typename _IntType, typename _RealType,
	   typename _CharT, typename _Traits>
    std::basic_ostream<_CharT, _Traits>&
    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
	       const binomial_distribution<_IntType, _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(__gnu_cxx::__numeric_traits<_RealType>::__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 _RealType,
	   typename _CharT, typename _Traits>
    std::basic_istream<_CharT, _Traits>&
    operator>>(std::basic_istream<_CharT, _Traits>& __is,
	       binomial_distribution<_IntType, _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);

      __is >> __x._M_t >> __x._M_p >> __x._M_nd;
      __x._M_initialize();

      __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<_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(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);

      __os << __x.min() << __space << __x.max();

      __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<_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);

      __is >> __x._M_min >> __x._M_max;

      __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(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);

      __os << __x.lambda();

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


  /**
   * 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<class _UniformRandomNumberGenerator>
      typename normal_distribution<_RealType>::result_type
      normal_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng)
      {
	result_type __ret;

	if (_M_saved_available)
	  {
	    _M_saved_available = false;
	    __ret = _M_saved;
	  }
	else
	  {
	    result_type __x, __y, __r2;
	    do
	      {
		__x = result_type(2.0) * __urng() - 1.0;
		__y = result_type(2.0) * __urng() - 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 * _M_sigma + _M_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(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);

      __os << __x._M_saved_available << __space
	   << __x.mean() << __space
	   << __x.sigma();
      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);

      __is >> __x._M_saved_available >> __x._M_mean
	   >> __x._M_sigma;
      if (__x._M_saved_available)
	__is >> __x._M_saved;

      __is.flags(__flags);
      return __is;
    }


  template<typename _RealType>
    void
    gamma_distribution<_RealType>::
    _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<class _UniformRandomNumberGenerator>
      typename gamma_distribution<_RealType>::result_type
      gamma_distribution<_RealType>::
      operator()(_UniformRandomNumberGenerator& __urng)
      {
	result_type __x;

	bool __reject;
	if (_M_alpha >= 1)
	  {
	    // alpha - log(4)
	    const result_type __b = _M_alpha
	      - result_type(1.3862943611198906188344642429163531L);
	    const result_type __c = _M_alpha + _M_l_d;
	    const result_type __1l = 1 / _M_l_d;

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

	    do
	      {
		const result_type __u = __urng();
		const result_type __v = __urng();

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

	    do
	      {
		const result_type __z = -std::log(__urng());
		const result_type __e = -std::log(__urng());

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

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

	return __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();
      __os.flags(__ios_base::scientific | __ios_base::left);
      __os.fill(__os.widen(' '));
      __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);

      __os << __x.alpha();

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

_GLIBCXX_END_NAMESPACE
}