path: root/libstdc++-v3/include/ext/random

// Random number extensions -*- C++ -*-

// Copyright (C) 2012 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.

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

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

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

/** @file ext/random
 *  This file is a GNU extension to the Standard C++ Library.
 */

#ifndef _EXT_RANDOM
#define _EXT_RANDOM 1

#pragma GCC system_header

#include <random>
#include <array>
#ifdef __SSE2__
# include <x86intrin.h>
#endif


namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  /* Mersenne twister implementation optimized for vector operations.
   *
   * Reference: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/
   */
  template<typename _UIntType, size_t __m,
	   size_t __pos1, size_t __sl1, size_t __sl2,
	   size_t __sr1, size_t __sr2,
	   uint32_t __msk1, uint32_t __msk2,
	   uint32_t __msk3, uint32_t __msk4,
	   uint32_t __parity1, uint32_t __parity2,
	   uint32_t __parity3, uint32_t __parity4>
    class simd_fast_mersenne_twister_engine
    {
      static_assert(std::is_unsigned<_UIntType>::value, "template argument "
		    "substituting _UIntType not an unsigned integral type");
      static_assert(__sr1 < 32, "first right shift too large");
      static_assert(__sr2 < 16, "second right shift too large");
      static_assert(__sl1 < 32, "first left shift too large");
      static_assert(__sl2 < 16, "second left shift too large");

    public:
      typedef _UIntType result_type;

    private:
      static constexpr size_t m_w = sizeof(result_type) * 8;
      static constexpr size_t _M_nstate = __m / 128 + 1;
      static constexpr size_t _M_nstate32 = _M_nstate * 4;

      static_assert(std::is_unsigned<_UIntType>::value, "template argument "
		    "substituting _UIntType not an unsigned integral type");
      static_assert(__pos1 < _M_nstate, "POS1 not smaller than state size");
      static_assert(16 % sizeof(_UIntType) == 0,
		    "UIntType size must divide 16");

    public:
      static constexpr size_t state_size = _M_nstate * (16
							/ sizeof(result_type));
      static constexpr result_type default_seed = 5489u;

      // constructors and member function
      explicit
      simd_fast_mersenne_twister_engine(result_type __sd = default_seed)
      { seed(__sd); }

      template<typename _Sseq, typename = typename
	std::enable_if<!std::is_same<_Sseq,
				     simd_fast_mersenne_twister_engine>::value>
	       ::type>
	explicit
	simd_fast_mersenne_twister_engine(_Sseq& __q)
	{ seed(__q); }

      void
      seed(result_type __sd = default_seed);

      template<typename _Sseq>
	typename std::enable_if<std::is_class<_Sseq>::value>::type
	seed(_Sseq& __q);

      static constexpr result_type
      min()
      { return 0; };

      static constexpr result_type
      max()
      { return std::numeric_limits<result_type>::max(); }

      void
      discard(unsigned long long __z);

      result_type
      operator()()
      {
	if (__builtin_expect(_M_pos >= state_size, 0))
	  _M_gen_rand();

	return _M_stateT[_M_pos++];
      }

#ifdef __SSE2__
      friend bool
      operator==(const simd_fast_mersenne_twister_engine& __lhs,
		 const simd_fast_mersenne_twister_engine& __rhs)
      { __m128i __res = _mm_cmpeq_epi8(__lhs._M_state[0], __rhs._M_state[0]);
	for (size_t __i = 1; __i < __lhs._M_nstate; ++__i)
	  __res = _mm_and_si128(__res, _mm_cmpeq_epi8(__lhs._M_state[__i],
						      __rhs._M_state[__i]));
	return (_mm_movemask_epi8(__res) == 0xffff
		&& __lhs._M_pos == __rhs._M_pos); }
#else
      friend bool
      operator==(const simd_fast_mersenne_twister_engine& __lhs,
		 const simd_fast_mersenne_twister_engine& __rhs)
      { return (std::equal(__lhs._M_stateT, __lhs._M_stateT + state_size,
			   __rhs._M_stateT)
		&& __lhs._M_pos == __rhs._M_pos); }
#endif

      template<typename _UIntType_2, size_t __m_2,
	       size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
	       size_t __sr1_2, size_t __sr2_2,
	       uint32_t __msk1_2, uint32_t __msk2_2,
	       uint32_t __msk3_2, uint32_t __msk4_2,
	       uint32_t __parity1_2, uint32_t __parity2_2,
	       uint32_t __parity3_2, uint32_t __parity4_2,
	       typename _CharT, typename _Traits>
	friend std::basic_ostream<_CharT, _Traits>&
	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
		   const __gnu_cxx::simd_fast_mersenne_twister_engine
		   <_UIntType_2,
		   __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
		   __msk1_2, __msk2_2, __msk3_2, __msk4_2,
		   __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);

      template<typename _UIntType_2, size_t __m_2,
	       size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
	       size_t __sr1_2, size_t __sr2_2,
	       uint32_t __msk1_2, uint32_t __msk2_2,
	       uint32_t __msk3_2, uint32_t __msk4_2,
	       uint32_t __parity1_2, uint32_t __parity2_2,
	       uint32_t __parity3_2, uint32_t __parity4_2,
	       typename _CharT, typename _Traits>
	friend std::basic_istream<_CharT, _Traits>&
	operator>>(std::basic_istream<_CharT, _Traits>& __is,
		   __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType_2,
		   __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
		   __msk1_2, __msk2_2, __msk3_2, __msk4_2,
		   __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);

    private:
      union
      {
#ifdef __SSE2__
	__m128i _M_state[_M_nstate];
#endif
	uint32_t _M_state32[_M_nstate32];
	result_type _M_stateT[state_size];
      } __attribute__ ((__aligned__ (16)));
      size_t _M_pos;

      void _M_gen_rand(void);
      void _M_period_certification();
  };


  template<typename _UIntType, size_t __m,
	   size_t __pos1, size_t __sl1, size_t __sl2,
	   size_t __sr1, size_t __sr2,
	   uint32_t __msk1, uint32_t __msk2,
	   uint32_t __msk3, uint32_t __msk4,
	   uint32_t __parity1, uint32_t __parity2,
	   uint32_t __parity3, uint32_t __parity4>
    inline bool
    operator!=(const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
	       __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
	       __msk4, __parity1, __parity2, __parity3, __parity4>& __lhs,
	       const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
	       __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
	       __msk4, __parity1, __parity2, __parity3, __parity4>& __rhs)
    { return !(__lhs == __rhs); }


  /* Definitions for the SIMD-oriented Fast Mersenne Twister as defined
   * in the C implementation by Daito and Matsumoto, as both a 32-bit
   * and 64-bit version.
   */
  typedef simd_fast_mersenne_twister_engine<uint32_t, 607, 2,
					    15, 3, 13, 3,
					    0xfdff37ffU, 0xef7f3f7dU,
					    0xff777b7dU, 0x7ff7fb2fU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x5986f054U>
    sfmt607;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 607, 2,
					    15, 3, 13, 3,
					    0xfdff37ffU, 0xef7f3f7dU,
					    0xff777b7dU, 0x7ff7fb2fU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x5986f054U>
    sfmt607_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 1279, 7,
					    14, 3, 5, 1,
					    0xf7fefffdU, 0x7fefcfffU,
					    0xaff3ef3fU, 0xb5ffff7fU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x20000000U>
    sfmt1279;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 1279, 7,
					    14, 3, 5, 1,
					    0xf7fefffdU, 0x7fefcfffU,
					    0xaff3ef3fU, 0xb5ffff7fU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x20000000U>
    sfmt1279_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 2281, 12,
					    19, 1, 5, 1,
					    0xbff7ffbfU, 0xfdfffffeU,
					    0xf7ffef7fU, 0xf2f7cbbfU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x41dfa600U>
    sfmt2281;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 2281, 12,
					    19, 1, 5, 1,
					    0xbff7ffbfU, 0xfdfffffeU,
					    0xf7ffef7fU, 0xf2f7cbbfU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x41dfa600U>
    sfmt2281_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 4253, 17,
					    20, 1, 7, 1,
					    0x9f7bffffU, 0x9fffff5fU,
					    0x3efffffbU, 0xfffff7bbU,
					    0xa8000001U, 0xaf5390a3U,
					    0xb740b3f8U, 0x6c11486dU>
    sfmt4253;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 4253, 17,
					    20, 1, 7, 1,
					    0x9f7bffffU, 0x9fffff5fU,
					    0x3efffffbU, 0xfffff7bbU,
					    0xa8000001U, 0xaf5390a3U,
					    0xb740b3f8U, 0x6c11486dU>
    sfmt4253_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 11213, 68,
					    14, 3, 7, 3,
					    0xeffff7fbU, 0xffffffefU,
					    0xdfdfbfffU, 0x7fffdbfdU,
					    0x00000001U, 0x00000000U,
					    0xe8148000U, 0xd0c7afa3U>
    sfmt11213;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 11213, 68,
					    14, 3, 7, 3,
					    0xeffff7fbU, 0xffffffefU,
					    0xdfdfbfffU, 0x7fffdbfdU,
					    0x00000001U, 0x00000000U,
					    0xe8148000U, 0xd0c7afa3U>
    sfmt11213_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 19937, 122,
					    18, 1, 11, 1,
					    0xdfffffefU, 0xddfecb7fU,
					    0xbffaffffU, 0xbffffff6U,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x13c9e684U>
    sfmt19937;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 19937, 122,
					    18, 1, 11, 1,
					    0xdfffffefU, 0xddfecb7fU,
					    0xbffaffffU, 0xbffffff6U,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0x13c9e684U>
    sfmt19937_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 44497, 330,
					    5, 3, 9, 3,
					    0xeffffffbU, 0xdfbebfffU,
					    0xbfbf7befU, 0x9ffd7bffU,
					    0x00000001U, 0x00000000U,
					    0xa3ac4000U, 0xecc1327aU>
    sfmt44497;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 44497, 330,
					    5, 3, 9, 3,
					    0xeffffffbU, 0xdfbebfffU,
					    0xbfbf7befU, 0x9ffd7bffU,
					    0x00000001U, 0x00000000U,
					    0xa3ac4000U, 0xecc1327aU>
    sfmt44497_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 86243, 366,
					    6, 7, 19, 1,
					    0xfdbffbffU, 0xbff7ff3fU,
					    0xfd77efffU, 0xbf9ff3ffU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0xe9528d85U>
    sfmt86243;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 86243, 366,
					    6, 7, 19, 1,
					    0xfdbffbffU, 0xbff7ff3fU,
					    0xfd77efffU, 0xbf9ff3ffU,
					    0x00000001U, 0x00000000U,
					    0x00000000U, 0xe9528d85U>
    sfmt86243_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 132049, 110,
					    19, 1, 21, 1,
					    0xffffbb5fU, 0xfb6ebf95U,
					    0xfffefffaU, 0xcff77fffU,
					    0x00000001U, 0x00000000U,
					    0xcb520000U, 0xc7e91c7dU>
    sfmt132049;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 132049, 110,
					    19, 1, 21, 1,
					    0xffffbb5fU, 0xfb6ebf95U,
					    0xfffefffaU, 0xcff77fffU,
					    0x00000001U, 0x00000000U,
					    0xcb520000U, 0xc7e91c7dU>
    sfmt132049_64;


  typedef simd_fast_mersenne_twister_engine<uint32_t, 216091, 627,
					    11, 3, 10, 1,
					    0xbff7bff7U, 0xbfffffffU,
					    0xbffffa7fU, 0xffddfbfbU,
					    0xf8000001U, 0x89e80709U,
					    0x3bd2b64bU, 0x0c64b1e4U>
    sfmt216091;

  typedef simd_fast_mersenne_twister_engine<uint64_t, 216091, 627,
					    11, 3, 10, 1,
					    0xbff7bff7U, 0xbfffffffU,
					    0xbffffa7fU, 0xffddfbfbU,
					    0xf8000001U, 0x89e80709U,
					    0x3bd2b64bU, 0x0c64b1e4U>
    sfmt216091_64;


  /**
   * @brief A beta continuous distribution for random numbers.
   *
   * The formula for the beta probability density function is:
   * @f[
   *     p(x|\alpha,\beta) = \frac{1}{B(\alpha,\beta)}
   *                         x^{\alpha - 1} (1 - x)^{\beta - 1}
   * @f]
   */
  template<typename _RealType = double>
    class beta_distribution
    {
      static_assert(std::is_floating_point<_RealType>::value,
		    "template argument not a floating point type");

    public:
      /** The type of the range of the distribution. */
      typedef _RealType result_type;
      /** Parameter type. */
      struct param_type
      {
	typedef beta_distribution<_RealType> distribution_type;
	friend class beta_distribution<_RealType>;

	explicit
	param_type(_RealType __alpha_val = _RealType(1),
		   _RealType __beta_val = _RealType(1))
	: _M_alpha(__alpha_val), _M_beta(__beta_val)
	{
	  _GLIBCXX_DEBUG_ASSERT(_M_alpha > _RealType(0));
	  _GLIBCXX_DEBUG_ASSERT(_M_beta > _RealType(0));
	}

	_RealType
	alpha() const
	{ return _M_alpha; }

	_RealType
	beta() const
	{ return _M_beta; }

	friend bool
	operator==(const param_type& __p1, const param_type& __p2)
	{ return (__p1._M_alpha == __p2._M_alpha
		  && __p1._M_beta == __p2._M_beta); }

      private:
	void
	_M_initialize();

	_RealType _M_alpha;
	_RealType _M_beta;
      };

    public:
      /**
       * @brief Constructs a beta distribution with parameters
       * @f$\alpha@f$ and @f$\beta@f$.
       */
      explicit
      beta_distribution(_RealType __alpha_val = _RealType(1),
			_RealType __beta_val = _RealType(1))
      : _M_param(__alpha_val, __beta_val)
      { }

      explicit
      beta_distribution(const param_type& __p)
      : _M_param(__p)
      { }

      /**
       * @brief Resets the distribution state.
       */
      void
      reset()
      { }

      /**
       * @brief Returns the @f$\alpha@f$ of the distribution.
       */
      _RealType
      alpha() const
      { return _M_param.alpha(); }

      /**
       * @brief Returns the @f$\beta@f$ of the distribution.
       */
      _RealType
      beta() const
      { return _M_param.beta(); }

      /**
       * @brief Returns the parameter set of the distribution.
       */
      param_type
      param() const
      { return _M_param; }

      /**
       * @brief Sets the parameter set of the distribution.
       * @param __param The new parameter set of the distribution.
       */
      void
      param(const param_type& __param)
      { _M_param = __param; }

      /**
       * @brief Returns the greatest lower bound value of the distribution.
       */
      result_type
      min() const
      { return result_type(0); }

      /**
       * @brief Returns the least upper bound value of the distribution.
       */
      result_type
      max() const
      { return result_type(1); }

      /**
       * @brief Generating functions.
       */
      template<typename _UniformRandomNumberGenerator>
	result_type
	operator()(_UniformRandomNumberGenerator& __urng)
	{ return this->operator()(__urng, this->param()); }

      template<typename _UniformRandomNumberGenerator>
	result_type
	operator()(_UniformRandomNumberGenerator& __urng,
		   const param_type& __p);

      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate(_ForwardIterator __f, _ForwardIterator __t,
		   _UniformRandomNumberGenerator& __urng)
	{ this->__generate(__f, __t, __urng, this->param()); }

      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate(_ForwardIterator __f, _ForwardIterator __t,
		   _UniformRandomNumberGenerator& __urng,
		   const param_type& __p)
	{ this->__generate_impl(__f, __t, __urng, __p); }

      template<typename _UniformRandomNumberGenerator>
	void
	__generate(result_type* __f, result_type* __t,
		   _UniformRandomNumberGenerator& __urng,
		   const param_type& __p)
	{ this->__generate_impl(__f, __t, __urng, __p); }

      /**
       * @brief Inserts a %beta_distribution random number distribution
       * @p __x into the output stream @p __os.
       *
       * @param __os An output stream.
       * @param __x  A %beta_distribution random number distribution.
       *
       * @returns The output stream with the state of @p __x inserted or in
       * an error state.
       */
      template<typename _RealType1, typename _CharT, typename _Traits>
	friend std::basic_ostream<_CharT, _Traits>&
	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
		   const __gnu_cxx::beta_distribution<_RealType1>& __x);

      /**
       * @brief Extracts a %beta_distribution random number distribution
       * @p __x from the input stream @p __is.
       *
       * @param __is An input stream.
       * @param __x  A %beta_distribution random number generator engine.
       *
       * @returns The input stream with @p __x extracted or in an error state.
       */
      template<typename _RealType1, typename _CharT, typename _Traits>
	friend std::basic_istream<_CharT, _Traits>&
	operator>>(std::basic_istream<_CharT, _Traits>& __is,
		   __gnu_cxx::beta_distribution<_RealType1>& __x);

    private:
      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
			_UniformRandomNumberGenerator& __urng,
			const param_type& __p);

      param_type _M_param;
    };

  /**
   * @brief Return true if two beta distributions have the same
   *        parameters and the sequences that would be generated
   *        are equal.
   */
  template<typename _RealType>
    inline bool
    operator==(const __gnu_cxx::beta_distribution<_RealType>& __d1,
	       const __gnu_cxx::beta_distribution<_RealType>& __d2)
    { return __d1.param() == __d2.param(); }

  /**
   * @brief Return true if two beta distributions are different.
   */
  template<typename _RealType>
    inline bool
    operator!=(const __gnu_cxx::beta_distribution<_RealType>& __d1,
	       const __gnu_cxx::beta_distribution<_RealType>& __d2)
   { return !(__d1 == __d2); }


  /**
   * @brief A multi-variate normal continuous distribution for random numbers.
   *
   * The formula for the normal probability density function is
   * @f[
   *     p(\overrightarrow{x}|\overrightarrow{\mu },\Sigma) =
   *       \frac{1}{\sqrt{(2\pi )^k\det(\Sigma))}}
   *       e^{-\frac{1}{2}(\overrightarrow{x}-\overrightarrow{\mu})^\text{T}
   *          \Sigma ^{-1}(\overrightarrow{x}-\overrightarrow{\mu})}
   * @f]
   *
   * where @f$\overrightarrow{x}@f$ and @f$\overrightarrow{\mu}@f$ are
   * vectors of dimension @f$k@f$ and @f$\Sigma@f$ is the covariance
   * matrix (which must be positive-definite).
   */
  template<std::size_t _Dimen, typename _RealType = double>
    class normal_mv_distribution
    {
      static_assert(std::is_floating_point<_RealType>::value,
		    "template argument not a floating point type");
      static_assert(_Dimen != 0, "dimension is zero");

    public:
      /** The type of the range of the distribution. */
      typedef std::array<_RealType, _Dimen> result_type;
      /** Parameter type. */
      class param_type
      {
	static constexpr size_t _M_t_size = _Dimen * (_Dimen + 1) / 2;

      public:
	typedef normal_mv_distribution<_Dimen, _RealType> distribution_type;
	friend class normal_mv_distribution<_Dimen, _RealType>;

	param_type()
	{
	  std::fill(_M_mean.begin(), _M_mean.end(), _RealType(0));
	  auto __it = _M_t.begin();
	  for (size_t __i = 0; __i < _Dimen; ++__i)
	    {
	      std::fill_n(__it, __i, _RealType(0));
	      __it += __i;
	      *__it++ = _RealType(1);
	    }
	}

	template<typename _ForwardIterator1, typename _ForwardIterator2>
	  param_type(_ForwardIterator1 __meanbegin,
		     _ForwardIterator1 __meanend,
		     _ForwardIterator2 __varcovbegin,
		     _ForwardIterator2 __varcovend)
	{
	  __glibcxx_function_requires(_ForwardIteratorConcept<
				      _ForwardIterator1>)
	  __glibcxx_function_requires(_ForwardIteratorConcept<
				      _ForwardIterator2>)
	  _GLIBCXX_DEBUG_ASSERT(std::distance(__meanbegin, __meanend)
				<= _Dimen);
	  const auto __dist = std::distance(__varcovbegin, __varcovend);
	  _GLIBCXX_DEBUG_ASSERT(__dist == _Dimen * _Dimen
				|| __dist == _Dimen * (_Dimen + 1) / 2
				|| __dist == _Dimen);

	  if (__dist == _Dimen * _Dimen)
	    _M_init_full(__meanbegin, __meanend, __varcovbegin, __varcovend);
	  else if (__dist == _Dimen * (_Dimen + 1) / 2)
	    _M_init_lower(__meanbegin, __meanend, __varcovbegin, __varcovend);
	  else
	    _M_init_diagonal(__meanbegin, __meanend,
			     __varcovbegin, __varcovend);
	}

	param_type(std::initializer_list<_RealType> __mean,
		   std::initializer_list<_RealType> __varcov)
	{
	  _GLIBCXX_DEBUG_ASSERT(__mean.size() <= _Dimen);
	  _GLIBCXX_DEBUG_ASSERT(__varcov.size() == _Dimen * _Dimen
				|| __varcov.size() == _Dimen * (_Dimen + 1) / 2
				|| __varcov.size() == _Dimen);

	  if (__varcov.size() == _Dimen * _Dimen)
	    _M_init_full(__mean.begin(), __mean.end(),
			 __varcov.begin(), __varcov.end());
	  else if (__varcov.size() == _Dimen * (_Dimen + 1) / 2)
	    _M_init_lower(__mean.begin(), __mean.end(),
			  __varcov.begin(), __varcov.end());
	  else
	    _M_init_diagonal(__mean.begin(), __mean.end(),
			     __varcov.begin(), __varcov.end());
	}

	std::array<_RealType, _Dimen>
	mean() const
	{ return _M_mean; }

	std::array<_RealType, _M_t_size>
	varcov() const
	{ return _M_t; }

	friend bool
	operator==(const param_type& __p1, const param_type& __p2)
	{ return __p1._M_mean == __p2._M_mean && __p1._M_t == __p2._M_t; }

      private:
	template <typename _InputIterator1, typename _InputIterator2>
	  void _M_init_full(_InputIterator1 __meanbegin,
			    _InputIterator1 __meanend,
			    _InputIterator2 __varcovbegin,
			    _InputIterator2 __varcovend);
	template <typename _InputIterator1, typename _InputIterator2>
	  void _M_init_lower(_InputIterator1 __meanbegin,
			     _InputIterator1 __meanend,
			     _InputIterator2 __varcovbegin,
			     _InputIterator2 __varcovend);
	template <typename _InputIterator1, typename _InputIterator2>
	  void _M_init_diagonal(_InputIterator1 __meanbegin,
				_InputIterator1 __meanend,
				_InputIterator2 __varbegin,
				_InputIterator2 __varend);

	std::array<_RealType, _Dimen> _M_mean;
	std::array<_RealType, _M_t_size> _M_t;
      };

    public:
      normal_mv_distribution()
      : _M_param(), _M_nd()
      { }

      template<typename _ForwardIterator1, typename _ForwardIterator2>
	normal_mv_distribution(_ForwardIterator1 __meanbegin,
			       _ForwardIterator1 __meanend,
			       _ForwardIterator2 __varcovbegin,
			       _ForwardIterator2 __varcovend)
	: _M_param(__meanbegin, __meanend, __varcovbegin, __varcovend),
	  _M_nd()
	{ }

      normal_mv_distribution(std::initializer_list<_RealType> __mean,
			     std::initializer_list<_RealType> __varcov)
      : _M_param(__mean, __varcov), _M_nd()
      { }

      explicit
      normal_mv_distribution(const param_type& __p)
      : _M_param(__p), _M_nd()
      { }

      /**
       * @brief Resets the distribution state.
       */
      void
      reset()
      { _M_nd.reset(); }

      /**
       * @brief Returns the mean of the distribution.
       */
      result_type
      mean() const
      { return _M_param.mean(); }

      /**
       * @brief Returns the compact form of the variance/covariance
       * matrix of the distribution.
       */
      std::array<_RealType, _Dimen * (_Dimen + 1) / 2>
      varcov() const
      { return _M_param.varcov(); }

      /**
       * @brief Returns the parameter set of the distribution.
       */
      param_type
      param() const
      { return _M_param; }

      /**
       * @brief Sets the parameter set of the distribution.
       * @param __param The new parameter set of the distribution.
       */
      void
      param(const param_type& __param)
      { _M_param = __param; }

      /**
       * @brief Returns the greatest lower bound value of the distribution.
       */
      result_type
      min() const
      { result_type __res;
	__res.fill(std::numeric_limits<_RealType>::min());
	return __res; }

      /**
       * @brief Returns the least upper bound value of the distribution.
       */
      result_type
      max() const
      { result_type __res;
	__res.fill(std::numeric_limits<_RealType>::max());
	return __res; }

      /**
       * @brief Generating functions.
       */
      template<typename _UniformRandomNumberGenerator>
	result_type
	operator()(_UniformRandomNumberGenerator& __urng)
	{ return this->operator()(__urng, this->param()); }

      template<typename _UniformRandomNumberGenerator>
	result_type
	operator()(_UniformRandomNumberGenerator& __urng,
		   const param_type& __p);

      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate(_ForwardIterator __f, _ForwardIterator __t,
		   _UniformRandomNumberGenerator& __urng)
	{ return this->__generate_impl(__f, __t, __urng, this->param()); }

      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate(_ForwardIterator __f, _ForwardIterator __t,
		   _UniformRandomNumberGenerator& __urng,
		   const param_type& __p)
	{ return this->__generate_impl(__f, __t, __urng, __p); }

      /**
       * @brief Return true if two multi-variant normal distributions have
       *        the same parameters and the sequences that would
       *        be generated are equal.
       */
      template<size_t _Dimen1, typename _RealType1>
	friend bool
	operator==(const
		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
		   __d1,
		   const
		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
		   __d2);

      /**
       * @brief Inserts a %normal_mv_distribution random number distribution
       * @p __x into the output stream @p __os.
       *
       * @param __os An output stream.
       * @param __x  A %normal_mv_distribution random number distribution.
       *
       * @returns The output stream with the state of @p __x inserted or in
       * an error state.
       */
      template<size_t _Dimen1, typename _RealType1,
	       typename _CharT, typename _Traits>
	friend std::basic_ostream<_CharT, _Traits>&
	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
		   const
		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
		   __x);

      /**
       * @brief Extracts a %normal_mv_distribution random number distribution
       * @p __x from the input stream @p __is.
       *
       * @param __is An input stream.
       * @param __x  A %normal_mv_distribution random number generator engine.
       *
       * @returns The input stream with @p __x extracted or in an error
       *          state.
       */
      template<size_t _Dimen1, typename _RealType1,
	       typename _CharT, typename _Traits>
	friend std::basic_istream<_CharT, _Traits>&
	operator>>(std::basic_istream<_CharT, _Traits>& __is,
		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
		   __x);

    private:
      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
			_UniformRandomNumberGenerator& __urng,
			const param_type& __p);

      param_type _M_param;
      std::normal_distribution<_RealType> _M_nd;
  };

  /**
   * @brief Return true if two multi-variate normal distributions are
   * different.
   */
  template<size_t _Dimen, typename _RealType>
    inline bool
    operator!=(const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
	       __d1,
	       const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
	       __d2)
    { return !(__d1 == __d2); }


  /**
   * @brief A Rice continuous distribution for random numbers.
   *
   * The formula for the Rice probability density function is
   * @f[
   *     p(x|\nu,\sigma) = \frac{x}{\sigma^2}
   *                       \exp\left(-\frac{x^2+\nu^2}{2\sigma^2}\right)
   *                       I_0\left(\frac{x \nu}{\sigma^2}\right)
   * @f]
   * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
   * of order 0 and @f$\nu >= 0@f$ and @f$\sigma > 0@f$.
   *
   * <table border=1 cellpadding=10 cellspacing=0>
   * <caption align=top>Distribution Statistics</caption>
   * <tr><td>Mean</td><td>@f$\sqrt{\pi/2}L_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
   * <tr><td>Variance</td><td>@f$2\sigma^2 + \nu^2
   *                   + (\pi\sigma^2/2)L^2_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
   * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
   * </table>
   * where @f$L_{1/2}(x)@f$ is the Laguerre polynomial of order 1/2.
   */
  template<typename _RealType = double>
    class
    rice_distribution
    {
      static_assert(std::is_floating_point<_RealType>::value,
		    "template argument not a floating point type");
    public:
      /** The type of the range of the distribution. */
      typedef _RealType result_type;
      /** Parameter type. */
      struct param_type
      {
	typedef rice_distribution<result_type> distribution_type;

	param_type(result_type __nu = result_type(0),
		   result_type __sigma = result_type(1))
	: _M_nu(__nu), _M_sigma(__sigma)
	{
	  _GLIBCXX_DEBUG_ASSERT(_M_nu >= result_type(0));
	  _GLIBCXX_DEBUG_ASSERT(_M_sigma > result_type(0));
	}

	result_type
	nu() const
	{ return _M_nu; }

	result_type
	sigma() const
	{ return _M_sigma; }

	friend bool
	operator==(const param_type& __p1, const param_type& __p2)
	{ return __p1._M_nu == __p2._M_nu
              && __p1._M_sigma == __p2._M_sigma; }

      private:
	void _M_initialize();

	result_type _M_nu;
	result_type _M_sigma;
      };

      /**
       * @brief Constructors.
       */
      explicit
      rice_distribution(result_type __nu = result_type(0),
			result_type __sigma = result_type(1))
      : _M_param(__nu, __sigma),
	_M_ndx(__nu, __sigma),
	_M_ndy(result_type(0), __sigma)
      { }

      explicit
      rice_distribution(const param_type& __p)
      : _M_param(__p),
	_M_ndx(__p.nu(), __p.sigma()),
	_M_ndy(result_type(0), __p.sigma())
      { }

      /**
       * @brief Resets the distribution state.
       */
      void
      reset()
      {
	_M_ndx.reset();
	_M_ndy.reset();
      }

      /**
       * @brief Return the parameters of the distribution.
       */
      result_type
      nu() const
      { return _M_param.nu(); }

      result_type
      sigma() const
      { return _M_param.sigma(); }

      /**
       * @brief Returns the parameter set of the distribution.
       */
      param_type
      param() const
      { return _M_param; }

      /**
       * @brief Sets the parameter set of the distribution.
       * @param __param The new parameter set of the distribution.
       */
      void
      param(const param_type& __param)
      { _M_param = __param; }

      /**
       * @brief Returns the greatest lower bound value of the distribution.
       */
      result_type
      min() const
      { return result_type(0); }

      /**
       * @brief Returns the least upper bound value of the distribution.
       */
      result_type
      max() const
      { return std::numeric_limits<result_type>::max(); }

      /**
       * @brief Generating functions.
       */
      template<typename _UniformRandomNumberGenerator>
	result_type
	operator()(_UniformRandomNumberGenerator& __urng)
	{
	  result_type __x = this->_M_ndx(__urng);
	  result_type __y = this->_M_ndy(__urng);
	  return std::hypot(__x, __y);
	}

      template<typename _UniformRandomNumberGenerator>
	result_type
	operator()(_UniformRandomNumberGenerator& __urng,
		   const param_type& __p)
        {
	  typename std::normal_distribution<result_type>::param_type
	    __px(__p.nu(), __p.sigma()), __py(result_type(0), __p.sigma());
	  result_type __x = this->_M_ndx(__px, __urng);
	  result_type __y = this->_M_ndy(__py, __urng);
	  return std::hypot(__x, __y);
	}

      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate(_ForwardIterator __f, _ForwardIterator __t,
		   _UniformRandomNumberGenerator& __urng)
	{ this->__generate(__f, __t, __urng, this->param()); }

      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate(_ForwardIterator __f, _ForwardIterator __t,
		   _UniformRandomNumberGenerator& __urng,
		   const param_type& __p)
	{ this->__generate_impl(__f, __t, __urng, __p); }

      template<typename _UniformRandomNumberGenerator>
	void
	__generate(result_type* __f, result_type* __t,
		   _UniformRandomNumberGenerator& __urng,
		   const param_type& __p)
	{ this->__generate_impl(__f, __t, __urng, __p); }

      /**
       * @brief Return true if two Rice distributions have
       *        the same parameters and the sequences that would
       *        be generated are equal.
       */
      friend bool
      operator==(const rice_distribution& __d1,
		 const rice_distribution& __d2)
      { return (__d1.param() == __d2.param()
		&& __d1._M_ndx == __d2._M_ndx
		&& __d1._M_ndy == __d2._M_ndy); }

      /**
       * @brief Inserts a %rice_distribution random number distribution
       * @p __x into the output stream @p __os.
       *
       * @param __os An output stream.
       * @param __x  A %rice_distribution random number distribution.
       *
       * @returns The output stream with the state of @p __x inserted or in
       * an error state.
       */
      template<typename _RealType1, typename _CharT, typename _Traits>
	friend std::basic_ostream<_CharT, _Traits>&
	operator<<(std::basic_ostream<_CharT, _Traits>&,
		   const rice_distribution<_RealType1>&);

      /**
       * @brief Extracts a %rice_distribution random number distribution
       * @p __x from the input stream @p __is.
       *
       * @param __is An input stream.
       * @param __x A %rice_distribution random number
       *            generator engine.
       *
       * @returns The input stream with @p __x extracted or in an error state.
       */
      template<typename _RealType1, typename _CharT, typename _Traits>
	friend std::basic_istream<_CharT, _Traits>&
	operator>>(std::basic_istream<_CharT, _Traits>&,
		   rice_distribution<_RealType1>&);

    private:
      template<typename _ForwardIterator,
	       typename _UniformRandomNumberGenerator>
	void
	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
			_UniformRandomNumberGenerator& __urng,
			const param_type& __p);

      param_type _M_param;

      std::normal_distribution<result_type> _M_ndx;
      std::normal_distribution<result_type> _M_ndy;
    };

  /**
   * @brief Return true if two Rice distributions are not equal.
   */
  template<typename _RealType1>
    inline bool
    operator!=(const rice_distribution<_RealType1>& __d1,
	       const rice_distribution<_RealType1>& __d2)
    { return !(__d1 == __d2); }

_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std

#include "random.tcc"

#endif /* _EXT_RANDOM */