1// Random number extensions -*- C++ -*-
2
3// Copyright (C) 2012-2020 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library.  This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file ext/random
26 *  This file is a GNU extension to the Standard C++ Library.
27 */
28
29#ifndef _EXT_RANDOM
30#define _EXT_RANDOM 1
31
32#pragma GCC system_header
33
34#if __cplusplus < 201103L
35# include <bits/c++0x_warning.h>
36#else
37
38#include <random>
39#include <algorithm>
40#include <array>
41#include <ext/cmath>
42#ifdef __SSE2__
43# include <emmintrin.h>
44#endif
45
46#if defined(_GLIBCXX_USE_C99_STDINT_TR1) && defined(UINT32_C)
47
48namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
49{
50_GLIBCXX_BEGIN_NAMESPACE_VERSION
51
52#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
53
54  /* Mersenne twister implementation optimized for vector operations.
55   *
56   * Reference: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/
57   */
58  template<typename _UIntType, size_t __m,
59	   size_t __pos1, size_t __sl1, size_t __sl2,
60	   size_t __sr1, size_t __sr2,
61	   uint32_t __msk1, uint32_t __msk2,
62	   uint32_t __msk3, uint32_t __msk4,
63	   uint32_t __parity1, uint32_t __parity2,
64	   uint32_t __parity3, uint32_t __parity4>
65    class simd_fast_mersenne_twister_engine
66    {
67      static_assert(std::is_unsigned<_UIntType>::value, "template argument "
68		    "substituting _UIntType not an unsigned integral type");
69      static_assert(__sr1 < 32, "first right shift too large");
70      static_assert(__sr2 < 16, "second right shift too large");
71      static_assert(__sl1 < 32, "first left shift too large");
72      static_assert(__sl2 < 16, "second left shift too large");
73
74    public:
75      typedef _UIntType result_type;
76
77    private:
78      static constexpr size_t m_w = sizeof(result_type) * 8;
79      static constexpr size_t _M_nstate = __m / 128 + 1;
80      static constexpr size_t _M_nstate32 = _M_nstate * 4;
81
82      static_assert(std::is_unsigned<_UIntType>::value, "template argument "
83		    "substituting _UIntType not an unsigned integral type");
84      static_assert(__pos1 < _M_nstate, "POS1 not smaller than state size");
85      static_assert(16 % sizeof(_UIntType) == 0,
86		    "UIntType size must divide 16");
87
88      template<typename _Sseq>
89	using _If_seed_seq
90	  = typename std::enable_if<std::__detail::__is_seed_seq<
91	    _Sseq, simd_fast_mersenne_twister_engine, result_type>::value
92	    >::type;
93
94    public:
95      static constexpr size_t state_size = _M_nstate * (16
96							/ sizeof(result_type));
97      static constexpr result_type default_seed = 5489u;
98
99      // constructors and member functions
100
101      simd_fast_mersenne_twister_engine()
102      : simd_fast_mersenne_twister_engine(default_seed)
103      { }
104
105      explicit
106      simd_fast_mersenne_twister_engine(result_type __sd)
107      { seed(__sd); }
108
109      template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
110	explicit
111	simd_fast_mersenne_twister_engine(_Sseq& __q)
112	{ seed(__q); }
113
114      void
115      seed(result_type __sd = default_seed);
116
117      template<typename _Sseq>
118	_If_seed_seq<_Sseq>
119	seed(_Sseq& __q);
120
121      static constexpr result_type
122      min()
123      { return 0; }
124
125      static constexpr result_type
126      max()
127      { return std::numeric_limits<result_type>::max(); }
128
129      void
130      discard(unsigned long long __z);
131
132      result_type
133      operator()()
134      {
135	if (__builtin_expect(_M_pos >= state_size, 0))
136	  _M_gen_rand();
137
138	return _M_stateT[_M_pos++];
139      }
140
141      template<typename _UIntType_2, size_t __m_2,
142	       size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
143	       size_t __sr1_2, size_t __sr2_2,
144	       uint32_t __msk1_2, uint32_t __msk2_2,
145	       uint32_t __msk3_2, uint32_t __msk4_2,
146	       uint32_t __parity1_2, uint32_t __parity2_2,
147	       uint32_t __parity3_2, uint32_t __parity4_2>
148	friend bool
149	operator==(const simd_fast_mersenne_twister_engine<_UIntType_2,
150		   __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
151		   __msk1_2, __msk2_2, __msk3_2, __msk4_2,
152		   __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __lhs,
153		   const simd_fast_mersenne_twister_engine<_UIntType_2,
154		   __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
155		   __msk1_2, __msk2_2, __msk3_2, __msk4_2,
156		   __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __rhs);
157
158      template<typename _UIntType_2, size_t __m_2,
159	       size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
160	       size_t __sr1_2, size_t __sr2_2,
161	       uint32_t __msk1_2, uint32_t __msk2_2,
162	       uint32_t __msk3_2, uint32_t __msk4_2,
163	       uint32_t __parity1_2, uint32_t __parity2_2,
164	       uint32_t __parity3_2, uint32_t __parity4_2,
165	       typename _CharT, typename _Traits>
166	friend std::basic_ostream<_CharT, _Traits>&
167	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
168		   const __gnu_cxx::simd_fast_mersenne_twister_engine
169		   <_UIntType_2,
170		   __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
171		   __msk1_2, __msk2_2, __msk3_2, __msk4_2,
172		   __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);
173
174      template<typename _UIntType_2, size_t __m_2,
175	       size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
176	       size_t __sr1_2, size_t __sr2_2,
177	       uint32_t __msk1_2, uint32_t __msk2_2,
178	       uint32_t __msk3_2, uint32_t __msk4_2,
179	       uint32_t __parity1_2, uint32_t __parity2_2,
180	       uint32_t __parity3_2, uint32_t __parity4_2,
181	       typename _CharT, typename _Traits>
182	friend std::basic_istream<_CharT, _Traits>&
183	operator>>(std::basic_istream<_CharT, _Traits>& __is,
184		   __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType_2,
185		   __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
186		   __msk1_2, __msk2_2, __msk3_2, __msk4_2,
187		   __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);
188
189    private:
190      union
191      {
192#ifdef __SSE2__
193	__m128i _M_state[_M_nstate];
194#endif
195#ifdef __ARM_NEON
196#ifdef __aarch64__
197	__Uint32x4_t _M_state[_M_nstate];
198#endif
199#endif
200	uint32_t _M_state32[_M_nstate32];
201	result_type _M_stateT[state_size];
202      } __attribute__ ((__aligned__ (16)));
203      size_t _M_pos;
204
205      void _M_gen_rand(void);
206      void _M_period_certification();
207  };
208
209
210  template<typename _UIntType, size_t __m,
211	   size_t __pos1, size_t __sl1, size_t __sl2,
212	   size_t __sr1, size_t __sr2,
213	   uint32_t __msk1, uint32_t __msk2,
214	   uint32_t __msk3, uint32_t __msk4,
215	   uint32_t __parity1, uint32_t __parity2,
216	   uint32_t __parity3, uint32_t __parity4>
217    inline bool
218    operator!=(const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
219	       __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
220	       __msk4, __parity1, __parity2, __parity3, __parity4>& __lhs,
221	       const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
222	       __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
223	       __msk4, __parity1, __parity2, __parity3, __parity4>& __rhs)
224    { return !(__lhs == __rhs); }
225
226
227  /* Definitions for the SIMD-oriented Fast Mersenne Twister as defined
228   * in the C implementation by Daito and Matsumoto, as both a 32-bit
229   * and 64-bit version.
230   */
231  typedef simd_fast_mersenne_twister_engine<uint32_t, 607, 2,
232					    15, 3, 13, 3,
233					    0xfdff37ffU, 0xef7f3f7dU,
234					    0xff777b7dU, 0x7ff7fb2fU,
235					    0x00000001U, 0x00000000U,
236					    0x00000000U, 0x5986f054U>
237    sfmt607;
238
239  typedef simd_fast_mersenne_twister_engine<uint64_t, 607, 2,
240					    15, 3, 13, 3,
241					    0xfdff37ffU, 0xef7f3f7dU,
242					    0xff777b7dU, 0x7ff7fb2fU,
243					    0x00000001U, 0x00000000U,
244					    0x00000000U, 0x5986f054U>
245    sfmt607_64;
246
247
248  typedef simd_fast_mersenne_twister_engine<uint32_t, 1279, 7,
249					    14, 3, 5, 1,
250					    0xf7fefffdU, 0x7fefcfffU,
251					    0xaff3ef3fU, 0xb5ffff7fU,
252					    0x00000001U, 0x00000000U,
253					    0x00000000U, 0x20000000U>
254    sfmt1279;
255
256  typedef simd_fast_mersenne_twister_engine<uint64_t, 1279, 7,
257					    14, 3, 5, 1,
258					    0xf7fefffdU, 0x7fefcfffU,
259					    0xaff3ef3fU, 0xb5ffff7fU,
260					    0x00000001U, 0x00000000U,
261					    0x00000000U, 0x20000000U>
262    sfmt1279_64;
263
264
265  typedef simd_fast_mersenne_twister_engine<uint32_t, 2281, 12,
266					    19, 1, 5, 1,
267					    0xbff7ffbfU, 0xfdfffffeU,
268					    0xf7ffef7fU, 0xf2f7cbbfU,
269					    0x00000001U, 0x00000000U,
270					    0x00000000U, 0x41dfa600U>
271    sfmt2281;
272
273  typedef simd_fast_mersenne_twister_engine<uint64_t, 2281, 12,
274					    19, 1, 5, 1,
275					    0xbff7ffbfU, 0xfdfffffeU,
276					    0xf7ffef7fU, 0xf2f7cbbfU,
277					    0x00000001U, 0x00000000U,
278					    0x00000000U, 0x41dfa600U>
279    sfmt2281_64;
280
281
282  typedef simd_fast_mersenne_twister_engine<uint32_t, 4253, 17,
283					    20, 1, 7, 1,
284					    0x9f7bffffU, 0x9fffff5fU,
285					    0x3efffffbU, 0xfffff7bbU,
286					    0xa8000001U, 0xaf5390a3U,
287					    0xb740b3f8U, 0x6c11486dU>
288    sfmt4253;
289
290  typedef simd_fast_mersenne_twister_engine<uint64_t, 4253, 17,
291					    20, 1, 7, 1,
292					    0x9f7bffffU, 0x9fffff5fU,
293					    0x3efffffbU, 0xfffff7bbU,
294					    0xa8000001U, 0xaf5390a3U,
295					    0xb740b3f8U, 0x6c11486dU>
296    sfmt4253_64;
297
298
299  typedef simd_fast_mersenne_twister_engine<uint32_t, 11213, 68,
300					    14, 3, 7, 3,
301					    0xeffff7fbU, 0xffffffefU,
302					    0xdfdfbfffU, 0x7fffdbfdU,
303					    0x00000001U, 0x00000000U,
304					    0xe8148000U, 0xd0c7afa3U>
305    sfmt11213;
306
307  typedef simd_fast_mersenne_twister_engine<uint64_t, 11213, 68,
308					    14, 3, 7, 3,
309					    0xeffff7fbU, 0xffffffefU,
310					    0xdfdfbfffU, 0x7fffdbfdU,
311					    0x00000001U, 0x00000000U,
312					    0xe8148000U, 0xd0c7afa3U>
313    sfmt11213_64;
314
315
316  typedef simd_fast_mersenne_twister_engine<uint32_t, 19937, 122,
317					    18, 1, 11, 1,
318					    0xdfffffefU, 0xddfecb7fU,
319					    0xbffaffffU, 0xbffffff6U,
320					    0x00000001U, 0x00000000U,
321					    0x00000000U, 0x13c9e684U>
322    sfmt19937;
323
324  typedef simd_fast_mersenne_twister_engine<uint64_t, 19937, 122,
325					    18, 1, 11, 1,
326					    0xdfffffefU, 0xddfecb7fU,
327					    0xbffaffffU, 0xbffffff6U,
328					    0x00000001U, 0x00000000U,
329					    0x00000000U, 0x13c9e684U>
330    sfmt19937_64;
331
332
333  typedef simd_fast_mersenne_twister_engine<uint32_t, 44497, 330,
334					    5, 3, 9, 3,
335					    0xeffffffbU, 0xdfbebfffU,
336					    0xbfbf7befU, 0x9ffd7bffU,
337					    0x00000001U, 0x00000000U,
338					    0xa3ac4000U, 0xecc1327aU>
339    sfmt44497;
340
341  typedef simd_fast_mersenne_twister_engine<uint64_t, 44497, 330,
342					    5, 3, 9, 3,
343					    0xeffffffbU, 0xdfbebfffU,
344					    0xbfbf7befU, 0x9ffd7bffU,
345					    0x00000001U, 0x00000000U,
346					    0xa3ac4000U, 0xecc1327aU>
347    sfmt44497_64;
348
349
350  typedef simd_fast_mersenne_twister_engine<uint32_t, 86243, 366,
351					    6, 7, 19, 1,
352					    0xfdbffbffU, 0xbff7ff3fU,
353					    0xfd77efffU, 0xbf9ff3ffU,
354					    0x00000001U, 0x00000000U,
355					    0x00000000U, 0xe9528d85U>
356    sfmt86243;
357
358  typedef simd_fast_mersenne_twister_engine<uint64_t, 86243, 366,
359					    6, 7, 19, 1,
360					    0xfdbffbffU, 0xbff7ff3fU,
361					    0xfd77efffU, 0xbf9ff3ffU,
362					    0x00000001U, 0x00000000U,
363					    0x00000000U, 0xe9528d85U>
364    sfmt86243_64;
365
366
367  typedef simd_fast_mersenne_twister_engine<uint32_t, 132049, 110,
368					    19, 1, 21, 1,
369					    0xffffbb5fU, 0xfb6ebf95U,
370					    0xfffefffaU, 0xcff77fffU,
371					    0x00000001U, 0x00000000U,
372					    0xcb520000U, 0xc7e91c7dU>
373    sfmt132049;
374
375  typedef simd_fast_mersenne_twister_engine<uint64_t, 132049, 110,
376					    19, 1, 21, 1,
377					    0xffffbb5fU, 0xfb6ebf95U,
378					    0xfffefffaU, 0xcff77fffU,
379					    0x00000001U, 0x00000000U,
380					    0xcb520000U, 0xc7e91c7dU>
381    sfmt132049_64;
382
383
384  typedef simd_fast_mersenne_twister_engine<uint32_t, 216091, 627,
385					    11, 3, 10, 1,
386					    0xbff7bff7U, 0xbfffffffU,
387					    0xbffffa7fU, 0xffddfbfbU,
388					    0xf8000001U, 0x89e80709U,
389					    0x3bd2b64bU, 0x0c64b1e4U>
390    sfmt216091;
391
392  typedef simd_fast_mersenne_twister_engine<uint64_t, 216091, 627,
393					    11, 3, 10, 1,
394					    0xbff7bff7U, 0xbfffffffU,
395					    0xbffffa7fU, 0xffddfbfbU,
396					    0xf8000001U, 0x89e80709U,
397					    0x3bd2b64bU, 0x0c64b1e4U>
398    sfmt216091_64;
399
400#endif // __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
401
402  /**
403   * @brief A beta continuous distribution for random numbers.
404   *
405   * The formula for the beta probability density function is:
406   * @f[
407   *     p(x|\alpha,\beta) = \frac{1}{B(\alpha,\beta)}
408   *                         x^{\alpha - 1} (1 - x)^{\beta - 1}
409   * @f]
410   */
411  template<typename _RealType = double>
412    class beta_distribution
413    {
414      static_assert(std::is_floating_point<_RealType>::value,
415		    "template argument not a floating point type");
416
417    public:
418      /** The type of the range of the distribution. */
419      typedef _RealType result_type;
420
421      /** Parameter type. */
422      struct param_type
423      {
424	typedef beta_distribution<_RealType> distribution_type;
425	friend class beta_distribution<_RealType>;
426
427	param_type() : param_type(1) { }
428
429	explicit
430	param_type(_RealType __alpha_val, _RealType __beta_val = _RealType(1))
431	: _M_alpha(__alpha_val), _M_beta(__beta_val)
432	{
433	  __glibcxx_assert(_M_alpha > _RealType(0));
434	  __glibcxx_assert(_M_beta > _RealType(0));
435	}
436
437	_RealType
438	alpha() const
439	{ return _M_alpha; }
440
441	_RealType
442	beta() const
443	{ return _M_beta; }
444
445	friend bool
446	operator==(const param_type& __p1, const param_type& __p2)
447	{ return (__p1._M_alpha == __p2._M_alpha
448		  && __p1._M_beta == __p2._M_beta); }
449
450	friend bool
451	operator!=(const param_type& __p1, const param_type& __p2)
452	{ return !(__p1 == __p2); }
453
454      private:
455	void
456	_M_initialize();
457
458	_RealType _M_alpha;
459	_RealType _M_beta;
460      };
461
462    public:
463      beta_distribution() : beta_distribution(1.0) { }
464
465      /**
466       * @brief Constructs a beta distribution with parameters
467       * @f$\alpha@f$ and @f$\beta@f$.
468       */
469      explicit
470      beta_distribution(_RealType __alpha_val,
471			_RealType __beta_val = _RealType(1))
472      : _M_param(__alpha_val, __beta_val)
473      { }
474
475      explicit
476      beta_distribution(const param_type& __p)
477      : _M_param(__p)
478      { }
479
480      /**
481       * @brief Resets the distribution state.
482       */
483      void
484      reset()
485      { }
486
487      /**
488       * @brief Returns the @f$\alpha@f$ of the distribution.
489       */
490      _RealType
491      alpha() const
492      { return _M_param.alpha(); }
493
494      /**
495       * @brief Returns the @f$\beta@f$ of the distribution.
496       */
497      _RealType
498      beta() const
499      { return _M_param.beta(); }
500
501      /**
502       * @brief Returns the parameter set of the distribution.
503       */
504      param_type
505      param() const
506      { return _M_param; }
507
508      /**
509       * @brief Sets the parameter set of the distribution.
510       * @param __param The new parameter set of the distribution.
511       */
512      void
513      param(const param_type& __param)
514      { _M_param = __param; }
515
516      /**
517       * @brief Returns the greatest lower bound value of the distribution.
518       */
519      result_type
520      min() const
521      { return result_type(0); }
522
523      /**
524       * @brief Returns the least upper bound value of the distribution.
525       */
526      result_type
527      max() const
528      { return result_type(1); }
529
530      /**
531       * @brief Generating functions.
532       */
533      template<typename _UniformRandomNumberGenerator>
534	result_type
535	operator()(_UniformRandomNumberGenerator& __urng)
536	{ return this->operator()(__urng, _M_param); }
537
538      template<typename _UniformRandomNumberGenerator>
539	result_type
540	operator()(_UniformRandomNumberGenerator& __urng,
541		   const param_type& __p);
542
543      template<typename _ForwardIterator,
544	       typename _UniformRandomNumberGenerator>
545	void
546	__generate(_ForwardIterator __f, _ForwardIterator __t,
547		   _UniformRandomNumberGenerator& __urng)
548	{ this->__generate(__f, __t, __urng, _M_param); }
549
550      template<typename _ForwardIterator,
551	       typename _UniformRandomNumberGenerator>
552	void
553	__generate(_ForwardIterator __f, _ForwardIterator __t,
554		   _UniformRandomNumberGenerator& __urng,
555		   const param_type& __p)
556	{ this->__generate_impl(__f, __t, __urng, __p); }
557
558      template<typename _UniformRandomNumberGenerator>
559	void
560	__generate(result_type* __f, result_type* __t,
561		   _UniformRandomNumberGenerator& __urng,
562		   const param_type& __p)
563	{ this->__generate_impl(__f, __t, __urng, __p); }
564
565      /**
566       * @brief Return true if two beta distributions have the same
567       *        parameters and the sequences that would be generated
568       *        are equal.
569       */
570      friend bool
571      operator==(const beta_distribution& __d1,
572		 const beta_distribution& __d2)
573      { return __d1._M_param == __d2._M_param; }
574
575      /**
576       * @brief Inserts a %beta_distribution random number distribution
577       * @p __x into the output stream @p __os.
578       *
579       * @param __os An output stream.
580       * @param __x  A %beta_distribution random number distribution.
581       *
582       * @returns The output stream with the state of @p __x inserted or in
583       * an error state.
584       */
585      template<typename _RealType1, typename _CharT, typename _Traits>
586	friend std::basic_ostream<_CharT, _Traits>&
587	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
588		   const __gnu_cxx::beta_distribution<_RealType1>& __x);
589
590      /**
591       * @brief Extracts a %beta_distribution random number distribution
592       * @p __x from the input stream @p __is.
593       *
594       * @param __is An input stream.
595       * @param __x  A %beta_distribution random number generator engine.
596       *
597       * @returns The input stream with @p __x extracted or in an error state.
598       */
599      template<typename _RealType1, typename _CharT, typename _Traits>
600	friend std::basic_istream<_CharT, _Traits>&
601	operator>>(std::basic_istream<_CharT, _Traits>& __is,
602		   __gnu_cxx::beta_distribution<_RealType1>& __x);
603
604    private:
605      template<typename _ForwardIterator,
606	       typename _UniformRandomNumberGenerator>
607	void
608	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
609			_UniformRandomNumberGenerator& __urng,
610			const param_type& __p);
611
612      param_type _M_param;
613    };
614
615  /**
616   * @brief Return true if two beta distributions are different.
617   */
618  template<typename _RealType>
619    inline bool
620    operator!=(const __gnu_cxx::beta_distribution<_RealType>& __d1,
621	       const __gnu_cxx::beta_distribution<_RealType>& __d2)
622    { return !(__d1 == __d2); }
623
624
625  /**
626   * @brief A multi-variate normal continuous distribution for random numbers.
627   *
628   * The formula for the normal probability density function is
629   * @f[
630   *     p(\overrightarrow{x}|\overrightarrow{\mu },\Sigma) =
631   *       \frac{1}{\sqrt{(2\pi )^k\det(\Sigma))}}
632   *       e^{-\frac{1}{2}(\overrightarrow{x}-\overrightarrow{\mu})^\text{T}
633   *          \Sigma ^{-1}(\overrightarrow{x}-\overrightarrow{\mu})}
634   * @f]
635   *
636   * where @f$\overrightarrow{x}@f$ and @f$\overrightarrow{\mu}@f$ are
637   * vectors of dimension @f$k@f$ and @f$\Sigma@f$ is the covariance
638   * matrix (which must be positive-definite).
639   */
640  template<std::size_t _Dimen, typename _RealType = double>
641    class normal_mv_distribution
642    {
643      static_assert(std::is_floating_point<_RealType>::value,
644		    "template argument not a floating point type");
645      static_assert(_Dimen != 0, "dimension is zero");
646
647    public:
648      /** The type of the range of the distribution. */
649      typedef std::array<_RealType, _Dimen> result_type;
650      /** Parameter type. */
651      class param_type
652      {
653	static constexpr size_t _M_t_size = _Dimen * (_Dimen + 1) / 2;
654
655      public:
656	typedef normal_mv_distribution<_Dimen, _RealType> distribution_type;
657	friend class normal_mv_distribution<_Dimen, _RealType>;
658
659	param_type()
660	{
661	  std::fill(_M_mean.begin(), _M_mean.end(), _RealType(0));
662	  auto __it = _M_t.begin();
663	  for (size_t __i = 0; __i < _Dimen; ++__i)
664	    {
665	      std::fill_n(__it, __i, _RealType(0));
666	      __it += __i;
667	      *__it++ = _RealType(1);
668	    }
669	}
670
671	template<typename _ForwardIterator1, typename _ForwardIterator2>
672	  param_type(_ForwardIterator1 __meanbegin,
673		     _ForwardIterator1 __meanend,
674		     _ForwardIterator2 __varcovbegin,
675		     _ForwardIterator2 __varcovend)
676	{
677	  __glibcxx_function_requires(_ForwardIteratorConcept<
678				      _ForwardIterator1>)
679	  __glibcxx_function_requires(_ForwardIteratorConcept<
680				      _ForwardIterator2>)
681	  _GLIBCXX_DEBUG_ASSERT(std::distance(__meanbegin, __meanend)
682				<= _Dimen);
683	  const auto __dist = std::distance(__varcovbegin, __varcovend);
684	  _GLIBCXX_DEBUG_ASSERT(__dist == _Dimen * _Dimen
685				|| __dist == _Dimen * (_Dimen + 1) / 2
686				|| __dist == _Dimen);
687
688	  if (__dist == _Dimen * _Dimen)
689	    _M_init_full(__meanbegin, __meanend, __varcovbegin, __varcovend);
690	  else if (__dist == _Dimen * (_Dimen + 1) / 2)
691	    _M_init_lower(__meanbegin, __meanend, __varcovbegin, __varcovend);
692	  else
693	    {
694	      __glibcxx_assert(__dist == _Dimen);
695	      _M_init_diagonal(__meanbegin, __meanend,
696			       __varcovbegin, __varcovend);
697	    }
698	}
699
700	param_type(std::initializer_list<_RealType> __mean,
701		   std::initializer_list<_RealType> __varcov)
702	{
703	  _GLIBCXX_DEBUG_ASSERT(__mean.size() <= _Dimen);
704	  _GLIBCXX_DEBUG_ASSERT(__varcov.size() == _Dimen * _Dimen
705				|| __varcov.size() == _Dimen * (_Dimen + 1) / 2
706				|| __varcov.size() == _Dimen);
707
708	  if (__varcov.size() == _Dimen * _Dimen)
709	    _M_init_full(__mean.begin(), __mean.end(),
710			 __varcov.begin(), __varcov.end());
711	  else if (__varcov.size() == _Dimen * (_Dimen + 1) / 2)
712	    _M_init_lower(__mean.begin(), __mean.end(),
713			  __varcov.begin(), __varcov.end());
714	  else
715	    {
716	      __glibcxx_assert(__varcov.size() == _Dimen);
717	      _M_init_diagonal(__mean.begin(), __mean.end(),
718			       __varcov.begin(), __varcov.end());
719	    }
720	}
721
722	std::array<_RealType, _Dimen>
723	mean() const
724	{ return _M_mean; }
725
726	std::array<_RealType, _M_t_size>
727	varcov() const
728	{ return _M_t; }
729
730	friend bool
731	operator==(const param_type& __p1, const param_type& __p2)
732	{ return __p1._M_mean == __p2._M_mean && __p1._M_t == __p2._M_t; }
733
734	friend bool
735	operator!=(const param_type& __p1, const param_type& __p2)
736	{ return !(__p1 == __p2); }
737
738      private:
739	template <typename _InputIterator1, typename _InputIterator2>
740	  void _M_init_full(_InputIterator1 __meanbegin,
741			    _InputIterator1 __meanend,
742			    _InputIterator2 __varcovbegin,
743			    _InputIterator2 __varcovend);
744	template <typename _InputIterator1, typename _InputIterator2>
745	  void _M_init_lower(_InputIterator1 __meanbegin,
746			     _InputIterator1 __meanend,
747			     _InputIterator2 __varcovbegin,
748			     _InputIterator2 __varcovend);
749	template <typename _InputIterator1, typename _InputIterator2>
750	  void _M_init_diagonal(_InputIterator1 __meanbegin,
751				_InputIterator1 __meanend,
752				_InputIterator2 __varbegin,
753				_InputIterator2 __varend);
754
755	// param_type constructors apply Cholesky decomposition to the
756	// varcov matrix in _M_init_full and _M_init_lower, but the
757	// varcov matrix output ot a stream is already decomposed, so
758	// we need means to restore it as-is when reading it back in.
759	template<size_t _Dimen1, typename _RealType1,
760		 typename _CharT, typename _Traits>
761	friend std::basic_istream<_CharT, _Traits>&
762	operator>>(std::basic_istream<_CharT, _Traits>& __is,
763		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
764		   __x);
765	param_type(std::array<_RealType, _Dimen> const &__mean,
766		   std::array<_RealType, _M_t_size> const &__varcov)
767	  : _M_mean (__mean), _M_t (__varcov)
768	{}
769
770	std::array<_RealType, _Dimen> _M_mean;
771	std::array<_RealType, _M_t_size> _M_t;
772      };
773
774    public:
775      normal_mv_distribution()
776      : _M_param(), _M_nd()
777      { }
778
779      template<typename _ForwardIterator1, typename _ForwardIterator2>
780	normal_mv_distribution(_ForwardIterator1 __meanbegin,
781			       _ForwardIterator1 __meanend,
782			       _ForwardIterator2 __varcovbegin,
783			       _ForwardIterator2 __varcovend)
784	: _M_param(__meanbegin, __meanend, __varcovbegin, __varcovend),
785	  _M_nd()
786	{ }
787
788      normal_mv_distribution(std::initializer_list<_RealType> __mean,
789			     std::initializer_list<_RealType> __varcov)
790      : _M_param(__mean, __varcov), _M_nd()
791      { }
792
793      explicit
794      normal_mv_distribution(const param_type& __p)
795      : _M_param(__p), _M_nd()
796      { }
797
798      /**
799       * @brief Resets the distribution state.
800       */
801      void
802      reset()
803      { _M_nd.reset(); }
804
805      /**
806       * @brief Returns the mean of the distribution.
807       */
808      result_type
809      mean() const
810      { return _M_param.mean(); }
811
812      /**
813       * @brief Returns the compact form of the variance/covariance
814       * matrix of the distribution.
815       */
816      std::array<_RealType, _Dimen * (_Dimen + 1) / 2>
817      varcov() const
818      { return _M_param.varcov(); }
819
820      /**
821       * @brief Returns the parameter set of the distribution.
822       */
823      param_type
824      param() const
825      { return _M_param; }
826
827      /**
828       * @brief Sets the parameter set of the distribution.
829       * @param __param The new parameter set of the distribution.
830       */
831      void
832      param(const param_type& __param)
833      { _M_param = __param; }
834
835      /**
836       * @brief Returns the greatest lower bound value of the distribution.
837       */
838      result_type
839      min() const
840      { result_type __res;
841	__res.fill(std::numeric_limits<_RealType>::lowest());
842	return __res; }
843
844      /**
845       * @brief Returns the least upper bound value of the distribution.
846       */
847      result_type
848      max() const
849      { result_type __res;
850	__res.fill(std::numeric_limits<_RealType>::max());
851	return __res; }
852
853      /**
854       * @brief Generating functions.
855       */
856      template<typename _UniformRandomNumberGenerator>
857	result_type
858	operator()(_UniformRandomNumberGenerator& __urng)
859	{ return this->operator()(__urng, _M_param); }
860
861      template<typename _UniformRandomNumberGenerator>
862	result_type
863	operator()(_UniformRandomNumberGenerator& __urng,
864		   const param_type& __p);
865
866      template<typename _ForwardIterator,
867	       typename _UniformRandomNumberGenerator>
868	void
869	__generate(_ForwardIterator __f, _ForwardIterator __t,
870		   _UniformRandomNumberGenerator& __urng)
871	{ return this->__generate_impl(__f, __t, __urng, _M_param); }
872
873      template<typename _ForwardIterator,
874	       typename _UniformRandomNumberGenerator>
875	void
876	__generate(_ForwardIterator __f, _ForwardIterator __t,
877		   _UniformRandomNumberGenerator& __urng,
878		   const param_type& __p)
879	{ return this->__generate_impl(__f, __t, __urng, __p); }
880
881      /**
882       * @brief Return true if two multi-variant normal distributions have
883       *        the same parameters and the sequences that would
884       *        be generated are equal.
885       */
886      template<size_t _Dimen1, typename _RealType1>
887	friend bool
888	operator==(const
889		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
890		   __d1,
891		   const
892		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
893		   __d2);
894
895      /**
896       * @brief Inserts a %normal_mv_distribution random number distribution
897       * @p __x into the output stream @p __os.
898       *
899       * @param __os An output stream.
900       * @param __x  A %normal_mv_distribution random number distribution.
901       *
902       * @returns The output stream with the state of @p __x inserted or in
903       * an error state.
904       */
905      template<size_t _Dimen1, typename _RealType1,
906	       typename _CharT, typename _Traits>
907	friend std::basic_ostream<_CharT, _Traits>&
908	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
909		   const
910		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
911		   __x);
912
913      /**
914       * @brief Extracts a %normal_mv_distribution random number distribution
915       * @p __x from the input stream @p __is.
916       *
917       * @param __is An input stream.
918       * @param __x  A %normal_mv_distribution random number generator engine.
919       *
920       * @returns The input stream with @p __x extracted or in an error
921       *          state.
922       */
923      template<size_t _Dimen1, typename _RealType1,
924	       typename _CharT, typename _Traits>
925	friend std::basic_istream<_CharT, _Traits>&
926	operator>>(std::basic_istream<_CharT, _Traits>& __is,
927		   __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
928		   __x);
929
930    private:
931      template<typename _ForwardIterator,
932	       typename _UniformRandomNumberGenerator>
933	void
934	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
935			_UniformRandomNumberGenerator& __urng,
936			const param_type& __p);
937
938      param_type _M_param;
939      std::normal_distribution<_RealType> _M_nd;
940  };
941
942  /**
943   * @brief Return true if two multi-variate normal distributions are
944   * different.
945   */
946  template<size_t _Dimen, typename _RealType>
947    inline bool
948    operator!=(const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
949	       __d1,
950	       const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
951	       __d2)
952    { return !(__d1 == __d2); }
953
954
955  /**
956   * @brief A Rice continuous distribution for random numbers.
957   *
958   * The formula for the Rice probability density function is
959   * @f[
960   *     p(x|\nu,\sigma) = \frac{x}{\sigma^2}
961   *                       \exp\left(-\frac{x^2+\nu^2}{2\sigma^2}\right)
962   *                       I_0\left(\frac{x \nu}{\sigma^2}\right)
963   * @f]
964   * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
965   * of order 0 and @f$\nu >= 0@f$ and @f$\sigma > 0@f$.
966   *
967   * <table border=1 cellpadding=10 cellspacing=0>
968   * <caption align=top>Distribution Statistics</caption>
969   * <tr><td>Mean</td><td>@f$\sqrt{\pi/2}L_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
970   * <tr><td>Variance</td><td>@f$2\sigma^2 + \nu^2
971   *                   + (\pi\sigma^2/2)L^2_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
972   * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
973   * </table>
974   * where @f$L_{1/2}(x)@f$ is the Laguerre polynomial of order 1/2.
975   */
976  template<typename _RealType = double>
977    class
978    rice_distribution
979    {
980      static_assert(std::is_floating_point<_RealType>::value,
981		    "template argument not a floating point type");
982    public:
983      /** The type of the range of the distribution. */
984      typedef _RealType result_type;
985
986      /** Parameter type. */
987      struct param_type
988      {
989	typedef rice_distribution<result_type> distribution_type;
990
991	param_type() : param_type(0) { }
992
993	param_type(result_type __nu_val,
994		   result_type __sigma_val = result_type(1))
995	: _M_nu(__nu_val), _M_sigma(__sigma_val)
996	{
997	  __glibcxx_assert(_M_nu >= result_type(0));
998	  __glibcxx_assert(_M_sigma > result_type(0));
999	}
1000
1001	result_type
1002	nu() const
1003	{ return _M_nu; }
1004
1005	result_type
1006	sigma() const
1007	{ return _M_sigma; }
1008
1009	friend bool
1010	operator==(const param_type& __p1, const param_type& __p2)
1011	{ return __p1._M_nu == __p2._M_nu && __p1._M_sigma == __p2._M_sigma; }
1012
1013	friend bool
1014	operator!=(const param_type& __p1, const param_type& __p2)
1015	{ return !(__p1 == __p2); }
1016
1017      private:
1018	void _M_initialize();
1019
1020	result_type _M_nu;
1021	result_type _M_sigma;
1022      };
1023
1024      /**
1025       * @brief Constructors.
1026       * @{
1027       */
1028
1029      rice_distribution() : rice_distribution(0) { }
1030
1031      explicit
1032      rice_distribution(result_type __nu_val,
1033			result_type __sigma_val = result_type(1))
1034      : _M_param(__nu_val, __sigma_val),
1035	_M_ndx(__nu_val, __sigma_val),
1036	_M_ndy(result_type(0), __sigma_val)
1037      { }
1038
1039      explicit
1040      rice_distribution(const param_type& __p)
1041      : _M_param(__p),
1042	_M_ndx(__p.nu(), __p.sigma()),
1043	_M_ndy(result_type(0), __p.sigma())
1044      { }
1045
1046      /// @}
1047
1048      /**
1049       * @brief Resets the distribution state.
1050       */
1051      void
1052      reset()
1053      {
1054	_M_ndx.reset();
1055	_M_ndy.reset();
1056      }
1057
1058      /**
1059       * @brief Return the parameters of the distribution.
1060       */
1061      result_type
1062      nu() const
1063      { return _M_param.nu(); }
1064
1065      result_type
1066      sigma() const
1067      { return _M_param.sigma(); }
1068
1069      /**
1070       * @brief Returns the parameter set of the distribution.
1071       */
1072      param_type
1073      param() const
1074      { return _M_param; }
1075
1076      /**
1077       * @brief Sets the parameter set of the distribution.
1078       * @param __param The new parameter set of the distribution.
1079       */
1080      void
1081      param(const param_type& __param)
1082      { _M_param = __param; }
1083
1084      /**
1085       * @brief Returns the greatest lower bound value of the distribution.
1086       */
1087      result_type
1088      min() const
1089      { return result_type(0); }
1090
1091      /**
1092       * @brief Returns the least upper bound value of the distribution.
1093       */
1094      result_type
1095      max() const
1096      { return std::numeric_limits<result_type>::max(); }
1097
1098      /**
1099       * @brief Generating functions.
1100       */
1101      template<typename _UniformRandomNumberGenerator>
1102	result_type
1103	operator()(_UniformRandomNumberGenerator& __urng)
1104	{
1105	  result_type __x = this->_M_ndx(__urng);
1106	  result_type __y = this->_M_ndy(__urng);
1107#if _GLIBCXX_USE_C99_MATH_TR1
1108	  return std::hypot(__x, __y);
1109#else
1110	  return std::sqrt(__x * __x + __y * __y);
1111#endif
1112	}
1113
1114      template<typename _UniformRandomNumberGenerator>
1115	result_type
1116	operator()(_UniformRandomNumberGenerator& __urng,
1117		   const param_type& __p)
1118	{
1119	  typename std::normal_distribution<result_type>::param_type
1120	    __px(__p.nu(), __p.sigma()), __py(result_type(0), __p.sigma());
1121	  result_type __x = this->_M_ndx(__px, __urng);
1122	  result_type __y = this->_M_ndy(__py, __urng);
1123#if _GLIBCXX_USE_C99_MATH_TR1
1124	  return std::hypot(__x, __y);
1125#else
1126	  return std::sqrt(__x * __x + __y * __y);
1127#endif
1128	}
1129
1130      template<typename _ForwardIterator,
1131	       typename _UniformRandomNumberGenerator>
1132	void
1133	__generate(_ForwardIterator __f, _ForwardIterator __t,
1134		   _UniformRandomNumberGenerator& __urng)
1135	{ this->__generate(__f, __t, __urng, _M_param); }
1136
1137      template<typename _ForwardIterator,
1138	       typename _UniformRandomNumberGenerator>
1139	void
1140	__generate(_ForwardIterator __f, _ForwardIterator __t,
1141		   _UniformRandomNumberGenerator& __urng,
1142		   const param_type& __p)
1143	{ this->__generate_impl(__f, __t, __urng, __p); }
1144
1145      template<typename _UniformRandomNumberGenerator>
1146	void
1147	__generate(result_type* __f, result_type* __t,
1148		   _UniformRandomNumberGenerator& __urng,
1149		   const param_type& __p)
1150	{ this->__generate_impl(__f, __t, __urng, __p); }
1151
1152      /**
1153       * @brief Return true if two Rice distributions have
1154       *        the same parameters and the sequences that would
1155       *        be generated are equal.
1156       */
1157      friend bool
1158      operator==(const rice_distribution& __d1,
1159		 const rice_distribution& __d2)
1160      { return (__d1._M_param == __d2._M_param
1161		&& __d1._M_ndx == __d2._M_ndx
1162		&& __d1._M_ndy == __d2._M_ndy); }
1163
1164      /**
1165       * @brief Inserts a %rice_distribution random number distribution
1166       * @p __x into the output stream @p __os.
1167       *
1168       * @param __os An output stream.
1169       * @param __x  A %rice_distribution random number distribution.
1170       *
1171       * @returns The output stream with the state of @p __x inserted or in
1172       * an error state.
1173       */
1174      template<typename _RealType1, typename _CharT, typename _Traits>
1175	friend std::basic_ostream<_CharT, _Traits>&
1176	operator<<(std::basic_ostream<_CharT, _Traits>&,
1177		   const rice_distribution<_RealType1>&);
1178
1179      /**
1180       * @brief Extracts a %rice_distribution random number distribution
1181       * @p __x from the input stream @p __is.
1182       *
1183       * @param __is An input stream.
1184       * @param __x A %rice_distribution random number
1185       *            generator engine.
1186       *
1187       * @returns The input stream with @p __x extracted or in an error state.
1188       */
1189      template<typename _RealType1, typename _CharT, typename _Traits>
1190	friend std::basic_istream<_CharT, _Traits>&
1191	operator>>(std::basic_istream<_CharT, _Traits>&,
1192		   rice_distribution<_RealType1>&);
1193
1194    private:
1195      template<typename _ForwardIterator,
1196	       typename _UniformRandomNumberGenerator>
1197	void
1198	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1199			_UniformRandomNumberGenerator& __urng,
1200			const param_type& __p);
1201
1202      param_type _M_param;
1203
1204      std::normal_distribution<result_type> _M_ndx;
1205      std::normal_distribution<result_type> _M_ndy;
1206    };
1207
1208  /**
1209   * @brief Return true if two Rice distributions are not equal.
1210   */
1211  template<typename _RealType1>
1212    inline bool
1213    operator!=(const rice_distribution<_RealType1>& __d1,
1214	       const rice_distribution<_RealType1>& __d2)
1215    { return !(__d1 == __d2); }
1216
1217
1218  /**
1219   * @brief A Nakagami continuous distribution for random numbers.
1220   *
1221   * The formula for the Nakagami probability density function is
1222   * @f[
1223   *     p(x|\mu,\omega) = \frac{2\mu^\mu}{\Gamma(\mu)\omega^\mu}
1224   *                       x^{2\mu-1}e^{-\mu x / \omega}
1225   * @f]
1226   * where @f$\Gamma(z)@f$ is the gamma function and @f$\mu >= 0.5@f$
1227   * and @f$\omega > 0@f$.
1228   */
1229  template<typename _RealType = double>
1230    class
1231    nakagami_distribution
1232    {
1233      static_assert(std::is_floating_point<_RealType>::value,
1234		    "template argument not a floating point type");
1235
1236    public:
1237      /** The type of the range of the distribution. */
1238      typedef _RealType result_type;
1239
1240      /** Parameter type. */
1241      struct param_type
1242      {
1243	typedef nakagami_distribution<result_type> distribution_type;
1244
1245	param_type() : param_type(1) { }
1246
1247	param_type(result_type __mu_val,
1248		   result_type __omega_val = result_type(1))
1249	: _M_mu(__mu_val), _M_omega(__omega_val)
1250	{
1251	  __glibcxx_assert(_M_mu >= result_type(0.5L));
1252	  __glibcxx_assert(_M_omega > result_type(0));
1253	}
1254
1255	result_type
1256	mu() const
1257	{ return _M_mu; }
1258
1259	result_type
1260	omega() const
1261	{ return _M_omega; }
1262
1263	friend bool
1264	operator==(const param_type& __p1, const param_type& __p2)
1265	{ return __p1._M_mu == __p2._M_mu && __p1._M_omega == __p2._M_omega; }
1266
1267	friend bool
1268	operator!=(const param_type& __p1, const param_type& __p2)
1269	{ return !(__p1 == __p2); }
1270
1271      private:
1272	void _M_initialize();
1273
1274	result_type _M_mu;
1275	result_type _M_omega;
1276      };
1277
1278      /**
1279       * @brief Constructors.
1280       * @{
1281       */
1282
1283      nakagami_distribution() : nakagami_distribution(1) { }
1284
1285      explicit
1286      nakagami_distribution(result_type __mu_val,
1287			    result_type __omega_val = result_type(1))
1288      : _M_param(__mu_val, __omega_val),
1289	_M_gd(__mu_val, __omega_val / __mu_val)
1290      { }
1291
1292      explicit
1293      nakagami_distribution(const param_type& __p)
1294      : _M_param(__p),
1295	_M_gd(__p.mu(), __p.omega() / __p.mu())
1296      { }
1297
1298      /// @}
1299
1300      /**
1301       * @brief Resets the distribution state.
1302       */
1303      void
1304      reset()
1305      { _M_gd.reset(); }
1306
1307      /**
1308       * @brief Return the parameters of the distribution.
1309       */
1310      result_type
1311      mu() const
1312      { return _M_param.mu(); }
1313
1314      result_type
1315      omega() const
1316      { return _M_param.omega(); }
1317
1318      /**
1319       * @brief Returns the parameter set of the distribution.
1320       */
1321      param_type
1322      param() const
1323      { return _M_param; }
1324
1325      /**
1326       * @brief Sets the parameter set of the distribution.
1327       * @param __param The new parameter set of the distribution.
1328       */
1329      void
1330      param(const param_type& __param)
1331      { _M_param = __param; }
1332
1333      /**
1334       * @brief Returns the greatest lower bound value of the distribution.
1335       */
1336      result_type
1337      min() const
1338      { return result_type(0); }
1339
1340      /**
1341       * @brief Returns the least upper bound value of the distribution.
1342       */
1343      result_type
1344      max() const
1345      { return std::numeric_limits<result_type>::max(); }
1346
1347      /**
1348       * @brief Generating functions.
1349       */
1350      template<typename _UniformRandomNumberGenerator>
1351	result_type
1352	operator()(_UniformRandomNumberGenerator& __urng)
1353	{ return std::sqrt(this->_M_gd(__urng)); }
1354
1355      template<typename _UniformRandomNumberGenerator>
1356	result_type
1357	operator()(_UniformRandomNumberGenerator& __urng,
1358		   const param_type& __p)
1359	{
1360	  typename std::gamma_distribution<result_type>::param_type
1361	    __pg(__p.mu(), __p.omega() / __p.mu());
1362	  return std::sqrt(this->_M_gd(__pg, __urng));
1363	}
1364
1365      template<typename _ForwardIterator,
1366	       typename _UniformRandomNumberGenerator>
1367	void
1368	__generate(_ForwardIterator __f, _ForwardIterator __t,
1369		   _UniformRandomNumberGenerator& __urng)
1370	{ this->__generate(__f, __t, __urng, _M_param); }
1371
1372      template<typename _ForwardIterator,
1373	       typename _UniformRandomNumberGenerator>
1374	void
1375	__generate(_ForwardIterator __f, _ForwardIterator __t,
1376		   _UniformRandomNumberGenerator& __urng,
1377		   const param_type& __p)
1378	{ this->__generate_impl(__f, __t, __urng, __p); }
1379
1380      template<typename _UniformRandomNumberGenerator>
1381	void
1382	__generate(result_type* __f, result_type* __t,
1383		   _UniformRandomNumberGenerator& __urng,
1384		   const param_type& __p)
1385	{ this->__generate_impl(__f, __t, __urng, __p); }
1386
1387      /**
1388       * @brief Return true if two Nakagami distributions have
1389       *        the same parameters and the sequences that would
1390       *        be generated are equal.
1391       */
1392      friend bool
1393      operator==(const nakagami_distribution& __d1,
1394		 const nakagami_distribution& __d2)
1395      { return (__d1._M_param == __d2._M_param
1396		&& __d1._M_gd == __d2._M_gd); }
1397
1398      /**
1399       * @brief Inserts a %nakagami_distribution random number distribution
1400       * @p __x into the output stream @p __os.
1401       *
1402       * @param __os An output stream.
1403       * @param __x  A %nakagami_distribution random number distribution.
1404       *
1405       * @returns The output stream with the state of @p __x inserted or in
1406       * an error state.
1407       */
1408      template<typename _RealType1, typename _CharT, typename _Traits>
1409	friend std::basic_ostream<_CharT, _Traits>&
1410	operator<<(std::basic_ostream<_CharT, _Traits>&,
1411		   const nakagami_distribution<_RealType1>&);
1412
1413      /**
1414       * @brief Extracts a %nakagami_distribution random number distribution
1415       * @p __x from the input stream @p __is.
1416       *
1417       * @param __is An input stream.
1418       * @param __x A %nakagami_distribution random number
1419       *            generator engine.
1420       *
1421       * @returns The input stream with @p __x extracted or in an error state.
1422       */
1423      template<typename _RealType1, typename _CharT, typename _Traits>
1424	friend std::basic_istream<_CharT, _Traits>&
1425	operator>>(std::basic_istream<_CharT, _Traits>&,
1426		   nakagami_distribution<_RealType1>&);
1427
1428    private:
1429      template<typename _ForwardIterator,
1430	       typename _UniformRandomNumberGenerator>
1431	void
1432	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1433			_UniformRandomNumberGenerator& __urng,
1434			const param_type& __p);
1435
1436      param_type _M_param;
1437
1438      std::gamma_distribution<result_type> _M_gd;
1439    };
1440
1441  /**
1442   * @brief Return true if two Nakagami distributions are not equal.
1443   */
1444  template<typename _RealType>
1445    inline bool
1446    operator!=(const nakagami_distribution<_RealType>& __d1,
1447	       const nakagami_distribution<_RealType>& __d2)
1448    { return !(__d1 == __d2); }
1449
1450
1451  /**
1452   * @brief A Pareto continuous distribution for random numbers.
1453   *
1454   * The formula for the Pareto cumulative probability function is
1455   * @f[
1456   *     P(x|\alpha,\mu) = 1 - \left(\frac{\mu}{x}\right)^\alpha
1457   * @f]
1458   * The formula for the Pareto probability density function is
1459   * @f[
1460   *     p(x|\alpha,\mu) = \frac{\alpha + 1}{\mu}
1461   *                       \left(\frac{\mu}{x}\right)^{\alpha + 1}
1462   * @f]
1463   * where @f$x >= \mu@f$ and @f$\mu > 0@f$, @f$\alpha > 0@f$.
1464   *
1465   * <table border=1 cellpadding=10 cellspacing=0>
1466   * <caption align=top>Distribution Statistics</caption>
1467   * <tr><td>Mean</td><td>@f$\alpha \mu / (\alpha - 1)@f$
1468   *              for @f$\alpha > 1@f$</td></tr>
1469   * <tr><td>Variance</td><td>@f$\alpha \mu^2 / [(\alpha - 1)^2(\alpha - 2)]@f$
1470   *              for @f$\alpha > 2@f$</td></tr>
1471   * <tr><td>Range</td><td>@f$[\mu, \infty)@f$</td></tr>
1472   * </table>
1473   */
1474  template<typename _RealType = double>
1475    class
1476    pareto_distribution
1477    {
1478      static_assert(std::is_floating_point<_RealType>::value,
1479		    "template argument not a floating point type");
1480
1481    public:
1482      /** The type of the range of the distribution. */
1483      typedef _RealType result_type;
1484
1485      /** Parameter type. */
1486      struct param_type
1487      {
1488	typedef pareto_distribution<result_type> distribution_type;
1489
1490	param_type() : param_type(1) { }
1491
1492	param_type(result_type __alpha_val,
1493		   result_type __mu_val = result_type(1))
1494	: _M_alpha(__alpha_val), _M_mu(__mu_val)
1495	{
1496	  __glibcxx_assert(_M_alpha > result_type(0));
1497	  __glibcxx_assert(_M_mu > result_type(0));
1498	}
1499
1500	result_type
1501	alpha() const
1502	{ return _M_alpha; }
1503
1504	result_type
1505	mu() const
1506	{ return _M_mu; }
1507
1508	friend bool
1509	operator==(const param_type& __p1, const param_type& __p2)
1510	{ return __p1._M_alpha == __p2._M_alpha && __p1._M_mu == __p2._M_mu; }
1511
1512	friend bool
1513	operator!=(const param_type& __p1, const param_type& __p2)
1514	{ return !(__p1 == __p2); }
1515
1516      private:
1517	void _M_initialize();
1518
1519	result_type _M_alpha;
1520	result_type _M_mu;
1521      };
1522
1523      /**
1524       * @brief Constructors.
1525       * @{
1526       */
1527
1528      pareto_distribution() : pareto_distribution(1) { }
1529
1530      explicit
1531      pareto_distribution(result_type __alpha_val,
1532			  result_type __mu_val = result_type(1))
1533      : _M_param(__alpha_val, __mu_val),
1534	_M_ud()
1535      { }
1536
1537      explicit
1538      pareto_distribution(const param_type& __p)
1539      : _M_param(__p),
1540	_M_ud()
1541      { }
1542
1543      /// @}
1544
1545      /**
1546       * @brief Resets the distribution state.
1547       */
1548      void
1549      reset()
1550      {
1551	_M_ud.reset();
1552      }
1553
1554      /**
1555       * @brief Return the parameters of the distribution.
1556       */
1557      result_type
1558      alpha() const
1559      { return _M_param.alpha(); }
1560
1561      result_type
1562      mu() const
1563      { return _M_param.mu(); }
1564
1565      /**
1566       * @brief Returns the parameter set of the distribution.
1567       */
1568      param_type
1569      param() const
1570      { return _M_param; }
1571
1572      /**
1573       * @brief Sets the parameter set of the distribution.
1574       * @param __param The new parameter set of the distribution.
1575       */
1576      void
1577      param(const param_type& __param)
1578      { _M_param = __param; }
1579
1580      /**
1581       * @brief Returns the greatest lower bound value of the distribution.
1582       */
1583      result_type
1584      min() const
1585      { return this->mu(); }
1586
1587      /**
1588       * @brief Returns the least upper bound value of the distribution.
1589       */
1590      result_type
1591      max() const
1592      { return std::numeric_limits<result_type>::max(); }
1593
1594      /**
1595       * @brief Generating functions.
1596       */
1597      template<typename _UniformRandomNumberGenerator>
1598	result_type
1599	operator()(_UniformRandomNumberGenerator& __urng)
1600	{
1601	  return this->mu() * std::pow(this->_M_ud(__urng),
1602				       -result_type(1) / this->alpha());
1603	}
1604
1605      template<typename _UniformRandomNumberGenerator>
1606	result_type
1607	operator()(_UniformRandomNumberGenerator& __urng,
1608		   const param_type& __p)
1609	{
1610	  return __p.mu() * std::pow(this->_M_ud(__urng),
1611					   -result_type(1) / __p.alpha());
1612	}
1613
1614      template<typename _ForwardIterator,
1615	       typename _UniformRandomNumberGenerator>
1616	void
1617	__generate(_ForwardIterator __f, _ForwardIterator __t,
1618		   _UniformRandomNumberGenerator& __urng)
1619	{ this->__generate(__f, __t, __urng, _M_param); }
1620
1621      template<typename _ForwardIterator,
1622	       typename _UniformRandomNumberGenerator>
1623	void
1624	__generate(_ForwardIterator __f, _ForwardIterator __t,
1625		   _UniformRandomNumberGenerator& __urng,
1626		   const param_type& __p)
1627	{ this->__generate_impl(__f, __t, __urng, __p); }
1628
1629      template<typename _UniformRandomNumberGenerator>
1630	void
1631	__generate(result_type* __f, result_type* __t,
1632		   _UniformRandomNumberGenerator& __urng,
1633		   const param_type& __p)
1634	{ this->__generate_impl(__f, __t, __urng, __p); }
1635
1636      /**
1637       * @brief Return true if two Pareto distributions have
1638       *        the same parameters and the sequences that would
1639       *        be generated are equal.
1640       */
1641      friend bool
1642      operator==(const pareto_distribution& __d1,
1643		 const pareto_distribution& __d2)
1644      { return (__d1._M_param == __d2._M_param
1645		&& __d1._M_ud == __d2._M_ud); }
1646
1647      /**
1648       * @brief Inserts a %pareto_distribution random number distribution
1649       * @p __x into the output stream @p __os.
1650       *
1651       * @param __os An output stream.
1652       * @param __x  A %pareto_distribution random number distribution.
1653       *
1654       * @returns The output stream with the state of @p __x inserted or in
1655       * an error state.
1656       */
1657      template<typename _RealType1, typename _CharT, typename _Traits>
1658	friend std::basic_ostream<_CharT, _Traits>&
1659	operator<<(std::basic_ostream<_CharT, _Traits>&,
1660		   const pareto_distribution<_RealType1>&);
1661
1662      /**
1663       * @brief Extracts a %pareto_distribution random number distribution
1664       * @p __x from the input stream @p __is.
1665       *
1666       * @param __is An input stream.
1667       * @param __x A %pareto_distribution random number
1668       *            generator engine.
1669       *
1670       * @returns The input stream with @p __x extracted or in an error state.
1671       */
1672      template<typename _RealType1, typename _CharT, typename _Traits>
1673	friend std::basic_istream<_CharT, _Traits>&
1674	operator>>(std::basic_istream<_CharT, _Traits>&,
1675		   pareto_distribution<_RealType1>&);
1676
1677    private:
1678      template<typename _ForwardIterator,
1679	       typename _UniformRandomNumberGenerator>
1680	void
1681	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1682			_UniformRandomNumberGenerator& __urng,
1683			const param_type& __p);
1684
1685      param_type _M_param;
1686
1687      std::uniform_real_distribution<result_type> _M_ud;
1688    };
1689
1690  /**
1691   * @brief Return true if two Pareto distributions are not equal.
1692   */
1693  template<typename _RealType>
1694    inline bool
1695    operator!=(const pareto_distribution<_RealType>& __d1,
1696	       const pareto_distribution<_RealType>& __d2)
1697    { return !(__d1 == __d2); }
1698
1699
1700  /**
1701   * @brief A K continuous distribution for random numbers.
1702   *
1703   * The formula for the K probability density function is
1704   * @f[
1705   *     p(x|\lambda, \mu, \nu) = \frac{2}{x}
1706   *             \left(\frac{\lambda\nu x}{\mu}\right)^{\frac{\lambda + \nu}{2}}
1707   *             \frac{1}{\Gamma(\lambda)\Gamma(\nu)}
1708   *             K_{\nu - \lambda}\left(2\sqrt{\frac{\lambda\nu x}{\mu}}\right)
1709   * @f]
1710   * where @f$I_0(z)@f$ is the modified Bessel function of the second kind
1711   * of order @f$\nu - \lambda@f$ and @f$\lambda > 0@f$, @f$\mu > 0@f$
1712   * and @f$\nu > 0@f$.
1713   *
1714   * <table border=1 cellpadding=10 cellspacing=0>
1715   * <caption align=top>Distribution Statistics</caption>
1716   * <tr><td>Mean</td><td>@f$\mu@f$</td></tr>
1717   * <tr><td>Variance</td><td>@f$\mu^2\frac{\lambda + \nu + 1}{\lambda\nu}@f$</td></tr>
1718   * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
1719   * </table>
1720   */
1721  template<typename _RealType = double>
1722    class
1723    k_distribution
1724    {
1725      static_assert(std::is_floating_point<_RealType>::value,
1726		    "template argument not a floating point type");
1727
1728    public:
1729      /** The type of the range of the distribution. */
1730      typedef _RealType result_type;
1731
1732      /** Parameter type. */
1733      struct param_type
1734      {
1735	typedef k_distribution<result_type> distribution_type;
1736
1737	param_type() : param_type(1) { }
1738
1739	param_type(result_type __lambda_val,
1740		   result_type __mu_val = result_type(1),
1741		   result_type __nu_val = result_type(1))
1742	: _M_lambda(__lambda_val), _M_mu(__mu_val), _M_nu(__nu_val)
1743	{
1744	  __glibcxx_assert(_M_lambda > result_type(0));
1745	  __glibcxx_assert(_M_mu > result_type(0));
1746	  __glibcxx_assert(_M_nu > result_type(0));
1747	}
1748
1749	result_type
1750	lambda() const
1751	{ return _M_lambda; }
1752
1753	result_type
1754	mu() const
1755	{ return _M_mu; }
1756
1757	result_type
1758	nu() const
1759	{ return _M_nu; }
1760
1761	friend bool
1762	operator==(const param_type& __p1, const param_type& __p2)
1763	{
1764	  return __p1._M_lambda == __p2._M_lambda
1765	      && __p1._M_mu == __p2._M_mu
1766	      && __p1._M_nu == __p2._M_nu;
1767	}
1768
1769	friend bool
1770	operator!=(const param_type& __p1, const param_type& __p2)
1771	{ return !(__p1 == __p2); }
1772
1773      private:
1774	void _M_initialize();
1775
1776	result_type _M_lambda;
1777	result_type _M_mu;
1778	result_type _M_nu;
1779      };
1780
1781      /**
1782       * @brief Constructors.
1783       * @{
1784       */
1785
1786      k_distribution() : k_distribution(1) { }
1787
1788      explicit
1789      k_distribution(result_type __lambda_val,
1790		     result_type __mu_val = result_type(1),
1791		     result_type __nu_val = result_type(1))
1792      : _M_param(__lambda_val, __mu_val, __nu_val),
1793	_M_gd1(__lambda_val, result_type(1) / __lambda_val),
1794	_M_gd2(__nu_val, __mu_val / __nu_val)
1795      { }
1796
1797      explicit
1798      k_distribution(const param_type& __p)
1799      : _M_param(__p),
1800	_M_gd1(__p.lambda(), result_type(1) / __p.lambda()),
1801	_M_gd2(__p.nu(), __p.mu() / __p.nu())
1802      { }
1803
1804      /// @}
1805
1806      /**
1807       * @brief Resets the distribution state.
1808       */
1809      void
1810      reset()
1811      {
1812	_M_gd1.reset();
1813	_M_gd2.reset();
1814      }
1815
1816      /**
1817       * @brief Return the parameters of the distribution.
1818       */
1819      result_type
1820      lambda() const
1821      { return _M_param.lambda(); }
1822
1823      result_type
1824      mu() const
1825      { return _M_param.mu(); }
1826
1827      result_type
1828      nu() const
1829      { return _M_param.nu(); }
1830
1831      /**
1832       * @brief Returns the parameter set of the distribution.
1833       */
1834      param_type
1835      param() const
1836      { return _M_param; }
1837
1838      /**
1839       * @brief Sets the parameter set of the distribution.
1840       * @param __param The new parameter set of the distribution.
1841       */
1842      void
1843      param(const param_type& __param)
1844      { _M_param = __param; }
1845
1846      /**
1847       * @brief Returns the greatest lower bound value of the distribution.
1848       */
1849      result_type
1850      min() const
1851      { return result_type(0); }
1852
1853      /**
1854       * @brief Returns the least upper bound value of the distribution.
1855       */
1856      result_type
1857      max() const
1858      { return std::numeric_limits<result_type>::max(); }
1859
1860      /**
1861       * @brief Generating functions.
1862       */
1863      template<typename _UniformRandomNumberGenerator>
1864	result_type
1865	operator()(_UniformRandomNumberGenerator&);
1866
1867      template<typename _UniformRandomNumberGenerator>
1868	result_type
1869	operator()(_UniformRandomNumberGenerator&, const param_type&);
1870
1871      template<typename _ForwardIterator,
1872	       typename _UniformRandomNumberGenerator>
1873	void
1874	__generate(_ForwardIterator __f, _ForwardIterator __t,
1875		   _UniformRandomNumberGenerator& __urng)
1876	{ this->__generate(__f, __t, __urng, _M_param); }
1877
1878      template<typename _ForwardIterator,
1879	       typename _UniformRandomNumberGenerator>
1880	void
1881	__generate(_ForwardIterator __f, _ForwardIterator __t,
1882		   _UniformRandomNumberGenerator& __urng,
1883		   const param_type& __p)
1884	{ this->__generate_impl(__f, __t, __urng, __p); }
1885
1886      template<typename _UniformRandomNumberGenerator>
1887	void
1888	__generate(result_type* __f, result_type* __t,
1889		   _UniformRandomNumberGenerator& __urng,
1890		   const param_type& __p)
1891	{ this->__generate_impl(__f, __t, __urng, __p); }
1892
1893      /**
1894       * @brief Return true if two K distributions have
1895       *        the same parameters and the sequences that would
1896       *        be generated are equal.
1897       */
1898      friend bool
1899      operator==(const k_distribution& __d1,
1900		 const k_distribution& __d2)
1901      { return (__d1._M_param == __d2._M_param
1902		&& __d1._M_gd1 == __d2._M_gd1
1903		&& __d1._M_gd2 == __d2._M_gd2); }
1904
1905      /**
1906       * @brief Inserts a %k_distribution random number distribution
1907       * @p __x into the output stream @p __os.
1908       *
1909       * @param __os An output stream.
1910       * @param __x  A %k_distribution random number distribution.
1911       *
1912       * @returns The output stream with the state of @p __x inserted or in
1913       * an error state.
1914       */
1915      template<typename _RealType1, typename _CharT, typename _Traits>
1916	friend std::basic_ostream<_CharT, _Traits>&
1917	operator<<(std::basic_ostream<_CharT, _Traits>&,
1918		   const k_distribution<_RealType1>&);
1919
1920      /**
1921       * @brief Extracts a %k_distribution random number distribution
1922       * @p __x from the input stream @p __is.
1923       *
1924       * @param __is An input stream.
1925       * @param __x A %k_distribution random number
1926       *            generator engine.
1927       *
1928       * @returns The input stream with @p __x extracted or in an error state.
1929       */
1930      template<typename _RealType1, typename _CharT, typename _Traits>
1931	friend std::basic_istream<_CharT, _Traits>&
1932	operator>>(std::basic_istream<_CharT, _Traits>&,
1933		   k_distribution<_RealType1>&);
1934
1935    private:
1936      template<typename _ForwardIterator,
1937	       typename _UniformRandomNumberGenerator>
1938	void
1939	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1940			_UniformRandomNumberGenerator& __urng,
1941			const param_type& __p);
1942
1943      param_type _M_param;
1944
1945      std::gamma_distribution<result_type> _M_gd1;
1946      std::gamma_distribution<result_type> _M_gd2;
1947    };
1948
1949  /**
1950   * @brief Return true if two K distributions are not equal.
1951   */
1952  template<typename _RealType>
1953    inline bool
1954    operator!=(const k_distribution<_RealType>& __d1,
1955	       const k_distribution<_RealType>& __d2)
1956    { return !(__d1 == __d2); }
1957
1958
1959  /**
1960   * @brief An arcsine continuous distribution for random numbers.
1961   *
1962   * The formula for the arcsine probability density function is
1963   * @f[
1964   *     p(x|a,b) = \frac{1}{\pi \sqrt{(x - a)(b - x)}}
1965   * @f]
1966   * where @f$x >= a@f$ and @f$x <= b@f$.
1967   *
1968   * <table border=1 cellpadding=10 cellspacing=0>
1969   * <caption align=top>Distribution Statistics</caption>
1970   * <tr><td>Mean</td><td>@f$ (a + b) / 2 @f$</td></tr>
1971   * <tr><td>Variance</td><td>@f$ (b - a)^2 / 8 @f$</td></tr>
1972   * <tr><td>Range</td><td>@f$[a, b]@f$</td></tr>
1973   * </table>
1974   */
1975  template<typename _RealType = double>
1976    class
1977    arcsine_distribution
1978    {
1979      static_assert(std::is_floating_point<_RealType>::value,
1980		    "template argument not a floating point type");
1981
1982    public:
1983      /** The type of the range of the distribution. */
1984      typedef _RealType result_type;
1985
1986      /** Parameter type. */
1987      struct param_type
1988      {
1989	typedef arcsine_distribution<result_type> distribution_type;
1990
1991	param_type() : param_type(0) { }
1992
1993	param_type(result_type __a, result_type __b = result_type(1))
1994	: _M_a(__a), _M_b(__b)
1995	{
1996	  __glibcxx_assert(_M_a <= _M_b);
1997	}
1998
1999	result_type
2000	a() const
2001	{ return _M_a; }
2002
2003	result_type
2004	b() const
2005	{ return _M_b; }
2006
2007	friend bool
2008	operator==(const param_type& __p1, const param_type& __p2)
2009	{ return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
2010
2011	friend bool
2012	operator!=(const param_type& __p1, const param_type& __p2)
2013	{ return !(__p1 == __p2); }
2014
2015      private:
2016	void _M_initialize();
2017
2018	result_type _M_a;
2019	result_type _M_b;
2020      };
2021
2022      /**
2023       * @brief Constructors.
2024       * :{
2025       */
2026
2027      arcsine_distribution() : arcsine_distribution(0) { }
2028
2029      explicit
2030      arcsine_distribution(result_type __a, result_type __b = result_type(1))
2031      : _M_param(__a, __b),
2032	_M_ud(-1.5707963267948966192313216916397514L,
2033	      +1.5707963267948966192313216916397514L)
2034      { }
2035
2036      explicit
2037      arcsine_distribution(const param_type& __p)
2038      : _M_param(__p),
2039	_M_ud(-1.5707963267948966192313216916397514L,
2040	      +1.5707963267948966192313216916397514L)
2041      { }
2042
2043      /// @}
2044
2045      /**
2046       * @brief Resets the distribution state.
2047       */
2048      void
2049      reset()
2050      { _M_ud.reset(); }
2051
2052      /**
2053       * @brief Return the parameters of the distribution.
2054       */
2055      result_type
2056      a() const
2057      { return _M_param.a(); }
2058
2059      result_type
2060      b() const
2061      { return _M_param.b(); }
2062
2063      /**
2064       * @brief Returns the parameter set of the distribution.
2065       */
2066      param_type
2067      param() const
2068      { return _M_param; }
2069
2070      /**
2071       * @brief Sets the parameter set of the distribution.
2072       * @param __param The new parameter set of the distribution.
2073       */
2074      void
2075      param(const param_type& __param)
2076      { _M_param = __param; }
2077
2078      /**
2079       * @brief Returns the greatest lower bound value of the distribution.
2080       */
2081      result_type
2082      min() const
2083      { return this->a(); }
2084
2085      /**
2086       * @brief Returns the least upper bound value of the distribution.
2087       */
2088      result_type
2089      max() const
2090      { return this->b(); }
2091
2092      /**
2093       * @brief Generating functions.
2094       */
2095      template<typename _UniformRandomNumberGenerator>
2096	result_type
2097	operator()(_UniformRandomNumberGenerator& __urng)
2098	{
2099	  result_type __x = std::sin(this->_M_ud(__urng));
2100	  return (__x * (this->b() - this->a())
2101		  + this->a() + this->b()) / result_type(2);
2102	}
2103
2104      template<typename _UniformRandomNumberGenerator>
2105	result_type
2106	operator()(_UniformRandomNumberGenerator& __urng,
2107		   const param_type& __p)
2108	{
2109	  result_type __x = std::sin(this->_M_ud(__urng));
2110	  return (__x * (__p.b() - __p.a())
2111		  + __p.a() + __p.b()) / result_type(2);
2112	}
2113
2114      template<typename _ForwardIterator,
2115	       typename _UniformRandomNumberGenerator>
2116	void
2117	__generate(_ForwardIterator __f, _ForwardIterator __t,
2118		   _UniformRandomNumberGenerator& __urng)
2119	{ this->__generate(__f, __t, __urng, _M_param); }
2120
2121      template<typename _ForwardIterator,
2122	       typename _UniformRandomNumberGenerator>
2123	void
2124	__generate(_ForwardIterator __f, _ForwardIterator __t,
2125		   _UniformRandomNumberGenerator& __urng,
2126		   const param_type& __p)
2127	{ this->__generate_impl(__f, __t, __urng, __p); }
2128
2129      template<typename _UniformRandomNumberGenerator>
2130	void
2131	__generate(result_type* __f, result_type* __t,
2132		   _UniformRandomNumberGenerator& __urng,
2133		   const param_type& __p)
2134	{ this->__generate_impl(__f, __t, __urng, __p); }
2135
2136      /**
2137       * @brief Return true if two arcsine distributions have
2138       *        the same parameters and the sequences that would
2139       *        be generated are equal.
2140       */
2141      friend bool
2142      operator==(const arcsine_distribution& __d1,
2143		 const arcsine_distribution& __d2)
2144      { return (__d1._M_param == __d2._M_param
2145		&& __d1._M_ud == __d2._M_ud); }
2146
2147      /**
2148       * @brief Inserts a %arcsine_distribution random number distribution
2149       * @p __x into the output stream @p __os.
2150       *
2151       * @param __os An output stream.
2152       * @param __x  A %arcsine_distribution random number distribution.
2153       *
2154       * @returns The output stream with the state of @p __x inserted or in
2155       * an error state.
2156       */
2157      template<typename _RealType1, typename _CharT, typename _Traits>
2158	friend std::basic_ostream<_CharT, _Traits>&
2159	operator<<(std::basic_ostream<_CharT, _Traits>&,
2160		   const arcsine_distribution<_RealType1>&);
2161
2162      /**
2163       * @brief Extracts a %arcsine_distribution random number distribution
2164       * @p __x from the input stream @p __is.
2165       *
2166       * @param __is An input stream.
2167       * @param __x A %arcsine_distribution random number
2168       *            generator engine.
2169       *
2170       * @returns The input stream with @p __x extracted or in an error state.
2171       */
2172      template<typename _RealType1, typename _CharT, typename _Traits>
2173	friend std::basic_istream<_CharT, _Traits>&
2174	operator>>(std::basic_istream<_CharT, _Traits>&,
2175		   arcsine_distribution<_RealType1>&);
2176
2177    private:
2178      template<typename _ForwardIterator,
2179	       typename _UniformRandomNumberGenerator>
2180	void
2181	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2182			_UniformRandomNumberGenerator& __urng,
2183			const param_type& __p);
2184
2185      param_type _M_param;
2186
2187      std::uniform_real_distribution<result_type> _M_ud;
2188    };
2189
2190  /**
2191   * @brief Return true if two arcsine distributions are not equal.
2192   */
2193  template<typename _RealType>
2194    inline bool
2195    operator!=(const arcsine_distribution<_RealType>& __d1,
2196	       const arcsine_distribution<_RealType>& __d2)
2197    { return !(__d1 == __d2); }
2198
2199
2200  /**
2201   * @brief A Hoyt continuous distribution for random numbers.
2202   *
2203   * The formula for the Hoyt probability density function is
2204   * @f[
2205   *     p(x|q,\omega) = \frac{(1 + q^2)x}{q\omega}
2206   *                     \exp\left(-\frac{(1 + q^2)^2 x^2}{4 q^2 \omega}\right)
2207   *                       I_0\left(\frac{(1 - q^4) x^2}{4 q^2 \omega}\right)
2208   * @f]
2209   * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
2210   * of order 0 and @f$0 < q < 1@f$.
2211   *
2212   * <table border=1 cellpadding=10 cellspacing=0>
2213   * <caption align=top>Distribution Statistics</caption>
2214   * <tr><td>Mean</td><td>@f$ \sqrt{\frac{2}{\pi}} \sqrt{\frac{\omega}{1 + q^2}}
2215   *                       E(1 - q^2) @f$</td></tr>
2216   * <tr><td>Variance</td><td>@f$ \omega \left(1 - \frac{2E^2(1 - q^2)}
2217   *                                      {\pi (1 + q^2)}\right) @f$</td></tr>
2218   * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
2219   * </table>
2220   * where @f$E(x)@f$ is the elliptic function of the second kind.
2221   */
2222  template<typename _RealType = double>
2223    class
2224    hoyt_distribution
2225    {
2226      static_assert(std::is_floating_point<_RealType>::value,
2227		    "template argument not a floating point type");
2228
2229    public:
2230      /** The type of the range of the distribution. */
2231      typedef _RealType result_type;
2232
2233      /** Parameter type. */
2234      struct param_type
2235      {
2236	typedef hoyt_distribution<result_type> distribution_type;
2237
2238	param_type() : param_type(0.5) { }
2239
2240	param_type(result_type __q, result_type __omega = result_type(1))
2241	: _M_q(__q), _M_omega(__omega)
2242	{
2243	  __glibcxx_assert(_M_q > result_type(0));
2244	  __glibcxx_assert(_M_q < result_type(1));
2245	}
2246
2247	result_type
2248	q() const
2249	{ return _M_q; }
2250
2251	result_type
2252	omega() const
2253	{ return _M_omega; }
2254
2255	friend bool
2256	operator==(const param_type& __p1, const param_type& __p2)
2257	{ return __p1._M_q == __p2._M_q && __p1._M_omega == __p2._M_omega; }
2258
2259	friend bool
2260	operator!=(const param_type& __p1, const param_type& __p2)
2261	{ return !(__p1 == __p2); }
2262
2263      private:
2264	void _M_initialize();
2265
2266	result_type _M_q;
2267	result_type _M_omega;
2268      };
2269
2270      /**
2271       * @brief Constructors.
2272       * @{
2273       */
2274
2275      hoyt_distribution() : hoyt_distribution(0.5) { }
2276
2277      explicit
2278      hoyt_distribution(result_type __q, result_type __omega = result_type(1))
2279      : _M_param(__q, __omega),
2280	_M_ad(result_type(0.5L) * (result_type(1) + __q * __q),
2281	      result_type(0.5L) * (result_type(1) + __q * __q)
2282				/ (__q * __q)),
2283	_M_ed(result_type(1))
2284      { }
2285
2286      explicit
2287      hoyt_distribution(const param_type& __p)
2288      : _M_param(__p),
2289	_M_ad(result_type(0.5L) * (result_type(1) + __p.q() * __p.q()),
2290	      result_type(0.5L) * (result_type(1) + __p.q() * __p.q())
2291				/ (__p.q() * __p.q())),
2292	_M_ed(result_type(1))
2293      { }
2294
2295      /**
2296       * @brief Resets the distribution state.
2297       */
2298      void
2299      reset()
2300      {
2301	_M_ad.reset();
2302	_M_ed.reset();
2303      }
2304
2305      /**
2306       * @brief Return the parameters of the distribution.
2307       */
2308      result_type
2309      q() const
2310      { return _M_param.q(); }
2311
2312      result_type
2313      omega() const
2314      { return _M_param.omega(); }
2315
2316      /**
2317       * @brief Returns the parameter set of the distribution.
2318       */
2319      param_type
2320      param() const
2321      { return _M_param; }
2322
2323      /**
2324       * @brief Sets the parameter set of the distribution.
2325       * @param __param The new parameter set of the distribution.
2326       */
2327      void
2328      param(const param_type& __param)
2329      { _M_param = __param; }
2330
2331      /**
2332       * @brief Returns the greatest lower bound value of the distribution.
2333       */
2334      result_type
2335      min() const
2336      { return result_type(0); }
2337
2338      /**
2339       * @brief Returns the least upper bound value of the distribution.
2340       */
2341      result_type
2342      max() const
2343      { return std::numeric_limits<result_type>::max(); }
2344
2345      /**
2346       * @brief Generating functions.
2347       */
2348      template<typename _UniformRandomNumberGenerator>
2349	result_type
2350	operator()(_UniformRandomNumberGenerator& __urng);
2351
2352      template<typename _UniformRandomNumberGenerator>
2353	result_type
2354	operator()(_UniformRandomNumberGenerator& __urng,
2355		   const param_type& __p);
2356
2357      template<typename _ForwardIterator,
2358	       typename _UniformRandomNumberGenerator>
2359	void
2360	__generate(_ForwardIterator __f, _ForwardIterator __t,
2361		   _UniformRandomNumberGenerator& __urng)
2362	{ this->__generate(__f, __t, __urng, _M_param); }
2363
2364      template<typename _ForwardIterator,
2365	       typename _UniformRandomNumberGenerator>
2366	void
2367	__generate(_ForwardIterator __f, _ForwardIterator __t,
2368		   _UniformRandomNumberGenerator& __urng,
2369		   const param_type& __p)
2370	{ this->__generate_impl(__f, __t, __urng, __p); }
2371
2372      template<typename _UniformRandomNumberGenerator>
2373	void
2374	__generate(result_type* __f, result_type* __t,
2375		   _UniformRandomNumberGenerator& __urng,
2376		   const param_type& __p)
2377	{ this->__generate_impl(__f, __t, __urng, __p); }
2378
2379      /**
2380       * @brief Return true if two Hoyt distributions have
2381       *        the same parameters and the sequences that would
2382       *        be generated are equal.
2383       */
2384      friend bool
2385      operator==(const hoyt_distribution& __d1,
2386		 const hoyt_distribution& __d2)
2387      { return (__d1._M_param == __d2._M_param
2388		&& __d1._M_ad == __d2._M_ad
2389		&& __d1._M_ed == __d2._M_ed); }
2390
2391      /**
2392       * @brief Inserts a %hoyt_distribution random number distribution
2393       * @p __x into the output stream @p __os.
2394       *
2395       * @param __os An output stream.
2396       * @param __x  A %hoyt_distribution random number distribution.
2397       *
2398       * @returns The output stream with the state of @p __x inserted or in
2399       * an error state.
2400       */
2401      template<typename _RealType1, typename _CharT, typename _Traits>
2402	friend std::basic_ostream<_CharT, _Traits>&
2403	operator<<(std::basic_ostream<_CharT, _Traits>&,
2404		   const hoyt_distribution<_RealType1>&);
2405
2406      /**
2407       * @brief Extracts a %hoyt_distribution random number distribution
2408       * @p __x from the input stream @p __is.
2409       *
2410       * @param __is An input stream.
2411       * @param __x A %hoyt_distribution random number
2412       *            generator engine.
2413       *
2414       * @returns The input stream with @p __x extracted or in an error state.
2415       */
2416      template<typename _RealType1, typename _CharT, typename _Traits>
2417	friend std::basic_istream<_CharT, _Traits>&
2418	operator>>(std::basic_istream<_CharT, _Traits>&,
2419		   hoyt_distribution<_RealType1>&);
2420
2421    private:
2422      template<typename _ForwardIterator,
2423	       typename _UniformRandomNumberGenerator>
2424	void
2425	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2426			_UniformRandomNumberGenerator& __urng,
2427			const param_type& __p);
2428
2429      param_type _M_param;
2430
2431      __gnu_cxx::arcsine_distribution<result_type> _M_ad;
2432      std::exponential_distribution<result_type> _M_ed;
2433    };
2434
2435  /**
2436   * @brief Return true if two Hoyt distributions are not equal.
2437   */
2438  template<typename _RealType>
2439    inline bool
2440    operator!=(const hoyt_distribution<_RealType>& __d1,
2441	       const hoyt_distribution<_RealType>& __d2)
2442    { return !(__d1 == __d2); }
2443
2444
2445  /**
2446   * @brief A triangular distribution for random numbers.
2447   *
2448   * The formula for the triangular probability density function is
2449   * @f[
2450   *                  / 0                          for x < a
2451   *     p(x|a,b,c) = | \frac{2(x-a)}{(c-a)(b-a)}  for a <= x <= b
2452   *                  | \frac{2(c-x)}{(c-a)(c-b)}  for b < x <= c
2453   *                  \ 0                          for c < x
2454   * @f]
2455   *
2456   * <table border=1 cellpadding=10 cellspacing=0>
2457   * <caption align=top>Distribution Statistics</caption>
2458   * <tr><td>Mean</td><td>@f$ \frac{a+b+c}{2} @f$</td></tr>
2459   * <tr><td>Variance</td><td>@f$ \frac{a^2+b^2+c^2-ab-ac-bc}
2460   *                                   {18}@f$</td></tr>
2461   * <tr><td>Range</td><td>@f$[a, c]@f$</td></tr>
2462   * </table>
2463   */
2464  template<typename _RealType = double>
2465    class triangular_distribution
2466    {
2467      static_assert(std::is_floating_point<_RealType>::value,
2468		    "template argument not a floating point type");
2469
2470    public:
2471      /** The type of the range of the distribution. */
2472      typedef _RealType result_type;
2473
2474      /** Parameter type. */
2475      struct param_type
2476      {
2477	friend class triangular_distribution<_RealType>;
2478
2479	param_type() : param_type(0) { }
2480
2481	explicit
2482	param_type(_RealType __a,
2483		   _RealType __b = _RealType(0.5),
2484		   _RealType __c = _RealType(1))
2485	: _M_a(__a), _M_b(__b), _M_c(__c)
2486	{
2487	  __glibcxx_assert(_M_a <= _M_b);
2488	  __glibcxx_assert(_M_b <= _M_c);
2489	  __glibcxx_assert(_M_a < _M_c);
2490
2491	  _M_r_ab = (_M_b - _M_a) / (_M_c - _M_a);
2492	  _M_f_ab_ac = (_M_b - _M_a) * (_M_c - _M_a);
2493	  _M_f_bc_ac = (_M_c - _M_b) * (_M_c - _M_a);
2494	}
2495
2496	_RealType
2497	a() const
2498	{ return _M_a; }
2499
2500	_RealType
2501	b() const
2502	{ return _M_b; }
2503
2504	_RealType
2505	c() const
2506	{ return _M_c; }
2507
2508	friend bool
2509	operator==(const param_type& __p1, const param_type& __p2)
2510	{
2511	  return (__p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b
2512		  && __p1._M_c == __p2._M_c);
2513	}
2514
2515	friend bool
2516	operator!=(const param_type& __p1, const param_type& __p2)
2517	{ return !(__p1 == __p2); }
2518
2519      private:
2520
2521	_RealType _M_a;
2522	_RealType _M_b;
2523	_RealType _M_c;
2524	_RealType _M_r_ab;
2525	_RealType _M_f_ab_ac;
2526	_RealType _M_f_bc_ac;
2527      };
2528
2529      triangular_distribution() : triangular_distribution(0.0) { }
2530
2531      /**
2532       * @brief Constructs a triangle distribution with parameters
2533       * @f$ a @f$, @f$ b @f$ and @f$ c @f$.
2534       */
2535      explicit
2536      triangular_distribution(result_type __a,
2537			      result_type __b = result_type(0.5),
2538			      result_type __c = result_type(1))
2539      : _M_param(__a, __b, __c)
2540      { }
2541
2542      explicit
2543      triangular_distribution(const param_type& __p)
2544      : _M_param(__p)
2545      { }
2546
2547      /**
2548       * @brief Resets the distribution state.
2549       */
2550      void
2551      reset()
2552      { }
2553
2554      /**
2555       * @brief Returns the @f$ a @f$ of the distribution.
2556       */
2557      result_type
2558      a() const
2559      { return _M_param.a(); }
2560
2561      /**
2562       * @brief Returns the @f$ b @f$ of the distribution.
2563       */
2564      result_type
2565      b() const
2566      { return _M_param.b(); }
2567
2568      /**
2569       * @brief Returns the @f$ c @f$ of the distribution.
2570       */
2571      result_type
2572      c() const
2573      { return _M_param.c(); }
2574
2575      /**
2576       * @brief Returns the parameter set of the distribution.
2577       */
2578      param_type
2579      param() const
2580      { return _M_param; }
2581
2582      /**
2583       * @brief Sets the parameter set of the distribution.
2584       * @param __param The new parameter set of the distribution.
2585       */
2586      void
2587      param(const param_type& __param)
2588      { _M_param = __param; }
2589
2590      /**
2591       * @brief Returns the greatest lower bound value of the distribution.
2592       */
2593      result_type
2594      min() const
2595      { return _M_param._M_a; }
2596
2597      /**
2598       * @brief Returns the least upper bound value of the distribution.
2599       */
2600      result_type
2601      max() const
2602      { return _M_param._M_c; }
2603
2604      /**
2605       * @brief Generating functions.
2606       */
2607      template<typename _UniformRandomNumberGenerator>
2608	result_type
2609	operator()(_UniformRandomNumberGenerator& __urng)
2610	{ return this->operator()(__urng, _M_param); }
2611
2612      template<typename _UniformRandomNumberGenerator>
2613	result_type
2614	operator()(_UniformRandomNumberGenerator& __urng,
2615		   const param_type& __p)
2616	{
2617	  std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2618	    __aurng(__urng);
2619	  result_type __rnd = __aurng();
2620	  if (__rnd <= __p._M_r_ab)
2621	    return __p.a() + std::sqrt(__rnd * __p._M_f_ab_ac);
2622	  else
2623	    return __p.c() - std::sqrt((result_type(1) - __rnd)
2624				       * __p._M_f_bc_ac);
2625	}
2626
2627      template<typename _ForwardIterator,
2628	       typename _UniformRandomNumberGenerator>
2629	void
2630	__generate(_ForwardIterator __f, _ForwardIterator __t,
2631		   _UniformRandomNumberGenerator& __urng)
2632	{ this->__generate(__f, __t, __urng, _M_param); }
2633
2634      template<typename _ForwardIterator,
2635	       typename _UniformRandomNumberGenerator>
2636	void
2637	__generate(_ForwardIterator __f, _ForwardIterator __t,
2638		   _UniformRandomNumberGenerator& __urng,
2639		   const param_type& __p)
2640	{ this->__generate_impl(__f, __t, __urng, __p); }
2641
2642      template<typename _UniformRandomNumberGenerator>
2643	void
2644	__generate(result_type* __f, result_type* __t,
2645		   _UniformRandomNumberGenerator& __urng,
2646		   const param_type& __p)
2647	{ this->__generate_impl(__f, __t, __urng, __p); }
2648
2649      /**
2650       * @brief Return true if two triangle distributions have the same
2651       *        parameters and the sequences that would be generated
2652       *        are equal.
2653       */
2654      friend bool
2655      operator==(const triangular_distribution& __d1,
2656		 const triangular_distribution& __d2)
2657      { return __d1._M_param == __d2._M_param; }
2658
2659      /**
2660       * @brief Inserts a %triangular_distribution random number distribution
2661       * @p __x into the output stream @p __os.
2662       *
2663       * @param __os An output stream.
2664       * @param __x  A %triangular_distribution random number distribution.
2665       *
2666       * @returns The output stream with the state of @p __x inserted or in
2667       * an error state.
2668       */
2669      template<typename _RealType1, typename _CharT, typename _Traits>
2670	friend std::basic_ostream<_CharT, _Traits>&
2671	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2672		   const __gnu_cxx::triangular_distribution<_RealType1>& __x);
2673
2674      /**
2675       * @brief Extracts a %triangular_distribution random number distribution
2676       * @p __x from the input stream @p __is.
2677       *
2678       * @param __is An input stream.
2679       * @param __x  A %triangular_distribution random number generator engine.
2680       *
2681       * @returns The input stream with @p __x extracted or in an error state.
2682       */
2683      template<typename _RealType1, typename _CharT, typename _Traits>
2684	friend std::basic_istream<_CharT, _Traits>&
2685	operator>>(std::basic_istream<_CharT, _Traits>& __is,
2686		   __gnu_cxx::triangular_distribution<_RealType1>& __x);
2687
2688    private:
2689      template<typename _ForwardIterator,
2690	       typename _UniformRandomNumberGenerator>
2691	void
2692	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2693			_UniformRandomNumberGenerator& __urng,
2694			const param_type& __p);
2695
2696      param_type _M_param;
2697    };
2698
2699  /**
2700   * @brief Return true if two triangle distributions are different.
2701   */
2702  template<typename _RealType>
2703    inline bool
2704    operator!=(const __gnu_cxx::triangular_distribution<_RealType>& __d1,
2705	       const __gnu_cxx::triangular_distribution<_RealType>& __d2)
2706    { return !(__d1 == __d2); }
2707
2708
2709  /**
2710   * @brief A von Mises distribution for random numbers.
2711   *
2712   * The formula for the von Mises probability density function is
2713   * @f[
2714   *     p(x|\mu,\kappa) = \frac{e^{\kappa \cos(x-\mu)}}
2715   *                            {2\pi I_0(\kappa)}
2716   * @f]
2717   *
2718   * The generating functions use the method according to:
2719   *
2720   * D. J. Best and N. I. Fisher, 1979. "Efficient Simulation of the
2721   * von Mises Distribution", Journal of the Royal Statistical Society.
2722   * Series C (Applied Statistics), Vol. 28, No. 2, pp. 152-157.
2723   *
2724   * <table border=1 cellpadding=10 cellspacing=0>
2725   * <caption align=top>Distribution Statistics</caption>
2726   * <tr><td>Mean</td><td>@f$ \mu @f$</td></tr>
2727   * <tr><td>Variance</td><td>@f$ 1-I_1(\kappa)/I_0(\kappa) @f$</td></tr>
2728   * <tr><td>Range</td><td>@f$[-\pi, \pi]@f$</td></tr>
2729   * </table>
2730   */
2731  template<typename _RealType = double>
2732    class von_mises_distribution
2733    {
2734      static_assert(std::is_floating_point<_RealType>::value,
2735		    "template argument not a floating point type");
2736
2737    public:
2738      /** The type of the range of the distribution. */
2739      typedef _RealType result_type;
2740
2741      /** Parameter type. */
2742      struct param_type
2743      {
2744	friend class von_mises_distribution<_RealType>;
2745
2746	param_type() : param_type(0) { }
2747
2748	explicit
2749	param_type(_RealType __mu, _RealType __kappa = _RealType(1))
2750	: _M_mu(__mu), _M_kappa(__kappa)
2751	{
2752	  const _RealType __pi = __gnu_cxx::__math_constants<_RealType>::__pi;
2753	  __glibcxx_assert(_M_mu >= -__pi && _M_mu <= __pi);
2754	  __glibcxx_assert(_M_kappa >= _RealType(0));
2755
2756	  auto __tau = std::sqrt(_RealType(4) * _M_kappa * _M_kappa
2757				 + _RealType(1)) + _RealType(1);
2758	  auto __rho = ((__tau - std::sqrt(_RealType(2) * __tau))
2759			/ (_RealType(2) * _M_kappa));
2760	  _M_r = (_RealType(1) + __rho * __rho) / (_RealType(2) * __rho);
2761	}
2762
2763	_RealType
2764	mu() const
2765	{ return _M_mu; }
2766
2767	_RealType
2768	kappa() const
2769	{ return _M_kappa; }
2770
2771	friend bool
2772	operator==(const param_type& __p1, const param_type& __p2)
2773	{ return __p1._M_mu == __p2._M_mu && __p1._M_kappa == __p2._M_kappa; }
2774
2775	friend bool
2776	operator!=(const param_type& __p1, const param_type& __p2)
2777	{ return !(__p1 == __p2); }
2778
2779      private:
2780	_RealType _M_mu;
2781	_RealType _M_kappa;
2782	_RealType _M_r;
2783      };
2784
2785      von_mises_distribution() : von_mises_distribution(0.0) { }
2786
2787      /**
2788       * @brief Constructs a von Mises distribution with parameters
2789       * @f$\mu@f$ and @f$\kappa@f$.
2790       */
2791      explicit
2792      von_mises_distribution(result_type __mu,
2793			     result_type __kappa = result_type(1))
2794      : _M_param(__mu, __kappa)
2795      { }
2796
2797      explicit
2798      von_mises_distribution(const param_type& __p)
2799      : _M_param(__p)
2800      { }
2801
2802      /**
2803       * @brief Resets the distribution state.
2804       */
2805      void
2806      reset()
2807      { }
2808
2809      /**
2810       * @brief Returns the @f$ \mu @f$ of the distribution.
2811       */
2812      result_type
2813      mu() const
2814      { return _M_param.mu(); }
2815
2816      /**
2817       * @brief Returns the @f$ \kappa @f$ of the distribution.
2818       */
2819      result_type
2820      kappa() const
2821      { return _M_param.kappa(); }
2822
2823      /**
2824       * @brief Returns the parameter set of the distribution.
2825       */
2826      param_type
2827      param() const
2828      { return _M_param; }
2829
2830      /**
2831       * @brief Sets the parameter set of the distribution.
2832       * @param __param The new parameter set of the distribution.
2833       */
2834      void
2835      param(const param_type& __param)
2836      { _M_param = __param; }
2837
2838      /**
2839       * @brief Returns the greatest lower bound value of the distribution.
2840       */
2841      result_type
2842      min() const
2843      {
2844	return -__gnu_cxx::__math_constants<result_type>::__pi;
2845      }
2846
2847      /**
2848       * @brief Returns the least upper bound value of the distribution.
2849       */
2850      result_type
2851      max() const
2852      {
2853	return __gnu_cxx::__math_constants<result_type>::__pi;
2854      }
2855
2856      /**
2857       * @brief Generating functions.
2858       */
2859      template<typename _UniformRandomNumberGenerator>
2860	result_type
2861	operator()(_UniformRandomNumberGenerator& __urng)
2862	{ return this->operator()(__urng, _M_param); }
2863
2864      template<typename _UniformRandomNumberGenerator>
2865	result_type
2866	operator()(_UniformRandomNumberGenerator& __urng,
2867		   const param_type& __p);
2868
2869      template<typename _ForwardIterator,
2870	       typename _UniformRandomNumberGenerator>
2871	void
2872	__generate(_ForwardIterator __f, _ForwardIterator __t,
2873		   _UniformRandomNumberGenerator& __urng)
2874	{ this->__generate(__f, __t, __urng, _M_param); }
2875
2876      template<typename _ForwardIterator,
2877	       typename _UniformRandomNumberGenerator>
2878	void
2879	__generate(_ForwardIterator __f, _ForwardIterator __t,
2880		   _UniformRandomNumberGenerator& __urng,
2881		   const param_type& __p)
2882	{ this->__generate_impl(__f, __t, __urng, __p); }
2883
2884      template<typename _UniformRandomNumberGenerator>
2885	void
2886	__generate(result_type* __f, result_type* __t,
2887		   _UniformRandomNumberGenerator& __urng,
2888		   const param_type& __p)
2889	{ this->__generate_impl(__f, __t, __urng, __p); }
2890
2891      /**
2892       * @brief Return true if two von Mises distributions have the same
2893       *        parameters and the sequences that would be generated
2894       *        are equal.
2895       */
2896      friend bool
2897      operator==(const von_mises_distribution& __d1,
2898		 const von_mises_distribution& __d2)
2899      { return __d1._M_param == __d2._M_param; }
2900
2901      /**
2902       * @brief Inserts a %von_mises_distribution random number distribution
2903       * @p __x into the output stream @p __os.
2904       *
2905       * @param __os An output stream.
2906       * @param __x  A %von_mises_distribution random number distribution.
2907       *
2908       * @returns The output stream with the state of @p __x inserted or in
2909       * an error state.
2910       */
2911      template<typename _RealType1, typename _CharT, typename _Traits>
2912	friend std::basic_ostream<_CharT, _Traits>&
2913	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2914		   const __gnu_cxx::von_mises_distribution<_RealType1>& __x);
2915
2916      /**
2917       * @brief Extracts a %von_mises_distribution random number distribution
2918       * @p __x from the input stream @p __is.
2919       *
2920       * @param __is An input stream.
2921       * @param __x  A %von_mises_distribution random number generator engine.
2922       *
2923       * @returns The input stream with @p __x extracted or in an error state.
2924       */
2925      template<typename _RealType1, typename _CharT, typename _Traits>
2926	friend std::basic_istream<_CharT, _Traits>&
2927	operator>>(std::basic_istream<_CharT, _Traits>& __is,
2928		   __gnu_cxx::von_mises_distribution<_RealType1>& __x);
2929
2930    private:
2931      template<typename _ForwardIterator,
2932	       typename _UniformRandomNumberGenerator>
2933	void
2934	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2935			_UniformRandomNumberGenerator& __urng,
2936			const param_type& __p);
2937
2938      param_type _M_param;
2939    };
2940
2941  /**
2942   * @brief Return true if two von Mises distributions are different.
2943   */
2944  template<typename _RealType>
2945    inline bool
2946    operator!=(const __gnu_cxx::von_mises_distribution<_RealType>& __d1,
2947	       const __gnu_cxx::von_mises_distribution<_RealType>& __d2)
2948    { return !(__d1 == __d2); }
2949
2950
2951  /**
2952   * @brief A discrete hypergeometric random number distribution.
2953   *
2954   * The hypergeometric distribution is a discrete probability distribution
2955   * that describes the probability of @p k successes in @p n draws @a without
2956   * replacement from a finite population of size @p N containing exactly @p K
2957   * successes.
2958   *
2959   * The formula for the hypergeometric probability density function is
2960   * @f[
2961   *   p(k|N,K,n) = \frac{\binom{K}{k} \binom{N-K}{n-k}}{\binom{N}{n}}
2962   * @f]
2963   * where @f$N@f$ is the total population of the distribution,
2964   * @f$K@f$ is the total population of the distribution.
2965   *
2966   * <table border=1 cellpadding=10 cellspacing=0>
2967   * <caption align=top>Distribution Statistics</caption>
2968   * <tr><td>Mean</td><td>@f$ n\frac{K}{N} @f$</td></tr>
2969   * <tr><td>Variance</td><td>@f$ n\frac{K}{N}\frac{N-K}{N}\frac{N-n}{N-1}
2970   *   @f$</td></tr>
2971   * <tr><td>Range</td><td>@f$[max(0, n+K-N), min(K, n)]@f$</td></tr>
2972   * </table>
2973   */
2974  template<typename _UIntType = unsigned int>
2975    class hypergeometric_distribution
2976    {
2977      static_assert(std::is_unsigned<_UIntType>::value, "template argument "
2978		    "substituting _UIntType not an unsigned integral type");
2979
2980    public:
2981      /** The type of the range of the distribution. */
2982      typedef _UIntType  result_type;
2983
2984      /** Parameter type. */
2985      struct param_type
2986      {
2987	typedef hypergeometric_distribution<_UIntType> distribution_type;
2988	friend class hypergeometric_distribution<_UIntType>;
2989
2990	param_type() : param_type(10) { }
2991
2992	explicit
2993	param_type(result_type __N, result_type __K = 5,
2994		   result_type __n = 1)
2995	: _M_N{__N}, _M_K{__K}, _M_n{__n}
2996	{
2997	  __glibcxx_assert(_M_N >= _M_K);
2998	  __glibcxx_assert(_M_N >= _M_n);
2999	}
3000
3001	result_type
3002	total_size() const
3003	{ return _M_N; }
3004
3005	result_type
3006	successful_size() const
3007	{ return _M_K; }
3008
3009	result_type
3010	unsuccessful_size() const
3011	{ return _M_N - _M_K; }
3012
3013	result_type
3014	total_draws() const
3015	{ return _M_n; }
3016
3017	friend bool
3018	operator==(const param_type& __p1, const param_type& __p2)
3019	{ return (__p1._M_N == __p2._M_N)
3020	      && (__p1._M_K == __p2._M_K)
3021	      && (__p1._M_n == __p2._M_n); }
3022
3023	friend bool
3024	operator!=(const param_type& __p1, const param_type& __p2)
3025	{ return !(__p1 == __p2); }
3026
3027      private:
3028
3029	result_type _M_N;
3030	result_type _M_K;
3031	result_type _M_n;
3032      };
3033
3034      // constructors and member functions
3035
3036      hypergeometric_distribution() : hypergeometric_distribution(10) { }
3037
3038      explicit
3039      hypergeometric_distribution(result_type __N, result_type __K = 5,
3040				  result_type __n = 1)
3041      : _M_param{__N, __K, __n}
3042      { }
3043
3044      explicit
3045      hypergeometric_distribution(const param_type& __p)
3046      : _M_param{__p}
3047      { }
3048
3049      /**
3050       * @brief Resets the distribution state.
3051       */
3052      void
3053      reset()
3054      { }
3055
3056      /**
3057       * @brief Returns the distribution parameter @p N,
3058       *	the total number of items.
3059       */
3060      result_type
3061      total_size() const
3062      { return this->_M_param.total_size(); }
3063
3064      /**
3065       * @brief Returns the distribution parameter @p K,
3066       *	the total number of successful items.
3067       */
3068      result_type
3069      successful_size() const
3070      { return this->_M_param.successful_size(); }
3071
3072      /**
3073       * @brief Returns the total number of unsuccessful items @f$ N - K @f$.
3074       */
3075      result_type
3076      unsuccessful_size() const
3077      { return this->_M_param.unsuccessful_size(); }
3078
3079      /**
3080       * @brief Returns the distribution parameter @p n,
3081       *	the total number of draws.
3082       */
3083      result_type
3084      total_draws() const
3085      { return this->_M_param.total_draws(); }
3086
3087      /**
3088       * @brief Returns the parameter set of the distribution.
3089       */
3090      param_type
3091      param() const
3092      { return this->_M_param; }
3093
3094      /**
3095       * @brief Sets the parameter set of the distribution.
3096       * @param __param The new parameter set of the distribution.
3097       */
3098      void
3099      param(const param_type& __param)
3100      { this->_M_param = __param; }
3101
3102      /**
3103       * @brief Returns the greatest lower bound value of the distribution.
3104       */
3105      result_type
3106      min() const
3107      {
3108	using _IntType = typename std::make_signed<result_type>::type;
3109	return static_cast<result_type>(std::max(static_cast<_IntType>(0),
3110				static_cast<_IntType>(this->total_draws()
3111						- this->unsuccessful_size())));
3112      }
3113
3114      /**
3115       * @brief Returns the least upper bound value of the distribution.
3116       */
3117      result_type
3118      max() const
3119      { return std::min(this->successful_size(), this->total_draws()); }
3120
3121      /**
3122       * @brief Generating functions.
3123       */
3124      template<typename _UniformRandomNumberGenerator>
3125	result_type
3126	operator()(_UniformRandomNumberGenerator& __urng)
3127	{ return this->operator()(__urng, this->_M_param); }
3128
3129      template<typename _UniformRandomNumberGenerator>
3130	result_type
3131	operator()(_UniformRandomNumberGenerator& __urng,
3132		   const param_type& __p);
3133
3134      template<typename _ForwardIterator,
3135	       typename _UniformRandomNumberGenerator>
3136	void
3137	__generate(_ForwardIterator __f, _ForwardIterator __t,
3138		   _UniformRandomNumberGenerator& __urng)
3139	{ this->__generate(__f, __t, __urng, this->_M_param); }
3140
3141      template<typename _ForwardIterator,
3142	       typename _UniformRandomNumberGenerator>
3143	void
3144	__generate(_ForwardIterator __f, _ForwardIterator __t,
3145		   _UniformRandomNumberGenerator& __urng,
3146		   const param_type& __p)
3147	{ this->__generate_impl(__f, __t, __urng, __p); }
3148
3149      template<typename _UniformRandomNumberGenerator>
3150	void
3151	__generate(result_type* __f, result_type* __t,
3152		   _UniformRandomNumberGenerator& __urng,
3153		   const param_type& __p)
3154	{ this->__generate_impl(__f, __t, __urng, __p); }
3155
3156       /**
3157	* @brief Return true if two hypergeometric distributions have the same
3158	*        parameters and the sequences that would be generated
3159	*        are equal.
3160	*/
3161      friend bool
3162      operator==(const hypergeometric_distribution& __d1,
3163		 const hypergeometric_distribution& __d2)
3164      { return __d1._M_param == __d2._M_param; }
3165
3166      /**
3167       * @brief Inserts a %hypergeometric_distribution random number
3168       * distribution @p __x into the output stream @p __os.
3169       *
3170       * @param __os An output stream.
3171       * @param __x  A %hypergeometric_distribution random number
3172       *             distribution.
3173       *
3174       * @returns The output stream with the state of @p __x inserted or in
3175       * an error state.
3176       */
3177      template<typename _UIntType1, typename _CharT, typename _Traits>
3178	friend std::basic_ostream<_CharT, _Traits>&
3179	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3180		   const __gnu_cxx::hypergeometric_distribution<_UIntType1>&
3181		   __x);
3182
3183      /**
3184       * @brief Extracts a %hypergeometric_distribution random number
3185       * distribution @p __x from the input stream @p __is.
3186       *
3187       * @param __is An input stream.
3188       * @param __x  A %hypergeometric_distribution random number generator
3189       *             distribution.
3190       *
3191       * @returns The input stream with @p __x extracted or in an error
3192       *          state.
3193       */
3194      template<typename _UIntType1, typename _CharT, typename _Traits>
3195	friend std::basic_istream<_CharT, _Traits>&
3196	operator>>(std::basic_istream<_CharT, _Traits>& __is,
3197		   __gnu_cxx::hypergeometric_distribution<_UIntType1>& __x);
3198
3199    private:
3200
3201      template<typename _ForwardIterator,
3202	       typename _UniformRandomNumberGenerator>
3203	void
3204	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3205			_UniformRandomNumberGenerator& __urng,
3206			const param_type& __p);
3207
3208      param_type _M_param;
3209    };
3210
3211  /**
3212   * @brief Return true if two hypergeometric distributions are different.
3213   */
3214  template<typename _UIntType>
3215    inline bool
3216    operator!=(const __gnu_cxx::hypergeometric_distribution<_UIntType>& __d1,
3217	       const __gnu_cxx::hypergeometric_distribution<_UIntType>& __d2)
3218    { return !(__d1 == __d2); }
3219
3220  /**
3221   * @brief A logistic continuous distribution for random numbers.
3222   *
3223   * The formula for the logistic probability density function is
3224   * @f[
3225   *     p(x|\a,\b) = \frac{e^{(x - a)/b}}{b[1 + e^{(x - a)/b}]^2}
3226   * @f]
3227   * where @f$b > 0@f$.
3228   *
3229   * The formula for the logistic probability function is
3230   * @f[
3231   *     cdf(x|\a,\b) = \frac{e^{(x - a)/b}}{1 + e^{(x - a)/b}}
3232   * @f]
3233   * where @f$b > 0@f$.
3234   *
3235   * <table border=1 cellpadding=10 cellspacing=0>
3236   * <caption align=top>Distribution Statistics</caption>
3237   * <tr><td>Mean</td><td>@f$a@f$</td></tr>
3238   * <tr><td>Variance</td><td>@f$b^2\pi^2/3@f$</td></tr>
3239   * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
3240   * </table>
3241   */
3242  template<typename _RealType = double>
3243    class
3244    logistic_distribution
3245    {
3246      static_assert(std::is_floating_point<_RealType>::value,
3247		    "template argument not a floating point type");
3248
3249    public:
3250      /** The type of the range of the distribution. */
3251      typedef _RealType result_type;
3252
3253      /** Parameter type. */
3254      struct param_type
3255      {
3256	typedef logistic_distribution<result_type> distribution_type;
3257
3258	param_type() : param_type(0) { }
3259
3260	explicit
3261	param_type(result_type __a, result_type __b = result_type(1))
3262	: _M_a(__a), _M_b(__b)
3263	{
3264	  __glibcxx_assert(_M_b > result_type(0));
3265	}
3266
3267	result_type
3268	a() const
3269	{ return _M_a; }
3270
3271	result_type
3272	b() const
3273	{ return _M_b; }
3274
3275	friend bool
3276	operator==(const param_type& __p1, const param_type& __p2)
3277	{ return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
3278
3279	friend bool
3280	operator!=(const param_type& __p1, const param_type& __p2)
3281	{ return !(__p1 == __p2); }
3282
3283      private:
3284	void _M_initialize();
3285
3286	result_type _M_a;
3287	result_type _M_b;
3288      };
3289
3290      /**
3291       * @brief Constructors.
3292       * @{
3293       */
3294      logistic_distribution() : logistic_distribution(0.0) { }
3295
3296      explicit
3297      logistic_distribution(result_type __a, result_type __b = result_type(1))
3298      : _M_param(__a, __b)
3299      { }
3300
3301      explicit
3302      logistic_distribution(const param_type& __p)
3303      : _M_param(__p)
3304      { }
3305
3306      /// @}
3307
3308      /**
3309       * @brief Resets the distribution state.
3310       */
3311      void
3312      reset()
3313      { }
3314
3315      /**
3316       * @brief Return the parameters of the distribution.
3317       */
3318      result_type
3319      a() const
3320      { return _M_param.a(); }
3321
3322      result_type
3323      b() const
3324      { return _M_param.b(); }
3325
3326      /**
3327       * @brief Returns the parameter set of the distribution.
3328       */
3329      param_type
3330      param() const
3331      { return _M_param; }
3332
3333      /**
3334       * @brief Sets the parameter set of the distribution.
3335       * @param __param The new parameter set of the distribution.
3336       */
3337      void
3338      param(const param_type& __param)
3339      { _M_param = __param; }
3340
3341      /**
3342       * @brief Returns the greatest lower bound value of the distribution.
3343       */
3344      result_type
3345      min() const
3346      { return -std::numeric_limits<result_type>::max(); }
3347
3348      /**
3349       * @brief Returns the least upper bound value of the distribution.
3350       */
3351      result_type
3352      max() const
3353      { return std::numeric_limits<result_type>::max(); }
3354
3355      /**
3356       * @brief Generating functions.
3357       */
3358      template<typename _UniformRandomNumberGenerator>
3359	result_type
3360	operator()(_UniformRandomNumberGenerator& __urng)
3361	{ return this->operator()(__urng, this->_M_param); }
3362
3363      template<typename _UniformRandomNumberGenerator>
3364	result_type
3365	operator()(_UniformRandomNumberGenerator&,
3366		   const param_type&);
3367
3368      template<typename _ForwardIterator,
3369	       typename _UniformRandomNumberGenerator>
3370	void
3371	__generate(_ForwardIterator __f, _ForwardIterator __t,
3372		   _UniformRandomNumberGenerator& __urng)
3373	{ this->__generate(__f, __t, __urng, this->param()); }
3374
3375      template<typename _ForwardIterator,
3376	       typename _UniformRandomNumberGenerator>
3377	void
3378	__generate(_ForwardIterator __f, _ForwardIterator __t,
3379		   _UniformRandomNumberGenerator& __urng,
3380		   const param_type& __p)
3381	{ this->__generate_impl(__f, __t, __urng, __p); }
3382
3383      template<typename _UniformRandomNumberGenerator>
3384	void
3385	__generate(result_type* __f, result_type* __t,
3386		   _UniformRandomNumberGenerator& __urng,
3387		   const param_type& __p)
3388	{ this->__generate_impl(__f, __t, __urng, __p); }
3389
3390      /**
3391       * @brief Return true if two logistic distributions have
3392       *        the same parameters and the sequences that would
3393       *        be generated are equal.
3394       */
3395      template<typename _RealType1>
3396	friend bool
3397	operator==(const logistic_distribution<_RealType1>& __d1,
3398		   const logistic_distribution<_RealType1>& __d2)
3399	{ return __d1.param() == __d2.param(); }
3400
3401      /**
3402       * @brief Inserts a %logistic_distribution random number distribution
3403       * @p __x into the output stream @p __os.
3404       *
3405       * @param __os An output stream.
3406       * @param __x  A %logistic_distribution random number distribution.
3407       *
3408       * @returns The output stream with the state of @p __x inserted or in
3409       * an error state.
3410       */
3411      template<typename _RealType1, typename _CharT, typename _Traits>
3412	friend std::basic_ostream<_CharT, _Traits>&
3413	operator<<(std::basic_ostream<_CharT, _Traits>&,
3414		   const logistic_distribution<_RealType1>&);
3415
3416      /**
3417       * @brief Extracts a %logistic_distribution random number distribution
3418       * @p __x from the input stream @p __is.
3419       *
3420       * @param __is An input stream.
3421       * @param __x A %logistic_distribution random number
3422       *            generator engine.
3423       *
3424       * @returns The input stream with @p __x extracted or in an error state.
3425       */
3426      template<typename _RealType1, typename _CharT, typename _Traits>
3427	friend std::basic_istream<_CharT, _Traits>&
3428	operator>>(std::basic_istream<_CharT, _Traits>&,
3429		   logistic_distribution<_RealType1>&);
3430
3431    private:
3432      template<typename _ForwardIterator,
3433	       typename _UniformRandomNumberGenerator>
3434	void
3435	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3436			_UniformRandomNumberGenerator& __urng,
3437			const param_type& __p);
3438
3439      param_type _M_param;
3440    };
3441
3442  /**
3443   * @brief Return true if two logistic distributions are not equal.
3444   */
3445  template<typename _RealType1>
3446    inline bool
3447    operator!=(const logistic_distribution<_RealType1>& __d1,
3448	       const logistic_distribution<_RealType1>& __d2)
3449    { return !(__d1 == __d2); }
3450
3451
3452  /**
3453   * @brief A distribution for random coordinates on a unit sphere.
3454   *
3455   * The method used in the generation function is attributed by Donald Knuth
3456   * to G. W. Brown, Modern Mathematics for the Engineer (1956).
3457   */
3458  template<std::size_t _Dimen, typename _RealType = double>
3459    class uniform_on_sphere_distribution
3460    {
3461      static_assert(std::is_floating_point<_RealType>::value,
3462		    "template argument not a floating point type");
3463      static_assert(_Dimen != 0, "dimension is zero");
3464
3465    public:
3466      /** The type of the range of the distribution. */
3467      typedef std::array<_RealType, _Dimen> result_type;
3468
3469      /** Parameter type. */
3470      struct param_type
3471      {
3472	param_type() { }
3473
3474	friend bool
3475	operator==(const param_type&, const param_type&)
3476	{ return true; }
3477
3478	friend bool
3479	operator!=(const param_type&, const param_type&)
3480	{ return false; }
3481      };
3482
3483      /**
3484       * @brief Constructs a uniform on sphere distribution.
3485       */
3486      uniform_on_sphere_distribution()
3487      : _M_param(), _M_nd()
3488      { }
3489
3490      explicit
3491      uniform_on_sphere_distribution(const param_type& __p)
3492      : _M_param(__p), _M_nd()
3493      { }
3494
3495      /**
3496       * @brief Resets the distribution state.
3497       */
3498      void
3499      reset()
3500      { _M_nd.reset(); }
3501
3502      /**
3503       * @brief Returns the parameter set of the distribution.
3504       */
3505      param_type
3506      param() const
3507      { return _M_param; }
3508
3509      /**
3510       * @brief Sets the parameter set of the distribution.
3511       * @param __param The new parameter set of the distribution.
3512       */
3513      void
3514      param(const param_type& __param)
3515      { _M_param = __param; }
3516
3517      /**
3518       * @brief Returns the greatest lower bound value of the distribution.
3519       * This function makes no sense for this distribution.
3520       */
3521      result_type
3522      min() const
3523      {
3524	result_type __res;
3525	__res.fill(0);
3526	return __res;
3527      }
3528
3529      /**
3530       * @brief Returns the least upper bound value of the distribution.
3531       * This function makes no sense for this distribution.
3532       */
3533      result_type
3534      max() const
3535      {
3536	result_type __res;
3537	__res.fill(0);
3538	return __res;
3539      }
3540
3541      /**
3542       * @brief Generating functions.
3543       */
3544      template<typename _UniformRandomNumberGenerator>
3545	result_type
3546	operator()(_UniformRandomNumberGenerator& __urng)
3547	{ return this->operator()(__urng, _M_param); }
3548
3549      template<typename _UniformRandomNumberGenerator>
3550	result_type
3551	operator()(_UniformRandomNumberGenerator& __urng,
3552		   const param_type& __p);
3553
3554      template<typename _ForwardIterator,
3555	       typename _UniformRandomNumberGenerator>
3556	void
3557	__generate(_ForwardIterator __f, _ForwardIterator __t,
3558		   _UniformRandomNumberGenerator& __urng)
3559	{ this->__generate(__f, __t, __urng, this->param()); }
3560
3561      template<typename _ForwardIterator,
3562	       typename _UniformRandomNumberGenerator>
3563	void
3564	__generate(_ForwardIterator __f, _ForwardIterator __t,
3565		   _UniformRandomNumberGenerator& __urng,
3566		   const param_type& __p)
3567	{ this->__generate_impl(__f, __t, __urng, __p); }
3568
3569      template<typename _UniformRandomNumberGenerator>
3570	void
3571	__generate(result_type* __f, result_type* __t,
3572		   _UniformRandomNumberGenerator& __urng,
3573		   const param_type& __p)
3574	{ this->__generate_impl(__f, __t, __urng, __p); }
3575
3576      /**
3577       * @brief Return true if two uniform on sphere distributions have
3578       *        the same parameters and the sequences that would be
3579       *        generated are equal.
3580       */
3581      friend bool
3582      operator==(const uniform_on_sphere_distribution& __d1,
3583		 const uniform_on_sphere_distribution& __d2)
3584      { return __d1._M_nd == __d2._M_nd; }
3585
3586      /**
3587       * @brief Inserts a %uniform_on_sphere_distribution random number
3588       *        distribution @p __x into the output stream @p __os.
3589       *
3590       * @param __os An output stream.
3591       * @param __x  A %uniform_on_sphere_distribution random number
3592       *             distribution.
3593       *
3594       * @returns The output stream with the state of @p __x inserted or in
3595       * an error state.
3596       */
3597      template<size_t _Dimen1, typename _RealType1, typename _CharT,
3598	       typename _Traits>
3599	friend std::basic_ostream<_CharT, _Traits>&
3600	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3601		   const __gnu_cxx::uniform_on_sphere_distribution<_Dimen1,
3602								   _RealType1>&
3603		   __x);
3604
3605      /**
3606       * @brief Extracts a %uniform_on_sphere_distribution random number
3607       *        distribution
3608       * @p __x from the input stream @p __is.
3609       *
3610       * @param __is An input stream.
3611       * @param __x  A %uniform_on_sphere_distribution random number
3612       *             generator engine.
3613       *
3614       * @returns The input stream with @p __x extracted or in an error state.
3615       */
3616      template<std::size_t _Dimen1, typename _RealType1, typename _CharT,
3617	       typename _Traits>
3618	friend std::basic_istream<_CharT, _Traits>&
3619	operator>>(std::basic_istream<_CharT, _Traits>& __is,
3620		   __gnu_cxx::uniform_on_sphere_distribution<_Dimen1,
3621							     _RealType1>& __x);
3622
3623    private:
3624      template<typename _ForwardIterator,
3625	       typename _UniformRandomNumberGenerator>
3626	void
3627	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3628			_UniformRandomNumberGenerator& __urng,
3629			const param_type& __p);
3630
3631      param_type _M_param;
3632      std::normal_distribution<_RealType> _M_nd;
3633    };
3634
3635  /**
3636   * @brief Return true if two uniform on sphere distributions are different.
3637   */
3638  template<std::size_t _Dimen, typename _RealType>
3639    inline bool
3640    operator!=(const __gnu_cxx::uniform_on_sphere_distribution<_Dimen,
3641	       _RealType>& __d1,
3642	       const __gnu_cxx::uniform_on_sphere_distribution<_Dimen,
3643	       _RealType>& __d2)
3644    { return !(__d1 == __d2); }
3645
3646
3647  /**
3648   * @brief A distribution for random coordinates inside a unit sphere.
3649   */
3650  template<std::size_t _Dimen, typename _RealType = double>
3651    class uniform_inside_sphere_distribution
3652    {
3653      static_assert(std::is_floating_point<_RealType>::value,
3654		    "template argument not a floating point type");
3655      static_assert(_Dimen != 0, "dimension is zero");
3656
3657    public:
3658      /** The type of the range of the distribution. */
3659      using result_type = std::array<_RealType, _Dimen>;
3660
3661      /** Parameter type. */
3662      struct param_type
3663      {
3664	using distribution_type
3665	  = uniform_inside_sphere_distribution<_Dimen, _RealType>;
3666	friend class uniform_inside_sphere_distribution<_Dimen, _RealType>;
3667
3668	param_type() : param_type(1.0) { }
3669
3670	explicit
3671	param_type(_RealType __radius)
3672	: _M_radius(__radius)
3673	{
3674	  __glibcxx_assert(_M_radius > _RealType(0));
3675	}
3676
3677	_RealType
3678	radius() const
3679	{ return _M_radius; }
3680
3681	friend bool
3682	operator==(const param_type& __p1, const param_type& __p2)
3683	{ return __p1._M_radius == __p2._M_radius; }
3684
3685	friend bool
3686	operator!=(const param_type& __p1, const param_type& __p2)
3687	{ return !(__p1 == __p2); }
3688
3689      private:
3690	_RealType _M_radius;
3691      };
3692
3693      /**
3694       * @brief Constructors.
3695       * @{
3696       */
3697
3698      uniform_inside_sphere_distribution()
3699      : uniform_inside_sphere_distribution(1.0)
3700      { }
3701
3702      explicit
3703      uniform_inside_sphere_distribution(_RealType __radius)
3704      : _M_param(__radius), _M_uosd()
3705      { }
3706
3707      explicit
3708      uniform_inside_sphere_distribution(const param_type& __p)
3709      : _M_param(__p), _M_uosd()
3710      { }
3711
3712      /// @}
3713
3714      /**
3715       * @brief Resets the distribution state.
3716       */
3717      void
3718      reset()
3719      { _M_uosd.reset(); }
3720
3721      /**
3722       * @brief Returns the @f$radius@f$ of the distribution.
3723       */
3724      _RealType
3725      radius() const
3726      { return _M_param.radius(); }
3727
3728      /**
3729       * @brief Returns the parameter set of the distribution.
3730       */
3731      param_type
3732      param() const
3733      { return _M_param; }
3734
3735      /**
3736       * @brief Sets the parameter set of the distribution.
3737       * @param __param The new parameter set of the distribution.
3738       */
3739      void
3740      param(const param_type& __param)
3741      { _M_param = __param; }
3742
3743      /**
3744       * @brief Returns the greatest lower bound value of the distribution.
3745       * This function makes no sense for this distribution.
3746       */
3747      result_type
3748      min() const
3749      {
3750	result_type __res;
3751	__res.fill(0);
3752	return __res;
3753      }
3754
3755      /**
3756       * @brief Returns the least upper bound value of the distribution.
3757       * This function makes no sense for this distribution.
3758       */
3759      result_type
3760      max() const
3761      {
3762	result_type __res;
3763	__res.fill(0);
3764	return __res;
3765      }
3766
3767      /**
3768       * @brief Generating functions.
3769       */
3770      template<typename _UniformRandomNumberGenerator>
3771	result_type
3772	operator()(_UniformRandomNumberGenerator& __urng)
3773	{ return this->operator()(__urng, _M_param); }
3774
3775      template<typename _UniformRandomNumberGenerator>
3776	result_type
3777	operator()(_UniformRandomNumberGenerator& __urng,
3778		   const param_type& __p);
3779
3780      template<typename _ForwardIterator,
3781	       typename _UniformRandomNumberGenerator>
3782	void
3783	__generate(_ForwardIterator __f, _ForwardIterator __t,
3784		   _UniformRandomNumberGenerator& __urng)
3785	{ this->__generate(__f, __t, __urng, this->param()); }
3786
3787      template<typename _ForwardIterator,
3788	       typename _UniformRandomNumberGenerator>
3789	void
3790	__generate(_ForwardIterator __f, _ForwardIterator __t,
3791		   _UniformRandomNumberGenerator& __urng,
3792		   const param_type& __p)
3793	{ this->__generate_impl(__f, __t, __urng, __p); }
3794
3795      template<typename _UniformRandomNumberGenerator>
3796	void
3797	__generate(result_type* __f, result_type* __t,
3798		   _UniformRandomNumberGenerator& __urng,
3799		   const param_type& __p)
3800	{ this->__generate_impl(__f, __t, __urng, __p); }
3801
3802      /**
3803       * @brief Return true if two uniform on sphere distributions have
3804       *        the same parameters and the sequences that would be
3805       *        generated are equal.
3806       */
3807      friend bool
3808      operator==(const uniform_inside_sphere_distribution& __d1,
3809		 const uniform_inside_sphere_distribution& __d2)
3810      { return __d1._M_param == __d2._M_param && __d1._M_uosd == __d2._M_uosd; }
3811
3812      /**
3813       * @brief Inserts a %uniform_inside_sphere_distribution random number
3814       *        distribution @p __x into the output stream @p __os.
3815       *
3816       * @param __os An output stream.
3817       * @param __x  A %uniform_inside_sphere_distribution random number
3818       *             distribution.
3819       *
3820       * @returns The output stream with the state of @p __x inserted or in
3821       * an error state.
3822       */
3823      template<size_t _Dimen1, typename _RealType1, typename _CharT,
3824	       typename _Traits>
3825	friend std::basic_ostream<_CharT, _Traits>&
3826	operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3827		   const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen1,
3828								   _RealType1>&
3829		   );
3830
3831      /**
3832       * @brief Extracts a %uniform_inside_sphere_distribution random number
3833       *        distribution
3834       * @p __x from the input stream @p __is.
3835       *
3836       * @param __is An input stream.
3837       * @param __x  A %uniform_inside_sphere_distribution random number
3838       *             generator engine.
3839       *
3840       * @returns The input stream with @p __x extracted or in an error state.
3841       */
3842      template<std::size_t _Dimen1, typename _RealType1, typename _CharT,
3843	       typename _Traits>
3844	friend std::basic_istream<_CharT, _Traits>&
3845	operator>>(std::basic_istream<_CharT, _Traits>& __is,
3846		   __gnu_cxx::uniform_inside_sphere_distribution<_Dimen1,
3847								 _RealType1>&);
3848
3849    private:
3850      template<typename _ForwardIterator,
3851	       typename _UniformRandomNumberGenerator>
3852	void
3853	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3854			_UniformRandomNumberGenerator& __urng,
3855			const param_type& __p);
3856
3857      param_type _M_param;
3858      uniform_on_sphere_distribution<_Dimen, _RealType> _M_uosd;
3859    };
3860
3861  /**
3862   * @brief Return true if two uniform on sphere distributions are different.
3863   */
3864  template<std::size_t _Dimen, typename _RealType>
3865    inline bool
3866    operator!=(const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen,
3867	       _RealType>& __d1,
3868	       const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen,
3869	       _RealType>& __d2)
3870    { return !(__d1 == __d2); }
3871
3872_GLIBCXX_END_NAMESPACE_VERSION
3873} // namespace __gnu_cxx
3874
3875#include <ext/opt_random.h>
3876#include <ext/random.tcc>
3877
3878#endif // _GLIBCXX_USE_C99_STDINT_TR1 && UINT32_C
3879
3880#endif // C++11
3881
3882#endif // _EXT_RANDOM
3883