1 // Random number extensions -*- C++ -*-
2 
3 // Copyright (C) 2012-2018 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.tcc
26  *  This is an internal header file, included by other library headers.
27  *  Do not attempt to use it directly. @headername{ext/random}
28  */
29 
30 #ifndef _EXT_RANDOM_TCC
31 #define _EXT_RANDOM_TCC 1
32 
33 #pragma GCC system_header
34 
35 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
36 {
37 _GLIBCXX_BEGIN_NAMESPACE_VERSION
38 
39 #if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
40 
41   template<typename _UIntType, size_t __m,
42 	   size_t __pos1, size_t __sl1, size_t __sl2,
43 	   size_t __sr1, size_t __sr2,
44 	   uint32_t __msk1, uint32_t __msk2,
45 	   uint32_t __msk3, uint32_t __msk4,
46 	   uint32_t __parity1, uint32_t __parity2,
47 	   uint32_t __parity3, uint32_t __parity4>
48     void simd_fast_mersenne_twister_engine<_UIntType, __m,
49 					   __pos1, __sl1, __sl2, __sr1, __sr2,
50 					   __msk1, __msk2, __msk3, __msk4,
51 					   __parity1, __parity2, __parity3,
52 					   __parity4>::
53     seed(_UIntType __seed)
54     {
55       _M_state32[0] = static_cast<uint32_t>(__seed);
56       for (size_t __i = 1; __i < _M_nstate32; ++__i)
57 	_M_state32[__i] = (1812433253UL
58 			   * (_M_state32[__i - 1] ^ (_M_state32[__i - 1] >> 30))
59 			   + __i);
60       _M_pos = state_size;
61       _M_period_certification();
62     }
63 
64 
65   namespace {
66 
67     inline uint32_t _Func1(uint32_t __x)
68     {
69       return (__x ^ (__x >> 27)) * UINT32_C(1664525);
70     }
71 
72     inline uint32_t _Func2(uint32_t __x)
73     {
74       return (__x ^ (__x >> 27)) * UINT32_C(1566083941);
75     }
76 
77   }
78 
79 
80   template<typename _UIntType, size_t __m,
81 	   size_t __pos1, size_t __sl1, size_t __sl2,
82 	   size_t __sr1, size_t __sr2,
83 	   uint32_t __msk1, uint32_t __msk2,
84 	   uint32_t __msk3, uint32_t __msk4,
85 	   uint32_t __parity1, uint32_t __parity2,
86 	   uint32_t __parity3, uint32_t __parity4>
87     template<typename _Sseq>
88       typename std::enable_if<std::is_class<_Sseq>::value>::type
89       simd_fast_mersenne_twister_engine<_UIntType, __m,
90 					__pos1, __sl1, __sl2, __sr1, __sr2,
91 					__msk1, __msk2, __msk3, __msk4,
92 					__parity1, __parity2, __parity3,
93 					__parity4>::
94       seed(_Sseq& __q)
95       {
96 	size_t __lag;
97 
98 	if (_M_nstate32 >= 623)
99 	  __lag = 11;
100 	else if (_M_nstate32 >= 68)
101 	  __lag = 7;
102 	else if (_M_nstate32 >= 39)
103 	  __lag = 5;
104 	else
105 	  __lag = 3;
106 	const size_t __mid = (_M_nstate32 - __lag) / 2;
107 
108 	std::fill(_M_state32, _M_state32 + _M_nstate32, UINT32_C(0x8b8b8b8b));
109 	uint32_t __arr[_M_nstate32];
110 	__q.generate(__arr + 0, __arr + _M_nstate32);
111 
112 	uint32_t __r = _Func1(_M_state32[0] ^ _M_state32[__mid]
113 			      ^ _M_state32[_M_nstate32  - 1]);
114 	_M_state32[__mid] += __r;
115 	__r += _M_nstate32;
116 	_M_state32[__mid + __lag] += __r;
117 	_M_state32[0] = __r;
118 
119 	for (size_t __i = 1, __j = 0; __j < _M_nstate32; ++__j)
120 	  {
121 	    __r = _Func1(_M_state32[__i]
122 			 ^ _M_state32[(__i + __mid) % _M_nstate32]
123 			 ^ _M_state32[(__i + _M_nstate32 - 1) % _M_nstate32]);
124 	    _M_state32[(__i + __mid) % _M_nstate32] += __r;
125 	    __r += __arr[__j] + __i;
126 	    _M_state32[(__i + __mid + __lag) % _M_nstate32] += __r;
127 	    _M_state32[__i] = __r;
128 	    __i = (__i + 1) % _M_nstate32;
129 	  }
130 	for (size_t __j = 0; __j < _M_nstate32; ++__j)
131 	  {
132 	    const size_t __i = (__j + 1) % _M_nstate32;
133 	    __r = _Func2(_M_state32[__i]
134 			 + _M_state32[(__i + __mid) % _M_nstate32]
135 			 + _M_state32[(__i + _M_nstate32 - 1) % _M_nstate32]);
136 	    _M_state32[(__i + __mid) % _M_nstate32] ^= __r;
137 	    __r -= __i;
138 	    _M_state32[(__i + __mid + __lag) % _M_nstate32] ^= __r;
139 	    _M_state32[__i] = __r;
140 	  }
141 
142 	_M_pos = state_size;
143 	_M_period_certification();
144       }
145 
146 
147   template<typename _UIntType, size_t __m,
148 	   size_t __pos1, size_t __sl1, size_t __sl2,
149 	   size_t __sr1, size_t __sr2,
150 	   uint32_t __msk1, uint32_t __msk2,
151 	   uint32_t __msk3, uint32_t __msk4,
152 	   uint32_t __parity1, uint32_t __parity2,
153 	   uint32_t __parity3, uint32_t __parity4>
154     void simd_fast_mersenne_twister_engine<_UIntType, __m,
155 					   __pos1, __sl1, __sl2, __sr1, __sr2,
156 					   __msk1, __msk2, __msk3, __msk4,
157 					   __parity1, __parity2, __parity3,
158 					   __parity4>::
159     _M_period_certification(void)
160     {
161       static const uint32_t __parity[4] = { __parity1, __parity2,
162 					    __parity3, __parity4 };
163       uint32_t __inner = 0;
164       for (size_t __i = 0; __i < 4; ++__i)
165 	if (__parity[__i] != 0)
166 	  __inner ^= _M_state32[__i] & __parity[__i];
167 
168       if (__builtin_parity(__inner) & 1)
169 	return;
170       for (size_t __i = 0; __i < 4; ++__i)
171 	if (__parity[__i] != 0)
172 	  {
173 	    _M_state32[__i] ^= 1 << (__builtin_ffs(__parity[__i]) - 1);
174 	    return;
175 	  }
176       __builtin_unreachable();
177     }
178 
179 
180   template<typename _UIntType, size_t __m,
181 	   size_t __pos1, size_t __sl1, size_t __sl2,
182 	   size_t __sr1, size_t __sr2,
183 	   uint32_t __msk1, uint32_t __msk2,
184 	   uint32_t __msk3, uint32_t __msk4,
185 	   uint32_t __parity1, uint32_t __parity2,
186 	   uint32_t __parity3, uint32_t __parity4>
187     void simd_fast_mersenne_twister_engine<_UIntType, __m,
188 					   __pos1, __sl1, __sl2, __sr1, __sr2,
189 					   __msk1, __msk2, __msk3, __msk4,
190 					   __parity1, __parity2, __parity3,
191 					   __parity4>::
192     discard(unsigned long long __z)
193     {
194       while (__z > state_size - _M_pos)
195 	{
196 	  __z -= state_size - _M_pos;
197 
198 	  _M_gen_rand();
199 	}
200 
201       _M_pos += __z;
202     }
203 
204 
205 #ifndef  _GLIBCXX_OPT_HAVE_RANDOM_SFMT_GEN_READ
206 
207   namespace {
208 
209     template<size_t __shift>
210       inline void __rshift(uint32_t *__out, const uint32_t *__in)
211       {
212 	uint64_t __th = ((static_cast<uint64_t>(__in[3]) << 32)
213 			 | static_cast<uint64_t>(__in[2]));
214 	uint64_t __tl = ((static_cast<uint64_t>(__in[1]) << 32)
215 			 | static_cast<uint64_t>(__in[0]));
216 
217 	uint64_t __oh = __th >> (__shift * 8);
218 	uint64_t __ol = __tl >> (__shift * 8);
219 	__ol |= __th << (64 - __shift * 8);
220 	__out[1] = static_cast<uint32_t>(__ol >> 32);
221 	__out[0] = static_cast<uint32_t>(__ol);
222 	__out[3] = static_cast<uint32_t>(__oh >> 32);
223 	__out[2] = static_cast<uint32_t>(__oh);
224       }
225 
226 
227     template<size_t __shift>
228       inline void __lshift(uint32_t *__out, const uint32_t *__in)
229       {
230 	uint64_t __th = ((static_cast<uint64_t>(__in[3]) << 32)
231 			 | static_cast<uint64_t>(__in[2]));
232 	uint64_t __tl = ((static_cast<uint64_t>(__in[1]) << 32)
233 			 | static_cast<uint64_t>(__in[0]));
234 
235 	uint64_t __oh = __th << (__shift * 8);
236 	uint64_t __ol = __tl << (__shift * 8);
237 	__oh |= __tl >> (64 - __shift * 8);
238 	__out[1] = static_cast<uint32_t>(__ol >> 32);
239 	__out[0] = static_cast<uint32_t>(__ol);
240 	__out[3] = static_cast<uint32_t>(__oh >> 32);
241 	__out[2] = static_cast<uint32_t>(__oh);
242       }
243 
244 
245     template<size_t __sl1, size_t __sl2, size_t __sr1, size_t __sr2,
246 	     uint32_t __msk1, uint32_t __msk2, uint32_t __msk3, uint32_t __msk4>
247       inline void __recursion(uint32_t *__r,
248 			      const uint32_t *__a, const uint32_t *__b,
249 			      const uint32_t *__c, const uint32_t *__d)
250       {
251 	uint32_t __x[4];
252 	uint32_t __y[4];
253 
254 	__lshift<__sl2>(__x, __a);
255 	__rshift<__sr2>(__y, __c);
256 	__r[0] = (__a[0] ^ __x[0] ^ ((__b[0] >> __sr1) & __msk1)
257 		  ^ __y[0] ^ (__d[0] << __sl1));
258 	__r[1] = (__a[1] ^ __x[1] ^ ((__b[1] >> __sr1) & __msk2)
259 		  ^ __y[1] ^ (__d[1] << __sl1));
260 	__r[2] = (__a[2] ^ __x[2] ^ ((__b[2] >> __sr1) & __msk3)
261 		  ^ __y[2] ^ (__d[2] << __sl1));
262 	__r[3] = (__a[3] ^ __x[3] ^ ((__b[3] >> __sr1) & __msk4)
263 		  ^ __y[3] ^ (__d[3] << __sl1));
264       }
265 
266   }
267 
268 
269   template<typename _UIntType, size_t __m,
270 	   size_t __pos1, size_t __sl1, size_t __sl2,
271 	   size_t __sr1, size_t __sr2,
272 	   uint32_t __msk1, uint32_t __msk2,
273 	   uint32_t __msk3, uint32_t __msk4,
274 	   uint32_t __parity1, uint32_t __parity2,
275 	   uint32_t __parity3, uint32_t __parity4>
276     void simd_fast_mersenne_twister_engine<_UIntType, __m,
277 					   __pos1, __sl1, __sl2, __sr1, __sr2,
278 					   __msk1, __msk2, __msk3, __msk4,
279 					   __parity1, __parity2, __parity3,
280 					   __parity4>::
281     _M_gen_rand(void)
282     {
283       const uint32_t *__r1 = &_M_state32[_M_nstate32 - 8];
284       const uint32_t *__r2 = &_M_state32[_M_nstate32 - 4];
285       static constexpr size_t __pos1_32 = __pos1 * 4;
286 
287       size_t __i;
288       for (__i = 0; __i < _M_nstate32 - __pos1_32; __i += 4)
289 	{
290 	  __recursion<__sl1, __sl2, __sr1, __sr2,
291 		      __msk1, __msk2, __msk3, __msk4>
292 	    (&_M_state32[__i], &_M_state32[__i],
293 	     &_M_state32[__i + __pos1_32], __r1, __r2);
294 	  __r1 = __r2;
295 	  __r2 = &_M_state32[__i];
296 	}
297 
298       for (; __i < _M_nstate32; __i += 4)
299 	{
300 	  __recursion<__sl1, __sl2, __sr1, __sr2,
301 		      __msk1, __msk2, __msk3, __msk4>
302 	    (&_M_state32[__i], &_M_state32[__i],
303 	     &_M_state32[__i + __pos1_32 - _M_nstate32], __r1, __r2);
304 	  __r1 = __r2;
305 	  __r2 = &_M_state32[__i];
306 	}
307 
308       _M_pos = 0;
309     }
310 
311 #endif
312 
313 #ifndef _GLIBCXX_OPT_HAVE_RANDOM_SFMT_OPERATOREQUAL
314   template<typename _UIntType, size_t __m,
315 	   size_t __pos1, size_t __sl1, size_t __sl2,
316 	   size_t __sr1, size_t __sr2,
317 	   uint32_t __msk1, uint32_t __msk2,
318 	   uint32_t __msk3, uint32_t __msk4,
319 	   uint32_t __parity1, uint32_t __parity2,
320 	   uint32_t __parity3, uint32_t __parity4>
321     bool
322     operator==(const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
323 	       __m, __pos1, __sl1, __sl2, __sr1, __sr2,
324 	       __msk1, __msk2, __msk3, __msk4,
325 	       __parity1, __parity2, __parity3, __parity4>& __lhs,
326 	       const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
327 	       __m, __pos1, __sl1, __sl2, __sr1, __sr2,
328 	       __msk1, __msk2, __msk3, __msk4,
329 	       __parity1, __parity2, __parity3, __parity4>& __rhs)
330     {
331       typedef __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
332 	       __m, __pos1, __sl1, __sl2, __sr1, __sr2,
333 	       __msk1, __msk2, __msk3, __msk4,
334 	       __parity1, __parity2, __parity3, __parity4> __engine;
335       return (std::equal(__lhs._M_stateT,
336 			 __lhs._M_stateT + __engine::state_size,
337 			 __rhs._M_stateT)
338 	      && __lhs._M_pos == __rhs._M_pos);
339     }
340 #endif
341 
342   template<typename _UIntType, size_t __m,
343 	   size_t __pos1, size_t __sl1, size_t __sl2,
344 	   size_t __sr1, size_t __sr2,
345 	   uint32_t __msk1, uint32_t __msk2,
346 	   uint32_t __msk3, uint32_t __msk4,
347 	   uint32_t __parity1, uint32_t __parity2,
348 	   uint32_t __parity3, uint32_t __parity4,
349 	   typename _CharT, typename _Traits>
350     std::basic_ostream<_CharT, _Traits>&
351     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
352 	       const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
353 	       __m, __pos1, __sl1, __sl2, __sr1, __sr2,
354 	       __msk1, __msk2, __msk3, __msk4,
355 	       __parity1, __parity2, __parity3, __parity4>& __x)
356     {
357       typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
358       typedef typename __ostream_type::ios_base __ios_base;
359 
360       const typename __ios_base::fmtflags __flags = __os.flags();
361       const _CharT __fill = __os.fill();
362       const _CharT __space = __os.widen(' ');
363       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
364       __os.fill(__space);
365 
366       for (size_t __i = 0; __i < __x._M_nstate32; ++__i)
367 	__os << __x._M_state32[__i] << __space;
368       __os << __x._M_pos;
369 
370       __os.flags(__flags);
371       __os.fill(__fill);
372       return __os;
373     }
374 
375 
376   template<typename _UIntType, size_t __m,
377 	   size_t __pos1, size_t __sl1, size_t __sl2,
378 	   size_t __sr1, size_t __sr2,
379 	   uint32_t __msk1, uint32_t __msk2,
380 	   uint32_t __msk3, uint32_t __msk4,
381 	   uint32_t __parity1, uint32_t __parity2,
382 	   uint32_t __parity3, uint32_t __parity4,
383 	   typename _CharT, typename _Traits>
384     std::basic_istream<_CharT, _Traits>&
385     operator>>(std::basic_istream<_CharT, _Traits>& __is,
386 	       __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
387 	       __m, __pos1, __sl1, __sl2, __sr1, __sr2,
388 	       __msk1, __msk2, __msk3, __msk4,
389 	       __parity1, __parity2, __parity3, __parity4>& __x)
390     {
391       typedef std::basic_istream<_CharT, _Traits> __istream_type;
392       typedef typename __istream_type::ios_base __ios_base;
393 
394       const typename __ios_base::fmtflags __flags = __is.flags();
395       __is.flags(__ios_base::dec | __ios_base::skipws);
396 
397       for (size_t __i = 0; __i < __x._M_nstate32; ++__i)
398 	__is >> __x._M_state32[__i];
399       __is >> __x._M_pos;
400 
401       __is.flags(__flags);
402       return __is;
403     }
404 
405 #endif // __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
406 
407   /**
408    * Iteration method due to M.D. J<o:>hnk.
409    *
410    * M.D. J<o:>hnk, Erzeugung von betaverteilten und gammaverteilten
411    * Zufallszahlen, Metrika, Volume 8, 1964
412    */
413   template<typename _RealType>
414     template<typename _UniformRandomNumberGenerator>
415       typename beta_distribution<_RealType>::result_type
416       beta_distribution<_RealType>::
417       operator()(_UniformRandomNumberGenerator& __urng,
418 		 const param_type& __param)
419       {
420 	std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
421 	  __aurng(__urng);
422 
423 	result_type __x, __y;
424 	do
425 	  {
426 	    __x = std::exp(std::log(__aurng()) / __param.alpha());
427 	    __y = std::exp(std::log(__aurng()) / __param.beta());
428 	  }
429 	while (__x + __y > result_type(1));
430 
431 	return __x / (__x + __y);
432       }
433 
434   template<typename _RealType>
435     template<typename _OutputIterator,
436 	     typename _UniformRandomNumberGenerator>
437       void
438       beta_distribution<_RealType>::
439       __generate_impl(_OutputIterator __f, _OutputIterator __t,
440 		      _UniformRandomNumberGenerator& __urng,
441 		      const param_type& __param)
442       {
443 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
444 	    result_type>)
445 
446 	std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
447 	  __aurng(__urng);
448 
449 	while (__f != __t)
450 	  {
451 	    result_type __x, __y;
452 	    do
453 	      {
454 		__x = std::exp(std::log(__aurng()) / __param.alpha());
455 		__y = std::exp(std::log(__aurng()) / __param.beta());
456 	      }
457 	    while (__x + __y > result_type(1));
458 
459 	    *__f++ = __x / (__x + __y);
460 	  }
461       }
462 
463   template<typename _RealType, typename _CharT, typename _Traits>
464     std::basic_ostream<_CharT, _Traits>&
465     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
466 	       const __gnu_cxx::beta_distribution<_RealType>& __x)
467     {
468       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
469       typedef typename __ostream_type::ios_base    __ios_base;
470 
471       const typename __ios_base::fmtflags __flags = __os.flags();
472       const _CharT __fill = __os.fill();
473       const std::streamsize __precision = __os.precision();
474       const _CharT __space = __os.widen(' ');
475       __os.flags(__ios_base::scientific | __ios_base::left);
476       __os.fill(__space);
477       __os.precision(std::numeric_limits<_RealType>::max_digits10);
478 
479       __os << __x.alpha() << __space << __x.beta();
480 
481       __os.flags(__flags);
482       __os.fill(__fill);
483       __os.precision(__precision);
484       return __os;
485     }
486 
487   template<typename _RealType, typename _CharT, typename _Traits>
488     std::basic_istream<_CharT, _Traits>&
489     operator>>(std::basic_istream<_CharT, _Traits>& __is,
490 	       __gnu_cxx::beta_distribution<_RealType>& __x)
491     {
492       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
493       typedef typename __istream_type::ios_base    __ios_base;
494 
495       const typename __ios_base::fmtflags __flags = __is.flags();
496       __is.flags(__ios_base::dec | __ios_base::skipws);
497 
498       _RealType __alpha_val, __beta_val;
499       __is >> __alpha_val >> __beta_val;
500       __x.param(typename __gnu_cxx::beta_distribution<_RealType>::
501 		param_type(__alpha_val, __beta_val));
502 
503       __is.flags(__flags);
504       return __is;
505     }
506 
507 
508   template<std::size_t _Dimen, typename _RealType>
509     template<typename _InputIterator1, typename _InputIterator2>
510       void
511       normal_mv_distribution<_Dimen, _RealType>::param_type::
512       _M_init_full(_InputIterator1 __meanbegin, _InputIterator1 __meanend,
513 		   _InputIterator2 __varcovbegin, _InputIterator2 __varcovend)
514       {
515 	__glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
516 	__glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
517 	std::fill(std::copy(__meanbegin, __meanend, _M_mean.begin()),
518 		  _M_mean.end(), _RealType(0));
519 
520 	// Perform the Cholesky decomposition
521 	auto __w = _M_t.begin();
522 	for (size_t __j = 0; __j < _Dimen; ++__j)
523 	  {
524 	    _RealType __sum = _RealType(0);
525 
526 	    auto __slitbegin = __w;
527 	    auto __cit = _M_t.begin();
528 	    for (size_t __i = 0; __i < __j; ++__i)
529 	      {
530 		auto __slit = __slitbegin;
531 		_RealType __s = *__varcovbegin++;
532 		for (size_t __k = 0; __k < __i; ++__k)
533 		  __s -= *__slit++ * *__cit++;
534 
535 		*__w++ = __s /= *__cit++;
536 		__sum += __s * __s;
537 	      }
538 
539 	    __sum = *__varcovbegin - __sum;
540 	    if (__builtin_expect(__sum <= _RealType(0), 0))
541 	      std::__throw_runtime_error(__N("normal_mv_distribution::"
542 					     "param_type::_M_init_full"));
543 	    *__w++ = std::sqrt(__sum);
544 
545 	    std::advance(__varcovbegin, _Dimen - __j);
546 	  }
547       }
548 
549   template<std::size_t _Dimen, typename _RealType>
550     template<typename _InputIterator1, typename _InputIterator2>
551       void
552       normal_mv_distribution<_Dimen, _RealType>::param_type::
553       _M_init_lower(_InputIterator1 __meanbegin, _InputIterator1 __meanend,
554 		    _InputIterator2 __varcovbegin, _InputIterator2 __varcovend)
555       {
556 	__glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
557 	__glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
558 	std::fill(std::copy(__meanbegin, __meanend, _M_mean.begin()),
559 		  _M_mean.end(), _RealType(0));
560 
561 	// Perform the Cholesky decomposition
562 	auto __w = _M_t.begin();
563 	for (size_t __j = 0; __j < _Dimen; ++__j)
564 	  {
565 	    _RealType __sum = _RealType(0);
566 
567 	    auto __slitbegin = __w;
568 	    auto __cit = _M_t.begin();
569 	    for (size_t __i = 0; __i < __j; ++__i)
570 	      {
571 		auto __slit = __slitbegin;
572 		_RealType __s = *__varcovbegin++;
573 		for (size_t __k = 0; __k < __i; ++__k)
574 		  __s -= *__slit++ * *__cit++;
575 
576 		*__w++ = __s /= *__cit++;
577 		__sum += __s * __s;
578 	      }
579 
580 	    __sum = *__varcovbegin++ - __sum;
581 	    if (__builtin_expect(__sum <= _RealType(0), 0))
582 	      std::__throw_runtime_error(__N("normal_mv_distribution::"
583 					     "param_type::_M_init_full"));
584 	    *__w++ = std::sqrt(__sum);
585 	  }
586       }
587 
588   template<std::size_t _Dimen, typename _RealType>
589     template<typename _InputIterator1, typename _InputIterator2>
590       void
591       normal_mv_distribution<_Dimen, _RealType>::param_type::
592       _M_init_diagonal(_InputIterator1 __meanbegin, _InputIterator1 __meanend,
593 		       _InputIterator2 __varbegin, _InputIterator2 __varend)
594       {
595 	__glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
596 	__glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
597 	std::fill(std::copy(__meanbegin, __meanend, _M_mean.begin()),
598 		  _M_mean.end(), _RealType(0));
599 
600 	auto __w = _M_t.begin();
601 	size_t __step = 0;
602 	while (__varbegin != __varend)
603 	  {
604 	    std::fill_n(__w, __step, _RealType(0));
605 	    __w += __step++;
606 	    if (__builtin_expect(*__varbegin < _RealType(0), 0))
607 	      std::__throw_runtime_error(__N("normal_mv_distribution::"
608 					     "param_type::_M_init_diagonal"));
609 	    *__w++ = std::sqrt(*__varbegin++);
610 	  }
611       }
612 
613   template<std::size_t _Dimen, typename _RealType>
614     template<typename _UniformRandomNumberGenerator>
615       typename normal_mv_distribution<_Dimen, _RealType>::result_type
616       normal_mv_distribution<_Dimen, _RealType>::
617       operator()(_UniformRandomNumberGenerator& __urng,
618 		 const param_type& __param)
619       {
620 	result_type __ret;
621 
622 	_M_nd.__generate(__ret.begin(), __ret.end(), __urng);
623 
624 	auto __t_it = __param._M_t.crbegin();
625 	for (size_t __i = _Dimen; __i > 0; --__i)
626 	  {
627 	    _RealType __sum = _RealType(0);
628 	    for (size_t __j = __i; __j > 0; --__j)
629 	      __sum += __ret[__j - 1] * *__t_it++;
630 	    __ret[__i - 1] = __sum;
631 	  }
632 
633 	return __ret;
634       }
635 
636   template<std::size_t _Dimen, typename _RealType>
637     template<typename _ForwardIterator, typename _UniformRandomNumberGenerator>
638       void
639       normal_mv_distribution<_Dimen, _RealType>::
640       __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
641 		      _UniformRandomNumberGenerator& __urng,
642 		      const param_type& __param)
643       {
644 	__glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
645 				    _ForwardIterator>)
646 	while (__f != __t)
647 	  *__f++ = this->operator()(__urng, __param);
648       }
649 
650   template<size_t _Dimen, typename _RealType>
651     bool
652     operator==(const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
653 	       __d1,
654 	       const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
655 	       __d2)
656     {
657       return __d1._M_param == __d2._M_param && __d1._M_nd == __d2._M_nd;
658     }
659 
660   template<size_t _Dimen, typename _RealType, typename _CharT, typename _Traits>
661     std::basic_ostream<_CharT, _Traits>&
662     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
663 	       const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>& __x)
664     {
665       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
666       typedef typename __ostream_type::ios_base    __ios_base;
667 
668       const typename __ios_base::fmtflags __flags = __os.flags();
669       const _CharT __fill = __os.fill();
670       const std::streamsize __precision = __os.precision();
671       const _CharT __space = __os.widen(' ');
672       __os.flags(__ios_base::scientific | __ios_base::left);
673       __os.fill(__space);
674       __os.precision(std::numeric_limits<_RealType>::max_digits10);
675 
676       auto __mean = __x._M_param.mean();
677       for (auto __it : __mean)
678 	__os << __it << __space;
679       auto __t = __x._M_param.varcov();
680       for (auto __it : __t)
681 	__os << __it << __space;
682 
683       __os << __x._M_nd;
684 
685       __os.flags(__flags);
686       __os.fill(__fill);
687       __os.precision(__precision);
688       return __os;
689     }
690 
691   template<size_t _Dimen, typename _RealType, typename _CharT, typename _Traits>
692     std::basic_istream<_CharT, _Traits>&
693     operator>>(std::basic_istream<_CharT, _Traits>& __is,
694 	       __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>& __x)
695     {
696       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
697       typedef typename __istream_type::ios_base    __ios_base;
698 
699       const typename __ios_base::fmtflags __flags = __is.flags();
700       __is.flags(__ios_base::dec | __ios_base::skipws);
701 
702       std::array<_RealType, _Dimen> __mean;
703       for (auto& __it : __mean)
704 	__is >> __it;
705       std::array<_RealType, _Dimen * (_Dimen + 1) / 2> __varcov;
706       for (auto& __it : __varcov)
707 	__is >> __it;
708 
709       __is >> __x._M_nd;
710 
711       __x.param(typename normal_mv_distribution<_Dimen, _RealType>::
712 		param_type(__mean.begin(), __mean.end(),
713 			   __varcov.begin(), __varcov.end()));
714 
715       __is.flags(__flags);
716       return __is;
717     }
718 
719 
720   template<typename _RealType>
721     template<typename _OutputIterator,
722 	     typename _UniformRandomNumberGenerator>
723       void
724       rice_distribution<_RealType>::
725       __generate_impl(_OutputIterator __f, _OutputIterator __t,
726 		      _UniformRandomNumberGenerator& __urng,
727 		      const param_type& __p)
728       {
729 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
730 	    result_type>)
731 
732 	while (__f != __t)
733 	  {
734 	    typename std::normal_distribution<result_type>::param_type
735 	      __px(__p.nu(), __p.sigma()), __py(result_type(0), __p.sigma());
736 	    result_type __x = this->_M_ndx(__px, __urng);
737 	    result_type __y = this->_M_ndy(__py, __urng);
738 #if _GLIBCXX_USE_C99_MATH_TR1
739 	    *__f++ = std::hypot(__x, __y);
740 #else
741 	    *__f++ = std::sqrt(__x * __x + __y * __y);
742 #endif
743 	  }
744       }
745 
746   template<typename _RealType, typename _CharT, typename _Traits>
747     std::basic_ostream<_CharT, _Traits>&
748     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
749 	       const rice_distribution<_RealType>& __x)
750     {
751       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
752       typedef typename __ostream_type::ios_base    __ios_base;
753 
754       const typename __ios_base::fmtflags __flags = __os.flags();
755       const _CharT __fill = __os.fill();
756       const std::streamsize __precision = __os.precision();
757       const _CharT __space = __os.widen(' ');
758       __os.flags(__ios_base::scientific | __ios_base::left);
759       __os.fill(__space);
760       __os.precision(std::numeric_limits<_RealType>::max_digits10);
761 
762       __os << __x.nu() << __space << __x.sigma();
763       __os << __space << __x._M_ndx;
764       __os << __space << __x._M_ndy;
765 
766       __os.flags(__flags);
767       __os.fill(__fill);
768       __os.precision(__precision);
769       return __os;
770     }
771 
772   template<typename _RealType, typename _CharT, typename _Traits>
773     std::basic_istream<_CharT, _Traits>&
774     operator>>(std::basic_istream<_CharT, _Traits>& __is,
775 	       rice_distribution<_RealType>& __x)
776     {
777       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
778       typedef typename __istream_type::ios_base    __ios_base;
779 
780       const typename __ios_base::fmtflags __flags = __is.flags();
781       __is.flags(__ios_base::dec | __ios_base::skipws);
782 
783       _RealType __nu_val, __sigma_val;
784       __is >> __nu_val >> __sigma_val;
785       __is >> __x._M_ndx;
786       __is >> __x._M_ndy;
787       __x.param(typename rice_distribution<_RealType>::
788 		param_type(__nu_val, __sigma_val));
789 
790       __is.flags(__flags);
791       return __is;
792     }
793 
794 
795   template<typename _RealType>
796     template<typename _OutputIterator,
797 	     typename _UniformRandomNumberGenerator>
798       void
799       nakagami_distribution<_RealType>::
800       __generate_impl(_OutputIterator __f, _OutputIterator __t,
801 		      _UniformRandomNumberGenerator& __urng,
802 		      const param_type& __p)
803       {
804 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
805 	    result_type>)
806 
807 	typename std::gamma_distribution<result_type>::param_type
808 	  __pg(__p.mu(), __p.omega() / __p.mu());
809 	while (__f != __t)
810 	  *__f++ = std::sqrt(this->_M_gd(__pg, __urng));
811       }
812 
813   template<typename _RealType, typename _CharT, typename _Traits>
814     std::basic_ostream<_CharT, _Traits>&
815     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
816 	       const nakagami_distribution<_RealType>& __x)
817     {
818       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
819       typedef typename __ostream_type::ios_base    __ios_base;
820 
821       const typename __ios_base::fmtflags __flags = __os.flags();
822       const _CharT __fill = __os.fill();
823       const std::streamsize __precision = __os.precision();
824       const _CharT __space = __os.widen(' ');
825       __os.flags(__ios_base::scientific | __ios_base::left);
826       __os.fill(__space);
827       __os.precision(std::numeric_limits<_RealType>::max_digits10);
828 
829       __os << __x.mu() << __space << __x.omega();
830       __os << __space << __x._M_gd;
831 
832       __os.flags(__flags);
833       __os.fill(__fill);
834       __os.precision(__precision);
835       return __os;
836     }
837 
838   template<typename _RealType, typename _CharT, typename _Traits>
839     std::basic_istream<_CharT, _Traits>&
840     operator>>(std::basic_istream<_CharT, _Traits>& __is,
841 	       nakagami_distribution<_RealType>& __x)
842     {
843       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
844       typedef typename __istream_type::ios_base    __ios_base;
845 
846       const typename __ios_base::fmtflags __flags = __is.flags();
847       __is.flags(__ios_base::dec | __ios_base::skipws);
848 
849       _RealType __mu_val, __omega_val;
850       __is >> __mu_val >> __omega_val;
851       __is >> __x._M_gd;
852       __x.param(typename nakagami_distribution<_RealType>::
853 		param_type(__mu_val, __omega_val));
854 
855       __is.flags(__flags);
856       return __is;
857     }
858 
859 
860   template<typename _RealType>
861     template<typename _OutputIterator,
862 	     typename _UniformRandomNumberGenerator>
863       void
864       pareto_distribution<_RealType>::
865       __generate_impl(_OutputIterator __f, _OutputIterator __t,
866 		      _UniformRandomNumberGenerator& __urng,
867 		      const param_type& __p)
868       {
869 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
870 	    result_type>)
871 
872 	result_type __mu_val = __p.mu();
873 	result_type __malphinv = -result_type(1) / __p.alpha();
874 	while (__f != __t)
875 	  *__f++ = __mu_val * std::pow(this->_M_ud(__urng), __malphinv);
876       }
877 
878   template<typename _RealType, typename _CharT, typename _Traits>
879     std::basic_ostream<_CharT, _Traits>&
880     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
881 	       const pareto_distribution<_RealType>& __x)
882     {
883       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
884       typedef typename __ostream_type::ios_base    __ios_base;
885 
886       const typename __ios_base::fmtflags __flags = __os.flags();
887       const _CharT __fill = __os.fill();
888       const std::streamsize __precision = __os.precision();
889       const _CharT __space = __os.widen(' ');
890       __os.flags(__ios_base::scientific | __ios_base::left);
891       __os.fill(__space);
892       __os.precision(std::numeric_limits<_RealType>::max_digits10);
893 
894       __os << __x.alpha() << __space << __x.mu();
895       __os << __space << __x._M_ud;
896 
897       __os.flags(__flags);
898       __os.fill(__fill);
899       __os.precision(__precision);
900       return __os;
901     }
902 
903   template<typename _RealType, typename _CharT, typename _Traits>
904     std::basic_istream<_CharT, _Traits>&
905     operator>>(std::basic_istream<_CharT, _Traits>& __is,
906 	       pareto_distribution<_RealType>& __x)
907     {
908       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
909       typedef typename __istream_type::ios_base    __ios_base;
910 
911       const typename __ios_base::fmtflags __flags = __is.flags();
912       __is.flags(__ios_base::dec | __ios_base::skipws);
913 
914       _RealType __alpha_val, __mu_val;
915       __is >> __alpha_val >> __mu_val;
916       __is >> __x._M_ud;
917       __x.param(typename pareto_distribution<_RealType>::
918 		param_type(__alpha_val, __mu_val));
919 
920       __is.flags(__flags);
921       return __is;
922     }
923 
924 
925   template<typename _RealType>
926     template<typename _UniformRandomNumberGenerator>
927       typename k_distribution<_RealType>::result_type
928       k_distribution<_RealType>::
929       operator()(_UniformRandomNumberGenerator& __urng)
930       {
931 	result_type __x = this->_M_gd1(__urng);
932 	result_type __y = this->_M_gd2(__urng);
933 	return std::sqrt(__x * __y);
934       }
935 
936   template<typename _RealType>
937     template<typename _UniformRandomNumberGenerator>
938       typename k_distribution<_RealType>::result_type
939       k_distribution<_RealType>::
940       operator()(_UniformRandomNumberGenerator& __urng,
941 		 const param_type& __p)
942       {
943 	typename std::gamma_distribution<result_type>::param_type
944 	  __p1(__p.lambda(), result_type(1) / __p.lambda()),
945 	  __p2(__p.nu(), __p.mu() / __p.nu());
946 	result_type __x = this->_M_gd1(__p1, __urng);
947 	result_type __y = this->_M_gd2(__p2, __urng);
948 	return std::sqrt(__x * __y);
949       }
950 
951   template<typename _RealType>
952     template<typename _OutputIterator,
953 	     typename _UniformRandomNumberGenerator>
954       void
955       k_distribution<_RealType>::
956       __generate_impl(_OutputIterator __f, _OutputIterator __t,
957 		      _UniformRandomNumberGenerator& __urng,
958 		      const param_type& __p)
959       {
960 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
961 	    result_type>)
962 
963 	typename std::gamma_distribution<result_type>::param_type
964 	  __p1(__p.lambda(), result_type(1) / __p.lambda()),
965 	  __p2(__p.nu(), __p.mu() / __p.nu());
966 	while (__f != __t)
967 	  {
968 	    result_type __x = this->_M_gd1(__p1, __urng);
969 	    result_type __y = this->_M_gd2(__p2, __urng);
970 	    *__f++ = std::sqrt(__x * __y);
971 	  }
972       }
973 
974   template<typename _RealType, typename _CharT, typename _Traits>
975     std::basic_ostream<_CharT, _Traits>&
976     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
977 	       const k_distribution<_RealType>& __x)
978     {
979       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
980       typedef typename __ostream_type::ios_base    __ios_base;
981 
982       const typename __ios_base::fmtflags __flags = __os.flags();
983       const _CharT __fill = __os.fill();
984       const std::streamsize __precision = __os.precision();
985       const _CharT __space = __os.widen(' ');
986       __os.flags(__ios_base::scientific | __ios_base::left);
987       __os.fill(__space);
988       __os.precision(std::numeric_limits<_RealType>::max_digits10);
989 
990       __os << __x.lambda() << __space << __x.mu() << __space << __x.nu();
991       __os << __space << __x._M_gd1;
992       __os << __space << __x._M_gd2;
993 
994       __os.flags(__flags);
995       __os.fill(__fill);
996       __os.precision(__precision);
997       return __os;
998     }
999 
1000   template<typename _RealType, typename _CharT, typename _Traits>
1001     std::basic_istream<_CharT, _Traits>&
1002     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1003 	       k_distribution<_RealType>& __x)
1004     {
1005       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1006       typedef typename __istream_type::ios_base    __ios_base;
1007 
1008       const typename __ios_base::fmtflags __flags = __is.flags();
1009       __is.flags(__ios_base::dec | __ios_base::skipws);
1010 
1011       _RealType __lambda_val, __mu_val, __nu_val;
1012       __is >> __lambda_val >> __mu_val >> __nu_val;
1013       __is >> __x._M_gd1;
1014       __is >> __x._M_gd2;
1015       __x.param(typename k_distribution<_RealType>::
1016 		param_type(__lambda_val, __mu_val, __nu_val));
1017 
1018       __is.flags(__flags);
1019       return __is;
1020     }
1021 
1022 
1023   template<typename _RealType>
1024     template<typename _OutputIterator,
1025 	     typename _UniformRandomNumberGenerator>
1026       void
1027       arcsine_distribution<_RealType>::
1028       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1029 		      _UniformRandomNumberGenerator& __urng,
1030 		      const param_type& __p)
1031       {
1032 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1033 	    result_type>)
1034 
1035 	result_type __dif = __p.b() - __p.a();
1036 	result_type __sum = __p.a() + __p.b();
1037 	while (__f != __t)
1038 	  {
1039 	    result_type __x = std::sin(this->_M_ud(__urng));
1040 	    *__f++ = (__x * __dif + __sum) / result_type(2);
1041 	  }
1042       }
1043 
1044   template<typename _RealType, typename _CharT, typename _Traits>
1045     std::basic_ostream<_CharT, _Traits>&
1046     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1047 	       const arcsine_distribution<_RealType>& __x)
1048     {
1049       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1050       typedef typename __ostream_type::ios_base    __ios_base;
1051 
1052       const typename __ios_base::fmtflags __flags = __os.flags();
1053       const _CharT __fill = __os.fill();
1054       const std::streamsize __precision = __os.precision();
1055       const _CharT __space = __os.widen(' ');
1056       __os.flags(__ios_base::scientific | __ios_base::left);
1057       __os.fill(__space);
1058       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1059 
1060       __os << __x.a() << __space << __x.b();
1061       __os << __space << __x._M_ud;
1062 
1063       __os.flags(__flags);
1064       __os.fill(__fill);
1065       __os.precision(__precision);
1066       return __os;
1067     }
1068 
1069   template<typename _RealType, typename _CharT, typename _Traits>
1070     std::basic_istream<_CharT, _Traits>&
1071     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1072 	       arcsine_distribution<_RealType>& __x)
1073     {
1074       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1075       typedef typename __istream_type::ios_base    __ios_base;
1076 
1077       const typename __ios_base::fmtflags __flags = __is.flags();
1078       __is.flags(__ios_base::dec | __ios_base::skipws);
1079 
1080       _RealType __a, __b;
1081       __is >> __a >> __b;
1082       __is >> __x._M_ud;
1083       __x.param(typename arcsine_distribution<_RealType>::
1084 		param_type(__a, __b));
1085 
1086       __is.flags(__flags);
1087       return __is;
1088     }
1089 
1090 
1091   template<typename _RealType>
1092     template<typename _UniformRandomNumberGenerator>
1093       typename hoyt_distribution<_RealType>::result_type
1094       hoyt_distribution<_RealType>::
1095       operator()(_UniformRandomNumberGenerator& __urng)
1096       {
1097 	result_type __x = this->_M_ad(__urng);
1098 	result_type __y = this->_M_ed(__urng);
1099 	return (result_type(2) * this->q()
1100 		  / (result_type(1) + this->q() * this->q()))
1101 	       * std::sqrt(this->omega() * __x * __y);
1102       }
1103 
1104   template<typename _RealType>
1105     template<typename _UniformRandomNumberGenerator>
1106       typename hoyt_distribution<_RealType>::result_type
1107       hoyt_distribution<_RealType>::
1108       operator()(_UniformRandomNumberGenerator& __urng,
1109 		 const param_type& __p)
1110       {
1111 	result_type __q2 = __p.q() * __p.q();
1112 	result_type __num = result_type(0.5L) * (result_type(1) + __q2);
1113 	typename __gnu_cxx::arcsine_distribution<result_type>::param_type
1114 	  __pa(__num, __num / __q2);
1115 	result_type __x = this->_M_ad(__pa, __urng);
1116 	result_type __y = this->_M_ed(__urng);
1117 	return (result_type(2) * __p.q() / (result_type(1) + __q2))
1118 	       * std::sqrt(__p.omega() * __x * __y);
1119       }
1120 
1121   template<typename _RealType>
1122     template<typename _OutputIterator,
1123 	     typename _UniformRandomNumberGenerator>
1124       void
1125       hoyt_distribution<_RealType>::
1126       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1127 		      _UniformRandomNumberGenerator& __urng,
1128 		      const param_type& __p)
1129       {
1130 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1131 	    result_type>)
1132 
1133 	result_type __2q = result_type(2) * __p.q();
1134 	result_type __q2 = __p.q() * __p.q();
1135 	result_type __q2p1 = result_type(1) + __q2;
1136 	result_type __num = result_type(0.5L) * __q2p1;
1137 	result_type __omega = __p.omega();
1138 	typename __gnu_cxx::arcsine_distribution<result_type>::param_type
1139 	  __pa(__num, __num / __q2);
1140 	while (__f != __t)
1141 	  {
1142 	    result_type __x = this->_M_ad(__pa, __urng);
1143 	    result_type __y = this->_M_ed(__urng);
1144 	    *__f++ = (__2q / __q2p1) * std::sqrt(__omega * __x * __y);
1145 	  }
1146       }
1147 
1148   template<typename _RealType, typename _CharT, typename _Traits>
1149     std::basic_ostream<_CharT, _Traits>&
1150     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1151 	       const hoyt_distribution<_RealType>& __x)
1152     {
1153       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1154       typedef typename __ostream_type::ios_base    __ios_base;
1155 
1156       const typename __ios_base::fmtflags __flags = __os.flags();
1157       const _CharT __fill = __os.fill();
1158       const std::streamsize __precision = __os.precision();
1159       const _CharT __space = __os.widen(' ');
1160       __os.flags(__ios_base::scientific | __ios_base::left);
1161       __os.fill(__space);
1162       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1163 
1164       __os << __x.q() << __space << __x.omega();
1165       __os << __space << __x._M_ad;
1166       __os << __space << __x._M_ed;
1167 
1168       __os.flags(__flags);
1169       __os.fill(__fill);
1170       __os.precision(__precision);
1171       return __os;
1172     }
1173 
1174   template<typename _RealType, typename _CharT, typename _Traits>
1175     std::basic_istream<_CharT, _Traits>&
1176     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1177 	       hoyt_distribution<_RealType>& __x)
1178     {
1179       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1180       typedef typename __istream_type::ios_base    __ios_base;
1181 
1182       const typename __ios_base::fmtflags __flags = __is.flags();
1183       __is.flags(__ios_base::dec | __ios_base::skipws);
1184 
1185       _RealType __q, __omega;
1186       __is >> __q >> __omega;
1187       __is >> __x._M_ad;
1188       __is >> __x._M_ed;
1189       __x.param(typename hoyt_distribution<_RealType>::
1190 		param_type(__q, __omega));
1191 
1192       __is.flags(__flags);
1193       return __is;
1194     }
1195 
1196 
1197   template<typename _RealType>
1198     template<typename _OutputIterator,
1199 	     typename _UniformRandomNumberGenerator>
1200       void
1201       triangular_distribution<_RealType>::
1202       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1203 		      _UniformRandomNumberGenerator& __urng,
1204 		      const param_type& __param)
1205       {
1206 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1207 	    result_type>)
1208 
1209 	while (__f != __t)
1210 	  *__f++ = this->operator()(__urng, __param);
1211       }
1212 
1213   template<typename _RealType, typename _CharT, typename _Traits>
1214     std::basic_ostream<_CharT, _Traits>&
1215     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1216 	       const __gnu_cxx::triangular_distribution<_RealType>& __x)
1217     {
1218       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1219       typedef typename __ostream_type::ios_base    __ios_base;
1220 
1221       const typename __ios_base::fmtflags __flags = __os.flags();
1222       const _CharT __fill = __os.fill();
1223       const std::streamsize __precision = __os.precision();
1224       const _CharT __space = __os.widen(' ');
1225       __os.flags(__ios_base::scientific | __ios_base::left);
1226       __os.fill(__space);
1227       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1228 
1229       __os << __x.a() << __space << __x.b() << __space << __x.c();
1230 
1231       __os.flags(__flags);
1232       __os.fill(__fill);
1233       __os.precision(__precision);
1234       return __os;
1235     }
1236 
1237   template<typename _RealType, typename _CharT, typename _Traits>
1238     std::basic_istream<_CharT, _Traits>&
1239     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1240 	       __gnu_cxx::triangular_distribution<_RealType>& __x)
1241     {
1242       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1243       typedef typename __istream_type::ios_base    __ios_base;
1244 
1245       const typename __ios_base::fmtflags __flags = __is.flags();
1246       __is.flags(__ios_base::dec | __ios_base::skipws);
1247 
1248       _RealType __a, __b, __c;
1249       __is >> __a >> __b >> __c;
1250       __x.param(typename __gnu_cxx::triangular_distribution<_RealType>::
1251 		param_type(__a, __b, __c));
1252 
1253       __is.flags(__flags);
1254       return __is;
1255     }
1256 
1257 
1258   template<typename _RealType>
1259     template<typename _UniformRandomNumberGenerator>
1260       typename von_mises_distribution<_RealType>::result_type
1261       von_mises_distribution<_RealType>::
1262       operator()(_UniformRandomNumberGenerator& __urng,
1263 		 const param_type& __p)
1264       {
1265 	const result_type __pi
1266 	  = __gnu_cxx::__math_constants<result_type>::__pi;
1267 	std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1268 	  __aurng(__urng);
1269 
1270 	result_type __f;
1271 	while (1)
1272 	  {
1273 	    result_type __rnd = std::cos(__pi * __aurng());
1274 	    __f = (result_type(1) + __p._M_r * __rnd) / (__p._M_r + __rnd);
1275 	    result_type __c = __p._M_kappa * (__p._M_r - __f);
1276 
1277 	    result_type __rnd2 = __aurng();
1278 	    if (__c * (result_type(2) - __c) > __rnd2)
1279 	      break;
1280 	    if (std::log(__c / __rnd2) >= __c - result_type(1))
1281 	      break;
1282 	  }
1283 
1284 	result_type __res = std::acos(__f);
1285 #if _GLIBCXX_USE_C99_MATH_TR1
1286 	__res = std::copysign(__res, __aurng() - result_type(0.5));
1287 #else
1288 	if (__aurng() < result_type(0.5))
1289 	  __res = -__res;
1290 #endif
1291 	__res += __p._M_mu;
1292 	if (__res > __pi)
1293 	  __res -= result_type(2) * __pi;
1294 	else if (__res < -__pi)
1295 	  __res += result_type(2) * __pi;
1296 	return __res;
1297       }
1298 
1299   template<typename _RealType>
1300     template<typename _OutputIterator,
1301 	     typename _UniformRandomNumberGenerator>
1302       void
1303       von_mises_distribution<_RealType>::
1304       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1305 		      _UniformRandomNumberGenerator& __urng,
1306 		      const param_type& __param)
1307       {
1308 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1309 	    result_type>)
1310 
1311 	while (__f != __t)
1312 	  *__f++ = this->operator()(__urng, __param);
1313       }
1314 
1315   template<typename _RealType, typename _CharT, typename _Traits>
1316     std::basic_ostream<_CharT, _Traits>&
1317     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1318 	       const __gnu_cxx::von_mises_distribution<_RealType>& __x)
1319     {
1320       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1321       typedef typename __ostream_type::ios_base    __ios_base;
1322 
1323       const typename __ios_base::fmtflags __flags = __os.flags();
1324       const _CharT __fill = __os.fill();
1325       const std::streamsize __precision = __os.precision();
1326       const _CharT __space = __os.widen(' ');
1327       __os.flags(__ios_base::scientific | __ios_base::left);
1328       __os.fill(__space);
1329       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1330 
1331       __os << __x.mu() << __space << __x.kappa();
1332 
1333       __os.flags(__flags);
1334       __os.fill(__fill);
1335       __os.precision(__precision);
1336       return __os;
1337     }
1338 
1339   template<typename _RealType, typename _CharT, typename _Traits>
1340     std::basic_istream<_CharT, _Traits>&
1341     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1342 	       __gnu_cxx::von_mises_distribution<_RealType>& __x)
1343     {
1344       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1345       typedef typename __istream_type::ios_base    __ios_base;
1346 
1347       const typename __ios_base::fmtflags __flags = __is.flags();
1348       __is.flags(__ios_base::dec | __ios_base::skipws);
1349 
1350       _RealType __mu, __kappa;
1351       __is >> __mu >> __kappa;
1352       __x.param(typename __gnu_cxx::von_mises_distribution<_RealType>::
1353 		param_type(__mu, __kappa));
1354 
1355       __is.flags(__flags);
1356       return __is;
1357     }
1358 
1359 
1360   template<typename _UIntType>
1361     template<typename _UniformRandomNumberGenerator>
1362       typename hypergeometric_distribution<_UIntType>::result_type
1363       hypergeometric_distribution<_UIntType>::
1364       operator()(_UniformRandomNumberGenerator& __urng,
1365 		 const param_type& __param)
1366       {
1367 	std::__detail::_Adaptor<_UniformRandomNumberGenerator, double>
1368 	  __aurng(__urng);
1369 
1370 	result_type __a = __param.successful_size();
1371 	result_type __b = __param.total_size();
1372 	result_type __k = 0;
1373 
1374 	if (__param.total_draws() < __param.total_size() / 2)
1375 	  {
1376 	    for (result_type __i = 0; __i < __param.total_draws(); ++__i)
1377 	      {
1378 		if (__b * __aurng() < __a)
1379 		  {
1380 		    ++__k;
1381 		    if (__k == __param.successful_size())
1382 		      return __k;
1383 		   --__a;
1384 		  }
1385 		--__b;
1386 	      }
1387 	    return __k;
1388 	  }
1389 	else
1390 	  {
1391 	    for (result_type __i = 0; __i < __param.unsuccessful_size(); ++__i)
1392 	      {
1393 		if (__b * __aurng() < __a)
1394 		  {
1395 		    ++__k;
1396 		    if (__k == __param.successful_size())
1397 		      return __param.successful_size() - __k;
1398 		    --__a;
1399 		  }
1400 		--__b;
1401 	      }
1402 	    return __param.successful_size() - __k;
1403 	  }
1404       }
1405 
1406   template<typename _UIntType>
1407     template<typename _OutputIterator,
1408 	     typename _UniformRandomNumberGenerator>
1409       void
1410       hypergeometric_distribution<_UIntType>::
1411       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1412 		      _UniformRandomNumberGenerator& __urng,
1413 		      const param_type& __param)
1414       {
1415 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1416 	    result_type>)
1417 
1418 	while (__f != __t)
1419 	  *__f++ = this->operator()(__urng);
1420       }
1421 
1422   template<typename _UIntType, typename _CharT, typename _Traits>
1423     std::basic_ostream<_CharT, _Traits>&
1424     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1425 	       const __gnu_cxx::hypergeometric_distribution<_UIntType>& __x)
1426     {
1427       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1428       typedef typename __ostream_type::ios_base    __ios_base;
1429 
1430       const typename __ios_base::fmtflags __flags = __os.flags();
1431       const _CharT __fill = __os.fill();
1432       const std::streamsize __precision = __os.precision();
1433       const _CharT __space = __os.widen(' ');
1434       __os.flags(__ios_base::scientific | __ios_base::left);
1435       __os.fill(__space);
1436       __os.precision(std::numeric_limits<_UIntType>::max_digits10);
1437 
1438       __os << __x.total_size() << __space << __x.successful_size() << __space
1439 	   << __x.total_draws();
1440 
1441       __os.flags(__flags);
1442       __os.fill(__fill);
1443       __os.precision(__precision);
1444       return __os;
1445     }
1446 
1447   template<typename _UIntType, typename _CharT, typename _Traits>
1448     std::basic_istream<_CharT, _Traits>&
1449     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1450 	       __gnu_cxx::hypergeometric_distribution<_UIntType>& __x)
1451     {
1452       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1453       typedef typename __istream_type::ios_base    __ios_base;
1454 
1455       const typename __ios_base::fmtflags __flags = __is.flags();
1456       __is.flags(__ios_base::dec | __ios_base::skipws);
1457 
1458       _UIntType __total_size, __successful_size, __total_draws;
1459       __is >> __total_size >> __successful_size >> __total_draws;
1460       __x.param(typename __gnu_cxx::hypergeometric_distribution<_UIntType>::
1461 		param_type(__total_size, __successful_size, __total_draws));
1462 
1463       __is.flags(__flags);
1464       return __is;
1465     }
1466 
1467 
1468   template<typename _RealType>
1469     template<typename _UniformRandomNumberGenerator>
1470       typename logistic_distribution<_RealType>::result_type
1471       logistic_distribution<_RealType>::
1472       operator()(_UniformRandomNumberGenerator& __urng,
1473 		 const param_type& __p)
1474       {
1475 	std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1476 	  __aurng(__urng);
1477 
1478 	result_type __arg = result_type(1);
1479 	while (__arg == result_type(1) || __arg == result_type(0))
1480 	  __arg = __aurng();
1481 	return __p.a()
1482 	     + __p.b() * std::log(__arg / (result_type(1) - __arg));
1483       }
1484 
1485   template<typename _RealType>
1486     template<typename _OutputIterator,
1487 	     typename _UniformRandomNumberGenerator>
1488       void
1489       logistic_distribution<_RealType>::
1490       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1491 		      _UniformRandomNumberGenerator& __urng,
1492 		      const param_type& __p)
1493       {
1494 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1495 	    result_type>)
1496 
1497 	std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1498 	  __aurng(__urng);
1499 
1500 	while (__f != __t)
1501 	  {
1502 	    result_type __arg = result_type(1);
1503 	    while (__arg == result_type(1) || __arg == result_type(0))
1504 	      __arg = __aurng();
1505 	    *__f++ = __p.a()
1506 		   + __p.b() * std::log(__arg / (result_type(1) - __arg));
1507 	  }
1508       }
1509 
1510   template<typename _RealType, typename _CharT, typename _Traits>
1511     std::basic_ostream<_CharT, _Traits>&
1512     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1513 	       const logistic_distribution<_RealType>& __x)
1514     {
1515       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1516       typedef typename __ostream_type::ios_base    __ios_base;
1517 
1518       const typename __ios_base::fmtflags __flags = __os.flags();
1519       const _CharT __fill = __os.fill();
1520       const std::streamsize __precision = __os.precision();
1521       const _CharT __space = __os.widen(' ');
1522       __os.flags(__ios_base::scientific | __ios_base::left);
1523       __os.fill(__space);
1524       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1525 
1526       __os << __x.a() << __space << __x.b();
1527 
1528       __os.flags(__flags);
1529       __os.fill(__fill);
1530       __os.precision(__precision);
1531       return __os;
1532     }
1533 
1534   template<typename _RealType, typename _CharT, typename _Traits>
1535     std::basic_istream<_CharT, _Traits>&
1536     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1537 	       logistic_distribution<_RealType>& __x)
1538     {
1539       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1540       typedef typename __istream_type::ios_base    __ios_base;
1541 
1542       const typename __ios_base::fmtflags __flags = __is.flags();
1543       __is.flags(__ios_base::dec | __ios_base::skipws);
1544 
1545       _RealType __a, __b;
1546       __is >> __a >> __b;
1547       __x.param(typename logistic_distribution<_RealType>::
1548 		param_type(__a, __b));
1549 
1550       __is.flags(__flags);
1551       return __is;
1552     }
1553 
1554 
1555   namespace {
1556 
1557     // Helper class for the uniform_on_sphere_distribution generation
1558     // function.
1559     template<std::size_t _Dimen, typename _RealType>
1560       class uniform_on_sphere_helper
1561       {
1562 	typedef typename uniform_on_sphere_distribution<_Dimen, _RealType>::
1563 	  result_type result_type;
1564 
1565       public:
1566 	template<typename _NormalDistribution,
1567 		 typename _UniformRandomNumberGenerator>
1568 	result_type operator()(_NormalDistribution& __nd,
1569 			       _UniformRandomNumberGenerator& __urng)
1570         {
1571 	  result_type __ret;
1572 	  typename result_type::value_type __norm;
1573 
1574 	  do
1575 	    {
1576 	      auto __sum = _RealType(0);
1577 
1578 	      std::generate(__ret.begin(), __ret.end(),
1579 			    [&__nd, &__urng, &__sum](){
1580 			      _RealType __t = __nd(__urng);
1581 			      __sum += __t * __t;
1582 			      return __t; });
1583 	      __norm = std::sqrt(__sum);
1584 	    }
1585 	  while (__norm == _RealType(0) || ! __builtin_isfinite(__norm));
1586 
1587 	  std::transform(__ret.begin(), __ret.end(), __ret.begin(),
1588 			 [__norm](_RealType __val){ return __val / __norm; });
1589 
1590 	  return __ret;
1591         }
1592       };
1593 
1594 
1595     template<typename _RealType>
1596       class uniform_on_sphere_helper<2, _RealType>
1597       {
1598 	typedef typename uniform_on_sphere_distribution<2, _RealType>::
1599 	  result_type result_type;
1600 
1601       public:
1602 	template<typename _NormalDistribution,
1603 		 typename _UniformRandomNumberGenerator>
1604 	result_type operator()(_NormalDistribution&,
1605 			       _UniformRandomNumberGenerator& __urng)
1606         {
1607 	  result_type __ret;
1608 	  _RealType __sq;
1609 	  std::__detail::_Adaptor<_UniformRandomNumberGenerator,
1610 				  _RealType> __aurng(__urng);
1611 
1612 	  do
1613 	    {
1614 	      __ret[0] = _RealType(2) * __aurng() - _RealType(1);
1615 	      __ret[1] = _RealType(2) * __aurng() - _RealType(1);
1616 
1617 	      __sq = __ret[0] * __ret[0] + __ret[1] * __ret[1];
1618 	    }
1619 	  while (__sq == _RealType(0) || __sq > _RealType(1));
1620 
1621 #if _GLIBCXX_USE_C99_MATH_TR1
1622 	  // Yes, we do not just use sqrt(__sq) because hypot() is more
1623 	  // accurate.
1624 	  auto __norm = std::hypot(__ret[0], __ret[1]);
1625 #else
1626 	  auto __norm = std::sqrt(__sq);
1627 #endif
1628 	  __ret[0] /= __norm;
1629 	  __ret[1] /= __norm;
1630 
1631 	  return __ret;
1632         }
1633       };
1634 
1635   }
1636 
1637 
1638   template<std::size_t _Dimen, typename _RealType>
1639     template<typename _UniformRandomNumberGenerator>
1640       typename uniform_on_sphere_distribution<_Dimen, _RealType>::result_type
1641       uniform_on_sphere_distribution<_Dimen, _RealType>::
1642       operator()(_UniformRandomNumberGenerator& __urng,
1643 		 const param_type& __p)
1644       {
1645         uniform_on_sphere_helper<_Dimen, _RealType> __helper;
1646         return __helper(_M_nd, __urng);
1647       }
1648 
1649   template<std::size_t _Dimen, typename _RealType>
1650     template<typename _OutputIterator,
1651 	     typename _UniformRandomNumberGenerator>
1652       void
1653       uniform_on_sphere_distribution<_Dimen, _RealType>::
1654       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1655 		      _UniformRandomNumberGenerator& __urng,
1656 		      const param_type& __param)
1657       {
1658 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1659 	    result_type>)
1660 
1661 	while (__f != __t)
1662 	  *__f++ = this->operator()(__urng, __param);
1663       }
1664 
1665   template<std::size_t _Dimen, typename _RealType, typename _CharT,
1666 	   typename _Traits>
1667     std::basic_ostream<_CharT, _Traits>&
1668     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1669 	       const __gnu_cxx::uniform_on_sphere_distribution<_Dimen,
1670 							       _RealType>& __x)
1671     {
1672       return __os << __x._M_nd;
1673     }
1674 
1675   template<std::size_t _Dimen, typename _RealType, typename _CharT,
1676 	   typename _Traits>
1677     std::basic_istream<_CharT, _Traits>&
1678     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1679 	       __gnu_cxx::uniform_on_sphere_distribution<_Dimen,
1680 							 _RealType>& __x)
1681     {
1682       return __is >> __x._M_nd;
1683     }
1684 
1685 
1686   namespace {
1687 
1688     // Helper class for the uniform_inside_sphere_distribution generation
1689     // function.
1690     template<std::size_t _Dimen, bool _SmallDimen, typename _RealType>
1691       class uniform_inside_sphere_helper;
1692 
1693     template<std::size_t _Dimen, typename _RealType>
1694       class uniform_inside_sphere_helper<_Dimen, false, _RealType>
1695       {
1696 	using result_type
1697 	  = typename uniform_inside_sphere_distribution<_Dimen, _RealType>::
1698 	    result_type;
1699 
1700       public:
1701 	template<typename _UniformOnSphereDistribution,
1702 		 typename _UniformRandomNumberGenerator>
1703 	result_type
1704 	operator()(_UniformOnSphereDistribution& __uosd,
1705 		   _UniformRandomNumberGenerator& __urng,
1706 		   _RealType __radius)
1707         {
1708 	  std::__detail::_Adaptor<_UniformRandomNumberGenerator,
1709 				  _RealType> __aurng(__urng);
1710 
1711 	  _RealType __pow = 1 / _RealType(_Dimen);
1712 	  _RealType __urt = __radius * std::pow(__aurng(), __pow);
1713 	  result_type __ret = __uosd(__aurng);
1714 
1715 	  std::transform(__ret.begin(), __ret.end(), __ret.begin(),
1716 			 [__urt](_RealType __val)
1717 			 { return __val * __urt; });
1718 
1719 	  return __ret;
1720         }
1721       };
1722 
1723     // Helper class for the uniform_inside_sphere_distribution generation
1724     // function specialized for small dimensions.
1725     template<std::size_t _Dimen, typename _RealType>
1726       class uniform_inside_sphere_helper<_Dimen, true, _RealType>
1727       {
1728 	using result_type
1729 	  = typename uniform_inside_sphere_distribution<_Dimen, _RealType>::
1730 	    result_type;
1731 
1732       public:
1733 	template<typename _UniformOnSphereDistribution,
1734 		 typename _UniformRandomNumberGenerator>
1735 	result_type
1736 	operator()(_UniformOnSphereDistribution&,
1737 		   _UniformRandomNumberGenerator& __urng,
1738 		   _RealType __radius)
1739         {
1740 	  result_type __ret;
1741 	  _RealType __sq;
1742 	  _RealType __radsq = __radius * __radius;
1743 	  std::__detail::_Adaptor<_UniformRandomNumberGenerator,
1744 				  _RealType> __aurng(__urng);
1745 
1746 	  do
1747 	    {
1748 	      __sq = _RealType(0);
1749 	      for (int i = 0; i < _Dimen; ++i)
1750 		{
1751 		  __ret[i] = _RealType(2) * __aurng() - _RealType(1);
1752 		  __sq += __ret[i] * __ret[i];
1753 		}
1754 	    }
1755 	  while (__sq > _RealType(1));
1756 
1757 	  for (int i = 0; i < _Dimen; ++i)
1758             __ret[i] *= __radius;
1759 
1760 	  return __ret;
1761         }
1762       };
1763   } // namespace
1764 
1765   //
1766   //  Experiments have shown that rejection is more efficient than transform
1767   //  for dimensions less than 8.
1768   //
1769   template<std::size_t _Dimen, typename _RealType>
1770     template<typename _UniformRandomNumberGenerator>
1771       typename uniform_inside_sphere_distribution<_Dimen, _RealType>::result_type
1772       uniform_inside_sphere_distribution<_Dimen, _RealType>::
1773       operator()(_UniformRandomNumberGenerator& __urng,
1774 		 const param_type& __p)
1775       {
1776         uniform_inside_sphere_helper<_Dimen, _Dimen < 8, _RealType> __helper;
1777         return __helper(_M_uosd, __urng, __p.radius());
1778       }
1779 
1780   template<std::size_t _Dimen, typename _RealType>
1781     template<typename _OutputIterator,
1782 	     typename _UniformRandomNumberGenerator>
1783       void
1784       uniform_inside_sphere_distribution<_Dimen, _RealType>::
1785       __generate_impl(_OutputIterator __f, _OutputIterator __t,
1786 		      _UniformRandomNumberGenerator& __urng,
1787 		      const param_type& __param)
1788       {
1789 	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
1790 	    result_type>)
1791 
1792 	while (__f != __t)
1793 	  *__f++ = this->operator()(__urng, __param);
1794       }
1795 
1796   template<std::size_t _Dimen, typename _RealType, typename _CharT,
1797 	   typename _Traits>
1798     std::basic_ostream<_CharT, _Traits>&
1799     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1800 	       const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen,
1801 								_RealType>& __x)
1802     {
1803       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1804       typedef typename __ostream_type::ios_base    __ios_base;
1805 
1806       const typename __ios_base::fmtflags __flags = __os.flags();
1807       const _CharT __fill = __os.fill();
1808       const std::streamsize __precision = __os.precision();
1809       const _CharT __space = __os.widen(' ');
1810       __os.flags(__ios_base::scientific | __ios_base::left);
1811       __os.fill(__space);
1812       __os.precision(std::numeric_limits<_RealType>::max_digits10);
1813 
1814       __os << __x.radius() << __space << __x._M_uosd;
1815 
1816       __os.flags(__flags);
1817       __os.fill(__fill);
1818       __os.precision(__precision);
1819 
1820       return __os;
1821     }
1822 
1823   template<std::size_t _Dimen, typename _RealType, typename _CharT,
1824 	   typename _Traits>
1825     std::basic_istream<_CharT, _Traits>&
1826     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1827 	       __gnu_cxx::uniform_inside_sphere_distribution<_Dimen,
1828 							     _RealType>& __x)
1829     {
1830       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1831       typedef typename __istream_type::ios_base    __ios_base;
1832 
1833       const typename __ios_base::fmtflags __flags = __is.flags();
1834       __is.flags(__ios_base::dec | __ios_base::skipws);
1835 
1836       _RealType __radius_val;
1837       __is >> __radius_val >> __x._M_uosd;
1838       __x.param(typename uniform_inside_sphere_distribution<_Dimen, _RealType>::
1839 		param_type(__radius_val));
1840 
1841       __is.flags(__flags);
1842 
1843       return __is;
1844     }
1845 
1846 _GLIBCXX_END_NAMESPACE_VERSION
1847 } // namespace __gnu_cxx
1848 
1849 
1850 #endif // _EXT_RANDOM_TCC
1851