xref: /netbsd-src/external/gpl3/gcc.old/dist/libstdc++-v3/include/tr1/random.h (revision b7b7574d3bf8eeb51a1fa3977b59142ec6434a55)
1 // random number generation -*- C++ -*-
2 
3 // Copyright (C) 2009, 2010 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 /**
26  * @file tr1/random.h
27  *  This is an internal header file, included by other library headers.
28  *  You should not attempt to use it directly.
29  */
30 
31 #ifndef _GLIBCXX_TR1_RANDOM_H
32 #define _GLIBCXX_TR1_RANDOM_H 1
33 
34 #pragma GCC system_header
35 
36 namespace std
37 {
38 namespace tr1
39 {
40   // [5.1] Random number generation
41 
42   /**
43    * @addtogroup tr1_random Random Number Generation
44    * A facility for generating random numbers on selected distributions.
45    * @{
46    */
47 
48   /*
49    * Implementation-space details.
50    */
51   namespace __detail
52   {
53     template<typename _UIntType, int __w,
54 	     bool = __w < std::numeric_limits<_UIntType>::digits>
55       struct _Shift
56       { static const _UIntType __value = 0; };
57 
58     template<typename _UIntType, int __w>
59       struct _Shift<_UIntType, __w, true>
60       { static const _UIntType __value = _UIntType(1) << __w; };
61 
62     template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool>
63       struct _Mod;
64 
65     // Dispatch based on modulus value to prevent divide-by-zero compile-time
66     // errors when m == 0.
67     template<typename _Tp, _Tp __a, _Tp __c, _Tp __m>
68       inline _Tp
69       __mod(_Tp __x)
70       { return _Mod<_Tp, __a, __c, __m, __m == 0>::__calc(__x); }
71 
72     typedef __gnu_cxx::__conditional_type<(sizeof(unsigned) == 4),
73 		    unsigned, unsigned long>::__type _UInt32Type;
74 
75     /*
76      * An adaptor class for converting the output of any Generator into
77      * the input for a specific Distribution.
78      */
79     template<typename _Engine, typename _Distribution>
80       struct _Adaptor
81       {
82 	typedef typename remove_reference<_Engine>::type _BEngine;
83 	typedef typename _BEngine::result_type           _Engine_result_type;
84 	typedef typename _Distribution::input_type       result_type;
85 
86       public:
87 	_Adaptor(const _Engine& __g)
88 	: _M_g(__g) { }
89 
90 	result_type
91 	min() const
92 	{
93 	  result_type __return_value;
94 	  if (is_integral<_Engine_result_type>::value
95 	      && is_integral<result_type>::value)
96 	    __return_value = _M_g.min();
97 	  else
98 	    __return_value = result_type(0);
99 	  return __return_value;
100 	}
101 
102 	result_type
103 	max() const
104 	{
105 	  result_type __return_value;
106 	  if (is_integral<_Engine_result_type>::value
107 	      && is_integral<result_type>::value)
108 	    __return_value = _M_g.max();
109 	  else if (!is_integral<result_type>::value)
110 	    __return_value = result_type(1);
111 	  else
112 	    __return_value = std::numeric_limits<result_type>::max() - 1;
113 	  return __return_value;
114 	}
115 
116 	/*
117 	 * Converts a value generated by the adapted random number generator
118 	 * into a value in the input domain for the dependent random number
119 	 * distribution.
120 	 *
121 	 * Because the type traits are compile time constants only the
122 	 * appropriate clause of the if statements will actually be emitted
123 	 * by the compiler.
124 	 */
125 	result_type
126 	operator()()
127 	{
128 	  result_type __return_value;
129 	  if (is_integral<_Engine_result_type>::value
130 	      && is_integral<result_type>::value)
131 	    __return_value = _M_g();
132 	  else if (!is_integral<_Engine_result_type>::value
133 		   && !is_integral<result_type>::value)
134 	    __return_value = result_type(_M_g() - _M_g.min())
135 	      / result_type(_M_g.max() - _M_g.min());
136 	  else if (is_integral<_Engine_result_type>::value
137 		   && !is_integral<result_type>::value)
138 	    __return_value = result_type(_M_g() - _M_g.min())
139 	      / result_type(_M_g.max() - _M_g.min() + result_type(1));
140 	  else
141 	    __return_value = (((_M_g() - _M_g.min())
142 			       / (_M_g.max() - _M_g.min()))
143 			      * std::numeric_limits<result_type>::max());
144 	  return __return_value;
145 	}
146 
147       private:
148 	_Engine _M_g;
149       };
150 
151     // Specialization for _Engine*.
152     template<typename _Engine, typename _Distribution>
153       struct _Adaptor<_Engine*, _Distribution>
154       {
155 	typedef typename _Engine::result_type      _Engine_result_type;
156 	typedef typename _Distribution::input_type result_type;
157 
158       public:
159 	_Adaptor(_Engine* __g)
160 	: _M_g(__g) { }
161 
162 	result_type
163 	min() const
164 	{
165 	  result_type __return_value;
166 	  if (is_integral<_Engine_result_type>::value
167 	      && is_integral<result_type>::value)
168 	    __return_value = _M_g->min();
169 	  else
170 	    __return_value = result_type(0);
171 	  return __return_value;
172 	}
173 
174 	result_type
175 	max() const
176 	{
177 	  result_type __return_value;
178 	  if (is_integral<_Engine_result_type>::value
179 	      && is_integral<result_type>::value)
180 	    __return_value = _M_g->max();
181 	  else if (!is_integral<result_type>::value)
182 	    __return_value = result_type(1);
183 	  else
184 	    __return_value = std::numeric_limits<result_type>::max() - 1;
185 	  return __return_value;
186 	}
187 
188 	result_type
189 	operator()()
190 	{
191 	  result_type __return_value;
192 	  if (is_integral<_Engine_result_type>::value
193 	      && is_integral<result_type>::value)
194 	    __return_value = (*_M_g)();
195 	  else if (!is_integral<_Engine_result_type>::value
196 		   && !is_integral<result_type>::value)
197 	    __return_value = result_type((*_M_g)() - _M_g->min())
198 	      / result_type(_M_g->max() - _M_g->min());
199 	  else if (is_integral<_Engine_result_type>::value
200 		   && !is_integral<result_type>::value)
201 	    __return_value = result_type((*_M_g)() - _M_g->min())
202 	      / result_type(_M_g->max() - _M_g->min() + result_type(1));
203 	  else
204 	    __return_value = ((((*_M_g)() - _M_g->min())
205 			       / (_M_g->max() - _M_g->min()))
206 			      * std::numeric_limits<result_type>::max());
207 	  return __return_value;
208 	}
209 
210       private:
211 	_Engine* _M_g;
212       };
213   } // namespace __detail
214 
215   /**
216    * Produces random numbers on a given distribution function using a
217    * non-uniform random number generation engine.
218    *
219    * @todo the engine_value_type needs to be studied more carefully.
220    */
221   template<typename _Engine, typename _Dist>
222     class variate_generator
223     {
224       // Concept requirements.
225       __glibcxx_class_requires(_Engine, _CopyConstructibleConcept)
226       //  __glibcxx_class_requires(_Engine, _EngineConcept)
227       //  __glibcxx_class_requires(_Dist, _EngineConcept)
228 
229     public:
230       typedef _Engine                                engine_type;
231       typedef __detail::_Adaptor<_Engine, _Dist>     engine_value_type;
232       typedef _Dist                                  distribution_type;
233       typedef typename _Dist::result_type            result_type;
234 
235       // tr1:5.1.1 table 5.1 requirement
236       typedef typename __gnu_cxx::__enable_if<
237 	is_arithmetic<result_type>::value, result_type>::__type _IsValidType;
238 
239       /**
240        * Constructs a variate generator with the uniform random number
241        * generator @p __eng for the random distribution @p __dist.
242        *
243        * @throws Any exceptions which may thrown by the copy constructors of
244        * the @p _Engine or @p _Dist objects.
245        */
246       variate_generator(engine_type __eng, distribution_type __dist)
247       : _M_engine(__eng), _M_dist(__dist) { }
248 
249       /**
250        * Gets the next generated value on the distribution.
251        */
252       result_type
253       operator()()
254       { return _M_dist(_M_engine); }
255 
256       /**
257        * WTF?
258        */
259       template<typename _Tp>
260         result_type
261         operator()(_Tp __value)
262         { return _M_dist(_M_engine, __value); }
263 
264       /**
265        * Gets a reference to the underlying uniform random number generator
266        * object.
267        */
268       engine_value_type&
269       engine()
270       { return _M_engine; }
271 
272       /**
273        * Gets a const reference to the underlying uniform random number
274        * generator object.
275        */
276       const engine_value_type&
277       engine() const
278       { return _M_engine; }
279 
280       /**
281        * Gets a reference to the underlying random distribution.
282        */
283       distribution_type&
284       distribution()
285       { return _M_dist; }
286 
287       /**
288        * Gets a const reference to the underlying random distribution.
289        */
290       const distribution_type&
291       distribution() const
292       { return _M_dist; }
293 
294       /**
295        * Gets the closed lower bound of the distribution interval.
296        */
297       result_type
298       min() const
299       { return this->distribution().min(); }
300 
301       /**
302        * Gets the closed upper bound of the distribution interval.
303        */
304       result_type
305       max() const
306       { return this->distribution().max(); }
307 
308     private:
309       engine_value_type _M_engine;
310       distribution_type _M_dist;
311     };
312 
313 
314   /**
315    * @addtogroup tr1_random_generators Random Number Generators
316    * @ingroup tr1_random
317    *
318    * These classes define objects which provide random or pseudorandom
319    * numbers, either from a discrete or a continuous interval.  The
320    * random number generator supplied as a part of this library are
321    * all uniform random number generators which provide a sequence of
322    * random number uniformly distributed over their range.
323    *
324    * A number generator is a function object with an operator() that
325    * takes zero arguments and returns a number.
326    *
327    * A compliant random number generator must satisfy the following
328    * requirements.  <table border=1 cellpadding=10 cellspacing=0>
329    * <caption align=top>Random Number Generator Requirements</caption>
330    * <tr><td>To be documented.</td></tr> </table>
331    *
332    * @{
333    */
334 
335   /**
336    * @brief A model of a linear congruential random number generator.
337    *
338    * A random number generator that produces pseudorandom numbers using the
339    * linear function @f$x_{i+1}\leftarrow(ax_{i} + c) \bmod m @f$.
340    *
341    * The template parameter @p _UIntType must be an unsigned integral type
342    * large enough to store values up to (__m-1). If the template parameter
343    * @p __m is 0, the modulus @p __m used is
344    * std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template
345    * parameters @p __a and @p __c must be less than @p __m.
346    *
347    * The size of the state is @f$ 1 @f$.
348    */
349   template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
350     class linear_congruential
351     {
352       __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
353       //  __glibcpp_class_requires(__a < __m && __c < __m)
354 
355     public:
356       /** The type of the generated random value. */
357       typedef _UIntType result_type;
358 
359       /** The multiplier. */
360       static const _UIntType multiplier = __a;
361       /** An increment. */
362       static const _UIntType increment = __c;
363       /** The modulus. */
364       static const _UIntType modulus = __m;
365 
366       /**
367        * Constructs a %linear_congruential random number generator engine with
368        * seed @p __s.  The default seed value is 1.
369        *
370        * @param __s The initial seed value.
371        */
372       explicit
373       linear_congruential(unsigned long __x0 = 1)
374       { this->seed(__x0); }
375 
376       /**
377        * Constructs a %linear_congruential random number generator engine
378        * seeded from the generator function @p __g.
379        *
380        * @param __g The seed generator function.
381        */
382       template<class _Gen>
383         linear_congruential(_Gen& __g)
384         { this->seed(__g); }
385 
386       /**
387        * Reseeds the %linear_congruential random number generator engine
388        * sequence to the seed @g __s.
389        *
390        * @param __s The new seed.
391        */
392       void
393       seed(unsigned long __s = 1);
394 
395       /**
396        * Reseeds the %linear_congruential random number generator engine
397        * sequence using values from the generator function @p __g.
398        *
399        * @param __g the seed generator function.
400        */
401       template<class _Gen>
402         void
403         seed(_Gen& __g)
404         { seed(__g, typename is_fundamental<_Gen>::type()); }
405 
406       /**
407        * Gets the smallest possible value in the output range.
408        *
409        * The minimum depends on the @p __c parameter: if it is zero, the
410        * minimum generated must be > 0, otherwise 0 is allowed.
411        */
412       result_type
413       min() const
414       { return (__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0) ? 1 : 0; }
415 
416       /**
417        * Gets the largest possible value in the output range.
418        */
419       result_type
420       max() const
421       { return __m - 1; }
422 
423       /**
424        * Gets the next random number in the sequence.
425        */
426       result_type
427       operator()();
428 
429       /**
430        * Compares two linear congruential random number generator
431        * objects of the same type for equality.
432        *
433        * @param __lhs A linear congruential random number generator object.
434        * @param __rhs Another linear congruential random number generator obj.
435        *
436        * @returns true if the two objects are equal, false otherwise.
437        */
438       friend bool
439       operator==(const linear_congruential& __lhs,
440 		 const linear_congruential& __rhs)
441       { return __lhs._M_x == __rhs._M_x; }
442 
443       /**
444        * Compares two linear congruential random number generator
445        * objects of the same type for inequality.
446        *
447        * @param __lhs A linear congruential random number generator object.
448        * @param __rhs Another linear congruential random number generator obj.
449        *
450        * @returns true if the two objects are not equal, false otherwise.
451        */
452       friend bool
453       operator!=(const linear_congruential& __lhs,
454 		 const linear_congruential& __rhs)
455       { return !(__lhs == __rhs); }
456 
457       /**
458        * Writes the textual representation of the state x(i) of x to @p __os.
459        *
460        * @param __os  The output stream.
461        * @param __lcr A % linear_congruential random number generator.
462        * @returns __os.
463        */
464       template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
465 	       _UIntType1 __m1,
466 	       typename _CharT, typename _Traits>
467         friend std::basic_ostream<_CharT, _Traits>&
468         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
469 		   const linear_congruential<_UIntType1, __a1, __c1,
470 		   __m1>& __lcr);
471 
472       /**
473        * Sets the state of the engine by reading its textual
474        * representation from @p __is.
475        *
476        * The textual representation must have been previously written using an
477        * output stream whose imbued locale and whose type's template
478        * specialization arguments _CharT and _Traits were the same as those of
479        * @p __is.
480        *
481        * @param __is  The input stream.
482        * @param __lcr A % linear_congruential random number generator.
483        * @returns __is.
484        */
485       template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
486 	       _UIntType1 __m1,
487 	       typename _CharT, typename _Traits>
488         friend std::basic_istream<_CharT, _Traits>&
489         operator>>(std::basic_istream<_CharT, _Traits>& __is,
490 		   linear_congruential<_UIntType1, __a1, __c1, __m1>& __lcr);
491 
492     private:
493       template<class _Gen>
494         void
495         seed(_Gen& __g, true_type)
496         { return seed(static_cast<unsigned long>(__g)); }
497 
498       template<class _Gen>
499         void
500         seed(_Gen& __g, false_type);
501 
502       _UIntType _M_x;
503     };
504 
505   /**
506    * The classic Minimum Standard rand0 of Lewis, Goodman, and Miller.
507    */
508   typedef linear_congruential<unsigned long, 16807, 0, 2147483647> minstd_rand0;
509 
510   /**
511    * An alternative LCR (Lehmer Generator function) .
512    */
513   typedef linear_congruential<unsigned long, 48271, 0, 2147483647> minstd_rand;
514 
515 
516   /**
517    * A generalized feedback shift register discrete random number generator.
518    *
519    * This algorithm avoids multiplication and division and is designed to be
520    * friendly to a pipelined architecture.  If the parameters are chosen
521    * correctly, this generator will produce numbers with a very long period and
522    * fairly good apparent entropy, although still not cryptographically strong.
523    *
524    * The best way to use this generator is with the predefined mt19937 class.
525    *
526    * This algorithm was originally invented by Makoto Matsumoto and
527    * Takuji Nishimura.
528    *
529    * @var word_size   The number of bits in each element of the state vector.
530    * @var state_size  The degree of recursion.
531    * @var shift_size  The period parameter.
532    * @var mask_bits   The separation point bit index.
533    * @var parameter_a The last row of the twist matrix.
534    * @var output_u    The first right-shift tempering matrix parameter.
535    * @var output_s    The first left-shift tempering matrix parameter.
536    * @var output_b    The first left-shift tempering matrix mask.
537    * @var output_t    The second left-shift tempering matrix parameter.
538    * @var output_c    The second left-shift tempering matrix mask.
539    * @var output_l    The second right-shift tempering matrix parameter.
540    */
541   template<class _UIntType, int __w, int __n, int __m, int __r,
542 	   _UIntType __a, int __u, int __s, _UIntType __b, int __t,
543 	   _UIntType __c, int __l>
544     class mersenne_twister
545     {
546       __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
547 
548     public:
549       // types
550       typedef _UIntType result_type;
551 
552       // parameter values
553       static const int       word_size   = __w;
554       static const int       state_size  = __n;
555       static const int       shift_size  = __m;
556       static const int       mask_bits   = __r;
557       static const _UIntType parameter_a = __a;
558       static const int       output_u    = __u;
559       static const int       output_s    = __s;
560       static const _UIntType output_b    = __b;
561       static const int       output_t    = __t;
562       static const _UIntType output_c    = __c;
563       static const int       output_l    = __l;
564 
565       // constructors and member function
566       mersenne_twister()
567       { seed(); }
568 
569       explicit
570       mersenne_twister(unsigned long __value)
571       { seed(__value); }
572 
573       template<class _Gen>
574         mersenne_twister(_Gen& __g)
575         { seed(__g); }
576 
577       void
578       seed()
579       { seed(5489UL); }
580 
581       void
582       seed(unsigned long __value);
583 
584       template<class _Gen>
585         void
586         seed(_Gen& __g)
587         { seed(__g, typename is_fundamental<_Gen>::type()); }
588 
589       result_type
590       min() const
591       { return 0; };
592 
593       result_type
594       max() const
595       { return __detail::_Shift<_UIntType, __w>::__value - 1; }
596 
597       result_type
598       operator()();
599 
600       /**
601        * Compares two % mersenne_twister random number generator objects of
602        * the same type for equality.
603        *
604        * @param __lhs A % mersenne_twister random number generator object.
605        * @param __rhs Another % mersenne_twister random number generator
606        *              object.
607        *
608        * @returns true if the two objects are equal, false otherwise.
609        */
610       friend bool
611       operator==(const mersenne_twister& __lhs,
612 		 const mersenne_twister& __rhs)
613       { return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); }
614 
615       /**
616        * Compares two % mersenne_twister random number generator objects of
617        * the same type for inequality.
618        *
619        * @param __lhs A % mersenne_twister random number generator object.
620        * @param __rhs Another % mersenne_twister random number generator
621        *              object.
622        *
623        * @returns true if the two objects are not equal, false otherwise.
624        */
625       friend bool
626       operator!=(const mersenne_twister& __lhs,
627 		 const mersenne_twister& __rhs)
628       { return !(__lhs == __rhs); }
629 
630       /**
631        * Inserts the current state of a % mersenne_twister random number
632        * generator engine @p __x into the output stream @p __os.
633        *
634        * @param __os An output stream.
635        * @param __x  A % mersenne_twister random number generator engine.
636        *
637        * @returns The output stream with the state of @p __x inserted or in
638        * an error state.
639        */
640       template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
641 	       _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
642 	       _UIntType1 __c1, int __l1,
643 	       typename _CharT, typename _Traits>
644         friend std::basic_ostream<_CharT, _Traits>&
645         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
646 		   const mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
647 		   __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
648 
649       /**
650        * Extracts the current state of a % mersenne_twister random number
651        * generator engine @p __x from the input stream @p __is.
652        *
653        * @param __is An input stream.
654        * @param __x  A % mersenne_twister random number generator engine.
655        *
656        * @returns The input stream with the state of @p __x extracted or in
657        * an error state.
658        */
659       template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
660 	       _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
661 	       _UIntType1 __c1, int __l1,
662 	       typename _CharT, typename _Traits>
663         friend std::basic_istream<_CharT, _Traits>&
664         operator>>(std::basic_istream<_CharT, _Traits>& __is,
665 		   mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
666 		   __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
667 
668     private:
669       template<class _Gen>
670         void
671         seed(_Gen& __g, true_type)
672         { return seed(static_cast<unsigned long>(__g)); }
673 
674       template<class _Gen>
675         void
676         seed(_Gen& __g, false_type);
677 
678       _UIntType _M_x[state_size];
679       int       _M_p;
680     };
681 
682   /**
683    * The classic Mersenne Twister.
684    *
685    * Reference:
686    * M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-Dimensionally
687    * Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions
688    * on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
689    */
690   typedef mersenne_twister<
691     unsigned long, 32, 624, 397, 31,
692     0x9908b0dful, 11, 7,
693     0x9d2c5680ul, 15,
694     0xefc60000ul, 18
695     > mt19937;
696 
697 
698   /**
699    * @brief The Marsaglia-Zaman generator.
700    *
701    * This is a model of a Generalized Fibonacci discrete random number
702    * generator, sometimes referred to as the SWC generator.
703    *
704    * A discrete random number generator that produces pseudorandom
705    * numbers using @f$x_{i}\leftarrow(x_{i - s} - x_{i - r} -
706    * carry_{i-1}) \bmod m @f$.
707    *
708    * The size of the state is @f$ r @f$
709    * and the maximum period of the generator is @f$ m^r - m^s -1 @f$.
710    *
711    * N1688[4.13] says <em>the template parameter _IntType shall denote
712    * an integral type large enough to store values up to m</em>.
713    *
714    * @var _M_x     The state of the generator.  This is a ring buffer.
715    * @var _M_carry The carry.
716    * @var _M_p     Current index of x(i - r).
717    */
718   template<typename _IntType, _IntType __m, int __s, int __r>
719     class subtract_with_carry
720     {
721       __glibcxx_class_requires(_IntType, _IntegerConcept)
722 
723     public:
724       /** The type of the generated random value. */
725       typedef _IntType result_type;
726 
727       // parameter values
728       static const _IntType modulus   = __m;
729       static const int      long_lag  = __r;
730       static const int      short_lag = __s;
731 
732       /**
733        * Constructs a default-initialized % subtract_with_carry random number
734        * generator.
735        */
736       subtract_with_carry()
737       { this->seed(); }
738 
739       /**
740        * Constructs an explicitly seeded % subtract_with_carry random number
741        * generator.
742        */
743       explicit
744       subtract_with_carry(unsigned long __value)
745       { this->seed(__value); }
746 
747       /**
748        * Constructs a %subtract_with_carry random number generator engine
749        * seeded from the generator function @p __g.
750        *
751        * @param __g The seed generator function.
752        */
753       template<class _Gen>
754         subtract_with_carry(_Gen& __g)
755         { this->seed(__g); }
756 
757       /**
758        * Seeds the initial state @f$ x_0 @f$ of the random number generator.
759        *
760        * N1688[4.19] modifies this as follows.  If @p __value == 0,
761        * sets value to 19780503.  In any case, with a linear
762        * congruential generator lcg(i) having parameters @f$ m_{lcg} =
763        * 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value
764        * @f$, sets @f$ x_{-r} \dots x_{-1} @f$ to @f$ lcg(1) \bmod m
765        * \dots lcg(r) \bmod m @f$ respectively.  If @f$ x_{-1} = 0 @f$
766        * set carry to 1, otherwise sets carry to 0.
767        */
768       void
769       seed(unsigned long __value = 19780503);
770 
771       /**
772        * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry
773        * random number generator.
774        */
775       template<class _Gen>
776         void
777         seed(_Gen& __g)
778         { seed(__g, typename is_fundamental<_Gen>::type()); }
779 
780       /**
781        * Gets the inclusive minimum value of the range of random integers
782        * returned by this generator.
783        */
784       result_type
785       min() const
786       { return 0; }
787 
788       /**
789        * Gets the inclusive maximum value of the range of random integers
790        * returned by this generator.
791        */
792       result_type
793       max() const
794       { return this->modulus - 1; }
795 
796       /**
797        * Gets the next random number in the sequence.
798        */
799       result_type
800       operator()();
801 
802       /**
803        * Compares two % subtract_with_carry random number generator objects of
804        * the same type for equality.
805        *
806        * @param __lhs A % subtract_with_carry random number generator object.
807        * @param __rhs Another % subtract_with_carry random number generator
808        *              object.
809        *
810        * @returns true if the two objects are equal, false otherwise.
811        */
812       friend bool
813       operator==(const subtract_with_carry& __lhs,
814 		 const subtract_with_carry& __rhs)
815       { return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); }
816 
817       /**
818        * Compares two % subtract_with_carry random number generator objects of
819        * the same type for inequality.
820        *
821        * @param __lhs A % subtract_with_carry random number generator object.
822        * @param __rhs Another % subtract_with_carry random number generator
823        *              object.
824        *
825        * @returns true if the two objects are not equal, false otherwise.
826        */
827       friend bool
828       operator!=(const subtract_with_carry& __lhs,
829 		 const subtract_with_carry& __rhs)
830       { return !(__lhs == __rhs); }
831 
832       /**
833        * Inserts the current state of a % subtract_with_carry random number
834        * generator engine @p __x into the output stream @p __os.
835        *
836        * @param __os An output stream.
837        * @param __x  A % subtract_with_carry random number generator engine.
838        *
839        * @returns The output stream with the state of @p __x inserted or in
840        * an error state.
841        */
842       template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
843 	       typename _CharT, typename _Traits>
844         friend std::basic_ostream<_CharT, _Traits>&
845         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
846 		   const subtract_with_carry<_IntType1, __m1, __s1,
847 		   __r1>& __x);
848 
849       /**
850        * Extracts the current state of a % subtract_with_carry random number
851        * generator engine @p __x from the input stream @p __is.
852        *
853        * @param __is An input stream.
854        * @param __x  A % subtract_with_carry random number generator engine.
855        *
856        * @returns The input stream with the state of @p __x extracted or in
857        * an error state.
858        */
859       template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
860 	       typename _CharT, typename _Traits>
861         friend std::basic_istream<_CharT, _Traits>&
862         operator>>(std::basic_istream<_CharT, _Traits>& __is,
863 		   subtract_with_carry<_IntType1, __m1, __s1, __r1>& __x);
864 
865     private:
866       template<class _Gen>
867         void
868         seed(_Gen& __g, true_type)
869         { return seed(static_cast<unsigned long>(__g)); }
870 
871       template<class _Gen>
872         void
873         seed(_Gen& __g, false_type);
874 
875       typedef typename __gnu_cxx::__add_unsigned<_IntType>::__type _UIntType;
876 
877       _UIntType  _M_x[long_lag];
878       _UIntType  _M_carry;
879       int        _M_p;
880     };
881 
882 
883   /**
884    * @brief The Marsaglia-Zaman generator (floats version).
885    *
886    * @var _M_x     The state of the generator.  This is a ring buffer.
887    * @var _M_carry The carry.
888    * @var _M_p     Current index of x(i - r).
889    * @var _M_npows Precomputed negative powers of 2.
890    */
891   template<typename _RealType, int __w, int __s, int __r>
892     class subtract_with_carry_01
893     {
894     public:
895       /** The type of the generated random value. */
896       typedef _RealType result_type;
897 
898       // parameter values
899       static const int      word_size = __w;
900       static const int      long_lag  = __r;
901       static const int      short_lag = __s;
902 
903       /**
904        * Constructs a default-initialized % subtract_with_carry_01 random
905        * number generator.
906        */
907       subtract_with_carry_01()
908       {
909 	this->seed();
910 	_M_initialize_npows();
911       }
912 
913       /**
914        * Constructs an explicitly seeded % subtract_with_carry_01 random number
915        * generator.
916        */
917       explicit
918       subtract_with_carry_01(unsigned long __value)
919       {
920 	this->seed(__value);
921 	_M_initialize_npows();
922       }
923 
924       /**
925        * Constructs a % subtract_with_carry_01 random number generator engine
926        * seeded from the generator function @p __g.
927        *
928        * @param __g The seed generator function.
929        */
930       template<class _Gen>
931         subtract_with_carry_01(_Gen& __g)
932         {
933 	  this->seed(__g);
934 	  _M_initialize_npows();
935 	}
936 
937       /**
938        * Seeds the initial state @f$ x_0 @f$ of the random number generator.
939        */
940       void
941       seed(unsigned long __value = 19780503);
942 
943       /**
944        * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry_01
945        * random number generator.
946        */
947       template<class _Gen>
948         void
949         seed(_Gen& __g)
950         { seed(__g, typename is_fundamental<_Gen>::type()); }
951 
952       /**
953        * Gets the minimum value of the range of random floats
954        * returned by this generator.
955        */
956       result_type
957       min() const
958       { return 0.0; }
959 
960       /**
961        * Gets the maximum value of the range of random floats
962        * returned by this generator.
963        */
964       result_type
965       max() const
966       { return 1.0; }
967 
968       /**
969        * Gets the next random number in the sequence.
970        */
971       result_type
972       operator()();
973 
974       /**
975        * Compares two % subtract_with_carry_01 random number generator objects
976        * of the same type for equality.
977        *
978        * @param __lhs A % subtract_with_carry_01 random number
979        *              generator object.
980        * @param __rhs Another % subtract_with_carry_01 random number generator
981        *              object.
982        *
983        * @returns true if the two objects are equal, false otherwise.
984        */
985       friend bool
986       operator==(const subtract_with_carry_01& __lhs,
987 		 const subtract_with_carry_01& __rhs)
988       {
989 	for (int __i = 0; __i < long_lag; ++__i)
990 	  if (!std::equal(__lhs._M_x[__i], __lhs._M_x[__i] + __n,
991 			  __rhs._M_x[__i]))
992 	    return false;
993 	return true;
994       }
995 
996       /**
997        * Compares two % subtract_with_carry_01 random number generator objects
998        * of the same type for inequality.
999        *
1000        * @param __lhs A % subtract_with_carry_01 random number
1001        *              generator object.
1002        *
1003        * @param __rhs Another % subtract_with_carry_01 random number generator
1004        *              object.
1005        *
1006        * @returns true if the two objects are not equal, false otherwise.
1007        */
1008       friend bool
1009       operator!=(const subtract_with_carry_01& __lhs,
1010 		 const subtract_with_carry_01& __rhs)
1011       { return !(__lhs == __rhs); }
1012 
1013       /**
1014        * Inserts the current state of a % subtract_with_carry_01 random number
1015        * generator engine @p __x into the output stream @p __os.
1016        *
1017        * @param __os An output stream.
1018        * @param __x  A % subtract_with_carry_01 random number generator engine.
1019        *
1020        * @returns The output stream with the state of @p __x inserted or in
1021        * an error state.
1022        */
1023       template<typename _RealType1, int __w1, int __s1, int __r1,
1024 	       typename _CharT, typename _Traits>
1025         friend std::basic_ostream<_CharT, _Traits>&
1026         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1027 		   const subtract_with_carry_01<_RealType1, __w1, __s1,
1028 		   __r1>& __x);
1029 
1030       /**
1031        * Extracts the current state of a % subtract_with_carry_01 random number
1032        * generator engine @p __x from the input stream @p __is.
1033        *
1034        * @param __is An input stream.
1035        * @param __x  A % subtract_with_carry_01 random number generator engine.
1036        *
1037        * @returns The input stream with the state of @p __x extracted or in
1038        * an error state.
1039        */
1040       template<typename _RealType1, int __w1, int __s1, int __r1,
1041 	       typename _CharT, typename _Traits>
1042         friend std::basic_istream<_CharT, _Traits>&
1043         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1044 		   subtract_with_carry_01<_RealType1, __w1, __s1, __r1>& __x);
1045 
1046     private:
1047       template<class _Gen>
1048         void
1049         seed(_Gen& __g, true_type)
1050         { return seed(static_cast<unsigned long>(__g)); }
1051 
1052       template<class _Gen>
1053         void
1054         seed(_Gen& __g, false_type);
1055 
1056       void
1057       _M_initialize_npows();
1058 
1059       static const int __n = (__w + 31) / 32;
1060 
1061       typedef __detail::_UInt32Type _UInt32Type;
1062       _UInt32Type  _M_x[long_lag][__n];
1063       _RealType    _M_npows[__n];
1064       _UInt32Type  _M_carry;
1065       int          _M_p;
1066     };
1067 
1068   typedef subtract_with_carry_01<float, 24, 10, 24>   ranlux_base_01;
1069 
1070   // _GLIBCXX_RESOLVE_LIB_DEFECTS
1071   // 508. Bad parameters for ranlux64_base_01.
1072   typedef subtract_with_carry_01<double, 48, 5, 12> ranlux64_base_01;
1073 
1074 
1075   /**
1076    * Produces random numbers from some base engine by discarding blocks of
1077    * data.
1078    *
1079    * 0 <= @p __r <= @p __p
1080    */
1081   template<class _UniformRandomNumberGenerator, int __p, int __r>
1082     class discard_block
1083     {
1084       // __glibcxx_class_requires(typename base_type::result_type,
1085       //                          ArithmeticTypeConcept)
1086 
1087     public:
1088       /** The type of the underlying generator engine. */
1089       typedef _UniformRandomNumberGenerator   base_type;
1090       /** The type of the generated random value. */
1091       typedef typename base_type::result_type result_type;
1092 
1093       // parameter values
1094       static const int block_size = __p;
1095       static const int used_block = __r;
1096 
1097       /**
1098        * Constructs a default %discard_block engine.
1099        *
1100        * The underlying engine is default constructed as well.
1101        */
1102       discard_block()
1103       : _M_n(0) { }
1104 
1105       /**
1106        * Copy constructs a %discard_block engine.
1107        *
1108        * Copies an existing base class random number generator.
1109        * @param rng An existing (base class) engine object.
1110        */
1111       explicit
1112       discard_block(const base_type& __rng)
1113       : _M_b(__rng), _M_n(0) { }
1114 
1115       /**
1116        * Seed constructs a %discard_block engine.
1117        *
1118        * Constructs the underlying generator engine seeded with @p __s.
1119        * @param __s A seed value for the base class engine.
1120        */
1121       explicit
1122       discard_block(unsigned long __s)
1123       : _M_b(__s), _M_n(0) { }
1124 
1125       /**
1126        * Generator construct a %discard_block engine.
1127        *
1128        * @param __g A seed generator function.
1129        */
1130       template<class _Gen>
1131         discard_block(_Gen& __g)
1132 	: _M_b(__g), _M_n(0) { }
1133 
1134       /**
1135        * Reseeds the %discard_block object with the default seed for the
1136        * underlying base class generator engine.
1137        */
1138       void seed()
1139       {
1140 	_M_b.seed();
1141 	_M_n = 0;
1142       }
1143 
1144       /**
1145        * Reseeds the %discard_block object with the given seed generator
1146        * function.
1147        * @param __g A seed generator function.
1148        */
1149       template<class _Gen>
1150         void seed(_Gen& __g)
1151         {
1152 	  _M_b.seed(__g);
1153 	  _M_n = 0;
1154 	}
1155 
1156       /**
1157        * Gets a const reference to the underlying generator engine object.
1158        */
1159       const base_type&
1160       base() const
1161       { return _M_b; }
1162 
1163       /**
1164        * Gets the minimum value in the generated random number range.
1165        */
1166       result_type
1167       min() const
1168       { return _M_b.min(); }
1169 
1170       /**
1171        * Gets the maximum value in the generated random number range.
1172        */
1173       result_type
1174       max() const
1175       { return _M_b.max(); }
1176 
1177       /**
1178        * Gets the next value in the generated random number sequence.
1179        */
1180       result_type
1181       operator()();
1182 
1183       /**
1184        * Compares two %discard_block random number generator objects of
1185        * the same type for equality.
1186        *
1187        * @param __lhs A %discard_block random number generator object.
1188        * @param __rhs Another %discard_block random number generator
1189        *              object.
1190        *
1191        * @returns true if the two objects are equal, false otherwise.
1192        */
1193       friend bool
1194       operator==(const discard_block& __lhs, const discard_block& __rhs)
1195       { return (__lhs._M_b == __rhs._M_b) && (__lhs._M_n == __rhs._M_n); }
1196 
1197       /**
1198        * Compares two %discard_block random number generator objects of
1199        * the same type for inequality.
1200        *
1201        * @param __lhs A %discard_block random number generator object.
1202        * @param __rhs Another %discard_block random number generator
1203        *              object.
1204        *
1205        * @returns true if the two objects are not equal, false otherwise.
1206        */
1207       friend bool
1208       operator!=(const discard_block& __lhs, const discard_block& __rhs)
1209       { return !(__lhs == __rhs); }
1210 
1211       /**
1212        * Inserts the current state of a %discard_block random number
1213        * generator engine @p __x into the output stream @p __os.
1214        *
1215        * @param __os An output stream.
1216        * @param __x  A %discard_block random number generator engine.
1217        *
1218        * @returns The output stream with the state of @p __x inserted or in
1219        * an error state.
1220        */
1221       template<class _UniformRandomNumberGenerator1, int __p1, int __r1,
1222 	       typename _CharT, typename _Traits>
1223         friend std::basic_ostream<_CharT, _Traits>&
1224         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1225 		   const discard_block<_UniformRandomNumberGenerator1,
1226 		   __p1, __r1>& __x);
1227 
1228       /**
1229        * Extracts the current state of a % subtract_with_carry random number
1230        * generator engine @p __x from the input stream @p __is.
1231        *
1232        * @param __is An input stream.
1233        * @param __x  A %discard_block random number generator engine.
1234        *
1235        * @returns The input stream with the state of @p __x extracted or in
1236        * an error state.
1237        */
1238       template<class _UniformRandomNumberGenerator1, int __p1, int __r1,
1239 	       typename _CharT, typename _Traits>
1240         friend std::basic_istream<_CharT, _Traits>&
1241         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1242 		   discard_block<_UniformRandomNumberGenerator1,
1243 		   __p1, __r1>& __x);
1244 
1245     private:
1246       base_type _M_b;
1247       int       _M_n;
1248     };
1249 
1250 
1251   /**
1252    * James's luxury-level-3 integer adaptation of Luescher's generator.
1253    */
1254   typedef discard_block<
1255     subtract_with_carry<unsigned long, (1UL << 24), 10, 24>,
1256       223,
1257       24
1258       > ranlux3;
1259 
1260   /**
1261    * James's luxury-level-4 integer adaptation of Luescher's generator.
1262    */
1263   typedef discard_block<
1264     subtract_with_carry<unsigned long, (1UL << 24), 10, 24>,
1265       389,
1266       24
1267       > ranlux4;
1268 
1269   typedef discard_block<
1270     subtract_with_carry_01<float, 24, 10, 24>,
1271       223,
1272       24
1273       > ranlux3_01;
1274 
1275   typedef discard_block<
1276     subtract_with_carry_01<float, 24, 10, 24>,
1277       389,
1278       24
1279       > ranlux4_01;
1280 
1281 
1282   /**
1283    * A random number generator adaptor class that combines two random number
1284    * generator engines into a single output sequence.
1285    */
1286   template<class _UniformRandomNumberGenerator1, int __s1,
1287 	   class _UniformRandomNumberGenerator2, int __s2>
1288     class xor_combine
1289     {
1290       // __glibcxx_class_requires(typename _UniformRandomNumberGenerator1::
1291       //                          result_type, ArithmeticTypeConcept)
1292       // __glibcxx_class_requires(typename _UniformRandomNumberGenerator2::
1293       //                          result_type, ArithmeticTypeConcept)
1294 
1295     public:
1296       /** The type of the first underlying generator engine. */
1297       typedef _UniformRandomNumberGenerator1   base1_type;
1298       /** The type of the second underlying generator engine. */
1299       typedef _UniformRandomNumberGenerator2   base2_type;
1300 
1301     private:
1302       typedef typename base1_type::result_type _Result_type1;
1303       typedef typename base2_type::result_type _Result_type2;
1304 
1305     public:
1306       /** The type of the generated random value. */
1307       typedef typename __gnu_cxx::__conditional_type<(sizeof(_Result_type1)
1308 						      > sizeof(_Result_type2)),
1309 	_Result_type1, _Result_type2>::__type result_type;
1310 
1311       // parameter values
1312       static const int shift1 = __s1;
1313       static const int shift2 = __s2;
1314 
1315       // constructors and member function
1316       xor_combine()
1317       : _M_b1(), _M_b2()
1318       { _M_initialize_max(); }
1319 
1320       xor_combine(const base1_type& __rng1, const base2_type& __rng2)
1321       : _M_b1(__rng1), _M_b2(__rng2)
1322       { _M_initialize_max(); }
1323 
1324       xor_combine(unsigned long __s)
1325       : _M_b1(__s), _M_b2(__s + 1)
1326       { _M_initialize_max(); }
1327 
1328       template<class _Gen>
1329         xor_combine(_Gen& __g)
1330 	: _M_b1(__g), _M_b2(__g)
1331         { _M_initialize_max(); }
1332 
1333       void
1334       seed()
1335       {
1336 	_M_b1.seed();
1337 	_M_b2.seed();
1338       }
1339 
1340       template<class _Gen>
1341         void
1342         seed(_Gen& __g)
1343         {
1344 	  _M_b1.seed(__g);
1345 	  _M_b2.seed(__g);
1346 	}
1347 
1348       const base1_type&
1349       base1() const
1350       { return _M_b1; }
1351 
1352       const base2_type&
1353       base2() const
1354       { return _M_b2; }
1355 
1356       result_type
1357       min() const
1358       { return 0; }
1359 
1360       result_type
1361       max() const
1362       { return _M_max; }
1363 
1364       /**
1365        * Gets the next random number in the sequence.
1366        */
1367       // NB: Not exactly the TR1 formula, per N2079 instead.
1368       result_type
1369       operator()()
1370       {
1371 	return ((result_type(_M_b1() - _M_b1.min()) << shift1)
1372 		^ (result_type(_M_b2() - _M_b2.min()) << shift2));
1373       }
1374 
1375       /**
1376        * Compares two %xor_combine random number generator objects of
1377        * the same type for equality.
1378        *
1379        * @param __lhs A %xor_combine random number generator object.
1380        * @param __rhs Another %xor_combine random number generator
1381        *              object.
1382        *
1383        * @returns true if the two objects are equal, false otherwise.
1384        */
1385       friend bool
1386       operator==(const xor_combine& __lhs, const xor_combine& __rhs)
1387       {
1388 	return (__lhs.base1() == __rhs.base1())
1389 	        && (__lhs.base2() == __rhs.base2());
1390       }
1391 
1392       /**
1393        * Compares two %xor_combine random number generator objects of
1394        * the same type for inequality.
1395        *
1396        * @param __lhs A %xor_combine random number generator object.
1397        * @param __rhs Another %xor_combine random number generator
1398        *              object.
1399        *
1400        * @returns true if the two objects are not equal, false otherwise.
1401        */
1402       friend bool
1403       operator!=(const xor_combine& __lhs, const xor_combine& __rhs)
1404       { return !(__lhs == __rhs); }
1405 
1406       /**
1407        * Inserts the current state of a %xor_combine random number
1408        * generator engine @p __x into the output stream @p __os.
1409        *
1410        * @param __os An output stream.
1411        * @param __x  A %xor_combine random number generator engine.
1412        *
1413        * @returns The output stream with the state of @p __x inserted or in
1414        * an error state.
1415        */
1416       template<class _UniformRandomNumberGenerator11, int __s11,
1417 	       class _UniformRandomNumberGenerator21, int __s21,
1418 	       typename _CharT, typename _Traits>
1419         friend std::basic_ostream<_CharT, _Traits>&
1420         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1421 		   const xor_combine<_UniformRandomNumberGenerator11, __s11,
1422 		   _UniformRandomNumberGenerator21, __s21>& __x);
1423 
1424       /**
1425        * Extracts the current state of a %xor_combine random number
1426        * generator engine @p __x from the input stream @p __is.
1427        *
1428        * @param __is An input stream.
1429        * @param __x  A %xor_combine random number generator engine.
1430        *
1431        * @returns The input stream with the state of @p __x extracted or in
1432        * an error state.
1433        */
1434       template<class _UniformRandomNumberGenerator11, int __s11,
1435 	       class _UniformRandomNumberGenerator21, int __s21,
1436 	       typename _CharT, typename _Traits>
1437         friend std::basic_istream<_CharT, _Traits>&
1438         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1439 		   xor_combine<_UniformRandomNumberGenerator11, __s11,
1440 		   _UniformRandomNumberGenerator21, __s21>& __x);
1441 
1442     private:
1443       void
1444       _M_initialize_max();
1445 
1446       result_type
1447       _M_initialize_max_aux(result_type, result_type, int);
1448 
1449       base1_type  _M_b1;
1450       base2_type  _M_b2;
1451       result_type _M_max;
1452     };
1453 
1454 
1455   /**
1456    * A standard interface to a platform-specific non-deterministic
1457    * random number generator (if any are available).
1458    */
1459   class random_device
1460   {
1461   public:
1462     // types
1463     typedef unsigned int result_type;
1464 
1465     // constructors, destructors and member functions
1466 
1467 #ifdef _GLIBCXX_USE_RANDOM_TR1
1468 
1469     explicit
1470     random_device(const std::string& __token = "/dev/urandom")
1471     {
1472       if ((__token != "/dev/urandom" && __token != "/dev/random")
1473 	  || !(_M_file = std::fopen(__token.c_str(), "rb")))
1474 	std::__throw_runtime_error(__N("random_device::"
1475 				       "random_device(const std::string&)"));
1476     }
1477 
1478     ~random_device()
1479     { std::fclose(_M_file); }
1480 
1481 #else
1482 
1483     explicit
1484     random_device(const std::string& __token = "mt19937")
1485     : _M_mt(_M_strtoul(__token)) { }
1486 
1487   private:
1488     static unsigned long
1489     _M_strtoul(const std::string& __str)
1490     {
1491       unsigned long __ret = 5489UL;
1492       if (__str != "mt19937")
1493 	{
1494 	  const char* __nptr = __str.c_str();
1495 	  char* __endptr;
1496 	  __ret = std::strtoul(__nptr, &__endptr, 0);
1497 	  if (*__nptr == '\0' || *__endptr != '\0')
1498 	    std::__throw_runtime_error(__N("random_device::_M_strtoul"
1499 					   "(const std::string&)"));
1500 	}
1501       return __ret;
1502     }
1503 
1504   public:
1505 
1506 #endif
1507 
1508     result_type
1509     min() const
1510     { return std::numeric_limits<result_type>::min(); }
1511 
1512     result_type
1513     max() const
1514     { return std::numeric_limits<result_type>::max(); }
1515 
1516     double
1517     entropy() const
1518     { return 0.0; }
1519 
1520     result_type
1521     operator()()
1522     {
1523 #ifdef _GLIBCXX_USE_RANDOM_TR1
1524       result_type __ret;
1525       std::fread(reinterpret_cast<void*>(&__ret), sizeof(result_type),
1526 		 1, _M_file);
1527       return __ret;
1528 #else
1529       return _M_mt();
1530 #endif
1531     }
1532 
1533   private:
1534     random_device(const random_device&);
1535     void operator=(const random_device&);
1536 
1537 #ifdef _GLIBCXX_USE_RANDOM_TR1
1538     FILE*        _M_file;
1539 #else
1540     mt19937      _M_mt;
1541 #endif
1542   };
1543 
1544   /* @} */ // group tr1_random_generators
1545 
1546   /**
1547    * @addtogroup tr1_random_distributions Random Number Distributions
1548    * @ingroup tr1_random
1549    * @{
1550    */
1551 
1552   /**
1553    * @addtogroup tr1_random_distributions_discrete Discrete Distributions
1554    * @ingroup tr1_random_distributions
1555    * @{
1556    */
1557 
1558   /**
1559    * @brief Uniform discrete distribution for random numbers.
1560    * A discrete random distribution on the range @f$[min, max]@f$ with equal
1561    * probability throughout the range.
1562    */
1563   template<typename _IntType = int>
1564     class uniform_int
1565     {
1566       __glibcxx_class_requires(_IntType, _IntegerConcept)
1567 
1568     public:
1569       /** The type of the parameters of the distribution. */
1570       typedef _IntType input_type;
1571       /** The type of the range of the distribution. */
1572       typedef _IntType result_type;
1573 
1574     public:
1575       /**
1576        * Constructs a uniform distribution object.
1577        */
1578       explicit
1579       uniform_int(_IntType __min = 0, _IntType __max = 9)
1580       : _M_min(__min), _M_max(__max)
1581       {
1582 	_GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
1583       }
1584 
1585       /**
1586        * Gets the inclusive lower bound of the distribution range.
1587        */
1588       result_type
1589       min() const
1590       { return _M_min; }
1591 
1592       /**
1593        * Gets the inclusive upper bound of the distribution range.
1594        */
1595       result_type
1596       max() const
1597       { return _M_max; }
1598 
1599       /**
1600        * Resets the distribution state.
1601        *
1602        * Does nothing for the uniform integer distribution.
1603        */
1604       void
1605       reset() { }
1606 
1607       /**
1608        * Gets a uniformly distributed random number in the range
1609        * @f$(min, max)@f$.
1610        */
1611       template<typename _UniformRandomNumberGenerator>
1612         result_type
1613         operator()(_UniformRandomNumberGenerator& __urng)
1614         {
1615 	  typedef typename _UniformRandomNumberGenerator::result_type
1616 	    _UResult_type;
1617 	  return _M_call(__urng, _M_min, _M_max,
1618 			 typename is_integral<_UResult_type>::type());
1619 	}
1620 
1621       /**
1622        * Gets a uniform random number in the range @f$[0, n)@f$.
1623        *
1624        * This function is aimed at use with std::random_shuffle.
1625        */
1626       template<typename _UniformRandomNumberGenerator>
1627         result_type
1628         operator()(_UniformRandomNumberGenerator& __urng, result_type __n)
1629         {
1630 	  typedef typename _UniformRandomNumberGenerator::result_type
1631 	    _UResult_type;
1632 	  return _M_call(__urng, 0, __n - 1,
1633 			 typename is_integral<_UResult_type>::type());
1634 	}
1635 
1636       /**
1637        * Inserts a %uniform_int random number distribution @p __x into the
1638        * output stream @p os.
1639        *
1640        * @param __os An output stream.
1641        * @param __x  A %uniform_int random number distribution.
1642        *
1643        * @returns The output stream with the state of @p __x inserted or in
1644        * an error state.
1645        */
1646       template<typename _IntType1, typename _CharT, typename _Traits>
1647         friend std::basic_ostream<_CharT, _Traits>&
1648         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1649 		   const uniform_int<_IntType1>& __x);
1650 
1651       /**
1652        * Extracts a %uniform_int random number distribution
1653        * @p __x from the input stream @p __is.
1654        *
1655        * @param __is An input stream.
1656        * @param __x  A %uniform_int random number generator engine.
1657        *
1658        * @returns The input stream with @p __x extracted or in an error state.
1659        */
1660       template<typename _IntType1, typename _CharT, typename _Traits>
1661         friend std::basic_istream<_CharT, _Traits>&
1662         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1663 		   uniform_int<_IntType1>& __x);
1664 
1665     private:
1666       template<typename _UniformRandomNumberGenerator>
1667         result_type
1668         _M_call(_UniformRandomNumberGenerator& __urng,
1669 		result_type __min, result_type __max, true_type);
1670 
1671       template<typename _UniformRandomNumberGenerator>
1672         result_type
1673         _M_call(_UniformRandomNumberGenerator& __urng,
1674 		result_type __min, result_type __max, false_type)
1675         {
1676 	  return result_type((__urng() - __urng.min())
1677 			     / (__urng.max() - __urng.min())
1678 			     * (__max - __min + 1)) + __min;
1679 	}
1680 
1681       _IntType _M_min;
1682       _IntType _M_max;
1683     };
1684 
1685 
1686   /**
1687    * @brief A Bernoulli random number distribution.
1688    *
1689    * Generates a sequence of true and false values with likelihood @f$ p @f$
1690    * that true will come up and @f$ (1 - p) @f$ that false will appear.
1691    */
1692   class bernoulli_distribution
1693   {
1694   public:
1695     typedef int  input_type;
1696     typedef bool result_type;
1697 
1698   public:
1699     /**
1700      * Constructs a Bernoulli distribution with likelihood @p p.
1701      *
1702      * @param __p  [IN]  The likelihood of a true result being returned.  Must
1703      * be in the interval @f$ [0, 1] @f$.
1704      */
1705     explicit
1706     bernoulli_distribution(double __p = 0.5)
1707     : _M_p(__p)
1708     {
1709       _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0));
1710     }
1711 
1712     /**
1713      * Gets the @p p parameter of the distribution.
1714      */
1715     double
1716     p() const
1717     { return _M_p; }
1718 
1719     /**
1720      * Resets the distribution state.
1721      *
1722      * Does nothing for a Bernoulli distribution.
1723      */
1724     void
1725     reset() { }
1726 
1727     /**
1728      * Gets the next value in the Bernoullian sequence.
1729      */
1730     template<class _UniformRandomNumberGenerator>
1731       result_type
1732       operator()(_UniformRandomNumberGenerator& __urng)
1733       {
1734 	if ((__urng() - __urng.min()) < _M_p * (__urng.max() - __urng.min()))
1735 	  return true;
1736 	return false;
1737       }
1738 
1739     /**
1740      * Inserts a %bernoulli_distribution random number distribution
1741      * @p __x into the output stream @p __os.
1742      *
1743      * @param __os An output stream.
1744      * @param __x  A %bernoulli_distribution random number distribution.
1745      *
1746      * @returns The output stream with the state of @p __x inserted or in
1747      * an error state.
1748      */
1749     template<typename _CharT, typename _Traits>
1750       friend std::basic_ostream<_CharT, _Traits>&
1751       operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1752 		 const bernoulli_distribution& __x);
1753 
1754     /**
1755      * Extracts a %bernoulli_distribution random number distribution
1756      * @p __x from the input stream @p __is.
1757      *
1758      * @param __is An input stream.
1759      * @param __x  A %bernoulli_distribution random number generator engine.
1760      *
1761      * @returns The input stream with @p __x extracted or in an error state.
1762      */
1763     template<typename _CharT, typename _Traits>
1764       friend std::basic_istream<_CharT, _Traits>&
1765       operator>>(std::basic_istream<_CharT, _Traits>& __is,
1766 		 bernoulli_distribution& __x)
1767       { return __is >> __x._M_p; }
1768 
1769   private:
1770     double _M_p;
1771   };
1772 
1773 
1774   /**
1775    * @brief A discrete geometric random number distribution.
1776    *
1777    * The formula for the geometric probability mass function is
1778    * @f$ p(i) = (1 - p)p^{i-1} @f$ where @f$ p @f$ is the parameter of the
1779    * distribution.
1780    */
1781   template<typename _IntType = int, typename _RealType = double>
1782     class geometric_distribution
1783     {
1784     public:
1785       // types
1786       typedef _RealType input_type;
1787       typedef _IntType  result_type;
1788 
1789       // constructors and member function
1790       explicit
1791       geometric_distribution(const _RealType& __p = _RealType(0.5))
1792       : _M_p(__p)
1793       {
1794 	_GLIBCXX_DEBUG_ASSERT((_M_p > 0.0) && (_M_p < 1.0));
1795 	_M_initialize();
1796       }
1797 
1798       /**
1799        * Gets the distribution parameter @p p.
1800        */
1801       _RealType
1802       p() const
1803       { return _M_p; }
1804 
1805       void
1806       reset() { }
1807 
1808       template<class _UniformRandomNumberGenerator>
1809         result_type
1810         operator()(_UniformRandomNumberGenerator& __urng);
1811 
1812       /**
1813        * Inserts a %geometric_distribution random number distribution
1814        * @p __x into the output stream @p __os.
1815        *
1816        * @param __os An output stream.
1817        * @param __x  A %geometric_distribution random number distribution.
1818        *
1819        * @returns The output stream with the state of @p __x inserted or in
1820        * an error state.
1821        */
1822       template<typename _IntType1, typename _RealType1,
1823 	       typename _CharT, typename _Traits>
1824         friend std::basic_ostream<_CharT, _Traits>&
1825         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1826 		   const geometric_distribution<_IntType1, _RealType1>& __x);
1827 
1828       /**
1829        * Extracts a %geometric_distribution random number distribution
1830        * @p __x from the input stream @p __is.
1831        *
1832        * @param __is An input stream.
1833        * @param __x  A %geometric_distribution random number generator engine.
1834        *
1835        * @returns The input stream with @p __x extracted or in an error state.
1836        */
1837       template<typename _CharT, typename _Traits>
1838         friend std::basic_istream<_CharT, _Traits>&
1839         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1840 		   geometric_distribution& __x)
1841         {
1842 	  __is >> __x._M_p;
1843 	  __x._M_initialize();
1844 	  return __is;
1845 	}
1846 
1847     private:
1848       void
1849       _M_initialize()
1850       { _M_log_p = std::log(_M_p); }
1851 
1852       _RealType _M_p;
1853       _RealType _M_log_p;
1854     };
1855 
1856 
1857   template<typename _RealType>
1858     class normal_distribution;
1859 
1860   /**
1861    * @brief A discrete Poisson random number distribution.
1862    *
1863    * The formula for the Poisson probability mass function is
1864    * @f$ p(i) = \frac{mean^i}{i!} e^{-mean} @f$ where @f$ mean @f$ is the
1865    * parameter of the distribution.
1866    */
1867   template<typename _IntType = int, typename _RealType = double>
1868     class poisson_distribution
1869     {
1870     public:
1871       // types
1872       typedef _RealType input_type;
1873       typedef _IntType  result_type;
1874 
1875       // constructors and member function
1876       explicit
1877       poisson_distribution(const _RealType& __mean = _RealType(1))
1878       : _M_mean(__mean), _M_nd()
1879       {
1880 	_GLIBCXX_DEBUG_ASSERT(_M_mean > 0.0);
1881 	_M_initialize();
1882       }
1883 
1884       /**
1885        * Gets the distribution parameter @p mean.
1886        */
1887       _RealType
1888       mean() const
1889       { return _M_mean; }
1890 
1891       void
1892       reset()
1893       { _M_nd.reset(); }
1894 
1895       template<class _UniformRandomNumberGenerator>
1896         result_type
1897         operator()(_UniformRandomNumberGenerator& __urng);
1898 
1899       /**
1900        * Inserts a %poisson_distribution random number distribution
1901        * @p __x into the output stream @p __os.
1902        *
1903        * @param __os An output stream.
1904        * @param __x  A %poisson_distribution random number distribution.
1905        *
1906        * @returns The output stream with the state of @p __x inserted or in
1907        * an error state.
1908        */
1909       template<typename _IntType1, typename _RealType1,
1910 	       typename _CharT, typename _Traits>
1911         friend std::basic_ostream<_CharT, _Traits>&
1912         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1913 		   const poisson_distribution<_IntType1, _RealType1>& __x);
1914 
1915       /**
1916        * Extracts a %poisson_distribution random number distribution
1917        * @p __x from the input stream @p __is.
1918        *
1919        * @param __is An input stream.
1920        * @param __x  A %poisson_distribution random number generator engine.
1921        *
1922        * @returns The input stream with @p __x extracted or in an error state.
1923        */
1924       template<typename _IntType1, typename _RealType1,
1925 	       typename _CharT, typename _Traits>
1926         friend std::basic_istream<_CharT, _Traits>&
1927         operator>>(std::basic_istream<_CharT, _Traits>& __is,
1928 		   poisson_distribution<_IntType1, _RealType1>& __x);
1929 
1930     private:
1931       void
1932       _M_initialize();
1933 
1934       // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
1935       normal_distribution<_RealType> _M_nd;
1936 
1937       _RealType _M_mean;
1938 
1939       // Hosts either log(mean) or the threshold of the simple method.
1940       _RealType _M_lm_thr;
1941 #if _GLIBCXX_USE_C99_MATH_TR1
1942       _RealType _M_lfm, _M_sm, _M_d, _M_scx, _M_1cx, _M_c2b, _M_cb;
1943 #endif
1944     };
1945 
1946 
1947   /**
1948    * @brief A discrete binomial random number distribution.
1949    *
1950    * The formula for the binomial probability mass function is
1951    * @f$ p(i) = \binom{n}{i} p^i (1 - p)^{t - i} @f$ where @f$ t @f$
1952    * and @f$ p @f$ are the parameters of the distribution.
1953    */
1954   template<typename _IntType = int, typename _RealType = double>
1955     class binomial_distribution
1956     {
1957     public:
1958       // types
1959       typedef _RealType input_type;
1960       typedef _IntType  result_type;
1961 
1962       // constructors and member function
1963       explicit
1964       binomial_distribution(_IntType __t = 1,
1965 			    const _RealType& __p = _RealType(0.5))
1966       : _M_t(__t), _M_p(__p), _M_nd()
1967       {
1968 	_GLIBCXX_DEBUG_ASSERT((_M_t >= 0) && (_M_p >= 0.0) && (_M_p <= 1.0));
1969 	_M_initialize();
1970       }
1971 
1972       /**
1973        * Gets the distribution @p t parameter.
1974        */
1975       _IntType
1976       t() const
1977       { return _M_t; }
1978 
1979       /**
1980        * Gets the distribution @p p parameter.
1981        */
1982       _RealType
1983       p() const
1984       { return _M_p; }
1985 
1986       void
1987       reset()
1988       { _M_nd.reset(); }
1989 
1990       template<class _UniformRandomNumberGenerator>
1991         result_type
1992         operator()(_UniformRandomNumberGenerator& __urng);
1993 
1994       /**
1995        * Inserts a %binomial_distribution random number distribution
1996        * @p __x into the output stream @p __os.
1997        *
1998        * @param __os An output stream.
1999        * @param __x  A %binomial_distribution random number distribution.
2000        *
2001        * @returns The output stream with the state of @p __x inserted or in
2002        * an error state.
2003        */
2004       template<typename _IntType1, typename _RealType1,
2005 	       typename _CharT, typename _Traits>
2006         friend std::basic_ostream<_CharT, _Traits>&
2007         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2008 		   const binomial_distribution<_IntType1, _RealType1>& __x);
2009 
2010       /**
2011        * Extracts a %binomial_distribution random number distribution
2012        * @p __x from the input stream @p __is.
2013        *
2014        * @param __is An input stream.
2015        * @param __x  A %binomial_distribution random number generator engine.
2016        *
2017        * @returns The input stream with @p __x extracted or in an error state.
2018        */
2019       template<typename _IntType1, typename _RealType1,
2020 	       typename _CharT, typename _Traits>
2021         friend std::basic_istream<_CharT, _Traits>&
2022         operator>>(std::basic_istream<_CharT, _Traits>& __is,
2023 		   binomial_distribution<_IntType1, _RealType1>& __x);
2024 
2025     private:
2026       void
2027       _M_initialize();
2028 
2029       template<class _UniformRandomNumberGenerator>
2030         result_type
2031         _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t);
2032 
2033       // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
2034       normal_distribution<_RealType> _M_nd;
2035 
2036       _RealType _M_q;
2037 #if _GLIBCXX_USE_C99_MATH_TR1
2038       _RealType _M_d1, _M_d2, _M_s1, _M_s2, _M_c,
2039 	        _M_a1, _M_a123, _M_s, _M_lf, _M_lp1p;
2040 #endif
2041       _RealType _M_p;
2042       _IntType  _M_t;
2043 
2044       bool      _M_easy;
2045     };
2046 
2047   /* @} */ // group tr1_random_distributions_discrete
2048 
2049   /**
2050    * @addtogroup tr1_random_distributions_continuous Continuous Distributions
2051    * @ingroup tr1_random_distributions
2052    * @{
2053    */
2054 
2055   /**
2056    * @brief Uniform continuous distribution for random numbers.
2057    *
2058    * A continuous random distribution on the range [min, max) with equal
2059    * probability throughout the range.  The URNG should be real-valued and
2060    * deliver number in the range [0, 1).
2061    */
2062   template<typename _RealType = double>
2063     class uniform_real
2064     {
2065     public:
2066       // types
2067       typedef _RealType input_type;
2068       typedef _RealType result_type;
2069 
2070     public:
2071       /**
2072        * Constructs a uniform_real object.
2073        *
2074        * @param __min [IN]  The lower bound of the distribution.
2075        * @param __max [IN]  The upper bound of the distribution.
2076        */
2077       explicit
2078       uniform_real(_RealType __min = _RealType(0),
2079 		   _RealType __max = _RealType(1))
2080       : _M_min(__min), _M_max(__max)
2081       {
2082 	_GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
2083       }
2084 
2085       result_type
2086       min() const
2087       { return _M_min; }
2088 
2089       result_type
2090       max() const
2091       { return _M_max; }
2092 
2093       void
2094       reset() { }
2095 
2096       template<class _UniformRandomNumberGenerator>
2097         result_type
2098         operator()(_UniformRandomNumberGenerator& __urng)
2099         { return (__urng() * (_M_max - _M_min)) + _M_min; }
2100 
2101       /**
2102        * Inserts a %uniform_real random number distribution @p __x into the
2103        * output stream @p __os.
2104        *
2105        * @param __os An output stream.
2106        * @param __x  A %uniform_real random number distribution.
2107        *
2108        * @returns The output stream with the state of @p __x inserted or in
2109        * an error state.
2110        */
2111       template<typename _RealType1, typename _CharT, typename _Traits>
2112         friend std::basic_ostream<_CharT, _Traits>&
2113         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2114 		   const uniform_real<_RealType1>& __x);
2115 
2116       /**
2117        * Extracts a %uniform_real random number distribution
2118        * @p __x from the input stream @p __is.
2119        *
2120        * @param __is An input stream.
2121        * @param __x  A %uniform_real random number generator engine.
2122        *
2123        * @returns The input stream with @p __x extracted or in an error state.
2124        */
2125       template<typename _RealType1, typename _CharT, typename _Traits>
2126         friend std::basic_istream<_CharT, _Traits>&
2127         operator>>(std::basic_istream<_CharT, _Traits>& __is,
2128 		   uniform_real<_RealType1>& __x);
2129 
2130     private:
2131       _RealType _M_min;
2132       _RealType _M_max;
2133     };
2134 
2135 
2136   /**
2137    * @brief An exponential continuous distribution for random numbers.
2138    *
2139    * The formula for the exponential probability mass function is
2140    * @f$ p(x) = \lambda e^{-\lambda x} @f$.
2141    *
2142    * <table border=1 cellpadding=10 cellspacing=0>
2143    * <caption align=top>Distribution Statistics</caption>
2144    * <tr><td>Mean</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
2145    * <tr><td>Median</td><td>@f$ \frac{\ln 2}{\lambda} @f$</td></tr>
2146    * <tr><td>Mode</td><td>@f$ zero @f$</td></tr>
2147    * <tr><td>Range</td><td>@f$[0, \infty]@f$</td></tr>
2148    * <tr><td>Standard Deviation</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
2149    * </table>
2150    */
2151   template<typename _RealType = double>
2152     class exponential_distribution
2153     {
2154     public:
2155       // types
2156       typedef _RealType input_type;
2157       typedef _RealType result_type;
2158 
2159     public:
2160       /**
2161        * Constructs an exponential distribution with inverse scale parameter
2162        * @f$ \lambda @f$.
2163        */
2164       explicit
2165       exponential_distribution(const result_type& __lambda = result_type(1))
2166       : _M_lambda(__lambda)
2167       {
2168 	_GLIBCXX_DEBUG_ASSERT(_M_lambda > 0);
2169       }
2170 
2171       /**
2172        * Gets the inverse scale parameter of the distribution.
2173        */
2174       _RealType
2175       lambda() const
2176       { return _M_lambda; }
2177 
2178       /**
2179        * Resets the distribution.
2180        *
2181        * Has no effect on exponential distributions.
2182        */
2183       void
2184       reset() { }
2185 
2186       template<class _UniformRandomNumberGenerator>
2187         result_type
2188         operator()(_UniformRandomNumberGenerator& __urng)
2189         { return -std::log(__urng()) / _M_lambda; }
2190 
2191       /**
2192        * Inserts a %exponential_distribution random number distribution
2193        * @p __x into the output stream @p __os.
2194        *
2195        * @param __os An output stream.
2196        * @param __x  A %exponential_distribution random number distribution.
2197        *
2198        * @returns The output stream with the state of @p __x inserted or in
2199        * an error state.
2200        */
2201       template<typename _RealType1, typename _CharT, typename _Traits>
2202         friend std::basic_ostream<_CharT, _Traits>&
2203         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2204 		   const exponential_distribution<_RealType1>& __x);
2205 
2206       /**
2207        * Extracts a %exponential_distribution random number distribution
2208        * @p __x from the input stream @p __is.
2209        *
2210        * @param __is An input stream.
2211        * @param __x A %exponential_distribution random number
2212        *            generator engine.
2213        *
2214        * @returns The input stream with @p __x extracted or in an error state.
2215        */
2216       template<typename _CharT, typename _Traits>
2217         friend std::basic_istream<_CharT, _Traits>&
2218         operator>>(std::basic_istream<_CharT, _Traits>& __is,
2219 		   exponential_distribution& __x)
2220         { return __is >> __x._M_lambda; }
2221 
2222     private:
2223       result_type _M_lambda;
2224     };
2225 
2226 
2227   /**
2228    * @brief A normal continuous distribution for random numbers.
2229    *
2230    * The formula for the normal probability mass function is
2231    * @f$ p(x) = \frac{1}{\sigma \sqrt{2 \pi}}
2232    *            e^{- \frac{{x - mean}^ {2}}{2 \sigma ^ {2}} } @f$.
2233    */
2234   template<typename _RealType = double>
2235     class normal_distribution
2236     {
2237     public:
2238       // types
2239       typedef _RealType input_type;
2240       typedef _RealType result_type;
2241 
2242     public:
2243       /**
2244        * Constructs a normal distribution with parameters @f$ mean @f$ and
2245        * @f$ \sigma @f$.
2246        */
2247       explicit
2248       normal_distribution(const result_type& __mean = result_type(0),
2249 			  const result_type& __sigma = result_type(1))
2250       : _M_mean(__mean), _M_sigma(__sigma), _M_saved_available(false)
2251       {
2252 	_GLIBCXX_DEBUG_ASSERT(_M_sigma > 0);
2253       }
2254 
2255       /**
2256        * Gets the mean of the distribution.
2257        */
2258       _RealType
2259       mean() const
2260       { return _M_mean; }
2261 
2262       /**
2263        * Gets the @f$ \sigma @f$ of the distribution.
2264        */
2265       _RealType
2266       sigma() const
2267       { return _M_sigma; }
2268 
2269       /**
2270        * Resets the distribution.
2271        */
2272       void
2273       reset()
2274       { _M_saved_available = false; }
2275 
2276       template<class _UniformRandomNumberGenerator>
2277         result_type
2278         operator()(_UniformRandomNumberGenerator& __urng);
2279 
2280       /**
2281        * Inserts a %normal_distribution random number distribution
2282        * @p __x into the output stream @p __os.
2283        *
2284        * @param __os An output stream.
2285        * @param __x  A %normal_distribution random number distribution.
2286        *
2287        * @returns The output stream with the state of @p __x inserted or in
2288        * an error state.
2289        */
2290       template<typename _RealType1, typename _CharT, typename _Traits>
2291         friend std::basic_ostream<_CharT, _Traits>&
2292         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2293 		   const normal_distribution<_RealType1>& __x);
2294 
2295       /**
2296        * Extracts a %normal_distribution random number distribution
2297        * @p __x from the input stream @p __is.
2298        *
2299        * @param __is An input stream.
2300        * @param __x  A %normal_distribution random number generator engine.
2301        *
2302        * @returns The input stream with @p __x extracted or in an error state.
2303        */
2304       template<typename _RealType1, typename _CharT, typename _Traits>
2305         friend std::basic_istream<_CharT, _Traits>&
2306         operator>>(std::basic_istream<_CharT, _Traits>& __is,
2307 		   normal_distribution<_RealType1>& __x);
2308 
2309     private:
2310       result_type _M_mean;
2311       result_type _M_sigma;
2312       result_type _M_saved;
2313       bool        _M_saved_available;
2314     };
2315 
2316 
2317   /**
2318    * @brief A gamma continuous distribution for random numbers.
2319    *
2320    * The formula for the gamma probability mass function is
2321    * @f$ p(x) = \frac{1}{\Gamma(\alpha)} x^{\alpha - 1} e^{-x} @f$.
2322    */
2323   template<typename _RealType = double>
2324     class gamma_distribution
2325     {
2326     public:
2327       // types
2328       typedef _RealType input_type;
2329       typedef _RealType result_type;
2330 
2331     public:
2332       /**
2333        * Constructs a gamma distribution with parameters @f$ \alpha @f$.
2334        */
2335       explicit
2336       gamma_distribution(const result_type& __alpha_val = result_type(1))
2337       : _M_alpha(__alpha_val)
2338       {
2339 	_GLIBCXX_DEBUG_ASSERT(_M_alpha > 0);
2340 	_M_initialize();
2341       }
2342 
2343       /**
2344        * Gets the @f$ \alpha @f$ of the distribution.
2345        */
2346       _RealType
2347       alpha() const
2348       { return _M_alpha; }
2349 
2350       /**
2351        * Resets the distribution.
2352        */
2353       void
2354       reset() { }
2355 
2356       template<class _UniformRandomNumberGenerator>
2357         result_type
2358         operator()(_UniformRandomNumberGenerator& __urng);
2359 
2360       /**
2361        * Inserts a %gamma_distribution random number distribution
2362        * @p __x into the output stream @p __os.
2363        *
2364        * @param __os An output stream.
2365        * @param __x  A %gamma_distribution random number distribution.
2366        *
2367        * @returns The output stream with the state of @p __x inserted or in
2368        * an error state.
2369        */
2370       template<typename _RealType1, typename _CharT, typename _Traits>
2371         friend std::basic_ostream<_CharT, _Traits>&
2372         operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2373 		   const gamma_distribution<_RealType1>& __x);
2374 
2375       /**
2376        * Extracts a %gamma_distribution random number distribution
2377        * @p __x from the input stream @p __is.
2378        *
2379        * @param __is An input stream.
2380        * @param __x  A %gamma_distribution random number generator engine.
2381        *
2382        * @returns The input stream with @p __x extracted or in an error state.
2383        */
2384       template<typename _CharT, typename _Traits>
2385         friend std::basic_istream<_CharT, _Traits>&
2386         operator>>(std::basic_istream<_CharT, _Traits>& __is,
2387 		   gamma_distribution& __x)
2388         {
2389 	  __is >> __x._M_alpha;
2390 	  __x._M_initialize();
2391 	  return __is;
2392 	}
2393 
2394     private:
2395       void
2396       _M_initialize();
2397 
2398       result_type _M_alpha;
2399 
2400       // Hosts either lambda of GB or d of modified Vaduva's.
2401       result_type _M_l_d;
2402     };
2403 
2404   /* @} */ // group tr1_random_distributions_continuous
2405   /* @} */ // group tr1_random_distributions
2406   /* @} */ // group tr1_random
2407 }
2408 }
2409 
2410 #endif // _GLIBCXX_TR1_RANDOM_H
2411