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[1166]1// random number generation -*- C++ -*-
2
3// Copyright (C) 2009-2021 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 * Do not attempt to use it directly. @headername{tr1/random}
29 */
30
31#ifndef _GLIBCXX_TR1_RANDOM_H
32#define _GLIBCXX_TR1_RANDOM_H 1
33
34#pragma GCC system_header
35
36namespace std _GLIBCXX_VISIBILITY(default)
37{
38_GLIBCXX_BEGIN_NAMESPACE_VERSION
39
40namespace tr1
41{
42 // [5.1] Random number generation
43
44 /**
45 * @addtogroup tr1_random Random Number Generation
46 * A facility for generating random numbers on selected distributions.
47 * @{
48 */
49
50 /*
51 * Implementation-space details.
52 */
53 namespace __detail
54 {
55 template<typename _UIntType, int __w,
56 bool = __w < std::numeric_limits<_UIntType>::digits>
57 struct _Shift
58 { static const _UIntType __value = 0; };
59
60 template<typename _UIntType, int __w>
61 struct _Shift<_UIntType, __w, true>
62 { static const _UIntType __value = _UIntType(1) << __w; };
63
64 template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool>
65 struct _Mod;
66
67 // Dispatch based on modulus value to prevent divide-by-zero compile-time
68 // errors when m == 0.
69 template<typename _Tp, _Tp __a, _Tp __c, _Tp __m>
70 inline _Tp
71 __mod(_Tp __x)
72 { return _Mod<_Tp, __a, __c, __m, __m == 0>::__calc(__x); }
73
74 typedef __gnu_cxx::__conditional_type<(sizeof(unsigned) == 4),
75 unsigned, unsigned long>::__type _UInt32Type;
76
77 /*
78 * An adaptor class for converting the output of any Generator into
79 * the input for a specific Distribution.
80 */
81 template<typename _Engine, typename _Distribution>
82 struct _Adaptor
83 {
84 typedef typename remove_reference<_Engine>::type _BEngine;
85 typedef typename _BEngine::result_type _Engine_result_type;
86 typedef typename _Distribution::input_type result_type;
87
88 public:
89 _Adaptor(const _Engine& __g)
90 : _M_g(__g) { }
91
92 result_type
93 min() const
94 {
95 result_type __return_value;
96 if (is_integral<_Engine_result_type>::value
97 && is_integral<result_type>::value)
98 __return_value = _M_g.min();
99 else
100 __return_value = result_type(0);
101 return __return_value;
102 }
103
104 result_type
105 max() const
106 {
107 result_type __return_value;
108 if (is_integral<_Engine_result_type>::value
109 && is_integral<result_type>::value)
110 __return_value = _M_g.max();
111 else if (!is_integral<result_type>::value)
112 __return_value = result_type(1);
113 else
114 __return_value = std::numeric_limits<result_type>::max() - 1;
115 return __return_value;
116 }
117
118 /*
119 * Converts a value generated by the adapted random number generator
120 * into a value in the input domain for the dependent random number
121 * distribution.
122 *
123 * Because the type traits are compile time constants only the
124 * appropriate clause of the if statements will actually be emitted
125 * by the compiler.
126 */
127 result_type
128 operator()()
129 {
130 result_type __return_value;
131 if (is_integral<_Engine_result_type>::value
132 && is_integral<result_type>::value)
133 __return_value = _M_g();
134 else if (!is_integral<_Engine_result_type>::value
135 && !is_integral<result_type>::value)
136 __return_value = result_type(_M_g() - _M_g.min())
137 / result_type(_M_g.max() - _M_g.min());
138 else if (is_integral<_Engine_result_type>::value
139 && !is_integral<result_type>::value)
140 __return_value = result_type(_M_g() - _M_g.min())
141 / result_type(_M_g.max() - _M_g.min() + result_type(1));
142 else
143 __return_value = (((_M_g() - _M_g.min())
144 / (_M_g.max() - _M_g.min()))
145 * std::numeric_limits<result_type>::max());
146 return __return_value;
147 }
148
149 private:
150 _Engine _M_g;
151 };
152
153 // Specialization for _Engine*.
154 template<typename _Engine, typename _Distribution>
155 struct _Adaptor<_Engine*, _Distribution>
156 {
157 typedef typename _Engine::result_type _Engine_result_type;
158 typedef typename _Distribution::input_type result_type;
159
160 public:
161 _Adaptor(_Engine* __g)
162 : _M_g(__g) { }
163
164 result_type
165 min() const
166 {
167 result_type __return_value;
168 if (is_integral<_Engine_result_type>::value
169 && is_integral<result_type>::value)
170 __return_value = _M_g->min();
171 else
172 __return_value = result_type(0);
173 return __return_value;
174 }
175
176 result_type
177 max() const
178 {
179 result_type __return_value;
180 if (is_integral<_Engine_result_type>::value
181 && is_integral<result_type>::value)
182 __return_value = _M_g->max();
183 else if (!is_integral<result_type>::value)
184 __return_value = result_type(1);
185 else
186 __return_value = std::numeric_limits<result_type>::max() - 1;
187 return __return_value;
188 }
189
190 result_type
191 operator()()
192 {
193 result_type __return_value;
194 if (is_integral<_Engine_result_type>::value
195 && is_integral<result_type>::value)
196 __return_value = (*_M_g)();
197 else if (!is_integral<_Engine_result_type>::value
198 && !is_integral<result_type>::value)
199 __return_value = result_type((*_M_g)() - _M_g->min())
200 / result_type(_M_g->max() - _M_g->min());
201 else if (is_integral<_Engine_result_type>::value
202 && !is_integral<result_type>::value)
203 __return_value = result_type((*_M_g)() - _M_g->min())
204 / result_type(_M_g->max() - _M_g->min() + result_type(1));
205 else
206 __return_value = ((((*_M_g)() - _M_g->min())
207 / (_M_g->max() - _M_g->min()))
208 * std::numeric_limits<result_type>::max());
209 return __return_value;
210 }
211
212 private:
213 _Engine* _M_g;
214 };
215 } // namespace __detail
216
217 /**
218 * Produces random numbers on a given distribution function using a
219 * non-uniform random number generation engine.
220 *
221 * @todo the engine_value_type needs to be studied more carefully.
222 */
223 template<typename _Engine, typename _Dist>
224 class variate_generator
225 {
226 // Concept requirements.
227 __glibcxx_class_requires(_Engine, _CopyConstructibleConcept)
228 // __glibcxx_class_requires(_Engine, _EngineConcept)
229 // __glibcxx_class_requires(_Dist, _EngineConcept)
230
231 public:
232 typedef _Engine engine_type;
233 typedef __detail::_Adaptor<_Engine, _Dist> engine_value_type;
234 typedef _Dist distribution_type;
235 typedef typename _Dist::result_type result_type;
236
237 // tr1:5.1.1 table 5.1 requirement
238 typedef typename __gnu_cxx::__enable_if<
239 is_arithmetic<result_type>::value, result_type>::__type _IsValidType;
240
241 /**
242 * Constructs a variate generator with the uniform random number
243 * generator @p __eng for the random distribution @p __dist.
244 *
245 * @throws Any exceptions which may thrown by the copy constructors of
246 * the @p _Engine or @p _Dist objects.
247 */
248 variate_generator(engine_type __eng, distribution_type __dist)
249 : _M_engine(__eng), _M_dist(__dist) { }
250
251 /**
252 * Gets the next generated value on the distribution.
253 */
254 result_type
255 operator()()
256 { return _M_dist(_M_engine); }
257
258 /**
259 * WTF?
260 */
261 template<typename _Tp>
262 result_type
263 operator()(_Tp __value)
264 { return _M_dist(_M_engine, __value); }
265
266 /**
267 * Gets a reference to the underlying uniform random number generator
268 * object.
269 */
270 engine_value_type&
271 engine()
272 { return _M_engine; }
273
274 /**
275 * Gets a const reference to the underlying uniform random number
276 * generator object.
277 */
278 const engine_value_type&
279 engine() const
280 { return _M_engine; }
281
282 /**
283 * Gets a reference to the underlying random distribution.
284 */
285 distribution_type&
286 distribution()
287 { return _M_dist; }
288
289 /**
290 * Gets a const reference to the underlying random distribution.
291 */
292 const distribution_type&
293 distribution() const
294 { return _M_dist; }
295
296 /**
297 * Gets the closed lower bound of the distribution interval.
298 */
299 result_type
300 min() const
301 { return this->distribution().min(); }
302
303 /**
304 * Gets the closed upper bound of the distribution interval.
305 */
306 result_type
307 max() const
308 { return this->distribution().max(); }
309
310 private:
311 engine_value_type _M_engine;
312 distribution_type _M_dist;
313 };
314
315
316 /**
317 * @addtogroup tr1_random_generators Random Number Generators
318 * @ingroup tr1_random
319 *
320 * These classes define objects which provide random or pseudorandom
321 * numbers, either from a discrete or a continuous interval. The
322 * random number generator supplied as a part of this library are
323 * all uniform random number generators which provide a sequence of
324 * random number uniformly distributed over their range.
325 *
326 * A number generator is a function object with an operator() that
327 * takes zero arguments and returns a number.
328 *
329 * A compliant random number generator must satisfy the following
330 * requirements. <table border=1 cellpadding=10 cellspacing=0>
331 * <caption align=top>Random Number Generator Requirements</caption>
332 * <tr><td>To be documented.</td></tr> </table>
333 *
334 * @{
335 */
336
337 /**
338 * @brief A model of a linear congruential random number generator.
339 *
340 * A random number generator that produces pseudorandom numbers using the
341 * linear function @f$x_{i+1}\leftarrow(ax_{i} + c) \bmod m @f$.
342 *
343 * The template parameter @p _UIntType must be an unsigned integral type
344 * large enough to store values up to (__m-1). If the template parameter
345 * @p __m is 0, the modulus @p __m used is
346 * std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template
347 * parameters @p __a and @p __c must be less than @p __m.
348 *
349 * The size of the state is @f$ 1 @f$.
350 */
351 template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
352 class linear_congruential
353 {
354 __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
355 // __glibcpp_class_requires(__a < __m && __c < __m)
356
357 public:
358 /** The type of the generated random value. */
359 typedef _UIntType result_type;
360
361 /** The multiplier. */
362 static const _UIntType multiplier = __a;
363 /** An increment. */
364 static const _UIntType increment = __c;
365 /** The modulus. */
366 static const _UIntType modulus = __m;
367
368 /**
369 * Constructs a %linear_congruential random number generator engine with
370 * seed @p __s. The default seed value is 1.
371 *
372 * @param __s The initial seed value.
373 */
374 explicit
375 linear_congruential(unsigned long __x0 = 1)
376 { this->seed(__x0); }
377
378 /**
379 * Constructs a %linear_congruential random number generator engine
380 * seeded from the generator function @p __g.
381 *
382 * @param __g The seed generator function.
383 */
384 template<class _Gen>
385 linear_congruential(_Gen& __g)
386 { this->seed(__g); }
387
388 /**
389 * Reseeds the %linear_congruential random number generator engine
390 * sequence to the seed @g __s.
391 *
392 * @param __s The new seed.
393 */
394 void
395 seed(unsigned long __s = 1);
396
397 /**
398 * Reseeds the %linear_congruential random number generator engine
399 * sequence using values from the generator function @p __g.
400 *
401 * @param __g the seed generator function.
402 */
403 template<class _Gen>
404 void
405 seed(_Gen& __g)
406 { seed(__g, typename is_fundamental<_Gen>::type()); }
407
408 /**
409 * Gets the smallest possible value in the output range.
410 *
411 * The minimum depends on the @p __c parameter: if it is zero, the
412 * minimum generated must be > 0, otherwise 0 is allowed.
413 */
414 result_type
415 min() const
416 { return (__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0) ? 1 : 0; }
417
418 /**
419 * Gets the largest possible value in the output range.
420 */
421 result_type
422 max() const
423 { return __m - 1; }
424
425 /**
426 * Gets the next random number in the sequence.
427 */
428 result_type
429 operator()();
430
431 /**
432 * Compares two linear congruential random number generator
433 * objects of the same type for equality.
434 *
435 * @param __lhs A linear congruential random number generator object.
436 * @param __rhs Another linear congruential random number generator obj.
437 *
438 * @returns true if the two objects are equal, false otherwise.
439 */
440 friend bool
441 operator==(const linear_congruential& __lhs,
442 const linear_congruential& __rhs)
443 { return __lhs._M_x == __rhs._M_x; }
444
445 /**
446 * Compares two linear congruential random number generator
447 * objects of the same type for inequality.
448 *
449 * @param __lhs A linear congruential random number generator object.
450 * @param __rhs Another linear congruential random number generator obj.
451 *
452 * @returns true if the two objects are not equal, false otherwise.
453 */
454 friend bool
455 operator!=(const linear_congruential& __lhs,
456 const linear_congruential& __rhs)
457 { return !(__lhs == __rhs); }
458
459 /**
460 * Writes the textual representation of the state x(i) of x to @p __os.
461 *
462 * @param __os The output stream.
463 * @param __lcr A % linear_congruential random number generator.
464 * @returns __os.
465 */
466 template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
467 _UIntType1 __m1,
468 typename _CharT, typename _Traits>
469 friend std::basic_ostream<_CharT, _Traits>&
470 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
471 const linear_congruential<_UIntType1, __a1, __c1,
472 __m1>& __lcr);
473
474 /**
475 * Sets the state of the engine by reading its textual
476 * representation from @p __is.
477 *
478 * The textual representation must have been previously written using an
479 * output stream whose imbued locale and whose type's template
480 * specialization arguments _CharT and _Traits were the same as those of
481 * @p __is.
482 *
483 * @param __is The input stream.
484 * @param __lcr A % linear_congruential random number generator.
485 * @returns __is.
486 */
487 template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
488 _UIntType1 __m1,
489 typename _CharT, typename _Traits>
490 friend std::basic_istream<_CharT, _Traits>&
491 operator>>(std::basic_istream<_CharT, _Traits>& __is,
492 linear_congruential<_UIntType1, __a1, __c1, __m1>& __lcr);
493
494 private:
495 template<class _Gen>
496 void
497 seed(_Gen& __g, true_type)
498 { return seed(static_cast<unsigned long>(__g)); }
499
500 template<class _Gen>
501 void
502 seed(_Gen& __g, false_type);
503
504 _UIntType _M_x;
505 };
506
507 /**
508 * The classic Minimum Standard rand0 of Lewis, Goodman, and Miller.
509 */
510 typedef linear_congruential<unsigned long, 16807, 0, 2147483647> minstd_rand0;
511
512 /**
513 * An alternative LCR (Lehmer Generator function) .
514 */
515 typedef linear_congruential<unsigned long, 48271, 0, 2147483647> minstd_rand;
516
517
518 /**
519 * A generalized feedback shift register discrete random number generator.
520 *
521 * This algorithm avoids multiplication and division and is designed to be
522 * friendly to a pipelined architecture. If the parameters are chosen
523 * correctly, this generator will produce numbers with a very long period and
524 * fairly good apparent entropy, although still not cryptographically strong.
525 *
526 * The best way to use this generator is with the predefined mt19937 class.
527 *
528 * This algorithm was originally invented by Makoto Matsumoto and
529 * Takuji Nishimura.
530 *
531 * @var word_size The number of bits in each element of the state vector.
532 * @var state_size The degree of recursion.
533 * @var shift_size The period parameter.
534 * @var mask_bits The separation point bit index.
535 * @var parameter_a The last row of the twist matrix.
536 * @var output_u The first right-shift tempering matrix parameter.
537 * @var output_s The first left-shift tempering matrix parameter.
538 * @var output_b The first left-shift tempering matrix mask.
539 * @var output_t The second left-shift tempering matrix parameter.
540 * @var output_c The second left-shift tempering matrix mask.
541 * @var output_l The second right-shift tempering matrix parameter.
542 */
543 template<class _UIntType, int __w, int __n, int __m, int __r,
544 _UIntType __a, int __u, int __s, _UIntType __b, int __t,
545 _UIntType __c, int __l>
546 class mersenne_twister
547 {
548 __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
549
550 public:
551 // types
552 typedef _UIntType result_type;
553
554 // parameter values
555 static const int word_size = __w;
556 static const int state_size = __n;
557 static const int shift_size = __m;
558 static const int mask_bits = __r;
559 static const _UIntType parameter_a = __a;
560 static const int output_u = __u;
561 static const int output_s = __s;
562 static const _UIntType output_b = __b;
563 static const int output_t = __t;
564 static const _UIntType output_c = __c;
565 static const int output_l = __l;
566
567 // constructors and member function
568 mersenne_twister()
569 { seed(); }
570
571 explicit
572 mersenne_twister(unsigned long __value)
573 { seed(__value); }
574
575 template<class _Gen>
576 mersenne_twister(_Gen& __g)
577 { seed(__g); }
578
579 void
580 seed()
581 { seed(5489UL); }
582
583 void
584 seed(unsigned long __value);
585
586 template<class _Gen>
587 void
588 seed(_Gen& __g)
589 { seed(__g, typename is_fundamental<_Gen>::type()); }
590
591 result_type
592 min() const
593 { return 0; }
594
595 result_type
596 max() const
597 { return __detail::_Shift<_UIntType, __w>::__value - 1; }
598
599 result_type
600 operator()();
601
602 /**
603 * Compares two % mersenne_twister random number generator objects of
604 * the same type for equality.
605 *
606 * @param __lhs A % mersenne_twister random number generator object.
607 * @param __rhs Another % mersenne_twister random number generator
608 * object.
609 *
610 * @returns true if the two objects are equal, false otherwise.
611 */
612 friend bool
613 operator==(const mersenne_twister& __lhs,
614 const mersenne_twister& __rhs)
615 { return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); }
616
617 /**
618 * Compares two % mersenne_twister random number generator objects of
619 * the same type for inequality.
620 *
621 * @param __lhs A % mersenne_twister random number generator object.
622 * @param __rhs Another % mersenne_twister random number generator
623 * object.
624 *
625 * @returns true if the two objects are not equal, false otherwise.
626 */
627 friend bool
628 operator!=(const mersenne_twister& __lhs,
629 const mersenne_twister& __rhs)
630 { return !(__lhs == __rhs); }
631
632 /**
633 * Inserts the current state of a % mersenne_twister random number
634 * generator engine @p __x into the output stream @p __os.
635 *
636 * @param __os An output stream.
637 * @param __x A % mersenne_twister random number generator engine.
638 *
639 * @returns The output stream with the state of @p __x inserted or in
640 * an error state.
641 */
642 template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
643 _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
644 _UIntType1 __c1, int __l1,
645 typename _CharT, typename _Traits>
646 friend std::basic_ostream<_CharT, _Traits>&
647 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
648 const mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
649 __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
650
651 /**
652 * Extracts the current state of a % mersenne_twister random number
653 * generator engine @p __x from the input stream @p __is.
654 *
655 * @param __is An input stream.
656 * @param __x A % mersenne_twister random number generator engine.
657 *
658 * @returns The input stream with the state of @p __x extracted or in
659 * an error state.
660 */
661 template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
662 _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
663 _UIntType1 __c1, int __l1,
664 typename _CharT, typename _Traits>
665 friend std::basic_istream<_CharT, _Traits>&
666 operator>>(std::basic_istream<_CharT, _Traits>& __is,
667 mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
668 __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
669
670 private:
671 template<class _Gen>
672 void
673 seed(_Gen& __g, true_type)
674 { return seed(static_cast<unsigned long>(__g)); }
675
676 template<class _Gen>
677 void
678 seed(_Gen& __g, false_type);
679
680 _UIntType _M_x[state_size];
681 int _M_p;
682 };
683
684 /**
685 * The classic Mersenne Twister.
686 *
687 * Reference:
688 * M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-Dimensionally
689 * Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions
690 * on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
691 */
692 typedef mersenne_twister<
693 unsigned long, 32, 624, 397, 31,
694 0x9908b0dful, 11, 7,
695 0x9d2c5680ul, 15,
696 0xefc60000ul, 18
697 > mt19937;
698
699
700 /**
701 * @brief The Marsaglia-Zaman generator.
702 *
703 * This is a model of a Generalized Fibonacci discrete random number
704 * generator, sometimes referred to as the SWC generator.
705 *
706 * A discrete random number generator that produces pseudorandom
707 * numbers using @f$x_{i}\leftarrow(x_{i - s} - x_{i - r} -
708 * carry_{i-1}) \bmod m @f$.
709 *
710 * The size of the state is @f$ r @f$
711 * and the maximum period of the generator is @f$ m^r - m^s -1 @f$.
712 *
713 * N1688[4.13] says <em>the template parameter _IntType shall denote
714 * an integral type large enough to store values up to m</em>.
715 *
716 * @var _M_x The state of the generator. This is a ring buffer.
717 * @var _M_carry The carry.
718 * @var _M_p Current index of x(i - r).
719 */
720 template<typename _IntType, _IntType __m, int __s, int __r>
721 class subtract_with_carry
722 {
723 __glibcxx_class_requires(_IntType, _IntegerConcept)
724
725 public:
726 /** The type of the generated random value. */
727 typedef _IntType result_type;
728
729 // parameter values
730 static const _IntType modulus = __m;
731 static const int long_lag = __r;
732 static const int short_lag = __s;
733
734 /**
735 * Constructs a default-initialized % subtract_with_carry random number
736 * generator.
737 */
738 subtract_with_carry()
739 { this->seed(); }
740
741 /**
742 * Constructs an explicitly seeded % subtract_with_carry random number
743 * generator.
744 */
745 explicit
746 subtract_with_carry(unsigned long __value)
747 { this->seed(__value); }
748
749 /**
750 * Constructs a %subtract_with_carry random number generator engine
751 * seeded from the generator function @p __g.
752 *
753 * @param __g The seed generator function.
754 */
755 template<class _Gen>
756 subtract_with_carry(_Gen& __g)
757 { this->seed(__g); }
758
759 /**
760 * Seeds the initial state @f$ x_0 @f$ of the random number generator.
761 *
762 * N1688[4.19] modifies this as follows. If @p __value == 0,
763 * sets value to 19780503. In any case, with a linear
764 * congruential generator lcg(i) having parameters @f$ m_{lcg} =
765 * 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value
766 * @f$, sets @f$ x_{-r} \dots x_{-1} @f$ to @f$ lcg(1) \bmod m
767 * \dots lcg(r) \bmod m @f$ respectively. If @f$ x_{-1} = 0 @f$
768 * set carry to 1, otherwise sets carry to 0.
769 */
770 void
771 seed(unsigned long __value = 19780503);
772
773 /**
774 * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry
775 * random number generator.
776 */
777 template<class _Gen>
778 void
779 seed(_Gen& __g)
780 { seed(__g, typename is_fundamental<_Gen>::type()); }
781
782 /**
783 * Gets the inclusive minimum value of the range of random integers
784 * returned by this generator.
785 */
786 result_type
787 min() const
788 { return 0; }
789
790 /**
791 * Gets the inclusive maximum value of the range of random integers
792 * returned by this generator.
793 */
794 result_type
795 max() const
796 { return this->modulus - 1; }
797
798 /**
799 * Gets the next random number in the sequence.
800 */
801 result_type
802 operator()();
803
804 /**
805 * Compares two % subtract_with_carry random number generator objects of
806 * the same type for equality.
807 *
808 * @param __lhs A % subtract_with_carry random number generator object.
809 * @param __rhs Another % subtract_with_carry random number generator
810 * object.
811 *
812 * @returns true if the two objects are equal, false otherwise.
813 */
814 friend bool
815 operator==(const subtract_with_carry& __lhs,
816 const subtract_with_carry& __rhs)
817 { return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); }
818
819 /**
820 * Compares two % subtract_with_carry random number generator objects of
821 * the same type for inequality.
822 *
823 * @param __lhs A % subtract_with_carry random number generator object.
824 * @param __rhs Another % subtract_with_carry random number generator
825 * object.
826 *
827 * @returns true if the two objects are not equal, false otherwise.
828 */
829 friend bool
830 operator!=(const subtract_with_carry& __lhs,
831 const subtract_with_carry& __rhs)
832 { return !(__lhs == __rhs); }
833
834 /**
835 * Inserts the current state of a % subtract_with_carry random number
836 * generator engine @p __x into the output stream @p __os.
837 *
838 * @param __os An output stream.
839 * @param __x A % subtract_with_carry random number generator engine.
840 *
841 * @returns The output stream with the state of @p __x inserted or in
842 * an error state.
843 */
844 template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
845 typename _CharT, typename _Traits>
846 friend std::basic_ostream<_CharT, _Traits>&
847 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
848 const subtract_with_carry<_IntType1, __m1, __s1,
849 __r1>& __x);
850
851 /**
852 * Extracts the current state of a % subtract_with_carry random number
853 * generator engine @p __x from the input stream @p __is.
854 *
855 * @param __is An input stream.
856 * @param __x A % subtract_with_carry random number generator engine.
857 *
858 * @returns The input stream with the state of @p __x extracted or in
859 * an error state.
860 */
861 template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
862 typename _CharT, typename _Traits>
863 friend std::basic_istream<_CharT, _Traits>&
864 operator>>(std::basic_istream<_CharT, _Traits>& __is,
865 subtract_with_carry<_IntType1, __m1, __s1, __r1>& __x);
866
867 private:
868 template<class _Gen>
869 void
870 seed(_Gen& __g, true_type)
871 { return seed(static_cast<unsigned long>(__g)); }
872
873 template<class _Gen>
874 void
875 seed(_Gen& __g, false_type);
876
877 typedef typename __gnu_cxx::__add_unsigned<_IntType>::__type _UIntType;
878
879 _UIntType _M_x[long_lag];
880 _UIntType _M_carry;
881 int _M_p;
882 };
883
884
885 /**
886 * @brief The Marsaglia-Zaman generator (floats version).
887 *
888 * @var _M_x The state of the generator. This is a ring buffer.
889 * @var _M_carry The carry.
890 * @var _M_p Current index of x(i - r).
891 * @var _M_npows Precomputed negative powers of 2.
892 */
893 template<typename _RealType, int __w, int __s, int __r>
894 class subtract_with_carry_01
895 {
896 public:
897 /** The type of the generated random value. */
898 typedef _RealType result_type;
899
900 // parameter values
901 static const int word_size = __w;
902 static const int long_lag = __r;
903 static const int short_lag = __s;
904
905 /**
906 * Constructs a default-initialized % subtract_with_carry_01 random
907 * number generator.
908 */
909 subtract_with_carry_01()
910 {
911 this->seed();
912 _M_initialize_npows();
913 }
914
915 /**
916 * Constructs an explicitly seeded % subtract_with_carry_01 random number
917 * generator.
918 */
919 explicit
920 subtract_with_carry_01(unsigned long __value)
921 {
922 this->seed(__value);
923 _M_initialize_npows();
924 }
925
926 /**
927 * Constructs a % subtract_with_carry_01 random number generator engine
928 * seeded from the generator function @p __g.
929 *
930 * @param __g The seed generator function.
931 */
932 template<class _Gen>
933 subtract_with_carry_01(_Gen& __g)
934 {
935 this->seed(__g);
936 _M_initialize_npows();
937 }
938
939 /**
940 * Seeds the initial state @f$ x_0 @f$ of the random number generator.
941 */
942 void
943 seed(unsigned long __value = 19780503);
944
945 /**
946 * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry_01
947 * random number generator.
948 */
949 template<class _Gen>
950 void
951 seed(_Gen& __g)
952 { seed(__g, typename is_fundamental<_Gen>::type()); }
953
954 /**
955 * Gets the minimum value of the range of random floats
956 * returned by this generator.
957 */
958 result_type
959 min() const
960 { return 0.0; }
961
962 /**
963 * Gets the maximum value of the range of random floats
964 * returned by this generator.
965 */
966 result_type
967 max() const
968 { return 1.0; }
969
970 /**
971 * Gets the next random number in the sequence.
972 */
973 result_type
974 operator()();
975
976 /**
977 * Compares two % subtract_with_carry_01 random number generator objects
978 * of the same type for equality.
979 *
980 * @param __lhs A % subtract_with_carry_01 random number
981 * generator object.
982 * @param __rhs Another % subtract_with_carry_01 random number generator
983 * object.
984 *
985 * @returns true if the two objects are equal, false otherwise.
986 */
987 friend bool
988 operator==(const subtract_with_carry_01& __lhs,
989 const subtract_with_carry_01& __rhs)
990 {
991 for (int __i = 0; __i < long_lag; ++__i)
992 if (!std::equal(__lhs._M_x[__i], __lhs._M_x[__i] + __n,
993 __rhs._M_x[__i]))
994 return false;
995 return true;
996 }
997
998 /**
999 * Compares two % subtract_with_carry_01 random number generator objects
1000 * of the same type for inequality.
1001 *
1002 * @param __lhs A % subtract_with_carry_01 random number
1003 * generator object.
1004 *
1005 * @param __rhs Another % subtract_with_carry_01 random number generator
1006 * object.
1007 *
1008 * @returns true if the two objects are not equal, false otherwise.
1009 */
1010 friend bool
1011 operator!=(const subtract_with_carry_01& __lhs,
1012 const subtract_with_carry_01& __rhs)
1013 { return !(__lhs == __rhs); }
1014
1015 /**
1016 * Inserts the current state of a % subtract_with_carry_01 random number
1017 * generator engine @p __x into the output stream @p __os.
1018 *
1019 * @param __os An output stream.
1020 * @param __x A % subtract_with_carry_01 random number generator engine.
1021 *
1022 * @returns The output stream with the state of @p __x inserted or in
1023 * an error state.
1024 */
1025 template<typename _RealType1, int __w1, int __s1, int __r1,
1026 typename _CharT, typename _Traits>
1027 friend std::basic_ostream<_CharT, _Traits>&
1028 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1029 const subtract_with_carry_01<_RealType1, __w1, __s1,
1030 __r1>& __x);
1031
1032 /**
1033 * Extracts the current state of a % subtract_with_carry_01 random number
1034 * generator engine @p __x from the input stream @p __is.
1035 *
1036 * @param __is An input stream.
1037 * @param __x A % subtract_with_carry_01 random number generator engine.
1038 *
1039 * @returns The input stream with the state of @p __x extracted or in
1040 * an error state.
1041 */
1042 template<typename _RealType1, int __w1, int __s1, int __r1,
1043 typename _CharT, typename _Traits>
1044 friend std::basic_istream<_CharT, _Traits>&
1045 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1046 subtract_with_carry_01<_RealType1, __w1, __s1, __r1>& __x);
1047
1048 private:
1049 template<class _Gen>
1050 void
1051 seed(_Gen& __g, true_type)
1052 { return seed(static_cast<unsigned long>(__g)); }
1053
1054 template<class _Gen>
1055 void
1056 seed(_Gen& __g, false_type);
1057
1058 void
1059 _M_initialize_npows();
1060
1061 static const int __n = (__w + 31) / 32;
1062
1063 typedef __detail::_UInt32Type _UInt32Type;
1064 _UInt32Type _M_x[long_lag][__n];
1065 _RealType _M_npows[__n];
1066 _UInt32Type _M_carry;
1067 int _M_p;
1068 };
1069
1070 typedef subtract_with_carry_01<float, 24, 10, 24> ranlux_base_01;
1071
1072 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1073 // 508. Bad parameters for ranlux64_base_01.
1074 typedef subtract_with_carry_01<double, 48, 5, 12> ranlux64_base_01;
1075
1076
1077 /**
1078 * Produces random numbers from some base engine by discarding blocks of
1079 * data.
1080 *
1081 * 0 <= @p __r <= @p __p
1082 */
1083 template<class _UniformRandomNumberGenerator, int __p, int __r>
1084 class discard_block
1085 {
1086 // __glibcxx_class_requires(typename base_type::result_type,
1087 // ArithmeticTypeConcept)
1088
1089 public:
1090 /** The type of the underlying generator engine. */
1091 typedef _UniformRandomNumberGenerator base_type;
1092 /** The type of the generated random value. */
1093 typedef typename base_type::result_type result_type;
1094
1095 // parameter values
1096 static const int block_size = __p;
1097 static const int used_block = __r;
1098
1099 /**
1100 * Constructs a default %discard_block engine.
1101 *
1102 * The underlying engine is default constructed as well.
1103 */
1104 discard_block()
1105 : _M_n(0) { }
1106
1107 /**
1108 * Copy constructs a %discard_block engine.
1109 *
1110 * Copies an existing base class random number generator.
1111 * @param rng An existing (base class) engine object.
1112 */
1113 explicit
1114 discard_block(const base_type& __rng)
1115 : _M_b(__rng), _M_n(0) { }
1116
1117 /**
1118 * Seed constructs a %discard_block engine.
1119 *
1120 * Constructs the underlying generator engine seeded with @p __s.
1121 * @param __s A seed value for the base class engine.
1122 */
1123 explicit
1124 discard_block(unsigned long __s)
1125 : _M_b(__s), _M_n(0) { }
1126
1127 /**
1128 * Generator construct a %discard_block engine.
1129 *
1130 * @param __g A seed generator function.
1131 */
1132 template<class _Gen>
1133 discard_block(_Gen& __g)
1134 : _M_b(__g), _M_n(0) { }
1135
1136 /**
1137 * Reseeds the %discard_block object with the default seed for the
1138 * underlying base class generator engine.
1139 */
1140 void seed()
1141 {
1142 _M_b.seed();
1143 _M_n = 0;
1144 }
1145
1146 /**
1147 * Reseeds the %discard_block object with the given seed generator
1148 * function.
1149 * @param __g A seed generator function.
1150 */
1151 template<class _Gen>
1152 void seed(_Gen& __g)
1153 {
1154 _M_b.seed(__g);
1155 _M_n = 0;
1156 }
1157
1158 /**
1159 * Gets a const reference to the underlying generator engine object.
1160 */
1161 const base_type&
1162 base() const
1163 { return _M_b; }
1164
1165 /**
1166 * Gets the minimum value in the generated random number range.
1167 */
1168 result_type
1169 min() const
1170 { return _M_b.min(); }
1171
1172 /**
1173 * Gets the maximum value in the generated random number range.
1174 */
1175 result_type
1176 max() const
1177 { return _M_b.max(); }
1178
1179 /**
1180 * Gets the next value in the generated random number sequence.
1181 */
1182 result_type
1183 operator()();
1184
1185 /**
1186 * Compares two %discard_block random number generator objects of
1187 * the same type for equality.
1188 *
1189 * @param __lhs A %discard_block random number generator object.
1190 * @param __rhs Another %discard_block random number generator
1191 * object.
1192 *
1193 * @returns true if the two objects are equal, false otherwise.
1194 */
1195 friend bool
1196 operator==(const discard_block& __lhs, const discard_block& __rhs)
1197 { return (__lhs._M_b == __rhs._M_b) && (__lhs._M_n == __rhs._M_n); }
1198
1199 /**
1200 * Compares two %discard_block random number generator objects of
1201 * the same type for inequality.
1202 *
1203 * @param __lhs A %discard_block random number generator object.
1204 * @param __rhs Another %discard_block random number generator
1205 * object.
1206 *
1207 * @returns true if the two objects are not equal, false otherwise.
1208 */
1209 friend bool
1210 operator!=(const discard_block& __lhs, const discard_block& __rhs)
1211 { return !(__lhs == __rhs); }
1212
1213 /**
1214 * Inserts the current state of a %discard_block random number
1215 * generator engine @p __x into the output stream @p __os.
1216 *
1217 * @param __os An output stream.
1218 * @param __x A %discard_block random number generator engine.
1219 *
1220 * @returns The output stream with the state of @p __x inserted or in
1221 * an error state.
1222 */
1223 template<class _UniformRandomNumberGenerator1, int __p1, int __r1,
1224 typename _CharT, typename _Traits>
1225 friend std::basic_ostream<_CharT, _Traits>&
1226 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1227 const discard_block<_UniformRandomNumberGenerator1,
1228 __p1, __r1>& __x);
1229
1230 /**
1231 * Extracts the current state of a % subtract_with_carry random number
1232 * generator engine @p __x from the input stream @p __is.
1233 *
1234 * @param __is An input stream.
1235 * @param __x A %discard_block random number generator engine.
1236 *
1237 * @returns The input stream with the state of @p __x extracted or in
1238 * an error state.
1239 */
1240 template<class _UniformRandomNumberGenerator1, int __p1, int __r1,
1241 typename _CharT, typename _Traits>
1242 friend std::basic_istream<_CharT, _Traits>&
1243 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1244 discard_block<_UniformRandomNumberGenerator1,
1245 __p1, __r1>& __x);
1246
1247 private:
1248 base_type _M_b;
1249 int _M_n;
1250 };
1251
1252
1253 /**
1254 * James's luxury-level-3 integer adaptation of Luescher's generator.
1255 */
1256 typedef discard_block<
1257 subtract_with_carry<unsigned long, (1UL << 24), 10, 24>,
1258 223,
1259 24
1260 > ranlux3;
1261
1262 /**
1263 * James's luxury-level-4 integer adaptation of Luescher's generator.
1264 */
1265 typedef discard_block<
1266 subtract_with_carry<unsigned long, (1UL << 24), 10, 24>,
1267 389,
1268 24
1269 > ranlux4;
1270
1271 typedef discard_block<
1272 subtract_with_carry_01<float, 24, 10, 24>,
1273 223,
1274 24
1275 > ranlux3_01;
1276
1277 typedef discard_block<
1278 subtract_with_carry_01<float, 24, 10, 24>,
1279 389,
1280 24
1281 > ranlux4_01;
1282
1283
1284 /**
1285 * A random number generator adaptor class that combines two random number
1286 * generator engines into a single output sequence.
1287 */
1288 template<class _UniformRandomNumberGenerator1, int __s1,
1289 class _UniformRandomNumberGenerator2, int __s2>
1290 class xor_combine
1291 {
1292 // __glibcxx_class_requires(typename _UniformRandomNumberGenerator1::
1293 // result_type, ArithmeticTypeConcept)
1294 // __glibcxx_class_requires(typename _UniformRandomNumberGenerator2::
1295 // result_type, ArithmeticTypeConcept)
1296
1297 public:
1298 /** The type of the first underlying generator engine. */
1299 typedef _UniformRandomNumberGenerator1 base1_type;
1300 /** The type of the second underlying generator engine. */
1301 typedef _UniformRandomNumberGenerator2 base2_type;
1302
1303 private:
1304 typedef typename base1_type::result_type _Result_type1;
1305 typedef typename base2_type::result_type _Result_type2;
1306
1307 public:
1308 /** The type of the generated random value. */
1309 typedef typename __gnu_cxx::__conditional_type<(sizeof(_Result_type1)
1310 > sizeof(_Result_type2)),
1311 _Result_type1, _Result_type2>::__type result_type;
1312
1313 // parameter values
1314 static const int shift1 = __s1;
1315 static const int shift2 = __s2;
1316
1317 // constructors and member function
1318 xor_combine()
1319 : _M_b1(), _M_b2()
1320 { _M_initialize_max(); }
1321
1322 xor_combine(const base1_type& __rng1, const base2_type& __rng2)
1323 : _M_b1(__rng1), _M_b2(__rng2)
1324 { _M_initialize_max(); }
1325
1326 xor_combine(unsigned long __s)
1327 : _M_b1(__s), _M_b2(__s + 1)
1328 { _M_initialize_max(); }
1329
1330 template<class _Gen>
1331 xor_combine(_Gen& __g)
1332 : _M_b1(__g), _M_b2(__g)
1333 { _M_initialize_max(); }
1334
1335 void
1336 seed()
1337 {
1338 _M_b1.seed();
1339 _M_b2.seed();
1340 }
1341
1342 template<class _Gen>
1343 void
1344 seed(_Gen& __g)
1345 {
1346 _M_b1.seed(__g);
1347 _M_b2.seed(__g);
1348 }
1349
1350 const base1_type&
1351 base1() const
1352 { return _M_b1; }
1353
1354 const base2_type&
1355 base2() const
1356 { return _M_b2; }
1357
1358 result_type
1359 min() const
1360 { return 0; }
1361
1362 result_type
1363 max() const
1364 { return _M_max; }
1365
1366 /**
1367 * Gets the next random number in the sequence.
1368 */
1369 // NB: Not exactly the TR1 formula, per N2079 instead.
1370 result_type
1371 operator()()
1372 {
1373 return ((result_type(_M_b1() - _M_b1.min()) << shift1)
1374 ^ (result_type(_M_b2() - _M_b2.min()) << shift2));
1375 }
1376
1377 /**
1378 * Compares two %xor_combine random number generator objects of
1379 * the same type for equality.
1380 *
1381 * @param __lhs A %xor_combine random number generator object.
1382 * @param __rhs Another %xor_combine random number generator
1383 * object.
1384 *
1385 * @returns true if the two objects are equal, false otherwise.
1386 */
1387 friend bool
1388 operator==(const xor_combine& __lhs, const xor_combine& __rhs)
1389 {
1390 return (__lhs.base1() == __rhs.base1())
1391 && (__lhs.base2() == __rhs.base2());
1392 }
1393
1394 /**
1395 * Compares two %xor_combine random number generator objects of
1396 * the same type for inequality.
1397 *
1398 * @param __lhs A %xor_combine random number generator object.
1399 * @param __rhs Another %xor_combine random number generator
1400 * object.
1401 *
1402 * @returns true if the two objects are not equal, false otherwise.
1403 */
1404 friend bool
1405 operator!=(const xor_combine& __lhs, const xor_combine& __rhs)
1406 { return !(__lhs == __rhs); }
1407
1408 /**
1409 * Inserts the current state of a %xor_combine random number
1410 * generator engine @p __x into the output stream @p __os.
1411 *
1412 * @param __os An output stream.
1413 * @param __x A %xor_combine random number generator engine.
1414 *
1415 * @returns The output stream with the state of @p __x inserted or in
1416 * an error state.
1417 */
1418 template<class _UniformRandomNumberGenerator11, int __s11,
1419 class _UniformRandomNumberGenerator21, int __s21,
1420 typename _CharT, typename _Traits>
1421 friend std::basic_ostream<_CharT, _Traits>&
1422 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1423 const xor_combine<_UniformRandomNumberGenerator11, __s11,
1424 _UniformRandomNumberGenerator21, __s21>& __x);
1425
1426 /**
1427 * Extracts the current state of a %xor_combine random number
1428 * generator engine @p __x from the input stream @p __is.
1429 *
1430 * @param __is An input stream.
1431 * @param __x A %xor_combine random number generator engine.
1432 *
1433 * @returns The input stream with the state of @p __x extracted or in
1434 * an error state.
1435 */
1436 template<class _UniformRandomNumberGenerator11, int __s11,
1437 class _UniformRandomNumberGenerator21, int __s21,
1438 typename _CharT, typename _Traits>
1439 friend std::basic_istream<_CharT, _Traits>&
1440 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1441 xor_combine<_UniformRandomNumberGenerator11, __s11,
1442 _UniformRandomNumberGenerator21, __s21>& __x);
1443
1444 private:
1445 void
1446 _M_initialize_max();
1447
1448 result_type
1449 _M_initialize_max_aux(result_type, result_type, int);
1450
1451 base1_type _M_b1;
1452 base2_type _M_b2;
1453 result_type _M_max;
1454 };
1455
1456
1457 /**
1458 * A standard interface to a platform-specific non-deterministic
1459 * random number generator (if any are available).
1460 */
1461 class random_device
1462 {
1463 public:
1464 // types
1465 typedef unsigned int result_type;
1466
1467 // constructors, destructors and member functions
1468
1469#ifdef _GLIBCXX_USE_RANDOM_TR1
1470
1471 explicit
1472 random_device(const std::string& __token = "/dev/urandom")
1473 {
1474 if ((__token != "/dev/urandom" && __token != "/dev/random")
1475 || !(_M_file = std::fopen(__token.c_str(), "rb")))
1476 std::__throw_runtime_error(__N("random_device::"
1477 "random_device(const std::string&)"));
1478 }
1479
1480 ~random_device()
1481 { std::fclose(_M_file); }
1482
1483#else
1484
1485 explicit
1486 random_device(const std::string& __token = "mt19937")
1487 : _M_mt(_M_strtoul(__token)) { }
1488
1489 private:
1490 static unsigned long
1491 _M_strtoul(const std::string& __str)
1492 {
1493 unsigned long __ret = 5489UL;
1494 if (__str != "mt19937")
1495 {
1496 const char* __nptr = __str.c_str();
1497 char* __endptr;
1498 __ret = std::strtoul(__nptr, &__endptr, 0);
1499 if (*__nptr == '\0' || *__endptr != '\0')
1500 std::__throw_runtime_error(__N("random_device::_M_strtoul"
1501 "(const std::string&)"));
1502 }
1503 return __ret;
1504 }
1505
1506 public:
1507
1508#endif
1509
1510 result_type
1511 min() const
1512 { return std::numeric_limits<result_type>::min(); }
1513
1514 result_type
1515 max() const
1516 { return std::numeric_limits<result_type>::max(); }
1517
1518 double
1519 entropy() const
1520 { return 0.0; }
1521
1522 result_type
1523 operator()()
1524 {
1525#ifdef _GLIBCXX_USE_RANDOM_TR1
1526 result_type __ret;
1527 std::fread(reinterpret_cast<void*>(&__ret), sizeof(result_type),
1528 1, _M_file);
1529 return __ret;
1530#else
1531 return _M_mt();
1532#endif
1533 }
1534
1535 private:
1536 random_device(const random_device&);
1537 void operator=(const random_device&);
1538
1539#ifdef _GLIBCXX_USE_RANDOM_TR1
1540 FILE* _M_file;
1541#else
1542 mt19937 _M_mt;
1543#endif
1544 };
1545
1546 /// @} group tr1_random_generators
1547
1548 /**
1549 * @addtogroup tr1_random_distributions Random Number Distributions
1550 * @ingroup tr1_random
1551 * @{
1552 */
1553
1554 /**
1555 * @addtogroup tr1_random_distributions_discrete Discrete Distributions
1556 * @ingroup tr1_random_distributions
1557 * @{
1558 */
1559
1560 /**
1561 * @brief Uniform discrete distribution for random numbers.
1562 * A discrete random distribution on the range @f$[min, max]@f$ with equal
1563 * probability throughout the range.
1564 */
1565 template<typename _IntType = int>
1566 class uniform_int
1567 {
1568 __glibcxx_class_requires(_IntType, _IntegerConcept)
1569
1570 public:
1571 /** The type of the parameters of the distribution. */
1572 typedef _IntType input_type;
1573 /** The type of the range of the distribution. */
1574 typedef _IntType result_type;
1575
1576 public:
1577 /**
1578 * Constructs a uniform distribution object.
1579 */
1580 explicit
1581 uniform_int(_IntType __min = 0, _IntType __max = 9)
1582 : _M_min(__min), _M_max(__max)
1583 {
1584 _GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
1585 }
1586
1587 /**
1588 * Gets the inclusive lower bound of the distribution range.
1589 */
1590 result_type
1591 min() const
1592 { return _M_min; }
1593
1594 /**
1595 * Gets the inclusive upper bound of the distribution range.
1596 */
1597 result_type
1598 max() const
1599 { return _M_max; }
1600
1601 /**
1602 * Resets the distribution state.
1603 *
1604 * Does nothing for the uniform integer distribution.
1605 */
1606 void
1607 reset() { }
1608
1609 /**
1610 * Gets a uniformly distributed random number in the range
1611 * @f$(min, max)@f$.
1612 */
1613 template<typename _UniformRandomNumberGenerator>
1614 result_type
1615 operator()(_UniformRandomNumberGenerator& __urng)
1616 {
1617 typedef typename _UniformRandomNumberGenerator::result_type
1618 _UResult_type;
1619 return _M_call(__urng, _M_min, _M_max,
1620 typename is_integral<_UResult_type>::type());
1621 }
1622
1623 /**
1624 * Gets a uniform random number in the range @f$[0, n)@f$.
1625 *
1626 * This function is aimed at use with std::random_shuffle.
1627 */
1628 template<typename _UniformRandomNumberGenerator>
1629 result_type
1630 operator()(_UniformRandomNumberGenerator& __urng, result_type __n)
1631 {
1632 typedef typename _UniformRandomNumberGenerator::result_type
1633 _UResult_type;
1634 return _M_call(__urng, 0, __n - 1,
1635 typename is_integral<_UResult_type>::type());
1636 }
1637
1638 /**
1639 * Inserts a %uniform_int random number distribution @p __x into the
1640 * output stream @p os.
1641 *
1642 * @param __os An output stream.
1643 * @param __x A %uniform_int random number distribution.
1644 *
1645 * @returns The output stream with the state of @p __x inserted or in
1646 * an error state.
1647 */
1648 template<typename _IntType1, typename _CharT, typename _Traits>
1649 friend std::basic_ostream<_CharT, _Traits>&
1650 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1651 const uniform_int<_IntType1>& __x);
1652
1653 /**
1654 * Extracts a %uniform_int random number distribution
1655 * @p __x from the input stream @p __is.
1656 *
1657 * @param __is An input stream.
1658 * @param __x A %uniform_int random number generator engine.
1659 *
1660 * @returns The input stream with @p __x extracted or in an error state.
1661 */
1662 template<typename _IntType1, typename _CharT, typename _Traits>
1663 friend std::basic_istream<_CharT, _Traits>&
1664 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1665 uniform_int<_IntType1>& __x);
1666
1667 private:
1668 template<typename _UniformRandomNumberGenerator>
1669 result_type
1670 _M_call(_UniformRandomNumberGenerator& __urng,
1671 result_type __min, result_type __max, true_type);
1672
1673 template<typename _UniformRandomNumberGenerator>
1674 result_type
1675 _M_call(_UniformRandomNumberGenerator& __urng,
1676 result_type __min, result_type __max, false_type)
1677 {
1678 return result_type((__urng() - __urng.min())
1679 / (__urng.max() - __urng.min())
1680 * (__max - __min + 1)) + __min;
1681 }
1682
1683 _IntType _M_min;
1684 _IntType _M_max;
1685 };
1686
1687
1688 /**
1689 * @brief A Bernoulli random number distribution.
1690 *
1691 * Generates a sequence of true and false values with likelihood @f$ p @f$
1692 * that true will come up and @f$ (1 - p) @f$ that false will appear.
1693 */
1694 class bernoulli_distribution
1695 {
1696 public:
1697 typedef int input_type;
1698 typedef bool result_type;
1699
1700 public:
1701 /**
1702 * Constructs a Bernoulli distribution with likelihood @p p.
1703 *
1704 * @param __p [IN] The likelihood of a true result being returned. Must
1705 * be in the interval @f$ [0, 1] @f$.
1706 */
1707 explicit
1708 bernoulli_distribution(double __p = 0.5)
1709 : _M_p(__p)
1710 {
1711 _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0));
1712 }
1713
1714 /**
1715 * Gets the @p p parameter of the distribution.
1716 */
1717 double
1718 p() const
1719 { return _M_p; }
1720
1721 /**
1722 * Resets the distribution state.
1723 *
1724 * Does nothing for a Bernoulli distribution.
1725 */
1726 void
1727 reset() { }
1728
1729 /**
1730 * Gets the next value in the Bernoullian sequence.
1731 */
1732 template<class _UniformRandomNumberGenerator>
1733 result_type
1734 operator()(_UniformRandomNumberGenerator& __urng)
1735 {
1736 if ((__urng() - __urng.min()) < _M_p * (__urng.max() - __urng.min()))
1737 return true;
1738 return false;
1739 }
1740
1741 /**
1742 * Inserts a %bernoulli_distribution random number distribution
1743 * @p __x into the output stream @p __os.
1744 *
1745 * @param __os An output stream.
1746 * @param __x A %bernoulli_distribution random number distribution.
1747 *
1748 * @returns The output stream with the state of @p __x inserted or in
1749 * an error state.
1750 */
1751 template<typename _CharT, typename _Traits>
1752 friend std::basic_ostream<_CharT, _Traits>&
1753 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1754 const bernoulli_distribution& __x);
1755
1756 /**
1757 * Extracts a %bernoulli_distribution random number distribution
1758 * @p __x from the input stream @p __is.
1759 *
1760 * @param __is An input stream.
1761 * @param __x A %bernoulli_distribution random number generator engine.
1762 *
1763 * @returns The input stream with @p __x extracted or in an error state.
1764 */
1765 template<typename _CharT, typename _Traits>
1766 friend std::basic_istream<_CharT, _Traits>&
1767 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1768 bernoulli_distribution& __x)
1769 { return __is >> __x._M_p; }
1770
1771 private:
1772 double _M_p;
1773 };
1774
1775
1776 /**
1777 * @brief A discrete geometric random number distribution.
1778 *
1779 * The formula for the geometric probability mass function is
1780 * @f$ p(i) = (1 - p)p^{i-1} @f$ where @f$ p @f$ is the parameter of the
1781 * distribution.
1782 */
1783 template<typename _IntType = int, typename _RealType = double>
1784 class geometric_distribution
1785 {
1786 public:
1787 // types
1788 typedef _RealType input_type;
1789 typedef _IntType result_type;
1790
1791 // constructors and member function
1792 explicit
1793 geometric_distribution(const _RealType& __p = _RealType(0.5))
1794 : _M_p(__p)
1795 {
1796 _GLIBCXX_DEBUG_ASSERT((_M_p > 0.0) && (_M_p < 1.0));
1797 _M_initialize();
1798 }
1799
1800 /**
1801 * Gets the distribution parameter @p p.
1802 */
1803 _RealType
1804 p() const
1805 { return _M_p; }
1806
1807 void
1808 reset() { }
1809
1810 template<class _UniformRandomNumberGenerator>
1811 result_type
1812 operator()(_UniformRandomNumberGenerator& __urng);
1813
1814 /**
1815 * Inserts a %geometric_distribution random number distribution
1816 * @p __x into the output stream @p __os.
1817 *
1818 * @param __os An output stream.
1819 * @param __x A %geometric_distribution random number distribution.
1820 *
1821 * @returns The output stream with the state of @p __x inserted or in
1822 * an error state.
1823 */
1824 template<typename _IntType1, typename _RealType1,
1825 typename _CharT, typename _Traits>
1826 friend std::basic_ostream<_CharT, _Traits>&
1827 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1828 const geometric_distribution<_IntType1, _RealType1>& __x);
1829
1830 /**
1831 * Extracts a %geometric_distribution random number distribution
1832 * @p __x from the input stream @p __is.
1833 *
1834 * @param __is An input stream.
1835 * @param __x A %geometric_distribution random number generator engine.
1836 *
1837 * @returns The input stream with @p __x extracted or in an error state.
1838 */
1839 template<typename _CharT, typename _Traits>
1840 friend std::basic_istream<_CharT, _Traits>&
1841 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1842 geometric_distribution& __x)
1843 {
1844 __is >> __x._M_p;
1845 __x._M_initialize();
1846 return __is;
1847 }
1848
1849 private:
1850 void
1851 _M_initialize()
1852 { _M_log_p = std::log(_M_p); }
1853
1854 _RealType _M_p;
1855 _RealType _M_log_p;
1856 };
1857
1858
1859 template<typename _RealType>
1860 class normal_distribution;
1861
1862 /**
1863 * @brief A discrete Poisson random number distribution.
1864 *
1865 * The formula for the Poisson probability mass function is
1866 * @f$ p(i) = \frac{mean^i}{i!} e^{-mean} @f$ where @f$ mean @f$ is the
1867 * parameter of the distribution.
1868 */
1869 template<typename _IntType = int, typename _RealType = double>
1870 class poisson_distribution
1871 {
1872 public:
1873 // types
1874 typedef _RealType input_type;
1875 typedef _IntType result_type;
1876
1877 // constructors and member function
1878 explicit
1879 poisson_distribution(const _RealType& __mean = _RealType(1))
1880 : _M_mean(__mean), _M_nd()
1881 {
1882 _GLIBCXX_DEBUG_ASSERT(_M_mean > 0.0);
1883 _M_initialize();
1884 }
1885
1886 /**
1887 * Gets the distribution parameter @p mean.
1888 */
1889 _RealType
1890 mean() const
1891 { return _M_mean; }
1892
1893 void
1894 reset()
1895 { _M_nd.reset(); }
1896
1897 template<class _UniformRandomNumberGenerator>
1898 result_type
1899 operator()(_UniformRandomNumberGenerator& __urng);
1900
1901 /**
1902 * Inserts a %poisson_distribution random number distribution
1903 * @p __x into the output stream @p __os.
1904 *
1905 * @param __os An output stream.
1906 * @param __x A %poisson_distribution random number distribution.
1907 *
1908 * @returns The output stream with the state of @p __x inserted or in
1909 * an error state.
1910 */
1911 template<typename _IntType1, typename _RealType1,
1912 typename _CharT, typename _Traits>
1913 friend std::basic_ostream<_CharT, _Traits>&
1914 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1915 const poisson_distribution<_IntType1, _RealType1>& __x);
1916
1917 /**
1918 * Extracts a %poisson_distribution random number distribution
1919 * @p __x from the input stream @p __is.
1920 *
1921 * @param __is An input stream.
1922 * @param __x A %poisson_distribution random number generator engine.
1923 *
1924 * @returns The input stream with @p __x extracted or in an error state.
1925 */
1926 template<typename _IntType1, typename _RealType1,
1927 typename _CharT, typename _Traits>
1928 friend std::basic_istream<_CharT, _Traits>&
1929 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1930 poisson_distribution<_IntType1, _RealType1>& __x);
1931
1932 private:
1933 void
1934 _M_initialize();
1935
1936 // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
1937 normal_distribution<_RealType> _M_nd;
1938
1939 _RealType _M_mean;
1940
1941 // Hosts either log(mean) or the threshold of the simple method.
1942 _RealType _M_lm_thr;
1943#if _GLIBCXX_USE_C99_MATH_TR1
1944 _RealType _M_lfm, _M_sm, _M_d, _M_scx, _M_1cx, _M_c2b, _M_cb;
1945#endif
1946 };
1947
1948
1949 /**
1950 * @brief A discrete binomial random number distribution.
1951 *
1952 * The formula for the binomial probability mass function is
1953 * @f$ p(i) = \binom{n}{i} p^i (1 - p)^{t - i} @f$ where @f$ t @f$
1954 * and @f$ p @f$ are the parameters of the distribution.
1955 */
1956 template<typename _IntType = int, typename _RealType = double>
1957 class binomial_distribution
1958 {
1959 public:
1960 // types
1961 typedef _RealType input_type;
1962 typedef _IntType result_type;
1963
1964 // constructors and member function
1965 explicit
1966 binomial_distribution(_IntType __t = 1,
1967 const _RealType& __p = _RealType(0.5))
1968 : _M_t(__t), _M_p(__p), _M_nd()
1969 {
1970 _GLIBCXX_DEBUG_ASSERT((_M_t >= 0) && (_M_p >= 0.0) && (_M_p <= 1.0));
1971 _M_initialize();
1972 }
1973
1974 /**
1975 * Gets the distribution @p t parameter.
1976 */
1977 _IntType
1978 t() const
1979 { return _M_t; }
1980
1981 /**
1982 * Gets the distribution @p p parameter.
1983 */
1984 _RealType
1985 p() const
1986 { return _M_p; }
1987
1988 void
1989 reset()
1990 { _M_nd.reset(); }
1991
1992 template<class _UniformRandomNumberGenerator>
1993 result_type
1994 operator()(_UniformRandomNumberGenerator& __urng);
1995
1996 /**
1997 * Inserts a %binomial_distribution random number distribution
1998 * @p __x into the output stream @p __os.
1999 *
2000 * @param __os An output stream.
2001 * @param __x A %binomial_distribution random number distribution.
2002 *
2003 * @returns The output stream with the state of @p __x inserted or in
2004 * an error state.
2005 */
2006 template<typename _IntType1, typename _RealType1,
2007 typename _CharT, typename _Traits>
2008 friend std::basic_ostream<_CharT, _Traits>&
2009 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2010 const binomial_distribution<_IntType1, _RealType1>& __x);
2011
2012 /**
2013 * Extracts a %binomial_distribution random number distribution
2014 * @p __x from the input stream @p __is.
2015 *
2016 * @param __is An input stream.
2017 * @param __x A %binomial_distribution random number generator engine.
2018 *
2019 * @returns The input stream with @p __x extracted or in an error state.
2020 */
2021 template<typename _IntType1, typename _RealType1,
2022 typename _CharT, typename _Traits>
2023 friend std::basic_istream<_CharT, _Traits>&
2024 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2025 binomial_distribution<_IntType1, _RealType1>& __x);
2026
2027 private:
2028 void
2029 _M_initialize();
2030
2031 template<class _UniformRandomNumberGenerator>
2032 result_type
2033 _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t);
2034
2035 // NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
2036 normal_distribution<_RealType> _M_nd;
2037
2038 _RealType _M_q;
2039#if _GLIBCXX_USE_C99_MATH_TR1
2040 _RealType _M_d1, _M_d2, _M_s1, _M_s2, _M_c,
2041 _M_a1, _M_a123, _M_s, _M_lf, _M_lp1p;
2042#endif
2043 _RealType _M_p;
2044 _IntType _M_t;
2045
2046 bool _M_easy;
2047 };
2048
2049 /// @} group tr1_random_distributions_discrete
2050
2051 /**
2052 * @addtogroup tr1_random_distributions_continuous Continuous Distributions
2053 * @ingroup tr1_random_distributions
2054 * @{
2055 */
2056
2057 /**
2058 * @brief Uniform continuous distribution for random numbers.
2059 *
2060 * A continuous random distribution on the range [min, max) with equal
2061 * probability throughout the range. The URNG should be real-valued and
2062 * deliver number in the range [0, 1).
2063 */
2064 template<typename _RealType = double>
2065 class uniform_real
2066 {
2067 public:
2068 // types
2069 typedef _RealType input_type;
2070 typedef _RealType result_type;
2071
2072 public:
2073 /**
2074 * Constructs a uniform_real object.
2075 *
2076 * @param __min [IN] The lower bound of the distribution.
2077 * @param __max [IN] The upper bound of the distribution.
2078 */
2079 explicit
2080 uniform_real(_RealType __min = _RealType(0),
2081 _RealType __max = _RealType(1))
2082 : _M_min(__min), _M_max(__max)
2083 {
2084 _GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
2085 }
2086
2087 result_type
2088 min() const
2089 { return _M_min; }
2090
2091 result_type
2092 max() const
2093 { return _M_max; }
2094
2095 void
2096 reset() { }
2097
2098 template<class _UniformRandomNumberGenerator>
2099 result_type
2100 operator()(_UniformRandomNumberGenerator& __urng)
2101 { return (__urng() * (_M_max - _M_min)) + _M_min; }
2102
2103 /**
2104 * Inserts a %uniform_real random number distribution @p __x into the
2105 * output stream @p __os.
2106 *
2107 * @param __os An output stream.
2108 * @param __x A %uniform_real random number distribution.
2109 *
2110 * @returns The output stream with the state of @p __x inserted or in
2111 * an error state.
2112 */
2113 template<typename _RealType1, typename _CharT, typename _Traits>
2114 friend std::basic_ostream<_CharT, _Traits>&
2115 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2116 const uniform_real<_RealType1>& __x);
2117
2118 /**
2119 * Extracts a %uniform_real random number distribution
2120 * @p __x from the input stream @p __is.
2121 *
2122 * @param __is An input stream.
2123 * @param __x A %uniform_real random number generator engine.
2124 *
2125 * @returns The input stream with @p __x extracted or in an error state.
2126 */
2127 template<typename _RealType1, typename _CharT, typename _Traits>
2128 friend std::basic_istream<_CharT, _Traits>&
2129 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2130 uniform_real<_RealType1>& __x);
2131
2132 private:
2133 _RealType _M_min;
2134 _RealType _M_max;
2135 };
2136
2137
2138 /**
2139 * @brief An exponential continuous distribution for random numbers.
2140 *
2141 * The formula for the exponential probability mass function is
2142 * @f$ p(x) = \lambda e^{-\lambda x} @f$.
2143 *
2144 * <table border=1 cellpadding=10 cellspacing=0>
2145 * <caption align=top>Distribution Statistics</caption>
2146 * <tr><td>Mean</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
2147 * <tr><td>Median</td><td>@f$ \frac{\ln 2}{\lambda} @f$</td></tr>
2148 * <tr><td>Mode</td><td>@f$ zero @f$</td></tr>
2149 * <tr><td>Range</td><td>@f$[0, \infty]@f$</td></tr>
2150 * <tr><td>Standard Deviation</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
2151 * </table>
2152 */
2153 template<typename _RealType = double>
2154 class exponential_distribution
2155 {
2156 public:
2157 // types
2158 typedef _RealType input_type;
2159 typedef _RealType result_type;
2160
2161 public:
2162 /**
2163 * Constructs an exponential distribution with inverse scale parameter
2164 * @f$ \lambda @f$.
2165 */
2166 explicit
2167 exponential_distribution(const result_type& __lambda = result_type(1))
2168 : _M_lambda(__lambda)
2169 {
2170 _GLIBCXX_DEBUG_ASSERT(_M_lambda > 0);
2171 }
2172
2173 /**
2174 * Gets the inverse scale parameter of the distribution.
2175 */
2176 _RealType
2177 lambda() const
2178 { return _M_lambda; }
2179
2180 /**
2181 * Resets the distribution.
2182 *
2183 * Has no effect on exponential distributions.
2184 */
2185 void
2186 reset() { }
2187
2188 template<class _UniformRandomNumberGenerator>
2189 result_type
2190 operator()(_UniformRandomNumberGenerator& __urng)
2191 { return -std::log(__urng()) / _M_lambda; }
2192
2193 /**
2194 * Inserts a %exponential_distribution random number distribution
2195 * @p __x into the output stream @p __os.
2196 *
2197 * @param __os An output stream.
2198 * @param __x A %exponential_distribution random number distribution.
2199 *
2200 * @returns The output stream with the state of @p __x inserted or in
2201 * an error state.
2202 */
2203 template<typename _RealType1, typename _CharT, typename _Traits>
2204 friend std::basic_ostream<_CharT, _Traits>&
2205 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2206 const exponential_distribution<_RealType1>& __x);
2207
2208 /**
2209 * Extracts a %exponential_distribution random number distribution
2210 * @p __x from the input stream @p __is.
2211 *
2212 * @param __is An input stream.
2213 * @param __x A %exponential_distribution random number
2214 * generator engine.
2215 *
2216 * @returns The input stream with @p __x extracted or in an error state.
2217 */
2218 template<typename _CharT, typename _Traits>
2219 friend std::basic_istream<_CharT, _Traits>&
2220 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2221 exponential_distribution& __x)
2222 { return __is >> __x._M_lambda; }
2223
2224 private:
2225 result_type _M_lambda;
2226 };
2227
2228
2229 /**
2230 * @brief A normal continuous distribution for random numbers.
2231 *
2232 * The formula for the normal probability mass function is
2233 * @f$ p(x) = \frac{1}{\sigma \sqrt{2 \pi}}
2234 * e^{- \frac{{x - mean}^ {2}}{2 \sigma ^ {2}} } @f$.
2235 */
2236 template<typename _RealType = double>
2237 class normal_distribution
2238 {
2239 public:
2240 // types
2241 typedef _RealType input_type;
2242 typedef _RealType result_type;
2243
2244 public:
2245 /**
2246 * Constructs a normal distribution with parameters @f$ mean @f$ and
2247 * @f$ \sigma @f$.
2248 */
2249 explicit
2250 normal_distribution(const result_type& __mean = result_type(0),
2251 const result_type& __sigma = result_type(1))
2252 : _M_mean(__mean), _M_sigma(__sigma), _M_saved_available(false)
2253 {
2254 _GLIBCXX_DEBUG_ASSERT(_M_sigma > 0);
2255 }
2256
2257 /**
2258 * Gets the mean of the distribution.
2259 */
2260 _RealType
2261 mean() const
2262 { return _M_mean; }
2263
2264 /**
2265 * Gets the @f$ \sigma @f$ of the distribution.
2266 */
2267 _RealType
2268 sigma() const
2269 { return _M_sigma; }
2270
2271 /**
2272 * Resets the distribution.
2273 */
2274 void
2275 reset()
2276 { _M_saved_available = false; }
2277
2278 template<class _UniformRandomNumberGenerator>
2279 result_type
2280 operator()(_UniformRandomNumberGenerator& __urng);
2281
2282 /**
2283 * Inserts a %normal_distribution random number distribution
2284 * @p __x into the output stream @p __os.
2285 *
2286 * @param __os An output stream.
2287 * @param __x A %normal_distribution random number distribution.
2288 *
2289 * @returns The output stream with the state of @p __x inserted or in
2290 * an error state.
2291 */
2292 template<typename _RealType1, typename _CharT, typename _Traits>
2293 friend std::basic_ostream<_CharT, _Traits>&
2294 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2295 const normal_distribution<_RealType1>& __x);
2296
2297 /**
2298 * Extracts a %normal_distribution random number distribution
2299 * @p __x from the input stream @p __is.
2300 *
2301 * @param __is An input stream.
2302 * @param __x A %normal_distribution random number generator engine.
2303 *
2304 * @returns The input stream with @p __x extracted or in an error state.
2305 */
2306 template<typename _RealType1, typename _CharT, typename _Traits>
2307 friend std::basic_istream<_CharT, _Traits>&
2308 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2309 normal_distribution<_RealType1>& __x);
2310
2311 private:
2312 result_type _M_mean;
2313 result_type _M_sigma;
2314 result_type _M_saved;
2315 bool _M_saved_available;
2316 };
2317
2318
2319 /**
2320 * @brief A gamma continuous distribution for random numbers.
2321 *
2322 * The formula for the gamma probability mass function is
2323 * @f$ p(x) = \frac{1}{\Gamma(\alpha)} x^{\alpha - 1} e^{-x} @f$.
2324 */
2325 template<typename _RealType = double>
2326 class gamma_distribution
2327 {
2328 public:
2329 // types
2330 typedef _RealType input_type;
2331 typedef _RealType result_type;
2332
2333 public:
2334 /**
2335 * Constructs a gamma distribution with parameters @f$ \alpha @f$.
2336 */
2337 explicit
2338 gamma_distribution(const result_type& __alpha_val = result_type(1))
2339 : _M_alpha(__alpha_val)
2340 {
2341 _GLIBCXX_DEBUG_ASSERT(_M_alpha > 0);
2342 _M_initialize();
2343 }
2344
2345 /**
2346 * Gets the @f$ \alpha @f$ of the distribution.
2347 */
2348 _RealType
2349 alpha() const
2350 { return _M_alpha; }
2351
2352 /**
2353 * Resets the distribution.
2354 */
2355 void
2356 reset() { }
2357
2358 template<class _UniformRandomNumberGenerator>
2359 result_type
2360 operator()(_UniformRandomNumberGenerator& __urng);
2361
2362 /**
2363 * Inserts a %gamma_distribution random number distribution
2364 * @p __x into the output stream @p __os.
2365 *
2366 * @param __os An output stream.
2367 * @param __x A %gamma_distribution random number distribution.
2368 *
2369 * @returns The output stream with the state of @p __x inserted or in
2370 * an error state.
2371 */
2372 template<typename _RealType1, typename _CharT, typename _Traits>
2373 friend std::basic_ostream<_CharT, _Traits>&
2374 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2375 const gamma_distribution<_RealType1>& __x);
2376
2377 /**
2378 * Extracts a %gamma_distribution random number distribution
2379 * @p __x from the input stream @p __is.
2380 *
2381 * @param __is An input stream.
2382 * @param __x A %gamma_distribution random number generator engine.
2383 *
2384 * @returns The input stream with @p __x extracted or in an error state.
2385 */
2386 template<typename _CharT, typename _Traits>
2387 friend std::basic_istream<_CharT, _Traits>&
2388 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2389 gamma_distribution& __x)
2390 {
2391 __is >> __x._M_alpha;
2392 __x._M_initialize();
2393 return __is;
2394 }
2395
2396 private:
2397 void
2398 _M_initialize();
2399
2400 result_type _M_alpha;
2401
2402 // Hosts either lambda of GB or d of modified Vaduva's.
2403 result_type _M_l_d;
2404 };
2405
2406 /// @} group tr1_random_distributions_continuous
2407 /// @} group tr1_random_distributions
2408 /// @} group tr1_random
2409}
2410
2411_GLIBCXX_END_NAMESPACE_VERSION
2412}
2413
2414#endif // _GLIBCXX_TR1_RANDOM_H
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