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1 // random number generation -*- C++ -*-
3 // Copyright (C) 2006 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 2, or (at your option)
9 // any later version.
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.
16 // You should have received a copy of the GNU General Public License along
17 // with this library; see the file COPYING. If not, write to the Free
18 // Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
19 // USA.
21 // As a special exception, you may use this file as part of a free software
22 // library without restriction. Specifically, if other files instantiate
23 // templates or use macros or inline functions from this file, or you compile
24 // this file and link it with other files to produce an executable, this
25 // file does not by itself cause the resulting executable to be covered by
26 // the GNU General Public License. This exception does not however
27 // invalidate any other reasons why the executable file might be covered by
28 // the GNU General Public License.
30 #ifndef _STD_TR1_RANDOM
31 #define _STD_TR1_RANDOM 1
33 /**
34 * @file
35 * This is a TR1 C++ Library header.
36 */
38 #include <algorithm>
39 #include <bits/concept_check.h>
40 #include <bits/cpp_type_traits.h>
41 #include <cmath>
42 #include <debug/debug.h>
43 #include <iterator>
44 #include <iosfwd>
45 #include <limits>
46 #include <tr1/type_traits>
47 #include <fstream>
49 namespace std
50 {
51 _GLIBCXX_BEGIN_NAMESPACE(tr1)
53 // [5.1] Random number generation
55 /**
56 * @addtogroup tr1_random Random Number Generation
57 * A facility for generating random numbers on selected distributions.
58 * @{
59 */
61 /*
62 * Implementation-space details.
63 */
64 namespace _Private
65 {
66 // Type selectors -- are these already implemented elsewhere?
67 template<bool, typename _TpTrue, typename _TpFalse>
68 struct _Select
69 {
70 typedef _TpTrue _Type;
71 };
73 template<typename _TpTrue, typename _TpFalse>
74 struct _Select<false, _TpTrue, _TpFalse>
75 {
76 typedef _TpFalse _Type;
77 };
79 /*
80 * An adaptor class for converting the output of any Generator into
81 * the input for a specific Distribution.
82 */
83 template<typename _Engine, typename _Distribution>
84 struct _Adaptor
85 {
86 typedef typename _Engine::result_type _Engine_result_type;
87 typedef typename _Distribution::input_type result_type;
89 public:
90 _Adaptor(const _Engine& __g)
91 : _M_g(__g) { }
93 result_type
94 operator()();
96 private:
97 _Engine _M_g;
98 };
100 /*
101 * Converts a value generated by the adapted random number generator into a
102 * value in the input domain for the dependent random number distribution.
103 *
104 * Because the type traits are compile time constants only the appropriate
105 * clause of the if statements will actually be emitted by the compiler.
106 */
107 template<typename _Engine, typename _Distribution>
108 typename _Adaptor<_Engine, _Distribution>::result_type
109 _Adaptor<_Engine, _Distribution>::
110 operator()()
111 {
112 result_type __return_value = 0;
113 if (is_integral<_Engine_result_type>::value
114 && is_integral<result_type>::value)
115 __return_value = _M_g();
116 else if (is_integral<_Engine_result_type>::value
117 && !is_integral<result_type>::value)
118 __return_value = result_type(_M_g())
119 / result_type(_M_g.max() - _M_g.min() + result_type(1));
120 else if (!is_integral<_Engine_result_type>::value
121 && !is_integral<result_type>::value)
122 __return_value = result_type(_M_g())
123 / result_type(_M_g.max() - _M_g.min());
124 return __return_value;
125 }
127 template<typename _UIntType, int __w, bool =
128 __w != std::numeric_limits<_UIntType>::digits>
129 struct _Shift
130 { static const _UIntType __value = 0; };
132 template<typename _UIntType, int __w>
133 struct _Shift<_UIntType, __w, true>
134 { static const _UIntType __value = _UIntType(1) << __w; };
136 } // namespace std::tr1::_Private
139 /**
140 * Produces random numbers on a given disribution function using a un uniform
141 * random number generation engine.
142 *
143 * @todo the engine_value_type needs to be studied more carefully.
144 */
145 template<typename _Engine, typename _Dist>
146 class variate_generator
147 {
148 // Concept requirements.
149 __glibcxx_class_requires(_Engine, _CopyConstructibleConcept)
150 // __glibcxx_class_requires(_Engine, _EngineConcept)
151 // __glibcxx_class_requires(_Dist, _EngineConcept)
153 public:
154 typedef _Engine engine_type;
155 typedef _Private::_Adaptor<_Engine, _Dist> engine_value_type;
156 typedef _Dist distribution_type;
157 typedef typename _Dist::result_type result_type;
159 // tr1:5.1.1 table 5.1 requirement
160 typedef typename std::__enable_if<result_type,
161 is_arithmetic<result_type>::value
162 >::__type _IsValidType;
164 public:
165 /**
166 * Constructs a variate generator with the uniform random number
167 * generator @p __eng for the random distribution @p __dist.
168 *
169 * @throws Any exceptions which may thrown by the copy constructors of
170 * the @p _Engine or @p _Dist objects.
171 */
172 variate_generator(engine_type __eng, distribution_type __dist)
173 : _M_engine(__eng), _M_dist(__dist) { }
175 /**
176 * Gets the next generated value on the distribution.
177 */
178 result_type
179 operator()()
180 { return _M_dist(_M_engine); }
182 /**
183 * WTF?
184 */
185 template<typename _Tp>
186 result_type
187 operator()(_Tp __value)
188 { return _M_dist(_M_engine, __value); }
190 /**
191 * Gets a reference to the underlying uniform random number generator
192 * object.
193 */
194 engine_value_type&
195 engine()
196 { return _M_engine; }
198 /**
199 * Gets a const reference to the underlying uniform random number
200 * generator object.
201 */
202 const engine_value_type&
203 engine() const
204 { return _M_engine; }
206 /**
207 * Gets a reference to the underlying random distribution.
208 */
209 distribution_type&
210 distribution()
211 { return _M_dist; }
213 /**
214 * Gets a const reference to the underlying random distribution.
215 */
216 const distribution_type&
217 distribution() const
218 { return _M_dist; }
220 /**
221 * Gets the closed lower bound of the distribution interval.
222 */
223 result_type
224 min() const
225 { return this->distribution().min(); }
227 /**
228 * Gets the closed upper bound of the distribution interval.
229 */
230 result_type
231 max() const
232 { return this->distribution().max(); }
234 private:
235 engine_value_type _M_engine;
236 distribution_type _M_dist;
237 };
240 /**
241 * @addtogroup tr1_random_generators Random Number Generators
242 * @ingroup tr1_random
243 *
244 * These classes define objects which provide random or pseudorandom numbers,
245 * either from a discrete or a continuous interval. The random number
246 * generator supplied as a part of this library are all uniform random number
247 * generators which provide a sequence of random number uniformly distributed
248 * over their range.
249 *
250 * A number generator is a function object with an operator() that takes zero
251 * arguments and returns a number.
252 *
253 * A compliant random number generator must satisy the following requirements.
254 * <table border=1 cellpadding=10 cellspacing=0>
255 * <caption align=top>Random Number Generator Requirements</caption>
256 * <tr><td>To be documented.</td></tr>
257 * </table>
258 *
259 * @{
260 */
262 /**
263 * @brief A model of a linear congruential random number generator.
264 *
265 * A random number generator that produces pseudorandom numbers using the
266 * linear function @f$x_{i+1}\leftarrow(ax_{i} + c) \bmod m @f$.
267 *
268 * The template parameter @p _UIntType must be an unsigned integral type
269 * large enough to store values up to (__m-1). If the template parameter
270 * @p __m is 0, the modulus @p __m used is
271 * std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template
272 * parameters @p __a and @p __c must be less than @p __m.
273 *
274 * The size of the state is @f$ 1 @f$.
275 */
276 template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
277 class linear_congruential;
279 template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
280 typename _CharT, typename _Traits>
281 std::basic_ostream<_CharT, _Traits>&
282 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
283 const linear_congruential<_UIntType, __a, __c, __m>& __lcr);
285 template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
286 typename _CharT, typename _Traits>
287 std::basic_istream<_CharT, _Traits>&
288 operator>>(std::basic_istream<_CharT, _Traits>& __is,
289 linear_congruential<_UIntType, __a, __c, __m>& __lcr);
291 template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
292 class linear_congruential
293 {
294 __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
295 // __glibcpp_class_requires(__a < __m && __c < __m)
297 public:
298 /** The type of the generated random value. */
299 typedef _UIntType result_type;
301 /** The multiplier. */
302 static const _UIntType multiplier = __a;
303 /** An increment. */
304 static const _UIntType increment = __c;
305 /** The modulus. */
306 static const _UIntType modulus = __m;
308 /**
309 * Constructs a %linear_congruential random number generator engine with
310 * seed @p __s. The default seed value is 1.
311 *
312 * @param __s The initial seed value.
313 */
314 explicit
315 linear_congruential(unsigned long __x0 = 1)
316 { this->seed(__x0); }
318 /**
319 * Constructs a %linear_congruential random number generator engine
320 * seeded from the generator function @p __g.
321 *
322 * @param __g The seed generator function.
323 */
324 template<class _Gen>
325 linear_congruential(_Gen& __g)
326 { this->seed(__g); }
328 /**
329 * Reseeds the %linear_congruential random number generator engine
330 * sequence to the seed @g __s.
331 *
332 * @param __s The new seed.
333 */
334 void
335 seed(unsigned long __s = 1);
337 /**
338 * Reseeds the %linear_congruential random number generator engine
339 * sequence using values from the generator function @p __g.
340 *
341 * @param __g the seed generator function.
342 */
343 template<class _Gen>
344 void
345 seed(_Gen& __g)
346 { seed(__g, typename is_fundamental<_Gen>::type()); }
348 /**
349 * Gets the smallest possible value in the output range.
350 */
351 result_type
352 min() const;
354 /**
355 * Gets the largest possible value in the output range.
356 */
357 result_type
358 max() const;
360 /**
361 * Gets the next random number in the sequence.
362 */
363 result_type
364 operator()();
366 /**
367 * Compares two linear congruential random number generator objects of the
368 * same type for equality.
369 *
370 * @param __lhs A linear congruential random number generator object.
371 * @param __rhs Another linear congruential random number generator obj.
372 *
373 * @returns true if the two objects are equal, false otherwise.
374 */
375 friend bool
376 operator==(const linear_congruential& __lhs,
377 const linear_congruential& __rhs)
378 { return __lhs._M_x == __rhs._M_x; }
380 /**
381 * Compares two linear congruential random number generator objects of the
382 * same type for inequality.
383 *
384 * @param __lhs A linear congruential random number generator object.
385 * @param __rhs Another linear congruential random number generator obj.
386 *
387 * @returns true if the two objects are not equal, false otherwise.
388 */
389 friend bool
390 operator!=(const linear_congruential& __lhs,
391 const linear_congruential& __rhs)
392 { return !(__lhs == __rhs); }
394 /**
395 * Writes the textual representation of the state x(i) of x to @p __os.
396 *
397 * @param __os The output stream.
398 * @param __lcr A % linear_congruential random number generator.
399 * @returns __os.
400 */
401 template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
402 _UIntType1 __m1,
403 typename _CharT, typename _Traits>
404 friend std::basic_ostream<_CharT, _Traits>&
405 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
406 const linear_congruential<_UIntType1, __a1, __c1,
407 __m1>& __lcr);
409 /**
410 * Sets the state of the engine by reading its textual
411 * representation from @p __is.
412 *
413 * The textual representation must have been previously written using an
414 * output stream whose imbued locale and whose type's template
415 * specialization arguments _CharT and _Traits were the same as those of
416 * @p __is.
417 *
418 * @param __is The input stream.
419 * @param __lcr A % linear_congruential random number generator.
420 * @returns __is.
421 */
422 template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
423 _UIntType1 __m1,
424 typename _CharT, typename _Traits>
425 friend std::basic_istream<_CharT, _Traits>&
426 operator>>(std::basic_istream<_CharT, _Traits>& __is,
427 linear_congruential<_UIntType1, __a1, __c1, __m1>& __lcr);
429 private:
430 template<class _Gen>
431 void
432 seed(_Gen& __g, true_type)
433 { return seed(static_cast<unsigned long>(__g)); }
435 template<class _Gen>
436 void
437 seed(_Gen& __g, false_type);
439 private:
440 _UIntType _M_x;
441 };
443 /**
444 * The classic Minimum Standard rand0 of Lewis, Goodman, and Miller.
445 */
446 typedef linear_congruential<unsigned int, 16807, 0, 2147483647> minstd_rand0;
448 /**
449 * An alternative LCR (Lehmer Generator function) .
450 */
451 typedef linear_congruential<unsigned int, 48271, 0, 2147483647> minstd_rand;
454 /**
455 * A generalized feedback shift register discrete random number generator.
456 *
457 * This algorithm avoind multiplication and division and is designed to be
458 * friendly to a pipelined architecture. If the parameters are chosen
459 * correctly, this generator will produce numbers with a very long period and
460 * fairly good apparent entropy, although still not cryptographically strong.
461 *
462 * The best way to use this generator is with the predefined mt19937 class.
463 *
464 * This algorithm was originally invented by Makoto Matsumoto and
465 * Takuji Nishimura.
466 *
467 * @var word_size The number of bits in each element of the state vector.
468 * @var state_size The degree of recursion.
469 * @var shift_size The period parameter.
470 * @var mask_bits The separation point bit index.
471 * @var parameter_a The last row of the twist matrix.
472 * @var output_u The first right-shift tempering matrix parameter.
473 * @var output_s The first left-shift tempering matrix parameter.
474 * @var output_b The first left-shift tempering matrix mask.
475 * @var output_t The second left-shift tempering matrix parameter.
476 * @var output_c The second left-shift tempering matrix mask.
477 * @var output_l The second right-shift tempering matrix parameter.
478 */
479 template<class _UIntType, int __w, int __n, int __m, int __r,
480 _UIntType __a, int __u, int __s, _UIntType __b, int __t,
481 _UIntType __c, int __l>
482 class mersenne_twister;
484 template<class _UIntType, int __w, int __n, int __m, int __r,
485 _UIntType __a, int __u, int __s, _UIntType __b, int __t,
486 _UIntType __c, int __l,
487 typename _CharT, typename _Traits>
488 std::basic_ostream<_CharT, _Traits>&
489 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
490 const mersenne_twister<_UIntType, __w, __n, __m,
491 __r, __a, __u, __s, __b, __t, __c, __l>& __x);
493 template<class _UIntType, int __w, int __n, int __m, int __r,
494 _UIntType __a, int __u, int __s, _UIntType __b, int __t,
495 _UIntType __c, int __l,
496 typename _CharT, typename _Traits>
497 std::basic_istream<_CharT, _Traits>&
498 operator>>(std::basic_istream<_CharT, _Traits>& __is,
499 mersenne_twister<_UIntType, __w, __n, __m,
500 __r, __a, __u, __s, __b, __t, __c, __l>& __x);
502 template<class _UIntType, int __w, int __n, int __m, int __r,
503 _UIntType __a, int __u, int __s, _UIntType __b, int __t,
504 _UIntType __c, int __l>
505 class mersenne_twister
506 {
507 __glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
509 public:
510 // types
511 typedef _UIntType result_type;
513 // parameter values
514 static const int word_size = __w;
515 static const int state_size = __n;
516 static const int shift_size = __m;
517 static const int mask_bits = __r;
518 static const _UIntType parameter_a = __a;
519 static const int output_u = __u;
520 static const int output_s = __s;
521 static const _UIntType output_b = __b;
522 static const int output_t = __t;
523 static const _UIntType output_c = __c;
524 static const int output_l = __l;
526 // constructors and member function
527 mersenne_twister()
528 { seed(); }
530 explicit
531 mersenne_twister(unsigned long __value)
532 { seed(__value); }
534 template<class _Gen>
535 mersenne_twister(_Gen& __g)
536 { seed(__g); }
538 void
539 seed()
540 { seed(5489UL); }
542 void
543 seed(unsigned long __value);
545 template<class _Gen>
546 void
547 seed(_Gen& __g)
548 { seed(__g, typename is_fundamental<_Gen>::type()); }
550 result_type
551 min() const
552 { return 0; };
554 result_type
555 max() const
556 { return _Private::_Shift<_UIntType, __w>::__value - 1; }
558 result_type
559 operator()();
561 /**
562 * Compares two % mersenne_twister random number generator objects of
563 * the same type for equality.
564 *
565 * @param __lhs A % mersenne_twister random number generator object.
566 * @param __rhs Another % mersenne_twister random number generator
567 * object.
568 *
569 * @returns true if the two objects are equal, false otherwise.
570 */
571 friend bool
572 operator==(const mersenne_twister& __lhs,
573 const mersenne_twister& __rhs)
574 { return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); }
576 /**
577 * Compares two % mersenne_twister random number generator objects of
578 * the same type for inequality.
579 *
580 * @param __lhs A % mersenne_twister random number generator object.
581 * @param __rhs Another % mersenne_twister random number generator
582 * object.
583 *
584 * @returns true if the two objects are not equal, false otherwise.
585 */
586 friend bool
587 operator!=(const mersenne_twister& __lhs,
588 const mersenne_twister& __rhs)
589 { return !(__lhs == __rhs); }
591 /**
592 * Inserts the current state of a % mersenne_twister random number
593 * generator engine @p __x into the output stream @p __os.
594 *
595 * @param __os An output stream.
596 * @param __x A % mersenne_twister random number generator engine.
597 *
598 * @returns The output stream with the state of @p __x inserted or in
599 * an error state.
600 */
601 template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
602 _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
603 _UIntType1 __c1, int __l1,
604 typename _CharT, typename _Traits>
605 friend std::basic_ostream<_CharT, _Traits>&
606 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
607 const mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
608 __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
610 /**
611 * Extracts the current state of a % mersenne_twister random number
612 * generator engine @p __x from the input stream @p __is.
613 *
614 * @param __is An input stream.
615 * @param __x A % mersenne_twister random number generator engine.
616 *
617 * @returns The input stream with the state of @p __x extracted or in
618 * an error state.
619 */
620 template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
621 _UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
622 _UIntType1 __c1, int __l1,
623 typename _CharT, typename _Traits>
624 friend std::basic_istream<_CharT, _Traits>&
625 operator>>(std::basic_istream<_CharT, _Traits>& __is,
626 mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
627 __a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
629 private:
630 template<class _Gen>
631 void
632 seed(_Gen& __g, true_type)
633 { return seed(static_cast<unsigned long>(__g)); }
635 template<class _Gen>
636 void
637 seed(_Gen& __g, false_type);
639 private:
640 _UIntType _M_x[state_size];
641 int _M_p;
642 };
644 /**
645 * The classic Mersenne Twister.
646 *
647 * Reference:
648 * M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
649 * Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions
650 * on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
651 */
652 typedef mersenne_twister<
653 unsigned long, 32, 624, 397, 31,
654 0x9908b0dful, 11, 7,
655 0x9d2c5680ul, 15,
656 0xefc60000ul, 18
657 > mt19937;
660 /**
661 * @brief The Marsaglia-Zaman generator.
662 *
663 * This is a model of a Generalized Fibonacci discrete random number
664 * generator, sometimes referred to as the SWC generator.
665 *
666 * A discrete random number generator that produces pseudorandom numbers using
667 * @f$x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m @f$.
668 *
669 * The size of the state is @f$ r @f$
670 * and the maximum period of the generator is @f$ m^r - m^s -1 @f$.
671 *
672 * N1688[4.13] says "the template parameter _IntType shall denote an integral
673 * type large enough to store values up to m."
674 *
675 * @if maint
676 * @var _M_x The state of te generator. This is a ring buffer.
677 * @var _M_carry The carry.
678 * @var _M_p Current index of x(i - r).
679 * @endif
680 */
681 template<typename _IntType, _IntType __m, int __s, int __r>
682 class subtract_with_carry;
684 template<typename _IntType, _IntType __m, int __s, int __r,
685 typename _CharT, typename _Traits>
686 std::basic_ostream<_CharT, _Traits>&
687 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
688 const subtract_with_carry<_IntType, __m, __s, __r>& __x);
690 template<typename _IntType, _IntType __m, int __s, int __r,
691 typename _CharT, typename _Traits>
692 std::basic_istream<_CharT, _Traits>&
693 operator>>(std::basic_istream<_CharT, _Traits>& __is,
694 subtract_with_carry<_IntType, __m, __s, __r>& __x);
696 template<typename _IntType, _IntType __m, int __s, int __r>
697 class subtract_with_carry
698 {
699 __glibcxx_class_requires(_IntType, _IntegerConcept)
701 public:
702 /** The type of the generated random value. */
703 typedef _IntType result_type;
705 // parameter values
706 static const _IntType modulus = __m;
707 static const int long_lag = __r;
708 static const int short_lag = __s;
710 public:
711 /**
712 * Constructs a default-initialized % subtract_with_carry random number
713 * generator.
714 */
715 subtract_with_carry()
716 { this->seed(); }
718 /**
719 * Constructs an explicitly seeded % subtract_with_carry random number
720 * generator.
721 */
722 explicit
723 subtract_with_carry(unsigned long __value)
724 { this->seed(__value); }
726 /**
727 * Constructs a % subtract_with_carry random number generator seeded from
728 * the PAD iterated by [__first, last).
729 */
730 template<class _Gen>
731 subtract_with_carry(_Gen& __g)
732 { this->seed(__g); }
734 /**
735 * Seeds the initial state @f$ x_0 @f$ of the random number generator.
736 *
737 * @note This implementation follows the tr1 specification but will
738 * obviously not work correctly on all platforms, since it has hardcoded
739 * values that may overflow ints on some platforms.
740 *
741 * N1688[4.19] modifies this as follows.
742 * If @p __value == 0, sets value to 19780503. In any case, with a linear
743 * congruential generator lcg(i) having parameters @f$ m_{lcg} =
744 * 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value @f$, sets
745 * @f$ x_{-r} \dots x_{-1} @f$ to
746 * @f$ lcg(1) \bmod m \dots lcg(r) \bmod m @f$ respectively.
747 * If @f$ x_{-1} = 0 @f$ set carry to 1, otherwise sets carry to 0.
748 */
749 void
750 seed(unsigned long __value = 19780503);
752 /**
753 * Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry
754 * random number generator.
755 */
756 template<class _Gen>
757 void
758 seed(_Gen& __g)
759 { seed(__g, typename is_fundamental<_Gen>::type()); }
761 /**
762 * Gets the inclusive minimum value of the range of random integers
763 * returned by this generator.
764 */
765 result_type
766 min() const
767 { return 0; }
769 /**
770 * Gets the inclusive maximum value of the range of random integers
771 * returned by this generator.
772 */
773 result_type
774 max() const
775 { return this->modulus - 1; }
777 /**
778 * Gets the next random number in the sequence.
779 */
780 result_type
781 operator()();
783 /**
784 * Compares two % subtract_with_carry random number generator objects of
785 * the same type for equality.
786 *
787 * @param __lhs A % subtract_with_carry random number generator object.
788 * @param __rhs Another % subtract_with_carry random number generator
789 * object.
790 *
791 * @returns true if the two objects are equal, false otherwise.
792 */
793 friend bool
794 operator==(const subtract_with_carry& __lhs,
795 const subtract_with_carry& __rhs)
796 { return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); }
798 /**
799 * Compares two % subtract_with_carry random number generator objects of
800 * the same type for inequality.
801 *
802 * @param __lhs A % subtract_with_carry random number generator object.
803 * @param __rhs Another % subtract_with_carry random number generator
804 * object.
805 *
806 * @returns true if the two objects are not equal, false otherwise.
807 */
808 friend bool
809 operator!=(const subtract_with_carry& __lhs,
810 const subtract_with_carry& __rhs)
811 { return !(__lhs == __rhs); }
813 /**
814 * Inserts the current state of a % subtract_with_carry random number
815 * generator engine @p __x into the output stream @p __os.
816 *
817 * @param __os An output stream.
818 * @param __x A % subtract_with_carry random number generator engine.
819 *
820 * @returns The output stream with the state of @p __x inserted or in
821 * an error state.
822 */
823 template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
824 typename _CharT, typename _Traits>
825 friend std::basic_ostream<_CharT, _Traits>&
826 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
827 const subtract_with_carry<_IntType1, __m1, __s1,
828 __r1>& __x);
830 /**
831 * Extracts the current state of a % subtract_with_carry random number
832 * generator engine @p __x from the input stream @p __is.
833 *
834 * @param __is An input stream.
835 * @param __x A % subtract_with_carry random number generator engine.
836 *
837 * @returns The input stream with the state of @p __x extracted or in
838 * an error state.
839 */
840 template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
841 typename _CharT, typename _Traits>
842 friend std::basic_istream<_CharT, _Traits>&
843 operator>>(std::basic_istream<_CharT, _Traits>& __is,
844 subtract_with_carry<_IntType1, __m1, __s1, __r1>& __x);
846 private:
847 template<class _Gen>
848 void
849 seed(_Gen& __g, true_type)
850 { return seed(static_cast<unsigned long>(__g)); }
852 template<class _Gen>
853 void
854 seed(_Gen& __g, false_type);
856 private:
857 int _M_p;
858 result_type _M_x[long_lag];
859 result_type _M_carry;
860 };
863 /**
864 * Produces random numbers from some base engine by discarding blocks of
865 * data.
866 *
867 * 0 <= @p __r <= @p __p
868 */
869 template<class _UniformRandomNumberGenerator, int __p, int __r>
870 class discard_block;
872 template<class _UniformRandomNumberGenerator, int __p, int __r,
873 typename _CharT, typename _Traits>
874 std::basic_ostream<_CharT, _Traits>&
875 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
876 const discard_block<_UniformRandomNumberGenerator,
877 __p, __r>& __x);
879 template<class _UniformRandomNumberGenerator, int __p, int __r,
880 typename _CharT, typename _Traits>
881 std::basic_istream<_CharT, _Traits>&
882 operator>>(std::basic_istream<_CharT, _Traits>& __is,
883 discard_block<_UniformRandomNumberGenerator, __p, __r>& __x);
885 template<class _UniformRandomNumberGenerator, int __p, int __r>
886 class discard_block
887 {
888 // __glibcxx_class_requires(typename base_type::result_type,
889 // ArithmeticTypeConcept)
891 public:
892 /** The type of the underlying generator engine. */
893 typedef _UniformRandomNumberGenerator base_type;
894 /** The type of the generated random value. */
895 typedef typename base_type::result_type result_type;
897 // parameter values
898 static const int block_size = __p;
899 static const int used_block = __r;
901 /**
902 * Constructs a default %discard_block engine.
903 *
904 * The underlying engine is default constructed as well.
905 */
906 discard_block()
907 : _M_n(0) { }
909 /**
910 * Copy constructs a %discard_block engine.
911 *
912 * Copies an existing base class random number geenerator.
913 * @param rng An existing (base class) engine object.
914 */
915 explicit
916 discard_block(const base_type& __rng)
917 : _M_b(__rng), _M_n(0) { }
919 /**
920 * Seed constructs a %discard_block engine.
921 *
922 * Constructs the underlying generator engine seeded with @p __s.
923 * @param __s A seed value for the base class engine.
924 */
925 explicit
926 discard_block(unsigned long __s)
927 : _M_b(__s), _M_n(0) { }
929 /**
930 * Generator constructs a %discard_block engine.
931 *
932 * @param __g A seed generator function.
933 */
934 template<class _Gen>
935 discard_block(_Gen& __g)
936 : _M_b(__g), _M_n(0) { }
938 /**
939 * Reseeds the %discard_block object with the default seed for the
940 * underlying base class generator engine.
941 */
942 void seed()
943 {
944 _M_b.seed();
945 _M_n = 0;
946 }
948 /**
949 * Reseeds the %discard_block object with the given seed generator
950 * function.
951 * @param __g A seed generator function.
952 */
953 template<class _Gen>
954 void seed(_Gen& __g)
955 {
956 _M_b.seed(__g);
957 _M_n = 0;
958 }
960 /**
961 * Gets a const reference to the underlying generator engine object.
962 */
963 const base_type&
964 base() const
965 { return _M_b; }
967 /**
968 * Gets the minimum value in the generated random number range.
969 */
970 result_type
971 min() const
972 { return _M_b.min(); }
974 /**
975 * Gets the maximum value in the generated random number range.
976 */
977 result_type
978 max() const
979 { return _M_b.max(); }
981 /**
982 * Gets the next value in the generated random number sequence.
983 */
984 result_type
985 operator()();
987 /**
988 * Compares two %discard_block random number generator objects of
989 * the same type for equality.
990 *
991 * @param __lhs A %discard_block random number generator object.
992 * @param __rhs Another %discard_block random number generator
993 * object.
994 *
995 * @returns true if the two objects are equal, false otherwise.
996 */
997 friend bool
998 operator==(const discard_block& __lhs, const discard_block& __rhs)
999 { return (__lhs._M_b == __rhs._M_b) && (__lhs._M_n == __rhs._M_n); }
1001 /**
1002 * Compares two %discard_block random number generator objects of
1003 * the same type for inequality.
1004 *
1005 * @param __lhs A %discard_block random number generator object.
1006 * @param __rhs Another %discard_block random number generator
1007 * object.
1008 *
1009 * @returns true if the two objects are not equal, false otherwise.
1010 */
1011 friend bool
1012 operator!=(const discard_block& __lhs, const discard_block& __rhs)
1013 { return !(__lhs == __rhs); }
1015 /**
1016 * Inserts the current state of a %discard_block random number
1017 * generator engine @p __x into the output stream @p __os.
1018 *
1019 * @param __os An output stream.
1020 * @param __x A %discard_block 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<class _UniformRandomNumberGenerator1, int __p1, int __r1,
1026 typename _CharT, typename _Traits>
1027 friend std::basic_ostream<_CharT, _Traits>&
1028 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1029 const discard_block<_UniformRandomNumberGenerator1,
1030 __p1, __r1>& __x);
1032 /**
1033 * Extracts the current state of a % subtract_with_carry random number
1034 * generator engine @p __x from the input stream @p __is.
1035 *
1036 * @param __is An input stream.
1037 * @param __x A %discard_block 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<class _UniformRandomNumberGenerator1, int __p1, int __r1,
1043 typename _CharT, typename _Traits>
1044 friend std::basic_istream<_CharT, _Traits>&
1045 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1046 discard_block<_UniformRandomNumberGenerator1,
1047 __p1, __r1>& __x);
1049 private:
1050 base_type _M_b;
1051 int _M_n;
1052 };
1055 /**
1056 * James's luxury-level-3 integer adaptation of Luescher's generator.
1057 */
1058 typedef discard_block<
1059 subtract_with_carry<int, (1 << 24), 10, 24>,
1060 223,
1061 24
1062 > ranlux3;
1064 /**
1065 * James's luxury-level-4 integer adaptation of Luescher's generator.
1066 */
1067 typedef discard_block<
1068 subtract_with_carry<int, (1 << 24), 10, 24>,
1069 389,
1070 24
1071 > ranlux4;
1074 /**
1075 * A random number generator adaptor class that combines two random number
1076 * generator engines into a single output sequence.
1077 */
1078 template<class _UniformRandomNumberGenerator1, int __s1,
1079 class _UniformRandomNumberGenerator2, int __s2>
1080 class xor_combine;
1082 template<class _UniformRandomNumberGenerator1, int __s1,
1083 class _UniformRandomNumberGenerator2, int __s2,
1084 typename _CharT, typename _Traits>
1085 std::basic_ostream<_CharT, _Traits>&
1086 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1087 const xor_combine<_UniformRandomNumberGenerator1, __s1,
1088 _UniformRandomNumberGenerator2, __s2>& __x);
1090 template<class _UniformRandomNumberGenerator1, int __s1,
1091 class _UniformRandomNumberGenerator2, int __s2,
1092 typename _CharT, typename _Traits>
1093 std::basic_istream<_CharT, _Traits>&
1094 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1095 xor_combine<_UniformRandomNumberGenerator1, __s1,
1096 _UniformRandomNumberGenerator2, __s2>& __x);
1098 template<class _UniformRandomNumberGenerator1, int __s1,
1099 class _UniformRandomNumberGenerator2, int __s2>
1100 class xor_combine
1101 {
1102 // __glibcxx_class_requires(typename _UniformRandomNumberGenerator1::
1103 // result_type, ArithmeticTypeConcept)
1104 // __glibcxx_class_requires(typename _UniformRandomNumberGenerator2::
1105 // result_type, ArithmeticTypeConcept)
1107 public:
1108 /** The type of the the first underlying generator engine. */
1109 typedef _UniformRandomNumberGenerator1 base1_type;
1110 /** The type of the the second underlying generator engine. */
1111 typedef _UniformRandomNumberGenerator2 base2_type;
1113 private:
1114 typedef typename base1_type::result_type _Result_type1;
1115 typedef typename base2_type::result_type _Result_type2;
1117 public:
1118 /** The type of the generated random value. */
1119 typedef typename _Private::_Select<
1120 (sizeof(_Result_type1) > sizeof(_Result_type2)),
1121 _Result_type1, _Result_type2>::_Type result_type;
1123 // parameter values
1124 static const int shift1 = __s1;
1125 static const int shift2 = __s2;
1127 // constructors and member function
1128 xor_combine() { }
1130 xor_combine(const base1_type& __rng1, const base2_type& __rng2)
1131 : _M_b1(__rng1), _M_b2(__rng2) { }
1133 xor_combine(unsigned long __s)
1134 : _M_b1(__s), _M_b2(__s + 1) { }
1136 template<class _Gen>
1137 xor_combine(_Gen& __g)
1138 : _M_b1(__g), _M_b2(__g) { }
1140 void
1141 seed()
1142 {
1143 _M_b1.seed();
1144 _M_b2.seed();
1145 }
1147 template<class _Gen>
1148 void
1149 seed(_Gen& __g)
1150 {
1151 _M_b1.seed(__g);
1152 _M_b2.seed(__g);
1153 }
1155 const base1_type&
1156 base1() const
1157 { return _M_b1; }
1159 const base2_type&
1160 base2() const
1161 { return _M_b2; }
1163 result_type
1164 min() const
1165 { return _M_b1.min() ^ _M_b2.min(); }
1167 result_type
1168 max() const
1169 { return _M_b1.max() | _M_b2.max(); }
1171 /**
1172 * Gets the next random number in the sequence.
1173 */
1174 result_type
1175 operator()()
1176 { return ((_M_b1() << shift1) ^ (_M_b2() << shift2)); }
1178 /**
1179 * Compares two %xor_combine random number generator objects of
1180 * the same type for equality.
1181 *
1182 * @param __lhs A %xor_combine random number generator object.
1183 * @param __rhs Another %xor_combine random number generator
1184 * object.
1185 *
1186 * @returns true if the two objects are equal, false otherwise.
1187 */
1188 friend bool
1189 operator==(const xor_combine& __lhs, const xor_combine& __rhs)
1190 {
1191 return (__lhs.base1() == __rhs.base1())
1192 && (__lhs.base2() == __rhs.base2());
1193 }
1195 /**
1196 * Compares two %xor_combine random number generator objects of
1197 * the same type for inequality.
1198 *
1199 * @param __lhs A %xor_combine random number generator object.
1200 * @param __rhs Another %xor_combine random number generator
1201 * object.
1202 *
1203 * @returns true if the two objects are not equal, false otherwise.
1204 */
1205 friend bool
1206 operator!=(const xor_combine& __lhs, const xor_combine& __rhs)
1207 { return !(__lhs == __rhs); }
1209 /**
1210 * Inserts the current state of a %xor_combine random number
1211 * generator engine @p __x into the output stream @p __os.
1212 *
1213 * @param __os An output stream.
1214 * @param __x A %xor_combine random number generator engine.
1215 *
1216 * @returns The output stream with the state of @p __x inserted or in
1217 * an error state.
1218 */
1219 template<class _UniformRandomNumberGenerator11, int __s11,
1220 class _UniformRandomNumberGenerator21, int __s21,
1221 typename _CharT, typename _Traits>
1222 friend std::basic_ostream<_CharT, _Traits>&
1223 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1224 const xor_combine<_UniformRandomNumberGenerator11, __s11,
1225 _UniformRandomNumberGenerator21, __s21>& __x);
1227 /**
1228 * Extracts the current state of a %xor_combine random number
1229 * generator engine @p __x from the input stream @p __is.
1230 *
1231 * @param __is An input stream.
1232 * @param __x A %xor_combine random number generator engine.
1233 *
1234 * @returns The input stream with the state of @p __x extracted or in
1235 * an error state.
1236 */
1237 template<class _UniformRandomNumberGenerator11, int __s11,
1238 class _UniformRandomNumberGenerator21, int __s21,
1239 typename _CharT, typename _Traits>
1240 friend std::basic_istream<_CharT, _Traits>&
1241 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1242 xor_combine<_UniformRandomNumberGenerator11, __s11,
1243 _UniformRandomNumberGenerator21, __s21>& __x);
1245 private:
1246 base1_type _M_b1;
1247 base2_type _M_b2;
1248 };
1251 /**
1252 * A standard interface to a platform-specific non-deterministic random number
1253 * generator (if any are available).
1254 */
1255 class random_device
1256 {
1257 public:
1258 // types
1259 typedef unsigned int result_type;
1261 // constructors, destructors and member functions
1263 #ifdef _GLIBCXX_USE_RANDOM_TR1
1265 explicit
1266 random_device(const std::string& __token = "/dev/urandom")
1267 {
1268 if ((__token != "/dev/urandom" && __token != "/dev/random")
1269 || !_M_filebuf.open(__token.c_str(),
1270 std::ios_base::in | std::ios_base::binary))
1271 std::__throw_runtime_error(__N("random_device::"
1272 "random_device(const std::string&)"));
1273 }
1275 ~random_device()
1276 { _M_filebuf.close(); }
1278 #else
1280 explicit
1281 random_device(const std::string& __token = "mt19937")
1282 : _M_mt(_M_strtoul(__token)) { }
1284 private:
1285 static unsigned long
1286 _M_strtoul(const std::string& __str)
1287 {
1288 unsigned long __ret = 5489UL;
1289 if (__str != "mt19937")
1290 {
1291 const char* __nptr = __str.c_str();
1292 char* __endptr;
1293 __ret = std::strtoul(__nptr, &__endptr, 0);
1294 if (*__nptr == '\0' || *__endptr != '\0')
1295 std::__throw_runtime_error(__N("random_device::_M_strtoul"
1296 "(const std::string&)"));
1297 }
1298 return __ret;
1299 }
1301 public:
1303 #endif
1305 result_type
1306 min() const
1307 { return std::numeric_limits<result_type>::min(); }
1309 result_type
1310 max() const
1311 { return std::numeric_limits<result_type>::max(); }
1313 double
1314 entropy() const
1315 { return 0.0; }
1317 result_type
1318 operator()()
1319 {
1320 #ifdef _GLIBCXX_USE_RANDOM_TR1
1321 result_type __ret;
1322 _M_filebuf.sgetn(reinterpret_cast<char*>(&__ret), sizeof(result_type));
1323 return __ret;
1324 #else
1325 return _M_mt();
1326 #endif
1327 }
1329 private:
1330 random_device(const random_device&);
1331 void operator=(const random_device&);
1333 #ifdef _GLIBCXX_USE_RANDOM_TR1
1334 std::filebuf _M_filebuf;
1335 #else
1336 mt19937 _M_mt;
1337 #endif
1338 };
1340 /* @} */ // group tr1_random_generators
1342 /**
1343 * @addtogroup tr1_random_distributions Random Number Distributions
1344 * @ingroup tr1_random
1345 * @{
1346 */
1348 /**
1349 * @addtogroup tr1_random_distributions_discrete Discrete Distributions
1350 * @ingroup tr1_random_distributions
1351 * @{
1352 */
1354 /**
1355 * @brief Uniform discrete distribution for random numbers.
1356 * A discrete random distribution on the range @f$[min, max]@f$ with equal
1357 * probability throughout the range.
1358 */
1359 template<typename _IntType = int>
1360 class uniform_int;
1362 template<typename _IntType, typename _CharT, typename _Traits>
1363 std::basic_ostream<_CharT, _Traits>&
1364 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1365 const uniform_int<_IntType>& __x);
1367 template<typename _IntType, typename _CharT, typename _Traits>
1368 std::basic_istream<_CharT, _Traits>&
1369 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1370 uniform_int<_IntType>& __x);
1372 template<typename _IntType>
1373 class uniform_int
1374 {
1375 __glibcxx_class_requires(_IntType, _IntegerConcept)
1377 public:
1378 /** The type of the parameters of the distribution. */
1379 typedef _IntType input_type;
1380 /** The type of the range of the distribution. */
1381 typedef _IntType result_type;
1383 public:
1384 /**
1385 * Constructs a uniform distribution object.
1386 */
1387 explicit
1388 uniform_int(_IntType __min = 0, _IntType __max = 9)
1389 : _M_min(__min), _M_max(__max)
1390 {
1391 _GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
1392 }
1394 /**
1395 * Gets the inclusive lower bound of the distribution range.
1396 */
1397 result_type
1398 min() const
1399 { return _M_min; }
1401 /**
1402 * Gets the inclusive upper bound of the distribution range.
1403 */
1404 result_type
1405 max() const
1406 { return _M_max; }
1408 /**
1409 * Resets the distribution state.
1410 *
1411 * Does nothing for the uniform integer distribution.
1412 */
1413 void
1414 reset() { }
1416 /**
1417 * Gets a uniformly distributed random number in the range
1418 * @f$(min, max)@f$.
1419 */
1420 template<typename _UniformRandomNumberGenerator>
1421 result_type
1422 operator()(_UniformRandomNumberGenerator& __urng)
1423 { return (__urng() % (_M_max - _M_min + 1)) + _M_min; }
1425 /**
1426 * Gets a uniform random number in the range @f$[0, n)@f$.
1427 *
1428 * This function is aimed at use with std::random_shuffle.
1429 */
1430 template<typename _UniformRandomNumberGenerator>
1431 result_type
1432 operator()(_UniformRandomNumberGenerator& __urng, result_type __n)
1433 { return __urng() % __n; }
1435 /**
1436 * Inserts a %uniform_int random number distribution @p __x into the
1437 * output stream @p os.
1438 *
1439 * @param __os An output stream.
1440 * @param __x A %uniform_int random number distribution.
1441 *
1442 * @returns The output stream with the state of @p __x inserted or in
1443 * an error state.
1444 */
1445 template<typename _IntType1, typename _CharT, typename _Traits>
1446 friend std::basic_ostream<_CharT, _Traits>&
1447 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1448 const uniform_int<_IntType1>& __x);
1450 /**
1451 * Extracts a %unform_int random number distribution
1452 * @p __x from the input stream @p __is.
1453 *
1454 * @param __is An input stream.
1455 * @param __x A %uniform_int random number generator engine.
1456 *
1457 * @returns The input stream with @p __x extracted or in an error state.
1458 */
1459 template<typename _IntType1, typename _CharT, typename _Traits>
1460 friend std::basic_istream<_CharT, _Traits>&
1461 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1462 uniform_int<_IntType1>& __x);
1464 private:
1465 _IntType _M_min;
1466 _IntType _M_max;
1467 };
1470 /**
1471 * @brief A Bernoulli random number distribution.
1472 *
1473 * Generates a sequence of true and false values with likelihood @f$ p @f$
1474 * that true will come up and @f$ (1 - p) @f$ that false will appear.
1475 */
1476 class bernoulli_distribution;
1478 template<typename _CharT, typename _Traits>
1479 std::basic_ostream<_CharT, _Traits>&
1480 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1481 const bernoulli_distribution& __x);
1483 class bernoulli_distribution
1484 {
1485 public:
1486 typedef int input_type;
1487 typedef bool result_type;
1489 public:
1490 /**
1491 * Constructs a Bernoulli distribution with likelihood @p p.
1492 *
1493 * @param __p [IN] The likelihood of a true result being returned. Must
1494 * be in the interval @f$ [0, 1] @f$.
1495 */
1496 explicit
1497 bernoulli_distribution(double __p = 0.5)
1498 : _M_p(__p)
1499 {
1500 _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0));
1501 }
1503 /**
1504 * Gets the @p p parameter of the distribution.
1505 */
1506 double
1507 p() const
1508 { return _M_p; }
1510 /**
1511 * Resets the distribution state.
1512 *
1513 * Does nothing for a bernoulli distribution.
1514 */
1515 void
1516 reset() { }
1518 /**
1519 * Gets the next value in the Bernoullian sequence.
1520 */
1521 template<class UniformRandomNumberGenerator>
1522 result_type
1523 operator()(UniformRandomNumberGenerator& __urng)
1524 {
1525 if (__urng() < _M_p)
1526 return true;
1527 return false;
1528 }
1530 /**
1531 * Inserts a %bernoulli_distribution random number distribution
1532 * @p __x into the output stream @p __os.
1533 *
1534 * @param __os An output stream.
1535 * @param __x A %bernoulli_distribution random number distribution.
1536 *
1537 * @returns The output stream with the state of @p __x inserted or in
1538 * an error state.
1539 */
1540 template<typename _CharT, typename _Traits>
1541 friend std::basic_ostream<_CharT, _Traits>&
1542 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1543 const bernoulli_distribution& __x);
1545 /**
1546 * Extracts a %bernoulli_distribution random number distribution
1547 * @p __x from the input stream @p __is.
1548 *
1549 * @param __is An input stream.
1550 * @param __x A %bernoulli_distribution random number generator engine.
1551 *
1552 * @returns The input stream with @p __x extracted or in an error state.
1553 */
1554 template<typename _CharT, typename _Traits>
1555 friend std::basic_istream<_CharT, _Traits>&
1556 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1557 bernoulli_distribution& __x)
1558 { return __is >> __x._M_p; }
1560 protected:
1561 double _M_p;
1562 };
1565 /**
1566 * @brief A discrete geometric random number distribution.
1567 *
1568 * The formula for the geometric probability mass function is
1569 * @f$ p(i) = (1 - p)p^{i-1} @f$ where @f$ p @f$ is the parameter of the
1570 * distribution.
1571 */
1572 template<typename _IntType = int, typename _RealType = double>
1573 class geometric_distribution;
1575 template<typename _IntType, typename _RealType,
1576 typename _CharT, typename _Traits>
1577 std::basic_ostream<_CharT, _Traits>&
1578 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1579 const geometric_distribution<_IntType, _RealType>& __x);
1581 template<typename _IntType, typename _RealType>
1582 class geometric_distribution
1583 {
1584 public:
1585 // types
1586 typedef _RealType input_type;
1587 typedef _IntType result_type;
1589 // constructors and member function
1591 explicit
1592 geometric_distribution(const _RealType& __p = _RealType(0.5))
1593 : _M_p(__p), _M_log_p(std::log(_M_p))
1594 {
1595 _GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0));
1596 }
1598 /**
1599 * Gets the distribution parameter @p p.
1600 */
1601 _RealType
1602 p() const
1603 { return _M_p; }
1605 void
1606 reset() { }
1608 template<class _UniformRandomNumberGenerator>
1609 result_type
1610 operator()(_UniformRandomNumberGenerator& __urng)
1611 { return result_type(std::ceil(std::log(__urng()) / _M_log_p)); }
1613 /**
1614 * Inserts a %geometric_distribution random number distribution
1615 * @p __x into the output stream @p __os.
1616 *
1617 * @param __os An output stream.
1618 * @param __x A %geometric_distribution random number distribution.
1619 *
1620 * @returns The output stream with the state of @p __x inserted or in
1621 * an error state.
1622 */
1623 template<typename _IntType1, typename _RealType1,
1624 typename _CharT, typename _Traits>
1625 friend std::basic_ostream<_CharT, _Traits>&
1626 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1627 const geometric_distribution<_IntType1, _RealType1>& __x);
1629 /**
1630 * Extracts a %geometric_distribution random number distribution
1631 * @p __x from the input stream @p __is.
1632 *
1633 * @param __is An input stream.
1634 * @param __x A %geometric_distribution random number generator engine.
1635 *
1636 * @returns The input stream with @p __x extracted or in an error state.
1637 */
1638 template<typename _CharT, typename _Traits>
1639 friend std::basic_istream<_CharT, _Traits>&
1640 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1641 geometric_distribution& __x)
1642 {
1643 __is >> __x._M_p;
1644 __x._M_log_p = std::log(__x._M_p);
1645 return __is;
1646 }
1648 protected:
1649 _RealType _M_p;
1650 _RealType _M_log_p;
1651 };
1653 /* @} */ // group tr1_random_distributions_discrete
1655 /**
1656 * @addtogroup tr1_random_distributions_continuous Continuous Distributions
1657 * @ingroup tr1_random_distributions
1658 * @{
1659 */
1661 /**
1662 * @brief Uniform continuous distribution for random numbers.
1663 *
1664 * A continuous random distribution on the range [min, max) with equal
1665 * probability throughout the range. The URNG should be real-valued and
1666 * deliver number in the range [0, 1).
1667 */
1668 template<typename _RealType = double>
1669 class uniform_real;
1671 template<typename _RealType, typename _CharT, typename _Traits>
1672 std::basic_ostream<_CharT, _Traits>&
1673 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1674 const uniform_real<_RealType>& __x);
1676 template<typename _RealType, typename _CharT, typename _Traits>
1677 std::basic_istream<_CharT, _Traits>&
1678 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1679 uniform_real<_RealType>& __x);
1681 template<typename _RealType>
1682 class uniform_real
1683 {
1684 public:
1685 // types
1686 typedef _RealType input_type;
1687 typedef _RealType result_type;
1689 public:
1690 /**
1691 * Constructs a uniform_real object.
1692 *
1693 * @param __min [IN] The lower bound of the distribution.
1694 * @param __max [IN] The upper bound of the distribution.
1695 */
1696 explicit
1697 uniform_real(_RealType __min = _RealType(0),
1698 _RealType __max = _RealType(1))
1699 : _M_min(__min), _M_max(__max)
1700 {
1701 _GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
1702 }
1704 result_type
1705 min() const
1706 { return _M_min; }
1708 result_type
1709 max() const
1710 { return _M_max; }
1712 void
1713 reset() { }
1715 template<class _UniformRandomNumberGenerator>
1716 result_type
1717 operator()(_UniformRandomNumberGenerator& __urng)
1718 { return (__urng() * (_M_max - _M_min)) + _M_min; }
1720 /**
1721 * Inserts a %uniform_real random number distribution @p __x into the
1722 * output stream @p __os.
1723 *
1724 * @param __os An output stream.
1725 * @param __x A %uniform_real random number distribution.
1726 *
1727 * @returns The output stream with the state of @p __x inserted or in
1728 * an error state.
1729 */
1730 template<typename _RealType1, typename _CharT, typename _Traits>
1731 friend std::basic_ostream<_CharT, _Traits>&
1732 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1733 const uniform_real<_RealType1>& __x);
1735 /**
1736 * Extracts a %unform_real random number distribution
1737 * @p __x from the input stream @p __is.
1738 *
1739 * @param __is An input stream.
1740 * @param __x A %uniform_real random number generator engine.
1741 *
1742 * @returns The input stream with @p __x extracted or in an error state.
1743 */
1744 template<typename _RealType1, typename _CharT, typename _Traits>
1745 friend std::basic_istream<_CharT, _Traits>&
1746 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1747 uniform_real<_RealType1>& __x);
1749 protected:
1750 _RealType _M_min;
1751 _RealType _M_max;
1752 };
1755 /**
1756 * @brief An exponential continuous distribution for random numbers.
1757 *
1758 * The formula for the exponential probability mass function is
1759 * @f$ p(x) = \lambda e^{-\lambda x} @f$.
1760 *
1761 * <table border=1 cellpadding=10 cellspacing=0>
1762 * <caption align=top>Distribution Statistics</caption>
1763 * <tr><td>Mean</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
1764 * <tr><td>Median</td><td>@f$ \frac{\ln 2}{\lambda} @f$</td></tr>
1765 * <tr><td>Mode</td><td>@f$ zero @f$</td></tr>
1766 * <tr><td>Range</td><td>@f$[0, \infty]@f$</td></tr>
1767 * <tr><td>Standard Deviation</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
1768 * </table>
1769 */
1770 template<typename _RealType = double>
1771 class exponential_distribution;
1773 template<typename _RealType, typename _CharT, typename _Traits>
1774 std::basic_ostream<_CharT, _Traits>&
1775 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1776 const exponential_distribution<_RealType>& __x);
1778 template<typename _RealType>
1779 class exponential_distribution
1780 {
1781 public:
1782 // types
1783 typedef _RealType input_type;
1784 typedef _RealType result_type;
1786 public:
1787 /**
1788 * Constructs an exponential distribution with inverse scale parameter
1789 * @f$ \lambda @f$.
1790 */
1791 explicit
1792 exponential_distribution(const result_type& __lambda = result_type(1))
1793 : _M_lambda(__lambda)
1794 {
1795 _GLIBCXX_DEBUG_ASSERT(_M_lambda > 0);
1796 }
1798 /**
1799 * Gets the inverse scale parameter of the distribution.
1800 */
1801 _RealType
1802 lambda() const
1803 { return _M_lambda; }
1805 /**
1806 * Resets the distribution.
1807 *
1808 * Has no effect on exponential distributions.
1809 */
1810 void
1811 reset() { }
1813 template<class _UniformRandomNumberGenerator>
1814 result_type
1815 operator()(_UniformRandomNumberGenerator& __urng)
1816 { return -std::log(__urng()) / _M_lambda; }
1818 /**
1819 * Inserts a %exponential_distribution random number distribution
1820 * @p __x into the output stream @p __os.
1821 *
1822 * @param __os An output stream.
1823 * @param __x A %exponential_distribution random number distribution.
1824 *
1825 * @returns The output stream with the state of @p __x inserted or in
1826 * an error state.
1827 */
1828 template<typename _RealType1, typename _CharT, typename _Traits>
1829 friend std::basic_ostream<_CharT, _Traits>&
1830 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1831 const exponential_distribution<_RealType1>& __x);
1833 /**
1834 * Extracts a %exponential_distribution random number distribution
1835 * @p __x from the input stream @p __is.
1836 *
1837 * @param __is An input stream.
1838 * @param __x A %exponential_distribution random number generator engine.
1839 *
1840 * @returns The input stream with @p __x extracted or in an error state.
1841 */
1842 template<typename _CharT, typename _Traits>
1843 friend std::basic_istream<_CharT, _Traits>&
1844 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1845 exponential_distribution& __x)
1846 { return __is >> __x._M_lambda; }
1848 private:
1849 result_type _M_lambda;
1850 };
1853 /**
1854 * @brief A normal continuous distribution for random numbers.
1855 *
1856 * The formula for the normal probability mass function is
1857 * @f$ p(x) = \frac{1}{\sigma \sqrt{2 \pi}}
1858 * e^{- \frac{{x - mean}^ {2}}{2 \sigma ^ {2}} } @f$.
1859 */
1860 template<typename _RealType = double>
1861 class normal_distribution;
1863 template<typename _RealType, typename _CharT, typename _Traits>
1864 std::basic_ostream<_CharT, _Traits>&
1865 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1866 const normal_distribution<_RealType>& __x);
1868 template<typename _RealType, typename _CharT, typename _Traits>
1869 std::basic_istream<_CharT, _Traits>&
1870 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1871 normal_distribution<_RealType>& __x);
1873 template<typename _RealType>
1874 class normal_distribution
1875 {
1876 public:
1877 // types
1878 typedef _RealType input_type;
1879 typedef _RealType result_type;
1881 public:
1882 /**
1883 * Constructs a normal distribution with parameters @f$ mean @f$ and
1884 * @f$ \sigma @f$.
1885 */
1886 explicit
1887 normal_distribution(const result_type& __mean = result_type(0),
1888 const result_type& __sigma = result_type(1))
1889 : _M_mean(__mean), _M_sigma(__sigma), _M_saved_available(false)
1890 {
1891 _GLIBCXX_DEBUG_ASSERT(_M_sigma > 0);
1892 }
1894 /**
1895 * Gets the mean of the distribution.
1896 */
1897 _RealType
1898 mean() const
1899 { return _M_mean; }
1901 /**
1902 * Gets the @f$ \sigma @f$ of the distribution.
1903 */
1904 _RealType
1905 sigma() const
1906 { return _M_sigma; }
1908 /**
1909 * Resets the distribution.
1910 */
1911 void
1912 reset()
1913 { _M_saved_available = false; }
1915 template<class _UniformRandomNumberGenerator>
1916 result_type
1917 operator()(_UniformRandomNumberGenerator& __urng);
1919 /**
1920 * Inserts a %normal_distribution random number distribution
1921 * @p __x into the output stream @p __os.
1922 *
1923 * @param __os An output stream.
1924 * @param __x A %normal_distribution random number distribution.
1925 *
1926 * @returns The output stream with the state of @p __x inserted or in
1927 * an error state.
1928 */
1929 template<typename _RealType1, typename _CharT, typename _Traits>
1930 friend std::basic_ostream<_CharT, _Traits>&
1931 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1932 const normal_distribution<_RealType1>& __x);
1934 /**
1935 * Extracts a %normal_distribution random number distribution
1936 * @p __x from the input stream @p __is.
1937 *
1938 * @param __is An input stream.
1939 * @param __x A %normal_distribution random number generator engine.
1940 *
1941 * @returns The input stream with @p __x extracted or in an error state.
1942 */
1943 template<typename _RealType1, typename _CharT, typename _Traits>
1944 friend std::basic_istream<_CharT, _Traits>&
1945 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1946 normal_distribution<_RealType1>& __x);
1948 private:
1949 result_type _M_mean;
1950 result_type _M_sigma;
1951 result_type _M_saved;
1952 bool _M_saved_available;
1953 };
1955 /* @} */ // group tr1_random_distributions_continuous
1956 /* @} */ // group tr1_random_distributions
1957 /* @} */ // group tr1_random
1959 _GLIBCXX_END_NAMESPACE
1960 }
1962 #include <tr1/random.tcc>
1964 #endif // _STD_TR1_RANDOM