| blob | adf8a241187cac7a7f42e67d72a2dc50098bb059 |
1 // Random number extensions -*- C++ -*-
3 // Copyright (C) 2012 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.
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 // 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.
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/>.
25 /** @file ext/random
26 * This file is a GNU extension to the Standard C++ Library.
27 */
29 #ifndef _EXT_RANDOM
30 #define _EXT_RANDOM 1
32 #pragma GCC system_header
34 #ifndef __GXX_EXPERIMENTAL_CXX0X__
35 # include <bits/c++0x_warning.h>
36 #else
38 #include <random>
39 #include <array>
40 #ifdef __SSE2__
41 # include <x86intrin.h>
42 #endif
44 #ifdef _GLIBCXX_USE_C99_STDINT_TR1
46 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
47 {
48 _GLIBCXX_BEGIN_NAMESPACE_VERSION
50 #if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
52 /* Mersenne twister implementation optimized for vector operations.
53 *
54 * Reference: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/
55 */
56 template<typename _UIntType, size_t __m,
57 size_t __pos1, size_t __sl1, size_t __sl2,
58 size_t __sr1, size_t __sr2,
59 uint32_t __msk1, uint32_t __msk2,
60 uint32_t __msk3, uint32_t __msk4,
61 uint32_t __parity1, uint32_t __parity2,
62 uint32_t __parity3, uint32_t __parity4>
63 class simd_fast_mersenne_twister_engine
64 {
65 static_assert(std::is_unsigned<_UIntType>::value, "template argument "
66 "substituting _UIntType not an unsigned integral type");
67 static_assert(__sr1 < 32, "first right shift too large");
68 static_assert(__sr2 < 16, "second right shift too large");
69 static_assert(__sl1 < 32, "first left shift too large");
70 static_assert(__sl2 < 16, "second left shift too large");
72 public:
73 typedef _UIntType result_type;
75 private:
76 static constexpr size_t m_w = sizeof(result_type) * 8;
77 static constexpr size_t _M_nstate = __m / 128 + 1;
78 static constexpr size_t _M_nstate32 = _M_nstate * 4;
80 static_assert(std::is_unsigned<_UIntType>::value, "template argument "
81 "substituting _UIntType not an unsigned integral type");
82 static_assert(__pos1 < _M_nstate, "POS1 not smaller than state size");
83 static_assert(16 % sizeof(_UIntType) == 0,
84 "UIntType size must divide 16");
86 public:
87 static constexpr size_t state_size = _M_nstate * (16
88 / sizeof(result_type));
89 static constexpr result_type default_seed = 5489u;
91 // constructors and member function
92 explicit
93 simd_fast_mersenne_twister_engine(result_type __sd = default_seed)
94 { seed(__sd); }
96 template<typename _Sseq, typename = typename
97 std::enable_if<!std::is_same<_Sseq,
98 simd_fast_mersenne_twister_engine>::value>
99 ::type>
100 explicit
101 simd_fast_mersenne_twister_engine(_Sseq& __q)
102 { seed(__q); }
104 void
105 seed(result_type __sd = default_seed);
107 template<typename _Sseq>
108 typename std::enable_if<std::is_class<_Sseq>::value>::type
109 seed(_Sseq& __q);
111 static constexpr result_type
112 min()
113 { return 0; };
115 static constexpr result_type
116 max()
117 { return std::numeric_limits<result_type>::max(); }
119 void
120 discard(unsigned long long __z);
122 result_type
123 operator()()
124 {
125 if (__builtin_expect(_M_pos >= state_size, 0))
126 _M_gen_rand();
128 return _M_stateT[_M_pos++];
129 }
131 template<typename _UIntType_2, size_t __m_2,
132 size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
133 size_t __sr1_2, size_t __sr2_2,
134 uint32_t __msk1_2, uint32_t __msk2_2,
135 uint32_t __msk3_2, uint32_t __msk4_2,
136 uint32_t __parity1_2, uint32_t __parity2_2,
137 uint32_t __parity3_2, uint32_t __parity4_2>
138 friend bool
139 operator==(const simd_fast_mersenne_twister_engine<_UIntType_2,
140 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
141 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
142 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __lhs,
143 const simd_fast_mersenne_twister_engine<_UIntType_2,
144 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
145 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
146 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __rhs);
148 template<typename _UIntType_2, size_t __m_2,
149 size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
150 size_t __sr1_2, size_t __sr2_2,
151 uint32_t __msk1_2, uint32_t __msk2_2,
152 uint32_t __msk3_2, uint32_t __msk4_2,
153 uint32_t __parity1_2, uint32_t __parity2_2,
154 uint32_t __parity3_2, uint32_t __parity4_2,
155 typename _CharT, typename _Traits>
156 friend std::basic_ostream<_CharT, _Traits>&
157 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
158 const __gnu_cxx::simd_fast_mersenne_twister_engine
159 <_UIntType_2,
160 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
161 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
162 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);
164 template<typename _UIntType_2, size_t __m_2,
165 size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
166 size_t __sr1_2, size_t __sr2_2,
167 uint32_t __msk1_2, uint32_t __msk2_2,
168 uint32_t __msk3_2, uint32_t __msk4_2,
169 uint32_t __parity1_2, uint32_t __parity2_2,
170 uint32_t __parity3_2, uint32_t __parity4_2,
171 typename _CharT, typename _Traits>
172 friend std::basic_istream<_CharT, _Traits>&
173 operator>>(std::basic_istream<_CharT, _Traits>& __is,
174 __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType_2,
175 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
176 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
177 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);
179 private:
180 union
181 {
182 #ifdef __SSE2__
183 __m128i _M_state[_M_nstate];
184 #endif
185 uint32_t _M_state32[_M_nstate32];
186 result_type _M_stateT[state_size];
187 } __attribute__ ((__aligned__ (16)));
188 size_t _M_pos;
190 void _M_gen_rand(void);
191 void _M_period_certification();
192 };
195 template<typename _UIntType, size_t __m,
196 size_t __pos1, size_t __sl1, size_t __sl2,
197 size_t __sr1, size_t __sr2,
198 uint32_t __msk1, uint32_t __msk2,
199 uint32_t __msk3, uint32_t __msk4,
200 uint32_t __parity1, uint32_t __parity2,
201 uint32_t __parity3, uint32_t __parity4>
202 inline bool
203 operator!=(const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
204 __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
205 __msk4, __parity1, __parity2, __parity3, __parity4>& __lhs,
206 const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
207 __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
208 __msk4, __parity1, __parity2, __parity3, __parity4>& __rhs)
209 { return !(__lhs == __rhs); }
212 /* Definitions for the SIMD-oriented Fast Mersenne Twister as defined
213 * in the C implementation by Daito and Matsumoto, as both a 32-bit
214 * and 64-bit version.
215 */
216 typedef simd_fast_mersenne_twister_engine<uint32_t, 607, 2,
217 15, 3, 13, 3,
218 0xfdff37ffU, 0xef7f3f7dU,
219 0xff777b7dU, 0x7ff7fb2fU,
220 0x00000001U, 0x00000000U,
221 0x00000000U, 0x5986f054U>
222 sfmt607;
224 typedef simd_fast_mersenne_twister_engine<uint64_t, 607, 2,
225 15, 3, 13, 3,
226 0xfdff37ffU, 0xef7f3f7dU,
227 0xff777b7dU, 0x7ff7fb2fU,
228 0x00000001U, 0x00000000U,
229 0x00000000U, 0x5986f054U>
230 sfmt607_64;
233 typedef simd_fast_mersenne_twister_engine<uint32_t, 1279, 7,
234 14, 3, 5, 1,
235 0xf7fefffdU, 0x7fefcfffU,
236 0xaff3ef3fU, 0xb5ffff7fU,
237 0x00000001U, 0x00000000U,
238 0x00000000U, 0x20000000U>
239 sfmt1279;
241 typedef simd_fast_mersenne_twister_engine<uint64_t, 1279, 7,
242 14, 3, 5, 1,
243 0xf7fefffdU, 0x7fefcfffU,
244 0xaff3ef3fU, 0xb5ffff7fU,
245 0x00000001U, 0x00000000U,
246 0x00000000U, 0x20000000U>
247 sfmt1279_64;
250 typedef simd_fast_mersenne_twister_engine<uint32_t, 2281, 12,
251 19, 1, 5, 1,
252 0xbff7ffbfU, 0xfdfffffeU,
253 0xf7ffef7fU, 0xf2f7cbbfU,
254 0x00000001U, 0x00000000U,
255 0x00000000U, 0x41dfa600U>
256 sfmt2281;
258 typedef simd_fast_mersenne_twister_engine<uint64_t, 2281, 12,
259 19, 1, 5, 1,
260 0xbff7ffbfU, 0xfdfffffeU,
261 0xf7ffef7fU, 0xf2f7cbbfU,
262 0x00000001U, 0x00000000U,
263 0x00000000U, 0x41dfa600U>
264 sfmt2281_64;
267 typedef simd_fast_mersenne_twister_engine<uint32_t, 4253, 17,
268 20, 1, 7, 1,
269 0x9f7bffffU, 0x9fffff5fU,
270 0x3efffffbU, 0xfffff7bbU,
271 0xa8000001U, 0xaf5390a3U,
272 0xb740b3f8U, 0x6c11486dU>
273 sfmt4253;
275 typedef simd_fast_mersenne_twister_engine<uint64_t, 4253, 17,
276 20, 1, 7, 1,
277 0x9f7bffffU, 0x9fffff5fU,
278 0x3efffffbU, 0xfffff7bbU,
279 0xa8000001U, 0xaf5390a3U,
280 0xb740b3f8U, 0x6c11486dU>
281 sfmt4253_64;
284 typedef simd_fast_mersenne_twister_engine<uint32_t, 11213, 68,
285 14, 3, 7, 3,
286 0xeffff7fbU, 0xffffffefU,
287 0xdfdfbfffU, 0x7fffdbfdU,
288 0x00000001U, 0x00000000U,
289 0xe8148000U, 0xd0c7afa3U>
290 sfmt11213;
292 typedef simd_fast_mersenne_twister_engine<uint64_t, 11213, 68,
293 14, 3, 7, 3,
294 0xeffff7fbU, 0xffffffefU,
295 0xdfdfbfffU, 0x7fffdbfdU,
296 0x00000001U, 0x00000000U,
297 0xe8148000U, 0xd0c7afa3U>
298 sfmt11213_64;
301 typedef simd_fast_mersenne_twister_engine<uint32_t, 19937, 122,
302 18, 1, 11, 1,
303 0xdfffffefU, 0xddfecb7fU,
304 0xbffaffffU, 0xbffffff6U,
305 0x00000001U, 0x00000000U,
306 0x00000000U, 0x13c9e684U>
307 sfmt19937;
309 typedef simd_fast_mersenne_twister_engine<uint64_t, 19937, 122,
310 18, 1, 11, 1,
311 0xdfffffefU, 0xddfecb7fU,
312 0xbffaffffU, 0xbffffff6U,
313 0x00000001U, 0x00000000U,
314 0x00000000U, 0x13c9e684U>
315 sfmt19937_64;
318 typedef simd_fast_mersenne_twister_engine<uint32_t, 44497, 330,
319 5, 3, 9, 3,
320 0xeffffffbU, 0xdfbebfffU,
321 0xbfbf7befU, 0x9ffd7bffU,
322 0x00000001U, 0x00000000U,
323 0xa3ac4000U, 0xecc1327aU>
324 sfmt44497;
326 typedef simd_fast_mersenne_twister_engine<uint64_t, 44497, 330,
327 5, 3, 9, 3,
328 0xeffffffbU, 0xdfbebfffU,
329 0xbfbf7befU, 0x9ffd7bffU,
330 0x00000001U, 0x00000000U,
331 0xa3ac4000U, 0xecc1327aU>
332 sfmt44497_64;
335 typedef simd_fast_mersenne_twister_engine<uint32_t, 86243, 366,
336 6, 7, 19, 1,
337 0xfdbffbffU, 0xbff7ff3fU,
338 0xfd77efffU, 0xbf9ff3ffU,
339 0x00000001U, 0x00000000U,
340 0x00000000U, 0xe9528d85U>
341 sfmt86243;
343 typedef simd_fast_mersenne_twister_engine<uint64_t, 86243, 366,
344 6, 7, 19, 1,
345 0xfdbffbffU, 0xbff7ff3fU,
346 0xfd77efffU, 0xbf9ff3ffU,
347 0x00000001U, 0x00000000U,
348 0x00000000U, 0xe9528d85U>
349 sfmt86243_64;
352 typedef simd_fast_mersenne_twister_engine<uint32_t, 132049, 110,
353 19, 1, 21, 1,
354 0xffffbb5fU, 0xfb6ebf95U,
355 0xfffefffaU, 0xcff77fffU,
356 0x00000001U, 0x00000000U,
357 0xcb520000U, 0xc7e91c7dU>
358 sfmt132049;
360 typedef simd_fast_mersenne_twister_engine<uint64_t, 132049, 110,
361 19, 1, 21, 1,
362 0xffffbb5fU, 0xfb6ebf95U,
363 0xfffefffaU, 0xcff77fffU,
364 0x00000001U, 0x00000000U,
365 0xcb520000U, 0xc7e91c7dU>
366 sfmt132049_64;
369 typedef simd_fast_mersenne_twister_engine<uint32_t, 216091, 627,
370 11, 3, 10, 1,
371 0xbff7bff7U, 0xbfffffffU,
372 0xbffffa7fU, 0xffddfbfbU,
373 0xf8000001U, 0x89e80709U,
374 0x3bd2b64bU, 0x0c64b1e4U>
375 sfmt216091;
377 typedef simd_fast_mersenne_twister_engine<uint64_t, 216091, 627,
378 11, 3, 10, 1,
379 0xbff7bff7U, 0xbfffffffU,
380 0xbffffa7fU, 0xffddfbfbU,
381 0xf8000001U, 0x89e80709U,
382 0x3bd2b64bU, 0x0c64b1e4U>
383 sfmt216091_64;
385 #endif // __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
387 /**
388 * @brief A beta continuous distribution for random numbers.
389 *
390 * The formula for the beta probability density function is:
391 * @f[
392 * p(x|\alpha,\beta) = \frac{1}{B(\alpha,\beta)}
393 * x^{\alpha - 1} (1 - x)^{\beta - 1}
394 * @f]
395 */
396 template<typename _RealType = double>
397 class beta_distribution
398 {
399 static_assert(std::is_floating_point<_RealType>::value,
400 "template argument not a floating point type");
402 public:
403 /** The type of the range of the distribution. */
404 typedef _RealType result_type;
405 /** Parameter type. */
406 struct param_type
407 {
408 typedef beta_distribution<_RealType> distribution_type;
409 friend class beta_distribution<_RealType>;
411 explicit
412 param_type(_RealType __alpha_val = _RealType(1),
413 _RealType __beta_val = _RealType(1))
414 : _M_alpha(__alpha_val), _M_beta(__beta_val)
415 {
416 _GLIBCXX_DEBUG_ASSERT(_M_alpha > _RealType(0));
417 _GLIBCXX_DEBUG_ASSERT(_M_beta > _RealType(0));
418 }
420 _RealType
421 alpha() const
422 { return _M_alpha; }
424 _RealType
425 beta() const
426 { return _M_beta; }
428 friend bool
429 operator==(const param_type& __p1, const param_type& __p2)
430 { return (__p1._M_alpha == __p2._M_alpha
431 && __p1._M_beta == __p2._M_beta); }
433 private:
434 void
435 _M_initialize();
437 _RealType _M_alpha;
438 _RealType _M_beta;
439 };
441 public:
442 /**
443 * @brief Constructs a beta distribution with parameters
444 * @f$\alpha@f$ and @f$\beta@f$.
445 */
446 explicit
447 beta_distribution(_RealType __alpha_val = _RealType(1),
448 _RealType __beta_val = _RealType(1))
449 : _M_param(__alpha_val, __beta_val)
450 { }
452 explicit
453 beta_distribution(const param_type& __p)
454 : _M_param(__p)
455 { }
457 /**
458 * @brief Resets the distribution state.
459 */
460 void
461 reset()
462 { }
464 /**
465 * @brief Returns the @f$\alpha@f$ of the distribution.
466 */
467 _RealType
468 alpha() const
469 { return _M_param.alpha(); }
471 /**
472 * @brief Returns the @f$\beta@f$ of the distribution.
473 */
474 _RealType
475 beta() const
476 { return _M_param.beta(); }
478 /**
479 * @brief Returns the parameter set of the distribution.
480 */
481 param_type
482 param() const
483 { return _M_param; }
485 /**
486 * @brief Sets the parameter set of the distribution.
487 * @param __param The new parameter set of the distribution.
488 */
489 void
490 param(const param_type& __param)
491 { _M_param = __param; }
493 /**
494 * @brief Returns the greatest lower bound value of the distribution.
495 */
496 result_type
497 min() const
498 { return result_type(0); }
500 /**
501 * @brief Returns the least upper bound value of the distribution.
502 */
503 result_type
504 max() const
505 { return result_type(1); }
507 /**
508 * @brief Generating functions.
509 */
510 template<typename _UniformRandomNumberGenerator>
511 result_type
512 operator()(_UniformRandomNumberGenerator& __urng)
513 { return this->operator()(__urng, this->param()); }
515 template<typename _UniformRandomNumberGenerator>
516 result_type
517 operator()(_UniformRandomNumberGenerator& __urng,
518 const param_type& __p);
520 template<typename _ForwardIterator,
521 typename _UniformRandomNumberGenerator>
522 void
523 __generate(_ForwardIterator __f, _ForwardIterator __t,
524 _UniformRandomNumberGenerator& __urng)
525 { this->__generate(__f, __t, __urng, this->param()); }
527 template<typename _ForwardIterator,
528 typename _UniformRandomNumberGenerator>
529 void
530 __generate(_ForwardIterator __f, _ForwardIterator __t,
531 _UniformRandomNumberGenerator& __urng,
532 const param_type& __p)
533 { this->__generate_impl(__f, __t, __urng, __p); }
535 template<typename _UniformRandomNumberGenerator>
536 void
537 __generate(result_type* __f, result_type* __t,
538 _UniformRandomNumberGenerator& __urng,
539 const param_type& __p)
540 { this->__generate_impl(__f, __t, __urng, __p); }
542 /**
543 * @brief Inserts a %beta_distribution random number distribution
544 * @p __x into the output stream @p __os.
545 *
546 * @param __os An output stream.
547 * @param __x A %beta_distribution random number distribution.
548 *
549 * @returns The output stream with the state of @p __x inserted or in
550 * an error state.
551 */
552 template<typename _RealType1, typename _CharT, typename _Traits>
553 friend std::basic_ostream<_CharT, _Traits>&
554 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
555 const __gnu_cxx::beta_distribution<_RealType1>& __x);
557 /**
558 * @brief Extracts a %beta_distribution random number distribution
559 * @p __x from the input stream @p __is.
560 *
561 * @param __is An input stream.
562 * @param __x A %beta_distribution random number generator engine.
563 *
564 * @returns The input stream with @p __x extracted or in an error state.
565 */
566 template<typename _RealType1, typename _CharT, typename _Traits>
567 friend std::basic_istream<_CharT, _Traits>&
568 operator>>(std::basic_istream<_CharT, _Traits>& __is,
569 __gnu_cxx::beta_distribution<_RealType1>& __x);
571 private:
572 template<typename _ForwardIterator,
573 typename _UniformRandomNumberGenerator>
574 void
575 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
576 _UniformRandomNumberGenerator& __urng,
577 const param_type& __p);
579 param_type _M_param;
580 };
582 /**
583 * @brief Return true if two beta distributions have the same
584 * parameters and the sequences that would be generated
585 * are equal.
586 */
587 template<typename _RealType>
588 inline bool
589 operator==(const __gnu_cxx::beta_distribution<_RealType>& __d1,
590 const __gnu_cxx::beta_distribution<_RealType>& __d2)
591 { return __d1.param() == __d2.param(); }
593 /**
594 * @brief Return true if two beta distributions are different.
595 */
596 template<typename _RealType>
597 inline bool
598 operator!=(const __gnu_cxx::beta_distribution<_RealType>& __d1,
599 const __gnu_cxx::beta_distribution<_RealType>& __d2)
600 { return !(__d1 == __d2); }
603 /**
604 * @brief A multi-variate normal continuous distribution for random numbers.
605 *
606 * The formula for the normal probability density function is
607 * @f[
608 * p(\overrightarrow{x}|\overrightarrow{\mu },\Sigma) =
609 * \frac{1}{\sqrt{(2\pi )^k\det(\Sigma))}}
610 * e^{-\frac{1}{2}(\overrightarrow{x}-\overrightarrow{\mu})^\text{T}
611 * \Sigma ^{-1}(\overrightarrow{x}-\overrightarrow{\mu})}
612 * @f]
613 *
614 * where @f$\overrightarrow{x}@f$ and @f$\overrightarrow{\mu}@f$ are
615 * vectors of dimension @f$k@f$ and @f$\Sigma@f$ is the covariance
616 * matrix (which must be positive-definite).
617 */
618 template<std::size_t _Dimen, typename _RealType = double>
619 class normal_mv_distribution
620 {
621 static_assert(std::is_floating_point<_RealType>::value,
622 "template argument not a floating point type");
623 static_assert(_Dimen != 0, "dimension is zero");
625 public:
626 /** The type of the range of the distribution. */
627 typedef std::array<_RealType, _Dimen> result_type;
628 /** Parameter type. */
629 class param_type
630 {
631 static constexpr size_t _M_t_size = _Dimen * (_Dimen + 1) / 2;
633 public:
634 typedef normal_mv_distribution<_Dimen, _RealType> distribution_type;
635 friend class normal_mv_distribution<_Dimen, _RealType>;
637 param_type()
638 {
639 std::fill(_M_mean.begin(), _M_mean.end(), _RealType(0));
640 auto __it = _M_t.begin();
641 for (size_t __i = 0; __i < _Dimen; ++__i)
642 {
643 std::fill_n(__it, __i, _RealType(0));
644 __it += __i;
645 *__it++ = _RealType(1);
646 }
647 }
649 template<typename _ForwardIterator1, typename _ForwardIterator2>
650 param_type(_ForwardIterator1 __meanbegin,
651 _ForwardIterator1 __meanend,
652 _ForwardIterator2 __varcovbegin,
653 _ForwardIterator2 __varcovend)
654 {
655 __glibcxx_function_requires(_ForwardIteratorConcept<
656 _ForwardIterator1>)
657 __glibcxx_function_requires(_ForwardIteratorConcept<
658 _ForwardIterator2>)
659 _GLIBCXX_DEBUG_ASSERT(std::distance(__meanbegin, __meanend)
660 <= _Dimen);
661 const auto __dist = std::distance(__varcovbegin, __varcovend);
662 _GLIBCXX_DEBUG_ASSERT(__dist == _Dimen * _Dimen
663 || __dist == _Dimen * (_Dimen + 1) / 2
664 || __dist == _Dimen);
666 if (__dist == _Dimen * _Dimen)
667 _M_init_full(__meanbegin, __meanend, __varcovbegin, __varcovend);
668 else if (__dist == _Dimen * (_Dimen + 1) / 2)
669 _M_init_lower(__meanbegin, __meanend, __varcovbegin, __varcovend);
670 else
671 _M_init_diagonal(__meanbegin, __meanend,
672 __varcovbegin, __varcovend);
673 }
675 param_type(std::initializer_list<_RealType> __mean,
676 std::initializer_list<_RealType> __varcov)
677 {
678 _GLIBCXX_DEBUG_ASSERT(__mean.size() <= _Dimen);
679 _GLIBCXX_DEBUG_ASSERT(__varcov.size() == _Dimen * _Dimen
680 || __varcov.size() == _Dimen * (_Dimen + 1) / 2
681 || __varcov.size() == _Dimen);
683 if (__varcov.size() == _Dimen * _Dimen)
684 _M_init_full(__mean.begin(), __mean.end(),
685 __varcov.begin(), __varcov.end());
686 else if (__varcov.size() == _Dimen * (_Dimen + 1) / 2)
687 _M_init_lower(__mean.begin(), __mean.end(),
688 __varcov.begin(), __varcov.end());
689 else
690 _M_init_diagonal(__mean.begin(), __mean.end(),
691 __varcov.begin(), __varcov.end());
692 }
694 std::array<_RealType, _Dimen>
695 mean() const
696 { return _M_mean; }
698 std::array<_RealType, _M_t_size>
699 varcov() const
700 { return _M_t; }
702 friend bool
703 operator==(const param_type& __p1, const param_type& __p2)
704 { return __p1._M_mean == __p2._M_mean && __p1._M_t == __p2._M_t; }
706 private:
707 template <typename _InputIterator1, typename _InputIterator2>
708 void _M_init_full(_InputIterator1 __meanbegin,
709 _InputIterator1 __meanend,
710 _InputIterator2 __varcovbegin,
711 _InputIterator2 __varcovend);
712 template <typename _InputIterator1, typename _InputIterator2>
713 void _M_init_lower(_InputIterator1 __meanbegin,
714 _InputIterator1 __meanend,
715 _InputIterator2 __varcovbegin,
716 _InputIterator2 __varcovend);
717 template <typename _InputIterator1, typename _InputIterator2>
718 void _M_init_diagonal(_InputIterator1 __meanbegin,
719 _InputIterator1 __meanend,
720 _InputIterator2 __varbegin,
721 _InputIterator2 __varend);
723 std::array<_RealType, _Dimen> _M_mean;
724 std::array<_RealType, _M_t_size> _M_t;
725 };
727 public:
728 normal_mv_distribution()
729 : _M_param(), _M_nd()
730 { }
732 template<typename _ForwardIterator1, typename _ForwardIterator2>
733 normal_mv_distribution(_ForwardIterator1 __meanbegin,
734 _ForwardIterator1 __meanend,
735 _ForwardIterator2 __varcovbegin,
736 _ForwardIterator2 __varcovend)
737 : _M_param(__meanbegin, __meanend, __varcovbegin, __varcovend),
738 _M_nd()
739 { }
741 normal_mv_distribution(std::initializer_list<_RealType> __mean,
742 std::initializer_list<_RealType> __varcov)
743 : _M_param(__mean, __varcov), _M_nd()
744 { }
746 explicit
747 normal_mv_distribution(const param_type& __p)
748 : _M_param(__p), _M_nd()
749 { }
751 /**
752 * @brief Resets the distribution state.
753 */
754 void
755 reset()
756 { _M_nd.reset(); }
758 /**
759 * @brief Returns the mean of the distribution.
760 */
761 result_type
762 mean() const
763 { return _M_param.mean(); }
765 /**
766 * @brief Returns the compact form of the variance/covariance
767 * matrix of the distribution.
768 */
769 std::array<_RealType, _Dimen * (_Dimen + 1) / 2>
770 varcov() const
771 { return _M_param.varcov(); }
773 /**
774 * @brief Returns the parameter set of the distribution.
775 */
776 param_type
777 param() const
778 { return _M_param; }
780 /**
781 * @brief Sets the parameter set of the distribution.
782 * @param __param The new parameter set of the distribution.
783 */
784 void
785 param(const param_type& __param)
786 { _M_param = __param; }
788 /**
789 * @brief Returns the greatest lower bound value of the distribution.
790 */
791 result_type
792 min() const
793 { result_type __res;
794 __res.fill(std::numeric_limits<_RealType>::min());
795 return __res; }
797 /**
798 * @brief Returns the least upper bound value of the distribution.
799 */
800 result_type
801 max() const
802 { result_type __res;
803 __res.fill(std::numeric_limits<_RealType>::max());
804 return __res; }
806 /**
807 * @brief Generating functions.
808 */
809 template<typename _UniformRandomNumberGenerator>
810 result_type
811 operator()(_UniformRandomNumberGenerator& __urng)
812 { return this->operator()(__urng, this->param()); }
814 template<typename _UniformRandomNumberGenerator>
815 result_type
816 operator()(_UniformRandomNumberGenerator& __urng,
817 const param_type& __p);
819 template<typename _ForwardIterator,
820 typename _UniformRandomNumberGenerator>
821 void
822 __generate(_ForwardIterator __f, _ForwardIterator __t,
823 _UniformRandomNumberGenerator& __urng)
824 { return this->__generate_impl(__f, __t, __urng, this->param()); }
826 template<typename _ForwardIterator,
827 typename _UniformRandomNumberGenerator>
828 void
829 __generate(_ForwardIterator __f, _ForwardIterator __t,
830 _UniformRandomNumberGenerator& __urng,
831 const param_type& __p)
832 { return this->__generate_impl(__f, __t, __urng, __p); }
834 /**
835 * @brief Return true if two multi-variant normal distributions have
836 * the same parameters and the sequences that would
837 * be generated are equal.
838 */
839 template<size_t _Dimen1, typename _RealType1>
840 friend bool
841 operator==(const
842 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
843 __d1,
844 const
845 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
846 __d2);
848 /**
849 * @brief Inserts a %normal_mv_distribution random number distribution
850 * @p __x into the output stream @p __os.
851 *
852 * @param __os An output stream.
853 * @param __x A %normal_mv_distribution random number distribution.
854 *
855 * @returns The output stream with the state of @p __x inserted or in
856 * an error state.
857 */
858 template<size_t _Dimen1, typename _RealType1,
859 typename _CharT, typename _Traits>
860 friend std::basic_ostream<_CharT, _Traits>&
861 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
862 const
863 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
864 __x);
866 /**
867 * @brief Extracts a %normal_mv_distribution random number distribution
868 * @p __x from the input stream @p __is.
869 *
870 * @param __is An input stream.
871 * @param __x A %normal_mv_distribution random number generator engine.
872 *
873 * @returns The input stream with @p __x extracted or in an error
874 * state.
875 */
876 template<size_t _Dimen1, typename _RealType1,
877 typename _CharT, typename _Traits>
878 friend std::basic_istream<_CharT, _Traits>&
879 operator>>(std::basic_istream<_CharT, _Traits>& __is,
880 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
881 __x);
883 private:
884 template<typename _ForwardIterator,
885 typename _UniformRandomNumberGenerator>
886 void
887 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
888 _UniformRandomNumberGenerator& __urng,
889 const param_type& __p);
891 param_type _M_param;
892 std::normal_distribution<_RealType> _M_nd;
893 };
895 /**
896 * @brief Return true if two multi-variate normal distributions are
897 * different.
898 */
899 template<size_t _Dimen, typename _RealType>
900 inline bool
901 operator!=(const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
902 __d1,
903 const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
904 __d2)
905 { return !(__d1 == __d2); }
908 /**
909 * @brief A Rice continuous distribution for random numbers.
910 *
911 * The formula for the Rice probability density function is
912 * @f[
913 * p(x|\nu,\sigma) = \frac{x}{\sigma^2}
914 * \exp\left(-\frac{x^2+\nu^2}{2\sigma^2}\right)
915 * I_0\left(\frac{x \nu}{\sigma^2}\right)
916 * @f]
917 * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
918 * of order 0 and @f$\nu >= 0@f$ and @f$\sigma > 0@f$.
919 *
920 * <table border=1 cellpadding=10 cellspacing=0>
921 * <caption align=top>Distribution Statistics</caption>
922 * <tr><td>Mean</td><td>@f$\sqrt{\pi/2}L_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
923 * <tr><td>Variance</td><td>@f$2\sigma^2 + \nu^2
924 * + (\pi\sigma^2/2)L^2_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
925 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
926 * </table>
927 * where @f$L_{1/2}(x)@f$ is the Laguerre polynomial of order 1/2.
928 */
929 template<typename _RealType = double>
930 class
931 rice_distribution
932 {
933 static_assert(std::is_floating_point<_RealType>::value,
934 "template argument not a floating point type");
935 public:
936 /** The type of the range of the distribution. */
937 typedef _RealType result_type;
938 /** Parameter type. */
939 struct param_type
940 {
941 typedef rice_distribution<result_type> distribution_type;
943 param_type(result_type __nu_val = result_type(0),
944 result_type __sigma_val = result_type(1))
945 : _M_nu(__nu_val), _M_sigma(__sigma_val)
946 {
947 _GLIBCXX_DEBUG_ASSERT(_M_nu >= result_type(0));
948 _GLIBCXX_DEBUG_ASSERT(_M_sigma > result_type(0));
949 }
951 result_type
952 nu() const
953 { return _M_nu; }
955 result_type
956 sigma() const
957 { return _M_sigma; }
959 friend bool
960 operator==(const param_type& __p1, const param_type& __p2)
961 { return __p1._M_nu == __p2._M_nu
962 && __p1._M_sigma == __p2._M_sigma; }
964 private:
965 void _M_initialize();
967 result_type _M_nu;
968 result_type _M_sigma;
969 };
971 /**
972 * @brief Constructors.
973 */
974 explicit
975 rice_distribution(result_type __nu_val = result_type(0),
976 result_type __sigma_val = result_type(1))
977 : _M_param(__nu_val, __sigma_val),
978 _M_ndx(__nu_val, __sigma_val),
979 _M_ndy(result_type(0), __sigma_val)
980 { }
982 explicit
983 rice_distribution(const param_type& __p)
984 : _M_param(__p),
985 _M_ndx(__p.nu(), __p.sigma()),
986 _M_ndy(result_type(0), __p.sigma())
987 { }
989 /**
990 * @brief Resets the distribution state.
991 */
992 void
993 reset()
994 {
995 _M_ndx.reset();
996 _M_ndy.reset();
997 }
999 /**
1000 * @brief Return the parameters of the distribution.
1001 */
1002 result_type
1003 nu() const
1004 { return _M_param.nu(); }
1006 result_type
1007 sigma() const
1008 { return _M_param.sigma(); }
1010 /**
1011 * @brief Returns the parameter set of the distribution.
1012 */
1013 param_type
1014 param() const
1015 { return _M_param; }
1017 /**
1018 * @brief Sets the parameter set of the distribution.
1019 * @param __param The new parameter set of the distribution.
1020 */
1021 void
1022 param(const param_type& __param)
1023 { _M_param = __param; }
1025 /**
1026 * @brief Returns the greatest lower bound value of the distribution.
1027 */
1028 result_type
1029 min() const
1030 { return result_type(0); }
1032 /**
1033 * @brief Returns the least upper bound value of the distribution.
1034 */
1035 result_type
1036 max() const
1037 { return std::numeric_limits<result_type>::max(); }
1039 /**
1040 * @brief Generating functions.
1041 */
1042 template<typename _UniformRandomNumberGenerator>
1043 result_type
1044 operator()(_UniformRandomNumberGenerator& __urng)
1045 {
1046 result_type __x = this->_M_ndx(__urng);
1047 result_type __y = this->_M_ndy(__urng);
1048 #if _GLIBCXX_USE_C99_MATH_TR1
1049 return std::hypot(__x, __y);
1050 #else
1051 return std::sqrt(__x * __x + __y * __y);
1052 #endif
1053 }
1055 template<typename _UniformRandomNumberGenerator>
1056 result_type
1057 operator()(_UniformRandomNumberGenerator& __urng,
1058 const param_type& __p)
1059 {
1060 typename std::normal_distribution<result_type>::param_type
1061 __px(__p.nu(), __p.sigma()), __py(result_type(0), __p.sigma());
1062 result_type __x = this->_M_ndx(__px, __urng);
1063 result_type __y = this->_M_ndy(__py, __urng);
1064 #if _GLIBCXX_USE_C99_MATH_TR1
1065 return std::hypot(__x, __y);
1066 #else
1067 return std::sqrt(__x * __x + __y * __y);
1068 #endif
1069 }
1071 template<typename _ForwardIterator,
1072 typename _UniformRandomNumberGenerator>
1073 void
1074 __generate(_ForwardIterator __f, _ForwardIterator __t,
1075 _UniformRandomNumberGenerator& __urng)
1076 { this->__generate(__f, __t, __urng, this->param()); }
1078 template<typename _ForwardIterator,
1079 typename _UniformRandomNumberGenerator>
1080 void
1081 __generate(_ForwardIterator __f, _ForwardIterator __t,
1082 _UniformRandomNumberGenerator& __urng,
1083 const param_type& __p)
1084 { this->__generate_impl(__f, __t, __urng, __p); }
1086 template<typename _UniformRandomNumberGenerator>
1087 void
1088 __generate(result_type* __f, result_type* __t,
1089 _UniformRandomNumberGenerator& __urng,
1090 const param_type& __p)
1091 { this->__generate_impl(__f, __t, __urng, __p); }
1093 /**
1094 * @brief Return true if two Rice distributions have
1095 * the same parameters and the sequences that would
1096 * be generated are equal.
1097 */
1098 friend bool
1099 operator==(const rice_distribution& __d1,
1100 const rice_distribution& __d2)
1101 { return (__d1.param() == __d2.param()
1102 && __d1._M_ndx == __d2._M_ndx
1103 && __d1._M_ndy == __d2._M_ndy); }
1105 /**
1106 * @brief Inserts a %rice_distribution random number distribution
1107 * @p __x into the output stream @p __os.
1108 *
1109 * @param __os An output stream.
1110 * @param __x A %rice_distribution random number distribution.
1111 *
1112 * @returns The output stream with the state of @p __x inserted or in
1113 * an error state.
1114 */
1115 template<typename _RealType1, typename _CharT, typename _Traits>
1116 friend std::basic_ostream<_CharT, _Traits>&
1117 operator<<(std::basic_ostream<_CharT, _Traits>&,
1118 const rice_distribution<_RealType1>&);
1120 /**
1121 * @brief Extracts a %rice_distribution random number distribution
1122 * @p __x from the input stream @p __is.
1123 *
1124 * @param __is An input stream.
1125 * @param __x A %rice_distribution random number
1126 * generator engine.
1127 *
1128 * @returns The input stream with @p __x extracted or in an error state.
1129 */
1130 template<typename _RealType1, typename _CharT, typename _Traits>
1131 friend std::basic_istream<_CharT, _Traits>&
1132 operator>>(std::basic_istream<_CharT, _Traits>&,
1133 rice_distribution<_RealType1>&);
1135 private:
1136 template<typename _ForwardIterator,
1137 typename _UniformRandomNumberGenerator>
1138 void
1139 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1140 _UniformRandomNumberGenerator& __urng,
1141 const param_type& __p);
1143 param_type _M_param;
1145 std::normal_distribution<result_type> _M_ndx;
1146 std::normal_distribution<result_type> _M_ndy;
1147 };
1149 /**
1150 * @brief Return true if two Rice distributions are not equal.
1151 */
1152 template<typename _RealType1>
1153 inline bool
1154 operator!=(const rice_distribution<_RealType1>& __d1,
1155 const rice_distribution<_RealType1>& __d2)
1156 { return !(__d1 == __d2); }
1159 /**
1160 * @brief A Nakagami continuous distribution for random numbers.
1161 *
1162 * The formula for the Nakagami probability density function is
1163 * @f[
1164 * p(x|\mu,\omega) = \frac{2\mu^\mu}{\Gamma(\mu)\omega^\mu}
1165 * x^{2\mu-1}e^{-\mu x / \omega}
1166 * @f]
1167 * where @f$\Gamma(z)@f$ is the gamma function and @f$\mu >= 0.5@f$
1168 * and @f$\omega > 0@f$.
1169 */
1170 template<typename _RealType = double>
1171 class
1172 nakagami_distribution
1173 {
1174 static_assert(std::is_floating_point<_RealType>::value,
1175 "template argument not a floating point type");
1177 public:
1178 /** The type of the range of the distribution. */
1179 typedef _RealType result_type;
1180 /** Parameter type. */
1181 struct param_type
1182 {
1183 typedef nakagami_distribution<result_type> distribution_type;
1185 param_type(result_type __mu_val = result_type(1),
1186 result_type __omega_val = result_type(1))
1187 : _M_mu(__mu_val), _M_omega(__omega_val)
1188 {
1189 _GLIBCXX_DEBUG_ASSERT(_M_mu >= result_type(0.5L));
1190 _GLIBCXX_DEBUG_ASSERT(_M_omega > result_type(0));
1191 }
1193 result_type
1194 mu() const
1195 { return _M_mu; }
1197 result_type
1198 omega() const
1199 { return _M_omega; }
1201 friend bool
1202 operator==(const param_type& __p1, const param_type& __p2)
1203 { return __p1._M_mu == __p2._M_mu
1204 && __p1._M_omega == __p2._M_omega; }
1206 private:
1207 void _M_initialize();
1209 result_type _M_mu;
1210 result_type _M_omega;
1211 };
1213 /**
1214 * @brief Constructors.
1215 */
1216 explicit
1217 nakagami_distribution(result_type __mu_val = result_type(1),
1218 result_type __omega_val = result_type(1))
1219 : _M_param(__mu_val, __omega_val),
1220 _M_gd(__mu_val, __omega_val / __mu_val)
1221 { }
1223 explicit
1224 nakagami_distribution(const param_type& __p)
1225 : _M_param(__p),
1226 _M_gd(__p.mu(), __p.omega() / __p.mu())
1227 { }
1229 /**
1230 * @brief Resets the distribution state.
1231 */
1232 void
1233 reset()
1234 { _M_gd.reset(); }
1236 /**
1237 * @brief Return the parameters of the distribution.
1238 */
1239 result_type
1240 mu() const
1241 { return _M_param.mu(); }
1243 result_type
1244 omega() const
1245 { return _M_param.omega(); }
1247 /**
1248 * @brief Returns the parameter set of the distribution.
1249 */
1250 param_type
1251 param() const
1252 { return _M_param; }
1254 /**
1255 * @brief Sets the parameter set of the distribution.
1256 * @param __param The new parameter set of the distribution.
1257 */
1258 void
1259 param(const param_type& __param)
1260 { _M_param = __param; }
1262 /**
1263 * @brief Returns the greatest lower bound value of the distribution.
1264 */
1265 result_type
1266 min() const
1267 { return result_type(0); }
1269 /**
1270 * @brief Returns the least upper bound value of the distribution.
1271 */
1272 result_type
1273 max() const
1274 { return std::numeric_limits<result_type>::max(); }
1276 /**
1277 * @brief Generating functions.
1278 */
1279 template<typename _UniformRandomNumberGenerator>
1280 result_type
1281 operator()(_UniformRandomNumberGenerator& __urng)
1282 { return std::sqrt(this->_M_gd(__urng)); }
1284 template<typename _UniformRandomNumberGenerator>
1285 result_type
1286 operator()(_UniformRandomNumberGenerator& __urng,
1287 const param_type& __p)
1288 {
1289 typename std::gamma_distribution<result_type>::param_type
1290 __pg(__p.mu(), __p.omega() / __p.mu());
1291 return std::sqrt(this->_M_gd(__pg, __urng));
1292 }
1294 template<typename _ForwardIterator,
1295 typename _UniformRandomNumberGenerator>
1296 void
1297 __generate(_ForwardIterator __f, _ForwardIterator __t,
1298 _UniformRandomNumberGenerator& __urng)
1299 { this->__generate(__f, __t, __urng, this->param()); }
1301 template<typename _ForwardIterator,
1302 typename _UniformRandomNumberGenerator>
1303 void
1304 __generate(_ForwardIterator __f, _ForwardIterator __t,
1305 _UniformRandomNumberGenerator& __urng,
1306 const param_type& __p)
1307 { this->__generate_impl(__f, __t, __urng, __p); }
1309 template<typename _UniformRandomNumberGenerator>
1310 void
1311 __generate(result_type* __f, result_type* __t,
1312 _UniformRandomNumberGenerator& __urng,
1313 const param_type& __p)
1314 { this->__generate_impl(__f, __t, __urng, __p); }
1316 /**
1317 * @brief Return true if two Nakagami distributions have
1318 * the same parameters and the sequences that would
1319 * be generated are equal.
1320 */
1321 friend bool
1322 operator==(const nakagami_distribution& __d1,
1323 const nakagami_distribution& __d2)
1324 { return (__d1.param() == __d2.param()
1325 && __d1._M_gd == __d2._M_gd); }
1327 /**
1328 * @brief Inserts a %nakagami_distribution random number distribution
1329 * @p __x into the output stream @p __os.
1330 *
1331 * @param __os An output stream.
1332 * @param __x A %nakagami_distribution random number distribution.
1333 *
1334 * @returns The output stream with the state of @p __x inserted or in
1335 * an error state.
1336 */
1337 template<typename _RealType1, typename _CharT, typename _Traits>
1338 friend std::basic_ostream<_CharT, _Traits>&
1339 operator<<(std::basic_ostream<_CharT, _Traits>&,
1340 const nakagami_distribution<_RealType1>&);
1342 /**
1343 * @brief Extracts a %nakagami_distribution random number distribution
1344 * @p __x from the input stream @p __is.
1345 *
1346 * @param __is An input stream.
1347 * @param __x A %nakagami_distribution random number
1348 * generator engine.
1349 *
1350 * @returns The input stream with @p __x extracted or in an error state.
1351 */
1352 template<typename _RealType1, typename _CharT, typename _Traits>
1353 friend std::basic_istream<_CharT, _Traits>&
1354 operator>>(std::basic_istream<_CharT, _Traits>&,
1355 nakagami_distribution<_RealType1>&);
1357 private:
1358 template<typename _ForwardIterator,
1359 typename _UniformRandomNumberGenerator>
1360 void
1361 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1362 _UniformRandomNumberGenerator& __urng,
1363 const param_type& __p);
1365 param_type _M_param;
1367 std::gamma_distribution<result_type> _M_gd;
1368 };
1370 /**
1371 * @brief Return true if two Nakagami distributions are not equal.
1372 */
1373 template<typename _RealType>
1374 inline bool
1375 operator!=(const nakagami_distribution<_RealType>& __d1,
1376 const nakagami_distribution<_RealType>& __d2)
1377 { return !(__d1 == __d2); }
1380 /**
1381 * @brief A Pareto continuous distribution for random numbers.
1382 *
1383 * The formula for the Pareto cumulative probability function is
1384 * @f[
1385 * P(x|\alpha,\mu) = 1 - \left(\frac{\mu}{x}\right)^\alpha
1386 * @f]
1387 * The formula for the Pareto probability density function is
1388 * @f[
1389 * p(x|\alpha,\mu) = \frac{\alpha + 1}{\mu}
1390 * \left(\frac{\mu}{x}\right)^{\alpha + 1}
1391 * @f]
1392 * where @f$x >= \mu@f$ and @f$\mu > 0@f$, @f$\alpha > 0@f$.
1393 *
1394 * <table border=1 cellpadding=10 cellspacing=0>
1395 * <caption align=top>Distribution Statistics</caption>
1396 * <tr><td>Mean</td><td>@f$\alpha \mu / (\alpha - 1)@f$
1397 * for @f$\alpha > 1@f$</td></tr>
1398 * <tr><td>Variance</td><td>@f$\alpha \mu^2 / [(\alpha - 1)^2(\alpha - 2)]@f$
1399 * for @f$\alpha > 2@f$</td></tr>
1400 * <tr><td>Range</td><td>@f$[\mu, \infty)@f$</td></tr>
1401 * </table>
1402 */
1403 template<typename _RealType = double>
1404 class
1405 pareto_distribution
1406 {
1407 static_assert(std::is_floating_point<_RealType>::value,
1408 "template argument not a floating point type");
1410 public:
1411 /** The type of the range of the distribution. */
1412 typedef _RealType result_type;
1413 /** Parameter type. */
1414 struct param_type
1415 {
1416 typedef pareto_distribution<result_type> distribution_type;
1418 param_type(result_type __alpha_val = result_type(1),
1419 result_type __mu_val = result_type(1))
1420 : _M_alpha(__alpha_val), _M_mu(__mu_val)
1421 {
1422 _GLIBCXX_DEBUG_ASSERT(_M_alpha > result_type(0));
1423 _GLIBCXX_DEBUG_ASSERT(_M_mu > result_type(0));
1424 }
1426 result_type
1427 alpha() const
1428 { return _M_alpha; }
1430 result_type
1431 mu() const
1432 { return _M_mu; }
1434 friend bool
1435 operator==(const param_type& __p1, const param_type& __p2)
1436 { return __p1._M_alpha == __p2._M_alpha && __p1._M_mu == __p2._M_mu; }
1438 private:
1439 void _M_initialize();
1441 result_type _M_alpha;
1442 result_type _M_mu;
1443 };
1445 /**
1446 * @brief Constructors.
1447 */
1448 explicit
1449 pareto_distribution(result_type __alpha_val = result_type(1),
1450 result_type __mu_val = result_type(1))
1451 : _M_param(__alpha_val, __mu_val),
1452 _M_ud()
1453 { }
1455 explicit
1456 pareto_distribution(const param_type& __p)
1457 : _M_param(__p),
1458 _M_ud()
1459 { }
1461 /**
1462 * @brief Resets the distribution state.
1463 */
1464 void
1465 reset()
1466 {
1467 _M_ud.reset();
1468 }
1470 /**
1471 * @brief Return the parameters of the distribution.
1472 */
1473 result_type
1474 alpha() const
1475 { return _M_param.alpha(); }
1477 result_type
1478 mu() const
1479 { return _M_param.mu(); }
1481 /**
1482 * @brief Returns the parameter set of the distribution.
1483 */
1484 param_type
1485 param() const
1486 { return _M_param; }
1488 /**
1489 * @brief Sets the parameter set of the distribution.
1490 * @param __param The new parameter set of the distribution.
1491 */
1492 void
1493 param(const param_type& __param)
1494 { _M_param = __param; }
1496 /**
1497 * @brief Returns the greatest lower bound value of the distribution.
1498 */
1499 result_type
1500 min() const
1501 { return this->mu(); }
1503 /**
1504 * @brief Returns the least upper bound value of the distribution.
1505 */
1506 result_type
1507 max() const
1508 { return std::numeric_limits<result_type>::max(); }
1510 /**
1511 * @brief Generating functions.
1512 */
1513 template<typename _UniformRandomNumberGenerator>
1514 result_type
1515 operator()(_UniformRandomNumberGenerator& __urng)
1516 {
1517 return this->mu() * std::pow(this->_M_ud(__urng),
1518 -result_type(1) / this->alpha());
1519 }
1521 template<typename _UniformRandomNumberGenerator>
1522 result_type
1523 operator()(_UniformRandomNumberGenerator& __urng,
1524 const param_type& __p)
1525 {
1526 return __p.mu() * std::pow(this->_M_ud(__urng),
1527 -result_type(1) / __p.alpha());
1528 }
1530 template<typename _ForwardIterator,
1531 typename _UniformRandomNumberGenerator>
1532 void
1533 __generate(_ForwardIterator __f, _ForwardIterator __t,
1534 _UniformRandomNumberGenerator& __urng)
1535 { this->__generate(__f, __t, __urng, this->param()); }
1537 template<typename _ForwardIterator,
1538 typename _UniformRandomNumberGenerator>
1539 void
1540 __generate(_ForwardIterator __f, _ForwardIterator __t,
1541 _UniformRandomNumberGenerator& __urng,
1542 const param_type& __p)
1543 { this->__generate_impl(__f, __t, __urng, __p); }
1545 template<typename _UniformRandomNumberGenerator>
1546 void
1547 __generate(result_type* __f, result_type* __t,
1548 _UniformRandomNumberGenerator& __urng,
1549 const param_type& __p)
1550 { this->__generate_impl(__f, __t, __urng, __p); }
1552 /**
1553 * @brief Return true if two Pareto distributions have
1554 * the same parameters and the sequences that would
1555 * be generated are equal.
1556 */
1557 friend bool
1558 operator==(const pareto_distribution& __d1,
1559 const pareto_distribution& __d2)
1560 { return (__d1.param() == __d2.param()
1561 && __d1._M_ud == __d2._M_ud); }
1563 /**
1564 * @brief Inserts a %pareto_distribution random number distribution
1565 * @p __x into the output stream @p __os.
1566 *
1567 * @param __os An output stream.
1568 * @param __x A %pareto_distribution random number distribution.
1569 *
1570 * @returns The output stream with the state of @p __x inserted or in
1571 * an error state.
1572 */
1573 template<typename _RealType1, typename _CharT, typename _Traits>
1574 friend std::basic_ostream<_CharT, _Traits>&
1575 operator<<(std::basic_ostream<_CharT, _Traits>&,
1576 const pareto_distribution<_RealType1>&);
1578 /**
1579 * @brief Extracts a %pareto_distribution random number distribution
1580 * @p __x from the input stream @p __is.
1581 *
1582 * @param __is An input stream.
1583 * @param __x A %pareto_distribution random number
1584 * generator engine.
1585 *
1586 * @returns The input stream with @p __x extracted or in an error state.
1587 */
1588 template<typename _RealType1, typename _CharT, typename _Traits>
1589 friend std::basic_istream<_CharT, _Traits>&
1590 operator>>(std::basic_istream<_CharT, _Traits>&,
1591 pareto_distribution<_RealType1>&);
1593 private:
1594 template<typename _ForwardIterator,
1595 typename _UniformRandomNumberGenerator>
1596 void
1597 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1598 _UniformRandomNumberGenerator& __urng,
1599 const param_type& __p);
1601 param_type _M_param;
1603 std::uniform_real_distribution<result_type> _M_ud;
1604 };
1606 /**
1607 * @brief Return true if two Pareto distributions are not equal.
1608 */
1609 template<typename _RealType>
1610 inline bool
1611 operator!=(const pareto_distribution<_RealType>& __d1,
1612 const pareto_distribution<_RealType>& __d2)
1613 { return !(__d1 == __d2); }
1616 /**
1617 * @brief A K continuous distribution for random numbers.
1618 *
1619 * The formula for the K probability density function is
1620 * @f[
1621 * p(x|\lambda, \mu, \nu) = \frac{2}{x}
1622 * \left(\frac{\lambda\nu x}{\mu}\right)^{\frac{\lambda + \nu}{2}}
1623 * \frac{1}{\Gamma(\lambda)\Gamma(\nu)}
1624 * K_{\nu - \lambda}\left(2\sqrt{\frac{\lambda\nu x}{\mu}}\right)
1625 * @f]
1626 * where @f$I_0(z)@f$ is the modified Bessel function of the second kind
1627 * of order @f$\nu - \lambda@f$ and @f$\lambda > 0@f$, @f$\mu > 0@f$
1628 * and @f$\nu > 0@f$.
1629 *
1630 * <table border=1 cellpadding=10 cellspacing=0>
1631 * <caption align=top>Distribution Statistics</caption>
1632 * <tr><td>Mean</td><td>@f$\mu@f$</td></tr>
1633 * <tr><td>Variance</td><td>@f$\mu^2\frac{\lambda + \nu + 1}{\lambda\nu}@f$</td></tr>
1634 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
1635 * </table>
1636 */
1637 template<typename _RealType = double>
1638 class
1639 k_distribution
1640 {
1641 static_assert(std::is_floating_point<_RealType>::value,
1642 "template argument not a floating point type");
1644 public:
1645 /** The type of the range of the distribution. */
1646 typedef _RealType result_type;
1647 /** Parameter type. */
1648 struct param_type
1649 {
1650 typedef k_distribution<result_type> distribution_type;
1652 param_type(result_type __lambda_val = result_type(1),
1653 result_type __mu_val = result_type(1),
1654 result_type __nu_val = result_type(1))
1655 : _M_lambda(__lambda_val), _M_mu(__mu_val), _M_nu(__nu_val)
1656 {
1657 _GLIBCXX_DEBUG_ASSERT(_M_lambda > result_type(0));
1658 _GLIBCXX_DEBUG_ASSERT(_M_mu > result_type(0));
1659 _GLIBCXX_DEBUG_ASSERT(_M_nu > result_type(0));
1660 }
1662 result_type
1663 lambda() const
1664 { return _M_lambda; }
1666 result_type
1667 mu() const
1668 { return _M_mu; }
1670 result_type
1671 nu() const
1672 { return _M_nu; }
1674 friend bool
1675 operator==(const param_type& __p1, const param_type& __p2)
1676 { return __p1._M_lambda == __p2._M_lambda
1677 && __p1._M_mu == __p2._M_mu
1678 && __p1._M_nu == __p2._M_nu; }
1680 private:
1681 void _M_initialize();
1683 result_type _M_lambda;
1684 result_type _M_mu;
1685 result_type _M_nu;
1686 };
1688 /**
1689 * @brief Constructors.
1690 */
1691 explicit
1692 k_distribution(result_type __lambda_val = result_type(1),
1693 result_type __mu_val = result_type(1),
1694 result_type __nu_val = result_type(1))
1695 : _M_param(__lambda_val, __mu_val, __nu_val),
1696 _M_gd1(__lambda_val, result_type(1) / __lambda_val),
1697 _M_gd2(__nu_val, __mu_val / __nu_val)
1698 { }
1700 explicit
1701 k_distribution(const param_type& __p)
1702 : _M_param(__p),
1703 _M_gd1(__p.lambda(), result_type(1) / __p.lambda()),
1704 _M_gd2(__p.nu(), __p.mu() / __p.nu())
1705 { }
1707 /**
1708 * @brief Resets the distribution state.
1709 */
1710 void
1711 reset()
1712 {
1713 _M_gd1.reset();
1714 _M_gd2.reset();
1715 }
1717 /**
1718 * @brief Return the parameters of the distribution.
1719 */
1720 result_type
1721 lambda() const
1722 { return _M_param.lambda(); }
1724 result_type
1725 mu() const
1726 { return _M_param.mu(); }
1728 result_type
1729 nu() const
1730 { return _M_param.nu(); }
1732 /**
1733 * @brief Returns the parameter set of the distribution.
1734 */
1735 param_type
1736 param() const
1737 { return _M_param; }
1739 /**
1740 * @brief Sets the parameter set of the distribution.
1741 * @param __param The new parameter set of the distribution.
1742 */
1743 void
1744 param(const param_type& __param)
1745 { _M_param = __param; }
1747 /**
1748 * @brief Returns the greatest lower bound value of the distribution.
1749 */
1750 result_type
1751 min() const
1752 { return result_type(0); }
1754 /**
1755 * @brief Returns the least upper bound value of the distribution.
1756 */
1757 result_type
1758 max() const
1759 { return std::numeric_limits<result_type>::max(); }
1761 /**
1762 * @brief Generating functions.
1763 */
1764 template<typename _UniformRandomNumberGenerator>
1765 result_type
1766 operator()(_UniformRandomNumberGenerator&);
1768 template<typename _UniformRandomNumberGenerator>
1769 result_type
1770 operator()(_UniformRandomNumberGenerator&, const param_type&);
1772 template<typename _ForwardIterator,
1773 typename _UniformRandomNumberGenerator>
1774 void
1775 __generate(_ForwardIterator __f, _ForwardIterator __t,
1776 _UniformRandomNumberGenerator& __urng)
1777 { this->__generate(__f, __t, __urng, this->param()); }
1779 template<typename _ForwardIterator,
1780 typename _UniformRandomNumberGenerator>
1781 void
1782 __generate(_ForwardIterator __f, _ForwardIterator __t,
1783 _UniformRandomNumberGenerator& __urng,
1784 const param_type& __p)
1785 { this->__generate_impl(__f, __t, __urng, __p); }
1787 template<typename _UniformRandomNumberGenerator>
1788 void
1789 __generate(result_type* __f, result_type* __t,
1790 _UniformRandomNumberGenerator& __urng,
1791 const param_type& __p)
1792 { this->__generate_impl(__f, __t, __urng, __p); }
1794 /**
1795 * @brief Return true if two K distributions have
1796 * the same parameters and the sequences that would
1797 * be generated are equal.
1798 */
1799 friend bool
1800 operator==(const k_distribution& __d1,
1801 const k_distribution& __d2)
1802 { return (__d1.param() == __d2.param()
1803 && __d1._M_gd1 == __d2._M_gd1
1804 && __d1._M_gd2 == __d2._M_gd2); }
1806 /**
1807 * @brief Inserts a %k_distribution random number distribution
1808 * @p __x into the output stream @p __os.
1809 *
1810 * @param __os An output stream.
1811 * @param __x A %k_distribution random number distribution.
1812 *
1813 * @returns The output stream with the state of @p __x inserted or in
1814 * an error state.
1815 */
1816 template<typename _RealType1, typename _CharT, typename _Traits>
1817 friend std::basic_ostream<_CharT, _Traits>&
1818 operator<<(std::basic_ostream<_CharT, _Traits>&,
1819 const k_distribution<_RealType1>&);
1821 /**
1822 * @brief Extracts a %k_distribution random number distribution
1823 * @p __x from the input stream @p __is.
1824 *
1825 * @param __is An input stream.
1826 * @param __x A %k_distribution random number
1827 * generator engine.
1828 *
1829 * @returns The input stream with @p __x extracted or in an error state.
1830 */
1831 template<typename _RealType1, typename _CharT, typename _Traits>
1832 friend std::basic_istream<_CharT, _Traits>&
1833 operator>>(std::basic_istream<_CharT, _Traits>&,
1834 k_distribution<_RealType1>&);
1836 private:
1837 template<typename _ForwardIterator,
1838 typename _UniformRandomNumberGenerator>
1839 void
1840 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1841 _UniformRandomNumberGenerator& __urng,
1842 const param_type& __p);
1844 param_type _M_param;
1846 std::gamma_distribution<result_type> _M_gd1;
1847 std::gamma_distribution<result_type> _M_gd2;
1848 };
1850 /**
1851 * @brief Return true if two K distributions are not equal.
1852 */
1853 template<typename _RealType>
1854 inline bool
1855 operator!=(const k_distribution<_RealType>& __d1,
1856 const k_distribution<_RealType>& __d2)
1857 { return !(__d1 == __d2); }
1860 /**
1861 * @brief An arcsine continuous distribution for random numbers.
1862 *
1863 * The formula for the arcsine probability density function is
1864 * @f[
1865 * p(x|a,b) = \frac{1}{\pi \sqrt{(x - a)(b - x)}}
1866 * @f]
1867 * where @f$x >= a@f$ and @f$x <= b@f$.
1868 *
1869 * <table border=1 cellpadding=10 cellspacing=0>
1870 * <caption align=top>Distribution Statistics</caption>
1871 * <tr><td>Mean</td><td>@f$ (a + b) / 2 @f$</td></tr>
1872 * <tr><td>Variance</td><td>@f$ (b - a)^2 / 8 @f$</td></tr>
1873 * <tr><td>Range</td><td>@f$[a, b]@f$</td></tr>
1874 * </table>
1875 */
1876 template<typename _RealType = double>
1877 class
1878 arcsine_distribution
1879 {
1880 static_assert(std::is_floating_point<_RealType>::value,
1881 "template argument not a floating point type");
1883 public:
1884 /** The type of the range of the distribution. */
1885 typedef _RealType result_type;
1886 /** Parameter type. */
1887 struct param_type
1888 {
1889 typedef arcsine_distribution<result_type> distribution_type;
1891 param_type(result_type __a = result_type(0),
1892 result_type __b = result_type(1))
1893 : _M_a(__a), _M_b(__b)
1894 {
1895 _GLIBCXX_DEBUG_ASSERT(_M_a <= _M_b);
1896 }
1898 result_type
1899 a() const
1900 { return _M_a; }
1902 result_type
1903 b() const
1904 { return _M_b; }
1906 friend bool
1907 operator==(const param_type& __p1, const param_type& __p2)
1908 { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
1910 private:
1911 void _M_initialize();
1913 result_type _M_a;
1914 result_type _M_b;
1915 };
1917 /**
1918 * @brief Constructors.
1919 */
1920 explicit
1921 arcsine_distribution(result_type __a = result_type(0),
1922 result_type __b = result_type(1))
1923 : _M_param(__a, __b),
1924 _M_ud(-1.5707963267948966192313216916397514L,
1925 +1.5707963267948966192313216916397514L)
1926 { }
1928 explicit
1929 arcsine_distribution(const param_type& __p)
1930 : _M_param(__p),
1931 _M_ud(-1.5707963267948966192313216916397514L,
1932 +1.5707963267948966192313216916397514L)
1933 { }
1935 /**
1936 * @brief Resets the distribution state.
1937 */
1938 void
1939 reset()
1940 { _M_ud.reset(); }
1942 /**
1943 * @brief Return the parameters of the distribution.
1944 */
1945 result_type
1946 a() const
1947 { return _M_param.a(); }
1949 result_type
1950 b() const
1951 { return _M_param.b(); }
1953 /**
1954 * @brief Returns the parameter set of the distribution.
1955 */
1956 param_type
1957 param() const
1958 { return _M_param; }
1960 /**
1961 * @brief Sets the parameter set of the distribution.
1962 * @param __param The new parameter set of the distribution.
1963 */
1964 void
1965 param(const param_type& __param)
1966 { _M_param = __param; }
1968 /**
1969 * @brief Returns the greatest lower bound value of the distribution.
1970 */
1971 result_type
1972 min() const
1973 { return this->a(); }
1975 /**
1976 * @brief Returns the least upper bound value of the distribution.
1977 */
1978 result_type
1979 max() const
1980 { return this->b(); }
1982 /**
1983 * @brief Generating functions.
1984 */
1985 template<typename _UniformRandomNumberGenerator>
1986 result_type
1987 operator()(_UniformRandomNumberGenerator& __urng)
1988 {
1989 result_type __x = std::sin(this->_M_ud(__urng));
1990 return (__x * (this->b() - this->a())
1991 + this->a() + this->b()) / result_type(2);
1992 }
1994 template<typename _UniformRandomNumberGenerator>
1995 result_type
1996 operator()(_UniformRandomNumberGenerator& __urng,
1997 const param_type& __p)
1998 {
1999 result_type __x = std::sin(this->_M_ud(__urng));
2000 return (__x * (__p.b() - __p.a())
2001 + __p.a() + __p.b()) / result_type(2);
2002 }
2004 template<typename _ForwardIterator,
2005 typename _UniformRandomNumberGenerator>
2006 void
2007 __generate(_ForwardIterator __f, _ForwardIterator __t,
2008 _UniformRandomNumberGenerator& __urng)
2009 { this->__generate(__f, __t, __urng, this->param()); }
2011 template<typename _ForwardIterator,
2012 typename _UniformRandomNumberGenerator>
2013 void
2014 __generate(_ForwardIterator __f, _ForwardIterator __t,
2015 _UniformRandomNumberGenerator& __urng,
2016 const param_type& __p)
2017 { this->__generate_impl(__f, __t, __urng, __p); }
2019 template<typename _UniformRandomNumberGenerator>
2020 void
2021 __generate(result_type* __f, result_type* __t,
2022 _UniformRandomNumberGenerator& __urng,
2023 const param_type& __p)
2024 { this->__generate_impl(__f, __t, __urng, __p); }
2026 /**
2027 * @brief Return true if two arcsine distributions have
2028 * the same parameters and the sequences that would
2029 * be generated are equal.
2030 */
2031 friend bool
2032 operator==(const arcsine_distribution& __d1,
2033 const arcsine_distribution& __d2)
2034 { return (__d1.param() == __d2.param()
2035 && __d1._M_ud == __d2._M_ud); }
2037 /**
2038 * @brief Inserts a %arcsine_distribution random number distribution
2039 * @p __x into the output stream @p __os.
2040 *
2041 * @param __os An output stream.
2042 * @param __x A %arcsine_distribution random number distribution.
2043 *
2044 * @returns The output stream with the state of @p __x inserted or in
2045 * an error state.
2046 */
2047 template<typename _RealType1, typename _CharT, typename _Traits>
2048 friend std::basic_ostream<_CharT, _Traits>&
2049 operator<<(std::basic_ostream<_CharT, _Traits>&,
2050 const arcsine_distribution<_RealType1>&);
2052 /**
2053 * @brief Extracts a %arcsine_distribution random number distribution
2054 * @p __x from the input stream @p __is.
2055 *
2056 * @param __is An input stream.
2057 * @param __x A %arcsine_distribution random number
2058 * generator engine.
2059 *
2060 * @returns The input stream with @p __x extracted or in an error state.
2061 */
2062 template<typename _RealType1, typename _CharT, typename _Traits>
2063 friend std::basic_istream<_CharT, _Traits>&
2064 operator>>(std::basic_istream<_CharT, _Traits>&,
2065 arcsine_distribution<_RealType1>&);
2067 private:
2068 template<typename _ForwardIterator,
2069 typename _UniformRandomNumberGenerator>
2070 void
2071 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2072 _UniformRandomNumberGenerator& __urng,
2073 const param_type& __p);
2075 param_type _M_param;
2077 std::uniform_real_distribution<result_type> _M_ud;
2078 };
2080 /**
2081 * @brief Return true if two arcsine distributions are not equal.
2082 */
2083 template<typename _RealType>
2084 inline bool
2085 operator!=(const arcsine_distribution<_RealType>& __d1,
2086 const arcsine_distribution<_RealType>& __d2)
2087 { return !(__d1 == __d2); }
2090 /**
2091 * @brief A Hoyt continuous distribution for random numbers.
2092 *
2093 * The formula for the Hoyt probability density function is
2094 * @f[
2095 * p(x|q,\omega) = \frac{(1 + q^2)x}{q\omega}
2096 * \exp\left(-\frac{(1 + q^2)^2 x^2}{4 q^2 \omega}\right)
2097 * I_0\left(\frac{(1 - q^4) x^2}{4 q^2 \omega}\right)
2098 * @f]
2099 * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
2100 * of order 0 and @f$0 < q < 1@f$.
2101 *
2102 * <table border=1 cellpadding=10 cellspacing=0>
2103 * <caption align=top>Distribution Statistics</caption>
2104 * <tr><td>Mean</td><td>@f$ \sqrt{\frac{2}{\pi}} \sqrt{\frac{\omega}{1 + q^2}}
2105 * E(1 - q^2) @f$</td></tr>
2106 * <tr><td>Variance</td><td>@f$ \omega \left(1 - \frac{2E^2(1 - q^2)}
2107 * {\pi (1 + q^2)}\right) @f$</td></tr>
2108 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
2109 * </table>
2110 * where @f$E(x)@f$ is the elliptic function of the second kind.
2111 */
2112 template<typename _RealType = double>
2113 class
2114 hoyt_distribution
2115 {
2116 static_assert(std::is_floating_point<_RealType>::value,
2117 "template argument not a floating point type");
2119 public:
2120 /** The type of the range of the distribution. */
2121 typedef _RealType result_type;
2122 /** Parameter type. */
2123 struct param_type
2124 {
2125 typedef hoyt_distribution<result_type> distribution_type;
2127 param_type(result_type __q = result_type(0.5L),
2128 result_type __omega = result_type(1))
2129 : _M_q(__q), _M_omega(__omega)
2130 {
2131 _GLIBCXX_DEBUG_ASSERT(_M_q > result_type(0));
2132 _GLIBCXX_DEBUG_ASSERT(_M_q < result_type(1));
2133 }
2135 result_type
2136 q() const
2137 { return _M_q; }
2139 result_type
2140 omega() const
2141 { return _M_omega; }
2143 friend bool
2144 operator==(const param_type& __p1, const param_type& __p2)
2145 { return __p1._M_q == __p2._M_q
2146 && __p1._M_omega == __p2._M_omega; }
2148 private:
2149 void _M_initialize();
2151 result_type _M_q;
2152 result_type _M_omega;
2153 };
2155 /**
2156 * @brief Constructors.
2157 */
2158 explicit
2159 hoyt_distribution(result_type __q = result_type(0.5L),
2160 result_type __omega = result_type(1))
2161 : _M_param(__q, __omega),
2162 _M_ad(result_type(0.5L) * (result_type(1) + __q * __q),
2163 result_type(0.5L) * (result_type(1) + __q * __q)
2164 / (__q * __q)),
2165 _M_ed(result_type(1))
2166 { }
2168 explicit
2169 hoyt_distribution(const param_type& __p)
2170 : _M_param(__p),
2171 _M_ad(result_type(0.5L) * (result_type(1) + __p.q() * __p.q()),
2172 result_type(0.5L) * (result_type(1) + __p.q() * __p.q())
2173 / (__p.q() * __p.q())),
2174 _M_ed(result_type(1))
2175 { }
2177 /**
2178 * @brief Resets the distribution state.
2179 */
2180 void
2181 reset()
2182 {
2183 _M_ad.reset();
2184 _M_ed.reset();
2185 }
2187 /**
2188 * @brief Return the parameters of the distribution.
2189 */
2190 result_type
2191 q() const
2192 { return _M_param.q(); }
2194 result_type
2195 omega() const
2196 { return _M_param.omega(); }
2198 /**
2199 * @brief Returns the parameter set of the distribution.
2200 */
2201 param_type
2202 param() const
2203 { return _M_param; }
2205 /**
2206 * @brief Sets the parameter set of the distribution.
2207 * @param __param The new parameter set of the distribution.
2208 */
2209 void
2210 param(const param_type& __param)
2211 { _M_param = __param; }
2213 /**
2214 * @brief Returns the greatest lower bound value of the distribution.
2215 */
2216 result_type
2217 min() const
2218 { return result_type(0); }
2220 /**
2221 * @brief Returns the least upper bound value of the distribution.
2222 */
2223 result_type
2224 max() const
2225 { return std::numeric_limits<result_type>::max(); }
2227 /**
2228 * @brief Generating functions.
2229 */
2230 template<typename _UniformRandomNumberGenerator>
2231 result_type
2232 operator()(_UniformRandomNumberGenerator& __urng);
2234 template<typename _UniformRandomNumberGenerator>
2235 result_type
2236 operator()(_UniformRandomNumberGenerator& __urng,
2237 const param_type& __p);
2239 template<typename _ForwardIterator,
2240 typename _UniformRandomNumberGenerator>
2241 void
2242 __generate(_ForwardIterator __f, _ForwardIterator __t,
2243 _UniformRandomNumberGenerator& __urng)
2244 { this->__generate(__f, __t, __urng, this->param()); }
2246 template<typename _ForwardIterator,
2247 typename _UniformRandomNumberGenerator>
2248 void
2249 __generate(_ForwardIterator __f, _ForwardIterator __t,
2250 _UniformRandomNumberGenerator& __urng,
2251 const param_type& __p)
2252 { this->__generate_impl(__f, __t, __urng, __p); }
2254 template<typename _UniformRandomNumberGenerator>
2255 void
2256 __generate(result_type* __f, result_type* __t,
2257 _UniformRandomNumberGenerator& __urng,
2258 const param_type& __p)
2259 { this->__generate_impl(__f, __t, __urng, __p); }
2261 /**
2262 * @brief Return true if two Hoyt distributions have
2263 * the same parameters and the sequences that would
2264 * be generated are equal.
2265 */
2266 friend bool
2267 operator==(const hoyt_distribution& __d1,
2268 const hoyt_distribution& __d2)
2269 { return (__d1.param() == __d2.param()
2270 && __d1._M_ad == __d2._M_ad
2271 && __d1._M_ed == __d2._M_ed); }
2273 /**
2274 * @brief Inserts a %hoyt_distribution random number distribution
2275 * @p __x into the output stream @p __os.
2276 *
2277 * @param __os An output stream.
2278 * @param __x A %hoyt_distribution random number distribution.
2279 *
2280 * @returns The output stream with the state of @p __x inserted or in
2281 * an error state.
2282 */
2283 template<typename _RealType1, typename _CharT, typename _Traits>
2284 friend std::basic_ostream<_CharT, _Traits>&
2285 operator<<(std::basic_ostream<_CharT, _Traits>&,
2286 const hoyt_distribution<_RealType1>&);
2288 /**
2289 * @brief Extracts a %hoyt_distribution random number distribution
2290 * @p __x from the input stream @p __is.
2291 *
2292 * @param __is An input stream.
2293 * @param __x A %hoyt_distribution random number
2294 * generator engine.
2295 *
2296 * @returns The input stream with @p __x extracted or in an error state.
2297 */
2298 template<typename _RealType1, typename _CharT, typename _Traits>
2299 friend std::basic_istream<_CharT, _Traits>&
2300 operator>>(std::basic_istream<_CharT, _Traits>&,
2301 hoyt_distribution<_RealType1>&);
2303 private:
2304 template<typename _ForwardIterator,
2305 typename _UniformRandomNumberGenerator>
2306 void
2307 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2308 _UniformRandomNumberGenerator& __urng,
2309 const param_type& __p);
2311 param_type _M_param;
2313 __gnu_cxx::arcsine_distribution<result_type> _M_ad;
2314 std::exponential_distribution<result_type> _M_ed;
2315 };
2317 /**
2318 * @brief Return true if two Hoyt distributions are not equal.
2319 */
2320 template<typename _RealType>
2321 inline bool
2322 operator!=(const hoyt_distribution<_RealType>& __d1,
2323 const hoyt_distribution<_RealType>& __d2)
2324 { return !(__d1 == __d2); }
2326 _GLIBCXX_END_NAMESPACE_VERSION
2327 } // namespace __gnu_cxx
2329 #include "opt_random.h"
2330 #include "random.tcc"
2332 #endif // _GLIBCXX_USE_C99_STDINT_TR1
2334 #endif // __GXX_EXPERIMENTAL_CXX0X__
2336 #endif // _EXT_RANDOM