| blob | 01957599f2fb81a24a62083d6530d5d96cf7f59e |
1 // Random number extensions -*- C++ -*-
3 // Copyright (C) 2012-2024 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 #include <bits/requires_hosted.h> // GNU extensions are currently omitted
36 #if __cplusplus < 201103L
37 # include <bits/c++0x_warning.h>
38 #else
40 #include <random>
41 #include <algorithm>
42 #include <array>
43 #include <ext/cmath>
44 #ifdef __SSE2__
45 # include <emmintrin.h>
46 #endif
48 #ifdef UINT32_C
50 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
51 {
52 _GLIBCXX_BEGIN_NAMESPACE_VERSION
54 #if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
56 /* Mersenne twister implementation optimized for vector operations.
57 *
58 * Reference: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/
59 */
60 template<typename _UIntType, size_t __m,
61 size_t __pos1, size_t __sl1, size_t __sl2,
62 size_t __sr1, size_t __sr2,
63 uint32_t __msk1, uint32_t __msk2,
64 uint32_t __msk3, uint32_t __msk4,
65 uint32_t __parity1, uint32_t __parity2,
66 uint32_t __parity3, uint32_t __parity4>
67 class simd_fast_mersenne_twister_engine
68 {
69 static_assert(std::is_unsigned<_UIntType>::value, "template argument "
70 "substituting _UIntType not an unsigned integral type");
71 static_assert(__sr1 < 32, "first right shift too large");
72 static_assert(__sr2 < 16, "second right shift too large");
73 static_assert(__sl1 < 32, "first left shift too large");
74 static_assert(__sl2 < 16, "second left shift too large");
76 public:
77 typedef _UIntType result_type;
79 private:
80 static constexpr size_t m_w = sizeof(result_type) * 8;
81 static constexpr size_t _M_nstate = __m / 128 + 1;
82 static constexpr size_t _M_nstate32 = _M_nstate * 4;
84 static_assert(std::is_unsigned<_UIntType>::value, "template argument "
85 "substituting _UIntType not an unsigned integral type");
86 static_assert(__pos1 < _M_nstate, "POS1 not smaller than state size");
87 static_assert(16 % sizeof(_UIntType) == 0,
88 "UIntType size must divide 16");
90 template<typename _Sseq>
91 using _If_seed_seq
92 = std::__detail::_If_seed_seq_for<_Sseq,
93 simd_fast_mersenne_twister_engine,
94 result_type>;
96 public:
97 static constexpr size_t state_size = _M_nstate * (16
98 / sizeof(result_type));
99 static constexpr result_type default_seed = 5489u;
101 // constructors and member functions
103 simd_fast_mersenne_twister_engine()
104 : simd_fast_mersenne_twister_engine(default_seed)
105 { }
107 explicit
108 simd_fast_mersenne_twister_engine(result_type __sd)
109 { seed(__sd); }
111 template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
112 explicit
113 simd_fast_mersenne_twister_engine(_Sseq& __q)
114 { seed(__q); }
116 void
117 seed(result_type __sd = default_seed);
119 template<typename _Sseq>
120 _If_seed_seq<_Sseq>
121 seed(_Sseq& __q);
123 static constexpr result_type
124 min()
125 { return 0; }
127 static constexpr result_type
128 max()
129 { return std::numeric_limits<result_type>::max(); }
131 void
132 discard(unsigned long long __z);
134 result_type
135 operator()()
136 {
137 if (__builtin_expect(_M_pos >= state_size, 0))
138 _M_gen_rand();
140 return _M_stateT[_M_pos++];
141 }
143 template<typename _UIntType_2, size_t __m_2,
144 size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
145 size_t __sr1_2, size_t __sr2_2,
146 uint32_t __msk1_2, uint32_t __msk2_2,
147 uint32_t __msk3_2, uint32_t __msk4_2,
148 uint32_t __parity1_2, uint32_t __parity2_2,
149 uint32_t __parity3_2, uint32_t __parity4_2>
150 friend bool
151 operator==(const simd_fast_mersenne_twister_engine<_UIntType_2,
152 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
153 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
154 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __lhs,
155 const simd_fast_mersenne_twister_engine<_UIntType_2,
156 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
157 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
158 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __rhs);
160 template<typename _UIntType_2, size_t __m_2,
161 size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
162 size_t __sr1_2, size_t __sr2_2,
163 uint32_t __msk1_2, uint32_t __msk2_2,
164 uint32_t __msk3_2, uint32_t __msk4_2,
165 uint32_t __parity1_2, uint32_t __parity2_2,
166 uint32_t __parity3_2, uint32_t __parity4_2,
167 typename _CharT, typename _Traits>
168 friend std::basic_ostream<_CharT, _Traits>&
169 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
170 const __gnu_cxx::simd_fast_mersenne_twister_engine
171 <_UIntType_2,
172 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
173 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
174 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);
176 template<typename _UIntType_2, size_t __m_2,
177 size_t __pos1_2, size_t __sl1_2, size_t __sl2_2,
178 size_t __sr1_2, size_t __sr2_2,
179 uint32_t __msk1_2, uint32_t __msk2_2,
180 uint32_t __msk3_2, uint32_t __msk4_2,
181 uint32_t __parity1_2, uint32_t __parity2_2,
182 uint32_t __parity3_2, uint32_t __parity4_2,
183 typename _CharT, typename _Traits>
184 friend std::basic_istream<_CharT, _Traits>&
185 operator>>(std::basic_istream<_CharT, _Traits>& __is,
186 __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType_2,
187 __m_2, __pos1_2, __sl1_2, __sl2_2, __sr1_2, __sr2_2,
188 __msk1_2, __msk2_2, __msk3_2, __msk4_2,
189 __parity1_2, __parity2_2, __parity3_2, __parity4_2>& __x);
191 private:
192 union
193 {
194 #ifdef __SSE2__
195 __m128i _M_state[_M_nstate];
196 #endif
197 #ifdef __ARM_NEON
198 #ifdef __aarch64__
199 __Uint32x4_t _M_state[_M_nstate];
200 #endif
201 #endif
202 uint32_t _M_state32[_M_nstate32];
203 result_type _M_stateT[state_size];
204 } __attribute__ ((__aligned__ (16)));
205 size_t _M_pos;
207 void _M_gen_rand(void);
208 void _M_period_certification();
209 };
211 #if __cpp_impl_three_way_comparison < 201907L
212 template<typename _UIntType, size_t __m,
213 size_t __pos1, size_t __sl1, size_t __sl2,
214 size_t __sr1, size_t __sr2,
215 uint32_t __msk1, uint32_t __msk2,
216 uint32_t __msk3, uint32_t __msk4,
217 uint32_t __parity1, uint32_t __parity2,
218 uint32_t __parity3, uint32_t __parity4>
219 inline bool
220 operator!=(const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
221 __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
222 __msk4, __parity1, __parity2, __parity3, __parity4>& __lhs,
223 const __gnu_cxx::simd_fast_mersenne_twister_engine<_UIntType,
224 __m, __pos1, __sl1, __sl2, __sr1, __sr2, __msk1, __msk2, __msk3,
225 __msk4, __parity1, __parity2, __parity3, __parity4>& __rhs)
226 { return !(__lhs == __rhs); }
227 #endif
229 /* Definitions for the SIMD-oriented Fast Mersenne Twister as defined
230 * in the C implementation by Daito and Matsumoto, as both a 32-bit
231 * and 64-bit version.
232 */
233 typedef simd_fast_mersenne_twister_engine<uint32_t, 607, 2,
234 15, 3, 13, 3,
235 0xfdff37ffU, 0xef7f3f7dU,
236 0xff777b7dU, 0x7ff7fb2fU,
237 0x00000001U, 0x00000000U,
238 0x00000000U, 0x5986f054U>
239 sfmt607;
241 typedef simd_fast_mersenne_twister_engine<uint64_t, 607, 2,
242 15, 3, 13, 3,
243 0xfdff37ffU, 0xef7f3f7dU,
244 0xff777b7dU, 0x7ff7fb2fU,
245 0x00000001U, 0x00000000U,
246 0x00000000U, 0x5986f054U>
247 sfmt607_64;
250 typedef simd_fast_mersenne_twister_engine<uint32_t, 1279, 7,
251 14, 3, 5, 1,
252 0xf7fefffdU, 0x7fefcfffU,
253 0xaff3ef3fU, 0xb5ffff7fU,
254 0x00000001U, 0x00000000U,
255 0x00000000U, 0x20000000U>
256 sfmt1279;
258 typedef simd_fast_mersenne_twister_engine<uint64_t, 1279, 7,
259 14, 3, 5, 1,
260 0xf7fefffdU, 0x7fefcfffU,
261 0xaff3ef3fU, 0xb5ffff7fU,
262 0x00000001U, 0x00000000U,
263 0x00000000U, 0x20000000U>
264 sfmt1279_64;
267 typedef simd_fast_mersenne_twister_engine<uint32_t, 2281, 12,
268 19, 1, 5, 1,
269 0xbff7ffbfU, 0xfdfffffeU,
270 0xf7ffef7fU, 0xf2f7cbbfU,
271 0x00000001U, 0x00000000U,
272 0x00000000U, 0x41dfa600U>
273 sfmt2281;
275 typedef simd_fast_mersenne_twister_engine<uint64_t, 2281, 12,
276 19, 1, 5, 1,
277 0xbff7ffbfU, 0xfdfffffeU,
278 0xf7ffef7fU, 0xf2f7cbbfU,
279 0x00000001U, 0x00000000U,
280 0x00000000U, 0x41dfa600U>
281 sfmt2281_64;
284 typedef simd_fast_mersenne_twister_engine<uint32_t, 4253, 17,
285 20, 1, 7, 1,
286 0x9f7bffffU, 0x9fffff5fU,
287 0x3efffffbU, 0xfffff7bbU,
288 0xa8000001U, 0xaf5390a3U,
289 0xb740b3f8U, 0x6c11486dU>
290 sfmt4253;
292 typedef simd_fast_mersenne_twister_engine<uint64_t, 4253, 17,
293 20, 1, 7, 1,
294 0x9f7bffffU, 0x9fffff5fU,
295 0x3efffffbU, 0xfffff7bbU,
296 0xa8000001U, 0xaf5390a3U,
297 0xb740b3f8U, 0x6c11486dU>
298 sfmt4253_64;
301 typedef simd_fast_mersenne_twister_engine<uint32_t, 11213, 68,
302 14, 3, 7, 3,
303 0xeffff7fbU, 0xffffffefU,
304 0xdfdfbfffU, 0x7fffdbfdU,
305 0x00000001U, 0x00000000U,
306 0xe8148000U, 0xd0c7afa3U>
307 sfmt11213;
309 typedef simd_fast_mersenne_twister_engine<uint64_t, 11213, 68,
310 14, 3, 7, 3,
311 0xeffff7fbU, 0xffffffefU,
312 0xdfdfbfffU, 0x7fffdbfdU,
313 0x00000001U, 0x00000000U,
314 0xe8148000U, 0xd0c7afa3U>
315 sfmt11213_64;
318 typedef simd_fast_mersenne_twister_engine<uint32_t, 19937, 122,
319 18, 1, 11, 1,
320 0xdfffffefU, 0xddfecb7fU,
321 0xbffaffffU, 0xbffffff6U,
322 0x00000001U, 0x00000000U,
323 0x00000000U, 0x13c9e684U>
324 sfmt19937;
326 typedef simd_fast_mersenne_twister_engine<uint64_t, 19937, 122,
327 18, 1, 11, 1,
328 0xdfffffefU, 0xddfecb7fU,
329 0xbffaffffU, 0xbffffff6U,
330 0x00000001U, 0x00000000U,
331 0x00000000U, 0x13c9e684U>
332 sfmt19937_64;
335 typedef simd_fast_mersenne_twister_engine<uint32_t, 44497, 330,
336 5, 3, 9, 3,
337 0xeffffffbU, 0xdfbebfffU,
338 0xbfbf7befU, 0x9ffd7bffU,
339 0x00000001U, 0x00000000U,
340 0xa3ac4000U, 0xecc1327aU>
341 sfmt44497;
343 typedef simd_fast_mersenne_twister_engine<uint64_t, 44497, 330,
344 5, 3, 9, 3,
345 0xeffffffbU, 0xdfbebfffU,
346 0xbfbf7befU, 0x9ffd7bffU,
347 0x00000001U, 0x00000000U,
348 0xa3ac4000U, 0xecc1327aU>
349 sfmt44497_64;
351 #if __SIZE_WIDTH__ >= 32
353 typedef simd_fast_mersenne_twister_engine<uint32_t, 86243, 366,
354 6, 7, 19, 1,
355 0xfdbffbffU, 0xbff7ff3fU,
356 0xfd77efffU, 0xbf9ff3ffU,
357 0x00000001U, 0x00000000U,
358 0x00000000U, 0xe9528d85U>
359 sfmt86243;
361 typedef simd_fast_mersenne_twister_engine<uint64_t, 86243, 366,
362 6, 7, 19, 1,
363 0xfdbffbffU, 0xbff7ff3fU,
364 0xfd77efffU, 0xbf9ff3ffU,
365 0x00000001U, 0x00000000U,
366 0x00000000U, 0xe9528d85U>
367 sfmt86243_64;
370 typedef simd_fast_mersenne_twister_engine<uint32_t, 132049, 110,
371 19, 1, 21, 1,
372 0xffffbb5fU, 0xfb6ebf95U,
373 0xfffefffaU, 0xcff77fffU,
374 0x00000001U, 0x00000000U,
375 0xcb520000U, 0xc7e91c7dU>
376 sfmt132049;
378 typedef simd_fast_mersenne_twister_engine<uint64_t, 132049, 110,
379 19, 1, 21, 1,
380 0xffffbb5fU, 0xfb6ebf95U,
381 0xfffefffaU, 0xcff77fffU,
382 0x00000001U, 0x00000000U,
383 0xcb520000U, 0xc7e91c7dU>
384 sfmt132049_64;
387 typedef simd_fast_mersenne_twister_engine<uint32_t, 216091, 627,
388 11, 3, 10, 1,
389 0xbff7bff7U, 0xbfffffffU,
390 0xbffffa7fU, 0xffddfbfbU,
391 0xf8000001U, 0x89e80709U,
392 0x3bd2b64bU, 0x0c64b1e4U>
393 sfmt216091;
395 typedef simd_fast_mersenne_twister_engine<uint64_t, 216091, 627,
396 11, 3, 10, 1,
397 0xbff7bff7U, 0xbfffffffU,
398 0xbffffa7fU, 0xffddfbfbU,
399 0xf8000001U, 0x89e80709U,
400 0x3bd2b64bU, 0x0c64b1e4U>
401 sfmt216091_64;
402 #endif // __SIZE_WIDTH__ >= 32
404 #endif // __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
406 /**
407 * @brief A beta continuous distribution for random numbers.
408 *
409 * The formula for the beta probability density function is:
410 * @f[
411 * p(x|\alpha,\beta) = \frac{1}{B(\alpha,\beta)}
412 * x^{\alpha - 1} (1 - x)^{\beta - 1}
413 * @f]
414 */
415 template<typename _RealType = double>
416 class beta_distribution
417 {
418 static_assert(std::is_floating_point<_RealType>::value,
419 "template argument not a floating point type");
421 public:
422 /** The type of the range of the distribution. */
423 typedef _RealType result_type;
425 /** Parameter type. */
426 struct param_type
427 {
428 typedef beta_distribution<_RealType> distribution_type;
429 friend class beta_distribution<_RealType>;
431 param_type() : param_type(1) { }
433 explicit
434 param_type(_RealType __alpha_val, _RealType __beta_val = _RealType(1))
435 : _M_alpha(__alpha_val), _M_beta(__beta_val)
436 {
437 __glibcxx_assert(_M_alpha > _RealType(0));
438 __glibcxx_assert(_M_beta > _RealType(0));
439 }
441 _RealType
442 alpha() const
443 { return _M_alpha; }
445 _RealType
446 beta() const
447 { return _M_beta; }
449 friend bool
450 operator==(const param_type& __p1, const param_type& __p2)
451 { return (__p1._M_alpha == __p2._M_alpha
452 && __p1._M_beta == __p2._M_beta); }
454 #if __cpp_impl_three_way_comparison < 201907L
455 friend bool
456 operator!=(const param_type& __p1, const param_type& __p2)
457 { return !(__p1 == __p2); }
458 #endif
460 private:
461 void
462 _M_initialize();
464 _RealType _M_alpha;
465 _RealType _M_beta;
466 };
468 public:
469 beta_distribution() : beta_distribution(1.0) { }
471 /**
472 * @brief Constructs a beta distribution with parameters
473 * @f$\alpha@f$ and @f$\beta@f$.
474 */
475 explicit
476 beta_distribution(_RealType __alpha_val,
477 _RealType __beta_val = _RealType(1))
478 : _M_param(__alpha_val, __beta_val)
479 { }
481 explicit
482 beta_distribution(const param_type& __p)
483 : _M_param(__p)
484 { }
486 /**
487 * @brief Resets the distribution state.
488 */
489 void
490 reset()
491 { }
493 /**
494 * @brief Returns the @f$\alpha@f$ of the distribution.
495 */
496 _RealType
497 alpha() const
498 { return _M_param.alpha(); }
500 /**
501 * @brief Returns the @f$\beta@f$ of the distribution.
502 */
503 _RealType
504 beta() const
505 { return _M_param.beta(); }
507 /**
508 * @brief Returns the parameter set of the distribution.
509 */
510 param_type
511 param() const
512 { return _M_param; }
514 /**
515 * @brief Sets the parameter set of the distribution.
516 * @param __param The new parameter set of the distribution.
517 */
518 void
519 param(const param_type& __param)
520 { _M_param = __param; }
522 /**
523 * @brief Returns the greatest lower bound value of the distribution.
524 */
525 result_type
526 min() const
527 { return result_type(0); }
529 /**
530 * @brief Returns the least upper bound value of the distribution.
531 */
532 result_type
533 max() const
534 { return result_type(1); }
536 /**
537 * @brief Generating functions.
538 */
539 template<typename _UniformRandomNumberGenerator>
540 result_type
541 operator()(_UniformRandomNumberGenerator& __urng)
542 { return this->operator()(__urng, _M_param); }
544 template<typename _UniformRandomNumberGenerator>
545 result_type
546 operator()(_UniformRandomNumberGenerator& __urng,
547 const param_type& __p);
549 template<typename _ForwardIterator,
550 typename _UniformRandomNumberGenerator>
551 void
552 __generate(_ForwardIterator __f, _ForwardIterator __t,
553 _UniformRandomNumberGenerator& __urng)
554 { this->__generate(__f, __t, __urng, _M_param); }
556 template<typename _ForwardIterator,
557 typename _UniformRandomNumberGenerator>
558 void
559 __generate(_ForwardIterator __f, _ForwardIterator __t,
560 _UniformRandomNumberGenerator& __urng,
561 const param_type& __p)
562 { this->__generate_impl(__f, __t, __urng, __p); }
564 template<typename _UniformRandomNumberGenerator>
565 void
566 __generate(result_type* __f, result_type* __t,
567 _UniformRandomNumberGenerator& __urng,
568 const param_type& __p)
569 { this->__generate_impl(__f, __t, __urng, __p); }
571 /**
572 * @brief Return true if two beta distributions have the same
573 * parameters and the sequences that would be generated
574 * are equal.
575 */
576 friend bool
577 operator==(const beta_distribution& __d1,
578 const beta_distribution& __d2)
579 { return __d1._M_param == __d2._M_param; }
581 /**
582 * @brief Inserts a %beta_distribution random number distribution
583 * @p __x into the output stream @p __os.
584 *
585 * @param __os An output stream.
586 * @param __x A %beta_distribution random number distribution.
587 *
588 * @returns The output stream with the state of @p __x inserted or in
589 * an error state.
590 */
591 template<typename _RealType1, typename _CharT, typename _Traits>
592 friend std::basic_ostream<_CharT, _Traits>&
593 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
594 const __gnu_cxx::beta_distribution<_RealType1>& __x);
596 /**
597 * @brief Extracts a %beta_distribution random number distribution
598 * @p __x from the input stream @p __is.
599 *
600 * @param __is An input stream.
601 * @param __x A %beta_distribution random number generator engine.
602 *
603 * @returns The input stream with @p __x extracted or in an error state.
604 */
605 template<typename _RealType1, typename _CharT, typename _Traits>
606 friend std::basic_istream<_CharT, _Traits>&
607 operator>>(std::basic_istream<_CharT, _Traits>& __is,
608 __gnu_cxx::beta_distribution<_RealType1>& __x);
610 private:
611 template<typename _ForwardIterator,
612 typename _UniformRandomNumberGenerator>
613 void
614 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
615 _UniformRandomNumberGenerator& __urng,
616 const param_type& __p);
618 param_type _M_param;
619 };
621 #if __cpp_impl_three_way_comparison < 201907L
622 /**
623 * @brief Return true if two beta distributions are different.
624 */
625 template<typename _RealType>
626 inline bool
627 operator!=(const __gnu_cxx::beta_distribution<_RealType>& __d1,
628 const __gnu_cxx::beta_distribution<_RealType>& __d2)
629 { return !(__d1 == __d2); }
630 #endif
632 /**
633 * @brief A multi-variate normal continuous distribution for random numbers.
634 *
635 * The formula for the normal probability density function is
636 * @f[
637 * p(\overrightarrow{x}|\overrightarrow{\mu },\Sigma) =
638 * \frac{1}{\sqrt{(2\pi )^k\det(\Sigma))}}
639 * e^{-\frac{1}{2}(\overrightarrow{x}-\overrightarrow{\mu})^\text{T}
640 * \Sigma ^{-1}(\overrightarrow{x}-\overrightarrow{\mu})}
641 * @f]
642 *
643 * where @f$\overrightarrow{x}@f$ and @f$\overrightarrow{\mu}@f$ are
644 * vectors of dimension @f$k@f$ and @f$\Sigma@f$ is the covariance
645 * matrix (which must be positive-definite).
646 */
647 template<std::size_t _Dimen, typename _RealType = double>
648 class normal_mv_distribution
649 {
650 static_assert(std::is_floating_point<_RealType>::value,
651 "template argument not a floating point type");
652 static_assert(_Dimen != 0, "dimension is zero");
654 public:
655 /** The type of the range of the distribution. */
656 typedef std::array<_RealType, _Dimen> result_type;
657 /** Parameter type. */
658 class param_type
659 {
660 static constexpr size_t _M_t_size = _Dimen * (_Dimen + 1) / 2;
662 public:
663 typedef normal_mv_distribution<_Dimen, _RealType> distribution_type;
664 friend class normal_mv_distribution<_Dimen, _RealType>;
666 param_type()
667 {
668 std::fill(_M_mean.begin(), _M_mean.end(), _RealType(0));
669 auto __it = _M_t.begin();
670 for (size_t __i = 0; __i < _Dimen; ++__i)
671 {
672 std::fill_n(__it, __i, _RealType(0));
673 __it += __i;
674 *__it++ = _RealType(1);
675 }
676 }
678 template<typename _ForwardIterator1, typename _ForwardIterator2>
679 param_type(_ForwardIterator1 __meanbegin,
680 _ForwardIterator1 __meanend,
681 _ForwardIterator2 __varcovbegin,
682 _ForwardIterator2 __varcovend)
683 {
684 __glibcxx_function_requires(_ForwardIteratorConcept<
685 _ForwardIterator1>)
686 __glibcxx_function_requires(_ForwardIteratorConcept<
687 _ForwardIterator2>)
688 _GLIBCXX_DEBUG_ASSERT(std::distance(__meanbegin, __meanend)
689 <= _Dimen);
690 const auto __dist = std::distance(__varcovbegin, __varcovend);
691 _GLIBCXX_DEBUG_ASSERT(__dist == _Dimen * _Dimen
692 || __dist == _Dimen * (_Dimen + 1) / 2
693 || __dist == _Dimen);
695 if (__dist == _Dimen * _Dimen)
696 _M_init_full(__meanbegin, __meanend, __varcovbegin, __varcovend);
697 else if (__dist == _Dimen * (_Dimen + 1) / 2)
698 _M_init_lower(__meanbegin, __meanend, __varcovbegin, __varcovend);
699 else
700 {
701 __glibcxx_assert(__dist == _Dimen);
702 _M_init_diagonal(__meanbegin, __meanend,
703 __varcovbegin, __varcovend);
704 }
705 }
707 param_type(std::initializer_list<_RealType> __mean,
708 std::initializer_list<_RealType> __varcov)
709 {
710 _GLIBCXX_DEBUG_ASSERT(__mean.size() <= _Dimen);
711 _GLIBCXX_DEBUG_ASSERT(__varcov.size() == _Dimen * _Dimen
712 || __varcov.size() == _Dimen * (_Dimen + 1) / 2
713 || __varcov.size() == _Dimen);
715 if (__varcov.size() == _Dimen * _Dimen)
716 _M_init_full(__mean.begin(), __mean.end(),
717 __varcov.begin(), __varcov.end());
718 else if (__varcov.size() == _Dimen * (_Dimen + 1) / 2)
719 _M_init_lower(__mean.begin(), __mean.end(),
720 __varcov.begin(), __varcov.end());
721 else
722 {
723 __glibcxx_assert(__varcov.size() == _Dimen);
724 _M_init_diagonal(__mean.begin(), __mean.end(),
725 __varcov.begin(), __varcov.end());
726 }
727 }
729 std::array<_RealType, _Dimen>
730 mean() const
731 { return _M_mean; }
733 std::array<_RealType, _M_t_size>
734 varcov() const
735 { return _M_t; }
737 friend bool
738 operator==(const param_type& __p1, const param_type& __p2)
739 { return __p1._M_mean == __p2._M_mean && __p1._M_t == __p2._M_t; }
741 #if __cpp_impl_three_way_comparison < 201907L
742 friend bool
743 operator!=(const param_type& __p1, const param_type& __p2)
744 { return !(__p1 == __p2); }
745 #endif
747 private:
748 template <typename _InputIterator1, typename _InputIterator2>
749 void _M_init_full(_InputIterator1 __meanbegin,
750 _InputIterator1 __meanend,
751 _InputIterator2 __varcovbegin,
752 _InputIterator2 __varcovend);
753 template <typename _InputIterator1, typename _InputIterator2>
754 void _M_init_lower(_InputIterator1 __meanbegin,
755 _InputIterator1 __meanend,
756 _InputIterator2 __varcovbegin,
757 _InputIterator2 __varcovend);
758 template <typename _InputIterator1, typename _InputIterator2>
759 void _M_init_diagonal(_InputIterator1 __meanbegin,
760 _InputIterator1 __meanend,
761 _InputIterator2 __varbegin,
762 _InputIterator2 __varend);
764 // param_type constructors apply Cholesky decomposition to the
765 // varcov matrix in _M_init_full and _M_init_lower, but the
766 // varcov matrix output ot a stream is already decomposed, so
767 // we need means to restore it as-is when reading it back in.
768 template<size_t _Dimen1, typename _RealType1,
769 typename _CharT, typename _Traits>
770 friend std::basic_istream<_CharT, _Traits>&
771 operator>>(std::basic_istream<_CharT, _Traits>& __is,
772 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
773 __x);
774 param_type(std::array<_RealType, _Dimen> const &__mean,
775 std::array<_RealType, _M_t_size> const &__varcov)
776 : _M_mean (__mean), _M_t (__varcov)
777 {}
779 std::array<_RealType, _Dimen> _M_mean;
780 std::array<_RealType, _M_t_size> _M_t;
781 };
783 public:
784 normal_mv_distribution()
785 : _M_param(), _M_nd()
786 { }
788 template<typename _ForwardIterator1, typename _ForwardIterator2>
789 normal_mv_distribution(_ForwardIterator1 __meanbegin,
790 _ForwardIterator1 __meanend,
791 _ForwardIterator2 __varcovbegin,
792 _ForwardIterator2 __varcovend)
793 : _M_param(__meanbegin, __meanend, __varcovbegin, __varcovend),
794 _M_nd()
795 { }
797 normal_mv_distribution(std::initializer_list<_RealType> __mean,
798 std::initializer_list<_RealType> __varcov)
799 : _M_param(__mean, __varcov), _M_nd()
800 { }
802 explicit
803 normal_mv_distribution(const param_type& __p)
804 : _M_param(__p), _M_nd()
805 { }
807 /**
808 * @brief Resets the distribution state.
809 */
810 void
811 reset()
812 { _M_nd.reset(); }
814 /**
815 * @brief Returns the mean of the distribution.
816 */
817 result_type
818 mean() const
819 { return _M_param.mean(); }
821 /**
822 * @brief Returns the compact form of the variance/covariance
823 * matrix of the distribution.
824 */
825 std::array<_RealType, _Dimen * (_Dimen + 1) / 2>
826 varcov() const
827 { return _M_param.varcov(); }
829 /**
830 * @brief Returns the parameter set of the distribution.
831 */
832 param_type
833 param() const
834 { return _M_param; }
836 /**
837 * @brief Sets the parameter set of the distribution.
838 * @param __param The new parameter set of the distribution.
839 */
840 void
841 param(const param_type& __param)
842 { _M_param = __param; }
844 /**
845 * @brief Returns the greatest lower bound value of the distribution.
846 */
847 result_type
848 min() const
849 { result_type __res;
850 __res.fill(std::numeric_limits<_RealType>::lowest());
851 return __res; }
853 /**
854 * @brief Returns the least upper bound value of the distribution.
855 */
856 result_type
857 max() const
858 { result_type __res;
859 __res.fill(std::numeric_limits<_RealType>::max());
860 return __res; }
862 /**
863 * @brief Generating functions.
864 */
865 template<typename _UniformRandomNumberGenerator>
866 result_type
867 operator()(_UniformRandomNumberGenerator& __urng)
868 { return this->operator()(__urng, _M_param); }
870 template<typename _UniformRandomNumberGenerator>
871 result_type
872 operator()(_UniformRandomNumberGenerator& __urng,
873 const param_type& __p);
875 template<typename _ForwardIterator,
876 typename _UniformRandomNumberGenerator>
877 void
878 __generate(_ForwardIterator __f, _ForwardIterator __t,
879 _UniformRandomNumberGenerator& __urng)
880 { return this->__generate_impl(__f, __t, __urng, _M_param); }
882 template<typename _ForwardIterator,
883 typename _UniformRandomNumberGenerator>
884 void
885 __generate(_ForwardIterator __f, _ForwardIterator __t,
886 _UniformRandomNumberGenerator& __urng,
887 const param_type& __p)
888 { return this->__generate_impl(__f, __t, __urng, __p); }
890 /**
891 * @brief Return true if two multi-variant normal distributions have
892 * the same parameters and the sequences that would
893 * be generated are equal.
894 */
895 template<size_t _Dimen1, typename _RealType1>
896 friend bool
897 operator==(const
898 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
899 __d1,
900 const
901 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
902 __d2);
904 /**
905 * @brief Inserts a %normal_mv_distribution random number distribution
906 * @p __x into the output stream @p __os.
907 *
908 * @param __os An output stream.
909 * @param __x A %normal_mv_distribution random number distribution.
910 *
911 * @returns The output stream with the state of @p __x inserted or in
912 * an error state.
913 */
914 template<size_t _Dimen1, typename _RealType1,
915 typename _CharT, typename _Traits>
916 friend std::basic_ostream<_CharT, _Traits>&
917 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
918 const
919 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
920 __x);
922 /**
923 * @brief Extracts a %normal_mv_distribution random number distribution
924 * @p __x from the input stream @p __is.
925 *
926 * @param __is An input stream.
927 * @param __x A %normal_mv_distribution random number generator engine.
928 *
929 * @returns The input stream with @p __x extracted or in an error
930 * state.
931 */
932 template<size_t _Dimen1, typename _RealType1,
933 typename _CharT, typename _Traits>
934 friend std::basic_istream<_CharT, _Traits>&
935 operator>>(std::basic_istream<_CharT, _Traits>& __is,
936 __gnu_cxx::normal_mv_distribution<_Dimen1, _RealType1>&
937 __x);
939 private:
940 template<typename _ForwardIterator,
941 typename _UniformRandomNumberGenerator>
942 void
943 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
944 _UniformRandomNumberGenerator& __urng,
945 const param_type& __p);
947 param_type _M_param;
948 std::normal_distribution<_RealType> _M_nd;
949 };
951 #if __cpp_impl_three_way_comparison < 201907L
952 /**
953 * @brief Return true if two multi-variate normal distributions are
954 * different.
955 */
956 template<size_t _Dimen, typename _RealType>
957 inline bool
958 operator!=(const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
959 __d1,
960 const __gnu_cxx::normal_mv_distribution<_Dimen, _RealType>&
961 __d2)
962 { return !(__d1 == __d2); }
963 #endif
965 /**
966 * @brief A Rice continuous distribution for random numbers.
967 *
968 * The formula for the Rice probability density function is
969 * @f[
970 * p(x|\nu,\sigma) = \frac{x}{\sigma^2}
971 * \exp\left(-\frac{x^2+\nu^2}{2\sigma^2}\right)
972 * I_0\left(\frac{x \nu}{\sigma^2}\right)
973 * @f]
974 * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
975 * of order 0 and @f$\nu >= 0@f$ and @f$\sigma > 0@f$.
976 *
977 * <table border=1 cellpadding=10 cellspacing=0>
978 * <caption align=top>Distribution Statistics</caption>
979 * <tr><td>Mean</td><td>@f$\sqrt{\pi/2}L_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
980 * <tr><td>Variance</td><td>@f$2\sigma^2 + \nu^2
981 * + (\pi\sigma^2/2)L^2_{1/2}(-\nu^2/2\sigma^2)@f$</td></tr>
982 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
983 * </table>
984 * where @f$L_{1/2}(x)@f$ is the Laguerre polynomial of order 1/2.
985 */
986 template<typename _RealType = double>
987 class
988 rice_distribution
989 {
990 static_assert(std::is_floating_point<_RealType>::value,
991 "template argument not a floating point type");
992 public:
993 /** The type of the range of the distribution. */
994 typedef _RealType result_type;
996 /** Parameter type. */
997 struct param_type
998 {
999 typedef rice_distribution<result_type> distribution_type;
1001 param_type() : param_type(0) { }
1003 param_type(result_type __nu_val,
1004 result_type __sigma_val = result_type(1))
1005 : _M_nu(__nu_val), _M_sigma(__sigma_val)
1006 {
1007 __glibcxx_assert(_M_nu >= result_type(0));
1008 __glibcxx_assert(_M_sigma > result_type(0));
1009 }
1011 result_type
1012 nu() const
1013 { return _M_nu; }
1015 result_type
1016 sigma() const
1017 { return _M_sigma; }
1019 friend bool
1020 operator==(const param_type& __p1, const param_type& __p2)
1021 { return __p1._M_nu == __p2._M_nu && __p1._M_sigma == __p2._M_sigma; }
1023 #if __cpp_impl_three_way_comparison < 201907L
1024 friend bool
1025 operator!=(const param_type& __p1, const param_type& __p2)
1026 { return !(__p1 == __p2); }
1027 #endif
1029 private:
1030 void _M_initialize();
1032 result_type _M_nu;
1033 result_type _M_sigma;
1034 };
1036 /**
1037 * @brief Constructors.
1038 * @{
1039 */
1041 rice_distribution() : rice_distribution(0) { }
1043 explicit
1044 rice_distribution(result_type __nu_val,
1045 result_type __sigma_val = result_type(1))
1046 : _M_param(__nu_val, __sigma_val),
1047 _M_ndx(__nu_val, __sigma_val),
1048 _M_ndy(result_type(0), __sigma_val)
1049 { }
1051 explicit
1052 rice_distribution(const param_type& __p)
1053 : _M_param(__p),
1054 _M_ndx(__p.nu(), __p.sigma()),
1055 _M_ndy(result_type(0), __p.sigma())
1056 { }
1058 /// @}
1060 /**
1061 * @brief Resets the distribution state.
1062 */
1063 void
1064 reset()
1065 {
1066 _M_ndx.reset();
1067 _M_ndy.reset();
1068 }
1070 /**
1071 * @brief Return the parameters of the distribution.
1072 */
1073 result_type
1074 nu() const
1075 { return _M_param.nu(); }
1077 result_type
1078 sigma() const
1079 { return _M_param.sigma(); }
1081 /**
1082 * @brief Returns the parameter set of the distribution.
1083 */
1084 param_type
1085 param() const
1086 { return _M_param; }
1088 /**
1089 * @brief Sets the parameter set of the distribution.
1090 * @param __param The new parameter set of the distribution.
1091 */
1092 void
1093 param(const param_type& __param)
1094 { _M_param = __param; }
1096 /**
1097 * @brief Returns the greatest lower bound value of the distribution.
1098 */
1099 result_type
1100 min() const
1101 { return result_type(0); }
1103 /**
1104 * @brief Returns the least upper bound value of the distribution.
1105 */
1106 result_type
1107 max() const
1108 { return std::numeric_limits<result_type>::max(); }
1110 /**
1111 * @brief Generating functions.
1112 */
1113 template<typename _UniformRandomNumberGenerator>
1114 result_type
1115 operator()(_UniformRandomNumberGenerator& __urng)
1116 {
1117 result_type __x = this->_M_ndx(__urng);
1118 result_type __y = this->_M_ndy(__urng);
1119 #if _GLIBCXX_USE_C99_MATH_FUNCS
1120 return std::hypot(__x, __y);
1121 #else
1122 return std::sqrt(__x * __x + __y * __y);
1123 #endif
1124 }
1126 template<typename _UniformRandomNumberGenerator>
1127 result_type
1128 operator()(_UniformRandomNumberGenerator& __urng,
1129 const param_type& __p)
1130 {
1131 typename std::normal_distribution<result_type>::param_type
1132 __px(__p.nu(), __p.sigma()), __py(result_type(0), __p.sigma());
1133 result_type __x = this->_M_ndx(__px, __urng);
1134 result_type __y = this->_M_ndy(__py, __urng);
1135 #if _GLIBCXX_USE_C99_MATH_FUNCS
1136 return std::hypot(__x, __y);
1137 #else
1138 return std::sqrt(__x * __x + __y * __y);
1139 #endif
1140 }
1142 template<typename _ForwardIterator,
1143 typename _UniformRandomNumberGenerator>
1144 void
1145 __generate(_ForwardIterator __f, _ForwardIterator __t,
1146 _UniformRandomNumberGenerator& __urng)
1147 { this->__generate(__f, __t, __urng, _M_param); }
1149 template<typename _ForwardIterator,
1150 typename _UniformRandomNumberGenerator>
1151 void
1152 __generate(_ForwardIterator __f, _ForwardIterator __t,
1153 _UniformRandomNumberGenerator& __urng,
1154 const param_type& __p)
1155 { this->__generate_impl(__f, __t, __urng, __p); }
1157 template<typename _UniformRandomNumberGenerator>
1158 void
1159 __generate(result_type* __f, result_type* __t,
1160 _UniformRandomNumberGenerator& __urng,
1161 const param_type& __p)
1162 { this->__generate_impl(__f, __t, __urng, __p); }
1164 /**
1165 * @brief Return true if two Rice distributions have
1166 * the same parameters and the sequences that would
1167 * be generated are equal.
1168 */
1169 friend bool
1170 operator==(const rice_distribution& __d1,
1171 const rice_distribution& __d2)
1172 { return (__d1._M_param == __d2._M_param
1173 && __d1._M_ndx == __d2._M_ndx
1174 && __d1._M_ndy == __d2._M_ndy); }
1176 /**
1177 * @brief Inserts a %rice_distribution random number distribution
1178 * @p __x into the output stream @p __os.
1179 *
1180 * @param __os An output stream.
1181 * @param __x A %rice_distribution random number distribution.
1182 *
1183 * @returns The output stream with the state of @p __x inserted or in
1184 * an error state.
1185 */
1186 template<typename _RealType1, typename _CharT, typename _Traits>
1187 friend std::basic_ostream<_CharT, _Traits>&
1188 operator<<(std::basic_ostream<_CharT, _Traits>&,
1189 const rice_distribution<_RealType1>&);
1191 /**
1192 * @brief Extracts a %rice_distribution random number distribution
1193 * @p __x from the input stream @p __is.
1194 *
1195 * @param __is An input stream.
1196 * @param __x A %rice_distribution random number
1197 * generator engine.
1198 *
1199 * @returns The input stream with @p __x extracted or in an error state.
1200 */
1201 template<typename _RealType1, typename _CharT, typename _Traits>
1202 friend std::basic_istream<_CharT, _Traits>&
1203 operator>>(std::basic_istream<_CharT, _Traits>&,
1204 rice_distribution<_RealType1>&);
1206 private:
1207 template<typename _ForwardIterator,
1208 typename _UniformRandomNumberGenerator>
1209 void
1210 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1211 _UniformRandomNumberGenerator& __urng,
1212 const param_type& __p);
1214 param_type _M_param;
1216 std::normal_distribution<result_type> _M_ndx;
1217 std::normal_distribution<result_type> _M_ndy;
1218 };
1220 #if __cpp_impl_three_way_comparison < 201907L
1221 /**
1222 * @brief Return true if two Rice distributions are not equal.
1223 */
1224 template<typename _RealType1>
1225 inline bool
1226 operator!=(const rice_distribution<_RealType1>& __d1,
1227 const rice_distribution<_RealType1>& __d2)
1228 { return !(__d1 == __d2); }
1229 #endif
1231 /**
1232 * @brief A Nakagami continuous distribution for random numbers.
1233 *
1234 * The formula for the Nakagami probability density function is
1235 * @f[
1236 * p(x|\mu,\omega) = \frac{2\mu^\mu}{\Gamma(\mu)\omega^\mu}
1237 * x^{2\mu-1}e^{-\mu x / \omega}
1238 * @f]
1239 * where @f$\Gamma(z)@f$ is the gamma function and @f$\mu >= 0.5@f$
1240 * and @f$\omega > 0@f$.
1241 */
1242 template<typename _RealType = double>
1243 class
1244 nakagami_distribution
1245 {
1246 static_assert(std::is_floating_point<_RealType>::value,
1247 "template argument not a floating point type");
1249 public:
1250 /** The type of the range of the distribution. */
1251 typedef _RealType result_type;
1253 /** Parameter type. */
1254 struct param_type
1255 {
1256 typedef nakagami_distribution<result_type> distribution_type;
1258 param_type() : param_type(1) { }
1260 param_type(result_type __mu_val,
1261 result_type __omega_val = result_type(1))
1262 : _M_mu(__mu_val), _M_omega(__omega_val)
1263 {
1264 __glibcxx_assert(_M_mu >= result_type(0.5L));
1265 __glibcxx_assert(_M_omega > result_type(0));
1266 }
1268 result_type
1269 mu() const
1270 { return _M_mu; }
1272 result_type
1273 omega() const
1274 { return _M_omega; }
1276 friend bool
1277 operator==(const param_type& __p1, const param_type& __p2)
1278 { return __p1._M_mu == __p2._M_mu && __p1._M_omega == __p2._M_omega; }
1280 #if __cpp_impl_three_way_comparison < 201907L
1281 friend bool
1282 operator!=(const param_type& __p1, const param_type& __p2)
1283 { return !(__p1 == __p2); }
1284 #endif
1286 private:
1287 void _M_initialize();
1289 result_type _M_mu;
1290 result_type _M_omega;
1291 };
1293 /**
1294 * @brief Constructors.
1295 * @{
1296 */
1298 nakagami_distribution() : nakagami_distribution(1) { }
1300 explicit
1301 nakagami_distribution(result_type __mu_val,
1302 result_type __omega_val = result_type(1))
1303 : _M_param(__mu_val, __omega_val),
1304 _M_gd(__mu_val, __omega_val / __mu_val)
1305 { }
1307 explicit
1308 nakagami_distribution(const param_type& __p)
1309 : _M_param(__p),
1310 _M_gd(__p.mu(), __p.omega() / __p.mu())
1311 { }
1313 /// @}
1315 /**
1316 * @brief Resets the distribution state.
1317 */
1318 void
1319 reset()
1320 { _M_gd.reset(); }
1322 /**
1323 * @brief Return the parameters of the distribution.
1324 */
1325 result_type
1326 mu() const
1327 { return _M_param.mu(); }
1329 result_type
1330 omega() const
1331 { return _M_param.omega(); }
1333 /**
1334 * @brief Returns the parameter set of the distribution.
1335 */
1336 param_type
1337 param() const
1338 { return _M_param; }
1340 /**
1341 * @brief Sets the parameter set of the distribution.
1342 * @param __param The new parameter set of the distribution.
1343 */
1344 void
1345 param(const param_type& __param)
1346 { _M_param = __param; }
1348 /**
1349 * @brief Returns the greatest lower bound value of the distribution.
1350 */
1351 result_type
1352 min() const
1353 { return result_type(0); }
1355 /**
1356 * @brief Returns the least upper bound value of the distribution.
1357 */
1358 result_type
1359 max() const
1360 { return std::numeric_limits<result_type>::max(); }
1362 /**
1363 * @brief Generating functions.
1364 */
1365 template<typename _UniformRandomNumberGenerator>
1366 result_type
1367 operator()(_UniformRandomNumberGenerator& __urng)
1368 { return std::sqrt(this->_M_gd(__urng)); }
1370 template<typename _UniformRandomNumberGenerator>
1371 result_type
1372 operator()(_UniformRandomNumberGenerator& __urng,
1373 const param_type& __p)
1374 {
1375 typename std::gamma_distribution<result_type>::param_type
1376 __pg(__p.mu(), __p.omega() / __p.mu());
1377 return std::sqrt(this->_M_gd(__pg, __urng));
1378 }
1380 template<typename _ForwardIterator,
1381 typename _UniformRandomNumberGenerator>
1382 void
1383 __generate(_ForwardIterator __f, _ForwardIterator __t,
1384 _UniformRandomNumberGenerator& __urng)
1385 { this->__generate(__f, __t, __urng, _M_param); }
1387 template<typename _ForwardIterator,
1388 typename _UniformRandomNumberGenerator>
1389 void
1390 __generate(_ForwardIterator __f, _ForwardIterator __t,
1391 _UniformRandomNumberGenerator& __urng,
1392 const param_type& __p)
1393 { this->__generate_impl(__f, __t, __urng, __p); }
1395 template<typename _UniformRandomNumberGenerator>
1396 void
1397 __generate(result_type* __f, result_type* __t,
1398 _UniformRandomNumberGenerator& __urng,
1399 const param_type& __p)
1400 { this->__generate_impl(__f, __t, __urng, __p); }
1402 /**
1403 * @brief Return true if two Nakagami distributions have
1404 * the same parameters and the sequences that would
1405 * be generated are equal.
1406 */
1407 friend bool
1408 operator==(const nakagami_distribution& __d1,
1409 const nakagami_distribution& __d2)
1410 { return (__d1._M_param == __d2._M_param
1411 && __d1._M_gd == __d2._M_gd); }
1413 /**
1414 * @brief Inserts a %nakagami_distribution random number distribution
1415 * @p __x into the output stream @p __os.
1416 *
1417 * @param __os An output stream.
1418 * @param __x A %nakagami_distribution random number distribution.
1419 *
1420 * @returns The output stream with the state of @p __x inserted or in
1421 * an error state.
1422 */
1423 template<typename _RealType1, typename _CharT, typename _Traits>
1424 friend std::basic_ostream<_CharT, _Traits>&
1425 operator<<(std::basic_ostream<_CharT, _Traits>&,
1426 const nakagami_distribution<_RealType1>&);
1428 /**
1429 * @brief Extracts a %nakagami_distribution random number distribution
1430 * @p __x from the input stream @p __is.
1431 *
1432 * @param __is An input stream.
1433 * @param __x A %nakagami_distribution random number
1434 * generator engine.
1435 *
1436 * @returns The input stream with @p __x extracted or in an error state.
1437 */
1438 template<typename _RealType1, typename _CharT, typename _Traits>
1439 friend std::basic_istream<_CharT, _Traits>&
1440 operator>>(std::basic_istream<_CharT, _Traits>&,
1441 nakagami_distribution<_RealType1>&);
1443 private:
1444 template<typename _ForwardIterator,
1445 typename _UniformRandomNumberGenerator>
1446 void
1447 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1448 _UniformRandomNumberGenerator& __urng,
1449 const param_type& __p);
1451 param_type _M_param;
1453 std::gamma_distribution<result_type> _M_gd;
1454 };
1456 #if __cpp_impl_three_way_comparison < 201907L
1457 /**
1458 * @brief Return true if two Nakagami distributions are not equal.
1459 */
1460 template<typename _RealType>
1461 inline bool
1462 operator!=(const nakagami_distribution<_RealType>& __d1,
1463 const nakagami_distribution<_RealType>& __d2)
1464 { return !(__d1 == __d2); }
1465 #endif
1467 /**
1468 * @brief A Pareto continuous distribution for random numbers.
1469 *
1470 * The formula for the Pareto cumulative probability function is
1471 * @f[
1472 * P(x|\alpha,\mu) = 1 - \left(\frac{\mu}{x}\right)^\alpha
1473 * @f]
1474 * The formula for the Pareto probability density function is
1475 * @f[
1476 * p(x|\alpha,\mu) = \frac{\alpha + 1}{\mu}
1477 * \left(\frac{\mu}{x}\right)^{\alpha + 1}
1478 * @f]
1479 * where @f$x >= \mu@f$ and @f$\mu > 0@f$, @f$\alpha > 0@f$.
1480 *
1481 * <table border=1 cellpadding=10 cellspacing=0>
1482 * <caption align=top>Distribution Statistics</caption>
1483 * <tr><td>Mean</td><td>@f$\alpha \mu / (\alpha - 1)@f$
1484 * for @f$\alpha > 1@f$</td></tr>
1485 * <tr><td>Variance</td><td>@f$\alpha \mu^2 / [(\alpha - 1)^2(\alpha - 2)]@f$
1486 * for @f$\alpha > 2@f$</td></tr>
1487 * <tr><td>Range</td><td>@f$[\mu, \infty)@f$</td></tr>
1488 * </table>
1489 */
1490 template<typename _RealType = double>
1491 class
1492 pareto_distribution
1493 {
1494 static_assert(std::is_floating_point<_RealType>::value,
1495 "template argument not a floating point type");
1497 public:
1498 /** The type of the range of the distribution. */
1499 typedef _RealType result_type;
1501 /** Parameter type. */
1502 struct param_type
1503 {
1504 typedef pareto_distribution<result_type> distribution_type;
1506 param_type() : param_type(1) { }
1508 param_type(result_type __alpha_val,
1509 result_type __mu_val = result_type(1))
1510 : _M_alpha(__alpha_val), _M_mu(__mu_val)
1511 {
1512 __glibcxx_assert(_M_alpha > result_type(0));
1513 __glibcxx_assert(_M_mu > result_type(0));
1514 }
1516 result_type
1517 alpha() const
1518 { return _M_alpha; }
1520 result_type
1521 mu() const
1522 { return _M_mu; }
1524 friend bool
1525 operator==(const param_type& __p1, const param_type& __p2)
1526 { return __p1._M_alpha == __p2._M_alpha && __p1._M_mu == __p2._M_mu; }
1528 #if __cpp_impl_three_way_comparison < 201907L
1529 friend bool
1530 operator!=(const param_type& __p1, const param_type& __p2)
1531 { return !(__p1 == __p2); }
1532 #endif
1534 private:
1535 void _M_initialize();
1537 result_type _M_alpha;
1538 result_type _M_mu;
1539 };
1541 /**
1542 * @brief Constructors.
1543 * @{
1544 */
1546 pareto_distribution() : pareto_distribution(1) { }
1548 explicit
1549 pareto_distribution(result_type __alpha_val,
1550 result_type __mu_val = result_type(1))
1551 : _M_param(__alpha_val, __mu_val),
1552 _M_ud()
1553 { }
1555 explicit
1556 pareto_distribution(const param_type& __p)
1557 : _M_param(__p),
1558 _M_ud()
1559 { }
1561 /// @}
1563 /**
1564 * @brief Resets the distribution state.
1565 */
1566 void
1567 reset()
1568 {
1569 _M_ud.reset();
1570 }
1572 /**
1573 * @brief Return the parameters of the distribution.
1574 */
1575 result_type
1576 alpha() const
1577 { return _M_param.alpha(); }
1579 result_type
1580 mu() const
1581 { return _M_param.mu(); }
1583 /**
1584 * @brief Returns the parameter set of the distribution.
1585 */
1586 param_type
1587 param() const
1588 { return _M_param; }
1590 /**
1591 * @brief Sets the parameter set of the distribution.
1592 * @param __param The new parameter set of the distribution.
1593 */
1594 void
1595 param(const param_type& __param)
1596 { _M_param = __param; }
1598 /**
1599 * @brief Returns the greatest lower bound value of the distribution.
1600 */
1601 result_type
1602 min() const
1603 { return this->mu(); }
1605 /**
1606 * @brief Returns the least upper bound value of the distribution.
1607 */
1608 result_type
1609 max() const
1610 { return std::numeric_limits<result_type>::max(); }
1612 /**
1613 * @brief Generating functions.
1614 */
1615 template<typename _UniformRandomNumberGenerator>
1616 result_type
1617 operator()(_UniformRandomNumberGenerator& __urng)
1618 {
1619 return this->mu() * std::pow(this->_M_ud(__urng),
1620 -result_type(1) / this->alpha());
1621 }
1623 template<typename _UniformRandomNumberGenerator>
1624 result_type
1625 operator()(_UniformRandomNumberGenerator& __urng,
1626 const param_type& __p)
1627 {
1628 return __p.mu() * std::pow(this->_M_ud(__urng),
1629 -result_type(1) / __p.alpha());
1630 }
1632 template<typename _ForwardIterator,
1633 typename _UniformRandomNumberGenerator>
1634 void
1635 __generate(_ForwardIterator __f, _ForwardIterator __t,
1636 _UniformRandomNumberGenerator& __urng)
1637 { this->__generate(__f, __t, __urng, _M_param); }
1639 template<typename _ForwardIterator,
1640 typename _UniformRandomNumberGenerator>
1641 void
1642 __generate(_ForwardIterator __f, _ForwardIterator __t,
1643 _UniformRandomNumberGenerator& __urng,
1644 const param_type& __p)
1645 { this->__generate_impl(__f, __t, __urng, __p); }
1647 template<typename _UniformRandomNumberGenerator>
1648 void
1649 __generate(result_type* __f, result_type* __t,
1650 _UniformRandomNumberGenerator& __urng,
1651 const param_type& __p)
1652 { this->__generate_impl(__f, __t, __urng, __p); }
1654 /**
1655 * @brief Return true if two Pareto distributions have
1656 * the same parameters and the sequences that would
1657 * be generated are equal.
1658 */
1659 friend bool
1660 operator==(const pareto_distribution& __d1,
1661 const pareto_distribution& __d2)
1662 { return (__d1._M_param == __d2._M_param
1663 && __d1._M_ud == __d2._M_ud); }
1665 /**
1666 * @brief Inserts a %pareto_distribution random number distribution
1667 * @p __x into the output stream @p __os.
1668 *
1669 * @param __os An output stream.
1670 * @param __x A %pareto_distribution random number distribution.
1671 *
1672 * @returns The output stream with the state of @p __x inserted or in
1673 * an error state.
1674 */
1675 template<typename _RealType1, typename _CharT, typename _Traits>
1676 friend std::basic_ostream<_CharT, _Traits>&
1677 operator<<(std::basic_ostream<_CharT, _Traits>&,
1678 const pareto_distribution<_RealType1>&);
1680 /**
1681 * @brief Extracts a %pareto_distribution random number distribution
1682 * @p __x from the input stream @p __is.
1683 *
1684 * @param __is An input stream.
1685 * @param __x A %pareto_distribution random number
1686 * generator engine.
1687 *
1688 * @returns The input stream with @p __x extracted or in an error state.
1689 */
1690 template<typename _RealType1, typename _CharT, typename _Traits>
1691 friend std::basic_istream<_CharT, _Traits>&
1692 operator>>(std::basic_istream<_CharT, _Traits>&,
1693 pareto_distribution<_RealType1>&);
1695 private:
1696 template<typename _ForwardIterator,
1697 typename _UniformRandomNumberGenerator>
1698 void
1699 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1700 _UniformRandomNumberGenerator& __urng,
1701 const param_type& __p);
1703 param_type _M_param;
1705 std::uniform_real_distribution<result_type> _M_ud;
1706 };
1708 #if __cpp_impl_three_way_comparison < 201907L
1709 /**
1710 * @brief Return true if two Pareto distributions are not equal.
1711 */
1712 template<typename _RealType>
1713 inline bool
1714 operator!=(const pareto_distribution<_RealType>& __d1,
1715 const pareto_distribution<_RealType>& __d2)
1716 { return !(__d1 == __d2); }
1717 #endif
1719 /**
1720 * @brief A K continuous distribution for random numbers.
1721 *
1722 * The formula for the K probability density function is
1723 * @f[
1724 * p(x|\lambda, \mu, \nu) = \frac{2}{x}
1725 * \left(\frac{\lambda\nu x}{\mu}\right)^{\frac{\lambda + \nu}{2}}
1726 * \frac{1}{\Gamma(\lambda)\Gamma(\nu)}
1727 * K_{\nu - \lambda}\left(2\sqrt{\frac{\lambda\nu x}{\mu}}\right)
1728 * @f]
1729 * where @f$I_0(z)@f$ is the modified Bessel function of the second kind
1730 * of order @f$\nu - \lambda@f$ and @f$\lambda > 0@f$, @f$\mu > 0@f$
1731 * and @f$\nu > 0@f$.
1732 *
1733 * <table border=1 cellpadding=10 cellspacing=0>
1734 * <caption align=top>Distribution Statistics</caption>
1735 * <tr><td>Mean</td><td>@f$\mu@f$</td></tr>
1736 * <tr><td>Variance</td><td>@f$\mu^2\frac{\lambda + \nu + 1}{\lambda\nu}@f$</td></tr>
1737 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
1738 * </table>
1739 */
1740 template<typename _RealType = double>
1741 class
1742 k_distribution
1743 {
1744 static_assert(std::is_floating_point<_RealType>::value,
1745 "template argument not a floating point type");
1747 public:
1748 /** The type of the range of the distribution. */
1749 typedef _RealType result_type;
1751 /** Parameter type. */
1752 struct param_type
1753 {
1754 typedef k_distribution<result_type> distribution_type;
1756 param_type() : param_type(1) { }
1758 param_type(result_type __lambda_val,
1759 result_type __mu_val = result_type(1),
1760 result_type __nu_val = result_type(1))
1761 : _M_lambda(__lambda_val), _M_mu(__mu_val), _M_nu(__nu_val)
1762 {
1763 __glibcxx_assert(_M_lambda > result_type(0));
1764 __glibcxx_assert(_M_mu > result_type(0));
1765 __glibcxx_assert(_M_nu > result_type(0));
1766 }
1768 result_type
1769 lambda() const
1770 { return _M_lambda; }
1772 result_type
1773 mu() const
1774 { return _M_mu; }
1776 result_type
1777 nu() const
1778 { return _M_nu; }
1780 friend bool
1781 operator==(const param_type& __p1, const param_type& __p2)
1782 {
1783 return __p1._M_lambda == __p2._M_lambda
1784 && __p1._M_mu == __p2._M_mu
1785 && __p1._M_nu == __p2._M_nu;
1786 }
1788 #if __cpp_impl_three_way_comparison < 201907L
1789 friend bool
1790 operator!=(const param_type& __p1, const param_type& __p2)
1791 { return !(__p1 == __p2); }
1792 #endif
1794 private:
1795 void _M_initialize();
1797 result_type _M_lambda;
1798 result_type _M_mu;
1799 result_type _M_nu;
1800 };
1802 /**
1803 * @brief Constructors.
1804 * @{
1805 */
1807 k_distribution() : k_distribution(1) { }
1809 explicit
1810 k_distribution(result_type __lambda_val,
1811 result_type __mu_val = result_type(1),
1812 result_type __nu_val = result_type(1))
1813 : _M_param(__lambda_val, __mu_val, __nu_val),
1814 _M_gd1(__lambda_val, result_type(1) / __lambda_val),
1815 _M_gd2(__nu_val, __mu_val / __nu_val)
1816 { }
1818 explicit
1819 k_distribution(const param_type& __p)
1820 : _M_param(__p),
1821 _M_gd1(__p.lambda(), result_type(1) / __p.lambda()),
1822 _M_gd2(__p.nu(), __p.mu() / __p.nu())
1823 { }
1825 /// @}
1827 /**
1828 * @brief Resets the distribution state.
1829 */
1830 void
1831 reset()
1832 {
1833 _M_gd1.reset();
1834 _M_gd2.reset();
1835 }
1837 /**
1838 * @brief Return the parameters of the distribution.
1839 */
1840 result_type
1841 lambda() const
1842 { return _M_param.lambda(); }
1844 result_type
1845 mu() const
1846 { return _M_param.mu(); }
1848 result_type
1849 nu() const
1850 { return _M_param.nu(); }
1852 /**
1853 * @brief Returns the parameter set of the distribution.
1854 */
1855 param_type
1856 param() const
1857 { return _M_param; }
1859 /**
1860 * @brief Sets the parameter set of the distribution.
1861 * @param __param The new parameter set of the distribution.
1862 */
1863 void
1864 param(const param_type& __param)
1865 { _M_param = __param; }
1867 /**
1868 * @brief Returns the greatest lower bound value of the distribution.
1869 */
1870 result_type
1871 min() const
1872 { return result_type(0); }
1874 /**
1875 * @brief Returns the least upper bound value of the distribution.
1876 */
1877 result_type
1878 max() const
1879 { return std::numeric_limits<result_type>::max(); }
1881 /**
1882 * @brief Generating functions.
1883 */
1884 template<typename _UniformRandomNumberGenerator>
1885 result_type
1886 operator()(_UniformRandomNumberGenerator&);
1888 template<typename _UniformRandomNumberGenerator>
1889 result_type
1890 operator()(_UniformRandomNumberGenerator&, const param_type&);
1892 template<typename _ForwardIterator,
1893 typename _UniformRandomNumberGenerator>
1894 void
1895 __generate(_ForwardIterator __f, _ForwardIterator __t,
1896 _UniformRandomNumberGenerator& __urng)
1897 { this->__generate(__f, __t, __urng, _M_param); }
1899 template<typename _ForwardIterator,
1900 typename _UniformRandomNumberGenerator>
1901 void
1902 __generate(_ForwardIterator __f, _ForwardIterator __t,
1903 _UniformRandomNumberGenerator& __urng,
1904 const param_type& __p)
1905 { this->__generate_impl(__f, __t, __urng, __p); }
1907 template<typename _UniformRandomNumberGenerator>
1908 void
1909 __generate(result_type* __f, result_type* __t,
1910 _UniformRandomNumberGenerator& __urng,
1911 const param_type& __p)
1912 { this->__generate_impl(__f, __t, __urng, __p); }
1914 /**
1915 * @brief Return true if two K distributions have
1916 * the same parameters and the sequences that would
1917 * be generated are equal.
1918 */
1919 friend bool
1920 operator==(const k_distribution& __d1,
1921 const k_distribution& __d2)
1922 { return (__d1._M_param == __d2._M_param
1923 && __d1._M_gd1 == __d2._M_gd1
1924 && __d1._M_gd2 == __d2._M_gd2); }
1926 /**
1927 * @brief Inserts a %k_distribution random number distribution
1928 * @p __x into the output stream @p __os.
1929 *
1930 * @param __os An output stream.
1931 * @param __x A %k_distribution random number distribution.
1932 *
1933 * @returns The output stream with the state of @p __x inserted or in
1934 * an error state.
1935 */
1936 template<typename _RealType1, typename _CharT, typename _Traits>
1937 friend std::basic_ostream<_CharT, _Traits>&
1938 operator<<(std::basic_ostream<_CharT, _Traits>&,
1939 const k_distribution<_RealType1>&);
1941 /**
1942 * @brief Extracts a %k_distribution random number distribution
1943 * @p __x from the input stream @p __is.
1944 *
1945 * @param __is An input stream.
1946 * @param __x A %k_distribution random number
1947 * generator engine.
1948 *
1949 * @returns The input stream with @p __x extracted or in an error state.
1950 */
1951 template<typename _RealType1, typename _CharT, typename _Traits>
1952 friend std::basic_istream<_CharT, _Traits>&
1953 operator>>(std::basic_istream<_CharT, _Traits>&,
1954 k_distribution<_RealType1>&);
1956 private:
1957 template<typename _ForwardIterator,
1958 typename _UniformRandomNumberGenerator>
1959 void
1960 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1961 _UniformRandomNumberGenerator& __urng,
1962 const param_type& __p);
1964 param_type _M_param;
1966 std::gamma_distribution<result_type> _M_gd1;
1967 std::gamma_distribution<result_type> _M_gd2;
1968 };
1970 #if __cpp_impl_three_way_comparison < 201907L
1971 /**
1972 * @brief Return true if two K distributions are not equal.
1973 */
1974 template<typename _RealType>
1975 inline bool
1976 operator!=(const k_distribution<_RealType>& __d1,
1977 const k_distribution<_RealType>& __d2)
1978 { return !(__d1 == __d2); }
1979 #endif
1981 /**
1982 * @brief An arcsine continuous distribution for random numbers.
1983 *
1984 * The formula for the arcsine probability density function is
1985 * @f[
1986 * p(x|a,b) = \frac{1}{\pi \sqrt{(x - a)(b - x)}}
1987 * @f]
1988 * where @f$x >= a@f$ and @f$x <= b@f$.
1989 *
1990 * <table border=1 cellpadding=10 cellspacing=0>
1991 * <caption align=top>Distribution Statistics</caption>
1992 * <tr><td>Mean</td><td>@f$ (a + b) / 2 @f$</td></tr>
1993 * <tr><td>Variance</td><td>@f$ (b - a)^2 / 8 @f$</td></tr>
1994 * <tr><td>Range</td><td>@f$[a, b]@f$</td></tr>
1995 * </table>
1996 */
1997 template<typename _RealType = double>
1998 class
1999 arcsine_distribution
2000 {
2001 static_assert(std::is_floating_point<_RealType>::value,
2002 "template argument not a floating point type");
2004 public:
2005 /** The type of the range of the distribution. */
2006 typedef _RealType result_type;
2008 /** Parameter type. */
2009 struct param_type
2010 {
2011 typedef arcsine_distribution<result_type> distribution_type;
2013 param_type() : param_type(0) { }
2015 param_type(result_type __a, result_type __b = result_type(1))
2016 : _M_a(__a), _M_b(__b)
2017 {
2018 __glibcxx_assert(_M_a <= _M_b);
2019 }
2021 result_type
2022 a() const
2023 { return _M_a; }
2025 result_type
2026 b() const
2027 { return _M_b; }
2029 friend bool
2030 operator==(const param_type& __p1, const param_type& __p2)
2031 { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
2033 #if __cpp_impl_three_way_comparison < 201907L
2034 friend bool
2035 operator!=(const param_type& __p1, const param_type& __p2)
2036 { return !(__p1 == __p2); }
2037 #endif
2039 private:
2040 void _M_initialize();
2042 result_type _M_a;
2043 result_type _M_b;
2044 };
2046 /**
2047 * @brief Constructors.
2048 * :{
2049 */
2051 arcsine_distribution() : arcsine_distribution(0) { }
2053 explicit
2054 arcsine_distribution(result_type __a, result_type __b = result_type(1))
2055 : _M_param(__a, __b),
2056 _M_ud(-1.5707963267948966192313216916397514L,
2057 +1.5707963267948966192313216916397514L)
2058 { }
2060 explicit
2061 arcsine_distribution(const param_type& __p)
2062 : _M_param(__p),
2063 _M_ud(-1.5707963267948966192313216916397514L,
2064 +1.5707963267948966192313216916397514L)
2065 { }
2067 /// @}
2069 /**
2070 * @brief Resets the distribution state.
2071 */
2072 void
2073 reset()
2074 { _M_ud.reset(); }
2076 /**
2077 * @brief Return the parameters of the distribution.
2078 */
2079 result_type
2080 a() const
2081 { return _M_param.a(); }
2083 result_type
2084 b() const
2085 { return _M_param.b(); }
2087 /**
2088 * @brief Returns the parameter set of the distribution.
2089 */
2090 param_type
2091 param() const
2092 { return _M_param; }
2094 /**
2095 * @brief Sets the parameter set of the distribution.
2096 * @param __param The new parameter set of the distribution.
2097 */
2098 void
2099 param(const param_type& __param)
2100 { _M_param = __param; }
2102 /**
2103 * @brief Returns the greatest lower bound value of the distribution.
2104 */
2105 result_type
2106 min() const
2107 { return this->a(); }
2109 /**
2110 * @brief Returns the least upper bound value of the distribution.
2111 */
2112 result_type
2113 max() const
2114 { return this->b(); }
2116 /**
2117 * @brief Generating functions.
2118 */
2119 template<typename _UniformRandomNumberGenerator>
2120 result_type
2121 operator()(_UniformRandomNumberGenerator& __urng)
2122 {
2123 result_type __x = std::sin(this->_M_ud(__urng));
2124 return (__x * (this->b() - this->a())
2125 + this->a() + this->b()) / result_type(2);
2126 }
2128 template<typename _UniformRandomNumberGenerator>
2129 result_type
2130 operator()(_UniformRandomNumberGenerator& __urng,
2131 const param_type& __p)
2132 {
2133 result_type __x = std::sin(this->_M_ud(__urng));
2134 return (__x * (__p.b() - __p.a())
2135 + __p.a() + __p.b()) / result_type(2);
2136 }
2138 template<typename _ForwardIterator,
2139 typename _UniformRandomNumberGenerator>
2140 void
2141 __generate(_ForwardIterator __f, _ForwardIterator __t,
2142 _UniformRandomNumberGenerator& __urng)
2143 { this->__generate(__f, __t, __urng, _M_param); }
2145 template<typename _ForwardIterator,
2146 typename _UniformRandomNumberGenerator>
2147 void
2148 __generate(_ForwardIterator __f, _ForwardIterator __t,
2149 _UniformRandomNumberGenerator& __urng,
2150 const param_type& __p)
2151 { this->__generate_impl(__f, __t, __urng, __p); }
2153 template<typename _UniformRandomNumberGenerator>
2154 void
2155 __generate(result_type* __f, result_type* __t,
2156 _UniformRandomNumberGenerator& __urng,
2157 const param_type& __p)
2158 { this->__generate_impl(__f, __t, __urng, __p); }
2160 /**
2161 * @brief Return true if two arcsine distributions have
2162 * the same parameters and the sequences that would
2163 * be generated are equal.
2164 */
2165 friend bool
2166 operator==(const arcsine_distribution& __d1,
2167 const arcsine_distribution& __d2)
2168 { return (__d1._M_param == __d2._M_param
2169 && __d1._M_ud == __d2._M_ud); }
2171 /**
2172 * @brief Inserts a %arcsine_distribution random number distribution
2173 * @p __x into the output stream @p __os.
2174 *
2175 * @param __os An output stream.
2176 * @param __x A %arcsine_distribution random number distribution.
2177 *
2178 * @returns The output stream with the state of @p __x inserted or in
2179 * an error state.
2180 */
2181 template<typename _RealType1, typename _CharT, typename _Traits>
2182 friend std::basic_ostream<_CharT, _Traits>&
2183 operator<<(std::basic_ostream<_CharT, _Traits>&,
2184 const arcsine_distribution<_RealType1>&);
2186 /**
2187 * @brief Extracts a %arcsine_distribution random number distribution
2188 * @p __x from the input stream @p __is.
2189 *
2190 * @param __is An input stream.
2191 * @param __x A %arcsine_distribution random number
2192 * generator engine.
2193 *
2194 * @returns The input stream with @p __x extracted or in an error state.
2195 */
2196 template<typename _RealType1, typename _CharT, typename _Traits>
2197 friend std::basic_istream<_CharT, _Traits>&
2198 operator>>(std::basic_istream<_CharT, _Traits>&,
2199 arcsine_distribution<_RealType1>&);
2201 private:
2202 template<typename _ForwardIterator,
2203 typename _UniformRandomNumberGenerator>
2204 void
2205 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2206 _UniformRandomNumberGenerator& __urng,
2207 const param_type& __p);
2209 param_type _M_param;
2211 std::uniform_real_distribution<result_type> _M_ud;
2212 };
2214 #if __cpp_impl_three_way_comparison < 201907L
2215 /**
2216 * @brief Return true if two arcsine distributions are not equal.
2217 */
2218 template<typename _RealType>
2219 inline bool
2220 operator!=(const arcsine_distribution<_RealType>& __d1,
2221 const arcsine_distribution<_RealType>& __d2)
2222 { return !(__d1 == __d2); }
2223 #endif
2225 /**
2226 * @brief A Hoyt continuous distribution for random numbers.
2227 *
2228 * The formula for the Hoyt probability density function is
2229 * @f[
2230 * p(x|q,\omega) = \frac{(1 + q^2)x}{q\omega}
2231 * \exp\left(-\frac{(1 + q^2)^2 x^2}{4 q^2 \omega}\right)
2232 * I_0\left(\frac{(1 - q^4) x^2}{4 q^2 \omega}\right)
2233 * @f]
2234 * where @f$I_0(z)@f$ is the modified Bessel function of the first kind
2235 * of order 0 and @f$0 < q < 1@f$.
2236 *
2237 * <table border=1 cellpadding=10 cellspacing=0>
2238 * <caption align=top>Distribution Statistics</caption>
2239 * <tr><td>Mean</td><td>@f$ \sqrt{\frac{2}{\pi}} \sqrt{\frac{\omega}{1 + q^2}}
2240 * E(1 - q^2) @f$</td></tr>
2241 * <tr><td>Variance</td><td>@f$ \omega \left(1 - \frac{2E^2(1 - q^2)}
2242 * {\pi (1 + q^2)}\right) @f$</td></tr>
2243 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
2244 * </table>
2245 * where @f$E(x)@f$ is the elliptic function of the second kind.
2246 */
2247 template<typename _RealType = double>
2248 class
2249 hoyt_distribution
2250 {
2251 static_assert(std::is_floating_point<_RealType>::value,
2252 "template argument not a floating point type");
2254 public:
2255 /** The type of the range of the distribution. */
2256 typedef _RealType result_type;
2258 /** Parameter type. */
2259 struct param_type
2260 {
2261 typedef hoyt_distribution<result_type> distribution_type;
2263 param_type() : param_type(0.5) { }
2265 param_type(result_type __q, result_type __omega = result_type(1))
2266 : _M_q(__q), _M_omega(__omega)
2267 {
2268 __glibcxx_assert(_M_q > result_type(0));
2269 __glibcxx_assert(_M_q < result_type(1));
2270 }
2272 result_type
2273 q() const
2274 { return _M_q; }
2276 result_type
2277 omega() const
2278 { return _M_omega; }
2280 friend bool
2281 operator==(const param_type& __p1, const param_type& __p2)
2282 { return __p1._M_q == __p2._M_q && __p1._M_omega == __p2._M_omega; }
2284 #if __cpp_impl_three_way_comparison < 201907L
2285 friend bool
2286 operator!=(const param_type& __p1, const param_type& __p2)
2287 { return !(__p1 == __p2); }
2288 #endif
2290 private:
2291 void _M_initialize();
2293 result_type _M_q;
2294 result_type _M_omega;
2295 };
2297 /**
2298 * @brief Constructors.
2299 * @{
2300 */
2302 hoyt_distribution() : hoyt_distribution(0.5) { }
2304 explicit
2305 hoyt_distribution(result_type __q, result_type __omega = result_type(1))
2306 : _M_param(__q, __omega),
2307 _M_ad(result_type(0.5L) * (result_type(1) + __q * __q),
2308 result_type(0.5L) * (result_type(1) + __q * __q)
2309 / (__q * __q)),
2310 _M_ed(result_type(1))
2311 { }
2313 explicit
2314 hoyt_distribution(const param_type& __p)
2315 : _M_param(__p),
2316 _M_ad(result_type(0.5L) * (result_type(1) + __p.q() * __p.q()),
2317 result_type(0.5L) * (result_type(1) + __p.q() * __p.q())
2318 / (__p.q() * __p.q())),
2319 _M_ed(result_type(1))
2320 { }
2322 /**
2323 * @brief Resets the distribution state.
2324 */
2325 void
2326 reset()
2327 {
2328 _M_ad.reset();
2329 _M_ed.reset();
2330 }
2332 /**
2333 * @brief Return the parameters of the distribution.
2334 */
2335 result_type
2336 q() const
2337 { return _M_param.q(); }
2339 result_type
2340 omega() const
2341 { return _M_param.omega(); }
2343 /**
2344 * @brief Returns the parameter set of the distribution.
2345 */
2346 param_type
2347 param() const
2348 { return _M_param; }
2350 /**
2351 * @brief Sets the parameter set of the distribution.
2352 * @param __param The new parameter set of the distribution.
2353 */
2354 void
2355 param(const param_type& __param)
2356 { _M_param = __param; }
2358 /**
2359 * @brief Returns the greatest lower bound value of the distribution.
2360 */
2361 result_type
2362 min() const
2363 { return result_type(0); }
2365 /**
2366 * @brief Returns the least upper bound value of the distribution.
2367 */
2368 result_type
2369 max() const
2370 { return std::numeric_limits<result_type>::max(); }
2372 /**
2373 * @brief Generating functions.
2374 */
2375 template<typename _UniformRandomNumberGenerator>
2376 result_type
2377 operator()(_UniformRandomNumberGenerator& __urng);
2379 template<typename _UniformRandomNumberGenerator>
2380 result_type
2381 operator()(_UniformRandomNumberGenerator& __urng,
2382 const param_type& __p);
2384 template<typename _ForwardIterator,
2385 typename _UniformRandomNumberGenerator>
2386 void
2387 __generate(_ForwardIterator __f, _ForwardIterator __t,
2388 _UniformRandomNumberGenerator& __urng)
2389 { this->__generate(__f, __t, __urng, _M_param); }
2391 template<typename _ForwardIterator,
2392 typename _UniformRandomNumberGenerator>
2393 void
2394 __generate(_ForwardIterator __f, _ForwardIterator __t,
2395 _UniformRandomNumberGenerator& __urng,
2396 const param_type& __p)
2397 { this->__generate_impl(__f, __t, __urng, __p); }
2399 template<typename _UniformRandomNumberGenerator>
2400 void
2401 __generate(result_type* __f, result_type* __t,
2402 _UniformRandomNumberGenerator& __urng,
2403 const param_type& __p)
2404 { this->__generate_impl(__f, __t, __urng, __p); }
2406 /**
2407 * @brief Return true if two Hoyt distributions have
2408 * the same parameters and the sequences that would
2409 * be generated are equal.
2410 */
2411 friend bool
2412 operator==(const hoyt_distribution& __d1,
2413 const hoyt_distribution& __d2)
2414 { return (__d1._M_param == __d2._M_param
2415 && __d1._M_ad == __d2._M_ad
2416 && __d1._M_ed == __d2._M_ed); }
2418 /**
2419 * @brief Inserts a %hoyt_distribution random number distribution
2420 * @p __x into the output stream @p __os.
2421 *
2422 * @param __os An output stream.
2423 * @param __x A %hoyt_distribution random number distribution.
2424 *
2425 * @returns The output stream with the state of @p __x inserted or in
2426 * an error state.
2427 */
2428 template<typename _RealType1, typename _CharT, typename _Traits>
2429 friend std::basic_ostream<_CharT, _Traits>&
2430 operator<<(std::basic_ostream<_CharT, _Traits>&,
2431 const hoyt_distribution<_RealType1>&);
2433 /**
2434 * @brief Extracts a %hoyt_distribution random number distribution
2435 * @p __x from the input stream @p __is.
2436 *
2437 * @param __is An input stream.
2438 * @param __x A %hoyt_distribution random number
2439 * generator engine.
2440 *
2441 * @returns The input stream with @p __x extracted or in an error state.
2442 */
2443 template<typename _RealType1, typename _CharT, typename _Traits>
2444 friend std::basic_istream<_CharT, _Traits>&
2445 operator>>(std::basic_istream<_CharT, _Traits>&,
2446 hoyt_distribution<_RealType1>&);
2448 private:
2449 template<typename _ForwardIterator,
2450 typename _UniformRandomNumberGenerator>
2451 void
2452 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2453 _UniformRandomNumberGenerator& __urng,
2454 const param_type& __p);
2456 param_type _M_param;
2458 __gnu_cxx::arcsine_distribution<result_type> _M_ad;
2459 std::exponential_distribution<result_type> _M_ed;
2460 };
2462 #if __cpp_impl_three_way_comparison < 201907L
2463 /**
2464 * @brief Return true if two Hoyt distributions are not equal.
2465 */
2466 template<typename _RealType>
2467 inline bool
2468 operator!=(const hoyt_distribution<_RealType>& __d1,
2469 const hoyt_distribution<_RealType>& __d2)
2470 { return !(__d1 == __d2); }
2471 #endif
2473 /**
2474 * @brief A triangular distribution for random numbers.
2475 *
2476 * The formula for the triangular probability density function is
2477 * @f[
2478 * / 0 for x < a
2479 * p(x|a,b,c) = | \frac{2(x-a)}{(c-a)(b-a)} for a <= x <= b
2480 * | \frac{2(c-x)}{(c-a)(c-b)} for b < x <= c
2481 * \ 0 for c < x
2482 * @f]
2483 *
2484 * <table border=1 cellpadding=10 cellspacing=0>
2485 * <caption align=top>Distribution Statistics</caption>
2486 * <tr><td>Mean</td><td>@f$ \frac{a+b+c}{2} @f$</td></tr>
2487 * <tr><td>Variance</td><td>@f$ \frac{a^2+b^2+c^2-ab-ac-bc}
2488 * {18}@f$</td></tr>
2489 * <tr><td>Range</td><td>@f$[a, c]@f$</td></tr>
2490 * </table>
2491 */
2492 template<typename _RealType = double>
2493 class triangular_distribution
2494 {
2495 static_assert(std::is_floating_point<_RealType>::value,
2496 "template argument not a floating point type");
2498 public:
2499 /** The type of the range of the distribution. */
2500 typedef _RealType result_type;
2502 /** Parameter type. */
2503 struct param_type
2504 {
2505 friend class triangular_distribution<_RealType>;
2507 param_type() : param_type(0) { }
2509 explicit
2510 param_type(_RealType __a,
2511 _RealType __b = _RealType(0.5),
2512 _RealType __c = _RealType(1))
2513 : _M_a(__a), _M_b(__b), _M_c(__c)
2514 {
2515 __glibcxx_assert(_M_a <= _M_b);
2516 __glibcxx_assert(_M_b <= _M_c);
2517 __glibcxx_assert(_M_a < _M_c);
2519 _M_r_ab = (_M_b - _M_a) / (_M_c - _M_a);
2520 _M_f_ab_ac = (_M_b - _M_a) * (_M_c - _M_a);
2521 _M_f_bc_ac = (_M_c - _M_b) * (_M_c - _M_a);
2522 }
2524 _RealType
2525 a() const
2526 { return _M_a; }
2528 _RealType
2529 b() const
2530 { return _M_b; }
2532 _RealType
2533 c() const
2534 { return _M_c; }
2536 friend bool
2537 operator==(const param_type& __p1, const param_type& __p2)
2538 {
2539 return (__p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b
2540 && __p1._M_c == __p2._M_c);
2541 }
2543 #if __cpp_impl_three_way_comparison < 201907L
2544 friend bool
2545 operator!=(const param_type& __p1, const param_type& __p2)
2546 { return !(__p1 == __p2); }
2547 #endif
2549 private:
2551 _RealType _M_a;
2552 _RealType _M_b;
2553 _RealType _M_c;
2554 _RealType _M_r_ab;
2555 _RealType _M_f_ab_ac;
2556 _RealType _M_f_bc_ac;
2557 };
2559 triangular_distribution() : triangular_distribution(0.0) { }
2561 /**
2562 * @brief Constructs a triangle distribution with parameters
2563 * @f$ a @f$, @f$ b @f$ and @f$ c @f$.
2564 */
2565 explicit
2566 triangular_distribution(result_type __a,
2567 result_type __b = result_type(0.5),
2568 result_type __c = result_type(1))
2569 : _M_param(__a, __b, __c)
2570 { }
2572 explicit
2573 triangular_distribution(const param_type& __p)
2574 : _M_param(__p)
2575 { }
2577 /**
2578 * @brief Resets the distribution state.
2579 */
2580 void
2581 reset()
2582 { }
2584 /**
2585 * @brief Returns the @f$ a @f$ of the distribution.
2586 */
2587 result_type
2588 a() const
2589 { return _M_param.a(); }
2591 /**
2592 * @brief Returns the @f$ b @f$ of the distribution.
2593 */
2594 result_type
2595 b() const
2596 { return _M_param.b(); }
2598 /**
2599 * @brief Returns the @f$ c @f$ of the distribution.
2600 */
2601 result_type
2602 c() const
2603 { return _M_param.c(); }
2605 /**
2606 * @brief Returns the parameter set of the distribution.
2607 */
2608 param_type
2609 param() const
2610 { return _M_param; }
2612 /**
2613 * @brief Sets the parameter set of the distribution.
2614 * @param __param The new parameter set of the distribution.
2615 */
2616 void
2617 param(const param_type& __param)
2618 { _M_param = __param; }
2620 /**
2621 * @brief Returns the greatest lower bound value of the distribution.
2622 */
2623 result_type
2624 min() const
2625 { return _M_param._M_a; }
2627 /**
2628 * @brief Returns the least upper bound value of the distribution.
2629 */
2630 result_type
2631 max() const
2632 { return _M_param._M_c; }
2634 /**
2635 * @brief Generating functions.
2636 */
2637 template<typename _UniformRandomNumberGenerator>
2638 result_type
2639 operator()(_UniformRandomNumberGenerator& __urng)
2640 { return this->operator()(__urng, _M_param); }
2642 template<typename _UniformRandomNumberGenerator>
2643 result_type
2644 operator()(_UniformRandomNumberGenerator& __urng,
2645 const param_type& __p)
2646 {
2647 std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2648 __aurng(__urng);
2649 result_type __rnd = __aurng();
2650 if (__rnd <= __p._M_r_ab)
2651 return __p.a() + std::sqrt(__rnd * __p._M_f_ab_ac);
2652 else
2653 return __p.c() - std::sqrt((result_type(1) - __rnd)
2654 * __p._M_f_bc_ac);
2655 }
2657 template<typename _ForwardIterator,
2658 typename _UniformRandomNumberGenerator>
2659 void
2660 __generate(_ForwardIterator __f, _ForwardIterator __t,
2661 _UniformRandomNumberGenerator& __urng)
2662 { this->__generate(__f, __t, __urng, _M_param); }
2664 template<typename _ForwardIterator,
2665 typename _UniformRandomNumberGenerator>
2666 void
2667 __generate(_ForwardIterator __f, _ForwardIterator __t,
2668 _UniformRandomNumberGenerator& __urng,
2669 const param_type& __p)
2670 { this->__generate_impl(__f, __t, __urng, __p); }
2672 template<typename _UniformRandomNumberGenerator>
2673 void
2674 __generate(result_type* __f, result_type* __t,
2675 _UniformRandomNumberGenerator& __urng,
2676 const param_type& __p)
2677 { this->__generate_impl(__f, __t, __urng, __p); }
2679 /**
2680 * @brief Return true if two triangle distributions have the same
2681 * parameters and the sequences that would be generated
2682 * are equal.
2683 */
2684 friend bool
2685 operator==(const triangular_distribution& __d1,
2686 const triangular_distribution& __d2)
2687 { return __d1._M_param == __d2._M_param; }
2689 /**
2690 * @brief Inserts a %triangular_distribution random number distribution
2691 * @p __x into the output stream @p __os.
2692 *
2693 * @param __os An output stream.
2694 * @param __x A %triangular_distribution random number distribution.
2695 *
2696 * @returns The output stream with the state of @p __x inserted or in
2697 * an error state.
2698 */
2699 template<typename _RealType1, typename _CharT, typename _Traits>
2700 friend std::basic_ostream<_CharT, _Traits>&
2701 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2702 const __gnu_cxx::triangular_distribution<_RealType1>& __x);
2704 /**
2705 * @brief Extracts a %triangular_distribution random number distribution
2706 * @p __x from the input stream @p __is.
2707 *
2708 * @param __is An input stream.
2709 * @param __x A %triangular_distribution random number generator engine.
2710 *
2711 * @returns The input stream with @p __x extracted or in an error state.
2712 */
2713 template<typename _RealType1, typename _CharT, typename _Traits>
2714 friend std::basic_istream<_CharT, _Traits>&
2715 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2716 __gnu_cxx::triangular_distribution<_RealType1>& __x);
2718 private:
2719 template<typename _ForwardIterator,
2720 typename _UniformRandomNumberGenerator>
2721 void
2722 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2723 _UniformRandomNumberGenerator& __urng,
2724 const param_type& __p);
2726 param_type _M_param;
2727 };
2729 #if __cpp_impl_three_way_comparison < 201907L
2730 /**
2731 * @brief Return true if two triangle distributions are different.
2732 */
2733 template<typename _RealType>
2734 inline bool
2735 operator!=(const __gnu_cxx::triangular_distribution<_RealType>& __d1,
2736 const __gnu_cxx::triangular_distribution<_RealType>& __d2)
2737 { return !(__d1 == __d2); }
2738 #endif
2740 /**
2741 * @brief A von Mises distribution for random numbers.
2742 *
2743 * The formula for the von Mises probability density function is
2744 * @f[
2745 * p(x|\mu,\kappa) = \frac{e^{\kappa \cos(x-\mu)}}
2746 * {2\pi I_0(\kappa)}
2747 * @f]
2748 *
2749 * The generating functions use the method according to:
2750 *
2751 * D. J. Best and N. I. Fisher, 1979. "Efficient Simulation of the
2752 * von Mises Distribution", Journal of the Royal Statistical Society.
2753 * Series C (Applied Statistics), Vol. 28, No. 2, pp. 152-157.
2754 *
2755 * <table border=1 cellpadding=10 cellspacing=0>
2756 * <caption align=top>Distribution Statistics</caption>
2757 * <tr><td>Mean</td><td>@f$ \mu @f$</td></tr>
2758 * <tr><td>Variance</td><td>@f$ 1-I_1(\kappa)/I_0(\kappa) @f$</td></tr>
2759 * <tr><td>Range</td><td>@f$[-\pi, \pi]@f$</td></tr>
2760 * </table>
2761 */
2762 template<typename _RealType = double>
2763 class von_mises_distribution
2764 {
2765 static_assert(std::is_floating_point<_RealType>::value,
2766 "template argument not a floating point type");
2768 public:
2769 /** The type of the range of the distribution. */
2770 typedef _RealType result_type;
2772 /** Parameter type. */
2773 struct param_type
2774 {
2775 friend class von_mises_distribution<_RealType>;
2777 param_type() : param_type(0) { }
2779 explicit
2780 param_type(_RealType __mu, _RealType __kappa = _RealType(1))
2781 : _M_mu(__mu), _M_kappa(__kappa)
2782 {
2783 const _RealType __pi = __gnu_cxx::__math_constants<_RealType>::__pi;
2784 __glibcxx_assert(_M_mu >= -__pi && _M_mu <= __pi);
2785 __glibcxx_assert(_M_kappa >= _RealType(0));
2787 auto __tau = std::sqrt(_RealType(4) * _M_kappa * _M_kappa
2788 + _RealType(1)) + _RealType(1);
2789 auto __rho = ((__tau - std::sqrt(_RealType(2) * __tau))
2790 / (_RealType(2) * _M_kappa));
2791 _M_r = (_RealType(1) + __rho * __rho) / (_RealType(2) * __rho);
2792 }
2794 _RealType
2795 mu() const
2796 { return _M_mu; }
2798 _RealType
2799 kappa() const
2800 { return _M_kappa; }
2802 friend bool
2803 operator==(const param_type& __p1, const param_type& __p2)
2804 { return __p1._M_mu == __p2._M_mu && __p1._M_kappa == __p2._M_kappa; }
2806 #if __cpp_impl_three_way_comparison < 201907L
2807 friend bool
2808 operator!=(const param_type& __p1, const param_type& __p2)
2809 { return !(__p1 == __p2); }
2810 #endif
2812 private:
2813 _RealType _M_mu;
2814 _RealType _M_kappa;
2815 _RealType _M_r;
2816 };
2818 von_mises_distribution() : von_mises_distribution(0.0) { }
2820 /**
2821 * @brief Constructs a von Mises distribution with parameters
2822 * @f$\mu@f$ and @f$\kappa@f$.
2823 */
2824 explicit
2825 von_mises_distribution(result_type __mu,
2826 result_type __kappa = result_type(1))
2827 : _M_param(__mu, __kappa)
2828 { }
2830 explicit
2831 von_mises_distribution(const param_type& __p)
2832 : _M_param(__p)
2833 { }
2835 /**
2836 * @brief Resets the distribution state.
2837 */
2838 void
2839 reset()
2840 { }
2842 /**
2843 * @brief Returns the @f$ \mu @f$ of the distribution.
2844 */
2845 result_type
2846 mu() const
2847 { return _M_param.mu(); }
2849 /**
2850 * @brief Returns the @f$ \kappa @f$ of the distribution.
2851 */
2852 result_type
2853 kappa() const
2854 { return _M_param.kappa(); }
2856 /**
2857 * @brief Returns the parameter set of the distribution.
2858 */
2859 param_type
2860 param() const
2861 { return _M_param; }
2863 /**
2864 * @brief Sets the parameter set of the distribution.
2865 * @param __param The new parameter set of the distribution.
2866 */
2867 void
2868 param(const param_type& __param)
2869 { _M_param = __param; }
2871 /**
2872 * @brief Returns the greatest lower bound value of the distribution.
2873 */
2874 result_type
2875 min() const
2876 {
2877 return -__gnu_cxx::__math_constants<result_type>::__pi;
2878 }
2880 /**
2881 * @brief Returns the least upper bound value of the distribution.
2882 */
2883 result_type
2884 max() const
2885 {
2886 return __gnu_cxx::__math_constants<result_type>::__pi;
2887 }
2889 /**
2890 * @brief Generating functions.
2891 */
2892 template<typename _UniformRandomNumberGenerator>
2893 result_type
2894 operator()(_UniformRandomNumberGenerator& __urng)
2895 { return this->operator()(__urng, _M_param); }
2897 template<typename _UniformRandomNumberGenerator>
2898 result_type
2899 operator()(_UniformRandomNumberGenerator& __urng,
2900 const param_type& __p);
2902 template<typename _ForwardIterator,
2903 typename _UniformRandomNumberGenerator>
2904 void
2905 __generate(_ForwardIterator __f, _ForwardIterator __t,
2906 _UniformRandomNumberGenerator& __urng)
2907 { this->__generate(__f, __t, __urng, _M_param); }
2909 template<typename _ForwardIterator,
2910 typename _UniformRandomNumberGenerator>
2911 void
2912 __generate(_ForwardIterator __f, _ForwardIterator __t,
2913 _UniformRandomNumberGenerator& __urng,
2914 const param_type& __p)
2915 { this->__generate_impl(__f, __t, __urng, __p); }
2917 template<typename _UniformRandomNumberGenerator>
2918 void
2919 __generate(result_type* __f, result_type* __t,
2920 _UniformRandomNumberGenerator& __urng,
2921 const param_type& __p)
2922 { this->__generate_impl(__f, __t, __urng, __p); }
2924 /**
2925 * @brief Return true if two von Mises distributions have the same
2926 * parameters and the sequences that would be generated
2927 * are equal.
2928 */
2929 friend bool
2930 operator==(const von_mises_distribution& __d1,
2931 const von_mises_distribution& __d2)
2932 { return __d1._M_param == __d2._M_param; }
2934 /**
2935 * @brief Inserts a %von_mises_distribution random number distribution
2936 * @p __x into the output stream @p __os.
2937 *
2938 * @param __os An output stream.
2939 * @param __x A %von_mises_distribution random number distribution.
2940 *
2941 * @returns The output stream with the state of @p __x inserted or in
2942 * an error state.
2943 */
2944 template<typename _RealType1, typename _CharT, typename _Traits>
2945 friend std::basic_ostream<_CharT, _Traits>&
2946 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2947 const __gnu_cxx::von_mises_distribution<_RealType1>& __x);
2949 /**
2950 * @brief Extracts a %von_mises_distribution random number distribution
2951 * @p __x from the input stream @p __is.
2952 *
2953 * @param __is An input stream.
2954 * @param __x A %von_mises_distribution random number generator engine.
2955 *
2956 * @returns The input stream with @p __x extracted or in an error state.
2957 */
2958 template<typename _RealType1, typename _CharT, typename _Traits>
2959 friend std::basic_istream<_CharT, _Traits>&
2960 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2961 __gnu_cxx::von_mises_distribution<_RealType1>& __x);
2963 private:
2964 template<typename _ForwardIterator,
2965 typename _UniformRandomNumberGenerator>
2966 void
2967 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2968 _UniformRandomNumberGenerator& __urng,
2969 const param_type& __p);
2971 param_type _M_param;
2972 };
2974 #if __cpp_impl_three_way_comparison < 201907L
2975 /**
2976 * @brief Return true if two von Mises distributions are different.
2977 */
2978 template<typename _RealType>
2979 inline bool
2980 operator!=(const __gnu_cxx::von_mises_distribution<_RealType>& __d1,
2981 const __gnu_cxx::von_mises_distribution<_RealType>& __d2)
2982 { return !(__d1 == __d2); }
2983 #endif
2985 /**
2986 * @brief A discrete hypergeometric random number distribution.
2987 *
2988 * The hypergeometric distribution is a discrete probability distribution
2989 * that describes the probability of @p k successes in @p n draws @a without
2990 * replacement from a finite population of size @p N containing exactly @p K
2991 * successes.
2992 *
2993 * The formula for the hypergeometric probability density function is
2994 * @f[
2995 * p(k|N,K,n) = \frac{\binom{K}{k} \binom{N-K}{n-k}}{\binom{N}{n}}
2996 * @f]
2997 * where @f$N@f$ is the total population of the distribution,
2998 * @f$K@f$ is the total population of the distribution.
2999 *
3000 * <table border=1 cellpadding=10 cellspacing=0>
3001 * <caption align=top>Distribution Statistics</caption>
3002 * <tr><td>Mean</td><td>@f$ n\frac{K}{N} @f$</td></tr>
3003 * <tr><td>Variance</td><td>@f$ n\frac{K}{N}\frac{N-K}{N}\frac{N-n}{N-1}
3004 * @f$</td></tr>
3005 * <tr><td>Range</td><td>@f$[max(0, n+K-N), min(K, n)]@f$</td></tr>
3006 * </table>
3007 */
3008 template<typename _UIntType = unsigned int>
3009 class hypergeometric_distribution
3010 {
3011 static_assert(std::is_unsigned<_UIntType>::value, "template argument "
3012 "substituting _UIntType not an unsigned integral type");
3014 public:
3015 /** The type of the range of the distribution. */
3016 typedef _UIntType result_type;
3018 /** Parameter type. */
3019 struct param_type
3020 {
3021 typedef hypergeometric_distribution<_UIntType> distribution_type;
3022 friend class hypergeometric_distribution<_UIntType>;
3024 param_type() : param_type(10) { }
3026 explicit
3027 param_type(result_type __N, result_type __K = 5,
3028 result_type __n = 1)
3029 : _M_N{__N}, _M_K{__K}, _M_n{__n}
3030 {
3031 __glibcxx_assert(_M_N >= _M_K);
3032 __glibcxx_assert(_M_N >= _M_n);
3033 }
3035 result_type
3036 total_size() const
3037 { return _M_N; }
3039 result_type
3040 successful_size() const
3041 { return _M_K; }
3043 result_type
3044 unsuccessful_size() const
3045 { return _M_N - _M_K; }
3047 result_type
3048 total_draws() const
3049 { return _M_n; }
3051 friend bool
3052 operator==(const param_type& __p1, const param_type& __p2)
3053 { return (__p1._M_N == __p2._M_N)
3054 && (__p1._M_K == __p2._M_K)
3055 && (__p1._M_n == __p2._M_n); }
3057 #if __cpp_impl_three_way_comparison < 201907L
3058 friend bool
3059 operator!=(const param_type& __p1, const param_type& __p2)
3060 { return !(__p1 == __p2); }
3061 #endif
3063 private:
3065 result_type _M_N;
3066 result_type _M_K;
3067 result_type _M_n;
3068 };
3070 // constructors and member functions
3072 hypergeometric_distribution() : hypergeometric_distribution(10) { }
3074 explicit
3075 hypergeometric_distribution(result_type __N, result_type __K = 5,
3076 result_type __n = 1)
3077 : _M_param{__N, __K, __n}
3078 { }
3080 explicit
3081 hypergeometric_distribution(const param_type& __p)
3082 : _M_param{__p}
3083 { }
3085 /**
3086 * @brief Resets the distribution state.
3087 */
3088 void
3089 reset()
3090 { }
3092 /**
3093 * @brief Returns the distribution parameter @p N,
3094 * the total number of items.
3095 */
3096 result_type
3097 total_size() const
3098 { return this->_M_param.total_size(); }
3100 /**
3101 * @brief Returns the distribution parameter @p K,
3102 * the total number of successful items.
3103 */
3104 result_type
3105 successful_size() const
3106 { return this->_M_param.successful_size(); }
3108 /**
3109 * @brief Returns the total number of unsuccessful items @f$ N - K @f$.
3110 */
3111 result_type
3112 unsuccessful_size() const
3113 { return this->_M_param.unsuccessful_size(); }
3115 /**
3116 * @brief Returns the distribution parameter @p n,
3117 * the total number of draws.
3118 */
3119 result_type
3120 total_draws() const
3121 { return this->_M_param.total_draws(); }
3123 /**
3124 * @brief Returns the parameter set of the distribution.
3125 */
3126 param_type
3127 param() const
3128 { return this->_M_param; }
3130 /**
3131 * @brief Sets the parameter set of the distribution.
3132 * @param __param The new parameter set of the distribution.
3133 */
3134 void
3135 param(const param_type& __param)
3136 { this->_M_param = __param; }
3138 /**
3139 * @brief Returns the greatest lower bound value of the distribution.
3140 */
3141 result_type
3142 min() const
3143 {
3144 using _IntType = typename std::make_signed<result_type>::type;
3145 return static_cast<result_type>(std::max(static_cast<_IntType>(0),
3146 static_cast<_IntType>(this->total_draws()
3147 - this->unsuccessful_size())));
3148 }
3150 /**
3151 * @brief Returns the least upper bound value of the distribution.
3152 */
3153 result_type
3154 max() const
3155 { return std::min(this->successful_size(), this->total_draws()); }
3157 /**
3158 * @brief Generating functions.
3159 */
3160 template<typename _UniformRandomNumberGenerator>
3161 result_type
3162 operator()(_UniformRandomNumberGenerator& __urng)
3163 { return this->operator()(__urng, this->_M_param); }
3165 template<typename _UniformRandomNumberGenerator>
3166 result_type
3167 operator()(_UniformRandomNumberGenerator& __urng,
3168 const param_type& __p);
3170 template<typename _ForwardIterator,
3171 typename _UniformRandomNumberGenerator>
3172 void
3173 __generate(_ForwardIterator __f, _ForwardIterator __t,
3174 _UniformRandomNumberGenerator& __urng)
3175 { this->__generate(__f, __t, __urng, this->_M_param); }
3177 template<typename _ForwardIterator,
3178 typename _UniformRandomNumberGenerator>
3179 void
3180 __generate(_ForwardIterator __f, _ForwardIterator __t,
3181 _UniformRandomNumberGenerator& __urng,
3182 const param_type& __p)
3183 { this->__generate_impl(__f, __t, __urng, __p); }
3185 template<typename _UniformRandomNumberGenerator>
3186 void
3187 __generate(result_type* __f, result_type* __t,
3188 _UniformRandomNumberGenerator& __urng,
3189 const param_type& __p)
3190 { this->__generate_impl(__f, __t, __urng, __p); }
3192 /**
3193 * @brief Return true if two hypergeometric distributions have the same
3194 * parameters and the sequences that would be generated
3195 * are equal.
3196 */
3197 friend bool
3198 operator==(const hypergeometric_distribution& __d1,
3199 const hypergeometric_distribution& __d2)
3200 { return __d1._M_param == __d2._M_param; }
3202 /**
3203 * @brief Inserts a %hypergeometric_distribution random number
3204 * distribution @p __x into the output stream @p __os.
3205 *
3206 * @param __os An output stream.
3207 * @param __x A %hypergeometric_distribution random number
3208 * distribution.
3209 *
3210 * @returns The output stream with the state of @p __x inserted or in
3211 * an error state.
3212 */
3213 template<typename _UIntType1, typename _CharT, typename _Traits>
3214 friend std::basic_ostream<_CharT, _Traits>&
3215 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3216 const __gnu_cxx::hypergeometric_distribution<_UIntType1>&
3217 __x);
3219 /**
3220 * @brief Extracts a %hypergeometric_distribution random number
3221 * distribution @p __x from the input stream @p __is.
3222 *
3223 * @param __is An input stream.
3224 * @param __x A %hypergeometric_distribution random number generator
3225 * distribution.
3226 *
3227 * @returns The input stream with @p __x extracted or in an error
3228 * state.
3229 */
3230 template<typename _UIntType1, typename _CharT, typename _Traits>
3231 friend std::basic_istream<_CharT, _Traits>&
3232 operator>>(std::basic_istream<_CharT, _Traits>& __is,
3233 __gnu_cxx::hypergeometric_distribution<_UIntType1>& __x);
3235 private:
3237 template<typename _ForwardIterator,
3238 typename _UniformRandomNumberGenerator>
3239 void
3240 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3241 _UniformRandomNumberGenerator& __urng,
3242 const param_type& __p);
3244 param_type _M_param;
3245 };
3247 #if __cpp_impl_three_way_comparison < 201907L
3248 /**
3249 * @brief Return true if two hypergeometric distributions are different.
3250 */
3251 template<typename _UIntType>
3252 inline bool
3253 operator!=(const __gnu_cxx::hypergeometric_distribution<_UIntType>& __d1,
3254 const __gnu_cxx::hypergeometric_distribution<_UIntType>& __d2)
3255 { return !(__d1 == __d2); }
3256 #endif
3258 /**
3259 * @brief A logistic continuous distribution for random numbers.
3260 *
3261 * The formula for the logistic probability density function is
3262 * @f[
3263 * p(x|\a,\b) = \frac{e^{(x - a)/b}}{b[1 + e^{(x - a)/b}]^2}
3264 * @f]
3265 * where @f$b > 0@f$.
3266 *
3267 * The formula for the logistic probability function is
3268 * @f[
3269 * cdf(x|\a,\b) = \frac{e^{(x - a)/b}}{1 + e^{(x - a)/b}}
3270 * @f]
3271 * where @f$b > 0@f$.
3272 *
3273 * <table border=1 cellpadding=10 cellspacing=0>
3274 * <caption align=top>Distribution Statistics</caption>
3275 * <tr><td>Mean</td><td>@f$a@f$</td></tr>
3276 * <tr><td>Variance</td><td>@f$b^2\pi^2/3@f$</td></tr>
3277 * <tr><td>Range</td><td>@f$[0, \infty)@f$</td></tr>
3278 * </table>
3279 */
3280 template<typename _RealType = double>
3281 class
3282 logistic_distribution
3283 {
3284 static_assert(std::is_floating_point<_RealType>::value,
3285 "template argument not a floating point type");
3287 public:
3288 /** The type of the range of the distribution. */
3289 typedef _RealType result_type;
3291 /** Parameter type. */
3292 struct param_type
3293 {
3294 typedef logistic_distribution<result_type> distribution_type;
3296 param_type() : param_type(0) { }
3298 explicit
3299 param_type(result_type __a, result_type __b = result_type(1))
3300 : _M_a(__a), _M_b(__b)
3301 {
3302 __glibcxx_assert(_M_b > result_type(0));
3303 }
3305 result_type
3306 a() const
3307 { return _M_a; }
3309 result_type
3310 b() const
3311 { return _M_b; }
3313 friend bool
3314 operator==(const param_type& __p1, const param_type& __p2)
3315 { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
3317 #if __cpp_impl_three_way_comparison < 201907L
3318 friend bool
3319 operator!=(const param_type& __p1, const param_type& __p2)
3320 { return !(__p1 == __p2); }
3321 #endif
3323 private:
3324 void _M_initialize();
3326 result_type _M_a;
3327 result_type _M_b;
3328 };
3330 /**
3331 * @brief Constructors.
3332 * @{
3333 */
3334 logistic_distribution() : logistic_distribution(0.0) { }
3336 explicit
3337 logistic_distribution(result_type __a, result_type __b = result_type(1))
3338 : _M_param(__a, __b)
3339 { }
3341 explicit
3342 logistic_distribution(const param_type& __p)
3343 : _M_param(__p)
3344 { }
3346 /// @}
3348 /**
3349 * @brief Resets the distribution state.
3350 */
3351 void
3352 reset()
3353 { }
3355 /**
3356 * @brief Return the parameters of the distribution.
3357 */
3358 result_type
3359 a() const
3360 { return _M_param.a(); }
3362 result_type
3363 b() const
3364 { return _M_param.b(); }
3366 /**
3367 * @brief Returns the parameter set of the distribution.
3368 */
3369 param_type
3370 param() const
3371 { return _M_param; }
3373 /**
3374 * @brief Sets the parameter set of the distribution.
3375 * @param __param The new parameter set of the distribution.
3376 */
3377 void
3378 param(const param_type& __param)
3379 { _M_param = __param; }
3381 /**
3382 * @brief Returns the greatest lower bound value of the distribution.
3383 */
3384 result_type
3385 min() const
3386 { return -std::numeric_limits<result_type>::max(); }
3388 /**
3389 * @brief Returns the least upper bound value of the distribution.
3390 */
3391 result_type
3392 max() const
3393 { return std::numeric_limits<result_type>::max(); }
3395 /**
3396 * @brief Generating functions.
3397 */
3398 template<typename _UniformRandomNumberGenerator>
3399 result_type
3400 operator()(_UniformRandomNumberGenerator& __urng)
3401 { return this->operator()(__urng, this->_M_param); }
3403 template<typename _UniformRandomNumberGenerator>
3404 result_type
3405 operator()(_UniformRandomNumberGenerator&,
3406 const param_type&);
3408 template<typename _ForwardIterator,
3409 typename _UniformRandomNumberGenerator>
3410 void
3411 __generate(_ForwardIterator __f, _ForwardIterator __t,
3412 _UniformRandomNumberGenerator& __urng)
3413 { this->__generate(__f, __t, __urng, this->param()); }
3415 template<typename _ForwardIterator,
3416 typename _UniformRandomNumberGenerator>
3417 void
3418 __generate(_ForwardIterator __f, _ForwardIterator __t,
3419 _UniformRandomNumberGenerator& __urng,
3420 const param_type& __p)
3421 { this->__generate_impl(__f, __t, __urng, __p); }
3423 template<typename _UniformRandomNumberGenerator>
3424 void
3425 __generate(result_type* __f, result_type* __t,
3426 _UniformRandomNumberGenerator& __urng,
3427 const param_type& __p)
3428 { this->__generate_impl(__f, __t, __urng, __p); }
3430 /**
3431 * @brief Return true if two logistic distributions have
3432 * the same parameters and the sequences that would
3433 * be generated are equal.
3434 */
3435 template<typename _RealType1>
3436 friend bool
3437 operator==(const logistic_distribution<_RealType1>& __d1,
3438 const logistic_distribution<_RealType1>& __d2)
3439 { return __d1.param() == __d2.param(); }
3441 /**
3442 * @brief Inserts a %logistic_distribution random number distribution
3443 * @p __x into the output stream @p __os.
3444 *
3445 * @param __os An output stream.
3446 * @param __x A %logistic_distribution random number distribution.
3447 *
3448 * @returns The output stream with the state of @p __x inserted or in
3449 * an error state.
3450 */
3451 template<typename _RealType1, typename _CharT, typename _Traits>
3452 friend std::basic_ostream<_CharT, _Traits>&
3453 operator<<(std::basic_ostream<_CharT, _Traits>&,
3454 const logistic_distribution<_RealType1>&);
3456 /**
3457 * @brief Extracts a %logistic_distribution random number distribution
3458 * @p __x from the input stream @p __is.
3459 *
3460 * @param __is An input stream.
3461 * @param __x A %logistic_distribution random number
3462 * generator engine.
3463 *
3464 * @returns The input stream with @p __x extracted or in an error state.
3465 */
3466 template<typename _RealType1, typename _CharT, typename _Traits>
3467 friend std::basic_istream<_CharT, _Traits>&
3468 operator>>(std::basic_istream<_CharT, _Traits>&,
3469 logistic_distribution<_RealType1>&);
3471 private:
3472 template<typename _ForwardIterator,
3473 typename _UniformRandomNumberGenerator>
3474 void
3475 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3476 _UniformRandomNumberGenerator& __urng,
3477 const param_type& __p);
3479 param_type _M_param;
3480 };
3482 #if __cpp_impl_three_way_comparison < 201907L
3483 /**
3484 * @brief Return true if two logistic distributions are not equal.
3485 */
3486 template<typename _RealType1>
3487 inline bool
3488 operator!=(const logistic_distribution<_RealType1>& __d1,
3489 const logistic_distribution<_RealType1>& __d2)
3490 { return !(__d1 == __d2); }
3491 #endif
3493 /**
3494 * @brief A distribution for random coordinates on a unit sphere.
3495 *
3496 * The method used in the generation function is attributed by Donald Knuth
3497 * to G. W. Brown, Modern Mathematics for the Engineer (1956).
3498 */
3499 template<std::size_t _Dimen, typename _RealType = double>
3500 class uniform_on_sphere_distribution
3501 {
3502 static_assert(std::is_floating_point<_RealType>::value,
3503 "template argument not a floating point type");
3504 static_assert(_Dimen != 0, "dimension is zero");
3506 public:
3507 /** The type of the range of the distribution. */
3508 typedef std::array<_RealType, _Dimen> result_type;
3510 /** Parameter type. */
3511 struct param_type
3512 {
3513 param_type() { }
3515 friend bool
3516 operator==(const param_type&, const param_type&)
3517 { return true; }
3519 #if __cpp_impl_three_way_comparison < 201907L
3520 friend bool
3521 operator!=(const param_type&, const param_type&)
3522 { return false; }
3523 #endif
3524 };
3526 /**
3527 * @brief Constructs a uniform on sphere distribution.
3528 */
3529 uniform_on_sphere_distribution()
3530 : _M_param(), _M_nd()
3531 { }
3533 explicit
3534 uniform_on_sphere_distribution(const param_type& __p)
3535 : _M_param(__p), _M_nd()
3536 { }
3538 /**
3539 * @brief Resets the distribution state.
3540 */
3541 void
3542 reset()
3543 { _M_nd.reset(); }
3545 /**
3546 * @brief Returns the parameter set of the distribution.
3547 */
3548 param_type
3549 param() const
3550 { return _M_param; }
3552 /**
3553 * @brief Sets the parameter set of the distribution.
3554 * @param __param The new parameter set of the distribution.
3555 */
3556 void
3557 param(const param_type& __param)
3558 { _M_param = __param; }
3560 /**
3561 * @brief Returns the greatest lower bound value of the distribution.
3562 * This function makes no sense for this distribution.
3563 */
3564 result_type
3565 min() const
3566 {
3567 result_type __res;
3568 __res.fill(0);
3569 return __res;
3570 }
3572 /**
3573 * @brief Returns the least upper bound value of the distribution.
3574 * This function makes no sense for this distribution.
3575 */
3576 result_type
3577 max() const
3578 {
3579 result_type __res;
3580 __res.fill(0);
3581 return __res;
3582 }
3584 /**
3585 * @brief Generating functions.
3586 */
3587 template<typename _UniformRandomNumberGenerator>
3588 result_type
3589 operator()(_UniformRandomNumberGenerator& __urng)
3590 { return this->operator()(__urng, _M_param); }
3592 template<typename _UniformRandomNumberGenerator>
3593 result_type
3594 operator()(_UniformRandomNumberGenerator& __urng,
3595 const param_type& __p);
3597 template<typename _ForwardIterator,
3598 typename _UniformRandomNumberGenerator>
3599 void
3600 __generate(_ForwardIterator __f, _ForwardIterator __t,
3601 _UniformRandomNumberGenerator& __urng)
3602 { this->__generate(__f, __t, __urng, this->param()); }
3604 template<typename _ForwardIterator,
3605 typename _UniformRandomNumberGenerator>
3606 void
3607 __generate(_ForwardIterator __f, _ForwardIterator __t,
3608 _UniformRandomNumberGenerator& __urng,
3609 const param_type& __p)
3610 { this->__generate_impl(__f, __t, __urng, __p); }
3612 template<typename _UniformRandomNumberGenerator>
3613 void
3614 __generate(result_type* __f, result_type* __t,
3615 _UniformRandomNumberGenerator& __urng,
3616 const param_type& __p)
3617 { this->__generate_impl(__f, __t, __urng, __p); }
3619 /**
3620 * @brief Return true if two uniform on sphere distributions have
3621 * the same parameters and the sequences that would be
3622 * generated are equal.
3623 */
3624 friend bool
3625 operator==(const uniform_on_sphere_distribution& __d1,
3626 const uniform_on_sphere_distribution& __d2)
3627 { return __d1._M_nd == __d2._M_nd; }
3629 /**
3630 * @brief Inserts a %uniform_on_sphere_distribution random number
3631 * distribution @p __x into the output stream @p __os.
3632 *
3633 * @param __os An output stream.
3634 * @param __x A %uniform_on_sphere_distribution random number
3635 * distribution.
3636 *
3637 * @returns The output stream with the state of @p __x inserted or in
3638 * an error state.
3639 */
3640 template<size_t _Dimen1, typename _RealType1, typename _CharT,
3641 typename _Traits>
3642 friend std::basic_ostream<_CharT, _Traits>&
3643 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3644 const __gnu_cxx::uniform_on_sphere_distribution<_Dimen1,
3645 _RealType1>&
3646 __x);
3648 /**
3649 * @brief Extracts a %uniform_on_sphere_distribution random number
3650 * distribution
3651 * @p __x from the input stream @p __is.
3652 *
3653 * @param __is An input stream.
3654 * @param __x A %uniform_on_sphere_distribution random number
3655 * generator engine.
3656 *
3657 * @returns The input stream with @p __x extracted or in an error state.
3658 */
3659 template<std::size_t _Dimen1, typename _RealType1, typename _CharT,
3660 typename _Traits>
3661 friend std::basic_istream<_CharT, _Traits>&
3662 operator>>(std::basic_istream<_CharT, _Traits>& __is,
3663 __gnu_cxx::uniform_on_sphere_distribution<_Dimen1,
3664 _RealType1>& __x);
3666 private:
3667 template<typename _ForwardIterator,
3668 typename _UniformRandomNumberGenerator>
3669 void
3670 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3671 _UniformRandomNumberGenerator& __urng,
3672 const param_type& __p);
3674 param_type _M_param;
3675 std::normal_distribution<_RealType> _M_nd;
3676 };
3678 #if __cpp_impl_three_way_comparison < 201907L
3679 /**
3680 * @brief Return true if two uniform on sphere distributions are different.
3681 */
3682 template<std::size_t _Dimen, typename _RealType>
3683 inline bool
3684 operator!=(const __gnu_cxx::uniform_on_sphere_distribution<_Dimen,
3685 _RealType>& __d1,
3686 const __gnu_cxx::uniform_on_sphere_distribution<_Dimen,
3687 _RealType>& __d2)
3688 { return !(__d1 == __d2); }
3689 #endif
3691 /**
3692 * @brief A distribution for random coordinates inside a unit sphere.
3693 */
3694 template<std::size_t _Dimen, typename _RealType = double>
3695 class uniform_inside_sphere_distribution
3696 {
3697 static_assert(std::is_floating_point<_RealType>::value,
3698 "template argument not a floating point type");
3699 static_assert(_Dimen != 0, "dimension is zero");
3701 public:
3702 /** The type of the range of the distribution. */
3703 using result_type = std::array<_RealType, _Dimen>;
3705 /** Parameter type. */
3706 struct param_type
3707 {
3708 using distribution_type
3709 = uniform_inside_sphere_distribution<_Dimen, _RealType>;
3710 friend class uniform_inside_sphere_distribution<_Dimen, _RealType>;
3712 param_type() : param_type(1.0) { }
3714 explicit
3715 param_type(_RealType __radius)
3716 : _M_radius(__radius)
3717 {
3718 __glibcxx_assert(_M_radius > _RealType(0));
3719 }
3721 _RealType
3722 radius() const
3723 { return _M_radius; }
3725 friend bool
3726 operator==(const param_type& __p1, const param_type& __p2)
3727 { return __p1._M_radius == __p2._M_radius; }
3729 #if __cpp_impl_three_way_comparison < 201907L
3730 friend bool
3731 operator!=(const param_type& __p1, const param_type& __p2)
3732 { return !(__p1 == __p2); }
3733 #endif
3735 private:
3736 _RealType _M_radius;
3737 };
3739 /**
3740 * @brief Constructors.
3741 * @{
3742 */
3744 uniform_inside_sphere_distribution()
3745 : uniform_inside_sphere_distribution(1.0)
3746 { }
3748 explicit
3749 uniform_inside_sphere_distribution(_RealType __radius)
3750 : _M_param(__radius), _M_uosd()
3751 { }
3753 explicit
3754 uniform_inside_sphere_distribution(const param_type& __p)
3755 : _M_param(__p), _M_uosd()
3756 { }
3758 /// @}
3760 /**
3761 * @brief Resets the distribution state.
3762 */
3763 void
3764 reset()
3765 { _M_uosd.reset(); }
3767 /**
3768 * @brief Returns the @f$radius@f$ of the distribution.
3769 */
3770 _RealType
3771 radius() const
3772 { return _M_param.radius(); }
3774 /**
3775 * @brief Returns the parameter set of the distribution.
3776 */
3777 param_type
3778 param() const
3779 { return _M_param; }
3781 /**
3782 * @brief Sets the parameter set of the distribution.
3783 * @param __param The new parameter set of the distribution.
3784 */
3785 void
3786 param(const param_type& __param)
3787 { _M_param = __param; }
3789 /**
3790 * @brief Returns the greatest lower bound value of the distribution.
3791 * This function makes no sense for this distribution.
3792 */
3793 result_type
3794 min() const
3795 {
3796 result_type __res;
3797 __res.fill(0);
3798 return __res;
3799 }
3801 /**
3802 * @brief Returns the least upper bound value of the distribution.
3803 * This function makes no sense for this distribution.
3804 */
3805 result_type
3806 max() const
3807 {
3808 result_type __res;
3809 __res.fill(0);
3810 return __res;
3811 }
3813 /**
3814 * @brief Generating functions.
3815 */
3816 template<typename _UniformRandomNumberGenerator>
3817 result_type
3818 operator()(_UniformRandomNumberGenerator& __urng)
3819 { return this->operator()(__urng, _M_param); }
3821 template<typename _UniformRandomNumberGenerator>
3822 result_type
3823 operator()(_UniformRandomNumberGenerator& __urng,
3824 const param_type& __p);
3826 template<typename _ForwardIterator,
3827 typename _UniformRandomNumberGenerator>
3828 void
3829 __generate(_ForwardIterator __f, _ForwardIterator __t,
3830 _UniformRandomNumberGenerator& __urng)
3831 { this->__generate(__f, __t, __urng, this->param()); }
3833 template<typename _ForwardIterator,
3834 typename _UniformRandomNumberGenerator>
3835 void
3836 __generate(_ForwardIterator __f, _ForwardIterator __t,
3837 _UniformRandomNumberGenerator& __urng,
3838 const param_type& __p)
3839 { this->__generate_impl(__f, __t, __urng, __p); }
3841 template<typename _UniformRandomNumberGenerator>
3842 void
3843 __generate(result_type* __f, result_type* __t,
3844 _UniformRandomNumberGenerator& __urng,
3845 const param_type& __p)
3846 { this->__generate_impl(__f, __t, __urng, __p); }
3848 /**
3849 * @brief Return true if two uniform on sphere distributions have
3850 * the same parameters and the sequences that would be
3851 * generated are equal.
3852 */
3853 friend bool
3854 operator==(const uniform_inside_sphere_distribution& __d1,
3855 const uniform_inside_sphere_distribution& __d2)
3856 { return __d1._M_param == __d2._M_param && __d1._M_uosd == __d2._M_uosd; }
3858 /**
3859 * @brief Inserts a %uniform_inside_sphere_distribution random number
3860 * distribution @p __x into the output stream @p __os.
3861 *
3862 * @param __os An output stream.
3863 * @param __x A %uniform_inside_sphere_distribution random number
3864 * distribution.
3865 *
3866 * @returns The output stream with the state of @p __x inserted or in
3867 * an error state.
3868 */
3869 template<size_t _Dimen1, typename _RealType1, typename _CharT,
3870 typename _Traits>
3871 friend std::basic_ostream<_CharT, _Traits>&
3872 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3873 const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen1,
3874 _RealType1>&
3875 );
3877 /**
3878 * @brief Extracts a %uniform_inside_sphere_distribution random number
3879 * distribution
3880 * @p __x from the input stream @p __is.
3881 *
3882 * @param __is An input stream.
3883 * @param __x A %uniform_inside_sphere_distribution random number
3884 * generator engine.
3885 *
3886 * @returns The input stream with @p __x extracted or in an error state.
3887 */
3888 template<std::size_t _Dimen1, typename _RealType1, typename _CharT,
3889 typename _Traits>
3890 friend std::basic_istream<_CharT, _Traits>&
3891 operator>>(std::basic_istream<_CharT, _Traits>& __is,
3892 __gnu_cxx::uniform_inside_sphere_distribution<_Dimen1,
3893 _RealType1>&);
3895 private:
3896 template<typename _ForwardIterator,
3897 typename _UniformRandomNumberGenerator>
3898 void
3899 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3900 _UniformRandomNumberGenerator& __urng,
3901 const param_type& __p);
3903 param_type _M_param;
3904 uniform_on_sphere_distribution<_Dimen, _RealType> _M_uosd;
3905 };
3907 #if __cpp_impl_three_way_comparison < 201907L
3908 /**
3909 * @brief Return true if two uniform on sphere distributions are different.
3910 */
3911 template<std::size_t _Dimen, typename _RealType>
3912 inline bool
3913 operator!=(const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen,
3914 _RealType>& __d1,
3915 const __gnu_cxx::uniform_inside_sphere_distribution<_Dimen,
3916 _RealType>& __d2)
3917 { return !(__d1 == __d2); }
3918 #endif
3920 _GLIBCXX_END_NAMESPACE_VERSION
3921 } // namespace __gnu_cxx
3923 #include <ext/opt_random.h>
3924 #include <ext/random.tcc>
3926 #endif // UINT32_C
3928 #endif // C++11
3930 #endif // _EXT_RANDOM