libstdc++
bits/random.tcc
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1// random number generation (out of line) -*- C++ -*-
2
3// Copyright (C) 2009-2022 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file bits/random.tcc
26 * This is an internal header file, included by other library headers.
27 * Do not attempt to use it directly. @headername{random}
28 */
29
30#ifndef _RANDOM_TCC
31#define _RANDOM_TCC 1
32
33#include <numeric> // std::accumulate and std::partial_sum
34
35namespace std _GLIBCXX_VISIBILITY(default)
36{
37_GLIBCXX_BEGIN_NAMESPACE_VERSION
38
39 /// @cond undocumented
40 // (Further) implementation-space details.
41 namespace __detail
42 {
43 // General case for x = (ax + c) mod m -- use Schrage's algorithm
44 // to avoid integer overflow.
45 //
46 // Preconditions: a > 0, m > 0.
47 //
48 // Note: only works correctly for __m % __a < __m / __a.
49 template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
50 _Tp
51 _Mod<_Tp, __m, __a, __c, false, true>::
52 __calc(_Tp __x)
53 {
54 if (__a == 1)
55 __x %= __m;
56 else
57 {
58 static const _Tp __q = __m / __a;
59 static const _Tp __r = __m % __a;
60
61 _Tp __t1 = __a * (__x % __q);
62 _Tp __t2 = __r * (__x / __q);
63 if (__t1 >= __t2)
64 __x = __t1 - __t2;
65 else
66 __x = __m - __t2 + __t1;
67 }
68
69 if (__c != 0)
70 {
71 const _Tp __d = __m - __x;
72 if (__d > __c)
73 __x += __c;
74 else
75 __x = __c - __d;
76 }
77 return __x;
78 }
79
80 template<typename _InputIterator, typename _OutputIterator,
81 typename _Tp>
82 _OutputIterator
83 __normalize(_InputIterator __first, _InputIterator __last,
84 _OutputIterator __result, const _Tp& __factor)
85 {
86 for (; __first != __last; ++__first, ++__result)
87 *__result = *__first / __factor;
88 return __result;
89 }
90
91 } // namespace __detail
92 /// @endcond
93
94#if ! __cpp_inline_variables
95 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
96 constexpr _UIntType
98
99 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
100 constexpr _UIntType
102
103 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
104 constexpr _UIntType
106
107 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
108 constexpr _UIntType
109 linear_congruential_engine<_UIntType, __a, __c, __m>::default_seed;
110#endif
111
112 /**
113 * Seeds the LCR with integral value @p __s, adjusted so that the
114 * ring identity is never a member of the convergence set.
115 */
116 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
117 void
120 {
121 if ((__detail::__mod<_UIntType, __m>(__c) == 0)
122 && (__detail::__mod<_UIntType, __m>(__s) == 0))
123 _M_x = 1;
124 else
125 _M_x = __detail::__mod<_UIntType, __m>(__s);
126 }
127
128 /**
129 * Seeds the LCR engine with a value generated by @p __q.
130 */
131 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
132 template<typename _Sseq>
133 auto
135 seed(_Sseq& __q)
137 {
138 const _UIntType __k0 = __m == 0 ? std::numeric_limits<_UIntType>::digits
139 : std::__lg(__m);
140 const _UIntType __k = (__k0 + 31) / 32;
141 uint_least32_t __arr[__k + 3];
142 __q.generate(__arr + 0, __arr + __k + 3);
143 _UIntType __factor = 1u;
144 _UIntType __sum = 0u;
145 for (size_t __j = 0; __j < __k; ++__j)
146 {
147 __sum += __arr[__j + 3] * __factor;
148 __factor *= __detail::_Shift<_UIntType, 32>::__value;
149 }
150 seed(__sum);
151 }
152
153 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
154 typename _CharT, typename _Traits>
157 const linear_congruential_engine<_UIntType,
158 __a, __c, __m>& __lcr)
159 {
161
162 const typename __ios_base::fmtflags __flags = __os.flags();
163 const _CharT __fill = __os.fill();
164 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
165 __os.fill(__os.widen(' '));
166
167 __os << __lcr._M_x;
168
169 __os.flags(__flags);
170 __os.fill(__fill);
171 return __os;
172 }
173
174 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
175 typename _CharT, typename _Traits>
178 linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
179 {
180 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
181
182 const typename __ios_base::fmtflags __flags = __is.flags();
183 __is.flags(__ios_base::dec);
184
185 __is >> __lcr._M_x;
186
187 __is.flags(__flags);
188 return __is;
189 }
190
191#if ! __cpp_inline_variables
192 template<typename _UIntType,
193 size_t __w, size_t __n, size_t __m, size_t __r,
194 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
195 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
196 _UIntType __f>
197 constexpr size_t
198 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
199 __s, __b, __t, __c, __l, __f>::word_size;
200
201 template<typename _UIntType,
202 size_t __w, size_t __n, size_t __m, size_t __r,
203 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
204 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
205 _UIntType __f>
206 constexpr size_t
207 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
208 __s, __b, __t, __c, __l, __f>::state_size;
209
210 template<typename _UIntType,
211 size_t __w, size_t __n, size_t __m, size_t __r,
212 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
213 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
214 _UIntType __f>
215 constexpr size_t
216 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
217 __s, __b, __t, __c, __l, __f>::shift_size;
218
219 template<typename _UIntType,
220 size_t __w, size_t __n, size_t __m, size_t __r,
221 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
222 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
223 _UIntType __f>
224 constexpr size_t
225 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
226 __s, __b, __t, __c, __l, __f>::mask_bits;
227
228 template<typename _UIntType,
229 size_t __w, size_t __n, size_t __m, size_t __r,
230 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
231 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
232 _UIntType __f>
233 constexpr _UIntType
234 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
235 __s, __b, __t, __c, __l, __f>::xor_mask;
236
237 template<typename _UIntType,
238 size_t __w, size_t __n, size_t __m, size_t __r,
239 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
240 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
241 _UIntType __f>
242 constexpr size_t
243 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
244 __s, __b, __t, __c, __l, __f>::tempering_u;
245
246 template<typename _UIntType,
247 size_t __w, size_t __n, size_t __m, size_t __r,
248 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
249 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
250 _UIntType __f>
251 constexpr _UIntType
252 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
253 __s, __b, __t, __c, __l, __f>::tempering_d;
254
255 template<typename _UIntType,
256 size_t __w, size_t __n, size_t __m, size_t __r,
257 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
258 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
259 _UIntType __f>
260 constexpr size_t
261 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
262 __s, __b, __t, __c, __l, __f>::tempering_s;
263
264 template<typename _UIntType,
265 size_t __w, size_t __n, size_t __m, size_t __r,
266 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
267 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
268 _UIntType __f>
269 constexpr _UIntType
270 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
271 __s, __b, __t, __c, __l, __f>::tempering_b;
272
273 template<typename _UIntType,
274 size_t __w, size_t __n, size_t __m, size_t __r,
275 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
276 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
277 _UIntType __f>
278 constexpr size_t
279 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
280 __s, __b, __t, __c, __l, __f>::tempering_t;
281
282 template<typename _UIntType,
283 size_t __w, size_t __n, size_t __m, size_t __r,
284 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
285 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
286 _UIntType __f>
287 constexpr _UIntType
288 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
289 __s, __b, __t, __c, __l, __f>::tempering_c;
290
291 template<typename _UIntType,
292 size_t __w, size_t __n, size_t __m, size_t __r,
293 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
294 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
295 _UIntType __f>
296 constexpr size_t
297 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
298 __s, __b, __t, __c, __l, __f>::tempering_l;
299
300 template<typename _UIntType,
301 size_t __w, size_t __n, size_t __m, size_t __r,
302 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
303 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
304 _UIntType __f>
305 constexpr _UIntType
306 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
307 __s, __b, __t, __c, __l, __f>::
308 initialization_multiplier;
309
310 template<typename _UIntType,
311 size_t __w, size_t __n, size_t __m, size_t __r,
312 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
313 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
314 _UIntType __f>
315 constexpr _UIntType
316 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
317 __s, __b, __t, __c, __l, __f>::default_seed;
318#endif
319
320 template<typename _UIntType,
321 size_t __w, size_t __n, size_t __m, size_t __r,
322 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
323 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
324 _UIntType __f>
325 void
326 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
327 __s, __b, __t, __c, __l, __f>::
328 seed(result_type __sd)
329 {
330 _M_x[0] = __detail::__mod<_UIntType,
331 __detail::_Shift<_UIntType, __w>::__value>(__sd);
332
333 for (size_t __i = 1; __i < state_size; ++__i)
334 {
335 _UIntType __x = _M_x[__i - 1];
336 __x ^= __x >> (__w - 2);
337 __x *= __f;
338 __x += __detail::__mod<_UIntType, __n>(__i);
339 _M_x[__i] = __detail::__mod<_UIntType,
340 __detail::_Shift<_UIntType, __w>::__value>(__x);
341 }
342 _M_p = state_size;
343 }
344
345 template<typename _UIntType,
346 size_t __w, size_t __n, size_t __m, size_t __r,
347 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
348 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
349 _UIntType __f>
350 template<typename _Sseq>
351 auto
352 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
353 __s, __b, __t, __c, __l, __f>::
354 seed(_Sseq& __q)
355 -> _If_seed_seq<_Sseq>
356 {
357 const _UIntType __upper_mask = (~_UIntType()) << __r;
358 const size_t __k = (__w + 31) / 32;
359 uint_least32_t __arr[__n * __k];
360 __q.generate(__arr + 0, __arr + __n * __k);
361
362 bool __zero = true;
363 for (size_t __i = 0; __i < state_size; ++__i)
364 {
365 _UIntType __factor = 1u;
366 _UIntType __sum = 0u;
367 for (size_t __j = 0; __j < __k; ++__j)
368 {
369 __sum += __arr[__k * __i + __j] * __factor;
370 __factor *= __detail::_Shift<_UIntType, 32>::__value;
371 }
372 _M_x[__i] = __detail::__mod<_UIntType,
373 __detail::_Shift<_UIntType, __w>::__value>(__sum);
374
375 if (__zero)
376 {
377 if (__i == 0)
378 {
379 if ((_M_x[0] & __upper_mask) != 0u)
380 __zero = false;
381 }
382 else if (_M_x[__i] != 0u)
383 __zero = false;
384 }
385 }
386 if (__zero)
387 _M_x[0] = __detail::_Shift<_UIntType, __w - 1>::__value;
388 _M_p = state_size;
389 }
390
391 template<typename _UIntType, size_t __w,
392 size_t __n, size_t __m, size_t __r,
393 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
394 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
395 _UIntType __f>
396 void
397 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
398 __s, __b, __t, __c, __l, __f>::
399 _M_gen_rand(void)
400 {
401 const _UIntType __upper_mask = (~_UIntType()) << __r;
402 const _UIntType __lower_mask = ~__upper_mask;
403
404 for (size_t __k = 0; __k < (__n - __m); ++__k)
405 {
406 _UIntType __y = ((_M_x[__k] & __upper_mask)
407 | (_M_x[__k + 1] & __lower_mask));
408 _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
409 ^ ((__y & 0x01) ? __a : 0));
410 }
411
412 for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
413 {
414 _UIntType __y = ((_M_x[__k] & __upper_mask)
415 | (_M_x[__k + 1] & __lower_mask));
416 _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
417 ^ ((__y & 0x01) ? __a : 0));
418 }
419
420 _UIntType __y = ((_M_x[__n - 1] & __upper_mask)
421 | (_M_x[0] & __lower_mask));
422 _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
423 ^ ((__y & 0x01) ? __a : 0));
424 _M_p = 0;
425 }
426
427 template<typename _UIntType, size_t __w,
428 size_t __n, size_t __m, size_t __r,
429 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
430 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
431 _UIntType __f>
432 void
433 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
434 __s, __b, __t, __c, __l, __f>::
435 discard(unsigned long long __z)
436 {
437 while (__z > state_size - _M_p)
438 {
439 __z -= state_size - _M_p;
440 _M_gen_rand();
441 }
442 _M_p += __z;
443 }
444
445 template<typename _UIntType, size_t __w,
446 size_t __n, size_t __m, size_t __r,
447 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
448 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
449 _UIntType __f>
450 typename
451 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
452 __s, __b, __t, __c, __l, __f>::result_type
453 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
454 __s, __b, __t, __c, __l, __f>::
455 operator()()
456 {
457 // Reload the vector - cost is O(n) amortized over n calls.
458 if (_M_p >= state_size)
459 _M_gen_rand();
460
461 // Calculate o(x(i)).
462 result_type __z = _M_x[_M_p++];
463 __z ^= (__z >> __u) & __d;
464 __z ^= (__z << __s) & __b;
465 __z ^= (__z << __t) & __c;
466 __z ^= (__z >> __l);
467
468 return __z;
469 }
470
471 template<typename _UIntType, size_t __w,
472 size_t __n, size_t __m, size_t __r,
473 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
474 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
475 _UIntType __f, typename _CharT, typename _Traits>
478 const mersenne_twister_engine<_UIntType, __w, __n, __m,
479 __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
480 {
481 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
482
483 const typename __ios_base::fmtflags __flags = __os.flags();
484 const _CharT __fill = __os.fill();
485 const _CharT __space = __os.widen(' ');
486 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
487 __os.fill(__space);
488
489 for (size_t __i = 0; __i < __n; ++__i)
490 __os << __x._M_x[__i] << __space;
491 __os << __x._M_p;
492
493 __os.flags(__flags);
494 __os.fill(__fill);
495 return __os;
496 }
497
498 template<typename _UIntType, size_t __w,
499 size_t __n, size_t __m, size_t __r,
500 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
501 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
502 _UIntType __f, typename _CharT, typename _Traits>
505 mersenne_twister_engine<_UIntType, __w, __n, __m,
506 __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
507 {
508 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
509
510 const typename __ios_base::fmtflags __flags = __is.flags();
511 __is.flags(__ios_base::dec | __ios_base::skipws);
512
513 for (size_t __i = 0; __i < __n; ++__i)
514 __is >> __x._M_x[__i];
515 __is >> __x._M_p;
516
517 __is.flags(__flags);
518 return __is;
519 }
520
521#if ! __cpp_inline_variables
522 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
523 constexpr size_t
524 subtract_with_carry_engine<_UIntType, __w, __s, __r>::word_size;
525
526 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
527 constexpr size_t
528 subtract_with_carry_engine<_UIntType, __w, __s, __r>::short_lag;
529
530 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
531 constexpr size_t
532 subtract_with_carry_engine<_UIntType, __w, __s, __r>::long_lag;
533
534 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
535 constexpr uint_least32_t
536 subtract_with_carry_engine<_UIntType, __w, __s, __r>::default_seed;
537#endif
538
539 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
540 void
542 seed(result_type __value)
543 {
544 // _GLIBCXX_RESOLVE_LIB_DEFECTS
545 // 3809. Is std::subtract_with_carry_engine<uint16_t> supposed to work?
546 // 4014. LWG 3809 changes behavior of some existing code
548 __lcg(__value == 0u ? default_seed : __value % 2147483563u);
549
550 const size_t __n = (__w + 31) / 32;
551
552 for (size_t __i = 0; __i < long_lag; ++__i)
553 {
554 _UIntType __sum = 0u;
555 _UIntType __factor = 1u;
556 for (size_t __j = 0; __j < __n; ++__j)
557 {
558 __sum += __detail::__mod<uint_least32_t,
559 __detail::_Shift<uint_least32_t, 32>::__value>
560 (__lcg()) * __factor;
561 __factor *= __detail::_Shift<_UIntType, 32>::__value;
562 }
563 _M_x[__i] = __detail::__mod<_UIntType,
564 __detail::_Shift<_UIntType, __w>::__value>(__sum);
565 }
566 _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
567 _M_p = 0;
568 }
569
570 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
571 template<typename _Sseq>
572 auto
574 seed(_Sseq& __q)
576 {
577 const size_t __k = (__w + 31) / 32;
578 uint_least32_t __arr[__r * __k];
579 __q.generate(__arr + 0, __arr + __r * __k);
580
581 for (size_t __i = 0; __i < long_lag; ++__i)
582 {
583 _UIntType __sum = 0u;
584 _UIntType __factor = 1u;
585 for (size_t __j = 0; __j < __k; ++__j)
586 {
587 __sum += __arr[__k * __i + __j] * __factor;
588 __factor *= __detail::_Shift<_UIntType, 32>::__value;
589 }
590 _M_x[__i] = __detail::__mod<_UIntType,
591 __detail::_Shift<_UIntType, __w>::__value>(__sum);
592 }
593 _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
594 _M_p = 0;
595 }
596
597 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
599 result_type
602 {
603 // Derive short lag index from current index.
604 long __ps = _M_p - short_lag;
605 if (__ps < 0)
606 __ps += long_lag;
607
608 // Calculate new x(i) without overflow or division.
609 // NB: Thanks to the requirements for _UIntType, _M_x[_M_p] + _M_carry
610 // cannot overflow.
611 _UIntType __xi;
612 if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
613 {
614 __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
615 _M_carry = 0;
616 }
617 else
618 {
619 __xi = (__detail::_Shift<_UIntType, __w>::__value
620 - _M_x[_M_p] - _M_carry + _M_x[__ps]);
621 _M_carry = 1;
622 }
623 _M_x[_M_p] = __xi;
624
625 // Adjust current index to loop around in ring buffer.
626 if (++_M_p >= long_lag)
627 _M_p = 0;
628
629 return __xi;
630 }
631
632 template<typename _UIntType, size_t __w, size_t __s, size_t __r,
633 typename _CharT, typename _Traits>
636 const subtract_with_carry_engine<_UIntType,
637 __w, __s, __r>& __x)
638 {
640
641 const typename __ios_base::fmtflags __flags = __os.flags();
642 const _CharT __fill = __os.fill();
643 const _CharT __space = __os.widen(' ');
644 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
645 __os.fill(__space);
646
647 for (size_t __i = 0; __i < __r; ++__i)
648 __os << __x._M_x[__i] << __space;
649 __os << __x._M_carry << __space << __x._M_p;
650
651 __os.flags(__flags);
652 __os.fill(__fill);
653 return __os;
654 }
655
656 template<typename _UIntType, size_t __w, size_t __s, size_t __r,
657 typename _CharT, typename _Traits>
660 subtract_with_carry_engine<_UIntType, __w, __s, __r>& __x)
661 {
662 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
663
664 const typename __ios_base::fmtflags __flags = __is.flags();
665 __is.flags(__ios_base::dec | __ios_base::skipws);
666
667 for (size_t __i = 0; __i < __r; ++__i)
668 __is >> __x._M_x[__i];
669 __is >> __x._M_carry;
670 __is >> __x._M_p;
671
672 __is.flags(__flags);
673 return __is;
674 }
675
676#if ! __cpp_inline_variables
677 template<typename _RandomNumberEngine, size_t __p, size_t __r>
678 constexpr size_t
679 discard_block_engine<_RandomNumberEngine, __p, __r>::block_size;
680
681 template<typename _RandomNumberEngine, size_t __p, size_t __r>
682 constexpr size_t
683 discard_block_engine<_RandomNumberEngine, __p, __r>::used_block;
684#endif
685
686 template<typename _RandomNumberEngine, size_t __p, size_t __r>
687 typename discard_block_engine<_RandomNumberEngine,
688 __p, __r>::result_type
691 {
692 if (_M_n >= used_block)
693 {
694 _M_b.discard(block_size - _M_n);
695 _M_n = 0;
696 }
697 ++_M_n;
698 return _M_b();
699 }
700
701 template<typename _RandomNumberEngine, size_t __p, size_t __r,
702 typename _CharT, typename _Traits>
705 const discard_block_engine<_RandomNumberEngine,
706 __p, __r>& __x)
707 {
709
710 const typename __ios_base::fmtflags __flags = __os.flags();
711 const _CharT __fill = __os.fill();
712 const _CharT __space = __os.widen(' ');
713 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
714 __os.fill(__space);
715
716 __os << __x.base() << __space << __x._M_n;
717
718 __os.flags(__flags);
719 __os.fill(__fill);
720 return __os;
721 }
722
723 template<typename _RandomNumberEngine, size_t __p, size_t __r,
724 typename _CharT, typename _Traits>
727 discard_block_engine<_RandomNumberEngine, __p, __r>& __x)
728 {
729 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
730
731 const typename __ios_base::fmtflags __flags = __is.flags();
732 __is.flags(__ios_base::dec | __ios_base::skipws);
733
734 __is >> __x._M_b >> __x._M_n;
735
736 __is.flags(__flags);
737 return __is;
738 }
739
740
741 template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
742 typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
743 result_type
746 {
747 typedef typename _RandomNumberEngine::result_type _Eresult_type;
748 const _Eresult_type __r
749 = (_M_b.max() - _M_b.min() < std::numeric_limits<_Eresult_type>::max()
750 ? _M_b.max() - _M_b.min() + 1 : 0);
752 const unsigned __m = __r ? std::__lg(__r) : __edig;
753
755 __ctype;
757
758 unsigned __n, __n0;
760
761 for (size_t __i = 0; __i < 2; ++__i)
762 {
763 __n = (__w + __m - 1) / __m + __i;
764 __n0 = __n - __w % __n;
765 const unsigned __w0 = __w / __n; // __w0 <= __m
766
767 __s0 = 0;
768 __s1 = 0;
769 if (__w0 < __cdig)
770 {
771 __s0 = __ctype(1) << __w0;
772 __s1 = __s0 << 1;
773 }
774
775 __y0 = 0;
776 __y1 = 0;
777 if (__r)
778 {
779 __y0 = __s0 * (__r / __s0);
780 if (__s1)
781 __y1 = __s1 * (__r / __s1);
782
783 if (__r - __y0 <= __y0 / __n)
784 break;
785 }
786 else
787 break;
788 }
789
790 result_type __sum = 0;
791 for (size_t __k = 0; __k < __n0; ++__k)
792 {
793 __ctype __u;
794 do
795 __u = _M_b() - _M_b.min();
796 while (__y0 && __u >= __y0);
797 __sum = __s0 * __sum + (__s0 ? __u % __s0 : __u);
798 }
799 for (size_t __k = __n0; __k < __n; ++__k)
800 {
801 __ctype __u;
802 do
803 __u = _M_b() - _M_b.min();
804 while (__y1 && __u >= __y1);
805 __sum = __s1 * __sum + (__s1 ? __u % __s1 : __u);
806 }
807 return __sum;
808 }
809
810#if ! __cpp_inline_variables
811 template<typename _RandomNumberEngine, size_t __k>
812 constexpr size_t
814#endif
815
816 namespace __detail
817 {
818 // Determine whether an integer is representable as double.
819 template<typename _Tp>
820 constexpr bool
821 __representable_as_double(_Tp __x) noexcept
822 {
823 static_assert(numeric_limits<_Tp>::is_integer, "");
824 static_assert(!numeric_limits<_Tp>::is_signed, "");
825 // All integers <= 2^53 are representable.
826 return (__x <= (1ull << __DBL_MANT_DIG__))
827 // Between 2^53 and 2^54 only even numbers are representable.
828 || (!(__x & 1) && __detail::__representable_as_double(__x >> 1));
829 }
830
831 // Determine whether x+1 is representable as double.
832 template<typename _Tp>
833 constexpr bool
834 __p1_representable_as_double(_Tp __x) noexcept
835 {
836 static_assert(numeric_limits<_Tp>::is_integer, "");
837 static_assert(!numeric_limits<_Tp>::is_signed, "");
838 return numeric_limits<_Tp>::digits < __DBL_MANT_DIG__
839 || (bool(__x + 1u) // return false if x+1 wraps around to zero
840 && __detail::__representable_as_double(__x + 1u));
841 }
842 }
843
844 template<typename _RandomNumberEngine, size_t __k>
848 {
849 constexpr result_type __range = max() - min();
850 size_t __j = __k;
851 const result_type __y = _M_y - min();
852 // Avoid using slower long double arithmetic if possible.
853 if _GLIBCXX17_CONSTEXPR (__detail::__p1_representable_as_double(__range))
854 __j *= __y / (__range + 1.0);
855 else
856 __j *= __y / (__range + 1.0L);
857 _M_y = _M_v[__j];
858 _M_v[__j] = _M_b();
859
860 return _M_y;
861 }
862
863 template<typename _RandomNumberEngine, size_t __k,
864 typename _CharT, typename _Traits>
868 {
870
871 const typename __ios_base::fmtflags __flags = __os.flags();
872 const _CharT __fill = __os.fill();
873 const _CharT __space = __os.widen(' ');
874 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
875 __os.fill(__space);
876
877 __os << __x.base();
878 for (size_t __i = 0; __i < __k; ++__i)
879 __os << __space << __x._M_v[__i];
880 __os << __space << __x._M_y;
881
882 __os.flags(__flags);
883 __os.fill(__fill);
884 return __os;
885 }
886
887 template<typename _RandomNumberEngine, size_t __k,
888 typename _CharT, typename _Traits>
892 {
894
895 const typename __ios_base::fmtflags __flags = __is.flags();
896 __is.flags(__ios_base::dec | __ios_base::skipws);
897
898 __is >> __x._M_b;
899 for (size_t __i = 0; __i < __k; ++__i)
900 __is >> __x._M_v[__i];
901 __is >> __x._M_y;
902
903 __is.flags(__flags);
904 return __is;
905 }
906
907
908 template<typename _IntType, typename _CharT, typename _Traits>
911 const uniform_int_distribution<_IntType>& __x)
912 {
913 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
914
915 const typename __ios_base::fmtflags __flags = __os.flags();
916 const _CharT __fill = __os.fill();
917 const _CharT __space = __os.widen(' ');
918 __os.flags(__ios_base::scientific | __ios_base::left);
919 __os.fill(__space);
920
921 __os << __x.a() << __space << __x.b();
922
923 __os.flags(__flags);
924 __os.fill(__fill);
925 return __os;
926 }
927
928 template<typename _IntType, typename _CharT, typename _Traits>
932 {
933 using param_type
936
937 const typename __ios_base::fmtflags __flags = __is.flags();
938 __is.flags(__ios_base::dec | __ios_base::skipws);
939
940 _IntType __a, __b;
941 if (__is >> __a >> __b)
942 __x.param(param_type(__a, __b));
943
944 __is.flags(__flags);
945 return __is;
946 }
947
948
949 template<typename _RealType>
950 template<typename _ForwardIterator,
951 typename _UniformRandomNumberGenerator>
952 void
956 const param_type& __p)
957 {
958 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
959 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
961 auto __range = __p.b() - __p.a();
962 while (__f != __t)
963 *__f++ = __aurng() * __range + __p.a();
964 }
965
966 template<typename _RealType, typename _CharT, typename _Traits>
969 const uniform_real_distribution<_RealType>& __x)
970 {
971 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
972
973 const typename __ios_base::fmtflags __flags = __os.flags();
974 const _CharT __fill = __os.fill();
975 const std::streamsize __precision = __os.precision();
976 const _CharT __space = __os.widen(' ');
977 __os.flags(__ios_base::scientific | __ios_base::left);
978 __os.fill(__space);
980
981 __os << __x.a() << __space << __x.b();
982
983 __os.flags(__flags);
984 __os.fill(__fill);
985 __os.precision(__precision);
986 return __os;
987 }
988
989 template<typename _RealType, typename _CharT, typename _Traits>
993 {
994 using param_type
997
998 const typename __ios_base::fmtflags __flags = __is.flags();
999 __is.flags(__ios_base::skipws);
1000
1001 _RealType __a, __b;
1002 if (__is >> __a >> __b)
1003 __x.param(param_type(__a, __b));
1004
1005 __is.flags(__flags);
1006 return __is;
1007 }
1008
1009
1010 template<typename _ForwardIterator,
1011 typename _UniformRandomNumberGenerator>
1012 void
1013 std::bernoulli_distribution::
1014 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1016 const param_type& __p)
1017 {
1018 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1019 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1020 __aurng(__urng);
1021 auto __limit = __p.p() * (__aurng.max() - __aurng.min());
1022
1023 while (__f != __t)
1024 *__f++ = (__aurng() - __aurng.min()) < __limit;
1025 }
1026
1027 template<typename _CharT, typename _Traits>
1030 const bernoulli_distribution& __x)
1031 {
1032 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1033
1034 const typename __ios_base::fmtflags __flags = __os.flags();
1035 const _CharT __fill = __os.fill();
1036 const std::streamsize __precision = __os.precision();
1037 __os.flags(__ios_base::scientific | __ios_base::left);
1038 __os.fill(__os.widen(' '));
1040
1041 __os << __x.p();
1042
1043 __os.flags(__flags);
1044 __os.fill(__fill);
1045 __os.precision(__precision);
1046 return __os;
1047 }
1048
1049
1050 template<typename _IntType>
1051 template<typename _UniformRandomNumberGenerator>
1054 operator()(_UniformRandomNumberGenerator& __urng,
1055 const param_type& __param)
1056 {
1057 // About the epsilon thing see this thread:
1058 // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1059 const double __naf =
1061 // The largest _RealType convertible to _IntType.
1062 const double __thr =
1064 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1065 __aurng(__urng);
1066
1067 double __cand;
1068 do
1069 __cand = std::floor(std::log(1.0 - __aurng()) / __param._M_log_1_p);
1070 while (__cand >= __thr);
1071
1072 return result_type(__cand + __naf);
1073 }
1074
1075 template<typename _IntType>
1076 template<typename _ForwardIterator,
1077 typename _UniformRandomNumberGenerator>
1078 void
1082 const param_type& __param)
1083 {
1084 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1085 // About the epsilon thing see this thread:
1086 // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1087 const double __naf =
1089 // The largest _RealType convertible to _IntType.
1090 const double __thr =
1092 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1093 __aurng(__urng);
1094
1095 while (__f != __t)
1096 {
1097 double __cand;
1098 do
1099 __cand = std::floor(std::log(1.0 - __aurng())
1100 / __param._M_log_1_p);
1101 while (__cand >= __thr);
1102
1103 *__f++ = __cand + __naf;
1104 }
1105 }
1106
1107 template<typename _IntType,
1108 typename _CharT, typename _Traits>
1111 const geometric_distribution<_IntType>& __x)
1112 {
1113 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1114
1115 const typename __ios_base::fmtflags __flags = __os.flags();
1116 const _CharT __fill = __os.fill();
1117 const std::streamsize __precision = __os.precision();
1118 __os.flags(__ios_base::scientific | __ios_base::left);
1119 __os.fill(__os.widen(' '));
1121
1122 __os << __x.p();
1123
1124 __os.flags(__flags);
1125 __os.fill(__fill);
1126 __os.precision(__precision);
1127 return __os;
1128 }
1129
1130 template<typename _IntType,
1131 typename _CharT, typename _Traits>
1135 {
1136 using param_type = typename geometric_distribution<_IntType>::param_type;
1138
1139 const typename __ios_base::fmtflags __flags = __is.flags();
1140 __is.flags(__ios_base::skipws);
1141
1142 double __p;
1143 if (__is >> __p)
1144 __x.param(param_type(__p));
1145
1146 __is.flags(__flags);
1147 return __is;
1148 }
1149
1150 // This is Leger's algorithm, also in Devroye, Ch. X, Example 1.5.
1151 template<typename _IntType>
1152 template<typename _UniformRandomNumberGenerator>
1156 {
1157 const double __y = _M_gd(__urng);
1158
1159 // XXX Is the constructor too slow?
1161 return __poisson(__urng);
1162 }
1163
1164 template<typename _IntType>
1165 template<typename _UniformRandomNumberGenerator>
1169 const param_type& __p)
1170 {
1172 param_type;
1173
1174 const double __y =
1175 _M_gd(__urng, param_type(__p.k(), (1.0 - __p.p()) / __p.p()));
1176
1178 return __poisson(__urng);
1179 }
1180
1181 template<typename _IntType>
1182 template<typename _ForwardIterator,
1183 typename _UniformRandomNumberGenerator>
1184 void
1185 negative_binomial_distribution<_IntType>::
1186 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1187 _UniformRandomNumberGenerator& __urng)
1188 {
1189 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1190 while (__f != __t)
1191 {
1192 const double __y = _M_gd(__urng);
1193
1194 // XXX Is the constructor too slow?
1196 *__f++ = __poisson(__urng);
1197 }
1198 }
1199
1200 template<typename _IntType>
1201 template<typename _ForwardIterator,
1202 typename _UniformRandomNumberGenerator>
1203 void
1204 negative_binomial_distribution<_IntType>::
1205 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1206 _UniformRandomNumberGenerator& __urng,
1207 const param_type& __p)
1208 {
1209 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1211 __p2(__p.k(), (1.0 - __p.p()) / __p.p());
1212
1213 while (__f != __t)
1214 {
1215 const double __y = _M_gd(__urng, __p2);
1216
1218 *__f++ = __poisson(__urng);
1219 }
1220 }
1221
1222 template<typename _IntType, typename _CharT, typename _Traits>
1225 const negative_binomial_distribution<_IntType>& __x)
1226 {
1227 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1228
1229 const typename __ios_base::fmtflags __flags = __os.flags();
1230 const _CharT __fill = __os.fill();
1231 const std::streamsize __precision = __os.precision();
1232 const _CharT __space = __os.widen(' ');
1233 __os.flags(__ios_base::scientific | __ios_base::left);
1234 __os.fill(__os.widen(' '));
1236
1237 __os << __x.k() << __space << __x.p()
1238 << __space << __x._M_gd;
1239
1240 __os.flags(__flags);
1241 __os.fill(__fill);
1242 __os.precision(__precision);
1243 return __os;
1244 }
1245
1246 template<typename _IntType, typename _CharT, typename _Traits>
1249 negative_binomial_distribution<_IntType>& __x)
1250 {
1251 using param_type
1252 = typename negative_binomial_distribution<_IntType>::param_type;
1253 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1254
1255 const typename __ios_base::fmtflags __flags = __is.flags();
1256 __is.flags(__ios_base::skipws);
1257
1258 _IntType __k;
1259 double __p;
1260 if (__is >> __k >> __p >> __x._M_gd)
1261 __x.param(param_type(__k, __p));
1262
1263 __is.flags(__flags);
1264 return __is;
1265 }
1266
1267
1268 template<typename _IntType>
1269 void
1270 poisson_distribution<_IntType>::param_type::
1271 _M_initialize()
1272 {
1273#if _GLIBCXX_USE_C99_MATH_TR1
1274 if (_M_mean >= 12)
1275 {
1276 const double __m = std::floor(_M_mean);
1277 _M_lm_thr = std::log(_M_mean);
1278 _M_lfm = std::lgamma(__m + 1);
1279 _M_sm = std::sqrt(__m);
1280
1281 const double __pi_4 = 0.7853981633974483096156608458198757L;
1282 const double __dx = std::sqrt(2 * __m * std::log(32 * __m
1283 / __pi_4));
1284 _M_d = std::round(std::max<double>(6.0, std::min(__m, __dx)));
1285 const double __cx = 2 * __m + _M_d;
1286 _M_scx = std::sqrt(__cx / 2);
1287 _M_1cx = 1 / __cx;
1288
1289 _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
1290 _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2))
1291 / _M_d;
1292 }
1293 else
1294#endif
1295 _M_lm_thr = std::exp(-_M_mean);
1296 }
1297
1298 /**
1299 * A rejection algorithm when mean >= 12 and a simple method based
1300 * upon the multiplication of uniform random variates otherwise.
1301 * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1302 * is defined.
1303 *
1304 * Reference:
1305 * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1306 * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
1307 */
1308 template<typename _IntType>
1309 template<typename _UniformRandomNumberGenerator>
1313 const param_type& __param)
1314 {
1315 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1316 __aurng(__urng);
1317#if _GLIBCXX_USE_C99_MATH_TR1
1318 if (__param.mean() >= 12)
1319 {
1320 double __x;
1321
1322 // See comments above...
1323 const double __naf =
1325 const double __thr =
1327
1328 const double __m = std::floor(__param.mean());
1329 // sqrt(pi / 2)
1330 const double __spi_2 = 1.2533141373155002512078826424055226L;
1331 const double __c1 = __param._M_sm * __spi_2;
1332 const double __c2 = __param._M_c2b + __c1;
1333 const double __c3 = __c2 + 1;
1334 const double __c4 = __c3 + 1;
1335 // 1 / 78
1336 const double __178 = 0.0128205128205128205128205128205128L;
1337 // e^(1 / 78)
1338 const double __e178 = 1.0129030479320018583185514777512983L;
1339 const double __c5 = __c4 + __e178;
1340 const double __c = __param._M_cb + __c5;
1341 const double __2cx = 2 * (2 * __m + __param._M_d);
1342
1343 bool __reject = true;
1344 do
1345 {
1346 const double __u = __c * __aurng();
1347 const double __e = -std::log(1.0 - __aurng());
1348
1349 double __w = 0.0;
1350
1351 if (__u <= __c1)
1352 {
1353 const double __n = _M_nd(__urng);
1354 const double __y = -std::abs(__n) * __param._M_sm - 1;
1355 __x = std::floor(__y);
1356 __w = -__n * __n / 2;
1357 if (__x < -__m)
1358 continue;
1359 }
1360 else if (__u <= __c2)
1361 {
1362 const double __n = _M_nd(__urng);
1363 const double __y = 1 + std::abs(__n) * __param._M_scx;
1364 __x = std::ceil(__y);
1365 __w = __y * (2 - __y) * __param._M_1cx;
1366 if (__x > __param._M_d)
1367 continue;
1368 }
1369 else if (__u <= __c3)
1370 // NB: This case not in the book, nor in the Errata,
1371 // but should be ok...
1372 __x = -1;
1373 else if (__u <= __c4)
1374 __x = 0;
1375 else if (__u <= __c5)
1376 {
1377 __x = 1;
1378 // Only in the Errata, see libstdc++/83237.
1379 __w = __178;
1380 }
1381 else
1382 {
1383 const double __v = -std::log(1.0 - __aurng());
1384 const double __y = __param._M_d
1385 + __v * __2cx / __param._M_d;
1386 __x = std::ceil(__y);
1387 __w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
1388 }
1389
1390 __reject = (__w - __e - __x * __param._M_lm_thr
1391 > __param._M_lfm - std::lgamma(__x + __m + 1));
1392
1393 __reject |= __x + __m >= __thr;
1394
1395 } while (__reject);
1396
1397 return result_type(__x + __m + __naf);
1398 }
1399 else
1400#endif
1401 {
1402 _IntType __x = 0;
1403 double __prod = 1.0;
1404
1405 do
1406 {
1407 __prod *= __aurng();
1408 __x += 1;
1409 }
1410 while (__prod > __param._M_lm_thr);
1411
1412 return __x - 1;
1413 }
1414 }
1415
1416 template<typename _IntType>
1417 template<typename _ForwardIterator,
1419 void
1423 const param_type& __param)
1424 {
1425 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1426 // We could duplicate everything from operator()...
1427 while (__f != __t)
1428 *__f++ = this->operator()(__urng, __param);
1429 }
1430
1431 template<typename _IntType,
1432 typename _CharT, typename _Traits>
1435 const poisson_distribution<_IntType>& __x)
1436 {
1437 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1438
1439 const typename __ios_base::fmtflags __flags = __os.flags();
1440 const _CharT __fill = __os.fill();
1441 const std::streamsize __precision = __os.precision();
1442 const _CharT __space = __os.widen(' ');
1443 __os.flags(__ios_base::scientific | __ios_base::left);
1444 __os.fill(__space);
1446
1447 __os << __x.mean() << __space << __x._M_nd;
1448
1449 __os.flags(__flags);
1450 __os.fill(__fill);
1451 __os.precision(__precision);
1452 return __os;
1453 }
1454
1455 template<typename _IntType,
1456 typename _CharT, typename _Traits>
1459 poisson_distribution<_IntType>& __x)
1460 {
1461 using param_type = typename poisson_distribution<_IntType>::param_type;
1462 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1463
1464 const typename __ios_base::fmtflags __flags = __is.flags();
1465 __is.flags(__ios_base::skipws);
1466
1467 double __mean;
1468 if (__is >> __mean >> __x._M_nd)
1469 __x.param(param_type(__mean));
1470
1471 __is.flags(__flags);
1472 return __is;
1473 }
1474
1475
1476 template<typename _IntType>
1477 void
1478 binomial_distribution<_IntType>::param_type::
1479 _M_initialize()
1480 {
1481 const double __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
1482
1483 _M_easy = true;
1484
1485#if _GLIBCXX_USE_C99_MATH_TR1
1486 if (_M_t * __p12 >= 8)
1487 {
1488 _M_easy = false;
1489 const double __np = std::floor(_M_t * __p12);
1490 const double __pa = __np / _M_t;
1491 const double __1p = 1 - __pa;
1492
1493 const double __pi_4 = 0.7853981633974483096156608458198757L;
1494 const double __d1x =
1495 std::sqrt(__np * __1p * std::log(32 * __np
1496 / (81 * __pi_4 * __1p)));
1497 _M_d1 = std::round(std::max<double>(1.0, __d1x));
1498 const double __d2x =
1499 std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
1500 / (__pi_4 * __pa)));
1501 _M_d2 = std::round(std::max<double>(1.0, __d2x));
1502
1503 // sqrt(pi / 2)
1504 const double __spi_2 = 1.2533141373155002512078826424055226L;
1505 _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
1506 _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * (_M_t * __1p)));
1507 _M_c = 2 * _M_d1 / __np;
1508 _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
1509 const double __a12 = _M_a1 + _M_s2 * __spi_2;
1510 const double __s1s = _M_s1 * _M_s1;
1511 _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
1512 * 2 * __s1s / _M_d1
1513 * std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
1514 const double __s2s = _M_s2 * _M_s2;
1515 _M_s = (_M_a123 + 2 * __s2s / _M_d2
1516 * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
1517 _M_lf = (std::lgamma(__np + 1)
1518 + std::lgamma(_M_t - __np + 1));
1519 _M_lp1p = std::log(__pa / __1p);
1520
1521 _M_q = -std::log(1 - (__p12 - __pa) / __1p);
1522 }
1523 else
1524#endif
1525 _M_q = -std::log(1 - __p12);
1526 }
1527
1528 template<typename _IntType>
1529 template<typename _UniformRandomNumberGenerator>
1531 binomial_distribution<_IntType>::
1532 _M_waiting(_UniformRandomNumberGenerator& __urng,
1533 _IntType __t, double __q)
1534 {
1535 _IntType __x = 0;
1536 double __sum = 0.0;
1537 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1538 __aurng(__urng);
1539
1540 do
1541 {
1542 if (__t == __x)
1543 return __x;
1544 const double __e = -std::log(1.0 - __aurng());
1545 __sum += __e / (__t - __x);
1546 __x += 1;
1547 }
1548 while (__sum <= __q);
1549
1550 return __x - 1;
1551 }
1552
1553 /**
1554 * A rejection algorithm when t * p >= 8 and a simple waiting time
1555 * method - the second in the referenced book - otherwise.
1556 * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1557 * is defined.
1558 *
1559 * Reference:
1560 * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1561 * New York, 1986, Ch. X, Sect. 4 (+ Errata!).
1562 */
1563 template<typename _IntType>
1564 template<typename _UniformRandomNumberGenerator>
1568 const param_type& __param)
1569 {
1571 const _IntType __t = __param.t();
1572 const double __p = __param.p();
1573 const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
1574 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1575 __aurng(__urng);
1576
1577#if _GLIBCXX_USE_C99_MATH_TR1
1578 if (!__param._M_easy)
1579 {
1580 double __x;
1581
1582 // See comments above...
1583 const double __naf =
1585 const double __thr =
1587
1588 const double __np = std::floor(__t * __p12);
1589
1590 // sqrt(pi / 2)
1591 const double __spi_2 = 1.2533141373155002512078826424055226L;
1592 const double __a1 = __param._M_a1;
1593 const double __a12 = __a1 + __param._M_s2 * __spi_2;
1594 const double __a123 = __param._M_a123;
1595 const double __s1s = __param._M_s1 * __param._M_s1;
1596 const double __s2s = __param._M_s2 * __param._M_s2;
1597
1598 bool __reject;
1599 do
1600 {
1601 const double __u = __param._M_s * __aurng();
1602
1603 double __v;
1604
1605 if (__u <= __a1)
1606 {
1607 const double __n = _M_nd(__urng);
1608 const double __y = __param._M_s1 * std::abs(__n);
1609 __reject = __y >= __param._M_d1;
1610 if (!__reject)
1611 {
1612 const double __e = -std::log(1.0 - __aurng());
1613 __x = std::floor(__y);
1614 __v = -__e - __n * __n / 2 + __param._M_c;
1615 }
1616 }
1617 else if (__u <= __a12)
1618 {
1619 const double __n = _M_nd(__urng);
1620 const double __y = __param._M_s2 * std::abs(__n);
1621 __reject = __y >= __param._M_d2;
1622 if (!__reject)
1623 {
1624 const double __e = -std::log(1.0 - __aurng());
1625 __x = std::floor(-__y);
1626 __v = -__e - __n * __n / 2;
1627 }
1628 }
1629 else if (__u <= __a123)
1630 {
1631 const double __e1 = -std::log(1.0 - __aurng());
1632 const double __e2 = -std::log(1.0 - __aurng());
1633
1634 const double __y = __param._M_d1
1635 + 2 * __s1s * __e1 / __param._M_d1;
1636 __x = std::floor(__y);
1637 __v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
1638 -__y / (2 * __s1s)));
1639 __reject = false;
1640 }
1641 else
1642 {
1643 const double __e1 = -std::log(1.0 - __aurng());
1644 const double __e2 = -std::log(1.0 - __aurng());
1645
1646 const double __y = __param._M_d2
1647 + 2 * __s2s * __e1 / __param._M_d2;
1648 __x = std::floor(-__y);
1649 __v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
1650 __reject = false;
1651 }
1652
1653 __reject = __reject || __x < -__np || __x > __t - __np;
1654 if (!__reject)
1655 {
1656 const double __lfx =
1657 std::lgamma(__np + __x + 1)
1658 + std::lgamma(__t - (__np + __x) + 1);
1659 __reject = __v > __param._M_lf - __lfx
1660 + __x * __param._M_lp1p;
1661 }
1662
1663 __reject |= __x + __np >= __thr;
1664 }
1665 while (__reject);
1666
1667 __x += __np + __naf;
1668
1669 const _IntType __z = _M_waiting(__urng, __t - _IntType(__x),
1670 __param._M_q);
1671 __ret = _IntType(__x) + __z;
1672 }
1673 else
1674#endif
1675 __ret = _M_waiting(__urng, __t, __param._M_q);
1676
1677 if (__p12 != __p)
1678 __ret = __t - __ret;
1679 return __ret;
1680 }
1681
1682 template<typename _IntType>
1683 template<typename _ForwardIterator,
1685 void
1689 const param_type& __param)
1690 {
1691 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1692 // We could duplicate everything from operator()...
1693 while (__f != __t)
1694 *__f++ = this->operator()(__urng, __param);
1695 }
1696
1697 template<typename _IntType,
1698 typename _CharT, typename _Traits>
1701 const binomial_distribution<_IntType>& __x)
1702 {
1703 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1704
1705 const typename __ios_base::fmtflags __flags = __os.flags();
1706 const _CharT __fill = __os.fill();
1707 const std::streamsize __precision = __os.precision();
1708 const _CharT __space = __os.widen(' ');
1709 __os.flags(__ios_base::scientific | __ios_base::left);
1710 __os.fill(__space);
1712
1713 __os << __x.t() << __space << __x.p()
1714 << __space << __x._M_nd;
1715
1716 __os.flags(__flags);
1717 __os.fill(__fill);
1718 __os.precision(__precision);
1719 return __os;
1720 }
1721
1722 template<typename _IntType,
1723 typename _CharT, typename _Traits>
1726 binomial_distribution<_IntType>& __x)
1727 {
1728 using param_type = typename binomial_distribution<_IntType>::param_type;
1729 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1730
1731 const typename __ios_base::fmtflags __flags = __is.flags();
1732 __is.flags(__ios_base::dec | __ios_base::skipws);
1733
1734 _IntType __t;
1735 double __p;
1736 if (__is >> __t >> __p >> __x._M_nd)
1737 __x.param(param_type(__t, __p));
1738
1739 __is.flags(__flags);
1740 return __is;
1741 }
1742
1743
1744 template<typename _RealType>
1745 template<typename _ForwardIterator,
1746 typename _UniformRandomNumberGenerator>
1747 void
1751 const param_type& __p)
1752 {
1753 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1754 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1755 __aurng(__urng);
1756 while (__f != __t)
1757 *__f++ = -std::log(result_type(1) - __aurng()) / __p.lambda();
1758 }
1759
1760 template<typename _RealType, typename _CharT, typename _Traits>
1763 const exponential_distribution<_RealType>& __x)
1764 {
1765 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1766
1767 const typename __ios_base::fmtflags __flags = __os.flags();
1768 const _CharT __fill = __os.fill();
1769 const std::streamsize __precision = __os.precision();
1770 __os.flags(__ios_base::scientific | __ios_base::left);
1771 __os.fill(__os.widen(' '));
1773
1774 __os << __x.lambda();
1775
1776 __os.flags(__flags);
1777 __os.fill(__fill);
1778 __os.precision(__precision);
1779 return __os;
1780 }
1781
1782 template<typename _RealType, typename _CharT, typename _Traits>
1786 {
1787 using param_type
1790
1791 const typename __ios_base::fmtflags __flags = __is.flags();
1792 __is.flags(__ios_base::dec | __ios_base::skipws);
1793
1794 _RealType __lambda;
1795 if (__is >> __lambda)
1796 __x.param(param_type(__lambda));
1797
1798 __is.flags(__flags);
1799 return __is;
1800 }
1801
1802
1803 /**
1804 * Polar method due to Marsaglia.
1805 *
1806 * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1807 * New York, 1986, Ch. V, Sect. 4.4.
1808 */
1809 template<typename _RealType>
1810 template<typename _UniformRandomNumberGenerator>
1814 const param_type& __param)
1815 {
1817 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1818 __aurng(__urng);
1819
1820 if (_M_saved_available)
1821 {
1822 _M_saved_available = false;
1823 __ret = _M_saved;
1824 }
1825 else
1826 {
1827 result_type __x, __y, __r2;
1828 do
1829 {
1830 __x = result_type(2.0) * __aurng() - 1.0;
1831 __y = result_type(2.0) * __aurng() - 1.0;
1832 __r2 = __x * __x + __y * __y;
1833 }
1834 while (__r2 > 1.0 || __r2 == 0.0);
1835
1836 const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1837 _M_saved = __x * __mult;
1838 _M_saved_available = true;
1839 __ret = __y * __mult;
1840 }
1841
1842 __ret = __ret * __param.stddev() + __param.mean();
1843 return __ret;
1844 }
1845
1846 template<typename _RealType>
1847 template<typename _ForwardIterator,
1849 void
1853 const param_type& __param)
1854 {
1855 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1856
1857 if (__f == __t)
1858 return;
1859
1860 if (_M_saved_available)
1861 {
1862 _M_saved_available = false;
1863 *__f++ = _M_saved * __param.stddev() + __param.mean();
1864
1865 if (__f == __t)
1866 return;
1867 }
1868
1869 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1870 __aurng(__urng);
1871
1872 while (__f + 1 < __t)
1873 {
1874 result_type __x, __y, __r2;
1875 do
1876 {
1877 __x = result_type(2.0) * __aurng() - 1.0;
1878 __y = result_type(2.0) * __aurng() - 1.0;
1879 __r2 = __x * __x + __y * __y;
1880 }
1881 while (__r2 > 1.0 || __r2 == 0.0);
1882
1883 const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1884 *__f++ = __y * __mult * __param.stddev() + __param.mean();
1885 *__f++ = __x * __mult * __param.stddev() + __param.mean();
1886 }
1887
1888 if (__f != __t)
1889 {
1890 result_type __x, __y, __r2;
1891 do
1892 {
1893 __x = result_type(2.0) * __aurng() - 1.0;
1894 __y = result_type(2.0) * __aurng() - 1.0;
1895 __r2 = __x * __x + __y * __y;
1896 }
1897 while (__r2 > 1.0 || __r2 == 0.0);
1898
1899 const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1900 _M_saved = __x * __mult;
1901 _M_saved_available = true;
1902 *__f = __y * __mult * __param.stddev() + __param.mean();
1903 }
1904 }
1905
1906 template<typename _RealType>
1907 bool
1910 {
1911 if (__d1._M_param == __d2._M_param
1912 && __d1._M_saved_available == __d2._M_saved_available)
1913 {
1914 if (__d1._M_saved_available
1915 && __d1._M_saved == __d2._M_saved)
1916 return true;
1917 else if(!__d1._M_saved_available)
1918 return true;
1919 else
1920 return false;
1921 }
1922 else
1923 return false;
1924 }
1925
1926 template<typename _RealType, typename _CharT, typename _Traits>
1929 const normal_distribution<_RealType>& __x)
1930 {
1931 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1932
1933 const typename __ios_base::fmtflags __flags = __os.flags();
1934 const _CharT __fill = __os.fill();
1935 const std::streamsize __precision = __os.precision();
1936 const _CharT __space = __os.widen(' ');
1937 __os.flags(__ios_base::scientific | __ios_base::left);
1938 __os.fill(__space);
1940
1941 __os << __x.mean() << __space << __x.stddev()
1942 << __space << __x._M_saved_available;
1943 if (__x._M_saved_available)
1944 __os << __space << __x._M_saved;
1945
1946 __os.flags(__flags);
1947 __os.fill(__fill);
1948 __os.precision(__precision);
1949 return __os;
1950 }
1951
1952 template<typename _RealType, typename _CharT, typename _Traits>
1955 normal_distribution<_RealType>& __x)
1956 {
1957 using param_type = typename normal_distribution<_RealType>::param_type;
1958 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1959
1960 const typename __ios_base::fmtflags __flags = __is.flags();
1961 __is.flags(__ios_base::dec | __ios_base::skipws);
1962
1963 double __mean, __stddev;
1964 bool __saved_avail;
1965 if (__is >> __mean >> __stddev >> __saved_avail)
1966 {
1967 if (!__saved_avail || (__is >> __x._M_saved))
1968 {
1969 __x._M_saved_available = __saved_avail;
1970 __x.param(param_type(__mean, __stddev));
1971 }
1972 }
1973
1974 __is.flags(__flags);
1975 return __is;
1976 }
1977
1978
1979 template<typename _RealType>
1980 template<typename _ForwardIterator,
1981 typename _UniformRandomNumberGenerator>
1982 void
1983 lognormal_distribution<_RealType>::
1984 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1985 _UniformRandomNumberGenerator& __urng,
1986 const param_type& __p)
1987 {
1988 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1989 while (__f != __t)
1990 *__f++ = std::exp(__p.s() * _M_nd(__urng) + __p.m());
1991 }
1992
1993 template<typename _RealType, typename _CharT, typename _Traits>
1996 const lognormal_distribution<_RealType>& __x)
1997 {
1998 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1999
2000 const typename __ios_base::fmtflags __flags = __os.flags();
2001 const _CharT __fill = __os.fill();
2002 const std::streamsize __precision = __os.precision();
2003 const _CharT __space = __os.widen(' ');
2004 __os.flags(__ios_base::scientific | __ios_base::left);
2005 __os.fill(__space);
2007
2008 __os << __x.m() << __space << __x.s()
2009 << __space << __x._M_nd;
2010
2011 __os.flags(__flags);
2012 __os.fill(__fill);
2013 __os.precision(__precision);
2014 return __os;
2015 }
2016
2017 template<typename _RealType, typename _CharT, typename _Traits>
2020 lognormal_distribution<_RealType>& __x)
2021 {
2022 using param_type
2023 = typename lognormal_distribution<_RealType>::param_type;
2024 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2025
2026 const typename __ios_base::fmtflags __flags = __is.flags();
2027 __is.flags(__ios_base::dec | __ios_base::skipws);
2028
2029 _RealType __m, __s;
2030 if (__is >> __m >> __s >> __x._M_nd)
2031 __x.param(param_type(__m, __s));
2032
2033 __is.flags(__flags);
2034 return __is;
2035 }
2036
2037 template<typename _RealType>
2038 template<typename _ForwardIterator,
2039 typename _UniformRandomNumberGenerator>
2040 void
2042 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2043 _UniformRandomNumberGenerator& __urng)
2044 {
2045 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2046 while (__f != __t)
2047 *__f++ = 2 * _M_gd(__urng);
2048 }
2049
2050 template<typename _RealType>
2051 template<typename _ForwardIterator,
2052 typename _UniformRandomNumberGenerator>
2053 void
2055 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2056 _UniformRandomNumberGenerator& __urng,
2057 const typename
2059 {
2060 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2061 while (__f != __t)
2062 *__f++ = 2 * _M_gd(__urng, __p);
2063 }
2064
2065 template<typename _RealType, typename _CharT, typename _Traits>
2068 const chi_squared_distribution<_RealType>& __x)
2069 {
2070 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2071
2072 const typename __ios_base::fmtflags __flags = __os.flags();
2073 const _CharT __fill = __os.fill();
2074 const std::streamsize __precision = __os.precision();
2075 const _CharT __space = __os.widen(' ');
2076 __os.flags(__ios_base::scientific | __ios_base::left);
2077 __os.fill(__space);
2079
2080 __os << __x.n() << __space << __x._M_gd;
2081
2082 __os.flags(__flags);
2083 __os.fill(__fill);
2084 __os.precision(__precision);
2085 return __os;
2086 }
2087
2088 template<typename _RealType, typename _CharT, typename _Traits>
2091 chi_squared_distribution<_RealType>& __x)
2092 {
2093 using param_type
2094 = typename chi_squared_distribution<_RealType>::param_type;
2095 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2096
2097 const typename __ios_base::fmtflags __flags = __is.flags();
2098 __is.flags(__ios_base::dec | __ios_base::skipws);
2099
2100 _RealType __n;
2101 if (__is >> __n >> __x._M_gd)
2102 __x.param(param_type(__n));
2103
2104 __is.flags(__flags);
2105 return __is;
2106 }
2107
2108
2109 template<typename _RealType>
2110 template<typename _UniformRandomNumberGenerator>
2114 const param_type& __p)
2115 {
2116 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2117 __aurng(__urng);
2118 _RealType __u;
2119 do
2120 __u = __aurng();
2121 while (__u == 0.5);
2122
2123 const _RealType __pi = 3.1415926535897932384626433832795029L;
2124 return __p.a() + __p.b() * std::tan(__pi * __u);
2125 }
2126
2127 template<typename _RealType>
2128 template<typename _ForwardIterator,
2129 typename _UniformRandomNumberGenerator>
2130 void
2134 const param_type& __p)
2135 {
2136 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2137 const _RealType __pi = 3.1415926535897932384626433832795029L;
2138 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2139 __aurng(__urng);
2140 while (__f != __t)
2141 {
2142 _RealType __u;
2143 do
2144 __u = __aurng();
2145 while (__u == 0.5);
2146
2147 *__f++ = __p.a() + __p.b() * std::tan(__pi * __u);
2148 }
2149 }
2150
2151 template<typename _RealType, typename _CharT, typename _Traits>
2154 const cauchy_distribution<_RealType>& __x)
2155 {
2156 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2157
2158 const typename __ios_base::fmtflags __flags = __os.flags();
2159 const _CharT __fill = __os.fill();
2160 const std::streamsize __precision = __os.precision();
2161 const _CharT __space = __os.widen(' ');
2162 __os.flags(__ios_base::scientific | __ios_base::left);
2163 __os.fill(__space);
2165
2166 __os << __x.a() << __space << __x.b();
2167
2168 __os.flags(__flags);
2169 __os.fill(__fill);
2170 __os.precision(__precision);
2171 return __os;
2172 }
2173
2174 template<typename _RealType, typename _CharT, typename _Traits>
2178 {
2179 using param_type = typename cauchy_distribution<_RealType>::param_type;
2181
2182 const typename __ios_base::fmtflags __flags = __is.flags();
2183 __is.flags(__ios_base::dec | __ios_base::skipws);
2184
2185 _RealType __a, __b;
2186 if (__is >> __a >> __b)
2187 __x.param(param_type(__a, __b));
2188
2189 __is.flags(__flags);
2190 return __is;
2191 }
2192
2193
2194 template<typename _RealType>
2195 template<typename _ForwardIterator,
2196 typename _UniformRandomNumberGenerator>
2197 void
2199 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2200 _UniformRandomNumberGenerator& __urng)
2201 {
2202 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2203 while (__f != __t)
2204 *__f++ = ((_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()));
2205 }
2206
2207 template<typename _RealType>
2208 template<typename _ForwardIterator,
2209 typename _UniformRandomNumberGenerator>
2210 void
2212 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2213 _UniformRandomNumberGenerator& __urng,
2214 const param_type& __p)
2215 {
2216 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2218 param_type;
2219 param_type __p1(__p.m() / 2);
2220 param_type __p2(__p.n() / 2);
2221 while (__f != __t)
2222 *__f++ = ((_M_gd_x(__urng, __p1) * n())
2223 / (_M_gd_y(__urng, __p2) * m()));
2224 }
2225
2226 template<typename _RealType, typename _CharT, typename _Traits>
2229 const fisher_f_distribution<_RealType>& __x)
2230 {
2231 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2232
2233 const typename __ios_base::fmtflags __flags = __os.flags();
2234 const _CharT __fill = __os.fill();
2235 const std::streamsize __precision = __os.precision();
2236 const _CharT __space = __os.widen(' ');
2237 __os.flags(__ios_base::scientific | __ios_base::left);
2238 __os.fill(__space);
2240
2241 __os << __x.m() << __space << __x.n()
2242 << __space << __x._M_gd_x << __space << __x._M_gd_y;
2243
2244 __os.flags(__flags);
2245 __os.fill(__fill);
2246 __os.precision(__precision);
2247 return __os;
2248 }
2249
2250 template<typename _RealType, typename _CharT, typename _Traits>
2253 fisher_f_distribution<_RealType>& __x)
2254 {
2255 using param_type
2256 = typename fisher_f_distribution<_RealType>::param_type;
2257 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2258
2259 const typename __ios_base::fmtflags __flags = __is.flags();
2260 __is.flags(__ios_base::dec | __ios_base::skipws);
2261
2262 _RealType __m, __n;
2263 if (__is >> __m >> __n >> __x._M_gd_x >> __x._M_gd_y)
2264 __x.param(param_type(__m, __n));
2265
2266 __is.flags(__flags);
2267 return __is;
2268 }
2269
2270
2271 template<typename _RealType>
2272 template<typename _ForwardIterator,
2273 typename _UniformRandomNumberGenerator>
2274 void
2276 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2277 _UniformRandomNumberGenerator& __urng)
2278 {
2279 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2280 while (__f != __t)
2281 *__f++ = _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng));
2282 }
2283
2284 template<typename _RealType>
2285 template<typename _ForwardIterator,
2286 typename _UniformRandomNumberGenerator>
2287 void
2289 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2290 _UniformRandomNumberGenerator& __urng,
2291 const param_type& __p)
2292 {
2293 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2295 __p2(__p.n() / 2, 2);
2296 while (__f != __t)
2297 *__f++ = _M_nd(__urng) * std::sqrt(__p.n() / _M_gd(__urng, __p2));
2298 }
2299
2300 template<typename _RealType, typename _CharT, typename _Traits>
2303 const student_t_distribution<_RealType>& __x)
2304 {
2305 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2306
2307 const typename __ios_base::fmtflags __flags = __os.flags();
2308 const _CharT __fill = __os.fill();
2309 const std::streamsize __precision = __os.precision();
2310 const _CharT __space = __os.widen(' ');
2311 __os.flags(__ios_base::scientific | __ios_base::left);
2312 __os.fill(__space);
2314
2315 __os << __x.n() << __space << __x._M_nd << __space << __x._M_gd;
2316
2317 __os.flags(__flags);
2318 __os.fill(__fill);
2319 __os.precision(__precision);
2320 return __os;
2321 }
2322
2323 template<typename _RealType, typename _CharT, typename _Traits>
2326 student_t_distribution<_RealType>& __x)
2327 {
2328 using param_type
2329 = typename student_t_distribution<_RealType>::param_type;
2330 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2331
2332 const typename __ios_base::fmtflags __flags = __is.flags();
2333 __is.flags(__ios_base::dec | __ios_base::skipws);
2334
2335 _RealType __n;
2336 if (__is >> __n >> __x._M_nd >> __x._M_gd)
2337 __x.param(param_type(__n));
2338
2339 __is.flags(__flags);
2340 return __is;
2341 }
2342
2343
2344 template<typename _RealType>
2345 void
2346 gamma_distribution<_RealType>::param_type::
2347 _M_initialize()
2348 {
2349 _M_malpha = _M_alpha < 1.0 ? _M_alpha + _RealType(1.0) : _M_alpha;
2350
2351 const _RealType __a1 = _M_malpha - _RealType(1.0) / _RealType(3.0);
2352 _M_a2 = _RealType(1.0) / std::sqrt(_RealType(9.0) * __a1);
2353 }
2354
2355 /**
2356 * Marsaglia, G. and Tsang, W. W.
2357 * "A Simple Method for Generating Gamma Variables"
2358 * ACM Transactions on Mathematical Software, 26, 3, 363-372, 2000.
2359 */
2360 template<typename _RealType>
2361 template<typename _UniformRandomNumberGenerator>
2365 const param_type& __param)
2366 {
2367 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2368 __aurng(__urng);
2369
2370 result_type __u, __v, __n;
2371 const result_type __a1 = (__param._M_malpha
2372 - _RealType(1.0) / _RealType(3.0));
2373
2374 do
2375 {
2376 do
2377 {
2378 __n = _M_nd(__urng);
2379 __v = result_type(1.0) + __param._M_a2 * __n;
2380 }
2381 while (__v <= 0.0);
2382
2383 __v = __v * __v * __v;
2384 __u = __aurng();
2385 }
2386 while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2387 && (std::log(__u) > (0.5 * __n * __n + __a1
2388 * (1.0 - __v + std::log(__v)))));
2389
2390 if (__param.alpha() == __param._M_malpha)
2391 return __a1 * __v * __param.beta();
2392 else
2393 {
2394 do
2395 __u = __aurng();
2396 while (__u == 0.0);
2397
2398 return (std::pow(__u, result_type(1.0) / __param.alpha())
2399 * __a1 * __v * __param.beta());
2400 }
2401 }
2402
2403 template<typename _RealType>
2404 template<typename _ForwardIterator,
2406 void
2410 const param_type& __param)
2411 {
2412 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2413 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2414 __aurng(__urng);
2415
2416 result_type __u, __v, __n;
2417 const result_type __a1 = (__param._M_malpha
2418 - _RealType(1.0) / _RealType(3.0));
2419
2420 if (__param.alpha() == __param._M_malpha)
2421 while (__f != __t)
2422 {
2423 do
2424 {
2425 do
2426 {
2427 __n = _M_nd(__urng);
2428 __v = result_type(1.0) + __param._M_a2 * __n;
2429 }
2430 while (__v <= 0.0);
2431
2432 __v = __v * __v * __v;
2433 __u = __aurng();
2434 }
2435 while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2436 && (std::log(__u) > (0.5 * __n * __n + __a1
2437 * (1.0 - __v + std::log(__v)))));
2438
2439 *__f++ = __a1 * __v * __param.beta();
2440 }
2441 else
2442 while (__f != __t)
2443 {
2444 do
2445 {
2446 do
2447 {
2448 __n = _M_nd(__urng);
2449 __v = result_type(1.0) + __param._M_a2 * __n;
2450 }
2451 while (__v <= 0.0);
2452
2453 __v = __v * __v * __v;
2454 __u = __aurng();
2455 }
2456 while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2457 && (std::log(__u) > (0.5 * __n * __n + __a1
2458 * (1.0 - __v + std::log(__v)))));
2459
2460 do
2461 __u = __aurng();
2462 while (__u == 0.0);
2463
2464 *__f++ = (std::pow(__u, result_type(1.0) / __param.alpha())
2465 * __a1 * __v * __param.beta());
2466 }
2467 }
2468
2469 template<typename _RealType, typename _CharT, typename _Traits>
2472 const gamma_distribution<_RealType>& __x)
2473 {
2474 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2475
2476 const typename __ios_base::fmtflags __flags = __os.flags();
2477 const _CharT __fill = __os.fill();
2478 const std::streamsize __precision = __os.precision();
2479 const _CharT __space = __os.widen(' ');
2480 __os.flags(__ios_base::scientific | __ios_base::left);
2481 __os.fill(__space);
2483
2484 __os << __x.alpha() << __space << __x.beta()
2485 << __space << __x._M_nd;
2486
2487 __os.flags(__flags);
2488 __os.fill(__fill);
2489 __os.precision(__precision);
2490 return __os;
2491 }
2492
2493 template<typename _RealType, typename _CharT, typename _Traits>
2496 gamma_distribution<_RealType>& __x)
2497 {
2498 using param_type = typename gamma_distribution<_RealType>::param_type;
2499 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2500
2501 const typename __ios_base::fmtflags __flags = __is.flags();
2502 __is.flags(__ios_base::dec | __ios_base::skipws);
2503
2504 _RealType __alpha_val, __beta_val;
2505 if (__is >> __alpha_val >> __beta_val >> __x._M_nd)
2506 __x.param(param_type(__alpha_val, __beta_val));
2507
2508 __is.flags(__flags);
2509 return __is;
2510 }
2511
2512
2513 template<typename _RealType>
2514 template<typename _UniformRandomNumberGenerator>
2517 operator()(_UniformRandomNumberGenerator& __urng,
2518 const param_type& __p)
2519 {
2520 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2521 __aurng(__urng);
2522 return __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2523 result_type(1) / __p.a());
2524 }
2525
2526 template<typename _RealType>
2527 template<typename _ForwardIterator,
2528 typename _UniformRandomNumberGenerator>
2529 void
2533 const param_type& __p)
2534 {
2535 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2536 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2537 __aurng(__urng);
2538 auto __inv_a = result_type(1) / __p.a();
2539
2540 while (__f != __t)
2541 *__f++ = __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2542 __inv_a);
2543 }
2544
2545 template<typename _RealType, typename _CharT, typename _Traits>
2549 {
2551
2552 const typename __ios_base::fmtflags __flags = __os.flags();
2553 const _CharT __fill = __os.fill();
2554 const std::streamsize __precision = __os.precision();
2555 const _CharT __space = __os.widen(' ');
2556 __os.flags(__ios_base::scientific | __ios_base::left);
2557 __os.fill(__space);
2559
2560 __os << __x.a() << __space << __x.b();
2561
2562 __os.flags(__flags);
2563 __os.fill(__fill);
2564 __os.precision(__precision);
2565 return __os;
2566 }
2567
2568 template<typename _RealType, typename _CharT, typename _Traits>
2572 {
2573 using param_type = typename weibull_distribution<_RealType>::param_type;
2575
2576 const typename __ios_base::fmtflags __flags = __is.flags();
2577 __is.flags(__ios_base::dec | __ios_base::skipws);
2578
2579 _RealType __a, __b;
2580 if (__is >> __a >> __b)
2581 __x.param(param_type(__a, __b));
2582
2583 __is.flags(__flags);
2584 return __is;
2585 }
2586
2587
2588 template<typename _RealType>
2589 template<typename _UniformRandomNumberGenerator>
2592 operator()(_UniformRandomNumberGenerator& __urng,
2593 const param_type& __p)
2594 {
2595 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2596 __aurng(__urng);
2597 return __p.a() - __p.b() * std::log(-std::log(result_type(1)
2598 - __aurng()));
2599 }
2600
2601 template<typename _RealType>
2602 template<typename _ForwardIterator,
2603 typename _UniformRandomNumberGenerator>
2604 void
2608 const param_type& __p)
2609 {
2610 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2611 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2612 __aurng(__urng);
2613
2614 while (__f != __t)
2615 *__f++ = __p.a() - __p.b() * std::log(-std::log(result_type(1)
2616 - __aurng()));
2617 }
2618
2619 template<typename _RealType, typename _CharT, typename _Traits>
2622 const extreme_value_distribution<_RealType>& __x)
2623 {
2624 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2625
2626 const typename __ios_base::fmtflags __flags = __os.flags();
2627 const _CharT __fill = __os.fill();
2628 const std::streamsize __precision = __os.precision();
2629 const _CharT __space = __os.widen(' ');
2630 __os.flags(__ios_base::scientific | __ios_base::left);
2631 __os.fill(__space);
2633
2634 __os << __x.a() << __space << __x.b();
2635
2636 __os.flags(__flags);
2637 __os.fill(__fill);
2638 __os.precision(__precision);
2639 return __os;
2640 }
2641
2642 template<typename _RealType, typename _CharT, typename _Traits>
2646 {
2647 using param_type
2650
2651 const typename __ios_base::fmtflags __flags = __is.flags();
2652 __is.flags(__ios_base::dec | __ios_base::skipws);
2653
2654 _RealType __a, __b;
2655 if (__is >> __a >> __b)
2656 __x.param(param_type(__a, __b));
2657
2658 __is.flags(__flags);
2659 return __is;
2660 }
2661
2662
2663 template<typename _IntType>
2664 void
2665 discrete_distribution<_IntType>::param_type::
2666 _M_initialize()
2667 {
2668 if (_M_prob.size() < 2)
2669 {
2670 _M_prob.clear();
2671 return;
2672 }
2673
2674 const double __sum = std::accumulate(_M_prob.begin(),
2675 _M_prob.end(), 0.0);
2676 __glibcxx_assert(__sum > 0);
2677 // Now normalize the probabilites.
2678 __detail::__normalize(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
2679 __sum);
2680 // Accumulate partial sums.
2681 _M_cp.reserve(_M_prob.size());
2682 std::partial_sum(_M_prob.begin(), _M_prob.end(),
2683 std::back_inserter(_M_cp));
2684 // Make sure the last cumulative probability is one.
2685 _M_cp[_M_cp.size() - 1] = 1.0;
2686 }
2687
2688 template<typename _IntType>
2689 template<typename _Func>
2690 discrete_distribution<_IntType>::param_type::
2691 param_type(size_t __nw, double __xmin, double __xmax, _Func __fw)
2692 : _M_prob(), _M_cp()
2693 {
2694 const size_t __n = __nw == 0 ? 1 : __nw;
2695 const double __delta = (__xmax - __xmin) / __n;
2696
2697 _M_prob.reserve(__n);
2698 for (size_t __k = 0; __k < __nw; ++__k)
2699 _M_prob.push_back(__fw(__xmin + __k * __delta + 0.5 * __delta));
2700
2701 _M_initialize();
2702 }
2703
2704 template<typename _IntType>
2705 template<typename _UniformRandomNumberGenerator>
2706 typename discrete_distribution<_IntType>::result_type
2707 discrete_distribution<_IntType>::
2708 operator()(_UniformRandomNumberGenerator& __urng,
2709 const param_type& __param)
2710 {
2711 if (__param._M_cp.empty())
2712 return result_type(0);
2713
2714 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2715 __aurng(__urng);
2716
2717 const double __p = __aurng();
2718 auto __pos = std::lower_bound(__param._M_cp.begin(),
2719 __param._M_cp.end(), __p);
2720
2721 return __pos - __param._M_cp.begin();
2722 }
2723
2724 template<typename _IntType>
2725 template<typename _ForwardIterator,
2726 typename _UniformRandomNumberGenerator>
2727 void
2728 discrete_distribution<_IntType>::
2729 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2730 _UniformRandomNumberGenerator& __urng,
2731 const param_type& __param)
2732 {
2733 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2734
2735 if (__param._M_cp.empty())
2736 {
2737 while (__f != __t)
2738 *__f++ = result_type(0);
2739 return;
2740 }
2741
2742 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2743 __aurng(__urng);
2744
2745 while (__f != __t)
2746 {
2747 const double __p = __aurng();
2748 auto __pos = std::lower_bound(__param._M_cp.begin(),
2749 __param._M_cp.end(), __p);
2750
2751 *__f++ = __pos - __param._M_cp.begin();
2752 }
2753 }
2754
2755 template<typename _IntType, typename _CharT, typename _Traits>
2758 const discrete_distribution<_IntType>& __x)
2759 {
2760 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2761
2762 const typename __ios_base::fmtflags __flags = __os.flags();
2763 const _CharT __fill = __os.fill();
2764 const std::streamsize __precision = __os.precision();
2765 const _CharT __space = __os.widen(' ');
2766 __os.flags(__ios_base::scientific | __ios_base::left);
2767 __os.fill(__space);
2769
2770 std::vector<double> __prob = __x.probabilities();
2771 __os << __prob.size();
2772 for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
2773 __os << __space << *__dit;
2774
2775 __os.flags(__flags);
2776 __os.fill(__fill);
2777 __os.precision(__precision);
2778 return __os;
2779 }
2780
2781namespace __detail
2782{
2783 template<typename _ValT, typename _CharT, typename _Traits>
2784 basic_istream<_CharT, _Traits>&
2785 __extract_params(basic_istream<_CharT, _Traits>& __is,
2786 vector<_ValT>& __vals, size_t __n)
2787 {
2788 __vals.reserve(__n);
2789 while (__n--)
2790 {
2791 _ValT __val;
2792 if (__is >> __val)
2793 __vals.push_back(__val);
2794 else
2795 break;
2796 }
2797 return __is;
2798 }
2799} // namespace __detail
2800
2801 template<typename _IntType, typename _CharT, typename _Traits>
2804 discrete_distribution<_IntType>& __x)
2805 {
2806 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2807
2808 const typename __ios_base::fmtflags __flags = __is.flags();
2809 __is.flags(__ios_base::dec | __ios_base::skipws);
2810
2811 size_t __n;
2812 if (__is >> __n)
2813 {
2814 std::vector<double> __prob_vec;
2815 if (__detail::__extract_params(__is, __prob_vec, __n))
2816 __x.param({__prob_vec.begin(), __prob_vec.end()});
2817 }
2818
2819 __is.flags(__flags);
2820 return __is;
2821 }
2822
2823
2824 template<typename _RealType>
2825 void
2826 piecewise_constant_distribution<_RealType>::param_type::
2827 _M_initialize()
2828 {
2829 if (_M_int.size() < 2
2830 || (_M_int.size() == 2
2831 && _M_int[0] == _RealType(0)
2832 && _M_int[1] == _RealType(1)))
2833 {
2834 _M_int.clear();
2835 _M_den.clear();
2836 return;
2837 }
2838
2839 const double __sum = std::accumulate(_M_den.begin(),
2840 _M_den.end(), 0.0);
2841 __glibcxx_assert(__sum > 0);
2842
2843 __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
2844 __sum);
2845
2846 _M_cp.reserve(_M_den.size());
2847 std::partial_sum(_M_den.begin(), _M_den.end(),
2848 std::back_inserter(_M_cp));
2849
2850 // Make sure the last cumulative probability is one.
2851 _M_cp[_M_cp.size() - 1] = 1.0;
2852
2853 for (size_t __k = 0; __k < _M_den.size(); ++__k)
2854 _M_den[__k] /= _M_int[__k + 1] - _M_int[__k];
2855 }
2856
2857 template<typename _RealType>
2858 template<typename _InputIteratorB, typename _InputIteratorW>
2859 piecewise_constant_distribution<_RealType>::param_type::
2860 param_type(_InputIteratorB __bbegin,
2861 _InputIteratorB __bend,
2862 _InputIteratorW __wbegin)
2863 : _M_int(), _M_den(), _M_cp()
2864 {
2865 if (__bbegin != __bend)
2866 {
2867 for (;;)
2868 {
2869 _M_int.push_back(*__bbegin);
2870 ++__bbegin;
2871 if (__bbegin == __bend)
2872 break;
2873
2874 _M_den.push_back(*__wbegin);
2875 ++__wbegin;
2876 }
2877 }
2878
2879 _M_initialize();
2880 }
2881
2882 template<typename _RealType>
2883 template<typename _Func>
2884 piecewise_constant_distribution<_RealType>::param_type::
2885 param_type(initializer_list<_RealType> __bl, _Func __fw)
2886 : _M_int(), _M_den(), _M_cp()
2887 {
2888 _M_int.reserve(__bl.size());
2889 for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
2890 _M_int.push_back(*__biter);
2891
2892 _M_den.reserve(_M_int.size() - 1);
2893 for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
2894 _M_den.push_back(__fw(0.5 * (_M_int[__k + 1] + _M_int[__k])));
2895
2896 _M_initialize();
2897 }
2898
2899 template<typename _RealType>
2900 template<typename _Func>
2901 piecewise_constant_distribution<_RealType>::param_type::
2902 param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
2903 : _M_int(), _M_den(), _M_cp()
2904 {
2905 const size_t __n = __nw == 0 ? 1 : __nw;
2906 const _RealType __delta = (__xmax - __xmin) / __n;
2907
2908 _M_int.reserve(__n + 1);
2909 for (size_t __k = 0; __k <= __nw; ++__k)
2910 _M_int.push_back(__xmin + __k * __delta);
2911
2912 _M_den.reserve(__n);
2913 for (size_t __k = 0; __k < __nw; ++__k)
2914 _M_den.push_back(__fw(_M_int[__k] + 0.5 * __delta));
2915
2916 _M_initialize();
2917 }
2918
2919 template<typename _RealType>
2920 template<typename _UniformRandomNumberGenerator>
2921 typename piecewise_constant_distribution<_RealType>::result_type
2922 piecewise_constant_distribution<_RealType>::
2923 operator()(_UniformRandomNumberGenerator& __urng,
2924 const param_type& __param)
2925 {
2926 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2927 __aurng(__urng);
2928
2929 const double __p = __aurng();
2930 if (__param._M_cp.empty())
2931 return __p;
2932
2933 auto __pos = std::lower_bound(__param._M_cp.begin(),
2934 __param._M_cp.end(), __p);
2935 const size_t __i = __pos - __param._M_cp.begin();
2936
2937 const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2938
2939 return __param._M_int[__i] + (__p - __pref) / __param._M_den[__i];
2940 }
2941
2942 template<typename _RealType>
2943 template<typename _ForwardIterator,
2944 typename _UniformRandomNumberGenerator>
2945 void
2946 piecewise_constant_distribution<_RealType>::
2947 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2948 _UniformRandomNumberGenerator& __urng,
2949 const param_type& __param)
2950 {
2951 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2952 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2953 __aurng(__urng);
2954
2955 if (__param._M_cp.empty())
2956 {
2957 while (__f != __t)
2958 *__f++ = __aurng();
2959 return;
2960 }
2961
2962 while (__f != __t)
2963 {
2964 const double __p = __aurng();
2965
2966 auto __pos = std::lower_bound(__param._M_cp.begin(),
2967 __param._M_cp.end(), __p);
2968 const size_t __i = __pos - __param._M_cp.begin();
2969
2970 const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2971
2972 *__f++ = (__param._M_int[__i]
2973 + (__p - __pref) / __param._M_den[__i]);
2974 }
2975 }
2976
2977 template<typename _RealType, typename _CharT, typename _Traits>
2980 const piecewise_constant_distribution<_RealType>& __x)
2981 {
2982 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2983
2984 const typename __ios_base::fmtflags __flags = __os.flags();
2985 const _CharT __fill = __os.fill();
2986 const std::streamsize __precision = __os.precision();
2987 const _CharT __space = __os.widen(' ');
2988 __os.flags(__ios_base::scientific | __ios_base::left);
2989 __os.fill(__space);
2991
2992 std::vector<_RealType> __int = __x.intervals();
2993 __os << __int.size() - 1;
2994
2995 for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
2996 __os << __space << *__xit;
2997
2998 std::vector<double> __den = __x.densities();
2999 for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
3000 __os << __space << *__dit;
3001
3002 __os.flags(__flags);
3003 __os.fill(__fill);
3004 __os.precision(__precision);
3005 return __os;
3006 }
3007
3008 template<typename _RealType, typename _CharT, typename _Traits>
3011 piecewise_constant_distribution<_RealType>& __x)
3012 {
3013 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
3014
3015 const typename __ios_base::fmtflags __flags = __is.flags();
3016 __is.flags(__ios_base::dec | __ios_base::skipws);
3017
3018 size_t __n;
3019 if (__is >> __n)
3020 {
3021 std::vector<_RealType> __int_vec;
3022 if (__detail::__extract_params(__is, __int_vec, __n + 1))
3023 {
3024 std::vector<double> __den_vec;
3025 if (__detail::__extract_params(__is, __den_vec, __n))
3026 {
3027 __x.param({ __int_vec.begin(), __int_vec.end(),
3028 __den_vec.begin() });
3029 }
3030 }
3031 }
3032
3033 __is.flags(__flags);
3034 return __is;
3035 }
3036
3037
3038 template<typename _RealType>
3039 void
3040 piecewise_linear_distribution<_RealType>::param_type::
3041 _M_initialize()
3042 {
3043 if (_M_int.size() < 2
3044 || (_M_int.size() == 2
3045 && _M_int[0] == _RealType(0)
3046 && _M_int[1] == _RealType(1)
3047 && _M_den[0] == _M_den[1]))
3048 {
3049 _M_int.clear();
3050 _M_den.clear();
3051 return;
3052 }
3053
3054 double __sum = 0.0;
3055 _M_cp.reserve(_M_int.size() - 1);
3056 _M_m.reserve(_M_int.size() - 1);
3057 for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
3058 {
3059 const _RealType __delta = _M_int[__k + 1] - _M_int[__k];
3060 __sum += 0.5 * (_M_den[__k + 1] + _M_den[__k]) * __delta;
3061 _M_cp.push_back(__sum);
3062 _M_m.push_back((_M_den[__k + 1] - _M_den[__k]) / __delta);
3063 }
3064 __glibcxx_assert(__sum > 0);
3065
3066 // Now normalize the densities...
3067 __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
3068 __sum);
3069 // ... and partial sums...
3070 __detail::__normalize(_M_cp.begin(), _M_cp.end(), _M_cp.begin(), __sum);
3071 // ... and slopes.
3072 __detail::__normalize(_M_m.begin(), _M_m.end(), _M_m.begin(), __sum);
3073
3074 // Make sure the last cumulative probablility is one.
3075 _M_cp[_M_cp.size() - 1] = 1.0;
3076 }
3077
3078 template<typename _RealType>
3079 template<typename _InputIteratorB, typename _InputIteratorW>
3080 piecewise_linear_distribution<_RealType>::param_type::
3081 param_type(_InputIteratorB __bbegin,
3082 _InputIteratorB __bend,
3083 _InputIteratorW __wbegin)
3084 : _M_int(), _M_den(), _M_cp(), _M_m()
3085 {
3086 for (; __bbegin != __bend; ++__bbegin, ++__wbegin)
3087 {
3088 _M_int.push_back(*__bbegin);
3089 _M_den.push_back(*__wbegin);
3090 }
3091
3092 _M_initialize();
3093 }
3094
3095 template<typename _RealType>
3096 template<typename _Func>
3097 piecewise_linear_distribution<_RealType>::param_type::
3098 param_type(initializer_list<_RealType> __bl, _Func __fw)
3099 : _M_int(), _M_den(), _M_cp(), _M_m()
3100 {
3101 _M_int.reserve(__bl.size());
3102 _M_den.reserve(__bl.size());
3103 for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
3104 {
3105 _M_int.push_back(*__biter);
3106 _M_den.push_back(__fw(*__biter));
3107 }
3108
3109 _M_initialize();
3110 }
3111
3112 template<typename _RealType>
3113 template<typename _Func>
3114 piecewise_linear_distribution<_RealType>::param_type::
3115 param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
3116 : _M_int(), _M_den(), _M_cp(), _M_m()
3117 {
3118 const size_t __n = __nw == 0 ? 1 : __nw;
3119 const _RealType __delta = (__xmax - __xmin) / __n;
3120
3121 _M_int.reserve(__n + 1);
3122 _M_den.reserve(__n + 1);
3123 for (size_t __k = 0; __k <= __nw; ++__k)
3124 {
3125 _M_int.push_back(__xmin + __k * __delta);
3126 _M_den.push_back(__fw(_M_int[__k] + __delta));
3127 }
3128
3129 _M_initialize();
3130 }
3131
3132 template<typename _RealType>
3133 template<typename _UniformRandomNumberGenerator>
3134 typename piecewise_linear_distribution<_RealType>::result_type
3135 piecewise_linear_distribution<_RealType>::
3136 operator()(_UniformRandomNumberGenerator& __urng,
3137 const param_type& __param)
3138 {
3139 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
3140 __aurng(__urng);
3141
3142 const double __p = __aurng();
3143 if (__param._M_cp.empty())
3144 return __p;
3145
3146 auto __pos = std::lower_bound(__param._M_cp.begin(),
3147 __param._M_cp.end(), __p);
3148 const size_t __i = __pos - __param._M_cp.begin();
3149
3150 const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
3151
3152 const double __a = 0.5 * __param._M_m[__i];
3153 const double __b = __param._M_den[__i];
3154 const double __cm = __p - __pref;
3155
3156 _RealType __x = __param._M_int[__i];
3157 if (__a == 0)
3158 __x += __cm / __b;
3159 else
3160 {
3161 const double __d = __b * __b + 4.0 * __a * __cm;
3162 __x += 0.5 * (std::sqrt(__d) - __b) / __a;
3163 }
3164
3165 return __x;
3166 }
3167
3168 template<typename _RealType>
3169 template<typename _ForwardIterator,
3170 typename _UniformRandomNumberGenerator>
3171 void
3172 piecewise_linear_distribution<_RealType>::
3173 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3174 _UniformRandomNumberGenerator& __urng,
3175 const param_type& __param)
3176 {
3177 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
3178 // We could duplicate everything from operator()...
3179 while (__f != __t)
3180 *__f++ = this->operator()(__urng, __param);
3181 }
3182
3183 template<typename _RealType, typename _CharT, typename _Traits>
3186 const piecewise_linear_distribution<_RealType>& __x)
3187 {
3188 using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
3189
3190 const typename __ios_base::fmtflags __flags = __os.flags();
3191 const _CharT __fill = __os.fill();
3192 const std::streamsize __precision = __os.precision();
3193 const _CharT __space = __os.widen(' ');
3194 __os.flags(__ios_base::scientific | __ios_base::left);
3195 __os.fill(__space);
3197
3198 std::vector<_RealType> __int = __x.intervals();
3199 __os << __int.size() - 1;
3200
3201 for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
3202 __os << __space << *__xit;
3203
3204 std::vector<double> __den = __x.densities();
3205 for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
3206 __os << __space << *__dit;
3207
3208 __os.flags(__flags);
3209 __os.fill(__fill);
3210 __os.precision(__precision);
3211 return __os;
3212 }
3213
3214 template<typename _RealType, typename _CharT, typename _Traits>
3217 piecewise_linear_distribution<_RealType>& __x)
3218 {
3219 using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
3220
3221 const typename __ios_base::fmtflags __flags = __is.flags();
3222 __is.flags(__ios_base::dec | __ios_base::skipws);
3223
3224 size_t __n;
3225 if (__is >> __n)
3226 {
3227 vector<_RealType> __int_vec;
3228 if (__detail::__extract_params(__is, __int_vec, __n + 1))
3229 {
3230 vector<double> __den_vec;
3231 if (__detail::__extract_params(__is, __den_vec, __n + 1))
3232 {
3233 __x.param({ __int_vec.begin(), __int_vec.end(),
3234 __den_vec.begin() });
3235 }
3236 }
3237 }
3238 __is.flags(__flags);
3239 return __is;
3240 }
3241
3242
3243 template<typename _IntType, typename>
3244 seed_seq::seed_seq(std::initializer_list<_IntType> __il)
3245 {
3246 _M_v.reserve(__il.size());
3247 for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
3248 _M_v.push_back(__detail::__mod<result_type,
3249 __detail::_Shift<result_type, 32>::__value>(*__iter));
3250 }
3251
3252 template<typename _InputIterator>
3253 seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
3254 {
3255 if _GLIBCXX17_CONSTEXPR (__is_random_access_iter<_InputIterator>::value)
3256 _M_v.reserve(std::distance(__begin, __end));
3257
3258 for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
3259 _M_v.push_back(__detail::__mod<result_type,
3260 __detail::_Shift<result_type, 32>::__value>(*__iter));
3261 }
3262
3263 template<typename _RandomAccessIterator>
3264 void
3265 seed_seq::generate(_RandomAccessIterator __begin,
3266 _RandomAccessIterator __end)
3267 {
3268 typedef typename iterator_traits<_RandomAccessIterator>::value_type
3269 _Type;
3270
3271 if (__begin == __end)
3272 return;
3273
3274 std::fill(__begin, __end, _Type(0x8b8b8b8bu));
3275
3276 const size_t __n = __end - __begin;
3277 const size_t __s = _M_v.size();
3278 const size_t __t = (__n >= 623) ? 11
3279 : (__n >= 68) ? 7
3280 : (__n >= 39) ? 5
3281 : (__n >= 7) ? 3
3282 : (__n - 1) / 2;
3283 const size_t __p = (__n - __t) / 2;
3284 const size_t __q = __p + __t;
3285 const size_t __m = std::max(size_t(__s + 1), __n);
3286
3287#ifndef __UINT32_TYPE__
3288 struct _Up
3289 {
3290 _Up(uint_least32_t v) : _M_v(v & 0xffffffffu) { }
3291
3292 operator uint_least32_t() const { return _M_v; }
3293
3294 uint_least32_t _M_v;
3295 };
3296 using uint32_t = _Up;
3297#endif
3298
3299 // k == 0, every element in [begin,end) equals 0x8b8b8b8bu
3300 {
3301 uint32_t __r1 = 1371501266u;
3302 uint32_t __r2 = __r1 + __s;
3303 __begin[__p] += __r1;
3304 __begin[__q] = (uint32_t)__begin[__q] + __r2;
3305 __begin[0] = __r2;
3306 }
3307
3308 for (size_t __k = 1; __k <= __s; ++__k)
3309 {
3310 const size_t __kn = __k % __n;
3311 const size_t __kpn = (__k + __p) % __n;
3312 const size_t __kqn = (__k + __q) % __n;
3313 uint32_t __arg = (__begin[__kn]
3314 ^ __begin[__kpn]
3315 ^ __begin[(__k - 1) % __n]);
3316 uint32_t __r1 = 1664525u * (__arg ^ (__arg >> 27));
3317 uint32_t __r2 = __r1 + (uint32_t)__kn + _M_v[__k - 1];
3318 __begin[__kpn] = (uint32_t)__begin[__kpn] + __r1;
3319 __begin[__kqn] = (uint32_t)__begin[__kqn] + __r2;
3320 __begin[__kn] = __r2;
3321 }
3322
3323 for (size_t __k = __s + 1; __k < __m; ++__k)
3324 {
3325 const size_t __kn = __k % __n;
3326 const size_t __kpn = (__k + __p) % __n;
3327 const size_t __kqn = (__k + __q) % __n;
3328 uint32_t __arg = (__begin[__kn]
3329 ^ __begin[__kpn]
3330 ^ __begin[(__k - 1) % __n]);
3331 uint32_t __r1 = 1664525u * (__arg ^ (__arg >> 27));
3332 uint32_t __r2 = __r1 + (uint32_t)__kn;
3333 __begin[__kpn] = (uint32_t)__begin[__kpn] + __r1;
3334 __begin[__kqn] = (uint32_t)__begin[__kqn] + __r2;
3335 __begin[__kn] = __r2;
3336 }
3337
3338 for (size_t __k = __m; __k < __m + __n; ++__k)
3339 {
3340 const size_t __kn = __k % __n;
3341 const size_t __kpn = (__k + __p) % __n;
3342 const size_t __kqn = (__k + __q) % __n;
3343 uint32_t __arg = (__begin[__kn]
3344 + __begin[__kpn]
3345 + __begin[(__k - 1) % __n]);
3346 uint32_t __r3 = 1566083941u * (__arg ^ (__arg >> 27));
3347 uint32_t __r4 = __r3 - __kn;
3348 __begin[__kpn] ^= __r3;
3349 __begin[__kqn] ^= __r4;
3350 __begin[__kn] = __r4;
3351 }
3352 }
3353
3354 template<typename _RealType, size_t __bits,
3355 typename _UniformRandomNumberGenerator>
3356 _RealType
3358 {
3360 "template argument must be a floating point type");
3361
3362 const size_t __b
3363 = std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
3364 __bits);
3365 const long double __r = static_cast<long double>(__urng.max())
3366 - static_cast<long double>(__urng.min()) + 1.0L;
3367 const size_t __log2r = std::log(__r) / std::log(2.0L);
3368 const size_t __m = std::max<size_t>(1UL,
3369 (__b + __log2r - 1UL) / __log2r);
3370 _RealType __ret;
3371 _RealType __sum = _RealType(0);
3372 _RealType __tmp = _RealType(1);
3373 for (size_t __k = __m; __k != 0; --__k)
3374 {
3375 __sum += _RealType(__urng() - __urng.min()) * __tmp;
3376 __tmp *= __r;
3377 }
3378 __ret = __sum / __tmp;
3379 if (__builtin_expect(__ret >= _RealType(1), 0))
3380 {
3381#if _GLIBCXX_USE_C99_MATH_TR1
3382 __ret = std::nextafter(_RealType(1), _RealType(0));
3383#else
3384 __ret = _RealType(1)
3385 - std::numeric_limits<_RealType>::epsilon() / _RealType(2);
3386#endif
3387 }
3388 return __ret;
3389 }
3390
3391_GLIBCXX_END_NAMESPACE_VERSION
3392} // namespace
3393
3394#endif
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition complex:824
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition complex:960
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition complex:630
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition complex:797
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
Definition complex:1019
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition complex:933
constexpr const _Tp & max(const _Tp &, const _Tp &)
This does what you think it does.
constexpr const _Tp & min(const _Tp &, const _Tp &)
This does what you think it does.
_RealType generate_canonical(_UniformRandomNumberGenerator &__g)
A function template for converting the output of a (integral) uniform random number generator to a fl...
constexpr back_insert_iterator< _Container > back_inserter(_Container &__x)
constexpr _Tp accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
Accumulate values in a range.
constexpr _OutputIterator partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
Return list of partial sums.
ISO C++ entities toplevel namespace is std.
ptrdiff_t streamsize
Integral type for I/O operation counts and buffer sizes.
Definition postypes.h:68
constexpr iterator_traits< _InputIterator >::difference_type distance(_InputIterator __first, _InputIterator __last)
A generalization of pointer arithmetic.
constexpr int __lg(int __n)
This is a helper function for the sort routines and for random.tcc.
std::basic_istream< _CharT, _Traits > & operator>>(std::basic_istream< _CharT, _Traits > &__is, bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition bitset:1475
std::basic_ostream< _CharT, _Traits > & operator<<(std::basic_ostream< _CharT, _Traits > &__os, const bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition bitset:1543
Template class basic_istream.
Definition istream:59
Template class basic_ostream.
Definition ostream:59
static constexpr bool is_integer
Definition limits:226
static constexpr int digits
Definition limits:211
static constexpr bool is_signed
Definition limits:223
Properties of fundamental types.
Definition limits:313
static constexpr _Tp max() noexcept
Definition limits:321
static constexpr _Tp epsilon() noexcept
Definition limits:333
is_floating_point
Definition type_traits:445
common_type
Definition type_traits:2259
A model of a linear congruential random number generator.
Definition random.h:259
static constexpr result_type multiplier
Definition random.h:274
static constexpr result_type modulus
Definition random.h:278
void seed(result_type __s=default_seed)
Reseeds the linear_congruential_engine random number generator engine sequence to the seed __s.
static constexpr result_type increment
Definition random.h:276
The Marsaglia-Zaman generator.
Definition random.h:696
void seed(result_type __sd=0u)
Seeds the initial state of the random number generator.
result_type operator()()
Gets the next random number in the sequence.
result_type operator()()
Gets the next value in the generated random number sequence.
result_type operator()()
Gets the next value in the generated random number sequence.
Produces random numbers by reordering random numbers from some base engine.
Definition random.h:1330
_RandomNumberEngine::result_type result_type
Definition random.h:1336
Uniform continuous distribution for random numbers.
Definition random.h:1746
A normal continuous distribution for random numbers.
Definition random.h:1976
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:2093
A gamma continuous distribution for random numbers.
Definition random.h:2408
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:2535
A chi_squared_distribution random number distribution.
Definition random.h:2636
A cauchy_distribution random number distribution.
Definition random.h:2860
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:2965
A fisher_f_distribution random number distribution.
Definition random.h:3068
A student_t_distribution random number distribution.
Definition random.h:3300
A discrete binomial random number distribution.
Definition random.h:3744
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:3870
A discrete geometric random number distribution.
Definition random.h:3984
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:4093
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
A discrete Poisson random number distribution.
Definition random.h:4425
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:4536
friend bool operator==(const poisson_distribution &__d1, const poisson_distribution &__d2)
Return true if two Poisson distributions have the same parameters and the sequences that would be gen...
Definition random.h:4572
friend std::basic_ostream< _CharT, _Traits > & operator<<(std::basic_ostream< _CharT, _Traits > &__os, const std::poisson_distribution< _IntType1 > &__x)
Inserts a poisson_distribution random number distribution __x into the output stream __os.
friend std::basic_istream< _CharT, _Traits > & operator>>(std::basic_istream< _CharT, _Traits > &__is, std::poisson_distribution< _IntType1 > &__x)
Extracts a poisson_distribution random number distribution __x from the input stream __is.
An exponential continuous distribution for random numbers.
Definition random.h:4651
A weibull_distribution random number distribution.
Definition random.h:4866
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:4974
A extreme_value_distribution random number distribution.
Definition random.h:5076
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition random.h:5184
Parallel STL function calls corresponding to stl_numeric.h. The functions defined here mainly do case...