libstdc++
bits/random.tcc
Go to the documentation of this file.
1 // random number generation (out of line) -*- C++ -*-
2 
3 // Copyright (C) 2009-2020 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 
35 namespace std _GLIBCXX_VISIBILITY(default)
36 {
37 _GLIBCXX_BEGIN_NAMESPACE_VERSION
38 
39  /*
40  * (Further) implementation-space details.
41  */
42  namespace __detail
43  {
44  // General case for x = (ax + c) mod m -- use Schrage's algorithm
45  // to avoid integer overflow.
46  //
47  // Preconditions: a > 0, m > 0.
48  //
49  // Note: only works correctly for __m % __a < __m / __a.
50  template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
51  _Tp
52  _Mod<_Tp, __m, __a, __c, false, true>::
53  __calc(_Tp __x)
54  {
55  if (__a == 1)
56  __x %= __m;
57  else
58  {
59  static const _Tp __q = __m / __a;
60  static const _Tp __r = __m % __a;
61 
62  _Tp __t1 = __a * (__x % __q);
63  _Tp __t2 = __r * (__x / __q);
64  if (__t1 >= __t2)
65  __x = __t1 - __t2;
66  else
67  __x = __m - __t2 + __t1;
68  }
69 
70  if (__c != 0)
71  {
72  const _Tp __d = __m - __x;
73  if (__d > __c)
74  __x += __c;
75  else
76  __x = __c - __d;
77  }
78  return __x;
79  }
80 
81  template<typename _InputIterator, typename _OutputIterator,
82  typename _Tp>
83  _OutputIterator
84  __normalize(_InputIterator __first, _InputIterator __last,
85  _OutputIterator __result, const _Tp& __factor)
86  {
87  for (; __first != __last; ++__first, ++__result)
88  *__result = *__first / __factor;
89  return __result;
90  }
91 
92  } // namespace __detail
93 
94  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
95  constexpr _UIntType
96  linear_congruential_engine<_UIntType, __a, __c, __m>::multiplier;
97 
98  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
99  constexpr _UIntType
100  linear_congruential_engine<_UIntType, __a, __c, __m>::increment;
101 
102  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
103  constexpr _UIntType
104  linear_congruential_engine<_UIntType, __a, __c, __m>::modulus;
105 
106  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
107  constexpr _UIntType
108  linear_congruential_engine<_UIntType, __a, __c, __m>::default_seed;
109 
110  /**
111  * Seeds the LCR with integral value @p __s, adjusted so that the
112  * ring identity is never a member of the convergence set.
113  */
114  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
115  void
116  linear_congruential_engine<_UIntType, __a, __c, __m>::
117  seed(result_type __s)
118  {
119  if ((__detail::__mod<_UIntType, __m>(__c) == 0)
120  && (__detail::__mod<_UIntType, __m>(__s) == 0))
121  _M_x = 1;
122  else
123  _M_x = __detail::__mod<_UIntType, __m>(__s);
124  }
125 
126  /**
127  * Seeds the LCR engine with a value generated by @p __q.
128  */
129  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
130  template<typename _Sseq>
131  auto
132  linear_congruential_engine<_UIntType, __a, __c, __m>::
133  seed(_Sseq& __q)
134  -> _If_seed_seq<_Sseq>
135  {
136  const _UIntType __k0 = __m == 0 ? std::numeric_limits<_UIntType>::digits
137  : std::__lg(__m);
138  const _UIntType __k = (__k0 + 31) / 32;
139  uint_least32_t __arr[__k + 3];
140  __q.generate(__arr + 0, __arr + __k + 3);
141  _UIntType __factor = 1u;
142  _UIntType __sum = 0u;
143  for (size_t __j = 0; __j < __k; ++__j)
144  {
145  __sum += __arr[__j + 3] * __factor;
146  __factor *= __detail::_Shift<_UIntType, 32>::__value;
147  }
148  seed(__sum);
149  }
150 
151  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
152  typename _CharT, typename _Traits>
153  std::basic_ostream<_CharT, _Traits>&
154  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
155  const linear_congruential_engine<_UIntType,
156  __a, __c, __m>& __lcr)
157  {
158  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
159 
160  const typename __ios_base::fmtflags __flags = __os.flags();
161  const _CharT __fill = __os.fill();
162  __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
163  __os.fill(__os.widen(' '));
164 
165  __os << __lcr._M_x;
166 
167  __os.flags(__flags);
168  __os.fill(__fill);
169  return __os;
170  }
171 
172  template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
173  typename _CharT, typename _Traits>
174  std::basic_istream<_CharT, _Traits>&
175  operator>>(std::basic_istream<_CharT, _Traits>& __is,
176  linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
177  {
178  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
179 
180  const typename __ios_base::fmtflags __flags = __is.flags();
181  __is.flags(__ios_base::dec);
182 
183  __is >> __lcr._M_x;
184 
185  __is.flags(__flags);
186  return __is;
187  }
188 
189 
190  template<typename _UIntType,
191  size_t __w, size_t __n, size_t __m, size_t __r,
192  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
193  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
194  _UIntType __f>
195  constexpr size_t
196  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
197  __s, __b, __t, __c, __l, __f>::word_size;
198 
199  template<typename _UIntType,
200  size_t __w, size_t __n, size_t __m, size_t __r,
201  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
202  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
203  _UIntType __f>
204  constexpr size_t
205  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
206  __s, __b, __t, __c, __l, __f>::state_size;
207 
208  template<typename _UIntType,
209  size_t __w, size_t __n, size_t __m, size_t __r,
210  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
211  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
212  _UIntType __f>
213  constexpr size_t
214  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
215  __s, __b, __t, __c, __l, __f>::shift_size;
216 
217  template<typename _UIntType,
218  size_t __w, size_t __n, size_t __m, size_t __r,
219  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
220  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
221  _UIntType __f>
222  constexpr size_t
223  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
224  __s, __b, __t, __c, __l, __f>::mask_bits;
225 
226  template<typename _UIntType,
227  size_t __w, size_t __n, size_t __m, size_t __r,
228  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
229  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
230  _UIntType __f>
231  constexpr _UIntType
232  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
233  __s, __b, __t, __c, __l, __f>::xor_mask;
234 
235  template<typename _UIntType,
236  size_t __w, size_t __n, size_t __m, size_t __r,
237  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
238  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
239  _UIntType __f>
240  constexpr size_t
241  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
242  __s, __b, __t, __c, __l, __f>::tempering_u;
243 
244  template<typename _UIntType,
245  size_t __w, size_t __n, size_t __m, size_t __r,
246  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
247  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
248  _UIntType __f>
249  constexpr _UIntType
250  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
251  __s, __b, __t, __c, __l, __f>::tempering_d;
252 
253  template<typename _UIntType,
254  size_t __w, size_t __n, size_t __m, size_t __r,
255  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
256  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
257  _UIntType __f>
258  constexpr size_t
259  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
260  __s, __b, __t, __c, __l, __f>::tempering_s;
261 
262  template<typename _UIntType,
263  size_t __w, size_t __n, size_t __m, size_t __r,
264  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
265  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
266  _UIntType __f>
267  constexpr _UIntType
268  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
269  __s, __b, __t, __c, __l, __f>::tempering_b;
270 
271  template<typename _UIntType,
272  size_t __w, size_t __n, size_t __m, size_t __r,
273  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
274  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
275  _UIntType __f>
276  constexpr size_t
277  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
278  __s, __b, __t, __c, __l, __f>::tempering_t;
279 
280  template<typename _UIntType,
281  size_t __w, size_t __n, size_t __m, size_t __r,
282  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
283  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
284  _UIntType __f>
285  constexpr _UIntType
286  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
287  __s, __b, __t, __c, __l, __f>::tempering_c;
288 
289  template<typename _UIntType,
290  size_t __w, size_t __n, size_t __m, size_t __r,
291  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
292  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
293  _UIntType __f>
294  constexpr size_t
295  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
296  __s, __b, __t, __c, __l, __f>::tempering_l;
297 
298  template<typename _UIntType,
299  size_t __w, size_t __n, size_t __m, size_t __r,
300  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
301  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
302  _UIntType __f>
303  constexpr _UIntType
304  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
305  __s, __b, __t, __c, __l, __f>::
306  initialization_multiplier;
307 
308  template<typename _UIntType,
309  size_t __w, size_t __n, size_t __m, size_t __r,
310  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
311  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
312  _UIntType __f>
313  constexpr _UIntType
314  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
315  __s, __b, __t, __c, __l, __f>::default_seed;
316 
317  template<typename _UIntType,
318  size_t __w, size_t __n, size_t __m, size_t __r,
319  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
320  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
321  _UIntType __f>
322  void
323  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
324  __s, __b, __t, __c, __l, __f>::
325  seed(result_type __sd)
326  {
327  _M_x[0] = __detail::__mod<_UIntType,
328  __detail::_Shift<_UIntType, __w>::__value>(__sd);
329 
330  for (size_t __i = 1; __i < state_size; ++__i)
331  {
332  _UIntType __x = _M_x[__i - 1];
333  __x ^= __x >> (__w - 2);
334  __x *= __f;
335  __x += __detail::__mod<_UIntType, __n>(__i);
336  _M_x[__i] = __detail::__mod<_UIntType,
337  __detail::_Shift<_UIntType, __w>::__value>(__x);
338  }
339  _M_p = state_size;
340  }
341 
342  template<typename _UIntType,
343  size_t __w, size_t __n, size_t __m, size_t __r,
344  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
345  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
346  _UIntType __f>
347  template<typename _Sseq>
348  auto
349  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
350  __s, __b, __t, __c, __l, __f>::
351  seed(_Sseq& __q)
352  -> _If_seed_seq<_Sseq>
353  {
354  const _UIntType __upper_mask = (~_UIntType()) << __r;
355  const size_t __k = (__w + 31) / 32;
356  uint_least32_t __arr[__n * __k];
357  __q.generate(__arr + 0, __arr + __n * __k);
358 
359  bool __zero = true;
360  for (size_t __i = 0; __i < state_size; ++__i)
361  {
362  _UIntType __factor = 1u;
363  _UIntType __sum = 0u;
364  for (size_t __j = 0; __j < __k; ++__j)
365  {
366  __sum += __arr[__k * __i + __j] * __factor;
367  __factor *= __detail::_Shift<_UIntType, 32>::__value;
368  }
369  _M_x[__i] = __detail::__mod<_UIntType,
370  __detail::_Shift<_UIntType, __w>::__value>(__sum);
371 
372  if (__zero)
373  {
374  if (__i == 0)
375  {
376  if ((_M_x[0] & __upper_mask) != 0u)
377  __zero = false;
378  }
379  else if (_M_x[__i] != 0u)
380  __zero = false;
381  }
382  }
383  if (__zero)
384  _M_x[0] = __detail::_Shift<_UIntType, __w - 1>::__value;
385  _M_p = state_size;
386  }
387 
388  template<typename _UIntType, size_t __w,
389  size_t __n, size_t __m, size_t __r,
390  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
391  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
392  _UIntType __f>
393  void
394  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
395  __s, __b, __t, __c, __l, __f>::
396  _M_gen_rand(void)
397  {
398  const _UIntType __upper_mask = (~_UIntType()) << __r;
399  const _UIntType __lower_mask = ~__upper_mask;
400 
401  for (size_t __k = 0; __k < (__n - __m); ++__k)
402  {
403  _UIntType __y = ((_M_x[__k] & __upper_mask)
404  | (_M_x[__k + 1] & __lower_mask));
405  _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
406  ^ ((__y & 0x01) ? __a : 0));
407  }
408 
409  for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
410  {
411  _UIntType __y = ((_M_x[__k] & __upper_mask)
412  | (_M_x[__k + 1] & __lower_mask));
413  _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
414  ^ ((__y & 0x01) ? __a : 0));
415  }
416 
417  _UIntType __y = ((_M_x[__n - 1] & __upper_mask)
418  | (_M_x[0] & __lower_mask));
419  _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
420  ^ ((__y & 0x01) ? __a : 0));
421  _M_p = 0;
422  }
423 
424  template<typename _UIntType, size_t __w,
425  size_t __n, size_t __m, size_t __r,
426  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
427  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
428  _UIntType __f>
429  void
430  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
431  __s, __b, __t, __c, __l, __f>::
432  discard(unsigned long long __z)
433  {
434  while (__z > state_size - _M_p)
435  {
436  __z -= state_size - _M_p;
437  _M_gen_rand();
438  }
439  _M_p += __z;
440  }
441 
442  template<typename _UIntType, size_t __w,
443  size_t __n, size_t __m, size_t __r,
444  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
445  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
446  _UIntType __f>
447  typename
448  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
449  __s, __b, __t, __c, __l, __f>::result_type
450  mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
451  __s, __b, __t, __c, __l, __f>::
452  operator()()
453  {
454  // Reload the vector - cost is O(n) amortized over n calls.
455  if (_M_p >= state_size)
456  _M_gen_rand();
457 
458  // Calculate o(x(i)).
459  result_type __z = _M_x[_M_p++];
460  __z ^= (__z >> __u) & __d;
461  __z ^= (__z << __s) & __b;
462  __z ^= (__z << __t) & __c;
463  __z ^= (__z >> __l);
464 
465  return __z;
466  }
467 
468  template<typename _UIntType, size_t __w,
469  size_t __n, size_t __m, size_t __r,
470  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
471  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
472  _UIntType __f, typename _CharT, typename _Traits>
473  std::basic_ostream<_CharT, _Traits>&
474  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
475  const mersenne_twister_engine<_UIntType, __w, __n, __m,
476  __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
477  {
478  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
479 
480  const typename __ios_base::fmtflags __flags = __os.flags();
481  const _CharT __fill = __os.fill();
482  const _CharT __space = __os.widen(' ');
483  __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
484  __os.fill(__space);
485 
486  for (size_t __i = 0; __i < __n; ++__i)
487  __os << __x._M_x[__i] << __space;
488  __os << __x._M_p;
489 
490  __os.flags(__flags);
491  __os.fill(__fill);
492  return __os;
493  }
494 
495  template<typename _UIntType, size_t __w,
496  size_t __n, size_t __m, size_t __r,
497  _UIntType __a, size_t __u, _UIntType __d, size_t __s,
498  _UIntType __b, size_t __t, _UIntType __c, size_t __l,
499  _UIntType __f, typename _CharT, typename _Traits>
500  std::basic_istream<_CharT, _Traits>&
501  operator>>(std::basic_istream<_CharT, _Traits>& __is,
502  mersenne_twister_engine<_UIntType, __w, __n, __m,
503  __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
504  {
505  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
506 
507  const typename __ios_base::fmtflags __flags = __is.flags();
508  __is.flags(__ios_base::dec | __ios_base::skipws);
509 
510  for (size_t __i = 0; __i < __n; ++__i)
511  __is >> __x._M_x[__i];
512  __is >> __x._M_p;
513 
514  __is.flags(__flags);
515  return __is;
516  }
517 
518 
519  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
520  constexpr size_t
521  subtract_with_carry_engine<_UIntType, __w, __s, __r>::word_size;
522 
523  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
524  constexpr size_t
525  subtract_with_carry_engine<_UIntType, __w, __s, __r>::short_lag;
526 
527  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
528  constexpr size_t
529  subtract_with_carry_engine<_UIntType, __w, __s, __r>::long_lag;
530 
531  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
532  constexpr _UIntType
533  subtract_with_carry_engine<_UIntType, __w, __s, __r>::default_seed;
534 
535  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
536  void
537  subtract_with_carry_engine<_UIntType, __w, __s, __r>::
538  seed(result_type __value)
539  {
540  std::linear_congruential_engine<result_type, 40014u, 0u, 2147483563u>
541  __lcg(__value == 0u ? default_seed : __value);
542 
543  const size_t __n = (__w + 31) / 32;
544 
545  for (size_t __i = 0; __i < long_lag; ++__i)
546  {
547  _UIntType __sum = 0u;
548  _UIntType __factor = 1u;
549  for (size_t __j = 0; __j < __n; ++__j)
550  {
551  __sum += __detail::__mod<uint_least32_t,
552  __detail::_Shift<uint_least32_t, 32>::__value>
553  (__lcg()) * __factor;
554  __factor *= __detail::_Shift<_UIntType, 32>::__value;
555  }
556  _M_x[__i] = __detail::__mod<_UIntType,
557  __detail::_Shift<_UIntType, __w>::__value>(__sum);
558  }
559  _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
560  _M_p = 0;
561  }
562 
563  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
564  template<typename _Sseq>
565  auto
566  subtract_with_carry_engine<_UIntType, __w, __s, __r>::
567  seed(_Sseq& __q)
568  -> _If_seed_seq<_Sseq>
569  {
570  const size_t __k = (__w + 31) / 32;
571  uint_least32_t __arr[__r * __k];
572  __q.generate(__arr + 0, __arr + __r * __k);
573 
574  for (size_t __i = 0; __i < long_lag; ++__i)
575  {
576  _UIntType __sum = 0u;
577  _UIntType __factor = 1u;
578  for (size_t __j = 0; __j < __k; ++__j)
579  {
580  __sum += __arr[__k * __i + __j] * __factor;
581  __factor *= __detail::_Shift<_UIntType, 32>::__value;
582  }
583  _M_x[__i] = __detail::__mod<_UIntType,
584  __detail::_Shift<_UIntType, __w>::__value>(__sum);
585  }
586  _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
587  _M_p = 0;
588  }
589 
590  template<typename _UIntType, size_t __w, size_t __s, size_t __r>
591  typename subtract_with_carry_engine<_UIntType, __w, __s, __r>::
592  result_type
593  subtract_with_carry_engine<_UIntType, __w, __s, __r>::
594  operator()()
595  {
596  // Derive short lag index from current index.
597  long __ps = _M_p - short_lag;
598  if (__ps < 0)
599  __ps += long_lag;
600 
601  // Calculate new x(i) without overflow or division.
602  // NB: Thanks to the requirements for _UIntType, _M_x[_M_p] + _M_carry
603  // cannot overflow.
604  _UIntType __xi;
605  if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
606  {
607  __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
608  _M_carry = 0;
609  }
610  else
611  {
612  __xi = (__detail::_Shift<_UIntType, __w>::__value
613  - _M_x[_M_p] - _M_carry + _M_x[__ps]);
614  _M_carry = 1;
615  }
616  _M_x[_M_p] = __xi;
617 
618  // Adjust current index to loop around in ring buffer.
619  if (++_M_p >= long_lag)
620  _M_p = 0;
621 
622  return __xi;
623  }
624 
625  template<typename _UIntType, size_t __w, size_t __s, size_t __r,
626  typename _CharT, typename _Traits>
627  std::basic_ostream<_CharT, _Traits>&
628  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
629  const subtract_with_carry_engine<_UIntType,
630  __w, __s, __r>& __x)
631  {
632  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
633 
634  const typename __ios_base::fmtflags __flags = __os.flags();
635  const _CharT __fill = __os.fill();
636  const _CharT __space = __os.widen(' ');
637  __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
638  __os.fill(__space);
639 
640  for (size_t __i = 0; __i < __r; ++__i)
641  __os << __x._M_x[__i] << __space;
642  __os << __x._M_carry << __space << __x._M_p;
643 
644  __os.flags(__flags);
645  __os.fill(__fill);
646  return __os;
647  }
648 
649  template<typename _UIntType, size_t __w, size_t __s, size_t __r,
650  typename _CharT, typename _Traits>
651  std::basic_istream<_CharT, _Traits>&
652  operator>>(std::basic_istream<_CharT, _Traits>& __is,
653  subtract_with_carry_engine<_UIntType, __w, __s, __r>& __x)
654  {
655  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
656 
657  const typename __ios_base::fmtflags __flags = __is.flags();
658  __is.flags(__ios_base::dec | __ios_base::skipws);
659 
660  for (size_t __i = 0; __i < __r; ++__i)
661  __is >> __x._M_x[__i];
662  __is >> __x._M_carry;
663  __is >> __x._M_p;
664 
665  __is.flags(__flags);
666  return __is;
667  }
668 
669 
670  template<typename _RandomNumberEngine, size_t __p, size_t __r>
671  constexpr size_t
672  discard_block_engine<_RandomNumberEngine, __p, __r>::block_size;
673 
674  template<typename _RandomNumberEngine, size_t __p, size_t __r>
675  constexpr size_t
676  discard_block_engine<_RandomNumberEngine, __p, __r>::used_block;
677 
678  template<typename _RandomNumberEngine, size_t __p, size_t __r>
679  typename discard_block_engine<_RandomNumberEngine,
680  __p, __r>::result_type
681  discard_block_engine<_RandomNumberEngine, __p, __r>::
682  operator()()
683  {
684  if (_M_n >= used_block)
685  {
686  _M_b.discard(block_size - _M_n);
687  _M_n = 0;
688  }
689  ++_M_n;
690  return _M_b();
691  }
692 
693  template<typename _RandomNumberEngine, size_t __p, size_t __r,
694  typename _CharT, typename _Traits>
695  std::basic_ostream<_CharT, _Traits>&
696  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
697  const discard_block_engine<_RandomNumberEngine,
698  __p, __r>& __x)
699  {
700  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
701 
702  const typename __ios_base::fmtflags __flags = __os.flags();
703  const _CharT __fill = __os.fill();
704  const _CharT __space = __os.widen(' ');
705  __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
706  __os.fill(__space);
707 
708  __os << __x.base() << __space << __x._M_n;
709 
710  __os.flags(__flags);
711  __os.fill(__fill);
712  return __os;
713  }
714 
715  template<typename _RandomNumberEngine, size_t __p, size_t __r,
716  typename _CharT, typename _Traits>
717  std::basic_istream<_CharT, _Traits>&
718  operator>>(std::basic_istream<_CharT, _Traits>& __is,
719  discard_block_engine<_RandomNumberEngine, __p, __r>& __x)
720  {
721  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
722 
723  const typename __ios_base::fmtflags __flags = __is.flags();
724  __is.flags(__ios_base::dec | __ios_base::skipws);
725 
726  __is >> __x._M_b >> __x._M_n;
727 
728  __is.flags(__flags);
729  return __is;
730  }
731 
732 
733  template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
734  typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
735  result_type
736  independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
737  operator()()
738  {
739  typedef typename _RandomNumberEngine::result_type _Eresult_type;
740  const _Eresult_type __r
741  = (_M_b.max() - _M_b.min() < std::numeric_limits<_Eresult_type>::max()
742  ? _M_b.max() - _M_b.min() + 1 : 0);
743  const unsigned __edig = std::numeric_limits<_Eresult_type>::digits;
744  const unsigned __m = __r ? std::__lg(__r) : __edig;
745 
746  typedef typename std::common_type<_Eresult_type, result_type>::type
747  __ctype;
748  const unsigned __cdig = std::numeric_limits<__ctype>::digits;
749 
750  unsigned __n, __n0;
751  __ctype __s0, __s1, __y0, __y1;
752 
753  for (size_t __i = 0; __i < 2; ++__i)
754  {
755  __n = (__w + __m - 1) / __m + __i;
756  __n0 = __n - __w % __n;
757  const unsigned __w0 = __w / __n; // __w0 <= __m
758 
759  __s0 = 0;
760  __s1 = 0;
761  if (__w0 < __cdig)
762  {
763  __s0 = __ctype(1) << __w0;
764  __s1 = __s0 << 1;
765  }
766 
767  __y0 = 0;
768  __y1 = 0;
769  if (__r)
770  {
771  __y0 = __s0 * (__r / __s0);
772  if (__s1)
773  __y1 = __s1 * (__r / __s1);
774 
775  if (__r - __y0 <= __y0 / __n)
776  break;
777  }
778  else
779  break;
780  }
781 
782  result_type __sum = 0;
783  for (size_t __k = 0; __k < __n0; ++__k)
784  {
785  __ctype __u;
786  do
787  __u = _M_b() - _M_b.min();
788  while (__y0 && __u >= __y0);
789  __sum = __s0 * __sum + (__s0 ? __u % __s0 : __u);
790  }
791  for (size_t __k = __n0; __k < __n; ++__k)
792  {
793  __ctype __u;
794  do
795  __u = _M_b() - _M_b.min();
796  while (__y1 && __u >= __y1);
797  __sum = __s1 * __sum + (__s1 ? __u % __s1 : __u);
798  }
799  return __sum;
800  }
801 
802 
803  template<typename _RandomNumberEngine, size_t __k>
804  constexpr size_t
805  shuffle_order_engine<_RandomNumberEngine, __k>::table_size;
806 
807  template<typename _RandomNumberEngine, size_t __k>
808  typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
809  shuffle_order_engine<_RandomNumberEngine, __k>::
810  operator()()
811  {
812  size_t __j = __k * ((_M_y - _M_b.min())
813  / (_M_b.max() - _M_b.min() + 1.0L));
814  _M_y = _M_v[__j];
815  _M_v[__j] = _M_b();
816 
817  return _M_y;
818  }
819 
820  template<typename _RandomNumberEngine, size_t __k,
821  typename _CharT, typename _Traits>
822  std::basic_ostream<_CharT, _Traits>&
823  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
824  const shuffle_order_engine<_RandomNumberEngine, __k>& __x)
825  {
826  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
827 
828  const typename __ios_base::fmtflags __flags = __os.flags();
829  const _CharT __fill = __os.fill();
830  const _CharT __space = __os.widen(' ');
831  __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
832  __os.fill(__space);
833 
834  __os << __x.base();
835  for (size_t __i = 0; __i < __k; ++__i)
836  __os << __space << __x._M_v[__i];
837  __os << __space << __x._M_y;
838 
839  __os.flags(__flags);
840  __os.fill(__fill);
841  return __os;
842  }
843 
844  template<typename _RandomNumberEngine, size_t __k,
845  typename _CharT, typename _Traits>
846  std::basic_istream<_CharT, _Traits>&
847  operator>>(std::basic_istream<_CharT, _Traits>& __is,
848  shuffle_order_engine<_RandomNumberEngine, __k>& __x)
849  {
850  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
851 
852  const typename __ios_base::fmtflags __flags = __is.flags();
853  __is.flags(__ios_base::dec | __ios_base::skipws);
854 
855  __is >> __x._M_b;
856  for (size_t __i = 0; __i < __k; ++__i)
857  __is >> __x._M_v[__i];
858  __is >> __x._M_y;
859 
860  __is.flags(__flags);
861  return __is;
862  }
863 
864 
865  template<typename _IntType, typename _CharT, typename _Traits>
866  std::basic_ostream<_CharT, _Traits>&
867  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
868  const uniform_int_distribution<_IntType>& __x)
869  {
870  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
871 
872  const typename __ios_base::fmtflags __flags = __os.flags();
873  const _CharT __fill = __os.fill();
874  const _CharT __space = __os.widen(' ');
875  __os.flags(__ios_base::scientific | __ios_base::left);
876  __os.fill(__space);
877 
878  __os << __x.a() << __space << __x.b();
879 
880  __os.flags(__flags);
881  __os.fill(__fill);
882  return __os;
883  }
884 
885  template<typename _IntType, typename _CharT, typename _Traits>
886  std::basic_istream<_CharT, _Traits>&
887  operator>>(std::basic_istream<_CharT, _Traits>& __is,
888  uniform_int_distribution<_IntType>& __x)
889  {
890  using param_type
891  = typename uniform_int_distribution<_IntType>::param_type;
892  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
893 
894  const typename __ios_base::fmtflags __flags = __is.flags();
895  __is.flags(__ios_base::dec | __ios_base::skipws);
896 
897  _IntType __a, __b;
898  if (__is >> __a >> __b)
899  __x.param(param_type(__a, __b));
900 
901  __is.flags(__flags);
902  return __is;
903  }
904 
905 
906  template<typename _RealType>
907  template<typename _ForwardIterator,
908  typename _UniformRandomNumberGenerator>
909  void
910  uniform_real_distribution<_RealType>::
911  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
912  _UniformRandomNumberGenerator& __urng,
913  const param_type& __p)
914  {
915  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
916  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
917  __aurng(__urng);
918  auto __range = __p.b() - __p.a();
919  while (__f != __t)
920  *__f++ = __aurng() * __range + __p.a();
921  }
922 
923  template<typename _RealType, typename _CharT, typename _Traits>
924  std::basic_ostream<_CharT, _Traits>&
925  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
926  const uniform_real_distribution<_RealType>& __x)
927  {
928  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
929 
930  const typename __ios_base::fmtflags __flags = __os.flags();
931  const _CharT __fill = __os.fill();
932  const std::streamsize __precision = __os.precision();
933  const _CharT __space = __os.widen(' ');
934  __os.flags(__ios_base::scientific | __ios_base::left);
935  __os.fill(__space);
936  __os.precision(std::numeric_limits<_RealType>::max_digits10);
937 
938  __os << __x.a() << __space << __x.b();
939 
940  __os.flags(__flags);
941  __os.fill(__fill);
942  __os.precision(__precision);
943  return __os;
944  }
945 
946  template<typename _RealType, typename _CharT, typename _Traits>
947  std::basic_istream<_CharT, _Traits>&
948  operator>>(std::basic_istream<_CharT, _Traits>& __is,
949  uniform_real_distribution<_RealType>& __x)
950  {
951  using param_type
952  = typename uniform_real_distribution<_RealType>::param_type;
953  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
954 
955  const typename __ios_base::fmtflags __flags = __is.flags();
956  __is.flags(__ios_base::skipws);
957 
958  _RealType __a, __b;
959  if (__is >> __a >> __b)
960  __x.param(param_type(__a, __b));
961 
962  __is.flags(__flags);
963  return __is;
964  }
965 
966 
967  template<typename _ForwardIterator,
968  typename _UniformRandomNumberGenerator>
969  void
970  std::bernoulli_distribution::
971  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
972  _UniformRandomNumberGenerator& __urng,
973  const param_type& __p)
974  {
975  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
976  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
977  __aurng(__urng);
978  auto __limit = __p.p() * (__aurng.max() - __aurng.min());
979 
980  while (__f != __t)
981  *__f++ = (__aurng() - __aurng.min()) < __limit;
982  }
983 
984  template<typename _CharT, typename _Traits>
985  std::basic_ostream<_CharT, _Traits>&
986  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
987  const bernoulli_distribution& __x)
988  {
989  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
990 
991  const typename __ios_base::fmtflags __flags = __os.flags();
992  const _CharT __fill = __os.fill();
993  const std::streamsize __precision = __os.precision();
994  __os.flags(__ios_base::scientific | __ios_base::left);
995  __os.fill(__os.widen(' '));
996  __os.precision(std::numeric_limits<double>::max_digits10);
997 
998  __os << __x.p();
999 
1000  __os.flags(__flags);
1001  __os.fill(__fill);
1002  __os.precision(__precision);
1003  return __os;
1004  }
1005 
1006 
1007  template<typename _IntType>
1008  template<typename _UniformRandomNumberGenerator>
1009  typename geometric_distribution<_IntType>::result_type
1010  geometric_distribution<_IntType>::
1011  operator()(_UniformRandomNumberGenerator& __urng,
1012  const param_type& __param)
1013  {
1014  // About the epsilon thing see this thread:
1015  // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1016  const double __naf =
1017  (1 - std::numeric_limits<double>::epsilon()) / 2;
1018  // The largest _RealType convertible to _IntType.
1019  const double __thr =
1020  std::numeric_limits<_IntType>::max() + __naf;
1021  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1022  __aurng(__urng);
1023 
1024  double __cand;
1025  do
1026  __cand = std::floor(std::log(1.0 - __aurng()) / __param._M_log_1_p);
1027  while (__cand >= __thr);
1028 
1029  return result_type(__cand + __naf);
1030  }
1031 
1032  template<typename _IntType>
1033  template<typename _ForwardIterator,
1034  typename _UniformRandomNumberGenerator>
1035  void
1036  geometric_distribution<_IntType>::
1037  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1038  _UniformRandomNumberGenerator& __urng,
1039  const param_type& __param)
1040  {
1041  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1042  // About the epsilon thing see this thread:
1043  // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1044  const double __naf =
1045  (1 - std::numeric_limits<double>::epsilon()) / 2;
1046  // The largest _RealType convertible to _IntType.
1047  const double __thr =
1048  std::numeric_limits<_IntType>::max() + __naf;
1049  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1050  __aurng(__urng);
1051 
1052  while (__f != __t)
1053  {
1054  double __cand;
1055  do
1056  __cand = std::floor(std::log(1.0 - __aurng())
1057  / __param._M_log_1_p);
1058  while (__cand >= __thr);
1059 
1060  *__f++ = __cand + __naf;
1061  }
1062  }
1063 
1064  template<typename _IntType,
1065  typename _CharT, typename _Traits>
1066  std::basic_ostream<_CharT, _Traits>&
1067  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1068  const geometric_distribution<_IntType>& __x)
1069  {
1070  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1071 
1072  const typename __ios_base::fmtflags __flags = __os.flags();
1073  const _CharT __fill = __os.fill();
1074  const std::streamsize __precision = __os.precision();
1075  __os.flags(__ios_base::scientific | __ios_base::left);
1076  __os.fill(__os.widen(' '));
1077  __os.precision(std::numeric_limits<double>::max_digits10);
1078 
1079  __os << __x.p();
1080 
1081  __os.flags(__flags);
1082  __os.fill(__fill);
1083  __os.precision(__precision);
1084  return __os;
1085  }
1086 
1087  template<typename _IntType,
1088  typename _CharT, typename _Traits>
1089  std::basic_istream<_CharT, _Traits>&
1090  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1091  geometric_distribution<_IntType>& __x)
1092  {
1093  using param_type = typename geometric_distribution<_IntType>::param_type;
1094  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1095 
1096  const typename __ios_base::fmtflags __flags = __is.flags();
1097  __is.flags(__ios_base::skipws);
1098 
1099  double __p;
1100  if (__is >> __p)
1101  __x.param(param_type(__p));
1102 
1103  __is.flags(__flags);
1104  return __is;
1105  }
1106 
1107  // This is Leger's algorithm, also in Devroye, Ch. X, Example 1.5.
1108  template<typename _IntType>
1109  template<typename _UniformRandomNumberGenerator>
1110  typename negative_binomial_distribution<_IntType>::result_type
1111  negative_binomial_distribution<_IntType>::
1112  operator()(_UniformRandomNumberGenerator& __urng)
1113  {
1114  const double __y = _M_gd(__urng);
1115 
1116  // XXX Is the constructor too slow?
1117  std::poisson_distribution<result_type> __poisson(__y);
1118  return __poisson(__urng);
1119  }
1120 
1121  template<typename _IntType>
1122  template<typename _UniformRandomNumberGenerator>
1123  typename negative_binomial_distribution<_IntType>::result_type
1124  negative_binomial_distribution<_IntType>::
1125  operator()(_UniformRandomNumberGenerator& __urng,
1126  const param_type& __p)
1127  {
1128  typedef typename std::gamma_distribution<double>::param_type
1129  param_type;
1130 
1131  const double __y =
1132  _M_gd(__urng, param_type(__p.k(), (1.0 - __p.p()) / __p.p()));
1133 
1134  std::poisson_distribution<result_type> __poisson(__y);
1135  return __poisson(__urng);
1136  }
1137 
1138  template<typename _IntType>
1139  template<typename _ForwardIterator,
1140  typename _UniformRandomNumberGenerator>
1141  void
1142  negative_binomial_distribution<_IntType>::
1143  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1144  _UniformRandomNumberGenerator& __urng)
1145  {
1146  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1147  while (__f != __t)
1148  {
1149  const double __y = _M_gd(__urng);
1150 
1151  // XXX Is the constructor too slow?
1152  std::poisson_distribution<result_type> __poisson(__y);
1153  *__f++ = __poisson(__urng);
1154  }
1155  }
1156 
1157  template<typename _IntType>
1158  template<typename _ForwardIterator,
1159  typename _UniformRandomNumberGenerator>
1160  void
1161  negative_binomial_distribution<_IntType>::
1162  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1163  _UniformRandomNumberGenerator& __urng,
1164  const param_type& __p)
1165  {
1166  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1167  typename std::gamma_distribution<result_type>::param_type
1168  __p2(__p.k(), (1.0 - __p.p()) / __p.p());
1169 
1170  while (__f != __t)
1171  {
1172  const double __y = _M_gd(__urng, __p2);
1173 
1174  std::poisson_distribution<result_type> __poisson(__y);
1175  *__f++ = __poisson(__urng);
1176  }
1177  }
1178 
1179  template<typename _IntType, typename _CharT, typename _Traits>
1180  std::basic_ostream<_CharT, _Traits>&
1181  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1182  const negative_binomial_distribution<_IntType>& __x)
1183  {
1184  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1185 
1186  const typename __ios_base::fmtflags __flags = __os.flags();
1187  const _CharT __fill = __os.fill();
1188  const std::streamsize __precision = __os.precision();
1189  const _CharT __space = __os.widen(' ');
1190  __os.flags(__ios_base::scientific | __ios_base::left);
1191  __os.fill(__os.widen(' '));
1192  __os.precision(std::numeric_limits<double>::max_digits10);
1193 
1194  __os << __x.k() << __space << __x.p()
1195  << __space << __x._M_gd;
1196 
1197  __os.flags(__flags);
1198  __os.fill(__fill);
1199  __os.precision(__precision);
1200  return __os;
1201  }
1202 
1203  template<typename _IntType, typename _CharT, typename _Traits>
1204  std::basic_istream<_CharT, _Traits>&
1205  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1206  negative_binomial_distribution<_IntType>& __x)
1207  {
1208  using param_type
1209  = typename negative_binomial_distribution<_IntType>::param_type;
1210  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1211 
1212  const typename __ios_base::fmtflags __flags = __is.flags();
1213  __is.flags(__ios_base::skipws);
1214 
1215  _IntType __k;
1216  double __p;
1217  if (__is >> __k >> __p >> __x._M_gd)
1218  __x.param(param_type(__k, __p));
1219 
1220  __is.flags(__flags);
1221  return __is;
1222  }
1223 
1224 
1225  template<typename _IntType>
1226  void
1227  poisson_distribution<_IntType>::param_type::
1228  _M_initialize()
1229  {
1230 #if _GLIBCXX_USE_C99_MATH_TR1
1231  if (_M_mean >= 12)
1232  {
1233  const double __m = std::floor(_M_mean);
1234  _M_lm_thr = std::log(_M_mean);
1235  _M_lfm = std::lgamma(__m + 1);
1236  _M_sm = std::sqrt(__m);
1237 
1238  const double __pi_4 = 0.7853981633974483096156608458198757L;
1239  const double __dx = std::sqrt(2 * __m * std::log(32 * __m
1240  / __pi_4));
1241  _M_d = std::round(std::max<double>(6.0, std::min(__m, __dx)));
1242  const double __cx = 2 * __m + _M_d;
1243  _M_scx = std::sqrt(__cx / 2);
1244  _M_1cx = 1 / __cx;
1245 
1246  _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
1247  _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2))
1248  / _M_d;
1249  }
1250  else
1251 #endif
1252  _M_lm_thr = std::exp(-_M_mean);
1253  }
1254 
1255  /**
1256  * A rejection algorithm when mean >= 12 and a simple method based
1257  * upon the multiplication of uniform random variates otherwise.
1258  * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1259  * is defined.
1260  *
1261  * Reference:
1262  * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1263  * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
1264  */
1265  template<typename _IntType>
1266  template<typename _UniformRandomNumberGenerator>
1267  typename poisson_distribution<_IntType>::result_type
1268  poisson_distribution<_IntType>::
1269  operator()(_UniformRandomNumberGenerator& __urng,
1270  const param_type& __param)
1271  {
1272  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1273  __aurng(__urng);
1274 #if _GLIBCXX_USE_C99_MATH_TR1
1275  if (__param.mean() >= 12)
1276  {
1277  double __x;
1278 
1279  // See comments above...
1280  const double __naf =
1281  (1 - std::numeric_limits<double>::epsilon()) / 2;
1282  const double __thr =
1283  std::numeric_limits<_IntType>::max() + __naf;
1284 
1285  const double __m = std::floor(__param.mean());
1286  // sqrt(pi / 2)
1287  const double __spi_2 = 1.2533141373155002512078826424055226L;
1288  const double __c1 = __param._M_sm * __spi_2;
1289  const double __c2 = __param._M_c2b + __c1;
1290  const double __c3 = __c2 + 1;
1291  const double __c4 = __c3 + 1;
1292  // 1 / 78
1293  const double __178 = 0.0128205128205128205128205128205128L;
1294  // e^(1 / 78)
1295  const double __e178 = 1.0129030479320018583185514777512983L;
1296  const double __c5 = __c4 + __e178;
1297  const double __c = __param._M_cb + __c5;
1298  const double __2cx = 2 * (2 * __m + __param._M_d);
1299 
1300  bool __reject = true;
1301  do
1302  {
1303  const double __u = __c * __aurng();
1304  const double __e = -std::log(1.0 - __aurng());
1305 
1306  double __w = 0.0;
1307 
1308  if (__u <= __c1)
1309  {
1310  const double __n = _M_nd(__urng);
1311  const double __y = -std::abs(__n) * __param._M_sm - 1;
1312  __x = std::floor(__y);
1313  __w = -__n * __n / 2;
1314  if (__x < -__m)
1315  continue;
1316  }
1317  else if (__u <= __c2)
1318  {
1319  const double __n = _M_nd(__urng);
1320  const double __y = 1 + std::abs(__n) * __param._M_scx;
1321  __x = std::ceil(__y);
1322  __w = __y * (2 - __y) * __param._M_1cx;
1323  if (__x > __param._M_d)
1324  continue;
1325  }
1326  else if (__u <= __c3)
1327  // NB: This case not in the book, nor in the Errata,
1328  // but should be ok...
1329  __x = -1;
1330  else if (__u <= __c4)
1331  __x = 0;
1332  else if (__u <= __c5)
1333  {
1334  __x = 1;
1335  // Only in the Errata, see libstdc++/83237.
1336  __w = __178;
1337  }
1338  else
1339  {
1340  const double __v = -std::log(1.0 - __aurng());
1341  const double __y = __param._M_d
1342  + __v * __2cx / __param._M_d;
1343  __x = std::ceil(__y);
1344  __w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
1345  }
1346 
1347  __reject = (__w - __e - __x * __param._M_lm_thr
1348  > __param._M_lfm - std::lgamma(__x + __m + 1));
1349 
1350  __reject |= __x + __m >= __thr;
1351 
1352  } while (__reject);
1353 
1354  return result_type(__x + __m + __naf);
1355  }
1356  else
1357 #endif
1358  {
1359  _IntType __x = 0;
1360  double __prod = 1.0;
1361 
1362  do
1363  {
1364  __prod *= __aurng();
1365  __x += 1;
1366  }
1367  while (__prod > __param._M_lm_thr);
1368 
1369  return __x - 1;
1370  }
1371  }
1372 
1373  template<typename _IntType>
1374  template<typename _ForwardIterator,
1375  typename _UniformRandomNumberGenerator>
1376  void
1377  poisson_distribution<_IntType>::
1378  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1379  _UniformRandomNumberGenerator& __urng,
1380  const param_type& __param)
1381  {
1382  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1383  // We could duplicate everything from operator()...
1384  while (__f != __t)
1385  *__f++ = this->operator()(__urng, __param);
1386  }
1387 
1388  template<typename _IntType,
1389  typename _CharT, typename _Traits>
1390  std::basic_ostream<_CharT, _Traits>&
1391  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1392  const poisson_distribution<_IntType>& __x)
1393  {
1394  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1395 
1396  const typename __ios_base::fmtflags __flags = __os.flags();
1397  const _CharT __fill = __os.fill();
1398  const std::streamsize __precision = __os.precision();
1399  const _CharT __space = __os.widen(' ');
1400  __os.flags(__ios_base::scientific | __ios_base::left);
1401  __os.fill(__space);
1402  __os.precision(std::numeric_limits<double>::max_digits10);
1403 
1404  __os << __x.mean() << __space << __x._M_nd;
1405 
1406  __os.flags(__flags);
1407  __os.fill(__fill);
1408  __os.precision(__precision);
1409  return __os;
1410  }
1411 
1412  template<typename _IntType,
1413  typename _CharT, typename _Traits>
1414  std::basic_istream<_CharT, _Traits>&
1415  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1416  poisson_distribution<_IntType>& __x)
1417  {
1418  using param_type = typename poisson_distribution<_IntType>::param_type;
1419  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1420 
1421  const typename __ios_base::fmtflags __flags = __is.flags();
1422  __is.flags(__ios_base::skipws);
1423 
1424  double __mean;
1425  if (__is >> __mean >> __x._M_nd)
1426  __x.param(param_type(__mean));
1427 
1428  __is.flags(__flags);
1429  return __is;
1430  }
1431 
1432 
1433  template<typename _IntType>
1434  void
1435  binomial_distribution<_IntType>::param_type::
1436  _M_initialize()
1437  {
1438  const double __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
1439 
1440  _M_easy = true;
1441 
1442 #if _GLIBCXX_USE_C99_MATH_TR1
1443  if (_M_t * __p12 >= 8)
1444  {
1445  _M_easy = false;
1446  const double __np = std::floor(_M_t * __p12);
1447  const double __pa = __np / _M_t;
1448  const double __1p = 1 - __pa;
1449 
1450  const double __pi_4 = 0.7853981633974483096156608458198757L;
1451  const double __d1x =
1452  std::sqrt(__np * __1p * std::log(32 * __np
1453  / (81 * __pi_4 * __1p)));
1454  _M_d1 = std::round(std::max<double>(1.0, __d1x));
1455  const double __d2x =
1456  std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
1457  / (__pi_4 * __pa)));
1458  _M_d2 = std::round(std::max<double>(1.0, __d2x));
1459 
1460  // sqrt(pi / 2)
1461  const double __spi_2 = 1.2533141373155002512078826424055226L;
1462  _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
1463  _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p));
1464  _M_c = 2 * _M_d1 / __np;
1465  _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
1466  const double __a12 = _M_a1 + _M_s2 * __spi_2;
1467  const double __s1s = _M_s1 * _M_s1;
1468  _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
1469  * 2 * __s1s / _M_d1
1470  * std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
1471  const double __s2s = _M_s2 * _M_s2;
1472  _M_s = (_M_a123 + 2 * __s2s / _M_d2
1473  * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
1474  _M_lf = (std::lgamma(__np + 1)
1475  + std::lgamma(_M_t - __np + 1));
1476  _M_lp1p = std::log(__pa / __1p);
1477 
1478  _M_q = -std::log(1 - (__p12 - __pa) / __1p);
1479  }
1480  else
1481 #endif
1482  _M_q = -std::log(1 - __p12);
1483  }
1484 
1485  template<typename _IntType>
1486  template<typename _UniformRandomNumberGenerator>
1487  typename binomial_distribution<_IntType>::result_type
1488  binomial_distribution<_IntType>::
1489  _M_waiting(_UniformRandomNumberGenerator& __urng,
1490  _IntType __t, double __q)
1491  {
1492  _IntType __x = 0;
1493  double __sum = 0.0;
1494  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1495  __aurng(__urng);
1496 
1497  do
1498  {
1499  if (__t == __x)
1500  return __x;
1501  const double __e = -std::log(1.0 - __aurng());
1502  __sum += __e / (__t - __x);
1503  __x += 1;
1504  }
1505  while (__sum <= __q);
1506 
1507  return __x - 1;
1508  }
1509 
1510  /**
1511  * A rejection algorithm when t * p >= 8 and a simple waiting time
1512  * method - the second in the referenced book - otherwise.
1513  * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1514  * is defined.
1515  *
1516  * Reference:
1517  * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1518  * New York, 1986, Ch. X, Sect. 4 (+ Errata!).
1519  */
1520  template<typename _IntType>
1521  template<typename _UniformRandomNumberGenerator>
1522  typename binomial_distribution<_IntType>::result_type
1523  binomial_distribution<_IntType>::
1524  operator()(_UniformRandomNumberGenerator& __urng,
1525  const param_type& __param)
1526  {
1527  result_type __ret;
1528  const _IntType __t = __param.t();
1529  const double __p = __param.p();
1530  const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
1531  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1532  __aurng(__urng);
1533 
1534 #if _GLIBCXX_USE_C99_MATH_TR1
1535  if (!__param._M_easy)
1536  {
1537  double __x;
1538 
1539  // See comments above...
1540  const double __naf =
1541  (1 - std::numeric_limits<double>::epsilon()) / 2;
1542  const double __thr =
1543  std::numeric_limits<_IntType>::max() + __naf;
1544 
1545  const double __np = std::floor(__t * __p12);
1546 
1547  // sqrt(pi / 2)
1548  const double __spi_2 = 1.2533141373155002512078826424055226L;
1549  const double __a1 = __param._M_a1;
1550  const double __a12 = __a1 + __param._M_s2 * __spi_2;
1551  const double __a123 = __param._M_a123;
1552  const double __s1s = __param._M_s1 * __param._M_s1;
1553  const double __s2s = __param._M_s2 * __param._M_s2;
1554 
1555  bool __reject;
1556  do
1557  {
1558  const double __u = __param._M_s * __aurng();
1559 
1560  double __v;
1561 
1562  if (__u <= __a1)
1563  {
1564  const double __n = _M_nd(__urng);
1565  const double __y = __param._M_s1 * std::abs(__n);
1566  __reject = __y >= __param._M_d1;
1567  if (!__reject)
1568  {
1569  const double __e = -std::log(1.0 - __aurng());
1570  __x = std::floor(__y);
1571  __v = -__e - __n * __n / 2 + __param._M_c;
1572  }
1573  }
1574  else if (__u <= __a12)
1575  {
1576  const double __n = _M_nd(__urng);
1577  const double __y = __param._M_s2 * std::abs(__n);
1578  __reject = __y >= __param._M_d2;
1579  if (!__reject)
1580  {
1581  const double __e = -std::log(1.0 - __aurng());
1582  __x = std::floor(-__y);
1583  __v = -__e - __n * __n / 2;
1584  }
1585  }
1586  else if (__u <= __a123)
1587  {
1588  const double __e1 = -std::log(1.0 - __aurng());
1589  const double __e2 = -std::log(1.0 - __aurng());
1590 
1591  const double __y = __param._M_d1
1592  + 2 * __s1s * __e1 / __param._M_d1;
1593  __x = std::floor(__y);
1594  __v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
1595  -__y / (2 * __s1s)));
1596  __reject = false;
1597  }
1598  else
1599  {
1600  const double __e1 = -std::log(1.0 - __aurng());
1601  const double __e2 = -std::log(1.0 - __aurng());
1602 
1603  const double __y = __param._M_d2
1604  + 2 * __s2s * __e1 / __param._M_d2;
1605  __x = std::floor(-__y);
1606  __v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
1607  __reject = false;
1608  }
1609 
1610  __reject = __reject || __x < -__np || __x > __t - __np;
1611  if (!__reject)
1612  {
1613  const double __lfx =
1614  std::lgamma(__np + __x + 1)
1615  + std::lgamma(__t - (__np + __x) + 1);
1616  __reject = __v > __param._M_lf - __lfx
1617  + __x * __param._M_lp1p;
1618  }
1619 
1620  __reject |= __x + __np >= __thr;
1621  }
1622  while (__reject);
1623 
1624  __x += __np + __naf;
1625 
1626  const _IntType __z = _M_waiting(__urng, __t - _IntType(__x),
1627  __param._M_q);
1628  __ret = _IntType(__x) + __z;
1629  }
1630  else
1631 #endif
1632  __ret = _M_waiting(__urng, __t, __param._M_q);
1633 
1634  if (__p12 != __p)
1635  __ret = __t - __ret;
1636  return __ret;
1637  }
1638 
1639  template<typename _IntType>
1640  template<typename _ForwardIterator,
1641  typename _UniformRandomNumberGenerator>
1642  void
1643  binomial_distribution<_IntType>::
1644  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1645  _UniformRandomNumberGenerator& __urng,
1646  const param_type& __param)
1647  {
1648  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1649  // We could duplicate everything from operator()...
1650  while (__f != __t)
1651  *__f++ = this->operator()(__urng, __param);
1652  }
1653 
1654  template<typename _IntType,
1655  typename _CharT, typename _Traits>
1656  std::basic_ostream<_CharT, _Traits>&
1657  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1658  const binomial_distribution<_IntType>& __x)
1659  {
1660  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1661 
1662  const typename __ios_base::fmtflags __flags = __os.flags();
1663  const _CharT __fill = __os.fill();
1664  const std::streamsize __precision = __os.precision();
1665  const _CharT __space = __os.widen(' ');
1666  __os.flags(__ios_base::scientific | __ios_base::left);
1667  __os.fill(__space);
1668  __os.precision(std::numeric_limits<double>::max_digits10);
1669 
1670  __os << __x.t() << __space << __x.p()
1671  << __space << __x._M_nd;
1672 
1673  __os.flags(__flags);
1674  __os.fill(__fill);
1675  __os.precision(__precision);
1676  return __os;
1677  }
1678 
1679  template<typename _IntType,
1680  typename _CharT, typename _Traits>
1681  std::basic_istream<_CharT, _Traits>&
1682  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1683  binomial_distribution<_IntType>& __x)
1684  {
1685  using param_type = typename binomial_distribution<_IntType>::param_type;
1686  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1687 
1688  const typename __ios_base::fmtflags __flags = __is.flags();
1689  __is.flags(__ios_base::dec | __ios_base::skipws);
1690 
1691  _IntType __t;
1692  double __p;
1693  if (__is >> __t >> __p >> __x._M_nd)
1694  __x.param(param_type(__t, __p));
1695 
1696  __is.flags(__flags);
1697  return __is;
1698  }
1699 
1700 
1701  template<typename _RealType>
1702  template<typename _ForwardIterator,
1703  typename _UniformRandomNumberGenerator>
1704  void
1705  std::exponential_distribution<_RealType>::
1706  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1707  _UniformRandomNumberGenerator& __urng,
1708  const param_type& __p)
1709  {
1710  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1711  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1712  __aurng(__urng);
1713  while (__f != __t)
1714  *__f++ = -std::log(result_type(1) - __aurng()) / __p.lambda();
1715  }
1716 
1717  template<typename _RealType, typename _CharT, typename _Traits>
1718  std::basic_ostream<_CharT, _Traits>&
1719  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1720  const exponential_distribution<_RealType>& __x)
1721  {
1722  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1723 
1724  const typename __ios_base::fmtflags __flags = __os.flags();
1725  const _CharT __fill = __os.fill();
1726  const std::streamsize __precision = __os.precision();
1727  __os.flags(__ios_base::scientific | __ios_base::left);
1728  __os.fill(__os.widen(' '));
1729  __os.precision(std::numeric_limits<_RealType>::max_digits10);
1730 
1731  __os << __x.lambda();
1732 
1733  __os.flags(__flags);
1734  __os.fill(__fill);
1735  __os.precision(__precision);
1736  return __os;
1737  }
1738 
1739  template<typename _RealType, typename _CharT, typename _Traits>
1740  std::basic_istream<_CharT, _Traits>&
1741  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1742  exponential_distribution<_RealType>& __x)
1743  {
1744  using param_type
1745  = typename exponential_distribution<_RealType>::param_type;
1746  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1747 
1748  const typename __ios_base::fmtflags __flags = __is.flags();
1749  __is.flags(__ios_base::dec | __ios_base::skipws);
1750 
1751  _RealType __lambda;
1752  if (__is >> __lambda)
1753  __x.param(param_type(__lambda));
1754 
1755  __is.flags(__flags);
1756  return __is;
1757  }
1758 
1759 
1760  /**
1761  * Polar method due to Marsaglia.
1762  *
1763  * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1764  * New York, 1986, Ch. V, Sect. 4.4.
1765  */
1766  template<typename _RealType>
1767  template<typename _UniformRandomNumberGenerator>
1768  typename normal_distribution<_RealType>::result_type
1769  normal_distribution<_RealType>::
1770  operator()(_UniformRandomNumberGenerator& __urng,
1771  const param_type& __param)
1772  {
1773  result_type __ret;
1774  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1775  __aurng(__urng);
1776 
1777  if (_M_saved_available)
1778  {
1779  _M_saved_available = false;
1780  __ret = _M_saved;
1781  }
1782  else
1783  {
1784  result_type __x, __y, __r2;
1785  do
1786  {
1787  __x = result_type(2.0) * __aurng() - 1.0;
1788  __y = result_type(2.0) * __aurng() - 1.0;
1789  __r2 = __x * __x + __y * __y;
1790  }
1791  while (__r2 > 1.0 || __r2 == 0.0);
1792 
1793  const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1794  _M_saved = __x * __mult;
1795  _M_saved_available = true;
1796  __ret = __y * __mult;
1797  }
1798 
1799  __ret = __ret * __param.stddev() + __param.mean();
1800  return __ret;
1801  }
1802 
1803  template<typename _RealType>
1804  template<typename _ForwardIterator,
1805  typename _UniformRandomNumberGenerator>
1806  void
1807  normal_distribution<_RealType>::
1808  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1809  _UniformRandomNumberGenerator& __urng,
1810  const param_type& __param)
1811  {
1812  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1813 
1814  if (__f == __t)
1815  return;
1816 
1817  if (_M_saved_available)
1818  {
1819  _M_saved_available = false;
1820  *__f++ = _M_saved * __param.stddev() + __param.mean();
1821 
1822  if (__f == __t)
1823  return;
1824  }
1825 
1826  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1827  __aurng(__urng);
1828 
1829  while (__f + 1 < __t)
1830  {
1831  result_type __x, __y, __r2;
1832  do
1833  {
1834  __x = result_type(2.0) * __aurng() - 1.0;
1835  __y = result_type(2.0) * __aurng() - 1.0;
1836  __r2 = __x * __x + __y * __y;
1837  }
1838  while (__r2 > 1.0 || __r2 == 0.0);
1839 
1840  const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1841  *__f++ = __y * __mult * __param.stddev() + __param.mean();
1842  *__f++ = __x * __mult * __param.stddev() + __param.mean();
1843  }
1844 
1845  if (__f != __t)
1846  {
1847  result_type __x, __y, __r2;
1848  do
1849  {
1850  __x = result_type(2.0) * __aurng() - 1.0;
1851  __y = result_type(2.0) * __aurng() - 1.0;
1852  __r2 = __x * __x + __y * __y;
1853  }
1854  while (__r2 > 1.0 || __r2 == 0.0);
1855 
1856  const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1857  _M_saved = __x * __mult;
1858  _M_saved_available = true;
1859  *__f = __y * __mult * __param.stddev() + __param.mean();
1860  }
1861  }
1862 
1863  template<typename _RealType>
1864  bool
1865  operator==(const std::normal_distribution<_RealType>& __d1,
1866  const std::normal_distribution<_RealType>& __d2)
1867  {
1868  if (__d1._M_param == __d2._M_param
1869  && __d1._M_saved_available == __d2._M_saved_available)
1870  {
1871  if (__d1._M_saved_available
1872  && __d1._M_saved == __d2._M_saved)
1873  return true;
1874  else if(!__d1._M_saved_available)
1875  return true;
1876  else
1877  return false;
1878  }
1879  else
1880  return false;
1881  }
1882 
1883  template<typename _RealType, typename _CharT, typename _Traits>
1884  std::basic_ostream<_CharT, _Traits>&
1885  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1886  const normal_distribution<_RealType>& __x)
1887  {
1888  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1889 
1890  const typename __ios_base::fmtflags __flags = __os.flags();
1891  const _CharT __fill = __os.fill();
1892  const std::streamsize __precision = __os.precision();
1893  const _CharT __space = __os.widen(' ');
1894  __os.flags(__ios_base::scientific | __ios_base::left);
1895  __os.fill(__space);
1896  __os.precision(std::numeric_limits<_RealType>::max_digits10);
1897 
1898  __os << __x.mean() << __space << __x.stddev()
1899  << __space << __x._M_saved_available;
1900  if (__x._M_saved_available)
1901  __os << __space << __x._M_saved;
1902 
1903  __os.flags(__flags);
1904  __os.fill(__fill);
1905  __os.precision(__precision);
1906  return __os;
1907  }
1908 
1909  template<typename _RealType, typename _CharT, typename _Traits>
1910  std::basic_istream<_CharT, _Traits>&
1911  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1912  normal_distribution<_RealType>& __x)
1913  {
1914  using param_type = typename normal_distribution<_RealType>::param_type;
1915  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1916 
1917  const typename __ios_base::fmtflags __flags = __is.flags();
1918  __is.flags(__ios_base::dec | __ios_base::skipws);
1919 
1920  double __mean, __stddev;
1921  bool __saved_avail;
1922  if (__is >> __mean >> __stddev >> __saved_avail)
1923  {
1924  if (!__saved_avail || (__is >> __x._M_saved))
1925  {
1926  __x._M_saved_available = __saved_avail;
1927  __x.param(param_type(__mean, __stddev));
1928  }
1929  }
1930 
1931  __is.flags(__flags);
1932  return __is;
1933  }
1934 
1935 
1936  template<typename _RealType>
1937  template<typename _ForwardIterator,
1938  typename _UniformRandomNumberGenerator>
1939  void
1940  lognormal_distribution<_RealType>::
1941  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1942  _UniformRandomNumberGenerator& __urng,
1943  const param_type& __p)
1944  {
1945  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1946  while (__f != __t)
1947  *__f++ = std::exp(__p.s() * _M_nd(__urng) + __p.m());
1948  }
1949 
1950  template<typename _RealType, typename _CharT, typename _Traits>
1951  std::basic_ostream<_CharT, _Traits>&
1952  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1953  const lognormal_distribution<_RealType>& __x)
1954  {
1955  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
1956 
1957  const typename __ios_base::fmtflags __flags = __os.flags();
1958  const _CharT __fill = __os.fill();
1959  const std::streamsize __precision = __os.precision();
1960  const _CharT __space = __os.widen(' ');
1961  __os.flags(__ios_base::scientific | __ios_base::left);
1962  __os.fill(__space);
1963  __os.precision(std::numeric_limits<_RealType>::max_digits10);
1964 
1965  __os << __x.m() << __space << __x.s()
1966  << __space << __x._M_nd;
1967 
1968  __os.flags(__flags);
1969  __os.fill(__fill);
1970  __os.precision(__precision);
1971  return __os;
1972  }
1973 
1974  template<typename _RealType, typename _CharT, typename _Traits>
1975  std::basic_istream<_CharT, _Traits>&
1976  operator>>(std::basic_istream<_CharT, _Traits>& __is,
1977  lognormal_distribution<_RealType>& __x)
1978  {
1979  using param_type
1980  = typename lognormal_distribution<_RealType>::param_type;
1981  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
1982 
1983  const typename __ios_base::fmtflags __flags = __is.flags();
1984  __is.flags(__ios_base::dec | __ios_base::skipws);
1985 
1986  _RealType __m, __s;
1987  if (__is >> __m >> __s >> __x._M_nd)
1988  __x.param(param_type(__m, __s));
1989 
1990  __is.flags(__flags);
1991  return __is;
1992  }
1993 
1994  template<typename _RealType>
1995  template<typename _ForwardIterator,
1996  typename _UniformRandomNumberGenerator>
1997  void
1998  std::chi_squared_distribution<_RealType>::
1999  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2000  _UniformRandomNumberGenerator& __urng)
2001  {
2002  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2003  while (__f != __t)
2004  *__f++ = 2 * _M_gd(__urng);
2005  }
2006 
2007  template<typename _RealType>
2008  template<typename _ForwardIterator,
2009  typename _UniformRandomNumberGenerator>
2010  void
2011  std::chi_squared_distribution<_RealType>::
2012  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2013  _UniformRandomNumberGenerator& __urng,
2014  const typename
2015  std::gamma_distribution<result_type>::param_type& __p)
2016  {
2017  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2018  while (__f != __t)
2019  *__f++ = 2 * _M_gd(__urng, __p);
2020  }
2021 
2022  template<typename _RealType, typename _CharT, typename _Traits>
2023  std::basic_ostream<_CharT, _Traits>&
2024  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2025  const chi_squared_distribution<_RealType>& __x)
2026  {
2027  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2028 
2029  const typename __ios_base::fmtflags __flags = __os.flags();
2030  const _CharT __fill = __os.fill();
2031  const std::streamsize __precision = __os.precision();
2032  const _CharT __space = __os.widen(' ');
2033  __os.flags(__ios_base::scientific | __ios_base::left);
2034  __os.fill(__space);
2035  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2036 
2037  __os << __x.n() << __space << __x._M_gd;
2038 
2039  __os.flags(__flags);
2040  __os.fill(__fill);
2041  __os.precision(__precision);
2042  return __os;
2043  }
2044 
2045  template<typename _RealType, typename _CharT, typename _Traits>
2046  std::basic_istream<_CharT, _Traits>&
2047  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2048  chi_squared_distribution<_RealType>& __x)
2049  {
2050  using param_type
2051  = typename chi_squared_distribution<_RealType>::param_type;
2052  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2053 
2054  const typename __ios_base::fmtflags __flags = __is.flags();
2055  __is.flags(__ios_base::dec | __ios_base::skipws);
2056 
2057  _RealType __n;
2058  if (__is >> __n >> __x._M_gd)
2059  __x.param(param_type(__n));
2060 
2061  __is.flags(__flags);
2062  return __is;
2063  }
2064 
2065 
2066  template<typename _RealType>
2067  template<typename _UniformRandomNumberGenerator>
2068  typename cauchy_distribution<_RealType>::result_type
2069  cauchy_distribution<_RealType>::
2070  operator()(_UniformRandomNumberGenerator& __urng,
2071  const param_type& __p)
2072  {
2073  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2074  __aurng(__urng);
2075  _RealType __u;
2076  do
2077  __u = __aurng();
2078  while (__u == 0.5);
2079 
2080  const _RealType __pi = 3.1415926535897932384626433832795029L;
2081  return __p.a() + __p.b() * std::tan(__pi * __u);
2082  }
2083 
2084  template<typename _RealType>
2085  template<typename _ForwardIterator,
2086  typename _UniformRandomNumberGenerator>
2087  void
2088  cauchy_distribution<_RealType>::
2089  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2090  _UniformRandomNumberGenerator& __urng,
2091  const param_type& __p)
2092  {
2093  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2094  const _RealType __pi = 3.1415926535897932384626433832795029L;
2095  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2096  __aurng(__urng);
2097  while (__f != __t)
2098  {
2099  _RealType __u;
2100  do
2101  __u = __aurng();
2102  while (__u == 0.5);
2103 
2104  *__f++ = __p.a() + __p.b() * std::tan(__pi * __u);
2105  }
2106  }
2107 
2108  template<typename _RealType, typename _CharT, typename _Traits>
2109  std::basic_ostream<_CharT, _Traits>&
2110  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2111  const cauchy_distribution<_RealType>& __x)
2112  {
2113  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2114 
2115  const typename __ios_base::fmtflags __flags = __os.flags();
2116  const _CharT __fill = __os.fill();
2117  const std::streamsize __precision = __os.precision();
2118  const _CharT __space = __os.widen(' ');
2119  __os.flags(__ios_base::scientific | __ios_base::left);
2120  __os.fill(__space);
2121  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2122 
2123  __os << __x.a() << __space << __x.b();
2124 
2125  __os.flags(__flags);
2126  __os.fill(__fill);
2127  __os.precision(__precision);
2128  return __os;
2129  }
2130 
2131  template<typename _RealType, typename _CharT, typename _Traits>
2132  std::basic_istream<_CharT, _Traits>&
2133  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2134  cauchy_distribution<_RealType>& __x)
2135  {
2136  using param_type = typename cauchy_distribution<_RealType>::param_type;
2137  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2138 
2139  const typename __ios_base::fmtflags __flags = __is.flags();
2140  __is.flags(__ios_base::dec | __ios_base::skipws);
2141 
2142  _RealType __a, __b;
2143  if (__is >> __a >> __b)
2144  __x.param(param_type(__a, __b));
2145 
2146  __is.flags(__flags);
2147  return __is;
2148  }
2149 
2150 
2151  template<typename _RealType>
2152  template<typename _ForwardIterator,
2153  typename _UniformRandomNumberGenerator>
2154  void
2155  std::fisher_f_distribution<_RealType>::
2156  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2157  _UniformRandomNumberGenerator& __urng)
2158  {
2159  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2160  while (__f != __t)
2161  *__f++ = ((_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()));
2162  }
2163 
2164  template<typename _RealType>
2165  template<typename _ForwardIterator,
2166  typename _UniformRandomNumberGenerator>
2167  void
2168  std::fisher_f_distribution<_RealType>::
2169  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2170  _UniformRandomNumberGenerator& __urng,
2171  const param_type& __p)
2172  {
2173  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2174  typedef typename std::gamma_distribution<result_type>::param_type
2175  param_type;
2176  param_type __p1(__p.m() / 2);
2177  param_type __p2(__p.n() / 2);
2178  while (__f != __t)
2179  *__f++ = ((_M_gd_x(__urng, __p1) * n())
2180  / (_M_gd_y(__urng, __p2) * m()));
2181  }
2182 
2183  template<typename _RealType, typename _CharT, typename _Traits>
2184  std::basic_ostream<_CharT, _Traits>&
2185  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2186  const fisher_f_distribution<_RealType>& __x)
2187  {
2188  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2189 
2190  const typename __ios_base::fmtflags __flags = __os.flags();
2191  const _CharT __fill = __os.fill();
2192  const std::streamsize __precision = __os.precision();
2193  const _CharT __space = __os.widen(' ');
2194  __os.flags(__ios_base::scientific | __ios_base::left);
2195  __os.fill(__space);
2196  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2197 
2198  __os << __x.m() << __space << __x.n()
2199  << __space << __x._M_gd_x << __space << __x._M_gd_y;
2200 
2201  __os.flags(__flags);
2202  __os.fill(__fill);
2203  __os.precision(__precision);
2204  return __os;
2205  }
2206 
2207  template<typename _RealType, typename _CharT, typename _Traits>
2208  std::basic_istream<_CharT, _Traits>&
2209  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2210  fisher_f_distribution<_RealType>& __x)
2211  {
2212  using param_type
2213  = typename fisher_f_distribution<_RealType>::param_type;
2214  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2215 
2216  const typename __ios_base::fmtflags __flags = __is.flags();
2217  __is.flags(__ios_base::dec | __ios_base::skipws);
2218 
2219  _RealType __m, __n;
2220  if (__is >> __m >> __n >> __x._M_gd_x >> __x._M_gd_y)
2221  __x.param(param_type(__m, __n));
2222 
2223  __is.flags(__flags);
2224  return __is;
2225  }
2226 
2227 
2228  template<typename _RealType>
2229  template<typename _ForwardIterator,
2230  typename _UniformRandomNumberGenerator>
2231  void
2232  std::student_t_distribution<_RealType>::
2233  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2234  _UniformRandomNumberGenerator& __urng)
2235  {
2236  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2237  while (__f != __t)
2238  *__f++ = _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng));
2239  }
2240 
2241  template<typename _RealType>
2242  template<typename _ForwardIterator,
2243  typename _UniformRandomNumberGenerator>
2244  void
2245  std::student_t_distribution<_RealType>::
2246  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2247  _UniformRandomNumberGenerator& __urng,
2248  const param_type& __p)
2249  {
2250  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2251  typename std::gamma_distribution<result_type>::param_type
2252  __p2(__p.n() / 2, 2);
2253  while (__f != __t)
2254  *__f++ = _M_nd(__urng) * std::sqrt(__p.n() / _M_gd(__urng, __p2));
2255  }
2256 
2257  template<typename _RealType, typename _CharT, typename _Traits>
2258  std::basic_ostream<_CharT, _Traits>&
2259  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2260  const student_t_distribution<_RealType>& __x)
2261  {
2262  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2263 
2264  const typename __ios_base::fmtflags __flags = __os.flags();
2265  const _CharT __fill = __os.fill();
2266  const std::streamsize __precision = __os.precision();
2267  const _CharT __space = __os.widen(' ');
2268  __os.flags(__ios_base::scientific | __ios_base::left);
2269  __os.fill(__space);
2270  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2271 
2272  __os << __x.n() << __space << __x._M_nd << __space << __x._M_gd;
2273 
2274  __os.flags(__flags);
2275  __os.fill(__fill);
2276  __os.precision(__precision);
2277  return __os;
2278  }
2279 
2280  template<typename _RealType, typename _CharT, typename _Traits>
2281  std::basic_istream<_CharT, _Traits>&
2282  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2283  student_t_distribution<_RealType>& __x)
2284  {
2285  using param_type
2286  = typename student_t_distribution<_RealType>::param_type;
2287  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2288 
2289  const typename __ios_base::fmtflags __flags = __is.flags();
2290  __is.flags(__ios_base::dec | __ios_base::skipws);
2291 
2292  _RealType __n;
2293  if (__is >> __n >> __x._M_nd >> __x._M_gd)
2294  __x.param(param_type(__n));
2295 
2296  __is.flags(__flags);
2297  return __is;
2298  }
2299 
2300 
2301  template<typename _RealType>
2302  void
2303  gamma_distribution<_RealType>::param_type::
2304  _M_initialize()
2305  {
2306  _M_malpha = _M_alpha < 1.0 ? _M_alpha + _RealType(1.0) : _M_alpha;
2307 
2308  const _RealType __a1 = _M_malpha - _RealType(1.0) / _RealType(3.0);
2309  _M_a2 = _RealType(1.0) / std::sqrt(_RealType(9.0) * __a1);
2310  }
2311 
2312  /**
2313  * Marsaglia, G. and Tsang, W. W.
2314  * "A Simple Method for Generating Gamma Variables"
2315  * ACM Transactions on Mathematical Software, 26, 3, 363-372, 2000.
2316  */
2317  template<typename _RealType>
2318  template<typename _UniformRandomNumberGenerator>
2319  typename gamma_distribution<_RealType>::result_type
2320  gamma_distribution<_RealType>::
2321  operator()(_UniformRandomNumberGenerator& __urng,
2322  const param_type& __param)
2323  {
2324  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2325  __aurng(__urng);
2326 
2327  result_type __u, __v, __n;
2328  const result_type __a1 = (__param._M_malpha
2329  - _RealType(1.0) / _RealType(3.0));
2330 
2331  do
2332  {
2333  do
2334  {
2335  __n = _M_nd(__urng);
2336  __v = result_type(1.0) + __param._M_a2 * __n;
2337  }
2338  while (__v <= 0.0);
2339 
2340  __v = __v * __v * __v;
2341  __u = __aurng();
2342  }
2343  while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2344  && (std::log(__u) > (0.5 * __n * __n + __a1
2345  * (1.0 - __v + std::log(__v)))));
2346 
2347  if (__param.alpha() == __param._M_malpha)
2348  return __a1 * __v * __param.beta();
2349  else
2350  {
2351  do
2352  __u = __aurng();
2353  while (__u == 0.0);
2354 
2355  return (std::pow(__u, result_type(1.0) / __param.alpha())
2356  * __a1 * __v * __param.beta());
2357  }
2358  }
2359 
2360  template<typename _RealType>
2361  template<typename _ForwardIterator,
2362  typename _UniformRandomNumberGenerator>
2363  void
2364  gamma_distribution<_RealType>::
2365  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2366  _UniformRandomNumberGenerator& __urng,
2367  const param_type& __param)
2368  {
2369  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2370  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2371  __aurng(__urng);
2372 
2373  result_type __u, __v, __n;
2374  const result_type __a1 = (__param._M_malpha
2375  - _RealType(1.0) / _RealType(3.0));
2376 
2377  if (__param.alpha() == __param._M_malpha)
2378  while (__f != __t)
2379  {
2380  do
2381  {
2382  do
2383  {
2384  __n = _M_nd(__urng);
2385  __v = result_type(1.0) + __param._M_a2 * __n;
2386  }
2387  while (__v <= 0.0);
2388 
2389  __v = __v * __v * __v;
2390  __u = __aurng();
2391  }
2392  while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2393  && (std::log(__u) > (0.5 * __n * __n + __a1
2394  * (1.0 - __v + std::log(__v)))));
2395 
2396  *__f++ = __a1 * __v * __param.beta();
2397  }
2398  else
2399  while (__f != __t)
2400  {
2401  do
2402  {
2403  do
2404  {
2405  __n = _M_nd(__urng);
2406  __v = result_type(1.0) + __param._M_a2 * __n;
2407  }
2408  while (__v <= 0.0);
2409 
2410  __v = __v * __v * __v;
2411  __u = __aurng();
2412  }
2413  while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2414  && (std::log(__u) > (0.5 * __n * __n + __a1
2415  * (1.0 - __v + std::log(__v)))));
2416 
2417  do
2418  __u = __aurng();
2419  while (__u == 0.0);
2420 
2421  *__f++ = (std::pow(__u, result_type(1.0) / __param.alpha())
2422  * __a1 * __v * __param.beta());
2423  }
2424  }
2425 
2426  template<typename _RealType, typename _CharT, typename _Traits>
2427  std::basic_ostream<_CharT, _Traits>&
2428  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2429  const gamma_distribution<_RealType>& __x)
2430  {
2431  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2432 
2433  const typename __ios_base::fmtflags __flags = __os.flags();
2434  const _CharT __fill = __os.fill();
2435  const std::streamsize __precision = __os.precision();
2436  const _CharT __space = __os.widen(' ');
2437  __os.flags(__ios_base::scientific | __ios_base::left);
2438  __os.fill(__space);
2439  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2440 
2441  __os << __x.alpha() << __space << __x.beta()
2442  << __space << __x._M_nd;
2443 
2444  __os.flags(__flags);
2445  __os.fill(__fill);
2446  __os.precision(__precision);
2447  return __os;
2448  }
2449 
2450  template<typename _RealType, typename _CharT, typename _Traits>
2451  std::basic_istream<_CharT, _Traits>&
2452  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2453  gamma_distribution<_RealType>& __x)
2454  {
2455  using param_type = typename gamma_distribution<_RealType>::param_type;
2456  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2457 
2458  const typename __ios_base::fmtflags __flags = __is.flags();
2459  __is.flags(__ios_base::dec | __ios_base::skipws);
2460 
2461  _RealType __alpha_val, __beta_val;
2462  if (__is >> __alpha_val >> __beta_val >> __x._M_nd)
2463  __x.param(param_type(__alpha_val, __beta_val));
2464 
2465  __is.flags(__flags);
2466  return __is;
2467  }
2468 
2469 
2470  template<typename _RealType>
2471  template<typename _UniformRandomNumberGenerator>
2472  typename weibull_distribution<_RealType>::result_type
2473  weibull_distribution<_RealType>::
2474  operator()(_UniformRandomNumberGenerator& __urng,
2475  const param_type& __p)
2476  {
2477  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2478  __aurng(__urng);
2479  return __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2480  result_type(1) / __p.a());
2481  }
2482 
2483  template<typename _RealType>
2484  template<typename _ForwardIterator,
2485  typename _UniformRandomNumberGenerator>
2486  void
2487  weibull_distribution<_RealType>::
2488  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2489  _UniformRandomNumberGenerator& __urng,
2490  const param_type& __p)
2491  {
2492  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2493  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2494  __aurng(__urng);
2495  auto __inv_a = result_type(1) / __p.a();
2496 
2497  while (__f != __t)
2498  *__f++ = __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2499  __inv_a);
2500  }
2501 
2502  template<typename _RealType, typename _CharT, typename _Traits>
2503  std::basic_ostream<_CharT, _Traits>&
2504  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2505  const weibull_distribution<_RealType>& __x)
2506  {
2507  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2508 
2509  const typename __ios_base::fmtflags __flags = __os.flags();
2510  const _CharT __fill = __os.fill();
2511  const std::streamsize __precision = __os.precision();
2512  const _CharT __space = __os.widen(' ');
2513  __os.flags(__ios_base::scientific | __ios_base::left);
2514  __os.fill(__space);
2515  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2516 
2517  __os << __x.a() << __space << __x.b();
2518 
2519  __os.flags(__flags);
2520  __os.fill(__fill);
2521  __os.precision(__precision);
2522  return __os;
2523  }
2524 
2525  template<typename _RealType, typename _CharT, typename _Traits>
2526  std::basic_istream<_CharT, _Traits>&
2527  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2528  weibull_distribution<_RealType>& __x)
2529  {
2530  using param_type = typename weibull_distribution<_RealType>::param_type;
2531  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2532 
2533  const typename __ios_base::fmtflags __flags = __is.flags();
2534  __is.flags(__ios_base::dec | __ios_base::skipws);
2535 
2536  _RealType __a, __b;
2537  if (__is >> __a >> __b)
2538  __x.param(param_type(__a, __b));
2539 
2540  __is.flags(__flags);
2541  return __is;
2542  }
2543 
2544 
2545  template<typename _RealType>
2546  template<typename _UniformRandomNumberGenerator>
2547  typename extreme_value_distribution<_RealType>::result_type
2548  extreme_value_distribution<_RealType>::
2549  operator()(_UniformRandomNumberGenerator& __urng,
2550  const param_type& __p)
2551  {
2552  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2553  __aurng(__urng);
2554  return __p.a() - __p.b() * std::log(-std::log(result_type(1)
2555  - __aurng()));
2556  }
2557 
2558  template<typename _RealType>
2559  template<typename _ForwardIterator,
2560  typename _UniformRandomNumberGenerator>
2561  void
2562  extreme_value_distribution<_RealType>::
2563  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2564  _UniformRandomNumberGenerator& __urng,
2565  const param_type& __p)
2566  {
2567  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2568  __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2569  __aurng(__urng);
2570 
2571  while (__f != __t)
2572  *__f++ = __p.a() - __p.b() * std::log(-std::log(result_type(1)
2573  - __aurng()));
2574  }
2575 
2576  template<typename _RealType, typename _CharT, typename _Traits>
2577  std::basic_ostream<_CharT, _Traits>&
2578  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2579  const extreme_value_distribution<_RealType>& __x)
2580  {
2581  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2582 
2583  const typename __ios_base::fmtflags __flags = __os.flags();
2584  const _CharT __fill = __os.fill();
2585  const std::streamsize __precision = __os.precision();
2586  const _CharT __space = __os.widen(' ');
2587  __os.flags(__ios_base::scientific | __ios_base::left);
2588  __os.fill(__space);
2589  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2590 
2591  __os << __x.a() << __space << __x.b();
2592 
2593  __os.flags(__flags);
2594  __os.fill(__fill);
2595  __os.precision(__precision);
2596  return __os;
2597  }
2598 
2599  template<typename _RealType, typename _CharT, typename _Traits>
2600  std::basic_istream<_CharT, _Traits>&
2601  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2602  extreme_value_distribution<_RealType>& __x)
2603  {
2604  using param_type
2605  = typename extreme_value_distribution<_RealType>::param_type;
2606  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2607 
2608  const typename __ios_base::fmtflags __flags = __is.flags();
2609  __is.flags(__ios_base::dec | __ios_base::skipws);
2610 
2611  _RealType __a, __b;
2612  if (__is >> __a >> __b)
2613  __x.param(param_type(__a, __b));
2614 
2615  __is.flags(__flags);
2616  return __is;
2617  }
2618 
2619 
2620  template<typename _IntType>
2621  void
2622  discrete_distribution<_IntType>::param_type::
2623  _M_initialize()
2624  {
2625  if (_M_prob.size() < 2)
2626  {
2627  _M_prob.clear();
2628  return;
2629  }
2630 
2631  const double __sum = std::accumulate(_M_prob.begin(),
2632  _M_prob.end(), 0.0);
2633  __glibcxx_assert(__sum > 0);
2634  // Now normalize the probabilites.
2635  __detail::__normalize(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
2636  __sum);
2637  // Accumulate partial sums.
2638  _M_cp.reserve(_M_prob.size());
2639  std::partial_sum(_M_prob.begin(), _M_prob.end(),
2640  std::back_inserter(_M_cp));
2641  // Make sure the last cumulative probability is one.
2642  _M_cp[_M_cp.size() - 1] = 1.0;
2643  }
2644 
2645  template<typename _IntType>
2646  template<typename _Func>
2647  discrete_distribution<_IntType>::param_type::
2648  param_type(size_t __nw, double __xmin, double __xmax, _Func __fw)
2649  : _M_prob(), _M_cp()
2650  {
2651  const size_t __n = __nw == 0 ? 1 : __nw;
2652  const double __delta = (__xmax - __xmin) / __n;
2653 
2654  _M_prob.reserve(__n);
2655  for (size_t __k = 0; __k < __nw; ++__k)
2656  _M_prob.push_back(__fw(__xmin + __k * __delta + 0.5 * __delta));
2657 
2658  _M_initialize();
2659  }
2660 
2661  template<typename _IntType>
2662  template<typename _UniformRandomNumberGenerator>
2663  typename discrete_distribution<_IntType>::result_type
2664  discrete_distribution<_IntType>::
2665  operator()(_UniformRandomNumberGenerator& __urng,
2666  const param_type& __param)
2667  {
2668  if (__param._M_cp.empty())
2669  return result_type(0);
2670 
2671  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2672  __aurng(__urng);
2673 
2674  const double __p = __aurng();
2675  auto __pos = std::lower_bound(__param._M_cp.begin(),
2676  __param._M_cp.end(), __p);
2677 
2678  return __pos - __param._M_cp.begin();
2679  }
2680 
2681  template<typename _IntType>
2682  template<typename _ForwardIterator,
2683  typename _UniformRandomNumberGenerator>
2684  void
2685  discrete_distribution<_IntType>::
2686  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2687  _UniformRandomNumberGenerator& __urng,
2688  const param_type& __param)
2689  {
2690  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2691 
2692  if (__param._M_cp.empty())
2693  {
2694  while (__f != __t)
2695  *__f++ = result_type(0);
2696  return;
2697  }
2698 
2699  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2700  __aurng(__urng);
2701 
2702  while (__f != __t)
2703  {
2704  const double __p = __aurng();
2705  auto __pos = std::lower_bound(__param._M_cp.begin(),
2706  __param._M_cp.end(), __p);
2707 
2708  *__f++ = __pos - __param._M_cp.begin();
2709  }
2710  }
2711 
2712  template<typename _IntType, typename _CharT, typename _Traits>
2713  std::basic_ostream<_CharT, _Traits>&
2714  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2715  const discrete_distribution<_IntType>& __x)
2716  {
2717  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2718 
2719  const typename __ios_base::fmtflags __flags = __os.flags();
2720  const _CharT __fill = __os.fill();
2721  const std::streamsize __precision = __os.precision();
2722  const _CharT __space = __os.widen(' ');
2723  __os.flags(__ios_base::scientific | __ios_base::left);
2724  __os.fill(__space);
2725  __os.precision(std::numeric_limits<double>::max_digits10);
2726 
2727  std::vector<double> __prob = __x.probabilities();
2728  __os << __prob.size();
2729  for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
2730  __os << __space << *__dit;
2731 
2732  __os.flags(__flags);
2733  __os.fill(__fill);
2734  __os.precision(__precision);
2735  return __os;
2736  }
2737 
2738 namespace __detail
2739 {
2740  template<typename _ValT, typename _CharT, typename _Traits>
2741  basic_istream<_CharT, _Traits>&
2742  __extract_params(basic_istream<_CharT, _Traits>& __is,
2743  vector<_ValT>& __vals, size_t __n)
2744  {
2745  __vals.reserve(__n);
2746  while (__n--)
2747  {
2748  _ValT __val;
2749  if (__is >> __val)
2750  __vals.push_back(__val);
2751  else
2752  break;
2753  }
2754  return __is;
2755  }
2756 } // namespace __detail
2757 
2758  template<typename _IntType, typename _CharT, typename _Traits>
2759  std::basic_istream<_CharT, _Traits>&
2760  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2761  discrete_distribution<_IntType>& __x)
2762  {
2763  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2764 
2765  const typename __ios_base::fmtflags __flags = __is.flags();
2766  __is.flags(__ios_base::dec | __ios_base::skipws);
2767 
2768  size_t __n;
2769  if (__is >> __n)
2770  {
2771  std::vector<double> __prob_vec;
2772  if (__detail::__extract_params(__is, __prob_vec, __n))
2773  __x.param({__prob_vec.begin(), __prob_vec.end()});
2774  }
2775 
2776  __is.flags(__flags);
2777  return __is;
2778  }
2779 
2780 
2781  template<typename _RealType>
2782  void
2783  piecewise_constant_distribution<_RealType>::param_type::
2784  _M_initialize()
2785  {
2786  if (_M_int.size() < 2
2787  || (_M_int.size() == 2
2788  && _M_int[0] == _RealType(0)
2789  && _M_int[1] == _RealType(1)))
2790  {
2791  _M_int.clear();
2792  _M_den.clear();
2793  return;
2794  }
2795 
2796  const double __sum = std::accumulate(_M_den.begin(),
2797  _M_den.end(), 0.0);
2798  __glibcxx_assert(__sum > 0);
2799 
2800  __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
2801  __sum);
2802 
2803  _M_cp.reserve(_M_den.size());
2804  std::partial_sum(_M_den.begin(), _M_den.end(),
2805  std::back_inserter(_M_cp));
2806 
2807  // Make sure the last cumulative probability is one.
2808  _M_cp[_M_cp.size() - 1] = 1.0;
2809 
2810  for (size_t __k = 0; __k < _M_den.size(); ++__k)
2811  _M_den[__k] /= _M_int[__k + 1] - _M_int[__k];
2812  }
2813 
2814  template<typename _RealType>
2815  template<typename _InputIteratorB, typename _InputIteratorW>
2816  piecewise_constant_distribution<_RealType>::param_type::
2817  param_type(_InputIteratorB __bbegin,
2818  _InputIteratorB __bend,
2819  _InputIteratorW __wbegin)
2820  : _M_int(), _M_den(), _M_cp()
2821  {
2822  if (__bbegin != __bend)
2823  {
2824  for (;;)
2825  {
2826  _M_int.push_back(*__bbegin);
2827  ++__bbegin;
2828  if (__bbegin == __bend)
2829  break;
2830 
2831  _M_den.push_back(*__wbegin);
2832  ++__wbegin;
2833  }
2834  }
2835 
2836  _M_initialize();
2837  }
2838 
2839  template<typename _RealType>
2840  template<typename _Func>
2841  piecewise_constant_distribution<_RealType>::param_type::
2842  param_type(initializer_list<_RealType> __bl, _Func __fw)
2843  : _M_int(), _M_den(), _M_cp()
2844  {
2845  _M_int.reserve(__bl.size());
2846  for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
2847  _M_int.push_back(*__biter);
2848 
2849  _M_den.reserve(_M_int.size() - 1);
2850  for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
2851  _M_den.push_back(__fw(0.5 * (_M_int[__k + 1] + _M_int[__k])));
2852 
2853  _M_initialize();
2854  }
2855 
2856  template<typename _RealType>
2857  template<typename _Func>
2858  piecewise_constant_distribution<_RealType>::param_type::
2859  param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
2860  : _M_int(), _M_den(), _M_cp()
2861  {
2862  const size_t __n = __nw == 0 ? 1 : __nw;
2863  const _RealType __delta = (__xmax - __xmin) / __n;
2864 
2865  _M_int.reserve(__n + 1);
2866  for (size_t __k = 0; __k <= __nw; ++__k)
2867  _M_int.push_back(__xmin + __k * __delta);
2868 
2869  _M_den.reserve(__n);
2870  for (size_t __k = 0; __k < __nw; ++__k)
2871  _M_den.push_back(__fw(_M_int[__k] + 0.5 * __delta));
2872 
2873  _M_initialize();
2874  }
2875 
2876  template<typename _RealType>
2877  template<typename _UniformRandomNumberGenerator>
2878  typename piecewise_constant_distribution<_RealType>::result_type
2879  piecewise_constant_distribution<_RealType>::
2880  operator()(_UniformRandomNumberGenerator& __urng,
2881  const param_type& __param)
2882  {
2883  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2884  __aurng(__urng);
2885 
2886  const double __p = __aurng();
2887  if (__param._M_cp.empty())
2888  return __p;
2889 
2890  auto __pos = std::lower_bound(__param._M_cp.begin(),
2891  __param._M_cp.end(), __p);
2892  const size_t __i = __pos - __param._M_cp.begin();
2893 
2894  const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2895 
2896  return __param._M_int[__i] + (__p - __pref) / __param._M_den[__i];
2897  }
2898 
2899  template<typename _RealType>
2900  template<typename _ForwardIterator,
2901  typename _UniformRandomNumberGenerator>
2902  void
2903  piecewise_constant_distribution<_RealType>::
2904  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2905  _UniformRandomNumberGenerator& __urng,
2906  const param_type& __param)
2907  {
2908  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2909  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2910  __aurng(__urng);
2911 
2912  if (__param._M_cp.empty())
2913  {
2914  while (__f != __t)
2915  *__f++ = __aurng();
2916  return;
2917  }
2918 
2919  while (__f != __t)
2920  {
2921  const double __p = __aurng();
2922 
2923  auto __pos = std::lower_bound(__param._M_cp.begin(),
2924  __param._M_cp.end(), __p);
2925  const size_t __i = __pos - __param._M_cp.begin();
2926 
2927  const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2928 
2929  *__f++ = (__param._M_int[__i]
2930  + (__p - __pref) / __param._M_den[__i]);
2931  }
2932  }
2933 
2934  template<typename _RealType, typename _CharT, typename _Traits>
2935  std::basic_ostream<_CharT, _Traits>&
2936  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2937  const piecewise_constant_distribution<_RealType>& __x)
2938  {
2939  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
2940 
2941  const typename __ios_base::fmtflags __flags = __os.flags();
2942  const _CharT __fill = __os.fill();
2943  const std::streamsize __precision = __os.precision();
2944  const _CharT __space = __os.widen(' ');
2945  __os.flags(__ios_base::scientific | __ios_base::left);
2946  __os.fill(__space);
2947  __os.precision(std::numeric_limits<_RealType>::max_digits10);
2948 
2949  std::vector<_RealType> __int = __x.intervals();
2950  __os << __int.size() - 1;
2951 
2952  for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
2953  __os << __space << *__xit;
2954 
2955  std::vector<double> __den = __x.densities();
2956  for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
2957  __os << __space << *__dit;
2958 
2959  __os.flags(__flags);
2960  __os.fill(__fill);
2961  __os.precision(__precision);
2962  return __os;
2963  }
2964 
2965  template<typename _RealType, typename _CharT, typename _Traits>
2966  std::basic_istream<_CharT, _Traits>&
2967  operator>>(std::basic_istream<_CharT, _Traits>& __is,
2968  piecewise_constant_distribution<_RealType>& __x)
2969  {
2970  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
2971 
2972  const typename __ios_base::fmtflags __flags = __is.flags();
2973  __is.flags(__ios_base::dec | __ios_base::skipws);
2974 
2975  size_t __n;
2976  if (__is >> __n)
2977  {
2978  std::vector<_RealType> __int_vec;
2979  if (__detail::__extract_params(__is, __int_vec, __n + 1))
2980  {
2981  std::vector<double> __den_vec;
2982  if (__detail::__extract_params(__is, __den_vec, __n))
2983  {
2984  __x.param({ __int_vec.begin(), __int_vec.end(),
2985  __den_vec.begin() });
2986  }
2987  }
2988  }
2989 
2990  __is.flags(__flags);
2991  return __is;
2992  }
2993 
2994 
2995  template<typename _RealType>
2996  void
2997  piecewise_linear_distribution<_RealType>::param_type::
2998  _M_initialize()
2999  {
3000  if (_M_int.size() < 2
3001  || (_M_int.size() == 2
3002  && _M_int[0] == _RealType(0)
3003  && _M_int[1] == _RealType(1)
3004  && _M_den[0] == _M_den[1]))
3005  {
3006  _M_int.clear();
3007  _M_den.clear();
3008  return;
3009  }
3010 
3011  double __sum = 0.0;
3012  _M_cp.reserve(_M_int.size() - 1);
3013  _M_m.reserve(_M_int.size() - 1);
3014  for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
3015  {
3016  const _RealType __delta = _M_int[__k + 1] - _M_int[__k];
3017  __sum += 0.5 * (_M_den[__k + 1] + _M_den[__k]) * __delta;
3018  _M_cp.push_back(__sum);
3019  _M_m.push_back((_M_den[__k + 1] - _M_den[__k]) / __delta);
3020  }
3021  __glibcxx_assert(__sum > 0);
3022 
3023  // Now normalize the densities...
3024  __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
3025  __sum);
3026  // ... and partial sums...
3027  __detail::__normalize(_M_cp.begin(), _M_cp.end(), _M_cp.begin(), __sum);
3028  // ... and slopes.
3029  __detail::__normalize(_M_m.begin(), _M_m.end(), _M_m.begin(), __sum);
3030 
3031  // Make sure the last cumulative probablility is one.
3032  _M_cp[_M_cp.size() - 1] = 1.0;
3033  }
3034 
3035  template<typename _RealType>
3036  template<typename _InputIteratorB, typename _InputIteratorW>
3037  piecewise_linear_distribution<_RealType>::param_type::
3038  param_type(_InputIteratorB __bbegin,
3039  _InputIteratorB __bend,
3040  _InputIteratorW __wbegin)
3041  : _M_int(), _M_den(), _M_cp(), _M_m()
3042  {
3043  for (; __bbegin != __bend; ++__bbegin, ++__wbegin)
3044  {
3045  _M_int.push_back(*__bbegin);
3046  _M_den.push_back(*__wbegin);
3047  }
3048 
3049  _M_initialize();
3050  }
3051 
3052  template<typename _RealType>
3053  template<typename _Func>
3054  piecewise_linear_distribution<_RealType>::param_type::
3055  param_type(initializer_list<_RealType> __bl, _Func __fw)
3056  : _M_int(), _M_den(), _M_cp(), _M_m()
3057  {
3058  _M_int.reserve(__bl.size());
3059  _M_den.reserve(__bl.size());
3060  for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
3061  {
3062  _M_int.push_back(*__biter);
3063  _M_den.push_back(__fw(*__biter));
3064  }
3065 
3066  _M_initialize();
3067  }
3068 
3069  template<typename _RealType>
3070  template<typename _Func>
3071  piecewise_linear_distribution<_RealType>::param_type::
3072  param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
3073  : _M_int(), _M_den(), _M_cp(), _M_m()
3074  {
3075  const size_t __n = __nw == 0 ? 1 : __nw;
3076  const _RealType __delta = (__xmax - __xmin) / __n;
3077 
3078  _M_int.reserve(__n + 1);
3079  _M_den.reserve(__n + 1);
3080  for (size_t __k = 0; __k <= __nw; ++__k)
3081  {
3082  _M_int.push_back(__xmin + __k * __delta);
3083  _M_den.push_back(__fw(_M_int[__k] + __delta));
3084  }
3085 
3086  _M_initialize();
3087  }
3088 
3089  template<typename _RealType>
3090  template<typename _UniformRandomNumberGenerator>
3091  typename piecewise_linear_distribution<_RealType>::result_type
3092  piecewise_linear_distribution<_RealType>::
3093  operator()(_UniformRandomNumberGenerator& __urng,
3094  const param_type& __param)
3095  {
3096  __detail::_Adaptor<_UniformRandomNumberGenerator, double>
3097  __aurng(__urng);
3098 
3099  const double __p = __aurng();
3100  if (__param._M_cp.empty())
3101  return __p;
3102 
3103  auto __pos = std::lower_bound(__param._M_cp.begin(),
3104  __param._M_cp.end(), __p);
3105  const size_t __i = __pos - __param._M_cp.begin();
3106 
3107  const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
3108 
3109  const double __a = 0.5 * __param._M_m[__i];
3110  const double __b = __param._M_den[__i];
3111  const double __cm = __p - __pref;
3112 
3113  _RealType __x = __param._M_int[__i];
3114  if (__a == 0)
3115  __x += __cm / __b;
3116  else
3117  {
3118  const double __d = __b * __b + 4.0 * __a * __cm;
3119  __x += 0.5 * (std::sqrt(__d) - __b) / __a;
3120  }
3121 
3122  return __x;
3123  }
3124 
3125  template<typename _RealType>
3126  template<typename _ForwardIterator,
3127  typename _UniformRandomNumberGenerator>
3128  void
3129  piecewise_linear_distribution<_RealType>::
3130  __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3131  _UniformRandomNumberGenerator& __urng,
3132  const param_type& __param)
3133  {
3134  __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
3135  // We could duplicate everything from operator()...
3136  while (__f != __t)
3137  *__f++ = this->operator()(__urng, __param);
3138  }
3139 
3140  template<typename _RealType, typename _CharT, typename _Traits>
3141  std::basic_ostream<_CharT, _Traits>&
3142  operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3143  const piecewise_linear_distribution<_RealType>& __x)
3144  {
3145  using __ios_base = typename basic_ostream<_CharT, _Traits>::ios_base;
3146 
3147  const typename __ios_base::fmtflags __flags = __os.flags();
3148  const _CharT __fill = __os.fill();
3149  const std::streamsize __precision = __os.precision();
3150  const _CharT __space = __os.widen(' ');
3151  __os.flags(__ios_base::scientific | __ios_base::left);
3152  __os.fill(__space);
3153  __os.precision(std::numeric_limits<_RealType>::max_digits10);
3154 
3155  std::vector<_RealType> __int = __x.intervals();
3156  __os << __int.size() - 1;
3157 
3158  for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
3159  __os << __space << *__xit;
3160 
3161  std::vector<double> __den = __x.densities();
3162  for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
3163  __os << __space << *__dit;
3164 
3165  __os.flags(__flags);
3166  __os.fill(__fill);
3167  __os.precision(__precision);
3168  return __os;
3169  }
3170 
3171  template<typename _RealType, typename _CharT, typename _Traits>
3172  std::basic_istream<_CharT, _Traits>&
3173  operator>>(std::basic_istream<_CharT, _Traits>& __is,
3174  piecewise_linear_distribution<_RealType>& __x)
3175  {
3176  using __ios_base = typename basic_istream<_CharT, _Traits>::ios_base;
3177 
3178  const typename __ios_base::fmtflags __flags = __is.flags();
3179  __is.flags(__ios_base::dec | __ios_base::skipws);
3180 
3181  size_t __n;
3182  if (__is >> __n)
3183  {
3184  vector<_RealType> __int_vec;
3185  if (__detail::__extract_params(__is, __int_vec, __n + 1))
3186  {
3187  vector<double> __den_vec;
3188  if (__detail::__extract_params(__is, __den_vec, __n + 1))
3189  {
3190  __x.param({ __int_vec.begin(), __int_vec.end(),
3191  __den_vec.begin() });
3192  }
3193  }
3194  }
3195  __is.flags(__flags);
3196  return __is;
3197  }
3198 
3199 
3200  template<typename _IntType, typename>
3201  seed_seq::seed_seq(std::initializer_list<_IntType> __il)
3202  {
3203  _M_v.reserve(__il.size());
3204  for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
3205  _M_v.push_back(__detail::__mod<result_type,
3206  __detail::_Shift<result_type, 32>::__value>(*__iter));
3207  }
3208 
3209  template<typename _InputIterator>
3210  seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
3211  {
3212  if _GLIBCXX17_CONSTEXPR (__is_random_access_iter<_InputIterator>::value)
3213  _M_v.reserve(std::distance(__begin, __end));
3214 
3215  for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
3216  _M_v.push_back(__detail::__mod<result_type,
3217  __detail::_Shift<result_type, 32>::__value>(*__iter));
3218  }
3219 
3220  template<typename _RandomAccessIterator>
3221  void
3222  seed_seq::generate(_RandomAccessIterator __begin,
3223  _RandomAccessIterator __end)
3224  {
3225  typedef typename iterator_traits<_RandomAccessIterator>::value_type
3226  _Type;
3227 
3228  if (__begin == __end)
3229  return;
3230 
3231  std::fill(__begin, __end, _Type(0x8b8b8b8bu));
3232 
3233  const size_t __n = __end - __begin;
3234  const size_t __s = _M_v.size();
3235  const size_t __t = (__n >= 623) ? 11
3236  : (__n >= 68) ? 7
3237  : (__n >= 39) ? 5
3238  : (__n >= 7) ? 3
3239  : (__n - 1) / 2;
3240  const size_t __p = (__n - __t) / 2;
3241  const size_t __q = __p + __t;
3242  const size_t __m = std::max(size_t(__s + 1), __n);
3243 
3244  for (size_t __k = 0; __k < __m; ++__k)
3245  {
3246  _Type __arg = (__begin[__k % __n]
3247  ^ __begin[(__k + __p) % __n]
3248  ^ __begin[(__k - 1) % __n]);
3249  _Type __r1 = __arg ^ (__arg >> 27);
3250  __r1 = __detail::__mod<_Type,
3251  __detail::_Shift<_Type, 32>::__value>(1664525u * __r1);
3252  _Type __r2 = __r1;
3253  if (__k == 0)
3254  __r2 += __s;
3255  else if (__k <= __s)
3256  __r2 += __k % __n + _M_v[__k - 1];
3257  else
3258  __r2 += __k % __n;
3259  __r2 = __detail::__mod<_Type,
3260  __detail::_Shift<_Type, 32>::__value>(__r2);
3261  __begin[(__k + __p) % __n] += __r1;
3262  __begin[(__k + __q) % __n] += __r2;
3263  __begin[__k % __n] = __r2;
3264  }
3265 
3266  for (size_t __k = __m; __k < __m + __n; ++__k)
3267  {
3268  _Type __arg = (__begin[__k % __n]
3269  + __begin[(__k + __p) % __n]
3270  + __begin[(__k - 1) % __n]);
3271  _Type __r3 = __arg ^ (__arg >> 27);
3272  __r3 = __detail::__mod<_Type,
3273  __detail::_Shift<_Type, 32>::__value>(1566083941u * __r3);
3274  _Type __r4 = __r3 - __k % __n;
3275  __r4 = __detail::__mod<_Type,
3276  __detail::_Shift<_Type, 32>::__value>(__r4);
3277  __begin[(__k + __p) % __n] ^= __r3;
3278  __begin[(__k + __q) % __n] ^= __r4;
3279  __begin[__k % __n] = __r4;
3280  }
3281  }
3282 
3283  template<typename _RealType, size_t __bits,
3284  typename _UniformRandomNumberGenerator>
3285  _RealType
3286  generate_canonical(_UniformRandomNumberGenerator& __urng)
3287  {
3288  static_assert(std::is_floating_point<_RealType>::value,
3289  "template argument must be a floating point type");
3290 
3291  const size_t __b
3292  = std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
3293  __bits);
3294  const long double __r = static_cast<long double>(__urng.max())
3295  - static_cast<long double>(__urng.min()) + 1.0L;
3296  const size_t __log2r = std::log(__r) / std::log(2.0L);
3297  const size_t __m = std::max<size_t>(1UL,
3298  (__b + __log2r - 1UL) / __log2r);
3299  _RealType __ret;
3300  _RealType __sum = _RealType(0);
3301  _RealType __tmp = _RealType(1);
3302  for (size_t __k = __m; __k != 0; --__k)
3303  {
3304  __sum += _RealType(__urng() - __urng.min()) * __tmp;
3305  __tmp *= __r;
3306  }
3307  __ret = __sum / __tmp;
3308  if (__builtin_expect(__ret >= _RealType(1), 0))
3309  {
3310 #if _GLIBCXX_USE_C99_MATH_TR1
3311  __ret = std::nextafter(_RealType(1), _RealType(0));
3312 #else
3313  __ret = _RealType(1)
3314  - std::numeric_limits<_RealType>::epsilon() / _RealType(2);
3315 #endif
3316  }
3317  return __ret;
3318  }
3319 
3320 _GLIBCXX_END_NAMESPACE_VERSION
3321 } // namespace
3322 
3323 #endif
std::log
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition: complex:823
std::tan
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition: complex:959
std::abs
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition: complex:629
std::exp
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition: complex:796
std::pow
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
Definition: complex:1018
std::sqrt
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition: complex:932
std::max
constexpr const _Tp & max(const _Tp &, const _Tp &)
This does what you think it does.
Definition: stl_algobase.h:254
std::min
constexpr const _Tp & min(const _Tp &, const _Tp &)
This does what you think it does.
Definition: stl_algobase.h:230
std::generate_canonical
_RealType generate_canonical(_UniformRandomNumberGenerator &__g)
A function template for converting the output of a (integral) uniform random number generator to a fl...
Definition: bits/random.tcc:3286
std::sub_match::operator<<
basic_ostream< _Ch_type, _Ch_traits > & operator<<(basic_ostream< _Ch_type, _Ch_traits > &__os, const sub_match< _Bi_iter > &__m)
Inserts a matched string into an output stream.
Definition: regex.h:1647
std::back_inserter
constexpr back_insert_iterator< _Container > back_inserter(_Container &__x)
Definition: bits/stl_iterator.h:705
std::accumulate
constexpr _Tp accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
Accumulate values in a range.
Definition: stl_numeric.h:134
std::partial_sum
constexpr _OutputIterator partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
Return list of partial sums.
Definition: stl_numeric.h:256
std
ISO C++ entities toplevel namespace is std.
std::operator>>
std::basic_istream< _CharT, _Traits > & operator>>(std::basic_istream< _CharT, _Traits > &__is, bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition: bitset:1472
std::streamsize
ptrdiff_t streamsize
Integral type for I/O operation counts and buffer sizes.
Definition: postypes.h:98
std::distance
constexpr iterator_traits< _InputIterator >::difference_type distance(_InputIterator __first, _InputIterator __last)
A generalization of pointer arithmetic.
Definition: stl_iterator_base_funcs.h:138
std::operator<<
std::basic_ostream< _CharT, _Traits > & operator<<(std::basic_ostream< _CharT, _Traits > &__os, const bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition: bitset:1540
std::scientific
ios_base & scientific(ios_base &__base)
Calls base.setf(ios_base::scientific, ios_base::floatfield).
Definition: ios_base.h:1079
std::dec
ios_base & dec(ios_base &__base)
Calls base.setf(ios_base::dec, ios_base::basefield).
Definition: ios_base.h:1046
std::__lg
constexpr int __lg(int __n)
This is a helper function for the sort routines and for random.tcc.
Definition: stl_algobase.h:1364
std::left
ios_base & left(ios_base &__base)
Calls base.setf(ios_base::left, ios_base::adjustfield).
Definition: ios_base.h:1029
std::skipws
ios_base & skipws(ios_base &__base)
Calls base.setf(ios_base::skipws).
Definition: ios_base.h:972
std::fixed
ios_base & fixed(ios_base &__base)
Calls base.setf(ios_base::fixed, ios_base::floatfield).
Definition: ios_base.h:1071
std::initializer_list
initializer_list
Definition: initializer_list:48
std::basic_ios::clear
void clear(iostate __state=goodbit)
[Re]sets the error state.
Definition: basic_ios.tcc:41
std::basic_ios::widen
char_type widen(char __c) const
Widens characters.
Definition: basic_ios.h:449
std::basic_ios::fill
char_type fill() const
Retrieves the empty character.
Definition: basic_ios.h:370
std::basic_istream
Template class basic_istream.
Definition: istream:59
std::basic_ostream
Template class basic_ostream.
Definition: ostream:59
std::numeric_limits
Properties of fundamental types.
Definition: limits:313
std::numeric_limits::max
static constexpr _Tp max() noexcept
Definition: limits:321
std::numeric_limits::epsilon
static constexpr _Tp epsilon() noexcept
Definition: limits:333
std::numeric_limits::min
static constexpr _Tp min() noexcept
Definition: limits:317
std::is_floating_point
is_floating_point
Definition: type_traits:395
std::common_type
common_type
Definition: type_traits:2215
std::ios_base::precision
streamsize precision() const
Flags access.
Definition: ios_base.h:719
std::ios_base::flags
fmtflags flags() const
Access to format flags.
Definition: ios_base.h:649
std::linear_congruential_engine
A model of a linear congruential random number generator.
Definition: random.h:256
std::linear_congruential_engine::multiplier
static constexpr result_type multiplier
Definition: random.h:271
std::linear_congruential_engine::modulus
static constexpr result_type modulus
Definition: random.h:275
std::linear_congruential_engine::seed
void seed(result_type __s=default_seed)
Reseeds the linear_congruential_engine random number generator engine sequence to the seed __s.
Definition: bits/random.tcc:117
std::linear_congruential_engine::increment
static constexpr result_type increment
Definition: random.h:273
std::subtract_with_carry_engine
The Marsaglia-Zaman generator.
Definition: random.h:693
std::subtract_with_carry_engine::seed
void seed(result_type __sd=default_seed)
Seeds the initial state of the random number generator.
Definition: bits/random.tcc:538
std::subtract_with_carry_engine::operator()
result_type operator()()
Gets the next random number in the sequence.
Definition: bits/random.tcc:594
std::discard_block_engine::operator()
result_type operator()()
Gets the next value in the generated random number sequence.
Definition: bits/random.tcc:682
std::independent_bits_engine::operator()
result_type operator()()
Gets the next value in the generated random number sequence.
Definition: bits/random.tcc:737
std::shuffle_order_engine
Produces random numbers by combining random numbers from some base engine to produce random numbers w...
Definition: random.h:1325
std::shuffle_order_engine::result_type
_RandomNumberEngine::result_type result_type
Definition: random.h:1327
std::shuffle_order_engine::base
const _RandomNumberEngine & base() const noexcept
Definition: random.h:1431
std::uniform_real_distribution
Uniform continuous distribution for random numbers.
Definition: random.h:1741
std::uniform_real_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: random.h:1828
std::normal_distribution
A normal continuous distribution for random numbers.
Definition: random.h:1971
std::normal_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:2088
std::gamma_distribution
A gamma continuous distribution for random numbers.
Definition: random.h:2403
std::gamma_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:2530
std::gamma_distribution::result_type
_RealType result_type
Definition: random.h:2405
std::chi_squared_distribution
A chi_squared_distribution random number distribution.
Definition: random.h:2631
std::cauchy_distribution
A cauchy_distribution random number distribution.
Definition: random.h:2855
std::cauchy_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: random.h:2930
std::cauchy_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:2960
std::fisher_f_distribution
A fisher_f_distribution random number distribution.
Definition: random.h:3063
std::student_t_distribution
A student_t_distribution random number distribution.
Definition: random.h:3295
std::binomial_distribution
A discrete binomial random number distribution.
Definition: random.h:3739
std::binomial_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:3865
std::geometric_distribution
A discrete geometric random number distribution.
Definition: random.h:3979
std::geometric_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:4088
std::geometric_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: random.h:4058
std::negative_binomial_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: bits/random.tcc:1112
std::poisson_distribution
A discrete Poisson random number distribution.
Definition: random.h:4420
std::poisson_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:4531
std::poisson_distribution::operator<<
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.
std::poisson_distribution::operator==
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:4567
std::poisson_distribution::operator>>
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.
std::exponential_distribution
An exponential continuous distribution for random numbers.
Definition: random.h:4646
std::exponential_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: random.h:4724
std::weibull_distribution
A weibull_distribution random number distribution.
Definition: random.h:4861
std::weibull_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: random.h:4939
std::weibull_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:4969
std::extreme_value_distribution
A extreme_value_distribution random number distribution.
Definition: random.h:5071
std::extreme_value_distribution::operator()
result_type operator()(_UniformRandomNumberGenerator &__urng)
Generating functions.
Definition: random.h:5179
std::extreme_value_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: random.h:5149
std::vector::begin
iterator begin() noexcept
Definition: stl_vector.h:811
std::vector::end
iterator end() noexcept
Definition: stl_vector.h:829
std::vector::size
size_type size() const noexcept
Definition: stl_vector.h:918
std::uniform_int_distribution
Uniform discrete distribution for random numbers. A discrete random distribution on the range with e...
Definition: uniform_int_dist.h:75
std::uniform_int_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: uniform_int_dist.h:158